Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3675,2,Mod(1,3675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3675, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3675.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3675.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: | \(29.3450227428\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.88404.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 7x^{2} + 5x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 525) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.70285\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3675.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.70285 | −1.91121 | −0.955603 | − | 0.294657i | \(-0.904795\pi\) | ||||
−0.955603 | + | 0.294657i | \(0.904795\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 5.30542 | 2.65271 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.70285 | −1.10344 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.93406 | −3.15867 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.82550 | 0.851921 | 0.425960 | − | 0.904742i | \(-0.359936\pi\) | ||||
0.425960 | + | 0.904742i | \(0.359936\pi\) | |||||||
\(12\) | 5.30542 | 1.53154 | ||||||||
\(13\) | 4.47992 | 1.24251 | 0.621253 | − | 0.783610i | \(-0.286624\pi\) | ||||
0.621253 | + | 0.783610i | \(0.286624\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 13.5366 | 3.38416 | ||||||||
\(17\) | −4.23121 | −1.02622 | −0.513109 | − | 0.858323i | \(-0.671506\pi\) | ||||
−0.513109 | + | 0.858323i | \(0.671506\pi\) | |||||||
\(18\) | −2.70285 | −0.637069 | ||||||||
\(19\) | 2.10029 | 0.481839 | 0.240920 | − | 0.970545i | \(-0.422551\pi\) | ||||
0.240920 | + | 0.970545i | \(0.422551\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.63692 | −1.62820 | ||||||||
\(23\) | 6.61084 | 1.37845 | 0.689227 | − | 0.724545i | \(-0.257950\pi\) | ||||
0.689227 | + | 0.724545i | \(0.257950\pi\) | |||||||
\(24\) | −8.93406 | −1.82366 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −12.1086 | −2.37468 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.00000 | 0.742781 | 0.371391 | − | 0.928477i | \(-0.378881\pi\) | ||||
0.371391 | + | 0.928477i | \(0.378881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.33150 | 1.67599 | 0.837993 | − | 0.545681i | \(-0.183729\pi\) | ||||
0.837993 | + | 0.545681i | \(0.183729\pi\) | |||||||
\(32\) | −18.7194 | −3.30915 | ||||||||
\(33\) | 2.82550 | 0.491857 | ||||||||
\(34\) | 11.4363 | 1.96132 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.30542 | 0.884236 | ||||||||
\(37\) | −4.20513 | −0.691319 | −0.345659 | − | 0.938360i | \(-0.612345\pi\) | ||||
−0.345659 | + | 0.938360i | \(0.612345\pi\) | |||||||
\(38\) | −5.67677 | −0.920894 | ||||||||
\(39\) | 4.47992 | 0.717361 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.37963 | 0.371635 | 0.185818 | − | 0.982584i | \(-0.440507\pi\) | ||||
0.185818 | + | 0.982584i | \(0.440507\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.13092 | 0.477461 | 0.238730 | − | 0.971086i | \(-0.423269\pi\) | ||||
0.238730 | + | 0.971086i | \(0.423269\pi\) | |||||||
\(44\) | 14.9905 | 2.25990 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −17.8681 | −2.63451 | ||||||||
\(47\) | −7.78534 | −1.13561 | −0.567804 | − | 0.823164i | \(-0.692207\pi\) | ||||
−0.567804 | + | 0.823164i | \(0.692207\pi\) | |||||||
\(48\) | 13.5366 | 1.95384 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.23121 | −0.592488 | ||||||||
\(52\) | 23.7678 | 3.29601 | ||||||||
\(53\) | −2.58021 | −0.354419 | −0.177209 | − | 0.984173i | \(-0.556707\pi\) | ||||
−0.177209 | + | 0.984173i | \(0.556707\pi\) | |||||||
\(54\) | −2.70285 | −0.367812 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.10029 | 0.278190 | ||||||||
\(58\) | −10.8114 | −1.41961 | ||||||||
\(59\) | −3.78534 | −0.492809 | −0.246404 | − | 0.969167i | \(-0.579249\pi\) | ||||
−0.246404 | + | 0.969167i | \(0.579249\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.00000 | −0.640184 | −0.320092 | − | 0.947386i | \(-0.603714\pi\) | ||||
−0.320092 | + | 0.947386i | \(0.603714\pi\) | |||||||
\(62\) | −25.2217 | −3.20316 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 23.5225 | 2.94032 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7.63692 | −0.940039 | ||||||||
\(67\) | 3.30542 | 0.403821 | 0.201911 | − | 0.979404i | \(-0.435285\pi\) | ||||
0.201911 | + | 0.979404i | \(0.435285\pi\) | |||||||
\(68\) | −22.4483 | −2.72226 | ||||||||
\(69\) | 6.61084 | 0.795851 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.4223 | −1.35557 | −0.677786 | − | 0.735259i | \(-0.737060\pi\) | ||||
−0.677786 | + | 0.735259i | \(0.737060\pi\) | |||||||
\(72\) | −8.93406 | −1.05289 | ||||||||
\(73\) | −2.65100 | −0.310276 | −0.155138 | − | 0.987893i | \(-0.549582\pi\) | ||||
−0.155138 | + | 0.987893i | \(0.549582\pi\) | |||||||
\(74\) | 11.3658 | 1.32125 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11.1429 | 1.27818 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −12.1086 | −1.37102 | ||||||||
\(79\) | 12.6369 | 1.42176 | 0.710882 | − | 0.703311i | \(-0.248296\pi\) | ||||
0.710882 | + | 0.703311i | \(0.248296\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.43179 | −0.710272 | ||||||||
\(83\) | 3.02608 | 0.332155 | 0.166078 | − | 0.986113i | \(-0.446890\pi\) | ||||
0.166078 | + | 0.986113i | \(0.446890\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8.46242 | −0.912526 | ||||||||
\(87\) | 4.00000 | 0.428845 | ||||||||
\(88\) | −25.2432 | −2.69093 | ||||||||
\(89\) | −8.23121 | −0.872506 | −0.436253 | − | 0.899824i | \(-0.643695\pi\) | ||||
−0.436253 | + | 0.899824i | \(0.643695\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 35.0733 | 3.65664 | ||||||||
\(93\) | 9.33150 | 0.967631 | ||||||||
\(94\) | 21.0426 | 2.17038 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −18.7194 | −1.91054 | ||||||||
\(97\) | 15.0165 | 1.52470 | 0.762350 | − | 0.647166i | \(-0.224046\pi\) | ||||
0.762350 | + | 0.647166i | \(0.224046\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.82550 | 0.283974 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.23121 | −0.222014 | −0.111007 | − | 0.993820i | \(-0.535408\pi\) | ||||
−0.111007 | + | 0.993820i | \(0.535408\pi\) | |||||||
\(102\) | 11.4363 | 1.13237 | ||||||||
\(103\) | −7.84205 | −0.772700 | −0.386350 | − | 0.922352i | \(-0.626264\pi\) | ||||
−0.386350 | + | 0.922352i | \(0.626264\pi\) | |||||||
\(104\) | −40.0239 | −3.92466 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.97392 | 0.677367 | ||||||||
\(107\) | 15.6369 | 1.51168 | 0.755839 | − | 0.654758i | \(-0.227229\pi\) | ||||
0.755839 | + | 0.654758i | \(0.227229\pi\) | |||||||
\(108\) | 5.30542 | 0.510514 | ||||||||
\(109\) | 3.07421 | 0.294456 | 0.147228 | − | 0.989103i | \(-0.452965\pi\) | ||||
0.147228 | + | 0.989103i | \(0.452965\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.20513 | −0.399133 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.348998 | −0.0328310 | −0.0164155 | − | 0.999865i | \(-0.505225\pi\) | ||||
−0.0164155 | + | 0.999865i | \(0.505225\pi\) | |||||||
\(114\) | −5.67677 | −0.531679 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 21.2217 | 1.97038 | ||||||||
\(117\) | 4.47992 | 0.414169 | ||||||||
\(118\) | 10.2312 | 0.941859 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.01654 | −0.274231 | ||||||||
\(122\) | 13.5143 | 1.22352 | ||||||||
\(123\) | 2.37963 | 0.214564 | ||||||||
\(124\) | 49.5075 | 4.44590 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.27137 | 0.201552 | 0.100776 | − | 0.994909i | \(-0.467867\pi\) | ||||
0.100776 | + | 0.994909i | \(0.467867\pi\) | |||||||
\(128\) | −26.1392 | −2.31040 | ||||||||
\(129\) | 3.13092 | 0.275662 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.2217 | 1.67941 | 0.839703 | − | 0.543046i | \(-0.182729\pi\) | ||||
0.839703 | + | 0.543046i | \(0.182729\pi\) | |||||||
\(132\) | 14.9905 | 1.30475 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −8.93406 | −0.771785 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 37.8019 | 3.24148 | ||||||||
\(137\) | −8.26184 | −0.705857 | −0.352928 | − | 0.935650i | \(-0.614814\pi\) | ||||
−0.352928 | + | 0.935650i | \(0.614814\pi\) | |||||||
\(138\) | −17.8681 | −1.52104 | ||||||||
\(139\) | 0.985914 | 0.0836241 | 0.0418121 | − | 0.999125i | \(-0.486687\pi\) | ||||
0.0418121 | + | 0.999125i | \(0.486687\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.78534 | −0.655644 | ||||||||
\(142\) | 30.8727 | 2.59078 | ||||||||
\(143\) | 12.6580 | 1.05852 | ||||||||
\(144\) | 13.5366 | 1.12805 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.16527 | 0.593002 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −22.3100 | −1.83387 | ||||||||
\(149\) | 7.82095 | 0.640717 | 0.320359 | − | 0.947296i | \(-0.396197\pi\) | ||||
0.320359 | + | 0.947296i | \(0.396197\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.13433 | −0.255068 | −0.127534 | − | 0.991834i | \(-0.540706\pi\) | ||||
−0.127534 | + | 0.991834i | \(0.540706\pi\) | |||||||
\(152\) | −18.7641 | −1.52197 | ||||||||
\(153\) | −4.23121 | −0.342073 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 23.7678 | 1.90295 | ||||||||
\(157\) | −23.4790 | −1.87383 | −0.936913 | − | 0.349564i | \(-0.886330\pi\) | ||||
−0.936913 | + | 0.349564i | \(0.886330\pi\) | |||||||
\(158\) | −34.1557 | −2.71728 | ||||||||
\(159\) | −2.58021 | −0.204624 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.70285 | −0.212356 | ||||||||
\(163\) | −12.4363 | −0.974089 | −0.487045 | − | 0.873377i | \(-0.661925\pi\) | ||||
−0.487045 | + | 0.873377i | \(0.661925\pi\) | |||||||
\(164\) | 12.6249 | 0.985841 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.17905 | −0.634817 | ||||||||
\(167\) | 18.4483 | 1.42757 | 0.713787 | − | 0.700362i | \(-0.246978\pi\) | ||||
0.713787 | + | 0.700362i | \(0.246978\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.06966 | 0.543820 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.10029 | 0.160613 | ||||||||
\(172\) | 16.6108 | 1.26656 | ||||||||
\(173\) | 7.65100 | 0.581695 | 0.290847 | − | 0.956769i | \(-0.406063\pi\) | ||||
0.290847 | + | 0.956769i | \(0.406063\pi\) | |||||||
\(174\) | −10.8114 | −0.819611 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 38.2478 | 2.88303 | ||||||||
\(177\) | −3.78534 | −0.284523 | ||||||||
\(178\) | 22.2478 | 1.66754 | ||||||||
\(179\) | −2.41026 | −0.180151 | −0.0900756 | − | 0.995935i | \(-0.528711\pi\) | ||||
−0.0900756 | + | 0.995935i | \(0.528711\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.6970 | −1.01809 | −0.509046 | − | 0.860739i | \(-0.670002\pi\) | ||||
−0.509046 | + | 0.860739i | \(0.670002\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.00000 | −0.369611 | ||||||||
\(184\) | −59.0616 | −4.35408 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −25.2217 | −1.84934 | ||||||||
\(187\) | −11.9553 | −0.874257 | ||||||||
\(188\) | −41.3045 | −3.01244 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.1343 | −0.878010 | −0.439005 | − | 0.898485i | \(-0.644669\pi\) | ||||
−0.439005 | + | 0.898485i | \(0.644669\pi\) | |||||||
\(192\) | 23.5225 | 1.69759 | ||||||||
\(193\) | 11.9258 | 0.858437 | 0.429219 | − | 0.903201i | \(-0.358789\pi\) | ||||
0.429219 | + | 0.903201i | \(0.358789\pi\) | |||||||
\(194\) | −40.5875 | −2.91401 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.50258 | −0.392043 | −0.196021 | − | 0.980600i | \(-0.562802\pi\) | ||||
−0.196021 | + | 0.980600i | \(0.562802\pi\) | |||||||
\(198\) | −7.63692 | −0.542732 | ||||||||
\(199\) | −11.3281 | −0.803027 | −0.401513 | − | 0.915853i | \(-0.631516\pi\) | ||||
−0.401513 | + | 0.915853i | \(0.631516\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.30542 | 0.233146 | ||||||||
\(202\) | 6.03063 | 0.424314 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −22.4483 | −1.57170 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 21.1959 | 1.47679 | ||||||||
\(207\) | 6.61084 | 0.459485 | ||||||||
\(208\) | 60.6430 | 4.20483 | ||||||||
\(209\) | 5.93437 | 0.410489 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.82095 | 0.607259 | 0.303630 | − | 0.952790i | \(-0.401801\pi\) | ||||
0.303630 | + | 0.952790i | \(0.401801\pi\) | |||||||
\(212\) | −13.6891 | −0.940170 | ||||||||
\(213\) | −11.4223 | −0.782640 | ||||||||
\(214\) | −42.2643 | −2.88913 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −8.93406 | −0.607886 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −8.30914 | −0.562766 | ||||||||
\(219\) | −2.65100 | −0.179138 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.9555 | −1.27508 | ||||||||
\(222\) | 11.3658 | 0.762826 | ||||||||
\(223\) | 26.4885 | 1.77380 | 0.886900 | − | 0.461961i | \(-0.152854\pi\) | ||||
0.886900 | + | 0.461961i | \(0.152854\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.943291 | 0.0627468 | ||||||||
\(227\) | −17.7712 | −1.17952 | −0.589760 | − | 0.807579i | \(-0.700778\pi\) | ||||
−0.589760 | + | 0.807579i | \(0.700778\pi\) | |||||||
\(228\) | 11.1429 | 0.737957 | ||||||||
\(229\) | 18.6449 | 1.23209 | 0.616044 | − | 0.787712i | \(-0.288734\pi\) | ||||
0.616044 | + | 0.787712i | \(0.288734\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −35.7362 | −2.34620 | ||||||||
\(233\) | −9.76879 | −0.639975 | −0.319987 | − | 0.947422i | \(-0.603679\pi\) | ||||
−0.319987 | + | 0.947422i | \(0.603679\pi\) | |||||||
\(234\) | −12.1086 | −0.791561 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −20.0828 | −1.30728 | ||||||||
\(237\) | 12.6369 | 0.820856 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.20058 | −0.401082 | −0.200541 | − | 0.979685i | \(-0.564270\pi\) | ||||
−0.200541 | + | 0.979685i | \(0.564270\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.2382 | −1.30366 | −0.651829 | − | 0.758366i | \(-0.725998\pi\) | ||||
−0.651829 | + | 0.758366i | \(0.725998\pi\) | |||||||
\(242\) | 8.15328 | 0.524113 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −26.5271 | −1.69822 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.43179 | −0.410076 | ||||||||
\(247\) | 9.40912 | 0.598688 | ||||||||
\(248\) | −83.3682 | −5.29388 | ||||||||
\(249\) | 3.02608 | 0.191770 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.21466 | −0.392266 | −0.196133 | − | 0.980577i | \(-0.562838\pi\) | ||||
−0.196133 | + | 0.980577i | \(0.562838\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.6789 | 1.17433 | ||||||||
\(254\) | −6.13919 | −0.385207 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 23.6053 | 1.47533 | ||||||||
\(257\) | 5.65346 | 0.352653 | 0.176327 | − | 0.984332i | \(-0.443579\pi\) | ||||
0.176327 | + | 0.984332i | \(0.443579\pi\) | |||||||
\(258\) | −8.46242 | −0.526847 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.00000 | 0.247594 | ||||||||
\(262\) | −51.9534 | −3.20969 | ||||||||
\(263\) | 25.0120 | 1.54231 | 0.771153 | − | 0.636650i | \(-0.219680\pi\) | ||||
0.771153 | + | 0.636650i | \(0.219680\pi\) | |||||||
\(264\) | −25.2432 | −1.55361 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.23121 | −0.503742 | ||||||||
\(268\) | 17.5366 | 1.07122 | ||||||||
\(269\) | −7.88221 | −0.480587 | −0.240293 | − | 0.970700i | \(-0.577244\pi\) | ||||
−0.240293 | + | 0.970700i | \(0.577244\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.74271 | 0.288099 | 0.144050 | − | 0.989570i | \(-0.453988\pi\) | ||||
0.144050 | + | 0.989570i | \(0.453988\pi\) | |||||||
\(272\) | −57.2763 | −3.47289 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 22.3305 | 1.34904 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 35.0733 | 2.11116 | ||||||||
\(277\) | 7.73721 | 0.464884 | 0.232442 | − | 0.972610i | \(-0.425328\pi\) | ||||
0.232442 | + | 0.972610i | \(0.425328\pi\) | |||||||
\(278\) | −2.66478 | −0.159823 | ||||||||
\(279\) | 9.33150 | 0.558662 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.11779 | 0.126337 | 0.0631684 | − | 0.998003i | \(-0.479879\pi\) | ||||
0.0631684 | + | 0.998003i | \(0.479879\pi\) | |||||||
\(282\) | 21.0426 | 1.25307 | ||||||||
\(283\) | 4.39774 | 0.261419 | 0.130709 | − | 0.991421i | \(-0.458275\pi\) | ||||
0.130709 | + | 0.991421i | \(0.458275\pi\) | |||||||
\(284\) | −60.5998 | −3.59594 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −34.2128 | −2.02304 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −18.7194 | −1.10305 | ||||||||
\(289\) | 0.903125 | 0.0531250 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.0165 | 0.880285 | ||||||||
\(292\) | −14.0647 | −0.823073 | ||||||||
\(293\) | −14.2006 | −0.829607 | −0.414803 | − | 0.909911i | \(-0.636150\pi\) | ||||
−0.414803 | + | 0.909911i | \(0.636150\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 37.5689 | 2.18365 | ||||||||
\(297\) | 2.82550 | 0.163952 | ||||||||
\(298\) | −21.1389 | −1.22454 | ||||||||
\(299\) | 29.6160 | 1.71274 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.47165 | 0.487488 | ||||||||
\(303\) | −2.23121 | −0.128180 | ||||||||
\(304\) | 28.4308 | 1.63062 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 11.4363 | 0.653772 | ||||||||
\(307\) | −13.9423 | −0.795731 | −0.397866 | − | 0.917444i | \(-0.630249\pi\) | ||||
−0.397866 | + | 0.917444i | \(0.630249\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.84205 | −0.446118 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.79942 | −0.215445 | −0.107723 | − | 0.994181i | \(-0.534356\pi\) | ||||
−0.107723 | + | 0.994181i | \(0.534356\pi\) | |||||||
\(312\) | −40.0239 | −2.26590 | ||||||||
\(313\) | 27.8976 | 1.57687 | 0.788433 | − | 0.615120i | \(-0.210893\pi\) | ||||
0.788433 | + | 0.615120i | \(0.210893\pi\) | |||||||
\(314\) | 63.4602 | 3.58127 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 67.0441 | 3.77153 | ||||||||
\(317\) | 34.4955 | 1.93746 | 0.968730 | − | 0.248116i | \(-0.0798115\pi\) | ||||
0.968730 | + | 0.248116i | \(0.0798115\pi\) | |||||||
\(318\) | 6.97392 | 0.391078 | ||||||||
\(319\) | 11.3020 | 0.632791 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.6369 | 0.872768 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.88676 | −0.494473 | ||||||||
\(324\) | 5.30542 | 0.294745 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 33.6136 | 1.86169 | ||||||||
\(327\) | 3.07421 | 0.170004 | ||||||||
\(328\) | −21.2597 | −1.17387 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.8942 | −1.64313 | −0.821567 | − | 0.570112i | \(-0.806900\pi\) | ||||
−0.821567 | + | 0.570112i | \(0.806900\pi\) | |||||||
\(332\) | 16.0546 | 0.881112 | ||||||||
\(333\) | −4.20513 | −0.230440 | ||||||||
\(334\) | −49.8631 | −2.72839 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.3480 | 1.05395 | 0.526977 | − | 0.849879i | \(-0.323325\pi\) | ||||
0.526977 | + | 0.849879i | \(0.323325\pi\) | |||||||
\(338\) | −19.1083 | −1.03935 | ||||||||
\(339\) | −0.348998 | −0.0189550 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 26.3662 | 1.42781 | ||||||||
\(342\) | −5.67677 | −0.306965 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −27.9718 | −1.50814 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −20.6795 | −1.11174 | ||||||||
\(347\) | 26.2999 | 1.41185 | 0.705927 | − | 0.708285i | \(-0.250531\pi\) | ||||
0.705927 | + | 0.708285i | \(0.250531\pi\) | |||||||
\(348\) | 21.2217 | 1.13760 | ||||||||
\(349\) | −14.9083 | −0.798022 | −0.399011 | − | 0.916946i | \(-0.630647\pi\) | ||||
−0.399011 | + | 0.916946i | \(0.630647\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.47992 | 0.239120 | ||||||||
\(352\) | −52.8917 | −2.81914 | ||||||||
\(353\) | −15.8210 | −0.842064 | −0.421032 | − | 0.907046i | \(-0.638332\pi\) | ||||
−0.421032 | + | 0.907046i | \(0.638332\pi\) | |||||||
\(354\) | 10.2312 | 0.543783 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −43.6700 | −2.31451 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.51458 | 0.344306 | ||||||||
\(359\) | 16.6771 | 0.880183 | 0.440091 | − | 0.897953i | \(-0.354946\pi\) | ||||
0.440091 | + | 0.897953i | \(0.354946\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.5888 | −0.767831 | ||||||||
\(362\) | 37.0211 | 1.94579 | ||||||||
\(363\) | −3.01654 | −0.158328 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 13.5143 | 0.706402 | ||||||||
\(367\) | 28.1876 | 1.47138 | 0.735691 | − | 0.677317i | \(-0.236858\pi\) | ||||
0.735691 | + | 0.677317i | \(0.236858\pi\) | |||||||
\(368\) | 89.4884 | 4.66491 | ||||||||
\(369\) | 2.37963 | 0.123878 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 49.5075 | 2.56684 | ||||||||
\(373\) | 23.9990 | 1.24262 | 0.621312 | − | 0.783564i | \(-0.286600\pi\) | ||||
0.621312 | + | 0.783564i | \(0.286600\pi\) | |||||||
\(374\) | 32.3134 | 1.67089 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 69.5547 | 3.58701 | ||||||||
\(377\) | 17.9197 | 0.922910 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.8550 | 0.711683 | 0.355842 | − | 0.934546i | \(-0.384194\pi\) | ||||
0.355842 | + | 0.934546i | \(0.384194\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.27137 | 0.116366 | ||||||||
\(382\) | 32.7973 | 1.67806 | ||||||||
\(383\) | −30.7764 | −1.57260 | −0.786301 | − | 0.617844i | \(-0.788006\pi\) | ||||
−0.786301 | + | 0.617844i | \(0.788006\pi\) | |||||||
\(384\) | −26.1392 | −1.33391 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −32.2337 | −1.64065 | ||||||||
\(387\) | 3.13092 | 0.159154 | ||||||||
\(388\) | 79.6690 | 4.04458 | ||||||||
\(389\) | 38.4127 | 1.94760 | 0.973801 | − | 0.227402i | \(-0.0730231\pi\) | ||||
0.973801 | + | 0.227402i | \(0.0730231\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.9718 | −1.41460 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 19.2217 | 0.969605 | ||||||||
\(394\) | 14.8727 | 0.749275 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 14.9905 | 0.753299 | ||||||||
\(397\) | −33.4615 | −1.67938 | −0.839691 | − | 0.543064i | \(-0.817264\pi\) | ||||
−0.839691 | + | 0.543064i | \(0.817264\pi\) | |||||||
\(398\) | 30.6182 | 1.53475 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.8420 | 0.741176 | 0.370588 | − | 0.928797i | \(-0.379156\pi\) | ||||
0.370588 | + | 0.928797i | \(0.379156\pi\) | |||||||
\(402\) | −8.93406 | −0.445591 | ||||||||
\(403\) | 41.8043 | 2.08242 | ||||||||
\(404\) | −11.8375 | −0.588937 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.8816 | −0.588949 | ||||||||
\(408\) | 37.8019 | 1.87147 | ||||||||
\(409\) | 8.44492 | 0.417574 | 0.208787 | − | 0.977961i | \(-0.433048\pi\) | ||||
0.208787 | + | 0.977961i | \(0.433048\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.26184 | −0.407526 | ||||||||
\(412\) | −41.6053 | −2.04975 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −17.8681 | −0.878170 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −83.8614 | −4.11164 | ||||||||
\(417\) | 0.985914 | 0.0482804 | ||||||||
\(418\) | −16.0397 | −0.784529 | ||||||||
\(419\) | −18.8427 | −0.920524 | −0.460262 | − | 0.887783i | \(-0.652245\pi\) | ||||
−0.460262 | + | 0.887783i | \(0.652245\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.09687 | −0.443355 | −0.221677 | − | 0.975120i | \(-0.571153\pi\) | ||||
−0.221677 | + | 0.975120i | \(0.571153\pi\) | |||||||
\(422\) | −23.8417 | −1.16060 | ||||||||
\(423\) | −7.78534 | −0.378536 | ||||||||
\(424\) | 23.0517 | 1.11949 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 30.8727 | 1.49579 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 82.9604 | 4.01004 | ||||||||
\(429\) | 12.6580 | 0.611135 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.95983 | −0.238907 | −0.119453 | − | 0.992840i | \(-0.538114\pi\) | ||||
−0.119453 | + | 0.992840i | \(0.538114\pi\) | |||||||
\(432\) | 13.5366 | 0.651281 | ||||||||
\(433\) | −2.61696 | −0.125763 | −0.0628815 | − | 0.998021i | \(-0.520029\pi\) | ||||
−0.0628815 | + | 0.998021i | \(0.520029\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16.3100 | 0.781106 | ||||||||
\(437\) | 13.8847 | 0.664194 | ||||||||
\(438\) | 7.16527 | 0.342370 | ||||||||
\(439\) | −26.5050 | −1.26502 | −0.632508 | − | 0.774554i | \(-0.717975\pi\) | ||||
−0.632508 | + | 0.774554i | \(0.717975\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 51.2338 | 2.43695 | ||||||||
\(443\) | 39.4903 | 1.87624 | 0.938121 | − | 0.346307i | \(-0.112564\pi\) | ||||
0.938121 | + | 0.346307i | \(0.112564\pi\) | |||||||
\(444\) | −22.3100 | −1.05878 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −71.5945 | −3.39010 | ||||||||
\(447\) | 7.82095 | 0.369918 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.3045 | 1.00542 | 0.502710 | − | 0.864455i | \(-0.332336\pi\) | ||||
0.502710 | + | 0.864455i | \(0.332336\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.72364 | 0.316604 | ||||||||
\(452\) | −1.85158 | −0.0870910 | ||||||||
\(453\) | −3.13433 | −0.147264 | ||||||||
\(454\) | 48.0331 | 2.25430 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −18.7641 | −0.878710 | ||||||||
\(457\) | 27.8801 | 1.30418 | 0.652088 | − | 0.758143i | \(-0.273893\pi\) | ||||
0.652088 | + | 0.758143i | \(0.273893\pi\) | |||||||
\(458\) | −50.3944 | −2.35478 | ||||||||
\(459\) | −4.23121 | −0.197496 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.5237 | 1.04903 | 0.524516 | − | 0.851401i | \(-0.324246\pi\) | ||||
0.524516 | + | 0.851401i | \(0.324246\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.69301 | −0.0786809 | −0.0393405 | − | 0.999226i | \(-0.512526\pi\) | ||||
−0.0393405 | + | 0.999226i | \(0.512526\pi\) | |||||||
\(464\) | 54.1465 | 2.51369 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 26.4036 | 1.22312 | ||||||||
\(467\) | −0.0803308 | −0.00371727 | −0.00185863 | − | 0.999998i | \(-0.500592\pi\) | ||||
−0.00185863 | + | 0.999998i | \(0.500592\pi\) | |||||||
\(468\) | 23.7678 | 1.09867 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.4790 | −1.08185 | ||||||||
\(472\) | 33.8184 | 1.55662 | ||||||||
\(473\) | 8.84642 | 0.406759 | ||||||||
\(474\) | −34.1557 | −1.56882 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.58021 | −0.118140 | ||||||||
\(478\) | 16.7593 | 0.766551 | ||||||||
\(479\) | −38.7783 | −1.77182 | −0.885912 | − | 0.463853i | \(-0.846466\pi\) | ||||
−0.885912 | + | 0.463853i | \(0.846466\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.8386 | −0.858968 | ||||||||
\(482\) | 54.7009 | 2.49156 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −16.0040 | −0.727456 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.70285 | −0.122604 | ||||||||
\(487\) | −27.1309 | −1.22942 | −0.614710 | − | 0.788753i | \(-0.710727\pi\) | ||||
−0.614710 | + | 0.788753i | \(0.710727\pi\) | |||||||
\(488\) | 44.6703 | 2.02213 | ||||||||
\(489\) | −12.4363 | −0.562391 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.7243 | 0.754755 | 0.377378 | − | 0.926059i | \(-0.376826\pi\) | ||||
0.377378 | + | 0.926059i | \(0.376826\pi\) | |||||||
\(492\) | 12.6249 | 0.569175 | ||||||||
\(493\) | −16.9248 | −0.762256 | ||||||||
\(494\) | −25.4315 | −1.14422 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 126.317 | 5.67180 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −8.17905 | −0.366512 | ||||||||
\(499\) | 19.7844 | 0.885670 | 0.442835 | − | 0.896603i | \(-0.353973\pi\) | ||||
0.442835 | + | 0.896603i | \(0.353973\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.4483 | 0.824211 | ||||||||
\(502\) | 16.7973 | 0.749701 | ||||||||
\(503\) | −6.75015 | −0.300975 | −0.150487 | − | 0.988612i | \(-0.548084\pi\) | ||||
−0.150487 | + | 0.988612i | \(0.548084\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −50.4864 | −2.24439 | ||||||||
\(507\) | 7.06966 | 0.313975 | ||||||||
\(508\) | 12.0506 | 0.534658 | ||||||||
\(509\) | −40.3471 | −1.78835 | −0.894177 | − | 0.447715i | \(-0.852238\pi\) | ||||
−0.894177 | + | 0.447715i | \(0.852238\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −11.5234 | −0.509266 | ||||||||
\(513\) | 2.10029 | 0.0927300 | ||||||||
\(514\) | −15.2805 | −0.673993 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 16.6108 | 0.731251 | ||||||||
\(517\) | −21.9975 | −0.967448 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.65100 | 0.335842 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.6038 | 1.64745 | 0.823725 | − | 0.566989i | \(-0.191892\pi\) | ||||
0.823725 | + | 0.566989i | \(0.191892\pi\) | |||||||
\(522\) | −10.8114 | −0.473203 | ||||||||
\(523\) | 39.3124 | 1.71901 | 0.859506 | − | 0.511125i | \(-0.170771\pi\) | ||||
0.859506 | + | 0.511125i | \(0.170771\pi\) | |||||||
\(524\) | 101.979 | 4.45497 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −67.6038 | −2.94766 | ||||||||
\(527\) | −39.4835 | −1.71993 | ||||||||
\(528\) | 38.2478 | 1.66452 | ||||||||
\(529\) | 20.7032 | 0.900137 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.78534 | −0.164270 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.6605 | 0.461759 | ||||||||
\(534\) | 22.2478 | 0.962754 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −29.5308 | −1.27554 | ||||||||
\(537\) | −2.41026 | −0.104010 | ||||||||
\(538\) | 21.3045 | 0.918501 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.5722 | 0.927463 | 0.463732 | − | 0.885976i | \(-0.346510\pi\) | ||||
0.463732 | + | 0.885976i | \(0.346510\pi\) | |||||||
\(542\) | −12.8189 | −0.550617 | ||||||||
\(543\) | −13.6970 | −0.587796 | ||||||||
\(544\) | 79.2057 | 3.39592 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.3707 | −0.913745 | −0.456873 | − | 0.889532i | \(-0.651031\pi\) | ||||
−0.456873 | + | 0.889532i | \(0.651031\pi\) | |||||||
\(548\) | −43.8325 | −1.87243 | ||||||||
\(549\) | −5.00000 | −0.213395 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.40116 | 0.357901 | ||||||||
\(552\) | −59.0616 | −2.51383 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −20.9125 | −0.888488 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.23069 | 0.221830 | ||||||||
\(557\) | 14.2618 | 0.604293 | 0.302147 | − | 0.953261i | \(-0.402297\pi\) | ||||
0.302147 | + | 0.953261i | \(0.402297\pi\) | |||||||
\(558\) | −25.2217 | −1.06772 | ||||||||
\(559\) | 14.0263 | 0.593248 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.9553 | −0.504752 | ||||||||
\(562\) | −5.72408 | −0.241456 | ||||||||
\(563\) | −2.36308 | −0.0995921 | −0.0497961 | − | 0.998759i | \(-0.515857\pi\) | ||||
−0.0497961 | + | 0.998759i | \(0.515857\pi\) | |||||||
\(564\) | −41.3045 | −1.73923 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −11.8865 | −0.499625 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 102.047 | 4.28180 | ||||||||
\(569\) | −12.7458 | −0.534331 | −0.267166 | − | 0.963651i | \(-0.586087\pi\) | ||||
−0.267166 | + | 0.963651i | \(0.586087\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.361514 | 0.0151289 | 0.00756444 | − | 0.999971i | \(-0.497592\pi\) | ||||
0.00756444 | + | 0.999971i | \(0.497592\pi\) | |||||||
\(572\) | 67.1560 | 2.80794 | ||||||||
\(573\) | −12.1343 | −0.506919 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 23.5225 | 0.980106 | ||||||||
\(577\) | 9.59334 | 0.399376 | 0.199688 | − | 0.979860i | \(-0.436007\pi\) | ||||
0.199688 | + | 0.979860i | \(0.436007\pi\) | |||||||
\(578\) | −2.44102 | −0.101533 | ||||||||
\(579\) | 11.9258 | 0.495619 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −40.5875 | −1.68241 | ||||||||
\(583\) | −7.29038 | −0.301937 | ||||||||
\(584\) | 23.6842 | 0.980060 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 38.3821 | 1.58555 | ||||||||
\(587\) | 19.2217 | 0.793363 | 0.396682 | − | 0.917956i | \(-0.370162\pi\) | ||||
0.396682 | + | 0.917956i | \(0.370162\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.5988 | 0.807556 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.50258 | −0.226346 | ||||||||
\(592\) | −56.9233 | −2.33953 | ||||||||
\(593\) | 11.7994 | 0.484544 | 0.242272 | − | 0.970208i | \(-0.422107\pi\) | ||||
0.242272 | + | 0.970208i | \(0.422107\pi\) | |||||||
\(594\) | −7.63692 | −0.313346 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 41.4934 | 1.69964 | ||||||||
\(597\) | −11.3281 | −0.463628 | ||||||||
\(598\) | −80.0477 | −3.27339 | ||||||||
\(599\) | 40.3962 | 1.65054 | 0.825271 | − | 0.564736i | \(-0.191022\pi\) | ||||
0.825271 | + | 0.564736i | \(0.191022\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.9073 | −0.852828 | −0.426414 | − | 0.904528i | \(-0.640223\pi\) | ||||
−0.426414 | + | 0.904528i | \(0.640223\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.30542 | 0.134607 | ||||||||
\(604\) | −16.6290 | −0.676622 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 6.03063 | 0.244978 | ||||||||
\(607\) | −4.20759 | −0.170781 | −0.0853903 | − | 0.996348i | \(-0.527214\pi\) | ||||
−0.0853903 | + | 0.996348i | \(0.527214\pi\) | |||||||
\(608\) | −39.3161 | −1.59448 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −34.8777 | −1.41100 | ||||||||
\(612\) | −22.4483 | −0.907420 | ||||||||
\(613\) | −16.4268 | −0.663472 | −0.331736 | − | 0.943372i | \(-0.607634\pi\) | ||||
−0.331736 | + | 0.943372i | \(0.607634\pi\) | |||||||
\(614\) | 37.6841 | 1.52081 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.9037 | −0.881811 | −0.440906 | − | 0.897553i | \(-0.645343\pi\) | ||||
−0.440906 | + | 0.897553i | \(0.645343\pi\) | |||||||
\(618\) | 21.1959 | 0.852624 | ||||||||
\(619\) | 0.319504 | 0.0128420 | 0.00642098 | − | 0.999979i | \(-0.497956\pi\) | ||||
0.00642098 | + | 0.999979i | \(0.497956\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.61084 | 0.265284 | ||||||||
\(622\) | 10.2693 | 0.411761 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 60.6430 | 2.42766 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −75.4032 | −3.01372 | ||||||||
\(627\) | 5.93437 | 0.236996 | ||||||||
\(628\) | −124.566 | −4.97071 | ||||||||
\(629\) | 17.7928 | 0.709445 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.3090 | 0.689061 | 0.344530 | − | 0.938775i | \(-0.388038\pi\) | ||||
0.344530 | + | 0.938775i | \(0.388038\pi\) | |||||||
\(632\) | −112.899 | −4.49088 | ||||||||
\(633\) | 8.82095 | 0.350601 | ||||||||
\(634\) | −93.2363 | −3.70289 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −13.6891 | −0.542807 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −30.5477 | −1.20939 | ||||||||
\(639\) | −11.4223 | −0.451857 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 48.2858 | 1.90718 | 0.953588 | − | 0.301115i | \(-0.0973589\pi\) | ||||
0.953588 | + | 0.301115i | \(0.0973589\pi\) | |||||||
\(642\) | −42.2643 | −1.66804 | ||||||||
\(643\) | −12.6460 | −0.498710 | −0.249355 | − | 0.968412i | \(-0.580219\pi\) | ||||
−0.249355 | + | 0.968412i | \(0.580219\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24.0196 | 0.945039 | ||||||||
\(647\) | 15.8534 | 0.623262 | 0.311631 | − | 0.950203i | \(-0.399125\pi\) | ||||
0.311631 | + | 0.950203i | \(0.399125\pi\) | |||||||
\(648\) | −8.93406 | −0.350963 | ||||||||
\(649\) | −10.6955 | −0.419834 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −65.9800 | −2.58398 | ||||||||
\(653\) | −1.15795 | −0.0453143 | −0.0226571 | − | 0.999743i | \(-0.507213\pi\) | ||||
−0.0226571 | + | 0.999743i | \(0.507213\pi\) | |||||||
\(654\) | −8.30914 | −0.324913 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 32.2121 | 1.25767 | ||||||||
\(657\) | −2.65100 | −0.103425 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.5617 | −1.34633 | −0.673167 | − | 0.739490i | \(-0.735067\pi\) | ||||
−0.673167 | + | 0.739490i | \(0.735067\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.28030 | −0.0497977 | −0.0248989 | − | 0.999690i | \(-0.507926\pi\) | ||||
−0.0248989 | + | 0.999690i | \(0.507926\pi\) | |||||||
\(662\) | 80.7997 | 3.14037 | ||||||||
\(663\) | −18.9555 | −0.736169 | ||||||||
\(664\) | −27.0352 | −1.04917 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11.3658 | 0.440418 | ||||||||
\(667\) | 26.4433 | 1.02389 | ||||||||
\(668\) | 97.8761 | 3.78694 | ||||||||
\(669\) | 26.4885 | 1.02410 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.1275 | −0.545386 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −45.9058 | −1.76954 | −0.884769 | − | 0.466031i | \(-0.845684\pi\) | ||||
−0.884769 | + | 0.466031i | \(0.845684\pi\) | |||||||
\(674\) | −52.2949 | −2.01433 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 37.5075 | 1.44260 | ||||||||
\(677\) | −19.7100 | −0.757516 | −0.378758 | − | 0.925496i | \(-0.623649\pi\) | ||||
−0.378758 | + | 0.925496i | \(0.623649\pi\) | |||||||
\(678\) | 0.943291 | 0.0362269 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.7712 | −0.680996 | ||||||||
\(682\) | −71.2639 | −2.72883 | ||||||||
\(683\) | −1.44317 | −0.0552212 | −0.0276106 | − | 0.999619i | \(-0.508790\pi\) | ||||
−0.0276106 | + | 0.999619i | \(0.508790\pi\) | |||||||
\(684\) | 11.1429 | 0.426060 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.6449 | 0.711347 | ||||||||
\(688\) | 42.3821 | 1.61580 | ||||||||
\(689\) | −11.5591 | −0.440367 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.9221 | −1.17633 | −0.588167 | − | 0.808740i | \(-0.700150\pi\) | ||||
−0.588167 | + | 0.808740i | \(0.700150\pi\) | |||||||
\(692\) | 40.5918 | 1.54307 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −71.0848 | −2.69834 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −35.7362 | −1.35458 | ||||||||
\(697\) | −10.0687 | −0.381379 | ||||||||
\(698\) | 40.2949 | 1.52519 | ||||||||
\(699\) | −9.76879 | −0.369490 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 50.6746 | 1.91395 | 0.956976 | − | 0.290168i | \(-0.0937111\pi\) | ||||
0.956976 | + | 0.290168i | \(0.0937111\pi\) | |||||||
\(702\) | −12.1086 | −0.457008 | ||||||||
\(703\) | −8.83199 | −0.333105 | ||||||||
\(704\) | 66.4630 | 2.50492 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 42.7617 | 1.60936 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −20.0828 | −0.754757 | ||||||||
\(709\) | −20.1770 | −0.757762 | −0.378881 | − | 0.925445i | \(-0.623691\pi\) | ||||
−0.378881 | + | 0.925445i | \(0.623691\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.6369 | 0.473921 | ||||||||
\(712\) | 73.5381 | 2.75596 | ||||||||
\(713\) | 61.6890 | 2.31027 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.7874 | −0.477889 | ||||||||
\(717\) | −6.20058 | −0.231565 | ||||||||
\(718\) | −45.0757 | −1.68221 | ||||||||
\(719\) | 45.3278 | 1.69044 | 0.845221 | − | 0.534416i | \(-0.179468\pi\) | ||||
0.845221 | + | 0.534416i | \(0.179468\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 39.4314 | 1.46748 | ||||||||
\(723\) | −20.2382 | −0.752667 | ||||||||
\(724\) | −72.6685 | −2.70070 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 8.15328 | 0.302597 | ||||||||
\(727\) | 16.9117 | 0.627220 | 0.313610 | − | 0.949552i | \(-0.398461\pi\) | ||||
0.313610 | + | 0.949552i | \(0.398461\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.2476 | −0.489979 | ||||||||
\(732\) | −26.5271 | −0.980470 | ||||||||
\(733\) | 7.16558 | 0.264667 | 0.132333 | − | 0.991205i | \(-0.457753\pi\) | ||||
0.132333 | + | 0.991205i | \(0.457753\pi\) | |||||||
\(734\) | −76.1870 | −2.81211 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −123.751 | −4.56152 | ||||||||
\(737\) | 9.33946 | 0.344024 | ||||||||
\(738\) | −6.43179 | −0.236757 | ||||||||
\(739\) | −20.3848 | −0.749867 | −0.374933 | − | 0.927052i | \(-0.622334\pi\) | ||||
−0.374933 | + | 0.927052i | \(0.622334\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.40912 | 0.345653 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.9267 | 0.620982 | 0.310491 | − | 0.950576i | \(-0.399507\pi\) | ||||
0.310491 | + | 0.950576i | \(0.399507\pi\) | |||||||
\(744\) | −83.3682 | −3.05643 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −64.8659 | −2.37491 | ||||||||
\(747\) | 3.02608 | 0.110718 | ||||||||
\(748\) | −63.4278 | −2.31915 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39.0877 | 1.42633 | 0.713165 | − | 0.700996i | \(-0.247261\pi\) | ||||
0.713165 | + | 0.700996i | \(0.247261\pi\) | |||||||
\(752\) | −105.387 | −3.84308 | ||||||||
\(753\) | −6.21466 | −0.226475 | ||||||||
\(754\) | −48.4342 | −1.76387 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.6675 | −0.823866 | −0.411933 | − | 0.911214i | \(-0.635146\pi\) | ||||
−0.411933 | + | 0.911214i | \(0.635146\pi\) | |||||||
\(758\) | −37.4480 | −1.36017 | ||||||||
\(759\) | 18.6789 | 0.678002 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.3275 | 0.374370 | 0.187185 | − | 0.982325i | \(-0.440064\pi\) | ||||
0.187185 | + | 0.982325i | \(0.440064\pi\) | |||||||
\(762\) | −6.13919 | −0.222399 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −64.3777 | −2.32910 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 83.1841 | 3.00557 | ||||||||
\(767\) | −16.9580 | −0.612318 | ||||||||
\(768\) | 23.6053 | 0.851784 | ||||||||
\(769\) | −25.8785 | −0.933204 | −0.466602 | − | 0.884467i | \(-0.654522\pi\) | ||||
−0.466602 | + | 0.884467i | \(0.654522\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.65346 | 0.203604 | ||||||||
\(772\) | 63.2713 | 2.27718 | ||||||||
\(773\) | 9.35416 | 0.336446 | 0.168223 | − | 0.985749i | \(-0.446197\pi\) | ||||
0.168223 | + | 0.985749i | \(0.446197\pi\) | |||||||
\(774\) | −8.46242 | −0.304175 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −134.159 | −4.81602 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −103.824 | −3.72227 | ||||||||
\(779\) | 4.99791 | 0.179069 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.2736 | −1.15484 | ||||||||
\(782\) | 75.6038 | 2.70358 | ||||||||
\(783\) | 4.00000 | 0.142948 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −51.9534 | −1.85312 | ||||||||
\(787\) | −2.80188 | −0.0998762 | −0.0499381 | − | 0.998752i | \(-0.515902\pi\) | ||||
−0.0499381 | + | 0.998752i | \(0.515902\pi\) | |||||||
\(788\) | −29.1935 | −1.03998 | ||||||||
\(789\) | 25.0120 | 0.890451 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −25.2432 | −0.896978 | ||||||||
\(793\) | −22.3996 | −0.795433 | ||||||||
\(794\) | 90.4414 | 3.20965 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −60.1002 | −2.13020 | ||||||||
\(797\) | 13.0211 | 0.461231 | 0.230615 | − | 0.973045i | \(-0.425926\pi\) | ||||
0.230615 | + | 0.973045i | \(0.425926\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32.9414 | 1.16538 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.23121 | −0.290835 | ||||||||
\(802\) | −40.1159 | −1.41654 | ||||||||
\(803\) | −7.49041 | −0.264331 | ||||||||
\(804\) | 17.5366 | 0.618469 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −112.991 | −3.97994 | ||||||||
\(807\) | −7.88221 | −0.277467 | ||||||||
\(808\) | 19.9338 | 0.701267 | ||||||||
\(809\) | 21.0211 | 0.739062 | 0.369531 | − | 0.929218i | \(-0.379518\pi\) | ||||
0.369531 | + | 0.929218i | \(0.379518\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −46.2591 | −1.62438 | −0.812189 | − | 0.583395i | \(-0.801724\pi\) | ||||
−0.812189 | + | 0.583395i | \(0.801724\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.74271 | 0.166334 | ||||||||
\(814\) | 32.1142 | 1.12560 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −57.2763 | −2.00507 | ||||||||
\(817\) | 6.57584 | 0.230059 | ||||||||
\(818\) | −22.8254 | −0.798070 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.9383 | 0.591151 | 0.295575 | − | 0.955319i | \(-0.404489\pi\) | ||||
0.295575 | + | 0.955319i | \(0.404489\pi\) | |||||||
\(822\) | 22.3305 | 0.778867 | ||||||||
\(823\) | 18.5332 | 0.646027 | 0.323014 | − | 0.946394i | \(-0.395304\pi\) | ||||
0.323014 | + | 0.946394i | \(0.395304\pi\) | |||||||
\(824\) | 70.0613 | 2.44070 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32.5496 | −1.13186 | −0.565930 | − | 0.824453i | \(-0.691483\pi\) | ||||
−0.565930 | + | 0.824453i | \(0.691483\pi\) | |||||||
\(828\) | 35.0733 | 1.21888 | ||||||||
\(829\) | −10.9553 | −0.380493 | −0.190246 | − | 0.981736i | \(-0.560929\pi\) | ||||
−0.190246 | + | 0.981736i | \(0.560929\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.73721 | 0.268401 | ||||||||
\(832\) | 105.379 | 3.65336 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2.66478 | −0.0922738 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 31.4843 | 1.08891 | ||||||||
\(837\) | 9.33150 | 0.322544 | ||||||||
\(838\) | 50.9290 | 1.75931 | ||||||||
\(839\) | 1.24074 | 0.0428352 | 0.0214176 | − | 0.999771i | \(-0.493182\pi\) | ||||
0.0214176 | + | 0.999771i | \(0.493182\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | 24.5875 | 0.847342 | ||||||||
\(843\) | 2.11779 | 0.0729405 | ||||||||
\(844\) | 46.7988 | 1.61088 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 21.0426 | 0.723460 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −34.9273 | −1.19941 | ||||||||
\(849\) | 4.39774 | 0.150930 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27.7994 | −0.952952 | ||||||||
\(852\) | −60.5998 | −2.07612 | ||||||||
\(853\) | −44.8500 | −1.53564 | −0.767818 | − | 0.640669i | \(-0.778657\pi\) | ||||
−0.767818 | + | 0.640669i | \(0.778657\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −139.701 | −4.77489 | ||||||||
\(857\) | −38.6108 | −1.31892 | −0.659461 | − | 0.751739i | \(-0.729215\pi\) | ||||
−0.659461 | + | 0.751739i | \(0.729215\pi\) | |||||||
\(858\) | −34.2128 | −1.16800 | ||||||||
\(859\) | 35.1083 | 1.19788 | 0.598939 | − | 0.800795i | \(-0.295589\pi\) | ||||
0.598939 | + | 0.800795i | \(0.295589\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13.4057 | 0.456600 | ||||||||
\(863\) | −4.94575 | −0.168355 | −0.0841776 | − | 0.996451i | \(-0.526826\pi\) | ||||
−0.0841776 | + | 0.996451i | \(0.526826\pi\) | |||||||
\(864\) | −18.7194 | −0.636847 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 7.07325 | 0.240359 | ||||||||
\(867\) | 0.903125 | 0.0306717 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 35.7056 | 1.21123 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.8080 | 0.501750 | ||||||||
\(872\) | −27.4652 | −0.930088 | ||||||||
\(873\) | 15.0165 | 0.508233 | ||||||||
\(874\) | −37.5282 | −1.26941 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −14.0647 | −0.475201 | ||||||||
\(877\) | 10.7123 | 0.361727 | 0.180864 | − | 0.983508i | \(-0.442111\pi\) | ||||
0.180864 | + | 0.983508i | \(0.442111\pi\) | |||||||
\(878\) | 71.6392 | 2.41771 | ||||||||
\(879\) | −14.2006 | −0.478974 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.2527 | 1.35615 | 0.678075 | − | 0.734993i | \(-0.262815\pi\) | ||||
0.678075 | + | 0.734993i | \(0.262815\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.2228 | 0.882468 | 0.441234 | − | 0.897392i | \(-0.354541\pi\) | ||||
0.441234 | + | 0.897392i | \(0.354541\pi\) | |||||||
\(884\) | −100.567 | −3.38242 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −106.737 | −3.58589 | ||||||||
\(887\) | −49.3964 | −1.65857 | −0.829284 | − | 0.558828i | \(-0.811251\pi\) | ||||
−0.829284 | + | 0.558828i | \(0.811251\pi\) | |||||||
\(888\) | 37.5689 | 1.26073 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.82550 | 0.0946578 | ||||||||
\(892\) | 140.533 | 4.70538 | ||||||||
\(893\) | −16.3515 | −0.547181 | ||||||||
\(894\) | −21.1389 | −0.706990 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 29.6160 | 0.988850 | ||||||||
\(898\) | −57.5828 | −1.92156 | ||||||||
\(899\) | 37.3260 | 1.24489 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.9174 | 0.363711 | ||||||||
\(902\) | −18.1730 | −0.605095 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.11797 | 0.103702 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 8.47165 | 0.281452 | ||||||||
\(907\) | −56.1629 | −1.86486 | −0.932429 | − | 0.361354i | \(-0.882315\pi\) | ||||
−0.932429 | + | 0.361354i | \(0.882315\pi\) | |||||||
\(908\) | −94.2839 | −3.12892 | ||||||||
\(909\) | −2.23121 | −0.0740045 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35.9981 | −1.19267 | −0.596335 | − | 0.802736i | \(-0.703377\pi\) | ||||
−0.596335 | + | 0.802736i | \(0.703377\pi\) | |||||||
\(912\) | 28.4308 | 0.941439 | ||||||||
\(913\) | 8.55019 | 0.282970 | ||||||||
\(914\) | −75.3559 | −2.49255 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 98.9189 | 3.26837 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 11.4363 | 0.377455 | ||||||||
\(919\) | −7.54801 | −0.248986 | −0.124493 | − | 0.992221i | \(-0.539730\pi\) | ||||
−0.124493 | + | 0.992221i | \(0.539730\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.9423 | −0.459416 | ||||||||
\(922\) | −60.8782 | −2.00492 | ||||||||
\(923\) | −51.1707 | −1.68431 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 4.57596 | 0.150375 | ||||||||
\(927\) | −7.84205 | −0.257567 | ||||||||
\(928\) | −74.8776 | −2.45798 | ||||||||
\(929\) | 5.19104 | 0.170313 | 0.0851563 | − | 0.996368i | \(-0.472861\pi\) | ||||
0.0851563 | + | 0.996368i | \(0.472861\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −51.8275 | −1.69767 | ||||||||
\(933\) | −3.79942 | −0.124387 | ||||||||
\(934\) | 0.217122 | 0.00710446 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −40.0239 | −1.30822 | ||||||||
\(937\) | 5.23690 | 0.171082 | 0.0855410 | − | 0.996335i | \(-0.472738\pi\) | ||||
0.0855410 | + | 0.996335i | \(0.472738\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.8976 | 0.910404 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.9439 | −0.421959 | −0.210980 | − | 0.977490i | \(-0.567665\pi\) | ||||
−0.210980 | + | 0.977490i | \(0.567665\pi\) | |||||||
\(942\) | 63.4602 | 2.06764 | ||||||||
\(943\) | 15.7313 | 0.512283 | ||||||||
\(944\) | −51.2407 | −1.66774 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −23.9106 | −0.777400 | ||||||||
\(947\) | 23.0143 | 0.747863 | 0.373932 | − | 0.927456i | \(-0.378009\pi\) | ||||
0.373932 | + | 0.927456i | \(0.378009\pi\) | |||||||
\(948\) | 67.0441 | 2.17749 | ||||||||
\(949\) | −11.8763 | −0.385520 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 34.4955 | 1.11859 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.1560 | 0.490952 | 0.245476 | − | 0.969403i | \(-0.421056\pi\) | ||||
0.245476 | + | 0.969403i | \(0.421056\pi\) | |||||||
\(954\) | 6.97392 | 0.225789 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −32.8967 | −1.06395 | ||||||||
\(957\) | 11.3020 | 0.365342 | ||||||||
\(958\) | 104.812 | 3.38632 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 56.0768 | 1.80893 | ||||||||
\(962\) | 50.9181 | 1.64166 | ||||||||
\(963\) | 15.6369 | 0.503893 | ||||||||
\(964\) | −107.372 | −3.45823 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.5145 | 1.46365 | 0.731824 | − | 0.681494i | \(-0.238669\pi\) | ||||
0.731824 | + | 0.681494i | \(0.238669\pi\) | |||||||
\(968\) | 26.9500 | 0.866206 | ||||||||
\(969\) | −8.88676 | −0.285484 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.60192 | −0.243957 | −0.121979 | − | 0.992533i | \(-0.538924\pi\) | ||||
−0.121979 | + | 0.992533i | \(0.538924\pi\) | |||||||
\(972\) | 5.30542 | 0.170171 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 73.3309 | 2.34967 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −67.6831 | −2.16648 | ||||||||
\(977\) | 34.6936 | 1.10995 | 0.554974 | − | 0.831868i | \(-0.312728\pi\) | ||||
0.554974 | + | 0.831868i | \(0.312728\pi\) | |||||||
\(978\) | 33.6136 | 1.07484 | ||||||||
\(979\) | −23.2573 | −0.743306 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.07421 | 0.0981520 | ||||||||
\(982\) | −45.2032 | −1.44249 | ||||||||
\(983\) | −15.5779 | −0.496859 | −0.248429 | − | 0.968650i | \(-0.579914\pi\) | ||||
−0.248429 | + | 0.968650i | \(0.579914\pi\) | |||||||
\(984\) | −21.2597 | −0.677736 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 45.7454 | 1.45683 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 49.9193 | 1.58815 | ||||||||
\(989\) | 20.6980 | 0.658158 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45.9589 | −1.45993 | −0.729966 | − | 0.683484i | \(-0.760464\pi\) | ||||
−0.729966 | + | 0.683484i | \(0.760464\pi\) | |||||||
\(992\) | −174.680 | −5.54610 | ||||||||
\(993\) | −29.8942 | −0.948664 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 16.0546 | 0.508710 | ||||||||
\(997\) | −41.0687 | −1.30066 | −0.650329 | − | 0.759652i | \(-0.725369\pi\) | ||||
−0.650329 | + | 0.759652i | \(0.725369\pi\) | |||||||
\(998\) | −53.4743 | −1.69270 | ||||||||
\(999\) | −4.20513 | −0.133044 |
(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 | 3675.2.a.br.1.1 | 4 | ||
5.4 | even | 2 | 3675.2.a.bw.1.4 | 4 | |||
7.2 | even | 3 | 525.2.i.j.151.4 | yes | 8 | ||
7.4 | even | 3 | 525.2.i.j.226.4 | yes | 8 | ||
7.6 | odd | 2 | 3675.2.a.bq.1.1 | 4 | |||
35.2 | odd | 12 | 525.2.r.h.424.1 | 16 | |||
35.4 | even | 6 | 525.2.i.i.226.1 | yes | 8 | ||
35.9 | even | 6 | 525.2.i.i.151.1 | ✓ | 8 | ||
35.18 | odd | 12 | 525.2.r.h.499.1 | 16 | |||
35.23 | odd | 12 | 525.2.r.h.424.8 | 16 | |||
35.32 | odd | 12 | 525.2.r.h.499.8 | 16 | |||
35.34 | odd | 2 | 3675.2.a.bx.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.i.i.151.1 | ✓ | 8 | 35.9 | even | 6 | ||
525.2.i.i.226.1 | yes | 8 | 35.4 | even | 6 | ||
525.2.i.j.151.4 | yes | 8 | 7.2 | even | 3 | ||
525.2.i.j.226.4 | yes | 8 | 7.4 | even | 3 | ||
525.2.r.h.424.1 | 16 | 35.2 | odd | 12 | |||
525.2.r.h.424.8 | 16 | 35.23 | odd | 12 | |||
525.2.r.h.499.1 | 16 | 35.18 | odd | 12 | |||
525.2.r.h.499.8 | 16 | 35.32 | odd | 12 | |||
3675.2.a.bq.1.1 | 4 | 7.6 | odd | 2 | |||
3675.2.a.br.1.1 | 4 | 1.1 | even | 1 | trivial | ||
3675.2.a.bw.1.4 | 4 | 5.4 | even | 2 | |||
3675.2.a.bx.1.4 | 4 | 35.34 | odd | 2 |