Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1850,2,Mod(1,1850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1850, 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("1850.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1850 = 2 \cdot 5^{2} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1850.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: | \(14.7723243739\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.1791440.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{5} - 9x^{3} + 13x - 4 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 370) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-2.62545\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1850.1 |
$q$-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 | ||||||||
\(3\) | 2.62545 | 1.51581 | 0.757903 | − | 0.652367i | \(-0.226224\pi\) | ||||
0.757903 | + | 0.652367i | \(0.226224\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.62545 | 1.07184 | ||||||||
\(7\) | −1.83227 | −0.692532 | −0.346266 | − | 0.938136i | \(-0.612551\pi\) | ||||
−0.346266 | + | 0.938136i | \(0.612551\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 3.89300 | 1.29767 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.19017 | 1.26338 | 0.631692 | − | 0.775219i | \(-0.282361\pi\) | ||||
0.631692 | + | 0.775219i | \(0.282361\pi\) | |||||||
\(12\) | 2.62545 | 0.757903 | ||||||||
\(13\) | −0.369454 | −0.102468 | −0.0512340 | − | 0.998687i | \(-0.516315\pi\) | ||||
−0.0512340 | + | 0.998687i | \(0.516315\pi\) | |||||||
\(14\) | −1.83227 | −0.489694 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.08317 | −1.23285 | −0.616425 | − | 0.787414i | \(-0.711420\pi\) | ||||
−0.616425 | + | 0.787414i | \(0.711420\pi\) | |||||||
\(18\) | 3.89300 | 0.917589 | ||||||||
\(19\) | 3.55963 | 0.816634 | 0.408317 | − | 0.912840i | \(-0.366116\pi\) | ||||
0.408317 | + | 0.912840i | \(0.366116\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.81053 | −1.04974 | ||||||||
\(22\) | 4.19017 | 0.893348 | ||||||||
\(23\) | 5.62036 | 1.17193 | 0.585963 | − | 0.810338i | \(-0.300716\pi\) | ||||
0.585963 | + | 0.810338i | \(0.300716\pi\) | |||||||
\(24\) | 2.62545 | 0.535918 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.369454 | −0.0724559 | ||||||||
\(27\) | 2.34453 | 0.451205 | ||||||||
\(28\) | −1.83227 | −0.346266 | ||||||||
\(29\) | 1.20681 | 0.224100 | 0.112050 | − | 0.993703i | \(-0.464258\pi\) | ||||
0.112050 | + | 0.993703i | \(0.464258\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.1030 | 1.81455 | 0.907276 | − | 0.420535i | \(-0.138158\pi\) | ||||
0.907276 | + | 0.420535i | \(0.138158\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 11.0011 | 1.91504 | ||||||||
\(34\) | −5.08317 | −0.871757 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.89300 | 0.648833 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | 3.55963 | 0.577447 | ||||||||
\(39\) | −0.969984 | −0.155322 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.01447 | −1.25165 | −0.625825 | − | 0.779964i | \(-0.715238\pi\) | ||||
−0.625825 | + | 0.779964i | \(0.715238\pi\) | |||||||
\(42\) | −4.81053 | −0.742281 | ||||||||
\(43\) | −2.27264 | −0.346575 | −0.173287 | − | 0.984871i | \(-0.555439\pi\) | ||||
−0.173287 | + | 0.984871i | \(0.555439\pi\) | |||||||
\(44\) | 4.19017 | 0.631692 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.62036 | 0.828677 | ||||||||
\(47\) | 10.9154 | 1.59218 | 0.796090 | − | 0.605178i | \(-0.206898\pi\) | ||||
0.796090 | + | 0.605178i | \(0.206898\pi\) | |||||||
\(48\) | 2.62545 | 0.378951 | ||||||||
\(49\) | −3.64280 | −0.520400 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −13.3456 | −1.86876 | ||||||||
\(52\) | −0.369454 | −0.0512340 | ||||||||
\(53\) | −9.94355 | −1.36585 | −0.682926 | − | 0.730488i | \(-0.739293\pi\) | ||||
−0.682926 | + | 0.730488i | \(0.739293\pi\) | |||||||
\(54\) | 2.34453 | 0.319050 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.83227 | −0.244847 | ||||||||
\(57\) | 9.34563 | 1.23786 | ||||||||
\(58\) | 1.20681 | 0.158463 | ||||||||
\(59\) | −5.34563 | −0.695941 | −0.347971 | − | 0.937505i | \(-0.613129\pi\) | ||||
−0.347971 | + | 0.937505i | \(0.613129\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.79428 | −1.25403 | −0.627015 | − | 0.779008i | \(-0.715723\pi\) | ||||
−0.627015 | + | 0.779008i | \(0.715723\pi\) | |||||||
\(62\) | 10.1030 | 1.28308 | ||||||||
\(63\) | −7.13302 | −0.898676 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 11.0011 | 1.35414 | ||||||||
\(67\) | 1.85073 | 0.226103 | 0.113052 | − | 0.993589i | \(-0.463937\pi\) | ||||
0.113052 | + | 0.993589i | \(0.463937\pi\) | |||||||
\(68\) | −5.08317 | −0.616425 | ||||||||
\(69\) | 14.7560 | 1.77641 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.86038 | 0.339464 | 0.169732 | − | 0.985490i | \(-0.445710\pi\) | ||||
0.169732 | + | 0.985490i | \(0.445710\pi\) | |||||||
\(72\) | 3.89300 | 0.458795 | ||||||||
\(73\) | −8.09942 | −0.947966 | −0.473983 | − | 0.880534i | \(-0.657184\pi\) | ||||
−0.473983 | + | 0.880534i | \(0.657184\pi\) | |||||||
\(74\) | 1.00000 | 0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.55963 | 0.408317 | ||||||||
\(77\) | −7.67751 | −0.874934 | ||||||||
\(78\) | −0.969984 | −0.109829 | ||||||||
\(79\) | 6.06361 | 0.682209 | 0.341105 | − | 0.940025i | \(-0.389199\pi\) | ||||
0.341105 | + | 0.940025i | \(0.389199\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.52355 | −0.613727 | ||||||||
\(82\) | −8.01447 | −0.885050 | ||||||||
\(83\) | −8.93200 | −0.980414 | −0.490207 | − | 0.871606i | \(-0.663079\pi\) | ||||
−0.490207 | + | 0.871606i | \(0.663079\pi\) | |||||||
\(84\) | −4.81053 | −0.524872 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.27264 | −0.245065 | ||||||||
\(87\) | 3.16843 | 0.339692 | ||||||||
\(88\) | 4.19017 | 0.446674 | ||||||||
\(89\) | 11.4773 | 1.21659 | 0.608295 | − | 0.793711i | \(-0.291854\pi\) | ||||
0.608295 | + | 0.793711i | \(0.291854\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.676938 | 0.0709624 | ||||||||
\(92\) | 5.62036 | 0.585963 | ||||||||
\(93\) | 26.5249 | 2.75051 | ||||||||
\(94\) | 10.9154 | 1.12584 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.62545 | 0.267959 | ||||||||
\(97\) | 6.05864 | 0.615162 | 0.307581 | − | 0.951522i | \(-0.400480\pi\) | ||||
0.307581 | + | 0.951522i | \(0.400480\pi\) | |||||||
\(98\) | −3.64280 | −0.367978 | ||||||||
\(99\) | 16.3123 | 1.63945 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.96528 | 0.494064 | 0.247032 | − | 0.969007i | \(-0.420545\pi\) | ||||
0.247032 | + | 0.969007i | \(0.420545\pi\) | |||||||
\(102\) | −13.3456 | −1.32141 | ||||||||
\(103\) | −7.33338 | −0.722579 | −0.361289 | − | 0.932454i | \(-0.617663\pi\) | ||||
−0.361289 | + | 0.932454i | \(0.617663\pi\) | |||||||
\(104\) | −0.369454 | −0.0362279 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.94355 | −0.965803 | ||||||||
\(107\) | −8.21182 | −0.793867 | −0.396933 | − | 0.917847i | \(-0.629926\pi\) | ||||
−0.396933 | + | 0.917847i | \(0.629926\pi\) | |||||||
\(108\) | 2.34453 | 0.225603 | ||||||||
\(109\) | −20.5503 | −1.96836 | −0.984179 | − | 0.177175i | \(-0.943304\pi\) | ||||
−0.984179 | + | 0.177175i | \(0.943304\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.62545 | 0.249197 | ||||||||
\(112\) | −1.83227 | −0.173133 | ||||||||
\(113\) | −0.652984 | −0.0614276 | −0.0307138 | − | 0.999528i | \(-0.509778\pi\) | ||||
−0.0307138 | + | 0.999528i | \(0.509778\pi\) | |||||||
\(114\) | 9.34563 | 0.875298 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.20681 | 0.112050 | ||||||||
\(117\) | −1.43828 | −0.132969 | ||||||||
\(118\) | −5.34563 | −0.492105 | ||||||||
\(119\) | 9.31373 | 0.853788 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.55754 | 0.596140 | ||||||||
\(122\) | −9.79428 | −0.886733 | ||||||||
\(123\) | −21.0416 | −1.89726 | ||||||||
\(124\) | 10.1030 | 0.907276 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −7.13302 | −0.635460 | ||||||||
\(127\) | −19.2856 | −1.71132 | −0.855660 | − | 0.517539i | \(-0.826848\pi\) | ||||
−0.855660 | + | 0.517539i | \(0.826848\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −5.96671 | −0.525340 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.82072 | −0.770670 | −0.385335 | − | 0.922777i | \(-0.625914\pi\) | ||||
−0.385335 | + | 0.922777i | \(0.625914\pi\) | |||||||
\(132\) | 11.0011 | 0.957522 | ||||||||
\(133\) | −6.52218 | −0.565545 | ||||||||
\(134\) | 1.85073 | 0.159879 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.08317 | −0.435878 | ||||||||
\(137\) | 4.66126 | 0.398239 | 0.199119 | − | 0.979975i | \(-0.436192\pi\) | ||||
0.199119 | + | 0.979975i | \(0.436192\pi\) | |||||||
\(138\) | 14.7560 | 1.25611 | ||||||||
\(139\) | 16.4050 | 1.39145 | 0.695727 | − | 0.718306i | \(-0.255082\pi\) | ||||
0.695727 | + | 0.718306i | \(0.255082\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 28.6580 | 2.41344 | ||||||||
\(142\) | 2.86038 | 0.240037 | ||||||||
\(143\) | −1.54808 | −0.129457 | ||||||||
\(144\) | 3.89300 | 0.324417 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.09942 | −0.670313 | ||||||||
\(147\) | −9.56399 | −0.788825 | ||||||||
\(148\) | 1.00000 | 0.0821995 | ||||||||
\(149\) | −5.86259 | −0.480282 | −0.240141 | − | 0.970738i | \(-0.577194\pi\) | ||||
−0.240141 | + | 0.970738i | \(0.577194\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.1460 | 1.06981 | 0.534903 | − | 0.844913i | \(-0.320348\pi\) | ||||
0.534903 | + | 0.844913i | \(0.320348\pi\) | |||||||
\(152\) | 3.55963 | 0.288724 | ||||||||
\(153\) | −19.7888 | −1.59983 | ||||||||
\(154\) | −7.67751 | −0.618672 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.969984 | −0.0776609 | ||||||||
\(157\) | −7.33629 | −0.585500 | −0.292750 | − | 0.956189i | \(-0.594570\pi\) | ||||
−0.292750 | + | 0.956189i | \(0.594570\pi\) | |||||||
\(158\) | 6.06361 | 0.482395 | ||||||||
\(159\) | −26.1063 | −2.07037 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.2980 | −0.811596 | ||||||||
\(162\) | −5.52355 | −0.433971 | ||||||||
\(163\) | −18.7968 | −1.47228 | −0.736138 | − | 0.676831i | \(-0.763353\pi\) | ||||
−0.736138 | + | 0.676831i | \(0.763353\pi\) | |||||||
\(164\) | −8.01447 | −0.625825 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.93200 | −0.693257 | ||||||||
\(167\) | −5.92772 | −0.458700 | −0.229350 | − | 0.973344i | \(-0.573660\pi\) | ||||
−0.229350 | + | 0.973344i | \(0.573660\pi\) | |||||||
\(168\) | −4.81053 | −0.371140 | ||||||||
\(169\) | −12.8635 | −0.989500 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 13.8576 | 1.05972 | ||||||||
\(172\) | −2.27264 | −0.173287 | ||||||||
\(173\) | 5.78242 | 0.439629 | 0.219815 | − | 0.975542i | \(-0.429455\pi\) | ||||
0.219815 | + | 0.975542i | \(0.429455\pi\) | |||||||
\(174\) | 3.16843 | 0.240198 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.19017 | 0.315846 | ||||||||
\(177\) | −14.0347 | −1.05491 | ||||||||
\(178\) | 11.4773 | 0.860259 | ||||||||
\(179\) | 7.13581 | 0.533355 | 0.266678 | − | 0.963786i | \(-0.414074\pi\) | ||||
0.266678 | + | 0.963786i | \(0.414074\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.5365 | 0.857503 | 0.428752 | − | 0.903422i | \(-0.358954\pi\) | ||||
0.428752 | + | 0.903422i | \(0.358954\pi\) | |||||||
\(182\) | 0.676938 | 0.0501780 | ||||||||
\(183\) | −25.7144 | −1.90086 | ||||||||
\(184\) | 5.62036 | 0.414338 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 26.5249 | 1.94490 | ||||||||
\(187\) | −21.2994 | −1.55756 | ||||||||
\(188\) | 10.9154 | 0.796090 | ||||||||
\(189\) | −4.29581 | −0.312474 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.6048 | −1.49091 | −0.745456 | − | 0.666555i | \(-0.767768\pi\) | ||||
−0.745456 | + | 0.666555i | \(0.767768\pi\) | |||||||
\(192\) | 2.62545 | 0.189476 | ||||||||
\(193\) | −26.1663 | −1.88349 | −0.941747 | − | 0.336321i | \(-0.890817\pi\) | ||||
−0.941747 | + | 0.336321i | \(0.890817\pi\) | |||||||
\(194\) | 6.05864 | 0.434985 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.64280 | −0.260200 | ||||||||
\(197\) | 14.6067 | 1.04069 | 0.520343 | − | 0.853957i | \(-0.325804\pi\) | ||||
0.520343 | + | 0.853957i | \(0.325804\pi\) | |||||||
\(198\) | 16.3123 | 1.15927 | ||||||||
\(199\) | 5.81275 | 0.412055 | 0.206027 | − | 0.978546i | \(-0.433946\pi\) | ||||
0.206027 | + | 0.978546i | \(0.433946\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.85901 | 0.342728 | ||||||||
\(202\) | 4.96528 | 0.349356 | ||||||||
\(203\) | −2.21121 | −0.155196 | ||||||||
\(204\) | −13.3456 | −0.934381 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −7.33338 | −0.510940 | ||||||||
\(207\) | 21.8801 | 1.52077 | ||||||||
\(208\) | −0.369454 | −0.0256170 | ||||||||
\(209\) | 14.9154 | 1.03172 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.0976 | 1.10821 | 0.554104 | − | 0.832448i | \(-0.313061\pi\) | ||||
0.554104 | + | 0.832448i | \(0.313061\pi\) | |||||||
\(212\) | −9.94355 | −0.682926 | ||||||||
\(213\) | 7.50978 | 0.514562 | ||||||||
\(214\) | −8.21182 | −0.561349 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.34453 | 0.159525 | ||||||||
\(217\) | −18.5114 | −1.25664 | ||||||||
\(218\) | −20.5503 | −1.39184 | ||||||||
\(219\) | −21.2646 | −1.43693 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.87800 | 0.126328 | ||||||||
\(222\) | 2.62545 | 0.176209 | ||||||||
\(223\) | 25.3608 | 1.69828 | 0.849142 | − | 0.528164i | \(-0.177119\pi\) | ||||
0.849142 | + | 0.528164i | \(0.177119\pi\) | |||||||
\(224\) | −1.83227 | −0.122423 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.652984 | −0.0434359 | ||||||||
\(227\) | −5.57339 | −0.369919 | −0.184960 | − | 0.982746i | \(-0.559215\pi\) | ||||
−0.184960 | + | 0.982746i | \(0.559215\pi\) | |||||||
\(228\) | 9.34563 | 0.618929 | ||||||||
\(229\) | 9.02035 | 0.596081 | 0.298041 | − | 0.954553i | \(-0.403667\pi\) | ||||
0.298041 | + | 0.954553i | \(0.403667\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −20.1569 | −1.32623 | ||||||||
\(232\) | 1.20681 | 0.0792313 | ||||||||
\(233\) | 11.8100 | 0.773696 | 0.386848 | − | 0.922144i | \(-0.373564\pi\) | ||||
0.386848 | + | 0.922144i | \(0.373564\pi\) | |||||||
\(234\) | −1.43828 | −0.0940236 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.34563 | −0.347971 | ||||||||
\(237\) | 15.9197 | 1.03410 | ||||||||
\(238\) | 9.31373 | 0.603719 | ||||||||
\(239\) | 0.907160 | 0.0586793 | 0.0293396 | − | 0.999569i | \(-0.490660\pi\) | ||||
0.0293396 | + | 0.999569i | \(0.490660\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.15616 | −0.267722 | −0.133861 | − | 0.991000i | \(-0.542738\pi\) | ||||
−0.133861 | + | 0.991000i | \(0.542738\pi\) | |||||||
\(242\) | 6.55754 | 0.421534 | ||||||||
\(243\) | −21.5354 | −1.38150 | ||||||||
\(244\) | −9.79428 | −0.627015 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −21.0416 | −1.34156 | ||||||||
\(247\) | −1.31512 | −0.0836789 | ||||||||
\(248\) | 10.1030 | 0.641541 | ||||||||
\(249\) | −23.4505 | −1.48612 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.31888 | 0.588203 | 0.294101 | − | 0.955774i | \(-0.404980\pi\) | ||||
0.294101 | + | 0.955774i | \(0.404980\pi\) | |||||||
\(252\) | −7.13302 | −0.449338 | ||||||||
\(253\) | 23.5503 | 1.48059 | ||||||||
\(254\) | −19.2856 | −1.21009 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −13.6312 | −0.850294 | −0.425147 | − | 0.905124i | \(-0.639778\pi\) | ||||
−0.425147 | + | 0.905124i | \(0.639778\pi\) | |||||||
\(258\) | −5.96671 | −0.371471 | ||||||||
\(259\) | −1.83227 | −0.113852 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.69813 | 0.290807 | ||||||||
\(262\) | −8.82072 | −0.544946 | ||||||||
\(263\) | 27.2170 | 1.67827 | 0.839137 | − | 0.543921i | \(-0.183061\pi\) | ||||
0.839137 | + | 0.543921i | \(0.183061\pi\) | |||||||
\(264\) | 11.0011 | 0.677071 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6.52218 | −0.399901 | ||||||||
\(267\) | 30.1331 | 1.84411 | ||||||||
\(268\) | 1.85073 | 0.113052 | ||||||||
\(269\) | 23.0550 | 1.40569 | 0.702845 | − | 0.711343i | \(-0.251913\pi\) | ||||
0.702845 | + | 0.711343i | \(0.251913\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.9320 | 1.39302 | 0.696510 | − | 0.717547i | \(-0.254735\pi\) | ||||
0.696510 | + | 0.717547i | \(0.254735\pi\) | |||||||
\(272\) | −5.08317 | −0.308213 | ||||||||
\(273\) | 1.77727 | 0.107565 | ||||||||
\(274\) | 4.66126 | 0.281597 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 14.7560 | 0.888206 | ||||||||
\(277\) | −11.7534 | −0.706192 | −0.353096 | − | 0.935587i | \(-0.614871\pi\) | ||||
−0.353096 | + | 0.935587i | \(0.614871\pi\) | |||||||
\(278\) | 16.4050 | 0.983906 | ||||||||
\(279\) | 39.3310 | 2.35468 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.0962 | −1.73573 | −0.867865 | − | 0.496799i | \(-0.834508\pi\) | ||||
−0.867865 | + | 0.496799i | \(0.834508\pi\) | |||||||
\(282\) | 28.6580 | 1.70656 | ||||||||
\(283\) | −10.1829 | −0.605311 | −0.302655 | − | 0.953100i | \(-0.597873\pi\) | ||||
−0.302655 | + | 0.953100i | \(0.597873\pi\) | |||||||
\(284\) | 2.86038 | 0.169732 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.54808 | −0.0915396 | ||||||||
\(287\) | 14.6846 | 0.866807 | ||||||||
\(288\) | 3.89300 | 0.229397 | ||||||||
\(289\) | 8.83864 | 0.519920 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.9067 | 0.932466 | ||||||||
\(292\) | −8.09942 | −0.473983 | ||||||||
\(293\) | 18.1243 | 1.05883 | 0.529415 | − | 0.848363i | \(-0.322411\pi\) | ||||
0.529415 | + | 0.848363i | \(0.322411\pi\) | |||||||
\(294\) | −9.56399 | −0.557783 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.00000 | 0.0581238 | ||||||||
\(297\) | 9.82399 | 0.570046 | ||||||||
\(298\) | −5.86259 | −0.339611 | ||||||||
\(299\) | −2.07646 | −0.120085 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.16409 | 0.240014 | ||||||||
\(302\) | 13.1460 | 0.756467 | ||||||||
\(303\) | 13.0361 | 0.748905 | ||||||||
\(304\) | 3.55963 | 0.204159 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −19.7888 | −1.13125 | ||||||||
\(307\) | −6.15561 | −0.351319 | −0.175660 | − | 0.984451i | \(-0.556206\pi\) | ||||
−0.175660 | + | 0.984451i | \(0.556206\pi\) | |||||||
\(308\) | −7.67751 | −0.437467 | ||||||||
\(309\) | −19.2534 | −1.09529 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.4512 | −1.67002 | −0.835011 | − | 0.550234i | \(-0.814539\pi\) | ||||
−0.835011 | + | 0.550234i | \(0.814539\pi\) | |||||||
\(312\) | −0.969984 | −0.0549145 | ||||||||
\(313\) | 13.0102 | 0.735378 | 0.367689 | − | 0.929949i | \(-0.380149\pi\) | ||||
0.367689 | + | 0.929949i | \(0.380149\pi\) | |||||||
\(314\) | −7.33629 | −0.414011 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.06361 | 0.341105 | ||||||||
\(317\) | −7.39826 | −0.415528 | −0.207764 | − | 0.978179i | \(-0.566619\pi\) | ||||
−0.207764 | + | 0.978179i | \(0.566619\pi\) | |||||||
\(318\) | −26.1063 | −1.46397 | ||||||||
\(319\) | 5.05676 | 0.283124 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −21.5598 | −1.20335 | ||||||||
\(322\) | −10.2980 | −0.573885 | ||||||||
\(323\) | −18.0942 | −1.00679 | ||||||||
\(324\) | −5.52355 | −0.306864 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −18.7968 | −1.04106 | ||||||||
\(327\) | −53.9537 | −2.98365 | ||||||||
\(328\) | −8.01447 | −0.442525 | ||||||||
\(329\) | −20.0000 | −1.10264 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.2545 | 1.82783 | 0.913916 | − | 0.405903i | \(-0.133043\pi\) | ||||
0.913916 | + | 0.405903i | \(0.133043\pi\) | |||||||
\(332\) | −8.93200 | −0.490207 | ||||||||
\(333\) | 3.89300 | 0.213335 | ||||||||
\(334\) | −5.92772 | −0.324350 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.81053 | −0.262436 | ||||||||
\(337\) | 22.6288 | 1.23267 | 0.616334 | − | 0.787485i | \(-0.288617\pi\) | ||||
0.616334 | + | 0.787485i | \(0.288617\pi\) | |||||||
\(338\) | −12.8635 | −0.699682 | ||||||||
\(339\) | −1.71438 | −0.0931123 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 42.3333 | 2.29248 | ||||||||
\(342\) | 13.8576 | 0.749334 | ||||||||
\(343\) | 19.5004 | 1.05293 | ||||||||
\(344\) | −2.27264 | −0.122533 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.78242 | 0.310865 | ||||||||
\(347\) | −24.1396 | −1.29588 | −0.647941 | − | 0.761691i | \(-0.724370\pi\) | ||||
−0.647941 | + | 0.761691i | \(0.724370\pi\) | |||||||
\(348\) | 3.16843 | 0.169846 | ||||||||
\(349\) | −10.3702 | −0.555102 | −0.277551 | − | 0.960711i | \(-0.589523\pi\) | ||||
−0.277551 | + | 0.960711i | \(0.589523\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.866196 | −0.0462341 | ||||||||
\(352\) | 4.19017 | 0.223337 | ||||||||
\(353\) | −3.92699 | −0.209013 | −0.104506 | − | 0.994524i | \(-0.533326\pi\) | ||||
−0.104506 | + | 0.994524i | \(0.533326\pi\) | |||||||
\(354\) | −14.0347 | −0.745935 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 11.4773 | 0.608295 | ||||||||
\(357\) | 24.4528 | 1.29418 | ||||||||
\(358\) | 7.13581 | 0.377139 | ||||||||
\(359\) | −9.85179 | −0.519957 | −0.259979 | − | 0.965614i | \(-0.583716\pi\) | ||||
−0.259979 | + | 0.965614i | \(0.583716\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.32907 | −0.333109 | ||||||||
\(362\) | 11.5365 | 0.606346 | ||||||||
\(363\) | 17.2165 | 0.903632 | ||||||||
\(364\) | 0.676938 | 0.0354812 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −25.7144 | −1.34411 | ||||||||
\(367\) | 33.2559 | 1.73594 | 0.867972 | − | 0.496614i | \(-0.165423\pi\) | ||||
0.867972 | + | 0.496614i | \(0.165423\pi\) | |||||||
\(368\) | 5.62036 | 0.292981 | ||||||||
\(369\) | −31.2003 | −1.62422 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.2192 | 0.945896 | ||||||||
\(372\) | 26.5249 | 1.37525 | ||||||||
\(373\) | −28.5387 | −1.47768 | −0.738839 | − | 0.673882i | \(-0.764625\pi\) | ||||
−0.738839 | + | 0.673882i | \(0.764625\pi\) | |||||||
\(374\) | −21.2994 | −1.10136 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.9154 | 0.562921 | ||||||||
\(377\) | −0.445862 | −0.0229631 | ||||||||
\(378\) | −4.29581 | −0.220953 | ||||||||
\(379\) | 0.476554 | 0.0244789 | 0.0122395 | − | 0.999925i | \(-0.496104\pi\) | ||||
0.0122395 | + | 0.999925i | \(0.496104\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −50.6334 | −2.59403 | ||||||||
\(382\) | −20.6048 | −1.05423 | ||||||||
\(383\) | 7.13962 | 0.364818 | 0.182409 | − | 0.983223i | \(-0.441611\pi\) | ||||
0.182409 | + | 0.983223i | \(0.441611\pi\) | |||||||
\(384\) | 2.62545 | 0.133980 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −26.1663 | −1.33183 | ||||||||
\(387\) | −8.84740 | −0.449738 | ||||||||
\(388\) | 6.05864 | 0.307581 | ||||||||
\(389\) | −24.2060 | −1.22729 | −0.613646 | − | 0.789581i | \(-0.710298\pi\) | ||||
−0.613646 | + | 0.789581i | \(0.710298\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −28.5693 | −1.44481 | ||||||||
\(392\) | −3.64280 | −0.183989 | ||||||||
\(393\) | −23.1584 | −1.16819 | ||||||||
\(394\) | 14.6067 | 0.735876 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 16.3123 | 0.819726 | ||||||||
\(397\) | 20.7491 | 1.04137 | 0.520684 | − | 0.853750i | \(-0.325677\pi\) | ||||
0.520684 | + | 0.853750i | \(0.325677\pi\) | |||||||
\(398\) | 5.81275 | 0.291367 | ||||||||
\(399\) | −17.1237 | −0.857256 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −34.8410 | −1.73988 | −0.869939 | − | 0.493159i | \(-0.835842\pi\) | ||||
−0.869939 | + | 0.493159i | \(0.835842\pi\) | |||||||
\(402\) | 4.85901 | 0.242346 | ||||||||
\(403\) | −3.73259 | −0.185934 | ||||||||
\(404\) | 4.96528 | 0.247032 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.21121 | −0.109740 | ||||||||
\(407\) | 4.19017 | 0.207699 | ||||||||
\(408\) | −13.3456 | −0.660707 | ||||||||
\(409\) | 25.2132 | 1.24671 | 0.623356 | − | 0.781938i | \(-0.285769\pi\) | ||||
0.623356 | + | 0.781938i | \(0.285769\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.2379 | 0.603652 | ||||||||
\(412\) | −7.33338 | −0.361289 | ||||||||
\(413\) | 9.79462 | 0.481962 | ||||||||
\(414\) | 21.8801 | 1.07535 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.369454 | −0.0181140 | ||||||||
\(417\) | 43.0705 | 2.10917 | ||||||||
\(418\) | 14.9154 | 0.729538 | ||||||||
\(419\) | 5.69695 | 0.278314 | 0.139157 | − | 0.990270i | \(-0.455561\pi\) | ||||
0.139157 | + | 0.990270i | \(0.455561\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.38092 | 0.164776 | 0.0823880 | − | 0.996600i | \(-0.473745\pi\) | ||||
0.0823880 | + | 0.996600i | \(0.473745\pi\) | |||||||
\(422\) | 16.0976 | 0.783621 | ||||||||
\(423\) | 42.4938 | 2.06612 | ||||||||
\(424\) | −9.94355 | −0.482901 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.50978 | 0.363850 | ||||||||
\(427\) | 17.9457 | 0.868455 | ||||||||
\(428\) | −8.21182 | −0.396933 | ||||||||
\(429\) | −4.06440 | −0.196231 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.381731 | −0.0183873 | −0.00919367 | − | 0.999958i | \(-0.502926\pi\) | ||||
−0.00919367 | + | 0.999958i | \(0.502926\pi\) | |||||||
\(432\) | 2.34453 | 0.112801 | ||||||||
\(433\) | −21.6393 | −1.03992 | −0.519958 | − | 0.854192i | \(-0.674052\pi\) | ||||
−0.519958 | + | 0.854192i | \(0.674052\pi\) | |||||||
\(434\) | −18.5114 | −0.888575 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −20.5503 | −0.984179 | ||||||||
\(437\) | 20.0064 | 0.957035 | ||||||||
\(438\) | −21.2646 | −1.01606 | ||||||||
\(439\) | 26.4663 | 1.26317 | 0.631583 | − | 0.775308i | \(-0.282405\pi\) | ||||
0.631583 | + | 0.775308i | \(0.282405\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.1814 | −0.675305 | ||||||||
\(442\) | 1.87800 | 0.0893273 | ||||||||
\(443\) | −4.65489 | −0.221161 | −0.110580 | − | 0.993867i | \(-0.535271\pi\) | ||||
−0.110580 | + | 0.993867i | \(0.535271\pi\) | |||||||
\(444\) | 2.62545 | 0.124598 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 25.3608 | 1.20087 | ||||||||
\(447\) | −15.3920 | −0.728015 | ||||||||
\(448\) | −1.83227 | −0.0865665 | ||||||||
\(449\) | −26.5531 | −1.25312 | −0.626558 | − | 0.779375i | \(-0.715537\pi\) | ||||
−0.626558 | + | 0.779375i | \(0.715537\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −33.5820 | −1.58131 | ||||||||
\(452\) | −0.652984 | −0.0307138 | ||||||||
\(453\) | 34.5142 | 1.62162 | ||||||||
\(454\) | −5.57339 | −0.261572 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 9.34563 | 0.437649 | ||||||||
\(457\) | 4.27264 | 0.199866 | 0.0999329 | − | 0.994994i | \(-0.468137\pi\) | ||||
0.0999329 | + | 0.994994i | \(0.468137\pi\) | |||||||
\(458\) | 9.02035 | 0.421493 | ||||||||
\(459\) | −11.9177 | −0.556269 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.1873 | 1.49911 | 0.749555 | − | 0.661942i | \(-0.230267\pi\) | ||||
0.749555 | + | 0.661942i | \(0.230267\pi\) | |||||||
\(462\) | −20.1569 | −0.937786 | ||||||||
\(463\) | 18.4014 | 0.855186 | 0.427593 | − | 0.903971i | \(-0.359362\pi\) | ||||
0.427593 | + | 0.903971i | \(0.359362\pi\) | |||||||
\(464\) | 1.20681 | 0.0560250 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.8100 | 0.547086 | ||||||||
\(467\) | −3.06777 | −0.141959 | −0.0709797 | − | 0.997478i | \(-0.522613\pi\) | ||||
−0.0709797 | + | 0.997478i | \(0.522613\pi\) | |||||||
\(468\) | −1.43828 | −0.0664847 | ||||||||
\(469\) | −3.39104 | −0.156584 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.2611 | −0.887504 | ||||||||
\(472\) | −5.34563 | −0.246052 | ||||||||
\(473\) | −9.52276 | −0.437857 | ||||||||
\(474\) | 15.9197 | 0.731217 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 9.31373 | 0.426894 | ||||||||
\(477\) | −38.7102 | −1.77242 | ||||||||
\(478\) | 0.907160 | 0.0414925 | ||||||||
\(479\) | 8.78798 | 0.401533 | 0.200767 | − | 0.979639i | \(-0.435657\pi\) | ||||
0.200767 | + | 0.979639i | \(0.435657\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.369454 | −0.0168457 | ||||||||
\(482\) | −4.15616 | −0.189308 | ||||||||
\(483\) | −27.0369 | −1.23022 | ||||||||
\(484\) | 6.55754 | 0.298070 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −21.5354 | −0.976866 | ||||||||
\(487\) | −22.4814 | −1.01873 | −0.509366 | − | 0.860550i | \(-0.670120\pi\) | ||||
−0.509366 | + | 0.860550i | \(0.670120\pi\) | |||||||
\(488\) | −9.79428 | −0.443366 | ||||||||
\(489\) | −49.3500 | −2.23168 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.0441752 | −0.00199360 | −0.000996799 | − | 1.00000i | \(-0.500317\pi\) | ||||
−0.000996799 | 1.00000i | \(0.500317\pi\) | ||||||||
\(492\) | −21.0416 | −0.948629 | ||||||||
\(493\) | −6.13445 | −0.276282 | ||||||||
\(494\) | −1.31512 | −0.0591699 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.1030 | 0.453638 | ||||||||
\(497\) | −5.24097 | −0.235090 | ||||||||
\(498\) | −23.4505 | −1.05084 | ||||||||
\(499\) | 28.2445 | 1.26440 | 0.632199 | − | 0.774806i | \(-0.282153\pi\) | ||||
0.632199 | + | 0.774806i | \(0.282153\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.5629 | −0.695301 | ||||||||
\(502\) | 9.31888 | 0.415922 | ||||||||
\(503\) | −19.7713 | −0.881560 | −0.440780 | − | 0.897615i | \(-0.645298\pi\) | ||||
−0.440780 | + | 0.897615i | \(0.645298\pi\) | |||||||
\(504\) | −7.13302 | −0.317730 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 23.5503 | 1.04694 | ||||||||
\(507\) | −33.7725 | −1.49989 | ||||||||
\(508\) | −19.2856 | −0.855660 | ||||||||
\(509\) | 43.4809 | 1.92726 | 0.963628 | − | 0.267247i | \(-0.0861141\pi\) | ||||
0.963628 | + | 0.267247i | \(0.0861141\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.8403 | 0.656496 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 8.34565 | 0.368470 | ||||||||
\(514\) | −13.6312 | −0.601249 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.96671 | −0.262670 | ||||||||
\(517\) | 45.7376 | 2.01154 | ||||||||
\(518\) | −1.83227 | −0.0805052 | ||||||||
\(519\) | 15.1815 | 0.666393 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.0325 | −0.790019 | −0.395009 | − | 0.918677i | \(-0.629259\pi\) | ||||
−0.395009 | + | 0.918677i | \(0.629259\pi\) | |||||||
\(522\) | 4.69813 | 0.205632 | ||||||||
\(523\) | 31.6788 | 1.38522 | 0.692610 | − | 0.721313i | \(-0.256461\pi\) | ||||
0.692610 | + | 0.721313i | \(0.256461\pi\) | |||||||
\(524\) | −8.82072 | −0.385335 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 27.2170 | 1.18672 | ||||||||
\(527\) | −51.3553 | −2.23707 | ||||||||
\(528\) | 11.0011 | 0.478761 | ||||||||
\(529\) | 8.58844 | 0.373410 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20.8105 | −0.903100 | ||||||||
\(532\) | −6.52218 | −0.282773 | ||||||||
\(533\) | 2.96098 | 0.128254 | ||||||||
\(534\) | 30.1331 | 1.30398 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.85073 | 0.0799395 | ||||||||
\(537\) | 18.7347 | 0.808463 | ||||||||
\(538\) | 23.0550 | 0.993973 | ||||||||
\(539\) | −15.2639 | −0.657465 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.39442 | 0.403898 | 0.201949 | − | 0.979396i | \(-0.435273\pi\) | ||||
0.201949 | + | 0.979396i | \(0.435273\pi\) | |||||||
\(542\) | 22.9320 | 0.985014 | ||||||||
\(543\) | 30.2886 | 1.29981 | ||||||||
\(544\) | −5.08317 | −0.217939 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.77727 | 0.0760601 | ||||||||
\(547\) | 24.7824 | 1.05962 | 0.529809 | − | 0.848117i | \(-0.322263\pi\) | ||||
0.529809 | + | 0.848117i | \(0.322263\pi\) | |||||||
\(548\) | 4.66126 | 0.199119 | ||||||||
\(549\) | −38.1291 | −1.62731 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.29581 | 0.183008 | ||||||||
\(552\) | 14.7560 | 0.628056 | ||||||||
\(553\) | −11.1102 | −0.472452 | ||||||||
\(554\) | −11.7534 | −0.499353 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.4050 | 0.695727 | ||||||||
\(557\) | −22.1627 | −0.939062 | −0.469531 | − | 0.882916i | \(-0.655577\pi\) | ||||
−0.469531 | + | 0.882916i | \(0.655577\pi\) | |||||||
\(558\) | 39.3310 | 1.66501 | ||||||||
\(559\) | 0.839637 | 0.0355128 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −55.9205 | −2.36096 | ||||||||
\(562\) | −29.0962 | −1.22735 | ||||||||
\(563\) | 6.46846 | 0.272613 | 0.136306 | − | 0.990667i | \(-0.456477\pi\) | ||||
0.136306 | + | 0.990667i | \(0.456477\pi\) | |||||||
\(564\) | 28.6580 | 1.20672 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −10.1829 | −0.428019 | ||||||||
\(567\) | 10.1206 | 0.425026 | ||||||||
\(568\) | 2.86038 | 0.120019 | ||||||||
\(569\) | 8.26550 | 0.346508 | 0.173254 | − | 0.984877i | \(-0.444572\pi\) | ||||
0.173254 | + | 0.984877i | \(0.444572\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.5179 | 1.44453 | 0.722264 | − | 0.691618i | \(-0.243102\pi\) | ||||
0.722264 | + | 0.691618i | \(0.243102\pi\) | |||||||
\(572\) | −1.54808 | −0.0647283 | ||||||||
\(573\) | −54.0970 | −2.25993 | ||||||||
\(574\) | 14.6846 | 0.612925 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.89300 | 0.162208 | ||||||||
\(577\) | −3.05347 | −0.127117 | −0.0635587 | − | 0.997978i | \(-0.520245\pi\) | ||||
−0.0635587 | + | 0.997978i | \(0.520245\pi\) | |||||||
\(578\) | 8.83864 | 0.367639 | ||||||||
\(579\) | −68.6985 | −2.85501 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.3658 | 0.678968 | ||||||||
\(582\) | 15.9067 | 0.659353 | ||||||||
\(583\) | −41.6652 | −1.72559 | ||||||||
\(584\) | −8.09942 | −0.335156 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.1243 | 0.748706 | ||||||||
\(587\) | −35.1344 | −1.45015 | −0.725076 | − | 0.688668i | \(-0.758196\pi\) | ||||
−0.725076 | + | 0.688668i | \(0.758196\pi\) | |||||||
\(588\) | −9.56399 | −0.394412 | ||||||||
\(589\) | 35.9629 | 1.48183 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 38.3492 | 1.57748 | ||||||||
\(592\) | 1.00000 | 0.0410997 | ||||||||
\(593\) | −12.0400 | −0.494424 | −0.247212 | − | 0.968961i | \(-0.579514\pi\) | ||||
−0.247212 | + | 0.968961i | \(0.579514\pi\) | |||||||
\(594\) | 9.82399 | 0.403083 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.86259 | −0.240141 | ||||||||
\(597\) | 15.2611 | 0.624595 | ||||||||
\(598\) | −2.07646 | −0.0849129 | ||||||||
\(599\) | −17.4701 | −0.713810 | −0.356905 | − | 0.934141i | \(-0.616168\pi\) | ||||
−0.356905 | + | 0.934141i | \(0.616168\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.7044 | 1.57878 | 0.789392 | − | 0.613890i | \(-0.210396\pi\) | ||||
0.789392 | + | 0.613890i | \(0.210396\pi\) | |||||||
\(602\) | 4.16409 | 0.169716 | ||||||||
\(603\) | 7.20491 | 0.293406 | ||||||||
\(604\) | 13.1460 | 0.534903 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 13.0361 | 0.529556 | ||||||||
\(607\) | −28.7903 | −1.16856 | −0.584282 | − | 0.811551i | \(-0.698624\pi\) | ||||
−0.584282 | + | 0.811551i | \(0.698624\pi\) | |||||||
\(608\) | 3.55963 | 0.144362 | ||||||||
\(609\) | −5.80542 | −0.235247 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.03275 | −0.163148 | ||||||||
\(612\) | −19.7888 | −0.799915 | ||||||||
\(613\) | −7.66539 | −0.309602 | −0.154801 | − | 0.987946i | \(-0.549474\pi\) | ||||
−0.154801 | + | 0.987946i | \(0.549474\pi\) | |||||||
\(614\) | −6.15561 | −0.248420 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.67751 | −0.309336 | ||||||||
\(617\) | 36.5388 | 1.47100 | 0.735498 | − | 0.677527i | \(-0.236948\pi\) | ||||
0.735498 | + | 0.677527i | \(0.236948\pi\) | |||||||
\(618\) | −19.2534 | −0.774487 | ||||||||
\(619\) | −45.8085 | −1.84120 | −0.920599 | − | 0.390510i | \(-0.872299\pi\) | ||||
−0.920599 | + | 0.390510i | \(0.872299\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.1771 | 0.528779 | ||||||||
\(622\) | −29.4512 | −1.18088 | ||||||||
\(623\) | −21.0294 | −0.842527 | ||||||||
\(624\) | −0.969984 | −0.0388304 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 13.0102 | 0.519991 | ||||||||
\(627\) | 39.1598 | 1.56389 | ||||||||
\(628\) | −7.33629 | −0.292750 | ||||||||
\(629\) | −5.08317 | −0.202679 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.42682 | 0.136420 | 0.0682098 | − | 0.997671i | \(-0.478271\pi\) | ||||
0.0682098 | + | 0.997671i | \(0.478271\pi\) | |||||||
\(632\) | 6.06361 | 0.241197 | ||||||||
\(633\) | 42.2636 | 1.67983 | ||||||||
\(634\) | −7.39826 | −0.293823 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −26.1063 | −1.03518 | ||||||||
\(637\) | 1.34585 | 0.0533244 | ||||||||
\(638\) | 5.05676 | 0.200199 | ||||||||
\(639\) | 11.1354 | 0.440511 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.3241 | 1.51371 | 0.756855 | − | 0.653583i | \(-0.226735\pi\) | ||||
0.756855 | + | 0.653583i | \(0.226735\pi\) | |||||||
\(642\) | −21.5598 | −0.850896 | ||||||||
\(643\) | 1.36660 | 0.0538935 | 0.0269468 | − | 0.999637i | \(-0.491422\pi\) | ||||
0.0269468 | + | 0.999637i | \(0.491422\pi\) | |||||||
\(644\) | −10.2980 | −0.405798 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18.0942 | −0.711906 | ||||||||
\(647\) | 11.2690 | 0.443028 | 0.221514 | − | 0.975157i | \(-0.428900\pi\) | ||||
0.221514 | + | 0.975157i | \(0.428900\pi\) | |||||||
\(648\) | −5.52355 | −0.216985 | ||||||||
\(649\) | −22.3991 | −0.879241 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −48.6008 | −1.90482 | ||||||||
\(652\) | −18.7968 | −0.736138 | ||||||||
\(653\) | −29.5439 | −1.15614 | −0.578070 | − | 0.815987i | \(-0.696194\pi\) | ||||
−0.578070 | + | 0.815987i | \(0.696194\pi\) | |||||||
\(654\) | −53.9537 | −2.10976 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −8.01447 | −0.312912 | ||||||||
\(657\) | −31.5311 | −1.23014 | ||||||||
\(658\) | −20.0000 | −0.779681 | ||||||||
\(659\) | −49.9126 | −1.94432 | −0.972159 | − | 0.234324i | \(-0.924712\pi\) | ||||
−0.972159 | + | 0.234324i | \(0.924712\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.9950 | 1.01109 | 0.505545 | − | 0.862800i | \(-0.331292\pi\) | ||||
0.505545 | + | 0.862800i | \(0.331292\pi\) | |||||||
\(662\) | 33.2545 | 1.29247 | ||||||||
\(663\) | 4.93059 | 0.191488 | ||||||||
\(664\) | −8.93200 | −0.346629 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.89300 | 0.150851 | ||||||||
\(667\) | 6.78273 | 0.262628 | ||||||||
\(668\) | −5.92772 | −0.229350 | ||||||||
\(669\) | 66.5836 | 2.57427 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −41.0397 | −1.58432 | ||||||||
\(672\) | −4.81053 | −0.185570 | ||||||||
\(673\) | 6.91054 | 0.266382 | 0.133191 | − | 0.991090i | \(-0.457478\pi\) | ||||
0.133191 | + | 0.991090i | \(0.457478\pi\) | |||||||
\(674\) | 22.6288 | 0.871627 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.8635 | −0.494750 | ||||||||
\(677\) | −15.6913 | −0.603065 | −0.301532 | − | 0.953456i | \(-0.597498\pi\) | ||||
−0.301532 | + | 0.953456i | \(0.597498\pi\) | |||||||
\(678\) | −1.71438 | −0.0658403 | ||||||||
\(679\) | −11.1011 | −0.426019 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.6327 | −0.560725 | ||||||||
\(682\) | 42.3333 | 1.62103 | ||||||||
\(683\) | −18.2002 | −0.696412 | −0.348206 | − | 0.937418i | \(-0.613209\pi\) | ||||
−0.348206 | + | 0.937418i | \(0.613209\pi\) | |||||||
\(684\) | 13.8576 | 0.529859 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 19.5004 | 0.744531 | ||||||||
\(687\) | 23.6825 | 0.903544 | ||||||||
\(688\) | −2.27264 | −0.0866437 | ||||||||
\(689\) | 3.67368 | 0.139956 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.58658 | −0.0983982 | −0.0491991 | − | 0.998789i | \(-0.515667\pi\) | ||||
−0.0491991 | + | 0.998789i | \(0.515667\pi\) | |||||||
\(692\) | 5.78242 | 0.219815 | ||||||||
\(693\) | −29.8886 | −1.13537 | ||||||||
\(694\) | −24.1396 | −0.916327 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.16843 | 0.120099 | ||||||||
\(697\) | 40.7389 | 1.54310 | ||||||||
\(698\) | −10.3702 | −0.392516 | ||||||||
\(699\) | 31.0065 | 1.17277 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.5092 | −1.00124 | −0.500620 | − | 0.865667i | \(-0.666895\pi\) | ||||
−0.500620 | + | 0.865667i | \(0.666895\pi\) | |||||||
\(702\) | −0.866196 | −0.0326925 | ||||||||
\(703\) | 3.55963 | 0.134254 | ||||||||
\(704\) | 4.19017 | 0.157923 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.92699 | −0.147794 | ||||||||
\(707\) | −9.09773 | −0.342155 | ||||||||
\(708\) | −14.0347 | −0.527456 | ||||||||
\(709\) | −25.0474 | −0.940674 | −0.470337 | − | 0.882487i | \(-0.655868\pi\) | ||||
−0.470337 | + | 0.882487i | \(0.655868\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23.6056 | 0.885281 | ||||||||
\(712\) | 11.4773 | 0.430129 | ||||||||
\(713\) | 56.7825 | 2.12652 | ||||||||
\(714\) | 24.4528 | 0.915121 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.13581 | 0.266678 | ||||||||
\(717\) | 2.38171 | 0.0889464 | ||||||||
\(718\) | −9.85179 | −0.367665 | ||||||||
\(719\) | 24.9551 | 0.930668 | 0.465334 | − | 0.885135i | \(-0.345934\pi\) | ||||
0.465334 | + | 0.885135i | \(0.345934\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.4367 | 0.500409 | ||||||||
\(722\) | −6.32907 | −0.235544 | ||||||||
\(723\) | −10.9118 | −0.405814 | ||||||||
\(724\) | 11.5365 | 0.428752 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 17.2165 | 0.638964 | ||||||||
\(727\) | −21.6774 | −0.803970 | −0.401985 | − | 0.915646i | \(-0.631680\pi\) | ||||
−0.401985 | + | 0.915646i | \(0.631680\pi\) | |||||||
\(728\) | 0.676938 | 0.0250890 | ||||||||
\(729\) | −39.9695 | −1.48035 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.5522 | 0.427275 | ||||||||
\(732\) | −25.7144 | −0.950432 | ||||||||
\(733\) | 6.33267 | 0.233903 | 0.116951 | − | 0.993138i | \(-0.462688\pi\) | ||||
0.116951 | + | 0.993138i | \(0.462688\pi\) | |||||||
\(734\) | 33.2559 | 1.22750 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.62036 | 0.207169 | ||||||||
\(737\) | 7.75489 | 0.285655 | ||||||||
\(738\) | −31.2003 | −1.14850 | ||||||||
\(739\) | 12.8076 | 0.471136 | 0.235568 | − | 0.971858i | \(-0.424305\pi\) | ||||
0.235568 | + | 0.971858i | \(0.424305\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.45278 | −0.126841 | ||||||||
\(742\) | 18.2192 | 0.668849 | ||||||||
\(743\) | 11.0694 | 0.406097 | 0.203048 | − | 0.979169i | \(-0.434915\pi\) | ||||
0.203048 | + | 0.979169i | \(0.434915\pi\) | |||||||
\(744\) | 26.5249 | 0.972452 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −28.5387 | −1.04488 | ||||||||
\(747\) | −34.7723 | −1.27225 | ||||||||
\(748\) | −21.2994 | −0.778782 | ||||||||
\(749\) | 15.0463 | 0.549778 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −46.5316 | −1.69796 | −0.848981 | − | 0.528423i | \(-0.822784\pi\) | ||||
−0.848981 | + | 0.528423i | \(0.822784\pi\) | |||||||
\(752\) | 10.9154 | 0.398045 | ||||||||
\(753\) | 24.4663 | 0.891601 | ||||||||
\(754\) | −0.445862 | −0.0162374 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.29581 | −0.156237 | ||||||||
\(757\) | 32.9872 | 1.19894 | 0.599470 | − | 0.800397i | \(-0.295378\pi\) | ||||
0.599470 | + | 0.800397i | \(0.295378\pi\) | |||||||
\(758\) | 0.476554 | 0.0173092 | ||||||||
\(759\) | 61.8301 | 2.24429 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.7913 | 1.04369 | 0.521843 | − | 0.853042i | \(-0.325245\pi\) | ||||
0.521843 | + | 0.853042i | \(0.325245\pi\) | |||||||
\(762\) | −50.6334 | −1.83426 | ||||||||
\(763\) | 37.6536 | 1.36315 | ||||||||
\(764\) | −20.6048 | −0.745456 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.13962 | 0.257965 | ||||||||
\(767\) | 1.97496 | 0.0713118 | ||||||||
\(768\) | 2.62545 | 0.0947379 | ||||||||
\(769\) | 41.9025 | 1.51104 | 0.755521 | − | 0.655124i | \(-0.227384\pi\) | ||||
0.755521 | + | 0.655124i | \(0.227384\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −35.7882 | −1.28888 | ||||||||
\(772\) | −26.1663 | −0.941747 | ||||||||
\(773\) | 31.0931 | 1.11834 | 0.559171 | − | 0.829052i | \(-0.311119\pi\) | ||||
0.559171 | + | 0.829052i | \(0.311119\pi\) | |||||||
\(774\) | −8.84740 | −0.318013 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.05864 | 0.217493 | ||||||||
\(777\) | −4.81053 | −0.172577 | ||||||||
\(778\) | −24.2060 | −0.867827 | ||||||||
\(779\) | −28.5285 | −1.02214 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.9855 | 0.428874 | ||||||||
\(782\) | −28.5693 | −1.02163 | ||||||||
\(783\) | 2.82941 | 0.101115 | ||||||||
\(784\) | −3.64280 | −0.130100 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −23.1584 | −0.826032 | ||||||||
\(787\) | −18.2842 | −0.651760 | −0.325880 | − | 0.945411i | \(-0.605661\pi\) | ||||
−0.325880 | + | 0.945411i | \(0.605661\pi\) | |||||||
\(788\) | 14.6067 | 0.520343 | ||||||||
\(789\) | 71.4570 | 2.54394 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.19644 | 0.0425406 | ||||||||
\(792\) | 16.3123 | 0.579634 | ||||||||
\(793\) | 3.61854 | 0.128498 | ||||||||
\(794\) | 20.7491 | 0.736358 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.81275 | 0.206027 | ||||||||
\(797\) | −40.6025 | −1.43821 | −0.719106 | − | 0.694900i | \(-0.755449\pi\) | ||||
−0.719106 | + | 0.694900i | \(0.755449\pi\) | |||||||
\(798\) | −17.1237 | −0.606172 | ||||||||
\(799\) | −55.4851 | −1.96292 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 44.6811 | 1.57873 | ||||||||
\(802\) | −34.8410 | −1.23028 | ||||||||
\(803\) | −33.9380 | −1.19764 | ||||||||
\(804\) | 4.85901 | 0.171364 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.73259 | −0.131475 | ||||||||
\(807\) | 60.5299 | 2.13075 | ||||||||
\(808\) | 4.96528 | 0.174678 | ||||||||
\(809\) | 41.1512 | 1.44680 | 0.723400 | − | 0.690429i | \(-0.242578\pi\) | ||||
0.723400 | + | 0.690429i | \(0.242578\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.71866 | −0.235924 | −0.117962 | − | 0.993018i | \(-0.537636\pi\) | ||||
−0.117962 | + | 0.993018i | \(0.537636\pi\) | |||||||
\(812\) | −2.21121 | −0.0775981 | ||||||||
\(813\) | 60.2069 | 2.11155 | ||||||||
\(814\) | 4.19017 | 0.146865 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −13.3456 | −0.467190 | ||||||||
\(817\) | −8.08975 | −0.283025 | ||||||||
\(818\) | 25.2132 | 0.881558 | ||||||||
\(819\) | 2.63532 | 0.0920856 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.5263 | −0.402272 | −0.201136 | − | 0.979563i | \(-0.564463\pi\) | ||||
−0.201136 | + | 0.979563i | \(0.564463\pi\) | |||||||
\(822\) | 12.2379 | 0.426847 | ||||||||
\(823\) | −4.69569 | −0.163681 | −0.0818407 | − | 0.996645i | \(-0.526080\pi\) | ||||
−0.0818407 | + | 0.996645i | \(0.526080\pi\) | |||||||
\(824\) | −7.33338 | −0.255470 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.79462 | 0.340798 | ||||||||
\(827\) | −28.4859 | −0.990550 | −0.495275 | − | 0.868736i | \(-0.664933\pi\) | ||||
−0.495275 | + | 0.868736i | \(0.664933\pi\) | |||||||
\(828\) | 21.8801 | 0.760385 | ||||||||
\(829\) | −40.2771 | −1.39888 | −0.699441 | − | 0.714691i | \(-0.746567\pi\) | ||||
−0.699441 | + | 0.714691i | \(0.746567\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −30.8579 | −1.07045 | ||||||||
\(832\) | −0.369454 | −0.0128085 | ||||||||
\(833\) | 18.5170 | 0.641575 | ||||||||
\(834\) | 43.0705 | 1.49141 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 14.9154 | 0.515861 | ||||||||
\(837\) | 23.6868 | 0.818736 | ||||||||
\(838\) | 5.69695 | 0.196798 | ||||||||
\(839\) | −9.99007 | −0.344895 | −0.172448 | − | 0.985019i | \(-0.555168\pi\) | ||||
−0.172448 | + | 0.985019i | \(0.555168\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.5436 | −0.949779 | ||||||||
\(842\) | 3.38092 | 0.116514 | ||||||||
\(843\) | −76.3906 | −2.63103 | ||||||||
\(844\) | 16.0976 | 0.554104 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 42.4938 | 1.46097 | ||||||||
\(847\) | −12.0152 | −0.412846 | ||||||||
\(848\) | −9.94355 | −0.341463 | ||||||||
\(849\) | −26.7347 | −0.917533 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.62036 | 0.192663 | ||||||||
\(852\) | 7.50978 | 0.257281 | ||||||||
\(853\) | −18.0500 | −0.618019 | −0.309010 | − | 0.951059i | \(-0.599998\pi\) | ||||
−0.309010 | + | 0.951059i | \(0.599998\pi\) | |||||||
\(854\) | 17.9457 | 0.614091 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.21182 | −0.280674 | ||||||||
\(857\) | 24.3118 | 0.830474 | 0.415237 | − | 0.909713i | \(-0.363699\pi\) | ||||
0.415237 | + | 0.909713i | \(0.363699\pi\) | |||||||
\(858\) | −4.06440 | −0.138756 | ||||||||
\(859\) | 35.2112 | 1.20139 | 0.600696 | − | 0.799477i | \(-0.294890\pi\) | ||||
0.600696 | + | 0.799477i | \(0.294890\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 38.5538 | 1.31391 | ||||||||
\(862\) | −0.381731 | −0.0130018 | ||||||||
\(863\) | 23.2986 | 0.793093 | 0.396546 | − | 0.918015i | \(-0.370209\pi\) | ||||
0.396546 | + | 0.918015i | \(0.370209\pi\) | |||||||
\(864\) | 2.34453 | 0.0797626 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −21.6393 | −0.735332 | ||||||||
\(867\) | 23.2054 | 0.788098 | ||||||||
\(868\) | −18.5114 | −0.628318 | ||||||||
\(869\) | 25.4076 | 0.861893 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.683761 | −0.0231684 | ||||||||
\(872\) | −20.5503 | −0.695920 | ||||||||
\(873\) | 23.5863 | 0.798275 | ||||||||
\(874\) | 20.0064 | 0.676726 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −21.2646 | −0.718466 | ||||||||
\(877\) | 47.8713 | 1.61650 | 0.808250 | − | 0.588839i | \(-0.200415\pi\) | ||||
0.808250 | + | 0.588839i | \(0.200415\pi\) | |||||||
\(878\) | 26.4663 | 0.893194 | ||||||||
\(879\) | 47.5844 | 1.60498 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40.1274 | −1.35193 | −0.675963 | − | 0.736936i | \(-0.736272\pi\) | ||||
−0.675963 | + | 0.736936i | \(0.736272\pi\) | |||||||
\(882\) | −14.1814 | −0.477513 | ||||||||
\(883\) | 45.6747 | 1.53708 | 0.768539 | − | 0.639803i | \(-0.220984\pi\) | ||||
0.768539 | + | 0.639803i | \(0.220984\pi\) | |||||||
\(884\) | 1.87800 | 0.0631639 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.65489 | −0.156384 | ||||||||
\(887\) | −17.5417 | −0.588992 | −0.294496 | − | 0.955653i | \(-0.595152\pi\) | ||||
−0.294496 | + | 0.955653i | \(0.595152\pi\) | |||||||
\(888\) | 2.62545 | 0.0881044 | ||||||||
\(889\) | 35.3364 | 1.18514 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −23.1446 | −0.775374 | ||||||||
\(892\) | 25.3608 | 0.849142 | ||||||||
\(893\) | 38.8549 | 1.30023 | ||||||||
\(894\) | −15.3920 | −0.514784 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.83227 | −0.0612117 | ||||||||
\(897\) | −5.45166 | −0.182026 | ||||||||
\(898\) | −26.5531 | −0.886087 | ||||||||
\(899\) | 12.1924 | 0.406641 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 50.5448 | 1.68389 | ||||||||
\(902\) | −33.5820 | −1.11816 | ||||||||
\(903\) | 10.9326 | 0.363815 | ||||||||
\(904\) | −0.652984 | −0.0217179 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 34.5142 | 1.14666 | ||||||||
\(907\) | −2.04294 | −0.0678347 | −0.0339173 | − | 0.999425i | \(-0.510798\pi\) | ||||
−0.0339173 | + | 0.999425i | \(0.510798\pi\) | |||||||
\(908\) | −5.57339 | −0.184960 | ||||||||
\(909\) | 19.3299 | 0.641131 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.3145 | 1.79952 | 0.899760 | − | 0.436385i | \(-0.143742\pi\) | ||||
0.899760 | + | 0.436385i | \(0.143742\pi\) | |||||||
\(912\) | 9.34563 | 0.309465 | ||||||||
\(913\) | −37.4266 | −1.23864 | ||||||||
\(914\) | 4.27264 | 0.141326 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.02035 | 0.298041 | ||||||||
\(917\) | 16.1619 | 0.533713 | ||||||||
\(918\) | −11.9177 | −0.393341 | ||||||||
\(919\) | 40.9771 | 1.35171 | 0.675855 | − | 0.737034i | \(-0.263774\pi\) | ||||
0.675855 | + | 0.737034i | \(0.263774\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.1613 | −0.532531 | ||||||||
\(922\) | 32.1873 | 1.06003 | ||||||||
\(923\) | −1.05678 | −0.0347842 | ||||||||
\(924\) | −20.1569 | −0.663115 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 18.4014 | 0.604708 | ||||||||
\(927\) | −28.5488 | −0.937667 | ||||||||
\(928\) | 1.20681 | 0.0396156 | ||||||||
\(929\) | −22.2458 | −0.729860 | −0.364930 | − | 0.931035i | \(-0.618907\pi\) | ||||
−0.364930 | + | 0.931035i | \(0.618907\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.9670 | −0.424976 | ||||||||
\(932\) | 11.8100 | 0.386848 | ||||||||
\(933\) | −77.3226 | −2.53143 | ||||||||
\(934\) | −3.06777 | −0.100380 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.43828 | −0.0470118 | ||||||||
\(937\) | −0.989771 | −0.0323344 | −0.0161672 | − | 0.999869i | \(-0.505146\pi\) | ||||
−0.0161672 | + | 0.999869i | \(0.505146\pi\) | |||||||
\(938\) | −3.39104 | −0.110721 | ||||||||
\(939\) | 34.1576 | 1.11469 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.255111 | 0.00831639 | 0.00415820 | − | 0.999991i | \(-0.498676\pi\) | ||||
0.00415820 | + | 0.999991i | \(0.498676\pi\) | |||||||
\(942\) | −19.2611 | −0.627560 | ||||||||
\(943\) | −45.0442 | −1.46684 | ||||||||
\(944\) | −5.34563 | −0.173985 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.52276 | −0.309612 | ||||||||
\(947\) | 58.4983 | 1.90094 | 0.950469 | − | 0.310819i | \(-0.100603\pi\) | ||||
0.950469 | + | 0.310819i | \(0.100603\pi\) | |||||||
\(948\) | 15.9197 | 0.517048 | ||||||||
\(949\) | 2.99236 | 0.0971362 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.4238 | −0.629860 | ||||||||
\(952\) | 9.31373 | 0.301860 | ||||||||
\(953\) | 34.4365 | 1.11551 | 0.557755 | − | 0.830006i | \(-0.311663\pi\) | ||||
0.557755 | + | 0.830006i | \(0.311663\pi\) | |||||||
\(954\) | −38.7102 | −1.25329 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.907160 | 0.0293396 | ||||||||
\(957\) | 13.2763 | 0.429161 | ||||||||
\(958\) | 8.78798 | 0.283927 | ||||||||
\(959\) | −8.54068 | −0.275793 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 71.0706 | 2.29260 | ||||||||
\(962\) | −0.369454 | −0.0119117 | ||||||||
\(963\) | −31.9686 | −1.03017 | ||||||||
\(964\) | −4.15616 | −0.133861 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −27.0369 | −0.869898 | ||||||||
\(967\) | 19.0310 | 0.611997 | 0.305998 | − | 0.952032i | \(-0.401010\pi\) | ||||
0.305998 | + | 0.952032i | \(0.401010\pi\) | |||||||
\(968\) | 6.55754 | 0.210767 | ||||||||
\(969\) | −47.5054 | −1.52609 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.9856 | 1.63621 | 0.818103 | − | 0.575071i | \(-0.195026\pi\) | ||||
0.818103 | + | 0.575071i | \(0.195026\pi\) | |||||||
\(972\) | −21.5354 | −0.690748 | ||||||||
\(973\) | −30.0583 | −0.963626 | ||||||||
\(974\) | −22.4814 | −0.720352 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.79428 | −0.313507 | ||||||||
\(977\) | −26.8574 | −0.859245 | −0.429622 | − | 0.903009i | \(-0.641353\pi\) | ||||
−0.429622 | + | 0.903009i | \(0.641353\pi\) | |||||||
\(978\) | −49.3500 | −1.57804 | ||||||||
\(979\) | 48.0918 | 1.53702 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −80.0022 | −2.55427 | ||||||||
\(982\) | −0.0441752 | −0.00140969 | ||||||||
\(983\) | −7.09389 | −0.226260 | −0.113130 | − | 0.993580i | \(-0.536088\pi\) | ||||
−0.113130 | + | 0.993580i | \(0.536088\pi\) | |||||||
\(984\) | −21.0416 | −0.670782 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −6.13445 | −0.195361 | ||||||||
\(987\) | −52.5091 | −1.67138 | ||||||||
\(988\) | −1.31512 | −0.0418395 | ||||||||
\(989\) | −12.7731 | −0.406160 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.2573 | −0.865856 | −0.432928 | − | 0.901429i | \(-0.642520\pi\) | ||||
−0.432928 | + | 0.901429i | \(0.642520\pi\) | |||||||
\(992\) | 10.1030 | 0.320771 | ||||||||
\(993\) | 87.3081 | 2.77064 | ||||||||
\(994\) | −5.24097 | −0.166234 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −23.4505 | −0.743059 | ||||||||
\(997\) | −24.6984 | −0.782207 | −0.391103 | − | 0.920347i | \(-0.627906\pi\) | ||||
−0.391103 | + | 0.920347i | \(0.627906\pi\) | |||||||
\(998\) | 28.2445 | 0.894064 | ||||||||
\(999\) | 2.34453 | 0.0741777 |
(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 | 1850.2.a.be.1.5 | 5 | ||
5.2 | odd | 4 | 370.2.b.d.149.6 | yes | 10 | ||
5.3 | odd | 4 | 370.2.b.d.149.5 | ✓ | 10 | ||
5.4 | even | 2 | 1850.2.a.bd.1.1 | 5 | |||
15.2 | even | 4 | 3330.2.d.p.1999.3 | 10 | |||
15.8 | even | 4 | 3330.2.d.p.1999.8 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.b.d.149.5 | ✓ | 10 | 5.3 | odd | 4 | ||
370.2.b.d.149.6 | yes | 10 | 5.2 | odd | 4 | ||
1850.2.a.bd.1.1 | 5 | 5.4 | even | 2 | |||
1850.2.a.be.1.5 | 5 | 1.1 | even | 1 | trivial | ||
3330.2.d.p.1999.3 | 10 | 15.2 | even | 4 | |||
3330.2.d.p.1999.8 | 10 | 15.8 | even | 4 |