Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9251,2,Mod(1,9251)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9251, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9251.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9251 = 11 \cdot 29^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9251.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: | \(73.8696069099\) |
Analytic rank: | \(1\) |
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: | \( x^{18} - 24 x^{16} - x^{15} + 233 x^{14} + 24 x^{13} - 1184 x^{12} - 207 x^{11} + 3413 x^{10} + \cdots - 41 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Root | \(-2.48400\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9251.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.48400 | 1.75645 | 0.878226 | − | 0.478245i | \(-0.158727\pi\) | ||||
0.878226 | + | 0.478245i | \(0.158727\pi\) | |||||||
\(3\) | 1.60954 | 0.929267 | 0.464634 | − | 0.885503i | \(-0.346186\pi\) | ||||
0.464634 | + | 0.885503i | \(0.346186\pi\) | |||||||
\(4\) | 4.17025 | 2.08513 | ||||||||
\(5\) | −1.24863 | −0.558406 | −0.279203 | − | 0.960232i | \(-0.590070\pi\) | ||||
−0.279203 | + | 0.960232i | \(0.590070\pi\) | |||||||
\(6\) | 3.99809 | 1.63221 | ||||||||
\(7\) | −4.33788 | −1.63957 | −0.819783 | − | 0.572674i | \(-0.805906\pi\) | ||||
−0.819783 | + | 0.572674i | \(0.805906\pi\) | |||||||
\(8\) | 5.39091 | 1.90597 | ||||||||
\(9\) | −0.409386 | −0.136462 | ||||||||
\(10\) | −3.10161 | −0.980814 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 6.71218 | 1.93764 | ||||||||
\(13\) | 3.41292 | 0.946575 | 0.473287 | − | 0.880908i | \(-0.343067\pi\) | ||||
0.473287 | + | 0.880908i | \(0.343067\pi\) | |||||||
\(14\) | −10.7753 | −2.87982 | ||||||||
\(15\) | −2.00972 | −0.518909 | ||||||||
\(16\) | 5.05050 | 1.26263 | ||||||||
\(17\) | −3.22679 | −0.782612 | −0.391306 | − | 0.920261i | \(-0.627977\pi\) | ||||
−0.391306 | + | 0.920261i | \(0.627977\pi\) | |||||||
\(18\) | −1.01691 | −0.239689 | ||||||||
\(19\) | 7.88973 | 1.81003 | 0.905014 | − | 0.425381i | \(-0.139860\pi\) | ||||
0.905014 | + | 0.425381i | \(0.139860\pi\) | |||||||
\(20\) | −5.20712 | −1.16435 | ||||||||
\(21\) | −6.98199 | −1.52360 | ||||||||
\(22\) | −2.48400 | −0.529590 | ||||||||
\(23\) | −5.25089 | −1.09489 | −0.547443 | − | 0.836843i | \(-0.684399\pi\) | ||||
−0.547443 | + | 0.836843i | \(0.684399\pi\) | |||||||
\(24\) | 8.67687 | 1.77116 | ||||||||
\(25\) | −3.44091 | −0.688183 | ||||||||
\(26\) | 8.47770 | 1.66261 | ||||||||
\(27\) | −5.48754 | −1.05608 | ||||||||
\(28\) | −18.0901 | −3.41870 | ||||||||
\(29\) | 0 | 0 | ||||||||
\(30\) | −4.99215 | −0.911438 | ||||||||
\(31\) | −7.46621 | −1.34097 | −0.670486 | − | 0.741922i | \(-0.733914\pi\) | ||||
−0.670486 | + | 0.741922i | \(0.733914\pi\) | |||||||
\(32\) | 1.76363 | 0.311769 | ||||||||
\(33\) | −1.60954 | −0.280185 | ||||||||
\(34\) | −8.01535 | −1.37462 | ||||||||
\(35\) | 5.41643 | 0.915544 | ||||||||
\(36\) | −1.70724 | −0.284540 | ||||||||
\(37\) | 0.156756 | 0.0257705 | 0.0128852 | − | 0.999917i | \(-0.495898\pi\) | ||||
0.0128852 | + | 0.999917i | \(0.495898\pi\) | |||||||
\(38\) | 19.5981 | 3.17923 | ||||||||
\(39\) | 5.49323 | 0.879621 | ||||||||
\(40\) | −6.73127 | −1.06431 | ||||||||
\(41\) | 5.92116 | 0.924731 | 0.462365 | − | 0.886690i | \(-0.347001\pi\) | ||||
0.462365 | + | 0.886690i | \(0.347001\pi\) | |||||||
\(42\) | −17.3433 | −2.67612 | ||||||||
\(43\) | −3.19801 | −0.487691 | −0.243846 | − | 0.969814i | \(-0.578409\pi\) | ||||
−0.243846 | + | 0.969814i | \(0.578409\pi\) | |||||||
\(44\) | −4.17025 | −0.628689 | ||||||||
\(45\) | 0.511173 | 0.0762012 | ||||||||
\(46\) | −13.0432 | −1.92312 | ||||||||
\(47\) | −3.78287 | −0.551789 | −0.275894 | − | 0.961188i | \(-0.588974\pi\) | ||||
−0.275894 | + | 0.961188i | \(0.588974\pi\) | |||||||
\(48\) | 8.12898 | 1.17332 | ||||||||
\(49\) | 11.8172 | 1.68818 | ||||||||
\(50\) | −8.54723 | −1.20876 | ||||||||
\(51\) | −5.19364 | −0.727256 | ||||||||
\(52\) | 14.2328 | 1.97373 | ||||||||
\(53\) | −12.7243 | −1.74782 | −0.873909 | − | 0.486089i | \(-0.838423\pi\) | ||||
−0.873909 | + | 0.486089i | \(0.838423\pi\) | |||||||
\(54\) | −13.6310 | −1.85495 | ||||||||
\(55\) | 1.24863 | 0.168366 | ||||||||
\(56\) | −23.3851 | −3.12497 | ||||||||
\(57\) | 12.6988 | 1.68200 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.93175 | −0.642060 | −0.321030 | − | 0.947069i | \(-0.604029\pi\) | ||||
−0.321030 | + | 0.947069i | \(0.604029\pi\) | |||||||
\(60\) | −8.38106 | −1.08199 | ||||||||
\(61\) | 10.8056 | 1.38351 | 0.691756 | − | 0.722132i | \(-0.256838\pi\) | ||||
0.691756 | + | 0.722132i | \(0.256838\pi\) | |||||||
\(62\) | −18.5461 | −2.35535 | ||||||||
\(63\) | 1.77587 | 0.223738 | ||||||||
\(64\) | −5.72015 | −0.715018 | ||||||||
\(65\) | −4.26149 | −0.528573 | ||||||||
\(66\) | −3.99809 | −0.492131 | ||||||||
\(67\) | −4.44829 | −0.543446 | −0.271723 | − | 0.962376i | \(-0.587593\pi\) | ||||
−0.271723 | + | 0.962376i | \(0.587593\pi\) | |||||||
\(68\) | −13.4565 | −1.63184 | ||||||||
\(69\) | −8.45151 | −1.01744 | ||||||||
\(70\) | 13.4544 | 1.60811 | ||||||||
\(71\) | −6.95540 | −0.825454 | −0.412727 | − | 0.910855i | \(-0.635424\pi\) | ||||
−0.412727 | + | 0.910855i | \(0.635424\pi\) | |||||||
\(72\) | −2.20696 | −0.260093 | ||||||||
\(73\) | 3.38107 | 0.395724 | 0.197862 | − | 0.980230i | \(-0.436600\pi\) | ||||
0.197862 | + | 0.980230i | \(0.436600\pi\) | |||||||
\(74\) | 0.389381 | 0.0452647 | ||||||||
\(75\) | −5.53828 | −0.639506 | ||||||||
\(76\) | 32.9022 | 3.77414 | ||||||||
\(77\) | 4.33788 | 0.494348 | ||||||||
\(78\) | 13.6452 | 1.54501 | ||||||||
\(79\) | −11.8638 | −1.33478 | −0.667390 | − | 0.744708i | \(-0.732589\pi\) | ||||
−0.667390 | + | 0.744708i | \(0.732589\pi\) | |||||||
\(80\) | −6.30623 | −0.705058 | ||||||||
\(81\) | −7.60425 | −0.844916 | ||||||||
\(82\) | 14.7082 | 1.62425 | ||||||||
\(83\) | 10.8180 | 1.18743 | 0.593713 | − | 0.804677i | \(-0.297661\pi\) | ||||
0.593713 | + | 0.804677i | \(0.297661\pi\) | |||||||
\(84\) | −29.1167 | −3.17689 | ||||||||
\(85\) | 4.02908 | 0.437015 | ||||||||
\(86\) | −7.94384 | −0.856607 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.39091 | −0.574673 | ||||||||
\(89\) | −2.57416 | −0.272860 | −0.136430 | − | 0.990650i | \(-0.543563\pi\) | ||||
−0.136430 | + | 0.990650i | \(0.543563\pi\) | |||||||
\(90\) | 1.26975 | 0.133844 | ||||||||
\(91\) | −14.8049 | −1.55197 | ||||||||
\(92\) | −21.8976 | −2.28298 | ||||||||
\(93\) | −12.0172 | −1.24612 | ||||||||
\(94\) | −9.39666 | −0.969191 | ||||||||
\(95\) | −9.85139 | −1.01073 | ||||||||
\(96\) | 2.83863 | 0.289717 | ||||||||
\(97\) | −13.6920 | −1.39021 | −0.695104 | − | 0.718909i | \(-0.744642\pi\) | ||||
−0.695104 | + | 0.718909i | \(0.744642\pi\) | |||||||
\(98\) | 29.3540 | 2.96520 | ||||||||
\(99\) | 0.409386 | 0.0411448 | ||||||||
\(100\) | −14.3495 | −1.43495 | ||||||||
\(101\) | −15.2789 | −1.52031 | −0.760153 | − | 0.649744i | \(-0.774876\pi\) | ||||
−0.760153 | + | 0.649744i | \(0.774876\pi\) | |||||||
\(102\) | −12.9010 | −1.27739 | ||||||||
\(103\) | 17.3172 | 1.70632 | 0.853158 | − | 0.521652i | \(-0.174684\pi\) | ||||
0.853158 | + | 0.521652i | \(0.174684\pi\) | |||||||
\(104\) | 18.3988 | 1.80415 | ||||||||
\(105\) | 8.71795 | 0.850785 | ||||||||
\(106\) | −31.6072 | −3.06996 | ||||||||
\(107\) | −4.57513 | −0.442294 | −0.221147 | − | 0.975240i | \(-0.570980\pi\) | ||||
−0.221147 | + | 0.975240i | \(0.570980\pi\) | |||||||
\(108\) | −22.8844 | −2.20205 | ||||||||
\(109\) | −8.58602 | −0.822391 | −0.411196 | − | 0.911547i | \(-0.634889\pi\) | ||||
−0.411196 | + | 0.911547i | \(0.634889\pi\) | |||||||
\(110\) | 3.10161 | 0.295727 | ||||||||
\(111\) | 0.252304 | 0.0239477 | ||||||||
\(112\) | −21.9085 | −2.07016 | ||||||||
\(113\) | 4.50753 | 0.424033 | 0.212017 | − | 0.977266i | \(-0.431997\pi\) | ||||
0.212017 | + | 0.977266i | \(0.431997\pi\) | |||||||
\(114\) | 31.5439 | 2.95435 | ||||||||
\(115\) | 6.55644 | 0.611391 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.39720 | −0.129171 | ||||||||
\(118\) | −12.2505 | −1.12775 | ||||||||
\(119\) | 13.9974 | 1.28314 | ||||||||
\(120\) | −10.8342 | −0.989026 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 26.8410 | 2.43007 | ||||||||
\(123\) | 9.53034 | 0.859322 | ||||||||
\(124\) | −31.1360 | −2.79610 | ||||||||
\(125\) | 10.5396 | 0.942691 | ||||||||
\(126\) | 4.41126 | 0.392986 | ||||||||
\(127\) | 7.87006 | 0.698355 | 0.349177 | − | 0.937057i | \(-0.386461\pi\) | ||||
0.349177 | + | 0.937057i | \(0.386461\pi\) | |||||||
\(128\) | −17.7361 | −1.56766 | ||||||||
\(129\) | −5.14731 | −0.453196 | ||||||||
\(130\) | −10.5855 | −0.928414 | ||||||||
\(131\) | 0.585436 | 0.0511498 | 0.0255749 | − | 0.999673i | \(-0.491858\pi\) | ||||
0.0255749 | + | 0.999673i | \(0.491858\pi\) | |||||||
\(132\) | −6.71218 | −0.584220 | ||||||||
\(133\) | −34.2247 | −2.96766 | ||||||||
\(134\) | −11.0496 | −0.954537 | ||||||||
\(135\) | 6.85193 | 0.589720 | ||||||||
\(136\) | −17.3953 | −1.49164 | ||||||||
\(137\) | 13.0489 | 1.11484 | 0.557421 | − | 0.830230i | \(-0.311791\pi\) | ||||
0.557421 | + | 0.830230i | \(0.311791\pi\) | |||||||
\(138\) | −20.9936 | −1.78709 | ||||||||
\(139\) | 9.78669 | 0.830096 | 0.415048 | − | 0.909799i | \(-0.363765\pi\) | ||||
0.415048 | + | 0.909799i | \(0.363765\pi\) | |||||||
\(140\) | 22.5879 | 1.90902 | ||||||||
\(141\) | −6.08868 | −0.512759 | ||||||||
\(142\) | −17.2772 | −1.44987 | ||||||||
\(143\) | −3.41292 | −0.285403 | ||||||||
\(144\) | −2.06760 | −0.172300 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.39856 | 0.695070 | ||||||||
\(147\) | 19.0203 | 1.56877 | ||||||||
\(148\) | 0.653711 | 0.0537347 | ||||||||
\(149\) | 3.59653 | 0.294639 | 0.147319 | − | 0.989089i | \(-0.452935\pi\) | ||||
0.147319 | + | 0.989089i | \(0.452935\pi\) | |||||||
\(150\) | −13.7571 | −1.12326 | ||||||||
\(151\) | −13.3410 | −1.08567 | −0.542837 | − | 0.839838i | \(-0.682650\pi\) | ||||
−0.542837 | + | 0.839838i | \(0.682650\pi\) | |||||||
\(152\) | 42.5328 | 3.44987 | ||||||||
\(153\) | 1.32100 | 0.106797 | ||||||||
\(154\) | 10.7753 | 0.868299 | ||||||||
\(155\) | 9.32257 | 0.748807 | ||||||||
\(156\) | 22.9082 | 1.83412 | ||||||||
\(157\) | −15.2824 | −1.21967 | −0.609836 | − | 0.792528i | \(-0.708765\pi\) | ||||
−0.609836 | + | 0.792528i | \(0.708765\pi\) | |||||||
\(158\) | −29.4696 | −2.34448 | ||||||||
\(159\) | −20.4803 | −1.62419 | ||||||||
\(160\) | −2.20213 | −0.174094 | ||||||||
\(161\) | 22.7778 | 1.79514 | ||||||||
\(162\) | −18.8889 | −1.48406 | ||||||||
\(163\) | −10.6468 | −0.833923 | −0.416961 | − | 0.908924i | \(-0.636905\pi\) | ||||
−0.416961 | + | 0.908924i | \(0.636905\pi\) | |||||||
\(164\) | 24.6928 | 1.92818 | ||||||||
\(165\) | 2.00972 | 0.156457 | ||||||||
\(166\) | 26.8718 | 2.08566 | ||||||||
\(167\) | 18.7552 | 1.45132 | 0.725661 | − | 0.688052i | \(-0.241534\pi\) | ||||
0.725661 | + | 0.688052i | \(0.241534\pi\) | |||||||
\(168\) | −37.6393 | −2.90393 | ||||||||
\(169\) | −1.35195 | −0.103996 | ||||||||
\(170\) | 10.0082 | 0.767597 | ||||||||
\(171\) | −3.22994 | −0.247000 | ||||||||
\(172\) | −13.3365 | −1.01690 | ||||||||
\(173\) | −0.562371 | −0.0427563 | −0.0213782 | − | 0.999771i | \(-0.506805\pi\) | ||||
−0.0213782 | + | 0.999771i | \(0.506805\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.9263 | 1.12832 | ||||||||
\(176\) | −5.05050 | −0.380696 | ||||||||
\(177\) | −7.93785 | −0.596645 | ||||||||
\(178\) | −6.39421 | −0.479267 | ||||||||
\(179\) | 8.72682 | 0.652273 | 0.326137 | − | 0.945323i | \(-0.394253\pi\) | ||||
0.326137 | + | 0.945323i | \(0.394253\pi\) | |||||||
\(180\) | 2.13172 | 0.158889 | ||||||||
\(181\) | −21.4433 | −1.59387 | −0.796934 | − | 0.604066i | \(-0.793546\pi\) | ||||
−0.796934 | + | 0.604066i | \(0.793546\pi\) | |||||||
\(182\) | −36.7753 | −2.72597 | ||||||||
\(183\) | 17.3920 | 1.28565 | ||||||||
\(184\) | −28.3071 | −2.08682 | ||||||||
\(185\) | −0.195731 | −0.0143904 | ||||||||
\(186\) | −29.8506 | −2.18875 | ||||||||
\(187\) | 3.22679 | 0.235966 | ||||||||
\(188\) | −15.7755 | −1.15055 | ||||||||
\(189\) | 23.8043 | 1.73151 | ||||||||
\(190\) | −24.4708 | −1.77530 | ||||||||
\(191\) | −1.16055 | −0.0839745 | −0.0419872 | − | 0.999118i | \(-0.513369\pi\) | ||||
−0.0419872 | + | 0.999118i | \(0.513369\pi\) | |||||||
\(192\) | −9.20680 | −0.664443 | ||||||||
\(193\) | −3.20830 | −0.230938 | −0.115469 | − | 0.993311i | \(-0.536837\pi\) | ||||
−0.115469 | + | 0.993311i | \(0.536837\pi\) | |||||||
\(194\) | −34.0108 | −2.44183 | ||||||||
\(195\) | −6.85904 | −0.491186 | ||||||||
\(196\) | 49.2809 | 3.52006 | ||||||||
\(197\) | 15.8476 | 1.12909 | 0.564546 | − | 0.825402i | \(-0.309051\pi\) | ||||
0.564546 | + | 0.825402i | \(0.309051\pi\) | |||||||
\(198\) | 1.01691 | 0.0722690 | ||||||||
\(199\) | 8.30490 | 0.588719 | 0.294359 | − | 0.955695i | \(-0.404894\pi\) | ||||
0.294359 | + | 0.955695i | \(0.404894\pi\) | |||||||
\(200\) | −18.5496 | −1.31166 | ||||||||
\(201\) | −7.15970 | −0.505006 | ||||||||
\(202\) | −37.9527 | −2.67035 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −21.6588 | −1.51642 | ||||||||
\(205\) | −7.39337 | −0.516375 | ||||||||
\(206\) | 43.0160 | 2.99706 | ||||||||
\(207\) | 2.14964 | 0.149410 | ||||||||
\(208\) | 17.2370 | 1.19517 | ||||||||
\(209\) | −7.88973 | −0.545744 | ||||||||
\(210\) | 21.6554 | 1.49436 | ||||||||
\(211\) | 1.95912 | 0.134871 | 0.0674357 | − | 0.997724i | \(-0.478518\pi\) | ||||
0.0674357 | + | 0.997724i | \(0.478518\pi\) | |||||||
\(212\) | −53.0636 | −3.64442 | ||||||||
\(213\) | −11.1950 | −0.767068 | ||||||||
\(214\) | −11.3646 | −0.776869 | ||||||||
\(215\) | 3.99314 | 0.272330 | ||||||||
\(216\) | −29.5828 | −2.01285 | ||||||||
\(217\) | 32.3876 | 2.19861 | ||||||||
\(218\) | −21.3277 | −1.44449 | ||||||||
\(219\) | 5.44196 | 0.367733 | ||||||||
\(220\) | 5.20712 | 0.351064 | ||||||||
\(221\) | −11.0128 | −0.740801 | ||||||||
\(222\) | 0.626724 | 0.0420630 | ||||||||
\(223\) | −3.34094 | −0.223726 | −0.111863 | − | 0.993724i | \(-0.535682\pi\) | ||||
−0.111863 | + | 0.993724i | \(0.535682\pi\) | |||||||
\(224\) | −7.65042 | −0.511165 | ||||||||
\(225\) | 1.40866 | 0.0939108 | ||||||||
\(226\) | 11.1967 | 0.744794 | ||||||||
\(227\) | 24.6860 | 1.63847 | 0.819234 | − | 0.573459i | \(-0.194399\pi\) | ||||
0.819234 | + | 0.573459i | \(0.194399\pi\) | |||||||
\(228\) | 52.9573 | 3.50718 | ||||||||
\(229\) | 27.8093 | 1.83769 | 0.918844 | − | 0.394620i | \(-0.129124\pi\) | ||||
0.918844 | + | 0.394620i | \(0.129124\pi\) | |||||||
\(230\) | 16.2862 | 1.07388 | ||||||||
\(231\) | 6.98199 | 0.459381 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.55755 | −0.429600 | −0.214800 | − | 0.976658i | \(-0.568910\pi\) | ||||
−0.214800 | + | 0.976658i | \(0.568910\pi\) | |||||||
\(234\) | −3.47065 | −0.226884 | ||||||||
\(235\) | 4.72342 | 0.308122 | ||||||||
\(236\) | −20.5667 | −1.33878 | ||||||||
\(237\) | −19.0952 | −1.24037 | ||||||||
\(238\) | 34.7696 | 2.25378 | ||||||||
\(239\) | 25.4157 | 1.64401 | 0.822003 | − | 0.569483i | \(-0.192857\pi\) | ||||
0.822003 | + | 0.569483i | \(0.192857\pi\) | |||||||
\(240\) | −10.1501 | −0.655187 | ||||||||
\(241\) | −3.09174 | −0.199156 | −0.0995781 | − | 0.995030i | \(-0.531749\pi\) | ||||
−0.0995781 | + | 0.995030i | \(0.531749\pi\) | |||||||
\(242\) | 2.48400 | 0.159678 | ||||||||
\(243\) | 4.22329 | 0.270924 | ||||||||
\(244\) | 45.0619 | 2.88480 | ||||||||
\(245\) | −14.7554 | −0.942688 | ||||||||
\(246\) | 23.6734 | 1.50936 | ||||||||
\(247\) | 26.9270 | 1.71333 | ||||||||
\(248\) | −40.2497 | −2.55586 | ||||||||
\(249\) | 17.4119 | 1.10344 | ||||||||
\(250\) | 26.1804 | 1.65579 | ||||||||
\(251\) | 9.93897 | 0.627342 | 0.313671 | − | 0.949532i | \(-0.398441\pi\) | ||||
0.313671 | + | 0.949532i | \(0.398441\pi\) | |||||||
\(252\) | 7.40582 | 0.466523 | ||||||||
\(253\) | 5.25089 | 0.330121 | ||||||||
\(254\) | 19.5492 | 1.22663 | ||||||||
\(255\) | 6.48496 | 0.406104 | ||||||||
\(256\) | −32.6162 | −2.03851 | ||||||||
\(257\) | 25.8038 | 1.60960 | 0.804798 | − | 0.593549i | \(-0.202274\pi\) | ||||
0.804798 | + | 0.593549i | \(0.202274\pi\) | |||||||
\(258\) | −12.7859 | −0.796017 | ||||||||
\(259\) | −0.679988 | −0.0422524 | ||||||||
\(260\) | −17.7715 | −1.10214 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.45422 | 0.0898422 | ||||||||
\(263\) | −26.7419 | −1.64898 | −0.824488 | − | 0.565880i | \(-0.808537\pi\) | ||||
−0.824488 | + | 0.565880i | \(0.808537\pi\) | |||||||
\(264\) | −8.67687 | −0.534024 | ||||||||
\(265\) | 15.8880 | 0.975993 | ||||||||
\(266\) | −85.0142 | −5.21256 | ||||||||
\(267\) | −4.14321 | −0.253560 | ||||||||
\(268\) | −18.5505 | −1.13315 | ||||||||
\(269\) | −20.1985 | −1.23152 | −0.615762 | − | 0.787932i | \(-0.711152\pi\) | ||||
−0.615762 | + | 0.787932i | \(0.711152\pi\) | |||||||
\(270\) | 17.0202 | 1.03582 | ||||||||
\(271\) | 1.03904 | 0.0631173 | 0.0315586 | − | 0.999502i | \(-0.489953\pi\) | ||||
0.0315586 | + | 0.999502i | \(0.489953\pi\) | |||||||
\(272\) | −16.2969 | −0.988146 | ||||||||
\(273\) | −23.8290 | −1.44220 | ||||||||
\(274\) | 32.4134 | 1.95817 | ||||||||
\(275\) | 3.44091 | 0.207495 | ||||||||
\(276\) | −35.2449 | −2.12150 | ||||||||
\(277\) | −19.3845 | −1.16470 | −0.582351 | − | 0.812937i | \(-0.697867\pi\) | ||||
−0.582351 | + | 0.812937i | \(0.697867\pi\) | |||||||
\(278\) | 24.3101 | 1.45803 | ||||||||
\(279\) | 3.05656 | 0.182992 | ||||||||
\(280\) | 29.1995 | 1.74500 | ||||||||
\(281\) | 21.2565 | 1.26806 | 0.634028 | − | 0.773310i | \(-0.281400\pi\) | ||||
0.634028 | + | 0.773310i | \(0.281400\pi\) | |||||||
\(282\) | −15.1243 | −0.900638 | ||||||||
\(283\) | 13.5808 | 0.807293 | 0.403646 | − | 0.914915i | \(-0.367743\pi\) | ||||
0.403646 | + | 0.914915i | \(0.367743\pi\) | |||||||
\(284\) | −29.0058 | −1.72118 | ||||||||
\(285\) | −15.8562 | −0.939239 | ||||||||
\(286\) | −8.47770 | −0.501297 | ||||||||
\(287\) | −25.6853 | −1.51616 | ||||||||
\(288\) | −0.722006 | −0.0425446 | ||||||||
\(289\) | −6.58782 | −0.387519 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −22.0377 | −1.29187 | ||||||||
\(292\) | 14.0999 | 0.825134 | ||||||||
\(293\) | 3.61548 | 0.211219 | 0.105609 | − | 0.994408i | \(-0.466321\pi\) | ||||
0.105609 | + | 0.994408i | \(0.466321\pi\) | |||||||
\(294\) | 47.2464 | 2.75547 | ||||||||
\(295\) | 6.15795 | 0.358530 | ||||||||
\(296\) | 0.845056 | 0.0491179 | ||||||||
\(297\) | 5.48754 | 0.318419 | ||||||||
\(298\) | 8.93377 | 0.517519 | ||||||||
\(299\) | −17.9209 | −1.03639 | ||||||||
\(300\) | −23.0960 | −1.33345 | ||||||||
\(301\) | 13.8726 | 0.799602 | ||||||||
\(302\) | −33.1390 | −1.90693 | ||||||||
\(303\) | −24.5920 | −1.41277 | ||||||||
\(304\) | 39.8471 | 2.28539 | ||||||||
\(305\) | −13.4922 | −0.772561 | ||||||||
\(306\) | 3.28137 | 0.187583 | ||||||||
\(307\) | 11.3363 | 0.646998 | 0.323499 | − | 0.946228i | \(-0.395141\pi\) | ||||
0.323499 | + | 0.946228i | \(0.395141\pi\) | |||||||
\(308\) | 18.0901 | 1.03078 | ||||||||
\(309\) | 27.8727 | 1.58562 | ||||||||
\(310\) | 23.1573 | 1.31524 | ||||||||
\(311\) | −6.55098 | −0.371472 | −0.185736 | − | 0.982600i | \(-0.559467\pi\) | ||||
−0.185736 | + | 0.982600i | \(0.559467\pi\) | |||||||
\(312\) | 29.6135 | 1.67653 | ||||||||
\(313\) | −26.1586 | −1.47857 | −0.739284 | − | 0.673393i | \(-0.764836\pi\) | ||||
−0.739284 | + | 0.673393i | \(0.764836\pi\) | |||||||
\(314\) | −37.9616 | −2.14230 | ||||||||
\(315\) | −2.21741 | −0.124937 | ||||||||
\(316\) | −49.4750 | −2.78319 | ||||||||
\(317\) | −24.5458 | −1.37863 | −0.689315 | − | 0.724461i | \(-0.742089\pi\) | ||||
−0.689315 | + | 0.724461i | \(0.742089\pi\) | |||||||
\(318\) | −50.8730 | −2.85282 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 7.14237 | 0.399271 | ||||||||
\(321\) | −7.36384 | −0.411010 | ||||||||
\(322\) | 56.5800 | 3.15308 | ||||||||
\(323\) | −25.4585 | −1.41655 | ||||||||
\(324\) | −31.7116 | −1.76176 | ||||||||
\(325\) | −11.7436 | −0.651416 | ||||||||
\(326\) | −26.4467 | −1.46475 | ||||||||
\(327\) | −13.8195 | −0.764222 | ||||||||
\(328\) | 31.9204 | 1.76251 | ||||||||
\(329\) | 16.4097 | 0.904694 | ||||||||
\(330\) | 4.99215 | 0.274809 | ||||||||
\(331\) | 9.23848 | 0.507793 | 0.253896 | − | 0.967231i | \(-0.418288\pi\) | ||||
0.253896 | + | 0.967231i | \(0.418288\pi\) | |||||||
\(332\) | 45.1136 | 2.47593 | ||||||||
\(333\) | −0.0641736 | −0.00351669 | ||||||||
\(334\) | 46.5880 | 2.54918 | ||||||||
\(335\) | 5.55429 | 0.303463 | ||||||||
\(336\) | −35.2626 | −1.92373 | ||||||||
\(337\) | 7.74981 | 0.422159 | 0.211080 | − | 0.977469i | \(-0.432302\pi\) | ||||
0.211080 | + | 0.977469i | \(0.432302\pi\) | |||||||
\(338\) | −3.35824 | −0.182664 | ||||||||
\(339\) | 7.25505 | 0.394040 | ||||||||
\(340\) | 16.8023 | 0.911232 | ||||||||
\(341\) | 7.46621 | 0.404318 | ||||||||
\(342\) | −8.02318 | −0.433844 | ||||||||
\(343\) | −20.8966 | −1.12831 | ||||||||
\(344\) | −17.2401 | −0.929527 | ||||||||
\(345\) | 10.5528 | 0.568146 | ||||||||
\(346\) | −1.39693 | −0.0750994 | ||||||||
\(347\) | −15.5385 | −0.834151 | −0.417076 | − | 0.908872i | \(-0.636945\pi\) | ||||
−0.417076 | + | 0.908872i | \(0.636945\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.8052 | −1.54191 | −0.770954 | − | 0.636890i | \(-0.780220\pi\) | ||||
−0.770954 | + | 0.636890i | \(0.780220\pi\) | |||||||
\(350\) | 37.0769 | 1.98184 | ||||||||
\(351\) | −18.7285 | −0.999656 | ||||||||
\(352\) | −1.76363 | −0.0940018 | ||||||||
\(353\) | 4.64212 | 0.247075 | 0.123537 | − | 0.992340i | \(-0.460576\pi\) | ||||
0.123537 | + | 0.992340i | \(0.460576\pi\) | |||||||
\(354\) | −19.7176 | −1.04798 | ||||||||
\(355\) | 8.68475 | 0.460939 | ||||||||
\(356\) | −10.7349 | −0.568949 | ||||||||
\(357\) | 22.5294 | 1.19238 | ||||||||
\(358\) | 21.6774 | 1.14569 | ||||||||
\(359\) | −9.64431 | −0.509007 | −0.254504 | − | 0.967072i | \(-0.581912\pi\) | ||||
−0.254504 | + | 0.967072i | \(0.581912\pi\) | |||||||
\(360\) | 2.75569 | 0.145237 | ||||||||
\(361\) | 43.2478 | 2.27620 | ||||||||
\(362\) | −53.2652 | −2.79955 | ||||||||
\(363\) | 1.60954 | 0.0844789 | ||||||||
\(364\) | −61.7400 | −3.23606 | ||||||||
\(365\) | −4.22171 | −0.220975 | ||||||||
\(366\) | 43.2017 | 2.25819 | ||||||||
\(367\) | −20.7081 | −1.08095 | −0.540477 | − | 0.841359i | \(-0.681756\pi\) | ||||
−0.540477 | + | 0.841359i | \(0.681756\pi\) | |||||||
\(368\) | −26.5196 | −1.38243 | ||||||||
\(369\) | −2.42404 | −0.126191 | ||||||||
\(370\) | −0.486195 | −0.0252761 | ||||||||
\(371\) | 55.1966 | 2.86566 | ||||||||
\(372\) | −50.1146 | −2.59832 | ||||||||
\(373\) | 9.52134 | 0.492996 | 0.246498 | − | 0.969143i | \(-0.420720\pi\) | ||||
0.246498 | + | 0.969143i | \(0.420720\pi\) | |||||||
\(374\) | 8.01535 | 0.414464 | ||||||||
\(375\) | 16.9639 | 0.876012 | ||||||||
\(376\) | −20.3931 | −1.05169 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 59.1299 | 3.04131 | ||||||||
\(379\) | −0.203466 | −0.0104513 | −0.00522566 | − | 0.999986i | \(-0.501663\pi\) | ||||
−0.00522566 | + | 0.999986i | \(0.501663\pi\) | |||||||
\(380\) | −41.0828 | −2.10750 | ||||||||
\(381\) | 12.6672 | 0.648958 | ||||||||
\(382\) | −2.88281 | −0.147497 | ||||||||
\(383\) | 33.2197 | 1.69745 | 0.848723 | − | 0.528838i | \(-0.177372\pi\) | ||||
0.848723 | + | 0.528838i | \(0.177372\pi\) | |||||||
\(384\) | −28.5469 | −1.45678 | ||||||||
\(385\) | −5.41643 | −0.276047 | ||||||||
\(386\) | −7.96941 | −0.405632 | ||||||||
\(387\) | 1.30922 | 0.0665513 | ||||||||
\(388\) | −57.0989 | −2.89876 | ||||||||
\(389\) | 5.39070 | 0.273319 | 0.136660 | − | 0.990618i | \(-0.456363\pi\) | ||||
0.136660 | + | 0.990618i | \(0.456363\pi\) | |||||||
\(390\) | −17.0378 | −0.862745 | ||||||||
\(391\) | 16.9435 | 0.856871 | ||||||||
\(392\) | 63.7056 | 3.21762 | ||||||||
\(393\) | 0.942282 | 0.0475318 | ||||||||
\(394\) | 39.3653 | 1.98320 | ||||||||
\(395\) | 14.8135 | 0.745349 | ||||||||
\(396\) | 1.70724 | 0.0857922 | ||||||||
\(397\) | 2.58905 | 0.129941 | 0.0649703 | − | 0.997887i | \(-0.479305\pi\) | ||||
0.0649703 | + | 0.997887i | \(0.479305\pi\) | |||||||
\(398\) | 20.6294 | 1.03406 | ||||||||
\(399\) | −55.0860 | −2.75775 | ||||||||
\(400\) | −17.3783 | −0.868917 | ||||||||
\(401\) | −30.9159 | −1.54387 | −0.771933 | − | 0.635704i | \(-0.780710\pi\) | ||||
−0.771933 | + | 0.635704i | \(0.780710\pi\) | |||||||
\(402\) | −17.7847 | −0.887020 | ||||||||
\(403\) | −25.4816 | −1.26933 | ||||||||
\(404\) | −63.7168 | −3.17003 | ||||||||
\(405\) | 9.49492 | 0.471806 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.156756 | −0.00777010 | ||||||||
\(408\) | −27.9985 | −1.38613 | ||||||||
\(409\) | −27.3291 | −1.35134 | −0.675668 | − | 0.737206i | \(-0.736145\pi\) | ||||
−0.675668 | + | 0.737206i | \(0.736145\pi\) | |||||||
\(410\) | −18.3651 | −0.906989 | ||||||||
\(411\) | 21.0027 | 1.03599 | ||||||||
\(412\) | 72.2172 | 3.55789 | ||||||||
\(413\) | 21.3934 | 1.05270 | ||||||||
\(414\) | 5.33971 | 0.262432 | ||||||||
\(415\) | −13.5077 | −0.663066 | ||||||||
\(416\) | 6.01914 | 0.295112 | ||||||||
\(417\) | 15.7521 | 0.771382 | ||||||||
\(418\) | −19.5981 | −0.958574 | ||||||||
\(419\) | 32.0078 | 1.56368 | 0.781842 | − | 0.623477i | \(-0.214280\pi\) | ||||
0.781842 | + | 0.623477i | \(0.214280\pi\) | |||||||
\(420\) | 36.3561 | 1.77399 | ||||||||
\(421\) | −16.6276 | −0.810378 | −0.405189 | − | 0.914233i | \(-0.632794\pi\) | ||||
−0.405189 | + | 0.914233i | \(0.632794\pi\) | |||||||
\(422\) | 4.86645 | 0.236895 | ||||||||
\(423\) | 1.54866 | 0.0752982 | ||||||||
\(424\) | −68.5956 | −3.33130 | ||||||||
\(425\) | 11.1031 | 0.538580 | ||||||||
\(426\) | −27.8083 | −1.34732 | ||||||||
\(427\) | −46.8733 | −2.26836 | ||||||||
\(428\) | −19.0794 | −0.922239 | ||||||||
\(429\) | −5.49323 | −0.265216 | ||||||||
\(430\) | 9.91895 | 0.478334 | ||||||||
\(431\) | 14.2553 | 0.686652 | 0.343326 | − | 0.939216i | \(-0.388446\pi\) | ||||
0.343326 | + | 0.939216i | \(0.388446\pi\) | |||||||
\(432\) | −27.7148 | −1.33343 | ||||||||
\(433\) | 4.19527 | 0.201612 | 0.100806 | − | 0.994906i | \(-0.467858\pi\) | ||||
0.100806 | + | 0.994906i | \(0.467858\pi\) | |||||||
\(434\) | 80.4507 | 3.86176 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −35.8059 | −1.71479 | ||||||||
\(437\) | −41.4281 | −1.98178 | ||||||||
\(438\) | 13.5178 | 0.645906 | ||||||||
\(439\) | 15.8189 | 0.754993 | 0.377497 | − | 0.926011i | \(-0.376785\pi\) | ||||
0.377497 | + | 0.926011i | \(0.376785\pi\) | |||||||
\(440\) | 6.73127 | 0.320901 | ||||||||
\(441\) | −4.83781 | −0.230372 | ||||||||
\(442\) | −27.3558 | −1.30118 | ||||||||
\(443\) | −26.3718 | −1.25296 | −0.626480 | − | 0.779437i | \(-0.715505\pi\) | ||||
−0.626480 | + | 0.779437i | \(0.715505\pi\) | |||||||
\(444\) | 1.05217 | 0.0499339 | ||||||||
\(445\) | 3.21418 | 0.152367 | ||||||||
\(446\) | −8.29888 | −0.392964 | ||||||||
\(447\) | 5.78875 | 0.273798 | ||||||||
\(448\) | 24.8133 | 1.17232 | ||||||||
\(449\) | 10.0615 | 0.474832 | 0.237416 | − | 0.971408i | \(-0.423699\pi\) | ||||
0.237416 | + | 0.971408i | \(0.423699\pi\) | |||||||
\(450\) | 3.49911 | 0.164950 | ||||||||
\(451\) | −5.92116 | −0.278817 | ||||||||
\(452\) | 18.7976 | 0.884163 | ||||||||
\(453\) | −21.4728 | −1.00888 | ||||||||
\(454\) | 61.3200 | 2.87789 | ||||||||
\(455\) | 18.4859 | 0.866631 | ||||||||
\(456\) | 68.4582 | 3.20585 | ||||||||
\(457\) | −19.0783 | −0.892447 | −0.446223 | − | 0.894922i | \(-0.647231\pi\) | ||||
−0.446223 | + | 0.894922i | \(0.647231\pi\) | |||||||
\(458\) | 69.0782 | 3.22781 | ||||||||
\(459\) | 17.7071 | 0.826498 | ||||||||
\(460\) | 27.3420 | 1.27483 | ||||||||
\(461\) | 31.3326 | 1.45930 | 0.729652 | − | 0.683819i | \(-0.239682\pi\) | ||||
0.729652 | + | 0.683819i | \(0.239682\pi\) | |||||||
\(462\) | 17.3433 | 0.806882 | ||||||||
\(463\) | −39.7402 | −1.84688 | −0.923442 | − | 0.383738i | \(-0.874637\pi\) | ||||
−0.923442 | + | 0.383738i | \(0.874637\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 15.0050 | 0.695842 | ||||||||
\(466\) | −16.2890 | −0.754571 | ||||||||
\(467\) | −9.22574 | −0.426917 | −0.213458 | − | 0.976952i | \(-0.568473\pi\) | ||||
−0.213458 | + | 0.976952i | \(0.568473\pi\) | |||||||
\(468\) | −5.82669 | −0.269339 | ||||||||
\(469\) | 19.2962 | 0.891015 | ||||||||
\(470\) | 11.7330 | 0.541202 | ||||||||
\(471\) | −24.5977 | −1.13340 | ||||||||
\(472\) | −26.5866 | −1.22375 | ||||||||
\(473\) | 3.19801 | 0.147044 | ||||||||
\(474\) | −47.4325 | −2.17865 | ||||||||
\(475\) | −27.1479 | −1.24563 | ||||||||
\(476\) | 58.3729 | 2.67552 | ||||||||
\(477\) | 5.20916 | 0.238511 | ||||||||
\(478\) | 63.1326 | 2.88762 | ||||||||
\(479\) | −6.28701 | −0.287261 | −0.143630 | − | 0.989631i | \(-0.545878\pi\) | ||||
−0.143630 | + | 0.989631i | \(0.545878\pi\) | |||||||
\(480\) | −3.54441 | −0.161779 | ||||||||
\(481\) | 0.534996 | 0.0243937 | ||||||||
\(482\) | −7.67987 | −0.349808 | ||||||||
\(483\) | 36.6617 | 1.66816 | ||||||||
\(484\) | 4.17025 | 0.189557 | ||||||||
\(485\) | 17.0962 | 0.776300 | ||||||||
\(486\) | 10.4906 | 0.475865 | ||||||||
\(487\) | 21.1188 | 0.956985 | 0.478492 | − | 0.878092i | \(-0.341183\pi\) | ||||
0.478492 | + | 0.878092i | \(0.341183\pi\) | |||||||
\(488\) | 58.2518 | 2.63694 | ||||||||
\(489\) | −17.1365 | −0.774937 | ||||||||
\(490\) | −36.6524 | −1.65579 | ||||||||
\(491\) | 36.3430 | 1.64014 | 0.820069 | − | 0.572265i | \(-0.193935\pi\) | ||||
0.820069 | + | 0.572265i | \(0.193935\pi\) | |||||||
\(492\) | 39.7439 | 1.79179 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 66.8868 | 3.00938 | ||||||||
\(495\) | −0.511173 | −0.0229755 | ||||||||
\(496\) | −37.7081 | −1.69314 | ||||||||
\(497\) | 30.1717 | 1.35339 | ||||||||
\(498\) | 43.2512 | 1.93813 | ||||||||
\(499\) | −42.3905 | −1.89766 | −0.948830 | − | 0.315788i | \(-0.897731\pi\) | ||||
−0.948830 | + | 0.315788i | \(0.897731\pi\) | |||||||
\(500\) | 43.9528 | 1.96563 | ||||||||
\(501\) | 30.1872 | 1.34867 | ||||||||
\(502\) | 24.6884 | 1.10190 | ||||||||
\(503\) | −14.9151 | −0.665033 | −0.332516 | − | 0.943097i | \(-0.607898\pi\) | ||||
−0.332516 | + | 0.943097i | \(0.607898\pi\) | |||||||
\(504\) | 9.57354 | 0.426439 | ||||||||
\(505\) | 19.0777 | 0.848948 | ||||||||
\(506\) | 13.0432 | 0.579842 | ||||||||
\(507\) | −2.17602 | −0.0966403 | ||||||||
\(508\) | 32.8201 | 1.45616 | ||||||||
\(509\) | 23.7542 | 1.05289 | 0.526443 | − | 0.850210i | \(-0.323525\pi\) | ||||
0.526443 | + | 0.850210i | \(0.323525\pi\) | |||||||
\(510\) | 16.1086 | 0.713303 | ||||||||
\(511\) | −14.6667 | −0.648815 | ||||||||
\(512\) | −45.5463 | −2.01288 | ||||||||
\(513\) | −43.2952 | −1.91153 | ||||||||
\(514\) | 64.0966 | 2.82718 | ||||||||
\(515\) | −21.6229 | −0.952818 | ||||||||
\(516\) | −21.4656 | −0.944970 | ||||||||
\(517\) | 3.78287 | 0.166371 | ||||||||
\(518\) | −1.68909 | −0.0742144 | ||||||||
\(519\) | −0.905158 | −0.0397320 | ||||||||
\(520\) | −22.9733 | −1.00745 | ||||||||
\(521\) | −7.05079 | −0.308901 | −0.154450 | − | 0.988001i | \(-0.549361\pi\) | ||||
−0.154450 | + | 0.988001i | \(0.549361\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.8210 | 0.516896 | 0.258448 | − | 0.966025i | \(-0.416789\pi\) | ||||
0.258448 | + | 0.966025i | \(0.416789\pi\) | |||||||
\(524\) | 2.44142 | 0.106654 | ||||||||
\(525\) | 24.0244 | 1.04851 | ||||||||
\(526\) | −66.4268 | −2.89635 | ||||||||
\(527\) | 24.0919 | 1.04946 | ||||||||
\(528\) | −8.12898 | −0.353768 | ||||||||
\(529\) | 4.57188 | 0.198777 | ||||||||
\(530\) | 39.4658 | 1.71429 | ||||||||
\(531\) | 2.01899 | 0.0876167 | ||||||||
\(532\) | −142.726 | −6.18795 | ||||||||
\(533\) | 20.2085 | 0.875327 | ||||||||
\(534\) | −10.2917 | −0.445367 | ||||||||
\(535\) | 5.71266 | 0.246980 | ||||||||
\(536\) | −23.9803 | −1.03579 | ||||||||
\(537\) | 14.0462 | 0.606136 | ||||||||
\(538\) | −50.1731 | −2.16312 | ||||||||
\(539\) | −11.8172 | −0.509005 | ||||||||
\(540\) | 28.5743 | 1.22964 | ||||||||
\(541\) | 10.4848 | 0.450777 | 0.225388 | − | 0.974269i | \(-0.427635\pi\) | ||||
0.225388 | + | 0.974269i | \(0.427635\pi\) | |||||||
\(542\) | 2.58098 | 0.110863 | ||||||||
\(543\) | −34.5138 | −1.48113 | ||||||||
\(544\) | −5.69087 | −0.243994 | ||||||||
\(545\) | 10.7208 | 0.459228 | ||||||||
\(546\) | −59.1912 | −2.53315 | ||||||||
\(547\) | 27.2345 | 1.16446 | 0.582231 | − | 0.813024i | \(-0.302180\pi\) | ||||
0.582231 | + | 0.813024i | \(0.302180\pi\) | |||||||
\(548\) | 54.4171 | 2.32459 | ||||||||
\(549\) | −4.42365 | −0.188797 | ||||||||
\(550\) | 8.54723 | 0.364455 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −45.5613 | −1.93922 | ||||||||
\(553\) | 51.4637 | 2.18846 | ||||||||
\(554\) | −48.1511 | −2.04575 | ||||||||
\(555\) | −0.315036 | −0.0133725 | ||||||||
\(556\) | 40.8130 | 1.73086 | ||||||||
\(557\) | 22.2134 | 0.941214 | 0.470607 | − | 0.882343i | \(-0.344035\pi\) | ||||
0.470607 | + | 0.882343i | \(0.344035\pi\) | |||||||
\(558\) | 7.59250 | 0.321416 | ||||||||
\(559\) | −10.9146 | −0.461636 | ||||||||
\(560\) | 27.3557 | 1.15599 | ||||||||
\(561\) | 5.19364 | 0.219276 | ||||||||
\(562\) | 52.8011 | 2.22728 | ||||||||
\(563\) | −40.8563 | −1.72189 | −0.860944 | − | 0.508699i | \(-0.830126\pi\) | ||||
−0.860944 | + | 0.508699i | \(0.830126\pi\) | |||||||
\(564\) | −25.3913 | −1.06917 | ||||||||
\(565\) | −5.62826 | −0.236783 | ||||||||
\(566\) | 33.7346 | 1.41797 | ||||||||
\(567\) | 32.9863 | 1.38530 | ||||||||
\(568\) | −37.4959 | −1.57329 | ||||||||
\(569\) | −8.88645 | −0.372540 | −0.186270 | − | 0.982499i | \(-0.559640\pi\) | ||||
−0.186270 | + | 0.982499i | \(0.559640\pi\) | |||||||
\(570\) | −39.3867 | −1.64973 | ||||||||
\(571\) | 29.0605 | 1.21615 | 0.608073 | − | 0.793881i | \(-0.291943\pi\) | ||||
0.608073 | + | 0.793881i | \(0.291943\pi\) | |||||||
\(572\) | −14.2328 | −0.595101 | ||||||||
\(573\) | −1.86795 | −0.0780348 | ||||||||
\(574\) | −63.8023 | −2.66306 | ||||||||
\(575\) | 18.0679 | 0.753482 | ||||||||
\(576\) | 2.34175 | 0.0975728 | ||||||||
\(577\) | 22.5698 | 0.939595 | 0.469798 | − | 0.882774i | \(-0.344327\pi\) | ||||
0.469798 | + | 0.882774i | \(0.344327\pi\) | |||||||
\(578\) | −16.3641 | −0.680658 | ||||||||
\(579\) | −5.16388 | −0.214604 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −46.9271 | −1.94686 | ||||||||
\(582\) | −54.7417 | −2.26912 | ||||||||
\(583\) | 12.7243 | 0.526987 | ||||||||
\(584\) | 18.2270 | 0.754239 | ||||||||
\(585\) | 1.74460 | 0.0721301 | ||||||||
\(586\) | 8.98085 | 0.370995 | ||||||||
\(587\) | 19.8969 | 0.821234 | 0.410617 | − | 0.911808i | \(-0.365313\pi\) | ||||
0.410617 | + | 0.911808i | \(0.365313\pi\) | |||||||
\(588\) | 79.3195 | 3.27108 | ||||||||
\(589\) | −58.9064 | −2.42720 | ||||||||
\(590\) | 15.2964 | 0.629741 | ||||||||
\(591\) | 25.5073 | 1.04923 | ||||||||
\(592\) | 0.791695 | 0.0325385 | ||||||||
\(593\) | −10.0453 | −0.412512 | −0.206256 | − | 0.978498i | \(-0.566128\pi\) | ||||
−0.206256 | + | 0.978498i | \(0.566128\pi\) | |||||||
\(594\) | 13.6310 | 0.559288 | ||||||||
\(595\) | −17.4777 | −0.716515 | ||||||||
\(596\) | 14.9984 | 0.614359 | ||||||||
\(597\) | 13.3671 | 0.547077 | ||||||||
\(598\) | −44.5155 | −1.82037 | ||||||||
\(599\) | 23.3547 | 0.954246 | 0.477123 | − | 0.878836i | \(-0.341680\pi\) | ||||
0.477123 | + | 0.878836i | \(0.341680\pi\) | |||||||
\(600\) | −29.8564 | −1.21888 | ||||||||
\(601\) | −43.1901 | −1.76176 | −0.880881 | − | 0.473339i | \(-0.843049\pi\) | ||||
−0.880881 | + | 0.473339i | \(0.843049\pi\) | |||||||
\(602\) | 34.4595 | 1.40446 | ||||||||
\(603\) | 1.82107 | 0.0741597 | ||||||||
\(604\) | −55.6352 | −2.26377 | ||||||||
\(605\) | −1.24863 | −0.0507642 | ||||||||
\(606\) | −61.0864 | −2.48147 | ||||||||
\(607\) | 32.3539 | 1.31320 | 0.656602 | − | 0.754237i | \(-0.271993\pi\) | ||||
0.656602 | + | 0.754237i | \(0.271993\pi\) | |||||||
\(608\) | 13.9146 | 0.564310 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −33.5146 | −1.35697 | ||||||||
\(611\) | −12.9107 | −0.522309 | ||||||||
\(612\) | 5.50892 | 0.222685 | ||||||||
\(613\) | 41.6093 | 1.68059 | 0.840293 | − | 0.542133i | \(-0.182383\pi\) | ||||
0.840293 | + | 0.542133i | \(0.182383\pi\) | |||||||
\(614\) | 28.1594 | 1.13642 | ||||||||
\(615\) | −11.8999 | −0.479851 | ||||||||
\(616\) | 23.3851 | 0.942214 | ||||||||
\(617\) | 17.9049 | 0.720823 | 0.360412 | − | 0.932793i | \(-0.382636\pi\) | ||||
0.360412 | + | 0.932793i | \(0.382636\pi\) | |||||||
\(618\) | 69.2359 | 2.78507 | ||||||||
\(619\) | −15.8354 | −0.636477 | −0.318239 | − | 0.948011i | \(-0.603091\pi\) | ||||
−0.318239 | + | 0.948011i | \(0.603091\pi\) | |||||||
\(620\) | 38.8775 | 1.56136 | ||||||||
\(621\) | 28.8145 | 1.15629 | ||||||||
\(622\) | −16.2726 | −0.652473 | ||||||||
\(623\) | 11.1664 | 0.447373 | ||||||||
\(624\) | 27.7436 | 1.11063 | ||||||||
\(625\) | 4.04445 | 0.161778 | ||||||||
\(626\) | −64.9778 | −2.59704 | ||||||||
\(627\) | −12.6988 | −0.507142 | ||||||||
\(628\) | −63.7317 | −2.54317 | ||||||||
\(629\) | −0.505818 | −0.0201683 | ||||||||
\(630\) | −5.50805 | −0.219446 | ||||||||
\(631\) | −40.1785 | −1.59948 | −0.799740 | − | 0.600346i | \(-0.795030\pi\) | ||||
−0.799740 | + | 0.600346i | \(0.795030\pi\) | |||||||
\(632\) | −63.9565 | −2.54405 | ||||||||
\(633\) | 3.15328 | 0.125332 | ||||||||
\(634\) | −60.9718 | −2.42150 | ||||||||
\(635\) | −9.82682 | −0.389965 | ||||||||
\(636\) | −85.4079 | −3.38664 | ||||||||
\(637\) | 40.3313 | 1.59799 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.84744 | 0.112643 | ||||||||
\(640\) | 22.1459 | 0.875393 | ||||||||
\(641\) | −14.6768 | −0.579701 | −0.289850 | − | 0.957072i | \(-0.593606\pi\) | ||||
−0.289850 | + | 0.957072i | \(0.593606\pi\) | |||||||
\(642\) | −18.2918 | −0.721919 | ||||||||
\(643\) | −23.6287 | −0.931827 | −0.465913 | − | 0.884830i | \(-0.654274\pi\) | ||||
−0.465913 | + | 0.884830i | \(0.654274\pi\) | |||||||
\(644\) | 94.9890 | 3.74309 | ||||||||
\(645\) | 6.42711 | 0.253067 | ||||||||
\(646\) | −63.2389 | −2.48810 | ||||||||
\(647\) | −15.7214 | −0.618073 | −0.309037 | − | 0.951050i | \(-0.600007\pi\) | ||||
−0.309037 | + | 0.951050i | \(0.600007\pi\) | |||||||
\(648\) | −40.9938 | −1.61039 | ||||||||
\(649\) | 4.93175 | 0.193588 | ||||||||
\(650\) | −29.1710 | −1.14418 | ||||||||
\(651\) | 52.1290 | 2.04310 | ||||||||
\(652\) | −44.3999 | −1.73883 | ||||||||
\(653\) | 40.7072 | 1.59300 | 0.796498 | − | 0.604641i | \(-0.206683\pi\) | ||||
0.796498 | + | 0.604641i | \(0.206683\pi\) | |||||||
\(654\) | −34.3277 | −1.34232 | ||||||||
\(655\) | −0.730995 | −0.0285623 | ||||||||
\(656\) | 29.9049 | 1.16759 | ||||||||
\(657\) | −1.38416 | −0.0540013 | ||||||||
\(658\) | 40.7616 | 1.58905 | ||||||||
\(659\) | −0.583461 | −0.0227284 | −0.0113642 | − | 0.999935i | \(-0.503617\pi\) | ||||
−0.0113642 | + | 0.999935i | \(0.503617\pi\) | |||||||
\(660\) | 8.38106 | 0.326232 | ||||||||
\(661\) | 6.57327 | 0.255671 | 0.127835 | − | 0.991795i | \(-0.459197\pi\) | ||||
0.127835 | + | 0.991795i | \(0.459197\pi\) | |||||||
\(662\) | 22.9484 | 0.891914 | ||||||||
\(663\) | −17.7255 | −0.688402 | ||||||||
\(664\) | 58.3186 | 2.26320 | ||||||||
\(665\) | 42.7342 | 1.65716 | ||||||||
\(666\) | −0.159407 | −0.00617690 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 78.2140 | 3.02619 | ||||||||
\(669\) | −5.37737 | −0.207901 | ||||||||
\(670\) | 13.7969 | 0.533019 | ||||||||
\(671\) | −10.8056 | −0.417144 | ||||||||
\(672\) | −12.3137 | −0.475009 | ||||||||
\(673\) | −8.76740 | −0.337958 | −0.168979 | − | 0.985620i | \(-0.554047\pi\) | ||||
−0.168979 | + | 0.985620i | \(0.554047\pi\) | |||||||
\(674\) | 19.2505 | 0.741502 | ||||||||
\(675\) | 18.8821 | 0.726774 | ||||||||
\(676\) | −5.63797 | −0.216845 | ||||||||
\(677\) | 3.06135 | 0.117657 | 0.0588286 | − | 0.998268i | \(-0.481263\pi\) | ||||
0.0588286 | + | 0.998268i | \(0.481263\pi\) | |||||||
\(678\) | 18.0215 | 0.692113 | ||||||||
\(679\) | 59.3941 | 2.27934 | ||||||||
\(680\) | 21.7204 | 0.832939 | ||||||||
\(681\) | 39.7331 | 1.52257 | ||||||||
\(682\) | 18.5461 | 0.710166 | ||||||||
\(683\) | −13.0361 | −0.498812 | −0.249406 | − | 0.968399i | \(-0.580235\pi\) | ||||
−0.249406 | + | 0.968399i | \(0.580235\pi\) | |||||||
\(684\) | −13.4697 | −0.515026 | ||||||||
\(685\) | −16.2933 | −0.622534 | ||||||||
\(686\) | −51.9072 | −1.98183 | ||||||||
\(687\) | 44.7601 | 1.70770 | ||||||||
\(688\) | −16.1515 | −0.615771 | ||||||||
\(689\) | −43.4271 | −1.65444 | ||||||||
\(690\) | 26.2133 | 0.997922 | ||||||||
\(691\) | −5.54561 | −0.210965 | −0.105483 | − | 0.994421i | \(-0.533639\pi\) | ||||
−0.105483 | + | 0.994421i | \(0.533639\pi\) | |||||||
\(692\) | −2.34523 | −0.0891523 | ||||||||
\(693\) | −1.77587 | −0.0674597 | ||||||||
\(694\) | −38.5977 | −1.46515 | ||||||||
\(695\) | −12.2200 | −0.463531 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.1064 | −0.723705 | ||||||||
\(698\) | −71.5522 | −2.70829 | ||||||||
\(699\) | −10.5546 | −0.399213 | ||||||||
\(700\) | 62.2464 | 2.35269 | ||||||||
\(701\) | −10.6100 | −0.400734 | −0.200367 | − | 0.979721i | \(-0.564213\pi\) | ||||
−0.200367 | + | 0.979721i | \(0.564213\pi\) | |||||||
\(702\) | −46.5217 | −1.75585 | ||||||||
\(703\) | 1.23676 | 0.0466453 | ||||||||
\(704\) | 5.72015 | 0.215586 | ||||||||
\(705\) | 7.60253 | 0.286328 | ||||||||
\(706\) | 11.5310 | 0.433975 | ||||||||
\(707\) | 66.2780 | 2.49264 | ||||||||
\(708\) | −33.1028 | −1.24408 | ||||||||
\(709\) | −37.6366 | −1.41347 | −0.706735 | − | 0.707478i | \(-0.749833\pi\) | ||||
−0.706735 | + | 0.707478i | \(0.749833\pi\) | |||||||
\(710\) | 21.5729 | 0.809617 | ||||||||
\(711\) | 4.85687 | 0.182147 | ||||||||
\(712\) | −13.8771 | −0.520065 | ||||||||
\(713\) | 39.2043 | 1.46821 | ||||||||
\(714\) | 55.9631 | 2.09437 | ||||||||
\(715\) | 4.26149 | 0.159371 | ||||||||
\(716\) | 36.3930 | 1.36007 | ||||||||
\(717\) | 40.9076 | 1.52772 | ||||||||
\(718\) | −23.9565 | −0.894047 | ||||||||
\(719\) | −43.8029 | −1.63357 | −0.816786 | − | 0.576941i | \(-0.804246\pi\) | ||||
−0.816786 | + | 0.576941i | \(0.804246\pi\) | |||||||
\(720\) | 2.58168 | 0.0962136 | ||||||||
\(721\) | −75.1201 | −2.79762 | ||||||||
\(722\) | 107.428 | 3.99804 | ||||||||
\(723\) | −4.97627 | −0.185069 | ||||||||
\(724\) | −89.4240 | −3.32342 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.99809 | 0.148383 | ||||||||
\(727\) | −2.87556 | −0.106649 | −0.0533243 | − | 0.998577i | \(-0.516982\pi\) | ||||
−0.0533243 | + | 0.998577i | \(0.516982\pi\) | |||||||
\(728\) | −79.8117 | −2.95802 | ||||||||
\(729\) | 29.6103 | 1.09668 | ||||||||
\(730\) | −10.4867 | −0.388131 | ||||||||
\(731\) | 10.3193 | 0.381673 | ||||||||
\(732\) | 72.5289 | 2.68075 | ||||||||
\(733\) | 20.9951 | 0.775473 | 0.387737 | − | 0.921770i | \(-0.373257\pi\) | ||||
0.387737 | + | 0.921770i | \(0.373257\pi\) | |||||||
\(734\) | −51.4389 | −1.89864 | ||||||||
\(735\) | −23.7494 | −0.876010 | ||||||||
\(736\) | −9.26064 | −0.341352 | ||||||||
\(737\) | 4.44829 | 0.163855 | ||||||||
\(738\) | −6.02132 | −0.221648 | ||||||||
\(739\) | −37.5062 | −1.37969 | −0.689844 | − | 0.723958i | \(-0.742321\pi\) | ||||
−0.689844 | + | 0.723958i | \(0.742321\pi\) | |||||||
\(740\) | −0.816246 | −0.0300058 | ||||||||
\(741\) | 43.3401 | 1.59214 | ||||||||
\(742\) | 137.108 | 5.03340 | ||||||||
\(743\) | 14.9862 | 0.549789 | 0.274894 | − | 0.961474i | \(-0.411357\pi\) | ||||
0.274894 | + | 0.961474i | \(0.411357\pi\) | |||||||
\(744\) | −64.7834 | −2.37507 | ||||||||
\(745\) | −4.49074 | −0.164528 | ||||||||
\(746\) | 23.6510 | 0.865925 | ||||||||
\(747\) | −4.42872 | −0.162038 | ||||||||
\(748\) | 13.4565 | 0.492020 | ||||||||
\(749\) | 19.8464 | 0.725171 | ||||||||
\(750\) | 42.1383 | 1.53867 | ||||||||
\(751\) | −30.2396 | −1.10346 | −0.551728 | − | 0.834024i | \(-0.686032\pi\) | ||||
−0.551728 | + | 0.834024i | \(0.686032\pi\) | |||||||
\(752\) | −19.1054 | −0.696703 | ||||||||
\(753\) | 15.9972 | 0.582969 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.6580 | 0.606247 | ||||||||
\(756\) | 99.2700 | 3.61041 | ||||||||
\(757\) | −11.9060 | −0.432730 | −0.216365 | − | 0.976313i | \(-0.569420\pi\) | ||||
−0.216365 | + | 0.976313i | \(0.569420\pi\) | |||||||
\(758\) | −0.505408 | −0.0183573 | ||||||||
\(759\) | 8.45151 | 0.306771 | ||||||||
\(760\) | −53.1079 | −1.92643 | ||||||||
\(761\) | 2.34210 | 0.0849009 | 0.0424505 | − | 0.999099i | \(-0.486484\pi\) | ||||
0.0424505 | + | 0.999099i | \(0.486484\pi\) | |||||||
\(762\) | 31.4652 | 1.13986 | ||||||||
\(763\) | 37.2452 | 1.34836 | ||||||||
\(764\) | −4.83979 | −0.175097 | ||||||||
\(765\) | −1.64945 | −0.0596360 | ||||||||
\(766\) | 82.5176 | 2.98148 | ||||||||
\(767\) | −16.8317 | −0.607757 | ||||||||
\(768\) | −52.4970 | −1.89432 | ||||||||
\(769\) | 10.0078 | 0.360890 | 0.180445 | − | 0.983585i | \(-0.442246\pi\) | ||||
0.180445 | + | 0.983585i | \(0.442246\pi\) | |||||||
\(770\) | −13.4544 | −0.484863 | ||||||||
\(771\) | 41.5322 | 1.49574 | ||||||||
\(772\) | −13.3794 | −0.481536 | ||||||||
\(773\) | 8.26441 | 0.297250 | 0.148625 | − | 0.988894i | \(-0.452515\pi\) | ||||
0.148625 | + | 0.988894i | \(0.452515\pi\) | |||||||
\(774\) | 3.25210 | 0.116894 | ||||||||
\(775\) | 25.6906 | 0.922833 | ||||||||
\(776\) | −73.8120 | −2.64970 | ||||||||
\(777\) | −1.09447 | −0.0392638 | ||||||||
\(778\) | 13.3905 | 0.480072 | ||||||||
\(779\) | 46.7164 | 1.67379 | ||||||||
\(780\) | −28.6039 | −1.02418 | ||||||||
\(781\) | 6.95540 | 0.248884 | ||||||||
\(782\) | 42.0877 | 1.50505 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 59.6830 | 2.13154 | ||||||||
\(785\) | 19.0822 | 0.681072 | ||||||||
\(786\) | 2.34063 | 0.0834874 | ||||||||
\(787\) | 32.1568 | 1.14626 | 0.573132 | − | 0.819463i | \(-0.305728\pi\) | ||||
0.573132 | + | 0.819463i | \(0.305728\pi\) | |||||||
\(788\) | 66.0883 | 2.35430 | ||||||||
\(789\) | −43.0421 | −1.53234 | ||||||||
\(790\) | 36.7968 | 1.30917 | ||||||||
\(791\) | −19.5532 | −0.695230 | ||||||||
\(792\) | 2.20696 | 0.0784209 | ||||||||
\(793\) | 36.8786 | 1.30960 | ||||||||
\(794\) | 6.43120 | 0.228235 | ||||||||
\(795\) | 25.5724 | 0.906958 | ||||||||
\(796\) | 34.6335 | 1.22755 | ||||||||
\(797\) | 21.1780 | 0.750164 | 0.375082 | − | 0.926992i | \(-0.377614\pi\) | ||||
0.375082 | + | 0.926992i | \(0.377614\pi\) | |||||||
\(798\) | −136.834 | −4.84386 | ||||||||
\(799\) | 12.2065 | 0.431837 | ||||||||
\(800\) | −6.06850 | −0.214554 | ||||||||
\(801\) | 1.05383 | 0.0372351 | ||||||||
\(802\) | −76.7951 | −2.71173 | ||||||||
\(803\) | −3.38107 | −0.119315 | ||||||||
\(804\) | −29.8578 | −1.05300 | ||||||||
\(805\) | −28.4411 | −1.00242 | ||||||||
\(806\) | −63.2963 | −2.22952 | ||||||||
\(807\) | −32.5103 | −1.14442 | ||||||||
\(808\) | −82.3671 | −2.89766 | ||||||||
\(809\) | −30.4346 | −1.07002 | −0.535011 | − | 0.844845i | \(-0.679693\pi\) | ||||
−0.535011 | + | 0.844845i | \(0.679693\pi\) | |||||||
\(810\) | 23.5854 | 0.828705 | ||||||||
\(811\) | −25.3347 | −0.889623 | −0.444811 | − | 0.895624i | \(-0.646729\pi\) | ||||
−0.444811 | + | 0.895624i | \(0.646729\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.67238 | 0.0586528 | ||||||||
\(814\) | −0.389381 | −0.0136478 | ||||||||
\(815\) | 13.2940 | 0.465667 | ||||||||
\(816\) | −26.2305 | −0.918252 | ||||||||
\(817\) | −25.2314 | −0.882735 | ||||||||
\(818\) | −67.8854 | −2.37356 | ||||||||
\(819\) | 6.06091 | 0.211785 | ||||||||
\(820\) | −30.8322 | −1.07671 | ||||||||
\(821\) | 11.5343 | 0.402548 | 0.201274 | − | 0.979535i | \(-0.435492\pi\) | ||||
0.201274 | + | 0.979535i | \(0.435492\pi\) | |||||||
\(822\) | 52.1706 | 1.81966 | ||||||||
\(823\) | −52.1878 | −1.81915 | −0.909577 | − | 0.415536i | \(-0.863594\pi\) | ||||
−0.909577 | + | 0.415536i | \(0.863594\pi\) | |||||||
\(824\) | 93.3555 | 3.25219 | ||||||||
\(825\) | 5.53828 | 0.192818 | ||||||||
\(826\) | 53.1411 | 1.84902 | ||||||||
\(827\) | 45.2613 | 1.57389 | 0.786945 | − | 0.617023i | \(-0.211662\pi\) | ||||
0.786945 | + | 0.617023i | \(0.211662\pi\) | |||||||
\(828\) | 8.96455 | 0.311540 | ||||||||
\(829\) | −7.36913 | −0.255940 | −0.127970 | − | 0.991778i | \(-0.540846\pi\) | ||||
−0.127970 | + | 0.991778i | \(0.540846\pi\) | |||||||
\(830\) | −33.5531 | −1.16464 | ||||||||
\(831\) | −31.2001 | −1.08232 | ||||||||
\(832\) | −19.5224 | −0.676818 | ||||||||
\(833\) | −38.1318 | −1.32119 | ||||||||
\(834\) | 39.1281 | 1.35490 | ||||||||
\(835\) | −23.4184 | −0.810427 | ||||||||
\(836\) | −32.9022 | −1.13795 | ||||||||
\(837\) | 40.9711 | 1.41617 | ||||||||
\(838\) | 79.5074 | 2.74654 | ||||||||
\(839\) | 23.7615 | 0.820338 | 0.410169 | − | 0.912010i | \(-0.365470\pi\) | ||||
0.410169 | + | 0.912010i | \(0.365470\pi\) | |||||||
\(840\) | 46.9977 | 1.62157 | ||||||||
\(841\) | 0 | 0 | ||||||||
\(842\) | −41.3029 | −1.42339 | ||||||||
\(843\) | 34.2131 | 1.17836 | ||||||||
\(844\) | 8.17002 | 0.281224 | ||||||||
\(845\) | 1.68809 | 0.0580721 | ||||||||
\(846\) | 3.84686 | 0.132258 | ||||||||
\(847\) | −4.33788 | −0.149051 | ||||||||
\(848\) | −64.2642 | −2.20684 | ||||||||
\(849\) | 21.8588 | 0.750191 | ||||||||
\(850\) | 27.5801 | 0.945990 | ||||||||
\(851\) | −0.823108 | −0.0282158 | ||||||||
\(852\) | −46.6859 | −1.59943 | ||||||||
\(853\) | −10.1896 | −0.348884 | −0.174442 | − | 0.984667i | \(-0.555812\pi\) | ||||
−0.174442 | + | 0.984667i | \(0.555812\pi\) | |||||||
\(854\) | −116.433 | −3.98426 | ||||||||
\(855\) | 4.03302 | 0.137926 | ||||||||
\(856\) | −24.6641 | −0.843001 | ||||||||
\(857\) | 32.5344 | 1.11135 | 0.555676 | − | 0.831399i | \(-0.312459\pi\) | ||||
0.555676 | + | 0.831399i | \(0.312459\pi\) | |||||||
\(858\) | −13.6452 | −0.465839 | ||||||||
\(859\) | −38.1391 | −1.30129 | −0.650644 | − | 0.759383i | \(-0.725501\pi\) | ||||
−0.650644 | + | 0.759383i | \(0.725501\pi\) | |||||||
\(860\) | 16.6524 | 0.567842 | ||||||||
\(861\) | −41.3415 | −1.40892 | ||||||||
\(862\) | 35.4101 | 1.20607 | ||||||||
\(863\) | 8.23738 | 0.280404 | 0.140202 | − | 0.990123i | \(-0.455225\pi\) | ||||
0.140202 | + | 0.990123i | \(0.455225\pi\) | |||||||
\(864\) | −9.67799 | −0.329252 | ||||||||
\(865\) | 0.702196 | 0.0238754 | ||||||||
\(866\) | 10.4211 | 0.354122 | ||||||||
\(867\) | −10.6033 | −0.360109 | ||||||||
\(868\) | 135.064 | 4.58438 | ||||||||
\(869\) | 11.8638 | 0.402451 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.1817 | −0.514412 | ||||||||
\(872\) | −46.2864 | −1.56746 | ||||||||
\(873\) | 5.60529 | 0.189710 | ||||||||
\(874\) | −102.907 | −3.48090 | ||||||||
\(875\) | −45.7196 | −1.54560 | ||||||||
\(876\) | 22.6943 | 0.766770 | ||||||||
\(877\) | −50.9996 | −1.72213 | −0.861067 | − | 0.508491i | \(-0.830203\pi\) | ||||
−0.861067 | + | 0.508491i | \(0.830203\pi\) | |||||||
\(878\) | 39.2940 | 1.32611 | ||||||||
\(879\) | 5.81925 | 0.196279 | ||||||||
\(880\) | 6.30623 | 0.212583 | ||||||||
\(881\) | −0.875343 | −0.0294911 | −0.0147455 | − | 0.999891i | \(-0.504694\pi\) | ||||
−0.0147455 | + | 0.999891i | \(0.504694\pi\) | |||||||
\(882\) | −12.0171 | −0.404638 | ||||||||
\(883\) | −1.89418 | −0.0637442 | −0.0318721 | − | 0.999492i | \(-0.510147\pi\) | ||||
−0.0318721 | + | 0.999492i | \(0.510147\pi\) | |||||||
\(884\) | −45.9261 | −1.54466 | ||||||||
\(885\) | 9.91147 | 0.333170 | ||||||||
\(886\) | −65.5074 | −2.20077 | ||||||||
\(887\) | −46.7093 | −1.56835 | −0.784173 | − | 0.620543i | \(-0.786912\pi\) | ||||
−0.784173 | + | 0.620543i | \(0.786912\pi\) | |||||||
\(888\) | 1.36015 | 0.0456436 | ||||||||
\(889\) | −34.1394 | −1.14500 | ||||||||
\(890\) | 7.98403 | 0.267625 | ||||||||
\(891\) | 7.60425 | 0.254752 | ||||||||
\(892\) | −13.9325 | −0.466496 | ||||||||
\(893\) | −29.8459 | −0.998754 | ||||||||
\(894\) | 14.3792 | 0.480914 | ||||||||
\(895\) | −10.8966 | −0.364233 | ||||||||
\(896\) | 76.9371 | 2.57029 | ||||||||
\(897\) | −28.8444 | −0.963086 | ||||||||
\(898\) | 24.9928 | 0.834021 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 5.87447 | 0.195816 | ||||||||
\(901\) | 41.0587 | 1.36786 | ||||||||
\(902\) | −14.7082 | −0.489728 | ||||||||
\(903\) | 22.3285 | 0.743044 | ||||||||
\(904\) | 24.2997 | 0.808196 | ||||||||
\(905\) | 26.7748 | 0.890026 | ||||||||
\(906\) | −53.3385 | −1.77205 | ||||||||
\(907\) | 55.4693 | 1.84183 | 0.920913 | − | 0.389768i | \(-0.127445\pi\) | ||||
0.920913 | + | 0.389768i | \(0.127445\pi\) | |||||||
\(908\) | 102.947 | 3.41641 | ||||||||
\(909\) | 6.25496 | 0.207464 | ||||||||
\(910\) | 45.9189 | 1.52220 | ||||||||
\(911\) | 51.6651 | 1.71174 | 0.855871 | − | 0.517189i | \(-0.173022\pi\) | ||||
0.855871 | + | 0.517189i | \(0.173022\pi\) | |||||||
\(912\) | 64.1354 | 2.12374 | ||||||||
\(913\) | −10.8180 | −0.358022 | ||||||||
\(914\) | −47.3906 | −1.56754 | ||||||||
\(915\) | −21.7162 | −0.717916 | ||||||||
\(916\) | 115.972 | 3.83181 | ||||||||
\(917\) | −2.53955 | −0.0838634 | ||||||||
\(918\) | 43.9845 | 1.45171 | ||||||||
\(919\) | −19.2269 | −0.634237 | −0.317119 | − | 0.948386i | \(-0.602715\pi\) | ||||
−0.317119 | + | 0.948386i | \(0.602715\pi\) | |||||||
\(920\) | 35.3452 | 1.16530 | ||||||||
\(921\) | 18.2462 | 0.601234 | ||||||||
\(922\) | 77.8301 | 2.56320 | ||||||||
\(923\) | −23.7383 | −0.781354 | ||||||||
\(924\) | 29.1167 | 0.957868 | ||||||||
\(925\) | −0.539383 | −0.0177348 | ||||||||
\(926\) | −98.7147 | −3.24396 | ||||||||
\(927\) | −7.08943 | −0.232847 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −47.9439 | −1.57299 | −0.786494 | − | 0.617598i | \(-0.788106\pi\) | ||||
−0.786494 | + | 0.617598i | \(0.788106\pi\) | |||||||
\(930\) | 37.2725 | 1.22221 | ||||||||
\(931\) | 93.2348 | 3.05565 | ||||||||
\(932\) | −27.3467 | −0.895769 | ||||||||
\(933\) | −10.5440 | −0.345197 | ||||||||
\(934\) | −22.9167 | −0.749859 | ||||||||
\(935\) | −4.02908 | −0.131765 | ||||||||
\(936\) | −7.53219 | −0.246197 | ||||||||
\(937\) | −8.76405 | −0.286309 | −0.143154 | − | 0.989700i | \(-0.545725\pi\) | ||||
−0.143154 | + | 0.989700i | \(0.545725\pi\) | |||||||
\(938\) | 47.9317 | 1.56503 | ||||||||
\(939\) | −42.1032 | −1.37399 | ||||||||
\(940\) | 19.6979 | 0.642474 | ||||||||
\(941\) | −13.4937 | −0.439883 | −0.219941 | − | 0.975513i | \(-0.570587\pi\) | ||||
−0.219941 | + | 0.975513i | \(0.570587\pi\) | |||||||
\(942\) | −61.1006 | −1.99077 | ||||||||
\(943\) | −31.0914 | −1.01248 | ||||||||
\(944\) | −24.9078 | −0.810681 | ||||||||
\(945\) | −29.7229 | −0.966885 | ||||||||
\(946\) | 7.94384 | 0.258277 | ||||||||
\(947\) | 53.9459 | 1.75300 | 0.876502 | − | 0.481397i | \(-0.159871\pi\) | ||||
0.876502 | + | 0.481397i | \(0.159871\pi\) | |||||||
\(948\) | −79.6319 | −2.58632 | ||||||||
\(949\) | 11.5393 | 0.374582 | ||||||||
\(950\) | −67.4353 | −2.18789 | ||||||||
\(951\) | −39.5075 | −1.28112 | ||||||||
\(952\) | 75.4589 | 2.44564 | ||||||||
\(953\) | 0.580291 | 0.0187975 | 0.00939874 | − | 0.999956i | \(-0.497008\pi\) | ||||
0.00939874 | + | 0.999956i | \(0.497008\pi\) | |||||||
\(954\) | 12.9395 | 0.418933 | ||||||||
\(955\) | 1.44910 | 0.0468919 | ||||||||
\(956\) | 105.990 | 3.42796 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −15.6169 | −0.504560 | ||||||||
\(959\) | −56.6046 | −1.82786 | ||||||||
\(960\) | 11.4959 | 0.371029 | ||||||||
\(961\) | 24.7443 | 0.798205 | ||||||||
\(962\) | 1.32893 | 0.0428464 | ||||||||
\(963\) | 1.87299 | 0.0603564 | ||||||||
\(964\) | −12.8933 | −0.415266 | ||||||||
\(965\) | 4.00599 | 0.128957 | ||||||||
\(966\) | 91.0676 | 2.93005 | ||||||||
\(967\) | 30.7659 | 0.989363 | 0.494682 | − | 0.869074i | \(-0.335285\pi\) | ||||
0.494682 | + | 0.869074i | \(0.335285\pi\) | |||||||
\(968\) | 5.39091 | 0.173270 | ||||||||
\(969\) | −40.9765 | −1.31635 | ||||||||
\(970\) | 42.4670 | 1.36353 | ||||||||
\(971\) | −7.74336 | −0.248496 | −0.124248 | − | 0.992251i | \(-0.539652\pi\) | ||||
−0.124248 | + | 0.992251i | \(0.539652\pi\) | |||||||
\(972\) | 17.6122 | 0.564911 | ||||||||
\(973\) | −42.4535 | −1.36100 | ||||||||
\(974\) | 52.4591 | 1.68090 | ||||||||
\(975\) | −18.9017 | −0.605340 | ||||||||
\(976\) | 54.5735 | 1.74686 | ||||||||
\(977\) | −31.9055 | −1.02075 | −0.510373 | − | 0.859953i | \(-0.670493\pi\) | ||||
−0.510373 | + | 0.859953i | \(0.670493\pi\) | |||||||
\(978\) | −42.5669 | −1.36114 | ||||||||
\(979\) | 2.57416 | 0.0822705 | ||||||||
\(980\) | −61.5338 | −1.96562 | ||||||||
\(981\) | 3.51500 | 0.112225 | ||||||||
\(982\) | 90.2760 | 2.88082 | ||||||||
\(983\) | 34.6333 | 1.10463 | 0.552316 | − | 0.833635i | \(-0.313744\pi\) | ||||
0.552316 | + | 0.833635i | \(0.313744\pi\) | |||||||
\(984\) | 51.3772 | 1.63784 | ||||||||
\(985\) | −19.7878 | −0.630492 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 26.4120 | 0.840703 | ||||||||
\(988\) | 112.293 | 3.57250 | ||||||||
\(989\) | 16.7924 | 0.533967 | ||||||||
\(990\) | −1.26975 | −0.0403554 | ||||||||
\(991\) | −26.8122 | −0.851717 | −0.425859 | − | 0.904790i | \(-0.640028\pi\) | ||||
−0.425859 | + | 0.904790i | \(0.640028\pi\) | |||||||
\(992\) | −13.1676 | −0.418073 | ||||||||
\(993\) | 14.8697 | 0.471875 | ||||||||
\(994\) | 74.9465 | 2.37716 | ||||||||
\(995\) | −10.3698 | −0.328744 | ||||||||
\(996\) | 72.6121 | 2.30080 | ||||||||
\(997\) | 16.2461 | 0.514519 | 0.257259 | − | 0.966342i | \(-0.417180\pi\) | ||||
0.257259 | + | 0.966342i | \(0.417180\pi\) | |||||||
\(998\) | −105.298 | −3.33315 | ||||||||
\(999\) | −0.860203 | −0.0272156 |
(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 | 9251.2.a.t.1.17 | yes | 18 | |
29.28 | even | 2 | 9251.2.a.s.1.2 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9251.2.a.s.1.2 | ✓ | 18 | 29.28 | even | 2 | ||
9251.2.a.t.1.17 | yes | 18 | 1.1 | even | 1 | trivial |