Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0650408 | −0.0459908 | −0.0229954 | − | 0.999736i | \(-0.507320\pi\) | ||||
−0.0229954 | + | 0.999736i | \(0.507320\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.99577 | −0.997885 | ||||||||
\(5\) | −2.65358 | −1.18672 | −0.593358 | − | 0.804939i | \(-0.702198\pi\) | ||||
−0.593358 | + | 0.804939i | \(0.702198\pi\) | |||||||
\(6\) | −0.0650408 | −0.0265528 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.259888 | 0.0918843 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.172591 | 0.0545779 | ||||||||
\(11\) | −5.47071 | −1.64948 | −0.824740 | − | 0.565512i | \(-0.808678\pi\) | ||||
−0.824740 | + | 0.565512i | \(0.808678\pi\) | |||||||
\(12\) | −1.99577 | −0.576129 | ||||||||
\(13\) | −3.40299 | −0.943819 | −0.471909 | − | 0.881647i | \(-0.656435\pi\) | ||||
−0.471909 | + | 0.881647i | \(0.656435\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.65358 | −0.685150 | ||||||||
\(16\) | 3.97464 | 0.993659 | ||||||||
\(17\) | −6.28311 | −1.52388 | −0.761939 | − | 0.647649i | \(-0.775752\pi\) | ||||
−0.761939 | + | 0.647649i | \(0.775752\pi\) | |||||||
\(18\) | −0.0650408 | −0.0153303 | ||||||||
\(19\) | −4.25848 | −0.976962 | −0.488481 | − | 0.872574i | \(-0.662449\pi\) | ||||
−0.488481 | + | 0.872574i | \(0.662449\pi\) | |||||||
\(20\) | 5.29593 | 1.18421 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.355819 | 0.0758608 | ||||||||
\(23\) | −1.06746 | −0.222581 | −0.111291 | − | 0.993788i | \(-0.535498\pi\) | ||||
−0.111291 | + | 0.993788i | \(0.535498\pi\) | |||||||
\(24\) | 0.259888 | 0.0530494 | ||||||||
\(25\) | 2.04147 | 0.408293 | ||||||||
\(26\) | 0.221333 | 0.0434069 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.10576 | −1.13381 | −0.566906 | − | 0.823783i | \(-0.691860\pi\) | ||||
−0.566906 | + | 0.823783i | \(0.691860\pi\) | |||||||
\(30\) | 0.172591 | 0.0315106 | ||||||||
\(31\) | −10.4918 | −1.88438 | −0.942192 | − | 0.335072i | \(-0.891239\pi\) | ||||
−0.942192 | + | 0.335072i | \(0.891239\pi\) | |||||||
\(32\) | −0.778289 | −0.137583 | ||||||||
\(33\) | −5.47071 | −0.952328 | ||||||||
\(34\) | 0.408658 | 0.0700843 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.99577 | −0.332628 | ||||||||
\(37\) | 3.83754 | 0.630888 | 0.315444 | − | 0.948944i | \(-0.397847\pi\) | ||||
0.315444 | + | 0.948944i | \(0.397847\pi\) | |||||||
\(38\) | 0.276975 | 0.0449312 | ||||||||
\(39\) | −3.40299 | −0.544914 | ||||||||
\(40\) | −0.689632 | −0.109040 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.68577 | −0.714573 | −0.357286 | − | 0.933995i | \(-0.616298\pi\) | ||||
−0.357286 | + | 0.933995i | \(0.616298\pi\) | |||||||
\(44\) | 10.9183 | 1.64599 | ||||||||
\(45\) | −2.65358 | −0.395572 | ||||||||
\(46\) | 0.0694285 | 0.0102367 | ||||||||
\(47\) | 11.1163 | 1.62148 | 0.810741 | − | 0.585405i | \(-0.199064\pi\) | ||||
0.810741 | + | 0.585405i | \(0.199064\pi\) | |||||||
\(48\) | 3.97464 | 0.573689 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.132779 | −0.0187777 | ||||||||
\(51\) | −6.28311 | −0.879811 | ||||||||
\(52\) | 6.79158 | 0.941822 | ||||||||
\(53\) | 8.14739 | 1.11913 | 0.559565 | − | 0.828786i | \(-0.310968\pi\) | ||||
0.559565 | + | 0.828786i | \(0.310968\pi\) | |||||||
\(54\) | −0.0650408 | −0.00885093 | ||||||||
\(55\) | 14.5169 | 1.95746 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.25848 | −0.564049 | ||||||||
\(58\) | 0.397124 | 0.0521449 | ||||||||
\(59\) | 14.0580 | 1.83020 | 0.915100 | − | 0.403228i | \(-0.132112\pi\) | ||||
0.915100 | + | 0.403228i | \(0.132112\pi\) | |||||||
\(60\) | 5.29593 | 0.683701 | ||||||||
\(61\) | −14.1386 | −1.81027 | −0.905133 | − | 0.425128i | \(-0.860229\pi\) | ||||
−0.905133 | + | 0.425128i | \(0.860229\pi\) | |||||||
\(62\) | 0.682395 | 0.0866643 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.89865 | −0.987331 | ||||||||
\(65\) | 9.03008 | 1.12004 | ||||||||
\(66\) | 0.355819 | 0.0437983 | ||||||||
\(67\) | −6.51962 | −0.796498 | −0.398249 | − | 0.917277i | \(-0.630382\pi\) | ||||
−0.398249 | + | 0.917277i | \(0.630382\pi\) | |||||||
\(68\) | 12.5396 | 1.52065 | ||||||||
\(69\) | −1.06746 | −0.128507 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.1718 | −1.20717 | −0.603587 | − | 0.797297i | \(-0.706262\pi\) | ||||
−0.603587 | + | 0.797297i | \(0.706262\pi\) | |||||||
\(72\) | 0.259888 | 0.0306281 | ||||||||
\(73\) | −4.82870 | −0.565157 | −0.282578 | − | 0.959244i | \(-0.591190\pi\) | ||||
−0.282578 | + | 0.959244i | \(0.591190\pi\) | |||||||
\(74\) | −0.249597 | −0.0290150 | ||||||||
\(75\) | 2.04147 | 0.235728 | ||||||||
\(76\) | 8.49894 | 0.974896 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.221333 | 0.0250610 | ||||||||
\(79\) | 9.32274 | 1.04889 | 0.524445 | − | 0.851444i | \(-0.324273\pi\) | ||||
0.524445 | + | 0.851444i | \(0.324273\pi\) | |||||||
\(80\) | −10.5470 | −1.17919 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.0650408 | 0.00718255 | ||||||||
\(83\) | −5.03523 | −0.552688 | −0.276344 | − | 0.961059i | \(-0.589123\pi\) | ||||
−0.276344 | + | 0.961059i | \(0.589123\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.6727 | 1.80841 | ||||||||
\(86\) | 0.304766 | 0.0328637 | ||||||||
\(87\) | −6.10576 | −0.654607 | ||||||||
\(88\) | −1.42177 | −0.151561 | ||||||||
\(89\) | 8.62706 | 0.914466 | 0.457233 | − | 0.889347i | \(-0.348841\pi\) | ||||
0.457233 | + | 0.889347i | \(0.348841\pi\) | |||||||
\(90\) | 0.172591 | 0.0181926 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.13041 | 0.222110 | ||||||||
\(93\) | −10.4918 | −1.08795 | ||||||||
\(94\) | −0.723014 | −0.0745732 | ||||||||
\(95\) | 11.3002 | 1.15938 | ||||||||
\(96\) | −0.778289 | −0.0794338 | ||||||||
\(97\) | −16.5259 | −1.67795 | −0.838977 | − | 0.544167i | \(-0.816846\pi\) | ||||
−0.838977 | + | 0.544167i | \(0.816846\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.47071 | −0.549827 | ||||||||
\(100\) | −4.07430 | −0.407430 | ||||||||
\(101\) | −12.2461 | −1.21853 | −0.609264 | − | 0.792968i | \(-0.708535\pi\) | ||||
−0.609264 | + | 0.792968i | \(0.708535\pi\) | |||||||
\(102\) | 0.408658 | 0.0404632 | ||||||||
\(103\) | −4.18464 | −0.412325 | −0.206163 | − | 0.978518i | \(-0.566098\pi\) | ||||
−0.206163 | + | 0.978518i | \(0.566098\pi\) | |||||||
\(104\) | −0.884395 | −0.0867221 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.529913 | −0.0514697 | ||||||||
\(107\) | 4.55230 | 0.440087 | 0.220044 | − | 0.975490i | \(-0.429380\pi\) | ||||
0.220044 | + | 0.975490i | \(0.429380\pi\) | |||||||
\(108\) | −1.99577 | −0.192043 | ||||||||
\(109\) | −9.25158 | −0.886141 | −0.443070 | − | 0.896487i | \(-0.646111\pi\) | ||||
−0.443070 | + | 0.896487i | \(0.646111\pi\) | |||||||
\(110\) | −0.944192 | −0.0900252 | ||||||||
\(111\) | 3.83754 | 0.364243 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.81242 | 0.640858 | 0.320429 | − | 0.947272i | \(-0.396173\pi\) | ||||
0.320429 | + | 0.947272i | \(0.396173\pi\) | |||||||
\(114\) | 0.276975 | 0.0259411 | ||||||||
\(115\) | 2.83259 | 0.264140 | ||||||||
\(116\) | 12.1857 | 1.13141 | ||||||||
\(117\) | −3.40299 | −0.314606 | ||||||||
\(118\) | −0.914345 | −0.0841723 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.689632 | −0.0629545 | ||||||||
\(121\) | 18.9286 | 1.72078 | ||||||||
\(122\) | 0.919587 | 0.0832555 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | 20.9392 | 1.88040 | ||||||||
\(125\) | 7.85069 | 0.702187 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.5337 | −1.20092 | −0.600461 | − | 0.799654i | \(-0.705016\pi\) | ||||
−0.600461 | + | 0.799654i | \(0.705016\pi\) | |||||||
\(128\) | 2.07031 | 0.182992 | ||||||||
\(129\) | −4.68577 | −0.412559 | ||||||||
\(130\) | −0.587324 | −0.0515117 | ||||||||
\(131\) | 4.69146 | 0.409895 | 0.204948 | − | 0.978773i | \(-0.434298\pi\) | ||||
0.204948 | + | 0.978773i | \(0.434298\pi\) | |||||||
\(132\) | 10.9183 | 0.950313 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.424041 | 0.0366316 | ||||||||
\(135\) | −2.65358 | −0.228383 | ||||||||
\(136\) | −1.63290 | −0.140020 | ||||||||
\(137\) | −12.7773 | −1.09164 | −0.545818 | − | 0.837904i | \(-0.683781\pi\) | ||||
−0.545818 | + | 0.837904i | \(0.683781\pi\) | |||||||
\(138\) | 0.0694285 | 0.00591015 | ||||||||
\(139\) | −12.5370 | −1.06338 | −0.531688 | − | 0.846940i | \(-0.678442\pi\) | ||||
−0.531688 | + | 0.846940i | \(0.678442\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.1163 | 0.936163 | ||||||||
\(142\) | 0.661584 | 0.0555189 | ||||||||
\(143\) | 18.6167 | 1.55681 | ||||||||
\(144\) | 3.97464 | 0.331220 | ||||||||
\(145\) | 16.2021 | 1.34551 | ||||||||
\(146\) | 0.314063 | 0.0259920 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.65885 | −0.629553 | ||||||||
\(149\) | 2.62732 | 0.215238 | 0.107619 | − | 0.994192i | \(-0.465677\pi\) | ||||
0.107619 | + | 0.994192i | \(0.465677\pi\) | |||||||
\(150\) | −0.132779 | −0.0108413 | ||||||||
\(151\) | −5.95876 | −0.484917 | −0.242458 | − | 0.970162i | \(-0.577954\pi\) | ||||
−0.242458 | + | 0.970162i | \(0.577954\pi\) | |||||||
\(152\) | −1.10673 | −0.0897675 | ||||||||
\(153\) | −6.28311 | −0.507959 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 27.8408 | 2.23623 | ||||||||
\(156\) | 6.79158 | 0.543761 | ||||||||
\(157\) | 13.8828 | 1.10797 | 0.553983 | − | 0.832528i | \(-0.313107\pi\) | ||||
0.553983 | + | 0.832528i | \(0.313107\pi\) | |||||||
\(158\) | −0.606358 | −0.0482393 | ||||||||
\(159\) | 8.14739 | 0.646130 | ||||||||
\(160\) | 2.06525 | 0.163272 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.0650408 | −0.00511009 | ||||||||
\(163\) | −0.962223 | −0.0753671 | −0.0376836 | − | 0.999290i | \(-0.511998\pi\) | ||||
−0.0376836 | + | 0.999290i | \(0.511998\pi\) | |||||||
\(164\) | 1.99577 | 0.155843 | ||||||||
\(165\) | 14.5169 | 1.13014 | ||||||||
\(166\) | 0.327495 | 0.0254185 | ||||||||
\(167\) | −10.9165 | −0.844743 | −0.422371 | − | 0.906423i | \(-0.638802\pi\) | ||||
−0.422371 | + | 0.906423i | \(0.638802\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.41969 | −0.109207 | ||||||||
\(170\) | −1.08441 | −0.0831701 | ||||||||
\(171\) | −4.25848 | −0.325654 | ||||||||
\(172\) | 9.35171 | 0.713061 | ||||||||
\(173\) | −18.1821 | −1.38236 | −0.691182 | − | 0.722681i | \(-0.742910\pi\) | ||||
−0.691182 | + | 0.722681i | \(0.742910\pi\) | |||||||
\(174\) | 0.397124 | 0.0301059 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −21.7441 | −1.63902 | ||||||||
\(177\) | 14.0580 | 1.05667 | ||||||||
\(178\) | −0.561110 | −0.0420570 | ||||||||
\(179\) | 14.3377 | 1.07165 | 0.535823 | − | 0.844330i | \(-0.320001\pi\) | ||||
0.535823 | + | 0.844330i | \(0.320001\pi\) | |||||||
\(180\) | 5.29593 | 0.394735 | ||||||||
\(181\) | 26.4209 | 1.96385 | 0.981925 | − | 0.189272i | \(-0.0606128\pi\) | ||||
0.981925 | + | 0.189272i | \(0.0606128\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.1386 | −1.04516 | ||||||||
\(184\) | −0.277420 | −0.0204517 | ||||||||
\(185\) | −10.1832 | −0.748684 | ||||||||
\(186\) | 0.682395 | 0.0500357 | ||||||||
\(187\) | 34.3730 | 2.51360 | ||||||||
\(188\) | −22.1856 | −1.61805 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.734974 | −0.0533206 | ||||||||
\(191\) | 4.42857 | 0.320440 | 0.160220 | − | 0.987081i | \(-0.448780\pi\) | ||||
0.160220 | + | 0.987081i | \(0.448780\pi\) | |||||||
\(192\) | −7.89865 | −0.570036 | ||||||||
\(193\) | 4.70814 | 0.338899 | 0.169450 | − | 0.985539i | \(-0.445801\pi\) | ||||
0.169450 | + | 0.985539i | \(0.445801\pi\) | |||||||
\(194\) | 1.07486 | 0.0771704 | ||||||||
\(195\) | 9.03008 | 0.646658 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.9342 | 1.84774 | 0.923868 | − | 0.382712i | \(-0.125010\pi\) | ||||
0.923868 | + | 0.382712i | \(0.125010\pi\) | |||||||
\(198\) | 0.355819 | 0.0252869 | ||||||||
\(199\) | −14.9384 | −1.05896 | −0.529479 | − | 0.848323i | \(-0.677612\pi\) | ||||
−0.529479 | + | 0.848323i | \(0.677612\pi\) | |||||||
\(200\) | 0.530552 | 0.0375157 | ||||||||
\(201\) | −6.51962 | −0.459859 | ||||||||
\(202\) | 0.796493 | 0.0560410 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 12.5396 | 0.877950 | ||||||||
\(205\) | 2.65358 | 0.185334 | ||||||||
\(206\) | 0.272172 | 0.0189632 | ||||||||
\(207\) | −1.06746 | −0.0741937 | ||||||||
\(208\) | −13.5256 | −0.937834 | ||||||||
\(209\) | 23.2969 | 1.61148 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.7550 | 0.878091 | 0.439045 | − | 0.898465i | \(-0.355317\pi\) | ||||
0.439045 | + | 0.898465i | \(0.355317\pi\) | |||||||
\(212\) | −16.2603 | −1.11676 | ||||||||
\(213\) | −10.1718 | −0.696962 | ||||||||
\(214\) | −0.296085 | −0.0202400 | ||||||||
\(215\) | 12.4340 | 0.847994 | ||||||||
\(216\) | 0.259888 | 0.0176831 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.601730 | 0.0407543 | ||||||||
\(219\) | −4.82870 | −0.326294 | ||||||||
\(220\) | −28.9725 | −1.95332 | ||||||||
\(221\) | 21.3813 | 1.43826 | ||||||||
\(222\) | −0.249597 | −0.0167518 | ||||||||
\(223\) | 7.54896 | 0.505515 | 0.252758 | − | 0.967530i | \(-0.418662\pi\) | ||||
0.252758 | + | 0.967530i | \(0.418662\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.04147 | 0.136098 | ||||||||
\(226\) | −0.443085 | −0.0294736 | ||||||||
\(227\) | −7.98410 | −0.529923 | −0.264962 | − | 0.964259i | \(-0.585359\pi\) | ||||
−0.264962 | + | 0.964259i | \(0.585359\pi\) | |||||||
\(228\) | 8.49894 | 0.562856 | ||||||||
\(229\) | −15.2575 | −1.00825 | −0.504123 | − | 0.863632i | \(-0.668184\pi\) | ||||
−0.504123 | + | 0.863632i | \(0.668184\pi\) | |||||||
\(230\) | −0.184234 | −0.0121480 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.58681 | −0.104179 | ||||||||
\(233\) | −13.1497 | −0.861468 | −0.430734 | − | 0.902479i | \(-0.641745\pi\) | ||||
−0.430734 | + | 0.902479i | \(0.641745\pi\) | |||||||
\(234\) | 0.221333 | 0.0144690 | ||||||||
\(235\) | −29.4980 | −1.92424 | ||||||||
\(236\) | −28.0566 | −1.82633 | ||||||||
\(237\) | 9.32274 | 0.605577 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.1988 | 1.56529 | 0.782645 | − | 0.622469i | \(-0.213870\pi\) | ||||
0.782645 | + | 0.622469i | \(0.213870\pi\) | |||||||
\(240\) | −10.5470 | −0.680806 | ||||||||
\(241\) | 15.7240 | 1.01287 | 0.506436 | − | 0.862278i | \(-0.330963\pi\) | ||||
0.506436 | + | 0.862278i | \(0.330963\pi\) | |||||||
\(242\) | −1.23113 | −0.0791401 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 28.2175 | 1.80644 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.0650408 | 0.00414685 | ||||||||
\(247\) | 14.4915 | 0.922075 | ||||||||
\(248\) | −2.72669 | −0.173145 | ||||||||
\(249\) | −5.03523 | −0.319095 | ||||||||
\(250\) | −0.510615 | −0.0322941 | ||||||||
\(251\) | 2.62369 | 0.165606 | 0.0828028 | − | 0.996566i | \(-0.473613\pi\) | ||||
0.0828028 | + | 0.996566i | \(0.473613\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.83977 | 0.367143 | ||||||||
\(254\) | 0.880243 | 0.0552313 | ||||||||
\(255\) | 16.6727 | 1.04409 | ||||||||
\(256\) | 15.6626 | 0.978916 | ||||||||
\(257\) | −19.5935 | −1.22221 | −0.611104 | − | 0.791550i | \(-0.709274\pi\) | ||||
−0.611104 | + | 0.791550i | \(0.709274\pi\) | |||||||
\(258\) | 0.304766 | 0.0189739 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −18.0220 | −1.11767 | ||||||||
\(261\) | −6.10576 | −0.377937 | ||||||||
\(262\) | −0.305136 | −0.0188514 | ||||||||
\(263\) | 1.27756 | 0.0787776 | 0.0393888 | − | 0.999224i | \(-0.487459\pi\) | ||||
0.0393888 | + | 0.999224i | \(0.487459\pi\) | |||||||
\(264\) | −1.42177 | −0.0875039 | ||||||||
\(265\) | −21.6197 | −1.32809 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.62706 | 0.527967 | ||||||||
\(268\) | 13.0117 | 0.794814 | ||||||||
\(269\) | −10.3127 | −0.628779 | −0.314389 | − | 0.949294i | \(-0.601800\pi\) | ||||
−0.314389 | + | 0.949294i | \(0.601800\pi\) | |||||||
\(270\) | 0.172591 | 0.0105035 | ||||||||
\(271\) | −6.53411 | −0.396919 | −0.198459 | − | 0.980109i | \(-0.563594\pi\) | ||||
−0.198459 | + | 0.980109i | \(0.563594\pi\) | |||||||
\(272\) | −24.9731 | −1.51421 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.831044 | 0.0502052 | ||||||||
\(275\) | −11.1683 | −0.673471 | ||||||||
\(276\) | 2.13041 | 0.128235 | ||||||||
\(277\) | −14.7541 | −0.886486 | −0.443243 | − | 0.896401i | \(-0.646172\pi\) | ||||
−0.443243 | + | 0.896401i | \(0.646172\pi\) | |||||||
\(278\) | 0.815417 | 0.0489055 | ||||||||
\(279\) | −10.4918 | −0.628128 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.67355 | −0.577075 | −0.288538 | − | 0.957469i | \(-0.593169\pi\) | ||||
−0.288538 | + | 0.957469i | \(0.593169\pi\) | |||||||
\(282\) | −0.723014 | −0.0430549 | ||||||||
\(283\) | −18.0256 | −1.07151 | −0.535756 | − | 0.844373i | \(-0.679973\pi\) | ||||
−0.535756 | + | 0.844373i | \(0.679973\pi\) | |||||||
\(284\) | 20.3006 | 1.20462 | ||||||||
\(285\) | 11.3002 | 0.669366 | ||||||||
\(286\) | −1.21085 | −0.0715989 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.778289 | −0.0458611 | ||||||||
\(289\) | 22.4774 | 1.32220 | ||||||||
\(290\) | −1.05380 | −0.0618811 | ||||||||
\(291\) | −16.5259 | −0.968767 | ||||||||
\(292\) | 9.63698 | 0.563962 | ||||||||
\(293\) | 30.2323 | 1.76619 | 0.883094 | − | 0.469195i | \(-0.155456\pi\) | ||||
0.883094 | + | 0.469195i | \(0.155456\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −37.3040 | −2.17193 | ||||||||
\(296\) | 0.997330 | 0.0579686 | ||||||||
\(297\) | −5.47071 | −0.317443 | ||||||||
\(298\) | −0.170883 | −0.00989898 | ||||||||
\(299\) | 3.63256 | 0.210076 | ||||||||
\(300\) | −4.07430 | −0.235230 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.387562 | 0.0223017 | ||||||||
\(303\) | −12.2461 | −0.703517 | ||||||||
\(304\) | −16.9259 | −0.970767 | ||||||||
\(305\) | 37.5179 | 2.14827 | ||||||||
\(306\) | 0.408658 | 0.0233614 | ||||||||
\(307\) | −5.59004 | −0.319040 | −0.159520 | − | 0.987195i | \(-0.550995\pi\) | ||||
−0.159520 | + | 0.987195i | \(0.550995\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.18464 | −0.238056 | ||||||||
\(310\) | −1.81079 | −0.102846 | ||||||||
\(311\) | −2.84702 | −0.161440 | −0.0807200 | − | 0.996737i | \(-0.525722\pi\) | ||||
−0.0807200 | + | 0.996737i | \(0.525722\pi\) | |||||||
\(312\) | −0.884395 | −0.0500690 | ||||||||
\(313\) | 7.97569 | 0.450813 | 0.225406 | − | 0.974265i | \(-0.427629\pi\) | ||||
0.225406 | + | 0.974265i | \(0.427629\pi\) | |||||||
\(314\) | −0.902947 | −0.0509562 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −18.6060 | −1.04667 | ||||||||
\(317\) | −9.27505 | −0.520939 | −0.260469 | − | 0.965482i | \(-0.583877\pi\) | ||||
−0.260469 | + | 0.965482i | \(0.583877\pi\) | |||||||
\(318\) | −0.529913 | −0.0297160 | ||||||||
\(319\) | 33.4028 | 1.87020 | ||||||||
\(320\) | 20.9597 | 1.17168 | ||||||||
\(321\) | 4.55230 | 0.254085 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 26.7565 | 1.48877 | ||||||||
\(324\) | −1.99577 | −0.110876 | ||||||||
\(325\) | −6.94708 | −0.385355 | ||||||||
\(326\) | 0.0625837 | 0.00346619 | ||||||||
\(327\) | −9.25158 | −0.511613 | ||||||||
\(328\) | −0.259888 | −0.0143499 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.944192 | −0.0519761 | ||||||||
\(331\) | 14.6322 | 0.804257 | 0.402129 | − | 0.915583i | \(-0.368270\pi\) | ||||
0.402129 | + | 0.915583i | \(0.368270\pi\) | |||||||
\(332\) | 10.0492 | 0.551519 | ||||||||
\(333\) | 3.83754 | 0.210296 | ||||||||
\(334\) | 0.710016 | 0.0388504 | ||||||||
\(335\) | 17.3003 | 0.945217 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.1264 | 0.769517 | 0.384758 | − | 0.923017i | \(-0.374285\pi\) | ||||
0.384758 | + | 0.923017i | \(0.374285\pi\) | |||||||
\(338\) | 0.0923374 | 0.00502249 | ||||||||
\(339\) | 6.81242 | 0.370000 | ||||||||
\(340\) | −33.2749 | −1.80458 | ||||||||
\(341\) | 57.3976 | 3.10825 | ||||||||
\(342\) | 0.276975 | 0.0149771 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.21777 | −0.0656580 | ||||||||
\(345\) | 2.83259 | 0.152502 | ||||||||
\(346\) | 1.18258 | 0.0635759 | ||||||||
\(347\) | 20.2540 | 1.08729 | 0.543645 | − | 0.839315i | \(-0.317044\pi\) | ||||
0.543645 | + | 0.839315i | \(0.317044\pi\) | |||||||
\(348\) | 12.1857 | 0.653222 | ||||||||
\(349\) | −23.8877 | −1.27868 | −0.639339 | − | 0.768925i | \(-0.720792\pi\) | ||||
−0.639339 | + | 0.768925i | \(0.720792\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.40299 | −0.181638 | ||||||||
\(352\) | 4.25779 | 0.226941 | ||||||||
\(353\) | 19.9546 | 1.06208 | 0.531039 | − | 0.847347i | \(-0.321802\pi\) | ||||
0.531039 | + | 0.847347i | \(0.321802\pi\) | |||||||
\(354\) | −0.914345 | −0.0485969 | ||||||||
\(355\) | 26.9917 | 1.43257 | ||||||||
\(356\) | −17.2176 | −0.912532 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.932532 | −0.0492859 | ||||||||
\(359\) | −4.70206 | −0.248165 | −0.124082 | − | 0.992272i | \(-0.539599\pi\) | ||||
−0.124082 | + | 0.992272i | \(0.539599\pi\) | |||||||
\(360\) | −0.689632 | −0.0363468 | ||||||||
\(361\) | −0.865350 | −0.0455448 | ||||||||
\(362\) | −1.71844 | −0.0903189 | ||||||||
\(363\) | 18.9286 | 0.993495 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.8133 | 0.670680 | ||||||||
\(366\) | 0.919587 | 0.0480676 | ||||||||
\(367\) | −12.9579 | −0.676398 | −0.338199 | − | 0.941075i | \(-0.609818\pi\) | ||||
−0.338199 | + | 0.941075i | \(0.609818\pi\) | |||||||
\(368\) | −4.24277 | −0.221170 | ||||||||
\(369\) | −1.00000 | −0.0520579 | ||||||||
\(370\) | 0.662323 | 0.0344326 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 20.9392 | 1.08565 | ||||||||
\(373\) | 24.5509 | 1.27120 | 0.635599 | − | 0.772019i | \(-0.280753\pi\) | ||||
0.635599 | + | 0.772019i | \(0.280753\pi\) | |||||||
\(374\) | −2.23565 | −0.115603 | ||||||||
\(375\) | 7.85069 | 0.405408 | ||||||||
\(376\) | 2.88900 | 0.148989 | ||||||||
\(377\) | 20.7778 | 1.07011 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.8102 | 1.73671 | 0.868356 | − | 0.495941i | \(-0.165177\pi\) | ||||
0.868356 | + | 0.495941i | \(0.165177\pi\) | |||||||
\(380\) | −22.5526 | −1.15692 | ||||||||
\(381\) | −13.5337 | −0.693353 | ||||||||
\(382\) | −0.288038 | −0.0147373 | ||||||||
\(383\) | −23.0463 | −1.17761 | −0.588805 | − | 0.808275i | \(-0.700401\pi\) | ||||
−0.588805 | + | 0.808275i | \(0.700401\pi\) | |||||||
\(384\) | 2.07031 | 0.105650 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.306221 | −0.0155862 | ||||||||
\(387\) | −4.68577 | −0.238191 | ||||||||
\(388\) | 32.9820 | 1.67440 | ||||||||
\(389\) | −4.13177 | −0.209489 | −0.104745 | − | 0.994499i | \(-0.533402\pi\) | ||||
−0.104745 | + | 0.994499i | \(0.533402\pi\) | |||||||
\(390\) | −0.587324 | −0.0297403 | ||||||||
\(391\) | 6.70697 | 0.339186 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.69146 | 0.236653 | ||||||||
\(394\) | −1.68678 | −0.0849788 | ||||||||
\(395\) | −24.7386 | −1.24473 | ||||||||
\(396\) | 10.9183 | 0.548664 | ||||||||
\(397\) | 25.3153 | 1.27054 | 0.635268 | − | 0.772292i | \(-0.280890\pi\) | ||||
0.635268 | + | 0.772292i | \(0.280890\pi\) | |||||||
\(398\) | 0.971607 | 0.0487023 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.11409 | 0.405704 | ||||||||
\(401\) | 27.0679 | 1.35171 | 0.675853 | − | 0.737037i | \(-0.263776\pi\) | ||||
0.675853 | + | 0.737037i | \(0.263776\pi\) | |||||||
\(402\) | 0.424041 | 0.0211492 | ||||||||
\(403\) | 35.7035 | 1.77852 | ||||||||
\(404\) | 24.4403 | 1.21595 | ||||||||
\(405\) | −2.65358 | −0.131857 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.9941 | −1.04064 | ||||||||
\(408\) | −1.63290 | −0.0808408 | ||||||||
\(409\) | −36.0335 | −1.78174 | −0.890870 | − | 0.454258i | \(-0.849904\pi\) | ||||
−0.890870 | + | 0.454258i | \(0.849904\pi\) | |||||||
\(410\) | −0.172591 | −0.00852364 | ||||||||
\(411\) | −12.7773 | −0.630256 | ||||||||
\(412\) | 8.35159 | 0.411453 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.0694285 | 0.00341223 | ||||||||
\(415\) | 13.3614 | 0.655883 | ||||||||
\(416\) | 2.64851 | 0.129854 | ||||||||
\(417\) | −12.5370 | −0.613940 | ||||||||
\(418\) | −1.51525 | −0.0741132 | ||||||||
\(419\) | 28.2596 | 1.38057 | 0.690287 | − | 0.723536i | \(-0.257484\pi\) | ||||
0.690287 | + | 0.723536i | \(0.257484\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.5570 | 0.904415 | 0.452207 | − | 0.891913i | \(-0.350637\pi\) | ||||
0.452207 | + | 0.891913i | \(0.350637\pi\) | |||||||
\(422\) | −0.829595 | −0.0403841 | ||||||||
\(423\) | 11.1163 | 0.540494 | ||||||||
\(424\) | 2.11741 | 0.102830 | ||||||||
\(425\) | −12.8268 | −0.622189 | ||||||||
\(426\) | 0.661584 | 0.0320538 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −9.08534 | −0.439157 | ||||||||
\(429\) | 18.6167 | 0.898824 | ||||||||
\(430\) | −0.808719 | −0.0389999 | ||||||||
\(431\) | −1.77967 | −0.0857239 | −0.0428619 | − | 0.999081i | \(-0.513648\pi\) | ||||
−0.0428619 | + | 0.999081i | \(0.513648\pi\) | |||||||
\(432\) | 3.97464 | 0.191230 | ||||||||
\(433\) | −28.5720 | −1.37308 | −0.686541 | − | 0.727092i | \(-0.740872\pi\) | ||||
−0.686541 | + | 0.727092i | \(0.740872\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.2021 | 0.776832 | ||||||||
\(436\) | 18.4640 | 0.884266 | ||||||||
\(437\) | 4.54576 | 0.217453 | ||||||||
\(438\) | 0.314063 | 0.0150065 | ||||||||
\(439\) | −6.39885 | −0.305400 | −0.152700 | − | 0.988273i | \(-0.548797\pi\) | ||||
−0.152700 | + | 0.988273i | \(0.548797\pi\) | |||||||
\(440\) | 3.77278 | 0.179860 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.39066 | −0.0661468 | ||||||||
\(443\) | −25.5094 | −1.21199 | −0.605995 | − | 0.795468i | \(-0.707225\pi\) | ||||
−0.605995 | + | 0.795468i | \(0.707225\pi\) | |||||||
\(444\) | −7.65885 | −0.363473 | ||||||||
\(445\) | −22.8925 | −1.08521 | ||||||||
\(446\) | −0.490990 | −0.0232490 | ||||||||
\(447\) | 2.62732 | 0.124268 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.3343 | −0.723671 | −0.361835 | − | 0.932242i | \(-0.617850\pi\) | ||||
−0.361835 | + | 0.932242i | \(0.617850\pi\) | |||||||
\(450\) | −0.132779 | −0.00625924 | ||||||||
\(451\) | 5.47071 | 0.257605 | ||||||||
\(452\) | −13.5960 | −0.639503 | ||||||||
\(453\) | −5.95876 | −0.279967 | ||||||||
\(454\) | 0.519292 | 0.0243716 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.10673 | −0.0518273 | ||||||||
\(457\) | −12.4509 | −0.582430 | −0.291215 | − | 0.956658i | \(-0.594059\pi\) | ||||
−0.291215 | + | 0.956658i | \(0.594059\pi\) | |||||||
\(458\) | 0.992361 | 0.0463700 | ||||||||
\(459\) | −6.28311 | −0.293270 | ||||||||
\(460\) | −5.65320 | −0.263582 | ||||||||
\(461\) | −37.9754 | −1.76869 | −0.884345 | − | 0.466833i | \(-0.845395\pi\) | ||||
−0.884345 | + | 0.466833i | \(0.845395\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.28313 | 0.338476 | 0.169238 | − | 0.985575i | \(-0.445869\pi\) | ||||
0.169238 | + | 0.985575i | \(0.445869\pi\) | |||||||
\(464\) | −24.2682 | −1.12662 | ||||||||
\(465\) | 27.8408 | 1.29109 | ||||||||
\(466\) | 0.855269 | 0.0396196 | ||||||||
\(467\) | −12.6148 | −0.583743 | −0.291871 | − | 0.956458i | \(-0.594278\pi\) | ||||
−0.291871 | + | 0.956458i | \(0.594278\pi\) | |||||||
\(468\) | 6.79158 | 0.313941 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.91857 | 0.0884972 | ||||||||
\(471\) | 13.8828 | 0.639685 | ||||||||
\(472\) | 3.65351 | 0.168166 | ||||||||
\(473\) | 25.6344 | 1.17867 | ||||||||
\(474\) | −0.606358 | −0.0278509 | ||||||||
\(475\) | −8.69354 | −0.398887 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.14739 | 0.373043 | ||||||||
\(478\) | −1.57391 | −0.0719888 | ||||||||
\(479\) | −42.8999 | −1.96015 | −0.980073 | − | 0.198638i | \(-0.936348\pi\) | ||||
−0.980073 | + | 0.198638i | \(0.936348\pi\) | |||||||
\(480\) | 2.06525 | 0.0942653 | ||||||||
\(481\) | −13.0591 | −0.595443 | ||||||||
\(482\) | −1.02270 | −0.0465827 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −37.7772 | −1.71714 | ||||||||
\(485\) | 43.8528 | 1.99125 | ||||||||
\(486\) | −0.0650408 | −0.00295031 | ||||||||
\(487\) | −31.2404 | −1.41564 | −0.707819 | − | 0.706394i | \(-0.750321\pi\) | ||||
−0.707819 | + | 0.706394i | \(0.750321\pi\) | |||||||
\(488\) | −3.67446 | −0.166335 | ||||||||
\(489\) | −0.962223 | −0.0435132 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.3972 | 1.77797 | 0.888985 | − | 0.457936i | \(-0.151411\pi\) | ||||
0.888985 | + | 0.457936i | \(0.151411\pi\) | |||||||
\(492\) | 1.99577 | 0.0899762 | ||||||||
\(493\) | 38.3632 | 1.72779 | ||||||||
\(494\) | −0.942541 | −0.0424069 | ||||||||
\(495\) | 14.5169 | 0.652488 | ||||||||
\(496\) | −41.7011 | −1.87244 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.327495 | 0.0146754 | ||||||||
\(499\) | 11.5175 | 0.515594 | 0.257797 | − | 0.966199i | \(-0.417003\pi\) | ||||
0.257797 | + | 0.966199i | \(0.417003\pi\) | |||||||
\(500\) | −15.6682 | −0.700702 | ||||||||
\(501\) | −10.9165 | −0.487712 | ||||||||
\(502\) | −0.170647 | −0.00761633 | ||||||||
\(503\) | −4.15133 | −0.185099 | −0.0925494 | − | 0.995708i | \(-0.529502\pi\) | ||||
−0.0925494 | + | 0.995708i | \(0.529502\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 32.4958 | 1.44605 | ||||||||
\(506\) | −0.379823 | −0.0168852 | ||||||||
\(507\) | −1.41969 | −0.0630505 | ||||||||
\(508\) | 27.0102 | 1.19838 | ||||||||
\(509\) | 5.60204 | 0.248306 | 0.124153 | − | 0.992263i | \(-0.460379\pi\) | ||||
0.124153 | + | 0.992263i | \(0.460379\pi\) | |||||||
\(510\) | −1.08441 | −0.0480183 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −5.15934 | −0.228013 | ||||||||
\(513\) | −4.25848 | −0.188016 | ||||||||
\(514\) | 1.27437 | 0.0562103 | ||||||||
\(515\) | 11.1043 | 0.489313 | ||||||||
\(516\) | 9.35171 | 0.411686 | ||||||||
\(517\) | −60.8141 | −2.67460 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.1821 | −0.798108 | ||||||||
\(520\) | 2.34681 | 0.102914 | ||||||||
\(521\) | −6.60586 | −0.289408 | −0.144704 | − | 0.989475i | \(-0.546223\pi\) | ||||
−0.144704 | + | 0.989475i | \(0.546223\pi\) | |||||||
\(522\) | 0.397124 | 0.0173816 | ||||||||
\(523\) | −14.2512 | −0.623163 | −0.311581 | − | 0.950219i | \(-0.600859\pi\) | ||||
−0.311581 | + | 0.950219i | \(0.600859\pi\) | |||||||
\(524\) | −9.36308 | −0.409028 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.0830934 | −0.00362304 | ||||||||
\(527\) | 65.9212 | 2.87157 | ||||||||
\(528\) | −21.7441 | −0.946289 | ||||||||
\(529\) | −21.8605 | −0.950458 | ||||||||
\(530\) | 1.40616 | 0.0610798 | ||||||||
\(531\) | 14.0580 | 0.610066 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.40299 | 0.147400 | ||||||||
\(534\) | −0.561110 | −0.0242816 | ||||||||
\(535\) | −12.0799 | −0.522259 | ||||||||
\(536\) | −1.69437 | −0.0731857 | ||||||||
\(537\) | 14.3377 | 0.618715 | ||||||||
\(538\) | 0.670748 | 0.0289180 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5.29593 | 0.227900 | ||||||||
\(541\) | 40.0215 | 1.72066 | 0.860329 | − | 0.509738i | \(-0.170258\pi\) | ||||
0.860329 | + | 0.509738i | \(0.170258\pi\) | |||||||
\(542\) | 0.424983 | 0.0182546 | ||||||||
\(543\) | 26.4209 | 1.13383 | ||||||||
\(544\) | 4.89007 | 0.209660 | ||||||||
\(545\) | 24.5498 | 1.05160 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.9488 | −0.553651 | −0.276826 | − | 0.960920i | \(-0.589282\pi\) | ||||
−0.276826 | + | 0.960920i | \(0.589282\pi\) | |||||||
\(548\) | 25.5005 | 1.08933 | ||||||||
\(549\) | −14.1386 | −0.603422 | ||||||||
\(550\) | 0.726392 | 0.0309735 | ||||||||
\(551\) | 26.0013 | 1.10769 | ||||||||
\(552\) | −0.277420 | −0.0118078 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.959616 | 0.0407702 | ||||||||
\(555\) | −10.1832 | −0.432253 | ||||||||
\(556\) | 25.0210 | 1.06113 | ||||||||
\(557\) | −11.4145 | −0.483648 | −0.241824 | − | 0.970320i | \(-0.577746\pi\) | ||||
−0.241824 | + | 0.970320i | \(0.577746\pi\) | |||||||
\(558\) | 0.682395 | 0.0288881 | ||||||||
\(559\) | 15.9456 | 0.674427 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 34.3730 | 1.45123 | ||||||||
\(562\) | 0.629175 | 0.0265401 | ||||||||
\(563\) | −34.8335 | −1.46806 | −0.734028 | − | 0.679119i | \(-0.762362\pi\) | ||||
−0.734028 | + | 0.679119i | \(0.762362\pi\) | |||||||
\(564\) | −22.1856 | −0.934183 | ||||||||
\(565\) | −18.0773 | −0.760516 | ||||||||
\(566\) | 1.17240 | 0.0492796 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.64354 | −0.110920 | ||||||||
\(569\) | −41.6149 | −1.74459 | −0.872294 | − | 0.488982i | \(-0.837369\pi\) | ||||
−0.872294 | + | 0.488982i | \(0.837369\pi\) | |||||||
\(570\) | −0.734974 | −0.0307847 | ||||||||
\(571\) | −40.2264 | −1.68342 | −0.841711 | − | 0.539929i | \(-0.818451\pi\) | ||||
−0.841711 | + | 0.539929i | \(0.818451\pi\) | |||||||
\(572\) | −37.1547 | −1.55352 | ||||||||
\(573\) | 4.42857 | 0.185006 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.17919 | −0.0908784 | ||||||||
\(576\) | −7.89865 | −0.329110 | ||||||||
\(577\) | 22.0329 | 0.917242 | 0.458621 | − | 0.888632i | \(-0.348343\pi\) | ||||
0.458621 | + | 0.888632i | \(0.348343\pi\) | |||||||
\(578\) | −1.46195 | −0.0608091 | ||||||||
\(579\) | 4.70814 | 0.195664 | ||||||||
\(580\) | −32.3357 | −1.34267 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.07486 | 0.0445544 | ||||||||
\(583\) | −44.5720 | −1.84598 | ||||||||
\(584\) | −1.25492 | −0.0519290 | ||||||||
\(585\) | 9.03008 | 0.373348 | ||||||||
\(586\) | −1.96633 | −0.0812284 | ||||||||
\(587\) | −14.1762 | −0.585116 | −0.292558 | − | 0.956248i | \(-0.594506\pi\) | ||||
−0.292558 | + | 0.956248i | \(0.594506\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 44.6792 | 1.84097 | ||||||||
\(590\) | 2.42628 | 0.0998885 | ||||||||
\(591\) | 25.9342 | 1.06679 | ||||||||
\(592\) | 15.2528 | 0.626887 | ||||||||
\(593\) | −0.457779 | −0.0187987 | −0.00939936 | − | 0.999956i | \(-0.502992\pi\) | ||||
−0.00939936 | + | 0.999956i | \(0.502992\pi\) | |||||||
\(594\) | 0.355819 | 0.0145994 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.24352 | −0.214783 | ||||||||
\(597\) | −14.9384 | −0.611389 | ||||||||
\(598\) | −0.236264 | −0.00966156 | ||||||||
\(599\) | −27.7858 | −1.13530 | −0.567648 | − | 0.823271i | \(-0.692147\pi\) | ||||
−0.567648 | + | 0.823271i | \(0.692147\pi\) | |||||||
\(600\) | 0.530552 | 0.0216597 | ||||||||
\(601\) | −30.0070 | −1.22401 | −0.612007 | − | 0.790853i | \(-0.709637\pi\) | ||||
−0.612007 | + | 0.790853i | \(0.709637\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.51962 | −0.265499 | ||||||||
\(604\) | 11.8923 | 0.483891 | ||||||||
\(605\) | −50.2285 | −2.04208 | ||||||||
\(606\) | 0.796493 | 0.0323553 | ||||||||
\(607\) | −24.6437 | −1.00026 | −0.500129 | − | 0.865951i | \(-0.666714\pi\) | ||||
−0.500129 | + | 0.865951i | \(0.666714\pi\) | |||||||
\(608\) | 3.31433 | 0.134414 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.44020 | −0.0988006 | ||||||||
\(611\) | −37.8287 | −1.53038 | ||||||||
\(612\) | 12.5396 | 0.506885 | ||||||||
\(613\) | 31.1894 | 1.25973 | 0.629865 | − | 0.776705i | \(-0.283110\pi\) | ||||
0.629865 | + | 0.776705i | \(0.283110\pi\) | |||||||
\(614\) | 0.363580 | 0.0146729 | ||||||||
\(615\) | 2.65358 | 0.107003 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.2034 | −1.41724 | −0.708619 | − | 0.705592i | \(-0.750681\pi\) | ||||
−0.708619 | + | 0.705592i | \(0.750681\pi\) | |||||||
\(618\) | 0.272172 | 0.0109484 | ||||||||
\(619\) | −32.5283 | −1.30742 | −0.653711 | − | 0.756744i | \(-0.726789\pi\) | ||||
−0.653711 | + | 0.756744i | \(0.726789\pi\) | |||||||
\(620\) | −55.5639 | −2.23150 | ||||||||
\(621\) | −1.06746 | −0.0428358 | ||||||||
\(622\) | 0.185173 | 0.00742475 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −13.5256 | −0.541459 | ||||||||
\(625\) | −31.0397 | −1.24159 | ||||||||
\(626\) | −0.518745 | −0.0207332 | ||||||||
\(627\) | 23.2969 | 0.930388 | ||||||||
\(628\) | −27.7068 | −1.10562 | ||||||||
\(629\) | −24.1117 | −0.961395 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.97175 | 0.0784943 | 0.0392471 | − | 0.999230i | \(-0.487504\pi\) | ||||
0.0392471 | + | 0.999230i | \(0.487504\pi\) | |||||||
\(632\) | 2.42287 | 0.0963765 | ||||||||
\(633\) | 12.7550 | 0.506966 | ||||||||
\(634\) | 0.603257 | 0.0239584 | ||||||||
\(635\) | 35.9127 | 1.42515 | ||||||||
\(636\) | −16.2603 | −0.644764 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.17255 | −0.0860119 | ||||||||
\(639\) | −10.1718 | −0.402391 | ||||||||
\(640\) | −5.49373 | −0.217159 | ||||||||
\(641\) | 5.94124 | 0.234665 | 0.117333 | − | 0.993093i | \(-0.462566\pi\) | ||||
0.117333 | + | 0.993093i | \(0.462566\pi\) | |||||||
\(642\) | −0.296085 | −0.0116855 | ||||||||
\(643\) | −0.918004 | −0.0362025 | −0.0181013 | − | 0.999836i | \(-0.505762\pi\) | ||||
−0.0181013 | + | 0.999836i | \(0.505762\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.4340 | 0.489590 | ||||||||
\(646\) | −1.74026 | −0.0684697 | ||||||||
\(647\) | 41.6269 | 1.63652 | 0.818260 | − | 0.574848i | \(-0.194939\pi\) | ||||
0.818260 | + | 0.574848i | \(0.194939\pi\) | |||||||
\(648\) | 0.259888 | 0.0102094 | ||||||||
\(649\) | −76.9073 | −3.01888 | ||||||||
\(650\) | 0.451844 | 0.0177228 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.92038 | 0.0752077 | ||||||||
\(653\) | −16.7700 | −0.656260 | −0.328130 | − | 0.944633i | \(-0.606418\pi\) | ||||
−0.328130 | + | 0.944633i | \(0.606418\pi\) | |||||||
\(654\) | 0.601730 | 0.0235295 | ||||||||
\(655\) | −12.4492 | −0.486429 | ||||||||
\(656\) | −3.97464 | −0.155183 | ||||||||
\(657\) | −4.82870 | −0.188386 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.2319 | 1.17767 | 0.588833 | − | 0.808255i | \(-0.299588\pi\) | ||||
0.588833 | + | 0.808255i | \(0.299588\pi\) | |||||||
\(660\) | −28.9725 | −1.12775 | ||||||||
\(661\) | 1.62355 | 0.0631488 | 0.0315744 | − | 0.999501i | \(-0.489948\pi\) | ||||
0.0315744 | + | 0.999501i | \(0.489948\pi\) | |||||||
\(662\) | −0.951688 | −0.0369884 | ||||||||
\(663\) | 21.3813 | 0.830382 | ||||||||
\(664\) | −1.30859 | −0.0507833 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.249597 | −0.00967167 | ||||||||
\(667\) | 6.51767 | 0.252365 | ||||||||
\(668\) | 21.7868 | 0.842956 | ||||||||
\(669\) | 7.54896 | 0.291859 | ||||||||
\(670\) | −1.12523 | −0.0434712 | ||||||||
\(671\) | 77.3483 | 2.98600 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.1360 | −1.08456 | −0.542282 | − | 0.840196i | \(-0.682440\pi\) | ||||
−0.542282 | + | 0.840196i | \(0.682440\pi\) | |||||||
\(674\) | −0.918795 | −0.0353907 | ||||||||
\(675\) | 2.04147 | 0.0785761 | ||||||||
\(676\) | 2.83337 | 0.108976 | ||||||||
\(677\) | −17.6912 | −0.679929 | −0.339964 | − | 0.940438i | \(-0.610415\pi\) | ||||
−0.339964 | + | 0.940438i | \(0.610415\pi\) | |||||||
\(678\) | −0.443085 | −0.0170166 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.33303 | 0.166164 | ||||||||
\(681\) | −7.98410 | −0.305951 | ||||||||
\(682\) | −3.73318 | −0.142951 | ||||||||
\(683\) | 3.62028 | 0.138526 | 0.0692630 | − | 0.997598i | \(-0.477935\pi\) | ||||
0.0692630 | + | 0.997598i | \(0.477935\pi\) | |||||||
\(684\) | 8.49894 | 0.324965 | ||||||||
\(685\) | 33.9055 | 1.29546 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.2575 | −0.582111 | ||||||||
\(688\) | −18.6242 | −0.710042 | ||||||||
\(689\) | −27.7255 | −1.05626 | ||||||||
\(690\) | −0.184234 | −0.00701366 | ||||||||
\(691\) | −10.5745 | −0.402273 | −0.201136 | − | 0.979563i | \(-0.564463\pi\) | ||||
−0.201136 | + | 0.979563i | \(0.564463\pi\) | |||||||
\(692\) | 36.2874 | 1.37944 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.31733 | −0.0500053 | ||||||||
\(695\) | 33.2679 | 1.26192 | ||||||||
\(696\) | −1.58681 | −0.0601480 | ||||||||
\(697\) | 6.28311 | 0.237990 | ||||||||
\(698\) | 1.55367 | 0.0588073 | ||||||||
\(699\) | −13.1497 | −0.497369 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.8486 | −1.46729 | −0.733645 | − | 0.679533i | \(-0.762182\pi\) | ||||
−0.733645 | + | 0.679533i | \(0.762182\pi\) | |||||||
\(702\) | 0.221333 | 0.00835367 | ||||||||
\(703\) | −16.3421 | −0.616353 | ||||||||
\(704\) | 43.2112 | 1.62858 | ||||||||
\(705\) | −29.4980 | −1.11096 | ||||||||
\(706\) | −1.29786 | −0.0488458 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −28.0566 | −1.05443 | ||||||||
\(709\) | 29.2915 | 1.10006 | 0.550032 | − | 0.835144i | \(-0.314616\pi\) | ||||
0.550032 | + | 0.835144i | \(0.314616\pi\) | |||||||
\(710\) | −1.75556 | −0.0658851 | ||||||||
\(711\) | 9.32274 | 0.349630 | ||||||||
\(712\) | 2.24207 | 0.0840250 | ||||||||
\(713\) | 11.1996 | 0.419428 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −49.4009 | −1.84749 | ||||||||
\(716\) | −28.6147 | −1.06938 | ||||||||
\(717\) | 24.1988 | 0.903720 | ||||||||
\(718\) | 0.305825 | 0.0114133 | ||||||||
\(719\) | −8.04364 | −0.299977 | −0.149989 | − | 0.988688i | \(-0.547924\pi\) | ||||
−0.149989 | + | 0.988688i | \(0.547924\pi\) | |||||||
\(720\) | −10.5470 | −0.393063 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.0562831 | 0.00209464 | ||||||||
\(723\) | 15.7240 | 0.584782 | ||||||||
\(724\) | −52.7300 | −1.95970 | ||||||||
\(725\) | −12.4647 | −0.462928 | ||||||||
\(726\) | −1.23113 | −0.0456916 | ||||||||
\(727\) | 45.4403 | 1.68529 | 0.842643 | − | 0.538472i | \(-0.180998\pi\) | ||||
0.842643 | + | 0.538472i | \(0.180998\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.833389 | −0.0308451 | ||||||||
\(731\) | 29.4412 | 1.08892 | ||||||||
\(732\) | 28.2175 | 1.04295 | ||||||||
\(733\) | −36.2630 | −1.33940 | −0.669702 | − | 0.742630i | \(-0.733578\pi\) | ||||
−0.669702 | + | 0.742630i | \(0.733578\pi\) | |||||||
\(734\) | 0.842794 | 0.0311081 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.830794 | 0.0306235 | ||||||||
\(737\) | 35.6669 | 1.31381 | ||||||||
\(738\) | 0.0650408 | 0.00239418 | ||||||||
\(739\) | −34.1511 | −1.25627 | −0.628134 | − | 0.778105i | \(-0.716181\pi\) | ||||
−0.628134 | + | 0.778105i | \(0.716181\pi\) | |||||||
\(740\) | 20.3233 | 0.747101 | ||||||||
\(741\) | 14.4915 | 0.532360 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.8077 | 0.726673 | 0.363337 | − | 0.931658i | \(-0.381637\pi\) | ||||
0.363337 | + | 0.931658i | \(0.381637\pi\) | |||||||
\(744\) | −2.72669 | −0.0999655 | ||||||||
\(745\) | −6.97179 | −0.255427 | ||||||||
\(746\) | −1.59681 | −0.0584634 | ||||||||
\(747\) | −5.03523 | −0.184229 | ||||||||
\(748\) | −68.6006 | −2.50829 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.510615 | −0.0186450 | ||||||||
\(751\) | 22.2356 | 0.811387 | 0.405694 | − | 0.914009i | \(-0.367030\pi\) | ||||
0.405694 | + | 0.914009i | \(0.367030\pi\) | |||||||
\(752\) | 44.1833 | 1.61120 | ||||||||
\(753\) | 2.62369 | 0.0956124 | ||||||||
\(754\) | −1.35141 | −0.0492153 | ||||||||
\(755\) | 15.8120 | 0.575458 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.0167 | −1.38174 | −0.690870 | − | 0.722979i | \(-0.742772\pi\) | ||||
−0.690870 | + | 0.722979i | \(0.742772\pi\) | |||||||
\(758\) | −2.19904 | −0.0798727 | ||||||||
\(759\) | 5.83977 | 0.211970 | ||||||||
\(760\) | 2.93679 | 0.106528 | ||||||||
\(761\) | −18.8243 | −0.682382 | −0.341191 | − | 0.939994i | \(-0.610830\pi\) | ||||
−0.341191 | + | 0.939994i | \(0.610830\pi\) | |||||||
\(762\) | 0.880243 | 0.0318878 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −8.83841 | −0.319762 | ||||||||
\(765\) | 16.6727 | 0.602803 | ||||||||
\(766\) | 1.49895 | 0.0541591 | ||||||||
\(767\) | −47.8393 | −1.72738 | ||||||||
\(768\) | 15.6626 | 0.565177 | ||||||||
\(769\) | −2.09557 | −0.0755682 | −0.0377841 | − | 0.999286i | \(-0.512030\pi\) | ||||
−0.0377841 | + | 0.999286i | \(0.512030\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.5935 | −0.705642 | ||||||||
\(772\) | −9.39637 | −0.338183 | ||||||||
\(773\) | 6.12334 | 0.220241 | 0.110121 | − | 0.993918i | \(-0.464876\pi\) | ||||
0.110121 | + | 0.993918i | \(0.464876\pi\) | |||||||
\(774\) | 0.304766 | 0.0109546 | ||||||||
\(775\) | −21.4187 | −0.769382 | ||||||||
\(776\) | −4.29489 | −0.154178 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.268734 | 0.00963456 | ||||||||
\(779\) | 4.25848 | 0.152576 | ||||||||
\(780\) | −18.0220 | −0.645290 | ||||||||
\(781\) | 55.6471 | 1.99121 | ||||||||
\(782\) | −0.436227 | −0.0155994 | ||||||||
\(783\) | −6.10576 | −0.218202 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −36.8390 | −1.31484 | ||||||||
\(786\) | −0.305136 | −0.0108839 | ||||||||
\(787\) | 25.8179 | 0.920310 | 0.460155 | − | 0.887839i | \(-0.347794\pi\) | ||||
0.460155 | + | 0.887839i | \(0.347794\pi\) | |||||||
\(788\) | −51.7587 | −1.84383 | ||||||||
\(789\) | 1.27756 | 0.0454823 | ||||||||
\(790\) | 1.60902 | 0.0572463 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.42177 | −0.0505204 | ||||||||
\(793\) | 48.1136 | 1.70856 | ||||||||
\(794\) | −1.64652 | −0.0584329 | ||||||||
\(795\) | −21.6197 | −0.766773 | ||||||||
\(796\) | 29.8137 | 1.05672 | ||||||||
\(797\) | 17.1847 | 0.608714 | 0.304357 | − | 0.952558i | \(-0.401558\pi\) | ||||
0.304357 | + | 0.952558i | \(0.401558\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −69.8450 | −2.47094 | ||||||||
\(800\) | −1.58885 | −0.0561744 | ||||||||
\(801\) | 8.62706 | 0.304822 | ||||||||
\(802\) | −1.76052 | −0.0621660 | ||||||||
\(803\) | 26.4164 | 0.932215 | ||||||||
\(804\) | 13.0117 | 0.458886 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.32218 | −0.0817954 | ||||||||
\(807\) | −10.3127 | −0.363026 | ||||||||
\(808\) | −3.18260 | −0.111964 | ||||||||
\(809\) | −4.69562 | −0.165089 | −0.0825446 | − | 0.996587i | \(-0.526305\pi\) | ||||
−0.0825446 | + | 0.996587i | \(0.526305\pi\) | |||||||
\(810\) | 0.172591 | 0.00606422 | ||||||||
\(811\) | 18.8630 | 0.662371 | 0.331185 | − | 0.943566i | \(-0.392551\pi\) | ||||
0.331185 | + | 0.943566i | \(0.392551\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.53411 | −0.229161 | ||||||||
\(814\) | 1.36547 | 0.0478597 | ||||||||
\(815\) | 2.55333 | 0.0894393 | ||||||||
\(816\) | −24.9731 | −0.874232 | ||||||||
\(817\) | 19.9542 | 0.698110 | ||||||||
\(818\) | 2.34364 | 0.0819436 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.29593 | −0.184942 | ||||||||
\(821\) | 37.6024 | 1.31233 | 0.656167 | − | 0.754616i | \(-0.272177\pi\) | ||||
0.656167 | + | 0.754616i | \(0.272177\pi\) | |||||||
\(822\) | 0.831044 | 0.0289860 | ||||||||
\(823\) | −45.6703 | −1.59197 | −0.795983 | − | 0.605320i | \(-0.793045\pi\) | ||||
−0.795983 | + | 0.605320i | \(0.793045\pi\) | |||||||
\(824\) | −1.08754 | −0.0378862 | ||||||||
\(825\) | −11.1683 | −0.388829 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.4857 | −0.816678 | −0.408339 | − | 0.912830i | \(-0.633892\pi\) | ||||
−0.408339 | + | 0.912830i | \(0.633892\pi\) | |||||||
\(828\) | 2.13041 | 0.0740368 | ||||||||
\(829\) | −27.5826 | −0.957982 | −0.478991 | − | 0.877820i | \(-0.658997\pi\) | ||||
−0.478991 | + | 0.877820i | \(0.658997\pi\) | |||||||
\(830\) | −0.869033 | −0.0301646 | ||||||||
\(831\) | −14.7541 | −0.511813 | ||||||||
\(832\) | 26.8790 | 0.931862 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0.815417 | 0.0282356 | ||||||||
\(835\) | 28.9677 | 1.00247 | ||||||||
\(836\) | −46.4952 | −1.60807 | ||||||||
\(837\) | −10.4918 | −0.362650 | ||||||||
\(838\) | −1.83803 | −0.0634937 | ||||||||
\(839\) | 11.7966 | 0.407263 | 0.203631 | − | 0.979048i | \(-0.434726\pi\) | ||||
0.203631 | + | 0.979048i | \(0.434726\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.28036 | 0.285530 | ||||||||
\(842\) | −1.20696 | −0.0415947 | ||||||||
\(843\) | −9.67355 | −0.333175 | ||||||||
\(844\) | −25.4561 | −0.876233 | ||||||||
\(845\) | 3.76724 | 0.129597 | ||||||||
\(846\) | −0.723014 | −0.0248577 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 32.3829 | 1.11203 | ||||||||
\(849\) | −18.0256 | −0.618637 | ||||||||
\(850\) | 0.834262 | 0.0286149 | ||||||||
\(851\) | −4.09643 | −0.140424 | ||||||||
\(852\) | 20.3006 | 0.695488 | ||||||||
\(853\) | −6.50215 | −0.222629 | −0.111315 | − | 0.993785i | \(-0.535506\pi\) | ||||
−0.111315 | + | 0.993785i | \(0.535506\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.3002 | 0.386459 | ||||||||
\(856\) | 1.18309 | 0.0404371 | ||||||||
\(857\) | 50.2945 | 1.71803 | 0.859014 | − | 0.511952i | \(-0.171078\pi\) | ||||
0.859014 | + | 0.511952i | \(0.171078\pi\) | |||||||
\(858\) | −1.21085 | −0.0413376 | ||||||||
\(859\) | 0.973780 | 0.0332249 | 0.0166125 | − | 0.999862i | \(-0.494712\pi\) | ||||
0.0166125 | + | 0.999862i | \(0.494712\pi\) | |||||||
\(860\) | −24.8155 | −0.846201 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.115751 | 0.00394251 | ||||||||
\(863\) | −40.4421 | −1.37667 | −0.688333 | − | 0.725395i | \(-0.741657\pi\) | ||||
−0.688333 | + | 0.725395i | \(0.741657\pi\) | |||||||
\(864\) | −0.778289 | −0.0264779 | ||||||||
\(865\) | 48.2477 | 1.64047 | ||||||||
\(866\) | 1.85834 | 0.0631491 | ||||||||
\(867\) | 22.4774 | 0.763373 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −51.0019 | −1.73012 | ||||||||
\(870\) | −1.05380 | −0.0357271 | ||||||||
\(871\) | 22.1862 | 0.751750 | ||||||||
\(872\) | −2.40437 | −0.0814224 | ||||||||
\(873\) | −16.5259 | −0.559318 | ||||||||
\(874\) | −0.295660 | −0.0100008 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 9.63698 | 0.325603 | ||||||||
\(877\) | −35.9374 | −1.21352 | −0.606760 | − | 0.794885i | \(-0.707531\pi\) | ||||
−0.606760 | + | 0.794885i | \(0.707531\pi\) | |||||||
\(878\) | 0.416186 | 0.0140456 | ||||||||
\(879\) | 30.2323 | 1.01971 | ||||||||
\(880\) | 57.6995 | 1.94505 | ||||||||
\(881\) | 4.34713 | 0.146459 | 0.0732293 | − | 0.997315i | \(-0.476669\pi\) | ||||
0.0732293 | + | 0.997315i | \(0.476669\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.4854 | 0.824000 | 0.412000 | − | 0.911184i | \(-0.364830\pi\) | ||||
0.412000 | + | 0.911184i | \(0.364830\pi\) | |||||||
\(884\) | −42.6722 | −1.43522 | ||||||||
\(885\) | −37.3040 | −1.25396 | ||||||||
\(886\) | 1.65915 | 0.0557404 | ||||||||
\(887\) | −5.39213 | −0.181050 | −0.0905250 | − | 0.995894i | \(-0.528854\pi\) | ||||
−0.0905250 | + | 0.995894i | \(0.528854\pi\) | |||||||
\(888\) | 0.997330 | 0.0334682 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.48895 | 0.0499097 | ||||||||
\(891\) | −5.47071 | −0.183276 | ||||||||
\(892\) | −15.0660 | −0.504446 | ||||||||
\(893\) | −47.3386 | −1.58413 | ||||||||
\(894\) | −0.170883 | −0.00571518 | ||||||||
\(895\) | −38.0461 | −1.27174 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.63256 | 0.121288 | ||||||||
\(898\) | 0.997355 | 0.0332822 | ||||||||
\(899\) | 64.0605 | 2.13654 | ||||||||
\(900\) | −4.07430 | −0.135810 | ||||||||
\(901\) | −51.1909 | −1.70542 | ||||||||
\(902\) | −0.355819 | −0.0118475 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.77046 | 0.0588848 | ||||||||
\(905\) | −70.1098 | −2.33053 | ||||||||
\(906\) | 0.387562 | 0.0128759 | ||||||||
\(907\) | 25.2422 | 0.838154 | 0.419077 | − | 0.907951i | \(-0.362354\pi\) | ||||
0.419077 | + | 0.907951i | \(0.362354\pi\) | |||||||
\(908\) | 15.9344 | 0.528802 | ||||||||
\(909\) | −12.2461 | −0.406176 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.07772 | −0.234495 | −0.117248 | − | 0.993103i | \(-0.537407\pi\) | ||||
−0.117248 | + | 0.993103i | \(0.537407\pi\) | |||||||
\(912\) | −16.9259 | −0.560473 | ||||||||
\(913\) | 27.5462 | 0.911648 | ||||||||
\(914\) | 0.809818 | 0.0267864 | ||||||||
\(915\) | 37.5179 | 1.24030 | ||||||||
\(916\) | 30.4505 | 1.00611 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.408658 | 0.0134877 | ||||||||
\(919\) | −9.66161 | −0.318707 | −0.159353 | − | 0.987222i | \(-0.550941\pi\) | ||||
−0.159353 | + | 0.987222i | \(0.550941\pi\) | |||||||
\(920\) | 0.736156 | 0.0242703 | ||||||||
\(921\) | −5.59004 | −0.184198 | ||||||||
\(922\) | 2.46995 | 0.0813435 | ||||||||
\(923\) | 34.6146 | 1.13935 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.83421 | 0.257587 | ||||||||
\(926\) | −0.473700 | −0.0155668 | ||||||||
\(927\) | −4.18464 | −0.137442 | ||||||||
\(928\) | 4.75205 | 0.155994 | ||||||||
\(929\) | −11.2288 | −0.368404 | −0.184202 | − | 0.982888i | \(-0.558970\pi\) | ||||
−0.184202 | + | 0.982888i | \(0.558970\pi\) | |||||||
\(930\) | −1.81079 | −0.0593781 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 26.2438 | 0.859646 | ||||||||
\(933\) | −2.84702 | −0.0932074 | ||||||||
\(934\) | 0.820475 | 0.0268468 | ||||||||
\(935\) | −91.2114 | −2.98293 | ||||||||
\(936\) | −0.884395 | −0.0289074 | ||||||||
\(937\) | 34.3993 | 1.12378 | 0.561888 | − | 0.827214i | \(-0.310075\pi\) | ||||
0.561888 | + | 0.827214i | \(0.310075\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.97569 | 0.260277 | ||||||||
\(940\) | 58.8712 | 1.92017 | ||||||||
\(941\) | 28.0008 | 0.912801 | 0.456401 | − | 0.889774i | \(-0.349138\pi\) | ||||
0.456401 | + | 0.889774i | \(0.349138\pi\) | |||||||
\(942\) | −0.902947 | −0.0294196 | ||||||||
\(943\) | 1.06746 | 0.0347613 | ||||||||
\(944\) | 55.8755 | 1.81859 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.66728 | −0.0542081 | ||||||||
\(947\) | −1.50126 | −0.0487845 | −0.0243922 | − | 0.999702i | \(-0.507765\pi\) | ||||
−0.0243922 | + | 0.999702i | \(0.507765\pi\) | |||||||
\(948\) | −18.6060 | −0.604296 | ||||||||
\(949\) | 16.4320 | 0.533406 | ||||||||
\(950\) | 0.565435 | 0.0183451 | ||||||||
\(951\) | −9.27505 | −0.300764 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.3166 | 0.852479 | 0.426240 | − | 0.904610i | \(-0.359838\pi\) | ||||
0.426240 | + | 0.904610i | \(0.359838\pi\) | |||||||
\(954\) | −0.529913 | −0.0171566 | ||||||||
\(955\) | −11.7516 | −0.380271 | ||||||||
\(956\) | −48.2952 | −1.56198 | ||||||||
\(957\) | 33.4028 | 1.07976 | ||||||||
\(958\) | 2.79024 | 0.0901486 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 20.9597 | 0.676471 | ||||||||
\(961\) | 79.0781 | 2.55091 | ||||||||
\(962\) | 0.849374 | 0.0273849 | ||||||||
\(963\) | 4.55230 | 0.146696 | ||||||||
\(964\) | −31.3815 | −1.01073 | ||||||||
\(965\) | −12.4934 | −0.402177 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.1209 | −0.647045 | −0.323523 | − | 0.946220i | \(-0.604867\pi\) | ||||
−0.323523 | + | 0.946220i | \(0.604867\pi\) | |||||||
\(968\) | 4.91932 | 0.158113 | ||||||||
\(969\) | 26.7565 | 0.859542 | ||||||||
\(970\) | −2.85222 | −0.0915793 | ||||||||
\(971\) | −24.1292 | −0.774341 | −0.387171 | − | 0.922008i | \(-0.626548\pi\) | ||||
−0.387171 | + | 0.922008i | \(0.626548\pi\) | |||||||
\(972\) | −1.99577 | −0.0640143 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.03190 | 0.0651063 | ||||||||
\(975\) | −6.94708 | −0.222485 | ||||||||
\(976\) | −56.1959 | −1.79879 | ||||||||
\(977\) | 29.1755 | 0.933408 | 0.466704 | − | 0.884414i | \(-0.345441\pi\) | ||||
0.466704 | + | 0.884414i | \(0.345441\pi\) | |||||||
\(978\) | 0.0625837 | 0.00200121 | ||||||||
\(979\) | −47.1961 | −1.50839 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.25158 | −0.295380 | ||||||||
\(982\) | −2.56242 | −0.0817702 | ||||||||
\(983\) | −7.77819 | −0.248086 | −0.124043 | − | 0.992277i | \(-0.539586\pi\) | ||||
−0.124043 | + | 0.992277i | \(0.539586\pi\) | |||||||
\(984\) | −0.259888 | −0.00828492 | ||||||||
\(985\) | −68.8184 | −2.19274 | ||||||||
\(986\) | −2.49517 | −0.0794624 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −28.9218 | −0.920125 | ||||||||
\(989\) | 5.00187 | 0.159050 | ||||||||
\(990\) | −0.944192 | −0.0300084 | ||||||||
\(991\) | −24.9735 | −0.793310 | −0.396655 | − | 0.917968i | \(-0.629829\pi\) | ||||
−0.396655 | + | 0.917968i | \(0.629829\pi\) | |||||||
\(992\) | 8.16566 | 0.259260 | ||||||||
\(993\) | 14.6322 | 0.464338 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 39.6403 | 1.25668 | ||||||||
\(996\) | 10.0492 | 0.318420 | ||||||||
\(997\) | −38.1977 | −1.20973 | −0.604866 | − | 0.796327i | \(-0.706773\pi\) | ||||
−0.604866 | + | 0.796327i | \(0.706773\pi\) | |||||||
\(998\) | −0.749106 | −0.0237125 | ||||||||
\(999\) | 3.83754 | 0.121414 |
(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 | 6027.2.a.bo.1.11 | yes | 24 | |
7.6 | odd | 2 | 6027.2.a.bn.1.11 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.bn.1.11 | ✓ | 24 | 7.6 | odd | 2 | ||
6027.2.a.bo.1.11 | yes | 24 | 1.1 | even | 1 | trivial |