Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2009,2,Mod(1,2009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2009, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2009 = 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2009.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: | \(16.0419457661\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 3 x^{16} - 25 x^{15} + 77 x^{14} + 247 x^{13} - 790 x^{12} - 1231 x^{11} + 4173 x^{10} + \cdots - 464 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 287) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Root | \(2.57424\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.57424 | 1.82027 | 0.910133 | − | 0.414317i | \(-0.135979\pi\) | ||||
0.910133 | + | 0.414317i | \(0.135979\pi\) | |||||||
\(3\) | −0.468252 | −0.270345 | −0.135173 | − | 0.990822i | \(-0.543159\pi\) | ||||
−0.135173 | + | 0.990822i | \(0.543159\pi\) | |||||||
\(4\) | 4.62673 | 2.31337 | ||||||||
\(5\) | −2.24224 | −1.00276 | −0.501380 | − | 0.865227i | \(-0.667174\pi\) | ||||
−0.501380 | + | 0.865227i | \(0.667174\pi\) | |||||||
\(6\) | −1.20539 | −0.492100 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 6.76185 | 2.39067 | ||||||||
\(9\) | −2.78074 | −0.926913 | ||||||||
\(10\) | −5.77207 | −1.82529 | ||||||||
\(11\) | 5.76768 | 1.73902 | 0.869511 | − | 0.493914i | \(-0.164434\pi\) | ||||
0.869511 | + | 0.493914i | \(0.164434\pi\) | |||||||
\(12\) | −2.16648 | −0.625408 | ||||||||
\(13\) | 0.0725380 | 0.0201184 | 0.0100592 | − | 0.999949i | \(-0.496798\pi\) | ||||
0.0100592 | + | 0.999949i | \(0.496798\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.04993 | 0.271091 | ||||||||
\(16\) | 8.15319 | 2.03830 | ||||||||
\(17\) | 5.01002 | 1.21511 | 0.607554 | − | 0.794279i | \(-0.292151\pi\) | ||||
0.607554 | + | 0.794279i | \(0.292151\pi\) | |||||||
\(18\) | −7.15830 | −1.68723 | ||||||||
\(19\) | 5.06540 | 1.16208 | 0.581041 | − | 0.813874i | \(-0.302646\pi\) | ||||
0.581041 | + | 0.813874i | \(0.302646\pi\) | |||||||
\(20\) | −10.3742 | −2.31975 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 14.8474 | 3.16548 | ||||||||
\(23\) | 1.90926 | 0.398108 | 0.199054 | − | 0.979988i | \(-0.436213\pi\) | ||||
0.199054 | + | 0.979988i | \(0.436213\pi\) | |||||||
\(24\) | −3.16625 | −0.646308 | ||||||||
\(25\) | 0.0276364 | 0.00552728 | ||||||||
\(26\) | 0.186731 | 0.0366209 | ||||||||
\(27\) | 2.70684 | 0.520932 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.90161 | 1.28160 | 0.640798 | − | 0.767709i | \(-0.278603\pi\) | ||||
0.640798 | + | 0.767709i | \(0.278603\pi\) | |||||||
\(30\) | 2.70278 | 0.493458 | ||||||||
\(31\) | −4.57558 | −0.821799 | −0.410899 | − | 0.911681i | \(-0.634785\pi\) | ||||
−0.410899 | + | 0.911681i | \(0.634785\pi\) | |||||||
\(32\) | 7.46459 | 1.31957 | ||||||||
\(33\) | −2.70073 | −0.470136 | ||||||||
\(34\) | 12.8970 | 2.21182 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −12.8657 | −2.14429 | ||||||||
\(37\) | −4.99460 | −0.821107 | −0.410554 | − | 0.911836i | \(-0.634665\pi\) | ||||
−0.410554 | + | 0.911836i | \(0.634665\pi\) | |||||||
\(38\) | 13.0396 | 2.11530 | ||||||||
\(39\) | −0.0339661 | −0.00543893 | ||||||||
\(40\) | −15.1617 | −2.39727 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.83836 | −1.04284 | −0.521420 | − | 0.853300i | \(-0.674597\pi\) | ||||
−0.521420 | + | 0.853300i | \(0.674597\pi\) | |||||||
\(44\) | 26.6855 | 4.02299 | ||||||||
\(45\) | 6.23508 | 0.929472 | ||||||||
\(46\) | 4.91490 | 0.724663 | ||||||||
\(47\) | 9.65313 | 1.40805 | 0.704027 | − | 0.710173i | \(-0.251383\pi\) | ||||
0.704027 | + | 0.710173i | \(0.251383\pi\) | |||||||
\(48\) | −3.81774 | −0.551044 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.0711428 | 0.0100611 | ||||||||
\(51\) | −2.34595 | −0.328499 | ||||||||
\(52\) | 0.335614 | 0.0465413 | ||||||||
\(53\) | 12.2714 | 1.68560 | 0.842802 | − | 0.538224i | \(-0.180905\pi\) | ||||
0.842802 | + | 0.538224i | \(0.180905\pi\) | |||||||
\(54\) | 6.96807 | 0.948235 | ||||||||
\(55\) | −12.9325 | −1.74382 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.37188 | −0.314163 | ||||||||
\(58\) | 17.7664 | 2.33285 | ||||||||
\(59\) | 2.22331 | 0.289451 | 0.144725 | − | 0.989472i | \(-0.453770\pi\) | ||||
0.144725 | + | 0.989472i | \(0.453770\pi\) | |||||||
\(60\) | 4.85776 | 0.627134 | ||||||||
\(61\) | 2.59124 | 0.331774 | 0.165887 | − | 0.986145i | \(-0.446951\pi\) | ||||
0.165887 | + | 0.986145i | \(0.446951\pi\) | |||||||
\(62\) | −11.7787 | −1.49589 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.90930 | 0.363663 | ||||||||
\(65\) | −0.162648 | −0.0201740 | ||||||||
\(66\) | −6.95233 | −0.855773 | ||||||||
\(67\) | −1.01182 | −0.123613 | −0.0618065 | − | 0.998088i | \(-0.519686\pi\) | ||||
−0.0618065 | + | 0.998088i | \(0.519686\pi\) | |||||||
\(68\) | 23.1800 | 2.81099 | ||||||||
\(69\) | −0.894015 | −0.107627 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.95904 | −0.469851 | −0.234926 | − | 0.972013i | \(-0.575485\pi\) | ||||
−0.234926 | + | 0.972013i | \(0.575485\pi\) | |||||||
\(72\) | −18.8029 | −2.21595 | ||||||||
\(73\) | 15.3317 | 1.79444 | 0.897220 | − | 0.441584i | \(-0.145583\pi\) | ||||
0.897220 | + | 0.441584i | \(0.145583\pi\) | |||||||
\(74\) | −12.8573 | −1.49463 | ||||||||
\(75\) | −0.0129408 | −0.00149427 | ||||||||
\(76\) | 23.4362 | 2.68832 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.0874370 | −0.00990029 | ||||||||
\(79\) | −5.48336 | −0.616927 | −0.308463 | − | 0.951236i | \(-0.599815\pi\) | ||||
−0.308463 | + | 0.951236i | \(0.599815\pi\) | |||||||
\(80\) | −18.2814 | −2.04392 | ||||||||
\(81\) | 7.07474 | 0.786082 | ||||||||
\(82\) | −2.57424 | −0.284278 | ||||||||
\(83\) | −4.84224 | −0.531505 | −0.265752 | − | 0.964041i | \(-0.585620\pi\) | ||||
−0.265752 | + | 0.964041i | \(0.585620\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.2337 | −1.21846 | ||||||||
\(86\) | −17.6036 | −1.89824 | ||||||||
\(87\) | −3.23169 | −0.346474 | ||||||||
\(88\) | 39.0002 | 4.15743 | ||||||||
\(89\) | −12.5800 | −1.33348 | −0.666739 | − | 0.745291i | \(-0.732310\pi\) | ||||
−0.666739 | + | 0.745291i | \(0.732310\pi\) | |||||||
\(90\) | 16.0506 | 1.69188 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.83364 | 0.920970 | ||||||||
\(93\) | 2.14252 | 0.222169 | ||||||||
\(94\) | 24.8495 | 2.56303 | ||||||||
\(95\) | −11.3578 | −1.16529 | ||||||||
\(96\) | −3.49531 | −0.356738 | ||||||||
\(97\) | −18.1362 | −1.84145 | −0.920724 | − | 0.390216i | \(-0.872400\pi\) | ||||
−0.920724 | + | 0.390216i | \(0.872400\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −16.0384 | −1.61192 | ||||||||
\(100\) | 0.127866 | 0.0127866 | ||||||||
\(101\) | −10.1764 | −1.01259 | −0.506295 | − | 0.862361i | \(-0.668985\pi\) | ||||
−0.506295 | + | 0.862361i | \(0.668985\pi\) | |||||||
\(102\) | −6.03905 | −0.597955 | ||||||||
\(103\) | 0.543194 | 0.0535225 | 0.0267613 | − | 0.999642i | \(-0.491481\pi\) | ||||
0.0267613 | + | 0.999642i | \(0.491481\pi\) | |||||||
\(104\) | 0.490491 | 0.0480966 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 31.5895 | 3.06825 | ||||||||
\(107\) | −0.396784 | −0.0383585 | −0.0191793 | − | 0.999816i | \(-0.506105\pi\) | ||||
−0.0191793 | + | 0.999816i | \(0.506105\pi\) | |||||||
\(108\) | 12.5238 | 1.20511 | ||||||||
\(109\) | −6.33114 | −0.606413 | −0.303206 | − | 0.952925i | \(-0.598057\pi\) | ||||
−0.303206 | + | 0.952925i | \(0.598057\pi\) | |||||||
\(110\) | −33.2915 | −3.17422 | ||||||||
\(111\) | 2.33873 | 0.221983 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.39846 | −0.413773 | −0.206886 | − | 0.978365i | \(-0.566333\pi\) | ||||
−0.206886 | + | 0.978365i | \(0.566333\pi\) | |||||||
\(114\) | −6.10580 | −0.571861 | ||||||||
\(115\) | −4.28102 | −0.399207 | ||||||||
\(116\) | 31.9319 | 2.96480 | ||||||||
\(117\) | −0.201709 | −0.0186480 | ||||||||
\(118\) | 5.72335 | 0.526877 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 7.09949 | 0.648091 | ||||||||
\(121\) | 22.2662 | 2.02420 | ||||||||
\(122\) | 6.67049 | 0.603918 | ||||||||
\(123\) | 0.468252 | 0.0422208 | ||||||||
\(124\) | −21.1700 | −1.90112 | ||||||||
\(125\) | 11.1492 | 0.997217 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.7138 | −1.03943 | −0.519715 | − | 0.854340i | \(-0.673962\pi\) | ||||
−0.519715 | + | 0.854340i | \(0.673962\pi\) | |||||||
\(128\) | −7.43992 | −0.657602 | ||||||||
\(129\) | 3.20207 | 0.281927 | ||||||||
\(130\) | −0.418695 | −0.0367220 | ||||||||
\(131\) | −22.2136 | −1.94081 | −0.970404 | − | 0.241486i | \(-0.922365\pi\) | ||||
−0.970404 | + | 0.241486i | \(0.922365\pi\) | |||||||
\(132\) | −12.4955 | −1.08760 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.60466 | −0.225009 | ||||||||
\(135\) | −6.06939 | −0.522370 | ||||||||
\(136\) | 33.8770 | 2.90493 | ||||||||
\(137\) | −5.95204 | −0.508517 | −0.254259 | − | 0.967136i | \(-0.581831\pi\) | ||||
−0.254259 | + | 0.967136i | \(0.581831\pi\) | |||||||
\(138\) | −2.30141 | −0.195909 | ||||||||
\(139\) | −8.89834 | −0.754747 | −0.377374 | − | 0.926061i | \(-0.623173\pi\) | ||||
−0.377374 | + | 0.926061i | \(0.623173\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.52010 | −0.380661 | ||||||||
\(142\) | −10.1915 | −0.855254 | ||||||||
\(143\) | 0.418376 | 0.0349864 | ||||||||
\(144\) | −22.6719 | −1.88932 | ||||||||
\(145\) | −15.4751 | −1.28513 | ||||||||
\(146\) | 39.4675 | 3.26636 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −23.1087 | −1.89952 | ||||||||
\(149\) | 8.15378 | 0.667983 | 0.333992 | − | 0.942576i | \(-0.391604\pi\) | ||||
0.333992 | + | 0.942576i | \(0.391604\pi\) | |||||||
\(150\) | −0.0333127 | −0.00271997 | ||||||||
\(151\) | −8.19460 | −0.666867 | −0.333433 | − | 0.942774i | \(-0.608207\pi\) | ||||
−0.333433 | + | 0.942774i | \(0.608207\pi\) | |||||||
\(152\) | 34.2515 | 2.77816 | ||||||||
\(153\) | −13.9316 | −1.12630 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.2596 | 0.824067 | ||||||||
\(156\) | −0.157152 | −0.0125822 | ||||||||
\(157\) | 7.64841 | 0.610410 | 0.305205 | − | 0.952287i | \(-0.401275\pi\) | ||||
0.305205 | + | 0.952287i | \(0.401275\pi\) | |||||||
\(158\) | −14.1155 | −1.12297 | ||||||||
\(159\) | −5.74609 | −0.455695 | ||||||||
\(160\) | −16.7374 | −1.32321 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 18.2121 | 1.43088 | ||||||||
\(163\) | −0.821579 | −0.0643510 | −0.0321755 | − | 0.999482i | \(-0.510244\pi\) | ||||
−0.0321755 | + | 0.999482i | \(0.510244\pi\) | |||||||
\(164\) | −4.62673 | −0.361287 | ||||||||
\(165\) | 6.05568 | 0.471434 | ||||||||
\(166\) | −12.4651 | −0.967480 | ||||||||
\(167\) | −7.82917 | −0.605840 | −0.302920 | − | 0.953016i | \(-0.597961\pi\) | ||||
−0.302920 | + | 0.953016i | \(0.597961\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9947 | −0.999595 | ||||||||
\(170\) | −28.9182 | −2.21792 | ||||||||
\(171\) | −14.0856 | −1.07715 | ||||||||
\(172\) | −31.6392 | −2.41247 | ||||||||
\(173\) | 13.3628 | 1.01596 | 0.507978 | − | 0.861370i | \(-0.330393\pi\) | ||||
0.507978 | + | 0.861370i | \(0.330393\pi\) | |||||||
\(174\) | −8.31916 | −0.630674 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 47.0250 | 3.54464 | ||||||||
\(177\) | −1.04107 | −0.0782516 | ||||||||
\(178\) | −32.3840 | −2.42728 | ||||||||
\(179\) | 8.21937 | 0.614345 | 0.307172 | − | 0.951654i | \(-0.400617\pi\) | ||||
0.307172 | + | 0.951654i | \(0.400617\pi\) | |||||||
\(180\) | 28.8481 | 2.15021 | ||||||||
\(181\) | 13.3667 | 0.993542 | 0.496771 | − | 0.867882i | \(-0.334519\pi\) | ||||
0.496771 | + | 0.867882i | \(0.334519\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.21335 | −0.0896937 | ||||||||
\(184\) | 12.9101 | 0.951747 | ||||||||
\(185\) | 11.1991 | 0.823374 | ||||||||
\(186\) | 5.51538 | 0.404407 | ||||||||
\(187\) | 28.8962 | 2.11310 | ||||||||
\(188\) | 44.6625 | 3.25734 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −29.2378 | −2.12114 | ||||||||
\(191\) | −2.34794 | −0.169891 | −0.0849457 | − | 0.996386i | \(-0.527072\pi\) | ||||
−0.0849457 | + | 0.996386i | \(0.527072\pi\) | |||||||
\(192\) | −1.36229 | −0.0983146 | ||||||||
\(193\) | −4.71054 | −0.339072 | −0.169536 | − | 0.985524i | \(-0.554227\pi\) | ||||
−0.169536 | + | 0.985524i | \(0.554227\pi\) | |||||||
\(194\) | −46.6869 | −3.35192 | ||||||||
\(195\) | 0.0761601 | 0.00545394 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.92302 | −0.493245 | −0.246622 | − | 0.969112i | \(-0.579321\pi\) | ||||
−0.246622 | + | 0.969112i | \(0.579321\pi\) | |||||||
\(198\) | −41.2868 | −2.93413 | ||||||||
\(199\) | 23.7088 | 1.68068 | 0.840338 | − | 0.542063i | \(-0.182357\pi\) | ||||
0.840338 | + | 0.542063i | \(0.182357\pi\) | |||||||
\(200\) | 0.186873 | 0.0132139 | ||||||||
\(201\) | 0.473785 | 0.0334182 | ||||||||
\(202\) | −26.1965 | −1.84318 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −10.8541 | −0.759938 | ||||||||
\(205\) | 2.24224 | 0.156605 | ||||||||
\(206\) | 1.39831 | 0.0974252 | ||||||||
\(207\) | −5.30916 | −0.369012 | ||||||||
\(208\) | 0.591416 | 0.0410073 | ||||||||
\(209\) | 29.2156 | 2.02089 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.20963 | 0.496331 | 0.248166 | − | 0.968718i | \(-0.420172\pi\) | ||||
0.248166 | + | 0.968718i | \(0.420172\pi\) | |||||||
\(212\) | 56.7764 | 3.89942 | ||||||||
\(213\) | 1.85383 | 0.127022 | ||||||||
\(214\) | −1.02142 | −0.0698227 | ||||||||
\(215\) | 15.3332 | 1.04572 | ||||||||
\(216\) | 18.3033 | 1.24538 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −16.2979 | −1.10383 | ||||||||
\(219\) | −7.17910 | −0.485118 | ||||||||
\(220\) | −59.8353 | −4.03410 | ||||||||
\(221\) | 0.363417 | 0.0244461 | ||||||||
\(222\) | 6.02046 | 0.404067 | ||||||||
\(223\) | −1.24287 | −0.0832285 | −0.0416142 | − | 0.999134i | \(-0.513250\pi\) | ||||
−0.0416142 | + | 0.999134i | \(0.513250\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.0768496 | −0.00512331 | ||||||||
\(226\) | −11.3227 | −0.753176 | ||||||||
\(227\) | −15.5050 | −1.02911 | −0.514553 | − | 0.857459i | \(-0.672042\pi\) | ||||
−0.514553 | + | 0.857459i | \(0.672042\pi\) | |||||||
\(228\) | −10.9741 | −0.726775 | ||||||||
\(229\) | 3.24527 | 0.214454 | 0.107227 | − | 0.994235i | \(-0.465803\pi\) | ||||
0.107227 | + | 0.994235i | \(0.465803\pi\) | |||||||
\(230\) | −11.0204 | −0.726663 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 46.6676 | 3.06388 | ||||||||
\(233\) | −0.148664 | −0.00973932 | −0.00486966 | − | 0.999988i | \(-0.501550\pi\) | ||||
−0.00486966 | + | 0.999988i | \(0.501550\pi\) | |||||||
\(234\) | −0.519249 | −0.0339444 | ||||||||
\(235\) | −21.6446 | −1.41194 | ||||||||
\(236\) | 10.2867 | 0.669605 | ||||||||
\(237\) | 2.56759 | 0.166783 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.7243 | 1.01712 | 0.508561 | − | 0.861026i | \(-0.330178\pi\) | ||||
0.508561 | + | 0.861026i | \(0.330178\pi\) | |||||||
\(240\) | 8.56029 | 0.552565 | ||||||||
\(241\) | −14.5039 | −0.934275 | −0.467138 | − | 0.884185i | \(-0.654715\pi\) | ||||
−0.467138 | + | 0.884185i | \(0.654715\pi\) | |||||||
\(242\) | 57.3185 | 3.68457 | ||||||||
\(243\) | −11.4333 | −0.733446 | ||||||||
\(244\) | 11.9890 | 0.767516 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.20539 | 0.0768531 | ||||||||
\(247\) | 0.367434 | 0.0233793 | ||||||||
\(248\) | −30.9394 | −1.96465 | ||||||||
\(249\) | 2.26739 | 0.143690 | ||||||||
\(250\) | 28.7008 | 1.81520 | ||||||||
\(251\) | −17.6114 | −1.11162 | −0.555812 | − | 0.831308i | \(-0.687593\pi\) | ||||
−0.555812 | + | 0.831308i | \(0.687593\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.0120 | 0.692319 | ||||||||
\(254\) | −30.1541 | −1.89204 | ||||||||
\(255\) | 5.26018 | 0.329405 | ||||||||
\(256\) | −24.9708 | −1.56067 | ||||||||
\(257\) | −29.9238 | −1.86660 | −0.933298 | − | 0.359103i | \(-0.883083\pi\) | ||||
−0.933298 | + | 0.359103i | \(0.883083\pi\) | |||||||
\(258\) | 8.24292 | 0.513182 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.752527 | −0.0466698 | ||||||||
\(261\) | −19.1916 | −1.18793 | ||||||||
\(262\) | −57.1832 | −3.53279 | ||||||||
\(263\) | −30.0029 | −1.85006 | −0.925030 | − | 0.379894i | \(-0.875960\pi\) | ||||
−0.925030 | + | 0.379894i | \(0.875960\pi\) | |||||||
\(264\) | −18.2619 | −1.12394 | ||||||||
\(265\) | −27.5154 | −1.69026 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.89061 | 0.360499 | ||||||||
\(268\) | −4.68140 | −0.285962 | ||||||||
\(269\) | −4.67405 | −0.284982 | −0.142491 | − | 0.989796i | \(-0.545511\pi\) | ||||
−0.142491 | + | 0.989796i | \(0.545511\pi\) | |||||||
\(270\) | −15.6241 | −0.950852 | ||||||||
\(271\) | 8.70676 | 0.528898 | 0.264449 | − | 0.964400i | \(-0.414810\pi\) | ||||
0.264449 | + | 0.964400i | \(0.414810\pi\) | |||||||
\(272\) | 40.8476 | 2.47675 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.3220 | −0.925636 | ||||||||
\(275\) | 0.159398 | 0.00961205 | ||||||||
\(276\) | −4.13637 | −0.248980 | ||||||||
\(277\) | 6.53178 | 0.392457 | 0.196228 | − | 0.980558i | \(-0.437131\pi\) | ||||
0.196228 | + | 0.980558i | \(0.437131\pi\) | |||||||
\(278\) | −22.9065 | −1.37384 | ||||||||
\(279\) | 12.7235 | 0.761736 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.9384 | 1.36839 | 0.684195 | − | 0.729299i | \(-0.260154\pi\) | ||||
0.684195 | + | 0.729299i | \(0.260154\pi\) | |||||||
\(282\) | −11.6358 | −0.692904 | ||||||||
\(283\) | 17.9116 | 1.06474 | 0.532369 | − | 0.846513i | \(-0.321302\pi\) | ||||
0.532369 | + | 0.846513i | \(0.321302\pi\) | |||||||
\(284\) | −18.3174 | −1.08694 | ||||||||
\(285\) | 5.31833 | 0.315030 | ||||||||
\(286\) | 1.07700 | 0.0636845 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −20.7571 | −1.22312 | ||||||||
\(289\) | 8.10027 | 0.476486 | ||||||||
\(290\) | −39.8366 | −2.33928 | ||||||||
\(291\) | 8.49229 | 0.497827 | ||||||||
\(292\) | 70.9357 | 4.15120 | ||||||||
\(293\) | −0.775720 | −0.0453181 | −0.0226590 | − | 0.999743i | \(-0.507213\pi\) | ||||
−0.0226590 | + | 0.999743i | \(0.507213\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.98520 | −0.290249 | ||||||||
\(296\) | −33.7727 | −1.96300 | ||||||||
\(297\) | 15.6122 | 0.905912 | ||||||||
\(298\) | 20.9898 | 1.21591 | ||||||||
\(299\) | 0.138494 | 0.00800932 | ||||||||
\(300\) | −0.0598736 | −0.00345680 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −21.0949 | −1.21387 | ||||||||
\(303\) | 4.76512 | 0.273749 | ||||||||
\(304\) | 41.2991 | 2.36867 | ||||||||
\(305\) | −5.81018 | −0.332690 | ||||||||
\(306\) | −35.8632 | −2.05016 | ||||||||
\(307\) | 2.48064 | 0.141577 | 0.0707887 | − | 0.997491i | \(-0.477448\pi\) | ||||
0.0707887 | + | 0.997491i | \(0.477448\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.254352 | −0.0144696 | ||||||||
\(310\) | 26.4106 | 1.50002 | ||||||||
\(311\) | −1.49389 | −0.0847108 | −0.0423554 | − | 0.999103i | \(-0.513486\pi\) | ||||
−0.0423554 | + | 0.999103i | \(0.513486\pi\) | |||||||
\(312\) | −0.229673 | −0.0130027 | ||||||||
\(313\) | 14.7941 | 0.836210 | 0.418105 | − | 0.908399i | \(-0.362694\pi\) | ||||
0.418105 | + | 0.908399i | \(0.362694\pi\) | |||||||
\(314\) | 19.6889 | 1.11111 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −25.3701 | −1.42718 | ||||||||
\(317\) | 15.2392 | 0.855919 | 0.427960 | − | 0.903798i | \(-0.359233\pi\) | ||||
0.427960 | + | 0.903798i | \(0.359233\pi\) | |||||||
\(318\) | −14.7918 | −0.829486 | ||||||||
\(319\) | 39.8063 | 2.22872 | ||||||||
\(320\) | −6.52336 | −0.364667 | ||||||||
\(321\) | 0.185795 | 0.0103700 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 25.3777 | 1.41205 | ||||||||
\(324\) | 32.7329 | 1.81850 | ||||||||
\(325\) | 0.00200469 | 0.000111200 0 | ||||||||
\(326\) | −2.11495 | −0.117136 | ||||||||
\(327\) | 2.96457 | 0.163941 | ||||||||
\(328\) | −6.76185 | −0.373361 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 15.5888 | 0.858135 | ||||||||
\(331\) | 21.2847 | 1.16991 | 0.584957 | − | 0.811064i | \(-0.301111\pi\) | ||||
0.584957 | + | 0.811064i | \(0.301111\pi\) | |||||||
\(332\) | −22.4037 | −1.22957 | ||||||||
\(333\) | 13.8887 | 0.761095 | ||||||||
\(334\) | −20.1542 | −1.10279 | ||||||||
\(335\) | 2.26873 | 0.123954 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.3612 | −1.05467 | −0.527336 | − | 0.849657i | \(-0.676809\pi\) | ||||
−0.527336 | + | 0.849657i | \(0.676809\pi\) | |||||||
\(338\) | −33.4516 | −1.81953 | ||||||||
\(339\) | 2.05959 | 0.111861 | ||||||||
\(340\) | −51.9751 | −2.81875 | ||||||||
\(341\) | −26.3905 | −1.42913 | ||||||||
\(342\) | −36.2597 | −1.96070 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −46.2399 | −2.49309 | ||||||||
\(345\) | 2.00459 | 0.107924 | ||||||||
\(346\) | 34.3992 | 1.84931 | ||||||||
\(347\) | 9.20075 | 0.493922 | 0.246961 | − | 0.969025i | \(-0.420568\pi\) | ||||
0.246961 | + | 0.969025i | \(0.420568\pi\) | |||||||
\(348\) | −14.9522 | −0.801520 | ||||||||
\(349\) | −5.22287 | −0.279574 | −0.139787 | − | 0.990182i | \(-0.544642\pi\) | ||||
−0.139787 | + | 0.990182i | \(0.544642\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.196349 | 0.0104803 | ||||||||
\(352\) | 43.0534 | 2.29475 | ||||||||
\(353\) | 32.9848 | 1.75561 | 0.877803 | − | 0.479022i | \(-0.159008\pi\) | ||||
0.877803 | + | 0.479022i | \(0.159008\pi\) | |||||||
\(354\) | −2.67997 | −0.142439 | ||||||||
\(355\) | 8.87710 | 0.471148 | ||||||||
\(356\) | −58.2043 | −3.08482 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 21.1587 | 1.11827 | ||||||||
\(359\) | 10.6166 | 0.560322 | 0.280161 | − | 0.959953i | \(-0.409612\pi\) | ||||
0.280161 | + | 0.959953i | \(0.409612\pi\) | |||||||
\(360\) | 42.1607 | 2.22206 | ||||||||
\(361\) | 6.65826 | 0.350435 | ||||||||
\(362\) | 34.4092 | 1.80851 | ||||||||
\(363\) | −10.4262 | −0.547232 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −34.3773 | −1.79939 | ||||||||
\(366\) | −3.12347 | −0.163266 | ||||||||
\(367\) | 1.48836 | 0.0776916 | 0.0388458 | − | 0.999245i | \(-0.487632\pi\) | ||||
0.0388458 | + | 0.999245i | \(0.487632\pi\) | |||||||
\(368\) | 15.5666 | 0.811463 | ||||||||
\(369\) | 2.78074 | 0.144760 | ||||||||
\(370\) | 28.8292 | 1.49876 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 9.91289 | 0.513959 | ||||||||
\(373\) | −3.30390 | −0.171070 | −0.0855348 | − | 0.996335i | \(-0.527260\pi\) | ||||
−0.0855348 | + | 0.996335i | \(0.527260\pi\) | |||||||
\(374\) | 74.3858 | 3.84640 | ||||||||
\(375\) | −5.22065 | −0.269593 | ||||||||
\(376\) | 65.2730 | 3.36620 | ||||||||
\(377\) | 0.500629 | 0.0257837 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.2983 | 0.939922 | 0.469961 | − | 0.882687i | \(-0.344268\pi\) | ||||
0.469961 | + | 0.882687i | \(0.344268\pi\) | |||||||
\(380\) | −52.5497 | −2.69574 | ||||||||
\(381\) | 5.48500 | 0.281005 | ||||||||
\(382\) | −6.04418 | −0.309247 | ||||||||
\(383\) | −37.2631 | −1.90405 | −0.952027 | − | 0.306014i | \(-0.901004\pi\) | ||||
−0.952027 | + | 0.306014i | \(0.901004\pi\) | |||||||
\(384\) | 3.48376 | 0.177780 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.1261 | −0.617201 | ||||||||
\(387\) | 19.0157 | 0.966622 | ||||||||
\(388\) | −83.9111 | −4.25994 | ||||||||
\(389\) | −3.72353 | −0.188790 | −0.0943952 | − | 0.995535i | \(-0.530092\pi\) | ||||
−0.0943952 | + | 0.995535i | \(0.530092\pi\) | |||||||
\(390\) | 0.196055 | 0.00992761 | ||||||||
\(391\) | 9.56543 | 0.483744 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.4015 | 0.524689 | ||||||||
\(394\) | −17.8215 | −0.897836 | ||||||||
\(395\) | 12.2950 | 0.618629 | ||||||||
\(396\) | −74.2055 | −3.72897 | ||||||||
\(397\) | 10.1751 | 0.510672 | 0.255336 | − | 0.966852i | \(-0.417814\pi\) | ||||
0.255336 | + | 0.966852i | \(0.417814\pi\) | |||||||
\(398\) | 61.0323 | 3.05928 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.225325 | 0.0112662 | ||||||||
\(401\) | −35.0565 | −1.75064 | −0.875319 | − | 0.483546i | \(-0.839348\pi\) | ||||
−0.875319 | + | 0.483546i | \(0.839348\pi\) | |||||||
\(402\) | 1.21964 | 0.0608300 | ||||||||
\(403\) | −0.331904 | −0.0165333 | ||||||||
\(404\) | −47.0835 | −2.34249 | ||||||||
\(405\) | −15.8633 | −0.788251 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −28.8073 | −1.42792 | ||||||||
\(408\) | −15.8630 | −0.785333 | ||||||||
\(409\) | 16.5748 | 0.819573 | 0.409787 | − | 0.912181i | \(-0.365603\pi\) | ||||
0.409787 | + | 0.912181i | \(0.365603\pi\) | |||||||
\(410\) | 5.77207 | 0.285062 | ||||||||
\(411\) | 2.78705 | 0.137475 | ||||||||
\(412\) | 2.51321 | 0.123817 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −13.6671 | −0.671700 | ||||||||
\(415\) | 10.8575 | 0.532972 | ||||||||
\(416\) | 0.541467 | 0.0265476 | ||||||||
\(417\) | 4.16666 | 0.204042 | ||||||||
\(418\) | 75.2081 | 3.67855 | ||||||||
\(419\) | −8.81409 | −0.430597 | −0.215298 | − | 0.976548i | \(-0.569072\pi\) | ||||
−0.215298 | + | 0.976548i | \(0.569072\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.9405 | 1.55668 | 0.778342 | − | 0.627841i | \(-0.216061\pi\) | ||||
0.778342 | + | 0.627841i | \(0.216061\pi\) | |||||||
\(422\) | 18.5593 | 0.903455 | ||||||||
\(423\) | −26.8429 | −1.30514 | ||||||||
\(424\) | 82.9772 | 4.02973 | ||||||||
\(425\) | 0.138459 | 0.00671624 | ||||||||
\(426\) | 4.77220 | 0.231214 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.83581 | −0.0887373 | ||||||||
\(429\) | −0.195906 | −0.00945841 | ||||||||
\(430\) | 39.4715 | 1.90348 | ||||||||
\(431\) | 30.4762 | 1.46799 | 0.733994 | − | 0.679156i | \(-0.237654\pi\) | ||||
0.733994 | + | 0.679156i | \(0.237654\pi\) | |||||||
\(432\) | 22.0694 | 1.06181 | ||||||||
\(433\) | −26.5128 | −1.27412 | −0.637062 | − | 0.770813i | \(-0.719850\pi\) | ||||
−0.637062 | + | 0.770813i | \(0.719850\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.24622 | 0.347430 | ||||||||
\(436\) | −29.2925 | −1.40286 | ||||||||
\(437\) | 9.67116 | 0.462634 | ||||||||
\(438\) | −18.4807 | −0.883044 | ||||||||
\(439\) | 16.6922 | 0.796675 | 0.398338 | − | 0.917239i | \(-0.369587\pi\) | ||||
0.398338 | + | 0.917239i | \(0.369587\pi\) | |||||||
\(440\) | −87.4478 | −4.16891 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.935524 | 0.0444983 | ||||||||
\(443\) | 3.07898 | 0.146287 | 0.0731434 | − | 0.997321i | \(-0.476697\pi\) | ||||
0.0731434 | + | 0.997321i | \(0.476697\pi\) | |||||||
\(444\) | 10.8207 | 0.513527 | ||||||||
\(445\) | 28.2074 | 1.33716 | ||||||||
\(446\) | −3.19944 | −0.151498 | ||||||||
\(447\) | −3.81802 | −0.180586 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.4476 | −1.05937 | −0.529683 | − | 0.848196i | \(-0.677689\pi\) | ||||
−0.529683 | + | 0.848196i | \(0.677689\pi\) | |||||||
\(450\) | −0.197830 | −0.00932578 | ||||||||
\(451\) | −5.76768 | −0.271590 | ||||||||
\(452\) | −20.3505 | −0.957207 | ||||||||
\(453\) | 3.83713 | 0.180284 | ||||||||
\(454\) | −39.9137 | −1.87324 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −16.0383 | −0.751063 | ||||||||
\(457\) | −38.6363 | −1.80733 | −0.903666 | − | 0.428239i | \(-0.859134\pi\) | ||||
−0.903666 | + | 0.428239i | \(0.859134\pi\) | |||||||
\(458\) | 8.35412 | 0.390362 | ||||||||
\(459\) | 13.5613 | 0.632988 | ||||||||
\(460\) | −19.8071 | −0.923512 | ||||||||
\(461\) | 12.2417 | 0.570155 | 0.285077 | − | 0.958504i | \(-0.407981\pi\) | ||||
0.285077 | + | 0.958504i | \(0.407981\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.9753 | 1.53249 | 0.766246 | − | 0.642547i | \(-0.222122\pi\) | ||||
0.766246 | + | 0.642547i | \(0.222122\pi\) | |||||||
\(464\) | 56.2701 | 2.61227 | ||||||||
\(465\) | −4.80405 | −0.222783 | ||||||||
\(466\) | −0.382698 | −0.0177281 | ||||||||
\(467\) | −6.01914 | −0.278533 | −0.139266 | − | 0.990255i | \(-0.544474\pi\) | ||||
−0.139266 | + | 0.990255i | \(0.544474\pi\) | |||||||
\(468\) | −0.933256 | −0.0431398 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −55.7186 | −2.57011 | ||||||||
\(471\) | −3.58138 | −0.165021 | ||||||||
\(472\) | 15.0337 | 0.691982 | ||||||||
\(473\) | −39.4415 | −1.81352 | ||||||||
\(474\) | 6.60962 | 0.303590 | ||||||||
\(475\) | 0.139989 | 0.00642315 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −34.1235 | −1.56241 | ||||||||
\(478\) | 40.4783 | 1.85143 | ||||||||
\(479\) | −20.5836 | −0.940489 | −0.470245 | − | 0.882536i | \(-0.655834\pi\) | ||||
−0.470245 | + | 0.882536i | \(0.655834\pi\) | |||||||
\(480\) | 7.83732 | 0.357723 | ||||||||
\(481\) | −0.362299 | −0.0165194 | ||||||||
\(482\) | −37.3365 | −1.70063 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 103.020 | 4.68271 | ||||||||
\(485\) | 40.6656 | 1.84653 | ||||||||
\(486\) | −29.4321 | −1.33507 | ||||||||
\(487\) | −3.46374 | −0.156957 | −0.0784785 | − | 0.996916i | \(-0.525006\pi\) | ||||
−0.0784785 | + | 0.996916i | \(0.525006\pi\) | |||||||
\(488\) | 17.5216 | 0.793165 | ||||||||
\(489\) | 0.384706 | 0.0173970 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.93553 | −0.403255 | −0.201627 | − | 0.979462i | \(-0.564623\pi\) | ||||
−0.201627 | + | 0.979462i | \(0.564623\pi\) | |||||||
\(492\) | 2.16648 | 0.0976723 | ||||||||
\(493\) | 34.5772 | 1.55728 | ||||||||
\(494\) | 0.945865 | 0.0425565 | ||||||||
\(495\) | 35.9620 | 1.61637 | ||||||||
\(496\) | −37.3056 | −1.67507 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 5.83681 | 0.261554 | ||||||||
\(499\) | 6.58943 | 0.294984 | 0.147492 | − | 0.989063i | \(-0.452880\pi\) | ||||
0.147492 | + | 0.989063i | \(0.452880\pi\) | |||||||
\(500\) | 51.5845 | 2.30693 | ||||||||
\(501\) | 3.66602 | 0.163786 | ||||||||
\(502\) | −45.3362 | −2.02345 | ||||||||
\(503\) | 21.0935 | 0.940511 | 0.470255 | − | 0.882530i | \(-0.344162\pi\) | ||||
0.470255 | + | 0.882530i | \(0.344162\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.8179 | 1.01538 | ||||||||
\(506\) | 28.3476 | 1.26020 | ||||||||
\(507\) | 6.08481 | 0.270236 | ||||||||
\(508\) | −54.1965 | −2.40458 | ||||||||
\(509\) | 0.213577 | 0.00946663 | 0.00473332 | − | 0.999989i | \(-0.498493\pi\) | ||||
0.00473332 | + | 0.999989i | \(0.498493\pi\) | |||||||
\(510\) | 13.5410 | 0.599605 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −49.4010 | −2.18324 | ||||||||
\(513\) | 13.7112 | 0.605366 | ||||||||
\(514\) | −77.0312 | −3.39770 | ||||||||
\(515\) | −1.21797 | −0.0536702 | ||||||||
\(516\) | 14.8151 | 0.652200 | ||||||||
\(517\) | 55.6762 | 2.44864 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.25717 | −0.274659 | ||||||||
\(520\) | −1.09980 | −0.0482294 | ||||||||
\(521\) | 14.1315 | 0.619113 | 0.309556 | − | 0.950881i | \(-0.399819\pi\) | ||||
0.309556 | + | 0.950881i | \(0.399819\pi\) | |||||||
\(522\) | −49.4038 | −2.16235 | ||||||||
\(523\) | −38.4886 | −1.68299 | −0.841495 | − | 0.540265i | \(-0.818324\pi\) | ||||
−0.841495 | + | 0.540265i | \(0.818324\pi\) | |||||||
\(524\) | −102.776 | −4.48980 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −77.2349 | −3.36760 | ||||||||
\(527\) | −22.9237 | −0.998574 | ||||||||
\(528\) | −22.0195 | −0.958277 | ||||||||
\(529\) | −19.3547 | −0.841510 | ||||||||
\(530\) | −70.8313 | −3.07671 | ||||||||
\(531\) | −6.18245 | −0.268296 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.0725380 | −0.00314197 | ||||||||
\(534\) | 15.1639 | 0.656205 | ||||||||
\(535\) | 0.889684 | 0.0384644 | ||||||||
\(536\) | −6.84175 | −0.295519 | ||||||||
\(537\) | −3.84874 | −0.166085 | ||||||||
\(538\) | −12.0321 | −0.518743 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −28.0814 | −1.20843 | ||||||||
\(541\) | −9.77310 | −0.420179 | −0.210089 | − | 0.977682i | \(-0.567375\pi\) | ||||
−0.210089 | + | 0.977682i | \(0.567375\pi\) | |||||||
\(542\) | 22.4133 | 0.962735 | ||||||||
\(543\) | −6.25900 | −0.268599 | ||||||||
\(544\) | 37.3977 | 1.60341 | ||||||||
\(545\) | 14.1959 | 0.608087 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.3733 | −1.38418 | −0.692092 | − | 0.721810i | \(-0.743311\pi\) | ||||
−0.692092 | + | 0.721810i | \(0.743311\pi\) | |||||||
\(548\) | −27.5385 | −1.17639 | ||||||||
\(549\) | −7.20557 | −0.307526 | ||||||||
\(550\) | 0.410329 | 0.0174965 | ||||||||
\(551\) | 34.9594 | 1.48932 | ||||||||
\(552\) | −6.04519 | −0.257300 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 16.8144 | 0.714375 | ||||||||
\(555\) | −5.24399 | −0.222595 | ||||||||
\(556\) | −41.1702 | −1.74601 | ||||||||
\(557\) | −31.9026 | −1.35176 | −0.675879 | − | 0.737012i | \(-0.736236\pi\) | ||||
−0.675879 | + | 0.737012i | \(0.736236\pi\) | |||||||
\(558\) | 32.7534 | 1.38656 | ||||||||
\(559\) | −0.496041 | −0.0209803 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.5307 | −0.571266 | ||||||||
\(562\) | 59.0491 | 2.49083 | ||||||||
\(563\) | −32.5073 | −1.37002 | −0.685009 | − | 0.728535i | \(-0.740202\pi\) | ||||
−0.685009 | + | 0.728535i | \(0.740202\pi\) | |||||||
\(564\) | −20.9133 | −0.880608 | ||||||||
\(565\) | 9.86240 | 0.414914 | ||||||||
\(566\) | 46.1090 | 1.93810 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −26.7704 | −1.12326 | ||||||||
\(569\) | −35.5560 | −1.49059 | −0.745293 | − | 0.666737i | \(-0.767691\pi\) | ||||
−0.745293 | + | 0.666737i | \(0.767691\pi\) | |||||||
\(570\) | 13.6907 | 0.573439 | ||||||||
\(571\) | 5.13907 | 0.215063 | 0.107532 | − | 0.994202i | \(-0.465705\pi\) | ||||
0.107532 | + | 0.994202i | \(0.465705\pi\) | |||||||
\(572\) | 1.93572 | 0.0809363 | ||||||||
\(573\) | 1.09943 | 0.0459293 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.0527651 | 0.00220045 | ||||||||
\(576\) | −8.09002 | −0.337084 | ||||||||
\(577\) | 23.4023 | 0.974250 | 0.487125 | − | 0.873332i | \(-0.338046\pi\) | ||||
0.487125 | + | 0.873332i | \(0.338046\pi\) | |||||||
\(578\) | 20.8521 | 0.867332 | ||||||||
\(579\) | 2.20572 | 0.0916666 | ||||||||
\(580\) | −71.5989 | −2.97298 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 21.8612 | 0.906177 | ||||||||
\(583\) | 70.7774 | 2.93130 | ||||||||
\(584\) | 103.671 | 4.28992 | ||||||||
\(585\) | 0.452281 | 0.0186995 | ||||||||
\(586\) | −1.99689 | −0.0824909 | ||||||||
\(587\) | −21.6605 | −0.894023 | −0.447011 | − | 0.894528i | \(-0.647512\pi\) | ||||
−0.447011 | + | 0.894528i | \(0.647512\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.1771 | −0.954998 | ||||||||
\(590\) | −12.8331 | −0.528331 | ||||||||
\(591\) | 3.24172 | 0.133346 | ||||||||
\(592\) | −40.7219 | −1.67366 | ||||||||
\(593\) | −0.975484 | −0.0400583 | −0.0200292 | − | 0.999799i | \(-0.506376\pi\) | ||||
−0.0200292 | + | 0.999799i | \(0.506376\pi\) | |||||||
\(594\) | 40.1896 | 1.64900 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 37.7253 | 1.54529 | ||||||||
\(597\) | −11.1017 | −0.454363 | ||||||||
\(598\) | 0.356517 | 0.0145791 | ||||||||
\(599\) | 4.84115 | 0.197804 | 0.0989021 | − | 0.995097i | \(-0.468467\pi\) | ||||
0.0989021 | + | 0.995097i | \(0.468467\pi\) | |||||||
\(600\) | −0.0875037 | −0.00357232 | ||||||||
\(601\) | 19.3928 | 0.791048 | 0.395524 | − | 0.918456i | \(-0.370563\pi\) | ||||
0.395524 | + | 0.918456i | \(0.370563\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.81360 | 0.114579 | ||||||||
\(604\) | −37.9142 | −1.54271 | ||||||||
\(605\) | −49.9260 | −2.02978 | ||||||||
\(606\) | 12.2666 | 0.498295 | ||||||||
\(607\) | 5.15332 | 0.209167 | 0.104583 | − | 0.994516i | \(-0.466649\pi\) | ||||
0.104583 | + | 0.994516i | \(0.466649\pi\) | |||||||
\(608\) | 37.8111 | 1.53344 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14.9568 | −0.605584 | ||||||||
\(611\) | 0.700219 | 0.0283278 | ||||||||
\(612\) | −64.4576 | −2.60554 | ||||||||
\(613\) | 21.1298 | 0.853426 | 0.426713 | − | 0.904387i | \(-0.359672\pi\) | ||||
0.426713 | + | 0.904387i | \(0.359672\pi\) | |||||||
\(614\) | 6.38576 | 0.257708 | ||||||||
\(615\) | −1.04993 | −0.0423374 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.2828 | 0.413969 | 0.206985 | − | 0.978344i | \(-0.433635\pi\) | ||||
0.206985 | + | 0.978344i | \(0.433635\pi\) | |||||||
\(618\) | −0.654763 | −0.0263384 | ||||||||
\(619\) | 30.7100 | 1.23434 | 0.617170 | − | 0.786830i | \(-0.288279\pi\) | ||||
0.617170 | + | 0.786830i | \(0.288279\pi\) | |||||||
\(620\) | 47.4682 | 1.90637 | ||||||||
\(621\) | 5.16807 | 0.207387 | ||||||||
\(622\) | −3.84564 | −0.154196 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −0.276932 | −0.0110861 | ||||||||
\(625\) | −25.1374 | −1.00550 | ||||||||
\(626\) | 38.0835 | 1.52212 | ||||||||
\(627\) | −13.6803 | −0.546337 | ||||||||
\(628\) | 35.3871 | 1.41210 | ||||||||
\(629\) | −25.0230 | −0.997734 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.2191 | 1.32243 | 0.661216 | − | 0.750195i | \(-0.270041\pi\) | ||||
0.661216 | + | 0.750195i | \(0.270041\pi\) | |||||||
\(632\) | −37.0777 | −1.47487 | ||||||||
\(633\) | −3.37592 | −0.134181 | ||||||||
\(634\) | 39.2295 | 1.55800 | ||||||||
\(635\) | 26.2651 | 1.04230 | ||||||||
\(636\) | −26.5856 | −1.05419 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 102.471 | 4.05687 | ||||||||
\(639\) | 11.0090 | 0.435511 | ||||||||
\(640\) | 16.6821 | 0.659417 | ||||||||
\(641\) | 2.37937 | 0.0939794 | 0.0469897 | − | 0.998895i | \(-0.485037\pi\) | ||||
0.0469897 | + | 0.998895i | \(0.485037\pi\) | |||||||
\(642\) | 0.478281 | 0.0188762 | ||||||||
\(643\) | −21.1865 | −0.835515 | −0.417757 | − | 0.908559i | \(-0.637184\pi\) | ||||
−0.417757 | + | 0.908559i | \(0.637184\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.17981 | −0.282705 | ||||||||
\(646\) | 65.3285 | 2.57031 | ||||||||
\(647\) | 3.29111 | 0.129387 | 0.0646935 | − | 0.997905i | \(-0.479393\pi\) | ||||
0.0646935 | + | 0.997905i | \(0.479393\pi\) | |||||||
\(648\) | 47.8383 | 1.87927 | ||||||||
\(649\) | 12.8234 | 0.503361 | ||||||||
\(650\) | 0.00516056 | 0.000202414 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.80123 | −0.148868 | ||||||||
\(653\) | 33.1264 | 1.29634 | 0.648168 | − | 0.761497i | \(-0.275535\pi\) | ||||
0.648168 | + | 0.761497i | \(0.275535\pi\) | |||||||
\(654\) | 7.63152 | 0.298416 | ||||||||
\(655\) | 49.8081 | 1.94617 | ||||||||
\(656\) | −8.15319 | −0.318328 | ||||||||
\(657\) | −42.6335 | −1.66329 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.3837 | 0.599266 | 0.299633 | − | 0.954055i | \(-0.403136\pi\) | ||||
0.299633 | + | 0.954055i | \(0.403136\pi\) | |||||||
\(660\) | 28.0180 | 1.09060 | ||||||||
\(661\) | −48.9638 | −1.90447 | −0.952236 | − | 0.305364i | \(-0.901222\pi\) | ||||
−0.952236 | + | 0.305364i | \(0.901222\pi\) | |||||||
\(662\) | 54.7921 | 2.12955 | ||||||||
\(663\) | −0.170171 | −0.00660888 | ||||||||
\(664\) | −32.7425 | −1.27066 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 35.7529 | 1.38540 | ||||||||
\(667\) | 13.1770 | 0.510214 | ||||||||
\(668\) | −36.2235 | −1.40153 | ||||||||
\(669\) | 0.581975 | 0.0225004 | ||||||||
\(670\) | 5.84028 | 0.225630 | ||||||||
\(671\) | 14.9455 | 0.576963 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.9400 | 0.730082 | 0.365041 | − | 0.930992i | \(-0.381055\pi\) | ||||
0.365041 | + | 0.930992i | \(0.381055\pi\) | |||||||
\(674\) | −49.8405 | −1.91978 | ||||||||
\(675\) | 0.0748073 | 0.00287934 | ||||||||
\(676\) | −60.1232 | −2.31243 | ||||||||
\(677\) | −26.8445 | −1.03172 | −0.515859 | − | 0.856674i | \(-0.672527\pi\) | ||||
−0.515859 | + | 0.856674i | \(0.672527\pi\) | |||||||
\(678\) | 5.30188 | 0.203618 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −75.9603 | −2.91294 | ||||||||
\(681\) | 7.26026 | 0.278214 | ||||||||
\(682\) | −67.9356 | −2.60139 | ||||||||
\(683\) | 45.1368 | 1.72711 | 0.863556 | − | 0.504252i | \(-0.168232\pi\) | ||||
0.863556 | + | 0.504252i | \(0.168232\pi\) | |||||||
\(684\) | −65.1701 | −2.49184 | ||||||||
\(685\) | 13.3459 | 0.509920 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.51960 | −0.0579765 | ||||||||
\(688\) | −55.7544 | −2.12562 | ||||||||
\(689\) | 0.890142 | 0.0339117 | ||||||||
\(690\) | 5.16032 | 0.196450 | ||||||||
\(691\) | −27.1345 | −1.03225 | −0.516123 | − | 0.856515i | \(-0.672625\pi\) | ||||
−0.516123 | + | 0.856515i | \(0.672625\pi\) | |||||||
\(692\) | 61.8262 | 2.35028 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 23.6850 | 0.899070 | ||||||||
\(695\) | 19.9522 | 0.756830 | ||||||||
\(696\) | −21.8522 | −0.828306 | ||||||||
\(697\) | −5.01002 | −0.189768 | ||||||||
\(698\) | −13.4449 | −0.508899 | ||||||||
\(699\) | 0.0696123 | 0.00263298 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 48.7878 | 1.84269 | 0.921344 | − | 0.388748i | \(-0.127092\pi\) | ||||
0.921344 | + | 0.388748i | \(0.127092\pi\) | |||||||
\(702\) | 0.505450 | 0.0190770 | ||||||||
\(703\) | −25.2996 | −0.954194 | ||||||||
\(704\) | 16.7799 | 0.632418 | ||||||||
\(705\) | 10.1351 | 0.381711 | ||||||||
\(706\) | 84.9110 | 3.19567 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4.81675 | −0.181025 | ||||||||
\(709\) | 12.1945 | 0.457975 | 0.228987 | − | 0.973429i | \(-0.426459\pi\) | ||||
0.228987 | + | 0.973429i | \(0.426459\pi\) | |||||||
\(710\) | 22.8518 | 0.857614 | ||||||||
\(711\) | 15.2478 | 0.571837 | ||||||||
\(712\) | −85.0641 | −3.18791 | ||||||||
\(713\) | −8.73598 | −0.327165 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.938100 | −0.0350829 | ||||||||
\(716\) | 38.0288 | 1.42120 | ||||||||
\(717\) | −7.36295 | −0.274974 | ||||||||
\(718\) | 27.3297 | 1.01993 | ||||||||
\(719\) | −10.3736 | −0.386869 | −0.193434 | − | 0.981113i | \(-0.561963\pi\) | ||||
−0.193434 | + | 0.981113i | \(0.561963\pi\) | |||||||
\(720\) | 50.8358 | 1.89454 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 17.1400 | 0.637884 | ||||||||
\(723\) | 6.79146 | 0.252577 | ||||||||
\(724\) | 61.8443 | 2.29843 | ||||||||
\(725\) | 0.190736 | 0.00708374 | ||||||||
\(726\) | −26.8395 | −0.996107 | ||||||||
\(727\) | 34.5870 | 1.28276 | 0.641380 | − | 0.767224i | \(-0.278362\pi\) | ||||
0.641380 | + | 0.767224i | \(0.278362\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.8706 | −0.587798 | ||||||||
\(730\) | −88.4956 | −3.27537 | ||||||||
\(731\) | −34.2603 | −1.26716 | ||||||||
\(732\) | −5.61386 | −0.207494 | ||||||||
\(733\) | −27.3160 | −1.00894 | −0.504470 | − | 0.863429i | \(-0.668312\pi\) | ||||
−0.504470 | + | 0.863429i | \(0.668312\pi\) | |||||||
\(734\) | 3.83140 | 0.141419 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 14.2518 | 0.525330 | ||||||||
\(737\) | −5.83583 | −0.214966 | ||||||||
\(738\) | 7.15830 | 0.263501 | ||||||||
\(739\) | −32.9855 | −1.21339 | −0.606695 | − | 0.794935i | \(-0.707505\pi\) | ||||
−0.606695 | + | 0.794935i | \(0.707505\pi\) | |||||||
\(740\) | 51.8152 | 1.90476 | ||||||||
\(741\) | −0.172052 | −0.00632048 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.5846 | 1.23210 | 0.616049 | − | 0.787708i | \(-0.288732\pi\) | ||||
0.616049 | + | 0.787708i | \(0.288732\pi\) | |||||||
\(744\) | 14.4874 | 0.531135 | ||||||||
\(745\) | −18.2827 | −0.669827 | ||||||||
\(746\) | −8.50505 | −0.311392 | ||||||||
\(747\) | 13.4650 | 0.492659 | ||||||||
\(748\) | 133.695 | 4.88837 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −13.4392 | −0.490731 | ||||||||
\(751\) | 6.22654 | 0.227210 | 0.113605 | − | 0.993526i | \(-0.463760\pi\) | ||||
0.113605 | + | 0.993526i | \(0.463760\pi\) | |||||||
\(752\) | 78.7038 | 2.87003 | ||||||||
\(753\) | 8.24659 | 0.300523 | ||||||||
\(754\) | 1.28874 | 0.0469332 | ||||||||
\(755\) | 18.3742 | 0.668707 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.40058 | −0.196288 | −0.0981438 | − | 0.995172i | \(-0.531291\pi\) | ||||
−0.0981438 | + | 0.995172i | \(0.531291\pi\) | |||||||
\(758\) | 47.1044 | 1.71091 | ||||||||
\(759\) | −5.15639 | −0.187165 | ||||||||
\(760\) | −76.8000 | −2.78583 | ||||||||
\(761\) | 15.6306 | 0.566610 | 0.283305 | − | 0.959030i | \(-0.408569\pi\) | ||||
0.283305 | + | 0.959030i | \(0.408569\pi\) | |||||||
\(762\) | 14.1197 | 0.511504 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −10.8633 | −0.393021 | ||||||||
\(765\) | 31.2379 | 1.12941 | ||||||||
\(766\) | −95.9242 | −3.46588 | ||||||||
\(767\) | 0.161275 | 0.00582329 | ||||||||
\(768\) | 11.6926 | 0.421921 | ||||||||
\(769\) | 3.23902 | 0.116802 | 0.0584009 | − | 0.998293i | \(-0.481400\pi\) | ||||
0.0584009 | + | 0.998293i | \(0.481400\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.0119 | 0.504625 | ||||||||
\(772\) | −21.7944 | −0.784398 | ||||||||
\(773\) | −8.42218 | −0.302925 | −0.151462 | − | 0.988463i | \(-0.548398\pi\) | ||||
−0.151462 | + | 0.988463i | \(0.548398\pi\) | |||||||
\(774\) | 48.9510 | 1.75951 | ||||||||
\(775\) | −0.126453 | −0.00454231 | ||||||||
\(776\) | −122.634 | −4.40230 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.58527 | −0.343649 | ||||||||
\(779\) | −5.06540 | −0.181487 | ||||||||
\(780\) | 0.352372 | 0.0126169 | ||||||||
\(781\) | −22.8345 | −0.817081 | ||||||||
\(782\) | 24.6237 | 0.880543 | ||||||||
\(783\) | 18.6816 | 0.667625 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17.1496 | −0.612094 | ||||||||
\(786\) | 26.7761 | 0.955072 | ||||||||
\(787\) | 19.1587 | 0.682933 | 0.341467 | − | 0.939894i | \(-0.389076\pi\) | ||||
0.341467 | + | 0.939894i | \(0.389076\pi\) | |||||||
\(788\) | −32.0310 | −1.14106 | ||||||||
\(789\) | 14.0489 | 0.500155 | ||||||||
\(790\) | 31.6504 | 1.12607 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −108.449 | −3.85358 | ||||||||
\(793\) | 0.187964 | 0.00667478 | ||||||||
\(794\) | 26.1931 | 0.929558 | ||||||||
\(795\) | 12.8841 | 0.456953 | ||||||||
\(796\) | 109.694 | 3.88802 | ||||||||
\(797\) | −49.1450 | −1.74080 | −0.870402 | − | 0.492342i | \(-0.836141\pi\) | ||||
−0.870402 | + | 0.492342i | \(0.836141\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 48.3624 | 1.71094 | ||||||||
\(800\) | 0.206294 | 0.00729360 | ||||||||
\(801\) | 34.9817 | 1.23602 | ||||||||
\(802\) | −90.2440 | −3.18662 | ||||||||
\(803\) | 88.4284 | 3.12057 | ||||||||
\(804\) | 2.19208 | 0.0773086 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.854401 | −0.0300950 | ||||||||
\(807\) | 2.18863 | 0.0770435 | ||||||||
\(808\) | −68.8113 | −2.42077 | ||||||||
\(809\) | 43.9060 | 1.54365 | 0.771826 | − | 0.635834i | \(-0.219344\pi\) | ||||
0.771826 | + | 0.635834i | \(0.219344\pi\) | |||||||
\(810\) | −40.8359 | −1.43483 | ||||||||
\(811\) | −21.3942 | −0.751252 | −0.375626 | − | 0.926771i | \(-0.622572\pi\) | ||||
−0.375626 | + | 0.926771i | \(0.622572\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.07696 | −0.142985 | ||||||||
\(814\) | −74.1569 | −2.59920 | ||||||||
\(815\) | 1.84218 | 0.0645286 | ||||||||
\(816\) | −19.1270 | −0.669578 | ||||||||
\(817\) | −34.6390 | −1.21187 | ||||||||
\(818\) | 42.6677 | 1.49184 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.3742 | 0.362284 | ||||||||
\(821\) | −51.5951 | −1.80068 | −0.900340 | − | 0.435187i | \(-0.856682\pi\) | ||||
−0.900340 | + | 0.435187i | \(0.856682\pi\) | |||||||
\(822\) | 7.17456 | 0.250241 | ||||||||
\(823\) | 32.4684 | 1.13178 | 0.565889 | − | 0.824482i | \(-0.308533\pi\) | ||||
0.565889 | + | 0.824482i | \(0.308533\pi\) | |||||||
\(824\) | 3.67300 | 0.127955 | ||||||||
\(825\) | −0.0746383 | −0.00259857 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.7906 | 0.688187 | 0.344094 | − | 0.938935i | \(-0.388186\pi\) | ||||
0.344094 | + | 0.938935i | \(0.388186\pi\) | |||||||
\(828\) | −24.5640 | −0.853660 | ||||||||
\(829\) | −3.18668 | −0.110678 | −0.0553389 | − | 0.998468i | \(-0.517624\pi\) | ||||
−0.0553389 | + | 0.998468i | \(0.517624\pi\) | |||||||
\(830\) | 27.9498 | 0.970150 | ||||||||
\(831\) | −3.05852 | −0.106099 | ||||||||
\(832\) | 0.211035 | 0.00731633 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 10.7260 | 0.371411 | ||||||||
\(835\) | 17.5549 | 0.607512 | ||||||||
\(836\) | 135.173 | 4.67505 | ||||||||
\(837\) | −12.3854 | −0.428101 | ||||||||
\(838\) | −22.6896 | −0.783800 | ||||||||
\(839\) | 0.366627 | 0.0126574 | 0.00632868 | − | 0.999980i | \(-0.497986\pi\) | ||||
0.00632868 | + | 0.999980i | \(0.497986\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.6322 | 0.642490 | ||||||||
\(842\) | 82.2226 | 2.83358 | ||||||||
\(843\) | −10.7410 | −0.369938 | ||||||||
\(844\) | 33.3570 | 1.14820 | ||||||||
\(845\) | 29.1373 | 1.00235 | ||||||||
\(846\) | −69.1000 | −2.37571 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 100.051 | 3.43576 | ||||||||
\(849\) | −8.38716 | −0.287847 | ||||||||
\(850\) | 0.356427 | 0.0122253 | ||||||||
\(851\) | −9.53599 | −0.326890 | ||||||||
\(852\) | 8.57715 | 0.293848 | ||||||||
\(853\) | −26.5967 | −0.910654 | −0.455327 | − | 0.890324i | \(-0.650478\pi\) | ||||
−0.455327 | + | 0.890324i | \(0.650478\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 31.5832 | 1.08012 | ||||||||
\(856\) | −2.68299 | −0.0917028 | ||||||||
\(857\) | −25.9523 | −0.886514 | −0.443257 | − | 0.896395i | \(-0.646177\pi\) | ||||
−0.443257 | + | 0.896395i | \(0.646177\pi\) | |||||||
\(858\) | −0.504309 | −0.0172168 | ||||||||
\(859\) | −57.0932 | −1.94800 | −0.973998 | − | 0.226555i | \(-0.927254\pi\) | ||||
−0.973998 | + | 0.226555i | \(0.927254\pi\) | |||||||
\(860\) | 70.9428 | 2.41913 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 78.4532 | 2.67213 | ||||||||
\(863\) | −30.9029 | −1.05195 | −0.525974 | − | 0.850501i | \(-0.676299\pi\) | ||||
−0.525974 | + | 0.850501i | \(0.676299\pi\) | |||||||
\(864\) | 20.2055 | 0.687404 | ||||||||
\(865\) | −29.9627 | −1.01876 | ||||||||
\(866\) | −68.2504 | −2.31924 | ||||||||
\(867\) | −3.79297 | −0.128816 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −31.6263 | −1.07285 | ||||||||
\(870\) | 18.6535 | 0.632415 | ||||||||
\(871\) | −0.0733952 | −0.00248690 | ||||||||
\(872\) | −42.8102 | −1.44974 | ||||||||
\(873\) | 50.4319 | 1.70686 | ||||||||
\(874\) | 24.8959 | 0.842118 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −33.2158 | −1.12226 | ||||||||
\(877\) | −9.96410 | −0.336464 | −0.168232 | − | 0.985747i | \(-0.553806\pi\) | ||||
−0.168232 | + | 0.985747i | \(0.553806\pi\) | |||||||
\(878\) | 42.9698 | 1.45016 | ||||||||
\(879\) | 0.363232 | 0.0122515 | ||||||||
\(880\) | −105.441 | −3.55442 | ||||||||
\(881\) | 2.35418 | 0.0793143 | 0.0396572 | − | 0.999213i | \(-0.487373\pi\) | ||||
0.0396572 | + | 0.999213i | \(0.487373\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.5946 | 0.928631 | 0.464315 | − | 0.885670i | \(-0.346300\pi\) | ||||
0.464315 | + | 0.885670i | \(0.346300\pi\) | |||||||
\(884\) | 1.68143 | 0.0565527 | ||||||||
\(885\) | 2.33433 | 0.0784676 | ||||||||
\(886\) | 7.92605 | 0.266281 | ||||||||
\(887\) | 19.7827 | 0.664239 | 0.332119 | − | 0.943237i | \(-0.392236\pi\) | ||||
0.332119 | + | 0.943237i | \(0.392236\pi\) | |||||||
\(888\) | 15.8141 | 0.530688 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 72.6127 | 2.43398 | ||||||||
\(891\) | 40.8048 | 1.36701 | ||||||||
\(892\) | −5.75041 | −0.192538 | ||||||||
\(893\) | 48.8970 | 1.63627 | ||||||||
\(894\) | −9.82852 | −0.328715 | ||||||||
\(895\) | −18.4298 | −0.616040 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.0648501 | −0.00216528 | ||||||||
\(898\) | −57.7855 | −1.92833 | ||||||||
\(899\) | −31.5789 | −1.05321 | ||||||||
\(900\) | −0.355563 | −0.0118521 | ||||||||
\(901\) | 61.4798 | 2.04819 | ||||||||
\(902\) | −14.8474 | −0.494365 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −29.7417 | −0.989196 | ||||||||
\(905\) | −29.9714 | −0.996284 | ||||||||
\(906\) | 9.87772 | 0.328165 | ||||||||
\(907\) | −2.52400 | −0.0838082 | −0.0419041 | − | 0.999122i | \(-0.513342\pi\) | ||||
−0.0419041 | + | 0.999122i | \(0.513342\pi\) | |||||||
\(908\) | −71.7376 | −2.38070 | ||||||||
\(909\) | 28.2979 | 0.938583 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −44.3294 | −1.46870 | −0.734350 | − | 0.678771i | \(-0.762513\pi\) | ||||
−0.734350 | + | 0.678771i | \(0.762513\pi\) | |||||||
\(912\) | −19.3384 | −0.640358 | ||||||||
\(913\) | −27.9285 | −0.924298 | ||||||||
\(914\) | −99.4593 | −3.28982 | ||||||||
\(915\) | 2.72063 | 0.0899412 | ||||||||
\(916\) | 15.0150 | 0.496110 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 34.9102 | 1.15221 | ||||||||
\(919\) | 49.1888 | 1.62259 | 0.811294 | − | 0.584638i | \(-0.198764\pi\) | ||||
0.811294 | + | 0.584638i | \(0.198764\pi\) | |||||||
\(920\) | −28.9476 | −0.954374 | ||||||||
\(921\) | −1.16156 | −0.0382748 | ||||||||
\(922\) | 31.5132 | 1.03783 | ||||||||
\(923\) | −0.287181 | −0.00945267 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.138033 | −0.00453849 | ||||||||
\(926\) | 84.8865 | 2.78954 | ||||||||
\(927\) | −1.51048 | −0.0496107 | ||||||||
\(928\) | 51.5177 | 1.69115 | ||||||||
\(929\) | −7.57846 | −0.248641 | −0.124321 | − | 0.992242i | \(-0.539675\pi\) | ||||
−0.124321 | + | 0.992242i | \(0.539675\pi\) | |||||||
\(930\) | −12.3668 | −0.405524 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.687830 | −0.0225306 | ||||||||
\(933\) | 0.699517 | 0.0229012 | ||||||||
\(934\) | −15.4947 | −0.507003 | ||||||||
\(935\) | −64.7922 | −2.11893 | ||||||||
\(936\) | −1.36393 | −0.0445814 | ||||||||
\(937\) | 15.1160 | 0.493817 | 0.246909 | − | 0.969039i | \(-0.420585\pi\) | ||||
0.246909 | + | 0.969039i | \(0.420585\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.92735 | −0.226065 | ||||||||
\(940\) | −100.144 | −3.26633 | ||||||||
\(941\) | −28.8060 | −0.939050 | −0.469525 | − | 0.882919i | \(-0.655575\pi\) | ||||
−0.469525 | + | 0.882919i | \(0.655575\pi\) | |||||||
\(942\) | −9.21935 | −0.300383 | ||||||||
\(943\) | −1.90926 | −0.0621741 | ||||||||
\(944\) | 18.1271 | 0.589986 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −101.532 | −3.30109 | ||||||||
\(947\) | 40.6344 | 1.32044 | 0.660221 | − | 0.751072i | \(-0.270463\pi\) | ||||
0.660221 | + | 0.751072i | \(0.270463\pi\) | |||||||
\(948\) | 11.8796 | 0.385831 | ||||||||
\(949\) | 1.11213 | 0.0361013 | ||||||||
\(950\) | 0.360367 | 0.0116918 | ||||||||
\(951\) | −7.13579 | −0.231394 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.5104 | 1.21508 | 0.607541 | − | 0.794289i | \(-0.292156\pi\) | ||||
0.607541 | + | 0.794289i | \(0.292156\pi\) | |||||||
\(954\) | −87.8422 | −2.84400 | ||||||||
\(955\) | 5.26465 | 0.170360 | ||||||||
\(956\) | 72.7523 | 2.35298 | ||||||||
\(957\) | −18.6394 | −0.602525 | ||||||||
\(958\) | −52.9872 | −1.71194 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 3.05457 | 0.0985859 | ||||||||
\(961\) | −10.0640 | −0.324647 | ||||||||
\(962\) | −0.932645 | −0.0300697 | ||||||||
\(963\) | 1.10335 | 0.0355550 | ||||||||
\(964\) | −67.1054 | −2.16132 | ||||||||
\(965\) | 10.5622 | 0.340008 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35.6540 | −1.14655 | −0.573277 | − | 0.819361i | \(-0.694328\pi\) | ||||
−0.573277 | + | 0.819361i | \(0.694328\pi\) | |||||||
\(968\) | 150.560 | 4.83919 | ||||||||
\(969\) | −11.8832 | −0.381742 | ||||||||
\(970\) | 104.683 | 3.36117 | ||||||||
\(971\) | −17.5452 | −0.563052 | −0.281526 | − | 0.959554i | \(-0.590841\pi\) | ||||
−0.281526 | + | 0.959554i | \(0.590841\pi\) | |||||||
\(972\) | −52.8987 | −1.69673 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −8.91651 | −0.285703 | ||||||||
\(975\) | −0.000938700 0 | −3.00624e−5 0 | ||||||||
\(976\) | 21.1269 | 0.676255 | ||||||||
\(977\) | −49.9851 | −1.59917 | −0.799583 | − | 0.600555i | \(-0.794946\pi\) | ||||
−0.799583 | + | 0.600555i | \(0.794946\pi\) | |||||||
\(978\) | 0.990327 | 0.0316672 | ||||||||
\(979\) | −72.5575 | −2.31895 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.6052 | 0.562092 | ||||||||
\(982\) | −23.0022 | −0.734031 | ||||||||
\(983\) | 53.5608 | 1.70833 | 0.854163 | − | 0.520006i | \(-0.174070\pi\) | ||||
0.854163 | + | 0.520006i | \(0.174070\pi\) | |||||||
\(984\) | 3.16625 | 0.100936 | ||||||||
\(985\) | 15.5231 | 0.494606 | ||||||||
\(986\) | 89.0101 | 2.83466 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.70002 | 0.0540848 | ||||||||
\(989\) | −13.0562 | −0.415163 | ||||||||
\(990\) | 92.5749 | 2.94222 | ||||||||
\(991\) | 9.93145 | 0.315483 | 0.157741 | − | 0.987480i | \(-0.449579\pi\) | ||||
0.157741 | + | 0.987480i | \(0.449579\pi\) | |||||||
\(992\) | −34.1548 | −1.08442 | ||||||||
\(993\) | −9.96661 | −0.316281 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −53.1609 | −1.68531 | ||||||||
\(996\) | 10.4906 | 0.332407 | ||||||||
\(997\) | 17.2765 | 0.547153 | 0.273577 | − | 0.961850i | \(-0.411793\pi\) | ||||
0.273577 | + | 0.961850i | \(0.411793\pi\) | |||||||
\(998\) | 16.9628 | 0.536948 | ||||||||
\(999\) | −13.5196 | −0.427741 |
(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 | 2009.2.a.r.1.16 | 17 | ||
7.3 | odd | 6 | 287.2.e.d.247.2 | yes | 34 | ||
7.5 | odd | 6 | 287.2.e.d.165.2 | ✓ | 34 | ||
7.6 | odd | 2 | 2009.2.a.s.1.16 | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.2.e.d.165.2 | ✓ | 34 | 7.5 | odd | 6 | ||
287.2.e.d.247.2 | yes | 34 | 7.3 | odd | 6 | ||
2009.2.a.r.1.16 | 17 | 1.1 | even | 1 | trivial | ||
2009.2.a.s.1.16 | 17 | 7.6 | odd | 2 |