Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2009,2,Mod(1,2009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2009, 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("2009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2009 = 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2009.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: | \(16.0419457661\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 3 x^{16} - 25 x^{15} + 77 x^{14} + 247 x^{13} - 790 x^{12} - 1231 x^{11} + 4173 x^{10} + \cdots - 464 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 287) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(1.17557\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.17557 | 0.831252 | 0.415626 | − | 0.909536i | \(-0.363562\pi\) | ||||
0.415626 | + | 0.909536i | \(0.363562\pi\) | |||||||
\(3\) | −2.72860 | −1.57536 | −0.787680 | − | 0.616084i | \(-0.788718\pi\) | ||||
−0.787680 | + | 0.616084i | \(0.788718\pi\) | |||||||
\(4\) | −0.618039 | −0.309020 | ||||||||
\(5\) | 2.82853 | 1.26496 | 0.632478 | − | 0.774578i | \(-0.282038\pi\) | ||||
0.632478 | + | 0.774578i | \(0.282038\pi\) | |||||||
\(6\) | −3.20766 | −1.30952 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.07768 | −1.08813 | ||||||||
\(9\) | 4.44528 | 1.48176 | ||||||||
\(10\) | 3.32513 | 1.05150 | ||||||||
\(11\) | 4.71688 | 1.42219 | 0.711096 | − | 0.703095i | \(-0.248199\pi\) | ||||
0.711096 | + | 0.703095i | \(0.248199\pi\) | |||||||
\(12\) | 1.68638 | 0.486817 | ||||||||
\(13\) | −2.95777 | −0.820338 | −0.410169 | − | 0.912010i | \(-0.634530\pi\) | ||||
−0.410169 | + | 0.912010i | \(0.634530\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.71794 | −1.99276 | ||||||||
\(16\) | −2.38195 | −0.595487 | ||||||||
\(17\) | −5.06492 | −1.22842 | −0.614211 | − | 0.789142i | \(-0.710526\pi\) | ||||
−0.614211 | + | 0.789142i | \(0.710526\pi\) | |||||||
\(18\) | 5.22573 | 1.23172 | ||||||||
\(19\) | 4.50858 | 1.03434 | 0.517170 | − | 0.855883i | \(-0.326986\pi\) | ||||
0.517170 | + | 0.855883i | \(0.326986\pi\) | |||||||
\(20\) | −1.74814 | −0.390896 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.54501 | 1.18220 | ||||||||
\(23\) | 1.60921 | 0.335543 | 0.167772 | − | 0.985826i | \(-0.446343\pi\) | ||||
0.167772 | + | 0.985826i | \(0.446343\pi\) | |||||||
\(24\) | 8.39778 | 1.71419 | ||||||||
\(25\) | 3.00058 | 0.600116 | ||||||||
\(26\) | −3.47706 | −0.681908 | ||||||||
\(27\) | −3.94360 | −0.758946 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.93993 | 1.47441 | 0.737204 | − | 0.675670i | \(-0.236146\pi\) | ||||
0.737204 | + | 0.675670i | \(0.236146\pi\) | |||||||
\(30\) | −9.07296 | −1.65649 | ||||||||
\(31\) | −7.31455 | −1.31373 | −0.656866 | − | 0.754007i | \(-0.728118\pi\) | ||||
−0.656866 | + | 0.754007i | \(0.728118\pi\) | |||||||
\(32\) | 3.35522 | 0.593125 | ||||||||
\(33\) | −12.8705 | −2.24047 | ||||||||
\(34\) | −5.95416 | −1.02113 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.74736 | −0.457893 | ||||||||
\(37\) | 1.35260 | 0.222366 | 0.111183 | − | 0.993800i | \(-0.464536\pi\) | ||||
0.111183 | + | 0.993800i | \(0.464536\pi\) | |||||||
\(38\) | 5.30014 | 0.859797 | ||||||||
\(39\) | 8.07058 | 1.29233 | ||||||||
\(40\) | −8.70532 | −1.37643 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.02962 | −0.157016 | −0.0785080 | − | 0.996913i | \(-0.525016\pi\) | ||||
−0.0785080 | + | 0.996913i | \(0.525016\pi\) | |||||||
\(44\) | −2.91522 | −0.439485 | ||||||||
\(45\) | 12.5736 | 1.87436 | ||||||||
\(46\) | 1.89174 | 0.278921 | ||||||||
\(47\) | −7.85022 | −1.14507 | −0.572536 | − | 0.819880i | \(-0.694040\pi\) | ||||
−0.572536 | + | 0.819880i | \(0.694040\pi\) | |||||||
\(48\) | 6.49940 | 0.938107 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.52738 | 0.498847 | ||||||||
\(51\) | 13.8202 | 1.93521 | ||||||||
\(52\) | 1.82802 | 0.253500 | ||||||||
\(53\) | 1.72187 | 0.236517 | 0.118258 | − | 0.992983i | \(-0.462269\pi\) | ||||
0.118258 | + | 0.992983i | \(0.462269\pi\) | |||||||
\(54\) | −4.63597 | −0.630876 | ||||||||
\(55\) | 13.3418 | 1.79901 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.3021 | −1.62946 | ||||||||
\(58\) | 9.33393 | 1.22561 | ||||||||
\(59\) | 11.1850 | 1.45616 | 0.728079 | − | 0.685493i | \(-0.240413\pi\) | ||||
0.728079 | + | 0.685493i | \(0.240413\pi\) | |||||||
\(60\) | 4.76999 | 0.615803 | ||||||||
\(61\) | 6.96462 | 0.891728 | 0.445864 | − | 0.895101i | \(-0.352897\pi\) | ||||
0.445864 | + | 0.895101i | \(0.352897\pi\) | |||||||
\(62\) | −8.59876 | −1.09204 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.70819 | 1.08852 | ||||||||
\(65\) | −8.36614 | −1.03769 | ||||||||
\(66\) | −15.1301 | −1.86239 | ||||||||
\(67\) | 0.648015 | 0.0791677 | 0.0395838 | − | 0.999216i | \(-0.487397\pi\) | ||||
0.0395838 | + | 0.999216i | \(0.487397\pi\) | |||||||
\(68\) | 3.13032 | 0.379607 | ||||||||
\(69\) | −4.39090 | −0.528602 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.1249 | 1.43896 | 0.719479 | − | 0.694514i | \(-0.244381\pi\) | ||||
0.719479 | + | 0.694514i | \(0.244381\pi\) | |||||||
\(72\) | −13.6812 | −1.61234 | ||||||||
\(73\) | 12.0878 | 1.41477 | 0.707385 | − | 0.706829i | \(-0.249875\pi\) | ||||
0.707385 | + | 0.706829i | \(0.249875\pi\) | |||||||
\(74\) | 1.59007 | 0.184842 | ||||||||
\(75\) | −8.18739 | −0.945398 | ||||||||
\(76\) | −2.78648 | −0.319631 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 9.48752 | 1.07425 | ||||||||
\(79\) | 5.45115 | 0.613303 | 0.306651 | − | 0.951822i | \(-0.400791\pi\) | ||||
0.306651 | + | 0.951822i | \(0.400791\pi\) | |||||||
\(80\) | −6.73741 | −0.753266 | ||||||||
\(81\) | −2.57532 | −0.286147 | ||||||||
\(82\) | −1.17557 | −0.129820 | ||||||||
\(83\) | 12.1586 | 1.33458 | 0.667288 | − | 0.744800i | \(-0.267455\pi\) | ||||
0.667288 | + | 0.744800i | \(0.267455\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.3263 | −1.55390 | ||||||||
\(86\) | −1.21039 | −0.130520 | ||||||||
\(87\) | −21.6649 | −2.32272 | ||||||||
\(88\) | −14.5171 | −1.54752 | ||||||||
\(89\) | −5.93969 | −0.629606 | −0.314803 | − | 0.949157i | \(-0.601938\pi\) | ||||
−0.314803 | + | 0.949157i | \(0.601938\pi\) | |||||||
\(90\) | 14.7811 | 1.55807 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.994555 | −0.103690 | ||||||||
\(93\) | 19.9585 | 2.06960 | ||||||||
\(94\) | −9.22847 | −0.951844 | ||||||||
\(95\) | 12.7526 | 1.30839 | ||||||||
\(96\) | −9.15508 | −0.934386 | ||||||||
\(97\) | −6.86976 | −0.697518 | −0.348759 | − | 0.937212i | \(-0.613397\pi\) | ||||
−0.348759 | + | 0.937212i | \(0.613397\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 20.9679 | 2.10735 | ||||||||
\(100\) | −1.85448 | −0.185448 | ||||||||
\(101\) | 18.9155 | 1.88216 | 0.941080 | − | 0.338184i | \(-0.109813\pi\) | ||||
0.941080 | + | 0.338184i | \(0.109813\pi\) | |||||||
\(102\) | 16.2465 | 1.60865 | ||||||||
\(103\) | 7.85352 | 0.773831 | 0.386915 | − | 0.922115i | \(-0.373541\pi\) | ||||
0.386915 | + | 0.922115i | \(0.373541\pi\) | |||||||
\(104\) | 9.10308 | 0.892630 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.02417 | 0.196605 | ||||||||
\(107\) | 11.6249 | 1.12382 | 0.561910 | − | 0.827199i | \(-0.310067\pi\) | ||||
0.561910 | + | 0.827199i | \(0.310067\pi\) | |||||||
\(108\) | 2.43730 | 0.234529 | ||||||||
\(109\) | −7.62432 | −0.730278 | −0.365139 | − | 0.930953i | \(-0.618978\pi\) | ||||
−0.365139 | + | 0.930953i | \(0.618978\pi\) | |||||||
\(110\) | 15.6842 | 1.49543 | ||||||||
\(111\) | −3.69071 | −0.350307 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.64402 | −0.154657 | −0.0773283 | − | 0.997006i | \(-0.524639\pi\) | ||||
−0.0773283 | + | 0.997006i | \(0.524639\pi\) | |||||||
\(114\) | −14.4620 | −1.35449 | ||||||||
\(115\) | 4.55170 | 0.424448 | ||||||||
\(116\) | −4.90719 | −0.455621 | ||||||||
\(117\) | −13.1481 | −1.21554 | ||||||||
\(118\) | 13.1487 | 1.21043 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 23.7534 | 2.16838 | ||||||||
\(121\) | 11.2489 | 1.02263 | ||||||||
\(122\) | 8.18738 | 0.741251 | ||||||||
\(123\) | 2.72860 | 0.246030 | ||||||||
\(124\) | 4.52068 | 0.405969 | ||||||||
\(125\) | −5.65542 | −0.505836 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.19475 | 0.372224 | 0.186112 | − | 0.982529i | \(-0.440411\pi\) | ||||
0.186112 | + | 0.982529i | \(0.440411\pi\) | |||||||
\(128\) | 3.52663 | 0.311713 | ||||||||
\(129\) | 2.80943 | 0.247357 | ||||||||
\(130\) | −9.83497 | −0.862584 | ||||||||
\(131\) | 20.7949 | 1.81686 | 0.908430 | − | 0.418037i | \(-0.137282\pi\) | ||||
0.908430 | + | 0.418037i | \(0.137282\pi\) | |||||||
\(132\) | 7.95447 | 0.692348 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.761786 | 0.0658083 | ||||||||
\(135\) | −11.1546 | −0.960034 | ||||||||
\(136\) | 15.5882 | 1.33668 | ||||||||
\(137\) | 2.66542 | 0.227723 | 0.113861 | − | 0.993497i | \(-0.463678\pi\) | ||||
0.113861 | + | 0.993497i | \(0.463678\pi\) | |||||||
\(138\) | −5.16180 | −0.439401 | ||||||||
\(139\) | 7.95421 | 0.674668 | 0.337334 | − | 0.941385i | \(-0.390475\pi\) | ||||
0.337334 | + | 0.941385i | \(0.390475\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 21.4201 | 1.80390 | ||||||||
\(142\) | 14.2536 | 1.19614 | ||||||||
\(143\) | −13.9514 | −1.16668 | ||||||||
\(144\) | −10.5884 | −0.882369 | ||||||||
\(145\) | 22.4583 | 1.86506 | ||||||||
\(146\) | 14.2100 | 1.17603 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.835960 | −0.0687155 | ||||||||
\(149\) | −0.0794937 | −0.00651238 | −0.00325619 | − | 0.999995i | \(-0.501036\pi\) | ||||
−0.00325619 | + | 0.999995i | \(0.501036\pi\) | |||||||
\(150\) | −9.62484 | −0.785865 | ||||||||
\(151\) | 14.6821 | 1.19481 | 0.597406 | − | 0.801939i | \(-0.296198\pi\) | ||||
0.597406 | + | 0.801939i | \(0.296198\pi\) | |||||||
\(152\) | −13.8760 | −1.12549 | ||||||||
\(153\) | −22.5150 | −1.82023 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20.6894 | −1.66181 | ||||||||
\(156\) | −4.98794 | −0.399355 | ||||||||
\(157\) | −10.8291 | −0.864256 | −0.432128 | − | 0.901812i | \(-0.642237\pi\) | ||||
−0.432128 | + | 0.901812i | \(0.642237\pi\) | |||||||
\(158\) | 6.40820 | 0.509809 | ||||||||
\(159\) | −4.69829 | −0.372599 | ||||||||
\(160\) | 9.49035 | 0.750278 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −3.02747 | −0.237860 | ||||||||
\(163\) | 16.6528 | 1.30435 | 0.652174 | − | 0.758069i | \(-0.273857\pi\) | ||||
0.652174 | + | 0.758069i | \(0.273857\pi\) | |||||||
\(164\) | 0.618039 | 0.0482608 | ||||||||
\(165\) | −36.4046 | −2.83409 | ||||||||
\(166\) | 14.2932 | 1.10937 | ||||||||
\(167\) | −7.39264 | −0.572060 | −0.286030 | − | 0.958221i | \(-0.592336\pi\) | ||||
−0.286030 | + | 0.958221i | \(0.592336\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.25160 | −0.327046 | ||||||||
\(170\) | −16.8415 | −1.29168 | ||||||||
\(171\) | 20.0419 | 1.53264 | ||||||||
\(172\) | 0.636348 | 0.0485211 | ||||||||
\(173\) | 14.3518 | 1.09115 | 0.545573 | − | 0.838063i | \(-0.316312\pi\) | ||||
0.545573 | + | 0.838063i | \(0.316312\pi\) | |||||||
\(174\) | −25.4686 | −1.93077 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −11.2354 | −0.846898 | ||||||||
\(177\) | −30.5193 | −2.29397 | ||||||||
\(178\) | −6.98251 | −0.523361 | ||||||||
\(179\) | 2.36978 | 0.177125 | 0.0885627 | − | 0.996071i | \(-0.471773\pi\) | ||||
0.0885627 | + | 0.996071i | \(0.471773\pi\) | |||||||
\(180\) | −7.77098 | −0.579215 | ||||||||
\(181\) | −20.2014 | −1.50156 | −0.750780 | − | 0.660552i | \(-0.770322\pi\) | ||||
−0.750780 | + | 0.660552i | \(0.770322\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −19.0037 | −1.40479 | ||||||||
\(184\) | −4.95264 | −0.365113 | ||||||||
\(185\) | 3.82587 | 0.281284 | ||||||||
\(186\) | 23.4626 | 1.72036 | ||||||||
\(187\) | −23.8906 | −1.74705 | ||||||||
\(188\) | 4.85174 | 0.353850 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 14.9916 | 1.08761 | ||||||||
\(191\) | −16.2663 | −1.17699 | −0.588494 | − | 0.808501i | \(-0.700279\pi\) | ||||
−0.588494 | + | 0.808501i | \(0.700279\pi\) | |||||||
\(192\) | −23.7612 | −1.71482 | ||||||||
\(193\) | −24.7700 | −1.78298 | −0.891490 | − | 0.453040i | \(-0.850339\pi\) | ||||
−0.891490 | + | 0.453040i | \(0.850339\pi\) | |||||||
\(194\) | −8.07587 | −0.579814 | ||||||||
\(195\) | 22.8279 | 1.63474 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.8114 | −1.34025 | −0.670127 | − | 0.742246i | \(-0.733761\pi\) | ||||
−0.670127 | + | 0.742246i | \(0.733761\pi\) | |||||||
\(198\) | 24.6491 | 1.75174 | ||||||||
\(199\) | −4.66599 | −0.330763 | −0.165382 | − | 0.986230i | \(-0.552886\pi\) | ||||
−0.165382 | + | 0.986230i | \(0.552886\pi\) | |||||||
\(200\) | −9.23483 | −0.653001 | ||||||||
\(201\) | −1.76818 | −0.124718 | ||||||||
\(202\) | 22.2364 | 1.56455 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −8.54140 | −0.598017 | ||||||||
\(205\) | −2.82853 | −0.197553 | ||||||||
\(206\) | 9.23235 | 0.643249 | ||||||||
\(207\) | 7.15339 | 0.497195 | ||||||||
\(208\) | 7.04526 | 0.488501 | ||||||||
\(209\) | 21.2664 | 1.47103 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.7594 | −1.29145 | −0.645725 | − | 0.763570i | \(-0.723445\pi\) | ||||
−0.645725 | + | 0.763570i | \(0.723445\pi\) | |||||||
\(212\) | −1.06418 | −0.0730883 | ||||||||
\(213\) | −33.0840 | −2.26688 | ||||||||
\(214\) | 13.6658 | 0.934177 | ||||||||
\(215\) | −2.91232 | −0.198619 | ||||||||
\(216\) | 12.1372 | 0.825828 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −8.96291 | −0.607045 | ||||||||
\(219\) | −32.9828 | −2.22877 | ||||||||
\(220\) | −8.24578 | −0.555930 | ||||||||
\(221\) | 14.9809 | 1.00772 | ||||||||
\(222\) | −4.33868 | −0.291193 | ||||||||
\(223\) | 4.94608 | 0.331214 | 0.165607 | − | 0.986192i | \(-0.447042\pi\) | ||||
0.165607 | + | 0.986192i | \(0.447042\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.3384 | 0.889227 | ||||||||
\(226\) | −1.93266 | −0.128559 | ||||||||
\(227\) | 16.4193 | 1.08978 | 0.544892 | − | 0.838506i | \(-0.316571\pi\) | ||||
0.544892 | + | 0.838506i | \(0.316571\pi\) | |||||||
\(228\) | 7.60320 | 0.503534 | ||||||||
\(229\) | −2.22991 | −0.147356 | −0.0736782 | − | 0.997282i | \(-0.523474\pi\) | ||||
−0.0736782 | + | 0.997282i | \(0.523474\pi\) | |||||||
\(230\) | 5.35083 | 0.352823 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −24.4366 | −1.60434 | ||||||||
\(233\) | 12.6535 | 0.828957 | 0.414479 | − | 0.910059i | \(-0.363964\pi\) | ||||
0.414479 | + | 0.910059i | \(0.363964\pi\) | |||||||
\(234\) | −15.4565 | −1.01042 | ||||||||
\(235\) | −22.2046 | −1.44847 | ||||||||
\(236\) | −6.91275 | −0.449981 | ||||||||
\(237\) | −14.8740 | −0.966173 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.62327 | −0.363739 | −0.181870 | − | 0.983323i | \(-0.558215\pi\) | ||||
−0.181870 | + | 0.983323i | \(0.558215\pi\) | |||||||
\(240\) | 18.3837 | 1.18666 | ||||||||
\(241\) | −23.2442 | −1.49729 | −0.748645 | − | 0.662971i | \(-0.769295\pi\) | ||||
−0.748645 | + | 0.662971i | \(0.769295\pi\) | |||||||
\(242\) | 13.2239 | 0.850065 | ||||||||
\(243\) | 18.8578 | 1.20973 | ||||||||
\(244\) | −4.30441 | −0.275561 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.20766 | 0.204513 | ||||||||
\(247\) | −13.3353 | −0.848507 | ||||||||
\(248\) | 22.5119 | 1.42951 | ||||||||
\(249\) | −33.1759 | −2.10244 | ||||||||
\(250\) | −6.64834 | −0.420478 | ||||||||
\(251\) | 22.6110 | 1.42720 | 0.713598 | − | 0.700556i | \(-0.247065\pi\) | ||||
0.713598 | + | 0.700556i | \(0.247065\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.59045 | 0.477207 | ||||||||
\(254\) | 4.93121 | 0.309412 | ||||||||
\(255\) | 39.0907 | 2.44796 | ||||||||
\(256\) | −13.2706 | −0.829412 | ||||||||
\(257\) | −5.47074 | −0.341256 | −0.170628 | − | 0.985336i | \(-0.554580\pi\) | ||||
−0.170628 | + | 0.985336i | \(0.554580\pi\) | |||||||
\(258\) | 3.30268 | 0.205616 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 5.17060 | 0.320667 | ||||||||
\(261\) | 35.2952 | 2.18472 | ||||||||
\(262\) | 24.4458 | 1.51027 | ||||||||
\(263\) | −10.7545 | −0.663148 | −0.331574 | − | 0.943429i | \(-0.607580\pi\) | ||||
−0.331574 | + | 0.943429i | \(0.607580\pi\) | |||||||
\(264\) | 39.6113 | 2.43791 | ||||||||
\(265\) | 4.87035 | 0.299183 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.2071 | 0.991856 | ||||||||
\(268\) | −0.400499 | −0.0244644 | ||||||||
\(269\) | 20.4906 | 1.24933 | 0.624667 | − | 0.780891i | \(-0.285235\pi\) | ||||
0.624667 | + | 0.780891i | \(0.285235\pi\) | |||||||
\(270\) | −13.1130 | −0.798030 | ||||||||
\(271\) | −14.8238 | −0.900481 | −0.450240 | − | 0.892907i | \(-0.648662\pi\) | ||||
−0.450240 | + | 0.892907i | \(0.648662\pi\) | |||||||
\(272\) | 12.0644 | 0.731510 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.13339 | 0.189295 | ||||||||
\(275\) | 14.1534 | 0.853480 | ||||||||
\(276\) | 2.71375 | 0.163348 | ||||||||
\(277\) | 19.4149 | 1.16653 | 0.583265 | − | 0.812282i | \(-0.301775\pi\) | ||||
0.583265 | + | 0.812282i | \(0.301775\pi\) | |||||||
\(278\) | 9.35072 | 0.560819 | ||||||||
\(279\) | −32.5152 | −1.94664 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.51673 | 0.567720 | 0.283860 | − | 0.958866i | \(-0.408385\pi\) | ||||
0.283860 | + | 0.958866i | \(0.408385\pi\) | |||||||
\(282\) | 25.1808 | 1.49950 | ||||||||
\(283\) | −14.3030 | −0.850225 | −0.425112 | − | 0.905141i | \(-0.639765\pi\) | ||||
−0.425112 | + | 0.905141i | \(0.639765\pi\) | |||||||
\(284\) | −7.49365 | −0.444666 | ||||||||
\(285\) | −34.7969 | −2.06119 | ||||||||
\(286\) | −16.4009 | −0.969804 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 14.9149 | 0.878870 | ||||||||
\(289\) | 8.65339 | 0.509023 | ||||||||
\(290\) | 26.4013 | 1.55034 | ||||||||
\(291\) | 18.7448 | 1.09884 | ||||||||
\(292\) | −7.47073 | −0.437191 | ||||||||
\(293\) | 9.08991 | 0.531038 | 0.265519 | − | 0.964106i | \(-0.414457\pi\) | ||||
0.265519 | + | 0.964106i | \(0.414457\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 31.6370 | 1.84198 | ||||||||
\(296\) | −4.16288 | −0.241962 | ||||||||
\(297\) | −18.6015 | −1.07937 | ||||||||
\(298\) | −0.0934503 | −0.00541343 | ||||||||
\(299\) | −4.75967 | −0.275259 | ||||||||
\(300\) | 5.06013 | 0.292147 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 17.2598 | 0.993191 | ||||||||
\(303\) | −51.6128 | −2.96508 | ||||||||
\(304\) | −10.7392 | −0.615936 | ||||||||
\(305\) | 19.6996 | 1.12800 | ||||||||
\(306\) | −26.4679 | −1.51307 | ||||||||
\(307\) | −25.2170 | −1.43921 | −0.719606 | − | 0.694383i | \(-0.755677\pi\) | ||||
−0.719606 | + | 0.694383i | \(0.755677\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −21.4292 | −1.21906 | ||||||||
\(310\) | −24.3218 | −1.38139 | ||||||||
\(311\) | 16.9161 | 0.959225 | 0.479613 | − | 0.877480i | \(-0.340777\pi\) | ||||
0.479613 | + | 0.877480i | \(0.340777\pi\) | |||||||
\(312\) | −24.8387 | −1.40621 | ||||||||
\(313\) | 0.875735 | 0.0494995 | 0.0247497 | − | 0.999694i | \(-0.492121\pi\) | ||||
0.0247497 | + | 0.999694i | \(0.492121\pi\) | |||||||
\(314\) | −12.7303 | −0.718415 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.36903 | −0.189523 | ||||||||
\(317\) | −12.9270 | −0.726051 | −0.363026 | − | 0.931779i | \(-0.618256\pi\) | ||||
−0.363026 | + | 0.931779i | \(0.618256\pi\) | |||||||
\(318\) | −5.52317 | −0.309724 | ||||||||
\(319\) | 37.4517 | 2.09689 | ||||||||
\(320\) | 24.6314 | 1.37694 | ||||||||
\(321\) | −31.7197 | −1.77042 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −22.8356 | −1.27061 | ||||||||
\(324\) | 1.59165 | 0.0884250 | ||||||||
\(325\) | −8.87502 | −0.492297 | ||||||||
\(326\) | 19.5765 | 1.08424 | ||||||||
\(327\) | 20.8038 | 1.15045 | ||||||||
\(328\) | 3.07768 | 0.169937 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −42.7961 | −2.35585 | ||||||||
\(331\) | −22.3039 | −1.22594 | −0.612968 | − | 0.790108i | \(-0.710025\pi\) | ||||
−0.612968 | + | 0.790108i | \(0.710025\pi\) | |||||||
\(332\) | −7.51447 | −0.412410 | ||||||||
\(333\) | 6.01269 | 0.329493 | ||||||||
\(334\) | −8.69055 | −0.475526 | ||||||||
\(335\) | 1.83293 | 0.100144 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.3364 | −0.780953 | −0.390477 | − | 0.920613i | \(-0.627690\pi\) | ||||
−0.390477 | + | 0.920613i | \(0.627690\pi\) | |||||||
\(338\) | −4.99805 | −0.271858 | ||||||||
\(339\) | 4.48589 | 0.243640 | ||||||||
\(340\) | 8.85420 | 0.480186 | ||||||||
\(341\) | −34.5019 | −1.86838 | ||||||||
\(342\) | 23.5606 | 1.27401 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.16886 | 0.170853 | ||||||||
\(345\) | −12.4198 | −0.668658 | ||||||||
\(346\) | 16.8715 | 0.907017 | ||||||||
\(347\) | −33.4640 | −1.79644 | −0.898221 | − | 0.439545i | \(-0.855140\pi\) | ||||
−0.898221 | + | 0.439545i | \(0.855140\pi\) | |||||||
\(348\) | 13.3898 | 0.717767 | ||||||||
\(349\) | −7.30788 | −0.391182 | −0.195591 | − | 0.980686i | \(-0.562662\pi\) | ||||
−0.195591 | + | 0.980686i | \(0.562662\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.6643 | 0.622592 | ||||||||
\(352\) | 15.8262 | 0.843539 | ||||||||
\(353\) | −20.2309 | −1.07678 | −0.538392 | − | 0.842694i | \(-0.680968\pi\) | ||||
−0.538392 | + | 0.842694i | \(0.680968\pi\) | |||||||
\(354\) | −35.8776 | −1.90687 | ||||||||
\(355\) | 34.2956 | 1.82022 | ||||||||
\(356\) | 3.67096 | 0.194560 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.78583 | 0.147236 | ||||||||
\(359\) | 35.3862 | 1.86761 | 0.933805 | − | 0.357782i | \(-0.116467\pi\) | ||||
0.933805 | + | 0.357782i | \(0.116467\pi\) | |||||||
\(360\) | −38.6976 | −2.03954 | ||||||||
\(361\) | 1.32729 | 0.0698573 | ||||||||
\(362\) | −23.7482 | −1.24818 | ||||||||
\(363\) | −30.6939 | −1.61101 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 34.1907 | 1.78962 | ||||||||
\(366\) | −22.3401 | −1.16774 | ||||||||
\(367\) | 15.8701 | 0.828413 | 0.414207 | − | 0.910183i | \(-0.364059\pi\) | ||||
0.414207 | + | 0.910183i | \(0.364059\pi\) | |||||||
\(368\) | −3.83306 | −0.199812 | ||||||||
\(369\) | −4.44528 | −0.231412 | ||||||||
\(370\) | 4.49757 | 0.233818 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −12.3351 | −0.639548 | ||||||||
\(373\) | −4.94499 | −0.256042 | −0.128021 | − | 0.991771i | \(-0.540862\pi\) | ||||
−0.128021 | + | 0.991771i | \(0.540862\pi\) | |||||||
\(374\) | −28.0850 | −1.45224 | ||||||||
\(375\) | 15.4314 | 0.796875 | ||||||||
\(376\) | 24.1605 | 1.24598 | ||||||||
\(377\) | −23.4845 | −1.20951 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.4026 | 1.30484 | 0.652422 | − | 0.757856i | \(-0.273753\pi\) | ||||
0.652422 | + | 0.757856i | \(0.273753\pi\) | |||||||
\(380\) | −7.88164 | −0.404320 | ||||||||
\(381\) | −11.4458 | −0.586386 | ||||||||
\(382\) | −19.1221 | −0.978374 | ||||||||
\(383\) | 8.79723 | 0.449517 | 0.224759 | − | 0.974414i | \(-0.427841\pi\) | ||||
0.224759 | + | 0.974414i | \(0.427841\pi\) | |||||||
\(384\) | −9.62277 | −0.491060 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −29.1188 | −1.48211 | ||||||||
\(387\) | −4.57696 | −0.232660 | ||||||||
\(388\) | 4.24578 | 0.215547 | ||||||||
\(389\) | 14.9916 | 0.760107 | 0.380053 | − | 0.924965i | \(-0.375906\pi\) | ||||
0.380053 | + | 0.924965i | \(0.375906\pi\) | |||||||
\(390\) | 26.8357 | 1.35888 | ||||||||
\(391\) | −8.15051 | −0.412189 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −56.7411 | −2.86221 | ||||||||
\(394\) | −22.1141 | −1.11409 | ||||||||
\(395\) | 15.4187 | 0.775801 | ||||||||
\(396\) | −12.9590 | −0.651212 | ||||||||
\(397\) | −1.30202 | −0.0653464 | −0.0326732 | − | 0.999466i | \(-0.510402\pi\) | ||||
−0.0326732 | + | 0.999466i | \(0.510402\pi\) | |||||||
\(398\) | −5.48519 | −0.274948 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.14722 | −0.357361 | ||||||||
\(401\) | −22.9368 | −1.14541 | −0.572705 | − | 0.819761i | \(-0.694106\pi\) | ||||
−0.572705 | + | 0.819761i | \(0.694106\pi\) | |||||||
\(402\) | −2.07861 | −0.103672 | ||||||||
\(403\) | 21.6348 | 1.07770 | ||||||||
\(404\) | −11.6905 | −0.581624 | ||||||||
\(405\) | −7.28437 | −0.361963 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.38005 | 0.316247 | ||||||||
\(408\) | −42.5341 | −2.10575 | ||||||||
\(409\) | −9.78196 | −0.483687 | −0.241843 | − | 0.970315i | \(-0.577752\pi\) | ||||
−0.241843 | + | 0.970315i | \(0.577752\pi\) | |||||||
\(410\) | −3.32513 | −0.164216 | ||||||||
\(411\) | −7.27289 | −0.358745 | ||||||||
\(412\) | −4.85379 | −0.239129 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 8.40930 | 0.413294 | ||||||||
\(415\) | 34.3909 | 1.68818 | ||||||||
\(416\) | −9.92398 | −0.486563 | ||||||||
\(417\) | −21.7039 | −1.06284 | ||||||||
\(418\) | 25.0001 | 1.22280 | ||||||||
\(419\) | −17.0753 | −0.834182 | −0.417091 | − | 0.908865i | \(-0.636950\pi\) | ||||
−0.417091 | + | 0.908865i | \(0.636950\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.50171 | 0.121926 | 0.0609628 | − | 0.998140i | \(-0.480583\pi\) | ||||
0.0609628 | + | 0.998140i | \(0.480583\pi\) | |||||||
\(422\) | −22.0529 | −1.07352 | ||||||||
\(423\) | −34.8964 | −1.69672 | ||||||||
\(424\) | −5.29936 | −0.257360 | ||||||||
\(425\) | −15.1977 | −0.737196 | ||||||||
\(426\) | −38.8925 | −1.88435 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −7.18463 | −0.347282 | ||||||||
\(429\) | 38.0680 | 1.83794 | ||||||||
\(430\) | −3.42363 | −0.165102 | ||||||||
\(431\) | 6.17111 | 0.297252 | 0.148626 | − | 0.988893i | \(-0.452515\pi\) | ||||
0.148626 | + | 0.988893i | \(0.452515\pi\) | |||||||
\(432\) | 9.39345 | 0.451943 | ||||||||
\(433\) | 8.89038 | 0.427244 | 0.213622 | − | 0.976916i | \(-0.431474\pi\) | ||||
0.213622 | + | 0.976916i | \(0.431474\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −61.2799 | −2.93815 | ||||||||
\(436\) | 4.71213 | 0.225670 | ||||||||
\(437\) | 7.25525 | 0.347066 | ||||||||
\(438\) | −38.7735 | −1.85267 | ||||||||
\(439\) | 8.59031 | 0.409993 | 0.204997 | − | 0.978763i | \(-0.434282\pi\) | ||||
0.204997 | + | 0.978763i | \(0.434282\pi\) | |||||||
\(440\) | −41.0619 | −1.95755 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 17.6110 | 0.837671 | ||||||||
\(443\) | 4.32990 | 0.205720 | 0.102860 | − | 0.994696i | \(-0.467201\pi\) | ||||
0.102860 | + | 0.994696i | \(0.467201\pi\) | |||||||
\(444\) | 2.28100 | 0.108252 | ||||||||
\(445\) | −16.8006 | −0.796424 | ||||||||
\(446\) | 5.81445 | 0.275322 | ||||||||
\(447\) | 0.216907 | 0.0102593 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.4438 | 0.870416 | 0.435208 | − | 0.900330i | \(-0.356675\pi\) | ||||
0.435208 | + | 0.900330i | \(0.356675\pi\) | |||||||
\(450\) | 15.6802 | 0.739172 | ||||||||
\(451\) | −4.71688 | −0.222109 | ||||||||
\(452\) | 1.01607 | 0.0477920 | ||||||||
\(453\) | −40.0616 | −1.88226 | ||||||||
\(454\) | 19.3020 | 0.905886 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 37.8621 | 1.77305 | ||||||||
\(457\) | 29.0862 | 1.36059 | 0.680297 | − | 0.732937i | \(-0.261851\pi\) | ||||
0.680297 | + | 0.732937i | \(0.261851\pi\) | |||||||
\(458\) | −2.62141 | −0.122490 | ||||||||
\(459\) | 19.9740 | 0.932307 | ||||||||
\(460\) | −2.81313 | −0.131163 | ||||||||
\(461\) | 37.9708 | 1.76848 | 0.884238 | − | 0.467037i | \(-0.154679\pi\) | ||||
0.884238 | + | 0.467037i | \(0.154679\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.55999 | 0.444290 | 0.222145 | − | 0.975014i | \(-0.428694\pi\) | ||||
0.222145 | + | 0.975014i | \(0.428694\pi\) | |||||||
\(464\) | −18.9125 | −0.877991 | ||||||||
\(465\) | 56.4533 | 2.61796 | ||||||||
\(466\) | 14.8750 | 0.689073 | ||||||||
\(467\) | 14.9165 | 0.690253 | 0.345127 | − | 0.938556i | \(-0.387836\pi\) | ||||
0.345127 | + | 0.938556i | \(0.387836\pi\) | |||||||
\(468\) | 8.12605 | 0.375627 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −26.1030 | −1.20404 | ||||||||
\(471\) | 29.5483 | 1.36152 | ||||||||
\(472\) | −34.4238 | −1.58448 | ||||||||
\(473\) | −4.85661 | −0.223307 | ||||||||
\(474\) | −17.4854 | −0.803133 | ||||||||
\(475\) | 13.5283 | 0.620723 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.65418 | 0.350461 | ||||||||
\(478\) | −6.61054 | −0.302359 | ||||||||
\(479\) | −22.3841 | −1.02276 | −0.511378 | − | 0.859356i | \(-0.670865\pi\) | ||||
−0.511378 | + | 0.859356i | \(0.670865\pi\) | |||||||
\(480\) | −25.8954 | −1.18196 | ||||||||
\(481\) | −4.00068 | −0.182415 | ||||||||
\(482\) | −27.3251 | −1.24463 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.95229 | −0.316013 | ||||||||
\(485\) | −19.4313 | −0.882330 | ||||||||
\(486\) | 22.1687 | 1.00559 | ||||||||
\(487\) | −16.6500 | −0.754485 | −0.377242 | − | 0.926115i | \(-0.623128\pi\) | ||||
−0.377242 | + | 0.926115i | \(0.623128\pi\) | |||||||
\(488\) | −21.4349 | −0.970312 | ||||||||
\(489\) | −45.4389 | −2.05482 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.5654 | 1.28914 | 0.644570 | − | 0.764546i | \(-0.277037\pi\) | ||||
0.644570 | + | 0.764546i | \(0.277037\pi\) | |||||||
\(492\) | −1.68638 | −0.0760281 | ||||||||
\(493\) | −40.2151 | −1.81120 | ||||||||
\(494\) | −15.6766 | −0.705324 | ||||||||
\(495\) | 59.3082 | 2.66570 | ||||||||
\(496\) | 17.4229 | 0.782311 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −39.0005 | −1.74766 | ||||||||
\(499\) | −16.2914 | −0.729304 | −0.364652 | − | 0.931144i | \(-0.618812\pi\) | ||||
−0.364652 | + | 0.931144i | \(0.618812\pi\) | |||||||
\(500\) | 3.49527 | 0.156313 | ||||||||
\(501\) | 20.1716 | 0.901200 | ||||||||
\(502\) | 26.5808 | 1.18636 | ||||||||
\(503\) | −1.49014 | −0.0664419 | −0.0332210 | − | 0.999448i | \(-0.510577\pi\) | ||||
−0.0332210 | + | 0.999448i | \(0.510577\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 53.5030 | 2.38085 | ||||||||
\(506\) | 8.92309 | 0.396680 | ||||||||
\(507\) | 11.6009 | 0.515216 | ||||||||
\(508\) | −2.59252 | −0.115024 | ||||||||
\(509\) | −11.5080 | −0.510085 | −0.255042 | − | 0.966930i | \(-0.582089\pi\) | ||||
−0.255042 | + | 0.966930i | \(0.582089\pi\) | |||||||
\(510\) | 45.9538 | 2.03487 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.6537 | −1.00116 | ||||||||
\(513\) | −17.7800 | −0.785007 | ||||||||
\(514\) | −6.43123 | −0.283670 | ||||||||
\(515\) | 22.2139 | 0.978862 | ||||||||
\(516\) | −1.73634 | −0.0764381 | ||||||||
\(517\) | −37.0285 | −1.62851 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −39.1603 | −1.71895 | ||||||||
\(520\) | 25.7483 | 1.12914 | ||||||||
\(521\) | −25.5384 | −1.11886 | −0.559428 | − | 0.828879i | \(-0.688979\pi\) | ||||
−0.559428 | + | 0.828879i | \(0.688979\pi\) | |||||||
\(522\) | 41.4919 | 1.81605 | ||||||||
\(523\) | 22.5171 | 0.984604 | 0.492302 | − | 0.870424i | \(-0.336156\pi\) | ||||
0.492302 | + | 0.870424i | \(0.336156\pi\) | |||||||
\(524\) | −12.8521 | −0.561445 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.6426 | −0.551244 | ||||||||
\(527\) | 37.0476 | 1.61382 | ||||||||
\(528\) | 30.6569 | 1.33417 | ||||||||
\(529\) | −20.4104 | −0.887411 | ||||||||
\(530\) | 5.72543 | 0.248697 | ||||||||
\(531\) | 49.7203 | 2.15768 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.95777 | 0.128115 | ||||||||
\(534\) | 19.0525 | 0.824482 | ||||||||
\(535\) | 32.8813 | 1.42158 | ||||||||
\(536\) | −1.99439 | −0.0861444 | ||||||||
\(537\) | −6.46618 | −0.279036 | ||||||||
\(538\) | 24.0881 | 1.03851 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 6.89397 | 0.296669 | ||||||||
\(541\) | 29.4571 | 1.26646 | 0.633230 | − | 0.773964i | \(-0.281729\pi\) | ||||
0.633230 | + | 0.773964i | \(0.281729\pi\) | |||||||
\(542\) | −17.4264 | −0.748527 | ||||||||
\(543\) | 55.1217 | 2.36550 | ||||||||
\(544\) | −16.9939 | −0.728609 | ||||||||
\(545\) | −21.5656 | −0.923770 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.6629 | 0.541425 | 0.270713 | − | 0.962660i | \(-0.412741\pi\) | ||||
0.270713 | + | 0.962660i | \(0.412741\pi\) | |||||||
\(548\) | −1.64734 | −0.0703708 | ||||||||
\(549\) | 30.9597 | 1.32133 | ||||||||
\(550\) | 16.6382 | 0.709457 | ||||||||
\(551\) | 35.7978 | 1.52504 | ||||||||
\(552\) | 13.5138 | 0.575185 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 22.8236 | 0.969681 | ||||||||
\(555\) | −10.4393 | −0.443123 | ||||||||
\(556\) | −4.91602 | −0.208486 | ||||||||
\(557\) | 17.1721 | 0.727605 | 0.363802 | − | 0.931476i | \(-0.381478\pi\) | ||||
0.363802 | + | 0.931476i | \(0.381478\pi\) | |||||||
\(558\) | −38.2239 | −1.61815 | ||||||||
\(559\) | 3.04539 | 0.128806 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 65.1880 | 2.75224 | ||||||||
\(562\) | 11.1876 | 0.471919 | ||||||||
\(563\) | −9.82712 | −0.414164 | −0.207082 | − | 0.978324i | \(-0.566397\pi\) | ||||
−0.207082 | + | 0.978324i | \(0.566397\pi\) | |||||||
\(564\) | −13.2385 | −0.557441 | ||||||||
\(565\) | −4.65017 | −0.195634 | ||||||||
\(566\) | −16.8141 | −0.706751 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −37.3165 | −1.56577 | ||||||||
\(569\) | 6.30004 | 0.264111 | 0.132056 | − | 0.991242i | \(-0.457842\pi\) | ||||
0.132056 | + | 0.991242i | \(0.457842\pi\) | |||||||
\(570\) | −40.9062 | −1.71337 | ||||||||
\(571\) | −18.6795 | −0.781714 | −0.390857 | − | 0.920451i | \(-0.627821\pi\) | ||||
−0.390857 | + | 0.920451i | \(0.627821\pi\) | |||||||
\(572\) | 8.62254 | 0.360526 | ||||||||
\(573\) | 44.3843 | 1.85418 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.82856 | 0.201365 | ||||||||
\(576\) | 38.7104 | 1.61293 | ||||||||
\(577\) | −6.54037 | −0.272279 | −0.136140 | − | 0.990690i | \(-0.543470\pi\) | ||||
−0.136140 | + | 0.990690i | \(0.543470\pi\) | |||||||
\(578\) | 10.1726 | 0.423126 | ||||||||
\(579\) | 67.5874 | 2.80884 | ||||||||
\(580\) | −13.8801 | −0.576341 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 22.0358 | 0.913415 | ||||||||
\(583\) | 8.12184 | 0.336372 | ||||||||
\(584\) | −37.2024 | −1.53945 | ||||||||
\(585\) | −37.1898 | −1.53761 | ||||||||
\(586\) | 10.6858 | 0.441427 | ||||||||
\(587\) | 6.12081 | 0.252633 | 0.126316 | − | 0.991990i | \(-0.459685\pi\) | ||||
0.126316 | + | 0.991990i | \(0.459685\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −32.9782 | −1.35884 | ||||||||
\(590\) | 37.1914 | 1.53115 | ||||||||
\(591\) | 51.3288 | 2.11138 | ||||||||
\(592\) | −3.22182 | −0.132416 | ||||||||
\(593\) | 43.9787 | 1.80599 | 0.902995 | − | 0.429651i | \(-0.141363\pi\) | ||||
0.902995 | + | 0.429651i | \(0.141363\pi\) | |||||||
\(594\) | −21.8673 | −0.897227 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.0491303 | 0.00201245 | ||||||||
\(597\) | 12.7316 | 0.521071 | ||||||||
\(598\) | −5.59532 | −0.228810 | ||||||||
\(599\) | −45.0087 | −1.83901 | −0.919503 | − | 0.393082i | \(-0.871409\pi\) | ||||
−0.919503 | + | 0.393082i | \(0.871409\pi\) | |||||||
\(600\) | 25.1982 | 1.02871 | ||||||||
\(601\) | 16.6713 | 0.680038 | 0.340019 | − | 0.940419i | \(-0.389567\pi\) | ||||
0.340019 | + | 0.940419i | \(0.389567\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.88061 | 0.117308 | ||||||||
\(604\) | −9.07411 | −0.369220 | ||||||||
\(605\) | 31.8180 | 1.29359 | ||||||||
\(606\) | −60.6744 | −2.46473 | ||||||||
\(607\) | 20.0189 | 0.812543 | 0.406272 | − | 0.913752i | \(-0.366829\pi\) | ||||
0.406272 | + | 0.913752i | \(0.366829\pi\) | |||||||
\(608\) | 15.1273 | 0.613493 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 23.1582 | 0.937650 | ||||||||
\(611\) | 23.2191 | 0.939346 | ||||||||
\(612\) | 13.9151 | 0.562486 | ||||||||
\(613\) | 24.0654 | 0.971992 | 0.485996 | − | 0.873961i | \(-0.338457\pi\) | ||||
0.485996 | + | 0.873961i | \(0.338457\pi\) | |||||||
\(614\) | −29.6443 | −1.19635 | ||||||||
\(615\) | 7.71794 | 0.311217 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −34.0652 | −1.37141 | −0.685707 | − | 0.727878i | \(-0.740507\pi\) | ||||
−0.685707 | + | 0.727878i | \(0.740507\pi\) | |||||||
\(618\) | −25.1914 | −1.01335 | ||||||||
\(619\) | 6.76477 | 0.271899 | 0.135950 | − | 0.990716i | \(-0.456591\pi\) | ||||
0.135950 | + | 0.990716i | \(0.456591\pi\) | |||||||
\(620\) | 12.7869 | 0.513533 | ||||||||
\(621\) | −6.34608 | −0.254659 | ||||||||
\(622\) | 19.8861 | 0.797358 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −19.2237 | −0.769564 | ||||||||
\(625\) | −30.9994 | −1.23998 | ||||||||
\(626\) | 1.02949 | 0.0411465 | ||||||||
\(627\) | −58.0277 | −2.31740 | ||||||||
\(628\) | 6.69281 | 0.267072 | ||||||||
\(629\) | −6.85081 | −0.273160 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.90673 | −0.235143 | −0.117572 | − | 0.993064i | \(-0.537511\pi\) | ||||
−0.117572 | + | 0.993064i | \(0.537511\pi\) | |||||||
\(632\) | −16.7769 | −0.667350 | ||||||||
\(633\) | 51.1869 | 2.03450 | ||||||||
\(634\) | −15.1965 | −0.603532 | ||||||||
\(635\) | 11.8650 | 0.470847 | ||||||||
\(636\) | 2.90373 | 0.115140 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 44.0270 | 1.74305 | ||||||||
\(639\) | 53.8985 | 2.13219 | ||||||||
\(640\) | 9.97517 | 0.394303 | ||||||||
\(641\) | −6.29419 | −0.248605 | −0.124303 | − | 0.992244i | \(-0.539669\pi\) | ||||
−0.124303 | + | 0.992244i | \(0.539669\pi\) | |||||||
\(642\) | −37.2887 | −1.47167 | ||||||||
\(643\) | 6.27693 | 0.247538 | 0.123769 | − | 0.992311i | \(-0.460502\pi\) | ||||
0.123769 | + | 0.992311i | \(0.460502\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.94657 | 0.312896 | ||||||||
\(646\) | −26.8448 | −1.05619 | ||||||||
\(647\) | 8.45932 | 0.332570 | 0.166285 | − | 0.986078i | \(-0.446823\pi\) | ||||
0.166285 | + | 0.986078i | \(0.446823\pi\) | |||||||
\(648\) | 7.92603 | 0.311364 | ||||||||
\(649\) | 52.7581 | 2.07094 | ||||||||
\(650\) | −10.4332 | −0.409223 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.2921 | −0.403069 | ||||||||
\(653\) | −20.7360 | −0.811462 | −0.405731 | − | 0.913993i | \(-0.632983\pi\) | ||||
−0.405731 | + | 0.913993i | \(0.632983\pi\) | |||||||
\(654\) | 24.4562 | 0.956314 | ||||||||
\(655\) | 58.8190 | 2.29825 | ||||||||
\(656\) | 2.38195 | 0.0929995 | ||||||||
\(657\) | 53.7336 | 2.09635 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.2206 | −1.13827 | −0.569137 | − | 0.822243i | \(-0.692723\pi\) | ||||
−0.569137 | + | 0.822243i | \(0.692723\pi\) | |||||||
\(660\) | 22.4995 | 0.875790 | ||||||||
\(661\) | −16.2903 | −0.633621 | −0.316810 | − | 0.948489i | \(-0.602612\pi\) | ||||
−0.316810 | + | 0.948489i | \(0.602612\pi\) | |||||||
\(662\) | −26.2198 | −1.01906 | ||||||||
\(663\) | −40.8768 | −1.58752 | ||||||||
\(664\) | −37.4202 | −1.45219 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.06833 | 0.273892 | ||||||||
\(667\) | 12.7770 | 0.494728 | ||||||||
\(668\) | 4.56894 | 0.176778 | ||||||||
\(669\) | −13.4959 | −0.521781 | ||||||||
\(670\) | 2.15473 | 0.0832447 | ||||||||
\(671\) | 32.8512 | 1.26821 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −33.1283 | −1.27700 | −0.638502 | − | 0.769621i | \(-0.720445\pi\) | ||||
−0.638502 | + | 0.769621i | \(0.720445\pi\) | |||||||
\(674\) | −16.8534 | −0.649169 | ||||||||
\(675\) | −11.8331 | −0.455455 | ||||||||
\(676\) | 2.62766 | 0.101064 | ||||||||
\(677\) | −43.2111 | −1.66074 | −0.830369 | − | 0.557215i | \(-0.811870\pi\) | ||||
−0.830369 | + | 0.557215i | \(0.811870\pi\) | |||||||
\(678\) | 5.27347 | 0.202526 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 44.0917 | 1.69084 | ||||||||
\(681\) | −44.8016 | −1.71680 | ||||||||
\(682\) | −40.5593 | −1.55310 | ||||||||
\(683\) | −37.8993 | −1.45018 | −0.725088 | − | 0.688656i | \(-0.758201\pi\) | ||||
−0.725088 | + | 0.688656i | \(0.758201\pi\) | |||||||
\(684\) | −12.3867 | −0.473617 | ||||||||
\(685\) | 7.53923 | 0.288059 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.08453 | 0.232139 | ||||||||
\(688\) | 2.45251 | 0.0935011 | ||||||||
\(689\) | −5.09289 | −0.194024 | ||||||||
\(690\) | −14.6003 | −0.555824 | ||||||||
\(691\) | −30.9744 | −1.17832 | −0.589160 | − | 0.808016i | \(-0.700541\pi\) | ||||
−0.589160 | + | 0.808016i | \(0.700541\pi\) | |||||||
\(692\) | −8.86996 | −0.337185 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −39.3392 | −1.49330 | ||||||||
\(695\) | 22.4987 | 0.853425 | ||||||||
\(696\) | 66.6778 | 2.52742 | ||||||||
\(697\) | 5.06492 | 0.191847 | ||||||||
\(698\) | −8.59091 | −0.325171 | ||||||||
\(699\) | −34.5263 | −1.30591 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.2468 | −0.689173 | −0.344586 | − | 0.938755i | \(-0.611981\pi\) | ||||
−0.344586 | + | 0.938755i | \(0.611981\pi\) | |||||||
\(702\) | 13.7121 | 0.517531 | ||||||||
\(703\) | 6.09831 | 0.230002 | ||||||||
\(704\) | 41.0755 | 1.54809 | ||||||||
\(705\) | 60.5875 | 2.28186 | ||||||||
\(706\) | −23.7829 | −0.895080 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 18.8621 | 0.708883 | ||||||||
\(709\) | −44.8300 | −1.68363 | −0.841814 | − | 0.539768i | \(-0.818512\pi\) | ||||
−0.841814 | + | 0.539768i | \(0.818512\pi\) | |||||||
\(710\) | 40.3168 | 1.51306 | ||||||||
\(711\) | 24.2319 | 0.908767 | ||||||||
\(712\) | 18.2805 | 0.685090 | ||||||||
\(713\) | −11.7706 | −0.440814 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −39.4621 | −1.47580 | ||||||||
\(716\) | −1.46462 | −0.0547352 | ||||||||
\(717\) | 15.3437 | 0.573020 | ||||||||
\(718\) | 41.5988 | 1.55246 | ||||||||
\(719\) | −22.4791 | −0.838329 | −0.419165 | − | 0.907910i | \(-0.637677\pi\) | ||||
−0.419165 | + | 0.907910i | \(0.637677\pi\) | |||||||
\(720\) | −29.9497 | −1.11616 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.56032 | 0.0580691 | ||||||||
\(723\) | 63.4242 | 2.35877 | ||||||||
\(724\) | 12.4853 | 0.464012 | ||||||||
\(725\) | 23.8244 | 0.884815 | ||||||||
\(726\) | −36.0828 | −1.33916 | ||||||||
\(727\) | 14.9987 | 0.556271 | 0.278135 | − | 0.960542i | \(-0.410284\pi\) | ||||
0.278135 | + | 0.960542i | \(0.410284\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.7296 | −1.61961 | ||||||||
\(730\) | 40.1935 | 1.48763 | ||||||||
\(731\) | 5.21496 | 0.192882 | ||||||||
\(732\) | 11.7450 | 0.434108 | ||||||||
\(733\) | −7.35860 | −0.271796 | −0.135898 | − | 0.990723i | \(-0.543392\pi\) | ||||
−0.135898 | + | 0.990723i | \(0.543392\pi\) | |||||||
\(734\) | 18.6564 | 0.688620 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.39926 | 0.199019 | ||||||||
\(737\) | 3.05661 | 0.112592 | ||||||||
\(738\) | −5.22573 | −0.192362 | ||||||||
\(739\) | −1.92445 | −0.0707921 | −0.0353960 | − | 0.999373i | \(-0.511269\pi\) | ||||
−0.0353960 | + | 0.999373i | \(0.511269\pi\) | |||||||
\(740\) | −2.36454 | −0.0869221 | ||||||||
\(741\) | 36.3869 | 1.33670 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.15152 | −0.262364 | −0.131182 | − | 0.991358i | \(-0.541877\pi\) | ||||
−0.131182 | + | 0.991358i | \(0.541877\pi\) | |||||||
\(744\) | −61.4260 | −2.25199 | ||||||||
\(745\) | −0.224850 | −0.00823788 | ||||||||
\(746\) | −5.81317 | −0.212835 | ||||||||
\(747\) | 54.0482 | 1.97752 | ||||||||
\(748\) | 14.7653 | 0.539874 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 18.1407 | 0.662404 | ||||||||
\(751\) | 31.3196 | 1.14287 | 0.571434 | − | 0.820648i | \(-0.306387\pi\) | ||||
0.571434 | + | 0.820648i | \(0.306387\pi\) | |||||||
\(752\) | 18.6988 | 0.681876 | ||||||||
\(753\) | −61.6965 | −2.24835 | ||||||||
\(754\) | −27.6076 | −1.00541 | ||||||||
\(755\) | 41.5288 | 1.51139 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.0634 | 1.01998 | 0.509990 | − | 0.860180i | \(-0.329649\pi\) | ||||
0.509990 | + | 0.860180i | \(0.329649\pi\) | |||||||
\(758\) | 29.8625 | 1.08465 | ||||||||
\(759\) | −20.7113 | −0.751774 | ||||||||
\(760\) | −39.2486 | −1.42370 | ||||||||
\(761\) | −14.4551 | −0.523996 | −0.261998 | − | 0.965068i | \(-0.584381\pi\) | ||||
−0.261998 | + | 0.965068i | \(0.584381\pi\) | |||||||
\(762\) | −13.4553 | −0.487435 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 10.0532 | 0.363713 | ||||||||
\(765\) | −63.6843 | −2.30251 | ||||||||
\(766\) | 10.3417 | 0.373662 | ||||||||
\(767\) | −33.0825 | −1.19454 | ||||||||
\(768\) | 36.2102 | 1.30662 | ||||||||
\(769\) | 10.4927 | 0.378377 | 0.189189 | − | 0.981941i | \(-0.439414\pi\) | ||||
0.189189 | + | 0.981941i | \(0.439414\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.9275 | 0.537601 | ||||||||
\(772\) | 15.3088 | 0.550976 | ||||||||
\(773\) | −8.37676 | −0.301291 | −0.150646 | − | 0.988588i | \(-0.548135\pi\) | ||||
−0.150646 | + | 0.988588i | \(0.548135\pi\) | |||||||
\(774\) | −5.38053 | −0.193399 | ||||||||
\(775\) | −21.9479 | −0.788391 | ||||||||
\(776\) | 21.1429 | 0.758987 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17.6237 | 0.631840 | ||||||||
\(779\) | −4.50858 | −0.161537 | ||||||||
\(780\) | −14.1085 | −0.505166 | ||||||||
\(781\) | 57.1916 | 2.04648 | ||||||||
\(782\) | −9.58149 | −0.342633 | ||||||||
\(783\) | −31.3119 | −1.11900 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −30.6304 | −1.09325 | ||||||||
\(786\) | −66.7030 | −2.37922 | ||||||||
\(787\) | −32.1245 | −1.14512 | −0.572558 | − | 0.819864i | \(-0.694049\pi\) | ||||
−0.572558 | + | 0.819864i | \(0.694049\pi\) | |||||||
\(788\) | 11.6262 | 0.414165 | ||||||||
\(789\) | 29.3447 | 1.04470 | ||||||||
\(790\) | 18.1258 | 0.644887 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −64.5324 | −2.29306 | ||||||||
\(793\) | −20.5997 | −0.731518 | ||||||||
\(794\) | −1.53061 | −0.0543194 | ||||||||
\(795\) | −13.2893 | −0.471322 | ||||||||
\(796\) | 2.88377 | 0.102212 | ||||||||
\(797\) | −36.4800 | −1.29219 | −0.646094 | − | 0.763258i | \(-0.723599\pi\) | ||||
−0.646094 | + | 0.763258i | \(0.723599\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 39.7607 | 1.40663 | ||||||||
\(800\) | 10.0676 | 0.355944 | ||||||||
\(801\) | −26.4036 | −0.932924 | ||||||||
\(802\) | −26.9638 | −0.952125 | ||||||||
\(803\) | 57.0167 | 2.01207 | ||||||||
\(804\) | 1.09280 | 0.0385402 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 25.4331 | 0.895844 | ||||||||
\(807\) | −55.9107 | −1.96815 | ||||||||
\(808\) | −58.2159 | −2.04803 | ||||||||
\(809\) | 41.9241 | 1.47397 | 0.736987 | − | 0.675907i | \(-0.236248\pi\) | ||||
0.736987 | + | 0.675907i | \(0.236248\pi\) | |||||||
\(810\) | −8.56328 | −0.300883 | ||||||||
\(811\) | −4.59446 | −0.161333 | −0.0806666 | − | 0.996741i | \(-0.525705\pi\) | ||||
−0.0806666 | + | 0.996741i | \(0.525705\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 40.4482 | 1.41858 | ||||||||
\(814\) | 7.50019 | 0.262881 | ||||||||
\(815\) | 47.1029 | 1.64994 | ||||||||
\(816\) | −32.9189 | −1.15239 | ||||||||
\(817\) | −4.64214 | −0.162408 | ||||||||
\(818\) | −11.4994 | −0.402066 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.74814 | 0.0610478 | ||||||||
\(821\) | 19.6723 | 0.686567 | 0.343284 | − | 0.939232i | \(-0.388461\pi\) | ||||
0.343284 | + | 0.939232i | \(0.388461\pi\) | |||||||
\(822\) | −8.54978 | −0.298208 | ||||||||
\(823\) | 10.9571 | 0.381939 | 0.190970 | − | 0.981596i | \(-0.438837\pi\) | ||||
0.190970 | + | 0.981596i | \(0.438837\pi\) | |||||||
\(824\) | −24.1707 | −0.842025 | ||||||||
\(825\) | −38.6189 | −1.34454 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.3400 | −0.568197 | −0.284099 | − | 0.958795i | \(-0.591694\pi\) | ||||
−0.284099 | + | 0.958795i | \(0.591694\pi\) | |||||||
\(828\) | −4.42108 | −0.153643 | ||||||||
\(829\) | 23.6076 | 0.819927 | 0.409964 | − | 0.912102i | \(-0.365541\pi\) | ||||
0.409964 | + | 0.912102i | \(0.365541\pi\) | |||||||
\(830\) | 40.4288 | 1.40330 | ||||||||
\(831\) | −52.9757 | −1.83771 | ||||||||
\(832\) | −25.7568 | −0.892957 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −25.5144 | −0.883492 | ||||||||
\(835\) | −20.9103 | −0.723631 | ||||||||
\(836\) | −13.1435 | −0.454577 | ||||||||
\(837\) | 28.8457 | 0.997052 | ||||||||
\(838\) | −20.0731 | −0.693415 | ||||||||
\(839\) | 12.4470 | 0.429719 | 0.214860 | − | 0.976645i | \(-0.431071\pi\) | ||||
0.214860 | + | 0.976645i | \(0.431071\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 34.0425 | 1.17388 | ||||||||
\(842\) | 2.94093 | 0.101351 | ||||||||
\(843\) | −25.9674 | −0.894364 | ||||||||
\(844\) | 11.5940 | 0.399083 | ||||||||
\(845\) | −12.0258 | −0.413699 | ||||||||
\(846\) | −41.0231 | −1.41040 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.10140 | −0.140843 | ||||||||
\(849\) | 39.0272 | 1.33941 | ||||||||
\(850\) | −17.8659 | −0.612796 | ||||||||
\(851\) | 2.17662 | 0.0746135 | ||||||||
\(852\) | 20.4472 | 0.700510 | ||||||||
\(853\) | 51.3305 | 1.75752 | 0.878761 | − | 0.477262i | \(-0.158371\pi\) | ||||
0.878761 | + | 0.477262i | \(0.158371\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 56.6891 | 1.93873 | ||||||||
\(856\) | −35.7777 | −1.22286 | ||||||||
\(857\) | −11.8437 | −0.404572 | −0.202286 | − | 0.979326i | \(-0.564837\pi\) | ||||
−0.202286 | + | 0.979326i | \(0.564837\pi\) | |||||||
\(858\) | 44.7515 | 1.52779 | ||||||||
\(859\) | −30.3860 | −1.03676 | −0.518379 | − | 0.855151i | \(-0.673464\pi\) | ||||
−0.518379 | + | 0.855151i | \(0.673464\pi\) | |||||||
\(860\) | 1.79993 | 0.0613770 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.25456 | 0.247091 | ||||||||
\(863\) | 3.30286 | 0.112431 | 0.0562154 | − | 0.998419i | \(-0.482097\pi\) | ||||
0.0562154 | + | 0.998419i | \(0.482097\pi\) | |||||||
\(864\) | −13.2317 | −0.450150 | ||||||||
\(865\) | 40.5944 | 1.38025 | ||||||||
\(866\) | 10.4512 | 0.355148 | ||||||||
\(867\) | −23.6117 | −0.801894 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25.7124 | 0.872234 | ||||||||
\(870\) | −72.0387 | −2.44234 | ||||||||
\(871\) | −1.91668 | −0.0649442 | ||||||||
\(872\) | 23.4653 | 0.794634 | ||||||||
\(873\) | −30.5380 | −1.03355 | ||||||||
\(874\) | 8.52904 | 0.288499 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 20.3847 | 0.688734 | ||||||||
\(877\) | −6.28757 | −0.212316 | −0.106158 | − | 0.994349i | \(-0.533855\pi\) | ||||
−0.106158 | + | 0.994349i | \(0.533855\pi\) | |||||||
\(878\) | 10.0985 | 0.340808 | ||||||||
\(879\) | −24.8028 | −0.836577 | ||||||||
\(880\) | −31.7796 | −1.07129 | ||||||||
\(881\) | 26.0595 | 0.877967 | 0.438983 | − | 0.898495i | \(-0.355339\pi\) | ||||
0.438983 | + | 0.898495i | \(0.355339\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 52.5138 | 1.76723 | 0.883615 | − | 0.468214i | \(-0.155102\pi\) | ||||
0.883615 | + | 0.468214i | \(0.155102\pi\) | |||||||
\(884\) | −9.25876 | −0.311406 | ||||||||
\(885\) | −86.3248 | −2.90178 | ||||||||
\(886\) | 5.09009 | 0.171005 | ||||||||
\(887\) | −18.6179 | −0.625128 | −0.312564 | − | 0.949897i | \(-0.601188\pi\) | ||||
−0.312564 | + | 0.949897i | \(0.601188\pi\) | |||||||
\(888\) | 11.3588 | 0.381178 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −19.7502 | −0.662029 | ||||||||
\(891\) | −12.1475 | −0.406956 | ||||||||
\(892\) | −3.05687 | −0.102352 | ||||||||
\(893\) | −35.3933 | −1.18439 | ||||||||
\(894\) | 0.254989 | 0.00852810 | ||||||||
\(895\) | 6.70298 | 0.224056 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.9873 | 0.433632 | ||||||||
\(898\) | 21.6819 | 0.723535 | ||||||||
\(899\) | −58.0770 | −1.93698 | ||||||||
\(900\) | −8.24366 | −0.274789 | ||||||||
\(901\) | −8.72112 | −0.290542 | ||||||||
\(902\) | −5.54501 | −0.184629 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.05978 | 0.168286 | ||||||||
\(905\) | −57.1403 | −1.89941 | ||||||||
\(906\) | −47.0952 | −1.56463 | ||||||||
\(907\) | −15.8713 | −0.526998 | −0.263499 | − | 0.964660i | \(-0.584877\pi\) | ||||
−0.263499 | + | 0.964660i | \(0.584877\pi\) | |||||||
\(908\) | −10.1477 | −0.336765 | ||||||||
\(909\) | 84.0846 | 2.78891 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.5926 | −0.947315 | −0.473657 | − | 0.880709i | \(-0.657067\pi\) | ||||
−0.473657 | + | 0.880709i | \(0.657067\pi\) | |||||||
\(912\) | 29.3030 | 0.970321 | ||||||||
\(913\) | 57.3505 | 1.89802 | ||||||||
\(914\) | 34.1928 | 1.13100 | ||||||||
\(915\) | −53.7525 | −1.77700 | ||||||||
\(916\) | 1.37817 | 0.0455360 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 23.4808 | 0.774982 | ||||||||
\(919\) | −55.8471 | −1.84222 | −0.921112 | − | 0.389297i | \(-0.872718\pi\) | ||||
−0.921112 | + | 0.389297i | \(0.872718\pi\) | |||||||
\(920\) | −14.0087 | −0.461853 | ||||||||
\(921\) | 68.8073 | 2.26728 | ||||||||
\(922\) | 44.6372 | 1.47005 | ||||||||
\(923\) | −35.8626 | −1.18043 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.05858 | 0.133445 | ||||||||
\(926\) | 11.2384 | 0.369317 | ||||||||
\(927\) | 34.9111 | 1.14663 | ||||||||
\(928\) | 26.6402 | 0.874509 | ||||||||
\(929\) | −2.24329 | −0.0735999 | −0.0368000 | − | 0.999323i | \(-0.511716\pi\) | ||||
−0.0368000 | + | 0.999323i | \(0.511716\pi\) | |||||||
\(930\) | 66.3646 | 2.17618 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −7.82035 | −0.256164 | ||||||||
\(933\) | −46.1574 | −1.51113 | ||||||||
\(934\) | 17.5354 | 0.573775 | ||||||||
\(935\) | −67.5753 | −2.20995 | ||||||||
\(936\) | 40.4657 | 1.32266 | ||||||||
\(937\) | 15.8394 | 0.517450 | 0.258725 | − | 0.965951i | \(-0.416698\pi\) | ||||
0.258725 | + | 0.965951i | \(0.416698\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.38953 | −0.0779795 | ||||||||
\(940\) | 13.7233 | 0.447605 | ||||||||
\(941\) | 21.0187 | 0.685189 | 0.342594 | − | 0.939483i | \(-0.388694\pi\) | ||||
0.342594 | + | 0.939483i | \(0.388694\pi\) | |||||||
\(942\) | 34.7361 | 1.13176 | ||||||||
\(943\) | −1.60921 | −0.0524031 | ||||||||
\(944\) | −26.6420 | −0.867124 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.70928 | −0.185625 | ||||||||
\(947\) | 29.0720 | 0.944714 | 0.472357 | − | 0.881407i | \(-0.343403\pi\) | ||||
0.472357 | + | 0.881407i | \(0.343403\pi\) | |||||||
\(948\) | 9.19274 | 0.298566 | ||||||||
\(949\) | −35.7529 | −1.16059 | ||||||||
\(950\) | 15.9035 | 0.515977 | ||||||||
\(951\) | 35.2726 | 1.14379 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 56.7231 | 1.83744 | 0.918720 | − | 0.394909i | \(-0.129224\pi\) | ||||
0.918720 | + | 0.394909i | \(0.129224\pi\) | |||||||
\(954\) | 8.99802 | 0.291322 | ||||||||
\(955\) | −46.0097 | −1.48884 | ||||||||
\(956\) | 3.47540 | 0.112403 | ||||||||
\(957\) | −102.191 | −3.30336 | ||||||||
\(958\) | −26.3140 | −0.850168 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −67.2093 | −2.16917 | ||||||||
\(961\) | 22.5027 | 0.725893 | ||||||||
\(962\) | −4.70307 | −0.151633 | ||||||||
\(963\) | 51.6758 | 1.66523 | ||||||||
\(964\) | 14.3658 | 0.462692 | ||||||||
\(965\) | −70.0625 | −2.25539 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46.1274 | 1.48336 | 0.741678 | − | 0.670756i | \(-0.234030\pi\) | ||||
0.741678 | + | 0.670756i | \(0.234030\pi\) | |||||||
\(968\) | −34.6207 | −1.11275 | ||||||||
\(969\) | 62.3093 | 2.00166 | ||||||||
\(970\) | −22.8428 | −0.733439 | ||||||||
\(971\) | 15.3334 | 0.492073 | 0.246036 | − | 0.969261i | \(-0.420872\pi\) | ||||
0.246036 | + | 0.969261i | \(0.420872\pi\) | |||||||
\(972\) | −11.6549 | −0.373830 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −19.5732 | −0.627167 | ||||||||
\(975\) | 24.2164 | 0.775546 | ||||||||
\(976\) | −16.5894 | −0.531012 | ||||||||
\(977\) | 9.77789 | 0.312822 | 0.156411 | − | 0.987692i | \(-0.450008\pi\) | ||||
0.156411 | + | 0.987692i | \(0.450008\pi\) | |||||||
\(978\) | −53.4165 | −1.70807 | ||||||||
\(979\) | −28.0168 | −0.895420 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −33.8922 | −1.08210 | ||||||||
\(982\) | 33.5806 | 1.07160 | ||||||||
\(983\) | −7.31956 | −0.233458 | −0.116729 | − | 0.993164i | \(-0.537241\pi\) | ||||
−0.116729 | + | 0.993164i | \(0.537241\pi\) | |||||||
\(984\) | −8.39778 | −0.267711 | ||||||||
\(985\) | −53.2085 | −1.69536 | ||||||||
\(986\) | −47.2756 | −1.50556 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.24176 | 0.262205 | ||||||||
\(989\) | −1.65688 | −0.0526857 | ||||||||
\(990\) | 69.7208 | 2.21587 | ||||||||
\(991\) | −26.1469 | −0.830585 | −0.415292 | − | 0.909688i | \(-0.636321\pi\) | ||||
−0.415292 | + | 0.909688i | \(0.636321\pi\) | |||||||
\(992\) | −24.5420 | −0.779208 | ||||||||
\(993\) | 60.8586 | 1.93129 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.1979 | −0.418401 | ||||||||
\(996\) | 20.5040 | 0.649695 | ||||||||
\(997\) | 6.05871 | 0.191881 | 0.0959407 | − | 0.995387i | \(-0.469414\pi\) | ||||
0.0959407 | + | 0.995387i | \(0.469414\pi\) | |||||||
\(998\) | −19.1517 | −0.606236 | ||||||||
\(999\) | −5.33411 | −0.168764 |
(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 | 2009.2.a.r.1.11 | 17 | ||
7.3 | odd | 6 | 287.2.e.d.247.7 | yes | 34 | ||
7.5 | odd | 6 | 287.2.e.d.165.7 | ✓ | 34 | ||
7.6 | odd | 2 | 2009.2.a.s.1.11 | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.2.e.d.165.7 | ✓ | 34 | 7.5 | odd | 6 | ||
287.2.e.d.247.7 | yes | 34 | 7.3 | odd | 6 | ||
2009.2.a.r.1.11 | 17 | 1.1 | even | 1 | trivial | ||
2009.2.a.s.1.11 | 17 | 7.6 | odd | 2 |