Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [425,2,Mod(101,425)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(425, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("425.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 425 = 5^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 425.d (of order \(2\), degree \(1\), 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: | \(3.39364208590\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.93924352.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 17x^{4} + 73x^{2} + 67 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 101.2 | ||
Root | \(-2.21547i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 425.101 |
Dual form | 425.2.d.a.101.1 |
$q$-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 \(\left(\mathbb{Z}/425\mathbb{Z}\right)^\times\).
\(n\) | \(52\) | \(326\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.17009 | −1.53448 | −0.767241 | − | 0.641358i | \(-0.778371\pi\) | ||||
−0.767241 | + | 0.641358i | \(0.778371\pi\) | |||||||
\(3\) | 2.21547i | 1.27910i | 0.768749 | + | 0.639550i | \(0.220879\pi\) | ||||
−0.768749 | + | 0.639550i | \(0.779121\pi\) | |||||||
\(4\) | 2.70928 | 1.35464 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 4.80775i | − | 1.96276i | ||||||
\(7\) | − | 1.02091i | − | 0.385868i | −0.981212 | − | 0.192934i | \(-0.938200\pi\) | ||
0.981212 | − | 0.192934i | \(-0.0618004\pi\) | |||||||
\(8\) | −1.53919 | −0.544185 | ||||||||
\(9\) | −1.90829 | −0.636097 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.98140i | − | 1.50195i | −0.660332 | − | 0.750974i | \(-0.729584\pi\) | ||
0.660332 | − | 0.750974i | \(-0.270416\pi\) | |||||||
\(12\) | 6.00231i | 1.73272i | ||||||||
\(13\) | −3.87936 | −1.07594 | −0.537971 | − | 0.842964i | \(-0.680809\pi\) | ||||
−0.537971 | + | 0.842964i | \(0.680809\pi\) | |||||||
\(14\) | 2.21547i | 0.592108i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.07838 | −0.519594 | ||||||||
\(17\) | −1.63090 | − | 3.78684i | −0.395551 | − | 0.918444i | ||||
\(18\) | 4.14116 | 0.976080 | ||||||||
\(19\) | −4.04945 | −0.929007 | −0.464504 | − | 0.885571i | \(-0.653767\pi\) | ||||
−0.464504 | + | 0.885571i | \(0.653767\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.26180 | 0.493564 | ||||||||
\(22\) | 10.8101i | 2.30471i | ||||||||
\(23\) | − | 7.02322i | − | 1.46444i | −0.681067 | − | 0.732221i | \(-0.738484\pi\) | ||
0.681067 | − | 0.732221i | \(-0.261516\pi\) | |||||||
\(24\) | − | 3.41002i | − | 0.696068i | ||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 8.41855 | 1.65101 | ||||||||
\(27\) | 2.41864i | 0.465468i | ||||||||
\(28\) | − | 2.76593i | − | 0.522712i | ||||||
\(29\) | 0.644091i | 0.119605i | 0.998210 | + | 0.0598023i | \(0.0190470\pi\) | ||||
−0.998210 | + | 0.0598023i | \(0.980953\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.25729i | 0.764632i | 0.924032 | + | 0.382316i | \(0.124873\pi\) | ||||
−0.924032 | + | 0.382316i | \(0.875127\pi\) | |||||||
\(32\) | 7.58864 | 1.34149 | ||||||||
\(33\) | 11.0361 | 1.92114 | ||||||||
\(34\) | 3.53919 | + | 8.21777i | 0.606966 | + | 1.40934i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.17009 | −0.861681 | ||||||||
\(37\) | − | 10.2596i | − | 1.68667i | −0.537390 | − | 0.843334i | \(-0.680590\pi\) | ||
0.537390 | − | 0.843334i | \(-0.319410\pi\) | |||||||
\(38\) | 8.78765 | 1.42555 | ||||||||
\(39\) | − | 8.59460i | − | 1.37624i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.82867i | − | 0.910285i | −0.890419 | − | 0.455142i | \(-0.849588\pi\) | ||
0.890419 | − | 0.455142i | \(-0.150412\pi\) | |||||||
\(42\) | −4.90829 | −0.757366 | ||||||||
\(43\) | −5.86603 | −0.894561 | −0.447281 | − | 0.894394i | \(-0.647607\pi\) | ||||
−0.447281 | + | 0.894394i | \(0.647607\pi\) | |||||||
\(44\) | − | 13.4960i | − | 2.03459i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 15.2410i | 2.24716i | ||||||||
\(47\) | 10.3402 | 1.50827 | 0.754135 | − | 0.656720i | \(-0.228057\pi\) | ||||
0.754135 | + | 0.656720i | \(0.228057\pi\) | |||||||
\(48\) | − | 4.60458i | − | 0.664613i | ||||||
\(49\) | 5.95774 | 0.851106 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.38962 | − | 3.61320i | 1.17478 | − | 0.505949i | ||||
\(52\) | −10.5103 | −1.45751 | ||||||||
\(53\) | −11.3896 | −1.56448 | −0.782242 | − | 0.622974i | \(-0.785924\pi\) | ||||
−0.782242 | + | 0.622974i | \(0.785924\pi\) | |||||||
\(54\) | − | 5.24867i | − | 0.714253i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.57138i | 0.209984i | ||||||||
\(57\) | − | 8.97142i | − | 1.18829i | ||||||
\(58\) | − | 1.39773i | − | 0.183531i | ||||||
\(59\) | −0.447480 | −0.0582570 | −0.0291285 | − | 0.999576i | \(-0.509273\pi\) | ||||
−0.0291285 | + | 0.999576i | \(0.509273\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.14275i | 0.402388i | 0.979551 | + | 0.201194i | \(0.0644822\pi\) | ||||
−0.979551 | + | 0.201194i | \(0.935518\pi\) | |||||||
\(62\) | − | 9.23869i | − | 1.17331i | ||||||
\(63\) | 1.94820i | 0.245450i | ||||||||
\(64\) | −12.3112 | −1.53891 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −23.9493 | −2.94796 | ||||||||
\(67\) | 5.07838 | 0.620423 | 0.310211 | − | 0.950668i | \(-0.399600\pi\) | ||||
0.310211 | + | 0.950668i | \(0.399600\pi\) | |||||||
\(68\) | −4.41855 | − | 10.2596i | −0.535828 | − | 1.24416i | ||||
\(69\) | 15.5597 | 1.87317 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.41002i | − | 0.404695i | −0.979314 | − | 0.202348i | \(-0.935143\pi\) | ||
0.979314 | − | 0.202348i | \(-0.0648571\pi\) | |||||||
\(72\) | 2.93722 | 0.346155 | ||||||||
\(73\) | 3.78684i | 0.443216i | 0.975136 | + | 0.221608i | \(0.0711306\pi\) | ||||
−0.975136 | + | 0.221608i | \(0.928869\pi\) | |||||||
\(74\) | 22.2642i | 2.58816i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.9711 | −1.25847 | ||||||||
\(77\) | −5.08557 | −0.579554 | ||||||||
\(78\) | 18.6510i | 2.11181i | ||||||||
\(79\) | 0.376821i | 0.0423957i | 0.999775 | + | 0.0211978i | \(0.00674798\pi\) | ||||
−0.999775 | + | 0.0211978i | \(0.993252\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0833 | −1.23148 | ||||||||
\(82\) | 12.6487i | 1.39682i | ||||||||
\(83\) | 3.57531 | 0.392441 | 0.196220 | − | 0.980560i | \(-0.437133\pi\) | ||||
0.196220 | + | 0.980560i | \(0.437133\pi\) | |||||||
\(84\) | 6.12783 | 0.668601 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 12.7298 | 1.37269 | ||||||||
\(87\) | −1.42696 | −0.152986 | ||||||||
\(88\) | 7.66731i | 0.817338i | ||||||||
\(89\) | −2.63090 | −0.278875 | −0.139437 | − | 0.990231i | \(-0.544529\pi\) | ||||
−0.139437 | + | 0.990231i | \(0.544529\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.96049i | 0.415172i | ||||||||
\(92\) | − | 19.0278i | − | 1.98379i | ||||||
\(93\) | −9.43188 | −0.978041 | ||||||||
\(94\) | −22.4391 | −2.31441 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 16.8124i | 1.71591i | ||||||||
\(97\) | 10.9037i | 1.10710i | 0.832815 | + | 0.553551i | \(0.186728\pi\) | ||||
−0.832815 | + | 0.553551i | \(0.813272\pi\) | |||||||
\(98\) | −12.9288 | −1.30601 | ||||||||
\(99\) | 9.50596i | 0.955385i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.21953 | −0.618867 | −0.309433 | − | 0.950921i | \(-0.600139\pi\) | ||||
−0.309433 | + | 0.950921i | \(0.600139\pi\) | |||||||
\(102\) | −18.2062 | + | 7.84095i | −1.80268 | + | 0.776370i | ||||
\(103\) | 10.4969 | 1.03429 | 0.517147 | − | 0.855897i | \(-0.326994\pi\) | ||||
0.517147 | + | 0.855897i | \(0.326994\pi\) | |||||||
\(104\) | 5.97107 | 0.585512 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 24.7165 | 2.40068 | ||||||||
\(107\) | − | 5.15504i | − | 0.498357i | −0.968458 | − | 0.249178i | \(-0.919839\pi\) | ||
0.968458 | − | 0.249178i | \(-0.0801605\pi\) | |||||||
\(108\) | 6.55277i | 0.630541i | ||||||||
\(109\) | 6.92959i | 0.663735i | 0.943326 | + | 0.331867i | \(0.107679\pi\) | ||||
−0.943326 | + | 0.331867i | \(0.892321\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 22.7298 | 2.15742 | ||||||||
\(112\) | 2.12184i | 0.200495i | ||||||||
\(113\) | 19.5783i | 1.84177i | 0.389832 | + | 0.920886i | \(0.372533\pi\) | ||||
−0.389832 | + | 0.920886i | \(0.627467\pi\) | |||||||
\(114\) | 19.4687i | 1.82342i | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.74502i | 0.162021i | ||||||||
\(117\) | 7.40295 | 0.684403 | ||||||||
\(118\) | 0.971071 | 0.0893943 | ||||||||
\(119\) | −3.86603 | + | 1.66500i | −0.354398 | + | 0.152631i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.8143 | −1.25585 | ||||||||
\(122\) | − | 6.82004i | − | 0.617458i | ||||||
\(123\) | 12.9132 | 1.16435 | ||||||||
\(124\) | 11.5342i | 1.03580i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | − | 4.22776i | − | 0.376638i | ||||||
\(127\) | 2.20620 | 0.195769 | 0.0978845 | − | 0.995198i | \(-0.468792\pi\) | ||||
0.0978845 | + | 0.995198i | \(0.468792\pi\) | |||||||
\(128\) | 11.5392 | 1.01993 | ||||||||
\(129\) | − | 12.9960i | − | 1.14423i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 19.2015i | − | 1.67764i | −0.544408 | − | 0.838821i | \(-0.683246\pi\) | ||
0.544408 | − | 0.838821i | \(-0.316754\pi\) | |||||||
\(132\) | 29.8999 | 2.60245 | ||||||||
\(133\) | 4.13413i | 0.358474i | ||||||||
\(134\) | −11.0205 | −0.952028 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.51026 | + | 5.82867i | 0.215253 | + | 0.499804i | ||||
\(137\) | −0.304056 | −0.0259772 | −0.0129886 | − | 0.999916i | \(-0.504135\pi\) | ||||
−0.0129886 | + | 0.999916i | \(0.504135\pi\) | |||||||
\(138\) | −33.7659 | −2.87435 | ||||||||
\(139\) | − | 18.9478i | − | 1.60713i | −0.595215 | − | 0.803567i | \(-0.702933\pi\) | ||
0.595215 | − | 0.803567i | \(-0.297067\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 22.9083i | 1.92923i | ||||||||
\(142\) | 7.40004i | 0.620998i | ||||||||
\(143\) | 19.3246i | 1.61601i | ||||||||
\(144\) | 3.96615 | 0.330513 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 8.21777i | − | 0.680108i | ||||||
\(147\) | 13.1992i | 1.08865i | ||||||||
\(148\) | − | 27.7961i | − | 2.28482i | ||||||
\(149\) | −19.4969 | −1.59725 | −0.798625 | − | 0.601829i | \(-0.794439\pi\) | ||||
−0.798625 | + | 0.601829i | \(0.794439\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.1773 | −1.56062 | −0.780312 | − | 0.625390i | \(-0.784940\pi\) | ||||
−0.780312 | + | 0.625390i | \(0.784940\pi\) | |||||||
\(152\) | 6.23287 | 0.505552 | ||||||||
\(153\) | 3.11223 | + | 7.22640i | 0.251609 | + | 0.584220i | ||||
\(154\) | 11.0361 | 0.889316 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | − | 23.2851i | − | 1.86430i | ||||||
\(157\) | −14.6248 | −1.16718 | −0.583591 | − | 0.812048i | \(-0.698353\pi\) | ||||
−0.583591 | + | 0.812048i | \(0.698353\pi\) | |||||||
\(158\) | − | 0.817734i | − | 0.0650554i | ||||||
\(159\) | − | 25.2333i | − | 2.00113i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.17009 | −0.565082 | ||||||||
\(162\) | 24.0517 | 1.88968 | ||||||||
\(163\) | − | 13.5760i | − | 1.06335i | −0.846947 | − | 0.531677i | \(-0.821562\pi\) | ||
0.846947 | − | 0.531677i | \(-0.178438\pi\) | |||||||
\(164\) | − | 15.7915i | − | 1.23311i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.75872 | −0.602194 | ||||||||
\(167\) | − | 2.59229i | − | 0.200597i | −0.994957 | − | 0.100299i | \(-0.968020\pi\) | ||
0.994957 | − | 0.100299i | \(-0.0319798\pi\) | |||||||
\(168\) | −3.48133 | −0.268590 | ||||||||
\(169\) | 2.04945 | 0.157650 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.72753 | 0.590939 | ||||||||
\(172\) | −15.8927 | −1.21181 | ||||||||
\(173\) | − | 11.0132i | − | 0.837321i | −0.908143 | − | 0.418661i | \(-0.862500\pi\) | ||
0.908143 | − | 0.418661i | \(-0.137500\pi\) | |||||||
\(174\) | 3.09663 | 0.234755 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 10.3532i | 0.780404i | ||||||||
\(177\) | − | 0.991377i | − | 0.0745165i | ||||||
\(178\) | 5.70928 | 0.427928 | ||||||||
\(179\) | 24.9854 | 1.86750 | 0.933750 | − | 0.357926i | \(-0.116516\pi\) | ||||
0.933750 | + | 0.357926i | \(0.116516\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 14.3432i | − | 1.06612i | −0.846076 | − | 0.533062i | \(-0.821041\pi\) | ||
0.846076 | − | 0.533062i | \(-0.178959\pi\) | |||||||
\(182\) | − | 8.59460i | − | 0.637074i | ||||||
\(183\) | −6.96266 | −0.514695 | ||||||||
\(184\) | 10.8101i | 0.796928i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 20.4680 | 1.50079 | ||||||||
\(187\) | −18.8638 | + | 8.12415i | −1.37946 | + | 0.594097i | ||||
\(188\) | 28.0144 | 2.04316 | ||||||||
\(189\) | 2.46922 | 0.179609 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.39576 | 0.390424 | 0.195212 | − | 0.980761i | \(-0.437461\pi\) | ||||
0.195212 | + | 0.980761i | \(0.437461\pi\) | |||||||
\(192\) | − | 27.2751i | − | 1.96841i | ||||||
\(193\) | − | 16.1387i | − | 1.16169i | −0.814013 | − | 0.580846i | \(-0.802722\pi\) | ||
0.814013 | − | 0.580846i | \(-0.197278\pi\) | |||||||
\(194\) | − | 23.6619i | − | 1.69883i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 16.1412 | 1.15294 | ||||||||
\(197\) | − | 9.26822i | − | 0.660333i | −0.943923 | − | 0.330167i | \(-0.892895\pi\) | ||
0.943923 | − | 0.330167i | \(-0.107105\pi\) | |||||||
\(198\) | − | 20.6287i | − | 1.46602i | ||||||
\(199\) | 4.63411i | 0.328503i | 0.986418 | + | 0.164252i | \(0.0525209\pi\) | ||||
−0.986418 | + | 0.164252i | \(0.947479\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.2510i | 0.793583i | ||||||||
\(202\) | 13.4969 | 0.949641 | ||||||||
\(203\) | 0.657560 | 0.0461516 | ||||||||
\(204\) | 22.7298 | − | 9.78915i | 1.59140 | − | 0.685378i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −22.7792 | −1.58711 | ||||||||
\(207\) | 13.4023i | 0.931528i | ||||||||
\(208\) | 8.06278 | 0.559053 | ||||||||
\(209\) | 20.1719i | 1.39532i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.09593i | 0.419661i | 0.977738 | + | 0.209831i | \(0.0672913\pi\) | ||||
−0.977738 | + | 0.209831i | \(0.932709\pi\) | |||||||
\(212\) | −30.8576 | −2.11931 | ||||||||
\(213\) | 7.55479 | 0.517645 | ||||||||
\(214\) | 11.1869i | 0.764720i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 3.72275i | − | 0.253301i | ||||||
\(217\) | 4.34632 | 0.295047 | ||||||||
\(218\) | − | 15.0378i | − | 1.01849i | ||||||
\(219\) | −8.38962 | −0.566918 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.32684 | + | 14.6905i | 0.425589 | + | 0.988192i | ||||
\(222\) | −49.3256 | −3.31052 | ||||||||
\(223\) | 17.7009 | 1.18534 | 0.592669 | − | 0.805446i | \(-0.298074\pi\) | ||||
0.592669 | + | 0.805446i | \(0.298074\pi\) | |||||||
\(224\) | − | 7.74733i | − | 0.517640i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 42.4866i | − | 2.82617i | ||||||
\(227\) | 25.5806i | 1.69784i | 0.528518 | + | 0.848922i | \(0.322748\pi\) | ||||
−0.528518 | + | 0.848922i | \(0.677252\pi\) | |||||||
\(228\) | − | 24.3060i | − | 1.60971i | ||||||
\(229\) | 11.9867 | 0.792101 | 0.396051 | − | 0.918229i | \(-0.370380\pi\) | ||||
0.396051 | + | 0.918229i | \(0.370380\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 11.2669i | − | 0.741308i | ||||||
\(232\) | − | 0.991377i | − | 0.0650871i | ||||||
\(233\) | − | 4.72774i | − | 0.309724i | −0.987936 | − | 0.154862i | \(-0.950507\pi\) | ||
0.987936 | − | 0.154862i | \(-0.0494933\pi\) | |||||||
\(234\) | −16.0650 | −1.05020 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.21235 | −0.0789171 | ||||||||
\(237\) | −0.834834 | −0.0542283 | ||||||||
\(238\) | 8.38962 | − | 3.61320i | 0.543818 | − | 0.234209i | ||||
\(239\) | 10.7649 | 0.696321 | 0.348161 | − | 0.937435i | \(-0.386806\pi\) | ||||
0.348161 | + | 0.937435i | \(0.386806\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.6201i | 1.39267i | 0.717715 | + | 0.696337i | \(0.245188\pi\) | ||||
−0.717715 | + | 0.696337i | \(0.754812\pi\) | |||||||
\(242\) | 29.9783 | 1.92708 | ||||||||
\(243\) | − | 17.2987i | − | 1.10971i | ||||||
\(244\) | 8.51458i | 0.545090i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −28.0228 | −1.78667 | ||||||||
\(247\) | 15.7093 | 0.999557 | ||||||||
\(248\) | − | 6.55277i | − | 0.416101i | ||||||
\(249\) | 7.92097i | 0.501971i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.837101 | −0.0528374 | −0.0264187 | − | 0.999651i | \(-0.508410\pi\) | ||||
−0.0264187 | + | 0.999651i | \(0.508410\pi\) | |||||||
\(252\) | 5.27820i | 0.332495i | ||||||||
\(253\) | −34.9854 | −2.19952 | ||||||||
\(254\) | −4.78765 | −0.300404 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.418551 | −0.0261594 | ||||||||
\(257\) | −7.67316 | −0.478638 | −0.239319 | − | 0.970941i | \(-0.576924\pi\) | ||||
−0.239319 | + | 0.970941i | \(0.576924\pi\) | |||||||
\(258\) | 28.2024i | 1.75581i | ||||||||
\(259\) | −10.4741 | −0.650832 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 1.22911i | − | 0.0760802i | ||||||
\(262\) | 41.6689i | 2.57431i | ||||||||
\(263\) | −26.8371 | −1.65485 | −0.827423 | − | 0.561579i | \(-0.810194\pi\) | ||||
−0.827423 | + | 0.561579i | \(0.810194\pi\) | |||||||
\(264\) | −16.9867 | −1.04546 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 8.97142i | − | 0.550073i | ||||||
\(267\) | − | 5.82867i | − | 0.356709i | ||||||
\(268\) | 13.7587 | 0.840448 | ||||||||
\(269\) | − | 20.5192i | − | 1.25108i | −0.780193 | − | 0.625539i | \(-0.784879\pi\) | ||
0.780193 | − | 0.625539i | \(-0.215121\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.2062 | 0.741474 | 0.370737 | − | 0.928738i | \(-0.379105\pi\) | ||||
0.370737 | + | 0.928738i | \(0.379105\pi\) | |||||||
\(272\) | 3.38962 | + | 7.87049i | 0.205526 | + | 0.477218i | ||||
\(273\) | −8.77432 | −0.531046 | ||||||||
\(274\) | 0.659827 | 0.0398616 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 42.1555 | 2.53746 | ||||||||
\(277\) | 6.52324i | 0.391943i | 0.980610 | + | 0.195972i | \(0.0627861\pi\) | ||||
−0.980610 | + | 0.195972i | \(0.937214\pi\) | |||||||
\(278\) | 41.1184i | 2.46612i | ||||||||
\(279\) | − | 8.12415i | − | 0.486380i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.60811 | 0.0959319 | 0.0479659 | − | 0.998849i | \(-0.484726\pi\) | ||||
0.0479659 | + | 0.998849i | \(0.484726\pi\) | |||||||
\(282\) | − | 49.7130i | − | 2.96037i | ||||||
\(283\) | − | 2.18593i | − | 0.129940i | −0.997887 | − | 0.0649701i | \(-0.979305\pi\) | ||
0.997887 | − | 0.0649701i | \(-0.0206952\pi\) | |||||||
\(284\) | − | 9.23869i | − | 0.548215i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 41.9361i | − | 2.47974i | ||||||
\(287\) | −5.95055 | −0.351250 | ||||||||
\(288\) | −14.4813 | −0.853321 | ||||||||
\(289\) | −11.6803 | + | 12.3519i | −0.687079 | + | 0.726583i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −24.1568 | −1.41609 | ||||||||
\(292\) | 10.2596i | 0.600398i | ||||||||
\(293\) | 1.50307 | 0.0878104 | 0.0439052 | − | 0.999036i | \(-0.486020\pi\) | ||||
0.0439052 | + | 0.999036i | \(0.486020\pi\) | |||||||
\(294\) | − | 28.6433i | − | 1.67051i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 15.7915i | 0.917860i | ||||||||
\(297\) | 12.0482 | 0.699109 | ||||||||
\(298\) | 42.3100 | 2.45095 | ||||||||
\(299\) | 27.2456i | 1.57565i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.98870i | 0.345183i | ||||||||
\(302\) | 41.6163 | 2.39475 | ||||||||
\(303\) | − | 13.7792i | − | 0.791593i | ||||||
\(304\) | 8.41628 | 0.482707 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6.75380 | − | 15.6819i | −0.386089 | − | 0.896475i | ||||
\(307\) | 0.340173 | 0.0194147 | 0.00970735 | − | 0.999953i | \(-0.496910\pi\) | ||||
0.00970735 | + | 0.999953i | \(0.496910\pi\) | |||||||
\(308\) | −13.7782 | −0.785086 | ||||||||
\(309\) | 23.2556i | 1.32296i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 23.1915i | − | 1.31507i | −0.753424 | − | 0.657535i | \(-0.771599\pi\) | ||
0.753424 | − | 0.657535i | \(-0.228401\pi\) | |||||||
\(312\) | 13.2287i | 0.748928i | ||||||||
\(313\) | 25.4070i | 1.43609i | 0.695998 | + | 0.718043i | \(0.254962\pi\) | ||||
−0.695998 | + | 0.718043i | \(0.745038\pi\) | |||||||
\(314\) | 31.7370 | 1.79102 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.02091i | 0.0574308i | ||||||||
\(317\) | 6.76956i | 0.380216i | 0.981763 | + | 0.190108i | \(0.0608839\pi\) | ||||
−0.981763 | + | 0.190108i | \(0.939116\pi\) | |||||||
\(318\) | 54.7585i | 3.07070i | ||||||||
\(319\) | 3.20847 | 0.179640 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.4208 | 0.637448 | ||||||||
\(322\) | 15.5597 | 0.867109 | ||||||||
\(323\) | 6.60424 | + | 15.3346i | 0.367469 | + | 0.853241i | ||||
\(324\) | −30.0277 | −1.66821 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 29.4611i | 1.63170i | ||||||||
\(327\) | −15.3523 | −0.848983 | ||||||||
\(328\) | 8.97142i | 0.495364i | ||||||||
\(329\) | − | 10.5564i | − | 0.581993i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.8888 | 1.20312 | 0.601559 | − | 0.798828i | \(-0.294546\pi\) | ||||
0.601559 | + | 0.798828i | \(0.294546\pi\) | |||||||
\(332\) | 9.68649 | 0.531615 | ||||||||
\(333\) | 19.5783i | 1.07288i | ||||||||
\(334\) | 5.62549i | 0.307813i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.70086 | −0.256453 | ||||||||
\(337\) | − | 29.7283i | − | 1.61941i | −0.586840 | − | 0.809703i | \(-0.699628\pi\) | ||
0.586840 | − | 0.809703i | \(-0.300372\pi\) | |||||||
\(338\) | −4.44748 | −0.241911 | ||||||||
\(339\) | −43.3751 | −2.35581 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.2072 | 1.14844 | ||||||||
\(342\) | −16.7694 | −0.906785 | ||||||||
\(343\) | − | 13.2287i | − | 0.714283i | ||||||
\(344\) | 9.02893 | 0.486807 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 23.8997i | 1.28485i | ||||||||
\(347\) | 22.0474i | 1.18357i | 0.806097 | + | 0.591784i | \(0.201576\pi\) | ||||
−0.806097 | + | 0.591784i | \(0.798424\pi\) | |||||||
\(348\) | −3.86603 | −0.207241 | ||||||||
\(349\) | −15.0761 | −0.807006 | −0.403503 | − | 0.914978i | \(-0.632207\pi\) | ||||
−0.403503 | + | 0.914978i | \(0.632207\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 9.38280i | − | 0.500817i | ||||||
\(352\) | − | 37.8020i | − | 2.01485i | ||||||
\(353\) | 14.1194 | 0.751501 | 0.375750 | − | 0.926721i | \(-0.377385\pi\) | ||||
0.375750 | + | 0.926721i | \(0.377385\pi\) | |||||||
\(354\) | 2.15137i | 0.114344i | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.12783 | −0.377774 | ||||||||
\(357\) | −3.68876 | − | 8.56506i | −0.195230 | − | 0.453311i | ||||
\(358\) | −54.2206 | −2.86565 | ||||||||
\(359\) | 23.8082 | 1.25655 | 0.628274 | − | 0.777992i | \(-0.283762\pi\) | ||||
0.628274 | + | 0.777992i | \(0.283762\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.60197 | −0.136946 | ||||||||
\(362\) | 31.1261i | 1.63595i | ||||||||
\(363\) | − | 30.6052i | − | 1.60635i | ||||||
\(364\) | 10.7300i | 0.562407i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 15.1096 | 0.789790 | ||||||||
\(367\) | − | 3.77323i | − | 0.196961i | −0.995139 | − | 0.0984806i | \(-0.968602\pi\) | ||
0.995139 | − | 0.0984806i | \(-0.0313982\pi\) | |||||||
\(368\) | 14.5969i | 0.760916i | ||||||||
\(369\) | 11.1228i | 0.579029i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.6278i | 0.603685i | ||||||||
\(372\) | −25.5536 | −1.32489 | ||||||||
\(373\) | 1.54760 | 0.0801317 | 0.0400658 | − | 0.999197i | \(-0.487243\pi\) | ||||
0.0400658 | + | 0.999197i | \(0.487243\pi\) | |||||||
\(374\) | 40.9360 | − | 17.6301i | 2.11675 | − | 0.911631i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −15.9155 | −0.820778 | ||||||||
\(377\) | − | 2.49866i | − | 0.128688i | ||||||
\(378\) | −5.35842 | −0.275608 | ||||||||
\(379\) | 13.4824i | 0.692543i | 0.938134 | + | 0.346271i | \(0.112552\pi\) | ||||
−0.938134 | + | 0.346271i | \(0.887448\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.88777i | 0.250408i | ||||||||
\(382\) | −11.7093 | −0.599099 | ||||||||
\(383\) | −4.44748 | −0.227256 | −0.113628 | − | 0.993523i | \(-0.536247\pi\) | ||||
−0.113628 | + | 0.993523i | \(0.536247\pi\) | |||||||
\(384\) | 25.5647i | 1.30459i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 35.0225i | 1.78260i | ||||||||
\(387\) | 11.1941 | 0.569028 | ||||||||
\(388\) | 29.5411i | 1.49972i | ||||||||
\(389\) | −25.4680 | −1.29128 | −0.645639 | − | 0.763642i | \(-0.723409\pi\) | ||||
−0.645639 | + | 0.763642i | \(0.723409\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −26.5958 | + | 11.4542i | −1.34501 | + | 0.579261i | ||||
\(392\) | −9.17009 | −0.463159 | ||||||||
\(393\) | 42.5402 | 2.14587 | ||||||||
\(394\) | 20.1128i | 1.01327i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 25.7543i | 1.29420i | ||||||||
\(397\) | − | 14.3937i | − | 0.722400i | −0.932488 | − | 0.361200i | \(-0.882367\pi\) | ||
0.932488 | − | 0.361200i | \(-0.117633\pi\) | |||||||
\(398\) | − | 10.0564i | − | 0.504083i | ||||||
\(399\) | −9.15902 | −0.458525 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.456838i | 0.0228134i | 0.999935 | + | 0.0114067i | \(0.00363094\pi\) | ||||
−0.999935 | + | 0.0114067i | \(0.996369\pi\) | |||||||
\(402\) | − | 24.4156i | − | 1.21774i | ||||||
\(403\) | − | 16.5156i | − | 0.822699i | ||||||
\(404\) | −16.8504 | −0.838340 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.42696 | −0.0708189 | ||||||||
\(407\) | −51.1071 | −2.53329 | ||||||||
\(408\) | −12.9132 | + | 5.56140i | −0.639299 | + | 0.275330i | ||||
\(409\) | 26.7770 | 1.32404 | 0.662018 | − | 0.749488i | \(-0.269700\pi\) | ||||
0.662018 | + | 0.749488i | \(0.269700\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 0.673625i | − | 0.0332275i | ||||||
\(412\) | 28.4391 | 1.40109 | ||||||||
\(413\) | 0.456838i | 0.0224795i | ||||||||
\(414\) | − | 29.0843i | − | 1.42941i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −29.4391 | −1.44337 | ||||||||
\(417\) | 41.9783 | 2.05568 | ||||||||
\(418\) | − | 43.7748i | − | 2.14109i | ||||||
\(419\) | 16.2914i | 0.795889i | 0.917409 | + | 0.397944i | \(0.130276\pi\) | ||||
−0.917409 | + | 0.397944i | \(0.869724\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.21953 | −0.303122 | −0.151561 | − | 0.988448i | \(-0.548430\pi\) | ||||
−0.151561 | + | 0.988448i | \(0.548430\pi\) | |||||||
\(422\) | − | 13.2287i | − | 0.643963i | ||||||
\(423\) | −19.7321 | −0.959406 | ||||||||
\(424\) | 17.5308 | 0.851370 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −16.3945 | −0.794318 | ||||||||
\(427\) | 3.20847 | 0.155269 | ||||||||
\(428\) | − | 13.9664i | − | 0.675093i | ||||||
\(429\) | −42.8131 | −2.06704 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 24.4292i | − | 1.17671i | −0.808602 | − | 0.588357i | \(-0.799775\pi\) | ||
0.808602 | − | 0.588357i | \(-0.200225\pi\) | |||||||
\(432\) | − | 5.02686i | − | 0.241855i | ||||||
\(433\) | 6.85989 | 0.329665 | 0.164833 | − | 0.986322i | \(-0.447292\pi\) | ||||
0.164833 | + | 0.986322i | \(0.447292\pi\) | |||||||
\(434\) | −9.43188 | −0.452745 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.7742i | 0.899120i | ||||||||
\(437\) | 28.4402i | 1.36048i | ||||||||
\(438\) | 18.2062 | 0.869926 | ||||||||
\(439\) | 13.0255i | 0.621675i | 0.950463 | + | 0.310837i | \(0.100609\pi\) | ||||
−0.950463 | + | 0.310837i | \(0.899391\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.3691 | −0.541386 | ||||||||
\(442\) | −13.7298 | − | 31.8797i | −0.653060 | − | 1.51636i | ||||
\(443\) | 2.71542 | 0.129013 | 0.0645067 | − | 0.997917i | \(-0.479453\pi\) | ||||
0.0645067 | + | 0.997917i | \(0.479453\pi\) | |||||||
\(444\) | 61.5813 | 2.92252 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −38.4124 | −1.81888 | ||||||||
\(447\) | − | 43.1948i | − | 2.04304i | ||||||
\(448\) | 12.5687i | 0.593815i | ||||||||
\(449\) | 20.5697i | 0.970743i | 0.874308 | + | 0.485372i | \(0.161316\pi\) | ||||
−0.874308 | + | 0.485372i | \(0.838684\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.0349 | −1.36720 | ||||||||
\(452\) | 53.0430i | 2.49493i | ||||||||
\(453\) | − | 42.4866i | − | 1.99619i | ||||||
\(454\) | − | 55.5121i | − | 2.60531i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 13.8087i | 0.646652i | ||||||||
\(457\) | 15.0338 | 0.703254 | 0.351627 | − | 0.936140i | \(-0.385629\pi\) | ||||
0.351627 | + | 0.936140i | \(0.385629\pi\) | |||||||
\(458\) | −26.0121 | −1.21547 | ||||||||
\(459\) | 9.15902 | − | 3.94456i | 0.427507 | − | 0.184116i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.7382 | −0.593277 | −0.296639 | − | 0.954990i | \(-0.595866\pi\) | ||||
−0.296639 | + | 0.954990i | \(0.595866\pi\) | |||||||
\(462\) | 24.4501i | 1.13752i | ||||||||
\(463\) | 5.68261 | 0.264093 | 0.132047 | − | 0.991243i | \(-0.457845\pi\) | ||||
0.132047 | + | 0.991243i | \(0.457845\pi\) | |||||||
\(464\) | − | 1.33866i | − | 0.0621459i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.2596i | 0.475267i | ||||||||
\(467\) | −23.9155 | −1.10668 | −0.553338 | − | 0.832957i | \(-0.686646\pi\) | ||||
−0.553338 | + | 0.832957i | \(0.686646\pi\) | |||||||
\(468\) | 20.0566 | 0.927118 | ||||||||
\(469\) | − | 5.18457i | − | 0.239401i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 32.4007i | − | 1.49294i | ||||||
\(472\) | 0.688756 | 0.0317026 | ||||||||
\(473\) | 29.2210i | 1.34358i | ||||||||
\(474\) | 1.81166 | 0.0832124 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −10.4741 | + | 4.51095i | −0.480082 | + | 0.206759i | ||||
\(477\) | 21.7347 | 0.995164 | ||||||||
\(478\) | −23.3607 | −1.06849 | ||||||||
\(479\) | − | 11.6142i | − | 0.530666i | −0.964157 | − | 0.265333i | \(-0.914518\pi\) | ||
0.964157 | − | 0.265333i | \(-0.0854818\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 39.8007i | 1.81476i | ||||||||
\(482\) | − | 46.9175i | − | 2.13704i | ||||||
\(483\) | − | 15.8851i | − | 0.722796i | ||||||
\(484\) | −37.4268 | −1.70122 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 37.5398i | 1.70284i | ||||||||
\(487\) | − | 7.96411i | − | 0.360888i | −0.983585 | − | 0.180444i | \(-0.942246\pi\) | ||
0.983585 | − | 0.180444i | \(-0.0577535\pi\) | |||||||
\(488\) | − | 4.83729i | − | 0.218974i | ||||||
\(489\) | 30.0772 | 1.36014 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.2557 | 1.63619 | 0.818097 | − | 0.575080i | \(-0.195029\pi\) | ||||
0.818097 | + | 0.575080i | \(0.195029\pi\) | |||||||
\(492\) | 34.9854 | 1.57727 | ||||||||
\(493\) | 2.43907 | − | 1.05045i | 0.109850 | − | 0.0473097i | ||||
\(494\) | −34.0905 | −1.53380 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 8.84826i | − | 0.397298i | ||||||
\(497\) | −3.48133 | −0.156159 | ||||||||
\(498\) | − | 17.1892i | − | 0.770266i | ||||||
\(499\) | 20.1583i | 0.902409i | 0.892420 | + | 0.451205i | \(0.149006\pi\) | ||||
−0.892420 | + | 0.451205i | \(0.850994\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.74313 | 0.256584 | ||||||||
\(502\) | 1.81658 | 0.0810780 | ||||||||
\(503\) | − | 19.2151i | − | 0.856759i | −0.903599 | − | 0.428379i | \(-0.859085\pi\) | ||
0.903599 | − | 0.428379i | \(-0.140915\pi\) | |||||||
\(504\) | − | 2.99864i | − | 0.133570i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 75.9214 | 3.37512 | ||||||||
\(507\) | 4.54048i | 0.201650i | ||||||||
\(508\) | 5.97721 | 0.265196 | ||||||||
\(509\) | 1.52813 | 0.0677330 | 0.0338665 | − | 0.999426i | \(-0.489218\pi\) | ||||
0.0338665 | + | 0.999426i | \(0.489218\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.86603 | 0.171023 | ||||||||
\(512\) | −22.1701 | −0.979789 | ||||||||
\(513\) | − | 9.79417i | − | 0.432423i | ||||||
\(514\) | 16.6514 | 0.734462 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 35.2097i | − | 1.55002i | ||||||
\(517\) | − | 51.5085i | − | 2.26534i | ||||||
\(518\) | 22.7298 | 0.998690 | ||||||||
\(519\) | 24.3995 | 1.07102 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.96279i | 0.436478i | 0.975895 | + | 0.218239i | \(0.0700312\pi\) | ||||
−0.975895 | + | 0.218239i | \(0.929969\pi\) | |||||||
\(522\) | 2.66728i | 0.116744i | ||||||||
\(523\) | 31.2618 | 1.36698 | 0.683491 | − | 0.729959i | \(-0.260461\pi\) | ||||
0.683491 | + | 0.729959i | \(0.260461\pi\) | |||||||
\(524\) | − | 52.0221i | − | 2.27260i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 58.2388 | 2.53933 | ||||||||
\(527\) | 16.1217 | − | 6.94320i | 0.702272 | − | 0.302451i | ||||
\(528\) | −22.9372 | −0.998214 | ||||||||
\(529\) | −26.3256 | −1.14459 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.853922 | 0.0370571 | ||||||||
\(532\) | 11.2005i | 0.485603i | ||||||||
\(533\) | 22.6115i | 0.979413i | ||||||||
\(534\) | 12.6487i | 0.547363i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.81658 | −0.337625 | ||||||||
\(537\) | 55.3544i | 2.38872i | ||||||||
\(538\) | 44.5284i | 1.91976i | ||||||||
\(539\) | − | 29.6779i | − | 1.27832i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.1433i | 1.25297i | 0.779434 | + | 0.626485i | \(0.215507\pi\) | ||||
−0.779434 | + | 0.626485i | \(0.784493\pi\) | |||||||
\(542\) | −26.4885 | −1.13778 | ||||||||
\(543\) | 31.7770 | 1.36368 | ||||||||
\(544\) | −12.3763 | − | 28.7370i | −0.530629 | − | 1.23209i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 19.0410 | 0.814881 | ||||||||
\(547\) | − | 18.5069i | − | 0.791298i | −0.918402 | − | 0.395649i | \(-0.870520\pi\) | ||
0.918402 | − | 0.395649i | \(-0.129480\pi\) | |||||||
\(548\) | −0.823770 | −0.0351897 | ||||||||
\(549\) | − | 5.99729i | − | 0.255958i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2.60821i | − | 0.111114i | ||||||
\(552\) | −23.9493 | −1.01935 | ||||||||
\(553\) | 0.384701 | 0.0163591 | ||||||||
\(554\) | − | 14.1560i | − | 0.601430i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 51.3349i | − | 2.17708i | ||||||
\(557\) | −1.44029 | −0.0610271 | −0.0305136 | − | 0.999534i | \(-0.509714\pi\) | ||||
−0.0305136 | + | 0.999534i | \(0.509714\pi\) | |||||||
\(558\) | 17.6301i | 0.746342i | ||||||||
\(559\) | 22.7565 | 0.962496 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.9988 | − | 41.7920i | −0.759909 | − | 1.76446i | ||||
\(562\) | −3.48974 | −0.147206 | ||||||||
\(563\) | 2.47414 | 0.104273 | 0.0521363 | − | 0.998640i | \(-0.483397\pi\) | ||||
0.0521363 | + | 0.998640i | \(0.483397\pi\) | |||||||
\(564\) | 62.0649i | 2.61340i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.74366i | 0.199391i | ||||||||
\(567\) | 11.3151i | 0.475188i | ||||||||
\(568\) | 5.24867i | 0.220229i | ||||||||
\(569\) | 15.3919 | 0.645262 | 0.322631 | − | 0.946525i | \(-0.395433\pi\) | ||||
0.322631 | + | 0.946525i | \(0.395433\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 17.8974i | − | 0.748982i | −0.927231 | − | 0.374491i | \(-0.877817\pi\) | ||
0.927231 | − | 0.374491i | \(-0.122183\pi\) | |||||||
\(572\) | 52.3558i | 2.18910i | ||||||||
\(573\) | 11.9541i | 0.499391i | ||||||||
\(574\) | 12.9132 | 0.538987 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 23.4934 | 0.978893 | ||||||||
\(577\) | 44.1894 | 1.83963 | 0.919814 | − | 0.392355i | \(-0.128339\pi\) | ||||
0.919814 | + | 0.392355i | \(0.128339\pi\) | |||||||
\(578\) | 25.3474 | − | 26.8047i | 1.05431 | − | 1.11493i | ||||
\(579\) | 35.7548 | 1.48592 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 3.65007i | − | 0.151430i | ||||||
\(582\) | 52.4222 | 2.17297 | ||||||||
\(583\) | 56.7362i | 2.34977i | ||||||||
\(584\) | − | 5.82867i | − | 0.241192i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.26180 | −0.134744 | ||||||||
\(587\) | 3.04718 | 0.125771 | 0.0628853 | − | 0.998021i | \(-0.479970\pi\) | ||||
0.0628853 | + | 0.998021i | \(0.479970\pi\) | |||||||
\(588\) | 35.7602i | 1.47473i | ||||||||
\(589\) | − | 17.2397i | − | 0.710348i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.5334 | 0.844633 | ||||||||
\(592\) | 21.3233i | 0.876383i | ||||||||
\(593\) | −9.68876 | −0.397870 | −0.198935 | − | 0.980013i | \(-0.563748\pi\) | ||||
−0.198935 | + | 0.980013i | \(0.563748\pi\) | |||||||
\(594\) | −26.1457 | −1.07277 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −52.8225 | −2.16370 | ||||||||
\(597\) | −10.2667 | −0.420189 | ||||||||
\(598\) | − | 59.1253i | − | 2.41781i | ||||||
\(599\) | −33.2846 | −1.35997 | −0.679986 | − | 0.733225i | \(-0.738014\pi\) | ||||
−0.679986 | + | 0.733225i | \(0.738014\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 13.1055i | − | 0.534586i | −0.963615 | − | 0.267293i | \(-0.913871\pi\) | ||
0.963615 | − | 0.267293i | \(-0.0861292\pi\) | |||||||
\(602\) | − | 12.9960i | − | 0.529677i | ||||||
\(603\) | −9.69102 | −0.394649 | ||||||||
\(604\) | −51.9565 | −2.11408 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 29.9020i | 1.21469i | ||||||||
\(607\) | 8.34094i | 0.338548i | 0.985569 | + | 0.169274i | \(0.0541423\pi\) | ||||
−0.985569 | + | 0.169274i | \(0.945858\pi\) | |||||||
\(608\) | −30.7298 | −1.24626 | ||||||||
\(609\) | 1.45680i | 0.0590326i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −40.1133 | −1.62281 | ||||||||
\(612\) | 8.43188 | + | 19.5783i | 0.340839 | + | 0.791406i | ||||
\(613\) | −32.6430 | −1.31844 | −0.659219 | − | 0.751951i | \(-0.729113\pi\) | ||||
−0.659219 | + | 0.751951i | \(0.729113\pi\) | |||||||
\(614\) | −0.738205 | −0.0297915 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.82765 | 0.315385 | ||||||||
\(617\) | 31.5324i | 1.26945i | 0.772739 | + | 0.634724i | \(0.218886\pi\) | ||||
−0.772739 | + | 0.634724i | \(0.781114\pi\) | |||||||
\(618\) | − | 50.4666i | − | 2.03007i | ||||||
\(619\) | 42.1234i | 1.69308i | 0.532323 | + | 0.846541i | \(0.321319\pi\) | ||||
−0.532323 | + | 0.846541i | \(0.678681\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16.9867 | 0.681652 | ||||||||
\(622\) | 50.3276i | 2.01795i | ||||||||
\(623\) | 2.68591i | 0.107609i | ||||||||
\(624\) | 17.8628i | 0.715085i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 55.1353i | − | 2.20365i | ||||||
\(627\) | −44.6902 | −1.78475 | ||||||||
\(628\) | −39.6225 | −1.58111 | ||||||||
\(629\) | −38.8515 | + | 16.7324i | −1.54911 | + | 0.667163i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.7031 | 0.664941 | 0.332471 | − | 0.943114i | \(-0.392118\pi\) | ||||
0.332471 | + | 0.943114i | \(0.392118\pi\) | |||||||
\(632\) | − | 0.579999i | − | 0.0230711i | ||||||
\(633\) | −13.5053 | −0.536789 | ||||||||
\(634\) | − | 14.6905i | − | 0.583436i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 68.3640i | − | 2.71081i | ||||||
\(637\) | −23.1122 | −0.915740 | ||||||||
\(638\) | −6.96266 | −0.275654 | ||||||||
\(639\) | 6.50731i | 0.257425i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 16.3260i | − | 0.644838i | −0.946597 | − | 0.322419i | \(-0.895504\pi\) | ||
0.946597 | − | 0.322419i | \(-0.104496\pi\) | |||||||
\(642\) | −24.7842 | −0.978153 | ||||||||
\(643\) | − | 28.0633i | − | 1.10671i | −0.832945 | − | 0.553355i | \(-0.813347\pi\) | ||
0.832945 | − | 0.553355i | \(-0.186653\pi\) | |||||||
\(644\) | −19.4257 | −0.765481 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14.3318 | − | 33.2775i | −0.563876 | − | 1.30928i | ||||
\(647\) | 39.7815 | 1.56397 | 0.781986 | − | 0.623296i | \(-0.214207\pi\) | ||||
0.781986 | + | 0.623296i | \(0.214207\pi\) | |||||||
\(648\) | 17.0593 | 0.670152 | ||||||||
\(649\) | 2.22908i | 0.0874989i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.62912i | 0.377395i | ||||||||
\(652\) | − | 36.7811i | − | 1.44046i | ||||||
\(653\) | − | 35.7761i | − | 1.40003i | −0.714129 | − | 0.700014i | \(-0.753177\pi\) | ||
0.714129 | − | 0.700014i | \(-0.246823\pi\) | |||||||
\(654\) | 33.3158 | 1.30275 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 12.1142i | 0.472979i | ||||||||
\(657\) | − | 7.22640i | − | 0.281929i | ||||||
\(658\) | 22.9083i | 0.893059i | ||||||||
\(659\) | −5.18568 | −0.202006 | −0.101003 | − | 0.994886i | \(-0.532205\pi\) | ||||
−0.101003 | + | 0.994886i | \(0.532205\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.4079 | 1.22162 | 0.610812 | − | 0.791775i | \(-0.290843\pi\) | ||||
0.610812 | + | 0.791775i | \(0.290843\pi\) | |||||||
\(662\) | −47.5006 | −1.84616 | ||||||||
\(663\) | −32.5464 | + | 14.0169i | −1.26400 | + | 0.544372i | ||||
\(664\) | −5.50307 | −0.213561 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − | 42.4866i | − | 1.64632i | ||||||
\(667\) | 4.52359 | 0.175154 | ||||||||
\(668\) | − | 7.02322i | − | 0.271737i | ||||||
\(669\) | 39.2157i | 1.51617i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.6553 | 0.604366 | ||||||||
\(672\) | 17.1639 | 0.662113 | ||||||||
\(673\) | 17.8838i | 0.689368i | 0.938719 | + | 0.344684i | \(0.112014\pi\) | ||||
−0.938719 | + | 0.344684i | \(0.887986\pi\) | |||||||
\(674\) | 64.5131i | 2.48495i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.55252 | 0.213558 | ||||||||
\(677\) | 3.30278i | 0.126936i | 0.997984 | + | 0.0634682i | \(0.0202161\pi\) | ||||
−0.997984 | + | 0.0634682i | \(0.979784\pi\) | |||||||
\(678\) | 94.1276 | 3.61495 | ||||||||
\(679\) | 11.1317 | 0.427196 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −56.6730 | −2.17171 | ||||||||
\(682\) | −46.0216 | −1.76226 | ||||||||
\(683\) | 10.8742i | 0.416088i | 0.978119 | + | 0.208044i | \(0.0667097\pi\) | ||||
−0.978119 | + | 0.208044i | \(0.933290\pi\) | |||||||
\(684\) | 20.9360 | 0.800508 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 28.7074i | 1.09606i | ||||||||
\(687\) | 26.5561i | 1.01318i | ||||||||
\(688\) | 12.1918 | 0.464809 | ||||||||
\(689\) | 44.1845 | 1.68329 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.41002i | 0.129723i | 0.997894 | + | 0.0648617i | \(0.0206606\pi\) | ||||
−0.997894 | + | 0.0648617i | \(0.979339\pi\) | |||||||
\(692\) | − | 29.8379i | − | 1.13427i | ||||||
\(693\) | 9.70474 | 0.368653 | ||||||||
\(694\) | − | 47.8448i | − | 1.81616i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.19636 | 0.0832529 | ||||||||
\(697\) | −22.0722 | + | 9.50596i | −0.836046 | + | 0.360064i | ||||
\(698\) | 32.7165 | 1.23834 | ||||||||
\(699\) | 10.4741 | 0.396168 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.68422 | −0.101382 | −0.0506908 | − | 0.998714i | \(-0.516142\pi\) | ||||
−0.0506908 | + | 0.998714i | \(0.516142\pi\) | |||||||
\(702\) | 20.3615i | 0.768494i | ||||||||
\(703\) | 41.5457i | 1.56693i | ||||||||
\(704\) | 61.3272i | 2.31136i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −30.6404 | −1.15316 | ||||||||
\(707\) | 6.34959i | 0.238801i | ||||||||
\(708\) | − | 2.68591i | − | 0.100943i | ||||||
\(709\) | − | 46.9766i | − | 1.76424i | −0.471021 | − | 0.882122i | \(-0.656115\pi\) | ||
0.471021 | − | 0.882122i | \(-0.343885\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 0.719084i | − | 0.0269678i | ||||||
\(712\) | 4.04945 | 0.151759 | ||||||||
\(713\) | 29.8999 | 1.11976 | ||||||||
\(714\) | 8.00492 | + | 18.5869i | 0.299577 | + | 0.695598i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 67.6925 | 2.52979 | ||||||||
\(717\) | 23.8492i | 0.890665i | ||||||||
\(718\) | −51.6658 | −1.92815 | ||||||||
\(719\) | − | 37.4252i | − | 1.39572i | −0.716232 | − | 0.697862i | \(-0.754135\pi\) | ||
0.716232 | − | 0.697862i | \(-0.245865\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 10.7164i | − | 0.399101i | ||||||
\(722\) | 5.64650 | 0.210141 | ||||||||
\(723\) | −47.8987 | −1.78137 | ||||||||
\(724\) | − | 38.8598i | − | 1.44421i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 66.4158i | 2.46492i | ||||||||
\(727\) | −37.8537 | −1.40392 | −0.701959 | − | 0.712218i | \(-0.747691\pi\) | ||||
−0.701959 | + | 0.712218i | \(0.747691\pi\) | |||||||
\(728\) | − | 6.09593i | − | 0.225930i | ||||||
\(729\) | 5.07489 | 0.187959 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.56690 | + | 22.2137i | 0.353844 | + | 0.821605i | ||||
\(732\) | −18.8638 | −0.697225 | ||||||||
\(733\) | 36.0205 | 1.33045 | 0.665224 | − | 0.746644i | \(-0.268336\pi\) | ||||
0.665224 | + | 0.746644i | \(0.268336\pi\) | |||||||
\(734\) | 8.18824i | 0.302233i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 53.2967i | − | 1.96454i | ||||||
\(737\) | − | 25.2974i | − | 0.931842i | ||||||
\(738\) | − | 24.1374i | − | 0.888511i | ||||||
\(739\) | 19.0349 | 0.700210 | 0.350105 | − | 0.936710i | \(-0.386146\pi\) | ||||
0.350105 | + | 0.936710i | \(0.386146\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 34.8034i | 1.27853i | ||||||||
\(742\) | − | 25.2333i | − | 0.926344i | ||||||
\(743\) | − | 10.8901i | − | 0.399518i | −0.979845 | − | 0.199759i | \(-0.935984\pi\) | ||
0.979845 | − | 0.199759i | \(-0.0640160\pi\) | |||||||
\(744\) | 14.5174 | 0.532235 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.35842 | −0.122961 | ||||||||
\(747\) | −6.82273 | −0.249630 | ||||||||
\(748\) | −51.1071 | + | 22.0106i | −1.86866 | + | 0.804786i | ||||
\(749\) | −5.26284 | −0.192300 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.59232i | 0.0581047i | 0.999578 | + | 0.0290524i | \(0.00924895\pi\) | ||||
−0.999578 | + | 0.0290524i | \(0.990751\pi\) | |||||||
\(752\) | −21.4908 | −0.783688 | ||||||||
\(753\) | − | 1.85457i | − | 0.0675843i | ||||||
\(754\) | 5.42231i | 0.197469i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 6.68980 | 0.243306 | ||||||||
\(757\) | 7.42696 | 0.269937 | 0.134969 | − | 0.990850i | \(-0.456907\pi\) | ||||
0.134969 | + | 0.990850i | \(0.456907\pi\) | |||||||
\(758\) | − | 29.2579i | − | 1.06269i | ||||||
\(759\) | − | 77.5091i | − | 2.81340i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.3679 | 1.53583 | 0.767917 | − | 0.640549i | \(-0.221293\pi\) | ||||
0.767917 | + | 0.640549i | \(0.221293\pi\) | |||||||
\(762\) | − | 10.6069i | − | 0.384247i | ||||||
\(763\) | 7.07450 | 0.256114 | ||||||||
\(764\) | 14.6186 | 0.528883 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.65142 | 0.348720 | ||||||||
\(767\) | 1.73594 | 0.0626811 | ||||||||
\(768\) | − | 0.927285i | − | 0.0334605i | ||||||
\(769\) | −3.40522 | −0.122795 | −0.0613977 | − | 0.998113i | \(-0.519556\pi\) | ||||
−0.0613977 | + | 0.998113i | \(0.519556\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 16.9996i | − | 0.612226i | ||||||
\(772\) | − | 43.7243i | − | 1.57367i | ||||||
\(773\) | −49.7058 | −1.78779 | −0.893896 | − | 0.448274i | \(-0.852039\pi\) | ||||
−0.893896 | + | 0.448274i | \(0.852039\pi\) | |||||||
\(774\) | −24.2922 | −0.873163 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 16.7828i | − | 0.602469i | ||||||
\(777\) | − | 23.2051i | − | 0.832479i | ||||||
\(778\) | 55.2678 | 1.98145 | ||||||||
\(779\) | 23.6029i | 0.845661i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.9867 | −0.607831 | ||||||||
\(782\) | 57.7152 | − | 24.8565i | 2.06389 | − | 0.888867i | ||||
\(783\) | −1.55783 | −0.0556722 | ||||||||
\(784\) | −12.3824 | −0.442230 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −92.3160 | −3.29280 | ||||||||
\(787\) | 3.96049i | 0.141176i | 0.997506 | + | 0.0705880i | \(0.0224876\pi\) | ||||
−0.997506 | + | 0.0705880i | \(0.977512\pi\) | |||||||
\(788\) | − | 25.1102i | − | 0.894512i | ||||||
\(789\) | − | 59.4567i | − | 2.11671i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.9877 | 0.710681 |