Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6036,2,Mod(1,6036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6036, 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("6036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6036 = 2^{2} \cdot 3 \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6036.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1977026600\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 4 x^{14} - 27 x^{13} + 106 x^{12} + 266 x^{11} - 1004 x^{10} - 1105 x^{9} + 4076 x^{8} + \cdots - 44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Root | \(3.52096\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6036.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.52096 | 1.12741 | 0.563704 | − | 0.825977i | \(-0.309376\pi\) | ||||
0.563704 | + | 0.825977i | \(0.309376\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.02518 | −0.387480 | −0.193740 | − | 0.981053i | \(-0.562062\pi\) | ||||
−0.193740 | + | 0.981053i | \(0.562062\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.26772 | −0.985255 | −0.492628 | − | 0.870240i | \(-0.663964\pi\) | ||||
−0.492628 | + | 0.870240i | \(0.663964\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.87517 | −0.797430 | −0.398715 | − | 0.917075i | \(-0.630544\pi\) | ||||
−0.398715 | + | 0.917075i | \(0.630544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.52096 | 0.650909 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.377785 | 0.0916263 | 0.0458131 | − | 0.998950i | \(-0.485412\pi\) | ||||
0.0458131 | + | 0.998950i | \(0.485412\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.62078 | −0.371833 | −0.185917 | − | 0.982566i | \(-0.559525\pi\) | ||||
−0.185917 | + | 0.982566i | \(0.559525\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.02518 | −0.223712 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.17692 | −1.28798 | −0.643989 | − | 0.765035i | \(-0.722722\pi\) | ||||
−0.643989 | + | 0.765035i | \(0.722722\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.35524 | 0.271048 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.77725 | −1.07281 | −0.536404 | − | 0.843961i | \(-0.680218\pi\) | ||||
−0.536404 | + | 0.843961i | \(0.680218\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.59306 | 1.18415 | 0.592074 | − | 0.805883i | \(-0.298309\pi\) | ||||
0.592074 | + | 0.805883i | \(0.298309\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.26772 | −0.568837 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.58443 | −0.436848 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.04591 | 0.336345 | 0.168172 | − | 0.985758i | \(-0.446213\pi\) | ||||
0.168172 | + | 0.985758i | \(0.446213\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.87517 | −0.460396 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.64121 | 0.256313 | 0.128157 | − | 0.991754i | \(-0.459094\pi\) | ||||
0.128157 | + | 0.991754i | \(0.459094\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.25813 | −0.191863 | −0.0959316 | − | 0.995388i | \(-0.530583\pi\) | ||||
−0.0959316 | + | 0.995388i | \(0.530583\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.52096 | 0.375803 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.2278 | 1.78361 | 0.891803 | − | 0.452424i | \(-0.149440\pi\) | ||||
0.891803 | + | 0.452424i | \(0.149440\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.94901 | −0.849859 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.377785 | 0.0529004 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.59305 | −1.18035 | −0.590173 | − | 0.807277i | \(-0.700941\pi\) | ||||
−0.590173 | + | 0.807277i | \(0.700941\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.23780 | −1.11078 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.62078 | −0.214678 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.35721 | −1.21820 | −0.609102 | − | 0.793092i | \(-0.708470\pi\) | ||||
−0.609102 | + | 0.793092i | \(0.708470\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.13492 | −0.145311 | −0.0726555 | − | 0.997357i | \(-0.523147\pi\) | ||||
−0.0726555 | + | 0.997357i | \(0.523147\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.02518 | −0.129160 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.24820 | −0.899029 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.942111 | 0.115097 | 0.0575486 | − | 0.998343i | \(-0.481672\pi\) | ||||
0.0575486 | + | 0.998343i | \(0.481672\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.17692 | −0.743614 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.988908 | 0.117362 | 0.0586809 | − | 0.998277i | \(-0.481311\pi\) | ||||
0.0586809 | + | 0.998277i | \(0.481311\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.7507 | −1.49236 | −0.746178 | − | 0.665747i | \(-0.768113\pi\) | ||||
−0.746178 | + | 0.665747i | \(0.768113\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.35524 | 0.156490 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.34999 | 0.381767 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.81707 | −0.429454 | −0.214727 | − | 0.976674i | \(-0.568886\pi\) | ||||
−0.214727 | + | 0.976674i | \(0.568886\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.87138 | 0.534703 | 0.267352 | − | 0.963599i | \(-0.413851\pi\) | ||||
0.267352 | + | 0.963599i | \(0.413851\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.952380 | 0.103300 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.77725 | −0.619386 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.9858 | −1.80049 | −0.900246 | − | 0.435382i | \(-0.856613\pi\) | ||||
−0.900246 | + | 0.435382i | \(0.856613\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.94756 | 0.308988 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.59306 | 0.683668 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.08593 | −0.419208 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.17800 | 0.525746 | 0.262873 | − | 0.964830i | \(-0.415330\pi\) | ||||
0.262873 | + | 0.964830i | \(0.415330\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.26772 | −0.328418 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.78904 | 0.874542 | 0.437271 | − | 0.899330i | \(-0.355945\pi\) | ||||
0.437271 | + | 0.899330i | \(0.355945\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.6235 | −1.63796 | −0.818980 | − | 0.573822i | \(-0.805460\pi\) | ||||
−0.818980 | + | 0.573822i | \(0.805460\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.58443 | −0.252214 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.66433 | 0.160897 | 0.0804486 | − | 0.996759i | \(-0.474365\pi\) | ||||
0.0804486 | + | 0.996759i | \(0.474365\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.7496 | −1.70010 | −0.850050 | − | 0.526702i | \(-0.823428\pi\) | ||||
−0.850050 | + | 0.526702i | \(0.823428\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.04591 | 0.194189 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.24845 | −0.399661 | −0.199830 | − | 0.979831i | \(-0.564039\pi\) | ||||
−0.199830 | + | 0.979831i | \(0.564039\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.5718 | −1.45208 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.87517 | −0.265810 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.387296 | −0.0355034 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.321992 | −0.0292720 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.64121 | 0.147983 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.18830 | −0.821826 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.3085 | 0.914731 | 0.457365 | − | 0.889279i | \(-0.348793\pi\) | ||||
0.457365 | + | 0.889279i | \(0.348793\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.25813 | −0.110772 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.88317 | 0.776126 | 0.388063 | − | 0.921633i | \(-0.373144\pi\) | ||||
0.388063 | + | 0.921633i | \(0.373144\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.66159 | 0.144078 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.52096 | 0.216970 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.0387 | −0.943097 | −0.471549 | − | 0.881840i | \(-0.656305\pi\) | ||||
−0.471549 | + | 0.881840i | \(0.656305\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0393 | 0.851520 | 0.425760 | − | 0.904836i | \(-0.360007\pi\) | ||||
0.425760 | + | 0.904836i | \(0.360007\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.2278 | 1.02977 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.39527 | 0.785672 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.5642 | −1.20949 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.94901 | −0.490666 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.47326 | 0.366463 | 0.183232 | − | 0.983070i | \(-0.441344\pi\) | ||||
0.183232 | + | 0.983070i | \(0.441344\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.6111 | 1.51455 | 0.757275 | − | 0.653096i | \(-0.226530\pi\) | ||||
0.757275 | + | 0.653096i | \(0.226530\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.377785 | 0.0305421 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.6208 | 1.33502 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.3876 | −1.14826 | −0.574128 | − | 0.818766i | \(-0.694659\pi\) | ||||
−0.574128 | + | 0.818766i | \(0.694659\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.59305 | −0.681473 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.33243 | 0.499066 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.81245 | −0.376940 | −0.188470 | − | 0.982079i | \(-0.560353\pi\) | ||||
−0.188470 | + | 0.982079i | \(0.560353\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.23780 | −0.641312 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.760554 | 0.0588534 | 0.0294267 | − | 0.999567i | \(-0.490632\pi\) | ||||
0.0294267 | + | 0.999567i | \(0.490632\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.73337 | −0.364106 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.62078 | −0.123944 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.1595 | −0.772410 | −0.386205 | − | 0.922413i | \(-0.626214\pi\) | ||||
−0.386205 | + | 0.922413i | \(0.626214\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.38936 | −0.105026 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.35721 | −0.703331 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.1094 | 1.27882 | 0.639409 | − | 0.768867i | \(-0.279179\pi\) | ||||
0.639409 | + | 0.768867i | \(0.279179\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.61105 | 0.268407 | 0.134203 | − | 0.990954i | \(-0.457152\pi\) | ||||
0.134203 | + | 0.990954i | \(0.457152\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.13492 | −0.0838954 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.15765 | 0.379198 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.23450 | −0.0902753 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.02518 | −0.0745706 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.296153 | 0.0214289 | 0.0107144 | − | 0.999943i | \(-0.496589\pi\) | ||||
0.0107144 | + | 0.999943i | \(0.496589\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.8084 | 1.06593 | 0.532966 | − | 0.846137i | \(-0.321077\pi\) | ||||
0.532966 | + | 0.846137i | \(0.321077\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.24820 | −0.519054 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.2880 | −1.37421 | −0.687105 | − | 0.726558i | \(-0.741119\pi\) | ||||
−0.687105 | + | 0.726558i | \(0.741119\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.1845 | −1.07640 | −0.538201 | − | 0.842817i | \(-0.680896\pi\) | ||||
−0.538201 | + | 0.842817i | \(0.680896\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.942111 | 0.0664514 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.92270 | 0.415692 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.13742 | 0.288970 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.17692 | −0.429326 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.29627 | 0.366351 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.1254 | −1.52317 | −0.761587 | − | 0.648063i | \(-0.775579\pi\) | ||||
−0.761587 | + | 0.648063i | \(0.775579\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.988908 | 0.0677589 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.17170 | −0.216308 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.75905 | −0.458834 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.7507 | −0.861612 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.08620 | −0.0730655 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.7967 | −1.25872 | −0.629359 | − | 0.777115i | \(-0.716683\pi\) | ||||
−0.629359 | + | 0.777115i | \(0.716683\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.35524 | 0.0903493 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.1902 | −0.676350 | −0.338175 | − | 0.941083i | \(-0.609810\pi\) | ||||
−0.338175 | + | 0.941083i | \(0.609810\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.80690 | 0.581976 | 0.290988 | − | 0.956727i | \(-0.406016\pi\) | ||||
0.290988 | + | 0.956727i | \(0.406016\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.34999 | 0.220413 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.6965 | −0.766263 | −0.383131 | − | 0.923694i | \(-0.625154\pi\) | ||||
−0.383131 | + | 0.923694i | \(0.625154\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 30.8258 | 2.01085 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.81707 | −0.247945 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.7646 | −1.53721 | −0.768603 | − | 0.639725i | \(-0.779048\pi\) | ||||
−0.768603 | + | 0.639725i | \(0.779048\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.06074 | 0.261575 | 0.130788 | − | 0.991410i | \(-0.458249\pi\) | ||||
0.130788 | + | 0.991410i | \(0.458249\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.9972 | −0.958138 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.66004 | 0.296511 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.87138 | 0.308711 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.8288 | 1.88278 | 0.941388 | − | 0.337326i | \(-0.109522\pi\) | ||||
0.941388 | + | 0.337326i | \(0.109522\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.1845 | 1.26899 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.952380 | 0.0596404 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.936638 | −0.0584258 | −0.0292129 | − | 0.999573i | \(-0.509300\pi\) | ||||
−0.0292129 | + | 0.999573i | \(0.509300\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.09741 | −0.130327 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.77725 | −0.357603 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.88139 | −0.239337 | −0.119668 | − | 0.992814i | \(-0.538183\pi\) | ||||
−0.119668 | + | 0.992814i | \(0.538183\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −21.6627 | −1.33073 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −16.9858 | −1.03951 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 32.5695 | 1.98580 | 0.992898 | − | 0.118971i | \(-0.0379596\pi\) | ||||
0.992898 | + | 0.118971i | \(0.0379596\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.0539 | 1.40042 | 0.700211 | − | 0.713936i | \(-0.253089\pi\) | ||||
0.700211 | + | 0.713936i | \(0.253089\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.94756 | 0.178395 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.42854 | −0.267051 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.4849 | 1.47115 | 0.735577 | − | 0.677442i | \(-0.236911\pi\) | ||||
0.735577 | + | 0.677442i | \(0.236911\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.59306 | 0.394716 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.0539 | 0.659418 | 0.329709 | − | 0.944083i | \(-0.393049\pi\) | ||||
0.329709 | + | 0.944083i | \(0.393049\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.3703 | 1.03256 | 0.516278 | − | 0.856421i | \(-0.327317\pi\) | ||||
0.516278 | + | 0.856421i | \(0.327317\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.08593 | −0.242030 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.68253 | −0.0993164 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8573 | −0.991605 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.17800 | 0.303540 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.92081 | 0.170636 | 0.0853178 | − | 0.996354i | \(-0.472809\pi\) | ||||
0.0853178 | + | 0.996354i | \(0.472809\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −23.5891 | −1.37341 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.26772 | −0.189612 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.7597 | 1.02707 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.28981 | 0.0743432 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.78904 | 0.504917 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.86108 | −0.163825 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.5812 | 1.34585 | 0.672925 | − | 0.739711i | \(-0.265038\pi\) | ||||
0.672925 | + | 0.739711i | \(0.265038\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.6235 | −0.945677 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.0568 | −0.853793 | −0.426896 | − | 0.904301i | \(-0.640393\pi\) | ||||
−0.426896 | + | 0.904301i | \(0.640393\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.4291 | 0.985153 | 0.492577 | − | 0.870269i | \(-0.336055\pi\) | ||||
0.492577 | + | 0.870269i | \(0.336055\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.58443 | −0.145616 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.21009 | −0.348794 | −0.174397 | − | 0.984675i | \(-0.555798\pi\) | ||||
−0.174397 | + | 0.984675i | \(0.555798\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.8785 | 1.05699 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.66433 | 0.0928941 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.612307 | −0.0340697 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.89655 | −0.216142 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.7496 | −0.981553 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.5356 | −0.691112 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.0705 | −0.883314 | −0.441657 | − | 0.897184i | \(-0.645609\pi\) | ||||
−0.441657 | + | 0.897184i | \(0.645609\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.04591 | 0.112115 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.37502 | 0.129761 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.0344 | 0.873447 | 0.436724 | − | 0.899596i | \(-0.356139\pi\) | ||||
0.436724 | + | 0.899596i | \(0.356139\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.24845 | −0.230744 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.5443 | −1.16669 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.2750 | 0.716784 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −15.5718 | −0.838356 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 32.1269 | 1.72466 | 0.862331 | − | 0.506345i | \(-0.169004\pi\) | ||||
0.862331 | + | 0.506345i | \(0.169004\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.0352 | 0.858345 | 0.429173 | − | 0.903223i | \(-0.358805\pi\) | ||||
0.429173 | + | 0.903223i | \(0.358805\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.87517 | −0.153465 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.0322 | −1.22588 | −0.612940 | − | 0.790129i | \(-0.710013\pi\) | ||||
−0.612940 | + | 0.790129i | \(0.710013\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.49300 | 0.132315 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.387296 | −0.0204979 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.1002 | −0.533067 | −0.266533 | − | 0.963826i | \(-0.585878\pi\) | ||||
−0.266533 | + | 0.963826i | \(0.585878\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.3731 | −0.861740 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.321992 | −0.0169002 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −32.1440 | −1.68249 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.20738 | 0.480622 | 0.240311 | − | 0.970696i | \(-0.422751\pi\) | ||||
0.240311 | + | 0.970696i | \(0.422751\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.64121 | 0.0854378 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.80939 | 0.457361 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.8720 | 1.13249 | 0.566244 | − | 0.824237i | \(-0.308396\pi\) | ||||
0.566244 | + | 0.824237i | \(0.308396\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.18830 | −0.474482 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.6106 | 0.855490 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.3983 | 1.71556 | 0.857779 | − | 0.514019i | \(-0.171844\pi\) | ||||
0.857779 | + | 0.514019i | \(0.171844\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.3085 | 0.528120 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.2461 | 1.03453 | 0.517264 | − | 0.855826i | \(-0.326950\pi\) | ||||
0.517264 | + | 0.855826i | \(0.326950\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.44519 | 0.430407 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.25813 | −0.0639544 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −32.2980 | −1.63758 | −0.818788 | − | 0.574096i | \(-0.805354\pi\) | ||||
−0.818788 | + | 0.574096i | \(0.805354\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.33355 | −0.118013 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.88317 | 0.448097 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.62268 | −0.484170 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.3523 | 0.820697 | 0.410348 | − | 0.911929i | \(-0.365407\pi\) | ||||
0.410348 | + | 0.911929i | \(0.365407\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.66159 | 0.0831835 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.6189 | −1.37922 | −0.689612 | − | 0.724179i | \(-0.742219\pi\) | ||||
−0.689612 | + | 0.724179i | \(0.742219\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.9562 | −0.944275 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.52096 | 0.125268 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.68545 | −0.331385 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.45875 | −0.171024 | −0.0855121 | − | 0.996337i | \(-0.527253\pi\) | ||||
−0.0855121 | + | 0.996337i | \(0.527253\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.0387 | −0.544498 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.59279 | 0.472030 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.2806 | 0.602828 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.0393 | 0.491625 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.45922 | 0.315553 | 0.157777 | − | 0.987475i | \(-0.449567\pi\) | ||||
0.157777 | + | 0.987475i | \(0.449567\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.0739 | −1.56319 | −0.781593 | − | 0.623789i | \(-0.785593\pi\) | ||||
−0.781593 | + | 0.623789i | \(0.785593\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12.2278 | 0.594535 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.511989 | 0.0248351 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.16349 | 0.0563052 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.39527 | 0.453608 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.9616 | −1.05785 | −0.528926 | − | 0.848668i | \(-0.677405\pi\) | ||||
−0.528926 | + | 0.848668i | \(0.677405\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.1059 | 0.966226 | 0.483113 | − | 0.875558i | \(-0.339506\pi\) | ||||
0.483113 | + | 0.875558i | \(0.339506\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14.5642 | −0.698301 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.0115 | 0.478913 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.533793 | −0.0254766 | −0.0127383 | − | 0.999919i | \(-0.504055\pi\) | ||||
−0.0127383 | + | 0.999919i | \(0.504055\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.94901 | −0.283286 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −33.0425 | −1.56989 | −0.784947 | − | 0.619563i | \(-0.787310\pi\) | ||||
−0.784947 | + | 0.619563i | \(0.787310\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −42.8205 | −2.02989 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.47326 | 0.211578 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.1673 | −0.857366 | −0.428683 | − | 0.903455i | \(-0.641022\pi\) | ||||
−0.428683 | + | 0.903455i | \(0.641022\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.36301 | −0.252534 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.6111 | 0.874426 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.43068 | 0.348356 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.1718 | 1.08393 | 0.541965 | − | 0.840401i | \(-0.317680\pi\) | ||||
0.541965 | + | 0.840401i | \(0.317680\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.377785 | 0.0176335 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.8369 | −0.504725 | −0.252363 | − | 0.967633i | \(-0.581208\pi\) | ||||
−0.252363 | + | 0.967633i | \(0.581208\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.90221 | −0.274299 | −0.137149 | − | 0.990550i | \(-0.543794\pi\) | ||||
−0.137149 | + | 0.990550i | \(0.543794\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 16.6208 | 0.770773 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.2479 | −0.751864 | −0.375932 | − | 0.926647i | \(-0.622677\pi\) | ||||
−0.375932 | + | 0.926647i | \(0.622677\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.965830 | −0.0445979 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.3876 | −0.662946 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.11122 | 0.189034 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.19655 | −0.100785 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.59305 | −0.393449 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.2545 | 0.925452 | 0.462726 | − | 0.886501i | \(-0.346871\pi\) | ||||
0.462726 | + | 0.886501i | \(0.346871\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.88233 | −0.268211 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.33243 | 0.288136 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.0535 | 0.592730 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.32264 | −0.286506 | −0.143253 | − | 0.989686i | \(-0.545756\pi\) | ||||
−0.143253 | + | 0.989686i | \(0.545756\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.81245 | −0.217627 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.0921 | 0.997002 | 0.498501 | − | 0.866889i | \(-0.333884\pi\) | ||||
0.498501 | + | 0.866889i | \(0.333884\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.18256 | −0.0982975 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.23780 | −0.370261 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.01381 | −0.0454754 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.8788 | −1.20326 | −0.601631 | − | 0.798774i | \(-0.705482\pi\) | ||||
−0.601631 | + | 0.798774i | \(0.705482\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.760554 | 0.0339790 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.1568 | 0.985965 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.73337 | −0.210216 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 40.8050 | 1.80865 | 0.904325 | − | 0.426845i | \(-0.140375\pi\) | ||||
0.904325 | + | 0.426845i | \(0.140375\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.0717 | 0.578258 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.62078 | −0.0715594 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −41.9071 | −1.84665 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −39.9570 | −1.75731 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.1595 | −0.445951 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.1863 | 1.14724 | 0.573621 | − | 0.819121i | \(-0.305538\pi\) | ||||
0.573621 | + | 0.819121i | \(0.305538\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.3042 | 1.41256 | 0.706282 | − | 0.707930i | \(-0.250371\pi\) | ||||
0.706282 | + | 0.707930i | \(0.250371\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.38936 | −0.0606366 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.49076 | 0.108499 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.1543 | 0.658885 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.35721 | −0.406068 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.71876 | −0.204392 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.19572 | 0.181397 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.1094 | 0.738326 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19.4397 | 0.837328 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.2223 | −0.654458 | −0.327229 | − | 0.944945i | \(-0.606115\pi\) | ||||
−0.327229 | + | 0.944945i | \(0.606115\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.61105 | 0.154965 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −44.7459 | −1.91671 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.6856 | −0.969966 | −0.484983 | − | 0.874524i | \(-0.661174\pi\) | ||||
−0.484983 | + | 0.874524i | \(0.661174\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.13492 | −0.0484370 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.36368 | 0.398906 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.91317 | 0.166405 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.15765 | 0.218930 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.53786 | 0.0651614 | 0.0325807 | − | 0.999469i | \(-0.489627\pi\) | ||||
0.0325807 | + | 0.999469i | \(0.489627\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.61735 | 0.152998 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.23450 | −0.0521204 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −36.8937 | −1.55488 | −0.777442 | − | 0.628954i | \(-0.783483\pi\) | ||||
−0.777442 | + | 0.628954i | \(0.783483\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.7102 | −0.450581 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.02518 | −0.0430534 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.39067 | 0.100222 | 0.0501110 | − | 0.998744i | \(-0.484042\pi\) | ||||
0.0501110 | + | 0.998744i | \(0.484042\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.1095 | 0.548616 | 0.274308 | − | 0.961642i | \(-0.411551\pi\) | ||||
0.274308 | + | 0.961642i | \(0.411551\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.296153 | 0.0123720 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.37120 | −0.349103 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.33586 | −0.222135 | −0.111067 | − | 0.993813i | \(-0.535427\pi\) | ||||
−0.111067 | + | 0.993813i | \(0.535427\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.8084 | 0.615416 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.99402 | −0.207187 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28.0797 | 1.16294 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.24820 | −0.299676 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.35300 | 0.386040 | 0.193020 | − | 0.981195i | \(-0.438172\pi\) | ||||
0.193020 | + | 0.981195i | \(0.438172\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.6859 | −0.440306 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.2880 | −0.793401 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.61989 | −0.0665208 | −0.0332604 | − | 0.999447i | \(-0.510589\pi\) | ||||
−0.0332604 | + | 0.999447i | \(0.510589\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.976358 | −0.0400268 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15.1845 | −0.621461 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.44660 | −0.263401 | −0.131700 | − | 0.991290i | \(-0.542044\pi\) | ||||
−0.131700 | + | 0.991290i | \(0.542044\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.9643 | −0.528824 | −0.264412 | − | 0.964410i | \(-0.585178\pi\) | ||||
−0.264412 | + | 0.964410i | \(0.585178\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.942111 | 0.0383657 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.811729 | −0.0330015 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.4087 | −0.503654 | −0.251827 | − | 0.967772i | \(-0.581031\pi\) | ||||
−0.251827 | + | 0.967772i | \(0.581031\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.92270 | 0.240000 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −35.1570 | −1.42230 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.41520 | 0.0571593 | 0.0285796 | − | 0.999592i | \(-0.490902\pi\) | ||||
0.0285796 | + | 0.999592i | \(0.490902\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.13742 | 0.166837 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.0686 | −0.606638 | −0.303319 | − | 0.952889i | \(-0.598095\pi\) | ||||
−0.303319 | + | 0.952889i | \(0.598095\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.87864 | −0.316669 | −0.158335 | − | 0.987386i | \(-0.550612\pi\) | ||||
−0.158335 | + | 0.987386i | \(0.550612\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.17692 | −0.247871 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.4134 | 0.697655 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.9395 | −1.19758 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.29627 | 0.211513 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.772912 | 0.0308180 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.63840 | −0.343889 | −0.171945 | − | 0.985107i | \(-0.555005\pi\) | ||||
−0.171945 | + | 0.985107i | \(0.555005\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −22.1254 | −0.879405 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 25.9873 | 1.03127 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.1045 | 0.677703 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.988908 | 0.0391206 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 33.1040 | 1.30753 | 0.653764 | − | 0.756699i | \(-0.273189\pi\) | ||||
0.653764 | + | 0.756699i | \(0.273189\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.1720 | −0.874377 | −0.437188 | − | 0.899370i | \(-0.644026\pi\) | ||||
−0.437188 | + | 0.899370i | \(0.644026\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.17170 | −0.124886 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.66692 | −0.222790 | −0.111395 | − | 0.993776i | \(-0.535532\pi\) | ||||
−0.111395 | + | 0.993776i | \(0.535532\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30.5767 | 1.20024 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.75905 | −0.264908 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.2652 | −0.519108 | −0.259554 | − | 0.965729i | \(-0.583576\pi\) | ||||
−0.259554 | + | 0.965729i | \(0.583576\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.3941 | 0.875010 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.7507 | −0.497452 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −41.7765 | −1.62738 | −0.813692 | − | 0.581297i | \(-0.802545\pi\) | ||||
−0.813692 | + | 0.581297i | \(0.802545\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.9461 | −0.853605 | −0.426802 | − | 0.904345i | \(-0.640360\pi\) | ||||
−0.426802 | + | 0.904345i | \(0.640360\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.08620 | −0.0421844 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.18880 | 0.162435 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 35.6856 | 1.38175 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.7967 | −0.726721 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.70859 | 0.143168 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.398443 | −0.0153589 | −0.00767943 | − | 0.999971i | \(-0.502444\pi\) | ||||
−0.00767943 | + | 0.999971i | \(0.502444\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.35524 | 0.0521632 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27.1248 | −1.04249 | −0.521246 | − | 0.853407i | \(-0.674533\pi\) | ||||
−0.521246 | + | 0.853407i | \(0.674533\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.30836 | −0.203716 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.1902 | −0.390491 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.255415 | −0.00977319 | −0.00488660 | − | 0.999988i | \(-0.501555\pi\) | ||||
−0.00488660 | + | 0.999988i | \(0.501555\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −27.8281 | −1.06326 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.80690 | 0.336004 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 24.7065 | 0.941244 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.6261 | 0.442279 | 0.221140 | − | 0.975242i | \(-0.429022\pi\) | ||||
0.221140 | + | 0.975242i | \(0.429022\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.34999 | 0.127256 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 25.3086 | 0.960010 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.620023 | 0.0234850 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.6965 | −0.442402 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.8197 | 0.484193 | 0.242097 | − | 0.970252i | \(-0.422165\pi\) | ||||
0.242097 | + | 0.970252i | \(0.422165\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.31597 | −0.125064 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 30.8258 | 1.16097 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.01032 | −0.338868 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.8398 | 1.23333 | 0.616663 | − | 0.787227i | \(-0.288484\pi\) | ||||
0.616663 | + | 0.787227i | \(0.288484\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.81707 | −0.143151 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −40.7248 | −1.52516 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 23.6851 | 0.885773 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −23.7646 | −0.887507 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.3717 | −0.759735 | −0.379867 | − | 0.925041i | \(-0.624030\pi\) | ||||
−0.379867 | + | 0.925041i | \(0.624030\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.0420 | 0.634677 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.06074 | 0.151021 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.82956 | −0.290782 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.8350 | −0.921078 | −0.460539 | − | 0.887640i | \(-0.652344\pi\) | ||||
−0.460539 | + | 0.887640i | \(0.652344\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.475303 | −0.0175797 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.4421 | 0.865853 | 0.432927 | − | 0.901429i | \(-0.357481\pi\) | ||||
0.432927 | + | 0.901429i | \(0.357481\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −14.9972 | −0.553181 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.07856 | −0.113400 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.3235 | −0.490114 | −0.245057 | − | 0.969509i | \(-0.578807\pi\) | ||||
−0.245057 | + | 0.969509i | \(0.578807\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.66004 | 0.171191 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.6296 | −1.27044 | −0.635218 | − | 0.772333i | \(-0.719090\pi\) | ||||
−0.635218 | + | 0.772333i | \(0.719090\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.2769 | 0.413154 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.87138 | 0.178234 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.70624 | −0.0623445 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.2014 | 0.737158 | 0.368579 | − | 0.929596i | \(-0.379844\pi\) | ||||
0.368579 | + | 0.929596i | \(0.379844\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 29.8288 | 1.08702 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 46.9179 | 1.70752 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.8622 | 1.30343 | 0.651716 | − | 0.758463i | \(-0.274049\pi\) | ||||
0.651716 | + | 0.758463i | \(0.274049\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.1845 | 0.732650 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.8328 | 0.537690 | 0.268845 | − | 0.963184i | \(-0.413358\pi\) | ||||
0.268845 | + | 0.963184i | \(0.413358\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.1964 | 0.658755 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.952380 | 0.0344334 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 26.9036 | 0.971433 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.01654 | 0.0366574 | 0.0183287 | − | 0.999832i | \(-0.494165\pi\) | ||||
0.0183287 | + | 0.999832i | \(0.494165\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.936638 | −0.0337322 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.5917 | −0.632731 | −0.316365 | − | 0.948637i | \(-0.602463\pi\) | ||||
−0.316365 | + | 0.948637i | \(0.602463\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.93517 | 0.320961 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.09741 | −0.0752443 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.66004 | −0.0953059 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.23148 | −0.115631 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.77725 | −0.206462 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −36.2706 | −1.29455 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 49.1247 | 1.75111 | 0.875553 | − | 0.483121i | \(-0.160497\pi\) | ||||
0.875553 | + | 0.483121i | \(0.160497\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.88139 | −0.138181 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.35541 | 0.154861 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.26308 | 0.115875 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −21.6627 | −0.768298 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30.3445 | 1.07486 | 0.537429 | − | 0.843309i | \(-0.319396\pi\) | ||||
0.537429 | + | 0.843309i | \(0.319396\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.61947 | 0.163425 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.9858 | −0.600164 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 41.6657 | 1.47035 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.9638 | 0.562650 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 32.5695 | 1.14650 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.0475 | 0.529040 | 0.264520 | − | 0.964380i | \(-0.414786\pi\) | ||||
0.264520 | + | 0.964380i | \(0.414786\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.4681 | −1.10499 | −0.552497 | − | 0.833515i | \(-0.686325\pi\) | ||||
−0.552497 | + | 0.833515i | \(0.686325\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 23.0539 | 0.808534 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.1320 | −0.424965 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.03916 | 0.0713412 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.94756 | 0.102996 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.1869 | −1.47233 | −0.736167 | − | 0.676800i | \(-0.763366\pi\) | ||||
−0.736167 | + | 0.676800i | \(0.763366\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.0254204 | −0.000886100 0 | −0.000443050 | − | 1.00000i | \(-0.500141\pi\) | ||||
−0.000443050 | 1.00000i | \(0.500141\pi\) | ||||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.42854 | −0.154182 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.6664 | −0.822961 | −0.411480 | − | 0.911419i | \(-0.634988\pi\) | ||||
−0.411480 | + | 0.911419i | \(0.634988\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.0883 | 1.56598 | 0.782990 | − | 0.622034i | \(-0.213694\pi\) | ||||
0.782990 | + | 0.622034i | \(0.213694\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.4849 | 0.849371 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.24745 | −0.0778694 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.91733 | 0.0663518 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.59306 | 0.227889 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11.7537 | −0.405782 | −0.202891 | − | 0.979201i | \(-0.565034\pi\) | ||||
−0.202891 | + | 0.979201i | \(0.565034\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.37664 | 0.150919 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.0539 | 0.380715 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.9326 | −0.410495 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.330099 | 0.0113423 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 17.3703 | 0.596147 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.6374 | −0.433204 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.4368 | 0.597026 | 0.298513 | − | 0.954406i | \(-0.403509\pi\) | ||||
0.298513 | + | 0.954406i | \(0.403509\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.08593 | −0.139736 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.57857 | −0.327198 | −0.163599 | − | 0.986527i | \(-0.552310\pi\) | ||||
−0.163599 | + | 0.986527i | \(0.552310\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.8356 | −0.437944 | −0.218972 | − | 0.975731i | \(-0.570270\pi\) | ||||
−0.218972 | + | 0.975731i | \(0.570270\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.68253 | −0.0573403 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.5875 | −0.394443 | −0.197221 | − | 0.980359i | \(-0.563192\pi\) | ||||
−0.197221 | + | 0.980359i | \(0.563192\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −25.6116 | −0.870821 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.8573 | −0.572503 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.4731 | 0.423122 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.70873 | −0.0917819 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.17800 | 0.175249 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.41963 | 0.318441 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.17868 | −0.107336 | −0.0536682 | − | 0.998559i | \(-0.517091\pi\) | ||||
−0.0536682 | + | 0.998559i | \(0.517091\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.92081 | 0.0985165 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.9054 | 1.14230 | 0.571150 | − | 0.820845i | \(-0.306497\pi\) | ||||
0.571150 | + | 0.820845i | \(0.306497\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.7707 | 1.03552 | 0.517758 | − | 0.855527i | \(-0.326767\pi\) | ||||
0.517758 | + | 0.855527i | \(0.326767\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −23.5891 | −0.792940 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23.4377 | 0.786962 | 0.393481 | − | 0.919333i | \(-0.371271\pi\) | ||||
0.393481 | + | 0.919333i | \(0.371271\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.5680 | −0.354440 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.26772 | −0.109473 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −19.8186 | −0.663204 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 43.1322 | 1.44175 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.7597 | 0.592980 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −38.0898 | −1.27036 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.24632 | −0.108151 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.28981 | 0.0429221 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.10330 | 0.302604 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.7964 | 0.790148 | 0.395074 | − | 0.918649i | \(-0.370719\pi\) | ||||
0.395074 | + | 0.918649i | \(0.370719\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.78904 | 0.291514 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39.6175 | −1.31259 | −0.656293 | − | 0.754506i | \(-0.727877\pi\) | ||||
−0.656293 | + | 0.754506i | \(0.727877\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.9183 | −0.526819 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.86108 | −0.0945843 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.10681 | −0.300734 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.2164 | 1.16168 | 0.580840 | − | 0.814018i | \(-0.302724\pi\) | ||||
0.580840 | + | 0.814018i | \(0.302724\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.5812 | 0.777027 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.84328 | −0.0935878 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.77269 | 0.0911655 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.6235 | −0.545987 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.0219 | −0.788134 | −0.394067 | − | 0.919082i | \(-0.628932\pi\) | ||||
−0.394067 | + | 0.919082i | \(0.628932\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.64206 | 0.316006 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.0568 | −0.492938 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.11211 | −0.101777 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.3384 | 0.925775 | 0.462888 | − | 0.886417i | \(-0.346813\pi\) | ||||
0.462888 | + | 0.886417i | \(0.346813\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.4291 | 0.568778 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31.7155 | −1.03390 | −0.516948 | − | 0.856017i | \(-0.672932\pi\) | ||||
−0.516948 | + | 0.856017i | \(0.672932\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.1376 | −0.330126 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.58443 | −0.0840715 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41.0291 | −1.33327 | −0.666634 | − | 0.745385i | \(-0.732266\pi\) | ||||
−0.666634 | + | 0.745385i | \(0.732266\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 36.6605 | 1.19005 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.21009 | −0.201376 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.8897 | 1.38933 | 0.694667 | − | 0.719332i | \(-0.255552\pi\) | ||||
0.694667 | + | 0.719332i | \(0.255552\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.746590 | 0.0241591 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 18.8785 | 0.610254 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.3166 | 0.365432 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.4684 | 0.402207 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.66433 | 0.0536324 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 37.3314 | 1.20174 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45.9167 | −1.47658 | −0.738291 | − | 0.674482i | \(-0.764367\pi\) | ||||
−0.738291 | + | 0.674482i | \(0.764367\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.612307 | −0.0196701 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37.6867 | −1.20942 | −0.604712 | − | 0.796444i | \(-0.706712\pi\) | ||||
−0.604712 | + | 0.796444i | \(0.706712\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.2920 | −0.329947 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.89655 | −0.124789 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.87111 | −0.187834 | −0.0939168 | − | 0.995580i | \(-0.529939\pi\) | ||||
−0.0939168 | + | 0.995580i | \(0.529939\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 55.5049 | 1.77394 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.7496 | −0.566700 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.7567 | −1.07667 | −0.538336 | − | 0.842731i | \(-0.680947\pi\) | ||||
−0.538336 | + | 0.842731i | \(0.680947\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −48.6242 | −1.54930 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.5356 | −0.399014 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.77138 | 0.247115 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.4635 | 1.38066 | 0.690332 | − | 0.723493i | \(-0.257464\pi\) | ||||
0.690332 | + | 0.723493i | \(0.257464\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −16.0705 | −0.509982 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −38.2796 | −1.21354 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.9207 | 0.377532 | 0.188766 | − | 0.982022i | \(-0.439551\pi\) | ||||
0.188766 | + | 0.982022i | \(0.439551\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.04591 | 0.0647296 |
(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 | 6036.2.a.g.1.14 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6036.2.a.g.1.14 | ✓ | 15 | 1.1 | even | 1 | trivial |