Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.32739 | −1.64571 | −0.822857 | − | 0.568248i | \(-0.807621\pi\) | ||||
−0.822857 | + | 0.568248i | \(0.807621\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.41675 | 1.70838 | ||||||||
\(5\) | 3.32274 | 1.48597 | 0.742987 | − | 0.669306i | \(-0.233408\pi\) | ||||
0.742987 | + | 0.669306i | \(0.233408\pi\) | |||||||
\(6\) | 2.32739 | 0.950154 | ||||||||
\(7\) | 1.34387 | 0.507934 | 0.253967 | − | 0.967213i | \(-0.418265\pi\) | ||||
0.253967 | + | 0.967213i | \(0.418265\pi\) | |||||||
\(8\) | −3.29733 | −1.16578 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −7.73332 | −2.44549 | ||||||||
\(11\) | 6.61253 | 1.99375 | 0.996876 | − | 0.0789778i | \(-0.0251656\pi\) | ||||
0.996876 | + | 0.0789778i | \(0.0251656\pi\) | |||||||
\(12\) | −3.41675 | −0.986331 | ||||||||
\(13\) | −5.69091 | −1.57837 | −0.789187 | − | 0.614153i | \(-0.789498\pi\) | ||||
−0.789187 | + | 0.614153i | \(0.789498\pi\) | |||||||
\(14\) | −3.12770 | −0.835914 | ||||||||
\(15\) | −3.32274 | −0.857928 | ||||||||
\(16\) | 0.840683 | 0.210171 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −2.32739 | −0.548571 | ||||||||
\(19\) | 3.29674 | 0.756324 | 0.378162 | − | 0.925739i | \(-0.376556\pi\) | ||||
0.378162 | + | 0.925739i | \(0.376556\pi\) | |||||||
\(20\) | 11.3530 | 2.53860 | ||||||||
\(21\) | −1.34387 | −0.293256 | ||||||||
\(22\) | −15.3899 | −3.28115 | ||||||||
\(23\) | 9.15661 | 1.90929 | 0.954643 | − | 0.297753i | \(-0.0962372\pi\) | ||||
0.954643 | + | 0.297753i | \(0.0962372\pi\) | |||||||
\(24\) | 3.29733 | 0.673065 | ||||||||
\(25\) | 6.04060 | 1.20812 | ||||||||
\(26\) | 13.2450 | 2.59755 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.59166 | 0.867742 | ||||||||
\(29\) | 2.40186 | 0.446014 | 0.223007 | − | 0.974817i | \(-0.428413\pi\) | ||||
0.223007 | + | 0.974817i | \(0.428413\pi\) | |||||||
\(30\) | 7.73332 | 1.41190 | ||||||||
\(31\) | −0.697480 | −0.125271 | −0.0626356 | − | 0.998036i | \(-0.519951\pi\) | ||||
−0.0626356 | + | 0.998036i | \(0.519951\pi\) | |||||||
\(32\) | 4.63807 | 0.819902 | ||||||||
\(33\) | −6.61253 | −1.15109 | ||||||||
\(34\) | −2.32739 | −0.399144 | ||||||||
\(35\) | 4.46532 | 0.754777 | ||||||||
\(36\) | 3.41675 | 0.569458 | ||||||||
\(37\) | 8.01191 | 1.31715 | 0.658575 | − | 0.752515i | \(-0.271160\pi\) | ||||
0.658575 | + | 0.752515i | \(0.271160\pi\) | |||||||
\(38\) | −7.67281 | −1.24469 | ||||||||
\(39\) | 5.69091 | 0.911275 | ||||||||
\(40\) | −10.9562 | −1.73232 | ||||||||
\(41\) | −10.7539 | −1.67947 | −0.839736 | − | 0.542995i | \(-0.817290\pi\) | ||||
−0.839736 | + | 0.542995i | \(0.817290\pi\) | |||||||
\(42\) | 3.12770 | 0.482615 | ||||||||
\(43\) | 8.67047 | 1.32223 | 0.661117 | − | 0.750283i | \(-0.270083\pi\) | ||||
0.661117 | + | 0.750283i | \(0.270083\pi\) | |||||||
\(44\) | 22.5934 | 3.40608 | ||||||||
\(45\) | 3.32274 | 0.495325 | ||||||||
\(46\) | −21.3110 | −3.14214 | ||||||||
\(47\) | 2.02538 | 0.295432 | 0.147716 | − | 0.989030i | \(-0.452808\pi\) | ||||
0.147716 | + | 0.989030i | \(0.452808\pi\) | |||||||
\(48\) | −0.840683 | −0.121342 | ||||||||
\(49\) | −5.19402 | −0.742003 | ||||||||
\(50\) | −14.0588 | −1.98822 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −19.4444 | −2.69646 | ||||||||
\(53\) | −4.76109 | −0.653986 | −0.326993 | − | 0.945027i | \(-0.606035\pi\) | ||||
−0.326993 | + | 0.945027i | \(0.606035\pi\) | |||||||
\(54\) | 2.32739 | 0.316718 | ||||||||
\(55\) | 21.9717 | 2.96267 | ||||||||
\(56\) | −4.43118 | −0.592141 | ||||||||
\(57\) | −3.29674 | −0.436664 | ||||||||
\(58\) | −5.59007 | −0.734012 | ||||||||
\(59\) | −2.52293 | −0.328457 | −0.164228 | − | 0.986422i | \(-0.552513\pi\) | ||||
−0.164228 | + | 0.986422i | \(0.552513\pi\) | |||||||
\(60\) | −11.3530 | −1.46566 | ||||||||
\(61\) | −10.8784 | −1.39283 | −0.696416 | − | 0.717638i | \(-0.745223\pi\) | ||||
−0.696416 | + | 0.717638i | \(0.745223\pi\) | |||||||
\(62\) | 1.62331 | 0.206161 | ||||||||
\(63\) | 1.34387 | 0.169311 | ||||||||
\(64\) | −12.4760 | −1.55950 | ||||||||
\(65\) | −18.9094 | −2.34542 | ||||||||
\(66\) | 15.3899 | 1.89437 | ||||||||
\(67\) | −11.5508 | −1.41115 | −0.705575 | − | 0.708635i | \(-0.749311\pi\) | ||||
−0.705575 | + | 0.708635i | \(0.749311\pi\) | |||||||
\(68\) | 3.41675 | 0.414342 | ||||||||
\(69\) | −9.15661 | −1.10233 | ||||||||
\(70\) | −10.3925 | −1.24215 | ||||||||
\(71\) | 11.9722 | 1.42083 | 0.710417 | − | 0.703781i | \(-0.248507\pi\) | ||||
0.710417 | + | 0.703781i | \(0.248507\pi\) | |||||||
\(72\) | −3.29733 | −0.388594 | ||||||||
\(73\) | 6.20046 | 0.725708 | 0.362854 | − | 0.931846i | \(-0.381802\pi\) | ||||
0.362854 | + | 0.931846i | \(0.381802\pi\) | |||||||
\(74\) | −18.6468 | −2.16765 | ||||||||
\(75\) | −6.04060 | −0.697508 | ||||||||
\(76\) | 11.2641 | 1.29209 | ||||||||
\(77\) | 8.88636 | 1.01269 | ||||||||
\(78\) | −13.2450 | −1.49970 | ||||||||
\(79\) | −2.20634 | −0.248232 | −0.124116 | − | 0.992268i | \(-0.539610\pi\) | ||||
−0.124116 | + | 0.992268i | \(0.539610\pi\) | |||||||
\(80\) | 2.79337 | 0.312308 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 25.0285 | 2.76393 | ||||||||
\(83\) | 13.4909 | 1.48082 | 0.740411 | − | 0.672155i | \(-0.234631\pi\) | ||||
0.740411 | + | 0.672155i | \(0.234631\pi\) | |||||||
\(84\) | −4.59166 | −0.500991 | ||||||||
\(85\) | 3.32274 | 0.360402 | ||||||||
\(86\) | −20.1796 | −2.17602 | ||||||||
\(87\) | −2.40186 | −0.257507 | ||||||||
\(88\) | −21.8037 | −2.32428 | ||||||||
\(89\) | 13.4090 | 1.42135 | 0.710675 | − | 0.703521i | \(-0.248390\pi\) | ||||
0.710675 | + | 0.703521i | \(0.248390\pi\) | |||||||
\(90\) | −7.73332 | −0.815163 | ||||||||
\(91\) | −7.64783 | −0.801710 | ||||||||
\(92\) | 31.2859 | 3.26178 | ||||||||
\(93\) | 0.697480 | 0.0723253 | ||||||||
\(94\) | −4.71386 | −0.486197 | ||||||||
\(95\) | 10.9542 | 1.12388 | ||||||||
\(96\) | −4.63807 | −0.473371 | ||||||||
\(97\) | −7.16444 | −0.727438 | −0.363719 | − | 0.931509i | \(-0.618493\pi\) | ||||
−0.363719 | + | 0.931509i | \(0.618493\pi\) | |||||||
\(98\) | 12.0885 | 1.22112 | ||||||||
\(99\) | 6.61253 | 0.664584 | ||||||||
\(100\) | 20.6392 | 2.06392 | ||||||||
\(101\) | −8.47772 | −0.843565 | −0.421782 | − | 0.906697i | \(-0.638595\pi\) | ||||
−0.421782 | + | 0.906697i | \(0.638595\pi\) | |||||||
\(102\) | 2.32739 | 0.230446 | ||||||||
\(103\) | 16.6771 | 1.64324 | 0.821622 | − | 0.570032i | \(-0.193069\pi\) | ||||
0.821622 | + | 0.570032i | \(0.193069\pi\) | |||||||
\(104\) | 18.7648 | 1.84004 | ||||||||
\(105\) | −4.46532 | −0.435771 | ||||||||
\(106\) | 11.0809 | 1.07627 | ||||||||
\(107\) | −5.07153 | −0.490283 | −0.245142 | − | 0.969487i | \(-0.578834\pi\) | ||||
−0.245142 | + | 0.969487i | \(0.578834\pi\) | |||||||
\(108\) | −3.41675 | −0.328777 | ||||||||
\(109\) | 13.4840 | 1.29154 | 0.645768 | − | 0.763534i | \(-0.276537\pi\) | ||||
0.645768 | + | 0.763534i | \(0.276537\pi\) | |||||||
\(110\) | −51.1368 | −4.87570 | ||||||||
\(111\) | −8.01191 | −0.760457 | ||||||||
\(112\) | 1.12977 | 0.106753 | ||||||||
\(113\) | 1.05538 | 0.0992817 | 0.0496409 | − | 0.998767i | \(-0.484192\pi\) | ||||
0.0496409 | + | 0.998767i | \(0.484192\pi\) | |||||||
\(114\) | 7.67281 | 0.718624 | ||||||||
\(115\) | 30.4250 | 2.83715 | ||||||||
\(116\) | 8.20656 | 0.761960 | ||||||||
\(117\) | −5.69091 | −0.526125 | ||||||||
\(118\) | 5.87184 | 0.540546 | ||||||||
\(119\) | 1.34387 | 0.123192 | ||||||||
\(120\) | 10.9562 | 1.00016 | ||||||||
\(121\) | 32.7256 | 2.97505 | ||||||||
\(122\) | 25.3182 | 2.29220 | ||||||||
\(123\) | 10.7539 | 0.969643 | ||||||||
\(124\) | −2.38312 | −0.214010 | ||||||||
\(125\) | 3.45764 | 0.309261 | ||||||||
\(126\) | −3.12770 | −0.278638 | ||||||||
\(127\) | 15.6374 | 1.38759 | 0.693797 | − | 0.720170i | \(-0.255936\pi\) | ||||
0.693797 | + | 0.720170i | \(0.255936\pi\) | |||||||
\(128\) | 19.7603 | 1.74658 | ||||||||
\(129\) | −8.67047 | −0.763392 | ||||||||
\(130\) | 44.0096 | 3.85990 | ||||||||
\(131\) | −12.8581 | −1.12342 | −0.561709 | − | 0.827335i | \(-0.689856\pi\) | ||||
−0.561709 | + | 0.827335i | \(0.689856\pi\) | |||||||
\(132\) | −22.5934 | −1.96650 | ||||||||
\(133\) | 4.43038 | 0.384163 | ||||||||
\(134\) | 26.8832 | 2.32235 | ||||||||
\(135\) | −3.32274 | −0.285976 | ||||||||
\(136\) | −3.29733 | −0.282744 | ||||||||
\(137\) | 7.89727 | 0.674709 | 0.337355 | − | 0.941378i | \(-0.390468\pi\) | ||||
0.337355 | + | 0.941378i | \(0.390468\pi\) | |||||||
\(138\) | 21.3110 | 1.81411 | ||||||||
\(139\) | −14.2178 | −1.20594 | −0.602969 | − | 0.797765i | \(-0.706016\pi\) | ||||
−0.602969 | + | 0.797765i | \(0.706016\pi\) | |||||||
\(140\) | 15.2569 | 1.28944 | ||||||||
\(141\) | −2.02538 | −0.170568 | ||||||||
\(142\) | −27.8639 | −2.33829 | ||||||||
\(143\) | −37.6313 | −3.14689 | ||||||||
\(144\) | 0.840683 | 0.0700569 | ||||||||
\(145\) | 7.98076 | 0.662766 | ||||||||
\(146\) | −14.4309 | −1.19431 | ||||||||
\(147\) | 5.19402 | 0.428396 | ||||||||
\(148\) | 27.3747 | 2.25019 | ||||||||
\(149\) | −18.3865 | −1.50628 | −0.753139 | − | 0.657861i | \(-0.771461\pi\) | ||||
−0.753139 | + | 0.657861i | \(0.771461\pi\) | |||||||
\(150\) | 14.0588 | 1.14790 | ||||||||
\(151\) | −1.29175 | −0.105121 | −0.0525606 | − | 0.998618i | \(-0.516738\pi\) | ||||
−0.0525606 | + | 0.998618i | \(0.516738\pi\) | |||||||
\(152\) | −10.8705 | −0.881710 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −20.6820 | −1.66661 | ||||||||
\(155\) | −2.31755 | −0.186150 | ||||||||
\(156\) | 19.4444 | 1.55680 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | 5.13501 | 0.408519 | ||||||||
\(159\) | 4.76109 | 0.377579 | ||||||||
\(160\) | 15.4111 | 1.21835 | ||||||||
\(161\) | 12.3053 | 0.969791 | ||||||||
\(162\) | −2.32739 | −0.182857 | ||||||||
\(163\) | 13.7858 | 1.07979 | 0.539895 | − | 0.841732i | \(-0.318464\pi\) | ||||
0.539895 | + | 0.841732i | \(0.318464\pi\) | |||||||
\(164\) | −36.7433 | −2.86917 | ||||||||
\(165\) | −21.9717 | −1.71050 | ||||||||
\(166\) | −31.3987 | −2.43701 | ||||||||
\(167\) | 15.9001 | 1.23039 | 0.615195 | − | 0.788375i | \(-0.289077\pi\) | ||||
0.615195 | + | 0.788375i | \(0.289077\pi\) | |||||||
\(168\) | 4.43118 | 0.341873 | ||||||||
\(169\) | 19.3864 | 1.49127 | ||||||||
\(170\) | −7.73332 | −0.593118 | ||||||||
\(171\) | 3.29674 | 0.252108 | ||||||||
\(172\) | 29.6248 | 2.25887 | ||||||||
\(173\) | −13.1914 | −1.00292 | −0.501462 | − | 0.865180i | \(-0.667204\pi\) | ||||
−0.501462 | + | 0.865180i | \(0.667204\pi\) | |||||||
\(174\) | 5.59007 | 0.423782 | ||||||||
\(175\) | 8.11776 | 0.613645 | ||||||||
\(176\) | 5.55904 | 0.419029 | ||||||||
\(177\) | 2.52293 | 0.189635 | ||||||||
\(178\) | −31.2080 | −2.33914 | ||||||||
\(179\) | −16.0222 | −1.19756 | −0.598779 | − | 0.800914i | \(-0.704347\pi\) | ||||
−0.598779 | + | 0.800914i | \(0.704347\pi\) | |||||||
\(180\) | 11.3530 | 0.846201 | ||||||||
\(181\) | −5.64999 | −0.419960 | −0.209980 | − | 0.977706i | \(-0.567340\pi\) | ||||
−0.209980 | + | 0.977706i | \(0.567340\pi\) | |||||||
\(182\) | 17.7995 | 1.31939 | ||||||||
\(183\) | 10.8784 | 0.804152 | ||||||||
\(184\) | −30.1924 | −2.22581 | ||||||||
\(185\) | 26.6215 | 1.95725 | ||||||||
\(186\) | −1.62331 | −0.119027 | ||||||||
\(187\) | 6.61253 | 0.483556 | ||||||||
\(188\) | 6.92022 | 0.504709 | ||||||||
\(189\) | −1.34387 | −0.0977520 | ||||||||
\(190\) | −25.4947 | −1.84958 | ||||||||
\(191\) | 14.3928 | 1.04143 | 0.520713 | − | 0.853732i | \(-0.325666\pi\) | ||||
0.520713 | + | 0.853732i | \(0.325666\pi\) | |||||||
\(192\) | 12.4760 | 0.900375 | ||||||||
\(193\) | −20.5330 | −1.47800 | −0.739000 | − | 0.673706i | \(-0.764701\pi\) | ||||
−0.739000 | + | 0.673706i | \(0.764701\pi\) | |||||||
\(194\) | 16.6745 | 1.19716 | ||||||||
\(195\) | 18.9094 | 1.35413 | ||||||||
\(196\) | −17.7467 | −1.26762 | ||||||||
\(197\) | 12.5215 | 0.892121 | 0.446060 | − | 0.895003i | \(-0.352827\pi\) | ||||
0.446060 | + | 0.895003i | \(0.352827\pi\) | |||||||
\(198\) | −15.3899 | −1.09372 | ||||||||
\(199\) | 14.5813 | 1.03364 | 0.516822 | − | 0.856093i | \(-0.327115\pi\) | ||||
0.516822 | + | 0.856093i | \(0.327115\pi\) | |||||||
\(200\) | −19.9179 | −1.40841 | ||||||||
\(201\) | 11.5508 | 0.814728 | ||||||||
\(202\) | 19.7310 | 1.38827 | ||||||||
\(203\) | 3.22778 | 0.226546 | ||||||||
\(204\) | −3.41675 | −0.239220 | ||||||||
\(205\) | −35.7323 | −2.49565 | ||||||||
\(206\) | −38.8142 | −2.70431 | ||||||||
\(207\) | 9.15661 | 0.636429 | ||||||||
\(208\) | −4.78425 | −0.331728 | ||||||||
\(209\) | 21.7998 | 1.50792 | ||||||||
\(210\) | 10.3925 | 0.717154 | ||||||||
\(211\) | 3.27818 | 0.225679 | 0.112839 | − | 0.993613i | \(-0.464005\pi\) | ||||
0.112839 | + | 0.993613i | \(0.464005\pi\) | |||||||
\(212\) | −16.2674 | −1.11725 | ||||||||
\(213\) | −11.9722 | −0.820318 | ||||||||
\(214\) | 11.8034 | 0.806866 | ||||||||
\(215\) | 28.8097 | 1.96481 | ||||||||
\(216\) | 3.29733 | 0.224355 | ||||||||
\(217\) | −0.937321 | −0.0636295 | ||||||||
\(218\) | −31.3826 | −2.12550 | ||||||||
\(219\) | −6.20046 | −0.418988 | ||||||||
\(220\) | 75.0719 | 5.06134 | ||||||||
\(221\) | −5.69091 | −0.382812 | ||||||||
\(222\) | 18.6468 | 1.25149 | ||||||||
\(223\) | 4.16671 | 0.279023 | 0.139512 | − | 0.990220i | \(-0.455447\pi\) | ||||
0.139512 | + | 0.990220i | \(0.455447\pi\) | |||||||
\(224\) | 6.23295 | 0.416456 | ||||||||
\(225\) | 6.04060 | 0.402707 | ||||||||
\(226\) | −2.45628 | −0.163389 | ||||||||
\(227\) | 21.9351 | 1.45588 | 0.727942 | − | 0.685639i | \(-0.240477\pi\) | ||||
0.727942 | + | 0.685639i | \(0.240477\pi\) | |||||||
\(228\) | −11.2641 | −0.745986 | ||||||||
\(229\) | −4.46636 | −0.295145 | −0.147573 | − | 0.989051i | \(-0.547146\pi\) | ||||
−0.147573 | + | 0.989051i | \(0.547146\pi\) | |||||||
\(230\) | −70.8110 | −4.66914 | ||||||||
\(231\) | −8.88636 | −0.584680 | ||||||||
\(232\) | −7.91974 | −0.519956 | ||||||||
\(233\) | −6.53994 | −0.428446 | −0.214223 | − | 0.976785i | \(-0.568722\pi\) | ||||
−0.214223 | + | 0.976785i | \(0.568722\pi\) | |||||||
\(234\) | 13.2450 | 0.865851 | ||||||||
\(235\) | 6.72982 | 0.439005 | ||||||||
\(236\) | −8.62021 | −0.561128 | ||||||||
\(237\) | 2.20634 | 0.143317 | ||||||||
\(238\) | −3.12770 | −0.202739 | ||||||||
\(239\) | −9.55138 | −0.617827 | −0.308914 | − | 0.951090i | \(-0.599965\pi\) | ||||
−0.308914 | + | 0.951090i | \(0.599965\pi\) | |||||||
\(240\) | −2.79337 | −0.180311 | ||||||||
\(241\) | −16.2977 | −1.04983 | −0.524913 | − | 0.851156i | \(-0.675902\pi\) | ||||
−0.524913 | + | 0.851156i | \(0.675902\pi\) | |||||||
\(242\) | −76.1652 | −4.89608 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −37.1687 | −2.37948 | ||||||||
\(245\) | −17.2584 | −1.10260 | ||||||||
\(246\) | −25.0285 | −1.59576 | ||||||||
\(247\) | −18.7615 | −1.19376 | ||||||||
\(248\) | 2.29983 | 0.146039 | ||||||||
\(249\) | −13.4909 | −0.854953 | ||||||||
\(250\) | −8.04728 | −0.508955 | ||||||||
\(251\) | −23.7998 | −1.50223 | −0.751115 | − | 0.660171i | \(-0.770484\pi\) | ||||
−0.751115 | + | 0.660171i | \(0.770484\pi\) | |||||||
\(252\) | 4.59166 | 0.289247 | ||||||||
\(253\) | 60.5484 | 3.80664 | ||||||||
\(254\) | −36.3944 | −2.28358 | ||||||||
\(255\) | −3.32274 | −0.208078 | ||||||||
\(256\) | −21.0381 | −1.31488 | ||||||||
\(257\) | −13.8093 | −0.861401 | −0.430700 | − | 0.902495i | \(-0.641733\pi\) | ||||
−0.430700 | + | 0.902495i | \(0.641733\pi\) | |||||||
\(258\) | 20.1796 | 1.25633 | ||||||||
\(259\) | 10.7669 | 0.669025 | ||||||||
\(260\) | −64.6087 | −4.00686 | ||||||||
\(261\) | 2.40186 | 0.148671 | ||||||||
\(262\) | 29.9259 | 1.84883 | ||||||||
\(263\) | −18.3375 | −1.13074 | −0.565368 | − | 0.824839i | \(-0.691266\pi\) | ||||
−0.565368 | + | 0.824839i | \(0.691266\pi\) | |||||||
\(264\) | 21.8037 | 1.34193 | ||||||||
\(265\) | −15.8199 | −0.971806 | ||||||||
\(266\) | −10.3112 | −0.632222 | ||||||||
\(267\) | −13.4090 | −0.820617 | ||||||||
\(268\) | −39.4661 | −2.41077 | ||||||||
\(269\) | 6.94847 | 0.423656 | 0.211828 | − | 0.977307i | \(-0.432058\pi\) | ||||
0.211828 | + | 0.977307i | \(0.432058\pi\) | |||||||
\(270\) | 7.73332 | 0.470635 | ||||||||
\(271\) | 17.5830 | 1.06809 | 0.534046 | − | 0.845456i | \(-0.320671\pi\) | ||||
0.534046 | + | 0.845456i | \(0.320671\pi\) | |||||||
\(272\) | 0.840683 | 0.0509739 | ||||||||
\(273\) | 7.64783 | 0.462867 | ||||||||
\(274\) | −18.3800 | −1.11038 | ||||||||
\(275\) | 39.9436 | 2.40869 | ||||||||
\(276\) | −31.2859 | −1.88319 | ||||||||
\(277\) | 18.1426 | 1.09008 | 0.545042 | − | 0.838409i | \(-0.316514\pi\) | ||||
0.545042 | + | 0.838409i | \(0.316514\pi\) | |||||||
\(278\) | 33.0904 | 1.98463 | ||||||||
\(279\) | −0.697480 | −0.0417571 | ||||||||
\(280\) | −14.7236 | −0.879906 | ||||||||
\(281\) | −2.37433 | −0.141641 | −0.0708204 | − | 0.997489i | \(-0.522562\pi\) | ||||
−0.0708204 | + | 0.997489i | \(0.522562\pi\) | |||||||
\(282\) | 4.71386 | 0.280706 | ||||||||
\(283\) | 25.0080 | 1.48657 | 0.743287 | − | 0.668973i | \(-0.233266\pi\) | ||||
0.743287 | + | 0.668973i | \(0.233266\pi\) | |||||||
\(284\) | 40.9059 | 2.42732 | ||||||||
\(285\) | −10.9542 | −0.648872 | ||||||||
\(286\) | 87.5828 | 5.17888 | ||||||||
\(287\) | −14.4518 | −0.853061 | ||||||||
\(288\) | 4.63807 | 0.273301 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −18.5744 | −1.09072 | ||||||||
\(291\) | 7.16444 | 0.419987 | ||||||||
\(292\) | 21.1854 | 1.23978 | ||||||||
\(293\) | −7.01012 | −0.409535 | −0.204768 | − | 0.978811i | \(-0.565644\pi\) | ||||
−0.204768 | + | 0.978811i | \(0.565644\pi\) | |||||||
\(294\) | −12.0885 | −0.705017 | ||||||||
\(295\) | −8.38303 | −0.488079 | ||||||||
\(296\) | −26.4179 | −1.53551 | ||||||||
\(297\) | −6.61253 | −0.383698 | ||||||||
\(298\) | 42.7925 | 2.47890 | ||||||||
\(299\) | −52.1095 | −3.01357 | ||||||||
\(300\) | −20.6392 | −1.19161 | ||||||||
\(301\) | 11.6520 | 0.671608 | ||||||||
\(302\) | 3.00641 | 0.172999 | ||||||||
\(303\) | 8.47772 | 0.487032 | ||||||||
\(304\) | 2.77152 | 0.158957 | ||||||||
\(305\) | −36.1460 | −2.06971 | ||||||||
\(306\) | −2.32739 | −0.133048 | ||||||||
\(307\) | −23.0077 | −1.31312 | −0.656560 | − | 0.754273i | \(-0.727989\pi\) | ||||
−0.656560 | + | 0.754273i | \(0.727989\pi\) | |||||||
\(308\) | 30.3625 | 1.73006 | ||||||||
\(309\) | −16.6771 | −0.948728 | ||||||||
\(310\) | 5.39384 | 0.306349 | ||||||||
\(311\) | 5.75350 | 0.326251 | 0.163126 | − | 0.986605i | \(-0.447842\pi\) | ||||
0.163126 | + | 0.986605i | \(0.447842\pi\) | |||||||
\(312\) | −18.7648 | −1.06235 | ||||||||
\(313\) | −6.84090 | −0.386670 | −0.193335 | − | 0.981133i | \(-0.561930\pi\) | ||||
−0.193335 | + | 0.981133i | \(0.561930\pi\) | |||||||
\(314\) | 2.32739 | 0.131342 | ||||||||
\(315\) | 4.46532 | 0.251592 | ||||||||
\(316\) | −7.53850 | −0.424074 | ||||||||
\(317\) | 10.4124 | 0.584819 | 0.292409 | − | 0.956293i | \(-0.405543\pi\) | ||||
0.292409 | + | 0.956293i | \(0.405543\pi\) | |||||||
\(318\) | −11.0809 | −0.621387 | ||||||||
\(319\) | 15.8824 | 0.889243 | ||||||||
\(320\) | −41.4544 | −2.31737 | ||||||||
\(321\) | 5.07153 | 0.283065 | ||||||||
\(322\) | −28.6392 | −1.59600 | ||||||||
\(323\) | 3.29674 | 0.183436 | ||||||||
\(324\) | 3.41675 | 0.189819 | ||||||||
\(325\) | −34.3765 | −1.90687 | ||||||||
\(326\) | −32.0850 | −1.77703 | ||||||||
\(327\) | −13.4840 | −0.745668 | ||||||||
\(328\) | 35.4591 | 1.95790 | ||||||||
\(329\) | 2.72184 | 0.150060 | ||||||||
\(330\) | 51.1368 | 2.81499 | ||||||||
\(331\) | −35.5826 | −1.95580 | −0.977899 | − | 0.209080i | \(-0.932953\pi\) | ||||
−0.977899 | + | 0.209080i | \(0.932953\pi\) | |||||||
\(332\) | 46.0951 | 2.52980 | ||||||||
\(333\) | 8.01191 | 0.439050 | ||||||||
\(334\) | −37.0058 | −2.02487 | ||||||||
\(335\) | −38.3802 | −2.09693 | ||||||||
\(336\) | −1.12977 | −0.0616338 | ||||||||
\(337\) | 1.72703 | 0.0940772 | 0.0470386 | − | 0.998893i | \(-0.485022\pi\) | ||||
0.0470386 | + | 0.998893i | \(0.485022\pi\) | |||||||
\(338\) | −45.1198 | −2.45420 | ||||||||
\(339\) | −1.05538 | −0.0573203 | ||||||||
\(340\) | 11.3530 | 0.615701 | ||||||||
\(341\) | −4.61211 | −0.249760 | ||||||||
\(342\) | −7.67281 | −0.414898 | ||||||||
\(343\) | −16.3871 | −0.884823 | ||||||||
\(344\) | −28.5894 | −1.54144 | ||||||||
\(345\) | −30.4250 | −1.63803 | ||||||||
\(346\) | 30.7016 | 1.65053 | ||||||||
\(347\) | 9.72179 | 0.521893 | 0.260947 | − | 0.965353i | \(-0.415965\pi\) | ||||
0.260947 | + | 0.965353i | \(0.415965\pi\) | |||||||
\(348\) | −8.20656 | −0.439918 | ||||||||
\(349\) | −4.86787 | −0.260571 | −0.130285 | − | 0.991477i | \(-0.541589\pi\) | ||||
−0.130285 | + | 0.991477i | \(0.541589\pi\) | |||||||
\(350\) | −18.8932 | −1.00988 | ||||||||
\(351\) | 5.69091 | 0.303758 | ||||||||
\(352\) | 30.6694 | 1.63468 | ||||||||
\(353\) | 19.9469 | 1.06167 | 0.530833 | − | 0.847476i | \(-0.321879\pi\) | ||||
0.530833 | + | 0.847476i | \(0.321879\pi\) | |||||||
\(354\) | −5.87184 | −0.312085 | ||||||||
\(355\) | 39.7803 | 2.11132 | ||||||||
\(356\) | 45.8152 | 2.42820 | ||||||||
\(357\) | −1.34387 | −0.0711250 | ||||||||
\(358\) | 37.2900 | 1.97084 | ||||||||
\(359\) | −31.0406 | −1.63826 | −0.819130 | − | 0.573608i | \(-0.805543\pi\) | ||||
−0.819130 | + | 0.573608i | \(0.805543\pi\) | |||||||
\(360\) | −10.9562 | −0.577441 | ||||||||
\(361\) | −8.13149 | −0.427973 | ||||||||
\(362\) | 13.1497 | 0.691135 | ||||||||
\(363\) | −32.7256 | −1.71765 | ||||||||
\(364\) | −26.1307 | −1.36962 | ||||||||
\(365\) | 20.6025 | 1.07838 | ||||||||
\(366\) | −25.3182 | −1.32340 | ||||||||
\(367\) | 1.74313 | 0.0909906 | 0.0454953 | − | 0.998965i | \(-0.485513\pi\) | ||||
0.0454953 | + | 0.998965i | \(0.485513\pi\) | |||||||
\(368\) | 7.69781 | 0.401276 | ||||||||
\(369\) | −10.7539 | −0.559824 | ||||||||
\(370\) | −61.9586 | −3.22107 | ||||||||
\(371\) | −6.39827 | −0.332182 | ||||||||
\(372\) | 2.38312 | 0.123559 | ||||||||
\(373\) | 14.3852 | 0.744836 | 0.372418 | − | 0.928065i | \(-0.378529\pi\) | ||||
0.372418 | + | 0.928065i | \(0.378529\pi\) | |||||||
\(374\) | −15.3899 | −0.795795 | ||||||||
\(375\) | −3.45764 | −0.178552 | ||||||||
\(376\) | −6.67836 | −0.344410 | ||||||||
\(377\) | −13.6688 | −0.703978 | ||||||||
\(378\) | 3.12770 | 0.160872 | ||||||||
\(379\) | 19.6571 | 1.00972 | 0.504859 | − | 0.863202i | \(-0.331544\pi\) | ||||
0.504859 | + | 0.863202i | \(0.331544\pi\) | |||||||
\(380\) | 37.4278 | 1.92001 | ||||||||
\(381\) | −15.6374 | −0.801128 | ||||||||
\(382\) | −33.4976 | −1.71389 | ||||||||
\(383\) | −25.1687 | −1.28606 | −0.643031 | − | 0.765840i | \(-0.722323\pi\) | ||||
−0.643031 | + | 0.765840i | \(0.722323\pi\) | |||||||
\(384\) | −19.7603 | −1.00839 | ||||||||
\(385\) | 29.5271 | 1.50484 | ||||||||
\(386\) | 47.7884 | 2.43236 | ||||||||
\(387\) | 8.67047 | 0.440745 | ||||||||
\(388\) | −24.4791 | −1.24274 | ||||||||
\(389\) | −8.73440 | −0.442852 | −0.221426 | − | 0.975177i | \(-0.571071\pi\) | ||||
−0.221426 | + | 0.975177i | \(0.571071\pi\) | |||||||
\(390\) | −44.0096 | −2.22851 | ||||||||
\(391\) | 9.15661 | 0.463070 | ||||||||
\(392\) | 17.1264 | 0.865015 | ||||||||
\(393\) | 12.8581 | 0.648606 | ||||||||
\(394\) | −29.1425 | −1.46818 | ||||||||
\(395\) | −7.33108 | −0.368867 | ||||||||
\(396\) | 22.5934 | 1.13536 | ||||||||
\(397\) | 16.0492 | 0.805487 | 0.402744 | − | 0.915313i | \(-0.368057\pi\) | ||||
0.402744 | + | 0.915313i | \(0.368057\pi\) | |||||||
\(398\) | −33.9365 | −1.70108 | ||||||||
\(399\) | −4.43038 | −0.221797 | ||||||||
\(400\) | 5.07823 | 0.253911 | ||||||||
\(401\) | −15.3628 | −0.767180 | −0.383590 | − | 0.923503i | \(-0.625312\pi\) | ||||
−0.383590 | + | 0.923503i | \(0.625312\pi\) | |||||||
\(402\) | −26.8832 | −1.34081 | ||||||||
\(403\) | 3.96930 | 0.197725 | ||||||||
\(404\) | −28.9663 | −1.44113 | ||||||||
\(405\) | 3.32274 | 0.165108 | ||||||||
\(406\) | −7.51231 | −0.372830 | ||||||||
\(407\) | 52.9790 | 2.62607 | ||||||||
\(408\) | 3.29733 | 0.163242 | ||||||||
\(409\) | −1.99130 | −0.0984634 | −0.0492317 | − | 0.998787i | \(-0.515677\pi\) | ||||
−0.0492317 | + | 0.998787i | \(0.515677\pi\) | |||||||
\(410\) | 83.1630 | 4.10713 | ||||||||
\(411\) | −7.89727 | −0.389544 | ||||||||
\(412\) | 56.9815 | 2.80728 | ||||||||
\(413\) | −3.39048 | −0.166834 | ||||||||
\(414\) | −21.3110 | −1.04738 | ||||||||
\(415\) | 44.8268 | 2.20046 | ||||||||
\(416\) | −26.3948 | −1.29411 | ||||||||
\(417\) | 14.2178 | 0.696248 | ||||||||
\(418\) | −50.7367 | −2.48161 | ||||||||
\(419\) | 12.9930 | 0.634748 | 0.317374 | − | 0.948300i | \(-0.397199\pi\) | ||||
0.317374 | + | 0.948300i | \(0.397199\pi\) | |||||||
\(420\) | −15.2569 | −0.744460 | ||||||||
\(421\) | −6.93314 | −0.337901 | −0.168950 | − | 0.985625i | \(-0.554038\pi\) | ||||
−0.168950 | + | 0.985625i | \(0.554038\pi\) | |||||||
\(422\) | −7.62960 | −0.371403 | ||||||||
\(423\) | 2.02538 | 0.0984774 | ||||||||
\(424\) | 15.6989 | 0.762405 | ||||||||
\(425\) | 6.04060 | 0.293012 | ||||||||
\(426\) | 27.8639 | 1.35001 | ||||||||
\(427\) | −14.6191 | −0.707467 | ||||||||
\(428\) | −17.3281 | −0.837588 | ||||||||
\(429\) | 37.6313 | 1.81686 | ||||||||
\(430\) | −67.0515 | −3.23351 | ||||||||
\(431\) | 15.8071 | 0.761400 | 0.380700 | − | 0.924699i | \(-0.375683\pi\) | ||||
0.380700 | + | 0.924699i | \(0.375683\pi\) | |||||||
\(432\) | −0.840683 | −0.0404474 | ||||||||
\(433\) | 19.7601 | 0.949608 | 0.474804 | − | 0.880092i | \(-0.342519\pi\) | ||||
0.474804 | + | 0.880092i | \(0.342519\pi\) | |||||||
\(434\) | 2.18151 | 0.104716 | ||||||||
\(435\) | −7.98076 | −0.382648 | ||||||||
\(436\) | 46.0716 | 2.20643 | ||||||||
\(437\) | 30.1870 | 1.44404 | ||||||||
\(438\) | 14.4309 | 0.689534 | ||||||||
\(439\) | −13.9659 | −0.666555 | −0.333278 | − | 0.942829i | \(-0.608155\pi\) | ||||
−0.333278 | + | 0.942829i | \(0.608155\pi\) | |||||||
\(440\) | −72.4481 | −3.45383 | ||||||||
\(441\) | −5.19402 | −0.247334 | ||||||||
\(442\) | 13.2450 | 0.629999 | ||||||||
\(443\) | −11.5698 | −0.549698 | −0.274849 | − | 0.961487i | \(-0.588628\pi\) | ||||
−0.274849 | + | 0.961487i | \(0.588628\pi\) | |||||||
\(444\) | −27.3747 | −1.29915 | ||||||||
\(445\) | 44.5546 | 2.11209 | ||||||||
\(446\) | −9.69756 | −0.459193 | ||||||||
\(447\) | 18.3865 | 0.869650 | ||||||||
\(448\) | −16.7660 | −0.792121 | ||||||||
\(449\) | −39.4676 | −1.86259 | −0.931295 | − | 0.364265i | \(-0.881320\pi\) | ||||
−0.931295 | + | 0.364265i | \(0.881320\pi\) | |||||||
\(450\) | −14.0588 | −0.662740 | ||||||||
\(451\) | −71.1103 | −3.34845 | ||||||||
\(452\) | 3.60597 | 0.169610 | ||||||||
\(453\) | 1.29175 | 0.0606917 | ||||||||
\(454\) | −51.0516 | −2.39597 | ||||||||
\(455\) | −25.4117 | −1.19132 | ||||||||
\(456\) | 10.8705 | 0.509056 | ||||||||
\(457\) | −30.1436 | −1.41006 | −0.705030 | − | 0.709178i | \(-0.749066\pi\) | ||||
−0.705030 | + | 0.709178i | \(0.749066\pi\) | |||||||
\(458\) | 10.3950 | 0.485724 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 103.955 | 4.84692 | ||||||||
\(461\) | −1.31904 | −0.0614339 | −0.0307170 | − | 0.999528i | \(-0.509779\pi\) | ||||
−0.0307170 | + | 0.999528i | \(0.509779\pi\) | |||||||
\(462\) | 20.6820 | 0.962216 | ||||||||
\(463\) | 29.1315 | 1.35386 | 0.676929 | − | 0.736048i | \(-0.263310\pi\) | ||||
0.676929 | + | 0.736048i | \(0.263310\pi\) | |||||||
\(464\) | 2.01920 | 0.0937392 | ||||||||
\(465\) | 2.31755 | 0.107474 | ||||||||
\(466\) | 15.2210 | 0.705099 | ||||||||
\(467\) | −29.3480 | −1.35806 | −0.679032 | − | 0.734108i | \(-0.737600\pi\) | ||||
−0.679032 | + | 0.734108i | \(0.737600\pi\) | |||||||
\(468\) | −19.4444 | −0.898818 | ||||||||
\(469\) | −15.5227 | −0.716771 | ||||||||
\(470\) | −15.6629 | −0.722476 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | 8.31893 | 0.382910 | ||||||||
\(473\) | 57.3337 | 2.63621 | ||||||||
\(474\) | −5.13501 | −0.235859 | ||||||||
\(475\) | 19.9143 | 0.913731 | ||||||||
\(476\) | 4.59166 | 0.210458 | ||||||||
\(477\) | −4.76109 | −0.217995 | ||||||||
\(478\) | 22.2298 | 1.01677 | ||||||||
\(479\) | 25.5498 | 1.16740 | 0.583700 | − | 0.811969i | \(-0.301604\pi\) | ||||
0.583700 | + | 0.811969i | \(0.301604\pi\) | |||||||
\(480\) | −15.4111 | −0.703417 | ||||||||
\(481\) | −45.5950 | −2.07895 | ||||||||
\(482\) | 37.9311 | 1.72771 | ||||||||
\(483\) | −12.3053 | −0.559909 | ||||||||
\(484\) | 111.815 | 5.08250 | ||||||||
\(485\) | −23.8056 | −1.08095 | ||||||||
\(486\) | 2.32739 | 0.105573 | ||||||||
\(487\) | −38.5443 | −1.74661 | −0.873305 | − | 0.487174i | \(-0.838028\pi\) | ||||
−0.873305 | + | 0.487174i | \(0.838028\pi\) | |||||||
\(488\) | 35.8696 | 1.62374 | ||||||||
\(489\) | −13.7858 | −0.623417 | ||||||||
\(490\) | 40.1670 | 1.81456 | ||||||||
\(491\) | −11.9324 | −0.538503 | −0.269251 | − | 0.963070i | \(-0.586776\pi\) | ||||
−0.269251 | + | 0.963070i | \(0.586776\pi\) | |||||||
\(492\) | 36.7433 | 1.65651 | ||||||||
\(493\) | 2.40186 | 0.108174 | ||||||||
\(494\) | 43.6653 | 1.96459 | ||||||||
\(495\) | 21.9717 | 0.987555 | ||||||||
\(496\) | −0.586360 | −0.0263283 | ||||||||
\(497\) | 16.0890 | 0.721690 | ||||||||
\(498\) | 31.3987 | 1.40701 | ||||||||
\(499\) | −30.4419 | −1.36276 | −0.681382 | − | 0.731928i | \(-0.738621\pi\) | ||||
−0.681382 | + | 0.731928i | \(0.738621\pi\) | |||||||
\(500\) | 11.8139 | 0.528333 | ||||||||
\(501\) | −15.9001 | −0.710366 | ||||||||
\(502\) | 55.3915 | 2.47224 | ||||||||
\(503\) | −13.9165 | −0.620504 | −0.310252 | − | 0.950654i | \(-0.600413\pi\) | ||||
−0.310252 | + | 0.950654i | \(0.600413\pi\) | |||||||
\(504\) | −4.43118 | −0.197380 | ||||||||
\(505\) | −28.1693 | −1.25352 | ||||||||
\(506\) | −140.920 | −6.26465 | ||||||||
\(507\) | −19.3864 | −0.860982 | ||||||||
\(508\) | 53.4291 | 2.37053 | ||||||||
\(509\) | 33.7056 | 1.49397 | 0.746987 | − | 0.664838i | \(-0.231500\pi\) | ||||
0.746987 | + | 0.664838i | \(0.231500\pi\) | |||||||
\(510\) | 7.73332 | 0.342437 | ||||||||
\(511\) | 8.33259 | 0.368612 | ||||||||
\(512\) | 9.44317 | 0.417333 | ||||||||
\(513\) | −3.29674 | −0.145555 | ||||||||
\(514\) | 32.1397 | 1.41762 | ||||||||
\(515\) | 55.4137 | 2.44182 | ||||||||
\(516\) | −29.6248 | −1.30416 | ||||||||
\(517\) | 13.3929 | 0.589019 | ||||||||
\(518\) | −25.0589 | −1.10102 | ||||||||
\(519\) | 13.1914 | 0.579039 | ||||||||
\(520\) | 62.3506 | 2.73426 | ||||||||
\(521\) | 38.3145 | 1.67859 | 0.839293 | − | 0.543679i | \(-0.182969\pi\) | ||||
0.839293 | + | 0.543679i | \(0.182969\pi\) | |||||||
\(522\) | −5.59007 | −0.244671 | ||||||||
\(523\) | −19.0674 | −0.833761 | −0.416880 | − | 0.908961i | \(-0.636877\pi\) | ||||
−0.416880 | + | 0.908961i | \(0.636877\pi\) | |||||||
\(524\) | −43.9330 | −1.91922 | ||||||||
\(525\) | −8.11776 | −0.354288 | ||||||||
\(526\) | 42.6785 | 1.86087 | ||||||||
\(527\) | −0.697480 | −0.0303827 | ||||||||
\(528\) | −5.55904 | −0.241926 | ||||||||
\(529\) | 60.8436 | 2.64537 | ||||||||
\(530\) | 36.8190 | 1.59931 | ||||||||
\(531\) | −2.52293 | −0.109486 | ||||||||
\(532\) | 15.1375 | 0.656294 | ||||||||
\(533\) | 61.1993 | 2.65083 | ||||||||
\(534\) | 31.2080 | 1.35050 | ||||||||
\(535\) | −16.8514 | −0.728548 | ||||||||
\(536\) | 38.0867 | 1.64510 | ||||||||
\(537\) | 16.0222 | 0.691411 | ||||||||
\(538\) | −16.1718 | −0.697216 | ||||||||
\(539\) | −34.3456 | −1.47937 | ||||||||
\(540\) | −11.3530 | −0.488554 | ||||||||
\(541\) | 3.55653 | 0.152907 | 0.0764536 | − | 0.997073i | \(-0.475640\pi\) | ||||
0.0764536 | + | 0.997073i | \(0.475640\pi\) | |||||||
\(542\) | −40.9225 | −1.75777 | ||||||||
\(543\) | 5.64999 | 0.242464 | ||||||||
\(544\) | 4.63807 | 0.198855 | ||||||||
\(545\) | 44.8039 | 1.91919 | ||||||||
\(546\) | −17.7995 | −0.761748 | ||||||||
\(547\) | 31.7365 | 1.35696 | 0.678478 | − | 0.734621i | \(-0.262640\pi\) | ||||
0.678478 | + | 0.734621i | \(0.262640\pi\) | |||||||
\(548\) | 26.9830 | 1.15266 | ||||||||
\(549\) | −10.8784 | −0.464277 | ||||||||
\(550\) | −92.9645 | −3.96402 | ||||||||
\(551\) | 7.91832 | 0.337332 | ||||||||
\(552\) | 30.1924 | 1.28507 | ||||||||
\(553\) | −2.96502 | −0.126086 | ||||||||
\(554\) | −42.2250 | −1.79397 | ||||||||
\(555\) | −26.6215 | −1.13002 | ||||||||
\(556\) | −48.5786 | −2.06019 | ||||||||
\(557\) | 4.64363 | 0.196757 | 0.0983785 | − | 0.995149i | \(-0.468634\pi\) | ||||
0.0983785 | + | 0.995149i | \(0.468634\pi\) | |||||||
\(558\) | 1.62331 | 0.0687202 | ||||||||
\(559\) | −49.3429 | −2.08698 | ||||||||
\(560\) | 3.75392 | 0.158632 | ||||||||
\(561\) | −6.61253 | −0.279181 | ||||||||
\(562\) | 5.52600 | 0.233100 | ||||||||
\(563\) | −42.4376 | −1.78853 | −0.894266 | − | 0.447535i | \(-0.852302\pi\) | ||||
−0.894266 | + | 0.447535i | \(0.852302\pi\) | |||||||
\(564\) | −6.92022 | −0.291394 | ||||||||
\(565\) | 3.50675 | 0.147530 | ||||||||
\(566\) | −58.2035 | −2.44647 | ||||||||
\(567\) | 1.34387 | 0.0564371 | ||||||||
\(568\) | −39.4762 | −1.65638 | ||||||||
\(569\) | −26.7428 | −1.12112 | −0.560559 | − | 0.828114i | \(-0.689414\pi\) | ||||
−0.560559 | + | 0.828114i | \(0.689414\pi\) | |||||||
\(570\) | 25.4947 | 1.06786 | ||||||||
\(571\) | −12.1029 | −0.506492 | −0.253246 | − | 0.967402i | \(-0.581498\pi\) | ||||
−0.253246 | + | 0.967402i | \(0.581498\pi\) | |||||||
\(572\) | −128.577 | −5.37607 | ||||||||
\(573\) | −14.3928 | −0.601267 | ||||||||
\(574\) | 33.6349 | 1.40389 | ||||||||
\(575\) | 55.3114 | 2.30665 | ||||||||
\(576\) | −12.4760 | −0.519832 | ||||||||
\(577\) | 6.35422 | 0.264530 | 0.132265 | − | 0.991214i | \(-0.457775\pi\) | ||||
0.132265 | + | 0.991214i | \(0.457775\pi\) | |||||||
\(578\) | −2.32739 | −0.0968067 | ||||||||
\(579\) | 20.5330 | 0.853323 | ||||||||
\(580\) | 27.2683 | 1.13225 | ||||||||
\(581\) | 18.1300 | 0.752160 | ||||||||
\(582\) | −16.6745 | −0.691178 | ||||||||
\(583\) | −31.4828 | −1.30389 | ||||||||
\(584\) | −20.4450 | −0.846019 | ||||||||
\(585\) | −18.9094 | −0.781808 | ||||||||
\(586\) | 16.3153 | 0.673978 | ||||||||
\(587\) | −4.33028 | −0.178730 | −0.0893648 | − | 0.995999i | \(-0.528484\pi\) | ||||
−0.0893648 | + | 0.995999i | \(0.528484\pi\) | |||||||
\(588\) | 17.7467 | 0.731861 | ||||||||
\(589\) | −2.29941 | −0.0947457 | ||||||||
\(590\) | 19.5106 | 0.803238 | ||||||||
\(591\) | −12.5215 | −0.515066 | ||||||||
\(592\) | 6.73547 | 0.276826 | ||||||||
\(593\) | 1.81519 | 0.0745410 | 0.0372705 | − | 0.999305i | \(-0.488134\pi\) | ||||
0.0372705 | + | 0.999305i | \(0.488134\pi\) | |||||||
\(594\) | 15.3899 | 0.631457 | ||||||||
\(595\) | 4.46532 | 0.183060 | ||||||||
\(596\) | −62.8220 | −2.57329 | ||||||||
\(597\) | −14.5813 | −0.596775 | ||||||||
\(598\) | 121.279 | 4.95947 | ||||||||
\(599\) | 13.4305 | 0.548756 | 0.274378 | − | 0.961622i | \(-0.411528\pi\) | ||||
0.274378 | + | 0.961622i | \(0.411528\pi\) | |||||||
\(600\) | 19.9179 | 0.813144 | ||||||||
\(601\) | −18.5674 | −0.757379 | −0.378689 | − | 0.925524i | \(-0.623625\pi\) | ||||
−0.378689 | + | 0.925524i | \(0.623625\pi\) | |||||||
\(602\) | −27.1187 | −1.10527 | ||||||||
\(603\) | −11.5508 | −0.470384 | ||||||||
\(604\) | −4.41359 | −0.179586 | ||||||||
\(605\) | 108.738 | 4.42085 | ||||||||
\(606\) | −19.7310 | −0.801516 | ||||||||
\(607\) | 6.45040 | 0.261814 | 0.130907 | − | 0.991395i | \(-0.458211\pi\) | ||||
0.130907 | + | 0.991395i | \(0.458211\pi\) | |||||||
\(608\) | 15.2905 | 0.620112 | ||||||||
\(609\) | −3.22778 | −0.130796 | ||||||||
\(610\) | 84.1258 | 3.40616 | ||||||||
\(611\) | −11.5263 | −0.466303 | ||||||||
\(612\) | 3.41675 | 0.138114 | ||||||||
\(613\) | −48.2329 | −1.94811 | −0.974054 | − | 0.226315i | \(-0.927332\pi\) | ||||
−0.974054 | + | 0.226315i | \(0.927332\pi\) | |||||||
\(614\) | 53.5480 | 2.16102 | ||||||||
\(615\) | 35.7323 | 1.44087 | ||||||||
\(616\) | −29.3013 | −1.18058 | ||||||||
\(617\) | 27.5600 | 1.10952 | 0.554762 | − | 0.832009i | \(-0.312809\pi\) | ||||
0.554762 | + | 0.832009i | \(0.312809\pi\) | |||||||
\(618\) | 38.8142 | 1.56133 | ||||||||
\(619\) | 11.5015 | 0.462285 | 0.231142 | − | 0.972920i | \(-0.425754\pi\) | ||||
0.231142 | + | 0.972920i | \(0.425754\pi\) | |||||||
\(620\) | −7.91848 | −0.318014 | ||||||||
\(621\) | −9.15661 | −0.367442 | ||||||||
\(622\) | −13.3907 | −0.536916 | ||||||||
\(623\) | 18.0199 | 0.721952 | ||||||||
\(624\) | 4.78425 | 0.191523 | ||||||||
\(625\) | −18.7142 | −0.748566 | ||||||||
\(626\) | 15.9214 | 0.636349 | ||||||||
\(627\) | −21.7998 | −0.870600 | ||||||||
\(628\) | −3.41675 | −0.136343 | ||||||||
\(629\) | 8.01191 | 0.319456 | ||||||||
\(630\) | −10.3925 | −0.414049 | ||||||||
\(631\) | 12.3845 | 0.493017 | 0.246509 | − | 0.969141i | \(-0.420717\pi\) | ||||
0.246509 | + | 0.969141i | \(0.420717\pi\) | |||||||
\(632\) | 7.27503 | 0.289385 | ||||||||
\(633\) | −3.27818 | −0.130296 | ||||||||
\(634\) | −24.2337 | −0.962444 | ||||||||
\(635\) | 51.9590 | 2.06193 | ||||||||
\(636\) | 16.2674 | 0.645046 | ||||||||
\(637\) | 29.5587 | 1.17116 | ||||||||
\(638\) | −36.9645 | −1.46344 | ||||||||
\(639\) | 11.9722 | 0.473611 | ||||||||
\(640\) | 65.6584 | 2.59538 | ||||||||
\(641\) | 10.1901 | 0.402485 | 0.201243 | − | 0.979541i | \(-0.435502\pi\) | ||||
0.201243 | + | 0.979541i | \(0.435502\pi\) | |||||||
\(642\) | −11.8034 | −0.465844 | ||||||||
\(643\) | −22.1714 | −0.874354 | −0.437177 | − | 0.899376i | \(-0.644022\pi\) | ||||
−0.437177 | + | 0.899376i | \(0.644022\pi\) | |||||||
\(644\) | 42.0440 | 1.65677 | ||||||||
\(645\) | −28.8097 | −1.13438 | ||||||||
\(646\) | −7.67281 | −0.301883 | ||||||||
\(647\) | −0.718734 | −0.0282564 | −0.0141282 | − | 0.999900i | \(-0.504497\pi\) | ||||
−0.0141282 | + | 0.999900i | \(0.504497\pi\) | |||||||
\(648\) | −3.29733 | −0.129531 | ||||||||
\(649\) | −16.6829 | −0.654862 | ||||||||
\(650\) | 80.0076 | 3.13816 | ||||||||
\(651\) | 0.937321 | 0.0367365 | ||||||||
\(652\) | 47.1028 | 1.84469 | ||||||||
\(653\) | −5.19193 | −0.203176 | −0.101588 | − | 0.994827i | \(-0.532392\pi\) | ||||
−0.101588 | + | 0.994827i | \(0.532392\pi\) | |||||||
\(654\) | 31.3826 | 1.22716 | ||||||||
\(655\) | −42.7242 | −1.66937 | ||||||||
\(656\) | −9.04059 | −0.352976 | ||||||||
\(657\) | 6.20046 | 0.241903 | ||||||||
\(658\) | −6.33480 | −0.246956 | ||||||||
\(659\) | −13.0414 | −0.508021 | −0.254011 | − | 0.967201i | \(-0.581750\pi\) | ||||
−0.254011 | + | 0.967201i | \(0.581750\pi\) | |||||||
\(660\) | −75.0719 | −2.92217 | ||||||||
\(661\) | 26.3710 | 1.02571 | 0.512857 | − | 0.858474i | \(-0.328587\pi\) | ||||
0.512857 | + | 0.858474i | \(0.328587\pi\) | |||||||
\(662\) | 82.8147 | 3.21868 | ||||||||
\(663\) | 5.69091 | 0.221017 | ||||||||
\(664\) | −44.4841 | −1.72632 | ||||||||
\(665\) | 14.7210 | 0.570856 | ||||||||
\(666\) | −18.6468 | −0.722550 | ||||||||
\(667\) | 21.9929 | 0.851569 | ||||||||
\(668\) | 54.3268 | 2.10197 | ||||||||
\(669\) | −4.16671 | −0.161094 | ||||||||
\(670\) | 89.3257 | 3.45095 | ||||||||
\(671\) | −71.9335 | −2.77696 | ||||||||
\(672\) | −6.23295 | −0.240441 | ||||||||
\(673\) | −14.3105 | −0.551628 | −0.275814 | − | 0.961211i | \(-0.588947\pi\) | ||||
−0.275814 | + | 0.961211i | \(0.588947\pi\) | |||||||
\(674\) | −4.01947 | −0.154824 | ||||||||
\(675\) | −6.04060 | −0.232503 | ||||||||
\(676\) | 66.2387 | 2.54764 | ||||||||
\(677\) | −1.46380 | −0.0562583 | −0.0281291 | − | 0.999604i | \(-0.508955\pi\) | ||||
−0.0281291 | + | 0.999604i | \(0.508955\pi\) | |||||||
\(678\) | 2.45628 | 0.0943329 | ||||||||
\(679\) | −9.62805 | −0.369491 | ||||||||
\(680\) | −10.9562 | −0.420150 | ||||||||
\(681\) | −21.9351 | −0.840555 | ||||||||
\(682\) | 10.7342 | 0.411033 | ||||||||
\(683\) | 16.2029 | 0.619988 | 0.309994 | − | 0.950739i | \(-0.399673\pi\) | ||||
0.309994 | + | 0.950739i | \(0.399673\pi\) | |||||||
\(684\) | 11.2641 | 0.430695 | ||||||||
\(685\) | 26.2406 | 1.00260 | ||||||||
\(686\) | 38.1393 | 1.45617 | ||||||||
\(687\) | 4.46636 | 0.170402 | ||||||||
\(688\) | 7.28912 | 0.277895 | ||||||||
\(689\) | 27.0949 | 1.03223 | ||||||||
\(690\) | 70.8110 | 2.69573 | ||||||||
\(691\) | 43.6737 | 1.66143 | 0.830713 | − | 0.556701i | \(-0.187933\pi\) | ||||
0.830713 | + | 0.556701i | \(0.187933\pi\) | |||||||
\(692\) | −45.0718 | −1.71337 | ||||||||
\(693\) | 8.88636 | 0.337565 | ||||||||
\(694\) | −22.6264 | −0.858887 | ||||||||
\(695\) | −47.2420 | −1.79199 | ||||||||
\(696\) | 7.91974 | 0.300197 | ||||||||
\(697\) | −10.7539 | −0.407332 | ||||||||
\(698\) | 11.3294 | 0.428825 | ||||||||
\(699\) | 6.53994 | 0.247363 | ||||||||
\(700\) | 27.7364 | 1.04834 | ||||||||
\(701\) | 34.9340 | 1.31944 | 0.659720 | − | 0.751512i | \(-0.270675\pi\) | ||||
0.659720 | + | 0.751512i | \(0.270675\pi\) | |||||||
\(702\) | −13.2450 | −0.499899 | ||||||||
\(703\) | 26.4132 | 0.996192 | ||||||||
\(704\) | −82.4977 | −3.10925 | ||||||||
\(705\) | −6.72982 | −0.253460 | ||||||||
\(706\) | −46.4242 | −1.74720 | ||||||||
\(707\) | −11.3929 | −0.428475 | ||||||||
\(708\) | 8.62021 | 0.323967 | ||||||||
\(709\) | −26.1764 | −0.983076 | −0.491538 | − | 0.870856i | \(-0.663565\pi\) | ||||
−0.491538 | + | 0.870856i | \(0.663565\pi\) | |||||||
\(710\) | −92.5844 | −3.47463 | ||||||||
\(711\) | −2.20634 | −0.0827441 | ||||||||
\(712\) | −44.2139 | −1.65699 | ||||||||
\(713\) | −6.38656 | −0.239178 | ||||||||
\(714\) | 3.12770 | 0.117051 | ||||||||
\(715\) | −125.039 | −4.67619 | ||||||||
\(716\) | −54.7440 | −2.04588 | ||||||||
\(717\) | 9.55138 | 0.356703 | ||||||||
\(718\) | 72.2436 | 2.69611 | ||||||||
\(719\) | −48.8397 | −1.82141 | −0.910707 | − | 0.413052i | \(-0.864463\pi\) | ||||
−0.910707 | + | 0.413052i | \(0.864463\pi\) | |||||||
\(720\) | 2.79337 | 0.104103 | ||||||||
\(721\) | 22.4118 | 0.834660 | ||||||||
\(722\) | 18.9252 | 0.704322 | ||||||||
\(723\) | 16.2977 | 0.606117 | ||||||||
\(724\) | −19.3046 | −0.717450 | ||||||||
\(725\) | 14.5087 | 0.538839 | ||||||||
\(726\) | 76.1652 | 2.82675 | ||||||||
\(727\) | −0.921621 | −0.0341810 | −0.0170905 | − | 0.999854i | \(-0.505440\pi\) | ||||
−0.0170905 | + | 0.999854i | \(0.505440\pi\) | |||||||
\(728\) | 25.2174 | 0.934620 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −47.9501 | −1.77471 | ||||||||
\(731\) | 8.67047 | 0.320689 | ||||||||
\(732\) | 37.1687 | 1.37379 | ||||||||
\(733\) | −20.1621 | −0.744706 | −0.372353 | − | 0.928091i | \(-0.621449\pi\) | ||||
−0.372353 | + | 0.928091i | \(0.621449\pi\) | |||||||
\(734\) | −4.05695 | −0.149745 | ||||||||
\(735\) | 17.2584 | 0.636585 | ||||||||
\(736\) | 42.4690 | 1.56543 | ||||||||
\(737\) | −76.3798 | −2.81349 | ||||||||
\(738\) | 25.0285 | 0.921310 | ||||||||
\(739\) | −11.2639 | −0.414351 | −0.207176 | − | 0.978304i | \(-0.566427\pi\) | ||||
−0.207176 | + | 0.978304i | \(0.566427\pi\) | |||||||
\(740\) | 90.9590 | 3.34372 | ||||||||
\(741\) | 18.7615 | 0.689219 | ||||||||
\(742\) | 14.8913 | 0.546676 | ||||||||
\(743\) | 34.4926 | 1.26541 | 0.632705 | − | 0.774393i | \(-0.281945\pi\) | ||||
0.632705 | + | 0.774393i | \(0.281945\pi\) | |||||||
\(744\) | −2.29983 | −0.0843157 | ||||||||
\(745\) | −61.0935 | −2.23829 | ||||||||
\(746\) | −33.4799 | −1.22579 | ||||||||
\(747\) | 13.4909 | 0.493607 | ||||||||
\(748\) | 22.5934 | 0.826095 | ||||||||
\(749\) | −6.81546 | −0.249032 | ||||||||
\(750\) | 8.04728 | 0.293845 | ||||||||
\(751\) | 12.3314 | 0.449979 | 0.224990 | − | 0.974361i | \(-0.427765\pi\) | ||||
0.224990 | + | 0.974361i | \(0.427765\pi\) | |||||||
\(752\) | 1.70270 | 0.0620912 | ||||||||
\(753\) | 23.7998 | 0.867313 | ||||||||
\(754\) | 31.8126 | 1.15855 | ||||||||
\(755\) | −4.29215 | −0.156207 | ||||||||
\(756\) | −4.59166 | −0.166997 | ||||||||
\(757\) | 3.84629 | 0.139796 | 0.0698978 | − | 0.997554i | \(-0.477733\pi\) | ||||
0.0698978 | + | 0.997554i | \(0.477733\pi\) | |||||||
\(758\) | −45.7498 | −1.66171 | ||||||||
\(759\) | −60.5484 | −2.19777 | ||||||||
\(760\) | −36.1197 | −1.31020 | ||||||||
\(761\) | 16.7457 | 0.607030 | 0.303515 | − | 0.952827i | \(-0.401840\pi\) | ||||
0.303515 | + | 0.952827i | \(0.401840\pi\) | |||||||
\(762\) | 36.3944 | 1.31843 | ||||||||
\(763\) | 18.1207 | 0.656015 | ||||||||
\(764\) | 49.1766 | 1.77915 | ||||||||
\(765\) | 3.32274 | 0.120134 | ||||||||
\(766\) | 58.5775 | 2.11649 | ||||||||
\(767\) | 14.3577 | 0.518428 | ||||||||
\(768\) | 21.0381 | 0.759146 | ||||||||
\(769\) | −27.3621 | −0.986702 | −0.493351 | − | 0.869830i | \(-0.664228\pi\) | ||||
−0.493351 | + | 0.869830i | \(0.664228\pi\) | |||||||
\(770\) | −68.7210 | −2.47653 | ||||||||
\(771\) | 13.8093 | 0.497330 | ||||||||
\(772\) | −70.1562 | −2.52498 | ||||||||
\(773\) | 6.73634 | 0.242289 | 0.121145 | − | 0.992635i | \(-0.461343\pi\) | ||||
0.121145 | + | 0.992635i | \(0.461343\pi\) | |||||||
\(774\) | −20.1796 | −0.725340 | ||||||||
\(775\) | −4.21320 | −0.151343 | ||||||||
\(776\) | 23.6235 | 0.848036 | ||||||||
\(777\) | −10.7669 | −0.386262 | ||||||||
\(778\) | 20.3284 | 0.728807 | ||||||||
\(779\) | −35.4527 | −1.27023 | ||||||||
\(780\) | 64.6087 | 2.31336 | ||||||||
\(781\) | 79.1662 | 2.83279 | ||||||||
\(782\) | −21.3110 | −0.762081 | ||||||||
\(783\) | −2.40186 | −0.0858355 | ||||||||
\(784\) | −4.36653 | −0.155947 | ||||||||
\(785\) | −3.32274 | −0.118594 | ||||||||
\(786\) | −29.9259 | −1.06742 | ||||||||
\(787\) | −13.9835 | −0.498457 | −0.249228 | − | 0.968445i | \(-0.580177\pi\) | ||||
−0.249228 | + | 0.968445i | \(0.580177\pi\) | |||||||
\(788\) | 42.7829 | 1.52408 | ||||||||
\(789\) | 18.3375 | 0.652831 | ||||||||
\(790\) | 17.0623 | 0.607049 | ||||||||
\(791\) | 1.41829 | 0.0504286 | ||||||||
\(792\) | −21.8037 | −0.774761 | ||||||||
\(793\) | 61.9078 | 2.19841 | ||||||||
\(794\) | −37.3528 | −1.32560 | ||||||||
\(795\) | 15.8199 | 0.561072 | ||||||||
\(796\) | 49.8208 | 1.76585 | ||||||||
\(797\) | −14.7852 | −0.523720 | −0.261860 | − | 0.965106i | \(-0.584336\pi\) | ||||
−0.261860 | + | 0.965106i | \(0.584336\pi\) | |||||||
\(798\) | 10.3112 | 0.365014 | ||||||||
\(799\) | 2.02538 | 0.0716528 | ||||||||
\(800\) | 28.0167 | 0.990540 | ||||||||
\(801\) | 13.4090 | 0.473783 | ||||||||
\(802\) | 35.7552 | 1.26256 | ||||||||
\(803\) | 41.0007 | 1.44688 | ||||||||
\(804\) | 39.4661 | 1.39186 | ||||||||
\(805\) | 40.8872 | 1.44108 | ||||||||
\(806\) | −9.23811 | −0.325399 | ||||||||
\(807\) | −6.94847 | −0.244598 | ||||||||
\(808\) | 27.9539 | 0.983414 | ||||||||
\(809\) | 7.68490 | 0.270187 | 0.135093 | − | 0.990833i | \(-0.456867\pi\) | ||||
0.135093 | + | 0.990833i | \(0.456867\pi\) | |||||||
\(810\) | −7.73332 | −0.271721 | ||||||||
\(811\) | 40.3889 | 1.41825 | 0.709123 | − | 0.705085i | \(-0.249091\pi\) | ||||
0.709123 | + | 0.705085i | \(0.249091\pi\) | |||||||
\(812\) | 11.0285 | 0.387025 | ||||||||
\(813\) | −17.5830 | −0.616663 | ||||||||
\(814\) | −123.303 | −4.32176 | ||||||||
\(815\) | 45.8067 | 1.60454 | ||||||||
\(816\) | −0.840683 | −0.0294298 | ||||||||
\(817\) | 28.5843 | 1.00004 | ||||||||
\(818\) | 4.63453 | 0.162043 | ||||||||
\(819\) | −7.64783 | −0.267237 | ||||||||
\(820\) | −122.088 | −4.26351 | ||||||||
\(821\) | 47.1690 | 1.64621 | 0.823104 | − | 0.567890i | \(-0.192240\pi\) | ||||
0.823104 | + | 0.567890i | \(0.192240\pi\) | |||||||
\(822\) | 18.3800 | 0.641078 | ||||||||
\(823\) | −47.1418 | −1.64326 | −0.821630 | − | 0.570022i | \(-0.806935\pi\) | ||||
−0.821630 | + | 0.570022i | \(0.806935\pi\) | |||||||
\(824\) | −54.9900 | −1.91567 | ||||||||
\(825\) | −39.9436 | −1.39066 | ||||||||
\(826\) | 7.89097 | 0.274562 | ||||||||
\(827\) | −2.32575 | −0.0808742 | −0.0404371 | − | 0.999182i | \(-0.512875\pi\) | ||||
−0.0404371 | + | 0.999182i | \(0.512875\pi\) | |||||||
\(828\) | 31.2859 | 1.08726 | ||||||||
\(829\) | −1.25975 | −0.0437529 | −0.0218765 | − | 0.999761i | \(-0.506964\pi\) | ||||
−0.0218765 | + | 0.999761i | \(0.506964\pi\) | |||||||
\(830\) | −104.330 | −3.62133 | ||||||||
\(831\) | −18.1426 | −0.629360 | ||||||||
\(832\) | 70.9996 | 2.46147 | ||||||||
\(833\) | −5.19402 | −0.179962 | ||||||||
\(834\) | −33.0904 | −1.14583 | ||||||||
\(835\) | 52.8320 | 1.82833 | ||||||||
\(836\) | 74.4845 | 2.57610 | ||||||||
\(837\) | 0.697480 | 0.0241084 | ||||||||
\(838\) | −30.2397 | −1.04461 | ||||||||
\(839\) | 39.2346 | 1.35453 | 0.677264 | − | 0.735740i | \(-0.263166\pi\) | ||||
0.677264 | + | 0.735740i | \(0.263166\pi\) | |||||||
\(840\) | 14.7236 | 0.508014 | ||||||||
\(841\) | −23.2311 | −0.801071 | ||||||||
\(842\) | 16.1361 | 0.556088 | ||||||||
\(843\) | 2.37433 | 0.0817764 | ||||||||
\(844\) | 11.2007 | 0.385544 | ||||||||
\(845\) | 64.4161 | 2.21598 | ||||||||
\(846\) | −4.71386 | −0.162066 | ||||||||
\(847\) | 43.9788 | 1.51113 | ||||||||
\(848\) | −4.00257 | −0.137449 | ||||||||
\(849\) | −25.0080 | −0.858274 | ||||||||
\(850\) | −14.0588 | −0.482214 | ||||||||
\(851\) | 73.3619 | 2.51481 | ||||||||
\(852\) | −40.9059 | −1.40141 | ||||||||
\(853\) | 0.193812 | 0.00663599 | 0.00331800 | − | 0.999994i | \(-0.498944\pi\) | ||||
0.00331800 | + | 0.999994i | \(0.498944\pi\) | |||||||
\(854\) | 34.0243 | 1.16429 | ||||||||
\(855\) | 10.9542 | 0.374626 | ||||||||
\(856\) | 16.7225 | 0.571564 | ||||||||
\(857\) | 11.1660 | 0.381424 | 0.190712 | − | 0.981646i | \(-0.438920\pi\) | ||||
0.190712 | + | 0.981646i | \(0.438920\pi\) | |||||||
\(858\) | −87.5828 | −2.99003 | ||||||||
\(859\) | 37.7779 | 1.28897 | 0.644483 | − | 0.764619i | \(-0.277073\pi\) | ||||
0.644483 | + | 0.764619i | \(0.277073\pi\) | |||||||
\(860\) | 98.4356 | 3.35663 | ||||||||
\(861\) | 14.4518 | 0.492515 | ||||||||
\(862\) | −36.7892 | −1.25305 | ||||||||
\(863\) | 36.3519 | 1.23743 | 0.618716 | − | 0.785615i | \(-0.287653\pi\) | ||||
0.618716 | + | 0.785615i | \(0.287653\pi\) | |||||||
\(864\) | −4.63807 | −0.157790 | ||||||||
\(865\) | −43.8316 | −1.49032 | ||||||||
\(866\) | −45.9894 | −1.56278 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −3.20259 | −0.108703 | ||||||||
\(869\) | −14.5895 | −0.494914 | ||||||||
\(870\) | 18.5744 | 0.629729 | ||||||||
\(871\) | 65.7344 | 2.22732 | ||||||||
\(872\) | −44.4613 | −1.50565 | ||||||||
\(873\) | −7.16444 | −0.242479 | ||||||||
\(874\) | −70.2569 | −2.37648 | ||||||||
\(875\) | 4.64661 | 0.157084 | ||||||||
\(876\) | −21.1854 | −0.715789 | ||||||||
\(877\) | 1.64946 | 0.0556984 | 0.0278492 | − | 0.999612i | \(-0.491134\pi\) | ||||
0.0278492 | + | 0.999612i | \(0.491134\pi\) | |||||||
\(878\) | 32.5041 | 1.09696 | ||||||||
\(879\) | 7.01012 | 0.236445 | ||||||||
\(880\) | 18.4713 | 0.622666 | ||||||||
\(881\) | −16.5085 | −0.556186 | −0.278093 | − | 0.960554i | \(-0.589702\pi\) | ||||
−0.278093 | + | 0.960554i | \(0.589702\pi\) | |||||||
\(882\) | 12.0885 | 0.407042 | ||||||||
\(883\) | −6.45829 | −0.217339 | −0.108669 | − | 0.994078i | \(-0.534659\pi\) | ||||
−0.108669 | + | 0.994078i | \(0.534659\pi\) | |||||||
\(884\) | −19.4444 | −0.653987 | ||||||||
\(885\) | 8.38303 | 0.281792 | ||||||||
\(886\) | 26.9274 | 0.904645 | ||||||||
\(887\) | 0.737297 | 0.0247560 | 0.0123780 | − | 0.999923i | \(-0.496060\pi\) | ||||
0.0123780 | + | 0.999923i | \(0.496060\pi\) | |||||||
\(888\) | 26.4179 | 0.886527 | ||||||||
\(889\) | 21.0146 | 0.704807 | ||||||||
\(890\) | −103.696 | −3.47590 | ||||||||
\(891\) | 6.61253 | 0.221528 | ||||||||
\(892\) | 14.2366 | 0.476677 | ||||||||
\(893\) | 6.67716 | 0.223443 | ||||||||
\(894\) | −42.7925 | −1.43120 | ||||||||
\(895\) | −53.2377 | −1.77954 | ||||||||
\(896\) | 26.5552 | 0.887148 | ||||||||
\(897\) | 52.1095 | 1.73988 | ||||||||
\(898\) | 91.8565 | 3.06529 | ||||||||
\(899\) | −1.67525 | −0.0558728 | ||||||||
\(900\) | 20.6392 | 0.687974 | ||||||||
\(901\) | −4.76109 | −0.158615 | ||||||||
\(902\) | 165.501 | 5.51059 | ||||||||
\(903\) | −11.6520 | −0.387753 | ||||||||
\(904\) | −3.47994 | −0.115741 | ||||||||
\(905\) | −18.7734 | −0.624050 | ||||||||
\(906\) | −3.00641 | −0.0998812 | ||||||||
\(907\) | 5.40099 | 0.179337 | 0.0896685 | − | 0.995972i | \(-0.471419\pi\) | ||||
0.0896685 | + | 0.995972i | \(0.471419\pi\) | |||||||
\(908\) | 74.9468 | 2.48720 | ||||||||
\(909\) | −8.47772 | −0.281188 | ||||||||
\(910\) | 59.1431 | 1.96057 | ||||||||
\(911\) | 50.3897 | 1.66949 | 0.834743 | − | 0.550639i | \(-0.185616\pi\) | ||||
0.834743 | + | 0.550639i | \(0.185616\pi\) | |||||||
\(912\) | −2.77152 | −0.0917740 | ||||||||
\(913\) | 89.2091 | 2.95239 | ||||||||
\(914\) | 70.1560 | 2.32055 | ||||||||
\(915\) | 36.1460 | 1.19495 | ||||||||
\(916\) | −15.2604 | −0.504219 | ||||||||
\(917\) | −17.2796 | −0.570622 | ||||||||
\(918\) | 2.32739 | 0.0768154 | ||||||||
\(919\) | −51.5149 | −1.69932 | −0.849659 | − | 0.527332i | \(-0.823192\pi\) | ||||
−0.849659 | + | 0.527332i | \(0.823192\pi\) | |||||||
\(920\) | −100.321 | −3.30750 | ||||||||
\(921\) | 23.0077 | 0.758131 | ||||||||
\(922\) | 3.06993 | 0.101103 | ||||||||
\(923\) | −68.1324 | −2.24261 | ||||||||
\(924\) | −30.3625 | −0.998852 | ||||||||
\(925\) | 48.3967 | 1.59127 | ||||||||
\(926\) | −67.8005 | −2.22806 | ||||||||
\(927\) | 16.6771 | 0.547748 | ||||||||
\(928\) | 11.1400 | 0.365688 | ||||||||
\(929\) | 9.22204 | 0.302565 | 0.151283 | − | 0.988491i | \(-0.451660\pi\) | ||||
0.151283 | + | 0.988491i | \(0.451660\pi\) | |||||||
\(930\) | −5.39384 | −0.176871 | ||||||||
\(931\) | −17.1233 | −0.561195 | ||||||||
\(932\) | −22.3453 | −0.731946 | ||||||||
\(933\) | −5.75350 | −0.188361 | ||||||||
\(934\) | 68.3043 | 2.23499 | ||||||||
\(935\) | 21.9717 | 0.718552 | ||||||||
\(936\) | 18.7648 | 0.613347 | ||||||||
\(937\) | 6.78658 | 0.221708 | 0.110854 | − | 0.993837i | \(-0.464641\pi\) | ||||
0.110854 | + | 0.993837i | \(0.464641\pi\) | |||||||
\(938\) | 36.1274 | 1.17960 | ||||||||
\(939\) | 6.84090 | 0.223244 | ||||||||
\(940\) | 22.9941 | 0.749985 | ||||||||
\(941\) | −42.1257 | −1.37326 | −0.686630 | − | 0.727008i | \(-0.740911\pi\) | ||||
−0.686630 | + | 0.727008i | \(0.740911\pi\) | |||||||
\(942\) | −2.32739 | −0.0758305 | ||||||||
\(943\) | −98.4690 | −3.20659 | ||||||||
\(944\) | −2.12098 | −0.0690321 | ||||||||
\(945\) | −4.46532 | −0.145257 | ||||||||
\(946\) | −133.438 | −4.33844 | ||||||||
\(947\) | −11.0615 | −0.359450 | −0.179725 | − | 0.983717i | \(-0.557521\pi\) | ||||
−0.179725 | + | 0.983717i | \(0.557521\pi\) | |||||||
\(948\) | 7.53850 | 0.244839 | ||||||||
\(949\) | −35.2862 | −1.14544 | ||||||||
\(950\) | −46.3484 | −1.50374 | ||||||||
\(951\) | −10.4124 | −0.337645 | ||||||||
\(952\) | −4.43118 | −0.143615 | ||||||||
\(953\) | −3.12289 | −0.101160 | −0.0505802 | − | 0.998720i | \(-0.516107\pi\) | ||||
−0.0505802 | + | 0.998720i | \(0.516107\pi\) | |||||||
\(954\) | 11.0809 | 0.358758 | ||||||||
\(955\) | 47.8235 | 1.54753 | ||||||||
\(956\) | −32.6347 | −1.05548 | ||||||||
\(957\) | −15.8824 | −0.513404 | ||||||||
\(958\) | −59.4644 | −1.92121 | ||||||||
\(959\) | 10.6129 | 0.342708 | ||||||||
\(960\) | 41.4544 | 1.33793 | ||||||||
\(961\) | −30.5135 | −0.984307 | ||||||||
\(962\) | 106.117 | 3.42137 | ||||||||
\(963\) | −5.07153 | −0.163428 | ||||||||
\(964\) | −55.6851 | −1.79350 | ||||||||
\(965\) | −68.2259 | −2.19627 | ||||||||
\(966\) | 28.6392 | 0.921451 | ||||||||
\(967\) | 7.84030 | 0.252127 | 0.126064 | − | 0.992022i | \(-0.459766\pi\) | ||||
0.126064 | + | 0.992022i | \(0.459766\pi\) | |||||||
\(968\) | −107.907 | −3.46826 | ||||||||
\(969\) | −3.29674 | −0.105907 | ||||||||
\(970\) | 55.4049 | 1.77894 | ||||||||
\(971\) | 29.7540 | 0.954851 | 0.477425 | − | 0.878672i | \(-0.341570\pi\) | ||||
0.477425 | + | 0.878672i | \(0.341570\pi\) | |||||||
\(972\) | −3.41675 | −0.109592 | ||||||||
\(973\) | −19.1068 | −0.612537 | ||||||||
\(974\) | 89.7077 | 2.87442 | ||||||||
\(975\) | 34.3765 | 1.10093 | ||||||||
\(976\) | −9.14526 | −0.292733 | ||||||||
\(977\) | −12.4161 | −0.397227 | −0.198614 | − | 0.980078i | \(-0.563644\pi\) | ||||
−0.198614 | + | 0.980078i | \(0.563644\pi\) | |||||||
\(978\) | 32.0850 | 1.02597 | ||||||||
\(979\) | 88.6673 | 2.83382 | ||||||||
\(980\) | −58.9676 | −1.88365 | ||||||||
\(981\) | 13.4840 | 0.430512 | ||||||||
\(982\) | 27.7714 | 0.886221 | ||||||||
\(983\) | 0.206575 | 0.00658871 | 0.00329436 | − | 0.999995i | \(-0.498951\pi\) | ||||
0.00329436 | + | 0.999995i | \(0.498951\pi\) | |||||||
\(984\) | −35.4591 | −1.13039 | ||||||||
\(985\) | 41.6057 | 1.32567 | ||||||||
\(986\) | −5.59007 | −0.178024 | ||||||||
\(987\) | −2.72184 | −0.0866372 | ||||||||
\(988\) | −64.1032 | −2.03940 | ||||||||
\(989\) | 79.3921 | 2.52452 | ||||||||
\(990\) | −51.1368 | −1.62523 | ||||||||
\(991\) | 10.2608 | 0.325944 | 0.162972 | − | 0.986631i | \(-0.447892\pi\) | ||||
0.162972 | + | 0.986631i | \(0.447892\pi\) | |||||||
\(992\) | −3.23496 | −0.102710 | ||||||||
\(993\) | 35.5826 | 1.12918 | ||||||||
\(994\) | −37.4454 | −1.18769 | ||||||||
\(995\) | 48.4500 | 1.53597 | ||||||||
\(996\) | −46.0951 | −1.46058 | ||||||||
\(997\) | −10.8776 | −0.344497 | −0.172248 | − | 0.985054i | \(-0.555103\pi\) | ||||
−0.172248 | + | 0.985054i | \(0.555103\pi\) | |||||||
\(998\) | 70.8501 | 2.24272 | ||||||||
\(999\) | −8.01191 | −0.253486 |
(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 | 8007.2.a.j.1.9 | ✓ | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.j.1.9 | ✓ | 64 | 1.1 | even | 1 | trivial |