Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6010,2,Mod(1,6010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6010, 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("6010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6010 = 2 \cdot 5 \cdot 601 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6010.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: | \(47.9900916148\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 6010.1 |
$q$-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 | ||||||||
\(3\) | 1.25977 | 0.727330 | 0.363665 | − | 0.931530i | \(-0.381525\pi\) | ||||
0.363665 | + | 0.931530i | \(0.381525\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.25977 | 0.514300 | ||||||||
\(7\) | 3.22153 | 1.21762 | 0.608812 | − | 0.793315i | \(-0.291647\pi\) | ||||
0.608812 | + | 0.793315i | \(0.291647\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.41297 | −0.470991 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 5.03908 | 1.51934 | 0.759670 | − | 0.650309i | \(-0.225361\pi\) | ||||
0.759670 | + | 0.650309i | \(0.225361\pi\) | |||||||
\(12\) | 1.25977 | 0.363665 | ||||||||
\(13\) | 2.54225 | 0.705092 | 0.352546 | − | 0.935794i | \(-0.385316\pi\) | ||||
0.352546 | + | 0.935794i | \(0.385316\pi\) | |||||||
\(14\) | 3.22153 | 0.860990 | ||||||||
\(15\) | −1.25977 | −0.325272 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.741176 | 0.179762 | 0.0898808 | − | 0.995953i | \(-0.471351\pi\) | ||||
0.0898808 | + | 0.995953i | \(0.471351\pi\) | |||||||
\(18\) | −1.41297 | −0.333041 | ||||||||
\(19\) | 8.15755 | 1.87147 | 0.935735 | − | 0.352703i | \(-0.114737\pi\) | ||||
0.935735 | + | 0.352703i | \(0.114737\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 4.05839 | 0.885614 | ||||||||
\(22\) | 5.03908 | 1.07434 | ||||||||
\(23\) | −0.280998 | −0.0585922 | −0.0292961 | − | 0.999571i | \(-0.509327\pi\) | ||||
−0.0292961 | + | 0.999571i | \(0.509327\pi\) | |||||||
\(24\) | 1.25977 | 0.257150 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.54225 | 0.498575 | ||||||||
\(27\) | −5.55934 | −1.06990 | ||||||||
\(28\) | 3.22153 | 0.608812 | ||||||||
\(29\) | 3.73498 | 0.693569 | 0.346784 | − | 0.937945i | \(-0.387274\pi\) | ||||
0.346784 | + | 0.937945i | \(0.387274\pi\) | |||||||
\(30\) | −1.25977 | −0.230002 | ||||||||
\(31\) | −8.36407 | −1.50223 | −0.751115 | − | 0.660171i | \(-0.770484\pi\) | ||||
−0.751115 | + | 0.660171i | \(0.770484\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 6.34810 | 1.10506 | ||||||||
\(34\) | 0.741176 | 0.127111 | ||||||||
\(35\) | −3.22153 | −0.544538 | ||||||||
\(36\) | −1.41297 | −0.235495 | ||||||||
\(37\) | −0.170862 | −0.0280895 | −0.0140447 | − | 0.999901i | \(-0.504471\pi\) | ||||
−0.0140447 | + | 0.999901i | \(0.504471\pi\) | |||||||
\(38\) | 8.15755 | 1.32333 | ||||||||
\(39\) | 3.20265 | 0.512835 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −4.02927 | −0.629267 | −0.314633 | − | 0.949213i | \(-0.601882\pi\) | ||||
−0.314633 | + | 0.949213i | \(0.601882\pi\) | |||||||
\(42\) | 4.05839 | 0.626224 | ||||||||
\(43\) | −9.44017 | −1.43961 | −0.719806 | − | 0.694175i | \(-0.755769\pi\) | ||||
−0.719806 | + | 0.694175i | \(0.755769\pi\) | |||||||
\(44\) | 5.03908 | 0.759670 | ||||||||
\(45\) | 1.41297 | 0.210633 | ||||||||
\(46\) | −0.280998 | −0.0414310 | ||||||||
\(47\) | 6.34766 | 0.925902 | 0.462951 | − | 0.886384i | \(-0.346791\pi\) | ||||
0.462951 | + | 0.886384i | \(0.346791\pi\) | |||||||
\(48\) | 1.25977 | 0.181833 | ||||||||
\(49\) | 3.37824 | 0.482606 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 0.933714 | 0.130746 | ||||||||
\(52\) | 2.54225 | 0.352546 | ||||||||
\(53\) | 0.251008 | 0.0344786 | 0.0172393 | − | 0.999851i | \(-0.494512\pi\) | ||||
0.0172393 | + | 0.999851i | \(0.494512\pi\) | |||||||
\(54\) | −5.55934 | −0.756531 | ||||||||
\(55\) | −5.03908 | −0.679469 | ||||||||
\(56\) | 3.22153 | 0.430495 | ||||||||
\(57\) | 10.2767 | 1.36118 | ||||||||
\(58\) | 3.73498 | 0.490427 | ||||||||
\(59\) | 5.26832 | 0.685877 | 0.342939 | − | 0.939358i | \(-0.388578\pi\) | ||||
0.342939 | + | 0.939358i | \(0.388578\pi\) | |||||||
\(60\) | −1.25977 | −0.162636 | ||||||||
\(61\) | −3.17080 | −0.405979 | −0.202989 | − | 0.979181i | \(-0.565066\pi\) | ||||
−0.202989 | + | 0.979181i | \(0.565066\pi\) | |||||||
\(62\) | −8.36407 | −1.06224 | ||||||||
\(63\) | −4.55193 | −0.573489 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.54225 | −0.315327 | ||||||||
\(66\) | 6.34810 | 0.781397 | ||||||||
\(67\) | −6.76837 | −0.826888 | −0.413444 | − | 0.910529i | \(-0.635674\pi\) | ||||
−0.413444 | + | 0.910529i | \(0.635674\pi\) | |||||||
\(68\) | 0.741176 | 0.0898808 | ||||||||
\(69\) | −0.353994 | −0.0426159 | ||||||||
\(70\) | −3.22153 | −0.385046 | ||||||||
\(71\) | −5.09804 | −0.605026 | −0.302513 | − | 0.953145i | \(-0.597826\pi\) | ||||
−0.302513 | + | 0.953145i | \(0.597826\pi\) | |||||||
\(72\) | −1.41297 | −0.166520 | ||||||||
\(73\) | 12.0725 | 1.41298 | 0.706488 | − | 0.707725i | \(-0.250278\pi\) | ||||
0.706488 | + | 0.707725i | \(0.250278\pi\) | |||||||
\(74\) | −0.170862 | −0.0198623 | ||||||||
\(75\) | 1.25977 | 0.145466 | ||||||||
\(76\) | 8.15755 | 0.935735 | ||||||||
\(77\) | 16.2335 | 1.84998 | ||||||||
\(78\) | 3.20265 | 0.362629 | ||||||||
\(79\) | −4.38753 | −0.493636 | −0.246818 | − | 0.969062i | \(-0.579385\pi\) | ||||
−0.246818 | + | 0.969062i | \(0.579385\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −2.76459 | −0.307177 | ||||||||
\(82\) | −4.02927 | −0.444959 | ||||||||
\(83\) | −2.56246 | −0.281267 | −0.140633 | − | 0.990062i | \(-0.544914\pi\) | ||||
−0.140633 | + | 0.990062i | \(0.544914\pi\) | |||||||
\(84\) | 4.05839 | 0.442807 | ||||||||
\(85\) | −0.741176 | −0.0803919 | ||||||||
\(86\) | −9.44017 | −1.01796 | ||||||||
\(87\) | 4.70523 | 0.504454 | ||||||||
\(88\) | 5.03908 | 0.537168 | ||||||||
\(89\) | −13.3773 | −1.41800 | −0.708998 | − | 0.705211i | \(-0.750852\pi\) | ||||
−0.708998 | + | 0.705211i | \(0.750852\pi\) | |||||||
\(90\) | 1.41297 | 0.148940 | ||||||||
\(91\) | 8.18992 | 0.858537 | ||||||||
\(92\) | −0.280998 | −0.0292961 | ||||||||
\(93\) | −10.5368 | −1.09262 | ||||||||
\(94\) | 6.34766 | 0.654711 | ||||||||
\(95\) | −8.15755 | −0.836947 | ||||||||
\(96\) | 1.25977 | 0.128575 | ||||||||
\(97\) | −6.12982 | −0.622389 | −0.311195 | − | 0.950346i | \(-0.600729\pi\) | ||||
−0.311195 | + | 0.950346i | \(0.600729\pi\) | |||||||
\(98\) | 3.37824 | 0.341254 | ||||||||
\(99\) | −7.12008 | −0.715595 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 3.15971 | 0.314403 | 0.157202 | − | 0.987567i | \(-0.449753\pi\) | ||||
0.157202 | + | 0.987567i | \(0.449753\pi\) | |||||||
\(102\) | 0.933714 | 0.0924515 | ||||||||
\(103\) | 12.8371 | 1.26487 | 0.632437 | − | 0.774612i | \(-0.282055\pi\) | ||||
0.632437 | + | 0.774612i | \(0.282055\pi\) | |||||||
\(104\) | 2.54225 | 0.249288 | ||||||||
\(105\) | −4.05839 | −0.396059 | ||||||||
\(106\) | 0.251008 | 0.0243800 | ||||||||
\(107\) | 10.6960 | 1.03402 | 0.517011 | − | 0.855979i | \(-0.327045\pi\) | ||||
0.517011 | + | 0.855979i | \(0.327045\pi\) | |||||||
\(108\) | −5.55934 | −0.534948 | ||||||||
\(109\) | −2.06372 | −0.197668 | −0.0988340 | − | 0.995104i | \(-0.531511\pi\) | ||||
−0.0988340 | + | 0.995104i | \(0.531511\pi\) | |||||||
\(110\) | −5.03908 | −0.480457 | ||||||||
\(111\) | −0.215247 | −0.0204303 | ||||||||
\(112\) | 3.22153 | 0.304406 | ||||||||
\(113\) | −9.93713 | −0.934807 | −0.467403 | − | 0.884044i | \(-0.654810\pi\) | ||||
−0.467403 | + | 0.884044i | \(0.654810\pi\) | |||||||
\(114\) | 10.2767 | 0.962498 | ||||||||
\(115\) | 0.280998 | 0.0262032 | ||||||||
\(116\) | 3.73498 | 0.346784 | ||||||||
\(117\) | −3.59212 | −0.332092 | ||||||||
\(118\) | 5.26832 | 0.484988 | ||||||||
\(119\) | 2.38772 | 0.218882 | ||||||||
\(120\) | −1.25977 | −0.115001 | ||||||||
\(121\) | 14.3923 | 1.30839 | ||||||||
\(122\) | −3.17080 | −0.287070 | ||||||||
\(123\) | −5.07597 | −0.457685 | ||||||||
\(124\) | −8.36407 | −0.751115 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −4.55193 | −0.405518 | ||||||||
\(127\) | 6.10582 | 0.541804 | 0.270902 | − | 0.962607i | \(-0.412678\pi\) | ||||
0.270902 | + | 0.962607i | \(0.412678\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −11.8925 | −1.04707 | ||||||||
\(130\) | −2.54225 | −0.222970 | ||||||||
\(131\) | 6.40845 | 0.559908 | 0.279954 | − | 0.960013i | \(-0.409681\pi\) | ||||
0.279954 | + | 0.960013i | \(0.409681\pi\) | |||||||
\(132\) | 6.34810 | 0.552531 | ||||||||
\(133\) | 26.2798 | 2.27875 | ||||||||
\(134\) | −6.76837 | −0.584698 | ||||||||
\(135\) | 5.55934 | 0.478472 | ||||||||
\(136\) | 0.741176 | 0.0635553 | ||||||||
\(137\) | −8.97013 | −0.766370 | −0.383185 | − | 0.923672i | \(-0.625173\pi\) | ||||
−0.383185 | + | 0.923672i | \(0.625173\pi\) | |||||||
\(138\) | −0.353994 | −0.0301340 | ||||||||
\(139\) | 2.87367 | 0.243741 | 0.121871 | − | 0.992546i | \(-0.461111\pi\) | ||||
0.121871 | + | 0.992546i | \(0.461111\pi\) | |||||||
\(140\) | −3.22153 | −0.272269 | ||||||||
\(141\) | 7.99661 | 0.673436 | ||||||||
\(142\) | −5.09804 | −0.427818 | ||||||||
\(143\) | 12.8106 | 1.07127 | ||||||||
\(144\) | −1.41297 | −0.117748 | ||||||||
\(145\) | −3.73498 | −0.310173 | ||||||||
\(146\) | 12.0725 | 0.999125 | ||||||||
\(147\) | 4.25582 | 0.351014 | ||||||||
\(148\) | −0.170862 | −0.0140447 | ||||||||
\(149\) | −6.64556 | −0.544426 | −0.272213 | − | 0.962237i | \(-0.587755\pi\) | ||||
−0.272213 | + | 0.962237i | \(0.587755\pi\) | |||||||
\(150\) | 1.25977 | 0.102860 | ||||||||
\(151\) | 14.0599 | 1.14418 | 0.572090 | − | 0.820191i | \(-0.306133\pi\) | ||||
0.572090 | + | 0.820191i | \(0.306133\pi\) | |||||||
\(152\) | 8.15755 | 0.661665 | ||||||||
\(153\) | −1.04726 | −0.0846661 | ||||||||
\(154\) | 16.2335 | 1.30814 | ||||||||
\(155\) | 8.36407 | 0.671818 | ||||||||
\(156\) | 3.20265 | 0.256417 | ||||||||
\(157\) | −21.6550 | −1.72826 | −0.864128 | − | 0.503271i | \(-0.832130\pi\) | ||||
−0.864128 | + | 0.503271i | \(0.832130\pi\) | |||||||
\(158\) | −4.38753 | −0.349053 | ||||||||
\(159\) | 0.316213 | 0.0250773 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −0.905244 | −0.0713432 | ||||||||
\(162\) | −2.76459 | −0.217207 | ||||||||
\(163\) | 18.6235 | 1.45871 | 0.729354 | − | 0.684137i | \(-0.239821\pi\) | ||||
0.729354 | + | 0.684137i | \(0.239821\pi\) | |||||||
\(164\) | −4.02927 | −0.314633 | ||||||||
\(165\) | −6.34810 | −0.494199 | ||||||||
\(166\) | −2.56246 | −0.198885 | ||||||||
\(167\) | −11.3326 | −0.876941 | −0.438471 | − | 0.898746i | \(-0.644480\pi\) | ||||
−0.438471 | + | 0.898746i | \(0.644480\pi\) | |||||||
\(168\) | 4.05839 | 0.313112 | ||||||||
\(169\) | −6.53699 | −0.502845 | ||||||||
\(170\) | −0.741176 | −0.0568456 | ||||||||
\(171\) | −11.5264 | −0.881445 | ||||||||
\(172\) | −9.44017 | −0.719806 | ||||||||
\(173\) | 21.3455 | 1.62287 | 0.811433 | − | 0.584445i | \(-0.198688\pi\) | ||||
0.811433 | + | 0.584445i | \(0.198688\pi\) | |||||||
\(174\) | 4.70523 | 0.356703 | ||||||||
\(175\) | 3.22153 | 0.243525 | ||||||||
\(176\) | 5.03908 | 0.379835 | ||||||||
\(177\) | 6.63689 | 0.498859 | ||||||||
\(178\) | −13.3773 | −1.00267 | ||||||||
\(179\) | 13.5678 | 1.01411 | 0.507053 | − | 0.861915i | \(-0.330735\pi\) | ||||
0.507053 | + | 0.861915i | \(0.330735\pi\) | |||||||
\(180\) | 1.41297 | 0.105317 | ||||||||
\(181\) | 0.469172 | 0.0348733 | 0.0174366 | − | 0.999848i | \(-0.494449\pi\) | ||||
0.0174366 | + | 0.999848i | \(0.494449\pi\) | |||||||
\(182\) | 8.18992 | 0.607077 | ||||||||
\(183\) | −3.99448 | −0.295281 | ||||||||
\(184\) | −0.280998 | −0.0207155 | ||||||||
\(185\) | 0.170862 | 0.0125620 | ||||||||
\(186\) | −10.5368 | −0.772598 | ||||||||
\(187\) | 3.73485 | 0.273119 | ||||||||
\(188\) | 6.34766 | 0.462951 | ||||||||
\(189\) | −17.9096 | −1.30273 | ||||||||
\(190\) | −8.15755 | −0.591811 | ||||||||
\(191\) | 19.0017 | 1.37492 | 0.687458 | − | 0.726224i | \(-0.258727\pi\) | ||||
0.687458 | + | 0.726224i | \(0.258727\pi\) | |||||||
\(192\) | 1.25977 | 0.0909163 | ||||||||
\(193\) | 23.2684 | 1.67490 | 0.837449 | − | 0.546515i | \(-0.184046\pi\) | ||||
0.837449 | + | 0.546515i | \(0.184046\pi\) | |||||||
\(194\) | −6.12982 | −0.440096 | ||||||||
\(195\) | −3.20265 | −0.229347 | ||||||||
\(196\) | 3.37824 | 0.241303 | ||||||||
\(197\) | 3.41108 | 0.243029 | 0.121515 | − | 0.992590i | \(-0.461225\pi\) | ||||
0.121515 | + | 0.992590i | \(0.461225\pi\) | |||||||
\(198\) | −7.12008 | −0.506002 | ||||||||
\(199\) | −10.5463 | −0.747606 | −0.373803 | − | 0.927508i | \(-0.621946\pi\) | ||||
−0.373803 | + | 0.927508i | \(0.621946\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −8.52661 | −0.601421 | ||||||||
\(202\) | 3.15971 | 0.222317 | ||||||||
\(203\) | 12.0324 | 0.844505 | ||||||||
\(204\) | 0.933714 | 0.0653731 | ||||||||
\(205\) | 4.02927 | 0.281417 | ||||||||
\(206\) | 12.8371 | 0.894401 | ||||||||
\(207\) | 0.397043 | 0.0275964 | ||||||||
\(208\) | 2.54225 | 0.176273 | ||||||||
\(209\) | 41.1066 | 2.84340 | ||||||||
\(210\) | −4.05839 | −0.280056 | ||||||||
\(211\) | 17.4016 | 1.19798 | 0.598988 | − | 0.800758i | \(-0.295570\pi\) | ||||
0.598988 | + | 0.800758i | \(0.295570\pi\) | |||||||
\(212\) | 0.251008 | 0.0172393 | ||||||||
\(213\) | −6.42237 | −0.440054 | ||||||||
\(214\) | 10.6960 | 0.731164 | ||||||||
\(215\) | 9.44017 | 0.643814 | ||||||||
\(216\) | −5.55934 | −0.378265 | ||||||||
\(217\) | −26.9451 | −1.82915 | ||||||||
\(218\) | −2.06372 | −0.139772 | ||||||||
\(219\) | 15.2086 | 1.02770 | ||||||||
\(220\) | −5.03908 | −0.339735 | ||||||||
\(221\) | 1.88425 | 0.126749 | ||||||||
\(222\) | −0.215247 | −0.0144464 | ||||||||
\(223\) | −14.0516 | −0.940965 | −0.470483 | − | 0.882409i | \(-0.655920\pi\) | ||||
−0.470483 | + | 0.882409i | \(0.655920\pi\) | |||||||
\(224\) | 3.22153 | 0.215247 | ||||||||
\(225\) | −1.41297 | −0.0941981 | ||||||||
\(226\) | −9.93713 | −0.661008 | ||||||||
\(227\) | 4.38716 | 0.291186 | 0.145593 | − | 0.989345i | \(-0.453491\pi\) | ||||
0.145593 | + | 0.989345i | \(0.453491\pi\) | |||||||
\(228\) | 10.2767 | 0.680589 | ||||||||
\(229\) | −13.3580 | −0.882724 | −0.441362 | − | 0.897329i | \(-0.645505\pi\) | ||||
−0.441362 | + | 0.897329i | \(0.645505\pi\) | |||||||
\(230\) | 0.280998 | 0.0185285 | ||||||||
\(231\) | 20.4506 | 1.34555 | ||||||||
\(232\) | 3.73498 | 0.245214 | ||||||||
\(233\) | −5.42645 | −0.355498 | −0.177749 | − | 0.984076i | \(-0.556882\pi\) | ||||
−0.177749 | + | 0.984076i | \(0.556882\pi\) | |||||||
\(234\) | −3.59212 | −0.234824 | ||||||||
\(235\) | −6.34766 | −0.414076 | ||||||||
\(236\) | 5.26832 | 0.342939 | ||||||||
\(237\) | −5.52729 | −0.359036 | ||||||||
\(238\) | 2.38772 | 0.154773 | ||||||||
\(239\) | −20.8299 | −1.34737 | −0.673686 | − | 0.739017i | \(-0.735290\pi\) | ||||
−0.673686 | + | 0.739017i | \(0.735290\pi\) | |||||||
\(240\) | −1.25977 | −0.0813180 | ||||||||
\(241\) | −19.7899 | −1.27478 | −0.637390 | − | 0.770542i | \(-0.719986\pi\) | ||||
−0.637390 | + | 0.770542i | \(0.719986\pi\) | |||||||
\(242\) | 14.3923 | 0.925173 | ||||||||
\(243\) | 13.1953 | 0.846477 | ||||||||
\(244\) | −3.17080 | −0.202989 | ||||||||
\(245\) | −3.37824 | −0.215828 | ||||||||
\(246\) | −5.07597 | −0.323632 | ||||||||
\(247\) | 20.7385 | 1.31956 | ||||||||
\(248\) | −8.36407 | −0.531119 | ||||||||
\(249\) | −3.22812 | −0.204574 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 24.9665 | 1.57587 | 0.787937 | − | 0.615756i | \(-0.211149\pi\) | ||||
0.787937 | + | 0.615756i | \(0.211149\pi\) | |||||||
\(252\) | −4.55193 | −0.286745 | ||||||||
\(253\) | −1.41597 | −0.0890215 | ||||||||
\(254\) | 6.10582 | 0.383113 | ||||||||
\(255\) | −0.933714 | −0.0584714 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −26.5943 | −1.65891 | −0.829455 | − | 0.558574i | \(-0.811349\pi\) | ||||
−0.829455 | + | 0.558574i | \(0.811349\pi\) | |||||||
\(258\) | −11.8925 | −0.740393 | ||||||||
\(259\) | −0.550435 | −0.0342024 | ||||||||
\(260\) | −2.54225 | −0.157663 | ||||||||
\(261\) | −5.27743 | −0.326664 | ||||||||
\(262\) | 6.40845 | 0.395915 | ||||||||
\(263\) | 8.11125 | 0.500161 | 0.250080 | − | 0.968225i | \(-0.419543\pi\) | ||||
0.250080 | + | 0.968225i | \(0.419543\pi\) | |||||||
\(264\) | 6.34810 | 0.390698 | ||||||||
\(265\) | −0.251008 | −0.0154193 | ||||||||
\(266\) | 26.2798 | 1.61132 | ||||||||
\(267\) | −16.8524 | −1.03135 | ||||||||
\(268\) | −6.76837 | −0.413444 | ||||||||
\(269\) | −5.04811 | −0.307789 | −0.153894 | − | 0.988087i | \(-0.549182\pi\) | ||||
−0.153894 | + | 0.988087i | \(0.549182\pi\) | |||||||
\(270\) | 5.55934 | 0.338331 | ||||||||
\(271\) | 6.98247 | 0.424155 | 0.212078 | − | 0.977253i | \(-0.431977\pi\) | ||||
0.212078 | + | 0.977253i | \(0.431977\pi\) | |||||||
\(272\) | 0.741176 | 0.0449404 | ||||||||
\(273\) | 10.3174 | 0.624440 | ||||||||
\(274\) | −8.97013 | −0.541905 | ||||||||
\(275\) | 5.03908 | 0.303868 | ||||||||
\(276\) | −0.353994 | −0.0213080 | ||||||||
\(277\) | −3.01293 | −0.181029 | −0.0905147 | − | 0.995895i | \(-0.528851\pi\) | ||||
−0.0905147 | + | 0.995895i | \(0.528851\pi\) | |||||||
\(278\) | 2.87367 | 0.172351 | ||||||||
\(279\) | 11.8182 | 0.707537 | ||||||||
\(280\) | −3.22153 | −0.192523 | ||||||||
\(281\) | −12.0243 | −0.717312 | −0.358656 | − | 0.933470i | \(-0.616765\pi\) | ||||
−0.358656 | + | 0.933470i | \(0.616765\pi\) | |||||||
\(282\) | 7.99661 | 0.476191 | ||||||||
\(283\) | −31.6802 | −1.88319 | −0.941596 | − | 0.336743i | \(-0.890675\pi\) | ||||
−0.941596 | + | 0.336743i | \(0.890675\pi\) | |||||||
\(284\) | −5.09804 | −0.302513 | ||||||||
\(285\) | −10.2767 | −0.608737 | ||||||||
\(286\) | 12.8106 | 0.757505 | ||||||||
\(287\) | −12.9804 | −0.766210 | ||||||||
\(288\) | −1.41297 | −0.0832602 | ||||||||
\(289\) | −16.4507 | −0.967686 | ||||||||
\(290\) | −3.73498 | −0.219326 | ||||||||
\(291\) | −7.72219 | −0.452683 | ||||||||
\(292\) | 12.0725 | 0.706488 | ||||||||
\(293\) | 20.9078 | 1.22144 | 0.610722 | − | 0.791845i | \(-0.290879\pi\) | ||||
0.610722 | + | 0.791845i | \(0.290879\pi\) | |||||||
\(294\) | 4.25582 | 0.248204 | ||||||||
\(295\) | −5.26832 | −0.306734 | ||||||||
\(296\) | −0.170862 | −0.00993113 | ||||||||
\(297\) | −28.0140 | −1.62554 | ||||||||
\(298\) | −6.64556 | −0.384967 | ||||||||
\(299\) | −0.714367 | −0.0413129 | ||||||||
\(300\) | 1.25977 | 0.0727330 | ||||||||
\(301\) | −30.4118 | −1.75291 | ||||||||
\(302\) | 14.0599 | 0.809058 | ||||||||
\(303\) | 3.98052 | 0.228675 | ||||||||
\(304\) | 8.15755 | 0.467868 | ||||||||
\(305\) | 3.17080 | 0.181559 | ||||||||
\(306\) | −1.04726 | −0.0598679 | ||||||||
\(307\) | −4.36711 | −0.249244 | −0.124622 | − | 0.992204i | \(-0.539772\pi\) | ||||
−0.124622 | + | 0.992204i | \(0.539772\pi\) | |||||||
\(308\) | 16.2335 | 0.924991 | ||||||||
\(309\) | 16.1718 | 0.919981 | ||||||||
\(310\) | 8.36407 | 0.475047 | ||||||||
\(311\) | 16.7802 | 0.951516 | 0.475758 | − | 0.879576i | \(-0.342174\pi\) | ||||
0.475758 | + | 0.879576i | \(0.342174\pi\) | |||||||
\(312\) | 3.20265 | 0.181315 | ||||||||
\(313\) | −14.3726 | −0.812387 | −0.406194 | − | 0.913787i | \(-0.633144\pi\) | ||||
−0.406194 | + | 0.913787i | \(0.633144\pi\) | |||||||
\(314\) | −21.6550 | −1.22206 | ||||||||
\(315\) | 4.55193 | 0.256472 | ||||||||
\(316\) | −4.38753 | −0.246818 | ||||||||
\(317\) | 12.3187 | 0.691887 | 0.345944 | − | 0.938255i | \(-0.387559\pi\) | ||||
0.345944 | + | 0.938255i | \(0.387559\pi\) | |||||||
\(318\) | 0.316213 | 0.0177323 | ||||||||
\(319\) | 18.8209 | 1.05377 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 13.4745 | 0.752075 | ||||||||
\(322\) | −0.905244 | −0.0504473 | ||||||||
\(323\) | 6.04618 | 0.336419 | ||||||||
\(324\) | −2.76459 | −0.153589 | ||||||||
\(325\) | 2.54225 | 0.141018 | ||||||||
\(326\) | 18.6235 | 1.03146 | ||||||||
\(327\) | −2.59981 | −0.143770 | ||||||||
\(328\) | −4.02927 | −0.222479 | ||||||||
\(329\) | 20.4492 | 1.12740 | ||||||||
\(330\) | −6.34810 | −0.349451 | ||||||||
\(331\) | 1.64904 | 0.0906393 | 0.0453196 | − | 0.998973i | \(-0.485569\pi\) | ||||
0.0453196 | + | 0.998973i | \(0.485569\pi\) | |||||||
\(332\) | −2.56246 | −0.140633 | ||||||||
\(333\) | 0.241423 | 0.0132299 | ||||||||
\(334\) | −11.3326 | −0.620091 | ||||||||
\(335\) | 6.76837 | 0.369796 | ||||||||
\(336\) | 4.05839 | 0.221404 | ||||||||
\(337\) | 1.70474 | 0.0928629 | 0.0464314 | − | 0.998921i | \(-0.485215\pi\) | ||||
0.0464314 | + | 0.998921i | \(0.485215\pi\) | |||||||
\(338\) | −6.53699 | −0.355565 | ||||||||
\(339\) | −12.5185 | −0.679913 | ||||||||
\(340\) | −0.741176 | −0.0401959 | ||||||||
\(341\) | −42.1472 | −2.28240 | ||||||||
\(342\) | −11.5264 | −0.623276 | ||||||||
\(343\) | −11.6676 | −0.629991 | ||||||||
\(344\) | −9.44017 | −0.508980 | ||||||||
\(345\) | 0.353994 | 0.0190584 | ||||||||
\(346\) | 21.3455 | 1.14754 | ||||||||
\(347\) | −19.5187 | −1.04782 | −0.523909 | − | 0.851775i | \(-0.675527\pi\) | ||||
−0.523909 | + | 0.851775i | \(0.675527\pi\) | |||||||
\(348\) | 4.70523 | 0.252227 | ||||||||
\(349\) | 1.38647 | 0.0742160 | 0.0371080 | − | 0.999311i | \(-0.488185\pi\) | ||||
0.0371080 | + | 0.999311i | \(0.488185\pi\) | |||||||
\(350\) | 3.22153 | 0.172198 | ||||||||
\(351\) | −14.1332 | −0.754375 | ||||||||
\(352\) | 5.03908 | 0.268584 | ||||||||
\(353\) | −16.9064 | −0.899836 | −0.449918 | − | 0.893070i | \(-0.648547\pi\) | ||||
−0.449918 | + | 0.893070i | \(0.648547\pi\) | |||||||
\(354\) | 6.63689 | 0.352747 | ||||||||
\(355\) | 5.09804 | 0.270576 | ||||||||
\(356\) | −13.3773 | −0.708998 | ||||||||
\(357\) | 3.00799 | 0.159199 | ||||||||
\(358\) | 13.5678 | 0.717081 | ||||||||
\(359\) | 15.8749 | 0.837844 | 0.418922 | − | 0.908022i | \(-0.362408\pi\) | ||||
0.418922 | + | 0.908022i | \(0.362408\pi\) | |||||||
\(360\) | 1.41297 | 0.0744702 | ||||||||
\(361\) | 47.5457 | 2.50240 | ||||||||
\(362\) | 0.469172 | 0.0246591 | ||||||||
\(363\) | 18.1311 | 0.951634 | ||||||||
\(364\) | 8.18992 | 0.429268 | ||||||||
\(365\) | −12.0725 | −0.631902 | ||||||||
\(366\) | −3.99448 | −0.208795 | ||||||||
\(367\) | −28.6903 | −1.49762 | −0.748810 | − | 0.662785i | \(-0.769374\pi\) | ||||
−0.748810 | + | 0.662785i | \(0.769374\pi\) | |||||||
\(368\) | −0.280998 | −0.0146481 | ||||||||
\(369\) | 5.69325 | 0.296379 | ||||||||
\(370\) | 0.170862 | 0.00888267 | ||||||||
\(371\) | 0.808629 | 0.0419819 | ||||||||
\(372\) | −10.5368 | −0.546309 | ||||||||
\(373\) | 7.28543 | 0.377225 | 0.188613 | − | 0.982052i | \(-0.439601\pi\) | ||||
0.188613 | + | 0.982052i | \(0.439601\pi\) | |||||||
\(374\) | 3.73485 | 0.193124 | ||||||||
\(375\) | −1.25977 | −0.0650544 | ||||||||
\(376\) | 6.34766 | 0.327356 | ||||||||
\(377\) | 9.49524 | 0.489030 | ||||||||
\(378\) | −17.9096 | −0.921169 | ||||||||
\(379\) | −18.5808 | −0.954431 | −0.477215 | − | 0.878786i | \(-0.658354\pi\) | ||||
−0.477215 | + | 0.878786i | \(0.658354\pi\) | |||||||
\(380\) | −8.15755 | −0.418474 | ||||||||
\(381\) | 7.69195 | 0.394071 | ||||||||
\(382\) | 19.0017 | 0.972213 | ||||||||
\(383\) | 17.9746 | 0.918461 | 0.459231 | − | 0.888317i | \(-0.348125\pi\) | ||||
0.459231 | + | 0.888317i | \(0.348125\pi\) | |||||||
\(384\) | 1.25977 | 0.0642875 | ||||||||
\(385\) | −16.2335 | −0.827337 | ||||||||
\(386\) | 23.2684 | 1.18433 | ||||||||
\(387\) | 13.3387 | 0.678044 | ||||||||
\(388\) | −6.12982 | −0.311195 | ||||||||
\(389\) | −19.5925 | −0.993380 | −0.496690 | − | 0.867928i | \(-0.665451\pi\) | ||||
−0.496690 | + | 0.867928i | \(0.665451\pi\) | |||||||
\(390\) | −3.20265 | −0.162173 | ||||||||
\(391\) | −0.208269 | −0.0105326 | ||||||||
\(392\) | 3.37824 | 0.170627 | ||||||||
\(393\) | 8.07319 | 0.407238 | ||||||||
\(394\) | 3.41108 | 0.171848 | ||||||||
\(395\) | 4.38753 | 0.220761 | ||||||||
\(396\) | −7.12008 | −0.357797 | ||||||||
\(397\) | −5.94922 | −0.298583 | −0.149291 | − | 0.988793i | \(-0.547699\pi\) | ||||
−0.149291 | + | 0.988793i | \(0.547699\pi\) | |||||||
\(398\) | −10.5463 | −0.528637 | ||||||||
\(399\) | 33.1066 | 1.65740 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −12.8074 | −0.639569 | −0.319785 | − | 0.947490i | \(-0.603611\pi\) | ||||
−0.319785 | + | 0.947490i | \(0.603611\pi\) | |||||||
\(402\) | −8.52661 | −0.425269 | ||||||||
\(403\) | −21.2635 | −1.05921 | ||||||||
\(404\) | 3.15971 | 0.157202 | ||||||||
\(405\) | 2.76459 | 0.137374 | ||||||||
\(406\) | 12.0324 | 0.597156 | ||||||||
\(407\) | −0.860985 | −0.0426774 | ||||||||
\(408\) | 0.933714 | 0.0462257 | ||||||||
\(409\) | −4.36148 | −0.215661 | −0.107831 | − | 0.994169i | \(-0.534390\pi\) | ||||
−0.107831 | + | 0.994169i | \(0.534390\pi\) | |||||||
\(410\) | 4.02927 | 0.198992 | ||||||||
\(411\) | −11.3003 | −0.557404 | ||||||||
\(412\) | 12.8371 | 0.632437 | ||||||||
\(413\) | 16.9720 | 0.835140 | ||||||||
\(414\) | 0.397043 | 0.0195136 | ||||||||
\(415\) | 2.56246 | 0.125786 | ||||||||
\(416\) | 2.54225 | 0.124644 | ||||||||
\(417\) | 3.62017 | 0.177280 | ||||||||
\(418\) | 41.1066 | 2.01059 | ||||||||
\(419\) | 35.4723 | 1.73294 | 0.866468 | − | 0.499232i | \(-0.166385\pi\) | ||||
0.866468 | + | 0.499232i | \(0.166385\pi\) | |||||||
\(420\) | −4.05839 | −0.198029 | ||||||||
\(421\) | 25.0881 | 1.22272 | 0.611359 | − | 0.791353i | \(-0.290623\pi\) | ||||
0.611359 | + | 0.791353i | \(0.290623\pi\) | |||||||
\(422\) | 17.4016 | 0.847097 | ||||||||
\(423\) | −8.96907 | −0.436091 | ||||||||
\(424\) | 0.251008 | 0.0121900 | ||||||||
\(425\) | 0.741176 | 0.0359523 | ||||||||
\(426\) | −6.42237 | −0.311165 | ||||||||
\(427\) | −10.2148 | −0.494329 | ||||||||
\(428\) | 10.6960 | 0.517011 | ||||||||
\(429\) | 16.1384 | 0.779170 | ||||||||
\(430\) | 9.44017 | 0.455246 | ||||||||
\(431\) | −13.4052 | −0.645707 | −0.322854 | − | 0.946449i | \(-0.604642\pi\) | ||||
−0.322854 | + | 0.946449i | \(0.604642\pi\) | |||||||
\(432\) | −5.55934 | −0.267474 | ||||||||
\(433\) | −26.3427 | −1.26595 | −0.632976 | − | 0.774172i | \(-0.718167\pi\) | ||||
−0.632976 | + | 0.774172i | \(0.718167\pi\) | |||||||
\(434\) | −26.9451 | −1.29341 | ||||||||
\(435\) | −4.70523 | −0.225599 | ||||||||
\(436\) | −2.06372 | −0.0988340 | ||||||||
\(437\) | −2.29226 | −0.109654 | ||||||||
\(438\) | 15.2086 | 0.726694 | ||||||||
\(439\) | 5.64346 | 0.269347 | 0.134674 | − | 0.990890i | \(-0.457001\pi\) | ||||
0.134674 | + | 0.990890i | \(0.457001\pi\) | |||||||
\(440\) | −5.03908 | −0.240229 | ||||||||
\(441\) | −4.77336 | −0.227303 | ||||||||
\(442\) | 1.88425 | 0.0896248 | ||||||||
\(443\) | 3.44605 | 0.163727 | 0.0818634 | − | 0.996644i | \(-0.473913\pi\) | ||||
0.0818634 | + | 0.996644i | \(0.473913\pi\) | |||||||
\(444\) | −0.215247 | −0.0102152 | ||||||||
\(445\) | 13.3773 | 0.634147 | ||||||||
\(446\) | −14.0516 | −0.665363 | ||||||||
\(447\) | −8.37190 | −0.395977 | ||||||||
\(448\) | 3.22153 | 0.152203 | ||||||||
\(449\) | −8.44176 | −0.398391 | −0.199196 | − | 0.979960i | \(-0.563833\pi\) | ||||
−0.199196 | + | 0.979960i | \(0.563833\pi\) | |||||||
\(450\) | −1.41297 | −0.0666081 | ||||||||
\(451\) | −20.3038 | −0.956070 | ||||||||
\(452\) | −9.93713 | −0.467403 | ||||||||
\(453\) | 17.7123 | 0.832197 | ||||||||
\(454\) | 4.38716 | 0.205899 | ||||||||
\(455\) | −8.18992 | −0.383949 | ||||||||
\(456\) | 10.2767 | 0.481249 | ||||||||
\(457\) | −29.4900 | −1.37949 | −0.689743 | − | 0.724055i | \(-0.742276\pi\) | ||||
−0.689743 | + | 0.724055i | \(0.742276\pi\) | |||||||
\(458\) | −13.3580 | −0.624180 | ||||||||
\(459\) | −4.12045 | −0.192326 | ||||||||
\(460\) | 0.280998 | 0.0131016 | ||||||||
\(461\) | 1.82175 | 0.0848474 | 0.0424237 | − | 0.999100i | \(-0.486492\pi\) | ||||
0.0424237 | + | 0.999100i | \(0.486492\pi\) | |||||||
\(462\) | 20.4506 | 0.951447 | ||||||||
\(463\) | −13.7778 | −0.640311 | −0.320155 | − | 0.947365i | \(-0.603735\pi\) | ||||
−0.320155 | + | 0.947365i | \(0.603735\pi\) | |||||||
\(464\) | 3.73498 | 0.173392 | ||||||||
\(465\) | 10.5368 | 0.488634 | ||||||||
\(466\) | −5.42645 | −0.251375 | ||||||||
\(467\) | 10.3059 | 0.476899 | 0.238449 | − | 0.971155i | \(-0.423361\pi\) | ||||
0.238449 | + | 0.971155i | \(0.423361\pi\) | |||||||
\(468\) | −3.59212 | −0.166046 | ||||||||
\(469\) | −21.8045 | −1.00684 | ||||||||
\(470\) | −6.34766 | −0.292796 | ||||||||
\(471\) | −27.2804 | −1.25701 | ||||||||
\(472\) | 5.26832 | 0.242494 | ||||||||
\(473\) | −47.5698 | −2.18726 | ||||||||
\(474\) | −5.52729 | −0.253877 | ||||||||
\(475\) | 8.15755 | 0.374294 | ||||||||
\(476\) | 2.38772 | 0.109441 | ||||||||
\(477\) | −0.354667 | −0.0162391 | ||||||||
\(478\) | −20.8299 | −0.952736 | ||||||||
\(479\) | 27.5806 | 1.26019 | 0.630096 | − | 0.776517i | \(-0.283016\pi\) | ||||
0.630096 | + | 0.776517i | \(0.283016\pi\) | |||||||
\(480\) | −1.25977 | −0.0575005 | ||||||||
\(481\) | −0.434372 | −0.0198057 | ||||||||
\(482\) | −19.7899 | −0.901405 | ||||||||
\(483\) | −1.14040 | −0.0518901 | ||||||||
\(484\) | 14.3923 | 0.654196 | ||||||||
\(485\) | 6.12982 | 0.278341 | ||||||||
\(486\) | 13.1953 | 0.598549 | ||||||||
\(487\) | −2.18416 | −0.0989737 | −0.0494869 | − | 0.998775i | \(-0.515759\pi\) | ||||
−0.0494869 | + | 0.998775i | \(0.515759\pi\) | |||||||
\(488\) | −3.17080 | −0.143535 | ||||||||
\(489\) | 23.4614 | 1.06096 | ||||||||
\(490\) | −3.37824 | −0.152613 | ||||||||
\(491\) | −16.1287 | −0.727878 | −0.363939 | − | 0.931423i | \(-0.618568\pi\) | ||||
−0.363939 | + | 0.931423i | \(0.618568\pi\) | |||||||
\(492\) | −5.07597 | −0.228842 | ||||||||
\(493\) | 2.76828 | 0.124677 | ||||||||
\(494\) | 20.7385 | 0.933069 | ||||||||
\(495\) | 7.12008 | 0.320024 | ||||||||
\(496\) | −8.36407 | −0.375558 | ||||||||
\(497\) | −16.4235 | −0.736694 | ||||||||
\(498\) | −3.22812 | −0.144655 | ||||||||
\(499\) | −19.7758 | −0.885288 | −0.442644 | − | 0.896697i | \(-0.645959\pi\) | ||||
−0.442644 | + | 0.896697i | \(0.645959\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −14.2765 | −0.637826 | ||||||||
\(502\) | 24.9665 | 1.11431 | ||||||||
\(503\) | −11.3213 | −0.504791 | −0.252395 | − | 0.967624i | \(-0.581218\pi\) | ||||
−0.252395 | + | 0.967624i | \(0.581218\pi\) | |||||||
\(504\) | −4.55193 | −0.202759 | ||||||||
\(505\) | −3.15971 | −0.140605 | ||||||||
\(506\) | −1.41597 | −0.0629477 | ||||||||
\(507\) | −8.23512 | −0.365734 | ||||||||
\(508\) | 6.10582 | 0.270902 | ||||||||
\(509\) | 19.3310 | 0.856832 | 0.428416 | − | 0.903582i | \(-0.359072\pi\) | ||||
0.428416 | + | 0.903582i | \(0.359072\pi\) | |||||||
\(510\) | −0.933714 | −0.0413455 | ||||||||
\(511\) | 38.8918 | 1.72047 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −45.3506 | −2.00228 | ||||||||
\(514\) | −26.5943 | −1.17303 | ||||||||
\(515\) | −12.8371 | −0.565669 | ||||||||
\(516\) | −11.8925 | −0.523537 | ||||||||
\(517\) | 31.9864 | 1.40676 | ||||||||
\(518\) | −0.550435 | −0.0241847 | ||||||||
\(519\) | 26.8905 | 1.18036 | ||||||||
\(520\) | −2.54225 | −0.111485 | ||||||||
\(521\) | −9.93862 | −0.435419 | −0.217709 | − | 0.976014i | \(-0.569859\pi\) | ||||
−0.217709 | + | 0.976014i | \(0.569859\pi\) | |||||||
\(522\) | −5.27743 | −0.230987 | ||||||||
\(523\) | −19.5256 | −0.853795 | −0.426897 | − | 0.904300i | \(-0.640393\pi\) | ||||
−0.426897 | + | 0.904300i | \(0.640393\pi\) | |||||||
\(524\) | 6.40845 | 0.279954 | ||||||||
\(525\) | 4.05839 | 0.177123 | ||||||||
\(526\) | 8.11125 | 0.353667 | ||||||||
\(527\) | −6.19925 | −0.270044 | ||||||||
\(528\) | 6.34810 | 0.276265 | ||||||||
\(529\) | −22.9210 | −0.996567 | ||||||||
\(530\) | −0.251008 | −0.0109031 | ||||||||
\(531\) | −7.44399 | −0.323042 | ||||||||
\(532\) | 26.2798 | 1.13937 | ||||||||
\(533\) | −10.2434 | −0.443691 | ||||||||
\(534\) | −16.8524 | −0.729275 | ||||||||
\(535\) | −10.6960 | −0.462428 | ||||||||
\(536\) | −6.76837 | −0.292349 | ||||||||
\(537\) | 17.0924 | 0.737590 | ||||||||
\(538\) | −5.04811 | −0.217640 | ||||||||
\(539\) | 17.0232 | 0.733242 | ||||||||
\(540\) | 5.55934 | 0.239236 | ||||||||
\(541\) | 40.1237 | 1.72505 | 0.862526 | − | 0.506013i | \(-0.168881\pi\) | ||||
0.862526 | + | 0.506013i | \(0.168881\pi\) | |||||||
\(542\) | 6.98247 | 0.299923 | ||||||||
\(543\) | 0.591050 | 0.0253644 | ||||||||
\(544\) | 0.741176 | 0.0317777 | ||||||||
\(545\) | 2.06372 | 0.0883999 | ||||||||
\(546\) | 10.3174 | 0.441545 | ||||||||
\(547\) | 6.56622 | 0.280751 | 0.140376 | − | 0.990098i | \(-0.455169\pi\) | ||||
0.140376 | + | 0.990098i | \(0.455169\pi\) | |||||||
\(548\) | −8.97013 | −0.383185 | ||||||||
\(549\) | 4.48025 | 0.191212 | ||||||||
\(550\) | 5.03908 | 0.214867 | ||||||||
\(551\) | 30.4683 | 1.29799 | ||||||||
\(552\) | −0.353994 | −0.0150670 | ||||||||
\(553\) | −14.1345 | −0.601062 | ||||||||
\(554\) | −3.01293 | −0.128007 | ||||||||
\(555\) | 0.215247 | 0.00913672 | ||||||||
\(556\) | 2.87367 | 0.121871 | ||||||||
\(557\) | −13.3385 | −0.565172 | −0.282586 | − | 0.959242i | \(-0.591192\pi\) | ||||
−0.282586 | + | 0.959242i | \(0.591192\pi\) | |||||||
\(558\) | 11.8182 | 0.500304 | ||||||||
\(559\) | −23.9992 | −1.01506 | ||||||||
\(560\) | −3.22153 | −0.136134 | ||||||||
\(561\) | 4.70506 | 0.198648 | ||||||||
\(562\) | −12.0243 | −0.507216 | ||||||||
\(563\) | 11.4169 | 0.481164 | 0.240582 | − | 0.970629i | \(-0.422662\pi\) | ||||
0.240582 | + | 0.970629i | \(0.422662\pi\) | |||||||
\(564\) | 7.99661 | 0.336718 | ||||||||
\(565\) | 9.93713 | 0.418058 | ||||||||
\(566\) | −31.6802 | −1.33162 | ||||||||
\(567\) | −8.90622 | −0.374026 | ||||||||
\(568\) | −5.09804 | −0.213909 | ||||||||
\(569\) | −45.6664 | −1.91443 | −0.957217 | − | 0.289371i | \(-0.906554\pi\) | ||||
−0.957217 | + | 0.289371i | \(0.906554\pi\) | |||||||
\(570\) | −10.2767 | −0.430442 | ||||||||
\(571\) | 21.5389 | 0.901374 | 0.450687 | − | 0.892682i | \(-0.351179\pi\) | ||||
0.450687 | + | 0.892682i | \(0.351179\pi\) | |||||||
\(572\) | 12.8106 | 0.535637 | ||||||||
\(573\) | 23.9379 | 1.00002 | ||||||||
\(574\) | −12.9804 | −0.541792 | ||||||||
\(575\) | −0.280998 | −0.0117184 | ||||||||
\(576\) | −1.41297 | −0.0588738 | ||||||||
\(577\) | 11.0320 | 0.459269 | 0.229634 | − | 0.973277i | \(-0.426247\pi\) | ||||
0.229634 | + | 0.973277i | \(0.426247\pi\) | |||||||
\(578\) | −16.4507 | −0.684257 | ||||||||
\(579\) | 29.3130 | 1.21820 | ||||||||
\(580\) | −3.73498 | −0.155087 | ||||||||
\(581\) | −8.25504 | −0.342477 | ||||||||
\(582\) | −7.72219 | −0.320095 | ||||||||
\(583\) | 1.26485 | 0.0523847 | ||||||||
\(584\) | 12.0725 | 0.499562 | ||||||||
\(585\) | 3.59212 | 0.148516 | ||||||||
\(586\) | 20.9078 | 0.863691 | ||||||||
\(587\) | 20.4254 | 0.843045 | 0.421523 | − | 0.906818i | \(-0.361496\pi\) | ||||
0.421523 | + | 0.906818i | \(0.361496\pi\) | |||||||
\(588\) | 4.25582 | 0.175507 | ||||||||
\(589\) | −68.2303 | −2.81138 | ||||||||
\(590\) | −5.26832 | −0.216893 | ||||||||
\(591\) | 4.29719 | 0.176763 | ||||||||
\(592\) | −0.170862 | −0.00702237 | ||||||||
\(593\) | 47.7316 | 1.96010 | 0.980052 | − | 0.198743i | \(-0.0636858\pi\) | ||||
0.980052 | + | 0.198743i | \(0.0636858\pi\) | |||||||
\(594\) | −28.0140 | −1.14943 | ||||||||
\(595\) | −2.38772 | −0.0978870 | ||||||||
\(596\) | −6.64556 | −0.272213 | ||||||||
\(597\) | −13.2859 | −0.543756 | ||||||||
\(598\) | −0.714367 | −0.0292126 | ||||||||
\(599\) | −24.1441 | −0.986500 | −0.493250 | − | 0.869888i | \(-0.664191\pi\) | ||||
−0.493250 | + | 0.869888i | \(0.664191\pi\) | |||||||
\(600\) | 1.25977 | 0.0514300 | ||||||||
\(601\) | −1.00000 | −0.0407909 | ||||||||
\(602\) | −30.4118 | −1.23949 | ||||||||
\(603\) | 9.56352 | 0.389457 | ||||||||
\(604\) | 14.0599 | 0.572090 | ||||||||
\(605\) | −14.3923 | −0.585131 | ||||||||
\(606\) | 3.98052 | 0.161698 | ||||||||
\(607\) | −24.6591 | −1.00088 | −0.500441 | − | 0.865770i | \(-0.666829\pi\) | ||||
−0.500441 | + | 0.865770i | \(0.666829\pi\) | |||||||
\(608\) | 8.15755 | 0.330832 | ||||||||
\(609\) | 15.1580 | 0.614234 | ||||||||
\(610\) | 3.17080 | 0.128382 | ||||||||
\(611\) | 16.1373 | 0.652846 | ||||||||
\(612\) | −1.04726 | −0.0423330 | ||||||||
\(613\) | −13.9250 | −0.562424 | −0.281212 | − | 0.959646i | \(-0.590736\pi\) | ||||
−0.281212 | + | 0.959646i | \(0.590736\pi\) | |||||||
\(614\) | −4.36711 | −0.176242 | ||||||||
\(615\) | 5.07597 | 0.204683 | ||||||||
\(616\) | 16.2335 | 0.654068 | ||||||||
\(617\) | 14.3924 | 0.579415 | 0.289707 | − | 0.957115i | \(-0.406442\pi\) | ||||
0.289707 | + | 0.957115i | \(0.406442\pi\) | |||||||
\(618\) | 16.1718 | 0.650525 | ||||||||
\(619\) | 15.0658 | 0.605545 | 0.302772 | − | 0.953063i | \(-0.402088\pi\) | ||||
0.302772 | + | 0.953063i | \(0.402088\pi\) | |||||||
\(620\) | 8.36407 | 0.335909 | ||||||||
\(621\) | 1.56217 | 0.0626876 | ||||||||
\(622\) | 16.7802 | 0.672823 | ||||||||
\(623\) | −43.0955 | −1.72658 | ||||||||
\(624\) | 3.20265 | 0.128209 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −14.3726 | −0.574445 | ||||||||
\(627\) | 51.7849 | 2.06809 | ||||||||
\(628\) | −21.6550 | −0.864128 | ||||||||
\(629\) | −0.126639 | −0.00504941 | ||||||||
\(630\) | 4.55193 | 0.181353 | ||||||||
\(631\) | −21.8634 | −0.870369 | −0.435185 | − | 0.900341i | \(-0.643317\pi\) | ||||
−0.435185 | + | 0.900341i | \(0.643317\pi\) | |||||||
\(632\) | −4.38753 | −0.174527 | ||||||||
\(633\) | 21.9221 | 0.871325 | ||||||||
\(634\) | 12.3187 | 0.489238 | ||||||||
\(635\) | −6.10582 | −0.242302 | ||||||||
\(636\) | 0.316213 | 0.0125387 | ||||||||
\(637\) | 8.58832 | 0.340282 | ||||||||
\(638\) | 18.8209 | 0.745126 | ||||||||
\(639\) | 7.20339 | 0.284962 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −38.5068 | −1.52093 | −0.760464 | − | 0.649380i | \(-0.775028\pi\) | ||||
−0.760464 | + | 0.649380i | \(0.775028\pi\) | |||||||
\(642\) | 13.4745 | 0.531797 | ||||||||
\(643\) | −33.2238 | −1.31022 | −0.655109 | − | 0.755535i | \(-0.727377\pi\) | ||||
−0.655109 | + | 0.755535i | \(0.727377\pi\) | |||||||
\(644\) | −0.905244 | −0.0356716 | ||||||||
\(645\) | 11.8925 | 0.468266 | ||||||||
\(646\) | 6.04618 | 0.237884 | ||||||||
\(647\) | −10.0734 | −0.396025 | −0.198012 | − | 0.980200i | \(-0.563449\pi\) | ||||
−0.198012 | + | 0.980200i | \(0.563449\pi\) | |||||||
\(648\) | −2.76459 | −0.108604 | ||||||||
\(649\) | 26.5475 | 1.04208 | ||||||||
\(650\) | 2.54225 | 0.0997151 | ||||||||
\(651\) | −33.9447 | −1.33040 | ||||||||
\(652\) | 18.6235 | 0.729354 | ||||||||
\(653\) | 3.57503 | 0.139902 | 0.0699509 | − | 0.997550i | \(-0.477716\pi\) | ||||
0.0699509 | + | 0.997550i | \(0.477716\pi\) | |||||||
\(654\) | −2.59981 | −0.101661 | ||||||||
\(655\) | −6.40845 | −0.250399 | ||||||||
\(656\) | −4.02927 | −0.157317 | ||||||||
\(657\) | −17.0581 | −0.665498 | ||||||||
\(658\) | 20.4492 | 0.797192 | ||||||||
\(659\) | −17.5839 | −0.684970 | −0.342485 | − | 0.939523i | \(-0.611269\pi\) | ||||
−0.342485 | + | 0.939523i | \(0.611269\pi\) | |||||||
\(660\) | −6.34810 | −0.247099 | ||||||||
\(661\) | −8.76137 | −0.340778 | −0.170389 | − | 0.985377i | \(-0.554502\pi\) | ||||
−0.170389 | + | 0.985377i | \(0.554502\pi\) | |||||||
\(662\) | 1.64904 | 0.0640916 | ||||||||
\(663\) | 2.37373 | 0.0921881 | ||||||||
\(664\) | −2.56246 | −0.0994427 | ||||||||
\(665\) | −26.2798 | −1.01909 | ||||||||
\(666\) | 0.241423 | 0.00935494 | ||||||||
\(667\) | −1.04952 | −0.0406377 | ||||||||
\(668\) | −11.3326 | −0.438471 | ||||||||
\(669\) | −17.7018 | −0.684392 | ||||||||
\(670\) | 6.76837 | 0.261485 | ||||||||
\(671\) | −15.9779 | −0.616820 | ||||||||
\(672\) | 4.05839 | 0.156556 | ||||||||
\(673\) | −29.2081 | −1.12589 | −0.562946 | − | 0.826494i | \(-0.690332\pi\) | ||||
−0.562946 | + | 0.826494i | \(0.690332\pi\) | |||||||
\(674\) | 1.70474 | 0.0656640 | ||||||||
\(675\) | −5.55934 | −0.213979 | ||||||||
\(676\) | −6.53699 | −0.251423 | ||||||||
\(677\) | 19.6789 | 0.756320 | 0.378160 | − | 0.925740i | \(-0.376557\pi\) | ||||
0.378160 | + | 0.925740i | \(0.376557\pi\) | |||||||
\(678\) | −12.5185 | −0.480771 | ||||||||
\(679\) | −19.7474 | −0.757836 | ||||||||
\(680\) | −0.741176 | −0.0284228 | ||||||||
\(681\) | 5.52682 | 0.211788 | ||||||||
\(682\) | −42.1472 | −1.61390 | ||||||||
\(683\) | 43.5775 | 1.66745 | 0.833723 | − | 0.552183i | \(-0.186205\pi\) | ||||
0.833723 | + | 0.552183i | \(0.186205\pi\) | |||||||
\(684\) | −11.5264 | −0.440723 | ||||||||
\(685\) | 8.97013 | 0.342731 | ||||||||
\(686\) | −11.6676 | −0.445471 | ||||||||
\(687\) | −16.8281 | −0.642032 | ||||||||
\(688\) | −9.44017 | −0.359903 | ||||||||
\(689\) | 0.638124 | 0.0243106 | ||||||||
\(690\) | 0.353994 | 0.0134763 | ||||||||
\(691\) | −24.1315 | −0.918004 | −0.459002 | − | 0.888435i | \(-0.651793\pi\) | ||||
−0.459002 | + | 0.888435i | \(0.651793\pi\) | |||||||
\(692\) | 21.3455 | 0.811433 | ||||||||
\(693\) | −22.9375 | −0.871325 | ||||||||
\(694\) | −19.5187 | −0.740919 | ||||||||
\(695\) | −2.87367 | −0.109004 | ||||||||
\(696\) | 4.70523 | 0.178351 | ||||||||
\(697\) | −2.98640 | −0.113118 | ||||||||
\(698\) | 1.38647 | 0.0524786 | ||||||||
\(699\) | −6.83609 | −0.258565 | ||||||||
\(700\) | 3.22153 | 0.121762 | ||||||||
\(701\) | −6.48035 | −0.244760 | −0.122380 | − | 0.992483i | \(-0.539053\pi\) | ||||
−0.122380 | + | 0.992483i | \(0.539053\pi\) | |||||||
\(702\) | −14.1332 | −0.533424 | ||||||||
\(703\) | −1.39381 | −0.0525686 | ||||||||
\(704\) | 5.03908 | 0.189917 | ||||||||
\(705\) | −7.99661 | −0.301170 | ||||||||
\(706\) | −16.9064 | −0.636280 | ||||||||
\(707\) | 10.1791 | 0.382825 | ||||||||
\(708\) | 6.63689 | 0.249430 | ||||||||
\(709\) | −36.3625 | −1.36562 | −0.682812 | − | 0.730594i | \(-0.739243\pi\) | ||||
−0.682812 | + | 0.730594i | \(0.739243\pi\) | |||||||
\(710\) | 5.09804 | 0.191326 | ||||||||
\(711\) | 6.19945 | 0.232498 | ||||||||
\(712\) | −13.3773 | −0.501337 | ||||||||
\(713\) | 2.35029 | 0.0880191 | ||||||||
\(714\) | 3.00799 | 0.112571 | ||||||||
\(715\) | −12.8106 | −0.479088 | ||||||||
\(716\) | 13.5678 | 0.507053 | ||||||||
\(717\) | −26.2409 | −0.979985 | ||||||||
\(718\) | 15.8749 | 0.592445 | ||||||||
\(719\) | −42.1623 | −1.57239 | −0.786195 | − | 0.617979i | \(-0.787952\pi\) | ||||
−0.786195 | + | 0.617979i | \(0.787952\pi\) | |||||||
\(720\) | 1.41297 | 0.0526584 | ||||||||
\(721\) | 41.3550 | 1.54014 | ||||||||
\(722\) | 47.5457 | 1.76947 | ||||||||
\(723\) | −24.9308 | −0.927185 | ||||||||
\(724\) | 0.469172 | 0.0174366 | ||||||||
\(725\) | 3.73498 | 0.138714 | ||||||||
\(726\) | 18.1311 | 0.672907 | ||||||||
\(727\) | 16.9022 | 0.626870 | 0.313435 | − | 0.949610i | \(-0.398520\pi\) | ||||
0.313435 | + | 0.949610i | \(0.398520\pi\) | |||||||
\(728\) | 8.18992 | 0.303538 | ||||||||
\(729\) | 24.9168 | 0.922845 | ||||||||
\(730\) | −12.0725 | −0.446822 | ||||||||
\(731\) | −6.99683 | −0.258787 | ||||||||
\(732\) | −3.99448 | −0.147640 | ||||||||
\(733\) | 39.0107 | 1.44089 | 0.720447 | − | 0.693510i | \(-0.243937\pi\) | ||||
0.720447 | + | 0.693510i | \(0.243937\pi\) | |||||||
\(734\) | −28.6903 | −1.05898 | ||||||||
\(735\) | −4.25582 | −0.156978 | ||||||||
\(736\) | −0.280998 | −0.0103577 | ||||||||
\(737\) | −34.1064 | −1.25632 | ||||||||
\(738\) | 5.69325 | 0.209571 | ||||||||
\(739\) | 12.1590 | 0.447277 | 0.223639 | − | 0.974672i | \(-0.428206\pi\) | ||||
0.223639 | + | 0.974672i | \(0.428206\pi\) | |||||||
\(740\) | 0.170862 | 0.00628100 | ||||||||
\(741\) | 26.1258 | 0.959756 | ||||||||
\(742\) | 0.808629 | 0.0296857 | ||||||||
\(743\) | 17.8692 | 0.655558 | 0.327779 | − | 0.944754i | \(-0.393700\pi\) | ||||
0.327779 | + | 0.944754i | \(0.393700\pi\) | |||||||
\(744\) | −10.5368 | −0.386299 | ||||||||
\(745\) | 6.64556 | 0.243475 | ||||||||
\(746\) | 7.28543 | 0.266739 | ||||||||
\(747\) | 3.62068 | 0.132474 | ||||||||
\(748\) | 3.73485 | 0.136560 | ||||||||
\(749\) | 34.4575 | 1.25905 | ||||||||
\(750\) | −1.25977 | −0.0460004 | ||||||||
\(751\) | 34.6934 | 1.26598 | 0.632990 | − | 0.774160i | \(-0.281827\pi\) | ||||
0.632990 | + | 0.774160i | \(0.281827\pi\) | |||||||
\(752\) | 6.34766 | 0.231475 | ||||||||
\(753\) | 31.4522 | 1.14618 | ||||||||
\(754\) | 9.49524 | 0.345796 | ||||||||
\(755\) | −14.0599 | −0.511693 | ||||||||
\(756\) | −17.9096 | −0.651365 | ||||||||
\(757\) | 16.6387 | 0.604744 | 0.302372 | − | 0.953190i | \(-0.402222\pi\) | ||||
0.302372 | + | 0.953190i | \(0.402222\pi\) | |||||||
\(758\) | −18.5808 | −0.674885 | ||||||||
\(759\) | −1.78381 | −0.0647480 | ||||||||
\(760\) | −8.15755 | −0.295906 | ||||||||
\(761\) | −11.7680 | −0.426589 | −0.213295 | − | 0.976988i | \(-0.568419\pi\) | ||||
−0.213295 | + | 0.976988i | \(0.568419\pi\) | |||||||
\(762\) | 7.69195 | 0.278650 | ||||||||
\(763\) | −6.64832 | −0.240685 | ||||||||
\(764\) | 19.0017 | 0.687458 | ||||||||
\(765\) | 1.04726 | 0.0378638 | ||||||||
\(766\) | 17.9746 | 0.649450 | ||||||||
\(767\) | 13.3934 | 0.483607 | ||||||||
\(768\) | 1.25977 | 0.0454581 | ||||||||
\(769\) | 15.7651 | 0.568505 | 0.284252 | − | 0.958750i | \(-0.408255\pi\) | ||||
0.284252 | + | 0.958750i | \(0.408255\pi\) | |||||||
\(770\) | −16.2335 | −0.585016 | ||||||||
\(771\) | −33.5028 | −1.20658 | ||||||||
\(772\) | 23.2684 | 0.837449 | ||||||||
\(773\) | 43.5857 | 1.56767 | 0.783834 | − | 0.620970i | \(-0.213261\pi\) | ||||
0.783834 | + | 0.620970i | \(0.213261\pi\) | |||||||
\(774\) | 13.3387 | 0.479450 | ||||||||
\(775\) | −8.36407 | −0.300446 | ||||||||
\(776\) | −6.12982 | −0.220048 | ||||||||
\(777\) | −0.693424 | −0.0248764 | ||||||||
\(778\) | −19.5925 | −0.702426 | ||||||||
\(779\) | −32.8690 | −1.17765 | ||||||||
\(780\) | −3.20265 | −0.114673 | ||||||||
\(781\) | −25.6894 | −0.919240 | ||||||||
\(782\) | −0.208269 | −0.00744770 | ||||||||
\(783\) | −20.7640 | −0.742047 | ||||||||
\(784\) | 3.37824 | 0.120651 | ||||||||
\(785\) | 21.6550 | 0.772900 | ||||||||
\(786\) | 8.07319 | 0.287961 | ||||||||
\(787\) | 1.37031 | 0.0488462 | 0.0244231 | − | 0.999702i | \(-0.492225\pi\) | ||||
0.0244231 | + | 0.999702i | \(0.492225\pi\) | |||||||
\(788\) | 3.41108 | 0.121515 | ||||||||
\(789\) | 10.2183 | 0.363782 | ||||||||
\(790\) | 4.38753 | 0.156101 | ||||||||
\(791\) | −32.0127 | −1.13824 | ||||||||
\(792\) | −7.12008 | −0.253001 | ||||||||
\(793\) | −8.06094 | −0.286253 | ||||||||
\(794\) | −5.94922 | −0.211130 | ||||||||
\(795\) | −0.316213 | −0.0112149 | ||||||||
\(796\) | −10.5463 | −0.373803 | ||||||||
\(797\) | −25.8089 | −0.914199 | −0.457099 | − | 0.889416i | \(-0.651112\pi\) | ||||
−0.457099 | + | 0.889416i | \(0.651112\pi\) | |||||||
\(798\) | 33.1066 | 1.17196 | ||||||||
\(799\) | 4.70474 | 0.166442 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 18.9018 | 0.667862 | ||||||||
\(802\) | −12.8074 | −0.452244 | ||||||||
\(803\) | 60.8341 | 2.14679 | ||||||||
\(804\) | −8.52661 | −0.300710 | ||||||||
\(805\) | 0.905244 | 0.0319057 | ||||||||
\(806\) | −21.2635 | −0.748975 | ||||||||
\(807\) | −6.35948 | −0.223864 | ||||||||
\(808\) | 3.15971 | 0.111158 | ||||||||
\(809\) | 24.4027 | 0.857954 | 0.428977 | − | 0.903315i | \(-0.358874\pi\) | ||||
0.428977 | + | 0.903315i | \(0.358874\pi\) | |||||||
\(810\) | 2.76459 | 0.0971379 | ||||||||
\(811\) | −36.2526 | −1.27300 | −0.636501 | − | 0.771276i | \(-0.719619\pi\) | ||||
−0.636501 | + | 0.771276i | \(0.719619\pi\) | |||||||
\(812\) | 12.0324 | 0.422253 | ||||||||
\(813\) | 8.79633 | 0.308501 | ||||||||
\(814\) | −0.860985 | −0.0301775 | ||||||||
\(815\) | −18.6235 | −0.652354 | ||||||||
\(816\) | 0.933714 | 0.0326865 | ||||||||
\(817\) | −77.0087 | −2.69419 | ||||||||
\(818\) | −4.36148 | −0.152496 | ||||||||
\(819\) | −11.5721 | −0.404363 | ||||||||
\(820\) | 4.02927 | 0.140708 | ||||||||
\(821\) | −23.2190 | −0.810348 | −0.405174 | − | 0.914240i | \(-0.632789\pi\) | ||||
−0.405174 | + | 0.914240i | \(0.632789\pi\) | |||||||
\(822\) | −11.3003 | −0.394144 | ||||||||
\(823\) | 39.9434 | 1.39234 | 0.696171 | − | 0.717876i | \(-0.254886\pi\) | ||||
0.696171 | + | 0.717876i | \(0.254886\pi\) | |||||||
\(824\) | 12.8371 | 0.447200 | ||||||||
\(825\) | 6.34810 | 0.221012 | ||||||||
\(826\) | 16.9720 | 0.590533 | ||||||||
\(827\) | −5.54040 | −0.192659 | −0.0963293 | − | 0.995350i | \(-0.530710\pi\) | ||||
−0.0963293 | + | 0.995350i | \(0.530710\pi\) | |||||||
\(828\) | 0.397043 | 0.0137982 | ||||||||
\(829\) | 18.3189 | 0.636241 | 0.318120 | − | 0.948050i | \(-0.396948\pi\) | ||||
0.318120 | + | 0.948050i | \(0.396948\pi\) | |||||||
\(830\) | 2.56246 | 0.0889443 | ||||||||
\(831\) | −3.79561 | −0.131668 | ||||||||
\(832\) | 2.54225 | 0.0881365 | ||||||||
\(833\) | 2.50387 | 0.0867540 | ||||||||
\(834\) | 3.62017 | 0.125356 | ||||||||
\(835\) | 11.3326 | 0.392180 | ||||||||
\(836\) | 41.1066 | 1.42170 | ||||||||
\(837\) | 46.4987 | 1.60723 | ||||||||
\(838\) | 35.4723 | 1.22537 | ||||||||
\(839\) | −18.5585 | −0.640710 | −0.320355 | − | 0.947298i | \(-0.603802\pi\) | ||||
−0.320355 | + | 0.947298i | \(0.603802\pi\) | |||||||
\(840\) | −4.05839 | −0.140028 | ||||||||
\(841\) | −15.0499 | −0.518962 | ||||||||
\(842\) | 25.0881 | 0.864592 | ||||||||
\(843\) | −15.1479 | −0.521722 | ||||||||
\(844\) | 17.4016 | 0.598988 | ||||||||
\(845\) | 6.53699 | 0.224879 | ||||||||
\(846\) | −8.96907 | −0.308363 | ||||||||
\(847\) | 46.3653 | 1.59313 | ||||||||
\(848\) | 0.251008 | 0.00861964 | ||||||||
\(849\) | −39.9099 | −1.36970 | ||||||||
\(850\) | 0.741176 | 0.0254221 | ||||||||
\(851\) | 0.0480118 | 0.00164582 | ||||||||
\(852\) | −6.42237 | −0.220027 | ||||||||
\(853\) | 23.7844 | 0.814363 | 0.407182 | − | 0.913347i | \(-0.366512\pi\) | ||||
0.407182 | + | 0.913347i | \(0.366512\pi\) | |||||||
\(854\) | −10.2148 | −0.349544 | ||||||||
\(855\) | 11.5264 | 0.394194 | ||||||||
\(856\) | 10.6960 | 0.365582 | ||||||||
\(857\) | 45.5725 | 1.55673 | 0.778363 | − | 0.627814i | \(-0.216050\pi\) | ||||
0.778363 | + | 0.627814i | \(0.216050\pi\) | |||||||
\(858\) | 16.1384 | 0.550957 | ||||||||
\(859\) | 9.42055 | 0.321425 | 0.160712 | − | 0.987001i | \(-0.448621\pi\) | ||||
0.160712 | + | 0.987001i | \(0.448621\pi\) | |||||||
\(860\) | 9.44017 | 0.321907 | ||||||||
\(861\) | −16.3524 | −0.557287 | ||||||||
\(862\) | −13.4052 | −0.456584 | ||||||||
\(863\) | −27.4099 | −0.933044 | −0.466522 | − | 0.884510i | \(-0.654493\pi\) | ||||
−0.466522 | + | 0.884510i | \(0.654493\pi\) | |||||||
\(864\) | −5.55934 | −0.189133 | ||||||||
\(865\) | −21.3455 | −0.725768 | ||||||||
\(866\) | −26.3427 | −0.895163 | ||||||||
\(867\) | −20.7241 | −0.703827 | ||||||||
\(868\) | −26.9451 | −0.914576 | ||||||||
\(869\) | −22.1091 | −0.750000 | ||||||||
\(870\) | −4.70523 | −0.159522 | ||||||||
\(871\) | −17.2069 | −0.583033 | ||||||||
\(872\) | −2.06372 | −0.0698862 | ||||||||
\(873\) | 8.66127 | 0.293140 | ||||||||
\(874\) | −2.29226 | −0.0775368 | ||||||||
\(875\) | −3.22153 | −0.108908 | ||||||||
\(876\) | 15.2086 | 0.513850 | ||||||||
\(877\) | −17.0285 | −0.575011 | −0.287506 | − | 0.957779i | \(-0.592826\pi\) | ||||
−0.287506 | + | 0.957779i | \(0.592826\pi\) | |||||||
\(878\) | 5.64346 | 0.190457 | ||||||||
\(879\) | 26.3390 | 0.888393 | ||||||||
\(880\) | −5.03908 | −0.169867 | ||||||||
\(881\) | 17.1326 | 0.577213 | 0.288607 | − | 0.957448i | \(-0.406808\pi\) | ||||
0.288607 | + | 0.957448i | \(0.406808\pi\) | |||||||
\(882\) | −4.77336 | −0.160727 | ||||||||
\(883\) | 19.3023 | 0.649573 | 0.324786 | − | 0.945787i | \(-0.394708\pi\) | ||||
0.324786 | + | 0.945787i | \(0.394708\pi\) | |||||||
\(884\) | 1.88425 | 0.0633743 | ||||||||
\(885\) | −6.63689 | −0.223097 | ||||||||
\(886\) | 3.44605 | 0.115772 | ||||||||
\(887\) | −5.32017 | −0.178634 | −0.0893168 | − | 0.996003i | \(-0.528468\pi\) | ||||
−0.0893168 | + | 0.996003i | \(0.528468\pi\) | |||||||
\(888\) | −0.215247 | −0.00722321 | ||||||||
\(889\) | 19.6701 | 0.659713 | ||||||||
\(890\) | 13.3773 | 0.448409 | ||||||||
\(891\) | −13.9310 | −0.466706 | ||||||||
\(892\) | −14.0516 | −0.470483 | ||||||||
\(893\) | 51.7814 | 1.73280 | ||||||||
\(894\) | −8.37190 | −0.279998 | ||||||||
\(895\) | −13.5678 | −0.453522 | ||||||||
\(896\) | 3.22153 | 0.107624 | ||||||||
\(897\) | −0.899941 | −0.0300481 | ||||||||
\(898\) | −8.44176 | −0.281705 | ||||||||
\(899\) | −31.2396 | −1.04190 | ||||||||
\(900\) | −1.41297 | −0.0470991 | ||||||||
\(901\) | 0.186041 | 0.00619793 | ||||||||
\(902\) | −20.3038 | −0.676043 | ||||||||
\(903\) | −38.3119 | −1.27494 | ||||||||
\(904\) | −9.93713 | −0.330504 | ||||||||
\(905\) | −0.469172 | −0.0155958 | ||||||||
\(906\) | 17.7123 | 0.588452 | ||||||||
\(907\) | 27.5062 | 0.913328 | 0.456664 | − | 0.889639i | \(-0.349044\pi\) | ||||
0.456664 | + | 0.889639i | \(0.349044\pi\) | |||||||
\(908\) | 4.38716 | 0.145593 | ||||||||
\(909\) | −4.46459 | −0.148081 | ||||||||
\(910\) | −8.18992 | −0.271493 | ||||||||
\(911\) | −15.0129 | −0.497400 | −0.248700 | − | 0.968581i | \(-0.580003\pi\) | ||||
−0.248700 | + | 0.968581i | \(0.580003\pi\) | |||||||
\(912\) | 10.2767 | 0.340294 | ||||||||
\(913\) | −12.9124 | −0.427339 | ||||||||
\(914\) | −29.4900 | −0.975444 | ||||||||
\(915\) | 3.99448 | 0.132054 | ||||||||
\(916\) | −13.3580 | −0.441362 | ||||||||
\(917\) | 20.6450 | 0.681757 | ||||||||
\(918\) | −4.12045 | −0.135995 | ||||||||
\(919\) | −22.2628 | −0.734382 | −0.367191 | − | 0.930146i | \(-0.619681\pi\) | ||||
−0.367191 | + | 0.930146i | \(0.619681\pi\) | |||||||
\(920\) | 0.280998 | 0.00926424 | ||||||||
\(921\) | −5.50156 | −0.181283 | ||||||||
\(922\) | 1.82175 | 0.0599962 | ||||||||
\(923\) | −12.9605 | −0.426599 | ||||||||
\(924\) | 20.4506 | 0.672774 | ||||||||
\(925\) | −0.170862 | −0.00561790 | ||||||||
\(926\) | −13.7778 | −0.452768 | ||||||||
\(927\) | −18.1384 | −0.595744 | ||||||||
\(928\) | 3.73498 | 0.122607 | ||||||||
\(929\) | 16.3123 | 0.535190 | 0.267595 | − | 0.963531i | \(-0.413771\pi\) | ||||
0.267595 | + | 0.963531i | \(0.413771\pi\) | |||||||
\(930\) | 10.5368 | 0.345516 | ||||||||
\(931\) | 27.5582 | 0.903183 | ||||||||
\(932\) | −5.42645 | −0.177749 | ||||||||
\(933\) | 21.1392 | 0.692066 | ||||||||
\(934\) | 10.3059 | 0.337218 | ||||||||
\(935\) | −3.73485 | −0.122143 | ||||||||
\(936\) | −3.59212 | −0.117412 | ||||||||
\(937\) | −46.7438 | −1.52705 | −0.763527 | − | 0.645776i | \(-0.776534\pi\) | ||||
−0.763527 | + | 0.645776i | \(0.776534\pi\) | |||||||
\(938\) | −21.8045 | −0.711942 | ||||||||
\(939\) | −18.1062 | −0.590874 | ||||||||
\(940\) | −6.34766 | −0.207038 | ||||||||
\(941\) | −41.4625 | −1.35164 | −0.675820 | − | 0.737067i | \(-0.736210\pi\) | ||||
−0.675820 | + | 0.737067i | \(0.736210\pi\) | |||||||
\(942\) | −27.2804 | −0.888843 | ||||||||
\(943\) | 1.13222 | 0.0368701 | ||||||||
\(944\) | 5.26832 | 0.171469 | ||||||||
\(945\) | 17.9096 | 0.582599 | ||||||||
\(946\) | −47.5698 | −1.54663 | ||||||||
\(947\) | 9.45305 | 0.307183 | 0.153591 | − | 0.988134i | \(-0.450916\pi\) | ||||
0.153591 | + | 0.988134i | \(0.450916\pi\) | |||||||
\(948\) | −5.52729 | −0.179518 | ||||||||
\(949\) | 30.6912 | 0.996278 | ||||||||
\(950\) | 8.15755 | 0.264666 | ||||||||
\(951\) | 15.5188 | 0.503231 | ||||||||
\(952\) | 2.38772 | 0.0773865 | ||||||||
\(953\) | −11.9182 | −0.386068 | −0.193034 | − | 0.981192i | \(-0.561833\pi\) | ||||
−0.193034 | + | 0.981192i | \(0.561833\pi\) | |||||||
\(954\) | −0.354667 | −0.0114828 | ||||||||
\(955\) | −19.0017 | −0.614881 | ||||||||
\(956\) | −20.8299 | −0.673686 | ||||||||
\(957\) | 23.7100 | 0.766436 | ||||||||
\(958\) | 27.5806 | 0.891090 | ||||||||
\(959\) | −28.8975 | −0.933149 | ||||||||
\(960\) | −1.25977 | −0.0406590 | ||||||||
\(961\) | 38.9576 | 1.25670 | ||||||||
\(962\) | −0.434372 | −0.0140047 | ||||||||
\(963\) | −15.1131 | −0.487014 | ||||||||
\(964\) | −19.7899 | −0.637390 | ||||||||
\(965\) | −23.2684 | −0.749038 | ||||||||
\(966\) | −1.14040 | −0.0366918 | ||||||||
\(967\) | −5.09622 | −0.163883 | −0.0819417 | − | 0.996637i | \(-0.526112\pi\) | ||||
−0.0819417 | + | 0.996637i | \(0.526112\pi\) | |||||||
\(968\) | 14.3923 | 0.462587 | ||||||||
\(969\) | 7.61682 | 0.244688 | ||||||||
\(970\) | 6.12982 | 0.196817 | ||||||||
\(971\) | 26.0599 | 0.836301 | 0.418151 | − | 0.908378i | \(-0.362678\pi\) | ||||
0.418151 | + | 0.908378i | \(0.362678\pi\) | |||||||
\(972\) | 13.1953 | 0.423238 | ||||||||
\(973\) | 9.25759 | 0.296785 | ||||||||
\(974\) | −2.18416 | −0.0699850 | ||||||||
\(975\) | 3.20265 | 0.102567 | ||||||||
\(976\) | −3.17080 | −0.101495 | ||||||||
\(977\) | −49.9058 | −1.59663 | −0.798313 | − | 0.602242i | \(-0.794274\pi\) | ||||
−0.798313 | + | 0.602242i | \(0.794274\pi\) | |||||||
\(978\) | 23.4614 | 0.750214 | ||||||||
\(979\) | −67.4095 | −2.15442 | ||||||||
\(980\) | −3.37824 | −0.107914 | ||||||||
\(981\) | 2.91597 | 0.0930998 | ||||||||
\(982\) | −16.1287 | −0.514687 | ||||||||
\(983\) | 38.7628 | 1.23634 | 0.618170 | − | 0.786044i | \(-0.287874\pi\) | ||||
0.618170 | + | 0.786044i | \(0.287874\pi\) | |||||||
\(984\) | −5.07597 | −0.161816 | ||||||||
\(985\) | −3.41108 | −0.108686 | ||||||||
\(986\) | 2.76828 | 0.0881600 | ||||||||
\(987\) | 25.7613 | 0.819992 | ||||||||
\(988\) | 20.7385 | 0.659780 | ||||||||
\(989\) | 2.65267 | 0.0843501 | ||||||||
\(990\) | 7.12008 | 0.226291 | ||||||||
\(991\) | −21.6649 | −0.688207 | −0.344104 | − | 0.938932i | \(-0.611817\pi\) | ||||
−0.344104 | + | 0.938932i | \(0.611817\pi\) | |||||||
\(992\) | −8.36407 | −0.265559 | ||||||||
\(993\) | 2.07741 | 0.0659247 | ||||||||
\(994\) | −16.4235 | −0.520921 | ||||||||
\(995\) | 10.5463 | 0.334339 | ||||||||
\(996\) | −3.22812 | −0.102287 | ||||||||
\(997\) | −46.0481 | −1.45836 | −0.729179 | − | 0.684323i | \(-0.760098\pi\) | ||||
−0.729179 | + | 0.684323i | \(0.760098\pi\) | |||||||
\(998\) | −19.7758 | −0.625993 | ||||||||
\(999\) | 0.949878 | 0.0300528 |
(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 | 6010.2.a.h.1.19 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6010.2.a.h.1.19 | ✓ | 28 | 1.1 | even | 1 | trivial |