Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [503,2,Mod(1,503)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(503, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("503.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 503.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(4.01647522167\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 9x^{8} + 14x^{7} + 27x^{6} - 27x^{5} - 34x^{4} + 14x^{3} + 17x^{2} + x - 1 \) |
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 | 1.9 | ||
Root | \(-1.40552\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 503.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.36113 | 0.962467 | 0.481234 | − | 0.876592i | \(-0.340189\pi\) | ||||
0.481234 | + | 0.876592i | \(0.340189\pi\) | |||||||
\(3\) | −2.40552 | −1.38883 | −0.694415 | − | 0.719575i | \(-0.744337\pi\) | ||||
−0.694415 | + | 0.719575i | \(0.744337\pi\) | |||||||
\(4\) | −0.147314 | −0.0736568 | ||||||||
\(5\) | 0.590303 | 0.263991 | 0.131996 | − | 0.991250i | \(-0.457861\pi\) | ||||
0.131996 | + | 0.991250i | \(0.457861\pi\) | |||||||
\(6\) | −3.27424 | −1.33670 | ||||||||
\(7\) | 1.95900 | 0.740431 | 0.370216 | − | 0.928946i | \(-0.379284\pi\) | ||||
0.370216 | + | 0.928946i | \(0.379284\pi\) | |||||||
\(8\) | −2.92278 | −1.03336 | ||||||||
\(9\) | 2.78655 | 0.928849 | ||||||||
\(10\) | 0.803481 | 0.254083 | ||||||||
\(11\) | −1.52746 | −0.460546 | −0.230273 | − | 0.973126i | \(-0.573962\pi\) | ||||
−0.230273 | + | 0.973126i | \(0.573962\pi\) | |||||||
\(12\) | 0.354366 | 0.102297 | ||||||||
\(13\) | −4.67738 | −1.29727 | −0.648636 | − | 0.761099i | \(-0.724660\pi\) | ||||
−0.648636 | + | 0.761099i | \(0.724660\pi\) | |||||||
\(14\) | 2.66646 | 0.712641 | ||||||||
\(15\) | −1.41999 | −0.366639 | ||||||||
\(16\) | −3.68367 | −0.920918 | ||||||||
\(17\) | −3.04913 | −0.739523 | −0.369761 | − | 0.929127i | \(-0.620561\pi\) | ||||
−0.369761 | + | 0.929127i | \(0.620561\pi\) | |||||||
\(18\) | 3.79286 | 0.893986 | ||||||||
\(19\) | 0.338159 | 0.0775789 | 0.0387895 | − | 0.999247i | \(-0.487650\pi\) | ||||
0.0387895 | + | 0.999247i | \(0.487650\pi\) | |||||||
\(20\) | −0.0869597 | −0.0194448 | ||||||||
\(21\) | −4.71242 | −1.02833 | ||||||||
\(22\) | −2.07908 | −0.443261 | ||||||||
\(23\) | −7.98874 | −1.66577 | −0.832884 | − | 0.553448i | \(-0.813312\pi\) | ||||
−0.832884 | + | 0.553448i | \(0.813312\pi\) | |||||||
\(24\) | 7.03082 | 1.43516 | ||||||||
\(25\) | −4.65154 | −0.930309 | ||||||||
\(26\) | −6.36654 | −1.24858 | ||||||||
\(27\) | 0.513468 | 0.0988170 | ||||||||
\(28\) | −0.288587 | −0.0545378 | ||||||||
\(29\) | 6.01794 | 1.11750 | 0.558751 | − | 0.829335i | \(-0.311281\pi\) | ||||
0.558751 | + | 0.829335i | \(0.311281\pi\) | |||||||
\(30\) | −1.93279 | −0.352878 | ||||||||
\(31\) | −4.17447 | −0.749758 | −0.374879 | − | 0.927074i | \(-0.622316\pi\) | ||||
−0.374879 | + | 0.927074i | \(0.622316\pi\) | |||||||
\(32\) | 0.831593 | 0.147006 | ||||||||
\(33\) | 3.67434 | 0.639621 | ||||||||
\(34\) | −4.15028 | −0.711767 | ||||||||
\(35\) | 1.15640 | 0.195468 | ||||||||
\(36\) | −0.410496 | −0.0684160 | ||||||||
\(37\) | −11.0654 | −1.81914 | −0.909569 | − | 0.415553i | \(-0.863588\pi\) | ||||
−0.909569 | + | 0.415553i | \(0.863588\pi\) | |||||||
\(38\) | 0.460279 | 0.0746672 | ||||||||
\(39\) | 11.2515 | 1.80169 | ||||||||
\(40\) | −1.72533 | −0.272798 | ||||||||
\(41\) | −4.82359 | −0.753319 | −0.376659 | − | 0.926352i | \(-0.622927\pi\) | ||||
−0.376659 | + | 0.926352i | \(0.622927\pi\) | |||||||
\(42\) | −6.41423 | −0.989737 | ||||||||
\(43\) | 12.4475 | 1.89822 | 0.949111 | − | 0.314941i | \(-0.101985\pi\) | ||||
0.949111 | + | 0.314941i | \(0.101985\pi\) | |||||||
\(44\) | 0.225016 | 0.0339224 | ||||||||
\(45\) | 1.64491 | 0.245208 | ||||||||
\(46\) | −10.8737 | −1.60325 | ||||||||
\(47\) | 11.0094 | 1.60589 | 0.802945 | − | 0.596052i | \(-0.203265\pi\) | ||||
0.802945 | + | 0.596052i | \(0.203265\pi\) | |||||||
\(48\) | 8.86116 | 1.27900 | ||||||||
\(49\) | −3.16233 | −0.451761 | ||||||||
\(50\) | −6.33137 | −0.895391 | ||||||||
\(51\) | 7.33476 | 1.02707 | ||||||||
\(52\) | 0.689042 | 0.0955529 | ||||||||
\(53\) | −3.43684 | −0.472087 | −0.236043 | − | 0.971743i | \(-0.575851\pi\) | ||||
−0.236043 | + | 0.971743i | \(0.575851\pi\) | |||||||
\(54\) | 0.698899 | 0.0951081 | ||||||||
\(55\) | −0.901664 | −0.121580 | ||||||||
\(56\) | −5.72572 | −0.765132 | ||||||||
\(57\) | −0.813449 | −0.107744 | ||||||||
\(58\) | 8.19122 | 1.07556 | ||||||||
\(59\) | 2.63490 | 0.343034 | 0.171517 | − | 0.985181i | \(-0.445133\pi\) | ||||
0.171517 | + | 0.985181i | \(0.445133\pi\) | |||||||
\(60\) | 0.209184 | 0.0270055 | ||||||||
\(61\) | 11.4908 | 1.47125 | 0.735625 | − | 0.677389i | \(-0.236889\pi\) | ||||
0.735625 | + | 0.677389i | \(0.236889\pi\) | |||||||
\(62\) | −5.68202 | −0.721617 | ||||||||
\(63\) | 5.45884 | 0.687749 | ||||||||
\(64\) | 8.49925 | 1.06241 | ||||||||
\(65\) | −2.76107 | −0.342469 | ||||||||
\(66\) | 5.00127 | 0.615614 | ||||||||
\(67\) | −10.2554 | −1.25289 | −0.626445 | − | 0.779465i | \(-0.715491\pi\) | ||||
−0.626445 | + | 0.779465i | \(0.715491\pi\) | |||||||
\(68\) | 0.449179 | 0.0544709 | ||||||||
\(69\) | 19.2171 | 2.31347 | ||||||||
\(70\) | 1.57402 | 0.188131 | ||||||||
\(71\) | 9.66931 | 1.14754 | 0.573768 | − | 0.819018i | \(-0.305481\pi\) | ||||
0.573768 | + | 0.819018i | \(0.305481\pi\) | |||||||
\(72\) | −8.14447 | −0.959835 | ||||||||
\(73\) | −6.33688 | −0.741676 | −0.370838 | − | 0.928698i | \(-0.620929\pi\) | ||||
−0.370838 | + | 0.928698i | \(0.620929\pi\) | |||||||
\(74\) | −15.0615 | −1.75086 | ||||||||
\(75\) | 11.1894 | 1.29204 | ||||||||
\(76\) | −0.0498154 | −0.00571422 | ||||||||
\(77\) | −2.99229 | −0.341003 | ||||||||
\(78\) | 15.3149 | 1.73407 | ||||||||
\(79\) | −0.667323 | −0.0750798 | −0.0375399 | − | 0.999295i | \(-0.511952\pi\) | ||||
−0.0375399 | + | 0.999295i | \(0.511952\pi\) | |||||||
\(80\) | −2.17448 | −0.243114 | ||||||||
\(81\) | −9.59480 | −1.06609 | ||||||||
\(82\) | −6.56556 | −0.725045 | ||||||||
\(83\) | −2.26231 | −0.248321 | −0.124161 | − | 0.992262i | \(-0.539624\pi\) | ||||
−0.124161 | + | 0.992262i | \(0.539624\pi\) | |||||||
\(84\) | 0.694203 | 0.0757438 | ||||||||
\(85\) | −1.79991 | −0.195228 | ||||||||
\(86\) | 16.9427 | 1.82698 | ||||||||
\(87\) | −14.4763 | −1.55202 | ||||||||
\(88\) | 4.46443 | 0.475910 | ||||||||
\(89\) | 2.21979 | 0.235297 | 0.117649 | − | 0.993055i | \(-0.462464\pi\) | ||||
0.117649 | + | 0.993055i | \(0.462464\pi\) | |||||||
\(90\) | 2.23894 | 0.236005 | ||||||||
\(91\) | −9.16297 | −0.960541 | ||||||||
\(92\) | 1.17685 | 0.122695 | ||||||||
\(93\) | 10.0418 | 1.04129 | ||||||||
\(94\) | 14.9853 | 1.54562 | ||||||||
\(95\) | 0.199616 | 0.0204802 | ||||||||
\(96\) | −2.00042 | −0.204167 | ||||||||
\(97\) | 14.2878 | 1.45070 | 0.725352 | − | 0.688378i | \(-0.241677\pi\) | ||||
0.725352 | + | 0.688378i | \(0.241677\pi\) | |||||||
\(98\) | −4.30435 | −0.434806 | ||||||||
\(99\) | −4.25634 | −0.427778 | ||||||||
\(100\) | 0.685236 | 0.0685236 | ||||||||
\(101\) | −0.629834 | −0.0626708 | −0.0313354 | − | 0.999509i | \(-0.509976\pi\) | ||||
−0.0313354 | + | 0.999509i | \(0.509976\pi\) | |||||||
\(102\) | 9.98359 | 0.988523 | ||||||||
\(103\) | −4.51410 | −0.444788 | −0.222394 | − | 0.974957i | \(-0.571387\pi\) | ||||
−0.222394 | + | 0.974957i | \(0.571387\pi\) | |||||||
\(104\) | 13.6710 | 1.34055 | ||||||||
\(105\) | −2.78175 | −0.271471 | ||||||||
\(106\) | −4.67801 | −0.454368 | ||||||||
\(107\) | 3.43562 | 0.332134 | 0.166067 | − | 0.986115i | \(-0.446893\pi\) | ||||
0.166067 | + | 0.986115i | \(0.446893\pi\) | |||||||
\(108\) | −0.0756409 | −0.00727855 | ||||||||
\(109\) | 9.90039 | 0.948285 | 0.474142 | − | 0.880448i | \(-0.342758\pi\) | ||||
0.474142 | + | 0.880448i | \(0.342758\pi\) | |||||||
\(110\) | −1.22729 | −0.117017 | ||||||||
\(111\) | 26.6180 | 2.52647 | ||||||||
\(112\) | −7.21630 | −0.681876 | ||||||||
\(113\) | −9.47684 | −0.891506 | −0.445753 | − | 0.895156i | \(-0.647064\pi\) | ||||
−0.445753 | + | 0.895156i | \(0.647064\pi\) | |||||||
\(114\) | −1.10721 | −0.103700 | ||||||||
\(115\) | −4.71578 | −0.439748 | ||||||||
\(116\) | −0.886524 | −0.0823117 | ||||||||
\(117\) | −13.0337 | −1.20497 | ||||||||
\(118\) | 3.58645 | 0.330159 | ||||||||
\(119\) | −5.97324 | −0.547566 | ||||||||
\(120\) | 4.15031 | 0.378870 | ||||||||
\(121\) | −8.66687 | −0.787897 | ||||||||
\(122\) | 15.6406 | 1.41603 | ||||||||
\(123\) | 11.6033 | 1.04623 | ||||||||
\(124\) | 0.614957 | 0.0552248 | ||||||||
\(125\) | −5.69733 | −0.509585 | ||||||||
\(126\) | 7.43021 | 0.661936 | ||||||||
\(127\) | −11.3574 | −1.00781 | −0.503904 | − | 0.863760i | \(-0.668104\pi\) | ||||
−0.503904 | + | 0.863760i | \(0.668104\pi\) | |||||||
\(128\) | 9.90544 | 0.875525 | ||||||||
\(129\) | −29.9427 | −2.63631 | ||||||||
\(130\) | −3.75819 | −0.329615 | ||||||||
\(131\) | 15.9119 | 1.39023 | 0.695113 | − | 0.718900i | \(-0.255354\pi\) | ||||
0.695113 | + | 0.718900i | \(0.255354\pi\) | |||||||
\(132\) | −0.541281 | −0.0471124 | ||||||||
\(133\) | 0.662452 | 0.0574419 | ||||||||
\(134\) | −13.9589 | −1.20587 | ||||||||
\(135\) | 0.303102 | 0.0260868 | ||||||||
\(136\) | 8.91195 | 0.764193 | ||||||||
\(137\) | −15.0390 | −1.28486 | −0.642432 | − | 0.766343i | \(-0.722075\pi\) | ||||
−0.642432 | + | 0.766343i | \(0.722075\pi\) | |||||||
\(138\) | 26.1571 | 2.22664 | ||||||||
\(139\) | −16.6486 | −1.41212 | −0.706059 | − | 0.708153i | \(-0.749529\pi\) | ||||
−0.706059 | + | 0.708153i | \(0.749529\pi\) | |||||||
\(140\) | −0.170354 | −0.0143975 | ||||||||
\(141\) | −26.4835 | −2.23031 | ||||||||
\(142\) | 13.1612 | 1.10447 | ||||||||
\(143\) | 7.14451 | 0.597454 | ||||||||
\(144\) | −10.2647 | −0.855393 | ||||||||
\(145\) | 3.55241 | 0.295011 | ||||||||
\(146\) | −8.62534 | −0.713838 | ||||||||
\(147\) | 7.60706 | 0.627420 | ||||||||
\(148\) | 1.63008 | 0.133992 | ||||||||
\(149\) | −12.0657 | −0.988463 | −0.494232 | − | 0.869330i | \(-0.664550\pi\) | ||||
−0.494232 | + | 0.869330i | \(0.664550\pi\) | |||||||
\(150\) | 15.2303 | 1.24355 | ||||||||
\(151\) | −16.4897 | −1.34192 | −0.670958 | − | 0.741495i | \(-0.734117\pi\) | ||||
−0.670958 | + | 0.741495i | \(0.734117\pi\) | |||||||
\(152\) | −0.988364 | −0.0801669 | ||||||||
\(153\) | −8.49655 | −0.686905 | ||||||||
\(154\) | −4.07291 | −0.328204 | ||||||||
\(155\) | −2.46420 | −0.197930 | ||||||||
\(156\) | −1.65751 | −0.132707 | ||||||||
\(157\) | 4.10607 | 0.327700 | 0.163850 | − | 0.986485i | \(-0.447609\pi\) | ||||
0.163850 | + | 0.986485i | \(0.447609\pi\) | |||||||
\(158\) | −0.908317 | −0.0722618 | ||||||||
\(159\) | 8.26741 | 0.655648 | ||||||||
\(160\) | 0.490892 | 0.0388084 | ||||||||
\(161\) | −15.6499 | −1.23339 | ||||||||
\(162\) | −13.0598 | −1.02608 | ||||||||
\(163\) | 21.2459 | 1.66411 | 0.832053 | − | 0.554696i | \(-0.187165\pi\) | ||||
0.832053 | + | 0.554696i | \(0.187165\pi\) | |||||||
\(164\) | 0.710581 | 0.0554871 | ||||||||
\(165\) | 2.16897 | 0.168854 | ||||||||
\(166\) | −3.07931 | −0.239001 | ||||||||
\(167\) | −5.96545 | −0.461620 | −0.230810 | − | 0.972999i | \(-0.574138\pi\) | ||||
−0.230810 | + | 0.972999i | \(0.574138\pi\) | |||||||
\(168\) | 13.7734 | 1.06264 | ||||||||
\(169\) | 8.87787 | 0.682913 | ||||||||
\(170\) | −2.44992 | −0.187900 | ||||||||
\(171\) | 0.942295 | 0.0720591 | ||||||||
\(172\) | −1.83368 | −0.139817 | ||||||||
\(173\) | −16.2621 | −1.23638 | −0.618192 | − | 0.786027i | \(-0.712135\pi\) | ||||
−0.618192 | + | 0.786027i | \(0.712135\pi\) | |||||||
\(174\) | −19.7042 | −1.49377 | ||||||||
\(175\) | −9.11236 | −0.688830 | ||||||||
\(176\) | 5.62666 | 0.424125 | ||||||||
\(177\) | −6.33831 | −0.476416 | ||||||||
\(178\) | 3.02143 | 0.226466 | ||||||||
\(179\) | 9.36724 | 0.700140 | 0.350070 | − | 0.936723i | \(-0.386158\pi\) | ||||
0.350070 | + | 0.936723i | \(0.386158\pi\) | |||||||
\(180\) | −0.242317 | −0.0180612 | ||||||||
\(181\) | 1.62885 | 0.121072 | 0.0605358 | − | 0.998166i | \(-0.480719\pi\) | ||||
0.0605358 | + | 0.998166i | \(0.480719\pi\) | |||||||
\(182\) | −12.4720 | −0.924489 | ||||||||
\(183\) | −27.6415 | −2.04332 | ||||||||
\(184\) | 23.3493 | 1.72134 | ||||||||
\(185\) | −6.53193 | −0.480237 | ||||||||
\(186\) | 13.6682 | 1.00220 | ||||||||
\(187\) | 4.65742 | 0.340585 | ||||||||
\(188\) | −1.62184 | −0.118285 | ||||||||
\(189\) | 1.00588 | 0.0731672 | ||||||||
\(190\) | 0.271704 | 0.0197115 | ||||||||
\(191\) | −8.41952 | −0.609215 | −0.304607 | − | 0.952478i | \(-0.598525\pi\) | ||||
−0.304607 | + | 0.952478i | \(0.598525\pi\) | |||||||
\(192\) | −20.4452 | −1.47550 | ||||||||
\(193\) | −24.9514 | −1.79604 | −0.898022 | − | 0.439950i | \(-0.854996\pi\) | ||||
−0.898022 | + | 0.439950i | \(0.854996\pi\) | |||||||
\(194\) | 19.4476 | 1.39625 | ||||||||
\(195\) | 6.64182 | 0.475631 | ||||||||
\(196\) | 0.465854 | 0.0332753 | ||||||||
\(197\) | 2.36559 | 0.168541 | 0.0842705 | − | 0.996443i | \(-0.473144\pi\) | ||||
0.0842705 | + | 0.996443i | \(0.473144\pi\) | |||||||
\(198\) | −5.79345 | −0.411722 | ||||||||
\(199\) | 11.7817 | 0.835180 | 0.417590 | − | 0.908636i | \(-0.362875\pi\) | ||||
0.417590 | + | 0.908636i | \(0.362875\pi\) | |||||||
\(200\) | 13.5954 | 0.961343 | ||||||||
\(201\) | 24.6695 | 1.74005 | ||||||||
\(202\) | −0.857288 | −0.0603186 | ||||||||
\(203\) | 11.7891 | 0.827434 | ||||||||
\(204\) | −1.08051 | −0.0756508 | ||||||||
\(205\) | −2.84738 | −0.198870 | ||||||||
\(206\) | −6.14430 | −0.428094 | ||||||||
\(207\) | −22.2610 | −1.54725 | ||||||||
\(208\) | 17.2299 | 1.19468 | ||||||||
\(209\) | −0.516524 | −0.0357287 | ||||||||
\(210\) | −3.78634 | −0.261282 | ||||||||
\(211\) | −16.8124 | −1.15742 | −0.578708 | − | 0.815535i | \(-0.696443\pi\) | ||||
−0.578708 | + | 0.815535i | \(0.696443\pi\) | |||||||
\(212\) | 0.506294 | 0.0347724 | ||||||||
\(213\) | −23.2597 | −1.59373 | ||||||||
\(214\) | 4.67633 | 0.319668 | ||||||||
\(215\) | 7.34778 | 0.501115 | ||||||||
\(216\) | −1.50076 | −0.102114 | ||||||||
\(217\) | −8.17778 | −0.555144 | ||||||||
\(218\) | 13.4758 | 0.912693 | ||||||||
\(219\) | 15.2435 | 1.03006 | ||||||||
\(220\) | 0.132827 | 0.00895522 | ||||||||
\(221\) | 14.2619 | 0.959362 | ||||||||
\(222\) | 36.2307 | 2.43165 | ||||||||
\(223\) | 8.32490 | 0.557476 | 0.278738 | − | 0.960367i | \(-0.410084\pi\) | ||||
0.278738 | + | 0.960367i | \(0.410084\pi\) | |||||||
\(224\) | 1.62909 | 0.108848 | ||||||||
\(225\) | −12.9617 | −0.864116 | ||||||||
\(226\) | −12.8992 | −0.858045 | ||||||||
\(227\) | 6.35919 | 0.422074 | 0.211037 | − | 0.977478i | \(-0.432316\pi\) | ||||
0.211037 | + | 0.977478i | \(0.432316\pi\) | |||||||
\(228\) | 0.119832 | 0.00793607 | ||||||||
\(229\) | 11.4619 | 0.757426 | 0.378713 | − | 0.925514i | \(-0.376367\pi\) | ||||
0.378713 | + | 0.925514i | \(0.376367\pi\) | |||||||
\(230\) | −6.41880 | −0.423243 | ||||||||
\(231\) | 7.19802 | 0.473595 | ||||||||
\(232\) | −17.5891 | −1.15478 | ||||||||
\(233\) | 21.5891 | 1.41435 | 0.707175 | − | 0.707039i | \(-0.249969\pi\) | ||||
0.707175 | + | 0.707039i | \(0.249969\pi\) | |||||||
\(234\) | −17.7407 | −1.15974 | ||||||||
\(235\) | 6.49890 | 0.423941 | ||||||||
\(236\) | −0.388156 | −0.0252668 | ||||||||
\(237\) | 1.60526 | 0.104273 | ||||||||
\(238\) | −8.13038 | −0.527014 | ||||||||
\(239\) | −4.52568 | −0.292742 | −0.146371 | − | 0.989230i | \(-0.546759\pi\) | ||||
−0.146371 | + | 0.989230i | \(0.546759\pi\) | |||||||
\(240\) | 5.23077 | 0.337645 | ||||||||
\(241\) | −9.84982 | −0.634483 | −0.317241 | − | 0.948345i | \(-0.602757\pi\) | ||||
−0.317241 | + | 0.948345i | \(0.602757\pi\) | |||||||
\(242\) | −11.7968 | −0.758325 | ||||||||
\(243\) | 21.5401 | 1.38180 | ||||||||
\(244\) | −1.69276 | −0.108368 | ||||||||
\(245\) | −1.86673 | −0.119261 | ||||||||
\(246\) | 15.7936 | 1.00696 | ||||||||
\(247\) | −1.58170 | −0.100641 | ||||||||
\(248\) | 12.2011 | 0.774769 | ||||||||
\(249\) | 5.44205 | 0.344876 | ||||||||
\(250\) | −7.75483 | −0.490459 | ||||||||
\(251\) | 22.0558 | 1.39215 | 0.696075 | − | 0.717969i | \(-0.254928\pi\) | ||||
0.696075 | + | 0.717969i | \(0.254928\pi\) | |||||||
\(252\) | −0.804161 | −0.0506574 | ||||||||
\(253\) | 12.2025 | 0.767163 | ||||||||
\(254\) | −15.4590 | −0.969982 | ||||||||
\(255\) | 4.32973 | 0.271138 | ||||||||
\(256\) | −3.51587 | −0.219742 | ||||||||
\(257\) | 25.3211 | 1.57948 | 0.789742 | − | 0.613439i | \(-0.210214\pi\) | ||||
0.789742 | + | 0.613439i | \(0.210214\pi\) | |||||||
\(258\) | −40.7560 | −2.53736 | ||||||||
\(259\) | −21.6771 | −1.34695 | ||||||||
\(260\) | 0.406743 | 0.0252251 | ||||||||
\(261\) | 16.7693 | 1.03799 | ||||||||
\(262\) | 21.6582 | 1.33805 | ||||||||
\(263\) | 10.7243 | 0.661289 | 0.330644 | − | 0.943755i | \(-0.392734\pi\) | ||||
0.330644 | + | 0.943755i | \(0.392734\pi\) | |||||||
\(264\) | −10.7393 | −0.660958 | ||||||||
\(265\) | −2.02878 | −0.124627 | ||||||||
\(266\) | 0.901686 | 0.0552859 | ||||||||
\(267\) | −5.33975 | −0.326788 | ||||||||
\(268\) | 1.51075 | 0.0922839 | ||||||||
\(269\) | −11.9609 | −0.729266 | −0.364633 | − | 0.931151i | \(-0.618806\pi\) | ||||
−0.364633 | + | 0.931151i | \(0.618806\pi\) | |||||||
\(270\) | 0.412562 | 0.0251077 | ||||||||
\(271\) | −11.7258 | −0.712295 | −0.356147 | − | 0.934430i | \(-0.615910\pi\) | ||||
−0.356147 | + | 0.934430i | \(0.615910\pi\) | |||||||
\(272\) | 11.2320 | 0.681040 | ||||||||
\(273\) | 22.0418 | 1.33403 | ||||||||
\(274\) | −20.4700 | −1.23664 | ||||||||
\(275\) | 7.10504 | 0.428450 | ||||||||
\(276\) | −2.83094 | −0.170403 | ||||||||
\(277\) | −0.916745 | −0.0550819 | −0.0275409 | − | 0.999621i | \(-0.508768\pi\) | ||||
−0.0275409 | + | 0.999621i | \(0.508768\pi\) | |||||||
\(278\) | −22.6610 | −1.35912 | ||||||||
\(279\) | −11.6324 | −0.696411 | ||||||||
\(280\) | −3.37991 | −0.201988 | ||||||||
\(281\) | 21.7464 | 1.29728 | 0.648640 | − | 0.761096i | \(-0.275338\pi\) | ||||
0.648640 | + | 0.761096i | \(0.275338\pi\) | |||||||
\(282\) | −36.0475 | −2.14660 | ||||||||
\(283\) | −8.06684 | −0.479524 | −0.239762 | − | 0.970832i | \(-0.577069\pi\) | ||||
−0.239762 | + | 0.970832i | \(0.577069\pi\) | |||||||
\(284\) | −1.42442 | −0.0845238 | ||||||||
\(285\) | −0.480181 | −0.0284435 | ||||||||
\(286\) | 9.72463 | 0.575030 | ||||||||
\(287\) | −9.44941 | −0.557781 | ||||||||
\(288\) | 2.31727 | 0.136547 | ||||||||
\(289\) | −7.70280 | −0.453106 | ||||||||
\(290\) | 4.83530 | 0.283939 | ||||||||
\(291\) | −34.3696 | −2.01478 | ||||||||
\(292\) | 0.933509 | 0.0546295 | ||||||||
\(293\) | −2.16609 | −0.126544 | −0.0632722 | − | 0.997996i | \(-0.520154\pi\) | ||||
−0.0632722 | + | 0.997996i | \(0.520154\pi\) | |||||||
\(294\) | 10.3542 | 0.603871 | ||||||||
\(295\) | 1.55539 | 0.0905581 | ||||||||
\(296\) | 32.3417 | 1.87982 | ||||||||
\(297\) | −0.784302 | −0.0455098 | ||||||||
\(298\) | −16.4231 | −0.951363 | ||||||||
\(299\) | 37.3664 | 2.16095 | ||||||||
\(300\) | −1.64835 | −0.0951676 | ||||||||
\(301\) | 24.3846 | 1.40550 | ||||||||
\(302\) | −22.4448 | −1.29155 | ||||||||
\(303\) | 1.51508 | 0.0870391 | ||||||||
\(304\) | −1.24567 | −0.0714438 | ||||||||
\(305\) | 6.78307 | 0.388397 | ||||||||
\(306\) | −11.5649 | −0.661124 | ||||||||
\(307\) | 6.60523 | 0.376980 | 0.188490 | − | 0.982075i | \(-0.439641\pi\) | ||||
0.188490 | + | 0.982075i | \(0.439641\pi\) | |||||||
\(308\) | 0.440805 | 0.0251172 | ||||||||
\(309\) | 10.8588 | 0.617735 | ||||||||
\(310\) | −3.35411 | −0.190501 | ||||||||
\(311\) | 3.84184 | 0.217851 | 0.108925 | − | 0.994050i | \(-0.465259\pi\) | ||||
0.108925 | + | 0.994050i | \(0.465259\pi\) | |||||||
\(312\) | −32.8858 | −1.86179 | ||||||||
\(313\) | −25.4617 | −1.43918 | −0.719591 | − | 0.694398i | \(-0.755671\pi\) | ||||
−0.719591 | + | 0.694398i | \(0.755671\pi\) | |||||||
\(314\) | 5.58891 | 0.315401 | ||||||||
\(315\) | 3.22237 | 0.181560 | ||||||||
\(316\) | 0.0983058 | 0.00553014 | ||||||||
\(317\) | −8.23817 | −0.462702 | −0.231351 | − | 0.972870i | \(-0.574314\pi\) | ||||
−0.231351 | + | 0.972870i | \(0.574314\pi\) | |||||||
\(318\) | 11.2531 | 0.631040 | ||||||||
\(319\) | −9.19216 | −0.514662 | ||||||||
\(320\) | 5.01713 | 0.280466 | ||||||||
\(321\) | −8.26446 | −0.461277 | ||||||||
\(322\) | −21.3016 | −1.18709 | ||||||||
\(323\) | −1.03109 | −0.0573714 | ||||||||
\(324\) | 1.41344 | 0.0785247 | ||||||||
\(325\) | 21.7570 | 1.20686 | ||||||||
\(326\) | 28.9185 | 1.60165 | ||||||||
\(327\) | −23.8156 | −1.31701 | ||||||||
\(328\) | 14.0983 | 0.778449 | ||||||||
\(329\) | 21.5675 | 1.18905 | ||||||||
\(330\) | 2.95226 | 0.162517 | ||||||||
\(331\) | −6.68597 | −0.367494 | −0.183747 | − | 0.982974i | \(-0.558823\pi\) | ||||
−0.183747 | + | 0.982974i | \(0.558823\pi\) | |||||||
\(332\) | 0.333270 | 0.0182906 | ||||||||
\(333\) | −30.8342 | −1.68970 | ||||||||
\(334\) | −8.11977 | −0.444294 | ||||||||
\(335\) | −6.05376 | −0.330752 | ||||||||
\(336\) | 17.3590 | 0.947011 | ||||||||
\(337\) | −34.9491 | −1.90380 | −0.951899 | − | 0.306411i | \(-0.900872\pi\) | ||||
−0.951899 | + | 0.306411i | \(0.900872\pi\) | |||||||
\(338\) | 12.0840 | 0.657282 | ||||||||
\(339\) | 22.7968 | 1.23815 | ||||||||
\(340\) | 0.265151 | 0.0143799 | ||||||||
\(341\) | 6.37634 | 0.345298 | ||||||||
\(342\) | 1.28259 | 0.0693545 | ||||||||
\(343\) | −19.9080 | −1.07493 | ||||||||
\(344\) | −36.3813 | −1.96155 | ||||||||
\(345\) | 11.3439 | 0.610736 | ||||||||
\(346\) | −22.1349 | −1.18998 | ||||||||
\(347\) | −16.1317 | −0.865998 | −0.432999 | − | 0.901394i | \(-0.642545\pi\) | ||||
−0.432999 | + | 0.901394i | \(0.642545\pi\) | |||||||
\(348\) | 2.13256 | 0.114317 | ||||||||
\(349\) | −16.2651 | −0.870653 | −0.435326 | − | 0.900273i | \(-0.643367\pi\) | ||||
−0.435326 | + | 0.900273i | \(0.643367\pi\) | |||||||
\(350\) | −12.4031 | −0.662976 | ||||||||
\(351\) | −2.40169 | −0.128192 | ||||||||
\(352\) | −1.27022 | −0.0677032 | ||||||||
\(353\) | 15.5427 | 0.827254 | 0.413627 | − | 0.910446i | \(-0.364262\pi\) | ||||
0.413627 | + | 0.910446i | \(0.364262\pi\) | |||||||
\(354\) | −8.62729 | −0.458535 | ||||||||
\(355\) | 5.70782 | 0.302940 | ||||||||
\(356\) | −0.327005 | −0.0173312 | ||||||||
\(357\) | 14.3688 | 0.760476 | ||||||||
\(358\) | 12.7501 | 0.673862 | ||||||||
\(359\) | −16.5339 | −0.872625 | −0.436312 | − | 0.899795i | \(-0.643716\pi\) | ||||
−0.436312 | + | 0.899795i | \(0.643716\pi\) | |||||||
\(360\) | −4.80770 | −0.253388 | ||||||||
\(361\) | −18.8856 | −0.993982 | ||||||||
\(362\) | 2.21708 | 0.116527 | ||||||||
\(363\) | 20.8484 | 1.09425 | ||||||||
\(364\) | 1.34983 | 0.0707504 | ||||||||
\(365\) | −3.74068 | −0.195796 | ||||||||
\(366\) | −37.6237 | −1.96662 | ||||||||
\(367\) | 5.62500 | 0.293623 | 0.146811 | − | 0.989165i | \(-0.453099\pi\) | ||||
0.146811 | + | 0.989165i | \(0.453099\pi\) | |||||||
\(368\) | 29.4279 | 1.53403 | ||||||||
\(369\) | −13.4412 | −0.699719 | ||||||||
\(370\) | −8.89083 | −0.462212 | ||||||||
\(371\) | −6.73277 | −0.349548 | ||||||||
\(372\) | −1.47929 | −0.0766978 | ||||||||
\(373\) | −18.0602 | −0.935122 | −0.467561 | − | 0.883961i | \(-0.654867\pi\) | ||||
−0.467561 | + | 0.883961i | \(0.654867\pi\) | |||||||
\(374\) | 6.33938 | 0.327802 | ||||||||
\(375\) | 13.7051 | 0.707727 | ||||||||
\(376\) | −32.1782 | −1.65946 | ||||||||
\(377\) | −28.1482 | −1.44970 | ||||||||
\(378\) | 1.36914 | 0.0704211 | ||||||||
\(379\) | −2.42773 | −0.124704 | −0.0623521 | − | 0.998054i | \(-0.519860\pi\) | ||||
−0.0623521 | + | 0.998054i | \(0.519860\pi\) | |||||||
\(380\) | −0.0294062 | −0.00150850 | ||||||||
\(381\) | 27.3206 | 1.39967 | ||||||||
\(382\) | −11.4601 | −0.586349 | ||||||||
\(383\) | −16.2778 | −0.831757 | −0.415878 | − | 0.909420i | \(-0.636526\pi\) | ||||
−0.415878 | + | 0.909420i | \(0.636526\pi\) | |||||||
\(384\) | −23.8278 | −1.21596 | ||||||||
\(385\) | −1.76636 | −0.0900219 | ||||||||
\(386\) | −33.9623 | −1.72863 | ||||||||
\(387\) | 34.6855 | 1.76316 | ||||||||
\(388\) | −2.10478 | −0.106854 | ||||||||
\(389\) | −15.0862 | −0.764899 | −0.382450 | − | 0.923976i | \(-0.624919\pi\) | ||||
−0.382450 | + | 0.923976i | \(0.624919\pi\) | |||||||
\(390\) | 9.04041 | 0.457779 | ||||||||
\(391\) | 24.3587 | 1.23187 | ||||||||
\(392\) | 9.24280 | 0.466832 | ||||||||
\(393\) | −38.2764 | −1.93079 | ||||||||
\(394\) | 3.21988 | 0.162215 | ||||||||
\(395\) | −0.393923 | −0.0198204 | ||||||||
\(396\) | 0.627016 | 0.0315088 | ||||||||
\(397\) | −26.7523 | −1.34266 | −0.671329 | − | 0.741160i | \(-0.734276\pi\) | ||||
−0.671329 | + | 0.741160i | \(0.734276\pi\) | |||||||
\(398\) | 16.0364 | 0.803834 | ||||||||
\(399\) | −1.59354 | −0.0797770 | ||||||||
\(400\) | 17.1348 | 0.856738 | ||||||||
\(401\) | −21.1930 | −1.05833 | −0.529165 | − | 0.848519i | \(-0.677495\pi\) | ||||
−0.529165 | + | 0.848519i | \(0.677495\pi\) | |||||||
\(402\) | 33.5785 | 1.67474 | ||||||||
\(403\) | 19.5256 | 0.972639 | ||||||||
\(404\) | 0.0927831 | 0.00461613 | ||||||||
\(405\) | −5.66384 | −0.281438 | ||||||||
\(406\) | 16.0466 | 0.796378 | ||||||||
\(407\) | 16.9019 | 0.837797 | ||||||||
\(408\) | −21.4379 | −1.06133 | ||||||||
\(409\) | 14.2178 | 0.703023 | 0.351511 | − | 0.936184i | \(-0.385668\pi\) | ||||
0.351511 | + | 0.936184i | \(0.385668\pi\) | |||||||
\(410\) | −3.87567 | −0.191406 | ||||||||
\(411\) | 36.1766 | 1.78446 | ||||||||
\(412\) | 0.664989 | 0.0327617 | ||||||||
\(413\) | 5.16176 | 0.253993 | ||||||||
\(414\) | −30.3002 | −1.48917 | ||||||||
\(415\) | −1.33545 | −0.0655547 | ||||||||
\(416\) | −3.88968 | −0.190707 | ||||||||
\(417\) | 40.0487 | 1.96119 | ||||||||
\(418\) | −0.703058 | −0.0343877 | ||||||||
\(419\) | 40.7220 | 1.98940 | 0.994700 | − | 0.102818i | \(-0.0327858\pi\) | ||||
0.994700 | + | 0.102818i | \(0.0327858\pi\) | |||||||
\(420\) | 0.409790 | 0.0199957 | ||||||||
\(421\) | 30.2685 | 1.47519 | 0.737597 | − | 0.675241i | \(-0.235960\pi\) | ||||
0.737597 | + | 0.675241i | \(0.235960\pi\) | |||||||
\(422\) | −22.8840 | −1.11397 | ||||||||
\(423\) | 30.6783 | 1.49163 | ||||||||
\(424\) | 10.0451 | 0.487835 | ||||||||
\(425\) | 14.1832 | 0.687984 | ||||||||
\(426\) | −31.6596 | −1.53391 | ||||||||
\(427\) | 22.5105 | 1.08936 | ||||||||
\(428\) | −0.506113 | −0.0244639 | ||||||||
\(429\) | −17.1863 | −0.829762 | ||||||||
\(430\) | 10.0013 | 0.482306 | ||||||||
\(431\) | 14.3367 | 0.690572 | 0.345286 | − | 0.938497i | \(-0.387782\pi\) | ||||
0.345286 | + | 0.938497i | \(0.387782\pi\) | |||||||
\(432\) | −1.89145 | −0.0910024 | ||||||||
\(433\) | −26.4985 | −1.27344 | −0.636719 | − | 0.771096i | \(-0.719709\pi\) | ||||
−0.636719 | + | 0.771096i | \(0.719709\pi\) | |||||||
\(434\) | −11.1311 | −0.534308 | ||||||||
\(435\) | −8.54540 | −0.409720 | ||||||||
\(436\) | −1.45846 | −0.0698477 | ||||||||
\(437\) | −2.70146 | −0.129228 | ||||||||
\(438\) | 20.7485 | 0.991400 | ||||||||
\(439\) | 19.2176 | 0.917208 | 0.458604 | − | 0.888641i | \(-0.348350\pi\) | ||||
0.458604 | + | 0.888641i | \(0.348350\pi\) | |||||||
\(440\) | 2.63537 | 0.125636 | ||||||||
\(441\) | −8.81198 | −0.419618 | ||||||||
\(442\) | 19.4124 | 0.923355 | ||||||||
\(443\) | −5.97322 | −0.283796 | −0.141898 | − | 0.989881i | \(-0.545321\pi\) | ||||
−0.141898 | + | 0.989881i | \(0.545321\pi\) | |||||||
\(444\) | −3.92120 | −0.186092 | ||||||||
\(445\) | 1.31035 | 0.0621164 | ||||||||
\(446\) | 11.3313 | 0.536553 | ||||||||
\(447\) | 29.0244 | 1.37281 | ||||||||
\(448\) | 16.6500 | 0.786639 | ||||||||
\(449\) | 1.84304 | 0.0869784 | 0.0434892 | − | 0.999054i | \(-0.486153\pi\) | ||||
0.0434892 | + | 0.999054i | \(0.486153\pi\) | |||||||
\(450\) | −17.6427 | −0.831683 | ||||||||
\(451\) | 7.36785 | 0.346938 | ||||||||
\(452\) | 1.39607 | 0.0656655 | ||||||||
\(453\) | 39.6665 | 1.86369 | ||||||||
\(454\) | 8.65571 | 0.406233 | ||||||||
\(455\) | −5.40893 | −0.253575 | ||||||||
\(456\) | 2.37753 | 0.111338 | ||||||||
\(457\) | 27.3399 | 1.27891 | 0.639453 | − | 0.768830i | \(-0.279161\pi\) | ||||
0.639453 | + | 0.768830i | \(0.279161\pi\) | |||||||
\(458\) | 15.6012 | 0.728998 | ||||||||
\(459\) | −1.56563 | −0.0730774 | ||||||||
\(460\) | 0.694698 | 0.0323905 | ||||||||
\(461\) | 35.1434 | 1.63679 | 0.818395 | − | 0.574656i | \(-0.194864\pi\) | ||||
0.818395 | + | 0.574656i | \(0.194864\pi\) | |||||||
\(462\) | 9.79748 | 0.455820 | ||||||||
\(463\) | −18.6765 | −0.867969 | −0.433984 | − | 0.900920i | \(-0.642893\pi\) | ||||
−0.433984 | + | 0.900920i | \(0.642893\pi\) | |||||||
\(464\) | −22.1681 | −1.02913 | ||||||||
\(465\) | 5.92770 | 0.274891 | ||||||||
\(466\) | 29.3857 | 1.36126 | ||||||||
\(467\) | −16.9925 | −0.786318 | −0.393159 | − | 0.919470i | \(-0.628618\pi\) | ||||
−0.393159 | + | 0.919470i | \(0.628618\pi\) | |||||||
\(468\) | 1.92005 | 0.0887542 | ||||||||
\(469\) | −20.0902 | −0.927680 | ||||||||
\(470\) | 8.84588 | 0.408030 | ||||||||
\(471\) | −9.87725 | −0.455120 | ||||||||
\(472\) | −7.70123 | −0.354478 | ||||||||
\(473\) | −19.0130 | −0.874220 | ||||||||
\(474\) | 2.18498 | 0.100359 | ||||||||
\(475\) | −1.57296 | −0.0721723 | ||||||||
\(476\) | 0.879940 | 0.0403320 | ||||||||
\(477\) | −9.57692 | −0.438497 | ||||||||
\(478\) | −6.16006 | −0.281755 | ||||||||
\(479\) | −11.4554 | −0.523409 | −0.261705 | − | 0.965148i | \(-0.584285\pi\) | ||||
−0.261705 | + | 0.965148i | \(0.584285\pi\) | |||||||
\(480\) | −1.18085 | −0.0538983 | ||||||||
\(481\) | 51.7570 | 2.35992 | ||||||||
\(482\) | −13.4069 | −0.610669 | ||||||||
\(483\) | 37.6463 | 1.71296 | ||||||||
\(484\) | 1.27675 | 0.0580340 | ||||||||
\(485\) | 8.43411 | 0.382973 | ||||||||
\(486\) | 29.3190 | 1.32994 | ||||||||
\(487\) | −14.2183 | −0.644295 | −0.322147 | − | 0.946690i | \(-0.604405\pi\) | ||||
−0.322147 | + | 0.946690i | \(0.604405\pi\) | |||||||
\(488\) | −33.5852 | −1.52033 | ||||||||
\(489\) | −51.1075 | −2.31116 | ||||||||
\(490\) | −2.54087 | −0.114785 | ||||||||
\(491\) | −4.53402 | −0.204617 | −0.102309 | − | 0.994753i | \(-0.532623\pi\) | ||||
−0.102309 | + | 0.994753i | \(0.532623\pi\) | |||||||
\(492\) | −1.70932 | −0.0770621 | ||||||||
\(493\) | −18.3495 | −0.826419 | ||||||||
\(494\) | −2.15290 | −0.0968636 | ||||||||
\(495\) | −2.51253 | −0.112930 | ||||||||
\(496\) | 15.3774 | 0.690465 | ||||||||
\(497\) | 18.9421 | 0.849671 | ||||||||
\(498\) | 7.40736 | 0.331932 | ||||||||
\(499\) | −38.1411 | −1.70743 | −0.853715 | − | 0.520741i | \(-0.825656\pi\) | ||||
−0.853715 | + | 0.520741i | \(0.825656\pi\) | |||||||
\(500\) | 0.839295 | 0.0375344 | ||||||||
\(501\) | 14.3500 | 0.641112 | ||||||||
\(502\) | 30.0209 | 1.33990 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | −15.9550 | −0.710692 | ||||||||
\(505\) | −0.371793 | −0.0165446 | ||||||||
\(506\) | 16.6092 | 0.738369 | ||||||||
\(507\) | −21.3559 | −0.948451 | ||||||||
\(508\) | 1.67310 | 0.0742319 | ||||||||
\(509\) | 34.3114 | 1.52083 | 0.760413 | − | 0.649440i | \(-0.224997\pi\) | ||||
0.760413 | + | 0.649440i | \(0.224997\pi\) | |||||||
\(510\) | 5.89334 | 0.260962 | ||||||||
\(511\) | −12.4139 | −0.549160 | ||||||||
\(512\) | −24.5965 | −1.08702 | ||||||||
\(513\) | 0.173634 | 0.00766612 | ||||||||
\(514\) | 34.4654 | 1.52020 | ||||||||
\(515\) | −2.66469 | −0.117420 | ||||||||
\(516\) | 4.41097 | 0.194182 | ||||||||
\(517\) | −16.8165 | −0.739587 | ||||||||
\(518\) | −29.5054 | −1.29639 | ||||||||
\(519\) | 39.1189 | 1.71713 | ||||||||
\(520\) | 8.07001 | 0.353893 | ||||||||
\(521\) | 23.8175 | 1.04346 | 0.521732 | − | 0.853110i | \(-0.325286\pi\) | ||||
0.521732 | + | 0.853110i | \(0.325286\pi\) | |||||||
\(522\) | 22.8252 | 0.999032 | ||||||||
\(523\) | −2.16718 | −0.0947643 | −0.0473821 | − | 0.998877i | \(-0.515088\pi\) | ||||
−0.0473821 | + | 0.998877i | \(0.515088\pi\) | |||||||
\(524\) | −2.34404 | −0.102400 | ||||||||
\(525\) | 21.9200 | 0.956667 | ||||||||
\(526\) | 14.5972 | 0.636469 | ||||||||
\(527\) | 12.7285 | 0.554463 | ||||||||
\(528\) | −13.5351 | −0.589038 | ||||||||
\(529\) | 40.8200 | 1.77478 | ||||||||
\(530\) | −2.76144 | −0.119949 | ||||||||
\(531\) | 7.34226 | 0.318627 | ||||||||
\(532\) | −0.0975882 | −0.00423099 | ||||||||
\(533\) | 22.5618 | 0.977259 | ||||||||
\(534\) | −7.26812 | −0.314522 | ||||||||
\(535\) | 2.02805 | 0.0876804 | ||||||||
\(536\) | 29.9742 | 1.29469 | ||||||||
\(537\) | −22.5331 | −0.972376 | ||||||||
\(538\) | −16.2803 | −0.701895 | ||||||||
\(539\) | 4.83033 | 0.208057 | ||||||||
\(540\) | −0.0446510 | −0.00192147 | ||||||||
\(541\) | 13.5019 | 0.580493 | 0.290246 | − | 0.956952i | \(-0.406263\pi\) | ||||
0.290246 | + | 0.956952i | \(0.406263\pi\) | |||||||
\(542\) | −15.9605 | −0.685560 | ||||||||
\(543\) | −3.91824 | −0.168148 | ||||||||
\(544\) | −2.53564 | −0.108714 | ||||||||
\(545\) | 5.84423 | 0.250339 | ||||||||
\(546\) | 30.0018 | 1.28396 | ||||||||
\(547\) | −1.05880 | −0.0452710 | −0.0226355 | − | 0.999744i | \(-0.507206\pi\) | ||||
−0.0226355 | + | 0.999744i | \(0.507206\pi\) | |||||||
\(548\) | 2.21544 | 0.0946390 | ||||||||
\(549\) | 32.0197 | 1.36657 | ||||||||
\(550\) | 9.67092 | 0.412369 | ||||||||
\(551\) | 2.03502 | 0.0866947 | ||||||||
\(552\) | −56.1674 | −2.39064 | ||||||||
\(553\) | −1.30728 | −0.0555914 | ||||||||
\(554\) | −1.24781 | −0.0530145 | ||||||||
\(555\) | 15.7127 | 0.666967 | ||||||||
\(556\) | 2.45257 | 0.104012 | ||||||||
\(557\) | −9.20176 | −0.389891 | −0.194946 | − | 0.980814i | \(-0.562453\pi\) | ||||
−0.194946 | + | 0.980814i | \(0.562453\pi\) | |||||||
\(558\) | −15.8332 | −0.670273 | ||||||||
\(559\) | −58.2216 | −2.46251 | ||||||||
\(560\) | −4.25980 | −0.180010 | ||||||||
\(561\) | −11.2035 | −0.473014 | ||||||||
\(562\) | 29.5997 | 1.24859 | ||||||||
\(563\) | −29.6502 | −1.24961 | −0.624804 | − | 0.780782i | \(-0.714821\pi\) | ||||
−0.624804 | + | 0.780782i | \(0.714821\pi\) | |||||||
\(564\) | 3.90137 | 0.164277 | ||||||||
\(565\) | −5.59420 | −0.235350 | ||||||||
\(566\) | −10.9800 | −0.461526 | ||||||||
\(567\) | −18.7962 | −0.789366 | ||||||||
\(568\) | −28.2613 | −1.18582 | ||||||||
\(569\) | 22.6715 | 0.950439 | 0.475220 | − | 0.879867i | \(-0.342369\pi\) | ||||
0.475220 | + | 0.879867i | \(0.342369\pi\) | |||||||
\(570\) | −0.653591 | −0.0273759 | ||||||||
\(571\) | −31.2013 | −1.30573 | −0.652866 | − | 0.757473i | \(-0.726434\pi\) | ||||
−0.652866 | + | 0.757473i | \(0.726434\pi\) | |||||||
\(572\) | −1.05248 | −0.0440065 | ||||||||
\(573\) | 20.2533 | 0.846096 | ||||||||
\(574\) | −12.8619 | −0.536846 | ||||||||
\(575\) | 37.1600 | 1.54968 | ||||||||
\(576\) | 23.6836 | 0.986815 | ||||||||
\(577\) | −3.98191 | −0.165769 | −0.0828845 | − | 0.996559i | \(-0.526413\pi\) | ||||
−0.0828845 | + | 0.996559i | \(0.526413\pi\) | |||||||
\(578\) | −10.4845 | −0.436099 | ||||||||
\(579\) | 60.0213 | 2.49440 | ||||||||
\(580\) | −0.523318 | −0.0217296 | ||||||||
\(581\) | −4.43187 | −0.183865 | ||||||||
\(582\) | −46.7816 | −1.93916 | ||||||||
\(583\) | 5.24964 | 0.217418 | ||||||||
\(584\) | 18.5213 | 0.766418 | ||||||||
\(585\) | −7.69385 | −0.318102 | ||||||||
\(586\) | −2.94834 | −0.121795 | ||||||||
\(587\) | −12.7494 | −0.526225 | −0.263113 | − | 0.964765i | \(-0.584749\pi\) | ||||
−0.263113 | + | 0.964765i | \(0.584749\pi\) | |||||||
\(588\) | −1.12062 | −0.0462137 | ||||||||
\(589\) | −1.41163 | −0.0581654 | ||||||||
\(590\) | 2.11709 | 0.0871592 | ||||||||
\(591\) | −5.69048 | −0.234075 | ||||||||
\(592\) | 40.7612 | 1.67528 | ||||||||
\(593\) | −3.27771 | −0.134600 | −0.0672998 | − | 0.997733i | \(-0.521438\pi\) | ||||
−0.0672998 | + | 0.997733i | \(0.521438\pi\) | |||||||
\(594\) | −1.06754 | −0.0438017 | ||||||||
\(595\) | −3.52602 | −0.144553 | ||||||||
\(596\) | 1.77745 | 0.0728070 | ||||||||
\(597\) | −28.3411 | −1.15992 | ||||||||
\(598\) | 50.8606 | 2.07985 | ||||||||
\(599\) | 10.9237 | 0.446332 | 0.223166 | − | 0.974780i | \(-0.428361\pi\) | ||||
0.223166 | + | 0.974780i | \(0.428361\pi\) | |||||||
\(600\) | −32.7042 | −1.33514 | ||||||||
\(601\) | −29.7446 | −1.21331 | −0.606653 | − | 0.794967i | \(-0.707488\pi\) | ||||
−0.606653 | + | 0.794967i | \(0.707488\pi\) | |||||||
\(602\) | 33.1907 | 1.35275 | ||||||||
\(603\) | −28.5770 | −1.16375 | ||||||||
\(604\) | 2.42916 | 0.0988413 | ||||||||
\(605\) | −5.11608 | −0.207998 | ||||||||
\(606\) | 2.06223 | 0.0837723 | ||||||||
\(607\) | −43.8414 | −1.77947 | −0.889735 | − | 0.456478i | \(-0.849111\pi\) | ||||
−0.889735 | + | 0.456478i | \(0.849111\pi\) | |||||||
\(608\) | 0.281210 | 0.0114046 | ||||||||
\(609\) | −28.3590 | −1.14917 | ||||||||
\(610\) | 9.23267 | 0.373820 | ||||||||
\(611\) | −51.4953 | −2.08328 | ||||||||
\(612\) | 1.25166 | 0.0505952 | ||||||||
\(613\) | −32.3195 | −1.30537 | −0.652687 | − | 0.757628i | \(-0.726358\pi\) | ||||
−0.652687 | + | 0.757628i | \(0.726358\pi\) | |||||||
\(614\) | 8.99061 | 0.362831 | ||||||||
\(615\) | 6.84945 | 0.276196 | ||||||||
\(616\) | 8.74581 | 0.352379 | ||||||||
\(617\) | 40.9696 | 1.64937 | 0.824687 | − | 0.565589i | \(-0.191351\pi\) | ||||
0.824687 | + | 0.565589i | \(0.191351\pi\) | |||||||
\(618\) | 14.7803 | 0.594549 | ||||||||
\(619\) | 22.5775 | 0.907466 | 0.453733 | − | 0.891138i | \(-0.350092\pi\) | ||||
0.453733 | + | 0.891138i | \(0.350092\pi\) | |||||||
\(620\) | 0.363011 | 0.0145789 | ||||||||
\(621\) | −4.10196 | −0.164606 | ||||||||
\(622\) | 5.22926 | 0.209674 | ||||||||
\(623\) | 4.34856 | 0.174221 | ||||||||
\(624\) | −41.4470 | −1.65921 | ||||||||
\(625\) | 19.8946 | 0.795782 | ||||||||
\(626\) | −34.6568 | −1.38517 | ||||||||
\(627\) | 1.24251 | 0.0496211 | ||||||||
\(628\) | −0.604880 | −0.0241373 | ||||||||
\(629\) | 33.7398 | 1.34529 | ||||||||
\(630\) | 4.38607 | 0.174745 | ||||||||
\(631\) | 33.9719 | 1.35240 | 0.676199 | − | 0.736719i | \(-0.263626\pi\) | ||||
0.676199 | + | 0.736719i | \(0.263626\pi\) | |||||||
\(632\) | 1.95044 | 0.0775844 | ||||||||
\(633\) | 40.4427 | 1.60745 | ||||||||
\(634\) | −11.2132 | −0.445335 | ||||||||
\(635\) | −6.70432 | −0.266053 | ||||||||
\(636\) | −1.21790 | −0.0482930 | ||||||||
\(637\) | 14.7914 | 0.586057 | ||||||||
\(638\) | −12.5118 | −0.495345 | ||||||||
\(639\) | 26.9440 | 1.06589 | ||||||||
\(640\) | 5.84721 | 0.231131 | ||||||||
\(641\) | −4.53431 | −0.179095 | −0.0895473 | − | 0.995983i | \(-0.528542\pi\) | ||||
−0.0895473 | + | 0.995983i | \(0.528542\pi\) | |||||||
\(642\) | −11.2490 | −0.443964 | ||||||||
\(643\) | 38.3929 | 1.51407 | 0.757033 | − | 0.653376i | \(-0.226648\pi\) | ||||
0.757033 | + | 0.653376i | \(0.226648\pi\) | |||||||
\(644\) | 2.30545 | 0.0908473 | ||||||||
\(645\) | −17.6753 | −0.695963 | ||||||||
\(646\) | −1.40345 | −0.0552181 | ||||||||
\(647\) | −0.255028 | −0.0100262 | −0.00501309 | − | 0.999987i | \(-0.501596\pi\) | ||||
−0.00501309 | + | 0.999987i | \(0.501596\pi\) | |||||||
\(648\) | 28.0435 | 1.10165 | ||||||||
\(649\) | −4.02470 | −0.157983 | ||||||||
\(650\) | 29.6142 | 1.16157 | ||||||||
\(651\) | 19.6719 | 0.771001 | ||||||||
\(652\) | −3.12981 | −0.122573 | ||||||||
\(653\) | −2.04379 | −0.0799797 | −0.0399898 | − | 0.999200i | \(-0.512733\pi\) | ||||
−0.0399898 | + | 0.999200i | \(0.512733\pi\) | |||||||
\(654\) | −32.4163 | −1.26758 | ||||||||
\(655\) | 9.39282 | 0.367008 | ||||||||
\(656\) | 17.7685 | 0.693745 | ||||||||
\(657\) | −17.6580 | −0.688904 | ||||||||
\(658\) | 29.3562 | 1.14442 | ||||||||
\(659\) | 10.0768 | 0.392534 | 0.196267 | − | 0.980550i | \(-0.437118\pi\) | ||||
0.196267 | + | 0.980550i | \(0.437118\pi\) | |||||||
\(660\) | −0.319519 | −0.0124373 | ||||||||
\(661\) | −5.53010 | −0.215096 | −0.107548 | − | 0.994200i | \(-0.534300\pi\) | ||||
−0.107548 | + | 0.994200i | \(0.534300\pi\) | |||||||
\(662\) | −9.10050 | −0.353701 | ||||||||
\(663\) | −34.3074 | −1.33239 | ||||||||
\(664\) | 6.61225 | 0.256605 | ||||||||
\(665\) | 0.391047 | 0.0151642 | ||||||||
\(666\) | −41.9695 | −1.62628 | ||||||||
\(667\) | −48.0757 | −1.86150 | ||||||||
\(668\) | 0.878791 | 0.0340015 | ||||||||
\(669\) | −20.0257 | −0.774240 | ||||||||
\(670\) | −8.23998 | −0.318338 | ||||||||
\(671\) | −17.5518 | −0.677579 | ||||||||
\(672\) | −3.91881 | −0.151171 | ||||||||
\(673\) | −3.16280 | −0.121917 | −0.0609585 | − | 0.998140i | \(-0.519416\pi\) | ||||
−0.0609585 | + | 0.998140i | \(0.519416\pi\) | |||||||
\(674\) | −47.5704 | −1.83234 | ||||||||
\(675\) | −2.38842 | −0.0919303 | ||||||||
\(676\) | −1.30783 | −0.0503012 | ||||||||
\(677\) | −47.8219 | −1.83794 | −0.918972 | − | 0.394323i | \(-0.870979\pi\) | ||||
−0.918972 | + | 0.394323i | \(0.870979\pi\) | |||||||
\(678\) | 31.0295 | 1.19168 | ||||||||
\(679\) | 27.9897 | 1.07415 | ||||||||
\(680\) | 5.26075 | 0.201740 | ||||||||
\(681\) | −15.2972 | −0.586190 | ||||||||
\(682\) | 8.67906 | 0.332338 | ||||||||
\(683\) | 13.2468 | 0.506873 | 0.253437 | − | 0.967352i | \(-0.418439\pi\) | ||||
0.253437 | + | 0.967352i | \(0.418439\pi\) | |||||||
\(684\) | −0.138813 | −0.00530764 | ||||||||
\(685\) | −8.87754 | −0.339193 | ||||||||
\(686\) | −27.0974 | −1.03458 | ||||||||
\(687\) | −27.5720 | −1.05194 | ||||||||
\(688\) | −45.8524 | −1.74811 | ||||||||
\(689\) | 16.0754 | 0.612425 | ||||||||
\(690\) | 15.4406 | 0.587813 | ||||||||
\(691\) | −7.80850 | −0.297049 | −0.148525 | − | 0.988909i | \(-0.547452\pi\) | ||||
−0.148525 | + | 0.988909i | \(0.547452\pi\) | |||||||
\(692\) | 2.39563 | 0.0910681 | ||||||||
\(693\) | −8.33815 | −0.316740 | ||||||||
\(694\) | −21.9575 | −0.833494 | ||||||||
\(695\) | −9.82774 | −0.372787 | ||||||||
\(696\) | 42.3111 | 1.60380 | ||||||||
\(697\) | 14.7078 | 0.557097 | ||||||||
\(698\) | −22.1390 | −0.837975 | ||||||||
\(699\) | −51.9331 | −1.96429 | ||||||||
\(700\) | 1.34237 | 0.0507370 | ||||||||
\(701\) | 7.68972 | 0.290437 | 0.145218 | − | 0.989400i | \(-0.453612\pi\) | ||||
0.145218 | + | 0.989400i | \(0.453612\pi\) | |||||||
\(702\) | −3.26902 | −0.123381 | ||||||||
\(703\) | −3.74185 | −0.141127 | ||||||||
\(704\) | −12.9823 | −0.489288 | ||||||||
\(705\) | −15.6333 | −0.588783 | ||||||||
\(706\) | 21.1557 | 0.796205 | ||||||||
\(707\) | −1.23384 | −0.0464034 | ||||||||
\(708\) | 0.933719 | 0.0350913 | ||||||||
\(709\) | 31.0522 | 1.16619 | 0.583096 | − | 0.812403i | \(-0.301841\pi\) | ||||
0.583096 | + | 0.812403i | \(0.301841\pi\) | |||||||
\(710\) | 7.76911 | 0.291569 | ||||||||
\(711\) | −1.85953 | −0.0697377 | ||||||||
\(712\) | −6.48796 | −0.243146 | ||||||||
\(713\) | 33.3488 | 1.24892 | ||||||||
\(714\) | 19.5578 | 0.731933 | ||||||||
\(715\) | 4.21742 | 0.157723 | ||||||||
\(716\) | −1.37992 | −0.0515701 | ||||||||
\(717\) | 10.8866 | 0.406569 | ||||||||
\(718\) | −22.5048 | −0.839873 | ||||||||
\(719\) | −30.4494 | −1.13557 | −0.567786 | − | 0.823176i | \(-0.692200\pi\) | ||||
−0.567786 | + | 0.823176i | \(0.692200\pi\) | |||||||
\(720\) | −6.05929 | −0.225817 | ||||||||
\(721\) | −8.84312 | −0.329335 | ||||||||
\(722\) | −25.7059 | −0.956675 | ||||||||
\(723\) | 23.6940 | 0.881189 | ||||||||
\(724\) | −0.239952 | −0.00891774 | ||||||||
\(725\) | −27.9927 | −1.03962 | ||||||||
\(726\) | 28.3774 | 1.05318 | ||||||||
\(727\) | −6.14587 | −0.227938 | −0.113969 | − | 0.993484i | \(-0.536356\pi\) | ||||
−0.113969 | + | 0.993484i | \(0.536356\pi\) | |||||||
\(728\) | 26.7814 | 0.992584 | ||||||||
\(729\) | −23.0309 | −0.852995 | ||||||||
\(730\) | −5.09156 | −0.188447 | ||||||||
\(731\) | −37.9540 | −1.40378 | ||||||||
\(732\) | 4.07196 | 0.150504 | ||||||||
\(733\) | −25.4237 | −0.939046 | −0.469523 | − | 0.882920i | \(-0.655574\pi\) | ||||
−0.469523 | + | 0.882920i | \(0.655574\pi\) | |||||||
\(734\) | 7.65638 | 0.282602 | ||||||||
\(735\) | 4.49047 | 0.165633 | ||||||||
\(736\) | −6.64338 | −0.244878 | ||||||||
\(737\) | 15.6646 | 0.577014 | ||||||||
\(738\) | −18.2952 | −0.673457 | ||||||||
\(739\) | −19.8464 | −0.730063 | −0.365032 | − | 0.930995i | \(-0.618942\pi\) | ||||
−0.365032 | + | 0.930995i | \(0.618942\pi\) | |||||||
\(740\) | 0.962242 | 0.0353727 | ||||||||
\(741\) | 3.80481 | 0.139773 | ||||||||
\(742\) | −9.16420 | −0.336428 | ||||||||
\(743\) | −28.7154 | −1.05346 | −0.526732 | − | 0.850031i | \(-0.676583\pi\) | ||||
−0.526732 | + | 0.850031i | \(0.676583\pi\) | |||||||
\(744\) | −29.3500 | −1.07602 | ||||||||
\(745\) | −7.12243 | −0.260946 | ||||||||
\(746\) | −24.5824 | −0.900025 | ||||||||
\(747\) | −6.30404 | −0.230653 | ||||||||
\(748\) | −0.686102 | −0.0250864 | ||||||||
\(749\) | 6.73036 | 0.245922 | ||||||||
\(750\) | 18.6544 | 0.681164 | ||||||||
\(751\) | 24.0374 | 0.877139 | 0.438569 | − | 0.898697i | \(-0.355485\pi\) | ||||
0.438569 | + | 0.898697i | \(0.355485\pi\) | |||||||
\(752\) | −40.5551 | −1.47889 | ||||||||
\(753\) | −53.0558 | −1.93346 | ||||||||
\(754\) | −38.3134 | −1.39529 | ||||||||
\(755\) | −9.73394 | −0.354254 | ||||||||
\(756\) | −0.148180 | −0.00538926 | ||||||||
\(757\) | −23.2463 | −0.844902 | −0.422451 | − | 0.906386i | \(-0.638830\pi\) | ||||
−0.422451 | + | 0.906386i | \(0.638830\pi\) | |||||||
\(758\) | −3.30447 | −0.120024 | ||||||||
\(759\) | −29.3534 | −1.06546 | ||||||||
\(760\) | −0.583434 | −0.0211634 | ||||||||
\(761\) | 44.3555 | 1.60789 | 0.803943 | − | 0.594706i | \(-0.202732\pi\) | ||||
0.803943 | + | 0.594706i | \(0.202732\pi\) | |||||||
\(762\) | 37.1869 | 1.34714 | ||||||||
\(763\) | 19.3948 | 0.702140 | ||||||||
\(764\) | 1.24031 | 0.0448728 | ||||||||
\(765\) | −5.01553 | −0.181337 | ||||||||
\(766\) | −22.1563 | −0.800539 | ||||||||
\(767\) | −12.3244 | −0.445009 | ||||||||
\(768\) | 8.45752 | 0.305185 | ||||||||
\(769\) | −17.4534 | −0.629385 | −0.314693 | − | 0.949194i | \(-0.601901\pi\) | ||||
−0.314693 | + | 0.949194i | \(0.601901\pi\) | |||||||
\(770\) | −2.40425 | −0.0866431 | ||||||||
\(771\) | −60.9104 | −2.19364 | ||||||||
\(772\) | 3.67569 | 0.132291 | ||||||||
\(773\) | −1.73607 | −0.0624422 | −0.0312211 | − | 0.999513i | \(-0.509940\pi\) | ||||
−0.0312211 | + | 0.999513i | \(0.509940\pi\) | |||||||
\(774\) | 47.2116 | 1.69699 | ||||||||
\(775\) | 19.4177 | 0.697506 | ||||||||
\(776\) | −41.7600 | −1.49910 | ||||||||
\(777\) | 52.1447 | 1.87068 | ||||||||
\(778\) | −20.5343 | −0.736190 | ||||||||
\(779\) | −1.63114 | −0.0584417 | ||||||||
\(780\) | −0.978431 | −0.0350334 | ||||||||
\(781\) | −14.7695 | −0.528493 | ||||||||
\(782\) | 33.1555 | 1.18564 | ||||||||
\(783\) | 3.09002 | 0.110428 | ||||||||
\(784\) | 11.6490 | 0.416035 | ||||||||
\(785\) | 2.42383 | 0.0865100 | ||||||||
\(786\) | −52.0993 | −1.85832 | ||||||||
\(787\) | −16.1636 | −0.576169 | −0.288085 | − | 0.957605i | \(-0.593018\pi\) | ||||
−0.288085 | + | 0.957605i | \(0.593018\pi\) | |||||||
\(788\) | −0.348483 | −0.0124142 | ||||||||
\(789\) | −25.7976 | −0.918418 | ||||||||
\(790\) | −0.536182 | −0.0190765 | ||||||||
\(791\) | −18.5651 | −0.660099 | ||||||||
\(792\) | 12.4403 | 0.442048 | ||||||||
\(793\) | −53.7469 | −1.90861 | ||||||||
\(794\) | −36.4134 | −1.29226 | ||||||||
\(795\) | 4.88028 | 0.173086 | ||||||||
\(796\) | −1.73560 | −0.0615167 | ||||||||
\(797\) | −26.8208 | −0.950040 | −0.475020 | − | 0.879975i | \(-0.657559\pi\) | ||||
−0.475020 | + | 0.879975i | \(0.657559\pi\) | |||||||
\(798\) | −2.16903 | −0.0767827 | ||||||||
\(799\) | −33.5692 | −1.18759 | ||||||||
\(800\) | −3.86819 | −0.136761 | ||||||||
\(801\) | 6.18554 | 0.218555 | ||||||||
\(802\) | −28.8466 | −1.01861 | ||||||||
\(803\) | 9.67933 | 0.341576 | ||||||||
\(804\) | −3.63415 | −0.128167 | ||||||||
\(805\) | −9.23819 | −0.325603 | ||||||||
\(806\) | 26.5770 | 0.936133 | ||||||||
\(807\) | 28.7721 | 1.01283 | ||||||||
\(808\) | 1.84087 | 0.0647615 | ||||||||
\(809\) | 33.4065 | 1.17451 | 0.587255 | − | 0.809402i | \(-0.300209\pi\) | ||||
0.587255 | + | 0.809402i | \(0.300209\pi\) | |||||||
\(810\) | −7.70924 | −0.270875 | ||||||||
\(811\) | 34.8499 | 1.22375 | 0.611873 | − | 0.790956i | \(-0.290416\pi\) | ||||
0.611873 | + | 0.790956i | \(0.290416\pi\) | |||||||
\(812\) | −1.73670 | −0.0609462 | ||||||||
\(813\) | 28.2068 | 0.989256 | ||||||||
\(814\) | 23.0058 | 0.806352 | ||||||||
\(815\) | 12.5415 | 0.439310 | ||||||||
\(816\) | −27.0188 | −0.945849 | ||||||||
\(817\) | 4.20922 | 0.147262 | ||||||||
\(818\) | 19.3523 | 0.676636 | ||||||||
\(819\) | −25.5330 | −0.892197 | ||||||||
\(820\) | 0.419458 | 0.0146481 | ||||||||
\(821\) | −24.4182 | −0.852201 | −0.426101 | − | 0.904676i | \(-0.640113\pi\) | ||||
−0.426101 | + | 0.904676i | \(0.640113\pi\) | |||||||
\(822\) | 49.2412 | 1.71748 | ||||||||
\(823\) | 4.51039 | 0.157222 | 0.0786112 | − | 0.996905i | \(-0.474951\pi\) | ||||
0.0786112 | + | 0.996905i | \(0.474951\pi\) | |||||||
\(824\) | 13.1937 | 0.459626 | ||||||||
\(825\) | −17.0914 | −0.595045 | ||||||||
\(826\) | 7.02584 | 0.244460 | ||||||||
\(827\) | −2.91499 | −0.101364 | −0.0506821 | − | 0.998715i | \(-0.516140\pi\) | ||||
−0.0506821 | + | 0.998715i | \(0.516140\pi\) | |||||||
\(828\) | 3.27935 | 0.113965 | ||||||||
\(829\) | 35.2382 | 1.22387 | 0.611937 | − | 0.790906i | \(-0.290390\pi\) | ||||
0.611937 | + | 0.790906i | \(0.290390\pi\) | |||||||
\(830\) | −1.81773 | −0.0630943 | ||||||||
\(831\) | 2.20525 | 0.0764994 | ||||||||
\(832\) | −39.7542 | −1.37823 | ||||||||
\(833\) | 9.64236 | 0.334088 | ||||||||
\(834\) | 54.5116 | 1.88758 | ||||||||
\(835\) | −3.52142 | −0.121864 | ||||||||
\(836\) | 0.0760910 | 0.00263166 | ||||||||
\(837\) | −2.14346 | −0.0740888 | ||||||||
\(838\) | 55.4281 | 1.91473 | ||||||||
\(839\) | −14.4876 | −0.500166 | −0.250083 | − | 0.968224i | \(-0.580458\pi\) | ||||
−0.250083 | + | 0.968224i | \(0.580458\pi\) | |||||||
\(840\) | 8.13046 | 0.280527 | ||||||||
\(841\) | 7.21557 | 0.248813 | ||||||||
\(842\) | 41.1994 | 1.41983 | ||||||||
\(843\) | −52.3114 | −1.80170 | ||||||||
\(844\) | 2.47670 | 0.0852515 | ||||||||
\(845\) | 5.24063 | 0.180283 | ||||||||
\(846\) | 41.7573 | 1.43564 | ||||||||
\(847\) | −16.9784 | −0.583384 | ||||||||
\(848\) | 12.6602 | 0.434753 | ||||||||
\(849\) | 19.4050 | 0.665977 | ||||||||
\(850\) | 19.3052 | 0.662163 | ||||||||
\(851\) | 88.3985 | 3.03026 | ||||||||
\(852\) | 3.42648 | 0.117389 | ||||||||
\(853\) | 4.92917 | 0.168772 | 0.0843858 | − | 0.996433i | \(-0.473107\pi\) | ||||
0.0843858 | + | 0.996433i | \(0.473107\pi\) | |||||||
\(854\) | 30.6398 | 1.04847 | ||||||||
\(855\) | 0.556239 | 0.0190230 | ||||||||
\(856\) | −10.0416 | −0.343213 | ||||||||
\(857\) | 52.5344 | 1.79454 | 0.897270 | − | 0.441482i | \(-0.145547\pi\) | ||||
0.897270 | + | 0.441482i | \(0.145547\pi\) | |||||||
\(858\) | −23.3928 | −0.798618 | ||||||||
\(859\) | 32.5431 | 1.11036 | 0.555179 | − | 0.831731i | \(-0.312650\pi\) | ||||
0.555179 | + | 0.831731i | \(0.312650\pi\) | |||||||
\(860\) | −1.08243 | −0.0369105 | ||||||||
\(861\) | 22.7308 | 0.774663 | ||||||||
\(862\) | 19.5141 | 0.664653 | ||||||||
\(863\) | 51.5604 | 1.75514 | 0.877568 | − | 0.479451i | \(-0.159164\pi\) | ||||
0.877568 | + | 0.479451i | \(0.159164\pi\) | |||||||
\(864\) | 0.426997 | 0.0145267 | ||||||||
\(865\) | −9.59956 | −0.326395 | ||||||||
\(866\) | −36.0681 | −1.22564 | ||||||||
\(867\) | 18.5293 | 0.629287 | ||||||||
\(868\) | 1.20470 | 0.0408901 | ||||||||
\(869\) | 1.01931 | 0.0345777 | ||||||||
\(870\) | −11.6314 | −0.394342 | ||||||||
\(871\) | 47.9682 | 1.62534 | ||||||||
\(872\) | −28.9367 | −0.979919 | ||||||||
\(873\) | 39.8135 | 1.34748 | ||||||||
\(874\) | −3.67705 | −0.124378 | ||||||||
\(875\) | −11.1611 | −0.377313 | ||||||||
\(876\) | −2.24558 | −0.0758710 | ||||||||
\(877\) | 35.8616 | 1.21096 | 0.605481 | − | 0.795860i | \(-0.292981\pi\) | ||||
0.605481 | + | 0.795860i | \(0.292981\pi\) | |||||||
\(878\) | 26.1578 | 0.882783 | ||||||||
\(879\) | 5.21058 | 0.175749 | ||||||||
\(880\) | 3.32143 | 0.111965 | ||||||||
\(881\) | −41.2432 | −1.38952 | −0.694759 | − | 0.719243i | \(-0.744489\pi\) | ||||
−0.694759 | + | 0.719243i | \(0.744489\pi\) | |||||||
\(882\) | −11.9943 | −0.403869 | ||||||||
\(883\) | 24.3041 | 0.817898 | 0.408949 | − | 0.912557i | \(-0.365895\pi\) | ||||
0.408949 | + | 0.912557i | \(0.365895\pi\) | |||||||
\(884\) | −2.10098 | −0.0706636 | ||||||||
\(885\) | −3.74152 | −0.125770 | ||||||||
\(886\) | −8.13035 | −0.273144 | ||||||||
\(887\) | 51.7010 | 1.73595 | 0.867975 | − | 0.496608i | \(-0.165421\pi\) | ||||
0.867975 | + | 0.496608i | \(0.165421\pi\) | |||||||
\(888\) | −77.7987 | −2.61075 | ||||||||
\(889\) | −22.2492 | −0.746213 | ||||||||
\(890\) | 1.78356 | 0.0597850 | ||||||||
\(891\) | 14.6557 | 0.490983 | ||||||||
\(892\) | −1.22637 | −0.0410619 | ||||||||
\(893\) | 3.72294 | 0.124583 | ||||||||
\(894\) | 39.5061 | 1.32128 | ||||||||
\(895\) | 5.52951 | 0.184831 | ||||||||
\(896\) | 19.4047 | 0.648266 | ||||||||
\(897\) | −89.8857 | −3.00120 | ||||||||
\(898\) | 2.50862 | 0.0837138 | ||||||||
\(899\) | −25.1217 | −0.837856 | ||||||||
\(900\) | 1.90944 | 0.0636480 | ||||||||
\(901\) | 10.4794 | 0.349119 | ||||||||
\(902\) | 10.0286 | 0.333917 | ||||||||
\(903\) | −58.6577 | −1.95201 | ||||||||
\(904\) | 27.6987 | 0.921246 | ||||||||
\(905\) | 0.961515 | 0.0319618 | ||||||||
\(906\) | 53.9914 | 1.79374 | ||||||||
\(907\) | −5.06194 | −0.168079 | −0.0840395 | − | 0.996462i | \(-0.526782\pi\) | ||||
−0.0840395 | + | 0.996462i | \(0.526782\pi\) | |||||||
\(908\) | −0.936796 | −0.0310887 | ||||||||
\(909\) | −1.75506 | −0.0582117 | ||||||||
\(910\) | −7.36228 | −0.244057 | ||||||||
\(911\) | −40.4144 | −1.33899 | −0.669495 | − | 0.742817i | \(-0.733489\pi\) | ||||
−0.669495 | + | 0.742817i | \(0.733489\pi\) | |||||||
\(912\) | 2.99648 | 0.0992233 | ||||||||
\(913\) | 3.45559 | 0.114363 | ||||||||
\(914\) | 37.2133 | 1.23091 | ||||||||
\(915\) | −16.3168 | −0.539418 | ||||||||
\(916\) | −1.68850 | −0.0557896 | ||||||||
\(917\) | 31.1713 | 1.02937 | ||||||||
\(918\) | −2.13104 | −0.0703347 | ||||||||
\(919\) | 31.2276 | 1.03010 | 0.515052 | − | 0.857159i | \(-0.327773\pi\) | ||||
0.515052 | + | 0.857159i | \(0.327773\pi\) | |||||||
\(920\) | 13.7832 | 0.454418 | ||||||||
\(921\) | −15.8890 | −0.523562 | ||||||||
\(922\) | 47.8349 | 1.57536 | ||||||||
\(923\) | −45.2270 | −1.48867 | ||||||||
\(924\) | −1.06037 | −0.0348835 | ||||||||
\(925\) | 51.4711 | 1.69236 | ||||||||
\(926\) | −25.4212 | −0.835391 | ||||||||
\(927\) | −12.5788 | −0.413141 | ||||||||
\(928\) | 5.00447 | 0.164280 | ||||||||
\(929\) | −51.3773 | −1.68563 | −0.842817 | − | 0.538201i | \(-0.819104\pi\) | ||||
−0.842817 | + | 0.538201i | \(0.819104\pi\) | |||||||
\(930\) | 8.06840 | 0.264573 | ||||||||
\(931\) | −1.06937 | −0.0350472 | ||||||||
\(932\) | −3.18037 | −0.104176 | ||||||||
\(933\) | −9.24164 | −0.302558 | ||||||||
\(934\) | −23.1290 | −0.756805 | ||||||||
\(935\) | 2.74929 | 0.0899114 | ||||||||
\(936\) | 38.0948 | 1.24517 | ||||||||
\(937\) | 22.6093 | 0.738614 | 0.369307 | − | 0.929307i | \(-0.379595\pi\) | ||||
0.369307 | + | 0.929307i | \(0.379595\pi\) | |||||||
\(938\) | −27.3455 | −0.892861 | ||||||||
\(939\) | 61.2488 | 1.99878 | ||||||||
\(940\) | −0.957377 | −0.0312262 | ||||||||
\(941\) | −51.2485 | −1.67065 | −0.835326 | − | 0.549754i | \(-0.814721\pi\) | ||||
−0.835326 | + | 0.549754i | \(0.814721\pi\) | |||||||
\(942\) | −13.4443 | −0.438038 | ||||||||
\(943\) | 38.5344 | 1.25485 | ||||||||
\(944\) | −9.70610 | −0.315906 | ||||||||
\(945\) | 0.593776 | 0.0193155 | ||||||||
\(946\) | −25.8793 | −0.841408 | ||||||||
\(947\) | −54.1474 | −1.75955 | −0.879777 | − | 0.475387i | \(-0.842308\pi\) | ||||
−0.879777 | + | 0.475387i | \(0.842308\pi\) | |||||||
\(948\) | −0.236477 | −0.00768042 | ||||||||
\(949\) | 29.6400 | 0.962155 | ||||||||
\(950\) | −2.14101 | −0.0694635 | ||||||||
\(951\) | 19.8171 | 0.642614 | ||||||||
\(952\) | 17.4585 | 0.565833 | ||||||||
\(953\) | −34.0986 | −1.10456 | −0.552281 | − | 0.833658i | \(-0.686242\pi\) | ||||
−0.552281 | + | 0.833658i | \(0.686242\pi\) | |||||||
\(954\) | −13.0355 | −0.422039 | ||||||||
\(955\) | −4.97006 | −0.160827 | ||||||||
\(956\) | 0.666695 | 0.0215624 | ||||||||
\(957\) | 22.1120 | 0.714778 | ||||||||
\(958\) | −15.5923 | −0.503764 | ||||||||
\(959\) | −29.4613 | −0.951354 | ||||||||
\(960\) | −12.0688 | −0.389520 | ||||||||
\(961\) | −13.5738 | −0.437863 | ||||||||
\(962\) | 70.4482 | 2.27134 | ||||||||
\(963\) | 9.57350 | 0.308502 | ||||||||
\(964\) | 1.45101 | 0.0467340 | ||||||||
\(965\) | −14.7289 | −0.474140 | ||||||||
\(966\) | 51.2416 | 1.64867 | ||||||||
\(967\) | 20.9385 | 0.673336 | 0.336668 | − | 0.941623i | \(-0.390700\pi\) | ||||
0.336668 | + | 0.941623i | \(0.390700\pi\) | |||||||
\(968\) | 25.3314 | 0.814181 | ||||||||
\(969\) | 2.48031 | 0.0796791 | ||||||||
\(970\) | 11.4800 | 0.368599 | ||||||||
\(971\) | −5.00722 | −0.160689 | −0.0803447 | − | 0.996767i | \(-0.525602\pi\) | ||||
−0.0803447 | + | 0.996767i | \(0.525602\pi\) | |||||||
\(972\) | −3.17315 | −0.101779 | ||||||||
\(973\) | −32.6146 | −1.04558 | ||||||||
\(974\) | −19.3531 | −0.620113 | ||||||||
\(975\) | −52.3371 | −1.67613 | ||||||||
\(976\) | −42.3284 | −1.35490 | ||||||||
\(977\) | 12.5547 | 0.401662 | 0.200831 | − | 0.979626i | \(-0.435636\pi\) | ||||
0.200831 | + | 0.979626i | \(0.435636\pi\) | |||||||
\(978\) | −69.5642 | −2.22442 | ||||||||
\(979\) | −3.39064 | −0.108365 | ||||||||
\(980\) | 0.274995 | 0.00878440 | ||||||||
\(981\) | 27.5879 | 0.880813 | ||||||||
\(982\) | −6.17140 | −0.196937 | ||||||||
\(983\) | 1.43810 | 0.0458683 | 0.0229341 | − | 0.999737i | \(-0.492699\pi\) | ||||
0.0229341 | + | 0.999737i | \(0.492699\pi\) | |||||||
\(984\) | −33.9138 | −1.08113 | ||||||||
\(985\) | 1.39641 | 0.0444934 | ||||||||
\(986\) | −24.9761 | −0.795401 | ||||||||
\(987\) | −51.8810 | −1.65139 | ||||||||
\(988\) | 0.233005 | 0.00741289 | ||||||||
\(989\) | −99.4397 | −3.16200 | ||||||||
\(990\) | −3.41989 | −0.108691 | ||||||||
\(991\) | −41.6595 | −1.32336 | −0.661678 | − | 0.749788i | \(-0.730155\pi\) | ||||
−0.661678 | + | 0.749788i | \(0.730155\pi\) | |||||||
\(992\) | −3.47146 | −0.110219 | ||||||||
\(993\) | 16.0833 | 0.510387 | ||||||||
\(994\) | 25.7828 | 0.817781 | ||||||||
\(995\) | 6.95475 | 0.220480 | ||||||||
\(996\) | −0.801689 | −0.0254025 | ||||||||
\(997\) | 46.5145 | 1.47313 | 0.736564 | − | 0.676367i | \(-0.236447\pi\) | ||||
0.736564 | + | 0.676367i | \(0.236447\pi\) | |||||||
\(998\) | −51.9151 | −1.64334 | ||||||||
\(999\) | −5.68172 | −0.179762 |
(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 | 503.2.a.e.1.9 | ✓ | 10 | |
3.2 | odd | 2 | 4527.2.a.k.1.2 | 10 | |||
4.3 | odd | 2 | 8048.2.a.p.1.9 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
503.2.a.e.1.9 | ✓ | 10 | 1.1 | even | 1 | trivial | |
4527.2.a.k.1.2 | 10 | 3.2 | odd | 2 | |||
8048.2.a.p.1.9 | 10 | 4.3 | odd | 2 |