Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(1,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, 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("950.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 190) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.414214 | −0.239146 | −0.119573 | − | 0.992825i | \(-0.538153\pi\) | ||||
−0.119573 | + | 0.992825i | \(0.538153\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.414214 | 0.169102 | ||||||||
\(7\) | 4.41421 | 1.66842 | 0.834208 | − | 0.551450i | \(-0.185925\pi\) | ||||
0.834208 | + | 0.551450i | \(0.185925\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.82843 | −0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.41421 | −0.426401 | −0.213201 | − | 0.977008i | \(-0.568389\pi\) | ||||
−0.213201 | + | 0.977008i | \(0.568389\pi\) | |||||||
\(12\) | −0.414214 | −0.119573 | ||||||||
\(13\) | 5.82843 | 1.61651 | 0.808257 | − | 0.588829i | \(-0.200411\pi\) | ||||
0.808257 | + | 0.588829i | \(0.200411\pi\) | |||||||
\(14\) | −4.41421 | −1.17975 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | 0.242536 | 0.121268 | − | 0.992620i | \(-0.461304\pi\) | ||||
0.121268 | + | 0.992620i | \(0.461304\pi\) | |||||||
\(18\) | 2.82843 | 0.666667 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.82843 | −0.398996 | ||||||||
\(22\) | 1.41421 | 0.301511 | ||||||||
\(23\) | 0.757359 | 0.157920 | 0.0789602 | − | 0.996878i | \(-0.474840\pi\) | ||||
0.0789602 | + | 0.996878i | \(0.474840\pi\) | |||||||
\(24\) | 0.414214 | 0.0845510 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.82843 | −1.14305 | ||||||||
\(27\) | 2.41421 | 0.464616 | ||||||||
\(28\) | 4.41421 | 0.834208 | ||||||||
\(29\) | −0.171573 | −0.0318603 | −0.0159301 | − | 0.999873i | \(-0.505071\pi\) | ||||
−0.0159301 | + | 0.999873i | \(0.505071\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.24264 | 1.12121 | 0.560606 | − | 0.828083i | \(-0.310568\pi\) | ||||
0.560606 | + | 0.828083i | \(0.310568\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.585786 | 0.101972 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.82843 | −0.471405 | ||||||||
\(37\) | −8.48528 | −1.39497 | −0.697486 | − | 0.716599i | \(-0.745698\pi\) | ||||
−0.697486 | + | 0.716599i | \(0.745698\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | −2.41421 | −0.386584 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.24264 | −0.662589 | −0.331295 | − | 0.943527i | \(-0.607485\pi\) | ||||
−0.331295 | + | 0.943527i | \(0.607485\pi\) | |||||||
\(42\) | 1.82843 | 0.282132 | ||||||||
\(43\) | 1.75736 | 0.267995 | 0.133997 | − | 0.990982i | \(-0.457219\pi\) | ||||
0.133997 | + | 0.990982i | \(0.457219\pi\) | |||||||
\(44\) | −1.41421 | −0.213201 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.757359 | −0.111667 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | −0.414214 | −0.0597866 | ||||||||
\(49\) | 12.4853 | 1.78361 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.414214 | −0.0580015 | ||||||||
\(52\) | 5.82843 | 0.808257 | ||||||||
\(53\) | 5.48528 | 0.753461 | 0.376731 | − | 0.926323i | \(-0.377048\pi\) | ||||
0.376731 | + | 0.926323i | \(0.377048\pi\) | |||||||
\(54\) | −2.41421 | −0.328533 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.41421 | −0.589874 | ||||||||
\(57\) | 0.414214 | 0.0548639 | ||||||||
\(58\) | 0.171573 | 0.0225286 | ||||||||
\(59\) | 6.89949 | 0.898238 | 0.449119 | − | 0.893472i | \(-0.351738\pi\) | ||||
0.449119 | + | 0.893472i | \(0.351738\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.2426 | 1.82358 | 0.911792 | − | 0.410653i | \(-0.134699\pi\) | ||||
0.911792 | + | 0.410653i | \(0.134699\pi\) | |||||||
\(62\) | −6.24264 | −0.792816 | ||||||||
\(63\) | −12.4853 | −1.57300 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.585786 | −0.0721053 | ||||||||
\(67\) | 4.75736 | 0.581204 | 0.290602 | − | 0.956844i | \(-0.406144\pi\) | ||||
0.290602 | + | 0.956844i | \(0.406144\pi\) | |||||||
\(68\) | 1.00000 | 0.121268 | ||||||||
\(69\) | −0.313708 | −0.0377661 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.4142 | −1.59197 | −0.795987 | − | 0.605314i | \(-0.793048\pi\) | ||||
−0.795987 | + | 0.605314i | \(0.793048\pi\) | |||||||
\(72\) | 2.82843 | 0.333333 | ||||||||
\(73\) | 11.4853 | 1.34425 | 0.672125 | − | 0.740437i | \(-0.265382\pi\) | ||||
0.672125 | + | 0.740437i | \(0.265382\pi\) | |||||||
\(74\) | 8.48528 | 0.986394 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −6.24264 | −0.711415 | ||||||||
\(78\) | 2.41421 | 0.273356 | ||||||||
\(79\) | −6.48528 | −0.729651 | −0.364826 | − | 0.931076i | \(-0.618871\pi\) | ||||
−0.364826 | + | 0.931076i | \(0.618871\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.48528 | 0.831698 | ||||||||
\(82\) | 4.24264 | 0.468521 | ||||||||
\(83\) | 14.4853 | 1.58997 | 0.794983 | − | 0.606632i | \(-0.207480\pi\) | ||||
0.794983 | + | 0.606632i | \(0.207480\pi\) | |||||||
\(84\) | −1.82843 | −0.199498 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.75736 | −0.189501 | ||||||||
\(87\) | 0.0710678 | 0.00761927 | ||||||||
\(88\) | 1.41421 | 0.150756 | ||||||||
\(89\) | 7.07107 | 0.749532 | 0.374766 | − | 0.927119i | \(-0.377723\pi\) | ||||
0.374766 | + | 0.927119i | \(0.377723\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 25.7279 | 2.69702 | ||||||||
\(92\) | 0.757359 | 0.0789602 | ||||||||
\(93\) | −2.58579 | −0.268134 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.414214 | 0.0422755 | ||||||||
\(97\) | −0.343146 | −0.0348412 | −0.0174206 | − | 0.999848i | \(-0.505545\pi\) | ||||
−0.0174206 | + | 0.999848i | \(0.505545\pi\) | |||||||
\(98\) | −12.4853 | −1.26120 | ||||||||
\(99\) | 4.00000 | 0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.0711 | 1.30062 | 0.650310 | − | 0.759669i | \(-0.274639\pi\) | ||||
0.650310 | + | 0.759669i | \(0.274639\pi\) | |||||||
\(102\) | 0.414214 | 0.0410133 | ||||||||
\(103\) | 4.24264 | 0.418040 | 0.209020 | − | 0.977911i | \(-0.432973\pi\) | ||||
0.209020 | + | 0.977911i | \(0.432973\pi\) | |||||||
\(104\) | −5.82843 | −0.571524 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.48528 | −0.532778 | ||||||||
\(107\) | 19.7279 | 1.90717 | 0.953585 | − | 0.301124i | \(-0.0973617\pi\) | ||||
0.953585 | + | 0.301124i | \(0.0973617\pi\) | |||||||
\(108\) | 2.41421 | 0.232308 | ||||||||
\(109\) | −17.9706 | −1.72127 | −0.860634 | − | 0.509224i | \(-0.829932\pi\) | ||||
−0.860634 | + | 0.509224i | \(0.829932\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.51472 | 0.333602 | ||||||||
\(112\) | 4.41421 | 0.417104 | ||||||||
\(113\) | −10.2426 | −0.963547 | −0.481773 | − | 0.876296i | \(-0.660007\pi\) | ||||
−0.481773 | + | 0.876296i | \(0.660007\pi\) | |||||||
\(114\) | −0.414214 | −0.0387947 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.171573 | −0.0159301 | ||||||||
\(117\) | −16.4853 | −1.52406 | ||||||||
\(118\) | −6.89949 | −0.635150 | ||||||||
\(119\) | 4.41421 | 0.404650 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | −14.2426 | −1.28947 | ||||||||
\(123\) | 1.75736 | 0.158456 | ||||||||
\(124\) | 6.24264 | 0.560606 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 12.4853 | 1.11228 | ||||||||
\(127\) | −2.48528 | −0.220533 | −0.110267 | − | 0.993902i | \(-0.535170\pi\) | ||||
−0.110267 | + | 0.993902i | \(0.535170\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.727922 | −0.0640900 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.9706 | −1.48272 | −0.741362 | − | 0.671105i | \(-0.765820\pi\) | ||||
−0.741362 | + | 0.671105i | \(0.765820\pi\) | |||||||
\(132\) | 0.585786 | 0.0509862 | ||||||||
\(133\) | −4.41421 | −0.382761 | ||||||||
\(134\) | −4.75736 | −0.410973 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | 13.0000 | 1.11066 | 0.555332 | − | 0.831628i | \(-0.312591\pi\) | ||||
0.555332 | + | 0.831628i | \(0.312591\pi\) | |||||||
\(138\) | 0.313708 | 0.0267046 | ||||||||
\(139\) | −12.0000 | −1.01783 | −0.508913 | − | 0.860818i | \(-0.669953\pi\) | ||||
−0.508913 | + | 0.860818i | \(0.669953\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 13.4142 | 1.12570 | ||||||||
\(143\) | −8.24264 | −0.689284 | ||||||||
\(144\) | −2.82843 | −0.235702 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −11.4853 | −0.950529 | ||||||||
\(147\) | −5.17157 | −0.426544 | ||||||||
\(148\) | −8.48528 | −0.697486 | ||||||||
\(149\) | 17.6569 | 1.44651 | 0.723253 | − | 0.690583i | \(-0.242646\pi\) | ||||
0.723253 | + | 0.690583i | \(0.242646\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.4853 | −0.853280 | −0.426640 | − | 0.904422i | \(-0.640303\pi\) | ||||
−0.426640 | + | 0.904422i | \(0.640303\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −2.82843 | −0.228665 | ||||||||
\(154\) | 6.24264 | 0.503046 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.41421 | −0.193292 | ||||||||
\(157\) | 11.6569 | 0.930318 | 0.465159 | − | 0.885227i | \(-0.345997\pi\) | ||||
0.465159 | + | 0.885227i | \(0.345997\pi\) | |||||||
\(158\) | 6.48528 | 0.515941 | ||||||||
\(159\) | −2.27208 | −0.180188 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.34315 | 0.263477 | ||||||||
\(162\) | −7.48528 | −0.588099 | ||||||||
\(163\) | −10.2426 | −0.802266 | −0.401133 | − | 0.916020i | \(-0.631383\pi\) | ||||
−0.401133 | + | 0.916020i | \(0.631383\pi\) | |||||||
\(164\) | −4.24264 | −0.331295 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.4853 | −1.12428 | ||||||||
\(167\) | −18.2426 | −1.41166 | −0.705829 | − | 0.708382i | \(-0.749425\pi\) | ||||
−0.705829 | + | 0.708382i | \(0.749425\pi\) | |||||||
\(168\) | 1.82843 | 0.141066 | ||||||||
\(169\) | 20.9706 | 1.61312 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.82843 | 0.216295 | ||||||||
\(172\) | 1.75736 | 0.133997 | ||||||||
\(173\) | 0.485281 | 0.0368953 | 0.0184476 | − | 0.999830i | \(-0.494128\pi\) | ||||
0.0184476 | + | 0.999830i | \(0.494128\pi\) | |||||||
\(174\) | −0.0710678 | −0.00538764 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.41421 | −0.106600 | ||||||||
\(177\) | −2.85786 | −0.214810 | ||||||||
\(178\) | −7.07107 | −0.529999 | ||||||||
\(179\) | −11.6569 | −0.871274 | −0.435637 | − | 0.900122i | \(-0.643477\pi\) | ||||
−0.435637 | + | 0.900122i | \(0.643477\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.48528 | −0.630706 | −0.315353 | − | 0.948974i | \(-0.602123\pi\) | ||||
−0.315353 | + | 0.948974i | \(0.602123\pi\) | |||||||
\(182\) | −25.7279 | −1.90708 | ||||||||
\(183\) | −5.89949 | −0.436103 | ||||||||
\(184\) | −0.757359 | −0.0558333 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.58579 | 0.189599 | ||||||||
\(187\) | −1.41421 | −0.103418 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.6569 | 0.775172 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.5563 | 0.908546 | 0.454273 | − | 0.890863i | \(-0.349899\pi\) | ||||
0.454273 | + | 0.890863i | \(0.349899\pi\) | |||||||
\(192\) | −0.414214 | −0.0298933 | ||||||||
\(193\) | −0.343146 | −0.0247002 | −0.0123501 | − | 0.999924i | \(-0.503931\pi\) | ||||
−0.0123501 | + | 0.999924i | \(0.503931\pi\) | |||||||
\(194\) | 0.343146 | 0.0246364 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.4853 | 0.891806 | ||||||||
\(197\) | −11.7574 | −0.837677 | −0.418839 | − | 0.908061i | \(-0.637563\pi\) | ||||
−0.418839 | + | 0.908061i | \(0.637563\pi\) | |||||||
\(198\) | −4.00000 | −0.284268 | ||||||||
\(199\) | 9.24264 | 0.655193 | 0.327597 | − | 0.944818i | \(-0.393761\pi\) | ||||
0.327597 | + | 0.944818i | \(0.393761\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.97056 | −0.138993 | ||||||||
\(202\) | −13.0711 | −0.919677 | ||||||||
\(203\) | −0.757359 | −0.0531562 | ||||||||
\(204\) | −0.414214 | −0.0290008 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.24264 | −0.295599 | ||||||||
\(207\) | −2.14214 | −0.148889 | ||||||||
\(208\) | 5.82843 | 0.404129 | ||||||||
\(209\) | 1.41421 | 0.0978232 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.7279 | −1.35813 | −0.679063 | − | 0.734080i | \(-0.737614\pi\) | ||||
−0.679063 | + | 0.734080i | \(0.737614\pi\) | |||||||
\(212\) | 5.48528 | 0.376731 | ||||||||
\(213\) | 5.55635 | 0.380715 | ||||||||
\(214\) | −19.7279 | −1.34857 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.41421 | −0.164266 | ||||||||
\(217\) | 27.5563 | 1.87065 | ||||||||
\(218\) | 17.9706 | 1.21712 | ||||||||
\(219\) | −4.75736 | −0.321473 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.82843 | 0.392062 | ||||||||
\(222\) | −3.51472 | −0.235892 | ||||||||
\(223\) | −15.1716 | −1.01596 | −0.507982 | − | 0.861368i | \(-0.669608\pi\) | ||||
−0.507982 | + | 0.861368i | \(0.669608\pi\) | |||||||
\(224\) | −4.41421 | −0.294937 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.2426 | 0.681330 | ||||||||
\(227\) | −16.7574 | −1.11223 | −0.556113 | − | 0.831107i | \(-0.687708\pi\) | ||||
−0.556113 | + | 0.831107i | \(0.687708\pi\) | |||||||
\(228\) | 0.414214 | 0.0274320 | ||||||||
\(229\) | 14.9706 | 0.989283 | 0.494641 | − | 0.869097i | \(-0.335299\pi\) | ||||
0.494641 | + | 0.869097i | \(0.335299\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.58579 | 0.170132 | ||||||||
\(232\) | 0.171573 | 0.0112643 | ||||||||
\(233\) | −24.9706 | −1.63588 | −0.817938 | − | 0.575306i | \(-0.804883\pi\) | ||||
−0.817938 | + | 0.575306i | \(0.804883\pi\) | |||||||
\(234\) | 16.4853 | 1.07768 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.89949 | 0.449119 | ||||||||
\(237\) | 2.68629 | 0.174493 | ||||||||
\(238\) | −4.41421 | −0.286131 | ||||||||
\(239\) | −6.89949 | −0.446291 | −0.223146 | − | 0.974785i | \(-0.571633\pi\) | ||||
−0.223146 | + | 0.974785i | \(0.571633\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.97056 | 0.577845 | 0.288922 | − | 0.957353i | \(-0.406703\pi\) | ||||
0.288922 | + | 0.957353i | \(0.406703\pi\) | |||||||
\(242\) | 9.00000 | 0.578542 | ||||||||
\(243\) | −10.3431 | −0.663513 | ||||||||
\(244\) | 14.2426 | 0.911792 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.75736 | −0.112045 | ||||||||
\(247\) | −5.82843 | −0.370854 | ||||||||
\(248\) | −6.24264 | −0.396408 | ||||||||
\(249\) | −6.00000 | −0.380235 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.55635 | 0.224475 | 0.112237 | − | 0.993681i | \(-0.464198\pi\) | ||||
0.112237 | + | 0.993681i | \(0.464198\pi\) | |||||||
\(252\) | −12.4853 | −0.786499 | ||||||||
\(253\) | −1.07107 | −0.0673375 | ||||||||
\(254\) | 2.48528 | 0.155940 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.7279 | 1.29297 | 0.646486 | − | 0.762926i | \(-0.276238\pi\) | ||||
0.646486 | + | 0.762926i | \(0.276238\pi\) | |||||||
\(258\) | 0.727922 | 0.0453184 | ||||||||
\(259\) | −37.4558 | −2.32739 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.485281 | 0.0300382 | ||||||||
\(262\) | 16.9706 | 1.04844 | ||||||||
\(263\) | −26.9706 | −1.66308 | −0.831538 | − | 0.555468i | \(-0.812539\pi\) | ||||
−0.831538 | + | 0.555468i | \(0.812539\pi\) | |||||||
\(264\) | −0.585786 | −0.0360527 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.41421 | 0.270653 | ||||||||
\(267\) | −2.92893 | −0.179248 | ||||||||
\(268\) | 4.75736 | 0.290602 | ||||||||
\(269\) | −16.6274 | −1.01379 | −0.506896 | − | 0.862007i | \(-0.669207\pi\) | ||||
−0.506896 | + | 0.862007i | \(0.669207\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.2426 | −1.65487 | −0.827436 | − | 0.561560i | \(-0.810202\pi\) | ||||
−0.827436 | + | 0.561560i | \(0.810202\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | −10.6569 | −0.644982 | ||||||||
\(274\) | −13.0000 | −0.785359 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.313708 | −0.0188830 | ||||||||
\(277\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(278\) | 12.0000 | 0.719712 | ||||||||
\(279\) | −17.6569 | −1.05709 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.24264 | 0.253095 | 0.126547 | − | 0.991961i | \(-0.459610\pi\) | ||||
0.126547 | + | 0.991961i | \(0.459610\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 32.1421 | 1.91065 | 0.955326 | − | 0.295555i | \(-0.0955045\pi\) | ||||
0.955326 | + | 0.295555i | \(0.0955045\pi\) | |||||||
\(284\) | −13.4142 | −0.795987 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.24264 | 0.487398 | ||||||||
\(287\) | −18.7279 | −1.10547 | ||||||||
\(288\) | 2.82843 | 0.166667 | ||||||||
\(289\) | −16.0000 | −0.941176 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.142136 | 0.00833214 | ||||||||
\(292\) | 11.4853 | 0.672125 | ||||||||
\(293\) | −5.48528 | −0.320454 | −0.160227 | − | 0.987080i | \(-0.551223\pi\) | ||||
−0.160227 | + | 0.987080i | \(0.551223\pi\) | |||||||
\(294\) | 5.17157 | 0.301612 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8.48528 | 0.493197 | ||||||||
\(297\) | −3.41421 | −0.198113 | ||||||||
\(298\) | −17.6569 | −1.02283 | ||||||||
\(299\) | 4.41421 | 0.255281 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.75736 | 0.447127 | ||||||||
\(302\) | 10.4853 | 0.603360 | ||||||||
\(303\) | −5.41421 | −0.311038 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.82843 | 0.161690 | ||||||||
\(307\) | −17.6569 | −1.00773 | −0.503865 | − | 0.863782i | \(-0.668089\pi\) | ||||
−0.503865 | + | 0.863782i | \(0.668089\pi\) | |||||||
\(308\) | −6.24264 | −0.355707 | ||||||||
\(309\) | −1.75736 | −0.0999727 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.75736 | −0.269765 | −0.134883 | − | 0.990862i | \(-0.543066\pi\) | ||||
−0.134883 | + | 0.990862i | \(0.543066\pi\) | |||||||
\(312\) | 2.41421 | 0.136678 | ||||||||
\(313\) | −7.97056 | −0.450523 | −0.225261 | − | 0.974298i | \(-0.572324\pi\) | ||||
−0.225261 | + | 0.974298i | \(0.572324\pi\) | |||||||
\(314\) | −11.6569 | −0.657834 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.48528 | −0.364826 | ||||||||
\(317\) | −9.48528 | −0.532746 | −0.266373 | − | 0.963870i | \(-0.585825\pi\) | ||||
−0.266373 | + | 0.963870i | \(0.585825\pi\) | |||||||
\(318\) | 2.27208 | 0.127412 | ||||||||
\(319\) | 0.242641 | 0.0135853 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.17157 | −0.456093 | ||||||||
\(322\) | −3.34315 | −0.186306 | ||||||||
\(323\) | −1.00000 | −0.0556415 | ||||||||
\(324\) | 7.48528 | 0.415849 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.2426 | 0.567287 | ||||||||
\(327\) | 7.44365 | 0.411635 | ||||||||
\(328\) | 4.24264 | 0.234261 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.2426 | −1.05767 | −0.528836 | − | 0.848724i | \(-0.677371\pi\) | ||||
−0.528836 | + | 0.848724i | \(0.677371\pi\) | |||||||
\(332\) | 14.4853 | 0.794983 | ||||||||
\(333\) | 24.0000 | 1.31519 | ||||||||
\(334\) | 18.2426 | 0.998193 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.82843 | −0.0997489 | ||||||||
\(337\) | 14.1005 | 0.768103 | 0.384052 | − | 0.923312i | \(-0.374528\pi\) | ||||
0.384052 | + | 0.923312i | \(0.374528\pi\) | |||||||
\(338\) | −20.9706 | −1.14065 | ||||||||
\(339\) | 4.24264 | 0.230429 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.82843 | −0.478086 | ||||||||
\(342\) | −2.82843 | −0.152944 | ||||||||
\(343\) | 24.2132 | 1.30739 | ||||||||
\(344\) | −1.75736 | −0.0947505 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.485281 | −0.0260889 | ||||||||
\(347\) | −5.51472 | −0.296046 | −0.148023 | − | 0.988984i | \(-0.547291\pi\) | ||||
−0.148023 | + | 0.988984i | \(0.547291\pi\) | |||||||
\(348\) | 0.0710678 | 0.00380963 | ||||||||
\(349\) | 6.00000 | 0.321173 | 0.160586 | − | 0.987022i | \(-0.448662\pi\) | ||||
0.160586 | + | 0.987022i | \(0.448662\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.0711 | 0.751058 | ||||||||
\(352\) | 1.41421 | 0.0753778 | ||||||||
\(353\) | −2.51472 | −0.133845 | −0.0669225 | − | 0.997758i | \(-0.521318\pi\) | ||||
−0.0669225 | + | 0.997758i | \(0.521318\pi\) | |||||||
\(354\) | 2.85786 | 0.151894 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 7.07107 | 0.374766 | ||||||||
\(357\) | −1.82843 | −0.0967706 | ||||||||
\(358\) | 11.6569 | 0.616084 | ||||||||
\(359\) | −22.7574 | −1.20109 | −0.600544 | − | 0.799592i | \(-0.705049\pi\) | ||||
−0.600544 | + | 0.799592i | \(0.705049\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 8.48528 | 0.445976 | ||||||||
\(363\) | 3.72792 | 0.195665 | ||||||||
\(364\) | 25.7279 | 1.34851 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5.89949 | 0.308372 | ||||||||
\(367\) | −25.4558 | −1.32878 | −0.664392 | − | 0.747384i | \(-0.731309\pi\) | ||||
−0.664392 | + | 0.747384i | \(0.731309\pi\) | |||||||
\(368\) | 0.757359 | 0.0394801 | ||||||||
\(369\) | 12.0000 | 0.624695 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.2132 | 1.25709 | ||||||||
\(372\) | −2.58579 | −0.134067 | ||||||||
\(373\) | 9.00000 | 0.466002 | 0.233001 | − | 0.972476i | \(-0.425145\pi\) | ||||
0.233001 | + | 0.972476i | \(0.425145\pi\) | |||||||
\(374\) | 1.41421 | 0.0731272 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.00000 | −0.0515026 | ||||||||
\(378\) | −10.6569 | −0.548129 | ||||||||
\(379\) | 11.2426 | 0.577496 | 0.288748 | − | 0.957405i | \(-0.406761\pi\) | ||||
0.288748 | + | 0.957405i | \(0.406761\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.02944 | 0.0527397 | ||||||||
\(382\) | −12.5563 | −0.642439 | ||||||||
\(383\) | 12.2426 | 0.625570 | 0.312785 | − | 0.949824i | \(-0.398738\pi\) | ||||
0.312785 | + | 0.949824i | \(0.398738\pi\) | |||||||
\(384\) | 0.414214 | 0.0211377 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.343146 | 0.0174657 | ||||||||
\(387\) | −4.97056 | −0.252668 | ||||||||
\(388\) | −0.343146 | −0.0174206 | ||||||||
\(389\) | 22.9289 | 1.16254 | 0.581272 | − | 0.813710i | \(-0.302555\pi\) | ||||
0.581272 | + | 0.813710i | \(0.302555\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.757359 | 0.0383013 | ||||||||
\(392\) | −12.4853 | −0.630602 | ||||||||
\(393\) | 7.02944 | 0.354588 | ||||||||
\(394\) | 11.7574 | 0.592327 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.00000 | 0.201008 | ||||||||
\(397\) | 24.0000 | 1.20453 | 0.602263 | − | 0.798298i | \(-0.294266\pi\) | ||||
0.602263 | + | 0.798298i | \(0.294266\pi\) | |||||||
\(398\) | −9.24264 | −0.463292 | ||||||||
\(399\) | 1.82843 | 0.0915358 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.4142 | −1.26913 | −0.634563 | − | 0.772871i | \(-0.718820\pi\) | ||||
−0.634563 | + | 0.772871i | \(0.718820\pi\) | |||||||
\(402\) | 1.97056 | 0.0982827 | ||||||||
\(403\) | 36.3848 | 1.81245 | ||||||||
\(404\) | 13.0711 | 0.650310 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.757359 | 0.0375871 | ||||||||
\(407\) | 12.0000 | 0.594818 | ||||||||
\(408\) | 0.414214 | 0.0205066 | ||||||||
\(409\) | 25.2132 | 1.24671 | 0.623356 | − | 0.781938i | \(-0.285769\pi\) | ||||
0.623356 | + | 0.781938i | \(0.285769\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.38478 | −0.265611 | ||||||||
\(412\) | 4.24264 | 0.209020 | ||||||||
\(413\) | 30.4558 | 1.49863 | ||||||||
\(414\) | 2.14214 | 0.105280 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.82843 | −0.285762 | ||||||||
\(417\) | 4.97056 | 0.243410 | ||||||||
\(418\) | −1.41421 | −0.0691714 | ||||||||
\(419\) | 19.4142 | 0.948446 | 0.474223 | − | 0.880405i | \(-0.342729\pi\) | ||||
0.474223 | + | 0.880405i | \(0.342729\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.4853 | 0.949655 | 0.474827 | − | 0.880079i | \(-0.342511\pi\) | ||||
0.474827 | + | 0.880079i | \(0.342511\pi\) | |||||||
\(422\) | 19.7279 | 0.960340 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.48528 | −0.266389 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.55635 | −0.269206 | ||||||||
\(427\) | 62.8701 | 3.04250 | ||||||||
\(428\) | 19.7279 | 0.953585 | ||||||||
\(429\) | 3.41421 | 0.164840 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.38478 | −0.307544 | −0.153772 | − | 0.988106i | \(-0.549142\pi\) | ||||
−0.153772 | + | 0.988106i | \(0.549142\pi\) | |||||||
\(432\) | 2.41421 | 0.116154 | ||||||||
\(433\) | −9.55635 | −0.459249 | −0.229624 | − | 0.973279i | \(-0.573750\pi\) | ||||
−0.229624 | + | 0.973279i | \(0.573750\pi\) | |||||||
\(434\) | −27.5563 | −1.32275 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −17.9706 | −0.860634 | ||||||||
\(437\) | −0.757359 | −0.0362294 | ||||||||
\(438\) | 4.75736 | 0.227315 | ||||||||
\(439\) | −5.75736 | −0.274784 | −0.137392 | − | 0.990517i | \(-0.543872\pi\) | ||||
−0.137392 | + | 0.990517i | \(0.543872\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −35.3137 | −1.68161 | ||||||||
\(442\) | −5.82843 | −0.277230 | ||||||||
\(443\) | 4.24264 | 0.201574 | 0.100787 | − | 0.994908i | \(-0.467864\pi\) | ||||
0.100787 | + | 0.994908i | \(0.467864\pi\) | |||||||
\(444\) | 3.51472 | 0.166801 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 15.1716 | 0.718395 | ||||||||
\(447\) | −7.31371 | −0.345927 | ||||||||
\(448\) | 4.41421 | 0.208552 | ||||||||
\(449\) | 17.3137 | 0.817084 | 0.408542 | − | 0.912739i | \(-0.366037\pi\) | ||||
0.408542 | + | 0.912739i | \(0.366037\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.00000 | 0.282529 | ||||||||
\(452\) | −10.2426 | −0.481773 | ||||||||
\(453\) | 4.34315 | 0.204059 | ||||||||
\(454\) | 16.7574 | 0.786462 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.414214 | −0.0193973 | ||||||||
\(457\) | −3.00000 | −0.140334 | −0.0701670 | − | 0.997535i | \(-0.522353\pi\) | ||||
−0.0701670 | + | 0.997535i | \(0.522353\pi\) | |||||||
\(458\) | −14.9706 | −0.699528 | ||||||||
\(459\) | 2.41421 | 0.112686 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.55635 | −0.165636 | −0.0828178 | − | 0.996565i | \(-0.526392\pi\) | ||||
−0.0828178 | + | 0.996565i | \(0.526392\pi\) | |||||||
\(462\) | −2.58579 | −0.120302 | ||||||||
\(463\) | 14.1421 | 0.657241 | 0.328620 | − | 0.944462i | \(-0.393416\pi\) | ||||
0.328620 | + | 0.944462i | \(0.393416\pi\) | |||||||
\(464\) | −0.171573 | −0.00796507 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 24.9706 | 1.15674 | ||||||||
\(467\) | 0.727922 | 0.0336842 | 0.0168421 | − | 0.999858i | \(-0.494639\pi\) | ||||
0.0168421 | + | 0.999858i | \(0.494639\pi\) | |||||||
\(468\) | −16.4853 | −0.762032 | ||||||||
\(469\) | 21.0000 | 0.969690 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.82843 | −0.222482 | ||||||||
\(472\) | −6.89949 | −0.317575 | ||||||||
\(473\) | −2.48528 | −0.114273 | ||||||||
\(474\) | −2.68629 | −0.123385 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.41421 | 0.202325 | ||||||||
\(477\) | −15.5147 | −0.710370 | ||||||||
\(478\) | 6.89949 | 0.315576 | ||||||||
\(479\) | −31.1127 | −1.42158 | −0.710788 | − | 0.703407i | \(-0.751661\pi\) | ||||
−0.710788 | + | 0.703407i | \(0.751661\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −49.4558 | −2.25499 | ||||||||
\(482\) | −8.97056 | −0.408598 | ||||||||
\(483\) | −1.38478 | −0.0630095 | ||||||||
\(484\) | −9.00000 | −0.409091 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 10.3431 | 0.469175 | ||||||||
\(487\) | 37.7990 | 1.71284 | 0.856418 | − | 0.516283i | \(-0.172685\pi\) | ||||
0.856418 | + | 0.516283i | \(0.172685\pi\) | |||||||
\(488\) | −14.2426 | −0.644734 | ||||||||
\(489\) | 4.24264 | 0.191859 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.5563 | −1.51438 | −0.757188 | − | 0.653197i | \(-0.773428\pi\) | ||||
−0.757188 | + | 0.653197i | \(0.773428\pi\) | |||||||
\(492\) | 1.75736 | 0.0792279 | ||||||||
\(493\) | −0.171573 | −0.00772725 | ||||||||
\(494\) | 5.82843 | 0.262233 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.24264 | 0.280303 | ||||||||
\(497\) | −59.2132 | −2.65608 | ||||||||
\(498\) | 6.00000 | 0.268866 | ||||||||
\(499\) | −25.7574 | −1.15306 | −0.576529 | − | 0.817077i | \(-0.695593\pi\) | ||||
−0.576529 | + | 0.817077i | \(0.695593\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.55635 | 0.337593 | ||||||||
\(502\) | −3.55635 | −0.158728 | ||||||||
\(503\) | 14.2721 | 0.636361 | 0.318180 | − | 0.948030i | \(-0.396928\pi\) | ||||
0.318180 | + | 0.948030i | \(0.396928\pi\) | |||||||
\(504\) | 12.4853 | 0.556139 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.07107 | 0.0476148 | ||||||||
\(507\) | −8.68629 | −0.385772 | ||||||||
\(508\) | −2.48528 | −0.110267 | ||||||||
\(509\) | 28.9706 | 1.28410 | 0.642049 | − | 0.766664i | \(-0.278085\pi\) | ||||
0.642049 | + | 0.766664i | \(0.278085\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 50.6985 | 2.24277 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −2.41421 | −0.106590 | ||||||||
\(514\) | −20.7279 | −0.914269 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.727922 | −0.0320450 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 37.4558 | 1.64572 | ||||||||
\(519\) | −0.201010 | −0.00882337 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.3137 | 1.02139 | 0.510696 | − | 0.859761i | \(-0.329388\pi\) | ||||
0.510696 | + | 0.859761i | \(0.329388\pi\) | |||||||
\(522\) | −0.485281 | −0.0212402 | ||||||||
\(523\) | −2.27208 | −0.0993510 | −0.0496755 | − | 0.998765i | \(-0.515819\pi\) | ||||
−0.0496755 | + | 0.998765i | \(0.515819\pi\) | |||||||
\(524\) | −16.9706 | −0.741362 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 26.9706 | 1.17597 | ||||||||
\(527\) | 6.24264 | 0.271934 | ||||||||
\(528\) | 0.585786 | 0.0254931 | ||||||||
\(529\) | −22.4264 | −0.975061 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −19.5147 | −0.846867 | ||||||||
\(532\) | −4.41421 | −0.191380 | ||||||||
\(533\) | −24.7279 | −1.07109 | ||||||||
\(534\) | 2.92893 | 0.126747 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.75736 | −0.205487 | ||||||||
\(537\) | 4.82843 | 0.208362 | ||||||||
\(538\) | 16.6274 | 0.716859 | ||||||||
\(539\) | −17.6569 | −0.760535 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.75736 | 0.419502 | 0.209751 | − | 0.977755i | \(-0.432735\pi\) | ||||
0.209751 | + | 0.977755i | \(0.432735\pi\) | |||||||
\(542\) | 27.2426 | 1.17017 | ||||||||
\(543\) | 3.51472 | 0.150831 | ||||||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 10.6569 | 0.456071 | ||||||||
\(547\) | −17.3137 | −0.740281 | −0.370140 | − | 0.928976i | \(-0.620690\pi\) | ||||
−0.370140 | + | 0.928976i | \(0.620690\pi\) | |||||||
\(548\) | 13.0000 | 0.555332 | ||||||||
\(549\) | −40.2843 | −1.71929 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.171573 | 0.00730925 | ||||||||
\(552\) | 0.313708 | 0.0133523 | ||||||||
\(553\) | −28.6274 | −1.21736 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.0000 | −0.508913 | ||||||||
\(557\) | 16.0000 | 0.677942 | 0.338971 | − | 0.940797i | \(-0.389921\pi\) | ||||
0.338971 | + | 0.940797i | \(0.389921\pi\) | |||||||
\(558\) | 17.6569 | 0.747474 | ||||||||
\(559\) | 10.2426 | 0.433218 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.585786 | 0.0247319 | ||||||||
\(562\) | −4.24264 | −0.178965 | ||||||||
\(563\) | 4.97056 | 0.209484 | 0.104742 | − | 0.994499i | \(-0.466598\pi\) | ||||
0.104742 | + | 0.994499i | \(0.466598\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −32.1421 | −1.35103 | ||||||||
\(567\) | 33.0416 | 1.38762 | ||||||||
\(568\) | 13.4142 | 0.562848 | ||||||||
\(569\) | −28.2843 | −1.18574 | −0.592869 | − | 0.805299i | \(-0.702005\pi\) | ||||
−0.592869 | + | 0.805299i | \(0.702005\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.24264 | −0.0938516 | −0.0469258 | − | 0.998898i | \(-0.514942\pi\) | ||||
−0.0469258 | + | 0.998898i | \(0.514942\pi\) | |||||||
\(572\) | −8.24264 | −0.344642 | ||||||||
\(573\) | −5.20101 | −0.217275 | ||||||||
\(574\) | 18.7279 | 0.781688 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.82843 | −0.117851 | ||||||||
\(577\) | −20.3137 | −0.845671 | −0.422835 | − | 0.906207i | \(-0.638965\pi\) | ||||
−0.422835 | + | 0.906207i | \(0.638965\pi\) | |||||||
\(578\) | 16.0000 | 0.665512 | ||||||||
\(579\) | 0.142136 | 0.00590695 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 63.9411 | 2.65272 | ||||||||
\(582\) | −0.142136 | −0.00589171 | ||||||||
\(583\) | −7.75736 | −0.321277 | ||||||||
\(584\) | −11.4853 | −0.475264 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.48528 | 0.226595 | ||||||||
\(587\) | 30.2426 | 1.24825 | 0.624124 | − | 0.781326i | \(-0.285456\pi\) | ||||
0.624124 | + | 0.781326i | \(0.285456\pi\) | |||||||
\(588\) | −5.17157 | −0.213272 | ||||||||
\(589\) | −6.24264 | −0.257224 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.87006 | 0.200327 | ||||||||
\(592\) | −8.48528 | −0.348743 | ||||||||
\(593\) | 22.0000 | 0.903432 | 0.451716 | − | 0.892162i | \(-0.350812\pi\) | ||||
0.451716 | + | 0.892162i | \(0.350812\pi\) | |||||||
\(594\) | 3.41421 | 0.140087 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17.6569 | 0.723253 | ||||||||
\(597\) | −3.82843 | −0.156687 | ||||||||
\(598\) | −4.41421 | −0.180511 | ||||||||
\(599\) | −15.2132 | −0.621595 | −0.310797 | − | 0.950476i | \(-0.600596\pi\) | ||||
−0.310797 | + | 0.950476i | \(0.600596\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.2426 | −0.825715 | −0.412857 | − | 0.910796i | \(-0.635469\pi\) | ||||
−0.412857 | + | 0.910796i | \(0.635469\pi\) | |||||||
\(602\) | −7.75736 | −0.316166 | ||||||||
\(603\) | −13.4558 | −0.547964 | ||||||||
\(604\) | −10.4853 | −0.426640 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.41421 | 0.219937 | ||||||||
\(607\) | 3.17157 | 0.128730 | 0.0643651 | − | 0.997926i | \(-0.479498\pi\) | ||||
0.0643651 | + | 0.997926i | \(0.479498\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 0.313708 | 0.0127121 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2.82843 | −0.114332 | ||||||||
\(613\) | −11.6985 | −0.472497 | −0.236249 | − | 0.971693i | \(-0.575918\pi\) | ||||
−0.236249 | + | 0.971693i | \(0.575918\pi\) | |||||||
\(614\) | 17.6569 | 0.712573 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.24264 | 0.251523 | ||||||||
\(617\) | −4.48528 | −0.180571 | −0.0902853 | − | 0.995916i | \(-0.528778\pi\) | ||||
−0.0902853 | + | 0.995916i | \(0.528778\pi\) | |||||||
\(618\) | 1.75736 | 0.0706914 | ||||||||
\(619\) | 7.75736 | 0.311795 | 0.155897 | − | 0.987773i | \(-0.450173\pi\) | ||||
0.155897 | + | 0.987773i | \(0.450173\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.82843 | 0.0733723 | ||||||||
\(622\) | 4.75736 | 0.190753 | ||||||||
\(623\) | 31.2132 | 1.25053 | ||||||||
\(624\) | −2.41421 | −0.0966459 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7.97056 | 0.318568 | ||||||||
\(627\) | −0.585786 | −0.0233941 | ||||||||
\(628\) | 11.6569 | 0.465159 | ||||||||
\(629\) | −8.48528 | −0.338330 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.9706 | −1.55139 | −0.775697 | − | 0.631106i | \(-0.782601\pi\) | ||||
−0.775697 | + | 0.631106i | \(0.782601\pi\) | |||||||
\(632\) | 6.48528 | 0.257971 | ||||||||
\(633\) | 8.17157 | 0.324791 | ||||||||
\(634\) | 9.48528 | 0.376709 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.27208 | −0.0900938 | ||||||||
\(637\) | 72.7696 | 2.88323 | ||||||||
\(638\) | −0.242641 | −0.00960624 | ||||||||
\(639\) | 37.9411 | 1.50093 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.0416 | −0.712602 | −0.356301 | − | 0.934371i | \(-0.615962\pi\) | ||||
−0.356301 | + | 0.934371i | \(0.615962\pi\) | |||||||
\(642\) | 8.17157 | 0.322506 | ||||||||
\(643\) | −14.4853 | −0.571244 | −0.285622 | − | 0.958342i | \(-0.592200\pi\) | ||||
−0.285622 | + | 0.958342i | \(0.592200\pi\) | |||||||
\(644\) | 3.34315 | 0.131738 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.00000 | 0.0393445 | ||||||||
\(647\) | −18.7574 | −0.737428 | −0.368714 | − | 0.929543i | \(-0.620202\pi\) | ||||
−0.368714 | + | 0.929543i | \(0.620202\pi\) | |||||||
\(648\) | −7.48528 | −0.294050 | ||||||||
\(649\) | −9.75736 | −0.383010 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.4142 | −0.447358 | ||||||||
\(652\) | −10.2426 | −0.401133 | ||||||||
\(653\) | −28.9706 | −1.13371 | −0.566853 | − | 0.823819i | \(-0.691839\pi\) | ||||
−0.566853 | + | 0.823819i | \(0.691839\pi\) | |||||||
\(654\) | −7.44365 | −0.291070 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.24264 | −0.165647 | ||||||||
\(657\) | −32.4853 | −1.26737 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.8995 | 0.736220 | 0.368110 | − | 0.929782i | \(-0.380005\pi\) | ||||
0.368110 | + | 0.929782i | \(0.380005\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.4558 | −0.717849 | −0.358925 | − | 0.933367i | \(-0.616856\pi\) | ||||
−0.358925 | + | 0.933367i | \(0.616856\pi\) | |||||||
\(662\) | 19.2426 | 0.747886 | ||||||||
\(663\) | −2.41421 | −0.0937603 | ||||||||
\(664\) | −14.4853 | −0.562138 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −24.0000 | −0.929981 | ||||||||
\(667\) | −0.129942 | −0.00503139 | ||||||||
\(668\) | −18.2426 | −0.705829 | ||||||||
\(669\) | 6.28427 | 0.242964 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20.1421 | −0.777579 | ||||||||
\(672\) | 1.82843 | 0.0705331 | ||||||||
\(673\) | −12.0000 | −0.462566 | −0.231283 | − | 0.972887i | \(-0.574292\pi\) | ||||
−0.231283 | + | 0.972887i | \(0.574292\pi\) | |||||||
\(674\) | −14.1005 | −0.543131 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 20.9706 | 0.806560 | ||||||||
\(677\) | −40.9411 | −1.57350 | −0.786748 | − | 0.617275i | \(-0.788237\pi\) | ||||
−0.786748 | + | 0.617275i | \(0.788237\pi\) | |||||||
\(678\) | −4.24264 | −0.162938 | ||||||||
\(679\) | −1.51472 | −0.0581296 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.94113 | 0.265985 | ||||||||
\(682\) | 8.82843 | 0.338058 | ||||||||
\(683\) | 12.0000 | 0.459167 | 0.229584 | − | 0.973289i | \(-0.426264\pi\) | ||||
0.229584 | + | 0.973289i | \(0.426264\pi\) | |||||||
\(684\) | 2.82843 | 0.108148 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −24.2132 | −0.924464 | ||||||||
\(687\) | −6.20101 | −0.236583 | ||||||||
\(688\) | 1.75736 | 0.0669987 | ||||||||
\(689\) | 31.9706 | 1.21798 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.4853 | 0.855380 | 0.427690 | − | 0.903925i | \(-0.359327\pi\) | ||||
0.427690 | + | 0.903925i | \(0.359327\pi\) | |||||||
\(692\) | 0.485281 | 0.0184476 | ||||||||
\(693\) | 17.6569 | 0.670728 | ||||||||
\(694\) | 5.51472 | 0.209336 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.0710678 | −0.00269382 | ||||||||
\(697\) | −4.24264 | −0.160701 | ||||||||
\(698\) | −6.00000 | −0.227103 | ||||||||
\(699\) | 10.3431 | 0.391214 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.9706 | 0.640969 | 0.320485 | − | 0.947254i | \(-0.396154\pi\) | ||||
0.320485 | + | 0.947254i | \(0.396154\pi\) | |||||||
\(702\) | −14.0711 | −0.531078 | ||||||||
\(703\) | 8.48528 | 0.320028 | ||||||||
\(704\) | −1.41421 | −0.0533002 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.51472 | 0.0946427 | ||||||||
\(707\) | 57.6985 | 2.16997 | ||||||||
\(708\) | −2.85786 | −0.107405 | ||||||||
\(709\) | −34.0000 | −1.27690 | −0.638448 | − | 0.769665i | \(-0.720423\pi\) | ||||
−0.638448 | + | 0.769665i | \(0.720423\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 18.3431 | 0.687922 | ||||||||
\(712\) | −7.07107 | −0.264999 | ||||||||
\(713\) | 4.72792 | 0.177062 | ||||||||
\(714\) | 1.82843 | 0.0684272 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11.6569 | −0.435637 | ||||||||
\(717\) | 2.85786 | 0.106729 | ||||||||
\(718\) | 22.7574 | 0.849297 | ||||||||
\(719\) | −5.10051 | −0.190217 | −0.0951084 | − | 0.995467i | \(-0.530320\pi\) | ||||
−0.0951084 | + | 0.995467i | \(0.530320\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.7279 | 0.697464 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −3.71573 | −0.138189 | ||||||||
\(724\) | −8.48528 | −0.315353 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.72792 | −0.138356 | ||||||||
\(727\) | 9.72792 | 0.360789 | 0.180394 | − | 0.983594i | \(-0.442263\pi\) | ||||
0.180394 | + | 0.983594i | \(0.442263\pi\) | |||||||
\(728\) | −25.7279 | −0.953540 | ||||||||
\(729\) | −18.1716 | −0.673021 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.75736 | 0.0649983 | ||||||||
\(732\) | −5.89949 | −0.218052 | ||||||||
\(733\) | 12.0000 | 0.443230 | 0.221615 | − | 0.975134i | \(-0.428867\pi\) | ||||
0.221615 | + | 0.975134i | \(0.428867\pi\) | |||||||
\(734\) | 25.4558 | 0.939592 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.757359 | −0.0279166 | ||||||||
\(737\) | −6.72792 | −0.247826 | ||||||||
\(738\) | −12.0000 | −0.441726 | ||||||||
\(739\) | 1.27208 | 0.0467941 | 0.0233971 | − | 0.999726i | \(-0.492552\pi\) | ||||
0.0233971 | + | 0.999726i | \(0.492552\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.41421 | 0.0886884 | ||||||||
\(742\) | −24.2132 | −0.888895 | ||||||||
\(743\) | 6.72792 | 0.246824 | 0.123412 | − | 0.992356i | \(-0.460616\pi\) | ||||
0.123412 | + | 0.992356i | \(0.460616\pi\) | |||||||
\(744\) | 2.58579 | 0.0947995 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9.00000 | −0.329513 | ||||||||
\(747\) | −40.9706 | −1.49903 | ||||||||
\(748\) | −1.41421 | −0.0517088 | ||||||||
\(749\) | 87.0833 | 3.18195 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.7279 | −0.975316 | −0.487658 | − | 0.873035i | \(-0.662149\pi\) | ||||
−0.487658 | + | 0.873035i | \(0.662149\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.47309 | −0.0536823 | ||||||||
\(754\) | 1.00000 | 0.0364179 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 10.6569 | 0.387586 | ||||||||
\(757\) | 12.3431 | 0.448619 | 0.224310 | − | 0.974518i | \(-0.427987\pi\) | ||||
0.224310 | + | 0.974518i | \(0.427987\pi\) | |||||||
\(758\) | −11.2426 | −0.408351 | ||||||||
\(759\) | 0.443651 | 0.0161035 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 43.9706 | 1.59393 | 0.796966 | − | 0.604024i | \(-0.206437\pi\) | ||||
0.796966 | + | 0.604024i | \(0.206437\pi\) | |||||||
\(762\) | −1.02944 | −0.0372926 | ||||||||
\(763\) | −79.3259 | −2.87179 | ||||||||
\(764\) | 12.5563 | 0.454273 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12.2426 | −0.442345 | ||||||||
\(767\) | 40.2132 | 1.45201 | ||||||||
\(768\) | −0.414214 | −0.0149466 | ||||||||
\(769\) | −36.4558 | −1.31463 | −0.657316 | − | 0.753615i | \(-0.728308\pi\) | ||||
−0.657316 | + | 0.753615i | \(0.728308\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.58579 | −0.309210 | ||||||||
\(772\) | −0.343146 | −0.0123501 | ||||||||
\(773\) | 13.9706 | 0.502486 | 0.251243 | − | 0.967924i | \(-0.419161\pi\) | ||||
0.251243 | + | 0.967924i | \(0.419161\pi\) | |||||||
\(774\) | 4.97056 | 0.178663 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.343146 | 0.0123182 | ||||||||
\(777\) | 15.5147 | 0.556587 | ||||||||
\(778\) | −22.9289 | −0.822042 | ||||||||
\(779\) | 4.24264 | 0.152008 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.9706 | 0.678820 | ||||||||
\(782\) | −0.757359 | −0.0270831 | ||||||||
\(783\) | −0.414214 | −0.0148028 | ||||||||
\(784\) | 12.4853 | 0.445903 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −7.02944 | −0.250732 | ||||||||
\(787\) | −41.1838 | −1.46804 | −0.734021 | − | 0.679126i | \(-0.762359\pi\) | ||||
−0.734021 | + | 0.679126i | \(0.762359\pi\) | |||||||
\(788\) | −11.7574 | −0.418839 | ||||||||
\(789\) | 11.1716 | 0.397719 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −45.2132 | −1.60760 | ||||||||
\(792\) | −4.00000 | −0.142134 | ||||||||
\(793\) | 83.0122 | 2.94785 | ||||||||
\(794\) | −24.0000 | −0.851728 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.24264 | 0.327597 | ||||||||
\(797\) | −47.4853 | −1.68201 | −0.841007 | − | 0.541023i | \(-0.818037\pi\) | ||||
−0.841007 | + | 0.541023i | \(0.818037\pi\) | |||||||
\(798\) | −1.82843 | −0.0647256 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −20.0000 | −0.706665 | ||||||||
\(802\) | 25.4142 | 0.897407 | ||||||||
\(803\) | −16.2426 | −0.573190 | ||||||||
\(804\) | −1.97056 | −0.0694964 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −36.3848 | −1.28160 | ||||||||
\(807\) | 6.88730 | 0.242444 | ||||||||
\(808\) | −13.0711 | −0.459839 | ||||||||
\(809\) | −28.7990 | −1.01252 | −0.506259 | − | 0.862381i | \(-0.668972\pi\) | ||||
−0.506259 | + | 0.862381i | \(0.668972\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 52.6985 | 1.85049 | 0.925247 | − | 0.379365i | \(-0.123858\pi\) | ||||
0.925247 | + | 0.379365i | \(0.123858\pi\) | |||||||
\(812\) | −0.757359 | −0.0265781 | ||||||||
\(813\) | 11.2843 | 0.395757 | ||||||||
\(814\) | −12.0000 | −0.420600 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.414214 | −0.0145004 | ||||||||
\(817\) | −1.75736 | −0.0614822 | ||||||||
\(818\) | −25.2132 | −0.881559 | ||||||||
\(819\) | −72.7696 | −2.54277 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.34315 | 0.221377 | 0.110689 | − | 0.993855i | \(-0.464694\pi\) | ||||
0.110689 | + | 0.993855i | \(0.464694\pi\) | |||||||
\(822\) | 5.38478 | 0.187816 | ||||||||
\(823\) | −15.7279 | −0.548241 | −0.274120 | − | 0.961695i | \(-0.588387\pi\) | ||||
−0.274120 | + | 0.961695i | \(0.588387\pi\) | |||||||
\(824\) | −4.24264 | −0.147799 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −30.4558 | −1.05969 | ||||||||
\(827\) | −20.6985 | −0.719757 | −0.359878 | − | 0.932999i | \(-0.617182\pi\) | ||||
−0.359878 | + | 0.932999i | \(0.617182\pi\) | |||||||
\(828\) | −2.14214 | −0.0744444 | ||||||||
\(829\) | 10.4558 | 0.363146 | 0.181573 | − | 0.983377i | \(-0.441881\pi\) | ||||
0.181573 | + | 0.983377i | \(0.441881\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.82843 | 0.202064 | ||||||||
\(833\) | 12.4853 | 0.432589 | ||||||||
\(834\) | −4.97056 | −0.172117 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.41421 | 0.0489116 | ||||||||
\(837\) | 15.0711 | 0.520932 | ||||||||
\(838\) | −19.4142 | −0.670653 | ||||||||
\(839\) | 22.6274 | 0.781185 | 0.390593 | − | 0.920564i | \(-0.372270\pi\) | ||||
0.390593 | + | 0.920564i | \(0.372270\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9706 | −0.998985 | ||||||||
\(842\) | −19.4853 | −0.671507 | ||||||||
\(843\) | −1.75736 | −0.0605267 | ||||||||
\(844\) | −19.7279 | −0.679063 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −39.7279 | −1.36507 | ||||||||
\(848\) | 5.48528 | 0.188365 | ||||||||
\(849\) | −13.3137 | −0.456925 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.42641 | −0.220294 | ||||||||
\(852\) | 5.55635 | 0.190357 | ||||||||
\(853\) | −27.9411 | −0.956686 | −0.478343 | − | 0.878173i | \(-0.658762\pi\) | ||||
−0.478343 | + | 0.878173i | \(0.658762\pi\) | |||||||
\(854\) | −62.8701 | −2.15137 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −19.7279 | −0.674286 | ||||||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | −3.41421 | −0.116559 | ||||||||
\(859\) | 4.72792 | 0.161315 | 0.0806573 | − | 0.996742i | \(-0.474298\pi\) | ||||
0.0806573 | + | 0.996742i | \(0.474298\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.75736 | 0.264370 | ||||||||
\(862\) | 6.38478 | 0.217466 | ||||||||
\(863\) | 0.727922 | 0.0247788 | 0.0123894 | − | 0.999923i | \(-0.496056\pi\) | ||||
0.0123894 | + | 0.999923i | \(0.496056\pi\) | |||||||
\(864\) | −2.41421 | −0.0821332 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 9.55635 | 0.324738 | ||||||||
\(867\) | 6.62742 | 0.225079 | ||||||||
\(868\) | 27.5563 | 0.935323 | ||||||||
\(869\) | 9.17157 | 0.311124 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.7279 | 0.939525 | ||||||||
\(872\) | 17.9706 | 0.608560 | ||||||||
\(873\) | 0.970563 | 0.0328486 | ||||||||
\(874\) | 0.757359 | 0.0256181 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.75736 | −0.160736 | ||||||||
\(877\) | −18.8579 | −0.636785 | −0.318392 | − | 0.947959i | \(-0.603143\pi\) | ||||
−0.318392 | + | 0.947959i | \(0.603143\pi\) | |||||||
\(878\) | 5.75736 | 0.194301 | ||||||||
\(879\) | 2.27208 | 0.0766353 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.5980 | −1.33409 | −0.667045 | − | 0.745018i | \(-0.732441\pi\) | ||||
−0.667045 | + | 0.745018i | \(0.732441\pi\) | |||||||
\(882\) | 35.3137 | 1.18907 | ||||||||
\(883\) | 14.4853 | 0.487469 | 0.243734 | − | 0.969842i | \(-0.421628\pi\) | ||||
0.243734 | + | 0.969842i | \(0.421628\pi\) | |||||||
\(884\) | 5.82843 | 0.196031 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.24264 | −0.142534 | ||||||||
\(887\) | −45.2132 | −1.51811 | −0.759055 | − | 0.651026i | \(-0.774339\pi\) | ||||
−0.759055 | + | 0.651026i | \(0.774339\pi\) | |||||||
\(888\) | −3.51472 | −0.117946 | ||||||||
\(889\) | −10.9706 | −0.367941 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.5858 | −0.354637 | ||||||||
\(892\) | −15.1716 | −0.507982 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 7.31371 | 0.244607 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.41421 | −0.147469 | ||||||||
\(897\) | −1.82843 | −0.0610494 | ||||||||
\(898\) | −17.3137 | −0.577766 | ||||||||
\(899\) | −1.07107 | −0.0357221 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.48528 | 0.182741 | ||||||||
\(902\) | −6.00000 | −0.199778 | ||||||||
\(903\) | −3.21320 | −0.106929 | ||||||||
\(904\) | 10.2426 | 0.340665 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.34315 | −0.144291 | ||||||||
\(907\) | 38.6985 | 1.28496 | 0.642481 | − | 0.766302i | \(-0.277905\pi\) | ||||
0.642481 | + | 0.766302i | \(0.277905\pi\) | |||||||
\(908\) | −16.7574 | −0.556113 | ||||||||
\(909\) | −36.9706 | −1.22624 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.2843 | 1.33468 | 0.667339 | − | 0.744754i | \(-0.267433\pi\) | ||||
0.667339 | + | 0.744754i | \(0.267433\pi\) | |||||||
\(912\) | 0.414214 | 0.0137160 | ||||||||
\(913\) | −20.4853 | −0.677964 | ||||||||
\(914\) | 3.00000 | 0.0992312 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.9706 | 0.494641 | ||||||||
\(917\) | −74.9117 | −2.47380 | ||||||||
\(918\) | −2.41421 | −0.0796809 | ||||||||
\(919\) | −6.21320 | −0.204955 | −0.102477 | − | 0.994735i | \(-0.532677\pi\) | ||||
−0.102477 | + | 0.994735i | \(0.532677\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.31371 | 0.240995 | ||||||||
\(922\) | 3.55635 | 0.117122 | ||||||||
\(923\) | −78.1838 | −2.57345 | ||||||||
\(924\) | 2.58579 | 0.0850661 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −14.1421 | −0.464739 | ||||||||
\(927\) | −12.0000 | −0.394132 | ||||||||
\(928\) | 0.171573 | 0.00563216 | ||||||||
\(929\) | −12.1716 | −0.399336 | −0.199668 | − | 0.979864i | \(-0.563986\pi\) | ||||
−0.199668 | + | 0.979864i | \(0.563986\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.4853 | −0.409189 | ||||||||
\(932\) | −24.9706 | −0.817938 | ||||||||
\(933\) | 1.97056 | 0.0645133 | ||||||||
\(934\) | −0.727922 | −0.0238183 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 16.4853 | 0.538838 | ||||||||
\(937\) | 27.0000 | 0.882052 | 0.441026 | − | 0.897494i | \(-0.354615\pi\) | ||||
0.441026 | + | 0.897494i | \(0.354615\pi\) | |||||||
\(938\) | −21.0000 | −0.685674 | ||||||||
\(939\) | 3.30152 | 0.107741 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 53.1421 | 1.73238 | 0.866192 | − | 0.499711i | \(-0.166561\pi\) | ||||
0.866192 | + | 0.499711i | \(0.166561\pi\) | |||||||
\(942\) | 4.82843 | 0.157319 | ||||||||
\(943\) | −3.21320 | −0.104636 | ||||||||
\(944\) | 6.89949 | 0.224559 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.48528 | 0.0808035 | ||||||||
\(947\) | −12.0000 | −0.389948 | −0.194974 | − | 0.980808i | \(-0.562462\pi\) | ||||
−0.194974 | + | 0.980808i | \(0.562462\pi\) | |||||||
\(948\) | 2.68629 | 0.0872467 | ||||||||
\(949\) | 66.9411 | 2.17300 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.92893 | 0.127404 | ||||||||
\(952\) | −4.41421 | −0.143065 | ||||||||
\(953\) | 18.7279 | 0.606657 | 0.303328 | − | 0.952886i | \(-0.401902\pi\) | ||||
0.303328 | + | 0.952886i | \(0.401902\pi\) | |||||||
\(954\) | 15.5147 | 0.502308 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6.89949 | −0.223146 | ||||||||
\(957\) | −0.100505 | −0.00324887 | ||||||||
\(958\) | 31.1127 | 1.00521 | ||||||||
\(959\) | 57.3848 | 1.85305 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.97056 | 0.257115 | ||||||||
\(962\) | 49.4558 | 1.59452 | ||||||||
\(963\) | −55.7990 | −1.79810 | ||||||||
\(964\) | 8.97056 | 0.288922 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.38478 | 0.0445544 | ||||||||
\(967\) | 43.1127 | 1.38641 | 0.693205 | − | 0.720740i | \(-0.256198\pi\) | ||||
0.693205 | + | 0.720740i | \(0.256198\pi\) | |||||||
\(968\) | 9.00000 | 0.289271 | ||||||||
\(969\) | 0.414214 | 0.0133065 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.6569 | 1.33683 | 0.668416 | − | 0.743788i | \(-0.266973\pi\) | ||||
0.668416 | + | 0.743788i | \(0.266973\pi\) | |||||||
\(972\) | −10.3431 | −0.331757 | ||||||||
\(973\) | −52.9706 | −1.69816 | ||||||||
\(974\) | −37.7990 | −1.21116 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.2426 | 0.455896 | ||||||||
\(977\) | 0.242641 | 0.00776276 | 0.00388138 | − | 0.999992i | \(-0.498765\pi\) | ||||
0.00388138 | + | 0.999992i | \(0.498765\pi\) | |||||||
\(978\) | −4.24264 | −0.135665 | ||||||||
\(979\) | −10.0000 | −0.319601 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 50.8284 | 1.62283 | ||||||||
\(982\) | 33.5563 | 1.07083 | ||||||||
\(983\) | −51.4558 | −1.64119 | −0.820593 | − | 0.571513i | \(-0.806357\pi\) | ||||
−0.820593 | + | 0.571513i | \(0.806357\pi\) | |||||||
\(984\) | −1.75736 | −0.0560226 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.171573 | 0.00546399 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.82843 | −0.185427 | ||||||||
\(989\) | 1.33095 | 0.0423218 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.7574 | 0.437017 | 0.218508 | − | 0.975835i | \(-0.429881\pi\) | ||||
0.218508 | + | 0.975835i | \(0.429881\pi\) | |||||||
\(992\) | −6.24264 | −0.198204 | ||||||||
\(993\) | 7.97056 | 0.252938 | ||||||||
\(994\) | 59.2132 | 1.87813 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.00000 | −0.190117 | ||||||||
\(997\) | 48.7279 | 1.54323 | 0.771614 | − | 0.636091i | \(-0.219450\pi\) | ||||
0.771614 | + | 0.636091i | \(0.219450\pi\) | |||||||
\(998\) | 25.7574 | 0.815335 | ||||||||
\(999\) | −20.4853 | −0.648126 |
(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 | 950.2.a.f.1.1 | 2 | ||
3.2 | odd | 2 | 8550.2.a.cb.1.2 | 2 | |||
4.3 | odd | 2 | 7600.2.a.v.1.2 | 2 | |||
5.2 | odd | 4 | 190.2.b.a.39.2 | ✓ | 4 | ||
5.3 | odd | 4 | 190.2.b.a.39.3 | yes | 4 | ||
5.4 | even | 2 | 950.2.a.g.1.2 | 2 | |||
15.2 | even | 4 | 1710.2.d.c.1369.3 | 4 | |||
15.8 | even | 4 | 1710.2.d.c.1369.1 | 4 | |||
15.14 | odd | 2 | 8550.2.a.bn.1.1 | 2 | |||
20.3 | even | 4 | 1520.2.d.e.609.3 | 4 | |||
20.7 | even | 4 | 1520.2.d.e.609.2 | 4 | |||
20.19 | odd | 2 | 7600.2.a.bg.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
190.2.b.a.39.2 | ✓ | 4 | 5.2 | odd | 4 | ||
190.2.b.a.39.3 | yes | 4 | 5.3 | odd | 4 | ||
950.2.a.f.1.1 | 2 | 1.1 | even | 1 | trivial | ||
950.2.a.g.1.2 | 2 | 5.4 | even | 2 | |||
1520.2.d.e.609.2 | 4 | 20.7 | even | 4 | |||
1520.2.d.e.609.3 | 4 | 20.3 | even | 4 | |||
1710.2.d.c.1369.1 | 4 | 15.8 | even | 4 | |||
1710.2.d.c.1369.3 | 4 | 15.2 | even | 4 | |||
7600.2.a.v.1.2 | 2 | 4.3 | odd | 2 | |||
7600.2.a.bg.1.1 | 2 | 20.19 | odd | 2 | |||
8550.2.a.bn.1.1 | 2 | 15.14 | odd | 2 | |||
8550.2.a.cb.1.2 | 2 | 3.2 | odd | 2 |