Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9025,2,Mod(1,9025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9025, 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("9025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9025 = 5^{2} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9025.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: | \(72.0649878242\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.71593280.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 8x^{4} + 13x^{2} - 5 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.44118\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.44118 | −1.72617 | −0.863086 | − | 0.505057i | \(-0.831472\pi\) | ||||
−0.863086 | + | 0.505057i | \(0.831472\pi\) | |||||||
\(3\) | −1.94894 | −1.12522 | −0.562610 | − | 0.826722i | \(-0.690203\pi\) | ||||
−0.562610 | + | 0.826722i | \(0.690203\pi\) | |||||||
\(4\) | 3.95934 | 1.97967 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.75770 | 1.94232 | ||||||||
\(7\) | −4.16098 | −1.57270 | −0.786352 | − | 0.617779i | \(-0.788033\pi\) | ||||
−0.786352 | + | 0.617779i | \(0.788033\pi\) | |||||||
\(8\) | −4.78310 | −1.69108 | ||||||||
\(9\) | 0.798360 | 0.266120 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.75770 | −1.43450 | −0.717251 | − | 0.696815i | \(-0.754600\pi\) | ||||
−0.717251 | + | 0.696815i | \(0.754600\pi\) | |||||||
\(12\) | −7.71651 | −2.22757 | ||||||||
\(13\) | −2.83416 | −0.786054 | −0.393027 | − | 0.919527i | \(-0.628572\pi\) | ||||
−0.393027 | + | 0.919527i | \(0.628572\pi\) | |||||||
\(14\) | 10.1577 | 2.71476 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.75770 | 0.939425 | ||||||||
\(17\) | −4.16098 | −1.00919 | −0.504593 | − | 0.863357i | \(-0.668357\pi\) | ||||
−0.504593 | + | 0.863357i | \(0.668357\pi\) | |||||||
\(18\) | −1.94894 | −0.459369 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.10950 | 1.76964 | ||||||||
\(22\) | 11.6144 | 2.47620 | ||||||||
\(23\) | −7.31376 | −1.52503 | −0.762513 | − | 0.646973i | \(-0.776034\pi\) | ||||
−0.762513 | + | 0.646973i | \(0.776034\pi\) | |||||||
\(24\) | 9.32196 | 1.90284 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.91868 | 1.35687 | ||||||||
\(27\) | 4.29086 | 0.825776 | ||||||||
\(28\) | −16.4747 | −3.11343 | ||||||||
\(29\) | −10.1577 | −1.88624 | −0.943118 | − | 0.332459i | \(-0.892122\pi\) | ||||
−0.943118 | + | 0.332459i | \(0.892122\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.04819 | 0.367866 | 0.183933 | − | 0.982939i | \(-0.441117\pi\) | ||||
0.183933 | + | 0.982939i | \(0.441117\pi\) | |||||||
\(32\) | 0.392983 | 0.0694703 | ||||||||
\(33\) | 9.27247 | 1.61413 | ||||||||
\(34\) | 10.1577 | 1.74203 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.16098 | 0.526830 | ||||||||
\(37\) | −6.25981 | −1.02911 | −0.514553 | − | 0.857458i | \(-0.672042\pi\) | ||||
−0.514553 | + | 0.857458i | \(0.672042\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.52360 | 0.884484 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.69650 | 1.20199 | 0.600996 | − | 0.799252i | \(-0.294771\pi\) | ||||
0.600996 | + | 0.799252i | \(0.294771\pi\) | |||||||
\(42\) | −19.7967 | −3.05470 | ||||||||
\(43\) | 3.32196 | 0.506594 | 0.253297 | − | 0.967388i | \(-0.418485\pi\) | ||||
0.253297 | + | 0.967388i | \(0.418485\pi\) | |||||||
\(44\) | −18.8374 | −2.83984 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 17.8542 | 2.63246 | ||||||||
\(47\) | −8.15278 | −1.18921 | −0.594603 | − | 0.804020i | \(-0.702691\pi\) | ||||
−0.594603 | + | 0.804020i | \(0.702691\pi\) | |||||||
\(48\) | −7.32353 | −1.05706 | ||||||||
\(49\) | 10.3138 | 1.47339 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.10950 | 1.13556 | ||||||||
\(52\) | −11.2214 | −1.55613 | ||||||||
\(53\) | 8.20875 | 1.12756 | 0.563779 | − | 0.825926i | \(-0.309347\pi\) | ||||
0.563779 | + | 0.825926i | \(0.309347\pi\) | |||||||
\(54\) | −10.4747 | −1.42543 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 19.9024 | 2.65957 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 24.7967 | 3.25597 | ||||||||
\(59\) | −4.09639 | −0.533304 | −0.266652 | − | 0.963793i | \(-0.585917\pi\) | ||||
−0.266652 | + | 0.963793i | \(0.585917\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.76590 | 0.738248 | 0.369124 | − | 0.929380i | \(-0.379658\pi\) | ||||
0.369124 | + | 0.929380i | \(0.379658\pi\) | |||||||
\(62\) | −5.00000 | −0.635001 | ||||||||
\(63\) | −3.32196 | −0.418528 | ||||||||
\(64\) | −8.47474 | −1.05934 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −22.6357 | −2.78627 | ||||||||
\(67\) | −0.392983 | −0.0480105 | −0.0240053 | − | 0.999712i | \(-0.507642\pi\) | ||||
−0.0240053 | + | 0.999712i | \(0.507642\pi\) | |||||||
\(68\) | −16.4747 | −1.99786 | ||||||||
\(69\) | 14.2541 | 1.71599 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.412997 | 0.0490137 | 0.0245069 | − | 0.999700i | \(-0.492198\pi\) | ||||
0.0245069 | + | 0.999700i | \(0.492198\pi\) | |||||||
\(72\) | −3.81864 | −0.450031 | ||||||||
\(73\) | 2.31376 | 0.270806 | 0.135403 | − | 0.990791i | \(-0.456767\pi\) | ||||
0.135403 | + | 0.990791i | \(0.456767\pi\) | |||||||
\(74\) | 15.2813 | 1.77642 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 19.7967 | 2.25604 | ||||||||
\(78\) | −13.4841 | −1.52677 | ||||||||
\(79\) | 5.64831 | 0.635484 | 0.317742 | − | 0.948177i | \(-0.397075\pi\) | ||||
0.317742 | + | 0.948177i | \(0.397075\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.7577 | −1.19530 | ||||||||
\(82\) | −18.7885 | −2.07484 | ||||||||
\(83\) | 2.31376 | 0.253969 | 0.126984 | − | 0.991905i | \(-0.459470\pi\) | ||||
0.126984 | + | 0.991905i | \(0.459470\pi\) | |||||||
\(84\) | 32.1083 | 3.50330 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8.10950 | −0.874469 | ||||||||
\(87\) | 19.7967 | 2.12243 | ||||||||
\(88\) | 22.7566 | 2.42586 | ||||||||
\(89\) | 12.2059 | 1.29382 | 0.646910 | − | 0.762566i | \(-0.276061\pi\) | ||||
0.646910 | + | 0.762566i | \(0.276061\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.7929 | 1.23623 | ||||||||
\(92\) | −28.9577 | −3.01905 | ||||||||
\(93\) | −3.99180 | −0.413931 | ||||||||
\(94\) | 19.9024 | 2.05277 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.765900 | −0.0781694 | ||||||||
\(97\) | 18.4657 | 1.87491 | 0.937454 | − | 0.348110i | \(-0.113177\pi\) | ||||
0.937454 | + | 0.348110i | \(0.113177\pi\) | |||||||
\(98\) | −25.1777 | −2.54333 | ||||||||
\(99\) | −3.79836 | −0.381750 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.242298 | 0.0241096 | 0.0120548 | − | 0.999927i | \(-0.496163\pi\) | ||||
0.0120548 | + | 0.999927i | \(0.496163\pi\) | |||||||
\(102\) | −19.7967 | −1.96017 | ||||||||
\(103\) | 15.4530 | 1.52263 | 0.761317 | − | 0.648380i | \(-0.224553\pi\) | ||||
0.761317 | + | 0.648380i | \(0.224553\pi\) | |||||||
\(104\) | 13.5561 | 1.32928 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −20.0390 | −1.94636 | ||||||||
\(107\) | −1.65521 | −0.160015 | −0.0800076 | − | 0.996794i | \(-0.525494\pi\) | ||||
−0.0800076 | + | 0.996794i | \(0.525494\pi\) | |||||||
\(108\) | 16.9890 | 1.63477 | ||||||||
\(109\) | −3.60011 | −0.344828 | −0.172414 | − | 0.985025i | \(-0.555157\pi\) | ||||
−0.172414 | + | 0.985025i | \(0.555157\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.2000 | 1.15797 | ||||||||
\(112\) | −15.6357 | −1.47744 | ||||||||
\(113\) | −2.42116 | −0.227764 | −0.113882 | − | 0.993494i | \(-0.536329\pi\) | ||||
−0.113882 | + | 0.993494i | \(0.536329\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −40.2178 | −3.73412 | ||||||||
\(117\) | −2.26268 | −0.209185 | ||||||||
\(118\) | 10.0000 | 0.920575 | ||||||||
\(119\) | 17.3138 | 1.58715 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.6357 | 1.05779 | ||||||||
\(122\) | −14.0756 | −1.27434 | ||||||||
\(123\) | −15.0000 | −1.35250 | ||||||||
\(124\) | 8.10950 | 0.728254 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 8.10950 | 0.722451 | ||||||||
\(127\) | −16.1038 | −1.42898 | −0.714489 | − | 0.699647i | \(-0.753341\pi\) | ||||
−0.714489 | + | 0.699647i | \(0.753341\pi\) | |||||||
\(128\) | 19.9024 | 1.75914 | ||||||||
\(129\) | −6.47430 | −0.570030 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.3138 | −0.901118 | −0.450559 | − | 0.892747i | \(-0.648775\pi\) | ||||
−0.450559 | + | 0.892747i | \(0.648775\pi\) | |||||||
\(132\) | 36.7129 | 3.19544 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.959341 | 0.0828745 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 19.9024 | 1.70661 | ||||||||
\(137\) | −10.6357 | −0.908671 | −0.454336 | − | 0.890831i | \(-0.650123\pi\) | ||||
−0.454336 | + | 0.890831i | \(0.650123\pi\) | |||||||
\(138\) | −34.7967 | −2.96209 | ||||||||
\(139\) | −3.80656 | −0.322868 | −0.161434 | − | 0.986884i | \(-0.551612\pi\) | ||||
−0.161434 | + | 0.986884i | \(0.551612\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.8893 | 1.33812 | ||||||||
\(142\) | −1.00820 | −0.0846061 | ||||||||
\(143\) | 13.4841 | 1.12760 | ||||||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.64831 | −0.467457 | ||||||||
\(147\) | −20.1009 | −1.65789 | ||||||||
\(148\) | −24.7847 | −2.03729 | ||||||||
\(149\) | 12.7984 | 1.04848 | 0.524241 | − | 0.851570i | \(-0.324349\pi\) | ||||
0.524241 | + | 0.851570i | \(0.324349\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.7766 | −1.85353 | −0.926765 | − | 0.375641i | \(-0.877423\pi\) | ||||
−0.926765 | + | 0.375641i | \(0.877423\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.32196 | −0.268565 | ||||||||
\(154\) | −48.3273 | −3.89432 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 21.8698 | 1.75099 | ||||||||
\(157\) | 15.6357 | 1.24787 | 0.623933 | − | 0.781478i | \(-0.285534\pi\) | ||||
0.623933 | + | 0.781478i | \(0.285534\pi\) | |||||||
\(158\) | −13.7885 | −1.09695 | ||||||||
\(159\) | −15.9983 | −1.26875 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 30.4324 | 2.39841 | ||||||||
\(162\) | 26.2614 | 2.06329 | ||||||||
\(163\) | 6.47474 | 0.507141 | 0.253571 | − | 0.967317i | \(-0.418395\pi\) | ||||
0.253571 | + | 0.967317i | \(0.418395\pi\) | |||||||
\(164\) | 30.4731 | 2.37955 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.64831 | −0.438394 | ||||||||
\(167\) | 3.79862 | 0.293946 | 0.146973 | − | 0.989140i | \(-0.453047\pi\) | ||||
0.146973 | + | 0.989140i | \(0.453047\pi\) | |||||||
\(168\) | −38.7885 | −2.99260 | ||||||||
\(169\) | −4.96754 | −0.382118 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 13.1528 | 1.00289 | ||||||||
\(173\) | 6.43427 | 0.489189 | 0.244594 | − | 0.969626i | \(-0.421345\pi\) | ||||
0.244594 | + | 0.969626i | \(0.421345\pi\) | |||||||
\(174\) | −48.3273 | −3.66368 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −17.8780 | −1.34761 | ||||||||
\(177\) | 7.98360 | 0.600084 | ||||||||
\(178\) | −29.7967 | −2.23336 | ||||||||
\(179\) | 8.60577 | 0.643225 | 0.321613 | − | 0.946871i | \(-0.395775\pi\) | ||||
0.321613 | + | 0.946871i | \(0.395775\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.50938 | −0.335180 | −0.167590 | − | 0.985857i | \(-0.553598\pi\) | ||||
−0.167590 | + | 0.985857i | \(0.553598\pi\) | |||||||
\(182\) | −28.7885 | −2.13395 | ||||||||
\(183\) | −11.2374 | −0.830691 | ||||||||
\(184\) | 34.9824 | 2.57894 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 9.74469 | 0.714515 | ||||||||
\(187\) | 19.7967 | 1.44768 | ||||||||
\(188\) | −32.2797 | −2.35424 | ||||||||
\(189\) | −17.8542 | −1.29870 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.85542 | 0.206611 | 0.103305 | − | 0.994650i | \(-0.467058\pi\) | ||||
0.103305 | + | 0.994650i | \(0.467058\pi\) | |||||||
\(192\) | 16.5168 | 1.19199 | ||||||||
\(193\) | −4.19564 | −0.302009 | −0.151004 | − | 0.988533i | \(-0.548251\pi\) | ||||
−0.151004 | + | 0.988533i | \(0.548251\pi\) | |||||||
\(194\) | −45.0780 | −3.23641 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 40.8357 | 2.91684 | ||||||||
\(197\) | −10.8390 | −0.772248 | −0.386124 | − | 0.922447i | \(-0.626186\pi\) | ||||
−0.386124 | + | 0.922447i | \(0.626186\pi\) | |||||||
\(198\) | 9.27247 | 0.658966 | ||||||||
\(199\) | −13.7885 | −0.977441 | −0.488721 | − | 0.872440i | \(-0.662536\pi\) | ||||
−0.488721 | + | 0.872440i | \(0.662536\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.765900 | 0.0540224 | ||||||||
\(202\) | −0.591493 | −0.0416173 | ||||||||
\(203\) | 42.2659 | 2.96649 | ||||||||
\(204\) | 32.1083 | 2.24803 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −37.7236 | −2.62833 | ||||||||
\(207\) | −5.83902 | −0.405840 | ||||||||
\(208\) | −10.6499 | −0.738440 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.8060 | −1.08813 | −0.544065 | − | 0.839043i | \(-0.683115\pi\) | ||||
−0.544065 | + | 0.839043i | \(0.683115\pi\) | |||||||
\(212\) | 32.5012 | 2.23219 | ||||||||
\(213\) | −0.804906 | −0.0551512 | ||||||||
\(214\) | 4.04066 | 0.276214 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −20.5236 | −1.39645 | ||||||||
\(217\) | −8.52249 | −0.578544 | ||||||||
\(218\) | 8.78851 | 0.595233 | ||||||||
\(219\) | −4.50938 | −0.304716 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.7929 | 0.793275 | ||||||||
\(222\) | −29.7823 | −1.99886 | ||||||||
\(223\) | −3.91385 | −0.262091 | −0.131046 | − | 0.991376i | \(-0.541833\pi\) | ||||
−0.131046 | + | 0.991376i | \(0.541833\pi\) | |||||||
\(224\) | −1.63520 | −0.109256 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.91048 | 0.393160 | ||||||||
\(227\) | −2.85417 | −0.189438 | −0.0947191 | − | 0.995504i | \(-0.530195\pi\) | ||||
−0.0947191 | + | 0.995504i | \(0.530195\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.0570553 | −0.00377032 | −0.00188516 | − | 0.999998i | \(-0.500600\pi\) | ||||
−0.00188516 | + | 0.999998i | \(0.500600\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −38.5826 | −2.53855 | ||||||||
\(232\) | 48.5852 | 3.18978 | ||||||||
\(233\) | 12.1105 | 0.793383 | 0.396692 | − | 0.917952i | \(-0.370158\pi\) | ||||
0.396692 | + | 0.917952i | \(0.370158\pi\) | |||||||
\(234\) | 5.52360 | 0.361089 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −16.2190 | −1.05577 | ||||||||
\(237\) | −11.0082 | −0.715059 | ||||||||
\(238\) | −42.2659 | −2.73969 | ||||||||
\(239\) | 12.4911 | 0.807985 | 0.403992 | − | 0.914762i | \(-0.367622\pi\) | ||||
0.403992 | + | 0.914762i | \(0.367622\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.9155 | −1.54053 | −0.770266 | − | 0.637723i | \(-0.779877\pi\) | ||||
−0.770266 | + | 0.637723i | \(0.779877\pi\) | |||||||
\(242\) | −28.4049 | −1.82593 | ||||||||
\(243\) | 8.09352 | 0.519199 | ||||||||
\(244\) | 22.8292 | 1.46149 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 36.6176 | 2.33466 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −9.79671 | −0.622092 | ||||||||
\(249\) | −4.50938 | −0.285771 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.1528 | 0.830196 | 0.415098 | − | 0.909777i | \(-0.363747\pi\) | ||||
0.415098 | + | 0.909777i | \(0.363747\pi\) | |||||||
\(252\) | −13.1528 | −0.828547 | ||||||||
\(253\) | 34.7967 | 2.18765 | ||||||||
\(254\) | 39.3121 | 2.46666 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −31.6357 | −1.97723 | ||||||||
\(257\) | 1.75043 | 0.109189 | 0.0545944 | − | 0.998509i | \(-0.482613\pi\) | ||||
0.0545944 | + | 0.998509i | \(0.482613\pi\) | |||||||
\(258\) | 15.8049 | 0.983970 | ||||||||
\(259\) | 26.0470 | 1.61848 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.10950 | −0.501965 | ||||||||
\(262\) | 25.1777 | 1.55548 | ||||||||
\(263\) | −26.4747 | −1.63250 | −0.816251 | − | 0.577697i | \(-0.803952\pi\) | ||||
−0.816251 | + | 0.577697i | \(0.803952\pi\) | |||||||
\(264\) | −44.3511 | −2.72962 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −23.7885 | −1.45583 | ||||||||
\(268\) | −1.55595 | −0.0950451 | ||||||||
\(269\) | −2.46119 | −0.150061 | −0.0750307 | − | 0.997181i | \(-0.523905\pi\) | ||||
−0.0750307 | + | 0.997181i | \(0.523905\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.2423 | −0.925904 | −0.462952 | − | 0.886383i | \(-0.653210\pi\) | ||||
−0.462952 | + | 0.886383i | \(0.653210\pi\) | |||||||
\(272\) | −15.6357 | −0.948055 | ||||||||
\(273\) | −22.9836 | −1.39103 | ||||||||
\(274\) | 25.9637 | 1.56852 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 56.4367 | 3.39709 | ||||||||
\(277\) | 19.6275 | 1.17930 | 0.589652 | − | 0.807657i | \(-0.299265\pi\) | ||||
0.589652 | + | 0.807657i | \(0.299265\pi\) | |||||||
\(278\) | 9.29248 | 0.557326 | ||||||||
\(279\) | 1.63520 | 0.0978966 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.09639 | −0.244370 | −0.122185 | − | 0.992507i | \(-0.538990\pi\) | ||||
−0.122185 | + | 0.992507i | \(0.538990\pi\) | |||||||
\(282\) | −38.7885 | −2.30982 | ||||||||
\(283\) | 25.2633 | 1.50174 | 0.750872 | − | 0.660447i | \(-0.229633\pi\) | ||||
0.750872 | + | 0.660447i | \(0.229633\pi\) | |||||||
\(284\) | 1.63520 | 0.0970310 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −32.9170 | −1.94642 | ||||||||
\(287\) | −32.0250 | −1.89038 | ||||||||
\(288\) | 0.313742 | 0.0184874 | ||||||||
\(289\) | 0.313764 | 0.0184567 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −35.9885 | −2.10968 | ||||||||
\(292\) | 9.16098 | 0.536106 | ||||||||
\(293\) | −15.9052 | −0.929195 | −0.464597 | − | 0.885522i | \(-0.653801\pi\) | ||||
−0.464597 | + | 0.885522i | \(0.653801\pi\) | |||||||
\(294\) | 49.0698 | 2.86181 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 29.9413 | 1.74030 | ||||||||
\(297\) | −20.4146 | −1.18458 | ||||||||
\(298\) | −31.2431 | −1.80986 | ||||||||
\(299\) | 20.7284 | 1.19875 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.8226 | −0.796723 | ||||||||
\(302\) | 55.6016 | 3.19951 | ||||||||
\(303\) | −0.472224 | −0.0271286 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 8.10950 | 0.463589 | ||||||||
\(307\) | −13.7378 | −0.784057 | −0.392028 | − | 0.919953i | \(-0.628227\pi\) | ||||
−0.392028 | + | 0.919953i | \(0.628227\pi\) | |||||||
\(308\) | 78.3819 | 4.46622 | ||||||||
\(309\) | −30.1170 | −1.71330 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.74950 | −0.212615 | −0.106307 | − | 0.994333i | \(-0.533903\pi\) | ||||
−0.106307 | + | 0.994333i | \(0.533903\pi\) | |||||||
\(312\) | −26.4199 | −1.49573 | ||||||||
\(313\) | 12.1105 | 0.684524 | 0.342262 | − | 0.939605i | \(-0.388807\pi\) | ||||
0.342262 | + | 0.939605i | \(0.388807\pi\) | |||||||
\(314\) | −38.1696 | −2.15403 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 22.3636 | 1.25805 | ||||||||
\(317\) | −26.4399 | −1.48502 | −0.742508 | − | 0.669838i | \(-0.766364\pi\) | ||||
−0.742508 | + | 0.669838i | \(0.766364\pi\) | |||||||
\(318\) | 39.0548 | 2.19008 | ||||||||
\(319\) | 48.3273 | 2.70581 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.22590 | 0.180052 | ||||||||
\(322\) | −74.2909 | −4.14007 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −42.5934 | −2.36630 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −15.8060 | −0.875413 | ||||||||
\(327\) | 7.01640 | 0.388008 | ||||||||
\(328\) | −36.8131 | −2.03266 | ||||||||
\(329\) | 33.9236 | 1.87027 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.6802 | 1.02676 | 0.513378 | − | 0.858163i | \(-0.328394\pi\) | ||||
0.513378 | + | 0.858163i | \(0.328394\pi\) | |||||||
\(332\) | 9.16098 | 0.502774 | ||||||||
\(333\) | −4.99759 | −0.273866 | ||||||||
\(334\) | −9.27311 | −0.507402 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 30.4731 | 1.66244 | ||||||||
\(337\) | 19.0131 | 1.03571 | 0.517855 | − | 0.855468i | \(-0.326731\pi\) | ||||
0.517855 | + | 0.855468i | \(0.326731\pi\) | |||||||
\(338\) | 12.1266 | 0.659602 | ||||||||
\(339\) | 4.71870 | 0.256284 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.74469 | −0.527705 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.7885 | −0.744509 | ||||||||
\(344\) | −15.8893 | −0.856692 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.7072 | −0.844424 | ||||||||
\(347\) | −2.85542 | −0.153287 | −0.0766434 | − | 0.997059i | \(-0.524420\pi\) | ||||
−0.0766434 | + | 0.997059i | \(0.524420\pi\) | |||||||
\(348\) | 78.3819 | 4.20171 | ||||||||
\(349\) | 29.7967 | 1.59498 | 0.797491 | − | 0.603331i | \(-0.206160\pi\) | ||||
0.797491 | + | 0.603331i | \(0.206160\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.1610 | −0.649105 | ||||||||
\(352\) | −1.86970 | −0.0996552 | ||||||||
\(353\) | −13.4911 | −0.718061 | −0.359031 | − | 0.933326i | \(-0.616893\pi\) | ||||
−0.359031 | + | 0.933326i | \(0.616893\pi\) | |||||||
\(354\) | −19.4894 | −1.03585 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 48.3273 | 2.56134 | ||||||||
\(357\) | −33.7435 | −1.78589 | ||||||||
\(358\) | −21.0082 | −1.11032 | ||||||||
\(359\) | 6.95934 | 0.367300 | 0.183650 | − | 0.982992i | \(-0.441209\pi\) | ||||
0.183650 | + | 0.982992i | \(0.441209\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 11.0082 | 0.578578 | ||||||||
\(363\) | −22.6773 | −1.19025 | ||||||||
\(364\) | 46.6921 | 2.44733 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 27.4324 | 1.43392 | ||||||||
\(367\) | 28.9577 | 1.51158 | 0.755790 | − | 0.654815i | \(-0.227253\pi\) | ||||
0.755790 | + | 0.654815i | \(0.227253\pi\) | |||||||
\(368\) | −27.4829 | −1.43265 | ||||||||
\(369\) | 6.14458 | 0.319874 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −34.1565 | −1.77331 | ||||||||
\(372\) | −15.8049 | −0.819446 | ||||||||
\(373\) | 25.8644 | 1.33921 | 0.669605 | − | 0.742718i | \(-0.266464\pi\) | ||||
0.669605 | + | 0.742718i | \(0.266464\pi\) | |||||||
\(374\) | −48.3273 | −2.49894 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 38.9956 | 2.01104 | ||||||||
\(377\) | 28.7885 | 1.48268 | ||||||||
\(378\) | 43.5852 | 2.24178 | ||||||||
\(379\) | 14.1708 | 0.727905 | 0.363952 | − | 0.931418i | \(-0.381427\pi\) | ||||
0.363952 | + | 0.931418i | \(0.381427\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 31.3852 | 1.60791 | ||||||||
\(382\) | −6.97057 | −0.356646 | ||||||||
\(383\) | 36.9706 | 1.88911 | 0.944555 | − | 0.328354i | \(-0.106494\pi\) | ||||
0.944555 | + | 0.328354i | \(0.106494\pi\) | |||||||
\(384\) | −38.7885 | −1.97942 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.2423 | 0.521319 | ||||||||
\(387\) | 2.65212 | 0.134815 | ||||||||
\(388\) | 73.1120 | 3.71170 | ||||||||
\(389\) | −28.2551 | −1.43259 | −0.716294 | − | 0.697799i | \(-0.754163\pi\) | ||||
−0.716294 | + | 0.697799i | \(0.754163\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.4324 | 1.53903 | ||||||||
\(392\) | −49.3317 | −2.49163 | ||||||||
\(393\) | 20.1009 | 1.01396 | ||||||||
\(394\) | 26.4600 | 1.33303 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −15.0390 | −0.755738 | ||||||||
\(397\) | 24.4242 | 1.22582 | 0.612909 | − | 0.790154i | \(-0.289999\pi\) | ||||
0.612909 | + | 0.790154i | \(0.289999\pi\) | |||||||
\(398\) | 33.6602 | 1.68723 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.9637 | 1.29656 | 0.648282 | − | 0.761400i | \(-0.275488\pi\) | ||||
0.648282 | + | 0.761400i | \(0.275488\pi\) | |||||||
\(402\) | −1.86970 | −0.0932520 | ||||||||
\(403\) | −5.80491 | −0.289163 | ||||||||
\(404\) | 0.959341 | 0.0477290 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −103.179 | −5.12067 | ||||||||
\(407\) | 29.7823 | 1.47625 | ||||||||
\(408\) | −38.7885 | −1.92032 | ||||||||
\(409\) | 4.01311 | 0.198435 | 0.0992177 | − | 0.995066i | \(-0.468366\pi\) | ||||
0.0992177 | + | 0.995066i | \(0.468366\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.7284 | 1.02246 | ||||||||
\(412\) | 61.1839 | 3.01431 | ||||||||
\(413\) | 17.0450 | 0.838729 | ||||||||
\(414\) | 14.2541 | 0.700550 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.11378 | −0.0546074 | ||||||||
\(417\) | 7.41875 | 0.363298 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.1187 | 0.689742 | 0.344871 | − | 0.938650i | \(-0.387923\pi\) | ||||
0.344871 | + | 0.938650i | \(0.387923\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.2672 | 0.890288 | 0.445144 | − | 0.895459i | \(-0.353152\pi\) | ||||
0.445144 | + | 0.895459i | \(0.353152\pi\) | |||||||
\(422\) | 38.5852 | 1.87830 | ||||||||
\(423\) | −6.50886 | −0.316472 | ||||||||
\(424\) | −39.2633 | −1.90679 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.96492 | 0.0952005 | ||||||||
\(427\) | −23.9918 | −1.16104 | ||||||||
\(428\) | −6.55354 | −0.316777 | ||||||||
\(429\) | −26.2797 | −1.26879 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.1765 | −0.923697 | −0.461849 | − | 0.886959i | \(-0.652814\pi\) | ||||
−0.461849 | + | 0.886959i | \(0.652814\pi\) | |||||||
\(432\) | 16.1238 | 0.775755 | ||||||||
\(433\) | 18.6201 | 0.894827 | 0.447413 | − | 0.894327i | \(-0.352345\pi\) | ||||
0.447413 | + | 0.894327i | \(0.352345\pi\) | |||||||
\(434\) | 20.8049 | 0.998667 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.2541 | −0.682646 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 11.0082 | 0.525992 | ||||||||
\(439\) | 14.2541 | 0.680310 | 0.340155 | − | 0.940369i | \(-0.389520\pi\) | ||||
0.340155 | + | 0.940369i | \(0.389520\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.23410 | 0.392100 | ||||||||
\(442\) | −28.7885 | −1.36933 | ||||||||
\(443\) | −27.2797 | −1.29610 | −0.648048 | − | 0.761600i | \(-0.724414\pi\) | ||||
−0.648048 | + | 0.761600i | \(0.724414\pi\) | |||||||
\(444\) | 48.3039 | 2.29240 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9.55441 | 0.452414 | ||||||||
\(447\) | −24.9432 | −1.17977 | ||||||||
\(448\) | 35.2633 | 1.66603 | ||||||||
\(449\) | 1.22220 | 0.0576791 | 0.0288396 | − | 0.999584i | \(-0.490819\pi\) | ||||
0.0288396 | + | 0.999584i | \(0.490819\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −36.6176 | −1.72426 | ||||||||
\(452\) | −9.58621 | −0.450897 | ||||||||
\(453\) | 44.3901 | 2.08563 | ||||||||
\(454\) | 6.96754 | 0.327003 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.1692 | −0.475694 | −0.237847 | − | 0.971303i | \(-0.576442\pi\) | ||||
−0.237847 | + | 0.971303i | \(0.576442\pi\) | |||||||
\(458\) | 0.139282 | 0.00650822 | ||||||||
\(459\) | −17.8542 | −0.833362 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.4911 | −0.721494 | −0.360747 | − | 0.932664i | \(-0.617478\pi\) | ||||
−0.360747 | + | 0.932664i | \(0.617478\pi\) | |||||||
\(462\) | 94.1868 | 4.38197 | ||||||||
\(463\) | 1.47474 | 0.0685372 | 0.0342686 | − | 0.999413i | \(-0.489090\pi\) | ||||
0.0342686 | + | 0.999413i | \(0.489090\pi\) | |||||||
\(464\) | −38.1696 | −1.77198 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −29.5638 | −1.36952 | ||||||||
\(467\) | −30.6357 | −1.41765 | −0.708826 | − | 0.705383i | \(-0.750775\pi\) | ||||
−0.708826 | + | 0.705383i | \(0.750775\pi\) | |||||||
\(468\) | −8.95872 | −0.414117 | ||||||||
\(469\) | 1.63520 | 0.0755063 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −30.4731 | −1.40412 | ||||||||
\(472\) | 19.5934 | 0.901860 | ||||||||
\(473\) | −15.8049 | −0.726710 | ||||||||
\(474\) | 26.8730 | 1.23432 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 68.5511 | 3.14203 | ||||||||
\(477\) | 6.55354 | 0.300066 | ||||||||
\(478\) | −30.4931 | −1.39472 | ||||||||
\(479\) | 21.7560 | 0.994059 | 0.497030 | − | 0.867734i | \(-0.334424\pi\) | ||||
0.497030 | + | 0.867734i | \(0.334424\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.7413 | 0.808934 | ||||||||
\(482\) | 58.3819 | 2.65922 | ||||||||
\(483\) | −59.3109 | −2.69874 | ||||||||
\(484\) | 46.0698 | 2.09408 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −19.7577 | −0.896228 | ||||||||
\(487\) | 6.99059 | 0.316774 | 0.158387 | − | 0.987377i | \(-0.449371\pi\) | ||||
0.158387 | + | 0.987377i | \(0.449371\pi\) | |||||||
\(488\) | −27.5789 | −1.24844 | ||||||||
\(489\) | −12.6189 | −0.570645 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −40.9741 | −1.84913 | −0.924567 | − | 0.381019i | \(-0.875573\pi\) | ||||
−0.924567 | + | 0.381019i | \(0.875573\pi\) | |||||||
\(492\) | −59.3901 | −2.67751 | ||||||||
\(493\) | 42.2659 | 1.90356 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.69650 | 0.345583 | ||||||||
\(497\) | −1.71847 | −0.0770840 | ||||||||
\(498\) | 11.0082 | 0.493289 | ||||||||
\(499\) | 22.9675 | 1.02817 | 0.514084 | − | 0.857740i | \(-0.328132\pi\) | ||||
0.514084 | + | 0.857740i | \(0.328132\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.40328 | −0.330754 | ||||||||
\(502\) | −32.1083 | −1.43306 | ||||||||
\(503\) | −17.5171 | −0.781047 | −0.390523 | − | 0.920593i | \(-0.627706\pi\) | ||||
−0.390523 | + | 0.920593i | \(0.627706\pi\) | |||||||
\(504\) | 15.8893 | 0.707764 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −84.9449 | −3.77626 | ||||||||
\(507\) | 9.68143 | 0.429967 | ||||||||
\(508\) | −63.7603 | −2.82890 | ||||||||
\(509\) | −11.7929 | −0.522710 | −0.261355 | − | 0.965243i | \(-0.584169\pi\) | ||||
−0.261355 | + | 0.965243i | \(0.584169\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.62753 | −0.425897 | ||||||||
\(512\) | 37.4236 | 1.65391 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.27311 | −0.188479 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −25.6340 | −1.12847 | ||||||||
\(517\) | 38.7885 | 1.70592 | ||||||||
\(518\) | −63.5852 | −2.79377 | ||||||||
\(519\) | −12.5400 | −0.550445 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.92238 | 0.215653 | 0.107827 | − | 0.994170i | \(-0.465611\pi\) | ||||
0.107827 | + | 0.994170i | \(0.465611\pi\) | |||||||
\(522\) | 19.7967 | 0.866478 | ||||||||
\(523\) | 29.6630 | 1.29707 | 0.648537 | − | 0.761183i | \(-0.275381\pi\) | ||||
0.648537 | + | 0.761183i | \(0.275381\pi\) | |||||||
\(524\) | −40.8357 | −1.78392 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 64.6295 | 2.81798 | ||||||||
\(527\) | −8.52249 | −0.371246 | ||||||||
\(528\) | 34.8432 | 1.51635 | ||||||||
\(529\) | 30.4911 | 1.32570 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.27039 | −0.141923 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21.8131 | −0.944830 | ||||||||
\(534\) | 58.0719 | 2.51302 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.87968 | 0.0811897 | ||||||||
\(537\) | −16.7721 | −0.723770 | ||||||||
\(538\) | 6.00820 | 0.259032 | ||||||||
\(539\) | −49.0698 | −2.11359 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.22590 | 0.138692 | 0.0693462 | − | 0.997593i | \(-0.477909\pi\) | ||||
0.0693462 | + | 0.997593i | \(0.477909\pi\) | |||||||
\(542\) | 37.2091 | 1.59827 | ||||||||
\(543\) | 8.78851 | 0.377151 | ||||||||
\(544\) | −1.63520 | −0.0701085 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 56.1070 | 2.40116 | ||||||||
\(547\) | −13.5593 | −0.579753 | −0.289877 | − | 0.957064i | \(-0.593614\pi\) | ||||
−0.289877 | + | 0.957064i | \(0.593614\pi\) | |||||||
\(548\) | −42.1105 | −1.79887 | ||||||||
\(549\) | 4.60327 | 0.196463 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −68.1786 | −2.90188 | ||||||||
\(553\) | −23.5025 | −0.999428 | ||||||||
\(554\) | −47.9143 | −2.03568 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15.0715 | −0.639173 | ||||||||
\(557\) | −22.1446 | −0.938296 | −0.469148 | − | 0.883120i | \(-0.655439\pi\) | ||||
−0.469148 | + | 0.883120i | \(0.655439\pi\) | |||||||
\(558\) | −3.99180 | −0.168986 | ||||||||
\(559\) | −9.41497 | −0.398211 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −38.5826 | −1.62896 | ||||||||
\(562\) | 10.0000 | 0.421825 | ||||||||
\(563\) | 37.4428 | 1.57803 | 0.789013 | − | 0.614376i | \(-0.210592\pi\) | ||||
0.789013 | + | 0.614376i | \(0.210592\pi\) | |||||||
\(564\) | 62.9110 | 2.64903 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −61.6721 | −2.59227 | ||||||||
\(567\) | 44.7626 | 1.87985 | ||||||||
\(568\) | −1.97540 | −0.0828861 | ||||||||
\(569\) | −39.8048 | −1.66870 | −0.834351 | − | 0.551233i | \(-0.814157\pi\) | ||||
−0.834351 | + | 0.551233i | \(0.814157\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.55441 | −0.190596 | −0.0952980 | − | 0.995449i | \(-0.530380\pi\) | ||||
−0.0952980 | + | 0.995449i | \(0.530380\pi\) | |||||||
\(572\) | 53.3881 | 2.23227 | ||||||||
\(573\) | −5.56503 | −0.232482 | ||||||||
\(574\) | 78.1786 | 3.26311 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6.76590 | −0.281913 | ||||||||
\(577\) | −16.1774 | −0.673473 | −0.336737 | − | 0.941599i | \(-0.609323\pi\) | ||||
−0.336737 | + | 0.941599i | \(0.609323\pi\) | |||||||
\(578\) | −0.765953 | −0.0318594 | ||||||||
\(579\) | 8.17704 | 0.339826 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.62753 | −0.399417 | ||||||||
\(582\) | 87.8543 | 3.64168 | ||||||||
\(583\) | −39.0548 | −1.61748 | ||||||||
\(584\) | −11.0670 | −0.457954 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 38.8275 | 1.60395 | ||||||||
\(587\) | −1.17738 | −0.0485956 | −0.0242978 | − | 0.999705i | \(-0.507735\pi\) | ||||
−0.0242978 | + | 0.999705i | \(0.507735\pi\) | |||||||
\(588\) | −79.5863 | −3.28208 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.1246 | 0.868949 | ||||||||
\(592\) | −23.5225 | −0.966769 | ||||||||
\(593\) | 45.1351 | 1.85348 | 0.926738 | − | 0.375709i | \(-0.122601\pi\) | ||||
0.926738 | + | 0.375709i | \(0.122601\pi\) | |||||||
\(594\) | 49.8357 | 2.04478 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 50.6731 | 2.07565 | ||||||||
\(597\) | 26.8730 | 1.09984 | ||||||||
\(598\) | −50.6016 | −2.06925 | ||||||||
\(599\) | −5.23531 | −0.213909 | −0.106954 | − | 0.994264i | \(-0.534110\pi\) | ||||
−0.106954 | + | 0.994264i | \(0.534110\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.3010 | 1.64391 | 0.821957 | − | 0.569550i | \(-0.192883\pi\) | ||||
0.821957 | + | 0.569550i | \(0.192883\pi\) | |||||||
\(602\) | 33.7435 | 1.37528 | ||||||||
\(603\) | −0.313742 | −0.0127766 | ||||||||
\(604\) | −90.1802 | −3.66938 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.15278 | 0.0468286 | ||||||||
\(607\) | 14.9768 | 0.607889 | 0.303944 | − | 0.952690i | \(-0.401696\pi\) | ||||
0.303944 | + | 0.952690i | \(0.401696\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −82.3737 | −3.33795 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.1063 | 0.934780 | ||||||||
\(612\) | −13.1528 | −0.531670 | ||||||||
\(613\) | 11.4747 | 0.463461 | 0.231730 | − | 0.972780i | \(-0.425561\pi\) | ||||
0.231730 | + | 0.972780i | \(0.425561\pi\) | |||||||
\(614\) | 33.5364 | 1.35342 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −94.6896 | −3.81515 | ||||||||
\(617\) | 6.64392 | 0.267474 | 0.133737 | − | 0.991017i | \(-0.457302\pi\) | ||||
0.133737 | + | 0.991017i | \(0.457302\pi\) | |||||||
\(618\) | 73.5209 | 2.95745 | ||||||||
\(619\) | −3.84556 | −0.154566 | −0.0772831 | − | 0.997009i | \(-0.524625\pi\) | ||||
−0.0772831 | + | 0.997009i | \(0.524625\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −31.3823 | −1.25933 | ||||||||
\(622\) | 9.15320 | 0.367010 | ||||||||
\(623\) | −50.7884 | −2.03480 | ||||||||
\(624\) | 20.7560 | 0.830907 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −29.5638 | −1.18161 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 61.9072 | 2.47037 | ||||||||
\(629\) | 26.0470 | 1.03856 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.5544 | −1.37559 | −0.687795 | − | 0.725905i | \(-0.741421\pi\) | ||||
−0.687795 | + | 0.725905i | \(0.741421\pi\) | |||||||
\(632\) | −27.0164 | −1.07465 | ||||||||
\(633\) | 30.8049 | 1.22439 | ||||||||
\(634\) | 64.5446 | 2.56339 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −63.3429 | −2.51171 | ||||||||
\(637\) | −29.2309 | −1.15817 | ||||||||
\(638\) | −117.975 | −4.67069 | ||||||||
\(639\) | 0.329720 | 0.0130435 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.23899 | −0.0489372 | −0.0244686 | − | 0.999701i | \(-0.507789\pi\) | ||||
−0.0244686 | + | 0.999701i | \(0.507789\pi\) | |||||||
\(642\) | −7.87499 | −0.310801 | ||||||||
\(643\) | 31.2715 | 1.23323 | 0.616613 | − | 0.787267i | \(-0.288504\pi\) | ||||
0.616613 | + | 0.787267i | \(0.288504\pi\) | |||||||
\(644\) | 120.492 | 4.74807 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −43.9577 | −1.72816 | −0.864078 | − | 0.503359i | \(-0.832097\pi\) | ||||
−0.864078 | + | 0.503359i | \(0.832097\pi\) | |||||||
\(648\) | 51.4551 | 2.02135 | ||||||||
\(649\) | 19.4894 | 0.765025 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.6098 | 0.650990 | ||||||||
\(652\) | 25.6357 | 1.00397 | ||||||||
\(653\) | 10.2633 | 0.401632 | 0.200816 | − | 0.979629i | \(-0.435641\pi\) | ||||
0.200816 | + | 0.979629i | \(0.435641\pi\) | |||||||
\(654\) | −17.1283 | −0.669768 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 28.9211 | 1.12918 | ||||||||
\(657\) | 1.84722 | 0.0720668 | ||||||||
\(658\) | −82.8134 | −3.22840 | ||||||||
\(659\) | 29.1508 | 1.13555 | 0.567777 | − | 0.823182i | \(-0.307804\pi\) | ||||
0.567777 | + | 0.823182i | \(0.307804\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.83542 | −0.343658 | −0.171829 | − | 0.985127i | \(-0.554968\pi\) | ||||
−0.171829 | + | 0.985127i | \(0.554968\pi\) | |||||||
\(662\) | −45.6016 | −1.77236 | ||||||||
\(663\) | −22.9836 | −0.892609 | ||||||||
\(664\) | −11.0670 | −0.429481 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 12.2000 | 0.472740 | ||||||||
\(667\) | 74.2909 | 2.87656 | ||||||||
\(668\) | 15.0400 | 0.581917 | ||||||||
\(669\) | 7.62786 | 0.294910 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −27.4324 | −1.05902 | ||||||||
\(672\) | 3.18690 | 0.122937 | ||||||||
\(673\) | −35.8317 | −1.38121 | −0.690605 | − | 0.723232i | \(-0.742656\pi\) | ||||
−0.690605 | + | 0.723232i | \(0.742656\pi\) | |||||||
\(674\) | −46.4144 | −1.78782 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −19.6682 | −0.756469 | ||||||||
\(677\) | 23.0743 | 0.886819 | 0.443409 | − | 0.896319i | \(-0.353769\pi\) | ||||
0.443409 | + | 0.896319i | \(0.353769\pi\) | |||||||
\(678\) | −11.5192 | −0.442391 | ||||||||
\(679\) | −76.8354 | −2.94867 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.56261 | 0.213160 | ||||||||
\(682\) | 23.7885 | 0.910909 | ||||||||
\(683\) | −10.1737 | −0.389285 | −0.194642 | − | 0.980874i | \(-0.562355\pi\) | ||||
−0.194642 | + | 0.980874i | \(0.562355\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 33.6602 | 1.28515 | ||||||||
\(687\) | 0.111197 | 0.00424244 | ||||||||
\(688\) | 12.4829 | 0.475908 | ||||||||
\(689\) | −23.2649 | −0.886322 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.5298 | 1.38966 | 0.694830 | − | 0.719174i | \(-0.255480\pi\) | ||||
0.694830 | + | 0.719174i | \(0.255480\pi\) | |||||||
\(692\) | 25.4755 | 0.968432 | ||||||||
\(693\) | 15.8049 | 0.600379 | ||||||||
\(694\) | 6.97057 | 0.264599 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −94.6896 | −3.58920 | ||||||||
\(697\) | −32.0250 | −1.21303 | ||||||||
\(698\) | −72.7390 | −2.75321 | ||||||||
\(699\) | −23.6026 | −0.892731 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.78230 | 0.105086 | 0.0525430 | − | 0.998619i | \(-0.483267\pi\) | ||||
0.0525430 | + | 0.998619i | \(0.483267\pi\) | |||||||
\(702\) | 29.6871 | 1.12047 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 40.3203 | 1.51963 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 32.9343 | 1.23950 | ||||||||
\(707\) | −1.00820 | −0.0379172 | ||||||||
\(708\) | 31.6098 | 1.18797 | ||||||||
\(709\) | −22.7803 | −0.855533 | −0.427766 | − | 0.903889i | \(-0.640699\pi\) | ||||
−0.427766 | + | 0.903889i | \(0.640699\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.50938 | 0.169115 | ||||||||
\(712\) | −58.3819 | −2.18796 | ||||||||
\(713\) | −14.9800 | −0.561005 | ||||||||
\(714\) | 82.3737 | 3.08276 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 34.0732 | 1.27337 | ||||||||
\(717\) | −24.3445 | −0.909161 | ||||||||
\(718\) | −16.9890 | −0.634023 | ||||||||
\(719\) | 14.9429 | 0.557278 | 0.278639 | − | 0.960396i | \(-0.410117\pi\) | ||||
0.278639 | + | 0.960396i | \(0.410117\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −64.2998 | −2.39465 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 46.6098 | 1.73344 | ||||||||
\(724\) | −17.8542 | −0.663546 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 55.3593 | 2.05458 | ||||||||
\(727\) | −17.4488 | −0.647141 | −0.323571 | − | 0.946204i | \(-0.604883\pi\) | ||||
−0.323571 | + | 0.946204i | \(0.604883\pi\) | |||||||
\(728\) | −56.4065 | −2.09056 | ||||||||
\(729\) | 16.4993 | 0.611087 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.8226 | −0.511248 | ||||||||
\(732\) | −44.4926 | −1.64450 | ||||||||
\(733\) | −32.2387 | −1.19076 | −0.595381 | − | 0.803443i | \(-0.702999\pi\) | ||||
−0.595381 | + | 0.803443i | \(0.702999\pi\) | |||||||
\(734\) | −70.6908 | −2.60925 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.87419 | −0.105944 | ||||||||
\(737\) | 1.86970 | 0.0688712 | ||||||||
\(738\) | −15.0000 | −0.552158 | ||||||||
\(739\) | −29.7967 | −1.09609 | −0.548045 | − | 0.836449i | \(-0.684628\pi\) | ||||
−0.548045 | + | 0.836449i | \(0.684628\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 83.3819 | 3.06105 | ||||||||
\(743\) | 4.41013 | 0.161792 | 0.0808960 | − | 0.996723i | \(-0.474222\pi\) | ||||
0.0808960 | + | 0.996723i | \(0.474222\pi\) | |||||||
\(744\) | 19.0932 | 0.699990 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −63.1396 | −2.31171 | ||||||||
\(747\) | 1.84722 | 0.0675861 | ||||||||
\(748\) | 78.3819 | 2.86593 | ||||||||
\(749\) | 6.88730 | 0.251656 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.6953 | −1.15658 | −0.578288 | − | 0.815832i | \(-0.696279\pi\) | ||||
−0.578288 | + | 0.815832i | \(0.696279\pi\) | |||||||
\(752\) | −30.6357 | −1.11717 | ||||||||
\(753\) | −25.6340 | −0.934153 | ||||||||
\(754\) | −70.2778 | −2.55937 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −70.6908 | −2.57100 | ||||||||
\(757\) | −7.65212 | −0.278121 | −0.139061 | − | 0.990284i | \(-0.544408\pi\) | ||||
−0.139061 | + | 0.990284i | \(0.544408\pi\) | |||||||
\(758\) | −34.5934 | −1.25649 | ||||||||
\(759\) | −67.8166 | −2.46159 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.5544 | −0.890097 | −0.445048 | − | 0.895507i | \(-0.646813\pi\) | ||||
−0.445048 | + | 0.895507i | \(0.646813\pi\) | |||||||
\(762\) | −76.6169 | −2.77554 | ||||||||
\(763\) | 14.9800 | 0.542312 | ||||||||
\(764\) | 11.3056 | 0.409021 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −90.2517 | −3.26093 | ||||||||
\(767\) | 11.6098 | 0.419206 | ||||||||
\(768\) | 61.6561 | 2.22482 | ||||||||
\(769\) | 28.7705 | 1.03749 | 0.518745 | − | 0.854929i | \(-0.326400\pi\) | ||||
0.518745 | + | 0.854929i | \(0.326400\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.41148 | −0.122861 | ||||||||
\(772\) | −16.6120 | −0.597878 | ||||||||
\(773\) | 32.4812 | 1.16827 | 0.584134 | − | 0.811657i | \(-0.301434\pi\) | ||||
0.584134 | + | 0.811657i | \(0.301434\pi\) | |||||||
\(774\) | −6.47430 | −0.232714 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −88.3232 | −3.17062 | ||||||||
\(777\) | −50.7639 | −1.82115 | ||||||||
\(778\) | 68.9756 | 2.47289 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.96492 | −0.0703102 | ||||||||
\(782\) | −74.2909 | −2.65664 | ||||||||
\(783\) | −43.5852 | −1.55761 | ||||||||
\(784\) | 38.7560 | 1.38414 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −49.0698 | −1.75026 | ||||||||
\(787\) | −17.2427 | −0.614635 | −0.307318 | − | 0.951607i | \(-0.599431\pi\) | ||||
−0.307318 | + | 0.951607i | \(0.599431\pi\) | |||||||
\(788\) | −42.9154 | −1.52880 | ||||||||
\(789\) | 51.5976 | 1.83692 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.0744 | 0.358205 | ||||||||
\(792\) | 18.1679 | 0.645569 | ||||||||
\(793\) | −16.3415 | −0.580303 | ||||||||
\(794\) | −59.6239 | −2.11597 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −54.5934 | −1.93501 | ||||||||
\(797\) | −43.6034 | −1.54451 | −0.772255 | − | 0.635312i | \(-0.780871\pi\) | ||||
−0.772255 | + | 0.635312i | \(0.780871\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.9236 | 1.20013 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.74469 | 0.344312 | ||||||||
\(802\) | −63.3819 | −2.23809 | ||||||||
\(803\) | −11.0082 | −0.388471 | ||||||||
\(804\) | 3.03246 | 0.106947 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 14.1708 | 0.499145 | ||||||||
\(807\) | 4.79671 | 0.168852 | ||||||||
\(808\) | −1.15894 | −0.0407712 | ||||||||
\(809\) | 32.3737 | 1.13820 | 0.569100 | − | 0.822268i | \(-0.307292\pi\) | ||||
0.569100 | + | 0.822268i | \(0.307292\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.2659 | 1.48416 | 0.742079 | − | 0.670312i | \(-0.233840\pi\) | ||||
0.742079 | + | 0.670312i | \(0.233840\pi\) | |||||||
\(812\) | 167.345 | 5.87267 | ||||||||
\(813\) | 29.7063 | 1.04185 | ||||||||
\(814\) | −72.7039 | −2.54827 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 30.4731 | 1.06677 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −9.79671 | −0.342534 | ||||||||
\(819\) | 9.41497 | 0.328986 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33.5688 | −1.17156 | −0.585780 | − | 0.810470i | \(-0.699212\pi\) | ||||
−0.585780 | + | 0.810470i | \(0.699212\pi\) | |||||||
\(822\) | −50.6016 | −1.76493 | ||||||||
\(823\) | −36.1023 | −1.25845 | −0.629223 | − | 0.777225i | \(-0.716627\pi\) | ||||
−0.629223 | + | 0.777225i | \(0.716627\pi\) | |||||||
\(824\) | −73.9134 | −2.57489 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −41.6098 | −1.44779 | ||||||||
\(827\) | −43.2905 | −1.50536 | −0.752678 | − | 0.658389i | \(-0.771238\pi\) | ||||
−0.752678 | + | 0.658389i | \(0.771238\pi\) | |||||||
\(828\) | −23.1187 | −0.803429 | ||||||||
\(829\) | 10.4706 | 0.363660 | 0.181830 | − | 0.983330i | \(-0.441798\pi\) | ||||
0.181830 | + | 0.983330i | \(0.441798\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −38.2528 | −1.32698 | ||||||||
\(832\) | 24.0188 | 0.832701 | ||||||||
\(833\) | −42.9154 | −1.48693 | ||||||||
\(834\) | −18.1105 | −0.627114 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.78851 | 0.303775 | ||||||||
\(838\) | −34.4662 | −1.19061 | ||||||||
\(839\) | 30.5563 | 1.05492 | 0.527461 | − | 0.849579i | \(-0.323144\pi\) | ||||
0.527461 | + | 0.849579i | \(0.323144\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 74.1786 | 2.55788 | ||||||||
\(842\) | −44.5934 | −1.53679 | ||||||||
\(843\) | 7.98360 | 0.274970 | ||||||||
\(844\) | −62.5813 | −2.15414 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 15.8893 | 0.546284 | ||||||||
\(847\) | −48.4160 | −1.66359 | ||||||||
\(848\) | 30.8460 | 1.05926 | ||||||||
\(849\) | −49.2365 | −1.68979 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 45.7828 | 1.56941 | ||||||||
\(852\) | −3.18690 | −0.109181 | ||||||||
\(853\) | 24.1269 | 0.826088 | 0.413044 | − | 0.910711i | \(-0.364466\pi\) | ||||
0.413044 | + | 0.910711i | \(0.364466\pi\) | |||||||
\(854\) | 58.5682 | 2.00416 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.91703 | 0.270599 | ||||||||
\(857\) | −35.6932 | −1.21926 | −0.609628 | − | 0.792687i | \(-0.708681\pi\) | ||||
−0.609628 | + | 0.792687i | \(0.708681\pi\) | |||||||
\(858\) | 64.1533 | 2.19016 | ||||||||
\(859\) | −39.9236 | −1.36217 | −0.681087 | − | 0.732202i | \(-0.738493\pi\) | ||||
−0.681087 | + | 0.732202i | \(0.738493\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 62.4147 | 2.12709 | ||||||||
\(862\) | 46.8131 | 1.59446 | ||||||||
\(863\) | −4.90640 | −0.167016 | −0.0835079 | − | 0.996507i | \(-0.526612\pi\) | ||||
−0.0835079 | + | 0.996507i | \(0.526612\pi\) | |||||||
\(864\) | 1.68624 | 0.0573669 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −45.4550 | −1.54463 | ||||||||
\(867\) | −0.611506 | −0.0207678 | ||||||||
\(868\) | −33.7435 | −1.14533 | ||||||||
\(869\) | −26.8730 | −0.911602 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.11378 | 0.0377389 | ||||||||
\(872\) | 17.2197 | 0.583132 | ||||||||
\(873\) | 14.7423 | 0.498950 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −17.8542 | −0.603237 | ||||||||
\(877\) | 24.6103 | 0.831030 | 0.415515 | − | 0.909586i | \(-0.363601\pi\) | ||||
0.415515 | + | 0.909586i | \(0.363601\pi\) | |||||||
\(878\) | −34.7967 | −1.17433 | ||||||||
\(879\) | 30.9983 | 1.04555 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.0554 | 1.07997 | 0.539987 | − | 0.841673i | \(-0.318429\pi\) | ||||
0.539987 | + | 0.841673i | \(0.318429\pi\) | |||||||
\(882\) | −20.1009 | −0.676832 | ||||||||
\(883\) | −47.1105 | −1.58539 | −0.792697 | − | 0.609616i | \(-0.791324\pi\) | ||||
−0.792697 | + | 0.609616i | \(0.791324\pi\) | |||||||
\(884\) | 46.6921 | 1.57042 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 66.5944 | 2.23728 | ||||||||
\(887\) | −12.1426 | −0.407709 | −0.203855 | − | 0.979001i | \(-0.565347\pi\) | ||||
−0.203855 | + | 0.979001i | \(0.565347\pi\) | |||||||
\(888\) | −58.3537 | −1.95822 | ||||||||
\(889\) | 67.0074 | 2.24736 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 51.1819 | 1.71466 | ||||||||
\(892\) | −15.4963 | −0.518854 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 60.8908 | 2.03649 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −82.8134 | −2.76660 | ||||||||
\(897\) | −40.3983 | −1.34886 | ||||||||
\(898\) | −2.98360 | −0.0995641 | ||||||||
\(899\) | −20.8049 | −0.693882 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −34.1565 | −1.13792 | ||||||||
\(902\) | 89.3901 | 2.97637 | ||||||||
\(903\) | 26.9394 | 0.896488 | ||||||||
\(904\) | 11.5807 | 0.385167 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −108.364 | −3.60016 | ||||||||
\(907\) | 18.7002 | 0.620930 | 0.310465 | − | 0.950585i | \(-0.399515\pi\) | ||||
0.310465 | + | 0.950585i | \(0.399515\pi\) | |||||||
\(908\) | −11.3006 | −0.375025 | ||||||||
\(909\) | 0.193441 | 0.00641604 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.04819 | 0.0678597 | 0.0339298 | − | 0.999424i | \(-0.489198\pi\) | ||||
0.0339298 | + | 0.999424i | \(0.489198\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.0082 | −0.364318 | ||||||||
\(914\) | 24.8248 | 0.821130 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.225901 | −0.00746399 | ||||||||
\(917\) | 42.9154 | 1.41719 | ||||||||
\(918\) | 43.5852 | 1.43853 | ||||||||
\(919\) | −27.4911 | −0.906849 | −0.453425 | − | 0.891295i | \(-0.649798\pi\) | ||||
−0.453425 | + | 0.891295i | \(0.649798\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 26.7741 | 0.882237 | ||||||||
\(922\) | 37.8166 | 1.24542 | ||||||||
\(923\) | −1.17050 | −0.0385275 | ||||||||
\(924\) | −152.762 | −5.02549 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.60011 | −0.118307 | ||||||||
\(927\) | 12.3371 | 0.405203 | ||||||||
\(928\) | −3.99180 | −0.131037 | ||||||||
\(929\) | 25.6016 | 0.839962 | 0.419981 | − | 0.907533i | \(-0.362037\pi\) | ||||
0.419981 | + | 0.907533i | \(0.362037\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 47.9495 | 1.57064 | ||||||||
\(933\) | 7.30755 | 0.239238 | ||||||||
\(934\) | 74.7872 | 2.44711 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 10.8226 | 0.353748 | ||||||||
\(937\) | −43.7544 | −1.42939 | −0.714697 | − | 0.699434i | \(-0.753435\pi\) | ||||
−0.714697 | + | 0.699434i | \(0.753435\pi\) | |||||||
\(938\) | −3.99180 | −0.130337 | ||||||||
\(939\) | −23.6026 | −0.770240 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 55.5275 | 1.81014 | 0.905072 | − | 0.425258i | \(-0.139817\pi\) | ||||
0.905072 | + | 0.425258i | \(0.139817\pi\) | |||||||
\(942\) | 74.3901 | 2.42376 | ||||||||
\(943\) | −56.2904 | −1.83307 | ||||||||
\(944\) | −15.3930 | −0.500999 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 38.5826 | 1.25443 | ||||||||
\(947\) | −31.5347 | −1.02474 | −0.512370 | − | 0.858765i | \(-0.671232\pi\) | ||||
−0.512370 | + | 0.858765i | \(0.671232\pi\) | |||||||
\(948\) | −43.5852 | −1.41558 | ||||||||
\(949\) | −6.55758 | −0.212868 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 51.5298 | 1.67097 | ||||||||
\(952\) | −82.8134 | −2.68400 | ||||||||
\(953\) | 12.1899 | 0.394870 | 0.197435 | − | 0.980316i | \(-0.436739\pi\) | ||||
0.197435 | + | 0.980316i | \(0.436739\pi\) | |||||||
\(954\) | −15.9983 | −0.517966 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 49.4567 | 1.59954 | ||||||||
\(957\) | −94.1868 | −3.04463 | ||||||||
\(958\) | −53.1103 | −1.71592 | ||||||||
\(959\) | 44.2551 | 1.42907 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.8049 | −0.864674 | ||||||||
\(962\) | −43.3097 | −1.39636 | ||||||||
\(963\) | −1.32145 | −0.0425833 | ||||||||
\(964\) | −94.6896 | −3.04975 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 144.788 | 4.65849 | ||||||||
\(967\) | −26.8472 | −0.863348 | −0.431674 | − | 0.902030i | \(-0.642077\pi\) | ||||
−0.431674 | + | 0.902030i | \(0.642077\pi\) | |||||||
\(968\) | −55.6548 | −1.78881 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.1152 | 0.420885 | 0.210443 | − | 0.977606i | \(-0.432509\pi\) | ||||
0.210443 | + | 0.977606i | \(0.432509\pi\) | |||||||
\(972\) | 32.0450 | 1.02784 | ||||||||
\(973\) | 15.8390 | 0.507776 | ||||||||
\(974\) | −17.0653 | −0.546806 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 21.6665 | 0.693529 | ||||||||
\(977\) | 37.0106 | 1.18407 | 0.592037 | − | 0.805910i | \(-0.298324\pi\) | ||||
0.592037 | + | 0.805910i | \(0.298324\pi\) | |||||||
\(978\) | 30.8049 | 0.985032 | ||||||||
\(979\) | −58.0719 | −1.85599 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.87419 | −0.0917657 | ||||||||
\(982\) | 100.025 | 3.19192 | ||||||||
\(983\) | 26.3166 | 0.839370 | 0.419685 | − | 0.907670i | \(-0.362140\pi\) | ||||
0.419685 | + | 0.907670i | \(0.362140\pi\) | |||||||
\(984\) | 71.7465 | 2.28719 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −103.179 | −3.28588 | ||||||||
\(987\) | −66.1150 | −2.10446 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −24.2960 | −0.772569 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.1157 | −0.988423 | −0.494212 | − | 0.869342i | \(-0.664543\pi\) | ||||
−0.494212 | + | 0.869342i | \(0.664543\pi\) | |||||||
\(992\) | 0.804906 | 0.0255558 | ||||||||
\(993\) | −36.4065 | −1.15533 | ||||||||
\(994\) | 4.19509 | 0.133060 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −17.8542 | −0.565732 | ||||||||
\(997\) | −17.6521 | −0.559048 | −0.279524 | − | 0.960139i | \(-0.590177\pi\) | ||||
−0.279524 | + | 0.960139i | \(0.590177\pi\) | |||||||
\(998\) | −56.0678 | −1.77480 | ||||||||
\(999\) | −26.8600 | −0.849812 |
(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 | 9025.2.a.bv.1.1 | ✓ | 6 | |
5.4 | even | 2 | 9025.2.a.bw.1.6 | yes | 6 | ||
19.18 | odd | 2 | inner | 9025.2.a.bv.1.6 | yes | 6 | |
95.94 | odd | 2 | 9025.2.a.bw.1.1 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9025.2.a.bv.1.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
9025.2.a.bv.1.6 | yes | 6 | 19.18 | odd | 2 | inner | |
9025.2.a.bw.1.1 | yes | 6 | 95.94 | odd | 2 | ||
9025.2.a.bw.1.6 | yes | 6 | 5.4 | even | 2 |