Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5290,2,Mod(1,5290)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5290, 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("5290.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5290 = 2 \cdot 5 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5290.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: | \(42.2408626693\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.4752.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 3x^{2} + 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.219687\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5290.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.60020 | 0.923873 | 0.461937 | − | 0.886913i | \(-0.347155\pi\) | ||||
0.461937 | + | 0.886913i | \(0.347155\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.60020 | 0.653277 | ||||||||
\(7\) | 2.60020 | 0.982782 | 0.491391 | − | 0.870939i | \(-0.336489\pi\) | ||||
0.491391 | + | 0.870939i | \(0.336489\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.439374 | −0.146458 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −0.439374 | −0.132476 | −0.0662381 | − | 0.997804i | \(-0.521100\pi\) | ||||
−0.0662381 | + | 0.997804i | \(0.521100\pi\) | |||||||
\(12\) | 1.60020 | 0.461937 | ||||||||
\(13\) | −1.20039 | −0.332929 | −0.166464 | − | 0.986047i | \(-0.553235\pi\) | ||||
−0.166464 | + | 0.986047i | \(0.553235\pi\) | |||||||
\(14\) | 2.60020 | 0.694932 | ||||||||
\(15\) | 1.60020 | 0.413169 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.33225 | −0.565653 | −0.282826 | − | 0.959171i | \(-0.591272\pi\) | ||||
−0.282826 | + | 0.959171i | \(0.591272\pi\) | |||||||
\(18\) | −0.439374 | −0.103561 | ||||||||
\(19\) | 2.97103 | 0.681602 | 0.340801 | − | 0.940136i | \(-0.389302\pi\) | ||||
0.340801 | + | 0.940136i | \(0.389302\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 4.16082 | 0.907966 | ||||||||
\(22\) | −0.439374 | −0.0936748 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | 1.60020 | 0.326639 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.20039 | −0.235416 | ||||||||
\(27\) | −5.50367 | −1.05918 | ||||||||
\(28\) | 2.60020 | 0.491391 | ||||||||
\(29\) | 3.47894 | 0.646024 | 0.323012 | − | 0.946395i | \(-0.395305\pi\) | ||||
0.323012 | + | 0.946395i | \(0.395305\pi\) | |||||||
\(30\) | 1.60020 | 0.292154 | ||||||||
\(31\) | −0.600196 | −0.107798 | −0.0538992 | − | 0.998546i | \(-0.517165\pi\) | ||||
−0.0538992 | + | 0.998546i | \(0.517165\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.703084 | −0.122391 | ||||||||
\(34\) | −2.33225 | −0.399977 | ||||||||
\(35\) | 2.60020 | 0.439513 | ||||||||
\(36\) | −0.439374 | −0.0732290 | ||||||||
\(37\) | 7.20039 | 1.18374 | 0.591869 | − | 0.806035i | \(-0.298390\pi\) | ||||
0.591869 | + | 0.806035i | \(0.298390\pi\) | |||||||
\(38\) | 2.97103 | 0.481965 | ||||||||
\(39\) | −1.92086 | −0.307584 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 8.56797 | 1.33809 | 0.669046 | − | 0.743221i | \(-0.266703\pi\) | ||||
0.669046 | + | 0.743221i | \(0.266703\pi\) | |||||||
\(42\) | 4.16082 | 0.642029 | ||||||||
\(43\) | 10.1971 | 1.55505 | 0.777524 | − | 0.628853i | \(-0.216475\pi\) | ||||
0.777524 | + | 0.628853i | \(0.216475\pi\) | |||||||
\(44\) | −0.439374 | −0.0662381 | ||||||||
\(45\) | −0.439374 | −0.0654980 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.960431 | −0.140093 | −0.0700466 | − | 0.997544i | \(-0.522315\pi\) | ||||
−0.0700466 | + | 0.997544i | \(0.522315\pi\) | |||||||
\(48\) | 1.60020 | 0.230968 | ||||||||
\(49\) | −0.238982 | −0.0341403 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −3.73205 | −0.522592 | ||||||||
\(52\) | −1.20039 | −0.166464 | ||||||||
\(53\) | 8.60020 | 1.18133 | 0.590664 | − | 0.806918i | \(-0.298866\pi\) | ||||
0.590664 | + | 0.806918i | \(0.298866\pi\) | |||||||
\(54\) | −5.50367 | −0.748955 | ||||||||
\(55\) | −0.439374 | −0.0592451 | ||||||||
\(56\) | 2.60020 | 0.347466 | ||||||||
\(57\) | 4.75423 | 0.629714 | ||||||||
\(58\) | 3.47894 | 0.456808 | ||||||||
\(59\) | 0.824336 | 0.107319 | 0.0536597 | − | 0.998559i | \(-0.482911\pi\) | ||||
0.0536597 | + | 0.998559i | \(0.482911\pi\) | |||||||
\(60\) | 1.60020 | 0.206584 | ||||||||
\(61\) | 4.26371 | 0.545912 | 0.272956 | − | 0.962026i | \(-0.411999\pi\) | ||||
0.272956 | + | 0.962026i | \(0.411999\pi\) | |||||||
\(62\) | −0.600196 | −0.0762249 | ||||||||
\(63\) | −1.14246 | −0.143936 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.20039 | −0.148890 | ||||||||
\(66\) | −0.703084 | −0.0865437 | ||||||||
\(67\) | 11.2901 | 1.37931 | 0.689655 | − | 0.724138i | \(-0.257762\pi\) | ||||
0.689655 | + | 0.724138i | \(0.257762\pi\) | |||||||
\(68\) | −2.33225 | −0.282826 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.60020 | 0.310783 | ||||||||
\(71\) | 7.52840 | 0.893457 | 0.446728 | − | 0.894670i | \(-0.352589\pi\) | ||||
0.446728 | + | 0.894670i | \(0.352589\pi\) | |||||||
\(72\) | −0.439374 | −0.0517807 | ||||||||
\(73\) | −16.0716 | −1.88104 | −0.940522 | − | 0.339734i | \(-0.889663\pi\) | ||||
−0.940522 | + | 0.339734i | \(0.889663\pi\) | |||||||
\(74\) | 7.20039 | 0.837028 | ||||||||
\(75\) | 1.60020 | 0.184775 | ||||||||
\(76\) | 2.97103 | 0.340801 | ||||||||
\(77\) | −1.14246 | −0.130195 | ||||||||
\(78\) | −1.92086 | −0.217495 | ||||||||
\(79\) | 3.03957 | 0.341978 | 0.170989 | − | 0.985273i | \(-0.445304\pi\) | ||||
0.170989 | + | 0.985273i | \(0.445304\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −7.48883 | −0.832092 | ||||||||
\(82\) | 8.56797 | 0.946174 | ||||||||
\(83\) | 3.84342 | 0.421870 | 0.210935 | − | 0.977500i | \(-0.432349\pi\) | ||||
0.210935 | + | 0.977500i | \(0.432349\pi\) | |||||||
\(84\) | 4.16082 | 0.453983 | ||||||||
\(85\) | −2.33225 | −0.252968 | ||||||||
\(86\) | 10.1971 | 1.09958 | ||||||||
\(87\) | 5.56699 | 0.596844 | ||||||||
\(88\) | −0.439374 | −0.0468374 | ||||||||
\(89\) | 9.98261 | 1.05815 | 0.529077 | − | 0.848574i | \(-0.322538\pi\) | ||||
0.529077 | + | 0.848574i | \(0.322538\pi\) | |||||||
\(90\) | −0.439374 | −0.0463141 | ||||||||
\(91\) | −3.12125 | −0.327196 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.960431 | −0.0995920 | ||||||||
\(94\) | −0.960431 | −0.0990608 | ||||||||
\(95\) | 2.97103 | 0.304822 | ||||||||
\(96\) | 1.60020 | 0.163319 | ||||||||
\(97\) | 6.92820 | 0.703452 | 0.351726 | − | 0.936103i | \(-0.385595\pi\) | ||||
0.351726 | + | 0.936103i | \(0.385595\pi\) | |||||||
\(98\) | −0.238982 | −0.0241409 | ||||||||
\(99\) | 0.193049 | 0.0194022 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −9.32899 | −0.928269 | −0.464134 | − | 0.885765i | \(-0.653635\pi\) | ||||
−0.464134 | + | 0.885765i | \(0.653635\pi\) | |||||||
\(102\) | −3.73205 | −0.369528 | ||||||||
\(103\) | −19.0073 | −1.87285 | −0.936425 | − | 0.350869i | \(-0.885886\pi\) | ||||
−0.936425 | + | 0.350869i | \(0.885886\pi\) | |||||||
\(104\) | −1.20039 | −0.117708 | ||||||||
\(105\) | 4.16082 | 0.406055 | ||||||||
\(106\) | 8.60020 | 0.835325 | ||||||||
\(107\) | −13.9935 | −1.35280 | −0.676400 | − | 0.736534i | \(-0.736461\pi\) | ||||
−0.676400 | + | 0.736534i | \(0.736461\pi\) | |||||||
\(108\) | −5.50367 | −0.529591 | ||||||||
\(109\) | 3.51753 | 0.336919 | 0.168459 | − | 0.985709i | \(-0.446121\pi\) | ||||
0.168459 | + | 0.985709i | \(0.446121\pi\) | |||||||
\(110\) | −0.439374 | −0.0418926 | ||||||||
\(111\) | 11.5220 | 1.09362 | ||||||||
\(112\) | 2.60020 | 0.245695 | ||||||||
\(113\) | 6.02799 | 0.567065 | 0.283533 | − | 0.958963i | \(-0.408494\pi\) | ||||
0.283533 | + | 0.958963i | \(0.408494\pi\) | |||||||
\(114\) | 4.75423 | 0.445275 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.47894 | 0.323012 | ||||||||
\(117\) | 0.527420 | 0.0487600 | ||||||||
\(118\) | 0.824336 | 0.0758863 | ||||||||
\(119\) | −6.06430 | −0.555913 | ||||||||
\(120\) | 1.60020 | 0.146077 | ||||||||
\(121\) | −10.8070 | −0.982450 | ||||||||
\(122\) | 4.26371 | 0.386018 | ||||||||
\(123\) | 13.7104 | 1.23623 | ||||||||
\(124\) | −0.600196 | −0.0538992 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.14246 | −0.101778 | ||||||||
\(127\) | −17.0890 | −1.51641 | −0.758203 | − | 0.652019i | \(-0.773922\pi\) | ||||
−0.758203 | + | 0.652019i | \(0.773922\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 16.3174 | 1.43667 | ||||||||
\(130\) | −1.20039 | −0.105281 | ||||||||
\(131\) | 9.25480 | 0.808596 | 0.404298 | − | 0.914627i | \(-0.367516\pi\) | ||||
0.404298 | + | 0.914627i | \(0.367516\pi\) | |||||||
\(132\) | −0.703084 | −0.0611956 | ||||||||
\(133\) | 7.72527 | 0.669866 | ||||||||
\(134\) | 11.2901 | 0.975319 | ||||||||
\(135\) | −5.50367 | −0.473681 | ||||||||
\(136\) | −2.33225 | −0.199988 | ||||||||
\(137\) | −20.0126 | −1.70979 | −0.854894 | − | 0.518802i | \(-0.826378\pi\) | ||||
−0.854894 | + | 0.518802i | \(0.826378\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.7050 | −1.33208 | −0.666042 | − | 0.745914i | \(-0.732013\pi\) | ||||
−0.666042 | + | 0.745914i | \(0.732013\pi\) | |||||||
\(140\) | 2.60020 | 0.219757 | ||||||||
\(141\) | −1.53688 | −0.129428 | ||||||||
\(142\) | 7.52840 | 0.631769 | ||||||||
\(143\) | 0.527420 | 0.0441051 | ||||||||
\(144\) | −0.439374 | −0.0366145 | ||||||||
\(145\) | 3.47894 | 0.288911 | ||||||||
\(146\) | −16.0716 | −1.33010 | ||||||||
\(147\) | −0.382419 | −0.0315413 | ||||||||
\(148\) | 7.20039 | 0.591869 | ||||||||
\(149\) | −3.65461 | −0.299397 | −0.149699 | − | 0.988732i | \(-0.547830\pi\) | ||||
−0.149699 | + | 0.988732i | \(0.547830\pi\) | |||||||
\(150\) | 1.60020 | 0.130655 | ||||||||
\(151\) | 8.79309 | 0.715571 | 0.357786 | − | 0.933804i | \(-0.383532\pi\) | ||||
0.357786 | + | 0.933804i | \(0.383532\pi\) | |||||||
\(152\) | 2.97103 | 0.240983 | ||||||||
\(153\) | 1.02473 | 0.0828443 | ||||||||
\(154\) | −1.14246 | −0.0920619 | ||||||||
\(155\) | −0.600196 | −0.0482089 | ||||||||
\(156\) | −1.92086 | −0.153792 | ||||||||
\(157\) | −5.59270 | −0.446346 | −0.223173 | − | 0.974779i | \(-0.571641\pi\) | ||||
−0.223173 | + | 0.974779i | \(0.571641\pi\) | |||||||
\(158\) | 3.03957 | 0.241815 | ||||||||
\(159\) | 13.7620 | 1.09140 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −7.48883 | −0.588378 | ||||||||
\(163\) | 11.2498 | 0.881156 | 0.440578 | − | 0.897714i | \(-0.354774\pi\) | ||||
0.440578 | + | 0.897714i | \(0.354774\pi\) | |||||||
\(164\) | 8.56797 | 0.669046 | ||||||||
\(165\) | −0.703084 | −0.0547350 | ||||||||
\(166\) | 3.84342 | 0.298307 | ||||||||
\(167\) | −20.0257 | −1.54964 | −0.774818 | − | 0.632185i | \(-0.782158\pi\) | ||||
−0.774818 | + | 0.632185i | \(0.782158\pi\) | |||||||
\(168\) | 4.16082 | 0.321014 | ||||||||
\(169\) | −11.5591 | −0.889159 | ||||||||
\(170\) | −2.33225 | −0.178875 | ||||||||
\(171\) | −1.30539 | −0.0998260 | ||||||||
\(172\) | 10.1971 | 0.777524 | ||||||||
\(173\) | −1.08903 | −0.0827971 | −0.0413985 | − | 0.999143i | \(-0.513181\pi\) | ||||
−0.0413985 | + | 0.999143i | \(0.513181\pi\) | |||||||
\(174\) | 5.56699 | 0.422032 | ||||||||
\(175\) | 2.60020 | 0.196556 | ||||||||
\(176\) | −0.439374 | −0.0331190 | ||||||||
\(177\) | 1.31910 | 0.0991496 | ||||||||
\(178\) | 9.98261 | 0.748229 | ||||||||
\(179\) | 17.2746 | 1.29116 | 0.645581 | − | 0.763692i | \(-0.276615\pi\) | ||||
0.645581 | + | 0.763692i | \(0.276615\pi\) | |||||||
\(180\) | −0.439374 | −0.0327490 | ||||||||
\(181\) | −26.4155 | −1.96345 | −0.981723 | − | 0.190315i | \(-0.939049\pi\) | ||||
−0.981723 | + | 0.190315i | \(0.939049\pi\) | |||||||
\(182\) | −3.12125 | −0.231363 | ||||||||
\(183\) | 6.82277 | 0.504354 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.20039 | 0.529383 | ||||||||
\(186\) | −0.960431 | −0.0704222 | ||||||||
\(187\) | 1.02473 | 0.0749355 | ||||||||
\(188\) | −0.960431 | −0.0700466 | ||||||||
\(189\) | −14.3106 | −1.04094 | ||||||||
\(190\) | 2.97103 | 0.215541 | ||||||||
\(191\) | 16.6323 | 1.20347 | 0.601734 | − | 0.798696i | \(-0.294477\pi\) | ||||
0.601734 | + | 0.798696i | \(0.294477\pi\) | |||||||
\(192\) | 1.60020 | 0.115484 | ||||||||
\(193\) | −9.23996 | −0.665107 | −0.332553 | − | 0.943084i | \(-0.607910\pi\) | ||||
−0.332553 | + | 0.943084i | \(0.607910\pi\) | |||||||
\(194\) | 6.92820 | 0.497416 | ||||||||
\(195\) | −1.92086 | −0.137556 | ||||||||
\(196\) | −0.238982 | −0.0170702 | ||||||||
\(197\) | 7.52204 | 0.535923 | 0.267961 | − | 0.963430i | \(-0.413650\pi\) | ||||
0.267961 | + | 0.963430i | \(0.413650\pi\) | |||||||
\(198\) | 0.193049 | 0.0137194 | ||||||||
\(199\) | 2.23996 | 0.158787 | 0.0793933 | − | 0.996843i | \(-0.474702\pi\) | ||||
0.0793933 | + | 0.996843i | \(0.474702\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 18.0664 | 1.27431 | ||||||||
\(202\) | −9.32899 | −0.656385 | ||||||||
\(203\) | 9.04593 | 0.634900 | ||||||||
\(204\) | −3.73205 | −0.261296 | ||||||||
\(205\) | 8.56797 | 0.598413 | ||||||||
\(206\) | −19.0073 | −1.32430 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.20039 | −0.0832322 | ||||||||
\(209\) | −1.30539 | −0.0902960 | ||||||||
\(210\) | 4.16082 | 0.287124 | ||||||||
\(211\) | 10.8946 | 0.750013 | 0.375006 | − | 0.927022i | \(-0.377640\pi\) | ||||
0.375006 | + | 0.927022i | \(0.377640\pi\) | |||||||
\(212\) | 8.60020 | 0.590664 | ||||||||
\(213\) | 12.0469 | 0.825441 | ||||||||
\(214\) | −13.9935 | −0.956575 | ||||||||
\(215\) | 10.1971 | 0.695439 | ||||||||
\(216\) | −5.50367 | −0.374477 | ||||||||
\(217\) | −1.56063 | −0.105942 | ||||||||
\(218\) | 3.51753 | 0.238237 | ||||||||
\(219\) | −25.7178 | −1.73785 | ||||||||
\(220\) | −0.439374 | −0.0296226 | ||||||||
\(221\) | 2.79961 | 0.188322 | ||||||||
\(222\) | 11.5220 | 0.773308 | ||||||||
\(223\) | −11.2414 | −0.752778 | −0.376389 | − | 0.926462i | \(-0.622834\pi\) | ||||
−0.376389 | + | 0.926462i | \(0.622834\pi\) | |||||||
\(224\) | 2.60020 | 0.173733 | ||||||||
\(225\) | −0.439374 | −0.0292916 | ||||||||
\(226\) | 6.02799 | 0.400976 | ||||||||
\(227\) | −5.21099 | −0.345866 | −0.172933 | − | 0.984934i | \(-0.555324\pi\) | ||||
−0.172933 | + | 0.984934i | \(0.555324\pi\) | |||||||
\(228\) | 4.75423 | 0.314857 | ||||||||
\(229\) | −10.4542 | −0.690834 | −0.345417 | − | 0.938449i | \(-0.612263\pi\) | ||||
−0.345417 | + | 0.938449i | \(0.612263\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.82816 | −0.120284 | ||||||||
\(232\) | 3.47894 | 0.228404 | ||||||||
\(233\) | 9.44769 | 0.618939 | 0.309470 | − | 0.950909i | \(-0.399849\pi\) | ||||
0.309470 | + | 0.950909i | \(0.399849\pi\) | |||||||
\(234\) | 0.527420 | 0.0344786 | ||||||||
\(235\) | −0.960431 | −0.0626516 | ||||||||
\(236\) | 0.824336 | 0.0536597 | ||||||||
\(237\) | 4.86391 | 0.315945 | ||||||||
\(238\) | −6.06430 | −0.393090 | ||||||||
\(239\) | −15.9355 | −1.03078 | −0.515392 | − | 0.856954i | \(-0.672354\pi\) | ||||
−0.515392 | + | 0.856954i | \(0.672354\pi\) | |||||||
\(240\) | 1.60020 | 0.103292 | ||||||||
\(241\) | −25.4618 | −1.64014 | −0.820070 | − | 0.572263i | \(-0.806066\pi\) | ||||
−0.820070 | + | 0.572263i | \(0.806066\pi\) | |||||||
\(242\) | −10.8070 | −0.694697 | ||||||||
\(243\) | 4.52742 | 0.290434 | ||||||||
\(244\) | 4.26371 | 0.272956 | ||||||||
\(245\) | −0.238982 | −0.0152680 | ||||||||
\(246\) | 13.7104 | 0.874145 | ||||||||
\(247\) | −3.56640 | −0.226925 | ||||||||
\(248\) | −0.600196 | −0.0381125 | ||||||||
\(249\) | 6.15022 | 0.389754 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −12.0189 | −0.758628 | −0.379314 | − | 0.925268i | \(-0.623840\pi\) | ||||
−0.379314 | + | 0.925268i | \(0.623840\pi\) | |||||||
\(252\) | −1.14246 | −0.0719681 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −17.0890 | −1.07226 | ||||||||
\(255\) | −3.73205 | −0.233710 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −10.2350 | −0.638442 | −0.319221 | − | 0.947680i | \(-0.603421\pi\) | ||||
−0.319221 | + | 0.947680i | \(0.603421\pi\) | |||||||
\(258\) | 16.3174 | 1.01588 | ||||||||
\(259\) | 18.7224 | 1.16335 | ||||||||
\(260\) | −1.20039 | −0.0744451 | ||||||||
\(261\) | −1.52856 | −0.0946153 | ||||||||
\(262\) | 9.25480 | 0.571764 | ||||||||
\(263\) | −5.51356 | −0.339981 | −0.169990 | − | 0.985446i | \(-0.554374\pi\) | ||||
−0.169990 | + | 0.985446i | \(0.554374\pi\) | |||||||
\(264\) | −0.703084 | −0.0432718 | ||||||||
\(265\) | 8.60020 | 0.528306 | ||||||||
\(266\) | 7.72527 | 0.473667 | ||||||||
\(267\) | 15.9741 | 0.977601 | ||||||||
\(268\) | 11.2901 | 0.689655 | ||||||||
\(269\) | −29.2236 | −1.78179 | −0.890896 | − | 0.454208i | \(-0.849922\pi\) | ||||
−0.890896 | + | 0.454208i | \(0.849922\pi\) | |||||||
\(270\) | −5.50367 | −0.334943 | ||||||||
\(271\) | −13.6204 | −0.827382 | −0.413691 | − | 0.910417i | \(-0.635761\pi\) | ||||
−0.413691 | + | 0.910417i | \(0.635761\pi\) | |||||||
\(272\) | −2.33225 | −0.141413 | ||||||||
\(273\) | −4.99461 | −0.302288 | ||||||||
\(274\) | −20.0126 | −1.20900 | ||||||||
\(275\) | −0.439374 | −0.0264952 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.99550 | −0.480403 | −0.240201 | − | 0.970723i | \(-0.577214\pi\) | ||||
−0.240201 | + | 0.970723i | \(0.577214\pi\) | |||||||
\(278\) | −15.7050 | −0.941926 | ||||||||
\(279\) | 0.263710 | 0.0157879 | ||||||||
\(280\) | 2.60020 | 0.155391 | ||||||||
\(281\) | −31.5993 | −1.88506 | −0.942529 | − | 0.334125i | \(-0.891559\pi\) | ||||
−0.942529 | + | 0.334125i | \(0.891559\pi\) | |||||||
\(282\) | −1.53688 | −0.0915197 | ||||||||
\(283\) | −5.73841 | −0.341113 | −0.170557 | − | 0.985348i | \(-0.554557\pi\) | ||||
−0.170557 | + | 0.985348i | \(0.554557\pi\) | |||||||
\(284\) | 7.52840 | 0.446728 | ||||||||
\(285\) | 4.75423 | 0.281617 | ||||||||
\(286\) | 0.527420 | 0.0311870 | ||||||||
\(287\) | 22.2784 | 1.31505 | ||||||||
\(288\) | −0.439374 | −0.0258903 | ||||||||
\(289\) | −11.5606 | −0.680037 | ||||||||
\(290\) | 3.47894 | 0.204291 | ||||||||
\(291\) | 11.0865 | 0.649901 | ||||||||
\(292\) | −16.0716 | −0.940522 | ||||||||
\(293\) | 15.1425 | 0.884632 | 0.442316 | − | 0.896859i | \(-0.354157\pi\) | ||||
0.442316 | + | 0.896859i | \(0.354157\pi\) | |||||||
\(294\) | −0.382419 | −0.0223031 | ||||||||
\(295\) | 0.824336 | 0.0479947 | ||||||||
\(296\) | 7.20039 | 0.418514 | ||||||||
\(297\) | 2.41817 | 0.140316 | ||||||||
\(298\) | −3.65461 | −0.211706 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.60020 | 0.0923873 | ||||||||
\(301\) | 26.5145 | 1.52827 | ||||||||
\(302\) | 8.79309 | 0.505985 | ||||||||
\(303\) | −14.9282 | −0.857603 | ||||||||
\(304\) | 2.97103 | 0.170400 | ||||||||
\(305\) | 4.26371 | 0.244139 | ||||||||
\(306\) | 1.02473 | 0.0585798 | ||||||||
\(307\) | 27.1369 | 1.54879 | 0.774393 | − | 0.632705i | \(-0.218055\pi\) | ||||
0.774393 | + | 0.632705i | \(0.218055\pi\) | |||||||
\(308\) | −1.14246 | −0.0650976 | ||||||||
\(309\) | −30.4155 | −1.73028 | ||||||||
\(310\) | −0.600196 | −0.0340888 | ||||||||
\(311\) | −17.5991 | −0.997951 | −0.498976 | − | 0.866616i | \(-0.666290\pi\) | ||||
−0.498976 | + | 0.866616i | \(0.666290\pi\) | |||||||
\(312\) | −1.92086 | −0.108747 | ||||||||
\(313\) | −4.90021 | −0.276977 | −0.138488 | − | 0.990364i | \(-0.544224\pi\) | ||||
−0.138488 | + | 0.990364i | \(0.544224\pi\) | |||||||
\(314\) | −5.59270 | −0.315614 | ||||||||
\(315\) | −1.14246 | −0.0643702 | ||||||||
\(316\) | 3.03957 | 0.170989 | ||||||||
\(317\) | 26.3601 | 1.48053 | 0.740265 | − | 0.672316i | \(-0.234700\pi\) | ||||
0.740265 | + | 0.672316i | \(0.234700\pi\) | |||||||
\(318\) | 13.7620 | 0.771734 | ||||||||
\(319\) | −1.52856 | −0.0855827 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −22.3923 | −1.24982 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.92918 | −0.385550 | ||||||||
\(324\) | −7.48883 | −0.416046 | ||||||||
\(325\) | −1.20039 | −0.0665857 | ||||||||
\(326\) | 11.2498 | 0.623071 | ||||||||
\(327\) | 5.62874 | 0.311270 | ||||||||
\(328\) | 8.56797 | 0.473087 | ||||||||
\(329\) | −2.49731 | −0.137681 | ||||||||
\(330\) | −0.703084 | −0.0387035 | ||||||||
\(331\) | 28.7213 | 1.57866 | 0.789332 | − | 0.613966i | \(-0.210427\pi\) | ||||
0.789332 | + | 0.613966i | \(0.210427\pi\) | |||||||
\(332\) | 3.84342 | 0.210935 | ||||||||
\(333\) | −3.16366 | −0.173368 | ||||||||
\(334\) | −20.0257 | −1.09576 | ||||||||
\(335\) | 11.2901 | 0.616846 | ||||||||
\(336\) | 4.16082 | 0.226991 | ||||||||
\(337\) | −22.5206 | −1.22678 | −0.613389 | − | 0.789781i | \(-0.710194\pi\) | ||||
−0.613389 | + | 0.789781i | \(0.710194\pi\) | |||||||
\(338\) | −11.5591 | −0.628730 | ||||||||
\(339\) | 9.64596 | 0.523897 | ||||||||
\(340\) | −2.33225 | −0.126484 | ||||||||
\(341\) | 0.263710 | 0.0142807 | ||||||||
\(342\) | −1.30539 | −0.0705876 | ||||||||
\(343\) | −18.8228 | −1.01633 | ||||||||
\(344\) | 10.1971 | 0.549792 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.08903 | −0.0585464 | ||||||||
\(347\) | 23.3620 | 1.25414 | 0.627070 | − | 0.778963i | \(-0.284254\pi\) | ||||
0.627070 | + | 0.778963i | \(0.284254\pi\) | |||||||
\(348\) | 5.56699 | 0.298422 | ||||||||
\(349\) | −17.2645 | −0.924149 | −0.462075 | − | 0.886841i | \(-0.652895\pi\) | ||||
−0.462075 | + | 0.886841i | \(0.652895\pi\) | |||||||
\(350\) | 2.60020 | 0.138986 | ||||||||
\(351\) | 6.60656 | 0.352632 | ||||||||
\(352\) | −0.439374 | −0.0234187 | ||||||||
\(353\) | 21.4457 | 1.14144 | 0.570721 | − | 0.821144i | \(-0.306664\pi\) | ||||
0.570721 | + | 0.821144i | \(0.306664\pi\) | |||||||
\(354\) | 1.31910 | 0.0701094 | ||||||||
\(355\) | 7.52840 | 0.399566 | ||||||||
\(356\) | 9.98261 | 0.529077 | ||||||||
\(357\) | −9.70406 | −0.513593 | ||||||||
\(358\) | 17.2746 | 0.912990 | ||||||||
\(359\) | −12.9341 | −0.682638 | −0.341319 | − | 0.939948i | \(-0.610874\pi\) | ||||
−0.341319 | + | 0.939948i | \(0.610874\pi\) | |||||||
\(360\) | −0.439374 | −0.0231570 | ||||||||
\(361\) | −10.1730 | −0.535419 | ||||||||
\(362\) | −26.4155 | −1.38837 | ||||||||
\(363\) | −17.2932 | −0.907659 | ||||||||
\(364\) | −3.12125 | −0.163598 | ||||||||
\(365\) | −16.0716 | −0.841228 | ||||||||
\(366\) | 6.82277 | 0.356632 | ||||||||
\(367\) | 8.78672 | 0.458663 | 0.229332 | − | 0.973348i | \(-0.426346\pi\) | ||||
0.229332 | + | 0.973348i | \(0.426346\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.76454 | −0.195974 | ||||||||
\(370\) | 7.20039 | 0.374331 | ||||||||
\(371\) | 22.3622 | 1.16099 | ||||||||
\(372\) | −0.960431 | −0.0497960 | ||||||||
\(373\) | 33.7856 | 1.74935 | 0.874676 | − | 0.484709i | \(-0.161074\pi\) | ||||
0.874676 | + | 0.484709i | \(0.161074\pi\) | |||||||
\(374\) | 1.02473 | 0.0529874 | ||||||||
\(375\) | 1.60020 | 0.0826338 | ||||||||
\(376\) | −0.960431 | −0.0495304 | ||||||||
\(377\) | −4.17609 | −0.215080 | ||||||||
\(378\) | −14.3106 | −0.736059 | ||||||||
\(379\) | −8.61080 | −0.442307 | −0.221153 | − | 0.975239i | \(-0.570982\pi\) | ||||
−0.221153 | + | 0.975239i | \(0.570982\pi\) | |||||||
\(380\) | 2.97103 | 0.152411 | ||||||||
\(381\) | −27.3458 | −1.40097 | ||||||||
\(382\) | 16.6323 | 0.850981 | ||||||||
\(383\) | 15.9143 | 0.813185 | 0.406592 | − | 0.913610i | \(-0.366717\pi\) | ||||
0.406592 | + | 0.913610i | \(0.366717\pi\) | |||||||
\(384\) | 1.60020 | 0.0816596 | ||||||||
\(385\) | −1.14246 | −0.0582250 | ||||||||
\(386\) | −9.23996 | −0.470302 | ||||||||
\(387\) | −4.48035 | −0.227749 | ||||||||
\(388\) | 6.92820 | 0.351726 | ||||||||
\(389\) | 1.49183 | 0.0756387 | 0.0378193 | − | 0.999285i | \(-0.487959\pi\) | ||||
0.0378193 | + | 0.999285i | \(0.487959\pi\) | |||||||
\(390\) | −1.92086 | −0.0972666 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.238982 | −0.0120704 | ||||||||
\(393\) | 14.8095 | 0.747040 | ||||||||
\(394\) | 7.52204 | 0.378955 | ||||||||
\(395\) | 3.03957 | 0.152937 | ||||||||
\(396\) | 0.193049 | 0.00970109 | ||||||||
\(397\) | −18.0766 | −0.907238 | −0.453619 | − | 0.891196i | \(-0.649867\pi\) | ||||
−0.453619 | + | 0.891196i | \(0.649867\pi\) | |||||||
\(398\) | 2.23996 | 0.112279 | ||||||||
\(399\) | 12.3619 | 0.618871 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 22.5920 | 1.12819 | 0.564095 | − | 0.825710i | \(-0.309225\pi\) | ||||
0.564095 | + | 0.825710i | \(0.309225\pi\) | |||||||
\(402\) | 18.0664 | 0.901071 | ||||||||
\(403\) | 0.720470 | 0.0358892 | ||||||||
\(404\) | −9.32899 | −0.464134 | ||||||||
\(405\) | −7.48883 | −0.372123 | ||||||||
\(406\) | 9.04593 | 0.448942 | ||||||||
\(407\) | −3.16366 | −0.156817 | ||||||||
\(408\) | −3.73205 | −0.184764 | ||||||||
\(409\) | 16.3973 | 0.810792 | 0.405396 | − | 0.914141i | \(-0.367134\pi\) | ||||
0.405396 | + | 0.914141i | \(0.367134\pi\) | |||||||
\(410\) | 8.56797 | 0.423142 | ||||||||
\(411\) | −32.0240 | −1.57963 | ||||||||
\(412\) | −19.0073 | −0.936425 | ||||||||
\(413\) | 2.14344 | 0.105472 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.84342 | 0.188666 | ||||||||
\(416\) | −1.20039 | −0.0588540 | ||||||||
\(417\) | −25.1311 | −1.23068 | ||||||||
\(418\) | −1.30539 | −0.0638489 | ||||||||
\(419\) | −30.9768 | −1.51332 | −0.756658 | − | 0.653811i | \(-0.773169\pi\) | ||||
−0.756658 | + | 0.653811i | \(0.773169\pi\) | |||||||
\(420\) | 4.16082 | 0.203027 | ||||||||
\(421\) | 0.737698 | 0.0359532 | 0.0179766 | − | 0.999838i | \(-0.494278\pi\) | ||||
0.0179766 | + | 0.999838i | \(0.494278\pi\) | |||||||
\(422\) | 10.8946 | 0.530339 | ||||||||
\(423\) | 0.421988 | 0.0205178 | ||||||||
\(424\) | 8.60020 | 0.417662 | ||||||||
\(425\) | −2.33225 | −0.113131 | ||||||||
\(426\) | 12.0469 | 0.583675 | ||||||||
\(427\) | 11.0865 | 0.536512 | ||||||||
\(428\) | −13.9935 | −0.676400 | ||||||||
\(429\) | 0.843976 | 0.0407475 | ||||||||
\(430\) | 10.1971 | 0.491749 | ||||||||
\(431\) | 19.3502 | 0.932066 | 0.466033 | − | 0.884767i | \(-0.345683\pi\) | ||||
0.466033 | + | 0.884767i | \(0.345683\pi\) | |||||||
\(432\) | −5.50367 | −0.264795 | ||||||||
\(433\) | 15.0954 | 0.725438 | 0.362719 | − | 0.931899i | \(-0.381848\pi\) | ||||
0.362719 | + | 0.931899i | \(0.381848\pi\) | |||||||
\(434\) | −1.56063 | −0.0749125 | ||||||||
\(435\) | 5.56699 | 0.266917 | ||||||||
\(436\) | 3.51753 | 0.168459 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −25.7178 | −1.22884 | ||||||||
\(439\) | 22.3987 | 1.06903 | 0.534515 | − | 0.845159i | \(-0.320494\pi\) | ||||
0.534515 | + | 0.845159i | \(0.320494\pi\) | |||||||
\(440\) | −0.439374 | −0.0209463 | ||||||||
\(441\) | 0.105003 | 0.00500012 | ||||||||
\(442\) | 2.79961 | 0.133164 | ||||||||
\(443\) | 0.993636 | 0.0472091 | 0.0236045 | − | 0.999721i | \(-0.492486\pi\) | ||||
0.0236045 | + | 0.999721i | \(0.492486\pi\) | |||||||
\(444\) | 11.5220 | 0.546812 | ||||||||
\(445\) | 9.98261 | 0.473221 | ||||||||
\(446\) | −11.2414 | −0.532294 | ||||||||
\(447\) | −5.84809 | −0.276605 | ||||||||
\(448\) | 2.60020 | 0.122848 | ||||||||
\(449\) | 39.5737 | 1.86760 | 0.933800 | − | 0.357795i | \(-0.116471\pi\) | ||||
0.933800 | + | 0.357795i | \(0.116471\pi\) | |||||||
\(450\) | −0.439374 | −0.0207123 | ||||||||
\(451\) | −3.76454 | −0.177265 | ||||||||
\(452\) | 6.02799 | 0.283533 | ||||||||
\(453\) | 14.0707 | 0.661097 | ||||||||
\(454\) | −5.21099 | −0.244564 | ||||||||
\(455\) | −3.12125 | −0.146327 | ||||||||
\(456\) | 4.75423 | 0.222637 | ||||||||
\(457\) | 3.44290 | 0.161052 | 0.0805260 | − | 0.996753i | \(-0.474340\pi\) | ||||
0.0805260 | + | 0.996753i | \(0.474340\pi\) | |||||||
\(458\) | −10.4542 | −0.488493 | ||||||||
\(459\) | 12.8359 | 0.599129 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.61308 | 0.401151 | 0.200576 | − | 0.979678i | \(-0.435719\pi\) | ||||
0.200576 | + | 0.979678i | \(0.435719\pi\) | |||||||
\(462\) | −1.82816 | −0.0850535 | ||||||||
\(463\) | 0.934724 | 0.0434403 | 0.0217202 | − | 0.999764i | \(-0.493086\pi\) | ||||
0.0217202 | + | 0.999764i | \(0.493086\pi\) | |||||||
\(464\) | 3.47894 | 0.161506 | ||||||||
\(465\) | −0.960431 | −0.0445389 | ||||||||
\(466\) | 9.44769 | 0.437656 | ||||||||
\(467\) | −10.2340 | −0.473574 | −0.236787 | − | 0.971562i | \(-0.576094\pi\) | ||||
−0.236787 | + | 0.971562i | \(0.576094\pi\) | |||||||
\(468\) | 0.527420 | 0.0243800 | ||||||||
\(469\) | 29.3566 | 1.35556 | ||||||||
\(470\) | −0.960431 | −0.0443014 | ||||||||
\(471\) | −8.94941 | −0.412367 | ||||||||
\(472\) | 0.824336 | 0.0379432 | ||||||||
\(473\) | −4.48035 | −0.206007 | ||||||||
\(474\) | 4.86391 | 0.223407 | ||||||||
\(475\) | 2.97103 | 0.136320 | ||||||||
\(476\) | −6.06430 | −0.277957 | ||||||||
\(477\) | −3.77870 | −0.173015 | ||||||||
\(478\) | −15.9355 | −0.728875 | ||||||||
\(479\) | −9.83918 | −0.449564 | −0.224782 | − | 0.974409i | \(-0.572167\pi\) | ||||
−0.224782 | + | 0.974409i | \(0.572167\pi\) | |||||||
\(480\) | 1.60020 | 0.0730386 | ||||||||
\(481\) | −8.64329 | −0.394100 | ||||||||
\(482\) | −25.4618 | −1.15975 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.8070 | −0.491225 | ||||||||
\(485\) | 6.92820 | 0.314594 | ||||||||
\(486\) | 4.52742 | 0.205368 | ||||||||
\(487\) | 0.537855 | 0.0243726 | 0.0121863 | − | 0.999926i | \(-0.496121\pi\) | ||||
0.0121863 | + | 0.999926i | \(0.496121\pi\) | |||||||
\(488\) | 4.26371 | 0.193009 | ||||||||
\(489\) | 18.0020 | 0.814077 | ||||||||
\(490\) | −0.238982 | −0.0107961 | ||||||||
\(491\) | 13.9464 | 0.629393 | 0.314696 | − | 0.949192i | \(-0.398097\pi\) | ||||
0.314696 | + | 0.949192i | \(0.398097\pi\) | |||||||
\(492\) | 13.7104 | 0.618114 | ||||||||
\(493\) | −8.11375 | −0.365425 | ||||||||
\(494\) | −3.56640 | −0.160460 | ||||||||
\(495\) | 0.193049 | 0.00867692 | ||||||||
\(496\) | −0.600196 | −0.0269496 | ||||||||
\(497\) | 19.5753 | 0.878073 | ||||||||
\(498\) | 6.15022 | 0.275598 | ||||||||
\(499\) | −40.6847 | −1.82130 | −0.910648 | − | 0.413184i | \(-0.864417\pi\) | ||||
−0.910648 | + | 0.413184i | \(0.864417\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −32.0450 | −1.43167 | ||||||||
\(502\) | −12.0189 | −0.536431 | ||||||||
\(503\) | 16.8425 | 0.750972 | 0.375486 | − | 0.926828i | \(-0.377476\pi\) | ||||
0.375486 | + | 0.926828i | \(0.377476\pi\) | |||||||
\(504\) | −1.14246 | −0.0508891 | ||||||||
\(505\) | −9.32899 | −0.415134 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.4968 | −0.821470 | ||||||||
\(508\) | −17.0890 | −0.758203 | ||||||||
\(509\) | −15.9871 | −0.708616 | −0.354308 | − | 0.935129i | \(-0.615284\pi\) | ||||
−0.354308 | + | 0.935129i | \(0.615284\pi\) | |||||||
\(510\) | −3.73205 | −0.165258 | ||||||||
\(511\) | −41.7894 | −1.84865 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −16.3516 | −0.721940 | ||||||||
\(514\) | −10.2350 | −0.451447 | ||||||||
\(515\) | −19.0073 | −0.837564 | ||||||||
\(516\) | 16.3174 | 0.718334 | ||||||||
\(517\) | 0.421988 | 0.0185590 | ||||||||
\(518\) | 18.7224 | 0.822616 | ||||||||
\(519\) | −1.74265 | −0.0764940 | ||||||||
\(520\) | −1.20039 | −0.0526406 | ||||||||
\(521\) | 9.87575 | 0.432664 | 0.216332 | − | 0.976320i | \(-0.430591\pi\) | ||||
0.216332 | + | 0.976320i | \(0.430591\pi\) | |||||||
\(522\) | −1.52856 | −0.0669031 | ||||||||
\(523\) | −15.0356 | −0.657461 | −0.328730 | − | 0.944424i | \(-0.606621\pi\) | ||||
−0.328730 | + | 0.944424i | \(0.606621\pi\) | |||||||
\(524\) | 9.25480 | 0.404298 | ||||||||
\(525\) | 4.16082 | 0.181593 | ||||||||
\(526\) | −5.51356 | −0.240403 | ||||||||
\(527\) | 1.39980 | 0.0609764 | ||||||||
\(528\) | −0.703084 | −0.0305978 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 8.60020 | 0.373569 | ||||||||
\(531\) | −0.362192 | −0.0157178 | ||||||||
\(532\) | 7.72527 | 0.334933 | ||||||||
\(533\) | −10.2849 | −0.445489 | ||||||||
\(534\) | 15.9741 | 0.691268 | ||||||||
\(535\) | −13.9935 | −0.604991 | ||||||||
\(536\) | 11.2901 | 0.487659 | ||||||||
\(537\) | 27.6427 | 1.19287 | ||||||||
\(538\) | −29.2236 | −1.25992 | ||||||||
\(539\) | 0.105003 | 0.00452278 | ||||||||
\(540\) | −5.50367 | −0.236840 | ||||||||
\(541\) | 12.4269 | 0.534275 | 0.267137 | − | 0.963658i | \(-0.413922\pi\) | ||||
0.267137 | + | 0.963658i | \(0.413922\pi\) | |||||||
\(542\) | −13.6204 | −0.585047 | ||||||||
\(543\) | −42.2699 | −1.81398 | ||||||||
\(544\) | −2.33225 | −0.0999942 | ||||||||
\(545\) | 3.51753 | 0.150675 | ||||||||
\(546\) | −4.99461 | −0.213750 | ||||||||
\(547\) | −33.2966 | −1.42366 | −0.711830 | − | 0.702352i | \(-0.752133\pi\) | ||||
−0.711830 | + | 0.702352i | \(0.752133\pi\) | |||||||
\(548\) | −20.0126 | −0.854894 | ||||||||
\(549\) | −1.87336 | −0.0799532 | ||||||||
\(550\) | −0.439374 | −0.0187350 | ||||||||
\(551\) | 10.3361 | 0.440331 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.90348 | 0.336090 | ||||||||
\(554\) | −7.99550 | −0.339696 | ||||||||
\(555\) | 11.5220 | 0.489083 | ||||||||
\(556\) | −15.7050 | −0.666042 | ||||||||
\(557\) | 27.4659 | 1.16377 | 0.581884 | − | 0.813272i | \(-0.302316\pi\) | ||||
0.581884 | + | 0.813272i | \(0.302316\pi\) | |||||||
\(558\) | 0.263710 | 0.0111637 | ||||||||
\(559\) | −12.2405 | −0.517720 | ||||||||
\(560\) | 2.60020 | 0.109878 | ||||||||
\(561\) | 1.63977 | 0.0692309 | ||||||||
\(562\) | −31.5993 | −1.33294 | ||||||||
\(563\) | −19.6721 | −0.829080 | −0.414540 | − | 0.910031i | \(-0.636058\pi\) | ||||
−0.414540 | + | 0.910031i | \(0.636058\pi\) | |||||||
\(564\) | −1.53688 | −0.0647142 | ||||||||
\(565\) | 6.02799 | 0.253599 | ||||||||
\(566\) | −5.73841 | −0.241204 | ||||||||
\(567\) | −19.4724 | −0.817765 | ||||||||
\(568\) | 7.52840 | 0.315885 | ||||||||
\(569\) | 17.8150 | 0.746844 | 0.373422 | − | 0.927662i | \(-0.378184\pi\) | ||||
0.373422 | + | 0.927662i | \(0.378184\pi\) | |||||||
\(570\) | 4.75423 | 0.199133 | ||||||||
\(571\) | 19.7853 | 0.827990 | 0.413995 | − | 0.910279i | \(-0.364133\pi\) | ||||
0.413995 | + | 0.910279i | \(0.364133\pi\) | |||||||
\(572\) | 0.527420 | 0.0220526 | ||||||||
\(573\) | 26.6149 | 1.11185 | ||||||||
\(574\) | 22.2784 | 0.929882 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.439374 | −0.0183072 | ||||||||
\(577\) | −12.3098 | −0.512464 | −0.256232 | − | 0.966615i | \(-0.582481\pi\) | ||||
−0.256232 | + | 0.966615i | \(0.582481\pi\) | |||||||
\(578\) | −11.5606 | −0.480859 | ||||||||
\(579\) | −14.7857 | −0.614475 | ||||||||
\(580\) | 3.47894 | 0.144455 | ||||||||
\(581\) | 9.99364 | 0.414606 | ||||||||
\(582\) | 11.0865 | 0.459549 | ||||||||
\(583\) | −3.77870 | −0.156498 | ||||||||
\(584\) | −16.0716 | −0.665049 | ||||||||
\(585\) | 0.527420 | 0.0218062 | ||||||||
\(586\) | 15.1425 | 0.625529 | ||||||||
\(587\) | −9.96891 | −0.411461 | −0.205730 | − | 0.978609i | \(-0.565957\pi\) | ||||
−0.205730 | + | 0.978609i | \(0.565957\pi\) | |||||||
\(588\) | −0.382419 | −0.0157707 | ||||||||
\(589\) | −1.78320 | −0.0734755 | ||||||||
\(590\) | 0.824336 | 0.0339374 | ||||||||
\(591\) | 12.0367 | 0.495125 | ||||||||
\(592\) | 7.20039 | 0.295934 | ||||||||
\(593\) | 43.9968 | 1.80673 | 0.903367 | − | 0.428869i | \(-0.141088\pi\) | ||||
0.903367 | + | 0.428869i | \(0.141088\pi\) | |||||||
\(594\) | 2.41817 | 0.0992187 | ||||||||
\(595\) | −6.06430 | −0.248612 | ||||||||
\(596\) | −3.65461 | −0.149699 | ||||||||
\(597\) | 3.58438 | 0.146699 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.6584 | −0.884939 | −0.442470 | − | 0.896783i | \(-0.645898\pi\) | ||||
−0.442470 | + | 0.896783i | \(0.645898\pi\) | |||||||
\(600\) | 1.60020 | 0.0653277 | ||||||||
\(601\) | 29.0776 | 1.18610 | 0.593049 | − | 0.805166i | \(-0.297924\pi\) | ||||
0.593049 | + | 0.805166i | \(0.297924\pi\) | |||||||
\(602\) | 26.5145 | 1.08065 | ||||||||
\(603\) | −4.96059 | −0.202011 | ||||||||
\(604\) | 8.79309 | 0.357786 | ||||||||
\(605\) | −10.8070 | −0.439365 | ||||||||
\(606\) | −14.9282 | −0.606417 | ||||||||
\(607\) | 15.2091 | 0.617320 | 0.308660 | − | 0.951172i | \(-0.400119\pi\) | ||||
0.308660 | + | 0.951172i | \(0.400119\pi\) | |||||||
\(608\) | 2.97103 | 0.120491 | ||||||||
\(609\) | 14.4753 | 0.586567 | ||||||||
\(610\) | 4.26371 | 0.172633 | ||||||||
\(611\) | 1.15289 | 0.0466410 | ||||||||
\(612\) | 1.02473 | 0.0414222 | ||||||||
\(613\) | −8.38398 | −0.338626 | −0.169313 | − | 0.985562i | \(-0.554155\pi\) | ||||
−0.169313 | + | 0.985562i | \(0.554155\pi\) | |||||||
\(614\) | 27.1369 | 1.09516 | ||||||||
\(615\) | 13.7104 | 0.552858 | ||||||||
\(616\) | −1.14246 | −0.0460309 | ||||||||
\(617\) | −37.0585 | −1.49192 | −0.745959 | − | 0.665991i | \(-0.768009\pi\) | ||||
−0.745959 | + | 0.665991i | \(0.768009\pi\) | |||||||
\(618\) | −30.4155 | −1.22349 | ||||||||
\(619\) | −17.4815 | −0.702640 | −0.351320 | − | 0.936255i | \(-0.614267\pi\) | ||||
−0.351320 | + | 0.936255i | \(0.614267\pi\) | |||||||
\(620\) | −0.600196 | −0.0241044 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −17.5991 | −0.705658 | ||||||||
\(623\) | 25.9568 | 1.03994 | ||||||||
\(624\) | −1.92086 | −0.0768960 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −4.90021 | −0.195852 | ||||||||
\(627\) | −2.08889 | −0.0834221 | ||||||||
\(628\) | −5.59270 | −0.223173 | ||||||||
\(629\) | −16.7931 | −0.669584 | ||||||||
\(630\) | −1.14246 | −0.0455166 | ||||||||
\(631\) | 46.7247 | 1.86008 | 0.930040 | − | 0.367459i | \(-0.119772\pi\) | ||||
0.930040 | + | 0.367459i | \(0.119772\pi\) | |||||||
\(632\) | 3.03957 | 0.120908 | ||||||||
\(633\) | 17.4334 | 0.692917 | ||||||||
\(634\) | 26.3601 | 1.04689 | ||||||||
\(635\) | −17.0890 | −0.678157 | ||||||||
\(636\) | 13.7620 | 0.545699 | ||||||||
\(637\) | 0.286872 | 0.0113663 | ||||||||
\(638\) | −1.52856 | −0.0605161 | ||||||||
\(639\) | −3.30778 | −0.130854 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 11.1552 | 0.440603 | 0.220301 | − | 0.975432i | \(-0.429296\pi\) | ||||
0.220301 | + | 0.975432i | \(0.429296\pi\) | |||||||
\(642\) | −22.3923 | −0.883754 | ||||||||
\(643\) | 20.2487 | 0.798531 | 0.399266 | − | 0.916835i | \(-0.369265\pi\) | ||||
0.399266 | + | 0.916835i | \(0.369265\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16.3174 | 0.642497 | ||||||||
\(646\) | −6.92918 | −0.272625 | ||||||||
\(647\) | −38.6297 | −1.51869 | −0.759346 | − | 0.650688i | \(-0.774481\pi\) | ||||
−0.759346 | + | 0.650688i | \(0.774481\pi\) | |||||||
\(648\) | −7.48883 | −0.294189 | ||||||||
\(649\) | −0.362192 | −0.0142173 | ||||||||
\(650\) | −1.20039 | −0.0470832 | ||||||||
\(651\) | −2.49731 | −0.0978772 | ||||||||
\(652\) | 11.2498 | 0.440578 | ||||||||
\(653\) | −27.0805 | −1.05974 | −0.529872 | − | 0.848078i | \(-0.677760\pi\) | ||||
−0.529872 | + | 0.848078i | \(0.677760\pi\) | |||||||
\(654\) | 5.62874 | 0.220101 | ||||||||
\(655\) | 9.25480 | 0.361615 | ||||||||
\(656\) | 8.56797 | 0.334523 | ||||||||
\(657\) | 7.06146 | 0.275494 | ||||||||
\(658\) | −2.49731 | −0.0973552 | ||||||||
\(659\) | 3.29268 | 0.128264 | 0.0641322 | − | 0.997941i | \(-0.479572\pi\) | ||||
0.0641322 | + | 0.997941i | \(0.479572\pi\) | |||||||
\(660\) | −0.703084 | −0.0273675 | ||||||||
\(661\) | 2.18907 | 0.0851451 | 0.0425725 | − | 0.999093i | \(-0.486445\pi\) | ||||
0.0425725 | + | 0.999093i | \(0.486445\pi\) | |||||||
\(662\) | 28.7213 | 1.11628 | ||||||||
\(663\) | 4.47992 | 0.173986 | ||||||||
\(664\) | 3.84342 | 0.149154 | ||||||||
\(665\) | 7.72527 | 0.299573 | ||||||||
\(666\) | −3.16366 | −0.122589 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −20.0257 | −0.774818 | ||||||||
\(669\) | −17.9884 | −0.695471 | ||||||||
\(670\) | 11.2901 | 0.436176 | ||||||||
\(671\) | −1.87336 | −0.0723204 | ||||||||
\(672\) | 4.16082 | 0.160507 | ||||||||
\(673\) | −35.4026 | −1.36467 | −0.682335 | − | 0.731040i | \(-0.739035\pi\) | ||||
−0.682335 | + | 0.731040i | \(0.739035\pi\) | |||||||
\(674\) | −22.5206 | −0.867463 | ||||||||
\(675\) | −5.50367 | −0.211836 | ||||||||
\(676\) | −11.5591 | −0.444579 | ||||||||
\(677\) | 28.2998 | 1.08765 | 0.543824 | − | 0.839199i | \(-0.316976\pi\) | ||||
0.543824 | + | 0.839199i | \(0.316976\pi\) | |||||||
\(678\) | 9.64596 | 0.370451 | ||||||||
\(679\) | 18.0147 | 0.691340 | ||||||||
\(680\) | −2.33225 | −0.0894376 | ||||||||
\(681\) | −8.33861 | −0.319536 | ||||||||
\(682\) | 0.263710 | 0.0100980 | ||||||||
\(683\) | 10.8520 | 0.415240 | 0.207620 | − | 0.978210i | \(-0.433428\pi\) | ||||
0.207620 | + | 0.978210i | \(0.433428\pi\) | |||||||
\(684\) | −1.30539 | −0.0499130 | ||||||||
\(685\) | −20.0126 | −0.764641 | ||||||||
\(686\) | −18.8228 | −0.718657 | ||||||||
\(687\) | −16.7288 | −0.638243 | ||||||||
\(688\) | 10.1971 | 0.388762 | ||||||||
\(689\) | −10.3236 | −0.393298 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 46.0830 | 1.75308 | 0.876539 | − | 0.481331i | \(-0.159846\pi\) | ||||
0.876539 | + | 0.481331i | \(0.159846\pi\) | |||||||
\(692\) | −1.08903 | −0.0413985 | ||||||||
\(693\) | 0.501966 | 0.0190681 | ||||||||
\(694\) | 23.3620 | 0.886811 | ||||||||
\(695\) | −15.7050 | −0.595726 | ||||||||
\(696\) | 5.56699 | 0.211016 | ||||||||
\(697\) | −19.9826 | −0.756895 | ||||||||
\(698\) | −17.2645 | −0.653472 | ||||||||
\(699\) | 15.1182 | 0.571821 | ||||||||
\(700\) | 2.60020 | 0.0982782 | ||||||||
\(701\) | 14.5121 | 0.548116 | 0.274058 | − | 0.961713i | \(-0.411634\pi\) | ||||
0.274058 | + | 0.961713i | \(0.411634\pi\) | |||||||
\(702\) | 6.60656 | 0.249349 | ||||||||
\(703\) | 21.3926 | 0.806837 | ||||||||
\(704\) | −0.439374 | −0.0165595 | ||||||||
\(705\) | −1.53688 | −0.0578821 | ||||||||
\(706\) | 21.4457 | 0.807121 | ||||||||
\(707\) | −24.2572 | −0.912285 | ||||||||
\(708\) | 1.31910 | 0.0495748 | ||||||||
\(709\) | 3.73375 | 0.140224 | 0.0701119 | − | 0.997539i | \(-0.477664\pi\) | ||||
0.0701119 | + | 0.997539i | \(0.477664\pi\) | |||||||
\(710\) | 7.52840 | 0.282536 | ||||||||
\(711\) | −1.33551 | −0.0500854 | ||||||||
\(712\) | 9.98261 | 0.374114 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −9.70406 | −0.363165 | ||||||||
\(715\) | 0.527420 | 0.0197244 | ||||||||
\(716\) | 17.2746 | 0.645581 | ||||||||
\(717\) | −25.5000 | −0.952315 | ||||||||
\(718\) | −12.9341 | −0.482698 | ||||||||
\(719\) | −23.2794 | −0.868174 | −0.434087 | − | 0.900871i | \(-0.642929\pi\) | ||||
−0.434087 | + | 0.900871i | \(0.642929\pi\) | |||||||
\(720\) | −0.439374 | −0.0163745 | ||||||||
\(721\) | −49.4228 | −1.84060 | ||||||||
\(722\) | −10.1730 | −0.378598 | ||||||||
\(723\) | −40.7439 | −1.51528 | ||||||||
\(724\) | −26.4155 | −0.981723 | ||||||||
\(725\) | 3.47894 | 0.129205 | ||||||||
\(726\) | −17.2932 | −0.641812 | ||||||||
\(727\) | 30.7094 | 1.13895 | 0.569474 | − | 0.822009i | \(-0.307147\pi\) | ||||
0.569474 | + | 0.822009i | \(0.307147\pi\) | |||||||
\(728\) | −3.12125 | −0.115681 | ||||||||
\(729\) | 29.7112 | 1.10042 | ||||||||
\(730\) | −16.0716 | −0.594838 | ||||||||
\(731\) | −23.7822 | −0.879617 | ||||||||
\(732\) | 6.82277 | 0.252177 | ||||||||
\(733\) | 11.9801 | 0.442494 | 0.221247 | − | 0.975218i | \(-0.428987\pi\) | ||||
0.221247 | + | 0.975218i | \(0.428987\pi\) | |||||||
\(734\) | 8.78672 | 0.324324 | ||||||||
\(735\) | −0.382419 | −0.0141057 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.96059 | −0.182726 | ||||||||
\(738\) | −3.76454 | −0.138575 | ||||||||
\(739\) | −29.6248 | −1.08976 | −0.544882 | − | 0.838513i | \(-0.683426\pi\) | ||||
−0.544882 | + | 0.838513i | \(0.683426\pi\) | |||||||
\(740\) | 7.20039 | 0.264692 | ||||||||
\(741\) | −5.70694 | −0.209650 | ||||||||
\(742\) | 22.3622 | 0.820942 | ||||||||
\(743\) | −37.7890 | −1.38634 | −0.693172 | − | 0.720773i | \(-0.743787\pi\) | ||||
−0.693172 | + | 0.720773i | \(0.743787\pi\) | |||||||
\(744\) | −0.960431 | −0.0352111 | ||||||||
\(745\) | −3.65461 | −0.133894 | ||||||||
\(746\) | 33.7856 | 1.23698 | ||||||||
\(747\) | −1.68870 | −0.0617862 | ||||||||
\(748\) | 1.02473 | 0.0374678 | ||||||||
\(749\) | −36.3858 | −1.32951 | ||||||||
\(750\) | 1.60020 | 0.0584309 | ||||||||
\(751\) | −12.7668 | −0.465867 | −0.232933 | − | 0.972493i | \(-0.574832\pi\) | ||||
−0.232933 | + | 0.972493i | \(0.574832\pi\) | |||||||
\(752\) | −0.960431 | −0.0350233 | ||||||||
\(753\) | −19.2326 | −0.700876 | ||||||||
\(754\) | −4.17609 | −0.152084 | ||||||||
\(755\) | 8.79309 | 0.320013 | ||||||||
\(756\) | −14.3106 | −0.520472 | ||||||||
\(757\) | −2.00636 | −0.0729225 | −0.0364613 | − | 0.999335i | \(-0.511609\pi\) | ||||
−0.0364613 | + | 0.999335i | \(0.511609\pi\) | |||||||
\(758\) | −8.61080 | −0.312758 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.97103 | 0.107771 | ||||||||
\(761\) | 6.60499 | 0.239431 | 0.119715 | − | 0.992808i | \(-0.461802\pi\) | ||||
0.119715 | + | 0.992808i | \(0.461802\pi\) | |||||||
\(762\) | −27.3458 | −0.990633 | ||||||||
\(763\) | 9.14628 | 0.331117 | ||||||||
\(764\) | 16.6323 | 0.601734 | ||||||||
\(765\) | 1.02473 | 0.0370491 | ||||||||
\(766\) | 15.9143 | 0.575008 | ||||||||
\(767\) | −0.989526 | −0.0357297 | ||||||||
\(768\) | 1.60020 | 0.0577421 | ||||||||
\(769\) | −17.4382 | −0.628839 | −0.314419 | − | 0.949284i | \(-0.601810\pi\) | ||||
−0.314419 | + | 0.949284i | \(0.601810\pi\) | |||||||
\(770\) | −1.14246 | −0.0411713 | ||||||||
\(771\) | −16.3780 | −0.589840 | ||||||||
\(772\) | −9.23996 | −0.332553 | ||||||||
\(773\) | −0.990701 | −0.0356330 | −0.0178165 | − | 0.999841i | \(-0.505671\pi\) | ||||
−0.0178165 | + | 0.999841i | \(0.505671\pi\) | |||||||
\(774\) | −4.48035 | −0.161043 | ||||||||
\(775\) | −0.600196 | −0.0215597 | ||||||||
\(776\) | 6.92820 | 0.248708 | ||||||||
\(777\) | 29.9595 | 1.07479 | ||||||||
\(778\) | 1.49183 | 0.0534846 | ||||||||
\(779\) | 25.4557 | 0.912046 | ||||||||
\(780\) | −1.92086 | −0.0687779 | ||||||||
\(781\) | −3.30778 | −0.118362 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −19.1470 | −0.684256 | ||||||||
\(784\) | −0.238982 | −0.00853508 | ||||||||
\(785\) | −5.59270 | −0.199612 | ||||||||
\(786\) | 14.8095 | 0.528237 | ||||||||
\(787\) | 17.4983 | 0.623747 | 0.311873 | − | 0.950124i | \(-0.399044\pi\) | ||||
0.311873 | + | 0.950124i | \(0.399044\pi\) | |||||||
\(788\) | 7.52204 | 0.267961 | ||||||||
\(789\) | −8.82277 | −0.314099 | ||||||||
\(790\) | 3.03957 | 0.108143 | ||||||||
\(791\) | 15.6739 | 0.557301 | ||||||||
\(792\) | 0.193049 | 0.00685971 | ||||||||
\(793\) | −5.11812 | −0.181750 | ||||||||
\(794\) | −18.0766 | −0.641514 | ||||||||
\(795\) | 13.7620 | 0.488088 | ||||||||
\(796\) | 2.23996 | 0.0793933 | ||||||||
\(797\) | −28.4269 | −1.00693 | −0.503467 | − | 0.864015i | \(-0.667942\pi\) | ||||
−0.503467 | + | 0.864015i | \(0.667942\pi\) | |||||||
\(798\) | 12.3619 | 0.437608 | ||||||||
\(799\) | 2.23996 | 0.0792441 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −4.38610 | −0.154975 | ||||||||
\(802\) | 22.5920 | 0.797751 | ||||||||
\(803\) | 7.06146 | 0.249193 | ||||||||
\(804\) | 18.0664 | 0.637154 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.720470 | 0.0253775 | ||||||||
\(807\) | −46.7634 | −1.64615 | ||||||||
\(808\) | −9.32899 | −0.328193 | ||||||||
\(809\) | −17.7630 | −0.624513 | −0.312256 | − | 0.949998i | \(-0.601085\pi\) | ||||
−0.312256 | + | 0.949998i | \(0.601085\pi\) | |||||||
\(810\) | −7.48883 | −0.263131 | ||||||||
\(811\) | −12.4344 | −0.436631 | −0.218316 | − | 0.975878i | \(-0.570056\pi\) | ||||
−0.218316 | + | 0.975878i | \(0.570056\pi\) | |||||||
\(812\) | 9.04593 | 0.317450 | ||||||||
\(813\) | −21.7953 | −0.764396 | ||||||||
\(814\) | −3.16366 | −0.110886 | ||||||||
\(815\) | 11.2498 | 0.394065 | ||||||||
\(816\) | −3.73205 | −0.130648 | ||||||||
\(817\) | 30.2960 | 1.05992 | ||||||||
\(818\) | 16.3973 | 0.573317 | ||||||||
\(819\) | 1.37140 | 0.0479205 | ||||||||
\(820\) | 8.56797 | 0.299206 | ||||||||
\(821\) | 42.6000 | 1.48675 | 0.743376 | − | 0.668874i | \(-0.233223\pi\) | ||||
0.743376 | + | 0.668874i | \(0.233223\pi\) | |||||||
\(822\) | −32.0240 | −1.11697 | ||||||||
\(823\) | 1.33805 | 0.0466415 | 0.0233208 | − | 0.999728i | \(-0.492576\pi\) | ||||
0.0233208 | + | 0.999728i | \(0.492576\pi\) | |||||||
\(824\) | −19.0073 | −0.662152 | ||||||||
\(825\) | −0.703084 | −0.0244782 | ||||||||
\(826\) | 2.14344 | 0.0745797 | ||||||||
\(827\) | 52.1609 | 1.81381 | 0.906907 | − | 0.421332i | \(-0.138437\pi\) | ||||
0.906907 | + | 0.421332i | \(0.138437\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.13625 | −0.108927 | −0.0544633 | − | 0.998516i | \(-0.517345\pi\) | ||||
−0.0544633 | + | 0.998516i | \(0.517345\pi\) | |||||||
\(830\) | 3.84342 | 0.133407 | ||||||||
\(831\) | −12.7944 | −0.443832 | ||||||||
\(832\) | −1.20039 | −0.0416161 | ||||||||
\(833\) | 0.557366 | 0.0193116 | ||||||||
\(834\) | −25.1311 | −0.870220 | ||||||||
\(835\) | −20.0257 | −0.693018 | ||||||||
\(836\) | −1.30539 | −0.0451480 | ||||||||
\(837\) | 3.30328 | 0.114178 | ||||||||
\(838\) | −30.9768 | −1.07008 | ||||||||
\(839\) | 55.2928 | 1.90892 | 0.954459 | − | 0.298341i | \(-0.0964332\pi\) | ||||
0.954459 | + | 0.298341i | \(0.0964332\pi\) | |||||||
\(840\) | 4.16082 | 0.143562 | ||||||||
\(841\) | −16.8970 | −0.582654 | ||||||||
\(842\) | 0.737698 | 0.0254228 | ||||||||
\(843\) | −50.5651 | −1.74155 | ||||||||
\(844\) | 10.8946 | 0.375006 | ||||||||
\(845\) | −11.5591 | −0.397644 | ||||||||
\(846\) | 0.421988 | 0.0145082 | ||||||||
\(847\) | −28.1002 | −0.965534 | ||||||||
\(848\) | 8.60020 | 0.295332 | ||||||||
\(849\) | −9.18259 | −0.315146 | ||||||||
\(850\) | −2.33225 | −0.0799954 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 12.0469 | 0.412720 | ||||||||
\(853\) | 29.4030 | 1.00674 | 0.503370 | − | 0.864071i | \(-0.332093\pi\) | ||||
0.503370 | + | 0.864071i | \(0.332093\pi\) | |||||||
\(854\) | 11.0865 | 0.379372 | ||||||||
\(855\) | −1.30539 | −0.0446435 | ||||||||
\(856\) | −13.9935 | −0.478287 | ||||||||
\(857\) | −50.9453 | −1.74026 | −0.870129 | − | 0.492824i | \(-0.835965\pi\) | ||||
−0.870129 | + | 0.492824i | \(0.835965\pi\) | |||||||
\(858\) | 0.843976 | 0.0288129 | ||||||||
\(859\) | −25.2804 | −0.862554 | −0.431277 | − | 0.902219i | \(-0.641937\pi\) | ||||
−0.431277 | + | 0.902219i | \(0.641937\pi\) | |||||||
\(860\) | 10.1971 | 0.347719 | ||||||||
\(861\) | 35.6498 | 1.21494 | ||||||||
\(862\) | 19.3502 | 0.659070 | ||||||||
\(863\) | 7.86886 | 0.267859 | 0.133930 | − | 0.990991i | \(-0.457240\pi\) | ||||
0.133930 | + | 0.990991i | \(0.457240\pi\) | |||||||
\(864\) | −5.50367 | −0.187239 | ||||||||
\(865\) | −1.08903 | −0.0370280 | ||||||||
\(866\) | 15.0954 | 0.512962 | ||||||||
\(867\) | −18.4993 | −0.628268 | ||||||||
\(868\) | −1.56063 | −0.0529711 | ||||||||
\(869\) | −1.33551 | −0.0453040 | ||||||||
\(870\) | 5.56699 | 0.188739 | ||||||||
\(871\) | −13.5526 | −0.459212 | ||||||||
\(872\) | 3.51753 | 0.119119 | ||||||||
\(873\) | −3.04407 | −0.103026 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.60020 | 0.0879027 | ||||||||
\(876\) | −25.7178 | −0.868923 | ||||||||
\(877\) | −44.9494 | −1.51783 | −0.758917 | − | 0.651188i | \(-0.774271\pi\) | ||||
−0.758917 | + | 0.651188i | \(0.774271\pi\) | |||||||
\(878\) | 22.3987 | 0.755918 | ||||||||
\(879\) | 24.2309 | 0.817288 | ||||||||
\(880\) | −0.439374 | −0.0148113 | ||||||||
\(881\) | −0.782223 | −0.0263538 | −0.0131769 | − | 0.999913i | \(-0.504194\pi\) | ||||
−0.0131769 | + | 0.999913i | \(0.504194\pi\) | |||||||
\(882\) | 0.105003 | 0.00353562 | ||||||||
\(883\) | 23.4590 | 0.789458 | 0.394729 | − | 0.918798i | \(-0.370839\pi\) | ||||
0.394729 | + | 0.918798i | \(0.370839\pi\) | |||||||
\(884\) | 2.79961 | 0.0941610 | ||||||||
\(885\) | 1.31910 | 0.0443411 | ||||||||
\(886\) | 0.993636 | 0.0333819 | ||||||||
\(887\) | −22.7100 | −0.762526 | −0.381263 | − | 0.924467i | \(-0.624511\pi\) | ||||
−0.381263 | + | 0.924467i | \(0.624511\pi\) | |||||||
\(888\) | 11.5220 | 0.386654 | ||||||||
\(889\) | −44.4348 | −1.49030 | ||||||||
\(890\) | 9.98261 | 0.334618 | ||||||||
\(891\) | 3.29040 | 0.110232 | ||||||||
\(892\) | −11.2414 | −0.376389 | ||||||||
\(893\) | −2.85347 | −0.0954878 | ||||||||
\(894\) | −5.84809 | −0.195589 | ||||||||
\(895\) | 17.2746 | 0.577425 | ||||||||
\(896\) | 2.60020 | 0.0868664 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 39.5737 | 1.32059 | ||||||||
\(899\) | −2.08805 | −0.0696403 | ||||||||
\(900\) | −0.439374 | −0.0146458 | ||||||||
\(901\) | −20.0578 | −0.668221 | ||||||||
\(902\) | −3.76454 | −0.125345 | ||||||||
\(903\) | 42.4284 | 1.41193 | ||||||||
\(904\) | 6.02799 | 0.200488 | ||||||||
\(905\) | −26.4155 | −0.878080 | ||||||||
\(906\) | 14.0707 | 0.467466 | ||||||||
\(907\) | −28.4132 | −0.943446 | −0.471723 | − | 0.881747i | \(-0.656368\pi\) | ||||
−0.471723 | + | 0.881747i | \(0.656368\pi\) | |||||||
\(908\) | −5.21099 | −0.172933 | ||||||||
\(909\) | 4.09891 | 0.135952 | ||||||||
\(910\) | −3.12125 | −0.103469 | ||||||||
\(911\) | −58.0359 | −1.92281 | −0.961407 | − | 0.275129i | \(-0.911280\pi\) | ||||
−0.961407 | + | 0.275129i | \(0.911280\pi\) | |||||||
\(912\) | 4.75423 | 0.157428 | ||||||||
\(913\) | −1.68870 | −0.0558877 | ||||||||
\(914\) | 3.44290 | 0.113881 | ||||||||
\(915\) | 6.82277 | 0.225554 | ||||||||
\(916\) | −10.4542 | −0.345417 | ||||||||
\(917\) | 24.0643 | 0.794673 | ||||||||
\(918\) | 12.8359 | 0.423648 | ||||||||
\(919\) | −10.6732 | −0.352078 | −0.176039 | − | 0.984383i | \(-0.556328\pi\) | ||||
−0.176039 | + | 0.984383i | \(0.556328\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 43.4244 | 1.43088 | ||||||||
\(922\) | 8.61308 | 0.283657 | ||||||||
\(923\) | −9.03703 | −0.297457 | ||||||||
\(924\) | −1.82816 | −0.0601419 | ||||||||
\(925\) | 7.20039 | 0.236747 | ||||||||
\(926\) | 0.934724 | 0.0307169 | ||||||||
\(927\) | 8.35133 | 0.274294 | ||||||||
\(928\) | 3.47894 | 0.114202 | ||||||||
\(929\) | −2.17609 | −0.0713953 | −0.0356977 | − | 0.999363i | \(-0.511365\pi\) | ||||
−0.0356977 | + | 0.999363i | \(0.511365\pi\) | |||||||
\(930\) | −0.960431 | −0.0314938 | ||||||||
\(931\) | −0.710025 | −0.0232701 | ||||||||
\(932\) | 9.44769 | 0.309470 | ||||||||
\(933\) | −28.1619 | −0.921981 | ||||||||
\(934\) | −10.2340 | −0.334868 | ||||||||
\(935\) | 1.02473 | 0.0335122 | ||||||||
\(936\) | 0.527420 | 0.0172393 | ||||||||
\(937\) | 43.2102 | 1.41162 | 0.705809 | − | 0.708403i | \(-0.250584\pi\) | ||||
0.705809 | + | 0.708403i | \(0.250584\pi\) | |||||||
\(938\) | 29.3566 | 0.958525 | ||||||||
\(939\) | −7.84130 | −0.255891 | ||||||||
\(940\) | −0.960431 | −0.0313258 | ||||||||
\(941\) | 53.9929 | 1.76012 | 0.880059 | − | 0.474864i | \(-0.157503\pi\) | ||||
0.880059 | + | 0.474864i | \(0.157503\pi\) | |||||||
\(942\) | −8.94941 | −0.291587 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0.824336 | 0.0268299 | ||||||||
\(945\) | −14.3106 | −0.465525 | ||||||||
\(946\) | −4.48035 | −0.145669 | ||||||||
\(947\) | 16.7361 | 0.543851 | 0.271926 | − | 0.962318i | \(-0.412340\pi\) | ||||
0.271926 | + | 0.962318i | \(0.412340\pi\) | |||||||
\(948\) | 4.86391 | 0.157972 | ||||||||
\(949\) | 19.2923 | 0.626253 | ||||||||
\(950\) | 2.97103 | 0.0963930 | ||||||||
\(951\) | 42.1813 | 1.36782 | ||||||||
\(952\) | −6.06430 | −0.196545 | ||||||||
\(953\) | 3.82391 | 0.123868 | 0.0619342 | − | 0.998080i | \(-0.480273\pi\) | ||||
0.0619342 | + | 0.998080i | \(0.480273\pi\) | |||||||
\(954\) | −3.77870 | −0.122340 | ||||||||
\(955\) | 16.6323 | 0.538207 | ||||||||
\(956\) | −15.9355 | −0.515392 | ||||||||
\(957\) | −2.44599 | −0.0790676 | ||||||||
\(958\) | −9.83918 | −0.317889 | ||||||||
\(959\) | −52.0366 | −1.68035 | ||||||||
\(960\) | 1.60020 | 0.0516461 | ||||||||
\(961\) | −30.6398 | −0.988380 | ||||||||
\(962\) | −8.64329 | −0.278671 | ||||||||
\(963\) | 6.14837 | 0.198128 | ||||||||
\(964\) | −25.4618 | −0.820070 | ||||||||
\(965\) | −9.23996 | −0.297445 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.9748 | −0.674505 | −0.337253 | − | 0.941414i | \(-0.609498\pi\) | ||||
−0.337253 | + | 0.941414i | \(0.609498\pi\) | |||||||
\(968\) | −10.8070 | −0.347349 | ||||||||
\(969\) | −11.0880 | −0.356199 | ||||||||
\(970\) | 6.92820 | 0.222451 | ||||||||
\(971\) | −47.2203 | −1.51537 | −0.757685 | − | 0.652620i | \(-0.773670\pi\) | ||||
−0.757685 | + | 0.652620i | \(0.773670\pi\) | |||||||
\(972\) | 4.52742 | 0.145217 | ||||||||
\(973\) | −40.8362 | −1.30915 | ||||||||
\(974\) | 0.537855 | 0.0172340 | ||||||||
\(975\) | −1.92086 | −0.0615168 | ||||||||
\(976\) | 4.26371 | 0.136478 | ||||||||
\(977\) | 16.3988 | 0.524645 | 0.262322 | − | 0.964980i | \(-0.415512\pi\) | ||||
0.262322 | + | 0.964980i | \(0.415512\pi\) | |||||||
\(978\) | 18.0020 | 0.575639 | ||||||||
\(979\) | −4.38610 | −0.140180 | ||||||||
\(980\) | −0.238982 | −0.00763401 | ||||||||
\(981\) | −1.54551 | −0.0493444 | ||||||||
\(982\) | 13.9464 | 0.445048 | ||||||||
\(983\) | −13.5150 | −0.431061 | −0.215531 | − | 0.976497i | \(-0.569148\pi\) | ||||
−0.215531 | + | 0.976497i | \(0.569148\pi\) | |||||||
\(984\) | 13.7104 | 0.437072 | ||||||||
\(985\) | 7.52204 | 0.239672 | ||||||||
\(986\) | −8.11375 | −0.258395 | ||||||||
\(987\) | −3.99618 | −0.127200 | ||||||||
\(988\) | −3.56640 | −0.113462 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0.193049 | 0.00613551 | ||||||||
\(991\) | −14.8425 | −0.471489 | −0.235744 | − | 0.971815i | \(-0.575753\pi\) | ||||
−0.235744 | + | 0.971815i | \(0.575753\pi\) | |||||||
\(992\) | −0.600196 | −0.0190562 | ||||||||
\(993\) | 45.9597 | 1.45849 | ||||||||
\(994\) | 19.5753 | 0.620891 | ||||||||
\(995\) | 2.23996 | 0.0710115 | ||||||||
\(996\) | 6.15022 | 0.194877 | ||||||||
\(997\) | −39.8781 | −1.26295 | −0.631477 | − | 0.775395i | \(-0.717551\pi\) | ||||
−0.631477 | + | 0.775395i | \(0.717551\pi\) | |||||||
\(998\) | −40.6847 | −1.28785 | ||||||||
\(999\) | −39.6286 | −1.25379 |
(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 | 5290.2.a.bb.1.3 | yes | 4 | |
23.22 | odd | 2 | 5290.2.a.ba.1.3 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5290.2.a.ba.1.3 | ✓ | 4 | 23.22 | odd | 2 | ||
5290.2.a.bb.1.3 | yes | 4 | 1.1 | even | 1 | trivial |