Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,2,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.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: | \(2.30767661842\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{18})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.53209\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.53209 | 1.08335 | 0.541675 | − | 0.840588i | \(-0.317790\pi\) | ||||
0.541675 | + | 0.840588i | \(0.317790\pi\) | |||||||
\(3\) | −1.34730 | −0.777862 | −0.388931 | − | 0.921267i | \(-0.627156\pi\) | ||||
−0.388931 | + | 0.921267i | \(0.627156\pi\) | |||||||
\(4\) | 0.347296 | 0.173648 | ||||||||
\(5\) | −3.53209 | −1.57960 | −0.789799 | − | 0.613366i | \(-0.789815\pi\) | ||||
−0.789799 | + | 0.613366i | \(0.789815\pi\) | |||||||
\(6\) | −2.06418 | −0.842697 | ||||||||
\(7\) | 0.347296 | 0.131266 | 0.0656328 | − | 0.997844i | \(-0.479093\pi\) | ||||
0.0656328 | + | 0.997844i | \(0.479093\pi\) | |||||||
\(8\) | −2.53209 | −0.895229 | ||||||||
\(9\) | −1.18479 | −0.394931 | ||||||||
\(10\) | −5.41147 | −1.71126 | ||||||||
\(11\) | 1.75877 | 0.530289 | 0.265145 | − | 0.964209i | \(-0.414580\pi\) | ||||
0.265145 | + | 0.964209i | \(0.414580\pi\) | |||||||
\(12\) | −0.467911 | −0.135074 | ||||||||
\(13\) | −3.29086 | −0.912720 | −0.456360 | − | 0.889795i | \(-0.650847\pi\) | ||||
−0.456360 | + | 0.889795i | \(0.650847\pi\) | |||||||
\(14\) | 0.532089 | 0.142207 | ||||||||
\(15\) | 4.75877 | 1.22871 | ||||||||
\(16\) | −4.57398 | −1.14349 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −1.81521 | −0.427849 | ||||||||
\(19\) | 1.53209 | 0.351485 | 0.175743 | − | 0.984436i | \(-0.443767\pi\) | ||||
0.175743 | + | 0.984436i | \(0.443767\pi\) | |||||||
\(20\) | −1.22668 | −0.274294 | ||||||||
\(21\) | −0.467911 | −0.102107 | ||||||||
\(22\) | 2.69459 | 0.574489 | ||||||||
\(23\) | −2.81521 | −0.587011 | −0.293506 | − | 0.955957i | \(-0.594822\pi\) | ||||
−0.293506 | + | 0.955957i | \(0.594822\pi\) | |||||||
\(24\) | 3.41147 | 0.696364 | ||||||||
\(25\) | 7.47565 | 1.49513 | ||||||||
\(26\) | −5.04189 | −0.988796 | ||||||||
\(27\) | 5.63816 | 1.08506 | ||||||||
\(28\) | 0.120615 | 0.0227940 | ||||||||
\(29\) | 1.18479 | 0.220010 | 0.110005 | − | 0.993931i | \(-0.464913\pi\) | ||||
0.110005 | + | 0.993931i | \(0.464913\pi\) | |||||||
\(30\) | 7.29086 | 1.33112 | ||||||||
\(31\) | −7.10607 | −1.27629 | −0.638144 | − | 0.769917i | \(-0.720297\pi\) | ||||
−0.638144 | + | 0.769917i | \(0.720297\pi\) | |||||||
\(32\) | −1.94356 | −0.343577 | ||||||||
\(33\) | −2.36959 | −0.412492 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.22668 | −0.207347 | ||||||||
\(36\) | −0.411474 | −0.0685790 | ||||||||
\(37\) | 3.92127 | 0.644654 | 0.322327 | − | 0.946628i | \(-0.395535\pi\) | ||||
0.322327 | + | 0.946628i | \(0.395535\pi\) | |||||||
\(38\) | 2.34730 | 0.380782 | ||||||||
\(39\) | 4.43376 | 0.709970 | ||||||||
\(40\) | 8.94356 | 1.41410 | ||||||||
\(41\) | −4.92127 | −0.768574 | −0.384287 | − | 0.923214i | \(-0.625553\pi\) | ||||
−0.384287 | + | 0.923214i | \(0.625553\pi\) | |||||||
\(42\) | −0.716881 | −0.110617 | ||||||||
\(43\) | 10.9855 | 1.67527 | 0.837633 | − | 0.546234i | \(-0.183939\pi\) | ||||
0.837633 | + | 0.546234i | \(0.183939\pi\) | |||||||
\(44\) | 0.610815 | 0.0920838 | ||||||||
\(45\) | 4.18479 | 0.623832 | ||||||||
\(46\) | −4.31315 | −0.635939 | ||||||||
\(47\) | −5.12061 | −0.746918 | −0.373459 | − | 0.927647i | \(-0.621828\pi\) | ||||
−0.373459 | + | 0.927647i | \(0.621828\pi\) | |||||||
\(48\) | 6.16250 | 0.889481 | ||||||||
\(49\) | −6.87939 | −0.982769 | ||||||||
\(50\) | 11.4534 | 1.61975 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.14290 | −0.158492 | ||||||||
\(53\) | −8.36959 | −1.14965 | −0.574825 | − | 0.818276i | \(-0.694930\pi\) | ||||
−0.574825 | + | 0.818276i | \(0.694930\pi\) | |||||||
\(54\) | 8.63816 | 1.17550 | ||||||||
\(55\) | −6.21213 | −0.837644 | ||||||||
\(56\) | −0.879385 | −0.117513 | ||||||||
\(57\) | −2.06418 | −0.273407 | ||||||||
\(58\) | 1.81521 | 0.238348 | ||||||||
\(59\) | −10.8648 | −1.41448 | −0.707241 | − | 0.706973i | \(-0.750060\pi\) | ||||
−0.707241 | + | 0.706973i | \(0.750060\pi\) | |||||||
\(60\) | 1.65270 | 0.213363 | ||||||||
\(61\) | 4.41147 | 0.564831 | 0.282416 | − | 0.959292i | \(-0.408864\pi\) | ||||
0.282416 | + | 0.959292i | \(0.408864\pi\) | |||||||
\(62\) | −10.8871 | −1.38267 | ||||||||
\(63\) | −0.411474 | −0.0518409 | ||||||||
\(64\) | 6.17024 | 0.771281 | ||||||||
\(65\) | 11.6236 | 1.44173 | ||||||||
\(66\) | −3.63041 | −0.446873 | ||||||||
\(67\) | 8.07192 | 0.986142 | 0.493071 | − | 0.869989i | \(-0.335874\pi\) | ||||
0.493071 | + | 0.869989i | \(0.335874\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.79292 | 0.456614 | ||||||||
\(70\) | −1.87939 | −0.224630 | ||||||||
\(71\) | −11.2490 | −1.33501 | −0.667504 | − | 0.744607i | \(-0.732637\pi\) | ||||
−0.667504 | + | 0.744607i | \(0.732637\pi\) | |||||||
\(72\) | 3.00000 | 0.353553 | ||||||||
\(73\) | −1.70233 | −0.199243 | −0.0996215 | − | 0.995025i | \(-0.531763\pi\) | ||||
−0.0996215 | + | 0.995025i | \(0.531763\pi\) | |||||||
\(74\) | 6.00774 | 0.698386 | ||||||||
\(75\) | −10.0719 | −1.16300 | ||||||||
\(76\) | 0.532089 | 0.0610348 | ||||||||
\(77\) | 0.610815 | 0.0696088 | ||||||||
\(78\) | 6.79292 | 0.769147 | ||||||||
\(79\) | −11.5817 | −1.30305 | −0.651523 | − | 0.758629i | \(-0.725869\pi\) | ||||
−0.651523 | + | 0.758629i | \(0.725869\pi\) | |||||||
\(80\) | 16.1557 | 1.80626 | ||||||||
\(81\) | −4.04189 | −0.449099 | ||||||||
\(82\) | −7.53983 | −0.832635 | ||||||||
\(83\) | −2.14796 | −0.235769 | −0.117884 | − | 0.993027i | \(-0.537611\pi\) | ||||
−0.117884 | + | 0.993027i | \(0.537611\pi\) | |||||||
\(84\) | −0.162504 | −0.0177306 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 16.8307 | 1.81490 | ||||||||
\(87\) | −1.59627 | −0.171138 | ||||||||
\(88\) | −4.45336 | −0.474730 | ||||||||
\(89\) | 6.41921 | 0.680435 | 0.340218 | − | 0.940347i | \(-0.389499\pi\) | ||||
0.340218 | + | 0.940347i | \(0.389499\pi\) | |||||||
\(90\) | 6.41147 | 0.675829 | ||||||||
\(91\) | −1.14290 | −0.119809 | ||||||||
\(92\) | −0.977711 | −0.101933 | ||||||||
\(93\) | 9.57398 | 0.992775 | ||||||||
\(94\) | −7.84524 | −0.809174 | ||||||||
\(95\) | −5.41147 | −0.555206 | ||||||||
\(96\) | 2.61856 | 0.267255 | ||||||||
\(97\) | −4.08378 | −0.414645 | −0.207322 | − | 0.978273i | \(-0.566475\pi\) | ||||
−0.207322 | + | 0.978273i | \(0.566475\pi\) | |||||||
\(98\) | −10.5398 | −1.06468 | ||||||||
\(99\) | −2.08378 | −0.209428 | ||||||||
\(100\) | 2.59627 | 0.259627 | ||||||||
\(101\) | 5.26857 | 0.524242 | 0.262121 | − | 0.965035i | \(-0.415578\pi\) | ||||
0.262121 | + | 0.965035i | \(0.415578\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.4388 | −1.81683 | −0.908415 | − | 0.418069i | \(-0.862707\pi\) | ||||
−0.908415 | + | 0.418069i | \(0.862707\pi\) | |||||||
\(104\) | 8.33275 | 0.817093 | ||||||||
\(105\) | 1.65270 | 0.161287 | ||||||||
\(106\) | −12.8229 | −1.24547 | ||||||||
\(107\) | −5.36184 | −0.518349 | −0.259175 | − | 0.965831i | \(-0.583450\pi\) | ||||
−0.259175 | + | 0.965831i | \(0.583450\pi\) | |||||||
\(108\) | 1.95811 | 0.188419 | ||||||||
\(109\) | 15.5175 | 1.48631 | 0.743155 | − | 0.669119i | \(-0.233328\pi\) | ||||
0.743155 | + | 0.669119i | \(0.233328\pi\) | |||||||
\(110\) | −9.51754 | −0.907462 | ||||||||
\(111\) | −5.28312 | −0.501451 | ||||||||
\(112\) | −1.58853 | −0.150102 | ||||||||
\(113\) | 7.02734 | 0.661077 | 0.330538 | − | 0.943793i | \(-0.392770\pi\) | ||||
0.330538 | + | 0.943793i | \(0.392770\pi\) | |||||||
\(114\) | −3.16250 | −0.296196 | ||||||||
\(115\) | 9.94356 | 0.927242 | ||||||||
\(116\) | 0.411474 | 0.0382044 | ||||||||
\(117\) | 3.89899 | 0.360461 | ||||||||
\(118\) | −16.6459 | −1.53238 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −12.0496 | −1.09998 | ||||||||
\(121\) | −7.90673 | −0.718793 | ||||||||
\(122\) | 6.75877 | 0.611910 | ||||||||
\(123\) | 6.63041 | 0.597844 | ||||||||
\(124\) | −2.46791 | −0.221625 | ||||||||
\(125\) | −8.74422 | −0.782107 | ||||||||
\(126\) | −0.630415 | −0.0561618 | ||||||||
\(127\) | 7.74422 | 0.687189 | 0.343594 | − | 0.939118i | \(-0.388355\pi\) | ||||
0.343594 | + | 0.939118i | \(0.388355\pi\) | |||||||
\(128\) | 13.3405 | 1.17914 | ||||||||
\(129\) | −14.8007 | −1.30313 | ||||||||
\(130\) | 17.8084 | 1.56190 | ||||||||
\(131\) | −18.6186 | −1.62671 | −0.813355 | − | 0.581767i | \(-0.802361\pi\) | ||||
−0.813355 | + | 0.581767i | \(0.802361\pi\) | |||||||
\(132\) | −0.822948 | −0.0716285 | ||||||||
\(133\) | 0.532089 | 0.0461380 | ||||||||
\(134\) | 12.3669 | 1.06834 | ||||||||
\(135\) | −19.9145 | −1.71396 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.0719 | 0.860502 | 0.430251 | − | 0.902709i | \(-0.358425\pi\) | ||||
0.430251 | + | 0.902709i | \(0.358425\pi\) | |||||||
\(138\) | 5.81109 | 0.494673 | ||||||||
\(139\) | 8.55438 | 0.725573 | 0.362786 | − | 0.931872i | \(-0.381825\pi\) | ||||
0.362786 | + | 0.931872i | \(0.381825\pi\) | |||||||
\(140\) | −0.426022 | −0.0360054 | ||||||||
\(141\) | 6.89899 | 0.580999 | ||||||||
\(142\) | −17.2344 | −1.44628 | ||||||||
\(143\) | −5.78787 | −0.484006 | ||||||||
\(144\) | 5.41921 | 0.451601 | ||||||||
\(145\) | −4.18479 | −0.347528 | ||||||||
\(146\) | −2.60813 | −0.215850 | ||||||||
\(147\) | 9.26857 | 0.764459 | ||||||||
\(148\) | 1.36184 | 0.111943 | ||||||||
\(149\) | 11.8794 | 0.973197 | 0.486599 | − | 0.873626i | \(-0.338237\pi\) | ||||
0.486599 | + | 0.873626i | \(0.338237\pi\) | |||||||
\(150\) | −15.4311 | −1.25994 | ||||||||
\(151\) | 6.55943 | 0.533799 | 0.266899 | − | 0.963724i | \(-0.414001\pi\) | ||||
0.266899 | + | 0.963724i | \(0.414001\pi\) | |||||||
\(152\) | −3.87939 | −0.314660 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.935822 | 0.0754107 | ||||||||
\(155\) | 25.0993 | 2.01602 | ||||||||
\(156\) | 1.53983 | 0.123285 | ||||||||
\(157\) | 8.88444 | 0.709055 | 0.354528 | − | 0.935046i | \(-0.384642\pi\) | ||||
0.354528 | + | 0.935046i | \(0.384642\pi\) | |||||||
\(158\) | −17.7442 | −1.41165 | ||||||||
\(159\) | 11.2763 | 0.894270 | ||||||||
\(160\) | 6.86484 | 0.542713 | ||||||||
\(161\) | −0.977711 | −0.0770544 | ||||||||
\(162\) | −6.19253 | −0.486531 | ||||||||
\(163\) | 9.68004 | 0.758200 | 0.379100 | − | 0.925356i | \(-0.376234\pi\) | ||||
0.379100 | + | 0.925356i | \(0.376234\pi\) | |||||||
\(164\) | −1.70914 | −0.133461 | ||||||||
\(165\) | 8.36959 | 0.651571 | ||||||||
\(166\) | −3.29086 | −0.255420 | ||||||||
\(167\) | −1.83750 | −0.142190 | −0.0710949 | − | 0.997470i | \(-0.522649\pi\) | ||||
−0.0710949 | + | 0.997470i | \(0.522649\pi\) | |||||||
\(168\) | 1.18479 | 0.0914087 | ||||||||
\(169\) | −2.17024 | −0.166942 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.81521 | −0.138812 | ||||||||
\(172\) | 3.81521 | 0.290907 | ||||||||
\(173\) | −22.7597 | −1.73039 | −0.865194 | − | 0.501437i | \(-0.832805\pi\) | ||||
−0.865194 | + | 0.501437i | \(0.832805\pi\) | |||||||
\(174\) | −2.44562 | −0.185402 | ||||||||
\(175\) | 2.59627 | 0.196259 | ||||||||
\(176\) | −8.04458 | −0.606383 | ||||||||
\(177\) | 14.6382 | 1.10027 | ||||||||
\(178\) | 9.83481 | 0.737150 | ||||||||
\(179\) | −17.5253 | −1.30990 | −0.654951 | − | 0.755672i | \(-0.727311\pi\) | ||||
−0.654951 | + | 0.755672i | \(0.727311\pi\) | |||||||
\(180\) | 1.45336 | 0.108327 | ||||||||
\(181\) | 4.56212 | 0.339100 | 0.169550 | − | 0.985522i | \(-0.445769\pi\) | ||||
0.169550 | + | 0.985522i | \(0.445769\pi\) | |||||||
\(182\) | −1.75103 | −0.129795 | ||||||||
\(183\) | −5.94356 | −0.439361 | ||||||||
\(184\) | 7.12836 | 0.525509 | ||||||||
\(185\) | −13.8503 | −1.01829 | ||||||||
\(186\) | 14.6682 | 1.07552 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.77837 | −0.129701 | ||||||||
\(189\) | 1.95811 | 0.142432 | ||||||||
\(190\) | −8.29086 | −0.601482 | ||||||||
\(191\) | −9.72462 | −0.703649 | −0.351824 | − | 0.936066i | \(-0.614439\pi\) | ||||
−0.351824 | + | 0.936066i | \(0.614439\pi\) | |||||||
\(192\) | −8.31315 | −0.599950 | ||||||||
\(193\) | 0.844303 | 0.0607743 | 0.0303871 | − | 0.999538i | \(-0.490326\pi\) | ||||
0.0303871 | + | 0.999538i | \(0.490326\pi\) | |||||||
\(194\) | −6.25671 | −0.449206 | ||||||||
\(195\) | −15.6604 | −1.12147 | ||||||||
\(196\) | −2.38919 | −0.170656 | ||||||||
\(197\) | −17.0009 | −1.21127 | −0.605633 | − | 0.795744i | \(-0.707080\pi\) | ||||
−0.605633 | + | 0.795744i | \(0.707080\pi\) | |||||||
\(198\) | −3.19253 | −0.226883 | ||||||||
\(199\) | 12.6955 | 0.899962 | 0.449981 | − | 0.893038i | \(-0.351431\pi\) | ||||
0.449981 | + | 0.893038i | \(0.351431\pi\) | |||||||
\(200\) | −18.9290 | −1.33848 | ||||||||
\(201\) | −10.8753 | −0.767082 | ||||||||
\(202\) | 8.07192 | 0.567938 | ||||||||
\(203\) | 0.411474 | 0.0288798 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.3824 | 1.21404 | ||||||||
\(206\) | −28.2499 | −1.96826 | ||||||||
\(207\) | 3.33544 | 0.231829 | ||||||||
\(208\) | 15.0523 | 1.04369 | ||||||||
\(209\) | 2.69459 | 0.186389 | ||||||||
\(210\) | 2.53209 | 0.174731 | ||||||||
\(211\) | −23.5303 | −1.61990 | −0.809948 | − | 0.586502i | \(-0.800504\pi\) | ||||
−0.809948 | + | 0.586502i | \(0.800504\pi\) | |||||||
\(212\) | −2.90673 | −0.199635 | ||||||||
\(213\) | 15.1557 | 1.03845 | ||||||||
\(214\) | −8.21482 | −0.561554 | ||||||||
\(215\) | −38.8016 | −2.64625 | ||||||||
\(216\) | −14.2763 | −0.971380 | ||||||||
\(217\) | −2.46791 | −0.167533 | ||||||||
\(218\) | 23.7743 | 1.61020 | ||||||||
\(219\) | 2.29355 | 0.154984 | ||||||||
\(220\) | −2.15745 | −0.145455 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −8.09421 | −0.543248 | ||||||||
\(223\) | 4.97090 | 0.332876 | 0.166438 | − | 0.986052i | \(-0.446773\pi\) | ||||
0.166438 | + | 0.986052i | \(0.446773\pi\) | |||||||
\(224\) | −0.674992 | −0.0450998 | ||||||||
\(225\) | −8.85710 | −0.590473 | ||||||||
\(226\) | 10.7665 | 0.716178 | ||||||||
\(227\) | 5.25671 | 0.348900 | 0.174450 | − | 0.984666i | \(-0.444185\pi\) | ||||
0.174450 | + | 0.984666i | \(0.444185\pi\) | |||||||
\(228\) | −0.716881 | −0.0474766 | ||||||||
\(229\) | −24.2053 | −1.59953 | −0.799767 | − | 0.600311i | \(-0.795043\pi\) | ||||
−0.799767 | + | 0.600311i | \(0.795043\pi\) | |||||||
\(230\) | 15.2344 | 1.00453 | ||||||||
\(231\) | −0.822948 | −0.0541460 | ||||||||
\(232\) | −3.00000 | −0.196960 | ||||||||
\(233\) | 28.7219 | 1.88164 | 0.940818 | − | 0.338912i | \(-0.110059\pi\) | ||||
0.940818 | + | 0.338912i | \(0.110059\pi\) | |||||||
\(234\) | 5.97359 | 0.390506 | ||||||||
\(235\) | 18.0865 | 1.17983 | ||||||||
\(236\) | −3.77332 | −0.245622 | ||||||||
\(237\) | 15.6040 | 1.01359 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.63310 | −0.170321 | −0.0851606 | − | 0.996367i | \(-0.527140\pi\) | ||||
−0.0851606 | + | 0.996367i | \(0.527140\pi\) | |||||||
\(240\) | −21.7665 | −1.40502 | ||||||||
\(241\) | 25.3337 | 1.63189 | 0.815943 | − | 0.578132i | \(-0.196218\pi\) | ||||
0.815943 | + | 0.578132i | \(0.196218\pi\) | |||||||
\(242\) | −12.1138 | −0.778705 | ||||||||
\(243\) | −11.4688 | −0.735727 | ||||||||
\(244\) | 1.53209 | 0.0980819 | ||||||||
\(245\) | 24.2986 | 1.55238 | ||||||||
\(246\) | 10.1584 | 0.647675 | ||||||||
\(247\) | −5.04189 | −0.320808 | ||||||||
\(248\) | 17.9932 | 1.14257 | ||||||||
\(249\) | 2.89393 | 0.183396 | ||||||||
\(250\) | −13.3969 | −0.847296 | ||||||||
\(251\) | 10.6851 | 0.674437 | 0.337219 | − | 0.941426i | \(-0.390514\pi\) | ||||
0.337219 | + | 0.941426i | \(0.390514\pi\) | |||||||
\(252\) | −0.142903 | −0.00900207 | ||||||||
\(253\) | −4.95130 | −0.311286 | ||||||||
\(254\) | 11.8648 | 0.744466 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.09833 | 0.506145 | ||||||||
\(257\) | −3.73648 | −0.233075 | −0.116538 | − | 0.993186i | \(-0.537180\pi\) | ||||
−0.116538 | + | 0.993186i | \(0.537180\pi\) | |||||||
\(258\) | −22.6759 | −1.41174 | ||||||||
\(259\) | 1.36184 | 0.0846209 | ||||||||
\(260\) | 4.03684 | 0.250354 | ||||||||
\(261\) | −1.40373 | −0.0868889 | ||||||||
\(262\) | −28.5253 | −1.76230 | ||||||||
\(263\) | 10.2094 | 0.629541 | 0.314771 | − | 0.949168i | \(-0.398072\pi\) | ||||
0.314771 | + | 0.949168i | \(0.398072\pi\) | |||||||
\(264\) | 6.00000 | 0.369274 | ||||||||
\(265\) | 29.5621 | 1.81599 | ||||||||
\(266\) | 0.815207 | 0.0499836 | ||||||||
\(267\) | −8.64858 | −0.529285 | ||||||||
\(268\) | 2.80335 | 0.171242 | ||||||||
\(269\) | −11.7392 | −0.715750 | −0.357875 | − | 0.933770i | \(-0.616499\pi\) | ||||
−0.357875 | + | 0.933770i | \(0.616499\pi\) | |||||||
\(270\) | −30.5107 | −1.85682 | ||||||||
\(271\) | 17.0000 | 1.03268 | 0.516338 | − | 0.856385i | \(-0.327295\pi\) | ||||
0.516338 | + | 0.856385i | \(0.327295\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.53983 | 0.0931947 | ||||||||
\(274\) | 15.4311 | 0.932225 | ||||||||
\(275\) | 13.1480 | 0.792852 | ||||||||
\(276\) | 1.31727 | 0.0792901 | ||||||||
\(277\) | 24.3432 | 1.46264 | 0.731320 | − | 0.682035i | \(-0.238905\pi\) | ||||
0.731320 | + | 0.682035i | \(0.238905\pi\) | |||||||
\(278\) | 13.1061 | 0.786050 | ||||||||
\(279\) | 8.41921 | 0.504045 | ||||||||
\(280\) | 3.10607 | 0.185623 | ||||||||
\(281\) | −5.79385 | −0.345632 | −0.172816 | − | 0.984954i | \(-0.555287\pi\) | ||||
−0.172816 | + | 0.984954i | \(0.555287\pi\) | |||||||
\(282\) | 10.5699 | 0.629426 | ||||||||
\(283\) | 15.3200 | 0.910677 | 0.455338 | − | 0.890318i | \(-0.349518\pi\) | ||||
0.455338 | + | 0.890318i | \(0.349518\pi\) | |||||||
\(284\) | −3.90673 | −0.231822 | ||||||||
\(285\) | 7.29086 | 0.431873 | ||||||||
\(286\) | −8.86753 | −0.524348 | ||||||||
\(287\) | −1.70914 | −0.100887 | ||||||||
\(288\) | 2.30272 | 0.135689 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −6.41147 | −0.376495 | ||||||||
\(291\) | 5.50206 | 0.322536 | ||||||||
\(292\) | −0.591214 | −0.0345982 | ||||||||
\(293\) | 2.98040 | 0.174117 | 0.0870584 | − | 0.996203i | \(-0.472253\pi\) | ||||
0.0870584 | + | 0.996203i | \(0.472253\pi\) | |||||||
\(294\) | 14.2003 | 0.828177 | ||||||||
\(295\) | 38.3756 | 2.23431 | ||||||||
\(296\) | −9.92902 | −0.577112 | ||||||||
\(297\) | 9.91622 | 0.575398 | ||||||||
\(298\) | 18.2003 | 1.05431 | ||||||||
\(299\) | 9.26445 | 0.535777 | ||||||||
\(300\) | −3.49794 | −0.201954 | ||||||||
\(301\) | 3.81521 | 0.219905 | ||||||||
\(302\) | 10.0496 | 0.578291 | ||||||||
\(303\) | −7.09833 | −0.407788 | ||||||||
\(304\) | −7.00774 | −0.401921 | ||||||||
\(305\) | −15.5817 | −0.892207 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.26857 | −0.186547 | −0.0932736 | − | 0.995641i | \(-0.529733\pi\) | ||||
−0.0932736 | + | 0.995641i | \(0.529733\pi\) | |||||||
\(308\) | 0.212134 | 0.0120874 | ||||||||
\(309\) | 24.8425 | 1.41324 | ||||||||
\(310\) | 38.4543 | 2.18406 | ||||||||
\(311\) | −3.53209 | −0.200286 | −0.100143 | − | 0.994973i | \(-0.531930\pi\) | ||||
−0.100143 | + | 0.994973i | \(0.531930\pi\) | |||||||
\(312\) | −11.2267 | −0.635586 | ||||||||
\(313\) | −1.48246 | −0.0837935 | −0.0418968 | − | 0.999122i | \(-0.513340\pi\) | ||||
−0.0418968 | + | 0.999122i | \(0.513340\pi\) | |||||||
\(314\) | 13.6117 | 0.768155 | ||||||||
\(315\) | 1.45336 | 0.0818877 | ||||||||
\(316\) | −4.02229 | −0.226271 | ||||||||
\(317\) | 14.4638 | 0.812368 | 0.406184 | − | 0.913791i | \(-0.366859\pi\) | ||||
0.406184 | + | 0.913791i | \(0.366859\pi\) | |||||||
\(318\) | 17.2763 | 0.968807 | ||||||||
\(319\) | 2.08378 | 0.116669 | ||||||||
\(320\) | −21.7939 | −1.21831 | ||||||||
\(321\) | 7.22399 | 0.403204 | ||||||||
\(322\) | −1.49794 | −0.0834770 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.40373 | −0.0779852 | ||||||||
\(325\) | −24.6013 | −1.36464 | ||||||||
\(326\) | 14.8307 | 0.821396 | ||||||||
\(327\) | −20.9067 | −1.15614 | ||||||||
\(328\) | 12.4611 | 0.688049 | ||||||||
\(329\) | −1.77837 | −0.0980448 | ||||||||
\(330\) | 12.8229 | 0.705880 | ||||||||
\(331\) | −9.03508 | −0.496613 | −0.248307 | − | 0.968682i | \(-0.579874\pi\) | ||||
−0.248307 | + | 0.968682i | \(0.579874\pi\) | |||||||
\(332\) | −0.745977 | −0.0409408 | ||||||||
\(333\) | −4.64590 | −0.254594 | ||||||||
\(334\) | −2.81521 | −0.154041 | ||||||||
\(335\) | −28.5107 | −1.55771 | ||||||||
\(336\) | 2.14022 | 0.116758 | ||||||||
\(337\) | 17.9659 | 0.978662 | 0.489331 | − | 0.872098i | \(-0.337241\pi\) | ||||
0.489331 | + | 0.872098i | \(0.337241\pi\) | |||||||
\(338\) | −3.32501 | −0.180857 | ||||||||
\(339\) | −9.46791 | −0.514226 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.4979 | −0.676801 | ||||||||
\(342\) | −2.78106 | −0.150382 | ||||||||
\(343\) | −4.82026 | −0.260270 | ||||||||
\(344\) | −27.8161 | −1.49975 | ||||||||
\(345\) | −13.3969 | −0.721266 | ||||||||
\(346\) | −34.8699 | −1.87462 | ||||||||
\(347\) | 7.78375 | 0.417853 | 0.208927 | − | 0.977931i | \(-0.433003\pi\) | ||||
0.208927 | + | 0.977931i | \(0.433003\pi\) | |||||||
\(348\) | −0.554378 | −0.0297178 | ||||||||
\(349\) | −6.65002 | −0.355967 | −0.177984 | − | 0.984033i | \(-0.556957\pi\) | ||||
−0.177984 | + | 0.984033i | \(0.556957\pi\) | |||||||
\(350\) | 3.97771 | 0.212618 | ||||||||
\(351\) | −18.5544 | −0.990359 | ||||||||
\(352\) | −3.41828 | −0.182195 | ||||||||
\(353\) | 4.14559 | 0.220648 | 0.110324 | − | 0.993896i | \(-0.464811\pi\) | ||||
0.110324 | + | 0.993896i | \(0.464811\pi\) | |||||||
\(354\) | 22.4270 | 1.19198 | ||||||||
\(355\) | 39.7324 | 2.10877 | ||||||||
\(356\) | 2.22937 | 0.118156 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −26.8503 | −1.41908 | ||||||||
\(359\) | −17.0770 | −0.901288 | −0.450644 | − | 0.892704i | \(-0.648806\pi\) | ||||
−0.450644 | + | 0.892704i | \(0.648806\pi\) | |||||||
\(360\) | −10.5963 | −0.558472 | ||||||||
\(361\) | −16.6527 | −0.876458 | ||||||||
\(362\) | 6.98957 | 0.367364 | ||||||||
\(363\) | 10.6527 | 0.559122 | ||||||||
\(364\) | −0.396926 | −0.0208046 | ||||||||
\(365\) | 6.01279 | 0.314724 | ||||||||
\(366\) | −9.10607 | −0.475982 | ||||||||
\(367\) | −18.8307 | −0.982954 | −0.491477 | − | 0.870891i | \(-0.663543\pi\) | ||||
−0.491477 | + | 0.870891i | \(0.663543\pi\) | |||||||
\(368\) | 12.8767 | 0.671244 | ||||||||
\(369\) | 5.83069 | 0.303534 | ||||||||
\(370\) | −21.2199 | −1.10317 | ||||||||
\(371\) | −2.90673 | −0.150910 | ||||||||
\(372\) | 3.32501 | 0.172394 | ||||||||
\(373\) | −11.7314 | −0.607430 | −0.303715 | − | 0.952763i | \(-0.598227\pi\) | ||||
−0.303715 | + | 0.952763i | \(0.598227\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.7811 | 0.608371 | ||||||||
\(376\) | 12.9659 | 0.668663 | ||||||||
\(377\) | −3.89899 | −0.200808 | ||||||||
\(378\) | 3.00000 | 0.154303 | ||||||||
\(379\) | −8.16519 | −0.419418 | −0.209709 | − | 0.977764i | \(-0.567252\pi\) | ||||
−0.209709 | + | 0.977764i | \(0.567252\pi\) | |||||||
\(380\) | −1.87939 | −0.0964104 | ||||||||
\(381\) | −10.4338 | −0.534538 | ||||||||
\(382\) | −14.8990 | −0.762298 | ||||||||
\(383\) | 16.2540 | 0.830542 | 0.415271 | − | 0.909698i | \(-0.363687\pi\) | ||||
0.415271 | + | 0.909698i | \(0.363687\pi\) | |||||||
\(384\) | −17.9736 | −0.917211 | ||||||||
\(385\) | −2.15745 | −0.109954 | ||||||||
\(386\) | 1.29355 | 0.0658398 | ||||||||
\(387\) | −13.0155 | −0.661614 | ||||||||
\(388\) | −1.41828 | −0.0720023 | ||||||||
\(389\) | −5.80747 | −0.294450 | −0.147225 | − | 0.989103i | \(-0.547034\pi\) | ||||
−0.147225 | + | 0.989103i | \(0.547034\pi\) | |||||||
\(390\) | −23.9932 | −1.21494 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 17.4192 | 0.879803 | ||||||||
\(393\) | 25.0847 | 1.26536 | ||||||||
\(394\) | −26.0469 | −1.31223 | ||||||||
\(395\) | 40.9077 | 2.05829 | ||||||||
\(396\) | −0.723689 | −0.0363667 | ||||||||
\(397\) | −10.2517 | −0.514516 | −0.257258 | − | 0.966343i | \(-0.582819\pi\) | ||||
−0.257258 | + | 0.966343i | \(0.582819\pi\) | |||||||
\(398\) | 19.4507 | 0.974974 | ||||||||
\(399\) | −0.716881 | −0.0358890 | ||||||||
\(400\) | −34.1935 | −1.70967 | ||||||||
\(401\) | −30.5621 | −1.52620 | −0.763100 | − | 0.646281i | \(-0.776323\pi\) | ||||
−0.763100 | + | 0.646281i | \(0.776323\pi\) | |||||||
\(402\) | −16.6619 | −0.831019 | ||||||||
\(403\) | 23.3851 | 1.16489 | ||||||||
\(404\) | 1.82976 | 0.0910337 | ||||||||
\(405\) | 14.2763 | 0.709396 | ||||||||
\(406\) | 0.630415 | 0.0312870 | ||||||||
\(407\) | 6.89662 | 0.341853 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.9736 | 0.987631 | 0.493815 | − | 0.869567i | \(-0.335602\pi\) | ||||
0.493815 | + | 0.869567i | \(0.335602\pi\) | |||||||
\(410\) | 26.6313 | 1.31523 | ||||||||
\(411\) | −13.5699 | −0.669352 | ||||||||
\(412\) | −6.40373 | −0.315489 | ||||||||
\(413\) | −3.77332 | −0.185673 | ||||||||
\(414\) | 5.11019 | 0.251152 | ||||||||
\(415\) | 7.58677 | 0.372420 | ||||||||
\(416\) | 6.39599 | 0.313589 | ||||||||
\(417\) | −11.5253 | −0.564395 | ||||||||
\(418\) | 4.12836 | 0.201924 | ||||||||
\(419\) | 16.9290 | 0.827037 | 0.413518 | − | 0.910496i | \(-0.364300\pi\) | ||||
0.413518 | + | 0.910496i | \(0.364300\pi\) | |||||||
\(420\) | 0.573978 | 0.0280073 | ||||||||
\(421\) | −23.7297 | −1.15651 | −0.578257 | − | 0.815855i | \(-0.696267\pi\) | ||||
−0.578257 | + | 0.815855i | \(0.696267\pi\) | |||||||
\(422\) | −36.0506 | −1.75491 | ||||||||
\(423\) | 6.06687 | 0.294981 | ||||||||
\(424\) | 21.1925 | 1.02920 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 23.2199 | 1.12501 | ||||||||
\(427\) | 1.53209 | 0.0741430 | ||||||||
\(428\) | −1.86215 | −0.0900104 | ||||||||
\(429\) | 7.79797 | 0.376490 | ||||||||
\(430\) | −59.4475 | −2.86681 | ||||||||
\(431\) | −23.5921 | −1.13639 | −0.568197 | − | 0.822893i | \(-0.692359\pi\) | ||||
−0.568197 | + | 0.822893i | \(0.692359\pi\) | |||||||
\(432\) | −25.7888 | −1.24076 | ||||||||
\(433\) | −12.6946 | −0.610063 | −0.305032 | − | 0.952342i | \(-0.598667\pi\) | ||||
−0.305032 | + | 0.952342i | \(0.598667\pi\) | |||||||
\(434\) | −3.78106 | −0.181497 | ||||||||
\(435\) | 5.63816 | 0.270329 | ||||||||
\(436\) | 5.38919 | 0.258095 | ||||||||
\(437\) | −4.31315 | −0.206326 | ||||||||
\(438\) | 3.51392 | 0.167902 | ||||||||
\(439\) | −23.4706 | −1.12019 | −0.560095 | − | 0.828428i | \(-0.689235\pi\) | ||||
−0.560095 | + | 0.828428i | \(0.689235\pi\) | |||||||
\(440\) | 15.7297 | 0.749883 | ||||||||
\(441\) | 8.15064 | 0.388126 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.4124 | −0.922311 | −0.461156 | − | 0.887319i | \(-0.652565\pi\) | ||||
−0.461156 | + | 0.887319i | \(0.652565\pi\) | |||||||
\(444\) | −1.83481 | −0.0870761 | ||||||||
\(445\) | −22.6732 | −1.07481 | ||||||||
\(446\) | 7.61587 | 0.360622 | ||||||||
\(447\) | −16.0051 | −0.757013 | ||||||||
\(448\) | 2.14290 | 0.101243 | ||||||||
\(449\) | −17.6263 | −0.831836 | −0.415918 | − | 0.909402i | \(-0.636540\pi\) | ||||
−0.415918 | + | 0.909402i | \(0.636540\pi\) | |||||||
\(450\) | −13.5699 | −0.639689 | ||||||||
\(451\) | −8.65539 | −0.407566 | ||||||||
\(452\) | 2.44057 | 0.114795 | ||||||||
\(453\) | −8.83750 | −0.415222 | ||||||||
\(454\) | 8.05375 | 0.377981 | ||||||||
\(455\) | 4.03684 | 0.189250 | ||||||||
\(456\) | 5.22668 | 0.244762 | ||||||||
\(457\) | −37.1215 | −1.73647 | −0.868236 | − | 0.496151i | \(-0.834746\pi\) | ||||
−0.868236 | + | 0.496151i | \(0.834746\pi\) | |||||||
\(458\) | −37.0847 | −1.73285 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.45336 | 0.161014 | ||||||||
\(461\) | 29.4074 | 1.36964 | 0.684819 | − | 0.728714i | \(-0.259881\pi\) | ||||
0.684819 | + | 0.728714i | \(0.259881\pi\) | |||||||
\(462\) | −1.26083 | −0.0586591 | ||||||||
\(463\) | −9.72462 | −0.451942 | −0.225971 | − | 0.974134i | \(-0.572555\pi\) | ||||
−0.225971 | + | 0.974134i | \(0.572555\pi\) | |||||||
\(464\) | −5.41921 | −0.251581 | ||||||||
\(465\) | −33.8161 | −1.56819 | ||||||||
\(466\) | 44.0046 | 2.03847 | ||||||||
\(467\) | −4.62267 | −0.213912 | −0.106956 | − | 0.994264i | \(-0.534110\pi\) | ||||
−0.106956 | + | 0.994264i | \(0.534110\pi\) | |||||||
\(468\) | 1.35410 | 0.0625935 | ||||||||
\(469\) | 2.80335 | 0.129447 | ||||||||
\(470\) | 27.7101 | 1.27817 | ||||||||
\(471\) | −11.9700 | −0.551547 | ||||||||
\(472\) | 27.5107 | 1.26628 | ||||||||
\(473\) | 19.3209 | 0.888375 | ||||||||
\(474\) | 23.9067 | 1.09807 | ||||||||
\(475\) | 11.4534 | 0.525516 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.91622 | 0.454033 | ||||||||
\(478\) | −4.03415 | −0.184518 | ||||||||
\(479\) | −6.83656 | −0.312371 | −0.156185 | − | 0.987728i | \(-0.549920\pi\) | ||||
−0.156185 | + | 0.987728i | \(0.549920\pi\) | |||||||
\(480\) | −9.24897 | −0.422156 | ||||||||
\(481\) | −12.9044 | −0.588388 | ||||||||
\(482\) | 38.8135 | 1.76790 | ||||||||
\(483\) | 1.31727 | 0.0599377 | ||||||||
\(484\) | −2.74598 | −0.124817 | ||||||||
\(485\) | 14.4243 | 0.654972 | ||||||||
\(486\) | −17.5713 | −0.797050 | ||||||||
\(487\) | 7.66281 | 0.347235 | 0.173617 | − | 0.984813i | \(-0.444454\pi\) | ||||
0.173617 | + | 0.984813i | \(0.444454\pi\) | |||||||
\(488\) | −11.1702 | −0.505653 | ||||||||
\(489\) | −13.0419 | −0.589775 | ||||||||
\(490\) | 37.2276 | 1.68177 | ||||||||
\(491\) | 9.02465 | 0.407277 | 0.203638 | − | 0.979046i | \(-0.434723\pi\) | ||||
0.203638 | + | 0.979046i | \(0.434723\pi\) | |||||||
\(492\) | 2.30272 | 0.103815 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −7.72462 | −0.347547 | ||||||||
\(495\) | 7.36009 | 0.330811 | ||||||||
\(496\) | 32.5030 | 1.45943 | ||||||||
\(497\) | −3.90673 | −0.175241 | ||||||||
\(498\) | 4.43376 | 0.198682 | ||||||||
\(499\) | −26.6928 | −1.19494 | −0.597468 | − | 0.801893i | \(-0.703826\pi\) | ||||
−0.597468 | + | 0.801893i | \(0.703826\pi\) | |||||||
\(500\) | −3.03684 | −0.135811 | ||||||||
\(501\) | 2.47565 | 0.110604 | ||||||||
\(502\) | 16.3705 | 0.730652 | ||||||||
\(503\) | −12.9267 | −0.576371 | −0.288185 | − | 0.957575i | \(-0.593052\pi\) | ||||
−0.288185 | + | 0.957575i | \(0.593052\pi\) | |||||||
\(504\) | 1.04189 | 0.0464094 | ||||||||
\(505\) | −18.6091 | −0.828092 | ||||||||
\(506\) | −7.58584 | −0.337232 | ||||||||
\(507\) | 2.92396 | 0.129858 | ||||||||
\(508\) | 2.68954 | 0.119329 | ||||||||
\(509\) | −27.8753 | −1.23555 | −0.617775 | − | 0.786355i | \(-0.711966\pi\) | ||||
−0.617775 | + | 0.786355i | \(0.711966\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.591214 | −0.0261538 | ||||||||
\(512\) | −14.2736 | −0.630811 | ||||||||
\(513\) | 8.63816 | 0.381384 | ||||||||
\(514\) | −5.72462 | −0.252502 | ||||||||
\(515\) | 65.1275 | 2.86986 | ||||||||
\(516\) | −5.14022 | −0.226285 | ||||||||
\(517\) | −9.00599 | −0.396083 | ||||||||
\(518\) | 2.08647 | 0.0916741 | ||||||||
\(519\) | 30.6641 | 1.34600 | ||||||||
\(520\) | −29.4320 | −1.29068 | ||||||||
\(521\) | −5.11886 | −0.224261 | −0.112131 | − | 0.993693i | \(-0.535768\pi\) | ||||
−0.112131 | + | 0.993693i | \(0.535768\pi\) | |||||||
\(522\) | −2.15064 | −0.0941311 | ||||||||
\(523\) | 15.3182 | 0.669818 | 0.334909 | − | 0.942250i | \(-0.391294\pi\) | ||||
0.334909 | + | 0.942250i | \(0.391294\pi\) | |||||||
\(524\) | −6.46616 | −0.282475 | ||||||||
\(525\) | −3.49794 | −0.152663 | ||||||||
\(526\) | 15.6418 | 0.682014 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 10.8384 | 0.471682 | ||||||||
\(529\) | −15.0746 | −0.655418 | ||||||||
\(530\) | 45.2918 | 1.96735 | ||||||||
\(531\) | 12.8726 | 0.558622 | ||||||||
\(532\) | 0.184793 | 0.00801177 | ||||||||
\(533\) | 16.1952 | 0.701493 | ||||||||
\(534\) | −13.2504 | −0.573401 | ||||||||
\(535\) | 18.9385 | 0.818783 | ||||||||
\(536\) | −20.4388 | −0.882822 | ||||||||
\(537\) | 23.6117 | 1.01892 | ||||||||
\(538\) | −17.9855 | −0.775408 | ||||||||
\(539\) | −12.0993 | −0.521152 | ||||||||
\(540\) | −6.91622 | −0.297627 | ||||||||
\(541\) | −37.4466 | −1.60995 | −0.804977 | − | 0.593307i | \(-0.797822\pi\) | ||||
−0.804977 | + | 0.593307i | \(0.797822\pi\) | |||||||
\(542\) | 26.0455 | 1.11875 | ||||||||
\(543\) | −6.14653 | −0.263773 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −54.8093 | −2.34777 | ||||||||
\(546\) | 2.35916 | 0.100963 | ||||||||
\(547\) | −27.3928 | −1.17123 | −0.585616 | − | 0.810589i | \(-0.699147\pi\) | ||||
−0.585616 | + | 0.810589i | \(0.699147\pi\) | |||||||
\(548\) | 3.49794 | 0.149425 | ||||||||
\(549\) | −5.22668 | −0.223069 | ||||||||
\(550\) | 20.1438 | 0.858936 | ||||||||
\(551\) | 1.81521 | 0.0773304 | ||||||||
\(552\) | −9.60401 | −0.408774 | ||||||||
\(553\) | −4.02229 | −0.171045 | ||||||||
\(554\) | 37.2959 | 1.58455 | ||||||||
\(555\) | 18.6604 | 0.792092 | ||||||||
\(556\) | 2.97090 | 0.125994 | ||||||||
\(557\) | 9.07604 | 0.384564 | 0.192282 | − | 0.981340i | \(-0.438411\pi\) | ||||
0.192282 | + | 0.981340i | \(0.438411\pi\) | |||||||
\(558\) | 12.8990 | 0.546058 | ||||||||
\(559\) | −36.1516 | −1.52905 | ||||||||
\(560\) | 5.61081 | 0.237100 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.87670 | −0.374441 | ||||||||
\(563\) | −38.4894 | −1.62213 | −0.811067 | − | 0.584953i | \(-0.801113\pi\) | ||||
−0.811067 | + | 0.584953i | \(0.801113\pi\) | |||||||
\(564\) | 2.39599 | 0.100889 | ||||||||
\(565\) | −24.8212 | −1.04424 | ||||||||
\(566\) | 23.4715 | 0.986582 | ||||||||
\(567\) | −1.40373 | −0.0589513 | ||||||||
\(568\) | 28.4834 | 1.19514 | ||||||||
\(569\) | 45.1830 | 1.89417 | 0.947086 | − | 0.320981i | \(-0.104012\pi\) | ||||
0.947086 | + | 0.320981i | \(0.104012\pi\) | |||||||
\(570\) | 11.1702 | 0.467870 | ||||||||
\(571\) | 30.4570 | 1.27459 | 0.637293 | − | 0.770622i | \(-0.280054\pi\) | ||||
0.637293 | + | 0.770622i | \(0.280054\pi\) | |||||||
\(572\) | −2.01010 | −0.0840467 | ||||||||
\(573\) | 13.1019 | 0.547342 | ||||||||
\(574\) | −2.61856 | −0.109296 | ||||||||
\(575\) | −21.0455 | −0.877658 | ||||||||
\(576\) | −7.31046 | −0.304602 | ||||||||
\(577\) | −9.90167 | −0.412212 | −0.206106 | − | 0.978530i | \(-0.566079\pi\) | ||||
−0.206106 | + | 0.978530i | \(0.566079\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.13753 | −0.0472740 | ||||||||
\(580\) | −1.45336 | −0.0603476 | ||||||||
\(581\) | −0.745977 | −0.0309484 | ||||||||
\(582\) | 8.42964 | 0.349420 | ||||||||
\(583\) | −14.7202 | −0.609648 | ||||||||
\(584\) | 4.31046 | 0.178368 | ||||||||
\(585\) | −13.7716 | −0.569384 | ||||||||
\(586\) | 4.56624 | 0.188630 | ||||||||
\(587\) | −36.1343 | −1.49142 | −0.745712 | − | 0.666268i | \(-0.767890\pi\) | ||||
−0.745712 | + | 0.666268i | \(0.767890\pi\) | |||||||
\(588\) | 3.21894 | 0.132747 | ||||||||
\(589\) | −10.8871 | −0.448596 | ||||||||
\(590\) | 58.7948 | 2.42054 | ||||||||
\(591\) | 22.9053 | 0.942198 | ||||||||
\(592\) | −17.9358 | −0.737158 | ||||||||
\(593\) | −7.41653 | −0.304560 | −0.152280 | − | 0.988337i | \(-0.548662\pi\) | ||||
−0.152280 | + | 0.988337i | \(0.548662\pi\) | |||||||
\(594\) | 15.1925 | 0.623357 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.12567 | 0.168994 | ||||||||
\(597\) | −17.1046 | −0.700046 | ||||||||
\(598\) | 14.1940 | 0.580434 | ||||||||
\(599\) | 7.61350 | 0.311079 | 0.155540 | − | 0.987830i | \(-0.450288\pi\) | ||||
0.155540 | + | 0.987830i | \(0.450288\pi\) | |||||||
\(600\) | 25.5030 | 1.04116 | ||||||||
\(601\) | 32.5732 | 1.32869 | 0.664343 | − | 0.747427i | \(-0.268711\pi\) | ||||
0.664343 | + | 0.747427i | \(0.268711\pi\) | |||||||
\(602\) | 5.84524 | 0.238234 | ||||||||
\(603\) | −9.56355 | −0.389458 | ||||||||
\(604\) | 2.27807 | 0.0926932 | ||||||||
\(605\) | 27.9273 | 1.13540 | ||||||||
\(606\) | −10.8753 | −0.441778 | ||||||||
\(607\) | 3.01455 | 0.122357 | 0.0611784 | − | 0.998127i | \(-0.480514\pi\) | ||||
0.0611784 | + | 0.998127i | \(0.480514\pi\) | |||||||
\(608\) | −2.97771 | −0.120762 | ||||||||
\(609\) | −0.554378 | −0.0224645 | ||||||||
\(610\) | −23.8726 | −0.966572 | ||||||||
\(611\) | 16.8512 | 0.681728 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.26857 | 0.293575 | 0.146787 | − | 0.989168i | \(-0.453107\pi\) | ||||
0.146787 | + | 0.989168i | \(0.453107\pi\) | |||||||
\(614\) | −5.00774 | −0.202096 | ||||||||
\(615\) | −23.4192 | −0.944354 | ||||||||
\(616\) | −1.54664 | −0.0623158 | ||||||||
\(617\) | 34.2449 | 1.37865 | 0.689323 | − | 0.724454i | \(-0.257908\pi\) | ||||
0.689323 | + | 0.724454i | \(0.257908\pi\) | |||||||
\(618\) | 38.0610 | 1.53104 | ||||||||
\(619\) | −20.4296 | −0.821137 | −0.410568 | − | 0.911830i | \(-0.634670\pi\) | ||||
−0.410568 | + | 0.911830i | \(0.634670\pi\) | |||||||
\(620\) | 8.71688 | 0.350078 | ||||||||
\(621\) | −15.8726 | −0.636945 | ||||||||
\(622\) | −5.41147 | −0.216980 | ||||||||
\(623\) | 2.22937 | 0.0893178 | ||||||||
\(624\) | −20.2799 | −0.811847 | ||||||||
\(625\) | −6.49289 | −0.259716 | ||||||||
\(626\) | −2.27126 | −0.0907778 | ||||||||
\(627\) | −3.63041 | −0.144985 | ||||||||
\(628\) | 3.08553 | 0.123126 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 2.22668 | 0.0887131 | ||||||||
\(631\) | 15.5080 | 0.617366 | 0.308683 | − | 0.951165i | \(-0.400112\pi\) | ||||
0.308683 | + | 0.951165i | \(0.400112\pi\) | |||||||
\(632\) | 29.3259 | 1.16652 | ||||||||
\(633\) | 31.7023 | 1.26005 | ||||||||
\(634\) | 22.1598 | 0.880079 | ||||||||
\(635\) | −27.3533 | −1.08548 | ||||||||
\(636\) | 3.91622 | 0.155288 | ||||||||
\(637\) | 22.6391 | 0.896993 | ||||||||
\(638\) | 3.19253 | 0.126394 | ||||||||
\(639\) | 13.3277 | 0.527236 | ||||||||
\(640\) | −47.1198 | −1.86257 | ||||||||
\(641\) | −32.5945 | −1.28741 | −0.643703 | − | 0.765275i | \(-0.722603\pi\) | ||||
−0.643703 | + | 0.765275i | \(0.722603\pi\) | |||||||
\(642\) | 11.0678 | 0.436811 | ||||||||
\(643\) | 41.2080 | 1.62509 | 0.812543 | − | 0.582902i | \(-0.198083\pi\) | ||||
0.812543 | + | 0.582902i | \(0.198083\pi\) | |||||||
\(644\) | −0.339556 | −0.0133804 | ||||||||
\(645\) | 52.2772 | 2.05841 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.5131 | 1.04234 | 0.521169 | − | 0.853454i | \(-0.325496\pi\) | ||||
0.521169 | + | 0.853454i | \(0.325496\pi\) | |||||||
\(648\) | 10.2344 | 0.402046 | ||||||||
\(649\) | −19.1088 | −0.750084 | ||||||||
\(650\) | −37.6914 | −1.47838 | ||||||||
\(651\) | 3.32501 | 0.130317 | ||||||||
\(652\) | 3.36184 | 0.131660 | ||||||||
\(653\) | −14.1875 | −0.555199 | −0.277600 | − | 0.960697i | \(-0.589539\pi\) | ||||
−0.277600 | + | 0.960697i | \(0.589539\pi\) | |||||||
\(654\) | −32.0310 | −1.25251 | ||||||||
\(655\) | 65.7624 | 2.56955 | ||||||||
\(656\) | 22.5098 | 0.878860 | ||||||||
\(657\) | 2.01691 | 0.0786872 | ||||||||
\(658\) | −2.72462 | −0.106217 | ||||||||
\(659\) | −28.3628 | −1.10486 | −0.552428 | − | 0.833560i | \(-0.686299\pi\) | ||||
−0.552428 | + | 0.833560i | \(0.686299\pi\) | |||||||
\(660\) | 2.90673 | 0.113144 | ||||||||
\(661\) | 29.1661 | 1.13443 | 0.567215 | − | 0.823569i | \(-0.308021\pi\) | ||||
0.567215 | + | 0.823569i | \(0.308021\pi\) | |||||||
\(662\) | −13.8425 | −0.538006 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.43882 | 0.211067 | ||||||||
\(665\) | −1.87939 | −0.0728794 | ||||||||
\(666\) | −7.11793 | −0.275814 | ||||||||
\(667\) | −3.33544 | −0.129149 | ||||||||
\(668\) | −0.638156 | −0.0246910 | ||||||||
\(669\) | −6.69728 | −0.258932 | ||||||||
\(670\) | −43.6810 | −1.68754 | ||||||||
\(671\) | 7.75877 | 0.299524 | ||||||||
\(672\) | 0.909415 | 0.0350814 | ||||||||
\(673\) | −29.3678 | −1.13205 | −0.566023 | − | 0.824389i | \(-0.691519\pi\) | ||||
−0.566023 | + | 0.824389i | \(0.691519\pi\) | |||||||
\(674\) | 27.5253 | 1.06023 | ||||||||
\(675\) | 42.1489 | 1.62231 | ||||||||
\(676\) | −0.753718 | −0.0289892 | ||||||||
\(677\) | 39.3783 | 1.51343 | 0.756715 | − | 0.653745i | \(-0.226803\pi\) | ||||
0.756715 | + | 0.653745i | \(0.226803\pi\) | |||||||
\(678\) | −14.5057 | −0.557087 | ||||||||
\(679\) | −1.41828 | −0.0544286 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.08235 | −0.271396 | ||||||||
\(682\) | −19.1480 | −0.733213 | ||||||||
\(683\) | 27.1634 | 1.03938 | 0.519690 | − | 0.854355i | \(-0.326047\pi\) | ||||
0.519690 | + | 0.854355i | \(0.326047\pi\) | |||||||
\(684\) | −0.630415 | −0.0241045 | ||||||||
\(685\) | −35.5749 | −1.35925 | ||||||||
\(686\) | −7.38507 | −0.281963 | ||||||||
\(687\) | 32.6117 | 1.24422 | ||||||||
\(688\) | −50.2472 | −1.91566 | ||||||||
\(689\) | 27.5431 | 1.04931 | ||||||||
\(690\) | −20.5253 | −0.781384 | ||||||||
\(691\) | −33.8503 | −1.28773 | −0.643863 | − | 0.765141i | \(-0.722669\pi\) | ||||
−0.643863 | + | 0.765141i | \(0.722669\pi\) | |||||||
\(692\) | −7.90436 | −0.300479 | ||||||||
\(693\) | −0.723689 | −0.0274907 | ||||||||
\(694\) | 11.9254 | 0.452682 | ||||||||
\(695\) | −30.2148 | −1.14611 | ||||||||
\(696\) | 4.04189 | 0.153207 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −10.1884 | −0.385637 | ||||||||
\(699\) | −38.6970 | −1.46365 | ||||||||
\(700\) | 0.901674 | 0.0340801 | ||||||||
\(701\) | 20.9540 | 0.791421 | 0.395711 | − | 0.918375i | \(-0.370498\pi\) | ||||
0.395711 | + | 0.918375i | \(0.370498\pi\) | |||||||
\(702\) | −28.4270 | −1.07291 | ||||||||
\(703\) | 6.00774 | 0.226586 | ||||||||
\(704\) | 10.8520 | 0.409002 | ||||||||
\(705\) | −24.3678 | −0.917746 | ||||||||
\(706\) | 6.35142 | 0.239039 | ||||||||
\(707\) | 1.82976 | 0.0688150 | ||||||||
\(708\) | 5.08378 | 0.191060 | ||||||||
\(709\) | −31.3236 | −1.17638 | −0.588191 | − | 0.808722i | \(-0.700160\pi\) | ||||
−0.588191 | + | 0.808722i | \(0.700160\pi\) | |||||||
\(710\) | 60.8735 | 2.28454 | ||||||||
\(711\) | 13.7219 | 0.514613 | ||||||||
\(712\) | −16.2540 | −0.609145 | ||||||||
\(713\) | 20.0051 | 0.749195 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.4433 | 0.764535 | ||||||||
\(716\) | −6.08647 | −0.227462 | ||||||||
\(717\) | 3.54757 | 0.132486 | ||||||||
\(718\) | −26.1634 | −0.976411 | ||||||||
\(719\) | −44.4097 | −1.65620 | −0.828102 | − | 0.560578i | \(-0.810579\pi\) | ||||
−0.828102 | + | 0.560578i | \(0.810579\pi\) | |||||||
\(720\) | −19.1411 | −0.713348 | ||||||||
\(721\) | −6.40373 | −0.238487 | ||||||||
\(722\) | −25.5134 | −0.949511 | ||||||||
\(723\) | −34.1320 | −1.26938 | ||||||||
\(724\) | 1.58441 | 0.0588840 | ||||||||
\(725\) | 8.85710 | 0.328944 | ||||||||
\(726\) | 16.3209 | 0.605725 | ||||||||
\(727\) | −39.5354 | −1.46629 | −0.733143 | − | 0.680074i | \(-0.761947\pi\) | ||||
−0.733143 | + | 0.680074i | \(0.761947\pi\) | |||||||
\(728\) | 2.89393 | 0.107256 | ||||||||
\(729\) | 27.5776 | 1.02139 | ||||||||
\(730\) | 9.21213 | 0.340956 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −2.06418 | −0.0762942 | ||||||||
\(733\) | 13.8990 | 0.513371 | 0.256685 | − | 0.966495i | \(-0.417370\pi\) | ||||
0.256685 | + | 0.966495i | \(0.417370\pi\) | |||||||
\(734\) | −28.8503 | −1.06488 | ||||||||
\(735\) | −32.7374 | −1.20754 | ||||||||
\(736\) | 5.47153 | 0.201683 | ||||||||
\(737\) | 14.1967 | 0.522940 | ||||||||
\(738\) | 8.93313 | 0.328833 | ||||||||
\(739\) | 11.4037 | 0.419493 | 0.209747 | − | 0.977756i | \(-0.432736\pi\) | ||||
0.209747 | + | 0.977756i | \(0.432736\pi\) | |||||||
\(740\) | −4.81016 | −0.176825 | ||||||||
\(741\) | 6.79292 | 0.249544 | ||||||||
\(742\) | −4.45336 | −0.163488 | ||||||||
\(743\) | −14.6209 | −0.536390 | −0.268195 | − | 0.963365i | \(-0.586427\pi\) | ||||
−0.268195 | + | 0.963365i | \(0.586427\pi\) | |||||||
\(744\) | −24.2422 | −0.888761 | ||||||||
\(745\) | −41.9590 | −1.53726 | ||||||||
\(746\) | −17.9736 | −0.658060 | ||||||||
\(747\) | 2.54488 | 0.0931124 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.86215 | −0.0680414 | ||||||||
\(750\) | 18.0496 | 0.659079 | ||||||||
\(751\) | 28.0196 | 1.02245 | 0.511225 | − | 0.859447i | \(-0.329192\pi\) | ||||
0.511225 | + | 0.859447i | \(0.329192\pi\) | |||||||
\(752\) | 23.4216 | 0.854097 | ||||||||
\(753\) | −14.3960 | −0.524619 | ||||||||
\(754\) | −5.97359 | −0.217545 | ||||||||
\(755\) | −23.1685 | −0.843188 | ||||||||
\(756\) | 0.680045 | 0.0247330 | ||||||||
\(757\) | 15.6186 | 0.567666 | 0.283833 | − | 0.958874i | \(-0.408394\pi\) | ||||
0.283833 | + | 0.958874i | \(0.408394\pi\) | |||||||
\(758\) | −12.5098 | −0.454376 | ||||||||
\(759\) | 6.67087 | 0.242137 | ||||||||
\(760\) | 13.7023 | 0.497036 | ||||||||
\(761\) | 20.5868 | 0.746270 | 0.373135 | − | 0.927777i | \(-0.378283\pi\) | ||||
0.373135 | + | 0.927777i | \(0.378283\pi\) | |||||||
\(762\) | −15.9855 | −0.579092 | ||||||||
\(763\) | 5.38919 | 0.195102 | ||||||||
\(764\) | −3.37733 | −0.122187 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.9026 | 0.899768 | ||||||||
\(767\) | 35.7547 | 1.29103 | ||||||||
\(768\) | −10.9108 | −0.393711 | ||||||||
\(769\) | 22.2249 | 0.801451 | 0.400726 | − | 0.916198i | \(-0.368758\pi\) | ||||
0.400726 | + | 0.916198i | \(0.368758\pi\) | |||||||
\(770\) | −3.30541 | −0.119119 | ||||||||
\(771\) | 5.03415 | 0.181300 | ||||||||
\(772\) | 0.293223 | 0.0105533 | ||||||||
\(773\) | −27.0087 | −0.971434 | −0.485717 | − | 0.874116i | \(-0.661442\pi\) | ||||
−0.485717 | + | 0.874116i | \(0.661442\pi\) | |||||||
\(774\) | −19.9409 | −0.716760 | ||||||||
\(775\) | −53.1225 | −1.90822 | ||||||||
\(776\) | 10.3405 | 0.371202 | ||||||||
\(777\) | −1.83481 | −0.0658234 | ||||||||
\(778\) | −8.89756 | −0.318993 | ||||||||
\(779\) | −7.53983 | −0.270142 | ||||||||
\(780\) | −5.43882 | −0.194741 | ||||||||
\(781\) | −19.7844 | −0.707940 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.68004 | 0.238725 | ||||||||
\(784\) | 31.4662 | 1.12379 | ||||||||
\(785\) | −31.3806 | −1.12002 | ||||||||
\(786\) | 38.4320 | 1.37082 | ||||||||
\(787\) | 20.9810 | 0.747892 | 0.373946 | − | 0.927450i | \(-0.378004\pi\) | ||||
0.373946 | + | 0.927450i | \(0.378004\pi\) | |||||||
\(788\) | −5.90436 | −0.210334 | ||||||||
\(789\) | −13.7551 | −0.489696 | ||||||||
\(790\) | 62.6742 | 2.22985 | ||||||||
\(791\) | 2.44057 | 0.0867767 | ||||||||
\(792\) | 5.27631 | 0.187486 | ||||||||
\(793\) | −14.5175 | −0.515533 | ||||||||
\(794\) | −15.7065 | −0.557401 | ||||||||
\(795\) | −39.8289 | −1.41259 | ||||||||
\(796\) | 4.40911 | 0.156277 | ||||||||
\(797\) | 34.4347 | 1.21974 | 0.609870 | − | 0.792502i | \(-0.291222\pi\) | ||||
0.609870 | + | 0.792502i | \(0.291222\pi\) | |||||||
\(798\) | −1.09833 | −0.0388803 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −14.5294 | −0.513692 | ||||||||
\(801\) | −7.60544 | −0.268725 | ||||||||
\(802\) | −46.8239 | −1.65341 | ||||||||
\(803\) | −2.99401 | −0.105656 | ||||||||
\(804\) | −3.77694 | −0.133202 | ||||||||
\(805\) | 3.45336 | 0.121715 | ||||||||
\(806\) | 35.8280 | 1.26199 | ||||||||
\(807\) | 15.8161 | 0.556755 | ||||||||
\(808\) | −13.3405 | −0.469317 | ||||||||
\(809\) | 28.9246 | 1.01693 | 0.508467 | − | 0.861082i | \(-0.330212\pi\) | ||||
0.508467 | + | 0.861082i | \(0.330212\pi\) | |||||||
\(810\) | 21.8726 | 0.768524 | ||||||||
\(811\) | 38.6236 | 1.35626 | 0.678129 | − | 0.734943i | \(-0.262791\pi\) | ||||
0.678129 | + | 0.734943i | \(0.262791\pi\) | |||||||
\(812\) | 0.142903 | 0.00501493 | ||||||||
\(813\) | −22.9040 | −0.803280 | ||||||||
\(814\) | 10.5662 | 0.370346 | ||||||||
\(815\) | −34.1908 | −1.19765 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.8307 | 0.588831 | ||||||||
\(818\) | 30.6013 | 1.06995 | ||||||||
\(819\) | 1.35410 | 0.0473162 | ||||||||
\(820\) | 6.03684 | 0.210815 | ||||||||
\(821\) | 5.39599 | 0.188321 | 0.0941607 | − | 0.995557i | \(-0.469983\pi\) | ||||
0.0941607 | + | 0.995557i | \(0.469983\pi\) | |||||||
\(822\) | −20.7902 | −0.725143 | ||||||||
\(823\) | 30.6878 | 1.06971 | 0.534854 | − | 0.844944i | \(-0.320366\pi\) | ||||
0.534854 | + | 0.844944i | \(0.320366\pi\) | |||||||
\(824\) | 46.6887 | 1.62648 | ||||||||
\(825\) | −17.7142 | −0.616729 | ||||||||
\(826\) | −5.78106 | −0.201149 | ||||||||
\(827\) | 35.5381 | 1.23578 | 0.617890 | − | 0.786265i | \(-0.287988\pi\) | ||||
0.617890 | + | 0.786265i | \(0.287988\pi\) | |||||||
\(828\) | 1.15839 | 0.0402567 | ||||||||
\(829\) | 3.17200 | 0.110168 | 0.0550840 | − | 0.998482i | \(-0.482457\pi\) | ||||
0.0550840 | + | 0.998482i | \(0.482457\pi\) | |||||||
\(830\) | 11.6236 | 0.403461 | ||||||||
\(831\) | −32.7975 | −1.13773 | ||||||||
\(832\) | −20.3054 | −0.703963 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −17.6578 | −0.611438 | ||||||||
\(835\) | 6.49020 | 0.224603 | ||||||||
\(836\) | 0.935822 | 0.0323661 | ||||||||
\(837\) | −40.0651 | −1.38485 | ||||||||
\(838\) | 25.9368 | 0.895970 | ||||||||
\(839\) | −36.8152 | −1.27100 | −0.635501 | − | 0.772100i | \(-0.719206\pi\) | ||||
−0.635501 | + | 0.772100i | \(0.719206\pi\) | |||||||
\(840\) | −4.18479 | −0.144389 | ||||||||
\(841\) | −27.5963 | −0.951595 | ||||||||
\(842\) | −36.3560 | −1.25291 | ||||||||
\(843\) | 7.80604 | 0.268854 | ||||||||
\(844\) | −8.17200 | −0.281292 | ||||||||
\(845\) | 7.66550 | 0.263701 | ||||||||
\(846\) | 9.29498 | 0.319568 | ||||||||
\(847\) | −2.74598 | −0.0943529 | ||||||||
\(848\) | 38.2823 | 1.31462 | ||||||||
\(849\) | −20.6405 | −0.708381 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.0392 | −0.378419 | ||||||||
\(852\) | 5.26352 | 0.180325 | ||||||||
\(853\) | 20.0651 | 0.687016 | 0.343508 | − | 0.939150i | \(-0.388385\pi\) | ||||
0.343508 | + | 0.939150i | \(0.388385\pi\) | |||||||
\(854\) | 2.34730 | 0.0803228 | ||||||||
\(855\) | 6.41147 | 0.219268 | ||||||||
\(856\) | 13.5767 | 0.464041 | ||||||||
\(857\) | 19.9299 | 0.680794 | 0.340397 | − | 0.940282i | \(-0.389439\pi\) | ||||
0.340397 | + | 0.940282i | \(0.389439\pi\) | |||||||
\(858\) | 11.9472 | 0.407870 | ||||||||
\(859\) | −23.3527 | −0.796783 | −0.398391 | − | 0.917215i | \(-0.630431\pi\) | ||||
−0.398391 | + | 0.917215i | \(0.630431\pi\) | |||||||
\(860\) | −13.4757 | −0.459516 | ||||||||
\(861\) | 2.30272 | 0.0784765 | ||||||||
\(862\) | −36.1453 | −1.23111 | ||||||||
\(863\) | 44.3878 | 1.51098 | 0.755488 | − | 0.655162i | \(-0.227400\pi\) | ||||
0.755488 | + | 0.655162i | \(0.227400\pi\) | |||||||
\(864\) | −10.9581 | −0.372803 | ||||||||
\(865\) | 80.3893 | 2.73332 | ||||||||
\(866\) | −19.4492 | −0.660912 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.857097 | −0.0290918 | ||||||||
\(869\) | −20.3696 | −0.690991 | ||||||||
\(870\) | 8.63816 | 0.292861 | ||||||||
\(871\) | −26.5635 | −0.900072 | ||||||||
\(872\) | −39.2918 | −1.33059 | ||||||||
\(873\) | 4.83843 | 0.163756 | ||||||||
\(874\) | −6.60813 | −0.223523 | ||||||||
\(875\) | −3.03684 | −0.102664 | ||||||||
\(876\) | 0.796541 | 0.0269126 | ||||||||
\(877\) | −9.14971 | −0.308964 | −0.154482 | − | 0.987996i | \(-0.549371\pi\) | ||||
−0.154482 | + | 0.987996i | \(0.549371\pi\) | |||||||
\(878\) | −35.9590 | −1.21356 | ||||||||
\(879\) | −4.01548 | −0.135439 | ||||||||
\(880\) | 28.4142 | 0.957841 | ||||||||
\(881\) | −6.76794 | −0.228018 | −0.114009 | − | 0.993480i | \(-0.536369\pi\) | ||||
−0.114009 | + | 0.993480i | \(0.536369\pi\) | |||||||
\(882\) | 12.4875 | 0.420476 | ||||||||
\(883\) | −47.9760 | −1.61452 | −0.807260 | − | 0.590196i | \(-0.799050\pi\) | ||||
−0.807260 | + | 0.590196i | \(0.799050\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −51.7033 | −1.73799 | ||||||||
\(886\) | −29.7415 | −0.999186 | ||||||||
\(887\) | 41.6982 | 1.40009 | 0.700045 | − | 0.714099i | \(-0.253163\pi\) | ||||
0.700045 | + | 0.714099i | \(0.253163\pi\) | |||||||
\(888\) | 13.3773 | 0.448914 | ||||||||
\(889\) | 2.68954 | 0.0902043 | ||||||||
\(890\) | −34.7374 | −1.16440 | ||||||||
\(891\) | −7.10876 | −0.238152 | ||||||||
\(892\) | 1.72638 | 0.0578034 | ||||||||
\(893\) | −7.84524 | −0.262531 | ||||||||
\(894\) | −24.5212 | −0.820110 | ||||||||
\(895\) | 61.9009 | 2.06912 | ||||||||
\(896\) | 4.63310 | 0.154781 | ||||||||
\(897\) | −12.4820 | −0.416761 | ||||||||
\(898\) | −27.0051 | −0.901170 | ||||||||
\(899\) | −8.41921 | −0.280797 | ||||||||
\(900\) | −3.07604 | −0.102535 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −13.2608 | −0.441537 | ||||||||
\(903\) | −5.14022 | −0.171056 | ||||||||
\(904\) | −17.7939 | −0.591815 | ||||||||
\(905\) | −16.1138 | −0.535641 | ||||||||
\(906\) | −13.5398 | −0.449831 | ||||||||
\(907\) | −32.9350 | −1.09359 | −0.546794 | − | 0.837267i | \(-0.684152\pi\) | ||||
−0.546794 | + | 0.837267i | \(0.684152\pi\) | |||||||
\(908\) | 1.82564 | 0.0605859 | ||||||||
\(909\) | −6.24216 | −0.207039 | ||||||||
\(910\) | 6.18479 | 0.205024 | ||||||||
\(911\) | −18.4926 | −0.612686 | −0.306343 | − | 0.951921i | \(-0.599105\pi\) | ||||
−0.306343 | + | 0.951921i | \(0.599105\pi\) | |||||||
\(912\) | 9.44150 | 0.312639 | ||||||||
\(913\) | −3.77776 | −0.125026 | ||||||||
\(914\) | −56.8735 | −1.88121 | ||||||||
\(915\) | 20.9932 | 0.694014 | ||||||||
\(916\) | −8.40642 | −0.277756 | ||||||||
\(917\) | −6.46616 | −0.213531 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.3909 | −0.441726 | −0.220863 | − | 0.975305i | \(-0.570887\pi\) | ||||
−0.220863 | + | 0.975305i | \(0.570887\pi\) | |||||||
\(920\) | −25.1780 | −0.830094 | ||||||||
\(921\) | 4.40373 | 0.145108 | ||||||||
\(922\) | 45.0547 | 1.48380 | ||||||||
\(923\) | 37.0188 | 1.21849 | ||||||||
\(924\) | −0.285807 | −0.00940236 | ||||||||
\(925\) | 29.3141 | 0.963841 | ||||||||
\(926\) | −14.8990 | −0.489611 | ||||||||
\(927\) | 21.8462 | 0.717522 | ||||||||
\(928\) | −2.30272 | −0.0755905 | ||||||||
\(929\) | −5.33956 | −0.175185 | −0.0875926 | − | 0.996156i | \(-0.527917\pi\) | ||||
−0.0875926 | + | 0.996156i | \(0.527917\pi\) | |||||||
\(930\) | −51.8093 | −1.69889 | ||||||||
\(931\) | −10.5398 | −0.345429 | ||||||||
\(932\) | 9.97502 | 0.326743 | ||||||||
\(933\) | 4.75877 | 0.155795 | ||||||||
\(934\) | −7.08235 | −0.231741 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −9.87258 | −0.322695 | ||||||||
\(937\) | 41.4361 | 1.35366 | 0.676830 | − | 0.736140i | \(-0.263353\pi\) | ||||
0.676830 | + | 0.736140i | \(0.263353\pi\) | |||||||
\(938\) | 4.29498 | 0.140236 | ||||||||
\(939\) | 1.99731 | 0.0651798 | ||||||||
\(940\) | 6.28136 | 0.204876 | ||||||||
\(941\) | 42.0601 | 1.37112 | 0.685559 | − | 0.728017i | \(-0.259558\pi\) | ||||
0.685559 | + | 0.728017i | \(0.259558\pi\) | |||||||
\(942\) | −18.3391 | −0.597519 | ||||||||
\(943\) | 13.8544 | 0.451162 | ||||||||
\(944\) | 49.6955 | 1.61745 | ||||||||
\(945\) | −6.91622 | −0.224985 | ||||||||
\(946\) | 29.6013 | 0.962422 | ||||||||
\(947\) | 41.4270 | 1.34620 | 0.673098 | − | 0.739554i | \(-0.264963\pi\) | ||||
0.673098 | + | 0.739554i | \(0.264963\pi\) | |||||||
\(948\) | 5.41921 | 0.176008 | ||||||||
\(949\) | 5.60214 | 0.181853 | ||||||||
\(950\) | 17.5476 | 0.569318 | ||||||||
\(951\) | −19.4870 | −0.631910 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.0719 | 0.876945 | 0.438473 | − | 0.898744i | \(-0.355520\pi\) | ||||
0.438473 | + | 0.898744i | \(0.355520\pi\) | |||||||
\(954\) | 15.1925 | 0.491876 | ||||||||
\(955\) | 34.3482 | 1.11148 | ||||||||
\(956\) | −0.914467 | −0.0295760 | ||||||||
\(957\) | −2.80747 | −0.0907525 | ||||||||
\(958\) | −10.4742 | −0.338407 | ||||||||
\(959\) | 3.49794 | 0.112954 | ||||||||
\(960\) | 29.3628 | 0.947680 | ||||||||
\(961\) | 19.4962 | 0.628909 | ||||||||
\(962\) | −19.7706 | −0.637431 | ||||||||
\(963\) | 6.35267 | 0.204712 | ||||||||
\(964\) | 8.79830 | 0.283374 | ||||||||
\(965\) | −2.98215 | −0.0959989 | ||||||||
\(966\) | 2.01817 | 0.0649336 | ||||||||
\(967\) | −43.3637 | −1.39448 | −0.697241 | − | 0.716836i | \(-0.745589\pi\) | ||||
−0.697241 | + | 0.716836i | \(0.745589\pi\) | |||||||
\(968\) | 20.0205 | 0.643484 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 22.0993 | 0.709564 | ||||||||
\(971\) | −1.27126 | −0.0407966 | −0.0203983 | − | 0.999792i | \(-0.506493\pi\) | ||||
−0.0203983 | + | 0.999792i | \(0.506493\pi\) | |||||||
\(972\) | −3.98309 | −0.127758 | ||||||||
\(973\) | 2.97090 | 0.0952428 | ||||||||
\(974\) | 11.7401 | 0.376177 | ||||||||
\(975\) | 33.1453 | 1.06150 | ||||||||
\(976\) | −20.1780 | −0.645882 | ||||||||
\(977\) | −24.7641 | −0.792275 | −0.396138 | − | 0.918191i | \(-0.629650\pi\) | ||||
−0.396138 | + | 0.918191i | \(0.629650\pi\) | |||||||
\(978\) | −19.9813 | −0.638933 | ||||||||
\(979\) | 11.2899 | 0.360828 | ||||||||
\(980\) | 8.43882 | 0.269568 | ||||||||
\(981\) | −18.3851 | −0.586990 | ||||||||
\(982\) | 13.8266 | 0.441224 | ||||||||
\(983\) | −39.6144 | −1.26350 | −0.631752 | − | 0.775170i | \(-0.717664\pi\) | ||||
−0.631752 | + | 0.775170i | \(0.717664\pi\) | |||||||
\(984\) | −16.7888 | −0.535207 | ||||||||
\(985\) | 60.0488 | 1.91331 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.39599 | 0.0762653 | ||||||||
\(988\) | −1.75103 | −0.0557077 | ||||||||
\(989\) | −30.9263 | −0.983400 | ||||||||
\(990\) | 11.2763 | 0.358385 | ||||||||
\(991\) | −33.3138 | −1.05825 | −0.529123 | − | 0.848545i | \(-0.677479\pi\) | ||||
−0.529123 | + | 0.848545i | \(0.677479\pi\) | |||||||
\(992\) | 13.8111 | 0.438503 | ||||||||
\(993\) | 12.1729 | 0.386296 | ||||||||
\(994\) | −5.98545 | −0.189847 | ||||||||
\(995\) | −44.8417 | −1.42158 | ||||||||
\(996\) | 1.00505 | 0.0318463 | ||||||||
\(997\) | −25.8958 | −0.820128 | −0.410064 | − | 0.912057i | \(-0.634494\pi\) | ||||
−0.410064 | + | 0.912057i | \(0.634494\pi\) | |||||||
\(998\) | −40.8958 | −1.29453 | ||||||||
\(999\) | 22.1088 | 0.699490 |
(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 | 289.2.a.d.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 2601.2.a.x.1.1 | 3 | |||
4.3 | odd | 2 | 4624.2.a.bg.1.2 | 3 | |||
5.4 | even | 2 | 7225.2.a.t.1.1 | 3 | |||
17.2 | even | 8 | 289.2.c.d.38.5 | 12 | |||
17.3 | odd | 16 | 289.2.d.f.179.5 | 24 | |||
17.4 | even | 4 | 289.2.b.d.288.2 | 6 | |||
17.5 | odd | 16 | 289.2.d.f.110.2 | 24 | |||
17.6 | odd | 16 | 289.2.d.f.155.5 | 24 | |||
17.7 | odd | 16 | 289.2.d.f.134.2 | 24 | |||
17.8 | even | 8 | 289.2.c.d.251.2 | 12 | |||
17.9 | even | 8 | 289.2.c.d.251.1 | 12 | |||
17.10 | odd | 16 | 289.2.d.f.134.1 | 24 | |||
17.11 | odd | 16 | 289.2.d.f.155.6 | 24 | |||
17.12 | odd | 16 | 289.2.d.f.110.1 | 24 | |||
17.13 | even | 4 | 289.2.b.d.288.1 | 6 | |||
17.14 | odd | 16 | 289.2.d.f.179.6 | 24 | |||
17.15 | even | 8 | 289.2.c.d.38.6 | 12 | |||
17.16 | even | 2 | 289.2.a.e.1.3 | yes | 3 | ||
51.50 | odd | 2 | 2601.2.a.w.1.1 | 3 | |||
68.67 | odd | 2 | 4624.2.a.bd.1.2 | 3 | |||
85.84 | even | 2 | 7225.2.a.s.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.2.a.d.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
289.2.a.e.1.3 | yes | 3 | 17.16 | even | 2 | ||
289.2.b.d.288.1 | 6 | 17.13 | even | 4 | |||
289.2.b.d.288.2 | 6 | 17.4 | even | 4 | |||
289.2.c.d.38.5 | 12 | 17.2 | even | 8 | |||
289.2.c.d.38.6 | 12 | 17.15 | even | 8 | |||
289.2.c.d.251.1 | 12 | 17.9 | even | 8 | |||
289.2.c.d.251.2 | 12 | 17.8 | even | 8 | |||
289.2.d.f.110.1 | 24 | 17.12 | odd | 16 | |||
289.2.d.f.110.2 | 24 | 17.5 | odd | 16 | |||
289.2.d.f.134.1 | 24 | 17.10 | odd | 16 | |||
289.2.d.f.134.2 | 24 | 17.7 | odd | 16 | |||
289.2.d.f.155.5 | 24 | 17.6 | odd | 16 | |||
289.2.d.f.155.6 | 24 | 17.11 | odd | 16 | |||
289.2.d.f.179.5 | 24 | 17.3 | odd | 16 | |||
289.2.d.f.179.6 | 24 | 17.14 | odd | 16 | |||
2601.2.a.w.1.1 | 3 | 51.50 | odd | 2 | |||
2601.2.a.x.1.1 | 3 | 3.2 | odd | 2 | |||
4624.2.a.bd.1.2 | 3 | 68.67 | odd | 2 | |||
4624.2.a.bg.1.2 | 3 | 4.3 | odd | 2 | |||
7225.2.a.s.1.1 | 3 | 85.84 | even | 2 | |||
7225.2.a.t.1.1 | 3 | 5.4 | even | 2 |