Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} - 11 x^{16} + 123 x^{15} - 35 x^{14} - 982 x^{13} + 988 x^{12} + 3872 x^{11} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 5 \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.24824\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.24824 | −1.58975 | −0.794873 | − | 0.606776i | \(-0.792462\pi\) | ||||
−0.794873 | + | 0.606776i | \(0.792462\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.05458 | 1.52729 | ||||||||
\(5\) | 3.31434 | 1.48222 | 0.741109 | − | 0.671385i | \(-0.234300\pi\) | ||||
0.741109 | + | 0.671385i | \(0.234300\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.37095 | −0.838256 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −7.45143 | −2.35635 | ||||||||
\(11\) | −5.47711 | −1.65141 | −0.825705 | − | 0.564102i | \(-0.809222\pi\) | ||||
−0.825705 | + | 0.564102i | \(0.809222\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.39594 | −1.21921 | −0.609607 | − | 0.792703i | \(-0.708673\pi\) | ||||
−0.609607 | + | 0.792703i | \(0.708673\pi\) | |||||||
\(14\) | −2.24824 | −0.600867 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.778706 | −0.194676 | ||||||||
\(17\) | 2.99559 | 0.726538 | 0.363269 | − | 0.931684i | \(-0.381661\pi\) | ||||
0.363269 | + | 0.931684i | \(0.381661\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.499179 | −0.114519 | −0.0572597 | − | 0.998359i | \(-0.518236\pi\) | ||||
−0.0572597 | + | 0.998359i | \(0.518236\pi\) | |||||||
\(20\) | 10.1239 | 2.26378 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 12.3138 | 2.62532 | ||||||||
\(23\) | 6.47149 | 1.34940 | 0.674699 | − | 0.738093i | \(-0.264273\pi\) | ||||
0.674699 | + | 0.738093i | \(0.264273\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.98485 | 1.19697 | ||||||||
\(26\) | 9.88313 | 1.93824 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.05458 | 0.577261 | ||||||||
\(29\) | −2.28220 | −0.423793 | −0.211897 | − | 0.977292i | \(-0.567964\pi\) | ||||
−0.211897 | + | 0.977292i | \(0.567964\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.20474 | 0.755193 | 0.377597 | − | 0.925970i | \(-0.376751\pi\) | ||||
0.377597 | + | 0.925970i | \(0.376751\pi\) | |||||||
\(32\) | 6.49261 | 1.14774 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.73481 | −1.15501 | ||||||||
\(35\) | 3.31434 | 0.560226 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.84180 | −1.28918 | −0.644592 | − | 0.764526i | \(-0.722973\pi\) | ||||
−0.644592 | + | 0.764526i | \(0.722973\pi\) | |||||||
\(38\) | 1.12227 | 0.182057 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.85812 | −1.24248 | ||||||||
\(41\) | 7.43947 | 1.16185 | 0.580925 | − | 0.813957i | \(-0.302691\pi\) | ||||
0.580925 | + | 0.813957i | \(0.302691\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.74366 | 1.02840 | 0.514200 | − | 0.857671i | \(-0.328089\pi\) | ||||
0.514200 | + | 0.857671i | \(0.328089\pi\) | |||||||
\(44\) | −16.7303 | −2.52218 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −14.5494 | −2.14520 | ||||||||
\(47\) | 8.99909 | 1.31265 | 0.656326 | − | 0.754477i | \(-0.272110\pi\) | ||||
0.656326 | + | 0.754477i | \(0.272110\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −13.4554 | −1.90288 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −13.4278 | −1.86209 | ||||||||
\(53\) | 1.35946 | 0.186736 | 0.0933679 | − | 0.995632i | \(-0.470237\pi\) | ||||
0.0933679 | + | 0.995632i | \(0.470237\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18.1530 | −2.44775 | ||||||||
\(56\) | −2.37095 | −0.316831 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.13092 | 0.673723 | ||||||||
\(59\) | 5.28556 | 0.688121 | 0.344061 | − | 0.938947i | \(-0.388197\pi\) | ||||
0.344061 | + | 0.938947i | \(0.388197\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.533481 | 0.0683053 | 0.0341526 | − | 0.999417i | \(-0.489127\pi\) | ||||
0.0341526 | + | 0.999417i | \(0.489127\pi\) | |||||||
\(62\) | −9.45326 | −1.20057 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −13.0395 | −1.62994 | ||||||||
\(65\) | −14.5696 | −1.80714 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.0967 | −1.72218 | −0.861092 | − | 0.508449i | \(-0.830219\pi\) | ||||
−0.861092 | + | 0.508449i | \(0.830219\pi\) | |||||||
\(68\) | 9.15028 | 1.10963 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.45143 | −0.890616 | ||||||||
\(71\) | 6.62684 | 0.786461 | 0.393231 | − | 0.919440i | \(-0.371357\pi\) | ||||
0.393231 | + | 0.919440i | \(0.371357\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.36264 | 0.744691 | 0.372345 | − | 0.928094i | \(-0.378554\pi\) | ||||
0.372345 | + | 0.928094i | \(0.378554\pi\) | |||||||
\(74\) | 17.6302 | 2.04947 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.52478 | −0.174904 | ||||||||
\(77\) | −5.47711 | −0.624174 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.8144 | −1.77926 | −0.889628 | − | 0.456686i | \(-0.849036\pi\) | ||||
−0.889628 | + | 0.456686i | \(0.849036\pi\) | |||||||
\(80\) | −2.58089 | −0.288553 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −16.7257 | −1.84705 | ||||||||
\(83\) | −5.96805 | −0.655079 | −0.327539 | − | 0.944838i | \(-0.606219\pi\) | ||||
−0.327539 | + | 0.944838i | \(0.606219\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.92842 | 1.07689 | ||||||||
\(86\) | −15.1614 | −1.63489 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 12.9859 | 1.38430 | ||||||||
\(89\) | −6.57010 | −0.696429 | −0.348215 | − | 0.937415i | \(-0.613212\pi\) | ||||
−0.348215 | + | 0.937415i | \(0.613212\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.39594 | −0.460820 | ||||||||
\(92\) | 19.7677 | 2.06092 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −20.2321 | −2.08678 | ||||||||
\(95\) | −1.65445 | −0.169743 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.5689 | 1.27618 | 0.638092 | − | 0.769960i | \(-0.279724\pi\) | ||||
0.638092 | + | 0.769960i | \(0.279724\pi\) | |||||||
\(98\) | −2.24824 | −0.227106 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 18.2812 | 1.82812 | ||||||||
\(101\) | 4.31831 | 0.429688 | 0.214844 | − | 0.976648i | \(-0.431076\pi\) | ||||
0.214844 | + | 0.976648i | \(0.431076\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.67776 | −0.756512 | −0.378256 | − | 0.925701i | \(-0.623476\pi\) | ||||
−0.378256 | + | 0.925701i | \(0.623476\pi\) | |||||||
\(104\) | 10.4225 | 1.02201 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.05638 | −0.296862 | ||||||||
\(107\) | 6.15637 | 0.595159 | 0.297579 | − | 0.954697i | \(-0.403821\pi\) | ||||
0.297579 | + | 0.954697i | \(0.403821\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.1231 | −1.44853 | −0.724263 | − | 0.689524i | \(-0.757820\pi\) | ||||
−0.724263 | + | 0.689524i | \(0.757820\pi\) | |||||||
\(110\) | 40.8123 | 3.89130 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.778706 | −0.0735808 | ||||||||
\(113\) | −1.57617 | −0.148273 | −0.0741366 | − | 0.997248i | \(-0.523620\pi\) | ||||
−0.0741366 | + | 0.997248i | \(0.523620\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 21.4487 | 2.00010 | ||||||||
\(116\) | −6.97115 | −0.647255 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.8832 | −1.09394 | ||||||||
\(119\) | 2.99559 | 0.274606 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.9987 | 1.72715 | ||||||||
\(122\) | −1.19939 | −0.108588 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 12.8437 | 1.15340 | ||||||||
\(125\) | 3.26412 | 0.291951 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | 16.3307 | 1.44345 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 32.7560 | 2.87289 | ||||||||
\(131\) | −0.0249085 | −0.00217626 | −0.00108813 | − | 0.999999i | \(-0.500346\pi\) | ||||
−0.00108813 | + | 0.999999i | \(0.500346\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.499179 | −0.0432843 | ||||||||
\(134\) | 31.6927 | 2.73783 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.10239 | −0.609025 | ||||||||
\(137\) | −19.2352 | −1.64337 | −0.821685 | − | 0.569942i | \(-0.806966\pi\) | ||||
−0.821685 | + | 0.569942i | \(0.806966\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.80780 | 0.577430 | 0.288715 | − | 0.957415i | \(-0.406772\pi\) | ||||
0.288715 | + | 0.957415i | \(0.406772\pi\) | |||||||
\(140\) | 10.1239 | 0.855627 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −14.8987 | −1.25027 | ||||||||
\(143\) | 24.0770 | 2.01342 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.56397 | −0.628154 | ||||||||
\(146\) | −14.3047 | −1.18387 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −23.9534 | −1.96896 | ||||||||
\(149\) | 11.2791 | 0.924021 | 0.462010 | − | 0.886874i | \(-0.347128\pi\) | ||||
0.462010 | + | 0.886874i | \(0.347128\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.10031 | 0.170920 | 0.0854602 | − | 0.996342i | \(-0.472764\pi\) | ||||
0.0854602 | + | 0.996342i | \(0.472764\pi\) | |||||||
\(152\) | 1.18353 | 0.0959966 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 12.3138 | 0.992278 | ||||||||
\(155\) | 13.9359 | 1.11936 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.5687 | 1.16271 | 0.581353 | − | 0.813651i | \(-0.302523\pi\) | ||||
0.581353 | + | 0.813651i | \(0.302523\pi\) | |||||||
\(158\) | 35.5545 | 2.82856 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 21.5187 | 1.70120 | ||||||||
\(161\) | 6.47149 | 0.510025 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.35015 | −0.184078 | −0.0920390 | − | 0.995755i | \(-0.529338\pi\) | ||||
−0.0920390 | + | 0.995755i | \(0.529338\pi\) | |||||||
\(164\) | 22.7245 | 1.77448 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.4176 | 1.04141 | ||||||||
\(167\) | 23.4699 | 1.81616 | 0.908079 | − | 0.418800i | \(-0.137549\pi\) | ||||
0.908079 | + | 0.418800i | \(0.137549\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.32430 | 0.486485 | ||||||||
\(170\) | −22.3215 | −1.71198 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 20.5991 | 1.57066 | ||||||||
\(173\) | −2.47947 | −0.188511 | −0.0942555 | − | 0.995548i | \(-0.530047\pi\) | ||||
−0.0942555 | + | 0.995548i | \(0.530047\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.98485 | 0.452412 | ||||||||
\(176\) | 4.26505 | 0.321490 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 14.7712 | 1.10715 | ||||||||
\(179\) | −9.59334 | −0.717040 | −0.358520 | − | 0.933522i | \(-0.616718\pi\) | ||||
−0.358520 | + | 0.933522i | \(0.616718\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.01943 | 0.0757737 | 0.0378868 | − | 0.999282i | \(-0.487937\pi\) | ||||
0.0378868 | + | 0.999282i | \(0.487937\pi\) | |||||||
\(182\) | 9.88313 | 0.732586 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −15.3435 | −1.13114 | ||||||||
\(185\) | −25.9904 | −1.91085 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.4072 | −1.19981 | ||||||||
\(188\) | 27.4884 | 2.00480 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.71959 | 0.269848 | ||||||||
\(191\) | −9.93407 | −0.718804 | −0.359402 | − | 0.933183i | \(-0.617019\pi\) | ||||
−0.359402 | + | 0.933183i | \(0.617019\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.2597 | 1.09842 | 0.549209 | − | 0.835685i | \(-0.314929\pi\) | ||||
0.549209 | + | 0.835685i | \(0.314929\pi\) | |||||||
\(194\) | −28.2580 | −2.02881 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.05458 | 0.218184 | ||||||||
\(197\) | 12.0045 | 0.855287 | 0.427644 | − | 0.903947i | \(-0.359344\pi\) | ||||
0.427644 | + | 0.903947i | \(0.359344\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.0679 | 1.56435 | 0.782174 | − | 0.623060i | \(-0.214111\pi\) | ||||
0.782174 | + | 0.623060i | \(0.214111\pi\) | |||||||
\(200\) | −14.1897 | −1.00337 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.70860 | −0.683095 | ||||||||
\(203\) | −2.28220 | −0.160179 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 24.6569 | 1.72211 | ||||||||
\(206\) | 17.2614 | 1.20266 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.42314 | 0.237352 | ||||||||
\(209\) | 2.73405 | 0.189119 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.3444 | 1.60710 | 0.803548 | − | 0.595239i | \(-0.202943\pi\) | ||||
0.803548 | + | 0.595239i | \(0.202943\pi\) | |||||||
\(212\) | 4.15257 | 0.285200 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −13.8410 | −0.946151 | ||||||||
\(215\) | 22.3508 | 1.52431 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.20474 | 0.285436 | ||||||||
\(218\) | 34.0002 | 2.30279 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −55.4497 | −3.73842 | ||||||||
\(221\) | −13.1685 | −0.885807 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.33378 | 0.491106 | 0.245553 | − | 0.969383i | \(-0.421030\pi\) | ||||
0.245553 | + | 0.969383i | \(0.421030\pi\) | |||||||
\(224\) | 6.49261 | 0.433806 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.54360 | 0.235717 | ||||||||
\(227\) | 27.0309 | 1.79411 | 0.897053 | − | 0.441924i | \(-0.145704\pi\) | ||||
0.897053 | + | 0.441924i | \(0.145704\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.0556 | −0.862737 | −0.431368 | − | 0.902176i | \(-0.641969\pi\) | ||||
−0.431368 | + | 0.902176i | \(0.641969\pi\) | |||||||
\(230\) | −48.2218 | −3.17965 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.41096 | 0.355247 | ||||||||
\(233\) | 23.6719 | 1.55080 | 0.775398 | − | 0.631473i | \(-0.217549\pi\) | ||||
0.775398 | + | 0.631473i | \(0.217549\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 29.8260 | 1.94564 | ||||||||
\(236\) | 16.1452 | 1.05096 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.73481 | −0.436553 | ||||||||
\(239\) | −28.3744 | −1.83539 | −0.917693 | − | 0.397289i | \(-0.869951\pi\) | ||||
−0.917693 | + | 0.397289i | \(0.869951\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.89559 | −0.444184 | −0.222092 | − | 0.975026i | \(-0.571288\pi\) | ||||
−0.222092 | + | 0.975026i | \(0.571288\pi\) | |||||||
\(242\) | −42.7136 | −2.74573 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.62956 | 0.104322 | ||||||||
\(245\) | 3.31434 | 0.211745 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.19436 | 0.139624 | ||||||||
\(248\) | −9.96921 | −0.633045 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.33851 | −0.464128 | ||||||||
\(251\) | −18.5391 | −1.17018 | −0.585090 | − | 0.810968i | \(-0.698941\pi\) | ||||
−0.585090 | + | 0.810968i | \(0.698941\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −35.4450 | −2.22841 | ||||||||
\(254\) | −2.24824 | −0.141067 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.6364 | −0.664774 | ||||||||
\(257\) | −14.7593 | −0.920662 | −0.460331 | − | 0.887747i | \(-0.652269\pi\) | ||||
−0.460331 | + | 0.887747i | \(0.652269\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.84180 | −0.487266 | ||||||||
\(260\) | −44.5041 | −2.76003 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.0560002 | 0.00345971 | ||||||||
\(263\) | −10.8798 | −0.670877 | −0.335439 | − | 0.942062i | \(-0.608884\pi\) | ||||
−0.335439 | + | 0.942062i | \(0.608884\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.50570 | 0.276783 | ||||||||
\(266\) | 1.12227 | 0.0688110 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −43.0594 | −2.63027 | ||||||||
\(269\) | −10.9718 | −0.668960 | −0.334480 | − | 0.942403i | \(-0.608561\pi\) | ||||
−0.334480 | + | 0.942403i | \(0.608561\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.1714 | 0.739362 | 0.369681 | − | 0.929159i | \(-0.379467\pi\) | ||||
0.369681 | + | 0.929159i | \(0.379467\pi\) | |||||||
\(272\) | −2.33269 | −0.141440 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 43.2452 | 2.61254 | ||||||||
\(275\) | −32.7796 | −1.97669 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.1659 | 1.09149 | 0.545743 | − | 0.837953i | \(-0.316247\pi\) | ||||
0.545743 | + | 0.837953i | \(0.316247\pi\) | |||||||
\(278\) | −15.3056 | −0.917966 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.85812 | −0.469612 | ||||||||
\(281\) | 11.9874 | 0.715107 | 0.357554 | − | 0.933893i | \(-0.383611\pi\) | ||||
0.357554 | + | 0.933893i | \(0.383611\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.09385 | −0.183910 | −0.0919552 | − | 0.995763i | \(-0.529312\pi\) | ||||
−0.0919552 | + | 0.995763i | \(0.529312\pi\) | |||||||
\(284\) | 20.2422 | 1.20115 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −54.1309 | −3.20083 | ||||||||
\(287\) | 7.43947 | 0.439138 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.02641 | −0.472142 | ||||||||
\(290\) | 17.0056 | 0.998604 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 19.4352 | 1.13736 | ||||||||
\(293\) | 22.8848 | 1.33694 | 0.668471 | − | 0.743738i | \(-0.266949\pi\) | ||||
0.668471 | + | 0.743738i | \(0.266949\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.5181 | 1.01995 | ||||||||
\(296\) | 18.5925 | 1.08067 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −25.3581 | −1.46896 | ||||||||
\(299\) | −28.4483 | −1.64521 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.74366 | 0.388698 | ||||||||
\(302\) | −4.72199 | −0.271720 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.388713 | 0.0222942 | ||||||||
\(305\) | 1.76814 | 0.101243 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.6006 | −1.57525 | −0.787625 | − | 0.616155i | \(-0.788689\pi\) | ||||
−0.787625 | + | 0.616155i | \(0.788689\pi\) | |||||||
\(308\) | −16.7303 | −0.953295 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −31.3313 | −1.77950 | ||||||||
\(311\) | −11.1839 | −0.634182 | −0.317091 | − | 0.948395i | \(-0.602706\pi\) | ||||
−0.317091 | + | 0.948395i | \(0.602706\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 30.9402 | 1.74884 | 0.874422 | − | 0.485166i | \(-0.161241\pi\) | ||||
0.874422 | + | 0.485166i | \(0.161241\pi\) | |||||||
\(314\) | −32.7539 | −1.84841 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −48.3062 | −2.71744 | ||||||||
\(317\) | −5.00488 | −0.281102 | −0.140551 | − | 0.990073i | \(-0.544887\pi\) | ||||
−0.140551 | + | 0.990073i | \(0.544887\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.4998 | 0.699856 | ||||||||
\(320\) | −43.2174 | −2.41593 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −14.5494 | −0.810809 | ||||||||
\(323\) | −1.49534 | −0.0832028 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −26.3090 | −1.45936 | ||||||||
\(326\) | 5.28370 | 0.292637 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −17.6386 | −0.973928 | ||||||||
\(329\) | 8.99909 | 0.496136 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.7088 | 0.588609 | 0.294305 | − | 0.955712i | \(-0.404912\pi\) | ||||
0.294305 | + | 0.955712i | \(0.404912\pi\) | |||||||
\(332\) | −18.2299 | −1.00049 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −52.7660 | −2.88723 | ||||||||
\(335\) | −46.7212 | −2.55265 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.32836 | −0.453675 | −0.226837 | − | 0.973933i | \(-0.572839\pi\) | ||||
−0.226837 | + | 0.973933i | \(0.572839\pi\) | |||||||
\(338\) | −14.2185 | −0.773387 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 30.3271 | 1.64472 | ||||||||
\(341\) | −23.0298 | −1.24713 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −15.9889 | −0.862062 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.57445 | 0.299684 | ||||||||
\(347\) | −4.09711 | −0.219945 | −0.109972 | − | 0.993935i | \(-0.535076\pi\) | ||||
−0.109972 | + | 0.993935i | \(0.535076\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.8638 | 1.33093 | 0.665465 | − | 0.746429i | \(-0.268233\pi\) | ||||
0.665465 | + | 0.746429i | \(0.268233\pi\) | |||||||
\(350\) | −13.4554 | −0.719220 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −35.5607 | −1.89539 | ||||||||
\(353\) | 2.37283 | 0.126293 | 0.0631465 | − | 0.998004i | \(-0.479886\pi\) | ||||
0.0631465 | + | 0.998004i | \(0.479886\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.9636 | 1.16571 | ||||||||
\(356\) | −20.0689 | −1.06365 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 21.5681 | 1.13991 | ||||||||
\(359\) | 8.59806 | 0.453788 | 0.226894 | − | 0.973919i | \(-0.427143\pi\) | ||||
0.226894 | + | 0.973919i | \(0.427143\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7508 | −0.986885 | ||||||||
\(362\) | −2.29192 | −0.120461 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −13.4278 | −0.703805 | ||||||||
\(365\) | 21.0880 | 1.10379 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.33703 | 0.435189 | 0.217595 | − | 0.976039i | \(-0.430179\pi\) | ||||
0.217595 | + | 0.976039i | \(0.430179\pi\) | |||||||
\(368\) | −5.03938 | −0.262696 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 58.4326 | 3.03777 | ||||||||
\(371\) | 1.35946 | 0.0705795 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.4028 | 0.745747 | 0.372873 | − | 0.927882i | \(-0.378373\pi\) | ||||
0.372873 | + | 0.927882i | \(0.378373\pi\) | |||||||
\(374\) | 36.8873 | 1.90740 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −21.3364 | −1.10034 | ||||||||
\(377\) | 10.0324 | 0.516695 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.5035 | 0.693626 | 0.346813 | − | 0.937934i | \(-0.387264\pi\) | ||||
0.346813 | + | 0.937934i | \(0.387264\pi\) | |||||||
\(380\) | −5.05364 | −0.259246 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 22.3342 | 1.14272 | ||||||||
\(383\) | 11.1740 | 0.570962 | 0.285481 | − | 0.958384i | \(-0.407847\pi\) | ||||
0.285481 | + | 0.958384i | \(0.407847\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18.1530 | −0.925162 | ||||||||
\(386\) | −34.3075 | −1.74620 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 38.3928 | 1.94910 | ||||||||
\(389\) | 29.1166 | 1.47627 | 0.738134 | − | 0.674654i | \(-0.235707\pi\) | ||||
0.738134 | + | 0.674654i | \(0.235707\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.3860 | 0.980390 | ||||||||
\(392\) | −2.37095 | −0.119751 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −26.9891 | −1.35969 | ||||||||
\(395\) | −52.4142 | −2.63724 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.2799 | 0.766878 | 0.383439 | − | 0.923566i | \(-0.374740\pi\) | ||||
0.383439 | + | 0.923566i | \(0.374740\pi\) | |||||||
\(398\) | −49.6138 | −2.48692 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.66043 | −0.233022 | ||||||||
\(401\) | −27.6205 | −1.37930 | −0.689652 | − | 0.724141i | \(-0.742236\pi\) | ||||
−0.689652 | + | 0.724141i | \(0.742236\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.4838 | −0.920743 | ||||||||
\(404\) | 13.1906 | 0.656258 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.13092 | 0.254643 | ||||||||
\(407\) | 42.9504 | 2.12897 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.51095 | 0.272499 | 0.136249 | − | 0.990675i | \(-0.456495\pi\) | ||||
0.136249 | + | 0.990675i | \(0.456495\pi\) | |||||||
\(410\) | −55.4347 | −2.73772 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −23.4523 | −1.15541 | ||||||||
\(413\) | 5.28556 | 0.260085 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −19.7801 | −0.970969 | ||||||||
\(416\) | −28.5411 | −1.39934 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.14681 | −0.300650 | ||||||||
\(419\) | 26.9938 | 1.31873 | 0.659366 | − | 0.751822i | \(-0.270825\pi\) | ||||
0.659366 | + | 0.751822i | \(0.270825\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.9232 | −1.11721 | −0.558605 | − | 0.829434i | \(-0.688663\pi\) | ||||
−0.558605 | + | 0.829434i | \(0.688663\pi\) | |||||||
\(422\) | −52.4839 | −2.55487 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.22320 | −0.156532 | ||||||||
\(425\) | 17.9282 | 0.869644 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.533481 | 0.0258170 | ||||||||
\(428\) | 18.8051 | 0.908980 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −50.2499 | −2.42327 | ||||||||
\(431\) | 6.16714 | 0.297061 | 0.148530 | − | 0.988908i | \(-0.452546\pi\) | ||||
0.148530 | + | 0.988908i | \(0.452546\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.1082 | −0.966340 | −0.483170 | − | 0.875526i | \(-0.660515\pi\) | ||||
−0.483170 | + | 0.875526i | \(0.660515\pi\) | |||||||
\(434\) | −9.45326 | −0.453771 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −46.1946 | −2.21232 | ||||||||
\(437\) | −3.23043 | −0.154532 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.8552 | 0.661273 | 0.330636 | − | 0.943758i | \(-0.392737\pi\) | ||||
0.330636 | + | 0.943758i | \(0.392737\pi\) | |||||||
\(440\) | 43.0397 | 2.05184 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 29.6058 | 1.40821 | ||||||||
\(443\) | 14.4784 | 0.687890 | 0.343945 | − | 0.938990i | \(-0.388237\pi\) | ||||
0.343945 | + | 0.938990i | \(0.388237\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −21.7755 | −1.03226 | ||||||||
\(446\) | −16.4881 | −0.780734 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −13.0395 | −0.616060 | ||||||||
\(449\) | 27.1832 | 1.28286 | 0.641428 | − | 0.767183i | \(-0.278342\pi\) | ||||
0.641428 | + | 0.767183i | \(0.278342\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −40.7468 | −1.91869 | ||||||||
\(452\) | −4.81452 | −0.226456 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −60.7720 | −2.85217 | ||||||||
\(455\) | −14.5696 | −0.683035 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.56791 | 0.260456 | 0.130228 | − | 0.991484i | \(-0.458429\pi\) | ||||
0.130228 | + | 0.991484i | \(0.458429\pi\) | |||||||
\(458\) | 29.3521 | 1.37153 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 65.5168 | 3.05473 | ||||||||
\(461\) | 9.34013 | 0.435013 | 0.217507 | − | 0.976059i | \(-0.430208\pi\) | ||||
0.217507 | + | 0.976059i | \(0.430208\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.05307 | −0.0954144 | −0.0477072 | − | 0.998861i | \(-0.515191\pi\) | ||||
−0.0477072 | + | 0.998861i | \(0.515191\pi\) | |||||||
\(464\) | 1.77716 | 0.0825025 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −53.2200 | −2.46537 | ||||||||
\(467\) | 32.0662 | 1.48384 | 0.741922 | − | 0.670486i | \(-0.233914\pi\) | ||||
0.741922 | + | 0.670486i | \(0.233914\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.0967 | −0.650925 | ||||||||
\(470\) | −67.0561 | −3.09307 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −12.5318 | −0.576822 | ||||||||
\(473\) | −36.9358 | −1.69831 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.98751 | −0.137076 | ||||||||
\(476\) | 9.15028 | 0.419402 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 63.7924 | 2.91780 | ||||||||
\(479\) | 25.0510 | 1.14461 | 0.572305 | − | 0.820041i | \(-0.306049\pi\) | ||||
0.572305 | + | 0.820041i | \(0.306049\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.4721 | 1.57179 | ||||||||
\(482\) | 15.5029 | 0.706139 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 58.0330 | 2.63786 | ||||||||
\(485\) | 41.6578 | 1.89158 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.1154 | −1.09277 | −0.546386 | − | 0.837534i | \(-0.683997\pi\) | ||||
−0.546386 | + | 0.837534i | \(0.683997\pi\) | |||||||
\(488\) | −1.26486 | −0.0572573 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −7.45143 | −0.336621 | ||||||||
\(491\) | 41.4602 | 1.87107 | 0.935535 | − | 0.353233i | \(-0.114918\pi\) | ||||
0.935535 | + | 0.353233i | \(0.114918\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.83653 | −0.307902 | ||||||||
\(494\) | −4.93345 | −0.221966 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.27425 | −0.147018 | ||||||||
\(497\) | 6.62684 | 0.297254 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.32228 | 0.283024 | 0.141512 | − | 0.989937i | \(-0.454804\pi\) | ||||
0.141512 | + | 0.989937i | \(0.454804\pi\) | |||||||
\(500\) | 9.97050 | 0.445894 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 41.6804 | 1.86029 | ||||||||
\(503\) | 30.3857 | 1.35483 | 0.677416 | − | 0.735600i | \(-0.263100\pi\) | ||||
0.677416 | + | 0.735600i | \(0.263100\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.3124 | 0.636891 | ||||||||
\(506\) | 79.6889 | 3.54260 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.05458 | 0.135525 | ||||||||
\(509\) | 43.5835 | 1.93181 | 0.965903 | − | 0.258906i | \(-0.0833618\pi\) | ||||
0.965903 | + | 0.258906i | \(0.0833618\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.36264 | 0.281467 | ||||||||
\(512\) | −8.74837 | −0.386627 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 33.1825 | 1.46362 | ||||||||
\(515\) | −25.4467 | −1.12132 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −49.2890 | −2.16773 | ||||||||
\(518\) | 17.6302 | 0.774629 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 34.5438 | 1.51485 | ||||||||
\(521\) | −3.41203 | −0.149484 | −0.0747419 | − | 0.997203i | \(-0.523813\pi\) | ||||
−0.0747419 | + | 0.997203i | \(0.523813\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.13861 | −0.180969 | −0.0904844 | − | 0.995898i | \(-0.528842\pi\) | ||||
−0.0904844 | + | 0.995898i | \(0.528842\pi\) | |||||||
\(524\) | −0.0760849 | −0.00332379 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.4604 | 1.06652 | ||||||||
\(527\) | 12.5957 | 0.548677 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.8801 | 0.820876 | ||||||||
\(530\) | −10.1299 | −0.440015 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.52478 | −0.0661076 | ||||||||
\(533\) | −32.7035 | −1.41655 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20.4043 | 0.882155 | ||||||||
\(536\) | 33.4225 | 1.44363 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 24.6671 | 1.06348 | ||||||||
\(539\) | −5.47711 | −0.235916 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.5714 | 1.31437 | 0.657184 | − | 0.753730i | \(-0.271747\pi\) | ||||
0.657184 | + | 0.753730i | \(0.271747\pi\) | |||||||
\(542\) | −27.3643 | −1.17540 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 19.4492 | 0.833878 | ||||||||
\(545\) | −50.1229 | −2.14703 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.9946 | −1.49626 | −0.748131 | − | 0.663551i | \(-0.769049\pi\) | ||||
−0.748131 | + | 0.663551i | \(0.769049\pi\) | |||||||
\(548\) | −58.7553 | −2.50990 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 73.6965 | 3.14243 | ||||||||
\(551\) | 1.13922 | 0.0485325 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.8144 | −0.672495 | ||||||||
\(554\) | −40.8414 | −1.73518 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 20.7950 | 0.881903 | ||||||||
\(557\) | −2.88453 | −0.122222 | −0.0611108 | − | 0.998131i | \(-0.519464\pi\) | ||||
−0.0611108 | + | 0.998131i | \(0.519464\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29.6448 | −1.25384 | ||||||||
\(560\) | −2.58089 | −0.109063 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −26.9505 | −1.13684 | ||||||||
\(563\) | 12.0756 | 0.508924 | 0.254462 | − | 0.967083i | \(-0.418102\pi\) | ||||
0.254462 | + | 0.967083i | \(0.418102\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.22395 | −0.219773 | ||||||||
\(566\) | 6.95572 | 0.292371 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −15.7119 | −0.659256 | ||||||||
\(569\) | −4.27015 | −0.179014 | −0.0895070 | − | 0.995986i | \(-0.528529\pi\) | ||||
−0.0895070 | + | 0.995986i | \(0.528529\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.6795 | 1.28390 | 0.641949 | − | 0.766747i | \(-0.278126\pi\) | ||||
0.641949 | + | 0.766747i | \(0.278126\pi\) | |||||||
\(572\) | 73.5452 | 3.07508 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −16.7257 | −0.698118 | ||||||||
\(575\) | 38.7309 | 1.61519 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.83635 | −0.0764482 | −0.0382241 | − | 0.999269i | \(-0.512170\pi\) | ||||
−0.0382241 | + | 0.999269i | \(0.512170\pi\) | |||||||
\(578\) | 18.0453 | 0.750585 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −23.1047 | −0.959372 | ||||||||
\(581\) | −5.96805 | −0.247596 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.44589 | −0.308377 | ||||||||
\(584\) | −15.0855 | −0.624241 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −51.4504 | −2.12540 | ||||||||
\(587\) | 38.6222 | 1.59411 | 0.797054 | − | 0.603908i | \(-0.206390\pi\) | ||||
0.797054 | + | 0.603908i | \(0.206390\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.09892 | −0.0864843 | ||||||||
\(590\) | −39.3850 | −1.62145 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.10646 | 0.250974 | ||||||||
\(593\) | 19.1132 | 0.784886 | 0.392443 | − | 0.919776i | \(-0.371630\pi\) | ||||
0.392443 | + | 0.919776i | \(0.371630\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.92842 | 0.407025 | ||||||||
\(596\) | 34.4529 | 1.41125 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 63.9585 | 2.61546 | ||||||||
\(599\) | 9.55259 | 0.390308 | 0.195154 | − | 0.980773i | \(-0.437479\pi\) | ||||
0.195154 | + | 0.980773i | \(0.437479\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.7388 | 1.62098 | 0.810490 | − | 0.585752i | \(-0.199201\pi\) | ||||
0.810490 | + | 0.585752i | \(0.199201\pi\) | |||||||
\(602\) | −15.1614 | −0.617931 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.41555 | 0.261045 | ||||||||
\(605\) | 62.9681 | 2.56002 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.6818 | 1.28592 | 0.642962 | − | 0.765898i | \(-0.277705\pi\) | ||||
0.642962 | + | 0.765898i | \(0.277705\pi\) | |||||||
\(608\) | −3.24097 | −0.131439 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.97520 | −0.160951 | ||||||||
\(611\) | −39.5595 | −1.60041 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.6030 | −0.710980 | −0.355490 | − | 0.934680i | \(-0.615686\pi\) | ||||
−0.355490 | + | 0.934680i | \(0.615686\pi\) | |||||||
\(614\) | 62.0528 | 2.50425 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12.9859 | 0.523218 | ||||||||
\(617\) | 20.1237 | 0.810149 | 0.405075 | − | 0.914284i | \(-0.367246\pi\) | ||||
0.405075 | + | 0.914284i | \(0.367246\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.89268 | −0.196653 | −0.0983267 | − | 0.995154i | \(-0.531349\pi\) | ||||
−0.0983267 | + | 0.995154i | \(0.531349\pi\) | |||||||
\(620\) | 42.5684 | 1.70959 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 25.1441 | 1.00819 | ||||||||
\(623\) | −6.57010 | −0.263226 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.1058 | −0.764234 | ||||||||
\(626\) | −69.5610 | −2.78022 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 44.5012 | 1.77579 | ||||||||
\(629\) | −23.4909 | −0.936642 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.6120 | 0.581695 | 0.290848 | − | 0.956769i | \(-0.406063\pi\) | ||||
0.290848 | + | 0.956769i | \(0.406063\pi\) | |||||||
\(632\) | 37.4950 | 1.49147 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 11.2522 | 0.446880 | ||||||||
\(635\) | 3.31434 | 0.131526 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.39594 | −0.174174 | ||||||||
\(638\) | −28.1026 | −1.11259 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 54.1256 | 2.13950 | ||||||||
\(641\) | −30.1442 | −1.19062 | −0.595312 | − | 0.803495i | \(-0.702972\pi\) | ||||
−0.595312 | + | 0.803495i | \(0.702972\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.02706 | 0.0799396 | 0.0399698 | − | 0.999201i | \(-0.487274\pi\) | ||||
0.0399698 | + | 0.999201i | \(0.487274\pi\) | |||||||
\(644\) | 19.7677 | 0.778955 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.36188 | 0.132271 | ||||||||
\(647\) | −31.2618 | −1.22903 | −0.614514 | − | 0.788906i | \(-0.710648\pi\) | ||||
−0.614514 | + | 0.788906i | \(0.710648\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −28.9496 | −1.13637 | ||||||||
\(650\) | 59.1490 | 2.32001 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.17872 | −0.281140 | ||||||||
\(653\) | −40.2091 | −1.57350 | −0.786752 | − | 0.617270i | \(-0.788239\pi\) | ||||
−0.786752 | + | 0.617270i | \(0.788239\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.0825552 | −0.00322570 | ||||||||
\(656\) | −5.79316 | −0.226185 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −20.2321 | −0.788730 | ||||||||
\(659\) | 39.3476 | 1.53276 | 0.766382 | − | 0.642385i | \(-0.222055\pi\) | ||||
0.766382 | + | 0.642385i | \(0.222055\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.03809 | 0.0792724 | 0.0396362 | − | 0.999214i | \(-0.487380\pi\) | ||||
0.0396362 | + | 0.999214i | \(0.487380\pi\) | |||||||
\(662\) | −24.0760 | −0.935739 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.1499 | 0.549123 | ||||||||
\(665\) | −1.65445 | −0.0641567 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.7692 | −0.571866 | ||||||||
\(668\) | 71.6907 | 2.77380 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 105.040 | 4.05807 | ||||||||
\(671\) | −2.92193 | −0.112800 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.3745 | −1.40213 | −0.701067 | − | 0.713095i | \(-0.747293\pi\) | ||||
−0.701067 | + | 0.713095i | \(0.747293\pi\) | |||||||
\(674\) | 18.7241 | 0.721227 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 19.3181 | 0.743003 | ||||||||
\(677\) | 8.76754 | 0.336964 | 0.168482 | − | 0.985705i | \(-0.446113\pi\) | ||||
0.168482 | + | 0.985705i | \(0.446113\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.5689 | 0.482352 | ||||||||
\(680\) | −23.5397 | −0.902708 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 51.7765 | 1.98262 | ||||||||
\(683\) | −28.0592 | −1.07366 | −0.536828 | − | 0.843692i | \(-0.680377\pi\) | ||||
−0.536828 | + | 0.843692i | \(0.680377\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −63.7518 | −2.43583 | ||||||||
\(686\) | −2.24824 | −0.0858382 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.25133 | −0.200205 | ||||||||
\(689\) | −5.97609 | −0.227671 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 49.3493 | 1.87734 | 0.938668 | − | 0.344821i | \(-0.112060\pi\) | ||||
0.938668 | + | 0.344821i | \(0.112060\pi\) | |||||||
\(692\) | −7.57375 | −0.287911 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.21129 | 0.349656 | ||||||||
\(695\) | 22.5634 | 0.855877 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.2856 | 0.844129 | ||||||||
\(698\) | −55.8998 | −2.11584 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 18.2812 | 0.690964 | ||||||||
\(701\) | −43.6097 | −1.64712 | −0.823558 | − | 0.567232i | \(-0.808014\pi\) | ||||
−0.823558 | + | 0.567232i | \(0.808014\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.91446 | 0.147637 | ||||||||
\(704\) | 71.4188 | 2.69170 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.33469 | −0.200774 | ||||||||
\(707\) | 4.31831 | 0.162407 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.8878 | −1.42291 | −0.711454 | − | 0.702733i | \(-0.751963\pi\) | ||||
−0.711454 | + | 0.702733i | \(0.751963\pi\) | |||||||
\(710\) | −49.3794 | −1.85318 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15.5774 | 0.583786 | ||||||||
\(713\) | 27.2109 | 1.01906 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 79.7995 | 2.98433 | ||||||||
\(716\) | −29.3036 | −1.09513 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −19.3305 | −0.721407 | ||||||||
\(719\) | 50.6110 | 1.88747 | 0.943736 | − | 0.330699i | \(-0.107285\pi\) | ||||
0.943736 | + | 0.330699i | \(0.107285\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.67776 | −0.285935 | ||||||||
\(722\) | 42.1563 | 1.56890 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.11393 | 0.115728 | ||||||||
\(725\) | −13.6586 | −0.507267 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.5430 | 0.724809 | 0.362404 | − | 0.932021i | \(-0.381956\pi\) | ||||
0.362404 | + | 0.932021i | \(0.381956\pi\) | |||||||
\(728\) | 10.4225 | 0.386285 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −47.4108 | −1.75475 | ||||||||
\(731\) | 20.2013 | 0.747172 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.8762 | −0.660274 | −0.330137 | − | 0.943933i | \(-0.607095\pi\) | ||||
−0.330137 | + | 0.943933i | \(0.607095\pi\) | |||||||
\(734\) | −18.7436 | −0.691840 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 42.0168 | 1.54876 | ||||||||
\(737\) | 77.2091 | 2.84403 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.3724 | 0.859768 | 0.429884 | − | 0.902884i | \(-0.358554\pi\) | ||||
0.429884 | + | 0.902884i | \(0.358554\pi\) | |||||||
\(740\) | −79.3897 | −2.91842 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.05638 | −0.112203 | ||||||||
\(743\) | −21.1697 | −0.776640 | −0.388320 | − | 0.921525i | \(-0.626944\pi\) | ||||
−0.388320 | + | 0.921525i | \(0.626944\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 37.3828 | 1.36960 | ||||||||
\(746\) | −32.3809 | −1.18555 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −50.1171 | −1.83246 | ||||||||
\(749\) | 6.15637 | 0.224949 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 49.7278 | 1.81459 | 0.907296 | − | 0.420492i | \(-0.138142\pi\) | ||||
0.907296 | + | 0.420492i | \(0.138142\pi\) | |||||||
\(752\) | −7.00764 | −0.255542 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −22.5552 | −0.821413 | ||||||||
\(755\) | 6.96113 | 0.253341 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.699544 | 0.0254254 | 0.0127127 | − | 0.999919i | \(-0.495953\pi\) | ||||
0.0127127 | + | 0.999919i | \(0.495953\pi\) | |||||||
\(758\) | −30.3590 | −1.10269 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.92261 | 0.142288 | ||||||||
\(761\) | −14.4262 | −0.522949 | −0.261474 | − | 0.965210i | \(-0.584209\pi\) | ||||
−0.261474 | + | 0.965210i | \(0.584209\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.1231 | −0.547491 | ||||||||
\(764\) | −30.3444 | −1.09782 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25.1217 | −0.907685 | ||||||||
\(767\) | −23.2350 | −0.838968 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.0451 | −0.831026 | −0.415513 | − | 0.909587i | \(-0.636398\pi\) | ||||
−0.415513 | + | 0.909587i | \(0.636398\pi\) | |||||||
\(770\) | 40.8123 | 1.47077 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 46.6120 | 1.67760 | ||||||||
\(773\) | 1.43085 | 0.0514640 | 0.0257320 | − | 0.999669i | \(-0.491808\pi\) | ||||
0.0257320 | + | 0.999669i | \(0.491808\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 25.1647 | 0.903943 | ||||||||
\(776\) | −29.8003 | −1.06977 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −65.4610 | −2.34689 | ||||||||
\(779\) | −3.71363 | −0.133054 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.2959 | −1.29877 | ||||||||
\(782\) | −43.5843 | −1.55857 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.778706 | −0.0278109 | ||||||||
\(785\) | 48.2855 | 1.72338 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −50.3549 | −1.79496 | −0.897479 | − | 0.441057i | \(-0.854604\pi\) | ||||
−0.897479 | + | 0.441057i | \(0.854604\pi\) | |||||||
\(788\) | 36.6688 | 1.30627 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 117.840 | 4.19255 | ||||||||
\(791\) | −1.57617 | −0.0560420 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.34515 | −0.0832788 | ||||||||
\(794\) | −34.3530 | −1.21914 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 67.4080 | 2.38921 | ||||||||
\(797\) | −17.2393 | −0.610647 | −0.305323 | − | 0.952249i | \(-0.598765\pi\) | ||||
−0.305323 | + | 0.952249i | \(0.598765\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.9576 | 0.953692 | ||||||||
\(800\) | 38.8573 | 1.37381 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 62.0975 | 2.19274 | ||||||||
\(803\) | −34.8489 | −1.22979 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.4487 | 0.755967 | ||||||||
\(806\) | 41.5560 | 1.46375 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10.2385 | −0.360189 | ||||||||
\(809\) | −40.4761 | −1.42306 | −0.711532 | − | 0.702654i | \(-0.751998\pi\) | ||||
−0.711532 | + | 0.702654i | \(0.751998\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.44221 | −0.331561 | −0.165780 | − | 0.986163i | \(-0.553014\pi\) | ||||
−0.165780 | + | 0.986163i | \(0.553014\pi\) | |||||||
\(812\) | −6.97115 | −0.244639 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −96.5628 | −3.38452 | ||||||||
\(815\) | −7.78920 | −0.272844 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.36629 | −0.117772 | ||||||||
\(818\) | −12.3899 | −0.433204 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 75.3165 | 2.63017 | ||||||||
\(821\) | 26.8033 | 0.935440 | 0.467720 | − | 0.883877i | \(-0.345076\pi\) | ||||
0.467720 | + | 0.883877i | \(0.345076\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.0877 | −0.386492 | −0.193246 | − | 0.981150i | \(-0.561901\pi\) | ||||
−0.193246 | + | 0.981150i | \(0.561901\pi\) | |||||||
\(824\) | 18.2035 | 0.634150 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.8832 | −0.413469 | ||||||||
\(827\) | −20.6815 | −0.719167 | −0.359584 | − | 0.933113i | \(-0.617081\pi\) | ||||
−0.359584 | + | 0.933113i | \(0.617081\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.98033 | −0.207705 | −0.103853 | − | 0.994593i | \(-0.533117\pi\) | ||||
−0.103853 | + | 0.994593i | \(0.533117\pi\) | |||||||
\(830\) | 44.4705 | 1.54359 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 57.3210 | 1.98725 | ||||||||
\(833\) | 2.99559 | 0.103791 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 77.7873 | 2.69194 | ||||||||
\(836\) | 8.35139 | 0.288839 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −60.6885 | −2.09645 | ||||||||
\(839\) | 28.0769 | 0.969321 | 0.484661 | − | 0.874702i | \(-0.338943\pi\) | ||||
0.484661 | + | 0.874702i | \(0.338943\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.7916 | −0.820399 | ||||||||
\(842\) | 51.5369 | 1.77608 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 71.3074 | 2.45450 | ||||||||
\(845\) | 20.9609 | 0.721076 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.9987 | 0.652803 | ||||||||
\(848\) | −1.05862 | −0.0363530 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −40.3068 | −1.38251 | ||||||||
\(851\) | −50.7481 | −1.73962 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.3187 | −0.866894 | −0.433447 | − | 0.901179i | \(-0.642703\pi\) | ||||
−0.433447 | + | 0.901179i | \(0.642703\pi\) | |||||||
\(854\) | −1.19939 | −0.0410424 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.5964 | −0.498895 | ||||||||
\(857\) | 4.04901 | 0.138312 | 0.0691558 | − | 0.997606i | \(-0.477969\pi\) | ||||
0.0691558 | + | 0.997606i | \(0.477969\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.0822329 | −0.00280575 | −0.00140287 | − | 0.999999i | \(-0.500447\pi\) | ||||
−0.00140287 | + | 0.999999i | \(0.500447\pi\) | |||||||
\(860\) | 68.2723 | 2.32806 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −13.8652 | −0.472251 | ||||||||
\(863\) | 27.8324 | 0.947425 | 0.473712 | − | 0.880680i | \(-0.342914\pi\) | ||||
0.473712 | + | 0.880680i | \(0.342914\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.21782 | −0.279414 | ||||||||
\(866\) | 45.2081 | 1.53623 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 12.8437 | 0.435944 | ||||||||
\(869\) | 86.6170 | 2.93828 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 61.9682 | 2.09971 | ||||||||
\(872\) | 35.8559 | 1.21424 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7.26278 | 0.245667 | ||||||||
\(875\) | 3.26412 | 0.110347 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.7277 | −1.54412 | −0.772058 | − | 0.635553i | \(-0.780772\pi\) | ||||
−0.772058 | + | 0.635553i | \(0.780772\pi\) | |||||||
\(878\) | −31.1498 | −1.05126 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 14.1358 | 0.476519 | ||||||||
\(881\) | −47.0656 | −1.58568 | −0.792840 | − | 0.609430i | \(-0.791398\pi\) | ||||
−0.792840 | + | 0.609430i | \(0.791398\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.6005 | −1.06344 | −0.531721 | − | 0.846920i | \(-0.678454\pi\) | ||||
−0.531721 | + | 0.846920i | \(0.678454\pi\) | |||||||
\(884\) | −40.2241 | −1.35288 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −32.5509 | −1.09357 | ||||||||
\(887\) | 30.9114 | 1.03790 | 0.518951 | − | 0.854804i | \(-0.326323\pi\) | ||||
0.518951 | + | 0.854804i | \(0.326323\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | 48.9566 | 1.64103 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 22.4016 | 0.750062 | ||||||||
\(893\) | −4.49215 | −0.150324 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.7956 | −1.06281 | ||||||||
\(896\) | 16.3307 | 0.545572 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −61.1144 | −2.03942 | ||||||||
\(899\) | −9.59604 | −0.320046 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.07238 | 0.135671 | ||||||||
\(902\) | 91.6085 | 3.05023 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.73700 | 0.124291 | ||||||||
\(905\) | 3.37874 | 0.112313 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.1542 | −0.536390 | −0.268195 | − | 0.963365i | \(-0.586427\pi\) | ||||
−0.268195 | + | 0.963365i | \(0.586427\pi\) | |||||||
\(908\) | 82.5681 | 2.74012 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 32.7560 | 1.08585 | ||||||||
\(911\) | 30.7252 | 1.01797 | 0.508985 | − | 0.860775i | \(-0.330021\pi\) | ||||
0.508985 | + | 0.860775i | \(0.330021\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.6876 | 1.08180 | ||||||||
\(914\) | −12.5180 | −0.414058 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −39.8793 | −1.31765 | ||||||||
\(917\) | −0.0249085 | −0.000822551 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.6178 | 1.20791 | 0.603955 | − | 0.797018i | \(-0.293590\pi\) | ||||
0.603955 | + | 0.797018i | \(0.293590\pi\) | |||||||
\(920\) | −50.8537 | −1.67660 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −20.9988 | −0.691560 | ||||||||
\(923\) | −29.1312 | −0.958865 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −46.9320 | −1.54311 | ||||||||
\(926\) | 4.61580 | 0.151685 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −14.8174 | −0.486405 | ||||||||
\(929\) | 3.45942 | 0.113500 | 0.0567500 | − | 0.998388i | \(-0.481926\pi\) | ||||
0.0567500 | + | 0.998388i | \(0.481926\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.499179 | −0.0163599 | ||||||||
\(932\) | 72.3076 | 2.36851 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −72.0924 | −2.35893 | ||||||||
\(935\) | −54.3790 | −1.77838 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.2761 | 0.891073 | 0.445536 | − | 0.895264i | \(-0.353013\pi\) | ||||
0.445536 | + | 0.895264i | \(0.353013\pi\) | |||||||
\(938\) | 31.6927 | 1.03480 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 91.1060 | 2.97155 | ||||||||
\(941\) | 50.5133 | 1.64669 | 0.823343 | − | 0.567544i | \(-0.192106\pi\) | ||||
0.823343 | + | 0.567544i | \(0.192106\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 48.1444 | 1.56780 | ||||||||
\(944\) | −4.11589 | −0.133961 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 83.0404 | 2.69988 | ||||||||
\(947\) | −31.7991 | −1.03333 | −0.516666 | − | 0.856187i | \(-0.672827\pi\) | ||||
−0.516666 | + | 0.856187i | \(0.672827\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27.9698 | −0.907938 | ||||||||
\(950\) | 6.71663 | 0.217916 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.10239 | −0.230190 | ||||||||
\(953\) | −32.8952 | −1.06558 | −0.532790 | − | 0.846247i | \(-0.678856\pi\) | ||||
−0.532790 | + | 0.846247i | \(0.678856\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −32.9249 | −1.06542 | ||||||||
\(956\) | −86.6718 | −2.80317 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −56.3206 | −1.81964 | ||||||||
\(959\) | −19.2352 | −0.621136 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.3202 | −0.429683 | ||||||||
\(962\) | −77.5016 | −2.49875 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −21.0631 | −0.678397 | ||||||||
\(965\) | 50.5759 | 1.62809 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 60.1512 | 1.93433 | 0.967166 | − | 0.254147i | \(-0.0817947\pi\) | ||||
0.967166 | + | 0.254147i | \(0.0817947\pi\) | |||||||
\(968\) | −45.0449 | −1.44780 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −93.6566 | −3.00713 | ||||||||
\(971\) | 49.3664 | 1.58424 | 0.792122 | − | 0.610363i | \(-0.208976\pi\) | ||||
0.792122 | + | 0.610363i | \(0.208976\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.80780 | 0.218248 | ||||||||
\(974\) | 54.2171 | 1.73723 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.415425 | −0.0132974 | ||||||||
\(977\) | 1.19493 | 0.0382293 | 0.0191147 | − | 0.999817i | \(-0.493915\pi\) | ||||
0.0191147 | + | 0.999817i | \(0.493915\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35.9851 | 1.15009 | ||||||||
\(980\) | 10.1239 | 0.323396 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −93.2124 | −2.97453 | ||||||||
\(983\) | −45.1609 | −1.44041 | −0.720204 | − | 0.693762i | \(-0.755952\pi\) | ||||
−0.720204 | + | 0.693762i | \(0.755952\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 39.7871 | 1.26772 | ||||||||
\(986\) | 15.3702 | 0.489486 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.70285 | 0.213246 | ||||||||
\(989\) | 43.6415 | 1.38772 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.1543 | 0.322562 | 0.161281 | − | 0.986908i | \(-0.448437\pi\) | ||||
0.161281 | + | 0.986908i | \(0.448437\pi\) | |||||||
\(992\) | 27.2997 | 0.866767 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −14.8987 | −0.472559 | ||||||||
\(995\) | 73.1404 | 2.31871 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −59.1360 | −1.87286 | −0.936428 | − | 0.350860i | \(-0.885889\pi\) | ||||
−0.936428 | + | 0.350860i | \(0.885889\pi\) | |||||||
\(998\) | −14.2140 | −0.449936 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8001.2.a.u.1.2 | 18 | ||
3.2 | odd | 2 | 2667.2.a.p.1.17 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.p.1.17 | ✓ | 18 | 3.2 | odd | 2 | ||
8001.2.a.u.1.2 | 18 | 1.1 | even | 1 | trivial |