Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.12489\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.12489 | −1.50252 | −0.751260 | − | 0.660006i | \(-0.770554\pi\) | ||||
−0.751260 | + | 0.660006i | \(0.770554\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.51514 | 1.25757 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.12489 | −0.867481 | ||||||||
\(7\) | −3.64002 | −1.37580 | −0.687900 | − | 0.725806i | \(-0.741467\pi\) | ||||
−0.687900 | + | 0.725806i | \(0.741467\pi\) | |||||||
\(8\) | −1.09461 | −0.387003 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 2.51514 | 0.726058 | ||||||||
\(13\) | −1.51514 | −0.420224 | −0.210112 | − | 0.977677i | \(-0.567383\pi\) | ||||
−0.210112 | + | 0.977677i | \(0.567383\pi\) | |||||||
\(14\) | 7.73463 | 2.06717 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.70436 | −0.676089 | ||||||||
\(17\) | −1.15516 | −0.280168 | −0.140084 | − | 0.990140i | \(-0.544737\pi\) | ||||
−0.140084 | + | 0.990140i | \(0.544737\pi\) | |||||||
\(18\) | −2.12489 | −0.500840 | ||||||||
\(19\) | 2.60975 | 0.598717 | 0.299359 | − | 0.954141i | \(-0.403227\pi\) | ||||
0.299359 | + | 0.954141i | \(0.403227\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.64002 | −0.794318 | ||||||||
\(22\) | −2.12489 | −0.453027 | ||||||||
\(23\) | 5.73463 | 1.19575 | 0.597877 | − | 0.801588i | \(-0.296011\pi\) | ||||
0.597877 | + | 0.801588i | \(0.296011\pi\) | |||||||
\(24\) | −1.09461 | −0.223436 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.21949 | 0.631395 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −9.15516 | −1.73016 | ||||||||
\(29\) | 6.24977 | 1.16055 | 0.580277 | − | 0.814419i | \(-0.302944\pi\) | ||||
0.580277 | + | 0.814419i | \(0.302944\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.51514 | 0.990548 | 0.495274 | − | 0.868737i | \(-0.335068\pi\) | ||||
0.495274 | + | 0.868737i | \(0.335068\pi\) | |||||||
\(32\) | 7.93567 | 1.40284 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 2.45459 | 0.420958 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.51514 | 0.419190 | ||||||||
\(37\) | −0.454586 | −0.0747335 | −0.0373667 | − | 0.999302i | \(-0.511897\pi\) | ||||
−0.0373667 | + | 0.999302i | \(0.511897\pi\) | |||||||
\(38\) | −5.54541 | −0.899585 | ||||||||
\(39\) | −1.51514 | −0.242616 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.12489 | 0.644199 | 0.322099 | − | 0.946706i | \(-0.395611\pi\) | ||||
0.322099 | + | 0.946706i | \(0.395611\pi\) | |||||||
\(42\) | 7.73463 | 1.19348 | ||||||||
\(43\) | −11.7044 | −1.78490 | −0.892449 | − | 0.451149i | \(-0.851014\pi\) | ||||
−0.892449 | + | 0.451149i | \(0.851014\pi\) | |||||||
\(44\) | 2.51514 | 0.379171 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12.1854 | −1.79664 | ||||||||
\(47\) | 3.48486 | 0.508319 | 0.254160 | − | 0.967162i | \(-0.418201\pi\) | ||||
0.254160 | + | 0.967162i | \(0.418201\pi\) | |||||||
\(48\) | −2.70436 | −0.390340 | ||||||||
\(49\) | 6.24977 | 0.892824 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.15516 | −0.161755 | ||||||||
\(52\) | −3.81078 | −0.528460 | ||||||||
\(53\) | 12.5601 | 1.72526 | 0.862631 | − | 0.505834i | \(-0.168815\pi\) | ||||
0.862631 | + | 0.505834i | \(0.168815\pi\) | |||||||
\(54\) | −2.12489 | −0.289160 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.98440 | 0.532438 | ||||||||
\(57\) | 2.60975 | 0.345669 | ||||||||
\(58\) | −13.2800 | −1.74376 | ||||||||
\(59\) | −7.73463 | −1.00696 | −0.503482 | − | 0.864006i | \(-0.667948\pi\) | ||||
−0.503482 | + | 0.864006i | \(0.667948\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.0147 | −1.53832 | −0.769161 | − | 0.639055i | \(-0.779326\pi\) | ||||
−0.769161 | + | 0.639055i | \(0.779326\pi\) | |||||||
\(62\) | −11.7190 | −1.48832 | ||||||||
\(63\) | −3.64002 | −0.458600 | ||||||||
\(64\) | −11.4537 | −1.43171 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.12489 | −0.261555 | ||||||||
\(67\) | 14.2645 | 1.74268 | 0.871340 | − | 0.490680i | \(-0.163251\pi\) | ||||
0.871340 | + | 0.490680i | \(0.163251\pi\) | |||||||
\(68\) | −2.90539 | −0.352330 | ||||||||
\(69\) | 5.73463 | 0.690369 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.51514 | 1.01056 | 0.505280 | − | 0.862955i | \(-0.331389\pi\) | ||||
0.505280 | + | 0.862955i | \(0.331389\pi\) | |||||||
\(72\) | −1.09461 | −0.129001 | ||||||||
\(73\) | 9.21949 | 1.07906 | 0.539530 | − | 0.841966i | \(-0.318602\pi\) | ||||
0.539530 | + | 0.841966i | \(0.318602\pi\) | |||||||
\(74\) | 0.965943 | 0.112289 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.56387 | 0.752928 | ||||||||
\(77\) | −3.64002 | −0.414819 | ||||||||
\(78\) | 3.21949 | 0.364536 | ||||||||
\(79\) | 5.09461 | 0.573188 | 0.286594 | − | 0.958052i | \(-0.407477\pi\) | ||||
0.286594 | + | 0.958052i | \(0.407477\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −8.76491 | −0.967922 | ||||||||
\(83\) | 14.7493 | 1.61895 | 0.809474 | − | 0.587156i | \(-0.199753\pi\) | ||||
0.809474 | + | 0.587156i | \(0.199753\pi\) | |||||||
\(84\) | −9.15516 | −0.998910 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 24.8704 | 2.68185 | ||||||||
\(87\) | 6.24977 | 0.670046 | ||||||||
\(88\) | −1.09461 | −0.116686 | ||||||||
\(89\) | −10.4995 | −1.11295 | −0.556475 | − | 0.830865i | \(-0.687846\pi\) | ||||
−0.556475 | + | 0.830865i | \(0.687846\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.51514 | 0.578144 | ||||||||
\(92\) | 14.4234 | 1.50374 | ||||||||
\(93\) | 5.51514 | 0.571893 | ||||||||
\(94\) | −7.40493 | −0.763760 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 7.93567 | 0.809931 | ||||||||
\(97\) | 6.77959 | 0.688363 | 0.344181 | − | 0.938903i | \(-0.388156\pi\) | ||||
0.344181 | + | 0.938903i | \(0.388156\pi\) | |||||||
\(98\) | −13.2800 | −1.34149 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.40493 | 0.736818 | 0.368409 | − | 0.929664i | \(-0.379903\pi\) | ||||
0.368409 | + | 0.929664i | \(0.379903\pi\) | |||||||
\(102\) | 2.45459 | 0.243040 | ||||||||
\(103\) | 16.4995 | 1.62575 | 0.812874 | − | 0.582439i | \(-0.197902\pi\) | ||||
0.812874 | + | 0.582439i | \(0.197902\pi\) | |||||||
\(104\) | 1.65848 | 0.162628 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −26.6888 | −2.59224 | ||||||||
\(107\) | −3.93945 | −0.380841 | −0.190420 | − | 0.981703i | \(-0.560985\pi\) | ||||
−0.190420 | + | 0.981703i | \(0.560985\pi\) | |||||||
\(108\) | 2.51514 | 0.242019 | ||||||||
\(109\) | 6.73463 | 0.645061 | 0.322530 | − | 0.946559i | \(-0.395467\pi\) | ||||
0.322530 | + | 0.946559i | \(0.395467\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.454586 | −0.0431474 | ||||||||
\(112\) | 9.84392 | 0.930163 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | −5.54541 | −0.519376 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 15.7190 | 1.45948 | ||||||||
\(117\) | −1.51514 | −0.140075 | ||||||||
\(118\) | 16.4352 | 1.51298 | ||||||||
\(119\) | 4.20482 | 0.385455 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 25.5298 | 2.31136 | ||||||||
\(123\) | 4.12489 | 0.371928 | ||||||||
\(124\) | 13.8713 | 1.24568 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 7.73463 | 0.689056 | ||||||||
\(127\) | −8.06433 | −0.715594 | −0.357797 | − | 0.933799i | \(-0.616472\pi\) | ||||
−0.357797 | + | 0.933799i | \(0.616472\pi\) | |||||||
\(128\) | 8.46640 | 0.748331 | ||||||||
\(129\) | −11.7044 | −1.03051 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.8099 | −1.11920 | −0.559602 | − | 0.828762i | \(-0.689046\pi\) | ||||
−0.559602 | + | 0.828762i | \(0.689046\pi\) | |||||||
\(132\) | 2.51514 | 0.218915 | ||||||||
\(133\) | −9.49954 | −0.823715 | ||||||||
\(134\) | −30.3103 | −2.61841 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.26445 | 0.108426 | ||||||||
\(137\) | −22.8099 | −1.94878 | −0.974389 | − | 0.224868i | \(-0.927805\pi\) | ||||
−0.974389 | + | 0.224868i | \(0.927805\pi\) | |||||||
\(138\) | −12.1854 | −1.03729 | ||||||||
\(139\) | 7.59037 | 0.643807 | 0.321903 | − | 0.946773i | \(-0.395677\pi\) | ||||
0.321903 | + | 0.946773i | \(0.395677\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.48486 | 0.293478 | ||||||||
\(142\) | −18.0937 | −1.51839 | ||||||||
\(143\) | −1.51514 | −0.126702 | ||||||||
\(144\) | −2.70436 | −0.225363 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −19.5904 | −1.62131 | ||||||||
\(147\) | 6.24977 | 0.515472 | ||||||||
\(148\) | −1.14335 | −0.0939825 | ||||||||
\(149\) | −1.81456 | −0.148655 | −0.0743274 | − | 0.997234i | \(-0.523681\pi\) | ||||
−0.0743274 | + | 0.997234i | \(0.523681\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 24.3250 | 1.97954 | 0.989770 | − | 0.142670i | \(-0.0455687\pi\) | ||||
0.989770 | + | 0.142670i | \(0.0455687\pi\) | |||||||
\(152\) | −2.85665 | −0.231705 | ||||||||
\(153\) | −1.15516 | −0.0933893 | ||||||||
\(154\) | 7.73463 | 0.623274 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.81078 | −0.305107 | ||||||||
\(157\) | −9.76491 | −0.779325 | −0.389662 | − | 0.920958i | \(-0.627408\pi\) | ||||
−0.389662 | + | 0.920958i | \(0.627408\pi\) | |||||||
\(158\) | −10.8255 | −0.861227 | ||||||||
\(159\) | 12.5601 | 0.996080 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.8742 | −1.64512 | ||||||||
\(162\) | −2.12489 | −0.166947 | ||||||||
\(163\) | 6.98440 | 0.547061 | 0.273530 | − | 0.961863i | \(-0.411809\pi\) | ||||
0.273530 | + | 0.961863i | \(0.411809\pi\) | |||||||
\(164\) | 10.3747 | 0.810125 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −31.3406 | −2.43250 | ||||||||
\(167\) | 6.31032 | 0.488307 | 0.244154 | − | 0.969737i | \(-0.421490\pi\) | ||||
0.244154 | + | 0.969737i | \(0.421490\pi\) | |||||||
\(168\) | 3.98440 | 0.307403 | ||||||||
\(169\) | −10.7044 | −0.823412 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.60975 | 0.199572 | ||||||||
\(172\) | −29.4381 | −2.24463 | ||||||||
\(173\) | 12.8448 | 0.976575 | 0.488287 | − | 0.872683i | \(-0.337622\pi\) | ||||
0.488287 | + | 0.872683i | \(0.337622\pi\) | |||||||
\(174\) | −13.2800 | −1.00676 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.70436 | −0.203849 | ||||||||
\(177\) | −7.73463 | −0.581371 | ||||||||
\(178\) | 22.3103 | 1.67223 | ||||||||
\(179\) | 13.4849 | 1.00791 | 0.503953 | − | 0.863731i | \(-0.331878\pi\) | ||||
0.503953 | + | 0.863731i | \(0.331878\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.0899 | −1.71626 | −0.858130 | − | 0.513433i | \(-0.828374\pi\) | ||||
−0.858130 | + | 0.513433i | \(0.828374\pi\) | |||||||
\(182\) | −11.7190 | −0.868673 | ||||||||
\(183\) | −12.0147 | −0.888151 | ||||||||
\(184\) | −6.27718 | −0.462760 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −11.7190 | −0.859281 | ||||||||
\(187\) | −1.15516 | −0.0844738 | ||||||||
\(188\) | 8.76491 | 0.639247 | ||||||||
\(189\) | −3.64002 | −0.264773 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.98440 | −0.577731 | −0.288866 | − | 0.957370i | \(-0.593278\pi\) | ||||
−0.288866 | + | 0.957370i | \(0.593278\pi\) | |||||||
\(192\) | −11.4537 | −0.826597 | ||||||||
\(193\) | −11.7649 | −0.846857 | −0.423428 | − | 0.905930i | \(-0.639173\pi\) | ||||
−0.423428 | + | 0.905930i | \(0.639173\pi\) | |||||||
\(194\) | −14.4058 | −1.03428 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 15.7190 | 1.12279 | ||||||||
\(197\) | 3.81456 | 0.271776 | 0.135888 | − | 0.990724i | \(-0.456611\pi\) | ||||
0.135888 | + | 0.990724i | \(0.456611\pi\) | |||||||
\(198\) | −2.12489 | −0.151009 | ||||||||
\(199\) | −12.0752 | −0.855990 | −0.427995 | − | 0.903781i | \(-0.640780\pi\) | ||||
−0.427995 | + | 0.903781i | \(0.640780\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.2645 | 1.00614 | ||||||||
\(202\) | −15.7346 | −1.10708 | ||||||||
\(203\) | −22.7493 | −1.59669 | ||||||||
\(204\) | −2.90539 | −0.203418 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −35.0596 | −2.44272 | ||||||||
\(207\) | 5.73463 | 0.398585 | ||||||||
\(208\) | 4.09747 | 0.284109 | ||||||||
\(209\) | 2.60975 | 0.180520 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.2645 | 0.706634 | 0.353317 | − | 0.935504i | \(-0.385054\pi\) | ||||
0.353317 | + | 0.935504i | \(0.385054\pi\) | |||||||
\(212\) | 31.5904 | 2.16964 | ||||||||
\(213\) | 8.51514 | 0.583448 | ||||||||
\(214\) | 8.37088 | 0.572221 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.09461 | −0.0744787 | ||||||||
\(217\) | −20.0752 | −1.36280 | ||||||||
\(218\) | −14.3103 | −0.969217 | ||||||||
\(219\) | 9.21949 | 0.622996 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.75023 | 0.117733 | ||||||||
\(222\) | 0.965943 | 0.0648298 | ||||||||
\(223\) | −12.9239 | −0.865445 | −0.432723 | − | 0.901527i | \(-0.642447\pi\) | ||||
−0.432723 | + | 0.901527i | \(0.642447\pi\) | |||||||
\(224\) | −28.8860 | −1.93003 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.7493 | −0.848072 | ||||||||
\(227\) | −22.8099 | −1.51394 | −0.756972 | − | 0.653447i | \(-0.773322\pi\) | ||||
−0.756972 | + | 0.653447i | \(0.773322\pi\) | |||||||
\(228\) | 6.56387 | 0.434703 | ||||||||
\(229\) | 14.7796 | 0.976663 | 0.488331 | − | 0.872658i | \(-0.337606\pi\) | ||||
0.488331 | + | 0.872658i | \(0.337606\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.64002 | −0.239496 | ||||||||
\(232\) | −6.84106 | −0.449137 | ||||||||
\(233\) | −4.96594 | −0.325330 | −0.162665 | − | 0.986681i | \(-0.552009\pi\) | ||||
−0.162665 | + | 0.986681i | \(0.552009\pi\) | |||||||
\(234\) | 3.21949 | 0.210465 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −19.4537 | −1.26633 | ||||||||
\(237\) | 5.09461 | 0.330930 | ||||||||
\(238\) | −8.93475 | −0.579154 | ||||||||
\(239\) | −14.9991 | −0.970210 | −0.485105 | − | 0.874456i | \(-0.661219\pi\) | ||||
−0.485105 | + | 0.874456i | \(0.661219\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.04496 | 0.324974 | 0.162487 | − | 0.986711i | \(-0.448048\pi\) | ||||
0.162487 | + | 0.986711i | \(0.448048\pi\) | |||||||
\(242\) | −2.12489 | −0.136593 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −30.2186 | −1.93455 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.76491 | −0.558830 | ||||||||
\(247\) | −3.95413 | −0.251595 | ||||||||
\(248\) | −6.03692 | −0.383345 | ||||||||
\(249\) | 14.7493 | 0.934700 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.03028 | −0.191269 | −0.0956347 | − | 0.995417i | \(-0.530488\pi\) | ||||
−0.0956347 | + | 0.995417i | \(0.530488\pi\) | |||||||
\(252\) | −9.15516 | −0.576721 | ||||||||
\(253\) | 5.73463 | 0.360533 | ||||||||
\(254\) | 17.1358 | 1.07519 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.91721 | 0.307325 | ||||||||
\(257\) | 13.6509 | 0.851521 | 0.425761 | − | 0.904836i | \(-0.360007\pi\) | ||||
0.425761 | + | 0.904836i | \(0.360007\pi\) | |||||||
\(258\) | 24.8704 | 1.54836 | ||||||||
\(259\) | 1.65470 | 0.102818 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.24977 | 0.386851 | ||||||||
\(262\) | 27.2195 | 1.68163 | ||||||||
\(263\) | −12.5601 | −0.774489 | −0.387244 | − | 0.921977i | \(-0.626573\pi\) | ||||
−0.387244 | + | 0.921977i | \(0.626573\pi\) | |||||||
\(264\) | −1.09461 | −0.0673685 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 20.1854 | 1.23765 | ||||||||
\(267\) | −10.4995 | −0.642562 | ||||||||
\(268\) | 35.8771 | 2.19154 | ||||||||
\(269\) | −24.6888 | −1.50530 | −0.752650 | − | 0.658421i | \(-0.771225\pi\) | ||||
−0.752650 | + | 0.658421i | \(0.771225\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.56479 | 0.459528 | 0.229764 | − | 0.973246i | \(-0.426205\pi\) | ||||
0.229764 | + | 0.973246i | \(0.426205\pi\) | |||||||
\(272\) | 3.12397 | 0.189418 | ||||||||
\(273\) | 5.51514 | 0.333791 | ||||||||
\(274\) | 48.4683 | 2.92808 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 14.4234 | 0.868186 | ||||||||
\(277\) | −1.92477 | −0.115648 | −0.0578241 | − | 0.998327i | \(-0.518416\pi\) | ||||
−0.0578241 | + | 0.998327i | \(0.518416\pi\) | |||||||
\(278\) | −16.1287 | −0.967333 | ||||||||
\(279\) | 5.51514 | 0.330183 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.87511 | −0.111860 | −0.0559300 | − | 0.998435i | \(-0.517812\pi\) | ||||
−0.0559300 | + | 0.998435i | \(0.517812\pi\) | |||||||
\(282\) | −7.40493 | −0.440957 | ||||||||
\(283\) | −30.1396 | −1.79161 | −0.895806 | − | 0.444446i | \(-0.853401\pi\) | ||||
−0.895806 | + | 0.444446i | \(0.853401\pi\) | |||||||
\(284\) | 21.4167 | 1.27085 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.21949 | 0.190373 | ||||||||
\(287\) | −15.0147 | −0.886289 | ||||||||
\(288\) | 7.93567 | 0.467614 | ||||||||
\(289\) | −15.6656 | −0.921506 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.77959 | 0.397427 | ||||||||
\(292\) | 23.1883 | 1.35699 | ||||||||
\(293\) | 29.1552 | 1.70326 | 0.851631 | − | 0.524141i | \(-0.175614\pi\) | ||||
0.851631 | + | 0.524141i | \(0.175614\pi\) | |||||||
\(294\) | −13.2800 | −0.774508 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.497594 | 0.0289221 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 3.85574 | 0.223357 | ||||||||
\(299\) | −8.68876 | −0.502484 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 42.6041 | 2.45566 | ||||||||
\(302\) | −51.6878 | −2.97430 | ||||||||
\(303\) | 7.40493 | 0.425402 | ||||||||
\(304\) | −7.05769 | −0.404786 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.45459 | 0.140319 | ||||||||
\(307\) | −27.8548 | −1.58976 | −0.794879 | − | 0.606768i | \(-0.792466\pi\) | ||||
−0.794879 | + | 0.606768i | \(0.792466\pi\) | |||||||
\(308\) | −9.15516 | −0.521664 | ||||||||
\(309\) | 16.4995 | 0.938626 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.9083 | 1.35571 | 0.677856 | − | 0.735194i | \(-0.262909\pi\) | ||||
0.677856 | + | 0.735194i | \(0.262909\pi\) | |||||||
\(312\) | 1.65848 | 0.0938932 | ||||||||
\(313\) | −28.3094 | −1.60014 | −0.800071 | − | 0.599905i | \(-0.795205\pi\) | ||||
−0.800071 | + | 0.599905i | \(0.795205\pi\) | |||||||
\(314\) | 20.7493 | 1.17095 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.8136 | 0.720824 | ||||||||
\(317\) | 8.80986 | 0.494811 | 0.247406 | − | 0.968912i | \(-0.420422\pi\) | ||||
0.247406 | + | 0.968912i | \(0.420422\pi\) | |||||||
\(318\) | −26.6888 | −1.49663 | ||||||||
\(319\) | 6.24977 | 0.349920 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.93945 | −0.219879 | ||||||||
\(322\) | 44.3553 | 2.47182 | ||||||||
\(323\) | −3.01468 | −0.167741 | ||||||||
\(324\) | 2.51514 | 0.139730 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −14.8411 | −0.821970 | ||||||||
\(327\) | 6.73463 | 0.372426 | ||||||||
\(328\) | −4.51514 | −0.249307 | ||||||||
\(329\) | −12.6850 | −0.699346 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.2498 | 1.77261 | 0.886304 | − | 0.463104i | \(-0.153264\pi\) | ||||
0.886304 | + | 0.463104i | \(0.153264\pi\) | |||||||
\(332\) | 37.0966 | 2.03594 | ||||||||
\(333\) | −0.454586 | −0.0249112 | ||||||||
\(334\) | −13.4087 | −0.733692 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 9.84392 | 0.537030 | ||||||||
\(337\) | −28.9844 | −1.57888 | −0.789441 | − | 0.613827i | \(-0.789629\pi\) | ||||
−0.789441 | + | 0.613827i | \(0.789629\pi\) | |||||||
\(338\) | 22.7455 | 1.23719 | ||||||||
\(339\) | 6.00000 | 0.325875 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.51514 | 0.298661 | ||||||||
\(342\) | −5.54541 | −0.299862 | ||||||||
\(343\) | 2.73085 | 0.147452 | ||||||||
\(344\) | 12.8117 | 0.690760 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −27.2938 | −1.46732 | ||||||||
\(347\) | 35.7190 | 1.91750 | 0.958749 | − | 0.284253i | \(-0.0917457\pi\) | ||||
0.958749 | + | 0.284253i | \(0.0917457\pi\) | |||||||
\(348\) | 15.7190 | 0.842629 | ||||||||
\(349\) | −23.2800 | −1.24615 | −0.623076 | − | 0.782161i | \(-0.714117\pi\) | ||||
−0.623076 | + | 0.782161i | \(0.714117\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.51514 | −0.0808721 | ||||||||
\(352\) | 7.93567 | 0.422972 | ||||||||
\(353\) | 9.75023 | 0.518952 | 0.259476 | − | 0.965750i | \(-0.416450\pi\) | ||||
0.259476 | + | 0.965750i | \(0.416450\pi\) | |||||||
\(354\) | 16.4352 | 0.873521 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −26.4078 | −1.39961 | ||||||||
\(357\) | 4.20482 | 0.222542 | ||||||||
\(358\) | −28.6538 | −1.51440 | ||||||||
\(359\) | 33.9007 | 1.78921 | 0.894605 | − | 0.446858i | \(-0.147457\pi\) | ||||
0.894605 | + | 0.446858i | \(0.147457\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.1892 | −0.641538 | ||||||||
\(362\) | 49.0634 | 2.57872 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 13.8713 | 0.727055 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 25.5298 | 1.33446 | ||||||||
\(367\) | −1.88601 | −0.0984491 | −0.0492245 | − | 0.998788i | \(-0.515675\pi\) | ||||
−0.0492245 | + | 0.998788i | \(0.515675\pi\) | |||||||
\(368\) | −15.5085 | −0.808436 | ||||||||
\(369\) | 4.12489 | 0.214733 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −45.7190 | −2.37361 | ||||||||
\(372\) | 13.8713 | 0.719195 | ||||||||
\(373\) | 16.3250 | 0.845277 | 0.422638 | − | 0.906298i | \(-0.361104\pi\) | ||||
0.422638 | + | 0.906298i | \(0.361104\pi\) | |||||||
\(374\) | 2.45459 | 0.126924 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.81456 | −0.196721 | ||||||||
\(377\) | −9.46927 | −0.487692 | ||||||||
\(378\) | 7.73463 | 0.397827 | ||||||||
\(379\) | −26.0440 | −1.33779 | −0.668896 | − | 0.743356i | \(-0.733233\pi\) | ||||
−0.668896 | + | 0.743356i | \(0.733233\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.06433 | −0.413148 | ||||||||
\(382\) | 16.9659 | 0.868053 | ||||||||
\(383\) | −12.4702 | −0.637197 | −0.318598 | − | 0.947890i | \(-0.603212\pi\) | ||||
−0.318598 | + | 0.947890i | \(0.603212\pi\) | |||||||
\(384\) | 8.46640 | 0.432049 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 24.9991 | 1.27242 | ||||||||
\(387\) | −11.7044 | −0.594966 | ||||||||
\(388\) | 17.0516 | 0.865664 | ||||||||
\(389\) | −18.0899 | −0.917195 | −0.458597 | − | 0.888644i | \(-0.651648\pi\) | ||||
−0.458597 | + | 0.888644i | \(0.651648\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.62443 | −0.335012 | ||||||||
\(392\) | −6.84106 | −0.345526 | ||||||||
\(393\) | −12.8099 | −0.646172 | ||||||||
\(394\) | −8.10551 | −0.408350 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.51514 | 0.126390 | ||||||||
\(397\) | 15.2342 | 0.764581 | 0.382291 | − | 0.924042i | \(-0.375135\pi\) | ||||
0.382291 | + | 0.924042i | \(0.375135\pi\) | |||||||
\(398\) | 25.6585 | 1.28614 | ||||||||
\(399\) | −9.49954 | −0.475572 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.74931 | 0.137294 | 0.0686471 | − | 0.997641i | \(-0.478132\pi\) | ||||
0.0686471 | + | 0.997641i | \(0.478132\pi\) | |||||||
\(402\) | −30.3103 | −1.51174 | ||||||||
\(403\) | −8.35620 | −0.416252 | ||||||||
\(404\) | 18.6244 | 0.926600 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 48.3397 | 2.39906 | ||||||||
\(407\) | −0.454586 | −0.0225330 | ||||||||
\(408\) | 1.26445 | 0.0625996 | ||||||||
\(409\) | −3.98532 | −0.197061 | −0.0985307 | − | 0.995134i | \(-0.531414\pi\) | ||||
−0.0985307 | + | 0.995134i | \(0.531414\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.8099 | −1.12513 | ||||||||
\(412\) | 41.4986 | 2.04449 | ||||||||
\(413\) | 28.1542 | 1.38538 | ||||||||
\(414\) | −12.1854 | −0.598882 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −12.0236 | −0.589507 | ||||||||
\(417\) | 7.59037 | 0.371702 | ||||||||
\(418\) | −5.54541 | −0.271235 | ||||||||
\(419\) | −5.13578 | −0.250899 | −0.125450 | − | 0.992100i | \(-0.540037\pi\) | ||||
−0.125450 | + | 0.992100i | \(0.540037\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.94657 | −0.436029 | −0.218014 | − | 0.975946i | \(-0.569958\pi\) | ||||
−0.218014 | + | 0.975946i | \(0.569958\pi\) | |||||||
\(422\) | −21.8108 | −1.06173 | ||||||||
\(423\) | 3.48486 | 0.169440 | ||||||||
\(424\) | −13.7484 | −0.667681 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −18.0937 | −0.876642 | ||||||||
\(427\) | 43.7337 | 2.11642 | ||||||||
\(428\) | −9.90826 | −0.478934 | ||||||||
\(429\) | −1.51514 | −0.0731516 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.7493 | 1.09580 | 0.547898 | − | 0.836545i | \(-0.315428\pi\) | ||||
0.547898 | + | 0.836545i | \(0.315428\pi\) | |||||||
\(432\) | −2.70436 | −0.130113 | ||||||||
\(433\) | −7.58325 | −0.364428 | −0.182214 | − | 0.983259i | \(-0.558326\pi\) | ||||
−0.182214 | + | 0.983259i | \(0.558326\pi\) | |||||||
\(434\) | 42.6576 | 2.04763 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16.9385 | 0.811209 | ||||||||
\(437\) | 14.9659 | 0.715918 | ||||||||
\(438\) | −19.5904 | −0.936064 | ||||||||
\(439\) | 17.3903 | 0.829991 | 0.414996 | − | 0.909823i | \(-0.363783\pi\) | ||||
0.414996 | + | 0.909823i | \(0.363783\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.24977 | 0.297608 | ||||||||
\(442\) | −3.71904 | −0.176897 | ||||||||
\(443\) | −10.6438 | −0.505702 | −0.252851 | − | 0.967505i | \(-0.581368\pi\) | ||||
−0.252851 | + | 0.967505i | \(0.581368\pi\) | |||||||
\(444\) | −1.14335 | −0.0542608 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 27.4617 | 1.30035 | ||||||||
\(447\) | −1.81456 | −0.0858259 | ||||||||
\(448\) | 41.6916 | 1.96974 | ||||||||
\(449\) | −26.9310 | −1.27095 | −0.635476 | − | 0.772121i | \(-0.719196\pi\) | ||||
−0.635476 | + | 0.772121i | \(0.719196\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.12489 | 0.194233 | ||||||||
\(452\) | 15.0908 | 0.709813 | ||||||||
\(453\) | 24.3250 | 1.14289 | ||||||||
\(454\) | 48.4683 | 2.27473 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.85665 | −0.133775 | ||||||||
\(457\) | 15.7796 | 0.738138 | 0.369069 | − | 0.929402i | \(-0.379677\pi\) | ||||
0.369069 | + | 0.929402i | \(0.379677\pi\) | |||||||
\(458\) | −31.4049 | −1.46746 | ||||||||
\(459\) | −1.15516 | −0.0539183 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.18922 | 0.381410 | 0.190705 | − | 0.981647i | \(-0.438923\pi\) | ||||
0.190705 | + | 0.981647i | \(0.438923\pi\) | |||||||
\(462\) | 7.73463 | 0.359848 | ||||||||
\(463\) | −16.0899 | −0.747762 | −0.373881 | − | 0.927477i | \(-0.621973\pi\) | ||||
−0.373881 | + | 0.927477i | \(0.621973\pi\) | |||||||
\(464\) | −16.9016 | −0.784638 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.5521 | 0.488815 | ||||||||
\(467\) | 29.4693 | 1.36367 | 0.681837 | − | 0.731504i | \(-0.261181\pi\) | ||||
0.681837 | + | 0.731504i | \(0.261181\pi\) | |||||||
\(468\) | −3.81078 | −0.176153 | ||||||||
\(469\) | −51.9229 | −2.39758 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.76491 | −0.449943 | ||||||||
\(472\) | 8.46640 | 0.389698 | ||||||||
\(473\) | −11.7044 | −0.538167 | ||||||||
\(474\) | −10.8255 | −0.497230 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 10.5757 | 0.484736 | ||||||||
\(477\) | 12.5601 | 0.575087 | ||||||||
\(478\) | 31.8713 | 1.45776 | ||||||||
\(479\) | 32.2186 | 1.47210 | 0.736052 | − | 0.676925i | \(-0.236688\pi\) | ||||
0.736052 | + | 0.676925i | \(0.236688\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.688760 | 0.0314048 | ||||||||
\(482\) | −10.7200 | −0.488280 | ||||||||
\(483\) | −20.8742 | −0.949809 | ||||||||
\(484\) | 2.51514 | 0.114324 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.12489 | −0.0963868 | ||||||||
\(487\) | 35.8936 | 1.62649 | 0.813247 | − | 0.581919i | \(-0.197698\pi\) | ||||
0.813247 | + | 0.581919i | \(0.197698\pi\) | |||||||
\(488\) | 13.1514 | 0.595335 | ||||||||
\(489\) | 6.98440 | 0.315846 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.15894 | −0.323079 | −0.161539 | − | 0.986866i | \(-0.551646\pi\) | ||||
−0.161539 | + | 0.986866i | \(0.551646\pi\) | |||||||
\(492\) | 10.3747 | 0.467726 | ||||||||
\(493\) | −7.21949 | −0.325150 | ||||||||
\(494\) | 8.40207 | 0.378027 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.9149 | −0.669699 | ||||||||
\(497\) | −30.9953 | −1.39033 | ||||||||
\(498\) | −31.3406 | −1.40441 | ||||||||
\(499\) | 27.0743 | 1.21201 | 0.606006 | − | 0.795460i | \(-0.292771\pi\) | ||||
0.606006 | + | 0.795460i | \(0.292771\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.31032 | 0.281924 | ||||||||
\(502\) | 6.43899 | 0.287386 | ||||||||
\(503\) | −26.9991 | −1.20383 | −0.601915 | − | 0.798560i | \(-0.705595\pi\) | ||||
−0.601915 | + | 0.798560i | \(0.705595\pi\) | |||||||
\(504\) | 3.98440 | 0.177479 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −12.1854 | −0.541709 | ||||||||
\(507\) | −10.7044 | −0.475397 | ||||||||
\(508\) | −20.2829 | −0.899909 | ||||||||
\(509\) | 15.5904 | 0.691031 | 0.345515 | − | 0.938413i | \(-0.387704\pi\) | ||||
0.345515 | + | 0.938413i | \(0.387704\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −33.5592 | −1.48457 | ||||||||
\(512\) | −27.3813 | −1.21009 | ||||||||
\(513\) | 2.60975 | 0.115223 | ||||||||
\(514\) | −29.0066 | −1.27943 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −29.4381 | −1.29594 | ||||||||
\(517\) | 3.48486 | 0.153264 | ||||||||
\(518\) | −3.51605 | −0.154487 | ||||||||
\(519\) | 12.8448 | 0.563826 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.1589 | 0.488882 | 0.244441 | − | 0.969664i | \(-0.421396\pi\) | ||||
0.244441 | + | 0.969664i | \(0.421396\pi\) | |||||||
\(522\) | −13.2800 | −0.581252 | ||||||||
\(523\) | 10.5786 | 0.462568 | 0.231284 | − | 0.972886i | \(-0.425707\pi\) | ||||
0.231284 | + | 0.972886i | \(0.425707\pi\) | |||||||
\(524\) | −32.2186 | −1.40748 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 26.6888 | 1.16369 | ||||||||
\(527\) | −6.37088 | −0.277520 | ||||||||
\(528\) | −2.70436 | −0.117692 | ||||||||
\(529\) | 9.88601 | 0.429827 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.73463 | −0.335654 | ||||||||
\(532\) | −23.8927 | −1.03588 | ||||||||
\(533\) | −6.24977 | −0.270708 | ||||||||
\(534\) | 22.3103 | 0.965462 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −15.6140 | −0.674422 | ||||||||
\(537\) | 13.4849 | 0.581915 | ||||||||
\(538\) | 52.4608 | 2.26175 | ||||||||
\(539\) | 6.24977 | 0.269197 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.2947 | −0.485598 | −0.242799 | − | 0.970077i | \(-0.578066\pi\) | ||||
−0.242799 | + | 0.970077i | \(0.578066\pi\) | |||||||
\(542\) | −16.0743 | −0.690451 | ||||||||
\(543\) | −23.0899 | −0.990883 | ||||||||
\(544\) | −9.16698 | −0.393031 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −11.7190 | −0.501528 | ||||||||
\(547\) | −6.09369 | −0.260547 | −0.130274 | − | 0.991478i | \(-0.541586\pi\) | ||||
−0.130274 | + | 0.991478i | \(0.541586\pi\) | |||||||
\(548\) | −57.3700 | −2.45072 | ||||||||
\(549\) | −12.0147 | −0.512774 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.3103 | 0.694843 | ||||||||
\(552\) | −6.27718 | −0.267175 | ||||||||
\(553\) | −18.5445 | −0.788592 | ||||||||
\(554\) | 4.08991 | 0.173764 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 19.0908 | 0.809631 | ||||||||
\(557\) | 5.90069 | 0.250020 | 0.125010 | − | 0.992155i | \(-0.460104\pi\) | ||||
0.125010 | + | 0.992155i | \(0.460104\pi\) | |||||||
\(558\) | −11.7190 | −0.496106 | ||||||||
\(559\) | 17.7337 | 0.750056 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.15516 | −0.0487710 | ||||||||
\(562\) | 3.98440 | 0.168072 | ||||||||
\(563\) | −3.03028 | −0.127711 | −0.0638555 | − | 0.997959i | \(-0.520340\pi\) | ||||
−0.0638555 | + | 0.997959i | \(0.520340\pi\) | |||||||
\(564\) | 8.76491 | 0.369069 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 64.0431 | 2.69193 | ||||||||
\(567\) | −3.64002 | −0.152867 | ||||||||
\(568\) | −9.32075 | −0.391090 | ||||||||
\(569\) | 13.4049 | 0.561964 | 0.280982 | − | 0.959713i | \(-0.409340\pi\) | ||||
0.280982 | + | 0.959713i | \(0.409340\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.8851 | 1.12511 | 0.562553 | − | 0.826761i | \(-0.309819\pi\) | ||||
0.562553 | + | 0.826761i | \(0.309819\pi\) | |||||||
\(572\) | −3.81078 | −0.159337 | ||||||||
\(573\) | −7.98440 | −0.333553 | ||||||||
\(574\) | 31.9045 | 1.33167 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −11.4537 | −0.477236 | ||||||||
\(577\) | −2.03028 | −0.0845215 | −0.0422607 | − | 0.999107i | \(-0.513456\pi\) | ||||
−0.0422607 | + | 0.999107i | \(0.513456\pi\) | |||||||
\(578\) | 33.2876 | 1.38458 | ||||||||
\(579\) | −11.7649 | −0.488933 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −53.6878 | −2.22735 | ||||||||
\(582\) | −14.4058 | −0.597142 | ||||||||
\(583\) | 12.5601 | 0.520186 | ||||||||
\(584\) | −10.0917 | −0.417599 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −61.9514 | −2.55919 | ||||||||
\(587\) | −21.8245 | −0.900795 | −0.450398 | − | 0.892828i | \(-0.648718\pi\) | ||||
−0.450398 | + | 0.892828i | \(0.648718\pi\) | |||||||
\(588\) | 15.7190 | 0.648242 | ||||||||
\(589\) | 14.3931 | 0.593058 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.81456 | 0.156910 | ||||||||
\(592\) | 1.22936 | 0.0505265 | ||||||||
\(593\) | −8.06811 | −0.331318 | −0.165659 | − | 0.986183i | \(-0.552975\pi\) | ||||
−0.165659 | + | 0.986183i | \(0.552975\pi\) | |||||||
\(594\) | −2.12489 | −0.0871851 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.56387 | −0.186944 | ||||||||
\(597\) | −12.0752 | −0.494206 | ||||||||
\(598\) | 18.4626 | 0.754993 | ||||||||
\(599\) | 7.61353 | 0.311080 | 0.155540 | − | 0.987830i | \(-0.450288\pi\) | ||||
0.155540 | + | 0.987830i | \(0.450288\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.57569 | 0.145855 | 0.0729277 | − | 0.997337i | \(-0.476766\pi\) | ||||
0.0729277 | + | 0.997337i | \(0.476766\pi\) | |||||||
\(602\) | −90.5289 | −3.68968 | ||||||||
\(603\) | 14.2645 | 0.580893 | ||||||||
\(604\) | 61.1807 | 2.48941 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −15.7346 | −0.639176 | ||||||||
\(607\) | −17.5298 | −0.711513 | −0.355757 | − | 0.934579i | \(-0.615777\pi\) | ||||
−0.355757 | + | 0.934579i | \(0.615777\pi\) | |||||||
\(608\) | 20.7101 | 0.839905 | ||||||||
\(609\) | −22.7493 | −0.921849 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.28005 | −0.213608 | ||||||||
\(612\) | −2.90539 | −0.117443 | ||||||||
\(613\) | −12.5601 | −0.507297 | −0.253649 | − | 0.967296i | \(-0.581631\pi\) | ||||
−0.253649 | + | 0.967296i | \(0.581631\pi\) | |||||||
\(614\) | 59.1883 | 2.38865 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.98440 | 0.160536 | ||||||||
\(617\) | −15.9612 | −0.642576 | −0.321288 | − | 0.946982i | \(-0.604116\pi\) | ||||
−0.321288 | + | 0.946982i | \(0.604116\pi\) | |||||||
\(618\) | −35.0596 | −1.41031 | ||||||||
\(619\) | −9.23417 | −0.371153 | −0.185576 | − | 0.982630i | \(-0.559415\pi\) | ||||
−0.185576 | + | 0.982630i | \(0.559415\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.73463 | 0.230123 | ||||||||
\(622\) | −50.8023 | −2.03699 | ||||||||
\(623\) | 38.2186 | 1.53119 | ||||||||
\(624\) | 4.09747 | 0.164030 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 60.1542 | 2.40425 | ||||||||
\(627\) | 2.60975 | 0.104223 | ||||||||
\(628\) | −24.5601 | −0.980054 | ||||||||
\(629\) | 0.525120 | 0.0209379 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.2342 | 1.16379 | 0.581897 | − | 0.813262i | \(-0.302311\pi\) | ||||
0.581897 | + | 0.813262i | \(0.302311\pi\) | |||||||
\(632\) | −5.57661 | −0.221826 | ||||||||
\(633\) | 10.2645 | 0.407975 | ||||||||
\(634\) | −18.7200 | −0.743464 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 31.5904 | 1.25264 | ||||||||
\(637\) | −9.46927 | −0.375186 | ||||||||
\(638\) | −13.2800 | −0.525762 | ||||||||
\(639\) | 8.51514 | 0.336854 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.9612 | 0.551436 | 0.275718 | − | 0.961239i | \(-0.411084\pi\) | ||||
0.275718 | + | 0.961239i | \(0.411084\pi\) | |||||||
\(642\) | 8.37088 | 0.330372 | ||||||||
\(643\) | −12.6206 | −0.497710 | −0.248855 | − | 0.968541i | \(-0.580054\pi\) | ||||
−0.248855 | + | 0.968541i | \(0.580054\pi\) | |||||||
\(644\) | −52.5015 | −2.06885 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.40585 | 0.252035 | ||||||||
\(647\) | −29.6429 | −1.16538 | −0.582691 | − | 0.812694i | \(-0.698000\pi\) | ||||
−0.582691 | + | 0.812694i | \(0.698000\pi\) | |||||||
\(648\) | −1.09461 | −0.0430003 | ||||||||
\(649\) | −7.73463 | −0.303611 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −20.0752 | −0.786810 | ||||||||
\(652\) | 17.5667 | 0.687967 | ||||||||
\(653\) | −9.90069 | −0.387444 | −0.193722 | − | 0.981056i | \(-0.562056\pi\) | ||||
−0.193722 | + | 0.981056i | \(0.562056\pi\) | |||||||
\(654\) | −14.3103 | −0.559578 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −11.1552 | −0.435536 | ||||||||
\(657\) | 9.21949 | 0.359687 | ||||||||
\(658\) | 26.9541 | 1.05078 | ||||||||
\(659\) | −5.28005 | −0.205681 | −0.102841 | − | 0.994698i | \(-0.532793\pi\) | ||||
−0.102841 | + | 0.994698i | \(0.532793\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.8548 | −1.04453 | −0.522266 | − | 0.852783i | \(-0.674913\pi\) | ||||
−0.522266 | + | 0.852783i | \(0.674913\pi\) | |||||||
\(662\) | −68.5271 | −2.66338 | ||||||||
\(663\) | 1.75023 | 0.0679733 | ||||||||
\(664\) | −16.1447 | −0.626537 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.965943 | 0.0374295 | ||||||||
\(667\) | 35.8401 | 1.38774 | ||||||||
\(668\) | 15.8713 | 0.614080 | ||||||||
\(669\) | −12.9239 | −0.499665 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.0147 | −0.463822 | ||||||||
\(672\) | −28.8860 | −1.11430 | ||||||||
\(673\) | 3.81834 | 0.147186 | 0.0735932 | − | 0.997288i | \(-0.476553\pi\) | ||||
0.0735932 | + | 0.997288i | \(0.476553\pi\) | |||||||
\(674\) | 61.5885 | 2.37230 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −26.9229 | −1.03550 | ||||||||
\(677\) | 15.6897 | 0.603003 | 0.301502 | − | 0.953466i | \(-0.402512\pi\) | ||||
0.301502 | + | 0.953466i | \(0.402512\pi\) | |||||||
\(678\) | −12.7493 | −0.489634 | ||||||||
\(679\) | −24.6779 | −0.947049 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22.8099 | −0.874076 | ||||||||
\(682\) | −11.7190 | −0.448745 | ||||||||
\(683\) | 15.6353 | 0.598269 | 0.299135 | − | 0.954211i | \(-0.403302\pi\) | ||||
0.299135 | + | 0.954211i | \(0.403302\pi\) | |||||||
\(684\) | 6.56387 | 0.250976 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5.80275 | −0.221550 | ||||||||
\(687\) | 14.7796 | 0.563876 | ||||||||
\(688\) | 31.6528 | 1.20675 | ||||||||
\(689\) | −19.0303 | −0.724996 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.4305 | −1.19567 | −0.597836 | − | 0.801618i | \(-0.703973\pi\) | ||||
−0.597836 | + | 0.801618i | \(0.703973\pi\) | |||||||
\(692\) | 32.3065 | 1.22811 | ||||||||
\(693\) | −3.64002 | −0.138273 | ||||||||
\(694\) | −75.8989 | −2.88108 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6.84106 | −0.259310 | ||||||||
\(697\) | −4.76491 | −0.180484 | ||||||||
\(698\) | 49.4674 | 1.87237 | ||||||||
\(699\) | −4.96594 | −0.187829 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.24507 | 0.122565 | 0.0612824 | − | 0.998120i | \(-0.480481\pi\) | ||||
0.0612824 | + | 0.998120i | \(0.480481\pi\) | |||||||
\(702\) | 3.21949 | 0.121512 | ||||||||
\(703\) | −1.18635 | −0.0447442 | ||||||||
\(704\) | −11.4537 | −0.431676 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −20.7181 | −0.779737 | ||||||||
\(707\) | −26.9541 | −1.01371 | ||||||||
\(708\) | −19.4537 | −0.731114 | ||||||||
\(709\) | −26.7190 | −1.00345 | −0.501727 | − | 0.865026i | \(-0.667302\pi\) | ||||
−0.501727 | + | 0.865026i | \(0.667302\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.09461 | 0.191063 | ||||||||
\(712\) | 11.4929 | 0.430714 | ||||||||
\(713\) | 31.6273 | 1.18445 | ||||||||
\(714\) | −8.93475 | −0.334375 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 33.9163 | 1.26751 | ||||||||
\(717\) | −14.9991 | −0.560151 | ||||||||
\(718\) | −72.0351 | −2.68833 | ||||||||
\(719\) | −6.78807 | −0.253152 | −0.126576 | − | 0.991957i | \(-0.540399\pi\) | ||||
−0.126576 | + | 0.991957i | \(0.540399\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −60.0587 | −2.23670 | ||||||||
\(722\) | 25.9007 | 0.963924 | ||||||||
\(723\) | 5.04496 | 0.187624 | ||||||||
\(724\) | −58.0743 | −2.15831 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.12489 | −0.0788619 | ||||||||
\(727\) | 19.9154 | 0.738620 | 0.369310 | − | 0.929306i | \(-0.379594\pi\) | ||||
0.369310 | + | 0.929306i | \(0.379594\pi\) | |||||||
\(728\) | −6.03692 | −0.223743 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.5204 | 0.500071 | ||||||||
\(732\) | −30.2186 | −1.11691 | ||||||||
\(733\) | 31.3388 | 1.15752 | 0.578762 | − | 0.815497i | \(-0.303536\pi\) | ||||
0.578762 | + | 0.815497i | \(0.303536\pi\) | |||||||
\(734\) | 4.00756 | 0.147922 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 45.5081 | 1.67745 | ||||||||
\(737\) | 14.2645 | 0.525438 | ||||||||
\(738\) | −8.76491 | −0.322641 | ||||||||
\(739\) | −2.25355 | −0.0828982 | −0.0414491 | − | 0.999141i | \(-0.513197\pi\) | ||||
−0.0414491 | + | 0.999141i | \(0.513197\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.95413 | −0.145259 | ||||||||
\(742\) | 97.1477 | 3.56640 | ||||||||
\(743\) | 6.74931 | 0.247608 | 0.123804 | − | 0.992307i | \(-0.460491\pi\) | ||||
0.123804 | + | 0.992307i | \(0.460491\pi\) | |||||||
\(744\) | −6.03692 | −0.221324 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −34.6888 | −1.27005 | ||||||||
\(747\) | 14.7493 | 0.539649 | ||||||||
\(748\) | −2.90539 | −0.106232 | ||||||||
\(749\) | 14.3397 | 0.523961 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.4390 | 0.818810 | 0.409405 | − | 0.912353i | \(-0.365736\pi\) | ||||
0.409405 | + | 0.912353i | \(0.365736\pi\) | |||||||
\(752\) | −9.42431 | −0.343669 | ||||||||
\(753\) | −3.03028 | −0.110429 | ||||||||
\(754\) | 20.1211 | 0.732767 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −9.15516 | −0.332970 | ||||||||
\(757\) | −25.4158 | −0.923754 | −0.461877 | − | 0.886944i | \(-0.652824\pi\) | ||||
−0.461877 | + | 0.886944i | \(0.652824\pi\) | |||||||
\(758\) | 55.3406 | 2.01006 | ||||||||
\(759\) | 5.73463 | 0.208154 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.7493 | −1.11466 | −0.557331 | − | 0.830291i | \(-0.688174\pi\) | ||||
−0.557331 | + | 0.830291i | \(0.688174\pi\) | |||||||
\(762\) | 17.1358 | 0.620764 | ||||||||
\(763\) | −24.5142 | −0.887474 | ||||||||
\(764\) | −20.0819 | −0.726537 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 26.4977 | 0.957401 | ||||||||
\(767\) | 11.7190 | 0.423150 | ||||||||
\(768\) | 4.91721 | 0.177434 | ||||||||
\(769\) | −16.2956 | −0.587636 | −0.293818 | − | 0.955861i | \(-0.594926\pi\) | ||||
−0.293818 | + | 0.955861i | \(0.594926\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.6509 | 0.491626 | ||||||||
\(772\) | −29.5904 | −1.06498 | ||||||||
\(773\) | −48.7787 | −1.75445 | −0.877223 | − | 0.480082i | \(-0.840607\pi\) | ||||
−0.877223 | + | 0.480082i | \(0.840607\pi\) | |||||||
\(774\) | 24.8704 | 0.893949 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7.42100 | −0.266398 | ||||||||
\(777\) | 1.65470 | 0.0593621 | ||||||||
\(778\) | 38.4390 | 1.37810 | ||||||||
\(779\) | 10.7649 | 0.385693 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.51514 | 0.304696 | ||||||||
\(782\) | 14.0761 | 0.503362 | ||||||||
\(783\) | 6.24977 | 0.223349 | ||||||||
\(784\) | −16.9016 | −0.603629 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 27.2195 | 0.970887 | ||||||||
\(787\) | 46.2001 | 1.64686 | 0.823428 | − | 0.567421i | \(-0.192059\pi\) | ||||
0.823428 | + | 0.567421i | \(0.192059\pi\) | |||||||
\(788\) | 9.59415 | 0.341777 | ||||||||
\(789\) | −12.5601 | −0.447151 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.8401 | −0.776546 | ||||||||
\(792\) | −1.09461 | −0.0388952 | ||||||||
\(793\) | 18.2039 | 0.646439 | ||||||||
\(794\) | −32.3709 | −1.14880 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −30.3709 | −1.07647 | ||||||||
\(797\) | −36.3784 | −1.28859 | −0.644295 | − | 0.764777i | \(-0.722849\pi\) | ||||
−0.644295 | + | 0.764777i | \(0.722849\pi\) | |||||||
\(798\) | 20.1854 | 0.714557 | ||||||||
\(799\) | −4.02558 | −0.142415 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.4995 | −0.370983 | ||||||||
\(802\) | −5.84197 | −0.206287 | ||||||||
\(803\) | 9.21949 | 0.325349 | ||||||||
\(804\) | 35.8771 | 1.26529 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 17.7560 | 0.625427 | ||||||||
\(807\) | −24.6888 | −0.869086 | ||||||||
\(808\) | −8.10551 | −0.285151 | ||||||||
\(809\) | 11.3737 | 0.399879 | 0.199940 | − | 0.979808i | \(-0.435925\pi\) | ||||
0.199940 | + | 0.979808i | \(0.435925\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.3903 | −0.470195 | −0.235098 | − | 0.971972i | \(-0.575541\pi\) | ||||
−0.235098 | + | 0.971972i | \(0.575541\pi\) | |||||||
\(812\) | −57.2177 | −2.00795 | ||||||||
\(813\) | 7.56479 | 0.265309 | ||||||||
\(814\) | 0.965943 | 0.0338563 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.12397 | 0.109361 | ||||||||
\(817\) | −30.5454 | −1.06865 | ||||||||
\(818\) | 8.46835 | 0.296089 | ||||||||
\(819\) | 5.51514 | 0.192715 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.0975 | 1.12021 | 0.560105 | − | 0.828422i | \(-0.310761\pi\) | ||||
0.560105 | + | 0.828422i | \(0.310761\pi\) | |||||||
\(822\) | 48.4683 | 1.69053 | ||||||||
\(823\) | −16.7952 | −0.585443 | −0.292722 | − | 0.956198i | \(-0.594561\pi\) | ||||
−0.292722 | + | 0.956198i | \(0.594561\pi\) | |||||||
\(824\) | −18.0606 | −0.629169 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −59.8245 | −2.08156 | ||||||||
\(827\) | 45.5904 | 1.58533 | 0.792666 | − | 0.609656i | \(-0.208692\pi\) | ||||
0.792666 | + | 0.609656i | \(0.208692\pi\) | |||||||
\(828\) | 14.4234 | 0.501248 | ||||||||
\(829\) | 12.9385 | 0.449374 | 0.224687 | − | 0.974431i | \(-0.427864\pi\) | ||||
0.224687 | + | 0.974431i | \(0.427864\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.92477 | −0.0667695 | ||||||||
\(832\) | 17.3539 | 0.601638 | ||||||||
\(833\) | −7.21949 | −0.250141 | ||||||||
\(834\) | −16.1287 | −0.558490 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.56387 | 0.227016 | ||||||||
\(837\) | 5.51514 | 0.190631 | ||||||||
\(838\) | 10.9130 | 0.376982 | ||||||||
\(839\) | −1.59037 | −0.0549057 | −0.0274528 | − | 0.999623i | \(-0.508740\pi\) | ||||
−0.0274528 | + | 0.999623i | \(0.508740\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0596 | 0.346884 | ||||||||
\(842\) | 19.0104 | 0.655143 | ||||||||
\(843\) | −1.87511 | −0.0645824 | ||||||||
\(844\) | 25.8165 | 0.888641 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.40493 | −0.254587 | ||||||||
\(847\) | −3.64002 | −0.125073 | ||||||||
\(848\) | −33.9670 | −1.16643 | ||||||||
\(849\) | −30.1396 | −1.03439 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.60688 | −0.0893628 | ||||||||
\(852\) | 21.4167 | 0.733726 | ||||||||
\(853\) | −10.5161 | −0.360063 | −0.180031 | − | 0.983661i | \(-0.557620\pi\) | ||||
−0.180031 | + | 0.983661i | \(0.557620\pi\) | |||||||
\(854\) | −92.9291 | −3.17997 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.31216 | 0.147386 | ||||||||
\(857\) | 57.4637 | 1.96292 | 0.981460 | − | 0.191665i | \(-0.0613886\pi\) | ||||
0.981460 | + | 0.191665i | \(0.0613886\pi\) | |||||||
\(858\) | 3.21949 | 0.109912 | ||||||||
\(859\) | 32.7181 | 1.11633 | 0.558164 | − | 0.829731i | \(-0.311506\pi\) | ||||
0.558164 | + | 0.829731i | \(0.311506\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.0147 | −0.511699 | ||||||||
\(862\) | −48.3397 | −1.64646 | ||||||||
\(863\) | 43.1807 | 1.46989 | 0.734945 | − | 0.678127i | \(-0.237208\pi\) | ||||
0.734945 | + | 0.678127i | \(0.237208\pi\) | |||||||
\(864\) | 7.93567 | 0.269977 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 16.1135 | 0.547560 | ||||||||
\(867\) | −15.6656 | −0.532032 | ||||||||
\(868\) | −50.4920 | −1.71381 | ||||||||
\(869\) | 5.09461 | 0.172823 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.6126 | −0.732315 | ||||||||
\(872\) | −7.37179 | −0.249640 | ||||||||
\(873\) | 6.77959 | 0.229454 | ||||||||
\(874\) | −31.8009 | −1.07568 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 23.1883 | 0.783460 | ||||||||
\(877\) | 16.0752 | 0.542822 | 0.271411 | − | 0.962464i | \(-0.412510\pi\) | ||||
0.271411 | + | 0.962464i | \(0.412510\pi\) | |||||||
\(878\) | −36.9523 | −1.24708 | ||||||||
\(879\) | 29.1552 | 0.983379 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.2876 | 1.05411 | 0.527053 | − | 0.849832i | \(-0.323297\pi\) | ||||
0.527053 | + | 0.849832i | \(0.323297\pi\) | |||||||
\(882\) | −13.2800 | −0.447162 | ||||||||
\(883\) | −24.7640 | −0.833375 | −0.416687 | − | 0.909050i | \(-0.636809\pi\) | ||||
−0.416687 | + | 0.909050i | \(0.636809\pi\) | |||||||
\(884\) | 4.40207 | 0.148058 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 22.6169 | 0.759828 | ||||||||
\(887\) | 26.3085 | 0.883353 | 0.441676 | − | 0.897174i | \(-0.354384\pi\) | ||||
0.441676 | + | 0.897174i | \(0.354384\pi\) | |||||||
\(888\) | 0.497594 | 0.0166982 | ||||||||
\(889\) | 29.3544 | 0.984514 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | −32.5053 | −1.08836 | ||||||||
\(893\) | 9.09461 | 0.304339 | ||||||||
\(894\) | 3.85574 | 0.128955 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −30.8179 | −1.02955 | ||||||||
\(897\) | −8.68876 | −0.290109 | ||||||||
\(898\) | 57.2252 | 1.90963 | ||||||||
\(899\) | 34.4683 | 1.14958 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.5089 | −0.483363 | ||||||||
\(902\) | −8.76491 | −0.291840 | ||||||||
\(903\) | 42.6041 | 1.41778 | ||||||||
\(904\) | −6.56766 | −0.218437 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −51.6878 | −1.71721 | ||||||||
\(907\) | 55.9301 | 1.85713 | 0.928563 | − | 0.371174i | \(-0.121045\pi\) | ||||
0.928563 | + | 0.371174i | \(0.121045\pi\) | |||||||
\(908\) | −57.3700 | −1.90389 | ||||||||
\(909\) | 7.40493 | 0.245606 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.3931 | −0.509997 | −0.254998 | − | 0.966941i | \(-0.582075\pi\) | ||||
−0.254998 | + | 0.966941i | \(0.582075\pi\) | |||||||
\(912\) | −7.05769 | −0.233703 | ||||||||
\(913\) | 14.7493 | 0.488131 | ||||||||
\(914\) | −33.5298 | −1.10907 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 37.1727 | 1.22822 | ||||||||
\(917\) | 46.6282 | 1.53980 | ||||||||
\(918\) | 2.45459 | 0.0810134 | ||||||||
\(919\) | −51.2598 | −1.69090 | −0.845452 | − | 0.534052i | \(-0.820669\pi\) | ||||
−0.845452 | + | 0.534052i | \(0.820669\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −27.8548 | −0.917848 | ||||||||
\(922\) | −17.4012 | −0.573076 | ||||||||
\(923\) | −12.9016 | −0.424662 | ||||||||
\(924\) | −9.15516 | −0.301183 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 34.1892 | 1.12353 | ||||||||
\(927\) | 16.4995 | 0.541916 | ||||||||
\(928\) | 49.5961 | 1.62807 | ||||||||
\(929\) | 14.8099 | 0.485896 | 0.242948 | − | 0.970039i | \(-0.421886\pi\) | ||||
0.242948 | + | 0.970039i | \(0.421886\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.3103 | 0.534549 | ||||||||
\(932\) | −12.4900 | −0.409125 | ||||||||
\(933\) | 23.9083 | 0.782721 | ||||||||
\(934\) | −62.6188 | −2.04895 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.65848 | 0.0542093 | ||||||||
\(937\) | −27.2654 | −0.890721 | −0.445360 | − | 0.895351i | \(-0.646924\pi\) | ||||
−0.445360 | + | 0.895351i | \(0.646924\pi\) | |||||||
\(938\) | 110.330 | 3.60241 | ||||||||
\(939\) | −28.3094 | −0.923843 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −49.5630 | −1.61571 | −0.807853 | − | 0.589384i | \(-0.799371\pi\) | ||||
−0.807853 | + | 0.589384i | \(0.799371\pi\) | |||||||
\(942\) | 20.7493 | 0.676049 | ||||||||
\(943\) | 23.6547 | 0.770303 | ||||||||
\(944\) | 20.9172 | 0.680797 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 24.8704 | 0.808607 | ||||||||
\(947\) | 13.9844 | 0.454432 | 0.227216 | − | 0.973844i | \(-0.427038\pi\) | ||||
0.227216 | + | 0.973844i | \(0.427038\pi\) | |||||||
\(948\) | 12.8136 | 0.416168 | ||||||||
\(949\) | −13.9688 | −0.453447 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.80986 | 0.285679 | ||||||||
\(952\) | −4.60263 | −0.149172 | ||||||||
\(953\) | −17.1240 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(954\) | −26.6888 | −0.864081 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −37.7248 | −1.22011 | ||||||||
\(957\) | 6.24977 | 0.202026 | ||||||||
\(958\) | −68.4608 | −2.21187 | ||||||||
\(959\) | 83.0284 | 2.68113 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.583252 | −0.0188146 | ||||||||
\(962\) | −1.46354 | −0.0471863 | ||||||||
\(963\) | −3.93945 | −0.126947 | ||||||||
\(964\) | 12.6888 | 0.408677 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 44.3553 | 1.42711 | ||||||||
\(967\) | −1.90826 | −0.0613653 | −0.0306827 | − | 0.999529i | \(-0.509768\pi\) | ||||
−0.0306827 | + | 0.999529i | \(0.509768\pi\) | |||||||
\(968\) | −1.09461 | −0.0351821 | ||||||||
\(969\) | −3.01468 | −0.0968455 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.3856 | 1.00721 | 0.503605 | − | 0.863934i | \(-0.332007\pi\) | ||||
0.503605 | + | 0.863934i | \(0.332007\pi\) | |||||||
\(972\) | 2.51514 | 0.0806731 | ||||||||
\(973\) | −27.6291 | −0.885749 | ||||||||
\(974\) | −76.2697 | −2.44384 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 32.4920 | 1.04004 | ||||||||
\(977\) | −41.4693 | −1.32672 | −0.663360 | − | 0.748301i | \(-0.730870\pi\) | ||||
−0.663360 | + | 0.748301i | \(0.730870\pi\) | |||||||
\(978\) | −14.8411 | −0.474565 | ||||||||
\(979\) | −10.4995 | −0.335567 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.73463 | 0.215020 | ||||||||
\(982\) | 15.2119 | 0.485432 | ||||||||
\(983\) | 6.23601 | 0.198898 | 0.0994489 | − | 0.995043i | \(-0.468292\pi\) | ||||
0.0994489 | + | 0.995043i | \(0.468292\pi\) | |||||||
\(984\) | −4.51514 | −0.143937 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 15.3406 | 0.488544 | ||||||||
\(987\) | −12.6850 | −0.403767 | ||||||||
\(988\) | −9.94518 | −0.316398 | ||||||||
\(989\) | −67.1202 | −2.13430 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.2048 | 0.864189 | 0.432095 | − | 0.901828i | \(-0.357775\pi\) | ||||
0.432095 | + | 0.901828i | \(0.357775\pi\) | |||||||
\(992\) | 43.7663 | 1.38958 | ||||||||
\(993\) | 32.2498 | 1.02342 | ||||||||
\(994\) | 65.8615 | 2.08900 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 37.0966 | 1.17545 | ||||||||
\(997\) | −28.0606 | −0.888687 | −0.444343 | − | 0.895857i | \(-0.646563\pi\) | ||||
−0.444343 | + | 0.895857i | \(0.646563\pi\) | |||||||
\(998\) | −57.5298 | −1.82107 | ||||||||
\(999\) | −0.454586 | −0.0143825 |
(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 | 825.2.a.m.1.1 | yes | 3 | |
3.2 | odd | 2 | 2475.2.a.z.1.3 | 3 | |||
5.2 | odd | 4 | 825.2.c.f.199.2 | 6 | |||
5.3 | odd | 4 | 825.2.c.f.199.5 | 6 | |||
5.4 | even | 2 | 825.2.a.i.1.3 | ✓ | 3 | ||
11.10 | odd | 2 | 9075.2.a.cd.1.3 | 3 | |||
15.2 | even | 4 | 2475.2.c.q.199.5 | 6 | |||
15.8 | even | 4 | 2475.2.c.q.199.2 | 6 | |||
15.14 | odd | 2 | 2475.2.a.bd.1.1 | 3 | |||
55.54 | odd | 2 | 9075.2.a.cj.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.2.a.i.1.3 | ✓ | 3 | 5.4 | even | 2 | ||
825.2.a.m.1.1 | yes | 3 | 1.1 | even | 1 | trivial | |
825.2.c.f.199.2 | 6 | 5.2 | odd | 4 | |||
825.2.c.f.199.5 | 6 | 5.3 | odd | 4 | |||
2475.2.a.z.1.3 | 3 | 3.2 | odd | 2 | |||
2475.2.a.bd.1.1 | 3 | 15.14 | odd | 2 | |||
2475.2.c.q.199.2 | 6 | 15.8 | even | 4 | |||
2475.2.c.q.199.5 | 6 | 15.2 | even | 4 | |||
9075.2.a.cd.1.3 | 3 | 11.10 | odd | 2 | |||
9075.2.a.cj.1.1 | 3 | 55.54 | odd | 2 |