Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,2,Mod(1,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, 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("1875.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(14.9719503790\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.5444000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{8} - 4x^{7} - 2x^{6} + 20x^{5} - 4x^{4} - 30x^{3} + 7x^{2} + 12x + 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 75) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.35083\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.35083 | −0.955181 | −0.477590 | − | 0.878583i | \(-0.658490\pi\) | ||||
−0.477590 | + | 0.878583i | \(0.658490\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.175259 | −0.0876296 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.35083 | 0.551474 | ||||||||
\(7\) | 1.59580 | 0.603155 | 0.301577 | − | 0.953442i | \(-0.402487\pi\) | ||||
0.301577 | + | 0.953442i | \(0.402487\pi\) | |||||||
\(8\) | 2.93840 | 1.03888 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.33277 | 1.00487 | 0.502434 | − | 0.864616i | \(-0.332438\pi\) | ||||
0.502434 | + | 0.864616i | \(0.332438\pi\) | |||||||
\(12\) | 0.175259 | 0.0505930 | ||||||||
\(13\) | 7.05132 | 1.95568 | 0.977842 | − | 0.209345i | \(-0.0671333\pi\) | ||||
0.977842 | + | 0.209345i | \(0.0671333\pi\) | |||||||
\(14\) | −2.15565 | −0.576122 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.61877 | −0.904691 | ||||||||
\(17\) | 4.09625 | 0.993486 | 0.496743 | − | 0.867898i | \(-0.334529\pi\) | ||||
0.496743 | + | 0.867898i | \(0.334529\pi\) | |||||||
\(18\) | −1.35083 | −0.318394 | ||||||||
\(19\) | 0.567535 | 0.130201 | 0.0651007 | − | 0.997879i | \(-0.479263\pi\) | ||||
0.0651007 | + | 0.997879i | \(0.479263\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.59580 | −0.348231 | ||||||||
\(22\) | −4.50200 | −0.959830 | ||||||||
\(23\) | 6.30400 | 1.31448 | 0.657238 | − | 0.753683i | \(-0.271725\pi\) | ||||
0.657238 | + | 0.753683i | \(0.271725\pi\) | |||||||
\(24\) | −2.93840 | −0.599799 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −9.52513 | −1.86803 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.279678 | −0.0528542 | ||||||||
\(29\) | −2.78357 | −0.516897 | −0.258448 | − | 0.966025i | \(-0.583211\pi\) | ||||
−0.258448 | + | 0.966025i | \(0.583211\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.995824 | −0.178855 | −0.0894276 | − | 0.995993i | \(-0.528504\pi\) | ||||
−0.0894276 | + | 0.995993i | \(0.528504\pi\) | |||||||
\(32\) | −0.988473 | −0.174739 | ||||||||
\(33\) | −3.33277 | −0.580161 | ||||||||
\(34\) | −5.53333 | −0.948959 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.175259 | −0.0292099 | ||||||||
\(37\) | −3.55334 | −0.584165 | −0.292083 | − | 0.956393i | \(-0.594348\pi\) | ||||
−0.292083 | + | 0.956393i | \(0.594348\pi\) | |||||||
\(38\) | −0.766643 | −0.124366 | ||||||||
\(39\) | −7.05132 | −1.12911 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.16293 | 0.181618 | 0.0908092 | − | 0.995868i | \(-0.471055\pi\) | ||||
0.0908092 | + | 0.995868i | \(0.471055\pi\) | |||||||
\(42\) | 2.15565 | 0.332624 | ||||||||
\(43\) | 0.117022 | 0.0178456 | 0.00892281 | − | 0.999960i | \(-0.497160\pi\) | ||||
0.00892281 | + | 0.999960i | \(0.497160\pi\) | |||||||
\(44\) | −0.584098 | −0.0880561 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.51563 | −1.25556 | ||||||||
\(47\) | 7.64173 | 1.11466 | 0.557331 | − | 0.830291i | \(-0.311826\pi\) | ||||
0.557331 | + | 0.830291i | \(0.311826\pi\) | |||||||
\(48\) | 3.61877 | 0.522324 | ||||||||
\(49\) | −4.45343 | −0.636205 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.09625 | −0.573589 | ||||||||
\(52\) | −1.23581 | −0.171376 | ||||||||
\(53\) | 0.523635 | 0.0719268 | 0.0359634 | − | 0.999353i | \(-0.488550\pi\) | ||||
0.0359634 | + | 0.999353i | \(0.488550\pi\) | |||||||
\(54\) | 1.35083 | 0.183825 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.68910 | 0.626607 | ||||||||
\(57\) | −0.567535 | −0.0751718 | ||||||||
\(58\) | 3.76013 | 0.493730 | ||||||||
\(59\) | 0.983998 | 0.128106 | 0.0640528 | − | 0.997947i | \(-0.479597\pi\) | ||||
0.0640528 | + | 0.997947i | \(0.479597\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.6137 | 1.35895 | 0.679473 | − | 0.733701i | \(-0.262208\pi\) | ||||
0.679473 | + | 0.733701i | \(0.262208\pi\) | |||||||
\(62\) | 1.34519 | 0.170839 | ||||||||
\(63\) | 1.59580 | 0.201052 | ||||||||
\(64\) | 8.57279 | 1.07160 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.50200 | 0.554158 | ||||||||
\(67\) | −15.2159 | −1.85892 | −0.929461 | − | 0.368920i | \(-0.879728\pi\) | ||||
−0.929461 | + | 0.368920i | \(0.879728\pi\) | |||||||
\(68\) | −0.717905 | −0.0870588 | ||||||||
\(69\) | −6.30400 | −0.758913 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.6639 | −1.26558 | −0.632788 | − | 0.774325i | \(-0.718090\pi\) | ||||
−0.632788 | + | 0.774325i | \(0.718090\pi\) | |||||||
\(72\) | 2.93840 | 0.346294 | ||||||||
\(73\) | 5.55832 | 0.650552 | 0.325276 | − | 0.945619i | \(-0.394543\pi\) | ||||
0.325276 | + | 0.945619i | \(0.394543\pi\) | |||||||
\(74\) | 4.79996 | 0.557984 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.0994657 | −0.0114095 | ||||||||
\(77\) | 5.31842 | 0.606090 | ||||||||
\(78\) | 9.52513 | 1.07851 | ||||||||
\(79\) | −14.5969 | −1.64227 | −0.821137 | − | 0.570731i | \(-0.806660\pi\) | ||||
−0.821137 | + | 0.570731i | \(0.806660\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.57091 | −0.173478 | ||||||||
\(83\) | 5.02398 | 0.551453 | 0.275727 | − | 0.961236i | \(-0.411082\pi\) | ||||
0.275727 | + | 0.961236i | \(0.411082\pi\) | |||||||
\(84\) | 0.279678 | 0.0305154 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.158076 | −0.0170458 | ||||||||
\(87\) | 2.78357 | 0.298430 | ||||||||
\(88\) | 9.79302 | 1.04394 | ||||||||
\(89\) | 2.82350 | 0.299291 | 0.149645 | − | 0.988740i | \(-0.452187\pi\) | ||||
0.149645 | + | 0.988740i | \(0.452187\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.2525 | 1.17958 | ||||||||
\(92\) | −1.10483 | −0.115187 | ||||||||
\(93\) | 0.995824 | 0.103262 | ||||||||
\(94\) | −10.3227 | −1.06470 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.988473 | 0.100886 | ||||||||
\(97\) | −1.70592 | −0.173210 | −0.0866049 | − | 0.996243i | \(-0.527602\pi\) | ||||
−0.0866049 | + | 0.996243i | \(0.527602\pi\) | |||||||
\(98\) | 6.01583 | 0.607690 | ||||||||
\(99\) | 3.33277 | 0.334956 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.1747 | 1.31093 | 0.655464 | − | 0.755226i | \(-0.272473\pi\) | ||||
0.655464 | + | 0.755226i | \(0.272473\pi\) | |||||||
\(102\) | 5.53333 | 0.547882 | ||||||||
\(103\) | 10.8720 | 1.07125 | 0.535624 | − | 0.844456i | \(-0.320076\pi\) | ||||
0.535624 | + | 0.844456i | \(0.320076\pi\) | |||||||
\(104\) | 20.7196 | 2.03173 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.707341 | −0.0687031 | ||||||||
\(107\) | 9.37236 | 0.906060 | 0.453030 | − | 0.891495i | \(-0.350343\pi\) | ||||
0.453030 | + | 0.891495i | \(0.350343\pi\) | |||||||
\(108\) | 0.175259 | 0.0168643 | ||||||||
\(109\) | −15.5899 | −1.49324 | −0.746622 | − | 0.665249i | \(-0.768326\pi\) | ||||
−0.746622 | + | 0.665249i | \(0.768326\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.55334 | 0.337268 | ||||||||
\(112\) | −5.77482 | −0.545669 | ||||||||
\(113\) | −10.0481 | −0.945243 | −0.472622 | − | 0.881265i | \(-0.656692\pi\) | ||||
−0.472622 | + | 0.881265i | \(0.656692\pi\) | |||||||
\(114\) | 0.766643 | 0.0718027 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.487847 | 0.0452954 | ||||||||
\(117\) | 7.05132 | 0.651895 | ||||||||
\(118\) | −1.32921 | −0.122364 | ||||||||
\(119\) | 6.53678 | 0.599226 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.107347 | 0.00975880 | ||||||||
\(122\) | −14.3373 | −1.29804 | ||||||||
\(123\) | −1.16293 | −0.104857 | ||||||||
\(124\) | 0.174527 | 0.0156730 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.15565 | −0.192041 | ||||||||
\(127\) | 0.976784 | 0.0866756 | 0.0433378 | − | 0.999060i | \(-0.486201\pi\) | ||||
0.0433378 | + | 0.999060i | \(0.486201\pi\) | |||||||
\(128\) | −9.60343 | −0.848832 | ||||||||
\(129\) | −0.117022 | −0.0103032 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.0616 | 0.879086 | 0.439543 | − | 0.898221i | \(-0.355140\pi\) | ||||
0.439543 | + | 0.898221i | \(0.355140\pi\) | |||||||
\(132\) | 0.584098 | 0.0508392 | ||||||||
\(133\) | 0.905670 | 0.0785316 | ||||||||
\(134\) | 20.5541 | 1.77561 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.0364 | 1.03212 | ||||||||
\(137\) | 4.87244 | 0.416281 | 0.208140 | − | 0.978099i | \(-0.433259\pi\) | ||||
0.208140 | + | 0.978099i | \(0.433259\pi\) | |||||||
\(138\) | 8.51563 | 0.724899 | ||||||||
\(139\) | 0.185784 | 0.0157580 | 0.00787898 | − | 0.999969i | \(-0.497492\pi\) | ||||
0.00787898 | + | 0.999969i | \(0.497492\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.64173 | −0.643550 | ||||||||
\(142\) | 14.4052 | 1.20885 | ||||||||
\(143\) | 23.5004 | 1.96520 | ||||||||
\(144\) | −3.61877 | −0.301564 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −7.50834 | −0.621395 | ||||||||
\(147\) | 4.45343 | 0.367313 | ||||||||
\(148\) | 0.622755 | 0.0511902 | ||||||||
\(149\) | 3.88889 | 0.318590 | 0.159295 | − | 0.987231i | \(-0.449078\pi\) | ||||
0.159295 | + | 0.987231i | \(0.449078\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.1146 | −1.79966 | −0.899829 | − | 0.436242i | \(-0.856309\pi\) | ||||
−0.899829 | + | 0.436242i | \(0.856309\pi\) | |||||||
\(152\) | 1.66765 | 0.135264 | ||||||||
\(153\) | 4.09625 | 0.331162 | ||||||||
\(154\) | −7.18428 | −0.578926 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.23581 | 0.0989438 | ||||||||
\(157\) | −13.6058 | −1.08586 | −0.542931 | − | 0.839777i | \(-0.682686\pi\) | ||||
−0.542931 | + | 0.839777i | \(0.682686\pi\) | |||||||
\(158\) | 19.7179 | 1.56867 | ||||||||
\(159\) | −0.523635 | −0.0415269 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.0599 | 0.792832 | ||||||||
\(162\) | −1.35083 | −0.106131 | ||||||||
\(163\) | −8.62895 | −0.675871 | −0.337936 | − | 0.941169i | \(-0.609729\pi\) | ||||
−0.337936 | + | 0.941169i | \(0.609729\pi\) | |||||||
\(164\) | −0.203813 | −0.0159151 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.78654 | −0.526737 | ||||||||
\(167\) | −6.59891 | −0.510639 | −0.255319 | − | 0.966857i | \(-0.582181\pi\) | ||||
−0.255319 | + | 0.966857i | \(0.582181\pi\) | |||||||
\(168\) | −4.68910 | −0.361772 | ||||||||
\(169\) | 36.7211 | 2.82470 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.567535 | 0.0434005 | ||||||||
\(172\) | −0.0205091 | −0.00156381 | ||||||||
\(173\) | −13.6595 | −1.03851 | −0.519257 | − | 0.854618i | \(-0.673791\pi\) | ||||
−0.519257 | + | 0.854618i | \(0.673791\pi\) | |||||||
\(174\) | −3.76013 | −0.285055 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −12.0605 | −0.909095 | ||||||||
\(177\) | −0.983998 | −0.0739618 | ||||||||
\(178\) | −3.81407 | −0.285877 | ||||||||
\(179\) | 9.82880 | 0.734639 | 0.367320 | − | 0.930095i | \(-0.380276\pi\) | ||||
0.367320 | + | 0.930095i | \(0.380276\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.8687 | 1.32817 | 0.664085 | − | 0.747657i | \(-0.268821\pi\) | ||||
0.664085 | + | 0.747657i | \(0.268821\pi\) | |||||||
\(182\) | −15.2002 | −1.12671 | ||||||||
\(183\) | −10.6137 | −0.784588 | ||||||||
\(184\) | 18.5237 | 1.36559 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.34519 | −0.0986340 | ||||||||
\(187\) | 13.6518 | 0.998322 | ||||||||
\(188\) | −1.33928 | −0.0976773 | ||||||||
\(189\) | −1.59580 | −0.116077 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.325813 | 0.0235750 | 0.0117875 | − | 0.999931i | \(-0.496248\pi\) | ||||
0.0117875 | + | 0.999931i | \(0.496248\pi\) | |||||||
\(192\) | −8.57279 | −0.618688 | ||||||||
\(193\) | 2.90187 | 0.208881 | 0.104441 | − | 0.994531i | \(-0.466695\pi\) | ||||
0.104441 | + | 0.994531i | \(0.466695\pi\) | |||||||
\(194\) | 2.30441 | 0.165447 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.780505 | 0.0557503 | ||||||||
\(197\) | 18.1220 | 1.29114 | 0.645568 | − | 0.763702i | \(-0.276620\pi\) | ||||
0.645568 | + | 0.763702i | \(0.276620\pi\) | |||||||
\(198\) | −4.50200 | −0.319943 | ||||||||
\(199\) | 1.53256 | 0.108640 | 0.0543201 | − | 0.998524i | \(-0.482701\pi\) | ||||
0.0543201 | + | 0.998524i | \(0.482701\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.2159 | 1.07325 | ||||||||
\(202\) | −17.7967 | −1.25217 | ||||||||
\(203\) | −4.44202 | −0.311769 | ||||||||
\(204\) | 0.717905 | 0.0502634 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −14.6862 | −1.02324 | ||||||||
\(207\) | 6.30400 | 0.438158 | ||||||||
\(208\) | −25.5171 | −1.76929 | ||||||||
\(209\) | 1.89146 | 0.130835 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.3698 | −0.782727 | −0.391363 | − | 0.920236i | \(-0.627996\pi\) | ||||
−0.391363 | + | 0.920236i | \(0.627996\pi\) | |||||||
\(212\) | −0.0917718 | −0.00630291 | ||||||||
\(213\) | 10.6639 | 0.730681 | ||||||||
\(214\) | −12.6605 | −0.865451 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.93840 | −0.199933 | ||||||||
\(217\) | −1.58913 | −0.107877 | ||||||||
\(218\) | 21.0593 | 1.42632 | ||||||||
\(219\) | −5.55832 | −0.375596 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 28.8839 | 1.94294 | ||||||||
\(222\) | −4.79996 | −0.322152 | ||||||||
\(223\) | −16.9507 | −1.13510 | −0.567550 | − | 0.823339i | \(-0.692109\pi\) | ||||
−0.567550 | + | 0.823339i | \(0.692109\pi\) | |||||||
\(224\) | −1.57740 | −0.105395 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.5732 | 0.902878 | ||||||||
\(227\) | −14.1117 | −0.936627 | −0.468314 | − | 0.883562i | \(-0.655138\pi\) | ||||
−0.468314 | + | 0.883562i | \(0.655138\pi\) | |||||||
\(228\) | 0.0994657 | 0.00658728 | ||||||||
\(229\) | 0.0619945 | 0.00409671 | 0.00204835 | − | 0.999998i | \(-0.499348\pi\) | ||||
0.00204835 | + | 0.999998i | \(0.499348\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.31842 | −0.349926 | ||||||||
\(232\) | −8.17927 | −0.536995 | ||||||||
\(233\) | 26.0191 | 1.70457 | 0.852283 | − | 0.523081i | \(-0.175218\pi\) | ||||
0.852283 | + | 0.523081i | \(0.175218\pi\) | |||||||
\(234\) | −9.52513 | −0.622677 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.172455 | −0.0112258 | ||||||||
\(237\) | 14.5969 | 0.948168 | ||||||||
\(238\) | −8.83008 | −0.572369 | ||||||||
\(239\) | 19.4970 | 1.26116 | 0.630579 | − | 0.776125i | \(-0.282817\pi\) | ||||
0.630579 | + | 0.776125i | \(0.282817\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.09860 | −0.264014 | −0.132007 | − | 0.991249i | \(-0.542142\pi\) | ||||
−0.132007 | + | 0.991249i | \(0.542142\pi\) | |||||||
\(242\) | −0.145007 | −0.00932141 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.86015 | −0.119084 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.57091 | 0.100158 | ||||||||
\(247\) | 4.00187 | 0.254633 | ||||||||
\(248\) | −2.92613 | −0.185810 | ||||||||
\(249\) | −5.02398 | −0.318382 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.02933 | −0.0649704 | −0.0324852 | − | 0.999472i | \(-0.510342\pi\) | ||||
−0.0324852 | + | 0.999472i | \(0.510342\pi\) | |||||||
\(252\) | −0.279678 | −0.0176181 | ||||||||
\(253\) | 21.0098 | 1.32087 | ||||||||
\(254\) | −1.31947 | −0.0827909 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.17298 | −0.260811 | ||||||||
\(257\) | 18.5597 | 1.15772 | 0.578862 | − | 0.815426i | \(-0.303497\pi\) | ||||
0.578862 | + | 0.815426i | \(0.303497\pi\) | |||||||
\(258\) | 0.158076 | 0.00984140 | ||||||||
\(259\) | −5.67041 | −0.352342 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.78357 | −0.172299 | ||||||||
\(262\) | −13.5915 | −0.839686 | ||||||||
\(263\) | −12.3938 | −0.764231 | −0.382116 | − | 0.924114i | \(-0.624804\pi\) | ||||
−0.382116 | + | 0.924114i | \(0.624804\pi\) | |||||||
\(264\) | −9.79302 | −0.602719 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.22341 | −0.0750119 | ||||||||
\(267\) | −2.82350 | −0.172796 | ||||||||
\(268\) | 2.66673 | 0.162897 | ||||||||
\(269\) | −5.30032 | −0.323166 | −0.161583 | − | 0.986859i | \(-0.551660\pi\) | ||||
−0.161583 | + | 0.986859i | \(0.551660\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.797428 | 0.0484403 | 0.0242201 | − | 0.999707i | \(-0.492290\pi\) | ||||
0.0242201 | + | 0.999707i | \(0.492290\pi\) | |||||||
\(272\) | −14.8234 | −0.898798 | ||||||||
\(273\) | −11.2525 | −0.681031 | ||||||||
\(274\) | −6.58184 | −0.397624 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.10483 | 0.0665032 | ||||||||
\(277\) | 4.74425 | 0.285054 | 0.142527 | − | 0.989791i | \(-0.454477\pi\) | ||||
0.142527 | + | 0.989791i | \(0.454477\pi\) | |||||||
\(278\) | −0.250962 | −0.0150517 | ||||||||
\(279\) | −0.995824 | −0.0596184 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.7398 | −1.11792 | −0.558961 | − | 0.829194i | \(-0.688800\pi\) | ||||
−0.558961 | + | 0.829194i | \(0.688800\pi\) | |||||||
\(282\) | 10.3227 | 0.614707 | ||||||||
\(283\) | −11.7612 | −0.699130 | −0.349565 | − | 0.936912i | \(-0.613671\pi\) | ||||
−0.349565 | + | 0.936912i | \(0.613671\pi\) | |||||||
\(284\) | 1.86895 | 0.110902 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −31.7451 | −1.87712 | ||||||||
\(287\) | 1.85579 | 0.109544 | ||||||||
\(288\) | −0.988473 | −0.0582463 | ||||||||
\(289\) | −0.220750 | −0.0129853 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.70592 | 0.100003 | ||||||||
\(292\) | −0.974146 | −0.0570076 | ||||||||
\(293\) | −22.2819 | −1.30172 | −0.650860 | − | 0.759198i | \(-0.725592\pi\) | ||||
−0.650860 | + | 0.759198i | \(0.725592\pi\) | |||||||
\(294\) | −6.01583 | −0.350850 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −10.4411 | −0.606879 | ||||||||
\(297\) | −3.33277 | −0.193387 | ||||||||
\(298\) | −5.25322 | −0.304311 | ||||||||
\(299\) | 44.4515 | 2.57070 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.186743 | 0.0107637 | ||||||||
\(302\) | 29.8730 | 1.71900 | ||||||||
\(303\) | −13.1747 | −0.756865 | ||||||||
\(304\) | −2.05378 | −0.117792 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −5.53333 | −0.316320 | ||||||||
\(307\) | 15.3063 | 0.873574 | 0.436787 | − | 0.899565i | \(-0.356116\pi\) | ||||
0.436787 | + | 0.899565i | \(0.356116\pi\) | |||||||
\(308\) | −0.932102 | −0.0531115 | ||||||||
\(309\) | −10.8720 | −0.618486 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.8545 | −0.728913 | −0.364456 | − | 0.931220i | \(-0.618745\pi\) | ||||
−0.364456 | + | 0.931220i | \(0.618745\pi\) | |||||||
\(312\) | −20.7196 | −1.17302 | ||||||||
\(313\) | 10.5072 | 0.593901 | 0.296951 | − | 0.954893i | \(-0.404030\pi\) | ||||
0.296951 | + | 0.954893i | \(0.404030\pi\) | |||||||
\(314\) | 18.3791 | 1.03720 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.55823 | 0.143912 | ||||||||
\(317\) | 19.4806 | 1.09414 | 0.547071 | − | 0.837086i | \(-0.315743\pi\) | ||||
0.547071 | + | 0.837086i | \(0.315743\pi\) | |||||||
\(318\) | 0.707341 | 0.0396657 | ||||||||
\(319\) | −9.27701 | −0.519413 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.37236 | −0.523114 | ||||||||
\(322\) | −13.5892 | −0.757298 | ||||||||
\(323\) | 2.32476 | 0.129353 | ||||||||
\(324\) | −0.175259 | −0.00973662 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.6562 | 0.645579 | ||||||||
\(327\) | 15.5899 | 0.862125 | ||||||||
\(328\) | 3.41714 | 0.188680 | ||||||||
\(329\) | 12.1947 | 0.672313 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.4925 | −0.796579 | −0.398289 | − | 0.917260i | \(-0.630396\pi\) | ||||
−0.398289 | + | 0.917260i | \(0.630396\pi\) | |||||||
\(332\) | −0.880498 | −0.0483236 | ||||||||
\(333\) | −3.55334 | −0.194722 | ||||||||
\(334\) | 8.91400 | 0.487753 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5.77482 | 0.315042 | ||||||||
\(337\) | −9.33225 | −0.508360 | −0.254180 | − | 0.967157i | \(-0.581806\pi\) | ||||
−0.254180 | + | 0.967157i | \(0.581806\pi\) | |||||||
\(338\) | −49.6039 | −2.69810 | ||||||||
\(339\) | 10.0481 | 0.545737 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.31885 | −0.179726 | ||||||||
\(342\) | −0.766643 | −0.0414553 | ||||||||
\(343\) | −18.2774 | −0.986884 | ||||||||
\(344\) | 0.343857 | 0.0185395 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.4517 | 0.991968 | ||||||||
\(347\) | 1.05341 | 0.0565499 | 0.0282750 | − | 0.999600i | \(-0.490999\pi\) | ||||
0.0282750 | + | 0.999600i | \(0.490999\pi\) | |||||||
\(348\) | −0.487847 | −0.0261513 | ||||||||
\(349\) | −13.0715 | −0.699700 | −0.349850 | − | 0.936806i | \(-0.613767\pi\) | ||||
−0.349850 | + | 0.936806i | \(0.613767\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.05132 | −0.376371 | ||||||||
\(352\) | −3.29435 | −0.175590 | ||||||||
\(353\) | −33.9473 | −1.80683 | −0.903415 | − | 0.428767i | \(-0.858948\pi\) | ||||
−0.903415 | + | 0.428767i | \(0.858948\pi\) | |||||||
\(354\) | 1.32921 | 0.0706469 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.494845 | −0.0262267 | ||||||||
\(357\) | −6.53678 | −0.345963 | ||||||||
\(358\) | −13.2770 | −0.701713 | ||||||||
\(359\) | −6.09450 | −0.321656 | −0.160828 | − | 0.986982i | \(-0.551416\pi\) | ||||
−0.160828 | + | 0.986982i | \(0.551416\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6779 | −0.983048 | ||||||||
\(362\) | −24.1376 | −1.26864 | ||||||||
\(363\) | −0.107347 | −0.00563424 | ||||||||
\(364\) | −1.97210 | −0.103366 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 14.3373 | 0.749423 | ||||||||
\(367\) | 21.8636 | 1.14127 | 0.570636 | − | 0.821203i | \(-0.306697\pi\) | ||||
0.570636 | + | 0.821203i | \(0.306697\pi\) | |||||||
\(368\) | −22.8127 | −1.18919 | ||||||||
\(369\) | 1.16293 | 0.0605395 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.835615 | 0.0433830 | ||||||||
\(372\) | −0.174527 | −0.00904882 | ||||||||
\(373\) | 24.4559 | 1.26628 | 0.633140 | − | 0.774037i | \(-0.281766\pi\) | ||||
0.633140 | + | 0.774037i | \(0.281766\pi\) | |||||||
\(374\) | −18.4413 | −0.953578 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 22.4545 | 1.15800 | ||||||||
\(377\) | −19.6279 | −1.01089 | ||||||||
\(378\) | 2.15565 | 0.110875 | ||||||||
\(379\) | −6.27821 | −0.322490 | −0.161245 | − | 0.986914i | \(-0.551551\pi\) | ||||
−0.161245 | + | 0.986914i | \(0.551551\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.976784 | −0.0500422 | ||||||||
\(382\) | −0.440118 | −0.0225184 | ||||||||
\(383\) | −24.6876 | −1.26148 | −0.630738 | − | 0.775996i | \(-0.717248\pi\) | ||||
−0.630738 | + | 0.775996i | \(0.717248\pi\) | |||||||
\(384\) | 9.60343 | 0.490073 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.91993 | −0.199519 | ||||||||
\(387\) | 0.117022 | 0.00594854 | ||||||||
\(388\) | 0.298978 | 0.0151783 | ||||||||
\(389\) | −12.9236 | −0.655251 | −0.327626 | − | 0.944808i | \(-0.606248\pi\) | ||||
−0.327626 | + | 0.944808i | \(0.606248\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.8228 | 1.30591 | ||||||||
\(392\) | −13.0860 | −0.660942 | ||||||||
\(393\) | −10.0616 | −0.507541 | ||||||||
\(394\) | −24.4797 | −1.23327 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.584098 | −0.0293520 | ||||||||
\(397\) | 29.0214 | 1.45654 | 0.728272 | − | 0.685288i | \(-0.240324\pi\) | ||||
0.728272 | + | 0.685288i | \(0.240324\pi\) | |||||||
\(398\) | −2.07022 | −0.103771 | ||||||||
\(399\) | −0.905670 | −0.0453402 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.3926 | 1.16817 | 0.584084 | − | 0.811693i | \(-0.301454\pi\) | ||||
0.584084 | + | 0.811693i | \(0.301454\pi\) | |||||||
\(402\) | −20.5541 | −1.02515 | ||||||||
\(403\) | −7.02187 | −0.349784 | ||||||||
\(404\) | −2.30898 | −0.114876 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.00041 | 0.297795 | ||||||||
\(407\) | −11.8425 | −0.587009 | ||||||||
\(408\) | −12.0364 | −0.595892 | ||||||||
\(409\) | −15.9918 | −0.790742 | −0.395371 | − | 0.918521i | \(-0.629384\pi\) | ||||
−0.395371 | + | 0.918521i | \(0.629384\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.87244 | −0.240340 | ||||||||
\(412\) | −1.90542 | −0.0938731 | ||||||||
\(413\) | 1.57026 | 0.0772675 | ||||||||
\(414\) | −8.51563 | −0.418521 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.97004 | −0.341734 | ||||||||
\(417\) | −0.185784 | −0.00909787 | ||||||||
\(418\) | −2.55504 | −0.124971 | ||||||||
\(419\) | 32.3769 | 1.58172 | 0.790858 | − | 0.611999i | \(-0.209634\pi\) | ||||
0.790858 | + | 0.611999i | \(0.209634\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.0520 | 0.879801 | 0.439900 | − | 0.898047i | \(-0.355014\pi\) | ||||
0.439900 | + | 0.898047i | \(0.355014\pi\) | |||||||
\(422\) | 15.3586 | 0.747646 | ||||||||
\(423\) | 7.64173 | 0.371554 | ||||||||
\(424\) | 1.53865 | 0.0747235 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −14.4052 | −0.697932 | ||||||||
\(427\) | 16.9373 | 0.819654 | ||||||||
\(428\) | −1.64259 | −0.0793977 | ||||||||
\(429\) | −23.5004 | −1.13461 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.1353 | 1.59607 | 0.798035 | − | 0.602612i | \(-0.205873\pi\) | ||||
0.798035 | + | 0.602612i | \(0.205873\pi\) | |||||||
\(432\) | 3.61877 | 0.174108 | ||||||||
\(433\) | 22.6653 | 1.08922 | 0.544612 | − | 0.838688i | \(-0.316677\pi\) | ||||
0.544612 | + | 0.838688i | \(0.316677\pi\) | |||||||
\(434\) | 2.14665 | 0.103042 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.73228 | 0.130852 | ||||||||
\(437\) | 3.57774 | 0.171147 | ||||||||
\(438\) | 7.50834 | 0.358762 | ||||||||
\(439\) | −8.50436 | −0.405891 | −0.202945 | − | 0.979190i | \(-0.565051\pi\) | ||||
−0.202945 | + | 0.979190i | \(0.565051\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.45343 | −0.212068 | ||||||||
\(442\) | −39.0173 | −1.85586 | ||||||||
\(443\) | −6.35768 | −0.302063 | −0.151031 | − | 0.988529i | \(-0.548259\pi\) | ||||
−0.151031 | + | 0.988529i | \(0.548259\pi\) | |||||||
\(444\) | −0.622755 | −0.0295547 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 22.8975 | 1.08423 | ||||||||
\(447\) | −3.88889 | −0.183938 | ||||||||
\(448\) | 13.6804 | 0.646340 | ||||||||
\(449\) | −6.25726 | −0.295298 | −0.147649 | − | 0.989040i | \(-0.547171\pi\) | ||||
−0.147649 | + | 0.989040i | \(0.547171\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.87576 | 0.182502 | ||||||||
\(452\) | 1.76102 | 0.0828313 | ||||||||
\(453\) | 22.1146 | 1.03903 | ||||||||
\(454\) | 19.0625 | 0.894648 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.66765 | −0.0780947 | ||||||||
\(457\) | 11.0441 | 0.516620 | 0.258310 | − | 0.966062i | \(-0.416834\pi\) | ||||
0.258310 | + | 0.966062i | \(0.416834\pi\) | |||||||
\(458\) | −0.0837440 | −0.00391310 | ||||||||
\(459\) | −4.09625 | −0.191196 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.6622 | −1.10206 | −0.551029 | − | 0.834486i | \(-0.685765\pi\) | ||||
−0.551029 | + | 0.834486i | \(0.685765\pi\) | |||||||
\(462\) | 7.18428 | 0.334243 | ||||||||
\(463\) | 6.22442 | 0.289273 | 0.144637 | − | 0.989485i | \(-0.453799\pi\) | ||||
0.144637 | + | 0.989485i | \(0.453799\pi\) | |||||||
\(464\) | 10.0731 | 0.467632 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −35.1473 | −1.62817 | ||||||||
\(467\) | −4.94679 | −0.228910 | −0.114455 | − | 0.993428i | \(-0.536512\pi\) | ||||
−0.114455 | + | 0.993428i | \(0.536512\pi\) | |||||||
\(468\) | −1.23581 | −0.0571252 | ||||||||
\(469\) | −24.2815 | −1.12122 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.6058 | 0.626923 | ||||||||
\(472\) | 2.89138 | 0.133087 | ||||||||
\(473\) | 0.390006 | 0.0179325 | ||||||||
\(474\) | −19.7179 | −0.905671 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.14563 | −0.0525099 | ||||||||
\(477\) | 0.523635 | 0.0239756 | ||||||||
\(478\) | −26.3372 | −1.20463 | ||||||||
\(479\) | −30.0898 | −1.37484 | −0.687419 | − | 0.726261i | \(-0.741256\pi\) | ||||
−0.687419 | + | 0.726261i | \(0.741256\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.0557 | −1.14244 | ||||||||
\(482\) | 5.53651 | 0.252181 | ||||||||
\(483\) | −10.0599 | −0.457742 | ||||||||
\(484\) | −0.0188135 | −0.000855159 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.35083 | 0.0612749 | ||||||||
\(487\) | 34.2499 | 1.55201 | 0.776006 | − | 0.630726i | \(-0.217243\pi\) | ||||
0.776006 | + | 0.630726i | \(0.217243\pi\) | |||||||
\(488\) | 31.1874 | 1.41179 | ||||||||
\(489\) | 8.62895 | 0.390215 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.4193 | −0.470218 | −0.235109 | − | 0.971969i | \(-0.575545\pi\) | ||||
−0.235109 | + | 0.971969i | \(0.575545\pi\) | |||||||
\(492\) | 0.203813 | 0.00918861 | ||||||||
\(493\) | −11.4022 | −0.513530 | ||||||||
\(494\) | −5.40584 | −0.243220 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.60365 | 0.161809 | ||||||||
\(497\) | −17.0175 | −0.763338 | ||||||||
\(498\) | 6.78654 | 0.304112 | ||||||||
\(499\) | 8.83514 | 0.395515 | 0.197757 | − | 0.980251i | \(-0.436634\pi\) | ||||
0.197757 | + | 0.980251i | \(0.436634\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.59891 | 0.294818 | ||||||||
\(502\) | 1.39044 | 0.0620585 | ||||||||
\(503\) | −21.3734 | −0.952994 | −0.476497 | − | 0.879176i | \(-0.658094\pi\) | ||||
−0.476497 | + | 0.879176i | \(0.658094\pi\) | |||||||
\(504\) | 4.68910 | 0.208869 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −28.3806 | −1.26167 | ||||||||
\(507\) | −36.7211 | −1.63084 | ||||||||
\(508\) | −0.171190 | −0.00759535 | ||||||||
\(509\) | −16.7800 | −0.743759 | −0.371879 | − | 0.928281i | \(-0.621286\pi\) | ||||
−0.371879 | + | 0.928281i | \(0.621286\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.86994 | 0.392383 | ||||||||
\(512\) | 24.8438 | 1.09795 | ||||||||
\(513\) | −0.567535 | −0.0250573 | ||||||||
\(514\) | −25.0710 | −1.10584 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.0205091 | 0.000902863 0 | ||||||||
\(517\) | 25.4681 | 1.12009 | ||||||||
\(518\) | 7.65976 | 0.336550 | ||||||||
\(519\) | 13.6595 | 0.599586 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.60508 | −0.201752 | −0.100876 | − | 0.994899i | \(-0.532165\pi\) | ||||
−0.100876 | + | 0.994899i | \(0.532165\pi\) | |||||||
\(522\) | 3.76013 | 0.164577 | ||||||||
\(523\) | −12.9634 | −0.566852 | −0.283426 | − | 0.958994i | \(-0.591471\pi\) | ||||
−0.283426 | + | 0.958994i | \(0.591471\pi\) | |||||||
\(524\) | −1.76339 | −0.0770340 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.7418 | 0.729979 | ||||||||
\(527\) | −4.07914 | −0.177690 | ||||||||
\(528\) | 12.0605 | 0.524866 | ||||||||
\(529\) | 16.7405 | 0.727846 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.983998 | 0.0427019 | ||||||||
\(532\) | −0.158727 | −0.00688169 | ||||||||
\(533\) | 8.20015 | 0.355188 | ||||||||
\(534\) | 3.81407 | 0.165051 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −44.7106 | −1.93120 | ||||||||
\(537\) | −9.82880 | −0.424144 | ||||||||
\(538\) | 7.15983 | 0.308682 | ||||||||
\(539\) | −14.8423 | −0.639301 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.3641 | −1.17647 | −0.588237 | − | 0.808688i | \(-0.700178\pi\) | ||||
−0.588237 | + | 0.808688i | \(0.700178\pi\) | |||||||
\(542\) | −1.07719 | −0.0462692 | ||||||||
\(543\) | −17.8687 | −0.766819 | ||||||||
\(544\) | −4.04903 | −0.173601 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 15.2002 | 0.650507 | ||||||||
\(547\) | −27.6453 | −1.18203 | −0.591015 | − | 0.806661i | \(-0.701272\pi\) | ||||
−0.591015 | + | 0.806661i | \(0.701272\pi\) | |||||||
\(548\) | −0.853941 | −0.0364785 | ||||||||
\(549\) | 10.6137 | 0.452982 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.57978 | −0.0673007 | ||||||||
\(552\) | −18.5237 | −0.788422 | ||||||||
\(553\) | −23.2936 | −0.990545 | ||||||||
\(554\) | −6.40868 | −0.272279 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.0325603 | −0.00138086 | ||||||||
\(557\) | 6.17333 | 0.261572 | 0.130786 | − | 0.991411i | \(-0.458250\pi\) | ||||
0.130786 | + | 0.991411i | \(0.458250\pi\) | |||||||
\(558\) | 1.34519 | 0.0569464 | ||||||||
\(559\) | 0.825156 | 0.0349004 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.6518 | −0.576381 | ||||||||
\(562\) | 25.3143 | 1.06782 | ||||||||
\(563\) | −5.69934 | −0.240198 | −0.120099 | − | 0.992762i | \(-0.538321\pi\) | ||||
−0.120099 | + | 0.992762i | \(0.538321\pi\) | |||||||
\(564\) | 1.33928 | 0.0563940 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 15.8874 | 0.667796 | ||||||||
\(567\) | 1.59580 | 0.0670172 | ||||||||
\(568\) | −31.3350 | −1.31479 | ||||||||
\(569\) | 20.1708 | 0.845605 | 0.422802 | − | 0.906222i | \(-0.361046\pi\) | ||||
0.422802 | + | 0.906222i | \(0.361046\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.7554 | −0.659341 | −0.329671 | − | 0.944096i | \(-0.606938\pi\) | ||||
−0.329671 | + | 0.944096i | \(0.606938\pi\) | |||||||
\(572\) | −4.11866 | −0.172210 | ||||||||
\(573\) | −0.325813 | −0.0136111 | ||||||||
\(574\) | −2.50686 | −0.104634 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 8.57279 | 0.357200 | ||||||||
\(577\) | 16.1062 | 0.670509 | 0.335255 | − | 0.942128i | \(-0.391178\pi\) | ||||
0.335255 | + | 0.942128i | \(0.391178\pi\) | |||||||
\(578\) | 0.298195 | 0.0124033 | ||||||||
\(579\) | −2.90187 | −0.120598 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.01725 | 0.332611 | ||||||||
\(582\) | −2.30441 | −0.0955207 | ||||||||
\(583\) | 1.74515 | 0.0722769 | ||||||||
\(584\) | 16.3326 | 0.675847 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 30.0990 | 1.24338 | ||||||||
\(587\) | −2.00072 | −0.0825786 | −0.0412893 | − | 0.999147i | \(-0.513147\pi\) | ||||
−0.0412893 | + | 0.999147i | \(0.513147\pi\) | |||||||
\(588\) | −0.780505 | −0.0321875 | ||||||||
\(589\) | −0.565165 | −0.0232872 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.1220 | −0.745438 | ||||||||
\(592\) | 12.8587 | 0.528489 | ||||||||
\(593\) | 26.8231 | 1.10149 | 0.550747 | − | 0.834672i | \(-0.314343\pi\) | ||||
0.550747 | + | 0.834672i | \(0.314343\pi\) | |||||||
\(594\) | 4.50200 | 0.184719 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.681563 | −0.0279179 | ||||||||
\(597\) | −1.53256 | −0.0627234 | ||||||||
\(598\) | −60.0464 | −2.45548 | ||||||||
\(599\) | −44.8025 | −1.83058 | −0.915290 | − | 0.402796i | \(-0.868038\pi\) | ||||
−0.915290 | + | 0.402796i | \(0.868038\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.2298 | −0.580446 | −0.290223 | − | 0.956959i | \(-0.593729\pi\) | ||||
−0.290223 | + | 0.956959i | \(0.593729\pi\) | |||||||
\(602\) | −0.252258 | −0.0102813 | ||||||||
\(603\) | −15.2159 | −0.619641 | ||||||||
\(604\) | 3.87578 | 0.157703 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 17.7967 | 0.722943 | ||||||||
\(607\) | 20.3346 | 0.825356 | 0.412678 | − | 0.910877i | \(-0.364594\pi\) | ||||
0.412678 | + | 0.910877i | \(0.364594\pi\) | |||||||
\(608\) | −0.560993 | −0.0227513 | ||||||||
\(609\) | 4.44202 | 0.180000 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 53.8843 | 2.17993 | ||||||||
\(612\) | −0.717905 | −0.0290196 | ||||||||
\(613\) | 20.7921 | 0.839783 | 0.419892 | − | 0.907574i | \(-0.362068\pi\) | ||||
0.419892 | + | 0.907574i | \(0.362068\pi\) | |||||||
\(614\) | −20.6761 | −0.834421 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 15.6277 | 0.629657 | ||||||||
\(617\) | −4.94634 | −0.199132 | −0.0995660 | − | 0.995031i | \(-0.531745\pi\) | ||||
−0.0995660 | + | 0.995031i | \(0.531745\pi\) | |||||||
\(618\) | 14.6862 | 0.590766 | ||||||||
\(619\) | −45.9527 | −1.84700 | −0.923498 | − | 0.383603i | \(-0.874683\pi\) | ||||
−0.923498 | + | 0.383603i | \(0.874683\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.30400 | −0.252971 | ||||||||
\(622\) | 17.3643 | 0.696243 | ||||||||
\(623\) | 4.50574 | 0.180519 | ||||||||
\(624\) | 25.5171 | 1.02150 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −14.1934 | −0.567283 | ||||||||
\(627\) | −1.89146 | −0.0755377 | ||||||||
\(628\) | 2.38454 | 0.0951537 | ||||||||
\(629\) | −14.5554 | −0.580360 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.6636 | −0.862414 | −0.431207 | − | 0.902253i | \(-0.641912\pi\) | ||||
−0.431207 | + | 0.902253i | \(0.641912\pi\) | |||||||
\(632\) | −42.8915 | −1.70613 | ||||||||
\(633\) | 11.3698 | 0.451908 | ||||||||
\(634\) | −26.3150 | −1.04510 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.0917718 | 0.00363899 | ||||||||
\(637\) | −31.4026 | −1.24421 | ||||||||
\(638\) | 12.5317 | 0.496133 | ||||||||
\(639\) | −10.6639 | −0.421859 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.3870 | 1.43720 | 0.718600 | − | 0.695424i | \(-0.244783\pi\) | ||||
0.718600 | + | 0.695424i | \(0.244783\pi\) | |||||||
\(642\) | 12.6605 | 0.499668 | ||||||||
\(643\) | 1.01349 | 0.0399682 | 0.0199841 | − | 0.999800i | \(-0.493638\pi\) | ||||
0.0199841 | + | 0.999800i | \(0.493638\pi\) | |||||||
\(644\) | −1.76309 | −0.0694755 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.14036 | −0.123556 | ||||||||
\(647\) | −13.7007 | −0.538629 | −0.269315 | − | 0.963052i | \(-0.586797\pi\) | ||||
−0.269315 | + | 0.963052i | \(0.586797\pi\) | |||||||
\(648\) | 2.93840 | 0.115431 | ||||||||
\(649\) | 3.27944 | 0.128729 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.58913 | 0.0622830 | ||||||||
\(652\) | 1.51230 | 0.0592263 | ||||||||
\(653\) | 23.8372 | 0.932822 | 0.466411 | − | 0.884568i | \(-0.345547\pi\) | ||||
0.466411 | + | 0.884568i | \(0.345547\pi\) | |||||||
\(654\) | −21.0593 | −0.823485 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.20835 | −0.164309 | ||||||||
\(657\) | 5.55832 | 0.216851 | ||||||||
\(658\) | −16.4729 | −0.642181 | ||||||||
\(659\) | 14.7758 | 0.575583 | 0.287791 | − | 0.957693i | \(-0.407079\pi\) | ||||
0.287791 | + | 0.957693i | \(0.407079\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.55471 | 0.293844 | 0.146922 | − | 0.989148i | \(-0.453063\pi\) | ||||
0.146922 | + | 0.989148i | \(0.453063\pi\) | |||||||
\(662\) | 19.5769 | 0.760877 | ||||||||
\(663\) | −28.8839 | −1.12176 | ||||||||
\(664\) | 14.7625 | 0.572895 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.79996 | 0.185995 | ||||||||
\(667\) | −17.5477 | −0.679448 | ||||||||
\(668\) | 1.15652 | 0.0447471 | ||||||||
\(669\) | 16.9507 | 0.655351 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 35.3730 | 1.36556 | ||||||||
\(672\) | 1.57740 | 0.0608496 | ||||||||
\(673\) | 12.1947 | 0.470069 | 0.235035 | − | 0.971987i | \(-0.424480\pi\) | ||||
0.235035 | + | 0.971987i | \(0.424480\pi\) | |||||||
\(674\) | 12.6063 | 0.485576 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.43571 | −0.247527 | ||||||||
\(677\) | −17.9507 | −0.689900 | −0.344950 | − | 0.938621i | \(-0.612104\pi\) | ||||
−0.344950 | + | 0.938621i | \(0.612104\pi\) | |||||||
\(678\) | −13.5732 | −0.521277 | ||||||||
\(679\) | −2.72230 | −0.104472 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.1117 | 0.540762 | ||||||||
\(682\) | 4.48320 | 0.171671 | ||||||||
\(683\) | −10.0273 | −0.383685 | −0.191842 | − | 0.981426i | \(-0.561446\pi\) | ||||
−0.191842 | + | 0.981426i | \(0.561446\pi\) | |||||||
\(684\) | −0.0994657 | −0.00380317 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 24.6896 | 0.942653 | ||||||||
\(687\) | −0.0619945 | −0.00236524 | ||||||||
\(688\) | −0.423474 | −0.0161448 | ||||||||
\(689\) | 3.69231 | 0.140666 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.1296 | 0.727722 | 0.363861 | − | 0.931453i | \(-0.381458\pi\) | ||||
0.363861 | + | 0.931453i | \(0.381458\pi\) | |||||||
\(692\) | 2.39396 | 0.0910045 | ||||||||
\(693\) | 5.31842 | 0.202030 | ||||||||
\(694\) | −1.42297 | −0.0540154 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.17927 | 0.310034 | ||||||||
\(697\) | 4.76363 | 0.180435 | ||||||||
\(698\) | 17.6573 | 0.668340 | ||||||||
\(699\) | −26.0191 | −0.984131 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.81920 | −0.144249 | −0.0721246 | − | 0.997396i | \(-0.522978\pi\) | ||||
−0.0721246 | + | 0.997396i | \(0.522978\pi\) | |||||||
\(702\) | 9.52513 | 0.359503 | ||||||||
\(703\) | −2.01664 | −0.0760592 | ||||||||
\(704\) | 28.5711 | 1.07681 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 45.8570 | 1.72585 | ||||||||
\(707\) | 21.0241 | 0.790692 | ||||||||
\(708\) | 0.172455 | 0.00648124 | ||||||||
\(709\) | 38.0535 | 1.42913 | 0.714565 | − | 0.699569i | \(-0.246625\pi\) | ||||
0.714565 | + | 0.699569i | \(0.246625\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.5969 | −0.547425 | ||||||||
\(712\) | 8.29660 | 0.310928 | ||||||||
\(713\) | −6.27768 | −0.235101 | ||||||||
\(714\) | 8.83008 | 0.330457 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.72259 | −0.0643761 | ||||||||
\(717\) | −19.4970 | −0.728130 | ||||||||
\(718\) | 8.23264 | 0.307239 | ||||||||
\(719\) | 19.4340 | 0.724766 | 0.362383 | − | 0.932029i | \(-0.381963\pi\) | ||||
0.362383 | + | 0.932029i | \(0.381963\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.3495 | 0.646129 | ||||||||
\(722\) | 25.2307 | 0.938988 | ||||||||
\(723\) | 4.09860 | 0.152429 | ||||||||
\(724\) | −3.13165 | −0.116387 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.145007 | 0.00538172 | ||||||||
\(727\) | 38.0739 | 1.41208 | 0.706042 | − | 0.708170i | \(-0.250479\pi\) | ||||
0.706042 | + | 0.708170i | \(0.250479\pi\) | |||||||
\(728\) | 33.0643 | 1.22544 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.479350 | 0.0177294 | ||||||||
\(732\) | 1.86015 | 0.0687531 | ||||||||
\(733\) | −16.9591 | −0.626400 | −0.313200 | − | 0.949687i | \(-0.601401\pi\) | ||||
−0.313200 | + | 0.949687i | \(0.601401\pi\) | |||||||
\(734\) | −29.5341 | −1.09012 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.23134 | −0.229690 | ||||||||
\(737\) | −50.7112 | −1.86797 | ||||||||
\(738\) | −1.57091 | −0.0578261 | ||||||||
\(739\) | 13.2040 | 0.485716 | 0.242858 | − | 0.970062i | \(-0.421915\pi\) | ||||
0.242858 | + | 0.970062i | \(0.421915\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.00187 | −0.147012 | ||||||||
\(742\) | −1.12877 | −0.0414386 | ||||||||
\(743\) | −42.2364 | −1.54950 | −0.774752 | − | 0.632265i | \(-0.782125\pi\) | ||||
−0.774752 | + | 0.632265i | \(0.782125\pi\) | |||||||
\(744\) | 2.92613 | 0.107277 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −33.0358 | −1.20953 | ||||||||
\(747\) | 5.02398 | 0.183818 | ||||||||
\(748\) | −2.39261 | −0.0874825 | ||||||||
\(749\) | 14.9564 | 0.546494 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.04801 | −0.0382426 | −0.0191213 | − | 0.999817i | \(-0.506087\pi\) | ||||
−0.0191213 | + | 0.999817i | \(0.506087\pi\) | |||||||
\(752\) | −27.6536 | −1.00842 | ||||||||
\(753\) | 1.02933 | 0.0375107 | ||||||||
\(754\) | 26.5139 | 0.965579 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.279678 | 0.0101718 | ||||||||
\(757\) | −17.0074 | −0.618146 | −0.309073 | − | 0.951038i | \(-0.600019\pi\) | ||||
−0.309073 | + | 0.951038i | \(0.600019\pi\) | |||||||
\(758\) | 8.48079 | 0.308036 | ||||||||
\(759\) | −21.0098 | −0.762607 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.1244 | −0.874508 | −0.437254 | − | 0.899338i | \(-0.644049\pi\) | ||||
−0.437254 | + | 0.899338i | \(0.644049\pi\) | |||||||
\(762\) | 1.31947 | 0.0477993 | ||||||||
\(763\) | −24.8783 | −0.900657 | ||||||||
\(764\) | −0.0571018 | −0.00206587 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 33.3487 | 1.20494 | ||||||||
\(767\) | 6.93848 | 0.250534 | ||||||||
\(768\) | 4.17298 | 0.150579 | ||||||||
\(769\) | 49.7819 | 1.79518 | 0.897591 | − | 0.440830i | \(-0.145316\pi\) | ||||
0.897591 | + | 0.440830i | \(0.145316\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.5597 | −0.668412 | ||||||||
\(772\) | −0.508580 | −0.0183042 | ||||||||
\(773\) | 31.4743 | 1.13205 | 0.566025 | − | 0.824388i | \(-0.308480\pi\) | ||||
0.566025 | + | 0.824388i | \(0.308480\pi\) | |||||||
\(774\) | −0.158076 | −0.00568193 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.01268 | −0.179945 | ||||||||
\(777\) | 5.67041 | 0.203425 | ||||||||
\(778\) | 17.4575 | 0.625883 | ||||||||
\(779\) | 0.660001 | 0.0236470 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −35.5404 | −1.27174 | ||||||||
\(782\) | −34.8822 | −1.24738 | ||||||||
\(783\) | 2.78357 | 0.0994768 | ||||||||
\(784\) | 16.1159 | 0.575569 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 13.5915 | 0.484793 | ||||||||
\(787\) | 19.1415 | 0.682321 | 0.341161 | − | 0.940005i | \(-0.389180\pi\) | ||||
0.341161 | + | 0.940005i | \(0.389180\pi\) | |||||||
\(788\) | −3.17604 | −0.113142 | ||||||||
\(789\) | 12.3938 | 0.441229 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.0347 | −0.570128 | ||||||||
\(792\) | 9.79302 | 0.347980 | ||||||||
\(793\) | 74.8406 | 2.65767 | ||||||||
\(794\) | −39.2030 | −1.39126 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.268595 | −0.00952009 | ||||||||
\(797\) | 7.21437 | 0.255546 | 0.127773 | − | 0.991803i | \(-0.459217\pi\) | ||||
0.127773 | + | 0.991803i | \(0.459217\pi\) | |||||||
\(798\) | 1.22341 | 0.0433081 | ||||||||
\(799\) | 31.3024 | 1.10740 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.82350 | 0.0997636 | ||||||||
\(802\) | −31.5994 | −1.11581 | ||||||||
\(803\) | 18.5246 | 0.653718 | ||||||||
\(804\) | −2.66673 | −0.0940484 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.48535 | 0.334107 | ||||||||
\(807\) | 5.30032 | 0.186580 | ||||||||
\(808\) | 38.7125 | 1.36190 | ||||||||
\(809\) | 1.05941 | 0.0372469 | 0.0186234 | − | 0.999827i | \(-0.494072\pi\) | ||||
0.0186234 | + | 0.999827i | \(0.494072\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.6400 | 0.759883 | 0.379941 | − | 0.925011i | \(-0.375944\pi\) | ||||
0.379941 | + | 0.925011i | \(0.375944\pi\) | |||||||
\(812\) | 0.778504 | 0.0273202 | ||||||||
\(813\) | −0.797428 | −0.0279670 | ||||||||
\(814\) | 15.9971 | 0.560700 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 14.8234 | 0.518922 | ||||||||
\(817\) | 0.0664138 | 0.00232353 | ||||||||
\(818\) | 21.6022 | 0.755302 | ||||||||
\(819\) | 11.2525 | 0.393193 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.1828 | −0.809085 | −0.404543 | − | 0.914519i | \(-0.632569\pi\) | ||||
−0.404543 | + | 0.914519i | \(0.632569\pi\) | |||||||
\(822\) | 6.58184 | 0.229568 | ||||||||
\(823\) | 27.9769 | 0.975214 | 0.487607 | − | 0.873063i | \(-0.337870\pi\) | ||||
0.487607 | + | 0.873063i | \(0.337870\pi\) | |||||||
\(824\) | 31.9463 | 1.11290 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.12116 | −0.0738044 | ||||||||
\(827\) | 41.3045 | 1.43630 | 0.718150 | − | 0.695889i | \(-0.244989\pi\) | ||||
0.718150 | + | 0.695889i | \(0.244989\pi\) | |||||||
\(828\) | −1.10483 | −0.0383956 | ||||||||
\(829\) | 47.5687 | 1.65213 | 0.826064 | − | 0.563577i | \(-0.190575\pi\) | ||||
0.826064 | + | 0.563577i | \(0.190575\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.74425 | −0.164576 | ||||||||
\(832\) | 60.4495 | 2.09571 | ||||||||
\(833\) | −18.2424 | −0.632060 | ||||||||
\(834\) | 0.250962 | 0.00869011 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.331496 | −0.0114650 | ||||||||
\(837\) | 0.995824 | 0.0344207 | ||||||||
\(838\) | −43.7357 | −1.51083 | ||||||||
\(839\) | 49.0322 | 1.69278 | 0.846389 | − | 0.532565i | \(-0.178772\pi\) | ||||
0.846389 | + | 0.532565i | \(0.178772\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.2517 | −0.732818 | ||||||||
\(842\) | −24.3852 | −0.840369 | ||||||||
\(843\) | 18.7398 | 0.645433 | ||||||||
\(844\) | 1.99266 | 0.0685900 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −10.3227 | −0.354901 | ||||||||
\(847\) | 0.171304 | 0.00588606 | ||||||||
\(848\) | −1.89491 | −0.0650715 | ||||||||
\(849\) | 11.7612 | 0.403643 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.4003 | −0.767871 | ||||||||
\(852\) | −1.86895 | −0.0640293 | ||||||||
\(853\) | 32.5376 | 1.11407 | 0.557033 | − | 0.830490i | \(-0.311939\pi\) | ||||
0.557033 | + | 0.830490i | \(0.311939\pi\) | |||||||
\(854\) | −22.8794 | −0.782918 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 27.5398 | 0.941290 | ||||||||
\(857\) | 30.4813 | 1.04122 | 0.520610 | − | 0.853794i | \(-0.325704\pi\) | ||||
0.520610 | + | 0.853794i | \(0.325704\pi\) | |||||||
\(858\) | 31.7451 | 1.08376 | ||||||||
\(859\) | 4.12215 | 0.140646 | 0.0703231 | − | 0.997524i | \(-0.477597\pi\) | ||||
0.0703231 | + | 0.997524i | \(0.477597\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.85579 | −0.0632452 | ||||||||
\(862\) | −44.7601 | −1.52453 | ||||||||
\(863\) | 18.4184 | 0.626969 | 0.313485 | − | 0.949593i | \(-0.398504\pi\) | ||||
0.313485 | + | 0.949593i | \(0.398504\pi\) | |||||||
\(864\) | 0.988473 | 0.0336285 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −30.6169 | −1.04041 | ||||||||
\(867\) | 0.220750 | 0.00749705 | ||||||||
\(868\) | 0.278510 | 0.00945325 | ||||||||
\(869\) | −48.6479 | −1.65027 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −107.292 | −3.63546 | ||||||||
\(872\) | −45.8095 | −1.55131 | ||||||||
\(873\) | −1.70592 | −0.0577366 | ||||||||
\(874\) | −4.83292 | −0.163476 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.974146 | 0.0329133 | ||||||||
\(877\) | 18.9126 | 0.638634 | 0.319317 | − | 0.947648i | \(-0.396547\pi\) | ||||
0.319317 | + | 0.947648i | \(0.396547\pi\) | |||||||
\(878\) | 11.4879 | 0.387699 | ||||||||
\(879\) | 22.2819 | 0.751548 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.6336 | 1.16684 | 0.583418 | − | 0.812172i | \(-0.301715\pi\) | ||||
0.583418 | + | 0.812172i | \(0.301715\pi\) | |||||||
\(882\) | 6.01583 | 0.202563 | ||||||||
\(883\) | 32.6874 | 1.10002 | 0.550009 | − | 0.835158i | \(-0.314624\pi\) | ||||
0.550009 | + | 0.835158i | \(0.314624\pi\) | |||||||
\(884\) | −5.06218 | −0.170259 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.58814 | 0.288524 | ||||||||
\(887\) | −48.7918 | −1.63827 | −0.819134 | − | 0.573602i | \(-0.805545\pi\) | ||||
−0.819134 | + | 0.573602i | \(0.805545\pi\) | |||||||
\(888\) | 10.4411 | 0.350382 | ||||||||
\(889\) | 1.55875 | 0.0522788 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.33277 | 0.111652 | ||||||||
\(892\) | 2.97076 | 0.0994684 | ||||||||
\(893\) | 4.33695 | 0.145131 | ||||||||
\(894\) | 5.25322 | 0.175694 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −15.3251 | −0.511977 | ||||||||
\(897\) | −44.4515 | −1.48419 | ||||||||
\(898\) | 8.45249 | 0.282063 | ||||||||
\(899\) | 2.77195 | 0.0924497 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.14494 | 0.0714582 | ||||||||
\(902\) | −5.23549 | −0.174323 | ||||||||
\(903\) | −0.186743 | −0.00621441 | ||||||||
\(904\) | −29.5253 | −0.981997 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −29.8730 | −0.992465 | ||||||||
\(907\) | −45.0367 | −1.49542 | −0.747710 | − | 0.664025i | \(-0.768847\pi\) | ||||
−0.747710 | + | 0.664025i | \(0.768847\pi\) | |||||||
\(908\) | 2.47321 | 0.0820762 | ||||||||
\(909\) | 13.1747 | 0.436976 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.9449 | 0.428882 | 0.214441 | − | 0.976737i | \(-0.431207\pi\) | ||||
0.214441 | + | 0.976737i | \(0.431207\pi\) | |||||||
\(912\) | 2.05378 | 0.0680073 | ||||||||
\(913\) | 16.7438 | 0.554137 | ||||||||
\(914\) | −14.9187 | −0.493466 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.0108651 | −0.000358993 0 | ||||||||
\(917\) | 16.0563 | 0.530225 | ||||||||
\(918\) | 5.53333 | 0.182627 | ||||||||
\(919\) | 14.5719 | 0.480682 | 0.240341 | − | 0.970689i | \(-0.422741\pi\) | ||||
0.240341 | + | 0.970689i | \(0.422741\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.3063 | −0.504358 | ||||||||
\(922\) | 31.9636 | 1.05266 | ||||||||
\(923\) | −75.1948 | −2.47507 | ||||||||
\(924\) | 0.932102 | 0.0306639 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −8.40813 | −0.276308 | ||||||||
\(927\) | 10.8720 | 0.357083 | ||||||||
\(928\) | 2.75149 | 0.0903220 | ||||||||
\(929\) | −31.3591 | −1.02886 | −0.514430 | − | 0.857532i | \(-0.671996\pi\) | ||||
−0.514430 | + | 0.857532i | \(0.671996\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.52748 | −0.0828347 | ||||||||
\(932\) | −4.56008 | −0.149370 | ||||||||
\(933\) | 12.8545 | 0.420838 | ||||||||
\(934\) | 6.68227 | 0.218651 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 20.7196 | 0.677242 | ||||||||
\(937\) | 48.7726 | 1.59333 | 0.796666 | − | 0.604420i | \(-0.206595\pi\) | ||||
0.796666 | + | 0.604420i | \(0.206595\pi\) | |||||||
\(938\) | 32.8002 | 1.07097 | ||||||||
\(939\) | −10.5072 | −0.342889 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.2359 | −1.05086 | −0.525431 | − | 0.850836i | \(-0.676096\pi\) | ||||
−0.525431 | + | 0.850836i | \(0.676096\pi\) | |||||||
\(942\) | −18.3791 | −0.598825 | ||||||||
\(943\) | 7.33108 | 0.238733 | ||||||||
\(944\) | −3.56086 | −0.115896 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.526832 | −0.0171288 | ||||||||
\(947\) | 51.9235 | 1.68729 | 0.843644 | − | 0.536903i | \(-0.180406\pi\) | ||||
0.843644 | + | 0.536903i | \(0.180406\pi\) | |||||||
\(948\) | −2.55823 | −0.0830875 | ||||||||
\(949\) | 39.1935 | 1.27227 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.4806 | −0.631703 | ||||||||
\(952\) | 19.2077 | 0.622525 | ||||||||
\(953\) | 39.7788 | 1.28856 | 0.644281 | − | 0.764789i | \(-0.277157\pi\) | ||||
0.644281 | + | 0.764789i | \(0.277157\pi\) | |||||||
\(954\) | −0.707341 | −0.0229010 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.41703 | −0.110515 | ||||||||
\(957\) | 9.27701 | 0.299883 | ||||||||
\(958\) | 40.6462 | 1.31322 | ||||||||
\(959\) | 7.77543 | 0.251082 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0083 | −0.968011 | ||||||||
\(962\) | 33.8460 | 1.09124 | ||||||||
\(963\) | 9.37236 | 0.302020 | ||||||||
\(964\) | 0.718317 | 0.0231354 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 13.5892 | 0.437226 | ||||||||
\(967\) | 19.8817 | 0.639353 | 0.319677 | − | 0.947527i | \(-0.396426\pi\) | ||||
0.319677 | + | 0.947527i | \(0.396426\pi\) | |||||||
\(968\) | 0.315428 | 0.0101382 | ||||||||
\(969\) | −2.32476 | −0.0746822 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41.3841 | −1.32808 | −0.664039 | − | 0.747698i | \(-0.731159\pi\) | ||||
−0.664039 | + | 0.747698i | \(0.731159\pi\) | |||||||
\(972\) | 0.175259 | 0.00562144 | ||||||||
\(973\) | 0.296473 | 0.00950449 | ||||||||
\(974\) | −46.2658 | −1.48245 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −38.4085 | −1.22943 | ||||||||
\(977\) | 3.61991 | 0.115811 | 0.0579056 | − | 0.998322i | \(-0.481558\pi\) | ||||
0.0579056 | + | 0.998322i | \(0.481558\pi\) | |||||||
\(978\) | −11.6562 | −0.372725 | ||||||||
\(979\) | 9.41009 | 0.300748 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.5899 | −0.497748 | ||||||||
\(982\) | 14.0747 | 0.449143 | ||||||||
\(983\) | −20.1099 | −0.641405 | −0.320702 | − | 0.947180i | \(-0.603919\pi\) | ||||
−0.320702 | + | 0.947180i | \(0.603919\pi\) | |||||||
\(984\) | −3.41714 | −0.108935 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 15.4024 | 0.490514 | ||||||||
\(987\) | −12.1947 | −0.388160 | ||||||||
\(988\) | −0.701364 | −0.0223134 | ||||||||
\(989\) | 0.737705 | 0.0234576 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.43990 | 0.236336 | 0.118168 | − | 0.992994i | \(-0.462298\pi\) | ||||
0.118168 | + | 0.992994i | \(0.462298\pi\) | |||||||
\(992\) | 0.984345 | 0.0312530 | ||||||||
\(993\) | 14.4925 | 0.459905 | ||||||||
\(994\) | 22.9877 | 0.729126 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.880498 | 0.0278996 | ||||||||
\(997\) | −46.1472 | −1.46150 | −0.730748 | − | 0.682648i | \(-0.760828\pi\) | ||||
−0.730748 | + | 0.682648i | \(0.760828\pi\) | |||||||
\(998\) | −11.9348 | −0.377788 | ||||||||
\(999\) | 3.55334 | 0.112423 |
(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 | 1875.2.a.p.1.2 | 8 | ||
3.2 | odd | 2 | 5625.2.a.t.1.7 | 8 | |||
5.2 | odd | 4 | 1875.2.b.h.1249.5 | 16 | |||
5.3 | odd | 4 | 1875.2.b.h.1249.12 | 16 | |||
5.4 | even | 2 | 1875.2.a.m.1.7 | 8 | |||
15.14 | odd | 2 | 5625.2.a.bd.1.2 | 8 | |||
25.2 | odd | 20 | 375.2.i.c.274.2 | 16 | |||
25.9 | even | 10 | 375.2.g.e.151.4 | 16 | |||
25.11 | even | 5 | 375.2.g.d.226.1 | 16 | |||
25.12 | odd | 20 | 75.2.i.a.19.3 | yes | 16 | ||
25.13 | odd | 20 | 375.2.i.c.349.2 | 16 | |||
25.14 | even | 10 | 375.2.g.e.226.4 | 16 | |||
25.16 | even | 5 | 375.2.g.d.151.1 | 16 | |||
25.23 | odd | 20 | 75.2.i.a.4.3 | ✓ | 16 | ||
75.23 | even | 20 | 225.2.m.b.154.2 | 16 | |||
75.62 | even | 20 | 225.2.m.b.19.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.i.a.4.3 | ✓ | 16 | 25.23 | odd | 20 | ||
75.2.i.a.19.3 | yes | 16 | 25.12 | odd | 20 | ||
225.2.m.b.19.2 | 16 | 75.62 | even | 20 | |||
225.2.m.b.154.2 | 16 | 75.23 | even | 20 | |||
375.2.g.d.151.1 | 16 | 25.16 | even | 5 | |||
375.2.g.d.226.1 | 16 | 25.11 | even | 5 | |||
375.2.g.e.151.4 | 16 | 25.9 | even | 10 | |||
375.2.g.e.226.4 | 16 | 25.14 | even | 10 | |||
375.2.i.c.274.2 | 16 | 25.2 | odd | 20 | |||
375.2.i.c.349.2 | 16 | 25.13 | odd | 20 | |||
1875.2.a.m.1.7 | 8 | 5.4 | even | 2 | |||
1875.2.a.p.1.2 | 8 | 1.1 | even | 1 | trivial | ||
1875.2.b.h.1249.5 | 16 | 5.2 | odd | 4 | |||
1875.2.b.h.1249.12 | 16 | 5.3 | odd | 4 | |||
5625.2.a.t.1.7 | 8 | 3.2 | odd | 2 | |||
5625.2.a.bd.1.2 | 8 | 15.14 | odd | 2 |