Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.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: | \(28.3389076774\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 11x^{7} + 8x^{6} + 37x^{5} - 18x^{4} - 41x^{3} + 12x^{2} + 6x - 1 \) |
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 | 1.4 | ||
Root | \(-0.374817\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.374817 | −0.265036 | −0.132518 | − | 0.991181i | \(-0.542306\pi\) | ||||
−0.132518 | + | 0.991181i | \(0.542306\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.85951 | −0.929756 | ||||||||
\(5\) | 1.32690 | 0.593408 | 0.296704 | − | 0.954969i | \(-0.404112\pi\) | ||||
0.296704 | + | 0.954969i | \(0.404112\pi\) | |||||||
\(6\) | 0.374817 | 0.153018 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.44661 | 0.511454 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.497345 | −0.157274 | ||||||||
\(11\) | 5.82806 | 1.75723 | 0.878613 | − | 0.477534i | \(-0.158469\pi\) | ||||
0.878613 | + | 0.477534i | \(0.158469\pi\) | |||||||
\(12\) | 1.85951 | 0.536795 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.374817 | 0.100174 | ||||||||
\(15\) | −1.32690 | −0.342604 | ||||||||
\(16\) | 3.17681 | 0.794202 | ||||||||
\(17\) | −0.442994 | −0.107442 | −0.0537209 | − | 0.998556i | \(-0.517108\pi\) | ||||
−0.0537209 | + | 0.998556i | \(0.517108\pi\) | |||||||
\(18\) | −0.374817 | −0.0883452 | ||||||||
\(19\) | 1.34585 | 0.308758 | 0.154379 | − | 0.988012i | \(-0.450662\pi\) | ||||
0.154379 | + | 0.988012i | \(0.450662\pi\) | |||||||
\(20\) | −2.46739 | −0.551725 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −2.18446 | −0.465728 | ||||||||
\(23\) | −2.67807 | −0.558417 | −0.279209 | − | 0.960230i | \(-0.590072\pi\) | ||||
−0.279209 | + | 0.960230i | \(0.590072\pi\) | |||||||
\(24\) | −1.44661 | −0.295288 | ||||||||
\(25\) | −3.23933 | −0.647867 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.85951 | 0.351415 | ||||||||
\(29\) | 3.35417 | 0.622853 | 0.311427 | − | 0.950270i | \(-0.399193\pi\) | ||||
0.311427 | + | 0.950270i | \(0.399193\pi\) | |||||||
\(30\) | 0.497345 | 0.0908024 | ||||||||
\(31\) | 8.32825 | 1.49580 | 0.747899 | − | 0.663813i | \(-0.231063\pi\) | ||||
0.747899 | + | 0.663813i | \(0.231063\pi\) | |||||||
\(32\) | −4.08395 | −0.721946 | ||||||||
\(33\) | −5.82806 | −1.01454 | ||||||||
\(34\) | 0.166042 | 0.0284759 | ||||||||
\(35\) | −1.32690 | −0.224287 | ||||||||
\(36\) | −1.85951 | −0.309919 | ||||||||
\(37\) | 7.93555 | 1.30460 | 0.652298 | − | 0.757962i | \(-0.273805\pi\) | ||||
0.652298 | + | 0.757962i | \(0.273805\pi\) | |||||||
\(38\) | −0.504446 | −0.0818319 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.91951 | 0.303501 | ||||||||
\(41\) | −0.816015 | −0.127440 | −0.0637201 | − | 0.997968i | \(-0.520296\pi\) | ||||
−0.0637201 | + | 0.997968i | \(0.520296\pi\) | |||||||
\(42\) | −0.374817 | −0.0578355 | ||||||||
\(43\) | 3.16166 | 0.482149 | 0.241074 | − | 0.970507i | \(-0.422500\pi\) | ||||
0.241074 | + | 0.970507i | \(0.422500\pi\) | |||||||
\(44\) | −10.8373 | −1.63379 | ||||||||
\(45\) | 1.32690 | 0.197803 | ||||||||
\(46\) | 1.00379 | 0.148000 | ||||||||
\(47\) | 4.29060 | 0.625848 | 0.312924 | − | 0.949778i | \(-0.398692\pi\) | ||||
0.312924 | + | 0.949778i | \(0.398692\pi\) | |||||||
\(48\) | −3.17681 | −0.458533 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.21416 | 0.171708 | ||||||||
\(51\) | 0.442994 | 0.0620316 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.85465 | −0.254756 | −0.127378 | − | 0.991854i | \(-0.540656\pi\) | ||||
−0.127378 | + | 0.991854i | \(0.540656\pi\) | |||||||
\(54\) | 0.374817 | 0.0510061 | ||||||||
\(55\) | 7.73326 | 1.04275 | ||||||||
\(56\) | −1.44661 | −0.193312 | ||||||||
\(57\) | −1.34585 | −0.178262 | ||||||||
\(58\) | −1.25720 | −0.165078 | ||||||||
\(59\) | −6.16798 | −0.803002 | −0.401501 | − | 0.915858i | \(-0.631511\pi\) | ||||
−0.401501 | + | 0.915858i | \(0.631511\pi\) | |||||||
\(60\) | 2.46739 | 0.318539 | ||||||||
\(61\) | −11.0420 | −1.41379 | −0.706893 | − | 0.707320i | \(-0.749904\pi\) | ||||
−0.706893 | + | 0.707320i | \(0.749904\pi\) | |||||||
\(62\) | −3.12157 | −0.396440 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −4.82289 | −0.602861 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.18446 | 0.268888 | ||||||||
\(67\) | −1.64442 | −0.200898 | −0.100449 | − | 0.994942i | \(-0.532028\pi\) | ||||
−0.100449 | + | 0.994942i | \(0.532028\pi\) | |||||||
\(68\) | 0.823753 | 0.0998947 | ||||||||
\(69\) | 2.67807 | 0.322402 | ||||||||
\(70\) | 0.497345 | 0.0594441 | ||||||||
\(71\) | −12.9896 | −1.54158 | −0.770792 | − | 0.637087i | \(-0.780139\pi\) | ||||
−0.770792 | + | 0.637087i | \(0.780139\pi\) | |||||||
\(72\) | 1.44661 | 0.170485 | ||||||||
\(73\) | 7.20060 | 0.842767 | 0.421384 | − | 0.906883i | \(-0.361545\pi\) | ||||
0.421384 | + | 0.906883i | \(0.361545\pi\) | |||||||
\(74\) | −2.97438 | −0.345765 | ||||||||
\(75\) | 3.23933 | 0.374046 | ||||||||
\(76\) | −2.50262 | −0.287070 | ||||||||
\(77\) | −5.82806 | −0.664169 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.54704 | −0.286565 | −0.143282 | − | 0.989682i | \(-0.545766\pi\) | ||||
−0.143282 | + | 0.989682i | \(0.545766\pi\) | |||||||
\(80\) | 4.21531 | 0.471286 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.305856 | 0.0337762 | ||||||||
\(83\) | −16.2210 | −1.78049 | −0.890243 | − | 0.455486i | \(-0.849465\pi\) | ||||
−0.890243 | + | 0.455486i | \(0.849465\pi\) | |||||||
\(84\) | −1.85951 | −0.202889 | ||||||||
\(85\) | −0.587809 | −0.0637569 | ||||||||
\(86\) | −1.18504 | −0.127787 | ||||||||
\(87\) | −3.35417 | −0.359604 | ||||||||
\(88\) | 8.43094 | 0.898741 | ||||||||
\(89\) | −0.249528 | −0.0264499 | −0.0132249 | − | 0.999913i | \(-0.504210\pi\) | ||||
−0.0132249 | + | 0.999913i | \(0.504210\pi\) | |||||||
\(90\) | −0.497345 | −0.0524248 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.97991 | 0.519192 | ||||||||
\(93\) | −8.32825 | −0.863599 | ||||||||
\(94\) | −1.60819 | −0.165872 | ||||||||
\(95\) | 1.78580 | 0.183220 | ||||||||
\(96\) | 4.08395 | 0.416816 | ||||||||
\(97\) | −3.75470 | −0.381232 | −0.190616 | − | 0.981665i | \(-0.561048\pi\) | ||||
−0.190616 | + | 0.981665i | \(0.561048\pi\) | |||||||
\(98\) | −0.374817 | −0.0378622 | ||||||||
\(99\) | 5.82806 | 0.585742 | ||||||||
\(100\) | 6.02358 | 0.602358 | ||||||||
\(101\) | 2.83930 | 0.282521 | 0.141261 | − | 0.989972i | \(-0.454884\pi\) | ||||
0.141261 | + | 0.989972i | \(0.454884\pi\) | |||||||
\(102\) | −0.166042 | −0.0164406 | ||||||||
\(103\) | −13.0189 | −1.28279 | −0.641395 | − | 0.767211i | \(-0.721644\pi\) | ||||
−0.641395 | + | 0.767211i | \(0.721644\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.32690 | 0.129492 | ||||||||
\(106\) | 0.695154 | 0.0675194 | ||||||||
\(107\) | 14.5111 | 1.40284 | 0.701421 | − | 0.712748i | \(-0.252550\pi\) | ||||
0.701421 | + | 0.712748i | \(0.252550\pi\) | |||||||
\(108\) | 1.85951 | 0.178932 | ||||||||
\(109\) | 13.5778 | 1.30051 | 0.650257 | − | 0.759714i | \(-0.274661\pi\) | ||||
0.650257 | + | 0.759714i | \(0.274661\pi\) | |||||||
\(110\) | −2.89856 | −0.276367 | ||||||||
\(111\) | −7.93555 | −0.753209 | ||||||||
\(112\) | −3.17681 | −0.300180 | ||||||||
\(113\) | 15.8715 | 1.49306 | 0.746532 | − | 0.665349i | \(-0.231717\pi\) | ||||
0.746532 | + | 0.665349i | \(0.231717\pi\) | |||||||
\(114\) | 0.504446 | 0.0472457 | ||||||||
\(115\) | −3.55354 | −0.331369 | ||||||||
\(116\) | −6.23711 | −0.579101 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.31186 | 0.212824 | ||||||||
\(119\) | 0.442994 | 0.0406092 | ||||||||
\(120\) | −1.91951 | −0.175227 | ||||||||
\(121\) | 22.9663 | 2.08784 | ||||||||
\(122\) | 4.13874 | 0.374704 | ||||||||
\(123\) | 0.816015 | 0.0735776 | ||||||||
\(124\) | −15.4865 | −1.39073 | ||||||||
\(125\) | −10.9328 | −0.977858 | ||||||||
\(126\) | 0.374817 | 0.0333914 | ||||||||
\(127\) | −6.24679 | −0.554313 | −0.277157 | − | 0.960825i | \(-0.589392\pi\) | ||||
−0.277157 | + | 0.960825i | \(0.589392\pi\) | |||||||
\(128\) | 9.97559 | 0.881726 | ||||||||
\(129\) | −3.16166 | −0.278369 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.6868 | 1.28319 | 0.641596 | − | 0.767043i | \(-0.278273\pi\) | ||||
0.641596 | + | 0.767043i | \(0.278273\pi\) | |||||||
\(132\) | 10.8373 | 0.943270 | ||||||||
\(133\) | −1.34585 | −0.116700 | ||||||||
\(134\) | 0.616356 | 0.0532451 | ||||||||
\(135\) | −1.32690 | −0.114201 | ||||||||
\(136\) | −0.640840 | −0.0549516 | ||||||||
\(137\) | −0.933243 | −0.0797323 | −0.0398662 | − | 0.999205i | \(-0.512693\pi\) | ||||
−0.0398662 | + | 0.999205i | \(0.512693\pi\) | |||||||
\(138\) | −1.00379 | −0.0854481 | ||||||||
\(139\) | 20.0765 | 1.70287 | 0.851435 | − | 0.524461i | \(-0.175733\pi\) | ||||
0.851435 | + | 0.524461i | \(0.175733\pi\) | |||||||
\(140\) | 2.46739 | 0.208532 | ||||||||
\(141\) | −4.29060 | −0.361333 | ||||||||
\(142\) | 4.86873 | 0.408575 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.17681 | 0.264734 | ||||||||
\(145\) | 4.45065 | 0.369606 | ||||||||
\(146\) | −2.69891 | −0.223363 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −14.7563 | −1.21296 | ||||||||
\(149\) | 12.2978 | 1.00748 | 0.503739 | − | 0.863856i | \(-0.331957\pi\) | ||||
0.503739 | + | 0.863856i | \(0.331957\pi\) | |||||||
\(150\) | −1.21416 | −0.0991355 | ||||||||
\(151\) | 18.6796 | 1.52013 | 0.760064 | − | 0.649849i | \(-0.225168\pi\) | ||||
0.760064 | + | 0.649849i | \(0.225168\pi\) | |||||||
\(152\) | 1.94692 | 0.157916 | ||||||||
\(153\) | −0.442994 | −0.0358139 | ||||||||
\(154\) | 2.18446 | 0.176029 | ||||||||
\(155\) | 11.0508 | 0.887619 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.3864 | 1.94624 | 0.973122 | − | 0.230288i | \(-0.0739669\pi\) | ||||
0.973122 | + | 0.230288i | \(0.0739669\pi\) | |||||||
\(158\) | 0.954675 | 0.0759499 | ||||||||
\(159\) | 1.85465 | 0.147083 | ||||||||
\(160\) | −5.41899 | −0.428409 | ||||||||
\(161\) | 2.67807 | 0.211062 | ||||||||
\(162\) | −0.374817 | −0.0294484 | ||||||||
\(163\) | −22.2649 | −1.74392 | −0.871962 | − | 0.489574i | \(-0.837152\pi\) | ||||
−0.871962 | + | 0.489574i | \(0.837152\pi\) | |||||||
\(164\) | 1.51739 | 0.118488 | ||||||||
\(165\) | −7.73326 | −0.602034 | ||||||||
\(166\) | 6.07991 | 0.471892 | ||||||||
\(167\) | 18.3284 | 1.41829 | 0.709146 | − | 0.705062i | \(-0.249081\pi\) | ||||
0.709146 | + | 0.705062i | \(0.249081\pi\) | |||||||
\(168\) | 1.44661 | 0.111608 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0.220321 | 0.0168979 | ||||||||
\(171\) | 1.34585 | 0.102919 | ||||||||
\(172\) | −5.87914 | −0.448281 | ||||||||
\(173\) | −12.7444 | −0.968940 | −0.484470 | − | 0.874808i | \(-0.660988\pi\) | ||||
−0.484470 | + | 0.874808i | \(0.660988\pi\) | |||||||
\(174\) | 1.25720 | 0.0953080 | ||||||||
\(175\) | 3.23933 | 0.244871 | ||||||||
\(176\) | 18.5146 | 1.39559 | ||||||||
\(177\) | 6.16798 | 0.463614 | ||||||||
\(178\) | 0.0935273 | 0.00701016 | ||||||||
\(179\) | 3.10502 | 0.232080 | 0.116040 | − | 0.993245i | \(-0.462980\pi\) | ||||
0.116040 | + | 0.993245i | \(0.462980\pi\) | |||||||
\(180\) | −2.46739 | −0.183908 | ||||||||
\(181\) | −0.670686 | −0.0498517 | −0.0249259 | − | 0.999689i | \(-0.507935\pi\) | ||||
−0.0249259 | + | 0.999689i | \(0.507935\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.0420 | 0.816250 | ||||||||
\(184\) | −3.87413 | −0.285605 | ||||||||
\(185\) | 10.5297 | 0.774158 | ||||||||
\(186\) | 3.12157 | 0.228885 | ||||||||
\(187\) | −2.58180 | −0.188800 | ||||||||
\(188\) | −7.97841 | −0.581886 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −0.669350 | −0.0485598 | ||||||||
\(191\) | 17.8728 | 1.29323 | 0.646614 | − | 0.762817i | \(-0.276184\pi\) | ||||
0.646614 | + | 0.762817i | \(0.276184\pi\) | |||||||
\(192\) | 4.82289 | 0.348062 | ||||||||
\(193\) | −5.62386 | −0.404814 | −0.202407 | − | 0.979301i | \(-0.564876\pi\) | ||||
−0.202407 | + | 0.979301i | \(0.564876\pi\) | |||||||
\(194\) | 1.40732 | 0.101040 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.85951 | −0.132822 | ||||||||
\(197\) | 16.5783 | 1.18116 | 0.590579 | − | 0.806980i | \(-0.298900\pi\) | ||||
0.590579 | + | 0.806980i | \(0.298900\pi\) | |||||||
\(198\) | −2.18446 | −0.155243 | ||||||||
\(199\) | 24.4240 | 1.73137 | 0.865687 | − | 0.500585i | \(-0.166882\pi\) | ||||
0.865687 | + | 0.500585i | \(0.166882\pi\) | |||||||
\(200\) | −4.68605 | −0.331354 | ||||||||
\(201\) | 1.64442 | 0.115988 | ||||||||
\(202\) | −1.06422 | −0.0748782 | ||||||||
\(203\) | −3.35417 | −0.235416 | ||||||||
\(204\) | −0.823753 | −0.0576742 | ||||||||
\(205\) | −1.08277 | −0.0756240 | ||||||||
\(206\) | 4.87970 | 0.339985 | ||||||||
\(207\) | −2.67807 | −0.186139 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.84367 | 0.542558 | ||||||||
\(210\) | −0.497345 | −0.0343201 | ||||||||
\(211\) | −10.9881 | −0.756454 | −0.378227 | − | 0.925713i | \(-0.623466\pi\) | ||||
−0.378227 | + | 0.925713i | \(0.623466\pi\) | |||||||
\(212\) | 3.44874 | 0.236861 | ||||||||
\(213\) | 12.9896 | 0.890033 | ||||||||
\(214\) | −5.43901 | −0.371803 | ||||||||
\(215\) | 4.19521 | 0.286111 | ||||||||
\(216\) | −1.44661 | −0.0984294 | ||||||||
\(217\) | −8.32825 | −0.565358 | ||||||||
\(218\) | −5.08918 | −0.344683 | ||||||||
\(219\) | −7.20060 | −0.486572 | ||||||||
\(220\) | −14.3801 | −0.969506 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2.97438 | 0.199627 | ||||||||
\(223\) | −14.6782 | −0.982922 | −0.491461 | − | 0.870900i | \(-0.663537\pi\) | ||||
−0.491461 | + | 0.870900i | \(0.663537\pi\) | |||||||
\(224\) | 4.08395 | 0.272870 | ||||||||
\(225\) | −3.23933 | −0.215956 | ||||||||
\(226\) | −5.94891 | −0.395715 | ||||||||
\(227\) | −0.615870 | −0.0408767 | −0.0204384 | − | 0.999791i | \(-0.506506\pi\) | ||||
−0.0204384 | + | 0.999791i | \(0.506506\pi\) | |||||||
\(228\) | 2.50262 | 0.165740 | ||||||||
\(229\) | −9.47389 | −0.626053 | −0.313026 | − | 0.949744i | \(-0.601343\pi\) | ||||
−0.313026 | + | 0.949744i | \(0.601343\pi\) | |||||||
\(230\) | 1.33193 | 0.0878247 | ||||||||
\(231\) | 5.82806 | 0.383458 | ||||||||
\(232\) | 4.85218 | 0.318561 | ||||||||
\(233\) | −8.35195 | −0.547154 | −0.273577 | − | 0.961850i | \(-0.588207\pi\) | ||||
−0.273577 | + | 0.961850i | \(0.588207\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.69320 | 0.371383 | ||||||||
\(236\) | 11.4694 | 0.746596 | ||||||||
\(237\) | 2.54704 | 0.165448 | ||||||||
\(238\) | −0.166042 | −0.0107629 | ||||||||
\(239\) | −3.25440 | −0.210510 | −0.105255 | − | 0.994445i | \(-0.533566\pi\) | ||||
−0.105255 | + | 0.994445i | \(0.533566\pi\) | |||||||
\(240\) | −4.21531 | −0.272097 | ||||||||
\(241\) | 16.1085 | 1.03764 | 0.518819 | − | 0.854884i | \(-0.326372\pi\) | ||||
0.518819 | + | 0.854884i | \(0.326372\pi\) | |||||||
\(242\) | −8.60816 | −0.553353 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 20.5328 | 1.31448 | ||||||||
\(245\) | 1.32690 | 0.0847726 | ||||||||
\(246\) | −0.305856 | −0.0195007 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 12.0477 | 0.765032 | ||||||||
\(249\) | 16.2210 | 1.02796 | ||||||||
\(250\) | 4.09779 | 0.259167 | ||||||||
\(251\) | 20.4332 | 1.28973 | 0.644866 | − | 0.764296i | \(-0.276913\pi\) | ||||
0.644866 | + | 0.764296i | \(0.276913\pi\) | |||||||
\(252\) | 1.85951 | 0.117138 | ||||||||
\(253\) | −15.6080 | −0.981265 | ||||||||
\(254\) | 2.34141 | 0.146913 | ||||||||
\(255\) | 0.587809 | 0.0368101 | ||||||||
\(256\) | 5.90675 | 0.369172 | ||||||||
\(257\) | −15.8411 | −0.988142 | −0.494071 | − | 0.869422i | \(-0.664492\pi\) | ||||
−0.494071 | + | 0.869422i | \(0.664492\pi\) | |||||||
\(258\) | 1.18504 | 0.0737776 | ||||||||
\(259\) | −7.93555 | −0.493091 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.35417 | 0.207618 | ||||||||
\(262\) | −5.50487 | −0.340092 | ||||||||
\(263\) | 17.0251 | 1.04982 | 0.524908 | − | 0.851159i | \(-0.324100\pi\) | ||||
0.524908 | + | 0.851159i | \(0.324100\pi\) | |||||||
\(264\) | −8.43094 | −0.518888 | ||||||||
\(265\) | −2.46094 | −0.151174 | ||||||||
\(266\) | 0.504446 | 0.0309296 | ||||||||
\(267\) | 0.249528 | 0.0152708 | ||||||||
\(268\) | 3.05782 | 0.186786 | ||||||||
\(269\) | −16.0150 | −0.976454 | −0.488227 | − | 0.872717i | \(-0.662356\pi\) | ||||
−0.488227 | + | 0.872717i | \(0.662356\pi\) | |||||||
\(270\) | 0.497345 | 0.0302675 | ||||||||
\(271\) | −10.3553 | −0.629040 | −0.314520 | − | 0.949251i | \(-0.601844\pi\) | ||||
−0.314520 | + | 0.949251i | \(0.601844\pi\) | |||||||
\(272\) | −1.40731 | −0.0853306 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.349795 | 0.0211319 | ||||||||
\(275\) | −18.8790 | −1.13845 | ||||||||
\(276\) | −4.97991 | −0.299755 | ||||||||
\(277\) | −8.83806 | −0.531027 | −0.265514 | − | 0.964107i | \(-0.585542\pi\) | ||||
−0.265514 | + | 0.964107i | \(0.585542\pi\) | |||||||
\(278\) | −7.52503 | −0.451321 | ||||||||
\(279\) | 8.32825 | 0.498599 | ||||||||
\(280\) | −1.91951 | −0.114713 | ||||||||
\(281\) | 14.3408 | 0.855503 | 0.427752 | − | 0.903896i | \(-0.359306\pi\) | ||||
0.427752 | + | 0.903896i | \(0.359306\pi\) | |||||||
\(282\) | 1.60819 | 0.0957662 | ||||||||
\(283\) | 13.9259 | 0.827808 | 0.413904 | − | 0.910321i | \(-0.364165\pi\) | ||||
0.413904 | + | 0.910321i | \(0.364165\pi\) | |||||||
\(284\) | 24.1543 | 1.43330 | ||||||||
\(285\) | −1.78580 | −0.105782 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.816015 | 0.0481678 | ||||||||
\(288\) | −4.08395 | −0.240649 | ||||||||
\(289\) | −16.8038 | −0.988456 | ||||||||
\(290\) | −1.66818 | −0.0979589 | ||||||||
\(291\) | 3.75470 | 0.220104 | ||||||||
\(292\) | −13.3896 | −0.783568 | ||||||||
\(293\) | −24.0035 | −1.40230 | −0.701149 | − | 0.713015i | \(-0.747329\pi\) | ||||
−0.701149 | + | 0.713015i | \(0.747329\pi\) | |||||||
\(294\) | 0.374817 | 0.0218598 | ||||||||
\(295\) | −8.18430 | −0.476508 | ||||||||
\(296\) | 11.4797 | 0.667241 | ||||||||
\(297\) | −5.82806 | −0.338178 | ||||||||
\(298\) | −4.60944 | −0.267018 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −6.02358 | −0.347771 | ||||||||
\(301\) | −3.16166 | −0.182235 | ||||||||
\(302\) | −7.00145 | −0.402888 | ||||||||
\(303\) | −2.83930 | −0.163114 | ||||||||
\(304\) | 4.27550 | 0.245216 | ||||||||
\(305\) | −14.6517 | −0.838953 | ||||||||
\(306\) | 0.166042 | 0.00949197 | ||||||||
\(307\) | 20.6185 | 1.17676 | 0.588381 | − | 0.808584i | \(-0.299765\pi\) | ||||
0.588381 | + | 0.808584i | \(0.299765\pi\) | |||||||
\(308\) | 10.8373 | 0.617515 | ||||||||
\(309\) | 13.0189 | 0.740619 | ||||||||
\(310\) | −4.14202 | −0.235251 | ||||||||
\(311\) | 33.6435 | 1.90775 | 0.953873 | − | 0.300210i | \(-0.0970566\pi\) | ||||
0.953873 | + | 0.300210i | \(0.0970566\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.87809 | 0.558342 | 0.279171 | − | 0.960241i | \(-0.409940\pi\) | ||||
0.279171 | + | 0.960241i | \(0.409940\pi\) | |||||||
\(314\) | −9.14043 | −0.515824 | ||||||||
\(315\) | −1.32690 | −0.0747624 | ||||||||
\(316\) | 4.73626 | 0.266435 | ||||||||
\(317\) | −13.6053 | −0.764151 | −0.382075 | − | 0.924131i | \(-0.624791\pi\) | ||||
−0.382075 | + | 0.924131i | \(0.624791\pi\) | |||||||
\(318\) | −0.695154 | −0.0389823 | ||||||||
\(319\) | 19.5483 | 1.09449 | ||||||||
\(320\) | −6.39950 | −0.357743 | ||||||||
\(321\) | −14.5111 | −0.809931 | ||||||||
\(322\) | −1.00379 | −0.0559389 | ||||||||
\(323\) | −0.596202 | −0.0331735 | ||||||||
\(324\) | −1.85951 | −0.103306 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.34527 | 0.462202 | ||||||||
\(327\) | −13.5778 | −0.750853 | ||||||||
\(328\) | −1.18046 | −0.0651798 | ||||||||
\(329\) | −4.29060 | −0.236548 | ||||||||
\(330\) | 2.89856 | 0.159560 | ||||||||
\(331\) | −1.35950 | −0.0747251 | −0.0373625 | − | 0.999302i | \(-0.511896\pi\) | ||||
−0.0373625 | + | 0.999302i | \(0.511896\pi\) | |||||||
\(332\) | 30.1631 | 1.65542 | ||||||||
\(333\) | 7.93555 | 0.434865 | ||||||||
\(334\) | −6.86979 | −0.375898 | ||||||||
\(335\) | −2.18198 | −0.119214 | ||||||||
\(336\) | 3.17681 | 0.173309 | ||||||||
\(337\) | 31.6542 | 1.72432 | 0.862158 | − | 0.506640i | \(-0.169113\pi\) | ||||
0.862158 | + | 0.506640i | \(0.169113\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.8715 | −0.862021 | ||||||||
\(340\) | 1.09304 | 0.0592783 | ||||||||
\(341\) | 48.5375 | 2.62846 | ||||||||
\(342\) | −0.504446 | −0.0272773 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 4.57369 | 0.246597 | ||||||||
\(345\) | 3.55354 | 0.191316 | ||||||||
\(346\) | 4.77683 | 0.256804 | ||||||||
\(347\) | 18.5368 | 0.995108 | 0.497554 | − | 0.867433i | \(-0.334232\pi\) | ||||
0.497554 | + | 0.867433i | \(0.334232\pi\) | |||||||
\(348\) | 6.23711 | 0.334344 | ||||||||
\(349\) | −31.9333 | −1.70935 | −0.854674 | − | 0.519165i | \(-0.826243\pi\) | ||||
−0.854674 | + | 0.519165i | \(0.826243\pi\) | |||||||
\(350\) | −1.21416 | −0.0648994 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −23.8015 | −1.26862 | ||||||||
\(353\) | −1.62631 | −0.0865598 | −0.0432799 | − | 0.999063i | \(-0.513781\pi\) | ||||
−0.0432799 | + | 0.999063i | \(0.513781\pi\) | |||||||
\(354\) | −2.31186 | −0.122874 | ||||||||
\(355\) | −17.2359 | −0.914788 | ||||||||
\(356\) | 0.464000 | 0.0245919 | ||||||||
\(357\) | −0.442994 | −0.0234457 | ||||||||
\(358\) | −1.16381 | −0.0615095 | ||||||||
\(359\) | 24.7731 | 1.30747 | 0.653736 | − | 0.756722i | \(-0.273201\pi\) | ||||
0.653736 | + | 0.756722i | \(0.273201\pi\) | |||||||
\(360\) | 1.91951 | 0.101167 | ||||||||
\(361\) | −17.1887 | −0.904668 | ||||||||
\(362\) | 0.251385 | 0.0132125 | ||||||||
\(363\) | −22.9663 | −1.20542 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.55449 | 0.500105 | ||||||||
\(366\) | −4.13874 | −0.216335 | ||||||||
\(367\) | 5.26649 | 0.274909 | 0.137454 | − | 0.990508i | \(-0.456108\pi\) | ||||
0.137454 | + | 0.990508i | \(0.456108\pi\) | |||||||
\(368\) | −8.50773 | −0.443496 | ||||||||
\(369\) | −0.816015 | −0.0424800 | ||||||||
\(370\) | −3.94671 | −0.205180 | ||||||||
\(371\) | 1.85465 | 0.0962886 | ||||||||
\(372\) | 15.4865 | 0.802937 | ||||||||
\(373\) | −27.3669 | −1.41701 | −0.708503 | − | 0.705708i | \(-0.750629\pi\) | ||||
−0.708503 | + | 0.705708i | \(0.750629\pi\) | |||||||
\(374\) | 0.967701 | 0.0500386 | ||||||||
\(375\) | 10.9328 | 0.564566 | ||||||||
\(376\) | 6.20682 | 0.320092 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.374817 | −0.0192785 | ||||||||
\(379\) | 25.4725 | 1.30844 | 0.654218 | − | 0.756306i | \(-0.272998\pi\) | ||||
0.654218 | + | 0.756306i | \(0.272998\pi\) | |||||||
\(380\) | −3.32073 | −0.170350 | ||||||||
\(381\) | 6.24679 | 0.320033 | ||||||||
\(382\) | −6.69902 | −0.342752 | ||||||||
\(383\) | 22.9476 | 1.17257 | 0.586283 | − | 0.810106i | \(-0.300591\pi\) | ||||
0.586283 | + | 0.810106i | \(0.300591\pi\) | |||||||
\(384\) | −9.97559 | −0.509065 | ||||||||
\(385\) | −7.73326 | −0.394123 | ||||||||
\(386\) | 2.10792 | 0.107290 | ||||||||
\(387\) | 3.16166 | 0.160716 | ||||||||
\(388\) | 6.98190 | 0.354452 | ||||||||
\(389\) | 15.0422 | 0.762671 | 0.381335 | − | 0.924437i | \(-0.375464\pi\) | ||||
0.381335 | + | 0.924437i | \(0.375464\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.18637 | 0.0599974 | ||||||||
\(392\) | 1.44661 | 0.0730649 | ||||||||
\(393\) | −14.6868 | −0.740851 | ||||||||
\(394\) | −6.21384 | −0.313049 | ||||||||
\(395\) | −3.37967 | −0.170050 | ||||||||
\(396\) | −10.8373 | −0.544597 | ||||||||
\(397\) | −16.4236 | −0.824278 | −0.412139 | − | 0.911121i | \(-0.635218\pi\) | ||||
−0.412139 | + | 0.911121i | \(0.635218\pi\) | |||||||
\(398\) | −9.15455 | −0.458876 | ||||||||
\(399\) | 1.34585 | 0.0673766 | ||||||||
\(400\) | −10.2907 | −0.514537 | ||||||||
\(401\) | −17.7054 | −0.884168 | −0.442084 | − | 0.896974i | \(-0.645761\pi\) | ||||
−0.442084 | + | 0.896974i | \(0.645761\pi\) | |||||||
\(402\) | −0.616356 | −0.0307411 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −5.27972 | −0.262676 | ||||||||
\(405\) | 1.32690 | 0.0659343 | ||||||||
\(406\) | 1.25720 | 0.0623937 | ||||||||
\(407\) | 46.2489 | 2.29247 | ||||||||
\(408\) | 0.640840 | 0.0317263 | ||||||||
\(409\) | −4.05274 | −0.200395 | −0.100198 | − | 0.994968i | \(-0.531947\pi\) | ||||
−0.100198 | + | 0.994968i | \(0.531947\pi\) | |||||||
\(410\) | 0.405841 | 0.0200431 | ||||||||
\(411\) | 0.933243 | 0.0460335 | ||||||||
\(412\) | 24.2088 | 1.19268 | ||||||||
\(413\) | 6.16798 | 0.303506 | ||||||||
\(414\) | 1.00379 | 0.0493335 | ||||||||
\(415\) | −21.5237 | −1.05655 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −20.0765 | −0.983152 | ||||||||
\(418\) | −2.93994 | −0.143797 | ||||||||
\(419\) | −7.13923 | −0.348774 | −0.174387 | − | 0.984677i | \(-0.555794\pi\) | ||||
−0.174387 | + | 0.984677i | \(0.555794\pi\) | |||||||
\(420\) | −2.46739 | −0.120396 | ||||||||
\(421\) | 32.2979 | 1.57410 | 0.787052 | − | 0.616887i | \(-0.211606\pi\) | ||||
0.787052 | + | 0.616887i | \(0.211606\pi\) | |||||||
\(422\) | 4.11854 | 0.200487 | ||||||||
\(423\) | 4.29060 | 0.208616 | ||||||||
\(424\) | −2.68296 | −0.130296 | ||||||||
\(425\) | 1.43501 | 0.0696080 | ||||||||
\(426\) | −4.86873 | −0.235891 | ||||||||
\(427\) | 11.0420 | 0.534361 | ||||||||
\(428\) | −26.9836 | −1.30430 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.57244 | −0.0758296 | ||||||||
\(431\) | −13.3707 | −0.644046 | −0.322023 | − | 0.946732i | \(-0.604363\pi\) | ||||
−0.322023 | + | 0.946732i | \(0.604363\pi\) | |||||||
\(432\) | −3.17681 | −0.152844 | ||||||||
\(433\) | −30.7437 | −1.47745 | −0.738723 | − | 0.674009i | \(-0.764571\pi\) | ||||
−0.738723 | + | 0.674009i | \(0.764571\pi\) | |||||||
\(434\) | 3.12157 | 0.149840 | ||||||||
\(435\) | −4.45065 | −0.213392 | ||||||||
\(436\) | −25.2480 | −1.20916 | ||||||||
\(437\) | −3.60427 | −0.172416 | ||||||||
\(438\) | 2.69891 | 0.128959 | ||||||||
\(439\) | −22.4974 | −1.07374 | −0.536871 | − | 0.843664i | \(-0.680394\pi\) | ||||
−0.536871 | + | 0.843664i | \(0.680394\pi\) | |||||||
\(440\) | 11.1870 | 0.533320 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.6355 | −1.26549 | −0.632746 | − | 0.774359i | \(-0.718072\pi\) | ||||
−0.632746 | + | 0.774359i | \(0.718072\pi\) | |||||||
\(444\) | 14.7563 | 0.700301 | ||||||||
\(445\) | −0.331099 | −0.0156956 | ||||||||
\(446\) | 5.50162 | 0.260509 | ||||||||
\(447\) | −12.2978 | −0.581668 | ||||||||
\(448\) | 4.82289 | 0.227860 | ||||||||
\(449\) | 30.2908 | 1.42951 | 0.714757 | − | 0.699373i | \(-0.246537\pi\) | ||||
0.714757 | + | 0.699373i | \(0.246537\pi\) | |||||||
\(450\) | 1.21416 | 0.0572359 | ||||||||
\(451\) | −4.75578 | −0.223941 | ||||||||
\(452\) | −29.5132 | −1.38819 | ||||||||
\(453\) | −18.6796 | −0.877646 | ||||||||
\(454\) | 0.230839 | 0.0108338 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.94692 | −0.0911727 | ||||||||
\(457\) | −7.92047 | −0.370504 | −0.185252 | − | 0.982691i | \(-0.559310\pi\) | ||||
−0.185252 | + | 0.982691i | \(0.559310\pi\) | |||||||
\(458\) | 3.55098 | 0.165926 | ||||||||
\(459\) | 0.442994 | 0.0206772 | ||||||||
\(460\) | 6.60785 | 0.308093 | ||||||||
\(461\) | 10.9884 | 0.511783 | 0.255891 | − | 0.966706i | \(-0.417631\pi\) | ||||
0.255891 | + | 0.966706i | \(0.417631\pi\) | |||||||
\(462\) | −2.18446 | −0.101630 | ||||||||
\(463\) | 8.71786 | 0.405153 | 0.202577 | − | 0.979266i | \(-0.435068\pi\) | ||||
0.202577 | + | 0.979266i | \(0.435068\pi\) | |||||||
\(464\) | 10.6555 | 0.494671 | ||||||||
\(465\) | −11.0508 | −0.512467 | ||||||||
\(466\) | 3.13045 | 0.145015 | ||||||||
\(467\) | 33.7907 | 1.56365 | 0.781824 | − | 0.623499i | \(-0.214289\pi\) | ||||
0.781824 | + | 0.623499i | \(0.214289\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.64442 | 0.0759322 | ||||||||
\(470\) | −2.13391 | −0.0984298 | ||||||||
\(471\) | −24.3864 | −1.12367 | ||||||||
\(472\) | −8.92267 | −0.410699 | ||||||||
\(473\) | 18.4263 | 0.847244 | ||||||||
\(474\) | −0.954675 | −0.0438497 | ||||||||
\(475\) | −4.35964 | −0.200034 | ||||||||
\(476\) | −0.823753 | −0.0377566 | ||||||||
\(477\) | −1.85465 | −0.0849186 | ||||||||
\(478\) | 1.21981 | 0.0557926 | ||||||||
\(479\) | 39.0440 | 1.78396 | 0.891982 | − | 0.452071i | \(-0.149315\pi\) | ||||
0.891982 | + | 0.452071i | \(0.149315\pi\) | |||||||
\(480\) | 5.41899 | 0.247342 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −6.03773 | −0.275011 | ||||||||
\(483\) | −2.67807 | −0.121857 | ||||||||
\(484\) | −42.7061 | −1.94119 | ||||||||
\(485\) | −4.98211 | −0.226226 | ||||||||
\(486\) | 0.374817 | 0.0170020 | ||||||||
\(487\) | 12.0804 | 0.547416 | 0.273708 | − | 0.961813i | \(-0.411750\pi\) | ||||
0.273708 | + | 0.961813i | \(0.411750\pi\) | |||||||
\(488\) | −15.9735 | −0.723087 | ||||||||
\(489\) | 22.2649 | 1.00685 | ||||||||
\(490\) | −0.497345 | −0.0224678 | ||||||||
\(491\) | −42.4080 | −1.91385 | −0.956923 | − | 0.290343i | \(-0.906231\pi\) | ||||
−0.956923 | + | 0.290343i | \(0.906231\pi\) | |||||||
\(492\) | −1.51739 | −0.0684092 | ||||||||
\(493\) | −1.48588 | −0.0669205 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.73326 | 0.347584 | ||||||||
\(496\) | 26.4573 | 1.18797 | ||||||||
\(497\) | 12.9896 | 0.582664 | ||||||||
\(498\) | −6.07991 | −0.272447 | ||||||||
\(499\) | 23.7535 | 1.06335 | 0.531677 | − | 0.846947i | \(-0.321562\pi\) | ||||
0.531677 | + | 0.846947i | \(0.321562\pi\) | |||||||
\(500\) | 20.3296 | 0.909169 | ||||||||
\(501\) | −18.3284 | −0.818851 | ||||||||
\(502\) | −7.65871 | −0.341825 | ||||||||
\(503\) | −18.4558 | −0.822905 | −0.411453 | − | 0.911431i | \(-0.634978\pi\) | ||||
−0.411453 | + | 0.911431i | \(0.634978\pi\) | |||||||
\(504\) | −1.44661 | −0.0644372 | ||||||||
\(505\) | 3.76747 | 0.167650 | ||||||||
\(506\) | 5.85014 | 0.260070 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11.6160 | 0.515376 | ||||||||
\(509\) | −12.5610 | −0.556755 | −0.278378 | − | 0.960472i | \(-0.589797\pi\) | ||||
−0.278378 | + | 0.960472i | \(0.589797\pi\) | |||||||
\(510\) | −0.220321 | −0.00975598 | ||||||||
\(511\) | −7.20060 | −0.318536 | ||||||||
\(512\) | −22.1651 | −0.979570 | ||||||||
\(513\) | −1.34585 | −0.0594205 | ||||||||
\(514\) | 5.93752 | 0.261893 | ||||||||
\(515\) | −17.2748 | −0.761218 | ||||||||
\(516\) | 5.87914 | 0.258815 | ||||||||
\(517\) | 25.0058 | 1.09976 | ||||||||
\(518\) | 2.97438 | 0.130687 | ||||||||
\(519\) | 12.7444 | 0.559418 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.8796 | −1.04618 | −0.523092 | − | 0.852276i | \(-0.675221\pi\) | ||||
−0.523092 | + | 0.852276i | \(0.675221\pi\) | |||||||
\(522\) | −1.25720 | −0.0550261 | ||||||||
\(523\) | 27.5520 | 1.20476 | 0.602382 | − | 0.798208i | \(-0.294218\pi\) | ||||
0.602382 | + | 0.798208i | \(0.294218\pi\) | |||||||
\(524\) | −27.3103 | −1.19306 | ||||||||
\(525\) | −3.23933 | −0.141376 | ||||||||
\(526\) | −6.38132 | −0.278239 | ||||||||
\(527\) | −3.68937 | −0.160711 | ||||||||
\(528\) | −18.5146 | −0.805746 | ||||||||
\(529\) | −15.8279 | −0.688170 | ||||||||
\(530\) | 0.922401 | 0.0400666 | ||||||||
\(531\) | −6.16798 | −0.267667 | ||||||||
\(532\) | 2.50262 | 0.108502 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.0935273 | −0.00404732 | ||||||||
\(535\) | 19.2548 | 0.832458 | ||||||||
\(536\) | −2.37884 | −0.102750 | ||||||||
\(537\) | −3.10502 | −0.133992 | ||||||||
\(538\) | 6.00271 | 0.258795 | ||||||||
\(539\) | 5.82806 | 0.251032 | ||||||||
\(540\) | 2.46739 | 0.106180 | ||||||||
\(541\) | −8.30651 | −0.357125 | −0.178562 | − | 0.983929i | \(-0.557145\pi\) | ||||
−0.178562 | + | 0.983929i | \(0.557145\pi\) | |||||||
\(542\) | 3.88134 | 0.166718 | ||||||||
\(543\) | 0.670686 | 0.0287819 | ||||||||
\(544\) | 1.80916 | 0.0775672 | ||||||||
\(545\) | 18.0164 | 0.771736 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.1011 | −0.816705 | −0.408353 | − | 0.912824i | \(-0.633897\pi\) | ||||
−0.408353 | + | 0.912824i | \(0.633897\pi\) | |||||||
\(548\) | 1.73538 | 0.0741316 | ||||||||
\(549\) | −11.0420 | −0.471262 | ||||||||
\(550\) | 7.07618 | 0.301729 | ||||||||
\(551\) | 4.51419 | 0.192311 | ||||||||
\(552\) | 3.87413 | 0.164894 | ||||||||
\(553\) | 2.54704 | 0.108311 | ||||||||
\(554\) | 3.31266 | 0.140741 | ||||||||
\(555\) | −10.5297 | −0.446961 | ||||||||
\(556\) | −37.3326 | −1.58325 | ||||||||
\(557\) | 0.238603 | 0.0101099 | 0.00505496 | − | 0.999987i | \(-0.498391\pi\) | ||||
0.00505496 | + | 0.999987i | \(0.498391\pi\) | |||||||
\(558\) | −3.12157 | −0.132147 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −4.21531 | −0.178129 | ||||||||
\(561\) | 2.58180 | 0.109004 | ||||||||
\(562\) | −5.37519 | −0.226739 | ||||||||
\(563\) | 20.7512 | 0.874559 | 0.437279 | − | 0.899326i | \(-0.355942\pi\) | ||||
0.437279 | + | 0.899326i | \(0.355942\pi\) | |||||||
\(564\) | 7.97841 | 0.335952 | ||||||||
\(565\) | 21.0599 | 0.885997 | ||||||||
\(566\) | −5.21966 | −0.219399 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −18.7909 | −0.788449 | ||||||||
\(569\) | 6.55284 | 0.274709 | 0.137355 | − | 0.990522i | \(-0.456140\pi\) | ||||
0.137355 | + | 0.990522i | \(0.456140\pi\) | |||||||
\(570\) | 0.669350 | 0.0280360 | ||||||||
\(571\) | 1.75392 | 0.0733995 | 0.0366997 | − | 0.999326i | \(-0.488315\pi\) | ||||
0.0366997 | + | 0.999326i | \(0.488315\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.8728 | −0.746646 | ||||||||
\(574\) | −0.305856 | −0.0127662 | ||||||||
\(575\) | 8.67517 | 0.361780 | ||||||||
\(576\) | −4.82289 | −0.200954 | ||||||||
\(577\) | 3.46646 | 0.144311 | 0.0721553 | − | 0.997393i | \(-0.477012\pi\) | ||||
0.0721553 | + | 0.997393i | \(0.477012\pi\) | |||||||
\(578\) | 6.29834 | 0.261976 | ||||||||
\(579\) | 5.62386 | 0.233720 | ||||||||
\(580\) | −8.27603 | −0.343644 | ||||||||
\(581\) | 16.2210 | 0.672960 | ||||||||
\(582\) | −1.40732 | −0.0583355 | ||||||||
\(583\) | −10.8090 | −0.447663 | ||||||||
\(584\) | 10.4165 | 0.431037 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.99692 | 0.371659 | ||||||||
\(587\) | −38.9101 | −1.60599 | −0.802997 | − | 0.595984i | \(-0.796762\pi\) | ||||
−0.802997 | + | 0.595984i | \(0.796762\pi\) | |||||||
\(588\) | 1.85951 | 0.0766850 | ||||||||
\(589\) | 11.2085 | 0.461840 | ||||||||
\(590\) | 3.06762 | 0.126292 | ||||||||
\(591\) | −16.5783 | −0.681941 | ||||||||
\(592\) | 25.2097 | 1.03611 | ||||||||
\(593\) | −25.4135 | −1.04361 | −0.521803 | − | 0.853066i | \(-0.674740\pi\) | ||||
−0.521803 | + | 0.853066i | \(0.674740\pi\) | |||||||
\(594\) | 2.18446 | 0.0896293 | ||||||||
\(595\) | 0.587809 | 0.0240978 | ||||||||
\(596\) | −22.8680 | −0.936709 | ||||||||
\(597\) | −24.4240 | −0.999610 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.40004 | −0.302357 | −0.151179 | − | 0.988506i | \(-0.548307\pi\) | ||||
−0.151179 | + | 0.988506i | \(0.548307\pi\) | |||||||
\(600\) | 4.68605 | 0.191307 | ||||||||
\(601\) | −14.4392 | −0.588988 | −0.294494 | − | 0.955653i | \(-0.595151\pi\) | ||||
−0.294494 | + | 0.955653i | \(0.595151\pi\) | |||||||
\(602\) | 1.18504 | 0.0482988 | ||||||||
\(603\) | −1.64442 | −0.0669659 | ||||||||
\(604\) | −34.7350 | −1.41335 | ||||||||
\(605\) | 30.4740 | 1.23894 | ||||||||
\(606\) | 1.06422 | 0.0432309 | ||||||||
\(607\) | 6.40534 | 0.259985 | 0.129992 | − | 0.991515i | \(-0.458505\pi\) | ||||
0.129992 | + | 0.991515i | \(0.458505\pi\) | |||||||
\(608\) | −5.49636 | −0.222907 | ||||||||
\(609\) | 3.35417 | 0.135918 | ||||||||
\(610\) | 5.49170 | 0.222352 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.823753 | 0.0332982 | ||||||||
\(613\) | −9.33764 | −0.377144 | −0.188572 | − | 0.982059i | \(-0.560386\pi\) | ||||
−0.188572 | + | 0.982059i | \(0.560386\pi\) | |||||||
\(614\) | −7.72818 | −0.311884 | ||||||||
\(615\) | 1.08277 | 0.0436616 | ||||||||
\(616\) | −8.43094 | −0.339692 | ||||||||
\(617\) | −4.02033 | −0.161852 | −0.0809262 | − | 0.996720i | \(-0.525788\pi\) | ||||
−0.0809262 | + | 0.996720i | \(0.525788\pi\) | |||||||
\(618\) | −4.87970 | −0.196290 | ||||||||
\(619\) | −22.6258 | −0.909408 | −0.454704 | − | 0.890643i | \(-0.650255\pi\) | ||||
−0.454704 | + | 0.890643i | \(0.650255\pi\) | |||||||
\(620\) | −20.5490 | −0.825269 | ||||||||
\(621\) | 2.67807 | 0.107467 | ||||||||
\(622\) | −12.6102 | −0.505621 | ||||||||
\(623\) | 0.249528 | 0.00999712 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.68994 | 0.0675975 | ||||||||
\(626\) | −3.70248 | −0.147981 | ||||||||
\(627\) | −7.84367 | −0.313246 | ||||||||
\(628\) | −45.3468 | −1.80953 | ||||||||
\(629\) | −3.51540 | −0.140168 | ||||||||
\(630\) | 0.497345 | 0.0198147 | ||||||||
\(631\) | 24.6591 | 0.981665 | 0.490832 | − | 0.871254i | \(-0.336693\pi\) | ||||
0.490832 | + | 0.871254i | \(0.336693\pi\) | |||||||
\(632\) | −3.68458 | −0.146565 | ||||||||
\(633\) | 10.9881 | 0.436739 | ||||||||
\(634\) | 5.09951 | 0.202527 | ||||||||
\(635\) | −8.28888 | −0.328934 | ||||||||
\(636\) | −3.44874 | −0.136752 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −7.32703 | −0.290080 | ||||||||
\(639\) | −12.9896 | −0.513861 | ||||||||
\(640\) | 13.2366 | 0.523224 | ||||||||
\(641\) | 39.3652 | 1.55483 | 0.777416 | − | 0.628987i | \(-0.216530\pi\) | ||||
0.777416 | + | 0.628987i | \(0.216530\pi\) | |||||||
\(642\) | 5.43901 | 0.214661 | ||||||||
\(643\) | 40.6170 | 1.60178 | 0.800889 | − | 0.598812i | \(-0.204361\pi\) | ||||
0.800889 | + | 0.598812i | \(0.204361\pi\) | |||||||
\(644\) | −4.97991 | −0.196236 | ||||||||
\(645\) | −4.19521 | −0.165186 | ||||||||
\(646\) | 0.223467 | 0.00879217 | ||||||||
\(647\) | 4.38181 | 0.172267 | 0.0861333 | − | 0.996284i | \(-0.472549\pi\) | ||||
0.0861333 | + | 0.996284i | \(0.472549\pi\) | |||||||
\(648\) | 1.44661 | 0.0568283 | ||||||||
\(649\) | −35.9473 | −1.41106 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.32825 | 0.326410 | ||||||||
\(652\) | 41.4019 | 1.62142 | ||||||||
\(653\) | 18.0074 | 0.704683 | 0.352342 | − | 0.935871i | \(-0.385386\pi\) | ||||
0.352342 | + | 0.935871i | \(0.385386\pi\) | |||||||
\(654\) | 5.08918 | 0.199003 | ||||||||
\(655\) | 19.4879 | 0.761457 | ||||||||
\(656\) | −2.59232 | −0.101213 | ||||||||
\(657\) | 7.20060 | 0.280922 | ||||||||
\(658\) | 1.60819 | 0.0626937 | ||||||||
\(659\) | −9.85306 | −0.383821 | −0.191910 | − | 0.981412i | \(-0.561468\pi\) | ||||
−0.191910 | + | 0.981412i | \(0.561468\pi\) | |||||||
\(660\) | 14.3801 | 0.559744 | ||||||||
\(661\) | −27.3954 | −1.06556 | −0.532779 | − | 0.846254i | \(-0.678852\pi\) | ||||
−0.532779 | + | 0.846254i | \(0.678852\pi\) | |||||||
\(662\) | 0.509565 | 0.0198048 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −23.4655 | −0.910637 | ||||||||
\(665\) | −1.78580 | −0.0692505 | ||||||||
\(666\) | −2.97438 | −0.115255 | ||||||||
\(667\) | −8.98271 | −0.347812 | ||||||||
\(668\) | −34.0818 | −1.31867 | ||||||||
\(669\) | 14.6782 | 0.567490 | ||||||||
\(670\) | 0.817844 | 0.0315961 | ||||||||
\(671\) | −64.3536 | −2.48434 | ||||||||
\(672\) | −4.08395 | −0.157542 | ||||||||
\(673\) | −17.8948 | −0.689796 | −0.344898 | − | 0.938640i | \(-0.612086\pi\) | ||||
−0.344898 | + | 0.938640i | \(0.612086\pi\) | |||||||
\(674\) | −11.8645 | −0.457005 | ||||||||
\(675\) | 3.23933 | 0.124682 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −37.6226 | −1.44595 | −0.722977 | − | 0.690872i | \(-0.757227\pi\) | ||||
−0.722977 | + | 0.690872i | \(0.757227\pi\) | |||||||
\(678\) | 5.94891 | 0.228466 | ||||||||
\(679\) | 3.75470 | 0.144092 | ||||||||
\(680\) | −0.850332 | −0.0326087 | ||||||||
\(681\) | 0.615870 | 0.0236002 | ||||||||
\(682\) | −18.1927 | −0.696635 | ||||||||
\(683\) | 37.2441 | 1.42511 | 0.712553 | − | 0.701618i | \(-0.247539\pi\) | ||||
0.712553 | + | 0.701618i | \(0.247539\pi\) | |||||||
\(684\) | −2.50262 | −0.0956899 | ||||||||
\(685\) | −1.23832 | −0.0473138 | ||||||||
\(686\) | 0.374817 | 0.0143106 | ||||||||
\(687\) | 9.47389 | 0.361452 | ||||||||
\(688\) | 10.0440 | 0.382924 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −1.33193 | −0.0507056 | ||||||||
\(691\) | −13.3126 | −0.506437 | −0.253218 | − | 0.967409i | \(-0.581489\pi\) | ||||
−0.253218 | + | 0.967409i | \(0.581489\pi\) | |||||||
\(692\) | 23.6984 | 0.900878 | ||||||||
\(693\) | −5.82806 | −0.221390 | ||||||||
\(694\) | −6.94791 | −0.263739 | ||||||||
\(695\) | 26.6396 | 1.01050 | ||||||||
\(696\) | −4.85218 | −0.183921 | ||||||||
\(697\) | 0.361490 | 0.0136924 | ||||||||
\(698\) | 11.9691 | 0.453038 | ||||||||
\(699\) | 8.35195 | 0.315900 | ||||||||
\(700\) | −6.02358 | −0.227670 | ||||||||
\(701\) | 40.6477 | 1.53524 | 0.767622 | − | 0.640903i | \(-0.221440\pi\) | ||||
0.767622 | + | 0.640903i | \(0.221440\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.6800 | 0.402805 | ||||||||
\(704\) | −28.1081 | −1.05936 | ||||||||
\(705\) | −5.69320 | −0.214418 | ||||||||
\(706\) | 0.609570 | 0.0229415 | ||||||||
\(707\) | −2.83930 | −0.106783 | ||||||||
\(708\) | −11.4694 | −0.431048 | ||||||||
\(709\) | −22.3533 | −0.839497 | −0.419748 | − | 0.907641i | \(-0.637882\pi\) | ||||
−0.419748 | + | 0.907641i | \(0.637882\pi\) | |||||||
\(710\) | 6.46032 | 0.242452 | ||||||||
\(711\) | −2.54704 | −0.0955215 | ||||||||
\(712\) | −0.360970 | −0.0135279 | ||||||||
\(713\) | −22.3037 | −0.835279 | ||||||||
\(714\) | 0.166042 | 0.00621396 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.77382 | −0.215778 | ||||||||
\(717\) | 3.25440 | 0.121538 | ||||||||
\(718\) | −9.28537 | −0.346527 | ||||||||
\(719\) | −13.6829 | −0.510288 | −0.255144 | − | 0.966903i | \(-0.582123\pi\) | ||||
−0.255144 | + | 0.966903i | \(0.582123\pi\) | |||||||
\(720\) | 4.21531 | 0.157095 | ||||||||
\(721\) | 13.0189 | 0.484849 | ||||||||
\(722\) | 6.44262 | 0.239769 | ||||||||
\(723\) | −16.1085 | −0.599080 | ||||||||
\(724\) | 1.24715 | 0.0463499 | ||||||||
\(725\) | −10.8653 | −0.403526 | ||||||||
\(726\) | 8.60816 | 0.319479 | ||||||||
\(727\) | −9.65059 | −0.357920 | −0.178960 | − | 0.983856i | \(-0.557273\pi\) | ||||
−0.178960 | + | 0.983856i | \(0.557273\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −3.58119 | −0.132546 | ||||||||
\(731\) | −1.40060 | −0.0518029 | ||||||||
\(732\) | −20.5328 | −0.758914 | ||||||||
\(733\) | −42.0579 | −1.55344 | −0.776722 | − | 0.629844i | \(-0.783119\pi\) | ||||
−0.776722 | + | 0.629844i | \(0.783119\pi\) | |||||||
\(734\) | −1.97397 | −0.0728606 | ||||||||
\(735\) | −1.32690 | −0.0489435 | ||||||||
\(736\) | 10.9371 | 0.403147 | ||||||||
\(737\) | −9.58377 | −0.353023 | ||||||||
\(738\) | 0.305856 | 0.0112587 | ||||||||
\(739\) | −19.4048 | −0.713818 | −0.356909 | − | 0.934139i | \(-0.616169\pi\) | ||||
−0.356909 | + | 0.934139i | \(0.616169\pi\) | |||||||
\(740\) | −19.5801 | −0.719778 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.695154 | −0.0255199 | ||||||||
\(743\) | 35.6920 | 1.30941 | 0.654706 | − | 0.755884i | \(-0.272793\pi\) | ||||
0.654706 | + | 0.755884i | \(0.272793\pi\) | |||||||
\(744\) | −12.0477 | −0.441692 | ||||||||
\(745\) | 16.3180 | 0.597846 | ||||||||
\(746\) | 10.2576 | 0.375557 | ||||||||
\(747\) | −16.2210 | −0.593495 | ||||||||
\(748\) | 4.80088 | 0.175538 | ||||||||
\(749\) | −14.5111 | −0.530224 | ||||||||
\(750\) | −4.09779 | −0.149630 | ||||||||
\(751\) | 51.8856 | 1.89333 | 0.946666 | − | 0.322217i | \(-0.104428\pi\) | ||||
0.946666 | + | 0.322217i | \(0.104428\pi\) | |||||||
\(752\) | 13.6304 | 0.497050 | ||||||||
\(753\) | −20.4332 | −0.744627 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.7860 | 0.902056 | ||||||||
\(756\) | −1.85951 | −0.0676298 | ||||||||
\(757\) | −29.7035 | −1.07959 | −0.539796 | − | 0.841796i | \(-0.681499\pi\) | ||||
−0.539796 | + | 0.841796i | \(0.681499\pi\) | |||||||
\(758\) | −9.54754 | −0.346782 | ||||||||
\(759\) | 15.6080 | 0.566534 | ||||||||
\(760\) | 2.58336 | 0.0937085 | ||||||||
\(761\) | −11.5829 | −0.419879 | −0.209940 | − | 0.977714i | \(-0.567327\pi\) | ||||
−0.209940 | + | 0.977714i | \(0.567327\pi\) | |||||||
\(762\) | −2.34141 | −0.0848202 | ||||||||
\(763\) | −13.5778 | −0.491548 | ||||||||
\(764\) | −33.2346 | −1.20239 | ||||||||
\(765\) | −0.587809 | −0.0212523 | ||||||||
\(766\) | −8.60114 | −0.310772 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −5.90675 | −0.213142 | ||||||||
\(769\) | −7.72447 | −0.278551 | −0.139276 | − | 0.990254i | \(-0.544477\pi\) | ||||
−0.139276 | + | 0.990254i | \(0.544477\pi\) | |||||||
\(770\) | 2.89856 | 0.104457 | ||||||||
\(771\) | 15.8411 | 0.570504 | ||||||||
\(772\) | 10.4576 | 0.376378 | ||||||||
\(773\) | 5.56390 | 0.200120 | 0.100060 | − | 0.994981i | \(-0.468097\pi\) | ||||
0.100060 | + | 0.994981i | \(0.468097\pi\) | |||||||
\(774\) | −1.18504 | −0.0425955 | ||||||||
\(775\) | −26.9780 | −0.969077 | ||||||||
\(776\) | −5.43158 | −0.194983 | ||||||||
\(777\) | 7.93555 | 0.284686 | ||||||||
\(778\) | −5.63808 | −0.202135 | ||||||||
\(779\) | −1.09823 | −0.0393482 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −75.7042 | −2.70891 | ||||||||
\(782\) | −0.444672 | −0.0159014 | ||||||||
\(783\) | −3.35417 | −0.119868 | ||||||||
\(784\) | 3.17681 | 0.113457 | ||||||||
\(785\) | 32.3583 | 1.15492 | ||||||||
\(786\) | 5.50487 | 0.196352 | ||||||||
\(787\) | 1.31894 | 0.0470150 | 0.0235075 | − | 0.999724i | \(-0.492517\pi\) | ||||
0.0235075 | + | 0.999724i | \(0.492517\pi\) | |||||||
\(788\) | −30.8276 | −1.09819 | ||||||||
\(789\) | −17.0251 | −0.606111 | ||||||||
\(790\) | 1.26676 | 0.0450693 | ||||||||
\(791\) | −15.8715 | −0.564325 | ||||||||
\(792\) | 8.43094 | 0.299580 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 6.15586 | 0.218463 | ||||||||
\(795\) | 2.46094 | 0.0872805 | ||||||||
\(796\) | −45.4168 | −1.60976 | ||||||||
\(797\) | −15.5957 | −0.552429 | −0.276215 | − | 0.961096i | \(-0.589080\pi\) | ||||
−0.276215 | + | 0.961096i | \(0.589080\pi\) | |||||||
\(798\) | −0.504446 | −0.0178572 | ||||||||
\(799\) | −1.90071 | −0.0672422 | ||||||||
\(800\) | 13.2293 | 0.467725 | ||||||||
\(801\) | −0.249528 | −0.00881663 | ||||||||
\(802\) | 6.63631 | 0.234336 | ||||||||
\(803\) | 41.9656 | 1.48093 | ||||||||
\(804\) | −3.05782 | −0.107841 | ||||||||
\(805\) | 3.55354 | 0.125246 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.0150 | 0.563756 | ||||||||
\(808\) | 4.10737 | 0.144497 | ||||||||
\(809\) | −37.9340 | −1.33369 | −0.666844 | − | 0.745197i | \(-0.732355\pi\) | ||||
−0.666844 | + | 0.745197i | \(0.732355\pi\) | |||||||
\(810\) | −0.497345 | −0.0174749 | ||||||||
\(811\) | −23.0022 | −0.807718 | −0.403859 | − | 0.914821i | \(-0.632331\pi\) | ||||
−0.403859 | + | 0.914821i | \(0.632331\pi\) | |||||||
\(812\) | 6.23711 | 0.218880 | ||||||||
\(813\) | 10.3553 | 0.363176 | ||||||||
\(814\) | −17.3349 | −0.607587 | ||||||||
\(815\) | −29.5434 | −1.03486 | ||||||||
\(816\) | 1.40731 | 0.0492656 | ||||||||
\(817\) | 4.25511 | 0.148867 | ||||||||
\(818\) | 1.51904 | 0.0531118 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.01343 | 0.0703119 | ||||||||
\(821\) | 16.9276 | 0.590778 | 0.295389 | − | 0.955377i | \(-0.404551\pi\) | ||||
0.295389 | + | 0.955377i | \(0.404551\pi\) | |||||||
\(822\) | −0.349795 | −0.0122005 | ||||||||
\(823\) | 7.69045 | 0.268072 | 0.134036 | − | 0.990976i | \(-0.457206\pi\) | ||||
0.134036 | + | 0.990976i | \(0.457206\pi\) | |||||||
\(824\) | −18.8333 | −0.656088 | ||||||||
\(825\) | 18.8790 | 0.657283 | ||||||||
\(826\) | −2.31186 | −0.0804400 | ||||||||
\(827\) | −42.2818 | −1.47028 | −0.735140 | − | 0.677915i | \(-0.762884\pi\) | ||||
−0.735140 | + | 0.677915i | \(0.762884\pi\) | |||||||
\(828\) | 4.97991 | 0.173064 | ||||||||
\(829\) | 9.67366 | 0.335980 | 0.167990 | − | 0.985789i | \(-0.446272\pi\) | ||||
0.167990 | + | 0.985789i | \(0.446272\pi\) | |||||||
\(830\) | 8.06744 | 0.280025 | ||||||||
\(831\) | 8.83806 | 0.306589 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.442994 | −0.0153488 | ||||||||
\(834\) | 7.52503 | 0.260570 | ||||||||
\(835\) | 24.3199 | 0.841626 | ||||||||
\(836\) | −14.5854 | −0.504447 | ||||||||
\(837\) | −8.32825 | −0.287866 | ||||||||
\(838\) | 2.67591 | 0.0924377 | ||||||||
\(839\) | −12.2804 | −0.423967 | −0.211983 | − | 0.977273i | \(-0.567992\pi\) | ||||
−0.211983 | + | 0.977273i | \(0.567992\pi\) | |||||||
\(840\) | 1.91951 | 0.0662294 | ||||||||
\(841\) | −17.7496 | −0.612054 | ||||||||
\(842\) | −12.1058 | −0.417194 | ||||||||
\(843\) | −14.3408 | −0.493925 | ||||||||
\(844\) | 20.4326 | 0.703318 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.60819 | −0.0552907 | ||||||||
\(847\) | −22.9663 | −0.789131 | ||||||||
\(848\) | −5.89187 | −0.202328 | ||||||||
\(849\) | −13.9259 | −0.477935 | ||||||||
\(850\) | −0.537864 | −0.0184486 | ||||||||
\(851\) | −21.2520 | −0.728509 | ||||||||
\(852\) | −24.1543 | −0.827514 | ||||||||
\(853\) | 0.0616267 | 0.00211006 | 0.00105503 | − | 0.999999i | \(-0.499664\pi\) | ||||
0.00105503 | + | 0.999999i | \(0.499664\pi\) | |||||||
\(854\) | −4.13874 | −0.141625 | ||||||||
\(855\) | 1.78580 | 0.0610732 | ||||||||
\(856\) | 20.9919 | 0.717489 | ||||||||
\(857\) | 56.0433 | 1.91440 | 0.957202 | − | 0.289421i | \(-0.0934629\pi\) | ||||
0.957202 | + | 0.289421i | \(0.0934629\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.0721 | −0.548372 | −0.274186 | − | 0.961677i | \(-0.588408\pi\) | ||||
−0.274186 | + | 0.961677i | \(0.588408\pi\) | |||||||
\(860\) | −7.80104 | −0.266013 | ||||||||
\(861\) | −0.816015 | −0.0278097 | ||||||||
\(862\) | 5.01158 | 0.170695 | ||||||||
\(863\) | 5.29127 | 0.180117 | 0.0900585 | − | 0.995936i | \(-0.471295\pi\) | ||||
0.0900585 | + | 0.995936i | \(0.471295\pi\) | |||||||
\(864\) | 4.08395 | 0.138939 | ||||||||
\(865\) | −16.9106 | −0.574977 | ||||||||
\(866\) | 11.5233 | 0.391576 | ||||||||
\(867\) | 16.8038 | 0.570685 | ||||||||
\(868\) | 15.4865 | 0.525645 | ||||||||
\(869\) | −14.8443 | −0.503559 | ||||||||
\(870\) | 1.66818 | 0.0565566 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 19.6418 | 0.665154 | ||||||||
\(873\) | −3.75470 | −0.127077 | ||||||||
\(874\) | 1.35094 | 0.0456964 | ||||||||
\(875\) | 10.9328 | 0.369595 | ||||||||
\(876\) | 13.3896 | 0.452393 | ||||||||
\(877\) | 33.2558 | 1.12297 | 0.561484 | − | 0.827487i | \(-0.310230\pi\) | ||||
0.561484 | + | 0.827487i | \(0.310230\pi\) | |||||||
\(878\) | 8.43241 | 0.284580 | ||||||||
\(879\) | 24.0035 | 0.809617 | ||||||||
\(880\) | 24.5671 | 0.828157 | ||||||||
\(881\) | 35.0421 | 1.18060 | 0.590299 | − | 0.807185i | \(-0.299010\pi\) | ||||
0.590299 | + | 0.807185i | \(0.299010\pi\) | |||||||
\(882\) | −0.374817 | −0.0126207 | ||||||||
\(883\) | 31.8305 | 1.07118 | 0.535590 | − | 0.844478i | \(-0.320089\pi\) | ||||
0.535590 | + | 0.844478i | \(0.320089\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.18430 | 0.275112 | ||||||||
\(886\) | 9.98346 | 0.335401 | ||||||||
\(887\) | 49.6809 | 1.66812 | 0.834060 | − | 0.551673i | \(-0.186010\pi\) | ||||
0.834060 | + | 0.551673i | \(0.186010\pi\) | |||||||
\(888\) | −11.4797 | −0.385232 | ||||||||
\(889\) | 6.24679 | 0.209511 | ||||||||
\(890\) | 0.124101 | 0.00415989 | ||||||||
\(891\) | 5.82806 | 0.195247 | ||||||||
\(892\) | 27.2942 | 0.913878 | ||||||||
\(893\) | 5.77448 | 0.193236 | ||||||||
\(894\) | 4.60944 | 0.154163 | ||||||||
\(895\) | 4.12006 | 0.137718 | ||||||||
\(896\) | −9.97559 | −0.333261 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.3535 | −0.378872 | ||||||||
\(899\) | 27.9343 | 0.931662 | ||||||||
\(900\) | 6.02358 | 0.200786 | ||||||||
\(901\) | 0.821599 | 0.0273714 | ||||||||
\(902\) | 1.78255 | 0.0593524 | ||||||||
\(903\) | 3.16166 | 0.105213 | ||||||||
\(904\) | 22.9599 | 0.763634 | ||||||||
\(905\) | −0.889935 | −0.0295824 | ||||||||
\(906\) | 7.00145 | 0.232607 | ||||||||
\(907\) | −8.42301 | −0.279681 | −0.139841 | − | 0.990174i | \(-0.544659\pi\) | ||||
−0.139841 | + | 0.990174i | \(0.544659\pi\) | |||||||
\(908\) | 1.14522 | 0.0380054 | ||||||||
\(909\) | 2.83930 | 0.0941737 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.84825 | 0.0612351 | 0.0306176 | − | 0.999531i | \(-0.490253\pi\) | ||||
0.0306176 | + | 0.999531i | \(0.490253\pi\) | |||||||
\(912\) | −4.27550 | −0.141576 | ||||||||
\(913\) | −94.5369 | −3.12872 | ||||||||
\(914\) | 2.96873 | 0.0981968 | ||||||||
\(915\) | 14.6517 | 0.484370 | ||||||||
\(916\) | 17.6168 | 0.582076 | ||||||||
\(917\) | −14.6868 | −0.485001 | ||||||||
\(918\) | −0.166042 | −0.00548019 | ||||||||
\(919\) | 55.6552 | 1.83590 | 0.917948 | − | 0.396700i | \(-0.129845\pi\) | ||||
0.917948 | + | 0.396700i | \(0.129845\pi\) | |||||||
\(920\) | −5.14059 | −0.169480 | ||||||||
\(921\) | −20.6185 | −0.679404 | ||||||||
\(922\) | −4.11866 | −0.135641 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −10.8373 | −0.356523 | ||||||||
\(925\) | −25.7059 | −0.845204 | ||||||||
\(926\) | −3.26760 | −0.107380 | ||||||||
\(927\) | −13.0189 | −0.427596 | ||||||||
\(928\) | −13.6982 | −0.449667 | ||||||||
\(929\) | 39.2038 | 1.28624 | 0.643118 | − | 0.765767i | \(-0.277641\pi\) | ||||
0.643118 | + | 0.765767i | \(0.277641\pi\) | |||||||
\(930\) | 4.14202 | 0.135822 | ||||||||
\(931\) | 1.34585 | 0.0441083 | ||||||||
\(932\) | 15.5306 | 0.508720 | ||||||||
\(933\) | −33.6435 | −1.10144 | ||||||||
\(934\) | −12.6653 | −0.414423 | ||||||||
\(935\) | −3.42579 | −0.112035 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.6724 | −0.413989 | −0.206995 | − | 0.978342i | \(-0.566368\pi\) | ||||
−0.206995 | + | 0.978342i | \(0.566368\pi\) | |||||||
\(938\) | −0.616356 | −0.0201248 | ||||||||
\(939\) | −9.87809 | −0.322359 | ||||||||
\(940\) | −10.5866 | −0.345296 | ||||||||
\(941\) | 7.81644 | 0.254809 | 0.127404 | − | 0.991851i | \(-0.459335\pi\) | ||||
0.127404 | + | 0.991851i | \(0.459335\pi\) | |||||||
\(942\) | 9.14043 | 0.297811 | ||||||||
\(943\) | 2.18535 | 0.0711648 | ||||||||
\(944\) | −19.5945 | −0.637746 | ||||||||
\(945\) | 1.32690 | 0.0431641 | ||||||||
\(946\) | −6.90651 | −0.224550 | ||||||||
\(947\) | 48.1824 | 1.56572 | 0.782859 | − | 0.622199i | \(-0.213760\pi\) | ||||
0.782859 | + | 0.622199i | \(0.213760\pi\) | |||||||
\(948\) | −4.73626 | −0.153826 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 1.63407 | 0.0530162 | ||||||||
\(951\) | 13.6053 | 0.441183 | ||||||||
\(952\) | 0.640840 | 0.0207697 | ||||||||
\(953\) | 51.8052 | 1.67813 | 0.839067 | − | 0.544028i | \(-0.183101\pi\) | ||||
0.839067 | + | 0.544028i | \(0.183101\pi\) | |||||||
\(954\) | 0.695154 | 0.0225065 | ||||||||
\(955\) | 23.7154 | 0.767412 | ||||||||
\(956\) | 6.05160 | 0.195723 | ||||||||
\(957\) | −19.5483 | −0.631906 | ||||||||
\(958\) | −14.6343 | −0.472814 | ||||||||
\(959\) | 0.933243 | 0.0301360 | ||||||||
\(960\) | 6.39950 | 0.206543 | ||||||||
\(961\) | 38.3598 | 1.23741 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.5111 | 0.467614 | ||||||||
\(964\) | −29.9539 | −0.964750 | ||||||||
\(965\) | −7.46231 | −0.240220 | ||||||||
\(966\) | 1.00379 | 0.0322964 | ||||||||
\(967\) | −5.87478 | −0.188920 | −0.0944602 | − | 0.995529i | \(-0.530113\pi\) | ||||
−0.0944602 | + | 0.995529i | \(0.530113\pi\) | |||||||
\(968\) | 33.2233 | 1.06784 | ||||||||
\(969\) | 0.596202 | 0.0191528 | ||||||||
\(970\) | 1.86738 | 0.0599580 | ||||||||
\(971\) | 53.1421 | 1.70541 | 0.852705 | − | 0.522392i | \(-0.174960\pi\) | ||||
0.852705 | + | 0.522392i | \(0.174960\pi\) | |||||||
\(972\) | 1.85951 | 0.0596439 | ||||||||
\(973\) | −20.0765 | −0.643624 | ||||||||
\(974\) | −4.52795 | −0.145085 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −35.0784 | −1.12283 | ||||||||
\(977\) | 16.9292 | 0.541612 | 0.270806 | − | 0.962634i | \(-0.412710\pi\) | ||||
0.270806 | + | 0.962634i | \(0.412710\pi\) | |||||||
\(978\) | −8.34527 | −0.266852 | ||||||||
\(979\) | −1.45426 | −0.0464784 | ||||||||
\(980\) | −2.46739 | −0.0788179 | ||||||||
\(981\) | 13.5778 | 0.433505 | ||||||||
\(982\) | 15.8952 | 0.507237 | ||||||||
\(983\) | 34.7612 | 1.10871 | 0.554355 | − | 0.832281i | \(-0.312965\pi\) | ||||
0.554355 | + | 0.832281i | \(0.312965\pi\) | |||||||
\(984\) | 1.18046 | 0.0376316 | ||||||||
\(985\) | 21.9978 | 0.700908 | ||||||||
\(986\) | 0.556932 | 0.0177363 | ||||||||
\(987\) | 4.29060 | 0.136571 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.46716 | −0.269240 | ||||||||
\(990\) | −2.89856 | −0.0921222 | ||||||||
\(991\) | 33.6843 | 1.07002 | 0.535009 | − | 0.844846i | \(-0.320308\pi\) | ||||
0.535009 | + | 0.844846i | \(0.320308\pi\) | |||||||
\(992\) | −34.0121 | −1.07989 | ||||||||
\(993\) | 1.35950 | 0.0431426 | ||||||||
\(994\) | −4.86873 | −0.154427 | ||||||||
\(995\) | 32.4083 | 1.02741 | ||||||||
\(996\) | −30.1631 | −0.955756 | ||||||||
\(997\) | 9.21153 | 0.291732 | 0.145866 | − | 0.989304i | \(-0.453403\pi\) | ||||
0.145866 | + | 0.989304i | \(0.453403\pi\) | |||||||
\(998\) | −8.90322 | −0.281827 | ||||||||
\(999\) | −7.93555 | −0.251070 |
(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 | 3549.2.a.bf.1.4 | yes | 9 | |
13.12 | even | 2 | 3549.2.a.be.1.6 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3549.2.a.be.1.6 | ✓ | 9 | 13.12 | even | 2 | ||
3549.2.a.bf.1.4 | yes | 9 | 1.1 | even | 1 | trivial |