Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2001,2,Mod(1,2001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2001.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: | \(15.9780654445\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 9x^{5} + 10x^{4} + 19x^{3} - 20x^{2} - 5x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.13025\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.55072 | −1.09652 | −0.548261 | − | 0.836307i | \(-0.684710\pi\) | ||||
−0.548261 | + | 0.836307i | \(0.684710\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.404722 | 0.202361 | ||||||||
\(5\) | −0.920116 | −0.411489 | −0.205744 | − | 0.978606i | \(-0.565962\pi\) | ||||
−0.205744 | + | 0.978606i | \(0.565962\pi\) | |||||||
\(6\) | −1.55072 | −0.633077 | ||||||||
\(7\) | −2.53796 | −0.959260 | −0.479630 | − | 0.877471i | \(-0.659229\pi\) | ||||
−0.479630 | + | 0.877471i | \(0.659229\pi\) | |||||||
\(8\) | 2.47382 | 0.874629 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.42684 | 0.451206 | ||||||||
\(11\) | −0.294618 | −0.0888305 | −0.0444153 | − | 0.999013i | \(-0.514142\pi\) | ||||
−0.0444153 | + | 0.999013i | \(0.514142\pi\) | |||||||
\(12\) | 0.404722 | 0.116833 | ||||||||
\(13\) | 5.74171 | 1.59247 | 0.796233 | − | 0.604991i | \(-0.206823\pi\) | ||||
0.796233 | + | 0.604991i | \(0.206823\pi\) | |||||||
\(14\) | 3.93566 | 1.05185 | ||||||||
\(15\) | −0.920116 | −0.237573 | ||||||||
\(16\) | −4.64564 | −1.16141 | ||||||||
\(17\) | −1.70697 | −0.414001 | −0.207000 | − | 0.978341i | \(-0.566370\pi\) | ||||
−0.207000 | + | 0.978341i | \(0.566370\pi\) | |||||||
\(18\) | −1.55072 | −0.365507 | ||||||||
\(19\) | −4.65004 | −1.06679 | −0.533397 | − | 0.845865i | \(-0.679085\pi\) | ||||
−0.533397 | + | 0.845865i | \(0.679085\pi\) | |||||||
\(20\) | −0.372391 | −0.0832692 | ||||||||
\(21\) | −2.53796 | −0.553829 | ||||||||
\(22\) | 0.456868 | 0.0974046 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 2.47382 | 0.504967 | ||||||||
\(25\) | −4.15339 | −0.830677 | ||||||||
\(26\) | −8.90377 | −1.74617 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.02717 | −0.194117 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 1.42684 | 0.260504 | ||||||||
\(31\) | 4.26756 | 0.766477 | 0.383238 | − | 0.923650i | \(-0.374809\pi\) | ||||
0.383238 | + | 0.923650i | \(0.374809\pi\) | |||||||
\(32\) | 2.25643 | 0.398884 | ||||||||
\(33\) | −0.294618 | −0.0512863 | ||||||||
\(34\) | 2.64703 | 0.453961 | ||||||||
\(35\) | 2.33522 | 0.394724 | ||||||||
\(36\) | 0.404722 | 0.0674536 | ||||||||
\(37\) | −8.67527 | −1.42621 | −0.713103 | − | 0.701059i | \(-0.752711\pi\) | ||||
−0.713103 | + | 0.701059i | \(0.752711\pi\) | |||||||
\(38\) | 7.21090 | 1.16976 | ||||||||
\(39\) | 5.74171 | 0.919410 | ||||||||
\(40\) | −2.27621 | −0.359900 | ||||||||
\(41\) | 6.05542 | 0.945698 | 0.472849 | − | 0.881144i | \(-0.343226\pi\) | ||||
0.472849 | + | 0.881144i | \(0.343226\pi\) | |||||||
\(42\) | 3.93566 | 0.607286 | ||||||||
\(43\) | 10.0457 | 1.53195 | 0.765977 | − | 0.642868i | \(-0.222256\pi\) | ||||
0.765977 | + | 0.642868i | \(0.222256\pi\) | |||||||
\(44\) | −0.119238 | −0.0179758 | ||||||||
\(45\) | −0.920116 | −0.137163 | ||||||||
\(46\) | 1.55072 | 0.228641 | ||||||||
\(47\) | 1.68275 | 0.245455 | 0.122727 | − | 0.992440i | \(-0.460836\pi\) | ||||
0.122727 | + | 0.992440i | \(0.460836\pi\) | |||||||
\(48\) | −4.64564 | −0.670541 | ||||||||
\(49\) | −0.558745 | −0.0798208 | ||||||||
\(50\) | 6.44072 | 0.910856 | ||||||||
\(51\) | −1.70697 | −0.239024 | ||||||||
\(52\) | 2.32380 | 0.322253 | ||||||||
\(53\) | 3.05393 | 0.419489 | 0.209744 | − | 0.977756i | \(-0.432737\pi\) | ||||
0.209744 | + | 0.977756i | \(0.432737\pi\) | |||||||
\(54\) | −1.55072 | −0.211026 | ||||||||
\(55\) | 0.271082 | 0.0365527 | ||||||||
\(56\) | −6.27847 | −0.838996 | ||||||||
\(57\) | −4.65004 | −0.615913 | ||||||||
\(58\) | −1.55072 | −0.203619 | ||||||||
\(59\) | 3.88052 | 0.505201 | 0.252601 | − | 0.967571i | \(-0.418714\pi\) | ||||
0.252601 | + | 0.967571i | \(0.418714\pi\) | |||||||
\(60\) | −0.372391 | −0.0480755 | ||||||||
\(61\) | −1.83997 | −0.235584 | −0.117792 | − | 0.993038i | \(-0.537582\pi\) | ||||
−0.117792 | + | 0.993038i | \(0.537582\pi\) | |||||||
\(62\) | −6.61778 | −0.840459 | ||||||||
\(63\) | −2.53796 | −0.319753 | ||||||||
\(64\) | 5.79221 | 0.724026 | ||||||||
\(65\) | −5.28305 | −0.655281 | ||||||||
\(66\) | 0.456868 | 0.0562366 | ||||||||
\(67\) | −7.06076 | −0.862609 | −0.431305 | − | 0.902206i | \(-0.641947\pi\) | ||||
−0.431305 | + | 0.902206i | \(0.641947\pi\) | |||||||
\(68\) | −0.690848 | −0.0837776 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | −3.62127 | −0.432824 | ||||||||
\(71\) | 0.554787 | 0.0658411 | 0.0329206 | − | 0.999458i | \(-0.489519\pi\) | ||||
0.0329206 | + | 0.999458i | \(0.489519\pi\) | |||||||
\(72\) | 2.47382 | 0.291543 | ||||||||
\(73\) | −13.8773 | −1.62421 | −0.812106 | − | 0.583509i | \(-0.801679\pi\) | ||||
−0.812106 | + | 0.583509i | \(0.801679\pi\) | |||||||
\(74\) | 13.4529 | 1.56387 | ||||||||
\(75\) | −4.15339 | −0.479592 | ||||||||
\(76\) | −1.88197 | −0.215877 | ||||||||
\(77\) | 0.747728 | 0.0852116 | ||||||||
\(78\) | −8.90377 | −1.00815 | ||||||||
\(79\) | −11.6642 | −1.31233 | −0.656163 | − | 0.754620i | \(-0.727821\pi\) | ||||
−0.656163 | + | 0.754620i | \(0.727821\pi\) | |||||||
\(80\) | 4.27453 | 0.477907 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −9.39024 | −1.03698 | ||||||||
\(83\) | −9.84078 | −1.08017 | −0.540083 | − | 0.841612i | \(-0.681607\pi\) | ||||
−0.540083 | + | 0.841612i | \(0.681607\pi\) | |||||||
\(84\) | −1.02717 | −0.112073 | ||||||||
\(85\) | 1.57061 | 0.170357 | ||||||||
\(86\) | −15.5780 | −1.67982 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | −0.728832 | −0.0776938 | ||||||||
\(89\) | −0.967352 | −0.102539 | −0.0512696 | − | 0.998685i | \(-0.516327\pi\) | ||||
−0.0512696 | + | 0.998685i | \(0.516327\pi\) | |||||||
\(90\) | 1.42684 | 0.150402 | ||||||||
\(91\) | −14.5723 | −1.52759 | ||||||||
\(92\) | −0.404722 | −0.0421952 | ||||||||
\(93\) | 4.26756 | 0.442525 | ||||||||
\(94\) | −2.60947 | −0.269147 | ||||||||
\(95\) | 4.27858 | 0.438973 | ||||||||
\(96\) | 2.25643 | 0.230296 | ||||||||
\(97\) | 3.92233 | 0.398252 | 0.199126 | − | 0.979974i | \(-0.436190\pi\) | ||||
0.199126 | + | 0.979974i | \(0.436190\pi\) | |||||||
\(98\) | 0.866456 | 0.0875252 | ||||||||
\(99\) | −0.294618 | −0.0296102 | ||||||||
\(100\) | −1.68097 | −0.168097 | ||||||||
\(101\) | −3.92185 | −0.390238 | −0.195119 | − | 0.980780i | \(-0.562509\pi\) | ||||
−0.195119 | + | 0.980780i | \(0.562509\pi\) | |||||||
\(102\) | 2.64703 | 0.262095 | ||||||||
\(103\) | −6.54643 | −0.645039 | −0.322520 | − | 0.946563i | \(-0.604530\pi\) | ||||
−0.322520 | + | 0.946563i | \(0.604530\pi\) | |||||||
\(104\) | 14.2040 | 1.39282 | ||||||||
\(105\) | 2.33522 | 0.227894 | ||||||||
\(106\) | −4.73577 | −0.459979 | ||||||||
\(107\) | −11.9957 | −1.15966 | −0.579832 | − | 0.814736i | \(-0.696882\pi\) | ||||
−0.579832 | + | 0.814736i | \(0.696882\pi\) | |||||||
\(108\) | 0.404722 | 0.0389444 | ||||||||
\(109\) | −4.83555 | −0.463161 | −0.231581 | − | 0.972816i | \(-0.574390\pi\) | ||||
−0.231581 | + | 0.972816i | \(0.574390\pi\) | |||||||
\(110\) | −0.420372 | −0.0400809 | ||||||||
\(111\) | −8.67527 | −0.823421 | ||||||||
\(112\) | 11.7905 | 1.11409 | ||||||||
\(113\) | −5.84726 | −0.550064 | −0.275032 | − | 0.961435i | \(-0.588688\pi\) | ||||
−0.275032 | + | 0.961435i | \(0.588688\pi\) | |||||||
\(114\) | 7.21090 | 0.675363 | ||||||||
\(115\) | 0.920116 | 0.0858013 | ||||||||
\(116\) | 0.404722 | 0.0375775 | ||||||||
\(117\) | 5.74171 | 0.530822 | ||||||||
\(118\) | −6.01759 | −0.553964 | ||||||||
\(119\) | 4.33223 | 0.397134 | ||||||||
\(120\) | −2.27621 | −0.207788 | ||||||||
\(121\) | −10.9132 | −0.992109 | ||||||||
\(122\) | 2.85327 | 0.258323 | ||||||||
\(123\) | 6.05542 | 0.545999 | ||||||||
\(124\) | 1.72718 | 0.155105 | ||||||||
\(125\) | 8.42218 | 0.753303 | ||||||||
\(126\) | 3.93566 | 0.350617 | ||||||||
\(127\) | −9.54852 | −0.847294 | −0.423647 | − | 0.905827i | \(-0.639250\pi\) | ||||
−0.423647 | + | 0.905827i | \(0.639250\pi\) | |||||||
\(128\) | −13.4949 | −1.19279 | ||||||||
\(129\) | 10.0457 | 0.884474 | ||||||||
\(130\) | 8.19251 | 0.718530 | ||||||||
\(131\) | −8.35446 | −0.729932 | −0.364966 | − | 0.931021i | \(-0.618919\pi\) | ||||
−0.364966 | + | 0.931021i | \(0.618919\pi\) | |||||||
\(132\) | −0.119238 | −0.0103783 | ||||||||
\(133\) | 11.8016 | 1.02333 | ||||||||
\(134\) | 10.9492 | 0.945870 | ||||||||
\(135\) | −0.920116 | −0.0791910 | ||||||||
\(136\) | −4.22274 | −0.362097 | ||||||||
\(137\) | 15.5216 | 1.32610 | 0.663050 | − | 0.748575i | \(-0.269261\pi\) | ||||
0.663050 | + | 0.748575i | \(0.269261\pi\) | |||||||
\(138\) | 1.55072 | 0.132006 | ||||||||
\(139\) | −12.4550 | −1.05642 | −0.528211 | − | 0.849113i | \(-0.677137\pi\) | ||||
−0.528211 | + | 0.849113i | \(0.677137\pi\) | |||||||
\(140\) | 0.945115 | 0.0798768 | ||||||||
\(141\) | 1.68275 | 0.141713 | ||||||||
\(142\) | −0.860317 | −0.0721962 | ||||||||
\(143\) | −1.69161 | −0.141460 | ||||||||
\(144\) | −4.64564 | −0.387137 | ||||||||
\(145\) | −0.920116 | −0.0764115 | ||||||||
\(146\) | 21.5197 | 1.78099 | ||||||||
\(147\) | −0.558745 | −0.0460845 | ||||||||
\(148\) | −3.51107 | −0.288608 | ||||||||
\(149\) | 10.7891 | 0.883879 | 0.441940 | − | 0.897045i | \(-0.354290\pi\) | ||||
0.441940 | + | 0.897045i | \(0.354290\pi\) | |||||||
\(150\) | 6.44072 | 0.525883 | ||||||||
\(151\) | −13.3481 | −1.08625 | −0.543126 | − | 0.839651i | \(-0.682760\pi\) | ||||
−0.543126 | + | 0.839651i | \(0.682760\pi\) | |||||||
\(152\) | −11.5034 | −0.933048 | ||||||||
\(153\) | −1.70697 | −0.138000 | ||||||||
\(154\) | −1.15951 | −0.0934364 | ||||||||
\(155\) | −3.92665 | −0.315396 | ||||||||
\(156\) | 2.32380 | 0.186053 | ||||||||
\(157\) | −23.1432 | −1.84703 | −0.923515 | − | 0.383562i | \(-0.874697\pi\) | ||||
−0.923515 | + | 0.383562i | \(0.874697\pi\) | |||||||
\(158\) | 18.0879 | 1.43899 | ||||||||
\(159\) | 3.05393 | 0.242192 | ||||||||
\(160\) | −2.07618 | −0.164136 | ||||||||
\(161\) | 2.53796 | 0.200019 | ||||||||
\(162\) | −1.55072 | −0.121836 | ||||||||
\(163\) | −14.1699 | −1.10988 | −0.554938 | − | 0.831892i | \(-0.687258\pi\) | ||||
−0.554938 | + | 0.831892i | \(0.687258\pi\) | |||||||
\(164\) | 2.45076 | 0.191372 | ||||||||
\(165\) | 0.271082 | 0.0211037 | ||||||||
\(166\) | 15.2603 | 1.18443 | ||||||||
\(167\) | 0.670813 | 0.0519091 | 0.0259545 | − | 0.999663i | \(-0.491737\pi\) | ||||
0.0259545 | + | 0.999663i | \(0.491737\pi\) | |||||||
\(168\) | −6.27847 | −0.484395 | ||||||||
\(169\) | 19.9673 | 1.53594 | ||||||||
\(170\) | −2.43557 | −0.186800 | ||||||||
\(171\) | −4.65004 | −0.355598 | ||||||||
\(172\) | 4.06571 | 0.310008 | ||||||||
\(173\) | 5.72576 | 0.435322 | 0.217661 | − | 0.976024i | \(-0.430157\pi\) | ||||
0.217661 | + | 0.976024i | \(0.430157\pi\) | |||||||
\(174\) | −1.55072 | −0.117560 | ||||||||
\(175\) | 10.5411 | 0.796835 | ||||||||
\(176\) | 1.36869 | 0.103169 | ||||||||
\(177\) | 3.88052 | 0.291678 | ||||||||
\(178\) | 1.50009 | 0.112436 | ||||||||
\(179\) | 19.2578 | 1.43940 | 0.719698 | − | 0.694288i | \(-0.244280\pi\) | ||||
0.719698 | + | 0.694288i | \(0.244280\pi\) | |||||||
\(180\) | −0.372391 | −0.0277564 | ||||||||
\(181\) | −0.611032 | −0.0454177 | −0.0227088 | − | 0.999742i | \(-0.507229\pi\) | ||||
−0.0227088 | + | 0.999742i | \(0.507229\pi\) | |||||||
\(182\) | 22.5974 | 1.67503 | ||||||||
\(183\) | −1.83997 | −0.136015 | ||||||||
\(184\) | −2.47382 | −0.182373 | ||||||||
\(185\) | 7.98226 | 0.586868 | ||||||||
\(186\) | −6.61778 | −0.485239 | ||||||||
\(187\) | 0.502903 | 0.0367759 | ||||||||
\(188\) | 0.681047 | 0.0496705 | ||||||||
\(189\) | −2.53796 | −0.184610 | ||||||||
\(190\) | −6.63487 | −0.481344 | ||||||||
\(191\) | −10.8586 | −0.785699 | −0.392849 | − | 0.919603i | \(-0.628511\pi\) | ||||
−0.392849 | + | 0.919603i | \(0.628511\pi\) | |||||||
\(192\) | 5.79221 | 0.418017 | ||||||||
\(193\) | 9.44410 | 0.679801 | 0.339900 | − | 0.940461i | \(-0.389607\pi\) | ||||
0.339900 | + | 0.940461i | \(0.389607\pi\) | |||||||
\(194\) | −6.08242 | −0.436692 | ||||||||
\(195\) | −5.28305 | −0.378327 | ||||||||
\(196\) | −0.226136 | −0.0161526 | ||||||||
\(197\) | −17.0771 | −1.21669 | −0.608347 | − | 0.793671i | \(-0.708167\pi\) | ||||
−0.608347 | + | 0.793671i | \(0.708167\pi\) | |||||||
\(198\) | 0.456868 | 0.0324682 | ||||||||
\(199\) | −13.8211 | −0.979751 | −0.489876 | − | 0.871792i | \(-0.662958\pi\) | ||||
−0.489876 | + | 0.871792i | \(0.662958\pi\) | |||||||
\(200\) | −10.2747 | −0.726534 | ||||||||
\(201\) | −7.06076 | −0.498028 | ||||||||
\(202\) | 6.08167 | 0.427905 | ||||||||
\(203\) | −2.53796 | −0.178130 | ||||||||
\(204\) | −0.690848 | −0.0483690 | ||||||||
\(205\) | −5.57169 | −0.389144 | ||||||||
\(206\) | 10.1517 | 0.707300 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | −26.6740 | −1.84951 | ||||||||
\(209\) | 1.36998 | 0.0947638 | ||||||||
\(210\) | −3.62127 | −0.249891 | ||||||||
\(211\) | −2.77270 | −0.190880 | −0.0954401 | − | 0.995435i | \(-0.530426\pi\) | ||||
−0.0954401 | + | 0.995435i | \(0.530426\pi\) | |||||||
\(212\) | 1.23599 | 0.0848882 | ||||||||
\(213\) | 0.554787 | 0.0380134 | ||||||||
\(214\) | 18.6019 | 1.27160 | ||||||||
\(215\) | −9.24321 | −0.630382 | ||||||||
\(216\) | 2.47382 | 0.168322 | ||||||||
\(217\) | −10.8309 | −0.735250 | ||||||||
\(218\) | 7.49856 | 0.507867 | ||||||||
\(219\) | −13.8773 | −0.937740 | ||||||||
\(220\) | 0.109713 | 0.00739685 | ||||||||
\(221\) | −9.80093 | −0.659282 | ||||||||
\(222\) | 13.4529 | 0.902899 | ||||||||
\(223\) | 9.49038 | 0.635523 | 0.317762 | − | 0.948171i | \(-0.397069\pi\) | ||||
0.317762 | + | 0.948171i | \(0.397069\pi\) | |||||||
\(224\) | −5.72673 | −0.382633 | ||||||||
\(225\) | −4.15339 | −0.276892 | ||||||||
\(226\) | 9.06744 | 0.603157 | ||||||||
\(227\) | −19.2167 | −1.27546 | −0.637730 | − | 0.770260i | \(-0.720126\pi\) | ||||
−0.637730 | + | 0.770260i | \(0.720126\pi\) | |||||||
\(228\) | −1.88197 | −0.124637 | ||||||||
\(229\) | 10.3141 | 0.681573 | 0.340787 | − | 0.940141i | \(-0.389307\pi\) | ||||
0.340787 | + | 0.940141i | \(0.389307\pi\) | |||||||
\(230\) | −1.42684 | −0.0940830 | ||||||||
\(231\) | 0.747728 | 0.0491969 | ||||||||
\(232\) | 2.47382 | 0.162415 | ||||||||
\(233\) | 15.4420 | 1.01164 | 0.505819 | − | 0.862640i | \(-0.331190\pi\) | ||||
0.505819 | + | 0.862640i | \(0.331190\pi\) | |||||||
\(234\) | −8.90377 | −0.582058 | ||||||||
\(235\) | −1.54833 | −0.101002 | ||||||||
\(236\) | 1.57053 | 0.102233 | ||||||||
\(237\) | −11.6642 | −0.757671 | ||||||||
\(238\) | −6.71805 | −0.435467 | ||||||||
\(239\) | −0.257622 | −0.0166642 | −0.00833209 | − | 0.999965i | \(-0.502652\pi\) | ||||
−0.00833209 | + | 0.999965i | \(0.502652\pi\) | |||||||
\(240\) | 4.27453 | 0.275920 | ||||||||
\(241\) | −4.32351 | −0.278502 | −0.139251 | − | 0.990257i | \(-0.544469\pi\) | ||||
−0.139251 | + | 0.990257i | \(0.544469\pi\) | |||||||
\(242\) | 16.9233 | 1.08787 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −0.744677 | −0.0476730 | ||||||||
\(245\) | 0.514111 | 0.0328453 | ||||||||
\(246\) | −9.39024 | −0.598700 | ||||||||
\(247\) | −26.6992 | −1.69883 | ||||||||
\(248\) | 10.5572 | 0.670383 | ||||||||
\(249\) | −9.84078 | −0.623634 | ||||||||
\(250\) | −13.0604 | −0.826013 | ||||||||
\(251\) | −18.9394 | −1.19544 | −0.597722 | − | 0.801704i | \(-0.703927\pi\) | ||||
−0.597722 | + | 0.801704i | \(0.703927\pi\) | |||||||
\(252\) | −1.02717 | −0.0647056 | ||||||||
\(253\) | 0.294618 | 0.0185224 | ||||||||
\(254\) | 14.8070 | 0.929077 | ||||||||
\(255\) | 1.57061 | 0.0983554 | ||||||||
\(256\) | 9.34239 | 0.583900 | ||||||||
\(257\) | −18.9624 | −1.18284 | −0.591421 | − | 0.806363i | \(-0.701433\pi\) | ||||
−0.591421 | + | 0.806363i | \(0.701433\pi\) | |||||||
\(258\) | −15.5780 | −0.969846 | ||||||||
\(259\) | 22.0175 | 1.36810 | ||||||||
\(260\) | −2.13816 | −0.132603 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 12.9554 | 0.800387 | ||||||||
\(263\) | 9.48797 | 0.585053 | 0.292527 | − | 0.956257i | \(-0.405504\pi\) | ||||
0.292527 | + | 0.956257i | \(0.405504\pi\) | |||||||
\(264\) | −0.728832 | −0.0448565 | ||||||||
\(265\) | −2.80997 | −0.172615 | ||||||||
\(266\) | −18.3010 | −1.12211 | ||||||||
\(267\) | −0.967352 | −0.0592010 | ||||||||
\(268\) | −2.85764 | −0.174558 | ||||||||
\(269\) | 15.1348 | 0.922787 | 0.461394 | − | 0.887196i | \(-0.347350\pi\) | ||||
0.461394 | + | 0.887196i | \(0.347350\pi\) | |||||||
\(270\) | 1.42684 | 0.0868347 | ||||||||
\(271\) | −5.65542 | −0.343542 | −0.171771 | − | 0.985137i | \(-0.554949\pi\) | ||||
−0.171771 | + | 0.985137i | \(0.554949\pi\) | |||||||
\(272\) | 7.92997 | 0.480825 | ||||||||
\(273\) | −14.5723 | −0.881953 | ||||||||
\(274\) | −24.0696 | −1.45410 | ||||||||
\(275\) | 1.22366 | 0.0737895 | ||||||||
\(276\) | −0.404722 | −0.0243614 | ||||||||
\(277\) | −12.4470 | −0.747871 | −0.373935 | − | 0.927455i | \(-0.621992\pi\) | ||||
−0.373935 | + | 0.927455i | \(0.621992\pi\) | |||||||
\(278\) | 19.3142 | 1.15839 | ||||||||
\(279\) | 4.26756 | 0.255492 | ||||||||
\(280\) | 5.77693 | 0.345237 | ||||||||
\(281\) | 12.8006 | 0.763618 | 0.381809 | − | 0.924241i | \(-0.375301\pi\) | ||||
0.381809 | + | 0.924241i | \(0.375301\pi\) | |||||||
\(282\) | −2.60947 | −0.155392 | ||||||||
\(283\) | 6.43854 | 0.382732 | 0.191366 | − | 0.981519i | \(-0.438708\pi\) | ||||
0.191366 | + | 0.981519i | \(0.438708\pi\) | |||||||
\(284\) | 0.224534 | 0.0133237 | ||||||||
\(285\) | 4.27858 | 0.253441 | ||||||||
\(286\) | 2.62321 | 0.155113 | ||||||||
\(287\) | −15.3684 | −0.907170 | ||||||||
\(288\) | 2.25643 | 0.132961 | ||||||||
\(289\) | −14.0863 | −0.828603 | ||||||||
\(290\) | 1.42684 | 0.0837869 | ||||||||
\(291\) | 3.92233 | 0.229931 | ||||||||
\(292\) | −5.61644 | −0.328677 | ||||||||
\(293\) | −5.55778 | −0.324689 | −0.162344 | − | 0.986734i | \(-0.551906\pi\) | ||||
−0.162344 | + | 0.986734i | \(0.551906\pi\) | |||||||
\(294\) | 0.866456 | 0.0505327 | ||||||||
\(295\) | −3.57053 | −0.207884 | ||||||||
\(296\) | −21.4611 | −1.24740 | ||||||||
\(297\) | −0.294618 | −0.0170954 | ||||||||
\(298\) | −16.7309 | −0.969193 | ||||||||
\(299\) | −5.74171 | −0.332052 | ||||||||
\(300\) | −1.68097 | −0.0970506 | ||||||||
\(301\) | −25.4956 | −1.46954 | ||||||||
\(302\) | 20.6991 | 1.19110 | ||||||||
\(303\) | −3.92185 | −0.225304 | ||||||||
\(304\) | 21.6024 | 1.23899 | ||||||||
\(305\) | 1.69299 | 0.0969402 | ||||||||
\(306\) | 2.64703 | 0.151320 | ||||||||
\(307\) | −5.76163 | −0.328833 | −0.164417 | − | 0.986391i | \(-0.552574\pi\) | ||||
−0.164417 | + | 0.986391i | \(0.552574\pi\) | |||||||
\(308\) | 0.302622 | 0.0172435 | ||||||||
\(309\) | −6.54643 | −0.372414 | ||||||||
\(310\) | 6.08912 | 0.345839 | ||||||||
\(311\) | −23.2993 | −1.32118 | −0.660590 | − | 0.750747i | \(-0.729694\pi\) | ||||
−0.660590 | + | 0.750747i | \(0.729694\pi\) | |||||||
\(312\) | 14.2040 | 0.804143 | ||||||||
\(313\) | 16.4820 | 0.931616 | 0.465808 | − | 0.884886i | \(-0.345764\pi\) | ||||
0.465808 | + | 0.884886i | \(0.345764\pi\) | |||||||
\(314\) | 35.8886 | 2.02531 | ||||||||
\(315\) | 2.33522 | 0.131575 | ||||||||
\(316\) | −4.72076 | −0.265563 | ||||||||
\(317\) | 19.1446 | 1.07527 | 0.537633 | − | 0.843179i | \(-0.319319\pi\) | ||||
0.537633 | + | 0.843179i | \(0.319319\pi\) | |||||||
\(318\) | −4.73577 | −0.265569 | ||||||||
\(319\) | −0.294618 | −0.0164954 | ||||||||
\(320\) | −5.32950 | −0.297928 | ||||||||
\(321\) | −11.9957 | −0.669532 | ||||||||
\(322\) | −3.93566 | −0.219326 | ||||||||
\(323\) | 7.93748 | 0.441653 | ||||||||
\(324\) | 0.404722 | 0.0224845 | ||||||||
\(325\) | −23.8476 | −1.32282 | ||||||||
\(326\) | 21.9736 | 1.21700 | ||||||||
\(327\) | −4.83555 | −0.267406 | ||||||||
\(328\) | 14.9800 | 0.827135 | ||||||||
\(329\) | −4.27077 | −0.235455 | ||||||||
\(330\) | −0.420372 | −0.0231407 | ||||||||
\(331\) | 16.3110 | 0.896533 | 0.448266 | − | 0.893900i | \(-0.352042\pi\) | ||||
0.448266 | + | 0.893900i | \(0.352042\pi\) | |||||||
\(332\) | −3.98278 | −0.218583 | ||||||||
\(333\) | −8.67527 | −0.475402 | ||||||||
\(334\) | −1.04024 | −0.0569195 | ||||||||
\(335\) | 6.49672 | 0.354954 | ||||||||
\(336\) | 11.7905 | 0.643223 | ||||||||
\(337\) | −10.5552 | −0.574979 | −0.287490 | − | 0.957784i | \(-0.592821\pi\) | ||||
−0.287490 | + | 0.957784i | \(0.592821\pi\) | |||||||
\(338\) | −30.9636 | −1.68420 | ||||||||
\(339\) | −5.84726 | −0.317580 | ||||||||
\(340\) | 0.635660 | 0.0344735 | ||||||||
\(341\) | −1.25730 | −0.0680865 | ||||||||
\(342\) | 7.21090 | 0.389921 | ||||||||
\(343\) | 19.1838 | 1.03583 | ||||||||
\(344\) | 24.8513 | 1.33989 | ||||||||
\(345\) | 0.920116 | 0.0495374 | ||||||||
\(346\) | −8.87903 | −0.477340 | ||||||||
\(347\) | 31.6377 | 1.69840 | 0.849201 | − | 0.528070i | \(-0.177084\pi\) | ||||
0.849201 | + | 0.528070i | \(0.177084\pi\) | |||||||
\(348\) | 0.404722 | 0.0216954 | ||||||||
\(349\) | 6.92488 | 0.370681 | 0.185340 | − | 0.982674i | \(-0.440661\pi\) | ||||
0.185340 | + | 0.982674i | \(0.440661\pi\) | |||||||
\(350\) | −16.3463 | −0.873747 | ||||||||
\(351\) | 5.74171 | 0.306470 | ||||||||
\(352\) | −0.664783 | −0.0354331 | ||||||||
\(353\) | 29.7641 | 1.58418 | 0.792092 | − | 0.610402i | \(-0.208992\pi\) | ||||
0.792092 | + | 0.610402i | \(0.208992\pi\) | |||||||
\(354\) | −6.01759 | −0.319831 | ||||||||
\(355\) | −0.510469 | −0.0270929 | ||||||||
\(356\) | −0.391509 | −0.0207499 | ||||||||
\(357\) | 4.33223 | 0.229286 | ||||||||
\(358\) | −29.8634 | −1.57833 | ||||||||
\(359\) | 3.16103 | 0.166833 | 0.0834165 | − | 0.996515i | \(-0.473417\pi\) | ||||
0.0834165 | + | 0.996515i | \(0.473417\pi\) | |||||||
\(360\) | −2.27621 | −0.119967 | ||||||||
\(361\) | 2.62291 | 0.138048 | ||||||||
\(362\) | 0.947538 | 0.0498015 | ||||||||
\(363\) | −10.9132 | −0.572794 | ||||||||
\(364\) | −5.89771 | −0.309124 | ||||||||
\(365\) | 12.7687 | 0.668345 | ||||||||
\(366\) | 2.85327 | 0.149143 | ||||||||
\(367\) | 21.4343 | 1.11886 | 0.559431 | − | 0.828877i | \(-0.311020\pi\) | ||||
0.559431 | + | 0.828877i | \(0.311020\pi\) | |||||||
\(368\) | 4.64564 | 0.242171 | ||||||||
\(369\) | 6.05542 | 0.315233 | ||||||||
\(370\) | −12.3782 | −0.643513 | ||||||||
\(371\) | −7.75075 | −0.402399 | ||||||||
\(372\) | 1.72718 | 0.0895499 | ||||||||
\(373\) | 2.05560 | 0.106435 | 0.0532174 | − | 0.998583i | \(-0.483052\pi\) | ||||
0.0532174 | + | 0.998583i | \(0.483052\pi\) | |||||||
\(374\) | −0.779860 | −0.0403256 | ||||||||
\(375\) | 8.42218 | 0.434919 | ||||||||
\(376\) | 4.16284 | 0.214682 | ||||||||
\(377\) | 5.74171 | 0.295713 | ||||||||
\(378\) | 3.93566 | 0.202429 | ||||||||
\(379\) | −3.15343 | −0.161981 | −0.0809905 | − | 0.996715i | \(-0.525808\pi\) | ||||
−0.0809905 | + | 0.996715i | \(0.525808\pi\) | |||||||
\(380\) | 1.73164 | 0.0888310 | ||||||||
\(381\) | −9.54852 | −0.489185 | ||||||||
\(382\) | 16.8386 | 0.861536 | ||||||||
\(383\) | −35.3997 | −1.80884 | −0.904420 | − | 0.426643i | \(-0.859696\pi\) | ||||
−0.904420 | + | 0.426643i | \(0.859696\pi\) | |||||||
\(384\) | −13.4949 | −0.688660 | ||||||||
\(385\) | −0.687997 | −0.0350636 | ||||||||
\(386\) | −14.6451 | −0.745417 | ||||||||
\(387\) | 10.0457 | 0.510651 | ||||||||
\(388\) | 1.58745 | 0.0805907 | ||||||||
\(389\) | −39.1672 | −1.98585 | −0.992927 | − | 0.118723i | \(-0.962120\pi\) | ||||
−0.992927 | + | 0.118723i | \(0.962120\pi\) | |||||||
\(390\) | 8.19251 | 0.414844 | ||||||||
\(391\) | 1.70697 | 0.0863252 | ||||||||
\(392\) | −1.38224 | −0.0698136 | ||||||||
\(393\) | −8.35446 | −0.421427 | ||||||||
\(394\) | 26.4818 | 1.33413 | ||||||||
\(395\) | 10.7324 | 0.540007 | ||||||||
\(396\) | −0.119238 | −0.00599194 | ||||||||
\(397\) | 17.3448 | 0.870512 | 0.435256 | − | 0.900307i | \(-0.356658\pi\) | ||||
0.435256 | + | 0.900307i | \(0.356658\pi\) | |||||||
\(398\) | 21.4326 | 1.07432 | ||||||||
\(399\) | 11.8016 | 0.590821 | ||||||||
\(400\) | 19.2952 | 0.964758 | ||||||||
\(401\) | 23.1874 | 1.15793 | 0.578963 | − | 0.815354i | \(-0.303458\pi\) | ||||
0.578963 | + | 0.815354i | \(0.303458\pi\) | |||||||
\(402\) | 10.9492 | 0.546098 | ||||||||
\(403\) | 24.5031 | 1.22059 | ||||||||
\(404\) | −1.58726 | −0.0789690 | ||||||||
\(405\) | −0.920116 | −0.0457209 | ||||||||
\(406\) | 3.93566 | 0.195324 | ||||||||
\(407\) | 2.55589 | 0.126691 | ||||||||
\(408\) | −4.22274 | −0.209057 | ||||||||
\(409\) | −17.5081 | −0.865720 | −0.432860 | − | 0.901461i | \(-0.642496\pi\) | ||||
−0.432860 | + | 0.901461i | \(0.642496\pi\) | |||||||
\(410\) | 8.64011 | 0.426705 | ||||||||
\(411\) | 15.5216 | 0.765625 | ||||||||
\(412\) | −2.64948 | −0.130531 | ||||||||
\(413\) | −9.84862 | −0.484619 | ||||||||
\(414\) | 1.55072 | 0.0762136 | ||||||||
\(415\) | 9.05466 | 0.444476 | ||||||||
\(416\) | 12.9558 | 0.635209 | ||||||||
\(417\) | −12.4550 | −0.609925 | ||||||||
\(418\) | −2.12446 | −0.103911 | ||||||||
\(419\) | −38.1925 | −1.86582 | −0.932912 | − | 0.360103i | \(-0.882741\pi\) | ||||
−0.932912 | + | 0.360103i | \(0.882741\pi\) | |||||||
\(420\) | 0.945115 | 0.0461169 | ||||||||
\(421\) | 10.8222 | 0.527444 | 0.263722 | − | 0.964599i | \(-0.415050\pi\) | ||||
0.263722 | + | 0.964599i | \(0.415050\pi\) | |||||||
\(422\) | 4.29966 | 0.209304 | ||||||||
\(423\) | 1.68275 | 0.0818183 | ||||||||
\(424\) | 7.55487 | 0.366897 | ||||||||
\(425\) | 7.08970 | 0.343901 | ||||||||
\(426\) | −0.860317 | −0.0416825 | ||||||||
\(427\) | 4.66978 | 0.225986 | ||||||||
\(428\) | −4.85490 | −0.234671 | ||||||||
\(429\) | −1.69161 | −0.0816717 | ||||||||
\(430\) | 14.3336 | 0.691227 | ||||||||
\(431\) | −24.8260 | −1.19583 | −0.597914 | − | 0.801561i | \(-0.704003\pi\) | ||||
−0.597914 | + | 0.801561i | \(0.704003\pi\) | |||||||
\(432\) | −4.64564 | −0.223514 | ||||||||
\(433\) | 4.67395 | 0.224616 | 0.112308 | − | 0.993673i | \(-0.464176\pi\) | ||||
0.112308 | + | 0.993673i | \(0.464176\pi\) | |||||||
\(434\) | 16.7957 | 0.806218 | ||||||||
\(435\) | −0.920116 | −0.0441162 | ||||||||
\(436\) | −1.95705 | −0.0937257 | ||||||||
\(437\) | 4.65004 | 0.222442 | ||||||||
\(438\) | 21.5197 | 1.02825 | ||||||||
\(439\) | −7.10914 | −0.339301 | −0.169650 | − | 0.985504i | \(-0.554264\pi\) | ||||
−0.169650 | + | 0.985504i | \(0.554264\pi\) | |||||||
\(440\) | 0.670610 | 0.0319701 | ||||||||
\(441\) | −0.558745 | −0.0266069 | ||||||||
\(442\) | 15.1985 | 0.722917 | ||||||||
\(443\) | 4.20233 | 0.199659 | 0.0998293 | − | 0.995005i | \(-0.468170\pi\) | ||||
0.0998293 | + | 0.995005i | \(0.468170\pi\) | |||||||
\(444\) | −3.51107 | −0.166628 | ||||||||
\(445\) | 0.890076 | 0.0421937 | ||||||||
\(446\) | −14.7169 | −0.696865 | ||||||||
\(447\) | 10.7891 | 0.510308 | ||||||||
\(448\) | −14.7004 | −0.694529 | ||||||||
\(449\) | −19.1700 | −0.904688 | −0.452344 | − | 0.891843i | \(-0.649412\pi\) | ||||
−0.452344 | + | 0.891843i | \(0.649412\pi\) | |||||||
\(450\) | 6.44072 | 0.303619 | ||||||||
\(451\) | −1.78403 | −0.0840068 | ||||||||
\(452\) | −2.36651 | −0.111311 | ||||||||
\(453\) | −13.3481 | −0.627148 | ||||||||
\(454\) | 29.7997 | 1.39857 | ||||||||
\(455\) | 13.4082 | 0.628585 | ||||||||
\(456\) | −11.5034 | −0.538696 | ||||||||
\(457\) | 27.5937 | 1.29078 | 0.645389 | − | 0.763854i | \(-0.276695\pi\) | ||||
0.645389 | + | 0.763854i | \(0.276695\pi\) | |||||||
\(458\) | −15.9942 | −0.747360 | ||||||||
\(459\) | −1.70697 | −0.0796745 | ||||||||
\(460\) | 0.372391 | 0.0173628 | ||||||||
\(461\) | −17.6892 | −0.823868 | −0.411934 | − | 0.911214i | \(-0.635147\pi\) | ||||
−0.411934 | + | 0.911214i | \(0.635147\pi\) | |||||||
\(462\) | −1.15951 | −0.0539455 | ||||||||
\(463\) | 22.2642 | 1.03470 | 0.517352 | − | 0.855773i | \(-0.326918\pi\) | ||||
0.517352 | + | 0.855773i | \(0.326918\pi\) | |||||||
\(464\) | −4.64564 | −0.215669 | ||||||||
\(465\) | −3.92665 | −0.182094 | ||||||||
\(466\) | −23.9461 | −1.10928 | ||||||||
\(467\) | −4.91837 | −0.227595 | −0.113797 | − | 0.993504i | \(-0.536301\pi\) | ||||
−0.113797 | + | 0.993504i | \(0.536301\pi\) | |||||||
\(468\) | 2.32380 | 0.107418 | ||||||||
\(469\) | 17.9199 | 0.827466 | ||||||||
\(470\) | 2.40102 | 0.110751 | ||||||||
\(471\) | −23.1432 | −1.06638 | ||||||||
\(472\) | 9.59973 | 0.441863 | ||||||||
\(473\) | −2.95964 | −0.136084 | ||||||||
\(474\) | 18.0879 | 0.830803 | ||||||||
\(475\) | 19.3134 | 0.886161 | ||||||||
\(476\) | 1.75335 | 0.0803645 | ||||||||
\(477\) | 3.05393 | 0.139830 | ||||||||
\(478\) | 0.399499 | 0.0182726 | ||||||||
\(479\) | 7.39386 | 0.337834 | 0.168917 | − | 0.985630i | \(-0.445973\pi\) | ||||
0.168917 | + | 0.985630i | \(0.445973\pi\) | |||||||
\(480\) | −2.07618 | −0.0947641 | ||||||||
\(481\) | −49.8109 | −2.27118 | ||||||||
\(482\) | 6.70453 | 0.305383 | ||||||||
\(483\) | 2.53796 | 0.115481 | ||||||||
\(484\) | −4.41681 | −0.200764 | ||||||||
\(485\) | −3.60900 | −0.163876 | ||||||||
\(486\) | −1.55072 | −0.0703419 | ||||||||
\(487\) | 12.8052 | 0.580260 | 0.290130 | − | 0.956987i | \(-0.406301\pi\) | ||||
0.290130 | + | 0.956987i | \(0.406301\pi\) | |||||||
\(488\) | −4.55177 | −0.206049 | ||||||||
\(489\) | −14.1699 | −0.640787 | ||||||||
\(490\) | −0.797240 | −0.0360156 | ||||||||
\(491\) | 8.90802 | 0.402014 | 0.201007 | − | 0.979590i | \(-0.435579\pi\) | ||||
0.201007 | + | 0.979590i | \(0.435579\pi\) | |||||||
\(492\) | 2.45076 | 0.110489 | ||||||||
\(493\) | −1.70697 | −0.0768780 | ||||||||
\(494\) | 41.4029 | 1.86281 | ||||||||
\(495\) | 0.271082 | 0.0121842 | ||||||||
\(496\) | −19.8256 | −0.890194 | ||||||||
\(497\) | −1.40803 | −0.0631587 | ||||||||
\(498\) | 15.2603 | 0.683828 | ||||||||
\(499\) | −23.5854 | −1.05583 | −0.527914 | − | 0.849298i | \(-0.677026\pi\) | ||||
−0.527914 | + | 0.849298i | \(0.677026\pi\) | |||||||
\(500\) | 3.40864 | 0.152439 | ||||||||
\(501\) | 0.670813 | 0.0299697 | ||||||||
\(502\) | 29.3696 | 1.31083 | ||||||||
\(503\) | 1.13086 | 0.0504227 | 0.0252113 | − | 0.999682i | \(-0.491974\pi\) | ||||
0.0252113 | + | 0.999682i | \(0.491974\pi\) | |||||||
\(504\) | −6.27847 | −0.279665 | ||||||||
\(505\) | 3.60855 | 0.160579 | ||||||||
\(506\) | −0.456868 | −0.0203103 | ||||||||
\(507\) | 19.9673 | 0.886778 | ||||||||
\(508\) | −3.86449 | −0.171459 | ||||||||
\(509\) | 7.10342 | 0.314853 | 0.157427 | − | 0.987531i | \(-0.449680\pi\) | ||||
0.157427 | + | 0.987531i | \(0.449680\pi\) | |||||||
\(510\) | −2.43557 | −0.107849 | ||||||||
\(511\) | 35.2200 | 1.55804 | ||||||||
\(512\) | 12.5025 | 0.552535 | ||||||||
\(513\) | −4.65004 | −0.205304 | ||||||||
\(514\) | 29.4053 | 1.29701 | ||||||||
\(515\) | 6.02348 | 0.265426 | ||||||||
\(516\) | 4.06571 | 0.178983 | ||||||||
\(517\) | −0.495769 | −0.0218039 | ||||||||
\(518\) | −34.1429 | −1.50015 | ||||||||
\(519\) | 5.72576 | 0.251333 | ||||||||
\(520\) | −13.0693 | −0.573128 | ||||||||
\(521\) | 11.1529 | 0.488616 | 0.244308 | − | 0.969698i | \(-0.421439\pi\) | ||||
0.244308 | + | 0.969698i | \(0.421439\pi\) | |||||||
\(522\) | −1.55072 | −0.0678730 | ||||||||
\(523\) | 43.1168 | 1.88537 | 0.942683 | − | 0.333690i | \(-0.108294\pi\) | ||||
0.942683 | + | 0.333690i | \(0.108294\pi\) | |||||||
\(524\) | −3.38123 | −0.147710 | ||||||||
\(525\) | 10.5411 | 0.460053 | ||||||||
\(526\) | −14.7131 | −0.641524 | ||||||||
\(527\) | −7.28460 | −0.317322 | ||||||||
\(528\) | 1.36869 | 0.0595645 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 4.35746 | 0.189276 | ||||||||
\(531\) | 3.88052 | 0.168400 | ||||||||
\(532\) | 4.77638 | 0.207082 | ||||||||
\(533\) | 34.7685 | 1.50599 | ||||||||
\(534\) | 1.50009 | 0.0649152 | ||||||||
\(535\) | 11.0374 | 0.477188 | ||||||||
\(536\) | −17.4671 | −0.754463 | ||||||||
\(537\) | 19.2578 | 0.831035 | ||||||||
\(538\) | −23.4698 | −1.01186 | ||||||||
\(539\) | 0.164616 | 0.00709052 | ||||||||
\(540\) | −0.372391 | −0.0160252 | ||||||||
\(541\) | 31.8465 | 1.36919 | 0.684594 | − | 0.728925i | \(-0.259980\pi\) | ||||
0.684594 | + | 0.728925i | \(0.259980\pi\) | |||||||
\(542\) | 8.76996 | 0.376702 | ||||||||
\(543\) | −0.611032 | −0.0262219 | ||||||||
\(544\) | −3.85165 | −0.165138 | ||||||||
\(545\) | 4.44926 | 0.190586 | ||||||||
\(546\) | 22.5974 | 0.967081 | ||||||||
\(547\) | 36.8946 | 1.57750 | 0.788750 | − | 0.614714i | \(-0.210728\pi\) | ||||
0.788750 | + | 0.614714i | \(0.210728\pi\) | |||||||
\(548\) | 6.28194 | 0.268351 | ||||||||
\(549\) | −1.83997 | −0.0785281 | ||||||||
\(550\) | −1.89755 | −0.0809118 | ||||||||
\(551\) | −4.65004 | −0.198099 | ||||||||
\(552\) | −2.47382 | −0.105293 | ||||||||
\(553\) | 29.6033 | 1.25886 | ||||||||
\(554\) | 19.3018 | 0.820057 | ||||||||
\(555\) | 7.98226 | 0.338828 | ||||||||
\(556\) | −5.04082 | −0.213779 | ||||||||
\(557\) | −6.48485 | −0.274772 | −0.137386 | − | 0.990518i | \(-0.543870\pi\) | ||||
−0.137386 | + | 0.990518i | \(0.543870\pi\) | |||||||
\(558\) | −6.61778 | −0.280153 | ||||||||
\(559\) | 57.6795 | 2.43958 | ||||||||
\(560\) | −10.8486 | −0.458437 | ||||||||
\(561\) | 0.502903 | 0.0212326 | ||||||||
\(562\) | −19.8501 | −0.837324 | ||||||||
\(563\) | −10.5825 | −0.445998 | −0.222999 | − | 0.974819i | \(-0.571585\pi\) | ||||
−0.222999 | + | 0.974819i | \(0.571585\pi\) | |||||||
\(564\) | 0.681047 | 0.0286773 | ||||||||
\(565\) | 5.38016 | 0.226345 | ||||||||
\(566\) | −9.98436 | −0.419674 | ||||||||
\(567\) | −2.53796 | −0.106584 | ||||||||
\(568\) | 1.37245 | 0.0575865 | ||||||||
\(569\) | 25.5371 | 1.07057 | 0.535286 | − | 0.844671i | \(-0.320204\pi\) | ||||
0.535286 | + | 0.844671i | \(0.320204\pi\) | |||||||
\(570\) | −6.63487 | −0.277904 | ||||||||
\(571\) | 7.97917 | 0.333918 | 0.166959 | − | 0.985964i | \(-0.446605\pi\) | ||||
0.166959 | + | 0.985964i | \(0.446605\pi\) | |||||||
\(572\) | −0.684631 | −0.0286259 | ||||||||
\(573\) | −10.8586 | −0.453623 | ||||||||
\(574\) | 23.8321 | 0.994732 | ||||||||
\(575\) | 4.15339 | 0.173208 | ||||||||
\(576\) | 5.79221 | 0.241342 | ||||||||
\(577\) | 36.2622 | 1.50961 | 0.754807 | − | 0.655947i | \(-0.227731\pi\) | ||||
0.754807 | + | 0.655947i | \(0.227731\pi\) | |||||||
\(578\) | 21.8438 | 0.908582 | ||||||||
\(579\) | 9.44410 | 0.392483 | ||||||||
\(580\) | −0.372391 | −0.0154627 | ||||||||
\(581\) | 24.9755 | 1.03616 | ||||||||
\(582\) | −6.08242 | −0.252124 | ||||||||
\(583\) | −0.899740 | −0.0372634 | ||||||||
\(584\) | −34.3300 | −1.42058 | ||||||||
\(585\) | −5.28305 | −0.218427 | ||||||||
\(586\) | 8.61854 | 0.356029 | ||||||||
\(587\) | −8.65368 | −0.357175 | −0.178588 | − | 0.983924i | \(-0.557153\pi\) | ||||
−0.178588 | + | 0.983924i | \(0.557153\pi\) | |||||||
\(588\) | −0.226136 | −0.00932571 | ||||||||
\(589\) | −19.8443 | −0.817672 | ||||||||
\(590\) | 5.53688 | 0.227950 | ||||||||
\(591\) | −17.0771 | −0.702459 | ||||||||
\(592\) | 40.3022 | 1.65641 | ||||||||
\(593\) | 14.8793 | 0.611021 | 0.305510 | − | 0.952189i | \(-0.401173\pi\) | ||||
0.305510 | + | 0.952189i | \(0.401173\pi\) | |||||||
\(594\) | 0.456868 | 0.0187455 | ||||||||
\(595\) | −3.98615 | −0.163416 | ||||||||
\(596\) | 4.36659 | 0.178863 | ||||||||
\(597\) | −13.8211 | −0.565660 | ||||||||
\(598\) | 8.90377 | 0.364102 | ||||||||
\(599\) | 21.1474 | 0.864060 | 0.432030 | − | 0.901859i | \(-0.357798\pi\) | ||||
0.432030 | + | 0.901859i | \(0.357798\pi\) | |||||||
\(600\) | −10.2747 | −0.419465 | ||||||||
\(601\) | −2.18931 | −0.0893037 | −0.0446518 | − | 0.999003i | \(-0.514218\pi\) | ||||
−0.0446518 | + | 0.999003i | \(0.514218\pi\) | |||||||
\(602\) | 39.5365 | 1.61139 | ||||||||
\(603\) | −7.06076 | −0.287536 | ||||||||
\(604\) | −5.40227 | −0.219815 | ||||||||
\(605\) | 10.0414 | 0.408242 | ||||||||
\(606\) | 6.08167 | 0.247051 | ||||||||
\(607\) | 10.7539 | 0.436486 | 0.218243 | − | 0.975894i | \(-0.429968\pi\) | ||||
0.218243 | + | 0.975894i | \(0.429968\pi\) | |||||||
\(608\) | −10.4925 | −0.425527 | ||||||||
\(609\) | −2.53796 | −0.102843 | ||||||||
\(610\) | −2.62534 | −0.106297 | ||||||||
\(611\) | 9.66189 | 0.390878 | ||||||||
\(612\) | −0.690848 | −0.0279259 | ||||||||
\(613\) | −29.9979 | −1.21160 | −0.605801 | − | 0.795616i | \(-0.707147\pi\) | ||||
−0.605801 | + | 0.795616i | \(0.707147\pi\) | |||||||
\(614\) | 8.93465 | 0.360573 | ||||||||
\(615\) | −5.57169 | −0.224672 | ||||||||
\(616\) | 1.84975 | 0.0745285 | ||||||||
\(617\) | 41.8380 | 1.68433 | 0.842167 | − | 0.539217i | \(-0.181280\pi\) | ||||
0.842167 | + | 0.539217i | \(0.181280\pi\) | |||||||
\(618\) | 10.1517 | 0.408360 | ||||||||
\(619\) | −17.2717 | −0.694209 | −0.347104 | − | 0.937826i | \(-0.612835\pi\) | ||||
−0.347104 | + | 0.937826i | \(0.612835\pi\) | |||||||
\(620\) | −1.58920 | −0.0638239 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 36.1306 | 1.44870 | ||||||||
\(623\) | 2.45510 | 0.0983616 | ||||||||
\(624\) | −26.6740 | −1.06781 | ||||||||
\(625\) | 13.0175 | 0.520702 | ||||||||
\(626\) | −25.5589 | −1.02154 | ||||||||
\(627\) | 1.36998 | 0.0547119 | ||||||||
\(628\) | −9.36657 | −0.373767 | ||||||||
\(629\) | 14.8084 | 0.590451 | ||||||||
\(630\) | −3.62127 | −0.144275 | ||||||||
\(631\) | −6.56178 | −0.261220 | −0.130610 | − | 0.991434i | \(-0.541694\pi\) | ||||
−0.130610 | + | 0.991434i | \(0.541694\pi\) | |||||||
\(632\) | −28.8552 | −1.14780 | ||||||||
\(633\) | −2.77270 | −0.110205 | ||||||||
\(634\) | −29.6878 | −1.17905 | ||||||||
\(635\) | 8.78575 | 0.348652 | ||||||||
\(636\) | 1.23599 | 0.0490102 | ||||||||
\(637\) | −3.20816 | −0.127112 | ||||||||
\(638\) | 0.456868 | 0.0180876 | ||||||||
\(639\) | 0.554787 | 0.0219470 | ||||||||
\(640\) | 12.4169 | 0.490821 | ||||||||
\(641\) | 7.14245 | 0.282110 | 0.141055 | − | 0.990002i | \(-0.454951\pi\) | ||||
0.141055 | + | 0.990002i | \(0.454951\pi\) | |||||||
\(642\) | 18.6019 | 0.734157 | ||||||||
\(643\) | −3.73453 | −0.147276 | −0.0736378 | − | 0.997285i | \(-0.523461\pi\) | ||||
−0.0736378 | + | 0.997285i | \(0.523461\pi\) | |||||||
\(644\) | 1.02717 | 0.0404761 | ||||||||
\(645\) | −9.24321 | −0.363951 | ||||||||
\(646\) | −12.3088 | −0.484283 | ||||||||
\(647\) | −28.3980 | −1.11644 | −0.558221 | − | 0.829692i | \(-0.688516\pi\) | ||||
−0.558221 | + | 0.829692i | \(0.688516\pi\) | |||||||
\(648\) | 2.47382 | 0.0971810 | ||||||||
\(649\) | −1.14327 | −0.0448773 | ||||||||
\(650\) | 36.9808 | 1.45051 | ||||||||
\(651\) | −10.8309 | −0.424497 | ||||||||
\(652\) | −5.73488 | −0.224595 | ||||||||
\(653\) | −35.4484 | −1.38720 | −0.693601 | − | 0.720359i | \(-0.743977\pi\) | ||||
−0.693601 | + | 0.720359i | \(0.743977\pi\) | |||||||
\(654\) | 7.49856 | 0.293217 | ||||||||
\(655\) | 7.68707 | 0.300359 | ||||||||
\(656\) | −28.1313 | −1.09834 | ||||||||
\(657\) | −13.8773 | −0.541404 | ||||||||
\(658\) | 6.62275 | 0.258182 | ||||||||
\(659\) | 4.93354 | 0.192183 | 0.0960916 | − | 0.995372i | \(-0.469366\pi\) | ||||
0.0960916 | + | 0.995372i | \(0.469366\pi\) | |||||||
\(660\) | 0.109713 | 0.00427057 | ||||||||
\(661\) | −24.0960 | −0.937227 | −0.468614 | − | 0.883403i | \(-0.655246\pi\) | ||||
−0.468614 | + | 0.883403i | \(0.655246\pi\) | |||||||
\(662\) | −25.2937 | −0.983068 | ||||||||
\(663\) | −9.80093 | −0.380637 | ||||||||
\(664\) | −24.3444 | −0.944744 | ||||||||
\(665\) | −10.8589 | −0.421089 | ||||||||
\(666\) | 13.4529 | 0.521289 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 0.271493 | 0.0105044 | ||||||||
\(669\) | 9.49038 | 0.366919 | ||||||||
\(670\) | −10.0746 | −0.389215 | ||||||||
\(671\) | 0.542088 | 0.0209271 | ||||||||
\(672\) | −5.72673 | −0.220913 | ||||||||
\(673\) | −41.4624 | −1.59826 | −0.799129 | − | 0.601159i | \(-0.794706\pi\) | ||||
−0.799129 | + | 0.601159i | \(0.794706\pi\) | |||||||
\(674\) | 16.3682 | 0.630478 | ||||||||
\(675\) | −4.15339 | −0.159864 | ||||||||
\(676\) | 8.08120 | 0.310815 | ||||||||
\(677\) | 8.35422 | 0.321079 | 0.160539 | − | 0.987029i | \(-0.448677\pi\) | ||||
0.160539 | + | 0.987029i | \(0.448677\pi\) | |||||||
\(678\) | 9.06744 | 0.348233 | ||||||||
\(679\) | −9.95473 | −0.382027 | ||||||||
\(680\) | 3.88541 | 0.148999 | ||||||||
\(681\) | −19.2167 | −0.736387 | ||||||||
\(682\) | 1.94971 | 0.0746584 | ||||||||
\(683\) | −47.0105 | −1.79881 | −0.899403 | − | 0.437121i | \(-0.855998\pi\) | ||||
−0.899403 | + | 0.437121i | \(0.855998\pi\) | |||||||
\(684\) | −1.88197 | −0.0719591 | ||||||||
\(685\) | −14.2817 | −0.545675 | ||||||||
\(686\) | −29.7487 | −1.13581 | ||||||||
\(687\) | 10.3141 | 0.393507 | ||||||||
\(688\) | −46.6687 | −1.77923 | ||||||||
\(689\) | 17.5348 | 0.668021 | ||||||||
\(690\) | −1.42684 | −0.0543189 | ||||||||
\(691\) | −7.55835 | −0.287533 | −0.143767 | − | 0.989612i | \(-0.545921\pi\) | ||||
−0.143767 | + | 0.989612i | \(0.545921\pi\) | |||||||
\(692\) | 2.31734 | 0.0880921 | ||||||||
\(693\) | 0.747728 | 0.0284039 | ||||||||
\(694\) | −49.0611 | −1.86234 | ||||||||
\(695\) | 11.4601 | 0.434705 | ||||||||
\(696\) | 2.47382 | 0.0937701 | ||||||||
\(697\) | −10.3364 | −0.391520 | ||||||||
\(698\) | −10.7385 | −0.406459 | ||||||||
\(699\) | 15.4420 | 0.584069 | ||||||||
\(700\) | 4.26623 | 0.161248 | ||||||||
\(701\) | 47.4732 | 1.79304 | 0.896518 | − | 0.443007i | \(-0.146088\pi\) | ||||
0.896518 | + | 0.443007i | \(0.146088\pi\) | |||||||
\(702\) | −8.90377 | −0.336051 | ||||||||
\(703\) | 40.3404 | 1.52147 | ||||||||
\(704\) | −1.70649 | −0.0643156 | ||||||||
\(705\) | −1.54833 | −0.0583135 | ||||||||
\(706\) | −46.1557 | −1.73709 | ||||||||
\(707\) | 9.95350 | 0.374340 | ||||||||
\(708\) | 1.57053 | 0.0590242 | ||||||||
\(709\) | −13.4626 | −0.505600 | −0.252800 | − | 0.967519i | \(-0.581351\pi\) | ||||
−0.252800 | + | 0.967519i | \(0.581351\pi\) | |||||||
\(710\) | 0.791592 | 0.0297079 | ||||||||
\(711\) | −11.6642 | −0.437442 | ||||||||
\(712\) | −2.39306 | −0.0896837 | ||||||||
\(713\) | −4.26756 | −0.159821 | ||||||||
\(714\) | −6.71805 | −0.251417 | ||||||||
\(715\) | 1.55648 | 0.0582090 | ||||||||
\(716\) | 7.79405 | 0.291277 | ||||||||
\(717\) | −0.257622 | −0.00962107 | ||||||||
\(718\) | −4.90187 | −0.182936 | ||||||||
\(719\) | −0.150106 | −0.00559802 | −0.00279901 | − | 0.999996i | \(-0.500891\pi\) | ||||
−0.00279901 | + | 0.999996i | \(0.500891\pi\) | |||||||
\(720\) | 4.27453 | 0.159302 | ||||||||
\(721\) | 16.6146 | 0.618760 | ||||||||
\(722\) | −4.06739 | −0.151372 | ||||||||
\(723\) | −4.32351 | −0.160793 | ||||||||
\(724\) | −0.247298 | −0.00919076 | ||||||||
\(725\) | −4.15339 | −0.154253 | ||||||||
\(726\) | 16.9233 | 0.628082 | ||||||||
\(727\) | −22.0694 | −0.818508 | −0.409254 | − | 0.912421i | \(-0.634211\pi\) | ||||
−0.409254 | + | 0.912421i | \(0.634211\pi\) | |||||||
\(728\) | −36.0492 | −1.33607 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −19.8007 | −0.732855 | ||||||||
\(731\) | −17.1477 | −0.634231 | ||||||||
\(732\) | −0.744677 | −0.0275240 | ||||||||
\(733\) | 41.5903 | 1.53617 | 0.768087 | − | 0.640345i | \(-0.221209\pi\) | ||||
0.768087 | + | 0.640345i | \(0.221209\pi\) | |||||||
\(734\) | −33.2385 | −1.22686 | ||||||||
\(735\) | 0.514111 | 0.0189633 | ||||||||
\(736\) | −2.25643 | −0.0831731 | ||||||||
\(737\) | 2.08022 | 0.0766260 | ||||||||
\(738\) | −9.39024 | −0.345660 | ||||||||
\(739\) | −45.3933 | −1.66982 | −0.834910 | − | 0.550387i | \(-0.814480\pi\) | ||||
−0.834910 | + | 0.550387i | \(0.814480\pi\) | |||||||
\(740\) | 3.23060 | 0.118759 | ||||||||
\(741\) | −26.6992 | −0.980820 | ||||||||
\(742\) | 12.0192 | 0.441239 | ||||||||
\(743\) | 0.403704 | 0.0148105 | 0.00740524 | − | 0.999973i | \(-0.497643\pi\) | ||||
0.00740524 | + | 0.999973i | \(0.497643\pi\) | |||||||
\(744\) | 10.5572 | 0.387046 | ||||||||
\(745\) | −9.92725 | −0.363706 | ||||||||
\(746\) | −3.18765 | −0.116708 | ||||||||
\(747\) | −9.84078 | −0.360055 | ||||||||
\(748\) | 0.203536 | 0.00744201 | ||||||||
\(749\) | 30.4445 | 1.11242 | ||||||||
\(750\) | −13.0604 | −0.476899 | ||||||||
\(751\) | 3.41838 | 0.124738 | 0.0623692 | − | 0.998053i | \(-0.480134\pi\) | ||||
0.0623692 | + | 0.998053i | \(0.480134\pi\) | |||||||
\(752\) | −7.81748 | −0.285074 | ||||||||
\(753\) | −18.9394 | −0.690190 | ||||||||
\(754\) | −8.90377 | −0.324256 | ||||||||
\(755\) | 12.2818 | 0.446980 | ||||||||
\(756\) | −1.02717 | −0.0373578 | ||||||||
\(757\) | −32.6212 | −1.18564 | −0.592819 | − | 0.805335i | \(-0.701985\pi\) | ||||
−0.592819 | + | 0.805335i | \(0.701985\pi\) | |||||||
\(758\) | 4.89008 | 0.177616 | ||||||||
\(759\) | 0.294618 | 0.0106939 | ||||||||
\(760\) | 10.5845 | 0.383939 | ||||||||
\(761\) | 35.3195 | 1.28033 | 0.640166 | − | 0.768237i | \(-0.278866\pi\) | ||||
0.640166 | + | 0.768237i | \(0.278866\pi\) | |||||||
\(762\) | 14.8070 | 0.536403 | ||||||||
\(763\) | 12.2724 | 0.444292 | ||||||||
\(764\) | −4.39470 | −0.158995 | ||||||||
\(765\) | 1.57061 | 0.0567855 | ||||||||
\(766\) | 54.8949 | 1.98343 | ||||||||
\(767\) | 22.2809 | 0.804515 | ||||||||
\(768\) | 9.34239 | 0.337115 | ||||||||
\(769\) | −9.57460 | −0.345269 | −0.172634 | − | 0.984986i | \(-0.555228\pi\) | ||||
−0.172634 | + | 0.984986i | \(0.555228\pi\) | |||||||
\(770\) | 1.06689 | 0.0384480 | ||||||||
\(771\) | −18.9624 | −0.682914 | ||||||||
\(772\) | 3.82223 | 0.137565 | ||||||||
\(773\) | 3.28418 | 0.118124 | 0.0590619 | − | 0.998254i | \(-0.481189\pi\) | ||||
0.0590619 | + | 0.998254i | \(0.481189\pi\) | |||||||
\(774\) | −15.5780 | −0.559941 | ||||||||
\(775\) | −17.7248 | −0.636695 | ||||||||
\(776\) | 9.70315 | 0.348323 | ||||||||
\(777\) | 22.0175 | 0.789874 | ||||||||
\(778\) | 60.7372 | 2.17753 | ||||||||
\(779\) | −28.1580 | −1.00886 | ||||||||
\(780\) | −2.13816 | −0.0765585 | ||||||||
\(781\) | −0.163450 | −0.00584870 | ||||||||
\(782\) | −2.64703 | −0.0946575 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | 2.59573 | 0.0927047 | ||||||||
\(785\) | 21.2945 | 0.760032 | ||||||||
\(786\) | 12.9554 | 0.462104 | ||||||||
\(787\) | −22.7463 | −0.810817 | −0.405408 | − | 0.914136i | \(-0.632871\pi\) | ||||
−0.405408 | + | 0.914136i | \(0.632871\pi\) | |||||||
\(788\) | −6.91148 | −0.246211 | ||||||||
\(789\) | 9.48797 | 0.337781 | ||||||||
\(790\) | −16.6429 | −0.592129 | ||||||||
\(791\) | 14.8401 | 0.527654 | ||||||||
\(792\) | −0.728832 | −0.0258979 | ||||||||
\(793\) | −10.5646 | −0.375160 | ||||||||
\(794\) | −26.8969 | −0.954536 | ||||||||
\(795\) | −2.80997 | −0.0996592 | ||||||||
\(796\) | −5.59370 | −0.198263 | ||||||||
\(797\) | −18.0025 | −0.637680 | −0.318840 | − | 0.947809i | \(-0.603293\pi\) | ||||
−0.318840 | + | 0.947809i | \(0.603293\pi\) | |||||||
\(798\) | −18.3010 | −0.647848 | ||||||||
\(799\) | −2.87241 | −0.101619 | ||||||||
\(800\) | −9.37182 | −0.331344 | ||||||||
\(801\) | −0.967352 | −0.0341797 | ||||||||
\(802\) | −35.9571 | −1.26969 | ||||||||
\(803\) | 4.08849 | 0.144280 | ||||||||
\(804\) | −2.85764 | −0.100781 | ||||||||
\(805\) | −2.33522 | −0.0823057 | ||||||||
\(806\) | −37.9974 | −1.33840 | ||||||||
\(807\) | 15.1348 | 0.532771 | ||||||||
\(808\) | −9.70196 | −0.341314 | ||||||||
\(809\) | 13.8919 | 0.488414 | 0.244207 | − | 0.969723i | \(-0.421472\pi\) | ||||
0.244207 | + | 0.969723i | \(0.421472\pi\) | |||||||
\(810\) | 1.42684 | 0.0501340 | ||||||||
\(811\) | 23.9714 | 0.841748 | 0.420874 | − | 0.907119i | \(-0.361723\pi\) | ||||
0.420874 | + | 0.907119i | \(0.361723\pi\) | |||||||
\(812\) | −1.02717 | −0.0360466 | ||||||||
\(813\) | −5.65542 | −0.198344 | ||||||||
\(814\) | −3.96346 | −0.138919 | ||||||||
\(815\) | 13.0380 | 0.456701 | ||||||||
\(816\) | 7.92997 | 0.277605 | ||||||||
\(817\) | −46.7129 | −1.63428 | ||||||||
\(818\) | 27.1501 | 0.949282 | ||||||||
\(819\) | −14.5723 | −0.509196 | ||||||||
\(820\) | −2.25498 | −0.0787475 | ||||||||
\(821\) | −36.3813 | −1.26972 | −0.634858 | − | 0.772629i | \(-0.718942\pi\) | ||||
−0.634858 | + | 0.772629i | \(0.718942\pi\) | |||||||
\(822\) | −24.0696 | −0.839525 | ||||||||
\(823\) | 18.7577 | 0.653852 | 0.326926 | − | 0.945050i | \(-0.393987\pi\) | ||||
0.326926 | + | 0.945050i | \(0.393987\pi\) | |||||||
\(824\) | −16.1947 | −0.564170 | ||||||||
\(825\) | 1.22366 | 0.0426024 | ||||||||
\(826\) | 15.2724 | 0.531396 | ||||||||
\(827\) | −15.4047 | −0.535675 | −0.267837 | − | 0.963464i | \(-0.586309\pi\) | ||||
−0.267837 | + | 0.963464i | \(0.586309\pi\) | |||||||
\(828\) | −0.404722 | −0.0140651 | ||||||||
\(829\) | 53.0291 | 1.84178 | 0.920889 | − | 0.389824i | \(-0.127464\pi\) | ||||
0.920889 | + | 0.389824i | \(0.127464\pi\) | |||||||
\(830\) | −14.0412 | −0.487377 | ||||||||
\(831\) | −12.4470 | −0.431783 | ||||||||
\(832\) | 33.2572 | 1.15299 | ||||||||
\(833\) | 0.953761 | 0.0330459 | ||||||||
\(834\) | 19.3142 | 0.668797 | ||||||||
\(835\) | −0.617226 | −0.0213600 | ||||||||
\(836\) | 0.554463 | 0.0191765 | ||||||||
\(837\) | 4.26756 | 0.147508 | ||||||||
\(838\) | 59.2257 | 2.04592 | ||||||||
\(839\) | −1.52069 | −0.0525001 | −0.0262500 | − | 0.999655i | \(-0.508357\pi\) | ||||
−0.0262500 | + | 0.999655i | \(0.508357\pi\) | |||||||
\(840\) | 5.77693 | 0.199323 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −16.7822 | −0.578354 | ||||||||
\(843\) | 12.8006 | 0.440875 | ||||||||
\(844\) | −1.12217 | −0.0386267 | ||||||||
\(845\) | −18.3722 | −0.632024 | ||||||||
\(846\) | −2.60947 | −0.0897156 | ||||||||
\(847\) | 27.6973 | 0.951690 | ||||||||
\(848\) | −14.1875 | −0.487199 | ||||||||
\(849\) | 6.43854 | 0.220970 | ||||||||
\(850\) | −10.9941 | −0.377095 | ||||||||
\(851\) | 8.67527 | 0.297385 | ||||||||
\(852\) | 0.224534 | 0.00769242 | ||||||||
\(853\) | −38.0427 | −1.30256 | −0.651279 | − | 0.758839i | \(-0.725767\pi\) | ||||
−0.651279 | + | 0.758839i | \(0.725767\pi\) | |||||||
\(854\) | −7.24150 | −0.247799 | ||||||||
\(855\) | 4.27858 | 0.146324 | ||||||||
\(856\) | −29.6751 | −1.01428 | ||||||||
\(857\) | 0.572918 | 0.0195705 | 0.00978525 | − | 0.999952i | \(-0.496885\pi\) | ||||
0.00978525 | + | 0.999952i | \(0.496885\pi\) | |||||||
\(858\) | 2.62321 | 0.0895548 | ||||||||
\(859\) | 20.5437 | 0.700941 | 0.350471 | − | 0.936574i | \(-0.386022\pi\) | ||||
0.350471 | + | 0.936574i | \(0.386022\pi\) | |||||||
\(860\) | −3.74093 | −0.127565 | ||||||||
\(861\) | −15.3684 | −0.523755 | ||||||||
\(862\) | 38.4981 | 1.31125 | ||||||||
\(863\) | −32.0064 | −1.08951 | −0.544755 | − | 0.838595i | \(-0.683377\pi\) | ||||
−0.544755 | + | 0.838595i | \(0.683377\pi\) | |||||||
\(864\) | 2.25643 | 0.0767653 | ||||||||
\(865\) | −5.26837 | −0.179130 | ||||||||
\(866\) | −7.24798 | −0.246296 | ||||||||
\(867\) | −14.0863 | −0.478394 | ||||||||
\(868\) | −4.38351 | −0.148786 | ||||||||
\(869\) | 3.43648 | 0.116575 | ||||||||
\(870\) | 1.42684 | 0.0483744 | ||||||||
\(871\) | −40.5409 | −1.37368 | ||||||||
\(872\) | −11.9623 | −0.405094 | ||||||||
\(873\) | 3.92233 | 0.132751 | ||||||||
\(874\) | −7.21090 | −0.243912 | ||||||||
\(875\) | −21.3752 | −0.722613 | ||||||||
\(876\) | −5.61644 | −0.189762 | ||||||||
\(877\) | 21.9419 | 0.740924 | 0.370462 | − | 0.928848i | \(-0.379199\pi\) | ||||
0.370462 | + | 0.928848i | \(0.379199\pi\) | |||||||
\(878\) | 11.0243 | 0.372051 | ||||||||
\(879\) | −5.55778 | −0.187459 | ||||||||
\(880\) | −1.25935 | −0.0424528 | ||||||||
\(881\) | −56.8734 | −1.91612 | −0.958058 | − | 0.286576i | \(-0.907483\pi\) | ||||
−0.958058 | + | 0.286576i | \(0.907483\pi\) | |||||||
\(882\) | 0.866456 | 0.0291751 | ||||||||
\(883\) | −44.5561 | −1.49943 | −0.749717 | − | 0.661759i | \(-0.769810\pi\) | ||||
−0.749717 | + | 0.661759i | \(0.769810\pi\) | |||||||
\(884\) | −3.96665 | −0.133413 | ||||||||
\(885\) | −3.57053 | −0.120022 | ||||||||
\(886\) | −6.51662 | −0.218930 | ||||||||
\(887\) | 37.8541 | 1.27102 | 0.635508 | − | 0.772095i | \(-0.280791\pi\) | ||||
0.635508 | + | 0.772095i | \(0.280791\pi\) | |||||||
\(888\) | −21.4611 | −0.720187 | ||||||||
\(889\) | 24.2338 | 0.812775 | ||||||||
\(890\) | −1.38026 | −0.0462663 | ||||||||
\(891\) | −0.294618 | −0.00987006 | ||||||||
\(892\) | 3.84097 | 0.128605 | ||||||||
\(893\) | −7.82488 | −0.261850 | ||||||||
\(894\) | −16.7309 | −0.559564 | ||||||||
\(895\) | −17.7194 | −0.592295 | ||||||||
\(896\) | 34.2496 | 1.14420 | ||||||||
\(897\) | −5.74171 | −0.191710 | ||||||||
\(898\) | 29.7272 | 0.992011 | ||||||||
\(899\) | 4.26756 | 0.142331 | ||||||||
\(900\) | −1.68097 | −0.0560322 | ||||||||
\(901\) | −5.21296 | −0.173669 | ||||||||
\(902\) | 2.76653 | 0.0921154 | ||||||||
\(903\) | −25.4956 | −0.848440 | ||||||||
\(904\) | −14.4651 | −0.481102 | ||||||||
\(905\) | 0.562221 | 0.0186889 | ||||||||
\(906\) | 20.6991 | 0.687682 | ||||||||
\(907\) | −6.38111 | −0.211881 | −0.105941 | − | 0.994372i | \(-0.533785\pi\) | ||||
−0.105941 | + | 0.994372i | \(0.533785\pi\) | |||||||
\(908\) | −7.77743 | −0.258103 | ||||||||
\(909\) | −3.92185 | −0.130079 | ||||||||
\(910\) | −20.7923 | −0.689257 | ||||||||
\(911\) | 17.7182 | 0.587029 | 0.293515 | − | 0.955955i | \(-0.405175\pi\) | ||||
0.293515 | + | 0.955955i | \(0.405175\pi\) | |||||||
\(912\) | 21.6024 | 0.715329 | ||||||||
\(913\) | 2.89927 | 0.0959517 | ||||||||
\(914\) | −42.7900 | −1.41537 | ||||||||
\(915\) | 1.69299 | 0.0559684 | ||||||||
\(916\) | 4.17433 | 0.137924 | ||||||||
\(917\) | 21.2033 | 0.700195 | ||||||||
\(918\) | 2.64703 | 0.0873649 | ||||||||
\(919\) | −18.1235 | −0.597840 | −0.298920 | − | 0.954278i | \(-0.596626\pi\) | ||||
−0.298920 | + | 0.954278i | \(0.596626\pi\) | |||||||
\(920\) | 2.27621 | 0.0750443 | ||||||||
\(921\) | −5.76163 | −0.189852 | ||||||||
\(922\) | 27.4309 | 0.903390 | ||||||||
\(923\) | 3.18543 | 0.104850 | ||||||||
\(924\) | 0.302622 | 0.00995553 | ||||||||
\(925\) | 36.0318 | 1.18472 | ||||||||
\(926\) | −34.5254 | −1.13457 | ||||||||
\(927\) | −6.54643 | −0.215013 | ||||||||
\(928\) | 2.25643 | 0.0740709 | ||||||||
\(929\) | −30.2422 | −0.992215 | −0.496108 | − | 0.868261i | \(-0.665238\pi\) | ||||
−0.496108 | + | 0.868261i | \(0.665238\pi\) | |||||||
\(930\) | 6.08912 | 0.199670 | ||||||||
\(931\) | 2.59819 | 0.0851523 | ||||||||
\(932\) | 6.24970 | 0.204716 | ||||||||
\(933\) | −23.2993 | −0.762784 | ||||||||
\(934\) | 7.62700 | 0.249563 | ||||||||
\(935\) | −0.462729 | −0.0151329 | ||||||||
\(936\) | 14.2040 | 0.464272 | ||||||||
\(937\) | −21.6319 | −0.706684 | −0.353342 | − | 0.935494i | \(-0.614955\pi\) | ||||
−0.353342 | + | 0.935494i | \(0.614955\pi\) | |||||||
\(938\) | −27.7888 | −0.907335 | ||||||||
\(939\) | 16.4820 | 0.537869 | ||||||||
\(940\) | −0.626643 | −0.0204388 | ||||||||
\(941\) | 37.5162 | 1.22299 | 0.611497 | − | 0.791246i | \(-0.290568\pi\) | ||||
0.611497 | + | 0.791246i | \(0.290568\pi\) | |||||||
\(942\) | 35.8886 | 1.16931 | ||||||||
\(943\) | −6.05542 | −0.197192 | ||||||||
\(944\) | −18.0275 | −0.586746 | ||||||||
\(945\) | 2.33522 | 0.0759647 | ||||||||
\(946\) | 4.58956 | 0.149219 | ||||||||
\(947\) | 14.9169 | 0.484735 | 0.242367 | − | 0.970185i | \(-0.422076\pi\) | ||||
0.242367 | + | 0.970185i | \(0.422076\pi\) | |||||||
\(948\) | −4.72076 | −0.153323 | ||||||||
\(949\) | −79.6794 | −2.58650 | ||||||||
\(950\) | −29.9497 | −0.971695 | ||||||||
\(951\) | 19.1446 | 0.620805 | ||||||||
\(952\) | 10.7172 | 0.347345 | ||||||||
\(953\) | 51.2950 | 1.66161 | 0.830804 | − | 0.556565i | \(-0.187881\pi\) | ||||
0.830804 | + | 0.556565i | \(0.187881\pi\) | |||||||
\(954\) | −4.73577 | −0.153326 | ||||||||
\(955\) | 9.99115 | 0.323306 | ||||||||
\(956\) | −0.104265 | −0.00337218 | ||||||||
\(957\) | −0.294618 | −0.00952363 | ||||||||
\(958\) | −11.4658 | −0.370443 | ||||||||
\(959\) | −39.3933 | −1.27208 | ||||||||
\(960\) | −5.32950 | −0.172009 | ||||||||
\(961\) | −12.7879 | −0.412514 | ||||||||
\(962\) | 77.2427 | 2.49040 | ||||||||
\(963\) | −11.9957 | −0.386555 | ||||||||
\(964\) | −1.74982 | −0.0563578 | ||||||||
\(965\) | −8.68967 | −0.279730 | ||||||||
\(966\) | −3.93566 | −0.126628 | ||||||||
\(967\) | 24.8773 | 0.800000 | 0.400000 | − | 0.916515i | \(-0.369010\pi\) | ||||
0.400000 | + | 0.916515i | \(0.369010\pi\) | |||||||
\(968\) | −26.9973 | −0.867727 | ||||||||
\(969\) | 7.93748 | 0.254989 | ||||||||
\(970\) | 5.59654 | 0.179694 | ||||||||
\(971\) | 39.7251 | 1.27484 | 0.637420 | − | 0.770516i | \(-0.280002\pi\) | ||||
0.637420 | + | 0.770516i | \(0.280002\pi\) | |||||||
\(972\) | 0.404722 | 0.0129815 | ||||||||
\(973\) | 31.6104 | 1.01338 | ||||||||
\(974\) | −19.8573 | −0.636268 | ||||||||
\(975\) | −23.8476 | −0.763733 | ||||||||
\(976\) | 8.54785 | 0.273610 | ||||||||
\(977\) | 16.1055 | 0.515260 | 0.257630 | − | 0.966244i | \(-0.417058\pi\) | ||||
0.257630 | + | 0.966244i | \(0.417058\pi\) | |||||||
\(978\) | 21.9736 | 0.702637 | ||||||||
\(979\) | 0.284999 | 0.00910860 | ||||||||
\(980\) | 0.208072 | 0.00664661 | ||||||||
\(981\) | −4.83555 | −0.154387 | ||||||||
\(982\) | −13.8138 | −0.440817 | ||||||||
\(983\) | −25.5195 | −0.813946 | −0.406973 | − | 0.913440i | \(-0.633416\pi\) | ||||
−0.406973 | + | 0.913440i | \(0.633416\pi\) | |||||||
\(984\) | 14.9800 | 0.477546 | ||||||||
\(985\) | 15.7129 | 0.500656 | ||||||||
\(986\) | 2.64703 | 0.0842985 | ||||||||
\(987\) | −4.27077 | −0.135940 | ||||||||
\(988\) | −10.8058 | −0.343777 | ||||||||
\(989\) | −10.0457 | −0.319435 | ||||||||
\(990\) | −0.420372 | −0.0133603 | ||||||||
\(991\) | −48.8047 | −1.55033 | −0.775166 | − | 0.631757i | \(-0.782334\pi\) | ||||
−0.775166 | + | 0.631757i | \(0.782334\pi\) | |||||||
\(992\) | 9.62945 | 0.305735 | ||||||||
\(993\) | 16.3110 | 0.517613 | ||||||||
\(994\) | 2.18345 | 0.0692549 | ||||||||
\(995\) | 12.7170 | 0.403156 | ||||||||
\(996\) | −3.98278 | −0.126199 | ||||||||
\(997\) | −29.6198 | −0.938069 | −0.469035 | − | 0.883180i | \(-0.655398\pi\) | ||||
−0.469035 | + | 0.883180i | \(0.655398\pi\) | |||||||
\(998\) | 36.5743 | 1.15774 | ||||||||
\(999\) | −8.67527 | −0.274474 |
(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 | 2001.2.a.j.1.2 | ✓ | 7 | |
3.2 | odd | 2 | 6003.2.a.i.1.6 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.j.1.2 | ✓ | 7 | 1.1 | even | 1 | trivial | |
6003.2.a.i.1.6 | 7 | 3.2 | odd | 2 |