Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2550,2,Mod(1,2550)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2550, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2550.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2550.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: | \(20.3618525154\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 510) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.76156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2550.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 2.86464 | 1.08273 | 0.541366 | − | 0.840787i | \(-0.317907\pi\) | ||||
0.541366 | + | 0.840787i | \(0.317907\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.52311 | −1.06226 | −0.531129 | − | 0.847291i | \(-0.678232\pi\) | ||||
−0.531129 | + | 0.847291i | \(0.678232\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 2.86464 | 0.765607 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 5.52311 | 1.26709 | 0.633545 | − | 0.773706i | \(-0.281599\pi\) | ||||
0.633545 | + | 0.773706i | \(0.281599\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.86464 | 0.625116 | ||||||||
\(22\) | −3.52311 | −0.751131 | ||||||||
\(23\) | −8.11704 | −1.69252 | −0.846260 | − | 0.532771i | \(-0.821151\pi\) | ||||
−0.846260 | + | 0.532771i | \(0.821151\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.86464 | 0.541366 | ||||||||
\(29\) | 7.91087 | 1.46901 | 0.734506 | − | 0.678602i | \(-0.237414\pi\) | ||||
0.734506 | + | 0.678602i | \(0.237414\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.3878 | 1.86570 | 0.932848 | − | 0.360270i | \(-0.117316\pi\) | ||||
0.932848 | + | 0.360270i | \(0.117316\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −3.52311 | −0.613295 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 6.65847 | 1.09465 | 0.547323 | − | 0.836921i | \(-0.315647\pi\) | ||||
0.547323 | + | 0.836921i | \(0.315647\pi\) | |||||||
\(38\) | 5.52311 | 0.895967 | ||||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.7755 | −1.68285 | −0.841426 | − | 0.540372i | \(-0.818283\pi\) | ||||
−0.841426 | + | 0.540372i | \(0.818283\pi\) | |||||||
\(42\) | 2.86464 | 0.442024 | ||||||||
\(43\) | 1.52311 | 0.232273 | 0.116136 | − | 0.993233i | \(-0.462949\pi\) | ||||
0.116136 | + | 0.993233i | \(0.462949\pi\) | |||||||
\(44\) | −3.52311 | −0.531129 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.11704 | −1.19679 | ||||||||
\(47\) | 12.7755 | 1.86350 | 0.931750 | − | 0.363101i | \(-0.118282\pi\) | ||||
0.931750 | + | 0.363101i | \(0.118282\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.20617 | 0.172310 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | 0.270718 | 0.0371860 | 0.0185930 | − | 0.999827i | \(-0.494081\pi\) | ||||
0.0185930 | + | 0.999827i | \(0.494081\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.86464 | 0.382804 | ||||||||
\(57\) | 5.52311 | 0.731554 | ||||||||
\(58\) | 7.91087 | 1.03875 | ||||||||
\(59\) | −13.2524 | −1.72532 | −0.862658 | − | 0.505789i | \(-0.831202\pi\) | ||||
−0.862658 | + | 0.505789i | \(0.831202\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.929192 | 0.118971 | 0.0594854 | − | 0.998229i | \(-0.481054\pi\) | ||||
0.0594854 | + | 0.998229i | \(0.481054\pi\) | |||||||
\(62\) | 10.3878 | 1.31925 | ||||||||
\(63\) | 2.86464 | 0.360911 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.52311 | −0.433665 | ||||||||
\(67\) | −14.5048 | −1.77204 | −0.886021 | − | 0.463645i | \(-0.846541\pi\) | ||||
−0.886021 | + | 0.463645i | \(0.846541\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | −8.11704 | −0.977176 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.1633 | 1.32484 | 0.662418 | − | 0.749134i | \(-0.269530\pi\) | ||||
0.662418 | + | 0.749134i | \(0.269530\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 4.98168 | 0.583061 | 0.291531 | − | 0.956561i | \(-0.405835\pi\) | ||||
0.291531 | + | 0.956561i | \(0.405835\pi\) | |||||||
\(74\) | 6.65847 | 0.774032 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.52311 | 0.633545 | ||||||||
\(77\) | −10.0925 | −1.15014 | ||||||||
\(78\) | 2.00000 | 0.226455 | ||||||||
\(79\) | −2.38776 | −0.268643 | −0.134322 | − | 0.990938i | \(-0.542886\pi\) | ||||
−0.134322 | + | 0.990938i | \(0.542886\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −10.7755 | −1.18996 | ||||||||
\(83\) | −1.52311 | −0.167184 | −0.0835918 | − | 0.996500i | \(-0.526639\pi\) | ||||
−0.0835918 | + | 0.996500i | \(0.526639\pi\) | |||||||
\(84\) | 2.86464 | 0.312558 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.52311 | 0.164242 | ||||||||
\(87\) | 7.91087 | 0.848134 | ||||||||
\(88\) | −3.52311 | −0.375565 | ||||||||
\(89\) | −9.25240 | −0.980752 | −0.490376 | − | 0.871511i | \(-0.663141\pi\) | ||||
−0.490376 | + | 0.871511i | \(0.663141\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.72928 | 0.600592 | ||||||||
\(92\) | −8.11704 | −0.846260 | ||||||||
\(93\) | 10.3878 | 1.07716 | ||||||||
\(94\) | 12.7755 | 1.31769 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 0.747604 | 0.0759077 | 0.0379538 | − | 0.999279i | \(-0.487916\pi\) | ||||
0.0379538 | + | 0.999279i | \(0.487916\pi\) | |||||||
\(98\) | 1.20617 | 0.121841 | ||||||||
\(99\) | −3.52311 | −0.354086 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.2524 | −1.51767 | −0.758835 | − | 0.651283i | \(-0.774231\pi\) | ||||
−0.758835 | + | 0.651283i | \(0.774231\pi\) | |||||||
\(102\) | −1.00000 | −0.0990148 | ||||||||
\(103\) | −7.52311 | −0.741274 | −0.370637 | − | 0.928778i | \(-0.620861\pi\) | ||||
−0.370637 | + | 0.928778i | \(0.620861\pi\) | |||||||
\(104\) | 2.00000 | 0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.270718 | 0.0262945 | ||||||||
\(107\) | 19.8217 | 1.91624 | 0.958120 | − | 0.286367i | \(-0.0924477\pi\) | ||||
0.958120 | + | 0.286367i | \(0.0924477\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −4.92919 | −0.472131 | −0.236065 | − | 0.971737i | \(-0.575858\pi\) | ||||
−0.236065 | + | 0.971737i | \(0.575858\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.65847 | 0.631994 | ||||||||
\(112\) | 2.86464 | 0.270683 | ||||||||
\(113\) | 3.72928 | 0.350821 | 0.175411 | − | 0.984495i | \(-0.443875\pi\) | ||||
0.175411 | + | 0.984495i | \(0.443875\pi\) | |||||||
\(114\) | 5.52311 | 0.517287 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.91087 | 0.734506 | ||||||||
\(117\) | 2.00000 | 0.184900 | ||||||||
\(118\) | −13.2524 | −1.21998 | ||||||||
\(119\) | −2.86464 | −0.262601 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.41233 | 0.128394 | ||||||||
\(122\) | 0.929192 | 0.0841251 | ||||||||
\(123\) | −10.7755 | −0.971595 | ||||||||
\(124\) | 10.3878 | 0.932848 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.86464 | 0.255202 | ||||||||
\(127\) | 2.20617 | 0.195766 | 0.0978829 | − | 0.995198i | \(-0.468793\pi\) | ||||
0.0978829 | + | 0.995198i | \(0.468793\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 1.52311 | 0.134103 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.52311 | 0.307816 | 0.153908 | − | 0.988085i | \(-0.450814\pi\) | ||||
0.153908 | + | 0.988085i | \(0.450814\pi\) | |||||||
\(132\) | −3.52311 | −0.306648 | ||||||||
\(133\) | 15.8217 | 1.37192 | ||||||||
\(134\) | −14.5048 | −1.25302 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | 6.20617 | 0.530229 | 0.265114 | − | 0.964217i | \(-0.414590\pi\) | ||||
0.265114 | + | 0.964217i | \(0.414590\pi\) | |||||||
\(138\) | −8.11704 | −0.690968 | ||||||||
\(139\) | −12.2341 | −1.03768 | −0.518840 | − | 0.854871i | \(-0.673636\pi\) | ||||
−0.518840 | + | 0.854871i | \(0.673636\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.7755 | 1.07589 | ||||||||
\(142\) | 11.1633 | 0.936800 | ||||||||
\(143\) | −7.04623 | −0.589235 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.98168 | 0.412287 | ||||||||
\(147\) | 1.20617 | 0.0994830 | ||||||||
\(148\) | 6.65847 | 0.547323 | ||||||||
\(149\) | −3.01832 | −0.247271 | −0.123635 | − | 0.992328i | \(-0.539455\pi\) | ||||
−0.123635 | + | 0.992328i | \(0.539455\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.04623 | −0.247899 | −0.123949 | − | 0.992289i | \(-0.539556\pi\) | ||||
−0.123949 | + | 0.992289i | \(0.539556\pi\) | |||||||
\(152\) | 5.52311 | 0.447984 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −10.0925 | −0.813273 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.00000 | 0.160128 | ||||||||
\(157\) | 11.7293 | 0.936099 | 0.468049 | − | 0.883702i | \(-0.344957\pi\) | ||||
0.468049 | + | 0.883702i | \(0.344957\pi\) | |||||||
\(158\) | −2.38776 | −0.189960 | ||||||||
\(159\) | 0.270718 | 0.0214694 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −23.2524 | −1.83255 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −11.0462 | −0.865207 | −0.432604 | − | 0.901584i | \(-0.642405\pi\) | ||||
−0.432604 | + | 0.901584i | \(0.642405\pi\) | |||||||
\(164\) | −10.7755 | −0.841426 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.52311 | −0.118217 | ||||||||
\(167\) | −11.5756 | −0.895747 | −0.447873 | − | 0.894097i | \(-0.647818\pi\) | ||||
−0.447873 | + | 0.894097i | \(0.647818\pi\) | |||||||
\(168\) | 2.86464 | 0.221012 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.52311 | 0.422363 | ||||||||
\(172\) | 1.52311 | 0.116136 | ||||||||
\(173\) | 5.34153 | 0.406109 | 0.203054 | − | 0.979167i | \(-0.434913\pi\) | ||||
0.203054 | + | 0.979167i | \(0.434913\pi\) | |||||||
\(174\) | 7.91087 | 0.599721 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.52311 | −0.265565 | ||||||||
\(177\) | −13.2524 | −0.996111 | ||||||||
\(178\) | −9.25240 | −0.693496 | ||||||||
\(179\) | 10.2341 | 0.764931 | 0.382465 | − | 0.923970i | \(-0.375075\pi\) | ||||
0.382465 | + | 0.923970i | \(0.375075\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.88296 | −0.139960 | −0.0699798 | − | 0.997548i | \(-0.522293\pi\) | ||||
−0.0699798 | + | 0.997548i | \(0.522293\pi\) | |||||||
\(182\) | 5.72928 | 0.424683 | ||||||||
\(183\) | 0.929192 | 0.0686878 | ||||||||
\(184\) | −8.11704 | −0.598396 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 10.3878 | 0.761667 | ||||||||
\(187\) | 3.52311 | 0.257636 | ||||||||
\(188\) | 12.7755 | 0.931750 | ||||||||
\(189\) | 2.86464 | 0.208372 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.775511 | 0.0561140 | 0.0280570 | − | 0.999606i | \(-0.491068\pi\) | ||||
0.0280570 | + | 0.999606i | \(0.491068\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −14.2986 | −1.02924 | −0.514619 | − | 0.857419i | \(-0.672067\pi\) | ||||
−0.514619 | + | 0.857419i | \(0.672067\pi\) | |||||||
\(194\) | 0.747604 | 0.0536748 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.20617 | 0.0861548 | ||||||||
\(197\) | 7.61224 | 0.542350 | 0.271175 | − | 0.962530i | \(-0.412588\pi\) | ||||
0.271175 | + | 0.962530i | \(0.412588\pi\) | |||||||
\(198\) | −3.52311 | −0.250377 | ||||||||
\(199\) | 2.38776 | 0.169263 | 0.0846317 | − | 0.996412i | \(-0.473029\pi\) | ||||
0.0846317 | + | 0.996412i | \(0.473029\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.5048 | −1.02309 | ||||||||
\(202\) | −15.2524 | −1.07315 | ||||||||
\(203\) | 22.6618 | 1.59055 | ||||||||
\(204\) | −1.00000 | −0.0700140 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −7.52311 | −0.524160 | ||||||||
\(207\) | −8.11704 | −0.564173 | ||||||||
\(208\) | 2.00000 | 0.138675 | ||||||||
\(209\) | −19.4586 | −1.34598 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.18785 | −0.0817746 | −0.0408873 | − | 0.999164i | \(-0.513018\pi\) | ||||
−0.0408873 | + | 0.999164i | \(0.513018\pi\) | |||||||
\(212\) | 0.270718 | 0.0185930 | ||||||||
\(213\) | 11.1633 | 0.764894 | ||||||||
\(214\) | 19.8217 | 1.35499 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 29.7572 | 2.02005 | ||||||||
\(218\) | −4.92919 | −0.333847 | ||||||||
\(219\) | 4.98168 | 0.336631 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.00000 | −0.134535 | ||||||||
\(222\) | 6.65847 | 0.446887 | ||||||||
\(223\) | −14.0279 | −0.939378 | −0.469689 | − | 0.882832i | \(-0.655634\pi\) | ||||
−0.469689 | + | 0.882832i | \(0.655634\pi\) | |||||||
\(224\) | 2.86464 | 0.191402 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.72928 | 0.248068 | ||||||||
\(227\) | 10.5048 | 0.697228 | 0.348614 | − | 0.937266i | \(-0.386652\pi\) | ||||
0.348614 | + | 0.937266i | \(0.386652\pi\) | |||||||
\(228\) | 5.52311 | 0.365777 | ||||||||
\(229\) | 4.50479 | 0.297685 | 0.148843 | − | 0.988861i | \(-0.452445\pi\) | ||||
0.148843 | + | 0.988861i | \(0.452445\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.0925 | −0.664035 | ||||||||
\(232\) | 7.91087 | 0.519374 | ||||||||
\(233\) | 18.7755 | 1.23002 | 0.615012 | − | 0.788518i | \(-0.289151\pi\) | ||||
0.615012 | + | 0.788518i | \(0.289151\pi\) | |||||||
\(234\) | 2.00000 | 0.130744 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −13.2524 | −0.862658 | ||||||||
\(237\) | −2.38776 | −0.155101 | ||||||||
\(238\) | −2.86464 | −0.185687 | ||||||||
\(239\) | 12.2341 | 0.791356 | 0.395678 | − | 0.918389i | \(-0.370510\pi\) | ||||
0.395678 | + | 0.918389i | \(0.370510\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.7755 | 0.694112 | 0.347056 | − | 0.937844i | \(-0.387181\pi\) | ||||
0.347056 | + | 0.937844i | \(0.387181\pi\) | |||||||
\(242\) | 1.41233 | 0.0907883 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0.929192 | 0.0594854 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −10.7755 | −0.687021 | ||||||||
\(247\) | 11.0462 | 0.702855 | ||||||||
\(248\) | 10.3878 | 0.659623 | ||||||||
\(249\) | −1.52311 | −0.0965235 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.3632 | −1.41155 | −0.705776 | − | 0.708435i | \(-0.749401\pi\) | ||||
−0.705776 | + | 0.708435i | \(0.749401\pi\) | |||||||
\(252\) | 2.86464 | 0.180455 | ||||||||
\(253\) | 28.5972 | 1.79789 | ||||||||
\(254\) | 2.20617 | 0.138427 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.79383 | −0.610922 | −0.305461 | − | 0.952205i | \(-0.598811\pi\) | ||||
−0.305461 | + | 0.952205i | \(0.598811\pi\) | |||||||
\(258\) | 1.52311 | 0.0948250 | ||||||||
\(259\) | 19.0741 | 1.18521 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.91087 | 0.489671 | ||||||||
\(262\) | 3.52311 | 0.217659 | ||||||||
\(263\) | 8.77551 | 0.541121 | 0.270561 | − | 0.962703i | \(-0.412791\pi\) | ||||
0.270561 | + | 0.962703i | \(0.412791\pi\) | |||||||
\(264\) | −3.52311 | −0.216833 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 15.8217 | 0.970093 | ||||||||
\(267\) | −9.25240 | −0.566237 | ||||||||
\(268\) | −14.5048 | −0.886021 | ||||||||
\(269\) | −20.4523 | −1.24700 | −0.623500 | − | 0.781824i | \(-0.714290\pi\) | ||||
−0.623500 | + | 0.781824i | \(0.714290\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.5048 | −1.36707 | −0.683534 | − | 0.729918i | \(-0.739558\pi\) | ||||
−0.683534 | + | 0.729918i | \(0.739558\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | 5.72928 | 0.346752 | ||||||||
\(274\) | 6.20617 | 0.374928 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −8.11704 | −0.488588 | ||||||||
\(277\) | −29.9388 | −1.79885 | −0.899423 | − | 0.437078i | \(-0.856013\pi\) | ||||
−0.899423 | + | 0.437078i | \(0.856013\pi\) | |||||||
\(278\) | −12.2341 | −0.733751 | ||||||||
\(279\) | 10.3878 | 0.621899 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.1695 | −1.44183 | −0.720916 | − | 0.693022i | \(-0.756279\pi\) | ||||
−0.720916 | + | 0.693022i | \(0.756279\pi\) | |||||||
\(282\) | 12.7755 | 0.760771 | ||||||||
\(283\) | −8.23407 | −0.489465 | −0.244732 | − | 0.969591i | \(-0.578700\pi\) | ||||
−0.244732 | + | 0.969591i | \(0.578700\pi\) | |||||||
\(284\) | 11.1633 | 0.662418 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.04623 | −0.416652 | ||||||||
\(287\) | −30.8680 | −1.82208 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.747604 | 0.0438253 | ||||||||
\(292\) | 4.98168 | 0.291531 | ||||||||
\(293\) | 16.9171 | 0.988309 | 0.494155 | − | 0.869374i | \(-0.335478\pi\) | ||||
0.494155 | + | 0.869374i | \(0.335478\pi\) | |||||||
\(294\) | 1.20617 | 0.0703451 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.65847 | 0.387016 | ||||||||
\(297\) | −3.52311 | −0.204432 | ||||||||
\(298\) | −3.01832 | −0.174847 | ||||||||
\(299\) | −16.2341 | −0.938841 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.36318 | 0.251489 | ||||||||
\(302\) | −3.04623 | −0.175291 | ||||||||
\(303\) | −15.2524 | −0.876227 | ||||||||
\(304\) | 5.52311 | 0.316772 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.00000 | −0.0571662 | ||||||||
\(307\) | 6.47689 | 0.369655 | 0.184828 | − | 0.982771i | \(-0.440827\pi\) | ||||
0.184828 | + | 0.982771i | \(0.440827\pi\) | |||||||
\(308\) | −10.0925 | −0.575071 | ||||||||
\(309\) | −7.52311 | −0.427975 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.3878 | −0.815855 | −0.407927 | − | 0.913014i | \(-0.633748\pi\) | ||||
−0.407927 | + | 0.913014i | \(0.633748\pi\) | |||||||
\(312\) | 2.00000 | 0.113228 | ||||||||
\(313\) | −22.7110 | −1.28370 | −0.641850 | − | 0.766830i | \(-0.721833\pi\) | ||||
−0.641850 | + | 0.766830i | \(0.721833\pi\) | |||||||
\(314\) | 11.7293 | 0.661922 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.38776 | −0.134322 | ||||||||
\(317\) | 16.2095 | 0.910416 | 0.455208 | − | 0.890385i | \(-0.349565\pi\) | ||||
0.455208 | + | 0.890385i | \(0.349565\pi\) | |||||||
\(318\) | 0.270718 | 0.0151811 | ||||||||
\(319\) | −27.8709 | −1.56047 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.8217 | 1.10634 | ||||||||
\(322\) | −23.2524 | −1.29581 | ||||||||
\(323\) | −5.52311 | −0.307314 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −11.0462 | −0.611794 | ||||||||
\(327\) | −4.92919 | −0.272585 | ||||||||
\(328\) | −10.7755 | −0.594978 | ||||||||
\(329\) | 36.5972 | 2.01767 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.04623 | −0.167436 | −0.0837179 | − | 0.996489i | \(-0.526679\pi\) | ||||
−0.0837179 | + | 0.996489i | \(0.526679\pi\) | |||||||
\(332\) | −1.52311 | −0.0835918 | ||||||||
\(333\) | 6.65847 | 0.364882 | ||||||||
\(334\) | −11.5756 | −0.633389 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.86464 | 0.156279 | ||||||||
\(337\) | −8.44024 | −0.459769 | −0.229885 | − | 0.973218i | \(-0.573835\pi\) | ||||
−0.229885 | + | 0.973218i | \(0.573835\pi\) | |||||||
\(338\) | −9.00000 | −0.489535 | ||||||||
\(339\) | 3.72928 | 0.202547 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −36.5972 | −1.98185 | ||||||||
\(342\) | 5.52311 | 0.298656 | ||||||||
\(343\) | −16.5972 | −0.896167 | ||||||||
\(344\) | 1.52311 | 0.0821208 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.34153 | 0.287162 | ||||||||
\(347\) | −8.54144 | −0.458528 | −0.229264 | − | 0.973364i | \(-0.573632\pi\) | ||||
−0.229264 | + | 0.973364i | \(0.573632\pi\) | |||||||
\(348\) | 7.91087 | 0.424067 | ||||||||
\(349\) | −9.28030 | −0.496763 | −0.248382 | − | 0.968662i | \(-0.579899\pi\) | ||||
−0.248382 | + | 0.968662i | \(0.579899\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.00000 | 0.106752 | ||||||||
\(352\) | −3.52311 | −0.187783 | ||||||||
\(353\) | −15.0096 | −0.798880 | −0.399440 | − | 0.916759i | \(-0.630795\pi\) | ||||
−0.399440 | + | 0.916759i | \(0.630795\pi\) | |||||||
\(354\) | −13.2524 | −0.704357 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −9.25240 | −0.490376 | ||||||||
\(357\) | −2.86464 | −0.151613 | ||||||||
\(358\) | 10.2341 | 0.540888 | ||||||||
\(359\) | −32.4681 | −1.71360 | −0.856802 | − | 0.515646i | \(-0.827552\pi\) | ||||
−0.856802 | + | 0.515646i | \(0.827552\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.5048 | 0.605515 | ||||||||
\(362\) | −1.88296 | −0.0989663 | ||||||||
\(363\) | 1.41233 | 0.0741284 | ||||||||
\(364\) | 5.72928 | 0.300296 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.929192 | 0.0485696 | ||||||||
\(367\) | 15.8742 | 0.828628 | 0.414314 | − | 0.910134i | \(-0.364022\pi\) | ||||
0.414314 | + | 0.910134i | \(0.364022\pi\) | |||||||
\(368\) | −8.11704 | −0.423130 | ||||||||
\(369\) | −10.7755 | −0.560951 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.775511 | 0.0402625 | ||||||||
\(372\) | 10.3878 | 0.538580 | ||||||||
\(373\) | 5.45856 | 0.282634 | 0.141317 | − | 0.989964i | \(-0.454866\pi\) | ||||
0.141317 | + | 0.989964i | \(0.454866\pi\) | |||||||
\(374\) | 3.52311 | 0.182176 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12.7755 | 0.658847 | ||||||||
\(377\) | 15.8217 | 0.814861 | ||||||||
\(378\) | 2.86464 | 0.147341 | ||||||||
\(379\) | −21.5510 | −1.10700 | −0.553501 | − | 0.832849i | \(-0.686708\pi\) | ||||
−0.553501 | + | 0.832849i | \(0.686708\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.20617 | 0.113025 | ||||||||
\(382\) | 0.775511 | 0.0396786 | ||||||||
\(383\) | 19.2803 | 0.985177 | 0.492589 | − | 0.870262i | \(-0.336051\pi\) | ||||
0.492589 | + | 0.870262i | \(0.336051\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.2986 | −0.727781 | ||||||||
\(387\) | 1.52311 | 0.0774243 | ||||||||
\(388\) | 0.747604 | 0.0379538 | ||||||||
\(389\) | −6.06455 | −0.307485 | −0.153742 | − | 0.988111i | \(-0.549133\pi\) | ||||
−0.153742 | + | 0.988111i | \(0.549133\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.11704 | 0.410496 | ||||||||
\(392\) | 1.20617 | 0.0609207 | ||||||||
\(393\) | 3.52311 | 0.177718 | ||||||||
\(394\) | 7.61224 | 0.383499 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.52311 | −0.177043 | ||||||||
\(397\) | 6.65847 | 0.334179 | 0.167090 | − | 0.985942i | \(-0.446563\pi\) | ||||
0.167090 | + | 0.985942i | \(0.446563\pi\) | |||||||
\(398\) | 2.38776 | 0.119687 | ||||||||
\(399\) | 15.8217 | 0.792078 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.3265 | 0.615558 | 0.307779 | − | 0.951458i | \(-0.400414\pi\) | ||||
0.307779 | + | 0.951458i | \(0.400414\pi\) | |||||||
\(402\) | −14.5048 | −0.723433 | ||||||||
\(403\) | 20.7755 | 1.03490 | ||||||||
\(404\) | −15.2524 | −0.758835 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 22.6618 | 1.12469 | ||||||||
\(407\) | −23.4586 | −1.16280 | ||||||||
\(408\) | −1.00000 | −0.0495074 | ||||||||
\(409\) | −4.29862 | −0.212553 | −0.106277 | − | 0.994337i | \(-0.533893\pi\) | ||||
−0.106277 | + | 0.994337i | \(0.533893\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.20617 | 0.306128 | ||||||||
\(412\) | −7.52311 | −0.370637 | ||||||||
\(413\) | −37.9634 | −1.86805 | ||||||||
\(414\) | −8.11704 | −0.398931 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.00000 | 0.0980581 | ||||||||
\(417\) | −12.2341 | −0.599105 | ||||||||
\(418\) | −19.4586 | −0.951749 | ||||||||
\(419\) | 24.7110 | 1.20721 | 0.603605 | − | 0.797284i | \(-0.293731\pi\) | ||||
0.603605 | + | 0.797284i | \(0.293731\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.7755 | −1.49991 | −0.749953 | − | 0.661491i | \(-0.769924\pi\) | ||||
−0.749953 | + | 0.661491i | \(0.769924\pi\) | |||||||
\(422\) | −1.18785 | −0.0578234 | ||||||||
\(423\) | 12.7755 | 0.621167 | ||||||||
\(424\) | 0.270718 | 0.0131472 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 11.1633 | 0.540862 | ||||||||
\(427\) | 2.66180 | 0.128814 | ||||||||
\(428\) | 19.8217 | 0.958120 | ||||||||
\(429\) | −7.04623 | −0.340195 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.658473 | −0.0317176 | −0.0158588 | − | 0.999874i | \(-0.505048\pi\) | ||||
−0.0158588 | + | 0.999874i | \(0.505048\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −28.3911 | −1.36439 | −0.682194 | − | 0.731171i | \(-0.738974\pi\) | ||||
−0.682194 | + | 0.731171i | \(0.738974\pi\) | |||||||
\(434\) | 29.7572 | 1.42839 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.92919 | −0.236065 | ||||||||
\(437\) | −44.8313 | −2.14457 | ||||||||
\(438\) | 4.98168 | 0.238034 | ||||||||
\(439\) | 30.0804 | 1.43566 | 0.717829 | − | 0.696219i | \(-0.245136\pi\) | ||||
0.717829 | + | 0.696219i | \(0.245136\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.20617 | 0.0574365 | ||||||||
\(442\) | −2.00000 | −0.0951303 | ||||||||
\(443\) | 8.54144 | 0.405816 | 0.202908 | − | 0.979198i | \(-0.434961\pi\) | ||||
0.202908 | + | 0.979198i | \(0.434961\pi\) | |||||||
\(444\) | 6.65847 | 0.315997 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −14.0279 | −0.664241 | ||||||||
\(447\) | −3.01832 | −0.142762 | ||||||||
\(448\) | 2.86464 | 0.135342 | ||||||||
\(449\) | 23.3169 | 1.10039 | 0.550197 | − | 0.835035i | \(-0.314552\pi\) | ||||
0.550197 | + | 0.835035i | \(0.314552\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 37.9634 | 1.78762 | ||||||||
\(452\) | 3.72928 | 0.175411 | ||||||||
\(453\) | −3.04623 | −0.143124 | ||||||||
\(454\) | 10.5048 | 0.493014 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.52311 | 0.258644 | ||||||||
\(457\) | 10.2986 | 0.481749 | 0.240875 | − | 0.970556i | \(-0.422566\pi\) | ||||
0.240875 | + | 0.970556i | \(0.422566\pi\) | |||||||
\(458\) | 4.50479 | 0.210495 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.70138 | −0.0792409 | −0.0396205 | − | 0.999215i | \(-0.512615\pi\) | ||||
−0.0396205 | + | 0.999215i | \(0.512615\pi\) | |||||||
\(462\) | −10.0925 | −0.469544 | ||||||||
\(463\) | 34.6252 | 1.60917 | 0.804584 | − | 0.593839i | \(-0.202388\pi\) | ||||
0.804584 | + | 0.593839i | \(0.202388\pi\) | |||||||
\(464\) | 7.91087 | 0.367253 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.7755 | 0.869759 | ||||||||
\(467\) | −18.9171 | −0.875380 | −0.437690 | − | 0.899126i | \(-0.644203\pi\) | ||||
−0.437690 | + | 0.899126i | \(0.644203\pi\) | |||||||
\(468\) | 2.00000 | 0.0924500 | ||||||||
\(469\) | −41.5510 | −1.91865 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.7293 | 0.540457 | ||||||||
\(472\) | −13.2524 | −0.609991 | ||||||||
\(473\) | −5.36611 | −0.246734 | ||||||||
\(474\) | −2.38776 | −0.109673 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.86464 | −0.131301 | ||||||||
\(477\) | 0.270718 | 0.0123953 | ||||||||
\(478\) | 12.2341 | 0.559574 | ||||||||
\(479\) | −14.6218 | −0.668088 | −0.334044 | − | 0.942557i | \(-0.608413\pi\) | ||||
−0.334044 | + | 0.942557i | \(0.608413\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.3169 | 0.607201 | ||||||||
\(482\) | 10.7755 | 0.490811 | ||||||||
\(483\) | −23.2524 | −1.05802 | ||||||||
\(484\) | 1.41233 | 0.0641970 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 23.5110 | 1.06539 | 0.532694 | − | 0.846308i | \(-0.321180\pi\) | ||||
0.532694 | + | 0.846308i | \(0.321180\pi\) | |||||||
\(488\) | 0.929192 | 0.0420625 | ||||||||
\(489\) | −11.0462 | −0.499528 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.8584 | 0.896196 | 0.448098 | − | 0.893984i | \(-0.352102\pi\) | ||||
0.448098 | + | 0.893984i | \(0.352102\pi\) | |||||||
\(492\) | −10.7755 | −0.485798 | ||||||||
\(493\) | −7.91087 | −0.356288 | ||||||||
\(494\) | 11.0462 | 0.496993 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.3878 | 0.466424 | ||||||||
\(497\) | 31.9787 | 1.43444 | ||||||||
\(498\) | −1.52311 | −0.0682524 | ||||||||
\(499\) | −25.3728 | −1.13584 | −0.567920 | − | 0.823084i | \(-0.692252\pi\) | ||||
−0.567920 | + | 0.823084i | \(0.692252\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.5756 | −0.517160 | ||||||||
\(502\) | −22.3632 | −0.998117 | ||||||||
\(503\) | −25.5631 | −1.13980 | −0.569901 | − | 0.821713i | \(-0.693018\pi\) | ||||
−0.569901 | + | 0.821713i | \(0.693018\pi\) | |||||||
\(504\) | 2.86464 | 0.127601 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 28.5972 | 1.27130 | ||||||||
\(507\) | −9.00000 | −0.399704 | ||||||||
\(508\) | 2.20617 | 0.0978829 | ||||||||
\(509\) | 7.07414 | 0.313556 | 0.156778 | − | 0.987634i | \(-0.449889\pi\) | ||||
0.156778 | + | 0.987634i | \(0.449889\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.2707 | 0.631299 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 5.52311 | 0.243851 | ||||||||
\(514\) | −9.79383 | −0.431987 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.52311 | 0.0670514 | ||||||||
\(517\) | −45.0096 | −1.97952 | ||||||||
\(518\) | 19.0741 | 0.838069 | ||||||||
\(519\) | 5.34153 | 0.234467 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.141617 | 0.00620434 | 0.00310217 | − | 0.999995i | \(-0.499013\pi\) | ||||
0.00310217 | + | 0.999995i | \(0.499013\pi\) | |||||||
\(522\) | 7.91087 | 0.346249 | ||||||||
\(523\) | 9.49521 | 0.415196 | 0.207598 | − | 0.978214i | \(-0.433435\pi\) | ||||
0.207598 | + | 0.978214i | \(0.433435\pi\) | |||||||
\(524\) | 3.52311 | 0.153908 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.77551 | 0.382630 | ||||||||
\(527\) | −10.3878 | −0.452498 | ||||||||
\(528\) | −3.52311 | −0.153324 | ||||||||
\(529\) | 42.8863 | 1.86462 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.2524 | −0.575105 | ||||||||
\(532\) | 15.8217 | 0.685959 | ||||||||
\(533\) | −21.5510 | −0.933478 | ||||||||
\(534\) | −9.25240 | −0.400390 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −14.5048 | −0.626512 | ||||||||
\(537\) | 10.2341 | 0.441633 | ||||||||
\(538\) | −20.4523 | −0.881762 | ||||||||
\(539\) | −4.24947 | −0.183037 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.6218 | −0.714628 | −0.357314 | − | 0.933984i | \(-0.616307\pi\) | ||||
−0.357314 | + | 0.933984i | \(0.616307\pi\) | |||||||
\(542\) | −22.5048 | −0.966664 | ||||||||
\(543\) | −1.88296 | −0.0808057 | ||||||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 5.72928 | 0.245191 | ||||||||
\(547\) | −8.77551 | −0.375214 | −0.187607 | − | 0.982244i | \(-0.560073\pi\) | ||||
−0.187607 | + | 0.982244i | \(0.560073\pi\) | |||||||
\(548\) | 6.20617 | 0.265114 | ||||||||
\(549\) | 0.929192 | 0.0396569 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 43.6926 | 1.86137 | ||||||||
\(552\) | −8.11704 | −0.345484 | ||||||||
\(553\) | −6.84006 | −0.290869 | ||||||||
\(554\) | −29.9388 | −1.27198 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.2341 | −0.518840 | ||||||||
\(557\) | −10.3632 | −0.439102 | −0.219551 | − | 0.975601i | \(-0.570459\pi\) | ||||
−0.219551 | + | 0.975601i | \(0.570459\pi\) | |||||||
\(558\) | 10.3878 | 0.439749 | ||||||||
\(559\) | 3.04623 | 0.128842 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.52311 | 0.148746 | ||||||||
\(562\) | −24.1695 | −1.01953 | ||||||||
\(563\) | −33.1108 | −1.39545 | −0.697726 | − | 0.716364i | \(-0.745805\pi\) | ||||
−0.697726 | + | 0.716364i | \(0.745805\pi\) | |||||||
\(564\) | 12.7755 | 0.537946 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8.23407 | −0.346104 | ||||||||
\(567\) | 2.86464 | 0.120304 | ||||||||
\(568\) | 11.1633 | 0.468400 | ||||||||
\(569\) | −39.0096 | −1.63537 | −0.817683 | − | 0.575668i | \(-0.804742\pi\) | ||||
−0.817683 | + | 0.575668i | \(0.804742\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.4586 | 0.479526 | 0.239763 | − | 0.970831i | \(-0.422930\pi\) | ||||
0.239763 | + | 0.970831i | \(0.422930\pi\) | |||||||
\(572\) | −7.04623 | −0.294618 | ||||||||
\(573\) | 0.775511 | 0.0323974 | ||||||||
\(574\) | −30.8680 | −1.28840 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 1.96336 | 0.0817356 | 0.0408678 | − | 0.999165i | \(-0.486988\pi\) | ||||
0.0408678 | + | 0.999165i | \(0.486988\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | −14.2986 | −0.594231 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.36318 | −0.181015 | ||||||||
\(582\) | 0.747604 | 0.0309892 | ||||||||
\(583\) | −0.953771 | −0.0395012 | ||||||||
\(584\) | 4.98168 | 0.206143 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.9171 | 0.698840 | ||||||||
\(587\) | 4.00000 | 0.165098 | 0.0825488 | − | 0.996587i | \(-0.473694\pi\) | ||||
0.0825488 | + | 0.996587i | \(0.473694\pi\) | |||||||
\(588\) | 1.20617 | 0.0497415 | ||||||||
\(589\) | 57.3728 | 2.36400 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.61224 | 0.313126 | ||||||||
\(592\) | 6.65847 | 0.273662 | ||||||||
\(593\) | 31.3449 | 1.28718 | 0.643589 | − | 0.765371i | \(-0.277444\pi\) | ||||
0.643589 | + | 0.765371i | \(0.277444\pi\) | |||||||
\(594\) | −3.52311 | −0.144555 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.01832 | −0.123635 | ||||||||
\(597\) | 2.38776 | 0.0977243 | ||||||||
\(598\) | −16.2341 | −0.663861 | ||||||||
\(599\) | −17.1387 | −0.700268 | −0.350134 | − | 0.936700i | \(-0.613864\pi\) | ||||
−0.350134 | + | 0.936700i | \(0.613864\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.3757 | 0.504815 | 0.252407 | − | 0.967621i | \(-0.418778\pi\) | ||||
0.252407 | + | 0.967621i | \(0.418778\pi\) | |||||||
\(602\) | 4.36318 | 0.177830 | ||||||||
\(603\) | −14.5048 | −0.590681 | ||||||||
\(604\) | −3.04623 | −0.123949 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −15.2524 | −0.619586 | ||||||||
\(607\) | 38.4523 | 1.56073 | 0.780365 | − | 0.625324i | \(-0.215033\pi\) | ||||
0.780365 | + | 0.625324i | \(0.215033\pi\) | |||||||
\(608\) | 5.52311 | 0.223992 | ||||||||
\(609\) | 22.6618 | 0.918302 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 25.5510 | 1.03368 | ||||||||
\(612\) | −1.00000 | −0.0404226 | ||||||||
\(613\) | 2.77551 | 0.112102 | 0.0560509 | − | 0.998428i | \(-0.482149\pi\) | ||||
0.0560509 | + | 0.998428i | \(0.482149\pi\) | |||||||
\(614\) | 6.47689 | 0.261386 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.0925 | −0.406637 | ||||||||
\(617\) | −40.2707 | −1.62124 | −0.810619 | − | 0.585574i | \(-0.800869\pi\) | ||||
−0.810619 | + | 0.585574i | \(0.800869\pi\) | |||||||
\(618\) | −7.52311 | −0.302624 | ||||||||
\(619\) | 40.5972 | 1.63174 | 0.815871 | − | 0.578234i | \(-0.196258\pi\) | ||||
0.815871 | + | 0.578234i | \(0.196258\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.11704 | −0.325725 | ||||||||
\(622\) | −14.3878 | −0.576896 | ||||||||
\(623\) | −26.5048 | −1.06189 | ||||||||
\(624\) | 2.00000 | 0.0800641 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −22.7110 | −0.907713 | ||||||||
\(627\) | −19.4586 | −0.777100 | ||||||||
\(628\) | 11.7293 | 0.468049 | ||||||||
\(629\) | −6.65847 | −0.265491 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.3169 | 0.689377 | 0.344688 | − | 0.938717i | \(-0.387985\pi\) | ||||
0.344688 | + | 0.938717i | \(0.387985\pi\) | |||||||
\(632\) | −2.38776 | −0.0949798 | ||||||||
\(633\) | −1.18785 | −0.0472126 | ||||||||
\(634\) | 16.2095 | 0.643761 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.270718 | 0.0107347 | ||||||||
\(637\) | 2.41233 | 0.0955802 | ||||||||
\(638\) | −27.8709 | −1.10342 | ||||||||
\(639\) | 11.1633 | 0.441612 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.6926 | 0.856808 | 0.428404 | − | 0.903587i | \(-0.359076\pi\) | ||||
0.428404 | + | 0.903587i | \(0.359076\pi\) | |||||||
\(642\) | 19.8217 | 0.782302 | ||||||||
\(643\) | 37.0096 | 1.45952 | 0.729758 | − | 0.683706i | \(-0.239633\pi\) | ||||
0.729758 | + | 0.683706i | \(0.239633\pi\) | |||||||
\(644\) | −23.2524 | −0.916273 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.52311 | −0.217304 | ||||||||
\(647\) | 16.6464 | 0.654438 | 0.327219 | − | 0.944949i | \(-0.393889\pi\) | ||||
0.327219 | + | 0.944949i | \(0.393889\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 46.6897 | 1.83273 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 29.7572 | 1.16628 | ||||||||
\(652\) | −11.0462 | −0.432604 | ||||||||
\(653\) | 6.89255 | 0.269726 | 0.134863 | − | 0.990864i | \(-0.456941\pi\) | ||||
0.134863 | + | 0.990864i | \(0.456941\pi\) | |||||||
\(654\) | −4.92919 | −0.192747 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −10.7755 | −0.420713 | ||||||||
\(657\) | 4.98168 | 0.194354 | ||||||||
\(658\) | 36.5972 | 1.42671 | ||||||||
\(659\) | −14.2062 | −0.553394 | −0.276697 | − | 0.960957i | \(-0.589240\pi\) | ||||
−0.276697 | + | 0.960957i | \(0.589240\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.3265 | −1.10177 | −0.550887 | − | 0.834580i | \(-0.685711\pi\) | ||||
−0.550887 | + | 0.834580i | \(0.685711\pi\) | |||||||
\(662\) | −3.04623 | −0.118395 | ||||||||
\(663\) | −2.00000 | −0.0776736 | ||||||||
\(664\) | −1.52311 | −0.0591083 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.65847 | 0.258011 | ||||||||
\(667\) | −64.2128 | −2.48633 | ||||||||
\(668\) | −11.5756 | −0.447873 | ||||||||
\(669\) | −14.0279 | −0.542350 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.27365 | −0.126378 | ||||||||
\(672\) | 2.86464 | 0.110506 | ||||||||
\(673\) | −1.70138 | −0.0655832 | −0.0327916 | − | 0.999462i | \(-0.510440\pi\) | ||||
−0.0327916 | + | 0.999462i | \(0.510440\pi\) | |||||||
\(674\) | −8.44024 | −0.325106 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | 7.30488 | 0.280749 | 0.140375 | − | 0.990098i | \(-0.455169\pi\) | ||||
0.140375 | + | 0.990098i | \(0.455169\pi\) | |||||||
\(678\) | 3.72928 | 0.143222 | ||||||||
\(679\) | 2.14162 | 0.0821877 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.5048 | 0.402545 | ||||||||
\(682\) | −36.5972 | −1.40138 | ||||||||
\(683\) | 15.0462 | 0.575728 | 0.287864 | − | 0.957671i | \(-0.407055\pi\) | ||||
0.287864 | + | 0.957671i | \(0.407055\pi\) | |||||||
\(684\) | 5.52311 | 0.211182 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −16.5972 | −0.633686 | ||||||||
\(687\) | 4.50479 | 0.171869 | ||||||||
\(688\) | 1.52311 | 0.0580682 | ||||||||
\(689\) | 0.541436 | 0.0206271 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.78510 | −0.372243 | −0.186121 | − | 0.982527i | \(-0.559592\pi\) | ||||
−0.186121 | + | 0.982527i | \(0.559592\pi\) | |||||||
\(692\) | 5.34153 | 0.203054 | ||||||||
\(693\) | −10.0925 | −0.383381 | ||||||||
\(694\) | −8.54144 | −0.324228 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7.91087 | 0.299861 | ||||||||
\(697\) | 10.7755 | 0.408152 | ||||||||
\(698\) | −9.28030 | −0.351265 | ||||||||
\(699\) | 18.7755 | 0.710155 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.88629 | 0.373400 | 0.186700 | − | 0.982417i | \(-0.440221\pi\) | ||||
0.186700 | + | 0.982417i | \(0.440221\pi\) | |||||||
\(702\) | 2.00000 | 0.0754851 | ||||||||
\(703\) | 36.7755 | 1.38701 | ||||||||
\(704\) | −3.52311 | −0.132782 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15.0096 | −0.564893 | ||||||||
\(707\) | −43.6926 | −1.64323 | ||||||||
\(708\) | −13.2524 | −0.498056 | ||||||||
\(709\) | −34.7143 | −1.30372 | −0.651861 | − | 0.758338i | \(-0.726012\pi\) | ||||
−0.651861 | + | 0.758338i | \(0.726012\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.38776 | −0.0895478 | ||||||||
\(712\) | −9.25240 | −0.346748 | ||||||||
\(713\) | −84.3178 | −3.15773 | ||||||||
\(714\) | −2.86464 | −0.107206 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10.2341 | 0.382465 | ||||||||
\(717\) | 12.2341 | 0.456890 | ||||||||
\(718\) | −32.4681 | −1.21170 | ||||||||
\(719\) | 34.2095 | 1.27580 | 0.637899 | − | 0.770120i | \(-0.279804\pi\) | ||||
0.637899 | + | 0.770120i | \(0.279804\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.5510 | −0.802602 | ||||||||
\(722\) | 11.5048 | 0.428164 | ||||||||
\(723\) | 10.7755 | 0.400746 | ||||||||
\(724\) | −1.88296 | −0.0699798 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.41233 | 0.0524167 | ||||||||
\(727\) | 35.8863 | 1.33095 | 0.665474 | − | 0.746421i | \(-0.268229\pi\) | ||||
0.665474 | + | 0.746421i | \(0.268229\pi\) | |||||||
\(728\) | 5.72928 | 0.212341 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.52311 | −0.0563344 | ||||||||
\(732\) | 0.929192 | 0.0343439 | ||||||||
\(733\) | −20.3757 | −0.752593 | −0.376297 | − | 0.926499i | \(-0.622803\pi\) | ||||
−0.376297 | + | 0.926499i | \(0.622803\pi\) | |||||||
\(734\) | 15.8742 | 0.585928 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.11704 | −0.299198 | ||||||||
\(737\) | 51.1020 | 1.88237 | ||||||||
\(738\) | −10.7755 | −0.396652 | ||||||||
\(739\) | −18.4769 | −0.679683 | −0.339842 | − | 0.940483i | \(-0.610373\pi\) | ||||
−0.339842 | + | 0.940483i | \(0.610373\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.0462 | 0.405793 | ||||||||
\(742\) | 0.775511 | 0.0284699 | ||||||||
\(743\) | −20.7876 | −0.762622 | −0.381311 | − | 0.924447i | \(-0.624527\pi\) | ||||
−0.381311 | + | 0.924447i | \(0.624527\pi\) | |||||||
\(744\) | 10.3878 | 0.380834 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.45856 | 0.199852 | ||||||||
\(747\) | −1.52311 | −0.0557278 | ||||||||
\(748\) | 3.52311 | 0.128818 | ||||||||
\(749\) | 56.7822 | 2.07478 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.8559 | −0.688062 | −0.344031 | − | 0.938958i | \(-0.611792\pi\) | ||||
−0.344031 | + | 0.938958i | \(0.611792\pi\) | |||||||
\(752\) | 12.7755 | 0.465875 | ||||||||
\(753\) | −22.3632 | −0.814959 | ||||||||
\(754\) | 15.8217 | 0.576194 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.86464 | 0.104186 | ||||||||
\(757\) | −7.18785 | −0.261247 | −0.130623 | − | 0.991432i | \(-0.541698\pi\) | ||||
−0.130623 | + | 0.991432i | \(0.541698\pi\) | |||||||
\(758\) | −21.5510 | −0.782768 | ||||||||
\(759\) | 28.5972 | 1.03801 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.09246 | 0.148351 | 0.0741757 | − | 0.997245i | \(-0.476367\pi\) | ||||
0.0741757 | + | 0.997245i | \(0.476367\pi\) | |||||||
\(762\) | 2.20617 | 0.0799210 | ||||||||
\(763\) | −14.1204 | −0.511192 | ||||||||
\(764\) | 0.775511 | 0.0280570 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.2803 | 0.696626 | ||||||||
\(767\) | −26.5048 | −0.957033 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −53.2311 | −1.91956 | −0.959782 | − | 0.280746i | \(-0.909418\pi\) | ||||
−0.959782 | + | 0.280746i | \(0.909418\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.79383 | −0.352716 | ||||||||
\(772\) | −14.2986 | −0.514619 | ||||||||
\(773\) | 6.00000 | 0.215805 | 0.107903 | − | 0.994161i | \(-0.465587\pi\) | ||||
0.107903 | + | 0.994161i | \(0.465587\pi\) | |||||||
\(774\) | 1.52311 | 0.0547472 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.747604 | 0.0268374 | ||||||||
\(777\) | 19.0741 | 0.684281 | ||||||||
\(778\) | −6.06455 | −0.217425 | ||||||||
\(779\) | −59.5144 | −2.13232 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −39.3295 | −1.40732 | ||||||||
\(782\) | 8.11704 | 0.290265 | ||||||||
\(783\) | 7.91087 | 0.282711 | ||||||||
\(784\) | 1.20617 | 0.0430774 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.52311 | 0.125665 | ||||||||
\(787\) | 11.2245 | 0.400110 | 0.200055 | − | 0.979785i | \(-0.435888\pi\) | ||||
0.200055 | + | 0.979785i | \(0.435888\pi\) | |||||||
\(788\) | 7.61224 | 0.271175 | ||||||||
\(789\) | 8.77551 | 0.312416 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.6831 | 0.379846 | ||||||||
\(792\) | −3.52311 | −0.125188 | ||||||||
\(793\) | 1.85838 | 0.0659931 | ||||||||
\(794\) | 6.65847 | 0.236300 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.38776 | 0.0846317 | ||||||||
\(797\) | −8.27072 | −0.292964 | −0.146482 | − | 0.989213i | \(-0.546795\pi\) | ||||
−0.146482 | + | 0.989213i | \(0.546795\pi\) | |||||||
\(798\) | 15.8217 | 0.560083 | ||||||||
\(799\) | −12.7755 | −0.451965 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.25240 | −0.326917 | ||||||||
\(802\) | 12.3265 | 0.435265 | ||||||||
\(803\) | −17.5510 | −0.619362 | ||||||||
\(804\) | −14.5048 | −0.511545 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 20.7755 | 0.731786 | ||||||||
\(807\) | −20.4523 | −0.719955 | ||||||||
\(808\) | −15.2524 | −0.536577 | ||||||||
\(809\) | −34.3632 | −1.20814 | −0.604072 | − | 0.796929i | \(-0.706456\pi\) | ||||
−0.604072 | + | 0.796929i | \(0.706456\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.9634 | −1.05216 | −0.526078 | − | 0.850436i | \(-0.676338\pi\) | ||||
−0.526078 | + | 0.850436i | \(0.676338\pi\) | |||||||
\(812\) | 22.6618 | 0.795273 | ||||||||
\(813\) | −22.5048 | −0.789278 | ||||||||
\(814\) | −23.4586 | −0.822222 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.00000 | −0.0350070 | ||||||||
\(817\) | 8.41233 | 0.294310 | ||||||||
\(818\) | −4.29862 | −0.150298 | ||||||||
\(819\) | 5.72928 | 0.200197 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −49.2278 | −1.71806 | −0.859031 | − | 0.511923i | \(-0.828933\pi\) | ||||
−0.859031 | + | 0.511923i | \(0.828933\pi\) | |||||||
\(822\) | 6.20617 | 0.216465 | ||||||||
\(823\) | 13.3694 | 0.466029 | 0.233015 | − | 0.972473i | \(-0.425141\pi\) | ||||
0.233015 | + | 0.972473i | \(0.425141\pi\) | |||||||
\(824\) | −7.52311 | −0.262080 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −37.9634 | −1.32091 | ||||||||
\(827\) | −26.7389 | −0.929801 | −0.464901 | − | 0.885363i | \(-0.653910\pi\) | ||||
−0.464901 | + | 0.885363i | \(0.653910\pi\) | |||||||
\(828\) | −8.11704 | −0.282087 | ||||||||
\(829\) | −20.4490 | −0.710222 | −0.355111 | − | 0.934824i | \(-0.615557\pi\) | ||||
−0.355111 | + | 0.934824i | \(0.615557\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −29.9388 | −1.03856 | ||||||||
\(832\) | 2.00000 | 0.0693375 | ||||||||
\(833\) | −1.20617 | −0.0417912 | ||||||||
\(834\) | −12.2341 | −0.423631 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −19.4586 | −0.672988 | ||||||||
\(837\) | 10.3878 | 0.359053 | ||||||||
\(838\) | 24.7110 | 0.853626 | ||||||||
\(839\) | −23.8097 | −0.822001 | −0.411001 | − | 0.911635i | \(-0.634821\pi\) | ||||
−0.411001 | + | 0.911635i | \(0.634821\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33.5819 | 1.15800 | ||||||||
\(842\) | −30.7755 | −1.06059 | ||||||||
\(843\) | −24.1695 | −0.832443 | ||||||||
\(844\) | −1.18785 | −0.0408873 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 12.7755 | 0.439231 | ||||||||
\(847\) | 4.04583 | 0.139016 | ||||||||
\(848\) | 0.270718 | 0.00929650 | ||||||||
\(849\) | −8.23407 | −0.282593 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −54.0471 | −1.85271 | ||||||||
\(852\) | 11.1633 | 0.382447 | ||||||||
\(853\) | 23.9754 | 0.820903 | 0.410451 | − | 0.911882i | \(-0.365371\pi\) | ||||
0.410451 | + | 0.911882i | \(0.365371\pi\) | |||||||
\(854\) | 2.66180 | 0.0910849 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19.8217 | 0.677493 | ||||||||
\(857\) | −1.58767 | −0.0542336 | −0.0271168 | − | 0.999632i | \(-0.508633\pi\) | ||||
−0.0271168 | + | 0.999632i | \(0.508633\pi\) | |||||||
\(858\) | −7.04623 | −0.240554 | ||||||||
\(859\) | 39.4586 | 1.34631 | 0.673154 | − | 0.739502i | \(-0.264939\pi\) | ||||
0.673154 | + | 0.739502i | \(0.264939\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −30.8680 | −1.05198 | ||||||||
\(862\) | −0.658473 | −0.0224277 | ||||||||
\(863\) | 54.0192 | 1.83883 | 0.919417 | − | 0.393284i | \(-0.128661\pi\) | ||||
0.919417 | + | 0.393284i | \(0.128661\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −28.3911 | −0.964768 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 29.7572 | 1.01002 | ||||||||
\(869\) | 8.41233 | 0.285369 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.0096 | −0.982952 | ||||||||
\(872\) | −4.92919 | −0.166923 | ||||||||
\(873\) | 0.747604 | 0.0253026 | ||||||||
\(874\) | −44.8313 | −1.51644 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.98168 | 0.168315 | ||||||||
\(877\) | −32.6218 | −1.10156 | −0.550780 | − | 0.834650i | \(-0.685670\pi\) | ||||
−0.550780 | + | 0.834650i | \(0.685670\pi\) | |||||||
\(878\) | 30.0804 | 1.01516 | ||||||||
\(879\) | 16.9171 | 0.570601 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.50479 | −0.286534 | −0.143267 | − | 0.989684i | \(-0.545761\pi\) | ||||
−0.143267 | + | 0.989684i | \(0.545761\pi\) | |||||||
\(882\) | 1.20617 | 0.0406138 | ||||||||
\(883\) | 24.0558 | 0.809543 | 0.404771 | − | 0.914418i | \(-0.367351\pi\) | ||||
0.404771 | + | 0.914418i | \(0.367351\pi\) | |||||||
\(884\) | −2.00000 | −0.0672673 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.54144 | 0.286955 | ||||||||
\(887\) | 39.5264 | 1.32717 | 0.663584 | − | 0.748102i | \(-0.269035\pi\) | ||||
0.663584 | + | 0.748102i | \(0.269035\pi\) | |||||||
\(888\) | 6.65847 | 0.223444 | ||||||||
\(889\) | 6.31988 | 0.211962 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.52311 | −0.118029 | ||||||||
\(892\) | −14.0279 | −0.469689 | ||||||||
\(893\) | 70.5606 | 2.36122 | ||||||||
\(894\) | −3.01832 | −0.100948 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.86464 | 0.0957009 | ||||||||
\(897\) | −16.2341 | −0.542040 | ||||||||
\(898\) | 23.3169 | 0.778097 | ||||||||
\(899\) | 82.1762 | 2.74073 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.270718 | −0.00901893 | ||||||||
\(902\) | 37.9634 | 1.26404 | ||||||||
\(903\) | 4.36318 | 0.145197 | ||||||||
\(904\) | 3.72928 | 0.124034 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.04623 | −0.101204 | ||||||||
\(907\) | 14.3998 | 0.478138 | 0.239069 | − | 0.971003i | \(-0.423158\pi\) | ||||
0.239069 | + | 0.971003i | \(0.423158\pi\) | |||||||
\(908\) | 10.5048 | 0.348614 | ||||||||
\(909\) | −15.2524 | −0.505890 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.8097 | 1.58401 | 0.792003 | − | 0.610518i | \(-0.209039\pi\) | ||||
0.792003 | + | 0.610518i | \(0.209039\pi\) | |||||||
\(912\) | 5.52311 | 0.182889 | ||||||||
\(913\) | 5.36611 | 0.177592 | ||||||||
\(914\) | 10.2986 | 0.340648 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.50479 | 0.148843 | ||||||||
\(917\) | 10.0925 | 0.333282 | ||||||||
\(918\) | −1.00000 | −0.0330049 | ||||||||
\(919\) | 57.1945 | 1.88667 | 0.943336 | − | 0.331838i | \(-0.107669\pi\) | ||||
0.943336 | + | 0.331838i | \(0.107669\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.47689 | 0.213421 | ||||||||
\(922\) | −1.70138 | −0.0560318 | ||||||||
\(923\) | 22.3265 | 0.734887 | ||||||||
\(924\) | −10.0925 | −0.332017 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 34.6252 | 1.13785 | ||||||||
\(927\) | −7.52311 | −0.247091 | ||||||||
\(928\) | 7.91087 | 0.259687 | ||||||||
\(929\) | 18.7197 | 0.614173 | 0.307087 | − | 0.951682i | \(-0.400646\pi\) | ||||
0.307087 | + | 0.951682i | \(0.400646\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.66180 | 0.218332 | ||||||||
\(932\) | 18.7755 | 0.615012 | ||||||||
\(933\) | −14.3878 | −0.471034 | ||||||||
\(934\) | −18.9171 | −0.618987 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.00000 | 0.0653720 | ||||||||
\(937\) | 25.2158 | 0.823763 | 0.411881 | − | 0.911237i | \(-0.364872\pi\) | ||||
0.411881 | + | 0.911237i | \(0.364872\pi\) | |||||||
\(938\) | −41.5510 | −1.35669 | ||||||||
\(939\) | −22.7110 | −0.741144 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.0891 | 0.394094 | 0.197047 | − | 0.980394i | \(-0.436865\pi\) | ||||
0.197047 | + | 0.980394i | \(0.436865\pi\) | |||||||
\(942\) | 11.7293 | 0.382161 | ||||||||
\(943\) | 87.4652 | 2.84826 | ||||||||
\(944\) | −13.2524 | −0.431329 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.36611 | −0.174467 | ||||||||
\(947\) | −29.7851 | −0.967886 | −0.483943 | − | 0.875100i | \(-0.660796\pi\) | ||||
−0.483943 | + | 0.875100i | \(0.660796\pi\) | |||||||
\(948\) | −2.38776 | −0.0775507 | ||||||||
\(949\) | 9.96336 | 0.323424 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.2095 | 0.525629 | ||||||||
\(952\) | −2.86464 | −0.0928435 | ||||||||
\(953\) | −25.5144 | −0.826492 | −0.413246 | − | 0.910619i | \(-0.635605\pi\) | ||||
−0.413246 | + | 0.910619i | \(0.635605\pi\) | |||||||
\(954\) | 0.270718 | 0.00876483 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 12.2341 | 0.395678 | ||||||||
\(957\) | −27.8709 | −0.900938 | ||||||||
\(958\) | −14.6218 | −0.472410 | ||||||||
\(959\) | 17.7784 | 0.574096 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 76.9055 | 2.48082 | ||||||||
\(962\) | 13.3169 | 0.429356 | ||||||||
\(963\) | 19.8217 | 0.638747 | ||||||||
\(964\) | 10.7755 | 0.347056 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −23.2524 | −0.748134 | ||||||||
\(967\) | −31.5231 | −1.01372 | −0.506858 | − | 0.862030i | \(-0.669193\pi\) | ||||
−0.506858 | + | 0.862030i | \(0.669193\pi\) | |||||||
\(968\) | 1.41233 | 0.0453942 | ||||||||
\(969\) | −5.52311 | −0.177428 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.8959 | 1.18404 | 0.592022 | − | 0.805921i | \(-0.298330\pi\) | ||||
0.592022 | + | 0.805921i | \(0.298330\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −35.0462 | −1.12353 | ||||||||
\(974\) | 23.5110 | 0.753343 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.929192 | 0.0297427 | ||||||||
\(977\) | −36.2986 | −1.16130 | −0.580648 | − | 0.814155i | \(-0.697201\pi\) | ||||
−0.580648 | + | 0.814155i | \(0.697201\pi\) | |||||||
\(978\) | −11.0462 | −0.353219 | ||||||||
\(979\) | 32.5972 | 1.04181 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.92919 | −0.157377 | ||||||||
\(982\) | 19.8584 | 0.633706 | ||||||||
\(983\) | 3.21242 | 0.102460 | 0.0512302 | − | 0.998687i | \(-0.483686\pi\) | ||||
0.0512302 | + | 0.998687i | \(0.483686\pi\) | |||||||
\(984\) | −10.7755 | −0.343511 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.91087 | −0.251933 | ||||||||
\(987\) | 36.5972 | 1.16490 | ||||||||
\(988\) | 11.0462 | 0.351427 | ||||||||
\(989\) | −12.3632 | −0.393126 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.2461 | 0.770204 | 0.385102 | − | 0.922874i | \(-0.374166\pi\) | ||||
0.385102 | + | 0.922874i | \(0.374166\pi\) | |||||||
\(992\) | 10.3878 | 0.329812 | ||||||||
\(993\) | −3.04623 | −0.0966691 | ||||||||
\(994\) | 31.9787 | 1.01430 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.52311 | −0.0482617 | ||||||||
\(997\) | 40.3386 | 1.27754 | 0.638768 | − | 0.769399i | \(-0.279444\pi\) | ||||
0.638768 | + | 0.769399i | \(0.279444\pi\) | |||||||
\(998\) | −25.3728 | −0.803161 | ||||||||
\(999\) | 6.65847 | 0.210665 |
(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 | 2550.2.a.bo.1.2 | 3 | ||
3.2 | odd | 2 | 7650.2.a.dl.1.2 | 3 | |||
5.2 | odd | 4 | 510.2.d.d.409.5 | yes | 6 | ||
5.3 | odd | 4 | 510.2.d.d.409.2 | ✓ | 6 | ||
5.4 | even | 2 | 2550.2.a.bn.1.2 | 3 | |||
15.2 | even | 4 | 1530.2.d.i.919.2 | 6 | |||
15.8 | even | 4 | 1530.2.d.i.919.5 | 6 | |||
15.14 | odd | 2 | 7650.2.a.dm.1.2 | 3 | |||
20.3 | even | 4 | 4080.2.m.p.2449.2 | 6 | |||
20.7 | even | 4 | 4080.2.m.p.2449.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
510.2.d.d.409.2 | ✓ | 6 | 5.3 | odd | 4 | ||
510.2.d.d.409.5 | yes | 6 | 5.2 | odd | 4 | ||
1530.2.d.i.919.2 | 6 | 15.2 | even | 4 | |||
1530.2.d.i.919.5 | 6 | 15.8 | even | 4 | |||
2550.2.a.bn.1.2 | 3 | 5.4 | even | 2 | |||
2550.2.a.bo.1.2 | 3 | 1.1 | even | 1 | trivial | ||
4080.2.m.p.2449.2 | 6 | 20.3 | even | 4 | |||
4080.2.m.p.2449.5 | 6 | 20.7 | even | 4 | |||
7650.2.a.dl.1.2 | 3 | 3.2 | odd | 2 | |||
7650.2.a.dm.1.2 | 3 | 15.14 | odd | 2 |