Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3450,2,Mod(1,3450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3450, 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("3450.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3450.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: | \(27.5483886973\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.3368.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 15x + 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-3.76300\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3450.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 3.76300 | 1.42228 | 0.711141 | − | 0.703050i | \(-0.248179\pi\) | ||||
0.711141 | + | 0.703050i | \(0.248179\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.18291 | 0.959682 | 0.479841 | − | 0.877355i | \(-0.340694\pi\) | ||||
0.479841 | + | 0.877355i | \(0.340694\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 6.34310 | 1.75926 | 0.879630 | − | 0.475659i | \(-0.157790\pi\) | ||||
0.879630 | + | 0.475659i | \(0.157790\pi\) | |||||||
\(14\) | 3.76300 | 1.00570 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.58010 | 0.625765 | 0.312883 | − | 0.949792i | \(-0.398705\pi\) | ||||
0.312883 | + | 0.949792i | \(0.398705\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −6.34310 | −1.45521 | −0.727603 | − | 0.685998i | \(-0.759366\pi\) | ||||
−0.727603 | + | 0.685998i | \(0.759366\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.76300 | −0.821155 | ||||||||
\(22\) | 3.18291 | 0.678598 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.34310 | 1.24398 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.76300 | 0.711141 | ||||||||
\(29\) | −1.00000 | −0.185695 | −0.0928477 | − | 0.995680i | \(-0.529597\pi\) | ||||
−0.0928477 | + | 0.995680i | \(0.529597\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −3.18291 | −0.554073 | ||||||||
\(34\) | 2.58010 | 0.442483 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −2.58010 | −0.424165 | −0.212083 | − | 0.977252i | \(-0.568025\pi\) | ||||
−0.212083 | + | 0.977252i | \(0.568025\pi\) | |||||||
\(38\) | −6.34310 | −1.02899 | ||||||||
\(39\) | −6.34310 | −1.01571 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.3431 | 1.92767 | 0.963834 | − | 0.266503i | \(-0.0858681\pi\) | ||||
0.963834 | + | 0.266503i | \(0.0858681\pi\) | |||||||
\(42\) | −3.76300 | −0.580644 | ||||||||
\(43\) | −10.3431 | −1.57731 | −0.788654 | − | 0.614837i | \(-0.789222\pi\) | ||||
−0.788654 | + | 0.614837i | \(0.789222\pi\) | |||||||
\(44\) | 3.18291 | 0.479841 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −3.34310 | −0.487641 | −0.243821 | − | 0.969820i | \(-0.578401\pi\) | ||||
−0.243821 | + | 0.969820i | \(0.578401\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 7.16019 | 1.02288 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.58010 | −0.361286 | ||||||||
\(52\) | 6.34310 | 0.879630 | ||||||||
\(53\) | −7.16019 | −0.983528 | −0.491764 | − | 0.870728i | \(-0.663648\pi\) | ||||
−0.491764 | + | 0.870728i | \(0.663648\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.76300 | 0.502852 | ||||||||
\(57\) | 6.34310 | 0.840164 | ||||||||
\(58\) | −1.00000 | −0.131306 | ||||||||
\(59\) | −4.36581 | −0.568380 | −0.284190 | − | 0.958768i | \(-0.591725\pi\) | ||||
−0.284190 | + | 0.958768i | \(0.591725\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.52601 | −0.195385 | −0.0976926 | − | 0.995217i | \(-0.531146\pi\) | ||||
−0.0976926 | + | 0.995217i | \(0.531146\pi\) | |||||||
\(62\) | 6.00000 | 0.762001 | ||||||||
\(63\) | 3.76300 | 0.474094 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.18291 | −0.391789 | ||||||||
\(67\) | −10.6862 | −1.30553 | −0.652764 | − | 0.757562i | \(-0.726390\pi\) | ||||
−0.652764 | + | 0.757562i | \(0.726390\pi\) | |||||||
\(68\) | 2.58010 | 0.312883 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.81709 | 0.215649 | 0.107825 | − | 0.994170i | \(-0.465611\pi\) | ||||
0.107825 | + | 0.994170i | \(0.465611\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −8.52601 | −0.997894 | −0.498947 | − | 0.866633i | \(-0.666280\pi\) | ||||
−0.498947 | + | 0.866633i | \(0.666280\pi\) | |||||||
\(74\) | −2.58010 | −0.299930 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.34310 | −0.727603 | ||||||||
\(77\) | 11.9773 | 1.36494 | ||||||||
\(78\) | −6.34310 | −0.718215 | ||||||||
\(79\) | −3.18291 | −0.358105 | −0.179052 | − | 0.983840i | \(-0.557303\pi\) | ||||
−0.179052 | + | 0.983840i | \(0.557303\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 12.3431 | 1.36307 | ||||||||
\(83\) | 7.28901 | 0.800073 | 0.400036 | − | 0.916499i | \(-0.368997\pi\) | ||||
0.400036 | + | 0.916499i | \(0.368997\pi\) | |||||||
\(84\) | −3.76300 | −0.410577 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −10.3431 | −1.11533 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | 3.18291 | 0.339299 | ||||||||
\(89\) | 4.58010 | 0.485489 | 0.242745 | − | 0.970090i | \(-0.421952\pi\) | ||||
0.242745 | + | 0.970090i | \(0.421952\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 23.8691 | 2.50216 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −6.00000 | −0.622171 | ||||||||
\(94\) | −3.34310 | −0.344814 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −11.5260 | −1.17029 | −0.585144 | − | 0.810929i | \(-0.698962\pi\) | ||||
−0.585144 | + | 0.810929i | \(0.698962\pi\) | |||||||
\(98\) | 7.16019 | 0.723289 | ||||||||
\(99\) | 3.18291 | 0.319894 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.70891 | −0.767066 | −0.383533 | − | 0.923527i | \(-0.625293\pi\) | ||||
−0.383533 | + | 0.923527i | \(0.625293\pi\) | |||||||
\(102\) | −2.58010 | −0.255468 | ||||||||
\(103\) | −3.39719 | −0.334735 | −0.167368 | − | 0.985895i | \(-0.553527\pi\) | ||||
−0.167368 | + | 0.985895i | \(0.553527\pi\) | |||||||
\(104\) | 6.34310 | 0.621992 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.16019 | −0.695459 | ||||||||
\(107\) | −6.68620 | −0.646379 | −0.323190 | − | 0.946334i | \(-0.604755\pi\) | ||||
−0.323190 | + | 0.946334i | \(0.604755\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 5.78572 | 0.554171 | 0.277086 | − | 0.960845i | \(-0.410631\pi\) | ||||
0.277086 | + | 0.960845i | \(0.410631\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.58010 | 0.244892 | ||||||||
\(112\) | 3.76300 | 0.355570 | ||||||||
\(113\) | 0.580097 | 0.0545709 | 0.0272855 | − | 0.999628i | \(-0.491314\pi\) | ||||
0.0272855 | + | 0.999628i | \(0.491314\pi\) | |||||||
\(114\) | 6.34310 | 0.594086 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | 6.34310 | 0.586420 | ||||||||
\(118\) | −4.36581 | −0.401906 | ||||||||
\(119\) | 9.70891 | 0.890015 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.869107 | −0.0790097 | ||||||||
\(122\) | −1.52601 | −0.138158 | ||||||||
\(123\) | −12.3431 | −1.11294 | ||||||||
\(124\) | 6.00000 | 0.538816 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.76300 | 0.335235 | ||||||||
\(127\) | 14.3204 | 1.27073 | 0.635364 | − | 0.772212i | \(-0.280850\pi\) | ||||
0.635364 | + | 0.772212i | \(0.280850\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 10.3431 | 0.910659 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.8918 | 1.38847 | 0.694237 | − | 0.719746i | \(-0.255742\pi\) | ||||
0.694237 | + | 0.719746i | \(0.255742\pi\) | |||||||
\(132\) | −3.18291 | −0.277036 | ||||||||
\(133\) | −23.8691 | −2.06971 | ||||||||
\(134\) | −10.6862 | −0.923147 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.58010 | 0.221241 | ||||||||
\(137\) | 15.4199 | 1.31741 | 0.658706 | − | 0.752401i | \(-0.271104\pi\) | ||||
0.658706 | + | 0.752401i | \(0.271104\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | 3.02271 | 0.256383 | 0.128192 | − | 0.991749i | \(-0.459083\pi\) | ||||
0.128192 | + | 0.991749i | \(0.459083\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.34310 | 0.281540 | ||||||||
\(142\) | 1.81709 | 0.152487 | ||||||||
\(143\) | 20.1895 | 1.68833 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.52601 | −0.705617 | ||||||||
\(147\) | −7.16019 | −0.590563 | ||||||||
\(148\) | −2.58010 | −0.212083 | ||||||||
\(149\) | 16.6862 | 1.36699 | 0.683493 | − | 0.729957i | \(-0.260460\pi\) | ||||
0.683493 | + | 0.729957i | \(0.260460\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.16019 | −0.582688 | −0.291344 | − | 0.956618i | \(-0.594102\pi\) | ||||
−0.291344 | + | 0.956618i | \(0.594102\pi\) | |||||||
\(152\) | −6.34310 | −0.514493 | ||||||||
\(153\) | 2.58010 | 0.208588 | ||||||||
\(154\) | 11.9773 | 0.965157 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −6.34310 | −0.507854 | ||||||||
\(157\) | −22.2122 | −1.77273 | −0.886364 | − | 0.462990i | \(-0.846777\pi\) | ||||
−0.886364 | + | 0.462990i | \(0.846777\pi\) | |||||||
\(158\) | −3.18291 | −0.253218 | ||||||||
\(159\) | 7.16019 | 0.567840 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.76300 | 0.296566 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 8.68620 | 0.680356 | 0.340178 | − | 0.940361i | \(-0.389513\pi\) | ||||
0.340178 | + | 0.940361i | \(0.389513\pi\) | |||||||
\(164\) | 12.3431 | 0.963834 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.28901 | 0.565737 | ||||||||
\(167\) | 25.2349 | 1.95274 | 0.976368 | − | 0.216113i | \(-0.0693380\pi\) | ||||
0.976368 | + | 0.216113i | \(0.0693380\pi\) | |||||||
\(168\) | −3.76300 | −0.290322 | ||||||||
\(169\) | 27.2349 | 2.09499 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.34310 | −0.485069 | ||||||||
\(172\) | −10.3431 | −0.788654 | ||||||||
\(173\) | −0.817094 | −0.0621225 | −0.0310612 | − | 0.999517i | \(-0.509889\pi\) | ||||
−0.0310612 | + | 0.999517i | \(0.509889\pi\) | |||||||
\(174\) | 1.00000 | 0.0758098 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.18291 | 0.239921 | ||||||||
\(177\) | 4.36581 | 0.328155 | ||||||||
\(178\) | 4.58010 | 0.343293 | ||||||||
\(179\) | −3.16019 | −0.236204 | −0.118102 | − | 0.993001i | \(-0.537681\pi\) | ||||
−0.118102 | + | 0.993001i | \(0.537681\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.37448 | 0.250823 | 0.125411 | − | 0.992105i | \(-0.459975\pi\) | ||||
0.125411 | + | 0.992105i | \(0.459975\pi\) | |||||||
\(182\) | 23.8691 | 1.76930 | ||||||||
\(183\) | 1.52601 | 0.112806 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.00000 | −0.439941 | ||||||||
\(187\) | 8.21221 | 0.600536 | ||||||||
\(188\) | −3.34310 | −0.243821 | ||||||||
\(189\) | −3.76300 | −0.273718 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.8691 | −0.858818 | −0.429409 | − | 0.903110i | \(-0.641278\pi\) | ||||
−0.429409 | + | 0.903110i | \(0.641278\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 2.97729 | 0.214310 | 0.107155 | − | 0.994242i | \(-0.465826\pi\) | ||||
0.107155 | + | 0.994242i | \(0.465826\pi\) | |||||||
\(194\) | −11.5260 | −0.827519 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.16019 | 0.511442 | ||||||||
\(197\) | 24.8918 | 1.77347 | 0.886734 | − | 0.462279i | \(-0.152968\pi\) | ||||
0.886734 | + | 0.462279i | \(0.152968\pi\) | |||||||
\(198\) | 3.18291 | 0.226199 | ||||||||
\(199\) | 22.4492 | 1.59138 | 0.795691 | − | 0.605703i | \(-0.207108\pi\) | ||||
0.795691 | + | 0.605703i | \(0.207108\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.6862 | 0.753746 | ||||||||
\(202\) | −7.70891 | −0.542397 | ||||||||
\(203\) | −3.76300 | −0.264111 | ||||||||
\(204\) | −2.58010 | −0.180643 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.39719 | −0.236693 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 6.34310 | 0.439815 | ||||||||
\(209\) | −20.1895 | −1.39654 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.5553 | 1.34624 | 0.673121 | − | 0.739532i | \(-0.264953\pi\) | ||||
0.673121 | + | 0.739532i | \(0.264953\pi\) | |||||||
\(212\) | −7.16019 | −0.491764 | ||||||||
\(213\) | −1.81709 | −0.124505 | ||||||||
\(214\) | −6.68620 | −0.457059 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 22.5780 | 1.53270 | ||||||||
\(218\) | 5.78572 | 0.391858 | ||||||||
\(219\) | 8.52601 | 0.576134 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.3658 | 1.10088 | ||||||||
\(222\) | 2.58010 | 0.173165 | ||||||||
\(223\) | −28.8984 | −1.93518 | −0.967590 | − | 0.252525i | \(-0.918739\pi\) | ||||
−0.967590 | + | 0.252525i | \(0.918739\pi\) | |||||||
\(224\) | 3.76300 | 0.251426 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.580097 | 0.0385875 | ||||||||
\(227\) | −17.6321 | −1.17028 | −0.585142 | − | 0.810931i | \(-0.698961\pi\) | ||||
−0.585142 | + | 0.810931i | \(0.698961\pi\) | |||||||
\(228\) | 6.34310 | 0.420082 | ||||||||
\(229\) | −11.8918 | −0.785834 | −0.392917 | − | 0.919574i | \(-0.628534\pi\) | ||||
−0.392917 | + | 0.919574i | \(0.628534\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.9773 | −0.788048 | ||||||||
\(232\) | −1.00000 | −0.0656532 | ||||||||
\(233\) | −9.02930 | −0.591529 | −0.295765 | − | 0.955261i | \(-0.595574\pi\) | ||||
−0.295765 | + | 0.955261i | \(0.595574\pi\) | |||||||
\(234\) | 6.34310 | 0.414661 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.36581 | −0.284190 | ||||||||
\(237\) | 3.18291 | 0.206752 | ||||||||
\(238\) | 9.70891 | 0.629335 | ||||||||
\(239\) | −20.0747 | −1.29853 | −0.649263 | − | 0.760564i | \(-0.724923\pi\) | ||||
−0.649263 | + | 0.760564i | \(0.724923\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.0066 | −1.48198 | −0.740992 | − | 0.671514i | \(-0.765645\pi\) | ||||
−0.740992 | + | 0.671514i | \(0.765645\pi\) | |||||||
\(242\) | −0.869107 | −0.0558683 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.52601 | −0.0976926 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −12.3431 | −0.786967 | ||||||||
\(247\) | −40.2349 | −2.56009 | ||||||||
\(248\) | 6.00000 | 0.381000 | ||||||||
\(249\) | −7.28901 | −0.461922 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.9459 | −0.690900 | −0.345450 | − | 0.938437i | \(-0.612274\pi\) | ||||
−0.345450 | + | 0.938437i | \(0.612274\pi\) | |||||||
\(252\) | 3.76300 | 0.237047 | ||||||||
\(253\) | 3.18291 | 0.200108 | ||||||||
\(254\) | 14.3204 | 0.898541 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 16.3204 | 1.01804 | 0.509019 | − | 0.860755i | \(-0.330008\pi\) | ||||
0.509019 | + | 0.860755i | \(0.330008\pi\) | |||||||
\(258\) | 10.3431 | 0.643933 | ||||||||
\(259\) | −9.70891 | −0.603282 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | 15.8918 | 0.981800 | ||||||||
\(263\) | −29.0066 | −1.78862 | −0.894311 | − | 0.447445i | \(-0.852334\pi\) | ||||
−0.894311 | + | 0.447445i | \(0.852334\pi\) | |||||||
\(264\) | −3.18291 | −0.195894 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −23.8691 | −1.46351 | ||||||||
\(267\) | −4.58010 | −0.280297 | ||||||||
\(268\) | −10.6862 | −0.652764 | ||||||||
\(269\) | −26.1895 | −1.59680 | −0.798401 | − | 0.602126i | \(-0.794320\pi\) | ||||
−0.798401 | + | 0.602126i | \(0.794320\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.36581 | 0.386696 | 0.193348 | − | 0.981130i | \(-0.438065\pi\) | ||||
0.193348 | + | 0.981130i | \(0.438065\pi\) | |||||||
\(272\) | 2.58010 | 0.156441 | ||||||||
\(273\) | −23.8691 | −1.44462 | ||||||||
\(274\) | 15.4199 | 0.931550 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | 9.50329 | 0.570998 | 0.285499 | − | 0.958379i | \(-0.407841\pi\) | ||||
0.285499 | + | 0.958379i | \(0.407841\pi\) | |||||||
\(278\) | 3.02271 | 0.181290 | ||||||||
\(279\) | 6.00000 | 0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.2663 | 1.62657 | 0.813285 | − | 0.581865i | \(-0.197677\pi\) | ||||
0.813285 | + | 0.581865i | \(0.197677\pi\) | |||||||
\(282\) | 3.34310 | 0.199079 | ||||||||
\(283\) | 10.3204 | 0.613483 | 0.306742 | − | 0.951793i | \(-0.400761\pi\) | ||||
0.306742 | + | 0.951793i | \(0.400761\pi\) | |||||||
\(284\) | 1.81709 | 0.107825 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 20.1895 | 1.19383 | ||||||||
\(287\) | 46.4471 | 2.74169 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −10.3431 | −0.608418 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.5260 | 0.675666 | ||||||||
\(292\) | −8.52601 | −0.498947 | ||||||||
\(293\) | −8.36581 | −0.488736 | −0.244368 | − | 0.969683i | \(-0.578580\pi\) | ||||
−0.244368 | + | 0.969683i | \(0.578580\pi\) | |||||||
\(294\) | −7.16019 | −0.417591 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.58010 | −0.149965 | ||||||||
\(297\) | −3.18291 | −0.184691 | ||||||||
\(298\) | 16.6862 | 0.966606 | ||||||||
\(299\) | 6.34310 | 0.366831 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −38.9211 | −2.24338 | ||||||||
\(302\) | −7.16019 | −0.412023 | ||||||||
\(303\) | 7.70891 | 0.442865 | ||||||||
\(304\) | −6.34310 | −0.363802 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.58010 | 0.147494 | ||||||||
\(307\) | −33.7089 | −1.92387 | −0.961935 | − | 0.273280i | \(-0.911892\pi\) | ||||
−0.961935 | + | 0.273280i | \(0.911892\pi\) | |||||||
\(308\) | 11.9773 | 0.682469 | ||||||||
\(309\) | 3.39719 | 0.193259 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.86252 | −0.105614 | −0.0528069 | − | 0.998605i | \(-0.516817\pi\) | ||||
−0.0528069 | + | 0.998605i | \(0.516817\pi\) | |||||||
\(312\) | −6.34310 | −0.359107 | ||||||||
\(313\) | 26.8984 | 1.52039 | 0.760194 | − | 0.649696i | \(-0.225104\pi\) | ||||
0.760194 | + | 0.649696i | \(0.225104\pi\) | |||||||
\(314\) | −22.2122 | −1.25351 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.18291 | −0.179052 | ||||||||
\(317\) | 11.0000 | 0.617822 | 0.308911 | − | 0.951091i | \(-0.400036\pi\) | ||||
0.308911 | + | 0.951091i | \(0.400036\pi\) | |||||||
\(318\) | 7.16019 | 0.401524 | ||||||||
\(319\) | −3.18291 | −0.178209 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.68620 | 0.373187 | ||||||||
\(322\) | 3.76300 | 0.209704 | ||||||||
\(323\) | −16.3658 | −0.910618 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.68620 | 0.481084 | ||||||||
\(327\) | −5.78572 | −0.319951 | ||||||||
\(328\) | 12.3431 | 0.681534 | ||||||||
\(329\) | −12.5801 | −0.693563 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.18291 | −0.339843 | −0.169922 | − | 0.985458i | \(-0.554351\pi\) | ||||
−0.169922 | + | 0.985458i | \(0.554351\pi\) | |||||||
\(332\) | 7.28901 | 0.400036 | ||||||||
\(333\) | −2.58010 | −0.141388 | ||||||||
\(334\) | 25.2349 | 1.38079 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.76300 | −0.205289 | ||||||||
\(337\) | 15.1602 | 0.825828 | 0.412914 | − | 0.910770i | \(-0.364511\pi\) | ||||
0.412914 | + | 0.910770i | \(0.364511\pi\) | |||||||
\(338\) | 27.2349 | 1.48138 | ||||||||
\(339\) | −0.580097 | −0.0315065 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.0974 | 1.03418 | ||||||||
\(342\) | −6.34310 | −0.342996 | ||||||||
\(343\) | 0.602810 | 0.0325487 | ||||||||
\(344\) | −10.3431 | −0.557663 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.817094 | −0.0439272 | ||||||||
\(347\) | −29.8918 | −1.60468 | −0.802338 | − | 0.596869i | \(-0.796411\pi\) | ||||
−0.802338 | + | 0.596869i | \(0.796411\pi\) | |||||||
\(348\) | 1.00000 | 0.0536056 | ||||||||
\(349\) | 7.02930 | 0.376270 | 0.188135 | − | 0.982143i | \(-0.439756\pi\) | ||||
0.188135 | + | 0.982143i | \(0.439756\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.34310 | −0.338570 | ||||||||
\(352\) | 3.18291 | 0.169649 | ||||||||
\(353\) | −26.2349 | −1.39634 | −0.698172 | − | 0.715930i | \(-0.746003\pi\) | ||||
−0.698172 | + | 0.715930i | \(0.746003\pi\) | |||||||
\(354\) | 4.36581 | 0.232040 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.58010 | 0.242745 | ||||||||
\(357\) | −9.70891 | −0.513850 | ||||||||
\(358\) | −3.16019 | −0.167021 | ||||||||
\(359\) | 19.5033 | 1.02934 | 0.514672 | − | 0.857387i | \(-0.327914\pi\) | ||||
0.514672 | + | 0.857387i | \(0.327914\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.2349 | 1.11763 | ||||||||
\(362\) | 3.37448 | 0.177359 | ||||||||
\(363\) | 0.869107 | 0.0456163 | ||||||||
\(364\) | 23.8691 | 1.25108 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.52601 | 0.0797656 | ||||||||
\(367\) | −33.5033 | −1.74886 | −0.874429 | − | 0.485154i | \(-0.838764\pi\) | ||||
−0.874429 | + | 0.485154i | \(0.838764\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 12.3431 | 0.642556 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −26.9438 | −1.39885 | ||||||||
\(372\) | −6.00000 | −0.311086 | ||||||||
\(373\) | 10.1515 | 0.525626 | 0.262813 | − | 0.964847i | \(-0.415350\pi\) | ||||
0.262813 | + | 0.964847i | \(0.415350\pi\) | |||||||
\(374\) | 8.21221 | 0.424643 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.34310 | −0.172407 | ||||||||
\(377\) | −6.34310 | −0.326686 | ||||||||
\(378\) | −3.76300 | −0.193548 | ||||||||
\(379\) | 20.5780 | 1.05702 | 0.528511 | − | 0.848926i | \(-0.322751\pi\) | ||||
0.528511 | + | 0.848926i | \(0.322751\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.3204 | −0.733656 | ||||||||
\(382\) | −11.8691 | −0.607276 | ||||||||
\(383\) | −1.22833 | −0.0627648 | −0.0313824 | − | 0.999507i | \(-0.509991\pi\) | ||||
−0.0313824 | + | 0.999507i | \(0.509991\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.97729 | 0.151540 | ||||||||
\(387\) | −10.3431 | −0.525769 | ||||||||
\(388\) | −11.5260 | −0.585144 | ||||||||
\(389\) | 35.3724 | 1.79345 | 0.896726 | − | 0.442586i | \(-0.145939\pi\) | ||||
0.896726 | + | 0.442586i | \(0.145939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.58010 | 0.130481 | ||||||||
\(392\) | 7.16019 | 0.361644 | ||||||||
\(393\) | −15.8918 | −0.801636 | ||||||||
\(394\) | 24.8918 | 1.25403 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.18291 | 0.159947 | ||||||||
\(397\) | −31.0066 | −1.55618 | −0.778088 | − | 0.628155i | \(-0.783810\pi\) | ||||
−0.778088 | + | 0.628155i | \(0.783810\pi\) | |||||||
\(398\) | 22.4492 | 1.12528 | ||||||||
\(399\) | 23.8691 | 1.19495 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.2056 | 0.759332 | 0.379666 | − | 0.925124i | \(-0.376039\pi\) | ||||
0.379666 | + | 0.925124i | \(0.376039\pi\) | |||||||
\(402\) | 10.6862 | 0.532979 | ||||||||
\(403\) | 38.0586 | 1.89583 | ||||||||
\(404\) | −7.70891 | −0.383533 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.76300 | −0.186755 | ||||||||
\(407\) | −8.21221 | −0.407064 | ||||||||
\(408\) | −2.58010 | −0.127734 | ||||||||
\(409\) | −2.57143 | −0.127149 | −0.0635746 | − | 0.997977i | \(-0.520250\pi\) | ||||
−0.0635746 | + | 0.997977i | \(0.520250\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.4199 | −0.760608 | ||||||||
\(412\) | −3.39719 | −0.167368 | ||||||||
\(413\) | −16.4286 | −0.808397 | ||||||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6.34310 | 0.310996 | ||||||||
\(417\) | −3.02271 | −0.148023 | ||||||||
\(418\) | −20.1895 | −0.987500 | ||||||||
\(419\) | −19.0768 | −0.931963 | −0.465981 | − | 0.884795i | \(-0.654299\pi\) | ||||
−0.465981 | + | 0.884795i | \(0.654299\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.8918 | −0.774520 | −0.387260 | − | 0.921971i | \(-0.626578\pi\) | ||||
−0.387260 | + | 0.921971i | \(0.626578\pi\) | |||||||
\(422\) | 19.5553 | 0.951937 | ||||||||
\(423\) | −3.34310 | −0.162547 | ||||||||
\(424\) | −7.16019 | −0.347730 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.81709 | −0.0880385 | ||||||||
\(427\) | −5.74237 | −0.277893 | ||||||||
\(428\) | −6.68620 | −0.323190 | ||||||||
\(429\) | −20.1895 | −0.974758 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.2122 | −1.16626 | −0.583130 | − | 0.812379i | \(-0.698172\pi\) | ||||
−0.583130 | + | 0.812379i | \(0.698172\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 12.2122 | 0.586881 | 0.293441 | − | 0.955977i | \(-0.405200\pi\) | ||||
0.293441 | + | 0.955977i | \(0.405200\pi\) | |||||||
\(434\) | 22.5780 | 1.08378 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.78572 | 0.277086 | ||||||||
\(437\) | −6.34310 | −0.303432 | ||||||||
\(438\) | 8.52601 | 0.407388 | ||||||||
\(439\) | −0.794381 | −0.0379137 | −0.0189569 | − | 0.999820i | \(-0.506035\pi\) | ||||
−0.0189569 | + | 0.999820i | \(0.506035\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.16019 | 0.340962 | ||||||||
\(442\) | 16.3658 | 0.778442 | ||||||||
\(443\) | −14.2122 | −0.675242 | −0.337621 | − | 0.941282i | \(-0.609622\pi\) | ||||
−0.337621 | + | 0.941282i | \(0.609622\pi\) | |||||||
\(444\) | 2.58010 | 0.122446 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −28.8984 | −1.36838 | ||||||||
\(447\) | −16.6862 | −0.789230 | ||||||||
\(448\) | 3.76300 | 0.177785 | ||||||||
\(449\) | 1.05201 | 0.0496476 | 0.0248238 | − | 0.999692i | \(-0.492098\pi\) | ||||
0.0248238 | + | 0.999692i | \(0.492098\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 39.2869 | 1.84995 | ||||||||
\(452\) | 0.580097 | 0.0272855 | ||||||||
\(453\) | 7.16019 | 0.336415 | ||||||||
\(454\) | −17.6321 | −0.827516 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.34310 | 0.297043 | ||||||||
\(457\) | 0.686200 | 0.0320991 | 0.0160495 | − | 0.999871i | \(-0.494891\pi\) | ||||
0.0160495 | + | 0.999871i | \(0.494891\pi\) | |||||||
\(458\) | −11.8918 | −0.555668 | ||||||||
\(459\) | −2.58010 | −0.120429 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.5780 | −1.37759 | −0.688793 | − | 0.724958i | \(-0.741859\pi\) | ||||
−0.688793 | + | 0.724958i | \(0.741859\pi\) | |||||||
\(462\) | −11.9773 | −0.557234 | ||||||||
\(463\) | 12.0000 | 0.557687 | 0.278844 | − | 0.960337i | \(-0.410049\pi\) | ||||
0.278844 | + | 0.960337i | \(0.410049\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.02930 | −0.418274 | ||||||||
\(467\) | 29.2890 | 1.35533 | 0.677667 | − | 0.735369i | \(-0.262991\pi\) | ||||
0.677667 | + | 0.735369i | \(0.262991\pi\) | |||||||
\(468\) | 6.34310 | 0.293210 | ||||||||
\(469\) | −40.2122 | −1.85683 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.2122 | 1.02348 | ||||||||
\(472\) | −4.36581 | −0.200953 | ||||||||
\(473\) | −32.9211 | −1.51371 | ||||||||
\(474\) | 3.18291 | 0.146196 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 9.70891 | 0.445007 | ||||||||
\(477\) | −7.16019 | −0.327843 | ||||||||
\(478\) | −20.0747 | −0.918197 | ||||||||
\(479\) | 15.9145 | 0.727154 | 0.363577 | − | 0.931564i | \(-0.381555\pi\) | ||||
0.363577 | + | 0.931564i | \(0.381555\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.3658 | −0.746217 | ||||||||
\(482\) | −23.0066 | −1.04792 | ||||||||
\(483\) | −3.76300 | −0.171223 | ||||||||
\(484\) | −0.869107 | −0.0395049 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −38.9438 | −1.76471 | −0.882357 | − | 0.470581i | \(-0.844044\pi\) | ||||
−0.882357 | + | 0.470581i | \(0.844044\pi\) | |||||||
\(488\) | −1.52601 | −0.0690791 | ||||||||
\(489\) | −8.68620 | −0.392804 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.4806 | 1.24018 | 0.620091 | − | 0.784530i | \(-0.287096\pi\) | ||||
0.620091 | + | 0.784530i | \(0.287096\pi\) | |||||||
\(492\) | −12.3431 | −0.556470 | ||||||||
\(493\) | −2.58010 | −0.116202 | ||||||||
\(494\) | −40.2349 | −1.81025 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.00000 | 0.269408 | ||||||||
\(497\) | 6.83773 | 0.306714 | ||||||||
\(498\) | −7.28901 | −0.326628 | ||||||||
\(499\) | 6.97729 | 0.312346 | 0.156173 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156173 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −25.2349 | −1.12741 | ||||||||
\(502\) | −10.9459 | −0.488540 | ||||||||
\(503\) | −7.65690 | −0.341404 | −0.170702 | − | 0.985323i | \(-0.554604\pi\) | ||||
−0.170702 | + | 0.985323i | \(0.554604\pi\) | |||||||
\(504\) | 3.76300 | 0.167617 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.18291 | 0.141497 | ||||||||
\(507\) | −27.2349 | −1.20955 | ||||||||
\(508\) | 14.3204 | 0.635364 | ||||||||
\(509\) | −34.6073 | −1.53394 | −0.766971 | − | 0.641681i | \(-0.778237\pi\) | ||||
−0.766971 | + | 0.641681i | \(0.778237\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −32.0834 | −1.41929 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 6.34310 | 0.280055 | ||||||||
\(514\) | 16.3204 | 0.719861 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 10.3431 | 0.455330 | ||||||||
\(517\) | −10.6408 | −0.467981 | ||||||||
\(518\) | −9.70891 | −0.426585 | ||||||||
\(519\) | 0.817094 | 0.0358664 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.4199 | 1.11367 | 0.556833 | − | 0.830624i | \(-0.312016\pi\) | ||||
0.556833 | + | 0.830624i | \(0.312016\pi\) | |||||||
\(522\) | −1.00000 | −0.0437688 | ||||||||
\(523\) | −25.8691 | −1.13118 | −0.565589 | − | 0.824688i | \(-0.691351\pi\) | ||||
−0.565589 | + | 0.824688i | \(0.691351\pi\) | |||||||
\(524\) | 15.8918 | 0.694237 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −29.0066 | −1.26475 | ||||||||
\(527\) | 15.4806 | 0.674345 | ||||||||
\(528\) | −3.18291 | −0.138518 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.36581 | −0.189460 | ||||||||
\(532\) | −23.8691 | −1.03486 | ||||||||
\(533\) | 78.2935 | 3.39127 | ||||||||
\(534\) | −4.58010 | −0.198200 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −10.6862 | −0.461574 | ||||||||
\(537\) | 3.16019 | 0.136372 | ||||||||
\(538\) | −26.1895 | −1.12911 | ||||||||
\(539\) | 22.7902 | 0.981645 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.6007 | 1.48760 | 0.743801 | − | 0.668401i | \(-0.233021\pi\) | ||||
0.743801 | + | 0.668401i | \(0.233021\pi\) | |||||||
\(542\) | 6.36581 | 0.273435 | ||||||||
\(543\) | −3.37448 | −0.144813 | ||||||||
\(544\) | 2.58010 | 0.110621 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −23.8691 | −1.02150 | ||||||||
\(547\) | 3.55531 | 0.152014 | 0.0760070 | − | 0.997107i | \(-0.475783\pi\) | ||||
0.0760070 | + | 0.997107i | \(0.475783\pi\) | |||||||
\(548\) | 15.4199 | 0.658706 | ||||||||
\(549\) | −1.52601 | −0.0651284 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.34310 | 0.270225 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | −11.9773 | −0.509326 | ||||||||
\(554\) | 9.50329 | 0.403756 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.02271 | 0.128192 | ||||||||
\(557\) | −15.2642 | −0.646766 | −0.323383 | − | 0.946268i | \(-0.604820\pi\) | ||||
−0.323383 | + | 0.946268i | \(0.604820\pi\) | |||||||
\(558\) | 6.00000 | 0.254000 | ||||||||
\(559\) | −65.6073 | −2.77489 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.21221 | −0.346720 | ||||||||
\(562\) | 27.2663 | 1.15016 | ||||||||
\(563\) | −13.5487 | −0.571010 | −0.285505 | − | 0.958377i | \(-0.592161\pi\) | ||||
−0.285505 | + | 0.958377i | \(0.592161\pi\) | |||||||
\(564\) | 3.34310 | 0.140770 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 10.3204 | 0.433798 | ||||||||
\(567\) | 3.76300 | 0.158031 | ||||||||
\(568\) | 1.81709 | 0.0762436 | ||||||||
\(569\) | −18.4740 | −0.774470 | −0.387235 | − | 0.921981i | \(-0.626570\pi\) | ||||
−0.387235 | + | 0.921981i | \(0.626570\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.89182 | −0.413960 | −0.206980 | − | 0.978345i | \(-0.566363\pi\) | ||||
−0.206980 | + | 0.978345i | \(0.566363\pi\) | |||||||
\(572\) | 20.1895 | 0.844165 | ||||||||
\(573\) | 11.8691 | 0.495839 | ||||||||
\(574\) | 46.4471 | 1.93867 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −29.5033 | −1.22824 | −0.614119 | − | 0.789213i | \(-0.710489\pi\) | ||||
−0.614119 | + | 0.789213i | \(0.710489\pi\) | |||||||
\(578\) | −10.3431 | −0.430216 | ||||||||
\(579\) | −2.97729 | −0.123732 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 27.4286 | 1.13793 | ||||||||
\(582\) | 11.5260 | 0.477768 | ||||||||
\(583\) | −22.7902 | −0.943875 | ||||||||
\(584\) | −8.52601 | −0.352809 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.36581 | −0.345589 | ||||||||
\(587\) | 14.4740 | 0.597406 | 0.298703 | − | 0.954346i | \(-0.403446\pi\) | ||||
0.298703 | + | 0.954346i | \(0.403446\pi\) | |||||||
\(588\) | −7.16019 | −0.295281 | ||||||||
\(589\) | −38.0586 | −1.56818 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.8918 | −1.02391 | ||||||||
\(592\) | −2.58010 | −0.106041 | ||||||||
\(593\) | 5.86911 | 0.241015 | 0.120508 | − | 0.992712i | \(-0.461548\pi\) | ||||
0.120508 | + | 0.992712i | \(0.461548\pi\) | |||||||
\(594\) | −3.18291 | −0.130596 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.6862 | 0.683493 | ||||||||
\(597\) | −22.4492 | −0.918785 | ||||||||
\(598\) | 6.34310 | 0.259389 | ||||||||
\(599\) | −3.95457 | −0.161580 | −0.0807898 | − | 0.996731i | \(-0.525744\pi\) | ||||
−0.0807898 | + | 0.996731i | \(0.525744\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.23492 | 0.376700 | 0.188350 | − | 0.982102i | \(-0.439686\pi\) | ||||
0.188350 | + | 0.982102i | \(0.439686\pi\) | |||||||
\(602\) | −38.9211 | −1.58631 | ||||||||
\(603\) | −10.6862 | −0.435176 | ||||||||
\(604\) | −7.16019 | −0.291344 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7.70891 | 0.313153 | ||||||||
\(607\) | 48.7448 | 1.97849 | 0.989245 | − | 0.146266i | \(-0.0467257\pi\) | ||||
0.989245 | + | 0.146266i | \(0.0467257\pi\) | |||||||
\(608\) | −6.34310 | −0.257247 | ||||||||
\(609\) | 3.76300 | 0.152485 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21.2056 | −0.857888 | ||||||||
\(612\) | 2.58010 | 0.104294 | ||||||||
\(613\) | 3.67754 | 0.148534 | 0.0742671 | − | 0.997238i | \(-0.476338\pi\) | ||||
0.0742671 | + | 0.997238i | \(0.476338\pi\) | |||||||
\(614\) | −33.7089 | −1.36038 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.9773 | 0.482579 | ||||||||
\(617\) | 0.794381 | 0.0319806 | 0.0159903 | − | 0.999872i | \(-0.494910\pi\) | ||||
0.0159903 | + | 0.999872i | \(0.494910\pi\) | |||||||
\(618\) | 3.39719 | 0.136655 | ||||||||
\(619\) | −4.57802 | −0.184006 | −0.0920031 | − | 0.995759i | \(-0.529327\pi\) | ||||
−0.0920031 | + | 0.995759i | \(0.529327\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | −1.86252 | −0.0746802 | ||||||||
\(623\) | 17.2349 | 0.690502 | ||||||||
\(624\) | −6.34310 | −0.253927 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 26.8984 | 1.07508 | ||||||||
\(627\) | 20.1895 | 0.806291 | ||||||||
\(628\) | −22.2122 | −0.886364 | ||||||||
\(629\) | −6.65690 | −0.265428 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.1808 | −1.24129 | −0.620645 | − | 0.784092i | \(-0.713129\pi\) | ||||
−0.620645 | + | 0.784092i | \(0.713129\pi\) | |||||||
\(632\) | −3.18291 | −0.126609 | ||||||||
\(633\) | −19.5553 | −0.777254 | ||||||||
\(634\) | 11.0000 | 0.436866 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 7.16019 | 0.283920 | ||||||||
\(637\) | 45.4178 | 1.79952 | ||||||||
\(638\) | −3.18291 | −0.126012 | ||||||||
\(639\) | 1.81709 | 0.0718831 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 46.7295 | 1.84571 | 0.922853 | − | 0.385152i | \(-0.125851\pi\) | ||||
0.922853 | + | 0.385152i | \(0.125851\pi\) | |||||||
\(642\) | 6.68620 | 0.263883 | ||||||||
\(643\) | −4.81709 | −0.189968 | −0.0949838 | − | 0.995479i | \(-0.530280\pi\) | ||||
−0.0949838 | + | 0.995479i | \(0.530280\pi\) | |||||||
\(644\) | 3.76300 | 0.148283 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16.3658 | −0.643904 | ||||||||
\(647\) | −19.4967 | −0.766495 | −0.383247 | − | 0.923646i | \(-0.625194\pi\) | ||||
−0.383247 | + | 0.923646i | \(0.625194\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −13.8960 | −0.545465 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −22.5780 | −0.884902 | ||||||||
\(652\) | 8.68620 | 0.340178 | ||||||||
\(653\) | 30.5260 | 1.19457 | 0.597287 | − | 0.802027i | \(-0.296245\pi\) | ||||
0.597287 | + | 0.802027i | \(0.296245\pi\) | |||||||
\(654\) | −5.78572 | −0.226239 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 12.3431 | 0.481917 | ||||||||
\(657\) | −8.52601 | −0.332631 | ||||||||
\(658\) | −12.5801 | −0.490423 | ||||||||
\(659\) | −2.49463 | −0.0971769 | −0.0485885 | − | 0.998819i | \(-0.515472\pi\) | ||||
−0.0485885 | + | 0.998819i | \(0.515472\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.7337 | −0.650866 | −0.325433 | − | 0.945565i | \(-0.605510\pi\) | ||||
−0.325433 | + | 0.945565i | \(0.605510\pi\) | |||||||
\(662\) | −6.18291 | −0.240305 | ||||||||
\(663\) | −16.3658 | −0.635596 | ||||||||
\(664\) | 7.28901 | 0.282868 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.58010 | −0.0999767 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 25.2349 | 0.976368 | ||||||||
\(669\) | 28.8984 | 1.11728 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.85714 | −0.187508 | ||||||||
\(672\) | −3.76300 | −0.145161 | ||||||||
\(673\) | −2.73821 | −0.105550 | −0.0527752 | − | 0.998606i | \(-0.516807\pi\) | ||||
−0.0527752 | + | 0.998606i | \(0.516807\pi\) | |||||||
\(674\) | 15.1602 | 0.583949 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 27.2349 | 1.04750 | ||||||||
\(677\) | −38.1040 | −1.46446 | −0.732228 | − | 0.681059i | \(-0.761520\pi\) | ||||
−0.732228 | + | 0.681059i | \(0.761520\pi\) | |||||||
\(678\) | −0.580097 | −0.0222785 | ||||||||
\(679\) | −43.3724 | −1.66448 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.6321 | 0.675664 | ||||||||
\(682\) | 19.0974 | 0.731279 | ||||||||
\(683\) | 24.6234 | 0.942190 | 0.471095 | − | 0.882082i | \(-0.343859\pi\) | ||||
0.471095 | + | 0.882082i | \(0.343859\pi\) | |||||||
\(684\) | −6.34310 | −0.242534 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.602810 | 0.0230154 | ||||||||
\(687\) | 11.8918 | 0.453701 | ||||||||
\(688\) | −10.3431 | −0.394327 | ||||||||
\(689\) | −45.4178 | −1.73028 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.2935 | 1.64696 | 0.823482 | − | 0.567343i | \(-0.192029\pi\) | ||||
0.823482 | + | 0.567343i | \(0.192029\pi\) | |||||||
\(692\) | −0.817094 | −0.0310612 | ||||||||
\(693\) | 11.9773 | 0.454980 | ||||||||
\(694\) | −29.8918 | −1.13468 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.00000 | 0.0379049 | ||||||||
\(697\) | 31.8464 | 1.20627 | ||||||||
\(698\) | 7.02930 | 0.266063 | ||||||||
\(699\) | 9.02930 | 0.341520 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.00659 | 0.340174 | 0.170087 | − | 0.985429i | \(-0.445595\pi\) | ||||
0.170087 | + | 0.985429i | \(0.445595\pi\) | |||||||
\(702\) | −6.34310 | −0.239405 | ||||||||
\(703\) | 16.3658 | 0.617248 | ||||||||
\(704\) | 3.18291 | 0.119960 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −26.2349 | −0.987364 | ||||||||
\(707\) | −29.0087 | −1.09098 | ||||||||
\(708\) | 4.36581 | 0.164077 | ||||||||
\(709\) | 22.3183 | 0.838182 | 0.419091 | − | 0.907944i | \(-0.362349\pi\) | ||||
0.419091 | + | 0.907944i | \(0.362349\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.18291 | −0.119368 | ||||||||
\(712\) | 4.58010 | 0.171646 | ||||||||
\(713\) | 6.00000 | 0.224702 | ||||||||
\(714\) | −9.70891 | −0.363347 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.16019 | −0.118102 | ||||||||
\(717\) | 20.0747 | 0.749704 | ||||||||
\(718\) | 19.5033 | 0.727856 | ||||||||
\(719\) | −32.1829 | −1.20022 | −0.600110 | − | 0.799918i | \(-0.704877\pi\) | ||||
−0.600110 | + | 0.799918i | \(0.704877\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.7836 | −0.476088 | ||||||||
\(722\) | 21.2349 | 0.790282 | ||||||||
\(723\) | 23.0066 | 0.855624 | ||||||||
\(724\) | 3.37448 | 0.125411 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.869107 | 0.0322556 | ||||||||
\(727\) | −32.3658 | −1.20038 | −0.600191 | − | 0.799857i | \(-0.704909\pi\) | ||||
−0.600191 | + | 0.799857i | \(0.704909\pi\) | |||||||
\(728\) | 23.8691 | 0.884648 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26.6862 | −0.987025 | ||||||||
\(732\) | 1.52601 | 0.0564028 | ||||||||
\(733\) | 34.6841 | 1.28109 | 0.640544 | − | 0.767922i | \(-0.278709\pi\) | ||||
0.640544 | + | 0.767922i | \(0.278709\pi\) | |||||||
\(734\) | −33.5033 | −1.23663 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −34.0132 | −1.25289 | ||||||||
\(738\) | 12.3431 | 0.454356 | ||||||||
\(739\) | 45.1441 | 1.66065 | 0.830326 | − | 0.557278i | \(-0.188154\pi\) | ||||
0.830326 | + | 0.557278i | \(0.188154\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 40.2349 | 1.47807 | ||||||||
\(742\) | −26.9438 | −0.989139 | ||||||||
\(743\) | −3.02930 | −0.111134 | −0.0555671 | − | 0.998455i | \(-0.517697\pi\) | ||||
−0.0555671 | + | 0.998455i | \(0.517697\pi\) | |||||||
\(744\) | −6.00000 | −0.219971 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 10.1515 | 0.371674 | ||||||||
\(747\) | 7.28901 | 0.266691 | ||||||||
\(748\) | 8.21221 | 0.300268 | ||||||||
\(749\) | −25.1602 | −0.919333 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.3410 | −0.450330 | −0.225165 | − | 0.974321i | \(-0.572292\pi\) | ||||
−0.225165 | + | 0.974321i | \(0.572292\pi\) | |||||||
\(752\) | −3.34310 | −0.121910 | ||||||||
\(753\) | 10.9459 | 0.398891 | ||||||||
\(754\) | −6.34310 | −0.231002 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.76300 | −0.136859 | ||||||||
\(757\) | 6.00208 | 0.218149 | 0.109075 | − | 0.994034i | \(-0.465211\pi\) | ||||
0.109075 | + | 0.994034i | \(0.465211\pi\) | |||||||
\(758\) | 20.5780 | 0.747427 | ||||||||
\(759\) | −3.18291 | −0.115532 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.2977 | −0.953290 | −0.476645 | − | 0.879096i | \(-0.658147\pi\) | ||||
−0.476645 | + | 0.879096i | \(0.658147\pi\) | |||||||
\(762\) | −14.3204 | −0.518773 | ||||||||
\(763\) | 21.7717 | 0.788187 | ||||||||
\(764\) | −11.8691 | −0.429409 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.22833 | −0.0443814 | ||||||||
\(767\) | −27.6928 | −0.999929 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −45.8918 | −1.65490 | −0.827451 | − | 0.561538i | \(-0.810210\pi\) | ||||
−0.827451 | + | 0.561538i | \(0.810210\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.3204 | −0.587764 | ||||||||
\(772\) | 2.97729 | 0.107155 | ||||||||
\(773\) | 37.5846 | 1.35182 | 0.675912 | − | 0.736982i | \(-0.263750\pi\) | ||||
0.675912 | + | 0.736982i | \(0.263750\pi\) | |||||||
\(774\) | −10.3431 | −0.371775 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −11.5260 | −0.413760 | ||||||||
\(777\) | 9.70891 | 0.348305 | ||||||||
\(778\) | 35.3724 | 1.26816 | ||||||||
\(779\) | −78.2935 | −2.80516 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.78364 | 0.206955 | ||||||||
\(782\) | 2.58010 | 0.0922641 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | 7.16019 | 0.255721 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −15.8918 | −0.566842 | ||||||||
\(787\) | −20.9211 | −0.745757 | −0.372879 | − | 0.927880i | \(-0.621629\pi\) | ||||
−0.372879 | + | 0.927880i | \(0.621629\pi\) | |||||||
\(788\) | 24.8918 | 0.886734 | ||||||||
\(789\) | 29.0066 | 1.03266 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.18291 | 0.0776152 | ||||||||
\(792\) | 3.18291 | 0.113100 | ||||||||
\(793\) | −9.67961 | −0.343733 | ||||||||
\(794\) | −31.0066 | −1.10038 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 22.4492 | 0.795691 | ||||||||
\(797\) | 46.5326 | 1.64827 | 0.824135 | − | 0.566394i | \(-0.191662\pi\) | ||||
0.824135 | + | 0.566394i | \(0.191662\pi\) | |||||||
\(798\) | 23.8691 | 0.844957 | ||||||||
\(799\) | −8.62552 | −0.305149 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.58010 | 0.161830 | ||||||||
\(802\) | 15.2056 | 0.536929 | ||||||||
\(803\) | −27.1375 | −0.957661 | ||||||||
\(804\) | 10.6862 | 0.376873 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 38.0586 | 1.34056 | ||||||||
\(807\) | 26.1895 | 0.921914 | ||||||||
\(808\) | −7.70891 | −0.271199 | ||||||||
\(809\) | 26.1895 | 0.920774 | 0.460387 | − | 0.887718i | \(-0.347711\pi\) | ||||
0.460387 | + | 0.887718i | \(0.347711\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.4112 | 0.365588 | 0.182794 | − | 0.983151i | \(-0.441486\pi\) | ||||
0.182794 | + | 0.983151i | \(0.441486\pi\) | |||||||
\(812\) | −3.76300 | −0.132056 | ||||||||
\(813\) | −6.36581 | −0.223259 | ||||||||
\(814\) | −8.21221 | −0.287838 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.58010 | −0.0903215 | ||||||||
\(817\) | 65.6073 | 2.29531 | ||||||||
\(818\) | −2.57143 | −0.0899080 | ||||||||
\(819\) | 23.8691 | 0.834054 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.8171 | 1.14532 | 0.572662 | − | 0.819791i | \(-0.305911\pi\) | ||||
0.572662 | + | 0.819791i | \(0.305911\pi\) | |||||||
\(822\) | −15.4199 | −0.537831 | ||||||||
\(823\) | −20.5780 | −0.717305 | −0.358652 | − | 0.933471i | \(-0.616764\pi\) | ||||
−0.358652 | + | 0.933471i | \(0.616764\pi\) | |||||||
\(824\) | −3.39719 | −0.118347 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16.4286 | −0.571623 | ||||||||
\(827\) | 21.1982 | 0.737132 | 0.368566 | − | 0.929602i | \(-0.379849\pi\) | ||||
0.368566 | + | 0.929602i | \(0.379849\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | −3.29109 | −0.114304 | −0.0571521 | − | 0.998365i | \(-0.518202\pi\) | ||||
−0.0571521 | + | 0.998365i | \(0.518202\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.50329 | −0.329666 | ||||||||
\(832\) | 6.34310 | 0.219907 | ||||||||
\(833\) | 18.4740 | 0.640086 | ||||||||
\(834\) | −3.02271 | −0.104668 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −20.1895 | −0.698268 | ||||||||
\(837\) | −6.00000 | −0.207390 | ||||||||
\(838\) | −19.0768 | −0.658997 | ||||||||
\(839\) | −20.0813 | −0.693284 | −0.346642 | − | 0.937998i | \(-0.612678\pi\) | ||||
−0.346642 | + | 0.937998i | \(0.612678\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | −15.8918 | −0.547668 | ||||||||
\(843\) | −27.2663 | −0.939101 | ||||||||
\(844\) | 19.5553 | 0.673121 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.34310 | −0.114938 | ||||||||
\(847\) | −3.27045 | −0.112374 | ||||||||
\(848\) | −7.16019 | −0.245882 | ||||||||
\(849\) | −10.3204 | −0.354195 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.58010 | −0.0884446 | ||||||||
\(852\) | −1.81709 | −0.0622526 | ||||||||
\(853\) | −32.9211 | −1.12720 | −0.563599 | − | 0.826049i | \(-0.690584\pi\) | ||||
−0.563599 | + | 0.826049i | \(0.690584\pi\) | |||||||
\(854\) | −5.74237 | −0.196500 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.68620 | −0.228530 | ||||||||
\(857\) | 46.5780 | 1.59107 | 0.795537 | − | 0.605904i | \(-0.207189\pi\) | ||||
0.795537 | + | 0.605904i | \(0.207189\pi\) | |||||||
\(858\) | −20.1895 | −0.689258 | ||||||||
\(859\) | −42.0132 | −1.43347 | −0.716736 | − | 0.697345i | \(-0.754365\pi\) | ||||
−0.716736 | + | 0.697345i | \(0.754365\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −46.4471 | −1.58291 | ||||||||
\(862\) | −24.2122 | −0.824671 | ||||||||
\(863\) | −15.5553 | −0.529509 | −0.264754 | − | 0.964316i | \(-0.585291\pi\) | ||||
−0.264754 | + | 0.964316i | \(0.585291\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 12.2122 | 0.414988 | ||||||||
\(867\) | 10.3431 | 0.351270 | ||||||||
\(868\) | 22.5780 | 0.766348 | ||||||||
\(869\) | −10.1309 | −0.343667 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −67.7836 | −2.29676 | ||||||||
\(872\) | 5.78572 | 0.195929 | ||||||||
\(873\) | −11.5260 | −0.390096 | ||||||||
\(874\) | −6.34310 | −0.214559 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.52601 | 0.288067 | ||||||||
\(877\) | −14.0000 | −0.472746 | −0.236373 | − | 0.971662i | \(-0.575959\pi\) | ||||
−0.236373 | + | 0.971662i | \(0.575959\pi\) | |||||||
\(878\) | −0.794381 | −0.0268091 | ||||||||
\(879\) | 8.36581 | 0.282172 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.4740 | 0.352878 | 0.176439 | − | 0.984312i | \(-0.443542\pi\) | ||||
0.176439 | + | 0.984312i | \(0.443542\pi\) | |||||||
\(882\) | 7.16019 | 0.241096 | ||||||||
\(883\) | −35.8757 | −1.20731 | −0.603657 | − | 0.797244i | \(-0.706290\pi\) | ||||
−0.603657 | + | 0.797244i | \(0.706290\pi\) | |||||||
\(884\) | 16.3658 | 0.550442 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14.2122 | −0.477468 | ||||||||
\(887\) | −7.29767 | −0.245032 | −0.122516 | − | 0.992467i | \(-0.539096\pi\) | ||||
−0.122516 | + | 0.992467i | \(0.539096\pi\) | |||||||
\(888\) | 2.58010 | 0.0865824 | ||||||||
\(889\) | 53.8877 | 1.80733 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.18291 | 0.106631 | ||||||||
\(892\) | −28.8984 | −0.967590 | ||||||||
\(893\) | 21.2056 | 0.709619 | ||||||||
\(894\) | −16.6862 | −0.558070 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.76300 | 0.125713 | ||||||||
\(897\) | −6.34310 | −0.211790 | ||||||||
\(898\) | 1.05201 | 0.0351061 | ||||||||
\(899\) | −6.00000 | −0.200111 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.4740 | −0.615458 | ||||||||
\(902\) | 39.2869 | 1.30811 | ||||||||
\(903\) | 38.9211 | 1.29521 | ||||||||
\(904\) | 0.580097 | 0.0192937 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 7.16019 | 0.237882 | ||||||||
\(907\) | −40.7089 | −1.35172 | −0.675859 | − | 0.737031i | \(-0.736227\pi\) | ||||
−0.675859 | + | 0.737031i | \(0.736227\pi\) | |||||||
\(908\) | −17.6321 | −0.585142 | ||||||||
\(909\) | −7.70891 | −0.255689 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.7089 | 0.752380 | 0.376190 | − | 0.926543i | \(-0.377234\pi\) | ||||
0.376190 | + | 0.926543i | \(0.377234\pi\) | |||||||
\(912\) | 6.34310 | 0.210041 | ||||||||
\(913\) | 23.2002 | 0.767816 | ||||||||
\(914\) | 0.686200 | 0.0226975 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.8918 | −0.392917 | ||||||||
\(917\) | 59.8010 | 1.97480 | ||||||||
\(918\) | −2.58010 | −0.0851559 | ||||||||
\(919\) | −26.5801 | −0.876796 | −0.438398 | − | 0.898781i | \(-0.644454\pi\) | ||||
−0.438398 | + | 0.898781i | \(0.644454\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 33.7089 | 1.11075 | ||||||||
\(922\) | −29.5780 | −0.974100 | ||||||||
\(923\) | 11.5260 | 0.379383 | ||||||||
\(924\) | −11.9773 | −0.394024 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 12.0000 | 0.394344 | ||||||||
\(927\) | −3.39719 | −0.111578 | ||||||||
\(928\) | −1.00000 | −0.0328266 | ||||||||
\(929\) | 36.5553 | 1.19934 | 0.599670 | − | 0.800247i | \(-0.295298\pi\) | ||||
0.599670 | + | 0.800247i | \(0.295298\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −45.4178 | −1.48851 | ||||||||
\(932\) | −9.02930 | −0.295765 | ||||||||
\(933\) | 1.86252 | 0.0609761 | ||||||||
\(934\) | 29.2890 | 0.958366 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.34310 | 0.207331 | ||||||||
\(937\) | 19.3724 | 0.632869 | 0.316434 | − | 0.948614i | \(-0.397514\pi\) | ||||
0.316434 | + | 0.948614i | \(0.397514\pi\) | |||||||
\(938\) | −40.2122 | −1.31298 | ||||||||
\(939\) | −26.8984 | −0.877796 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36.3204 | −1.18401 | −0.592005 | − | 0.805934i | \(-0.701664\pi\) | ||||
−0.592005 | + | 0.805934i | \(0.701664\pi\) | |||||||
\(942\) | 22.2122 | 0.723713 | ||||||||
\(943\) | 12.3431 | 0.401947 | ||||||||
\(944\) | −4.36581 | −0.142095 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −32.9211 | −1.07036 | ||||||||
\(947\) | −5.63419 | −0.183086 | −0.0915432 | − | 0.995801i | \(-0.529180\pi\) | ||||
−0.0915432 | + | 0.995801i | \(0.529180\pi\) | |||||||
\(948\) | 3.18291 | 0.103376 | ||||||||
\(949\) | −54.0813 | −1.75555 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.0000 | −0.356699 | ||||||||
\(952\) | 9.70891 | 0.314668 | ||||||||
\(953\) | 28.9005 | 0.936179 | 0.468089 | − | 0.883681i | \(-0.344943\pi\) | ||||
0.468089 | + | 0.883681i | \(0.344943\pi\) | |||||||
\(954\) | −7.16019 | −0.231820 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −20.0747 | −0.649263 | ||||||||
\(957\) | 3.18291 | 0.102889 | ||||||||
\(958\) | 15.9145 | 0.514175 | ||||||||
\(959\) | 58.0251 | 1.87373 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | −16.3658 | −0.527655 | ||||||||
\(963\) | −6.68620 | −0.215460 | ||||||||
\(964\) | −23.0066 | −0.740992 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.76300 | −0.121073 | ||||||||
\(967\) | −12.3658 | −0.397658 | −0.198829 | − | 0.980034i | \(-0.563714\pi\) | ||||
−0.198829 | + | 0.980034i | \(0.563714\pi\) | |||||||
\(968\) | −0.869107 | −0.0279341 | ||||||||
\(969\) | 16.3658 | 0.525746 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.9125 | −1.08830 | −0.544151 | − | 0.838987i | \(-0.683148\pi\) | ||||
−0.544151 | + | 0.838987i | \(0.683148\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 11.3745 | 0.364649 | ||||||||
\(974\) | −38.9438 | −1.24784 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.52601 | −0.0488463 | ||||||||
\(977\) | −41.3703 | −1.32355 | −0.661777 | − | 0.749701i | \(-0.730197\pi\) | ||||
−0.661777 | + | 0.749701i | \(0.730197\pi\) | |||||||
\(978\) | −8.68620 | −0.277754 | ||||||||
\(979\) | 14.5780 | 0.465916 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.78572 | 0.184724 | ||||||||
\(982\) | 27.4806 | 0.876941 | ||||||||
\(983\) | −1.91453 | −0.0610641 | −0.0305320 | − | 0.999534i | \(-0.509720\pi\) | ||||
−0.0305320 | + | 0.999534i | \(0.509720\pi\) | |||||||
\(984\) | −12.3431 | −0.393484 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.58010 | −0.0821670 | ||||||||
\(987\) | 12.5801 | 0.400429 | ||||||||
\(988\) | −40.2349 | −1.28004 | ||||||||
\(989\) | −10.3431 | −0.328891 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.31380 | 0.105266 | 0.0526332 | − | 0.998614i | \(-0.483239\pi\) | ||||
0.0526332 | + | 0.998614i | \(0.483239\pi\) | |||||||
\(992\) | 6.00000 | 0.190500 | ||||||||
\(993\) | 6.18291 | 0.196209 | ||||||||
\(994\) | 6.83773 | 0.216880 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −7.28901 | −0.230961 | ||||||||
\(997\) | 8.70891 | 0.275814 | 0.137907 | − | 0.990445i | \(-0.455962\pi\) | ||||
0.137907 | + | 0.990445i | \(0.455962\pi\) | |||||||
\(998\) | 6.97729 | 0.220862 | ||||||||
\(999\) | 2.58010 | 0.0816307 |
(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 | 3450.2.a.bs.1.3 | yes | 3 | |
5.2 | odd | 4 | 3450.2.d.ba.2899.6 | 6 | |||
5.3 | odd | 4 | 3450.2.d.ba.2899.1 | 6 | |||
5.4 | even | 2 | 3450.2.a.bp.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3450.2.a.bp.1.1 | ✓ | 3 | 5.4 | even | 2 | ||
3450.2.a.bs.1.3 | yes | 3 | 1.1 | even | 1 | trivial | |
3450.2.d.ba.2899.1 | 6 | 5.3 | odd | 4 | |||
3450.2.d.ba.2899.6 | 6 | 5.2 | odd | 4 |