Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, 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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.43348 | −1.01362 | −0.506812 | − | 0.862057i | \(-0.669176\pi\) | ||||
−0.506812 | + | 0.862057i | \(0.669176\pi\) | |||||||
\(3\) | 2.46422 | 1.42272 | 0.711359 | − | 0.702829i | \(-0.248080\pi\) | ||||
0.711359 | + | 0.702829i | \(0.248080\pi\) | |||||||
\(4\) | 0.0548683 | 0.0274341 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.53241 | −1.44210 | ||||||||
\(7\) | 5.17959 | 1.95770 | 0.978851 | − | 0.204574i | \(-0.0655807\pi\) | ||||
0.978851 | + | 0.204574i | \(0.0655807\pi\) | |||||||
\(8\) | 2.78831 | 0.985816 | ||||||||
\(9\) | 3.07238 | 1.02413 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.79186 | 0.841777 | 0.420889 | − | 0.907112i | \(-0.361718\pi\) | ||||
0.420889 | + | 0.907112i | \(0.361718\pi\) | |||||||
\(12\) | 0.135207 | 0.0390310 | ||||||||
\(13\) | −1.04374 | −0.289481 | −0.144741 | − | 0.989470i | \(-0.546235\pi\) | ||||
−0.144741 | + | 0.989470i | \(0.546235\pi\) | |||||||
\(14\) | −7.42485 | −1.98437 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.10673 | −1.02668 | ||||||||
\(17\) | −1.22801 | −0.297836 | −0.148918 | − | 0.988850i | \(-0.547579\pi\) | ||||
−0.148918 | + | 0.988850i | \(0.547579\pi\) | |||||||
\(18\) | −4.40419 | −1.03808 | ||||||||
\(19\) | −0.657935 | −0.150941 | −0.0754704 | − | 0.997148i | \(-0.524046\pi\) | ||||
−0.0754704 | + | 0.997148i | \(0.524046\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.7637 | 2.78526 | ||||||||
\(22\) | −4.00208 | −0.853246 | ||||||||
\(23\) | −5.23420 | −1.09141 | −0.545703 | − | 0.837978i | \(-0.683737\pi\) | ||||
−0.545703 | + | 0.837978i | \(0.683737\pi\) | |||||||
\(24\) | 6.87101 | 1.40254 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.49618 | 0.293425 | ||||||||
\(27\) | 0.178351 | 0.0343237 | ||||||||
\(28\) | 0.284195 | 0.0537079 | ||||||||
\(29\) | 2.90874 | 0.540140 | 0.270070 | − | 0.962841i | \(-0.412953\pi\) | ||||
0.270070 | + | 0.962841i | \(0.412953\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.0888286 | −0.0159541 | −0.00797705 | − | 0.999968i | \(-0.502539\pi\) | ||||
−0.00797705 | + | 0.999968i | \(0.502539\pi\) | |||||||
\(32\) | 0.310295 | 0.0548529 | ||||||||
\(33\) | 6.87975 | 1.19761 | ||||||||
\(34\) | 1.76033 | 0.301894 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.168576 | 0.0280960 | ||||||||
\(37\) | 8.62366 | 1.41772 | 0.708861 | − | 0.705348i | \(-0.249209\pi\) | ||||
0.708861 | + | 0.705348i | \(0.249209\pi\) | |||||||
\(38\) | 0.943138 | 0.152997 | ||||||||
\(39\) | −2.57200 | −0.411850 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.475889 | 0.0743214 | 0.0371607 | − | 0.999309i | \(-0.488169\pi\) | ||||
0.0371607 | + | 0.999309i | \(0.488169\pi\) | |||||||
\(42\) | −18.2965 | −2.82320 | ||||||||
\(43\) | −9.62961 | −1.46850 | −0.734251 | − | 0.678878i | \(-0.762466\pi\) | ||||
−0.734251 | + | 0.678878i | \(0.762466\pi\) | |||||||
\(44\) | 0.153184 | 0.0230934 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.50313 | 1.10628 | ||||||||
\(47\) | 11.2840 | 1.64594 | 0.822969 | − | 0.568087i | \(-0.192316\pi\) | ||||
0.822969 | + | 0.568087i | \(0.192316\pi\) | |||||||
\(48\) | −10.1199 | −1.46068 | ||||||||
\(49\) | 19.8282 | 2.83260 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.02608 | −0.423736 | ||||||||
\(52\) | −0.0572681 | −0.00794166 | ||||||||
\(53\) | −4.33694 | −0.595725 | −0.297862 | − | 0.954609i | \(-0.596274\pi\) | ||||
−0.297862 | + | 0.954609i | \(0.596274\pi\) | |||||||
\(54\) | −0.255663 | −0.0347913 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 14.4423 | 1.92994 | ||||||||
\(57\) | −1.62130 | −0.214746 | ||||||||
\(58\) | −4.16963 | −0.547499 | ||||||||
\(59\) | 6.20571 | 0.807915 | 0.403957 | − | 0.914778i | \(-0.367634\pi\) | ||||
0.403957 | + | 0.914778i | \(0.367634\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.05916 | −0.263648 | −0.131824 | − | 0.991273i | \(-0.542083\pi\) | ||||
−0.131824 | + | 0.991273i | \(0.542083\pi\) | |||||||
\(62\) | 0.127334 | 0.0161715 | ||||||||
\(63\) | 15.9137 | 2.00493 | ||||||||
\(64\) | 7.76865 | 0.971081 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −9.86199 | −1.21393 | ||||||||
\(67\) | 9.29073 | 1.13504 | 0.567522 | − | 0.823358i | \(-0.307902\pi\) | ||||
0.567522 | + | 0.823358i | \(0.307902\pi\) | |||||||
\(68\) | −0.0673787 | −0.00817087 | ||||||||
\(69\) | −12.8982 | −1.55276 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.61695 | 0.191897 | 0.0959485 | − | 0.995386i | \(-0.469412\pi\) | ||||
0.0959485 | + | 0.995386i | \(0.469412\pi\) | |||||||
\(72\) | 8.56674 | 1.00960 | ||||||||
\(73\) | −15.5909 | −1.82478 | −0.912389 | − | 0.409324i | \(-0.865765\pi\) | ||||
−0.912389 | + | 0.409324i | \(0.865765\pi\) | |||||||
\(74\) | −12.3619 | −1.43704 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.0360998 | −0.00414093 | ||||||||
\(77\) | 14.4607 | 1.64795 | ||||||||
\(78\) | 3.68691 | 0.417461 | ||||||||
\(79\) | −0.552668 | −0.0621800 | −0.0310900 | − | 0.999517i | \(-0.509898\pi\) | ||||
−0.0310900 | + | 0.999517i | \(0.509898\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.77763 | −0.975293 | ||||||||
\(82\) | −0.682178 | −0.0753340 | ||||||||
\(83\) | 2.67927 | 0.294088 | 0.147044 | − | 0.989130i | \(-0.453024\pi\) | ||||
0.147044 | + | 0.989130i | \(0.453024\pi\) | |||||||
\(84\) | 0.700320 | 0.0764111 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 13.8039 | 1.48851 | ||||||||
\(87\) | 7.16778 | 0.768467 | ||||||||
\(88\) | 7.78457 | 0.829838 | ||||||||
\(89\) | 13.0002 | 1.37802 | 0.689011 | − | 0.724750i | \(-0.258045\pi\) | ||||
0.689011 | + | 0.724750i | \(0.258045\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.40614 | −0.566718 | ||||||||
\(92\) | −0.287192 | −0.0299418 | ||||||||
\(93\) | −0.218893 | −0.0226982 | ||||||||
\(94\) | −16.1754 | −1.66836 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.764635 | 0.0780402 | ||||||||
\(97\) | 7.94354 | 0.806545 | 0.403272 | − | 0.915080i | \(-0.367873\pi\) | ||||
0.403272 | + | 0.915080i | \(0.367873\pi\) | |||||||
\(98\) | −28.4233 | −2.87119 | ||||||||
\(99\) | 8.57764 | 0.862085 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.2339 | 1.01831 | 0.509155 | − | 0.860675i | \(-0.329958\pi\) | ||||
0.509155 | + | 0.860675i | \(0.329958\pi\) | |||||||
\(102\) | 4.33783 | 0.429509 | ||||||||
\(103\) | 15.7121 | 1.54816 | 0.774078 | − | 0.633091i | \(-0.218214\pi\) | ||||
0.774078 | + | 0.633091i | \(0.218214\pi\) | |||||||
\(104\) | −2.91027 | −0.285375 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.21693 | 0.603841 | ||||||||
\(107\) | 19.3889 | 1.87439 | 0.937196 | − | 0.348803i | \(-0.113412\pi\) | ||||
0.937196 | + | 0.348803i | \(0.113412\pi\) | |||||||
\(108\) | 0.00978582 | 0.000941641 0 | ||||||||
\(109\) | 6.76288 | 0.647767 | 0.323883 | − | 0.946097i | \(-0.395011\pi\) | ||||
0.323883 | + | 0.946097i | \(0.395011\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 21.2506 | 2.01702 | ||||||||
\(112\) | −21.2712 | −2.00994 | ||||||||
\(113\) | 9.10124 | 0.856173 | 0.428086 | − | 0.903738i | \(-0.359188\pi\) | ||||
0.428086 | + | 0.903738i | \(0.359188\pi\) | |||||||
\(114\) | 2.32410 | 0.217672 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.159598 | 0.0148183 | ||||||||
\(117\) | −3.20676 | −0.296465 | ||||||||
\(118\) | −8.89577 | −0.818922 | ||||||||
\(119\) | −6.36059 | −0.583074 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.20553 | −0.291411 | ||||||||
\(122\) | 2.95176 | 0.267240 | ||||||||
\(123\) | 1.17270 | 0.105738 | ||||||||
\(124\) | −0.00487387 | −0.000437687 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −22.8119 | −2.03225 | ||||||||
\(127\) | −0.727223 | −0.0645306 | −0.0322653 | − | 0.999479i | \(-0.510272\pi\) | ||||
−0.0322653 | + | 0.999479i | \(0.510272\pi\) | |||||||
\(128\) | −11.7568 | −1.03916 | ||||||||
\(129\) | −23.7295 | −2.08926 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.525880 | −0.0459464 | −0.0229732 | − | 0.999736i | \(-0.507313\pi\) | ||||
−0.0229732 | + | 0.999736i | \(0.507313\pi\) | |||||||
\(132\) | 0.377480 | 0.0328554 | ||||||||
\(133\) | −3.40784 | −0.295497 | ||||||||
\(134\) | −13.3181 | −1.15051 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.42407 | −0.293612 | ||||||||
\(137\) | −6.88081 | −0.587868 | −0.293934 | − | 0.955826i | \(-0.594965\pi\) | ||||
−0.293934 | + | 0.955826i | \(0.594965\pi\) | |||||||
\(138\) | 18.4894 | 1.57392 | ||||||||
\(139\) | 2.59618 | 0.220205 | 0.110103 | − | 0.993920i | \(-0.464882\pi\) | ||||
0.110103 | + | 0.993920i | \(0.464882\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 27.8062 | 2.34170 | ||||||||
\(142\) | −2.31787 | −0.194512 | ||||||||
\(143\) | −2.91397 | −0.243678 | ||||||||
\(144\) | −12.6174 | −1.05145 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 22.3493 | 1.84964 | ||||||||
\(147\) | 48.8610 | 4.02999 | ||||||||
\(148\) | 0.473166 | 0.0388940 | ||||||||
\(149\) | −17.9601 | −1.47135 | −0.735675 | − | 0.677335i | \(-0.763135\pi\) | ||||
−0.735675 | + | 0.677335i | \(0.763135\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.0714 | −1.71476 | −0.857382 | − | 0.514681i | \(-0.827910\pi\) | ||||
−0.857382 | + | 0.514681i | \(0.827910\pi\) | |||||||
\(152\) | −1.83453 | −0.148800 | ||||||||
\(153\) | −3.77291 | −0.305021 | ||||||||
\(154\) | −20.7291 | −1.67040 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.141121 | −0.0112987 | ||||||||
\(157\) | −10.0807 | −0.804529 | −0.402265 | − | 0.915523i | \(-0.631777\pi\) | ||||
−0.402265 | + | 0.915523i | \(0.631777\pi\) | |||||||
\(158\) | 0.792239 | 0.0630272 | ||||||||
\(159\) | −10.6872 | −0.847548 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −27.1110 | −2.13665 | ||||||||
\(162\) | 12.5826 | 0.988580 | ||||||||
\(163\) | 15.6749 | 1.22776 | 0.613878 | − | 0.789401i | \(-0.289609\pi\) | ||||
0.613878 | + | 0.789401i | \(0.289609\pi\) | |||||||
\(164\) | 0.0261112 | 0.00203894 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.84068 | −0.298095 | ||||||||
\(167\) | −2.23696 | −0.173101 | −0.0865505 | − | 0.996247i | \(-0.527584\pi\) | ||||
−0.0865505 | + | 0.996247i | \(0.527584\pi\) | |||||||
\(168\) | 35.5890 | 2.74575 | ||||||||
\(169\) | −11.9106 | −0.916201 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.02143 | −0.154582 | ||||||||
\(172\) | −0.528360 | −0.0402871 | ||||||||
\(173\) | 10.8730 | 0.826658 | 0.413329 | − | 0.910582i | \(-0.364366\pi\) | ||||
0.413329 | + | 0.910582i | \(0.364366\pi\) | |||||||
\(174\) | −10.2749 | −0.778936 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −11.4654 | −0.864237 | ||||||||
\(177\) | 15.2922 | 1.14943 | ||||||||
\(178\) | −18.6356 | −1.39680 | ||||||||
\(179\) | 4.70527 | 0.351688 | 0.175844 | − | 0.984418i | \(-0.443735\pi\) | ||||
0.175844 | + | 0.984418i | \(0.443735\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.72151 | −0.425277 | −0.212638 | − | 0.977131i | \(-0.568206\pi\) | ||||
−0.212638 | + | 0.977131i | \(0.568206\pi\) | |||||||
\(182\) | 7.74960 | 0.574439 | ||||||||
\(183\) | −5.07422 | −0.375097 | ||||||||
\(184\) | −14.5946 | −1.07593 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.313779 | 0.0230074 | ||||||||
\(187\) | −3.42843 | −0.250711 | ||||||||
\(188\) | 0.619132 | 0.0451549 | ||||||||
\(189\) | 0.923787 | 0.0671956 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.5048 | 1.41132 | 0.705660 | − | 0.708551i | \(-0.250651\pi\) | ||||
0.705660 | + | 0.708551i | \(0.250651\pi\) | |||||||
\(192\) | 19.1437 | 1.38157 | ||||||||
\(193\) | 21.3217 | 1.53477 | 0.767384 | − | 0.641187i | \(-0.221558\pi\) | ||||
0.767384 | + | 0.641187i | \(0.221558\pi\) | |||||||
\(194\) | −11.3869 | −0.817533 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.08794 | 0.0777099 | ||||||||
\(197\) | −22.8070 | −1.62493 | −0.812465 | − | 0.583010i | \(-0.801875\pi\) | ||||
−0.812465 | + | 0.583010i | \(0.801875\pi\) | |||||||
\(198\) | −12.2959 | −0.873831 | ||||||||
\(199\) | −18.7857 | −1.33168 | −0.665840 | − | 0.746095i | \(-0.731927\pi\) | ||||
−0.665840 | + | 0.746095i | \(0.731927\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 22.8944 | 1.61485 | ||||||||
\(202\) | −14.6701 | −1.03218 | ||||||||
\(203\) | 15.0661 | 1.05743 | ||||||||
\(204\) | −0.166036 | −0.0116248 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −22.5229 | −1.56925 | ||||||||
\(207\) | −16.0814 | −1.11774 | ||||||||
\(208\) | 4.28635 | 0.297205 | ||||||||
\(209\) | −1.83686 | −0.127058 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.886722 | −0.0610445 | −0.0305222 | − | 0.999534i | \(-0.509717\pi\) | ||||
−0.0305222 | + | 0.999534i | \(0.509717\pi\) | |||||||
\(212\) | −0.237961 | −0.0163432 | ||||||||
\(213\) | 3.98453 | 0.273015 | ||||||||
\(214\) | −27.7936 | −1.89993 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.497298 | 0.0338369 | ||||||||
\(217\) | −0.460096 | −0.0312334 | ||||||||
\(218\) | −9.69447 | −0.656592 | ||||||||
\(219\) | −38.4194 | −2.59614 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.28172 | 0.0862178 | ||||||||
\(222\) | −30.4623 | −2.04450 | ||||||||
\(223\) | −8.77254 | −0.587452 | −0.293726 | − | 0.955890i | \(-0.594895\pi\) | ||||
−0.293726 | + | 0.955890i | \(0.594895\pi\) | |||||||
\(224\) | 1.60720 | 0.107386 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.0465 | −0.867837 | ||||||||
\(227\) | −1.76117 | −0.116893 | −0.0584465 | − | 0.998291i | \(-0.518615\pi\) | ||||
−0.0584465 | + | 0.998291i | \(0.518615\pi\) | |||||||
\(228\) | −0.0889578 | −0.00589137 | ||||||||
\(229\) | 1.91528 | 0.126565 | 0.0632827 | − | 0.997996i | \(-0.479843\pi\) | ||||
0.0632827 | + | 0.997996i | \(0.479843\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 35.6343 | 2.34457 | ||||||||
\(232\) | 8.11048 | 0.532479 | ||||||||
\(233\) | −19.2871 | −1.26354 | −0.631771 | − | 0.775155i | \(-0.717672\pi\) | ||||
−0.631771 | + | 0.775155i | \(0.717672\pi\) | |||||||
\(234\) | 4.59683 | 0.300504 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.340497 | 0.0221645 | ||||||||
\(237\) | −1.36189 | −0.0884646 | ||||||||
\(238\) | 9.11778 | 0.591018 | ||||||||
\(239\) | −16.0031 | −1.03515 | −0.517577 | − | 0.855636i | \(-0.673166\pi\) | ||||
−0.517577 | + | 0.855636i | \(0.673166\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | 4.59506 | 0.295382 | ||||||||
\(243\) | −22.1651 | −1.42189 | ||||||||
\(244\) | −0.112982 | −0.00723296 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.68104 | −0.107179 | ||||||||
\(247\) | 0.686713 | 0.0436945 | ||||||||
\(248\) | −0.247682 | −0.0157278 | ||||||||
\(249\) | 6.60231 | 0.418404 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.12210 | 0.260185 | 0.130092 | − | 0.991502i | \(-0.458473\pi\) | ||||
0.130092 | + | 0.991502i | \(0.458473\pi\) | |||||||
\(252\) | 0.873155 | 0.0550036 | ||||||||
\(253\) | −14.6132 | −0.918721 | ||||||||
\(254\) | 1.04246 | 0.0654098 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.31586 | 0.0822410 | ||||||||
\(257\) | −20.2865 | −1.26543 | −0.632717 | − | 0.774383i | \(-0.718060\pi\) | ||||
−0.632717 | + | 0.774383i | \(0.718060\pi\) | |||||||
\(258\) | 34.0158 | 2.11773 | ||||||||
\(259\) | 44.6671 | 2.77548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.93675 | 0.553171 | ||||||||
\(262\) | 0.753839 | 0.0465723 | ||||||||
\(263\) | −5.48083 | −0.337962 | −0.168981 | − | 0.985619i | \(-0.554048\pi\) | ||||
−0.168981 | + | 0.985619i | \(0.554048\pi\) | |||||||
\(264\) | 19.1829 | 1.18062 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.88507 | 0.299523 | ||||||||
\(267\) | 32.0354 | 1.96054 | ||||||||
\(268\) | 0.509766 | 0.0311389 | ||||||||
\(269\) | −8.66729 | −0.528454 | −0.264227 | − | 0.964460i | \(-0.585117\pi\) | ||||
−0.264227 | + | 0.964460i | \(0.585117\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.56471 | 0.398778 | 0.199389 | − | 0.979920i | \(-0.436104\pi\) | ||||
0.199389 | + | 0.979920i | \(0.436104\pi\) | |||||||
\(272\) | 5.04310 | 0.305783 | ||||||||
\(273\) | −13.3219 | −0.806279 | ||||||||
\(274\) | 9.86352 | 0.595877 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.707703 | −0.0425987 | ||||||||
\(277\) | 11.5757 | 0.695515 | 0.347758 | − | 0.937584i | \(-0.386943\pi\) | ||||
0.347758 | + | 0.937584i | \(0.386943\pi\) | |||||||
\(278\) | −3.72158 | −0.223206 | ||||||||
\(279\) | −0.272915 | −0.0163390 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.1853 | 1.38312 | 0.691560 | − | 0.722319i | \(-0.256924\pi\) | ||||
0.691560 | + | 0.722319i | \(0.256924\pi\) | |||||||
\(282\) | −39.8597 | −2.37361 | ||||||||
\(283\) | −17.3530 | −1.03153 | −0.515766 | − | 0.856730i | \(-0.672493\pi\) | ||||
−0.515766 | + | 0.856730i | \(0.672493\pi\) | |||||||
\(284\) | 0.0887194 | 0.00526453 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.17712 | 0.246998 | ||||||||
\(287\) | 2.46491 | 0.145499 | ||||||||
\(288\) | 0.953343 | 0.0561763 | ||||||||
\(289\) | −15.4920 | −0.911294 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 19.5746 | 1.14749 | ||||||||
\(292\) | −0.855447 | −0.0500612 | ||||||||
\(293\) | 13.0688 | 0.763487 | 0.381744 | − | 0.924268i | \(-0.375324\pi\) | ||||
0.381744 | + | 0.924268i | \(0.375324\pi\) | |||||||
\(294\) | −70.0413 | −4.08489 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 24.0454 | 1.39761 | ||||||||
\(297\) | 0.497931 | 0.0288929 | ||||||||
\(298\) | 25.7455 | 1.49140 | ||||||||
\(299\) | 5.46314 | 0.315941 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −49.8775 | −2.87489 | ||||||||
\(302\) | 30.2054 | 1.73813 | ||||||||
\(303\) | 25.2185 | 1.44877 | ||||||||
\(304\) | 2.70196 | 0.154968 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 5.40839 | 0.309177 | ||||||||
\(307\) | 12.8961 | 0.736018 | 0.368009 | − | 0.929822i | \(-0.380040\pi\) | ||||
0.368009 | + | 0.929822i | \(0.380040\pi\) | |||||||
\(308\) | 0.793433 | 0.0452101 | ||||||||
\(309\) | 38.7180 | 2.20259 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.1630 | 1.20004 | 0.600022 | − | 0.799983i | \(-0.295158\pi\) | ||||
0.600022 | + | 0.799983i | \(0.295158\pi\) | |||||||
\(312\) | −7.17154 | −0.406008 | ||||||||
\(313\) | 8.30818 | 0.469606 | 0.234803 | − | 0.972043i | \(-0.424556\pi\) | ||||
0.234803 | + | 0.972043i | \(0.424556\pi\) | |||||||
\(314\) | 14.4505 | 0.815491 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.0303239 | −0.00170585 | ||||||||
\(317\) | 6.88752 | 0.386842 | 0.193421 | − | 0.981116i | \(-0.438042\pi\) | ||||
0.193421 | + | 0.981116i | \(0.438042\pi\) | |||||||
\(318\) | 15.3199 | 0.859095 | ||||||||
\(319\) | 8.12080 | 0.454677 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 47.7784 | 2.66673 | ||||||||
\(322\) | 38.8632 | 2.16576 | ||||||||
\(323\) | 0.807951 | 0.0449556 | ||||||||
\(324\) | −0.481614 | −0.0267563 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −22.4697 | −1.24448 | ||||||||
\(327\) | 16.6652 | 0.921589 | ||||||||
\(328\) | 1.32693 | 0.0732673 | ||||||||
\(329\) | 58.4464 | 3.22226 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.7637 | −1.03135 | −0.515674 | − | 0.856785i | \(-0.672459\pi\) | ||||
−0.515674 | + | 0.856785i | \(0.672459\pi\) | |||||||
\(332\) | 0.147007 | 0.00806805 | ||||||||
\(333\) | 26.4951 | 1.45192 | ||||||||
\(334\) | 3.20664 | 0.175459 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −52.4168 | −2.85957 | ||||||||
\(337\) | −1.51865 | −0.0827260 | −0.0413630 | − | 0.999144i | \(-0.513170\pi\) | ||||
−0.0413630 | + | 0.999144i | \(0.513170\pi\) | |||||||
\(338\) | 17.0736 | 0.928683 | ||||||||
\(339\) | 22.4274 | 1.21809 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.247997 | −0.0134298 | ||||||||
\(342\) | 2.89768 | 0.156688 | ||||||||
\(343\) | 66.4448 | 3.58768 | ||||||||
\(344\) | −26.8503 | −1.44767 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.5862 | −0.837920 | ||||||||
\(347\) | 30.3377 | 1.62861 | 0.814307 | − | 0.580435i | \(-0.197117\pi\) | ||||
0.814307 | + | 0.580435i | \(0.197117\pi\) | |||||||
\(348\) | 0.393284 | 0.0210822 | ||||||||
\(349\) | −12.8971 | −0.690363 | −0.345182 | − | 0.938536i | \(-0.612183\pi\) | ||||
−0.345182 | + | 0.938536i | \(0.612183\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.186152 | −0.00993606 | ||||||||
\(352\) | 0.866300 | 0.0461739 | ||||||||
\(353\) | −14.8812 | −0.792046 | −0.396023 | − | 0.918241i | \(-0.629610\pi\) | ||||
−0.396023 | + | 0.918241i | \(0.629610\pi\) | |||||||
\(354\) | −21.9211 | −1.16510 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.713301 | 0.0378049 | ||||||||
\(357\) | −15.6739 | −0.829550 | ||||||||
\(358\) | −6.74491 | −0.356480 | ||||||||
\(359\) | −6.68516 | −0.352829 | −0.176415 | − | 0.984316i | \(-0.556450\pi\) | ||||
−0.176415 | + | 0.984316i | \(0.556450\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5671 | −0.977217 | ||||||||
\(362\) | 8.20168 | 0.431071 | ||||||||
\(363\) | −7.89912 | −0.414596 | ||||||||
\(364\) | −0.296626 | −0.0155474 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 7.27379 | 0.380207 | ||||||||
\(367\) | −15.3030 | −0.798811 | −0.399405 | − | 0.916774i | \(-0.630783\pi\) | ||||
−0.399405 | + | 0.916774i | \(0.630783\pi\) | |||||||
\(368\) | 21.4954 | 1.12053 | ||||||||
\(369\) | 1.46211 | 0.0761144 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.4636 | −1.16625 | ||||||||
\(372\) | −0.0120103 | −0.000622705 0 | ||||||||
\(373\) | 12.1156 | 0.627324 | 0.313662 | − | 0.949535i | \(-0.398444\pi\) | ||||
0.313662 | + | 0.949535i | \(0.398444\pi\) | |||||||
\(374\) | 4.91459 | 0.254127 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 31.4632 | 1.62259 | ||||||||
\(377\) | −3.03597 | −0.156360 | ||||||||
\(378\) | −1.32423 | −0.0681111 | ||||||||
\(379\) | −7.60280 | −0.390530 | −0.195265 | − | 0.980751i | \(-0.562557\pi\) | ||||
−0.195265 | + | 0.980751i | \(0.562557\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.79204 | −0.0918088 | ||||||||
\(382\) | −27.9598 | −1.43055 | ||||||||
\(383\) | −5.69888 | −0.291199 | −0.145600 | − | 0.989344i | \(-0.546511\pi\) | ||||
−0.145600 | + | 0.989344i | \(0.546511\pi\) | |||||||
\(384\) | −28.9713 | −1.47844 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −30.5642 | −1.55568 | ||||||||
\(387\) | −29.5858 | −1.50393 | ||||||||
\(388\) | 0.435849 | 0.0221269 | ||||||||
\(389\) | 22.6246 | 1.14711 | 0.573557 | − | 0.819166i | \(-0.305563\pi\) | ||||
0.573557 | + | 0.819166i | \(0.305563\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.42765 | 0.325060 | ||||||||
\(392\) | 55.2871 | 2.79242 | ||||||||
\(393\) | −1.29588 | −0.0653687 | ||||||||
\(394\) | 32.6934 | 1.64707 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.470640 | 0.0236506 | ||||||||
\(397\) | 6.33449 | 0.317919 | 0.158959 | − | 0.987285i | \(-0.449186\pi\) | ||||
0.158959 | + | 0.987285i | \(0.449186\pi\) | |||||||
\(398\) | 26.9289 | 1.34982 | ||||||||
\(399\) | −8.39766 | −0.420409 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.3255 | 0.515633 | 0.257817 | − | 0.966194i | \(-0.416997\pi\) | ||||
0.257817 | + | 0.966194i | \(0.416997\pi\) | |||||||
\(402\) | −32.8187 | −1.63685 | ||||||||
\(403\) | 0.0927139 | 0.00461841 | ||||||||
\(404\) | 0.561515 | 0.0279364 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −21.5970 | −1.07184 | ||||||||
\(407\) | 24.0761 | 1.19341 | ||||||||
\(408\) | −8.43766 | −0.417726 | ||||||||
\(409\) | 29.2410 | 1.44587 | 0.722937 | − | 0.690914i | \(-0.242792\pi\) | ||||
0.722937 | + | 0.690914i | \(0.242792\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.9558 | −0.836369 | ||||||||
\(412\) | 0.862094 | 0.0424723 | ||||||||
\(413\) | 32.1431 | 1.58166 | ||||||||
\(414\) | 23.0524 | 1.13297 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.323867 | −0.0158789 | ||||||||
\(417\) | 6.39757 | 0.313290 | ||||||||
\(418\) | 2.63311 | 0.128790 | ||||||||
\(419\) | −16.1489 | −0.788928 | −0.394464 | − | 0.918911i | \(-0.629070\pi\) | ||||
−0.394464 | + | 0.918911i | \(0.629070\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.71549 | −0.181082 | −0.0905410 | − | 0.995893i | \(-0.528860\pi\) | ||||
−0.0905410 | + | 0.995893i | \(0.528860\pi\) | |||||||
\(422\) | 1.27110 | 0.0618761 | ||||||||
\(423\) | 34.6686 | 1.68565 | ||||||||
\(424\) | −12.0927 | −0.587275 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.71175 | −0.276735 | ||||||||
\(427\) | −10.6656 | −0.516145 | ||||||||
\(428\) | 1.06383 | 0.0514223 | ||||||||
\(429\) | −7.18066 | −0.346686 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.70077 | −0.322765 | −0.161382 | − | 0.986892i | \(-0.551595\pi\) | ||||
−0.161382 | + | 0.986892i | \(0.551595\pi\) | |||||||
\(432\) | −0.732440 | −0.0352395 | ||||||||
\(433\) | 39.5127 | 1.89886 | 0.949428 | − | 0.313983i | \(-0.101664\pi\) | ||||
0.949428 | + | 0.313983i | \(0.101664\pi\) | |||||||
\(434\) | 0.659539 | 0.0316589 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.371068 | 0.0177709 | ||||||||
\(437\) | 3.44377 | 0.164738 | ||||||||
\(438\) | 55.0735 | 2.63152 | ||||||||
\(439\) | −30.3954 | −1.45069 | −0.725346 | − | 0.688384i | \(-0.758320\pi\) | ||||
−0.725346 | + | 0.688384i | \(0.758320\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 60.9197 | 2.90094 | ||||||||
\(442\) | −1.83732 | −0.0873925 | ||||||||
\(443\) | −24.9368 | −1.18479 | −0.592393 | − | 0.805649i | \(-0.701817\pi\) | ||||
−0.592393 | + | 0.805649i | \(0.701817\pi\) | |||||||
\(444\) | 1.16598 | 0.0553351 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 12.5753 | 0.595456 | ||||||||
\(447\) | −44.2577 | −2.09332 | ||||||||
\(448\) | 40.2385 | 1.90109 | ||||||||
\(449\) | 16.5391 | 0.780530 | 0.390265 | − | 0.920703i | \(-0.372383\pi\) | ||||
0.390265 | + | 0.920703i | \(0.372383\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.32862 | 0.0625621 | ||||||||
\(452\) | 0.499369 | 0.0234884 | ||||||||
\(453\) | −51.9245 | −2.43962 | ||||||||
\(454\) | 2.52460 | 0.118486 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.52068 | −0.211700 | ||||||||
\(457\) | −28.7826 | −1.34639 | −0.673197 | − | 0.739463i | \(-0.735080\pi\) | ||||
−0.673197 | + | 0.739463i | \(0.735080\pi\) | |||||||
\(458\) | −2.74552 | −0.128290 | ||||||||
\(459\) | −0.219017 | −0.0102228 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.9485 | −1.44142 | −0.720708 | − | 0.693238i | \(-0.756183\pi\) | ||||
−0.720708 | + | 0.693238i | \(0.756183\pi\) | |||||||
\(462\) | −51.0811 | −2.37651 | ||||||||
\(463\) | −18.7109 | −0.869570 | −0.434785 | − | 0.900534i | \(-0.643176\pi\) | ||||
−0.434785 | + | 0.900534i | \(0.643176\pi\) | |||||||
\(464\) | −11.9454 | −0.554552 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 27.6477 | 1.28076 | ||||||||
\(467\) | 7.89229 | 0.365212 | 0.182606 | − | 0.983186i | \(-0.441547\pi\) | ||||
0.182606 | + | 0.983186i | \(0.441547\pi\) | |||||||
\(468\) | −0.175949 | −0.00813326 | ||||||||
\(469\) | 48.1222 | 2.22208 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −24.8411 | −1.14462 | ||||||||
\(472\) | 17.3034 | 0.796456 | ||||||||
\(473\) | −26.8845 | −1.23615 | ||||||||
\(474\) | 1.95225 | 0.0896698 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.348994 | −0.0159961 | ||||||||
\(477\) | −13.3247 | −0.610097 | ||||||||
\(478\) | 22.9402 | 1.04926 | ||||||||
\(479\) | −26.2048 | −1.19733 | −0.598665 | − | 0.801000i | \(-0.704302\pi\) | ||||
−0.598665 | + | 0.801000i | \(0.704302\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.00085 | −0.410404 | ||||||||
\(482\) | −1.43348 | −0.0652933 | ||||||||
\(483\) | −66.8075 | −3.03985 | ||||||||
\(484\) | −0.175882 | −0.00799462 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 31.7732 | 1.44126 | ||||||||
\(487\) | −8.82039 | −0.399690 | −0.199845 | − | 0.979827i | \(-0.564044\pi\) | ||||
−0.199845 | + | 0.979827i | \(0.564044\pi\) | |||||||
\(488\) | −5.74157 | −0.259909 | ||||||||
\(489\) | 38.6265 | 1.74675 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.1268 | −0.908309 | −0.454155 | − | 0.890923i | \(-0.650059\pi\) | ||||
−0.454155 | + | 0.890923i | \(0.650059\pi\) | |||||||
\(492\) | 0.0643438 | 0.00290084 | ||||||||
\(493\) | −3.57196 | −0.160873 | ||||||||
\(494\) | −0.984390 | −0.0442898 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.364795 | 0.0163798 | ||||||||
\(497\) | 8.37516 | 0.375677 | ||||||||
\(498\) | −9.46428 | −0.424105 | ||||||||
\(499\) | −23.4769 | −1.05097 | −0.525485 | − | 0.850803i | \(-0.676116\pi\) | ||||
−0.525485 | + | 0.850803i | \(0.676116\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.51235 | −0.246274 | ||||||||
\(502\) | −5.90896 | −0.263730 | ||||||||
\(503\) | 22.5386 | 1.00495 | 0.502474 | − | 0.864592i | \(-0.332423\pi\) | ||||
0.502474 | + | 0.864592i | \(0.332423\pi\) | |||||||
\(504\) | 44.3722 | 1.97650 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 20.9477 | 0.931238 | ||||||||
\(507\) | −29.3504 | −1.30349 | ||||||||
\(508\) | −0.0399015 | −0.00177034 | ||||||||
\(509\) | 3.72385 | 0.165057 | 0.0825283 | − | 0.996589i | \(-0.473701\pi\) | ||||
0.0825283 | + | 0.996589i | \(0.473701\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −80.7546 | −3.57237 | ||||||||
\(512\) | 21.6274 | 0.955803 | ||||||||
\(513\) | −0.117344 | −0.00518085 | ||||||||
\(514\) | 29.0803 | 1.28267 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.30200 | −0.0573172 | ||||||||
\(517\) | 31.5033 | 1.38551 | ||||||||
\(518\) | −64.0294 | −2.81329 | ||||||||
\(519\) | 26.7934 | 1.17610 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.2014 | 0.972659 | 0.486330 | − | 0.873775i | \(-0.338335\pi\) | ||||
0.486330 | + | 0.873775i | \(0.338335\pi\) | |||||||
\(522\) | −12.8107 | −0.560708 | ||||||||
\(523\) | 0.231478 | 0.0101218 | 0.00506091 | − | 0.999987i | \(-0.498389\pi\) | ||||
0.00506091 | + | 0.999987i | \(0.498389\pi\) | |||||||
\(524\) | −0.0288541 | −0.00126050 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.85666 | 0.342567 | ||||||||
\(527\) | 0.109082 | 0.00475170 | ||||||||
\(528\) | −28.2533 | −1.22957 | ||||||||
\(529\) | 4.39687 | 0.191168 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.0663 | 0.827406 | ||||||||
\(532\) | −0.186982 | −0.00810671 | ||||||||
\(533\) | −0.496704 | −0.0215146 | ||||||||
\(534\) | −45.9222 | −1.98725 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 25.9054 | 1.11894 | ||||||||
\(537\) | 11.5948 | 0.500353 | ||||||||
\(538\) | 12.4244 | 0.535654 | ||||||||
\(539\) | 55.3575 | 2.38442 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.5420 | −0.582215 | −0.291107 | − | 0.956690i | \(-0.594024\pi\) | ||||
−0.291107 | + | 0.956690i | \(0.594024\pi\) | |||||||
\(542\) | −9.41038 | −0.404211 | ||||||||
\(543\) | −14.0991 | −0.605048 | ||||||||
\(544\) | −0.381045 | −0.0163372 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 19.0967 | 0.817264 | ||||||||
\(547\) | −18.4978 | −0.790909 | −0.395455 | − | 0.918485i | \(-0.629413\pi\) | ||||
−0.395455 | + | 0.918485i | \(0.629413\pi\) | |||||||
\(548\) | −0.377538 | −0.0161276 | ||||||||
\(549\) | −6.32651 | −0.270009 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.91377 | −0.0815291 | ||||||||
\(552\) | −35.9642 | −1.53074 | ||||||||
\(553\) | −2.86260 | −0.121730 | ||||||||
\(554\) | −16.5935 | −0.704991 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.142448 | 0.00604115 | ||||||||
\(557\) | 21.1410 | 0.895771 | 0.447886 | − | 0.894091i | \(-0.352177\pi\) | ||||
0.447886 | + | 0.894091i | \(0.352177\pi\) | |||||||
\(558\) | 0.391219 | 0.0165616 | ||||||||
\(559\) | 10.0508 | 0.425104 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.44840 | −0.356692 | ||||||||
\(562\) | −33.2357 | −1.40196 | ||||||||
\(563\) | 33.7297 | 1.42154 | 0.710769 | − | 0.703426i | \(-0.248347\pi\) | ||||
0.710769 | + | 0.703426i | \(0.248347\pi\) | |||||||
\(564\) | 1.52568 | 0.0642426 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 24.8753 | 1.04559 | ||||||||
\(567\) | −45.4646 | −1.90933 | ||||||||
\(568\) | 4.50857 | 0.189175 | ||||||||
\(569\) | 11.0670 | 0.463953 | 0.231976 | − | 0.972721i | \(-0.425481\pi\) | ||||
0.231976 | + | 0.972721i | \(0.425481\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.61172 | 0.402238 | 0.201119 | − | 0.979567i | \(-0.435542\pi\) | ||||
0.201119 | + | 0.979567i | \(0.435542\pi\) | |||||||
\(572\) | −0.159885 | −0.00668511 | ||||||||
\(573\) | 48.0642 | 2.00791 | ||||||||
\(574\) | −3.53341 | −0.147482 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 23.8682 | 0.994509 | ||||||||
\(577\) | 11.8334 | 0.492632 | 0.246316 | − | 0.969190i | \(-0.420780\pi\) | ||||
0.246316 | + | 0.969190i | \(0.420780\pi\) | |||||||
\(578\) | 22.2075 | 0.923709 | ||||||||
\(579\) | 52.5413 | 2.18354 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.8775 | 0.575737 | ||||||||
\(582\) | −28.0599 | −1.16312 | ||||||||
\(583\) | −12.1081 | −0.501468 | ||||||||
\(584\) | −43.4723 | −1.79890 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.7339 | −0.773889 | ||||||||
\(587\) | −29.0431 | −1.19874 | −0.599369 | − | 0.800473i | \(-0.704582\pi\) | ||||
−0.599369 | + | 0.800473i | \(0.704582\pi\) | |||||||
\(588\) | 2.68092 | 0.110559 | ||||||||
\(589\) | 0.0584435 | 0.00240812 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −56.2014 | −2.31182 | ||||||||
\(592\) | −35.4150 | −1.45555 | ||||||||
\(593\) | −10.5632 | −0.433780 | −0.216890 | − | 0.976196i | \(-0.569591\pi\) | ||||
−0.216890 | + | 0.976196i | \(0.569591\pi\) | |||||||
\(594\) | −0.713775 | −0.0292866 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.985441 | −0.0403652 | ||||||||
\(597\) | −46.2920 | −1.89460 | ||||||||
\(598\) | −7.83131 | −0.320246 | ||||||||
\(599\) | 42.4874 | 1.73599 | 0.867995 | − | 0.496573i | \(-0.165409\pi\) | ||||
0.867995 | + | 0.496573i | \(0.165409\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.6920 | −0.558510 | −0.279255 | − | 0.960217i | \(-0.590087\pi\) | ||||
−0.279255 | + | 0.960217i | \(0.590087\pi\) | |||||||
\(602\) | 71.4984 | 2.91406 | ||||||||
\(603\) | 28.5446 | 1.16243 | ||||||||
\(604\) | −1.15615 | −0.0470431 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −36.1503 | −1.46850 | ||||||||
\(607\) | −29.5482 | −1.19932 | −0.599662 | − | 0.800253i | \(-0.704698\pi\) | ||||
−0.599662 | + | 0.800253i | \(0.704698\pi\) | |||||||
\(608\) | −0.204154 | −0.00827954 | ||||||||
\(609\) | 37.1262 | 1.50443 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.7775 | −0.476468 | ||||||||
\(612\) | −0.207013 | −0.00836800 | ||||||||
\(613\) | −6.84948 | −0.276648 | −0.138324 | − | 0.990387i | \(-0.544172\pi\) | ||||
−0.138324 | + | 0.990387i | \(0.544172\pi\) | |||||||
\(614\) | −18.4863 | −0.746046 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 40.3209 | 1.62458 | ||||||||
\(617\) | 18.9353 | 0.762306 | 0.381153 | − | 0.924512i | \(-0.375527\pi\) | ||||
0.381153 | + | 0.924512i | \(0.375527\pi\) | |||||||
\(618\) | −55.5015 | −2.23260 | ||||||||
\(619\) | 3.23449 | 0.130005 | 0.0650026 | − | 0.997885i | \(-0.479294\pi\) | ||||
0.0650026 | + | 0.997885i | \(0.479294\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.933526 | −0.0374611 | ||||||||
\(622\) | −30.3368 | −1.21639 | ||||||||
\(623\) | 67.3360 | 2.69776 | ||||||||
\(624\) | 10.5625 | 0.422839 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −11.9096 | −0.476004 | ||||||||
\(627\) | −4.52643 | −0.180768 | ||||||||
\(628\) | −0.553112 | −0.0220716 | ||||||||
\(629\) | −10.5899 | −0.422248 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.4292 | −1.33080 | −0.665398 | − | 0.746488i | \(-0.731738\pi\) | ||||
−0.665398 | + | 0.746488i | \(0.731738\pi\) | |||||||
\(632\) | −1.54101 | −0.0612981 | ||||||||
\(633\) | −2.18508 | −0.0868490 | ||||||||
\(634\) | −9.87313 | −0.392112 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.586387 | −0.0232518 | ||||||||
\(637\) | −20.6955 | −0.819984 | ||||||||
\(638\) | −11.6410 | −0.460872 | ||||||||
\(639\) | 4.96789 | 0.196527 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.4442 | 0.610010 | 0.305005 | − | 0.952351i | \(-0.401342\pi\) | ||||
0.305005 | + | 0.952351i | \(0.401342\pi\) | |||||||
\(642\) | −68.4895 | −2.70306 | ||||||||
\(643\) | −14.7173 | −0.580394 | −0.290197 | − | 0.956967i | \(-0.593721\pi\) | ||||
−0.290197 | + | 0.956967i | \(0.593721\pi\) | |||||||
\(644\) | −1.48754 | −0.0586171 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.15818 | −0.0455681 | ||||||||
\(647\) | 35.6625 | 1.40204 | 0.701019 | − | 0.713142i | \(-0.252729\pi\) | ||||
0.701019 | + | 0.713142i | \(0.252729\pi\) | |||||||
\(648\) | −24.4748 | −0.961459 | ||||||||
\(649\) | 17.3255 | 0.680084 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.13378 | −0.0444363 | ||||||||
\(652\) | 0.860057 | 0.0336824 | ||||||||
\(653\) | −43.0253 | −1.68371 | −0.841854 | − | 0.539705i | \(-0.818536\pi\) | ||||
−0.841854 | + | 0.539705i | \(0.818536\pi\) | |||||||
\(654\) | −23.8893 | −0.934145 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.95435 | −0.0763044 | ||||||||
\(657\) | −47.9012 | −1.86880 | ||||||||
\(658\) | −83.7818 | −3.26616 | ||||||||
\(659\) | −11.3198 | −0.440955 | −0.220478 | − | 0.975392i | \(-0.570762\pi\) | ||||
−0.220478 | + | 0.975392i | \(0.570762\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.1612 | 1.60099 | 0.800493 | − | 0.599342i | \(-0.204571\pi\) | ||||
0.800493 | + | 0.599342i | \(0.204571\pi\) | |||||||
\(662\) | 26.8975 | 1.04540 | ||||||||
\(663\) | 3.15844 | 0.122664 | ||||||||
\(664\) | 7.47063 | 0.289917 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −37.9803 | −1.47171 | ||||||||
\(667\) | −15.2249 | −0.589512 | ||||||||
\(668\) | −0.122738 | −0.00474888 | ||||||||
\(669\) | −21.6175 | −0.835779 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.74888 | −0.221933 | ||||||||
\(672\) | 3.96050 | 0.152780 | ||||||||
\(673\) | −27.0152 | −1.04136 | −0.520680 | − | 0.853752i | \(-0.674322\pi\) | ||||
−0.520680 | + | 0.853752i | \(0.674322\pi\) | |||||||
\(674\) | 2.17695 | 0.0838531 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.653515 | −0.0251352 | ||||||||
\(677\) | −51.7906 | −1.99047 | −0.995237 | − | 0.0974881i | \(-0.968919\pi\) | ||||
−0.995237 | + | 0.0974881i | \(0.968919\pi\) | |||||||
\(678\) | −32.1493 | −1.23469 | ||||||||
\(679\) | 41.1443 | 1.57897 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.33991 | −0.166306 | ||||||||
\(682\) | 0.355499 | 0.0136128 | ||||||||
\(683\) | −21.7709 | −0.833039 | −0.416520 | − | 0.909127i | \(-0.636750\pi\) | ||||
−0.416520 | + | 0.909127i | \(0.636750\pi\) | |||||||
\(684\) | −0.110912 | −0.00424083 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −95.2474 | −3.63656 | ||||||||
\(687\) | 4.71967 | 0.180067 | ||||||||
\(688\) | 39.5462 | 1.50768 | ||||||||
\(689\) | 4.52663 | 0.172451 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.9459 | −1.51961 | −0.759807 | − | 0.650148i | \(-0.774707\pi\) | ||||
−0.759807 | + | 0.650148i | \(0.774707\pi\) | |||||||
\(692\) | 0.596582 | 0.0226786 | ||||||||
\(693\) | 44.4287 | 1.68771 | ||||||||
\(694\) | −43.4885 | −1.65080 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 19.9860 | 0.757567 | ||||||||
\(697\) | −0.584396 | −0.0221356 | ||||||||
\(698\) | 18.4877 | 0.699769 | ||||||||
\(699\) | −47.5277 | −1.79766 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.8929 | 0.411419 | 0.205710 | − | 0.978613i | \(-0.434050\pi\) | ||||
0.205710 | + | 0.978613i | \(0.434050\pi\) | |||||||
\(702\) | 0.266846 | 0.0100714 | ||||||||
\(703\) | −5.67382 | −0.213992 | ||||||||
\(704\) | 21.6890 | 0.817434 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.3319 | 0.802837 | ||||||||
\(707\) | 53.0073 | 1.99355 | ||||||||
\(708\) | 0.839059 | 0.0315338 | ||||||||
\(709\) | −39.0384 | −1.46612 | −0.733060 | − | 0.680164i | \(-0.761908\pi\) | ||||
−0.733060 | + | 0.680164i | \(0.761908\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.69800 | −0.0636801 | ||||||||
\(712\) | 36.2487 | 1.35848 | ||||||||
\(713\) | 0.464947 | 0.0174124 | ||||||||
\(714\) | 22.4682 | 0.840852 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.258170 | 0.00964827 | ||||||||
\(717\) | −39.4352 | −1.47273 | ||||||||
\(718\) | 9.58305 | 0.357636 | ||||||||
\(719\) | −51.9115 | −1.93597 | −0.967986 | − | 0.251006i | \(-0.919239\pi\) | ||||
−0.967986 | + | 0.251006i | \(0.919239\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 81.3821 | 3.03083 | ||||||||
\(722\) | 26.6156 | 0.990531 | ||||||||
\(723\) | 2.46422 | 0.0916453 | ||||||||
\(724\) | −0.313929 | −0.0116671 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 11.3232 | 0.420245 | ||||||||
\(727\) | 38.9182 | 1.44340 | 0.721699 | − | 0.692207i | \(-0.243362\pi\) | ||||
0.721699 | + | 0.692207i | \(0.243362\pi\) | |||||||
\(728\) | −15.0740 | −0.558680 | ||||||||
\(729\) | −28.2867 | −1.04765 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.8252 | 0.437373 | ||||||||
\(732\) | −0.278413 | −0.0102905 | ||||||||
\(733\) | 41.2969 | 1.52534 | 0.762668 | − | 0.646790i | \(-0.223889\pi\) | ||||
0.762668 | + | 0.646790i | \(0.223889\pi\) | |||||||
\(734\) | 21.9366 | 0.809694 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.62415 | −0.0598668 | ||||||||
\(737\) | 25.9384 | 0.955454 | ||||||||
\(738\) | −2.09591 | −0.0771514 | ||||||||
\(739\) | −44.7870 | −1.64752 | −0.823758 | − | 0.566941i | \(-0.808127\pi\) | ||||
−0.823758 | + | 0.566941i | \(0.808127\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.69221 | 0.0621649 | ||||||||
\(742\) | 32.2011 | 1.18214 | ||||||||
\(743\) | 22.3140 | 0.818622 | 0.409311 | − | 0.912395i | \(-0.365769\pi\) | ||||
0.409311 | + | 0.912395i | \(0.365769\pi\) | |||||||
\(744\) | −0.610342 | −0.0223762 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −17.3675 | −0.635871 | ||||||||
\(747\) | 8.23172 | 0.301183 | ||||||||
\(748\) | −0.188112 | −0.00687805 | ||||||||
\(749\) | 100.426 | 3.66950 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.54056 | −0.275159 | −0.137580 | − | 0.990491i | \(-0.543932\pi\) | ||||
−0.137580 | + | 0.990491i | \(0.543932\pi\) | |||||||
\(752\) | −46.3402 | −1.68985 | ||||||||
\(753\) | 10.1578 | 0.370170 | ||||||||
\(754\) | 4.35200 | 0.158491 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.0506866 | 0.00184345 | ||||||||
\(757\) | 36.8147 | 1.33805 | 0.669026 | − | 0.743239i | \(-0.266711\pi\) | ||||
0.669026 | + | 0.743239i | \(0.266711\pi\) | |||||||
\(758\) | 10.8985 | 0.395850 | ||||||||
\(759\) | −36.0100 | −1.30708 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 45.4086 | 1.64606 | 0.823030 | − | 0.567998i | \(-0.192282\pi\) | ||||
0.823030 | + | 0.567998i | \(0.192282\pi\) | |||||||
\(762\) | 2.56885 | 0.0930596 | ||||||||
\(763\) | 35.0290 | 1.26813 | ||||||||
\(764\) | 1.07020 | 0.0387183 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.16924 | 0.295166 | ||||||||
\(767\) | −6.47714 | −0.233876 | ||||||||
\(768\) | 3.24256 | 0.117006 | ||||||||
\(769\) | −36.7641 | −1.32575 | −0.662873 | − | 0.748732i | \(-0.730663\pi\) | ||||
−0.662873 | + | 0.748732i | \(0.730663\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −49.9903 | −1.80036 | ||||||||
\(772\) | 1.16988 | 0.0421051 | ||||||||
\(773\) | −8.78587 | −0.316006 | −0.158003 | − | 0.987439i | \(-0.550506\pi\) | ||||
−0.158003 | + | 0.987439i | \(0.550506\pi\) | |||||||
\(774\) | 42.4107 | 1.52442 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 22.1491 | 0.795105 | ||||||||
\(777\) | 110.069 | 3.94872 | ||||||||
\(778\) | −32.4319 | −1.16274 | ||||||||
\(779\) | −0.313104 | −0.0112181 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.51431 | 0.161535 | ||||||||
\(782\) | −9.21391 | −0.329489 | ||||||||
\(783\) | 0.518778 | 0.0185396 | ||||||||
\(784\) | −81.4289 | −2.90818 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.85762 | 0.0662593 | ||||||||
\(787\) | −42.6718 | −1.52108 | −0.760542 | − | 0.649289i | \(-0.775067\pi\) | ||||
−0.760542 | + | 0.649289i | \(0.775067\pi\) | |||||||
\(788\) | −1.25138 | −0.0445785 | ||||||||
\(789\) | −13.5060 | −0.480825 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 47.1407 | 1.67613 | ||||||||
\(792\) | 23.9171 | 0.849858 | ||||||||
\(793\) | 2.14922 | 0.0763211 | ||||||||
\(794\) | −9.08037 | −0.322250 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.03074 | −0.0365335 | ||||||||
\(797\) | 45.6410 | 1.61669 | 0.808343 | − | 0.588711i | \(-0.200365\pi\) | ||||
0.808343 | + | 0.588711i | \(0.200365\pi\) | |||||||
\(798\) | 12.0379 | 0.426137 | ||||||||
\(799\) | −13.8568 | −0.490219 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 39.9416 | 1.41127 | ||||||||
\(802\) | −14.8015 | −0.522658 | ||||||||
\(803\) | −43.5276 | −1.53606 | ||||||||
\(804\) | 1.25618 | 0.0443019 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.132904 | −0.00468133 | ||||||||
\(807\) | −21.3581 | −0.751841 | ||||||||
\(808\) | 28.5352 | 1.00387 | ||||||||
\(809\) | 16.3698 | 0.575532 | 0.287766 | − | 0.957701i | \(-0.407088\pi\) | ||||
0.287766 | + | 0.957701i | \(0.407088\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 50.1149 | 1.75977 | 0.879886 | − | 0.475184i | \(-0.157619\pi\) | ||||
0.879886 | + | 0.475184i | \(0.157619\pi\) | |||||||
\(812\) | 0.826651 | 0.0290098 | ||||||||
\(813\) | 16.1769 | 0.567348 | ||||||||
\(814\) | −34.5126 | −1.20966 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 12.4273 | 0.435042 | ||||||||
\(817\) | 6.33566 | 0.221657 | ||||||||
\(818\) | −41.9164 | −1.46557 | ||||||||
\(819\) | −16.6097 | −0.580390 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.41793 | 0.189087 | 0.0945436 | − | 0.995521i | \(-0.469861\pi\) | ||||
0.0945436 | + | 0.995521i | \(0.469861\pi\) | |||||||
\(822\) | 24.3059 | 0.847764 | ||||||||
\(823\) | 18.4024 | 0.641468 | 0.320734 | − | 0.947169i | \(-0.396071\pi\) | ||||
0.320734 | + | 0.947169i | \(0.396071\pi\) | |||||||
\(824\) | 43.8101 | 1.52620 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −46.0765 | −1.60321 | ||||||||
\(827\) | −33.6753 | −1.17101 | −0.585503 | − | 0.810670i | \(-0.699103\pi\) | ||||
−0.585503 | + | 0.810670i | \(0.699103\pi\) | |||||||
\(828\) | −0.882361 | −0.0306642 | ||||||||
\(829\) | 10.5634 | 0.366881 | 0.183440 | − | 0.983031i | \(-0.441277\pi\) | ||||
0.183440 | + | 0.983031i | \(0.441277\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 28.5250 | 0.989522 | ||||||||
\(832\) | −8.10844 | −0.281110 | ||||||||
\(833\) | −24.3492 | −0.843650 | ||||||||
\(834\) | −9.17079 | −0.317559 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.100785 | −0.00348574 | ||||||||
\(837\) | −0.0158427 | −0.000547604 0 | ||||||||
\(838\) | 23.1492 | 0.799676 | ||||||||
\(839\) | 30.4519 | 1.05132 | 0.525658 | − | 0.850696i | \(-0.323819\pi\) | ||||
0.525658 | + | 0.850696i | \(0.323819\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.5392 | −0.708249 | ||||||||
\(842\) | 5.32609 | 0.183549 | ||||||||
\(843\) | 57.1337 | 1.96779 | ||||||||
\(844\) | −0.0486529 | −0.00167470 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −49.6968 | −1.70861 | ||||||||
\(847\) | −16.6033 | −0.570497 | ||||||||
\(848\) | 17.8106 | 0.611620 | ||||||||
\(849\) | −42.7617 | −1.46758 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −45.1380 | −1.54731 | ||||||||
\(852\) | 0.218624 | 0.00748994 | ||||||||
\(853\) | −10.3766 | −0.355287 | −0.177644 | − | 0.984095i | \(-0.556847\pi\) | ||||
−0.177644 | + | 0.984095i | \(0.556847\pi\) | |||||||
\(854\) | 15.2889 | 0.523177 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 54.0622 | 1.84781 | ||||||||
\(857\) | 37.3240 | 1.27496 | 0.637482 | − | 0.770466i | \(-0.279976\pi\) | ||||
0.637482 | + | 0.770466i | \(0.279976\pi\) | |||||||
\(858\) | 10.2933 | 0.351409 | ||||||||
\(859\) | −23.8640 | −0.814231 | −0.407115 | − | 0.913377i | \(-0.633465\pi\) | ||||
−0.407115 | + | 0.913377i | \(0.633465\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.07409 | 0.207004 | ||||||||
\(862\) | 9.60543 | 0.327162 | ||||||||
\(863\) | 38.6590 | 1.31597 | 0.657984 | − | 0.753032i | \(-0.271409\pi\) | ||||
0.657984 | + | 0.753032i | \(0.271409\pi\) | |||||||
\(864\) | 0.0553415 | 0.00188276 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −56.6406 | −1.92473 | ||||||||
\(867\) | −38.1757 | −1.29651 | ||||||||
\(868\) | −0.0252447 | −0.000856861 0 | ||||||||
\(869\) | −1.54297 | −0.0523417 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.69710 | −0.328574 | ||||||||
\(872\) | 18.8570 | 0.638579 | ||||||||
\(873\) | 24.4056 | 0.826003 | ||||||||
\(874\) | −4.93658 | −0.166982 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.10801 | −0.0712230 | ||||||||
\(877\) | −28.9135 | −0.976341 | −0.488170 | − | 0.872748i | \(-0.662335\pi\) | ||||
−0.488170 | + | 0.872748i | \(0.662335\pi\) | |||||||
\(878\) | 43.5712 | 1.47046 | ||||||||
\(879\) | 32.2044 | 1.08623 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.1236 | 0.475835 | 0.237918 | − | 0.971285i | \(-0.423535\pi\) | ||||
0.237918 | + | 0.971285i | \(0.423535\pi\) | |||||||
\(882\) | −87.3272 | −2.94046 | ||||||||
\(883\) | 18.6110 | 0.626310 | 0.313155 | − | 0.949702i | \(-0.398614\pi\) | ||||
0.313155 | + | 0.949702i | \(0.398614\pi\) | |||||||
\(884\) | 0.0703258 | 0.00236531 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 35.7465 | 1.20093 | ||||||||
\(887\) | 4.35743 | 0.146308 | 0.0731541 | − | 0.997321i | \(-0.476693\pi\) | ||||
0.0731541 | + | 0.997321i | \(0.476693\pi\) | |||||||
\(888\) | 59.2533 | 1.98841 | ||||||||
\(889\) | −3.76672 | −0.126332 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −24.5059 | −0.820979 | ||||||||
\(892\) | −0.481334 | −0.0161163 | ||||||||
\(893\) | −7.42413 | −0.248439 | ||||||||
\(894\) | 63.4425 | 2.12184 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −60.8955 | −2.03437 | ||||||||
\(897\) | 13.4624 | 0.449496 | ||||||||
\(898\) | −23.7085 | −0.791164 | ||||||||
\(899\) | −0.258380 | −0.00861744 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.32580 | 0.177428 | ||||||||
\(902\) | −1.90455 | −0.0634144 | ||||||||
\(903\) | −122.909 | −4.09016 | ||||||||
\(904\) | 25.3771 | 0.844029 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 74.4327 | 2.47286 | ||||||||
\(907\) | 53.9300 | 1.79072 | 0.895359 | − | 0.445345i | \(-0.146919\pi\) | ||||
0.895359 | + | 0.445345i | \(0.146919\pi\) | |||||||
\(908\) | −0.0966324 | −0.00320686 | ||||||||
\(909\) | 31.4423 | 1.04288 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.92385 | 0.0968714 | 0.0484357 | − | 0.998826i | \(-0.484576\pi\) | ||||
0.0484357 | + | 0.998826i | \(0.484576\pi\) | |||||||
\(912\) | 6.65822 | 0.220476 | ||||||||
\(913\) | 7.48014 | 0.247557 | ||||||||
\(914\) | 41.2594 | 1.36474 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.105088 | 0.00347221 | ||||||||
\(917\) | −2.72384 | −0.0899493 | ||||||||
\(918\) | 0.313957 | 0.0103621 | ||||||||
\(919\) | −51.8138 | −1.70918 | −0.854590 | − | 0.519303i | \(-0.826192\pi\) | ||||
−0.854590 | + | 0.519303i | \(0.826192\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 31.7788 | 1.04715 | ||||||||
\(922\) | 44.3641 | 1.46106 | ||||||||
\(923\) | −1.68768 | −0.0555506 | ||||||||
\(924\) | 1.95519 | 0.0643211 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 26.8217 | 0.881417 | ||||||||
\(927\) | 48.2734 | 1.58551 | ||||||||
\(928\) | 0.902568 | 0.0296283 | ||||||||
\(929\) | −4.04344 | −0.132661 | −0.0663306 | − | 0.997798i | \(-0.521129\pi\) | ||||
−0.0663306 | + | 0.997798i | \(0.521129\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.0457 | −0.427555 | ||||||||
\(932\) | −1.05825 | −0.0346642 | ||||||||
\(933\) | 52.1503 | 1.70732 | ||||||||
\(934\) | −11.3135 | −0.370188 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −8.94143 | −0.292260 | ||||||||
\(937\) | 30.4753 | 0.995586 | 0.497793 | − | 0.867296i | \(-0.334144\pi\) | ||||
0.497793 | + | 0.867296i | \(0.334144\pi\) | |||||||
\(938\) | −68.9823 | −2.25235 | ||||||||
\(939\) | 20.4732 | 0.668117 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31.1342 | −1.01495 | −0.507473 | − | 0.861668i | \(-0.669420\pi\) | ||||
−0.507473 | + | 0.861668i | \(0.669420\pi\) | |||||||
\(942\) | 35.6093 | 1.16021 | ||||||||
\(943\) | −2.49090 | −0.0811149 | ||||||||
\(944\) | −25.4852 | −0.829471 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 38.5384 | 1.25299 | ||||||||
\(947\) | 6.66732 | 0.216659 | 0.108329 | − | 0.994115i | \(-0.465450\pi\) | ||||
0.108329 | + | 0.994115i | \(0.465450\pi\) | |||||||
\(948\) | −0.0747248 | −0.00242695 | ||||||||
\(949\) | 16.2728 | 0.528239 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.9724 | 0.550367 | ||||||||
\(952\) | −17.7353 | −0.574804 | ||||||||
\(953\) | −48.4890 | −1.57071 | −0.785356 | − | 0.619045i | \(-0.787520\pi\) | ||||
−0.785356 | + | 0.619045i | \(0.787520\pi\) | |||||||
\(954\) | 19.1007 | 0.618409 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.878063 | −0.0283986 | ||||||||
\(957\) | 20.0114 | 0.646878 | ||||||||
\(958\) | 37.5641 | 1.21364 | ||||||||
\(959\) | −35.6398 | −1.15087 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9921 | −0.999745 | ||||||||
\(962\) | 12.9026 | 0.415995 | ||||||||
\(963\) | 59.5699 | 1.91961 | ||||||||
\(964\) | 0.0548683 | 0.00176719 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 95.7674 | 3.08126 | ||||||||
\(967\) | 36.4511 | 1.17219 | 0.586094 | − | 0.810243i | \(-0.300665\pi\) | ||||
0.586094 | + | 0.810243i | \(0.300665\pi\) | |||||||
\(968\) | −8.93800 | −0.287278 | ||||||||
\(969\) | 1.99097 | 0.0639591 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.64815 | −0.213349 | −0.106675 | − | 0.994294i | \(-0.534020\pi\) | ||||
−0.106675 | + | 0.994294i | \(0.534020\pi\) | |||||||
\(972\) | −1.21616 | −0.0390083 | ||||||||
\(973\) | 13.4472 | 0.431097 | ||||||||
\(974\) | 12.6439 | 0.405136 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.45640 | 0.270683 | ||||||||
\(977\) | −41.3101 | −1.32163 | −0.660814 | − | 0.750550i | \(-0.729789\pi\) | ||||
−0.660814 | + | 0.750550i | \(0.729789\pi\) | |||||||
\(978\) | −55.3704 | −1.77055 | ||||||||
\(979\) | 36.2948 | 1.15999 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.7781 | 0.663394 | ||||||||
\(982\) | 28.8514 | 0.920684 | ||||||||
\(983\) | 1.36032 | 0.0433874 | 0.0216937 | − | 0.999765i | \(-0.493094\pi\) | ||||
0.0216937 | + | 0.999765i | \(0.493094\pi\) | |||||||
\(984\) | 3.26984 | 0.104239 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.12034 | 0.163065 | ||||||||
\(987\) | 144.025 | 4.58436 | ||||||||
\(988\) | 0.0376787 | 0.00119872 | ||||||||
\(989\) | 50.4033 | 1.60273 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48.3616 | −1.53626 | −0.768128 | − | 0.640296i | \(-0.778811\pi\) | ||||
−0.768128 | + | 0.640296i | \(0.778811\pi\) | |||||||
\(992\) | −0.0275631 | −0.000875129 0 | ||||||||
\(993\) | −46.2380 | −1.46732 | ||||||||
\(994\) | −12.0056 | −0.380796 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.362257 | 0.0114786 | ||||||||
\(997\) | 40.6531 | 1.28750 | 0.643748 | − | 0.765238i | \(-0.277379\pi\) | ||||
0.643748 | + | 0.765238i | \(0.277379\pi\) | |||||||
\(998\) | 33.6537 | 1.06529 | ||||||||
\(999\) | 1.53804 | 0.0486615 |
(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 | 6025.2.a.n.1.10 | yes | 40 | |
5.4 | even | 2 | 6025.2.a.m.1.31 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6025.2.a.m.1.31 | ✓ | 40 | 5.4 | even | 2 | ||
6025.2.a.n.1.10 | yes | 40 | 1.1 | even | 1 | trivial |