Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4018,2,Mod(1,4018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4018, 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("4018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4018 = 2 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4018.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: | \(32.0838915322\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.5163008.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 5x^{2} - 6x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-1.14577\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4018.1 |
$q$-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 | ||||||||
\(3\) | 3.30757 | 1.90963 | 0.954814 | − | 0.297203i | \(-0.0960538\pi\) | ||||
0.954814 | + | 0.297203i | \(0.0960538\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.87277 | 1.73196 | 0.865979 | − | 0.500081i | \(-0.166696\pi\) | ||||
0.865979 | + | 0.500081i | \(0.166696\pi\) | |||||||
\(6\) | 3.30757 | 1.35031 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 7.94005 | 2.64668 | ||||||||
\(10\) | 3.87277 | 1.22468 | ||||||||
\(11\) | −6.05768 | −1.82646 | −0.913229 | − | 0.407446i | \(-0.866419\pi\) | ||||
−0.913229 | + | 0.407446i | \(0.866419\pi\) | |||||||
\(12\) | 3.30757 | 0.954814 | ||||||||
\(13\) | −2.22470 | −0.617020 | −0.308510 | − | 0.951221i | \(-0.599830\pi\) | ||||
−0.308510 | + | 0.951221i | \(0.599830\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 12.8095 | 3.30740 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.70041 | 1.14002 | 0.570008 | − | 0.821639i | \(-0.306940\pi\) | ||||
0.570008 | + | 0.821639i | \(0.306940\pi\) | |||||||
\(18\) | 7.94005 | 1.87149 | ||||||||
\(19\) | −3.59912 | −0.825694 | −0.412847 | − | 0.910800i | \(-0.635466\pi\) | ||||
−0.412847 | + | 0.910800i | \(0.635466\pi\) | |||||||
\(20\) | 3.87277 | 0.865979 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.05768 | −1.29150 | ||||||||
\(23\) | 0.533885 | 0.111323 | 0.0556613 | − | 0.998450i | \(-0.482273\pi\) | ||||
0.0556613 | + | 0.998450i | \(0.482273\pi\) | |||||||
\(24\) | 3.30757 | 0.675156 | ||||||||
\(25\) | 9.99839 | 1.99968 | ||||||||
\(26\) | −2.22470 | −0.436299 | ||||||||
\(27\) | 16.3396 | 3.14455 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.98064 | 1.29627 | 0.648136 | − | 0.761525i | \(-0.275549\pi\) | ||||
0.648136 | + | 0.761525i | \(0.275549\pi\) | |||||||
\(30\) | 12.8095 | 2.33868 | ||||||||
\(31\) | −9.52470 | −1.71069 | −0.855344 | − | 0.518061i | \(-0.826654\pi\) | ||||
−0.855344 | + | 0.518061i | \(0.826654\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −20.0362 | −3.48786 | ||||||||
\(34\) | 4.70041 | 0.806113 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 7.94005 | 1.32334 | ||||||||
\(37\) | −5.92259 | −0.973668 | −0.486834 | − | 0.873495i | \(-0.661848\pi\) | ||||
−0.486834 | + | 0.873495i | \(0.661848\pi\) | |||||||
\(38\) | −3.59912 | −0.583854 | ||||||||
\(39\) | −7.35835 | −1.17828 | ||||||||
\(40\) | 3.87277 | 0.612339 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.00835 | −0.458769 | −0.229385 | − | 0.973336i | \(-0.573671\pi\) | ||||
−0.229385 | + | 0.973336i | \(0.573671\pi\) | |||||||
\(44\) | −6.05768 | −0.913229 | ||||||||
\(45\) | 30.7500 | 4.58394 | ||||||||
\(46\) | 0.533885 | 0.0787170 | ||||||||
\(47\) | −11.6754 | −1.70303 | −0.851516 | − | 0.524329i | \(-0.824316\pi\) | ||||
−0.851516 | + | 0.524329i | \(0.824316\pi\) | |||||||
\(48\) | 3.30757 | 0.477407 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 9.99839 | 1.41399 | ||||||||
\(51\) | 15.5469 | 2.17701 | ||||||||
\(52\) | −2.22470 | −0.308510 | ||||||||
\(53\) | −11.2204 | −1.54124 | −0.770620 | − | 0.637295i | \(-0.780053\pi\) | ||||
−0.770620 | + | 0.637295i | \(0.780053\pi\) | |||||||
\(54\) | 16.3396 | 2.22353 | ||||||||
\(55\) | −23.4600 | −3.16335 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.9043 | −1.57677 | ||||||||
\(58\) | 6.98064 | 0.916603 | ||||||||
\(59\) | −6.19036 | −0.805916 | −0.402958 | − | 0.915219i | \(-0.632018\pi\) | ||||
−0.402958 | + | 0.915219i | \(0.632018\pi\) | |||||||
\(60\) | 12.8095 | 1.65370 | ||||||||
\(61\) | 3.60391 | 0.461433 | 0.230716 | − | 0.973021i | \(-0.425893\pi\) | ||||
0.230716 | + | 0.973021i | \(0.425893\pi\) | |||||||
\(62\) | −9.52470 | −1.20964 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −8.61575 | −1.06865 | ||||||||
\(66\) | −20.0362 | −2.46629 | ||||||||
\(67\) | 7.05464 | 0.861861 | 0.430931 | − | 0.902385i | \(-0.358185\pi\) | ||||
0.430931 | + | 0.902385i | \(0.358185\pi\) | |||||||
\(68\) | 4.70041 | 0.570008 | ||||||||
\(69\) | 1.76586 | 0.212585 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.41575 | 0.642732 | 0.321366 | − | 0.946955i | \(-0.395858\pi\) | ||||
0.321366 | + | 0.946955i | \(0.395858\pi\) | |||||||
\(72\) | 7.94005 | 0.935743 | ||||||||
\(73\) | 5.26340 | 0.616035 | 0.308017 | − | 0.951381i | \(-0.400335\pi\) | ||||
0.308017 | + | 0.951381i | \(0.400335\pi\) | |||||||
\(74\) | −5.92259 | −0.688487 | ||||||||
\(75\) | 33.0704 | 3.81864 | ||||||||
\(76\) | −3.59912 | −0.412847 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −7.35835 | −0.833169 | ||||||||
\(79\) | 0.401018 | 0.0451180 | 0.0225590 | − | 0.999746i | \(-0.492819\pi\) | ||||
0.0225590 | + | 0.999746i | \(0.492819\pi\) | |||||||
\(80\) | 3.87277 | 0.432989 | ||||||||
\(81\) | 30.2242 | 3.35824 | ||||||||
\(82\) | −1.00000 | −0.110432 | ||||||||
\(83\) | −4.69112 | −0.514917 | −0.257459 | − | 0.966289i | \(-0.582885\pi\) | ||||
−0.257459 | + | 0.966289i | \(0.582885\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.2036 | 1.97446 | ||||||||
\(86\) | −3.00835 | −0.324399 | ||||||||
\(87\) | 23.0890 | 2.47540 | ||||||||
\(88\) | −6.05768 | −0.645751 | ||||||||
\(89\) | 3.68437 | 0.390543 | 0.195271 | − | 0.980749i | \(-0.437441\pi\) | ||||
0.195271 | + | 0.980749i | \(0.437441\pi\) | |||||||
\(90\) | 30.7500 | 3.24134 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.533885 | 0.0556613 | ||||||||
\(93\) | −31.5037 | −3.26678 | ||||||||
\(94\) | −11.6754 | −1.20423 | ||||||||
\(95\) | −13.9386 | −1.43007 | ||||||||
\(96\) | 3.30757 | 0.337578 | ||||||||
\(97\) | 8.66450 | 0.879747 | 0.439873 | − | 0.898060i | \(-0.355023\pi\) | ||||
0.439873 | + | 0.898060i | \(0.355023\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −48.0982 | −4.83405 | ||||||||
\(100\) | 9.99839 | 0.999839 | ||||||||
\(101\) | 6.03142 | 0.600149 | 0.300075 | − | 0.953916i | \(-0.402988\pi\) | ||||
0.300075 | + | 0.953916i | \(0.402988\pi\) | |||||||
\(102\) | 15.5469 | 1.53938 | ||||||||
\(103\) | 8.47928 | 0.835488 | 0.417744 | − | 0.908565i | \(-0.362821\pi\) | ||||
0.417744 | + | 0.908565i | \(0.362821\pi\) | |||||||
\(104\) | −2.22470 | −0.218149 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.2204 | −1.08982 | ||||||||
\(107\) | 3.56345 | 0.344492 | 0.172246 | − | 0.985054i | \(-0.444898\pi\) | ||||
0.172246 | + | 0.985054i | \(0.444898\pi\) | |||||||
\(108\) | 16.3396 | 1.57228 | ||||||||
\(109\) | −4.11954 | −0.394581 | −0.197290 | − | 0.980345i | \(-0.563214\pi\) | ||||
−0.197290 | + | 0.980345i | \(0.563214\pi\) | |||||||
\(110\) | −23.4600 | −2.23683 | ||||||||
\(111\) | −19.5894 | −1.85934 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.96493 | −0.184845 | −0.0924227 | − | 0.995720i | \(-0.529461\pi\) | ||||
−0.0924227 | + | 0.995720i | \(0.529461\pi\) | |||||||
\(114\) | −11.9043 | −1.11494 | ||||||||
\(115\) | 2.06762 | 0.192806 | ||||||||
\(116\) | 6.98064 | 0.648136 | ||||||||
\(117\) | −17.6642 | −1.63306 | ||||||||
\(118\) | −6.19036 | −0.569868 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 12.8095 | 1.16934 | ||||||||
\(121\) | 25.6954 | 2.33595 | ||||||||
\(122\) | 3.60391 | 0.326282 | ||||||||
\(123\) | −3.30757 | −0.298234 | ||||||||
\(124\) | −9.52470 | −0.855344 | ||||||||
\(125\) | 19.3576 | 1.73140 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.907246 | 0.0805050 | 0.0402525 | − | 0.999190i | \(-0.487184\pi\) | ||||
0.0402525 | + | 0.999190i | \(0.487184\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −9.95034 | −0.876079 | ||||||||
\(130\) | −8.61575 | −0.755651 | ||||||||
\(131\) | −9.23740 | −0.807075 | −0.403538 | − | 0.914963i | \(-0.632220\pi\) | ||||
−0.403538 | + | 0.914963i | \(0.632220\pi\) | |||||||
\(132\) | −20.0362 | −1.74393 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 7.05464 | 0.609428 | ||||||||
\(135\) | 63.2795 | 5.44623 | ||||||||
\(136\) | 4.70041 | 0.403056 | ||||||||
\(137\) | −2.35366 | −0.201086 | −0.100543 | − | 0.994933i | \(-0.532058\pi\) | ||||
−0.100543 | + | 0.994933i | \(0.532058\pi\) | |||||||
\(138\) | 1.76586 | 0.150320 | ||||||||
\(139\) | 0.333978 | 0.0283276 | 0.0141638 | − | 0.999900i | \(-0.495491\pi\) | ||||
0.0141638 | + | 0.999900i | \(0.495491\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −38.6172 | −3.25216 | ||||||||
\(142\) | 5.41575 | 0.454480 | ||||||||
\(143\) | 13.4765 | 1.12696 | ||||||||
\(144\) | 7.94005 | 0.661670 | ||||||||
\(145\) | 27.0344 | 2.24509 | ||||||||
\(146\) | 5.26340 | 0.435602 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.92259 | −0.486834 | ||||||||
\(149\) | −7.44236 | −0.609702 | −0.304851 | − | 0.952400i | \(-0.598607\pi\) | ||||
−0.304851 | + | 0.952400i | \(0.598607\pi\) | |||||||
\(150\) | 33.0704 | 2.70019 | ||||||||
\(151\) | −7.22502 | −0.587964 | −0.293982 | − | 0.955811i | \(-0.594981\pi\) | ||||
−0.293982 | + | 0.955811i | \(0.594981\pi\) | |||||||
\(152\) | −3.59912 | −0.291927 | ||||||||
\(153\) | 37.3214 | 3.01726 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −36.8870 | −2.96284 | ||||||||
\(156\) | −7.35835 | −0.589139 | ||||||||
\(157\) | −12.8953 | −1.02916 | −0.514580 | − | 0.857442i | \(-0.672052\pi\) | ||||
−0.514580 | + | 0.857442i | \(0.672052\pi\) | |||||||
\(158\) | 0.401018 | 0.0319033 | ||||||||
\(159\) | −37.1123 | −2.94320 | ||||||||
\(160\) | 3.87277 | 0.306170 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 30.2242 | 2.37464 | ||||||||
\(163\) | 6.83948 | 0.535709 | 0.267855 | − | 0.963459i | \(-0.413685\pi\) | ||||
0.267855 | + | 0.963459i | \(0.413685\pi\) | |||||||
\(164\) | −1.00000 | −0.0780869 | ||||||||
\(165\) | −77.5957 | −6.04082 | ||||||||
\(166\) | −4.69112 | −0.364102 | ||||||||
\(167\) | 14.3011 | 1.10665 | 0.553327 | − | 0.832964i | \(-0.313358\pi\) | ||||
0.553327 | + | 0.832964i | \(0.313358\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.05072 | −0.619287 | ||||||||
\(170\) | 18.2036 | 1.39615 | ||||||||
\(171\) | −28.5771 | −2.18535 | ||||||||
\(172\) | −3.00835 | −0.229385 | ||||||||
\(173\) | 24.8199 | 1.88702 | 0.943510 | − | 0.331344i | \(-0.107502\pi\) | ||||
0.943510 | + | 0.331344i | \(0.107502\pi\) | |||||||
\(174\) | 23.0890 | 1.75037 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.05768 | −0.456615 | ||||||||
\(177\) | −20.4751 | −1.53900 | ||||||||
\(178\) | 3.68437 | 0.276155 | ||||||||
\(179\) | −24.3788 | −1.82216 | −0.911078 | − | 0.412234i | \(-0.864748\pi\) | ||||
−0.911078 | + | 0.412234i | \(0.864748\pi\) | |||||||
\(180\) | 30.7500 | 2.29197 | ||||||||
\(181\) | 0.0528641 | 0.00392936 | 0.00196468 | − | 0.999998i | \(-0.499375\pi\) | ||||
0.00196468 | + | 0.999998i | \(0.499375\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.9202 | 0.881166 | ||||||||
\(184\) | 0.533885 | 0.0393585 | ||||||||
\(185\) | −22.9369 | −1.68635 | ||||||||
\(186\) | −31.5037 | −2.30996 | ||||||||
\(187\) | −28.4735 | −2.08219 | ||||||||
\(188\) | −11.6754 | −0.851516 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −13.9386 | −1.01121 | ||||||||
\(191\) | −2.87401 | −0.207956 | −0.103978 | − | 0.994580i | \(-0.533157\pi\) | ||||
−0.103978 | + | 0.994580i | \(0.533157\pi\) | |||||||
\(192\) | 3.30757 | 0.238704 | ||||||||
\(193\) | −7.09383 | −0.510625 | −0.255312 | − | 0.966859i | \(-0.582178\pi\) | ||||
−0.255312 | + | 0.966859i | \(0.582178\pi\) | |||||||
\(194\) | 8.66450 | 0.622075 | ||||||||
\(195\) | −28.4972 | −2.04073 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.52134 | 0.108391 | 0.0541954 | − | 0.998530i | \(-0.482741\pi\) | ||||
0.0541954 | + | 0.998530i | \(0.482741\pi\) | |||||||
\(198\) | −48.0982 | −3.41819 | ||||||||
\(199\) | −4.90768 | −0.347896 | −0.173948 | − | 0.984755i | \(-0.555653\pi\) | ||||
−0.173948 | + | 0.984755i | \(0.555653\pi\) | |||||||
\(200\) | 9.99839 | 0.706993 | ||||||||
\(201\) | 23.3337 | 1.64583 | ||||||||
\(202\) | 6.03142 | 0.424369 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 15.5469 | 1.08850 | ||||||||
\(205\) | −3.87277 | −0.270486 | ||||||||
\(206\) | 8.47928 | 0.590779 | ||||||||
\(207\) | 4.23907 | 0.294636 | ||||||||
\(208\) | −2.22470 | −0.154255 | ||||||||
\(209\) | 21.8023 | 1.50810 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.33390 | 0.642572 | 0.321286 | − | 0.946982i | \(-0.395885\pi\) | ||||
0.321286 | + | 0.946982i | \(0.395885\pi\) | |||||||
\(212\) | −11.2204 | −0.770620 | ||||||||
\(213\) | 17.9130 | 1.22738 | ||||||||
\(214\) | 3.56345 | 0.243592 | ||||||||
\(215\) | −11.6507 | −0.794569 | ||||||||
\(216\) | 16.3396 | 1.11177 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4.11954 | −0.279011 | ||||||||
\(219\) | 17.4091 | 1.17640 | ||||||||
\(220\) | −23.4600 | −1.58167 | ||||||||
\(221\) | −10.4570 | −0.703412 | ||||||||
\(222\) | −19.5894 | −1.31475 | ||||||||
\(223\) | −6.43192 | −0.430713 | −0.215357 | − | 0.976535i | \(-0.569091\pi\) | ||||
−0.215357 | + | 0.976535i | \(0.569091\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 79.3876 | 5.29251 | ||||||||
\(226\) | −1.96493 | −0.130705 | ||||||||
\(227\) | 22.9617 | 1.52402 | 0.762011 | − | 0.647564i | \(-0.224212\pi\) | ||||
0.762011 | + | 0.647564i | \(0.224212\pi\) | |||||||
\(228\) | −11.9043 | −0.788384 | ||||||||
\(229\) | 8.12017 | 0.536596 | 0.268298 | − | 0.963336i | \(-0.413539\pi\) | ||||
0.268298 | + | 0.963336i | \(0.413539\pi\) | |||||||
\(230\) | 2.06762 | 0.136335 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.98064 | 0.458301 | ||||||||
\(233\) | −10.4623 | −0.685406 | −0.342703 | − | 0.939444i | \(-0.611342\pi\) | ||||
−0.342703 | + | 0.939444i | \(0.611342\pi\) | |||||||
\(234\) | −17.6642 | −1.15474 | ||||||||
\(235\) | −45.2162 | −2.94958 | ||||||||
\(236\) | −6.19036 | −0.402958 | ||||||||
\(237\) | 1.32640 | 0.0861586 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.5581 | −1.00637 | −0.503184 | − | 0.864180i | \(-0.667838\pi\) | ||||
−0.503184 | + | 0.864180i | \(0.667838\pi\) | |||||||
\(240\) | 12.8095 | 0.826849 | ||||||||
\(241\) | 2.30003 | 0.148158 | 0.0740789 | − | 0.997252i | \(-0.476398\pi\) | ||||
0.0740789 | + | 0.997252i | \(0.476398\pi\) | |||||||
\(242\) | 25.6954 | 1.65177 | ||||||||
\(243\) | 50.9500 | 3.26845 | ||||||||
\(244\) | 3.60391 | 0.230716 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.30757 | −0.210883 | ||||||||
\(247\) | 8.00694 | 0.509469 | ||||||||
\(248\) | −9.52470 | −0.604819 | ||||||||
\(249\) | −15.5162 | −0.983301 | ||||||||
\(250\) | 19.3576 | 1.22428 | ||||||||
\(251\) | 21.2686 | 1.34246 | 0.671231 | − | 0.741248i | \(-0.265766\pi\) | ||||
0.671231 | + | 0.741248i | \(0.265766\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.23410 | −0.203326 | ||||||||
\(254\) | 0.907246 | 0.0569257 | ||||||||
\(255\) | 60.2098 | 3.77048 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −16.4453 | −1.02583 | −0.512916 | − | 0.858439i | \(-0.671435\pi\) | ||||
−0.512916 | + | 0.858439i | \(0.671435\pi\) | |||||||
\(258\) | −9.95034 | −0.619481 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −8.61575 | −0.534326 | ||||||||
\(261\) | 55.4266 | 3.43082 | ||||||||
\(262\) | −9.23740 | −0.570688 | ||||||||
\(263\) | −2.06940 | −0.127604 | −0.0638022 | − | 0.997963i | \(-0.520323\pi\) | ||||
−0.0638022 | + | 0.997963i | \(0.520323\pi\) | |||||||
\(264\) | −20.0362 | −1.23314 | ||||||||
\(265\) | −43.4541 | −2.66936 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.1863 | 0.745792 | ||||||||
\(268\) | 7.05464 | 0.430931 | ||||||||
\(269\) | −10.1884 | −0.621197 | −0.310599 | − | 0.950541i | \(-0.600530\pi\) | ||||
−0.310599 | + | 0.950541i | \(0.600530\pi\) | |||||||
\(270\) | 63.2795 | 3.85107 | ||||||||
\(271\) | 18.1252 | 1.10103 | 0.550513 | − | 0.834827i | \(-0.314432\pi\) | ||||
0.550513 | + | 0.834827i | \(0.314432\pi\) | |||||||
\(272\) | 4.70041 | 0.285004 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.35366 | −0.142190 | ||||||||
\(275\) | −60.5670 | −3.65233 | ||||||||
\(276\) | 1.76586 | 0.106293 | ||||||||
\(277\) | 25.6514 | 1.54124 | 0.770622 | − | 0.637293i | \(-0.219946\pi\) | ||||
0.770622 | + | 0.637293i | \(0.219946\pi\) | |||||||
\(278\) | 0.333978 | 0.0200307 | ||||||||
\(279\) | −75.6266 | −4.52765 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.98688 | 0.595767 | 0.297884 | − | 0.954602i | \(-0.403719\pi\) | ||||
0.297884 | + | 0.954602i | \(0.403719\pi\) | |||||||
\(282\) | −38.6172 | −2.29962 | ||||||||
\(283\) | −10.8783 | −0.646647 | −0.323324 | − | 0.946288i | \(-0.604800\pi\) | ||||
−0.323324 | + | 0.946288i | \(0.604800\pi\) | |||||||
\(284\) | 5.41575 | 0.321366 | ||||||||
\(285\) | −46.1028 | −2.73090 | ||||||||
\(286\) | 13.4765 | 0.796882 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 7.94005 | 0.467872 | ||||||||
\(289\) | 5.09381 | 0.299636 | ||||||||
\(290\) | 27.0344 | 1.58752 | ||||||||
\(291\) | 28.6585 | 1.67999 | ||||||||
\(292\) | 5.26340 | 0.308017 | ||||||||
\(293\) | 22.7063 | 1.32652 | 0.663259 | − | 0.748390i | \(-0.269173\pi\) | ||||
0.663259 | + | 0.748390i | \(0.269173\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −23.9739 | −1.39581 | ||||||||
\(296\) | −5.92259 | −0.344243 | ||||||||
\(297\) | −98.9798 | −5.74339 | ||||||||
\(298\) | −7.44236 | −0.431125 | ||||||||
\(299\) | −1.18773 | −0.0686883 | ||||||||
\(300\) | 33.0704 | 1.90932 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −7.22502 | −0.415753 | ||||||||
\(303\) | 19.9494 | 1.14606 | ||||||||
\(304\) | −3.59912 | −0.206423 | ||||||||
\(305\) | 13.9571 | 0.799182 | ||||||||
\(306\) | 37.3214 | 2.13352 | ||||||||
\(307\) | −16.2095 | −0.925123 | −0.462562 | − | 0.886587i | \(-0.653070\pi\) | ||||
−0.462562 | + | 0.886587i | \(0.653070\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 28.0458 | 1.59547 | ||||||||
\(310\) | −36.8870 | −2.09504 | ||||||||
\(311\) | −2.08493 | −0.118225 | −0.0591127 | − | 0.998251i | \(-0.518827\pi\) | ||||
−0.0591127 | + | 0.998251i | \(0.518827\pi\) | |||||||
\(312\) | −7.35835 | −0.416584 | ||||||||
\(313\) | 26.8869 | 1.51974 | 0.759868 | − | 0.650078i | \(-0.225264\pi\) | ||||
0.759868 | + | 0.650078i | \(0.225264\pi\) | |||||||
\(314\) | −12.8953 | −0.727727 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.401018 | 0.0225590 | ||||||||
\(317\) | −17.2868 | −0.970922 | −0.485461 | − | 0.874258i | \(-0.661348\pi\) | ||||
−0.485461 | + | 0.874258i | \(0.661348\pi\) | |||||||
\(318\) | −37.1123 | −2.08115 | ||||||||
\(319\) | −42.2864 | −2.36759 | ||||||||
\(320\) | 3.87277 | 0.216495 | ||||||||
\(321\) | 11.7864 | 0.657851 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.9173 | −0.941304 | ||||||||
\(324\) | 30.2242 | 1.67912 | ||||||||
\(325\) | −22.2434 | −1.23384 | ||||||||
\(326\) | 6.83948 | 0.378804 | ||||||||
\(327\) | −13.6257 | −0.753503 | ||||||||
\(328\) | −1.00000 | −0.0552158 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −77.5957 | −4.27151 | ||||||||
\(331\) | 2.88391 | 0.158514 | 0.0792570 | − | 0.996854i | \(-0.474745\pi\) | ||||
0.0792570 | + | 0.996854i | \(0.474745\pi\) | |||||||
\(332\) | −4.69112 | −0.257459 | ||||||||
\(333\) | −47.0256 | −2.57699 | ||||||||
\(334\) | 14.3011 | 0.782522 | ||||||||
\(335\) | 27.3210 | 1.49271 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.9701 | 0.597581 | 0.298790 | − | 0.954319i | \(-0.403417\pi\) | ||||
0.298790 | + | 0.954319i | \(0.403417\pi\) | |||||||
\(338\) | −8.05072 | −0.437902 | ||||||||
\(339\) | −6.49917 | −0.352986 | ||||||||
\(340\) | 18.2036 | 0.987229 | ||||||||
\(341\) | 57.6976 | 3.12450 | ||||||||
\(342\) | −28.5771 | −1.54527 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.00835 | −0.162199 | ||||||||
\(345\) | 6.83879 | 0.368188 | ||||||||
\(346\) | 24.8199 | 1.33432 | ||||||||
\(347\) | −1.96054 | −0.105247 | −0.0526235 | − | 0.998614i | \(-0.516758\pi\) | ||||
−0.0526235 | + | 0.998614i | \(0.516758\pi\) | |||||||
\(348\) | 23.0890 | 1.23770 | ||||||||
\(349\) | 18.2795 | 0.978481 | 0.489241 | − | 0.872149i | \(-0.337274\pi\) | ||||
0.489241 | + | 0.872149i | \(0.337274\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −36.3506 | −1.94025 | ||||||||
\(352\) | −6.05768 | −0.322875 | ||||||||
\(353\) | −23.2747 | −1.23879 | −0.619394 | − | 0.785080i | \(-0.712622\pi\) | ||||
−0.619394 | + | 0.785080i | \(0.712622\pi\) | |||||||
\(354\) | −20.4751 | −1.08824 | ||||||||
\(355\) | 20.9740 | 1.11318 | ||||||||
\(356\) | 3.68437 | 0.195271 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −24.3788 | −1.28846 | ||||||||
\(359\) | 12.5000 | 0.659723 | 0.329862 | − | 0.944029i | \(-0.392998\pi\) | ||||
0.329862 | + | 0.944029i | \(0.392998\pi\) | |||||||
\(360\) | 30.7500 | 1.62067 | ||||||||
\(361\) | −6.04637 | −0.318230 | ||||||||
\(362\) | 0.0528641 | 0.00277848 | ||||||||
\(363\) | 84.9896 | 4.46080 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 20.3840 | 1.06695 | ||||||||
\(366\) | 11.9202 | 0.623078 | ||||||||
\(367\) | −8.45799 | −0.441503 | −0.220752 | − | 0.975330i | \(-0.570851\pi\) | ||||
−0.220752 | + | 0.975330i | \(0.570851\pi\) | |||||||
\(368\) | 0.533885 | 0.0278307 | ||||||||
\(369\) | −7.94005 | −0.413342 | ||||||||
\(370\) | −22.9369 | −1.19243 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −31.5037 | −1.63339 | ||||||||
\(373\) | 17.2826 | 0.894858 | 0.447429 | − | 0.894319i | \(-0.352340\pi\) | ||||
0.447429 | + | 0.894319i | \(0.352340\pi\) | |||||||
\(374\) | −28.4735 | −1.47233 | ||||||||
\(375\) | 64.0268 | 3.30633 | ||||||||
\(376\) | −11.6754 | −0.602113 | ||||||||
\(377\) | −15.5298 | −0.799825 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.5973 | 1.52031 | 0.760157 | − | 0.649740i | \(-0.225122\pi\) | ||||
0.760157 | + | 0.649740i | \(0.225122\pi\) | |||||||
\(380\) | −13.9386 | −0.715033 | ||||||||
\(381\) | 3.00078 | 0.153735 | ||||||||
\(382\) | −2.87401 | −0.147047 | ||||||||
\(383\) | 18.2590 | 0.932990 | 0.466495 | − | 0.884524i | \(-0.345517\pi\) | ||||
0.466495 | + | 0.884524i | \(0.345517\pi\) | |||||||
\(384\) | 3.30757 | 0.168789 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.09383 | −0.361066 | ||||||||
\(387\) | −23.8864 | −1.21422 | ||||||||
\(388\) | 8.66450 | 0.439873 | ||||||||
\(389\) | 22.9438 | 1.16329 | 0.581647 | − | 0.813441i | \(-0.302408\pi\) | ||||
0.581647 | + | 0.813441i | \(0.302408\pi\) | |||||||
\(390\) | −28.4972 | −1.44301 | ||||||||
\(391\) | 2.50948 | 0.126910 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −30.5534 | −1.54121 | ||||||||
\(394\) | 1.52134 | 0.0766439 | ||||||||
\(395\) | 1.55305 | 0.0781425 | ||||||||
\(396\) | −48.0982 | −2.41703 | ||||||||
\(397\) | −3.04357 | −0.152753 | −0.0763763 | − | 0.997079i | \(-0.524335\pi\) | ||||
−0.0763763 | + | 0.997079i | \(0.524335\pi\) | |||||||
\(398\) | −4.90768 | −0.246000 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.99839 | 0.499919 | ||||||||
\(401\) | 20.0372 | 1.00061 | 0.500304 | − | 0.865850i | \(-0.333221\pi\) | ||||
0.500304 | + | 0.865850i | \(0.333221\pi\) | |||||||
\(402\) | 23.3337 | 1.16378 | ||||||||
\(403\) | 21.1896 | 1.05553 | ||||||||
\(404\) | 6.03142 | 0.300075 | ||||||||
\(405\) | 117.051 | 5.81633 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 35.8771 | 1.77836 | ||||||||
\(408\) | 15.5469 | 0.769688 | ||||||||
\(409\) | 27.9562 | 1.38235 | 0.691173 | − | 0.722689i | \(-0.257094\pi\) | ||||
0.691173 | + | 0.722689i | \(0.257094\pi\) | |||||||
\(410\) | −3.87277 | −0.191263 | ||||||||
\(411\) | −7.78489 | −0.384001 | ||||||||
\(412\) | 8.47928 | 0.417744 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.23907 | 0.208339 | ||||||||
\(415\) | −18.1677 | −0.891815 | ||||||||
\(416\) | −2.22470 | −0.109075 | ||||||||
\(417\) | 1.10466 | 0.0540952 | ||||||||
\(418\) | 21.8023 | 1.06638 | ||||||||
\(419\) | −37.3753 | −1.82590 | −0.912950 | − | 0.408071i | \(-0.866202\pi\) | ||||
−0.912950 | + | 0.408071i | \(0.866202\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.99134 | −0.438211 | −0.219105 | − | 0.975701i | \(-0.570314\pi\) | ||||
−0.219105 | + | 0.975701i | \(0.570314\pi\) | |||||||
\(422\) | 9.33390 | 0.454367 | ||||||||
\(423\) | −92.7032 | −4.50738 | ||||||||
\(424\) | −11.2204 | −0.544910 | ||||||||
\(425\) | 46.9965 | 2.27966 | ||||||||
\(426\) | 17.9130 | 0.867888 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.56345 | 0.172246 | ||||||||
\(429\) | 44.5745 | 2.15208 | ||||||||
\(430\) | −11.6507 | −0.561845 | ||||||||
\(431\) | 0.851001 | 0.0409913 | 0.0204956 | − | 0.999790i | \(-0.493476\pi\) | ||||
0.0204956 | + | 0.999790i | \(0.493476\pi\) | |||||||
\(432\) | 16.3396 | 0.786138 | ||||||||
\(433\) | −33.1658 | −1.59385 | −0.796923 | − | 0.604080i | \(-0.793541\pi\) | ||||
−0.796923 | + | 0.604080i | \(0.793541\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 89.4184 | 4.28728 | ||||||||
\(436\) | −4.11954 | −0.197290 | ||||||||
\(437\) | −1.92151 | −0.0919184 | ||||||||
\(438\) | 17.4091 | 0.831839 | ||||||||
\(439\) | −25.0468 | −1.19542 | −0.597710 | − | 0.801713i | \(-0.703923\pi\) | ||||
−0.597710 | + | 0.801713i | \(0.703923\pi\) | |||||||
\(440\) | −23.4600 | −1.11841 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.4570 | −0.497388 | ||||||||
\(443\) | 1.65140 | 0.0784604 | 0.0392302 | − | 0.999230i | \(-0.487509\pi\) | ||||
0.0392302 | + | 0.999230i | \(0.487509\pi\) | |||||||
\(444\) | −19.5894 | −0.929672 | ||||||||
\(445\) | 14.2687 | 0.676403 | ||||||||
\(446\) | −6.43192 | −0.304560 | ||||||||
\(447\) | −24.6162 | −1.16430 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.7590 | −0.838098 | −0.419049 | − | 0.907964i | \(-0.637636\pi\) | ||||
−0.419049 | + | 0.907964i | \(0.637636\pi\) | |||||||
\(450\) | 79.3876 | 3.74237 | ||||||||
\(451\) | 6.05768 | 0.285245 | ||||||||
\(452\) | −1.96493 | −0.0924227 | ||||||||
\(453\) | −23.8973 | −1.12279 | ||||||||
\(454\) | 22.9617 | 1.07765 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −11.9043 | −0.557472 | ||||||||
\(457\) | 26.8026 | 1.25377 | 0.626886 | − | 0.779111i | \(-0.284329\pi\) | ||||
0.626886 | + | 0.779111i | \(0.284329\pi\) | |||||||
\(458\) | 8.12017 | 0.379431 | ||||||||
\(459\) | 76.8026 | 3.58484 | ||||||||
\(460\) | 2.06762 | 0.0964031 | ||||||||
\(461\) | −22.1793 | −1.03299 | −0.516496 | − | 0.856290i | \(-0.672764\pi\) | ||||
−0.516496 | + | 0.856290i | \(0.672764\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.4496 | −1.46159 | −0.730794 | − | 0.682598i | \(-0.760850\pi\) | ||||
−0.730794 | + | 0.682598i | \(0.760850\pi\) | |||||||
\(464\) | 6.98064 | 0.324068 | ||||||||
\(465\) | −122.007 | −5.65792 | ||||||||
\(466\) | −10.4623 | −0.484655 | ||||||||
\(467\) | 14.3411 | 0.663628 | 0.331814 | − | 0.943345i | \(-0.392339\pi\) | ||||
0.331814 | + | 0.943345i | \(0.392339\pi\) | |||||||
\(468\) | −17.6642 | −0.816528 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −45.2162 | −2.08567 | ||||||||
\(471\) | −42.6523 | −1.96532 | ||||||||
\(472\) | −6.19036 | −0.284934 | ||||||||
\(473\) | 18.2236 | 0.837923 | ||||||||
\(474\) | 1.32640 | 0.0609234 | ||||||||
\(475\) | −35.9853 | −1.65112 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −89.0904 | −4.07917 | ||||||||
\(478\) | −15.5581 | −0.711609 | ||||||||
\(479\) | 12.2351 | 0.559037 | 0.279518 | − | 0.960140i | \(-0.409825\pi\) | ||||
0.279518 | + | 0.960140i | \(0.409825\pi\) | |||||||
\(480\) | 12.8095 | 0.584671 | ||||||||
\(481\) | 13.1760 | 0.600772 | ||||||||
\(482\) | 2.30003 | 0.104763 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 25.6954 | 1.16797 | ||||||||
\(485\) | 33.5557 | 1.52368 | ||||||||
\(486\) | 50.9500 | 2.31114 | ||||||||
\(487\) | 5.21478 | 0.236304 | 0.118152 | − | 0.992996i | \(-0.462303\pi\) | ||||
0.118152 | + | 0.992996i | \(0.462303\pi\) | |||||||
\(488\) | 3.60391 | 0.163141 | ||||||||
\(489\) | 22.6221 | 1.02301 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.94577 | 0.403717 | 0.201858 | − | 0.979415i | \(-0.435302\pi\) | ||||
0.201858 | + | 0.979415i | \(0.435302\pi\) | |||||||
\(492\) | −3.30757 | −0.149117 | ||||||||
\(493\) | 32.8118 | 1.47777 | ||||||||
\(494\) | 8.00694 | 0.360249 | ||||||||
\(495\) | −186.274 | −8.37238 | ||||||||
\(496\) | −9.52470 | −0.427672 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −15.5162 | −0.695299 | ||||||||
\(499\) | 14.3264 | 0.641337 | 0.320669 | − | 0.947191i | \(-0.396092\pi\) | ||||
0.320669 | + | 0.947191i | \(0.396092\pi\) | |||||||
\(500\) | 19.3576 | 0.865699 | ||||||||
\(501\) | 47.3020 | 2.11330 | ||||||||
\(502\) | 21.2686 | 0.949264 | ||||||||
\(503\) | −41.7063 | −1.85959 | −0.929795 | − | 0.368077i | \(-0.880016\pi\) | ||||
−0.929795 | + | 0.368077i | \(0.880016\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.3583 | 1.03943 | ||||||||
\(506\) | −3.23410 | −0.143773 | ||||||||
\(507\) | −26.6284 | −1.18261 | ||||||||
\(508\) | 0.907246 | 0.0402525 | ||||||||
\(509\) | −6.39637 | −0.283514 | −0.141757 | − | 0.989901i | \(-0.545275\pi\) | ||||
−0.141757 | + | 0.989901i | \(0.545275\pi\) | |||||||
\(510\) | 60.2098 | 2.66613 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −58.8080 | −2.59644 | ||||||||
\(514\) | −16.4453 | −0.725373 | ||||||||
\(515\) | 32.8383 | 1.44703 | ||||||||
\(516\) | −9.95034 | −0.438039 | ||||||||
\(517\) | 70.7258 | 3.11052 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 82.0936 | 3.60351 | ||||||||
\(520\) | −8.61575 | −0.377826 | ||||||||
\(521\) | −11.9458 | −0.523353 | −0.261677 | − | 0.965156i | \(-0.584275\pi\) | ||||
−0.261677 | + | 0.965156i | \(0.584275\pi\) | |||||||
\(522\) | 55.4266 | 2.42596 | ||||||||
\(523\) | 24.1939 | 1.05792 | 0.528962 | − | 0.848645i | \(-0.322581\pi\) | ||||
0.528962 | + | 0.848645i | \(0.322581\pi\) | |||||||
\(524\) | −9.23740 | −0.403538 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.06940 | −0.0902299 | ||||||||
\(527\) | −44.7700 | −1.95021 | ||||||||
\(528\) | −20.0362 | −0.871964 | ||||||||
\(529\) | −22.7150 | −0.987607 | ||||||||
\(530\) | −43.4541 | −1.88752 | ||||||||
\(531\) | −49.1517 | −2.13300 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.22470 | 0.0963623 | ||||||||
\(534\) | 12.1863 | 0.527354 | ||||||||
\(535\) | 13.8004 | 0.596645 | ||||||||
\(536\) | 7.05464 | 0.304714 | ||||||||
\(537\) | −80.6346 | −3.47964 | ||||||||
\(538\) | −10.1884 | −0.439253 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 63.2795 | 2.72311 | ||||||||
\(541\) | −42.3740 | −1.82180 | −0.910901 | − | 0.412624i | \(-0.864612\pi\) | ||||
−0.910901 | + | 0.412624i | \(0.864612\pi\) | |||||||
\(542\) | 18.1252 | 0.778543 | ||||||||
\(543\) | 0.174852 | 0.00750362 | ||||||||
\(544\) | 4.70041 | 0.201528 | ||||||||
\(545\) | −15.9541 | −0.683397 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.5275 | −0.834935 | −0.417467 | − | 0.908692i | \(-0.637082\pi\) | ||||
−0.417467 | + | 0.908692i | \(0.637082\pi\) | |||||||
\(548\) | −2.35366 | −0.100543 | ||||||||
\(549\) | 28.6152 | 1.22127 | ||||||||
\(550\) | −60.5670 | −2.58259 | ||||||||
\(551\) | −25.1241 | −1.07032 | ||||||||
\(552\) | 1.76586 | 0.0751601 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 25.6514 | 1.08982 | ||||||||
\(555\) | −75.8653 | −3.22030 | ||||||||
\(556\) | 0.333978 | 0.0141638 | ||||||||
\(557\) | −13.3280 | −0.564724 | −0.282362 | − | 0.959308i | \(-0.591118\pi\) | ||||
−0.282362 | + | 0.959308i | \(0.591118\pi\) | |||||||
\(558\) | −75.6266 | −3.20153 | ||||||||
\(559\) | 6.69267 | 0.283070 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −94.1783 | −3.97621 | ||||||||
\(562\) | 9.98688 | 0.421271 | ||||||||
\(563\) | 17.1983 | 0.724822 | 0.362411 | − | 0.932018i | \(-0.381954\pi\) | ||||
0.362411 | + | 0.932018i | \(0.381954\pi\) | |||||||
\(564\) | −38.6172 | −1.62608 | ||||||||
\(565\) | −7.60975 | −0.320145 | ||||||||
\(566\) | −10.8783 | −0.457249 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.41575 | 0.227240 | ||||||||
\(569\) | −8.77605 | −0.367911 | −0.183956 | − | 0.982935i | \(-0.558890\pi\) | ||||
−0.183956 | + | 0.982935i | \(0.558890\pi\) | |||||||
\(570\) | −46.1028 | −1.93104 | ||||||||
\(571\) | 38.2957 | 1.60262 | 0.801312 | − | 0.598247i | \(-0.204136\pi\) | ||||
0.801312 | + | 0.598247i | \(0.204136\pi\) | |||||||
\(572\) | 13.4765 | 0.563480 | ||||||||
\(573\) | −9.50599 | −0.397118 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.33799 | 0.222609 | ||||||||
\(576\) | 7.94005 | 0.330835 | ||||||||
\(577\) | −44.6215 | −1.85762 | −0.928808 | − | 0.370561i | \(-0.879165\pi\) | ||||
−0.928808 | + | 0.370561i | \(0.879165\pi\) | |||||||
\(578\) | 5.09381 | 0.211875 | ||||||||
\(579\) | −23.4634 | −0.975104 | ||||||||
\(580\) | 27.0344 | 1.12254 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 28.6585 | 1.18793 | ||||||||
\(583\) | 67.9695 | 2.81501 | ||||||||
\(584\) | 5.26340 | 0.217801 | ||||||||
\(585\) | −68.4094 | −2.82838 | ||||||||
\(586\) | 22.7063 | 0.937989 | ||||||||
\(587\) | −5.54935 | −0.229046 | −0.114523 | − | 0.993421i | \(-0.536534\pi\) | ||||
−0.114523 | + | 0.993421i | \(0.536534\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 34.2805 | 1.41250 | ||||||||
\(590\) | −23.9739 | −0.986988 | ||||||||
\(591\) | 5.03194 | 0.206986 | ||||||||
\(592\) | −5.92259 | −0.243417 | ||||||||
\(593\) | 23.8376 | 0.978893 | 0.489446 | − | 0.872033i | \(-0.337199\pi\) | ||||
0.489446 | + | 0.872033i | \(0.337199\pi\) | |||||||
\(594\) | −98.9798 | −4.06119 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.44236 | −0.304851 | ||||||||
\(597\) | −16.2325 | −0.664353 | ||||||||
\(598\) | −1.18773 | −0.0485700 | ||||||||
\(599\) | −23.6738 | −0.967286 | −0.483643 | − | 0.875265i | \(-0.660687\pi\) | ||||
−0.483643 | + | 0.875265i | \(0.660687\pi\) | |||||||
\(600\) | 33.0704 | 1.35009 | ||||||||
\(601\) | −36.6358 | −1.49441 | −0.747203 | − | 0.664595i | \(-0.768604\pi\) | ||||
−0.747203 | + | 0.664595i | \(0.768604\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 56.0141 | 2.28107 | ||||||||
\(604\) | −7.22502 | −0.293982 | ||||||||
\(605\) | 99.5127 | 4.04577 | ||||||||
\(606\) | 19.9494 | 0.810388 | ||||||||
\(607\) | 16.6639 | 0.676369 | 0.338184 | − | 0.941080i | \(-0.390187\pi\) | ||||
0.338184 | + | 0.941080i | \(0.390187\pi\) | |||||||
\(608\) | −3.59912 | −0.145963 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 13.9571 | 0.565107 | ||||||||
\(611\) | 25.9742 | 1.05080 | ||||||||
\(612\) | 37.3214 | 1.50863 | ||||||||
\(613\) | −13.3045 | −0.537363 | −0.268682 | − | 0.963229i | \(-0.586588\pi\) | ||||
−0.268682 | + | 0.963229i | \(0.586588\pi\) | |||||||
\(614\) | −16.2095 | −0.654161 | ||||||||
\(615\) | −12.8095 | −0.516528 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.9486 | −0.601810 | −0.300905 | − | 0.953654i | \(-0.597289\pi\) | ||||
−0.300905 | + | 0.953654i | \(0.597289\pi\) | |||||||
\(618\) | 28.0458 | 1.12817 | ||||||||
\(619\) | 14.9047 | 0.599071 | 0.299535 | − | 0.954085i | \(-0.403168\pi\) | ||||
0.299535 | + | 0.954085i | \(0.403168\pi\) | |||||||
\(620\) | −36.8870 | −1.48142 | ||||||||
\(621\) | 8.72345 | 0.350060 | ||||||||
\(622\) | −2.08493 | −0.0835980 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −7.35835 | −0.294570 | ||||||||
\(625\) | 24.9758 | 0.999032 | ||||||||
\(626\) | 26.8869 | 1.07462 | ||||||||
\(627\) | 72.1126 | 2.87990 | ||||||||
\(628\) | −12.8953 | −0.514580 | ||||||||
\(629\) | −27.8386 | −1.11000 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.3314 | 0.729763 | 0.364882 | − | 0.931054i | \(-0.381109\pi\) | ||||
0.364882 | + | 0.931054i | \(0.381109\pi\) | |||||||
\(632\) | 0.401018 | 0.0159516 | ||||||||
\(633\) | 30.8726 | 1.22707 | ||||||||
\(634\) | −17.2868 | −0.686545 | ||||||||
\(635\) | 3.51356 | 0.139431 | ||||||||
\(636\) | −37.1123 | −1.47160 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −42.2864 | −1.67414 | ||||||||
\(639\) | 43.0013 | 1.70111 | ||||||||
\(640\) | 3.87277 | 0.153085 | ||||||||
\(641\) | −3.53353 | −0.139566 | −0.0697829 | − | 0.997562i | \(-0.522231\pi\) | ||||
−0.0697829 | + | 0.997562i | \(0.522231\pi\) | |||||||
\(642\) | 11.7864 | 0.465171 | ||||||||
\(643\) | 7.20916 | 0.284301 | 0.142151 | − | 0.989845i | \(-0.454598\pi\) | ||||
0.142151 | + | 0.989845i | \(0.454598\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −38.5354 | −1.51733 | ||||||||
\(646\) | −16.9173 | −0.665602 | ||||||||
\(647\) | 41.9515 | 1.64928 | 0.824642 | − | 0.565654i | \(-0.191376\pi\) | ||||
0.824642 | + | 0.565654i | \(0.191376\pi\) | |||||||
\(648\) | 30.2242 | 1.18732 | ||||||||
\(649\) | 37.4992 | 1.47197 | ||||||||
\(650\) | −22.2434 | −0.872457 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.83948 | 0.267855 | ||||||||
\(653\) | −44.2064 | −1.72993 | −0.864965 | − | 0.501833i | \(-0.832659\pi\) | ||||
−0.864965 | + | 0.501833i | \(0.832659\pi\) | |||||||
\(654\) | −13.6257 | −0.532807 | ||||||||
\(655\) | −35.7744 | −1.39782 | ||||||||
\(656\) | −1.00000 | −0.0390434 | ||||||||
\(657\) | 41.7917 | 1.63045 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 46.7615 | 1.82157 | 0.910785 | − | 0.412880i | \(-0.135477\pi\) | ||||
0.910785 | + | 0.412880i | \(0.135477\pi\) | |||||||
\(660\) | −77.5957 | −3.02041 | ||||||||
\(661\) | 4.68047 | 0.182049 | 0.0910247 | − | 0.995849i | \(-0.470986\pi\) | ||||
0.0910247 | + | 0.995849i | \(0.470986\pi\) | |||||||
\(662\) | 2.88391 | 0.112086 | ||||||||
\(663\) | −34.5872 | −1.34326 | ||||||||
\(664\) | −4.69112 | −0.182051 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −47.0256 | −1.82221 | ||||||||
\(667\) | 3.72686 | 0.144304 | ||||||||
\(668\) | 14.3011 | 0.553327 | ||||||||
\(669\) | −21.2740 | −0.822502 | ||||||||
\(670\) | 27.3210 | 1.05550 | ||||||||
\(671\) | −21.8313 | −0.842788 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.0725 | −1.39049 | −0.695247 | − | 0.718771i | \(-0.744705\pi\) | ||||
−0.695247 | + | 0.718771i | \(0.744705\pi\) | |||||||
\(674\) | 10.9701 | 0.422553 | ||||||||
\(675\) | 163.369 | 6.28809 | ||||||||
\(676\) | −8.05072 | −0.309643 | ||||||||
\(677\) | 39.0587 | 1.50115 | 0.750575 | − | 0.660786i | \(-0.229777\pi\) | ||||
0.750575 | + | 0.660786i | \(0.229777\pi\) | |||||||
\(678\) | −6.49917 | −0.249599 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 18.2036 | 0.698077 | ||||||||
\(681\) | 75.9475 | 2.91032 | ||||||||
\(682\) | 57.6976 | 2.20935 | ||||||||
\(683\) | 5.38884 | 0.206198 | 0.103099 | − | 0.994671i | \(-0.467124\pi\) | ||||
0.103099 | + | 0.994671i | \(0.467124\pi\) | |||||||
\(684\) | −28.5771 | −1.09267 | ||||||||
\(685\) | −9.11518 | −0.348273 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.8581 | 1.02470 | ||||||||
\(688\) | −3.00835 | −0.114692 | ||||||||
\(689\) | 24.9620 | 0.950975 | ||||||||
\(690\) | 6.83879 | 0.260348 | ||||||||
\(691\) | 42.1815 | 1.60466 | 0.802331 | − | 0.596880i | \(-0.203593\pi\) | ||||
0.802331 | + | 0.596880i | \(0.203593\pi\) | |||||||
\(692\) | 24.8199 | 0.943510 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.96054 | −0.0744209 | ||||||||
\(695\) | 1.29342 | 0.0490622 | ||||||||
\(696\) | 23.0890 | 0.875185 | ||||||||
\(697\) | −4.70041 | −0.178041 | ||||||||
\(698\) | 18.2795 | 0.691891 | ||||||||
\(699\) | −34.6047 | −1.30887 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.46425 | −0.206382 | −0.103191 | − | 0.994662i | \(-0.532905\pi\) | ||||
−0.103191 | + | 0.994662i | \(0.532905\pi\) | |||||||
\(702\) | −36.3506 | −1.37196 | ||||||||
\(703\) | 21.3161 | 0.803951 | ||||||||
\(704\) | −6.05768 | −0.228307 | ||||||||
\(705\) | −149.556 | −5.63260 | ||||||||
\(706\) | −23.2747 | −0.875955 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −20.4751 | −0.769500 | ||||||||
\(709\) | −48.2902 | −1.81358 | −0.906789 | − | 0.421585i | \(-0.861474\pi\) | ||||
−0.906789 | + | 0.421585i | \(0.861474\pi\) | |||||||
\(710\) | 20.9740 | 0.787140 | ||||||||
\(711\) | 3.18410 | 0.119413 | ||||||||
\(712\) | 3.68437 | 0.138078 | ||||||||
\(713\) | −5.08510 | −0.190438 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 52.1914 | 1.95185 | ||||||||
\(716\) | −24.3788 | −0.911078 | ||||||||
\(717\) | −51.4594 | −1.92179 | ||||||||
\(718\) | 12.5000 | 0.466495 | ||||||||
\(719\) | 52.1574 | 1.94514 | 0.972571 | − | 0.232606i | \(-0.0747251\pi\) | ||||
0.972571 | + | 0.232606i | \(0.0747251\pi\) | |||||||
\(720\) | 30.7500 | 1.14599 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −6.04637 | −0.225023 | ||||||||
\(723\) | 7.60752 | 0.282927 | ||||||||
\(724\) | 0.0528641 | 0.00196468 | ||||||||
\(725\) | 69.7951 | 2.59212 | ||||||||
\(726\) | 84.9896 | 3.15426 | ||||||||
\(727\) | 31.3575 | 1.16299 | 0.581493 | − | 0.813551i | \(-0.302469\pi\) | ||||
0.581493 | + | 0.813551i | \(0.302469\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 77.8484 | 2.88327 | ||||||||
\(730\) | 20.3840 | 0.754445 | ||||||||
\(731\) | −14.1405 | −0.523004 | ||||||||
\(732\) | 11.9202 | 0.440583 | ||||||||
\(733\) | −5.43860 | −0.200879 | −0.100440 | − | 0.994943i | \(-0.532025\pi\) | ||||
−0.100440 | + | 0.994943i | \(0.532025\pi\) | |||||||
\(734\) | −8.45799 | −0.312190 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.533885 | 0.0196793 | ||||||||
\(737\) | −42.7347 | −1.57415 | ||||||||
\(738\) | −7.94005 | −0.292277 | ||||||||
\(739\) | 48.4786 | 1.78331 | 0.891656 | − | 0.452713i | \(-0.149544\pi\) | ||||
0.891656 | + | 0.452713i | \(0.149544\pi\) | |||||||
\(740\) | −22.9369 | −0.843175 | ||||||||
\(741\) | 26.4835 | 0.972897 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.55894 | −0.0938786 | −0.0469393 | − | 0.998898i | \(-0.514947\pi\) | ||||
−0.0469393 | + | 0.998898i | \(0.514947\pi\) | |||||||
\(744\) | −31.5037 | −1.15498 | ||||||||
\(745\) | −28.8226 | −1.05598 | ||||||||
\(746\) | 17.2826 | 0.632760 | ||||||||
\(747\) | −37.2477 | −1.36282 | ||||||||
\(748\) | −28.4735 | −1.04110 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 64.0268 | 2.33793 | ||||||||
\(751\) | 30.6177 | 1.11726 | 0.558629 | − | 0.829418i | \(-0.311328\pi\) | ||||
0.558629 | + | 0.829418i | \(0.311328\pi\) | |||||||
\(752\) | −11.6754 | −0.425758 | ||||||||
\(753\) | 70.3475 | 2.56360 | ||||||||
\(754\) | −15.5298 | −0.565562 | ||||||||
\(755\) | −27.9809 | −1.01833 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.9086 | 0.541861 | 0.270930 | − | 0.962599i | \(-0.412669\pi\) | ||||
0.270930 | + | 0.962599i | \(0.412669\pi\) | |||||||
\(758\) | 29.5973 | 1.07502 | ||||||||
\(759\) | −10.6970 | −0.388278 | ||||||||
\(760\) | −13.9386 | −0.505605 | ||||||||
\(761\) | 35.1656 | 1.27475 | 0.637376 | − | 0.770553i | \(-0.280020\pi\) | ||||
0.637376 | + | 0.770553i | \(0.280020\pi\) | |||||||
\(762\) | 3.00078 | 0.108707 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.87401 | −0.103978 | ||||||||
\(765\) | 144.538 | 5.22576 | ||||||||
\(766\) | 18.2590 | 0.659723 | ||||||||
\(767\) | 13.7717 | 0.497266 | ||||||||
\(768\) | 3.30757 | 0.119352 | ||||||||
\(769\) | 25.9354 | 0.935256 | 0.467628 | − | 0.883925i | \(-0.345109\pi\) | ||||
0.467628 | + | 0.883925i | \(0.345109\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −54.3942 | −1.95896 | ||||||||
\(772\) | −7.09383 | −0.255312 | ||||||||
\(773\) | −39.6671 | −1.42673 | −0.713364 | − | 0.700794i | \(-0.752829\pi\) | ||||
−0.713364 | + | 0.700794i | \(0.752829\pi\) | |||||||
\(774\) | −23.8864 | −0.858580 | ||||||||
\(775\) | −95.2317 | −3.42082 | ||||||||
\(776\) | 8.66450 | 0.311037 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 22.9438 | 0.822574 | ||||||||
\(779\) | 3.59912 | 0.128952 | ||||||||
\(780\) | −28.4972 | −1.02036 | ||||||||
\(781\) | −32.8069 | −1.17392 | ||||||||
\(782\) | 2.50948 | 0.0897387 | ||||||||
\(783\) | 114.061 | 4.07619 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −49.9408 | −1.78246 | ||||||||
\(786\) | −30.5534 | −1.08980 | ||||||||
\(787\) | 4.36654 | 0.155650 | 0.0778252 | − | 0.996967i | \(-0.475202\pi\) | ||||
0.0778252 | + | 0.996967i | \(0.475202\pi\) | |||||||
\(788\) | 1.52134 | 0.0541954 | ||||||||
\(789\) | −6.84468 | −0.243677 | ||||||||
\(790\) | 1.55305 | 0.0552551 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −48.0982 | −1.70910 | ||||||||
\(793\) | −8.01760 | −0.284713 | ||||||||
\(794\) | −3.04357 | −0.108012 | ||||||||
\(795\) | −143.728 | −5.09749 | ||||||||
\(796\) | −4.90768 | −0.173948 | ||||||||
\(797\) | 10.4561 | 0.370375 | 0.185187 | − | 0.982703i | \(-0.440711\pi\) | ||||
0.185187 | + | 0.982703i | \(0.440711\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −54.8791 | −1.94148 | ||||||||
\(800\) | 9.99839 | 0.353496 | ||||||||
\(801\) | 29.2541 | 1.03364 | ||||||||
\(802\) | 20.0372 | 0.707537 | ||||||||
\(803\) | −31.8840 | −1.12516 | ||||||||
\(804\) | 23.3337 | 0.822917 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 21.1896 | 0.746371 | ||||||||
\(807\) | −33.6989 | −1.18626 | ||||||||
\(808\) | 6.03142 | 0.212185 | ||||||||
\(809\) | −41.8027 | −1.46971 | −0.734853 | − | 0.678226i | \(-0.762749\pi\) | ||||
−0.734853 | + | 0.678226i | \(0.762749\pi\) | |||||||
\(810\) | 117.051 | 4.11277 | ||||||||
\(811\) | 49.9521 | 1.75406 | 0.877028 | − | 0.480439i | \(-0.159523\pi\) | ||||
0.877028 | + | 0.480439i | \(0.159523\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 59.9504 | 2.10255 | ||||||||
\(814\) | 35.8771 | 1.25749 | ||||||||
\(815\) | 26.4878 | 0.927826 | ||||||||
\(816\) | 15.5469 | 0.544252 | ||||||||
\(817\) | 10.8274 | 0.378803 | ||||||||
\(818\) | 27.9562 | 0.977466 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.87277 | −0.135243 | ||||||||
\(821\) | −4.12898 | −0.144102 | −0.0720512 | − | 0.997401i | \(-0.522954\pi\) | ||||
−0.0720512 | + | 0.997401i | \(0.522954\pi\) | |||||||
\(822\) | −7.78489 | −0.271529 | ||||||||
\(823\) | −11.8683 | −0.413703 | −0.206851 | − | 0.978372i | \(-0.566322\pi\) | ||||
−0.206851 | + | 0.978372i | \(0.566322\pi\) | |||||||
\(824\) | 8.47928 | 0.295390 | ||||||||
\(825\) | −200.330 | −6.97459 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −53.8557 | −1.87274 | −0.936372 | − | 0.351008i | \(-0.885839\pi\) | ||||
−0.936372 | + | 0.351008i | \(0.885839\pi\) | |||||||
\(828\) | 4.23907 | 0.147318 | ||||||||
\(829\) | −37.5271 | −1.30337 | −0.651686 | − | 0.758489i | \(-0.725938\pi\) | ||||
−0.651686 | + | 0.758489i | \(0.725938\pi\) | |||||||
\(830\) | −18.1677 | −0.630609 | ||||||||
\(831\) | 84.8439 | 2.94320 | ||||||||
\(832\) | −2.22470 | −0.0771275 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.10466 | 0.0382511 | ||||||||
\(835\) | 55.3850 | 1.91668 | ||||||||
\(836\) | 21.8023 | 0.754048 | ||||||||
\(837\) | −155.630 | −5.37934 | ||||||||
\(838\) | −37.3753 | −1.29111 | ||||||||
\(839\) | −19.0531 | −0.657786 | −0.328893 | − | 0.944367i | \(-0.606676\pi\) | ||||
−0.328893 | + | 0.944367i | \(0.606676\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.7293 | 0.680320 | ||||||||
\(842\) | −8.99134 | −0.309862 | ||||||||
\(843\) | 33.0324 | 1.13769 | ||||||||
\(844\) | 9.33390 | 0.321286 | ||||||||
\(845\) | −31.1786 | −1.07258 | ||||||||
\(846\) | −92.7032 | −3.18720 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −11.2204 | −0.385310 | ||||||||
\(849\) | −35.9808 | −1.23486 | ||||||||
\(850\) | 46.9965 | 1.61197 | ||||||||
\(851\) | −3.16198 | −0.108391 | ||||||||
\(852\) | 17.9130 | 0.613689 | ||||||||
\(853\) | 25.5388 | 0.874430 | 0.437215 | − | 0.899357i | \(-0.355965\pi\) | ||||
0.437215 | + | 0.899357i | \(0.355965\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −110.673 | −3.78493 | ||||||||
\(856\) | 3.56345 | 0.121796 | ||||||||
\(857\) | 31.6247 | 1.08028 | 0.540139 | − | 0.841576i | \(-0.318372\pi\) | ||||
0.540139 | + | 0.841576i | \(0.318372\pi\) | |||||||
\(858\) | 44.5745 | 1.52175 | ||||||||
\(859\) | 53.3239 | 1.81939 | 0.909694 | − | 0.415280i | \(-0.136316\pi\) | ||||
0.909694 | + | 0.415280i | \(0.136316\pi\) | |||||||
\(860\) | −11.6507 | −0.397284 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.851001 | 0.0289852 | ||||||||
\(863\) | −2.73115 | −0.0929694 | −0.0464847 | − | 0.998919i | \(-0.514802\pi\) | ||||
−0.0464847 | + | 0.998919i | \(0.514802\pi\) | |||||||
\(864\) | 16.3396 | 0.555883 | ||||||||
\(865\) | 96.1218 | 3.26824 | ||||||||
\(866\) | −33.1658 | −1.12702 | ||||||||
\(867\) | 16.8482 | 0.572193 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.42924 | −0.0824062 | ||||||||
\(870\) | 89.4184 | 3.03157 | ||||||||
\(871\) | −15.6944 | −0.531785 | ||||||||
\(872\) | −4.11954 | −0.139505 | ||||||||
\(873\) | 68.7965 | 2.32841 | ||||||||
\(874\) | −1.92151 | −0.0649962 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 17.4091 | 0.588199 | ||||||||
\(877\) | −23.0478 | −0.778269 | −0.389135 | − | 0.921181i | \(-0.627226\pi\) | ||||
−0.389135 | + | 0.921181i | \(0.627226\pi\) | |||||||
\(878\) | −25.0468 | −0.845289 | ||||||||
\(879\) | 75.1028 | 2.53316 | ||||||||
\(880\) | −23.4600 | −0.790837 | ||||||||
\(881\) | 34.5243 | 1.16315 | 0.581576 | − | 0.813492i | \(-0.302436\pi\) | ||||
0.581576 | + | 0.813492i | \(0.302436\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.11188 | 0.205681 | 0.102841 | − | 0.994698i | \(-0.467207\pi\) | ||||
0.102841 | + | 0.994698i | \(0.467207\pi\) | |||||||
\(884\) | −10.4570 | −0.351706 | ||||||||
\(885\) | −79.2953 | −2.66548 | ||||||||
\(886\) | 1.65140 | 0.0554799 | ||||||||
\(887\) | −5.64372 | −0.189498 | −0.0947488 | − | 0.995501i | \(-0.530205\pi\) | ||||
−0.0947488 | + | 0.995501i | \(0.530205\pi\) | |||||||
\(888\) | −19.5894 | −0.657377 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 14.2687 | 0.478289 | ||||||||
\(891\) | −183.088 | −6.13369 | ||||||||
\(892\) | −6.43192 | −0.215357 | ||||||||
\(893\) | 42.0211 | 1.40618 | ||||||||
\(894\) | −24.6162 | −0.823288 | ||||||||
\(895\) | −94.4135 | −3.15590 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.92851 | −0.131169 | ||||||||
\(898\) | −17.7590 | −0.592625 | ||||||||
\(899\) | −66.4885 | −2.21752 | ||||||||
\(900\) | 79.3876 | 2.64625 | ||||||||
\(901\) | −52.7404 | −1.75704 | ||||||||
\(902\) | 6.05768 | 0.201699 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.96493 | −0.0653527 | ||||||||
\(905\) | 0.204731 | 0.00680548 | ||||||||
\(906\) | −23.8973 | −0.793934 | ||||||||
\(907\) | −21.1256 | −0.701464 | −0.350732 | − | 0.936476i | \(-0.614067\pi\) | ||||
−0.350732 | + | 0.936476i | \(0.614067\pi\) | |||||||
\(908\) | 22.9617 | 0.762011 | ||||||||
\(909\) | 47.8898 | 1.58840 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.5810 | −0.880667 | −0.440333 | − | 0.897834i | \(-0.645140\pi\) | ||||
−0.440333 | + | 0.897834i | \(0.645140\pi\) | |||||||
\(912\) | −11.9043 | −0.394192 | ||||||||
\(913\) | 28.4173 | 0.940475 | ||||||||
\(914\) | 26.8026 | 0.886551 | ||||||||
\(915\) | 46.1642 | 1.52614 | ||||||||
\(916\) | 8.12017 | 0.268298 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 76.8026 | 2.53486 | ||||||||
\(919\) | 20.1647 | 0.665172 | 0.332586 | − | 0.943073i | \(-0.392079\pi\) | ||||
0.332586 | + | 0.943073i | \(0.392079\pi\) | |||||||
\(920\) | 2.06762 | 0.0681673 | ||||||||
\(921\) | −53.6140 | −1.76664 | ||||||||
\(922\) | −22.1793 | −0.730435 | ||||||||
\(923\) | −12.0484 | −0.396578 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −59.2163 | −1.94702 | ||||||||
\(926\) | −31.4496 | −1.03350 | ||||||||
\(927\) | 67.3259 | 2.21127 | ||||||||
\(928\) | 6.98064 | 0.229151 | ||||||||
\(929\) | −20.0618 | −0.658205 | −0.329102 | − | 0.944294i | \(-0.606746\pi\) | ||||
−0.329102 | + | 0.944294i | \(0.606746\pi\) | |||||||
\(930\) | −122.007 | −4.00075 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −10.4623 | −0.342703 | ||||||||
\(933\) | −6.89606 | −0.225767 | ||||||||
\(934\) | 14.3411 | 0.469256 | ||||||||
\(935\) | −110.272 | −3.60627 | ||||||||
\(936\) | −17.6642 | −0.577372 | ||||||||
\(937\) | −18.2309 | −0.595578 | −0.297789 | − | 0.954632i | \(-0.596249\pi\) | ||||
−0.297789 | + | 0.954632i | \(0.596249\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 88.9303 | 2.90213 | ||||||||
\(940\) | −45.2162 | −1.47479 | ||||||||
\(941\) | −16.5589 | −0.539805 | −0.269902 | − | 0.962888i | \(-0.586991\pi\) | ||||
−0.269902 | + | 0.962888i | \(0.586991\pi\) | |||||||
\(942\) | −42.6523 | −1.38969 | ||||||||
\(943\) | −0.533885 | −0.0173857 | ||||||||
\(944\) | −6.19036 | −0.201479 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 18.2236 | 0.592501 | ||||||||
\(947\) | 57.4355 | 1.86640 | 0.933201 | − | 0.359354i | \(-0.117003\pi\) | ||||
0.933201 | + | 0.359354i | \(0.117003\pi\) | |||||||
\(948\) | 1.32640 | 0.0430793 | ||||||||
\(949\) | −11.7095 | −0.380106 | ||||||||
\(950\) | −35.9853 | −1.16752 | ||||||||
\(951\) | −57.1773 | −1.85410 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 56.6818 | 1.83610 | 0.918052 | − | 0.396460i | \(-0.129761\pi\) | ||||
0.918052 | + | 0.396460i | \(0.129761\pi\) | |||||||
\(954\) | −89.0904 | −2.88441 | ||||||||
\(955\) | −11.1304 | −0.360171 | ||||||||
\(956\) | −15.5581 | −0.503184 | ||||||||
\(957\) | −139.866 | −4.52121 | ||||||||
\(958\) | 12.2351 | 0.395299 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 12.8095 | 0.413424 | ||||||||
\(961\) | 59.7200 | 1.92645 | ||||||||
\(962\) | 13.1760 | 0.424810 | ||||||||
\(963\) | 28.2939 | 0.911759 | ||||||||
\(964\) | 2.30003 | 0.0740789 | ||||||||
\(965\) | −27.4728 | −0.884380 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35.7547 | −1.14979 | −0.574896 | − | 0.818226i | \(-0.694958\pi\) | ||||
−0.574896 | + | 0.818226i | \(0.694958\pi\) | |||||||
\(968\) | 25.6954 | 0.825883 | ||||||||
\(969\) | −55.9552 | −1.79754 | ||||||||
\(970\) | 33.5557 | 1.07741 | ||||||||
\(971\) | −19.6443 | −0.630414 | −0.315207 | − | 0.949023i | \(-0.602074\pi\) | ||||
−0.315207 | + | 0.949023i | \(0.602074\pi\) | |||||||
\(972\) | 50.9500 | 1.63422 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 5.21478 | 0.167092 | ||||||||
\(975\) | −73.5716 | −2.35618 | ||||||||
\(976\) | 3.60391 | 0.115358 | ||||||||
\(977\) | −27.9407 | −0.893904 | −0.446952 | − | 0.894558i | \(-0.647490\pi\) | ||||
−0.446952 | + | 0.894558i | \(0.647490\pi\) | |||||||
\(978\) | 22.6221 | 0.723374 | ||||||||
\(979\) | −22.3187 | −0.713310 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −32.7094 | −1.04433 | ||||||||
\(982\) | 8.94577 | 0.285471 | ||||||||
\(983\) | −58.7479 | −1.87377 | −0.936883 | − | 0.349643i | \(-0.886303\pi\) | ||||
−0.936883 | + | 0.349643i | \(0.886303\pi\) | |||||||
\(984\) | −3.30757 | −0.105442 | ||||||||
\(985\) | 5.89180 | 0.187728 | ||||||||
\(986\) | 32.8118 | 1.04494 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.00694 | 0.254735 | ||||||||
\(989\) | −1.60611 | −0.0510714 | ||||||||
\(990\) | −186.274 | −5.92016 | ||||||||
\(991\) | −36.0677 | −1.14573 | −0.572864 | − | 0.819650i | \(-0.694168\pi\) | ||||
−0.572864 | + | 0.819650i | \(0.694168\pi\) | |||||||
\(992\) | −9.52470 | −0.302410 | ||||||||
\(993\) | 9.53874 | 0.302703 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19.0064 | −0.602542 | ||||||||
\(996\) | −15.5162 | −0.491651 | ||||||||
\(997\) | −30.5916 | −0.968845 | −0.484423 | − | 0.874834i | \(-0.660970\pi\) | ||||
−0.484423 | + | 0.874834i | \(0.660970\pi\) | |||||||
\(998\) | 14.3264 | 0.453494 | ||||||||
\(999\) | −96.7725 | −3.06175 |
(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 | 4018.2.a.bq.1.6 | yes | 6 | |
7.6 | odd | 2 | 4018.2.a.bp.1.1 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4018.2.a.bp.1.1 | ✓ | 6 | 7.6 | odd | 2 | ||
4018.2.a.bq.1.6 | yes | 6 | 1.1 | even | 1 | trivial |