Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8047,2,Mod(1,8047)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8047, 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("8047.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8047 = 13 \cdot 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8047.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: | \(64.2556185065\) |
Analytic rank: | \(1\) |
Dimension: | \(151\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8047.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.59872 | −1.83757 | −0.918787 | − | 0.394755i | \(-0.870830\pi\) | ||||
−0.918787 | + | 0.394755i | \(0.870830\pi\) | |||||||
\(3\) | 0.688709 | 0.397627 | 0.198813 | − | 0.980037i | \(-0.436291\pi\) | ||||
0.198813 | + | 0.980037i | \(0.436291\pi\) | |||||||
\(4\) | 4.75335 | 2.37668 | ||||||||
\(5\) | −1.04737 | −0.468396 | −0.234198 | − | 0.972189i | \(-0.575246\pi\) | ||||
−0.234198 | + | 0.972189i | \(0.575246\pi\) | |||||||
\(6\) | −1.78976 | −0.730668 | ||||||||
\(7\) | 2.76372 | 1.04459 | 0.522294 | − | 0.852766i | \(-0.325077\pi\) | ||||
0.522294 | + | 0.852766i | \(0.325077\pi\) | |||||||
\(8\) | −7.15519 | −2.52974 | ||||||||
\(9\) | −2.52568 | −0.841893 | ||||||||
\(10\) | 2.72181 | 0.860713 | ||||||||
\(11\) | 2.17885 | 0.656949 | 0.328475 | − | 0.944513i | \(-0.393465\pi\) | ||||
0.328475 | + | 0.944513i | \(0.393465\pi\) | |||||||
\(12\) | 3.27368 | 0.945029 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −7.18213 | −1.91951 | ||||||||
\(15\) | −0.721331 | −0.186247 | ||||||||
\(16\) | 9.08764 | 2.27191 | ||||||||
\(17\) | −2.98651 | −0.724335 | −0.362167 | − | 0.932113i | \(-0.617963\pi\) | ||||
−0.362167 | + | 0.932113i | \(0.617963\pi\) | |||||||
\(18\) | 6.56354 | 1.54704 | ||||||||
\(19\) | 7.89798 | 1.81192 | 0.905961 | − | 0.423361i | \(-0.139150\pi\) | ||||
0.905961 | + | 0.423361i | \(0.139150\pi\) | |||||||
\(20\) | −4.97850 | −1.11323 | ||||||||
\(21\) | 1.90340 | 0.415356 | ||||||||
\(22\) | −5.66223 | −1.20719 | ||||||||
\(23\) | 9.29513 | 1.93817 | 0.969084 | − | 0.246729i | \(-0.0793558\pi\) | ||||
0.969084 | + | 0.246729i | \(0.0793558\pi\) | |||||||
\(24\) | −4.92785 | −1.00589 | ||||||||
\(25\) | −3.90302 | −0.780605 | ||||||||
\(26\) | 2.59872 | 0.509651 | ||||||||
\(27\) | −3.80559 | −0.732386 | ||||||||
\(28\) | 13.1369 | 2.48264 | ||||||||
\(29\) | −4.12598 | −0.766175 | −0.383087 | − | 0.923712i | \(-0.625139\pi\) | ||||
−0.383087 | + | 0.923712i | \(0.625139\pi\) | |||||||
\(30\) | 1.87454 | 0.342242 | ||||||||
\(31\) | 6.39056 | 1.14778 | 0.573889 | − | 0.818933i | \(-0.305434\pi\) | ||||
0.573889 | + | 0.818933i | \(0.305434\pi\) | |||||||
\(32\) | −9.30587 | −1.64506 | ||||||||
\(33\) | 1.50060 | 0.261220 | ||||||||
\(34\) | 7.76110 | 1.33102 | ||||||||
\(35\) | −2.89462 | −0.489281 | ||||||||
\(36\) | −12.0054 | −2.00091 | ||||||||
\(37\) | −6.47592 | −1.06463 | −0.532317 | − | 0.846545i | \(-0.678679\pi\) | ||||
−0.532317 | + | 0.846545i | \(0.678679\pi\) | |||||||
\(38\) | −20.5247 | −3.32954 | ||||||||
\(39\) | −0.688709 | −0.110282 | ||||||||
\(40\) | 7.49410 | 1.18492 | ||||||||
\(41\) | −5.96707 | −0.931899 | −0.465950 | − | 0.884811i | \(-0.654287\pi\) | ||||
−0.465950 | + | 0.884811i | \(0.654287\pi\) | |||||||
\(42\) | −4.94640 | −0.763246 | ||||||||
\(43\) | −6.98240 | −1.06481 | −0.532403 | − | 0.846491i | \(-0.678711\pi\) | ||||
−0.532403 | + | 0.846491i | \(0.678711\pi\) | |||||||
\(44\) | 10.3569 | 1.56136 | ||||||||
\(45\) | 2.64531 | 0.394340 | ||||||||
\(46\) | −24.1555 | −3.56153 | ||||||||
\(47\) | −8.32173 | −1.21385 | −0.606924 | − | 0.794760i | \(-0.707597\pi\) | ||||
−0.606924 | + | 0.794760i | \(0.707597\pi\) | |||||||
\(48\) | 6.25875 | 0.903372 | ||||||||
\(49\) | 0.638136 | 0.0911623 | ||||||||
\(50\) | 10.1429 | 1.43442 | ||||||||
\(51\) | −2.05684 | −0.288015 | ||||||||
\(52\) | −4.75335 | −0.659171 | ||||||||
\(53\) | −11.0940 | −1.52388 | −0.761940 | − | 0.647648i | \(-0.775753\pi\) | ||||
−0.761940 | + | 0.647648i | \(0.775753\pi\) | |||||||
\(54\) | 9.88966 | 1.34581 | ||||||||
\(55\) | −2.28206 | −0.307713 | ||||||||
\(56\) | −19.7749 | −2.64254 | ||||||||
\(57\) | 5.43942 | 0.720468 | ||||||||
\(58\) | 10.7223 | 1.40790 | ||||||||
\(59\) | 5.14294 | 0.669554 | 0.334777 | − | 0.942297i | \(-0.391339\pi\) | ||||
0.334777 | + | 0.942297i | \(0.391339\pi\) | |||||||
\(60\) | −3.42874 | −0.442648 | ||||||||
\(61\) | 9.66893 | 1.23798 | 0.618990 | − | 0.785399i | \(-0.287542\pi\) | ||||
0.618990 | + | 0.785399i | \(0.287542\pi\) | |||||||
\(62\) | −16.6073 | −2.10913 | ||||||||
\(63\) | −6.98026 | −0.879431 | ||||||||
\(64\) | 6.00807 | 0.751008 | ||||||||
\(65\) | 1.04737 | 0.129910 | ||||||||
\(66\) | −3.89963 | −0.480012 | ||||||||
\(67\) | −4.15316 | −0.507389 | −0.253694 | − | 0.967284i | \(-0.581646\pi\) | ||||
−0.253694 | + | 0.967284i | \(0.581646\pi\) | |||||||
\(68\) | −14.1959 | −1.72151 | ||||||||
\(69\) | 6.40164 | 0.770667 | ||||||||
\(70\) | 7.52232 | 0.899089 | ||||||||
\(71\) | −1.40495 | −0.166737 | −0.0833683 | − | 0.996519i | \(-0.526568\pi\) | ||||
−0.0833683 | + | 0.996519i | \(0.526568\pi\) | |||||||
\(72\) | 18.0717 | 2.12977 | ||||||||
\(73\) | −8.94604 | −1.04706 | −0.523528 | − | 0.852009i | \(-0.675384\pi\) | ||||
−0.523528 | + | 0.852009i | \(0.675384\pi\) | |||||||
\(74\) | 16.8291 | 1.95634 | ||||||||
\(75\) | −2.68805 | −0.310389 | ||||||||
\(76\) | 37.5419 | 4.30635 | ||||||||
\(77\) | 6.02174 | 0.686241 | ||||||||
\(78\) | 1.78976 | 0.202651 | ||||||||
\(79\) | 15.8910 | 1.78787 | 0.893937 | − | 0.448194i | \(-0.147932\pi\) | ||||
0.893937 | + | 0.448194i | \(0.147932\pi\) | |||||||
\(80\) | −9.51809 | −1.06415 | ||||||||
\(81\) | 4.95609 | 0.550677 | ||||||||
\(82\) | 15.5067 | 1.71243 | ||||||||
\(83\) | −10.6444 | −1.16838 | −0.584188 | − | 0.811619i | \(-0.698587\pi\) | ||||
−0.584188 | + | 0.811619i | \(0.698587\pi\) | |||||||
\(84\) | 9.04752 | 0.987165 | ||||||||
\(85\) | 3.12797 | 0.339276 | ||||||||
\(86\) | 18.1453 | 1.95666 | ||||||||
\(87\) | −2.84160 | −0.304651 | ||||||||
\(88\) | −15.5901 | −1.66191 | ||||||||
\(89\) | −7.65560 | −0.811492 | −0.405746 | − | 0.913986i | \(-0.632988\pi\) | ||||
−0.405746 | + | 0.913986i | \(0.632988\pi\) | |||||||
\(90\) | −6.87443 | −0.724628 | ||||||||
\(91\) | −2.76372 | −0.289716 | ||||||||
\(92\) | 44.1830 | 4.60640 | ||||||||
\(93\) | 4.40124 | 0.456387 | ||||||||
\(94\) | 21.6258 | 2.23054 | ||||||||
\(95\) | −8.27208 | −0.848698 | ||||||||
\(96\) | −6.40904 | −0.654120 | ||||||||
\(97\) | 5.80198 | 0.589102 | 0.294551 | − | 0.955636i | \(-0.404830\pi\) | ||||
0.294551 | + | 0.955636i | \(0.404830\pi\) | |||||||
\(98\) | −1.65834 | −0.167517 | ||||||||
\(99\) | −5.50309 | −0.553081 | ||||||||
\(100\) | −18.5524 | −1.85524 | ||||||||
\(101\) | 1.08317 | 0.107780 | 0.0538899 | − | 0.998547i | \(-0.482838\pi\) | ||||
0.0538899 | + | 0.998547i | \(0.482838\pi\) | |||||||
\(102\) | 5.34514 | 0.529248 | ||||||||
\(103\) | 3.95448 | 0.389646 | 0.194823 | − | 0.980838i | \(-0.437587\pi\) | ||||
0.194823 | + | 0.980838i | \(0.437587\pi\) | |||||||
\(104\) | 7.15519 | 0.701624 | ||||||||
\(105\) | −1.99356 | −0.194551 | ||||||||
\(106\) | 28.8302 | 2.80024 | ||||||||
\(107\) | −14.5159 | −1.40331 | −0.701654 | − | 0.712518i | \(-0.747555\pi\) | ||||
−0.701654 | + | 0.712518i | \(0.747555\pi\) | |||||||
\(108\) | −18.0893 | −1.74064 | ||||||||
\(109\) | −19.0446 | −1.82414 | −0.912071 | − | 0.410031i | \(-0.865518\pi\) | ||||
−0.912071 | + | 0.410031i | \(0.865518\pi\) | |||||||
\(110\) | 5.93043 | 0.565445 | ||||||||
\(111\) | −4.46003 | −0.423327 | ||||||||
\(112\) | 25.1157 | 2.37321 | ||||||||
\(113\) | −2.85441 | −0.268520 | −0.134260 | − | 0.990946i | \(-0.542866\pi\) | ||||
−0.134260 | + | 0.990946i | \(0.542866\pi\) | |||||||
\(114\) | −14.1355 | −1.32391 | ||||||||
\(115\) | −9.73541 | −0.907831 | ||||||||
\(116\) | −19.6122 | −1.82095 | ||||||||
\(117\) | 2.52568 | 0.233499 | ||||||||
\(118\) | −13.3651 | −1.23035 | ||||||||
\(119\) | −8.25387 | −0.756631 | ||||||||
\(120\) | 5.16126 | 0.471156 | ||||||||
\(121\) | −6.25259 | −0.568418 | ||||||||
\(122\) | −25.1268 | −2.27488 | ||||||||
\(123\) | −4.10958 | −0.370548 | ||||||||
\(124\) | 30.3766 | 2.72790 | ||||||||
\(125\) | 9.32473 | 0.834029 | ||||||||
\(126\) | 18.1398 | 1.61602 | ||||||||
\(127\) | 6.28579 | 0.557773 | 0.278887 | − | 0.960324i | \(-0.410035\pi\) | ||||
0.278887 | + | 0.960324i | \(0.410035\pi\) | |||||||
\(128\) | 2.99845 | 0.265028 | ||||||||
\(129\) | −4.80884 | −0.423395 | ||||||||
\(130\) | −2.72181 | −0.238719 | ||||||||
\(131\) | 11.2745 | 0.985055 | 0.492528 | − | 0.870297i | \(-0.336073\pi\) | ||||
0.492528 | + | 0.870297i | \(0.336073\pi\) | |||||||
\(132\) | 7.13287 | 0.620836 | ||||||||
\(133\) | 21.8278 | 1.89271 | ||||||||
\(134\) | 10.7929 | 0.932364 | ||||||||
\(135\) | 3.98584 | 0.343047 | ||||||||
\(136\) | 21.3690 | 1.83238 | ||||||||
\(137\) | 9.19000 | 0.785155 | 0.392577 | − | 0.919719i | \(-0.371583\pi\) | ||||
0.392577 | + | 0.919719i | \(0.371583\pi\) | |||||||
\(138\) | −16.6361 | −1.41616 | ||||||||
\(139\) | 3.59163 | 0.304638 | 0.152319 | − | 0.988331i | \(-0.451326\pi\) | ||||
0.152319 | + | 0.988331i | \(0.451326\pi\) | |||||||
\(140\) | −13.7592 | −1.16286 | ||||||||
\(141\) | −5.73125 | −0.482659 | ||||||||
\(142\) | 3.65107 | 0.306391 | ||||||||
\(143\) | −2.17885 | −0.182205 | ||||||||
\(144\) | −22.9525 | −1.91271 | ||||||||
\(145\) | 4.32141 | 0.358873 | ||||||||
\(146\) | 23.2483 | 1.92404 | ||||||||
\(147\) | 0.439490 | 0.0362486 | ||||||||
\(148\) | −30.7823 | −2.53029 | ||||||||
\(149\) | −9.10469 | −0.745885 | −0.372943 | − | 0.927854i | \(-0.621651\pi\) | ||||
−0.372943 | + | 0.927854i | \(0.621651\pi\) | |||||||
\(150\) | 6.98549 | 0.570363 | ||||||||
\(151\) | −0.944906 | −0.0768953 | −0.0384477 | − | 0.999261i | \(-0.512241\pi\) | ||||
−0.0384477 | + | 0.999261i | \(0.512241\pi\) | |||||||
\(152\) | −56.5116 | −4.58370 | ||||||||
\(153\) | 7.54296 | 0.609812 | ||||||||
\(154\) | −15.6488 | −1.26102 | ||||||||
\(155\) | −6.69326 | −0.537616 | ||||||||
\(156\) | −3.27368 | −0.262104 | ||||||||
\(157\) | 0.0201883 | 0.00161120 | 0.000805600 | − | 1.00000i | \(-0.499744\pi\) | ||||
0.000805600 | 1.00000i | \(0.499744\pi\) | ||||||||
\(158\) | −41.2962 | −3.28535 | ||||||||
\(159\) | −7.64055 | −0.605935 | ||||||||
\(160\) | 9.74665 | 0.770540 | ||||||||
\(161\) | 25.6891 | 2.02459 | ||||||||
\(162\) | −12.8795 | −1.01191 | ||||||||
\(163\) | 18.3239 | 1.43524 | 0.717619 | − | 0.696436i | \(-0.245232\pi\) | ||||
0.717619 | + | 0.696436i | \(0.245232\pi\) | |||||||
\(164\) | −28.3636 | −2.21482 | ||||||||
\(165\) | −1.57167 | −0.122355 | ||||||||
\(166\) | 27.6618 | 2.14697 | ||||||||
\(167\) | −17.3408 | −1.34187 | −0.670934 | − | 0.741517i | \(-0.734107\pi\) | ||||
−0.670934 | + | 0.741517i | \(0.734107\pi\) | |||||||
\(168\) | −13.6192 | −1.05074 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −8.12872 | −0.623444 | ||||||||
\(171\) | −19.9478 | −1.52544 | ||||||||
\(172\) | −33.1898 | −2.53070 | ||||||||
\(173\) | 19.4028 | 1.47517 | 0.737585 | − | 0.675254i | \(-0.235966\pi\) | ||||
0.737585 | + | 0.675254i | \(0.235966\pi\) | |||||||
\(174\) | 7.38452 | 0.559819 | ||||||||
\(175\) | −10.7869 | −0.815410 | ||||||||
\(176\) | 19.8006 | 1.49253 | ||||||||
\(177\) | 3.54199 | 0.266232 | ||||||||
\(178\) | 19.8948 | 1.49118 | ||||||||
\(179\) | −18.8738 | −1.41069 | −0.705345 | − | 0.708864i | \(-0.749208\pi\) | ||||
−0.705345 | + | 0.708864i | \(0.749208\pi\) | |||||||
\(180\) | 12.5741 | 0.937217 | ||||||||
\(181\) | −9.17970 | −0.682322 | −0.341161 | − | 0.940005i | \(-0.610820\pi\) | ||||
−0.341161 | + | 0.940005i | \(0.610820\pi\) | |||||||
\(182\) | 7.18213 | 0.532375 | ||||||||
\(183\) | 6.65908 | 0.492254 | ||||||||
\(184\) | −66.5084 | −4.90307 | ||||||||
\(185\) | 6.78266 | 0.498671 | ||||||||
\(186\) | −11.4376 | −0.838645 | ||||||||
\(187\) | −6.50717 | −0.475851 | ||||||||
\(188\) | −39.5561 | −2.88492 | ||||||||
\(189\) | −10.5176 | −0.765041 | ||||||||
\(190\) | 21.4968 | 1.55954 | ||||||||
\(191\) | 1.23686 | 0.0894960 | 0.0447480 | − | 0.998998i | \(-0.485752\pi\) | ||||
0.0447480 | + | 0.998998i | \(0.485752\pi\) | |||||||
\(192\) | 4.13781 | 0.298621 | ||||||||
\(193\) | 16.9145 | 1.21753 | 0.608765 | − | 0.793350i | \(-0.291665\pi\) | ||||
0.608765 | + | 0.793350i | \(0.291665\pi\) | |||||||
\(194\) | −15.0777 | −1.08252 | ||||||||
\(195\) | 0.721331 | 0.0516556 | ||||||||
\(196\) | 3.03329 | 0.216663 | ||||||||
\(197\) | −21.4795 | −1.53035 | −0.765175 | − | 0.643823i | \(-0.777347\pi\) | ||||
−0.765175 | + | 0.643823i | \(0.777347\pi\) | |||||||
\(198\) | 14.3010 | 1.01633 | ||||||||
\(199\) | −16.3287 | −1.15751 | −0.578754 | − | 0.815502i | \(-0.696461\pi\) | ||||
−0.578754 | + | 0.815502i | \(0.696461\pi\) | |||||||
\(200\) | 27.9269 | 1.97473 | ||||||||
\(201\) | −2.86032 | −0.201751 | ||||||||
\(202\) | −2.81486 | −0.198053 | ||||||||
\(203\) | −11.4030 | −0.800336 | ||||||||
\(204\) | −9.77687 | −0.684518 | ||||||||
\(205\) | 6.24970 | 0.436498 | ||||||||
\(206\) | −10.2766 | −0.716003 | ||||||||
\(207\) | −23.4765 | −1.63173 | ||||||||
\(208\) | −9.08764 | −0.630115 | ||||||||
\(209\) | 17.2086 | 1.19034 | ||||||||
\(210\) | 5.18069 | 0.357502 | ||||||||
\(211\) | 11.8390 | 0.815031 | 0.407516 | − | 0.913198i | \(-0.366395\pi\) | ||||
0.407516 | + | 0.913198i | \(0.366395\pi\) | |||||||
\(212\) | −52.7337 | −3.62177 | ||||||||
\(213\) | −0.967601 | −0.0662989 | ||||||||
\(214\) | 37.7228 | 2.57868 | ||||||||
\(215\) | 7.31313 | 0.498751 | ||||||||
\(216\) | 27.2297 | 1.85275 | ||||||||
\(217\) | 17.6617 | 1.19896 | ||||||||
\(218\) | 49.4916 | 3.35200 | ||||||||
\(219\) | −6.16122 | −0.416337 | ||||||||
\(220\) | −10.8474 | −0.731333 | ||||||||
\(221\) | 2.98651 | 0.200894 | ||||||||
\(222\) | 11.5904 | 0.777894 | ||||||||
\(223\) | −13.2083 | −0.884496 | −0.442248 | − | 0.896893i | \(-0.645819\pi\) | ||||
−0.442248 | + | 0.896893i | \(0.645819\pi\) | |||||||
\(224\) | −25.7188 | −1.71841 | ||||||||
\(225\) | 9.85779 | 0.657186 | ||||||||
\(226\) | 7.41781 | 0.493425 | ||||||||
\(227\) | 14.9772 | 0.994069 | 0.497034 | − | 0.867731i | \(-0.334422\pi\) | ||||
0.497034 | + | 0.867731i | \(0.334422\pi\) | |||||||
\(228\) | 25.8555 | 1.71232 | ||||||||
\(229\) | −0.684727 | −0.0452481 | −0.0226240 | − | 0.999744i | \(-0.507202\pi\) | ||||
−0.0226240 | + | 0.999744i | \(0.507202\pi\) | |||||||
\(230\) | 25.2996 | 1.66821 | ||||||||
\(231\) | 4.14723 | 0.272868 | ||||||||
\(232\) | 29.5222 | 1.93822 | ||||||||
\(233\) | −6.24751 | −0.409288 | −0.204644 | − | 0.978836i | \(-0.565604\pi\) | ||||
−0.204644 | + | 0.978836i | \(0.565604\pi\) | |||||||
\(234\) | −6.56354 | −0.429072 | ||||||||
\(235\) | 8.71590 | 0.568562 | ||||||||
\(236\) | 24.4462 | 1.59131 | ||||||||
\(237\) | 10.9443 | 0.710906 | ||||||||
\(238\) | 21.4495 | 1.39036 | ||||||||
\(239\) | −12.3898 | −0.801427 | −0.400713 | − | 0.916203i | \(-0.631238\pi\) | ||||
−0.400713 | + | 0.916203i | \(0.631238\pi\) | |||||||
\(240\) | −6.55520 | −0.423136 | ||||||||
\(241\) | −19.5597 | −1.25995 | −0.629977 | − | 0.776614i | \(-0.716936\pi\) | ||||
−0.629977 | + | 0.776614i | \(0.716936\pi\) | |||||||
\(242\) | 16.2487 | 1.04451 | ||||||||
\(243\) | 14.8301 | 0.951349 | ||||||||
\(244\) | 45.9598 | 2.94228 | ||||||||
\(245\) | −0.668362 | −0.0427001 | ||||||||
\(246\) | 10.6796 | 0.680909 | ||||||||
\(247\) | −7.89798 | −0.502537 | ||||||||
\(248\) | −45.7257 | −2.90358 | ||||||||
\(249\) | −7.33090 | −0.464577 | ||||||||
\(250\) | −24.2324 | −1.53259 | ||||||||
\(251\) | 20.6154 | 1.30123 | 0.650617 | − | 0.759406i | \(-0.274510\pi\) | ||||
0.650617 | + | 0.759406i | \(0.274510\pi\) | |||||||
\(252\) | −33.1796 | −2.09012 | ||||||||
\(253\) | 20.2527 | 1.27328 | ||||||||
\(254\) | −16.3350 | −1.02495 | ||||||||
\(255\) | 2.15426 | 0.134905 | ||||||||
\(256\) | −19.8083 | −1.23802 | ||||||||
\(257\) | 17.9214 | 1.11791 | 0.558953 | − | 0.829199i | \(-0.311203\pi\) | ||||
0.558953 | + | 0.829199i | \(0.311203\pi\) | |||||||
\(258\) | 12.4968 | 0.778020 | ||||||||
\(259\) | −17.8976 | −1.11210 | ||||||||
\(260\) | 4.97850 | 0.308753 | ||||||||
\(261\) | 10.4209 | 0.645037 | ||||||||
\(262\) | −29.2992 | −1.81011 | ||||||||
\(263\) | −24.2219 | −1.49359 | −0.746793 | − | 0.665056i | \(-0.768408\pi\) | ||||
−0.746793 | + | 0.665056i | \(0.768408\pi\) | |||||||
\(264\) | −10.7371 | −0.660820 | ||||||||
\(265\) | 11.6195 | 0.713780 | ||||||||
\(266\) | −56.7244 | −3.47799 | ||||||||
\(267\) | −5.27248 | −0.322671 | ||||||||
\(268\) | −19.7414 | −1.20590 | ||||||||
\(269\) | 11.2016 | 0.682972 | 0.341486 | − | 0.939887i | \(-0.389070\pi\) | ||||
0.341486 | + | 0.939887i | \(0.389070\pi\) | |||||||
\(270\) | −10.3581 | −0.630374 | ||||||||
\(271\) | −4.33678 | −0.263440 | −0.131720 | − | 0.991287i | \(-0.542050\pi\) | ||||
−0.131720 | + | 0.991287i | \(0.542050\pi\) | |||||||
\(272\) | −27.1403 | −1.64562 | ||||||||
\(273\) | −1.90340 | −0.115199 | ||||||||
\(274\) | −23.8823 | −1.44278 | ||||||||
\(275\) | −8.50412 | −0.512818 | ||||||||
\(276\) | 30.4293 | 1.83163 | ||||||||
\(277\) | 6.25708 | 0.375951 | 0.187976 | − | 0.982174i | \(-0.439807\pi\) | ||||
0.187976 | + | 0.982174i | \(0.439807\pi\) | |||||||
\(278\) | −9.33366 | −0.559796 | ||||||||
\(279\) | −16.1405 | −0.966307 | ||||||||
\(280\) | 20.7116 | 1.23775 | ||||||||
\(281\) | −19.4833 | −1.16227 | −0.581137 | − | 0.813806i | \(-0.697392\pi\) | ||||
−0.581137 | + | 0.813806i | \(0.697392\pi\) | |||||||
\(282\) | 14.8939 | 0.886920 | ||||||||
\(283\) | 2.43171 | 0.144550 | 0.0722751 | − | 0.997385i | \(-0.476974\pi\) | ||||
0.0722751 | + | 0.997385i | \(0.476974\pi\) | |||||||
\(284\) | −6.67821 | −0.396279 | ||||||||
\(285\) | −5.69706 | −0.337465 | ||||||||
\(286\) | 5.66223 | 0.334815 | ||||||||
\(287\) | −16.4913 | −0.973450 | ||||||||
\(288\) | 23.5036 | 1.38497 | ||||||||
\(289\) | −8.08077 | −0.475339 | ||||||||
\(290\) | −11.2301 | −0.659456 | ||||||||
\(291\) | 3.99588 | 0.234242 | ||||||||
\(292\) | −42.5237 | −2.48851 | ||||||||
\(293\) | 23.0117 | 1.34436 | 0.672179 | − | 0.740389i | \(-0.265359\pi\) | ||||
0.672179 | + | 0.740389i | \(0.265359\pi\) | |||||||
\(294\) | −1.14211 | −0.0666094 | ||||||||
\(295\) | −5.38654 | −0.313616 | ||||||||
\(296\) | 46.3364 | 2.69325 | ||||||||
\(297\) | −8.29182 | −0.481140 | ||||||||
\(298\) | 23.6605 | 1.37062 | ||||||||
\(299\) | −9.29513 | −0.537551 | ||||||||
\(300\) | −12.7772 | −0.737694 | ||||||||
\(301\) | −19.2974 | −1.11228 | ||||||||
\(302\) | 2.45555 | 0.141301 | ||||||||
\(303\) | 0.745992 | 0.0428561 | ||||||||
\(304\) | 71.7741 | 4.11652 | ||||||||
\(305\) | −10.1269 | −0.579865 | ||||||||
\(306\) | −19.6021 | −1.12058 | ||||||||
\(307\) | 24.3955 | 1.39233 | 0.696164 | − | 0.717883i | \(-0.254889\pi\) | ||||
0.696164 | + | 0.717883i | \(0.254889\pi\) | |||||||
\(308\) | 28.6234 | 1.63097 | ||||||||
\(309\) | 2.72349 | 0.154934 | ||||||||
\(310\) | 17.3939 | 0.987908 | ||||||||
\(311\) | −26.9813 | −1.52997 | −0.764984 | − | 0.644049i | \(-0.777253\pi\) | ||||
−0.764984 | + | 0.644049i | \(0.777253\pi\) | |||||||
\(312\) | 4.92785 | 0.278984 | ||||||||
\(313\) | 19.3728 | 1.09502 | 0.547509 | − | 0.836800i | \(-0.315576\pi\) | ||||
0.547509 | + | 0.836800i | \(0.315576\pi\) | |||||||
\(314\) | −0.0524637 | −0.00296070 | ||||||||
\(315\) | 7.31089 | 0.411922 | ||||||||
\(316\) | 75.5353 | 4.24919 | ||||||||
\(317\) | −9.00074 | −0.505532 | −0.252766 | − | 0.967527i | \(-0.581340\pi\) | ||||
−0.252766 | + | 0.967527i | \(0.581340\pi\) | |||||||
\(318\) | 19.8557 | 1.11345 | ||||||||
\(319\) | −8.98990 | −0.503338 | ||||||||
\(320\) | −6.29265 | −0.351770 | ||||||||
\(321\) | −9.99726 | −0.557992 | ||||||||
\(322\) | −66.7589 | −3.72033 | ||||||||
\(323\) | −23.5874 | −1.31244 | ||||||||
\(324\) | 23.5581 | 1.30878 | ||||||||
\(325\) | 3.90302 | 0.216501 | ||||||||
\(326\) | −47.6187 | −2.63736 | ||||||||
\(327\) | −13.1162 | −0.725328 | ||||||||
\(328\) | 42.6955 | 2.35746 | ||||||||
\(329\) | −22.9989 | −1.26797 | ||||||||
\(330\) | 4.08434 | 0.224836 | ||||||||
\(331\) | 27.5757 | 1.51570 | 0.757849 | − | 0.652430i | \(-0.226250\pi\) | ||||
0.757849 | + | 0.652430i | \(0.226250\pi\) | |||||||
\(332\) | −50.5966 | −2.77685 | ||||||||
\(333\) | 16.3561 | 0.896309 | ||||||||
\(334\) | 45.0638 | 2.46578 | ||||||||
\(335\) | 4.34988 | 0.237659 | ||||||||
\(336\) | 17.2974 | 0.943651 | ||||||||
\(337\) | −31.1307 | −1.69580 | −0.847898 | − | 0.530159i | \(-0.822132\pi\) | ||||
−0.847898 | + | 0.530159i | \(0.822132\pi\) | |||||||
\(338\) | −2.59872 | −0.141352 | ||||||||
\(339\) | −1.96586 | −0.106771 | ||||||||
\(340\) | 14.8683 | 0.806348 | ||||||||
\(341\) | 13.9241 | 0.754033 | ||||||||
\(342\) | 51.8387 | 2.80312 | ||||||||
\(343\) | −17.5824 | −0.949360 | ||||||||
\(344\) | 49.9604 | 2.69368 | ||||||||
\(345\) | −6.70487 | −0.360978 | ||||||||
\(346\) | −50.4226 | −2.71073 | ||||||||
\(347\) | −29.6154 | −1.58984 | −0.794920 | − | 0.606715i | \(-0.792487\pi\) | ||||
−0.794920 | + | 0.606715i | \(0.792487\pi\) | |||||||
\(348\) | −13.5071 | −0.724058 | ||||||||
\(349\) | −28.9624 | −1.55032 | −0.775162 | − | 0.631762i | \(-0.782332\pi\) | ||||
−0.775162 | + | 0.631762i | \(0.782332\pi\) | |||||||
\(350\) | 28.0320 | 1.49838 | ||||||||
\(351\) | 3.80559 | 0.203127 | ||||||||
\(352\) | −20.2761 | −1.08072 | ||||||||
\(353\) | −22.3910 | −1.19175 | −0.595877 | − | 0.803075i | \(-0.703196\pi\) | ||||
−0.595877 | + | 0.803075i | \(0.703196\pi\) | |||||||
\(354\) | −9.20464 | −0.489221 | ||||||||
\(355\) | 1.47150 | 0.0780989 | ||||||||
\(356\) | −36.3897 | −1.92865 | ||||||||
\(357\) | −5.68452 | −0.300857 | ||||||||
\(358\) | 49.0476 | 2.59225 | ||||||||
\(359\) | 1.15725 | 0.0610772 | 0.0305386 | − | 0.999534i | \(-0.490278\pi\) | ||||
0.0305386 | + | 0.999534i | \(0.490278\pi\) | |||||||
\(360\) | −18.9277 | −0.997578 | ||||||||
\(361\) | 43.3782 | 2.28306 | ||||||||
\(362\) | 23.8555 | 1.25382 | ||||||||
\(363\) | −4.30622 | −0.226018 | ||||||||
\(364\) | −13.1369 | −0.688562 | ||||||||
\(365\) | 9.36978 | 0.490437 | ||||||||
\(366\) | −17.3051 | −0.904552 | ||||||||
\(367\) | 20.8216 | 1.08688 | 0.543438 | − | 0.839449i | \(-0.317122\pi\) | ||||
0.543438 | + | 0.839449i | \(0.317122\pi\) | |||||||
\(368\) | 84.4708 | 4.40335 | ||||||||
\(369\) | 15.0709 | 0.784560 | ||||||||
\(370\) | −17.6262 | −0.916344 | ||||||||
\(371\) | −30.6607 | −1.59183 | ||||||||
\(372\) | 20.9206 | 1.08468 | ||||||||
\(373\) | −22.7516 | −1.17803 | −0.589017 | − | 0.808121i | \(-0.700485\pi\) | ||||
−0.589017 | + | 0.808121i | \(0.700485\pi\) | |||||||
\(374\) | 16.9103 | 0.874411 | ||||||||
\(375\) | 6.42203 | 0.331632 | ||||||||
\(376\) | 59.5436 | 3.07072 | ||||||||
\(377\) | 4.12598 | 0.212499 | ||||||||
\(378\) | 27.3322 | 1.40582 | ||||||||
\(379\) | −10.4205 | −0.535264 | −0.267632 | − | 0.963521i | \(-0.586241\pi\) | ||||
−0.267632 | + | 0.963521i | \(0.586241\pi\) | |||||||
\(380\) | −39.3201 | −2.01708 | ||||||||
\(381\) | 4.32908 | 0.221785 | ||||||||
\(382\) | −3.21425 | −0.164455 | ||||||||
\(383\) | −19.8913 | −1.01640 | −0.508199 | − | 0.861240i | \(-0.669689\pi\) | ||||
−0.508199 | + | 0.861240i | \(0.669689\pi\) | |||||||
\(384\) | 2.06506 | 0.105382 | ||||||||
\(385\) | −6.30696 | −0.321433 | ||||||||
\(386\) | −43.9560 | −2.23730 | ||||||||
\(387\) | 17.6353 | 0.896453 | ||||||||
\(388\) | 27.5788 | 1.40010 | ||||||||
\(389\) | 8.25398 | 0.418493 | 0.209247 | − | 0.977863i | \(-0.432899\pi\) | ||||
0.209247 | + | 0.977863i | \(0.432899\pi\) | |||||||
\(390\) | −1.87454 | −0.0949209 | ||||||||
\(391\) | −27.7600 | −1.40388 | ||||||||
\(392\) | −4.56599 | −0.230617 | ||||||||
\(393\) | 7.76484 | 0.391684 | ||||||||
\(394\) | 55.8192 | 2.81213 | ||||||||
\(395\) | −16.6437 | −0.837433 | ||||||||
\(396\) | −26.1581 | −1.31449 | ||||||||
\(397\) | −30.0695 | −1.50914 | −0.754571 | − | 0.656218i | \(-0.772155\pi\) | ||||
−0.754571 | + | 0.656218i | \(0.772155\pi\) | |||||||
\(398\) | 42.4336 | 2.12701 | ||||||||
\(399\) | 15.0330 | 0.752592 | ||||||||
\(400\) | −35.4693 | −1.77346 | ||||||||
\(401\) | −5.42244 | −0.270783 | −0.135392 | − | 0.990792i | \(-0.543229\pi\) | ||||
−0.135392 | + | 0.990792i | \(0.543229\pi\) | |||||||
\(402\) | 7.43317 | 0.370733 | ||||||||
\(403\) | −6.39056 | −0.318337 | ||||||||
\(404\) | 5.14870 | 0.256158 | ||||||||
\(405\) | −5.19085 | −0.257935 | ||||||||
\(406\) | 29.6333 | 1.47068 | ||||||||
\(407\) | −14.1101 | −0.699411 | ||||||||
\(408\) | 14.7171 | 0.728603 | ||||||||
\(409\) | 36.7863 | 1.81896 | 0.909482 | − | 0.415744i | \(-0.136479\pi\) | ||||
0.909482 | + | 0.415744i | \(0.136479\pi\) | |||||||
\(410\) | −16.2412 | −0.802098 | ||||||||
\(411\) | 6.32924 | 0.312198 | ||||||||
\(412\) | 18.7970 | 0.926063 | ||||||||
\(413\) | 14.2136 | 0.699407 | ||||||||
\(414\) | 61.0089 | 2.99843 | ||||||||
\(415\) | 11.1486 | 0.547263 | ||||||||
\(416\) | 9.30587 | 0.456258 | ||||||||
\(417\) | 2.47359 | 0.121132 | ||||||||
\(418\) | −44.7202 | −2.18734 | ||||||||
\(419\) | 13.9172 | 0.679899 | 0.339950 | − | 0.940444i | \(-0.389590\pi\) | ||||
0.339950 | + | 0.940444i | \(0.389590\pi\) | |||||||
\(420\) | −9.47607 | −0.462385 | ||||||||
\(421\) | −8.08024 | −0.393807 | −0.196903 | − | 0.980423i | \(-0.563089\pi\) | ||||
−0.196903 | + | 0.980423i | \(0.563089\pi\) | |||||||
\(422\) | −30.7663 | −1.49768 | ||||||||
\(423\) | 21.0180 | 1.02193 | ||||||||
\(424\) | 79.3798 | 3.85502 | ||||||||
\(425\) | 11.6564 | 0.565419 | ||||||||
\(426\) | 2.51453 | 0.121829 | ||||||||
\(427\) | 26.7222 | 1.29318 | ||||||||
\(428\) | −68.9993 | −3.33521 | ||||||||
\(429\) | −1.50060 | −0.0724495 | ||||||||
\(430\) | −19.0048 | −0.916492 | ||||||||
\(431\) | 15.1622 | 0.730340 | 0.365170 | − | 0.930941i | \(-0.381011\pi\) | ||||
0.365170 | + | 0.930941i | \(0.381011\pi\) | |||||||
\(432\) | −34.5838 | −1.66391 | ||||||||
\(433\) | 7.09373 | 0.340903 | 0.170451 | − | 0.985366i | \(-0.445477\pi\) | ||||
0.170451 | + | 0.985366i | \(0.445477\pi\) | |||||||
\(434\) | −45.8979 | −2.20317 | ||||||||
\(435\) | 2.97619 | 0.142698 | ||||||||
\(436\) | −90.5257 | −4.33540 | ||||||||
\(437\) | 73.4128 | 3.51181 | ||||||||
\(438\) | 16.0113 | 0.765050 | ||||||||
\(439\) | 40.8912 | 1.95163 | 0.975815 | − | 0.218597i | \(-0.0701479\pi\) | ||||
0.975815 | + | 0.218597i | \(0.0701479\pi\) | |||||||
\(440\) | 16.3286 | 0.778434 | ||||||||
\(441\) | −1.61173 | −0.0767489 | ||||||||
\(442\) | −7.76110 | −0.369158 | ||||||||
\(443\) | 17.6417 | 0.838180 | 0.419090 | − | 0.907945i | \(-0.362349\pi\) | ||||
0.419090 | + | 0.907945i | \(0.362349\pi\) | |||||||
\(444\) | −21.2001 | −1.00611 | ||||||||
\(445\) | 8.01821 | 0.380100 | ||||||||
\(446\) | 34.3248 | 1.62533 | ||||||||
\(447\) | −6.27049 | −0.296584 | ||||||||
\(448\) | 16.6046 | 0.784494 | ||||||||
\(449\) | −4.66444 | −0.220129 | −0.110064 | − | 0.993924i | \(-0.535106\pi\) | ||||
−0.110064 | + | 0.993924i | \(0.535106\pi\) | |||||||
\(450\) | −25.6176 | −1.20763 | ||||||||
\(451\) | −13.0014 | −0.612211 | ||||||||
\(452\) | −13.5680 | −0.638185 | ||||||||
\(453\) | −0.650765 | −0.0305756 | ||||||||
\(454\) | −38.9215 | −1.82667 | ||||||||
\(455\) | 2.89462 | 0.135702 | ||||||||
\(456\) | −38.9201 | −1.82260 | ||||||||
\(457\) | 40.8629 | 1.91149 | 0.955743 | − | 0.294203i | \(-0.0950542\pi\) | ||||
0.955743 | + | 0.294203i | \(0.0950542\pi\) | |||||||
\(458\) | 1.77942 | 0.0831466 | ||||||||
\(459\) | 11.3654 | 0.530492 | ||||||||
\(460\) | −46.2758 | −2.15762 | ||||||||
\(461\) | 17.0262 | 0.792991 | 0.396495 | − | 0.918037i | \(-0.370226\pi\) | ||||
0.396495 | + | 0.918037i | \(0.370226\pi\) | |||||||
\(462\) | −10.7775 | −0.501414 | ||||||||
\(463\) | −37.5228 | −1.74383 | −0.871917 | − | 0.489654i | \(-0.837123\pi\) | ||||
−0.871917 | + | 0.489654i | \(0.837123\pi\) | |||||||
\(464\) | −37.4954 | −1.74068 | ||||||||
\(465\) | −4.60971 | −0.213770 | ||||||||
\(466\) | 16.2355 | 0.752097 | ||||||||
\(467\) | −26.7958 | −1.23996 | −0.619980 | − | 0.784618i | \(-0.712859\pi\) | ||||
−0.619980 | + | 0.784618i | \(0.712859\pi\) | |||||||
\(468\) | 12.0054 | 0.554952 | ||||||||
\(469\) | −11.4782 | −0.530012 | ||||||||
\(470\) | −22.6502 | −1.04477 | ||||||||
\(471\) | 0.0139039 | 0.000640656 0 | ||||||||
\(472\) | −36.7987 | −1.69380 | ||||||||
\(473\) | −15.2136 | −0.699523 | ||||||||
\(474\) | −28.4411 | −1.30634 | ||||||||
\(475\) | −30.8260 | −1.41440 | ||||||||
\(476\) | −39.2335 | −1.79827 | ||||||||
\(477\) | 28.0199 | 1.28294 | ||||||||
\(478\) | 32.1975 | 1.47268 | ||||||||
\(479\) | −30.7475 | −1.40489 | −0.702445 | − | 0.711738i | \(-0.747908\pi\) | ||||
−0.702445 | + | 0.711738i | \(0.747908\pi\) | |||||||
\(480\) | 6.71261 | 0.306387 | ||||||||
\(481\) | 6.47592 | 0.295277 | ||||||||
\(482\) | 50.8303 | 2.31526 | ||||||||
\(483\) | 17.6923 | 0.805029 | ||||||||
\(484\) | −29.7208 | −1.35094 | ||||||||
\(485\) | −6.07680 | −0.275933 | ||||||||
\(486\) | −38.5392 | −1.74817 | ||||||||
\(487\) | 16.4350 | 0.744743 | 0.372371 | − | 0.928084i | \(-0.378545\pi\) | ||||
0.372371 | + | 0.928084i | \(0.378545\pi\) | |||||||
\(488\) | −69.1830 | −3.13177 | ||||||||
\(489\) | 12.6198 | 0.570689 | ||||||||
\(490\) | 1.73689 | 0.0784646 | ||||||||
\(491\) | 35.1988 | 1.58850 | 0.794250 | − | 0.607592i | \(-0.207864\pi\) | ||||
0.794250 | + | 0.607592i | \(0.207864\pi\) | |||||||
\(492\) | −19.5343 | −0.880672 | ||||||||
\(493\) | 12.3223 | 0.554967 | ||||||||
\(494\) | 20.5247 | 0.923448 | ||||||||
\(495\) | 5.76375 | 0.259061 | ||||||||
\(496\) | 58.0752 | 2.60765 | ||||||||
\(497\) | −3.88288 | −0.174171 | ||||||||
\(498\) | 19.0510 | 0.853694 | ||||||||
\(499\) | −17.4592 | −0.781582 | −0.390791 | − | 0.920479i | \(-0.627798\pi\) | ||||
−0.390791 | + | 0.920479i | \(0.627798\pi\) | |||||||
\(500\) | 44.3237 | 1.98222 | ||||||||
\(501\) | −11.9427 | −0.533563 | ||||||||
\(502\) | −53.5737 | −2.39111 | ||||||||
\(503\) | −20.8128 | −0.927998 | −0.463999 | − | 0.885836i | \(-0.653586\pi\) | ||||
−0.463999 | + | 0.885836i | \(0.653586\pi\) | |||||||
\(504\) | 49.9451 | 2.22473 | ||||||||
\(505\) | −1.13448 | −0.0504836 | ||||||||
\(506\) | −52.6312 | −2.33974 | ||||||||
\(507\) | 0.688709 | 0.0305867 | ||||||||
\(508\) | 29.8785 | 1.32565 | ||||||||
\(509\) | −24.1331 | −1.06968 | −0.534840 | − | 0.844953i | \(-0.679628\pi\) | ||||
−0.534840 | + | 0.844953i | \(0.679628\pi\) | |||||||
\(510\) | −5.59832 | −0.247898 | ||||||||
\(511\) | −24.7243 | −1.09374 | ||||||||
\(512\) | 45.4792 | 2.00992 | ||||||||
\(513\) | −30.0565 | −1.32703 | ||||||||
\(514\) | −46.5727 | −2.05423 | ||||||||
\(515\) | −4.14179 | −0.182509 | ||||||||
\(516\) | −22.8581 | −1.00627 | ||||||||
\(517\) | −18.1318 | −0.797437 | ||||||||
\(518\) | 46.5109 | 2.04357 | ||||||||
\(519\) | 13.3629 | 0.586567 | ||||||||
\(520\) | −7.49410 | −0.328638 | ||||||||
\(521\) | 24.1945 | 1.05998 | 0.529989 | − | 0.848004i | \(-0.322196\pi\) | ||||
0.529989 | + | 0.848004i | \(0.322196\pi\) | |||||||
\(522\) | −27.0810 | −1.18530 | ||||||||
\(523\) | 9.60899 | 0.420172 | 0.210086 | − | 0.977683i | \(-0.432626\pi\) | ||||
0.210086 | + | 0.977683i | \(0.432626\pi\) | |||||||
\(524\) | 53.5915 | 2.34116 | ||||||||
\(525\) | −7.42901 | −0.324229 | ||||||||
\(526\) | 62.9460 | 2.74457 | ||||||||
\(527\) | −19.0855 | −0.831376 | ||||||||
\(528\) | 13.6369 | 0.593470 | ||||||||
\(529\) | 63.3995 | 2.75650 | ||||||||
\(530\) | −30.1958 | −1.31162 | ||||||||
\(531\) | −12.9894 | −0.563693 | ||||||||
\(532\) | 103.755 | 4.49836 | ||||||||
\(533\) | 5.96707 | 0.258462 | ||||||||
\(534\) | 13.7017 | 0.592931 | ||||||||
\(535\) | 15.2035 | 0.657304 | ||||||||
\(536\) | 29.7166 | 1.28356 | ||||||||
\(537\) | −12.9985 | −0.560928 | ||||||||
\(538\) | −29.1098 | −1.25501 | ||||||||
\(539\) | 1.39041 | 0.0598890 | ||||||||
\(540\) | 18.9461 | 0.815311 | ||||||||
\(541\) | −19.1507 | −0.823353 | −0.411676 | − | 0.911330i | \(-0.635057\pi\) | ||||
−0.411676 | + | 0.911330i | \(0.635057\pi\) | |||||||
\(542\) | 11.2701 | 0.484091 | ||||||||
\(543\) | −6.32215 | −0.271309 | ||||||||
\(544\) | 27.7921 | 1.19157 | ||||||||
\(545\) | 19.9467 | 0.854422 | ||||||||
\(546\) | 4.94640 | 0.211686 | ||||||||
\(547\) | −25.7697 | −1.10183 | −0.550916 | − | 0.834561i | \(-0.685721\pi\) | ||||
−0.550916 | + | 0.834561i | \(0.685721\pi\) | |||||||
\(548\) | 43.6833 | 1.86606 | ||||||||
\(549\) | −24.4206 | −1.04225 | ||||||||
\(550\) | 22.0998 | 0.942340 | ||||||||
\(551\) | −32.5869 | −1.38825 | ||||||||
\(552\) | −45.8050 | −1.94959 | ||||||||
\(553\) | 43.9181 | 1.86759 | ||||||||
\(554\) | −16.2604 | −0.690838 | ||||||||
\(555\) | 4.67128 | 0.198285 | ||||||||
\(556\) | 17.0723 | 0.724027 | ||||||||
\(557\) | 43.2228 | 1.83141 | 0.915704 | − | 0.401853i | \(-0.131634\pi\) | ||||
0.915704 | + | 0.401853i | \(0.131634\pi\) | |||||||
\(558\) | 41.9447 | 1.77566 | ||||||||
\(559\) | 6.98240 | 0.295324 | ||||||||
\(560\) | −26.3053 | −1.11160 | ||||||||
\(561\) | −4.48155 | −0.189211 | ||||||||
\(562\) | 50.6316 | 2.13576 | ||||||||
\(563\) | 16.5646 | 0.698116 | 0.349058 | − | 0.937101i | \(-0.386502\pi\) | ||||
0.349058 | + | 0.937101i | \(0.386502\pi\) | |||||||
\(564\) | −27.2427 | −1.14712 | ||||||||
\(565\) | 2.98961 | 0.125774 | ||||||||
\(566\) | −6.31934 | −0.265622 | ||||||||
\(567\) | 13.6972 | 0.575230 | ||||||||
\(568\) | 10.0527 | 0.421801 | ||||||||
\(569\) | 11.4237 | 0.478904 | 0.239452 | − | 0.970908i | \(-0.423032\pi\) | ||||
0.239452 | + | 0.970908i | \(0.423032\pi\) | |||||||
\(570\) | 14.8051 | 0.620116 | ||||||||
\(571\) | −7.28710 | −0.304956 | −0.152478 | − | 0.988307i | \(-0.548725\pi\) | ||||
−0.152478 | + | 0.988307i | \(0.548725\pi\) | |||||||
\(572\) | −10.3569 | −0.433042 | ||||||||
\(573\) | 0.851836 | 0.0355860 | ||||||||
\(574\) | 42.8563 | 1.78879 | ||||||||
\(575\) | −36.2791 | −1.51294 | ||||||||
\(576\) | −15.1745 | −0.632269 | ||||||||
\(577\) | 9.90803 | 0.412477 | 0.206238 | − | 0.978502i | \(-0.433878\pi\) | ||||
0.206238 | + | 0.978502i | \(0.433878\pi\) | |||||||
\(578\) | 20.9997 | 0.873470 | ||||||||
\(579\) | 11.6492 | 0.484122 | ||||||||
\(580\) | 20.5412 | 0.852926 | ||||||||
\(581\) | −29.4181 | −1.22047 | ||||||||
\(582\) | −10.3842 | −0.430438 | ||||||||
\(583\) | −24.1722 | −1.00111 | ||||||||
\(584\) | 64.0106 | 2.64878 | ||||||||
\(585\) | −2.64531 | −0.109370 | ||||||||
\(586\) | −59.8010 | −2.47036 | ||||||||
\(587\) | 24.8505 | 1.02569 | 0.512845 | − | 0.858481i | \(-0.328591\pi\) | ||||
0.512845 | + | 0.858481i | \(0.328591\pi\) | |||||||
\(588\) | 2.08905 | 0.0861511 | ||||||||
\(589\) | 50.4726 | 2.07969 | ||||||||
\(590\) | 13.9981 | 0.576293 | ||||||||
\(591\) | −14.7931 | −0.608508 | ||||||||
\(592\) | −58.8508 | −2.41875 | ||||||||
\(593\) | −38.7850 | −1.59271 | −0.796354 | − | 0.604830i | \(-0.793241\pi\) | ||||
−0.796354 | + | 0.604830i | \(0.793241\pi\) | |||||||
\(594\) | 21.5481 | 0.884130 | ||||||||
\(595\) | 8.64482 | 0.354403 | ||||||||
\(596\) | −43.2778 | −1.77273 | ||||||||
\(597\) | −11.2457 | −0.460256 | ||||||||
\(598\) | 24.1555 | 0.987790 | ||||||||
\(599\) | 17.0945 | 0.698462 | 0.349231 | − | 0.937037i | \(-0.386443\pi\) | ||||
0.349231 | + | 0.937037i | \(0.386443\pi\) | |||||||
\(600\) | 19.2335 | 0.785205 | ||||||||
\(601\) | −21.2362 | −0.866244 | −0.433122 | − | 0.901335i | \(-0.642588\pi\) | ||||
−0.433122 | + | 0.901335i | \(0.642588\pi\) | |||||||
\(602\) | 50.1485 | 2.04390 | ||||||||
\(603\) | 10.4895 | 0.427167 | ||||||||
\(604\) | −4.49147 | −0.182755 | ||||||||
\(605\) | 6.54876 | 0.266245 | ||||||||
\(606\) | −1.93862 | −0.0787512 | ||||||||
\(607\) | −48.5361 | −1.97002 | −0.985010 | − | 0.172498i | \(-0.944816\pi\) | ||||
−0.985010 | + | 0.172498i | \(0.944816\pi\) | |||||||
\(608\) | −73.4976 | −2.98072 | ||||||||
\(609\) | −7.85338 | −0.318235 | ||||||||
\(610\) | 26.3170 | 1.06554 | ||||||||
\(611\) | 8.32173 | 0.336661 | ||||||||
\(612\) | 35.8544 | 1.44933 | ||||||||
\(613\) | −4.34559 | −0.175517 | −0.0877584 | − | 0.996142i | \(-0.527970\pi\) | ||||
−0.0877584 | + | 0.996142i | \(0.527970\pi\) | |||||||
\(614\) | −63.3972 | −2.55850 | ||||||||
\(615\) | 4.30423 | 0.173563 | ||||||||
\(616\) | −43.0867 | −1.73601 | ||||||||
\(617\) | −47.3895 | −1.90783 | −0.953914 | − | 0.300080i | \(-0.902986\pi\) | ||||
−0.953914 | + | 0.300080i | \(0.902986\pi\) | |||||||
\(618\) | −7.07758 | −0.284702 | ||||||||
\(619\) | −1.00000 | −0.0401934 | ||||||||
\(620\) | −31.8154 | −1.27774 | ||||||||
\(621\) | −35.3734 | −1.41949 | ||||||||
\(622\) | 70.1168 | 2.81143 | ||||||||
\(623\) | −21.1579 | −0.847674 | ||||||||
\(624\) | −6.25875 | −0.250550 | ||||||||
\(625\) | 9.74872 | 0.389949 | ||||||||
\(626\) | −50.3446 | −2.01217 | ||||||||
\(627\) | 11.8517 | 0.473311 | ||||||||
\(628\) | 0.0959620 | 0.00382930 | ||||||||
\(629\) | 19.3404 | 0.771152 | ||||||||
\(630\) | −18.9990 | −0.756937 | ||||||||
\(631\) | 10.0256 | 0.399113 | 0.199557 | − | 0.979886i | \(-0.436050\pi\) | ||||
0.199557 | + | 0.979886i | \(0.436050\pi\) | |||||||
\(632\) | −113.703 | −4.52286 | ||||||||
\(633\) | 8.15364 | 0.324078 | ||||||||
\(634\) | 23.3904 | 0.928952 | ||||||||
\(635\) | −6.58352 | −0.261259 | ||||||||
\(636\) | −36.3182 | −1.44011 | ||||||||
\(637\) | −0.638136 | −0.0252839 | ||||||||
\(638\) | 23.3622 | 0.924920 | ||||||||
\(639\) | 3.54845 | 0.140374 | ||||||||
\(640\) | −3.14047 | −0.124138 | ||||||||
\(641\) | −27.2086 | −1.07468 | −0.537338 | − | 0.843367i | \(-0.680570\pi\) | ||||
−0.537338 | + | 0.843367i | \(0.680570\pi\) | |||||||
\(642\) | 25.9801 | 1.02535 | ||||||||
\(643\) | −32.6845 | −1.28895 | −0.644476 | − | 0.764625i | \(-0.722924\pi\) | ||||
−0.644476 | + | 0.764625i | \(0.722924\pi\) | |||||||
\(644\) | 122.109 | 4.81178 | ||||||||
\(645\) | 5.03662 | 0.198317 | ||||||||
\(646\) | 61.2971 | 2.41170 | ||||||||
\(647\) | 7.71902 | 0.303466 | 0.151733 | − | 0.988422i | \(-0.451515\pi\) | ||||
0.151733 | + | 0.988422i | \(0.451515\pi\) | |||||||
\(648\) | −35.4618 | −1.39307 | ||||||||
\(649\) | 11.2057 | 0.439863 | ||||||||
\(650\) | −10.1429 | −0.397836 | ||||||||
\(651\) | 12.1638 | 0.476736 | ||||||||
\(652\) | 87.0999 | 3.41110 | ||||||||
\(653\) | 8.19855 | 0.320834 | 0.160417 | − | 0.987049i | \(-0.448716\pi\) | ||||
0.160417 | + | 0.987049i | \(0.448716\pi\) | |||||||
\(654\) | 34.0854 | 1.33284 | ||||||||
\(655\) | −11.8085 | −0.461396 | ||||||||
\(656\) | −54.2266 | −2.11719 | ||||||||
\(657\) | 22.5948 | 0.881508 | ||||||||
\(658\) | 59.7677 | 2.32999 | ||||||||
\(659\) | −1.86454 | −0.0726322 | −0.0363161 | − | 0.999340i | \(-0.511562\pi\) | ||||
−0.0363161 | + | 0.999340i | \(0.511562\pi\) | |||||||
\(660\) | −7.47072 | −0.290797 | ||||||||
\(661\) | −18.7343 | −0.728680 | −0.364340 | − | 0.931266i | \(-0.618705\pi\) | ||||
−0.364340 | + | 0.931266i | \(0.618705\pi\) | |||||||
\(662\) | −71.6616 | −2.78521 | ||||||||
\(663\) | 2.05684 | 0.0798809 | ||||||||
\(664\) | 76.1627 | 2.95569 | ||||||||
\(665\) | −22.8617 | −0.886539 | ||||||||
\(666\) | −42.5049 | −1.64703 | ||||||||
\(667\) | −38.3515 | −1.48498 | ||||||||
\(668\) | −82.4268 | −3.18919 | ||||||||
\(669\) | −9.09671 | −0.351699 | ||||||||
\(670\) | −11.3041 | −0.436716 | ||||||||
\(671\) | 21.0672 | 0.813290 | ||||||||
\(672\) | −17.7128 | −0.683285 | ||||||||
\(673\) | −11.3377 | −0.437036 | −0.218518 | − | 0.975833i | \(-0.570122\pi\) | ||||
−0.218518 | + | 0.975833i | \(0.570122\pi\) | |||||||
\(674\) | 80.8999 | 3.11615 | ||||||||
\(675\) | 14.8533 | 0.571704 | ||||||||
\(676\) | 4.75335 | 0.182821 | ||||||||
\(677\) | −1.04186 | −0.0400418 | −0.0200209 | − | 0.999800i | \(-0.506373\pi\) | ||||
−0.0200209 | + | 0.999800i | \(0.506373\pi\) | |||||||
\(678\) | 5.10872 | 0.196199 | ||||||||
\(679\) | 16.0350 | 0.615368 | ||||||||
\(680\) | −22.3812 | −0.858280 | ||||||||
\(681\) | 10.3149 | 0.395268 | ||||||||
\(682\) | −36.1849 | −1.38559 | ||||||||
\(683\) | 10.1832 | 0.389647 | 0.194824 | − | 0.980838i | \(-0.437587\pi\) | ||||
0.194824 | + | 0.980838i | \(0.437587\pi\) | |||||||
\(684\) | −94.8188 | −3.62549 | ||||||||
\(685\) | −9.62530 | −0.367764 | ||||||||
\(686\) | 45.6917 | 1.74452 | ||||||||
\(687\) | −0.471578 | −0.0179918 | ||||||||
\(688\) | −63.4536 | −2.41914 | ||||||||
\(689\) | 11.0940 | 0.422648 | ||||||||
\(690\) | 17.4241 | 0.663323 | ||||||||
\(691\) | −25.5194 | −0.970805 | −0.485402 | − | 0.874291i | \(-0.661327\pi\) | ||||
−0.485402 | + | 0.874291i | \(0.661327\pi\) | |||||||
\(692\) | 92.2285 | 3.50600 | ||||||||
\(693\) | −15.2090 | −0.577741 | ||||||||
\(694\) | 76.9622 | 2.92145 | ||||||||
\(695\) | −3.76176 | −0.142692 | ||||||||
\(696\) | 20.3322 | 0.770689 | ||||||||
\(697\) | 17.8207 | 0.675007 | ||||||||
\(698\) | 75.2653 | 2.84883 | ||||||||
\(699\) | −4.30272 | −0.162744 | ||||||||
\(700\) | −51.2737 | −1.93796 | ||||||||
\(701\) | 40.8717 | 1.54370 | 0.771851 | − | 0.635803i | \(-0.219331\pi\) | ||||
0.771851 | + | 0.635803i | \(0.219331\pi\) | |||||||
\(702\) | −9.88966 | −0.373261 | ||||||||
\(703\) | −51.1467 | −1.92903 | ||||||||
\(704\) | 13.0907 | 0.493374 | ||||||||
\(705\) | 6.00272 | 0.226075 | ||||||||
\(706\) | 58.1881 | 2.18994 | ||||||||
\(707\) | 2.99359 | 0.112585 | ||||||||
\(708\) | 16.8363 | 0.632748 | ||||||||
\(709\) | −27.5022 | −1.03287 | −0.516433 | − | 0.856328i | \(-0.672740\pi\) | ||||
−0.516433 | + | 0.856328i | \(0.672740\pi\) | |||||||
\(710\) | −3.82401 | −0.143512 | ||||||||
\(711\) | −40.1355 | −1.50520 | ||||||||
\(712\) | 54.7773 | 2.05286 | ||||||||
\(713\) | 59.4011 | 2.22459 | ||||||||
\(714\) | 14.7725 | 0.552846 | ||||||||
\(715\) | 2.28206 | 0.0853441 | ||||||||
\(716\) | −89.7136 | −3.35275 | ||||||||
\(717\) | −8.53294 | −0.318669 | ||||||||
\(718\) | −3.00736 | −0.112234 | ||||||||
\(719\) | −27.9410 | −1.04202 | −0.521012 | − | 0.853549i | \(-0.674445\pi\) | ||||
−0.521012 | + | 0.853549i | \(0.674445\pi\) | |||||||
\(720\) | 24.0396 | 0.895905 | ||||||||
\(721\) | 10.9291 | 0.407019 | ||||||||
\(722\) | −112.728 | −4.19529 | ||||||||
\(723\) | −13.4710 | −0.500991 | ||||||||
\(724\) | −43.6343 | −1.62166 | ||||||||
\(725\) | 16.1038 | 0.598080 | ||||||||
\(726\) | 11.1907 | 0.415325 | ||||||||
\(727\) | 30.5808 | 1.13418 | 0.567090 | − | 0.823656i | \(-0.308069\pi\) | ||||
0.567090 | + | 0.823656i | \(0.308069\pi\) | |||||||
\(728\) | 19.7749 | 0.732908 | ||||||||
\(729\) | −4.65467 | −0.172395 | ||||||||
\(730\) | −24.3494 | −0.901214 | ||||||||
\(731\) | 20.8530 | 0.771276 | ||||||||
\(732\) | 31.6530 | 1.16993 | ||||||||
\(733\) | 26.1846 | 0.967150 | 0.483575 | − | 0.875303i | \(-0.339338\pi\) | ||||
0.483575 | + | 0.875303i | \(0.339338\pi\) | |||||||
\(734\) | −54.1094 | −1.99722 | ||||||||
\(735\) | −0.460307 | −0.0169787 | ||||||||
\(736\) | −86.4993 | −3.18841 | ||||||||
\(737\) | −9.04912 | −0.333329 | ||||||||
\(738\) | −39.1651 | −1.44169 | ||||||||
\(739\) | −39.5814 | −1.45603 | −0.728013 | − | 0.685563i | \(-0.759556\pi\) | ||||
−0.728013 | + | 0.685563i | \(0.759556\pi\) | |||||||
\(740\) | 32.2404 | 1.18518 | ||||||||
\(741\) | −5.43942 | −0.199822 | ||||||||
\(742\) | 79.6787 | 2.92510 | ||||||||
\(743\) | 11.4306 | 0.419349 | 0.209675 | − | 0.977771i | \(-0.432759\pi\) | ||||
0.209675 | + | 0.977771i | \(0.432759\pi\) | |||||||
\(744\) | −31.4917 | −1.15454 | ||||||||
\(745\) | 9.53594 | 0.349370 | ||||||||
\(746\) | 59.1251 | 2.16472 | ||||||||
\(747\) | 26.8843 | 0.983647 | ||||||||
\(748\) | −30.9308 | −1.13094 | ||||||||
\(749\) | −40.1179 | −1.46588 | ||||||||
\(750\) | −16.6891 | −0.609398 | ||||||||
\(751\) | 32.6042 | 1.18974 | 0.594872 | − | 0.803821i | \(-0.297203\pi\) | ||||
0.594872 | + | 0.803821i | \(0.297203\pi\) | |||||||
\(752\) | −75.6249 | −2.75776 | ||||||||
\(753\) | 14.1980 | 0.517405 | ||||||||
\(754\) | −10.7223 | −0.390482 | ||||||||
\(755\) | 0.989662 | 0.0360175 | ||||||||
\(756\) | −49.9937 | −1.81825 | ||||||||
\(757\) | −43.1269 | −1.56747 | −0.783737 | − | 0.621093i | \(-0.786689\pi\) | ||||
−0.783737 | + | 0.621093i | \(0.786689\pi\) | |||||||
\(758\) | 27.0799 | 0.983586 | ||||||||
\(759\) | 13.9483 | 0.506289 | ||||||||
\(760\) | 59.1883 | 2.14699 | ||||||||
\(761\) | −38.3672 | −1.39081 | −0.695405 | − | 0.718618i | \(-0.744775\pi\) | ||||
−0.695405 | + | 0.718618i | \(0.744775\pi\) | |||||||
\(762\) | −11.2501 | −0.407547 | ||||||||
\(763\) | −52.6339 | −1.90548 | ||||||||
\(764\) | 5.87922 | 0.212703 | ||||||||
\(765\) | −7.90024 | −0.285634 | ||||||||
\(766\) | 51.6920 | 1.86771 | ||||||||
\(767\) | −5.14294 | −0.185701 | ||||||||
\(768\) | −13.6421 | −0.492268 | ||||||||
\(769\) | −33.8874 | −1.22201 | −0.611006 | − | 0.791626i | \(-0.709235\pi\) | ||||
−0.611006 | + | 0.791626i | \(0.709235\pi\) | |||||||
\(770\) | 16.3900 | 0.590656 | ||||||||
\(771\) | 12.3426 | 0.444509 | ||||||||
\(772\) | 80.4004 | 2.89367 | ||||||||
\(773\) | −29.0798 | −1.04593 | −0.522963 | − | 0.852355i | \(-0.675174\pi\) | ||||
−0.522963 | + | 0.852355i | \(0.675174\pi\) | |||||||
\(774\) | −45.8292 | −1.64730 | ||||||||
\(775\) | −24.9425 | −0.895962 | ||||||||
\(776\) | −41.5143 | −1.49028 | ||||||||
\(777\) | −12.3263 | −0.442202 | ||||||||
\(778\) | −21.4498 | −0.769012 | ||||||||
\(779\) | −47.1278 | −1.68853 | ||||||||
\(780\) | 3.42874 | 0.122769 | ||||||||
\(781\) | −3.06118 | −0.109538 | ||||||||
\(782\) | 72.1405 | 2.57974 | ||||||||
\(783\) | 15.7018 | 0.561135 | ||||||||
\(784\) | 5.79915 | 0.207113 | ||||||||
\(785\) | −0.0211445 | −0.000754681 0 | ||||||||
\(786\) | −20.1786 | −0.719748 | ||||||||
\(787\) | −6.19685 | −0.220894 | −0.110447 | − | 0.993882i | \(-0.535228\pi\) | ||||
−0.110447 | + | 0.993882i | \(0.535228\pi\) | |||||||
\(788\) | −102.099 | −3.63714 | ||||||||
\(789\) | −16.6819 | −0.593890 | ||||||||
\(790\) | 43.2522 | 1.53884 | ||||||||
\(791\) | −7.88878 | −0.280493 | ||||||||
\(792\) | 39.3756 | 1.39915 | ||||||||
\(793\) | −9.66893 | −0.343354 | ||||||||
\(794\) | 78.1421 | 2.77316 | ||||||||
\(795\) | 8.00245 | 0.283818 | ||||||||
\(796\) | −77.6158 | −2.75102 | ||||||||
\(797\) | 31.0023 | 1.09816 | 0.549079 | − | 0.835771i | \(-0.314979\pi\) | ||||
0.549079 | + | 0.835771i | \(0.314979\pi\) | |||||||
\(798\) | −39.0666 | −1.38294 | ||||||||
\(799\) | 24.8529 | 0.879233 | ||||||||
\(800\) | 36.3210 | 1.28414 | ||||||||
\(801\) | 19.3356 | 0.683189 | ||||||||
\(802\) | 14.0914 | 0.497585 | ||||||||
\(803\) | −19.4921 | −0.687862 | ||||||||
\(804\) | −13.5961 | −0.479497 | ||||||||
\(805\) | −26.9059 | −0.948309 | ||||||||
\(806\) | 16.6073 | 0.584967 | ||||||||
\(807\) | 7.71463 | 0.271568 | ||||||||
\(808\) | −7.75031 | −0.272655 | ||||||||
\(809\) | 6.11111 | 0.214855 | 0.107428 | − | 0.994213i | \(-0.465739\pi\) | ||||
0.107428 | + | 0.994213i | \(0.465739\pi\) | |||||||
\(810\) | 13.4896 | 0.473975 | ||||||||
\(811\) | 22.4734 | 0.789147 | 0.394573 | − | 0.918864i | \(-0.370892\pi\) | ||||
0.394573 | + | 0.918864i | \(0.370892\pi\) | |||||||
\(812\) | −54.2026 | −1.90214 | ||||||||
\(813\) | −2.98678 | −0.104751 | ||||||||
\(814\) | 36.6682 | 1.28522 | ||||||||
\(815\) | −19.1918 | −0.672261 | ||||||||
\(816\) | −18.6918 | −0.654344 | ||||||||
\(817\) | −55.1469 | −1.92935 | ||||||||
\(818\) | −95.5972 | −3.34248 | ||||||||
\(819\) | 6.98026 | 0.243910 | ||||||||
\(820\) | 29.7070 | 1.03741 | ||||||||
\(821\) | −38.2799 | −1.33598 | −0.667989 | − | 0.744171i | \(-0.732845\pi\) | ||||
−0.667989 | + | 0.744171i | \(0.732845\pi\) | |||||||
\(822\) | −16.4479 | −0.573688 | ||||||||
\(823\) | −48.1451 | −1.67823 | −0.839116 | − | 0.543952i | \(-0.816927\pi\) | ||||
−0.839116 | + | 0.543952i | \(0.816927\pi\) | |||||||
\(824\) | −28.2950 | −0.985704 | ||||||||
\(825\) | −5.85687 | −0.203910 | ||||||||
\(826\) | −36.9373 | −1.28521 | ||||||||
\(827\) | −37.7005 | −1.31098 | −0.655488 | − | 0.755206i | \(-0.727537\pi\) | ||||
−0.655488 | + | 0.755206i | \(0.727537\pi\) | |||||||
\(828\) | −111.592 | −3.87810 | ||||||||
\(829\) | −11.8709 | −0.412292 | −0.206146 | − | 0.978521i | \(-0.566092\pi\) | ||||
−0.206146 | + | 0.978521i | \(0.566092\pi\) | |||||||
\(830\) | −28.9721 | −1.00564 | ||||||||
\(831\) | 4.30931 | 0.149488 | ||||||||
\(832\) | −6.00807 | −0.208292 | ||||||||
\(833\) | −1.90580 | −0.0660320 | ||||||||
\(834\) | −6.42818 | −0.222590 | ||||||||
\(835\) | 18.1621 | 0.628527 | ||||||||
\(836\) | 81.7983 | 2.82905 | ||||||||
\(837\) | −24.3198 | −0.840617 | ||||||||
\(838\) | −36.1669 | −1.24936 | ||||||||
\(839\) | 39.7211 | 1.37132 | 0.685662 | − | 0.727920i | \(-0.259513\pi\) | ||||
0.685662 | + | 0.727920i | \(0.259513\pi\) | |||||||
\(840\) | 14.2643 | 0.492164 | ||||||||
\(841\) | −11.9763 | −0.412976 | ||||||||
\(842\) | 20.9983 | 0.723649 | ||||||||
\(843\) | −13.4183 | −0.462151 | ||||||||
\(844\) | 56.2750 | 1.93706 | ||||||||
\(845\) | −1.04737 | −0.0360305 | ||||||||
\(846\) | −54.6200 | −1.87787 | ||||||||
\(847\) | −17.2804 | −0.593762 | ||||||||
\(848\) | −100.818 | −3.46212 | ||||||||
\(849\) | 1.67474 | 0.0574770 | ||||||||
\(850\) | −30.2918 | −1.03900 | ||||||||
\(851\) | −60.1945 | −2.06344 | ||||||||
\(852\) | −4.59935 | −0.157571 | ||||||||
\(853\) | 36.9809 | 1.26620 | 0.633101 | − | 0.774069i | \(-0.281782\pi\) | ||||
0.633101 | + | 0.774069i | \(0.281782\pi\) | |||||||
\(854\) | −69.4435 | −2.37631 | ||||||||
\(855\) | 20.8926 | 0.714513 | ||||||||
\(856\) | 103.864 | 3.55001 | ||||||||
\(857\) | −21.2559 | −0.726088 | −0.363044 | − | 0.931772i | \(-0.618263\pi\) | ||||
−0.363044 | + | 0.931772i | \(0.618263\pi\) | |||||||
\(858\) | 3.89963 | 0.133131 | ||||||||
\(859\) | 29.1910 | 0.995983 | 0.497992 | − | 0.867182i | \(-0.334071\pi\) | ||||
0.497992 | + | 0.867182i | \(0.334071\pi\) | |||||||
\(860\) | 34.7619 | 1.18537 | ||||||||
\(861\) | −11.3577 | −0.387070 | ||||||||
\(862\) | −39.4024 | −1.34205 | ||||||||
\(863\) | 10.8183 | 0.368260 | 0.184130 | − | 0.982902i | \(-0.441053\pi\) | ||||
0.184130 | + | 0.982902i | \(0.441053\pi\) | |||||||
\(864\) | 35.4143 | 1.20482 | ||||||||
\(865\) | −20.3219 | −0.690965 | ||||||||
\(866\) | −18.4346 | −0.626434 | ||||||||
\(867\) | −5.56530 | −0.189007 | ||||||||
\(868\) | 83.9523 | 2.84953 | ||||||||
\(869\) | 34.6241 | 1.17454 | ||||||||
\(870\) | −7.73430 | −0.262217 | ||||||||
\(871\) | 4.15316 | 0.140724 | ||||||||
\(872\) | 136.268 | 4.61461 | ||||||||
\(873\) | −14.6539 | −0.495961 | ||||||||
\(874\) | −190.779 | −6.45321 | ||||||||
\(875\) | 25.7709 | 0.871216 | ||||||||
\(876\) | −29.2865 | −0.989498 | ||||||||
\(877\) | −38.4298 | −1.29768 | −0.648841 | − | 0.760924i | \(-0.724746\pi\) | ||||
−0.648841 | + | 0.760924i | \(0.724746\pi\) | |||||||
\(878\) | −106.265 | −3.58626 | ||||||||
\(879\) | 15.8484 | 0.534552 | ||||||||
\(880\) | −20.7385 | −0.699096 | ||||||||
\(881\) | 2.72589 | 0.0918375 | 0.0459187 | − | 0.998945i | \(-0.485378\pi\) | ||||
0.0459187 | + | 0.998945i | \(0.485378\pi\) | |||||||
\(882\) | 4.18843 | 0.141032 | ||||||||
\(883\) | 18.0096 | 0.606071 | 0.303035 | − | 0.952979i | \(-0.402000\pi\) | ||||
0.303035 | + | 0.952979i | \(0.402000\pi\) | |||||||
\(884\) | 14.1959 | 0.477461 | ||||||||
\(885\) | −3.70976 | −0.124702 | ||||||||
\(886\) | −45.8457 | −1.54022 | ||||||||
\(887\) | −8.47061 | −0.284415 | −0.142208 | − | 0.989837i | \(-0.545420\pi\) | ||||
−0.142208 | + | 0.989837i | \(0.545420\pi\) | |||||||
\(888\) | 31.9123 | 1.07091 | ||||||||
\(889\) | 17.3721 | 0.582643 | ||||||||
\(890\) | −20.8371 | −0.698461 | ||||||||
\(891\) | 10.7986 | 0.361767 | ||||||||
\(892\) | −62.7839 | −2.10216 | ||||||||
\(893\) | −65.7249 | −2.19940 | ||||||||
\(894\) | 16.2952 | 0.544994 | ||||||||
\(895\) | 19.7677 | 0.660762 | ||||||||
\(896\) | 8.28686 | 0.276844 | ||||||||
\(897\) | −6.40164 | −0.213745 | ||||||||
\(898\) | 12.1216 | 0.404503 | ||||||||
\(899\) | −26.3673 | −0.879399 | ||||||||
\(900\) | 46.8575 | 1.56192 | ||||||||
\(901\) | 33.1324 | 1.10380 | ||||||||
\(902\) | 33.7869 | 1.12498 | ||||||||
\(903\) | −13.2903 | −0.442273 | ||||||||
\(904\) | 20.4238 | 0.679287 | ||||||||
\(905\) | 9.61451 | 0.319597 | ||||||||
\(906\) | 1.69116 | 0.0561850 | ||||||||
\(907\) | −19.7512 | −0.655826 | −0.327913 | − | 0.944708i | \(-0.606345\pi\) | ||||
−0.327913 | + | 0.944708i | \(0.606345\pi\) | |||||||
\(908\) | 71.1917 | 2.36258 | ||||||||
\(909\) | −2.73575 | −0.0907390 | ||||||||
\(910\) | −7.52232 | −0.249363 | ||||||||
\(911\) | 4.90474 | 0.162501 | 0.0812507 | − | 0.996694i | \(-0.474109\pi\) | ||||
0.0812507 | + | 0.996694i | \(0.474109\pi\) | |||||||
\(912\) | 49.4315 | 1.63684 | ||||||||
\(913\) | −23.1926 | −0.767563 | ||||||||
\(914\) | −106.191 | −3.51250 | ||||||||
\(915\) | −6.97450 | −0.230570 | ||||||||
\(916\) | −3.25475 | −0.107540 | ||||||||
\(917\) | 31.1595 | 1.02898 | ||||||||
\(918\) | −29.5356 | −0.974819 | ||||||||
\(919\) | 29.1191 | 0.960551 | 0.480276 | − | 0.877118i | \(-0.340537\pi\) | ||||
0.480276 | + | 0.877118i | \(0.340537\pi\) | |||||||
\(920\) | 69.6587 | 2.29658 | ||||||||
\(921\) | 16.8014 | 0.553626 | ||||||||
\(922\) | −44.2464 | −1.45718 | ||||||||
\(923\) | 1.40495 | 0.0462444 | ||||||||
\(924\) | 19.7132 | 0.648518 | ||||||||
\(925\) | 25.2757 | 0.831059 | ||||||||
\(926\) | 97.5113 | 3.20442 | ||||||||
\(927\) | −9.98774 | −0.328040 | ||||||||
\(928\) | 38.3958 | 1.26040 | ||||||||
\(929\) | −54.8629 | −1.79999 | −0.899997 | − | 0.435896i | \(-0.856431\pi\) | ||||
−0.899997 | + | 0.435896i | \(0.856431\pi\) | |||||||
\(930\) | 11.9794 | 0.392818 | ||||||||
\(931\) | 5.03999 | 0.165179 | ||||||||
\(932\) | −29.6966 | −0.972745 | ||||||||
\(933\) | −18.5823 | −0.608356 | ||||||||
\(934\) | 69.6347 | 2.27852 | ||||||||
\(935\) | 6.81539 | 0.222887 | ||||||||
\(936\) | −18.0717 | −0.590693 | ||||||||
\(937\) | 3.01907 | 0.0986286 | 0.0493143 | − | 0.998783i | \(-0.484296\pi\) | ||||
0.0493143 | + | 0.998783i | \(0.484296\pi\) | |||||||
\(938\) | 29.8285 | 0.973936 | ||||||||
\(939\) | 13.3423 | 0.435408 | ||||||||
\(940\) | 41.4297 | 1.35129 | ||||||||
\(941\) | 12.6616 | 0.412758 | 0.206379 | − | 0.978472i | \(-0.433832\pi\) | ||||
0.206379 | + | 0.978472i | \(0.433832\pi\) | |||||||
\(942\) | −0.0361323 | −0.00117725 | ||||||||
\(943\) | −55.4647 | −1.80618 | ||||||||
\(944\) | 46.7372 | 1.52117 | ||||||||
\(945\) | 11.0157 | 0.358342 | ||||||||
\(946\) | 39.5360 | 1.28543 | ||||||||
\(947\) | −11.8605 | −0.385415 | −0.192708 | − | 0.981256i | \(-0.561727\pi\) | ||||
−0.192708 | + | 0.981256i | \(0.561727\pi\) | |||||||
\(948\) | 52.0219 | 1.68959 | ||||||||
\(949\) | 8.94604 | 0.290401 | ||||||||
\(950\) | 80.1082 | 2.59905 | ||||||||
\(951\) | −6.19890 | −0.201013 | ||||||||
\(952\) | 59.0580 | 1.91408 | ||||||||
\(953\) | −49.5246 | −1.60426 | −0.802129 | − | 0.597151i | \(-0.796299\pi\) | ||||
−0.802129 | + | 0.597151i | \(0.796299\pi\) | |||||||
\(954\) | −72.8160 | −2.35750 | ||||||||
\(955\) | −1.29544 | −0.0419196 | ||||||||
\(956\) | −58.8929 | −1.90473 | ||||||||
\(957\) | −6.19143 | −0.200141 | ||||||||
\(958\) | 79.9042 | 2.58159 | ||||||||
\(959\) | 25.3986 | 0.820163 | ||||||||
\(960\) | −4.33380 | −0.139873 | ||||||||
\(961\) | 9.83930 | 0.317397 | ||||||||
\(962\) | −16.8291 | −0.542592 | ||||||||
\(963\) | 36.6626 | 1.18144 | ||||||||
\(964\) | −92.9743 | −2.99450 | ||||||||
\(965\) | −17.7156 | −0.570287 | ||||||||
\(966\) | −45.9775 | −1.47930 | ||||||||
\(967\) | −50.4159 | −1.62127 | −0.810634 | − | 0.585554i | \(-0.800877\pi\) | ||||
−0.810634 | + | 0.585554i | \(0.800877\pi\) | |||||||
\(968\) | 44.7385 | 1.43795 | ||||||||
\(969\) | −16.2449 | −0.521860 | ||||||||
\(970\) | 15.7919 | 0.507047 | ||||||||
\(971\) | −8.01922 | −0.257349 | −0.128675 | − | 0.991687i | \(-0.541072\pi\) | ||||
−0.128675 | + | 0.991687i | \(0.541072\pi\) | |||||||
\(972\) | 70.4925 | 2.26105 | ||||||||
\(973\) | 9.92627 | 0.318221 | ||||||||
\(974\) | −42.7101 | −1.36852 | ||||||||
\(975\) | 2.68805 | 0.0860865 | ||||||||
\(976\) | 87.8678 | 2.81258 | ||||||||
\(977\) | −8.72755 | −0.279219 | −0.139610 | − | 0.990207i | \(-0.544585\pi\) | ||||
−0.139610 | + | 0.990207i | \(0.544585\pi\) | |||||||
\(978\) | −32.7955 | −1.04868 | ||||||||
\(979\) | −16.6804 | −0.533109 | ||||||||
\(980\) | −3.17696 | −0.101484 | ||||||||
\(981\) | 48.1006 | 1.53573 | ||||||||
\(982\) | −91.4718 | −2.91898 | ||||||||
\(983\) | 48.4105 | 1.54406 | 0.772028 | − | 0.635589i | \(-0.219243\pi\) | ||||
0.772028 | + | 0.635589i | \(0.219243\pi\) | |||||||
\(984\) | 29.4048 | 0.937391 | ||||||||
\(985\) | 22.4969 | 0.716810 | ||||||||
\(986\) | −32.0221 | −1.01979 | ||||||||
\(987\) | −15.8396 | −0.504179 | ||||||||
\(988\) | −37.5419 | −1.19437 | ||||||||
\(989\) | −64.9023 | −2.06377 | ||||||||
\(990\) | −14.9784 | −0.476044 | ||||||||
\(991\) | 9.26982 | 0.294466 | 0.147233 | − | 0.989102i | \(-0.452963\pi\) | ||||
0.147233 | + | 0.989102i | \(0.452963\pi\) | |||||||
\(992\) | −59.4697 | −1.88817 | ||||||||
\(993\) | 18.9916 | 0.602682 | ||||||||
\(994\) | 10.0905 | 0.320052 | ||||||||
\(995\) | 17.1021 | 0.542172 | ||||||||
\(996\) | −34.8463 | −1.10415 | ||||||||
\(997\) | −29.5072 | −0.934503 | −0.467251 | − | 0.884125i | \(-0.654756\pi\) | ||||
−0.467251 | + | 0.884125i | \(0.654756\pi\) | |||||||
\(998\) | 45.3716 | 1.43621 | ||||||||
\(999\) | 24.6447 | 0.779723 |
(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 | 8047.2.a.c.1.11 | ✓ | 151 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8047.2.a.c.1.11 | ✓ | 151 | 1.1 | even | 1 | trivial |