Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7098,2,Mod(1,7098)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7098, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7098.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7098.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: | \(56.6778153547\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.24698\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7098.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.692021 | −0.309481 | −0.154741 | − | 0.987955i | \(-0.549454\pi\) | ||||
−0.154741 | + | 0.987955i | \(0.549454\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.692021 | −0.218836 | ||||||||
\(11\) | −0.664874 | −0.200467 | −0.100234 | − | 0.994964i | \(-0.531959\pi\) | ||||
−0.100234 | + | 0.994964i | \(0.531959\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0.692021 | 0.178679 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.74094 | −1.87745 | −0.938727 | − | 0.344662i | \(-0.887993\pi\) | ||||
−0.938727 | + | 0.344662i | \(0.887993\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −3.89977 | −0.894669 | −0.447335 | − | 0.894367i | \(-0.647627\pi\) | ||||
−0.447335 | + | 0.894367i | \(0.647627\pi\) | |||||||
\(20\) | −0.692021 | −0.154741 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −0.664874 | −0.141752 | ||||||||
\(23\) | 0.841166 | 0.175395 | 0.0876977 | − | 0.996147i | \(-0.472049\pi\) | ||||
0.0876977 | + | 0.996147i | \(0.472049\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −4.52111 | −0.904221 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 8.98792 | 1.66901 | 0.834507 | − | 0.550997i | \(-0.185752\pi\) | ||||
0.834507 | + | 0.550997i | \(0.185752\pi\) | |||||||
\(30\) | 0.692021 | 0.126345 | ||||||||
\(31\) | 6.26875 | 1.12590 | 0.562950 | − | 0.826491i | \(-0.309666\pi\) | ||||
0.562950 | + | 0.826491i | \(0.309666\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.664874 | 0.115740 | ||||||||
\(34\) | −7.74094 | −1.32756 | ||||||||
\(35\) | 0.692021 | 0.116973 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 11.1685 | 1.83609 | 0.918047 | − | 0.396472i | \(-0.129766\pi\) | ||||
0.918047 | + | 0.396472i | \(0.129766\pi\) | |||||||
\(38\) | −3.89977 | −0.632627 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.692021 | −0.109418 | ||||||||
\(41\) | −11.7409 | −1.83363 | −0.916813 | − | 0.399316i | \(-0.869248\pi\) | ||||
−0.916813 | + | 0.399316i | \(0.869248\pi\) | |||||||
\(42\) | 1.00000 | 0.154303 | ||||||||
\(43\) | 9.87800 | 1.50638 | 0.753191 | − | 0.657802i | \(-0.228514\pi\) | ||||
0.753191 | + | 0.657802i | \(0.228514\pi\) | |||||||
\(44\) | −0.664874 | −0.100234 | ||||||||
\(45\) | −0.692021 | −0.103160 | ||||||||
\(46\) | 0.841166 | 0.124023 | ||||||||
\(47\) | −10.3177 | −1.50499 | −0.752493 | − | 0.658600i | \(-0.771149\pi\) | ||||
−0.752493 | + | 0.658600i | \(0.771149\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −4.52111 | −0.639381 | ||||||||
\(51\) | 7.74094 | 1.08395 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.92154 | −1.08811 | −0.544054 | − | 0.839050i | \(-0.683111\pi\) | ||||
−0.544054 | + | 0.839050i | \(0.683111\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0.460107 | 0.0620409 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 3.89977 | 0.516537 | ||||||||
\(58\) | 8.98792 | 1.18017 | ||||||||
\(59\) | 10.8901 | 1.41777 | 0.708884 | − | 0.705325i | \(-0.249199\pi\) | ||||
0.708884 | + | 0.705325i | \(0.249199\pi\) | |||||||
\(60\) | 0.692021 | 0.0893396 | ||||||||
\(61\) | −6.05429 | −0.775173 | −0.387586 | − | 0.921833i | \(-0.626691\pi\) | ||||
−0.387586 | + | 0.921833i | \(0.626691\pi\) | |||||||
\(62\) | 6.26875 | 0.796132 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.664874 | 0.0818404 | ||||||||
\(67\) | −2.98792 | −0.365032 | −0.182516 | − | 0.983203i | \(-0.558424\pi\) | ||||
−0.182516 | + | 0.983203i | \(0.558424\pi\) | |||||||
\(68\) | −7.74094 | −0.938727 | ||||||||
\(69\) | −0.841166 | −0.101265 | ||||||||
\(70\) | 0.692021 | 0.0827124 | ||||||||
\(71\) | 9.93661 | 1.17926 | 0.589629 | − | 0.807674i | \(-0.299274\pi\) | ||||
0.589629 | + | 0.807674i | \(0.299274\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 14.5918 | 1.70784 | 0.853920 | − | 0.520404i | \(-0.174219\pi\) | ||||
0.853920 | + | 0.520404i | \(0.174219\pi\) | |||||||
\(74\) | 11.1685 | 1.29831 | ||||||||
\(75\) | 4.52111 | 0.522052 | ||||||||
\(76\) | −3.89977 | −0.447335 | ||||||||
\(77\) | 0.664874 | 0.0757695 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.60388 | −0.180450 | −0.0902250 | − | 0.995921i | \(-0.528759\pi\) | ||||
−0.0902250 | + | 0.995921i | \(0.528759\pi\) | |||||||
\(80\) | −0.692021 | −0.0773704 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −11.7409 | −1.29657 | ||||||||
\(83\) | 4.39612 | 0.482537 | 0.241269 | − | 0.970458i | \(-0.422436\pi\) | ||||
0.241269 | + | 0.970458i | \(0.422436\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | 5.35690 | 0.581037 | ||||||||
\(86\) | 9.87800 | 1.06517 | ||||||||
\(87\) | −8.98792 | −0.963606 | ||||||||
\(88\) | −0.664874 | −0.0708758 | ||||||||
\(89\) | 0.454731 | 0.0482013 | 0.0241007 | − | 0.999710i | \(-0.492328\pi\) | ||||
0.0241007 | + | 0.999710i | \(0.492328\pi\) | |||||||
\(90\) | −0.692021 | −0.0729455 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.841166 | 0.0876977 | ||||||||
\(93\) | −6.26875 | −0.650039 | ||||||||
\(94\) | −10.3177 | −1.06419 | ||||||||
\(95\) | 2.69873 | 0.276883 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 8.61596 | 0.874818 | 0.437409 | − | 0.899263i | \(-0.355896\pi\) | ||||
0.437409 | + | 0.899263i | \(0.355896\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | −0.664874 | −0.0668224 | ||||||||
\(100\) | −4.52111 | −0.452111 | ||||||||
\(101\) | 17.7235 | 1.76355 | 0.881776 | − | 0.471668i | \(-0.156348\pi\) | ||||
0.881776 | + | 0.471668i | \(0.156348\pi\) | |||||||
\(102\) | 7.74094 | 0.766467 | ||||||||
\(103\) | −12.5972 | −1.24124 | −0.620618 | − | 0.784113i | \(-0.713118\pi\) | ||||
−0.620618 | + | 0.784113i | \(0.713118\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.692021 | −0.0675344 | ||||||||
\(106\) | −7.92154 | −0.769408 | ||||||||
\(107\) | −0.692021 | −0.0669002 | −0.0334501 | − | 0.999440i | \(-0.510649\pi\) | ||||
−0.0334501 | + | 0.999440i | \(0.510649\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 8.03923 | 0.770018 | 0.385009 | − | 0.922913i | \(-0.374198\pi\) | ||||
0.385009 | + | 0.922913i | \(0.374198\pi\) | |||||||
\(110\) | 0.460107 | 0.0438695 | ||||||||
\(111\) | −11.1685 | −1.06007 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 12.5918 | 1.18454 | 0.592268 | − | 0.805741i | \(-0.298233\pi\) | ||||
0.592268 | + | 0.805741i | \(0.298233\pi\) | |||||||
\(114\) | 3.89977 | 0.365247 | ||||||||
\(115\) | −0.582105 | −0.0542816 | ||||||||
\(116\) | 8.98792 | 0.834507 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.8901 | 1.00251 | ||||||||
\(119\) | 7.74094 | 0.709611 | ||||||||
\(120\) | 0.692021 | 0.0631726 | ||||||||
\(121\) | −10.5579 | −0.959813 | ||||||||
\(122\) | −6.05429 | −0.548130 | ||||||||
\(123\) | 11.7409 | 1.05864 | ||||||||
\(124\) | 6.26875 | 0.562950 | ||||||||
\(125\) | 6.58881 | 0.589321 | ||||||||
\(126\) | −1.00000 | −0.0890871 | ||||||||
\(127\) | 6.76809 | 0.600571 | 0.300285 | − | 0.953849i | \(-0.402918\pi\) | ||||
0.300285 | + | 0.953849i | \(0.402918\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −9.87800 | −0.869710 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.987918 | 0.0863148 | 0.0431574 | − | 0.999068i | \(-0.486258\pi\) | ||||
0.0431574 | + | 0.999068i | \(0.486258\pi\) | |||||||
\(132\) | 0.664874 | 0.0578699 | ||||||||
\(133\) | 3.89977 | 0.338153 | ||||||||
\(134\) | −2.98792 | −0.258117 | ||||||||
\(135\) | 0.692021 | 0.0595597 | ||||||||
\(136\) | −7.74094 | −0.663780 | ||||||||
\(137\) | −0.572417 | −0.0489048 | −0.0244524 | − | 0.999701i | \(-0.507784\pi\) | ||||
−0.0244524 | + | 0.999701i | \(0.507784\pi\) | |||||||
\(138\) | −0.841166 | −0.0716048 | ||||||||
\(139\) | 16.7627 | 1.42179 | 0.710897 | − | 0.703296i | \(-0.248289\pi\) | ||||
0.710897 | + | 0.703296i | \(0.248289\pi\) | |||||||
\(140\) | 0.692021 | 0.0584865 | ||||||||
\(141\) | 10.3177 | 0.868904 | ||||||||
\(142\) | 9.93661 | 0.833862 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −6.21983 | −0.516529 | ||||||||
\(146\) | 14.5918 | 1.20763 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 11.1685 | 0.918047 | ||||||||
\(149\) | −12.0194 | −0.984666 | −0.492333 | − | 0.870407i | \(-0.663856\pi\) | ||||
−0.492333 | + | 0.870407i | \(0.663856\pi\) | |||||||
\(150\) | 4.52111 | 0.369147 | ||||||||
\(151\) | −19.3491 | −1.57461 | −0.787305 | − | 0.616564i | \(-0.788524\pi\) | ||||
−0.787305 | + | 0.616564i | \(0.788524\pi\) | |||||||
\(152\) | −3.89977 | −0.316313 | ||||||||
\(153\) | −7.74094 | −0.625818 | ||||||||
\(154\) | 0.664874 | 0.0535771 | ||||||||
\(155\) | −4.33811 | −0.348445 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.19567 | −0.175233 | −0.0876167 | − | 0.996154i | \(-0.527925\pi\) | ||||
−0.0876167 | + | 0.996154i | \(0.527925\pi\) | |||||||
\(158\) | −1.60388 | −0.127597 | ||||||||
\(159\) | 7.92154 | 0.628219 | ||||||||
\(160\) | −0.692021 | −0.0547091 | ||||||||
\(161\) | −0.841166 | −0.0662932 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 19.3599 | 1.51638 | 0.758191 | − | 0.652032i | \(-0.226083\pi\) | ||||
0.758191 | + | 0.652032i | \(0.226083\pi\) | |||||||
\(164\) | −11.7409 | −0.916813 | ||||||||
\(165\) | −0.460107 | −0.0358193 | ||||||||
\(166\) | 4.39612 | 0.341205 | ||||||||
\(167\) | 20.5133 | 1.58737 | 0.793685 | − | 0.608329i | \(-0.208160\pi\) | ||||
0.793685 | + | 0.608329i | \(0.208160\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 5.35690 | 0.410855 | ||||||||
\(171\) | −3.89977 | −0.298223 | ||||||||
\(172\) | 9.87800 | 0.753191 | ||||||||
\(173\) | 9.08815 | 0.690959 | 0.345479 | − | 0.938426i | \(-0.387716\pi\) | ||||
0.345479 | + | 0.938426i | \(0.387716\pi\) | |||||||
\(174\) | −8.98792 | −0.681372 | ||||||||
\(175\) | 4.52111 | 0.341764 | ||||||||
\(176\) | −0.664874 | −0.0501168 | ||||||||
\(177\) | −10.8901 | −0.818549 | ||||||||
\(178\) | 0.454731 | 0.0340835 | ||||||||
\(179\) | 8.98792 | 0.671789 | 0.335894 | − | 0.941900i | \(-0.390962\pi\) | ||||
0.335894 | + | 0.941900i | \(0.390962\pi\) | |||||||
\(180\) | −0.692021 | −0.0515802 | ||||||||
\(181\) | −1.76941 | −0.131519 | −0.0657597 | − | 0.997835i | \(-0.520947\pi\) | ||||
−0.0657597 | + | 0.997835i | \(0.520947\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.05429 | 0.447546 | ||||||||
\(184\) | 0.841166 | 0.0620116 | ||||||||
\(185\) | −7.72886 | −0.568237 | ||||||||
\(186\) | −6.26875 | −0.459647 | ||||||||
\(187\) | 5.14675 | 0.376368 | ||||||||
\(188\) | −10.3177 | −0.752493 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 2.69873 | 0.195786 | ||||||||
\(191\) | −16.7657 | −1.21312 | −0.606561 | − | 0.795037i | \(-0.707452\pi\) | ||||
−0.606561 | + | 0.795037i | \(0.707452\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 16.9933 | 1.22320 | 0.611602 | − | 0.791166i | \(-0.290525\pi\) | ||||
0.611602 | + | 0.791166i | \(0.290525\pi\) | |||||||
\(194\) | 8.61596 | 0.618590 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −4.90946 | −0.349785 | −0.174892 | − | 0.984588i | \(-0.555958\pi\) | ||||
−0.174892 | + | 0.984588i | \(0.555958\pi\) | |||||||
\(198\) | −0.664874 | −0.0472506 | ||||||||
\(199\) | −14.9729 | −1.06140 | −0.530699 | − | 0.847561i | \(-0.678070\pi\) | ||||
−0.530699 | + | 0.847561i | \(0.678070\pi\) | |||||||
\(200\) | −4.52111 | −0.319690 | ||||||||
\(201\) | 2.98792 | 0.210752 | ||||||||
\(202\) | 17.7235 | 1.24702 | ||||||||
\(203\) | −8.98792 | −0.630828 | ||||||||
\(204\) | 7.74094 | 0.541974 | ||||||||
\(205\) | 8.12498 | 0.567473 | ||||||||
\(206\) | −12.5972 | −0.877686 | ||||||||
\(207\) | 0.841166 | 0.0584651 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.59286 | 0.179352 | ||||||||
\(210\) | −0.692021 | −0.0477540 | ||||||||
\(211\) | −6.98792 | −0.481068 | −0.240534 | − | 0.970641i | \(-0.577323\pi\) | ||||
−0.240534 | + | 0.970641i | \(0.577323\pi\) | |||||||
\(212\) | −7.92154 | −0.544054 | ||||||||
\(213\) | −9.93661 | −0.680845 | ||||||||
\(214\) | −0.692021 | −0.0473056 | ||||||||
\(215\) | −6.83579 | −0.466197 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −6.26875 | −0.425550 | ||||||||
\(218\) | 8.03923 | 0.544485 | ||||||||
\(219\) | −14.5918 | −0.986022 | ||||||||
\(220\) | 0.460107 | 0.0310204 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −11.1685 | −0.749582 | ||||||||
\(223\) | −1.13467 | −0.0759832 | −0.0379916 | − | 0.999278i | \(-0.512096\pi\) | ||||
−0.0379916 | + | 0.999278i | \(0.512096\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −4.52111 | −0.301407 | ||||||||
\(226\) | 12.5918 | 0.837594 | ||||||||
\(227\) | 5.26205 | 0.349254 | 0.174627 | − | 0.984635i | \(-0.444128\pi\) | ||||
0.174627 | + | 0.984635i | \(0.444128\pi\) | |||||||
\(228\) | 3.89977 | 0.258269 | ||||||||
\(229\) | 3.40821 | 0.225221 | 0.112610 | − | 0.993639i | \(-0.464079\pi\) | ||||
0.112610 | + | 0.993639i | \(0.464079\pi\) | |||||||
\(230\) | −0.582105 | −0.0383829 | ||||||||
\(231\) | −0.664874 | −0.0437455 | ||||||||
\(232\) | 8.98792 | 0.590086 | ||||||||
\(233\) | −23.6775 | −1.55117 | −0.775584 | − | 0.631245i | \(-0.782544\pi\) | ||||
−0.775584 | + | 0.631245i | \(0.782544\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.14005 | 0.465765 | ||||||||
\(236\) | 10.8901 | 0.708884 | ||||||||
\(237\) | 1.60388 | 0.104183 | ||||||||
\(238\) | 7.74094 | 0.501771 | ||||||||
\(239\) | −20.2610 | −1.31057 | −0.655287 | − | 0.755380i | \(-0.727452\pi\) | ||||
−0.655287 | + | 0.755380i | \(0.727452\pi\) | |||||||
\(240\) | 0.692021 | 0.0446698 | ||||||||
\(241\) | 0.0435405 | 0.00280469 | 0.00140235 | − | 0.999999i | \(-0.499554\pi\) | ||||
0.00140235 | + | 0.999999i | \(0.499554\pi\) | |||||||
\(242\) | −10.5579 | −0.678690 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −6.05429 | −0.387586 | ||||||||
\(245\) | −0.692021 | −0.0442116 | ||||||||
\(246\) | 11.7409 | 0.748575 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 6.26875 | 0.398066 | ||||||||
\(249\) | −4.39612 | −0.278593 | ||||||||
\(250\) | 6.58881 | 0.416713 | ||||||||
\(251\) | −27.3056 | −1.72351 | −0.861757 | − | 0.507322i | \(-0.830636\pi\) | ||||
−0.861757 | + | 0.507322i | \(0.830636\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | −0.559270 | −0.0351610 | ||||||||
\(254\) | 6.76809 | 0.424667 | ||||||||
\(255\) | −5.35690 | −0.335462 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 7.97584 | 0.497519 | 0.248760 | − | 0.968565i | \(-0.419977\pi\) | ||||
0.248760 | + | 0.968565i | \(0.419977\pi\) | |||||||
\(258\) | −9.87800 | −0.614978 | ||||||||
\(259\) | −11.1685 | −0.693978 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.98792 | 0.556338 | ||||||||
\(262\) | 0.987918 | 0.0610338 | ||||||||
\(263\) | 9.37867 | 0.578313 | 0.289157 | − | 0.957282i | \(-0.406625\pi\) | ||||
0.289157 | + | 0.957282i | \(0.406625\pi\) | |||||||
\(264\) | 0.664874 | 0.0409202 | ||||||||
\(265\) | 5.48188 | 0.336749 | ||||||||
\(266\) | 3.89977 | 0.239110 | ||||||||
\(267\) | −0.454731 | −0.0278291 | ||||||||
\(268\) | −2.98792 | −0.182516 | ||||||||
\(269\) | 7.96077 | 0.485377 | 0.242688 | − | 0.970104i | \(-0.421971\pi\) | ||||
0.242688 | + | 0.970104i | \(0.421971\pi\) | |||||||
\(270\) | 0.692021 | 0.0421151 | ||||||||
\(271\) | 10.6377 | 0.646196 | 0.323098 | − | 0.946366i | \(-0.395276\pi\) | ||||
0.323098 | + | 0.946366i | \(0.395276\pi\) | |||||||
\(272\) | −7.74094 | −0.469363 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.572417 | −0.0345809 | ||||||||
\(275\) | 3.00597 | 0.181267 | ||||||||
\(276\) | −0.841166 | −0.0506323 | ||||||||
\(277\) | 26.4674 | 1.59027 | 0.795136 | − | 0.606431i | \(-0.207399\pi\) | ||||
0.795136 | + | 0.606431i | \(0.207399\pi\) | |||||||
\(278\) | 16.7627 | 1.00536 | ||||||||
\(279\) | 6.26875 | 0.375300 | ||||||||
\(280\) | 0.692021 | 0.0413562 | ||||||||
\(281\) | 5.60388 | 0.334299 | 0.167150 | − | 0.985932i | \(-0.446544\pi\) | ||||
0.167150 | + | 0.985932i | \(0.446544\pi\) | |||||||
\(282\) | 10.3177 | 0.614408 | ||||||||
\(283\) | −11.3351 | −0.673803 | −0.336902 | − | 0.941540i | \(-0.609379\pi\) | ||||
−0.336902 | + | 0.941540i | \(0.609379\pi\) | |||||||
\(284\) | 9.93661 | 0.589629 | ||||||||
\(285\) | −2.69873 | −0.159859 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.7409 | 0.693046 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 42.9221 | 2.52483 | ||||||||
\(290\) | −6.21983 | −0.365241 | ||||||||
\(291\) | −8.61596 | −0.505076 | ||||||||
\(292\) | 14.5918 | 0.853920 | ||||||||
\(293\) | 20.7530 | 1.21240 | 0.606202 | − | 0.795311i | \(-0.292692\pi\) | ||||
0.606202 | + | 0.795311i | \(0.292692\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | −7.53617 | −0.438773 | ||||||||
\(296\) | 11.1685 | 0.649157 | ||||||||
\(297\) | 0.664874 | 0.0385799 | ||||||||
\(298\) | −12.0194 | −0.696264 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 4.52111 | 0.261026 | ||||||||
\(301\) | −9.87800 | −0.569359 | ||||||||
\(302\) | −19.3491 | −1.11342 | ||||||||
\(303\) | −17.7235 | −1.01819 | ||||||||
\(304\) | −3.89977 | −0.223667 | ||||||||
\(305\) | 4.18970 | 0.239902 | ||||||||
\(306\) | −7.74094 | −0.442520 | ||||||||
\(307\) | 14.5961 | 0.833044 | 0.416522 | − | 0.909126i | \(-0.363249\pi\) | ||||
0.416522 | + | 0.909126i | \(0.363249\pi\) | |||||||
\(308\) | 0.664874 | 0.0378847 | ||||||||
\(309\) | 12.5972 | 0.716628 | ||||||||
\(310\) | −4.33811 | −0.246388 | ||||||||
\(311\) | −1.82371 | −0.103413 | −0.0517065 | − | 0.998662i | \(-0.516466\pi\) | ||||
−0.0517065 | + | 0.998662i | \(0.516466\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 34.6112 | 1.95634 | 0.978170 | − | 0.207808i | \(-0.0666331\pi\) | ||||
0.978170 | + | 0.207808i | \(0.0666331\pi\) | |||||||
\(314\) | −2.19567 | −0.123909 | ||||||||
\(315\) | 0.692021 | 0.0389910 | ||||||||
\(316\) | −1.60388 | −0.0902250 | ||||||||
\(317\) | −4.49396 | −0.252406 | −0.126203 | − | 0.992004i | \(-0.540279\pi\) | ||||
−0.126203 | + | 0.992004i | \(0.540279\pi\) | |||||||
\(318\) | 7.92154 | 0.444218 | ||||||||
\(319\) | −5.97584 | −0.334583 | ||||||||
\(320\) | −0.692021 | −0.0386852 | ||||||||
\(321\) | 0.692021 | 0.0386249 | ||||||||
\(322\) | −0.841166 | −0.0468764 | ||||||||
\(323\) | 30.1879 | 1.67970 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 19.3599 | 1.07224 | ||||||||
\(327\) | −8.03923 | −0.444570 | ||||||||
\(328\) | −11.7409 | −0.648285 | ||||||||
\(329\) | 10.3177 | 0.568831 | ||||||||
\(330\) | −0.460107 | −0.0253281 | ||||||||
\(331\) | −8.75733 | −0.481347 | −0.240673 | − | 0.970606i | \(-0.577368\pi\) | ||||
−0.240673 | + | 0.970606i | \(0.577368\pi\) | |||||||
\(332\) | 4.39612 | 0.241269 | ||||||||
\(333\) | 11.1685 | 0.612031 | ||||||||
\(334\) | 20.5133 | 1.12244 | ||||||||
\(335\) | 2.06770 | 0.112971 | ||||||||
\(336\) | 1.00000 | 0.0545545 | ||||||||
\(337\) | 12.6136 | 0.687105 | 0.343552 | − | 0.939134i | \(-0.388370\pi\) | ||||
0.343552 | + | 0.939134i | \(0.388370\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.5918 | −0.683892 | ||||||||
\(340\) | 5.35690 | 0.290518 | ||||||||
\(341\) | −4.16793 | −0.225706 | ||||||||
\(342\) | −3.89977 | −0.210876 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 9.87800 | 0.532586 | ||||||||
\(345\) | 0.582105 | 0.0313395 | ||||||||
\(346\) | 9.08815 | 0.488582 | ||||||||
\(347\) | 19.4034 | 1.04163 | 0.520815 | − | 0.853670i | \(-0.325628\pi\) | ||||
0.520815 | + | 0.853670i | \(0.325628\pi\) | |||||||
\(348\) | −8.98792 | −0.481803 | ||||||||
\(349\) | 0.415502 | 0.0222413 | 0.0111207 | − | 0.999938i | \(-0.496460\pi\) | ||||
0.0111207 | + | 0.999938i | \(0.496460\pi\) | |||||||
\(350\) | 4.52111 | 0.241663 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.664874 | −0.0354379 | ||||||||
\(353\) | 16.4450 | 0.875281 | 0.437641 | − | 0.899150i | \(-0.355814\pi\) | ||||
0.437641 | + | 0.899150i | \(0.355814\pi\) | |||||||
\(354\) | −10.8901 | −0.578801 | ||||||||
\(355\) | −6.87635 | −0.364959 | ||||||||
\(356\) | 0.454731 | 0.0241007 | ||||||||
\(357\) | −7.74094 | −0.409694 | ||||||||
\(358\) | 8.98792 | 0.475026 | ||||||||
\(359\) | 6.61058 | 0.348893 | 0.174447 | − | 0.984667i | \(-0.444186\pi\) | ||||
0.174447 | + | 0.984667i | \(0.444186\pi\) | |||||||
\(360\) | −0.692021 | −0.0364727 | ||||||||
\(361\) | −3.79178 | −0.199567 | ||||||||
\(362\) | −1.76941 | −0.0929983 | ||||||||
\(363\) | 10.5579 | 0.554148 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.0978 | −0.528545 | ||||||||
\(366\) | 6.05429 | 0.316463 | ||||||||
\(367\) | 15.5773 | 0.813129 | 0.406565 | − | 0.913622i | \(-0.366727\pi\) | ||||
0.406565 | + | 0.913622i | \(0.366727\pi\) | |||||||
\(368\) | 0.841166 | 0.0438488 | ||||||||
\(369\) | −11.7409 | −0.611209 | ||||||||
\(370\) | −7.72886 | −0.401804 | ||||||||
\(371\) | 7.92154 | 0.411266 | ||||||||
\(372\) | −6.26875 | −0.325020 | ||||||||
\(373\) | −1.81940 | −0.0942048 | −0.0471024 | − | 0.998890i | \(-0.514999\pi\) | ||||
−0.0471024 | + | 0.998890i | \(0.514999\pi\) | |||||||
\(374\) | 5.14675 | 0.266132 | ||||||||
\(375\) | −6.58881 | −0.340245 | ||||||||
\(376\) | −10.3177 | −0.532093 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.00000 | 0.0514344 | ||||||||
\(379\) | −7.53617 | −0.387107 | −0.193554 | − | 0.981090i | \(-0.562001\pi\) | ||||
−0.193554 | + | 0.981090i | \(0.562001\pi\) | |||||||
\(380\) | 2.69873 | 0.138442 | ||||||||
\(381\) | −6.76809 | −0.346740 | ||||||||
\(382\) | −16.7657 | −0.857807 | ||||||||
\(383\) | 3.78017 | 0.193158 | 0.0965788 | − | 0.995325i | \(-0.469210\pi\) | ||||
0.0965788 | + | 0.995325i | \(0.469210\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −0.460107 | −0.0234492 | ||||||||
\(386\) | 16.9933 | 0.864936 | ||||||||
\(387\) | 9.87800 | 0.502127 | ||||||||
\(388\) | 8.61596 | 0.437409 | ||||||||
\(389\) | 5.01208 | 0.254123 | 0.127061 | − | 0.991895i | \(-0.459446\pi\) | ||||
0.127061 | + | 0.991895i | \(0.459446\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.51142 | −0.329297 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −0.987918 | −0.0498339 | ||||||||
\(394\) | −4.90946 | −0.247335 | ||||||||
\(395\) | 1.10992 | 0.0558459 | ||||||||
\(396\) | −0.664874 | −0.0334112 | ||||||||
\(397\) | −5.05562 | −0.253734 | −0.126867 | − | 0.991920i | \(-0.540492\pi\) | ||||
−0.126867 | + | 0.991920i | \(0.540492\pi\) | |||||||
\(398\) | −14.9729 | −0.750521 | ||||||||
\(399\) | −3.89977 | −0.195233 | ||||||||
\(400\) | −4.52111 | −0.226055 | ||||||||
\(401\) | 38.8745 | 1.94130 | 0.970651 | − | 0.240492i | \(-0.0773089\pi\) | ||||
0.970651 | + | 0.240492i | \(0.0773089\pi\) | |||||||
\(402\) | 2.98792 | 0.149024 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 17.7235 | 0.881776 | ||||||||
\(405\) | −0.692021 | −0.0343868 | ||||||||
\(406\) | −8.98792 | −0.446063 | ||||||||
\(407\) | −7.42566 | −0.368077 | ||||||||
\(408\) | 7.74094 | 0.383234 | ||||||||
\(409\) | 32.6461 | 1.61425 | 0.807123 | − | 0.590384i | \(-0.201024\pi\) | ||||
0.807123 | + | 0.590384i | \(0.201024\pi\) | |||||||
\(410\) | 8.12498 | 0.401264 | ||||||||
\(411\) | 0.572417 | 0.0282352 | ||||||||
\(412\) | −12.5972 | −0.620618 | ||||||||
\(413\) | −10.8901 | −0.535866 | ||||||||
\(414\) | 0.841166 | 0.0413411 | ||||||||
\(415\) | −3.04221 | −0.149336 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.7627 | −0.820873 | ||||||||
\(418\) | 2.59286 | 0.126821 | ||||||||
\(419\) | 23.3250 | 1.13950 | 0.569750 | − | 0.821818i | \(-0.307040\pi\) | ||||
0.569750 | + | 0.821818i | \(0.307040\pi\) | |||||||
\(420\) | −0.692021 | −0.0337672 | ||||||||
\(421\) | 18.2282 | 0.888388 | 0.444194 | − | 0.895931i | \(-0.353490\pi\) | ||||
0.444194 | + | 0.895931i | \(0.353490\pi\) | |||||||
\(422\) | −6.98792 | −0.340167 | ||||||||
\(423\) | −10.3177 | −0.501662 | ||||||||
\(424\) | −7.92154 | −0.384704 | ||||||||
\(425\) | 34.9976 | 1.69763 | ||||||||
\(426\) | −9.93661 | −0.481430 | ||||||||
\(427\) | 6.05429 | 0.292988 | ||||||||
\(428\) | −0.692021 | −0.0334501 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.83579 | −0.329651 | ||||||||
\(431\) | −4.02177 | −0.193722 | −0.0968609 | − | 0.995298i | \(-0.530880\pi\) | ||||
−0.0968609 | + | 0.995298i | \(0.530880\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −11.4470 | −0.550106 | −0.275053 | − | 0.961429i | \(-0.588695\pi\) | ||||
−0.275053 | + | 0.961429i | \(0.588695\pi\) | |||||||
\(434\) | −6.26875 | −0.300910 | ||||||||
\(435\) | 6.21983 | 0.298218 | ||||||||
\(436\) | 8.03923 | 0.385009 | ||||||||
\(437\) | −3.28036 | −0.156921 | ||||||||
\(438\) | −14.5918 | −0.697223 | ||||||||
\(439\) | −37.6450 | −1.79670 | −0.898349 | − | 0.439282i | \(-0.855233\pi\) | ||||
−0.898349 | + | 0.439282i | \(0.855233\pi\) | |||||||
\(440\) | 0.460107 | 0.0219348 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.7797 | −1.50990 | −0.754949 | − | 0.655783i | \(-0.772339\pi\) | ||||
−0.754949 | + | 0.655783i | \(0.772339\pi\) | |||||||
\(444\) | −11.1685 | −0.530035 | ||||||||
\(445\) | −0.314683 | −0.0149174 | ||||||||
\(446\) | −1.13467 | −0.0537282 | ||||||||
\(447\) | 12.0194 | 0.568497 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 1.82371 | 0.0860661 | 0.0430331 | − | 0.999074i | \(-0.486298\pi\) | ||||
0.0430331 | + | 0.999074i | \(0.486298\pi\) | |||||||
\(450\) | −4.52111 | −0.213127 | ||||||||
\(451\) | 7.80625 | 0.367582 | ||||||||
\(452\) | 12.5918 | 0.592268 | ||||||||
\(453\) | 19.3491 | 0.909101 | ||||||||
\(454\) | 5.26205 | 0.246960 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.89977 | 0.182624 | ||||||||
\(457\) | 11.0774 | 0.518179 | 0.259089 | − | 0.965853i | \(-0.416578\pi\) | ||||
0.259089 | + | 0.965853i | \(0.416578\pi\) | |||||||
\(458\) | 3.40821 | 0.159255 | ||||||||
\(459\) | 7.74094 | 0.361316 | ||||||||
\(460\) | −0.582105 | −0.0271408 | ||||||||
\(461\) | −3.82908 | −0.178338 | −0.0891691 | − | 0.996016i | \(-0.528421\pi\) | ||||
−0.0891691 | + | 0.996016i | \(0.528421\pi\) | |||||||
\(462\) | −0.664874 | −0.0309328 | ||||||||
\(463\) | 36.0737 | 1.67649 | 0.838243 | − | 0.545297i | \(-0.183583\pi\) | ||||
0.838243 | + | 0.545297i | \(0.183583\pi\) | |||||||
\(464\) | 8.98792 | 0.417254 | ||||||||
\(465\) | 4.33811 | 0.201175 | ||||||||
\(466\) | −23.6775 | −1.09684 | ||||||||
\(467\) | −38.3806 | −1.77604 | −0.888021 | − | 0.459803i | \(-0.847920\pi\) | ||||
−0.888021 | + | 0.459803i | \(0.847920\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.98792 | 0.137969 | ||||||||
\(470\) | 7.14005 | 0.329346 | ||||||||
\(471\) | 2.19567 | 0.101171 | ||||||||
\(472\) | 10.8901 | 0.501257 | ||||||||
\(473\) | −6.56763 | −0.301980 | ||||||||
\(474\) | 1.60388 | 0.0736684 | ||||||||
\(475\) | 17.6313 | 0.808979 | ||||||||
\(476\) | 7.74094 | 0.354805 | ||||||||
\(477\) | −7.92154 | −0.362703 | ||||||||
\(478\) | −20.2610 | −0.926716 | ||||||||
\(479\) | 11.3599 | 0.519046 | 0.259523 | − | 0.965737i | \(-0.416435\pi\) | ||||
0.259523 | + | 0.965737i | \(0.416435\pi\) | |||||||
\(480\) | 0.692021 | 0.0315863 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.0435405 | 0.00198322 | ||||||||
\(483\) | 0.841166 | 0.0382744 | ||||||||
\(484\) | −10.5579 | −0.479906 | ||||||||
\(485\) | −5.96243 | −0.270740 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 37.4577 | 1.69737 | 0.848686 | − | 0.528898i | \(-0.177395\pi\) | ||||
0.848686 | + | 0.528898i | \(0.177395\pi\) | |||||||
\(488\) | −6.05429 | −0.274065 | ||||||||
\(489\) | −19.3599 | −0.875484 | ||||||||
\(490\) | −0.692021 | −0.0312623 | ||||||||
\(491\) | 24.0200 | 1.08401 | 0.542003 | − | 0.840377i | \(-0.317666\pi\) | ||||
0.542003 | + | 0.840377i | \(0.317666\pi\) | |||||||
\(492\) | 11.7409 | 0.529322 | ||||||||
\(493\) | −69.5749 | −3.13350 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.460107 | 0.0206803 | ||||||||
\(496\) | 6.26875 | 0.281475 | ||||||||
\(497\) | −9.93661 | −0.445718 | ||||||||
\(498\) | −4.39612 | −0.196995 | ||||||||
\(499\) | 36.3043 | 1.62520 | 0.812601 | − | 0.582821i | \(-0.198051\pi\) | ||||
0.812601 | + | 0.582821i | \(0.198051\pi\) | |||||||
\(500\) | 6.58881 | 0.294661 | ||||||||
\(501\) | −20.5133 | −0.916468 | ||||||||
\(502\) | −27.3056 | −1.21871 | ||||||||
\(503\) | −15.6340 | −0.697086 | −0.348543 | − | 0.937293i | \(-0.613323\pi\) | ||||
−0.348543 | + | 0.937293i | \(0.613323\pi\) | |||||||
\(504\) | −1.00000 | −0.0445435 | ||||||||
\(505\) | −12.2650 | −0.545787 | ||||||||
\(506\) | −0.559270 | −0.0248626 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.76809 | 0.300285 | ||||||||
\(509\) | 12.0248 | 0.532988 | 0.266494 | − | 0.963837i | \(-0.414135\pi\) | ||||
0.266494 | + | 0.963837i | \(0.414135\pi\) | |||||||
\(510\) | −5.35690 | −0.237207 | ||||||||
\(511\) | −14.5918 | −0.645503 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 3.89977 | 0.172179 | ||||||||
\(514\) | 7.97584 | 0.351799 | ||||||||
\(515\) | 8.71751 | 0.384140 | ||||||||
\(516\) | −9.87800 | −0.434855 | ||||||||
\(517\) | 6.85995 | 0.301700 | ||||||||
\(518\) | −11.1685 | −0.490717 | ||||||||
\(519\) | −9.08815 | −0.398925 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.0054 | −0.701208 | −0.350604 | − | 0.936524i | \(-0.614024\pi\) | ||||
−0.350604 | + | 0.936524i | \(0.614024\pi\) | |||||||
\(522\) | 8.98792 | 0.393391 | ||||||||
\(523\) | 0.143768 | 0.00628654 | 0.00314327 | − | 0.999995i | \(-0.498999\pi\) | ||||
0.00314327 | + | 0.999995i | \(0.498999\pi\) | |||||||
\(524\) | 0.987918 | 0.0431574 | ||||||||
\(525\) | −4.52111 | −0.197317 | ||||||||
\(526\) | 9.37867 | 0.408929 | ||||||||
\(527\) | −48.5260 | −2.11383 | ||||||||
\(528\) | 0.664874 | 0.0289349 | ||||||||
\(529\) | −22.2924 | −0.969236 | ||||||||
\(530\) | 5.48188 | 0.238118 | ||||||||
\(531\) | 10.8901 | 0.472589 | ||||||||
\(532\) | 3.89977 | 0.169077 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.454731 | −0.0196781 | ||||||||
\(535\) | 0.478894 | 0.0207044 | ||||||||
\(536\) | −2.98792 | −0.129058 | ||||||||
\(537\) | −8.98792 | −0.387857 | ||||||||
\(538\) | 7.96077 | 0.343213 | ||||||||
\(539\) | −0.664874 | −0.0286382 | ||||||||
\(540\) | 0.692021 | 0.0297799 | ||||||||
\(541\) | −30.2717 | −1.30148 | −0.650742 | − | 0.759299i | \(-0.725542\pi\) | ||||
−0.650742 | + | 0.759299i | \(0.725542\pi\) | |||||||
\(542\) | 10.6377 | 0.456930 | ||||||||
\(543\) | 1.76941 | 0.0759328 | ||||||||
\(544\) | −7.74094 | −0.331890 | ||||||||
\(545\) | −5.56332 | −0.238306 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.7681 | 1.31555 | 0.657774 | − | 0.753215i | \(-0.271498\pi\) | ||||
0.657774 | + | 0.753215i | \(0.271498\pi\) | |||||||
\(548\) | −0.572417 | −0.0244524 | ||||||||
\(549\) | −6.05429 | −0.258391 | ||||||||
\(550\) | 3.00597 | 0.128175 | ||||||||
\(551\) | −35.0508 | −1.49322 | ||||||||
\(552\) | −0.841166 | −0.0358024 | ||||||||
\(553\) | 1.60388 | 0.0682037 | ||||||||
\(554\) | 26.4674 | 1.12449 | ||||||||
\(555\) | 7.72886 | 0.328072 | ||||||||
\(556\) | 16.7627 | 0.710897 | ||||||||
\(557\) | −5.01208 | −0.212369 | −0.106184 | − | 0.994346i | \(-0.533863\pi\) | ||||
−0.106184 | + | 0.994346i | \(0.533863\pi\) | |||||||
\(558\) | 6.26875 | 0.265377 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0.692021 | 0.0292432 | ||||||||
\(561\) | −5.14675 | −0.217296 | ||||||||
\(562\) | 5.60388 | 0.236385 | ||||||||
\(563\) | 23.3793 | 0.985318 | 0.492659 | − | 0.870222i | \(-0.336025\pi\) | ||||
0.492659 | + | 0.870222i | \(0.336025\pi\) | |||||||
\(564\) | 10.3177 | 0.434452 | ||||||||
\(565\) | −8.71379 | −0.366592 | ||||||||
\(566\) | −11.3351 | −0.476451 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 9.93661 | 0.416931 | ||||||||
\(569\) | 25.9168 | 1.08649 | 0.543243 | − | 0.839575i | \(-0.317196\pi\) | ||||
0.543243 | + | 0.839575i | \(0.317196\pi\) | |||||||
\(570\) | −2.69873 | −0.113037 | ||||||||
\(571\) | −19.3163 | −0.808364 | −0.404182 | − | 0.914679i | \(-0.632444\pi\) | ||||
−0.404182 | + | 0.914679i | \(0.632444\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.7657 | 0.700397 | ||||||||
\(574\) | 11.7409 | 0.490057 | ||||||||
\(575\) | −3.80300 | −0.158596 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 17.7802 | 0.740198 | 0.370099 | − | 0.928992i | \(-0.379324\pi\) | ||||
0.370099 | + | 0.928992i | \(0.379324\pi\) | |||||||
\(578\) | 42.9221 | 1.78533 | ||||||||
\(579\) | −16.9933 | −0.706217 | ||||||||
\(580\) | −6.21983 | −0.258264 | ||||||||
\(581\) | −4.39612 | −0.182382 | ||||||||
\(582\) | −8.61596 | −0.357143 | ||||||||
\(583\) | 5.26683 | 0.218130 | ||||||||
\(584\) | 14.5918 | 0.603813 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 20.7530 | 0.857299 | ||||||||
\(587\) | −2.95300 | −0.121883 | −0.0609417 | − | 0.998141i | \(-0.519410\pi\) | ||||
−0.0609417 | + | 0.998141i | \(0.519410\pi\) | |||||||
\(588\) | −1.00000 | −0.0412393 | ||||||||
\(589\) | −24.4467 | −1.00731 | ||||||||
\(590\) | −7.53617 | −0.310259 | ||||||||
\(591\) | 4.90946 | 0.201948 | ||||||||
\(592\) | 11.1685 | 0.459023 | ||||||||
\(593\) | −27.9758 | −1.14883 | −0.574415 | − | 0.818564i | \(-0.694770\pi\) | ||||
−0.574415 | + | 0.818564i | \(0.694770\pi\) | |||||||
\(594\) | 0.664874 | 0.0272801 | ||||||||
\(595\) | −5.35690 | −0.219611 | ||||||||
\(596\) | −12.0194 | −0.492333 | ||||||||
\(597\) | 14.9729 | 0.612798 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.53617 | −0.389637 | −0.194819 | − | 0.980839i | \(-0.562412\pi\) | ||||
−0.194819 | + | 0.980839i | \(0.562412\pi\) | |||||||
\(600\) | 4.52111 | 0.184573 | ||||||||
\(601\) | 21.9215 | 0.894198 | 0.447099 | − | 0.894484i | \(-0.352457\pi\) | ||||
0.447099 | + | 0.894484i | \(0.352457\pi\) | |||||||
\(602\) | −9.87800 | −0.402597 | ||||||||
\(603\) | −2.98792 | −0.121677 | ||||||||
\(604\) | −19.3491 | −0.787305 | ||||||||
\(605\) | 7.30632 | 0.297044 | ||||||||
\(606\) | −17.7235 | −0.719967 | ||||||||
\(607\) | −45.6625 | −1.85338 | −0.926691 | − | 0.375823i | \(-0.877360\pi\) | ||||
−0.926691 | + | 0.375823i | \(0.877360\pi\) | |||||||
\(608\) | −3.89977 | −0.158157 | ||||||||
\(609\) | 8.98792 | 0.364209 | ||||||||
\(610\) | 4.18970 | 0.169636 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −7.74094 | −0.312909 | ||||||||
\(613\) | 29.7071 | 1.19986 | 0.599929 | − | 0.800053i | \(-0.295195\pi\) | ||||
0.599929 | + | 0.800053i | \(0.295195\pi\) | |||||||
\(614\) | 14.5961 | 0.589051 | ||||||||
\(615\) | −8.12498 | −0.327631 | ||||||||
\(616\) | 0.664874 | 0.0267886 | ||||||||
\(617\) | −37.4034 | −1.50581 | −0.752903 | − | 0.658132i | \(-0.771347\pi\) | ||||
−0.752903 | + | 0.658132i | \(0.771347\pi\) | |||||||
\(618\) | 12.5972 | 0.506733 | ||||||||
\(619\) | −12.0000 | −0.482321 | −0.241160 | − | 0.970485i | \(-0.577528\pi\) | ||||
−0.241160 | + | 0.970485i | \(0.577528\pi\) | |||||||
\(620\) | −4.33811 | −0.174223 | ||||||||
\(621\) | −0.841166 | −0.0337548 | ||||||||
\(622\) | −1.82371 | −0.0731240 | ||||||||
\(623\) | −0.454731 | −0.0182184 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.0459 | 0.721837 | ||||||||
\(626\) | 34.6112 | 1.38334 | ||||||||
\(627\) | −2.59286 | −0.103549 | ||||||||
\(628\) | −2.19567 | −0.0876167 | ||||||||
\(629\) | −86.4548 | −3.44718 | ||||||||
\(630\) | 0.692021 | 0.0275708 | ||||||||
\(631\) | 17.3163 | 0.689353 | 0.344676 | − | 0.938722i | \(-0.387989\pi\) | ||||
0.344676 | + | 0.938722i | \(0.387989\pi\) | |||||||
\(632\) | −1.60388 | −0.0637987 | ||||||||
\(633\) | 6.98792 | 0.277745 | ||||||||
\(634\) | −4.49396 | −0.178478 | ||||||||
\(635\) | −4.68366 | −0.185865 | ||||||||
\(636\) | 7.92154 | 0.314110 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.97584 | −0.236586 | ||||||||
\(639\) | 9.93661 | 0.393086 | ||||||||
\(640\) | −0.692021 | −0.0273546 | ||||||||
\(641\) | −27.3599 | −1.08065 | −0.540325 | − | 0.841456i | \(-0.681699\pi\) | ||||
−0.540325 | + | 0.841456i | \(0.681699\pi\) | |||||||
\(642\) | 0.692021 | 0.0273119 | ||||||||
\(643\) | −19.1675 | −0.755891 | −0.377945 | − | 0.925828i | \(-0.623369\pi\) | ||||
−0.377945 | + | 0.925828i | \(0.623369\pi\) | |||||||
\(644\) | −0.841166 | −0.0331466 | ||||||||
\(645\) | 6.83579 | 0.269159 | ||||||||
\(646\) | 30.1879 | 1.18773 | ||||||||
\(647\) | −27.4711 | −1.08000 | −0.540001 | − | 0.841665i | \(-0.681576\pi\) | ||||
−0.540001 | + | 0.841665i | \(0.681576\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −7.24054 | −0.284216 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.26875 | 0.245692 | ||||||||
\(652\) | 19.3599 | 0.758191 | ||||||||
\(653\) | 43.2680 | 1.69321 | 0.846604 | − | 0.532223i | \(-0.178643\pi\) | ||||
0.846604 | + | 0.532223i | \(0.178643\pi\) | |||||||
\(654\) | −8.03923 | −0.314359 | ||||||||
\(655\) | −0.683661 | −0.0267128 | ||||||||
\(656\) | −11.7409 | −0.458407 | ||||||||
\(657\) | 14.5918 | 0.569280 | ||||||||
\(658\) | 10.3177 | 0.402225 | ||||||||
\(659\) | −19.8619 | −0.773709 | −0.386854 | − | 0.922141i | \(-0.626438\pi\) | ||||
−0.386854 | + | 0.922141i | \(0.626438\pi\) | |||||||
\(660\) | −0.460107 | −0.0179097 | ||||||||
\(661\) | −13.4625 | −0.523631 | −0.261815 | − | 0.965118i | \(-0.584321\pi\) | ||||
−0.261815 | + | 0.965118i | \(0.584321\pi\) | |||||||
\(662\) | −8.75733 | −0.340363 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.39612 | 0.170603 | ||||||||
\(665\) | −2.69873 | −0.104652 | ||||||||
\(666\) | 11.1685 | 0.432771 | ||||||||
\(667\) | 7.56033 | 0.292737 | ||||||||
\(668\) | 20.5133 | 0.793685 | ||||||||
\(669\) | 1.13467 | 0.0438689 | ||||||||
\(670\) | 2.06770 | 0.0798824 | ||||||||
\(671\) | 4.02535 | 0.155397 | ||||||||
\(672\) | 1.00000 | 0.0385758 | ||||||||
\(673\) | −19.2731 | −0.742922 | −0.371461 | − | 0.928449i | \(-0.621143\pi\) | ||||
−0.371461 | + | 0.928449i | \(0.621143\pi\) | |||||||
\(674\) | 12.6136 | 0.485856 | ||||||||
\(675\) | 4.52111 | 0.174017 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.5241 | −0.788805 | −0.394402 | − | 0.918938i | \(-0.629048\pi\) | ||||
−0.394402 | + | 0.918938i | \(0.629048\pi\) | |||||||
\(678\) | −12.5918 | −0.483585 | ||||||||
\(679\) | −8.61596 | −0.330650 | ||||||||
\(680\) | 5.35690 | 0.205428 | ||||||||
\(681\) | −5.26205 | −0.201642 | ||||||||
\(682\) | −4.16793 | −0.159598 | ||||||||
\(683\) | 4.07202 | 0.155811 | 0.0779057 | − | 0.996961i | \(-0.475177\pi\) | ||||
0.0779057 | + | 0.996961i | \(0.475177\pi\) | |||||||
\(684\) | −3.89977 | −0.149112 | ||||||||
\(685\) | 0.396125 | 0.0151351 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −3.40821 | −0.130031 | ||||||||
\(688\) | 9.87800 | 0.376595 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0.582105 | 0.0221604 | ||||||||
\(691\) | 35.3739 | 1.34569 | 0.672843 | − | 0.739785i | \(-0.265073\pi\) | ||||
0.672843 | + | 0.739785i | \(0.265073\pi\) | |||||||
\(692\) | 9.08815 | 0.345479 | ||||||||
\(693\) | 0.664874 | 0.0252565 | ||||||||
\(694\) | 19.4034 | 0.736544 | ||||||||
\(695\) | −11.6002 | −0.440019 | ||||||||
\(696\) | −8.98792 | −0.340686 | ||||||||
\(697\) | 90.8859 | 3.44255 | ||||||||
\(698\) | 0.415502 | 0.0157270 | ||||||||
\(699\) | 23.6775 | 0.895567 | ||||||||
\(700\) | 4.52111 | 0.170882 | ||||||||
\(701\) | −9.27280 | −0.350229 | −0.175114 | − | 0.984548i | \(-0.556030\pi\) | ||||
−0.175114 | + | 0.984548i | \(0.556030\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −43.5547 | −1.64270 | ||||||||
\(704\) | −0.664874 | −0.0250584 | ||||||||
\(705\) | −7.14005 | −0.268910 | ||||||||
\(706\) | 16.4450 | 0.618917 | ||||||||
\(707\) | −17.7235 | −0.666560 | ||||||||
\(708\) | −10.8901 | −0.409274 | ||||||||
\(709\) | −2.31527 | −0.0869520 | −0.0434760 | − | 0.999054i | \(-0.513843\pi\) | ||||
−0.0434760 | + | 0.999054i | \(0.513843\pi\) | |||||||
\(710\) | −6.87635 | −0.258065 | ||||||||
\(711\) | −1.60388 | −0.0601500 | ||||||||
\(712\) | 0.454731 | 0.0170417 | ||||||||
\(713\) | 5.27306 | 0.197478 | ||||||||
\(714\) | −7.74094 | −0.289697 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.98792 | 0.335894 | ||||||||
\(717\) | 20.2610 | 0.756660 | ||||||||
\(718\) | 6.61058 | 0.246705 | ||||||||
\(719\) | 0.987918 | 0.0368431 | 0.0184216 | − | 0.999830i | \(-0.494136\pi\) | ||||
0.0184216 | + | 0.999830i | \(0.494136\pi\) | |||||||
\(720\) | −0.692021 | −0.0257901 | ||||||||
\(721\) | 12.5972 | 0.469143 | ||||||||
\(722\) | −3.79178 | −0.141115 | ||||||||
\(723\) | −0.0435405 | −0.00161929 | ||||||||
\(724\) | −1.76941 | −0.0657597 | ||||||||
\(725\) | −40.6353 | −1.50916 | ||||||||
\(726\) | 10.5579 | 0.391842 | ||||||||
\(727\) | −23.1860 | −0.859920 | −0.429960 | − | 0.902848i | \(-0.641472\pi\) | ||||
−0.429960 | + | 0.902848i | \(0.641472\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −10.0978 | −0.373738 | ||||||||
\(731\) | −76.4650 | −2.82816 | ||||||||
\(732\) | 6.05429 | 0.223773 | ||||||||
\(733\) | 26.5435 | 0.980405 | 0.490203 | − | 0.871608i | \(-0.336923\pi\) | ||||
0.490203 | + | 0.871608i | \(0.336923\pi\) | |||||||
\(734\) | 15.5773 | 0.574969 | ||||||||
\(735\) | 0.692021 | 0.0255256 | ||||||||
\(736\) | 0.841166 | 0.0310058 | ||||||||
\(737\) | 1.98659 | 0.0731770 | ||||||||
\(738\) | −11.7409 | −0.432190 | ||||||||
\(739\) | 19.3491 | 0.711769 | 0.355885 | − | 0.934530i | \(-0.384180\pi\) | ||||
0.355885 | + | 0.934530i | \(0.384180\pi\) | |||||||
\(740\) | −7.72886 | −0.284118 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.92154 | 0.290809 | ||||||||
\(743\) | −51.8437 | −1.90196 | −0.950980 | − | 0.309252i | \(-0.899921\pi\) | ||||
−0.950980 | + | 0.309252i | \(0.899921\pi\) | |||||||
\(744\) | −6.26875 | −0.229824 | ||||||||
\(745\) | 8.31767 | 0.304736 | ||||||||
\(746\) | −1.81940 | −0.0666128 | ||||||||
\(747\) | 4.39612 | 0.160846 | ||||||||
\(748\) | 5.14675 | 0.188184 | ||||||||
\(749\) | 0.692021 | 0.0252859 | ||||||||
\(750\) | −6.58881 | −0.240589 | ||||||||
\(751\) | −16.9095 | −0.617035 | −0.308517 | − | 0.951219i | \(-0.599833\pi\) | ||||
−0.308517 | + | 0.951219i | \(0.599833\pi\) | |||||||
\(752\) | −10.3177 | −0.376247 | ||||||||
\(753\) | 27.3056 | 0.995071 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.3900 | 0.487312 | ||||||||
\(756\) | 1.00000 | 0.0363696 | ||||||||
\(757\) | −23.5297 | −0.855203 | −0.427601 | − | 0.903967i | \(-0.640641\pi\) | ||||
−0.427601 | + | 0.903967i | \(0.640641\pi\) | |||||||
\(758\) | −7.53617 | −0.273726 | ||||||||
\(759\) | 0.559270 | 0.0203002 | ||||||||
\(760\) | 2.69873 | 0.0978931 | ||||||||
\(761\) | −9.60627 | −0.348227 | −0.174113 | − | 0.984726i | \(-0.555706\pi\) | ||||
−0.174113 | + | 0.984726i | \(0.555706\pi\) | |||||||
\(762\) | −6.76809 | −0.245182 | ||||||||
\(763\) | −8.03923 | −0.291040 | ||||||||
\(764\) | −16.7657 | −0.606561 | ||||||||
\(765\) | 5.35690 | 0.193679 | ||||||||
\(766\) | 3.78017 | 0.136583 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −2.29829 | −0.0828785 | −0.0414392 | − | 0.999141i | \(-0.513194\pi\) | ||||
−0.0414392 | + | 0.999141i | \(0.513194\pi\) | |||||||
\(770\) | −0.460107 | −0.0165811 | ||||||||
\(771\) | −7.97584 | −0.287243 | ||||||||
\(772\) | 16.9933 | 0.611602 | ||||||||
\(773\) | 10.2828 | 0.369845 | 0.184922 | − | 0.982753i | \(-0.440797\pi\) | ||||
0.184922 | + | 0.982753i | \(0.440797\pi\) | |||||||
\(774\) | 9.87800 | 0.355057 | ||||||||
\(775\) | −28.3417 | −1.01806 | ||||||||
\(776\) | 8.61596 | 0.309295 | ||||||||
\(777\) | 11.1685 | 0.400669 | ||||||||
\(778\) | 5.01208 | 0.179692 | ||||||||
\(779\) | 45.7870 | 1.64049 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.60660 | −0.236403 | ||||||||
\(782\) | −6.51142 | −0.232848 | ||||||||
\(783\) | −8.98792 | −0.321202 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 1.51945 | 0.0542315 | ||||||||
\(786\) | −0.987918 | −0.0352379 | ||||||||
\(787\) | −26.2398 | −0.935348 | −0.467674 | − | 0.883901i | \(-0.654908\pi\) | ||||
−0.467674 | + | 0.883901i | \(0.654908\pi\) | |||||||
\(788\) | −4.90946 | −0.174892 | ||||||||
\(789\) | −9.37867 | −0.333889 | ||||||||
\(790\) | 1.10992 | 0.0394890 | ||||||||
\(791\) | −12.5918 | −0.447713 | ||||||||
\(792\) | −0.664874 | −0.0236253 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −5.05562 | −0.179417 | ||||||||
\(795\) | −5.48188 | −0.194422 | ||||||||
\(796\) | −14.9729 | −0.530699 | ||||||||
\(797\) | −10.6203 | −0.376189 | −0.188095 | − | 0.982151i | \(-0.560231\pi\) | ||||
−0.188095 | + | 0.982151i | \(0.560231\pi\) | |||||||
\(798\) | −3.89977 | −0.138050 | ||||||||
\(799\) | 79.8684 | 2.82554 | ||||||||
\(800\) | −4.52111 | −0.159845 | ||||||||
\(801\) | 0.454731 | 0.0160671 | ||||||||
\(802\) | 38.8745 | 1.37271 | ||||||||
\(803\) | −9.70171 | −0.342366 | ||||||||
\(804\) | 2.98792 | 0.105376 | ||||||||
\(805\) | 0.582105 | 0.0205165 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.96077 | −0.280232 | ||||||||
\(808\) | 17.7235 | 0.623510 | ||||||||
\(809\) | −32.0435 | −1.12659 | −0.563295 | − | 0.826256i | \(-0.690467\pi\) | ||||
−0.563295 | + | 0.826256i | \(0.690467\pi\) | |||||||
\(810\) | −0.692021 | −0.0243152 | ||||||||
\(811\) | −25.9909 | −0.912664 | −0.456332 | − | 0.889810i | \(-0.650837\pi\) | ||||
−0.456332 | + | 0.889810i | \(0.650837\pi\) | |||||||
\(812\) | −8.98792 | −0.315414 | ||||||||
\(813\) | −10.6377 | −0.373081 | ||||||||
\(814\) | −7.42566 | −0.260269 | ||||||||
\(815\) | −13.3975 | −0.469292 | ||||||||
\(816\) | 7.74094 | 0.270987 | ||||||||
\(817\) | −38.5220 | −1.34771 | ||||||||
\(818\) | 32.6461 | 1.14144 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.12498 | 0.283737 | ||||||||
\(821\) | −34.5133 | −1.20452 | −0.602262 | − | 0.798299i | \(-0.705734\pi\) | ||||
−0.602262 | + | 0.798299i | \(0.705734\pi\) | |||||||
\(822\) | 0.572417 | 0.0199653 | ||||||||
\(823\) | 9.84309 | 0.343108 | 0.171554 | − | 0.985175i | \(-0.445121\pi\) | ||||
0.171554 | + | 0.985175i | \(0.445121\pi\) | |||||||
\(824\) | −12.5972 | −0.438843 | ||||||||
\(825\) | −3.00597 | −0.104654 | ||||||||
\(826\) | −10.8901 | −0.378914 | ||||||||
\(827\) | 16.2892 | 0.566431 | 0.283215 | − | 0.959056i | \(-0.408599\pi\) | ||||
0.283215 | + | 0.959056i | \(0.408599\pi\) | |||||||
\(828\) | 0.841166 | 0.0292326 | ||||||||
\(829\) | 13.9323 | 0.483889 | 0.241944 | − | 0.970290i | \(-0.422215\pi\) | ||||
0.241944 | + | 0.970290i | \(0.422215\pi\) | |||||||
\(830\) | −3.04221 | −0.105597 | ||||||||
\(831\) | −26.4674 | −0.918144 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.74094 | −0.268208 | ||||||||
\(834\) | −16.7627 | −0.580445 | ||||||||
\(835\) | −14.1957 | −0.491261 | ||||||||
\(836\) | 2.59286 | 0.0896759 | ||||||||
\(837\) | −6.26875 | −0.216680 | ||||||||
\(838\) | 23.3250 | 0.805747 | ||||||||
\(839\) | −6.49396 | −0.224196 | −0.112098 | − | 0.993697i | \(-0.535757\pi\) | ||||
−0.112098 | + | 0.993697i | \(0.535757\pi\) | |||||||
\(840\) | −0.692021 | −0.0238770 | ||||||||
\(841\) | 51.7827 | 1.78561 | ||||||||
\(842\) | 18.2282 | 0.628185 | ||||||||
\(843\) | −5.60388 | −0.193008 | ||||||||
\(844\) | −6.98792 | −0.240534 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −10.3177 | −0.354729 | ||||||||
\(847\) | 10.5579 | 0.362775 | ||||||||
\(848\) | −7.92154 | −0.272027 | ||||||||
\(849\) | 11.3351 | 0.389021 | ||||||||
\(850\) | 34.9976 | 1.20041 | ||||||||
\(851\) | 9.39459 | 0.322042 | ||||||||
\(852\) | −9.93661 | −0.340423 | ||||||||
\(853\) | 45.1099 | 1.54453 | 0.772267 | − | 0.635298i | \(-0.219123\pi\) | ||||
0.772267 | + | 0.635298i | \(0.219123\pi\) | |||||||
\(854\) | 6.05429 | 0.207174 | ||||||||
\(855\) | 2.69873 | 0.0922945 | ||||||||
\(856\) | −0.692021 | −0.0236528 | ||||||||
\(857\) | −4.66189 | −0.159247 | −0.0796236 | − | 0.996825i | \(-0.525372\pi\) | ||||
−0.0796236 | + | 0.996825i | \(0.525372\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.6364 | −1.28414 | −0.642069 | − | 0.766647i | \(-0.721924\pi\) | ||||
−0.642069 | + | 0.766647i | \(0.721924\pi\) | |||||||
\(860\) | −6.83579 | −0.233098 | ||||||||
\(861\) | −11.7409 | −0.400130 | ||||||||
\(862\) | −4.02177 | −0.136982 | ||||||||
\(863\) | 14.1021 | 0.480043 | 0.240021 | − | 0.970768i | \(-0.422846\pi\) | ||||
0.240021 | + | 0.970768i | \(0.422846\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −6.28919 | −0.213839 | ||||||||
\(866\) | −11.4470 | −0.388984 | ||||||||
\(867\) | −42.9221 | −1.45771 | ||||||||
\(868\) | −6.26875 | −0.212775 | ||||||||
\(869\) | 1.06638 | 0.0361743 | ||||||||
\(870\) | 6.21983 | 0.210872 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 8.03923 | 0.272243 | ||||||||
\(873\) | 8.61596 | 0.291606 | ||||||||
\(874\) | −3.28036 | −0.110960 | ||||||||
\(875\) | −6.58881 | −0.222742 | ||||||||
\(876\) | −14.5918 | −0.493011 | ||||||||
\(877\) | −8.51765 | −0.287621 | −0.143810 | − | 0.989605i | \(-0.545936\pi\) | ||||
−0.143810 | + | 0.989605i | \(0.545936\pi\) | |||||||
\(878\) | −37.6450 | −1.27046 | ||||||||
\(879\) | −20.7530 | −0.699982 | ||||||||
\(880\) | 0.460107 | 0.0155102 | ||||||||
\(881\) | 5.84548 | 0.196939 | 0.0984696 | − | 0.995140i | \(-0.468605\pi\) | ||||
0.0984696 | + | 0.995140i | \(0.468605\pi\) | |||||||
\(882\) | 1.00000 | 0.0336718 | ||||||||
\(883\) | −26.8358 | −0.903096 | −0.451548 | − | 0.892247i | \(-0.649128\pi\) | ||||
−0.451548 | + | 0.892247i | \(0.649128\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.53617 | 0.253326 | ||||||||
\(886\) | −31.7797 | −1.06766 | ||||||||
\(887\) | −41.9758 | −1.40941 | −0.704705 | − | 0.709500i | \(-0.748921\pi\) | ||||
−0.704705 | + | 0.709500i | \(0.748921\pi\) | |||||||
\(888\) | −11.1685 | −0.374791 | ||||||||
\(889\) | −6.76809 | −0.226994 | ||||||||
\(890\) | −0.314683 | −0.0105482 | ||||||||
\(891\) | −0.664874 | −0.0222741 | ||||||||
\(892\) | −1.13467 | −0.0379916 | ||||||||
\(893\) | 40.2366 | 1.34646 | ||||||||
\(894\) | 12.0194 | 0.401988 | ||||||||
\(895\) | −6.21983 | −0.207906 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.82371 | 0.0608579 | ||||||||
\(899\) | 56.3430 | 1.87914 | ||||||||
\(900\) | −4.52111 | −0.150704 | ||||||||
\(901\) | 61.3202 | 2.04287 | ||||||||
\(902\) | 7.80625 | 0.259920 | ||||||||
\(903\) | 9.87800 | 0.328719 | ||||||||
\(904\) | 12.5918 | 0.418797 | ||||||||
\(905\) | 1.22447 | 0.0407028 | ||||||||
\(906\) | 19.3491 | 0.642832 | ||||||||
\(907\) | −34.3043 | −1.13905 | −0.569527 | − | 0.821973i | \(-0.692874\pi\) | ||||
−0.569527 | + | 0.821973i | \(0.692874\pi\) | |||||||
\(908\) | 5.26205 | 0.174627 | ||||||||
\(909\) | 17.7235 | 0.587851 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.4179 | −0.543949 | −0.271975 | − | 0.962304i | \(-0.587677\pi\) | ||||
−0.271975 | + | 0.962304i | \(0.587677\pi\) | |||||||
\(912\) | 3.89977 | 0.129134 | ||||||||
\(913\) | −2.92287 | −0.0967329 | ||||||||
\(914\) | 11.0774 | 0.366408 | ||||||||
\(915\) | −4.18970 | −0.138507 | ||||||||
\(916\) | 3.40821 | 0.112610 | ||||||||
\(917\) | −0.987918 | −0.0326239 | ||||||||
\(918\) | 7.74094 | 0.255489 | ||||||||
\(919\) | −44.9697 | −1.48341 | −0.741707 | − | 0.670724i | \(-0.765984\pi\) | ||||
−0.741707 | + | 0.670724i | \(0.765984\pi\) | |||||||
\(920\) | −0.582105 | −0.0191914 | ||||||||
\(921\) | −14.5961 | −0.480958 | ||||||||
\(922\) | −3.82908 | −0.126104 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −0.664874 | −0.0218728 | ||||||||
\(925\) | −50.4941 | −1.66024 | ||||||||
\(926\) | 36.0737 | 1.18545 | ||||||||
\(927\) | −12.5972 | −0.413745 | ||||||||
\(928\) | 8.98792 | 0.295043 | ||||||||
\(929\) | −16.5724 | −0.543723 | −0.271862 | − | 0.962336i | \(-0.587639\pi\) | ||||
−0.271862 | + | 0.962336i | \(0.587639\pi\) | |||||||
\(930\) | 4.33811 | 0.142252 | ||||||||
\(931\) | −3.89977 | −0.127810 | ||||||||
\(932\) | −23.6775 | −0.775584 | ||||||||
\(933\) | 1.82371 | 0.0597055 | ||||||||
\(934\) | −38.3806 | −1.25585 | ||||||||
\(935\) | −3.56166 | −0.116479 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50.5435 | 1.65118 | 0.825592 | − | 0.564268i | \(-0.190842\pi\) | ||||
0.825592 | + | 0.564268i | \(0.190842\pi\) | |||||||
\(938\) | 2.98792 | 0.0975590 | ||||||||
\(939\) | −34.6112 | −1.12949 | ||||||||
\(940\) | 7.14005 | 0.232883 | ||||||||
\(941\) | 37.9191 | 1.23613 | 0.618064 | − | 0.786127i | \(-0.287917\pi\) | ||||
0.618064 | + | 0.786127i | \(0.287917\pi\) | |||||||
\(942\) | 2.19567 | 0.0715388 | ||||||||
\(943\) | −9.87608 | −0.321610 | ||||||||
\(944\) | 10.8901 | 0.354442 | ||||||||
\(945\) | −0.692021 | −0.0225115 | ||||||||
\(946\) | −6.56763 | −0.213532 | ||||||||
\(947\) | 10.2067 | 0.331673 | 0.165836 | − | 0.986153i | \(-0.446968\pi\) | ||||
0.165836 | + | 0.986153i | \(0.446968\pi\) | |||||||
\(948\) | 1.60388 | 0.0520915 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 17.6313 | 0.572034 | ||||||||
\(951\) | 4.49396 | 0.145727 | ||||||||
\(952\) | 7.74094 | 0.250885 | ||||||||
\(953\) | 49.6292 | 1.60765 | 0.803824 | − | 0.594867i | \(-0.202795\pi\) | ||||
0.803824 | + | 0.594867i | \(0.202795\pi\) | |||||||
\(954\) | −7.92154 | −0.256469 | ||||||||
\(955\) | 11.6022 | 0.375439 | ||||||||
\(956\) | −20.2610 | −0.655287 | ||||||||
\(957\) | 5.97584 | 0.193171 | ||||||||
\(958\) | 11.3599 | 0.367021 | ||||||||
\(959\) | 0.572417 | 0.0184843 | ||||||||
\(960\) | 0.692021 | 0.0223349 | ||||||||
\(961\) | 8.29722 | 0.267652 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.692021 | −0.0223001 | ||||||||
\(964\) | 0.0435405 | 0.00140235 | ||||||||
\(965\) | −11.7597 | −0.378559 | ||||||||
\(966\) | 0.841166 | 0.0270641 | ||||||||
\(967\) | 38.5461 | 1.23956 | 0.619780 | − | 0.784776i | \(-0.287222\pi\) | ||||
0.619780 | + | 0.784776i | \(0.287222\pi\) | |||||||
\(968\) | −10.5579 | −0.339345 | ||||||||
\(969\) | −30.1879 | −0.969775 | ||||||||
\(970\) | −5.96243 | −0.191442 | ||||||||
\(971\) | −6.45904 | −0.207281 | −0.103640 | − | 0.994615i | \(-0.533049\pi\) | ||||
−0.103640 | + | 0.994615i | \(0.533049\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −16.7627 | −0.537388 | ||||||||
\(974\) | 37.4577 | 1.20022 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.05429 | −0.193793 | ||||||||
\(977\) | 9.85649 | 0.315337 | 0.157669 | − | 0.987492i | \(-0.449602\pi\) | ||||
0.157669 | + | 0.987492i | \(0.449602\pi\) | |||||||
\(978\) | −19.3599 | −0.619061 | ||||||||
\(979\) | −0.302339 | −0.00966279 | ||||||||
\(980\) | −0.692021 | −0.0221058 | ||||||||
\(981\) | 8.03923 | 0.256673 | ||||||||
\(982\) | 24.0200 | 0.766508 | ||||||||
\(983\) | 17.2728 | 0.550917 | 0.275458 | − | 0.961313i | \(-0.411170\pi\) | ||||
0.275458 | + | 0.961313i | \(0.411170\pi\) | |||||||
\(984\) | 11.7409 | 0.374287 | ||||||||
\(985\) | 3.39745 | 0.108252 | ||||||||
\(986\) | −69.5749 | −2.21572 | ||||||||
\(987\) | −10.3177 | −0.328415 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.30904 | 0.264212 | ||||||||
\(990\) | 0.460107 | 0.0146232 | ||||||||
\(991\) | 21.0992 | 0.670237 | 0.335118 | − | 0.942176i | \(-0.391224\pi\) | ||||
0.335118 | + | 0.942176i | \(0.391224\pi\) | |||||||
\(992\) | 6.26875 | 0.199033 | ||||||||
\(993\) | 8.75733 | 0.277906 | ||||||||
\(994\) | −9.93661 | −0.315170 | ||||||||
\(995\) | 10.3615 | 0.328483 | ||||||||
\(996\) | −4.39612 | −0.139297 | ||||||||
\(997\) | 4.86113 | 0.153954 | 0.0769768 | − | 0.997033i | \(-0.475473\pi\) | ||||
0.0769768 | + | 0.997033i | \(0.475473\pi\) | |||||||
\(998\) | 36.3043 | 1.14919 | ||||||||
\(999\) | −11.1685 | −0.353356 |
(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 | 7098.2.a.ck.1.1 | yes | 3 | |
13.12 | even | 2 | 7098.2.a.cb.1.3 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7098.2.a.cb.1.3 | ✓ | 3 | 13.12 | even | 2 | ||
7098.2.a.ck.1.1 | yes | 3 | 1.1 | even | 1 | trivial |