Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6033,2,Mod(1,6033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6033, 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("6033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6033 = 3 \cdot 2011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6033.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: | \(48.1737475394\) |
Analytic rank: | \(0\) |
Dimension: | \(82\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 6033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.34798 | −1.66027 | −0.830136 | − | 0.557561i | \(-0.811737\pi\) | ||||
−0.830136 | + | 0.557561i | \(0.811737\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.51301 | 1.75650 | ||||||||
\(5\) | 0.242883 | 0.108621 | 0.0543103 | − | 0.998524i | \(-0.482704\pi\) | ||||
0.0543103 | + | 0.998524i | \(0.482704\pi\) | |||||||
\(6\) | 2.34798 | 0.958559 | ||||||||
\(7\) | −0.571157 | −0.215877 | −0.107938 | − | 0.994158i | \(-0.534425\pi\) | ||||
−0.107938 | + | 0.994158i | \(0.534425\pi\) | |||||||
\(8\) | −3.55251 | −1.25600 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.570284 | −0.180340 | ||||||||
\(11\) | −0.420562 | −0.126804 | −0.0634021 | − | 0.997988i | \(-0.520195\pi\) | ||||
−0.0634021 | + | 0.997988i | \(0.520195\pi\) | |||||||
\(12\) | −3.51301 | −1.01412 | ||||||||
\(13\) | 2.88848 | 0.801121 | 0.400560 | − | 0.916270i | \(-0.368815\pi\) | ||||
0.400560 | + | 0.916270i | \(0.368815\pi\) | |||||||
\(14\) | 1.34106 | 0.358415 | ||||||||
\(15\) | −0.242883 | −0.0627121 | ||||||||
\(16\) | 1.31521 | 0.328803 | ||||||||
\(17\) | 1.47020 | 0.356575 | 0.178287 | − | 0.983978i | \(-0.442944\pi\) | ||||
0.178287 | + | 0.983978i | \(0.442944\pi\) | |||||||
\(18\) | −2.34798 | −0.553424 | ||||||||
\(19\) | 1.36494 | 0.313138 | 0.156569 | − | 0.987667i | \(-0.449957\pi\) | ||||
0.156569 | + | 0.987667i | \(0.449957\pi\) | |||||||
\(20\) | 0.853250 | 0.190793 | ||||||||
\(21\) | 0.571157 | 0.124637 | ||||||||
\(22\) | 0.987472 | 0.210530 | ||||||||
\(23\) | 5.83343 | 1.21635 | 0.608177 | − | 0.793801i | \(-0.291901\pi\) | ||||
0.608177 | + | 0.793801i | \(0.291901\pi\) | |||||||
\(24\) | 3.55251 | 0.725154 | ||||||||
\(25\) | −4.94101 | −0.988202 | ||||||||
\(26\) | −6.78210 | −1.33008 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.00648 | −0.379189 | ||||||||
\(29\) | 3.46112 | 0.642715 | 0.321357 | − | 0.946958i | \(-0.395861\pi\) | ||||
0.321357 | + | 0.946958i | \(0.395861\pi\) | |||||||
\(30\) | 0.570284 | 0.104119 | ||||||||
\(31\) | 4.76523 | 0.855860 | 0.427930 | − | 0.903812i | \(-0.359243\pi\) | ||||
0.427930 | + | 0.903812i | \(0.359243\pi\) | |||||||
\(32\) | 4.01693 | 0.710100 | ||||||||
\(33\) | 0.420562 | 0.0732105 | ||||||||
\(34\) | −3.45199 | −0.592011 | ||||||||
\(35\) | −0.138724 | −0.0234487 | ||||||||
\(36\) | 3.51301 | 0.585501 | ||||||||
\(37\) | 2.97447 | 0.489000 | 0.244500 | − | 0.969649i | \(-0.421376\pi\) | ||||
0.244500 | + | 0.969649i | \(0.421376\pi\) | |||||||
\(38\) | −3.20484 | −0.519894 | ||||||||
\(39\) | −2.88848 | −0.462527 | ||||||||
\(40\) | −0.862845 | −0.136428 | ||||||||
\(41\) | 9.02310 | 1.40917 | 0.704586 | − | 0.709619i | \(-0.251133\pi\) | ||||
0.704586 | + | 0.709619i | \(0.251133\pi\) | |||||||
\(42\) | −1.34106 | −0.206931 | ||||||||
\(43\) | −7.29688 | −1.11276 | −0.556382 | − | 0.830927i | \(-0.687811\pi\) | ||||
−0.556382 | + | 0.830927i | \(0.687811\pi\) | |||||||
\(44\) | −1.47744 | −0.222732 | ||||||||
\(45\) | 0.242883 | 0.0362069 | ||||||||
\(46\) | −13.6968 | −2.01948 | ||||||||
\(47\) | 7.37779 | 1.07616 | 0.538080 | − | 0.842893i | \(-0.319150\pi\) | ||||
0.538080 | + | 0.842893i | \(0.319150\pi\) | |||||||
\(48\) | −1.31521 | −0.189835 | ||||||||
\(49\) | −6.67378 | −0.953397 | ||||||||
\(50\) | 11.6014 | 1.64068 | ||||||||
\(51\) | −1.47020 | −0.205869 | ||||||||
\(52\) | 10.1473 | 1.40717 | ||||||||
\(53\) | −8.36187 | −1.14859 | −0.574296 | − | 0.818648i | \(-0.694724\pi\) | ||||
−0.574296 | + | 0.818648i | \(0.694724\pi\) | |||||||
\(54\) | 2.34798 | 0.319520 | ||||||||
\(55\) | −0.102147 | −0.0137736 | ||||||||
\(56\) | 2.02904 | 0.271142 | ||||||||
\(57\) | −1.36494 | −0.180790 | ||||||||
\(58\) | −8.12665 | −1.06708 | ||||||||
\(59\) | 0.215905 | 0.0281084 | 0.0140542 | − | 0.999901i | \(-0.495526\pi\) | ||||
0.0140542 | + | 0.999901i | \(0.495526\pi\) | |||||||
\(60\) | −0.853250 | −0.110154 | ||||||||
\(61\) | 2.51070 | 0.321462 | 0.160731 | − | 0.986998i | \(-0.448615\pi\) | ||||
0.160731 | + | 0.986998i | \(0.448615\pi\) | |||||||
\(62\) | −11.1887 | −1.42096 | ||||||||
\(63\) | −0.571157 | −0.0719590 | ||||||||
\(64\) | −12.0621 | −1.50776 | ||||||||
\(65\) | 0.701563 | 0.0870182 | ||||||||
\(66\) | −0.987472 | −0.121549 | ||||||||
\(67\) | 0.957142 | 0.116933 | 0.0584667 | − | 0.998289i | \(-0.481379\pi\) | ||||
0.0584667 | + | 0.998289i | \(0.481379\pi\) | |||||||
\(68\) | 5.16481 | 0.626325 | ||||||||
\(69\) | −5.83343 | −0.702263 | ||||||||
\(70\) | 0.325722 | 0.0389312 | ||||||||
\(71\) | −4.70798 | −0.558734 | −0.279367 | − | 0.960184i | \(-0.590125\pi\) | ||||
−0.279367 | + | 0.960184i | \(0.590125\pi\) | |||||||
\(72\) | −3.55251 | −0.418668 | ||||||||
\(73\) | −0.504793 | −0.0590815 | −0.0295408 | − | 0.999564i | \(-0.509404\pi\) | ||||
−0.0295408 | + | 0.999564i | \(0.509404\pi\) | |||||||
\(74\) | −6.98400 | −0.811874 | ||||||||
\(75\) | 4.94101 | 0.570538 | ||||||||
\(76\) | 4.79503 | 0.550028 | ||||||||
\(77\) | 0.240207 | 0.0273741 | ||||||||
\(78\) | 6.78210 | 0.767921 | ||||||||
\(79\) | 11.9252 | 1.34169 | 0.670844 | − | 0.741598i | \(-0.265932\pi\) | ||||
0.670844 | + | 0.741598i | \(0.265932\pi\) | |||||||
\(80\) | 0.319443 | 0.0357148 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −21.1861 | −2.33961 | ||||||||
\(83\) | 16.3840 | 1.79838 | 0.899189 | − | 0.437560i | \(-0.144157\pi\) | ||||
0.899189 | + | 0.437560i | \(0.144157\pi\) | |||||||
\(84\) | 2.00648 | 0.218925 | ||||||||
\(85\) | 0.357086 | 0.0387314 | ||||||||
\(86\) | 17.1329 | 1.84749 | ||||||||
\(87\) | −3.46112 | −0.371072 | ||||||||
\(88\) | 1.49405 | 0.159267 | ||||||||
\(89\) | 16.2594 | 1.72350 | 0.861748 | − | 0.507336i | \(-0.169370\pi\) | ||||
0.861748 | + | 0.507336i | \(0.169370\pi\) | |||||||
\(90\) | −0.570284 | −0.0601133 | ||||||||
\(91\) | −1.64978 | −0.172943 | ||||||||
\(92\) | 20.4929 | 2.13653 | ||||||||
\(93\) | −4.76523 | −0.494131 | ||||||||
\(94\) | −17.3229 | −1.78672 | ||||||||
\(95\) | 0.331520 | 0.0340132 | ||||||||
\(96\) | −4.01693 | −0.409977 | ||||||||
\(97\) | 9.69021 | 0.983891 | 0.491946 | − | 0.870626i | \(-0.336286\pi\) | ||||
0.491946 | + | 0.870626i | \(0.336286\pi\) | |||||||
\(98\) | 15.6699 | 1.58290 | ||||||||
\(99\) | −0.420562 | −0.0422681 | ||||||||
\(100\) | −17.3578 | −1.73578 | ||||||||
\(101\) | −5.12175 | −0.509633 | −0.254816 | − | 0.966989i | \(-0.582015\pi\) | ||||
−0.254816 | + | 0.966989i | \(0.582015\pi\) | |||||||
\(102\) | 3.45199 | 0.341798 | ||||||||
\(103\) | −6.14681 | −0.605663 | −0.302832 | − | 0.953044i | \(-0.597932\pi\) | ||||
−0.302832 | + | 0.953044i | \(0.597932\pi\) | |||||||
\(104\) | −10.2614 | −1.00621 | ||||||||
\(105\) | 0.138724 | 0.0135381 | ||||||||
\(106\) | 19.6335 | 1.90697 | ||||||||
\(107\) | 2.11389 | 0.204358 | 0.102179 | − | 0.994766i | \(-0.467419\pi\) | ||||
0.102179 | + | 0.994766i | \(0.467419\pi\) | |||||||
\(108\) | −3.51301 | −0.338039 | ||||||||
\(109\) | −14.1952 | −1.35965 | −0.679825 | − | 0.733374i | \(-0.737944\pi\) | ||||
−0.679825 | + | 0.733374i | \(0.737944\pi\) | |||||||
\(110\) | 0.239840 | 0.0228679 | ||||||||
\(111\) | −2.97447 | −0.282324 | ||||||||
\(112\) | −0.751193 | −0.0709810 | ||||||||
\(113\) | −3.02675 | −0.284733 | −0.142366 | − | 0.989814i | \(-0.545471\pi\) | ||||
−0.142366 | + | 0.989814i | \(0.545471\pi\) | |||||||
\(114\) | 3.20484 | 0.300161 | ||||||||
\(115\) | 1.41684 | 0.132121 | ||||||||
\(116\) | 12.1590 | 1.12893 | ||||||||
\(117\) | 2.88848 | 0.267040 | ||||||||
\(118\) | −0.506941 | −0.0466677 | ||||||||
\(119\) | −0.839712 | −0.0769763 | ||||||||
\(120\) | 0.862845 | 0.0787667 | ||||||||
\(121\) | −10.8231 | −0.983921 | ||||||||
\(122\) | −5.89507 | −0.533715 | ||||||||
\(123\) | −9.02310 | −0.813586 | ||||||||
\(124\) | 16.7403 | 1.50332 | ||||||||
\(125\) | −2.41450 | −0.215960 | ||||||||
\(126\) | 1.34106 | 0.119472 | ||||||||
\(127\) | −1.88632 | −0.167384 | −0.0836919 | − | 0.996492i | \(-0.526671\pi\) | ||||
−0.0836919 | + | 0.996492i | \(0.526671\pi\) | |||||||
\(128\) | 20.2877 | 1.79320 | ||||||||
\(129\) | 7.29688 | 0.642455 | ||||||||
\(130\) | −1.64726 | −0.144474 | ||||||||
\(131\) | −20.0670 | −1.75326 | −0.876631 | − | 0.481163i | \(-0.840215\pi\) | ||||
−0.876631 | + | 0.481163i | \(0.840215\pi\) | |||||||
\(132\) | 1.47744 | 0.128595 | ||||||||
\(133\) | −0.779593 | −0.0675993 | ||||||||
\(134\) | −2.24735 | −0.194141 | ||||||||
\(135\) | −0.242883 | −0.0209040 | ||||||||
\(136\) | −5.22289 | −0.447859 | ||||||||
\(137\) | 8.08966 | 0.691146 | 0.345573 | − | 0.938392i | \(-0.387684\pi\) | ||||
0.345573 | + | 0.938392i | \(0.387684\pi\) | |||||||
\(138\) | 13.6968 | 1.16595 | ||||||||
\(139\) | 9.04638 | 0.767304 | 0.383652 | − | 0.923478i | \(-0.374666\pi\) | ||||
0.383652 | + | 0.923478i | \(0.374666\pi\) | |||||||
\(140\) | −0.487340 | −0.0411877 | ||||||||
\(141\) | −7.37779 | −0.621322 | ||||||||
\(142\) | 11.0542 | 0.927651 | ||||||||
\(143\) | −1.21479 | −0.101586 | ||||||||
\(144\) | 1.31521 | 0.109601 | ||||||||
\(145\) | 0.840649 | 0.0698121 | ||||||||
\(146\) | 1.18524 | 0.0980914 | ||||||||
\(147\) | 6.67378 | 0.550444 | ||||||||
\(148\) | 10.4493 | 0.858931 | ||||||||
\(149\) | −8.51571 | −0.697634 | −0.348817 | − | 0.937191i | \(-0.613417\pi\) | ||||
−0.348817 | + | 0.937191i | \(0.613417\pi\) | |||||||
\(150\) | −11.6014 | −0.947249 | ||||||||
\(151\) | −13.2754 | −1.08034 | −0.540170 | − | 0.841556i | \(-0.681640\pi\) | ||||
−0.540170 | + | 0.841556i | \(0.681640\pi\) | |||||||
\(152\) | −4.84896 | −0.393302 | ||||||||
\(153\) | 1.47020 | 0.118858 | ||||||||
\(154\) | −0.564001 | −0.0454485 | ||||||||
\(155\) | 1.15739 | 0.0929641 | ||||||||
\(156\) | −10.1473 | −0.812431 | ||||||||
\(157\) | 13.3219 | 1.06320 | 0.531600 | − | 0.846995i | \(-0.321591\pi\) | ||||
0.531600 | + | 0.846995i | \(0.321591\pi\) | |||||||
\(158\) | −28.0001 | −2.22757 | ||||||||
\(159\) | 8.36187 | 0.663140 | ||||||||
\(160\) | 0.975645 | 0.0771315 | ||||||||
\(161\) | −3.33180 | −0.262583 | ||||||||
\(162\) | −2.34798 | −0.184475 | ||||||||
\(163\) | −1.55334 | −0.121667 | −0.0608335 | − | 0.998148i | \(-0.519376\pi\) | ||||
−0.0608335 | + | 0.998148i | \(0.519376\pi\) | |||||||
\(164\) | 31.6982 | 2.47522 | ||||||||
\(165\) | 0.102147 | 0.00795217 | ||||||||
\(166\) | −38.4693 | −2.98580 | ||||||||
\(167\) | −10.0948 | −0.781157 | −0.390578 | − | 0.920570i | \(-0.627725\pi\) | ||||
−0.390578 | + | 0.920570i | \(0.627725\pi\) | |||||||
\(168\) | −2.02904 | −0.156544 | ||||||||
\(169\) | −4.65667 | −0.358206 | ||||||||
\(170\) | −0.838430 | −0.0643046 | ||||||||
\(171\) | 1.36494 | 0.104379 | ||||||||
\(172\) | −25.6340 | −1.95458 | ||||||||
\(173\) | 17.2207 | 1.30927 | 0.654634 | − | 0.755946i | \(-0.272823\pi\) | ||||
0.654634 | + | 0.755946i | \(0.272823\pi\) | |||||||
\(174\) | 8.12665 | 0.616080 | ||||||||
\(175\) | 2.82209 | 0.213330 | ||||||||
\(176\) | −0.553129 | −0.0416937 | ||||||||
\(177\) | −0.215905 | −0.0162284 | ||||||||
\(178\) | −38.1768 | −2.86147 | ||||||||
\(179\) | 11.8324 | 0.884396 | 0.442198 | − | 0.896918i | \(-0.354199\pi\) | ||||
0.442198 | + | 0.896918i | \(0.354199\pi\) | |||||||
\(180\) | 0.853250 | 0.0635975 | ||||||||
\(181\) | 4.70237 | 0.349525 | 0.174762 | − | 0.984611i | \(-0.444084\pi\) | ||||
0.174762 | + | 0.984611i | \(0.444084\pi\) | |||||||
\(182\) | 3.87364 | 0.287133 | ||||||||
\(183\) | −2.51070 | −0.185596 | ||||||||
\(184\) | −20.7233 | −1.52775 | ||||||||
\(185\) | 0.722449 | 0.0531155 | ||||||||
\(186\) | 11.1887 | 0.820392 | ||||||||
\(187\) | −0.618309 | −0.0452152 | ||||||||
\(188\) | 25.9182 | 1.89028 | ||||||||
\(189\) | 0.571157 | 0.0415455 | ||||||||
\(190\) | −0.778402 | −0.0564712 | ||||||||
\(191\) | 18.1643 | 1.31432 | 0.657160 | − | 0.753752i | \(-0.271758\pi\) | ||||
0.657160 | + | 0.753752i | \(0.271758\pi\) | |||||||
\(192\) | 12.0621 | 0.870508 | ||||||||
\(193\) | 10.4894 | 0.755041 | 0.377520 | − | 0.926001i | \(-0.376777\pi\) | ||||
0.377520 | + | 0.926001i | \(0.376777\pi\) | |||||||
\(194\) | −22.7524 | −1.63353 | ||||||||
\(195\) | −0.701563 | −0.0502400 | ||||||||
\(196\) | −23.4450 | −1.67465 | ||||||||
\(197\) | 20.1704 | 1.43708 | 0.718540 | − | 0.695485i | \(-0.244811\pi\) | ||||
0.718540 | + | 0.695485i | \(0.244811\pi\) | |||||||
\(198\) | 0.987472 | 0.0701765 | ||||||||
\(199\) | 5.42185 | 0.384345 | 0.192172 | − | 0.981361i | \(-0.438447\pi\) | ||||
0.192172 | + | 0.981361i | \(0.438447\pi\) | |||||||
\(200\) | 17.5530 | 1.24118 | ||||||||
\(201\) | −0.957142 | −0.0675116 | ||||||||
\(202\) | 12.0258 | 0.846129 | ||||||||
\(203\) | −1.97684 | −0.138747 | ||||||||
\(204\) | −5.16481 | −0.361609 | ||||||||
\(205\) | 2.19156 | 0.153065 | ||||||||
\(206\) | 14.4326 | 1.00557 | ||||||||
\(207\) | 5.83343 | 0.405452 | ||||||||
\(208\) | 3.79897 | 0.263411 | ||||||||
\(209\) | −0.574041 | −0.0397072 | ||||||||
\(210\) | −0.325722 | −0.0224769 | ||||||||
\(211\) | −20.5328 | −1.41353 | −0.706767 | − | 0.707446i | \(-0.749847\pi\) | ||||
−0.706767 | + | 0.707446i | \(0.749847\pi\) | |||||||
\(212\) | −29.3753 | −2.01751 | ||||||||
\(213\) | 4.70798 | 0.322585 | ||||||||
\(214\) | −4.96338 | −0.339290 | ||||||||
\(215\) | −1.77229 | −0.120869 | ||||||||
\(216\) | 3.55251 | 0.241718 | ||||||||
\(217\) | −2.72169 | −0.184761 | ||||||||
\(218\) | 33.3300 | 2.25739 | ||||||||
\(219\) | 0.504793 | 0.0341107 | ||||||||
\(220\) | −0.358845 | −0.0241933 | ||||||||
\(221\) | 4.24663 | 0.285659 | ||||||||
\(222\) | 6.98400 | 0.468735 | ||||||||
\(223\) | 2.89841 | 0.194092 | 0.0970459 | − | 0.995280i | \(-0.469061\pi\) | ||||
0.0970459 | + | 0.995280i | \(0.469061\pi\) | |||||||
\(224\) | −2.29430 | −0.153294 | ||||||||
\(225\) | −4.94101 | −0.329401 | ||||||||
\(226\) | 7.10675 | 0.472734 | ||||||||
\(227\) | 21.4076 | 1.42087 | 0.710437 | − | 0.703761i | \(-0.248498\pi\) | ||||
0.710437 | + | 0.703761i | \(0.248498\pi\) | |||||||
\(228\) | −4.79503 | −0.317559 | ||||||||
\(229\) | 0.833593 | 0.0550854 | 0.0275427 | − | 0.999621i | \(-0.491232\pi\) | ||||
0.0275427 | + | 0.999621i | \(0.491232\pi\) | |||||||
\(230\) | −3.32672 | −0.219357 | ||||||||
\(231\) | −0.240207 | −0.0158045 | ||||||||
\(232\) | −12.2957 | −0.807252 | ||||||||
\(233\) | −26.1263 | −1.71159 | −0.855794 | − | 0.517316i | \(-0.826931\pi\) | ||||
−0.855794 | + | 0.517316i | \(0.826931\pi\) | |||||||
\(234\) | −6.78210 | −0.443360 | ||||||||
\(235\) | 1.79194 | 0.116893 | ||||||||
\(236\) | 0.758476 | 0.0493726 | ||||||||
\(237\) | −11.9252 | −0.774624 | ||||||||
\(238\) | 1.97163 | 0.127802 | ||||||||
\(239\) | −4.71233 | −0.304815 | −0.152408 | − | 0.988318i | \(-0.548703\pi\) | ||||
−0.152408 | + | 0.988318i | \(0.548703\pi\) | |||||||
\(240\) | −0.319443 | −0.0206200 | ||||||||
\(241\) | 0.841105 | 0.0541803 | 0.0270902 | − | 0.999633i | \(-0.491376\pi\) | ||||
0.0270902 | + | 0.999633i | \(0.491376\pi\) | |||||||
\(242\) | 25.4125 | 1.63358 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 8.82011 | 0.564650 | ||||||||
\(245\) | −1.62095 | −0.103559 | ||||||||
\(246\) | 21.1861 | 1.35077 | ||||||||
\(247\) | 3.94259 | 0.250861 | ||||||||
\(248\) | −16.9285 | −1.07496 | ||||||||
\(249\) | −16.3840 | −1.03829 | ||||||||
\(250\) | 5.66920 | 0.358552 | ||||||||
\(251\) | 3.16561 | 0.199811 | 0.0999056 | − | 0.994997i | \(-0.468146\pi\) | ||||
0.0999056 | + | 0.994997i | \(0.468146\pi\) | |||||||
\(252\) | −2.00648 | −0.126396 | ||||||||
\(253\) | −2.45332 | −0.154239 | ||||||||
\(254\) | 4.42904 | 0.277903 | ||||||||
\(255\) | −0.357086 | −0.0223616 | ||||||||
\(256\) | −23.5109 | −1.46943 | ||||||||
\(257\) | −26.0869 | −1.62726 | −0.813629 | − | 0.581384i | \(-0.802512\pi\) | ||||
−0.813629 | + | 0.581384i | \(0.802512\pi\) | |||||||
\(258\) | −17.1329 | −1.06665 | ||||||||
\(259\) | −1.69889 | −0.105564 | ||||||||
\(260\) | 2.46460 | 0.152848 | ||||||||
\(261\) | 3.46112 | 0.214238 | ||||||||
\(262\) | 47.1169 | 2.91089 | ||||||||
\(263\) | 1.35825 | 0.0837532 | 0.0418766 | − | 0.999123i | \(-0.486666\pi\) | ||||
0.0418766 | + | 0.999123i | \(0.486666\pi\) | |||||||
\(264\) | −1.49405 | −0.0919526 | ||||||||
\(265\) | −2.03096 | −0.124761 | ||||||||
\(266\) | 1.83047 | 0.112233 | ||||||||
\(267\) | −16.2594 | −0.995061 | ||||||||
\(268\) | 3.36245 | 0.205394 | ||||||||
\(269\) | −23.4519 | −1.42989 | −0.714944 | − | 0.699181i | \(-0.753548\pi\) | ||||
−0.714944 | + | 0.699181i | \(0.753548\pi\) | |||||||
\(270\) | 0.570284 | 0.0347064 | ||||||||
\(271\) | 10.1012 | 0.613602 | 0.306801 | − | 0.951774i | \(-0.400741\pi\) | ||||
0.306801 | + | 0.951774i | \(0.400741\pi\) | |||||||
\(272\) | 1.93362 | 0.117243 | ||||||||
\(273\) | 1.64978 | 0.0998490 | ||||||||
\(274\) | −18.9944 | −1.14749 | ||||||||
\(275\) | 2.07800 | 0.125308 | ||||||||
\(276\) | −20.4929 | −1.23353 | ||||||||
\(277\) | −26.4062 | −1.58660 | −0.793299 | − | 0.608832i | \(-0.791638\pi\) | ||||
−0.793299 | + | 0.608832i | \(0.791638\pi\) | |||||||
\(278\) | −21.2407 | −1.27393 | ||||||||
\(279\) | 4.76523 | 0.285287 | ||||||||
\(280\) | 0.492820 | 0.0294516 | ||||||||
\(281\) | −15.8352 | −0.944649 | −0.472325 | − | 0.881425i | \(-0.656585\pi\) | ||||
−0.472325 | + | 0.881425i | \(0.656585\pi\) | |||||||
\(282\) | 17.3229 | 1.03156 | ||||||||
\(283\) | −12.2934 | −0.730765 | −0.365382 | − | 0.930857i | \(-0.619062\pi\) | ||||
−0.365382 | + | 0.930857i | \(0.619062\pi\) | |||||||
\(284\) | −16.5392 | −0.981419 | ||||||||
\(285\) | −0.331520 | −0.0196375 | ||||||||
\(286\) | 2.85229 | 0.168660 | ||||||||
\(287\) | −5.15361 | −0.304208 | ||||||||
\(288\) | 4.01693 | 0.236700 | ||||||||
\(289\) | −14.8385 | −0.872854 | ||||||||
\(290\) | −1.97383 | −0.115907 | ||||||||
\(291\) | −9.69021 | −0.568050 | ||||||||
\(292\) | −1.77334 | −0.103777 | ||||||||
\(293\) | −19.3666 | −1.13141 | −0.565703 | − | 0.824609i | \(-0.691395\pi\) | ||||
−0.565703 | + | 0.824609i | \(0.691395\pi\) | |||||||
\(294\) | −15.6699 | −0.913887 | ||||||||
\(295\) | 0.0524397 | 0.00305316 | ||||||||
\(296\) | −10.5669 | −0.614186 | ||||||||
\(297\) | 0.420562 | 0.0244035 | ||||||||
\(298\) | 19.9947 | 1.15826 | ||||||||
\(299\) | 16.8498 | 0.974447 | ||||||||
\(300\) | 17.3578 | 1.00215 | ||||||||
\(301\) | 4.16766 | 0.240220 | ||||||||
\(302\) | 31.1705 | 1.79366 | ||||||||
\(303\) | 5.12175 | 0.294237 | ||||||||
\(304\) | 1.79518 | 0.102961 | ||||||||
\(305\) | 0.609806 | 0.0349174 | ||||||||
\(306\) | −3.45199 | −0.197337 | ||||||||
\(307\) | −19.2231 | −1.09712 | −0.548560 | − | 0.836112i | \(-0.684824\pi\) | ||||
−0.548560 | + | 0.836112i | \(0.684824\pi\) | |||||||
\(308\) | 0.843849 | 0.0480828 | ||||||||
\(309\) | 6.14681 | 0.349680 | ||||||||
\(310\) | −2.71754 | −0.154346 | ||||||||
\(311\) | −3.51765 | −0.199468 | −0.0997338 | − | 0.995014i | \(-0.531799\pi\) | ||||
−0.0997338 | + | 0.995014i | \(0.531799\pi\) | |||||||
\(312\) | 10.2614 | 0.580936 | ||||||||
\(313\) | 7.89578 | 0.446296 | 0.223148 | − | 0.974785i | \(-0.428367\pi\) | ||||
0.223148 | + | 0.974785i | \(0.428367\pi\) | |||||||
\(314\) | −31.2795 | −1.76520 | ||||||||
\(315\) | −0.138724 | −0.00781623 | ||||||||
\(316\) | 41.8933 | 2.35668 | ||||||||
\(317\) | 6.85000 | 0.384734 | 0.192367 | − | 0.981323i | \(-0.438384\pi\) | ||||
0.192367 | + | 0.981323i | \(0.438384\pi\) | |||||||
\(318\) | −19.6335 | −1.10099 | ||||||||
\(319\) | −1.45562 | −0.0814990 | ||||||||
\(320\) | −2.92968 | −0.163774 | ||||||||
\(321\) | −2.11389 | −0.117986 | ||||||||
\(322\) | 7.82301 | 0.435959 | ||||||||
\(323\) | 2.00672 | 0.111657 | ||||||||
\(324\) | 3.51301 | 0.195167 | ||||||||
\(325\) | −14.2720 | −0.791669 | ||||||||
\(326\) | 3.64721 | 0.202000 | ||||||||
\(327\) | 14.1952 | 0.784994 | ||||||||
\(328\) | −32.0547 | −1.76992 | ||||||||
\(329\) | −4.21387 | −0.232318 | ||||||||
\(330\) | −0.239840 | −0.0132028 | ||||||||
\(331\) | −2.96821 | −0.163147 | −0.0815737 | − | 0.996667i | \(-0.525995\pi\) | ||||
−0.0815737 | + | 0.996667i | \(0.525995\pi\) | |||||||
\(332\) | 57.5572 | 3.15886 | ||||||||
\(333\) | 2.97447 | 0.163000 | ||||||||
\(334\) | 23.7023 | 1.29693 | ||||||||
\(335\) | 0.232473 | 0.0127014 | ||||||||
\(336\) | 0.751193 | 0.0409809 | ||||||||
\(337\) | 4.12763 | 0.224846 | 0.112423 | − | 0.993660i | \(-0.464139\pi\) | ||||
0.112423 | + | 0.993660i | \(0.464139\pi\) | |||||||
\(338\) | 10.9338 | 0.594719 | ||||||||
\(339\) | 3.02675 | 0.164391 | ||||||||
\(340\) | 1.25444 | 0.0680318 | ||||||||
\(341\) | −2.00408 | −0.108527 | ||||||||
\(342\) | −3.20484 | −0.173298 | ||||||||
\(343\) | 7.80987 | 0.421693 | ||||||||
\(344\) | 25.9223 | 1.39764 | ||||||||
\(345\) | −1.41684 | −0.0762802 | ||||||||
\(346\) | −40.4339 | −2.17374 | ||||||||
\(347\) | −11.5145 | −0.618132 | −0.309066 | − | 0.951041i | \(-0.600016\pi\) | ||||
−0.309066 | + | 0.951041i | \(0.600016\pi\) | |||||||
\(348\) | −12.1590 | −0.651789 | ||||||||
\(349\) | 5.50371 | 0.294607 | 0.147303 | − | 0.989091i | \(-0.452941\pi\) | ||||
0.147303 | + | 0.989091i | \(0.452941\pi\) | |||||||
\(350\) | −6.62621 | −0.354186 | ||||||||
\(351\) | −2.88848 | −0.154176 | ||||||||
\(352\) | −1.68937 | −0.0900438 | ||||||||
\(353\) | 33.9358 | 1.80622 | 0.903111 | − | 0.429407i | \(-0.141277\pi\) | ||||
0.903111 | + | 0.429407i | \(0.141277\pi\) | |||||||
\(354\) | 0.506941 | 0.0269436 | ||||||||
\(355\) | −1.14349 | −0.0606901 | ||||||||
\(356\) | 57.1195 | 3.02733 | ||||||||
\(357\) | 0.839712 | 0.0444423 | ||||||||
\(358\) | −27.7823 | −1.46834 | ||||||||
\(359\) | −25.7415 | −1.35859 | −0.679293 | − | 0.733867i | \(-0.737713\pi\) | ||||
−0.679293 | + | 0.733867i | \(0.737713\pi\) | |||||||
\(360\) | −0.862845 | −0.0454759 | ||||||||
\(361\) | −17.1369 | −0.901945 | ||||||||
\(362\) | −11.0411 | −0.580306 | ||||||||
\(363\) | 10.8231 | 0.568067 | ||||||||
\(364\) | −5.79568 | −0.303776 | ||||||||
\(365\) | −0.122606 | −0.00641747 | ||||||||
\(366\) | 5.89507 | 0.308140 | ||||||||
\(367\) | 13.7226 | 0.716312 | 0.358156 | − | 0.933662i | \(-0.383406\pi\) | ||||
0.358156 | + | 0.933662i | \(0.383406\pi\) | |||||||
\(368\) | 7.67221 | 0.399941 | ||||||||
\(369\) | 9.02310 | 0.469724 | ||||||||
\(370\) | −1.69630 | −0.0881862 | ||||||||
\(371\) | 4.77594 | 0.247954 | ||||||||
\(372\) | −16.7403 | −0.867944 | ||||||||
\(373\) | 6.61625 | 0.342576 | 0.171288 | − | 0.985221i | \(-0.445207\pi\) | ||||
0.171288 | + | 0.985221i | \(0.445207\pi\) | |||||||
\(374\) | 1.45178 | 0.0750696 | ||||||||
\(375\) | 2.41450 | 0.124684 | ||||||||
\(376\) | −26.2097 | −1.35166 | ||||||||
\(377\) | 9.99740 | 0.514892 | ||||||||
\(378\) | −1.34106 | −0.0689769 | ||||||||
\(379\) | 12.1057 | 0.621830 | 0.310915 | − | 0.950438i | \(-0.399365\pi\) | ||||
0.310915 | + | 0.950438i | \(0.399365\pi\) | |||||||
\(380\) | 1.16463 | 0.0597444 | ||||||||
\(381\) | 1.88632 | 0.0966391 | ||||||||
\(382\) | −42.6493 | −2.18213 | ||||||||
\(383\) | 27.8995 | 1.42560 | 0.712798 | − | 0.701369i | \(-0.247427\pi\) | ||||
0.712798 | + | 0.701369i | \(0.247427\pi\) | |||||||
\(384\) | −20.2877 | −1.03530 | ||||||||
\(385\) | 0.0583422 | 0.00297339 | ||||||||
\(386\) | −24.6288 | −1.25357 | ||||||||
\(387\) | −7.29688 | −0.370921 | ||||||||
\(388\) | 34.0418 | 1.72821 | ||||||||
\(389\) | −18.8000 | −0.953196 | −0.476598 | − | 0.879121i | \(-0.658130\pi\) | ||||
−0.476598 | + | 0.879121i | \(0.658130\pi\) | |||||||
\(390\) | 1.64726 | 0.0834121 | ||||||||
\(391\) | 8.57628 | 0.433721 | ||||||||
\(392\) | 23.7087 | 1.19747 | ||||||||
\(393\) | 20.0670 | 1.01225 | ||||||||
\(394\) | −47.3597 | −2.38595 | ||||||||
\(395\) | 2.89643 | 0.145735 | ||||||||
\(396\) | −1.47744 | −0.0742441 | ||||||||
\(397\) | −24.8418 | −1.24677 | −0.623386 | − | 0.781914i | \(-0.714244\pi\) | ||||
−0.623386 | + | 0.781914i | \(0.714244\pi\) | |||||||
\(398\) | −12.7304 | −0.638117 | ||||||||
\(399\) | 0.779593 | 0.0390284 | ||||||||
\(400\) | −6.49848 | −0.324924 | ||||||||
\(401\) | 34.4751 | 1.72161 | 0.860803 | − | 0.508939i | \(-0.169962\pi\) | ||||
0.860803 | + | 0.508939i | \(0.169962\pi\) | |||||||
\(402\) | 2.24735 | 0.112088 | ||||||||
\(403\) | 13.7643 | 0.685647 | ||||||||
\(404\) | −17.9927 | −0.895172 | ||||||||
\(405\) | 0.242883 | 0.0120690 | ||||||||
\(406\) | 4.64159 | 0.230358 | ||||||||
\(407\) | −1.25095 | −0.0620073 | ||||||||
\(408\) | 5.22289 | 0.258572 | ||||||||
\(409\) | −20.5367 | −1.01548 | −0.507738 | − | 0.861512i | \(-0.669518\pi\) | ||||
−0.507738 | + | 0.861512i | \(0.669518\pi\) | |||||||
\(410\) | −5.14573 | −0.254130 | ||||||||
\(411\) | −8.08966 | −0.399034 | ||||||||
\(412\) | −21.5938 | −1.06385 | ||||||||
\(413\) | −0.123316 | −0.00606797 | ||||||||
\(414\) | −13.6968 | −0.673160 | ||||||||
\(415\) | 3.97940 | 0.195341 | ||||||||
\(416\) | 11.6028 | 0.568876 | ||||||||
\(417\) | −9.04638 | −0.443003 | ||||||||
\(418\) | 1.34784 | 0.0659248 | ||||||||
\(419\) | 25.9726 | 1.26884 | 0.634421 | − | 0.772988i | \(-0.281239\pi\) | ||||
0.634421 | + | 0.772988i | \(0.281239\pi\) | |||||||
\(420\) | 0.487340 | 0.0237797 | ||||||||
\(421\) | −16.9382 | −0.825516 | −0.412758 | − | 0.910841i | \(-0.635435\pi\) | ||||
−0.412758 | + | 0.910841i | \(0.635435\pi\) | |||||||
\(422\) | 48.2105 | 2.34685 | ||||||||
\(423\) | 7.37779 | 0.358720 | ||||||||
\(424\) | 29.7057 | 1.44263 | ||||||||
\(425\) | −7.26425 | −0.352368 | ||||||||
\(426\) | −11.0542 | −0.535580 | ||||||||
\(427\) | −1.43400 | −0.0693963 | ||||||||
\(428\) | 7.42613 | 0.358955 | ||||||||
\(429\) | 1.21479 | 0.0586504 | ||||||||
\(430\) | 4.16130 | 0.200676 | ||||||||
\(431\) | 37.6494 | 1.81351 | 0.906755 | − | 0.421658i | \(-0.138552\pi\) | ||||
0.906755 | + | 0.421658i | \(0.138552\pi\) | |||||||
\(432\) | −1.31521 | −0.0632782 | ||||||||
\(433\) | 17.6170 | 0.846619 | 0.423309 | − | 0.905985i | \(-0.360868\pi\) | ||||
0.423309 | + | 0.905985i | \(0.360868\pi\) | |||||||
\(434\) | 6.39048 | 0.306753 | ||||||||
\(435\) | −0.840649 | −0.0403060 | ||||||||
\(436\) | −49.8677 | −2.38823 | ||||||||
\(437\) | 7.96226 | 0.380887 | ||||||||
\(438\) | −1.18524 | −0.0566331 | ||||||||
\(439\) | 10.0292 | 0.478668 | 0.239334 | − | 0.970937i | \(-0.423071\pi\) | ||||
0.239334 | + | 0.970937i | \(0.423071\pi\) | |||||||
\(440\) | 0.362880 | 0.0172996 | ||||||||
\(441\) | −6.67378 | −0.317799 | ||||||||
\(442\) | −9.97101 | −0.474273 | ||||||||
\(443\) | −1.08124 | −0.0513711 | −0.0256856 | − | 0.999670i | \(-0.508177\pi\) | ||||
−0.0256856 | + | 0.999670i | \(0.508177\pi\) | |||||||
\(444\) | −10.4493 | −0.495904 | ||||||||
\(445\) | 3.94914 | 0.187207 | ||||||||
\(446\) | −6.80541 | −0.322245 | ||||||||
\(447\) | 8.51571 | 0.402779 | ||||||||
\(448\) | 6.88935 | 0.325491 | ||||||||
\(449\) | −6.71342 | −0.316826 | −0.158413 | − | 0.987373i | \(-0.550638\pi\) | ||||
−0.158413 | + | 0.987373i | \(0.550638\pi\) | |||||||
\(450\) | 11.6014 | 0.546895 | ||||||||
\(451\) | −3.79478 | −0.178689 | ||||||||
\(452\) | −10.6330 | −0.500134 | ||||||||
\(453\) | 13.2754 | 0.623735 | ||||||||
\(454\) | −50.2646 | −2.35904 | ||||||||
\(455\) | −0.400703 | −0.0187852 | ||||||||
\(456\) | 4.84896 | 0.227073 | ||||||||
\(457\) | 9.93143 | 0.464573 | 0.232286 | − | 0.972647i | \(-0.425379\pi\) | ||||
0.232286 | + | 0.972647i | \(0.425379\pi\) | |||||||
\(458\) | −1.95726 | −0.0914568 | ||||||||
\(459\) | −1.47020 | −0.0686229 | ||||||||
\(460\) | 4.97738 | 0.232071 | ||||||||
\(461\) | −12.6060 | −0.587118 | −0.293559 | − | 0.955941i | \(-0.594840\pi\) | ||||
−0.293559 | + | 0.955941i | \(0.594840\pi\) | |||||||
\(462\) | 0.564001 | 0.0262397 | ||||||||
\(463\) | 16.9520 | 0.787825 | 0.393913 | − | 0.919148i | \(-0.371121\pi\) | ||||
0.393913 | + | 0.919148i | \(0.371121\pi\) | |||||||
\(464\) | 4.55212 | 0.211327 | ||||||||
\(465\) | −1.15739 | −0.0536728 | ||||||||
\(466\) | 61.3439 | 2.84170 | ||||||||
\(467\) | 7.91921 | 0.366457 | 0.183229 | − | 0.983070i | \(-0.441345\pi\) | ||||
0.183229 | + | 0.983070i | \(0.441345\pi\) | |||||||
\(468\) | 10.1473 | 0.469057 | ||||||||
\(469\) | −0.546678 | −0.0252432 | ||||||||
\(470\) | −4.20744 | −0.194075 | ||||||||
\(471\) | −13.3219 | −0.613839 | ||||||||
\(472\) | −0.767006 | −0.0353043 | ||||||||
\(473\) | 3.06879 | 0.141103 | ||||||||
\(474\) | 28.0001 | 1.28609 | ||||||||
\(475\) | −6.74416 | −0.309443 | ||||||||
\(476\) | −2.94992 | −0.135209 | ||||||||
\(477\) | −8.36187 | −0.382864 | ||||||||
\(478\) | 11.0645 | 0.506076 | ||||||||
\(479\) | 5.12525 | 0.234179 | 0.117089 | − | 0.993121i | \(-0.462644\pi\) | ||||
0.117089 | + | 0.993121i | \(0.462644\pi\) | |||||||
\(480\) | −0.975645 | −0.0445319 | ||||||||
\(481\) | 8.59171 | 0.391748 | ||||||||
\(482\) | −1.97490 | −0.0899541 | ||||||||
\(483\) | 3.33180 | 0.151602 | ||||||||
\(484\) | −38.0217 | −1.72826 | ||||||||
\(485\) | 2.35359 | 0.106871 | ||||||||
\(486\) | 2.34798 | 0.106507 | ||||||||
\(487\) | 17.4201 | 0.789381 | 0.394691 | − | 0.918814i | \(-0.370852\pi\) | ||||
0.394691 | + | 0.918814i | \(0.370852\pi\) | |||||||
\(488\) | −8.91930 | −0.403758 | ||||||||
\(489\) | 1.55334 | 0.0702444 | ||||||||
\(490\) | 3.80595 | 0.171935 | ||||||||
\(491\) | −2.51520 | −0.113509 | −0.0567546 | − | 0.998388i | \(-0.518075\pi\) | ||||
−0.0567546 | + | 0.998388i | \(0.518075\pi\) | |||||||
\(492\) | −31.6982 | −1.42907 | ||||||||
\(493\) | 5.08853 | 0.229176 | ||||||||
\(494\) | −9.25713 | −0.416498 | ||||||||
\(495\) | −0.102147 | −0.00459119 | ||||||||
\(496\) | 6.26729 | 0.281410 | ||||||||
\(497\) | 2.68899 | 0.120618 | ||||||||
\(498\) | 38.4693 | 1.72385 | ||||||||
\(499\) | 14.6518 | 0.655903 | 0.327951 | − | 0.944695i | \(-0.393642\pi\) | ||||
0.327951 | + | 0.944695i | \(0.393642\pi\) | |||||||
\(500\) | −8.48217 | −0.379334 | ||||||||
\(501\) | 10.0948 | 0.451001 | ||||||||
\(502\) | −7.43278 | −0.331741 | ||||||||
\(503\) | 35.6179 | 1.58812 | 0.794062 | − | 0.607836i | \(-0.207962\pi\) | ||||
0.794062 | + | 0.607836i | \(0.207962\pi\) | |||||||
\(504\) | 2.02904 | 0.0903807 | ||||||||
\(505\) | −1.24399 | −0.0553566 | ||||||||
\(506\) | 5.76035 | 0.256079 | ||||||||
\(507\) | 4.65667 | 0.206810 | ||||||||
\(508\) | −6.62666 | −0.294010 | ||||||||
\(509\) | 4.89398 | 0.216922 | 0.108461 | − | 0.994101i | \(-0.465408\pi\) | ||||
0.108461 | + | 0.994101i | \(0.465408\pi\) | |||||||
\(510\) | 0.838430 | 0.0371263 | ||||||||
\(511\) | 0.288316 | 0.0127543 | ||||||||
\(512\) | 14.6278 | 0.646461 | ||||||||
\(513\) | −1.36494 | −0.0602634 | ||||||||
\(514\) | 61.2516 | 2.70169 | ||||||||
\(515\) | −1.49296 | −0.0657875 | ||||||||
\(516\) | 25.6340 | 1.12847 | ||||||||
\(517\) | −3.10282 | −0.136462 | ||||||||
\(518\) | 3.98896 | 0.175265 | ||||||||
\(519\) | −17.2207 | −0.755906 | ||||||||
\(520\) | −2.49231 | −0.109295 | ||||||||
\(521\) | 39.7084 | 1.73966 | 0.869829 | − | 0.493353i | \(-0.164229\pi\) | ||||
0.869829 | + | 0.493353i | \(0.164229\pi\) | |||||||
\(522\) | −8.12665 | −0.355694 | ||||||||
\(523\) | 2.27910 | 0.0996582 | 0.0498291 | − | 0.998758i | \(-0.484132\pi\) | ||||
0.0498291 | + | 0.998758i | \(0.484132\pi\) | |||||||
\(524\) | −70.4956 | −3.07961 | ||||||||
\(525\) | −2.82209 | −0.123166 | ||||||||
\(526\) | −3.18914 | −0.139053 | ||||||||
\(527\) | 7.00582 | 0.305178 | ||||||||
\(528\) | 0.553129 | 0.0240718 | ||||||||
\(529\) | 11.0289 | 0.479518 | ||||||||
\(530\) | 4.76865 | 0.207137 | ||||||||
\(531\) | 0.215905 | 0.00936948 | ||||||||
\(532\) | −2.73872 | −0.118738 | ||||||||
\(533\) | 26.0631 | 1.12892 | ||||||||
\(534\) | 38.1768 | 1.65207 | ||||||||
\(535\) | 0.513429 | 0.0221975 | ||||||||
\(536\) | −3.40026 | −0.146869 | ||||||||
\(537\) | −11.8324 | −0.510606 | ||||||||
\(538\) | 55.0646 | 2.37400 | ||||||||
\(539\) | 2.80674 | 0.120895 | ||||||||
\(540\) | −0.853250 | −0.0367180 | ||||||||
\(541\) | 21.4978 | 0.924263 | 0.462132 | − | 0.886811i | \(-0.347085\pi\) | ||||
0.462132 | + | 0.886811i | \(0.347085\pi\) | |||||||
\(542\) | −23.7173 | −1.01875 | ||||||||
\(543\) | −4.70237 | −0.201798 | ||||||||
\(544\) | 5.90568 | 0.253204 | ||||||||
\(545\) | −3.44776 | −0.147686 | ||||||||
\(546\) | −3.87364 | −0.165776 | ||||||||
\(547\) | 23.4522 | 1.00275 | 0.501373 | − | 0.865231i | \(-0.332829\pi\) | ||||
0.501373 | + | 0.865231i | \(0.332829\pi\) | |||||||
\(548\) | 28.4191 | 1.21400 | ||||||||
\(549\) | 2.51070 | 0.107154 | ||||||||
\(550\) | −4.87910 | −0.208046 | ||||||||
\(551\) | 4.72422 | 0.201258 | ||||||||
\(552\) | 20.7233 | 0.882044 | ||||||||
\(553\) | −6.81115 | −0.289640 | ||||||||
\(554\) | 62.0013 | 2.63418 | ||||||||
\(555\) | −0.722449 | −0.0306662 | ||||||||
\(556\) | 31.7800 | 1.34777 | ||||||||
\(557\) | −38.4501 | −1.62918 | −0.814592 | − | 0.580034i | \(-0.803039\pi\) | ||||
−0.814592 | + | 0.580034i | \(0.803039\pi\) | |||||||
\(558\) | −11.1887 | −0.473654 | ||||||||
\(559\) | −21.0769 | −0.891459 | ||||||||
\(560\) | −0.182452 | −0.00771000 | ||||||||
\(561\) | 0.618309 | 0.0261050 | ||||||||
\(562\) | 37.1807 | 1.56837 | ||||||||
\(563\) | 36.0730 | 1.52030 | 0.760148 | − | 0.649750i | \(-0.225126\pi\) | ||||
0.760148 | + | 0.649750i | \(0.225126\pi\) | |||||||
\(564\) | −25.9182 | −1.09135 | ||||||||
\(565\) | −0.735147 | −0.0309279 | ||||||||
\(566\) | 28.8646 | 1.21327 | ||||||||
\(567\) | −0.571157 | −0.0239863 | ||||||||
\(568\) | 16.7252 | 0.701772 | ||||||||
\(569\) | 40.0926 | 1.68077 | 0.840384 | − | 0.541991i | \(-0.182329\pi\) | ||||
0.840384 | + | 0.541991i | \(0.182329\pi\) | |||||||
\(570\) | 0.778402 | 0.0326037 | ||||||||
\(571\) | 3.53507 | 0.147938 | 0.0739691 | − | 0.997261i | \(-0.476433\pi\) | ||||
0.0739691 | + | 0.997261i | \(0.476433\pi\) | |||||||
\(572\) | −4.26756 | −0.178435 | ||||||||
\(573\) | −18.1643 | −0.758822 | ||||||||
\(574\) | 12.1006 | 0.505068 | ||||||||
\(575\) | −28.8230 | −1.20200 | ||||||||
\(576\) | −12.0621 | −0.502588 | ||||||||
\(577\) | 13.7405 | 0.572027 | 0.286013 | − | 0.958226i | \(-0.407670\pi\) | ||||
0.286013 | + | 0.958226i | \(0.407670\pi\) | |||||||
\(578\) | 34.8406 | 1.44918 | ||||||||
\(579\) | −10.4894 | −0.435923 | ||||||||
\(580\) | 2.95321 | 0.122625 | ||||||||
\(581\) | −9.35783 | −0.388228 | ||||||||
\(582\) | 22.7524 | 0.943118 | ||||||||
\(583\) | 3.51669 | 0.145646 | ||||||||
\(584\) | 1.79328 | 0.0742066 | ||||||||
\(585\) | 0.701563 | 0.0290061 | ||||||||
\(586\) | 45.4723 | 1.87844 | ||||||||
\(587\) | −36.3630 | −1.50086 | −0.750430 | − | 0.660950i | \(-0.770153\pi\) | ||||
−0.750430 | + | 0.660950i | \(0.770153\pi\) | |||||||
\(588\) | 23.4450 | 0.966857 | ||||||||
\(589\) | 6.50423 | 0.268002 | ||||||||
\(590\) | −0.123127 | −0.00506907 | ||||||||
\(591\) | −20.1704 | −0.829699 | ||||||||
\(592\) | 3.91206 | 0.160785 | ||||||||
\(593\) | 32.0091 | 1.31446 | 0.657229 | − | 0.753691i | \(-0.271728\pi\) | ||||
0.657229 | + | 0.753691i | \(0.271728\pi\) | |||||||
\(594\) | −0.987472 | −0.0405164 | ||||||||
\(595\) | −0.203952 | −0.00836121 | ||||||||
\(596\) | −29.9158 | −1.22540 | ||||||||
\(597\) | −5.42185 | −0.221901 | ||||||||
\(598\) | −39.5629 | −1.61785 | ||||||||
\(599\) | −17.4381 | −0.712503 | −0.356252 | − | 0.934390i | \(-0.615945\pi\) | ||||
−0.356252 | + | 0.934390i | \(0.615945\pi\) | |||||||
\(600\) | −17.5530 | −0.716598 | ||||||||
\(601\) | 15.4028 | 0.628292 | 0.314146 | − | 0.949375i | \(-0.398282\pi\) | ||||
0.314146 | + | 0.949375i | \(0.398282\pi\) | |||||||
\(602\) | −9.78559 | −0.398831 | ||||||||
\(603\) | 0.957142 | 0.0389778 | ||||||||
\(604\) | −46.6367 | −1.89762 | ||||||||
\(605\) | −2.62875 | −0.106874 | ||||||||
\(606\) | −12.0258 | −0.488513 | ||||||||
\(607\) | 36.8374 | 1.49518 | 0.747592 | − | 0.664158i | \(-0.231210\pi\) | ||||
0.747592 | + | 0.664158i | \(0.231210\pi\) | |||||||
\(608\) | 5.48286 | 0.222359 | ||||||||
\(609\) | 1.97684 | 0.0801058 | ||||||||
\(610\) | −1.43181 | −0.0579724 | ||||||||
\(611\) | 21.3106 | 0.862135 | ||||||||
\(612\) | 5.16481 | 0.208775 | ||||||||
\(613\) | 0.0760720 | 0.00307252 | 0.00153626 | − | 0.999999i | \(-0.499511\pi\) | ||||
0.00153626 | + | 0.999999i | \(0.499511\pi\) | |||||||
\(614\) | 45.1354 | 1.82152 | ||||||||
\(615\) | −2.19156 | −0.0883722 | ||||||||
\(616\) | −0.853338 | −0.0343820 | ||||||||
\(617\) | −1.78171 | −0.0717291 | −0.0358645 | − | 0.999357i | \(-0.511418\pi\) | ||||
−0.0358645 | + | 0.999357i | \(0.511418\pi\) | |||||||
\(618\) | −14.4326 | −0.580564 | ||||||||
\(619\) | −22.0114 | −0.884712 | −0.442356 | − | 0.896839i | \(-0.645857\pi\) | ||||
−0.442356 | + | 0.896839i | \(0.645857\pi\) | |||||||
\(620\) | 4.06593 | 0.163292 | ||||||||
\(621\) | −5.83343 | −0.234088 | ||||||||
\(622\) | 8.25937 | 0.331171 | ||||||||
\(623\) | −9.28668 | −0.372063 | ||||||||
\(624\) | −3.79897 | −0.152080 | ||||||||
\(625\) | 24.1186 | 0.964744 | ||||||||
\(626\) | −18.5391 | −0.740973 | ||||||||
\(627\) | 0.574041 | 0.0229250 | ||||||||
\(628\) | 46.7998 | 1.86752 | ||||||||
\(629\) | 4.37306 | 0.174365 | ||||||||
\(630\) | 0.325722 | 0.0129771 | ||||||||
\(631\) | −22.9548 | −0.913818 | −0.456909 | − | 0.889514i | \(-0.651043\pi\) | ||||
−0.456909 | + | 0.889514i | \(0.651043\pi\) | |||||||
\(632\) | −42.3644 | −1.68517 | ||||||||
\(633\) | 20.5328 | 0.816105 | ||||||||
\(634\) | −16.0837 | −0.638764 | ||||||||
\(635\) | −0.458155 | −0.0181813 | ||||||||
\(636\) | 29.3753 | 1.16481 | ||||||||
\(637\) | −19.2771 | −0.763786 | ||||||||
\(638\) | 3.41776 | 0.135310 | ||||||||
\(639\) | −4.70798 | −0.186245 | ||||||||
\(640\) | 4.92754 | 0.194778 | ||||||||
\(641\) | 47.0213 | 1.85723 | 0.928616 | − | 0.371043i | \(-0.121000\pi\) | ||||
0.928616 | + | 0.371043i | \(0.121000\pi\) | |||||||
\(642\) | 4.96338 | 0.195889 | ||||||||
\(643\) | 34.5170 | 1.36122 | 0.680609 | − | 0.732647i | \(-0.261715\pi\) | ||||
0.680609 | + | 0.732647i | \(0.261715\pi\) | |||||||
\(644\) | −11.7047 | −0.461228 | ||||||||
\(645\) | 1.77229 | 0.0697838 | ||||||||
\(646\) | −4.71175 | −0.185381 | ||||||||
\(647\) | 23.3820 | 0.919243 | 0.459621 | − | 0.888115i | \(-0.347985\pi\) | ||||
0.459621 | + | 0.888115i | \(0.347985\pi\) | |||||||
\(648\) | −3.55251 | −0.139556 | ||||||||
\(649\) | −0.0908015 | −0.00356427 | ||||||||
\(650\) | 33.5104 | 1.31439 | ||||||||
\(651\) | 2.72169 | 0.106672 | ||||||||
\(652\) | −5.45689 | −0.213708 | ||||||||
\(653\) | 16.5330 | 0.646987 | 0.323493 | − | 0.946230i | \(-0.395143\pi\) | ||||
0.323493 | + | 0.946230i | \(0.395143\pi\) | |||||||
\(654\) | −33.3300 | −1.30330 | ||||||||
\(655\) | −4.87394 | −0.190440 | ||||||||
\(656\) | 11.8673 | 0.463340 | ||||||||
\(657\) | −0.504793 | −0.0196938 | ||||||||
\(658\) | 9.89409 | 0.385712 | ||||||||
\(659\) | 26.8096 | 1.04435 | 0.522176 | − | 0.852838i | \(-0.325120\pi\) | ||||
0.522176 | + | 0.852838i | \(0.325120\pi\) | |||||||
\(660\) | 0.358845 | 0.0139680 | ||||||||
\(661\) | 12.3809 | 0.481563 | 0.240781 | − | 0.970579i | \(-0.422596\pi\) | ||||
0.240781 | + | 0.970579i | \(0.422596\pi\) | |||||||
\(662\) | 6.96929 | 0.270869 | ||||||||
\(663\) | −4.24663 | −0.164926 | ||||||||
\(664\) | −58.2044 | −2.25877 | ||||||||
\(665\) | −0.189350 | −0.00734267 | ||||||||
\(666\) | −6.98400 | −0.270625 | ||||||||
\(667\) | 20.1902 | 0.781769 | ||||||||
\(668\) | −35.4630 | −1.37211 | ||||||||
\(669\) | −2.89841 | −0.112059 | ||||||||
\(670\) | −0.545843 | −0.0210878 | ||||||||
\(671\) | −1.05591 | −0.0407628 | ||||||||
\(672\) | 2.29430 | 0.0885045 | ||||||||
\(673\) | −38.8502 | −1.49756 | −0.748782 | − | 0.662816i | \(-0.769361\pi\) | ||||
−0.748782 | + | 0.662816i | \(0.769361\pi\) | |||||||
\(674\) | −9.69159 | −0.373306 | ||||||||
\(675\) | 4.94101 | 0.190179 | ||||||||
\(676\) | −16.3589 | −0.629190 | ||||||||
\(677\) | 30.8470 | 1.18555 | 0.592773 | − | 0.805370i | \(-0.298033\pi\) | ||||
0.592773 | + | 0.805370i | \(0.298033\pi\) | |||||||
\(678\) | −7.10675 | −0.272933 | ||||||||
\(679\) | −5.53463 | −0.212399 | ||||||||
\(680\) | −1.26855 | −0.0486467 | ||||||||
\(681\) | −21.4076 | −0.820342 | ||||||||
\(682\) | 4.70553 | 0.180184 | ||||||||
\(683\) | −48.5825 | −1.85896 | −0.929478 | − | 0.368877i | \(-0.879742\pi\) | ||||
−0.929478 | + | 0.368877i | \(0.879742\pi\) | |||||||
\(684\) | 4.79503 | 0.183343 | ||||||||
\(685\) | 1.96484 | 0.0750727 | ||||||||
\(686\) | −18.3374 | −0.700126 | ||||||||
\(687\) | −0.833593 | −0.0318036 | ||||||||
\(688\) | −9.59696 | −0.365881 | ||||||||
\(689\) | −24.1531 | −0.920160 | ||||||||
\(690\) | 3.32672 | 0.126646 | ||||||||
\(691\) | 44.1216 | 1.67846 | 0.839232 | − | 0.543773i | \(-0.183005\pi\) | ||||
0.839232 | + | 0.543773i | \(0.183005\pi\) | |||||||
\(692\) | 60.4966 | 2.29973 | ||||||||
\(693\) | 0.240207 | 0.00912471 | ||||||||
\(694\) | 27.0359 | 1.02627 | ||||||||
\(695\) | 2.19721 | 0.0833450 | ||||||||
\(696\) | 12.2957 | 0.466067 | ||||||||
\(697\) | 13.2657 | 0.502475 | ||||||||
\(698\) | −12.9226 | −0.489128 | ||||||||
\(699\) | 26.1263 | 0.988186 | ||||||||
\(700\) | 9.91403 | 0.374715 | ||||||||
\(701\) | −29.7318 | −1.12296 | −0.561478 | − | 0.827492i | \(-0.689767\pi\) | ||||
−0.561478 | + | 0.827492i | \(0.689767\pi\) | |||||||
\(702\) | 6.78210 | 0.255974 | ||||||||
\(703\) | 4.05997 | 0.153124 | ||||||||
\(704\) | 5.07287 | 0.191191 | ||||||||
\(705\) | −1.79194 | −0.0674883 | ||||||||
\(706\) | −79.6806 | −2.99882 | ||||||||
\(707\) | 2.92532 | 0.110018 | ||||||||
\(708\) | −0.758476 | −0.0285053 | ||||||||
\(709\) | −14.6473 | −0.550091 | −0.275045 | − | 0.961431i | \(-0.588693\pi\) | ||||
−0.275045 | + | 0.961431i | \(0.588693\pi\) | |||||||
\(710\) | 2.68489 | 0.100762 | ||||||||
\(711\) | 11.9252 | 0.447229 | ||||||||
\(712\) | −57.7619 | −2.16472 | ||||||||
\(713\) | 27.7976 | 1.04103 | ||||||||
\(714\) | −1.97163 | −0.0737863 | ||||||||
\(715\) | −0.295051 | −0.0110343 | ||||||||
\(716\) | 41.5674 | 1.55344 | ||||||||
\(717\) | 4.71233 | 0.175985 | ||||||||
\(718\) | 60.4406 | 2.25562 | ||||||||
\(719\) | −4.36655 | −0.162845 | −0.0814225 | − | 0.996680i | \(-0.525946\pi\) | ||||
−0.0814225 | + | 0.996680i | \(0.525946\pi\) | |||||||
\(720\) | 0.319443 | 0.0119049 | ||||||||
\(721\) | 3.51079 | 0.130749 | ||||||||
\(722\) | 40.2372 | 1.49747 | ||||||||
\(723\) | −0.841105 | −0.0312810 | ||||||||
\(724\) | 16.5195 | 0.613942 | ||||||||
\(725\) | −17.1014 | −0.635132 | ||||||||
\(726\) | −25.4125 | −0.943146 | ||||||||
\(727\) | 6.10062 | 0.226259 | 0.113130 | − | 0.993580i | \(-0.463912\pi\) | ||||
0.113130 | + | 0.993580i | \(0.463912\pi\) | |||||||
\(728\) | 5.86085 | 0.217218 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.287875 | 0.0106547 | ||||||||
\(731\) | −10.7278 | −0.396784 | ||||||||
\(732\) | −8.82011 | −0.326001 | ||||||||
\(733\) | 44.6070 | 1.64760 | 0.823799 | − | 0.566882i | \(-0.191851\pi\) | ||||
0.823799 | + | 0.566882i | \(0.191851\pi\) | |||||||
\(734\) | −32.2203 | −1.18927 | ||||||||
\(735\) | 1.62095 | 0.0597896 | ||||||||
\(736\) | 23.4325 | 0.863734 | ||||||||
\(737\) | −0.402538 | −0.0148277 | ||||||||
\(738\) | −21.1861 | −0.779870 | ||||||||
\(739\) | 33.2116 | 1.22171 | 0.610853 | − | 0.791744i | \(-0.290826\pi\) | ||||
0.610853 | + | 0.791744i | \(0.290826\pi\) | |||||||
\(740\) | 2.53797 | 0.0932976 | ||||||||
\(741\) | −3.94259 | −0.144835 | ||||||||
\(742\) | −11.2138 | −0.411672 | ||||||||
\(743\) | 16.8702 | 0.618907 | 0.309453 | − | 0.950915i | \(-0.399854\pi\) | ||||
0.309453 | + | 0.950915i | \(0.399854\pi\) | |||||||
\(744\) | 16.9285 | 0.620630 | ||||||||
\(745\) | −2.06832 | −0.0757775 | ||||||||
\(746\) | −15.5348 | −0.568770 | ||||||||
\(747\) | 16.3840 | 0.599459 | ||||||||
\(748\) | −2.17212 | −0.0794207 | ||||||||
\(749\) | −1.20736 | −0.0441161 | ||||||||
\(750\) | −5.66920 | −0.207010 | ||||||||
\(751\) | −23.1859 | −0.846067 | −0.423034 | − | 0.906114i | \(-0.639035\pi\) | ||||
−0.423034 | + | 0.906114i | \(0.639035\pi\) | |||||||
\(752\) | 9.70336 | 0.353845 | ||||||||
\(753\) | −3.16561 | −0.115361 | ||||||||
\(754\) | −23.4737 | −0.854861 | ||||||||
\(755\) | −3.22438 | −0.117347 | ||||||||
\(756\) | 2.00648 | 0.0729749 | ||||||||
\(757\) | 1.46129 | 0.0531114 | 0.0265557 | − | 0.999647i | \(-0.491546\pi\) | ||||
0.0265557 | + | 0.999647i | \(0.491546\pi\) | |||||||
\(758\) | −28.4240 | −1.03241 | ||||||||
\(759\) | 2.45332 | 0.0890499 | ||||||||
\(760\) | −1.17773 | −0.0427207 | ||||||||
\(761\) | 34.3238 | 1.24424 | 0.622118 | − | 0.782924i | \(-0.286273\pi\) | ||||
0.622118 | + | 0.782924i | \(0.286273\pi\) | |||||||
\(762\) | −4.42904 | −0.160447 | ||||||||
\(763\) | 8.10766 | 0.293517 | ||||||||
\(764\) | 63.8112 | 2.30861 | ||||||||
\(765\) | 0.357086 | 0.0129105 | ||||||||
\(766\) | −65.5074 | −2.36688 | ||||||||
\(767\) | 0.623638 | 0.0225183 | ||||||||
\(768\) | 23.5109 | 0.848377 | ||||||||
\(769\) | −36.9790 | −1.33350 | −0.666749 | − | 0.745282i | \(-0.732315\pi\) | ||||
−0.666749 | + | 0.745282i | \(0.732315\pi\) | |||||||
\(770\) | −0.136986 | −0.00493664 | ||||||||
\(771\) | 26.0869 | 0.939498 | ||||||||
\(772\) | 36.8492 | 1.32623 | ||||||||
\(773\) | −1.06077 | −0.0381532 | −0.0190766 | − | 0.999818i | \(-0.506073\pi\) | ||||
−0.0190766 | + | 0.999818i | \(0.506073\pi\) | |||||||
\(774\) | 17.1329 | 0.615831 | ||||||||
\(775\) | −23.5450 | −0.845762 | ||||||||
\(776\) | −34.4246 | −1.23577 | ||||||||
\(777\) | 1.69889 | 0.0609473 | ||||||||
\(778\) | 44.1419 | 1.58257 | ||||||||
\(779\) | 12.3160 | 0.441265 | ||||||||
\(780\) | −2.46460 | −0.0882468 | ||||||||
\(781\) | 1.98000 | 0.0708499 | ||||||||
\(782\) | −20.1369 | −0.720096 | ||||||||
\(783\) | −3.46112 | −0.123691 | ||||||||
\(784\) | −8.77744 | −0.313480 | ||||||||
\(785\) | 3.23565 | 0.115485 | ||||||||
\(786\) | −47.1169 | −1.68061 | ||||||||
\(787\) | 24.3150 | 0.866735 | 0.433368 | − | 0.901217i | \(-0.357325\pi\) | ||||
0.433368 | + | 0.901217i | \(0.357325\pi\) | |||||||
\(788\) | 70.8588 | 2.52424 | ||||||||
\(789\) | −1.35825 | −0.0483550 | ||||||||
\(790\) | −6.80075 | −0.241960 | ||||||||
\(791\) | 1.72875 | 0.0614673 | ||||||||
\(792\) | 1.49405 | 0.0530889 | ||||||||
\(793\) | 7.25211 | 0.257530 | ||||||||
\(794\) | 58.3280 | 2.06998 | ||||||||
\(795\) | 2.03096 | 0.0720306 | ||||||||
\(796\) | 19.0470 | 0.675103 | ||||||||
\(797\) | −16.5812 | −0.587336 | −0.293668 | − | 0.955907i | \(-0.594876\pi\) | ||||
−0.293668 | + | 0.955907i | \(0.594876\pi\) | |||||||
\(798\) | −1.83047 | −0.0647979 | ||||||||
\(799\) | 10.8468 | 0.383732 | ||||||||
\(800\) | −19.8477 | −0.701722 | ||||||||
\(801\) | 16.2594 | 0.574499 | ||||||||
\(802\) | −80.9469 | −2.85833 | ||||||||
\(803\) | 0.212297 | 0.00749179 | ||||||||
\(804\) | −3.36245 | −0.118584 | ||||||||
\(805\) | −0.809239 | −0.0285219 | ||||||||
\(806\) | −32.3182 | −1.13836 | ||||||||
\(807\) | 23.4519 | 0.825547 | ||||||||
\(808\) | 18.1951 | 0.640100 | ||||||||
\(809\) | −32.4871 | −1.14218 | −0.571092 | − | 0.820886i | \(-0.693480\pi\) | ||||
−0.571092 | + | 0.820886i | \(0.693480\pi\) | |||||||
\(810\) | −0.570284 | −0.0200378 | ||||||||
\(811\) | 31.9035 | 1.12028 | 0.560142 | − | 0.828397i | \(-0.310747\pi\) | ||||
0.560142 | + | 0.828397i | \(0.310747\pi\) | |||||||
\(812\) | −6.94467 | −0.243710 | ||||||||
\(813\) | −10.1012 | −0.354263 | ||||||||
\(814\) | 2.93721 | 0.102949 | ||||||||
\(815\) | −0.377280 | −0.0132155 | ||||||||
\(816\) | −1.93362 | −0.0676903 | ||||||||
\(817\) | −9.95978 | −0.348449 | ||||||||
\(818\) | 48.2198 | 1.68597 | ||||||||
\(819\) | −1.64978 | −0.0576478 | ||||||||
\(820\) | 7.69896 | 0.268859 | ||||||||
\(821\) | −39.7609 | −1.38766 | −0.693832 | − | 0.720137i | \(-0.744079\pi\) | ||||
−0.693832 | + | 0.720137i | \(0.744079\pi\) | |||||||
\(822\) | 18.9944 | 0.662504 | ||||||||
\(823\) | −34.6368 | −1.20736 | −0.603681 | − | 0.797226i | \(-0.706300\pi\) | ||||
−0.603681 | + | 0.797226i | \(0.706300\pi\) | |||||||
\(824\) | 21.8366 | 0.760715 | ||||||||
\(825\) | −2.07800 | −0.0723467 | ||||||||
\(826\) | 0.289543 | 0.0100745 | ||||||||
\(827\) | 50.7365 | 1.76428 | 0.882141 | − | 0.470985i | \(-0.156101\pi\) | ||||
0.882141 | + | 0.470985i | \(0.156101\pi\) | |||||||
\(828\) | 20.4929 | 0.712177 | ||||||||
\(829\) | 16.7304 | 0.581072 | 0.290536 | − | 0.956864i | \(-0.406166\pi\) | ||||
0.290536 | + | 0.956864i | \(0.406166\pi\) | |||||||
\(830\) | −9.34354 | −0.324319 | ||||||||
\(831\) | 26.4062 | 0.916023 | ||||||||
\(832\) | −34.8412 | −1.20790 | ||||||||
\(833\) | −9.81176 | −0.339957 | ||||||||
\(834\) | 21.2407 | 0.735505 | ||||||||
\(835\) | −2.45185 | −0.0848497 | ||||||||
\(836\) | −2.01661 | −0.0697459 | ||||||||
\(837\) | −4.76523 | −0.164710 | ||||||||
\(838\) | −60.9830 | −2.10662 | ||||||||
\(839\) | −4.46605 | −0.154185 | −0.0770927 | − | 0.997024i | \(-0.524564\pi\) | ||||
−0.0770927 | + | 0.997024i | \(0.524564\pi\) | |||||||
\(840\) | −0.492820 | −0.0170039 | ||||||||
\(841\) | −17.0206 | −0.586918 | ||||||||
\(842\) | 39.7705 | 1.37058 | ||||||||
\(843\) | 15.8352 | 0.545393 | ||||||||
\(844\) | −72.1318 | −2.48288 | ||||||||
\(845\) | −1.13103 | −0.0389085 | ||||||||
\(846\) | −17.3229 | −0.595573 | ||||||||
\(847\) | 6.18170 | 0.212406 | ||||||||
\(848\) | −10.9976 | −0.377661 | ||||||||
\(849\) | 12.2934 | 0.421907 | ||||||||
\(850\) | 17.0563 | 0.585026 | ||||||||
\(851\) | 17.3514 | 0.594798 | ||||||||
\(852\) | 16.5392 | 0.566623 | ||||||||
\(853\) | 36.2916 | 1.24260 | 0.621301 | − | 0.783572i | \(-0.286605\pi\) | ||||
0.621301 | + | 0.783572i | \(0.286605\pi\) | |||||||
\(854\) | 3.36701 | 0.115217 | ||||||||
\(855\) | 0.331520 | 0.0113377 | ||||||||
\(856\) | −7.50964 | −0.256674 | ||||||||
\(857\) | 27.0531 | 0.924117 | 0.462058 | − | 0.886850i | \(-0.347111\pi\) | ||||
0.462058 | + | 0.886850i | \(0.347111\pi\) | |||||||
\(858\) | −2.85229 | −0.0973757 | ||||||||
\(859\) | 49.7342 | 1.69691 | 0.848454 | − | 0.529268i | \(-0.177534\pi\) | ||||
0.848454 | + | 0.529268i | \(0.177534\pi\) | |||||||
\(860\) | −6.22607 | −0.212307 | ||||||||
\(861\) | 5.15361 | 0.175634 | ||||||||
\(862\) | −88.4001 | −3.01092 | ||||||||
\(863\) | 11.5896 | 0.394513 | 0.197257 | − | 0.980352i | \(-0.436797\pi\) | ||||
0.197257 | + | 0.980352i | \(0.436797\pi\) | |||||||
\(864\) | −4.01693 | −0.136659 | ||||||||
\(865\) | 4.18262 | 0.142213 | ||||||||
\(866\) | −41.3644 | −1.40562 | ||||||||
\(867\) | 14.8385 | 0.503943 | ||||||||
\(868\) | −9.56133 | −0.324533 | ||||||||
\(869\) | −5.01528 | −0.170132 | ||||||||
\(870\) | 1.97383 | 0.0669190 | ||||||||
\(871\) | 2.76469 | 0.0936778 | ||||||||
\(872\) | 50.4285 | 1.70773 | ||||||||
\(873\) | 9.69021 | 0.327964 | ||||||||
\(874\) | −18.6952 | −0.632376 | ||||||||
\(875\) | 1.37906 | 0.0466207 | ||||||||
\(876\) | 1.77334 | 0.0599157 | ||||||||
\(877\) | 22.3115 | 0.753404 | 0.376702 | − | 0.926334i | \(-0.377058\pi\) | ||||
0.376702 | + | 0.926334i | \(0.377058\pi\) | |||||||
\(878\) | −23.5484 | −0.794719 | ||||||||
\(879\) | 19.3666 | 0.653218 | ||||||||
\(880\) | −0.134346 | −0.00452879 | ||||||||
\(881\) | −4.47136 | −0.150644 | −0.0753220 | − | 0.997159i | \(-0.523998\pi\) | ||||
−0.0753220 | + | 0.997159i | \(0.523998\pi\) | |||||||
\(882\) | 15.6699 | 0.527633 | ||||||||
\(883\) | −41.8469 | −1.40826 | −0.704130 | − | 0.710071i | \(-0.748663\pi\) | ||||
−0.704130 | + | 0.710071i | \(0.748663\pi\) | |||||||
\(884\) | 14.9185 | 0.501762 | ||||||||
\(885\) | −0.0524397 | −0.00176274 | ||||||||
\(886\) | 2.53872 | 0.0852900 | ||||||||
\(887\) | 33.3732 | 1.12056 | 0.560281 | − | 0.828303i | \(-0.310693\pi\) | ||||
0.560281 | + | 0.828303i | \(0.310693\pi\) | |||||||
\(888\) | 10.5669 | 0.354600 | ||||||||
\(889\) | 1.07738 | 0.0361343 | ||||||||
\(890\) | −9.27250 | −0.310815 | ||||||||
\(891\) | −0.420562 | −0.0140894 | ||||||||
\(892\) | 10.1821 | 0.340923 | ||||||||
\(893\) | 10.0702 | 0.336987 | ||||||||
\(894\) | −19.9947 | −0.668723 | ||||||||
\(895\) | 2.87389 | 0.0960636 | ||||||||
\(896\) | −11.5875 | −0.387110 | ||||||||
\(897\) | −16.8498 | −0.562597 | ||||||||
\(898\) | 15.7630 | 0.526017 | ||||||||
\(899\) | 16.4930 | 0.550074 | ||||||||
\(900\) | −17.3578 | −0.578593 | ||||||||
\(901\) | −12.2936 | −0.409559 | ||||||||
\(902\) | 8.91006 | 0.296672 | ||||||||
\(903\) | −4.16766 | −0.138691 | ||||||||
\(904\) | 10.7526 | 0.357625 | ||||||||
\(905\) | 1.14213 | 0.0379656 | ||||||||
\(906\) | −31.1705 | −1.03557 | ||||||||
\(907\) | 55.8614 | 1.85485 | 0.927424 | − | 0.374012i | \(-0.122018\pi\) | ||||
0.927424 | + | 0.374012i | \(0.122018\pi\) | |||||||
\(908\) | 75.2051 | 2.49577 | ||||||||
\(909\) | −5.12175 | −0.169878 | ||||||||
\(910\) | 0.940842 | 0.0311886 | ||||||||
\(911\) | −3.79744 | −0.125815 | −0.0629074 | − | 0.998019i | \(-0.520037\pi\) | ||||
−0.0629074 | + | 0.998019i | \(0.520037\pi\) | |||||||
\(912\) | −1.79518 | −0.0594444 | ||||||||
\(913\) | −6.89049 | −0.228042 | ||||||||
\(914\) | −23.3188 | −0.771318 | ||||||||
\(915\) | −0.609806 | −0.0201596 | ||||||||
\(916\) | 2.92842 | 0.0967577 | ||||||||
\(917\) | 11.4614 | 0.378489 | ||||||||
\(918\) | 3.45199 | 0.113933 | ||||||||
\(919\) | −18.2102 | −0.600700 | −0.300350 | − | 0.953829i | \(-0.597103\pi\) | ||||
−0.300350 | + | 0.953829i | \(0.597103\pi\) | |||||||
\(920\) | −5.03335 | −0.165945 | ||||||||
\(921\) | 19.2231 | 0.633422 | ||||||||
\(922\) | 29.5985 | 0.974776 | ||||||||
\(923\) | −13.5989 | −0.447614 | ||||||||
\(924\) | −0.843849 | −0.0277606 | ||||||||
\(925\) | −14.6969 | −0.483231 | ||||||||
\(926\) | −39.8029 | −1.30800 | ||||||||
\(927\) | −6.14681 | −0.201888 | ||||||||
\(928\) | 13.9031 | 0.456392 | ||||||||
\(929\) | 27.2118 | 0.892791 | 0.446395 | − | 0.894836i | \(-0.352707\pi\) | ||||
0.446395 | + | 0.894836i | \(0.352707\pi\) | |||||||
\(930\) | 2.71754 | 0.0891115 | ||||||||
\(931\) | −9.10929 | −0.298545 | ||||||||
\(932\) | −91.7818 | −3.00641 | ||||||||
\(933\) | 3.51765 | 0.115163 | ||||||||
\(934\) | −18.5941 | −0.608419 | ||||||||
\(935\) | −0.150177 | −0.00491130 | ||||||||
\(936\) | −10.2614 | −0.335403 | ||||||||
\(937\) | −34.1452 | −1.11548 | −0.557738 | − | 0.830017i | \(-0.688331\pi\) | ||||
−0.557738 | + | 0.830017i | \(0.688331\pi\) | |||||||
\(938\) | 1.28359 | 0.0419107 | ||||||||
\(939\) | −7.89578 | −0.257669 | ||||||||
\(940\) | 6.29510 | 0.205323 | ||||||||
\(941\) | −43.4405 | −1.41612 | −0.708060 | − | 0.706153i | \(-0.750429\pi\) | ||||
−0.708060 | + | 0.706153i | \(0.750429\pi\) | |||||||
\(942\) | 31.2795 | 1.01914 | ||||||||
\(943\) | 52.6356 | 1.71405 | ||||||||
\(944\) | 0.283961 | 0.00924215 | ||||||||
\(945\) | 0.138724 | 0.00451270 | ||||||||
\(946\) | −7.20546 | −0.234270 | ||||||||
\(947\) | −23.5708 | −0.765948 | −0.382974 | − | 0.923759i | \(-0.625100\pi\) | ||||
−0.382974 | + | 0.923759i | \(0.625100\pi\) | |||||||
\(948\) | −41.8933 | −1.36063 | ||||||||
\(949\) | −1.45808 | −0.0473314 | ||||||||
\(950\) | 15.8352 | 0.513760 | ||||||||
\(951\) | −6.85000 | −0.222126 | ||||||||
\(952\) | 2.98309 | 0.0966825 | ||||||||
\(953\) | 42.5899 | 1.37962 | 0.689812 | − | 0.723989i | \(-0.257693\pi\) | ||||
0.689812 | + | 0.723989i | \(0.257693\pi\) | |||||||
\(954\) | 19.6335 | 0.635658 | ||||||||
\(955\) | 4.41179 | 0.142762 | ||||||||
\(956\) | −16.5545 | −0.535409 | ||||||||
\(957\) | 1.45562 | 0.0470535 | ||||||||
\(958\) | −12.0340 | −0.388801 | ||||||||
\(959\) | −4.62046 | −0.149203 | ||||||||
\(960\) | 2.92968 | 0.0945551 | ||||||||
\(961\) | −8.29260 | −0.267503 | ||||||||
\(962\) | −20.1732 | −0.650409 | ||||||||
\(963\) | 2.11389 | 0.0681193 | ||||||||
\(964\) | 2.95481 | 0.0951680 | ||||||||
\(965\) | 2.54769 | 0.0820130 | ||||||||
\(966\) | −7.82301 | −0.251701 | ||||||||
\(967\) | −49.8924 | −1.60443 | −0.802215 | − | 0.597035i | \(-0.796345\pi\) | ||||
−0.802215 | + | 0.597035i | \(0.796345\pi\) | |||||||
\(968\) | 38.4493 | 1.23581 | ||||||||
\(969\) | −2.00672 | −0.0644652 | ||||||||
\(970\) | −5.52617 | −0.177435 | ||||||||
\(971\) | 18.8772 | 0.605800 | 0.302900 | − | 0.953022i | \(-0.402045\pi\) | ||||
0.302900 | + | 0.953022i | \(0.402045\pi\) | |||||||
\(972\) | −3.51301 | −0.112680 | ||||||||
\(973\) | −5.16690 | −0.165643 | ||||||||
\(974\) | −40.9021 | −1.31059 | ||||||||
\(975\) | 14.2720 | 0.457070 | ||||||||
\(976\) | 3.30211 | 0.105698 | ||||||||
\(977\) | −9.70661 | −0.310542 | −0.155271 | − | 0.987872i | \(-0.549625\pi\) | ||||
−0.155271 | + | 0.987872i | \(0.549625\pi\) | |||||||
\(978\) | −3.64721 | −0.116625 | ||||||||
\(979\) | −6.83810 | −0.218547 | ||||||||
\(980\) | −5.69440 | −0.181901 | ||||||||
\(981\) | −14.1952 | −0.453217 | ||||||||
\(982\) | 5.90563 | 0.188456 | ||||||||
\(983\) | −33.4815 | −1.06790 | −0.533948 | − | 0.845517i | \(-0.679292\pi\) | ||||
−0.533948 | + | 0.845517i | \(0.679292\pi\) | |||||||
\(984\) | 32.0547 | 1.02187 | ||||||||
\(985\) | 4.89905 | 0.156097 | ||||||||
\(986\) | −11.9478 | −0.380494 | ||||||||
\(987\) | 4.21387 | 0.134129 | ||||||||
\(988\) | 13.8504 | 0.440639 | ||||||||
\(989\) | −42.5659 | −1.35352 | ||||||||
\(990\) | 0.239840 | 0.00762262 | ||||||||
\(991\) | 49.4531 | 1.57093 | 0.785464 | − | 0.618907i | \(-0.212424\pi\) | ||||
0.785464 | + | 0.618907i | \(0.212424\pi\) | |||||||
\(992\) | 19.1416 | 0.607747 | ||||||||
\(993\) | 2.96821 | 0.0941932 | ||||||||
\(994\) | −6.31370 | −0.200259 | ||||||||
\(995\) | 1.31688 | 0.0417477 | ||||||||
\(996\) | −57.5572 | −1.82377 | ||||||||
\(997\) | 49.2921 | 1.56110 | 0.780548 | − | 0.625096i | \(-0.214940\pi\) | ||||
0.780548 | + | 0.625096i | \(0.214940\pi\) | |||||||
\(998\) | −34.4020 | −1.08898 | ||||||||
\(999\) | −2.97447 | −0.0941081 |
(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 | 6033.2.a.c.1.8 | ✓ | 82 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6033.2.a.c.1.8 | ✓ | 82 | 1.1 | even | 1 | trivial |