Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4235,2,Mod(1,4235)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4235, 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("4235.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4235 = 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4235.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: | \(33.8166452560\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 2 x^{17} - 28 x^{16} + 54 x^{15} + 317 x^{14} - 580 x^{13} - 1874 x^{12} + 3158 x^{11} + 6290 x^{10} - 9228 x^{9} - 12411 x^{8} + 14224 x^{7} + 14618 x^{6} - 10744 x^{5} + \cdots - 176 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 385) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.35862\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4235.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.35862 | −1.66780 | −0.833898 | − | 0.551919i | \(-0.813896\pi\) | ||||
−0.833898 | + | 0.551919i | \(0.813896\pi\) | |||||||
\(3\) | 3.12567 | 1.80461 | 0.902304 | − | 0.431100i | \(-0.141874\pi\) | ||||
0.902304 | + | 0.431100i | \(0.141874\pi\) | |||||||
\(4\) | 3.56309 | 1.78154 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −7.37227 | −3.00972 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −3.68672 | −1.30345 | ||||||||
\(9\) | 6.76983 | 2.25661 | ||||||||
\(10\) | −2.35862 | −0.745861 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 11.1370 | 3.21499 | ||||||||
\(13\) | −0.303615 | −0.0842076 | −0.0421038 | − | 0.999113i | \(-0.513406\pi\) | ||||
−0.0421038 | + | 0.999113i | \(0.513406\pi\) | |||||||
\(14\) | −2.35862 | −0.630368 | ||||||||
\(15\) | 3.12567 | 0.807045 | ||||||||
\(16\) | 1.56941 | 0.392352 | ||||||||
\(17\) | 1.03365 | 0.250698 | 0.125349 | − | 0.992113i | \(-0.459995\pi\) | ||||
0.125349 | + | 0.992113i | \(0.459995\pi\) | |||||||
\(18\) | −15.9675 | −3.76357 | ||||||||
\(19\) | 5.12290 | 1.17527 | 0.587636 | − | 0.809125i | \(-0.300059\pi\) | ||||
0.587636 | + | 0.809125i | \(0.300059\pi\) | |||||||
\(20\) | 3.56309 | 0.796730 | ||||||||
\(21\) | 3.12567 | 0.682078 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.52137 | 1.77683 | 0.888414 | − | 0.459043i | \(-0.151808\pi\) | ||||
0.888414 | + | 0.459043i | \(0.151808\pi\) | |||||||
\(24\) | −11.5235 | −2.35222 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.716112 | 0.140441 | ||||||||
\(27\) | 11.7833 | 2.26769 | ||||||||
\(28\) | 3.56309 | 0.673360 | ||||||||
\(29\) | −4.31946 | −0.802103 | −0.401052 | − | 0.916055i | \(-0.631355\pi\) | ||||
−0.401052 | + | 0.916055i | \(0.631355\pi\) | |||||||
\(30\) | −7.37227 | −1.34599 | ||||||||
\(31\) | −2.64939 | −0.475844 | −0.237922 | − | 0.971284i | \(-0.576466\pi\) | ||||
−0.237922 | + | 0.971284i | \(0.576466\pi\) | |||||||
\(32\) | 3.67181 | 0.649091 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.43800 | −0.418113 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 24.1215 | 4.02025 | ||||||||
\(37\) | −2.27545 | −0.374081 | −0.187041 | − | 0.982352i | \(-0.559890\pi\) | ||||
−0.187041 | + | 0.982352i | \(0.559890\pi\) | |||||||
\(38\) | −12.0830 | −1.96011 | ||||||||
\(39\) | −0.949001 | −0.151962 | ||||||||
\(40\) | −3.68672 | −0.582922 | ||||||||
\(41\) | 9.65845 | 1.50840 | 0.754198 | − | 0.656647i | \(-0.228026\pi\) | ||||
0.754198 | + | 0.656647i | \(0.228026\pi\) | |||||||
\(42\) | −7.37227 | −1.13757 | ||||||||
\(43\) | −1.37993 | −0.210438 | −0.105219 | − | 0.994449i | \(-0.533554\pi\) | ||||
−0.105219 | + | 0.994449i | \(0.533554\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.76983 | 1.00919 | ||||||||
\(46\) | −20.0987 | −2.96339 | ||||||||
\(47\) | 1.07602 | 0.156953 | 0.0784765 | − | 0.996916i | \(-0.474994\pi\) | ||||
0.0784765 | + | 0.996916i | \(0.474994\pi\) | |||||||
\(48\) | 4.90546 | 0.708042 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.35862 | −0.333559 | ||||||||
\(51\) | 3.23087 | 0.452412 | ||||||||
\(52\) | −1.08181 | −0.150019 | ||||||||
\(53\) | −9.21775 | −1.26616 | −0.633078 | − | 0.774088i | \(-0.718209\pi\) | ||||
−0.633078 | + | 0.774088i | \(0.718209\pi\) | |||||||
\(54\) | −27.7923 | −3.78205 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.68672 | −0.492659 | ||||||||
\(57\) | 16.0125 | 2.12091 | ||||||||
\(58\) | 10.1880 | 1.33774 | ||||||||
\(59\) | −8.81202 | −1.14723 | −0.573614 | − | 0.819126i | \(-0.694459\pi\) | ||||
−0.573614 | + | 0.819126i | \(0.694459\pi\) | |||||||
\(60\) | 11.1370 | 1.43779 | ||||||||
\(61\) | 10.5463 | 1.35031 | 0.675155 | − | 0.737675i | \(-0.264077\pi\) | ||||
0.675155 | + | 0.737675i | \(0.264077\pi\) | |||||||
\(62\) | 6.24889 | 0.793610 | ||||||||
\(63\) | 6.76983 | 0.852919 | ||||||||
\(64\) | −11.7992 | −1.47490 | ||||||||
\(65\) | −0.303615 | −0.0376588 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.6999 | 1.67371 | 0.836854 | − | 0.547427i | \(-0.184392\pi\) | ||||
0.836854 | + | 0.547427i | \(0.184392\pi\) | |||||||
\(68\) | 3.68300 | 0.446629 | ||||||||
\(69\) | 26.6350 | 3.20648 | ||||||||
\(70\) | −2.35862 | −0.281909 | ||||||||
\(71\) | −7.14373 | −0.847805 | −0.423903 | − | 0.905708i | \(-0.639340\pi\) | ||||
−0.423903 | + | 0.905708i | \(0.639340\pi\) | |||||||
\(72\) | −24.9585 | −2.94139 | ||||||||
\(73\) | −16.1243 | −1.88721 | −0.943605 | − | 0.331075i | \(-0.892589\pi\) | ||||
−0.943605 | + | 0.331075i | \(0.892589\pi\) | |||||||
\(74\) | 5.36691 | 0.623891 | ||||||||
\(75\) | 3.12567 | 0.360922 | ||||||||
\(76\) | 18.2533 | 2.09380 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.23833 | 0.253441 | ||||||||
\(79\) | 0.573402 | 0.0645127 | 0.0322564 | − | 0.999480i | \(-0.489731\pi\) | ||||
0.0322564 | + | 0.999480i | \(0.489731\pi\) | |||||||
\(80\) | 1.56941 | 0.175465 | ||||||||
\(81\) | 16.5212 | 1.83568 | ||||||||
\(82\) | −22.7806 | −2.51570 | ||||||||
\(83\) | −11.2134 | −1.23083 | −0.615413 | − | 0.788205i | \(-0.711011\pi\) | ||||
−0.615413 | + | 0.788205i | \(0.711011\pi\) | |||||||
\(84\) | 11.1370 | 1.21515 | ||||||||
\(85\) | 1.03365 | 0.112116 | ||||||||
\(86\) | 3.25473 | 0.350967 | ||||||||
\(87\) | −13.5012 | −1.44748 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.3947 | −1.52583 | −0.762917 | − | 0.646496i | \(-0.776234\pi\) | ||||
−0.762917 | + | 0.646496i | \(0.776234\pi\) | |||||||
\(90\) | −15.9675 | −1.68312 | ||||||||
\(91\) | −0.303615 | −0.0318275 | ||||||||
\(92\) | 30.3624 | 3.16550 | ||||||||
\(93\) | −8.28111 | −0.858712 | ||||||||
\(94\) | −2.53791 | −0.261766 | ||||||||
\(95\) | 5.12290 | 0.525598 | ||||||||
\(96\) | 11.4769 | 1.17135 | ||||||||
\(97\) | −3.94258 | −0.400308 | −0.200154 | − | 0.979764i | \(-0.564144\pi\) | ||||
−0.200154 | + | 0.979764i | \(0.564144\pi\) | |||||||
\(98\) | −2.35862 | −0.238257 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.56309 | 0.356309 | ||||||||
\(101\) | 10.1902 | 1.01397 | 0.506983 | − | 0.861956i | \(-0.330761\pi\) | ||||
0.506983 | + | 0.861956i | \(0.330761\pi\) | |||||||
\(102\) | −7.62038 | −0.754530 | ||||||||
\(103\) | 18.4463 | 1.81757 | 0.908783 | − | 0.417269i | \(-0.137013\pi\) | ||||
0.908783 | + | 0.417269i | \(0.137013\pi\) | |||||||
\(104\) | 1.11934 | 0.109761 | ||||||||
\(105\) | 3.12567 | 0.305034 | ||||||||
\(106\) | 21.7412 | 2.11169 | ||||||||
\(107\) | −17.9196 | −1.73235 | −0.866176 | − | 0.499738i | \(-0.833430\pi\) | ||||
−0.866176 | + | 0.499738i | \(0.833430\pi\) | |||||||
\(108\) | 41.9848 | 4.03999 | ||||||||
\(109\) | −1.01822 | −0.0975276 | −0.0487638 | − | 0.998810i | \(-0.515528\pi\) | ||||
−0.0487638 | + | 0.998810i | \(0.515528\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.11230 | −0.675070 | ||||||||
\(112\) | 1.56941 | 0.148295 | ||||||||
\(113\) | −1.79756 | −0.169100 | −0.0845501 | − | 0.996419i | \(-0.526945\pi\) | ||||
−0.0845501 | + | 0.996419i | \(0.526945\pi\) | |||||||
\(114\) | −37.7674 | −3.53724 | ||||||||
\(115\) | 8.52137 | 0.794622 | ||||||||
\(116\) | −15.3906 | −1.42898 | ||||||||
\(117\) | −2.05542 | −0.190024 | ||||||||
\(118\) | 20.7842 | 1.91334 | ||||||||
\(119\) | 1.03365 | 0.0947549 | ||||||||
\(120\) | −11.5235 | −1.05195 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −24.8746 | −2.25204 | ||||||||
\(123\) | 30.1892 | 2.72206 | ||||||||
\(124\) | −9.43999 | −0.847736 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −15.9675 | −1.42249 | ||||||||
\(127\) | 11.2516 | 0.998417 | 0.499209 | − | 0.866482i | \(-0.333624\pi\) | ||||
0.499209 | + | 0.866482i | \(0.333624\pi\) | |||||||
\(128\) | 20.4863 | 1.81075 | ||||||||
\(129\) | −4.31321 | −0.379757 | ||||||||
\(130\) | 0.716112 | 0.0628072 | ||||||||
\(131\) | −3.75923 | −0.328445 | −0.164223 | − | 0.986423i | \(-0.552512\pi\) | ||||
−0.164223 | + | 0.986423i | \(0.552512\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.12290 | 0.444211 | ||||||||
\(134\) | −32.3128 | −2.79140 | ||||||||
\(135\) | 11.7833 | 1.01414 | ||||||||
\(136\) | −3.81080 | −0.326773 | ||||||||
\(137\) | 15.0871 | 1.28898 | 0.644490 | − | 0.764613i | \(-0.277070\pi\) | ||||
0.644490 | + | 0.764613i | \(0.277070\pi\) | |||||||
\(138\) | −62.8219 | −5.34775 | ||||||||
\(139\) | 13.3265 | 1.13034 | 0.565171 | − | 0.824974i | \(-0.308810\pi\) | ||||
0.565171 | + | 0.824974i | \(0.308810\pi\) | |||||||
\(140\) | 3.56309 | 0.301136 | ||||||||
\(141\) | 3.36327 | 0.283239 | ||||||||
\(142\) | 16.8493 | 1.41397 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 10.6246 | 0.885386 | ||||||||
\(145\) | −4.31946 | −0.358712 | ||||||||
\(146\) | 38.0311 | 3.14748 | ||||||||
\(147\) | 3.12567 | 0.257801 | ||||||||
\(148\) | −8.10761 | −0.666441 | ||||||||
\(149\) | −2.12769 | −0.174307 | −0.0871534 | − | 0.996195i | \(-0.527777\pi\) | ||||
−0.0871534 | + | 0.996195i | \(0.527777\pi\) | |||||||
\(150\) | −7.37227 | −0.601944 | ||||||||
\(151\) | 15.7506 | 1.28177 | 0.640883 | − | 0.767639i | \(-0.278568\pi\) | ||||
0.640883 | + | 0.767639i | \(0.278568\pi\) | |||||||
\(152\) | −18.8867 | −1.53191 | ||||||||
\(153\) | 6.99767 | 0.565728 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.64939 | −0.212804 | ||||||||
\(156\) | −3.38137 | −0.270726 | ||||||||
\(157\) | −8.52511 | −0.680378 | −0.340189 | − | 0.940357i | \(-0.610491\pi\) | ||||
−0.340189 | + | 0.940357i | \(0.610491\pi\) | |||||||
\(158\) | −1.35244 | −0.107594 | ||||||||
\(159\) | −28.8117 | −2.28491 | ||||||||
\(160\) | 3.67181 | 0.290282 | ||||||||
\(161\) | 8.52137 | 0.671578 | ||||||||
\(162\) | −38.9671 | −3.06155 | ||||||||
\(163\) | −12.1811 | −0.954097 | −0.477049 | − | 0.878877i | \(-0.658293\pi\) | ||||
−0.477049 | + | 0.878877i | \(0.658293\pi\) | |||||||
\(164\) | 34.4139 | 2.68727 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 26.4480 | 2.05277 | ||||||||
\(167\) | −8.44915 | −0.653815 | −0.326908 | − | 0.945056i | \(-0.606007\pi\) | ||||
−0.326908 | + | 0.945056i | \(0.606007\pi\) | |||||||
\(168\) | −11.5235 | −0.889057 | ||||||||
\(169\) | −12.9078 | −0.992909 | ||||||||
\(170\) | −2.43800 | −0.186986 | ||||||||
\(171\) | 34.6812 | 2.65213 | ||||||||
\(172\) | −4.91681 | −0.374904 | ||||||||
\(173\) | −8.85874 | −0.673517 | −0.336759 | − | 0.941591i | \(-0.609331\pi\) | ||||
−0.336759 | + | 0.941591i | \(0.609331\pi\) | |||||||
\(174\) | 31.8442 | 2.41411 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −27.5435 | −2.07030 | ||||||||
\(178\) | 33.9516 | 2.54478 | ||||||||
\(179\) | 8.08279 | 0.604136 | 0.302068 | − | 0.953286i | \(-0.402323\pi\) | ||||
0.302068 | + | 0.953286i | \(0.402323\pi\) | |||||||
\(180\) | 24.1215 | 1.79791 | ||||||||
\(181\) | −1.35065 | −0.100393 | −0.0501966 | − | 0.998739i | \(-0.515985\pi\) | ||||
−0.0501966 | + | 0.998739i | \(0.515985\pi\) | |||||||
\(182\) | 0.716112 | 0.0530818 | ||||||||
\(183\) | 32.9642 | 2.43678 | ||||||||
\(184\) | −31.4159 | −2.31601 | ||||||||
\(185\) | −2.27545 | −0.167294 | ||||||||
\(186\) | 19.5320 | 1.43216 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.83394 | 0.279618 | ||||||||
\(189\) | 11.7833 | 0.857107 | ||||||||
\(190\) | −12.0830 | −0.876590 | ||||||||
\(191\) | 12.2917 | 0.889396 | 0.444698 | − | 0.895680i | \(-0.353311\pi\) | ||||
0.444698 | + | 0.895680i | \(0.353311\pi\) | |||||||
\(192\) | −36.8805 | −2.66162 | ||||||||
\(193\) | 18.5658 | 1.33640 | 0.668198 | − | 0.743983i | \(-0.267066\pi\) | ||||
0.668198 | + | 0.743983i | \(0.267066\pi\) | |||||||
\(194\) | 9.29904 | 0.667633 | ||||||||
\(195\) | −0.949001 | −0.0679594 | ||||||||
\(196\) | 3.56309 | 0.254506 | ||||||||
\(197\) | 12.8716 | 0.917062 | 0.458531 | − | 0.888678i | \(-0.348376\pi\) | ||||
0.458531 | + | 0.888678i | \(0.348376\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.93245 | 0.704093 | 0.352046 | − | 0.935983i | \(-0.385486\pi\) | ||||
0.352046 | + | 0.935983i | \(0.385486\pi\) | |||||||
\(200\) | −3.68672 | −0.260691 | ||||||||
\(201\) | 42.8214 | 3.02039 | ||||||||
\(202\) | −24.0349 | −1.69109 | ||||||||
\(203\) | −4.31946 | −0.303167 | ||||||||
\(204\) | 11.5119 | 0.805991 | ||||||||
\(205\) | 9.65845 | 0.674575 | ||||||||
\(206\) | −43.5078 | −3.03133 | ||||||||
\(207\) | 57.6882 | 4.00961 | ||||||||
\(208\) | −0.476496 | −0.0330390 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −7.37227 | −0.508735 | ||||||||
\(211\) | 17.1478 | 1.18050 | 0.590252 | − | 0.807219i | \(-0.299028\pi\) | ||||
0.590252 | + | 0.807219i | \(0.299028\pi\) | |||||||
\(212\) | −32.8436 | −2.25571 | ||||||||
\(213\) | −22.3290 | −1.52996 | ||||||||
\(214\) | 42.2655 | 2.88921 | ||||||||
\(215\) | −1.37993 | −0.0941105 | ||||||||
\(216\) | −43.4417 | −2.95583 | ||||||||
\(217\) | −2.64939 | −0.179852 | ||||||||
\(218\) | 2.40159 | 0.162656 | ||||||||
\(219\) | −50.3994 | −3.40567 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.313833 | −0.0211107 | ||||||||
\(222\) | 16.7752 | 1.12588 | ||||||||
\(223\) | 15.3328 | 1.02676 | 0.513380 | − | 0.858161i | \(-0.328393\pi\) | ||||
0.513380 | + | 0.858161i | \(0.328393\pi\) | |||||||
\(224\) | 3.67181 | 0.245333 | ||||||||
\(225\) | 6.76983 | 0.451322 | ||||||||
\(226\) | 4.23976 | 0.282025 | ||||||||
\(227\) | 2.01861 | 0.133980 | 0.0669899 | − | 0.997754i | \(-0.478660\pi\) | ||||
0.0669899 | + | 0.997754i | \(0.478660\pi\) | |||||||
\(228\) | 57.0539 | 3.77849 | ||||||||
\(229\) | −0.312306 | −0.0206377 | −0.0103189 | − | 0.999947i | \(-0.503285\pi\) | ||||
−0.0103189 | + | 0.999947i | \(0.503285\pi\) | |||||||
\(230\) | −20.0987 | −1.32527 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 15.9247 | 1.04550 | ||||||||
\(233\) | −17.3822 | −1.13874 | −0.569371 | − | 0.822080i | \(-0.692813\pi\) | ||||
−0.569371 | + | 0.822080i | \(0.692813\pi\) | |||||||
\(234\) | 4.84796 | 0.316921 | ||||||||
\(235\) | 1.07602 | 0.0701915 | ||||||||
\(236\) | −31.3980 | −2.04383 | ||||||||
\(237\) | 1.79227 | 0.116420 | ||||||||
\(238\) | −2.43800 | −0.158032 | ||||||||
\(239\) | −22.6580 | −1.46562 | −0.732812 | − | 0.680431i | \(-0.761793\pi\) | ||||
−0.732812 | + | 0.680431i | \(0.761793\pi\) | |||||||
\(240\) | 4.90546 | 0.316646 | ||||||||
\(241\) | −6.28549 | −0.404884 | −0.202442 | − | 0.979294i | \(-0.564888\pi\) | ||||
−0.202442 | + | 0.979294i | \(0.564888\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.2899 | 1.04500 | ||||||||
\(244\) | 37.5772 | 2.40564 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −71.2047 | −4.53985 | ||||||||
\(247\) | −1.55539 | −0.0989669 | ||||||||
\(248\) | 9.76755 | 0.620240 | ||||||||
\(249\) | −35.0493 | −2.22116 | ||||||||
\(250\) | −2.35862 | −0.149172 | ||||||||
\(251\) | −10.6760 | −0.673861 | −0.336931 | − | 0.941529i | \(-0.609389\pi\) | ||||
−0.336931 | + | 0.941529i | \(0.609389\pi\) | |||||||
\(252\) | 24.1215 | 1.51951 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −26.5382 | −1.66516 | ||||||||
\(255\) | 3.23087 | 0.202325 | ||||||||
\(256\) | −24.7208 | −1.54505 | ||||||||
\(257\) | −17.6734 | −1.10244 | −0.551220 | − | 0.834360i | \(-0.685837\pi\) | ||||
−0.551220 | + | 0.834360i | \(0.685837\pi\) | |||||||
\(258\) | 10.1732 | 0.633358 | ||||||||
\(259\) | −2.27545 | −0.141389 | ||||||||
\(260\) | −1.08181 | −0.0670908 | ||||||||
\(261\) | −29.2420 | −1.81004 | ||||||||
\(262\) | 8.86659 | 0.547780 | ||||||||
\(263\) | −12.2684 | −0.756499 | −0.378250 | − | 0.925704i | \(-0.623474\pi\) | ||||
−0.378250 | + | 0.925704i | \(0.623474\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.21775 | −0.566242 | ||||||||
\(266\) | −12.0830 | −0.740854 | ||||||||
\(267\) | −44.9931 | −2.75353 | ||||||||
\(268\) | 48.8139 | 2.98178 | ||||||||
\(269\) | 21.5065 | 1.31128 | 0.655639 | − | 0.755075i | \(-0.272399\pi\) | ||||
0.655639 | + | 0.755075i | \(0.272399\pi\) | |||||||
\(270\) | −27.7923 | −1.69138 | ||||||||
\(271\) | 4.38256 | 0.266221 | 0.133111 | − | 0.991101i | \(-0.457503\pi\) | ||||
0.133111 | + | 0.991101i | \(0.457503\pi\) | |||||||
\(272\) | 1.62223 | 0.0983619 | ||||||||
\(273\) | −0.949001 | −0.0574362 | ||||||||
\(274\) | −35.5848 | −2.14976 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 94.9028 | 5.71248 | ||||||||
\(277\) | −11.4465 | −0.687756 | −0.343878 | − | 0.939014i | \(-0.611741\pi\) | ||||
−0.343878 | + | 0.939014i | \(0.611741\pi\) | |||||||
\(278\) | −31.4322 | −1.88518 | ||||||||
\(279\) | −17.9359 | −1.07379 | ||||||||
\(280\) | −3.68672 | −0.220324 | ||||||||
\(281\) | −11.4639 | −0.683879 | −0.341940 | − | 0.939722i | \(-0.611084\pi\) | ||||
−0.341940 | + | 0.939722i | \(0.611084\pi\) | |||||||
\(282\) | −7.93268 | −0.472384 | ||||||||
\(283\) | 12.6804 | 0.753772 | 0.376886 | − | 0.926260i | \(-0.376995\pi\) | ||||
0.376886 | + | 0.926260i | \(0.376995\pi\) | |||||||
\(284\) | −25.4537 | −1.51040 | ||||||||
\(285\) | 16.0125 | 0.948498 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.65845 | 0.570120 | ||||||||
\(288\) | 24.8576 | 1.46475 | ||||||||
\(289\) | −15.9316 | −0.937151 | ||||||||
\(290\) | 10.1880 | 0.598258 | ||||||||
\(291\) | −12.3232 | −0.722400 | ||||||||
\(292\) | −57.4523 | −3.36214 | ||||||||
\(293\) | −8.25289 | −0.482139 | −0.241070 | − | 0.970508i | \(-0.577498\pi\) | ||||
−0.241070 | + | 0.970508i | \(0.577498\pi\) | |||||||
\(294\) | −7.37227 | −0.429960 | ||||||||
\(295\) | −8.81202 | −0.513056 | ||||||||
\(296\) | 8.38894 | 0.487597 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.01840 | 0.290708 | ||||||||
\(299\) | −2.58721 | −0.149622 | ||||||||
\(300\) | 11.1370 | 0.642997 | ||||||||
\(301\) | −1.37993 | −0.0795379 | ||||||||
\(302\) | −37.1497 | −2.13772 | ||||||||
\(303\) | 31.8513 | 1.82981 | ||||||||
\(304\) | 8.03991 | 0.461121 | ||||||||
\(305\) | 10.5463 | 0.603877 | ||||||||
\(306\) | −16.5048 | −0.943519 | ||||||||
\(307\) | −1.76640 | −0.100814 | −0.0504070 | − | 0.998729i | \(-0.516052\pi\) | ||||
−0.0504070 | + | 0.998729i | \(0.516052\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 57.6570 | 3.27999 | ||||||||
\(310\) | 6.24889 | 0.354913 | ||||||||
\(311\) | −4.51683 | −0.256126 | −0.128063 | − | 0.991766i | \(-0.540876\pi\) | ||||
−0.128063 | + | 0.991766i | \(0.540876\pi\) | |||||||
\(312\) | 3.49871 | 0.198075 | ||||||||
\(313\) | −6.29171 | −0.355628 | −0.177814 | − | 0.984064i | \(-0.556903\pi\) | ||||
−0.177814 | + | 0.984064i | \(0.556903\pi\) | |||||||
\(314\) | 20.1075 | 1.13473 | ||||||||
\(315\) | 6.76983 | 0.381437 | ||||||||
\(316\) | 2.04308 | 0.114932 | ||||||||
\(317\) | 3.69981 | 0.207802 | 0.103901 | − | 0.994588i | \(-0.466867\pi\) | ||||
0.103901 | + | 0.994588i | \(0.466867\pi\) | |||||||
\(318\) | 67.9558 | 3.81077 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −11.7992 | −0.659597 | ||||||||
\(321\) | −56.0108 | −3.12622 | ||||||||
\(322\) | −20.0987 | −1.12005 | ||||||||
\(323\) | 5.29530 | 0.294639 | ||||||||
\(324\) | 58.8663 | 3.27035 | ||||||||
\(325\) | −0.303615 | −0.0168415 | ||||||||
\(326\) | 28.7306 | 1.59124 | ||||||||
\(327\) | −3.18262 | −0.175999 | ||||||||
\(328\) | −35.6080 | −1.96612 | ||||||||
\(329\) | 1.07602 | 0.0593227 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.6957 | −1.13754 | −0.568769 | − | 0.822497i | \(-0.692580\pi\) | ||||
−0.568769 | + | 0.822497i | \(0.692580\pi\) | |||||||
\(332\) | −39.9541 | −2.19277 | ||||||||
\(333\) | −15.4044 | −0.844156 | ||||||||
\(334\) | 19.9283 | 1.09043 | ||||||||
\(335\) | 13.6999 | 0.748505 | ||||||||
\(336\) | 4.90546 | 0.267615 | ||||||||
\(337\) | −13.8060 | −0.752061 | −0.376030 | − | 0.926607i | \(-0.622711\pi\) | ||||
−0.376030 | + | 0.926607i | \(0.622711\pi\) | |||||||
\(338\) | 30.4446 | 1.65597 | ||||||||
\(339\) | −5.61858 | −0.305160 | ||||||||
\(340\) | 3.68300 | 0.199739 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −81.7996 | −4.42322 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 5.08743 | 0.274296 | ||||||||
\(345\) | 26.6350 | 1.43398 | ||||||||
\(346\) | 20.8944 | 1.12329 | ||||||||
\(347\) | −2.92092 | −0.156803 | −0.0784016 | − | 0.996922i | \(-0.524982\pi\) | ||||
−0.0784016 | + | 0.996922i | \(0.524982\pi\) | |||||||
\(348\) | −48.1060 | −2.57875 | ||||||||
\(349\) | −14.2115 | −0.760727 | −0.380363 | − | 0.924837i | \(-0.624201\pi\) | ||||
−0.380363 | + | 0.924837i | \(0.624201\pi\) | |||||||
\(350\) | −2.35862 | −0.126074 | ||||||||
\(351\) | −3.57758 | −0.190957 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.1977 | −1.28792 | −0.643958 | − | 0.765061i | \(-0.722709\pi\) | ||||
−0.643958 | + | 0.765061i | \(0.722709\pi\) | |||||||
\(354\) | 64.9646 | 3.45283 | ||||||||
\(355\) | −7.14373 | −0.379150 | ||||||||
\(356\) | −51.2895 | −2.71834 | ||||||||
\(357\) | 3.23087 | 0.170996 | ||||||||
\(358\) | −19.0642 | −1.00758 | ||||||||
\(359\) | 17.3847 | 0.917532 | 0.458766 | − | 0.888557i | \(-0.348292\pi\) | ||||
0.458766 | + | 0.888557i | \(0.348292\pi\) | |||||||
\(360\) | −24.9585 | −1.31543 | ||||||||
\(361\) | 7.24405 | 0.381266 | ||||||||
\(362\) | 3.18568 | 0.167435 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.08181 | −0.0567020 | ||||||||
\(365\) | −16.1243 | −0.843986 | ||||||||
\(366\) | −77.7500 | −4.06406 | ||||||||
\(367\) | −8.65437 | −0.451755 | −0.225877 | − | 0.974156i | \(-0.572525\pi\) | ||||
−0.225877 | + | 0.974156i | \(0.572525\pi\) | |||||||
\(368\) | 13.3735 | 0.697142 | ||||||||
\(369\) | 65.3861 | 3.40386 | ||||||||
\(370\) | 5.36691 | 0.279012 | ||||||||
\(371\) | −9.21775 | −0.478562 | ||||||||
\(372\) | −29.5063 | −1.52983 | ||||||||
\(373\) | −11.7827 | −0.610087 | −0.305044 | − | 0.952338i | \(-0.598671\pi\) | ||||
−0.305044 | + | 0.952338i | \(0.598671\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.12567 | 0.161409 | ||||||||
\(376\) | −3.96697 | −0.204581 | ||||||||
\(377\) | 1.31145 | 0.0675432 | ||||||||
\(378\) | −27.7923 | −1.42948 | ||||||||
\(379\) | 3.97512 | 0.204188 | 0.102094 | − | 0.994775i | \(-0.467446\pi\) | ||||
0.102094 | + | 0.994775i | \(0.467446\pi\) | |||||||
\(380\) | 18.2533 | 0.936375 | ||||||||
\(381\) | 35.1688 | 1.80175 | ||||||||
\(382\) | −28.9914 | −1.48333 | ||||||||
\(383\) | −18.7450 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(384\) | 64.0333 | 3.26769 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −43.7897 | −2.22884 | ||||||||
\(387\) | −9.34191 | −0.474876 | ||||||||
\(388\) | −14.0477 | −0.713166 | ||||||||
\(389\) | 2.31336 | 0.117292 | 0.0586459 | − | 0.998279i | \(-0.481322\pi\) | ||||
0.0586459 | + | 0.998279i | \(0.481322\pi\) | |||||||
\(390\) | 2.23833 | 0.113342 | ||||||||
\(391\) | 8.80815 | 0.445447 | ||||||||
\(392\) | −3.68672 | −0.186208 | ||||||||
\(393\) | −11.7501 | −0.592715 | ||||||||
\(394\) | −30.3592 | −1.52947 | ||||||||
\(395\) | 0.573402 | 0.0288510 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.3968 | 1.12406 | 0.562032 | − | 0.827116i | \(-0.310020\pi\) | ||||
0.562032 | + | 0.827116i | \(0.310020\pi\) | |||||||
\(398\) | −23.4269 | −1.17428 | ||||||||
\(399\) | 16.0125 | 0.801628 | ||||||||
\(400\) | 1.56941 | 0.0784704 | ||||||||
\(401\) | 24.2091 | 1.20894 | 0.604472 | − | 0.796626i | \(-0.293384\pi\) | ||||
0.604472 | + | 0.796626i | \(0.293384\pi\) | |||||||
\(402\) | −100.999 | −5.03739 | ||||||||
\(403\) | 0.804393 | 0.0400697 | ||||||||
\(404\) | 36.3086 | 1.80642 | ||||||||
\(405\) | 16.5212 | 0.820943 | ||||||||
\(406\) | 10.1880 | 0.505620 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −11.9113 | −0.589698 | ||||||||
\(409\) | 17.4252 | 0.861622 | 0.430811 | − | 0.902442i | \(-0.358228\pi\) | ||||
0.430811 | + | 0.902442i | \(0.358228\pi\) | |||||||
\(410\) | −22.7806 | −1.12505 | ||||||||
\(411\) | 47.1574 | 2.32610 | ||||||||
\(412\) | 65.7257 | 3.23807 | ||||||||
\(413\) | −8.81202 | −0.433611 | ||||||||
\(414\) | −136.065 | −6.68721 | ||||||||
\(415\) | −11.2134 | −0.550442 | ||||||||
\(416\) | −1.11482 | −0.0546584 | ||||||||
\(417\) | 41.6544 | 2.03982 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.0980 | 0.884145 | 0.442073 | − | 0.896979i | \(-0.354243\pi\) | ||||
0.442073 | + | 0.896979i | \(0.354243\pi\) | |||||||
\(420\) | 11.1370 | 0.543432 | ||||||||
\(421\) | 19.4325 | 0.947082 | 0.473541 | − | 0.880772i | \(-0.342976\pi\) | ||||
0.473541 | + | 0.880772i | \(0.342976\pi\) | |||||||
\(422\) | −40.4452 | −1.96884 | ||||||||
\(423\) | 7.28445 | 0.354182 | ||||||||
\(424\) | 33.9833 | 1.65037 | ||||||||
\(425\) | 1.03365 | 0.0501396 | ||||||||
\(426\) | 52.6656 | 2.55165 | ||||||||
\(427\) | 10.5463 | 0.510370 | ||||||||
\(428\) | −63.8491 | −3.08626 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.25473 | 0.156957 | ||||||||
\(431\) | −7.90822 | −0.380926 | −0.190463 | − | 0.981694i | \(-0.560999\pi\) | ||||
−0.190463 | + | 0.981694i | \(0.560999\pi\) | |||||||
\(432\) | 18.4928 | 0.889734 | ||||||||
\(433\) | 18.2620 | 0.877618 | 0.438809 | − | 0.898580i | \(-0.355400\pi\) | ||||
0.438809 | + | 0.898580i | \(0.355400\pi\) | |||||||
\(434\) | 6.24889 | 0.299956 | ||||||||
\(435\) | −13.5012 | −0.647334 | ||||||||
\(436\) | −3.62800 | −0.173750 | ||||||||
\(437\) | 43.6541 | 2.08826 | ||||||||
\(438\) | 118.873 | 5.67997 | ||||||||
\(439\) | 24.6331 | 1.17567 | 0.587837 | − | 0.808979i | \(-0.299980\pi\) | ||||
0.587837 | + | 0.808979i | \(0.299980\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.76983 | 0.322373 | ||||||||
\(442\) | 0.740212 | 0.0352083 | ||||||||
\(443\) | −16.6461 | −0.790881 | −0.395441 | − | 0.918492i | \(-0.629408\pi\) | ||||
−0.395441 | + | 0.918492i | \(0.629408\pi\) | |||||||
\(444\) | −25.3417 | −1.20267 | ||||||||
\(445\) | −14.3947 | −0.682374 | ||||||||
\(446\) | −36.1642 | −1.71243 | ||||||||
\(447\) | −6.65045 | −0.314555 | ||||||||
\(448\) | −11.7992 | −0.557461 | ||||||||
\(449\) | −8.05832 | −0.380296 | −0.190148 | − | 0.981755i | \(-0.560897\pi\) | ||||
−0.190148 | + | 0.981755i | \(0.560897\pi\) | |||||||
\(450\) | −15.9675 | −0.752713 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −6.40486 | −0.301259 | ||||||||
\(453\) | 49.2312 | 2.31309 | ||||||||
\(454\) | −4.76113 | −0.223451 | ||||||||
\(455\) | −0.303615 | −0.0142337 | ||||||||
\(456\) | −59.0337 | −2.76450 | ||||||||
\(457\) | −22.9712 | −1.07455 | −0.537273 | − | 0.843408i | \(-0.680546\pi\) | ||||
−0.537273 | + | 0.843408i | \(0.680546\pi\) | |||||||
\(458\) | 0.736610 | 0.0344195 | ||||||||
\(459\) | 12.1798 | 0.568506 | ||||||||
\(460\) | 30.3624 | 1.41565 | ||||||||
\(461\) | 15.0286 | 0.699951 | 0.349975 | − | 0.936759i | \(-0.386190\pi\) | ||||
0.349975 | + | 0.936759i | \(0.386190\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.9066 | −1.06456 | −0.532279 | − | 0.846569i | \(-0.678664\pi\) | ||||
−0.532279 | + | 0.846569i | \(0.678664\pi\) | |||||||
\(464\) | −6.77900 | −0.314707 | ||||||||
\(465\) | −8.28111 | −0.384027 | ||||||||
\(466\) | 40.9979 | 1.89919 | ||||||||
\(467\) | 1.64223 | 0.0759932 | 0.0379966 | − | 0.999278i | \(-0.487902\pi\) | ||||
0.0379966 | + | 0.999278i | \(0.487902\pi\) | |||||||
\(468\) | −7.32365 | −0.338536 | ||||||||
\(469\) | 13.6999 | 0.632602 | ||||||||
\(470\) | −2.53791 | −0.117065 | ||||||||
\(471\) | −26.6467 | −1.22781 | ||||||||
\(472\) | 32.4875 | 1.49536 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −4.22728 | −0.194165 | ||||||||
\(475\) | 5.12290 | 0.235055 | ||||||||
\(476\) | 3.68300 | 0.168810 | ||||||||
\(477\) | −62.4026 | −2.85722 | ||||||||
\(478\) | 53.4416 | 2.44436 | ||||||||
\(479\) | −6.50665 | −0.297296 | −0.148648 | − | 0.988890i | \(-0.547492\pi\) | ||||
−0.148648 | + | 0.988890i | \(0.547492\pi\) | |||||||
\(480\) | 11.4769 | 0.523846 | ||||||||
\(481\) | 0.690859 | 0.0315005 | ||||||||
\(482\) | 14.8251 | 0.675264 | ||||||||
\(483\) | 26.6350 | 1.21194 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.94258 | −0.179023 | ||||||||
\(486\) | −38.4217 | −1.74284 | ||||||||
\(487\) | 31.1060 | 1.40955 | 0.704774 | − | 0.709432i | \(-0.251048\pi\) | ||||
0.704774 | + | 0.709432i | \(0.251048\pi\) | |||||||
\(488\) | −38.8812 | −1.76007 | ||||||||
\(489\) | −38.0741 | −1.72177 | ||||||||
\(490\) | −2.35862 | −0.106552 | ||||||||
\(491\) | 19.2332 | 0.867984 | 0.433992 | − | 0.900917i | \(-0.357105\pi\) | ||||
0.433992 | + | 0.900917i | \(0.357105\pi\) | |||||||
\(492\) | 107.567 | 4.84947 | ||||||||
\(493\) | −4.46483 | −0.201086 | ||||||||
\(494\) | 3.66857 | 0.165057 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.15797 | −0.186698 | ||||||||
\(497\) | −7.14373 | −0.320440 | ||||||||
\(498\) | 82.6679 | 3.70444 | ||||||||
\(499\) | 12.4567 | 0.557636 | 0.278818 | − | 0.960344i | \(-0.410057\pi\) | ||||
0.278818 | + | 0.960344i | \(0.410057\pi\) | |||||||
\(500\) | 3.56309 | 0.159346 | ||||||||
\(501\) | −26.4093 | −1.17988 | ||||||||
\(502\) | 25.1806 | 1.12386 | ||||||||
\(503\) | −0.952980 | −0.0424913 | −0.0212456 | − | 0.999774i | \(-0.506763\pi\) | ||||
−0.0212456 | + | 0.999774i | \(0.506763\pi\) | |||||||
\(504\) | −24.9585 | −1.11174 | ||||||||
\(505\) | 10.1902 | 0.453459 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −40.3456 | −1.79181 | ||||||||
\(508\) | 40.0904 | 1.77872 | ||||||||
\(509\) | 30.0463 | 1.33178 | 0.665890 | − | 0.746050i | \(-0.268052\pi\) | ||||
0.665890 | + | 0.746050i | \(0.268052\pi\) | |||||||
\(510\) | −7.62038 | −0.337436 | ||||||||
\(511\) | −16.1243 | −0.713298 | ||||||||
\(512\) | 17.3345 | 0.766085 | ||||||||
\(513\) | 60.3645 | 2.66516 | ||||||||
\(514\) | 41.6849 | 1.83864 | ||||||||
\(515\) | 18.4463 | 0.812840 | ||||||||
\(516\) | −15.3684 | −0.676554 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 5.36691 | 0.235809 | ||||||||
\(519\) | −27.6895 | −1.21544 | ||||||||
\(520\) | 1.11934 | 0.0490865 | ||||||||
\(521\) | 35.3266 | 1.54769 | 0.773844 | − | 0.633376i | \(-0.218331\pi\) | ||||
0.773844 | + | 0.633376i | \(0.218331\pi\) | |||||||
\(522\) | 68.9708 | 3.01877 | ||||||||
\(523\) | 3.82511 | 0.167261 | 0.0836303 | − | 0.996497i | \(-0.473349\pi\) | ||||
0.0836303 | + | 0.996497i | \(0.473349\pi\) | |||||||
\(524\) | −13.3945 | −0.585140 | ||||||||
\(525\) | 3.12567 | 0.136416 | ||||||||
\(526\) | 28.9364 | 1.26169 | ||||||||
\(527\) | −2.73855 | −0.119293 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 49.6137 | 2.15712 | ||||||||
\(530\) | 21.7412 | 0.944376 | ||||||||
\(531\) | −59.6559 | −2.58885 | ||||||||
\(532\) | 18.2533 | 0.791382 | ||||||||
\(533\) | −2.93245 | −0.127018 | ||||||||
\(534\) | 106.122 | 4.59233 | ||||||||
\(535\) | −17.9196 | −0.774732 | ||||||||
\(536\) | −50.5077 | −2.18160 | ||||||||
\(537\) | 25.2642 | 1.09023 | ||||||||
\(538\) | −50.7258 | −2.18694 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 41.9848 | 1.80674 | ||||||||
\(541\) | −1.78673 | −0.0768175 | −0.0384087 | − | 0.999262i | \(-0.512229\pi\) | ||||
−0.0384087 | + | 0.999262i | \(0.512229\pi\) | |||||||
\(542\) | −10.3368 | −0.444003 | ||||||||
\(543\) | −4.22170 | −0.181170 | ||||||||
\(544\) | 3.79538 | 0.162726 | ||||||||
\(545\) | −1.01822 | −0.0436157 | ||||||||
\(546\) | 2.23833 | 0.0957918 | ||||||||
\(547\) | −33.1680 | −1.41816 | −0.709081 | − | 0.705127i | \(-0.750890\pi\) | ||||
−0.709081 | + | 0.705127i | \(0.750890\pi\) | |||||||
\(548\) | 53.7567 | 2.29637 | ||||||||
\(549\) | 71.3965 | 3.04713 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.1281 | −0.942690 | ||||||||
\(552\) | −98.1960 | −4.17950 | ||||||||
\(553\) | 0.573402 | 0.0243835 | ||||||||
\(554\) | 26.9980 | 1.14704 | ||||||||
\(555\) | −7.11230 | −0.301900 | ||||||||
\(556\) | 47.4836 | 2.01375 | ||||||||
\(557\) | 2.03928 | 0.0864070 | 0.0432035 | − | 0.999066i | \(-0.486244\pi\) | ||||
0.0432035 | + | 0.999066i | \(0.486244\pi\) | |||||||
\(558\) | 42.3040 | 1.79087 | ||||||||
\(559\) | 0.418968 | 0.0177204 | ||||||||
\(560\) | 1.56941 | 0.0663196 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 27.0390 | 1.14057 | ||||||||
\(563\) | 18.5776 | 0.782953 | 0.391476 | − | 0.920188i | \(-0.371964\pi\) | ||||
0.391476 | + | 0.920188i | \(0.371964\pi\) | |||||||
\(564\) | 11.9836 | 0.504602 | ||||||||
\(565\) | −1.79756 | −0.0756239 | ||||||||
\(566\) | −29.9083 | −1.25714 | ||||||||
\(567\) | 16.5212 | 0.693823 | ||||||||
\(568\) | 26.3370 | 1.10507 | ||||||||
\(569\) | −16.4095 | −0.687920 | −0.343960 | − | 0.938984i | \(-0.611768\pi\) | ||||
−0.343960 | + | 0.938984i | \(0.611768\pi\) | |||||||
\(570\) | −37.7674 | −1.58190 | ||||||||
\(571\) | −18.5329 | −0.775578 | −0.387789 | − | 0.921748i | \(-0.626761\pi\) | ||||
−0.387789 | + | 0.921748i | \(0.626761\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 38.4198 | 1.60501 | ||||||||
\(574\) | −22.7806 | −0.950844 | ||||||||
\(575\) | 8.52137 | 0.355366 | ||||||||
\(576\) | −79.8788 | −3.32828 | ||||||||
\(577\) | −23.7459 | −0.988554 | −0.494277 | − | 0.869304i | \(-0.664567\pi\) | ||||
−0.494277 | + | 0.869304i | \(0.664567\pi\) | |||||||
\(578\) | 37.5765 | 1.56298 | ||||||||
\(579\) | 58.0307 | 2.41167 | ||||||||
\(580\) | −15.3906 | −0.639060 | ||||||||
\(581\) | −11.2134 | −0.465208 | ||||||||
\(582\) | 29.0658 | 1.20482 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 59.4459 | 2.45989 | ||||||||
\(585\) | −2.05542 | −0.0849813 | ||||||||
\(586\) | 19.4654 | 0.804110 | ||||||||
\(587\) | 21.0434 | 0.868554 | 0.434277 | − | 0.900779i | \(-0.357004\pi\) | ||||
0.434277 | + | 0.900779i | \(0.357004\pi\) | |||||||
\(588\) | 11.1370 | 0.459284 | ||||||||
\(589\) | −13.5725 | −0.559246 | ||||||||
\(590\) | 20.7842 | 0.855672 | ||||||||
\(591\) | 40.2324 | 1.65494 | ||||||||
\(592\) | −3.57110 | −0.146771 | ||||||||
\(593\) | −46.2299 | −1.89843 | −0.949217 | − | 0.314621i | \(-0.898122\pi\) | ||||
−0.949217 | + | 0.314621i | \(0.898122\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.03365 | 0.0423757 | ||||||||
\(596\) | −7.58112 | −0.310535 | ||||||||
\(597\) | 31.0456 | 1.27061 | ||||||||
\(598\) | 6.10225 | 0.249540 | ||||||||
\(599\) | 16.7230 | 0.683282 | 0.341641 | − | 0.939831i | \(-0.389017\pi\) | ||||
0.341641 | + | 0.939831i | \(0.389017\pi\) | |||||||
\(600\) | −11.5235 | −0.470445 | ||||||||
\(601\) | 10.4475 | 0.426161 | 0.213080 | − | 0.977035i | \(-0.431650\pi\) | ||||
0.213080 | + | 0.977035i | \(0.431650\pi\) | |||||||
\(602\) | 3.25473 | 0.132653 | ||||||||
\(603\) | 92.7460 | 3.77691 | ||||||||
\(604\) | 56.1207 | 2.28352 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −75.1251 | −3.05175 | ||||||||
\(607\) | 19.9139 | 0.808279 | 0.404139 | − | 0.914697i | \(-0.367571\pi\) | ||||
0.404139 | + | 0.914697i | \(0.367571\pi\) | |||||||
\(608\) | 18.8103 | 0.762859 | ||||||||
\(609\) | −13.5012 | −0.547097 | ||||||||
\(610\) | −24.8746 | −1.00714 | ||||||||
\(611\) | −0.326694 | −0.0132166 | ||||||||
\(612\) | 24.9333 | 1.00787 | ||||||||
\(613\) | −17.4111 | −0.703229 | −0.351615 | − | 0.936145i | \(-0.614367\pi\) | ||||
−0.351615 | + | 0.936145i | \(0.614367\pi\) | |||||||
\(614\) | 4.16627 | 0.168137 | ||||||||
\(615\) | 30.1892 | 1.21734 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.6972 | −0.551427 | −0.275713 | − | 0.961240i | \(-0.588914\pi\) | ||||
−0.275713 | + | 0.961240i | \(0.588914\pi\) | |||||||
\(618\) | −135.991 | −5.47036 | ||||||||
\(619\) | −31.9100 | −1.28257 | −0.641286 | − | 0.767302i | \(-0.721599\pi\) | ||||
−0.641286 | + | 0.767302i | \(0.721599\pi\) | |||||||
\(620\) | −9.43999 | −0.379119 | ||||||||
\(621\) | 100.410 | 4.02930 | ||||||||
\(622\) | 10.6535 | 0.427165 | ||||||||
\(623\) | −14.3947 | −0.576711 | ||||||||
\(624\) | −1.48937 | −0.0596225 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 14.8397 | 0.593115 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −30.3757 | −1.21212 | ||||||||
\(629\) | −2.35203 | −0.0937814 | ||||||||
\(630\) | −15.9675 | −0.636159 | ||||||||
\(631\) | 22.1491 | 0.881742 | 0.440871 | − | 0.897570i | \(-0.354670\pi\) | ||||
0.440871 | + | 0.897570i | \(0.354670\pi\) | |||||||
\(632\) | −2.11397 | −0.0840894 | ||||||||
\(633\) | 53.5985 | 2.13035 | ||||||||
\(634\) | −8.72644 | −0.346571 | ||||||||
\(635\) | 11.2516 | 0.446506 | ||||||||
\(636\) | −102.658 | −4.07067 | ||||||||
\(637\) | −0.303615 | −0.0120297 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −48.3619 | −1.91317 | ||||||||
\(640\) | 20.4863 | 0.809790 | ||||||||
\(641\) | 47.0120 | 1.85686 | 0.928431 | − | 0.371506i | \(-0.121158\pi\) | ||||
0.928431 | + | 0.371506i | \(0.121158\pi\) | |||||||
\(642\) | 132.108 | 5.21389 | ||||||||
\(643\) | −16.2825 | −0.642117 | −0.321059 | − | 0.947059i | \(-0.604039\pi\) | ||||
−0.321059 | + | 0.947059i | \(0.604039\pi\) | |||||||
\(644\) | 30.3624 | 1.19644 | ||||||||
\(645\) | −4.31321 | −0.169833 | ||||||||
\(646\) | −12.4896 | −0.491397 | ||||||||
\(647\) | −40.8269 | −1.60507 | −0.802536 | − | 0.596604i | \(-0.796516\pi\) | ||||
−0.802536 | + | 0.596604i | \(0.796516\pi\) | |||||||
\(648\) | −60.9089 | −2.39273 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0.716112 | 0.0280882 | ||||||||
\(651\) | −8.28111 | −0.324562 | ||||||||
\(652\) | −43.4023 | −1.69976 | ||||||||
\(653\) | 23.2768 | 0.910893 | 0.455447 | − | 0.890263i | \(-0.349480\pi\) | ||||
0.455447 | + | 0.890263i | \(0.349480\pi\) | |||||||
\(654\) | 7.50658 | 0.293531 | ||||||||
\(655\) | −3.75923 | −0.146885 | ||||||||
\(656\) | 15.1580 | 0.591822 | ||||||||
\(657\) | −109.159 | −4.25870 | ||||||||
\(658\) | −2.53791 | −0.0989381 | ||||||||
\(659\) | −8.17158 | −0.318320 | −0.159160 | − | 0.987253i | \(-0.550879\pi\) | ||||
−0.159160 | + | 0.987253i | \(0.550879\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.64860 | 0.297496 | 0.148748 | − | 0.988875i | \(-0.452476\pi\) | ||||
0.148748 | + | 0.988875i | \(0.452476\pi\) | |||||||
\(662\) | 48.8133 | 1.89718 | ||||||||
\(663\) | −0.980939 | −0.0380965 | ||||||||
\(664\) | 41.3405 | 1.60432 | ||||||||
\(665\) | 5.12290 | 0.198657 | ||||||||
\(666\) | 36.3331 | 1.40788 | ||||||||
\(667\) | −36.8077 | −1.42520 | ||||||||
\(668\) | −30.1051 | −1.16480 | ||||||||
\(669\) | 47.9253 | 1.85290 | ||||||||
\(670\) | −32.3128 | −1.24835 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 11.4769 | 0.442730 | ||||||||
\(673\) | 14.2835 | 0.550590 | 0.275295 | − | 0.961360i | \(-0.411224\pi\) | ||||
0.275295 | + | 0.961360i | \(0.411224\pi\) | |||||||
\(674\) | 32.5631 | 1.25428 | ||||||||
\(675\) | 11.7833 | 0.453538 | ||||||||
\(676\) | −45.9917 | −1.76891 | ||||||||
\(677\) | −28.7655 | −1.10555 | −0.552774 | − | 0.833331i | \(-0.686431\pi\) | ||||
−0.552774 | + | 0.833331i | \(0.686431\pi\) | |||||||
\(678\) | 13.2521 | 0.508944 | ||||||||
\(679\) | −3.94258 | −0.151302 | ||||||||
\(680\) | −3.81080 | −0.146137 | ||||||||
\(681\) | 6.30952 | 0.241781 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.0519 | −0.843794 | −0.421897 | − | 0.906644i | \(-0.638636\pi\) | ||||
−0.421897 | + | 0.906644i | \(0.638636\pi\) | |||||||
\(684\) | 123.572 | 4.72489 | ||||||||
\(685\) | 15.0871 | 0.576449 | ||||||||
\(686\) | −2.35862 | −0.0900525 | ||||||||
\(687\) | −0.976166 | −0.0372430 | ||||||||
\(688\) | −2.16568 | −0.0825656 | ||||||||
\(689\) | 2.79865 | 0.106620 | ||||||||
\(690\) | −62.8219 | −2.39159 | ||||||||
\(691\) | 8.92737 | 0.339613 | 0.169807 | − | 0.985477i | \(-0.445686\pi\) | ||||
0.169807 | + | 0.985477i | \(0.445686\pi\) | |||||||
\(692\) | −31.5644 | −1.19990 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.88934 | 0.261516 | ||||||||
\(695\) | 13.3265 | 0.505504 | ||||||||
\(696\) | 49.7753 | 1.88673 | ||||||||
\(697\) | 9.98350 | 0.378152 | ||||||||
\(698\) | 33.5196 | 1.26874 | ||||||||
\(699\) | −54.3309 | −2.05499 | ||||||||
\(700\) | 3.56309 | 0.134672 | ||||||||
\(701\) | −0.0337866 | −0.00127610 | −0.000638050 | − | 1.00000i | \(-0.500203\pi\) | ||||
−0.000638050 | 1.00000i | \(0.500203\pi\) | ||||||||
\(702\) | 8.43814 | 0.318477 | ||||||||
\(703\) | −11.6569 | −0.439647 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.36327 | 0.126668 | ||||||||
\(706\) | 57.0733 | 2.14798 | ||||||||
\(707\) | 10.1902 | 0.383243 | ||||||||
\(708\) | −98.1398 | −3.68832 | ||||||||
\(709\) | −2.86944 | −0.107764 | −0.0538821 | − | 0.998547i | \(-0.517160\pi\) | ||||
−0.0538821 | + | 0.998547i | \(0.517160\pi\) | |||||||
\(710\) | 16.8493 | 0.632345 | ||||||||
\(711\) | 3.88184 | 0.145580 | ||||||||
\(712\) | 53.0693 | 1.98886 | ||||||||
\(713\) | −22.5764 | −0.845492 | ||||||||
\(714\) | −7.62038 | −0.285186 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 28.7997 | 1.07629 | ||||||||
\(717\) | −70.8215 | −2.64488 | ||||||||
\(718\) | −41.0040 | −1.53026 | ||||||||
\(719\) | 1.67521 | 0.0624749 | 0.0312375 | − | 0.999512i | \(-0.490055\pi\) | ||||
0.0312375 | + | 0.999512i | \(0.490055\pi\) | |||||||
\(720\) | 10.6246 | 0.395957 | ||||||||
\(721\) | 18.4463 | 0.686975 | ||||||||
\(722\) | −17.0860 | −0.635874 | ||||||||
\(723\) | −19.6464 | −0.730657 | ||||||||
\(724\) | −4.81249 | −0.178855 | ||||||||
\(725\) | −4.31946 | −0.160421 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.612732 | 0.0227250 | 0.0113625 | − | 0.999935i | \(-0.496383\pi\) | ||||
0.0113625 | + | 0.999935i | \(0.496383\pi\) | |||||||
\(728\) | 1.11934 | 0.0414857 | ||||||||
\(729\) | 1.35351 | 0.0501298 | ||||||||
\(730\) | 38.0311 | 1.40760 | ||||||||
\(731\) | −1.42637 | −0.0527563 | ||||||||
\(732\) | 117.454 | 4.34123 | ||||||||
\(733\) | −36.4732 | −1.34717 | −0.673584 | − | 0.739111i | \(-0.735246\pi\) | ||||
−0.673584 | + | 0.739111i | \(0.735246\pi\) | |||||||
\(734\) | 20.4124 | 0.753434 | ||||||||
\(735\) | 3.12567 | 0.115292 | ||||||||
\(736\) | 31.2889 | 1.15332 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −154.221 | −5.67695 | ||||||||
\(739\) | 44.7363 | 1.64565 | 0.822826 | − | 0.568293i | \(-0.192396\pi\) | ||||
0.822826 | + | 0.568293i | \(0.192396\pi\) | |||||||
\(740\) | −8.10761 | −0.298042 | ||||||||
\(741\) | −4.86163 | −0.178597 | ||||||||
\(742\) | 21.7412 | 0.798143 | ||||||||
\(743\) | 13.6791 | 0.501838 | 0.250919 | − | 0.968008i | \(-0.419267\pi\) | ||||
0.250919 | + | 0.968008i | \(0.419267\pi\) | |||||||
\(744\) | 30.5302 | 1.11929 | ||||||||
\(745\) | −2.12769 | −0.0779523 | ||||||||
\(746\) | 27.7910 | 1.01750 | ||||||||
\(747\) | −75.9125 | −2.77749 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.9196 | −0.654768 | ||||||||
\(750\) | −7.37227 | −0.269197 | ||||||||
\(751\) | −46.1908 | −1.68553 | −0.842764 | − | 0.538284i | \(-0.819073\pi\) | ||||
−0.842764 | + | 0.538284i | \(0.819073\pi\) | |||||||
\(752\) | 1.68871 | 0.0615808 | ||||||||
\(753\) | −33.3696 | −1.21606 | ||||||||
\(754\) | −3.09322 | −0.112648 | ||||||||
\(755\) | 15.7506 | 0.573223 | ||||||||
\(756\) | 41.9848 | 1.52697 | ||||||||
\(757\) | 51.4344 | 1.86942 | 0.934708 | − | 0.355417i | \(-0.115661\pi\) | ||||
0.934708 | + | 0.355417i | \(0.115661\pi\) | |||||||
\(758\) | −9.37579 | −0.340544 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −18.8867 | −0.685093 | ||||||||
\(761\) | −32.2686 | −1.16974 | −0.584869 | − | 0.811128i | \(-0.698854\pi\) | ||||
−0.584869 | + | 0.811128i | \(0.698854\pi\) | |||||||
\(762\) | −82.9498 | −3.00495 | ||||||||
\(763\) | −1.01822 | −0.0368620 | ||||||||
\(764\) | 43.7964 | 1.58450 | ||||||||
\(765\) | 6.99767 | 0.253001 | ||||||||
\(766\) | 44.2124 | 1.59746 | ||||||||
\(767\) | 2.67546 | 0.0966053 | ||||||||
\(768\) | −77.2692 | −2.78821 | ||||||||
\(769\) | −20.8369 | −0.751399 | −0.375699 | − | 0.926742i | \(-0.622597\pi\) | ||||
−0.375699 | + | 0.926742i | \(0.622597\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −55.2414 | −1.98947 | ||||||||
\(772\) | 66.1516 | 2.38085 | ||||||||
\(773\) | −39.5002 | −1.42072 | −0.710361 | − | 0.703838i | \(-0.751468\pi\) | ||||
−0.710361 | + | 0.703838i | \(0.751468\pi\) | |||||||
\(774\) | 22.0340 | 0.791996 | ||||||||
\(775\) | −2.64939 | −0.0951687 | ||||||||
\(776\) | 14.5352 | 0.521783 | ||||||||
\(777\) | −7.11230 | −0.255152 | ||||||||
\(778\) | −5.45633 | −0.195619 | ||||||||
\(779\) | 49.4792 | 1.77278 | ||||||||
\(780\) | −3.38137 | −0.121073 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −20.7751 | −0.742915 | ||||||||
\(783\) | −50.8974 | −1.81892 | ||||||||
\(784\) | 1.56941 | 0.0560503 | ||||||||
\(785\) | −8.52511 | −0.304274 | ||||||||
\(786\) | 27.7141 | 0.988528 | ||||||||
\(787\) | 23.4515 | 0.835954 | 0.417977 | − | 0.908458i | \(-0.362739\pi\) | ||||
0.417977 | + | 0.908458i | \(0.362739\pi\) | |||||||
\(788\) | 45.8626 | 1.63379 | ||||||||
\(789\) | −38.3469 | −1.36519 | ||||||||
\(790\) | −1.35244 | −0.0481175 | ||||||||
\(791\) | −1.79756 | −0.0639139 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.20200 | −0.113706 | ||||||||
\(794\) | −52.8255 | −1.87471 | ||||||||
\(795\) | −28.8117 | −1.02184 | ||||||||
\(796\) | 35.3902 | 1.25437 | ||||||||
\(797\) | 19.6169 | 0.694868 | 0.347434 | − | 0.937705i | \(-0.387053\pi\) | ||||
0.347434 | + | 0.937705i | \(0.387053\pi\) | |||||||
\(798\) | −37.7674 | −1.33695 | ||||||||
\(799\) | 1.11223 | 0.0393478 | ||||||||
\(800\) | 3.67181 | 0.129818 | ||||||||
\(801\) | −97.4497 | −3.44322 | ||||||||
\(802\) | −57.1001 | −2.01627 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 152.576 | 5.38095 | ||||||||
\(805\) | 8.52137 | 0.300339 | ||||||||
\(806\) | −1.89726 | −0.0668280 | ||||||||
\(807\) | 67.2224 | 2.36634 | ||||||||
\(808\) | −37.5686 | −1.32166 | ||||||||
\(809\) | 1.20245 | 0.0422757 | 0.0211379 | − | 0.999777i | \(-0.493271\pi\) | ||||
0.0211379 | + | 0.999777i | \(0.493271\pi\) | |||||||
\(810\) | −38.9671 | −1.36916 | ||||||||
\(811\) | 15.3789 | 0.540025 | 0.270012 | − | 0.962857i | \(-0.412972\pi\) | ||||
0.270012 | + | 0.962857i | \(0.412972\pi\) | |||||||
\(812\) | −15.3906 | −0.540104 | ||||||||
\(813\) | 13.6984 | 0.480425 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.1811 | −0.426685 | ||||||||
\(816\) | 5.07055 | 0.177505 | ||||||||
\(817\) | −7.06924 | −0.247322 | ||||||||
\(818\) | −41.0995 | −1.43701 | ||||||||
\(819\) | −2.05542 | −0.0718223 | ||||||||
\(820\) | 34.4139 | 1.20178 | ||||||||
\(821\) | 36.6757 | 1.27999 | 0.639996 | − | 0.768378i | \(-0.278936\pi\) | ||||
0.639996 | + | 0.768378i | \(0.278936\pi\) | |||||||
\(822\) | −111.226 | −3.87947 | ||||||||
\(823\) | −41.8158 | −1.45761 | −0.728804 | − | 0.684722i | \(-0.759924\pi\) | ||||
−0.728804 | + | 0.684722i | \(0.759924\pi\) | |||||||
\(824\) | −68.0063 | −2.36911 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 20.7842 | 0.723175 | ||||||||
\(827\) | −54.0547 | −1.87966 | −0.939832 | − | 0.341636i | \(-0.889019\pi\) | ||||
−0.939832 | + | 0.341636i | \(0.889019\pi\) | |||||||
\(828\) | 205.548 | 7.14329 | ||||||||
\(829\) | 26.8067 | 0.931034 | 0.465517 | − | 0.885039i | \(-0.345868\pi\) | ||||
0.465517 | + | 0.885039i | \(0.345868\pi\) | |||||||
\(830\) | 26.4480 | 0.918025 | ||||||||
\(831\) | −35.7782 | −1.24113 | ||||||||
\(832\) | 3.58242 | 0.124198 | ||||||||
\(833\) | 1.03365 | 0.0358140 | ||||||||
\(834\) | −98.2469 | −3.40201 | ||||||||
\(835\) | −8.44915 | −0.292395 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −31.2184 | −1.07907 | ||||||||
\(838\) | −42.6863 | −1.47457 | ||||||||
\(839\) | 16.2884 | 0.562338 | 0.281169 | − | 0.959658i | \(-0.409278\pi\) | ||||
0.281169 | + | 0.959658i | \(0.409278\pi\) | |||||||
\(840\) | −11.5235 | −0.397598 | ||||||||
\(841\) | −10.3423 | −0.356630 | ||||||||
\(842\) | −45.8339 | −1.57954 | ||||||||
\(843\) | −35.8324 | −1.23413 | ||||||||
\(844\) | 61.0991 | 2.10312 | ||||||||
\(845\) | −12.9078 | −0.444042 | ||||||||
\(846\) | −17.1812 | −0.590703 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −14.4664 | −0.496779 | ||||||||
\(849\) | 39.6348 | 1.36026 | ||||||||
\(850\) | −2.43800 | −0.0836226 | ||||||||
\(851\) | −19.3899 | −0.664678 | ||||||||
\(852\) | −79.5601 | −2.72568 | ||||||||
\(853\) | 30.6496 | 1.04942 | 0.524710 | − | 0.851281i | \(-0.324174\pi\) | ||||
0.524710 | + | 0.851281i | \(0.324174\pi\) | |||||||
\(854\) | −24.8746 | −0.851192 | ||||||||
\(855\) | 34.6812 | 1.18607 | ||||||||
\(856\) | 66.0646 | 2.25804 | ||||||||
\(857\) | −42.2735 | −1.44404 | −0.722018 | − | 0.691875i | \(-0.756785\pi\) | ||||
−0.722018 | + | 0.691875i | \(0.756785\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.3365 | −0.455036 | −0.227518 | − | 0.973774i | \(-0.573061\pi\) | ||||
−0.227518 | + | 0.973774i | \(0.573061\pi\) | |||||||
\(860\) | −4.91681 | −0.167662 | ||||||||
\(861\) | 30.1892 | 1.02884 | ||||||||
\(862\) | 18.6525 | 0.635306 | ||||||||
\(863\) | −37.7743 | −1.28585 | −0.642926 | − | 0.765929i | \(-0.722280\pi\) | ||||
−0.642926 | + | 0.765929i | \(0.722280\pi\) | |||||||
\(864\) | 43.2660 | 1.47194 | ||||||||
\(865\) | −8.85874 | −0.301206 | ||||||||
\(866\) | −43.0732 | −1.46369 | ||||||||
\(867\) | −49.7968 | −1.69119 | ||||||||
\(868\) | −9.43999 | −0.320414 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 31.8442 | 1.07962 | ||||||||
\(871\) | −4.15949 | −0.140939 | ||||||||
\(872\) | 3.75389 | 0.127123 | ||||||||
\(873\) | −26.6906 | −0.903340 | ||||||||
\(874\) | −102.963 | −3.48279 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −179.577 | −6.06735 | ||||||||
\(877\) | −8.69917 | −0.293750 | −0.146875 | − | 0.989155i | \(-0.546922\pi\) | ||||
−0.146875 | + | 0.989155i | \(0.546922\pi\) | |||||||
\(878\) | −58.1001 | −1.96078 | ||||||||
\(879\) | −25.7958 | −0.870072 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.89312 | −0.131163 | −0.0655814 | − | 0.997847i | \(-0.520890\pi\) | ||||
−0.0655814 | + | 0.997847i | \(0.520890\pi\) | |||||||
\(882\) | −15.9675 | −0.537652 | ||||||||
\(883\) | 45.1520 | 1.51948 | 0.759742 | − | 0.650225i | \(-0.225325\pi\) | ||||
0.759742 | + | 0.650225i | \(0.225325\pi\) | |||||||
\(884\) | −1.11821 | −0.0376096 | ||||||||
\(885\) | −27.5435 | −0.925864 | ||||||||
\(886\) | 39.2619 | 1.31903 | ||||||||
\(887\) | −15.6274 | −0.524718 | −0.262359 | − | 0.964970i | \(-0.584500\pi\) | ||||
−0.262359 | + | 0.964970i | \(0.584500\pi\) | |||||||
\(888\) | 26.2211 | 0.879922 | ||||||||
\(889\) | 11.2516 | 0.377366 | ||||||||
\(890\) | 33.9516 | 1.13806 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 54.6321 | 1.82922 | ||||||||
\(893\) | 5.51231 | 0.184463 | ||||||||
\(894\) | 15.6859 | 0.524614 | ||||||||
\(895\) | 8.08279 | 0.270178 | ||||||||
\(896\) | 20.4863 | 0.684398 | ||||||||
\(897\) | −8.08679 | −0.270010 | ||||||||
\(898\) | 19.0065 | 0.634256 | ||||||||
\(899\) | 11.4439 | 0.381676 | ||||||||
\(900\) | 24.1215 | 0.804050 | ||||||||
\(901\) | −9.52797 | −0.317423 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.31321 | −0.143535 | ||||||||
\(904\) | 6.62711 | 0.220414 | ||||||||
\(905\) | −1.35065 | −0.0448972 | ||||||||
\(906\) | −116.118 | −3.85775 | ||||||||
\(907\) | 22.9194 | 0.761027 | 0.380513 | − | 0.924775i | \(-0.375747\pi\) | ||||
0.380513 | + | 0.924775i | \(0.375747\pi\) | |||||||
\(908\) | 7.19248 | 0.238691 | ||||||||
\(909\) | 68.9861 | 2.28813 | ||||||||
\(910\) | 0.716112 | 0.0237389 | ||||||||
\(911\) | 39.8282 | 1.31957 | 0.659784 | − | 0.751455i | \(-0.270648\pi\) | ||||
0.659784 | + | 0.751455i | \(0.270648\pi\) | |||||||
\(912\) | 25.1301 | 0.832142 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 54.1803 | 1.79212 | ||||||||
\(915\) | 32.9642 | 1.08976 | ||||||||
\(916\) | −1.11277 | −0.0367670 | ||||||||
\(917\) | −3.75923 | −0.124141 | ||||||||
\(918\) | −28.7276 | −0.948152 | ||||||||
\(919\) | −9.94569 | −0.328078 | −0.164039 | − | 0.986454i | \(-0.552452\pi\) | ||||
−0.164039 | + | 0.986454i | \(0.552452\pi\) | |||||||
\(920\) | −31.4159 | −1.03575 | ||||||||
\(921\) | −5.52120 | −0.181930 | ||||||||
\(922\) | −35.4467 | −1.16737 | ||||||||
\(923\) | 2.16894 | 0.0713917 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.27545 | −0.0748162 | ||||||||
\(926\) | 54.0278 | 1.77547 | ||||||||
\(927\) | 124.878 | 4.10154 | ||||||||
\(928\) | −15.8602 | −0.520638 | ||||||||
\(929\) | −52.2385 | −1.71389 | −0.856944 | − | 0.515409i | \(-0.827640\pi\) | ||||
−0.856944 | + | 0.515409i | \(0.827640\pi\) | |||||||
\(930\) | 19.5320 | 0.640479 | ||||||||
\(931\) | 5.12290 | 0.167896 | ||||||||
\(932\) | −61.9341 | −2.02872 | ||||||||
\(933\) | −14.1181 | −0.462207 | ||||||||
\(934\) | −3.87339 | −0.126741 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.57778 | 0.247687 | ||||||||
\(937\) | 5.94143 | 0.194098 | 0.0970490 | − | 0.995280i | \(-0.469060\pi\) | ||||
0.0970490 | + | 0.995280i | \(0.469060\pi\) | |||||||
\(938\) | −32.3128 | −1.05505 | ||||||||
\(939\) | −19.6658 | −0.641770 | ||||||||
\(940\) | 3.83394 | 0.125049 | ||||||||
\(941\) | 15.7759 | 0.514281 | 0.257140 | − | 0.966374i | \(-0.417220\pi\) | ||||
0.257140 | + | 0.966374i | \(0.417220\pi\) | |||||||
\(942\) | 62.8494 | 2.04774 | ||||||||
\(943\) | 82.3032 | 2.68016 | ||||||||
\(944\) | −13.8297 | −0.450117 | ||||||||
\(945\) | 11.7833 | 0.383310 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 45.1583 | 1.46745 | 0.733723 | − | 0.679448i | \(-0.237781\pi\) | ||||
0.733723 | + | 0.679448i | \(0.237781\pi\) | |||||||
\(948\) | 6.38600 | 0.207408 | ||||||||
\(949\) | 4.89558 | 0.158917 | ||||||||
\(950\) | −12.0830 | −0.392023 | ||||||||
\(951\) | 11.5644 | 0.375001 | ||||||||
\(952\) | −3.81080 | −0.123509 | ||||||||
\(953\) | 38.0837 | 1.23365 | 0.616825 | − | 0.787100i | \(-0.288418\pi\) | ||||
0.616825 | + | 0.787100i | \(0.288418\pi\) | |||||||
\(954\) | 147.184 | 4.76526 | ||||||||
\(955\) | 12.2917 | 0.397750 | ||||||||
\(956\) | −80.7324 | −2.61107 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 15.3467 | 0.495830 | ||||||||
\(959\) | 15.0871 | 0.487189 | ||||||||
\(960\) | −36.8805 | −1.19031 | ||||||||
\(961\) | −23.9808 | −0.773573 | ||||||||
\(962\) | −1.62947 | −0.0525364 | ||||||||
\(963\) | −121.313 | −3.90925 | ||||||||
\(964\) | −22.3957 | −0.721318 | ||||||||
\(965\) | 18.5658 | 0.597655 | ||||||||
\(966\) | −62.8219 | −2.02126 | ||||||||
\(967\) | −15.4735 | −0.497593 | −0.248796 | − | 0.968556i | \(-0.580035\pi\) | ||||
−0.248796 | + | 0.968556i | \(0.580035\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.5514 | 0.531707 | ||||||||
\(970\) | 9.29904 | 0.298574 | ||||||||
\(971\) | 0.473814 | 0.0152054 | 0.00760270 | − | 0.999971i | \(-0.497580\pi\) | ||||
0.00760270 | + | 0.999971i | \(0.497580\pi\) | |||||||
\(972\) | 58.0424 | 1.86171 | ||||||||
\(973\) | 13.3265 | 0.427229 | ||||||||
\(974\) | −73.3673 | −2.35084 | ||||||||
\(975\) | −0.949001 | −0.0303924 | ||||||||
\(976\) | 16.5514 | 0.529797 | ||||||||
\(977\) | −46.1591 | −1.47676 | −0.738380 | − | 0.674384i | \(-0.764409\pi\) | ||||
−0.738380 | + | 0.674384i | \(0.764409\pi\) | |||||||
\(978\) | 89.8024 | 2.87156 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 3.56309 | 0.113819 | ||||||||
\(981\) | −6.89317 | −0.220082 | ||||||||
\(982\) | −45.3639 | −1.44762 | ||||||||
\(983\) | −51.4375 | −1.64060 | −0.820300 | − | 0.571934i | \(-0.806194\pi\) | ||||
−0.820300 | + | 0.571934i | \(0.806194\pi\) | |||||||
\(984\) | −111.299 | −3.54809 | ||||||||
\(985\) | 12.8716 | 0.410123 | ||||||||
\(986\) | 10.5308 | 0.335370 | ||||||||
\(987\) | 3.36327 | 0.107054 | ||||||||
\(988\) | −5.54198 | −0.176314 | ||||||||
\(989\) | −11.7589 | −0.373911 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.7757 | 0.914091 | 0.457046 | − | 0.889443i | \(-0.348908\pi\) | ||||
0.457046 | + | 0.889443i | \(0.348908\pi\) | |||||||
\(992\) | −9.72805 | −0.308866 | ||||||||
\(993\) | −64.6880 | −2.05281 | ||||||||
\(994\) | 16.8493 | 0.534429 | ||||||||
\(995\) | 9.93245 | 0.314880 | ||||||||
\(996\) | −124.884 | −3.95709 | ||||||||
\(997\) | −45.9499 | −1.45525 | −0.727625 | − | 0.685975i | \(-0.759376\pi\) | ||||
−0.727625 | + | 0.685975i | \(0.759376\pi\) | |||||||
\(998\) | −29.3805 | −0.930024 | ||||||||
\(999\) | −26.8122 | −0.848300 |
(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 | 4235.2.a.bp.1.3 | 18 | ||
11.7 | odd | 10 | 385.2.n.f.71.8 | ✓ | 36 | ||
11.8 | odd | 10 | 385.2.n.f.141.8 | yes | 36 | ||
11.10 | odd | 2 | 4235.2.a.bo.1.16 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
385.2.n.f.71.8 | ✓ | 36 | 11.7 | odd | 10 | ||
385.2.n.f.141.8 | yes | 36 | 11.8 | odd | 10 | ||
4235.2.a.bo.1.16 | 18 | 11.10 | odd | 2 | |||
4235.2.a.bp.1.3 | 18 | 1.1 | even | 1 | trivial |