Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1587,2,Mod(1,1587)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1587, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1587.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1587 = 3 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1587.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: | \(12.6722588008\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
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 | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1587.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.73205 | 1.93185 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.46410 | 2.73205 | ||||||||
\(5\) | −2.73205 | −1.22181 | −0.610905 | − | 0.791704i | \(-0.709194\pi\) | ||||
−0.610905 | + | 0.791704i | \(0.709194\pi\) | |||||||
\(6\) | −2.73205 | −1.11536 | ||||||||
\(7\) | 0.267949 | 0.101275 | 0.0506376 | − | 0.998717i | \(-0.483875\pi\) | ||||
0.0506376 | + | 0.998717i | \(0.483875\pi\) | |||||||
\(8\) | 9.46410 | 3.34607 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −7.46410 | −2.36036 | ||||||||
\(11\) | 1.26795 | 0.382301 | 0.191151 | − | 0.981561i | \(-0.438778\pi\) | ||||
0.191151 | + | 0.981561i | \(0.438778\pi\) | |||||||
\(12\) | −5.46410 | −1.57735 | ||||||||
\(13\) | 1.00000 | 0.277350 | 0.138675 | − | 0.990338i | \(-0.455716\pi\) | ||||
0.138675 | + | 0.990338i | \(0.455716\pi\) | |||||||
\(14\) | 0.732051 | 0.195649 | ||||||||
\(15\) | 2.73205 | 0.705412 | ||||||||
\(16\) | 14.9282 | 3.73205 | ||||||||
\(17\) | 6.73205 | 1.63276 | 0.816381 | − | 0.577514i | \(-0.195977\pi\) | ||||
0.816381 | + | 0.577514i | \(0.195977\pi\) | |||||||
\(18\) | 2.73205 | 0.643951 | ||||||||
\(19\) | −1.46410 | −0.335888 | −0.167944 | − | 0.985797i | \(-0.553713\pi\) | ||||
−0.167944 | + | 0.985797i | \(0.553713\pi\) | |||||||
\(20\) | −14.9282 | −3.33805 | ||||||||
\(21\) | −0.267949 | −0.0584713 | ||||||||
\(22\) | 3.46410 | 0.738549 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | −9.46410 | −1.93185 | ||||||||
\(25\) | 2.46410 | 0.492820 | ||||||||
\(26\) | 2.73205 | 0.535799 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.46410 | 0.276689 | ||||||||
\(29\) | 7.66025 | 1.42247 | 0.711237 | − | 0.702953i | \(-0.248135\pi\) | ||||
0.711237 | + | 0.702953i | \(0.248135\pi\) | |||||||
\(30\) | 7.46410 | 1.36275 | ||||||||
\(31\) | −2.00000 | −0.359211 | −0.179605 | − | 0.983739i | \(-0.557482\pi\) | ||||
−0.179605 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(32\) | 21.8564 | 3.86370 | ||||||||
\(33\) | −1.26795 | −0.220722 | ||||||||
\(34\) | 18.3923 | 3.15425 | ||||||||
\(35\) | −0.732051 | −0.123739 | ||||||||
\(36\) | 5.46410 | 0.910684 | ||||||||
\(37\) | 7.19615 | 1.18304 | 0.591520 | − | 0.806290i | \(-0.298528\pi\) | ||||
0.591520 | + | 0.806290i | \(0.298528\pi\) | |||||||
\(38\) | −4.00000 | −0.648886 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −25.8564 | −4.08826 | ||||||||
\(41\) | 2.53590 | 0.396041 | 0.198020 | − | 0.980198i | \(-0.436549\pi\) | ||||
0.198020 | + | 0.980198i | \(0.436549\pi\) | |||||||
\(42\) | −0.732051 | −0.112958 | ||||||||
\(43\) | 6.26795 | 0.955853 | 0.477927 | − | 0.878400i | \(-0.341388\pi\) | ||||
0.477927 | + | 0.878400i | \(0.341388\pi\) | |||||||
\(44\) | 6.92820 | 1.04447 | ||||||||
\(45\) | −2.73205 | −0.407270 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.19615 | −1.19553 | −0.597766 | − | 0.801671i | \(-0.703945\pi\) | ||||
−0.597766 | + | 0.801671i | \(0.703945\pi\) | |||||||
\(48\) | −14.9282 | −2.15470 | ||||||||
\(49\) | −6.92820 | −0.989743 | ||||||||
\(50\) | 6.73205 | 0.952056 | ||||||||
\(51\) | −6.73205 | −0.942676 | ||||||||
\(52\) | 5.46410 | 0.757735 | ||||||||
\(53\) | −8.92820 | −1.22638 | −0.613192 | − | 0.789934i | \(-0.710115\pi\) | ||||
−0.613192 | + | 0.789934i | \(0.710115\pi\) | |||||||
\(54\) | −2.73205 | −0.371785 | ||||||||
\(55\) | −3.46410 | −0.467099 | ||||||||
\(56\) | 2.53590 | 0.338874 | ||||||||
\(57\) | 1.46410 | 0.193925 | ||||||||
\(58\) | 20.9282 | 2.74801 | ||||||||
\(59\) | −9.66025 | −1.25766 | −0.628829 | − | 0.777544i | \(-0.716465\pi\) | ||||
−0.628829 | + | 0.777544i | \(0.716465\pi\) | |||||||
\(60\) | 14.9282 | 1.92722 | ||||||||
\(61\) | 3.19615 | 0.409225 | 0.204613 | − | 0.978843i | \(-0.434407\pi\) | ||||
0.204613 | + | 0.978843i | \(0.434407\pi\) | |||||||
\(62\) | −5.46410 | −0.693942 | ||||||||
\(63\) | 0.267949 | 0.0337584 | ||||||||
\(64\) | 29.8564 | 3.73205 | ||||||||
\(65\) | −2.73205 | −0.338869 | ||||||||
\(66\) | −3.46410 | −0.426401 | ||||||||
\(67\) | −10.2679 | −1.25443 | −0.627215 | − | 0.778846i | \(-0.715805\pi\) | ||||
−0.627215 | + | 0.778846i | \(0.715805\pi\) | |||||||
\(68\) | 36.7846 | 4.46079 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.00000 | −0.239046 | ||||||||
\(71\) | 4.19615 | 0.497992 | 0.248996 | − | 0.968505i | \(-0.419899\pi\) | ||||
0.248996 | + | 0.968505i | \(0.419899\pi\) | |||||||
\(72\) | 9.46410 | 1.11536 | ||||||||
\(73\) | 6.92820 | 0.810885 | 0.405442 | − | 0.914121i | \(-0.367117\pi\) | ||||
0.405442 | + | 0.914121i | \(0.367117\pi\) | |||||||
\(74\) | 19.6603 | 2.28546 | ||||||||
\(75\) | −2.46410 | −0.284530 | ||||||||
\(76\) | −8.00000 | −0.917663 | ||||||||
\(77\) | 0.339746 | 0.0387176 | ||||||||
\(78\) | −2.73205 | −0.309344 | ||||||||
\(79\) | 4.00000 | 0.450035 | 0.225018 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | −40.7846 | −4.55986 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.92820 | 0.765092 | ||||||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | −1.46410 | −0.159747 | ||||||||
\(85\) | −18.3923 | −1.99493 | ||||||||
\(86\) | 17.1244 | 1.84657 | ||||||||
\(87\) | −7.66025 | −0.821265 | ||||||||
\(88\) | 12.0000 | 1.27920 | ||||||||
\(89\) | 2.19615 | 0.232792 | 0.116396 | − | 0.993203i | \(-0.462866\pi\) | ||||
0.116396 | + | 0.993203i | \(0.462866\pi\) | |||||||
\(90\) | −7.46410 | −0.786785 | ||||||||
\(91\) | 0.267949 | 0.0280887 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.00000 | 0.207390 | ||||||||
\(94\) | −22.3923 | −2.30959 | ||||||||
\(95\) | 4.00000 | 0.410391 | ||||||||
\(96\) | −21.8564 | −2.23071 | ||||||||
\(97\) | −14.9282 | −1.51573 | −0.757865 | − | 0.652412i | \(-0.773757\pi\) | ||||
−0.757865 | + | 0.652412i | \(0.773757\pi\) | |||||||
\(98\) | −18.9282 | −1.91204 | ||||||||
\(99\) | 1.26795 | 0.127434 | ||||||||
\(100\) | 13.4641 | 1.34641 | ||||||||
\(101\) | 0.339746 | 0.0338060 | 0.0169030 | − | 0.999857i | \(-0.494619\pi\) | ||||
0.0169030 | + | 0.999857i | \(0.494619\pi\) | |||||||
\(102\) | −18.3923 | −1.82111 | ||||||||
\(103\) | −17.5885 | −1.73304 | −0.866521 | − | 0.499140i | \(-0.833649\pi\) | ||||
−0.866521 | + | 0.499140i | \(0.833649\pi\) | |||||||
\(104\) | 9.46410 | 0.928032 | ||||||||
\(105\) | 0.732051 | 0.0714408 | ||||||||
\(106\) | −24.3923 | −2.36919 | ||||||||
\(107\) | 11.8564 | 1.14620 | 0.573101 | − | 0.819485i | \(-0.305740\pi\) | ||||
0.573101 | + | 0.819485i | \(0.305740\pi\) | |||||||
\(108\) | −5.46410 | −0.525783 | ||||||||
\(109\) | −7.46410 | −0.714931 | −0.357466 | − | 0.933926i | \(-0.616359\pi\) | ||||
−0.357466 | + | 0.933926i | \(0.616359\pi\) | |||||||
\(110\) | −9.46410 | −0.902367 | ||||||||
\(111\) | −7.19615 | −0.683029 | ||||||||
\(112\) | 4.00000 | 0.377964 | ||||||||
\(113\) | −15.8564 | −1.49165 | −0.745823 | − | 0.666145i | \(-0.767943\pi\) | ||||
−0.745823 | + | 0.666145i | \(0.767943\pi\) | |||||||
\(114\) | 4.00000 | 0.374634 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 41.8564 | 3.88627 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −26.3923 | −2.42961 | ||||||||
\(119\) | 1.80385 | 0.165358 | ||||||||
\(120\) | 25.8564 | 2.36036 | ||||||||
\(121\) | −9.39230 | −0.853846 | ||||||||
\(122\) | 8.73205 | 0.790563 | ||||||||
\(123\) | −2.53590 | −0.228654 | ||||||||
\(124\) | −10.9282 | −0.981382 | ||||||||
\(125\) | 6.92820 | 0.619677 | ||||||||
\(126\) | 0.732051 | 0.0652163 | ||||||||
\(127\) | 9.39230 | 0.833432 | 0.416716 | − | 0.909037i | \(-0.363181\pi\) | ||||
0.416716 | + | 0.909037i | \(0.363181\pi\) | |||||||
\(128\) | 37.8564 | 3.34607 | ||||||||
\(129\) | −6.26795 | −0.551862 | ||||||||
\(130\) | −7.46410 | −0.654645 | ||||||||
\(131\) | 5.07180 | 0.443125 | 0.221562 | − | 0.975146i | \(-0.428884\pi\) | ||||
0.221562 | + | 0.975146i | \(0.428884\pi\) | |||||||
\(132\) | −6.92820 | −0.603023 | ||||||||
\(133\) | −0.392305 | −0.0340171 | ||||||||
\(134\) | −28.0526 | −2.42337 | ||||||||
\(135\) | 2.73205 | 0.235137 | ||||||||
\(136\) | 63.7128 | 5.46333 | ||||||||
\(137\) | −7.26795 | −0.620943 | −0.310471 | − | 0.950583i | \(-0.600487\pi\) | ||||
−0.310471 | + | 0.950583i | \(0.600487\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.5359 | −1.31774 | −0.658869 | − | 0.752258i | \(-0.728965\pi\) | ||||
−0.658869 | + | 0.752258i | \(0.728965\pi\) | |||||||
\(140\) | −4.00000 | −0.338062 | ||||||||
\(141\) | 8.19615 | 0.690241 | ||||||||
\(142\) | 11.4641 | 0.962046 | ||||||||
\(143\) | 1.26795 | 0.106031 | ||||||||
\(144\) | 14.9282 | 1.24402 | ||||||||
\(145\) | −20.9282 | −1.73799 | ||||||||
\(146\) | 18.9282 | 1.56651 | ||||||||
\(147\) | 6.92820 | 0.571429 | ||||||||
\(148\) | 39.3205 | 3.23213 | ||||||||
\(149\) | 20.9282 | 1.71451 | 0.857253 | − | 0.514896i | \(-0.172169\pi\) | ||||
0.857253 | + | 0.514896i | \(0.172169\pi\) | |||||||
\(150\) | −6.73205 | −0.549670 | ||||||||
\(151\) | −22.8564 | −1.86003 | −0.930014 | − | 0.367524i | \(-0.880206\pi\) | ||||
−0.930014 | + | 0.367524i | \(0.880206\pi\) | |||||||
\(152\) | −13.8564 | −1.12390 | ||||||||
\(153\) | 6.73205 | 0.544254 | ||||||||
\(154\) | 0.928203 | 0.0747967 | ||||||||
\(155\) | 5.46410 | 0.438887 | ||||||||
\(156\) | −5.46410 | −0.437478 | ||||||||
\(157\) | −0.535898 | −0.0427693 | −0.0213847 | − | 0.999771i | \(-0.506807\pi\) | ||||
−0.0213847 | + | 0.999771i | \(0.506807\pi\) | |||||||
\(158\) | 10.9282 | 0.869401 | ||||||||
\(159\) | 8.92820 | 0.708053 | ||||||||
\(160\) | −59.7128 | −4.72071 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.73205 | 0.214650 | ||||||||
\(163\) | −1.00000 | −0.0783260 | −0.0391630 | − | 0.999233i | \(-0.512469\pi\) | ||||
−0.0391630 | + | 0.999233i | \(0.512469\pi\) | |||||||
\(164\) | 13.8564 | 1.08200 | ||||||||
\(165\) | 3.46410 | 0.269680 | ||||||||
\(166\) | 16.3923 | 1.27229 | ||||||||
\(167\) | 0.535898 | 0.0414691 | 0.0207345 | − | 0.999785i | \(-0.493400\pi\) | ||||
0.0207345 | + | 0.999785i | \(0.493400\pi\) | |||||||
\(168\) | −2.53590 | −0.195649 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | −50.2487 | −3.85390 | ||||||||
\(171\) | −1.46410 | −0.111963 | ||||||||
\(172\) | 34.2487 | 2.61144 | ||||||||
\(173\) | −3.12436 | −0.237540 | −0.118770 | − | 0.992922i | \(-0.537895\pi\) | ||||
−0.118770 | + | 0.992922i | \(0.537895\pi\) | |||||||
\(174\) | −20.9282 | −1.58656 | ||||||||
\(175\) | 0.660254 | 0.0499105 | ||||||||
\(176\) | 18.9282 | 1.42677 | ||||||||
\(177\) | 9.66025 | 0.726109 | ||||||||
\(178\) | 6.00000 | 0.449719 | ||||||||
\(179\) | −5.80385 | −0.433800 | −0.216900 | − | 0.976194i | \(-0.569595\pi\) | ||||
−0.216900 | + | 0.976194i | \(0.569595\pi\) | |||||||
\(180\) | −14.9282 | −1.11268 | ||||||||
\(181\) | 0.535898 | 0.0398330 | 0.0199165 | − | 0.999802i | \(-0.493660\pi\) | ||||
0.0199165 | + | 0.999802i | \(0.493660\pi\) | |||||||
\(182\) | 0.732051 | 0.0542632 | ||||||||
\(183\) | −3.19615 | −0.236266 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −19.6603 | −1.44545 | ||||||||
\(186\) | 5.46410 | 0.400647 | ||||||||
\(187\) | 8.53590 | 0.624207 | ||||||||
\(188\) | −44.7846 | −3.26625 | ||||||||
\(189\) | −0.267949 | −0.0194904 | ||||||||
\(190\) | 10.9282 | 0.792815 | ||||||||
\(191\) | 2.00000 | 0.144715 | 0.0723575 | − | 0.997379i | \(-0.476948\pi\) | ||||
0.0723575 | + | 0.997379i | \(0.476948\pi\) | |||||||
\(192\) | −29.8564 | −2.15470 | ||||||||
\(193\) | −3.00000 | −0.215945 | −0.107972 | − | 0.994154i | \(-0.534436\pi\) | ||||
−0.107972 | + | 0.994154i | \(0.534436\pi\) | |||||||
\(194\) | −40.7846 | −2.92816 | ||||||||
\(195\) | 2.73205 | 0.195646 | ||||||||
\(196\) | −37.8564 | −2.70403 | ||||||||
\(197\) | −8.39230 | −0.597927 | −0.298963 | − | 0.954265i | \(-0.596641\pi\) | ||||
−0.298963 | + | 0.954265i | \(0.596641\pi\) | |||||||
\(198\) | 3.46410 | 0.246183 | ||||||||
\(199\) | 17.7321 | 1.25699 | 0.628496 | − | 0.777813i | \(-0.283671\pi\) | ||||
0.628496 | + | 0.777813i | \(0.283671\pi\) | |||||||
\(200\) | 23.3205 | 1.64901 | ||||||||
\(201\) | 10.2679 | 0.724245 | ||||||||
\(202\) | 0.928203 | 0.0653082 | ||||||||
\(203\) | 2.05256 | 0.144061 | ||||||||
\(204\) | −36.7846 | −2.57544 | ||||||||
\(205\) | −6.92820 | −0.483887 | ||||||||
\(206\) | −48.0526 | −3.34798 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 14.9282 | 1.03508 | ||||||||
\(209\) | −1.85641 | −0.128410 | ||||||||
\(210\) | 2.00000 | 0.138013 | ||||||||
\(211\) | −1.53590 | −0.105736 | −0.0528678 | − | 0.998602i | \(-0.516836\pi\) | ||||
−0.0528678 | + | 0.998602i | \(0.516836\pi\) | |||||||
\(212\) | −48.7846 | −3.35054 | ||||||||
\(213\) | −4.19615 | −0.287516 | ||||||||
\(214\) | 32.3923 | 2.21429 | ||||||||
\(215\) | −17.1244 | −1.16787 | ||||||||
\(216\) | −9.46410 | −0.643951 | ||||||||
\(217\) | −0.535898 | −0.0363792 | ||||||||
\(218\) | −20.3923 | −1.38114 | ||||||||
\(219\) | −6.92820 | −0.468165 | ||||||||
\(220\) | −18.9282 | −1.27614 | ||||||||
\(221\) | 6.73205 | 0.452847 | ||||||||
\(222\) | −19.6603 | −1.31951 | ||||||||
\(223\) | −19.9282 | −1.33449 | −0.667246 | − | 0.744838i | \(-0.732527\pi\) | ||||
−0.667246 | + | 0.744838i | \(0.732527\pi\) | |||||||
\(224\) | 5.85641 | 0.391298 | ||||||||
\(225\) | 2.46410 | 0.164273 | ||||||||
\(226\) | −43.3205 | −2.88164 | ||||||||
\(227\) | 4.73205 | 0.314077 | 0.157039 | − | 0.987592i | \(-0.449805\pi\) | ||||
0.157039 | + | 0.987592i | \(0.449805\pi\) | |||||||
\(228\) | 8.00000 | 0.529813 | ||||||||
\(229\) | 4.80385 | 0.317447 | 0.158724 | − | 0.987323i | \(-0.449262\pi\) | ||||
0.158724 | + | 0.987323i | \(0.449262\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.339746 | −0.0223536 | ||||||||
\(232\) | 72.4974 | 4.75969 | ||||||||
\(233\) | 10.9282 | 0.715930 | 0.357965 | − | 0.933735i | \(-0.383471\pi\) | ||||
0.357965 | + | 0.933735i | \(0.383471\pi\) | |||||||
\(234\) | 2.73205 | 0.178600 | ||||||||
\(235\) | 22.3923 | 1.46071 | ||||||||
\(236\) | −52.7846 | −3.43599 | ||||||||
\(237\) | −4.00000 | −0.259828 | ||||||||
\(238\) | 4.92820 | 0.319448 | ||||||||
\(239\) | 24.1962 | 1.56512 | 0.782559 | − | 0.622576i | \(-0.213914\pi\) | ||||
0.782559 | + | 0.622576i | \(0.213914\pi\) | |||||||
\(240\) | 40.7846 | 2.63264 | ||||||||
\(241\) | −8.80385 | −0.567106 | −0.283553 | − | 0.958957i | \(-0.591513\pi\) | ||||
−0.283553 | + | 0.958957i | \(0.591513\pi\) | |||||||
\(242\) | −25.6603 | −1.64950 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 17.4641 | 1.11802 | ||||||||
\(245\) | 18.9282 | 1.20928 | ||||||||
\(246\) | −6.92820 | −0.441726 | ||||||||
\(247\) | −1.46410 | −0.0931586 | ||||||||
\(248\) | −18.9282 | −1.20194 | ||||||||
\(249\) | −6.00000 | −0.380235 | ||||||||
\(250\) | 18.9282 | 1.19712 | ||||||||
\(251\) | 24.9282 | 1.57345 | 0.786727 | − | 0.617301i | \(-0.211774\pi\) | ||||
0.786727 | + | 0.617301i | \(0.211774\pi\) | |||||||
\(252\) | 1.46410 | 0.0922297 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 25.6603 | 1.61007 | ||||||||
\(255\) | 18.3923 | 1.15177 | ||||||||
\(256\) | 43.7128 | 2.73205 | ||||||||
\(257\) | 26.3923 | 1.64631 | 0.823153 | − | 0.567819i | \(-0.192213\pi\) | ||||
0.823153 | + | 0.567819i | \(0.192213\pi\) | |||||||
\(258\) | −17.1244 | −1.06612 | ||||||||
\(259\) | 1.92820 | 0.119813 | ||||||||
\(260\) | −14.9282 | −0.925808 | ||||||||
\(261\) | 7.66025 | 0.474158 | ||||||||
\(262\) | 13.8564 | 0.856052 | ||||||||
\(263\) | −27.1244 | −1.67256 | −0.836280 | − | 0.548303i | \(-0.815274\pi\) | ||||
−0.836280 | + | 0.548303i | \(0.815274\pi\) | |||||||
\(264\) | −12.0000 | −0.738549 | ||||||||
\(265\) | 24.3923 | 1.49841 | ||||||||
\(266\) | −1.07180 | −0.0657161 | ||||||||
\(267\) | −2.19615 | −0.134402 | ||||||||
\(268\) | −56.1051 | −3.42717 | ||||||||
\(269\) | 3.46410 | 0.211210 | 0.105605 | − | 0.994408i | \(-0.466322\pi\) | ||||
0.105605 | + | 0.994408i | \(0.466322\pi\) | |||||||
\(270\) | 7.46410 | 0.454251 | ||||||||
\(271\) | −2.60770 | −0.158406 | −0.0792031 | − | 0.996858i | \(-0.525238\pi\) | ||||
−0.0792031 | + | 0.996858i | \(0.525238\pi\) | |||||||
\(272\) | 100.497 | 6.09355 | ||||||||
\(273\) | −0.267949 | −0.0162170 | ||||||||
\(274\) | −19.8564 | −1.19957 | ||||||||
\(275\) | 3.12436 | 0.188406 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.0000 | 1.38194 | 0.690968 | − | 0.722885i | \(-0.257185\pi\) | ||||
0.690968 | + | 0.722885i | \(0.257185\pi\) | |||||||
\(278\) | −42.4449 | −2.54567 | ||||||||
\(279\) | −2.00000 | −0.119737 | ||||||||
\(280\) | −6.92820 | −0.414039 | ||||||||
\(281\) | −22.2487 | −1.32725 | −0.663623 | − | 0.748067i | \(-0.730982\pi\) | ||||
−0.663623 | + | 0.748067i | \(0.730982\pi\) | |||||||
\(282\) | 22.3923 | 1.33344 | ||||||||
\(283\) | −28.1244 | −1.67182 | −0.835910 | − | 0.548867i | \(-0.815059\pi\) | ||||
−0.835910 | + | 0.548867i | \(0.815059\pi\) | |||||||
\(284\) | 22.9282 | 1.36054 | ||||||||
\(285\) | −4.00000 | −0.236940 | ||||||||
\(286\) | 3.46410 | 0.204837 | ||||||||
\(287\) | 0.679492 | 0.0401091 | ||||||||
\(288\) | 21.8564 | 1.28790 | ||||||||
\(289\) | 28.3205 | 1.66591 | ||||||||
\(290\) | −57.1769 | −3.35754 | ||||||||
\(291\) | 14.9282 | 0.875107 | ||||||||
\(292\) | 37.8564 | 2.21538 | ||||||||
\(293\) | −13.2679 | −0.775122 | −0.387561 | − | 0.921844i | \(-0.626682\pi\) | ||||
−0.387561 | + | 0.921844i | \(0.626682\pi\) | |||||||
\(294\) | 18.9282 | 1.10392 | ||||||||
\(295\) | 26.3923 | 1.53662 | ||||||||
\(296\) | 68.1051 | 3.95853 | ||||||||
\(297\) | −1.26795 | −0.0735739 | ||||||||
\(298\) | 57.1769 | 3.31217 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −13.4641 | −0.777350 | ||||||||
\(301\) | 1.67949 | 0.0968043 | ||||||||
\(302\) | −62.4449 | −3.59330 | ||||||||
\(303\) | −0.339746 | −0.0195179 | ||||||||
\(304\) | −21.8564 | −1.25355 | ||||||||
\(305\) | −8.73205 | −0.499996 | ||||||||
\(306\) | 18.3923 | 1.05142 | ||||||||
\(307\) | −4.60770 | −0.262975 | −0.131488 | − | 0.991318i | \(-0.541975\pi\) | ||||
−0.131488 | + | 0.991318i | \(0.541975\pi\) | |||||||
\(308\) | 1.85641 | 0.105779 | ||||||||
\(309\) | 17.5885 | 1.00057 | ||||||||
\(310\) | 14.9282 | 0.847865 | ||||||||
\(311\) | −9.60770 | −0.544802 | −0.272401 | − | 0.962184i | \(-0.587818\pi\) | ||||
−0.272401 | + | 0.962184i | \(0.587818\pi\) | |||||||
\(312\) | −9.46410 | −0.535799 | ||||||||
\(313\) | 20.1244 | 1.13750 | 0.568748 | − | 0.822512i | \(-0.307428\pi\) | ||||
0.568748 | + | 0.822512i | \(0.307428\pi\) | |||||||
\(314\) | −1.46410 | −0.0826240 | ||||||||
\(315\) | −0.732051 | −0.0412464 | ||||||||
\(316\) | 21.8564 | 1.22952 | ||||||||
\(317\) | 15.8564 | 0.890585 | 0.445292 | − | 0.895385i | \(-0.353100\pi\) | ||||
0.445292 | + | 0.895385i | \(0.353100\pi\) | |||||||
\(318\) | 24.3923 | 1.36785 | ||||||||
\(319\) | 9.71281 | 0.543813 | ||||||||
\(320\) | −81.5692 | −4.55986 | ||||||||
\(321\) | −11.8564 | −0.661760 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.85641 | −0.548425 | ||||||||
\(324\) | 5.46410 | 0.303561 | ||||||||
\(325\) | 2.46410 | 0.136684 | ||||||||
\(326\) | −2.73205 | −0.151314 | ||||||||
\(327\) | 7.46410 | 0.412766 | ||||||||
\(328\) | 24.0000 | 1.32518 | ||||||||
\(329\) | −2.19615 | −0.121078 | ||||||||
\(330\) | 9.46410 | 0.520982 | ||||||||
\(331\) | −12.8564 | −0.706652 | −0.353326 | − | 0.935500i | \(-0.614949\pi\) | ||||
−0.353326 | + | 0.935500i | \(0.614949\pi\) | |||||||
\(332\) | 32.7846 | 1.79929 | ||||||||
\(333\) | 7.19615 | 0.394347 | ||||||||
\(334\) | 1.46410 | 0.0801121 | ||||||||
\(335\) | 28.0526 | 1.53268 | ||||||||
\(336\) | −4.00000 | −0.218218 | ||||||||
\(337\) | −23.7321 | −1.29277 | −0.646384 | − | 0.763013i | \(-0.723719\pi\) | ||||
−0.646384 | + | 0.763013i | \(0.723719\pi\) | |||||||
\(338\) | −32.7846 | −1.78325 | ||||||||
\(339\) | 15.8564 | 0.861202 | ||||||||
\(340\) | −100.497 | −5.45024 | ||||||||
\(341\) | −2.53590 | −0.137327 | ||||||||
\(342\) | −4.00000 | −0.216295 | ||||||||
\(343\) | −3.73205 | −0.201512 | ||||||||
\(344\) | 59.3205 | 3.19835 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.53590 | −0.458893 | ||||||||
\(347\) | 16.7321 | 0.898224 | 0.449112 | − | 0.893476i | \(-0.351740\pi\) | ||||
0.449112 | + | 0.893476i | \(0.351740\pi\) | |||||||
\(348\) | −41.8564 | −2.24374 | ||||||||
\(349\) | −11.0000 | −0.588817 | −0.294408 | − | 0.955680i | \(-0.595123\pi\) | ||||
−0.294408 | + | 0.955680i | \(0.595123\pi\) | |||||||
\(350\) | 1.80385 | 0.0964197 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 27.7128 | 1.47710 | ||||||||
\(353\) | −6.00000 | −0.319348 | −0.159674 | − | 0.987170i | \(-0.551044\pi\) | ||||
−0.159674 | + | 0.987170i | \(0.551044\pi\) | |||||||
\(354\) | 26.3923 | 1.40274 | ||||||||
\(355\) | −11.4641 | −0.608451 | ||||||||
\(356\) | 12.0000 | 0.635999 | ||||||||
\(357\) | −1.80385 | −0.0954697 | ||||||||
\(358\) | −15.8564 | −0.838037 | ||||||||
\(359\) | 10.9282 | 0.576769 | 0.288384 | − | 0.957515i | \(-0.406882\pi\) | ||||
0.288384 | + | 0.957515i | \(0.406882\pi\) | |||||||
\(360\) | −25.8564 | −1.36275 | ||||||||
\(361\) | −16.8564 | −0.887179 | ||||||||
\(362\) | 1.46410 | 0.0769515 | ||||||||
\(363\) | 9.39230 | 0.492968 | ||||||||
\(364\) | 1.46410 | 0.0767398 | ||||||||
\(365\) | −18.9282 | −0.990747 | ||||||||
\(366\) | −8.73205 | −0.456432 | ||||||||
\(367\) | 33.4641 | 1.74681 | 0.873406 | − | 0.486993i | \(-0.161906\pi\) | ||||
0.873406 | + | 0.486993i | \(0.161906\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.53590 | 0.132014 | ||||||||
\(370\) | −53.7128 | −2.79240 | ||||||||
\(371\) | −2.39230 | −0.124202 | ||||||||
\(372\) | 10.9282 | 0.566601 | ||||||||
\(373\) | 19.1962 | 0.993939 | 0.496970 | − | 0.867768i | \(-0.334446\pi\) | ||||
0.496970 | + | 0.867768i | \(0.334446\pi\) | |||||||
\(374\) | 23.3205 | 1.20587 | ||||||||
\(375\) | −6.92820 | −0.357771 | ||||||||
\(376\) | −77.5692 | −4.00033 | ||||||||
\(377\) | 7.66025 | 0.394523 | ||||||||
\(378\) | −0.732051 | −0.0376526 | ||||||||
\(379\) | −31.1962 | −1.60244 | −0.801219 | − | 0.598371i | \(-0.795815\pi\) | ||||
−0.801219 | + | 0.598371i | \(0.795815\pi\) | |||||||
\(380\) | 21.8564 | 1.12121 | ||||||||
\(381\) | −9.39230 | −0.481182 | ||||||||
\(382\) | 5.46410 | 0.279568 | ||||||||
\(383\) | 1.07180 | 0.0547663 | 0.0273831 | − | 0.999625i | \(-0.491283\pi\) | ||||
0.0273831 | + | 0.999625i | \(0.491283\pi\) | |||||||
\(384\) | −37.8564 | −1.93185 | ||||||||
\(385\) | −0.928203 | −0.0473056 | ||||||||
\(386\) | −8.19615 | −0.417173 | ||||||||
\(387\) | 6.26795 | 0.318618 | ||||||||
\(388\) | −81.5692 | −4.14105 | ||||||||
\(389\) | −13.5167 | −0.685322 | −0.342661 | − | 0.939459i | \(-0.611328\pi\) | ||||
−0.342661 | + | 0.939459i | \(0.611328\pi\) | |||||||
\(390\) | 7.46410 | 0.377959 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −65.5692 | −3.31175 | ||||||||
\(393\) | −5.07180 | −0.255838 | ||||||||
\(394\) | −22.9282 | −1.15511 | ||||||||
\(395\) | −10.9282 | −0.549858 | ||||||||
\(396\) | 6.92820 | 0.348155 | ||||||||
\(397\) | 20.4641 | 1.02706 | 0.513532 | − | 0.858070i | \(-0.328337\pi\) | ||||
0.513532 | + | 0.858070i | \(0.328337\pi\) | |||||||
\(398\) | 48.4449 | 2.42832 | ||||||||
\(399\) | 0.392305 | 0.0196398 | ||||||||
\(400\) | 36.7846 | 1.83923 | ||||||||
\(401\) | 2.53590 | 0.126637 | 0.0633184 | − | 0.997993i | \(-0.479832\pi\) | ||||
0.0633184 | + | 0.997993i | \(0.479832\pi\) | |||||||
\(402\) | 28.0526 | 1.39913 | ||||||||
\(403\) | −2.00000 | −0.0996271 | ||||||||
\(404\) | 1.85641 | 0.0923597 | ||||||||
\(405\) | −2.73205 | −0.135757 | ||||||||
\(406\) | 5.60770 | 0.278305 | ||||||||
\(407\) | 9.12436 | 0.452278 | ||||||||
\(408\) | −63.7128 | −3.15425 | ||||||||
\(409\) | 18.8564 | 0.932389 | 0.466195 | − | 0.884682i | \(-0.345625\pi\) | ||||
0.466195 | + | 0.884682i | \(0.345625\pi\) | |||||||
\(410\) | −18.9282 | −0.934797 | ||||||||
\(411\) | 7.26795 | 0.358501 | ||||||||
\(412\) | −96.1051 | −4.73476 | ||||||||
\(413\) | −2.58846 | −0.127370 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.3923 | −0.804667 | ||||||||
\(416\) | 21.8564 | 1.07160 | ||||||||
\(417\) | 15.5359 | 0.760796 | ||||||||
\(418\) | −5.07180 | −0.248070 | ||||||||
\(419\) | −4.73205 | −0.231176 | −0.115588 | − | 0.993297i | \(-0.536875\pi\) | ||||
−0.115588 | + | 0.993297i | \(0.536875\pi\) | |||||||
\(420\) | 4.00000 | 0.195180 | ||||||||
\(421\) | 1.33975 | 0.0652952 | 0.0326476 | − | 0.999467i | \(-0.489606\pi\) | ||||
0.0326476 | + | 0.999467i | \(0.489606\pi\) | |||||||
\(422\) | −4.19615 | −0.204266 | ||||||||
\(423\) | −8.19615 | −0.398511 | ||||||||
\(424\) | −84.4974 | −4.10356 | ||||||||
\(425\) | 16.5885 | 0.804658 | ||||||||
\(426\) | −11.4641 | −0.555438 | ||||||||
\(427\) | 0.856406 | 0.0414444 | ||||||||
\(428\) | 64.7846 | 3.13148 | ||||||||
\(429\) | −1.26795 | −0.0612172 | ||||||||
\(430\) | −46.7846 | −2.25615 | ||||||||
\(431\) | −24.3923 | −1.17494 | −0.587468 | − | 0.809247i | \(-0.699875\pi\) | ||||
−0.587468 | + | 0.809247i | \(0.699875\pi\) | |||||||
\(432\) | −14.9282 | −0.718234 | ||||||||
\(433\) | 3.19615 | 0.153597 | 0.0767986 | − | 0.997047i | \(-0.475530\pi\) | ||||
0.0767986 | + | 0.997047i | \(0.475530\pi\) | |||||||
\(434\) | −1.46410 | −0.0702791 | ||||||||
\(435\) | 20.9282 | 1.00343 | ||||||||
\(436\) | −40.7846 | −1.95323 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −18.9282 | −0.904425 | ||||||||
\(439\) | −31.7846 | −1.51700 | −0.758498 | − | 0.651675i | \(-0.774067\pi\) | ||||
−0.758498 | + | 0.651675i | \(0.774067\pi\) | |||||||
\(440\) | −32.7846 | −1.56294 | ||||||||
\(441\) | −6.92820 | −0.329914 | ||||||||
\(442\) | 18.3923 | 0.874833 | ||||||||
\(443\) | 23.6603 | 1.12413 | 0.562066 | − | 0.827092i | \(-0.310007\pi\) | ||||
0.562066 | + | 0.827092i | \(0.310007\pi\) | |||||||
\(444\) | −39.3205 | −1.86607 | ||||||||
\(445\) | −6.00000 | −0.284427 | ||||||||
\(446\) | −54.4449 | −2.57804 | ||||||||
\(447\) | −20.9282 | −0.989870 | ||||||||
\(448\) | 8.00000 | 0.377964 | ||||||||
\(449\) | 23.6603 | 1.11660 | 0.558298 | − | 0.829640i | \(-0.311455\pi\) | ||||
0.558298 | + | 0.829640i | \(0.311455\pi\) | |||||||
\(450\) | 6.73205 | 0.317352 | ||||||||
\(451\) | 3.21539 | 0.151407 | ||||||||
\(452\) | −86.6410 | −4.07525 | ||||||||
\(453\) | 22.8564 | 1.07389 | ||||||||
\(454\) | 12.9282 | 0.606751 | ||||||||
\(455\) | −0.732051 | −0.0343191 | ||||||||
\(456\) | 13.8564 | 0.648886 | ||||||||
\(457\) | 13.1962 | 0.617290 | 0.308645 | − | 0.951177i | \(-0.400124\pi\) | ||||
0.308645 | + | 0.951177i | \(0.400124\pi\) | |||||||
\(458\) | 13.1244 | 0.613261 | ||||||||
\(459\) | −6.73205 | −0.314225 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.0526 | 1.02709 | 0.513545 | − | 0.858063i | \(-0.328332\pi\) | ||||
0.513545 | + | 0.858063i | \(0.328332\pi\) | |||||||
\(462\) | −0.928203 | −0.0431839 | ||||||||
\(463\) | 6.07180 | 0.282180 | 0.141090 | − | 0.989997i | \(-0.454939\pi\) | ||||
0.141090 | + | 0.989997i | \(0.454939\pi\) | |||||||
\(464\) | 114.354 | 5.30874 | ||||||||
\(465\) | −5.46410 | −0.253392 | ||||||||
\(466\) | 29.8564 | 1.38307 | ||||||||
\(467\) | 25.6603 | 1.18741 | 0.593707 | − | 0.804681i | \(-0.297664\pi\) | ||||
0.593707 | + | 0.804681i | \(0.297664\pi\) | |||||||
\(468\) | 5.46410 | 0.252578 | ||||||||
\(469\) | −2.75129 | −0.127043 | ||||||||
\(470\) | 61.1769 | 2.82188 | ||||||||
\(471\) | 0.535898 | 0.0246929 | ||||||||
\(472\) | −91.4256 | −4.20821 | ||||||||
\(473\) | 7.94744 | 0.365424 | ||||||||
\(474\) | −10.9282 | −0.501949 | ||||||||
\(475\) | −3.60770 | −0.165532 | ||||||||
\(476\) | 9.85641 | 0.451768 | ||||||||
\(477\) | −8.92820 | −0.408794 | ||||||||
\(478\) | 66.1051 | 3.02358 | ||||||||
\(479\) | 10.3923 | 0.474837 | 0.237418 | − | 0.971408i | \(-0.423699\pi\) | ||||
0.237418 | + | 0.971408i | \(0.423699\pi\) | |||||||
\(480\) | 59.7128 | 2.72550 | ||||||||
\(481\) | 7.19615 | 0.328116 | ||||||||
\(482\) | −24.0526 | −1.09556 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −51.3205 | −2.33275 | ||||||||
\(485\) | 40.7846 | 1.85193 | ||||||||
\(486\) | −2.73205 | −0.123928 | ||||||||
\(487\) | −16.3205 | −0.739553 | −0.369776 | − | 0.929121i | \(-0.620566\pi\) | ||||
−0.369776 | + | 0.929121i | \(0.620566\pi\) | |||||||
\(488\) | 30.2487 | 1.36929 | ||||||||
\(489\) | 1.00000 | 0.0452216 | ||||||||
\(490\) | 51.7128 | 2.33615 | ||||||||
\(491\) | 10.0526 | 0.453666 | 0.226833 | − | 0.973934i | \(-0.427163\pi\) | ||||
0.226833 | + | 0.973934i | \(0.427163\pi\) | |||||||
\(492\) | −13.8564 | −0.624695 | ||||||||
\(493\) | 51.5692 | 2.32256 | ||||||||
\(494\) | −4.00000 | −0.179969 | ||||||||
\(495\) | −3.46410 | −0.155700 | ||||||||
\(496\) | −29.8564 | −1.34059 | ||||||||
\(497\) | 1.12436 | 0.0504342 | ||||||||
\(498\) | −16.3923 | −0.734557 | ||||||||
\(499\) | 26.3205 | 1.17827 | 0.589134 | − | 0.808035i | \(-0.299469\pi\) | ||||
0.589134 | + | 0.808035i | \(0.299469\pi\) | |||||||
\(500\) | 37.8564 | 1.69299 | ||||||||
\(501\) | −0.535898 | −0.0239422 | ||||||||
\(502\) | 68.1051 | 3.03968 | ||||||||
\(503\) | −12.7321 | −0.567694 | −0.283847 | − | 0.958870i | \(-0.591611\pi\) | ||||
−0.283847 | + | 0.958870i | \(0.591611\pi\) | |||||||
\(504\) | 2.53590 | 0.112958 | ||||||||
\(505\) | −0.928203 | −0.0413045 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.0000 | 0.532939 | ||||||||
\(508\) | 51.3205 | 2.27698 | ||||||||
\(509\) | 17.8564 | 0.791471 | 0.395736 | − | 0.918364i | \(-0.370490\pi\) | ||||
0.395736 | + | 0.918364i | \(0.370490\pi\) | |||||||
\(510\) | 50.2487 | 2.22505 | ||||||||
\(511\) | 1.85641 | 0.0821226 | ||||||||
\(512\) | 43.7128 | 1.93185 | ||||||||
\(513\) | 1.46410 | 0.0646417 | ||||||||
\(514\) | 72.1051 | 3.18042 | ||||||||
\(515\) | 48.0526 | 2.11745 | ||||||||
\(516\) | −34.2487 | −1.50772 | ||||||||
\(517\) | −10.3923 | −0.457053 | ||||||||
\(518\) | 5.26795 | 0.231460 | ||||||||
\(519\) | 3.12436 | 0.137144 | ||||||||
\(520\) | −25.8564 | −1.13388 | ||||||||
\(521\) | −19.8564 | −0.869925 | −0.434962 | − | 0.900449i | \(-0.643238\pi\) | ||||
−0.434962 | + | 0.900449i | \(0.643238\pi\) | |||||||
\(522\) | 20.9282 | 0.916003 | ||||||||
\(523\) | −21.4641 | −0.938560 | −0.469280 | − | 0.883050i | \(-0.655486\pi\) | ||||
−0.469280 | + | 0.883050i | \(0.655486\pi\) | |||||||
\(524\) | 27.7128 | 1.21064 | ||||||||
\(525\) | −0.660254 | −0.0288158 | ||||||||
\(526\) | −74.1051 | −3.23114 | ||||||||
\(527\) | −13.4641 | −0.586505 | ||||||||
\(528\) | −18.9282 | −0.823744 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 66.6410 | 2.89470 | ||||||||
\(531\) | −9.66025 | −0.419219 | ||||||||
\(532\) | −2.14359 | −0.0929366 | ||||||||
\(533\) | 2.53590 | 0.109842 | ||||||||
\(534\) | −6.00000 | −0.259645 | ||||||||
\(535\) | −32.3923 | −1.40044 | ||||||||
\(536\) | −97.1769 | −4.19740 | ||||||||
\(537\) | 5.80385 | 0.250455 | ||||||||
\(538\) | 9.46410 | 0.408026 | ||||||||
\(539\) | −8.78461 | −0.378380 | ||||||||
\(540\) | 14.9282 | 0.642408 | ||||||||
\(541\) | 13.4641 | 0.578867 | 0.289433 | − | 0.957198i | \(-0.406533\pi\) | ||||
0.289433 | + | 0.957198i | \(0.406533\pi\) | |||||||
\(542\) | −7.12436 | −0.306017 | ||||||||
\(543\) | −0.535898 | −0.0229976 | ||||||||
\(544\) | 147.138 | 6.30851 | ||||||||
\(545\) | 20.3923 | 0.873510 | ||||||||
\(546\) | −0.732051 | −0.0313289 | ||||||||
\(547\) | −38.1051 | −1.62926 | −0.814629 | − | 0.579983i | \(-0.803059\pi\) | ||||
−0.814629 | + | 0.579983i | \(0.803059\pi\) | |||||||
\(548\) | −39.7128 | −1.69645 | ||||||||
\(549\) | 3.19615 | 0.136408 | ||||||||
\(550\) | 8.53590 | 0.363972 | ||||||||
\(551\) | −11.2154 | −0.477792 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.07180 | 0.0455774 | ||||||||
\(554\) | 62.8372 | 2.66970 | ||||||||
\(555\) | 19.6603 | 0.834531 | ||||||||
\(556\) | −84.8897 | −3.60013 | ||||||||
\(557\) | −15.4641 | −0.655235 | −0.327618 | − | 0.944810i | \(-0.606246\pi\) | ||||
−0.327618 | + | 0.944810i | \(0.606246\pi\) | |||||||
\(558\) | −5.46410 | −0.231314 | ||||||||
\(559\) | 6.26795 | 0.265106 | ||||||||
\(560\) | −10.9282 | −0.461801 | ||||||||
\(561\) | −8.53590 | −0.360386 | ||||||||
\(562\) | −60.7846 | −2.56404 | ||||||||
\(563\) | −8.53590 | −0.359745 | −0.179873 | − | 0.983690i | \(-0.557569\pi\) | ||||
−0.179873 | + | 0.983690i | \(0.557569\pi\) | |||||||
\(564\) | 44.7846 | 1.88577 | ||||||||
\(565\) | 43.3205 | 1.82251 | ||||||||
\(566\) | −76.8372 | −3.22971 | ||||||||
\(567\) | 0.267949 | 0.0112528 | ||||||||
\(568\) | 39.7128 | 1.66631 | ||||||||
\(569\) | −10.3397 | −0.433465 | −0.216732 | − | 0.976231i | \(-0.569540\pi\) | ||||
−0.216732 | + | 0.976231i | \(0.569540\pi\) | |||||||
\(570\) | −10.9282 | −0.457732 | ||||||||
\(571\) | −21.7321 | −0.909458 | −0.454729 | − | 0.890630i | \(-0.650264\pi\) | ||||
−0.454729 | + | 0.890630i | \(0.650264\pi\) | |||||||
\(572\) | 6.92820 | 0.289683 | ||||||||
\(573\) | −2.00000 | −0.0835512 | ||||||||
\(574\) | 1.85641 | 0.0774849 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 29.8564 | 1.24402 | ||||||||
\(577\) | −28.0000 | −1.16566 | −0.582828 | − | 0.812596i | \(-0.698054\pi\) | ||||
−0.582828 | + | 0.812596i | \(0.698054\pi\) | |||||||
\(578\) | 77.3731 | 3.21830 | ||||||||
\(579\) | 3.00000 | 0.124676 | ||||||||
\(580\) | −114.354 | −4.74828 | ||||||||
\(581\) | 1.60770 | 0.0666984 | ||||||||
\(582\) | 40.7846 | 1.69058 | ||||||||
\(583\) | −11.3205 | −0.468848 | ||||||||
\(584\) | 65.5692 | 2.71327 | ||||||||
\(585\) | −2.73205 | −0.112956 | ||||||||
\(586\) | −36.2487 | −1.49742 | ||||||||
\(587\) | −35.6603 | −1.47186 | −0.735928 | − | 0.677060i | \(-0.763254\pi\) | ||||
−0.735928 | + | 0.677060i | \(0.763254\pi\) | |||||||
\(588\) | 37.8564 | 1.56117 | ||||||||
\(589\) | 2.92820 | 0.120655 | ||||||||
\(590\) | 72.1051 | 2.96852 | ||||||||
\(591\) | 8.39230 | 0.345213 | ||||||||
\(592\) | 107.426 | 4.41517 | ||||||||
\(593\) | −11.1244 | −0.456823 | −0.228411 | − | 0.973565i | \(-0.573353\pi\) | ||||
−0.228411 | + | 0.973565i | \(0.573353\pi\) | |||||||
\(594\) | −3.46410 | −0.142134 | ||||||||
\(595\) | −4.92820 | −0.202037 | ||||||||
\(596\) | 114.354 | 4.68412 | ||||||||
\(597\) | −17.7321 | −0.725725 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.5885 | 0.922939 | 0.461470 | − | 0.887156i | \(-0.347322\pi\) | ||||
0.461470 | + | 0.887156i | \(0.347322\pi\) | |||||||
\(600\) | −23.3205 | −0.952056 | ||||||||
\(601\) | −5.00000 | −0.203954 | −0.101977 | − | 0.994787i | \(-0.532517\pi\) | ||||
−0.101977 | + | 0.994787i | \(0.532517\pi\) | |||||||
\(602\) | 4.58846 | 0.187012 | ||||||||
\(603\) | −10.2679 | −0.418143 | ||||||||
\(604\) | −124.890 | −5.08169 | ||||||||
\(605\) | 25.6603 | 1.04324 | ||||||||
\(606\) | −0.928203 | −0.0377057 | ||||||||
\(607\) | 20.6077 | 0.836441 | 0.418220 | − | 0.908346i | \(-0.362654\pi\) | ||||
0.418220 | + | 0.908346i | \(0.362654\pi\) | |||||||
\(608\) | −32.0000 | −1.29777 | ||||||||
\(609\) | −2.05256 | −0.0831739 | ||||||||
\(610\) | −23.8564 | −0.965918 | ||||||||
\(611\) | −8.19615 | −0.331581 | ||||||||
\(612\) | 36.7846 | 1.48693 | ||||||||
\(613\) | 4.94744 | 0.199825 | 0.0999126 | − | 0.994996i | \(-0.468144\pi\) | ||||
0.0999126 | + | 0.994996i | \(0.468144\pi\) | |||||||
\(614\) | −12.5885 | −0.508029 | ||||||||
\(615\) | 6.92820 | 0.279372 | ||||||||
\(616\) | 3.21539 | 0.129552 | ||||||||
\(617\) | −12.7846 | −0.514689 | −0.257345 | − | 0.966320i | \(-0.582848\pi\) | ||||
−0.257345 | + | 0.966320i | \(0.582848\pi\) | |||||||
\(618\) | 48.0526 | 1.93296 | ||||||||
\(619\) | −25.0526 | −1.00695 | −0.503474 | − | 0.864011i | \(-0.667945\pi\) | ||||
−0.503474 | + | 0.864011i | \(0.667945\pi\) | |||||||
\(620\) | 29.8564 | 1.19906 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −26.2487 | −1.05248 | ||||||||
\(623\) | 0.588457 | 0.0235760 | ||||||||
\(624\) | −14.9282 | −0.597606 | ||||||||
\(625\) | −31.2487 | −1.24995 | ||||||||
\(626\) | 54.9808 | 2.19747 | ||||||||
\(627\) | 1.85641 | 0.0741377 | ||||||||
\(628\) | −2.92820 | −0.116848 | ||||||||
\(629\) | 48.4449 | 1.93162 | ||||||||
\(630\) | −2.00000 | −0.0796819 | ||||||||
\(631\) | 47.5885 | 1.89447 | 0.947233 | − | 0.320545i | \(-0.103866\pi\) | ||||
0.947233 | + | 0.320545i | \(0.103866\pi\) | |||||||
\(632\) | 37.8564 | 1.50585 | ||||||||
\(633\) | 1.53590 | 0.0610465 | ||||||||
\(634\) | 43.3205 | 1.72048 | ||||||||
\(635\) | −25.6603 | −1.01830 | ||||||||
\(636\) | 48.7846 | 1.93444 | ||||||||
\(637\) | −6.92820 | −0.274505 | ||||||||
\(638\) | 26.5359 | 1.05057 | ||||||||
\(639\) | 4.19615 | 0.165997 | ||||||||
\(640\) | −103.426 | −4.08826 | ||||||||
\(641\) | −4.53590 | −0.179157 | −0.0895786 | − | 0.995980i | \(-0.528552\pi\) | ||||
−0.0895786 | + | 0.995980i | \(0.528552\pi\) | |||||||
\(642\) | −32.3923 | −1.27842 | ||||||||
\(643\) | −31.0526 | −1.22459 | −0.612297 | − | 0.790628i | \(-0.709754\pi\) | ||||
−0.612297 | + | 0.790628i | \(0.709754\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17.1244 | 0.674271 | ||||||||
\(646\) | −26.9282 | −1.05948 | ||||||||
\(647\) | −2.87564 | −0.113053 | −0.0565266 | − | 0.998401i | \(-0.518003\pi\) | ||||
−0.0565266 | + | 0.998401i | \(0.518003\pi\) | |||||||
\(648\) | 9.46410 | 0.371785 | ||||||||
\(649\) | −12.2487 | −0.480804 | ||||||||
\(650\) | 6.73205 | 0.264053 | ||||||||
\(651\) | 0.535898 | 0.0210035 | ||||||||
\(652\) | −5.46410 | −0.213991 | ||||||||
\(653\) | 13.0718 | 0.511539 | 0.255769 | − | 0.966738i | \(-0.417671\pi\) | ||||
0.255769 | + | 0.966738i | \(0.417671\pi\) | |||||||
\(654\) | 20.3923 | 0.797402 | ||||||||
\(655\) | −13.8564 | −0.541415 | ||||||||
\(656\) | 37.8564 | 1.47804 | ||||||||
\(657\) | 6.92820 | 0.270295 | ||||||||
\(658\) | −6.00000 | −0.233904 | ||||||||
\(659\) | −39.2679 | −1.52966 | −0.764831 | − | 0.644231i | \(-0.777178\pi\) | ||||
−0.764831 | + | 0.644231i | \(0.777178\pi\) | |||||||
\(660\) | 18.9282 | 0.736779 | ||||||||
\(661\) | 24.0000 | 0.933492 | 0.466746 | − | 0.884391i | \(-0.345426\pi\) | ||||
0.466746 | + | 0.884391i | \(0.345426\pi\) | |||||||
\(662\) | −35.1244 | −1.36515 | ||||||||
\(663\) | −6.73205 | −0.261451 | ||||||||
\(664\) | 56.7846 | 2.20367 | ||||||||
\(665\) | 1.07180 | 0.0415625 | ||||||||
\(666\) | 19.6603 | 0.761819 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 2.92820 | 0.113296 | ||||||||
\(669\) | 19.9282 | 0.770469 | ||||||||
\(670\) | 76.6410 | 2.96090 | ||||||||
\(671\) | 4.05256 | 0.156447 | ||||||||
\(672\) | −5.85641 | −0.225916 | ||||||||
\(673\) | 43.7846 | 1.68777 | 0.843886 | − | 0.536522i | \(-0.180262\pi\) | ||||
0.843886 | + | 0.536522i | \(0.180262\pi\) | |||||||
\(674\) | −64.8372 | −2.49743 | ||||||||
\(675\) | −2.46410 | −0.0948433 | ||||||||
\(676\) | −65.5692 | −2.52189 | ||||||||
\(677\) | 11.2679 | 0.433062 | 0.216531 | − | 0.976276i | \(-0.430526\pi\) | ||||
0.216531 | + | 0.976276i | \(0.430526\pi\) | |||||||
\(678\) | 43.3205 | 1.66371 | ||||||||
\(679\) | −4.00000 | −0.153506 | ||||||||
\(680\) | −174.067 | −6.67515 | ||||||||
\(681\) | −4.73205 | −0.181333 | ||||||||
\(682\) | −6.92820 | −0.265295 | ||||||||
\(683\) | 44.1962 | 1.69112 | 0.845559 | − | 0.533881i | \(-0.179267\pi\) | ||||
0.845559 | + | 0.533881i | \(0.179267\pi\) | |||||||
\(684\) | −8.00000 | −0.305888 | ||||||||
\(685\) | 19.8564 | 0.758674 | ||||||||
\(686\) | −10.1962 | −0.389291 | ||||||||
\(687\) | −4.80385 | −0.183278 | ||||||||
\(688\) | 93.5692 | 3.56729 | ||||||||
\(689\) | −8.92820 | −0.340137 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.46410 | 0.321990 | 0.160995 | − | 0.986955i | \(-0.448530\pi\) | ||||
0.160995 | + | 0.986955i | \(0.448530\pi\) | |||||||
\(692\) | −17.0718 | −0.648972 | ||||||||
\(693\) | 0.339746 | 0.0129059 | ||||||||
\(694\) | 45.7128 | 1.73523 | ||||||||
\(695\) | 42.4449 | 1.61003 | ||||||||
\(696\) | −72.4974 | −2.74801 | ||||||||
\(697\) | 17.0718 | 0.646640 | ||||||||
\(698\) | −30.0526 | −1.13751 | ||||||||
\(699\) | −10.9282 | −0.413343 | ||||||||
\(700\) | 3.60770 | 0.136358 | ||||||||
\(701\) | −4.67949 | −0.176742 | −0.0883710 | − | 0.996088i | \(-0.528166\pi\) | ||||
−0.0883710 | + | 0.996088i | \(0.528166\pi\) | |||||||
\(702\) | −2.73205 | −0.103115 | ||||||||
\(703\) | −10.5359 | −0.397369 | ||||||||
\(704\) | 37.8564 | 1.42677 | ||||||||
\(705\) | −22.3923 | −0.843343 | ||||||||
\(706\) | −16.3923 | −0.616933 | ||||||||
\(707\) | 0.0910347 | 0.00342371 | ||||||||
\(708\) | 52.7846 | 1.98377 | ||||||||
\(709\) | 15.8756 | 0.596222 | 0.298111 | − | 0.954531i | \(-0.403643\pi\) | ||||
0.298111 | + | 0.954531i | \(0.403643\pi\) | |||||||
\(710\) | −31.3205 | −1.17544 | ||||||||
\(711\) | 4.00000 | 0.150012 | ||||||||
\(712\) | 20.7846 | 0.778936 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −4.92820 | −0.184433 | ||||||||
\(715\) | −3.46410 | −0.129550 | ||||||||
\(716\) | −31.7128 | −1.18516 | ||||||||
\(717\) | −24.1962 | −0.903622 | ||||||||
\(718\) | 29.8564 | 1.11423 | ||||||||
\(719\) | 15.8038 | 0.589384 | 0.294692 | − | 0.955592i | \(-0.404783\pi\) | ||||
0.294692 | + | 0.955592i | \(0.404783\pi\) | |||||||
\(720\) | −40.7846 | −1.51995 | ||||||||
\(721\) | −4.71281 | −0.175514 | ||||||||
\(722\) | −46.0526 | −1.71390 | ||||||||
\(723\) | 8.80385 | 0.327419 | ||||||||
\(724\) | 2.92820 | 0.108826 | ||||||||
\(725\) | 18.8756 | 0.701024 | ||||||||
\(726\) | 25.6603 | 0.952341 | ||||||||
\(727\) | −30.9282 | −1.14706 | −0.573532 | − | 0.819183i | \(-0.694427\pi\) | ||||
−0.573532 | + | 0.819183i | \(0.694427\pi\) | |||||||
\(728\) | 2.53590 | 0.0939866 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −51.7128 | −1.91398 | ||||||||
\(731\) | 42.1962 | 1.56068 | ||||||||
\(732\) | −17.4641 | −0.645492 | ||||||||
\(733\) | 17.7321 | 0.654948 | 0.327474 | − | 0.944860i | \(-0.393803\pi\) | ||||
0.327474 | + | 0.944860i | \(0.393803\pi\) | |||||||
\(734\) | 91.4256 | 3.37458 | ||||||||
\(735\) | −18.9282 | −0.698177 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.0192 | −0.479570 | ||||||||
\(738\) | 6.92820 | 0.255031 | ||||||||
\(739\) | −1.67949 | −0.0617811 | −0.0308906 | − | 0.999523i | \(-0.509834\pi\) | ||||
−0.0308906 | + | 0.999523i | \(0.509834\pi\) | |||||||
\(740\) | −107.426 | −3.94904 | ||||||||
\(741\) | 1.46410 | 0.0537851 | ||||||||
\(742\) | −6.53590 | −0.239940 | ||||||||
\(743\) | −19.6077 | −0.719337 | −0.359668 | − | 0.933080i | \(-0.617110\pi\) | ||||
−0.359668 | + | 0.933080i | \(0.617110\pi\) | |||||||
\(744\) | 18.9282 | 0.693942 | ||||||||
\(745\) | −57.1769 | −2.09480 | ||||||||
\(746\) | 52.4449 | 1.92014 | ||||||||
\(747\) | 6.00000 | 0.219529 | ||||||||
\(748\) | 46.6410 | 1.70536 | ||||||||
\(749\) | 3.17691 | 0.116082 | ||||||||
\(750\) | −18.9282 | −0.691160 | ||||||||
\(751\) | −29.4641 | −1.07516 | −0.537580 | − | 0.843213i | \(-0.680661\pi\) | ||||
−0.537580 | + | 0.843213i | \(0.680661\pi\) | |||||||
\(752\) | −122.354 | −4.46179 | ||||||||
\(753\) | −24.9282 | −0.908434 | ||||||||
\(754\) | 20.9282 | 0.762160 | ||||||||
\(755\) | 62.4449 | 2.27260 | ||||||||
\(756\) | −1.46410 | −0.0532489 | ||||||||
\(757\) | 15.1769 | 0.551614 | 0.275807 | − | 0.961213i | \(-0.411055\pi\) | ||||
0.275807 | + | 0.961213i | \(0.411055\pi\) | |||||||
\(758\) | −85.2295 | −3.09567 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 37.8564 | 1.37320 | ||||||||
\(761\) | −29.6603 | −1.07518 | −0.537592 | − | 0.843205i | \(-0.680666\pi\) | ||||
−0.537592 | + | 0.843205i | \(0.680666\pi\) | |||||||
\(762\) | −25.6603 | −0.929573 | ||||||||
\(763\) | −2.00000 | −0.0724049 | ||||||||
\(764\) | 10.9282 | 0.395369 | ||||||||
\(765\) | −18.3923 | −0.664975 | ||||||||
\(766\) | 2.92820 | 0.105800 | ||||||||
\(767\) | −9.66025 | −0.348812 | ||||||||
\(768\) | −43.7128 | −1.57735 | ||||||||
\(769\) | −22.1244 | −0.797825 | −0.398912 | − | 0.916989i | \(-0.630612\pi\) | ||||
−0.398912 | + | 0.916989i | \(0.630612\pi\) | |||||||
\(770\) | −2.53590 | −0.0913874 | ||||||||
\(771\) | −26.3923 | −0.950496 | ||||||||
\(772\) | −16.3923 | −0.589972 | ||||||||
\(773\) | 37.0333 | 1.33200 | 0.665998 | − | 0.745954i | \(-0.268006\pi\) | ||||
0.665998 | + | 0.745954i | \(0.268006\pi\) | |||||||
\(774\) | 17.1244 | 0.615522 | ||||||||
\(775\) | −4.92820 | −0.177026 | ||||||||
\(776\) | −141.282 | −5.07173 | ||||||||
\(777\) | −1.92820 | −0.0691739 | ||||||||
\(778\) | −36.9282 | −1.32394 | ||||||||
\(779\) | −3.71281 | −0.133025 | ||||||||
\(780\) | 14.9282 | 0.534515 | ||||||||
\(781\) | 5.32051 | 0.190383 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.66025 | −0.273755 | ||||||||
\(784\) | −103.426 | −3.69377 | ||||||||
\(785\) | 1.46410 | 0.0522560 | ||||||||
\(786\) | −13.8564 | −0.494242 | ||||||||
\(787\) | 49.1769 | 1.75297 | 0.876484 | − | 0.481431i | \(-0.159883\pi\) | ||||
0.876484 | + | 0.481431i | \(0.159883\pi\) | |||||||
\(788\) | −45.8564 | −1.63357 | ||||||||
\(789\) | 27.1244 | 0.965653 | ||||||||
\(790\) | −29.8564 | −1.06224 | ||||||||
\(791\) | −4.24871 | −0.151067 | ||||||||
\(792\) | 12.0000 | 0.426401 | ||||||||
\(793\) | 3.19615 | 0.113499 | ||||||||
\(794\) | 55.9090 | 1.98413 | ||||||||
\(795\) | −24.3923 | −0.865106 | ||||||||
\(796\) | 96.8897 | 3.43417 | ||||||||
\(797\) | −22.0526 | −0.781142 | −0.390571 | − | 0.920573i | \(-0.627722\pi\) | ||||
−0.390571 | + | 0.920573i | \(0.627722\pi\) | |||||||
\(798\) | 1.07180 | 0.0379412 | ||||||||
\(799\) | −55.1769 | −1.95202 | ||||||||
\(800\) | 53.8564 | 1.90411 | ||||||||
\(801\) | 2.19615 | 0.0775972 | ||||||||
\(802\) | 6.92820 | 0.244643 | ||||||||
\(803\) | 8.78461 | 0.310002 | ||||||||
\(804\) | 56.1051 | 1.97867 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.46410 | −0.192465 | ||||||||
\(807\) | −3.46410 | −0.121942 | ||||||||
\(808\) | 3.21539 | 0.113117 | ||||||||
\(809\) | 0.483340 | 0.0169933 | 0.00849666 | − | 0.999964i | \(-0.497295\pi\) | ||||
0.00849666 | + | 0.999964i | \(0.497295\pi\) | |||||||
\(810\) | −7.46410 | −0.262262 | ||||||||
\(811\) | −19.5359 | −0.685998 | −0.342999 | − | 0.939336i | \(-0.611443\pi\) | ||||
−0.342999 | + | 0.939336i | \(0.611443\pi\) | |||||||
\(812\) | 11.2154 | 0.393583 | ||||||||
\(813\) | 2.60770 | 0.0914559 | ||||||||
\(814\) | 24.9282 | 0.873733 | ||||||||
\(815\) | 2.73205 | 0.0956996 | ||||||||
\(816\) | −100.497 | −3.51811 | ||||||||
\(817\) | −9.17691 | −0.321060 | ||||||||
\(818\) | 51.5167 | 1.80124 | ||||||||
\(819\) | 0.267949 | 0.00936290 | ||||||||
\(820\) | −37.8564 | −1.32200 | ||||||||
\(821\) | −13.4641 | −0.469900 | −0.234950 | − | 0.972007i | \(-0.575493\pi\) | ||||
−0.234950 | + | 0.972007i | \(0.575493\pi\) | |||||||
\(822\) | 19.8564 | 0.692572 | ||||||||
\(823\) | −16.0000 | −0.557725 | −0.278862 | − | 0.960331i | \(-0.589957\pi\) | ||||
−0.278862 | + | 0.960331i | \(0.589957\pi\) | |||||||
\(824\) | −166.459 | −5.79887 | ||||||||
\(825\) | −3.12436 | −0.108776 | ||||||||
\(826\) | −7.07180 | −0.246059 | ||||||||
\(827\) | 39.7128 | 1.38095 | 0.690475 | − | 0.723356i | \(-0.257402\pi\) | ||||
0.690475 | + | 0.723356i | \(0.257402\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.7846 | 1.06919 | 0.534597 | − | 0.845107i | \(-0.320463\pi\) | ||||
0.534597 | + | 0.845107i | \(0.320463\pi\) | |||||||
\(830\) | −44.7846 | −1.55450 | ||||||||
\(831\) | −23.0000 | −0.797861 | ||||||||
\(832\) | 29.8564 | 1.03508 | ||||||||
\(833\) | −46.6410 | −1.61602 | ||||||||
\(834\) | 42.4449 | 1.46975 | ||||||||
\(835\) | −1.46410 | −0.0506673 | ||||||||
\(836\) | −10.1436 | −0.350824 | ||||||||
\(837\) | 2.00000 | 0.0691301 | ||||||||
\(838\) | −12.9282 | −0.446597 | ||||||||
\(839\) | −38.5359 | −1.33041 | −0.665203 | − | 0.746662i | \(-0.731655\pi\) | ||||
−0.665203 | + | 0.746662i | \(0.731655\pi\) | |||||||
\(840\) | 6.92820 | 0.239046 | ||||||||
\(841\) | 29.6795 | 1.02343 | ||||||||
\(842\) | 3.66025 | 0.126141 | ||||||||
\(843\) | 22.2487 | 0.766286 | ||||||||
\(844\) | −8.39230 | −0.288875 | ||||||||
\(845\) | 32.7846 | 1.12782 | ||||||||
\(846\) | −22.3923 | −0.769863 | ||||||||
\(847\) | −2.51666 | −0.0864735 | ||||||||
\(848\) | −133.282 | −4.57692 | ||||||||
\(849\) | 28.1244 | 0.965225 | ||||||||
\(850\) | 45.3205 | 1.55448 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −22.9282 | −0.785507 | ||||||||
\(853\) | 33.9282 | 1.16168 | 0.580840 | − | 0.814018i | \(-0.302724\pi\) | ||||
0.580840 | + | 0.814018i | \(0.302724\pi\) | |||||||
\(854\) | 2.33975 | 0.0800645 | ||||||||
\(855\) | 4.00000 | 0.136797 | ||||||||
\(856\) | 112.210 | 3.83527 | ||||||||
\(857\) | 43.5167 | 1.48650 | 0.743250 | − | 0.669013i | \(-0.233283\pi\) | ||||
0.743250 | + | 0.669013i | \(0.233283\pi\) | |||||||
\(858\) | −3.46410 | −0.118262 | ||||||||
\(859\) | −29.9282 | −1.02114 | −0.510569 | − | 0.859837i | \(-0.670565\pi\) | ||||
−0.510569 | + | 0.859837i | \(0.670565\pi\) | |||||||
\(860\) | −93.5692 | −3.19068 | ||||||||
\(861\) | −0.679492 | −0.0231570 | ||||||||
\(862\) | −66.6410 | −2.26980 | ||||||||
\(863\) | −48.9282 | −1.66554 | −0.832768 | − | 0.553623i | \(-0.813245\pi\) | ||||
−0.832768 | + | 0.553623i | \(0.813245\pi\) | |||||||
\(864\) | −21.8564 | −0.743570 | ||||||||
\(865\) | 8.53590 | 0.290229 | ||||||||
\(866\) | 8.73205 | 0.296727 | ||||||||
\(867\) | −28.3205 | −0.961815 | ||||||||
\(868\) | −2.92820 | −0.0993897 | ||||||||
\(869\) | 5.07180 | 0.172049 | ||||||||
\(870\) | 57.1769 | 1.93848 | ||||||||
\(871\) | −10.2679 | −0.347916 | ||||||||
\(872\) | −70.6410 | −2.39221 | ||||||||
\(873\) | −14.9282 | −0.505243 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.85641 | 0.0627580 | ||||||||
\(876\) | −37.8564 | −1.27905 | ||||||||
\(877\) | −53.4256 | −1.80406 | −0.902028 | − | 0.431678i | \(-0.857922\pi\) | ||||
−0.902028 | + | 0.431678i | \(0.857922\pi\) | |||||||
\(878\) | −86.8372 | −2.93061 | ||||||||
\(879\) | 13.2679 | 0.447517 | ||||||||
\(880\) | −51.7128 | −1.74324 | ||||||||
\(881\) | 25.1769 | 0.848232 | 0.424116 | − | 0.905608i | \(-0.360585\pi\) | ||||
0.424116 | + | 0.905608i | \(0.360585\pi\) | |||||||
\(882\) | −18.9282 | −0.637346 | ||||||||
\(883\) | 55.5692 | 1.87005 | 0.935027 | − | 0.354578i | \(-0.115375\pi\) | ||||
0.935027 | + | 0.354578i | \(0.115375\pi\) | |||||||
\(884\) | 36.7846 | 1.23720 | ||||||||
\(885\) | −26.3923 | −0.887168 | ||||||||
\(886\) | 64.6410 | 2.17166 | ||||||||
\(887\) | 13.0718 | 0.438908 | 0.219454 | − | 0.975623i | \(-0.429572\pi\) | ||||
0.219454 | + | 0.975623i | \(0.429572\pi\) | |||||||
\(888\) | −68.1051 | −2.28546 | ||||||||
\(889\) | 2.51666 | 0.0844061 | ||||||||
\(890\) | −16.3923 | −0.549471 | ||||||||
\(891\) | 1.26795 | 0.0424779 | ||||||||
\(892\) | −108.890 | −3.64590 | ||||||||
\(893\) | 12.0000 | 0.401565 | ||||||||
\(894\) | −57.1769 | −1.91228 | ||||||||
\(895\) | 15.8564 | 0.530021 | ||||||||
\(896\) | 10.1436 | 0.338874 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 64.6410 | 2.15710 | ||||||||
\(899\) | −15.3205 | −0.510968 | ||||||||
\(900\) | 13.4641 | 0.448803 | ||||||||
\(901\) | −60.1051 | −2.00239 | ||||||||
\(902\) | 8.78461 | 0.292496 | ||||||||
\(903\) | −1.67949 | −0.0558900 | ||||||||
\(904\) | −150.067 | −4.99114 | ||||||||
\(905\) | −1.46410 | −0.0486684 | ||||||||
\(906\) | 62.4449 | 2.07459 | ||||||||
\(907\) | −12.5167 | −0.415609 | −0.207804 | − | 0.978170i | \(-0.566632\pi\) | ||||
−0.207804 | + | 0.978170i | \(0.566632\pi\) | |||||||
\(908\) | 25.8564 | 0.858075 | ||||||||
\(909\) | 0.339746 | 0.0112687 | ||||||||
\(910\) | −2.00000 | −0.0662994 | ||||||||
\(911\) | −49.3205 | −1.63406 | −0.817031 | − | 0.576594i | \(-0.804381\pi\) | ||||
−0.817031 | + | 0.576594i | \(0.804381\pi\) | |||||||
\(912\) | 21.8564 | 0.723738 | ||||||||
\(913\) | 7.60770 | 0.251778 | ||||||||
\(914\) | 36.0526 | 1.19251 | ||||||||
\(915\) | 8.73205 | 0.288673 | ||||||||
\(916\) | 26.2487 | 0.867282 | ||||||||
\(917\) | 1.35898 | 0.0448776 | ||||||||
\(918\) | −18.3923 | −0.607037 | ||||||||
\(919\) | 33.8372 | 1.11619 | 0.558093 | − | 0.829779i | \(-0.311533\pi\) | ||||
0.558093 | + | 0.829779i | \(0.311533\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.60770 | 0.151829 | ||||||||
\(922\) | 60.2487 | 1.98419 | ||||||||
\(923\) | 4.19615 | 0.138118 | ||||||||
\(924\) | −1.85641 | −0.0610713 | ||||||||
\(925\) | 17.7321 | 0.583026 | ||||||||
\(926\) | 16.5885 | 0.545131 | ||||||||
\(927\) | −17.5885 | −0.577681 | ||||||||
\(928\) | 167.426 | 5.49602 | ||||||||
\(929\) | −39.8038 | −1.30592 | −0.652961 | − | 0.757392i | \(-0.726473\pi\) | ||||
−0.652961 | + | 0.757392i | \(0.726473\pi\) | |||||||
\(930\) | −14.9282 | −0.489515 | ||||||||
\(931\) | 10.1436 | 0.332443 | ||||||||
\(932\) | 59.7128 | 1.95596 | ||||||||
\(933\) | 9.60770 | 0.314542 | ||||||||
\(934\) | 70.1051 | 2.29391 | ||||||||
\(935\) | −23.3205 | −0.762662 | ||||||||
\(936\) | 9.46410 | 0.309344 | ||||||||
\(937\) | 5.98076 | 0.195383 | 0.0976915 | − | 0.995217i | \(-0.468854\pi\) | ||||
0.0976915 | + | 0.995217i | \(0.468854\pi\) | |||||||
\(938\) | −7.51666 | −0.245428 | ||||||||
\(939\) | −20.1244 | −0.656734 | ||||||||
\(940\) | 122.354 | 3.99074 | ||||||||
\(941\) | −28.0000 | −0.912774 | −0.456387 | − | 0.889781i | \(-0.650857\pi\) | ||||
−0.456387 | + | 0.889781i | \(0.650857\pi\) | |||||||
\(942\) | 1.46410 | 0.0477030 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −144.210 | −4.69364 | ||||||||
\(945\) | 0.732051 | 0.0238136 | ||||||||
\(946\) | 21.7128 | 0.705944 | ||||||||
\(947\) | 32.5885 | 1.05898 | 0.529491 | − | 0.848315i | \(-0.322383\pi\) | ||||
0.529491 | + | 0.848315i | \(0.322383\pi\) | |||||||
\(948\) | −21.8564 | −0.709863 | ||||||||
\(949\) | 6.92820 | 0.224899 | ||||||||
\(950\) | −9.85641 | −0.319784 | ||||||||
\(951\) | −15.8564 | −0.514179 | ||||||||
\(952\) | 17.0718 | 0.553300 | ||||||||
\(953\) | −26.0526 | −0.843925 | −0.421963 | − | 0.906613i | \(-0.638659\pi\) | ||||
−0.421963 | + | 0.906613i | \(0.638659\pi\) | |||||||
\(954\) | −24.3923 | −0.789730 | ||||||||
\(955\) | −5.46410 | −0.176814 | ||||||||
\(956\) | 132.210 | 4.27598 | ||||||||
\(957\) | −9.71281 | −0.313971 | ||||||||
\(958\) | 28.3923 | 0.917314 | ||||||||
\(959\) | −1.94744 | −0.0628862 | ||||||||
\(960\) | 81.5692 | 2.63264 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 19.6603 | 0.633872 | ||||||||
\(963\) | 11.8564 | 0.382067 | ||||||||
\(964\) | −48.1051 | −1.54936 | ||||||||
\(965\) | 8.19615 | 0.263843 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.2487 | 0.876259 | 0.438130 | − | 0.898912i | \(-0.355641\pi\) | ||||
0.438130 | + | 0.898912i | \(0.355641\pi\) | |||||||
\(968\) | −88.8897 | −2.85702 | ||||||||
\(969\) | 9.85641 | 0.316633 | ||||||||
\(970\) | 111.426 | 3.57766 | ||||||||
\(971\) | −8.14359 | −0.261340 | −0.130670 | − | 0.991426i | \(-0.541713\pi\) | ||||
−0.130670 | + | 0.991426i | \(0.541713\pi\) | |||||||
\(972\) | −5.46410 | −0.175261 | ||||||||
\(973\) | −4.16283 | −0.133454 | ||||||||
\(974\) | −44.5885 | −1.42871 | ||||||||
\(975\) | −2.46410 | −0.0789144 | ||||||||
\(976\) | 47.7128 | 1.52725 | ||||||||
\(977\) | 17.0718 | 0.546175 | 0.273088 | − | 0.961989i | \(-0.411955\pi\) | ||||
0.273088 | + | 0.961989i | \(0.411955\pi\) | |||||||
\(978\) | 2.73205 | 0.0873614 | ||||||||
\(979\) | 2.78461 | 0.0889965 | ||||||||
\(980\) | 103.426 | 3.30381 | ||||||||
\(981\) | −7.46410 | −0.238310 | ||||||||
\(982\) | 27.4641 | 0.876415 | ||||||||
\(983\) | 41.8038 | 1.33334 | 0.666668 | − | 0.745355i | \(-0.267720\pi\) | ||||
0.666668 | + | 0.745355i | \(0.267720\pi\) | |||||||
\(984\) | −24.0000 | −0.765092 | ||||||||
\(985\) | 22.9282 | 0.730553 | ||||||||
\(986\) | 140.890 | 4.48684 | ||||||||
\(987\) | 2.19615 | 0.0699043 | ||||||||
\(988\) | −8.00000 | −0.254514 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −9.46410 | −0.300789 | ||||||||
\(991\) | −25.6077 | −0.813455 | −0.406728 | − | 0.913549i | \(-0.633330\pi\) | ||||
−0.406728 | + | 0.913549i | \(0.633330\pi\) | |||||||
\(992\) | −43.7128 | −1.38788 | ||||||||
\(993\) | 12.8564 | 0.407986 | ||||||||
\(994\) | 3.07180 | 0.0974315 | ||||||||
\(995\) | −48.4449 | −1.53581 | ||||||||
\(996\) | −32.7846 | −1.03882 | ||||||||
\(997\) | 39.0000 | 1.23514 | 0.617571 | − | 0.786515i | \(-0.288117\pi\) | ||||
0.617571 | + | 0.786515i | \(0.288117\pi\) | |||||||
\(998\) | 71.9090 | 2.27624 | ||||||||
\(999\) | −7.19615 | −0.227676 |
(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 | 1587.2.a.k.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 4761.2.a.m.1.1 | 2 | |||
23.22 | odd | 2 | 1587.2.a.l.1.2 | yes | 2 | ||
69.68 | even | 2 | 4761.2.a.l.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1587.2.a.k.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1587.2.a.l.1.2 | yes | 2 | 23.22 | odd | 2 | ||
4761.2.a.l.1.1 | 2 | 69.68 | even | 2 | |||
4761.2.a.m.1.1 | 2 | 3.2 | odd | 2 |