Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 2 x^{14} - 16 x^{13} + 31 x^{12} + 99 x^{11} - 184 x^{10} - 296 x^{9} + 519 x^{8} + 437 x^{7} + \cdots - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1205) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.92974\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.92974 | −1.36453 | −0.682267 | − | 0.731103i | \(-0.739006\pi\) | ||||
−0.682267 | + | 0.731103i | \(0.739006\pi\) | |||||||
\(3\) | −0.860854 | −0.497014 | −0.248507 | − | 0.968630i | \(-0.579940\pi\) | ||||
−0.248507 | + | 0.968630i | \(0.579940\pi\) | |||||||
\(4\) | 1.72391 | 0.861956 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.66123 | 0.678194 | ||||||||
\(7\) | 4.27878 | 1.61723 | 0.808614 | − | 0.588339i | \(-0.200218\pi\) | ||||
0.808614 | + | 0.588339i | \(0.200218\pi\) | |||||||
\(8\) | 0.532780 | 0.188366 | ||||||||
\(9\) | −2.25893 | −0.752977 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.15941 | −1.25411 | −0.627054 | − | 0.778976i | \(-0.715740\pi\) | ||||
−0.627054 | + | 0.778976i | \(0.715740\pi\) | |||||||
\(12\) | −1.48404 | −0.428404 | ||||||||
\(13\) | −1.01359 | −0.281120 | −0.140560 | − | 0.990072i | \(-0.544890\pi\) | ||||
−0.140560 | + | 0.990072i | \(0.544890\pi\) | |||||||
\(14\) | −8.25696 | −2.20676 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.47595 | −1.11899 | ||||||||
\(17\) | −5.08984 | −1.23447 | −0.617234 | − | 0.786780i | \(-0.711747\pi\) | ||||
−0.617234 | + | 0.786780i | \(0.711747\pi\) | |||||||
\(18\) | 4.35916 | 1.02746 | ||||||||
\(19\) | −0.226708 | −0.0520105 | −0.0260052 | − | 0.999662i | \(-0.508279\pi\) | ||||
−0.0260052 | + | 0.999662i | \(0.508279\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.68341 | −0.803786 | ||||||||
\(22\) | 8.02659 | 1.71128 | ||||||||
\(23\) | 2.25775 | 0.470773 | 0.235387 | − | 0.971902i | \(-0.424364\pi\) | ||||
0.235387 | + | 0.971902i | \(0.424364\pi\) | |||||||
\(24\) | −0.458646 | −0.0936208 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.95598 | 0.383599 | ||||||||
\(27\) | 4.52717 | 0.871255 | ||||||||
\(28\) | 7.37624 | 1.39398 | ||||||||
\(29\) | −0.0980765 | −0.0182123 | −0.00910617 | − | 0.999959i | \(-0.502899\pi\) | ||||
−0.00910617 | + | 0.999959i | \(0.502899\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.03981 | 0.905176 | 0.452588 | − | 0.891720i | \(-0.350501\pi\) | ||||
0.452588 | + | 0.891720i | \(0.350501\pi\) | |||||||
\(32\) | 7.57188 | 1.33853 | ||||||||
\(33\) | 3.58064 | 0.623310 | ||||||||
\(34\) | 9.82208 | 1.68447 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.89420 | −0.649033 | ||||||||
\(37\) | 1.95298 | 0.321067 | 0.160534 | − | 0.987030i | \(-0.448678\pi\) | ||||
0.160534 | + | 0.987030i | \(0.448678\pi\) | |||||||
\(38\) | 0.437489 | 0.0709701 | ||||||||
\(39\) | 0.872557 | 0.139721 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.64124 | 0.256318 | 0.128159 | − | 0.991754i | \(-0.459093\pi\) | ||||
0.128159 | + | 0.991754i | \(0.459093\pi\) | |||||||
\(42\) | 7.10804 | 1.09679 | ||||||||
\(43\) | 10.2371 | 1.56115 | 0.780575 | − | 0.625063i | \(-0.214927\pi\) | ||||
0.780575 | + | 0.625063i | \(0.214927\pi\) | |||||||
\(44\) | −7.17045 | −1.08099 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.35688 | −0.642386 | ||||||||
\(47\) | −9.73665 | −1.42024 | −0.710118 | − | 0.704082i | \(-0.751359\pi\) | ||||
−0.710118 | + | 0.704082i | \(0.751359\pi\) | |||||||
\(48\) | 3.85314 | 0.556153 | ||||||||
\(49\) | 11.3080 | 1.61543 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.38161 | 0.613548 | ||||||||
\(52\) | −1.74735 | −0.242313 | ||||||||
\(53\) | 8.87850 | 1.21956 | 0.609778 | − | 0.792573i | \(-0.291259\pi\) | ||||
0.609778 | + | 0.792573i | \(0.291259\pi\) | |||||||
\(54\) | −8.73628 | −1.18886 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.27965 | 0.304631 | ||||||||
\(57\) | 0.195163 | 0.0258499 | ||||||||
\(58\) | 0.189262 | 0.0248514 | ||||||||
\(59\) | −12.3589 | −1.60899 | −0.804495 | − | 0.593959i | \(-0.797564\pi\) | ||||
−0.804495 | + | 0.593959i | \(0.797564\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.46892 | 0.700223 | 0.350112 | − | 0.936708i | \(-0.386144\pi\) | ||||
0.350112 | + | 0.936708i | \(0.386144\pi\) | |||||||
\(62\) | −9.72554 | −1.23514 | ||||||||
\(63\) | −9.66547 | −1.21774 | ||||||||
\(64\) | −5.65989 | −0.707486 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.90973 | −0.850528 | ||||||||
\(67\) | 5.19583 | 0.634772 | 0.317386 | − | 0.948296i | \(-0.397195\pi\) | ||||
0.317386 | + | 0.948296i | \(0.397195\pi\) | |||||||
\(68\) | −8.77443 | −1.06406 | ||||||||
\(69\) | −1.94359 | −0.233981 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.82517 | 0.335287 | 0.167643 | − | 0.985848i | \(-0.446384\pi\) | ||||
0.167643 | + | 0.985848i | \(0.446384\pi\) | |||||||
\(72\) | −1.20351 | −0.141835 | ||||||||
\(73\) | −12.6670 | −1.48256 | −0.741280 | − | 0.671195i | \(-0.765781\pi\) | ||||
−0.741280 | + | 0.671195i | \(0.765781\pi\) | |||||||
\(74\) | −3.76874 | −0.438108 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.390825 | −0.0448307 | ||||||||
\(77\) | −17.7972 | −2.02818 | ||||||||
\(78\) | −1.68381 | −0.190654 | ||||||||
\(79\) | −6.82909 | −0.768333 | −0.384167 | − | 0.923264i | \(-0.625511\pi\) | ||||
−0.384167 | + | 0.923264i | \(0.625511\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.87955 | 0.319950 | ||||||||
\(82\) | −3.16717 | −0.349755 | ||||||||
\(83\) | −0.598091 | −0.0656491 | −0.0328245 | − | 0.999461i | \(-0.510450\pi\) | ||||
−0.0328245 | + | 0.999461i | \(0.510450\pi\) | |||||||
\(84\) | −6.34987 | −0.692828 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −19.7551 | −2.13024 | ||||||||
\(87\) | 0.0844295 | 0.00905180 | ||||||||
\(88\) | −2.21605 | −0.236232 | ||||||||
\(89\) | 4.03281 | 0.427477 | 0.213739 | − | 0.976891i | \(-0.431436\pi\) | ||||
0.213739 | + | 0.976891i | \(0.431436\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.33695 | −0.454636 | ||||||||
\(92\) | 3.89216 | 0.405786 | ||||||||
\(93\) | −4.33854 | −0.449886 | ||||||||
\(94\) | 18.7892 | 1.93796 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −6.51829 | −0.665270 | ||||||||
\(97\) | 6.64220 | 0.674413 | 0.337207 | − | 0.941431i | \(-0.390518\pi\) | ||||
0.337207 | + | 0.941431i | \(0.390518\pi\) | |||||||
\(98\) | −21.8215 | −2.20431 | ||||||||
\(99\) | 9.39581 | 0.944315 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.208478 | 0.0207443 | 0.0103722 | − | 0.999946i | \(-0.496698\pi\) | ||||
0.0103722 | + | 0.999946i | \(0.496698\pi\) | |||||||
\(102\) | −8.45538 | −0.837208 | ||||||||
\(103\) | 2.18940 | 0.215728 | 0.107864 | − | 0.994166i | \(-0.465599\pi\) | ||||
0.107864 | + | 0.994166i | \(0.465599\pi\) | |||||||
\(104\) | −0.540023 | −0.0529536 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −17.1332 | −1.66413 | ||||||||
\(107\) | 13.9628 | 1.34983 | 0.674916 | − | 0.737895i | \(-0.264180\pi\) | ||||
0.674916 | + | 0.737895i | \(0.264180\pi\) | |||||||
\(108\) | 7.80444 | 0.750983 | ||||||||
\(109\) | −16.7010 | −1.59967 | −0.799833 | − | 0.600222i | \(-0.795079\pi\) | ||||
−0.799833 | + | 0.600222i | \(0.795079\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.68123 | −0.159575 | ||||||||
\(112\) | −19.1516 | −1.80966 | ||||||||
\(113\) | −14.9373 | −1.40518 | −0.702592 | − | 0.711593i | \(-0.747974\pi\) | ||||
−0.702592 | + | 0.711593i | \(0.747974\pi\) | |||||||
\(114\) | −0.376614 | −0.0352732 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.169075 | −0.0156982 | ||||||||
\(117\) | 2.28964 | 0.211677 | ||||||||
\(118\) | 23.8495 | 2.19552 | ||||||||
\(119\) | −21.7783 | −1.99642 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.30067 | 0.572788 | ||||||||
\(122\) | −10.5536 | −0.955479 | ||||||||
\(123\) | −1.41287 | −0.127394 | ||||||||
\(124\) | 8.68818 | 0.780222 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 18.6519 | 1.66164 | ||||||||
\(127\) | 7.99709 | 0.709627 | 0.354813 | − | 0.934937i | \(-0.384544\pi\) | ||||
0.354813 | + | 0.934937i | \(0.384544\pi\) | |||||||
\(128\) | −4.22163 | −0.373143 | ||||||||
\(129\) | −8.81269 | −0.775914 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.04129 | 0.0909775 | 0.0454887 | − | 0.998965i | \(-0.485515\pi\) | ||||
0.0454887 | + | 0.998965i | \(0.485515\pi\) | |||||||
\(132\) | 6.17271 | 0.537266 | ||||||||
\(133\) | −0.970036 | −0.0841128 | ||||||||
\(134\) | −10.0266 | −0.866168 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.71177 | −0.232532 | ||||||||
\(137\) | −0.348409 | −0.0297666 | −0.0148833 | − | 0.999889i | \(-0.504738\pi\) | ||||
−0.0148833 | + | 0.999889i | \(0.504738\pi\) | |||||||
\(138\) | 3.75064 | 0.319275 | ||||||||
\(139\) | 0.755352 | 0.0640681 | 0.0320340 | − | 0.999487i | \(-0.489802\pi\) | ||||
0.0320340 | + | 0.999487i | \(0.489802\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.38184 | 0.705878 | ||||||||
\(142\) | −5.45186 | −0.457510 | ||||||||
\(143\) | 4.21595 | 0.352555 | ||||||||
\(144\) | 10.1109 | 0.842572 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 24.4441 | 2.02301 | ||||||||
\(147\) | −9.73453 | −0.802891 | ||||||||
\(148\) | 3.36676 | 0.276746 | ||||||||
\(149\) | −17.7229 | −1.45192 | −0.725958 | − | 0.687739i | \(-0.758604\pi\) | ||||
−0.725958 | + | 0.687739i | \(0.758604\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.38376 | 0.600882 | 0.300441 | − | 0.953800i | \(-0.402866\pi\) | ||||
0.300441 | + | 0.953800i | \(0.402866\pi\) | |||||||
\(152\) | −0.120786 | −0.00979702 | ||||||||
\(153\) | 11.4976 | 0.929525 | ||||||||
\(154\) | 34.3441 | 2.76752 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.50421 | 0.120433 | ||||||||
\(157\) | −2.53136 | −0.202024 | −0.101012 | − | 0.994885i | \(-0.532208\pi\) | ||||
−0.101012 | + | 0.994885i | \(0.532208\pi\) | |||||||
\(158\) | 13.1784 | 1.04842 | ||||||||
\(159\) | −7.64309 | −0.606137 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.66042 | 0.761348 | ||||||||
\(162\) | −5.55680 | −0.436584 | ||||||||
\(163\) | 5.60586 | 0.439085 | 0.219543 | − | 0.975603i | \(-0.429544\pi\) | ||||
0.219543 | + | 0.975603i | \(0.429544\pi\) | |||||||
\(164\) | 2.82935 | 0.220935 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.15416 | 0.0895804 | ||||||||
\(167\) | 14.9994 | 1.16069 | 0.580344 | − | 0.814372i | \(-0.302918\pi\) | ||||
0.580344 | + | 0.814372i | \(0.302918\pi\) | |||||||
\(168\) | −1.96245 | −0.151406 | ||||||||
\(169\) | −11.9726 | −0.920971 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.512118 | 0.0391627 | ||||||||
\(172\) | 17.6479 | 1.34564 | ||||||||
\(173\) | 14.1212 | 1.07362 | 0.536808 | − | 0.843704i | \(-0.319630\pi\) | ||||
0.536808 | + | 0.843704i | \(0.319630\pi\) | |||||||
\(174\) | −0.162927 | −0.0123515 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 18.6173 | 1.40333 | ||||||||
\(177\) | 10.6392 | 0.799692 | ||||||||
\(178\) | −7.78229 | −0.583307 | ||||||||
\(179\) | −23.0755 | −1.72474 | −0.862372 | − | 0.506275i | \(-0.831022\pi\) | ||||
−0.862372 | + | 0.506275i | \(0.831022\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.2453 | −0.984517 | −0.492258 | − | 0.870449i | \(-0.663829\pi\) | ||||
−0.492258 | + | 0.870449i | \(0.663829\pi\) | |||||||
\(182\) | 8.36920 | 0.620366 | ||||||||
\(183\) | −4.70794 | −0.348021 | ||||||||
\(184\) | 1.20288 | 0.0886778 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 8.37227 | 0.613885 | ||||||||
\(187\) | 21.1707 | 1.54816 | ||||||||
\(188\) | −16.7851 | −1.22418 | ||||||||
\(189\) | 19.3708 | 1.40902 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.9302 | 1.58681 | 0.793406 | − | 0.608693i | \(-0.208306\pi\) | ||||
0.793406 | + | 0.608693i | \(0.208306\pi\) | |||||||
\(192\) | 4.87234 | 0.351631 | ||||||||
\(193\) | −20.0677 | −1.44450 | −0.722252 | − | 0.691630i | \(-0.756893\pi\) | ||||
−0.722252 | + | 0.691630i | \(0.756893\pi\) | |||||||
\(194\) | −12.8177 | −0.920260 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 19.4940 | 1.39243 | ||||||||
\(197\) | −15.4880 | −1.10348 | −0.551738 | − | 0.834017i | \(-0.686035\pi\) | ||||
−0.551738 | + | 0.834017i | \(0.686035\pi\) | |||||||
\(198\) | −18.1315 | −1.28855 | ||||||||
\(199\) | −12.6164 | −0.894354 | −0.447177 | − | 0.894445i | \(-0.647571\pi\) | ||||
−0.447177 | + | 0.894445i | \(0.647571\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.47285 | −0.315491 | ||||||||
\(202\) | −0.402309 | −0.0283063 | ||||||||
\(203\) | −0.419648 | −0.0294535 | ||||||||
\(204\) | 7.55350 | 0.528851 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.22498 | −0.294368 | ||||||||
\(207\) | −5.10010 | −0.354481 | ||||||||
\(208\) | 4.53680 | 0.314570 | ||||||||
\(209\) | 0.942972 | 0.0652268 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.4401 | 1.06294 | 0.531470 | − | 0.847077i | \(-0.321640\pi\) | ||||
0.531470 | + | 0.847077i | \(0.321640\pi\) | |||||||
\(212\) | 15.3057 | 1.05120 | ||||||||
\(213\) | −2.43206 | −0.166642 | ||||||||
\(214\) | −26.9446 | −1.84189 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.41199 | 0.164115 | ||||||||
\(217\) | 21.5643 | 1.46388 | ||||||||
\(218\) | 32.2287 | 2.18280 | ||||||||
\(219\) | 10.9044 | 0.736854 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.15903 | 0.347034 | ||||||||
\(222\) | 3.24434 | 0.217746 | ||||||||
\(223\) | −4.61995 | −0.309375 | −0.154687 | − | 0.987963i | \(-0.549437\pi\) | ||||
−0.154687 | + | 0.987963i | \(0.549437\pi\) | |||||||
\(224\) | 32.3984 | 2.16471 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 28.8252 | 1.91742 | ||||||||
\(227\) | −15.7557 | −1.04574 | −0.522870 | − | 0.852413i | \(-0.675139\pi\) | ||||
−0.522870 | + | 0.852413i | \(0.675139\pi\) | |||||||
\(228\) | 0.336443 | 0.0222815 | ||||||||
\(229\) | 10.3167 | 0.681744 | 0.340872 | − | 0.940110i | \(-0.389278\pi\) | ||||
0.340872 | + | 0.940110i | \(0.389278\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 15.3208 | 1.00803 | ||||||||
\(232\) | −0.0522532 | −0.00343059 | ||||||||
\(233\) | 28.7950 | 1.88642 | 0.943210 | − | 0.332197i | \(-0.107790\pi\) | ||||
0.943210 | + | 0.332197i | \(0.107790\pi\) | |||||||
\(234\) | −4.41841 | −0.288841 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −21.3056 | −1.38688 | ||||||||
\(237\) | 5.87885 | 0.381873 | ||||||||
\(238\) | 42.0266 | 2.72418 | ||||||||
\(239\) | 2.11916 | 0.137077 | 0.0685385 | − | 0.997648i | \(-0.478166\pi\) | ||||
0.0685385 | + | 0.997648i | \(0.478166\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −0.0644157 | ||||||||
\(242\) | −12.1587 | −0.781590 | ||||||||
\(243\) | −16.0604 | −1.03027 | ||||||||
\(244\) | 9.42793 | 0.603561 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.72647 | 0.173833 | ||||||||
\(247\) | 0.229790 | 0.0146212 | ||||||||
\(248\) | 2.68511 | 0.170505 | ||||||||
\(249\) | 0.514869 | 0.0326285 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.7992 | 0.934116 | 0.467058 | − | 0.884227i | \(-0.345314\pi\) | ||||
0.467058 | + | 0.884227i | \(0.345314\pi\) | |||||||
\(252\) | −16.6624 | −1.04963 | ||||||||
\(253\) | −9.39090 | −0.590401 | ||||||||
\(254\) | −15.4323 | −0.968310 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.4664 | 1.21665 | ||||||||
\(257\) | −3.44087 | −0.214635 | −0.107318 | − | 0.994225i | \(-0.534226\pi\) | ||||
−0.107318 | + | 0.994225i | \(0.534226\pi\) | |||||||
\(258\) | 17.0062 | 1.05876 | ||||||||
\(259\) | 8.35636 | 0.519239 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.221548 | 0.0137135 | ||||||||
\(262\) | −2.00941 | −0.124142 | ||||||||
\(263\) | −15.0960 | −0.930856 | −0.465428 | − | 0.885086i | \(-0.654100\pi\) | ||||
−0.465428 | + | 0.885086i | \(0.654100\pi\) | |||||||
\(264\) | 1.90770 | 0.117411 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.87192 | 0.114775 | ||||||||
\(267\) | −3.47166 | −0.212462 | ||||||||
\(268\) | 8.95715 | 0.547145 | ||||||||
\(269\) | −19.7140 | −1.20198 | −0.600990 | − | 0.799256i | \(-0.705227\pi\) | ||||
−0.600990 | + | 0.799256i | \(0.705227\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.40136 | 0.388855 | 0.194427 | − | 0.980917i | \(-0.437715\pi\) | ||||
0.194427 | + | 0.980917i | \(0.437715\pi\) | |||||||
\(272\) | 22.7819 | 1.38135 | ||||||||
\(273\) | 3.73348 | 0.225961 | ||||||||
\(274\) | 0.672341 | 0.0406176 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.35058 | −0.201681 | ||||||||
\(277\) | −0.0900030 | −0.00540775 | −0.00270388 | − | 0.999996i | \(-0.500861\pi\) | ||||
−0.00270388 | + | 0.999996i | \(0.500861\pi\) | |||||||
\(278\) | −1.45763 | −0.0874231 | ||||||||
\(279\) | −11.3846 | −0.681577 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −32.2937 | −1.92648 | −0.963241 | − | 0.268639i | \(-0.913426\pi\) | ||||
−0.963241 | + | 0.268639i | \(0.913426\pi\) | |||||||
\(282\) | −16.1748 | −0.963196 | ||||||||
\(283\) | 20.5936 | 1.22416 | 0.612082 | − | 0.790794i | \(-0.290332\pi\) | ||||
0.612082 | + | 0.790794i | \(0.290332\pi\) | |||||||
\(284\) | 4.87035 | 0.289002 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.13570 | −0.481074 | ||||||||
\(287\) | 7.02250 | 0.414525 | ||||||||
\(288\) | −17.1043 | −1.00788 | ||||||||
\(289\) | 8.90645 | 0.523909 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.71797 | −0.335193 | ||||||||
\(292\) | −21.8368 | −1.27790 | ||||||||
\(293\) | −30.9657 | −1.80904 | −0.904519 | − | 0.426433i | \(-0.859770\pi\) | ||||
−0.904519 | + | 0.426433i | \(0.859770\pi\) | |||||||
\(294\) | 18.7852 | 1.09557 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.04051 | 0.0604782 | ||||||||
\(297\) | −18.8304 | −1.09265 | ||||||||
\(298\) | 34.2007 | 1.98119 | ||||||||
\(299\) | −2.28844 | −0.132344 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 43.8025 | 2.52474 | ||||||||
\(302\) | −14.2488 | −0.819924 | ||||||||
\(303\) | −0.179469 | −0.0103102 | ||||||||
\(304\) | 1.01474 | 0.0581991 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −22.1874 | −1.26837 | ||||||||
\(307\) | 5.68955 | 0.324720 | 0.162360 | − | 0.986732i | \(-0.448089\pi\) | ||||
0.162360 | + | 0.986732i | \(0.448089\pi\) | |||||||
\(308\) | −30.6808 | −1.74820 | ||||||||
\(309\) | −1.88475 | −0.107220 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.2738 | 0.582571 | 0.291285 | − | 0.956636i | \(-0.405917\pi\) | ||||
0.291285 | + | 0.956636i | \(0.405917\pi\) | |||||||
\(312\) | 0.464881 | 0.0263187 | ||||||||
\(313\) | 6.76087 | 0.382147 | 0.191074 | − | 0.981576i | \(-0.438803\pi\) | ||||
0.191074 | + | 0.981576i | \(0.438803\pi\) | |||||||
\(314\) | 4.88487 | 0.275669 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.7728 | −0.662269 | ||||||||
\(317\) | −13.1784 | −0.740175 | −0.370088 | − | 0.928997i | \(-0.620672\pi\) | ||||
−0.370088 | + | 0.928997i | \(0.620672\pi\) | |||||||
\(318\) | 14.7492 | 0.827095 | ||||||||
\(319\) | 0.407940 | 0.0228403 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.0199 | −0.670886 | ||||||||
\(322\) | −18.6421 | −1.03889 | ||||||||
\(323\) | 1.15391 | 0.0642052 | ||||||||
\(324\) | 4.96410 | 0.275783 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −10.8179 | −0.599147 | ||||||||
\(327\) | 14.3771 | 0.795057 | ||||||||
\(328\) | 0.874419 | 0.0482817 | ||||||||
\(329\) | −41.6610 | −2.29685 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.3929 | −1.50565 | −0.752824 | − | 0.658222i | \(-0.771309\pi\) | ||||
−0.752824 | + | 0.658222i | \(0.771309\pi\) | |||||||
\(332\) | −1.03106 | −0.0565866 | ||||||||
\(333\) | −4.41164 | −0.241756 | ||||||||
\(334\) | −28.9450 | −1.58380 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 16.4868 | 0.899427 | ||||||||
\(337\) | −0.450778 | −0.0245554 | −0.0122777 | − | 0.999925i | \(-0.503908\pi\) | ||||
−0.0122777 | + | 0.999925i | \(0.503908\pi\) | |||||||
\(338\) | 23.1041 | 1.25670 | ||||||||
\(339\) | 12.8589 | 0.698397 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −20.9626 | −1.13519 | ||||||||
\(342\) | −0.988257 | −0.0534388 | ||||||||
\(343\) | 18.4330 | 0.995287 | ||||||||
\(344\) | 5.45415 | 0.294068 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −27.2503 | −1.46499 | ||||||||
\(347\) | −11.8401 | −0.635610 | −0.317805 | − | 0.948156i | \(-0.602946\pi\) | ||||
−0.317805 | + | 0.948156i | \(0.602946\pi\) | |||||||
\(348\) | 0.145549 | 0.00780225 | ||||||||
\(349\) | 16.6656 | 0.892087 | 0.446044 | − | 0.895011i | \(-0.352833\pi\) | ||||
0.446044 | + | 0.895011i | \(0.352833\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.58871 | −0.244927 | ||||||||
\(352\) | −31.4945 | −1.67866 | ||||||||
\(353\) | −23.4430 | −1.24775 | −0.623873 | − | 0.781526i | \(-0.714442\pi\) | ||||
−0.623873 | + | 0.781526i | \(0.714442\pi\) | |||||||
\(354\) | −20.5309 | −1.09121 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.95221 | 0.368466 | ||||||||
\(357\) | 18.7480 | 0.992247 | ||||||||
\(358\) | 44.5298 | 2.35347 | ||||||||
\(359\) | −20.3446 | −1.07375 | −0.536875 | − | 0.843662i | \(-0.680395\pi\) | ||||
−0.536875 | + | 0.843662i | \(0.680395\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9486 | −0.997295 | ||||||||
\(362\) | 25.5601 | 1.34341 | ||||||||
\(363\) | −5.42396 | −0.284684 | ||||||||
\(364\) | −7.47652 | −0.391876 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 9.08512 | 0.474887 | ||||||||
\(367\) | −33.0454 | −1.72495 | −0.862477 | − | 0.506096i | \(-0.831088\pi\) | ||||
−0.862477 | + | 0.506096i | \(0.831088\pi\) | |||||||
\(368\) | −10.1056 | −0.526790 | ||||||||
\(369\) | −3.70744 | −0.193002 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 37.9892 | 1.97230 | ||||||||
\(372\) | −7.47926 | −0.387782 | ||||||||
\(373\) | −24.2843 | −1.25740 | −0.628698 | − | 0.777650i | \(-0.716412\pi\) | ||||
−0.628698 | + | 0.777650i | \(0.716412\pi\) | |||||||
\(374\) | −40.8541 | −2.11251 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.18750 | −0.267525 | ||||||||
\(377\) | 0.0994097 | 0.00511986 | ||||||||
\(378\) | −37.3807 | −1.92265 | ||||||||
\(379\) | −26.0547 | −1.33834 | −0.669170 | − | 0.743110i | \(-0.733350\pi\) | ||||
−0.669170 | + | 0.743110i | \(0.733350\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.88433 | −0.352695 | ||||||||
\(382\) | −42.3196 | −2.16526 | ||||||||
\(383\) | −23.6290 | −1.20738 | −0.603692 | − | 0.797218i | \(-0.706304\pi\) | ||||
−0.603692 | + | 0.797218i | \(0.706304\pi\) | |||||||
\(384\) | 3.63421 | 0.185457 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 38.7255 | 1.97108 | ||||||||
\(387\) | −23.1250 | −1.17551 | ||||||||
\(388\) | 11.4506 | 0.581314 | ||||||||
\(389\) | 25.6016 | 1.29805 | 0.649026 | − | 0.760766i | \(-0.275176\pi\) | ||||
0.649026 | + | 0.760766i | \(0.275176\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.4916 | −0.581154 | ||||||||
\(392\) | 6.02468 | 0.304292 | ||||||||
\(393\) | −0.896395 | −0.0452171 | ||||||||
\(394\) | 29.8879 | 1.50573 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 16.1975 | 0.813957 | ||||||||
\(397\) | −3.25969 | −0.163599 | −0.0817996 | − | 0.996649i | \(-0.526067\pi\) | ||||
−0.0817996 | + | 0.996649i | \(0.526067\pi\) | |||||||
\(398\) | 24.3465 | 1.22038 | ||||||||
\(399\) | 0.835060 | 0.0418053 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.9043 | −1.39347 | −0.696736 | − | 0.717327i | \(-0.745365\pi\) | ||||
−0.696736 | + | 0.717327i | \(0.745365\pi\) | |||||||
\(402\) | 8.63146 | 0.430498 | ||||||||
\(403\) | −5.10832 | −0.254463 | ||||||||
\(404\) | 0.359397 | 0.0178807 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.809813 | 0.0401904 | ||||||||
\(407\) | −8.12322 | −0.402653 | ||||||||
\(408\) | 2.33443 | 0.115572 | ||||||||
\(409\) | 2.75895 | 0.136421 | 0.0682107 | − | 0.997671i | \(-0.478271\pi\) | ||||
0.0682107 | + | 0.997671i | \(0.478271\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.299930 | 0.0147944 | ||||||||
\(412\) | 3.77433 | 0.185948 | ||||||||
\(413\) | −52.8810 | −2.60211 | ||||||||
\(414\) | 9.84188 | 0.483702 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7.67481 | −0.376289 | ||||||||
\(417\) | −0.650248 | −0.0318428 | ||||||||
\(418\) | −1.81970 | −0.0890042 | ||||||||
\(419\) | 6.53907 | 0.319454 | 0.159727 | − | 0.987161i | \(-0.448939\pi\) | ||||
0.159727 | + | 0.987161i | \(0.448939\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.0767 | −0.929741 | −0.464871 | − | 0.885379i | \(-0.653899\pi\) | ||||
−0.464871 | + | 0.885379i | \(0.653899\pi\) | |||||||
\(422\) | −29.7954 | −1.45042 | ||||||||
\(423\) | 21.9944 | 1.06941 | ||||||||
\(424\) | 4.73029 | 0.229723 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.69326 | 0.227389 | ||||||||
\(427\) | 23.4003 | 1.13242 | ||||||||
\(428\) | 24.0706 | 1.16349 | ||||||||
\(429\) | −3.62932 | −0.175225 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.2304 | 0.589117 | 0.294559 | − | 0.955633i | \(-0.404827\pi\) | ||||
0.294559 | + | 0.955633i | \(0.404827\pi\) | |||||||
\(432\) | −20.2634 | −0.974924 | ||||||||
\(433\) | 36.0938 | 1.73456 | 0.867278 | − | 0.497824i | \(-0.165868\pi\) | ||||
0.867278 | + | 0.497824i | \(0.165868\pi\) | |||||||
\(434\) | −41.6135 | −1.99751 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −28.7911 | −1.37884 | ||||||||
\(437\) | −0.511850 | −0.0244851 | ||||||||
\(438\) | −21.0428 | −1.00546 | ||||||||
\(439\) | 22.7319 | 1.08494 | 0.542468 | − | 0.840077i | \(-0.317490\pi\) | ||||
0.542468 | + | 0.840077i | \(0.317490\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −25.5440 | −1.21638 | ||||||||
\(442\) | −9.95560 | −0.473540 | ||||||||
\(443\) | 35.9263 | 1.70691 | 0.853454 | − | 0.521168i | \(-0.174503\pi\) | ||||
0.853454 | + | 0.521168i | \(0.174503\pi\) | |||||||
\(444\) | −2.89829 | −0.137547 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8.91531 | 0.422152 | ||||||||
\(447\) | 15.2568 | 0.721624 | ||||||||
\(448\) | −24.2174 | −1.14417 | ||||||||
\(449\) | 32.4537 | 1.53159 | 0.765793 | − | 0.643088i | \(-0.222347\pi\) | ||||
0.765793 | + | 0.643088i | \(0.222347\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.82658 | −0.321451 | ||||||||
\(452\) | −25.7506 | −1.21121 | ||||||||
\(453\) | −6.35634 | −0.298647 | ||||||||
\(454\) | 30.4044 | 1.42695 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.103979 | 0.00486926 | ||||||||
\(457\) | 19.2139 | 0.898787 | 0.449394 | − | 0.893334i | \(-0.351640\pi\) | ||||
0.449394 | + | 0.893334i | \(0.351640\pi\) | |||||||
\(458\) | −19.9085 | −0.930263 | ||||||||
\(459\) | −23.0426 | −1.07554 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −39.6176 | −1.84517 | −0.922587 | − | 0.385789i | \(-0.873929\pi\) | ||||
−0.922587 | + | 0.385789i | \(0.873929\pi\) | |||||||
\(462\) | −29.5652 | −1.37550 | ||||||||
\(463\) | 9.54990 | 0.443821 | 0.221911 | − | 0.975067i | \(-0.428771\pi\) | ||||
0.221911 | + | 0.975067i | \(0.428771\pi\) | |||||||
\(464\) | 0.438986 | 0.0203794 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −55.5669 | −2.57409 | ||||||||
\(467\) | 15.3884 | 0.712089 | 0.356044 | − | 0.934469i | \(-0.384125\pi\) | ||||
0.356044 | + | 0.934469i | \(0.384125\pi\) | |||||||
\(468\) | 3.94713 | 0.182456 | ||||||||
\(469\) | 22.2318 | 1.02657 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.17913 | 0.100409 | ||||||||
\(472\) | −6.58457 | −0.303080 | ||||||||
\(473\) | −42.5804 | −1.95785 | ||||||||
\(474\) | −11.3447 | −0.521079 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −37.5439 | −1.72082 | ||||||||
\(477\) | −20.0559 | −0.918297 | ||||||||
\(478\) | −4.08943 | −0.187046 | ||||||||
\(479\) | −12.3599 | −0.564738 | −0.282369 | − | 0.959306i | \(-0.591120\pi\) | ||||
−0.282369 | + | 0.959306i | \(0.591120\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.97952 | −0.0902585 | ||||||||
\(482\) | 1.92974 | 0.0878974 | ||||||||
\(483\) | −8.31621 | −0.378401 | ||||||||
\(484\) | 10.8618 | 0.493718 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 30.9924 | 1.40585 | ||||||||
\(487\) | −13.2006 | −0.598176 | −0.299088 | − | 0.954226i | \(-0.596682\pi\) | ||||
−0.299088 | + | 0.954226i | \(0.596682\pi\) | |||||||
\(488\) | 2.91373 | 0.131898 | ||||||||
\(489\) | −4.82583 | −0.218232 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.26409 | 0.0570475 | 0.0285237 | − | 0.999593i | \(-0.490919\pi\) | ||||
0.0285237 | + | 0.999593i | \(0.490919\pi\) | |||||||
\(492\) | −2.43566 | −0.109808 | ||||||||
\(493\) | 0.499193 | 0.0224825 | ||||||||
\(494\) | −0.443436 | −0.0199511 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −22.5579 | −1.01288 | ||||||||
\(497\) | 12.0883 | 0.542235 | ||||||||
\(498\) | −0.993566 | −0.0445228 | ||||||||
\(499\) | −15.3594 | −0.687582 | −0.343791 | − | 0.939046i | \(-0.611711\pi\) | ||||
−0.343791 | + | 0.939046i | \(0.611711\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.9123 | −0.576878 | ||||||||
\(502\) | −28.5586 | −1.27463 | ||||||||
\(503\) | 34.7267 | 1.54839 | 0.774194 | − | 0.632949i | \(-0.218156\pi\) | ||||
0.774194 | + | 0.632949i | \(0.218156\pi\) | |||||||
\(504\) | −5.14957 | −0.229380 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 18.1220 | 0.805622 | ||||||||
\(507\) | 10.3067 | 0.457736 | ||||||||
\(508\) | 13.7863 | 0.611667 | ||||||||
\(509\) | −1.23400 | −0.0546960 | −0.0273480 | − | 0.999626i | \(-0.508706\pi\) | ||||
−0.0273480 | + | 0.999626i | \(0.508706\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −54.1994 | −2.39764 | ||||||||
\(512\) | −29.1220 | −1.28702 | ||||||||
\(513\) | −1.02635 | −0.0453144 | ||||||||
\(514\) | 6.63999 | 0.292877 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −15.1923 | −0.668803 | ||||||||
\(517\) | 40.4987 | 1.78113 | ||||||||
\(518\) | −16.1256 | −0.708520 | ||||||||
\(519\) | −12.1563 | −0.533603 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 41.5523 | 1.82044 | 0.910219 | − | 0.414128i | \(-0.135913\pi\) | ||||
0.910219 | + | 0.414128i | \(0.135913\pi\) | |||||||
\(522\) | −0.427531 | −0.0187125 | ||||||||
\(523\) | 1.16999 | 0.0511601 | 0.0255801 | − | 0.999673i | \(-0.491857\pi\) | ||||
0.0255801 | + | 0.999673i | \(0.491857\pi\) | |||||||
\(524\) | 1.79508 | 0.0784186 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 29.1313 | 1.27019 | ||||||||
\(527\) | −25.6518 | −1.11741 | ||||||||
\(528\) | −16.0268 | −0.697477 | ||||||||
\(529\) | −17.9026 | −0.778373 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 27.9179 | 1.21153 | ||||||||
\(532\) | −1.67226 | −0.0725015 | ||||||||
\(533\) | −1.66355 | −0.0720563 | ||||||||
\(534\) | 6.69942 | 0.289912 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.76824 | 0.119570 | ||||||||
\(537\) | 19.8646 | 0.857223 | ||||||||
\(538\) | 38.0429 | 1.64014 | ||||||||
\(539\) | −47.0346 | −2.02592 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.4142 | 0.576722 | 0.288361 | − | 0.957522i | \(-0.406890\pi\) | ||||
0.288361 | + | 0.957522i | \(0.406890\pi\) | |||||||
\(542\) | −12.3530 | −0.530606 | ||||||||
\(543\) | 11.4023 | 0.489319 | ||||||||
\(544\) | −38.5396 | −1.65237 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −7.20466 | −0.308331 | ||||||||
\(547\) | −15.1917 | −0.649550 | −0.324775 | − | 0.945791i | \(-0.605289\pi\) | ||||
−0.324775 | + | 0.945791i | \(0.605289\pi\) | |||||||
\(548\) | −0.600627 | −0.0256575 | ||||||||
\(549\) | −12.3539 | −0.527252 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.0222348 | 0.000947232 0 | ||||||||
\(552\) | −1.03551 | −0.0440741 | ||||||||
\(553\) | −29.2202 | −1.24257 | ||||||||
\(554\) | 0.173683 | 0.00737907 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.30216 | 0.0552238 | ||||||||
\(557\) | −39.8802 | −1.68978 | −0.844888 | − | 0.534943i | \(-0.820333\pi\) | ||||
−0.844888 | + | 0.534943i | \(0.820333\pi\) | |||||||
\(558\) | 21.9693 | 0.930035 | ||||||||
\(559\) | −10.3763 | −0.438871 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.2249 | −0.769456 | ||||||||
\(562\) | 62.3186 | 2.62875 | ||||||||
\(563\) | −0.395018 | −0.0166480 | −0.00832401 | − | 0.999965i | \(-0.502650\pi\) | ||||
−0.00832401 | + | 0.999965i | \(0.502650\pi\) | |||||||
\(564\) | 14.4495 | 0.608436 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −39.7404 | −1.67042 | ||||||||
\(567\) | 12.3210 | 0.517433 | ||||||||
\(568\) | 1.50520 | 0.0631567 | ||||||||
\(569\) | 0.348736 | 0.0146198 | 0.00730989 | − | 0.999973i | \(-0.497673\pi\) | ||||
0.00730989 | + | 0.999973i | \(0.497673\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.4391 | 1.77602 | 0.888010 | − | 0.459825i | \(-0.152088\pi\) | ||||
0.888010 | + | 0.459825i | \(0.152088\pi\) | |||||||
\(572\) | 7.26792 | 0.303887 | ||||||||
\(573\) | −18.8787 | −0.788668 | ||||||||
\(574\) | −13.5516 | −0.565634 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 12.7853 | 0.532720 | ||||||||
\(577\) | −12.1367 | −0.505257 | −0.252628 | − | 0.967563i | \(-0.581295\pi\) | ||||
−0.252628 | + | 0.967563i | \(0.581295\pi\) | |||||||
\(578\) | −17.1872 | −0.714892 | ||||||||
\(579\) | 17.2754 | 0.717939 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.55910 | −0.106170 | ||||||||
\(582\) | 11.0342 | 0.457383 | ||||||||
\(583\) | −36.9293 | −1.52945 | ||||||||
\(584\) | −6.74873 | −0.279264 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 59.7560 | 2.46850 | ||||||||
\(587\) | −1.30593 | −0.0539013 | −0.0269507 | − | 0.999637i | \(-0.508580\pi\) | ||||
−0.0269507 | + | 0.999637i | \(0.508580\pi\) | |||||||
\(588\) | −16.7815 | −0.692056 | ||||||||
\(589\) | −1.14257 | −0.0470786 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.3329 | 0.548444 | ||||||||
\(592\) | −8.74143 | −0.359270 | ||||||||
\(593\) | 7.46971 | 0.306744 | 0.153372 | − | 0.988169i | \(-0.450987\pi\) | ||||
0.153372 | + | 0.988169i | \(0.450987\pi\) | |||||||
\(594\) | 36.3378 | 1.49096 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −30.5527 | −1.25149 | ||||||||
\(597\) | 10.8609 | 0.444507 | ||||||||
\(598\) | 4.41610 | 0.180588 | ||||||||
\(599\) | 20.9641 | 0.856569 | 0.428285 | − | 0.903644i | \(-0.359118\pi\) | ||||
0.428285 | + | 0.903644i | \(0.359118\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.4369 | −1.32313 | −0.661565 | − | 0.749888i | \(-0.730108\pi\) | ||||
−0.661565 | + | 0.749888i | \(0.730108\pi\) | |||||||
\(602\) | −84.5276 | −3.44509 | ||||||||
\(603\) | −11.7370 | −0.477968 | ||||||||
\(604\) | 12.7289 | 0.517933 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.346329 | 0.0140687 | ||||||||
\(607\) | −2.08203 | −0.0845071 | −0.0422536 | − | 0.999107i | \(-0.513454\pi\) | ||||
−0.0422536 | + | 0.999107i | \(0.513454\pi\) | |||||||
\(608\) | −1.71661 | −0.0696177 | ||||||||
\(609\) | 0.361256 | 0.0146388 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.86901 | 0.399257 | ||||||||
\(612\) | 19.8208 | 0.801209 | ||||||||
\(613\) | 18.2956 | 0.738953 | 0.369476 | − | 0.929240i | \(-0.379537\pi\) | ||||
0.369476 | + | 0.929240i | \(0.379537\pi\) | |||||||
\(614\) | −10.9794 | −0.443091 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.48200 | −0.382041 | ||||||||
\(617\) | −40.2177 | −1.61911 | −0.809553 | − | 0.587047i | \(-0.800290\pi\) | ||||
−0.809553 | + | 0.587047i | \(0.800290\pi\) | |||||||
\(618\) | 3.63709 | 0.146305 | ||||||||
\(619\) | −18.5221 | −0.744468 | −0.372234 | − | 0.928139i | \(-0.621408\pi\) | ||||
−0.372234 | + | 0.928139i | \(0.621408\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.2212 | 0.410163 | ||||||||
\(622\) | −19.8257 | −0.794938 | ||||||||
\(623\) | 17.2555 | 0.691328 | ||||||||
\(624\) | −3.90552 | −0.156346 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −13.0468 | −0.521453 | ||||||||
\(627\) | −0.811762 | −0.0324186 | ||||||||
\(628\) | −4.36383 | −0.174136 | ||||||||
\(629\) | −9.94033 | −0.396347 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.1932 | −0.644640 | −0.322320 | − | 0.946631i | \(-0.604463\pi\) | ||||
−0.322320 | + | 0.946631i | \(0.604463\pi\) | |||||||
\(632\) | −3.63841 | −0.144728 | ||||||||
\(633\) | −13.2917 | −0.528296 | ||||||||
\(634\) | 25.4310 | 1.01000 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −13.1760 | −0.522463 | ||||||||
\(637\) | −11.4617 | −0.454130 | ||||||||
\(638\) | −0.787220 | −0.0311663 | ||||||||
\(639\) | −6.38187 | −0.252463 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.5279 | −0.494823 | −0.247411 | − | 0.968911i | \(-0.579580\pi\) | ||||
−0.247411 | + | 0.968911i | \(0.579580\pi\) | |||||||
\(642\) | 23.1953 | 0.915447 | ||||||||
\(643\) | −3.68823 | −0.145450 | −0.0727248 | − | 0.997352i | \(-0.523169\pi\) | ||||
−0.0727248 | + | 0.997352i | \(0.523169\pi\) | |||||||
\(644\) | 16.6537 | 0.656248 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.22675 | −0.0876102 | ||||||||
\(647\) | 2.22030 | 0.0872889 | 0.0436445 | − | 0.999047i | \(-0.486103\pi\) | ||||
0.0436445 | + | 0.999047i | \(0.486103\pi\) | |||||||
\(648\) | 1.53417 | 0.0602679 | ||||||||
\(649\) | 51.4057 | 2.01785 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −18.5637 | −0.727568 | ||||||||
\(652\) | 9.66401 | 0.378472 | ||||||||
\(653\) | 11.1287 | 0.435499 | 0.217750 | − | 0.976005i | \(-0.430128\pi\) | ||||
0.217750 | + | 0.976005i | \(0.430128\pi\) | |||||||
\(654\) | −27.7442 | −1.08488 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −7.34610 | −0.286817 | ||||||||
\(657\) | 28.6139 | 1.11633 | ||||||||
\(658\) | 80.3951 | 3.13413 | ||||||||
\(659\) | −48.7913 | −1.90064 | −0.950320 | − | 0.311274i | \(-0.899244\pi\) | ||||
−0.950320 | + | 0.311274i | \(0.899244\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.83428 | 0.382509 | 0.191255 | − | 0.981540i | \(-0.438744\pi\) | ||||
0.191255 | + | 0.981540i | \(0.438744\pi\) | |||||||
\(662\) | 52.8612 | 2.05451 | ||||||||
\(663\) | −4.44117 | −0.172481 | ||||||||
\(664\) | −0.318651 | −0.0123661 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.51333 | 0.329885 | ||||||||
\(667\) | −0.221432 | −0.00857388 | ||||||||
\(668\) | 25.8576 | 1.00046 | ||||||||
\(669\) | 3.97710 | 0.153764 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.7475 | −0.878156 | ||||||||
\(672\) | −27.8903 | −1.07589 | ||||||||
\(673\) | −7.68732 | −0.296325 | −0.148162 | − | 0.988963i | \(-0.547336\pi\) | ||||
−0.148162 | + | 0.988963i | \(0.547336\pi\) | |||||||
\(674\) | 0.869886 | 0.0335068 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −20.6397 | −0.793837 | ||||||||
\(677\) | −14.6186 | −0.561840 | −0.280920 | − | 0.959731i | \(-0.590639\pi\) | ||||
−0.280920 | + | 0.959731i | \(0.590639\pi\) | |||||||
\(678\) | −24.8143 | −0.952987 | ||||||||
\(679\) | 28.4205 | 1.09068 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.5633 | 0.519748 | ||||||||
\(682\) | 40.4525 | 1.54901 | ||||||||
\(683\) | −27.4320 | −1.04966 | −0.524828 | − | 0.851209i | \(-0.675870\pi\) | ||||
−0.524828 | + | 0.851209i | \(0.675870\pi\) | |||||||
\(684\) | 0.882846 | 0.0337565 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −35.5709 | −1.35810 | ||||||||
\(687\) | −8.88113 | −0.338836 | ||||||||
\(688\) | −45.8210 | −1.74691 | ||||||||
\(689\) | −8.99919 | −0.342842 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.6077 | −0.783955 | −0.391977 | − | 0.919975i | \(-0.628209\pi\) | ||||
−0.391977 | + | 0.919975i | \(0.628209\pi\) | |||||||
\(692\) | 24.3437 | 0.925410 | ||||||||
\(693\) | 40.2026 | 1.52717 | ||||||||
\(694\) | 22.8484 | 0.867312 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.0449824 | 0.00170505 | ||||||||
\(697\) | −8.35364 | −0.316417 | ||||||||
\(698\) | −32.1603 | −1.21728 | ||||||||
\(699\) | −24.7883 | −0.937578 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.40290 | −0.166295 | −0.0831476 | − | 0.996537i | \(-0.526497\pi\) | ||||
−0.0831476 | + | 0.996537i | \(0.526497\pi\) | |||||||
\(702\) | 8.85504 | 0.334212 | ||||||||
\(703\) | −0.442756 | −0.0166989 | ||||||||
\(704\) | 23.5418 | 0.887264 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 45.2390 | 1.70259 | ||||||||
\(707\) | 0.892032 | 0.0335483 | ||||||||
\(708\) | 18.3410 | 0.689299 | ||||||||
\(709\) | 14.6396 | 0.549803 | 0.274901 | − | 0.961472i | \(-0.411355\pi\) | ||||
0.274901 | + | 0.961472i | \(0.411355\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.4264 | 0.578537 | ||||||||
\(712\) | 2.14860 | 0.0805223 | ||||||||
\(713\) | 11.3786 | 0.426133 | ||||||||
\(714\) | −36.1788 | −1.35396 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −39.7801 | −1.48665 | ||||||||
\(717\) | −1.82429 | −0.0681292 | ||||||||
\(718\) | 39.2599 | 1.46517 | ||||||||
\(719\) | −10.3659 | −0.386582 | −0.193291 | − | 0.981141i | \(-0.561916\pi\) | ||||
−0.193291 | + | 0.981141i | \(0.561916\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.36796 | 0.348881 | ||||||||
\(722\) | 36.5660 | 1.36084 | ||||||||
\(723\) | 0.860854 | 0.0320155 | ||||||||
\(724\) | −22.8338 | −0.848610 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 10.4669 | 0.388461 | ||||||||
\(727\) | 20.6367 | 0.765375 | 0.382687 | − | 0.923878i | \(-0.374999\pi\) | ||||
0.382687 | + | 0.923878i | \(0.374999\pi\) | |||||||
\(728\) | −2.31064 | −0.0856381 | ||||||||
\(729\) | 5.18699 | 0.192111 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −52.1054 | −1.92719 | ||||||||
\(732\) | −8.11607 | −0.299979 | ||||||||
\(733\) | 14.1693 | 0.523355 | 0.261677 | − | 0.965155i | \(-0.415724\pi\) | ||||
0.261677 | + | 0.965155i | \(0.415724\pi\) | |||||||
\(734\) | 63.7691 | 2.35376 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 17.0954 | 0.630145 | ||||||||
\(737\) | −21.6116 | −0.796073 | ||||||||
\(738\) | 7.15441 | 0.263358 | ||||||||
\(739\) | −50.7411 | −1.86654 | −0.933270 | − | 0.359175i | \(-0.883058\pi\) | ||||
−0.933270 | + | 0.359175i | \(0.883058\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.197816 | −0.00726695 | ||||||||
\(742\) | −73.3094 | −2.69127 | ||||||||
\(743\) | 12.3212 | 0.452020 | 0.226010 | − | 0.974125i | \(-0.427432\pi\) | ||||
0.226010 | + | 0.974125i | \(0.427432\pi\) | |||||||
\(744\) | −2.31149 | −0.0847433 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 46.8626 | 1.71576 | ||||||||
\(747\) | 1.35105 | 0.0494322 | ||||||||
\(748\) | 36.4964 | 1.33444 | ||||||||
\(749\) | 59.7436 | 2.18299 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.0863 | −0.514018 | −0.257009 | − | 0.966409i | \(-0.582737\pi\) | ||||
−0.257009 | + | 0.966409i | \(0.582737\pi\) | |||||||
\(752\) | 43.5808 | 1.58923 | ||||||||
\(753\) | −12.7399 | −0.464269 | ||||||||
\(754\) | −0.191835 | −0.00698623 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 33.3935 | 1.21451 | ||||||||
\(757\) | −39.3962 | −1.43188 | −0.715940 | − | 0.698162i | \(-0.754002\pi\) | ||||
−0.715940 | + | 0.698162i | \(0.754002\pi\) | |||||||
\(758\) | 50.2789 | 1.82621 | ||||||||
\(759\) | 8.08419 | 0.293438 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.4776 | −0.416064 | −0.208032 | − | 0.978122i | \(-0.566706\pi\) | ||||
−0.208032 | + | 0.978122i | \(0.566706\pi\) | |||||||
\(762\) | 13.2850 | 0.481264 | ||||||||
\(763\) | −71.4600 | −2.58703 | ||||||||
\(764\) | 37.8057 | 1.36776 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 45.5978 | 1.64752 | ||||||||
\(767\) | 12.5269 | 0.452320 | ||||||||
\(768\) | −16.7578 | −0.604694 | ||||||||
\(769\) | −23.4598 | −0.845983 | −0.422991 | − | 0.906134i | \(-0.639020\pi\) | ||||
−0.422991 | + | 0.906134i | \(0.639020\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.96208 | 0.106677 | ||||||||
\(772\) | −34.5949 | −1.24510 | ||||||||
\(773\) | 43.3955 | 1.56083 | 0.780414 | − | 0.625263i | \(-0.215008\pi\) | ||||
0.780414 | + | 0.625263i | \(0.215008\pi\) | |||||||
\(774\) | 44.6253 | 1.60402 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.53883 | 0.127037 | ||||||||
\(777\) | −7.19361 | −0.258069 | ||||||||
\(778\) | −49.4045 | −1.77124 | ||||||||
\(779\) | −0.372082 | −0.0133312 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.7511 | −0.420486 | ||||||||
\(782\) | 22.1758 | 0.793005 | ||||||||
\(783\) | −0.444009 | −0.0158676 | ||||||||
\(784\) | −50.6140 | −1.80764 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.72981 | 0.0617004 | ||||||||
\(787\) | 6.18560 | 0.220493 | 0.110246 | − | 0.993904i | \(-0.464836\pi\) | ||||
0.110246 | + | 0.993904i | \(0.464836\pi\) | |||||||
\(788\) | −26.7000 | −0.951148 | ||||||||
\(789\) | 12.9954 | 0.462649 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −63.9136 | −2.27250 | ||||||||
\(792\) | 5.00590 | 0.177877 | ||||||||
\(793\) | −5.54326 | −0.196847 | ||||||||
\(794\) | 6.29037 | 0.223237 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −21.7496 | −0.770894 | ||||||||
\(797\) | 33.9504 | 1.20259 | 0.601293 | − | 0.799029i | \(-0.294653\pi\) | ||||
0.601293 | + | 0.799029i | \(0.294653\pi\) | |||||||
\(798\) | −1.61145 | −0.0570448 | ||||||||
\(799\) | 49.5580 | 1.75324 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.10984 | −0.321880 | ||||||||
\(802\) | 53.8481 | 1.90144 | ||||||||
\(803\) | 52.6872 | 1.85929 | ||||||||
\(804\) | −7.71080 | −0.271939 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.85775 | 0.347224 | ||||||||
\(807\) | 16.9708 | 0.597402 | ||||||||
\(808\) | 0.111073 | 0.00390753 | ||||||||
\(809\) | −17.0245 | −0.598550 | −0.299275 | − | 0.954167i | \(-0.596745\pi\) | ||||
−0.299275 | + | 0.954167i | \(0.596745\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35.1615 | −1.23469 | −0.617344 | − | 0.786694i | \(-0.711791\pi\) | ||||
−0.617344 | + | 0.786694i | \(0.711791\pi\) | |||||||
\(812\) | −0.723436 | −0.0253876 | ||||||||
\(813\) | −5.51064 | −0.193266 | ||||||||
\(814\) | 15.6757 | 0.549434 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −19.6119 | −0.686553 | ||||||||
\(817\) | −2.32085 | −0.0811961 | ||||||||
\(818\) | −5.32407 | −0.186152 | ||||||||
\(819\) | 9.79686 | 0.342330 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.68686 | 0.268273 | 0.134137 | − | 0.990963i | \(-0.457174\pi\) | ||||
0.134137 | + | 0.990963i | \(0.457174\pi\) | |||||||
\(822\) | −0.578787 | −0.0201875 | ||||||||
\(823\) | 26.4535 | 0.922113 | 0.461056 | − | 0.887371i | \(-0.347471\pi\) | ||||
0.461056 | + | 0.887371i | \(0.347471\pi\) | |||||||
\(824\) | 1.16647 | 0.0406359 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 102.047 | 3.55066 | ||||||||
\(827\) | −22.4623 | −0.781090 | −0.390545 | − | 0.920584i | \(-0.627713\pi\) | ||||
−0.390545 | + | 0.920584i | \(0.627713\pi\) | |||||||
\(828\) | −8.79211 | −0.305547 | ||||||||
\(829\) | 48.1972 | 1.67396 | 0.836979 | − | 0.547236i | \(-0.184320\pi\) | ||||
0.836979 | + | 0.547236i | \(0.184320\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.0774794 | 0.00268773 | ||||||||
\(832\) | 5.73683 | 0.198889 | ||||||||
\(833\) | −57.5559 | −1.99419 | ||||||||
\(834\) | 1.25481 | 0.0434506 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.62560 | 0.0562226 | ||||||||
\(837\) | 22.8161 | 0.788639 | ||||||||
\(838\) | −12.6187 | −0.435907 | ||||||||
\(839\) | −10.6726 | −0.368459 | −0.184229 | − | 0.982883i | \(-0.558979\pi\) | ||||
−0.184229 | + | 0.982883i | \(0.558979\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9904 | −0.999668 | ||||||||
\(842\) | 36.8131 | 1.26866 | ||||||||
\(843\) | 27.8002 | 0.957489 | ||||||||
\(844\) | 26.6173 | 0.916207 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −42.4436 | −1.45924 | ||||||||
\(847\) | 26.9592 | 0.926330 | ||||||||
\(848\) | −39.7397 | −1.36467 | ||||||||
\(849\) | −17.7281 | −0.608428 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.40933 | 0.151150 | ||||||||
\(852\) | −4.19266 | −0.143638 | ||||||||
\(853\) | −15.2826 | −0.523265 | −0.261633 | − | 0.965168i | \(-0.584261\pi\) | ||||
−0.261633 | + | 0.965168i | \(0.584261\pi\) | |||||||
\(854\) | −45.1566 | −1.54523 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.43908 | 0.254263 | ||||||||
\(857\) | −30.6509 | −1.04701 | −0.523507 | − | 0.852021i | \(-0.675377\pi\) | ||||
−0.523507 | + | 0.852021i | \(0.675377\pi\) | |||||||
\(858\) | 7.00366 | 0.239101 | ||||||||
\(859\) | −14.1900 | −0.484157 | −0.242078 | − | 0.970257i | \(-0.577829\pi\) | ||||
−0.242078 | + | 0.970257i | \(0.577829\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.04535 | −0.206025 | ||||||||
\(862\) | −23.6015 | −0.803871 | ||||||||
\(863\) | −55.4190 | −1.88649 | −0.943243 | − | 0.332104i | \(-0.892242\pi\) | ||||
−0.943243 | + | 0.332104i | \(0.892242\pi\) | |||||||
\(864\) | 34.2792 | 1.16620 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −69.6517 | −2.36686 | ||||||||
\(867\) | −7.66715 | −0.260390 | ||||||||
\(868\) | 37.1749 | 1.26180 | ||||||||
\(869\) | 28.4050 | 0.963573 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.26646 | −0.178447 | ||||||||
\(872\) | −8.89797 | −0.301323 | ||||||||
\(873\) | −15.0043 | −0.507817 | ||||||||
\(874\) | 0.987740 | 0.0334108 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 18.7983 | 0.635136 | ||||||||
\(877\) | 49.2029 | 1.66147 | 0.830733 | − | 0.556672i | \(-0.187922\pi\) | ||||
0.830733 | + | 0.556672i | \(0.187922\pi\) | |||||||
\(878\) | −43.8668 | −1.48043 | ||||||||
\(879\) | 26.6570 | 0.899118 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.9549 | −0.571226 | −0.285613 | − | 0.958345i | \(-0.592197\pi\) | ||||
−0.285613 | + | 0.958345i | \(0.592197\pi\) | |||||||
\(882\) | 49.2933 | 1.65979 | ||||||||
\(883\) | 4.68142 | 0.157542 | 0.0787712 | − | 0.996893i | \(-0.474900\pi\) | ||||
0.0787712 | + | 0.996893i | \(0.474900\pi\) | |||||||
\(884\) | 8.89371 | 0.299128 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −69.3285 | −2.32914 | ||||||||
\(887\) | −49.3729 | −1.65778 | −0.828889 | − | 0.559413i | \(-0.811027\pi\) | ||||
−0.828889 | + | 0.559413i | \(0.811027\pi\) | |||||||
\(888\) | −0.895725 | −0.0300586 | ||||||||
\(889\) | 34.2178 | 1.14763 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.9772 | −0.401253 | ||||||||
\(892\) | −7.96438 | −0.266667 | ||||||||
\(893\) | 2.20738 | 0.0738672 | ||||||||
\(894\) | −29.4418 | −0.984681 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −18.0634 | −0.603457 | ||||||||
\(897\) | 1.97001 | 0.0657768 | ||||||||
\(898\) | −62.6274 | −2.08990 | ||||||||
\(899\) | −0.494287 | −0.0164854 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −45.1901 | −1.50550 | ||||||||
\(902\) | 13.1736 | 0.438631 | ||||||||
\(903\) | −37.7076 | −1.25483 | ||||||||
\(904\) | −7.95831 | −0.264689 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 12.2661 | 0.407514 | ||||||||
\(907\) | 13.0437 | 0.433108 | 0.216554 | − | 0.976271i | \(-0.430518\pi\) | ||||
0.216554 | + | 0.976271i | \(0.430518\pi\) | |||||||
\(908\) | −27.1614 | −0.901381 | ||||||||
\(909\) | −0.470937 | −0.0156200 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.93310 | 0.0971779 | 0.0485889 | − | 0.998819i | \(-0.484528\pi\) | ||||
0.0485889 | + | 0.998819i | \(0.484528\pi\) | |||||||
\(912\) | −0.873540 | −0.0289258 | ||||||||
\(913\) | 2.48771 | 0.0823310 | ||||||||
\(914\) | −37.0779 | −1.22643 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.7850 | 0.587633 | ||||||||
\(917\) | 4.45543 | 0.147131 | ||||||||
\(918\) | 44.4663 | 1.46761 | ||||||||
\(919\) | −53.4647 | −1.76364 | −0.881820 | − | 0.471587i | \(-0.843681\pi\) | ||||
−0.881820 | + | 0.471587i | \(0.843681\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.89787 | −0.161390 | ||||||||
\(922\) | 76.4518 | 2.51780 | ||||||||
\(923\) | −2.86358 | −0.0942559 | ||||||||
\(924\) | 26.4117 | 0.868881 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −18.4289 | −0.605610 | ||||||||
\(927\) | −4.94570 | −0.162438 | ||||||||
\(928\) | −0.742623 | −0.0243778 | ||||||||
\(929\) | 3.79205 | 0.124413 | 0.0622065 | − | 0.998063i | \(-0.480186\pi\) | ||||
0.0622065 | + | 0.998063i | \(0.480186\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.56362 | −0.0840191 | ||||||||
\(932\) | 49.6400 | 1.62601 | ||||||||
\(933\) | −8.84420 | −0.289546 | ||||||||
\(934\) | −29.6956 | −0.971670 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.21987 | 0.0398728 | ||||||||
\(937\) | 39.6163 | 1.29421 | 0.647103 | − | 0.762402i | \(-0.275980\pi\) | ||||
0.647103 | + | 0.762402i | \(0.275980\pi\) | |||||||
\(938\) | −42.9018 | −1.40079 | ||||||||
\(939\) | −5.82013 | −0.189933 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39.7620 | 1.29620 | 0.648101 | − | 0.761554i | \(-0.275563\pi\) | ||||
0.648101 | + | 0.761554i | \(0.275563\pi\) | |||||||
\(942\) | −4.20516 | −0.137011 | ||||||||
\(943\) | 3.70550 | 0.120668 | ||||||||
\(944\) | 55.3178 | 1.80044 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 82.1694 | 2.67156 | ||||||||
\(947\) | −18.8648 | −0.613024 | −0.306512 | − | 0.951867i | \(-0.599162\pi\) | ||||
−0.306512 | + | 0.951867i | \(0.599162\pi\) | |||||||
\(948\) | 10.1346 | 0.329157 | ||||||||
\(949\) | 12.8392 | 0.416778 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.3447 | 0.367878 | ||||||||
\(952\) | −11.6031 | −0.376057 | ||||||||
\(953\) | 27.6442 | 0.895484 | 0.447742 | − | 0.894163i | \(-0.352228\pi\) | ||||
0.447742 | + | 0.894163i | \(0.352228\pi\) | |||||||
\(954\) | 38.7028 | 1.25305 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.65324 | 0.118154 | ||||||||
\(957\) | −0.351177 | −0.0113519 | ||||||||
\(958\) | 23.8514 | 0.770605 | ||||||||
\(959\) | −1.49077 | −0.0481394 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.60033 | −0.180656 | ||||||||
\(962\) | 3.81997 | 0.123161 | ||||||||
\(963\) | −31.5409 | −1.01639 | ||||||||
\(964\) | −1.72391 | −0.0555234 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 16.0482 | 0.516341 | ||||||||
\(967\) | −2.13869 | −0.0687757 | −0.0343878 | − | 0.999409i | \(-0.510948\pi\) | ||||
−0.0343878 | + | 0.999409i | \(0.510948\pi\) | |||||||
\(968\) | 3.35687 | 0.107894 | ||||||||
\(969\) | −0.993347 | −0.0319109 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34.3123 | 1.10113 | 0.550567 | − | 0.834791i | \(-0.314412\pi\) | ||||
0.550567 | + | 0.834791i | \(0.314412\pi\) | |||||||
\(972\) | −27.6867 | −0.888051 | ||||||||
\(973\) | 3.23199 | 0.103613 | ||||||||
\(974\) | 25.4738 | 0.816232 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −24.4786 | −0.783541 | ||||||||
\(977\) | 43.8976 | 1.40441 | 0.702204 | − | 0.711976i | \(-0.252200\pi\) | ||||
0.702204 | + | 0.711976i | \(0.252200\pi\) | |||||||
\(978\) | 9.31262 | 0.297785 | ||||||||
\(979\) | −16.7741 | −0.536103 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 37.7264 | 1.20451 | ||||||||
\(982\) | −2.43936 | −0.0778432 | ||||||||
\(983\) | −24.2230 | −0.772594 | −0.386297 | − | 0.922374i | \(-0.626246\pi\) | ||||
−0.386297 | + | 0.922374i | \(0.626246\pi\) | |||||||
\(984\) | −0.752748 | −0.0239967 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.963315 | −0.0306782 | ||||||||
\(987\) | 35.8641 | 1.14157 | ||||||||
\(988\) | 0.396138 | 0.0126028 | ||||||||
\(989\) | 23.1129 | 0.734947 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −51.0189 | −1.62067 | −0.810335 | − | 0.585967i | \(-0.800715\pi\) | ||||
−0.810335 | + | 0.585967i | \(0.800715\pi\) | |||||||
\(992\) | 38.1608 | 1.21161 | ||||||||
\(993\) | 23.5813 | 0.748329 | ||||||||
\(994\) | −23.3273 | −0.739899 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.887589 | 0.0281243 | ||||||||
\(997\) | 12.2863 | 0.389112 | 0.194556 | − | 0.980891i | \(-0.437673\pi\) | ||||
0.194556 | + | 0.980891i | \(0.437673\pi\) | |||||||
\(998\) | 29.6397 | 0.938230 | ||||||||
\(999\) | 8.84146 | 0.279731 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6025.2.a.i.1.4 | 15 | ||
5.4 | even | 2 | 1205.2.a.c.1.12 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1205.2.a.c.1.12 | ✓ | 15 | 5.4 | even | 2 | ||
6025.2.a.i.1.4 | 15 | 1.1 | even | 1 | trivial |