Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [325,2,Mod(1,325)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(325, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("325.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.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: | \(2.59513806569\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 65) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 325.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.73205 | 1.22474 | 0.612372 | − | 0.790569i | \(-0.290215\pi\) | ||||
0.612372 | + | 0.790569i | \(0.290215\pi\) | |||||||
\(3\) | −2.73205 | −1.57735 | −0.788675 | − | 0.614810i | \(-0.789233\pi\) | ||||
−0.788675 | + | 0.614810i | \(0.789233\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −4.73205 | −1.93185 | ||||||||
\(7\) | −2.00000 | −0.755929 | −0.377964 | − | 0.925820i | \(-0.623376\pi\) | ||||
−0.377964 | + | 0.925820i | \(0.623376\pi\) | |||||||
\(8\) | −1.73205 | −0.612372 | ||||||||
\(9\) | 4.46410 | 1.48803 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.73205 | −1.42677 | −0.713384 | − | 0.700774i | \(-0.752838\pi\) | ||||
−0.713384 | + | 0.700774i | \(0.752838\pi\) | |||||||
\(12\) | −2.73205 | −0.788675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −3.46410 | −0.925820 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.00000 | −1.25000 | ||||||||
\(17\) | 3.46410 | 0.840168 | 0.420084 | − | 0.907485i | \(-0.362001\pi\) | ||||
0.420084 | + | 0.907485i | \(0.362001\pi\) | |||||||
\(18\) | 7.73205 | 1.82246 | ||||||||
\(19\) | −6.19615 | −1.42149 | −0.710747 | − | 0.703447i | \(-0.751643\pi\) | ||||
−0.710747 | + | 0.703447i | \(0.751643\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.46410 | 1.19236 | ||||||||
\(22\) | −8.19615 | −1.74743 | ||||||||
\(23\) | −1.26795 | −0.264386 | −0.132193 | − | 0.991224i | \(-0.542202\pi\) | ||||
−0.132193 | + | 0.991224i | \(0.542202\pi\) | |||||||
\(24\) | 4.73205 | 0.965926 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.73205 | −0.339683 | ||||||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | −2.00000 | −0.377964 | ||||||||
\(29\) | −2.53590 | −0.470905 | −0.235452 | − | 0.971886i | \(-0.575657\pi\) | ||||
−0.235452 | + | 0.971886i | \(0.575657\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.1962 | 1.83128 | 0.915642 | − | 0.401996i | \(-0.131683\pi\) | ||||
0.915642 | + | 0.401996i | \(0.131683\pi\) | |||||||
\(32\) | −5.19615 | −0.918559 | ||||||||
\(33\) | 12.9282 | 2.25051 | ||||||||
\(34\) | 6.00000 | 1.02899 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.46410 | 0.744017 | ||||||||
\(37\) | 4.00000 | 0.657596 | 0.328798 | − | 0.944400i | \(-0.393356\pi\) | ||||
0.328798 | + | 0.944400i | \(0.393356\pi\) | |||||||
\(38\) | −10.7321 | −1.74097 | ||||||||
\(39\) | 2.73205 | 0.437478 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.46410 | 0.541002 | 0.270501 | − | 0.962720i | \(-0.412811\pi\) | ||||
0.270501 | + | 0.962720i | \(0.412811\pi\) | |||||||
\(42\) | 9.46410 | 1.46034 | ||||||||
\(43\) | 0.196152 | 0.0299130 | 0.0149565 | − | 0.999888i | \(-0.495239\pi\) | ||||
0.0149565 | + | 0.999888i | \(0.495239\pi\) | |||||||
\(44\) | −4.73205 | −0.713384 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.19615 | −0.323805 | ||||||||
\(47\) | −6.00000 | −0.875190 | −0.437595 | − | 0.899172i | \(-0.644170\pi\) | ||||
−0.437595 | + | 0.899172i | \(0.644170\pi\) | |||||||
\(48\) | 13.6603 | 1.97169 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.46410 | −1.32524 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | −10.3923 | −1.42749 | −0.713746 | − | 0.700404i | \(-0.753003\pi\) | ||||
−0.713746 | + | 0.700404i | \(0.753003\pi\) | |||||||
\(54\) | −6.92820 | −0.942809 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.46410 | 0.462910 | ||||||||
\(57\) | 16.9282 | 2.24220 | ||||||||
\(58\) | −4.39230 | −0.576738 | ||||||||
\(59\) | 9.12436 | 1.18789 | 0.593945 | − | 0.804506i | \(-0.297570\pi\) | ||||
0.593945 | + | 0.804506i | \(0.297570\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.39230 | −1.07452 | −0.537262 | − | 0.843415i | \(-0.680541\pi\) | ||||
−0.537262 | + | 0.843415i | \(0.680541\pi\) | |||||||
\(62\) | 17.6603 | 2.24285 | ||||||||
\(63\) | −8.92820 | −1.12485 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 22.3923 | 2.75630 | ||||||||
\(67\) | −6.39230 | −0.780944 | −0.390472 | − | 0.920615i | \(-0.627688\pi\) | ||||
−0.390472 | + | 0.920615i | \(0.627688\pi\) | |||||||
\(68\) | 3.46410 | 0.420084 | ||||||||
\(69\) | 3.46410 | 0.417029 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.73205 | 0.561591 | 0.280796 | − | 0.959768i | \(-0.409402\pi\) | ||||
0.280796 | + | 0.959768i | \(0.409402\pi\) | |||||||
\(72\) | −7.73205 | −0.911231 | ||||||||
\(73\) | 4.00000 | 0.468165 | 0.234082 | − | 0.972217i | \(-0.424791\pi\) | ||||
0.234082 | + | 0.972217i | \(0.424791\pi\) | |||||||
\(74\) | 6.92820 | 0.805387 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.19615 | −0.710747 | ||||||||
\(77\) | 9.46410 | 1.07853 | ||||||||
\(78\) | 4.73205 | 0.535799 | ||||||||
\(79\) | −8.39230 | −0.944208 | −0.472104 | − | 0.881543i | \(-0.656505\pi\) | ||||
−0.472104 | + | 0.881543i | \(0.656505\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.46410 | −0.273789 | ||||||||
\(82\) | 6.00000 | 0.662589 | ||||||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | 5.46410 | 0.596182 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.339746 | 0.0366357 | ||||||||
\(87\) | 6.92820 | 0.742781 | ||||||||
\(88\) | 8.19615 | 0.873713 | ||||||||
\(89\) | −12.9282 | −1.37039 | −0.685193 | − | 0.728361i | \(-0.740282\pi\) | ||||
−0.685193 | + | 0.728361i | \(0.740282\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | 0.209657 | ||||||||
\(92\) | −1.26795 | −0.132193 | ||||||||
\(93\) | −27.8564 | −2.88857 | ||||||||
\(94\) | −10.3923 | −1.07188 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 14.1962 | 1.44889 | ||||||||
\(97\) | −2.00000 | −0.203069 | −0.101535 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101535 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(98\) | −5.19615 | −0.524891 | ||||||||
\(99\) | −21.1244 | −2.12308 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.928203 | −0.0923597 | −0.0461798 | − | 0.998933i | \(-0.514705\pi\) | ||||
−0.0461798 | + | 0.998933i | \(0.514705\pi\) | |||||||
\(102\) | −16.3923 | −1.62308 | ||||||||
\(103\) | 0.196152 | 0.0193275 | 0.00966374 | − | 0.999953i | \(-0.496924\pi\) | ||||
0.00966374 | + | 0.999953i | \(0.496924\pi\) | |||||||
\(104\) | 1.73205 | 0.169842 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −18.0000 | −1.74831 | ||||||||
\(107\) | −17.6603 | −1.70728 | −0.853641 | − | 0.520862i | \(-0.825610\pi\) | ||||
−0.853641 | + | 0.520862i | \(0.825610\pi\) | |||||||
\(108\) | −4.00000 | −0.384900 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.9282 | −1.03726 | ||||||||
\(112\) | 10.0000 | 0.944911 | ||||||||
\(113\) | −8.53590 | −0.802990 | −0.401495 | − | 0.915861i | \(-0.631509\pi\) | ||||
−0.401495 | + | 0.915861i | \(0.631509\pi\) | |||||||
\(114\) | 29.3205 | 2.74612 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.53590 | −0.235452 | ||||||||
\(117\) | −4.46410 | −0.412706 | ||||||||
\(118\) | 15.8038 | 1.45486 | ||||||||
\(119\) | −6.92820 | −0.635107 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.3923 | 1.03566 | ||||||||
\(122\) | −14.5359 | −1.31602 | ||||||||
\(123\) | −9.46410 | −0.853349 | ||||||||
\(124\) | 10.1962 | 0.915642 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −15.4641 | −1.37765 | ||||||||
\(127\) | −16.1962 | −1.43718 | −0.718588 | − | 0.695436i | \(-0.755211\pi\) | ||||
−0.718588 | + | 0.695436i | \(0.755211\pi\) | |||||||
\(128\) | 12.1244 | 1.07165 | ||||||||
\(129\) | −0.535898 | −0.0471832 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 12.9282 | 1.12526 | ||||||||
\(133\) | 12.3923 | 1.07455 | ||||||||
\(134\) | −11.0718 | −0.956458 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.00000 | −0.514496 | ||||||||
\(137\) | −0.928203 | −0.0793018 | −0.0396509 | − | 0.999214i | \(-0.512625\pi\) | ||||
−0.0396509 | + | 0.999214i | \(0.512625\pi\) | |||||||
\(138\) | 6.00000 | 0.510754 | ||||||||
\(139\) | 12.3923 | 1.05110 | 0.525551 | − | 0.850762i | \(-0.323859\pi\) | ||||
0.525551 | + | 0.850762i | \(0.323859\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.3923 | 1.38048 | ||||||||
\(142\) | 8.19615 | 0.687806 | ||||||||
\(143\) | 4.73205 | 0.395714 | ||||||||
\(144\) | −22.3205 | −1.86004 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.92820 | 0.573382 | ||||||||
\(147\) | 8.19615 | 0.676007 | ||||||||
\(148\) | 4.00000 | 0.328798 | ||||||||
\(149\) | −7.85641 | −0.643622 | −0.321811 | − | 0.946804i | \(-0.604292\pi\) | ||||
−0.321811 | + | 0.946804i | \(0.604292\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.80385 | −0.146795 | −0.0733975 | − | 0.997303i | \(-0.523384\pi\) | ||||
−0.0733975 | + | 0.997303i | \(0.523384\pi\) | |||||||
\(152\) | 10.7321 | 0.870484 | ||||||||
\(153\) | 15.4641 | 1.25020 | ||||||||
\(154\) | 16.3923 | 1.32093 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.73205 | 0.218739 | ||||||||
\(157\) | 10.0000 | 0.798087 | 0.399043 | − | 0.916932i | \(-0.369342\pi\) | ||||
0.399043 | + | 0.916932i | \(0.369342\pi\) | |||||||
\(158\) | −14.5359 | −1.15641 | ||||||||
\(159\) | 28.3923 | 2.25166 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.53590 | 0.199857 | ||||||||
\(162\) | −4.26795 | −0.335322 | ||||||||
\(163\) | 14.3923 | 1.12729 | 0.563646 | − | 0.826016i | \(-0.309398\pi\) | ||||
0.563646 | + | 0.826016i | \(0.309398\pi\) | |||||||
\(164\) | 3.46410 | 0.270501 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.3923 | 0.806599 | ||||||||
\(167\) | 0.928203 | 0.0718265 | 0.0359133 | − | 0.999355i | \(-0.488566\pi\) | ||||
0.0359133 | + | 0.999355i | \(0.488566\pi\) | |||||||
\(168\) | −9.46410 | −0.730171 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −27.6603 | −2.11523 | ||||||||
\(172\) | 0.196152 | 0.0149565 | ||||||||
\(173\) | −8.53590 | −0.648972 | −0.324486 | − | 0.945890i | \(-0.605191\pi\) | ||||
−0.324486 | + | 0.945890i | \(0.605191\pi\) | |||||||
\(174\) | 12.0000 | 0.909718 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 23.6603 | 1.78346 | ||||||||
\(177\) | −24.9282 | −1.87372 | ||||||||
\(178\) | −22.3923 | −1.67837 | ||||||||
\(179\) | −18.9282 | −1.41476 | −0.707380 | − | 0.706833i | \(-0.750123\pi\) | ||||
−0.707380 | + | 0.706833i | \(0.750123\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.392305 | 0.0291598 | 0.0145799 | − | 0.999894i | \(-0.495359\pi\) | ||||
0.0145799 | + | 0.999894i | \(0.495359\pi\) | |||||||
\(182\) | 3.46410 | 0.256776 | ||||||||
\(183\) | 22.9282 | 1.69490 | ||||||||
\(184\) | 2.19615 | 0.161903 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −48.2487 | −3.53777 | ||||||||
\(187\) | −16.3923 | −1.19872 | ||||||||
\(188\) | −6.00000 | −0.437595 | ||||||||
\(189\) | 8.00000 | 0.581914 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.07180 | −0.366982 | −0.183491 | − | 0.983021i | \(-0.558740\pi\) | ||||
−0.183491 | + | 0.983021i | \(0.558740\pi\) | |||||||
\(192\) | −2.73205 | −0.197169 | ||||||||
\(193\) | 10.0000 | 0.719816 | 0.359908 | − | 0.932988i | \(-0.382808\pi\) | ||||
0.359908 | + | 0.932988i | \(0.382808\pi\) | |||||||
\(194\) | −3.46410 | −0.248708 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | 12.9282 | 0.921096 | 0.460548 | − | 0.887635i | \(-0.347653\pi\) | ||||
0.460548 | + | 0.887635i | \(0.347653\pi\) | |||||||
\(198\) | −36.5885 | −2.60023 | ||||||||
\(199\) | 20.0000 | 1.41776 | 0.708881 | − | 0.705328i | \(-0.249200\pi\) | ||||
0.708881 | + | 0.705328i | \(0.249200\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 17.4641 | 1.23182 | ||||||||
\(202\) | −1.60770 | −0.113117 | ||||||||
\(203\) | 5.07180 | 0.355970 | ||||||||
\(204\) | −9.46410 | −0.662620 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.339746 | 0.0236712 | ||||||||
\(207\) | −5.66025 | −0.393415 | ||||||||
\(208\) | 5.00000 | 0.346688 | ||||||||
\(209\) | 29.3205 | 2.02814 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.00000 | 0.550743 | 0.275371 | − | 0.961338i | \(-0.411199\pi\) | ||||
0.275371 | + | 0.961338i | \(0.411199\pi\) | |||||||
\(212\) | −10.3923 | −0.713746 | ||||||||
\(213\) | −12.9282 | −0.885826 | ||||||||
\(214\) | −30.5885 | −2.09098 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 6.92820 | 0.471405 | ||||||||
\(217\) | −20.3923 | −1.38432 | ||||||||
\(218\) | 3.46410 | 0.234619 | ||||||||
\(219\) | −10.9282 | −0.738460 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.46410 | −0.233021 | ||||||||
\(222\) | −18.9282 | −1.27038 | ||||||||
\(223\) | −2.00000 | −0.133930 | −0.0669650 | − | 0.997755i | \(-0.521332\pi\) | ||||
−0.0669650 | + | 0.997755i | \(0.521332\pi\) | |||||||
\(224\) | 10.3923 | 0.694365 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.7846 | −0.983458 | ||||||||
\(227\) | 3.46410 | 0.229920 | 0.114960 | − | 0.993370i | \(-0.463326\pi\) | ||||
0.114960 | + | 0.993370i | \(0.463326\pi\) | |||||||
\(228\) | 16.9282 | 1.12110 | ||||||||
\(229\) | 6.39230 | 0.422415 | 0.211208 | − | 0.977441i | \(-0.432260\pi\) | ||||
0.211208 | + | 0.977441i | \(0.432260\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −25.8564 | −1.70123 | ||||||||
\(232\) | 4.39230 | 0.288369 | ||||||||
\(233\) | 6.00000 | 0.393073 | 0.196537 | − | 0.980497i | \(-0.437031\pi\) | ||||
0.196537 | + | 0.980497i | \(0.437031\pi\) | |||||||
\(234\) | −7.73205 | −0.505460 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.12436 | 0.593945 | ||||||||
\(237\) | 22.9282 | 1.48935 | ||||||||
\(238\) | −12.0000 | −0.777844 | ||||||||
\(239\) | −14.1962 | −0.918273 | −0.459136 | − | 0.888366i | \(-0.651841\pi\) | ||||
−0.459136 | + | 0.888366i | \(0.651841\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.39230 | −0.154102 | −0.0770510 | − | 0.997027i | \(-0.524550\pi\) | ||||
−0.0770510 | + | 0.997027i | \(0.524550\pi\) | |||||||
\(242\) | 19.7321 | 1.26842 | ||||||||
\(243\) | 18.7321 | 1.20166 | ||||||||
\(244\) | −8.39230 | −0.537262 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −16.3923 | −1.04514 | ||||||||
\(247\) | 6.19615 | 0.394252 | ||||||||
\(248\) | −17.6603 | −1.12143 | ||||||||
\(249\) | −16.3923 | −1.03882 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.4641 | −1.35480 | −0.677401 | − | 0.735614i | \(-0.736894\pi\) | ||||
−0.677401 | + | 0.735614i | \(0.736894\pi\) | |||||||
\(252\) | −8.92820 | −0.562424 | ||||||||
\(253\) | 6.00000 | 0.377217 | ||||||||
\(254\) | −28.0526 | −1.76017 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.0000 | 1.18750 | ||||||||
\(257\) | −19.8564 | −1.23861 | −0.619304 | − | 0.785151i | \(-0.712585\pi\) | ||||
−0.619304 | + | 0.785151i | \(0.712585\pi\) | |||||||
\(258\) | −0.928203 | −0.0577874 | ||||||||
\(259\) | −8.00000 | −0.497096 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.3205 | −0.700722 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.26795 | −0.0781851 | −0.0390925 | − | 0.999236i | \(-0.512447\pi\) | ||||
−0.0390925 | + | 0.999236i | \(0.512447\pi\) | |||||||
\(264\) | −22.3923 | −1.37815 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 21.4641 | 1.31605 | ||||||||
\(267\) | 35.3205 | 2.16158 | ||||||||
\(268\) | −6.39230 | −0.390472 | ||||||||
\(269\) | −19.8564 | −1.21067 | −0.605333 | − | 0.795972i | \(-0.706960\pi\) | ||||
−0.605333 | + | 0.795972i | \(0.706960\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.9808 | 1.88195 | 0.940974 | − | 0.338480i | \(-0.109913\pi\) | ||||
0.940974 | + | 0.338480i | \(0.109913\pi\) | |||||||
\(272\) | −17.3205 | −1.05021 | ||||||||
\(273\) | −5.46410 | −0.330702 | ||||||||
\(274\) | −1.60770 | −0.0971244 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.46410 | 0.208514 | ||||||||
\(277\) | 26.3923 | 1.58576 | 0.792880 | − | 0.609378i | \(-0.208581\pi\) | ||||
0.792880 | + | 0.609378i | \(0.208581\pi\) | |||||||
\(278\) | 21.4641 | 1.28733 | ||||||||
\(279\) | 45.5167 | 2.72501 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.3923 | 1.33581 | 0.667906 | − | 0.744245i | \(-0.267191\pi\) | ||||
0.667906 | + | 0.744245i | \(0.267191\pi\) | |||||||
\(282\) | 28.3923 | 1.69074 | ||||||||
\(283\) | −32.5885 | −1.93718 | −0.968591 | − | 0.248658i | \(-0.920010\pi\) | ||||
−0.968591 | + | 0.248658i | \(0.920010\pi\) | |||||||
\(284\) | 4.73205 | 0.280796 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.19615 | 0.484649 | ||||||||
\(287\) | −6.92820 | −0.408959 | ||||||||
\(288\) | −23.1962 | −1.36685 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.46410 | 0.320311 | ||||||||
\(292\) | 4.00000 | 0.234082 | ||||||||
\(293\) | 5.07180 | 0.296298 | 0.148149 | − | 0.988965i | \(-0.452669\pi\) | ||||
0.148149 | + | 0.988965i | \(0.452669\pi\) | |||||||
\(294\) | 14.1962 | 0.827936 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.92820 | −0.402694 | ||||||||
\(297\) | 18.9282 | 1.09833 | ||||||||
\(298\) | −13.6077 | −0.788273 | ||||||||
\(299\) | 1.26795 | 0.0733274 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.392305 | −0.0226121 | ||||||||
\(302\) | −3.12436 | −0.179786 | ||||||||
\(303\) | 2.53590 | 0.145684 | ||||||||
\(304\) | 30.9808 | 1.77687 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 26.7846 | 1.53117 | ||||||||
\(307\) | 18.7846 | 1.07209 | 0.536047 | − | 0.844188i | \(-0.319917\pi\) | ||||
0.536047 | + | 0.844188i | \(0.319917\pi\) | |||||||
\(308\) | 9.46410 | 0.539267 | ||||||||
\(309\) | −0.535898 | −0.0304862 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.3923 | −0.929522 | −0.464761 | − | 0.885436i | \(-0.653860\pi\) | ||||
−0.464761 | + | 0.885436i | \(0.653860\pi\) | |||||||
\(312\) | −4.73205 | −0.267900 | ||||||||
\(313\) | 14.3923 | 0.813501 | 0.406751 | − | 0.913539i | \(-0.366662\pi\) | ||||
0.406751 | + | 0.913539i | \(0.366662\pi\) | |||||||
\(314\) | 17.3205 | 0.977453 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.39230 | −0.472104 | ||||||||
\(317\) | −24.0000 | −1.34797 | −0.673987 | − | 0.738743i | \(-0.735420\pi\) | ||||
−0.673987 | + | 0.738743i | \(0.735420\pi\) | |||||||
\(318\) | 49.1769 | 2.75770 | ||||||||
\(319\) | 12.0000 | 0.671871 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 48.2487 | 2.69298 | ||||||||
\(322\) | 4.39230 | 0.244774 | ||||||||
\(323\) | −21.4641 | −1.19429 | ||||||||
\(324\) | −2.46410 | −0.136895 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 24.9282 | 1.38065 | ||||||||
\(327\) | −5.46410 | −0.302166 | ||||||||
\(328\) | −6.00000 | −0.331295 | ||||||||
\(329\) | 12.0000 | 0.661581 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.58846 | 0.142274 | 0.0711372 | − | 0.997467i | \(-0.477337\pi\) | ||||
0.0711372 | + | 0.997467i | \(0.477337\pi\) | |||||||
\(332\) | 6.00000 | 0.329293 | ||||||||
\(333\) | 17.8564 | 0.978525 | ||||||||
\(334\) | 1.60770 | 0.0879692 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −27.3205 | −1.49046 | ||||||||
\(337\) | 26.3923 | 1.43768 | 0.718840 | − | 0.695175i | \(-0.244673\pi\) | ||||
0.718840 | + | 0.695175i | \(0.244673\pi\) | |||||||
\(338\) | 1.73205 | 0.0942111 | ||||||||
\(339\) | 23.3205 | 1.26660 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −48.2487 | −2.61281 | ||||||||
\(342\) | −47.9090 | −2.59062 | ||||||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | −0.339746 | −0.0183179 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.7846 | −0.794826 | ||||||||
\(347\) | 5.66025 | 0.303858 | 0.151929 | − | 0.988391i | \(-0.451451\pi\) | ||||
0.151929 | + | 0.988391i | \(0.451451\pi\) | |||||||
\(348\) | 6.92820 | 0.371391 | ||||||||
\(349\) | −14.3923 | −0.770402 | −0.385201 | − | 0.922833i | \(-0.625868\pi\) | ||||
−0.385201 | + | 0.922833i | \(0.625868\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.00000 | 0.213504 | ||||||||
\(352\) | 24.5885 | 1.31057 | ||||||||
\(353\) | 27.7128 | 1.47500 | 0.737502 | − | 0.675345i | \(-0.236005\pi\) | ||||
0.737502 | + | 0.675345i | \(0.236005\pi\) | |||||||
\(354\) | −43.1769 | −2.29483 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −12.9282 | −0.685193 | ||||||||
\(357\) | 18.9282 | 1.00179 | ||||||||
\(358\) | −32.7846 | −1.73272 | ||||||||
\(359\) | −2.19615 | −0.115908 | −0.0579542 | − | 0.998319i | \(-0.518458\pi\) | ||||
−0.0579542 | + | 0.998319i | \(0.518458\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.3923 | 1.02065 | ||||||||
\(362\) | 0.679492 | 0.0357133 | ||||||||
\(363\) | −31.1244 | −1.63361 | ||||||||
\(364\) | 2.00000 | 0.104828 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 39.7128 | 2.07582 | ||||||||
\(367\) | −11.8038 | −0.616156 | −0.308078 | − | 0.951361i | \(-0.599686\pi\) | ||||
−0.308078 | + | 0.951361i | \(0.599686\pi\) | |||||||
\(368\) | 6.33975 | 0.330482 | ||||||||
\(369\) | 15.4641 | 0.805029 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.7846 | 1.07908 | ||||||||
\(372\) | −27.8564 | −1.44429 | ||||||||
\(373\) | 10.0000 | 0.517780 | 0.258890 | − | 0.965907i | \(-0.416643\pi\) | ||||
0.258890 | + | 0.965907i | \(0.416643\pi\) | |||||||
\(374\) | −28.3923 | −1.46813 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.3923 | 0.535942 | ||||||||
\(377\) | 2.53590 | 0.130605 | ||||||||
\(378\) | 13.8564 | 0.712697 | ||||||||
\(379\) | 18.9808 | 0.974976 | 0.487488 | − | 0.873130i | \(-0.337913\pi\) | ||||
0.487488 | + | 0.873130i | \(0.337913\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 44.2487 | 2.26693 | ||||||||
\(382\) | −8.78461 | −0.449460 | ||||||||
\(383\) | −12.9282 | −0.660600 | −0.330300 | − | 0.943876i | \(-0.607150\pi\) | ||||
−0.330300 | + | 0.943876i | \(0.607150\pi\) | |||||||
\(384\) | −33.1244 | −1.69037 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.3205 | 0.881591 | ||||||||
\(387\) | 0.875644 | 0.0445115 | ||||||||
\(388\) | −2.00000 | −0.101535 | ||||||||
\(389\) | 6.00000 | 0.304212 | 0.152106 | − | 0.988364i | \(-0.451394\pi\) | ||||
0.152106 | + | 0.988364i | \(0.451394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.39230 | −0.222128 | ||||||||
\(392\) | 5.19615 | 0.262445 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 22.3923 | 1.12811 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −21.1244 | −1.06154 | ||||||||
\(397\) | −28.7846 | −1.44466 | −0.722329 | − | 0.691549i | \(-0.756928\pi\) | ||||
−0.722329 | + | 0.691549i | \(0.756928\pi\) | |||||||
\(398\) | 34.6410 | 1.73640 | ||||||||
\(399\) | −33.8564 | −1.69494 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −36.9282 | −1.84411 | −0.922053 | − | 0.387063i | \(-0.873490\pi\) | ||||
−0.922053 | + | 0.387063i | \(0.873490\pi\) | |||||||
\(402\) | 30.2487 | 1.50867 | ||||||||
\(403\) | −10.1962 | −0.507907 | ||||||||
\(404\) | −0.928203 | −0.0461798 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.78461 | 0.435973 | ||||||||
\(407\) | −18.9282 | −0.938236 | ||||||||
\(408\) | 16.3923 | 0.811540 | ||||||||
\(409\) | −17.6077 | −0.870644 | −0.435322 | − | 0.900275i | \(-0.643366\pi\) | ||||
−0.435322 | + | 0.900275i | \(0.643366\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.53590 | 0.125087 | ||||||||
\(412\) | 0.196152 | 0.00966374 | ||||||||
\(413\) | −18.2487 | −0.897960 | ||||||||
\(414\) | −9.80385 | −0.481833 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.19615 | 0.254762 | ||||||||
\(417\) | −33.8564 | −1.65796 | ||||||||
\(418\) | 50.7846 | 2.48396 | ||||||||
\(419\) | −2.53590 | −0.123887 | −0.0619434 | − | 0.998080i | \(-0.519730\pi\) | ||||
−0.0619434 | + | 0.998080i | \(0.519730\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.7846 | −1.50035 | −0.750175 | − | 0.661239i | \(-0.770031\pi\) | ||||
−0.750175 | + | 0.661239i | \(0.770031\pi\) | |||||||
\(422\) | 13.8564 | 0.674519 | ||||||||
\(423\) | −26.7846 | −1.30231 | ||||||||
\(424\) | 18.0000 | 0.874157 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −22.3923 | −1.08491 | ||||||||
\(427\) | 16.7846 | 0.812264 | ||||||||
\(428\) | −17.6603 | −0.853641 | ||||||||
\(429\) | −12.9282 | −0.624180 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.5167 | −1.22909 | −0.614547 | − | 0.788880i | \(-0.710661\pi\) | ||||
−0.614547 | + | 0.788880i | \(0.710661\pi\) | |||||||
\(432\) | 20.0000 | 0.962250 | ||||||||
\(433\) | −34.7846 | −1.67164 | −0.835821 | − | 0.549002i | \(-0.815008\pi\) | ||||
−0.835821 | + | 0.549002i | \(0.815008\pi\) | |||||||
\(434\) | −35.3205 | −1.69544 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | 0.0957826 | ||||||||
\(437\) | 7.85641 | 0.375823 | ||||||||
\(438\) | −18.9282 | −0.904425 | ||||||||
\(439\) | 32.0000 | 1.52728 | 0.763638 | − | 0.645644i | \(-0.223411\pi\) | ||||
0.763638 | + | 0.645644i | \(0.223411\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.3923 | −0.637729 | ||||||||
\(442\) | −6.00000 | −0.285391 | ||||||||
\(443\) | 16.9808 | 0.806780 | 0.403390 | − | 0.915028i | \(-0.367832\pi\) | ||||
0.403390 | + | 0.915028i | \(0.367832\pi\) | |||||||
\(444\) | −10.9282 | −0.518630 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.46410 | −0.164030 | ||||||||
\(447\) | 21.4641 | 1.01522 | ||||||||
\(448\) | −2.00000 | −0.0944911 | ||||||||
\(449\) | 20.5359 | 0.969149 | 0.484574 | − | 0.874750i | \(-0.338974\pi\) | ||||
0.484574 | + | 0.874750i | \(0.338974\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.3923 | −0.771883 | ||||||||
\(452\) | −8.53590 | −0.401495 | ||||||||
\(453\) | 4.92820 | 0.231547 | ||||||||
\(454\) | 6.00000 | 0.281594 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −29.3205 | −1.37306 | ||||||||
\(457\) | −10.7846 | −0.504483 | −0.252241 | − | 0.967664i | \(-0.581168\pi\) | ||||
−0.252241 | + | 0.967664i | \(0.581168\pi\) | |||||||
\(458\) | 11.0718 | 0.517351 | ||||||||
\(459\) | −13.8564 | −0.646762 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.46410 | −0.161339 | −0.0806696 | − | 0.996741i | \(-0.525706\pi\) | ||||
−0.0806696 | + | 0.996741i | \(0.525706\pi\) | |||||||
\(462\) | −44.7846 | −2.08357 | ||||||||
\(463\) | 2.39230 | 0.111180 | 0.0555899 | − | 0.998454i | \(-0.482296\pi\) | ||||
0.0555899 | + | 0.998454i | \(0.482296\pi\) | |||||||
\(464\) | 12.6795 | 0.588631 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.3923 | 0.481414 | ||||||||
\(467\) | −27.8038 | −1.28661 | −0.643304 | − | 0.765611i | \(-0.722437\pi\) | ||||
−0.643304 | + | 0.765611i | \(0.722437\pi\) | |||||||
\(468\) | −4.46410 | −0.206353 | ||||||||
\(469\) | 12.7846 | 0.590338 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −27.3205 | −1.25886 | ||||||||
\(472\) | −15.8038 | −0.727431 | ||||||||
\(473\) | −0.928203 | −0.0426788 | ||||||||
\(474\) | 39.7128 | 1.82407 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.92820 | −0.317554 | ||||||||
\(477\) | −46.3923 | −2.12416 | ||||||||
\(478\) | −24.5885 | −1.12465 | ||||||||
\(479\) | 35.6603 | 1.62936 | 0.814679 | − | 0.579912i | \(-0.196913\pi\) | ||||
0.814679 | + | 0.579912i | \(0.196913\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.00000 | −0.182384 | ||||||||
\(482\) | −4.14359 | −0.188736 | ||||||||
\(483\) | −6.92820 | −0.315244 | ||||||||
\(484\) | 11.3923 | 0.517832 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 32.4449 | 1.47173 | ||||||||
\(487\) | 26.3923 | 1.19595 | 0.597975 | − | 0.801515i | \(-0.295972\pi\) | ||||
0.597975 | + | 0.801515i | \(0.295972\pi\) | |||||||
\(488\) | 14.5359 | 0.658009 | ||||||||
\(489\) | −39.3205 | −1.77813 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.53590 | −0.114443 | −0.0572217 | − | 0.998361i | \(-0.518224\pi\) | ||||
−0.0572217 | + | 0.998361i | \(0.518224\pi\) | |||||||
\(492\) | −9.46410 | −0.426675 | ||||||||
\(493\) | −8.78461 | −0.395639 | ||||||||
\(494\) | 10.7321 | 0.482858 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −50.9808 | −2.28910 | ||||||||
\(497\) | −9.46410 | −0.424523 | ||||||||
\(498\) | −28.3923 | −1.27229 | ||||||||
\(499\) | −38.9808 | −1.74502 | −0.872509 | − | 0.488598i | \(-0.837509\pi\) | ||||
−0.872509 | + | 0.488598i | \(0.837509\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.53590 | −0.113296 | ||||||||
\(502\) | −37.1769 | −1.65929 | ||||||||
\(503\) | −19.5167 | −0.870205 | −0.435102 | − | 0.900381i | \(-0.643288\pi\) | ||||
−0.435102 | + | 0.900381i | \(0.643288\pi\) | |||||||
\(504\) | 15.4641 | 0.688826 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 10.3923 | 0.461994 | ||||||||
\(507\) | −2.73205 | −0.121335 | ||||||||
\(508\) | −16.1962 | −0.718588 | ||||||||
\(509\) | 39.4641 | 1.74922 | 0.874608 | − | 0.484831i | \(-0.161119\pi\) | ||||
0.874608 | + | 0.484831i | \(0.161119\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.00000 | −0.353899 | ||||||||
\(512\) | 8.66025 | 0.382733 | ||||||||
\(513\) | 24.7846 | 1.09427 | ||||||||
\(514\) | −34.3923 | −1.51698 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.535898 | −0.0235916 | ||||||||
\(517\) | 28.3923 | 1.24869 | ||||||||
\(518\) | −13.8564 | −0.608816 | ||||||||
\(519\) | 23.3205 | 1.02366 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.3923 | −1.24389 | −0.621945 | − | 0.783061i | \(-0.713657\pi\) | ||||
−0.621945 | + | 0.783061i | \(0.713657\pi\) | |||||||
\(522\) | −19.6077 | −0.858206 | ||||||||
\(523\) | 24.1962 | 1.05802 | 0.529012 | − | 0.848614i | \(-0.322563\pi\) | ||||
0.529012 | + | 0.848614i | \(0.322563\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.19615 | −0.0957568 | ||||||||
\(527\) | 35.3205 | 1.53859 | ||||||||
\(528\) | −64.6410 | −2.81314 | ||||||||
\(529\) | −21.3923 | −0.930100 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 40.7321 | 1.76762 | ||||||||
\(532\) | 12.3923 | 0.537275 | ||||||||
\(533\) | −3.46410 | −0.150047 | ||||||||
\(534\) | 61.1769 | 2.64738 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 11.0718 | 0.478229 | ||||||||
\(537\) | 51.7128 | 2.23157 | ||||||||
\(538\) | −34.3923 | −1.48276 | ||||||||
\(539\) | 14.1962 | 0.611472 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.3923 | −1.13469 | −0.567347 | − | 0.823479i | \(-0.692030\pi\) | ||||
−0.567347 | + | 0.823479i | \(0.692030\pi\) | |||||||
\(542\) | 53.6603 | 2.30491 | ||||||||
\(543\) | −1.07180 | −0.0459952 | ||||||||
\(544\) | −18.0000 | −0.771744 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −9.46410 | −0.405026 | ||||||||
\(547\) | 12.1962 | 0.521470 | 0.260735 | − | 0.965410i | \(-0.416035\pi\) | ||||
0.260735 | + | 0.965410i | \(0.416035\pi\) | |||||||
\(548\) | −0.928203 | −0.0396509 | ||||||||
\(549\) | −37.4641 | −1.59893 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.7128 | 0.669388 | ||||||||
\(552\) | −6.00000 | −0.255377 | ||||||||
\(553\) | 16.7846 | 0.713754 | ||||||||
\(554\) | 45.7128 | 1.94215 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.3923 | 0.525551 | ||||||||
\(557\) | −1.85641 | −0.0786585 | −0.0393292 | − | 0.999226i | \(-0.512522\pi\) | ||||
−0.0393292 | + | 0.999226i | \(0.512522\pi\) | |||||||
\(558\) | 78.8372 | 3.33744 | ||||||||
\(559\) | −0.196152 | −0.00829636 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 44.7846 | 1.89081 | ||||||||
\(562\) | 38.7846 | 1.63603 | ||||||||
\(563\) | 22.0526 | 0.929405 | 0.464702 | − | 0.885467i | \(-0.346161\pi\) | ||||
0.464702 | + | 0.885467i | \(0.346161\pi\) | |||||||
\(564\) | 16.3923 | 0.690241 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −56.4449 | −2.37255 | ||||||||
\(567\) | 4.92820 | 0.206965 | ||||||||
\(568\) | −8.19615 | −0.343903 | ||||||||
\(569\) | −2.53590 | −0.106310 | −0.0531552 | − | 0.998586i | \(-0.516928\pi\) | ||||
−0.0531552 | + | 0.998586i | \(0.516928\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.3923 | 1.52297 | 0.761485 | − | 0.648182i | \(-0.224470\pi\) | ||||
0.761485 | + | 0.648182i | \(0.224470\pi\) | |||||||
\(572\) | 4.73205 | 0.197857 | ||||||||
\(573\) | 13.8564 | 0.578860 | ||||||||
\(574\) | −12.0000 | −0.500870 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.46410 | 0.186004 | ||||||||
\(577\) | 4.00000 | 0.166522 | 0.0832611 | − | 0.996528i | \(-0.473466\pi\) | ||||
0.0832611 | + | 0.996528i | \(0.473466\pi\) | |||||||
\(578\) | −8.66025 | −0.360219 | ||||||||
\(579\) | −27.3205 | −1.13540 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.0000 | −0.497844 | ||||||||
\(582\) | 9.46410 | 0.392300 | ||||||||
\(583\) | 49.1769 | 2.03670 | ||||||||
\(584\) | −6.92820 | −0.286691 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.78461 | 0.362889 | ||||||||
\(587\) | 8.53590 | 0.352314 | 0.176157 | − | 0.984362i | \(-0.443633\pi\) | ||||
0.176157 | + | 0.984362i | \(0.443633\pi\) | |||||||
\(588\) | 8.19615 | 0.338004 | ||||||||
\(589\) | −63.1769 | −2.60316 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −35.3205 | −1.45289 | ||||||||
\(592\) | −20.0000 | −0.821995 | ||||||||
\(593\) | −26.7846 | −1.09991 | −0.549956 | − | 0.835194i | \(-0.685356\pi\) | ||||
−0.549956 | + | 0.835194i | \(0.685356\pi\) | |||||||
\(594\) | 32.7846 | 1.34517 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.85641 | −0.321811 | ||||||||
\(597\) | −54.6410 | −2.23631 | ||||||||
\(598\) | 2.19615 | 0.0898074 | ||||||||
\(599\) | −7.60770 | −0.310842 | −0.155421 | − | 0.987848i | \(-0.549673\pi\) | ||||
−0.155421 | + | 0.987848i | \(0.549673\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 43.5692 | 1.77723 | 0.888613 | − | 0.458658i | \(-0.151670\pi\) | ||||
0.888613 | + | 0.458658i | \(0.151670\pi\) | |||||||
\(602\) | −0.679492 | −0.0276940 | ||||||||
\(603\) | −28.5359 | −1.16207 | ||||||||
\(604\) | −1.80385 | −0.0733975 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.39230 | 0.178425 | ||||||||
\(607\) | −24.9808 | −1.01394 | −0.506969 | − | 0.861964i | \(-0.669234\pi\) | ||||
−0.506969 | + | 0.861964i | \(0.669234\pi\) | |||||||
\(608\) | 32.1962 | 1.30573 | ||||||||
\(609\) | −13.8564 | −0.561490 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.00000 | 0.242734 | ||||||||
\(612\) | 15.4641 | 0.625099 | ||||||||
\(613\) | −26.0000 | −1.05013 | −0.525065 | − | 0.851062i | \(-0.675959\pi\) | ||||
−0.525065 | + | 0.851062i | \(0.675959\pi\) | |||||||
\(614\) | 32.5359 | 1.31304 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −16.3923 | −0.660465 | ||||||||
\(617\) | −33.7128 | −1.35723 | −0.678613 | − | 0.734496i | \(-0.737419\pi\) | ||||
−0.678613 | + | 0.734496i | \(0.737419\pi\) | |||||||
\(618\) | −0.928203 | −0.0373378 | ||||||||
\(619\) | 6.98076 | 0.280581 | 0.140290 | − | 0.990110i | \(-0.455196\pi\) | ||||
0.140290 | + | 0.990110i | \(0.455196\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.07180 | 0.203524 | ||||||||
\(622\) | −28.3923 | −1.13843 | ||||||||
\(623\) | 25.8564 | 1.03592 | ||||||||
\(624\) | −13.6603 | −0.546848 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 24.9282 | 0.996331 | ||||||||
\(627\) | −80.1051 | −3.19909 | ||||||||
\(628\) | 10.0000 | 0.399043 | ||||||||
\(629\) | 13.8564 | 0.552491 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.80385 | 0.231048 | 0.115524 | − | 0.993305i | \(-0.463145\pi\) | ||||
0.115524 | + | 0.993305i | \(0.463145\pi\) | |||||||
\(632\) | 14.5359 | 0.578207 | ||||||||
\(633\) | −21.8564 | −0.868714 | ||||||||
\(634\) | −41.5692 | −1.65092 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 28.3923 | 1.12583 | ||||||||
\(637\) | 3.00000 | 0.118864 | ||||||||
\(638\) | 20.7846 | 0.822871 | ||||||||
\(639\) | 21.1244 | 0.835667 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.9282 | 0.510633 | 0.255317 | − | 0.966857i | \(-0.417820\pi\) | ||||
0.255317 | + | 0.966857i | \(0.417820\pi\) | |||||||
\(642\) | 83.5692 | 3.29821 | ||||||||
\(643\) | 6.78461 | 0.267559 | 0.133779 | − | 0.991011i | \(-0.457289\pi\) | ||||
0.133779 | + | 0.991011i | \(0.457289\pi\) | |||||||
\(644\) | 2.53590 | 0.0999284 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −37.1769 | −1.46271 | ||||||||
\(647\) | −22.0526 | −0.866976 | −0.433488 | − | 0.901159i | \(-0.642717\pi\) | ||||
−0.433488 | + | 0.901159i | \(0.642717\pi\) | |||||||
\(648\) | 4.26795 | 0.167661 | ||||||||
\(649\) | −43.1769 | −1.69484 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 55.7128 | 2.18356 | ||||||||
\(652\) | 14.3923 | 0.563646 | ||||||||
\(653\) | −7.85641 | −0.307445 | −0.153722 | − | 0.988114i | \(-0.549126\pi\) | ||||
−0.153722 | + | 0.988114i | \(0.549126\pi\) | |||||||
\(654\) | −9.46410 | −0.370076 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −17.3205 | −0.676252 | ||||||||
\(657\) | 17.8564 | 0.696645 | ||||||||
\(658\) | 20.7846 | 0.810268 | ||||||||
\(659\) | −21.4641 | −0.836123 | −0.418061 | − | 0.908419i | \(-0.637290\pi\) | ||||
−0.418061 | + | 0.908419i | \(0.637290\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.7846 | 0.419473 | 0.209736 | − | 0.977758i | \(-0.432739\pi\) | ||||
0.209736 | + | 0.977758i | \(0.432739\pi\) | |||||||
\(662\) | 4.48334 | 0.174250 | ||||||||
\(663\) | 9.46410 | 0.367555 | ||||||||
\(664\) | −10.3923 | −0.403300 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 30.9282 | 1.19844 | ||||||||
\(667\) | 3.21539 | 0.124500 | ||||||||
\(668\) | 0.928203 | 0.0359133 | ||||||||
\(669\) | 5.46410 | 0.211254 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 39.7128 | 1.53310 | ||||||||
\(672\) | −28.3923 | −1.09526 | ||||||||
\(673\) | 14.3923 | 0.554783 | 0.277391 | − | 0.960757i | \(-0.410530\pi\) | ||||
0.277391 | + | 0.960757i | \(0.410530\pi\) | |||||||
\(674\) | 45.7128 | 1.76079 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −10.3923 | −0.399409 | −0.199704 | − | 0.979856i | \(-0.563998\pi\) | ||||
−0.199704 | + | 0.979856i | \(0.563998\pi\) | |||||||
\(678\) | 40.3923 | 1.55126 | ||||||||
\(679\) | 4.00000 | 0.153506 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.46410 | −0.362665 | ||||||||
\(682\) | −83.5692 | −3.20003 | ||||||||
\(683\) | −32.5359 | −1.24495 | −0.622476 | − | 0.782639i | \(-0.713873\pi\) | ||||
−0.622476 | + | 0.782639i | \(0.713873\pi\) | |||||||
\(684\) | −27.6603 | −1.05762 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 34.6410 | 1.32260 | ||||||||
\(687\) | −17.4641 | −0.666297 | ||||||||
\(688\) | −0.980762 | −0.0373912 | ||||||||
\(689\) | 10.3923 | 0.395915 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −47.7654 | −1.81708 | −0.908540 | − | 0.417797i | \(-0.862802\pi\) | ||||
−0.908540 | + | 0.417797i | \(0.862802\pi\) | |||||||
\(692\) | −8.53590 | −0.324486 | ||||||||
\(693\) | 42.2487 | 1.60490 | ||||||||
\(694\) | 9.80385 | 0.372149 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −12.0000 | −0.454859 | ||||||||
\(697\) | 12.0000 | 0.454532 | ||||||||
\(698\) | −24.9282 | −0.943546 | ||||||||
\(699\) | −16.3923 | −0.620014 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.0000 | 1.58632 | 0.793159 | − | 0.609015i | \(-0.208435\pi\) | ||||
0.793159 | + | 0.609015i | \(0.208435\pi\) | |||||||
\(702\) | 6.92820 | 0.261488 | ||||||||
\(703\) | −24.7846 | −0.934769 | ||||||||
\(704\) | −4.73205 | −0.178346 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 48.0000 | 1.80650 | ||||||||
\(707\) | 1.85641 | 0.0698174 | ||||||||
\(708\) | −24.9282 | −0.936859 | ||||||||
\(709\) | 30.3923 | 1.14141 | 0.570703 | − | 0.821156i | \(-0.306671\pi\) | ||||
0.570703 | + | 0.821156i | \(0.306671\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −37.4641 | −1.40501 | ||||||||
\(712\) | 22.3923 | 0.839187 | ||||||||
\(713\) | −12.9282 | −0.484165 | ||||||||
\(714\) | 32.7846 | 1.22693 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −18.9282 | −0.707380 | ||||||||
\(717\) | 38.7846 | 1.44844 | ||||||||
\(718\) | −3.80385 | −0.141958 | ||||||||
\(719\) | −25.8564 | −0.964281 | −0.482141 | − | 0.876094i | \(-0.660141\pi\) | ||||
−0.482141 | + | 0.876094i | \(0.660141\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.392305 | −0.0146102 | ||||||||
\(722\) | 33.5885 | 1.25003 | ||||||||
\(723\) | 6.53590 | 0.243073 | ||||||||
\(724\) | 0.392305 | 0.0145799 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −53.9090 | −2.00075 | ||||||||
\(727\) | −44.5885 | −1.65369 | −0.826847 | − | 0.562427i | \(-0.809868\pi\) | ||||
−0.826847 | + | 0.562427i | \(0.809868\pi\) | |||||||
\(728\) | −3.46410 | −0.128388 | ||||||||
\(729\) | −43.7846 | −1.62165 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.679492 | 0.0251319 | ||||||||
\(732\) | 22.9282 | 0.847451 | ||||||||
\(733\) | −38.0000 | −1.40356 | −0.701781 | − | 0.712393i | \(-0.747612\pi\) | ||||
−0.701781 | + | 0.712393i | \(0.747612\pi\) | |||||||
\(734\) | −20.4449 | −0.754634 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.58846 | 0.242854 | ||||||||
\(737\) | 30.2487 | 1.11423 | ||||||||
\(738\) | 26.7846 | 0.985955 | ||||||||
\(739\) | −18.1962 | −0.669356 | −0.334678 | − | 0.942332i | \(-0.608628\pi\) | ||||
−0.334678 | + | 0.942332i | \(0.608628\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.9282 | −0.621873 | ||||||||
\(742\) | 36.0000 | 1.32160 | ||||||||
\(743\) | 16.1436 | 0.592251 | 0.296126 | − | 0.955149i | \(-0.404305\pi\) | ||||
0.296126 | + | 0.955149i | \(0.404305\pi\) | |||||||
\(744\) | 48.2487 | 1.76888 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 17.3205 | 0.634149 | ||||||||
\(747\) | 26.7846 | 0.979998 | ||||||||
\(748\) | −16.3923 | −0.599362 | ||||||||
\(749\) | 35.3205 | 1.29058 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.3923 | 1.32797 | 0.663987 | − | 0.747744i | \(-0.268863\pi\) | ||||
0.663987 | + | 0.747744i | \(0.268863\pi\) | |||||||
\(752\) | 30.0000 | 1.09399 | ||||||||
\(753\) | 58.6410 | 2.13700 | ||||||||
\(754\) | 4.39230 | 0.159958 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 8.00000 | 0.290957 | ||||||||
\(757\) | 2.39230 | 0.0869498 | 0.0434749 | − | 0.999055i | \(-0.486157\pi\) | ||||
0.0434749 | + | 0.999055i | \(0.486157\pi\) | |||||||
\(758\) | 32.8756 | 1.19410 | ||||||||
\(759\) | −16.3923 | −0.595003 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.8564 | −0.719794 | −0.359897 | − | 0.932992i | \(-0.617188\pi\) | ||||
−0.359897 | + | 0.932992i | \(0.617188\pi\) | |||||||
\(762\) | 76.6410 | 2.77641 | ||||||||
\(763\) | −4.00000 | −0.144810 | ||||||||
\(764\) | −5.07180 | −0.183491 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −22.3923 | −0.809067 | ||||||||
\(767\) | −9.12436 | −0.329461 | ||||||||
\(768\) | −51.9090 | −1.87310 | ||||||||
\(769\) | 34.7846 | 1.25437 | 0.627183 | − | 0.778872i | \(-0.284208\pi\) | ||||
0.627183 | + | 0.778872i | \(0.284208\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 54.2487 | 1.95372 | ||||||||
\(772\) | 10.0000 | 0.359908 | ||||||||
\(773\) | −6.92820 | −0.249190 | −0.124595 | − | 0.992208i | \(-0.539763\pi\) | ||||
−0.124595 | + | 0.992208i | \(0.539763\pi\) | |||||||
\(774\) | 1.51666 | 0.0545152 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.46410 | 0.124354 | ||||||||
\(777\) | 21.8564 | 0.784094 | ||||||||
\(778\) | 10.3923 | 0.372582 | ||||||||
\(779\) | −21.4641 | −0.769031 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.3923 | −0.801260 | ||||||||
\(782\) | −7.60770 | −0.272051 | ||||||||
\(783\) | 10.1436 | 0.362502 | ||||||||
\(784\) | 15.0000 | 0.535714 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.5692 | −1.12532 | −0.562661 | − | 0.826688i | \(-0.690222\pi\) | ||||
−0.562661 | + | 0.826688i | \(0.690222\pi\) | |||||||
\(788\) | 12.9282 | 0.460548 | ||||||||
\(789\) | 3.46410 | 0.123325 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.0718 | 0.607003 | ||||||||
\(792\) | 36.5885 | 1.30011 | ||||||||
\(793\) | 8.39230 | 0.298019 | ||||||||
\(794\) | −49.8564 | −1.76934 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.0000 | 0.708881 | ||||||||
\(797\) | 40.6410 | 1.43958 | 0.719789 | − | 0.694193i | \(-0.244238\pi\) | ||||
0.719789 | + | 0.694193i | \(0.244238\pi\) | |||||||
\(798\) | −58.6410 | −2.07587 | ||||||||
\(799\) | −20.7846 | −0.735307 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −57.7128 | −2.03918 | ||||||||
\(802\) | −63.9615 | −2.25856 | ||||||||
\(803\) | −18.9282 | −0.667962 | ||||||||
\(804\) | 17.4641 | 0.615911 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −17.6603 | −0.622056 | ||||||||
\(807\) | 54.2487 | 1.90965 | ||||||||
\(808\) | 1.60770 | 0.0565585 | ||||||||
\(809\) | −2.53590 | −0.0891574 | −0.0445787 | − | 0.999006i | \(-0.514195\pi\) | ||||
−0.0445787 | + | 0.999006i | \(0.514195\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.8038 | 0.625178 | 0.312589 | − | 0.949889i | \(-0.398804\pi\) | ||||
0.312589 | + | 0.949889i | \(0.398804\pi\) | |||||||
\(812\) | 5.07180 | 0.177985 | ||||||||
\(813\) | −84.6410 | −2.96849 | ||||||||
\(814\) | −32.7846 | −1.14910 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 47.3205 | 1.65655 | ||||||||
\(817\) | −1.21539 | −0.0425211 | ||||||||
\(818\) | −30.4974 | −1.06632 | ||||||||
\(819\) | 8.92820 | 0.311977 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.6410 | 0.999578 | 0.499789 | − | 0.866147i | \(-0.333411\pi\) | ||||
0.499789 | + | 0.866147i | \(0.333411\pi\) | |||||||
\(822\) | 4.39230 | 0.153199 | ||||||||
\(823\) | 15.4115 | 0.537213 | 0.268606 | − | 0.963250i | \(-0.413437\pi\) | ||||
0.268606 | + | 0.963250i | \(0.413437\pi\) | |||||||
\(824\) | −0.339746 | −0.0118356 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −31.6077 | −1.09977 | ||||||||
\(827\) | −18.0000 | −0.625921 | −0.312961 | − | 0.949766i | \(-0.601321\pi\) | ||||
−0.312961 | + | 0.949766i | \(0.601321\pi\) | |||||||
\(828\) | −5.66025 | −0.196707 | ||||||||
\(829\) | 0.392305 | 0.0136253 | 0.00681266 | − | 0.999977i | \(-0.497831\pi\) | ||||
0.00681266 | + | 0.999977i | \(0.497831\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −72.1051 | −2.50130 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | −10.3923 | −0.360072 | ||||||||
\(834\) | −58.6410 | −2.03057 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 29.3205 | 1.01407 | ||||||||
\(837\) | −40.7846 | −1.40972 | ||||||||
\(838\) | −4.39230 | −0.151730 | ||||||||
\(839\) | 0.339746 | 0.0117293 | 0.00586467 | − | 0.999983i | \(-0.498133\pi\) | ||||
0.00586467 | + | 0.999983i | \(0.498133\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.5692 | −0.778249 | ||||||||
\(842\) | −53.3205 | −1.83755 | ||||||||
\(843\) | −61.1769 | −2.10704 | ||||||||
\(844\) | 8.00000 | 0.275371 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −46.3923 | −1.59500 | ||||||||
\(847\) | −22.7846 | −0.782888 | ||||||||
\(848\) | 51.9615 | 1.78437 | ||||||||
\(849\) | 89.0333 | 3.05562 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.07180 | −0.173859 | ||||||||
\(852\) | −12.9282 | −0.442913 | ||||||||
\(853\) | −8.00000 | −0.273915 | −0.136957 | − | 0.990577i | \(-0.543732\pi\) | ||||
−0.136957 | + | 0.990577i | \(0.543732\pi\) | |||||||
\(854\) | 29.0718 | 0.994816 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 30.5885 | 1.04549 | ||||||||
\(857\) | 35.5692 | 1.21502 | 0.607511 | − | 0.794311i | \(-0.292168\pi\) | ||||
0.607511 | + | 0.794311i | \(0.292168\pi\) | |||||||
\(858\) | −22.3923 | −0.764461 | ||||||||
\(859\) | −17.1769 | −0.586069 | −0.293034 | − | 0.956102i | \(-0.594665\pi\) | ||||
−0.293034 | + | 0.956102i | \(0.594665\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.9282 | 0.645071 | ||||||||
\(862\) | −44.1962 | −1.50533 | ||||||||
\(863\) | 38.7846 | 1.32024 | 0.660122 | − | 0.751159i | \(-0.270505\pi\) | ||||
0.660122 | + | 0.751159i | \(0.270505\pi\) | |||||||
\(864\) | 20.7846 | 0.707107 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −60.2487 | −2.04733 | ||||||||
\(867\) | 13.6603 | 0.463927 | ||||||||
\(868\) | −20.3923 | −0.692160 | ||||||||
\(869\) | 39.7128 | 1.34716 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.39230 | 0.216595 | ||||||||
\(872\) | −3.46410 | −0.117309 | ||||||||
\(873\) | −8.92820 | −0.302174 | ||||||||
\(874\) | 13.6077 | 0.460287 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.9282 | −0.369230 | ||||||||
\(877\) | −2.00000 | −0.0675352 | −0.0337676 | − | 0.999430i | \(-0.510751\pi\) | ||||
−0.0337676 | + | 0.999430i | \(0.510751\pi\) | |||||||
\(878\) | 55.4256 | 1.87052 | ||||||||
\(879\) | −13.8564 | −0.467365 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −47.3205 | −1.59427 | −0.797134 | − | 0.603802i | \(-0.793652\pi\) | ||||
−0.797134 | + | 0.603802i | \(0.793652\pi\) | |||||||
\(882\) | −23.1962 | −0.781055 | ||||||||
\(883\) | −23.8038 | −0.801063 | −0.400532 | − | 0.916283i | \(-0.631175\pi\) | ||||
−0.400532 | + | 0.916283i | \(0.631175\pi\) | |||||||
\(884\) | −3.46410 | −0.116510 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 29.4115 | 0.988100 | ||||||||
\(887\) | 47.9090 | 1.60863 | 0.804313 | − | 0.594206i | \(-0.202534\pi\) | ||||
0.804313 | + | 0.594206i | \(0.202534\pi\) | |||||||
\(888\) | 18.9282 | 0.635189 | ||||||||
\(889\) | 32.3923 | 1.08640 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11.6603 | 0.390633 | ||||||||
\(892\) | −2.00000 | −0.0669650 | ||||||||
\(893\) | 37.1769 | 1.24408 | ||||||||
\(894\) | 37.1769 | 1.24338 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −24.2487 | −0.810093 | ||||||||
\(897\) | −3.46410 | −0.115663 | ||||||||
\(898\) | 35.5692 | 1.18696 | ||||||||
\(899\) | −25.8564 | −0.862359 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.0000 | −1.19933 | ||||||||
\(902\) | −28.3923 | −0.945360 | ||||||||
\(903\) | 1.07180 | 0.0356672 | ||||||||
\(904\) | 14.7846 | 0.491729 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 8.53590 | 0.283586 | ||||||||
\(907\) | 53.7654 | 1.78525 | 0.892625 | − | 0.450800i | \(-0.148861\pi\) | ||||
0.892625 | + | 0.450800i | \(0.148861\pi\) | |||||||
\(908\) | 3.46410 | 0.114960 | ||||||||
\(909\) | −4.14359 | −0.137434 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.0000 | −1.19273 | −0.596367 | − | 0.802712i | \(-0.703390\pi\) | ||||
−0.596367 | + | 0.802712i | \(0.703390\pi\) | |||||||
\(912\) | −84.6410 | −2.80274 | ||||||||
\(913\) | −28.3923 | −0.939648 | ||||||||
\(914\) | −18.6795 | −0.617863 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.39230 | 0.211208 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −24.0000 | −0.792118 | ||||||||
\(919\) | 9.17691 | 0.302718 | 0.151359 | − | 0.988479i | \(-0.451635\pi\) | ||||
0.151359 | + | 0.988479i | \(0.451635\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −51.3205 | −1.69107 | ||||||||
\(922\) | −6.00000 | −0.197599 | ||||||||
\(923\) | −4.73205 | −0.155757 | ||||||||
\(924\) | −25.8564 | −0.850613 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 4.14359 | 0.136167 | ||||||||
\(927\) | 0.875644 | 0.0287599 | ||||||||
\(928\) | 13.1769 | 0.432553 | ||||||||
\(929\) | 44.5359 | 1.46118 | 0.730588 | − | 0.682819i | \(-0.239246\pi\) | ||||
0.730588 | + | 0.682819i | \(0.239246\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.5885 | 0.609212 | ||||||||
\(932\) | 6.00000 | 0.196537 | ||||||||
\(933\) | 44.7846 | 1.46618 | ||||||||
\(934\) | −48.1577 | −1.57577 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.73205 | 0.252730 | ||||||||
\(937\) | −34.7846 | −1.13636 | −0.568182 | − | 0.822903i | \(-0.692353\pi\) | ||||
−0.568182 | + | 0.822903i | \(0.692353\pi\) | |||||||
\(938\) | 22.1436 | 0.723014 | ||||||||
\(939\) | −39.3205 | −1.28318 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.1769 | 1.01634 | 0.508169 | − | 0.861257i | \(-0.330322\pi\) | ||||
0.508169 | + | 0.861257i | \(0.330322\pi\) | |||||||
\(942\) | −47.3205 | −1.54179 | ||||||||
\(943\) | −4.39230 | −0.143033 | ||||||||
\(944\) | −45.6218 | −1.48486 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.60770 | −0.0522707 | ||||||||
\(947\) | −40.6410 | −1.32066 | −0.660328 | − | 0.750978i | \(-0.729583\pi\) | ||||
−0.660328 | + | 0.750978i | \(0.729583\pi\) | |||||||
\(948\) | 22.9282 | 0.744673 | ||||||||
\(949\) | −4.00000 | −0.129845 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 65.5692 | 2.12623 | ||||||||
\(952\) | 12.0000 | 0.388922 | ||||||||
\(953\) | −0.928203 | −0.0300675 | −0.0150337 | − | 0.999887i | \(-0.504786\pi\) | ||||
−0.0150337 | + | 0.999887i | \(0.504786\pi\) | |||||||
\(954\) | −80.3538 | −2.60155 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −14.1962 | −0.459136 | ||||||||
\(957\) | −32.7846 | −1.05978 | ||||||||
\(958\) | 61.7654 | 1.99555 | ||||||||
\(959\) | 1.85641 | 0.0599465 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 72.9615 | 2.35360 | ||||||||
\(962\) | −6.92820 | −0.223374 | ||||||||
\(963\) | −78.8372 | −2.54049 | ||||||||
\(964\) | −2.39230 | −0.0770510 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −12.0000 | −0.386094 | ||||||||
\(967\) | 50.3923 | 1.62051 | 0.810254 | − | 0.586079i | \(-0.199329\pi\) | ||||
0.810254 | + | 0.586079i | \(0.199329\pi\) | |||||||
\(968\) | −19.7321 | −0.634212 | ||||||||
\(969\) | 58.6410 | 1.88382 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.9282 | 0.607435 | 0.303717 | − | 0.952762i | \(-0.401772\pi\) | ||||
0.303717 | + | 0.952762i | \(0.401772\pi\) | |||||||
\(972\) | 18.7321 | 0.600831 | ||||||||
\(973\) | −24.7846 | −0.794558 | ||||||||
\(974\) | 45.7128 | 1.46473 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 41.9615 | 1.34316 | ||||||||
\(977\) | 15.7128 | 0.502697 | 0.251349 | − | 0.967897i | \(-0.419126\pi\) | ||||
0.251349 | + | 0.967897i | \(0.419126\pi\) | |||||||
\(978\) | −68.1051 | −2.17776 | ||||||||
\(979\) | 61.1769 | 1.95522 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.92820 | 0.285056 | ||||||||
\(982\) | −4.39230 | −0.140164 | ||||||||
\(983\) | 34.3923 | 1.09694 | 0.548472 | − | 0.836169i | \(-0.315210\pi\) | ||||
0.548472 | + | 0.836169i | \(0.315210\pi\) | |||||||
\(984\) | 16.3923 | 0.522568 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −15.2154 | −0.484557 | ||||||||
\(987\) | −32.7846 | −1.04355 | ||||||||
\(988\) | 6.19615 | 0.197126 | ||||||||
\(989\) | −0.248711 | −0.00790856 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.00000 | 0.254128 | 0.127064 | − | 0.991894i | \(-0.459445\pi\) | ||||
0.127064 | + | 0.991894i | \(0.459445\pi\) | |||||||
\(992\) | −52.9808 | −1.68214 | ||||||||
\(993\) | −7.07180 | −0.224417 | ||||||||
\(994\) | −16.3923 | −0.519932 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −16.3923 | −0.519410 | ||||||||
\(997\) | −33.6077 | −1.06437 | −0.532183 | − | 0.846629i | \(-0.678628\pi\) | ||||
−0.532183 | + | 0.846629i | \(0.678628\pi\) | |||||||
\(998\) | −67.5167 | −2.13720 | ||||||||
\(999\) | −16.0000 | −0.506218 |
(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 | 325.2.a.g.1.2 | 2 | ||
3.2 | odd | 2 | 2925.2.a.z.1.1 | 2 | |||
4.3 | odd | 2 | 5200.2.a.ca.1.2 | 2 | |||
5.2 | odd | 4 | 325.2.b.e.274.4 | 4 | |||
5.3 | odd | 4 | 325.2.b.e.274.1 | 4 | |||
5.4 | even | 2 | 65.2.a.c.1.1 | ✓ | 2 | ||
13.12 | even | 2 | 4225.2.a.w.1.1 | 2 | |||
15.2 | even | 4 | 2925.2.c.v.2224.1 | 4 | |||
15.8 | even | 4 | 2925.2.c.v.2224.4 | 4 | |||
15.14 | odd | 2 | 585.2.a.k.1.2 | 2 | |||
20.19 | odd | 2 | 1040.2.a.h.1.1 | 2 | |||
35.34 | odd | 2 | 3185.2.a.k.1.1 | 2 | |||
40.19 | odd | 2 | 4160.2.a.bj.1.2 | 2 | |||
40.29 | even | 2 | 4160.2.a.y.1.1 | 2 | |||
55.54 | odd | 2 | 7865.2.a.h.1.2 | 2 | |||
60.59 | even | 2 | 9360.2.a.cm.1.1 | 2 | |||
65.4 | even | 6 | 845.2.e.f.146.1 | 4 | |||
65.9 | even | 6 | 845.2.e.e.146.2 | 4 | |||
65.19 | odd | 12 | 845.2.m.c.361.1 | 4 | |||
65.24 | odd | 12 | 845.2.m.c.316.1 | 4 | |||
65.29 | even | 6 | 845.2.e.e.191.2 | 4 | |||
65.34 | odd | 4 | 845.2.c.e.506.2 | 4 | |||
65.44 | odd | 4 | 845.2.c.e.506.4 | 4 | |||
65.49 | even | 6 | 845.2.e.f.191.1 | 4 | |||
65.54 | odd | 12 | 845.2.m.a.316.1 | 4 | |||
65.59 | odd | 12 | 845.2.m.a.361.1 | 4 | |||
65.64 | even | 2 | 845.2.a.d.1.2 | 2 | |||
195.194 | odd | 2 | 7605.2.a.be.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.a.c.1.1 | ✓ | 2 | 5.4 | even | 2 | ||
325.2.a.g.1.2 | 2 | 1.1 | even | 1 | trivial | ||
325.2.b.e.274.1 | 4 | 5.3 | odd | 4 | |||
325.2.b.e.274.4 | 4 | 5.2 | odd | 4 | |||
585.2.a.k.1.2 | 2 | 15.14 | odd | 2 | |||
845.2.a.d.1.2 | 2 | 65.64 | even | 2 | |||
845.2.c.e.506.2 | 4 | 65.34 | odd | 4 | |||
845.2.c.e.506.4 | 4 | 65.44 | odd | 4 | |||
845.2.e.e.146.2 | 4 | 65.9 | even | 6 | |||
845.2.e.e.191.2 | 4 | 65.29 | even | 6 | |||
845.2.e.f.146.1 | 4 | 65.4 | even | 6 | |||
845.2.e.f.191.1 | 4 | 65.49 | even | 6 | |||
845.2.m.a.316.1 | 4 | 65.54 | odd | 12 | |||
845.2.m.a.361.1 | 4 | 65.59 | odd | 12 | |||
845.2.m.c.316.1 | 4 | 65.24 | odd | 12 | |||
845.2.m.c.361.1 | 4 | 65.19 | odd | 12 | |||
1040.2.a.h.1.1 | 2 | 20.19 | odd | 2 | |||
2925.2.a.z.1.1 | 2 | 3.2 | odd | 2 | |||
2925.2.c.v.2224.1 | 4 | 15.2 | even | 4 | |||
2925.2.c.v.2224.4 | 4 | 15.8 | even | 4 | |||
3185.2.a.k.1.1 | 2 | 35.34 | odd | 2 | |||
4160.2.a.y.1.1 | 2 | 40.29 | even | 2 | |||
4160.2.a.bj.1.2 | 2 | 40.19 | odd | 2 | |||
4225.2.a.w.1.1 | 2 | 13.12 | even | 2 | |||
5200.2.a.ca.1.2 | 2 | 4.3 | odd | 2 | |||
7605.2.a.be.1.1 | 2 | 195.194 | odd | 2 | |||
7865.2.a.h.1.2 | 2 | 55.54 | odd | 2 | |||
9360.2.a.cm.1.1 | 2 | 60.59 | even | 2 |