Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.446366 | 0.315628 | 0.157814 | − | 0.987469i | \(-0.449555\pi\) | ||||
0.157814 | + | 0.987469i | \(0.449555\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.80076 | −0.900379 | ||||||||
\(5\) | −2.33773 | −1.04547 | −0.522733 | − | 0.852496i | \(-0.675088\pi\) | ||||
−0.522733 | + | 0.852496i | \(0.675088\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.69653 | −0.599814 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.04348 | −0.329979 | ||||||||
\(11\) | 4.53166 | 1.36635 | 0.683174 | − | 0.730256i | \(-0.260599\pi\) | ||||
0.683174 | + | 0.730256i | \(0.260599\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.767582 | −0.212889 | −0.106445 | − | 0.994319i | \(-0.533947\pi\) | ||||
−0.106445 | + | 0.994319i | \(0.533947\pi\) | |||||||
\(14\) | 0.446366 | 0.119296 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.84424 | 0.711061 | ||||||||
\(17\) | 3.43169 | 0.832307 | 0.416154 | − | 0.909294i | \(-0.363378\pi\) | ||||
0.416154 | + | 0.909294i | \(0.363378\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.98922 | −1.14460 | −0.572302 | − | 0.820043i | \(-0.693950\pi\) | ||||
−0.572302 | + | 0.820043i | \(0.693950\pi\) | |||||||
\(20\) | 4.20969 | 0.941316 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.02278 | 0.431258 | ||||||||
\(23\) | −4.14751 | −0.864816 | −0.432408 | − | 0.901678i | \(-0.642336\pi\) | ||||
−0.432408 | + | 0.901678i | \(0.642336\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.464998 | 0.0929996 | ||||||||
\(26\) | −0.342623 | −0.0671938 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.80076 | −0.340311 | ||||||||
\(29\) | −9.37650 | −1.74117 | −0.870586 | − | 0.492016i | \(-0.836260\pi\) | ||||
−0.870586 | + | 0.492016i | \(0.836260\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.36743 | 0.964019 | 0.482009 | − | 0.876166i | \(-0.339907\pi\) | ||||
0.482009 | + | 0.876166i | \(0.339907\pi\) | |||||||
\(32\) | 4.66263 | 0.824244 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.53179 | 0.262700 | ||||||||
\(35\) | −2.33773 | −0.395149 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.44708 | −0.402297 | −0.201148 | − | 0.979561i | \(-0.564467\pi\) | ||||
−0.201148 | + | 0.979561i | \(0.564467\pi\) | |||||||
\(38\) | −2.22702 | −0.361270 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.96603 | 0.627085 | ||||||||
\(41\) | −1.04906 | −0.163835 | −0.0819176 | − | 0.996639i | \(-0.526104\pi\) | ||||
−0.0819176 | + | 0.996639i | \(0.526104\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.90570 | 0.443116 | 0.221558 | − | 0.975147i | \(-0.428886\pi\) | ||||
0.221558 | + | 0.975147i | \(0.428886\pi\) | |||||||
\(44\) | −8.16042 | −1.23023 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.85131 | −0.272961 | ||||||||
\(47\) | −1.19217 | −0.173896 | −0.0869481 | − | 0.996213i | \(-0.527711\pi\) | ||||
−0.0869481 | + | 0.996213i | \(0.527711\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.207559 | 0.0293533 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.38223 | 0.191681 | ||||||||
\(53\) | 10.5726 | 1.45226 | 0.726130 | − | 0.687557i | \(-0.241317\pi\) | ||||
0.726130 | + | 0.687557i | \(0.241317\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.5938 | −1.42847 | ||||||||
\(56\) | −1.69653 | −0.226708 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.18535 | −0.549563 | ||||||||
\(59\) | 1.68946 | 0.219949 | 0.109974 | − | 0.993934i | \(-0.464923\pi\) | ||||
0.109974 | + | 0.993934i | \(0.464923\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.42071 | 0.566014 | 0.283007 | − | 0.959118i | \(-0.408668\pi\) | ||||
0.283007 | + | 0.959118i | \(0.408668\pi\) | |||||||
\(62\) | 2.39584 | 0.304272 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.60724 | −0.450906 | ||||||||
\(65\) | 1.79440 | 0.222568 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.8999 | 1.45380 | 0.726901 | − | 0.686742i | \(-0.240960\pi\) | ||||
0.726901 | + | 0.686742i | \(0.240960\pi\) | |||||||
\(68\) | −6.17964 | −0.749392 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.04348 | −0.124720 | ||||||||
\(71\) | 5.39083 | 0.639773 | 0.319887 | − | 0.947456i | \(-0.396355\pi\) | ||||
0.319887 | + | 0.947456i | \(0.396355\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.28672 | 0.618764 | 0.309382 | − | 0.950938i | \(-0.399878\pi\) | ||||
0.309382 | + | 0.950938i | \(0.399878\pi\) | |||||||
\(74\) | −1.09229 | −0.126976 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.98437 | 1.03058 | ||||||||
\(77\) | 4.53166 | 0.516431 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.18146 | −0.582959 | −0.291480 | − | 0.956577i | \(-0.594148\pi\) | ||||
−0.291480 | + | 0.956577i | \(0.594148\pi\) | |||||||
\(80\) | −6.64908 | −0.743390 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.468264 | −0.0517111 | ||||||||
\(83\) | 6.33884 | 0.695778 | 0.347889 | − | 0.937536i | \(-0.386899\pi\) | ||||
0.347889 | + | 0.937536i | \(0.386899\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.02238 | −0.870149 | ||||||||
\(86\) | 1.29701 | 0.139860 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −7.68809 | −0.819554 | ||||||||
\(89\) | −1.35913 | −0.144068 | −0.0720339 | − | 0.997402i | \(-0.522949\pi\) | ||||
−0.0720339 | + | 0.997402i | \(0.522949\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.767582 | −0.0804645 | ||||||||
\(92\) | 7.46866 | 0.778662 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.532145 | −0.0548866 | ||||||||
\(95\) | 11.6635 | 1.19665 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.94618 | −0.908347 | −0.454173 | − | 0.890913i | \(-0.650065\pi\) | ||||
−0.454173 | + | 0.890913i | \(0.650065\pi\) | |||||||
\(98\) | 0.446366 | 0.0450898 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.837349 | −0.0837349 | ||||||||
\(101\) | 0.306288 | 0.0304768 | 0.0152384 | − | 0.999884i | \(-0.495149\pi\) | ||||
0.0152384 | + | 0.999884i | \(0.495149\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.08821 | −0.698422 | −0.349211 | − | 0.937044i | \(-0.613550\pi\) | ||||
−0.349211 | + | 0.937044i | \(0.613550\pi\) | |||||||
\(104\) | 1.30223 | 0.127694 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.71926 | 0.458375 | ||||||||
\(107\) | −9.23685 | −0.892960 | −0.446480 | − | 0.894794i | \(-0.647323\pi\) | ||||
−0.446480 | + | 0.894794i | \(0.647323\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.5036 | −1.00606 | −0.503031 | − | 0.864268i | \(-0.667782\pi\) | ||||
−0.503031 | + | 0.864268i | \(0.667782\pi\) | |||||||
\(110\) | −4.72872 | −0.450866 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.84424 | 0.268756 | ||||||||
\(113\) | 8.67620 | 0.816188 | 0.408094 | − | 0.912940i | \(-0.366193\pi\) | ||||
0.408094 | + | 0.912940i | \(0.366193\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.69578 | 0.904136 | ||||||||
\(116\) | 16.8848 | 1.56771 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.754117 | 0.0694221 | ||||||||
\(119\) | 3.43169 | 0.314583 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.53595 | 0.866905 | ||||||||
\(122\) | 1.97325 | 0.178650 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.66544 | −0.867982 | ||||||||
\(125\) | 10.6016 | 0.948238 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | −10.9354 | −0.966563 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.800960 | 0.0702489 | ||||||||
\(131\) | 10.2832 | 0.898445 | 0.449223 | − | 0.893420i | \(-0.351701\pi\) | ||||
0.449223 | + | 0.893420i | \(0.351701\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.98922 | −0.432620 | ||||||||
\(134\) | 5.31170 | 0.458861 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.82196 | −0.499229 | ||||||||
\(137\) | −0.222610 | −0.0190189 | −0.00950944 | − | 0.999955i | \(-0.503027\pi\) | ||||
−0.00950944 | + | 0.999955i | \(0.503027\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.73668 | 0.571398 | 0.285699 | − | 0.958319i | \(-0.407774\pi\) | ||||
0.285699 | + | 0.958319i | \(0.407774\pi\) | |||||||
\(140\) | 4.20969 | 0.355784 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.40628 | 0.201931 | ||||||||
\(143\) | −3.47842 | −0.290880 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 21.9198 | 1.82034 | ||||||||
\(146\) | 2.35981 | 0.195300 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.40659 | 0.362219 | ||||||||
\(149\) | 4.25733 | 0.348774 | 0.174387 | − | 0.984677i | \(-0.444206\pi\) | ||||
0.174387 | + | 0.984677i | \(0.444206\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.4936 | −1.50499 | −0.752495 | − | 0.658598i | \(-0.771150\pi\) | ||||
−0.752495 | + | 0.658598i | \(0.771150\pi\) | |||||||
\(152\) | 8.46435 | 0.686549 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.02278 | 0.163000 | ||||||||
\(155\) | −12.5476 | −1.00785 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.8175 | −0.863333 | −0.431666 | − | 0.902033i | \(-0.642074\pi\) | ||||
−0.431666 | + | 0.902033i | \(0.642074\pi\) | |||||||
\(158\) | −2.31283 | −0.183999 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −10.9000 | −0.861720 | ||||||||
\(161\) | −4.14751 | −0.326870 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.9398 | −1.32683 | −0.663415 | − | 0.748251i | \(-0.730894\pi\) | ||||
−0.663415 | + | 0.748251i | \(0.730894\pi\) | |||||||
\(164\) | 1.88910 | 0.147514 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.82944 | 0.219607 | ||||||||
\(167\) | −8.15215 | −0.630832 | −0.315416 | − | 0.948953i | \(-0.602144\pi\) | ||||
−0.315416 | + | 0.948953i | \(0.602144\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.4108 | −0.954678 | ||||||||
\(170\) | −3.58092 | −0.274644 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.23247 | −0.398972 | ||||||||
\(173\) | −16.1018 | −1.22420 | −0.612098 | − | 0.790782i | \(-0.709674\pi\) | ||||
−0.612098 | + | 0.790782i | \(0.709674\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.464998 | 0.0351506 | ||||||||
\(176\) | 12.8891 | 0.971556 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.606671 | −0.0454719 | ||||||||
\(179\) | 6.75542 | 0.504924 | 0.252462 | − | 0.967607i | \(-0.418760\pi\) | ||||
0.252462 | + | 0.967607i | \(0.418760\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.5449 | −1.22977 | −0.614885 | − | 0.788617i | \(-0.710798\pi\) | ||||
−0.614885 | + | 0.788617i | \(0.710798\pi\) | |||||||
\(182\) | −0.342623 | −0.0253969 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.03637 | 0.518728 | ||||||||
\(185\) | 5.72061 | 0.420588 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.5513 | 1.13722 | ||||||||
\(188\) | 2.14681 | 0.156572 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.20617 | 0.377695 | ||||||||
\(191\) | 4.01445 | 0.290475 | 0.145238 | − | 0.989397i | \(-0.453605\pi\) | ||||
0.145238 | + | 0.989397i | \(0.453605\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.60259 | −0.187339 | −0.0936693 | − | 0.995603i | \(-0.529860\pi\) | ||||
−0.0936693 | + | 0.995603i | \(0.529860\pi\) | |||||||
\(194\) | −3.99327 | −0.286700 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.80076 | −0.128626 | ||||||||
\(197\) | −3.22387 | −0.229691 | −0.114846 | − | 0.993383i | \(-0.536637\pi\) | ||||
−0.114846 | + | 0.993383i | \(0.536637\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.7767 | −0.905717 | −0.452859 | − | 0.891582i | \(-0.649596\pi\) | ||||
−0.452859 | + | 0.891582i | \(0.649596\pi\) | |||||||
\(200\) | −0.788883 | −0.0557824 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.136716 | 0.00961934 | ||||||||
\(203\) | −9.37650 | −0.658101 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.45242 | 0.171284 | ||||||||
\(206\) | −3.16393 | −0.220442 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.18319 | −0.151377 | ||||||||
\(209\) | −22.6094 | −1.56393 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.6650 | −1.35380 | −0.676898 | − | 0.736077i | \(-0.736676\pi\) | ||||
−0.676898 | + | 0.736077i | \(0.736676\pi\) | |||||||
\(212\) | −19.0387 | −1.30758 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.12302 | −0.281844 | ||||||||
\(215\) | −6.79276 | −0.463263 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.36743 | 0.364365 | ||||||||
\(218\) | −4.68845 | −0.317542 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 19.0769 | 1.28616 | ||||||||
\(221\) | −2.63411 | −0.177189 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.9512 | −0.733346 | −0.366673 | − | 0.930350i | \(-0.619503\pi\) | ||||
−0.366673 | + | 0.930350i | \(0.619503\pi\) | |||||||
\(224\) | 4.66263 | 0.311535 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.87276 | 0.257612 | ||||||||
\(227\) | −6.15209 | −0.408329 | −0.204164 | − | 0.978937i | \(-0.565448\pi\) | ||||
−0.204164 | + | 0.978937i | \(0.565448\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.4006 | 1.34811 | 0.674054 | − | 0.738682i | \(-0.264552\pi\) | ||||
0.674054 | + | 0.738682i | \(0.264552\pi\) | |||||||
\(230\) | 4.32787 | 0.285371 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 15.9075 | 1.04438 | ||||||||
\(233\) | −23.9319 | −1.56783 | −0.783914 | − | 0.620869i | \(-0.786780\pi\) | ||||
−0.783914 | + | 0.620869i | \(0.786780\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.78698 | 0.181803 | ||||||||
\(236\) | −3.04231 | −0.198037 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.53179 | 0.0992912 | ||||||||
\(239\) | 3.47377 | 0.224700 | 0.112350 | − | 0.993669i | \(-0.464162\pi\) | ||||
0.112350 | + | 0.993669i | \(0.464162\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.8457 | 0.698634 | 0.349317 | − | 0.937005i | \(-0.386414\pi\) | ||||
0.349317 | + | 0.937005i | \(0.386414\pi\) | |||||||
\(242\) | 4.25653 | 0.273620 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.96063 | −0.509627 | ||||||||
\(245\) | −2.33773 | −0.149352 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.82963 | 0.243674 | ||||||||
\(248\) | −9.10600 | −0.578231 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.73221 | 0.299291 | ||||||||
\(251\) | 11.2843 | 0.712260 | 0.356130 | − | 0.934437i | \(-0.384096\pi\) | ||||
0.356130 | + | 0.934437i | \(0.384096\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.7951 | −1.18164 | ||||||||
\(254\) | 0.446366 | 0.0280075 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.33329 | 0.145831 | ||||||||
\(257\) | −1.31385 | −0.0819559 | −0.0409779 | − | 0.999160i | \(-0.513047\pi\) | ||||
−0.0409779 | + | 0.999160i | \(0.513047\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.44708 | −0.152054 | ||||||||
\(260\) | −3.23128 | −0.200396 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.59006 | 0.283575 | ||||||||
\(263\) | −4.13412 | −0.254921 | −0.127460 | − | 0.991844i | \(-0.540683\pi\) | ||||
−0.127460 | + | 0.991844i | \(0.540683\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −24.7160 | −1.51829 | ||||||||
\(266\) | −2.22702 | −0.136547 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −21.4288 | −1.30897 | ||||||||
\(269\) | −19.5802 | −1.19382 | −0.596912 | − | 0.802307i | \(-0.703606\pi\) | ||||
−0.596912 | + | 0.802307i | \(0.703606\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.5373 | 1.55128 | 0.775641 | − | 0.631174i | \(-0.217427\pi\) | ||||
0.775641 | + | 0.631174i | \(0.217427\pi\) | |||||||
\(272\) | 9.76056 | 0.591821 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.0993656 | −0.00600290 | ||||||||
\(275\) | 2.10721 | 0.127070 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.17171 | −0.490991 | −0.245495 | − | 0.969398i | \(-0.578951\pi\) | ||||
−0.245495 | + | 0.969398i | \(0.578951\pi\) | |||||||
\(278\) | 3.00703 | 0.180349 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.96603 | 0.237016 | ||||||||
\(281\) | −11.2877 | −0.673366 | −0.336683 | − | 0.941618i | \(-0.609305\pi\) | ||||
−0.336683 | + | 0.941618i | \(0.609305\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.5510 | −0.864966 | −0.432483 | − | 0.901642i | \(-0.642362\pi\) | ||||
−0.432483 | + | 0.901642i | \(0.642362\pi\) | |||||||
\(284\) | −9.70757 | −0.576038 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.55265 | −0.0918101 | ||||||||
\(287\) | −1.04906 | −0.0619239 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.22350 | −0.307265 | ||||||||
\(290\) | 9.78423 | 0.574550 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.52011 | −0.557122 | ||||||||
\(293\) | −15.8252 | −0.924518 | −0.462259 | − | 0.886745i | \(-0.652961\pi\) | ||||
−0.462259 | + | 0.886745i | \(0.652961\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.94951 | −0.229949 | ||||||||
\(296\) | 4.15153 | 0.241303 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.90033 | 0.110083 | ||||||||
\(299\) | 3.18356 | 0.184110 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.90570 | 0.167482 | ||||||||
\(302\) | −8.25493 | −0.475018 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −14.1905 | −0.813883 | ||||||||
\(305\) | −10.3344 | −0.591749 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.2596 | 0.585544 | 0.292772 | − | 0.956182i | \(-0.405422\pi\) | ||||
0.292772 | + | 0.956182i | \(0.405422\pi\) | |||||||
\(308\) | −8.16042 | −0.464983 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.60083 | −0.318106 | ||||||||
\(311\) | 19.5160 | 1.10665 | 0.553325 | − | 0.832965i | \(-0.313359\pi\) | ||||
0.553325 | + | 0.832965i | \(0.313359\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.6729 | −1.39460 | −0.697298 | − | 0.716781i | \(-0.745615\pi\) | ||||
−0.697298 | + | 0.716781i | \(0.745615\pi\) | |||||||
\(314\) | −4.82858 | −0.272492 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.33055 | 0.524884 | ||||||||
\(317\) | −21.4107 | −1.20255 | −0.601273 | − | 0.799043i | \(-0.705340\pi\) | ||||
−0.601273 | + | 0.799043i | \(0.705340\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −42.4911 | −2.37905 | ||||||||
\(320\) | 8.43278 | 0.471407 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.85131 | −0.103169 | ||||||||
\(323\) | −17.1214 | −0.952663 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.356924 | −0.0197986 | ||||||||
\(326\) | −7.56137 | −0.418785 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.77976 | 0.0982706 | ||||||||
\(329\) | −1.19217 | −0.0657266 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.4219 | −1.01256 | −0.506280 | − | 0.862369i | \(-0.668980\pi\) | ||||
−0.506280 | + | 0.862369i | \(0.668980\pi\) | |||||||
\(332\) | −11.4147 | −0.626463 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.63884 | −0.199109 | ||||||||
\(335\) | −27.8188 | −1.51990 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.6053 | −1.28586 | −0.642930 | − | 0.765925i | \(-0.722281\pi\) | ||||
−0.642930 | + | 0.765925i | \(0.722281\pi\) | |||||||
\(338\) | −5.53977 | −0.301324 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 14.4464 | 0.783464 | ||||||||
\(341\) | 24.3234 | 1.31718 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −4.92961 | −0.265787 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.18728 | −0.386391 | ||||||||
\(347\) | 33.5517 | 1.80115 | 0.900576 | − | 0.434699i | \(-0.143145\pi\) | ||||
0.900576 | + | 0.434699i | \(0.143145\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −30.7293 | −1.64490 | −0.822450 | − | 0.568837i | \(-0.807394\pi\) | ||||
−0.822450 | + | 0.568837i | \(0.807394\pi\) | |||||||
\(350\) | 0.207559 | 0.0110945 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 21.1295 | 1.12620 | ||||||||
\(353\) | 18.2382 | 0.970722 | 0.485361 | − | 0.874314i | \(-0.338688\pi\) | ||||
0.485361 | + | 0.874314i | \(0.338688\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.6023 | −0.668862 | ||||||||
\(356\) | 2.44747 | 0.129716 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.01539 | 0.159368 | ||||||||
\(359\) | −11.3158 | −0.597223 | −0.298611 | − | 0.954375i | \(-0.596523\pi\) | ||||
−0.298611 | + | 0.954375i | \(0.596523\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.89227 | 0.310119 | ||||||||
\(362\) | −7.38507 | −0.388150 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.38223 | 0.0724485 | ||||||||
\(365\) | −12.3589 | −0.646897 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.5352 | −1.43732 | −0.718662 | − | 0.695360i | \(-0.755245\pi\) | ||||
−0.718662 | + | 0.695360i | \(0.755245\pi\) | |||||||
\(368\) | −11.7965 | −0.614937 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.55349 | 0.132749 | ||||||||
\(371\) | 10.5726 | 0.548903 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.92003 | 0.0994156 | 0.0497078 | − | 0.998764i | \(-0.484171\pi\) | ||||
0.0497078 | + | 0.998764i | \(0.484171\pi\) | |||||||
\(374\) | 6.94155 | 0.358939 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.02255 | 0.104305 | ||||||||
\(377\) | 7.19724 | 0.370677 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.18999 | 0.266592 | 0.133296 | − | 0.991076i | \(-0.457444\pi\) | ||||
0.133296 | + | 0.991076i | \(0.457444\pi\) | |||||||
\(380\) | −21.0031 | −1.07743 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.79191 | 0.0916823 | ||||||||
\(383\) | 37.3440 | 1.90819 | 0.954095 | − | 0.299505i | \(-0.0968215\pi\) | ||||
0.954095 | + | 0.299505i | \(0.0968215\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.5938 | −0.539911 | ||||||||
\(386\) | −1.16171 | −0.0591294 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 16.1099 | 0.817856 | ||||||||
\(389\) | −17.3932 | −0.881871 | −0.440935 | − | 0.897539i | \(-0.645353\pi\) | ||||
−0.440935 | + | 0.897539i | \(0.645353\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.2330 | −0.719793 | ||||||||
\(392\) | −1.69653 | −0.0856876 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.43903 | −0.0724971 | ||||||||
\(395\) | 12.1129 | 0.609464 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.97781 | −0.249829 | −0.124915 | − | 0.992167i | \(-0.539866\pi\) | ||||
−0.124915 | + | 0.992167i | \(0.539866\pi\) | |||||||
\(398\) | −5.70309 | −0.285870 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.32257 | 0.0661284 | ||||||||
\(401\) | 13.6687 | 0.682582 | 0.341291 | − | 0.939958i | \(-0.389136\pi\) | ||||
0.341291 | + | 0.939958i | \(0.389136\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.11994 | −0.205229 | ||||||||
\(404\) | −0.551550 | −0.0274406 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.18535 | −0.207715 | ||||||||
\(407\) | −11.0893 | −0.549677 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.1574 | 0.749485 | 0.374742 | − | 0.927129i | \(-0.377731\pi\) | ||||
0.374742 | + | 0.927129i | \(0.377731\pi\) | |||||||
\(410\) | 1.09468 | 0.0540622 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.7641 | 0.628844 | ||||||||
\(413\) | 1.68946 | 0.0831329 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.8185 | −0.727412 | ||||||||
\(416\) | −3.57895 | −0.175473 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −10.0921 | −0.493620 | ||||||||
\(419\) | −16.8436 | −0.822866 | −0.411433 | − | 0.911440i | \(-0.634972\pi\) | ||||
−0.411433 | + | 0.911440i | \(0.634972\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.0881303 | −0.00429521 | −0.00214760 | − | 0.999998i | \(-0.500684\pi\) | ||||
−0.00214760 | + | 0.999998i | \(0.500684\pi\) | |||||||
\(422\) | −8.77779 | −0.427296 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −17.9367 | −0.871085 | ||||||||
\(425\) | 1.59573 | 0.0774043 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.42071 | 0.213933 | ||||||||
\(428\) | 16.6333 | 0.804002 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.03206 | −0.146219 | ||||||||
\(431\) | −28.1319 | −1.35506 | −0.677532 | − | 0.735493i | \(-0.736951\pi\) | ||||
−0.677532 | + | 0.735493i | \(0.736951\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.5326 | 1.13090 | 0.565452 | − | 0.824781i | \(-0.308702\pi\) | ||||
0.565452 | + | 0.824781i | \(0.308702\pi\) | |||||||
\(434\) | 2.39584 | 0.115004 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.9144 | 0.905837 | ||||||||
\(437\) | 20.6928 | 0.989872 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.13019 | −0.0539411 | −0.0269705 | − | 0.999636i | \(-0.508586\pi\) | ||||
−0.0269705 | + | 0.999636i | \(0.508586\pi\) | |||||||
\(440\) | 17.9727 | 0.856816 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.17577 | −0.0559259 | ||||||||
\(443\) | −25.2206 | −1.19827 | −0.599134 | − | 0.800649i | \(-0.704488\pi\) | ||||
−0.599134 | + | 0.800649i | \(0.704488\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.17729 | 0.150618 | ||||||||
\(446\) | −4.88824 | −0.231465 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.60724 | −0.170426 | ||||||||
\(449\) | −2.99798 | −0.141483 | −0.0707416 | − | 0.997495i | \(-0.522537\pi\) | ||||
−0.0707416 | + | 0.997495i | \(0.522537\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.75397 | −0.223856 | ||||||||
\(452\) | −15.6237 | −0.734879 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.74608 | −0.128880 | ||||||||
\(455\) | 1.79440 | 0.0841229 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.3210 | 0.810242 | 0.405121 | − | 0.914263i | \(-0.367229\pi\) | ||||
0.405121 | + | 0.914263i | \(0.367229\pi\) | |||||||
\(458\) | 9.10612 | 0.425501 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −17.4597 | −0.814065 | ||||||||
\(461\) | 6.28572 | 0.292755 | 0.146377 | − | 0.989229i | \(-0.453239\pi\) | ||||
0.146377 | + | 0.989229i | \(0.453239\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.3025 | −0.525270 | −0.262635 | − | 0.964895i | \(-0.584591\pi\) | ||||
−0.262635 | + | 0.964895i | \(0.584591\pi\) | |||||||
\(464\) | −26.6690 | −1.23808 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.6824 | −0.494851 | ||||||||
\(467\) | −0.664225 | −0.0307367 | −0.0153683 | − | 0.999882i | \(-0.504892\pi\) | ||||
−0.0153683 | + | 0.999882i | \(0.504892\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.8999 | 0.549486 | ||||||||
\(470\) | 1.24401 | 0.0573821 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.86622 | −0.131928 | ||||||||
\(473\) | 13.1677 | 0.605450 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.31998 | −0.106448 | ||||||||
\(476\) | −6.17964 | −0.283243 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.55057 | 0.0709216 | ||||||||
\(479\) | −20.6417 | −0.943145 | −0.471572 | − | 0.881827i | \(-0.656313\pi\) | ||||
−0.471572 | + | 0.881827i | \(0.656313\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.87833 | 0.0856446 | ||||||||
\(482\) | 4.84116 | 0.220509 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −17.1719 | −0.780543 | ||||||||
\(485\) | 20.9138 | 0.949646 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.0401 | −1.49719 | −0.748594 | − | 0.663028i | \(-0.769271\pi\) | ||||
−0.748594 | + | 0.663028i | \(0.769271\pi\) | |||||||
\(488\) | −7.49986 | −0.339503 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.04348 | −0.0471398 | ||||||||
\(491\) | 38.1702 | 1.72260 | 0.861299 | − | 0.508099i | \(-0.169652\pi\) | ||||
0.861299 | + | 0.508099i | \(0.169652\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −32.1772 | −1.44919 | ||||||||
\(494\) | 1.70942 | 0.0769104 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 15.2663 | 0.685476 | ||||||||
\(497\) | 5.39083 | 0.241812 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.83156 | 0.305823 | 0.152911 | − | 0.988240i | \(-0.451135\pi\) | ||||
0.152911 | + | 0.988240i | \(0.451135\pi\) | |||||||
\(500\) | −19.0910 | −0.853774 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.03693 | 0.224809 | ||||||||
\(503\) | 24.9027 | 1.11036 | 0.555178 | − | 0.831732i | \(-0.312650\pi\) | ||||
0.555178 | + | 0.831732i | \(0.312650\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.716019 | −0.0318624 | ||||||||
\(506\) | −8.38950 | −0.372959 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.80076 | −0.0798957 | ||||||||
\(509\) | 19.4291 | 0.861180 | 0.430590 | − | 0.902548i | \(-0.358306\pi\) | ||||
0.430590 | + | 0.902548i | \(0.358306\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.28672 | 0.233871 | ||||||||
\(512\) | 22.9123 | 1.01259 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.586459 | −0.0258676 | ||||||||
\(515\) | 16.5703 | 0.730176 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.40252 | −0.237603 | ||||||||
\(518\) | −1.09229 | −0.0479925 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.04426 | −0.133499 | ||||||||
\(521\) | 23.0002 | 1.00766 | 0.503828 | − | 0.863804i | \(-0.331925\pi\) | ||||
0.503828 | + | 0.863804i | \(0.331925\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.0527 | −1.05175 | −0.525876 | − | 0.850561i | \(-0.676262\pi\) | ||||
−0.525876 | + | 0.850561i | \(0.676262\pi\) | |||||||
\(524\) | −18.5175 | −0.808941 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.84533 | −0.0804602 | ||||||||
\(527\) | 18.4194 | 0.802360 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.79814 | −0.252093 | ||||||||
\(530\) | −11.0324 | −0.479215 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.98437 | 0.389522 | ||||||||
\(533\) | 0.805238 | 0.0348787 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 21.5933 | 0.933560 | ||||||||
\(536\) | −20.1885 | −0.872010 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.73992 | −0.376805 | ||||||||
\(539\) | 4.53166 | 0.195192 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.8773 | 1.28452 | 0.642262 | − | 0.766485i | \(-0.277996\pi\) | ||||
0.642262 | + | 0.766485i | \(0.277996\pi\) | |||||||
\(542\) | 11.3990 | 0.489629 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 16.0007 | 0.686025 | ||||||||
\(545\) | 24.5546 | 1.05180 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.4196 | −1.00135 | −0.500675 | − | 0.865635i | \(-0.666915\pi\) | ||||
−0.500675 | + | 0.865635i | \(0.666915\pi\) | |||||||
\(548\) | 0.400867 | 0.0171242 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.940589 | 0.0401068 | ||||||||
\(551\) | 46.7814 | 1.99295 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.18146 | −0.220338 | ||||||||
\(554\) | −3.64757 | −0.154971 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.1311 | −0.514474 | ||||||||
\(557\) | −18.7404 | −0.794055 | −0.397028 | − | 0.917807i | \(-0.629958\pi\) | ||||
−0.397028 | + | 0.917807i | \(0.629958\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.23037 | −0.0943345 | ||||||||
\(560\) | −6.64908 | −0.280975 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.03843 | −0.212534 | ||||||||
\(563\) | 35.2058 | 1.48375 | 0.741874 | − | 0.670539i | \(-0.233937\pi\) | ||||
0.741874 | + | 0.670539i | \(0.233937\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.2826 | −0.853297 | ||||||||
\(566\) | −6.49506 | −0.273008 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.14569 | −0.383745 | ||||||||
\(569\) | −13.5337 | −0.567361 | −0.283681 | − | 0.958919i | \(-0.591556\pi\) | ||||
−0.283681 | + | 0.958919i | \(0.591556\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.0291 | −0.461552 | −0.230776 | − | 0.973007i | \(-0.574126\pi\) | ||||
−0.230776 | + | 0.973007i | \(0.574126\pi\) | |||||||
\(572\) | 6.26380 | 0.261902 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.468264 | −0.0195449 | ||||||||
\(575\) | −1.92859 | −0.0804276 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.1645 | −1.38066 | −0.690328 | − | 0.723496i | \(-0.742534\pi\) | ||||
−0.690328 | + | 0.723496i | \(0.742534\pi\) | |||||||
\(578\) | −2.33159 | −0.0969815 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −39.4722 | −1.63899 | ||||||||
\(581\) | 6.33884 | 0.262979 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 47.9115 | 1.98429 | ||||||||
\(584\) | −8.96908 | −0.371143 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.06383 | −0.291804 | ||||||||
\(587\) | 17.6262 | 0.727512 | 0.363756 | − | 0.931494i | \(-0.381494\pi\) | ||||
0.363756 | + | 0.931494i | \(0.381494\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.7793 | −1.10342 | ||||||||
\(590\) | −1.76293 | −0.0725785 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.96007 | −0.286057 | ||||||||
\(593\) | 11.9687 | 0.491497 | 0.245749 | − | 0.969334i | \(-0.420966\pi\) | ||||
0.245749 | + | 0.969334i | \(0.420966\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.02238 | −0.328885 | ||||||||
\(596\) | −7.66641 | −0.314028 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.42103 | 0.0581103 | ||||||||
\(599\) | 19.2882 | 0.788096 | 0.394048 | − | 0.919090i | \(-0.371074\pi\) | ||||
0.394048 | + | 0.919090i | \(0.371074\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −43.2184 | −1.76292 | −0.881458 | − | 0.472262i | \(-0.843438\pi\) | ||||
−0.881458 | + | 0.472262i | \(0.843438\pi\) | |||||||
\(602\) | 1.29701 | 0.0528621 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 33.3025 | 1.35506 | ||||||||
\(605\) | −22.2925 | −0.906320 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.6332 | −0.878064 | −0.439032 | − | 0.898471i | \(-0.644679\pi\) | ||||
−0.439032 | + | 0.898471i | \(0.644679\pi\) | |||||||
\(608\) | −23.2629 | −0.943434 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.61294 | −0.186773 | ||||||||
\(611\) | 0.915090 | 0.0370206 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.25536 | −0.252651 | −0.126326 | − | 0.991989i | \(-0.540318\pi\) | ||||
−0.126326 | + | 0.991989i | \(0.540318\pi\) | |||||||
\(614\) | 4.57952 | 0.184814 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.68809 | −0.309762 | ||||||||
\(617\) | −28.4663 | −1.14601 | −0.573005 | − | 0.819552i | \(-0.694223\pi\) | ||||
−0.573005 | + | 0.819552i | \(0.694223\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.3680 | 0.456920 | 0.228460 | − | 0.973553i | \(-0.426631\pi\) | ||||
0.228460 | + | 0.973553i | \(0.426631\pi\) | |||||||
\(620\) | 22.5952 | 0.907446 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.71128 | 0.349290 | ||||||||
\(623\) | −1.35913 | −0.0544525 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.1088 | −1.08435 | ||||||||
\(626\) | −11.0132 | −0.440174 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 19.4797 | 0.777326 | ||||||||
\(629\) | −8.39761 | −0.334834 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.9887 | 1.03459 | 0.517297 | − | 0.855806i | \(-0.326938\pi\) | ||||
0.517297 | + | 0.855806i | \(0.326938\pi\) | |||||||
\(632\) | 8.79049 | 0.349667 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9.55702 | −0.379558 | ||||||||
\(635\) | −2.33773 | −0.0927701 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.767582 | −0.0304127 | ||||||||
\(638\) | −18.9666 | −0.750895 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 25.5641 | 1.01051 | ||||||||
\(641\) | −18.8497 | −0.744517 | −0.372258 | − | 0.928129i | \(-0.621416\pi\) | ||||
−0.372258 | + | 0.928129i | \(0.621416\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.58722 | 0.378083 | 0.189042 | − | 0.981969i | \(-0.439462\pi\) | ||||
0.189042 | + | 0.981969i | \(0.439462\pi\) | |||||||
\(644\) | 7.46866 | 0.294307 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.64243 | −0.300687 | ||||||||
\(647\) | −7.25215 | −0.285111 | −0.142556 | − | 0.989787i | \(-0.545532\pi\) | ||||
−0.142556 | + | 0.989787i | \(0.545532\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.65606 | 0.300527 | ||||||||
\(650\) | −0.159319 | −0.00624900 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 30.5045 | 1.19465 | ||||||||
\(653\) | 15.6142 | 0.611030 | 0.305515 | − | 0.952187i | \(-0.401171\pi\) | ||||
0.305515 | + | 0.952187i | \(0.401171\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −24.0393 | −0.939294 | ||||||||
\(656\) | −2.98377 | −0.116497 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.532145 | −0.0207452 | ||||||||
\(659\) | 19.6781 | 0.766550 | 0.383275 | − | 0.923634i | \(-0.374796\pi\) | ||||
0.383275 | + | 0.923634i | \(0.374796\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.6371 | 0.647110 | 0.323555 | − | 0.946209i | \(-0.395122\pi\) | ||||
0.323555 | + | 0.946209i | \(0.395122\pi\) | |||||||
\(662\) | −8.22291 | −0.319593 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.7540 | −0.417337 | ||||||||
\(665\) | 11.6635 | 0.452289 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 38.8891 | 1.50579 | ||||||||
\(668\) | 14.6800 | 0.567988 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −12.4173 | −0.479724 | ||||||||
\(671\) | 20.0332 | 0.773372 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.85137 | 0.225554 | 0.112777 | − | 0.993620i | \(-0.464025\pi\) | ||||
0.112777 | + | 0.993620i | \(0.464025\pi\) | |||||||
\(674\) | −10.5366 | −0.405854 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 22.3489 | 0.859572 | ||||||||
\(677\) | 6.32236 | 0.242988 | 0.121494 | − | 0.992592i | \(-0.461231\pi\) | ||||
0.121494 | + | 0.992592i | \(0.461231\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.94618 | −0.343323 | ||||||||
\(680\) | 13.6102 | 0.521927 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10.8571 | 0.415741 | ||||||||
\(683\) | 47.3971 | 1.81360 | 0.906799 | − | 0.421563i | \(-0.138518\pi\) | ||||
0.906799 | + | 0.421563i | \(0.138518\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.520403 | 0.0198836 | ||||||||
\(686\) | 0.446366 | 0.0170423 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.26453 | 0.315082 | ||||||||
\(689\) | −8.11535 | −0.309170 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.46620 | −0.245986 | −0.122993 | − | 0.992408i | \(-0.539249\pi\) | ||||
−0.122993 | + | 0.992408i | \(0.539249\pi\) | |||||||
\(692\) | 28.9954 | 1.10224 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.9764 | 0.568495 | ||||||||
\(695\) | −15.7486 | −0.597377 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.60004 | −0.136361 | ||||||||
\(698\) | −13.7165 | −0.519177 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.837349 | −0.0316488 | ||||||||
\(701\) | −18.8826 | −0.713188 | −0.356594 | − | 0.934260i | \(-0.616062\pi\) | ||||
−0.356594 | + | 0.934260i | \(0.616062\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.2090 | 0.460471 | ||||||||
\(704\) | −16.3468 | −0.616094 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.14091 | 0.306387 | ||||||||
\(707\) | 0.306288 | 0.0115191 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.01518 | 0.188349 | 0.0941746 | − | 0.995556i | \(-0.469979\pi\) | ||||
0.0941746 | + | 0.995556i | \(0.469979\pi\) | |||||||
\(710\) | −5.62525 | −0.211112 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.30581 | 0.0864138 | ||||||||
\(713\) | −22.2615 | −0.833699 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.13163 | 0.304106 | ||||||||
\(716\) | −12.1649 | −0.454623 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.05097 | −0.188500 | ||||||||
\(719\) | −48.7874 | −1.81946 | −0.909731 | − | 0.415199i | \(-0.863712\pi\) | ||||
−0.909731 | + | 0.415199i | \(0.863712\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.08821 | −0.263979 | ||||||||
\(722\) | 2.63011 | 0.0978825 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 29.7933 | 1.10726 | ||||||||
\(725\) | −4.36006 | −0.161928 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.0214 | 0.631288 | 0.315644 | − | 0.948878i | \(-0.397780\pi\) | ||||
0.315644 | + | 0.948878i | \(0.397780\pi\) | |||||||
\(728\) | 1.30223 | 0.0482637 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.51661 | −0.204179 | ||||||||
\(731\) | 9.97148 | 0.368808 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.82439 | 0.325936 | 0.162968 | − | 0.986631i | \(-0.447893\pi\) | ||||
0.162968 | + | 0.986631i | \(0.447893\pi\) | |||||||
\(734\) | −12.2908 | −0.453660 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −19.3383 | −0.712820 | ||||||||
\(737\) | 53.9262 | 1.98640 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −44.0616 | −1.62083 | −0.810417 | − | 0.585854i | \(-0.800759\pi\) | ||||
−0.810417 | + | 0.585854i | \(0.800759\pi\) | |||||||
\(740\) | −10.3014 | −0.378688 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.71926 | 0.173249 | ||||||||
\(743\) | −8.57658 | −0.314644 | −0.157322 | − | 0.987547i | \(-0.550286\pi\) | ||||
−0.157322 | + | 0.987547i | \(0.550286\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.95250 | −0.364631 | ||||||||
\(746\) | 0.857038 | 0.0313784 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −28.0040 | −1.02393 | ||||||||
\(749\) | −9.23685 | −0.337507 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.2586 | −0.958191 | −0.479095 | − | 0.877763i | \(-0.659035\pi\) | ||||
−0.479095 | + | 0.877763i | \(0.659035\pi\) | |||||||
\(752\) | −3.39083 | −0.123651 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.21260 | 0.116996 | ||||||||
\(755\) | 43.2332 | 1.57342 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.31126 | 0.265732 | 0.132866 | − | 0.991134i | \(-0.457582\pi\) | ||||
0.132866 | + | 0.991134i | \(0.457582\pi\) | |||||||
\(758\) | 2.31663 | 0.0841439 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −19.7874 | −0.717764 | ||||||||
\(761\) | 10.9355 | 0.396410 | 0.198205 | − | 0.980161i | \(-0.436489\pi\) | ||||
0.198205 | + | 0.980161i | \(0.436489\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.5036 | −0.380256 | ||||||||
\(764\) | −7.22905 | −0.261538 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16.6691 | 0.602279 | ||||||||
\(767\) | −1.29680 | −0.0468247 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −52.1535 | −1.88070 | −0.940352 | − | 0.340203i | \(-0.889504\pi\) | ||||
−0.940352 | + | 0.340203i | \(0.889504\pi\) | |||||||
\(770\) | −4.72872 | −0.170411 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.68664 | 0.168676 | ||||||||
\(773\) | −5.87993 | −0.211486 | −0.105743 | − | 0.994393i | \(-0.533722\pi\) | ||||
−0.105743 | + | 0.994393i | \(0.533722\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.49584 | 0.0896534 | ||||||||
\(776\) | 15.1774 | 0.544839 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.76374 | −0.278343 | ||||||||
\(779\) | 5.23397 | 0.187527 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.4294 | 0.874153 | ||||||||
\(782\) | −6.35312 | −0.227187 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.84424 | 0.101580 | ||||||||
\(785\) | 25.2885 | 0.902585 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.5039 | −1.19428 | −0.597142 | − | 0.802135i | \(-0.703697\pi\) | ||||
−0.597142 | + | 0.802135i | \(0.703697\pi\) | |||||||
\(788\) | 5.80541 | 0.206809 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.40677 | 0.192364 | ||||||||
\(791\) | 8.67620 | 0.308490 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.39326 | −0.120498 | ||||||||
\(794\) | −2.22193 | −0.0788532 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 23.0078 | 0.815488 | ||||||||
\(797\) | −40.6842 | −1.44111 | −0.720554 | − | 0.693399i | \(-0.756112\pi\) | ||||
−0.720554 | + | 0.693399i | \(0.756112\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.09117 | −0.144735 | ||||||||
\(800\) | 2.16811 | 0.0766544 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.10124 | 0.215442 | ||||||||
\(803\) | 23.9576 | 0.845447 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.69578 | 0.341731 | ||||||||
\(806\) | −1.83900 | −0.0647761 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.519626 | −0.0182804 | ||||||||
\(809\) | 0.118941 | 0.00418173 | 0.00209087 | − | 0.999998i | \(-0.499334\pi\) | ||||
0.00209087 | + | 0.999998i | \(0.499334\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.5686 | −0.687148 | −0.343574 | − | 0.939126i | \(-0.611638\pi\) | ||||
−0.343574 | + | 0.939126i | \(0.611638\pi\) | |||||||
\(812\) | 16.8848 | 0.592540 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.94989 | −0.173494 | ||||||||
\(815\) | 39.6008 | 1.38716 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.4972 | −0.507192 | ||||||||
\(818\) | 6.76574 | 0.236559 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.41621 | −0.154221 | ||||||||
\(821\) | −48.0569 | −1.67720 | −0.838599 | − | 0.544749i | \(-0.816625\pi\) | ||||
−0.838599 | + | 0.544749i | \(0.816625\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −48.8400 | −1.70246 | −0.851228 | − | 0.524797i | \(-0.824141\pi\) | ||||
−0.851228 | + | 0.524797i | \(0.824141\pi\) | |||||||
\(824\) | 12.0253 | 0.418923 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.754117 | 0.0262391 | ||||||||
\(827\) | −18.4660 | −0.642125 | −0.321063 | − | 0.947058i | \(-0.604040\pi\) | ||||
−0.321063 | + | 0.947058i | \(0.604040\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.9964 | 1.11128 | 0.555641 | − | 0.831423i | \(-0.312473\pi\) | ||||
0.555641 | + | 0.831423i | \(0.312473\pi\) | |||||||
\(830\) | −6.61448 | −0.229592 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.76886 | 0.0959929 | ||||||||
\(833\) | 3.43169 | 0.118901 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.0576 | 0.659514 | ||||||||
\(836\) | 40.7141 | 1.40813 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7.51843 | −0.259720 | ||||||||
\(839\) | 49.5290 | 1.70993 | 0.854965 | − | 0.518685i | \(-0.173578\pi\) | ||||
0.854965 | + | 0.518685i | \(0.173578\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 58.9188 | 2.03168 | ||||||||
\(842\) | −0.0393384 | −0.00135569 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 35.4119 | 1.21893 | ||||||||
\(845\) | 29.0132 | 0.998084 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.53595 | 0.327659 | ||||||||
\(848\) | 30.0711 | 1.03264 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.712279 | 0.0244310 | ||||||||
\(851\) | 10.1493 | 0.347913 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −44.7512 | −1.53225 | −0.766126 | − | 0.642691i | \(-0.777818\pi\) | ||||
−0.766126 | + | 0.642691i | \(0.777818\pi\) | |||||||
\(854\) | 1.97325 | 0.0675234 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.6706 | 0.535609 | ||||||||
\(857\) | 36.3915 | 1.24311 | 0.621555 | − | 0.783371i | \(-0.286501\pi\) | ||||
0.621555 | + | 0.783371i | \(0.286501\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.6322 | 1.42047 | 0.710237 | − | 0.703963i | \(-0.248588\pi\) | ||||
0.710237 | + | 0.703963i | \(0.248588\pi\) | |||||||
\(860\) | 12.2321 | 0.417112 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12.5571 | −0.427697 | ||||||||
\(863\) | −27.8245 | −0.947158 | −0.473579 | − | 0.880751i | \(-0.657038\pi\) | ||||
−0.473579 | + | 0.880751i | \(0.657038\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 37.6417 | 1.27985 | ||||||||
\(866\) | 10.5042 | 0.356946 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −9.66544 | −0.328066 | ||||||||
\(869\) | −23.4806 | −0.796525 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.13414 | −0.309499 | ||||||||
\(872\) | 17.8197 | 0.603450 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.23658 | 0.312432 | ||||||||
\(875\) | 10.6016 | 0.358400 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.1138 | 0.577893 | 0.288946 | − | 0.957345i | \(-0.406695\pi\) | ||||
0.288946 | + | 0.957345i | \(0.406695\pi\) | |||||||
\(878\) | −0.504479 | −0.0170253 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −30.1314 | −1.01573 | ||||||||
\(881\) | −26.9903 | −0.909327 | −0.454663 | − | 0.890663i | \(-0.650240\pi\) | ||||
−0.454663 | + | 0.890663i | \(0.650240\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.5601 | −1.19669 | −0.598346 | − | 0.801238i | \(-0.704175\pi\) | ||||
−0.598346 | + | 0.801238i | \(0.704175\pi\) | |||||||
\(884\) | 4.74338 | 0.159537 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.2576 | −0.378207 | ||||||||
\(887\) | 7.42653 | 0.249359 | 0.124679 | − | 0.992197i | \(-0.460210\pi\) | ||||
0.124679 | + | 0.992197i | \(0.460210\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | 1.41823 | 0.0475393 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 19.7204 | 0.660289 | ||||||||
\(893\) | 5.94800 | 0.199042 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.7924 | −0.527881 | ||||||||
\(896\) | −10.9354 | −0.365326 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.33819 | −0.0446561 | ||||||||
\(899\) | −50.3277 | −1.67852 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.2819 | 1.20873 | ||||||||
\(902\) | −2.12201 | −0.0706553 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.7194 | −0.489561 | ||||||||
\(905\) | 38.6775 | 1.28568 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.3294 | 1.20630 | 0.603149 | − | 0.797628i | \(-0.293912\pi\) | ||||
0.603149 | + | 0.797628i | \(0.293912\pi\) | |||||||
\(908\) | 11.0784 | 0.367651 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.800960 | 0.0265516 | ||||||||
\(911\) | −5.05197 | −0.167379 | −0.0836896 | − | 0.996492i | \(-0.526670\pi\) | ||||
−0.0836896 | + | 0.996492i | \(0.526670\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.7255 | 0.950674 | ||||||||
\(914\) | 7.73150 | 0.255735 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −36.7365 | −1.21381 | ||||||||
\(917\) | 10.2832 | 0.339580 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41.5970 | 1.37216 | 0.686079 | − | 0.727527i | \(-0.259330\pi\) | ||||
0.686079 | + | 0.727527i | \(0.259330\pi\) | |||||||
\(920\) | −16.4492 | −0.542313 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.80573 | 0.0924018 | ||||||||
\(923\) | −4.13790 | −0.136201 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.13789 | −0.0374134 | ||||||||
\(926\) | −5.04503 | −0.165790 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −43.7192 | −1.43515 | ||||||||
\(929\) | −20.6724 | −0.678239 | −0.339120 | − | 0.940743i | \(-0.610129\pi\) | ||||
−0.339120 | + | 0.940743i | \(0.610129\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.98922 | −0.163515 | ||||||||
\(932\) | 43.0955 | 1.41164 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.296487 | −0.00970136 | ||||||||
\(935\) | −36.3547 | −1.18893 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.93386 | −0.0958452 | −0.0479226 | − | 0.998851i | \(-0.515260\pi\) | ||||
−0.0479226 | + | 0.998851i | \(0.515260\pi\) | |||||||
\(938\) | 5.31170 | 0.173433 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5.01868 | −0.163691 | ||||||||
\(941\) | −10.4399 | −0.340329 | −0.170165 | − | 0.985416i | \(-0.554430\pi\) | ||||
−0.170165 | + | 0.985416i | \(0.554430\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.35098 | 0.141687 | ||||||||
\(944\) | 4.80523 | 0.156397 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.87760 | 0.191097 | ||||||||
\(947\) | 25.7647 | 0.837240 | 0.418620 | − | 0.908161i | \(-0.362514\pi\) | ||||
0.418620 | + | 0.908161i | \(0.362514\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.05800 | −0.131728 | ||||||||
\(950\) | −1.03556 | −0.0335979 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.82196 | −0.188691 | ||||||||
\(953\) | 46.8318 | 1.51703 | 0.758516 | − | 0.651655i | \(-0.225925\pi\) | ||||
0.758516 | + | 0.651655i | \(0.225925\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.38471 | −0.303682 | ||||||||
\(956\) | −6.25542 | −0.202315 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9.21377 | −0.297683 | ||||||||
\(959\) | −0.222610 | −0.00718846 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.19070 | −0.0706678 | ||||||||
\(962\) | 0.838423 | 0.0270319 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −19.5305 | −0.629036 | ||||||||
\(965\) | 6.08416 | 0.195856 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.2505 | 0.522581 | 0.261290 | − | 0.965260i | \(-0.415852\pi\) | ||||
0.261290 | + | 0.965260i | \(0.415852\pi\) | |||||||
\(968\) | −16.1780 | −0.519981 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9.33520 | 0.299735 | ||||||||
\(971\) | 28.9833 | 0.930118 | 0.465059 | − | 0.885280i | \(-0.346033\pi\) | ||||
0.465059 | + | 0.885280i | \(0.346033\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.73668 | 0.215968 | ||||||||
\(974\) | −14.7480 | −0.472555 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.5736 | 0.402470 | ||||||||
\(977\) | −41.7762 | −1.33654 | −0.668269 | − | 0.743919i | \(-0.732965\pi\) | ||||
−0.668269 | + | 0.743919i | \(0.732965\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.15913 | −0.196847 | ||||||||
\(980\) | 4.20969 | 0.134474 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 17.0379 | 0.543701 | ||||||||
\(983\) | −5.70314 | −0.181902 | −0.0909509 | − | 0.995855i | \(-0.528991\pi\) | ||||
−0.0909509 | + | 0.995855i | \(0.528991\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.53655 | 0.240134 | ||||||||
\(986\) | −14.3628 | −0.457406 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.89624 | −0.219399 | ||||||||
\(989\) | −12.0514 | −0.383214 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.9263 | 0.347087 | 0.173543 | − | 0.984826i | \(-0.444478\pi\) | ||||
0.173543 | + | 0.984826i | \(0.444478\pi\) | |||||||
\(992\) | 25.0263 | 0.794587 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.40628 | 0.0763226 | ||||||||
\(995\) | 29.8685 | 0.946897 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.34051 | 0.137465 | 0.0687327 | − | 0.997635i | \(-0.478104\pi\) | ||||
0.0687327 | + | 0.997635i | \(0.478104\pi\) | |||||||
\(998\) | 3.04938 | 0.0965263 | ||||||||
\(999\) | 0 | 0 |
(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 | 8001.2.a.x.1.13 | yes | 22 | |
3.2 | odd | 2 | inner | 8001.2.a.x.1.10 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8001.2.a.x.1.10 | ✓ | 22 | 3.2 | odd | 2 | inner | |
8001.2.a.x.1.13 | yes | 22 | 1.1 | even | 1 | trivial |