Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4923,2,Mod(1,4923)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4923, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4923.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4923 = 3^{2} \cdot 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4923.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: | \(39.3103529151\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 4 x^{17} - 18 x^{16} + 84 x^{15} + 116 x^{14} - 708 x^{13} - 282 x^{12} + 3104 x^{11} - 137 x^{10} - 7703 x^{9} + 2068 x^{8} + 11068 x^{7} - 4274 x^{6} - 9021 x^{5} + \cdots + 328 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 547) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-0.735255\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4923.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.735255 | −0.519904 | −0.259952 | − | 0.965622i | \(-0.583707\pi\) | ||||
−0.259952 | + | 0.965622i | \(0.583707\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.45940 | −0.729700 | ||||||||
\(5\) | −0.962787 | −0.430571 | −0.215286 | − | 0.976551i | \(-0.569068\pi\) | ||||
−0.215286 | + | 0.976551i | \(0.569068\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.25298 | −1.22951 | −0.614755 | − | 0.788718i | \(-0.710745\pi\) | ||||
−0.614755 | + | 0.788718i | \(0.710745\pi\) | |||||||
\(8\) | 2.54354 | 0.899278 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.707894 | 0.223856 | ||||||||
\(11\) | 0.883096 | 0.266263 | 0.133132 | − | 0.991098i | \(-0.457497\pi\) | ||||
0.133132 | + | 0.991098i | \(0.457497\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.48154 | −1.24296 | −0.621478 | − | 0.783431i | \(-0.713468\pi\) | ||||
−0.621478 | + | 0.783431i | \(0.713468\pi\) | |||||||
\(14\) | 2.39177 | 0.639228 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.04865 | 0.262161 | ||||||||
\(17\) | 3.18294 | 0.771977 | 0.385988 | − | 0.922504i | \(-0.373860\pi\) | ||||
0.385988 | + | 0.922504i | \(0.373860\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.12466 | 0.946261 | 0.473131 | − | 0.880992i | \(-0.343124\pi\) | ||||
0.473131 | + | 0.880992i | \(0.343124\pi\) | |||||||
\(20\) | 1.40509 | 0.314188 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.649301 | −0.138431 | ||||||||
\(23\) | −3.73970 | −0.779781 | −0.389890 | − | 0.920861i | \(-0.627487\pi\) | ||||
−0.389890 | + | 0.920861i | \(0.627487\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.07304 | −0.814608 | ||||||||
\(26\) | 3.29508 | 0.646218 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.74740 | 0.897174 | ||||||||
\(29\) | −6.33388 | −1.17617 | −0.588086 | − | 0.808798i | \(-0.700119\pi\) | ||||
−0.588086 | + | 0.808798i | \(0.700119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.47939 | −1.52294 | −0.761472 | − | 0.648198i | \(-0.775523\pi\) | ||||
−0.761472 | + | 0.648198i | \(0.775523\pi\) | |||||||
\(32\) | −5.85811 | −1.03558 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.34028 | −0.401354 | ||||||||
\(35\) | 3.13193 | 0.529392 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.0375 | 1.81455 | 0.907276 | − | 0.420535i | \(-0.138158\pi\) | ||||
0.907276 | + | 0.420535i | \(0.138158\pi\) | |||||||
\(38\) | −3.03268 | −0.491965 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.44889 | −0.387203 | ||||||||
\(41\) | −1.41138 | −0.220421 | −0.110210 | − | 0.993908i | \(-0.535152\pi\) | ||||
−0.110210 | + | 0.993908i | \(0.535152\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.31097 | −1.41991 | −0.709955 | − | 0.704247i | \(-0.751285\pi\) | ||||
−0.709955 | + | 0.704247i | \(0.751285\pi\) | |||||||
\(44\) | −1.28879 | −0.194292 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.74963 | 0.405411 | ||||||||
\(47\) | 5.82191 | 0.849213 | 0.424606 | − | 0.905378i | \(-0.360413\pi\) | ||||
0.424606 | + | 0.905378i | \(0.360413\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.58188 | 0.511697 | ||||||||
\(50\) | 2.99473 | 0.423518 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.54036 | 0.906985 | ||||||||
\(53\) | 7.06826 | 0.970900 | 0.485450 | − | 0.874264i | \(-0.338656\pi\) | ||||
0.485450 | + | 0.874264i | \(0.338656\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.850233 | −0.114645 | ||||||||
\(56\) | −8.27409 | −1.10567 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.65702 | 0.611497 | ||||||||
\(59\) | −12.9274 | −1.68301 | −0.841503 | − | 0.540252i | \(-0.818329\pi\) | ||||
−0.841503 | + | 0.540252i | \(0.818329\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.04777 | −0.390227 | −0.195114 | − | 0.980781i | \(-0.562508\pi\) | ||||
−0.195114 | + | 0.980781i | \(0.562508\pi\) | |||||||
\(62\) | 6.23452 | 0.791784 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.20991 | 0.276239 | ||||||||
\(65\) | 4.31477 | 0.535182 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.15218 | −1.11812 | −0.559059 | − | 0.829128i | \(-0.688837\pi\) | ||||
−0.559059 | + | 0.829128i | \(0.688837\pi\) | |||||||
\(68\) | −4.64518 | −0.563311 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.30277 | −0.275233 | ||||||||
\(71\) | 4.57601 | 0.543072 | 0.271536 | − | 0.962428i | \(-0.412468\pi\) | ||||
0.271536 | + | 0.962428i | \(0.412468\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.4453 | −1.69070 | −0.845349 | − | 0.534215i | \(-0.820607\pi\) | ||||
−0.845349 | + | 0.534215i | \(0.820607\pi\) | |||||||
\(74\) | −8.11538 | −0.943393 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.01952 | −0.690486 | ||||||||
\(77\) | −2.87269 | −0.327374 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.20620 | 0.810761 | 0.405381 | − | 0.914148i | \(-0.367139\pi\) | ||||
0.405381 | + | 0.914148i | \(0.367139\pi\) | |||||||
\(80\) | −1.00962 | −0.112879 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.03773 | 0.114598 | ||||||||
\(83\) | −7.39056 | −0.811219 | −0.405610 | − | 0.914046i | \(-0.632941\pi\) | ||||
−0.405610 | + | 0.914046i | \(0.632941\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.06450 | −0.332391 | ||||||||
\(86\) | 6.84594 | 0.738217 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.24619 | 0.239445 | ||||||||
\(89\) | −0.838265 | −0.0888559 | −0.0444280 | − | 0.999013i | \(-0.514147\pi\) | ||||
−0.0444280 | + | 0.999013i | \(0.514147\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.5784 | 1.52823 | ||||||||
\(92\) | 5.45771 | 0.569006 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.28059 | −0.441509 | ||||||||
\(95\) | −3.97117 | −0.407433 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.475381 | 0.0482676 | 0.0241338 | − | 0.999709i | \(-0.492317\pi\) | ||||
0.0241338 | + | 0.999709i | \(0.492317\pi\) | |||||||
\(98\) | −2.63360 | −0.266033 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.94419 | 0.594419 | ||||||||
\(101\) | 3.07939 | 0.306411 | 0.153205 | − | 0.988194i | \(-0.451040\pi\) | ||||
0.153205 | + | 0.988194i | \(0.451040\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.71378 | −0.365929 | −0.182965 | − | 0.983119i | \(-0.558569\pi\) | ||||
−0.182965 | + | 0.983119i | \(0.558569\pi\) | |||||||
\(104\) | −11.3990 | −1.11776 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.19698 | −0.504775 | ||||||||
\(107\) | −16.1036 | −1.55680 | −0.778398 | − | 0.627771i | \(-0.783968\pi\) | ||||
−0.778398 | + | 0.627771i | \(0.783968\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.61098 | 0.250087 | 0.125043 | − | 0.992151i | \(-0.460093\pi\) | ||||
0.125043 | + | 0.992151i | \(0.460093\pi\) | |||||||
\(110\) | 0.625139 | 0.0596046 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.41122 | −0.322330 | ||||||||
\(113\) | 12.2204 | 1.14960 | 0.574798 | − | 0.818295i | \(-0.305081\pi\) | ||||
0.574798 | + | 0.818295i | \(0.305081\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.60053 | 0.335751 | ||||||||
\(116\) | 9.24367 | 0.858253 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.50495 | 0.875002 | ||||||||
\(119\) | −10.3540 | −0.949154 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.2201 | −0.929104 | ||||||||
\(122\) | 2.24089 | 0.202881 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 12.3748 | 1.11129 | ||||||||
\(125\) | 8.73541 | 0.781318 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.90845 | 0.524290 | 0.262145 | − | 0.965028i | \(-0.415570\pi\) | ||||
0.262145 | + | 0.965028i | \(0.415570\pi\) | |||||||
\(128\) | 10.0914 | 0.891959 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.17246 | −0.278243 | ||||||||
\(131\) | −4.91027 | −0.429012 | −0.214506 | − | 0.976723i | \(-0.568814\pi\) | ||||
−0.214506 | + | 0.976723i | \(0.568814\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.4174 | −1.16344 | ||||||||
\(134\) | 6.72919 | 0.581314 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.09595 | 0.694222 | ||||||||
\(137\) | 8.29905 | 0.709036 | 0.354518 | − | 0.935049i | \(-0.384645\pi\) | ||||
0.354518 | + | 0.935049i | \(0.384645\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.0776 | 1.78778 | 0.893889 | − | 0.448288i | \(-0.147966\pi\) | ||||
0.893889 | + | 0.448288i | \(0.147966\pi\) | |||||||
\(140\) | −4.57073 | −0.386297 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.36453 | −0.282345 | ||||||||
\(143\) | −3.95763 | −0.330954 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.09818 | 0.506426 | ||||||||
\(146\) | 10.6210 | 0.879001 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −16.1081 | −1.32408 | ||||||||
\(149\) | 20.9236 | 1.71413 | 0.857063 | − | 0.515212i | \(-0.172287\pi\) | ||||
0.857063 | + | 0.515212i | \(0.172287\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.2666 | −0.998241 | −0.499121 | − | 0.866533i | \(-0.666344\pi\) | ||||
−0.499121 | + | 0.866533i | \(0.666344\pi\) | |||||||
\(152\) | 10.4912 | 0.850952 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.11216 | 0.170203 | ||||||||
\(155\) | 8.16385 | 0.655736 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.63793 | 0.769191 | 0.384595 | − | 0.923085i | \(-0.374341\pi\) | ||||
0.384595 | + | 0.923085i | \(0.374341\pi\) | |||||||
\(158\) | −5.29840 | −0.421518 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.64011 | 0.445890 | ||||||||
\(161\) | 12.1652 | 0.958749 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.8440 | 0.927693 | 0.463847 | − | 0.885915i | \(-0.346469\pi\) | ||||
0.463847 | + | 0.885915i | \(0.346469\pi\) | |||||||
\(164\) | 2.05977 | 0.160841 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.43395 | 0.421756 | ||||||||
\(167\) | 18.8572 | 1.45922 | 0.729609 | − | 0.683865i | \(-0.239702\pi\) | ||||
0.729609 | + | 0.683865i | \(0.239702\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.08424 | 0.544941 | ||||||||
\(170\) | 2.25319 | 0.172812 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 13.5884 | 1.03611 | ||||||||
\(173\) | 15.1822 | 1.15428 | 0.577140 | − | 0.816645i | \(-0.304169\pi\) | ||||
0.577140 | + | 0.816645i | \(0.304169\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.2495 | 1.00157 | ||||||||
\(176\) | 0.926054 | 0.0698040 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.616339 | 0.0461966 | ||||||||
\(179\) | 2.57897 | 0.192761 | 0.0963806 | − | 0.995345i | \(-0.469273\pi\) | ||||
0.0963806 | + | 0.995345i | \(0.469273\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.50776 | −0.706706 | −0.353353 | − | 0.935490i | \(-0.614959\pi\) | ||||
−0.353353 | + | 0.935490i | \(0.614959\pi\) | |||||||
\(182\) | −10.7188 | −0.794532 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −9.51208 | −0.701240 | ||||||||
\(185\) | −10.6268 | −0.781295 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.81084 | 0.205549 | ||||||||
\(188\) | −8.49649 | −0.619670 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.91982 | 0.211826 | ||||||||
\(191\) | −6.20885 | −0.449257 | −0.224628 | − | 0.974444i | \(-0.572117\pi\) | ||||
−0.224628 | + | 0.974444i | \(0.572117\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.6307 | −1.41305 | −0.706526 | − | 0.707687i | \(-0.749739\pi\) | ||||
−0.706526 | + | 0.707687i | \(0.749739\pi\) | |||||||
\(194\) | −0.349526 | −0.0250945 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.22739 | −0.373385 | ||||||||
\(197\) | −26.3638 | −1.87834 | −0.939171 | − | 0.343449i | \(-0.888405\pi\) | ||||
−0.939171 | + | 0.343449i | \(0.888405\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.17965 | −0.367176 | −0.183588 | − | 0.983003i | \(-0.558771\pi\) | ||||
−0.183588 | + | 0.983003i | \(0.558771\pi\) | |||||||
\(200\) | −10.3600 | −0.732559 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.26414 | −0.159304 | ||||||||
\(203\) | 20.6040 | 1.44612 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.35886 | 0.0949069 | ||||||||
\(206\) | 2.73058 | 0.190248 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.69955 | −0.325855 | ||||||||
\(209\) | 3.64247 | 0.251955 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.3624 | 0.782217 | 0.391109 | − | 0.920344i | \(-0.372092\pi\) | ||||
0.391109 | + | 0.920344i | \(0.372092\pi\) | |||||||
\(212\) | −10.3154 | −0.708466 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 11.8403 | 0.809385 | ||||||||
\(215\) | 8.96448 | 0.611373 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 27.5833 | 1.87248 | ||||||||
\(218\) | −1.91974 | −0.130021 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.24083 | 0.0836567 | ||||||||
\(221\) | −14.2645 | −0.959534 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.9951 | 1.27201 | 0.636003 | − | 0.771686i | \(-0.280587\pi\) | ||||
0.636003 | + | 0.771686i | \(0.280587\pi\) | |||||||
\(224\) | 19.0563 | 1.27325 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.98510 | −0.597680 | ||||||||
\(227\) | −11.7708 | −0.781254 | −0.390627 | − | 0.920549i | \(-0.627742\pi\) | ||||
−0.390627 | + | 0.920549i | \(0.627742\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.31464 | 0.417283 | 0.208641 | − | 0.977992i | \(-0.433096\pi\) | ||||
0.208641 | + | 0.977992i | \(0.433096\pi\) | |||||||
\(230\) | −2.64731 | −0.174558 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −16.1105 | −1.05771 | ||||||||
\(233\) | −20.7839 | −1.36160 | −0.680799 | − | 0.732470i | \(-0.738367\pi\) | ||||
−0.680799 | + | 0.732470i | \(0.738367\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.60526 | −0.365647 | ||||||||
\(236\) | 18.8663 | 1.22809 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.61287 | 0.493469 | ||||||||
\(239\) | 23.8405 | 1.54212 | 0.771058 | − | 0.636765i | \(-0.219728\pi\) | ||||
0.771058 | + | 0.636765i | \(0.219728\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.62031 | 0.104374 | 0.0521868 | − | 0.998637i | \(-0.483381\pi\) | ||||
0.0521868 | + | 0.998637i | \(0.483381\pi\) | |||||||
\(242\) | 7.51442 | 0.483045 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.44792 | 0.284749 | ||||||||
\(245\) | −3.44859 | −0.220322 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.4848 | −1.17616 | ||||||||
\(248\) | −21.5677 | −1.36955 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.42276 | −0.406211 | ||||||||
\(251\) | 10.7109 | 0.676064 | 0.338032 | − | 0.941135i | \(-0.390239\pi\) | ||||
0.338032 | + | 0.941135i | \(0.390239\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.30251 | −0.207627 | ||||||||
\(254\) | −4.34422 | −0.272581 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.8396 | −0.739972 | ||||||||
\(257\) | 28.7954 | 1.79621 | 0.898105 | − | 0.439781i | \(-0.144944\pi\) | ||||
0.898105 | + | 0.439781i | \(0.144944\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −35.9047 | −2.23101 | ||||||||
\(260\) | −6.29698 | −0.390522 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.61030 | 0.223045 | ||||||||
\(263\) | 27.1652 | 1.67508 | 0.837539 | − | 0.546378i | \(-0.183994\pi\) | ||||
0.837539 | + | 0.546378i | \(0.183994\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.80523 | −0.418042 | ||||||||
\(266\) | 9.86523 | 0.604876 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 13.3567 | 0.815890 | ||||||||
\(269\) | 19.2182 | 1.17176 | 0.585878 | − | 0.810399i | \(-0.300750\pi\) | ||||
0.585878 | + | 0.810399i | \(0.300750\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.73786 | −0.591533 | −0.295766 | − | 0.955260i | \(-0.595575\pi\) | ||||
−0.295766 | + | 0.955260i | \(0.595575\pi\) | |||||||
\(272\) | 3.33778 | 0.202382 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.10192 | −0.368631 | ||||||||
\(275\) | −3.59689 | −0.216900 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.8931 | −1.61585 | −0.807925 | − | 0.589285i | \(-0.799409\pi\) | ||||
−0.807925 | + | 0.589285i | \(0.799409\pi\) | |||||||
\(278\) | −15.4974 | −0.929474 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7.96619 | 0.476071 | ||||||||
\(281\) | 4.21282 | 0.251316 | 0.125658 | − | 0.992074i | \(-0.459896\pi\) | ||||
0.125658 | + | 0.992074i | \(0.459896\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31.3587 | 1.86408 | 0.932039 | − | 0.362357i | \(-0.118028\pi\) | ||||
0.932039 | + | 0.362357i | \(0.118028\pi\) | |||||||
\(284\) | −6.67822 | −0.396280 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.90987 | 0.172064 | ||||||||
\(287\) | 4.59120 | 0.271010 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.86888 | −0.404052 | ||||||||
\(290\) | −4.48372 | −0.263293 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 21.0815 | 1.23370 | ||||||||
\(293\) | 15.8890 | 0.928244 | 0.464122 | − | 0.885771i | \(-0.346370\pi\) | ||||
0.464122 | + | 0.885771i | \(0.346370\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.4463 | 0.724654 | ||||||||
\(296\) | 28.0743 | 1.63179 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −15.3842 | −0.891181 | ||||||||
\(299\) | 16.7596 | 0.969234 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 30.2884 | 1.74579 | ||||||||
\(302\) | 9.01908 | 0.518990 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.32530 | 0.248073 | ||||||||
\(305\) | 2.93436 | 0.168021 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.7030 | −0.782070 | −0.391035 | − | 0.920376i | \(-0.627883\pi\) | ||||
−0.391035 | + | 0.920376i | \(0.627883\pi\) | |||||||
\(308\) | 4.19241 | 0.238884 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.00251 | −0.340920 | ||||||||
\(311\) | −6.49422 | −0.368253 | −0.184127 | − | 0.982903i | \(-0.558946\pi\) | ||||
−0.184127 | + | 0.982903i | \(0.558946\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.26403 | 0.467111 | 0.233555 | − | 0.972344i | \(-0.424964\pi\) | ||||
0.233555 | + | 0.972344i | \(0.424964\pi\) | |||||||
\(314\) | −7.08634 | −0.399905 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.5167 | −0.591612 | ||||||||
\(317\) | 28.1441 | 1.58073 | 0.790364 | − | 0.612638i | \(-0.209892\pi\) | ||||
0.790364 | + | 0.612638i | \(0.209892\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.59343 | −0.313172 | ||||||||
\(320\) | −2.12768 | −0.118941 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.94450 | −0.498457 | ||||||||
\(323\) | 13.1285 | 0.730492 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.2535 | 1.01252 | ||||||||
\(326\) | −8.70836 | −0.482312 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.58991 | −0.198220 | ||||||||
\(329\) | −18.9386 | −1.04412 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.78319 | −0.0980130 | −0.0490065 | − | 0.998798i | \(-0.515606\pi\) | ||||
−0.0490065 | + | 0.998798i | \(0.515606\pi\) | |||||||
\(332\) | 10.7858 | 0.591947 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −13.8649 | −0.758653 | ||||||||
\(335\) | 8.81160 | 0.481429 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.5528 | 0.956160 | 0.478080 | − | 0.878316i | \(-0.341333\pi\) | ||||
0.478080 | + | 0.878316i | \(0.341333\pi\) | |||||||
\(338\) | −5.20873 | −0.283317 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.47232 | 0.242546 | ||||||||
\(341\) | −7.48811 | −0.405504 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.1191 | 0.600374 | ||||||||
\(344\) | −23.6829 | −1.27689 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.1628 | −0.600115 | ||||||||
\(347\) | −14.8308 | −0.796160 | −0.398080 | − | 0.917351i | \(-0.630323\pi\) | ||||
−0.398080 | + | 0.917351i | \(0.630323\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34.3697 | −1.83977 | −0.919884 | − | 0.392190i | \(-0.871718\pi\) | ||||
−0.919884 | + | 0.392190i | \(0.871718\pi\) | |||||||
\(350\) | −9.74178 | −0.520720 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.17327 | −0.275736 | ||||||||
\(353\) | 16.1758 | 0.860949 | 0.430474 | − | 0.902603i | \(-0.358346\pi\) | ||||
0.430474 | + | 0.902603i | \(0.358346\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.40572 | −0.233831 | ||||||||
\(356\) | 1.22336 | 0.0648381 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.89620 | −0.100217 | ||||||||
\(359\) | −17.7167 | −0.935053 | −0.467526 | − | 0.883979i | \(-0.654855\pi\) | ||||
−0.467526 | + | 0.883979i | \(0.654855\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.98721 | −0.104590 | ||||||||
\(362\) | 6.99063 | 0.367419 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −21.2757 | −1.11515 | ||||||||
\(365\) | 13.9078 | 0.727966 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.29148 | 0.380612 | 0.190306 | − | 0.981725i | \(-0.439052\pi\) | ||||
0.190306 | + | 0.981725i | \(0.439052\pi\) | |||||||
\(368\) | −3.92162 | −0.204428 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7.81338 | 0.406198 | ||||||||
\(371\) | −22.9929 | −1.19373 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.4135 | 1.00520 | 0.502598 | − | 0.864520i | \(-0.332378\pi\) | ||||
0.502598 | + | 0.864520i | \(0.332378\pi\) | |||||||
\(374\) | −2.06669 | −0.106866 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 14.8083 | 0.763678 | ||||||||
\(377\) | 28.3856 | 1.46193 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.5543 | 1.10717 | 0.553586 | − | 0.832792i | \(-0.313259\pi\) | ||||
0.553586 | + | 0.832792i | \(0.313259\pi\) | |||||||
\(380\) | 5.79552 | 0.297304 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.56509 | 0.233571 | ||||||||
\(383\) | 8.69462 | 0.444274 | 0.222137 | − | 0.975015i | \(-0.428697\pi\) | ||||
0.222137 | + | 0.975015i | \(0.428697\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.76579 | 0.140958 | ||||||||
\(386\) | 14.4336 | 0.734652 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.693771 | −0.0352209 | ||||||||
\(389\) | −20.0986 | −1.01904 | −0.509520 | − | 0.860459i | \(-0.670177\pi\) | ||||
−0.509520 | + | 0.860459i | \(0.670177\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.9032 | −0.601973 | ||||||||
\(392\) | 9.11066 | 0.460158 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 19.3841 | 0.976558 | ||||||||
\(395\) | −6.93804 | −0.349091 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.3318 | −1.12080 | −0.560402 | − | 0.828221i | \(-0.689353\pi\) | ||||
−0.560402 | + | 0.828221i | \(0.689353\pi\) | |||||||
\(398\) | 3.80836 | 0.190896 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.27118 | −0.213559 | ||||||||
\(401\) | 1.95708 | 0.0977321 | 0.0488661 | − | 0.998805i | \(-0.484439\pi\) | ||||
0.0488661 | + | 0.998805i | \(0.484439\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 38.0008 | 1.89295 | ||||||||
\(404\) | −4.49406 | −0.223588 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.1492 | −0.751842 | ||||||||
\(407\) | 9.74716 | 0.483149 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.4716 | 0.715576 | 0.357788 | − | 0.933803i | \(-0.383531\pi\) | ||||
0.357788 | + | 0.933803i | \(0.383531\pi\) | |||||||
\(410\) | −0.999110 | −0.0493425 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.41989 | 0.267019 | ||||||||
\(413\) | 42.0526 | 2.06927 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.11554 | 0.349288 | ||||||||
\(416\) | 26.2534 | 1.28718 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.67814 | −0.130992 | ||||||||
\(419\) | 4.92102 | 0.240408 | 0.120204 | − | 0.992749i | \(-0.461645\pi\) | ||||
0.120204 | + | 0.992749i | \(0.461645\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.7810 | 0.817857 | 0.408928 | − | 0.912566i | \(-0.365903\pi\) | ||||
0.408928 | + | 0.912566i | \(0.365903\pi\) | |||||||
\(422\) | −8.35424 | −0.406678 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 17.9784 | 0.873109 | ||||||||
\(425\) | −12.9643 | −0.628859 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.91435 | 0.479789 | ||||||||
\(428\) | 23.5016 | 1.13599 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.59119 | −0.317855 | ||||||||
\(431\) | −10.5214 | −0.506800 | −0.253400 | − | 0.967362i | \(-0.581549\pi\) | ||||
−0.253400 | + | 0.967362i | \(0.581549\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.8135 | −0.567721 | −0.283860 | − | 0.958866i | \(-0.591615\pi\) | ||||
−0.283860 | + | 0.958866i | \(0.591615\pi\) | |||||||
\(434\) | −20.2808 | −0.973508 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.81047 | −0.182488 | ||||||||
\(437\) | −15.4250 | −0.737876 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.18885 | 0.390833 | 0.195416 | − | 0.980720i | \(-0.437394\pi\) | ||||
0.195416 | + | 0.980720i | \(0.437394\pi\) | |||||||
\(440\) | −2.16260 | −0.103098 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10.4880 | 0.498866 | ||||||||
\(443\) | 15.7119 | 0.746496 | 0.373248 | − | 0.927732i | \(-0.378244\pi\) | ||||
0.373248 | + | 0.927732i | \(0.378244\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.807071 | 0.0382588 | ||||||||
\(446\) | −13.9663 | −0.661321 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.18881 | −0.339639 | ||||||||
\(449\) | −9.89465 | −0.466957 | −0.233479 | − | 0.972362i | \(-0.575011\pi\) | ||||
−0.233479 | + | 0.972362i | \(0.575011\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.24639 | −0.0586900 | ||||||||
\(452\) | −17.8344 | −0.838860 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.65453 | 0.406177 | ||||||||
\(455\) | −14.0359 | −0.658012 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.4319 | 0.908985 | 0.454492 | − | 0.890751i | \(-0.349821\pi\) | ||||
0.454492 | + | 0.890751i | \(0.349821\pi\) | |||||||
\(458\) | −4.64287 | −0.216947 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5.25461 | −0.244998 | ||||||||
\(461\) | −28.4760 | −1.32626 | −0.663130 | − | 0.748504i | \(-0.730772\pi\) | ||||
−0.663130 | + | 0.748504i | \(0.730772\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.8095 | −0.502361 | −0.251181 | − | 0.967940i | \(-0.580819\pi\) | ||||
−0.251181 | + | 0.967940i | \(0.580819\pi\) | |||||||
\(464\) | −6.64200 | −0.308347 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15.2815 | 0.707901 | ||||||||
\(467\) | −26.3662 | −1.22008 | −0.610041 | − | 0.792369i | \(-0.708847\pi\) | ||||
−0.610041 | + | 0.792369i | \(0.708847\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 29.7719 | 1.37474 | ||||||||
\(470\) | 4.12130 | 0.190101 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −32.8814 | −1.51349 | ||||||||
\(473\) | −8.22248 | −0.378070 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.7999 | −0.770832 | ||||||||
\(476\) | 15.1107 | 0.692597 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −17.5289 | −0.801752 | ||||||||
\(479\) | 0.194030 | 0.00886547 | 0.00443274 | − | 0.999990i | \(-0.498589\pi\) | ||||
0.00443274 | + | 0.999990i | \(0.498589\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −49.4650 | −2.25541 | ||||||||
\(482\) | −1.19134 | −0.0542642 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 14.9153 | 0.677967 | ||||||||
\(485\) | −0.457691 | −0.0207827 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.65682 | −0.120392 | −0.0601959 | − | 0.998187i | \(-0.519173\pi\) | ||||
−0.0601959 | + | 0.998187i | \(0.519173\pi\) | |||||||
\(488\) | −7.75214 | −0.350923 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.53559 | 0.114546 | ||||||||
\(491\) | −11.0398 | −0.498219 | −0.249109 | − | 0.968475i | \(-0.580138\pi\) | ||||
−0.249109 | + | 0.968475i | \(0.580138\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.1604 | −0.907978 | ||||||||
\(494\) | 13.5911 | 0.611491 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.89187 | −0.399257 | ||||||||
\(497\) | −14.8857 | −0.667713 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.9966 | 1.38760 | 0.693799 | − | 0.720168i | \(-0.255935\pi\) | ||||
0.693799 | + | 0.720168i | \(0.255935\pi\) | |||||||
\(500\) | −12.7484 | −0.570128 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7.87523 | −0.351489 | ||||||||
\(503\) | 37.0982 | 1.65413 | 0.827063 | − | 0.562109i | \(-0.190010\pi\) | ||||
0.827063 | + | 0.562109i | \(0.190010\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.96480 | −0.131932 | ||||||||
\(506\) | 2.42819 | 0.107946 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.62279 | −0.382575 | ||||||||
\(509\) | 8.10275 | 0.359148 | 0.179574 | − | 0.983744i | \(-0.442528\pi\) | ||||
0.179574 | + | 0.983744i | \(0.442528\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 46.9904 | 2.07873 | ||||||||
\(512\) | −11.4776 | −0.507244 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −21.1720 | −0.933857 | ||||||||
\(515\) | 3.57558 | 0.157559 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.14130 | 0.226114 | ||||||||
\(518\) | 26.3992 | 1.15991 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10.9748 | 0.481277 | ||||||||
\(521\) | −9.96721 | −0.436671 | −0.218336 | − | 0.975874i | \(-0.570063\pi\) | ||||
−0.218336 | + | 0.975874i | \(0.570063\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.12073 | −0.311368 | −0.155684 | − | 0.987807i | \(-0.549758\pi\) | ||||
−0.155684 | + | 0.987807i | \(0.549758\pi\) | |||||||
\(524\) | 7.16604 | 0.313050 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.9734 | −0.870879 | ||||||||
\(527\) | −26.9894 | −1.17568 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.01467 | −0.391942 | ||||||||
\(530\) | 5.00358 | 0.217342 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 19.5814 | 0.848961 | ||||||||
\(533\) | 6.32517 | 0.273974 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.5044 | 0.670312 | ||||||||
\(536\) | −23.2790 | −1.00550 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −14.1303 | −0.609201 | ||||||||
\(539\) | 3.16314 | 0.136246 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 39.1006 | 1.68107 | 0.840533 | − | 0.541760i | \(-0.182242\pi\) | ||||
0.840533 | + | 0.541760i | \(0.182242\pi\) | |||||||
\(542\) | 7.15981 | 0.307540 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −18.6460 | −0.799441 | ||||||||
\(545\) | −2.51382 | −0.107680 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.00000 | −0.0427569 | ||||||||
\(548\) | −12.1116 | −0.517383 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.64463 | 0.112767 | ||||||||
\(551\) | −26.1251 | −1.11297 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −23.4416 | −0.996840 | ||||||||
\(554\) | 19.7733 | 0.840087 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −30.7606 | −1.30454 | ||||||||
\(557\) | −39.1227 | −1.65768 | −0.828841 | − | 0.559485i | \(-0.810999\pi\) | ||||
−0.828841 | + | 0.559485i | \(0.810999\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 41.7275 | 1.76489 | ||||||||
\(560\) | 3.28428 | 0.138786 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.09750 | −0.130660 | ||||||||
\(563\) | −32.3381 | −1.36289 | −0.681445 | − | 0.731869i | \(-0.738648\pi\) | ||||
−0.681445 | + | 0.731869i | \(0.738648\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.7656 | −0.494983 | ||||||||
\(566\) | −23.0566 | −0.969142 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.6393 | 0.488373 | ||||||||
\(569\) | −0.316254 | −0.0132581 | −0.00662903 | − | 0.999978i | \(-0.502110\pi\) | ||||
−0.00662903 | + | 0.999978i | \(0.502110\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.67642 | 0.195702 | 0.0978511 | − | 0.995201i | \(-0.468803\pi\) | ||||
0.0978511 | + | 0.995201i | \(0.468803\pi\) | |||||||
\(572\) | 5.77577 | 0.241497 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.37570 | −0.140899 | ||||||||
\(575\) | 15.2319 | 0.635216 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.4107 | 1.59906 | 0.799529 | − | 0.600627i | \(-0.205082\pi\) | ||||
0.799529 | + | 0.600627i | \(0.205082\pi\) | |||||||
\(578\) | 5.05038 | 0.210068 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −8.89968 | −0.369539 | ||||||||
\(581\) | 24.0413 | 0.997403 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.24195 | 0.258515 | ||||||||
\(584\) | −36.7423 | −1.52041 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.6825 | −0.482598 | ||||||||
\(587\) | −6.56995 | −0.271171 | −0.135586 | − | 0.990766i | \(-0.543292\pi\) | ||||
−0.135586 | + | 0.990766i | \(0.543292\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −34.9746 | −1.44110 | ||||||||
\(590\) | −9.15125 | −0.376751 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 11.5744 | 0.475706 | ||||||||
\(593\) | 0.570902 | 0.0234441 | 0.0117221 | − | 0.999931i | \(-0.496269\pi\) | ||||
0.0117221 | + | 0.999931i | \(0.496269\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.96874 | 0.408679 | ||||||||
\(596\) | −30.5359 | −1.25080 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −12.3226 | −0.503909 | ||||||||
\(599\) | −8.95352 | −0.365831 | −0.182915 | − | 0.983129i | \(-0.558553\pi\) | ||||
−0.182915 | + | 0.983129i | \(0.558553\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.7284 | −0.519202 | −0.259601 | − | 0.965716i | \(-0.583591\pi\) | ||||
−0.259601 | + | 0.965716i | \(0.583591\pi\) | |||||||
\(602\) | −22.2697 | −0.907646 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 17.9019 | 0.728416 | ||||||||
\(605\) | 9.83982 | 0.400046 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.7859 | 1.08721 | 0.543603 | − | 0.839342i | \(-0.317060\pi\) | ||||
0.543603 | + | 0.839342i | \(0.317060\pi\) | |||||||
\(608\) | −24.1627 | −0.979926 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.15750 | −0.0873547 | ||||||||
\(611\) | −26.0911 | −1.05553 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 31.3273 | 1.26530 | 0.632649 | − | 0.774439i | \(-0.281968\pi\) | ||||
0.632649 | + | 0.774439i | \(0.281968\pi\) | |||||||
\(614\) | 10.0752 | 0.406602 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.30682 | −0.294400 | ||||||||
\(617\) | 31.6103 | 1.27258 | 0.636292 | − | 0.771448i | \(-0.280467\pi\) | ||||
0.636292 | + | 0.771448i | \(0.280467\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.99712 | 0.321431 | 0.160716 | − | 0.987001i | \(-0.448620\pi\) | ||||
0.160716 | + | 0.987001i | \(0.448620\pi\) | |||||||
\(620\) | −11.9143 | −0.478490 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.77491 | 0.191457 | ||||||||
\(623\) | 2.72686 | 0.109249 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.9549 | 0.478195 | ||||||||
\(626\) | −6.07617 | −0.242853 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14.0656 | −0.561278 | ||||||||
\(629\) | 35.1317 | 1.40079 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.2164 | −1.76023 | −0.880113 | − | 0.474764i | \(-0.842534\pi\) | ||||
−0.880113 | + | 0.474764i | \(0.842534\pi\) | |||||||
\(632\) | 18.3293 | 0.729100 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −20.6931 | −0.821827 | ||||||||
\(635\) | −5.68858 | −0.225744 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.0523 | −0.636017 | ||||||||
\(638\) | 4.11260 | 0.162819 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −9.71583 | −0.384052 | ||||||||
\(641\) | 16.8320 | 0.664824 | 0.332412 | − | 0.943134i | \(-0.392138\pi\) | ||||
0.332412 | + | 0.943134i | \(0.392138\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.4597 | −0.491362 | −0.245681 | − | 0.969351i | \(-0.579012\pi\) | ||||
−0.245681 | + | 0.969351i | \(0.579012\pi\) | |||||||
\(644\) | −17.7538 | −0.699599 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.65283 | −0.379786 | ||||||||
\(647\) | 48.1533 | 1.89310 | 0.946551 | − | 0.322555i | \(-0.104542\pi\) | ||||
0.946551 | + | 0.322555i | \(0.104542\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.4161 | −0.448123 | ||||||||
\(650\) | −13.4210 | −0.526415 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −17.2851 | −0.676938 | ||||||||
\(653\) | 12.7505 | 0.498967 | 0.249484 | − | 0.968379i | \(-0.419739\pi\) | ||||
0.249484 | + | 0.968379i | \(0.419739\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.72754 | 0.184720 | ||||||||
\(656\) | −1.48004 | −0.0577858 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 13.9247 | 0.542840 | ||||||||
\(659\) | 29.8939 | 1.16450 | 0.582250 | − | 0.813010i | \(-0.302172\pi\) | ||||
0.582250 | + | 0.813010i | \(0.302172\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0815 | 0.858872 | 0.429436 | − | 0.903097i | \(-0.358712\pi\) | ||||
0.429436 | + | 0.903097i | \(0.358712\pi\) | |||||||
\(662\) | 1.31110 | 0.0509574 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −18.7982 | −0.729512 | ||||||||
\(665\) | 12.9181 | 0.500943 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 23.6868 | 0.917157 | ||||||||
\(668\) | −27.5203 | −1.06479 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.47878 | −0.250297 | ||||||||
\(671\) | −2.69148 | −0.103903 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.6133 | 0.948772 | 0.474386 | − | 0.880317i | \(-0.342670\pi\) | ||||
0.474386 | + | 0.880317i | \(0.342670\pi\) | |||||||
\(674\) | −12.9058 | −0.497112 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.3387 | −0.397644 | ||||||||
\(677\) | −15.1930 | −0.583913 | −0.291956 | − | 0.956432i | \(-0.594306\pi\) | ||||
−0.291956 | + | 0.956432i | \(0.594306\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.54640 | −0.0593456 | ||||||||
\(680\) | −7.79467 | −0.298912 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.50568 | 0.210823 | ||||||||
\(683\) | 23.5519 | 0.901189 | 0.450594 | − | 0.892729i | \(-0.351212\pi\) | ||||
0.450594 | + | 0.892729i | \(0.351212\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.99022 | −0.305291 | ||||||||
\(686\) | −8.17537 | −0.312137 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.76391 | −0.372245 | ||||||||
\(689\) | −31.6767 | −1.20679 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.0300 | −1.40869 | −0.704343 | − | 0.709860i | \(-0.748758\pi\) | ||||
−0.704343 | + | 0.709860i | \(0.748758\pi\) | |||||||
\(692\) | −22.1569 | −0.842278 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.9044 | 0.413927 | ||||||||
\(695\) | −20.2932 | −0.769766 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.49235 | −0.170160 | ||||||||
\(698\) | 25.2705 | 0.956503 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −19.3363 | −0.730845 | ||||||||
\(701\) | −35.5829 | −1.34395 | −0.671973 | − | 0.740576i | \(-0.734553\pi\) | ||||
−0.671973 | + | 0.740576i | \(0.734553\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 45.5259 | 1.71704 | ||||||||
\(704\) | 1.95157 | 0.0735524 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11.8933 | −0.447611 | ||||||||
\(707\) | −10.0172 | −0.376736 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.5125 | 1.52148 | 0.760739 | − | 0.649058i | \(-0.224837\pi\) | ||||
0.760739 | + | 0.649058i | \(0.224837\pi\) | |||||||
\(710\) | 3.23933 | 0.121570 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.13216 | −0.0799062 | ||||||||
\(713\) | 31.7103 | 1.18756 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.81036 | 0.142499 | ||||||||
\(716\) | −3.76375 | −0.140658 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13.0263 | 0.486138 | ||||||||
\(719\) | −6.36743 | −0.237465 | −0.118733 | − | 0.992926i | \(-0.537883\pi\) | ||||
−0.118733 | + | 0.992926i | \(0.537883\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.0808 | 0.449914 | ||||||||
\(722\) | 1.46111 | 0.0543767 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13.8756 | 0.515683 | ||||||||
\(725\) | 25.7982 | 0.958120 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35.1164 | −1.30240 | −0.651198 | − | 0.758908i | \(-0.725733\pi\) | ||||
−0.651198 | + | 0.758908i | \(0.725733\pi\) | |||||||
\(728\) | 37.0807 | 1.37430 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −10.2258 | −0.378473 | ||||||||
\(731\) | −29.6363 | −1.09614 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.1891 | 0.967315 | 0.483658 | − | 0.875257i | \(-0.339308\pi\) | ||||
0.483658 | + | 0.875257i | \(0.339308\pi\) | |||||||
\(734\) | −5.36110 | −0.197882 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 21.9075 | 0.807523 | ||||||||
\(737\) | −8.08225 | −0.297714 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.8483 | 0.582988 | 0.291494 | − | 0.956573i | \(-0.405848\pi\) | ||||
0.291494 | + | 0.956573i | \(0.405848\pi\) | |||||||
\(740\) | 15.5087 | 0.570110 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 16.9057 | 0.620626 | ||||||||
\(743\) | −13.1980 | −0.484189 | −0.242095 | − | 0.970253i | \(-0.577834\pi\) | ||||
−0.242095 | + | 0.970253i | \(0.577834\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.1449 | −0.738054 | ||||||||
\(746\) | −14.2739 | −0.522605 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.10214 | −0.149989 | ||||||||
\(749\) | 52.3848 | 1.91410 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.3729 | −0.633945 | −0.316973 | − | 0.948435i | \(-0.602666\pi\) | ||||
−0.316973 | + | 0.948435i | \(0.602666\pi\) | |||||||
\(752\) | 6.10512 | 0.222631 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −20.8707 | −0.760064 | ||||||||
\(755\) | 11.8101 | 0.429814 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.7514 | −1.40844 | −0.704222 | − | 0.709980i | \(-0.748704\pi\) | ||||
−0.704222 | + | 0.709980i | \(0.748704\pi\) | |||||||
\(758\) | −15.8479 | −0.575623 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −10.1008 | −0.366396 | ||||||||
\(761\) | 29.0280 | 1.05226 | 0.526132 | − | 0.850403i | \(-0.323642\pi\) | ||||
0.526132 | + | 0.850403i | \(0.323642\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.49347 | −0.307484 | ||||||||
\(764\) | 9.06120 | 0.327823 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.39277 | −0.230980 | ||||||||
\(767\) | 57.9348 | 2.09190 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.49451 | −0.306320 | −0.153160 | − | 0.988201i | \(-0.548945\pi\) | ||||
−0.153160 | + | 0.988201i | \(0.548945\pi\) | |||||||
\(770\) | −2.03356 | −0.0732845 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 28.6491 | 1.03110 | ||||||||
\(773\) | 30.2676 | 1.08865 | 0.544325 | − | 0.838875i | \(-0.316786\pi\) | ||||
0.544325 | + | 0.838875i | \(0.316786\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 34.5369 | 1.24060 | ||||||||
\(776\) | 1.20915 | 0.0434060 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 14.7776 | 0.529803 | ||||||||
\(779\) | −5.82147 | −0.208576 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.04105 | 0.144600 | ||||||||
\(782\) | 8.75192 | 0.312968 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.75612 | 0.134147 | ||||||||
\(785\) | −9.27927 | −0.331191 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.5339 | −0.910185 | −0.455093 | − | 0.890444i | \(-0.650394\pi\) | ||||
−0.455093 | + | 0.890444i | \(0.650394\pi\) | |||||||
\(788\) | 38.4753 | 1.37063 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.10123 | 0.181494 | ||||||||
\(791\) | −39.7526 | −1.41344 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.6587 | 0.485036 | ||||||||
\(794\) | 16.4196 | 0.582710 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.55918 | 0.267928 | ||||||||
\(797\) | 48.5429 | 1.71948 | 0.859738 | − | 0.510735i | \(-0.170627\pi\) | ||||
0.859738 | + | 0.510735i | \(0.170627\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.5308 | 0.655573 | ||||||||
\(800\) | 23.8603 | 0.843589 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.43896 | −0.0508113 | ||||||||
\(803\) | −12.7566 | −0.450171 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.7125 | −0.412810 | ||||||||
\(806\) | −27.9403 | −0.984154 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.83256 | 0.275549 | ||||||||
\(809\) | −30.1082 | −1.05855 | −0.529274 | − | 0.848451i | \(-0.677536\pi\) | ||||
−0.529274 | + | 0.848451i | \(0.677536\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26.6166 | −0.934634 | −0.467317 | − | 0.884090i | \(-0.654779\pi\) | ||||
−0.467317 | + | 0.884090i | \(0.654779\pi\) | |||||||
\(812\) | −30.0695 | −1.05523 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.16665 | −0.251191 | ||||||||
\(815\) | −11.4032 | −0.399438 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −38.4046 | −1.34361 | ||||||||
\(818\) | −10.6403 | −0.372031 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.98312 | −0.0692536 | ||||||||
\(821\) | 52.7820 | 1.84210 | 0.921052 | − | 0.389440i | \(-0.127332\pi\) | ||||
0.921052 | + | 0.389440i | \(0.127332\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.7992 | −0.725014 | −0.362507 | − | 0.931981i | \(-0.618079\pi\) | ||||
−0.362507 | + | 0.931981i | \(0.618079\pi\) | |||||||
\(824\) | −9.44615 | −0.329072 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −30.9194 | −1.07582 | ||||||||
\(827\) | −12.6722 | −0.440654 | −0.220327 | − | 0.975426i | \(-0.570713\pi\) | ||||
−0.220327 | + | 0.975426i | \(0.570713\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.4262 | 0.848357 | 0.424179 | − | 0.905579i | \(-0.360563\pi\) | ||||
0.424179 | + | 0.905579i | \(0.360563\pi\) | |||||||
\(830\) | −5.23174 | −0.181596 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −9.90383 | −0.343354 | ||||||||
\(833\) | 11.4009 | 0.395018 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.1555 | −0.628297 | ||||||||
\(836\) | −5.31581 | −0.183851 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.61821 | −0.124989 | ||||||||
\(839\) | −41.6208 | −1.43691 | −0.718455 | − | 0.695574i | \(-0.755150\pi\) | ||||
−0.718455 | + | 0.695574i | \(0.755150\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.1181 | 0.383383 | ||||||||
\(842\) | −12.3383 | −0.425207 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −16.5822 | −0.570784 | ||||||||
\(845\) | −6.82061 | −0.234636 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 33.2459 | 1.14234 | ||||||||
\(848\) | 7.41210 | 0.254533 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9.53204 | 0.326946 | ||||||||
\(851\) | −41.2769 | −1.41495 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.9436 | 0.408942 | 0.204471 | − | 0.978873i | \(-0.434453\pi\) | ||||
0.204471 | + | 0.978873i | \(0.434453\pi\) | |||||||
\(854\) | −7.28958 | −0.249444 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −40.9603 | −1.39999 | ||||||||
\(857\) | 17.0803 | 0.583452 | 0.291726 | − | 0.956502i | \(-0.405771\pi\) | ||||
0.291726 | + | 0.956502i | \(0.405771\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −45.1499 | −1.54049 | −0.770247 | − | 0.637745i | \(-0.779867\pi\) | ||||
−0.770247 | + | 0.637745i | \(0.779867\pi\) | |||||||
\(860\) | −13.0828 | −0.446118 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.73595 | 0.263487 | ||||||||
\(863\) | 42.9192 | 1.46099 | 0.730494 | − | 0.682919i | \(-0.239290\pi\) | ||||
0.730494 | + | 0.682919i | \(0.239290\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.6172 | −0.497000 | ||||||||
\(866\) | 8.68594 | 0.295160 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −40.2550 | −1.36634 | ||||||||
\(869\) | 6.36377 | 0.215876 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 41.0159 | 1.38977 | ||||||||
\(872\) | 6.64114 | 0.224897 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 11.3413 | 0.383625 | ||||||||
\(875\) | −28.4161 | −0.960640 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.1529 | −0.748050 | −0.374025 | − | 0.927419i | \(-0.622023\pi\) | ||||
−0.374025 | + | 0.927419i | \(0.622023\pi\) | |||||||
\(878\) | −6.02090 | −0.203196 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.891593 | −0.0300556 | ||||||||
\(881\) | 8.84872 | 0.298121 | 0.149060 | − | 0.988828i | \(-0.452375\pi\) | ||||
0.149060 | + | 0.988828i | \(0.452375\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.6632 | 0.493455 | 0.246728 | − | 0.969085i | \(-0.420645\pi\) | ||||
0.246728 | + | 0.969085i | \(0.420645\pi\) | |||||||
\(884\) | 20.8176 | 0.700172 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.5523 | −0.388107 | ||||||||
\(887\) | −17.3973 | −0.584143 | −0.292072 | − | 0.956396i | \(-0.594345\pi\) | ||||
−0.292072 | + | 0.956396i | \(0.594345\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.2201 | −0.644621 | ||||||||
\(890\) | −0.593403 | −0.0198909 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −27.7214 | −0.928183 | ||||||||
\(893\) | 24.0134 | 0.803577 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.48300 | −0.0829975 | ||||||||
\(896\) | −32.8270 | −1.09667 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.27509 | 0.242773 | ||||||||
\(899\) | 53.7075 | 1.79124 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.4979 | 0.749512 | ||||||||
\(902\) | 0.916412 | 0.0305132 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 31.0830 | 1.03381 | ||||||||
\(905\) | 9.15395 | 0.304288 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33.7438 | −1.12045 | −0.560223 | − | 0.828342i | \(-0.689285\pi\) | ||||
−0.560223 | + | 0.828342i | \(0.689285\pi\) | |||||||
\(908\) | 17.1783 | 0.570081 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 10.3199 | 0.342103 | ||||||||
\(911\) | −12.1001 | −0.400895 | −0.200447 | − | 0.979704i | \(-0.564240\pi\) | ||||
−0.200447 | + | 0.979704i | \(0.564240\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.52657 | −0.215998 | ||||||||
\(914\) | −14.2874 | −0.472585 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.21557 | −0.304491 | ||||||||
\(917\) | 15.9730 | 0.527475 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −31.4919 | −1.03882 | −0.519412 | − | 0.854524i | \(-0.673849\pi\) | ||||
−0.519412 | + | 0.854524i | \(0.673849\pi\) | |||||||
\(920\) | 9.15811 | 0.301934 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 20.9371 | 0.689528 | ||||||||
\(923\) | −20.5076 | −0.675015 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −44.9562 | −1.47815 | ||||||||
\(926\) | 7.94777 | 0.261180 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 37.1046 | 1.21802 | ||||||||
\(929\) | −28.6545 | −0.940123 | −0.470061 | − | 0.882634i | \(-0.655768\pi\) | ||||
−0.470061 | + | 0.882634i | \(0.655768\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.7740 | 0.484199 | ||||||||
\(932\) | 30.3320 | 0.993558 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 19.3859 | 0.634326 | ||||||||
\(935\) | −2.70624 | −0.0885036 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.14354 | 0.200701 | 0.100350 | − | 0.994952i | \(-0.468004\pi\) | ||||
0.100350 | + | 0.994952i | \(0.468004\pi\) | |||||||
\(938\) | −21.8899 | −0.714731 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.18031 | 0.266812 | ||||||||
\(941\) | 25.9528 | 0.846038 | 0.423019 | − | 0.906121i | \(-0.360970\pi\) | ||||
0.423019 | + | 0.906121i | \(0.360970\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.27814 | 0.171880 | ||||||||
\(944\) | −13.5563 | −0.441219 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.04562 | 0.196560 | ||||||||
\(947\) | −45.1337 | −1.46665 | −0.733324 | − | 0.679880i | \(-0.762032\pi\) | ||||
−0.733324 | + | 0.679880i | \(0.762032\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 64.7374 | 2.10146 | ||||||||
\(950\) | 12.3522 | 0.400759 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −26.3360 | −0.853553 | ||||||||
\(953\) | 6.09060 | 0.197294 | 0.0986469 | − | 0.995122i | \(-0.468549\pi\) | ||||
0.0986469 | + | 0.995122i | \(0.468549\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.97781 | 0.193437 | ||||||||
\(956\) | −34.7929 | −1.12528 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −0.142662 | −0.00460920 | ||||||||
\(959\) | −26.9966 | −0.871767 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 40.9000 | 1.31936 | ||||||||
\(962\) | 36.3694 | 1.17260 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.36468 | −0.0761614 | ||||||||
\(965\) | 18.9002 | 0.608420 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.8474 | −1.05630 | −0.528151 | − | 0.849150i | \(-0.677115\pi\) | ||||
−0.528151 | + | 0.849150i | \(0.677115\pi\) | |||||||
\(968\) | −25.9954 | −0.835523 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.336519 | 0.0108050 | ||||||||
\(971\) | −45.3642 | −1.45581 | −0.727903 | − | 0.685680i | \(-0.759505\pi\) | ||||
−0.727903 | + | 0.685680i | \(0.759505\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −68.5650 | −2.19809 | ||||||||
\(974\) | 1.95344 | 0.0625922 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.19603 | −0.102303 | ||||||||
\(977\) | −9.96515 | −0.318813 | −0.159407 | − | 0.987213i | \(-0.550958\pi\) | ||||
−0.159407 | + | 0.987213i | \(0.550958\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.740268 | −0.0236591 | ||||||||
\(980\) | 5.03286 | 0.160769 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8.11707 | 0.259026 | ||||||||
\(983\) | 8.37150 | 0.267009 | 0.133505 | − | 0.991048i | \(-0.457377\pi\) | ||||
0.133505 | + | 0.991048i | \(0.457377\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.3827 | 0.808761 | ||||||||
\(986\) | 14.8230 | 0.472062 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 26.9768 | 0.858245 | ||||||||
\(989\) | 34.8202 | 1.10722 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.8111 | 0.915215 | 0.457608 | − | 0.889154i | \(-0.348706\pi\) | ||||
0.457608 | + | 0.889154i | \(0.348706\pi\) | |||||||
\(992\) | 49.6732 | 1.57712 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10.9448 | 0.347147 | ||||||||
\(995\) | 4.98690 | 0.158095 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.3708 | 0.391788 | 0.195894 | − | 0.980625i | \(-0.437239\pi\) | ||||
0.195894 | + | 0.980625i | \(0.437239\pi\) | |||||||
\(998\) | −22.7904 | −0.721418 | ||||||||
\(999\) | 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 | 4923.2.a.l.1.8 | 18 | ||
3.2 | odd | 2 | 547.2.a.b.1.11 | ✓ | 18 | ||
12.11 | even | 2 | 8752.2.a.s.1.6 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
547.2.a.b.1.11 | ✓ | 18 | 3.2 | odd | 2 | ||
4923.2.a.l.1.8 | 18 | 1.1 | even | 1 | trivial | ||
8752.2.a.s.1.6 | 18 | 12.11 | even | 2 |