Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9075,2,Mod(1,9075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9075, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("9075.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9075 = 3 \cdot 5^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9075.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: | \(72.4642398343\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.725.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 3x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.35567\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9075.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.16215 | 0.821762 | 0.410881 | − | 0.911689i | \(-0.365221\pi\) | ||||
0.410881 | + | 0.911689i | \(0.365221\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.649414 | −0.324707 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.16215 | −0.474445 | ||||||||
\(7\) | −4.28684 | −1.62027 | −0.810137 | − | 0.586241i | \(-0.800607\pi\) | ||||
−0.810137 | + | 0.586241i | \(0.800607\pi\) | |||||||
\(8\) | −3.07901 | −1.08859 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.649414 | 0.187470 | ||||||||
\(13\) | 5.16724 | 1.43313 | 0.716567 | − | 0.697519i | \(-0.245713\pi\) | ||||
0.716567 | + | 0.697519i | \(0.245713\pi\) | |||||||
\(14\) | −4.98194 | −1.33148 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.27943 | −0.569858 | ||||||||
\(17\) | 5.00000 | 1.21268 | 0.606339 | − | 0.795206i | \(-0.292637\pi\) | ||||
0.606339 | + | 0.795206i | \(0.292637\pi\) | |||||||
\(18\) | 1.16215 | 0.273921 | ||||||||
\(19\) | −5.59998 | −1.28472 | −0.642361 | − | 0.766402i | \(-0.722045\pi\) | ||||
−0.642361 | + | 0.766402i | \(0.722045\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.28684 | 0.935466 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.219819 | 0.0458354 | 0.0229177 | − | 0.999737i | \(-0.492704\pi\) | ||||
0.0229177 | + | 0.999737i | \(0.492704\pi\) | |||||||
\(24\) | 3.07901 | 0.628500 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.00509 | 1.17769 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.78393 | 0.526114 | ||||||||
\(29\) | −6.41843 | −1.19187 | −0.595937 | − | 0.803031i | \(-0.703219\pi\) | ||||
−0.595937 | + | 0.803031i | \(0.703219\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.83095 | −0.508455 | −0.254227 | − | 0.967145i | \(-0.581821\pi\) | ||||
−0.254227 | + | 0.967145i | \(0.581821\pi\) | |||||||
\(32\) | 3.50898 | 0.620306 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.81074 | 0.996533 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.649414 | −0.108236 | ||||||||
\(37\) | −3.92802 | −0.645763 | −0.322881 | − | 0.946439i | \(-0.604652\pi\) | ||||
−0.322881 | + | 0.946439i | \(0.604652\pi\) | |||||||
\(38\) | −6.50800 | −1.05574 | ||||||||
\(39\) | −5.16724 | −0.827420 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.86100 | −0.915334 | −0.457667 | − | 0.889124i | \(-0.651315\pi\) | ||||
−0.457667 | + | 0.889124i | \(0.651315\pi\) | |||||||
\(42\) | 4.98194 | 0.768730 | ||||||||
\(43\) | −8.90173 | −1.35750 | −0.678751 | − | 0.734369i | \(-0.737478\pi\) | ||||
−0.678751 | + | 0.734369i | \(0.737478\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.255462 | 0.0376658 | ||||||||
\(47\) | 0.237878 | 0.0346980 | 0.0173490 | − | 0.999849i | \(-0.494477\pi\) | ||||
0.0173490 | + | 0.999849i | \(0.494477\pi\) | |||||||
\(48\) | 2.27943 | 0.329008 | ||||||||
\(49\) | 11.3770 | 1.62529 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.00000 | −0.700140 | ||||||||
\(52\) | −3.35567 | −0.465348 | ||||||||
\(53\) | −2.53671 | −0.348443 | −0.174222 | − | 0.984706i | \(-0.555741\pi\) | ||||
−0.174222 | + | 0.984706i | \(0.555741\pi\) | |||||||
\(54\) | −1.16215 | −0.158148 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 13.1992 | 1.76382 | ||||||||
\(57\) | 5.59998 | 0.741735 | ||||||||
\(58\) | −7.45917 | −0.979436 | ||||||||
\(59\) | −7.87035 | −1.02463 | −0.512316 | − | 0.858797i | \(-0.671212\pi\) | ||||
−0.512316 | + | 0.858797i | \(0.671212\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.85807 | 0.622012 | 0.311006 | − | 0.950408i | \(-0.399334\pi\) | ||||
0.311006 | + | 0.950408i | \(0.399334\pi\) | |||||||
\(62\) | −3.28999 | −0.417829 | ||||||||
\(63\) | −4.28684 | −0.540091 | ||||||||
\(64\) | 8.63682 | 1.07960 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.1280 | −1.48167 | −0.740834 | − | 0.671688i | \(-0.765569\pi\) | ||||
−0.740834 | + | 0.671688i | \(0.765569\pi\) | |||||||
\(68\) | −3.24707 | −0.393765 | ||||||||
\(69\) | −0.219819 | −0.0264631 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.98194 | −1.18464 | −0.592319 | − | 0.805703i | \(-0.701788\pi\) | ||||
−0.592319 | + | 0.805703i | \(0.701788\pi\) | |||||||
\(72\) | −3.07901 | −0.362865 | ||||||||
\(73\) | 14.5625 | 1.70441 | 0.852207 | − | 0.523205i | \(-0.175264\pi\) | ||||
0.852207 | + | 0.523205i | \(0.175264\pi\) | |||||||
\(74\) | −4.56494 | −0.530664 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.63670 | 0.417158 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.00509 | −0.679942 | ||||||||
\(79\) | −8.00194 | −0.900289 | −0.450144 | − | 0.892956i | \(-0.648628\pi\) | ||||
−0.450144 | + | 0.892956i | \(0.648628\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.81134 | −0.752187 | ||||||||
\(83\) | 12.5530 | 1.37787 | 0.688933 | − | 0.724825i | \(-0.258079\pi\) | ||||
0.688933 | + | 0.724825i | \(0.258079\pi\) | |||||||
\(84\) | −2.78393 | −0.303752 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −10.3451 | −1.11554 | ||||||||
\(87\) | 6.41843 | 0.688128 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.56545 | −0.271937 | −0.135969 | − | 0.990713i | \(-0.543415\pi\) | ||||
−0.135969 | + | 0.990713i | \(0.543415\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −22.1511 | −2.32207 | ||||||||
\(92\) | −0.142753 | −0.0148831 | ||||||||
\(93\) | 2.83095 | 0.293556 | ||||||||
\(94\) | 0.276449 | 0.0285135 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.50898 | −0.358134 | ||||||||
\(97\) | −2.01199 | −0.204286 | −0.102143 | − | 0.994770i | \(-0.532570\pi\) | ||||
−0.102143 | + | 0.994770i | \(0.532570\pi\) | |||||||
\(98\) | 13.2218 | 1.33560 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.58484 | 0.754720 | 0.377360 | − | 0.926067i | \(-0.376832\pi\) | ||||
0.377360 | + | 0.926067i | \(0.376832\pi\) | |||||||
\(102\) | −5.81074 | −0.575349 | ||||||||
\(103\) | 16.8685 | 1.66211 | 0.831053 | − | 0.556193i | \(-0.187738\pi\) | ||||
0.831053 | + | 0.556193i | \(0.187738\pi\) | |||||||
\(104\) | −15.9100 | −1.56010 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.94803 | −0.286338 | ||||||||
\(107\) | 7.76161 | 0.750343 | 0.375172 | − | 0.926955i | \(-0.377584\pi\) | ||||
0.375172 | + | 0.926955i | \(0.377584\pi\) | |||||||
\(108\) | 0.649414 | 0.0624899 | ||||||||
\(109\) | −4.45671 | −0.426876 | −0.213438 | − | 0.976957i | \(-0.568466\pi\) | ||||
−0.213438 | + | 0.976957i | \(0.568466\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.92802 | 0.372831 | ||||||||
\(112\) | 9.77157 | 0.923327 | ||||||||
\(113\) | 7.71247 | 0.725528 | 0.362764 | − | 0.931881i | \(-0.381833\pi\) | ||||
0.362764 | + | 0.931881i | \(0.381833\pi\) | |||||||
\(114\) | 6.50800 | 0.609530 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.16822 | 0.387010 | ||||||||
\(117\) | 5.16724 | 0.477711 | ||||||||
\(118\) | −9.14651 | −0.842004 | ||||||||
\(119\) | −21.4342 | −1.96487 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 5.64579 | 0.511146 | ||||||||
\(123\) | 5.86100 | 0.528469 | ||||||||
\(124\) | 1.83846 | 0.165099 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.98194 | −0.443827 | ||||||||
\(127\) | 1.53114 | 0.135867 | 0.0679335 | − | 0.997690i | \(-0.478359\pi\) | ||||
0.0679335 | + | 0.997690i | \(0.478359\pi\) | |||||||
\(128\) | 3.01930 | 0.266871 | ||||||||
\(129\) | 8.90173 | 0.783754 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.66108 | −0.232500 | −0.116250 | − | 0.993220i | \(-0.537087\pi\) | ||||
−0.116250 | + | 0.993220i | \(0.537087\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 24.0062 | 2.08160 | ||||||||
\(134\) | −14.0945 | −1.21758 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −15.3950 | −1.32011 | ||||||||
\(137\) | −10.2555 | −0.876183 | −0.438092 | − | 0.898930i | \(-0.644345\pi\) | ||||
−0.438092 | + | 0.898930i | \(0.644345\pi\) | |||||||
\(138\) | −0.255462 | −0.0217464 | ||||||||
\(139\) | 5.29507 | 0.449122 | 0.224561 | − | 0.974460i | \(-0.427905\pi\) | ||||
0.224561 | + | 0.974460i | \(0.427905\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.237878 | −0.0200329 | ||||||||
\(142\) | −11.6005 | −0.973491 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.27943 | −0.189953 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 16.9238 | 1.40062 | ||||||||
\(147\) | −11.3770 | −0.938360 | ||||||||
\(148\) | 2.55091 | 0.209684 | ||||||||
\(149\) | −3.78841 | −0.310359 | −0.155179 | − | 0.987886i | \(-0.549596\pi\) | ||||
−0.155179 | + | 0.987886i | \(0.549596\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.92001 | 0.481763 | 0.240882 | − | 0.970554i | \(-0.422563\pi\) | ||||
0.240882 | + | 0.970554i | \(0.422563\pi\) | |||||||
\(152\) | 17.2424 | 1.39854 | ||||||||
\(153\) | 5.00000 | 0.404226 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.35567 | 0.268669 | ||||||||
\(157\) | 7.42909 | 0.592906 | 0.296453 | − | 0.955048i | \(-0.404196\pi\) | ||||
0.296453 | + | 0.955048i | \(0.404196\pi\) | |||||||
\(158\) | −9.29944 | −0.739823 | ||||||||
\(159\) | 2.53671 | 0.201174 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.942328 | −0.0742659 | ||||||||
\(162\) | 1.16215 | 0.0913069 | ||||||||
\(163\) | −5.32086 | −0.416762 | −0.208381 | − | 0.978048i | \(-0.566819\pi\) | ||||
−0.208381 | + | 0.978048i | \(0.566819\pi\) | |||||||
\(164\) | 3.80621 | 0.297215 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.5884 | 1.13228 | ||||||||
\(167\) | −1.97139 | −0.152551 | −0.0762753 | − | 0.997087i | \(-0.524303\pi\) | ||||
−0.0762753 | + | 0.997087i | \(0.524303\pi\) | |||||||
\(168\) | −13.1992 | −1.01834 | ||||||||
\(169\) | 13.7003 | 1.05387 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.59998 | −0.428241 | ||||||||
\(172\) | 5.78091 | 0.440790 | ||||||||
\(173\) | −1.97504 | −0.150160 | −0.0750799 | − | 0.997178i | \(-0.523921\pi\) | ||||
−0.0750799 | + | 0.997178i | \(0.523921\pi\) | |||||||
\(174\) | 7.45917 | 0.565478 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.87035 | 0.591572 | ||||||||
\(178\) | −2.98143 | −0.223468 | ||||||||
\(179\) | −2.02315 | −0.151217 | −0.0756086 | − | 0.997138i | \(-0.524090\pi\) | ||||
−0.0756086 | + | 0.997138i | \(0.524090\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.1380 | 1.49685 | 0.748423 | − | 0.663221i | \(-0.230811\pi\) | ||||
0.748423 | + | 0.663221i | \(0.230811\pi\) | |||||||
\(182\) | −25.7429 | −1.90819 | ||||||||
\(183\) | −4.85807 | −0.359119 | ||||||||
\(184\) | −0.676824 | −0.0498961 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.28999 | 0.241234 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −0.154481 | −0.0112667 | ||||||||
\(189\) | 4.28684 | 0.311822 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.6652 | 0.916418 | 0.458209 | − | 0.888844i | \(-0.348491\pi\) | ||||
0.458209 | + | 0.888844i | \(0.348491\pi\) | |||||||
\(192\) | −8.63682 | −0.623309 | ||||||||
\(193\) | −13.9321 | −1.00286 | −0.501428 | − | 0.865199i | \(-0.667192\pi\) | ||||
−0.501428 | + | 0.865199i | \(0.667192\pi\) | |||||||
\(194\) | −2.33822 | −0.167875 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.38839 | −0.527742 | ||||||||
\(197\) | 14.6060 | 1.04064 | 0.520319 | − | 0.853972i | \(-0.325813\pi\) | ||||
0.520319 | + | 0.853972i | \(0.325813\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.8748 | −0.841784 | −0.420892 | − | 0.907111i | \(-0.638283\pi\) | ||||
−0.420892 | + | 0.907111i | \(0.638283\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.1280 | 0.855441 | ||||||||
\(202\) | 8.81471 | 0.620201 | ||||||||
\(203\) | 27.5148 | 1.93116 | ||||||||
\(204\) | 3.24707 | 0.227340 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 19.6037 | 1.36586 | ||||||||
\(207\) | 0.219819 | 0.0152785 | ||||||||
\(208\) | −11.7784 | −0.816683 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.3518 | 1.53876 | 0.769382 | − | 0.638789i | \(-0.220564\pi\) | ||||
0.769382 | + | 0.638789i | \(0.220564\pi\) | |||||||
\(212\) | 1.64737 | 0.113142 | ||||||||
\(213\) | 9.98194 | 0.683951 | ||||||||
\(214\) | 9.02014 | 0.616604 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.07901 | 0.209500 | ||||||||
\(217\) | 12.1359 | 0.823836 | ||||||||
\(218\) | −5.17936 | −0.350790 | ||||||||
\(219\) | −14.5625 | −0.984044 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25.8362 | 1.73793 | ||||||||
\(222\) | 4.56494 | 0.306379 | ||||||||
\(223\) | 19.1583 | 1.28294 | 0.641468 | − | 0.767150i | \(-0.278326\pi\) | ||||
0.641468 | + | 0.767150i | \(0.278326\pi\) | |||||||
\(224\) | −15.0424 | −1.00507 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.96302 | 0.596211 | ||||||||
\(227\) | 15.3759 | 1.02053 | 0.510267 | − | 0.860016i | \(-0.329547\pi\) | ||||
0.510267 | + | 0.860016i | \(0.329547\pi\) | |||||||
\(228\) | −3.63670 | −0.240846 | ||||||||
\(229\) | 8.90126 | 0.588212 | 0.294106 | − | 0.955773i | \(-0.404978\pi\) | ||||
0.294106 | + | 0.955773i | \(0.404978\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 19.7624 | 1.29747 | ||||||||
\(233\) | 22.8362 | 1.49605 | 0.748024 | − | 0.663672i | \(-0.231003\pi\) | ||||
0.748024 | + | 0.663672i | \(0.231003\pi\) | |||||||
\(234\) | 6.00509 | 0.392565 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.11112 | 0.332705 | ||||||||
\(237\) | 8.00194 | 0.519782 | ||||||||
\(238\) | −24.9097 | −1.61466 | ||||||||
\(239\) | −16.8605 | −1.09062 | −0.545308 | − | 0.838236i | \(-0.683587\pi\) | ||||
−0.545308 | + | 0.838236i | \(0.683587\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.9607 | 0.770459 | 0.385229 | − | 0.922821i | \(-0.374122\pi\) | ||||
0.385229 | + | 0.922821i | \(0.374122\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −3.15490 | −0.201972 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.81134 | 0.434275 | ||||||||
\(247\) | −28.9364 | −1.84118 | ||||||||
\(248\) | 8.71654 | 0.553501 | ||||||||
\(249\) | −12.5530 | −0.795511 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.0034 | 1.01013 | 0.505063 | − | 0.863082i | \(-0.331469\pi\) | ||||
0.505063 | + | 0.863082i | \(0.331469\pi\) | |||||||
\(252\) | 2.78393 | 0.175371 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 1.77941 | 0.111650 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.7648 | −0.860298 | ||||||||
\(257\) | −5.47446 | −0.341487 | −0.170744 | − | 0.985315i | \(-0.554617\pi\) | ||||
−0.170744 | + | 0.985315i | \(0.554617\pi\) | |||||||
\(258\) | 10.3451 | 0.644059 | ||||||||
\(259\) | 16.8388 | 1.04631 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.41843 | −0.397291 | ||||||||
\(262\) | −3.09257 | −0.191060 | ||||||||
\(263\) | 11.9841 | 0.738971 | 0.369486 | − | 0.929236i | \(-0.379534\pi\) | ||||
0.369486 | + | 0.929236i | \(0.379534\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 27.8987 | 1.71058 | ||||||||
\(267\) | 2.56545 | 0.157003 | ||||||||
\(268\) | 7.87607 | 0.481108 | ||||||||
\(269\) | 13.6465 | 0.832041 | 0.416020 | − | 0.909355i | \(-0.363424\pi\) | ||||
0.416020 | + | 0.909355i | \(0.363424\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.8379 | −0.719098 | −0.359549 | − | 0.933126i | \(-0.617070\pi\) | ||||
−0.359549 | + | 0.933126i | \(0.617070\pi\) | |||||||
\(272\) | −11.3972 | −0.691055 | ||||||||
\(273\) | 22.1511 | 1.34065 | ||||||||
\(274\) | −11.9184 | −0.720014 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.142753 | 0.00859274 | ||||||||
\(277\) | 10.2638 | 0.616694 | 0.308347 | − | 0.951274i | \(-0.400224\pi\) | ||||
0.308347 | + | 0.951274i | \(0.400224\pi\) | |||||||
\(278\) | 6.15366 | 0.369072 | ||||||||
\(279\) | −2.83095 | −0.169485 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.93889 | 0.175319 | 0.0876597 | − | 0.996150i | \(-0.472061\pi\) | ||||
0.0876597 | + | 0.996150i | \(0.472061\pi\) | |||||||
\(282\) | −0.276449 | −0.0164623 | ||||||||
\(283\) | 21.8279 | 1.29754 | 0.648768 | − | 0.760986i | \(-0.275284\pi\) | ||||
0.648768 | + | 0.760986i | \(0.275284\pi\) | |||||||
\(284\) | 6.48241 | 0.384660 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 25.1252 | 1.48309 | ||||||||
\(288\) | 3.50898 | 0.206769 | ||||||||
\(289\) | 8.00000 | 0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.01199 | 0.117945 | ||||||||
\(292\) | −9.45710 | −0.553435 | ||||||||
\(293\) | −24.7665 | −1.44688 | −0.723438 | − | 0.690390i | \(-0.757439\pi\) | ||||
−0.723438 | + | 0.690390i | \(0.757439\pi\) | |||||||
\(294\) | −13.2218 | −0.771109 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 12.0944 | 0.702974 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.40269 | −0.255041 | ||||||||
\(299\) | 1.13586 | 0.0656882 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 38.1603 | 2.19952 | ||||||||
\(302\) | 6.87992 | 0.395895 | ||||||||
\(303\) | −7.58484 | −0.435738 | ||||||||
\(304\) | 12.7648 | 0.732110 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 5.81074 | 0.332178 | ||||||||
\(307\) | −4.94023 | −0.281954 | −0.140977 | − | 0.990013i | \(-0.545024\pi\) | ||||
−0.140977 | + | 0.990013i | \(0.545024\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.8685 | −0.959618 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.8096 | −0.783070 | −0.391535 | − | 0.920163i | \(-0.628056\pi\) | ||||
−0.391535 | + | 0.920163i | \(0.628056\pi\) | |||||||
\(312\) | 15.9100 | 0.900724 | ||||||||
\(313\) | 4.06934 | 0.230013 | 0.115006 | − | 0.993365i | \(-0.463311\pi\) | ||||
0.115006 | + | 0.993365i | \(0.463311\pi\) | |||||||
\(314\) | 8.63369 | 0.487227 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.19657 | 0.292330 | ||||||||
\(317\) | −25.8199 | −1.45019 | −0.725096 | − | 0.688648i | \(-0.758205\pi\) | ||||
−0.725096 | + | 0.688648i | \(0.758205\pi\) | |||||||
\(318\) | 2.94803 | 0.165317 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.76161 | −0.433211 | ||||||||
\(322\) | −1.09512 | −0.0610289 | ||||||||
\(323\) | −27.9999 | −1.55795 | ||||||||
\(324\) | −0.649414 | −0.0360785 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.18362 | −0.342479 | ||||||||
\(327\) | 4.45671 | 0.246457 | ||||||||
\(328\) | 18.0461 | 0.996428 | ||||||||
\(329\) | −1.01974 | −0.0562203 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.35008 | −0.184137 | −0.0920684 | − | 0.995753i | \(-0.529348\pi\) | ||||
−0.0920684 | + | 0.995753i | \(0.529348\pi\) | |||||||
\(332\) | −8.15206 | −0.447403 | ||||||||
\(333\) | −3.92802 | −0.215254 | ||||||||
\(334\) | −2.29104 | −0.125360 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −9.77157 | −0.533083 | ||||||||
\(337\) | −27.3998 | −1.49256 | −0.746282 | − | 0.665630i | \(-0.768163\pi\) | ||||
−0.746282 | + | 0.665630i | \(0.768163\pi\) | |||||||
\(338\) | 15.9218 | 0.866031 | ||||||||
\(339\) | −7.71247 | −0.418884 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −6.50800 | −0.351912 | ||||||||
\(343\) | −18.7636 | −1.01314 | ||||||||
\(344\) | 27.4085 | 1.47777 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.29529 | −0.123396 | ||||||||
\(347\) | 15.8265 | 0.849610 | 0.424805 | − | 0.905285i | \(-0.360343\pi\) | ||||
0.424805 | + | 0.905285i | \(0.360343\pi\) | |||||||
\(348\) | −4.16822 | −0.223440 | ||||||||
\(349\) | 3.65930 | 0.195878 | 0.0979388 | − | 0.995192i | \(-0.468775\pi\) | ||||
0.0979388 | + | 0.995192i | \(0.468775\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.16724 | −0.275807 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 27.4937 | 1.46334 | 0.731671 | − | 0.681658i | \(-0.238741\pi\) | ||||
0.731671 | + | 0.681658i | \(0.238741\pi\) | |||||||
\(354\) | 9.14651 | 0.486131 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.66604 | 0.0882999 | ||||||||
\(357\) | 21.4342 | 1.13442 | ||||||||
\(358\) | −2.35119 | −0.124265 | ||||||||
\(359\) | −0.478740 | −0.0252670 | −0.0126335 | − | 0.999920i | \(-0.504021\pi\) | ||||
−0.0126335 | + | 0.999920i | \(0.504021\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.3597 | 0.650512 | ||||||||
\(362\) | 23.4033 | 1.23005 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 14.3852 | 0.753992 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.64579 | −0.295110 | ||||||||
\(367\) | 25.4582 | 1.32891 | 0.664453 | − | 0.747330i | \(-0.268665\pi\) | ||||
0.664453 | + | 0.747330i | \(0.268665\pi\) | |||||||
\(368\) | −0.501062 | −0.0261197 | ||||||||
\(369\) | −5.86100 | −0.305111 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.8745 | 0.564574 | ||||||||
\(372\) | −1.83846 | −0.0953198 | ||||||||
\(373\) | −2.75967 | −0.142890 | −0.0714451 | − | 0.997445i | \(-0.522761\pi\) | ||||
−0.0714451 | + | 0.997445i | \(0.522761\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.732428 | −0.0377721 | ||||||||
\(377\) | −33.1656 | −1.70811 | ||||||||
\(378\) | 4.98194 | 0.256243 | ||||||||
\(379\) | −21.6535 | −1.11227 | −0.556133 | − | 0.831093i | \(-0.687716\pi\) | ||||
−0.556133 | + | 0.831093i | \(0.687716\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.53114 | −0.0784428 | ||||||||
\(382\) | 14.7188 | 0.753078 | ||||||||
\(383\) | −16.2295 | −0.829287 | −0.414643 | − | 0.909984i | \(-0.636094\pi\) | ||||
−0.414643 | + | 0.909984i | \(0.636094\pi\) | |||||||
\(384\) | −3.01930 | −0.154078 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.1912 | −0.824109 | ||||||||
\(387\) | −8.90173 | −0.452500 | ||||||||
\(388\) | 1.30661 | 0.0663332 | ||||||||
\(389\) | −16.2916 | −0.826019 | −0.413009 | − | 0.910727i | \(-0.635522\pi\) | ||||
−0.413009 | + | 0.910727i | \(0.635522\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.09909 | 0.0555836 | ||||||||
\(392\) | −35.0299 | −1.76928 | ||||||||
\(393\) | 2.66108 | 0.134234 | ||||||||
\(394\) | 16.9744 | 0.855157 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.9673 | 1.00213 | 0.501064 | − | 0.865410i | \(-0.332942\pi\) | ||||
0.501064 | + | 0.865410i | \(0.332942\pi\) | |||||||
\(398\) | −13.8003 | −0.691747 | ||||||||
\(399\) | −24.0062 | −1.20181 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.3269 | −1.36464 | −0.682320 | − | 0.731053i | \(-0.739029\pi\) | ||||
−0.682320 | + | 0.731053i | \(0.739029\pi\) | |||||||
\(402\) | 14.0945 | 0.702969 | ||||||||
\(403\) | −14.6282 | −0.728683 | ||||||||
\(404\) | −4.92570 | −0.245063 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 31.9763 | 1.58696 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 15.3950 | 0.762168 | ||||||||
\(409\) | −24.9380 | −1.23310 | −0.616552 | − | 0.787314i | \(-0.711471\pi\) | ||||
−0.616552 | + | 0.787314i | \(0.711471\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.2555 | 0.505865 | ||||||||
\(412\) | −10.9547 | −0.539698 | ||||||||
\(413\) | 33.7389 | 1.66019 | ||||||||
\(414\) | 0.255462 | 0.0125553 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 18.1317 | 0.888981 | ||||||||
\(417\) | −5.29507 | −0.259301 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.8256 | 0.821986 | 0.410993 | − | 0.911639i | \(-0.365182\pi\) | ||||
0.410993 | + | 0.911639i | \(0.365182\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.6006 | 1.15022 | 0.575112 | − | 0.818074i | \(-0.304958\pi\) | ||||
0.575112 | + | 0.818074i | \(0.304958\pi\) | |||||||
\(422\) | 25.9761 | 1.26450 | ||||||||
\(423\) | 0.237878 | 0.0115660 | ||||||||
\(424\) | 7.81054 | 0.379313 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 11.6005 | 0.562045 | ||||||||
\(427\) | −20.8258 | −1.00783 | ||||||||
\(428\) | −5.04050 | −0.243642 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 37.6556 | 1.81381 | 0.906903 | − | 0.421339i | \(-0.138440\pi\) | ||||
0.906903 | + | 0.421339i | \(0.138440\pi\) | |||||||
\(432\) | 2.27943 | 0.109669 | ||||||||
\(433\) | 30.9752 | 1.48857 | 0.744286 | − | 0.667861i | \(-0.232790\pi\) | ||||
0.744286 | + | 0.667861i | \(0.232790\pi\) | |||||||
\(434\) | 14.1037 | 0.676997 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.89425 | 0.138609 | ||||||||
\(437\) | −1.23098 | −0.0588858 | ||||||||
\(438\) | −16.9238 | −0.808650 | ||||||||
\(439\) | 28.2131 | 1.34654 | 0.673268 | − | 0.739399i | \(-0.264890\pi\) | ||||
0.673268 | + | 0.739399i | \(0.264890\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.3770 | 0.541762 | ||||||||
\(442\) | 30.0254 | 1.42816 | ||||||||
\(443\) | −14.6420 | −0.695663 | −0.347831 | − | 0.937557i | \(-0.613082\pi\) | ||||
−0.347831 | + | 0.937557i | \(0.613082\pi\) | |||||||
\(444\) | −2.55091 | −0.121061 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 22.2648 | 1.05427 | ||||||||
\(447\) | 3.78841 | 0.179186 | ||||||||
\(448\) | −37.0247 | −1.74925 | ||||||||
\(449\) | 11.9977 | 0.566206 | 0.283103 | − | 0.959090i | \(-0.408636\pi\) | ||||
0.283103 | + | 0.959090i | \(0.408636\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −5.00858 | −0.235584 | ||||||||
\(453\) | −5.92001 | −0.278146 | ||||||||
\(454\) | 17.8691 | 0.838636 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −17.2424 | −0.807448 | ||||||||
\(457\) | 10.0437 | 0.469824 | 0.234912 | − | 0.972017i | \(-0.424520\pi\) | ||||
0.234912 | + | 0.972017i | \(0.424520\pi\) | |||||||
\(458\) | 10.3446 | 0.483370 | ||||||||
\(459\) | −5.00000 | −0.233380 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.4491 | 0.626386 | 0.313193 | − | 0.949689i | \(-0.398601\pi\) | ||||
0.313193 | + | 0.949689i | \(0.398601\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.7836 | −0.872946 | −0.436473 | − | 0.899717i | \(-0.643773\pi\) | ||||
−0.436473 | + | 0.899717i | \(0.643773\pi\) | |||||||
\(464\) | 14.6304 | 0.679199 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 26.5390 | 1.22940 | ||||||||
\(467\) | −26.5510 | −1.22863 | −0.614316 | − | 0.789060i | \(-0.710568\pi\) | ||||
−0.614316 | + | 0.789060i | \(0.710568\pi\) | |||||||
\(468\) | −3.35567 | −0.155116 | ||||||||
\(469\) | 51.9907 | 2.40071 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.42909 | −0.342314 | ||||||||
\(472\) | 24.2329 | 1.11541 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 9.29944 | 0.427137 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 13.9197 | 0.638007 | ||||||||
\(477\) | −2.53671 | −0.116148 | ||||||||
\(478\) | −19.5944 | −0.896228 | ||||||||
\(479\) | −10.7830 | −0.492689 | −0.246345 | − | 0.969182i | \(-0.579229\pi\) | ||||
−0.246345 | + | 0.969182i | \(0.579229\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.2970 | −0.925464 | ||||||||
\(482\) | 13.9001 | 0.633134 | ||||||||
\(483\) | 0.942328 | 0.0428774 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.16215 | −0.0527161 | ||||||||
\(487\) | −6.81095 | −0.308634 | −0.154317 | − | 0.988021i | \(-0.549318\pi\) | ||||
−0.154317 | + | 0.988021i | \(0.549318\pi\) | |||||||
\(488\) | −14.9580 | −0.677119 | ||||||||
\(489\) | 5.32086 | 0.240617 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.0954 | −1.17767 | −0.588834 | − | 0.808254i | \(-0.700413\pi\) | ||||
−0.588834 | + | 0.808254i | \(0.700413\pi\) | |||||||
\(492\) | −3.80621 | −0.171597 | ||||||||
\(493\) | −32.0922 | −1.44536 | ||||||||
\(494\) | −33.6283 | −1.51301 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.45297 | 0.289747 | ||||||||
\(497\) | 42.7910 | 1.91944 | ||||||||
\(498\) | −14.5884 | −0.653721 | ||||||||
\(499\) | 19.3834 | 0.867719 | 0.433860 | − | 0.900981i | \(-0.357151\pi\) | ||||
0.433860 | + | 0.900981i | \(0.357151\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.97139 | 0.0880751 | ||||||||
\(502\) | 18.5983 | 0.830084 | ||||||||
\(503\) | 18.8422 | 0.840134 | 0.420067 | − | 0.907493i | \(-0.362007\pi\) | ||||
0.420067 | + | 0.907493i | \(0.362007\pi\) | |||||||
\(504\) | 13.1992 | 0.587940 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13.7003 | −0.608453 | ||||||||
\(508\) | −0.994345 | −0.0441169 | ||||||||
\(509\) | −5.15120 | −0.228323 | −0.114162 | − | 0.993462i | \(-0.536418\pi\) | ||||
−0.114162 | + | 0.993462i | \(0.536418\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −62.4272 | −2.76162 | ||||||||
\(512\) | −22.0353 | −0.973831 | ||||||||
\(513\) | 5.59998 | 0.247245 | ||||||||
\(514\) | −6.36212 | −0.280621 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.78091 | −0.254490 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 19.5692 | 0.859820 | ||||||||
\(519\) | 1.97504 | 0.0866948 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −41.5022 | −1.81824 | −0.909121 | − | 0.416532i | \(-0.863246\pi\) | ||||
−0.909121 | + | 0.416532i | \(0.863246\pi\) | |||||||
\(522\) | −7.45917 | −0.326479 | ||||||||
\(523\) | −6.92280 | −0.302713 | −0.151356 | − | 0.988479i | \(-0.548364\pi\) | ||||
−0.151356 | + | 0.988479i | \(0.548364\pi\) | |||||||
\(524\) | 1.72815 | 0.0754944 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.9273 | 0.607259 | ||||||||
\(527\) | −14.1548 | −0.616592 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9517 | −0.997899 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.87035 | −0.341544 | ||||||||
\(532\) | −15.5900 | −0.675911 | ||||||||
\(533\) | −30.2852 | −1.31180 | ||||||||
\(534\) | 2.98143 | 0.129019 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 37.3421 | 1.61293 | ||||||||
\(537\) | 2.02315 | 0.0873052 | ||||||||
\(538\) | 15.8592 | 0.683740 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.4183 | 1.22180 | 0.610899 | − | 0.791709i | \(-0.290808\pi\) | ||||
0.610899 | + | 0.791709i | \(0.290808\pi\) | |||||||
\(542\) | −13.7573 | −0.590928 | ||||||||
\(543\) | −20.1380 | −0.864205 | ||||||||
\(544\) | 17.5449 | 0.752231 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 25.7429 | 1.10169 | ||||||||
\(547\) | 25.8592 | 1.10566 | 0.552829 | − | 0.833295i | \(-0.313548\pi\) | ||||
0.552829 | + | 0.833295i | \(0.313548\pi\) | |||||||
\(548\) | 6.66004 | 0.284503 | ||||||||
\(549\) | 4.85807 | 0.207337 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 35.9431 | 1.53123 | ||||||||
\(552\) | 0.676824 | 0.0288075 | ||||||||
\(553\) | 34.3031 | 1.45871 | ||||||||
\(554\) | 11.9281 | 0.506776 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.43869 | −0.145833 | ||||||||
\(557\) | −8.06409 | −0.341687 | −0.170843 | − | 0.985298i | \(-0.554649\pi\) | ||||
−0.170843 | + | 0.985298i | \(0.554649\pi\) | |||||||
\(558\) | −3.28999 | −0.139276 | ||||||||
\(559\) | −45.9973 | −1.94548 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.41542 | 0.144071 | ||||||||
\(563\) | 29.6516 | 1.24966 | 0.624832 | − | 0.780759i | \(-0.285167\pi\) | ||||
0.624832 | + | 0.780759i | \(0.285167\pi\) | |||||||
\(564\) | 0.154481 | 0.00650483 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 25.3673 | 1.06627 | ||||||||
\(567\) | −4.28684 | −0.180030 | ||||||||
\(568\) | 30.7345 | 1.28959 | ||||||||
\(569\) | 42.1026 | 1.76503 | 0.882517 | − | 0.470280i | \(-0.155847\pi\) | ||||
0.882517 | + | 0.470280i | \(0.155847\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.6823 | 1.11662 | 0.558311 | − | 0.829632i | \(-0.311450\pi\) | ||||
0.558311 | + | 0.829632i | \(0.311450\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.6652 | −0.529094 | ||||||||
\(574\) | 29.1992 | 1.21875 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 8.63682 | 0.359867 | ||||||||
\(577\) | 3.30818 | 0.137721 | 0.0688606 | − | 0.997626i | \(-0.478064\pi\) | ||||
0.0688606 | + | 0.997626i | \(0.478064\pi\) | |||||||
\(578\) | 9.29718 | 0.386712 | ||||||||
\(579\) | 13.9321 | 0.578999 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −53.8125 | −2.23252 | ||||||||
\(582\) | 2.33822 | 0.0969225 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −44.8381 | −1.85542 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28.7823 | −1.18899 | ||||||||
\(587\) | 8.52770 | 0.351976 | 0.175988 | − | 0.984392i | \(-0.443688\pi\) | ||||
0.175988 | + | 0.984392i | \(0.443688\pi\) | |||||||
\(588\) | 7.38839 | 0.304692 | ||||||||
\(589\) | 15.8533 | 0.653223 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.6060 | −0.600813 | ||||||||
\(592\) | 8.95367 | 0.367993 | ||||||||
\(593\) | −23.4343 | −0.962333 | −0.481167 | − | 0.876629i | \(-0.659787\pi\) | ||||
−0.481167 | + | 0.876629i | \(0.659787\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.46025 | 0.100776 | ||||||||
\(597\) | 11.8748 | 0.486004 | ||||||||
\(598\) | 1.32003 | 0.0539801 | ||||||||
\(599\) | 18.8344 | 0.769555 | 0.384777 | − | 0.923009i | \(-0.374278\pi\) | ||||
0.384777 | + | 0.923009i | \(0.374278\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.6585 | 1.53612 | 0.768062 | − | 0.640376i | \(-0.221221\pi\) | ||||
0.768062 | + | 0.640376i | \(0.221221\pi\) | |||||||
\(602\) | 44.3479 | 1.80749 | ||||||||
\(603\) | −12.1280 | −0.493889 | ||||||||
\(604\) | −3.84453 | −0.156432 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −8.81471 | −0.358073 | ||||||||
\(607\) | −29.3680 | −1.19201 | −0.596004 | − | 0.802981i | \(-0.703246\pi\) | ||||
−0.596004 | + | 0.802981i | \(0.703246\pi\) | |||||||
\(608\) | −19.6502 | −0.796921 | ||||||||
\(609\) | −27.5148 | −1.11496 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.22917 | 0.0497269 | ||||||||
\(612\) | −3.24707 | −0.131255 | ||||||||
\(613\) | −12.9111 | −0.521474 | −0.260737 | − | 0.965410i | \(-0.583965\pi\) | ||||
−0.260737 | + | 0.965410i | \(0.583965\pi\) | |||||||
\(614\) | −5.74127 | −0.231699 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −41.6041 | −1.67492 | −0.837459 | − | 0.546500i | \(-0.815960\pi\) | ||||
−0.837459 | + | 0.546500i | \(0.815960\pi\) | |||||||
\(618\) | −19.6037 | −0.788578 | ||||||||
\(619\) | 4.27117 | 0.171673 | 0.0858363 | − | 0.996309i | \(-0.472644\pi\) | ||||
0.0858363 | + | 0.996309i | \(0.472644\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.219819 | −0.00882102 | ||||||||
\(622\) | −16.0488 | −0.643497 | ||||||||
\(623\) | 10.9977 | 0.440613 | ||||||||
\(624\) | 11.7784 | 0.471512 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.72918 | 0.189016 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.82455 | −0.192521 | ||||||||
\(629\) | −19.6401 | −0.783103 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.5510 | −1.09679 | −0.548393 | − | 0.836221i | \(-0.684760\pi\) | ||||
−0.548393 | + | 0.836221i | \(0.684760\pi\) | |||||||
\(632\) | 24.6381 | 0.980049 | ||||||||
\(633\) | −22.3518 | −0.888406 | ||||||||
\(634\) | −30.0066 | −1.19171 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.64737 | −0.0653225 | ||||||||
\(637\) | 58.7877 | 2.32925 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.98194 | −0.394879 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.16806 | 0.362117 | 0.181058 | − | 0.983472i | \(-0.442048\pi\) | ||||
0.181058 | + | 0.983472i | \(0.442048\pi\) | |||||||
\(642\) | −9.02014 | −0.355996 | ||||||||
\(643\) | 3.40908 | 0.134441 | 0.0672206 | − | 0.997738i | \(-0.478587\pi\) | ||||
0.0672206 | + | 0.997738i | \(0.478587\pi\) | |||||||
\(644\) | 0.611961 | 0.0241146 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −32.5400 | −1.28027 | ||||||||
\(647\) | −22.3608 | −0.879092 | −0.439546 | − | 0.898220i | \(-0.644861\pi\) | ||||
−0.439546 | + | 0.898220i | \(0.644861\pi\) | |||||||
\(648\) | −3.07901 | −0.120955 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.1359 | −0.475642 | ||||||||
\(652\) | 3.45544 | 0.135325 | ||||||||
\(653\) | 14.7957 | 0.578999 | 0.289500 | − | 0.957178i | \(-0.406511\pi\) | ||||
0.289500 | + | 0.957178i | \(0.406511\pi\) | |||||||
\(654\) | 5.17936 | 0.202529 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 13.3598 | 0.521611 | ||||||||
\(657\) | 14.5625 | 0.568138 | ||||||||
\(658\) | −1.18509 | −0.0461997 | ||||||||
\(659\) | 47.4724 | 1.84926 | 0.924631 | − | 0.380864i | \(-0.124373\pi\) | ||||
0.924631 | + | 0.380864i | \(0.124373\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.6525 | −0.842184 | −0.421092 | − | 0.907018i | \(-0.638353\pi\) | ||||
−0.421092 | + | 0.907018i | \(0.638353\pi\) | |||||||
\(662\) | −3.89328 | −0.151317 | ||||||||
\(663\) | −25.8362 | −1.00339 | ||||||||
\(664\) | −38.6507 | −1.49994 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.56494 | −0.176888 | ||||||||
\(667\) | −1.41089 | −0.0546300 | ||||||||
\(668\) | 1.28025 | 0.0495342 | ||||||||
\(669\) | −19.1583 | −0.740703 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 15.0424 | 0.580275 | ||||||||
\(673\) | −38.3923 | −1.47991 | −0.739957 | − | 0.672654i | \(-0.765154\pi\) | ||||
−0.739957 | + | 0.672654i | \(0.765154\pi\) | |||||||
\(674\) | −31.8426 | −1.22653 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.89718 | −0.342199 | ||||||||
\(677\) | −22.9333 | −0.881398 | −0.440699 | − | 0.897655i | \(-0.645269\pi\) | ||||
−0.440699 | + | 0.897655i | \(0.645269\pi\) | |||||||
\(678\) | −8.96302 | −0.344223 | ||||||||
\(679\) | 8.62507 | 0.331000 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.3759 | −0.589206 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.9084 | −0.991359 | −0.495680 | − | 0.868505i | \(-0.665081\pi\) | ||||
−0.495680 | + | 0.868505i | \(0.665081\pi\) | |||||||
\(684\) | 3.63670 | 0.139053 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −21.8060 | −0.832557 | ||||||||
\(687\) | −8.90126 | −0.339604 | ||||||||
\(688\) | 20.2909 | 0.773584 | ||||||||
\(689\) | −13.1078 | −0.499366 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.8155 | 0.563608 | 0.281804 | − | 0.959472i | \(-0.409067\pi\) | ||||
0.281804 | + | 0.959472i | \(0.409067\pi\) | |||||||
\(692\) | 1.28262 | 0.0487579 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18.3927 | 0.698177 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −19.7624 | −0.749092 | ||||||||
\(697\) | −29.3050 | −1.11001 | ||||||||
\(698\) | 4.25264 | 0.160965 | ||||||||
\(699\) | −22.8362 | −0.863744 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.50632 | −0.207971 | −0.103985 | − | 0.994579i | \(-0.533160\pi\) | ||||
−0.103985 | + | 0.994579i | \(0.533160\pi\) | |||||||
\(702\) | −6.00509 | −0.226647 | ||||||||
\(703\) | 21.9968 | 0.829626 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 31.9517 | 1.20252 | ||||||||
\(707\) | −32.5150 | −1.22285 | ||||||||
\(708\) | −5.11112 | −0.192087 | ||||||||
\(709\) | −17.9007 | −0.672274 | −0.336137 | − | 0.941813i | \(-0.609120\pi\) | ||||
−0.336137 | + | 0.941813i | \(0.609120\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.00194 | −0.300096 | ||||||||
\(712\) | 7.89905 | 0.296029 | ||||||||
\(713\) | −0.622297 | −0.0233052 | ||||||||
\(714\) | 24.9097 | 0.932222 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.31386 | 0.0491012 | ||||||||
\(717\) | 16.8605 | 0.629668 | ||||||||
\(718\) | −0.556367 | −0.0207634 | ||||||||
\(719\) | 32.5918 | 1.21547 | 0.607734 | − | 0.794141i | \(-0.292079\pi\) | ||||
0.607734 | + | 0.794141i | \(0.292079\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −72.3128 | −2.69307 | ||||||||
\(722\) | 14.3638 | 0.534566 | ||||||||
\(723\) | −11.9607 | −0.444825 | ||||||||
\(724\) | −13.0779 | −0.486037 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 43.0199 | 1.59552 | 0.797759 | − | 0.602976i | \(-0.206018\pi\) | ||||
0.797759 | + | 0.602976i | \(0.206018\pi\) | |||||||
\(728\) | 68.2035 | 2.52779 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −44.5087 | −1.64621 | ||||||||
\(732\) | 3.15490 | 0.116608 | ||||||||
\(733\) | 40.7066 | 1.50353 | 0.751766 | − | 0.659429i | \(-0.229202\pi\) | ||||
0.751766 | + | 0.659429i | \(0.229202\pi\) | |||||||
\(734\) | 29.5862 | 1.09204 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.771340 | 0.0284320 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −6.81134 | −0.250729 | ||||||||
\(739\) | −38.1240 | −1.40241 | −0.701207 | − | 0.712958i | \(-0.747355\pi\) | ||||
−0.701207 | + | 0.712958i | \(0.747355\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 28.9364 | 1.06300 | ||||||||
\(742\) | 12.6377 | 0.463945 | ||||||||
\(743\) | −18.0381 | −0.661754 | −0.330877 | − | 0.943674i | \(-0.607345\pi\) | ||||
−0.330877 | + | 0.943674i | \(0.607345\pi\) | |||||||
\(744\) | −8.71654 | −0.319564 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.20714 | −0.117422 | ||||||||
\(747\) | 12.5530 | 0.459289 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −33.2728 | −1.21576 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.5349 | −0.639859 | −0.319929 | − | 0.947441i | \(-0.603659\pi\) | ||||
−0.319929 | + | 0.947441i | \(0.603659\pi\) | |||||||
\(752\) | −0.542227 | −0.0197730 | ||||||||
\(753\) | −16.0034 | −0.583197 | ||||||||
\(754\) | −38.5433 | −1.40366 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.78393 | −0.101251 | ||||||||
\(757\) | 25.9609 | 0.943565 | 0.471782 | − | 0.881715i | \(-0.343611\pi\) | ||||
0.471782 | + | 0.881715i | \(0.343611\pi\) | |||||||
\(758\) | −25.1646 | −0.914019 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.0059 | −1.01521 | −0.507607 | − | 0.861589i | \(-0.669470\pi\) | ||||
−0.507607 | + | 0.861589i | \(0.669470\pi\) | |||||||
\(762\) | −1.77941 | −0.0644613 | ||||||||
\(763\) | 19.1052 | 0.691655 | ||||||||
\(764\) | −8.22493 | −0.297567 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.8610 | −0.681477 | ||||||||
\(767\) | −40.6680 | −1.46843 | ||||||||
\(768\) | 13.7648 | 0.496693 | ||||||||
\(769\) | −22.9537 | −0.827732 | −0.413866 | − | 0.910338i | \(-0.635822\pi\) | ||||
−0.413866 | + | 0.910338i | \(0.635822\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.47446 | 0.197158 | ||||||||
\(772\) | 9.04772 | 0.325634 | ||||||||
\(773\) | 23.5282 | 0.846251 | 0.423126 | − | 0.906071i | \(-0.360933\pi\) | ||||
0.423126 | + | 0.906071i | \(0.360933\pi\) | |||||||
\(774\) | −10.3451 | −0.371848 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.19492 | 0.222385 | ||||||||
\(777\) | −16.8388 | −0.604089 | ||||||||
\(778\) | −18.9333 | −0.678791 | ||||||||
\(779\) | 32.8215 | 1.17595 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 1.27731 | 0.0456765 | ||||||||
\(783\) | 6.41843 | 0.229376 | ||||||||
\(784\) | −25.9331 | −0.926184 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.09257 | 0.110308 | ||||||||
\(787\) | −25.2725 | −0.900869 | −0.450434 | − | 0.892810i | \(-0.648731\pi\) | ||||
−0.450434 | + | 0.892810i | \(0.648731\pi\) | |||||||
\(788\) | −9.48537 | −0.337902 | ||||||||
\(789\) | −11.9841 | −0.426645 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −33.0621 | −1.17555 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.1028 | 0.891427 | ||||||||
\(794\) | 23.2049 | 0.823511 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.71168 | 0.273333 | ||||||||
\(797\) | −8.65645 | −0.306627 | −0.153314 | − | 0.988178i | \(-0.548994\pi\) | ||||
−0.153314 | + | 0.988178i | \(0.548994\pi\) | |||||||
\(798\) | −27.8987 | −0.987605 | ||||||||
\(799\) | 1.18939 | 0.0420775 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.56545 | −0.0906457 | ||||||||
\(802\) | −31.7579 | −1.12141 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −7.87607 | −0.277768 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −17.0001 | −0.598804 | ||||||||
\(807\) | −13.6465 | −0.480379 | ||||||||
\(808\) | −23.3538 | −0.821584 | ||||||||
\(809\) | 10.2124 | 0.359050 | 0.179525 | − | 0.983753i | \(-0.442544\pi\) | ||||
0.179525 | + | 0.983753i | \(0.442544\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.6224 | 1.67225 | 0.836124 | − | 0.548540i | \(-0.184816\pi\) | ||||
0.836124 | + | 0.548540i | \(0.184816\pi\) | |||||||
\(812\) | −17.8685 | −0.627061 | ||||||||
\(813\) | 11.8379 | 0.415172 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 11.3972 | 0.398981 | ||||||||
\(817\) | 49.8495 | 1.74401 | ||||||||
\(818\) | −28.9816 | −1.01332 | ||||||||
\(819\) | −22.1511 | −0.774023 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 47.5598 | 1.65985 | 0.829925 | − | 0.557875i | \(-0.188383\pi\) | ||||
0.829925 | + | 0.557875i | \(0.188383\pi\) | |||||||
\(822\) | 11.9184 | 0.415700 | ||||||||
\(823\) | 24.7360 | 0.862242 | 0.431121 | − | 0.902294i | \(-0.358118\pi\) | ||||
0.431121 | + | 0.902294i | \(0.358118\pi\) | |||||||
\(824\) | −51.9384 | −1.80936 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 39.2096 | 1.36428 | ||||||||
\(827\) | −1.56166 | −0.0543043 | −0.0271522 | − | 0.999631i | \(-0.508644\pi\) | ||||
−0.0271522 | + | 0.999631i | \(0.508644\pi\) | |||||||
\(828\) | −0.142753 | −0.00496102 | ||||||||
\(829\) | 42.1950 | 1.46549 | 0.732747 | − | 0.680501i | \(-0.238238\pi\) | ||||
0.732747 | + | 0.680501i | \(0.238238\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.2638 | −0.356048 | ||||||||
\(832\) | 44.6285 | 1.54721 | ||||||||
\(833\) | 56.8851 | 1.97095 | ||||||||
\(834\) | −6.15366 | −0.213084 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.83095 | 0.0978521 | ||||||||
\(838\) | 19.5539 | 0.675477 | ||||||||
\(839\) | −6.29451 | −0.217311 | −0.108655 | − | 0.994079i | \(-0.534654\pi\) | ||||
−0.108655 | + | 0.994079i | \(0.534654\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.1963 | 0.420562 | ||||||||
\(842\) | 27.4274 | 0.945211 | ||||||||
\(843\) | −2.93889 | −0.101221 | ||||||||
\(844\) | −14.5156 | −0.499647 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.276449 | 0.00950451 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.78225 | 0.198563 | ||||||||
\(849\) | −21.8279 | −0.749133 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.863453 | −0.0295988 | ||||||||
\(852\) | −6.48241 | −0.222084 | ||||||||
\(853\) | −7.27120 | −0.248961 | −0.124481 | − | 0.992222i | \(-0.539726\pi\) | ||||
−0.124481 | + | 0.992222i | \(0.539726\pi\) | |||||||
\(854\) | −24.2026 | −0.828197 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −23.8981 | −0.816819 | ||||||||
\(857\) | 39.8590 | 1.36156 | 0.680779 | − | 0.732489i | \(-0.261641\pi\) | ||||
0.680779 | + | 0.732489i | \(0.261641\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.5278 | 0.461564 | 0.230782 | − | 0.973006i | \(-0.425872\pi\) | ||||
0.230782 | + | 0.973006i | \(0.425872\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −25.1252 | −0.856264 | ||||||||
\(862\) | 43.7613 | 1.49052 | ||||||||
\(863\) | −50.3117 | −1.71263 | −0.856316 | − | 0.516453i | \(-0.827252\pi\) | ||||
−0.856316 | + | 0.516453i | \(0.827252\pi\) | |||||||
\(864\) | −3.50898 | −0.119378 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 35.9977 | 1.22325 | ||||||||
\(867\) | −8.00000 | −0.271694 | ||||||||
\(868\) | −7.88119 | −0.267505 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −62.6681 | −2.12343 | ||||||||
\(872\) | 13.7223 | 0.464694 | ||||||||
\(873\) | −2.01199 | −0.0680954 | ||||||||
\(874\) | −1.43058 | −0.0483901 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 9.45710 | 0.319526 | ||||||||
\(877\) | −1.20736 | −0.0407696 | −0.0203848 | − | 0.999792i | \(-0.506489\pi\) | ||||
−0.0203848 | + | 0.999792i | \(0.506489\pi\) | |||||||
\(878\) | 32.7877 | 1.10653 | ||||||||
\(879\) | 24.7665 | 0.835354 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.91816 | 0.0646245 | 0.0323123 | − | 0.999478i | \(-0.489713\pi\) | ||||
0.0323123 | + | 0.999478i | \(0.489713\pi\) | |||||||
\(882\) | 13.2218 | 0.445200 | ||||||||
\(883\) | −58.0890 | −1.95485 | −0.977425 | − | 0.211281i | \(-0.932237\pi\) | ||||
−0.977425 | + | 0.211281i | \(0.932237\pi\) | |||||||
\(884\) | −16.7784 | −0.564318 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −17.0162 | −0.571669 | ||||||||
\(887\) | 30.2427 | 1.01545 | 0.507725 | − | 0.861519i | \(-0.330487\pi\) | ||||
0.507725 | + | 0.861519i | \(0.330487\pi\) | |||||||
\(888\) | −12.0944 | −0.405862 | ||||||||
\(889\) | −6.56377 | −0.220142 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.4417 | −0.416578 | ||||||||
\(893\) | −1.33211 | −0.0445773 | ||||||||
\(894\) | 4.40269 | 0.147248 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −12.9432 | −0.432403 | ||||||||
\(897\) | −1.13586 | −0.0379251 | ||||||||
\(898\) | 13.9431 | 0.465286 | ||||||||
\(899\) | 18.1703 | 0.606013 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.6835 | −0.422550 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −38.1603 | −1.26990 | ||||||||
\(904\) | −23.7468 | −0.789805 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.87992 | −0.228570 | ||||||||
\(907\) | 31.9669 | 1.06144 | 0.530721 | − | 0.847547i | \(-0.321921\pi\) | ||||
0.530721 | + | 0.847547i | \(0.321921\pi\) | |||||||
\(908\) | −9.98532 | −0.331374 | ||||||||
\(909\) | 7.58484 | 0.251573 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.8454 | −1.71771 | −0.858857 | − | 0.512216i | \(-0.828825\pi\) | ||||
−0.858857 | + | 0.512216i | \(0.828825\pi\) | |||||||
\(912\) | −12.7648 | −0.422684 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 11.6722 | 0.386083 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.78060 | −0.190996 | ||||||||
\(917\) | 11.4076 | 0.376714 | ||||||||
\(918\) | −5.81074 | −0.191783 | ||||||||
\(919\) | 34.2084 | 1.12843 | 0.564215 | − | 0.825628i | \(-0.309179\pi\) | ||||
0.564215 | + | 0.825628i | \(0.309179\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.94023 | 0.162786 | ||||||||
\(922\) | 15.6298 | 0.514741 | ||||||||
\(923\) | −51.5790 | −1.69774 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −21.8293 | −0.717354 | ||||||||
\(927\) | 16.8685 | 0.554036 | ||||||||
\(928\) | −22.5222 | −0.739326 | ||||||||
\(929\) | 18.3482 | 0.601984 | 0.300992 | − | 0.953627i | \(-0.402682\pi\) | ||||
0.300992 | + | 0.953627i | \(0.402682\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −63.7110 | −2.08804 | ||||||||
\(932\) | −14.8301 | −0.485777 | ||||||||
\(933\) | 13.8096 | 0.452106 | ||||||||
\(934\) | −30.8561 | −1.00964 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −15.9100 | −0.520033 | ||||||||
\(937\) | 3.38415 | 0.110555 | 0.0552777 | − | 0.998471i | \(-0.482396\pi\) | ||||
0.0552777 | + | 0.998471i | \(0.482396\pi\) | |||||||
\(938\) | 60.4208 | 1.97281 | ||||||||
\(939\) | −4.06934 | −0.132798 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.1002 | 1.14423 | 0.572116 | − | 0.820172i | \(-0.306123\pi\) | ||||
0.572116 | + | 0.820172i | \(0.306123\pi\) | |||||||
\(942\) | −8.63369 | −0.281301 | ||||||||
\(943\) | −1.28836 | −0.0419547 | ||||||||
\(944\) | 17.9399 | 0.583895 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.0512 | 1.26899 | 0.634497 | − | 0.772925i | \(-0.281207\pi\) | ||||
0.634497 | + | 0.772925i | \(0.281207\pi\) | |||||||
\(948\) | −5.19657 | −0.168777 | ||||||||
\(949\) | 75.2480 | 2.44265 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.8199 | 0.837269 | ||||||||
\(952\) | 65.9961 | 2.13895 | ||||||||
\(953\) | 24.6783 | 0.799409 | 0.399705 | − | 0.916644i | \(-0.369113\pi\) | ||||
0.399705 | + | 0.916644i | \(0.369113\pi\) | |||||||
\(954\) | −2.94803 | −0.0954458 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 10.9495 | 0.354131 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.5315 | −0.404873 | ||||||||
\(959\) | 43.9635 | 1.41966 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.9857 | −0.741474 | ||||||||
\(962\) | −23.5881 | −0.760512 | ||||||||
\(963\) | 7.76161 | 0.250114 | ||||||||
\(964\) | −7.76747 | −0.250173 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.09512 | 0.0352350 | ||||||||
\(967\) | 1.20724 | 0.0388222 | 0.0194111 | − | 0.999812i | \(-0.493821\pi\) | ||||
0.0194111 | + | 0.999812i | \(0.493821\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 27.9999 | 0.899486 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.3821 | 1.61684 | 0.808418 | − | 0.588608i | \(-0.200324\pi\) | ||||
0.808418 | + | 0.588608i | \(0.200324\pi\) | |||||||
\(972\) | 0.649414 | 0.0208300 | ||||||||
\(973\) | −22.6991 | −0.727701 | ||||||||
\(974\) | −7.91533 | −0.253624 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.0737 | −0.354459 | ||||||||
\(977\) | 5.88330 | 0.188223 | 0.0941117 | − | 0.995562i | \(-0.469999\pi\) | ||||
0.0941117 | + | 0.995562i | \(0.469999\pi\) | |||||||
\(978\) | 6.18362 | 0.197730 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.45671 | −0.142292 | ||||||||
\(982\) | −30.3267 | −0.967763 | ||||||||
\(983\) | −36.4899 | −1.16385 | −0.581924 | − | 0.813243i | \(-0.697700\pi\) | ||||
−0.581924 | + | 0.813243i | \(0.697700\pi\) | |||||||
\(984\) | −18.0461 | −0.575288 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −37.2958 | −1.18774 | ||||||||
\(987\) | 1.01974 | 0.0324588 | ||||||||
\(988\) | 18.7917 | 0.597843 | ||||||||
\(989\) | −1.95677 | −0.0622216 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.8404 | −1.17027 | −0.585137 | − | 0.810934i | \(-0.698959\pi\) | ||||
−0.585137 | + | 0.810934i | \(0.698959\pi\) | |||||||
\(992\) | −9.93376 | −0.315397 | ||||||||
\(993\) | 3.35008 | 0.106311 | ||||||||
\(994\) | 49.7294 | 1.57732 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 8.15206 | 0.258308 | ||||||||
\(997\) | 34.8694 | 1.10432 | 0.552162 | − | 0.833737i | \(-0.313803\pi\) | ||||
0.552162 | + | 0.833737i | \(0.313803\pi\) | |||||||
\(998\) | 22.5263 | 0.713059 | ||||||||
\(999\) | 3.92802 | 0.124277 |
(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 | 9075.2.a.dj.1.2 | 4 | ||
5.4 | even | 2 | 1815.2.a.o.1.3 | 4 | |||
11.7 | odd | 10 | 825.2.n.k.676.2 | 8 | |||
11.8 | odd | 10 | 825.2.n.k.526.2 | 8 | |||
11.10 | odd | 2 | 9075.2.a.cl.1.3 | 4 | |||
15.14 | odd | 2 | 5445.2.a.bv.1.2 | 4 | |||
55.7 | even | 20 | 825.2.bx.h.49.3 | 16 | |||
55.8 | even | 20 | 825.2.bx.h.724.3 | 16 | |||
55.18 | even | 20 | 825.2.bx.h.49.2 | 16 | |||
55.19 | odd | 10 | 165.2.m.a.31.1 | yes | 8 | ||
55.29 | odd | 10 | 165.2.m.a.16.1 | ✓ | 8 | ||
55.52 | even | 20 | 825.2.bx.h.724.2 | 16 | |||
55.54 | odd | 2 | 1815.2.a.x.1.2 | 4 | |||
165.29 | even | 10 | 495.2.n.d.181.2 | 8 | |||
165.74 | even | 10 | 495.2.n.d.361.2 | 8 | |||
165.164 | even | 2 | 5445.2.a.be.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.m.a.16.1 | ✓ | 8 | 55.29 | odd | 10 | ||
165.2.m.a.31.1 | yes | 8 | 55.19 | odd | 10 | ||
495.2.n.d.181.2 | 8 | 165.29 | even | 10 | |||
495.2.n.d.361.2 | 8 | 165.74 | even | 10 | |||
825.2.n.k.526.2 | 8 | 11.8 | odd | 10 | |||
825.2.n.k.676.2 | 8 | 11.7 | odd | 10 | |||
825.2.bx.h.49.2 | 16 | 55.18 | even | 20 | |||
825.2.bx.h.49.3 | 16 | 55.7 | even | 20 | |||
825.2.bx.h.724.2 | 16 | 55.52 | even | 20 | |||
825.2.bx.h.724.3 | 16 | 55.8 | even | 20 | |||
1815.2.a.o.1.3 | 4 | 5.4 | even | 2 | |||
1815.2.a.x.1.2 | 4 | 55.54 | odd | 2 | |||
5445.2.a.be.1.3 | 4 | 165.164 | even | 2 | |||
5445.2.a.bv.1.2 | 4 | 15.14 | odd | 2 | |||
9075.2.a.cl.1.3 | 4 | 11.10 | odd | 2 | |||
9075.2.a.dj.1.2 | 4 | 1.1 | even | 1 | trivial |