Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [667,2,Mod(1,667)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(667, 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("667.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 667 = 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 667.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: | \(5.32602181482\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 13 x^{10} + 41 x^{9} + 54 x^{8} - 188 x^{7} - 77 x^{6} + 342 x^{5} + 13 x^{4} - 215 x^{3} + 9 x^{2} + 37 x - 5 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.58646\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 667.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.58646 | −1.82890 | −0.914452 | − | 0.404694i | \(-0.867378\pi\) | ||||
−0.914452 | + | 0.404694i | \(0.867378\pi\) | |||||||
\(3\) | −2.87567 | −1.66027 | −0.830136 | − | 0.557562i | \(-0.811737\pi\) | ||||
−0.830136 | + | 0.557562i | \(0.811737\pi\) | |||||||
\(4\) | 4.68978 | 2.34489 | ||||||||
\(5\) | −3.69848 | −1.65401 | −0.827005 | − | 0.562195i | \(-0.809957\pi\) | ||||
−0.827005 | + | 0.562195i | \(0.809957\pi\) | |||||||
\(6\) | 7.43782 | 3.03648 | ||||||||
\(7\) | −0.298143 | −0.112688 | −0.0563438 | − | 0.998411i | \(-0.517944\pi\) | ||||
−0.0563438 | + | 0.998411i | \(0.517944\pi\) | |||||||
\(8\) | −6.95702 | −2.45968 | ||||||||
\(9\) | 5.26950 | 1.75650 | ||||||||
\(10\) | 9.56597 | 3.02503 | ||||||||
\(11\) | −1.58434 | −0.477696 | −0.238848 | − | 0.971057i | \(-0.576770\pi\) | ||||
−0.238848 | + | 0.971057i | \(0.576770\pi\) | |||||||
\(12\) | −13.4863 | −3.89316 | ||||||||
\(13\) | −4.24524 | −1.17742 | −0.588709 | − | 0.808345i | \(-0.700364\pi\) | ||||
−0.588709 | + | 0.808345i | \(0.700364\pi\) | |||||||
\(14\) | 0.771137 | 0.206095 | ||||||||
\(15\) | 10.6356 | 2.74610 | ||||||||
\(16\) | 8.61451 | 2.15363 | ||||||||
\(17\) | 4.97869 | 1.20751 | 0.603754 | − | 0.797170i | \(-0.293671\pi\) | ||||
0.603754 | + | 0.797170i | \(0.293671\pi\) | |||||||
\(18\) | −13.6294 | −3.21247 | ||||||||
\(19\) | 8.32429 | 1.90972 | 0.954861 | − | 0.297053i | \(-0.0960037\pi\) | ||||
0.954861 | + | 0.297053i | \(0.0960037\pi\) | |||||||
\(20\) | −17.3451 | −3.87847 | ||||||||
\(21\) | 0.857363 | 0.187092 | ||||||||
\(22\) | 4.09783 | 0.873661 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 20.0061 | 4.08374 | ||||||||
\(25\) | 8.67874 | 1.73575 | ||||||||
\(26\) | 10.9802 | 2.15339 | ||||||||
\(27\) | −6.52634 | −1.25600 | ||||||||
\(28\) | −1.39823 | −0.264240 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | −27.5086 | −5.02236 | ||||||||
\(31\) | −0.692531 | −0.124382 | −0.0621911 | − | 0.998064i | \(-0.519809\pi\) | ||||
−0.0621911 | + | 0.998064i | \(0.519809\pi\) | |||||||
\(32\) | −8.36705 | −1.47910 | ||||||||
\(33\) | 4.55604 | 0.793106 | ||||||||
\(34\) | −12.8772 | −2.20842 | ||||||||
\(35\) | 1.10268 | 0.186386 | ||||||||
\(36\) | 24.7128 | 4.11880 | ||||||||
\(37\) | 7.77829 | 1.27874 | 0.639372 | − | 0.768898i | \(-0.279194\pi\) | ||||
0.639372 | + | 0.768898i | \(0.279194\pi\) | |||||||
\(38\) | −21.5304 | −3.49270 | ||||||||
\(39\) | 12.2079 | 1.95483 | ||||||||
\(40\) | 25.7304 | 4.06833 | ||||||||
\(41\) | 5.66508 | 0.884737 | 0.442368 | − | 0.896833i | \(-0.354138\pi\) | ||||
0.442368 | + | 0.896833i | \(0.354138\pi\) | |||||||
\(42\) | −2.21754 | −0.342173 | ||||||||
\(43\) | −2.82585 | −0.430939 | −0.215469 | − | 0.976511i | \(-0.569128\pi\) | ||||
−0.215469 | + | 0.976511i | \(0.569128\pi\) | |||||||
\(44\) | −7.43021 | −1.12015 | ||||||||
\(45\) | −19.4891 | −2.90527 | ||||||||
\(46\) | 2.58646 | 0.381353 | ||||||||
\(47\) | 0.941070 | 0.137269 | 0.0686346 | − | 0.997642i | \(-0.478136\pi\) | ||||
0.0686346 | + | 0.997642i | \(0.478136\pi\) | |||||||
\(48\) | −24.7725 | −3.57561 | ||||||||
\(49\) | −6.91111 | −0.987301 | ||||||||
\(50\) | −22.4472 | −3.17452 | ||||||||
\(51\) | −14.3171 | −2.00479 | ||||||||
\(52\) | −19.9093 | −2.76092 | ||||||||
\(53\) | −8.52596 | −1.17113 | −0.585565 | − | 0.810625i | \(-0.699127\pi\) | ||||
−0.585565 | + | 0.810625i | \(0.699127\pi\) | |||||||
\(54\) | 16.8801 | 2.29710 | ||||||||
\(55\) | 5.85965 | 0.790115 | ||||||||
\(56\) | 2.07419 | 0.277175 | ||||||||
\(57\) | −23.9379 | −3.17066 | ||||||||
\(58\) | 2.58646 | 0.339619 | ||||||||
\(59\) | −5.47010 | −0.712146 | −0.356073 | − | 0.934458i | \(-0.615885\pi\) | ||||
−0.356073 | + | 0.934458i | \(0.615885\pi\) | |||||||
\(60\) | 49.8788 | 6.43932 | ||||||||
\(61\) | −7.60438 | −0.973641 | −0.486820 | − | 0.873502i | \(-0.661843\pi\) | ||||
−0.486820 | + | 0.873502i | \(0.661843\pi\) | |||||||
\(62\) | 1.79121 | 0.227483 | ||||||||
\(63\) | −1.57107 | −0.197936 | ||||||||
\(64\) | 4.41204 | 0.551505 | ||||||||
\(65\) | 15.7009 | 1.94746 | ||||||||
\(66\) | −11.7840 | −1.45051 | ||||||||
\(67\) | 8.46657 | 1.03436 | 0.517178 | − | 0.855878i | \(-0.326983\pi\) | ||||
0.517178 | + | 0.855878i | \(0.326983\pi\) | |||||||
\(68\) | 23.3490 | 2.83148 | ||||||||
\(69\) | 2.87567 | 0.346190 | ||||||||
\(70\) | −2.85203 | −0.340883 | ||||||||
\(71\) | 14.1339 | 1.67738 | 0.838691 | − | 0.544608i | \(-0.183321\pi\) | ||||
0.838691 | + | 0.544608i | \(0.183321\pi\) | |||||||
\(72\) | −36.6600 | −4.32043 | ||||||||
\(73\) | −5.10834 | −0.597885 | −0.298943 | − | 0.954271i | \(-0.596634\pi\) | ||||
−0.298943 | + | 0.954271i | \(0.596634\pi\) | |||||||
\(74\) | −20.1183 | −2.33870 | ||||||||
\(75\) | −24.9572 | −2.88181 | ||||||||
\(76\) | 39.0391 | 4.47809 | ||||||||
\(77\) | 0.472361 | 0.0538305 | ||||||||
\(78\) | −31.5754 | −3.57520 | ||||||||
\(79\) | −0.828407 | −0.0932031 | −0.0466016 | − | 0.998914i | \(-0.514839\pi\) | ||||
−0.0466016 | + | 0.998914i | \(0.514839\pi\) | |||||||
\(80\) | −31.8606 | −3.56212 | ||||||||
\(81\) | 2.95913 | 0.328793 | ||||||||
\(82\) | −14.6525 | −1.61810 | ||||||||
\(83\) | −17.8414 | −1.95834 | −0.979172 | − | 0.203033i | \(-0.934920\pi\) | ||||
−0.979172 | + | 0.203033i | \(0.934920\pi\) | |||||||
\(84\) | 4.02085 | 0.438711 | ||||||||
\(85\) | −18.4136 | −1.99723 | ||||||||
\(86\) | 7.30896 | 0.788146 | ||||||||
\(87\) | 2.87567 | 0.308305 | ||||||||
\(88\) | 11.0223 | 1.17498 | ||||||||
\(89\) | −6.78344 | −0.719043 | −0.359522 | − | 0.933137i | \(-0.617060\pi\) | ||||
−0.359522 | + | 0.933137i | \(0.617060\pi\) | |||||||
\(90\) | 50.4079 | 5.31346 | ||||||||
\(91\) | 1.26569 | 0.132681 | ||||||||
\(92\) | −4.68978 | −0.488944 | ||||||||
\(93\) | 1.99149 | 0.206508 | ||||||||
\(94\) | −2.43404 | −0.251052 | ||||||||
\(95\) | −30.7872 | −3.15870 | ||||||||
\(96\) | 24.0609 | 2.45571 | ||||||||
\(97\) | 9.10860 | 0.924838 | 0.462419 | − | 0.886661i | \(-0.346982\pi\) | ||||
0.462419 | + | 0.886661i | \(0.346982\pi\) | |||||||
\(98\) | 17.8753 | 1.80568 | ||||||||
\(99\) | −8.34868 | −0.839074 | ||||||||
\(100\) | 40.7014 | 4.07014 | ||||||||
\(101\) | −16.9255 | −1.68415 | −0.842073 | − | 0.539364i | \(-0.818665\pi\) | ||||
−0.842073 | + | 0.539364i | \(0.818665\pi\) | |||||||
\(102\) | 37.0306 | 3.66657 | ||||||||
\(103\) | 0.342308 | 0.0337286 | 0.0168643 | − | 0.999858i | \(-0.494632\pi\) | ||||
0.0168643 | + | 0.999858i | \(0.494632\pi\) | |||||||
\(104\) | 29.5343 | 2.89607 | ||||||||
\(105\) | −3.17094 | −0.309452 | ||||||||
\(106\) | 22.0521 | 2.14189 | ||||||||
\(107\) | 16.6153 | 1.60626 | 0.803130 | − | 0.595804i | \(-0.203166\pi\) | ||||
0.803130 | + | 0.595804i | \(0.203166\pi\) | |||||||
\(108\) | −30.6071 | −2.94517 | ||||||||
\(109\) | −1.54247 | −0.147742 | −0.0738710 | − | 0.997268i | \(-0.523535\pi\) | ||||
−0.0738710 | + | 0.997268i | \(0.523535\pi\) | |||||||
\(110\) | −15.1558 | −1.44504 | ||||||||
\(111\) | −22.3678 | −2.12306 | ||||||||
\(112\) | −2.56836 | −0.242687 | ||||||||
\(113\) | 14.7265 | 1.38536 | 0.692678 | − | 0.721247i | \(-0.256431\pi\) | ||||
0.692678 | + | 0.721247i | \(0.256431\pi\) | |||||||
\(114\) | 61.9145 | 5.79883 | ||||||||
\(115\) | 3.69848 | 0.344885 | ||||||||
\(116\) | −4.68978 | −0.435436 | ||||||||
\(117\) | −22.3703 | −2.06814 | ||||||||
\(118\) | 14.1482 | 1.30245 | ||||||||
\(119\) | −1.48436 | −0.136071 | ||||||||
\(120\) | −73.9923 | −6.75454 | ||||||||
\(121\) | −8.48987 | −0.771806 | ||||||||
\(122\) | 19.6684 | 1.78070 | ||||||||
\(123\) | −16.2909 | −1.46890 | ||||||||
\(124\) | −3.24782 | −0.291663 | ||||||||
\(125\) | −13.6057 | −1.21693 | ||||||||
\(126\) | 4.06350 | 0.362006 | ||||||||
\(127\) | −0.462641 | −0.0410528 | −0.0205264 | − | 0.999789i | \(-0.506534\pi\) | ||||
−0.0205264 | + | 0.999789i | \(0.506534\pi\) | |||||||
\(128\) | 5.32254 | 0.470450 | ||||||||
\(129\) | 8.12624 | 0.715475 | ||||||||
\(130\) | −40.6099 | −3.56172 | ||||||||
\(131\) | 16.0399 | 1.40141 | 0.700707 | − | 0.713449i | \(-0.252868\pi\) | ||||
0.700707 | + | 0.713449i | \(0.252868\pi\) | |||||||
\(132\) | 21.3669 | 1.85975 | ||||||||
\(133\) | −2.48183 | −0.215202 | ||||||||
\(134\) | −21.8985 | −1.89174 | ||||||||
\(135\) | 24.1375 | 2.07743 | ||||||||
\(136\) | −34.6368 | −2.97008 | ||||||||
\(137\) | −3.85509 | −0.329363 | −0.164681 | − | 0.986347i | \(-0.552660\pi\) | ||||
−0.164681 | + | 0.986347i | \(0.552660\pi\) | |||||||
\(138\) | −7.43782 | −0.633149 | ||||||||
\(139\) | 8.07514 | 0.684924 | 0.342462 | − | 0.939532i | \(-0.388739\pi\) | ||||
0.342462 | + | 0.939532i | \(0.388739\pi\) | |||||||
\(140\) | 5.17132 | 0.437056 | ||||||||
\(141\) | −2.70621 | −0.227904 | ||||||||
\(142\) | −36.5567 | −3.06777 | ||||||||
\(143\) | 6.72591 | 0.562449 | ||||||||
\(144\) | 45.3942 | 3.78285 | ||||||||
\(145\) | 3.69848 | 0.307142 | ||||||||
\(146\) | 13.2125 | 1.09348 | ||||||||
\(147\) | 19.8741 | 1.63919 | ||||||||
\(148\) | 36.4785 | 2.99852 | ||||||||
\(149\) | 21.9397 | 1.79737 | 0.898683 | − | 0.438598i | \(-0.144525\pi\) | ||||
0.898683 | + | 0.438598i | \(0.144525\pi\) | |||||||
\(150\) | 64.5509 | 5.27056 | ||||||||
\(151\) | 0.452281 | 0.0368061 | 0.0184031 | − | 0.999831i | \(-0.494142\pi\) | ||||
0.0184031 | + | 0.999831i | \(0.494142\pi\) | |||||||
\(152\) | −57.9123 | −4.69730 | ||||||||
\(153\) | 26.2352 | 2.12099 | ||||||||
\(154\) | −1.22174 | −0.0984508 | ||||||||
\(155\) | 2.56131 | 0.205730 | ||||||||
\(156\) | 57.2526 | 4.58387 | ||||||||
\(157\) | −8.50054 | −0.678417 | −0.339208 | − | 0.940711i | \(-0.610159\pi\) | ||||
−0.339208 | + | 0.940711i | \(0.610159\pi\) | |||||||
\(158\) | 2.14264 | 0.170460 | ||||||||
\(159\) | 24.5179 | 1.94439 | ||||||||
\(160\) | 30.9454 | 2.44645 | ||||||||
\(161\) | 0.298143 | 0.0234970 | ||||||||
\(162\) | −7.65368 | −0.601330 | ||||||||
\(163\) | −7.14215 | −0.559417 | −0.279708 | − | 0.960085i | \(-0.590238\pi\) | ||||
−0.279708 | + | 0.960085i | \(0.590238\pi\) | |||||||
\(164\) | 26.5680 | 2.07461 | ||||||||
\(165\) | −16.8504 | −1.31180 | ||||||||
\(166\) | 46.1460 | 3.58162 | ||||||||
\(167\) | −1.47531 | −0.114163 | −0.0570813 | − | 0.998370i | \(-0.518179\pi\) | ||||
−0.0570813 | + | 0.998370i | \(0.518179\pi\) | |||||||
\(168\) | −5.96470 | −0.460186 | ||||||||
\(169\) | 5.02209 | 0.386314 | ||||||||
\(170\) | 47.6260 | 3.65275 | ||||||||
\(171\) | 43.8648 | 3.35443 | ||||||||
\(172\) | −13.2526 | −1.01050 | ||||||||
\(173\) | −18.0111 | −1.36936 | −0.684678 | − | 0.728846i | \(-0.740057\pi\) | ||||
−0.684678 | + | 0.728846i | \(0.740057\pi\) | |||||||
\(174\) | −7.43782 | −0.563860 | ||||||||
\(175\) | −2.58751 | −0.195597 | ||||||||
\(176\) | −13.6483 | −1.02878 | ||||||||
\(177\) | 15.7302 | 1.18236 | ||||||||
\(178\) | 17.5451 | 1.31506 | ||||||||
\(179\) | 15.7157 | 1.17465 | 0.587323 | − | 0.809353i | \(-0.300182\pi\) | ||||
0.587323 | + | 0.809353i | \(0.300182\pi\) | |||||||
\(180\) | −91.3998 | −6.81254 | ||||||||
\(181\) | −19.1187 | −1.42108 | −0.710541 | − | 0.703656i | \(-0.751550\pi\) | ||||
−0.710541 | + | 0.703656i | \(0.751550\pi\) | |||||||
\(182\) | −3.27366 | −0.242660 | ||||||||
\(183\) | 21.8677 | 1.61651 | ||||||||
\(184\) | 6.95702 | 0.512879 | ||||||||
\(185\) | −28.7679 | −2.11505 | ||||||||
\(186\) | −5.15092 | −0.377684 | ||||||||
\(187\) | −7.88793 | −0.576823 | ||||||||
\(188\) | 4.41342 | 0.321882 | ||||||||
\(189\) | 1.94579 | 0.141535 | ||||||||
\(190\) | 79.6299 | 5.77696 | ||||||||
\(191\) | 3.97520 | 0.287636 | 0.143818 | − | 0.989604i | \(-0.454062\pi\) | ||||
0.143818 | + | 0.989604i | \(0.454062\pi\) | |||||||
\(192\) | −12.6876 | −0.915647 | ||||||||
\(193\) | −20.0623 | −1.44412 | −0.722059 | − | 0.691832i | \(-0.756804\pi\) | ||||
−0.722059 | + | 0.691832i | \(0.756804\pi\) | |||||||
\(194\) | −23.5590 | −1.69144 | ||||||||
\(195\) | −45.1508 | −3.23331 | ||||||||
\(196\) | −32.4116 | −2.31512 | ||||||||
\(197\) | 11.0730 | 0.788916 | 0.394458 | − | 0.918914i | \(-0.370932\pi\) | ||||
0.394458 | + | 0.918914i | \(0.370932\pi\) | |||||||
\(198\) | 21.5935 | 1.53459 | ||||||||
\(199\) | −18.6961 | −1.32533 | −0.662665 | − | 0.748916i | \(-0.730575\pi\) | ||||
−0.662665 | + | 0.748916i | \(0.730575\pi\) | |||||||
\(200\) | −60.3782 | −4.26939 | ||||||||
\(201\) | −24.3471 | −1.71731 | ||||||||
\(202\) | 43.7770 | 3.08014 | ||||||||
\(203\) | 0.298143 | 0.0209256 | ||||||||
\(204\) | −67.1440 | −4.70102 | ||||||||
\(205\) | −20.9522 | −1.46336 | ||||||||
\(206\) | −0.885366 | −0.0616864 | ||||||||
\(207\) | −5.26950 | −0.366256 | ||||||||
\(208\) | −36.5707 | −2.53572 | ||||||||
\(209\) | −13.1885 | −0.912267 | ||||||||
\(210\) | 8.20151 | 0.565958 | ||||||||
\(211\) | 4.24605 | 0.292310 | 0.146155 | − | 0.989262i | \(-0.453310\pi\) | ||||
0.146155 | + | 0.989262i | \(0.453310\pi\) | |||||||
\(212\) | −39.9849 | −2.74617 | ||||||||
\(213\) | −40.6444 | −2.78491 | ||||||||
\(214\) | −42.9748 | −2.93770 | ||||||||
\(215\) | 10.4514 | 0.712777 | ||||||||
\(216\) | 45.4039 | 3.08935 | ||||||||
\(217\) | 0.206474 | 0.0140163 | ||||||||
\(218\) | 3.98954 | 0.270206 | ||||||||
\(219\) | 14.6899 | 0.992652 | ||||||||
\(220\) | 27.4805 | 1.85273 | ||||||||
\(221\) | −21.1357 | −1.42174 | ||||||||
\(222\) | 57.8536 | 3.88288 | ||||||||
\(223\) | 18.4472 | 1.23532 | 0.617658 | − | 0.786447i | \(-0.288082\pi\) | ||||
0.617658 | + | 0.786447i | \(0.288082\pi\) | |||||||
\(224\) | 2.49458 | 0.166676 | ||||||||
\(225\) | 45.7326 | 3.04884 | ||||||||
\(226\) | −38.0896 | −2.53368 | ||||||||
\(227\) | 20.0773 | 1.33257 | 0.666287 | − | 0.745695i | \(-0.267882\pi\) | ||||
0.666287 | + | 0.745695i | \(0.267882\pi\) | |||||||
\(228\) | −112.264 | −7.43485 | ||||||||
\(229\) | −3.04324 | −0.201103 | −0.100551 | − | 0.994932i | \(-0.532061\pi\) | ||||
−0.100551 | + | 0.994932i | \(0.532061\pi\) | |||||||
\(230\) | −9.56597 | −0.630762 | ||||||||
\(231\) | −1.35835 | −0.0893732 | ||||||||
\(232\) | 6.95702 | 0.456751 | ||||||||
\(233\) | 5.39180 | 0.353228 | 0.176614 | − | 0.984280i | \(-0.443486\pi\) | ||||
0.176614 | + | 0.984280i | \(0.443486\pi\) | |||||||
\(234\) | 57.8599 | 3.78242 | ||||||||
\(235\) | −3.48053 | −0.227045 | ||||||||
\(236\) | −25.6536 | −1.66991 | ||||||||
\(237\) | 2.38223 | 0.154742 | ||||||||
\(238\) | 3.83925 | 0.248861 | ||||||||
\(239\) | −14.2539 | −0.922008 | −0.461004 | − | 0.887398i | \(-0.652511\pi\) | ||||
−0.461004 | + | 0.887398i | \(0.652511\pi\) | |||||||
\(240\) | 91.6206 | 5.91409 | ||||||||
\(241\) | −7.87515 | −0.507283 | −0.253641 | − | 0.967298i | \(-0.581628\pi\) | ||||
−0.253641 | + | 0.967298i | \(0.581628\pi\) | |||||||
\(242\) | 21.9587 | 1.41156 | ||||||||
\(243\) | 11.0695 | 0.710111 | ||||||||
\(244\) | −35.6629 | −2.28308 | ||||||||
\(245\) | 25.5606 | 1.63301 | ||||||||
\(246\) | 42.1358 | 2.68648 | ||||||||
\(247\) | −35.3386 | −2.24854 | ||||||||
\(248\) | 4.81796 | 0.305941 | ||||||||
\(249\) | 51.3059 | 3.25138 | ||||||||
\(250\) | 35.1907 | 2.22566 | ||||||||
\(251\) | −7.81496 | −0.493276 | −0.246638 | − | 0.969108i | \(-0.579326\pi\) | ||||
−0.246638 | + | 0.969108i | \(0.579326\pi\) | |||||||
\(252\) | −7.36797 | −0.464138 | ||||||||
\(253\) | 1.58434 | 0.0996066 | ||||||||
\(254\) | 1.19660 | 0.0750816 | ||||||||
\(255\) | 52.9514 | 3.31595 | ||||||||
\(256\) | −22.5906 | −1.41191 | ||||||||
\(257\) | −29.9598 | −1.86884 | −0.934419 | − | 0.356175i | \(-0.884081\pi\) | ||||
−0.934419 | + | 0.356175i | \(0.884081\pi\) | |||||||
\(258\) | −21.0182 | −1.30854 | ||||||||
\(259\) | −2.31905 | −0.144099 | ||||||||
\(260\) | 73.6340 | 4.56659 | ||||||||
\(261\) | −5.26950 | −0.326174 | ||||||||
\(262\) | −41.4866 | −2.56305 | ||||||||
\(263\) | −13.9120 | −0.857853 | −0.428926 | − | 0.903339i | \(-0.641108\pi\) | ||||
−0.428926 | + | 0.903339i | \(0.641108\pi\) | |||||||
\(264\) | −31.6965 | −1.95079 | ||||||||
\(265\) | 31.5331 | 1.93706 | ||||||||
\(266\) | 6.41916 | 0.393584 | ||||||||
\(267\) | 19.5070 | 1.19381 | ||||||||
\(268\) | 39.7064 | 2.42545 | ||||||||
\(269\) | −24.8644 | −1.51601 | −0.758003 | − | 0.652251i | \(-0.773825\pi\) | ||||
−0.758003 | + | 0.652251i | \(0.773825\pi\) | |||||||
\(270\) | −62.4308 | −3.79942 | ||||||||
\(271\) | −11.0533 | −0.671439 | −0.335720 | − | 0.941962i | \(-0.608979\pi\) | ||||
−0.335720 | + | 0.941962i | \(0.608979\pi\) | |||||||
\(272\) | 42.8889 | 2.60052 | ||||||||
\(273\) | −3.63972 | −0.220286 | ||||||||
\(274\) | 9.97105 | 0.602373 | ||||||||
\(275\) | −13.7501 | −0.829161 | ||||||||
\(276\) | 13.4863 | 0.811779 | ||||||||
\(277\) | −23.3758 | −1.40451 | −0.702257 | − | 0.711923i | \(-0.747824\pi\) | ||||
−0.702257 | + | 0.711923i | \(0.747824\pi\) | |||||||
\(278\) | −20.8860 | −1.25266 | ||||||||
\(279\) | −3.64929 | −0.218478 | ||||||||
\(280\) | −7.67135 | −0.458451 | ||||||||
\(281\) | −10.6841 | −0.637358 | −0.318679 | − | 0.947863i | \(-0.603239\pi\) | ||||
−0.318679 | + | 0.947863i | \(0.603239\pi\) | |||||||
\(282\) | 6.99951 | 0.416815 | ||||||||
\(283\) | −18.4046 | −1.09404 | −0.547021 | − | 0.837119i | \(-0.684238\pi\) | ||||
−0.547021 | + | 0.837119i | \(0.684238\pi\) | |||||||
\(284\) | 66.2848 | 3.93328 | ||||||||
\(285\) | 88.5339 | 5.24430 | ||||||||
\(286\) | −17.3963 | −1.02866 | ||||||||
\(287\) | −1.68901 | −0.0996989 | ||||||||
\(288\) | −44.0902 | −2.59804 | ||||||||
\(289\) | 7.78731 | 0.458077 | ||||||||
\(290\) | −9.56597 | −0.561733 | ||||||||
\(291\) | −26.1934 | −1.53548 | ||||||||
\(292\) | −23.9570 | −1.40198 | ||||||||
\(293\) | −5.02693 | −0.293677 | −0.146838 | − | 0.989161i | \(-0.546910\pi\) | ||||
−0.146838 | + | 0.989161i | \(0.546910\pi\) | |||||||
\(294\) | −51.4036 | −2.99792 | ||||||||
\(295\) | 20.2310 | 1.17790 | ||||||||
\(296\) | −54.1138 | −3.14530 | ||||||||
\(297\) | 10.3399 | 0.599984 | ||||||||
\(298\) | −56.7461 | −3.28721 | ||||||||
\(299\) | 4.24524 | 0.245509 | ||||||||
\(300\) | −117.044 | −6.75754 | ||||||||
\(301\) | 0.842510 | 0.0485615 | ||||||||
\(302\) | −1.16981 | −0.0673149 | ||||||||
\(303\) | 48.6721 | 2.79614 | ||||||||
\(304\) | 71.7096 | 4.11283 | ||||||||
\(305\) | 28.1246 | 1.61041 | ||||||||
\(306\) | −67.8563 | −3.87909 | ||||||||
\(307\) | −15.6946 | −0.895736 | −0.447868 | − | 0.894100i | \(-0.647816\pi\) | ||||
−0.447868 | + | 0.894100i | \(0.647816\pi\) | |||||||
\(308\) | 2.21527 | 0.126227 | ||||||||
\(309\) | −0.984366 | −0.0559986 | ||||||||
\(310\) | −6.62474 | −0.376260 | ||||||||
\(311\) | 19.4424 | 1.10248 | 0.551238 | − | 0.834348i | \(-0.314156\pi\) | ||||
0.551238 | + | 0.834348i | \(0.314156\pi\) | |||||||
\(312\) | −84.9309 | −4.80827 | ||||||||
\(313\) | 20.3762 | 1.15173 | 0.575866 | − | 0.817544i | \(-0.304665\pi\) | ||||
0.575866 | + | 0.817544i | \(0.304665\pi\) | |||||||
\(314\) | 21.9863 | 1.24076 | ||||||||
\(315\) | 5.81056 | 0.327388 | ||||||||
\(316\) | −3.88505 | −0.218551 | ||||||||
\(317\) | 23.6273 | 1.32704 | 0.663519 | − | 0.748159i | \(-0.269062\pi\) | ||||
0.663519 | + | 0.748159i | \(0.269062\pi\) | |||||||
\(318\) | −63.4145 | −3.55611 | ||||||||
\(319\) | 1.58434 | 0.0887060 | ||||||||
\(320\) | −16.3178 | −0.912194 | ||||||||
\(321\) | −47.7801 | −2.66683 | ||||||||
\(322\) | −0.771137 | −0.0429738 | ||||||||
\(323\) | 41.4440 | 2.30601 | ||||||||
\(324\) | 13.8777 | 0.770983 | ||||||||
\(325\) | −36.8434 | −2.04370 | ||||||||
\(326\) | 18.4729 | 1.02312 | ||||||||
\(327\) | 4.43564 | 0.245292 | ||||||||
\(328\) | −39.4121 | −2.17617 | ||||||||
\(329\) | −0.280574 | −0.0154685 | ||||||||
\(330\) | 43.5830 | 2.39917 | ||||||||
\(331\) | 13.0745 | 0.718638 | 0.359319 | − | 0.933215i | \(-0.383009\pi\) | ||||
0.359319 | + | 0.933215i | \(0.383009\pi\) | |||||||
\(332\) | −83.6721 | −4.59210 | ||||||||
\(333\) | 40.9877 | 2.24611 | ||||||||
\(334\) | 3.81583 | 0.208793 | ||||||||
\(335\) | −31.3134 | −1.71083 | ||||||||
\(336\) | 7.38577 | 0.402927 | ||||||||
\(337\) | 14.7501 | 0.803490 | 0.401745 | − | 0.915752i | \(-0.368404\pi\) | ||||
0.401745 | + | 0.915752i | \(0.368404\pi\) | |||||||
\(338\) | −12.9894 | −0.706532 | ||||||||
\(339\) | −42.3487 | −2.30007 | ||||||||
\(340\) | −86.3556 | −4.68329 | ||||||||
\(341\) | 1.09720 | 0.0594170 | ||||||||
\(342\) | −113.455 | −6.13493 | ||||||||
\(343\) | 4.14751 | 0.223944 | ||||||||
\(344\) | 19.6595 | 1.05997 | ||||||||
\(345\) | −10.6356 | −0.572602 | ||||||||
\(346\) | 46.5849 | 2.50442 | ||||||||
\(347\) | −21.7437 | −1.16726 | −0.583631 | − | 0.812019i | \(-0.698369\pi\) | ||||
−0.583631 | + | 0.812019i | \(0.698369\pi\) | |||||||
\(348\) | 13.4863 | 0.722941 | ||||||||
\(349\) | −14.7938 | −0.791896 | −0.395948 | − | 0.918273i | \(-0.629584\pi\) | ||||
−0.395948 | + | 0.918273i | \(0.629584\pi\) | |||||||
\(350\) | 6.69250 | 0.357729 | ||||||||
\(351\) | 27.7059 | 1.47883 | ||||||||
\(352\) | 13.2563 | 0.706561 | ||||||||
\(353\) | 4.93410 | 0.262615 | 0.131308 | − | 0.991342i | \(-0.458082\pi\) | ||||
0.131308 | + | 0.991342i | \(0.458082\pi\) | |||||||
\(354\) | −40.6856 | −2.16242 | ||||||||
\(355\) | −52.2738 | −2.77441 | ||||||||
\(356\) | −31.8129 | −1.68608 | ||||||||
\(357\) | 4.26854 | 0.225915 | ||||||||
\(358\) | −40.6480 | −2.14832 | ||||||||
\(359\) | 15.7127 | 0.829282 | 0.414641 | − | 0.909985i | \(-0.363907\pi\) | ||||
0.414641 | + | 0.909985i | \(0.363907\pi\) | |||||||
\(360\) | 135.586 | 7.14603 | ||||||||
\(361\) | 50.2937 | 2.64704 | ||||||||
\(362\) | 49.4498 | 2.59902 | ||||||||
\(363\) | 24.4141 | 1.28141 | ||||||||
\(364\) | 5.93582 | 0.311121 | ||||||||
\(365\) | 18.8931 | 0.988908 | ||||||||
\(366\) | −56.5600 | −2.95644 | ||||||||
\(367\) | 7.48780 | 0.390860 | 0.195430 | − | 0.980718i | \(-0.437390\pi\) | ||||
0.195430 | + | 0.980718i | \(0.437390\pi\) | |||||||
\(368\) | −8.61451 | −0.449062 | ||||||||
\(369\) | 29.8521 | 1.55404 | ||||||||
\(370\) | 74.4070 | 3.86823 | ||||||||
\(371\) | 2.54196 | 0.131972 | ||||||||
\(372\) | 9.33968 | 0.484240 | ||||||||
\(373\) | 4.44612 | 0.230211 | 0.115106 | − | 0.993353i | \(-0.463279\pi\) | ||||
0.115106 | + | 0.993353i | \(0.463279\pi\) | |||||||
\(374\) | 20.4018 | 1.05495 | ||||||||
\(375\) | 39.1257 | 2.02044 | ||||||||
\(376\) | −6.54705 | −0.337638 | ||||||||
\(377\) | 4.24524 | 0.218641 | ||||||||
\(378\) | −5.03270 | −0.258854 | ||||||||
\(379\) | 2.88999 | 0.148449 | 0.0742243 | − | 0.997242i | \(-0.476352\pi\) | ||||
0.0742243 | + | 0.997242i | \(0.476352\pi\) | |||||||
\(380\) | −144.385 | −7.40681 | ||||||||
\(381\) | 1.33041 | 0.0681588 | ||||||||
\(382\) | −10.2817 | −0.526058 | ||||||||
\(383\) | −15.5570 | −0.794927 | −0.397463 | − | 0.917618i | \(-0.630109\pi\) | ||||
−0.397463 | + | 0.917618i | \(0.630109\pi\) | |||||||
\(384\) | −15.3059 | −0.781075 | ||||||||
\(385\) | −1.74702 | −0.0890361 | ||||||||
\(386\) | 51.8904 | 2.64115 | ||||||||
\(387\) | −14.8908 | −0.756944 | ||||||||
\(388\) | 42.7174 | 2.16865 | ||||||||
\(389\) | −27.6653 | −1.40269 | −0.701344 | − | 0.712823i | \(-0.747416\pi\) | ||||
−0.701344 | + | 0.712823i | \(0.747416\pi\) | |||||||
\(390\) | 116.781 | 5.91342 | ||||||||
\(391\) | −4.97869 | −0.251783 | ||||||||
\(392\) | 48.0808 | 2.42845 | ||||||||
\(393\) | −46.1256 | −2.32673 | ||||||||
\(394\) | −28.6398 | −1.44285 | ||||||||
\(395\) | 3.06385 | 0.154159 | ||||||||
\(396\) | −39.1535 | −1.96754 | ||||||||
\(397\) | 19.0031 | 0.953738 | 0.476869 | − | 0.878974i | \(-0.341772\pi\) | ||||
0.476869 | + | 0.878974i | \(0.341772\pi\) | |||||||
\(398\) | 48.3567 | 2.42390 | ||||||||
\(399\) | 7.13694 | 0.357294 | ||||||||
\(400\) | 74.7631 | 3.73816 | ||||||||
\(401\) | −16.3800 | −0.817977 | −0.408988 | − | 0.912540i | \(-0.634118\pi\) | ||||
−0.408988 | + | 0.912540i | \(0.634118\pi\) | |||||||
\(402\) | 62.9728 | 3.14080 | ||||||||
\(403\) | 2.93996 | 0.146450 | ||||||||
\(404\) | −79.3767 | −3.94914 | ||||||||
\(405\) | −10.9443 | −0.543826 | ||||||||
\(406\) | −0.771137 | −0.0382709 | ||||||||
\(407\) | −12.3235 | −0.610851 | ||||||||
\(408\) | 99.6043 | 4.93115 | ||||||||
\(409\) | 15.8224 | 0.782369 | 0.391184 | − | 0.920312i | \(-0.372065\pi\) | ||||
0.391184 | + | 0.920312i | \(0.372065\pi\) | |||||||
\(410\) | 54.1920 | 2.67635 | ||||||||
\(411\) | 11.0860 | 0.546832 | ||||||||
\(412\) | 1.60535 | 0.0790899 | ||||||||
\(413\) | 1.63087 | 0.0802500 | ||||||||
\(414\) | 13.6294 | 0.669847 | ||||||||
\(415\) | 65.9859 | 3.23912 | ||||||||
\(416\) | 35.5202 | 1.74152 | ||||||||
\(417\) | −23.2215 | −1.13716 | ||||||||
\(418\) | 34.1115 | 1.66845 | ||||||||
\(419\) | −28.0107 | −1.36841 | −0.684206 | − | 0.729289i | \(-0.739851\pi\) | ||||
−0.684206 | + | 0.729289i | \(0.739851\pi\) | |||||||
\(420\) | −14.8710 | −0.725632 | ||||||||
\(421\) | −4.24762 | −0.207017 | −0.103508 | − | 0.994629i | \(-0.533007\pi\) | ||||
−0.103508 | + | 0.994629i | \(0.533007\pi\) | |||||||
\(422\) | −10.9822 | −0.534607 | ||||||||
\(423\) | 4.95897 | 0.241113 | ||||||||
\(424\) | 59.3153 | 2.88061 | ||||||||
\(425\) | 43.2087 | 2.09593 | ||||||||
\(426\) | 105.125 | 5.09333 | ||||||||
\(427\) | 2.26719 | 0.109717 | ||||||||
\(428\) | 77.9221 | 3.76651 | ||||||||
\(429\) | −19.3415 | −0.933817 | ||||||||
\(430\) | −27.0320 | −1.30360 | ||||||||
\(431\) | −3.36941 | −0.162299 | −0.0811495 | − | 0.996702i | \(-0.525859\pi\) | ||||
−0.0811495 | + | 0.996702i | \(0.525859\pi\) | |||||||
\(432\) | −56.2212 | −2.70495 | ||||||||
\(433\) | 10.2719 | 0.493637 | 0.246818 | − | 0.969062i | \(-0.420615\pi\) | ||||
0.246818 | + | 0.969062i | \(0.420615\pi\) | |||||||
\(434\) | −0.534036 | −0.0256346 | ||||||||
\(435\) | −10.6356 | −0.509939 | ||||||||
\(436\) | −7.23386 | −0.346439 | ||||||||
\(437\) | −8.32429 | −0.398205 | ||||||||
\(438\) | −37.9949 | −1.81547 | ||||||||
\(439\) | 19.4763 | 0.929554 | 0.464777 | − | 0.885428i | \(-0.346135\pi\) | ||||
0.464777 | + | 0.885428i | \(0.346135\pi\) | |||||||
\(440\) | −40.7657 | −1.94343 | ||||||||
\(441\) | −36.4181 | −1.73420 | ||||||||
\(442\) | 54.6668 | 2.60023 | ||||||||
\(443\) | 0.131749 | 0.00625956 | 0.00312978 | − | 0.999995i | \(-0.499004\pi\) | ||||
0.00312978 | + | 0.999995i | \(0.499004\pi\) | |||||||
\(444\) | −104.900 | −4.97835 | ||||||||
\(445\) | 25.0884 | 1.18930 | ||||||||
\(446\) | −47.7130 | −2.25927 | ||||||||
\(447\) | −63.0913 | −2.98412 | ||||||||
\(448\) | −1.31542 | −0.0621478 | ||||||||
\(449\) | −27.9352 | −1.31835 | −0.659173 | − | 0.751992i | \(-0.729093\pi\) | ||||
−0.659173 | + | 0.751992i | \(0.729093\pi\) | |||||||
\(450\) | −118.286 | −5.57604 | ||||||||
\(451\) | −8.97541 | −0.422636 | ||||||||
\(452\) | 69.0643 | 3.24851 | ||||||||
\(453\) | −1.30061 | −0.0611082 | ||||||||
\(454\) | −51.9291 | −2.43715 | ||||||||
\(455\) | −4.68113 | −0.219455 | ||||||||
\(456\) | 166.537 | 7.79880 | ||||||||
\(457\) | −10.4880 | −0.490608 | −0.245304 | − | 0.969446i | \(-0.578888\pi\) | ||||
−0.245304 | + | 0.969446i | \(0.578888\pi\) | |||||||
\(458\) | 7.87122 | 0.367798 | ||||||||
\(459\) | −32.4926 | −1.51663 | ||||||||
\(460\) | 17.3451 | 0.808718 | ||||||||
\(461\) | 20.0869 | 0.935542 | 0.467771 | − | 0.883850i | \(-0.345057\pi\) | ||||
0.467771 | + | 0.883850i | \(0.345057\pi\) | |||||||
\(462\) | 3.51333 | 0.163455 | ||||||||
\(463\) | 8.02831 | 0.373107 | 0.186554 | − | 0.982445i | \(-0.440268\pi\) | ||||
0.186554 | + | 0.982445i | \(0.440268\pi\) | |||||||
\(464\) | −8.61451 | −0.399919 | ||||||||
\(465\) | −7.36550 | −0.341567 | ||||||||
\(466\) | −13.9457 | −0.646021 | ||||||||
\(467\) | 10.8557 | 0.502343 | 0.251171 | − | 0.967943i | \(-0.419184\pi\) | ||||
0.251171 | + | 0.967943i | \(0.419184\pi\) | |||||||
\(468\) | −104.912 | −4.84956 | ||||||||
\(469\) | −2.52425 | −0.116559 | ||||||||
\(470\) | 9.00225 | 0.415243 | ||||||||
\(471\) | 24.4448 | 1.12636 | ||||||||
\(472\) | 38.0556 | 1.75165 | ||||||||
\(473\) | 4.47711 | 0.205858 | ||||||||
\(474\) | −6.16155 | −0.283009 | ||||||||
\(475\) | 72.2443 | 3.31480 | ||||||||
\(476\) | −6.96134 | −0.319073 | ||||||||
\(477\) | −44.9275 | −2.05709 | ||||||||
\(478\) | 36.8672 | 1.68626 | ||||||||
\(479\) | 10.0793 | 0.460536 | 0.230268 | − | 0.973127i | \(-0.426040\pi\) | ||||
0.230268 | + | 0.973127i | \(0.426040\pi\) | |||||||
\(480\) | −88.9888 | −4.06176 | ||||||||
\(481\) | −33.0207 | −1.50562 | ||||||||
\(482\) | 20.3688 | 0.927772 | ||||||||
\(483\) | −0.857363 | −0.0390114 | ||||||||
\(484\) | −39.8156 | −1.80980 | ||||||||
\(485\) | −33.6880 | −1.52969 | ||||||||
\(486\) | −28.6309 | −1.29872 | ||||||||
\(487\) | −41.2202 | −1.86786 | −0.933932 | − | 0.357450i | \(-0.883646\pi\) | ||||
−0.933932 | + | 0.357450i | \(0.883646\pi\) | |||||||
\(488\) | 52.9038 | 2.39484 | ||||||||
\(489\) | 20.5385 | 0.928783 | ||||||||
\(490\) | −66.1115 | −2.98661 | ||||||||
\(491\) | −17.3868 | −0.784655 | −0.392328 | − | 0.919826i | \(-0.628330\pi\) | ||||
−0.392328 | + | 0.919826i | \(0.628330\pi\) | |||||||
\(492\) | −76.4009 | −3.44442 | ||||||||
\(493\) | −4.97869 | −0.224229 | ||||||||
\(494\) | 91.4020 | 4.11237 | ||||||||
\(495\) | 30.8774 | 1.38784 | ||||||||
\(496\) | −5.96582 | −0.267873 | ||||||||
\(497\) | −4.21392 | −0.189020 | ||||||||
\(498\) | −132.701 | −5.94647 | ||||||||
\(499\) | 11.0205 | 0.493346 | 0.246673 | − | 0.969099i | \(-0.420663\pi\) | ||||
0.246673 | + | 0.969099i | \(0.420663\pi\) | |||||||
\(500\) | −63.8080 | −2.85358 | ||||||||
\(501\) | 4.24250 | 0.189541 | ||||||||
\(502\) | 20.2131 | 0.902155 | ||||||||
\(503\) | −19.4469 | −0.867094 | −0.433547 | − | 0.901131i | \(-0.642738\pi\) | ||||
−0.433547 | + | 0.901131i | \(0.642738\pi\) | |||||||
\(504\) | 10.9300 | 0.486859 | ||||||||
\(505\) | 62.5984 | 2.78559 | ||||||||
\(506\) | −4.09783 | −0.182171 | ||||||||
\(507\) | −14.4419 | −0.641387 | ||||||||
\(508\) | −2.16969 | −0.0962644 | ||||||||
\(509\) | −23.9761 | −1.06272 | −0.531361 | − | 0.847145i | \(-0.678319\pi\) | ||||
−0.531361 | + | 0.847145i | \(0.678319\pi\) | |||||||
\(510\) | −136.957 | −6.06455 | ||||||||
\(511\) | 1.52302 | 0.0673743 | ||||||||
\(512\) | 47.7847 | 2.11180 | ||||||||
\(513\) | −54.3271 | −2.39860 | ||||||||
\(514\) | 77.4898 | 3.41793 | ||||||||
\(515\) | −1.26602 | −0.0557874 | ||||||||
\(516\) | 38.1103 | 1.67771 | ||||||||
\(517\) | −1.49098 | −0.0655730 | ||||||||
\(518\) | 5.99813 | 0.263543 | ||||||||
\(519\) | 51.7939 | 2.27350 | ||||||||
\(520\) | −109.232 | −4.79013 | ||||||||
\(521\) | −6.98559 | −0.306044 | −0.153022 | − | 0.988223i | \(-0.548901\pi\) | ||||
−0.153022 | + | 0.988223i | \(0.548901\pi\) | |||||||
\(522\) | 13.6294 | 0.596541 | ||||||||
\(523\) | 2.57278 | 0.112500 | 0.0562498 | − | 0.998417i | \(-0.482086\pi\) | ||||
0.0562498 | + | 0.998417i | \(0.482086\pi\) | |||||||
\(524\) | 75.2238 | 3.28617 | ||||||||
\(525\) | 7.44084 | 0.324745 | ||||||||
\(526\) | 35.9829 | 1.56893 | ||||||||
\(527\) | −3.44790 | −0.150193 | ||||||||
\(528\) | 39.2481 | 1.70805 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −81.5591 | −3.54270 | ||||||||
\(531\) | −28.8247 | −1.25088 | ||||||||
\(532\) | −11.6393 | −0.504626 | ||||||||
\(533\) | −24.0496 | −1.04171 | ||||||||
\(534\) | −50.4540 | −2.18336 | ||||||||
\(535\) | −61.4513 | −2.65677 | ||||||||
\(536\) | −58.9021 | −2.54418 | ||||||||
\(537\) | −45.1932 | −1.95023 | ||||||||
\(538\) | 64.3107 | 2.77263 | ||||||||
\(539\) | 10.9495 | 0.471630 | ||||||||
\(540\) | 113.200 | 4.87135 | ||||||||
\(541\) | −6.06745 | −0.260860 | −0.130430 | − | 0.991458i | \(-0.541636\pi\) | ||||
−0.130430 | + | 0.991458i | \(0.541636\pi\) | |||||||
\(542\) | 28.5889 | 1.22800 | ||||||||
\(543\) | 54.9791 | 2.35938 | ||||||||
\(544\) | −41.6569 | −1.78603 | ||||||||
\(545\) | 5.70480 | 0.244367 | ||||||||
\(546\) | 9.41399 | 0.402881 | ||||||||
\(547\) | −17.8606 | −0.763663 | −0.381831 | − | 0.924232i | \(-0.624707\pi\) | ||||
−0.381831 | + | 0.924232i | \(0.624707\pi\) | |||||||
\(548\) | −18.0796 | −0.772321 | ||||||||
\(549\) | −40.0713 | −1.71020 | ||||||||
\(550\) | 35.5640 | 1.51646 | ||||||||
\(551\) | −8.32429 | −0.354627 | ||||||||
\(552\) | −20.0061 | −0.851518 | ||||||||
\(553\) | 0.246984 | 0.0105028 | ||||||||
\(554\) | 60.4605 | 2.56872 | ||||||||
\(555\) | 82.7270 | 3.51156 | ||||||||
\(556\) | 37.8707 | 1.60607 | ||||||||
\(557\) | −24.5101 | −1.03853 | −0.519264 | − | 0.854614i | \(-0.673794\pi\) | ||||
−0.519264 | + | 0.854614i | \(0.673794\pi\) | |||||||
\(558\) | 9.43876 | 0.399575 | ||||||||
\(559\) | 11.9964 | 0.507395 | ||||||||
\(560\) | 9.49902 | 0.401407 | ||||||||
\(561\) | 22.6831 | 0.957682 | ||||||||
\(562\) | 27.6339 | 1.16567 | ||||||||
\(563\) | 19.6373 | 0.827614 | 0.413807 | − | 0.910365i | \(-0.364199\pi\) | ||||
0.413807 | + | 0.910365i | \(0.364199\pi\) | |||||||
\(564\) | −12.6915 | −0.534411 | ||||||||
\(565\) | −54.4658 | −2.29139 | ||||||||
\(566\) | 47.6028 | 2.00090 | ||||||||
\(567\) | −0.882246 | −0.0370509 | ||||||||
\(568\) | −98.3297 | −4.12582 | ||||||||
\(569\) | 12.2184 | 0.512220 | 0.256110 | − | 0.966648i | \(-0.417559\pi\) | ||||
0.256110 | + | 0.966648i | \(0.417559\pi\) | |||||||
\(570\) | −228.990 | −9.59132 | ||||||||
\(571\) | −14.8371 | −0.620912 | −0.310456 | − | 0.950588i | \(-0.600482\pi\) | ||||
−0.310456 | + | 0.950588i | \(0.600482\pi\) | |||||||
\(572\) | 31.5431 | 1.31888 | ||||||||
\(573\) | −11.4314 | −0.477553 | ||||||||
\(574\) | 4.36855 | 0.182340 | ||||||||
\(575\) | −8.67874 | −0.361929 | ||||||||
\(576\) | 23.2492 | 0.968718 | ||||||||
\(577\) | 3.27511 | 0.136345 | 0.0681724 | − | 0.997674i | \(-0.478283\pi\) | ||||
0.0681724 | + | 0.997674i | \(0.478283\pi\) | |||||||
\(578\) | −20.1416 | −0.837780 | ||||||||
\(579\) | 57.6927 | 2.39763 | ||||||||
\(580\) | 17.3451 | 0.720215 | ||||||||
\(581\) | 5.31928 | 0.220681 | ||||||||
\(582\) | 67.7481 | 2.80825 | ||||||||
\(583\) | 13.5080 | 0.559445 | ||||||||
\(584\) | 35.5388 | 1.47061 | ||||||||
\(585\) | 82.7361 | 3.42072 | ||||||||
\(586\) | 13.0020 | 0.537107 | ||||||||
\(587\) | −3.32253 | −0.137135 | −0.0685677 | − | 0.997646i | \(-0.521843\pi\) | ||||
−0.0685677 | + | 0.997646i | \(0.521843\pi\) | |||||||
\(588\) | 93.2052 | 3.84372 | ||||||||
\(589\) | −5.76483 | −0.237536 | ||||||||
\(590\) | −52.3268 | −2.15426 | ||||||||
\(591\) | −31.8422 | −1.30981 | ||||||||
\(592\) | 67.0062 | 2.75394 | ||||||||
\(593\) | 5.26774 | 0.216320 | 0.108160 | − | 0.994133i | \(-0.465504\pi\) | ||||
0.108160 | + | 0.994133i | \(0.465504\pi\) | |||||||
\(594\) | −26.7439 | −1.09731 | ||||||||
\(595\) | 5.48988 | 0.225063 | ||||||||
\(596\) | 102.892 | 4.21463 | ||||||||
\(597\) | 53.7639 | 2.20041 | ||||||||
\(598\) | −10.9802 | −0.449012 | ||||||||
\(599\) | −27.8838 | −1.13930 | −0.569651 | − | 0.821887i | \(-0.692922\pi\) | ||||
−0.569651 | + | 0.821887i | \(0.692922\pi\) | |||||||
\(600\) | 173.628 | 7.08834 | ||||||||
\(601\) | −41.4467 | −1.69064 | −0.845322 | − | 0.534256i | \(-0.820592\pi\) | ||||
−0.845322 | + | 0.534256i | \(0.820592\pi\) | |||||||
\(602\) | −2.17912 | −0.0888143 | ||||||||
\(603\) | 44.6146 | 1.81685 | ||||||||
\(604\) | 2.12110 | 0.0863064 | ||||||||
\(605\) | 31.3996 | 1.27657 | ||||||||
\(606\) | −125.888 | −5.11387 | ||||||||
\(607\) | −9.60082 | −0.389685 | −0.194843 | − | 0.980835i | \(-0.562420\pi\) | ||||
−0.194843 | + | 0.980835i | \(0.562420\pi\) | |||||||
\(608\) | −69.6497 | −2.82467 | ||||||||
\(609\) | −0.857363 | −0.0347421 | ||||||||
\(610\) | −72.7433 | −2.94529 | ||||||||
\(611\) | −3.99507 | −0.161623 | ||||||||
\(612\) | 123.037 | 4.97349 | ||||||||
\(613\) | −9.71648 | −0.392445 | −0.196222 | − | 0.980559i | \(-0.562867\pi\) | ||||
−0.196222 | + | 0.980559i | \(0.562867\pi\) | |||||||
\(614\) | 40.5934 | 1.63822 | ||||||||
\(615\) | 60.2516 | 2.42958 | ||||||||
\(616\) | −3.28622 | −0.132406 | ||||||||
\(617\) | 15.4612 | 0.622446 | 0.311223 | − | 0.950337i | \(-0.399261\pi\) | ||||
0.311223 | + | 0.950337i | \(0.399261\pi\) | |||||||
\(618\) | 2.54602 | 0.102416 | ||||||||
\(619\) | −32.2470 | −1.29612 | −0.648058 | − | 0.761591i | \(-0.724419\pi\) | ||||
−0.648058 | + | 0.761591i | \(0.724419\pi\) | |||||||
\(620\) | 12.0120 | 0.482414 | ||||||||
\(621\) | 6.52634 | 0.261893 | ||||||||
\(622\) | −50.2870 | −2.01632 | ||||||||
\(623\) | 2.02244 | 0.0810273 | ||||||||
\(624\) | 105.165 | 4.20998 | ||||||||
\(625\) | 6.92685 | 0.277074 | ||||||||
\(626\) | −52.7023 | −2.10641 | ||||||||
\(627\) | 37.9258 | 1.51461 | ||||||||
\(628\) | −39.8657 | −1.59081 | ||||||||
\(629\) | 38.7257 | 1.54409 | ||||||||
\(630\) | −15.0288 | −0.598761 | ||||||||
\(631\) | −0.388206 | −0.0154543 | −0.00772713 | − | 0.999970i | \(-0.502460\pi\) | ||||
−0.00772713 | + | 0.999970i | \(0.502460\pi\) | |||||||
\(632\) | 5.76325 | 0.229250 | ||||||||
\(633\) | −12.2102 | −0.485314 | ||||||||
\(634\) | −61.1110 | −2.42703 | ||||||||
\(635\) | 1.71107 | 0.0679017 | ||||||||
\(636\) | 114.984 | 4.55939 | ||||||||
\(637\) | 29.3393 | 1.16247 | ||||||||
\(638\) | −4.09783 | −0.162235 | ||||||||
\(639\) | 74.4784 | 2.94632 | ||||||||
\(640\) | −19.6853 | −0.778129 | ||||||||
\(641\) | −10.1116 | −0.399382 | −0.199691 | − | 0.979859i | \(-0.563994\pi\) | ||||
−0.199691 | + | 0.979859i | \(0.563994\pi\) | |||||||
\(642\) | 123.582 | 4.87737 | ||||||||
\(643\) | −2.00502 | −0.0790702 | −0.0395351 | − | 0.999218i | \(-0.512588\pi\) | ||||
−0.0395351 | + | 0.999218i | \(0.512588\pi\) | |||||||
\(644\) | 1.39823 | 0.0550979 | ||||||||
\(645\) | −30.0547 | −1.18340 | ||||||||
\(646\) | −107.193 | −4.21747 | ||||||||
\(647\) | −6.03637 | −0.237314 | −0.118657 | − | 0.992935i | \(-0.537859\pi\) | ||||
−0.118657 | + | 0.992935i | \(0.537859\pi\) | |||||||
\(648\) | −20.5868 | −0.808724 | ||||||||
\(649\) | 8.66649 | 0.340190 | ||||||||
\(650\) | 95.2940 | 3.73774 | ||||||||
\(651\) | −0.593751 | −0.0232709 | ||||||||
\(652\) | −33.4952 | −1.31177 | ||||||||
\(653\) | 29.0646 | 1.13739 | 0.568693 | − | 0.822550i | \(-0.307449\pi\) | ||||
0.568693 | + | 0.822550i | \(0.307449\pi\) | |||||||
\(654\) | −11.4726 | −0.448615 | ||||||||
\(655\) | −59.3233 | −2.31795 | ||||||||
\(656\) | 48.8019 | 1.90539 | ||||||||
\(657\) | −26.9184 | −1.05019 | ||||||||
\(658\) | 0.725694 | 0.0282905 | ||||||||
\(659\) | 3.50863 | 0.136677 | 0.0683383 | − | 0.997662i | \(-0.478230\pi\) | ||||
0.0683383 | + | 0.997662i | \(0.478230\pi\) | |||||||
\(660\) | −79.0249 | −3.07604 | ||||||||
\(661\) | −24.1713 | −0.940154 | −0.470077 | − | 0.882625i | \(-0.655774\pi\) | ||||
−0.470077 | + | 0.882625i | \(0.655774\pi\) | |||||||
\(662\) | −33.8166 | −1.31432 | ||||||||
\(663\) | 60.7795 | 2.36048 | ||||||||
\(664\) | 124.123 | 4.81690 | ||||||||
\(665\) | 9.17900 | 0.355946 | ||||||||
\(666\) | −106.013 | −4.10793 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | −6.91887 | −0.267699 | ||||||||
\(669\) | −53.0481 | −2.05096 | ||||||||
\(670\) | 80.9910 | 3.12895 | ||||||||
\(671\) | 12.0479 | 0.465105 | ||||||||
\(672\) | −7.17360 | −0.276728 | ||||||||
\(673\) | −21.8007 | −0.840356 | −0.420178 | − | 0.907442i | \(-0.638032\pi\) | ||||
−0.420178 | + | 0.907442i | \(0.638032\pi\) | |||||||
\(674\) | −38.1506 | −1.46951 | ||||||||
\(675\) | −56.6404 | −2.18009 | ||||||||
\(676\) | 23.5525 | 0.905865 | ||||||||
\(677\) | −25.6377 | −0.985338 | −0.492669 | − | 0.870217i | \(-0.663979\pi\) | ||||
−0.492669 | + | 0.870217i | \(0.663979\pi\) | |||||||
\(678\) | 109.533 | 4.20660 | ||||||||
\(679\) | −2.71567 | −0.104218 | ||||||||
\(680\) | 128.104 | 4.91255 | ||||||||
\(681\) | −57.7357 | −2.21244 | ||||||||
\(682\) | −2.83788 | −0.108668 | ||||||||
\(683\) | 22.5840 | 0.864153 | 0.432077 | − | 0.901837i | \(-0.357781\pi\) | ||||
0.432077 | + | 0.901837i | \(0.357781\pi\) | |||||||
\(684\) | 205.717 | 7.86577 | ||||||||
\(685\) | 14.2580 | 0.544769 | ||||||||
\(686\) | −10.7274 | −0.409573 | ||||||||
\(687\) | 8.75136 | 0.333885 | ||||||||
\(688\) | −24.3434 | −0.928082 | ||||||||
\(689\) | 36.1948 | 1.37891 | ||||||||
\(690\) | 27.5086 | 1.04724 | ||||||||
\(691\) | 18.2063 | 0.692601 | 0.346301 | − | 0.938124i | \(-0.387438\pi\) | ||||
0.346301 | + | 0.938124i | \(0.387438\pi\) | |||||||
\(692\) | −84.4680 | −3.21099 | ||||||||
\(693\) | 2.48910 | 0.0945532 | ||||||||
\(694\) | 56.2392 | 2.13481 | ||||||||
\(695\) | −29.8657 | −1.13287 | ||||||||
\(696\) | −20.0061 | −0.758331 | ||||||||
\(697\) | 28.2046 | 1.06833 | ||||||||
\(698\) | 38.2637 | 1.44830 | ||||||||
\(699\) | −15.5051 | −0.586455 | ||||||||
\(700\) | −12.1349 | −0.458655 | ||||||||
\(701\) | −26.0625 | −0.984367 | −0.492183 | − | 0.870492i | \(-0.663801\pi\) | ||||
−0.492183 | + | 0.870492i | \(0.663801\pi\) | |||||||
\(702\) | −71.6603 | −2.70464 | ||||||||
\(703\) | 64.7487 | 2.44205 | ||||||||
\(704\) | −6.99017 | −0.263452 | ||||||||
\(705\) | 10.0089 | 0.376956 | ||||||||
\(706\) | −12.7618 | −0.480299 | ||||||||
\(707\) | 5.04621 | 0.189782 | ||||||||
\(708\) | 73.7713 | 2.77250 | ||||||||
\(709\) | −8.21955 | −0.308692 | −0.154346 | − | 0.988017i | \(-0.549327\pi\) | ||||
−0.154346 | + | 0.988017i | \(0.549327\pi\) | |||||||
\(710\) | 135.204 | 5.07412 | ||||||||
\(711\) | −4.36529 | −0.163711 | ||||||||
\(712\) | 47.1926 | 1.76862 | ||||||||
\(713\) | 0.692531 | 0.0259355 | ||||||||
\(714\) | −11.0404 | −0.413177 | ||||||||
\(715\) | −24.8756 | −0.930296 | ||||||||
\(716\) | 73.7032 | 2.75442 | ||||||||
\(717\) | 40.9896 | 1.53078 | ||||||||
\(718\) | −40.6402 | −1.51668 | ||||||||
\(719\) | 22.3796 | 0.834620 | 0.417310 | − | 0.908764i | \(-0.362973\pi\) | ||||
0.417310 | + | 0.908764i | \(0.362973\pi\) | |||||||
\(720\) | −167.889 | −6.25687 | ||||||||
\(721\) | −0.102057 | −0.00380080 | ||||||||
\(722\) | −130.083 | −4.84118 | ||||||||
\(723\) | 22.6464 | 0.842227 | ||||||||
\(724\) | −89.6626 | −3.33228 | ||||||||
\(725\) | −8.67874 | −0.322320 | ||||||||
\(726\) | −63.1461 | −2.34357 | ||||||||
\(727\) | −22.5875 | −0.837724 | −0.418862 | − | 0.908050i | \(-0.637571\pi\) | ||||
−0.418862 | + | 0.908050i | \(0.637571\pi\) | |||||||
\(728\) | −8.80545 | −0.326352 | ||||||||
\(729\) | −40.7098 | −1.50777 | ||||||||
\(730\) | −48.8662 | −1.80862 | ||||||||
\(731\) | −14.0690 | −0.520362 | ||||||||
\(732\) | 102.555 | 3.79054 | ||||||||
\(733\) | −18.1058 | −0.668752 | −0.334376 | − | 0.942440i | \(-0.608526\pi\) | ||||
−0.334376 | + | 0.942440i | \(0.608526\pi\) | |||||||
\(734\) | −19.3669 | −0.714845 | ||||||||
\(735\) | −73.5039 | −2.71123 | ||||||||
\(736\) | 8.36705 | 0.308414 | ||||||||
\(737\) | −13.4139 | −0.494108 | ||||||||
\(738\) | −77.2114 | −2.84219 | ||||||||
\(739\) | 35.0206 | 1.28825 | 0.644126 | − | 0.764919i | \(-0.277221\pi\) | ||||
0.644126 | + | 0.764919i | \(0.277221\pi\) | |||||||
\(740\) | −134.915 | −4.95958 | ||||||||
\(741\) | 101.622 | 3.73319 | ||||||||
\(742\) | −6.57468 | −0.241364 | ||||||||
\(743\) | −49.7154 | −1.82388 | −0.911940 | − | 0.410324i | \(-0.865416\pi\) | ||||
−0.911940 | + | 0.410324i | \(0.865416\pi\) | |||||||
\(744\) | −13.8549 | −0.507944 | ||||||||
\(745\) | −81.1433 | −2.97286 | ||||||||
\(746\) | −11.4997 | −0.421035 | ||||||||
\(747\) | −94.0150 | −3.43983 | ||||||||
\(748\) | −36.9927 | −1.35259 | ||||||||
\(749\) | −4.95374 | −0.181006 | ||||||||
\(750\) | −101.197 | −3.69520 | ||||||||
\(751\) | −15.7405 | −0.574378 | −0.287189 | − | 0.957874i | \(-0.592721\pi\) | ||||
−0.287189 | + | 0.957874i | \(0.592721\pi\) | |||||||
\(752\) | 8.10686 | 0.295627 | ||||||||
\(753\) | 22.4733 | 0.818972 | ||||||||
\(754\) | −10.9802 | −0.399874 | ||||||||
\(755\) | −1.67275 | −0.0608777 | ||||||||
\(756\) | 9.12532 | 0.331885 | ||||||||
\(757\) | 1.52963 | 0.0555952 | 0.0277976 | − | 0.999614i | \(-0.491151\pi\) | ||||
0.0277976 | + | 0.999614i | \(0.491151\pi\) | |||||||
\(758\) | −7.47484 | −0.271498 | ||||||||
\(759\) | −4.55604 | −0.165374 | ||||||||
\(760\) | 214.187 | 7.76939 | ||||||||
\(761\) | −5.19360 | −0.188268 | −0.0941339 | − | 0.995560i | \(-0.530008\pi\) | ||||
−0.0941339 | + | 0.995560i | \(0.530008\pi\) | |||||||
\(762\) | −3.44104 | −0.124656 | ||||||||
\(763\) | 0.459878 | 0.0166487 | ||||||||
\(764\) | 18.6429 | 0.674475 | ||||||||
\(765\) | −97.0303 | −3.50814 | ||||||||
\(766\) | 40.2376 | 1.45385 | ||||||||
\(767\) | 23.2219 | 0.838494 | ||||||||
\(768\) | 64.9632 | 2.34416 | ||||||||
\(769\) | 0.710853 | 0.0256340 | 0.0128170 | − | 0.999918i | \(-0.495920\pi\) | ||||
0.0128170 | + | 0.999918i | \(0.495920\pi\) | |||||||
\(770\) | 4.51859 | 0.162839 | ||||||||
\(771\) | 86.1545 | 3.10278 | ||||||||
\(772\) | −94.0880 | −3.38630 | ||||||||
\(773\) | −11.8426 | −0.425950 | −0.212975 | − | 0.977058i | \(-0.568315\pi\) | ||||
−0.212975 | + | 0.977058i | \(0.568315\pi\) | |||||||
\(774\) | 38.5146 | 1.38438 | ||||||||
\(775\) | −6.01030 | −0.215896 | ||||||||
\(776\) | −63.3688 | −2.27481 | ||||||||
\(777\) | 6.66882 | 0.239243 | ||||||||
\(778\) | 71.5553 | 2.56538 | ||||||||
\(779\) | 47.1577 | 1.68960 | ||||||||
\(780\) | −211.747 | −7.58177 | ||||||||
\(781\) | −22.3929 | −0.801279 | ||||||||
\(782\) | 12.8772 | 0.460487 | ||||||||
\(783\) | 6.52634 | 0.233232 | ||||||||
\(784\) | −59.5358 | −2.12628 | ||||||||
\(785\) | 31.4391 | 1.12211 | ||||||||
\(786\) | 119.302 | 4.25536 | ||||||||
\(787\) | 18.9698 | 0.676199 | 0.338100 | − | 0.941110i | \(-0.390216\pi\) | ||||
0.338100 | + | 0.941110i | \(0.390216\pi\) | |||||||
\(788\) | 51.9298 | 1.84992 | ||||||||
\(789\) | 40.0065 | 1.42427 | ||||||||
\(790\) | −7.92452 | −0.281942 | ||||||||
\(791\) | −4.39062 | −0.156112 | ||||||||
\(792\) | 58.0820 | 2.06385 | ||||||||
\(793\) | 32.2824 | 1.14638 | ||||||||
\(794\) | −49.1508 | −1.74430 | ||||||||
\(795\) | −90.6788 | −3.21605 | ||||||||
\(796\) | −87.6806 | −3.10776 | ||||||||
\(797\) | −15.6956 | −0.555967 | −0.277984 | − | 0.960586i | \(-0.589666\pi\) | ||||
−0.277984 | + | 0.960586i | \(0.589666\pi\) | |||||||
\(798\) | −18.4594 | −0.653456 | ||||||||
\(799\) | 4.68529 | 0.165754 | ||||||||
\(800\) | −72.6155 | −2.56734 | ||||||||
\(801\) | −35.7454 | −1.26300 | ||||||||
\(802\) | 42.3662 | 1.49600 | ||||||||
\(803\) | 8.09334 | 0.285608 | ||||||||
\(804\) | −114.183 | −4.02691 | ||||||||
\(805\) | −1.10268 | −0.0388643 | ||||||||
\(806\) | −7.60410 | −0.267843 | ||||||||
\(807\) | 71.5018 | 2.51698 | ||||||||
\(808\) | 117.751 | 4.14246 | ||||||||
\(809\) | −1.92393 | −0.0676419 | −0.0338209 | − | 0.999428i | \(-0.510768\pi\) | ||||
−0.0338209 | + | 0.999428i | \(0.510768\pi\) | |||||||
\(810\) | 28.3070 | 0.994606 | ||||||||
\(811\) | −33.0097 | −1.15913 | −0.579563 | − | 0.814927i | \(-0.696777\pi\) | ||||
−0.579563 | + | 0.814927i | \(0.696777\pi\) | |||||||
\(812\) | 1.39823 | 0.0490682 | ||||||||
\(813\) | 31.7856 | 1.11477 | ||||||||
\(814\) | 31.8742 | 1.11719 | ||||||||
\(815\) | 26.4151 | 0.925281 | ||||||||
\(816\) | −123.335 | −4.31757 | ||||||||
\(817\) | −23.5232 | −0.822973 | ||||||||
\(818\) | −40.9241 | −1.43088 | ||||||||
\(819\) | 6.66956 | 0.233053 | ||||||||
\(820\) | −98.2612 | −3.43143 | ||||||||
\(821\) | 10.3352 | 0.360700 | 0.180350 | − | 0.983602i | \(-0.442277\pi\) | ||||
0.180350 | + | 0.983602i | \(0.442277\pi\) | |||||||
\(822\) | −28.6735 | −1.00010 | ||||||||
\(823\) | 7.36395 | 0.256691 | 0.128346 | − | 0.991730i | \(-0.459033\pi\) | ||||
0.128346 | + | 0.991730i | \(0.459033\pi\) | |||||||
\(824\) | −2.38144 | −0.0829615 | ||||||||
\(825\) | 39.5407 | 1.37663 | ||||||||
\(826\) | −4.21819 | −0.146770 | ||||||||
\(827\) | −28.2030 | −0.980713 | −0.490357 | − | 0.871522i | \(-0.663133\pi\) | ||||
−0.490357 | + | 0.871522i | \(0.663133\pi\) | |||||||
\(828\) | −24.7128 | −0.858830 | ||||||||
\(829\) | 47.8749 | 1.66277 | 0.831383 | − | 0.555700i | \(-0.187550\pi\) | ||||
0.831383 | + | 0.555700i | \(0.187550\pi\) | |||||||
\(830\) | −170.670 | −5.92404 | ||||||||
\(831\) | 67.2211 | 2.33187 | ||||||||
\(832\) | −18.7302 | −0.649352 | ||||||||
\(833\) | −34.4082 | −1.19218 | ||||||||
\(834\) | 60.0614 | 2.07976 | ||||||||
\(835\) | 5.45639 | 0.188826 | ||||||||
\(836\) | −61.8512 | −2.13917 | ||||||||
\(837\) | 4.51970 | 0.156224 | ||||||||
\(838\) | 72.4486 | 2.50270 | ||||||||
\(839\) | −21.2537 | −0.733760 | −0.366880 | − | 0.930268i | \(-0.619574\pi\) | ||||
−0.366880 | + | 0.930268i | \(0.619574\pi\) | |||||||
\(840\) | 22.0603 | 0.761153 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 10.9863 | 0.378613 | ||||||||
\(843\) | 30.7239 | 1.05819 | ||||||||
\(844\) | 19.9130 | 0.685435 | ||||||||
\(845\) | −18.5741 | −0.638968 | ||||||||
\(846\) | −12.8262 | −0.440973 | ||||||||
\(847\) | 2.53120 | 0.0869730 | ||||||||
\(848\) | −73.4469 | −2.52218 | ||||||||
\(849\) | 52.9257 | 1.81640 | ||||||||
\(850\) | −111.758 | −3.83326 | ||||||||
\(851\) | −7.77829 | −0.266636 | ||||||||
\(852\) | −190.613 | −6.53031 | ||||||||
\(853\) | 37.7663 | 1.29309 | 0.646547 | − | 0.762874i | \(-0.276212\pi\) | ||||
0.646547 | + | 0.762874i | \(0.276212\pi\) | |||||||
\(854\) | −5.86401 | −0.200662 | ||||||||
\(855\) | −162.233 | −5.54826 | ||||||||
\(856\) | −115.593 | −3.95089 | ||||||||
\(857\) | 21.6219 | 0.738591 | 0.369296 | − | 0.929312i | \(-0.379599\pi\) | ||||
0.369296 | + | 0.929312i | \(0.379599\pi\) | |||||||
\(858\) | 50.0261 | 1.70786 | ||||||||
\(859\) | −28.5224 | −0.973171 | −0.486586 | − | 0.873633i | \(-0.661758\pi\) | ||||
−0.486586 | + | 0.873633i | \(0.661758\pi\) | |||||||
\(860\) | 49.0146 | 1.67139 | ||||||||
\(861\) | 4.85703 | 0.165527 | ||||||||
\(862\) | 8.71486 | 0.296829 | ||||||||
\(863\) | −6.71401 | −0.228548 | −0.114274 | − | 0.993449i | \(-0.536454\pi\) | ||||
−0.114274 | + | 0.993449i | \(0.536454\pi\) | |||||||
\(864\) | 54.6062 | 1.85774 | ||||||||
\(865\) | 66.6135 | 2.26493 | ||||||||
\(866\) | −26.5679 | −0.902815 | ||||||||
\(867\) | −22.3938 | −0.760532 | ||||||||
\(868\) | 0.968317 | 0.0328668 | ||||||||
\(869\) | 1.31248 | 0.0445228 | ||||||||
\(870\) | 27.5086 | 0.932630 | ||||||||
\(871\) | −35.9426 | −1.21787 | ||||||||
\(872\) | 10.7310 | 0.363398 | ||||||||
\(873\) | 47.9978 | 1.62448 | ||||||||
\(874\) | 21.5304 | 0.728278 | ||||||||
\(875\) | 4.05646 | 0.137134 | ||||||||
\(876\) | 68.8925 | 2.32766 | ||||||||
\(877\) | 29.1648 | 0.984826 | 0.492413 | − | 0.870362i | \(-0.336115\pi\) | ||||
0.492413 | + | 0.870362i | \(0.336115\pi\) | |||||||
\(878\) | −50.3748 | −1.70007 | ||||||||
\(879\) | 14.4558 | 0.487583 | ||||||||
\(880\) | 50.4780 | 1.70161 | ||||||||
\(881\) | −39.6009 | −1.33419 | −0.667095 | − | 0.744973i | \(-0.732462\pi\) | ||||
−0.667095 | + | 0.744973i | \(0.732462\pi\) | |||||||
\(882\) | 94.1940 | 3.17168 | ||||||||
\(883\) | −51.2378 | −1.72429 | −0.862145 | − | 0.506662i | \(-0.830879\pi\) | ||||
−0.862145 | + | 0.506662i | \(0.830879\pi\) | |||||||
\(884\) | −99.1220 | −3.33383 | ||||||||
\(885\) | −58.1779 | −1.95563 | ||||||||
\(886\) | −0.340763 | −0.0114481 | ||||||||
\(887\) | −28.2673 | −0.949123 | −0.474561 | − | 0.880222i | \(-0.657393\pi\) | ||||
−0.474561 | + | 0.880222i | \(0.657393\pi\) | |||||||
\(888\) | 155.614 | 5.22205 | ||||||||
\(889\) | 0.137934 | 0.00462614 | ||||||||
\(890\) | −64.8902 | −2.17513 | ||||||||
\(891\) | −4.68827 | −0.157063 | ||||||||
\(892\) | 86.5134 | 2.89668 | ||||||||
\(893\) | 7.83374 | 0.262146 | ||||||||
\(894\) | 163.183 | 5.45766 | ||||||||
\(895\) | −58.1241 | −1.94288 | ||||||||
\(896\) | −1.58688 | −0.0530139 | ||||||||
\(897\) | −12.2079 | −0.407611 | ||||||||
\(898\) | 72.2534 | 2.41113 | ||||||||
\(899\) | 0.692531 | 0.0230972 | ||||||||
\(900\) | 214.476 | 7.14921 | ||||||||
\(901\) | −42.4481 | −1.41415 | ||||||||
\(902\) | 23.2146 | 0.772960 | ||||||||
\(903\) | −2.42278 | −0.0806252 | ||||||||
\(904\) | −102.453 | −3.40753 | ||||||||
\(905\) | 70.7101 | 2.35048 | ||||||||
\(906\) | 3.36399 | 0.111761 | ||||||||
\(907\) | −14.9606 | −0.496759 | −0.248380 | − | 0.968663i | \(-0.579898\pi\) | ||||
−0.248380 | + | 0.968663i | \(0.579898\pi\) | |||||||
\(908\) | 94.1580 | 3.12474 | ||||||||
\(909\) | −89.1887 | −2.95820 | ||||||||
\(910\) | 12.1076 | 0.401362 | ||||||||
\(911\) | 46.5789 | 1.54323 | 0.771614 | − | 0.636091i | \(-0.219450\pi\) | ||||
0.771614 | + | 0.636091i | \(0.219450\pi\) | |||||||
\(912\) | −206.214 | −6.82841 | ||||||||
\(913\) | 28.2668 | 0.935494 | ||||||||
\(914\) | 27.1268 | 0.897274 | ||||||||
\(915\) | −80.8772 | −2.67372 | ||||||||
\(916\) | −14.2721 | −0.471564 | ||||||||
\(917\) | −4.78220 | −0.157922 | ||||||||
\(918\) | 84.0409 | 2.77376 | ||||||||
\(919\) | −13.2992 | −0.438701 | −0.219351 | − | 0.975646i | \(-0.570394\pi\) | ||||
−0.219351 | + | 0.975646i | \(0.570394\pi\) | |||||||
\(920\) | −25.7304 | −0.848306 | ||||||||
\(921\) | 45.1324 | 1.48716 | ||||||||
\(922\) | −51.9541 | −1.71102 | ||||||||
\(923\) | −60.0017 | −1.97498 | ||||||||
\(924\) | −6.37039 | −0.209571 | ||||||||
\(925\) | 67.5058 | 2.21958 | ||||||||
\(926\) | −20.7649 | −0.682378 | ||||||||
\(927\) | 1.80379 | 0.0592443 | ||||||||
\(928\) | 8.36705 | 0.274662 | ||||||||
\(929\) | −53.8440 | −1.76657 | −0.883283 | − | 0.468840i | \(-0.844672\pi\) | ||||
−0.883283 | + | 0.468840i | \(0.844672\pi\) | |||||||
\(930\) | 19.0506 | 0.624693 | ||||||||
\(931\) | −57.5301 | −1.88547 | ||||||||
\(932\) | 25.2864 | 0.828283 | ||||||||
\(933\) | −55.9100 | −1.83041 | ||||||||
\(934\) | −28.0779 | −0.918737 | ||||||||
\(935\) | 29.1733 | 0.954070 | ||||||||
\(936\) | 155.631 | 5.08695 | ||||||||
\(937\) | −52.1527 | −1.70375 | −0.851877 | − | 0.523742i | \(-0.824536\pi\) | ||||
−0.851877 | + | 0.523742i | \(0.824536\pi\) | |||||||
\(938\) | 6.52888 | 0.213176 | ||||||||
\(939\) | −58.5953 | −1.91219 | ||||||||
\(940\) | −16.3229 | −0.532395 | ||||||||
\(941\) | 52.5915 | 1.71443 | 0.857217 | − | 0.514956i | \(-0.172192\pi\) | ||||
0.857217 | + | 0.514956i | \(0.172192\pi\) | |||||||
\(942\) | −63.2255 | −2.06000 | ||||||||
\(943\) | −5.66508 | −0.184480 | ||||||||
\(944\) | −47.1222 | −1.53370 | ||||||||
\(945\) | −7.19645 | −0.234101 | ||||||||
\(946\) | −11.5799 | −0.376494 | ||||||||
\(947\) | 43.6115 | 1.41718 | 0.708592 | − | 0.705618i | \(-0.249331\pi\) | ||||
0.708592 | + | 0.705618i | \(0.249331\pi\) | |||||||
\(948\) | 11.1721 | 0.362854 | ||||||||
\(949\) | 21.6861 | 0.703961 | ||||||||
\(950\) | −186.857 | −6.06245 | ||||||||
\(951\) | −67.9443 | −2.20324 | ||||||||
\(952\) | 10.3267 | 0.334692 | ||||||||
\(953\) | 29.9990 | 0.971763 | 0.485882 | − | 0.874025i | \(-0.338499\pi\) | ||||
0.485882 | + | 0.874025i | \(0.338499\pi\) | |||||||
\(954\) | 116.203 | 3.76222 | ||||||||
\(955\) | −14.7022 | −0.475752 | ||||||||
\(956\) | −66.8477 | −2.16201 | ||||||||
\(957\) | −4.55604 | −0.147276 | ||||||||
\(958\) | −26.0698 | −0.842276 | ||||||||
\(959\) | 1.14937 | 0.0371151 | ||||||||
\(960\) | 46.9247 | 1.51449 | ||||||||
\(961\) | −30.5204 | −0.984529 | ||||||||
\(962\) | 85.4069 | 2.75363 | ||||||||
\(963\) | 87.5543 | 2.82140 | ||||||||
\(964\) | −36.9328 | −1.18952 | ||||||||
\(965\) | 74.2001 | 2.38858 | ||||||||
\(966\) | 2.21754 | 0.0713481 | ||||||||
\(967\) | 13.5790 | 0.436670 | 0.218335 | − | 0.975874i | \(-0.429937\pi\) | ||||
0.218335 | + | 0.975874i | \(0.429937\pi\) | |||||||
\(968\) | 59.0642 | 1.89840 | ||||||||
\(969\) | −119.179 | −3.82860 | ||||||||
\(970\) | 87.1326 | 2.79766 | ||||||||
\(971\) | 31.8369 | 1.02169 | 0.510847 | − | 0.859672i | \(-0.329332\pi\) | ||||
0.510847 | + | 0.859672i | \(0.329332\pi\) | |||||||
\(972\) | 51.9137 | 1.66513 | ||||||||
\(973\) | −2.40755 | −0.0771825 | ||||||||
\(974\) | 106.614 | 3.41615 | ||||||||
\(975\) | 105.950 | 3.39310 | ||||||||
\(976\) | −65.5080 | −2.09686 | ||||||||
\(977\) | −25.6319 | −0.820038 | −0.410019 | − | 0.912077i | \(-0.634478\pi\) | ||||
−0.410019 | + | 0.912077i | \(0.634478\pi\) | |||||||
\(978\) | −53.1221 | −1.69866 | ||||||||
\(979\) | 10.7473 | 0.343485 | ||||||||
\(980\) | 119.874 | 3.82922 | ||||||||
\(981\) | −8.12805 | −0.259509 | ||||||||
\(982\) | 44.9703 | 1.43506 | ||||||||
\(983\) | −32.7361 | −1.04412 | −0.522060 | − | 0.852909i | \(-0.674836\pi\) | ||||
−0.522060 | + | 0.852909i | \(0.674836\pi\) | |||||||
\(984\) | 113.336 | 3.61303 | ||||||||
\(985\) | −40.9531 | −1.30487 | ||||||||
\(986\) | 12.8772 | 0.410093 | ||||||||
\(987\) | 0.806839 | 0.0256820 | ||||||||
\(988\) | −165.730 | −5.27259 | ||||||||
\(989\) | 2.82585 | 0.0898569 | ||||||||
\(990\) | −79.8632 | −2.53822 | ||||||||
\(991\) | −2.56233 | −0.0813950 | −0.0406975 | − | 0.999172i | \(-0.512958\pi\) | ||||
−0.0406975 | + | 0.999172i | \(0.512958\pi\) | |||||||
\(992\) | 5.79444 | 0.183974 | ||||||||
\(993\) | −37.5979 | −1.19313 | ||||||||
\(994\) | 10.8991 | 0.345700 | ||||||||
\(995\) | 69.1471 | 2.19211 | ||||||||
\(996\) | 240.614 | 7.62414 | ||||||||
\(997\) | 39.5107 | 1.25132 | 0.625658 | − | 0.780097i | \(-0.284830\pi\) | ||||
0.625658 | + | 0.780097i | \(0.284830\pi\) | |||||||
\(998\) | −28.5041 | −0.902283 | ||||||||
\(999\) | −50.7638 | −1.60610 |
(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 | 667.2.a.b.1.2 | ✓ | 12 | |
3.2 | odd | 2 | 6003.2.a.n.1.11 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
667.2.a.b.1.2 | ✓ | 12 | 1.1 | even | 1 | trivial | |
6003.2.a.n.1.11 | 12 | 3.2 | odd | 2 |