Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [580,2,Mod(1,580)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(580, 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("580.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 580 = 2^{2} \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 580.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: | \(4.63132331723\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.564.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.51414\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 580.1 |
$q$-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 | 0 | ||||||||
\(3\) | 3.32088 | 1.91731 | 0.958657 | − | 0.284565i | \(-0.0918491\pi\) | ||||
0.958657 | + | 0.284565i | \(0.0918491\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.32088 | 0.499247 | 0.249624 | − | 0.968343i | \(-0.419693\pi\) | ||||
0.249624 | + | 0.968343i | \(0.419693\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.02827 | 2.67609 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.32088 | 1.60431 | 0.802154 | − | 0.597118i | \(-0.203688\pi\) | ||||
0.802154 | + | 0.597118i | \(0.203688\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.02827 | −1.39459 | −0.697296 | − | 0.716783i | \(-0.745614\pi\) | ||||
−0.697296 | + | 0.716783i | \(0.745614\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.32088 | −0.857449 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.34916 | −1.53990 | −0.769949 | − | 0.638106i | \(-0.779718\pi\) | ||||
−0.769949 | + | 0.638106i | \(0.779718\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.34916 | −0.997765 | −0.498883 | − | 0.866670i | \(-0.666256\pi\) | ||||
−0.498883 | + | 0.866670i | \(0.666256\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.38650 | 0.957214 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.70739 | −0.356015 | −0.178008 | − | 0.984029i | \(-0.556965\pi\) | ||||
−0.178008 | + | 0.984029i | \(0.556965\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 16.6983 | 3.21359 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.34916 | 1.49955 | 0.749777 | − | 0.661691i | \(-0.230161\pi\) | ||||
0.749777 | + | 0.661691i | \(0.230161\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 17.6700 | 3.07596 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.32088 | −0.223270 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.93438 | −1.14000 | −0.570002 | − | 0.821643i | \(-0.693058\pi\) | ||||
−0.570002 | + | 0.821643i | \(0.693058\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −16.6983 | −2.67387 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.02827 | −0.160589 | −0.0802947 | − | 0.996771i | \(-0.525586\pi\) | ||||
−0.0802947 | + | 0.996771i | \(0.525586\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.7357 | 1.63717 | 0.818587 | − | 0.574383i | \(-0.194758\pi\) | ||||
0.818587 | + | 0.574383i | \(0.194758\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.02827 | −1.19678 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.679116 | −0.0990592 | −0.0495296 | − | 0.998773i | \(-0.515772\pi\) | ||||
−0.0495296 | + | 0.998773i | \(0.515772\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.25526 | −0.750752 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −21.0848 | −2.95247 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.38650 | 0.327812 | 0.163906 | − | 0.986476i | \(-0.447591\pi\) | ||||
0.163906 | + | 0.986476i | \(0.447591\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.32088 | −0.717468 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −14.4431 | −1.91303 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.4431 | 1.35957 | 0.679785 | − | 0.733412i | \(-0.262073\pi\) | ||||
0.679785 | + | 0.733412i | \(0.262073\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.38650 | −0.817708 | −0.408854 | − | 0.912600i | \(-0.634072\pi\) | ||||
−0.408854 | + | 0.912600i | \(0.634072\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 10.6044 | 1.33603 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.02827 | 0.623681 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.70739 | −0.697269 | −0.348634 | − | 0.937259i | \(-0.613354\pi\) | ||||
−0.348634 | + | 0.937259i | \(0.613354\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.67004 | −0.682593 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.61350 | −0.428843 | −0.214421 | − | 0.976741i | \(-0.568787\pi\) | ||||
−0.214421 | + | 0.976741i | \(0.568787\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.73566 | −0.788350 | −0.394175 | − | 0.919035i | \(-0.628970\pi\) | ||||
−0.394175 | + | 0.919035i | \(0.628970\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.32088 | 0.383463 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.02827 | 0.800946 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.3774 | −1.28006 | −0.640031 | − | 0.768349i | \(-0.721078\pi\) | ||||
−0.640031 | + | 0.768349i | \(0.721078\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 31.3684 | 3.48537 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.96265 | −0.434958 | −0.217479 | − | 0.976065i | \(-0.569783\pi\) | ||||
−0.217479 | + | 0.976065i | \(0.569783\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.34916 | 0.688663 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.32088 | −0.356036 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.58522 | 0.274033 | 0.137016 | − | 0.990569i | \(-0.456249\pi\) | ||||
0.137016 | + | 0.990569i | \(0.456249\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.64177 | −0.696247 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 27.7266 | 2.87511 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.34916 | 0.446214 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.3209 | −1.55560 | −0.777800 | − | 0.628512i | \(-0.783664\pi\) | ||||
−0.777800 | + | 0.628512i | \(0.783664\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 42.7175 | 4.29327 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.8688 | 1.18099 | 0.590493 | − | 0.807043i | \(-0.298933\pi\) | ||||
0.590493 | + | 0.807043i | \(0.298933\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.65084 | −0.359728 | −0.179864 | − | 0.983691i | \(-0.557566\pi\) | ||||
−0.179864 | + | 0.983691i | \(0.557566\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.38650 | −0.428079 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.32088 | −0.514389 | −0.257195 | − | 0.966360i | \(-0.582798\pi\) | ||||
−0.257195 | + | 0.966360i | \(0.582798\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.3118 | −1.37082 | −0.685411 | − | 0.728156i | \(-0.740378\pi\) | ||||
−0.685411 | + | 0.728156i | \(0.740378\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −23.0283 | −2.18575 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.03735 | 0.191657 | 0.0958287 | − | 0.995398i | \(-0.469450\pi\) | ||||
0.0958287 | + | 0.995398i | \(0.469450\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.70739 | 0.159215 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −40.3684 | −3.73206 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.38650 | −0.768790 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.3118 | 1.57380 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.41478 | −0.307900 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.26434 | −0.112192 | −0.0560959 | − | 0.998425i | \(-0.517865\pi\) | ||||
−0.0560959 | + | 0.998425i | \(0.517865\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 35.6519 | 3.13897 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.70739 | −0.149175 | −0.0745877 | − | 0.997214i | \(-0.523764\pi\) | ||||
−0.0745877 | + | 0.997214i | \(0.523764\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.74474 | −0.498132 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −16.6983 | −1.43716 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.7639 | 1.85942 | 0.929709 | − | 0.368294i | \(-0.120058\pi\) | ||||
0.929709 | + | 0.368294i | \(0.120058\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.6983 | −1.41633 | −0.708166 | − | 0.706046i | \(-0.750477\pi\) | ||||
−0.708166 | + | 0.706046i | \(0.750477\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.25526 | −0.189928 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −26.7549 | −2.23735 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.00000 | 0.0830455 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −17.4521 | −1.43943 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.0000 | 1.47462 | 0.737309 | − | 0.675556i | \(-0.236096\pi\) | ||||
0.737309 | + | 0.675556i | \(0.236096\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.44305 | 0.524328 | 0.262164 | − | 0.965023i | \(-0.415564\pi\) | ||||
0.262164 | + | 0.965023i | \(0.415564\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −50.9728 | −4.12091 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.34916 | −0.670621 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.7357 | 0.856799 | 0.428400 | − | 0.903589i | \(-0.359078\pi\) | ||||
0.428400 | + | 0.903589i | \(0.359078\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.92531 | 0.628518 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.25526 | −0.177740 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.90611 | 0.305950 | 0.152975 | − | 0.988230i | \(-0.451115\pi\) | ||||
0.152975 | + | 0.988230i | \(0.451115\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −17.6700 | −1.37561 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.51960 | −0.427120 | −0.213560 | − | 0.976930i | \(-0.568506\pi\) | ||||
−0.213560 | + | 0.976930i | \(0.568506\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.2835 | 0.944888 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −34.9162 | −2.67011 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.80128 | 0.441063 | 0.220532 | − | 0.975380i | \(-0.429221\pi\) | ||||
0.220532 | + | 0.975380i | \(0.429221\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.32088 | 0.0998495 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 34.6802 | 2.60672 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.0565 | 1.05064 | 0.525318 | − | 0.850906i | \(-0.323946\pi\) | ||||
0.525318 | + | 0.850906i | \(0.323946\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.08482 | −0.526611 | −0.263305 | − | 0.964713i | \(-0.584813\pi\) | ||||
−0.263305 | + | 0.964713i | \(0.584813\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −21.2088 | −1.56780 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.93438 | 0.509826 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −33.7831 | −2.47047 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 22.0565 | 1.60438 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.547875 | −0.0396428 | −0.0198214 | − | 0.999804i | \(-0.506310\pi\) | ||||
−0.0198214 | + | 0.999804i | \(0.506310\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.40571 | 0.317130 | 0.158565 | − | 0.987349i | \(-0.449313\pi\) | ||||
0.158565 | + | 0.987349i | \(0.449313\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 16.6983 | 1.19579 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.64177 | −0.330712 | −0.165356 | − | 0.986234i | \(-0.552877\pi\) | ||||
−0.165356 | + | 0.986234i | \(0.552877\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.4431 | 1.30739 | 0.653697 | − | 0.756757i | \(-0.273217\pi\) | ||||
0.653697 | + | 0.756757i | \(0.273217\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −18.9536 | −1.33688 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.32088 | −0.0927079 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.02827 | 0.0718178 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −13.7074 | −0.952729 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −23.1414 | −1.60072 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.54787 | −0.313089 | −0.156544 | − | 0.987671i | \(-0.550035\pi\) | ||||
−0.156544 | + | 0.987671i | \(0.550035\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.0000 | −0.822226 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.7357 | −0.732166 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.0283 | 0.748648 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −22.3684 | −1.51151 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 31.9253 | 2.14753 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.12217 | 0.0751459 | 0.0375730 | − | 0.999294i | \(-0.488037\pi\) | ||||
0.0375730 | + | 0.999294i | \(0.488037\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.02827 | 0.535218 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.63270 | 0.639345 | 0.319672 | − | 0.947528i | \(-0.396427\pi\) | ||||
0.319672 | + | 0.947528i | \(0.396427\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.00000 | 0.132164 | 0.0660819 | − | 0.997814i | \(-0.478950\pi\) | ||||
0.0660819 | + | 0.997814i | \(0.478950\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 23.3401 | 1.53566 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.05655 | −0.527802 | −0.263901 | − | 0.964550i | \(-0.585009\pi\) | ||||
−0.263901 | + | 0.964550i | \(0.585009\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.679116 | 0.0443006 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −37.7831 | −2.45428 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.6135 | 1.00995 | 0.504977 | − | 0.863133i | \(-0.331501\pi\) | ||||
0.504977 | + | 0.863133i | \(0.331501\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.5105 | 1.19237 | 0.596184 | − | 0.802848i | \(-0.296683\pi\) | ||||
0.596184 | + | 0.802848i | \(0.296683\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 54.0757 | 3.46896 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.25526 | 0.335747 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.8688 | 1.39148 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13.1595 | −0.833950 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.67912 | −0.421582 | −0.210791 | − | 0.977531i | \(-0.567604\pi\) | ||||
−0.210791 | + | 0.977531i | \(0.567604\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.08482 | −0.571158 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 21.0848 | 1.32038 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −26.4249 | −1.64834 | −0.824170 | − | 0.566342i | \(-0.808358\pi\) | ||||
−0.824170 | + | 0.566342i | \(0.808358\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.15951 | −0.569145 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.02827 | −0.496938 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 27.4340 | 1.69165 | 0.845826 | − | 0.533459i | \(-0.179108\pi\) | ||||
0.845826 | + | 0.533459i | \(0.179108\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.38650 | −0.146602 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.58522 | 0.525407 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.9717 | −0.668958 | −0.334479 | − | 0.942403i | \(-0.608560\pi\) | ||||
−0.334479 | + | 0.942403i | \(0.608560\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.1504 | 1.22405 | 0.612026 | − | 0.790838i | \(-0.290355\pi\) | ||||
0.612026 | + | 0.790838i | \(0.290355\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −22.0565 | −1.33492 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.32088 | 0.320861 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.15951 | 0.189837 | 0.0949184 | − | 0.995485i | \(-0.469741\pi\) | ||||
0.0949184 | + | 0.995485i | \(0.469741\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 67.0293 | 4.01294 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.3118 | −0.615151 | −0.307576 | − | 0.951524i | \(-0.599518\pi\) | ||||
−0.307576 | + | 0.951524i | \(0.599518\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.423851 | 0.0251953 | 0.0125977 | − | 0.999921i | \(-0.495990\pi\) | ||||
0.0125977 | + | 0.999921i | \(0.495990\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.4431 | 0.855533 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.35823 | −0.0801738 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 23.3118 | 1.37128 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −50.8789 | −2.98257 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.2462 | 1.12437 | 0.562187 | − | 0.827010i | \(-0.309960\pi\) | ||||
0.562187 | + | 0.827010i | \(0.309960\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.4431 | −0.608018 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 88.8498 | 5.15559 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.58522 | 0.496496 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.1806 | 0.817355 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 39.4148 | 2.26432 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.38650 | 0.365690 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.7357 | 1.29759 | 0.648796 | − | 0.760962i | \(-0.275273\pi\) | ||||
0.648796 | + | 0.760962i | \(0.275273\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.1240 | −0.689712 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.8031 | 0.839409 | 0.419704 | − | 0.907661i | \(-0.362134\pi\) | ||||
0.419704 | + | 0.907661i | \(0.362134\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.9717 | −0.846252 | −0.423126 | − | 0.906071i | \(-0.639067\pi\) | ||||
−0.423126 | + | 0.906071i | \(0.639067\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −10.6044 | −0.597492 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.1222 | 1.29867 | 0.649335 | − | 0.760502i | \(-0.275047\pi\) | ||||
0.649335 | + | 0.760502i | \(0.275047\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.32088 | −0.297912 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.6700 | −0.986246 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 27.6135 | 1.53646 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.02827 | −0.278918 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −47.5279 | −2.62830 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.897033 | −0.0494550 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.82048 | −0.539783 | −0.269891 | − | 0.962891i | \(-0.586988\pi\) | ||||
−0.269891 | + | 0.962891i | \(0.586988\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −55.6711 | −3.05076 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.70739 | 0.311828 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.09389 | −0.440903 | −0.220451 | − | 0.975398i | \(-0.570753\pi\) | ||||
−0.220451 | + | 0.975398i | \(0.570753\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.76579 | 0.367467 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 44.4249 | 2.40574 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.1878 | −0.874058 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.67004 | 0.305265 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.37743 | −0.396041 | −0.198021 | − | 0.980198i | \(-0.563451\pi\) | ||||
−0.198021 | + | 0.980198i | \(0.563451\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.82956 | 0.472635 | 0.236318 | − | 0.971676i | \(-0.424059\pi\) | ||||
0.236318 | + | 0.971676i | \(0.424059\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −83.9637 | −4.48165 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.7266 | 0.730593 | 0.365296 | − | 0.930891i | \(-0.380968\pi\) | ||||
0.365296 | + | 0.930891i | \(0.380968\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.61350 | 0.191784 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −27.8506 | −1.47401 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.70739 | −0.0901126 | −0.0450563 | − | 0.998984i | \(-0.514347\pi\) | ||||
−0.0450563 | + | 0.998984i | \(0.514347\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.0848216 | −0.00446429 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 57.4905 | 3.01747 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.73566 | 0.352561 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.9627 | −1.35524 | −0.677620 | − | 0.735412i | \(-0.736988\pi\) | ||||
−0.677620 | + | 0.735412i | \(0.736988\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.25526 | −0.429752 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.15230 | 0.163659 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.92531 | 0.513913 | 0.256956 | − | 0.966423i | \(-0.417280\pi\) | ||||
0.256956 | + | 0.966423i | \(0.417280\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.32088 | −0.171490 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.02827 | 0.258969 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.2070 | 1.75710 | 0.878548 | − | 0.477655i | \(-0.158513\pi\) | ||||
0.878548 | + | 0.477655i | \(0.158513\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.19872 | −0.215107 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.4340 | −1.09523 | −0.547613 | − | 0.836732i | \(-0.684463\pi\) | ||||
−0.547613 | + | 0.836732i | \(0.684463\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.02827 | −0.358194 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 86.1888 | 4.38123 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −36.3684 | −1.84395 | −0.921975 | − | 0.387251i | \(-0.873425\pi\) | ||||
−0.921975 | + | 0.387251i | \(0.873425\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.8405 | 0.548227 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.67004 | −0.286016 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.3774 | 0.572461 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.4713 | −1.37875 | −0.689373 | − | 0.724406i | \(-0.742114\pi\) | ||||
−0.689373 | + | 0.724406i | \(0.742114\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −19.0776 | −0.955075 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.3118 | 1.11420 | 0.557099 | − | 0.830446i | \(-0.311914\pi\) | ||||
0.557099 | + | 0.830446i | \(0.311914\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −41.9819 | −2.09127 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −31.3684 | −1.55871 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −36.8970 | −1.82892 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.95358 | 0.244939 | 0.122469 | − | 0.992472i | \(-0.460919\pi\) | ||||
0.122469 | + | 0.992472i | \(0.460919\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 72.2755 | 3.56509 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.7941 | 0.678762 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.96265 | 0.194519 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −55.4532 | −2.71555 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.198716 | −0.00970793 | −0.00485397 | − | 0.999988i | \(-0.501545\pi\) | ||||
−0.00485397 | + | 0.999988i | \(0.501545\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.4996 | 1.29151 | 0.645756 | − | 0.763544i | \(-0.276542\pi\) | ||||
0.645756 | + | 0.763544i | \(0.276542\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.45213 | −0.265091 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.34916 | −0.307979 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.43584 | −0.408239 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −88.8498 | −4.28971 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.2835 | −1.02519 | −0.512596 | − | 0.858630i | \(-0.671316\pi\) | ||||
−0.512596 | + | 0.858630i | \(0.671316\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.8031 | −1.19196 | −0.595981 | − | 0.802998i | \(-0.703237\pi\) | ||||
−0.595981 | + | 0.802998i | \(0.703237\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.32088 | 0.159224 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.42571 | 0.355220 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.3118 | −1.54216 | −0.771079 | − | 0.636739i | \(-0.780283\pi\) | ||||
−0.771079 | + | 0.636739i | \(0.780283\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −42.1907 | −2.00908 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.3774 | 1.20572 | 0.602859 | − | 0.797848i | \(-0.294028\pi\) | ||||
0.602859 | + | 0.797848i | \(0.294028\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.58522 | −0.122551 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 59.7759 | 2.82730 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.7266 | 0.647798 | 0.323899 | − | 0.946092i | \(-0.395006\pi\) | ||||
0.323899 | + | 0.946092i | \(0.395006\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.47133 | −0.257635 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 21.3966 | 1.00530 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.64177 | 0.311371 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.0101 | −0.702144 | −0.351072 | − | 0.936348i | \(-0.614183\pi\) | ||||
−0.351072 | + | 0.936348i | \(0.614183\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −106.020 | −4.94860 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.7549 | 1.52555 | 0.762773 | − | 0.646666i | \(-0.223837\pi\) | ||||
0.762773 | + | 0.646666i | \(0.223837\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.5369 | −1.14033 | −0.570164 | − | 0.821531i | \(-0.693120\pi\) | ||||
−0.570164 | + | 0.821531i | \(0.693120\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −27.7266 | −1.28579 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.60442 | −0.398165 | −0.199083 | − | 0.979983i | \(-0.563796\pi\) | ||||
−0.199083 | + | 0.979983i | \(0.563796\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.53880 | −0.348110 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 35.6519 | 1.64275 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 57.1232 | 2.62653 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.34916 | −0.199553 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 19.1595 | 0.877254 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.26434 | 0.149151 | 0.0745757 | − | 0.997215i | \(-0.476240\pi\) | ||||
0.0745757 | + | 0.997215i | \(0.476240\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.8680 | 1.58984 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.48947 | −0.340783 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.3209 | 0.695686 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.2070 | 1.55007 | 0.775033 | − | 0.631920i | \(-0.217733\pi\) | ||||
0.775033 | + | 0.631920i | \(0.217733\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.9717 | 0.586602 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.93438 | −0.403203 | −0.201601 | − | 0.979468i | \(-0.564615\pi\) | ||||
−0.201601 | + | 0.979468i | \(0.564615\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.34916 | 0.285952 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −42.7175 | −1.92001 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.77301 | −0.214099 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.6236 | 1.28137 | 0.640685 | − | 0.767804i | \(-0.278651\pi\) | ||||
0.640685 | + | 0.767804i | \(0.278651\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.3300 | −0.818922 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.0192012 | −0.000856140 0 | −0.000428070 | − | 1.00000i | \(-0.500136\pi\) | ||||
−0.000428070 | 1.00000i | \(0.500136\pi\) | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.8688 | −0.528153 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 40.7922 | 1.81165 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.25526 | −0.365908 | −0.182954 | − | 0.983121i | \(-0.558566\pi\) | ||||
−0.182954 | + | 0.983121i | \(0.558566\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.89703 | −0.393582 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −72.6236 | −3.20641 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.65084 | 0.160875 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.61350 | −0.158921 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.2654 | 0.845657 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.2553 | −0.887399 | −0.443700 | − | 0.896176i | \(-0.646334\pi\) | ||||
−0.443700 | + | 0.896176i | \(0.646334\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.82048 | 0.0796042 | 0.0398021 | − | 0.999208i | \(-0.487327\pi\) | ||||
0.0398021 | + | 0.999208i | \(0.487327\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.38650 | 0.191443 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −53.0101 | −2.30916 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.0848 | −0.873253 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 83.8397 | 3.63833 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.17044 | 0.223957 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.32088 | 0.230042 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 46.6802 | 2.01440 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −27.9627 | −1.20444 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.03920 | 0.0446788 | 0.0223394 | − | 0.999750i | \(-0.492889\pi\) | ||||
0.0223394 | + | 0.999750i | \(0.492889\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −23.5279 | −1.00968 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.3118 | 0.613051 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.7567 | 1.61436 | 0.807180 | − | 0.590305i | \(-0.200992\pi\) | ||||
0.807180 | + | 0.590305i | \(0.200992\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −51.2726 | −2.18826 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.34916 | 0.185280 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.0283 | −0.639067 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 23.0283 | 0.977496 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 45.8506 | 1.94275 | 0.971376 | − | 0.237545i | \(-0.0763429\pi\) | ||||
0.971376 | + | 0.237545i | \(0.0763429\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −53.9819 | −2.28319 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −112.190 | −4.73666 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 33.3027 | 1.40354 | 0.701772 | − | 0.712402i | \(-0.252393\pi\) | ||||
0.701772 | + | 0.712402i | \(0.252393\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.03735 | −0.0857118 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 41.4340 | 1.74006 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.6700 | −0.992300 | −0.496150 | − | 0.868237i | \(-0.665253\pi\) | ||||
−0.496150 | + | 0.868237i | \(0.665253\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.5671 | 0.609613 | 0.304807 | − | 0.952414i | \(-0.401408\pi\) | ||||
0.304807 | + | 0.952414i | \(0.401408\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.81943 | −0.0760077 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.70739 | −0.0712031 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.7639 | −0.573000 | −0.286500 | − | 0.958080i | \(-0.592492\pi\) | ||||
−0.286500 | + | 0.958080i | \(0.592492\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.6308 | 0.608037 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.23421 | −0.217152 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.6983 | 0.525911 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 40.3684 | 1.66903 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.04748 | −0.0432339 | −0.0216170 | − | 0.999766i | \(-0.506881\pi\) | ||||
−0.0216170 | + | 0.999766i | \(0.506881\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −36.3118 | −1.49620 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.4148 | −0.634079 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.3865 | 0.590783 | 0.295391 | − | 0.955376i | \(-0.404550\pi\) | ||||
0.295391 | + | 0.955376i | \(0.404550\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.38650 | 0.343813 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 61.2472 | 2.50668 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.98080 | −0.244369 | −0.122184 | − | 0.992507i | \(-0.538990\pi\) | ||||
−0.122184 | + | 0.992507i | \(0.538990\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.08482 | −0.288996 | −0.144498 | − | 0.989505i | \(-0.546157\pi\) | ||||
−0.144498 | + | 0.989505i | \(0.546157\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −45.8205 | −1.86595 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −17.3118 | −0.703825 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.7175 | 1.32796 | 0.663982 | − | 0.747749i | \(-0.268865\pi\) | ||||
0.663982 | + | 0.747749i | \(0.268865\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.38650 | −0.177750 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.41478 | 0.138147 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.22699 | 0.372675 | 0.186337 | − | 0.982486i | \(-0.440338\pi\) | ||||
0.186337 | + | 0.982486i | \(0.440338\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.41478 | 0.137697 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.281683 | 0.0113401 | 0.00567006 | − | 0.999984i | \(-0.498195\pi\) | ||||
0.00567006 | + | 0.999984i | \(0.498195\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.2462 | 0.853957 | 0.426978 | − | 0.904262i | \(-0.359578\pi\) | ||||
0.426978 | + | 0.904262i | \(0.359578\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −28.5105 | −1.14409 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.41478 | 0.136810 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −76.8498 | −3.06909 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 44.0275 | 1.75549 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.8688 | 1.50753 | 0.753766 | − | 0.657143i | \(-0.228235\pi\) | ||||
0.753766 | + | 0.657143i | \(0.228235\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −15.1030 | −0.600289 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.26434 | 0.0501737 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.4249 | 1.04699 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −29.0101 | −1.14762 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −36.7658 | −1.45216 | −0.726081 | − | 0.687609i | \(-0.758660\pi\) | ||||
−0.726081 | + | 0.687609i | \(0.758660\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.9728 | −0.984830 | −0.492415 | − | 0.870360i | \(-0.663886\pi\) | ||||
−0.492415 | + | 0.870360i | \(0.663886\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −35.6519 | −1.40379 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.56522 | −0.140163 | −0.0700816 | − | 0.997541i | \(-0.522326\pi\) | ||||
−0.0700816 | + | 0.997541i | \(0.522326\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 55.5663 | 2.18117 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 36.6236 | 1.43539 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.5652 | −0.843912 | −0.421956 | − | 0.906616i | \(-0.638656\pi\) | ||||
−0.421956 | + | 0.906616i | \(0.638656\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.70739 | 0.0667132 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −54.0757 | −2.10970 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −40.4623 | −1.57619 | −0.788093 | − | 0.615556i | \(-0.788931\pi\) | ||||
−0.788093 | + | 0.615556i | \(0.788931\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.1987 | 1.01901 | 0.509506 | − | 0.860467i | \(-0.329828\pi\) | ||||
0.509506 | + | 0.860467i | \(0.329828\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 106.020 | 4.11749 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.74474 | 0.222771 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.70739 | 0.0661104 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.72659 | 0.144078 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −33.9819 | −1.31185 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.35823 | 0.129450 | 0.0647251 | − | 0.997903i | \(-0.479383\pi\) | ||||
0.0647251 | + | 0.997903i | \(0.479383\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 16.6983 | 0.642719 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.6965 | −0.603264 | −0.301632 | − | 0.953424i | \(-0.597531\pi\) | ||||
−0.301632 | + | 0.953424i | \(0.597531\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.2371 | −0.776629 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 31.9891 | 1.22582 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −40.1998 | −1.53820 | −0.769101 | − | 0.639128i | \(-0.779296\pi\) | ||||
−0.769101 | + | 0.639128i | \(0.779296\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.7639 | −0.831557 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.64177 | 0.253399 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.0000 | −0.457164 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.7084 | 0.977995 | 0.488998 | − | 0.872285i | \(-0.337363\pi\) | ||||
0.488998 | + | 0.872285i | \(0.337363\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 56.4249 | 2.14340 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.6983 | 0.633403 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.52867 | 0.247291 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −26.7549 | −1.01196 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.51775 | −0.321711 | −0.160855 | − | 0.986978i | \(-0.551425\pi\) | ||||
−0.160855 | + | 0.986978i | \(0.551425\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.1587 | 1.13746 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.25526 | 0.0849382 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.6773 | 0.589604 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.0848 | 1.31764 | 0.658819 | − | 0.752301i | \(-0.271056\pi\) | ||||
0.658819 | + | 0.752301i | \(0.271056\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −91.3411 | −3.42556 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14.2553 | −0.533864 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 26.7549 | 1.00058 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 51.8506 | 1.93640 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31.3292 | 1.16838 | 0.584190 | − | 0.811617i | \(-0.301412\pi\) | ||||
0.584190 | + | 0.811617i | \(0.301412\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.82234 | −0.179593 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 61.4713 | 2.28614 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.00000 | −0.0371391 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.9627 | −0.517846 | −0.258923 | − | 0.965898i | \(-0.583368\pi\) | ||||
−0.258923 | + | 0.965898i | \(0.583368\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 85.4742 | 3.16571 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −68.1624 | −2.52108 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.5761 | −1.09242 | −0.546210 | − | 0.837648i | \(-0.683930\pi\) | ||||
−0.546210 | + | 0.837648i | \(0.683930\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 17.4521 | 0.643731 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −30.3684 | −1.11863 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.66819 | −0.245293 | −0.122647 | − | 0.992450i | \(-0.539138\pi\) | ||||
−0.122647 | + | 0.992450i | \(0.539138\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 72.6236 | 2.66790 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.7002 | −1.23634 | −0.618170 | − | 0.786045i | \(-0.712126\pi\) | ||||
−0.618170 | + | 0.786045i | \(0.712126\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.0000 | −0.659469 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −31.8133 | −1.16399 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.02827 | −0.256808 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −48.3129 | −1.76296 | −0.881481 | − | 0.472220i | \(-0.843453\pi\) | ||||
−0.881481 | + | 0.472220i | \(0.843453\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.1806 | −0.808305 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.44305 | −0.234487 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.3985 | 1.54100 | 0.770500 | − | 0.637440i | \(-0.220007\pi\) | ||||
0.770500 | + | 0.637440i | \(0.220007\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −30.1696 | −1.09509 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −44.7933 | −1.62375 | −0.811877 | − | 0.583828i | \(-0.801554\pi\) | ||||
−0.811877 | + | 0.583828i | \(0.801554\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.9043 | −0.684380 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 50.9728 | 1.84292 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −52.5105 | −1.89605 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −52.2080 | −1.88267 | −0.941335 | − | 0.337473i | \(-0.890428\pi\) | ||||
−0.941335 | + | 0.337473i | \(0.890428\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −87.7541 | −3.16039 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.2179 | −0.871058 | −0.435529 | − | 0.900175i | \(-0.643439\pi\) | ||||
−0.435529 | + | 0.900175i | \(0.643439\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.34916 | 0.299911 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −30.4177 | −1.09123 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.47213 | 0.160231 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.2270 | −0.687996 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −16.6983 | −0.596749 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.7357 | −0.383172 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.43398 | −0.0511159 | −0.0255579 | − | 0.999673i | \(-0.508136\pi\) | ||||
−0.0255579 | + | 0.999673i | \(0.508136\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 91.1051 | 3.24343 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.69110 | 0.0956845 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.1131 | 1.14037 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.92531 | −0.281082 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.4732 | −0.512666 | −0.256333 | − | 0.966588i | \(-0.582514\pi\) | ||||
−0.256333 | + | 0.966588i | \(0.582514\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.31181 | 0.152541 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 20.7549 | 0.733337 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −35.8397 | −1.26476 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.25526 | 0.0794876 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −36.4358 | −1.28260 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 49.2654 | 1.73208 | 0.866039 | − | 0.499976i | \(-0.166658\pi\) | ||||
0.866039 | + | 0.499976i | \(0.166658\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.69832 | −0.164980 | −0.0824901 | − | 0.996592i | \(-0.526287\pi\) | ||||
−0.0824901 | + | 0.996592i | \(0.526287\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 66.9173 | 2.34689 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.90611 | −0.136825 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −46.6911 | −1.63351 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −53.3219 | −1.86322 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34.7730 | 1.21359 | 0.606793 | − | 0.794860i | \(-0.292456\pi\) | ||||
0.606793 | + | 0.794860i | \(0.292456\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −44.1323 | −1.53836 | −0.769178 | − | 0.639035i | \(-0.779334\pi\) | ||||
−0.769178 | + | 0.639035i | \(0.779334\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 17.6700 | 0.615192 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.6610 | 0.787999 | 0.394000 | − | 0.919111i | \(-0.371091\pi\) | ||||
0.394000 | + | 0.919111i | \(0.371091\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −37.9144 | −1.31682 | −0.658410 | − | 0.752659i | \(-0.728771\pi\) | ||||
−0.658410 | + | 0.752659i | \(0.728771\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.4924 | 0.363977 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 33.3665 | 1.15608 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.51960 | 0.191014 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 139.417 | 4.81895 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.7175 | 1.06049 | 0.530243 | − | 0.847846i | \(-0.322101\pi\) | ||||
0.530243 | + | 0.847846i | \(0.322101\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −34.2443 | −1.17944 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.2835 | −0.422567 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.8669 | 0.785716 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.40756 | 0.0483074 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.8397 | 0.405859 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.25341 | 0.0429159 | 0.0214579 | − | 0.999770i | \(-0.493169\pi\) | ||||
0.0214579 | + | 0.999770i | \(0.493169\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 34.9162 | 1.19411 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.85783 | −0.268418 | −0.134209 | − | 0.990953i | \(-0.542849\pi\) | ||||
−0.134209 | + | 0.990953i | \(0.542849\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.4913 | −0.494438 | −0.247219 | − | 0.968960i | \(-0.579517\pi\) | ||||
−0.247219 | + | 0.968960i | \(0.579517\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.51053 | −0.153718 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.69646 | −0.330071 | −0.165036 | − | 0.986288i | \(-0.552774\pi\) | ||||
−0.165036 | + | 0.986288i | \(0.552774\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.80128 | −0.197250 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 77.4158 | 2.62918 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −60.5380 | −2.05361 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.6983 | 0.972405 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −123.000 | −4.16293 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.32088 | −0.0446540 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.27341 | 0.211838 | 0.105919 | − | 0.994375i | \(-0.466222\pi\) | ||||
0.105919 | + | 0.994375i | \(0.466222\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 63.9144 | 2.15578 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.5953 | 0.660184 | 0.330092 | − | 0.943949i | \(-0.392920\pi\) | ||||
0.330092 | + | 0.943949i | \(0.392920\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.24619 | −0.176548 | −0.0882742 | − | 0.996096i | \(-0.528135\pi\) | ||||
−0.0882742 | + | 0.996096i | \(0.528135\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −34.6802 | −1.16576 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32.6044 | −1.09475 | −0.547375 | − | 0.836888i | \(-0.684373\pi\) | ||||
−0.547375 | + | 0.836888i | \(0.684373\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.67004 | −0.0560114 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 166.907 | 5.59161 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.95358 | 0.0988378 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.0565 | −0.469859 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 28.5105 | 0.951939 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.34916 | −0.278460 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.1523 | −0.504796 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 47.0920 | 1.56712 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.08482 | 0.235507 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.96265 | −0.0651688 | −0.0325844 | − | 0.999469i | \(-0.510374\pi\) | ||||
−0.0325844 | + | 0.999469i | \(0.510374\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 95.2856 | 3.16043 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50.7066 | 1.67998 | 0.839992 | − | 0.542599i | \(-0.182560\pi\) | ||||
0.839992 | + | 0.542599i | \(0.182560\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.0848 | −0.697806 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 21.2088 | 0.701143 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.25526 | −0.0744754 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 56.2371 | 1.85509 | 0.927546 | − | 0.373710i | \(-0.121914\pi\) | ||||
0.927546 | + | 0.373710i | \(0.121914\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 75.5025 | 2.48789 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.1696 | 0.598061 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.93438 | −0.228001 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −29.3100 | −0.962665 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.34009 | −0.175203 | −0.0876013 | − | 0.996156i | \(-0.527920\pi\) | ||||
−0.0876013 | + | 0.996156i | \(0.527920\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.8560 | 0.749074 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 49.1595 | 1.60941 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 33.7831 | 1.10483 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.01013 | −0.0983366 | −0.0491683 | − | 0.998791i | \(-0.515657\pi\) | ||||
−0.0491683 | + | 0.998791i | \(0.515657\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −49.7194 | −1.62253 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.829557 | −0.0270428 | −0.0135214 | − | 0.999909i | \(-0.504304\pi\) | ||||
−0.0135214 | + | 0.999909i | \(0.504304\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.75566 | 0.0571723 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −22.0565 | −0.717500 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.3027 | 0.692246 | 0.346123 | − | 0.938189i | \(-0.387498\pi\) | ||||
0.346123 | + | 0.938189i | \(0.387498\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 33.8688 | 1.09943 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 76.7860 | 2.48996 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −40.0203 | −1.29638 | −0.648192 | − | 0.761477i | \(-0.724474\pi\) | ||||
−0.648192 | + | 0.761477i | \(0.724474\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.547875 | 0.0177288 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −17.6700 | −0.571191 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 28.7476 | 0.928310 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 38.7084 | 1.24866 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −42.7175 | −1.37655 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.40571 | −0.141825 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.0365 | −0.998068 | −0.499034 | − | 0.866582i | \(-0.666312\pi\) | ||||
−0.499034 | + | 0.866582i | \(0.666312\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 91.7012 | 2.94587 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.66819 | −0.0856262 | −0.0428131 | − | 0.999083i | \(-0.513632\pi\) | ||||
−0.0428131 | + | 0.999083i | \(0.513632\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.0565 | −0.707100 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −16.6983 | −0.534774 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 45.6519 | 1.46053 | 0.730267 | − | 0.683162i | \(-0.239396\pi\) | ||||
0.730267 | + | 0.683162i | \(0.239396\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.7557 | 0.439633 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −114.899 | −3.66845 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.4521 | −0.556636 | −0.278318 | − | 0.960489i | \(-0.589777\pi\) | ||||
−0.278318 | + | 0.960489i | \(0.589777\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.64177 | 0.147899 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.97894 | −0.0948208 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.3300 | −0.582859 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.49960 | −0.142935 | −0.0714673 | − | 0.997443i | \(-0.522768\pi\) | ||||
−0.0714673 | + | 0.997443i | \(0.522768\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −32.6127 | −1.03493 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18.4431 | −0.584684 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.1896 | −0.671083 | −0.335541 | − | 0.942025i | \(-0.608919\pi\) | ||||
−0.335541 | + | 0.942025i | \(0.608919\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −115.792 | −3.66351 |
(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 | 580.2.a.c.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 5220.2.a.x.1.3 | 3 | |||
4.3 | odd | 2 | 2320.2.a.m.1.1 | 3 | |||
5.2 | odd | 4 | 2900.2.c.f.349.1 | 6 | |||
5.3 | odd | 4 | 2900.2.c.f.349.6 | 6 | |||
5.4 | even | 2 | 2900.2.a.g.1.1 | 3 | |||
8.3 | odd | 2 | 9280.2.a.bw.1.3 | 3 | |||
8.5 | even | 2 | 9280.2.a.bk.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
580.2.a.c.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
2320.2.a.m.1.1 | 3 | 4.3 | odd | 2 | |||
2900.2.a.g.1.1 | 3 | 5.4 | even | 2 | |||
2900.2.c.f.349.1 | 6 | 5.2 | odd | 4 | |||
2900.2.c.f.349.6 | 6 | 5.3 | odd | 4 | |||
5220.2.a.x.1.3 | 3 | 3.2 | odd | 2 | |||
9280.2.a.bk.1.1 | 3 | 8.5 | even | 2 | |||
9280.2.a.bw.1.3 | 3 | 8.3 | odd | 2 |