Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,2,Mod(19,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.l (of order \(10\), degree \(4\), minimal) |
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: | no |
Analytic conductor: | \(3.59326809096\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 289.4 | ||
Root | \(0.0566033 - 1.17421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.289 |
Dual form | 450.2.l.d.109.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{10}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.587785 | + | 0.809017i | 0.415627 | + | 0.572061i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.309017 | + | 0.951057i | −0.154508 | + | 0.475528i | ||||
\(5\) | 1.87020 | + | 1.22570i | 0.836380 | + | 0.548150i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.26086i | 1.23249i | 0.787555 | + | 0.616244i | \(0.211346\pi\) | ||||
−0.787555 | + | 0.616244i | \(0.788654\pi\) | |||||||
\(8\) | −0.951057 | + | 0.309017i | −0.336249 | + | 0.109254i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.107666 | + | 2.23347i | 0.0340469 | + | 0.706287i | ||||
\(11\) | −1.44726 | + | 1.05149i | −0.436364 | + | 0.317037i | −0.784189 | − | 0.620523i | \(-0.786920\pi\) |
0.347825 | + | 0.937560i | \(0.386920\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.38313 | − | 4.65648i | 0.938312 | − | 1.29148i | −0.0182161 | − | 0.999834i | \(-0.505799\pi\) |
0.956528 | − | 0.291641i | \(-0.0942013\pi\) | |||||||
\(14\) | −2.63809 | + | 1.91668i | −0.705059 | + | 0.512255i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | −6.26221 | + | 2.03472i | −1.51881 | + | 0.493491i | −0.945438 | − | 0.325803i | \(-0.894365\pi\) |
−0.573373 | + | 0.819295i | \(0.694365\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.21533 | − | 3.74041i | −0.278816 | − | 0.858108i | −0.988184 | − | 0.153270i | \(-0.951020\pi\) |
0.709368 | − | 0.704838i | \(-0.248980\pi\) | |||||||
\(20\) | −1.74363 | + | 1.39991i | −0.389889 | + | 0.313029i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.70135 | − | 0.552802i | −0.362729 | − | 0.117858i | ||||
\(23\) | 4.91598 | + | 6.76626i | 1.02505 | + | 1.41086i | 0.908600 | + | 0.417667i | \(0.137152\pi\) |
0.116452 | + | 0.993196i | \(0.462848\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.99532 | + | 4.58462i | 0.399064 | + | 0.916923i | ||||
\(26\) | 5.75573 | 1.12879 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.10126 | − | 1.00766i | −0.586083 | − | 0.190430i | ||||
\(29\) | 0.442669 | − | 1.36239i | 0.0822015 | − | 0.252990i | −0.901506 | − | 0.432767i | \(-0.857537\pi\) |
0.983708 | + | 0.179776i | \(0.0575374\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.99827 | + | 6.15005i | 0.358900 | + | 1.10458i | 0.953713 | + | 0.300717i | \(0.0972261\pi\) |
−0.594813 | + | 0.803864i | \(0.702774\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.32696 | − | 3.87026i | −0.913566 | − | 0.663744i | ||||
\(35\) | −3.99683 | + | 6.09846i | −0.675588 | + | 1.03083i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.56303 | − | 9.03323i | 1.07895 | − | 1.48505i | 0.218289 | − | 0.975884i | \(-0.429953\pi\) |
0.860666 | − | 0.509170i | \(-0.170047\pi\) | |||||||
\(38\) | 2.31170 | − | 3.18178i | 0.375007 | − | 0.516153i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.15743 | − | 0.587785i | −0.341120 | − | 0.0929370i | ||||
\(41\) | −3.18453 | − | 2.31370i | −0.497340 | − | 0.361339i | 0.310660 | − | 0.950521i | \(-0.399450\pi\) |
−0.808000 | + | 0.589182i | \(0.799450\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.18577i | − | 0.333327i | −0.986014 | − | 0.166664i | \(-0.946701\pi\) | ||
0.986014 | − | 0.166664i | \(-0.0532994\pi\) | |||||||
\(44\) | −0.552802 | − | 1.70135i | −0.0833381 | − | 0.256488i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.58448 | + | 7.95422i | −0.381061 | + | 1.17279i | ||||
\(47\) | 6.88191 | + | 2.23607i | 1.00383 | + | 0.326164i | 0.764395 | − | 0.644748i | \(-0.223038\pi\) |
0.239435 | + | 0.970912i | \(0.423038\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.63318 | −0.519026 | ||||||||
\(50\) | −2.53621 | + | 4.30902i | −0.358675 | + | 0.609387i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.38313 | + | 4.65648i | 0.469156 | + | 0.645738i | ||||
\(53\) | −1.47281 | − | 0.478544i | −0.202306 | − | 0.0657330i | 0.206111 | − | 0.978529i | \(-0.433919\pi\) |
−0.408417 | + | 0.912795i | \(0.633919\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.99548 | + | 0.192604i | −0.538750 | + | 0.0259707i | ||||
\(56\) | −1.00766 | − | 3.10126i | −0.134654 | − | 0.414423i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.36239 | − | 0.442669i | 0.178891 | − | 0.0581253i | ||||
\(59\) | −8.85810 | − | 6.43579i | −1.15323 | − | 0.837868i | −0.164320 | − | 0.986407i | \(-0.552543\pi\) |
−0.988907 | + | 0.148539i | \(0.952543\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.637605 | − | 0.463247i | 0.0816370 | − | 0.0593128i | −0.546218 | − | 0.837643i | \(-0.683933\pi\) |
0.627855 | + | 0.778330i | \(0.283933\pi\) | |||||||
\(62\) | −3.80094 | + | 5.23154i | −0.482720 | + | 0.664407i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.809017 | − | 0.587785i | 0.101127 | − | 0.0734732i | ||||
\(65\) | 12.0346 | − | 4.56186i | 1.49271 | − | 0.565829i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.46309 | − | 2.42490i | 0.911762 | − | 0.296249i | 0.184679 | − | 0.982799i | \(-0.440876\pi\) |
0.727083 | + | 0.686550i | \(0.240876\pi\) | |||||||
\(68\) | − | 6.58448i | − | 0.798486i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.28304 | + | 0.351083i | −0.870489 | + | 0.0419624i | ||||
\(71\) | 2.12853 | − | 6.55093i | 0.252610 | − | 0.777452i | −0.741682 | − | 0.670752i | \(-0.765971\pi\) |
0.994291 | − | 0.106700i | \(-0.0340285\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.26733 | − | 10.0026i | −0.850577 | − | 1.17072i | −0.983735 | − | 0.179624i | \(-0.942512\pi\) |
0.133159 | − | 0.991095i | \(-0.457488\pi\) | |||||||
\(74\) | 11.1657 | 1.29798 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.93290 | 0.451134 | ||||||||
\(77\) | −3.42877 | − | 4.71929i | −0.390744 | − | 0.537813i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.18285 | − | 3.64043i | 0.133081 | − | 0.409580i | −0.862206 | − | 0.506558i | \(-0.830918\pi\) |
0.995287 | + | 0.0969777i | \(0.0309176\pi\) | |||||||
\(80\) | −0.792578 | − | 2.09089i | −0.0886129 | − | 0.233769i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 3.93630i | − | 0.434691i | ||||||
\(83\) | 6.37438 | − | 2.07116i | 0.699679 | − | 0.227339i | 0.0624883 | − | 0.998046i | \(-0.480096\pi\) |
0.637191 | + | 0.770706i | \(0.280096\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.2056 | − | 3.87026i | −1.54081 | − | 0.419789i | ||||
\(86\) | 1.76833 | − | 1.28477i | 0.190684 | − | 0.138540i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.05149 | − | 1.44726i | 0.112090 | − | 0.154278i | ||||
\(89\) | −1.29271 | + | 0.939207i | −0.137027 | + | 0.0995557i | −0.654187 | − | 0.756333i | \(-0.726989\pi\) |
0.517160 | + | 0.855889i | \(0.326989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.1841 | + | 11.0319i | 1.59173 | + | 1.15646i | ||||
\(92\) | −7.95422 | + | 2.58448i | −0.829285 | + | 0.269451i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.23607 | + | 6.88191i | 0.230633 | + | 0.709815i | ||||
\(95\) | 2.31170 | − | 8.48495i | 0.237175 | − | 0.870538i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.68131 | + | 2.82073i | 0.881454 | + | 0.286402i | 0.714561 | − | 0.699573i | \(-0.246627\pi\) |
0.166893 | + | 0.985975i | \(0.446627\pi\) | |||||||
\(98\) | −2.13553 | − | 2.93930i | −0.215721 | − | 0.296915i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.97682 | + | 0.480938i | −0.497682 | + | 0.0480938i | ||||
\(101\) | 4.57572 | 0.455302 | 0.227651 | − | 0.973743i | \(-0.426896\pi\) | ||||
0.227651 | + | 0.973743i | \(0.426896\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.54128 | + | 1.47555i | 0.447466 | + | 0.145390i | 0.524078 | − | 0.851671i | \(-0.324410\pi\) |
−0.0766118 | + | 0.997061i | \(0.524410\pi\) | |||||||
\(104\) | −1.77862 | + | 5.47402i | −0.174408 | + | 0.536772i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.478544 | − | 1.47281i | −0.0464803 | − | 0.143052i | ||||
\(107\) | − | 9.80214i | − | 0.947609i | −0.880630 | − | 0.473804i | \(-0.842880\pi\) | ||
0.880630 | − | 0.473804i | \(-0.157120\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.36472 | − | 5.35079i | −0.705413 | − | 0.512512i | 0.176278 | − | 0.984340i | \(-0.443594\pi\) |
−0.881691 | + | 0.471828i | \(0.843594\pi\) | |||||||
\(110\) | −2.50430 | − | 3.11920i | −0.238776 | − | 0.297404i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.91668 | − | 2.63809i | 0.181110 | − | 0.249276i | ||||
\(113\) | −2.67031 | + | 3.67537i | −0.251202 | + | 0.345750i | −0.915932 | − | 0.401334i | \(-0.868547\pi\) |
0.664730 | + | 0.747084i | \(0.268547\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.900470 | + | 18.6798i | 0.0839692 | + | 1.74190i | ||||
\(116\) | 1.15892 | + | 0.842006i | 0.107603 | + | 0.0781783i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 10.9492i | − | 1.00796i | ||||||
\(119\) | −6.63492 | − | 20.4202i | −0.608222 | − | 1.87191i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.41027 | + | 7.41806i | −0.219116 | + | 0.674369i | ||||
\(122\) | 0.749550 | + | 0.243544i | 0.0678611 | + | 0.0220494i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.46655 | −0.580713 | ||||||||
\(125\) | −1.88771 | + | 11.0198i | −0.168842 | + | 0.985643i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.88140 | + | 9.47144i | 0.610626 | + | 0.840454i | 0.996629 | − | 0.0820432i | \(-0.0261446\pi\) |
−0.386003 | + | 0.922498i | \(0.626145\pi\) | |||||||
\(128\) | 0.951057 | + | 0.309017i | 0.0840623 | + | 0.0273135i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 10.7644 | + | 7.05479i | 0.944098 | + | 0.618746i | ||||
\(131\) | −0.164308 | − | 0.505688i | −0.0143557 | − | 0.0441822i | 0.943622 | − | 0.331025i | \(-0.107394\pi\) |
−0.957978 | + | 0.286843i | \(0.907394\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.1969 | − | 3.96302i | 1.05761 | − | 0.343638i | ||||
\(134\) | 6.34848 | + | 4.61244i | 0.548425 | + | 0.398454i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.32696 | − | 3.87026i | 0.456783 | − | 0.331872i | ||||
\(137\) | 11.7483 | − | 16.1701i | 1.00372 | − | 1.38151i | 0.0807113 | − | 0.996738i | \(-0.474281\pi\) |
0.923013 | − | 0.384770i | \(-0.125719\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.8021 | + | 12.2075i | −1.42514 | + | 1.03542i | −0.434243 | + | 0.900796i | \(0.642984\pi\) |
−0.990896 | + | 0.134628i | \(0.957016\pi\) | |||||||
\(140\) | −4.56489 | − | 5.68574i | −0.385804 | − | 0.480533i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.55093 | − | 2.12853i | 0.549742 | − | 0.178622i | ||||
\(143\) | 10.2965i | 0.861033i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.49777 | − | 2.00538i | 0.207428 | − | 0.166537i | ||||
\(146\) | 3.82066 | − | 11.7588i | 0.316200 | − | 0.973164i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.56303 | + | 9.03323i | 0.539477 | + | 0.742527i | ||||
\(149\) | 3.80700 | 0.311882 | 0.155941 | − | 0.987766i | \(-0.450159\pi\) | ||||
0.155941 | + | 0.987766i | \(0.450159\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.9802 | −1.21907 | −0.609534 | − | 0.792760i | \(-0.708643\pi\) | ||||
−0.609534 | + | 0.792760i | \(0.708643\pi\) | |||||||
\(152\) | 2.31170 | + | 3.18178i | 0.187503 | + | 0.258076i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.80261 | − | 5.54786i | 0.145258 | − | 0.447059i | ||||
\(155\) | −3.80094 | + | 13.9511i | −0.305299 | + | 1.12058i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 0.333474i | − | 0.0266141i | −0.999911 | − | 0.0133071i | \(-0.995764\pi\) | ||
0.999911 | − | 0.0133071i | \(-0.00423589\pi\) | |||||||
\(158\) | 3.64043 | − | 1.18285i | 0.289617 | − | 0.0941023i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.22570 | − | 1.87020i | 0.0969001 | − | 0.147853i | ||||
\(161\) | −22.0638 | + | 16.0303i | −1.73887 | + | 1.26336i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.13075 | + | 1.55635i | −0.0885674 | + | 0.121903i | −0.851001 | − | 0.525163i | \(-0.824004\pi\) |
0.762434 | + | 0.647066i | \(0.224004\pi\) | |||||||
\(164\) | 3.18453 | − | 2.31370i | 0.248670 | − | 0.180669i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.42237 | + | 3.93958i | 0.420858 | + | 0.305771i | ||||
\(167\) | −1.34265 | + | 0.436254i | −0.103898 | + | 0.0337584i | −0.360504 | − | 0.932757i | \(-0.617395\pi\) |
0.256607 | + | 0.966516i | \(0.417395\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.22001 | − | 19.1432i | −0.478462 | − | 1.47256i | ||||
\(170\) | −5.21871 | − | 13.7674i | −0.400257 | − | 1.05591i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.07879 | + | 0.675441i | 0.158507 | + | 0.0515019i | ||||
\(173\) | −7.78821 | − | 10.7195i | −0.592126 | − | 0.814992i | 0.402833 | − | 0.915274i | \(-0.368026\pi\) |
−0.994959 | + | 0.100282i | \(0.968026\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.9498 | + | 6.50645i | −1.13010 | + | 0.491841i | ||||
\(176\) | 1.78891 | 0.134844 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.51967 | − | 0.493770i | −0.113904 | − | 0.0370096i | ||||
\(179\) | −7.39730 | + | 22.7665i | −0.552900 | + | 1.70165i | 0.148525 | + | 0.988909i | \(0.452547\pi\) |
−0.701425 | + | 0.712743i | \(0.747453\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.36799 | − | 10.3656i | −0.250340 | − | 0.770468i | −0.994712 | − | 0.102703i | \(-0.967251\pi\) |
0.744372 | − | 0.667766i | \(-0.232749\pi\) | |||||||
\(182\) | 18.7686i | 1.39122i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.76626 | − | 4.91598i | −0.498815 | − | 0.362411i | ||||
\(185\) | 23.3462 | − | 8.84968i | 1.71645 | − | 0.650641i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.92354 | − | 9.52943i | 0.506299 | − | 0.696861i | ||||
\(188\) | −4.25325 | + | 5.85410i | −0.310200 | + | 0.426954i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.22325 | − | 3.11713i | 0.596577 | − | 0.226140i | ||||
\(191\) | 4.22273 | + | 3.06799i | 0.305546 | + | 0.221992i | 0.729983 | − | 0.683465i | \(-0.239528\pi\) |
−0.424437 | + | 0.905458i | \(0.639528\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 5.70634i | − | 0.410751i | −0.978683 | − | 0.205376i | \(-0.934158\pi\) | ||
0.978683 | − | 0.205376i | \(-0.0658416\pi\) | |||||||
\(194\) | 2.82073 | + | 8.68131i | 0.202517 | + | 0.623282i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.12271 | − | 3.45536i | 0.0801939 | − | 0.246811i | ||||
\(197\) | 17.0025 | + | 5.52445i | 1.21138 | + | 0.393600i | 0.843935 | − | 0.536446i | \(-0.180233\pi\) |
0.367443 | + | 0.930046i | \(0.380233\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.6446 | −0.825461 | −0.412730 | − | 0.910853i | \(-0.635425\pi\) | ||||
−0.412730 | + | 0.910853i | \(0.635425\pi\) | |||||||
\(200\) | −3.31439 | − | 3.74364i | −0.234362 | − | 0.264715i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.68954 | + | 3.70184i | 0.189236 | + | 0.260460i | ||||
\(203\) | 4.44257 | + | 1.44348i | 0.311807 | + | 0.101312i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.11982 | − | 8.23036i | −0.217898 | − | 0.574833i | ||||
\(206\) | 1.47555 | + | 4.54128i | 0.102807 | + | 0.316406i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.47402 | + | 1.77862i | −0.379555 | + | 0.123325i | ||||
\(209\) | 5.69191 | + | 4.13541i | 0.393717 | + | 0.286052i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.96645 | − | 3.60834i | 0.341904 | − | 0.248408i | −0.403561 | − | 0.914953i | \(-0.632228\pi\) |
0.745465 | + | 0.666545i | \(0.232228\pi\) | |||||||
\(212\) | 0.910244 | − | 1.25284i | 0.0625158 | − | 0.0860457i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.93010 | − | 5.76156i | 0.542091 | − | 0.393852i | ||||
\(215\) | 2.67910 | − | 4.08784i | 0.182713 | − | 0.278788i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.0544 | + | 6.51608i | −1.36138 | + | 0.442340i | ||||
\(218\) | − | 9.10330i | − | 0.616553i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.05149 | − | 3.85944i | 0.0708916 | − | 0.260204i | ||||
\(221\) | −11.7113 | + | 36.0436i | −0.787785 | + | 2.42455i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.32111 | − | 5.94750i | −0.289363 | − | 0.398274i | 0.639444 | − | 0.768838i | \(-0.279165\pi\) |
−0.928807 | + | 0.370563i | \(0.879165\pi\) | |||||||
\(224\) | 3.26086 | 0.217875 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.54301 | −0.302196 | ||||||||
\(227\) | −9.42691 | − | 12.9750i | −0.625686 | − | 0.861183i | 0.372065 | − | 0.928207i | \(-0.378650\pi\) |
−0.997751 | + | 0.0670236i | \(0.978650\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.53767 | + | 10.8878i | −0.233776 | + | 0.719488i | 0.763506 | + | 0.645801i | \(0.223476\pi\) |
−0.997281 | + | 0.0736867i | \(0.976524\pi\) | |||||||
\(230\) | −14.5830 | + | 11.7082i | −0.961574 | + | 0.772016i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.43251i | 0.0940487i | ||||||||
\(233\) | −8.93253 | + | 2.90235i | −0.585189 | + | 0.190140i | −0.586624 | − | 0.809859i | \(-0.699543\pi\) |
0.00143462 | + | 0.999999i | \(0.499543\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.1298 | + | 12.6171i | 0.660797 | + | 0.823046i | ||||
\(236\) | 8.85810 | − | 6.43579i | 0.576613 | − | 0.418934i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 12.6204 | − | 17.3704i | 0.818057 | − | 1.12596i | ||||
\(239\) | −7.21159 | + | 5.23952i | −0.466479 | + | 0.338917i | −0.796067 | − | 0.605208i | \(-0.793090\pi\) |
0.329589 | + | 0.944125i | \(0.393090\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.06186 | + | 5.13074i | 0.454894 | + | 0.330500i | 0.791525 | − | 0.611137i | \(-0.209287\pi\) |
−0.336631 | + | 0.941637i | \(0.609287\pi\) | |||||||
\(242\) | −7.41806 | + | 2.41027i | −0.476851 | + | 0.154938i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.243544 | + | 0.749550i | 0.0155913 | + | 0.0479850i | ||||
\(245\) | −6.79478 | − | 4.45319i | −0.434103 | − | 0.284504i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −21.5288 | − | 6.99512i | −1.36984 | − | 0.445089i | ||||
\(248\) | −3.80094 | − | 5.23154i | −0.241360 | − | 0.332203i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10.0248 | + | 4.95010i | −0.634024 | + | 0.313072i | ||||
\(251\) | −12.6654 | −0.799434 | −0.399717 | − | 0.916639i | \(-0.630892\pi\) | ||||
−0.399717 | + | 0.916639i | \(0.630892\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.2294 | − | 4.62340i | −0.894592 | − | 0.290670i | ||||
\(254\) | −3.61777 | + | 11.1343i | −0.226999 | + | 0.698631i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | 23.3320i | 1.45541i | 0.685889 | + | 0.727706i | \(0.259413\pi\) | ||||
−0.685889 | + | 0.727706i | \(0.740587\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 29.4561 | + | 21.4011i | 1.83031 | + | 1.32980i | ||||
\(260\) | 0.619695 | + | 12.8553i | 0.0384319 | + | 0.797250i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.312532 | − | 0.430164i | 0.0193083 | − | 0.0265756i | ||||
\(263\) | −16.9057 | + | 23.2687i | −1.04245 | + | 1.43481i | −0.147274 | + | 0.989096i | \(0.547050\pi\) |
−0.895176 | + | 0.445713i | \(0.852950\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.16790 | − | 2.70019i | −0.133173 | − | 0.165872i | ||||
\(266\) | 10.3753 | + | 7.53811i | 0.636152 | + | 0.462191i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.84716i | 0.479341i | ||||||||
\(269\) | −8.10976 | − | 24.9593i | −0.494461 | − | 1.52179i | −0.817796 | − | 0.575508i | \(-0.804804\pi\) |
0.323335 | − | 0.946284i | \(-0.395196\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.54474 | + | 13.9873i | −0.276073 | + | 0.849666i | 0.712860 | + | 0.701306i | \(0.247399\pi\) |
−0.988933 | + | 0.148360i | \(0.952601\pi\) | |||||||
\(272\) | 6.26221 | + | 2.03472i | 0.379703 | + | 0.123373i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 19.9874 | 1.20748 | ||||||||
\(275\) | −7.70843 | − | 4.53705i | −0.464836 | − | 0.273594i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.80958 | + | 5.24344i | 0.228895 | + | 0.315048i | 0.907981 | − | 0.419012i | \(-0.137623\pi\) |
−0.679085 | + | 0.734059i | \(0.737623\pi\) | |||||||
\(278\) | −19.7521 | − | 6.41785i | −1.18465 | − | 0.384917i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.91668 | − | 7.03507i | 0.114544 | − | 0.420426i | ||||
\(281\) | −4.22790 | − | 13.0121i | −0.252215 | − | 0.776239i | −0.994366 | − | 0.106005i | \(-0.966194\pi\) |
0.742150 | − | 0.670234i | \(-0.233806\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.07176 | + | 1.64792i | −0.301485 | + | 0.0979584i | −0.455853 | − | 0.890055i | \(-0.650666\pi\) |
0.154368 | + | 0.988013i | \(0.450666\pi\) | |||||||
\(284\) | 5.57255 | + | 4.04870i | 0.330670 | + | 0.240246i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.33001 | + | 6.05210i | −0.492564 | + | 0.357868i | ||||
\(287\) | 7.54463 | − | 10.3843i | 0.445346 | − | 0.612966i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.3220 | − | 15.4913i | 1.25423 | − | 0.911254i | ||||
\(290\) | 3.09053 | + | 0.842006i | 0.181482 | + | 0.0494443i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.7588 | − | 3.82066i | 0.688131 | − | 0.223587i | ||||
\(293\) | 5.03444i | 0.294115i | 0.989128 | + | 0.147058i | \(0.0469803\pi\) | ||||
−0.989128 | + | 0.147058i | \(0.953020\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.67811 | − | 22.8936i | −0.505259 | − | 1.33292i | ||||
\(296\) | −3.45039 | + | 10.6192i | −0.200550 | + | 0.617228i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.23770 | + | 3.07993i | 0.129626 | + | 0.178415i | ||||
\(299\) | 48.1384 | 2.78391 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.12749 | 0.410822 | ||||||||
\(302\) | −8.80511 | − | 12.1192i | −0.506677 | − | 0.697382i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.21533 | + | 3.74041i | −0.0697041 | + | 0.214527i | ||||
\(305\) | 1.76025 | − | 0.0848540i | 0.100792 | − | 0.00485873i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.3668i | 0.934103i | 0.884230 | + | 0.467052i | \(0.154684\pi\) | ||||
−0.884230 | + | 0.467052i | \(0.845316\pi\) | |||||||
\(308\) | 5.54786 | − | 1.80261i | 0.316119 | − | 0.102713i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −13.5208 | + | 5.12524i | −0.767932 | + | 0.291094i | ||||
\(311\) | 16.7904 | − | 12.1989i | 0.952096 | − | 0.691738i | 0.000794562 | − | 1.00000i | \(-0.499747\pi\) |
0.951302 | + | 0.308261i | \(0.0997471\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.5274 | + | 24.1244i | −0.990707 | + | 1.36359i | −0.0598502 | + | 0.998207i | \(0.519062\pi\) |
−0.930857 | + | 0.365384i | \(0.880938\pi\) | |||||||
\(314\) | 0.269786 | − | 0.196011i | 0.0152249 | − | 0.0110615i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.09673 | + | 2.24991i | 0.174205 | + | 0.126567i | ||||
\(317\) | 23.6062 | − | 7.67013i | 1.32586 | − | 0.430797i | 0.441355 | − | 0.897332i | \(-0.354498\pi\) |
0.884503 | + | 0.466535i | \(0.154498\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.791893 | + | 2.43720i | 0.0443375 | + | 0.136457i | ||||
\(320\) | 2.23347 | − | 0.107666i | 0.124855 | − | 0.00601870i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −25.9376 | − | 8.42762i | −1.44544 | − | 0.469653i | ||||
\(323\) | 15.2213 | + | 20.9504i | 0.846938 | + | 1.16571i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 28.0986 | + | 6.21919i | 1.55863 | + | 0.344978i | ||||
\(326\) | −1.92375 | −0.106547 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.74364 | + | 1.21638i | 0.206708 | + | 0.0671635i | ||||
\(329\) | −7.29149 | + | 22.4409i | −0.401993 | + | 1.23721i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.629410 | + | 1.93712i | 0.0345955 | + | 0.106474i | 0.966863 | − | 0.255295i | \(-0.0821727\pi\) |
−0.932268 | + | 0.361769i | \(0.882173\pi\) | |||||||
\(332\) | 6.70242i | 0.367843i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.14213 | − | 0.829805i | −0.0624945 | − | 0.0454049i | ||||
\(335\) | 16.9297 | + | 4.61244i | 0.924968 | + | 0.252005i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.8274 | − | 20.4082i | 0.807700 | − | 1.11170i | −0.183974 | − | 0.982931i | \(-0.558896\pi\) |
0.991674 | − | 0.128773i | \(-0.0411038\pi\) | |||||||
\(338\) | 11.8312 | − | 16.2842i | 0.643531 | − | 0.885744i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8.07060 | − | 12.3143i | 0.437690 | − | 0.667838i | ||||
\(341\) | −9.35874 | − | 6.79953i | −0.506804 | − | 0.368215i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.9787i | 0.592795i | ||||||||
\(344\) | 0.675441 | + | 2.07879i | 0.0364173 | + | 0.112081i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.09450 | − | 12.6016i | 0.220122 | − | 0.677465i | ||||
\(347\) | −19.2892 | − | 6.26743i | −1.03550 | − | 0.336453i | −0.258535 | − | 0.966002i | \(-0.583240\pi\) |
−0.776961 | + | 0.629549i | \(0.783240\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.40434 | 0.0751724 | 0.0375862 | − | 0.999293i | \(-0.488033\pi\) | ||||
0.0375862 | + | 0.999293i | \(0.488033\pi\) | |||||||
\(350\) | −14.0511 | − | 8.27022i | −0.751062 | − | 0.442062i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.05149 | + | 1.44726i | 0.0560448 | + | 0.0771390i | ||||
\(353\) | −3.65495 | − | 1.18756i | −0.194533 | − | 0.0632077i | 0.210130 | − | 0.977673i | \(-0.432611\pi\) |
−0.404663 | + | 0.914466i | \(0.632611\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.0103 | − | 9.64264i | 0.637438 | − | 0.511778i | ||||
\(356\) | −0.493770 | − | 1.51967i | −0.0261698 | − | 0.0805423i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −22.7665 | + | 7.39730i | −1.20325 | + | 0.390959i | ||||
\(359\) | −19.8653 | − | 14.4330i | −1.04845 | − | 0.761744i | −0.0765337 | − | 0.997067i | \(-0.524385\pi\) |
−0.971917 | + | 0.235323i | \(0.924385\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.85771 | − | 2.07625i | 0.150406 | − | 0.109276i | ||||
\(362\) | 6.40629 | − | 8.81750i | 0.336707 | − | 0.463438i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −15.1841 | + | 11.0319i | −0.795864 | + | 0.578229i | ||||
\(365\) | −1.33117 | − | 27.6145i | −0.0696767 | − | 1.44541i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.243387 | − | 0.0790811i | 0.0127047 | − | 0.00412800i | −0.302658 | − | 0.953099i | \(-0.597874\pi\) |
0.315362 | + | 0.948971i | \(0.397874\pi\) | |||||||
\(368\) | − | 8.36356i | − | 0.435981i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 20.8821 | + | 13.6858i | 1.08561 | + | 0.711490i | ||||
\(371\) | 1.56046 | − | 4.80261i | 0.0810152 | − | 0.249339i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.79290 | + | 9.34963i | 0.351723 | + | 0.484105i | 0.947819 | − | 0.318808i | \(-0.103282\pi\) |
−0.596096 | + | 0.802913i | \(0.703282\pi\) | |||||||
\(374\) | 11.7790 | 0.609079 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.23607 | −0.373172 | ||||||||
\(377\) | −4.84636 | − | 6.67044i | −0.249600 | − | 0.343545i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.86925 | − | 11.9083i | 0.198750 | − | 0.611689i | −0.801162 | − | 0.598447i | \(-0.795785\pi\) |
0.999912 | − | 0.0132423i | \(-0.00421528\pi\) | |||||||
\(380\) | 7.35531 | + | 4.82055i | 0.377320 | + | 0.247289i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.21958i | 0.267057i | ||||||||
\(383\) | −0.620541 | + | 0.201626i | −0.0317082 | + | 0.0103026i | −0.324828 | − | 0.945773i | \(-0.605306\pi\) |
0.293120 | + | 0.956076i | \(0.405306\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.628054 | − | 13.0287i | −0.0320086 | − | 0.664003i | ||||
\(386\) | 4.61653 | − | 3.35410i | 0.234975 | − | 0.170719i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.36535 | + | 7.38477i | −0.272384 | + | 0.374905i | ||||
\(389\) | −27.5315 | + | 20.0028i | −1.39590 | + | 1.01418i | −0.400716 | + | 0.916202i | \(0.631239\pi\) |
−0.995188 | + | 0.0979818i | \(0.968761\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −44.5523 | − | 32.3692i | −2.25311 | − | 1.63698i | ||||
\(392\) | 3.45536 | − | 1.12271i | 0.174522 | − | 0.0567056i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.52445 | + | 17.0025i | 0.278318 | + | 0.856573i | ||||
\(395\) | 6.67424 | − | 5.35853i | 0.335817 | − | 0.269617i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.2990 | − | 9.19490i | −1.42029 | − | 0.461479i | −0.504592 | − | 0.863358i | \(-0.668357\pi\) |
−0.915693 | + | 0.401879i | \(0.868357\pi\) | |||||||
\(398\) | −6.84450 | − | 9.42064i | −0.343084 | − | 0.472214i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.08052 | − | 4.88185i | 0.0540261 | − | 0.244093i | ||||
\(401\) | −17.3426 | −0.866050 | −0.433025 | − | 0.901382i | \(-0.642554\pi\) | ||||
−0.433025 | + | 0.901382i | \(0.642554\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 35.3980 | + | 11.5015i | 1.76330 | + | 0.572931i | ||||
\(404\) | −1.41398 | + | 4.35177i | −0.0703480 | + | 0.216509i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.44348 | + | 4.44257i | 0.0716387 | + | 0.220481i | ||||
\(407\) | 19.9744i | 0.990093i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.90864 | + | 5.01942i | 0.341610 | + | 0.248195i | 0.745341 | − | 0.666683i | \(-0.232287\pi\) |
−0.403731 | + | 0.914878i | \(0.632287\pi\) | |||||||
\(410\) | 4.82472 | − | 7.36167i | 0.238276 | − | 0.363567i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.80667 | + | 3.86304i | −0.138275 | + | 0.190319i | ||||
\(413\) | 20.9862 | − | 28.8850i | 1.03266 | − | 1.42134i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.4600 | + | 3.93958i | 0.709814 | + | 0.193387i | ||||
\(416\) | −4.65648 | − | 3.38313i | −0.228303 | − | 0.165872i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.03558i | 0.344122i | ||||||||
\(419\) | −11.2825 | − | 34.7240i | −0.551186 | − | 1.69638i | −0.705809 | − | 0.708402i | \(-0.749416\pi\) |
0.154623 | − | 0.987974i | \(-0.450584\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.826416 | + | 2.54345i | −0.0402770 | + | 0.123960i | −0.969173 | − | 0.246380i | \(-0.920759\pi\) |
0.928896 | + | 0.370340i | \(0.120759\pi\) | |||||||
\(422\) | 5.83841 | + | 1.89701i | 0.284209 | + | 0.0923452i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.54860 | 0.0752067 | ||||||||
\(425\) | −21.8235 | − | 24.6499i | −1.05860 | − | 1.19570i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.51058 | + | 2.07914i | 0.0731022 | + | 0.100617i | ||||
\(428\) | 9.32239 | + | 3.02903i | 0.450615 | + | 0.146414i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.88187 | − | 0.235333i | 0.235425 | − | 0.0113488i | ||||
\(431\) | 2.67910 | + | 8.24543i | 0.129048 | + | 0.397168i | 0.994617 | − | 0.103621i | \(-0.0330430\pi\) |
−0.865569 | + | 0.500790i | \(0.833043\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.9977 | − | 6.17274i | 0.912973 | − | 0.296643i | 0.185392 | − | 0.982665i | \(-0.440644\pi\) |
0.727581 | + | 0.686022i | \(0.240644\pi\) | |||||||
\(434\) | −17.0593 | − | 12.3943i | −0.818873 | − | 0.594946i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.36472 | − | 5.35079i | 0.352706 | − | 0.256256i | ||||
\(437\) | 19.3340 | − | 26.6110i | 0.924872 | − | 1.27298i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.7988 | − | 10.7520i | 0.706310 | − | 0.513164i | −0.175671 | − | 0.984449i | \(-0.556210\pi\) |
0.881981 | + | 0.471285i | \(0.156210\pi\) | |||||||
\(440\) | 3.74041 | − | 1.41785i | 0.178317 | − | 0.0675932i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −36.0436 | + | 11.7113i | −1.71442 | + | 0.557048i | ||||
\(443\) | − | 12.0428i | − | 0.572170i | −0.958204 | − | 0.286085i | \(-0.907646\pi\) | ||
0.958204 | − | 0.286085i | \(-0.0923540\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.56881 | + | 0.172036i | −0.169178 | + | 0.00815531i | ||||
\(446\) | 2.27174 | − | 6.99171i | 0.107570 | − | 0.331067i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.91668 | + | 2.63809i | 0.0905548 | + | 0.124638i | ||||
\(449\) | 35.7261 | 1.68602 | 0.843010 | − | 0.537898i | \(-0.180782\pi\) | ||||
0.843010 | + | 0.537898i | \(0.180782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.04167 | 0.331579 | ||||||||
\(452\) | −2.67031 | − | 3.67537i | −0.125601 | − | 0.172875i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.95602 | − | 15.2531i | 0.232598 | − | 0.715862i | ||||
\(455\) | 14.8756 | + | 39.2431i | 0.697377 | + | 1.83974i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.79597i | 0.224346i | 0.993689 | + | 0.112173i | \(0.0357811\pi\) | ||||
−0.993689 | + | 0.112173i | \(0.964219\pi\) | |||||||
\(458\) | −10.8878 | + | 3.53767i | −0.508755 | + | 0.165304i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −18.0438 | − | 4.91598i | −0.841297 | − | 0.229209i | ||||
\(461\) | −0.416802 | + | 0.302824i | −0.0194124 | + | 0.0141039i | −0.597449 | − | 0.801907i | \(-0.703819\pi\) |
0.578037 | + | 0.816011i | \(0.303819\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.2736 | + | 18.2695i | −0.616876 | + | 0.849057i | −0.997121 | − | 0.0758291i | \(-0.975840\pi\) |
0.380245 | + | 0.924886i | \(0.375840\pi\) | |||||||
\(464\) | −1.15892 | + | 0.842006i | −0.0538016 | + | 0.0390892i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.59846 | − | 5.52061i | −0.351992 | − | 0.255737i | ||||
\(467\) | −37.5947 | + | 12.2153i | −1.73968 | + | 0.565255i | −0.994791 | − | 0.101936i | \(-0.967496\pi\) |
−0.744886 | + | 0.667191i | \(0.767496\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.90726 | + | 24.3361i | 0.365124 | + | 1.12373i | ||||
\(470\) | −4.25325 | + | 15.6113i | −0.196188 | + | 0.720096i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10.4133 | + | 3.38349i | 0.479312 | + | 0.155738i | ||||
\(473\) | 2.29833 | + | 3.16337i | 0.105677 | + | 0.145452i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.7233 | − | 13.0351i | 0.675554 | − | 0.598093i | ||||
\(476\) | 21.4710 | 0.984124 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.47773 | − | 2.75458i | −0.387762 | − | 0.125992i | ||||
\(479\) | 10.0117 | − | 30.8129i | 0.457447 | − | 1.40788i | −0.410791 | − | 0.911730i | \(-0.634747\pi\) |
0.868238 | − | 0.496148i | \(-0.165253\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.8595 | − | 61.1212i | −0.905514 | − | 2.78689i | ||||
\(482\) | 8.72894i | 0.397592i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.31018 | − | 4.58462i | −0.286826 | − | 0.208392i | ||||
\(485\) | 12.7785 | + | 15.9160i | 0.580240 | + | 0.722709i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.5148 | + | 29.6125i | −0.974928 | + | 1.34187i | −0.0354097 | + | 0.999373i | \(0.511274\pi\) |
−0.939518 | + | 0.342500i | \(0.888726\pi\) | |||||||
\(488\) | −0.463247 | + | 0.637605i | −0.0209702 | + | 0.0288630i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.391169 | − | 8.11461i | −0.0176712 | − | 0.366581i | ||||
\(491\) | 15.3601 | + | 11.1597i | 0.693190 | + | 0.503632i | 0.877707 | − | 0.479197i | \(-0.159072\pi\) |
−0.184517 | + | 0.982829i | \(0.559072\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.43231i | 0.424810i | ||||||||
\(494\) | −6.99512 | − | 21.5288i | −0.314725 | − | 0.968624i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.99827 | − | 6.15005i | 0.0897251 | − | 0.276145i | ||||
\(497\) | 21.3616 | + | 6.94082i | 0.958200 | + | 0.311338i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.2476 | 0.682578 | 0.341289 | − | 0.939958i | \(-0.389137\pi\) | ||||
0.341289 | + | 0.939958i | \(0.389137\pi\) | |||||||
\(500\) | −9.89714 | − | 5.20063i | −0.442614 | − | 0.232579i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7.44455 | − | 10.2465i | −0.332266 | − | 0.457325i | ||||
\(503\) | 9.83195 | + | 3.19460i | 0.438385 | + | 0.142440i | 0.519890 | − | 0.854233i | \(-0.325973\pi\) |
−0.0815053 | + | 0.996673i | \(0.525973\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.55753 | + | 5.60846i | 0.380805 | + | 0.249573i | ||||
\(506\) | −4.62340 | − | 14.2294i | −0.205535 | − | 0.632572i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11.1343 | + | 3.61777i | −0.494007 | + | 0.160512i | ||||
\(509\) | −11.0094 | − | 7.99881i | −0.487984 | − | 0.354541i | 0.316424 | − | 0.948618i | \(-0.397518\pi\) |
−0.804409 | + | 0.594077i | \(0.797518\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 32.6171 | − | 23.6977i | 1.44290 | − | 1.04833i | ||||
\(512\) | −0.587785 | + | 0.809017i | −0.0259767 | + | 0.0357538i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −18.8760 | + | 13.7142i | −0.832585 | + | 0.604908i | ||||
\(515\) | 6.68454 | + | 8.32583i | 0.294556 | + | 0.366880i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.3111 | + | 4.00012i | −0.541441 | + | 0.175925i | ||||
\(518\) | 36.4097i | 1.59975i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −10.0359 | + | 8.05748i | −0.440103 | + | 0.353344i | ||||
\(521\) | 12.9865 | − | 39.9683i | 0.568948 | − | 1.75104i | −0.0869703 | − | 0.996211i | \(-0.527719\pi\) |
0.655919 | − | 0.754832i | \(-0.272281\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.9423 | − | 26.0718i | −0.828287 | − | 1.14004i | −0.988239 | − | 0.152915i | \(-0.951134\pi\) |
0.159952 | − | 0.987125i | \(-0.448866\pi\) | |||||||
\(524\) | 0.531712 | 0.0232279 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −28.7617 | −1.25407 | ||||||||
\(527\) | −25.0272 | − | 34.4470i | −1.09020 | − | 1.50054i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.5081 | + | 44.6513i | −0.630786 | + | 1.94136i | ||||
\(530\) | 0.910244 | − | 3.34100i | 0.0395385 | − | 0.145124i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 12.8246i | 0.556017i | ||||||||
\(533\) | −21.5474 | + | 7.00116i | −0.933320 | + | 0.303254i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.0145 | − | 18.3320i | 0.519432 | − | 0.792561i | ||||
\(536\) | −6.34848 | + | 4.61244i | −0.274213 | + | 0.199227i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15.4257 | − | 21.2316i | 0.665048 | − | 0.915360i | ||||
\(539\) | 5.25814 | − | 3.82026i | 0.226484 | − | 0.164550i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.1531 | + | 11.7359i | 0.694476 | + | 0.504566i | 0.878128 | − | 0.478425i | \(-0.158792\pi\) |
−0.183653 | + | 0.982991i | \(0.558792\pi\) | |||||||
\(542\) | −13.9873 | + | 4.54474i | −0.600804 | + | 0.195213i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.03472 | + | 6.26221i | 0.0872378 | + | 0.268490i | ||||
\(545\) | −7.21507 | − | 19.0340i | −0.309060 | − | 0.815327i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.331447 | − | 0.107694i | −0.0141717 | − | 0.00460465i | 0.301923 | − | 0.953332i | \(-0.402372\pi\) |
−0.316094 | + | 0.948728i | \(0.602372\pi\) | |||||||
\(548\) | 11.7483 | + | 16.1701i | 0.501862 | + | 0.690754i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.860353 | − | 8.90306i | −0.0366856 | − | 0.379628i | ||||
\(551\) | −5.63390 | −0.240012 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.8709 | + | 3.85709i | 0.504803 | + | 0.164020i | ||||
\(554\) | −2.00281 | + | 6.16403i | −0.0850914 | + | 0.261885i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.41785 | − | 19.7521i | −0.272177 | − | 0.837676i | ||||
\(557\) | 21.1297i | 0.895294i | 0.894210 | + | 0.447647i | \(0.147738\pi\) | ||||
−0.894210 | + | 0.447647i | \(0.852262\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.1780 | − | 7.39476i | −0.430484 | − | 0.312765i | ||||
\(560\) | 6.81809 | − | 2.58448i | 0.288117 | − | 0.109214i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.04194 | − | 11.0688i | 0.339229 | − | 0.466908i | ||||
\(563\) | 17.9593 | − | 24.7188i | 0.756893 | − | 1.04177i | −0.240573 | − | 0.970631i | \(-0.577335\pi\) |
0.997466 | − | 0.0711432i | \(-0.0226647\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.49893 | + | 3.60069i | −0.399623 | + | 0.151482i | ||||
\(566\) | −4.31430 | − | 3.13452i | −0.181344 | − | 0.131754i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.88806i | 0.289016i | ||||||||
\(569\) | 7.63431 | + | 23.4960i | 0.320047 | + | 0.985003i | 0.973627 | + | 0.228146i | \(0.0732662\pi\) |
−0.653580 | + | 0.756857i | \(0.726734\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.9666 | − | 33.7519i | 0.458940 | − | 1.41247i | −0.407507 | − | 0.913202i | \(-0.633602\pi\) |
0.866447 | − | 0.499269i | \(-0.166398\pi\) | |||||||
\(572\) | −9.79251 | − | 3.18178i | −0.409445 | − | 0.133037i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 12.8357 | 0.535752 | ||||||||
\(575\) | −21.2118 | + | 36.0387i | −0.884592 | + | 1.50292i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.35546 | − | 4.61840i | −0.139690 | − | 0.192266i | 0.733440 | − | 0.679754i | \(-0.237913\pi\) |
−0.873130 | + | 0.487488i | \(0.837913\pi\) | |||||||
\(578\) | 25.0655 | + | 8.14427i | 1.04259 | + | 0.338757i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.13537 | + | 2.99521i | 0.0471438 | + | 0.124369i | ||||
\(581\) | 6.75376 | + | 20.7859i | 0.280193 | + | 0.862346i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.63471 | − | 0.856070i | 0.109119 | − | 0.0354548i | ||||
\(584\) | 10.0026 | + | 7.26733i | 0.413911 | + | 0.300724i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.07295 | + | 2.95917i | −0.168252 | + | 0.122242i | ||||
\(587\) | −11.2569 | + | 15.4938i | −0.464624 | + | 0.639499i | −0.975460 | − | 0.220179i | \(-0.929336\pi\) |
0.510836 | + | 0.859678i | \(0.329336\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.5751 | − | 14.9487i | 0.847783 | − | 0.615950i | ||||
\(590\) | 13.4205 | − | 20.4773i | 0.552511 | − | 0.843035i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −10.6192 | + | 3.45039i | −0.436446 | + | 0.141810i | ||||
\(593\) | − | 10.9253i | − | 0.448648i | −0.974515 | − | 0.224324i | \(-0.927983\pi\) | ||
0.974515 | − | 0.224324i | \(-0.0720174\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.6204 | − | 46.3223i | 0.517384 | − | 1.89903i | ||||
\(596\) | −1.17643 | + | 3.62067i | −0.0481884 | + | 0.148309i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 28.2950 | + | 38.9447i | 1.15707 | + | 1.59257i | ||||
\(599\) | −17.5722 | −0.717981 | −0.358991 | − | 0.933341i | \(-0.616879\pi\) | ||||
−0.358991 | + | 0.933341i | \(0.616879\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.9235 | −0.690325 | −0.345163 | − | 0.938543i | \(-0.612176\pi\) | ||||
−0.345163 | + | 0.938543i | \(0.612176\pi\) | |||||||
\(602\) | 4.18943 | + | 5.76626i | 0.170749 | + | 0.235015i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.62912 | − | 14.2470i | 0.188356 | − | 0.579701i | ||||
\(605\) | −13.6000 | + | 10.9190i | −0.552920 | + | 0.443921i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 35.3264i | − | 1.43386i | −0.697147 | − | 0.716928i | \(-0.745548\pi\) | ||
0.697147 | − | 0.716928i | \(-0.254452\pi\) | |||||||
\(608\) | −3.74041 | + | 1.21533i | −0.151694 | + | 0.0492882i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.10330 | + | 1.37420i | 0.0446713 | + | 0.0556397i | ||||
\(611\) | 33.6946 | − | 24.4806i | 1.36314 | − | 0.990378i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.9273 | + | 31.5567i | −0.926024 | + | 1.27456i | 0.0353661 | + | 0.999374i | \(0.488740\pi\) |
−0.961390 | + | 0.275188i | \(0.911260\pi\) | |||||||
\(614\) | −13.2410 | + | 9.62017i | −0.534364 | + | 0.388238i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.71929 | + | 3.42877i | 0.190146 | + | 0.138149i | ||||
\(617\) | −19.8036 | + | 6.43456i | −0.797261 | + | 0.259046i | −0.679193 | − | 0.733960i | \(-0.737670\pi\) |
−0.118068 | + | 0.993006i | \(0.537670\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.20465 | − | 6.78522i | −0.0886124 | − | 0.272721i | 0.896924 | − | 0.442185i | \(-0.145796\pi\) |
−0.985536 | + | 0.169464i | \(0.945796\pi\) | |||||||
\(620\) | −12.0938 | − | 7.92604i | −0.485697 | − | 0.318318i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 19.7383 | + | 6.41336i | 0.791434 | + | 0.257152i | ||||
\(623\) | −3.06262 | − | 4.21533i | −0.122701 | − | 0.168884i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.0374 | + | 18.2955i | −0.681496 | + | 0.731822i | ||||
\(626\) | −29.8194 | −1.19182 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.317153 | + | 0.103049i | 0.0126558 | + | 0.00411211i | ||||
\(629\) | −22.7190 | + | 69.9219i | −0.905866 | + | 2.78797i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.2234 | + | 34.5422i | 0.446798 | + | 1.37510i | 0.880499 | + | 0.474047i | \(0.157207\pi\) |
−0.433701 | + | 0.901057i | \(0.642793\pi\) | |||||||
\(632\) | 3.82777i | 0.152261i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 20.0807 | + | 14.5895i | 0.797505 | + | 0.579421i | ||||
\(635\) | 1.26048 | + | 26.1480i | 0.0500207 | + | 1.03765i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.2915 | + | 16.9178i | −0.487008 | + | 0.670309i | ||||
\(638\) | −1.50627 | + | 2.07320i | −0.0596338 | + | 0.0820789i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.39991 | + | 1.74363i | 0.0553362 | + | 0.0689232i | ||||
\(641\) | 0.245277 | + | 0.178204i | 0.00968787 | + | 0.00703865i | 0.592619 | − | 0.805483i | \(-0.298094\pi\) |
−0.582931 | + | 0.812522i | \(0.698094\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 45.5553i | 1.79652i | 0.439461 | + | 0.898262i | \(0.355170\pi\) | ||||
−0.439461 | + | 0.898262i | \(0.644830\pi\) | |||||||
\(644\) | −8.42762 | − | 25.9376i | −0.332095 | − | 1.02208i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.00233 | + | 24.6286i | −0.314847 | + | 0.969001i | ||||
\(647\) | 24.4716 | + | 7.95130i | 0.962078 | + | 0.312598i | 0.747614 | − | 0.664134i | \(-0.231200\pi\) |
0.214464 | + | 0.976732i | \(0.431200\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.5871 | 0.768862 | ||||||||
\(650\) | 11.4845 | + | 26.3878i | 0.450460 | + | 1.03501i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.13075 | − | 1.55635i | −0.0442837 | − | 0.0609513i | ||||
\(653\) | 3.37510 | + | 1.09664i | 0.132078 | + | 0.0429148i | 0.374310 | − | 0.927304i | \(-0.377880\pi\) |
−0.242232 | + | 0.970218i | \(0.577880\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.312532 | − | 1.14713i | 0.0122116 | − | 0.0448221i | ||||
\(656\) | 1.21638 | + | 3.74364i | 0.0474918 | + | 0.146165i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −22.4409 | + | 7.29149i | −0.874838 | + | 0.284252i | ||||
\(659\) | −7.87551 | − | 5.72189i | −0.306786 | − | 0.222893i | 0.423730 | − | 0.905789i | \(-0.360721\pi\) |
−0.730516 | + | 0.682895i | \(0.760721\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.8343 | + | 20.2228i | −1.08263 | + | 0.786575i | −0.978139 | − | 0.207952i | \(-0.933320\pi\) |
−0.104488 | + | 0.994526i | \(0.533320\pi\) | |||||||
\(662\) | −1.19721 | + | 1.64782i | −0.0465308 | + | 0.0640442i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.42237 | + | 3.93958i | −0.210429 | + | 0.152885i | ||||
\(665\) | 27.6682 | + | 7.53811i | 1.07293 | + | 0.292316i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.3945 | − | 3.70229i | 0.441196 | − | 0.143353i | ||||
\(668\) | − | 1.41175i | − | 0.0546222i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.21948 | + | 16.4075i | 0.240280 | + | 0.633879i | ||||
\(671\) | −0.435677 | + | 1.34088i | −0.0168191 | + | 0.0517639i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.6142 | + | 15.9856i | 0.447696 | + | 0.616200i | 0.971901 | − | 0.235392i | \(-0.0756374\pi\) |
−0.524205 | + | 0.851592i | \(0.675637\pi\) | |||||||
\(674\) | 25.2259 | 0.971665 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 20.1284 | 0.774169 | ||||||||
\(677\) | 12.1757 | + | 16.7585i | 0.467952 | + | 0.644081i | 0.976134 | − | 0.217169i | \(-0.0696823\pi\) |
−0.508182 | + | 0.861250i | \(0.669682\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.19799 | + | 28.3085i | −0.352987 | + | 1.08638i | ||||
\(680\) | 14.7063 | − | 0.708924i | 0.563960 | − | 0.0271860i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 11.5680i | − | 0.442963i | ||||||
\(683\) | 23.7317 | − | 7.71091i | 0.908069 | − | 0.295050i | 0.182506 | − | 0.983205i | \(-0.441579\pi\) |
0.725564 | + | 0.688155i | \(0.241579\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 41.7914 | − | 15.8416i | 1.59677 | − | 0.605275i | ||||
\(686\) | −8.88197 | + | 6.45313i | −0.339115 | + | 0.246382i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.28477 | + | 1.76833i | −0.0489812 | + | 0.0674169i | ||||
\(689\) | −7.21103 | + | 5.23912i | −0.274718 | + | 0.199594i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.52642 | − | 2.56210i | −0.134152 | − | 0.0974668i | 0.518686 | − | 0.854965i | \(-0.326421\pi\) |
−0.652837 | + | 0.757498i | \(0.726421\pi\) | |||||||
\(692\) | 12.6016 | − | 4.09450i | 0.479040 | − | 0.155650i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.26743 | − | 19.2892i | −0.237908 | − | 0.732206i | ||||
\(695\) | −46.3861 | + | 2.23607i | −1.75953 | + | 0.0848189i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.6499 | + | 8.00925i | 0.933683 | + | 0.303372i | ||||
\(698\) | 0.825448 | + | 1.13613i | 0.0312437 | + | 0.0430032i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.56827 | − | 16.2287i | −0.0592750 | − | 0.613386i | ||||
\(701\) | 1.08146 | 0.0408460 | 0.0204230 | − | 0.999791i | \(-0.493499\pi\) | ||||
0.0204230 | + | 0.999791i | \(0.493499\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −41.7642 | − | 13.5700i | −1.57517 | − | 0.511803i | ||||
\(704\) | −0.552802 | + | 1.70135i | −0.0208345 | + | 0.0641221i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.18756 | − | 3.65495i | −0.0446946 | − | 0.137556i | ||||
\(707\) | 14.9208i | 0.561154i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.0706 | + | 8.76980i | 0.453321 | + | 0.329357i | 0.790906 | − | 0.611938i | \(-0.209610\pi\) |
−0.337585 | + | 0.941295i | \(0.609610\pi\) | |||||||
\(710\) | 14.8605 | + | 4.04870i | 0.557705 | + | 0.151945i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.939207 | − | 1.29271i | 0.0351983 | − | 0.0484463i | ||||
\(713\) | −31.7894 | + | 43.7543i | −1.19052 | + | 1.63861i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.6204 | + | 19.2565i | −0.471975 | + | 0.720151i | ||||
\(716\) | −19.3664 | − | 14.0705i | −0.723756 | − | 0.525839i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 24.5549i | − | 0.916380i | ||||||
\(719\) | −12.4072 | − | 38.1853i | −0.462709 | − | 1.42407i | −0.861841 | − | 0.507178i | \(-0.830689\pi\) |
0.399132 | − | 0.916893i | \(-0.369311\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.81156 | + | 14.8085i | −0.179192 | + | 0.551496i | ||||
\(722\) | 3.35944 | + | 1.09155i | 0.125026 | + | 0.0406233i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 10.8990 | 0.405059 | ||||||||
\(725\) | 7.12932 | − | 0.688947i | 0.264776 | − | 0.0255868i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.3143 | − | 30.7130i | −0.827592 | − | 1.13908i | −0.988366 | − | 0.152092i | \(-0.951399\pi\) |
0.160774 | − | 0.986991i | \(-0.448601\pi\) | |||||||
\(728\) | −17.8500 | − | 5.79981i | −0.661565 | − | 0.214955i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 21.5582 | − | 17.3083i | 0.797903 | − | 0.640610i | ||||
\(731\) | 4.44743 | + | 13.6878i | 0.164494 | + | 0.506261i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.0797 | − | 7.49904i | 0.852468 | − | 0.276984i | 0.149988 | − | 0.988688i | \(-0.452076\pi\) |
0.702479 | + | 0.711704i | \(0.252076\pi\) | |||||||
\(734\) | 0.207037 | + | 0.150421i | 0.00764187 | + | 0.00555215i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.76626 | − | 4.91598i | 0.249408 | − | 0.181205i | ||||
\(737\) | −8.25123 | + | 11.3568i | −0.303938 | + | 0.418335i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.7190 | − | 22.3186i | 1.13002 | − | 0.821004i | 0.144318 | − | 0.989531i | \(-0.453901\pi\) |
0.985697 | + | 0.168527i | \(0.0539011\pi\) | |||||||
\(740\) | 1.20216 | + | 24.9383i | 0.0441924 | + | 0.916749i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.80261 | − | 1.56046i | 0.176309 | − | 0.0572864i | ||||
\(743\) | 27.7086i | 1.01653i | 0.861201 | + | 0.508265i | \(0.169713\pi\) | ||||
−0.861201 | + | 0.508265i | \(0.830287\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.11986 | + | 4.66624i | 0.260852 | + | 0.170958i | ||||
\(746\) | −3.57124 | + | 10.9911i | −0.130752 | + | 0.402415i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.92354 | + | 9.52943i | 0.253150 | + | 0.348430i | ||||
\(749\) | 31.9634 | 1.16792 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.1379 | −0.588882 | −0.294441 | − | 0.955670i | \(-0.595133\pi\) | ||||
−0.294441 | + | 0.955670i | \(0.595133\pi\) | |||||||
\(752\) | −4.25325 | − | 5.85410i | −0.155100 | − | 0.213477i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.54788 | − | 7.84157i | 0.0927883 | − | 0.285573i | ||||
\(755\) | −28.0159 | − | 18.3612i | −1.01960 | − | 0.668231i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.6556i | 0.387283i | 0.981072 | + | 0.193641i | \(0.0620298\pi\) | ||||
−0.981072 | + | 0.193641i | \(0.937970\pi\) | |||||||
\(758\) | 11.9083 | − | 3.86925i | 0.432530 | − | 0.140537i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.423439 | + | 8.78402i | 0.0153597 | + | 0.318630i | ||||
\(761\) | 1.57163 | − | 1.14185i | 0.0569714 | − | 0.0413922i | −0.558935 | − | 0.829211i | \(-0.688790\pi\) |
0.615906 | + | 0.787819i | \(0.288790\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.4481 | − | 24.0153i | 0.631665 | − | 0.869412i | ||||
\(764\) | −4.22273 | + | 3.06799i | −0.152773 | + | 0.110996i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.527864 | − | 0.383516i | −0.0190725 | − | 0.0138570i | ||||
\(767\) | −59.9362 | + | 19.4745i | −2.16417 | + | 0.703182i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.82372 | + | 8.69051i | 0.101826 | + | 0.313388i | 0.988972 | − | 0.148100i | \(-0.0473158\pi\) |
−0.887147 | + | 0.461488i | \(0.847316\pi\) | |||||||
\(770\) | 10.1713 | − | 8.16617i | 0.366547 | − | 0.294288i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.42705 | + | 1.76336i | 0.195324 | + | 0.0634646i | ||||
\(773\) | −24.7553 | − | 34.0728i | −0.890387 | − | 1.22551i | −0.973434 | − | 0.228967i | \(-0.926465\pi\) |
0.0830472 | − | 0.996546i | \(-0.473535\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24.2084 | + | 21.4326i | −0.869592 | + | 0.769883i | ||||
\(776\) | −9.12807 | −0.327679 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −32.3653 | − | 10.5161i | −1.16035 | − | 0.377021i | ||||
\(779\) | −4.78391 | + | 14.7233i | −0.171401 | + | 0.527519i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.80773 | + | 11.7190i | 0.136251 | + | 0.419339i | ||||
\(782\) | − | 55.0697i | − | 1.96929i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.93930 | + | 2.13553i | 0.104975 | + | 0.0762689i | ||||
\(785\) | 0.408739 | − | 0.623664i | 0.0145885 | − | 0.0222595i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.06835 | + | 2.84684i | −0.0737287 | + | 0.101479i | −0.844289 | − | 0.535889i | \(-0.819977\pi\) |
0.770560 | + | 0.637368i | \(0.219977\pi\) | |||||||
\(788\) | −10.5081 | + | 14.4632i | −0.374336 | + | 0.515230i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.25816 | + | 2.24991i | 0.293812 | + | 0.0800482i | ||||
\(791\) | −11.9849 | − | 8.70751i | −0.426132 | − | 0.309603i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 4.53622i | − | 0.161086i | ||||||
\(794\) | −9.19490 | − | 28.2990i | −0.326315 | − | 1.00429i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.59837 | − | 11.0746i | 0.127541 | − | 0.392530i | ||||
\(797\) | 31.5697 | + | 10.2576i | 1.11826 | + | 0.363344i | 0.809102 | − | 0.587668i | \(-0.199954\pi\) |
0.309155 | + | 0.951012i | \(0.399954\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −47.6458 | −1.68559 | ||||||||
\(800\) | 4.58462 | − | 1.99532i | 0.162091 | − | 0.0705452i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −10.1937 | − | 14.0305i | −0.359954 | − | 0.495434i | ||||
\(803\) | 21.0354 | + | 6.83481i | 0.742322 | + | 0.241195i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −60.9121 | + | 2.93630i | −2.14687 | + | 0.103491i | ||||
\(806\) | 11.5015 | + | 35.3980i | 0.405123 | + | 1.24684i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.35177 | + | 1.41398i | −0.153095 | + | 0.0497435i | ||||
\(809\) | 6.07490 | + | 4.41367i | 0.213582 | + | 0.155176i | 0.689433 | − | 0.724350i | \(-0.257860\pi\) |
−0.475851 | + | 0.879526i | \(0.657860\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.5051 | + | 22.1632i | −1.07118 | + | 0.778256i | −0.976124 | − | 0.217216i | \(-0.930302\pi\) |
−0.0950543 | + | 0.995472i | \(0.530302\pi\) | |||||||
\(812\) | −2.74566 | + | 3.77908i | −0.0963538 | + | 0.132620i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −16.1596 | + | 11.7406i | −0.566394 | + | 0.411509i | ||||
\(815\) | −4.02235 | + | 1.52472i | −0.140897 | + | 0.0534087i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.17568 | + | 2.65644i | −0.286031 | + | 0.0929371i | ||||
\(818\) | 8.53955i | 0.298579i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.79162 | − | 0.423805i | 0.307017 | − | 0.0147999i | ||||
\(821\) | 1.20526 | − | 3.70942i | 0.0420640 | − | 0.129460i | −0.927819 | − | 0.373030i | \(-0.878319\pi\) |
0.969883 | + | 0.243571i | \(0.0783187\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.3684 | − | 34.9166i | −0.884286 | − | 1.21711i | −0.975215 | − | 0.221258i | \(-0.928984\pi\) |
0.0909296 | − | 0.995857i | \(-0.471016\pi\) | |||||||
\(824\) | −4.77499 | −0.166345 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 35.7038 | 1.24229 | ||||||||
\(827\) | 1.65632 | + | 2.27973i | 0.0575960 | + | 0.0792741i | 0.836843 | − | 0.547442i | \(-0.184398\pi\) |
−0.779247 | + | 0.626716i | \(0.784398\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.4671 | − | 41.4475i | 0.467732 | − | 1.43953i | −0.387782 | − | 0.921751i | \(-0.626759\pi\) |
0.855514 | − | 0.517780i | \(-0.173241\pi\) | |||||||
\(830\) | 5.31219 | + | 14.0140i | 0.184389 | + | 0.486434i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 5.75573i | − | 0.199544i | ||||||
\(833\) | 22.7517 | − | 7.39249i | 0.788301 | − | 0.256135i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.04575 | − | 0.829805i | −0.105403 | − | 0.0287166i | ||||
\(836\) | −5.69191 | + | 4.13541i | −0.196859 | + | 0.143026i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 21.4606 | − | 29.5380i | 0.741344 | − | 1.02037i | ||||
\(839\) | 26.3904 | − | 19.1737i | 0.911098 | − | 0.661951i | −0.0301946 | − | 0.999544i | \(-0.509613\pi\) |
0.941292 | + | 0.337593i | \(0.109613\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.8013 | + | 15.8396i | 0.751770 | + | 0.546193i | ||||
\(842\) | −2.54345 | + | 0.826416i | −0.0876530 | + | 0.0284802i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.89701 | + | 5.83841i | 0.0652979 | + | 0.200966i | ||||
\(845\) | 11.8312 | − | 43.4256i | 0.407004 | − | 1.49389i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24.1892 | − | 7.85956i | −0.831152 | − | 0.270058i | ||||
\(848\) | 0.910244 | + | 1.25284i | 0.0312579 | + | 0.0430228i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 7.11468 | − | 32.1445i | 0.244031 | − | 1.10255i | ||||
\(851\) | 93.3849 | 3.20119 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.97505 | − | 0.966652i | −0.101864 | − | 0.0330975i | 0.257642 | − | 0.966241i | \(-0.417055\pi\) |
−0.359505 | + | 0.933143i | \(0.617055\pi\) | |||||||
\(854\) | −0.794161 | + | 2.44417i | −0.0271756 | + | 0.0836379i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.02903 | + | 9.32239i | 0.103530 | + | 0.318633i | ||||
\(857\) | − | 26.4837i | − | 0.904666i | −0.891849 | − | 0.452333i | \(-0.850592\pi\) | ||
0.891849 | − | 0.452333i | \(-0.149408\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.278666 | + | 0.202463i | 0.00950797 | + | 0.00690795i | 0.592529 | − | 0.805549i | \(-0.298130\pi\) |
−0.583021 | + | 0.812457i | \(0.698130\pi\) | |||||||
\(860\) | 3.05988 | + | 3.81119i | 0.104341 | + | 0.129960i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.09595 | + | 7.01398i | −0.173569 | + | 0.238897i | ||||
\(863\) | 12.3485 | − | 16.9962i | 0.420347 | − | 0.578558i | −0.545357 | − | 0.838204i | \(-0.683606\pi\) |
0.965704 | + | 0.259646i | \(0.0836058\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.42658 | − | 29.5937i | −0.0485052 | − | 1.00622i | ||||
\(866\) | 16.1604 | + | 11.7413i | 0.549154 | + | 0.398984i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 21.0865i | − | 0.715721i | ||||||
\(869\) | 2.11600 | + | 6.51239i | 0.0717805 | + | 0.220918i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.9571 | − | 42.9555i | 0.472918 | − | 1.45549i | ||||
\(872\) | 8.65775 | + | 2.81307i | 0.293188 | + | 0.0952627i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 32.8930 | 1.11262 | ||||||||
\(875\) | −35.9341 | − | 6.15555i | −1.21479 | − | 0.208095i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.6819 | + | 39.4773i | 0.968519 | + | 1.33305i | 0.942791 | + | 0.333384i | \(0.108190\pi\) |
0.0257283 | + | 0.999669i | \(0.491810\pi\) | |||||||
\(878\) | 17.3971 | + | 5.65265i | 0.587123 | + | 0.190768i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.34562 | + | 2.19266i | 0.112781 | + | 0.0739146i | ||||
\(881\) | −0.690898 | − | 2.12637i | −0.0232769 | − | 0.0716391i | 0.938743 | − | 0.344617i | \(-0.111991\pi\) |
−0.962020 | + | 0.272978i | \(0.911991\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.1665 | − | 3.30330i | 0.342130 | − | 0.111165i | −0.132912 | − | 0.991128i | \(-0.542433\pi\) |
0.475042 | + | 0.879963i | \(0.342433\pi\) | |||||||
\(884\) | −30.6605 | − | 22.2762i | −1.03122 | − | 0.749228i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.74282 | − | 7.07858i | 0.327317 | − | 0.237809i | ||||
\(887\) | 15.3734 | − | 21.1596i | 0.516187 | − | 0.710470i | −0.468761 | − | 0.883325i | \(-0.655299\pi\) |
0.984947 | + | 0.172855i | \(0.0552993\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −30.8850 | + | 22.4393i | −1.03585 | + | 0.752589i | ||||
\(890\) | −2.23687 | − | 2.78611i | −0.0749802 | − | 0.0933906i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.99171 | − | 2.27174i | 0.234100 | − | 0.0760636i | ||||
\(893\) | − | 28.4587i | − | 0.952334i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −41.7394 | + | 33.5112i | −1.39519 | + | 1.12016i | ||||
\(896\) | −1.00766 | + | 3.10126i | −0.0336636 | + | 0.103606i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 20.9993 | + | 28.9030i | 0.700755 | + | 0.964507i | ||||
\(899\) | 9.26337 | 0.308951 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.1967 | 0.339702 | ||||||||
\(902\) | 4.13899 | + | 5.69683i | 0.137813 | + | 0.189684i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.40387 | − | 4.32066i | 0.0466919 | − | 0.143703i | ||||
\(905\) | 6.40629 | − | 23.5139i | 0.212952 | − | 0.781629i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.59794i | 0.318694i | 0.987223 | + | 0.159347i | \(0.0509389\pi\) | ||||
−0.987223 | + | 0.159347i | \(0.949061\pi\) | |||||||
\(908\) | 15.2531 | − | 4.95602i | 0.506191 | − | 0.164471i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −23.0047 | + | 35.1011i | −0.762597 | + | 1.16359i | ||||
\(911\) | −34.8520 | + | 25.3215i | −1.15470 | + | 0.838937i | −0.989098 | − | 0.147256i | \(-0.952956\pi\) |
−0.165600 | + | 0.986193i | \(0.552956\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.04755 | + | 9.70011i | −0.233240 | + | 0.321027i | ||||
\(914\) | −3.88002 | + | 2.81900i | −0.128340 | + | 0.0932442i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.26174 | − | 6.72905i | −0.306016 | − | 0.222334i | ||||
\(917\) | 1.64898 | − | 0.535785i | 0.0544540 | − | 0.0176932i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.3901 | − | 31.9774i | −0.342737 | − | 1.05484i | −0.962784 | − | 0.270272i | \(-0.912886\pi\) |
0.620047 | − | 0.784565i | \(-0.287114\pi\) | |||||||
\(920\) | −6.62877 | − | 17.4873i | −0.218544 | − | 0.576539i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.489980 | − | 0.159204i | −0.0161366 | − | 0.00524311i | ||||
\(923\) | −23.3032 | − | 32.0741i | −0.767034 | − | 1.05573i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 54.5092 | + | 12.0648i | 1.79225 | + | 0.396687i | ||||
\(926\) | −22.5824 | −0.742103 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.36239 | − | 0.442669i | −0.0447228 | − | 0.0145313i | ||||
\(929\) | −7.76297 | + | 23.8920i | −0.254695 | + | 0.783870i | 0.739195 | + | 0.673492i | \(0.235206\pi\) |
−0.993890 | + | 0.110378i | \(0.964794\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.41552 | + | 13.5896i | 0.144713 | + | 0.445380i | ||||
\(932\) | − | 9.39222i | − | 0.307652i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −31.9800 | − | 23.2348i | −1.04642 | − | 0.760267i | ||||
\(935\) | 24.6286 | − | 9.33579i | 0.805443 | − | 0.305313i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.9522 | + | 30.2146i | −0.717146 | + | 0.987066i | 0.282468 | + | 0.959277i | \(0.408847\pi\) |
−0.999614 | + | 0.0277897i | \(0.991153\pi\) | |||||||
\(938\) | −15.0405 | + | 20.7015i | −0.491090 | + | 0.675928i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −15.1298 | + | 5.73515i | −0.493480 | + | 0.187060i | ||||
\(941\) | −45.5557 | − | 33.0981i | −1.48507 | − | 1.07897i | −0.975878 | − | 0.218317i | \(-0.929943\pi\) |
−0.509194 | − | 0.860652i | \(-0.670057\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 32.9215i | − | 1.07207i | ||||||
\(944\) | 3.38349 | + | 10.4133i | 0.110123 | + | 0.338925i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.20830 | + | 3.71877i | −0.0392853 | + | 0.120908i | ||||
\(947\) | 1.00257 | + | 0.325756i | 0.0325793 | + | 0.0105856i | 0.325261 | − | 0.945624i | \(-0.394548\pi\) |
−0.292682 | + | 0.956210i | \(0.594548\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −71.1633 | −2.31006 | ||||||||
\(950\) | 19.1998 | + | 4.24958i | 0.622924 | + | 0.137875i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 12.6204 | + | 17.3704i | 0.409028 | + | 0.562979i | ||||
\(953\) | −45.6210 | − | 14.8232i | −1.47781 | − | 0.480169i | −0.544351 | − | 0.838857i | \(-0.683224\pi\) |
−0.933457 | + | 0.358688i | \(0.883224\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.13693 | + | 10.9136i | 0.133868 | + | 0.353155i | ||||
\(956\) | −2.75458 | − | 8.47773i | −0.0890895 | − | 0.274189i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 30.8129 | − | 10.0117i | 0.995520 | − | 0.323464i | ||||
\(959\) | 52.7285 | + | 38.3095i | 1.70269 | + | 1.23708i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.75049 | + | 6.35761i | −0.282274 | + | 0.205084i | ||||
\(962\) | 37.7750 | − | 51.9928i | 1.21791 | − | 1.67632i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.06186 | + | 5.13074i | −0.227447 | + | 0.165250i | ||||
\(965\) | 6.99426 | − | 10.6720i | 0.225153 | − | 0.343544i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.7284 | − | 12.9085i | 1.27758 | − | 0.415111i | 0.409853 | − | 0.912152i | \(-0.365580\pi\) |
0.867727 | + | 0.497041i | \(0.165580\pi\) | |||||||
\(968\) | − | 7.79981i | − | 0.250696i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.36535 | + | 19.6932i | −0.172271 | + | 0.632310i | ||||
\(971\) | 5.52977 | − | 17.0189i | 0.177459 | − | 0.546162i | −0.822278 | − | 0.569085i | \(-0.807297\pi\) |
0.999737 | + | 0.0229233i | \(0.00729736\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −39.8068 | − | 54.7894i | −1.27615 | − | 1.75647i | ||||
\(974\) | −36.6031 | −1.17284 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.788124 | −0.0252272 | ||||||||
\(977\) | 10.0952 | + | 13.8949i | 0.322976 | + | 0.444538i | 0.939373 | − | 0.342898i | \(-0.111408\pi\) |
−0.616397 | + | 0.787435i | \(0.711408\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.883309 | − | 2.71854i | 0.0282307 | − | 0.0868851i | ||||
\(980\) | 6.33494 | − | 5.08611i | 0.202362 | − | 0.162470i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 18.9861i | 0.605870i | ||||||||
\(983\) | −14.6491 | + | 4.75978i | −0.467234 | + | 0.151813i | −0.533166 | − | 0.846011i | \(-0.678998\pi\) |
0.0659323 | + | 0.997824i | \(0.478998\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.0268 | + | 31.1718i | 0.797420 | + | 0.993216i | ||||
\(986\) | −7.63090 | + | 5.54417i | −0.243017 | + | 0.176562i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 13.3055 | − | 18.3135i | 0.423304 | − | 0.582629i | ||||
\(989\) | 14.7895 | − | 10.7452i | 0.470279 | − | 0.341678i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.05504 | − | 3.67270i | −0.160579 | − | 0.116667i | 0.504594 | − | 0.863357i | \(-0.331642\pi\) |
−0.665173 | + | 0.746689i | \(0.731642\pi\) | |||||||
\(992\) | 6.15005 | − | 1.99827i | 0.195264 | − | 0.0634452i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.94082 | + | 21.3616i | 0.220149 | + | 0.677550i | ||||
\(995\) | −21.7777 | − | 14.2727i | −0.690399 | − | 0.452476i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.04054 | + | 2.61253i | 0.254646 | + | 0.0827397i | 0.433559 | − | 0.901125i | \(-0.357258\pi\) |
−0.178912 | + | 0.983865i | \(0.557258\pi\) | |||||||
\(998\) | 8.96234 | + | 12.3356i | 0.283698 | + | 0.390477i | ||||
\(999\) | 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 | 450.2.l.d.289.4 | yes | 16 | |
3.2 | odd | 2 | inner | 450.2.l.d.289.1 | yes | 16 | |
25.9 | even | 10 | inner | 450.2.l.d.109.4 | yes | 16 | |
75.59 | odd | 10 | inner | 450.2.l.d.109.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.2.l.d.109.1 | ✓ | 16 | 75.59 | odd | 10 | inner | |
450.2.l.d.109.4 | yes | 16 | 25.9 | even | 10 | inner | |
450.2.l.d.289.1 | yes | 16 | 3.2 | odd | 2 | inner | |
450.2.l.d.289.4 | yes | 16 | 1.1 | even | 1 | trivial |