Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1710,2,Mod(1709,1710)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1710, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1710.1709");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1710.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(13.6544187456\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1709.18 | ||
Character | \(\chi\) | \(=\) | 1710.1709 |
Dual form | 1710.2.c.d.1709.19 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(1027\) | \(1351\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −0.586990 | + | 2.15765i | −0.262510 | + | 0.964929i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.03449i | − | 1.14693i | −0.819230 | − | 0.573465i | \(-0.805599\pi\) | ||
0.819230 | − | 0.573465i | \(-0.194401\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.15765 | + | 0.586990i | 0.682308 | + | 0.185623i | ||||
\(11\) | 2.90108i | 0.874709i | 0.899289 | + | 0.437354i | \(0.144084\pi\) | ||||
−0.899289 | + | 0.437354i | \(0.855916\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.78122 | 0.494021 | 0.247010 | − | 0.969013i | \(-0.420552\pi\) | ||||
0.247010 | + | 0.969013i | \(0.420552\pi\) | |||||||
\(14\) | −3.03449 | −0.811002 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.79113 | −0.434412 | −0.217206 | − | 0.976126i | \(-0.569694\pi\) | ||||
−0.217206 | + | 0.976126i | \(0.569694\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.39593 | − | 2.73270i | −0.779080 | − | 0.626924i | ||||
\(20\) | 0.586990 | − | 2.15765i | 0.131255 | − | 0.482465i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.90108 | 0.618513 | ||||||||
\(23\) | 5.93022 | 1.23654 | 0.618268 | − | 0.785968i | \(-0.287835\pi\) | ||||
0.618268 | + | 0.785968i | \(0.287835\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.31088 | − | 2.53304i | −0.862177 | − | 0.506607i | ||||
\(26\) | − | 1.78122i | − | 0.349325i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.03449i | 0.573465i | ||||||||
\(29\) | 4.19330 | 0.778675 | 0.389338 | − | 0.921095i | \(-0.372704\pi\) | ||||
0.389338 | + | 0.921095i | \(0.372704\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.66480i | 1.73585i | 0.496696 | + | 0.867925i | \(0.334546\pi\) | ||||
−0.496696 | + | 0.867925i | \(0.665454\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.79113i | 0.307176i | ||||||||
\(35\) | 6.54736 | + | 1.78122i | 1.10671 | + | 0.301081i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.75577 | 0.453046 | 0.226523 | − | 0.974006i | \(-0.427264\pi\) | ||||
0.226523 | + | 0.974006i | \(0.427264\pi\) | |||||||
\(38\) | −2.73270 | + | 3.39593i | −0.443302 | + | 0.550893i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.15765 | − | 0.586990i | −0.341154 | − | 0.0928113i | ||||
\(41\) | 7.22779 | 1.12879 | 0.564395 | − | 0.825505i | \(-0.309109\pi\) | ||||
0.564395 | + | 0.825505i | \(0.309109\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.85355i | 0.892659i | 0.894869 | + | 0.446329i | \(0.147269\pi\) | ||||
−0.894869 | + | 0.446329i | \(0.852731\pi\) | |||||||
\(44\) | − | 2.90108i | − | 0.437354i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 5.93022i | − | 0.874363i | ||||||
\(47\) | −4.29142 | −0.625968 | −0.312984 | − | 0.949758i | \(-0.601329\pi\) | ||||
−0.312984 | + | 0.949758i | \(0.601329\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.20814 | −0.315448 | ||||||||
\(50\) | −2.53304 | + | 4.31088i | −0.358225 | + | 0.609651i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.78122 | −0.247010 | ||||||||
\(53\) | 13.4136i | 1.84250i | 0.388966 | + | 0.921252i | \(0.372832\pi\) | ||||
−0.388966 | + | 0.921252i | \(0.627168\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.25951 | − | 1.70291i | −0.844032 | − | 0.229620i | ||||
\(56\) | 3.03449 | 0.405501 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 4.19330i | − | 0.550607i | ||||||
\(59\) | 6.22488 | 0.810410 | 0.405205 | − | 0.914226i | \(-0.367200\pi\) | ||||
0.405205 | + | 0.914226i | \(0.367200\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.10275 | −0.525303 | −0.262652 | − | 0.964891i | \(-0.584597\pi\) | ||||
−0.262652 | + | 0.964891i | \(0.584597\pi\) | |||||||
\(62\) | 9.66480 | 1.22743 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −1.04556 | + | 3.84324i | −0.129685 | + | 0.476695i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.97215 | 1.21829 | 0.609146 | − | 0.793058i | \(-0.291512\pi\) | ||||
0.609146 | + | 0.793058i | \(0.291512\pi\) | |||||||
\(68\) | 1.79113 | 0.217206 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.78122 | − | 6.54736i | 0.212896 | − | 0.782559i | ||||
\(71\) | 10.9196 | 1.29592 | 0.647961 | − | 0.761674i | \(-0.275622\pi\) | ||||
0.647961 | + | 0.761674i | \(0.275622\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.59911i | − | 0.889408i | −0.895677 | − | 0.444704i | \(-0.853309\pi\) | ||
0.895677 | − | 0.444704i | \(-0.146691\pi\) | |||||||
\(74\) | − | 2.75577i | − | 0.320352i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.39593 | + | 2.73270i | 0.389540 | + | 0.313462i | ||||
\(77\) | 8.80331 | 1.00323 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.50029i | 0.281305i | 0.990059 | + | 0.140652i | \(0.0449200\pi\) | ||||
−0.990059 | + | 0.140652i | \(0.955080\pi\) | |||||||
\(80\) | −0.586990 | + | 2.15765i | −0.0656275 | + | 0.241232i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 7.22779i | − | 0.798176i | ||||||
\(83\) | 15.1302 | 1.66076 | 0.830378 | − | 0.557201i | \(-0.188125\pi\) | ||||
0.830378 | + | 0.557201i | \(0.188125\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.05137 | − | 3.86462i | 0.114038 | − | 0.419177i | ||||
\(86\) | 5.85355 | 0.631205 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.90108 | −0.309256 | ||||||||
\(89\) | −17.3599 | −1.84015 | −0.920075 | − | 0.391743i | \(-0.871872\pi\) | ||||
−0.920075 | + | 0.391743i | \(0.871872\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 5.40509i | − | 0.566607i | ||||||
\(92\) | −5.93022 | −0.618268 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.29142i | 0.442626i | ||||||||
\(95\) | 7.88958 | − | 5.72316i | 0.809454 | − | 0.587183i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.94829 | 0.400888 | 0.200444 | − | 0.979705i | \(-0.435761\pi\) | ||||
0.200444 | + | 0.979705i | \(0.435761\pi\) | |||||||
\(98\) | 2.20814i | 0.223055i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.31088 | + | 2.53304i | 0.431088 | + | 0.253304i | ||||
\(101\) | 1.11986i | 0.111431i | 0.998447 | + | 0.0557153i | \(0.0177439\pi\) | ||||
−0.998447 | + | 0.0557153i | \(0.982256\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.26808 | 0.322014 | 0.161007 | − | 0.986953i | \(-0.448526\pi\) | ||||
0.161007 | + | 0.986953i | \(0.448526\pi\) | |||||||
\(104\) | 1.78122i | 0.174663i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.4136 | 1.30285 | ||||||||
\(107\) | 5.03804i | 0.487046i | 0.969895 | + | 0.243523i | \(0.0783031\pi\) | ||||
−0.969895 | + | 0.243523i | \(0.921697\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.90856i | 0.470155i | 0.971977 | + | 0.235078i | \(0.0755344\pi\) | ||||
−0.971977 | + | 0.235078i | \(0.924466\pi\) | |||||||
\(110\) | −1.70291 | + | 6.25951i | −0.162366 | + | 0.596821i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 3.03449i | − | 0.286732i | ||||||
\(113\) | 4.62177i | 0.434780i | 0.976085 | + | 0.217390i | \(0.0697543\pi\) | ||||
−0.976085 | + | 0.217390i | \(0.930246\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.48098 | + | 12.7953i | −0.324603 | + | 1.19317i | ||||
\(116\) | −4.19330 | −0.389338 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 6.22488i | − | 0.573046i | ||||||
\(119\) | 5.43516i | 0.498240i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.58373 | 0.234884 | ||||||||
\(122\) | 4.10275i | 0.371445i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 9.66480i | − | 0.867925i | ||||||
\(125\) | 7.99585 | − | 7.81450i | 0.715170 | − | 0.698950i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.2641 | 1.70941 | 0.854706 | − | 0.519113i | \(-0.173737\pi\) | ||||
0.854706 | + | 0.519113i | \(0.173737\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.84324 | + | 1.04556i | 0.337074 | + | 0.0917014i | ||||
\(131\) | 12.5062i | 1.09267i | 0.837565 | + | 0.546337i | \(0.183978\pi\) | ||||
−0.837565 | + | 0.546337i | \(0.816022\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.29235 | + | 10.3049i | −0.719038 | + | 0.893550i | ||||
\(134\) | − | 9.97215i | − | 0.861462i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 1.79113i | − | 0.153588i | ||||||
\(137\) | −4.44375 | −0.379655 | −0.189828 | − | 0.981817i | \(-0.560793\pi\) | ||||
−0.189828 | + | 0.981817i | \(0.560793\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.89461 | 0.245518 | 0.122759 | − | 0.992437i | \(-0.460826\pi\) | ||||
0.122759 | + | 0.992437i | \(0.460826\pi\) | |||||||
\(140\) | −6.54736 | − | 1.78122i | −0.553353 | − | 0.150540i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 10.9196i | − | 0.916355i | ||||||
\(143\) | 5.16745i | 0.432124i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.46142 | + | 9.04765i | −0.204410 | + | 0.751367i | ||||
\(146\) | −7.59911 | −0.628907 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.75577 | −0.226523 | ||||||||
\(149\) | 4.68230i | 0.383589i | 0.981435 | + | 0.191794i | \(0.0614307\pi\) | ||||
−0.981435 | + | 0.191794i | \(0.938569\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.36014i | 0.761717i | 0.924633 | + | 0.380859i | \(0.124372\pi\) | ||||
−0.924633 | + | 0.380859i | \(0.875628\pi\) | |||||||
\(152\) | 2.73270 | − | 3.39593i | 0.221651 | − | 0.275446i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 8.80331i | − | 0.709391i | ||||||
\(155\) | −20.8532 | − | 5.67314i | −1.67497 | − | 0.455678i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 15.8298i | − | 1.26336i | −0.775231 | − | 0.631678i | \(-0.782366\pi\) | ||
0.775231 | − | 0.631678i | \(-0.217634\pi\) | |||||||
\(158\) | 2.50029 | 0.198913 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.15765 | + | 0.586990i | 0.170577 | + | 0.0464057i | ||||
\(161\) | − | 17.9952i | − | 1.41822i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 13.6681i | − | 1.07057i | −0.844672 | − | 0.535284i | \(-0.820205\pi\) | ||
0.844672 | − | 0.535284i | \(-0.179795\pi\) | |||||||
\(164\) | −7.22779 | −0.564395 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 15.1302i | − | 1.17433i | ||||||
\(167\) | 9.93265i | 0.768612i | 0.923206 | + | 0.384306i | \(0.125559\pi\) | ||||
−0.923206 | + | 0.384306i | \(0.874441\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.82727 | −0.755944 | ||||||||
\(170\) | −3.86462 | − | 1.05137i | −0.296403 | − | 0.0806367i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 5.85355i | − | 0.446329i | ||||||
\(173\) | − | 12.0354i | − | 0.915035i | −0.889201 | − | 0.457517i | \(-0.848739\pi\) | ||
0.889201 | − | 0.457517i | \(-0.151261\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.68648 | + | 13.0813i | −0.581043 | + | 0.988856i | ||||
\(176\) | 2.90108i | 0.218677i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 17.3599i | 1.30118i | ||||||||
\(179\) | 18.2775 | 1.36613 | 0.683064 | − | 0.730359i | \(-0.260647\pi\) | ||||
0.683064 | + | 0.730359i | \(0.260647\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 23.6288i | − | 1.75632i | −0.478369 | − | 0.878159i | \(-0.658772\pi\) | ||
0.478369 | − | 0.878159i | \(-0.341228\pi\) | |||||||
\(182\) | −5.40509 | −0.400652 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.93022i | 0.437181i | ||||||||
\(185\) | −1.61761 | + | 5.94599i | −0.118929 | + | 0.437158i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 5.19621i | − | 0.379984i | ||||||
\(188\) | 4.29142 | 0.312984 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.72316 | − | 7.88958i | −0.415201 | − | 0.572370i | ||||
\(191\) | 16.3630i | 1.18399i | 0.805943 | + | 0.591993i | \(0.201659\pi\) | ||||
−0.805943 | + | 0.591993i | \(0.798341\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.10101 | 0.0792524 | 0.0396262 | − | 0.999215i | \(-0.487383\pi\) | ||||
0.0396262 | + | 0.999215i | \(0.487383\pi\) | |||||||
\(194\) | − | 3.94829i | − | 0.283471i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.20814 | 0.157724 | ||||||||
\(197\) | −27.5475 | −1.96268 | −0.981338 | − | 0.192292i | \(-0.938408\pi\) | ||||
−0.981338 | + | 0.192292i | \(0.938408\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.62177 | −0.185852 | −0.0929262 | − | 0.995673i | \(-0.529622\pi\) | ||||
−0.0929262 | + | 0.995673i | \(0.529622\pi\) | |||||||
\(200\) | 2.53304 | − | 4.31088i | 0.179113 | − | 0.304826i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.11986 | 0.0787934 | ||||||||
\(203\) | − | 12.7245i | − | 0.893086i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.24264 | + | 15.5950i | −0.296319 | + | 1.08920i | ||||
\(206\) | − | 3.26808i | − | 0.227698i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.78122 | 0.123505 | ||||||||
\(209\) | 7.92778 | − | 9.85187i | 0.548376 | − | 0.681468i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 8.64315i | − | 0.595019i | −0.954719 | − | 0.297509i | \(-0.903844\pi\) | ||
0.954719 | − | 0.297509i | \(-0.0961560\pi\) | |||||||
\(212\) | − | 13.4136i | − | 0.921252i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.03804 | 0.344393 | ||||||||
\(215\) | −12.6299 | − | 3.43598i | −0.861353 | − | 0.234332i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 29.3277 | 1.99090 | ||||||||
\(218\) | 4.90856 | 0.332450 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.25951 | + | 1.70291i | 0.422016 | + | 0.114810i | ||||
\(221\) | −3.19039 | −0.214609 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −29.1599 | −1.95269 | −0.976344 | − | 0.216223i | \(-0.930626\pi\) | ||||
−0.976344 | + | 0.216223i | \(0.930626\pi\) | |||||||
\(224\) | −3.03449 | −0.202750 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.62177 | 0.307436 | ||||||||
\(227\) | − | 21.7892i | − | 1.44620i | −0.690743 | − | 0.723101i | \(-0.742716\pi\) | ||
0.690743 | − | 0.723101i | \(-0.257284\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.0380 | 0.993742 | 0.496871 | − | 0.867824i | \(-0.334482\pi\) | ||||
0.496871 | + | 0.867824i | \(0.334482\pi\) | |||||||
\(230\) | 12.7953 | + | 3.48098i | 0.843698 | + | 0.229529i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.19330i | 0.275303i | ||||||||
\(233\) | −5.37338 | −0.352022 | −0.176011 | − | 0.984388i | \(-0.556319\pi\) | ||||
−0.176011 | + | 0.984388i | \(0.556319\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.51902 | − | 9.25937i | 0.164323 | − | 0.604015i | ||||
\(236\) | −6.22488 | −0.405205 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.43516 | 0.352309 | ||||||||
\(239\) | 7.36542i | 0.476429i | 0.971213 | + | 0.238215i | \(0.0765622\pi\) | ||||
−0.971213 | + | 0.238215i | \(0.923438\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.75247i | 0.177302i | 0.996063 | + | 0.0886509i | \(0.0282556\pi\) | ||||
−0.996063 | + | 0.0886509i | \(0.971744\pi\) | |||||||
\(242\) | − | 2.58373i | − | 0.166088i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.10275 | 0.262652 | ||||||||
\(245\) | 1.29615 | − | 4.76438i | 0.0828083 | − | 0.304385i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.04889 | − | 4.86753i | −0.384882 | − | 0.309714i | ||||
\(248\) | −9.66480 | −0.613715 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.81450 | − | 7.99585i | −0.494232 | − | 0.505702i | ||||
\(251\) | 20.0170i | 1.26346i | 0.775189 | + | 0.631729i | \(0.217655\pi\) | ||||
−0.775189 | + | 0.631729i | \(0.782345\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.2040i | 1.08161i | ||||||||
\(254\) | − | 19.2641i | − | 1.20874i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 11.0380i | − | 0.688534i | −0.938872 | − | 0.344267i | \(-0.888127\pi\) | ||
0.938872 | − | 0.344267i | \(-0.111873\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 8.36237i | − | 0.519612i | ||||||
\(260\) | 1.04556 | − | 3.84324i | 0.0648427 | − | 0.238348i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.5062 | 0.772637 | ||||||||
\(263\) | −12.1651 | −0.750132 | −0.375066 | − | 0.926998i | \(-0.622380\pi\) | ||||
−0.375066 | + | 0.926998i | \(0.622380\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −28.9419 | − | 7.87367i | −1.77789 | − | 0.483676i | ||||
\(266\) | 10.3049 | + | 8.29235i | 0.631835 | + | 0.508437i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.97215 | −0.609146 | ||||||||
\(269\) | 0.430855 | 0.0262697 | 0.0131348 | − | 0.999914i | \(-0.495819\pi\) | ||||
0.0131348 | + | 0.999914i | \(0.495819\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.1788 | −1.22578 | −0.612888 | − | 0.790169i | \(-0.709992\pi\) | ||||
−0.612888 | + | 0.790169i | \(0.709992\pi\) | |||||||
\(272\) | −1.79113 | −0.108603 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.44375i | 0.268457i | ||||||||
\(275\) | 7.34854 | − | 12.5062i | 0.443134 | − | 0.754154i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.78004i | 0.287205i | 0.989635 | + | 0.143603i | \(0.0458687\pi\) | ||||
−0.989635 | + | 0.143603i | \(0.954131\pi\) | |||||||
\(278\) | − | 2.89461i | − | 0.173607i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.78122 | + | 6.54736i | −0.106448 | + | 0.391280i | ||||
\(281\) | −7.31308 | −0.436262 | −0.218131 | − | 0.975920i | \(-0.569996\pi\) | ||||
−0.218131 | + | 0.975920i | \(0.569996\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.4364i | 1.15537i | 0.816259 | + | 0.577686i | \(0.196044\pi\) | ||||
−0.816259 | + | 0.577686i | \(0.803956\pi\) | |||||||
\(284\) | −10.9196 | −0.647961 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.16745 | 0.305558 | ||||||||
\(287\) | − | 21.9327i | − | 1.29464i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.7919 | −0.811286 | ||||||||
\(290\) | 9.04765 | + | 2.46142i | 0.531296 | + | 0.144540i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.59911i | 0.444704i | ||||||||
\(293\) | 24.7245i | 1.44442i | 0.691673 | + | 0.722211i | \(0.256874\pi\) | ||||
−0.691673 | + | 0.722211i | \(0.743126\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.65394 | + | 13.4311i | −0.212741 | + | 0.781988i | ||||
\(296\) | 2.75577i | 0.160176i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.68230 | 0.271238 | ||||||||
\(299\) | 10.5630 | 0.610874 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.7626 | 1.02382 | ||||||||
\(302\) | 9.36014 | 0.538616 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.39593 | − | 2.73270i | −0.194770 | − | 0.156731i | ||||
\(305\) | 2.40827 | − | 8.85228i | 0.137897 | − | 0.506880i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.48687 | −0.0848600 | −0.0424300 | − | 0.999099i | \(-0.513510\pi\) | ||||
−0.0424300 | + | 0.999099i | \(0.513510\pi\) | |||||||
\(308\) | −8.80331 | −0.501615 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.67314 | + | 20.8532i | −0.322213 | + | 1.18438i | ||||
\(311\) | 2.80957i | 0.159316i | 0.996822 | + | 0.0796581i | \(0.0253829\pi\) | ||||
−0.996822 | + | 0.0796581i | \(0.974617\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.9467i | 1.01441i | 0.861827 | + | 0.507203i | \(0.169321\pi\) | ||||
−0.861827 | + | 0.507203i | \(0.830679\pi\) | |||||||
\(314\) | −15.8298 | −0.893328 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 2.50029i | − | 0.140652i | ||||||
\(317\) | − | 25.2702i | − | 1.41932i | −0.704546 | − | 0.709658i | \(-0.748849\pi\) | ||
0.704546 | − | 0.709658i | \(-0.251151\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.1651i | 0.681114i | ||||||||
\(320\) | 0.586990 | − | 2.15765i | 0.0328138 | − | 0.120616i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −17.9952 | −1.00283 | ||||||||
\(323\) | 6.08255 | + | 4.89461i | 0.338442 | + | 0.272344i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.67862 | − | 4.51189i | −0.425933 | − | 0.250274i | ||||
\(326\) | −13.6681 | −0.757006 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.22779i | 0.399088i | ||||||||
\(329\) | 13.0223i | 0.717941i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.69911i | 0.0933915i | 0.998909 | + | 0.0466957i | \(0.0148691\pi\) | ||||
−0.998909 | + | 0.0466957i | \(0.985131\pi\) | |||||||
\(332\) | −15.1302 | −0.830378 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.93265 | 0.543491 | ||||||||
\(335\) | −5.85355 | + | 21.5164i | −0.319814 | + | 1.17557i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.1225 | −0.878246 | −0.439123 | − | 0.898427i | \(-0.644711\pi\) | ||||
−0.439123 | + | 0.898427i | \(0.644711\pi\) | |||||||
\(338\) | 9.82727i | 0.534533i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.05137 | + | 3.86462i | −0.0570188 | + | 0.209588i | ||||
\(341\) | −28.0384 | −1.51836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 14.5409i | − | 0.785133i | ||||||
\(344\) | −5.85355 | −0.315603 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.0354 | −0.647027 | ||||||||
\(347\) | −9.01595 | −0.484001 | −0.242001 | − | 0.970276i | \(-0.577804\pi\) | ||||
−0.242001 | + | 0.970276i | \(0.577804\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 36.5137 | 1.95454 | 0.977268 | − | 0.212008i | \(-0.0680003\pi\) | ||||
0.977268 | + | 0.212008i | \(0.0680003\pi\) | |||||||
\(350\) | 13.0813 | + | 7.68648i | 0.699227 | + | 0.410859i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.90108 | 0.154628 | ||||||||
\(353\) | −12.5379 | −0.667325 | −0.333662 | − | 0.942693i | \(-0.608285\pi\) | ||||
−0.333662 | + | 0.942693i | \(0.608285\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.40972 | + | 23.5607i | −0.340192 | + | 1.25047i | ||||
\(356\) | 17.3599 | 0.920075 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 18.2775i | − | 0.965998i | ||||||
\(359\) | 16.1413i | 0.851906i | 0.904745 | + | 0.425953i | \(0.140061\pi\) | ||||
−0.904745 | + | 0.425953i | \(0.859939\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.06471 | + | 18.5601i | 0.213932 | + | 0.976849i | ||||
\(362\) | −23.6288 | −1.24190 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.40509i | 0.283304i | ||||||||
\(365\) | 16.3962 | + | 4.46060i | 0.858216 | + | 0.233479i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 19.5812i | − | 1.02213i | −0.859542 | − | 0.511065i | \(-0.829251\pi\) | ||
0.859542 | − | 0.511065i | \(-0.170749\pi\) | |||||||
\(368\) | 5.93022 | 0.309134 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.94599 | + | 1.61761i | 0.309117 | + | 0.0840956i | ||||
\(371\) | 40.7036 | 2.11322 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.2394 | −0.789067 | −0.394533 | − | 0.918882i | \(-0.629094\pi\) | ||||
−0.394533 | + | 0.918882i | \(0.629094\pi\) | |||||||
\(374\) | −5.19621 | −0.268689 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 4.29142i | − | 0.221313i | ||||||
\(377\) | 7.46917 | 0.384682 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.0160i | 1.54182i | 0.636944 | + | 0.770910i | \(0.280198\pi\) | ||||
−0.636944 | + | 0.770910i | \(0.719802\pi\) | |||||||
\(380\) | −7.88958 | + | 5.72316i | −0.404727 | + | 0.293592i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16.3630 | 0.837204 | ||||||||
\(383\) | − | 28.2055i | − | 1.44123i | −0.693334 | − | 0.720617i | \(-0.743859\pi\) | ||
0.693334 | − | 0.720617i | \(-0.256141\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.16745 | + | 18.9944i | −0.263358 | + | 0.968046i | ||||
\(386\) | − | 1.10101i | − | 0.0560399i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.94829 | −0.200444 | ||||||||
\(389\) | 3.21428i | 0.162971i | 0.996675 | + | 0.0814854i | \(0.0259664\pi\) | ||||
−0.996675 | + | 0.0814854i | \(0.974034\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.6218 | −0.537166 | ||||||||
\(392\) | − | 2.20814i | − | 0.111528i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 27.5475i | 1.38782i | ||||||||
\(395\) | −5.39475 | − | 1.46765i | −0.271439 | − | 0.0738453i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 17.4901i | − | 0.877801i | −0.898536 | − | 0.438901i | \(-0.855368\pi\) | ||
0.898536 | − | 0.438901i | \(-0.144632\pi\) | |||||||
\(398\) | 2.62177i | 0.131417i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.31088 | − | 2.53304i | −0.215544 | − | 0.126652i | ||||
\(401\) | −6.13958 | −0.306596 | −0.153298 | − | 0.988180i | \(-0.548989\pi\) | ||||
−0.153298 | + | 0.988180i | \(0.548989\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.2151i | 0.857545i | ||||||||
\(404\) | − | 1.11986i | − | 0.0557153i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.7245 | −0.631507 | ||||||||
\(407\) | 7.99472i | 0.396284i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 10.0012i | − | 0.494526i | −0.968948 | − | 0.247263i | \(-0.920469\pi\) | ||
0.968948 | − | 0.247263i | \(-0.0795311\pi\) | |||||||
\(410\) | 15.5950 | + | 4.24264i | 0.770183 | + | 0.209529i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.26808 | −0.161007 | ||||||||
\(413\) | − | 18.8893i | − | 0.929483i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.88128 | + | 32.6456i | −0.435965 | + | 1.60251i | ||||
\(416\) | − | 1.78122i | − | 0.0873313i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −9.85187 | − | 7.92778i | −0.481871 | − | 0.387761i | ||||
\(419\) | 20.9915i | 1.02550i | 0.858537 | + | 0.512751i | \(0.171374\pi\) | ||||
−0.858537 | + | 0.512751i | \(0.828626\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 15.6553i | − | 0.762994i | −0.924370 | − | 0.381497i | \(-0.875409\pi\) | ||
0.924370 | − | 0.381497i | \(-0.124591\pi\) | |||||||
\(422\) | −8.64315 | −0.420742 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −13.4136 | −0.651424 | ||||||||
\(425\) | 7.72134 | + | 4.53699i | 0.374540 | + | 0.220076i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.4498i | 0.602486i | ||||||||
\(428\) | − | 5.03804i | − | 0.243523i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.43598 | + | 12.6299i | −0.165698 | + | 0.609068i | ||||
\(431\) | 0.430855 | 0.0207535 | 0.0103768 | − | 0.999946i | \(-0.496697\pi\) | ||||
0.0103768 | + | 0.999946i | \(0.496697\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.8894 | 1.67668 | 0.838338 | − | 0.545151i | \(-0.183528\pi\) | ||||
0.838338 | + | 0.545151i | \(0.183528\pi\) | |||||||
\(434\) | − | 29.3277i | − | 1.40778i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 4.90856i | − | 0.235078i | ||||||
\(437\) | −20.1386 | − | 16.2055i | −0.963360 | − | 0.775214i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 15.8997i | − | 0.758850i | −0.925222 | − | 0.379425i | \(-0.876122\pi\) | ||
0.925222 | − | 0.379425i | \(-0.123878\pi\) | |||||||
\(440\) | 1.70291 | − | 6.25951i | 0.0811829 | − | 0.298410i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.19039i | 0.151751i | ||||||||
\(443\) | 7.47699 | 0.355243 | 0.177621 | − | 0.984099i | \(-0.443160\pi\) | ||||
0.177621 | + | 0.984099i | \(0.443160\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.1901 | − | 37.4566i | 0.483058 | − | 1.77561i | ||||
\(446\) | 29.1599i | 1.38076i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.03449i | 0.143366i | ||||||||
\(449\) | −17.7055 | −0.835574 | −0.417787 | − | 0.908545i | \(-0.637194\pi\) | ||||
−0.417787 | + | 0.908545i | \(0.637194\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.9684i | 0.987363i | ||||||||
\(452\) | − | 4.62177i | − | 0.217390i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −21.7892 | −1.02262 | ||||||||
\(455\) | 11.6623 | + | 3.17273i | 0.546736 | + | 0.148740i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.7674i | 0.690788i | 0.938458 | + | 0.345394i | \(0.112255\pi\) | ||||
−0.938458 | + | 0.345394i | \(0.887745\pi\) | |||||||
\(458\) | − | 15.0380i | − | 0.702682i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.48098 | − | 12.7953i | 0.162301 | − | 0.596585i | ||||
\(461\) | 3.54358i | 0.165041i | 0.996589 | + | 0.0825205i | \(0.0262970\pi\) | ||||
−0.996589 | + | 0.0825205i | \(0.973703\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 23.7855i | − | 1.10541i | −0.833378 | − | 0.552704i | \(-0.813596\pi\) | ||
0.833378 | − | 0.552704i | \(-0.186404\pi\) | |||||||
\(464\) | 4.19330 | 0.194669 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.37338i | 0.248917i | ||||||||
\(467\) | −29.9479 | −1.38582 | −0.692912 | − | 0.721022i | \(-0.743673\pi\) | ||||
−0.692912 | + | 0.721022i | \(0.743673\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 30.2604i | − | 1.39730i | ||||||
\(470\) | −9.25937 | − | 2.51902i | −0.427103 | − | 0.116194i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.22488i | 0.286523i | ||||||||
\(473\) | −16.9816 | −0.780817 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.71744 | + | 20.3824i | 0.354101 | + | 0.935207i | ||||
\(476\) | − | 5.43516i | − | 0.249120i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.36542 | 0.336886 | ||||||||
\(479\) | 9.52876i | 0.435380i | 0.976018 | + | 0.217690i | \(0.0698522\pi\) | ||||
−0.976018 | + | 0.217690i | \(0.930148\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.90863 | 0.223814 | ||||||||
\(482\) | 2.75247 | 0.125371 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.58373 | −0.117442 | ||||||||
\(485\) | −2.31761 | + | 8.51902i | −0.105237 | + | 0.386829i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.7534 | 0.532596 | 0.266298 | − | 0.963891i | \(-0.414200\pi\) | ||||
0.266298 | + | 0.963891i | \(0.414200\pi\) | |||||||
\(488\) | − | 4.10275i | − | 0.185723i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.76438 | − | 1.29615i | −0.215233 | − | 0.0585543i | ||||
\(491\) | − | 9.05139i | − | 0.408484i | −0.978920 | − | 0.204242i | \(-0.934527\pi\) | ||
0.978920 | − | 0.204242i | \(-0.0654729\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.51073 | −0.338266 | ||||||||
\(494\) | −4.86753 | + | 6.04889i | −0.219001 | + | 0.272152i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.66480i | 0.433962i | ||||||||
\(497\) | − | 33.1355i | − | 1.48633i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −40.4464 | −1.81063 | −0.905315 | − | 0.424741i | \(-0.860365\pi\) | ||||
−0.905315 | + | 0.424741i | \(0.860365\pi\) | |||||||
\(500\) | −7.99585 | + | 7.81450i | −0.357585 | + | 0.349475i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 20.0170 | 0.893400 | ||||||||
\(503\) | −3.98676 | −0.177761 | −0.0888804 | − | 0.996042i | \(-0.528329\pi\) | ||||
−0.0888804 | + | 0.996042i | \(0.528329\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.41627 | − | 0.657350i | −0.107523 | − | 0.0292517i | ||||
\(506\) | 17.2040 | 0.764813 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −19.2641 | −0.854706 | ||||||||
\(509\) | 31.3589 | 1.38996 | 0.694979 | − | 0.719030i | \(-0.255414\pi\) | ||||
0.694979 | + | 0.719030i | \(0.255414\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.0594 | −1.02009 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −11.0380 | −0.486867 | ||||||||
\(515\) | −1.91833 | + | 7.05137i | −0.0845319 | + | 0.310721i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 12.4498i | − | 0.547540i | ||||||
\(518\) | −8.36237 | −0.367421 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.84324 | − | 1.04556i | −0.168537 | − | 0.0458507i | ||||
\(521\) | −4.99547 | −0.218856 | −0.109428 | − | 0.993995i | \(-0.534902\pi\) | ||||
−0.109428 | + | 0.993995i | \(0.534902\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.8934 | 0.826149 | 0.413074 | − | 0.910697i | \(-0.364455\pi\) | ||||
0.413074 | + | 0.910697i | \(0.364455\pi\) | |||||||
\(524\) | − | 12.5062i | − | 0.546337i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.1651i | 0.530423i | ||||||||
\(527\) | − | 17.3109i | − | 0.754074i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.1675 | 0.529020 | ||||||||
\(530\) | −7.87367 | + | 28.9419i | −0.342010 | + | 1.25716i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.29235 | − | 10.3049i | 0.359519 | − | 0.446775i | ||||
\(533\) | 12.8743 | 0.557646 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.8703 | − | 2.95728i | −0.469965 | − | 0.127854i | ||||
\(536\) | 9.97215i | 0.430731i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 0.430855i | − | 0.0185755i | ||||||
\(539\) | − | 6.40598i | − | 0.275925i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.1736 | 1.55522 | 0.777611 | − | 0.628745i | \(-0.216431\pi\) | ||||
0.777611 | + | 0.628745i | \(0.216431\pi\) | |||||||
\(542\) | 20.1788i | 0.866755i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.79113i | 0.0767939i | ||||||||
\(545\) | −10.5910 | − | 2.88128i | −0.453667 | − | 0.123420i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.4312 | 0.916330 | 0.458165 | − | 0.888867i | \(-0.348507\pi\) | ||||
0.458165 | + | 0.888867i | \(0.348507\pi\) | |||||||
\(548\) | 4.44375 | 0.189828 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −12.5062 | − | 7.34854i | −0.533267 | − | 0.313343i | ||||
\(551\) | −14.2401 | − | 11.4590i | −0.606651 | − | 0.488171i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.58711 | 0.322637 | ||||||||
\(554\) | 4.78004 | 0.203085 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.89461 | −0.122759 | ||||||||
\(557\) | 33.3778 | 1.41426 | 0.707132 | − | 0.707081i | \(-0.249989\pi\) | ||||
0.707132 | + | 0.707081i | \(0.249989\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.4265i | 0.440992i | ||||||||
\(560\) | 6.54736 | + | 1.78122i | 0.276677 | + | 0.0752702i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.31308i | 0.308484i | ||||||||
\(563\) | − | 35.3463i | − | 1.48967i | −0.667250 | − | 0.744834i | \(-0.732529\pi\) | ||
0.667250 | − | 0.744834i | \(-0.267471\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.97215 | − | 2.71293i | −0.419531 | − | 0.114134i | ||||
\(566\) | 19.4364 | 0.816971 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.9196i | 0.458177i | ||||||||
\(569\) | 34.2522 | 1.43593 | 0.717963 | − | 0.696081i | \(-0.245075\pi\) | ||||
0.717963 | + | 0.696081i | \(0.245075\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.9681 | −1.00303 | −0.501516 | − | 0.865148i | \(-0.667224\pi\) | ||||
−0.501516 | + | 0.865148i | \(0.667224\pi\) | |||||||
\(572\) | − | 5.16745i | − | 0.216062i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −21.9327 | −0.915451 | ||||||||
\(575\) | −25.5645 | − | 15.0215i | −1.06611 | − | 0.626438i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 30.0104i | − | 1.24935i | −0.780885 | − | 0.624675i | \(-0.785231\pi\) | ||
0.780885 | − | 0.624675i | \(-0.214769\pi\) | |||||||
\(578\) | 13.7919i | 0.573666i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.46142 | − | 9.04765i | 0.102205 | − | 0.375683i | ||||
\(581\) | − | 45.9125i | − | 1.90477i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −38.9140 | −1.61165 | ||||||||
\(584\) | 7.59911 | 0.314453 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.7245 | 1.02136 | ||||||||
\(587\) | −2.03548 | −0.0840130 | −0.0420065 | − | 0.999117i | \(-0.513375\pi\) | ||||
−0.0420065 | + | 0.999117i | \(0.513375\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.4110 | − | 32.8210i | 1.08825 | − | 1.35237i | ||||
\(590\) | 13.4311 | + | 3.65394i | 0.552949 | + | 0.150430i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.75577 | 0.113262 | ||||||||
\(593\) | 18.9568 | 0.778463 | 0.389231 | − | 0.921140i | \(-0.372741\pi\) | ||||
0.389231 | + | 0.921140i | \(0.372741\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.7272 | − | 3.19039i | −0.480767 | − | 0.130793i | ||||
\(596\) | − | 4.68230i | − | 0.191794i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 10.5630i | − | 0.431953i | ||||||
\(599\) | −37.6838 | −1.53972 | −0.769858 | − | 0.638215i | \(-0.779673\pi\) | ||||
−0.769858 | + | 0.638215i | \(0.779673\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.9446i | 0.487231i | 0.969872 | + | 0.243616i | \(0.0783335\pi\) | ||||
−0.969872 | + | 0.243616i | \(0.921666\pi\) | |||||||
\(602\) | − | 17.7626i | − | 0.723948i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 9.36014i | − | 0.380859i | ||||||
\(605\) | −1.51662 | + | 5.57477i | −0.0616595 | + | 0.226647i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.3675 | −0.461393 | −0.230696 | − | 0.973026i | \(-0.574100\pi\) | ||||
−0.230696 | + | 0.973026i | \(0.574100\pi\) | |||||||
\(608\) | −2.73270 | + | 3.39593i | −0.110826 | + | 0.137723i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.85228 | − | 2.40827i | −0.358419 | − | 0.0975081i | ||||
\(611\) | −7.64395 | −0.309241 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 28.9369i | − | 1.16875i | −0.811483 | − | 0.584375i | \(-0.801340\pi\) | ||
0.811483 | − | 0.584375i | \(-0.198660\pi\) | |||||||
\(614\) | 1.48687i | 0.0600051i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.80331i | 0.354695i | ||||||||
\(617\) | −17.4178 | −0.701216 | −0.350608 | − | 0.936522i | \(-0.614025\pi\) | ||||
−0.350608 | + | 0.936522i | \(0.614025\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.3782 | 0.698490 | 0.349245 | − | 0.937031i | \(-0.386438\pi\) | ||||
0.349245 | + | 0.937031i | \(0.386438\pi\) | |||||||
\(620\) | 20.8532 | + | 5.67314i | 0.837486 | + | 0.227839i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.80957 | 0.112654 | ||||||||
\(623\) | 52.6786i | 2.11052i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.1675 | + | 21.8393i | 0.486698 | + | 0.873570i | ||||
\(626\) | 17.9467 | 0.717294 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.8298i | 0.631678i | ||||||||
\(629\) | −4.93594 | −0.196809 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.5190 | 0.498374 | 0.249187 | − | 0.968455i | \(-0.419837\pi\) | ||||
0.249187 | + | 0.968455i | \(0.419837\pi\) | |||||||
\(632\) | −2.50029 | −0.0994563 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −25.2702 | −1.00361 | ||||||||
\(635\) | −11.3078 | + | 41.5651i | −0.448738 | + | 1.64946i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.93317 | −0.155838 | ||||||||
\(638\) | 12.1651 | 0.481621 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.15765 | − | 0.586990i | −0.0852885 | − | 0.0232028i | ||||
\(641\) | −37.1418 | −1.46701 | −0.733507 | − | 0.679682i | \(-0.762118\pi\) | ||||
−0.733507 | + | 0.679682i | \(0.762118\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.1315i | 1.58263i | 0.611408 | + | 0.791316i | \(0.290604\pi\) | ||||
−0.611408 | + | 0.791316i | \(0.709396\pi\) | |||||||
\(644\) | 17.9952i | 0.709110i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.89461 | − | 6.08255i | 0.192576 | − | 0.239315i | ||||
\(647\) | 11.6400 | 0.457614 | 0.228807 | − | 0.973472i | \(-0.426518\pi\) | ||||
0.228807 | + | 0.973472i | \(0.426518\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.0589i | 0.708873i | ||||||||
\(650\) | −4.51189 | + | 7.67862i | −0.176971 | + | 0.301180i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.6681i | 0.535284i | ||||||||
\(653\) | −26.3132 | −1.02971 | −0.514857 | − | 0.857276i | \(-0.672155\pi\) | ||||
−0.514857 | + | 0.857276i | \(0.672155\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26.9840 | − | 7.34103i | −1.05435 | − | 0.286838i | ||||
\(656\) | 7.22779 | 0.282198 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 13.0223 | 0.507661 | ||||||||
\(659\) | −2.07642 | −0.0808858 | −0.0404429 | − | 0.999182i | \(-0.512877\pi\) | ||||
−0.0404429 | + | 0.999182i | \(0.512877\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 9.42045i | − | 0.366413i | −0.983074 | − | 0.183207i | \(-0.941352\pi\) | ||
0.983074 | − | 0.183207i | \(-0.0586477\pi\) | |||||||
\(662\) | 1.69911 | 0.0660378 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15.1302i | 0.587166i | ||||||||
\(665\) | −17.3669 | − | 23.9409i | −0.673458 | − | 0.928387i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.8671 | 0.962860 | ||||||||
\(668\) | − | 9.93265i | − | 0.384306i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 21.5164 | + | 5.85355i | 0.831250 | + | 0.226143i | ||||
\(671\) | − | 11.9024i | − | 0.459487i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.5338 | −0.714426 | −0.357213 | − | 0.934023i | \(-0.616273\pi\) | ||||
−0.357213 | + | 0.934023i | \(0.616273\pi\) | |||||||
\(674\) | 16.1225i | 0.621014i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.82727 | 0.377972 | ||||||||
\(677\) | 27.5518i | 1.05890i | 0.848341 | + | 0.529451i | \(0.177602\pi\) | ||||
−0.848341 | + | 0.529451i | \(0.822398\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 11.9811i | − | 0.459791i | ||||||
\(680\) | 3.86462 | + | 1.05137i | 0.148201 | + | 0.0403184i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 28.0384i | 1.07364i | ||||||||
\(683\) | 6.30825i | 0.241378i | 0.992690 | + | 0.120689i | \(0.0385104\pi\) | ||||
−0.992690 | + | 0.120689i | \(0.961490\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.60844 | − | 9.58804i | 0.0996633 | − | 0.366340i | ||||
\(686\) | −14.5409 | −0.555173 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.85355i | 0.223165i | ||||||||
\(689\) | 23.8926i | 0.910235i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.0975 | 0.992795 | 0.496397 | − | 0.868095i | \(-0.334656\pi\) | ||||
0.496397 | + | 0.868095i | \(0.334656\pi\) | |||||||
\(692\) | 12.0354i | 0.457517i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.01595i | 0.342241i | ||||||||
\(695\) | −1.69911 | + | 6.24555i | −0.0644509 | + | 0.236907i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.9459 | −0.490360 | ||||||||
\(698\) | − | 36.5137i | − | 1.38207i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.68648 | − | 13.0813i | 0.290521 | − | 0.494428i | ||||
\(701\) | − | 39.8697i | − | 1.50586i | −0.658101 | − | 0.752930i | \(-0.728640\pi\) | ||
0.658101 | − | 0.752930i | \(-0.271360\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.35842 | − | 7.53070i | −0.352959 | − | 0.284026i | ||||
\(704\) | − | 2.90108i | − | 0.109339i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.5379i | 0.471870i | ||||||||
\(707\) | 3.39822 | 0.127803 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.6865 | 1.26512 | 0.632561 | − | 0.774510i | \(-0.282004\pi\) | ||||
0.632561 | + | 0.774510i | \(0.282004\pi\) | |||||||
\(710\) | 23.5607 | + | 6.40972i | 0.884218 | + | 0.240552i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 17.3599i | − | 0.650591i | ||||||
\(713\) | 57.3143i | 2.14644i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.1495 | − | 3.03325i | −0.416969 | − | 0.113437i | ||||
\(716\) | −18.2775 | −0.683064 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 16.1413 | 0.602389 | ||||||||
\(719\) | − | 28.9230i | − | 1.07865i | −0.842099 | − | 0.539324i | \(-0.818680\pi\) | ||
0.842099 | − | 0.539324i | \(-0.181320\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 9.91697i | − | 0.369327i | ||||||
\(722\) | 18.5601 | − | 4.06471i | 0.690736 | − | 0.151273i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 23.6288i | 0.878159i | ||||||||
\(725\) | −18.0768 | − | 10.6218i | −0.671356 | − | 0.394483i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 0.371322i | − | 0.0137716i | −0.999976 | − | 0.00688579i | \(-0.997808\pi\) | ||
0.999976 | − | 0.00688579i | \(-0.00219183\pi\) | |||||||
\(728\) | 5.40509 | 0.200326 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.46060 | − | 16.3962i | 0.165094 | − | 0.606850i | ||||
\(731\) | − | 10.4845i | − | 0.387782i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.2519i | 0.489471i | 0.969590 | + | 0.244736i | \(0.0787012\pi\) | ||||
−0.969590 | + | 0.244736i | \(0.921299\pi\) | |||||||
\(734\) | −19.5812 | −0.722754 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 5.93022i | − | 0.218591i | ||||||
\(737\) | 28.9300i | 1.06565i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.3135 | −0.526531 | −0.263266 | − | 0.964723i | \(-0.584800\pi\) | ||||
−0.263266 | + | 0.964723i | \(0.584800\pi\) | |||||||
\(740\) | 1.61761 | − | 5.94599i | 0.0594646 | − | 0.218579i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 40.7036i | − | 1.49427i | ||||||
\(743\) | − | 0.818528i | − | 0.0300289i | −0.999887 | − | 0.0150144i | \(-0.995221\pi\) | ||
0.999887 | − | 0.0150144i | \(-0.00477942\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.1027 | − | 2.74846i | −0.370136 | − | 0.100696i | ||||
\(746\) | 15.2394i | 0.557955i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.19621i | 0.189992i | ||||||||
\(749\) | 15.2879 | 0.558607 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.5063i | 1.22266i | 0.791375 | + | 0.611331i | \(0.209366\pi\) | ||||
−0.791375 | + | 0.611331i | \(0.790634\pi\) | |||||||
\(752\) | −4.29142 | −0.156492 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 7.46917i | − | 0.272011i | ||||||
\(755\) | −20.1959 | − | 5.49431i | −0.735003 | − | 0.199958i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 45.3130i | − | 1.64693i | −0.567368 | − | 0.823465i | \(-0.692038\pi\) | ||
0.567368 | − | 0.823465i | \(-0.307962\pi\) | |||||||
\(758\) | 30.0160 | 1.09023 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.72316 | + | 7.88958i | 0.207601 | + | 0.286185i | ||||
\(761\) | − | 9.60888i | − | 0.348322i | −0.984717 | − | 0.174161i | \(-0.944279\pi\) | ||
0.984717 | − | 0.174161i | \(-0.0557212\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.8950 | 0.539235 | ||||||||
\(764\) | − | 16.3630i | − | 0.591993i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −28.2055 | −1.01911 | ||||||||
\(767\) | 11.0879 | 0.400359 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.6191 | 1.42870 | 0.714351 | − | 0.699787i | \(-0.246722\pi\) | ||||
0.714351 | + | 0.699787i | \(0.246722\pi\) | |||||||
\(770\) | 18.9944 | + | 5.16745i | 0.684512 | + | 0.186222i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.10101 | −0.0396262 | ||||||||
\(773\) | − | 12.3436i | − | 0.443970i | −0.975050 | − | 0.221985i | \(-0.928746\pi\) | ||
0.975050 | − | 0.221985i | \(-0.0712536\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24.4813 | − | 41.6638i | 0.879394 | − | 1.49661i | ||||
\(776\) | 3.94829i | 0.141735i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.21428 | 0.115238 | ||||||||
\(779\) | −24.5451 | − | 19.7514i | −0.879418 | − | 0.707666i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31.6787i | 1.13355i | ||||||||
\(782\) | 10.6218i | 0.379834i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.20814 | −0.0788620 | ||||||||
\(785\) | 34.1551 | + | 9.29194i | 1.21905 | + | 0.331644i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 46.4248 | 1.65486 | 0.827432 | − | 0.561566i | \(-0.189801\pi\) | ||||
0.827432 | + | 0.561566i | \(0.189801\pi\) | |||||||
\(788\) | 27.5475 | 0.981338 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.46765 | + | 5.39475i | −0.0522165 | + | 0.191936i | ||||
\(791\) | 14.0247 | 0.498662 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.30788 | −0.259511 | ||||||||
\(794\) | −17.4901 | −0.620699 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.62177 | 0.0929262 | ||||||||
\(797\) | 6.83255i | 0.242021i | 0.992651 | + | 0.121011i | \(0.0386135\pi\) | ||||
−0.992651 | + | 0.121011i | \(0.961387\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.68648 | 0.271928 | ||||||||
\(800\) | −2.53304 | + | 4.31088i | −0.0895564 | + | 0.152413i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.13958i | 0.216796i | ||||||||
\(803\) | 22.0456 | 0.777973 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 38.8273 | + | 10.5630i | 1.36848 | + | 0.372297i | ||||
\(806\) | 17.2151 | 0.606376 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.11986 | −0.0393967 | ||||||||
\(809\) | 0.332058i | 0.0116745i | 0.999983 | + | 0.00583727i | \(0.00185807\pi\) | ||||
−0.999983 | + | 0.00583727i | \(0.998142\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 16.1280i | − | 0.566330i | −0.959071 | − | 0.283165i | \(-0.908616\pi\) | ||
0.959071 | − | 0.283165i | \(-0.0913843\pi\) | |||||||
\(812\) | 12.7245i | 0.446543i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.99472 | 0.280215 | ||||||||
\(815\) | 29.4909 | + | 8.02304i | 1.03302 | + | 0.281035i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.9960 | − | 19.8783i | 0.559629 | − | 0.695453i | ||||
\(818\) | −10.0012 | −0.349683 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.24264 | − | 15.5950i | 0.148159 | − | 0.544602i | ||||
\(821\) | 28.9230i | 1.00942i | 0.863289 | + | 0.504710i | \(0.168401\pi\) | ||||
−0.863289 | + | 0.504710i | \(0.831599\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 10.0726i | − | 0.351109i | −0.984470 | − | 0.175555i | \(-0.943828\pi\) | ||
0.984470 | − | 0.175555i | \(-0.0561719\pi\) | |||||||
\(824\) | 3.26808i | 0.113849i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18.8893 | −0.657244 | ||||||||
\(827\) | 48.7245i | 1.69432i | 0.531340 | + | 0.847159i | \(0.321689\pi\) | ||||
−0.531340 | + | 0.847159i | \(0.678311\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 51.7253i | − | 1.79649i | −0.439490 | − | 0.898247i | \(-0.644841\pi\) | ||
0.439490 | − | 0.898247i | \(-0.355159\pi\) | |||||||
\(830\) | 32.6456 | + | 8.88128i | 1.13315 | + | 0.308274i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.78122 | −0.0617526 | ||||||||
\(833\) | 3.95505 | 0.137034 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.4312 | − | 5.83037i | −0.741656 | − | 0.201768i | ||||
\(836\) | −7.92778 | + | 9.85187i | −0.274188 | + | 0.340734i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 20.9915 | 0.725140 | ||||||||
\(839\) | 35.9830 | 1.24227 | 0.621136 | − | 0.783703i | \(-0.286671\pi\) | ||||
0.621136 | + | 0.783703i | \(0.286671\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.4163 | −0.393665 | ||||||||
\(842\) | −15.6553 | −0.539518 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.64315i | 0.297509i | ||||||||
\(845\) | 5.76851 | − | 21.2038i | 0.198443 | − | 0.729432i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 7.84030i | − | 0.269396i | ||||||
\(848\) | 13.4136i | 0.460626i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.53699 | − | 7.72134i | 0.155617 | − | 0.264840i | ||||
\(851\) | 16.3423 | 0.560208 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 43.9645i | − | 1.50532i | −0.658411 | − | 0.752659i | \(-0.728771\pi\) | ||
0.658411 | − | 0.752659i | \(-0.271229\pi\) | |||||||
\(854\) | 12.4498 | 0.426022 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.03804 | −0.172197 | ||||||||
\(857\) | 0.308245i | 0.0105295i | 0.999986 | + | 0.00526473i | \(0.00167582\pi\) | ||||
−0.999986 | + | 0.00526473i | \(0.998324\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.75118 | −0.298586 | −0.149293 | − | 0.988793i | \(-0.547700\pi\) | ||||
−0.149293 | + | 0.988793i | \(0.547700\pi\) | |||||||
\(860\) | 12.6299 | + | 3.43598i | 0.430676 | + | 0.117166i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 0.430855i | − | 0.0146750i | ||||||
\(863\) | 50.4110i | 1.71601i | 0.513641 | + | 0.858005i | \(0.328296\pi\) | ||||
−0.513641 | + | 0.858005i | \(0.671704\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 25.9682 | + | 7.06466i | 0.882944 | + | 0.240206i | ||||
\(866\) | − | 34.8894i | − | 1.18559i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −29.3277 | −0.995449 | ||||||||
\(869\) | −7.25355 | −0.246060 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.7626 | 0.601861 | ||||||||
\(872\) | −4.90856 | −0.166225 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −16.2055 | + | 20.1386i | −0.548159 | + | 0.681199i | ||||
\(875\) | −23.7130 | − | 24.2633i | −0.801647 | − | 0.820250i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.6475 | −0.967359 | −0.483679 | − | 0.875245i | \(-0.660700\pi\) | ||||
−0.483679 | + | 0.875245i | \(0.660700\pi\) | |||||||
\(878\) | −15.8997 | −0.536588 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.25951 | − | 1.70291i | −0.211008 | − | 0.0574050i | ||||
\(881\) | − | 48.3201i | − | 1.62794i | −0.580904 | − | 0.813972i | \(-0.697301\pi\) | ||
0.580904 | − | 0.813972i | \(-0.302699\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 38.1257i | − | 1.28303i | −0.767110 | − | 0.641516i | \(-0.778306\pi\) | ||
0.767110 | − | 0.641516i | \(-0.221694\pi\) | |||||||
\(884\) | 3.19039 | 0.107304 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 7.47699i | − | 0.251195i | ||||||
\(887\) | − | 25.3056i | − | 0.849679i | −0.905269 | − | 0.424840i | \(-0.860331\pi\) | ||
0.905269 | − | 0.424840i | \(-0.139669\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 58.4567i | − | 1.96058i | ||||||
\(890\) | −37.4566 | − | 10.1901i | −1.25555 | − | 0.341573i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 29.1599 | 0.976344 | ||||||||
\(893\) | 14.5734 | + | 11.7272i | 0.487679 | + | 0.392434i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.7287 | + | 39.4365i | −0.358622 | + | 1.31822i | ||||
\(896\) | 3.03449 | 0.101375 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 17.7055i | 0.590840i | ||||||||
\(899\) | 40.5274i | 1.35166i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 24.0255i | − | 0.800406i | ||||||
\(902\) | 20.9684 | 0.698171 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.62177 | −0.153718 | ||||||||
\(905\) | 50.9827 | + | 13.8699i | 1.69472 | + | 0.461051i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.84570 | −0.326921 | −0.163460 | − | 0.986550i | \(-0.552266\pi\) | ||||
−0.163460 | + | 0.986550i | \(0.552266\pi\) | |||||||
\(908\) | 21.7892i | 0.723101i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.17273 | − | 11.6623i | 0.105175 | − | 0.386601i | ||||
\(911\) | −0.215427 | −0.00713743 | −0.00356871 | − | 0.999994i | \(-0.501136\pi\) | ||||
−0.00356871 | + | 0.999994i | \(0.501136\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 43.8939i | 1.45268i | ||||||||
\(914\) | 14.7674 | 0.488461 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −15.0380 | −0.496871 | ||||||||
\(917\) | 37.9500 | 1.25322 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 55.9628 | 1.84604 | 0.923021 | − | 0.384750i | \(-0.125712\pi\) | ||||
0.923021 | + | 0.384750i | \(0.125712\pi\) | |||||||
\(920\) | −12.7953 | − | 3.48098i | −0.421849 | − | 0.114764i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.54358 | 0.116702 | ||||||||
\(923\) | 19.4502 | 0.640212 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.8798 | − | 6.98047i | −0.390606 | − | 0.229517i | ||||
\(926\) | −23.7855 | −0.781641 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 4.19330i | − | 0.137652i | ||||||
\(929\) | − | 22.9718i | − | 0.753681i | −0.926278 | − | 0.376841i | \(-0.877010\pi\) | ||
0.926278 | − | 0.376841i | \(-0.122990\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.49868 | + | 6.03417i | 0.245759 | + | 0.197762i | ||||
\(932\) | 5.37338 | 0.176011 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 29.9479i | 0.979926i | ||||||||
\(935\) | 11.2116 | + | 3.05012i | 0.366658 | + | 0.0997497i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 0.215427i | − | 0.00703771i | −0.999994 | − | 0.00351885i | \(-0.998880\pi\) | ||
0.999994 | − | 0.00351885i | \(-0.00112009\pi\) | |||||||
\(938\) | −30.2604 | −0.988037 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.51902 | + | 9.25937i | −0.0821614 | + | 0.302007i | ||||
\(941\) | −49.4762 | −1.61288 | −0.806438 | − | 0.591318i | \(-0.798608\pi\) | ||||
−0.806438 | + | 0.591318i | \(0.798608\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 42.8623 | 1.39579 | ||||||||
\(944\) | 6.22488 | 0.202602 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.9816i | 0.552121i | ||||||||
\(947\) | −14.9462 | −0.485685 | −0.242843 | − | 0.970066i | \(-0.578080\pi\) | ||||
−0.242843 | + | 0.970066i | \(0.578080\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 13.5357i | − | 0.439386i | ||||||
\(950\) | 20.3824 | − | 7.71744i | 0.661291 | − | 0.250387i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.43516 | −0.176155 | ||||||||
\(953\) | 4.62177i | 0.149714i | 0.997194 | + | 0.0748569i | \(0.0238500\pi\) | ||||
−0.997194 | + | 0.0748569i | \(0.976150\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −35.3056 | − | 9.60493i | −1.14246 | − | 0.310808i | ||||
\(956\) | − | 7.36542i | − | 0.238215i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.52876 | 0.307860 | ||||||||
\(959\) | 13.4845i | 0.435438i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −62.4084 | −2.01317 | ||||||||
\(962\) | − | 4.90863i | − | 0.158261i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 2.75247i | − | 0.0886509i | ||||||
\(965\) | −0.646282 | + | 2.37559i | −0.0208046 | + | 0.0764730i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.94629i | 0.0625884i | 0.999510 | + | 0.0312942i | \(0.00996287\pi\) | ||||
−0.999510 | + | 0.0312942i | \(0.990037\pi\) | |||||||
\(968\) | 2.58373i | 0.0830441i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.51902 | + | 2.31761i | 0.273529 | + | 0.0744139i | ||||
\(971\) | −8.97334 | −0.287968 | −0.143984 | − | 0.989580i | \(-0.545991\pi\) | ||||
−0.143984 | + | 0.989580i | \(0.545991\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 8.78367i | − | 0.281592i | ||||||
\(974\) | − | 11.7534i | − | 0.376602i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.10275 | −0.131326 | ||||||||
\(977\) | 49.7573i | 1.59188i | 0.605378 | + | 0.795938i | \(0.293022\pi\) | ||||
−0.605378 | + | 0.795938i | \(0.706978\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 50.3626i | − | 1.60959i | ||||||
\(980\) | −1.29615 | + | 4.76438i | −0.0414041 | + | 0.152193i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −9.05139 | −0.288842 | ||||||||
\(983\) | − | 44.7546i | − | 1.42745i | −0.700425 | − | 0.713726i | \(-0.747006\pi\) | ||
0.700425 | − | 0.713726i | \(-0.252994\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.1701 | − | 59.4377i | 0.515222 | − | 1.89384i | ||||
\(986\) | 7.51073i | 0.239190i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.04889 | + | 4.86753i | 0.192441 | + | 0.154857i | ||||
\(989\) | 34.7128i | 1.10380i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 36.6476i | − | 1.16415i | −0.813135 | − | 0.582075i | \(-0.802241\pi\) | ||
0.813135 | − | 0.582075i | \(-0.197759\pi\) | |||||||
\(992\) | 9.66480 | 0.306858 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −33.1355 | −1.05099 | ||||||||
\(995\) | 1.53895 | − | 5.65685i | 0.0487881 | − | 0.179334i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.7325i | 0.783288i | 0.920117 | + | 0.391644i | \(0.128093\pi\) | ||||
−0.920117 | + | 0.391644i | \(0.871907\pi\) | |||||||
\(998\) | 40.4464i | 1.28031i | ||||||||
\(999\) | 0 | 0 |
(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 | 1710.2.c.d.1709.18 | yes | 24 | |
3.2 | odd | 2 | inner | 1710.2.c.d.1709.11 | yes | 24 | |
5.4 | even | 2 | inner | 1710.2.c.d.1709.12 | yes | 24 | |
15.14 | odd | 2 | inner | 1710.2.c.d.1709.17 | yes | 24 | |
19.18 | odd | 2 | inner | 1710.2.c.d.1709.20 | yes | 24 | |
57.56 | even | 2 | inner | 1710.2.c.d.1709.9 | ✓ | 24 | |
95.94 | odd | 2 | inner | 1710.2.c.d.1709.10 | yes | 24 | |
285.284 | even | 2 | inner | 1710.2.c.d.1709.19 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1710.2.c.d.1709.9 | ✓ | 24 | 57.56 | even | 2 | inner | |
1710.2.c.d.1709.10 | yes | 24 | 95.94 | odd | 2 | inner | |
1710.2.c.d.1709.11 | yes | 24 | 3.2 | odd | 2 | inner | |
1710.2.c.d.1709.12 | yes | 24 | 5.4 | even | 2 | inner | |
1710.2.c.d.1709.17 | yes | 24 | 15.14 | odd | 2 | inner | |
1710.2.c.d.1709.18 | yes | 24 | 1.1 | even | 1 | trivial | |
1710.2.c.d.1709.19 | yes | 24 | 285.284 | even | 2 | inner | |
1710.2.c.d.1709.20 | yes | 24 | 19.18 | odd | 2 | inner |