Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6014,2,Mod(1,6014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6014, 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("6014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6014 = 2 \cdot 31 \cdot 97 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6014.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.0220317756\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 6014.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.56192 | 0.901776 | 0.450888 | − | 0.892580i | \(-0.351107\pi\) | ||||
0.450888 | + | 0.892580i | \(0.351107\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.75184 | −1.67787 | −0.838937 | − | 0.544229i | \(-0.816822\pi\) | ||||
−0.838937 | + | 0.544229i | \(0.816822\pi\) | |||||||
\(6\) | 1.56192 | 0.637652 | ||||||||
\(7\) | −2.39374 | −0.904749 | −0.452374 | − | 0.891828i | \(-0.649423\pi\) | ||||
−0.452374 | + | 0.891828i | \(0.649423\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.560398 | −0.186799 | ||||||||
\(10\) | −3.75184 | −1.18644 | ||||||||
\(11\) | 2.24392 | 0.676568 | 0.338284 | − | 0.941044i | \(-0.390154\pi\) | ||||
0.338284 | + | 0.941044i | \(0.390154\pi\) | |||||||
\(12\) | 1.56192 | 0.450888 | ||||||||
\(13\) | 2.57839 | 0.715117 | 0.357558 | − | 0.933891i | \(-0.383609\pi\) | ||||
0.357558 | + | 0.933891i | \(0.383609\pi\) | |||||||
\(14\) | −2.39374 | −0.639754 | ||||||||
\(15\) | −5.86008 | −1.51307 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.0983609 | 0.0238560 | 0.0119280 | − | 0.999929i | \(-0.496203\pi\) | ||||
0.0119280 | + | 0.999929i | \(0.496203\pi\) | |||||||
\(18\) | −0.560398 | −0.132087 | ||||||||
\(19\) | 5.94294 | 1.36341 | 0.681703 | − | 0.731629i | \(-0.261240\pi\) | ||||
0.681703 | + | 0.731629i | \(0.261240\pi\) | |||||||
\(20\) | −3.75184 | −0.838937 | ||||||||
\(21\) | −3.73884 | −0.815881 | ||||||||
\(22\) | 2.24392 | 0.478406 | ||||||||
\(23\) | −1.87367 | −0.390686 | −0.195343 | − | 0.980735i | \(-0.562582\pi\) | ||||
−0.195343 | + | 0.980735i | \(0.562582\pi\) | |||||||
\(24\) | 1.56192 | 0.318826 | ||||||||
\(25\) | 9.07630 | 1.81526 | ||||||||
\(26\) | 2.57839 | 0.505664 | ||||||||
\(27\) | −5.56107 | −1.07023 | ||||||||
\(28\) | −2.39374 | −0.452374 | ||||||||
\(29\) | −7.16628 | −1.33074 | −0.665372 | − | 0.746512i | \(-0.731727\pi\) | ||||
−0.665372 | + | 0.746512i | \(0.731727\pi\) | |||||||
\(30\) | −5.86008 | −1.06990 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.50483 | 0.610113 | ||||||||
\(34\) | 0.0983609 | 0.0168687 | ||||||||
\(35\) | 8.98093 | 1.51805 | ||||||||
\(36\) | −0.560398 | −0.0933996 | ||||||||
\(37\) | 0.543246 | 0.0893091 | 0.0446545 | − | 0.999002i | \(-0.485781\pi\) | ||||
0.0446545 | + | 0.999002i | \(0.485781\pi\) | |||||||
\(38\) | 5.94294 | 0.964073 | ||||||||
\(39\) | 4.02725 | 0.644875 | ||||||||
\(40\) | −3.75184 | −0.593218 | ||||||||
\(41\) | 7.44368 | 1.16251 | 0.581253 | − | 0.813723i | \(-0.302562\pi\) | ||||
0.581253 | + | 0.813723i | \(0.302562\pi\) | |||||||
\(42\) | −3.73884 | −0.576915 | ||||||||
\(43\) | −5.45549 | −0.831954 | −0.415977 | − | 0.909375i | \(-0.636560\pi\) | ||||
−0.415977 | + | 0.909375i | \(0.636560\pi\) | |||||||
\(44\) | 2.24392 | 0.338284 | ||||||||
\(45\) | 2.10252 | 0.313426 | ||||||||
\(46\) | −1.87367 | −0.276257 | ||||||||
\(47\) | −8.90482 | −1.29890 | −0.649451 | − | 0.760404i | \(-0.725001\pi\) | ||||
−0.649451 | + | 0.760404i | \(0.725001\pi\) | |||||||
\(48\) | 1.56192 | 0.225444 | ||||||||
\(49\) | −1.27001 | −0.181430 | ||||||||
\(50\) | 9.07630 | 1.28358 | ||||||||
\(51\) | 0.153632 | 0.0215128 | ||||||||
\(52\) | 2.57839 | 0.357558 | ||||||||
\(53\) | 2.87792 | 0.395312 | 0.197656 | − | 0.980271i | \(-0.436667\pi\) | ||||
0.197656 | + | 0.980271i | \(0.436667\pi\) | |||||||
\(54\) | −5.56107 | −0.756765 | ||||||||
\(55\) | −8.41883 | −1.13519 | ||||||||
\(56\) | −2.39374 | −0.319877 | ||||||||
\(57\) | 9.28242 | 1.22949 | ||||||||
\(58\) | −7.16628 | −0.940978 | ||||||||
\(59\) | −8.47404 | −1.10323 | −0.551613 | − | 0.834100i | \(-0.685987\pi\) | ||||
−0.551613 | + | 0.834100i | \(0.685987\pi\) | |||||||
\(60\) | −5.86008 | −0.756533 | ||||||||
\(61\) | −7.57710 | −0.970149 | −0.485074 | − | 0.874473i | \(-0.661207\pi\) | ||||
−0.485074 | + | 0.874473i | \(0.661207\pi\) | |||||||
\(62\) | 1.00000 | 0.127000 | ||||||||
\(63\) | 1.34145 | 0.169006 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −9.67370 | −1.19988 | ||||||||
\(66\) | 3.50483 | 0.431415 | ||||||||
\(67\) | −11.3966 | −1.39232 | −0.696158 | − | 0.717888i | \(-0.745109\pi\) | ||||
−0.696158 | + | 0.717888i | \(0.745109\pi\) | |||||||
\(68\) | 0.0983609 | 0.0119280 | ||||||||
\(69\) | −2.92652 | −0.352312 | ||||||||
\(70\) | 8.98093 | 1.07343 | ||||||||
\(71\) | 3.15399 | 0.374310 | 0.187155 | − | 0.982330i | \(-0.440073\pi\) | ||||
0.187155 | + | 0.982330i | \(0.440073\pi\) | |||||||
\(72\) | −0.560398 | −0.0660435 | ||||||||
\(73\) | −9.85978 | −1.15400 | −0.577000 | − | 0.816744i | \(-0.695777\pi\) | ||||
−0.577000 | + | 0.816744i | \(0.695777\pi\) | |||||||
\(74\) | 0.543246 | 0.0631511 | ||||||||
\(75\) | 14.1765 | 1.63696 | ||||||||
\(76\) | 5.94294 | 0.681703 | ||||||||
\(77\) | −5.37136 | −0.612124 | ||||||||
\(78\) | 4.02725 | 0.455996 | ||||||||
\(79\) | −8.19488 | −0.921997 | −0.460998 | − | 0.887401i | \(-0.652509\pi\) | ||||
−0.460998 | + | 0.887401i | \(0.652509\pi\) | |||||||
\(80\) | −3.75184 | −0.419468 | ||||||||
\(81\) | −7.00476 | −0.778307 | ||||||||
\(82\) | 7.44368 | 0.822016 | ||||||||
\(83\) | 5.49596 | 0.603260 | 0.301630 | − | 0.953425i | \(-0.402469\pi\) | ||||
0.301630 | + | 0.953425i | \(0.402469\pi\) | |||||||
\(84\) | −3.73884 | −0.407940 | ||||||||
\(85\) | −0.369034 | −0.0400274 | ||||||||
\(86\) | −5.45549 | −0.588281 | ||||||||
\(87\) | −11.1932 | −1.20003 | ||||||||
\(88\) | 2.24392 | 0.239203 | ||||||||
\(89\) | 8.25650 | 0.875187 | 0.437593 | − | 0.899173i | \(-0.355831\pi\) | ||||
0.437593 | + | 0.899173i | \(0.355831\pi\) | |||||||
\(90\) | 2.10252 | 0.221625 | ||||||||
\(91\) | −6.17199 | −0.647001 | ||||||||
\(92\) | −1.87367 | −0.195343 | ||||||||
\(93\) | 1.56192 | 0.161964 | ||||||||
\(94\) | −8.90482 | −0.918462 | ||||||||
\(95\) | −22.2970 | −2.28762 | ||||||||
\(96\) | 1.56192 | 0.159413 | ||||||||
\(97\) | −1.00000 | −0.101535 | ||||||||
\(98\) | −1.27001 | −0.128290 | ||||||||
\(99\) | −1.25749 | −0.126382 | ||||||||
\(100\) | 9.07630 | 0.907630 | ||||||||
\(101\) | −8.27408 | −0.823302 | −0.411651 | − | 0.911342i | \(-0.635048\pi\) | ||||
−0.411651 | + | 0.911342i | \(0.635048\pi\) | |||||||
\(102\) | 0.153632 | 0.0152118 | ||||||||
\(103\) | −10.9834 | −1.08223 | −0.541115 | − | 0.840949i | \(-0.681997\pi\) | ||||
−0.541115 | + | 0.840949i | \(0.681997\pi\) | |||||||
\(104\) | 2.57839 | 0.252832 | ||||||||
\(105\) | 14.0275 | 1.36895 | ||||||||
\(106\) | 2.87792 | 0.279528 | ||||||||
\(107\) | 0.540399 | 0.0522423 | 0.0261212 | − | 0.999659i | \(-0.491684\pi\) | ||||
0.0261212 | + | 0.999659i | \(0.491684\pi\) | |||||||
\(108\) | −5.56107 | −0.535114 | ||||||||
\(109\) | −12.4265 | −1.19024 | −0.595122 | − | 0.803635i | \(-0.702896\pi\) | ||||
−0.595122 | + | 0.803635i | \(0.702896\pi\) | |||||||
\(110\) | −8.41883 | −0.802704 | ||||||||
\(111\) | 0.848508 | 0.0805368 | ||||||||
\(112\) | −2.39374 | −0.226187 | ||||||||
\(113\) | 2.36848 | 0.222808 | 0.111404 | − | 0.993775i | \(-0.464465\pi\) | ||||
0.111404 | + | 0.993775i | \(0.464465\pi\) | |||||||
\(114\) | 9.28242 | 0.869378 | ||||||||
\(115\) | 7.02969 | 0.655522 | ||||||||
\(116\) | −7.16628 | −0.665372 | ||||||||
\(117\) | −1.44492 | −0.133583 | ||||||||
\(118\) | −8.47404 | −0.780099 | ||||||||
\(119\) | −0.235450 | −0.0215837 | ||||||||
\(120\) | −5.86008 | −0.534950 | ||||||||
\(121\) | −5.96482 | −0.542256 | ||||||||
\(122\) | −7.57710 | −0.685999 | ||||||||
\(123\) | 11.6264 | 1.04832 | ||||||||
\(124\) | 1.00000 | 0.0898027 | ||||||||
\(125\) | −15.2936 | −1.36790 | ||||||||
\(126\) | 1.34145 | 0.119506 | ||||||||
\(127\) | −8.95664 | −0.794773 | −0.397387 | − | 0.917651i | \(-0.630083\pi\) | ||||
−0.397387 | + | 0.917651i | \(0.630083\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −8.52105 | −0.750237 | ||||||||
\(130\) | −9.67370 | −0.848440 | ||||||||
\(131\) | −1.81408 | −0.158497 | −0.0792486 | − | 0.996855i | \(-0.525252\pi\) | ||||
−0.0792486 | + | 0.996855i | \(0.525252\pi\) | |||||||
\(132\) | 3.50483 | 0.305056 | ||||||||
\(133\) | −14.2259 | −1.23354 | ||||||||
\(134\) | −11.3966 | −0.984516 | ||||||||
\(135\) | 20.8642 | 1.79571 | ||||||||
\(136\) | 0.0983609 | 0.00843437 | ||||||||
\(137\) | 8.60658 | 0.735310 | 0.367655 | − | 0.929962i | \(-0.380161\pi\) | ||||
0.367655 | + | 0.929962i | \(0.380161\pi\) | |||||||
\(138\) | −2.92652 | −0.249122 | ||||||||
\(139\) | −1.22561 | −0.103955 | −0.0519773 | − | 0.998648i | \(-0.516552\pi\) | ||||
−0.0519773 | + | 0.998648i | \(0.516552\pi\) | |||||||
\(140\) | 8.98093 | 0.759027 | ||||||||
\(141\) | −13.9086 | −1.17132 | ||||||||
\(142\) | 3.15399 | 0.264677 | ||||||||
\(143\) | 5.78570 | 0.483825 | ||||||||
\(144\) | −0.560398 | −0.0466998 | ||||||||
\(145\) | 26.8867 | 2.23282 | ||||||||
\(146\) | −9.85978 | −0.816001 | ||||||||
\(147\) | −1.98366 | −0.163609 | ||||||||
\(148\) | 0.543246 | 0.0446545 | ||||||||
\(149\) | 4.91409 | 0.402578 | 0.201289 | − | 0.979532i | \(-0.435487\pi\) | ||||
0.201289 | + | 0.979532i | \(0.435487\pi\) | |||||||
\(150\) | 14.1765 | 1.15750 | ||||||||
\(151\) | 5.25936 | 0.428001 | 0.214000 | − | 0.976834i | \(-0.431351\pi\) | ||||
0.214000 | + | 0.976834i | \(0.431351\pi\) | |||||||
\(152\) | 5.94294 | 0.482036 | ||||||||
\(153\) | −0.0551212 | −0.00445629 | ||||||||
\(154\) | −5.37136 | −0.432837 | ||||||||
\(155\) | −3.75184 | −0.301355 | ||||||||
\(156\) | 4.02725 | 0.322438 | ||||||||
\(157\) | −15.9814 | −1.27545 | −0.637726 | − | 0.770263i | \(-0.720125\pi\) | ||||
−0.637726 | + | 0.770263i | \(0.720125\pi\) | |||||||
\(158\) | −8.19488 | −0.651950 | ||||||||
\(159\) | 4.49508 | 0.356483 | ||||||||
\(160\) | −3.75184 | −0.296609 | ||||||||
\(161\) | 4.48507 | 0.353473 | ||||||||
\(162\) | −7.00476 | −0.550346 | ||||||||
\(163\) | 20.6002 | 1.61353 | 0.806766 | − | 0.590872i | \(-0.201216\pi\) | ||||
0.806766 | + | 0.590872i | \(0.201216\pi\) | |||||||
\(164\) | 7.44368 | 0.581253 | ||||||||
\(165\) | −13.1496 | −1.02369 | ||||||||
\(166\) | 5.49596 | 0.426569 | ||||||||
\(167\) | 6.52617 | 0.505010 | 0.252505 | − | 0.967596i | \(-0.418746\pi\) | ||||
0.252505 | + | 0.967596i | \(0.418746\pi\) | |||||||
\(168\) | −3.73884 | −0.288457 | ||||||||
\(169\) | −6.35191 | −0.488608 | ||||||||
\(170\) | −0.369034 | −0.0283036 | ||||||||
\(171\) | −3.33041 | −0.254683 | ||||||||
\(172\) | −5.45549 | −0.415977 | ||||||||
\(173\) | 2.24208 | 0.170462 | 0.0852311 | − | 0.996361i | \(-0.472837\pi\) | ||||
0.0852311 | + | 0.996361i | \(0.472837\pi\) | |||||||
\(174\) | −11.1932 | −0.848552 | ||||||||
\(175\) | −21.7263 | −1.64235 | ||||||||
\(176\) | 2.24392 | 0.169142 | ||||||||
\(177\) | −13.2358 | −0.994863 | ||||||||
\(178\) | 8.25650 | 0.618851 | ||||||||
\(179\) | 11.9848 | 0.895784 | 0.447892 | − | 0.894088i | \(-0.352175\pi\) | ||||
0.447892 | + | 0.894088i | \(0.352175\pi\) | |||||||
\(180\) | 2.10252 | 0.156713 | ||||||||
\(181\) | 15.6727 | 1.16494 | 0.582471 | − | 0.812852i | \(-0.302086\pi\) | ||||
0.582471 | + | 0.812852i | \(0.302086\pi\) | |||||||
\(182\) | −6.17199 | −0.457499 | ||||||||
\(183\) | −11.8348 | −0.874857 | ||||||||
\(184\) | −1.87367 | −0.138128 | ||||||||
\(185\) | −2.03817 | −0.149849 | ||||||||
\(186\) | 1.56192 | 0.114526 | ||||||||
\(187\) | 0.220714 | 0.0161402 | ||||||||
\(188\) | −8.90482 | −0.649451 | ||||||||
\(189\) | 13.3117 | 0.968287 | ||||||||
\(190\) | −22.2970 | −1.61759 | ||||||||
\(191\) | −2.91679 | −0.211052 | −0.105526 | − | 0.994417i | \(-0.533653\pi\) | ||||
−0.105526 | + | 0.994417i | \(0.533653\pi\) | |||||||
\(192\) | 1.56192 | 0.112722 | ||||||||
\(193\) | −6.67285 | −0.480322 | −0.240161 | − | 0.970733i | \(-0.577200\pi\) | ||||
−0.240161 | + | 0.970733i | \(0.577200\pi\) | |||||||
\(194\) | −1.00000 | −0.0717958 | ||||||||
\(195\) | −15.1096 | −1.08202 | ||||||||
\(196\) | −1.27001 | −0.0907150 | ||||||||
\(197\) | 0.343230 | 0.0244541 | 0.0122270 | − | 0.999925i | \(-0.496108\pi\) | ||||
0.0122270 | + | 0.999925i | \(0.496108\pi\) | |||||||
\(198\) | −1.25749 | −0.0893658 | ||||||||
\(199\) | −18.6347 | −1.32098 | −0.660491 | − | 0.750834i | \(-0.729652\pi\) | ||||
−0.660491 | + | 0.750834i | \(0.729652\pi\) | |||||||
\(200\) | 9.07630 | 0.641791 | ||||||||
\(201\) | −17.8006 | −1.25556 | ||||||||
\(202\) | −8.27408 | −0.582162 | ||||||||
\(203\) | 17.1542 | 1.20399 | ||||||||
\(204\) | 0.153632 | 0.0107564 | ||||||||
\(205\) | −27.9275 | −1.95054 | ||||||||
\(206\) | −10.9834 | −0.765251 | ||||||||
\(207\) | 1.05000 | 0.0729799 | ||||||||
\(208\) | 2.57839 | 0.178779 | ||||||||
\(209\) | 13.3355 | 0.922436 | ||||||||
\(210\) | 14.0275 | 0.967990 | ||||||||
\(211\) | −16.8159 | −1.15765 | −0.578827 | − | 0.815450i | \(-0.696490\pi\) | ||||
−0.578827 | + | 0.815450i | \(0.696490\pi\) | |||||||
\(212\) | 2.87792 | 0.197656 | ||||||||
\(213\) | 4.92629 | 0.337544 | ||||||||
\(214\) | 0.540399 | 0.0369409 | ||||||||
\(215\) | 20.4681 | 1.39591 | ||||||||
\(216\) | −5.56107 | −0.378383 | ||||||||
\(217\) | −2.39374 | −0.162498 | ||||||||
\(218\) | −12.4265 | −0.841630 | ||||||||
\(219\) | −15.4002 | −1.04065 | ||||||||
\(220\) | −8.41883 | −0.567597 | ||||||||
\(221\) | 0.253613 | 0.0170598 | ||||||||
\(222\) | 0.848508 | 0.0569481 | ||||||||
\(223\) | −7.80316 | −0.522538 | −0.261269 | − | 0.965266i | \(-0.584141\pi\) | ||||
−0.261269 | + | 0.965266i | \(0.584141\pi\) | |||||||
\(224\) | −2.39374 | −0.159938 | ||||||||
\(225\) | −5.08634 | −0.339089 | ||||||||
\(226\) | 2.36848 | 0.157549 | ||||||||
\(227\) | −15.0215 | −0.997009 | −0.498505 | − | 0.866887i | \(-0.666117\pi\) | ||||
−0.498505 | + | 0.866887i | \(0.666117\pi\) | |||||||
\(228\) | 9.28242 | 0.614743 | ||||||||
\(229\) | −10.1878 | −0.673226 | −0.336613 | − | 0.941643i | \(-0.609281\pi\) | ||||
−0.336613 | + | 0.941643i | \(0.609281\pi\) | |||||||
\(230\) | 7.02969 | 0.463524 | ||||||||
\(231\) | −8.38965 | −0.551999 | ||||||||
\(232\) | −7.16628 | −0.470489 | ||||||||
\(233\) | 24.7094 | 1.61876 | 0.809382 | − | 0.587282i | \(-0.199802\pi\) | ||||
0.809382 | + | 0.587282i | \(0.199802\pi\) | |||||||
\(234\) | −1.44492 | −0.0944576 | ||||||||
\(235\) | 33.4094 | 2.17939 | ||||||||
\(236\) | −8.47404 | −0.551613 | ||||||||
\(237\) | −12.7998 | −0.831435 | ||||||||
\(238\) | −0.235450 | −0.0152620 | ||||||||
\(239\) | −10.9021 | −0.705200 | −0.352600 | − | 0.935774i | \(-0.614702\pi\) | ||||
−0.352600 | + | 0.935774i | \(0.614702\pi\) | |||||||
\(240\) | −5.86008 | −0.378267 | ||||||||
\(241\) | −15.2459 | −0.982074 | −0.491037 | − | 0.871139i | \(-0.663382\pi\) | ||||
−0.491037 | + | 0.871139i | \(0.663382\pi\) | |||||||
\(242\) | −5.96482 | −0.383433 | ||||||||
\(243\) | 5.74230 | 0.368369 | ||||||||
\(244\) | −7.57710 | −0.485074 | ||||||||
\(245\) | 4.76487 | 0.304416 | ||||||||
\(246\) | 11.6264 | 0.741275 | ||||||||
\(247\) | 15.3232 | 0.974994 | ||||||||
\(248\) | 1.00000 | 0.0635001 | ||||||||
\(249\) | 8.58427 | 0.544006 | ||||||||
\(250\) | −15.2936 | −0.967253 | ||||||||
\(251\) | −0.275802 | −0.0174085 | −0.00870423 | − | 0.999962i | \(-0.502771\pi\) | ||||
−0.00870423 | + | 0.999962i | \(0.502771\pi\) | |||||||
\(252\) | 1.34145 | 0.0845032 | ||||||||
\(253\) | −4.20436 | −0.264326 | ||||||||
\(254\) | −8.95664 | −0.561990 | ||||||||
\(255\) | −0.576403 | −0.0360957 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.99659 | 0.374057 | 0.187028 | − | 0.982354i | \(-0.440114\pi\) | ||||
0.187028 | + | 0.982354i | \(0.440114\pi\) | |||||||
\(258\) | −8.52105 | −0.530498 | ||||||||
\(259\) | −1.30039 | −0.0808023 | ||||||||
\(260\) | −9.67370 | −0.599938 | ||||||||
\(261\) | 4.01597 | 0.248582 | ||||||||
\(262\) | −1.81408 | −0.112074 | ||||||||
\(263\) | −14.5509 | −0.897245 | −0.448623 | − | 0.893721i | \(-0.648085\pi\) | ||||
−0.448623 | + | 0.893721i | \(0.648085\pi\) | |||||||
\(264\) | 3.50483 | 0.215707 | ||||||||
\(265\) | −10.7975 | −0.663284 | ||||||||
\(266\) | −14.2259 | −0.872244 | ||||||||
\(267\) | 12.8960 | 0.789223 | ||||||||
\(268\) | −11.3966 | −0.696158 | ||||||||
\(269\) | 10.1366 | 0.618039 | 0.309019 | − | 0.951056i | \(-0.399999\pi\) | ||||
0.309019 | + | 0.951056i | \(0.399999\pi\) | |||||||
\(270\) | 20.8642 | 1.26976 | ||||||||
\(271\) | 12.2040 | 0.741340 | 0.370670 | − | 0.928765i | \(-0.379128\pi\) | ||||
0.370670 | + | 0.928765i | \(0.379128\pi\) | |||||||
\(272\) | 0.0983609 | 0.00596400 | ||||||||
\(273\) | −9.64018 | −0.583450 | ||||||||
\(274\) | 8.60658 | 0.519943 | ||||||||
\(275\) | 20.3665 | 1.22815 | ||||||||
\(276\) | −2.92652 | −0.176156 | ||||||||
\(277\) | −21.7743 | −1.30829 | −0.654147 | − | 0.756368i | \(-0.726972\pi\) | ||||
−0.654147 | + | 0.756368i | \(0.726972\pi\) | |||||||
\(278\) | −1.22561 | −0.0735070 | ||||||||
\(279\) | −0.560398 | −0.0335501 | ||||||||
\(280\) | 8.98093 | 0.536713 | ||||||||
\(281\) | −7.70986 | −0.459932 | −0.229966 | − | 0.973199i | \(-0.573861\pi\) | ||||
−0.229966 | + | 0.973199i | \(0.573861\pi\) | |||||||
\(282\) | −13.9086 | −0.828247 | ||||||||
\(283\) | 16.7327 | 0.994655 | 0.497328 | − | 0.867563i | \(-0.334315\pi\) | ||||
0.497328 | + | 0.867563i | \(0.334315\pi\) | |||||||
\(284\) | 3.15399 | 0.187155 | ||||||||
\(285\) | −34.8261 | −2.06292 | ||||||||
\(286\) | 5.78570 | 0.342116 | ||||||||
\(287\) | −17.8182 | −1.05178 | ||||||||
\(288\) | −0.560398 | −0.0330218 | ||||||||
\(289\) | −16.9903 | −0.999431 | ||||||||
\(290\) | 26.8867 | 1.57884 | ||||||||
\(291\) | −1.56192 | −0.0915615 | ||||||||
\(292\) | −9.85978 | −0.577000 | ||||||||
\(293\) | 25.5368 | 1.49187 | 0.745937 | − | 0.666017i | \(-0.232002\pi\) | ||||
0.745937 | + | 0.666017i | \(0.232002\pi\) | |||||||
\(294\) | −1.98366 | −0.115689 | ||||||||
\(295\) | 31.7932 | 1.85107 | ||||||||
\(296\) | 0.543246 | 0.0315755 | ||||||||
\(297\) | −12.4786 | −0.724081 | ||||||||
\(298\) | 4.91409 | 0.284666 | ||||||||
\(299\) | −4.83104 | −0.279386 | ||||||||
\(300\) | 14.1765 | 0.818479 | ||||||||
\(301\) | 13.0590 | 0.752710 | ||||||||
\(302\) | 5.25936 | 0.302642 | ||||||||
\(303\) | −12.9235 | −0.742434 | ||||||||
\(304\) | 5.94294 | 0.340851 | ||||||||
\(305\) | 28.4281 | 1.62779 | ||||||||
\(306\) | −0.0551212 | −0.00315107 | ||||||||
\(307\) | 9.96450 | 0.568704 | 0.284352 | − | 0.958720i | \(-0.408222\pi\) | ||||
0.284352 | + | 0.958720i | \(0.408222\pi\) | |||||||
\(308\) | −5.37136 | −0.306062 | ||||||||
\(309\) | −17.1553 | −0.975929 | ||||||||
\(310\) | −3.75184 | −0.213090 | ||||||||
\(311\) | 16.3760 | 0.928599 | 0.464299 | − | 0.885678i | \(-0.346306\pi\) | ||||
0.464299 | + | 0.885678i | \(0.346306\pi\) | |||||||
\(312\) | 4.02725 | 0.227998 | ||||||||
\(313\) | −30.9221 | −1.74782 | −0.873910 | − | 0.486087i | \(-0.838424\pi\) | ||||
−0.873910 | + | 0.486087i | \(0.838424\pi\) | |||||||
\(314\) | −15.9814 | −0.901881 | ||||||||
\(315\) | −5.03289 | −0.283571 | ||||||||
\(316\) | −8.19488 | −0.460998 | ||||||||
\(317\) | −2.71329 | −0.152394 | −0.0761968 | − | 0.997093i | \(-0.524278\pi\) | ||||
−0.0761968 | + | 0.997093i | \(0.524278\pi\) | |||||||
\(318\) | 4.49508 | 0.252072 | ||||||||
\(319\) | −16.0806 | −0.900339 | ||||||||
\(320\) | −3.75184 | −0.209734 | ||||||||
\(321\) | 0.844061 | 0.0471109 | ||||||||
\(322\) | 4.48507 | 0.249943 | ||||||||
\(323\) | 0.584553 | 0.0325254 | ||||||||
\(324\) | −7.00476 | −0.389153 | ||||||||
\(325\) | 23.4022 | 1.29812 | ||||||||
\(326\) | 20.6002 | 1.14094 | ||||||||
\(327\) | −19.4093 | −1.07333 | ||||||||
\(328\) | 7.44368 | 0.411008 | ||||||||
\(329\) | 21.3158 | 1.17518 | ||||||||
\(330\) | −13.1496 | −0.723860 | ||||||||
\(331\) | −26.5667 | −1.46024 | −0.730118 | − | 0.683321i | \(-0.760535\pi\) | ||||
−0.730118 | + | 0.683321i | \(0.760535\pi\) | |||||||
\(332\) | 5.49596 | 0.301630 | ||||||||
\(333\) | −0.304434 | −0.0166829 | ||||||||
\(334\) | 6.52617 | 0.357096 | ||||||||
\(335\) | 42.7582 | 2.33613 | ||||||||
\(336\) | −3.73884 | −0.203970 | ||||||||
\(337\) | 32.3828 | 1.76401 | 0.882003 | − | 0.471244i | \(-0.156195\pi\) | ||||
0.882003 | + | 0.471244i | \(0.156195\pi\) | |||||||
\(338\) | −6.35191 | −0.345498 | ||||||||
\(339\) | 3.69938 | 0.200923 | ||||||||
\(340\) | −0.369034 | −0.0200137 | ||||||||
\(341\) | 2.24392 | 0.121515 | ||||||||
\(342\) | −3.33041 | −0.180088 | ||||||||
\(343\) | 19.7963 | 1.06890 | ||||||||
\(344\) | −5.45549 | −0.294140 | ||||||||
\(345\) | 10.9798 | 0.591134 | ||||||||
\(346\) | 2.24208 | 0.120535 | ||||||||
\(347\) | 21.7246 | 1.16624 | 0.583119 | − | 0.812386i | \(-0.301832\pi\) | ||||
0.583119 | + | 0.812386i | \(0.301832\pi\) | |||||||
\(348\) | −11.1932 | −0.600017 | ||||||||
\(349\) | 17.4429 | 0.933697 | 0.466849 | − | 0.884337i | \(-0.345389\pi\) | ||||
0.466849 | + | 0.884337i | \(0.345389\pi\) | |||||||
\(350\) | −21.7263 | −1.16132 | ||||||||
\(351\) | −14.3386 | −0.765338 | ||||||||
\(352\) | 2.24392 | 0.119601 | ||||||||
\(353\) | −17.0303 | −0.906434 | −0.453217 | − | 0.891400i | \(-0.649724\pi\) | ||||
−0.453217 | + | 0.891400i | \(0.649724\pi\) | |||||||
\(354\) | −13.2358 | −0.703474 | ||||||||
\(355\) | −11.8333 | −0.628044 | ||||||||
\(356\) | 8.25650 | 0.437593 | ||||||||
\(357\) | −0.367755 | −0.0194637 | ||||||||
\(358\) | 11.9848 | 0.633415 | ||||||||
\(359\) | −6.88917 | −0.363596 | −0.181798 | − | 0.983336i | \(-0.558192\pi\) | ||||
−0.181798 | + | 0.983336i | \(0.558192\pi\) | |||||||
\(360\) | 2.10252 | 0.110813 | ||||||||
\(361\) | 16.3186 | 0.858873 | ||||||||
\(362\) | 15.6727 | 0.823738 | ||||||||
\(363\) | −9.31658 | −0.488994 | ||||||||
\(364\) | −6.17199 | −0.323500 | ||||||||
\(365\) | 36.9923 | 1.93627 | ||||||||
\(366\) | −11.8348 | −0.618618 | ||||||||
\(367\) | 28.0593 | 1.46468 | 0.732342 | − | 0.680937i | \(-0.238427\pi\) | ||||
0.732342 | + | 0.680937i | \(0.238427\pi\) | |||||||
\(368\) | −1.87367 | −0.0976715 | ||||||||
\(369\) | −4.17142 | −0.217155 | ||||||||
\(370\) | −2.03817 | −0.105960 | ||||||||
\(371\) | −6.88898 | −0.357658 | ||||||||
\(372\) | 1.56192 | 0.0809819 | ||||||||
\(373\) | 17.7996 | 0.921630 | 0.460815 | − | 0.887496i | \(-0.347557\pi\) | ||||
0.460815 | + | 0.887496i | \(0.347557\pi\) | |||||||
\(374\) | 0.220714 | 0.0114128 | ||||||||
\(375\) | −23.8874 | −1.23354 | ||||||||
\(376\) | −8.90482 | −0.459231 | ||||||||
\(377\) | −18.4775 | −0.951637 | ||||||||
\(378\) | 13.3117 | 0.684682 | ||||||||
\(379\) | −12.7562 | −0.655240 | −0.327620 | − | 0.944810i | \(-0.606247\pi\) | ||||
−0.327620 | + | 0.944810i | \(0.606247\pi\) | |||||||
\(380\) | −22.2970 | −1.14381 | ||||||||
\(381\) | −13.9896 | −0.716708 | ||||||||
\(382\) | −2.91679 | −0.149236 | ||||||||
\(383\) | −25.5429 | −1.30518 | −0.652590 | − | 0.757711i | \(-0.726317\pi\) | ||||
−0.652590 | + | 0.757711i | \(0.726317\pi\) | |||||||
\(384\) | 1.56192 | 0.0797065 | ||||||||
\(385\) | 20.1525 | 1.02707 | ||||||||
\(386\) | −6.67285 | −0.339639 | ||||||||
\(387\) | 3.05724 | 0.155408 | ||||||||
\(388\) | −1.00000 | −0.0507673 | ||||||||
\(389\) | 5.01300 | 0.254169 | 0.127085 | − | 0.991892i | \(-0.459438\pi\) | ||||
0.127085 | + | 0.991892i | \(0.459438\pi\) | |||||||
\(390\) | −15.1096 | −0.765103 | ||||||||
\(391\) | −0.184295 | −0.00932021 | ||||||||
\(392\) | −1.27001 | −0.0641452 | ||||||||
\(393\) | −2.83346 | −0.142929 | ||||||||
\(394\) | 0.343230 | 0.0172917 | ||||||||
\(395\) | 30.7459 | 1.54699 | ||||||||
\(396\) | −1.25749 | −0.0631912 | ||||||||
\(397\) | −28.8266 | −1.44676 | −0.723382 | − | 0.690448i | \(-0.757413\pi\) | ||||
−0.723382 | + | 0.690448i | \(0.757413\pi\) | |||||||
\(398\) | −18.6347 | −0.934076 | ||||||||
\(399\) | −22.2197 | −1.11238 | ||||||||
\(400\) | 9.07630 | 0.453815 | ||||||||
\(401\) | 15.1201 | 0.755064 | 0.377532 | − | 0.925997i | \(-0.376773\pi\) | ||||
0.377532 | + | 0.925997i | \(0.376773\pi\) | |||||||
\(402\) | −17.8006 | −0.887814 | ||||||||
\(403\) | 2.57839 | 0.128439 | ||||||||
\(404\) | −8.27408 | −0.411651 | ||||||||
\(405\) | 26.2807 | 1.30590 | ||||||||
\(406\) | 17.1542 | 0.851349 | ||||||||
\(407\) | 1.21900 | 0.0604236 | ||||||||
\(408\) | 0.153632 | 0.00760592 | ||||||||
\(409\) | −13.3584 | −0.660532 | −0.330266 | − | 0.943888i | \(-0.607138\pi\) | ||||
−0.330266 | + | 0.943888i | \(0.607138\pi\) | |||||||
\(410\) | −27.9275 | −1.37924 | ||||||||
\(411\) | 13.4428 | 0.663085 | ||||||||
\(412\) | −10.9834 | −0.541115 | ||||||||
\(413\) | 20.2846 | 0.998142 | ||||||||
\(414\) | 1.05000 | 0.0516046 | ||||||||
\(415\) | −20.6200 | −1.01219 | ||||||||
\(416\) | 2.57839 | 0.126416 | ||||||||
\(417\) | −1.91430 | −0.0937438 | ||||||||
\(418\) | 13.3355 | 0.652261 | ||||||||
\(419\) | −11.4278 | −0.558285 | −0.279143 | − | 0.960250i | \(-0.590050\pi\) | ||||
−0.279143 | + | 0.960250i | \(0.590050\pi\) | |||||||
\(420\) | 14.0275 | 0.684473 | ||||||||
\(421\) | −34.7650 | −1.69434 | −0.847172 | − | 0.531319i | \(-0.821697\pi\) | ||||
−0.847172 | + | 0.531319i | \(0.821697\pi\) | |||||||
\(422\) | −16.8159 | −0.818586 | ||||||||
\(423\) | 4.99024 | 0.242634 | ||||||||
\(424\) | 2.87792 | 0.139764 | ||||||||
\(425\) | 0.892752 | 0.0433049 | ||||||||
\(426\) | 4.92629 | 0.238679 | ||||||||
\(427\) | 18.1376 | 0.877741 | ||||||||
\(428\) | 0.540399 | 0.0261212 | ||||||||
\(429\) | 9.03682 | 0.436302 | ||||||||
\(430\) | 20.4681 | 0.987060 | ||||||||
\(431\) | 10.8643 | 0.523313 | 0.261657 | − | 0.965161i | \(-0.415731\pi\) | ||||
0.261657 | + | 0.965161i | \(0.415731\pi\) | |||||||
\(432\) | −5.56107 | −0.267557 | ||||||||
\(433\) | 39.8552 | 1.91532 | 0.957659 | − | 0.287903i | \(-0.0929582\pi\) | ||||
0.957659 | + | 0.287903i | \(0.0929582\pi\) | |||||||
\(434\) | −2.39374 | −0.114903 | ||||||||
\(435\) | 41.9950 | 2.01350 | ||||||||
\(436\) | −12.4265 | −0.595122 | ||||||||
\(437\) | −11.1351 | −0.532664 | ||||||||
\(438\) | −15.4002 | −0.735851 | ||||||||
\(439\) | 1.11217 | 0.0530809 | 0.0265405 | − | 0.999648i | \(-0.491551\pi\) | ||||
0.0265405 | + | 0.999648i | \(0.491551\pi\) | |||||||
\(440\) | −8.41883 | −0.401352 | ||||||||
\(441\) | 0.711711 | 0.0338910 | ||||||||
\(442\) | 0.253613 | 0.0120631 | ||||||||
\(443\) | −20.0217 | −0.951259 | −0.475629 | − | 0.879646i | \(-0.657780\pi\) | ||||
−0.475629 | + | 0.879646i | \(0.657780\pi\) | |||||||
\(444\) | 0.848508 | 0.0402684 | ||||||||
\(445\) | −30.9771 | −1.46845 | ||||||||
\(446\) | −7.80316 | −0.369490 | ||||||||
\(447\) | 7.67543 | 0.363035 | ||||||||
\(448\) | −2.39374 | −0.113094 | ||||||||
\(449\) | −11.6894 | −0.551657 | −0.275828 | − | 0.961207i | \(-0.588952\pi\) | ||||
−0.275828 | + | 0.961207i | \(0.588952\pi\) | |||||||
\(450\) | −5.08634 | −0.239772 | ||||||||
\(451\) | 16.7030 | 0.786515 | ||||||||
\(452\) | 2.36848 | 0.111404 | ||||||||
\(453\) | 8.21472 | 0.385961 | ||||||||
\(454\) | −15.0215 | −0.704992 | ||||||||
\(455\) | 23.1563 | 1.08559 | ||||||||
\(456\) | 9.28242 | 0.434689 | ||||||||
\(457\) | 14.8909 | 0.696567 | 0.348284 | − | 0.937389i | \(-0.386765\pi\) | ||||
0.348284 | + | 0.937389i | \(0.386765\pi\) | |||||||
\(458\) | −10.1878 | −0.476042 | ||||||||
\(459\) | −0.546991 | −0.0255314 | ||||||||
\(460\) | 7.02969 | 0.327761 | ||||||||
\(461\) | −26.1101 | −1.21607 | −0.608035 | − | 0.793910i | \(-0.708042\pi\) | ||||
−0.608035 | + | 0.793910i | \(0.708042\pi\) | |||||||
\(462\) | −8.38965 | −0.390322 | ||||||||
\(463\) | −5.62200 | −0.261277 | −0.130638 | − | 0.991430i | \(-0.541703\pi\) | ||||
−0.130638 | + | 0.991430i | \(0.541703\pi\) | |||||||
\(464\) | −7.16628 | −0.332686 | ||||||||
\(465\) | −5.86008 | −0.271755 | ||||||||
\(466\) | 24.7094 | 1.14464 | ||||||||
\(467\) | −38.7588 | −1.79354 | −0.896771 | − | 0.442494i | \(-0.854094\pi\) | ||||
−0.896771 | + | 0.442494i | \(0.854094\pi\) | |||||||
\(468\) | −1.44492 | −0.0667916 | ||||||||
\(469\) | 27.2805 | 1.25970 | ||||||||
\(470\) | 33.4094 | 1.54106 | ||||||||
\(471\) | −24.9617 | −1.15017 | ||||||||
\(472\) | −8.47404 | −0.390049 | ||||||||
\(473\) | −12.2417 | −0.562873 | ||||||||
\(474\) | −12.7998 | −0.587913 | ||||||||
\(475\) | 53.9399 | 2.47493 | ||||||||
\(476\) | −0.235450 | −0.0107918 | ||||||||
\(477\) | −1.61278 | −0.0738440 | ||||||||
\(478\) | −10.9021 | −0.498651 | ||||||||
\(479\) | 14.2225 | 0.649843 | 0.324921 | − | 0.945741i | \(-0.394662\pi\) | ||||
0.324921 | + | 0.945741i | \(0.394662\pi\) | |||||||
\(480\) | −5.86008 | −0.267475 | ||||||||
\(481\) | 1.40070 | 0.0638664 | ||||||||
\(482\) | −15.2459 | −0.694431 | ||||||||
\(483\) | 7.00533 | 0.318753 | ||||||||
\(484\) | −5.96482 | −0.271128 | ||||||||
\(485\) | 3.75184 | 0.170362 | ||||||||
\(486\) | 5.74230 | 0.260476 | ||||||||
\(487\) | 37.2537 | 1.68812 | 0.844062 | − | 0.536245i | \(-0.180158\pi\) | ||||
0.844062 | + | 0.536245i | \(0.180158\pi\) | |||||||
\(488\) | −7.57710 | −0.342999 | ||||||||
\(489\) | 32.1759 | 1.45504 | ||||||||
\(490\) | 4.76487 | 0.215255 | ||||||||
\(491\) | 36.7869 | 1.66017 | 0.830085 | − | 0.557637i | \(-0.188292\pi\) | ||||
0.830085 | + | 0.557637i | \(0.188292\pi\) | |||||||
\(492\) | 11.6264 | 0.524161 | ||||||||
\(493\) | −0.704881 | −0.0317463 | ||||||||
\(494\) | 15.3232 | 0.689425 | ||||||||
\(495\) | 4.71789 | 0.212054 | ||||||||
\(496\) | 1.00000 | 0.0449013 | ||||||||
\(497\) | −7.54983 | −0.338656 | ||||||||
\(498\) | 8.58427 | 0.384670 | ||||||||
\(499\) | 4.29955 | 0.192474 | 0.0962372 | − | 0.995358i | \(-0.469319\pi\) | ||||
0.0962372 | + | 0.995358i | \(0.469319\pi\) | |||||||
\(500\) | −15.2936 | −0.683951 | ||||||||
\(501\) | 10.1934 | 0.455406 | ||||||||
\(502\) | −0.275802 | −0.0123096 | ||||||||
\(503\) | 26.5264 | 1.18275 | 0.591377 | − | 0.806395i | \(-0.298585\pi\) | ||||
0.591377 | + | 0.806395i | \(0.298585\pi\) | |||||||
\(504\) | 1.34145 | 0.0597528 | ||||||||
\(505\) | 31.0430 | 1.38140 | ||||||||
\(506\) | −4.20436 | −0.186906 | ||||||||
\(507\) | −9.92119 | −0.440615 | ||||||||
\(508\) | −8.95664 | −0.397387 | ||||||||
\(509\) | 0.727766 | 0.0322577 | 0.0161288 | − | 0.999870i | \(-0.494866\pi\) | ||||
0.0161288 | + | 0.999870i | \(0.494866\pi\) | |||||||
\(510\) | −0.576403 | −0.0255235 | ||||||||
\(511\) | 23.6017 | 1.04408 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −33.0491 | −1.45915 | ||||||||
\(514\) | 5.99659 | 0.264498 | ||||||||
\(515\) | 41.2080 | 1.81584 | ||||||||
\(516\) | −8.52105 | −0.375118 | ||||||||
\(517\) | −19.9817 | −0.878794 | ||||||||
\(518\) | −1.30039 | −0.0571358 | ||||||||
\(519\) | 3.50196 | 0.153719 | ||||||||
\(520\) | −9.67370 | −0.424220 | ||||||||
\(521\) | 12.4453 | 0.545237 | 0.272618 | − | 0.962122i | \(-0.412110\pi\) | ||||
0.272618 | + | 0.962122i | \(0.412110\pi\) | |||||||
\(522\) | 4.01597 | 0.175774 | ||||||||
\(523\) | 16.9889 | 0.742871 | 0.371435 | − | 0.928459i | \(-0.378866\pi\) | ||||
0.371435 | + | 0.928459i | \(0.378866\pi\) | |||||||
\(524\) | −1.81408 | −0.0792486 | ||||||||
\(525\) | −33.9348 | −1.48104 | ||||||||
\(526\) | −14.5509 | −0.634448 | ||||||||
\(527\) | 0.0983609 | 0.00428467 | ||||||||
\(528\) | 3.50483 | 0.152528 | ||||||||
\(529\) | −19.4894 | −0.847364 | ||||||||
\(530\) | −10.7975 | −0.469013 | ||||||||
\(531\) | 4.74883 | 0.206082 | ||||||||
\(532\) | −14.2259 | −0.616769 | ||||||||
\(533\) | 19.1927 | 0.831328 | ||||||||
\(534\) | 12.8960 | 0.558065 | ||||||||
\(535\) | −2.02749 | −0.0876560 | ||||||||
\(536\) | −11.3966 | −0.492258 | ||||||||
\(537\) | 18.7193 | 0.807797 | ||||||||
\(538\) | 10.1366 | 0.437019 | ||||||||
\(539\) | −2.84980 | −0.122750 | ||||||||
\(540\) | 20.8642 | 0.897853 | ||||||||
\(541\) | −2.19717 | −0.0944636 | −0.0472318 | − | 0.998884i | \(-0.515040\pi\) | ||||
−0.0472318 | + | 0.998884i | \(0.515040\pi\) | |||||||
\(542\) | 12.2040 | 0.524207 | ||||||||
\(543\) | 24.4795 | 1.05052 | ||||||||
\(544\) | 0.0983609 | 0.00421719 | ||||||||
\(545\) | 46.6223 | 1.99708 | ||||||||
\(546\) | −9.64018 | −0.412561 | ||||||||
\(547\) | 17.2689 | 0.738364 | 0.369182 | − | 0.929357i | \(-0.379638\pi\) | ||||
0.369182 | + | 0.929357i | \(0.379638\pi\) | |||||||
\(548\) | 8.60658 | 0.367655 | ||||||||
\(549\) | 4.24619 | 0.181223 | ||||||||
\(550\) | 20.3665 | 0.868430 | ||||||||
\(551\) | −42.5888 | −1.81434 | ||||||||
\(552\) | −2.92652 | −0.124561 | ||||||||
\(553\) | 19.6164 | 0.834175 | ||||||||
\(554\) | −21.7743 | −0.925103 | ||||||||
\(555\) | −3.18347 | −0.135131 | ||||||||
\(556\) | −1.22561 | −0.0519773 | ||||||||
\(557\) | −17.7728 | −0.753058 | −0.376529 | − | 0.926405i | \(-0.622883\pi\) | ||||
−0.376529 | + | 0.926405i | \(0.622883\pi\) | |||||||
\(558\) | −0.560398 | −0.0237235 | ||||||||
\(559\) | −14.0664 | −0.594944 | ||||||||
\(560\) | 8.98093 | 0.379513 | ||||||||
\(561\) | 0.344738 | 0.0145549 | ||||||||
\(562\) | −7.70986 | −0.325221 | ||||||||
\(563\) | −23.9880 | −1.01097 | −0.505486 | − | 0.862835i | \(-0.668687\pi\) | ||||
−0.505486 | + | 0.862835i | \(0.668687\pi\) | |||||||
\(564\) | −13.9086 | −0.585659 | ||||||||
\(565\) | −8.88616 | −0.373844 | ||||||||
\(566\) | 16.7327 | 0.703328 | ||||||||
\(567\) | 16.7676 | 0.704172 | ||||||||
\(568\) | 3.15399 | 0.132338 | ||||||||
\(569\) | −42.9240 | −1.79947 | −0.899735 | − | 0.436437i | \(-0.856240\pi\) | ||||
−0.899735 | + | 0.436437i | \(0.856240\pi\) | |||||||
\(570\) | −34.8261 | −1.45871 | ||||||||
\(571\) | 9.53021 | 0.398827 | 0.199413 | − | 0.979915i | \(-0.436096\pi\) | ||||
0.199413 | + | 0.979915i | \(0.436096\pi\) | |||||||
\(572\) | 5.78570 | 0.241912 | ||||||||
\(573\) | −4.55580 | −0.190321 | ||||||||
\(574\) | −17.8182 | −0.743718 | ||||||||
\(575\) | −17.0059 | −0.709197 | ||||||||
\(576\) | −0.560398 | −0.0233499 | ||||||||
\(577\) | −9.93712 | −0.413688 | −0.206844 | − | 0.978374i | \(-0.566319\pi\) | ||||
−0.206844 | + | 0.978374i | \(0.566319\pi\) | |||||||
\(578\) | −16.9903 | −0.706704 | ||||||||
\(579\) | −10.4225 | −0.433143 | ||||||||
\(580\) | 26.8867 | 1.11641 | ||||||||
\(581\) | −13.1559 | −0.545799 | ||||||||
\(582\) | −1.56192 | −0.0647438 | ||||||||
\(583\) | 6.45782 | 0.267455 | ||||||||
\(584\) | −9.85978 | −0.408001 | ||||||||
\(585\) | 5.42112 | 0.224136 | ||||||||
\(586\) | 25.5368 | 1.05491 | ||||||||
\(587\) | 0.481022 | 0.0198539 | 0.00992695 | − | 0.999951i | \(-0.496840\pi\) | ||||
0.00992695 | + | 0.999951i | \(0.496840\pi\) | |||||||
\(588\) | −1.98366 | −0.0818046 | ||||||||
\(589\) | 5.94294 | 0.244875 | ||||||||
\(590\) | 31.7932 | 1.30891 | ||||||||
\(591\) | 0.536098 | 0.0220521 | ||||||||
\(592\) | 0.543246 | 0.0223273 | ||||||||
\(593\) | 28.4099 | 1.16666 | 0.583328 | − | 0.812237i | \(-0.301750\pi\) | ||||
0.583328 | + | 0.812237i | \(0.301750\pi\) | |||||||
\(594\) | −12.4786 | −0.512003 | ||||||||
\(595\) | 0.883372 | 0.0362147 | ||||||||
\(596\) | 4.91409 | 0.201289 | ||||||||
\(597\) | −29.1060 | −1.19123 | ||||||||
\(598\) | −4.83104 | −0.197556 | ||||||||
\(599\) | 25.1564 | 1.02786 | 0.513932 | − | 0.857831i | \(-0.328188\pi\) | ||||
0.513932 | + | 0.857831i | \(0.328188\pi\) | |||||||
\(600\) | 14.1765 | 0.578752 | ||||||||
\(601\) | −4.95961 | −0.202307 | −0.101153 | − | 0.994871i | \(-0.532253\pi\) | ||||
−0.101153 | + | 0.994871i | \(0.532253\pi\) | |||||||
\(602\) | 13.0590 | 0.532246 | ||||||||
\(603\) | 6.38663 | 0.260084 | ||||||||
\(604\) | 5.25936 | 0.214000 | ||||||||
\(605\) | 22.3790 | 0.909837 | ||||||||
\(606\) | −12.9235 | −0.524980 | ||||||||
\(607\) | 33.7791 | 1.37105 | 0.685525 | − | 0.728049i | \(-0.259573\pi\) | ||||
0.685525 | + | 0.728049i | \(0.259573\pi\) | |||||||
\(608\) | 5.94294 | 0.241018 | ||||||||
\(609\) | 26.7935 | 1.08573 | ||||||||
\(610\) | 28.4281 | 1.15102 | ||||||||
\(611\) | −22.9601 | −0.928866 | ||||||||
\(612\) | −0.0551212 | −0.00222814 | ||||||||
\(613\) | 19.3378 | 0.781045 | 0.390523 | − | 0.920593i | \(-0.372294\pi\) | ||||
0.390523 | + | 0.920593i | \(0.372294\pi\) | |||||||
\(614\) | 9.96450 | 0.402135 | ||||||||
\(615\) | −43.6206 | −1.75895 | ||||||||
\(616\) | −5.37136 | −0.216418 | ||||||||
\(617\) | 44.3819 | 1.78675 | 0.893374 | − | 0.449314i | \(-0.148331\pi\) | ||||
0.893374 | + | 0.449314i | \(0.148331\pi\) | |||||||
\(618\) | −17.1553 | −0.690086 | ||||||||
\(619\) | 0.993756 | 0.0399424 | 0.0199712 | − | 0.999801i | \(-0.493643\pi\) | ||||
0.0199712 | + | 0.999801i | \(0.493643\pi\) | |||||||
\(620\) | −3.75184 | −0.150677 | ||||||||
\(621\) | 10.4196 | 0.418123 | ||||||||
\(622\) | 16.3760 | 0.656619 | ||||||||
\(623\) | −19.7639 | −0.791824 | ||||||||
\(624\) | 4.02725 | 0.161219 | ||||||||
\(625\) | 11.9977 | 0.479908 | ||||||||
\(626\) | −30.9221 | −1.23590 | ||||||||
\(627\) | 20.8290 | 0.831831 | ||||||||
\(628\) | −15.9814 | −0.637726 | ||||||||
\(629\) | 0.0534341 | 0.00213056 | ||||||||
\(630\) | −5.03289 | −0.200515 | ||||||||
\(631\) | 5.90755 | 0.235176 | 0.117588 | − | 0.993062i | \(-0.462484\pi\) | ||||
0.117588 | + | 0.993062i | \(0.462484\pi\) | |||||||
\(632\) | −8.19488 | −0.325975 | ||||||||
\(633\) | −26.2651 | −1.04395 | ||||||||
\(634\) | −2.71329 | −0.107759 | ||||||||
\(635\) | 33.6039 | 1.33353 | ||||||||
\(636\) | 4.49508 | 0.178242 | ||||||||
\(637\) | −3.27458 | −0.129744 | ||||||||
\(638\) | −16.0806 | −0.636635 | ||||||||
\(639\) | −1.76749 | −0.0699208 | ||||||||
\(640\) | −3.75184 | −0.148304 | ||||||||
\(641\) | 21.3085 | 0.841634 | 0.420817 | − | 0.907146i | \(-0.361743\pi\) | ||||
0.420817 | + | 0.907146i | \(0.361743\pi\) | |||||||
\(642\) | 0.844061 | 0.0333124 | ||||||||
\(643\) | −4.76022 | −0.187725 | −0.0938623 | − | 0.995585i | \(-0.529921\pi\) | ||||
−0.0938623 | + | 0.995585i | \(0.529921\pi\) | |||||||
\(644\) | 4.48507 | 0.176736 | ||||||||
\(645\) | 31.9696 | 1.25880 | ||||||||
\(646\) | 0.584553 | 0.0229989 | ||||||||
\(647\) | −27.2597 | −1.07169 | −0.535845 | − | 0.844316i | \(-0.680007\pi\) | ||||
−0.535845 | + | 0.844316i | \(0.680007\pi\) | |||||||
\(648\) | −7.00476 | −0.275173 | ||||||||
\(649\) | −19.0151 | −0.746407 | ||||||||
\(650\) | 23.4022 | 0.917911 | ||||||||
\(651\) | −3.73884 | −0.146537 | ||||||||
\(652\) | 20.6002 | 0.806766 | ||||||||
\(653\) | 38.1641 | 1.49348 | 0.746738 | − | 0.665118i | \(-0.231619\pi\) | ||||
0.746738 | + | 0.665118i | \(0.231619\pi\) | |||||||
\(654\) | −19.4093 | −0.758962 | ||||||||
\(655\) | 6.80614 | 0.265938 | ||||||||
\(656\) | 7.44368 | 0.290627 | ||||||||
\(657\) | 5.52540 | 0.215566 | ||||||||
\(658\) | 21.3158 | 0.830977 | ||||||||
\(659\) | 23.1460 | 0.901640 | 0.450820 | − | 0.892615i | \(-0.351132\pi\) | ||||
0.450820 | + | 0.892615i | \(0.351132\pi\) | |||||||
\(660\) | −13.1496 | −0.511846 | ||||||||
\(661\) | 24.0712 | 0.936259 | 0.468130 | − | 0.883660i | \(-0.344928\pi\) | ||||
0.468130 | + | 0.883660i | \(0.344928\pi\) | |||||||
\(662\) | −26.5667 | −1.03254 | ||||||||
\(663\) | 0.396123 | 0.0153842 | ||||||||
\(664\) | 5.49596 | 0.213285 | ||||||||
\(665\) | 53.3732 | 2.06972 | ||||||||
\(666\) | −0.304434 | −0.0117966 | ||||||||
\(667\) | 13.4272 | 0.519903 | ||||||||
\(668\) | 6.52617 | 0.252505 | ||||||||
\(669\) | −12.1879 | −0.471212 | ||||||||
\(670\) | 42.7582 | 1.65189 | ||||||||
\(671\) | −17.0024 | −0.656371 | ||||||||
\(672\) | −3.73884 | −0.144229 | ||||||||
\(673\) | −21.7421 | −0.838097 | −0.419048 | − | 0.907964i | \(-0.637636\pi\) | ||||
−0.419048 | + | 0.907964i | \(0.637636\pi\) | |||||||
\(674\) | 32.3828 | 1.24734 | ||||||||
\(675\) | −50.4739 | −1.94274 | ||||||||
\(676\) | −6.35191 | −0.244304 | ||||||||
\(677\) | 6.56881 | 0.252460 | 0.126230 | − | 0.992001i | \(-0.459712\pi\) | ||||
0.126230 | + | 0.992001i | \(0.459712\pi\) | |||||||
\(678\) | 3.69938 | 0.142074 | ||||||||
\(679\) | 2.39374 | 0.0918633 | ||||||||
\(680\) | −0.369034 | −0.0141518 | ||||||||
\(681\) | −23.4624 | −0.899079 | ||||||||
\(682\) | 2.24392 | 0.0859242 | ||||||||
\(683\) | 8.44591 | 0.323174 | 0.161587 | − | 0.986859i | \(-0.448339\pi\) | ||||
0.161587 | + | 0.986859i | \(0.448339\pi\) | |||||||
\(684\) | −3.33041 | −0.127342 | ||||||||
\(685\) | −32.2905 | −1.23376 | ||||||||
\(686\) | 19.7963 | 0.755824 | ||||||||
\(687\) | −15.9125 | −0.607099 | ||||||||
\(688\) | −5.45549 | −0.207989 | ||||||||
\(689\) | 7.42039 | 0.282694 | ||||||||
\(690\) | 10.9798 | 0.417995 | ||||||||
\(691\) | 28.1775 | 1.07192 | 0.535960 | − | 0.844243i | \(-0.319950\pi\) | ||||
0.535960 | + | 0.844243i | \(0.319950\pi\) | |||||||
\(692\) | 2.24208 | 0.0852311 | ||||||||
\(693\) | 3.01010 | 0.114344 | ||||||||
\(694\) | 21.7246 | 0.824655 | ||||||||
\(695\) | 4.59828 | 0.174423 | ||||||||
\(696\) | −11.1932 | −0.424276 | ||||||||
\(697\) | 0.732166 | 0.0277328 | ||||||||
\(698\) | 17.4429 | 0.660224 | ||||||||
\(699\) | 38.5941 | 1.45976 | ||||||||
\(700\) | −21.7263 | −0.821177 | ||||||||
\(701\) | −37.2466 | −1.40678 | −0.703392 | − | 0.710802i | \(-0.748332\pi\) | ||||
−0.703392 | + | 0.710802i | \(0.748332\pi\) | |||||||
\(702\) | −14.3386 | −0.541175 | ||||||||
\(703\) | 3.22848 | 0.121764 | ||||||||
\(704\) | 2.24392 | 0.0845710 | ||||||||
\(705\) | 52.1830 | 1.96532 | ||||||||
\(706\) | −17.0303 | −0.640945 | ||||||||
\(707\) | 19.8060 | 0.744881 | ||||||||
\(708\) | −13.2358 | −0.497432 | ||||||||
\(709\) | 38.7576 | 1.45557 | 0.727786 | − | 0.685805i | \(-0.240550\pi\) | ||||
0.727786 | + | 0.685805i | \(0.240550\pi\) | |||||||
\(710\) | −11.8333 | −0.444094 | ||||||||
\(711\) | 4.59240 | 0.172228 | ||||||||
\(712\) | 8.25650 | 0.309425 | ||||||||
\(713\) | −1.87367 | −0.0701693 | ||||||||
\(714\) | −0.367755 | −0.0137629 | ||||||||
\(715\) | −21.7070 | −0.811797 | ||||||||
\(716\) | 11.9848 | 0.447892 | ||||||||
\(717\) | −17.0283 | −0.635932 | ||||||||
\(718\) | −6.88917 | −0.257101 | ||||||||
\(719\) | −40.1264 | −1.49646 | −0.748231 | − | 0.663438i | \(-0.769097\pi\) | ||||
−0.748231 | + | 0.663438i | \(0.769097\pi\) | |||||||
\(720\) | 2.10252 | 0.0783564 | ||||||||
\(721\) | 26.2915 | 0.979145 | ||||||||
\(722\) | 16.3186 | 0.607315 | ||||||||
\(723\) | −23.8129 | −0.885611 | ||||||||
\(724\) | 15.6727 | 0.582471 | ||||||||
\(725\) | −65.0433 | −2.41565 | ||||||||
\(726\) | −9.31658 | −0.345771 | ||||||||
\(727\) | 22.4005 | 0.830787 | 0.415394 | − | 0.909642i | \(-0.363644\pi\) | ||||
0.415394 | + | 0.909642i | \(0.363644\pi\) | |||||||
\(728\) | −6.17199 | −0.228749 | ||||||||
\(729\) | 29.9833 | 1.11049 | ||||||||
\(730\) | 36.9923 | 1.36915 | ||||||||
\(731\) | −0.536607 | −0.0198471 | ||||||||
\(732\) | −11.8348 | −0.437429 | ||||||||
\(733\) | 23.5236 | 0.868862 | 0.434431 | − | 0.900705i | \(-0.356949\pi\) | ||||
0.434431 | + | 0.900705i | \(0.356949\pi\) | |||||||
\(734\) | 28.0593 | 1.03569 | ||||||||
\(735\) | 7.44236 | 0.274516 | ||||||||
\(736\) | −1.87367 | −0.0690642 | ||||||||
\(737\) | −25.5731 | −0.941996 | ||||||||
\(738\) | −4.17142 | −0.153552 | ||||||||
\(739\) | −3.74419 | −0.137732 | −0.0688661 | − | 0.997626i | \(-0.521938\pi\) | ||||
−0.0688661 | + | 0.997626i | \(0.521938\pi\) | |||||||
\(740\) | −2.03817 | −0.0749247 | ||||||||
\(741\) | 23.9337 | 0.879226 | ||||||||
\(742\) | −6.88898 | −0.252903 | ||||||||
\(743\) | −30.1601 | −1.10647 | −0.553233 | − | 0.833026i | \(-0.686606\pi\) | ||||
−0.553233 | + | 0.833026i | \(0.686606\pi\) | |||||||
\(744\) | 1.56192 | 0.0572629 | ||||||||
\(745\) | −18.4369 | −0.675475 | ||||||||
\(746\) | 17.7996 | 0.651691 | ||||||||
\(747\) | −3.07992 | −0.112689 | ||||||||
\(748\) | 0.220714 | 0.00807010 | ||||||||
\(749\) | −1.29357 | −0.0472662 | ||||||||
\(750\) | −23.8874 | −0.872246 | ||||||||
\(751\) | −48.6350 | −1.77472 | −0.887358 | − | 0.461082i | \(-0.847461\pi\) | ||||
−0.887358 | + | 0.461082i | \(0.847461\pi\) | |||||||
\(752\) | −8.90482 | −0.324725 | ||||||||
\(753\) | −0.430781 | −0.0156985 | ||||||||
\(754\) | −18.4775 | −0.672909 | ||||||||
\(755\) | −19.7323 | −0.718131 | ||||||||
\(756\) | 13.3117 | 0.484143 | ||||||||
\(757\) | −42.7839 | −1.55501 | −0.777504 | − | 0.628878i | \(-0.783515\pi\) | ||||
−0.777504 | + | 0.628878i | \(0.783515\pi\) | |||||||
\(758\) | −12.7562 | −0.463324 | ||||||||
\(759\) | −6.56688 | −0.238363 | ||||||||
\(760\) | −22.2970 | −0.808796 | ||||||||
\(761\) | −23.4138 | −0.848748 | −0.424374 | − | 0.905487i | \(-0.639506\pi\) | ||||
−0.424374 | + | 0.905487i | \(0.639506\pi\) | |||||||
\(762\) | −13.9896 | −0.506789 | ||||||||
\(763\) | 29.7458 | 1.07687 | ||||||||
\(764\) | −2.91679 | −0.105526 | ||||||||
\(765\) | 0.206806 | 0.00747708 | ||||||||
\(766\) | −25.5429 | −0.922901 | ||||||||
\(767\) | −21.8494 | −0.788935 | ||||||||
\(768\) | 1.56192 | 0.0563610 | ||||||||
\(769\) | −8.73251 | −0.314902 | −0.157451 | − | 0.987527i | \(-0.550328\pi\) | ||||
−0.157451 | + | 0.987527i | \(0.550328\pi\) | |||||||
\(770\) | 20.1525 | 0.726245 | ||||||||
\(771\) | 9.36621 | 0.337316 | ||||||||
\(772\) | −6.67285 | −0.240161 | ||||||||
\(773\) | −19.6191 | −0.705650 | −0.352825 | − | 0.935689i | \(-0.614779\pi\) | ||||
−0.352825 | + | 0.935689i | \(0.614779\pi\) | |||||||
\(774\) | 3.05724 | 0.109890 | ||||||||
\(775\) | 9.07630 | 0.326030 | ||||||||
\(776\) | −1.00000 | −0.0358979 | ||||||||
\(777\) | −2.03111 | −0.0728656 | ||||||||
\(778\) | 5.01300 | 0.179725 | ||||||||
\(779\) | 44.2374 | 1.58497 | ||||||||
\(780\) | −15.1096 | −0.541010 | ||||||||
\(781\) | 7.07730 | 0.253246 | ||||||||
\(782\) | −0.184295 | −0.00659039 | ||||||||
\(783\) | 39.8521 | 1.42420 | ||||||||
\(784\) | −1.27001 | −0.0453575 | ||||||||
\(785\) | 59.9596 | 2.14005 | ||||||||
\(786\) | −2.83346 | −0.101066 | ||||||||
\(787\) | −11.4801 | −0.409221 | −0.204611 | − | 0.978843i | \(-0.565593\pi\) | ||||
−0.204611 | + | 0.978843i | \(0.565593\pi\) | |||||||
\(788\) | 0.343230 | 0.0122270 | ||||||||
\(789\) | −22.7273 | −0.809115 | ||||||||
\(790\) | 30.7459 | 1.09389 | ||||||||
\(791\) | −5.66953 | −0.201585 | ||||||||
\(792\) | −1.25749 | −0.0446829 | ||||||||
\(793\) | −19.5367 | −0.693769 | ||||||||
\(794\) | −28.8266 | −1.02302 | ||||||||
\(795\) | −16.8648 | −0.598134 | ||||||||
\(796\) | −18.6347 | −0.660491 | ||||||||
\(797\) | −12.9066 | −0.457175 | −0.228588 | − | 0.973523i | \(-0.573411\pi\) | ||||
−0.228588 | + | 0.973523i | \(0.573411\pi\) | |||||||
\(798\) | −22.2197 | −0.786569 | ||||||||
\(799\) | −0.875885 | −0.0309866 | ||||||||
\(800\) | 9.07630 | 0.320896 | ||||||||
\(801\) | −4.62692 | −0.163484 | ||||||||
\(802\) | 15.1201 | 0.533911 | ||||||||
\(803\) | −22.1246 | −0.780759 | ||||||||
\(804\) | −17.8006 | −0.627779 | ||||||||
\(805\) | −16.8273 | −0.593083 | ||||||||
\(806\) | 2.57839 | 0.0908199 | ||||||||
\(807\) | 15.8326 | 0.557333 | ||||||||
\(808\) | −8.27408 | −0.291081 | ||||||||
\(809\) | −32.3221 | −1.13638 | −0.568191 | − | 0.822896i | \(-0.692357\pi\) | ||||
−0.568191 | + | 0.822896i | \(0.692357\pi\) | |||||||
\(810\) | 26.2807 | 0.923411 | ||||||||
\(811\) | 45.8968 | 1.61165 | 0.805827 | − | 0.592151i | \(-0.201721\pi\) | ||||
0.805827 | + | 0.592151i | \(0.201721\pi\) | |||||||
\(812\) | 17.1542 | 0.601995 | ||||||||
\(813\) | 19.0617 | 0.668523 | ||||||||
\(814\) | 1.21900 | 0.0427260 | ||||||||
\(815\) | −77.2886 | −2.70730 | ||||||||
\(816\) | 0.153632 | 0.00537820 | ||||||||
\(817\) | −32.4217 | −1.13429 | ||||||||
\(818\) | −13.3584 | −0.467067 | ||||||||
\(819\) | 3.45877 | 0.120859 | ||||||||
\(820\) | −27.9275 | −0.975270 | ||||||||
\(821\) | 4.74026 | 0.165436 | 0.0827182 | − | 0.996573i | \(-0.473640\pi\) | ||||
0.0827182 | + | 0.996573i | \(0.473640\pi\) | |||||||
\(822\) | 13.4428 | 0.468872 | ||||||||
\(823\) | 31.3979 | 1.09446 | 0.547231 | − | 0.836981i | \(-0.315682\pi\) | ||||
0.547231 | + | 0.836981i | \(0.315682\pi\) | |||||||
\(824\) | −10.9834 | −0.382626 | ||||||||
\(825\) | 31.8109 | 1.10751 | ||||||||
\(826\) | 20.2846 | 0.705793 | ||||||||
\(827\) | −6.81237 | −0.236889 | −0.118445 | − | 0.992961i | \(-0.537791\pi\) | ||||
−0.118445 | + | 0.992961i | \(0.537791\pi\) | |||||||
\(828\) | 1.05000 | 0.0364900 | ||||||||
\(829\) | −16.8112 | −0.583878 | −0.291939 | − | 0.956437i | \(-0.594300\pi\) | ||||
−0.291939 | + | 0.956437i | \(0.594300\pi\) | |||||||
\(830\) | −20.6200 | −0.715729 | ||||||||
\(831\) | −34.0098 | −1.17979 | ||||||||
\(832\) | 2.57839 | 0.0893896 | ||||||||
\(833\) | −0.124919 | −0.00432819 | ||||||||
\(834\) | −1.91430 | −0.0662869 | ||||||||
\(835\) | −24.4851 | −0.847343 | ||||||||
\(836\) | 13.3355 | 0.461218 | ||||||||
\(837\) | −5.56107 | −0.192219 | ||||||||
\(838\) | −11.4278 | −0.394767 | ||||||||
\(839\) | −1.04239 | −0.0359875 | −0.0179937 | − | 0.999838i | \(-0.505728\pi\) | ||||
−0.0179937 | + | 0.999838i | \(0.505728\pi\) | |||||||
\(840\) | 14.0275 | 0.483995 | ||||||||
\(841\) | 22.3555 | 0.770880 | ||||||||
\(842\) | −34.7650 | −1.19808 | ||||||||
\(843\) | −12.0422 | −0.414756 | ||||||||
\(844\) | −16.8159 | −0.578827 | ||||||||
\(845\) | 23.8313 | 0.819823 | ||||||||
\(846\) | 4.99024 | 0.171568 | ||||||||
\(847\) | 14.2782 | 0.490606 | ||||||||
\(848\) | 2.87792 | 0.0988281 | ||||||||
\(849\) | 26.1352 | 0.896957 | ||||||||
\(850\) | 0.892752 | 0.0306212 | ||||||||
\(851\) | −1.01786 | −0.0348918 | ||||||||
\(852\) | 4.92629 | 0.168772 | ||||||||
\(853\) | −26.5391 | −0.908682 | −0.454341 | − | 0.890828i | \(-0.650125\pi\) | ||||
−0.454341 | + | 0.890828i | \(0.650125\pi\) | |||||||
\(854\) | 18.1376 | 0.620656 | ||||||||
\(855\) | 12.4952 | 0.427326 | ||||||||
\(856\) | 0.540399 | 0.0184704 | ||||||||
\(857\) | −45.5640 | −1.55644 | −0.778218 | − | 0.627994i | \(-0.783876\pi\) | ||||
−0.778218 | + | 0.627994i | \(0.783876\pi\) | |||||||
\(858\) | 9.03682 | 0.308512 | ||||||||
\(859\) | −36.2295 | −1.23613 | −0.618067 | − | 0.786126i | \(-0.712084\pi\) | ||||
−0.618067 | + | 0.786126i | \(0.712084\pi\) | |||||||
\(860\) | 20.4681 | 0.697957 | ||||||||
\(861\) | −27.8307 | −0.948467 | ||||||||
\(862\) | 10.8643 | 0.370038 | ||||||||
\(863\) | 14.3389 | 0.488100 | 0.244050 | − | 0.969763i | \(-0.421524\pi\) | ||||
0.244050 | + | 0.969763i | \(0.421524\pi\) | |||||||
\(864\) | −5.56107 | −0.189191 | ||||||||
\(865\) | −8.41193 | −0.286014 | ||||||||
\(866\) | 39.8552 | 1.35434 | ||||||||
\(867\) | −26.5376 | −0.901263 | ||||||||
\(868\) | −2.39374 | −0.0812488 | ||||||||
\(869\) | −18.3887 | −0.623793 | ||||||||
\(870\) | 41.9950 | 1.42376 | ||||||||
\(871\) | −29.3849 | −0.995669 | ||||||||
\(872\) | −12.4265 | −0.420815 | ||||||||
\(873\) | 0.560398 | 0.0189666 | ||||||||
\(874\) | −11.1351 | −0.376650 | ||||||||
\(875\) | 36.6089 | 1.23761 | ||||||||
\(876\) | −15.4002 | −0.520325 | ||||||||
\(877\) | −30.5967 | −1.03318 | −0.516589 | − | 0.856233i | \(-0.672799\pi\) | ||||
−0.516589 | + | 0.856233i | \(0.672799\pi\) | |||||||
\(878\) | 1.11217 | 0.0375339 | ||||||||
\(879\) | 39.8864 | 1.34534 | ||||||||
\(880\) | −8.41883 | −0.283799 | ||||||||
\(881\) | 9.82117 | 0.330884 | 0.165442 | − | 0.986220i | \(-0.447095\pi\) | ||||
0.165442 | + | 0.986220i | \(0.447095\pi\) | |||||||
\(882\) | 0.711711 | 0.0239645 | ||||||||
\(883\) | 40.5589 | 1.36492 | 0.682458 | − | 0.730925i | \(-0.260911\pi\) | ||||
0.682458 | + | 0.730925i | \(0.260911\pi\) | |||||||
\(884\) | 0.253613 | 0.00852992 | ||||||||
\(885\) | 49.6586 | 1.66925 | ||||||||
\(886\) | −20.0217 | −0.672642 | ||||||||
\(887\) | 18.6428 | 0.625963 | 0.312982 | − | 0.949759i | \(-0.398672\pi\) | ||||
0.312982 | + | 0.949759i | \(0.398672\pi\) | |||||||
\(888\) | 0.848508 | 0.0284741 | ||||||||
\(889\) | 21.4399 | 0.719070 | ||||||||
\(890\) | −30.9771 | −1.03835 | ||||||||
\(891\) | −15.7181 | −0.526577 | ||||||||
\(892\) | −7.80316 | −0.261269 | ||||||||
\(893\) | −52.9208 | −1.77093 | ||||||||
\(894\) | 7.67543 | 0.256705 | ||||||||
\(895\) | −44.9649 | −1.50301 | ||||||||
\(896\) | −2.39374 | −0.0799692 | ||||||||
\(897\) | −7.54571 | −0.251944 | ||||||||
\(898\) | −11.6894 | −0.390080 | ||||||||
\(899\) | −7.16628 | −0.239009 | ||||||||
\(900\) | −5.08634 | −0.169545 | ||||||||
\(901\) | 0.283074 | 0.00943057 | ||||||||
\(902\) | 16.7030 | 0.556150 | ||||||||
\(903\) | 20.3972 | 0.678776 | ||||||||
\(904\) | 2.36848 | 0.0787745 | ||||||||
\(905\) | −58.8014 | −1.95462 | ||||||||
\(906\) | 8.21472 | 0.272916 | ||||||||
\(907\) | 46.1852 | 1.53355 | 0.766777 | − | 0.641913i | \(-0.221859\pi\) | ||||
0.766777 | + | 0.641913i | \(0.221859\pi\) | |||||||
\(908\) | −15.0215 | −0.498505 | ||||||||
\(909\) | 4.63678 | 0.153792 | ||||||||
\(910\) | 23.1563 | 0.767625 | ||||||||
\(911\) | 27.5874 | 0.914011 | 0.457006 | − | 0.889464i | \(-0.348922\pi\) | ||||
0.457006 | + | 0.889464i | \(0.348922\pi\) | |||||||
\(912\) | 9.28242 | 0.307372 | ||||||||
\(913\) | 12.3325 | 0.408146 | ||||||||
\(914\) | 14.8909 | 0.492547 | ||||||||
\(915\) | 44.4025 | 1.46790 | ||||||||
\(916\) | −10.1878 | −0.336613 | ||||||||
\(917\) | 4.34244 | 0.143400 | ||||||||
\(918\) | −0.546991 | −0.0180534 | ||||||||
\(919\) | −52.9597 | −1.74698 | −0.873490 | − | 0.486842i | \(-0.838149\pi\) | ||||
−0.873490 | + | 0.486842i | \(0.838149\pi\) | |||||||
\(920\) | 7.02969 | 0.231762 | ||||||||
\(921\) | 15.5638 | 0.512844 | ||||||||
\(922\) | −26.1101 | −0.859891 | ||||||||
\(923\) | 8.13221 | 0.267675 | ||||||||
\(924\) | −8.38965 | −0.275999 | ||||||||
\(925\) | 4.93066 | 0.162119 | ||||||||
\(926\) | −5.62200 | −0.184750 | ||||||||
\(927\) | 6.15509 | 0.202160 | ||||||||
\(928\) | −7.16628 | −0.235245 | ||||||||
\(929\) | 40.9581 | 1.34379 | 0.671896 | − | 0.740645i | \(-0.265480\pi\) | ||||
0.671896 | + | 0.740645i | \(0.265480\pi\) | |||||||
\(930\) | −5.86008 | −0.192160 | ||||||||
\(931\) | −7.54760 | −0.247362 | ||||||||
\(932\) | 24.7094 | 0.809382 | ||||||||
\(933\) | 25.5781 | 0.837389 | ||||||||
\(934\) | −38.7588 | −1.26823 | ||||||||
\(935\) | −0.828083 | −0.0270812 | ||||||||
\(936\) | −1.44492 | −0.0472288 | ||||||||
\(937\) | −32.6865 | −1.06782 | −0.533911 | − | 0.845541i | \(-0.679278\pi\) | ||||
−0.533911 | + | 0.845541i | \(0.679278\pi\) | |||||||
\(938\) | 27.2805 | 0.890740 | ||||||||
\(939\) | −48.2979 | −1.57614 | ||||||||
\(940\) | 33.4094 | 1.08970 | ||||||||
\(941\) | −44.9518 | −1.46539 | −0.732694 | − | 0.680558i | \(-0.761737\pi\) | ||||
−0.732694 | + | 0.680558i | \(0.761737\pi\) | |||||||
\(942\) | −24.9617 | −0.813295 | ||||||||
\(943\) | −13.9470 | −0.454175 | ||||||||
\(944\) | −8.47404 | −0.275806 | ||||||||
\(945\) | −49.9435 | −1.62466 | ||||||||
\(946\) | −12.2417 | −0.398012 | ||||||||
\(947\) | 24.3199 | 0.790289 | 0.395145 | − | 0.918619i | \(-0.370694\pi\) | ||||
0.395145 | + | 0.918619i | \(0.370694\pi\) | |||||||
\(948\) | −12.7998 | −0.415717 | ||||||||
\(949\) | −25.4224 | −0.825245 | ||||||||
\(950\) | 53.9399 | 1.75004 | ||||||||
\(951\) | −4.23795 | −0.137425 | ||||||||
\(952\) | −0.235450 | −0.00763099 | ||||||||
\(953\) | −27.9528 | −0.905479 | −0.452740 | − | 0.891643i | \(-0.649553\pi\) | ||||
−0.452740 | + | 0.891643i | \(0.649553\pi\) | |||||||
\(954\) | −1.61278 | −0.0522156 | ||||||||
\(955\) | 10.9433 | 0.354118 | ||||||||
\(956\) | −10.9021 | −0.352600 | ||||||||
\(957\) | −25.1166 | −0.811904 | ||||||||
\(958\) | 14.2225 | 0.459508 | ||||||||
\(959\) | −20.6019 | −0.665271 | ||||||||
\(960\) | −5.86008 | −0.189133 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 1.40070 | 0.0451604 | ||||||||
\(963\) | −0.302838 | −0.00975883 | ||||||||
\(964\) | −15.2459 | −0.491037 | ||||||||
\(965\) | 25.0354 | 0.805919 | ||||||||
\(966\) | 7.00533 | 0.225393 | ||||||||
\(967\) | 17.2667 | 0.555260 | 0.277630 | − | 0.960688i | \(-0.410451\pi\) | ||||
0.277630 | + | 0.960688i | \(0.410451\pi\) | |||||||
\(968\) | −5.96482 | −0.191717 | ||||||||
\(969\) | 0.913027 | 0.0293306 | ||||||||
\(970\) | 3.75184 | 0.120464 | ||||||||
\(971\) | 39.9411 | 1.28177 | 0.640885 | − | 0.767637i | \(-0.278567\pi\) | ||||
0.640885 | + | 0.767637i | \(0.278567\pi\) | |||||||
\(972\) | 5.74230 | 0.184184 | ||||||||
\(973\) | 2.93378 | 0.0940528 | ||||||||
\(974\) | 37.2537 | 1.19368 | ||||||||
\(975\) | 36.5525 | 1.17062 | ||||||||
\(976\) | −7.57710 | −0.242537 | ||||||||
\(977\) | −3.10021 | −0.0991846 | −0.0495923 | − | 0.998770i | \(-0.515792\pi\) | ||||
−0.0495923 | + | 0.998770i | \(0.515792\pi\) | |||||||
\(978\) | 32.1759 | 1.02887 | ||||||||
\(979\) | 18.5269 | 0.592123 | ||||||||
\(980\) | 4.76487 | 0.152208 | ||||||||
\(981\) | 6.96379 | 0.222337 | ||||||||
\(982\) | 36.7869 | 1.17392 | ||||||||
\(983\) | 32.6254 | 1.04059 | 0.520294 | − | 0.853987i | \(-0.325823\pi\) | ||||
0.520294 | + | 0.853987i | \(0.325823\pi\) | |||||||
\(984\) | 11.6264 | 0.370638 | ||||||||
\(985\) | −1.28774 | −0.0410309 | ||||||||
\(986\) | −0.704881 | −0.0224480 | ||||||||
\(987\) | 33.2937 | 1.05975 | ||||||||
\(988\) | 15.3232 | 0.487497 | ||||||||
\(989\) | 10.2218 | 0.325033 | ||||||||
\(990\) | 4.71789 | 0.149945 | ||||||||
\(991\) | −37.0927 | −1.17829 | −0.589145 | − | 0.808028i | \(-0.700535\pi\) | ||||
−0.589145 | + | 0.808028i | \(0.700535\pi\) | |||||||
\(992\) | 1.00000 | 0.0317500 | ||||||||
\(993\) | −41.4951 | −1.31681 | ||||||||
\(994\) | −7.54983 | −0.239466 | ||||||||
\(995\) | 69.9146 | 2.21644 | ||||||||
\(996\) | 8.58427 | 0.272003 | ||||||||
\(997\) | −26.0630 | −0.825423 | −0.412711 | − | 0.910862i | \(-0.635418\pi\) | ||||
−0.412711 | + | 0.910862i | \(0.635418\pi\) | |||||||
\(998\) | 4.29955 | 0.136100 | ||||||||
\(999\) | −3.02103 | −0.0955811 |
(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 | 6014.2.a.e.1.17 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6014.2.a.e.1.17 | ✓ | 21 | 1.1 | even | 1 | trivial |