Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4022,2,Mod(1,4022)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4022, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4022.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4022 = 2 \cdot 2011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4022.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1158316930\) |
Analytic rank: | \(0\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 4022.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.848137 | −0.489672 | −0.244836 | − | 0.969564i | \(-0.578734\pi\) | ||||
−0.244836 | + | 0.969564i | \(0.578734\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.52415 | 1.12883 | 0.564416 | − | 0.825490i | \(-0.309101\pi\) | ||||
0.564416 | + | 0.825490i | \(0.309101\pi\) | |||||||
\(6\) | 0.848137 | 0.346251 | ||||||||
\(7\) | 4.28843 | 1.62087 | 0.810436 | − | 0.585827i | \(-0.199230\pi\) | ||||
0.810436 | + | 0.585827i | \(0.199230\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.28066 | −0.760221 | ||||||||
\(10\) | −2.52415 | −0.798205 | ||||||||
\(11\) | 1.39012 | 0.419136 | 0.209568 | − | 0.977794i | \(-0.432794\pi\) | ||||
0.209568 | + | 0.977794i | \(0.432794\pi\) | |||||||
\(12\) | −0.848137 | −0.244836 | ||||||||
\(13\) | 3.63558 | 1.00833 | 0.504164 | − | 0.863608i | \(-0.331801\pi\) | ||||
0.504164 | + | 0.863608i | \(0.331801\pi\) | |||||||
\(14\) | −4.28843 | −1.14613 | ||||||||
\(15\) | −2.14082 | −0.552758 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.705537 | −0.171118 | −0.0855589 | − | 0.996333i | \(-0.527268\pi\) | ||||
−0.0855589 | + | 0.996333i | \(0.527268\pi\) | |||||||
\(18\) | 2.28066 | 0.537557 | ||||||||
\(19\) | 6.44216 | 1.47793 | 0.738966 | − | 0.673743i | \(-0.235314\pi\) | ||||
0.738966 | + | 0.673743i | \(0.235314\pi\) | |||||||
\(20\) | 2.52415 | 0.564416 | ||||||||
\(21\) | −3.63717 | −0.793697 | ||||||||
\(22\) | −1.39012 | −0.296374 | ||||||||
\(23\) | 3.81495 | 0.795473 | 0.397736 | − | 0.917500i | \(-0.369796\pi\) | ||||
0.397736 | + | 0.917500i | \(0.369796\pi\) | |||||||
\(24\) | 0.848137 | 0.173125 | ||||||||
\(25\) | 1.37132 | 0.274264 | ||||||||
\(26\) | −3.63558 | −0.712996 | ||||||||
\(27\) | 4.47873 | 0.861932 | ||||||||
\(28\) | 4.28843 | 0.810436 | ||||||||
\(29\) | −6.00320 | −1.11477 | −0.557383 | − | 0.830255i | \(-0.688195\pi\) | ||||
−0.557383 | + | 0.830255i | \(0.688195\pi\) | |||||||
\(30\) | 2.14082 | 0.390859 | ||||||||
\(31\) | 1.54915 | 0.278235 | 0.139118 | − | 0.990276i | \(-0.455573\pi\) | ||||
0.139118 | + | 0.990276i | \(0.455573\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.17901 | −0.205239 | ||||||||
\(34\) | 0.705537 | 0.120999 | ||||||||
\(35\) | 10.8246 | 1.82969 | ||||||||
\(36\) | −2.28066 | −0.380111 | ||||||||
\(37\) | 4.11262 | 0.676111 | 0.338056 | − | 0.941126i | \(-0.390231\pi\) | ||||
0.338056 | + | 0.941126i | \(0.390231\pi\) | |||||||
\(38\) | −6.44216 | −1.04506 | ||||||||
\(39\) | −3.08347 | −0.493750 | ||||||||
\(40\) | −2.52415 | −0.399103 | ||||||||
\(41\) | −8.44136 | −1.31832 | −0.659159 | − | 0.752003i | \(-0.729088\pi\) | ||||
−0.659159 | + | 0.752003i | \(0.729088\pi\) | |||||||
\(42\) | 3.63717 | 0.561228 | ||||||||
\(43\) | 3.11793 | 0.475481 | 0.237740 | − | 0.971329i | \(-0.423593\pi\) | ||||
0.237740 | + | 0.971329i | \(0.423593\pi\) | |||||||
\(44\) | 1.39012 | 0.209568 | ||||||||
\(45\) | −5.75673 | −0.858162 | ||||||||
\(46\) | −3.81495 | −0.562484 | ||||||||
\(47\) | −1.17750 | −0.171756 | −0.0858780 | − | 0.996306i | \(-0.527370\pi\) | ||||
−0.0858780 | + | 0.996306i | \(0.527370\pi\) | |||||||
\(48\) | −0.848137 | −0.122418 | ||||||||
\(49\) | 11.3906 | 1.62723 | ||||||||
\(50\) | −1.37132 | −0.193934 | ||||||||
\(51\) | 0.598392 | 0.0837917 | ||||||||
\(52\) | 3.63558 | 0.504164 | ||||||||
\(53\) | −2.19908 | −0.302067 | −0.151033 | − | 0.988529i | \(-0.548260\pi\) | ||||
−0.151033 | + | 0.988529i | \(0.548260\pi\) | |||||||
\(54\) | −4.47873 | −0.609478 | ||||||||
\(55\) | 3.50886 | 0.473134 | ||||||||
\(56\) | −4.28843 | −0.573065 | ||||||||
\(57\) | −5.46383 | −0.723702 | ||||||||
\(58\) | 6.00320 | 0.788259 | ||||||||
\(59\) | −0.124586 | −0.0162197 | −0.00810985 | − | 0.999967i | \(-0.502581\pi\) | ||||
−0.00810985 | + | 0.999967i | \(0.502581\pi\) | |||||||
\(60\) | −2.14082 | −0.276379 | ||||||||
\(61\) | 12.4020 | 1.58791 | 0.793955 | − | 0.607977i | \(-0.208019\pi\) | ||||
0.793955 | + | 0.607977i | \(0.208019\pi\) | |||||||
\(62\) | −1.54915 | −0.196742 | ||||||||
\(63\) | −9.78046 | −1.23222 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 9.17674 | 1.13823 | ||||||||
\(66\) | 1.17901 | 0.145126 | ||||||||
\(67\) | −7.81056 | −0.954212 | −0.477106 | − | 0.878846i | \(-0.658314\pi\) | ||||
−0.477106 | + | 0.878846i | \(0.658314\pi\) | |||||||
\(68\) | −0.705537 | −0.0855589 | ||||||||
\(69\) | −3.23560 | −0.389521 | ||||||||
\(70\) | −10.8246 | −1.29379 | ||||||||
\(71\) | 13.0693 | 1.55104 | 0.775519 | − | 0.631324i | \(-0.217488\pi\) | ||||
0.775519 | + | 0.631324i | \(0.217488\pi\) | |||||||
\(72\) | 2.28066 | 0.268779 | ||||||||
\(73\) | 6.28186 | 0.735236 | 0.367618 | − | 0.929977i | \(-0.380173\pi\) | ||||
0.367618 | + | 0.929977i | \(0.380173\pi\) | |||||||
\(74\) | −4.11262 | −0.478083 | ||||||||
\(75\) | −1.16307 | −0.134299 | ||||||||
\(76\) | 6.44216 | 0.738966 | ||||||||
\(77\) | 5.96141 | 0.679366 | ||||||||
\(78\) | 3.08347 | 0.349134 | ||||||||
\(79\) | 7.77058 | 0.874258 | 0.437129 | − | 0.899399i | \(-0.355995\pi\) | ||||
0.437129 | + | 0.899399i | \(0.355995\pi\) | |||||||
\(80\) | 2.52415 | 0.282208 | ||||||||
\(81\) | 3.04341 | 0.338157 | ||||||||
\(82\) | 8.44136 | 0.932192 | ||||||||
\(83\) | 1.46305 | 0.160591 | 0.0802954 | − | 0.996771i | \(-0.474414\pi\) | ||||
0.0802954 | + | 0.996771i | \(0.474414\pi\) | |||||||
\(84\) | −3.63717 | −0.396848 | ||||||||
\(85\) | −1.78088 | −0.193163 | ||||||||
\(86\) | −3.11793 | −0.336216 | ||||||||
\(87\) | 5.09154 | 0.545870 | ||||||||
\(88\) | −1.39012 | −0.148187 | ||||||||
\(89\) | 16.1746 | 1.71451 | 0.857254 | − | 0.514893i | \(-0.172168\pi\) | ||||
0.857254 | + | 0.514893i | \(0.172168\pi\) | |||||||
\(90\) | 5.75673 | 0.606812 | ||||||||
\(91\) | 15.5909 | 1.63437 | ||||||||
\(92\) | 3.81495 | 0.397736 | ||||||||
\(93\) | −1.31389 | −0.136244 | ||||||||
\(94\) | 1.17750 | 0.121450 | ||||||||
\(95\) | 16.2609 | 1.66834 | ||||||||
\(96\) | 0.848137 | 0.0865627 | ||||||||
\(97\) | −18.6424 | −1.89285 | −0.946426 | − | 0.322922i | \(-0.895335\pi\) | ||||
−0.946426 | + | 0.322922i | \(0.895335\pi\) | |||||||
\(98\) | −11.3906 | −1.15062 | ||||||||
\(99\) | −3.17039 | −0.318636 | ||||||||
\(100\) | 1.37132 | 0.137132 | ||||||||
\(101\) | −11.9626 | −1.19033 | −0.595163 | − | 0.803605i | \(-0.702913\pi\) | ||||
−0.595163 | + | 0.803605i | \(0.702913\pi\) | |||||||
\(102\) | −0.598392 | −0.0592497 | ||||||||
\(103\) | −17.7134 | −1.74535 | −0.872675 | − | 0.488302i | \(-0.837616\pi\) | ||||
−0.872675 | + | 0.488302i | \(0.837616\pi\) | |||||||
\(104\) | −3.63558 | −0.356498 | ||||||||
\(105\) | −9.18076 | −0.895951 | ||||||||
\(106\) | 2.19908 | 0.213593 | ||||||||
\(107\) | −20.0166 | −1.93508 | −0.967539 | − | 0.252723i | \(-0.918674\pi\) | ||||
−0.967539 | + | 0.252723i | \(0.918674\pi\) | |||||||
\(108\) | 4.47873 | 0.430966 | ||||||||
\(109\) | 2.26646 | 0.217087 | 0.108544 | − | 0.994092i | \(-0.465381\pi\) | ||||
0.108544 | + | 0.994092i | \(0.465381\pi\) | |||||||
\(110\) | −3.50886 | −0.334557 | ||||||||
\(111\) | −3.48807 | −0.331073 | ||||||||
\(112\) | 4.28843 | 0.405218 | ||||||||
\(113\) | −14.5570 | −1.36941 | −0.684703 | − | 0.728822i | \(-0.740068\pi\) | ||||
−0.684703 | + | 0.728822i | \(0.740068\pi\) | |||||||
\(114\) | 5.46383 | 0.511735 | ||||||||
\(115\) | 9.62950 | 0.897956 | ||||||||
\(116\) | −6.00320 | −0.557383 | ||||||||
\(117\) | −8.29153 | −0.766552 | ||||||||
\(118\) | 0.124586 | 0.0114691 | ||||||||
\(119\) | −3.02564 | −0.277360 | ||||||||
\(120\) | 2.14082 | 0.195430 | ||||||||
\(121\) | −9.06758 | −0.824325 | ||||||||
\(122\) | −12.4020 | −1.12282 | ||||||||
\(123\) | 7.15943 | 0.645544 | ||||||||
\(124\) | 1.54915 | 0.139118 | ||||||||
\(125\) | −9.15933 | −0.819235 | ||||||||
\(126\) | 9.78046 | 0.871312 | ||||||||
\(127\) | 3.25025 | 0.288413 | 0.144207 | − | 0.989548i | \(-0.453937\pi\) | ||||
0.144207 | + | 0.989548i | \(0.453937\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −2.64444 | −0.232830 | ||||||||
\(130\) | −9.17674 | −0.804853 | ||||||||
\(131\) | 1.95777 | 0.171051 | 0.0855255 | − | 0.996336i | \(-0.472743\pi\) | ||||
0.0855255 | + | 0.996336i | \(0.472743\pi\) | |||||||
\(132\) | −1.17901 | −0.102620 | ||||||||
\(133\) | 27.6267 | 2.39554 | ||||||||
\(134\) | 7.81056 | 0.674729 | ||||||||
\(135\) | 11.3050 | 0.972977 | ||||||||
\(136\) | 0.705537 | 0.0604993 | ||||||||
\(137\) | 21.4160 | 1.82969 | 0.914845 | − | 0.403806i | \(-0.132313\pi\) | ||||
0.914845 | + | 0.403806i | \(0.132313\pi\) | |||||||
\(138\) | 3.23560 | 0.275433 | ||||||||
\(139\) | −8.89425 | −0.754401 | −0.377200 | − | 0.926132i | \(-0.623113\pi\) | ||||
−0.377200 | + | 0.926132i | \(0.623113\pi\) | |||||||
\(140\) | 10.8246 | 0.914847 | ||||||||
\(141\) | 0.998681 | 0.0841041 | ||||||||
\(142\) | −13.0693 | −1.09675 | ||||||||
\(143\) | 5.05388 | 0.422627 | ||||||||
\(144\) | −2.28066 | −0.190055 | ||||||||
\(145\) | −15.1530 | −1.25839 | ||||||||
\(146\) | −6.28186 | −0.519890 | ||||||||
\(147\) | −9.66079 | −0.796809 | ||||||||
\(148\) | 4.11262 | 0.338056 | ||||||||
\(149\) | −15.8776 | −1.30075 | −0.650373 | − | 0.759615i | \(-0.725387\pi\) | ||||
−0.650373 | + | 0.759615i | \(0.725387\pi\) | |||||||
\(150\) | 1.16307 | 0.0949639 | ||||||||
\(151\) | 14.3115 | 1.16465 | 0.582326 | − | 0.812956i | \(-0.302143\pi\) | ||||
0.582326 | + | 0.812956i | \(0.302143\pi\) | |||||||
\(152\) | −6.44216 | −0.522528 | ||||||||
\(153\) | 1.60909 | 0.130087 | ||||||||
\(154\) | −5.96141 | −0.480384 | ||||||||
\(155\) | 3.91028 | 0.314081 | ||||||||
\(156\) | −3.08347 | −0.246875 | ||||||||
\(157\) | 16.3527 | 1.30509 | 0.652543 | − | 0.757752i | \(-0.273702\pi\) | ||||
0.652543 | + | 0.757752i | \(0.273702\pi\) | |||||||
\(158\) | −7.77058 | −0.618194 | ||||||||
\(159\) | 1.86512 | 0.147914 | ||||||||
\(160\) | −2.52415 | −0.199551 | ||||||||
\(161\) | 16.3601 | 1.28936 | ||||||||
\(162\) | −3.04341 | −0.239113 | ||||||||
\(163\) | −6.71678 | −0.526099 | −0.263049 | − | 0.964782i | \(-0.584728\pi\) | ||||
−0.263049 | + | 0.964782i | \(0.584728\pi\) | |||||||
\(164\) | −8.44136 | −0.659159 | ||||||||
\(165\) | −2.97599 | −0.231681 | ||||||||
\(166\) | −1.46305 | −0.113555 | ||||||||
\(167\) | −11.3429 | −0.877740 | −0.438870 | − | 0.898551i | \(-0.644621\pi\) | ||||
−0.438870 | + | 0.898551i | \(0.644621\pi\) | |||||||
\(168\) | 3.63717 | 0.280614 | ||||||||
\(169\) | 0.217437 | 0.0167259 | ||||||||
\(170\) | 1.78088 | 0.136587 | ||||||||
\(171\) | −14.6924 | −1.12355 | ||||||||
\(172\) | 3.11793 | 0.237740 | ||||||||
\(173\) | 2.96943 | 0.225761 | 0.112881 | − | 0.993609i | \(-0.463992\pi\) | ||||
0.112881 | + | 0.993609i | \(0.463992\pi\) | |||||||
\(174\) | −5.09154 | −0.385989 | ||||||||
\(175\) | 5.88080 | 0.444546 | ||||||||
\(176\) | 1.39012 | 0.104784 | ||||||||
\(177\) | 0.105666 | 0.00794234 | ||||||||
\(178\) | −16.1746 | −1.21234 | ||||||||
\(179\) | −14.4536 | −1.08031 | −0.540156 | − | 0.841565i | \(-0.681635\pi\) | ||||
−0.540156 | + | 0.841565i | \(0.681635\pi\) | |||||||
\(180\) | −5.75673 | −0.429081 | ||||||||
\(181\) | −16.4568 | −1.22322 | −0.611612 | − | 0.791158i | \(-0.709479\pi\) | ||||
−0.611612 | + | 0.791158i | \(0.709479\pi\) | |||||||
\(182\) | −15.5909 | −1.15568 | ||||||||
\(183\) | −10.5186 | −0.777555 | ||||||||
\(184\) | −3.81495 | −0.281242 | ||||||||
\(185\) | 10.3809 | 0.763217 | ||||||||
\(186\) | 1.31389 | 0.0963391 | ||||||||
\(187\) | −0.980779 | −0.0717216 | ||||||||
\(188\) | −1.17750 | −0.0858780 | ||||||||
\(189\) | 19.2067 | 1.39708 | ||||||||
\(190\) | −16.2609 | −1.17969 | ||||||||
\(191\) | −6.67151 | −0.482734 | −0.241367 | − | 0.970434i | \(-0.577596\pi\) | ||||
−0.241367 | + | 0.970434i | \(0.577596\pi\) | |||||||
\(192\) | −0.848137 | −0.0612090 | ||||||||
\(193\) | −22.3603 | −1.60953 | −0.804763 | − | 0.593596i | \(-0.797708\pi\) | ||||
−0.804763 | + | 0.593596i | \(0.797708\pi\) | |||||||
\(194\) | 18.6424 | 1.33845 | ||||||||
\(195\) | −7.78313 | −0.557362 | ||||||||
\(196\) | 11.3906 | 0.813614 | ||||||||
\(197\) | 5.84586 | 0.416500 | 0.208250 | − | 0.978076i | \(-0.433223\pi\) | ||||
0.208250 | + | 0.978076i | \(0.433223\pi\) | |||||||
\(198\) | 3.17039 | 0.225310 | ||||||||
\(199\) | 27.1617 | 1.92544 | 0.962721 | − | 0.270496i | \(-0.0871877\pi\) | ||||
0.962721 | + | 0.270496i | \(0.0871877\pi\) | |||||||
\(200\) | −1.37132 | −0.0969668 | ||||||||
\(201\) | 6.62443 | 0.467251 | ||||||||
\(202\) | 11.9626 | 0.841688 | ||||||||
\(203\) | −25.7443 | −1.80689 | ||||||||
\(204\) | 0.598392 | 0.0418958 | ||||||||
\(205\) | −21.3072 | −1.48816 | ||||||||
\(206\) | 17.7134 | 1.23415 | ||||||||
\(207\) | −8.70062 | −0.604735 | ||||||||
\(208\) | 3.63558 | 0.252082 | ||||||||
\(209\) | 8.95535 | 0.619454 | ||||||||
\(210\) | 9.18076 | 0.633533 | ||||||||
\(211\) | −23.6704 | −1.62954 | −0.814768 | − | 0.579787i | \(-0.803136\pi\) | ||||
−0.814768 | + | 0.579787i | \(0.803136\pi\) | |||||||
\(212\) | −2.19908 | −0.151033 | ||||||||
\(213\) | −11.0845 | −0.759501 | ||||||||
\(214\) | 20.0166 | 1.36831 | ||||||||
\(215\) | 7.87013 | 0.536738 | ||||||||
\(216\) | −4.47873 | −0.304739 | ||||||||
\(217\) | 6.64341 | 0.450984 | ||||||||
\(218\) | −2.26646 | −0.153504 | ||||||||
\(219\) | −5.32788 | −0.360025 | ||||||||
\(220\) | 3.50886 | 0.236567 | ||||||||
\(221\) | −2.56504 | −0.172543 | ||||||||
\(222\) | 3.48807 | 0.234104 | ||||||||
\(223\) | 17.8834 | 1.19756 | 0.598779 | − | 0.800914i | \(-0.295653\pi\) | ||||
0.598779 | + | 0.800914i | \(0.295653\pi\) | |||||||
\(224\) | −4.28843 | −0.286533 | ||||||||
\(225\) | −3.12751 | −0.208501 | ||||||||
\(226\) | 14.5570 | 0.968317 | ||||||||
\(227\) | 23.6615 | 1.57047 | 0.785235 | − | 0.619197i | \(-0.212542\pi\) | ||||
0.785235 | + | 0.619197i | \(0.212542\pi\) | |||||||
\(228\) | −5.46383 | −0.361851 | ||||||||
\(229\) | 5.12897 | 0.338932 | 0.169466 | − | 0.985536i | \(-0.445796\pi\) | ||||
0.169466 | + | 0.985536i | \(0.445796\pi\) | |||||||
\(230\) | −9.62950 | −0.634951 | ||||||||
\(231\) | −5.05610 | −0.332667 | ||||||||
\(232\) | 6.00320 | 0.394129 | ||||||||
\(233\) | 22.6401 | 1.48320 | 0.741601 | − | 0.670841i | \(-0.234067\pi\) | ||||
0.741601 | + | 0.670841i | \(0.234067\pi\) | |||||||
\(234\) | 8.29153 | 0.542034 | ||||||||
\(235\) | −2.97218 | −0.193884 | ||||||||
\(236\) | −0.124586 | −0.00810985 | ||||||||
\(237\) | −6.59052 | −0.428100 | ||||||||
\(238\) | 3.02564 | 0.196123 | ||||||||
\(239\) | −0.757583 | −0.0490040 | −0.0245020 | − | 0.999700i | \(-0.507800\pi\) | ||||
−0.0245020 | + | 0.999700i | \(0.507800\pi\) | |||||||
\(240\) | −2.14082 | −0.138190 | ||||||||
\(241\) | 15.3907 | 0.991400 | 0.495700 | − | 0.868494i | \(-0.334912\pi\) | ||||
0.495700 | + | 0.868494i | \(0.334912\pi\) | |||||||
\(242\) | 9.06758 | 0.582886 | ||||||||
\(243\) | −16.0174 | −1.02752 | ||||||||
\(244\) | 12.4020 | 0.793955 | ||||||||
\(245\) | 28.7516 | 1.83687 | ||||||||
\(246\) | −7.15943 | −0.456469 | ||||||||
\(247\) | 23.4210 | 1.49024 | ||||||||
\(248\) | −1.54915 | −0.0983710 | ||||||||
\(249\) | −1.24087 | −0.0786369 | ||||||||
\(250\) | 9.15933 | 0.579287 | ||||||||
\(251\) | −5.72343 | −0.361260 | −0.180630 | − | 0.983551i | \(-0.557814\pi\) | ||||
−0.180630 | + | 0.983551i | \(0.557814\pi\) | |||||||
\(252\) | −9.78046 | −0.616111 | ||||||||
\(253\) | 5.30323 | 0.333411 | ||||||||
\(254\) | −3.25025 | −0.203939 | ||||||||
\(255\) | 1.51043 | 0.0945868 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −0.205041 | −0.0127901 | −0.00639504 | − | 0.999980i | \(-0.502036\pi\) | ||||
−0.00639504 | + | 0.999980i | \(0.502036\pi\) | |||||||
\(258\) | 2.64444 | 0.164635 | ||||||||
\(259\) | 17.6367 | 1.09589 | ||||||||
\(260\) | 9.17674 | 0.569117 | ||||||||
\(261\) | 13.6913 | 0.847469 | ||||||||
\(262\) | −1.95777 | −0.120951 | ||||||||
\(263\) | −25.7819 | −1.58978 | −0.794891 | − | 0.606753i | \(-0.792472\pi\) | ||||
−0.794891 | + | 0.606753i | \(0.792472\pi\) | |||||||
\(264\) | 1.17901 | 0.0725630 | ||||||||
\(265\) | −5.55079 | −0.340983 | ||||||||
\(266\) | −27.6267 | −1.69390 | ||||||||
\(267\) | −13.7183 | −0.839547 | ||||||||
\(268\) | −7.81056 | −0.477106 | ||||||||
\(269\) | 16.2087 | 0.988261 | 0.494130 | − | 0.869388i | \(-0.335487\pi\) | ||||
0.494130 | + | 0.869388i | \(0.335487\pi\) | |||||||
\(270\) | −11.3050 | −0.687998 | ||||||||
\(271\) | −16.8037 | −1.02075 | −0.510376 | − | 0.859951i | \(-0.670494\pi\) | ||||
−0.510376 | + | 0.859951i | \(0.670494\pi\) | |||||||
\(272\) | −0.705537 | −0.0427795 | ||||||||
\(273\) | −13.2232 | −0.800307 | ||||||||
\(274\) | −21.4160 | −1.29379 | ||||||||
\(275\) | 1.90629 | 0.114954 | ||||||||
\(276\) | −3.23560 | −0.194760 | ||||||||
\(277\) | 3.73395 | 0.224351 | 0.112176 | − | 0.993688i | \(-0.464218\pi\) | ||||
0.112176 | + | 0.993688i | \(0.464218\pi\) | |||||||
\(278\) | 8.89425 | 0.533442 | ||||||||
\(279\) | −3.53308 | −0.211520 | ||||||||
\(280\) | −10.8246 | −0.646895 | ||||||||
\(281\) | 32.0279 | 1.91062 | 0.955312 | − | 0.295600i | \(-0.0955196\pi\) | ||||
0.955312 | + | 0.295600i | \(0.0955196\pi\) | |||||||
\(282\) | −0.998681 | −0.0594706 | ||||||||
\(283\) | 11.3164 | 0.672691 | 0.336345 | − | 0.941739i | \(-0.390809\pi\) | ||||
0.336345 | + | 0.941739i | \(0.390809\pi\) | |||||||
\(284\) | 13.0693 | 0.775519 | ||||||||
\(285\) | −13.7915 | −0.816939 | ||||||||
\(286\) | −5.05388 | −0.298842 | ||||||||
\(287\) | −36.2002 | −2.13683 | ||||||||
\(288\) | 2.28066 | 0.134389 | ||||||||
\(289\) | −16.5022 | −0.970719 | ||||||||
\(290\) | 15.1530 | 0.889813 | ||||||||
\(291\) | 15.8113 | 0.926877 | ||||||||
\(292\) | 6.28186 | 0.367618 | ||||||||
\(293\) | 31.4834 | 1.83928 | 0.919639 | − | 0.392765i | \(-0.128481\pi\) | ||||
0.919639 | + | 0.392765i | \(0.128481\pi\) | |||||||
\(294\) | 9.66079 | 0.563429 | ||||||||
\(295\) | −0.314473 | −0.0183093 | ||||||||
\(296\) | −4.11262 | −0.239041 | ||||||||
\(297\) | 6.22595 | 0.361267 | ||||||||
\(298\) | 15.8776 | 0.919766 | ||||||||
\(299\) | 13.8696 | 0.802098 | ||||||||
\(300\) | −1.16307 | −0.0671496 | ||||||||
\(301\) | 13.3710 | 0.770694 | ||||||||
\(302\) | −14.3115 | −0.823533 | ||||||||
\(303\) | 10.1460 | 0.582870 | ||||||||
\(304\) | 6.44216 | 0.369483 | ||||||||
\(305\) | 31.3044 | 1.79248 | ||||||||
\(306\) | −1.60909 | −0.0919857 | ||||||||
\(307\) | −28.2044 | −1.60971 | −0.804856 | − | 0.593470i | \(-0.797758\pi\) | ||||
−0.804856 | + | 0.593470i | \(0.797758\pi\) | |||||||
\(308\) | 5.96141 | 0.339683 | ||||||||
\(309\) | 15.0234 | 0.854649 | ||||||||
\(310\) | −3.91028 | −0.222089 | ||||||||
\(311\) | 7.16541 | 0.406313 | 0.203156 | − | 0.979146i | \(-0.434880\pi\) | ||||
0.203156 | + | 0.979146i | \(0.434880\pi\) | |||||||
\(312\) | 3.08347 | 0.174567 | ||||||||
\(313\) | 31.5578 | 1.78375 | 0.891875 | − | 0.452281i | \(-0.149390\pi\) | ||||
0.891875 | + | 0.452281i | \(0.149390\pi\) | |||||||
\(314\) | −16.3527 | −0.922835 | ||||||||
\(315\) | −24.6873 | −1.39097 | ||||||||
\(316\) | 7.77058 | 0.437129 | ||||||||
\(317\) | 7.84681 | 0.440721 | 0.220360 | − | 0.975419i | \(-0.429277\pi\) | ||||
0.220360 | + | 0.975419i | \(0.429277\pi\) | |||||||
\(318\) | −1.86512 | −0.104591 | ||||||||
\(319\) | −8.34515 | −0.467239 | ||||||||
\(320\) | 2.52415 | 0.141104 | ||||||||
\(321\) | 16.9768 | 0.947554 | ||||||||
\(322\) | −16.3601 | −0.911715 | ||||||||
\(323\) | −4.54518 | −0.252901 | ||||||||
\(324\) | 3.04341 | 0.169079 | ||||||||
\(325\) | 4.98553 | 0.276548 | ||||||||
\(326\) | 6.71678 | 0.372008 | ||||||||
\(327\) | −1.92227 | −0.106302 | ||||||||
\(328\) | 8.44136 | 0.466096 | ||||||||
\(329\) | −5.04962 | −0.278395 | ||||||||
\(330\) | 2.97599 | 0.163823 | ||||||||
\(331\) | 18.8782 | 1.03764 | 0.518821 | − | 0.854883i | \(-0.326371\pi\) | ||||
0.518821 | + | 0.854883i | \(0.326371\pi\) | |||||||
\(332\) | 1.46305 | 0.0802954 | ||||||||
\(333\) | −9.37951 | −0.513994 | ||||||||
\(334\) | 11.3429 | 0.620656 | ||||||||
\(335\) | −19.7150 | −1.07715 | ||||||||
\(336\) | −3.63717 | −0.198424 | ||||||||
\(337\) | 29.7801 | 1.62222 | 0.811112 | − | 0.584891i | \(-0.198863\pi\) | ||||
0.811112 | + | 0.584891i | \(0.198863\pi\) | |||||||
\(338\) | −0.217437 | −0.0118270 | ||||||||
\(339\) | 12.3463 | 0.670561 | ||||||||
\(340\) | −1.78088 | −0.0965817 | ||||||||
\(341\) | 2.15350 | 0.116618 | ||||||||
\(342\) | 14.6924 | 0.794473 | ||||||||
\(343\) | 18.8288 | 1.01666 | ||||||||
\(344\) | −3.11793 | −0.168108 | ||||||||
\(345\) | −8.16714 | −0.439704 | ||||||||
\(346\) | −2.96943 | −0.159637 | ||||||||
\(347\) | 13.5235 | 0.725978 | 0.362989 | − | 0.931793i | \(-0.381756\pi\) | ||||
0.362989 | + | 0.931793i | \(0.381756\pi\) | |||||||
\(348\) | 5.09154 | 0.272935 | ||||||||
\(349\) | −17.9453 | −0.960592 | −0.480296 | − | 0.877106i | \(-0.659471\pi\) | ||||
−0.480296 | + | 0.877106i | \(0.659471\pi\) | |||||||
\(350\) | −5.88080 | −0.314342 | ||||||||
\(351\) | 16.2828 | 0.869110 | ||||||||
\(352\) | −1.39012 | −0.0740935 | ||||||||
\(353\) | −1.58860 | −0.0845525 | −0.0422762 | − | 0.999106i | \(-0.513461\pi\) | ||||
−0.0422762 | + | 0.999106i | \(0.513461\pi\) | |||||||
\(354\) | −0.105666 | −0.00561608 | ||||||||
\(355\) | 32.9888 | 1.75086 | ||||||||
\(356\) | 16.1746 | 0.857254 | ||||||||
\(357\) | 2.56616 | 0.135816 | ||||||||
\(358\) | 14.4536 | 0.763895 | ||||||||
\(359\) | −7.53761 | −0.397820 | −0.198910 | − | 0.980018i | \(-0.563740\pi\) | ||||
−0.198910 | + | 0.980018i | \(0.563740\pi\) | |||||||
\(360\) | 5.75673 | 0.303406 | ||||||||
\(361\) | 22.5014 | 1.18428 | ||||||||
\(362\) | 16.4568 | 0.864950 | ||||||||
\(363\) | 7.69055 | 0.403649 | ||||||||
\(364\) | 15.5909 | 0.817186 | ||||||||
\(365\) | 15.8563 | 0.829958 | ||||||||
\(366\) | 10.5186 | 0.549815 | ||||||||
\(367\) | −22.2254 | −1.16016 | −0.580078 | − | 0.814561i | \(-0.696978\pi\) | ||||
−0.580078 | + | 0.814561i | \(0.696978\pi\) | |||||||
\(368\) | 3.81495 | 0.198868 | ||||||||
\(369\) | 19.2519 | 1.00221 | ||||||||
\(370\) | −10.3809 | −0.539676 | ||||||||
\(371\) | −9.43058 | −0.489611 | ||||||||
\(372\) | −1.31389 | −0.0681220 | ||||||||
\(373\) | −3.50558 | −0.181512 | −0.0907560 | − | 0.995873i | \(-0.528928\pi\) | ||||
−0.0907560 | + | 0.995873i | \(0.528928\pi\) | |||||||
\(374\) | 0.980779 | 0.0507149 | ||||||||
\(375\) | 7.76837 | 0.401157 | ||||||||
\(376\) | 1.17750 | 0.0607249 | ||||||||
\(377\) | −21.8251 | −1.12405 | ||||||||
\(378\) | −19.2067 | −0.987886 | ||||||||
\(379\) | 31.1315 | 1.59912 | 0.799560 | − | 0.600587i | \(-0.205066\pi\) | ||||
0.799560 | + | 0.600587i | \(0.205066\pi\) | |||||||
\(380\) | 16.2609 | 0.834169 | ||||||||
\(381\) | −2.75666 | −0.141228 | ||||||||
\(382\) | 6.67151 | 0.341344 | ||||||||
\(383\) | 1.47085 | 0.0751571 | 0.0375786 | − | 0.999294i | \(-0.488036\pi\) | ||||
0.0375786 | + | 0.999294i | \(0.488036\pi\) | |||||||
\(384\) | 0.848137 | 0.0432813 | ||||||||
\(385\) | 15.0475 | 0.766891 | ||||||||
\(386\) | 22.3603 | 1.13811 | ||||||||
\(387\) | −7.11096 | −0.361470 | ||||||||
\(388\) | −18.6424 | −0.946426 | ||||||||
\(389\) | −6.12789 | −0.310697 | −0.155348 | − | 0.987860i | \(-0.549650\pi\) | ||||
−0.155348 | + | 0.987860i | \(0.549650\pi\) | |||||||
\(390\) | 7.78313 | 0.394114 | ||||||||
\(391\) | −2.69159 | −0.136120 | ||||||||
\(392\) | −11.3906 | −0.575312 | ||||||||
\(393\) | −1.66046 | −0.0837589 | ||||||||
\(394\) | −5.84586 | −0.294510 | ||||||||
\(395\) | 19.6141 | 0.986891 | ||||||||
\(396\) | −3.17039 | −0.159318 | ||||||||
\(397\) | −24.6791 | −1.23861 | −0.619304 | − | 0.785151i | \(-0.712585\pi\) | ||||
−0.619304 | + | 0.785151i | \(0.712585\pi\) | |||||||
\(398\) | −27.1617 | −1.36149 | ||||||||
\(399\) | −23.4312 | −1.17303 | ||||||||
\(400\) | 1.37132 | 0.0685659 | ||||||||
\(401\) | −12.5963 | −0.629030 | −0.314515 | − | 0.949252i | \(-0.601842\pi\) | ||||
−0.314515 | + | 0.949252i | \(0.601842\pi\) | |||||||
\(402\) | −6.62443 | −0.330396 | ||||||||
\(403\) | 5.63205 | 0.280552 | ||||||||
\(404\) | −11.9626 | −0.595163 | ||||||||
\(405\) | 7.68202 | 0.381723 | ||||||||
\(406\) | 25.7443 | 1.27767 | ||||||||
\(407\) | 5.71703 | 0.283383 | ||||||||
\(408\) | −0.598392 | −0.0296248 | ||||||||
\(409\) | −26.8009 | −1.32522 | −0.662610 | − | 0.748964i | \(-0.730551\pi\) | ||||
−0.662610 | + | 0.748964i | \(0.730551\pi\) | |||||||
\(410\) | 21.3072 | 1.05229 | ||||||||
\(411\) | −18.1637 | −0.895948 | ||||||||
\(412\) | −17.7134 | −0.872675 | ||||||||
\(413\) | −0.534277 | −0.0262901 | ||||||||
\(414\) | 8.70062 | 0.427612 | ||||||||
\(415\) | 3.69296 | 0.181280 | ||||||||
\(416\) | −3.63558 | −0.178249 | ||||||||
\(417\) | 7.54355 | 0.369409 | ||||||||
\(418\) | −8.95535 | −0.438020 | ||||||||
\(419\) | −17.4599 | −0.852971 | −0.426486 | − | 0.904494i | \(-0.640249\pi\) | ||||
−0.426486 | + | 0.904494i | \(0.640249\pi\) | |||||||
\(420\) | −9.18076 | −0.447975 | ||||||||
\(421\) | 27.1884 | 1.32508 | 0.662541 | − | 0.749025i | \(-0.269478\pi\) | ||||
0.662541 | + | 0.749025i | \(0.269478\pi\) | |||||||
\(422\) | 23.6704 | 1.15226 | ||||||||
\(423\) | 2.68548 | 0.130572 | ||||||||
\(424\) | 2.19908 | 0.106797 | ||||||||
\(425\) | −0.967515 | −0.0469314 | ||||||||
\(426\) | 11.0845 | 0.537048 | ||||||||
\(427\) | 53.1849 | 2.57380 | ||||||||
\(428\) | −20.0166 | −0.967539 | ||||||||
\(429\) | −4.28638 | −0.206949 | ||||||||
\(430\) | −7.87013 | −0.379531 | ||||||||
\(431\) | 1.99033 | 0.0958706 | 0.0479353 | − | 0.998850i | \(-0.484736\pi\) | ||||
0.0479353 | + | 0.998850i | \(0.484736\pi\) | |||||||
\(432\) | 4.47873 | 0.215483 | ||||||||
\(433\) | −13.7589 | −0.661210 | −0.330605 | − | 0.943769i | \(-0.607253\pi\) | ||||
−0.330605 | + | 0.943769i | \(0.607253\pi\) | |||||||
\(434\) | −6.64341 | −0.318894 | ||||||||
\(435\) | 12.8518 | 0.616196 | ||||||||
\(436\) | 2.26646 | 0.108544 | ||||||||
\(437\) | 24.5765 | 1.17565 | ||||||||
\(438\) | 5.32788 | 0.254576 | ||||||||
\(439\) | 9.47256 | 0.452101 | 0.226050 | − | 0.974116i | \(-0.427419\pi\) | ||||
0.226050 | + | 0.974116i | \(0.427419\pi\) | |||||||
\(440\) | −3.50886 | −0.167278 | ||||||||
\(441\) | −25.9781 | −1.23705 | ||||||||
\(442\) | 2.56504 | 0.122006 | ||||||||
\(443\) | 24.4260 | 1.16052 | 0.580258 | − | 0.814433i | \(-0.302952\pi\) | ||||
0.580258 | + | 0.814433i | \(0.302952\pi\) | |||||||
\(444\) | −3.48807 | −0.165536 | ||||||||
\(445\) | 40.8272 | 1.93539 | ||||||||
\(446\) | −17.8834 | −0.846801 | ||||||||
\(447\) | 13.4664 | 0.636939 | ||||||||
\(448\) | 4.28843 | 0.202609 | ||||||||
\(449\) | −32.5829 | −1.53768 | −0.768841 | − | 0.639441i | \(-0.779166\pi\) | ||||
−0.768841 | + | 0.639441i | \(0.779166\pi\) | |||||||
\(450\) | 3.12751 | 0.147432 | ||||||||
\(451\) | −11.7345 | −0.552555 | ||||||||
\(452\) | −14.5570 | −0.684703 | ||||||||
\(453\) | −12.1381 | −0.570297 | ||||||||
\(454\) | −23.6615 | −1.11049 | ||||||||
\(455\) | 39.3538 | 1.84493 | ||||||||
\(456\) | 5.46383 | 0.255867 | ||||||||
\(457\) | 41.3262 | 1.93316 | 0.966580 | − | 0.256367i | \(-0.0825255\pi\) | ||||
0.966580 | + | 0.256367i | \(0.0825255\pi\) | |||||||
\(458\) | −5.12897 | −0.239661 | ||||||||
\(459\) | −3.15991 | −0.147492 | ||||||||
\(460\) | 9.62950 | 0.448978 | ||||||||
\(461\) | −19.6357 | −0.914528 | −0.457264 | − | 0.889331i | \(-0.651171\pi\) | ||||
−0.457264 | + | 0.889331i | \(0.651171\pi\) | |||||||
\(462\) | 5.05610 | 0.235231 | ||||||||
\(463\) | 42.8568 | 1.99172 | 0.995861 | − | 0.0908841i | \(-0.0289693\pi\) | ||||
0.995861 | + | 0.0908841i | \(0.0289693\pi\) | |||||||
\(464\) | −6.00320 | −0.278692 | ||||||||
\(465\) | −3.31645 | −0.153797 | ||||||||
\(466\) | −22.6401 | −1.04878 | ||||||||
\(467\) | −33.6907 | −1.55902 | −0.779509 | − | 0.626391i | \(-0.784531\pi\) | ||||
−0.779509 | + | 0.626391i | \(0.784531\pi\) | |||||||
\(468\) | −8.29153 | −0.383276 | ||||||||
\(469\) | −33.4950 | −1.54666 | ||||||||
\(470\) | 2.97218 | 0.137097 | ||||||||
\(471\) | −13.8693 | −0.639065 | ||||||||
\(472\) | 0.124586 | 0.00573453 | ||||||||
\(473\) | 4.33429 | 0.199291 | ||||||||
\(474\) | 6.59052 | 0.302712 | ||||||||
\(475\) | 8.83424 | 0.405343 | ||||||||
\(476\) | −3.02564 | −0.138680 | ||||||||
\(477\) | 5.01535 | 0.229637 | ||||||||
\(478\) | 0.757583 | 0.0346511 | ||||||||
\(479\) | 12.7300 | 0.581647 | 0.290824 | − | 0.956777i | \(-0.406071\pi\) | ||||
0.290824 | + | 0.956777i | \(0.406071\pi\) | |||||||
\(480\) | 2.14082 | 0.0977148 | ||||||||
\(481\) | 14.9518 | 0.681742 | ||||||||
\(482\) | −15.3907 | −0.701026 | ||||||||
\(483\) | −13.8757 | −0.631364 | ||||||||
\(484\) | −9.06758 | −0.412163 | ||||||||
\(485\) | −47.0562 | −2.13671 | ||||||||
\(486\) | 16.0174 | 0.726565 | ||||||||
\(487\) | −13.2547 | −0.600627 | −0.300313 | − | 0.953841i | \(-0.597091\pi\) | ||||
−0.300313 | + | 0.953841i | \(0.597091\pi\) | |||||||
\(488\) | −12.4020 | −0.561411 | ||||||||
\(489\) | 5.69675 | 0.257616 | ||||||||
\(490\) | −28.7516 | −1.29886 | ||||||||
\(491\) | 35.4462 | 1.59967 | 0.799833 | − | 0.600223i | \(-0.204921\pi\) | ||||
0.799833 | + | 0.600223i | \(0.204921\pi\) | |||||||
\(492\) | 7.15943 | 0.322772 | ||||||||
\(493\) | 4.23548 | 0.190756 | ||||||||
\(494\) | −23.4210 | −1.05376 | ||||||||
\(495\) | −8.00253 | −0.359687 | ||||||||
\(496\) | 1.54915 | 0.0695588 | ||||||||
\(497\) | 56.0467 | 2.51404 | ||||||||
\(498\) | 1.24087 | 0.0556047 | ||||||||
\(499\) | −19.7405 | −0.883706 | −0.441853 | − | 0.897087i | \(-0.645679\pi\) | ||||
−0.441853 | + | 0.897087i | \(0.645679\pi\) | |||||||
\(500\) | −9.15933 | −0.409618 | ||||||||
\(501\) | 9.62034 | 0.429805 | ||||||||
\(502\) | 5.72343 | 0.255449 | ||||||||
\(503\) | −43.3502 | −1.93289 | −0.966445 | − | 0.256875i | \(-0.917307\pi\) | ||||
−0.966445 | + | 0.256875i | \(0.917307\pi\) | |||||||
\(504\) | 9.78046 | 0.435656 | ||||||||
\(505\) | −30.1954 | −1.34368 | ||||||||
\(506\) | −5.30323 | −0.235757 | ||||||||
\(507\) | −0.184417 | −0.00819023 | ||||||||
\(508\) | 3.25025 | 0.144207 | ||||||||
\(509\) | −11.3968 | −0.505154 | −0.252577 | − | 0.967577i | \(-0.581278\pi\) | ||||
−0.252577 | + | 0.967577i | \(0.581278\pi\) | |||||||
\(510\) | −1.51043 | −0.0668830 | ||||||||
\(511\) | 26.9393 | 1.19172 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 28.8527 | 1.27388 | ||||||||
\(514\) | 0.205041 | 0.00904395 | ||||||||
\(515\) | −44.7111 | −1.97021 | ||||||||
\(516\) | −2.64444 | −0.116415 | ||||||||
\(517\) | −1.63686 | −0.0719891 | ||||||||
\(518\) | −17.6367 | −0.774912 | ||||||||
\(519\) | −2.51848 | −0.110549 | ||||||||
\(520\) | −9.17674 | −0.402427 | ||||||||
\(521\) | 31.7470 | 1.39086 | 0.695432 | − | 0.718592i | \(-0.255213\pi\) | ||||
0.695432 | + | 0.718592i | \(0.255213\pi\) | |||||||
\(522\) | −13.6913 | −0.599251 | ||||||||
\(523\) | 2.45982 | 0.107560 | 0.0537802 | − | 0.998553i | \(-0.482873\pi\) | ||||
0.0537802 | + | 0.998553i | \(0.482873\pi\) | |||||||
\(524\) | 1.95777 | 0.0855255 | ||||||||
\(525\) | −4.98772 | −0.217682 | ||||||||
\(526\) | 25.7819 | 1.12415 | ||||||||
\(527\) | −1.09298 | −0.0476110 | ||||||||
\(528\) | −1.17901 | −0.0513098 | ||||||||
\(529\) | −8.44613 | −0.367223 | ||||||||
\(530\) | 5.55079 | 0.241111 | ||||||||
\(531\) | 0.284138 | 0.0123306 | ||||||||
\(532\) | 27.6267 | 1.19777 | ||||||||
\(533\) | −30.6892 | −1.32930 | ||||||||
\(534\) | 13.7183 | 0.593650 | ||||||||
\(535\) | −50.5248 | −2.18438 | ||||||||
\(536\) | 7.81056 | 0.337365 | ||||||||
\(537\) | 12.2586 | 0.528999 | ||||||||
\(538\) | −16.2087 | −0.698806 | ||||||||
\(539\) | 15.8343 | 0.682030 | ||||||||
\(540\) | 11.3050 | 0.486488 | ||||||||
\(541\) | 32.2425 | 1.38621 | 0.693106 | − | 0.720836i | \(-0.256242\pi\) | ||||
0.693106 | + | 0.720836i | \(0.256242\pi\) | |||||||
\(542\) | 16.8037 | 0.721781 | ||||||||
\(543\) | 13.9576 | 0.598979 | ||||||||
\(544\) | 0.705537 | 0.0302496 | ||||||||
\(545\) | 5.72087 | 0.245055 | ||||||||
\(546\) | 13.2232 | 0.565902 | ||||||||
\(547\) | 4.14648 | 0.177291 | 0.0886454 | − | 0.996063i | \(-0.471746\pi\) | ||||
0.0886454 | + | 0.996063i | \(0.471746\pi\) | |||||||
\(548\) | 21.4160 | 0.914845 | ||||||||
\(549\) | −28.2847 | −1.20716 | ||||||||
\(550\) | −1.90629 | −0.0812846 | ||||||||
\(551\) | −38.6736 | −1.64755 | ||||||||
\(552\) | 3.23560 | 0.137716 | ||||||||
\(553\) | 33.3235 | 1.41706 | ||||||||
\(554\) | −3.73395 | −0.158640 | ||||||||
\(555\) | −8.80440 | −0.373726 | ||||||||
\(556\) | −8.89425 | −0.377200 | ||||||||
\(557\) | −37.4512 | −1.58686 | −0.793429 | − | 0.608663i | \(-0.791706\pi\) | ||||
−0.793429 | + | 0.608663i | \(0.791706\pi\) | |||||||
\(558\) | 3.53308 | 0.149567 | ||||||||
\(559\) | 11.3355 | 0.479441 | ||||||||
\(560\) | 10.8246 | 0.457424 | ||||||||
\(561\) | 0.831835 | 0.0351201 | ||||||||
\(562\) | −32.0279 | −1.35101 | ||||||||
\(563\) | 15.3689 | 0.647722 | 0.323861 | − | 0.946105i | \(-0.395019\pi\) | ||||
0.323861 | + | 0.946105i | \(0.395019\pi\) | |||||||
\(564\) | 0.998681 | 0.0420521 | ||||||||
\(565\) | −36.7440 | −1.54583 | ||||||||
\(566\) | −11.3164 | −0.475664 | ||||||||
\(567\) | 13.0515 | 0.548110 | ||||||||
\(568\) | −13.0693 | −0.548375 | ||||||||
\(569\) | −35.2378 | −1.47725 | −0.738623 | − | 0.674119i | \(-0.764524\pi\) | ||||
−0.738623 | + | 0.674119i | \(0.764524\pi\) | |||||||
\(570\) | 13.7915 | 0.577663 | ||||||||
\(571\) | −4.23440 | −0.177204 | −0.0886021 | − | 0.996067i | \(-0.528240\pi\) | ||||
−0.0886021 | + | 0.996067i | \(0.528240\pi\) | |||||||
\(572\) | 5.05388 | 0.211313 | ||||||||
\(573\) | 5.65836 | 0.236381 | ||||||||
\(574\) | 36.2002 | 1.51097 | ||||||||
\(575\) | 5.23151 | 0.218169 | ||||||||
\(576\) | −2.28066 | −0.0950276 | ||||||||
\(577\) | 18.6658 | 0.777069 | 0.388534 | − | 0.921434i | \(-0.372981\pi\) | ||||
0.388534 | + | 0.921434i | \(0.372981\pi\) | |||||||
\(578\) | 16.5022 | 0.686402 | ||||||||
\(579\) | 18.9646 | 0.788141 | ||||||||
\(580\) | −15.1530 | −0.629193 | ||||||||
\(581\) | 6.27419 | 0.260297 | ||||||||
\(582\) | −15.8113 | −0.655401 | ||||||||
\(583\) | −3.05697 | −0.126607 | ||||||||
\(584\) | −6.28186 | −0.259945 | ||||||||
\(585\) | −20.9290 | −0.865309 | ||||||||
\(586\) | −31.4834 | −1.30057 | ||||||||
\(587\) | 13.8080 | 0.569917 | 0.284958 | − | 0.958540i | \(-0.408020\pi\) | ||||
0.284958 | + | 0.958540i | \(0.408020\pi\) | |||||||
\(588\) | −9.66079 | −0.398404 | ||||||||
\(589\) | 9.97985 | 0.411213 | ||||||||
\(590\) | 0.314473 | 0.0129466 | ||||||||
\(591\) | −4.95809 | −0.203949 | ||||||||
\(592\) | 4.11262 | 0.169028 | ||||||||
\(593\) | 34.9226 | 1.43410 | 0.717049 | − | 0.697023i | \(-0.245492\pi\) | ||||
0.717049 | + | 0.697023i | \(0.245492\pi\) | |||||||
\(594\) | −6.22595 | −0.255454 | ||||||||
\(595\) | −7.63717 | −0.313093 | ||||||||
\(596\) | −15.8776 | −0.650373 | ||||||||
\(597\) | −23.0369 | −0.942836 | ||||||||
\(598\) | −13.8696 | −0.567169 | ||||||||
\(599\) | −2.59642 | −0.106087 | −0.0530433 | − | 0.998592i | \(-0.516892\pi\) | ||||
−0.0530433 | + | 0.998592i | \(0.516892\pi\) | |||||||
\(600\) | 1.16307 | 0.0474820 | ||||||||
\(601\) | −27.0250 | −1.10237 | −0.551186 | − | 0.834382i | \(-0.685825\pi\) | ||||
−0.551186 | + | 0.834382i | \(0.685825\pi\) | |||||||
\(602\) | −13.3710 | −0.544963 | ||||||||
\(603\) | 17.8133 | 0.725412 | ||||||||
\(604\) | 14.3115 | 0.582326 | ||||||||
\(605\) | −22.8879 | −0.930525 | ||||||||
\(606\) | −10.1460 | −0.412151 | ||||||||
\(607\) | −31.8214 | −1.29159 | −0.645795 | − | 0.763511i | \(-0.723474\pi\) | ||||
−0.645795 | + | 0.763511i | \(0.723474\pi\) | |||||||
\(608\) | −6.44216 | −0.261264 | ||||||||
\(609\) | 21.8347 | 0.884786 | ||||||||
\(610\) | −31.3044 | −1.26748 | ||||||||
\(611\) | −4.28089 | −0.173186 | ||||||||
\(612\) | 1.60909 | 0.0650437 | ||||||||
\(613\) | 37.5120 | 1.51510 | 0.757549 | − | 0.652779i | \(-0.226397\pi\) | ||||
0.757549 | + | 0.652779i | \(0.226397\pi\) | |||||||
\(614\) | 28.2044 | 1.13824 | ||||||||
\(615\) | 18.0715 | 0.728712 | ||||||||
\(616\) | −5.96141 | −0.240192 | ||||||||
\(617\) | 6.35395 | 0.255800 | 0.127900 | − | 0.991787i | \(-0.459176\pi\) | ||||
0.127900 | + | 0.991787i | \(0.459176\pi\) | |||||||
\(618\) | −15.0234 | −0.604328 | ||||||||
\(619\) | −38.1690 | −1.53414 | −0.767070 | − | 0.641563i | \(-0.778286\pi\) | ||||
−0.767070 | + | 0.641563i | \(0.778286\pi\) | |||||||
\(620\) | 3.91028 | 0.157040 | ||||||||
\(621\) | 17.0861 | 0.685643 | ||||||||
\(622\) | −7.16541 | −0.287307 | ||||||||
\(623\) | 69.3638 | 2.77900 | ||||||||
\(624\) | −3.08347 | −0.123438 | ||||||||
\(625\) | −29.9761 | −1.19904 | ||||||||
\(626\) | −31.5578 | −1.26130 | ||||||||
\(627\) | −7.59537 | −0.303330 | ||||||||
\(628\) | 16.3527 | 0.652543 | ||||||||
\(629\) | −2.90161 | −0.115695 | ||||||||
\(630\) | 24.6873 | 0.983566 | ||||||||
\(631\) | −15.5718 | −0.619904 | −0.309952 | − | 0.950752i | \(-0.600313\pi\) | ||||
−0.309952 | + | 0.950752i | \(0.600313\pi\) | |||||||
\(632\) | −7.77058 | −0.309097 | ||||||||
\(633\) | 20.0757 | 0.797939 | ||||||||
\(634\) | −7.84681 | −0.311637 | ||||||||
\(635\) | 8.20411 | 0.325570 | ||||||||
\(636\) | 1.86512 | 0.0739568 | ||||||||
\(637\) | 41.4114 | 1.64078 | ||||||||
\(638\) | 8.34515 | 0.330388 | ||||||||
\(639\) | −29.8066 | −1.17913 | ||||||||
\(640\) | −2.52415 | −0.0997757 | ||||||||
\(641\) | −26.1849 | −1.03424 | −0.517121 | − | 0.855913i | \(-0.672996\pi\) | ||||
−0.517121 | + | 0.855913i | \(0.672996\pi\) | |||||||
\(642\) | −16.9768 | −0.670022 | ||||||||
\(643\) | 6.17217 | 0.243407 | 0.121703 | − | 0.992567i | \(-0.461164\pi\) | ||||
0.121703 | + | 0.992567i | \(0.461164\pi\) | |||||||
\(644\) | 16.3601 | 0.644680 | ||||||||
\(645\) | −6.67495 | −0.262826 | ||||||||
\(646\) | 4.54518 | 0.178828 | ||||||||
\(647\) | −10.5034 | −0.412931 | −0.206465 | − | 0.978454i | \(-0.566196\pi\) | ||||
−0.206465 | + | 0.978454i | \(0.566196\pi\) | |||||||
\(648\) | −3.04341 | −0.119557 | ||||||||
\(649\) | −0.173189 | −0.00679826 | ||||||||
\(650\) | −4.98553 | −0.195549 | ||||||||
\(651\) | −5.63452 | −0.220834 | ||||||||
\(652\) | −6.71678 | −0.263049 | ||||||||
\(653\) | 12.3841 | 0.484628 | 0.242314 | − | 0.970198i | \(-0.422094\pi\) | ||||
0.242314 | + | 0.970198i | \(0.422094\pi\) | |||||||
\(654\) | 1.92227 | 0.0751666 | ||||||||
\(655\) | 4.94169 | 0.193088 | ||||||||
\(656\) | −8.44136 | −0.329580 | ||||||||
\(657\) | −14.3268 | −0.558942 | ||||||||
\(658\) | 5.04962 | 0.196855 | ||||||||
\(659\) | −8.97817 | −0.349740 | −0.174870 | − | 0.984592i | \(-0.555951\pi\) | ||||
−0.174870 | + | 0.984592i | \(0.555951\pi\) | |||||||
\(660\) | −2.97599 | −0.115840 | ||||||||
\(661\) | −26.8418 | −1.04403 | −0.522013 | − | 0.852938i | \(-0.674819\pi\) | ||||
−0.522013 | + | 0.852938i | \(0.674819\pi\) | |||||||
\(662\) | −18.8782 | −0.733723 | ||||||||
\(663\) | 2.17550 | 0.0844895 | ||||||||
\(664\) | −1.46305 | −0.0567774 | ||||||||
\(665\) | 69.7339 | 2.70416 | ||||||||
\(666\) | 9.37951 | 0.363449 | ||||||||
\(667\) | −22.9019 | −0.886766 | ||||||||
\(668\) | −11.3429 | −0.438870 | ||||||||
\(669\) | −15.1675 | −0.586411 | ||||||||
\(670\) | 19.7150 | 0.761657 | ||||||||
\(671\) | 17.2402 | 0.665550 | ||||||||
\(672\) | 3.63717 | 0.140307 | ||||||||
\(673\) | 14.8725 | 0.573294 | 0.286647 | − | 0.958036i | \(-0.407459\pi\) | ||||
0.286647 | + | 0.958036i | \(0.407459\pi\) | |||||||
\(674\) | −29.7801 | −1.14709 | ||||||||
\(675\) | 6.14176 | 0.236396 | ||||||||
\(676\) | 0.217437 | 0.00836297 | ||||||||
\(677\) | 2.44642 | 0.0940237 | 0.0470118 | − | 0.998894i | \(-0.485030\pi\) | ||||
0.0470118 | + | 0.998894i | \(0.485030\pi\) | |||||||
\(678\) | −12.3463 | −0.474158 | ||||||||
\(679\) | −79.9467 | −3.06807 | ||||||||
\(680\) | 1.78088 | 0.0682936 | ||||||||
\(681\) | −20.0682 | −0.769016 | ||||||||
\(682\) | −2.15350 | −0.0824616 | ||||||||
\(683\) | 7.15665 | 0.273842 | 0.136921 | − | 0.990582i | \(-0.456279\pi\) | ||||
0.136921 | + | 0.990582i | \(0.456279\pi\) | |||||||
\(684\) | −14.6924 | −0.561777 | ||||||||
\(685\) | 54.0570 | 2.06541 | ||||||||
\(686\) | −18.8288 | −0.718886 | ||||||||
\(687\) | −4.35007 | −0.165965 | ||||||||
\(688\) | 3.11793 | 0.118870 | ||||||||
\(689\) | −7.99492 | −0.304582 | ||||||||
\(690\) | 8.16714 | 0.310918 | ||||||||
\(691\) | −27.0859 | −1.03040 | −0.515198 | − | 0.857071i | \(-0.672282\pi\) | ||||
−0.515198 | + | 0.857071i | \(0.672282\pi\) | |||||||
\(692\) | 2.96943 | 0.112881 | ||||||||
\(693\) | −13.5960 | −0.516468 | ||||||||
\(694\) | −13.5235 | −0.513344 | ||||||||
\(695\) | −22.4504 | −0.851592 | ||||||||
\(696\) | −5.09154 | −0.192994 | ||||||||
\(697\) | 5.95569 | 0.225588 | ||||||||
\(698\) | 17.9453 | 0.679241 | ||||||||
\(699\) | −19.2019 | −0.726283 | ||||||||
\(700\) | 5.88080 | 0.222273 | ||||||||
\(701\) | 50.3868 | 1.90308 | 0.951542 | − | 0.307518i | \(-0.0994984\pi\) | ||||
0.951542 | + | 0.307518i | \(0.0994984\pi\) | |||||||
\(702\) | −16.2828 | −0.614554 | ||||||||
\(703\) | 26.4942 | 0.999246 | ||||||||
\(704\) | 1.39012 | 0.0523920 | ||||||||
\(705\) | 2.52082 | 0.0949395 | ||||||||
\(706\) | 1.58860 | 0.0597876 | ||||||||
\(707\) | −51.3009 | −1.92937 | ||||||||
\(708\) | 0.105666 | 0.00397117 | ||||||||
\(709\) | 11.8120 | 0.443610 | 0.221805 | − | 0.975091i | \(-0.428805\pi\) | ||||
0.221805 | + | 0.975091i | \(0.428805\pi\) | |||||||
\(710\) | −32.9888 | −1.23805 | ||||||||
\(711\) | −17.7221 | −0.664629 | ||||||||
\(712\) | −16.1746 | −0.606170 | ||||||||
\(713\) | 5.90993 | 0.221328 | ||||||||
\(714\) | −2.56616 | −0.0960362 | ||||||||
\(715\) | 12.7567 | 0.477075 | ||||||||
\(716\) | −14.4536 | −0.540156 | ||||||||
\(717\) | 0.642535 | 0.0239959 | ||||||||
\(718\) | 7.53761 | 0.281301 | ||||||||
\(719\) | 30.3062 | 1.13023 | 0.565115 | − | 0.825012i | \(-0.308832\pi\) | ||||
0.565115 | + | 0.825012i | \(0.308832\pi\) | |||||||
\(720\) | −5.75673 | −0.214541 | ||||||||
\(721\) | −75.9624 | −2.82899 | ||||||||
\(722\) | −22.5014 | −0.837414 | ||||||||
\(723\) | −13.0534 | −0.485461 | ||||||||
\(724\) | −16.4568 | −0.611612 | ||||||||
\(725\) | −8.23230 | −0.305740 | ||||||||
\(726\) | −7.69055 | −0.285423 | ||||||||
\(727\) | 6.54366 | 0.242691 | 0.121345 | − | 0.992610i | \(-0.461279\pi\) | ||||
0.121345 | + | 0.992610i | \(0.461279\pi\) | |||||||
\(728\) | −15.5909 | −0.577838 | ||||||||
\(729\) | 4.45473 | 0.164990 | ||||||||
\(730\) | −15.8563 | −0.586869 | ||||||||
\(731\) | −2.19982 | −0.0813632 | ||||||||
\(732\) | −10.5186 | −0.388778 | ||||||||
\(733\) | −1.62664 | −0.0600813 | −0.0300406 | − | 0.999549i | \(-0.509564\pi\) | ||||
−0.0300406 | + | 0.999549i | \(0.509564\pi\) | |||||||
\(734\) | 22.2254 | 0.820354 | ||||||||
\(735\) | −24.3853 | −0.899464 | ||||||||
\(736\) | −3.81495 | −0.140621 | ||||||||
\(737\) | −10.8576 | −0.399944 | ||||||||
\(738\) | −19.2519 | −0.708672 | ||||||||
\(739\) | 40.7557 | 1.49922 | 0.749612 | − | 0.661878i | \(-0.230240\pi\) | ||||
0.749612 | + | 0.661878i | \(0.230240\pi\) | |||||||
\(740\) | 10.3809 | 0.381608 | ||||||||
\(741\) | −19.8642 | −0.729730 | ||||||||
\(742\) | 9.43058 | 0.346208 | ||||||||
\(743\) | 5.56392 | 0.204120 | 0.102060 | − | 0.994778i | \(-0.467457\pi\) | ||||
0.102060 | + | 0.994778i | \(0.467457\pi\) | |||||||
\(744\) | 1.31389 | 0.0481695 | ||||||||
\(745\) | −40.0775 | −1.46832 | ||||||||
\(746\) | 3.50558 | 0.128348 | ||||||||
\(747\) | −3.33673 | −0.122085 | ||||||||
\(748\) | −0.980779 | −0.0358608 | ||||||||
\(749\) | −85.8397 | −3.13651 | ||||||||
\(750\) | −7.76837 | −0.283661 | ||||||||
\(751\) | −26.1738 | −0.955096 | −0.477548 | − | 0.878606i | \(-0.658474\pi\) | ||||
−0.477548 | + | 0.878606i | \(0.658474\pi\) | |||||||
\(752\) | −1.17750 | −0.0429390 | ||||||||
\(753\) | 4.85426 | 0.176899 | ||||||||
\(754\) | 21.8251 | 0.794824 | ||||||||
\(755\) | 36.1243 | 1.31470 | ||||||||
\(756\) | 19.2067 | 0.698541 | ||||||||
\(757\) | −8.97940 | −0.326362 | −0.163181 | − | 0.986596i | \(-0.552175\pi\) | ||||
−0.163181 | + | 0.986596i | \(0.552175\pi\) | |||||||
\(758\) | −31.1315 | −1.13075 | ||||||||
\(759\) | −4.49787 | −0.163262 | ||||||||
\(760\) | −16.2609 | −0.589847 | ||||||||
\(761\) | 22.7813 | 0.825821 | 0.412911 | − | 0.910772i | \(-0.364512\pi\) | ||||
0.412911 | + | 0.910772i | \(0.364512\pi\) | |||||||
\(762\) | 2.75666 | 0.0998632 | ||||||||
\(763\) | 9.71954 | 0.351871 | ||||||||
\(764\) | −6.67151 | −0.241367 | ||||||||
\(765\) | 4.06158 | 0.146847 | ||||||||
\(766\) | −1.47085 | −0.0531441 | ||||||||
\(767\) | −0.452942 | −0.0163548 | ||||||||
\(768\) | −0.848137 | −0.0306045 | ||||||||
\(769\) | −9.53046 | −0.343677 | −0.171839 | − | 0.985125i | \(-0.554971\pi\) | ||||
−0.171839 | + | 0.985125i | \(0.554971\pi\) | |||||||
\(770\) | −15.0475 | −0.542274 | ||||||||
\(771\) | 0.173903 | 0.00626295 | ||||||||
\(772\) | −22.3603 | −0.804763 | ||||||||
\(773\) | −46.0981 | −1.65803 | −0.829016 | − | 0.559225i | \(-0.811099\pi\) | ||||
−0.829016 | + | 0.559225i | \(0.811099\pi\) | |||||||
\(774\) | 7.11096 | 0.255598 | ||||||||
\(775\) | 2.12437 | 0.0763098 | ||||||||
\(776\) | 18.6424 | 0.669224 | ||||||||
\(777\) | −14.9583 | −0.536627 | ||||||||
\(778\) | 6.12789 | 0.219696 | ||||||||
\(779\) | −54.3806 | −1.94839 | ||||||||
\(780\) | −7.78313 | −0.278681 | ||||||||
\(781\) | 18.1678 | 0.650096 | ||||||||
\(782\) | 2.69159 | 0.0962511 | ||||||||
\(783\) | −26.8867 | −0.960852 | ||||||||
\(784\) | 11.3906 | 0.406807 | ||||||||
\(785\) | 41.2766 | 1.47322 | ||||||||
\(786\) | 1.66046 | 0.0592265 | ||||||||
\(787\) | 27.5820 | 0.983193 | 0.491596 | − | 0.870823i | \(-0.336414\pi\) | ||||
0.491596 | + | 0.870823i | \(0.336414\pi\) | |||||||
\(788\) | 5.84586 | 0.208250 | ||||||||
\(789\) | 21.8666 | 0.778472 | ||||||||
\(790\) | −19.6141 | −0.697838 | ||||||||
\(791\) | −62.4266 | −2.21963 | ||||||||
\(792\) | 3.17039 | 0.112655 | ||||||||
\(793\) | 45.0883 | 1.60113 | ||||||||
\(794\) | 24.6791 | 0.875829 | ||||||||
\(795\) | 4.70784 | 0.166970 | ||||||||
\(796\) | 27.1617 | 0.962721 | ||||||||
\(797\) | 5.33961 | 0.189139 | 0.0945693 | − | 0.995518i | \(-0.469853\pi\) | ||||
0.0945693 | + | 0.995518i | \(0.469853\pi\) | |||||||
\(798\) | 23.4312 | 0.829457 | ||||||||
\(799\) | 0.830769 | 0.0293905 | ||||||||
\(800\) | −1.37132 | −0.0484834 | ||||||||
\(801\) | −36.8889 | −1.30341 | ||||||||
\(802\) | 12.5963 | 0.444791 | ||||||||
\(803\) | 8.73252 | 0.308164 | ||||||||
\(804\) | 6.62443 | 0.233626 | ||||||||
\(805\) | 41.2954 | 1.45547 | ||||||||
\(806\) | −5.63205 | −0.198380 | ||||||||
\(807\) | −13.7472 | −0.483924 | ||||||||
\(808\) | 11.9626 | 0.420844 | ||||||||
\(809\) | 54.8261 | 1.92758 | 0.963792 | − | 0.266656i | \(-0.0859186\pi\) | ||||
0.963792 | + | 0.266656i | \(0.0859186\pi\) | |||||||
\(810\) | −7.68202 | −0.269919 | ||||||||
\(811\) | 21.9104 | 0.769377 | 0.384689 | − | 0.923046i | \(-0.374309\pi\) | ||||
0.384689 | + | 0.923046i | \(0.374309\pi\) | |||||||
\(812\) | −25.7443 | −0.903447 | ||||||||
\(813\) | 14.2519 | 0.499834 | ||||||||
\(814\) | −5.71703 | −0.200382 | ||||||||
\(815\) | −16.9541 | −0.593878 | ||||||||
\(816\) | 0.598392 | 0.0209479 | ||||||||
\(817\) | 20.0862 | 0.702728 | ||||||||
\(818\) | 26.8009 | 0.937073 | ||||||||
\(819\) | −35.5576 | −1.24248 | ||||||||
\(820\) | −21.3072 | −0.744081 | ||||||||
\(821\) | −5.04146 | −0.175948 | −0.0879742 | − | 0.996123i | \(-0.528039\pi\) | ||||
−0.0879742 | + | 0.996123i | \(0.528039\pi\) | |||||||
\(822\) | 18.1637 | 0.633531 | ||||||||
\(823\) | −1.29802 | −0.0452462 | −0.0226231 | − | 0.999744i | \(-0.507202\pi\) | ||||
−0.0226231 | + | 0.999744i | \(0.507202\pi\) | |||||||
\(824\) | 17.7134 | 0.617074 | ||||||||
\(825\) | −1.61680 | −0.0562897 | ||||||||
\(826\) | 0.534277 | 0.0185899 | ||||||||
\(827\) | 46.6641 | 1.62267 | 0.811336 | − | 0.584581i | \(-0.198741\pi\) | ||||
0.811336 | + | 0.584581i | \(0.198741\pi\) | |||||||
\(828\) | −8.70062 | −0.302368 | ||||||||
\(829\) | −26.0194 | −0.903691 | −0.451845 | − | 0.892096i | \(-0.649234\pi\) | ||||
−0.451845 | + | 0.892096i | \(0.649234\pi\) | |||||||
\(830\) | −3.69296 | −0.128184 | ||||||||
\(831\) | −3.16690 | −0.109858 | ||||||||
\(832\) | 3.63558 | 0.126041 | ||||||||
\(833\) | −8.03649 | −0.278448 | ||||||||
\(834\) | −7.54355 | −0.261212 | ||||||||
\(835\) | −28.6312 | −0.990822 | ||||||||
\(836\) | 8.95535 | 0.309727 | ||||||||
\(837\) | 6.93821 | 0.239820 | ||||||||
\(838\) | 17.4599 | 0.603142 | ||||||||
\(839\) | −14.8946 | −0.514219 | −0.257109 | − | 0.966382i | \(-0.582770\pi\) | ||||
−0.257109 | + | 0.966382i | \(0.582770\pi\) | |||||||
\(840\) | 9.18076 | 0.316766 | ||||||||
\(841\) | 7.03843 | 0.242704 | ||||||||
\(842\) | −27.1884 | −0.936975 | ||||||||
\(843\) | −27.1640 | −0.935579 | ||||||||
\(844\) | −23.6704 | −0.814768 | ||||||||
\(845\) | 0.548843 | 0.0188808 | ||||||||
\(846\) | −2.68548 | −0.0923287 | ||||||||
\(847\) | −38.8856 | −1.33613 | ||||||||
\(848\) | −2.19908 | −0.0755166 | ||||||||
\(849\) | −9.59787 | −0.329398 | ||||||||
\(850\) | 0.967515 | 0.0331855 | ||||||||
\(851\) | 15.6895 | 0.537828 | ||||||||
\(852\) | −11.0845 | −0.379750 | ||||||||
\(853\) | −3.99597 | −0.136819 | −0.0684097 | − | 0.997657i | \(-0.521793\pi\) | ||||
−0.0684097 | + | 0.997657i | \(0.521793\pi\) | |||||||
\(854\) | −53.1849 | −1.81995 | ||||||||
\(855\) | −37.0857 | −1.26831 | ||||||||
\(856\) | 20.0166 | 0.684153 | ||||||||
\(857\) | 18.8330 | 0.643324 | 0.321662 | − | 0.946854i | \(-0.395758\pi\) | ||||
0.321662 | + | 0.946854i | \(0.395758\pi\) | |||||||
\(858\) | 4.28638 | 0.146335 | ||||||||
\(859\) | 9.39350 | 0.320502 | 0.160251 | − | 0.987076i | \(-0.448770\pi\) | ||||
0.160251 | + | 0.987076i | \(0.448770\pi\) | |||||||
\(860\) | 7.87013 | 0.268369 | ||||||||
\(861\) | 30.7027 | 1.04635 | ||||||||
\(862\) | −1.99033 | −0.0677908 | ||||||||
\(863\) | −4.32213 | −0.147127 | −0.0735636 | − | 0.997291i | \(-0.523437\pi\) | ||||
−0.0735636 | + | 0.997291i | \(0.523437\pi\) | |||||||
\(864\) | −4.47873 | −0.152369 | ||||||||
\(865\) | 7.49527 | 0.254847 | ||||||||
\(866\) | 13.7589 | 0.467546 | ||||||||
\(867\) | 13.9961 | 0.475334 | ||||||||
\(868\) | 6.64341 | 0.225492 | ||||||||
\(869\) | 10.8020 | 0.366433 | ||||||||
\(870\) | −12.8518 | −0.435717 | ||||||||
\(871\) | −28.3959 | −0.962159 | ||||||||
\(872\) | −2.26646 | −0.0767520 | ||||||||
\(873\) | 42.5171 | 1.43899 | ||||||||
\(874\) | −24.5765 | −0.831313 | ||||||||
\(875\) | −39.2791 | −1.32788 | ||||||||
\(876\) | −5.32788 | −0.180012 | ||||||||
\(877\) | −33.1618 | −1.11979 | −0.559897 | − | 0.828562i | \(-0.689159\pi\) | ||||
−0.559897 | + | 0.828562i | \(0.689159\pi\) | |||||||
\(878\) | −9.47256 | −0.319683 | ||||||||
\(879\) | −26.7022 | −0.900643 | ||||||||
\(880\) | 3.50886 | 0.118284 | ||||||||
\(881\) | −13.3574 | −0.450023 | −0.225012 | − | 0.974356i | \(-0.572242\pi\) | ||||
−0.225012 | + | 0.974356i | \(0.572242\pi\) | |||||||
\(882\) | 25.9781 | 0.874729 | ||||||||
\(883\) | 20.9771 | 0.705936 | 0.352968 | − | 0.935635i | \(-0.385172\pi\) | ||||
0.352968 | + | 0.935635i | \(0.385172\pi\) | |||||||
\(884\) | −2.56504 | −0.0862715 | ||||||||
\(885\) | 0.266716 | 0.00896557 | ||||||||
\(886\) | −24.4260 | −0.820609 | ||||||||
\(887\) | −28.5477 | −0.958537 | −0.479269 | − | 0.877668i | \(-0.659098\pi\) | ||||
−0.479269 | + | 0.877668i | \(0.659098\pi\) | |||||||
\(888\) | 3.48807 | 0.117052 | ||||||||
\(889\) | 13.9385 | 0.467481 | ||||||||
\(890\) | −40.8272 | −1.36853 | ||||||||
\(891\) | 4.23070 | 0.141734 | ||||||||
\(892\) | 17.8834 | 0.598779 | ||||||||
\(893\) | −7.58564 | −0.253844 | ||||||||
\(894\) | −13.4664 | −0.450384 | ||||||||
\(895\) | −36.4830 | −1.21949 | ||||||||
\(896\) | −4.28843 | −0.143266 | ||||||||
\(897\) | −11.7633 | −0.392765 | ||||||||
\(898\) | 32.5829 | 1.08730 | ||||||||
\(899\) | −9.29985 | −0.310167 | ||||||||
\(900\) | −3.12751 | −0.104250 | ||||||||
\(901\) | 1.55153 | 0.0516890 | ||||||||
\(902\) | 11.7345 | 0.390715 | ||||||||
\(903\) | −11.3405 | −0.377387 | ||||||||
\(904\) | 14.5570 | 0.484158 | ||||||||
\(905\) | −41.5394 | −1.38082 | ||||||||
\(906\) | 12.1381 | 0.403261 | ||||||||
\(907\) | 9.71651 | 0.322632 | 0.161316 | − | 0.986903i | \(-0.448426\pi\) | ||||
0.161316 | + | 0.986903i | \(0.448426\pi\) | |||||||
\(908\) | 23.6615 | 0.785235 | ||||||||
\(909\) | 27.2827 | 0.904911 | ||||||||
\(910\) | −39.3538 | −1.30456 | ||||||||
\(911\) | 5.99946 | 0.198771 | 0.0993855 | − | 0.995049i | \(-0.468312\pi\) | ||||
0.0993855 | + | 0.995049i | \(0.468312\pi\) | |||||||
\(912\) | −5.46383 | −0.180926 | ||||||||
\(913\) | 2.03381 | 0.0673094 | ||||||||
\(914\) | −41.3262 | −1.36695 | ||||||||
\(915\) | −26.5504 | −0.877730 | ||||||||
\(916\) | 5.12897 | 0.169466 | ||||||||
\(917\) | 8.39574 | 0.277252 | ||||||||
\(918\) | 3.15991 | 0.104292 | ||||||||
\(919\) | −27.5373 | −0.908372 | −0.454186 | − | 0.890907i | \(-0.650070\pi\) | ||||
−0.454186 | + | 0.890907i | \(0.650070\pi\) | |||||||
\(920\) | −9.62950 | −0.317475 | ||||||||
\(921\) | 23.9212 | 0.788232 | ||||||||
\(922\) | 19.6357 | 0.646669 | ||||||||
\(923\) | 47.5144 | 1.56396 | ||||||||
\(924\) | −5.05610 | −0.166333 | ||||||||
\(925\) | 5.63972 | 0.185433 | ||||||||
\(926\) | −42.8568 | −1.40836 | ||||||||
\(927\) | 40.3982 | 1.32685 | ||||||||
\(928\) | 6.00320 | 0.197065 | ||||||||
\(929\) | −47.4312 | −1.55617 | −0.778083 | − | 0.628161i | \(-0.783808\pi\) | ||||
−0.778083 | + | 0.628161i | \(0.783808\pi\) | |||||||
\(930\) | 3.31645 | 0.108751 | ||||||||
\(931\) | 73.3800 | 2.40493 | ||||||||
\(932\) | 22.6401 | 0.741601 | ||||||||
\(933\) | −6.07725 | −0.198960 | ||||||||
\(934\) | 33.6907 | 1.10239 | ||||||||
\(935\) | −2.47563 | −0.0809617 | ||||||||
\(936\) | 8.29153 | 0.271017 | ||||||||
\(937\) | 37.8678 | 1.23709 | 0.618543 | − | 0.785751i | \(-0.287723\pi\) | ||||
0.618543 | + | 0.785751i | \(0.287723\pi\) | |||||||
\(938\) | 33.4950 | 1.09365 | ||||||||
\(939\) | −26.7653 | −0.873453 | ||||||||
\(940\) | −2.97218 | −0.0969419 | ||||||||
\(941\) | −7.09904 | −0.231422 | −0.115711 | − | 0.993283i | \(-0.536915\pi\) | ||||
−0.115711 | + | 0.993283i | \(0.536915\pi\) | |||||||
\(942\) | 13.8693 | 0.451887 | ||||||||
\(943\) | −32.2034 | −1.04869 | ||||||||
\(944\) | −0.124586 | −0.00405492 | ||||||||
\(945\) | 48.4805 | 1.57707 | ||||||||
\(946\) | −4.33429 | −0.140920 | ||||||||
\(947\) | 22.4187 | 0.728511 | 0.364255 | − | 0.931299i | \(-0.381323\pi\) | ||||
0.364255 | + | 0.931299i | \(0.381323\pi\) | |||||||
\(948\) | −6.59052 | −0.214050 | ||||||||
\(949\) | 22.8382 | 0.741359 | ||||||||
\(950\) | −8.83424 | −0.286621 | ||||||||
\(951\) | −6.65517 | −0.215809 | ||||||||
\(952\) | 3.02564 | 0.0980617 | ||||||||
\(953\) | 26.0659 | 0.844357 | 0.422178 | − | 0.906513i | \(-0.361266\pi\) | ||||
0.422178 | + | 0.906513i | \(0.361266\pi\) | |||||||
\(954\) | −5.01535 | −0.162378 | ||||||||
\(955\) | −16.8399 | −0.544926 | ||||||||
\(956\) | −0.757583 | −0.0245020 | ||||||||
\(957\) | 7.07783 | 0.228794 | ||||||||
\(958\) | −12.7300 | −0.411287 | ||||||||
\(959\) | 91.8408 | 2.96569 | ||||||||
\(960\) | −2.14082 | −0.0690948 | ||||||||
\(961\) | −28.6001 | −0.922585 | ||||||||
\(962\) | −14.9518 | −0.482065 | ||||||||
\(963\) | 45.6511 | 1.47109 | ||||||||
\(964\) | 15.3907 | 0.495700 | ||||||||
\(965\) | −56.4406 | −1.81689 | ||||||||
\(966\) | 13.8757 | 0.446442 | ||||||||
\(967\) | −16.8371 | −0.541444 | −0.270722 | − | 0.962658i | \(-0.587262\pi\) | ||||
−0.270722 | + | 0.962658i | \(0.587262\pi\) | |||||||
\(968\) | 9.06758 | 0.291443 | ||||||||
\(969\) | 3.85494 | 0.123838 | ||||||||
\(970\) | 47.0562 | 1.51088 | ||||||||
\(971\) | 7.81667 | 0.250849 | 0.125424 | − | 0.992103i | \(-0.459971\pi\) | ||||
0.125424 | + | 0.992103i | \(0.459971\pi\) | |||||||
\(972\) | −16.0174 | −0.513759 | ||||||||
\(973\) | −38.1423 | −1.22279 | ||||||||
\(974\) | 13.2547 | 0.424707 | ||||||||
\(975\) | −4.22842 | −0.135418 | ||||||||
\(976\) | 12.4020 | 0.396977 | ||||||||
\(977\) | −35.0066 | −1.11996 | −0.559980 | − | 0.828506i | \(-0.689191\pi\) | ||||
−0.559980 | + | 0.828506i | \(0.689191\pi\) | |||||||
\(978\) | −5.69675 | −0.182162 | ||||||||
\(979\) | 22.4846 | 0.718612 | ||||||||
\(980\) | 28.7516 | 0.918435 | ||||||||
\(981\) | −5.16903 | −0.165034 | ||||||||
\(982\) | −35.4462 | −1.13113 | ||||||||
\(983\) | −53.0322 | −1.69146 | −0.845732 | − | 0.533608i | \(-0.820836\pi\) | ||||
−0.845732 | + | 0.533608i | \(0.820836\pi\) | |||||||
\(984\) | −7.15943 | −0.228234 | ||||||||
\(985\) | 14.7558 | 0.470159 | ||||||||
\(986\) | −4.23548 | −0.134885 | ||||||||
\(987\) | 4.28277 | 0.136322 | ||||||||
\(988\) | 23.4210 | 0.745120 | ||||||||
\(989\) | 11.8948 | 0.378232 | ||||||||
\(990\) | 8.00253 | 0.254337 | ||||||||
\(991\) | 37.6006 | 1.19442 | 0.597211 | − | 0.802084i | \(-0.296276\pi\) | ||||
0.597211 | + | 0.802084i | \(0.296276\pi\) | |||||||
\(992\) | −1.54915 | −0.0491855 | ||||||||
\(993\) | −16.0113 | −0.508104 | ||||||||
\(994\) | −56.0467 | −1.77769 | ||||||||
\(995\) | 68.5601 | 2.17350 | ||||||||
\(996\) | −1.24087 | −0.0393184 | ||||||||
\(997\) | −33.2451 | −1.05288 | −0.526441 | − | 0.850212i | \(-0.676474\pi\) | ||||
−0.526441 | + | 0.850212i | \(0.676474\pi\) | |||||||
\(998\) | 19.7405 | 0.624874 | ||||||||
\(999\) | 18.4193 | 0.582762 |
(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 | 4022.2.a.e.1.18 | ✓ | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4022.2.a.e.1.18 | ✓ | 46 | 1.1 | even | 1 | trivial |