Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.78055 | −1.96615 | −0.983073 | − | 0.183213i | \(-0.941350\pi\) | ||||
−0.983073 | + | 0.183213i | \(0.941350\pi\) | |||||||
\(3\) | 0.298033 | 0.172070 | 0.0860348 | − | 0.996292i | \(-0.472580\pi\) | ||||
0.0860348 | + | 0.996292i | \(0.472580\pi\) | |||||||
\(4\) | 5.73146 | 2.86573 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −0.828697 | −0.338314 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −10.3755 | −3.66830 | ||||||||
\(9\) | −2.91118 | −0.970392 | ||||||||
\(10\) | 2.78055 | 0.879287 | ||||||||
\(11\) | 1.93021 | 0.581979 | 0.290990 | − | 0.956726i | \(-0.406015\pi\) | ||||
0.290990 | + | 0.956726i | \(0.406015\pi\) | |||||||
\(12\) | 1.70817 | 0.493105 | ||||||||
\(13\) | 0.800858 | 0.222118 | 0.111059 | − | 0.993814i | \(-0.464576\pi\) | ||||
0.111059 | + | 0.993814i | \(0.464576\pi\) | |||||||
\(14\) | 2.78055 | 0.743133 | ||||||||
\(15\) | −0.298033 | −0.0769519 | ||||||||
\(16\) | 17.3867 | 4.34668 | ||||||||
\(17\) | 0.984021 | 0.238660 | 0.119330 | − | 0.992855i | \(-0.461925\pi\) | ||||
0.119330 | + | 0.992855i | \(0.461925\pi\) | |||||||
\(18\) | 8.09467 | 1.90793 | ||||||||
\(19\) | −7.86576 | −1.80453 | −0.902264 | − | 0.431183i | \(-0.858096\pi\) | ||||
−0.902264 | + | 0.431183i | \(0.858096\pi\) | |||||||
\(20\) | −5.73146 | −1.28159 | ||||||||
\(21\) | −0.298033 | −0.0650362 | ||||||||
\(22\) | −5.36704 | −1.14426 | ||||||||
\(23\) | 3.94812 | 0.823239 | 0.411620 | − | 0.911356i | \(-0.364963\pi\) | ||||
0.411620 | + | 0.911356i | \(0.364963\pi\) | |||||||
\(24\) | −3.09225 | −0.631203 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.22683 | −0.436717 | ||||||||
\(27\) | −1.76173 | −0.339045 | ||||||||
\(28\) | −5.73146 | −1.08314 | ||||||||
\(29\) | −9.46879 | −1.75831 | −0.879155 | − | 0.476535i | \(-0.841892\pi\) | ||||
−0.879155 | + | 0.476535i | \(0.841892\pi\) | |||||||
\(30\) | 0.828697 | 0.151299 | ||||||||
\(31\) | −2.41133 | −0.433088 | −0.216544 | − | 0.976273i | \(-0.569478\pi\) | ||||
−0.216544 | + | 0.976273i | \(0.569478\pi\) | |||||||
\(32\) | −27.5937 | −4.87792 | ||||||||
\(33\) | 0.575266 | 0.100141 | ||||||||
\(34\) | −2.73612 | −0.469241 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −16.6853 | −2.78088 | ||||||||
\(37\) | 9.35326 | 1.53767 | 0.768833 | − | 0.639449i | \(-0.220838\pi\) | ||||
0.768833 | + | 0.639449i | \(0.220838\pi\) | |||||||
\(38\) | 21.8711 | 3.54797 | ||||||||
\(39\) | 0.238682 | 0.0382198 | ||||||||
\(40\) | 10.3755 | 1.64051 | ||||||||
\(41\) | −4.16333 | −0.650203 | −0.325102 | − | 0.945679i | \(-0.605398\pi\) | ||||
−0.325102 | + | 0.945679i | \(0.605398\pi\) | |||||||
\(42\) | 0.828697 | 0.127871 | ||||||||
\(43\) | −6.96297 | −1.06184 | −0.530922 | − | 0.847421i | \(-0.678154\pi\) | ||||
−0.530922 | + | 0.847421i | \(0.678154\pi\) | |||||||
\(44\) | 11.0629 | 1.66780 | ||||||||
\(45\) | 2.91118 | 0.433973 | ||||||||
\(46\) | −10.9779 | −1.61861 | ||||||||
\(47\) | −8.50129 | −1.24004 | −0.620020 | − | 0.784586i | \(-0.712876\pi\) | ||||
−0.620020 | + | 0.784586i | \(0.712876\pi\) | |||||||
\(48\) | 5.18183 | 0.747933 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.78055 | −0.393229 | ||||||||
\(51\) | 0.293271 | 0.0410662 | ||||||||
\(52\) | 4.59009 | 0.636531 | ||||||||
\(53\) | 5.63325 | 0.773786 | 0.386893 | − | 0.922125i | \(-0.373548\pi\) | ||||
0.386893 | + | 0.922125i | \(0.373548\pi\) | |||||||
\(54\) | 4.89857 | 0.666612 | ||||||||
\(55\) | −1.93021 | −0.260269 | ||||||||
\(56\) | 10.3755 | 1.38649 | ||||||||
\(57\) | −2.34426 | −0.310505 | ||||||||
\(58\) | 26.3285 | 3.45710 | ||||||||
\(59\) | 1.48487 | 0.193313 | 0.0966567 | − | 0.995318i | \(-0.469185\pi\) | ||||
0.0966567 | + | 0.995318i | \(0.469185\pi\) | |||||||
\(60\) | −1.70817 | −0.220523 | ||||||||
\(61\) | 8.07188 | 1.03350 | 0.516749 | − | 0.856137i | \(-0.327142\pi\) | ||||
0.516749 | + | 0.856137i | \(0.327142\pi\) | |||||||
\(62\) | 6.70483 | 0.851514 | ||||||||
\(63\) | 2.91118 | 0.366774 | ||||||||
\(64\) | 41.9521 | 5.24401 | ||||||||
\(65\) | −0.800858 | −0.0993342 | ||||||||
\(66\) | −1.59956 | −0.196892 | ||||||||
\(67\) | −13.2763 | −1.62196 | −0.810982 | − | 0.585071i | \(-0.801066\pi\) | ||||
−0.810982 | + | 0.585071i | \(0.801066\pi\) | |||||||
\(68\) | 5.63988 | 0.683936 | ||||||||
\(69\) | 1.17667 | 0.141655 | ||||||||
\(70\) | −2.78055 | −0.332339 | ||||||||
\(71\) | −3.56191 | −0.422720 | −0.211360 | − | 0.977408i | \(-0.567789\pi\) | ||||
−0.211360 | + | 0.977408i | \(0.567789\pi\) | |||||||
\(72\) | 30.2050 | 3.55969 | ||||||||
\(73\) | 13.7107 | 1.60471 | 0.802357 | − | 0.596844i | \(-0.203579\pi\) | ||||
0.802357 | + | 0.596844i | \(0.203579\pi\) | |||||||
\(74\) | −26.0072 | −3.02328 | ||||||||
\(75\) | 0.298033 | 0.0344139 | ||||||||
\(76\) | −45.0823 | −5.17130 | ||||||||
\(77\) | −1.93021 | −0.219968 | ||||||||
\(78\) | −0.663669 | −0.0751457 | ||||||||
\(79\) | −4.47244 | −0.503189 | −0.251594 | − | 0.967833i | \(-0.580955\pi\) | ||||
−0.251594 | + | 0.967833i | \(0.580955\pi\) | |||||||
\(80\) | −17.3867 | −1.94390 | ||||||||
\(81\) | 8.20847 | 0.912053 | ||||||||
\(82\) | 11.5764 | 1.27839 | ||||||||
\(83\) | −7.65176 | −0.839890 | −0.419945 | − | 0.907549i | \(-0.637951\pi\) | ||||
−0.419945 | + | 0.907549i | \(0.637951\pi\) | |||||||
\(84\) | −1.70817 | −0.186376 | ||||||||
\(85\) | −0.984021 | −0.106732 | ||||||||
\(86\) | 19.3609 | 2.08774 | ||||||||
\(87\) | −2.82202 | −0.302552 | ||||||||
\(88\) | −20.0269 | −2.13488 | ||||||||
\(89\) | 5.62676 | 0.596436 | 0.298218 | − | 0.954498i | \(-0.403608\pi\) | ||||
0.298218 | + | 0.954498i | \(0.403608\pi\) | |||||||
\(90\) | −8.09467 | −0.853253 | ||||||||
\(91\) | −0.800858 | −0.0839527 | ||||||||
\(92\) | 22.6285 | 2.35918 | ||||||||
\(93\) | −0.718657 | −0.0745213 | ||||||||
\(94\) | 23.6383 | 2.43810 | ||||||||
\(95\) | 7.86576 | 0.807010 | ||||||||
\(96\) | −8.22384 | −0.839342 | ||||||||
\(97\) | 18.7585 | 1.90464 | 0.952319 | − | 0.305104i | \(-0.0986913\pi\) | ||||
0.952319 | + | 0.305104i | \(0.0986913\pi\) | |||||||
\(98\) | −2.78055 | −0.280878 | ||||||||
\(99\) | −5.61917 | −0.564748 | ||||||||
\(100\) | 5.73146 | 0.573146 | ||||||||
\(101\) | −15.0894 | −1.50145 | −0.750724 | − | 0.660616i | \(-0.770295\pi\) | ||||
−0.750724 | + | 0.660616i | \(0.770295\pi\) | |||||||
\(102\) | −0.815455 | −0.0807421 | ||||||||
\(103\) | 3.53153 | 0.347972 | 0.173986 | − | 0.984748i | \(-0.444335\pi\) | ||||
0.173986 | + | 0.984748i | \(0.444335\pi\) | |||||||
\(104\) | −8.30932 | −0.814796 | ||||||||
\(105\) | 0.298033 | 0.0290851 | ||||||||
\(106\) | −15.6635 | −1.52138 | ||||||||
\(107\) | −19.6309 | −1.89779 | −0.948894 | − | 0.315595i | \(-0.897796\pi\) | ||||
−0.948894 | + | 0.315595i | \(0.897796\pi\) | |||||||
\(108\) | −10.0973 | −0.971611 | ||||||||
\(109\) | 1.25448 | 0.120157 | 0.0600787 | − | 0.998194i | \(-0.480865\pi\) | ||||
0.0600787 | + | 0.998194i | \(0.480865\pi\) | |||||||
\(110\) | 5.36704 | 0.511727 | ||||||||
\(111\) | 2.78758 | 0.264586 | ||||||||
\(112\) | −17.3867 | −1.64289 | ||||||||
\(113\) | −5.15218 | −0.484676 | −0.242338 | − | 0.970192i | \(-0.577914\pi\) | ||||
−0.242338 | + | 0.970192i | \(0.577914\pi\) | |||||||
\(114\) | 6.51833 | 0.610498 | ||||||||
\(115\) | −3.94812 | −0.368164 | ||||||||
\(116\) | −54.2700 | −5.03885 | ||||||||
\(117\) | −2.33144 | −0.215542 | ||||||||
\(118\) | −4.12875 | −0.380082 | ||||||||
\(119\) | −0.984021 | −0.0902050 | ||||||||
\(120\) | 3.09225 | 0.282283 | ||||||||
\(121\) | −7.27430 | −0.661300 | ||||||||
\(122\) | −22.4443 | −2.03201 | ||||||||
\(123\) | −1.24081 | −0.111880 | ||||||||
\(124\) | −13.8204 | −1.24111 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −8.09467 | −0.721131 | ||||||||
\(127\) | 14.0867 | 1.24999 | 0.624995 | − | 0.780629i | \(-0.285101\pi\) | ||||
0.624995 | + | 0.780629i | \(0.285101\pi\) | |||||||
\(128\) | −61.4626 | −5.43258 | ||||||||
\(129\) | −2.07520 | −0.182711 | ||||||||
\(130\) | 2.22683 | 0.195306 | ||||||||
\(131\) | −19.8616 | −1.73532 | −0.867660 | − | 0.497158i | \(-0.834377\pi\) | ||||
−0.867660 | + | 0.497158i | \(0.834377\pi\) | |||||||
\(132\) | 3.29712 | 0.286977 | ||||||||
\(133\) | 7.86576 | 0.682048 | ||||||||
\(134\) | 36.9155 | 3.18902 | ||||||||
\(135\) | 1.76173 | 0.151625 | ||||||||
\(136\) | −10.2097 | −0.875477 | ||||||||
\(137\) | 14.7868 | 1.26332 | 0.631662 | − | 0.775244i | \(-0.282373\pi\) | ||||
0.631662 | + | 0.775244i | \(0.282373\pi\) | |||||||
\(138\) | −3.27179 | −0.278514 | ||||||||
\(139\) | −21.9510 | −1.86186 | −0.930931 | − | 0.365196i | \(-0.881002\pi\) | ||||
−0.930931 | + | 0.365196i | \(0.881002\pi\) | |||||||
\(140\) | 5.73146 | 0.484397 | ||||||||
\(141\) | −2.53367 | −0.213373 | ||||||||
\(142\) | 9.90406 | 0.831130 | ||||||||
\(143\) | 1.54582 | 0.129268 | ||||||||
\(144\) | −50.6159 | −4.21799 | ||||||||
\(145\) | 9.46879 | 0.786341 | ||||||||
\(146\) | −38.1233 | −3.15510 | ||||||||
\(147\) | 0.298033 | 0.0245814 | ||||||||
\(148\) | 53.6079 | 4.40654 | ||||||||
\(149\) | 13.3356 | 1.09250 | 0.546249 | − | 0.837623i | \(-0.316055\pi\) | ||||
0.546249 | + | 0.837623i | \(0.316055\pi\) | |||||||
\(150\) | −0.828697 | −0.0676628 | ||||||||
\(151\) | −1.52962 | −0.124479 | −0.0622395 | − | 0.998061i | \(-0.519824\pi\) | ||||
−0.0622395 | + | 0.998061i | \(0.519824\pi\) | |||||||
\(152\) | 81.6114 | 6.61955 | ||||||||
\(153\) | −2.86466 | −0.231594 | ||||||||
\(154\) | 5.36704 | 0.432488 | ||||||||
\(155\) | 2.41133 | 0.193683 | ||||||||
\(156\) | 1.36800 | 0.109528 | ||||||||
\(157\) | −13.7258 | −1.09543 | −0.547717 | − | 0.836663i | \(-0.684503\pi\) | ||||
−0.547717 | + | 0.836663i | \(0.684503\pi\) | |||||||
\(158\) | 12.4358 | 0.989343 | ||||||||
\(159\) | 1.67890 | 0.133145 | ||||||||
\(160\) | 27.5937 | 2.18147 | ||||||||
\(161\) | −3.94812 | −0.311155 | ||||||||
\(162\) | −22.8241 | −1.79323 | ||||||||
\(163\) | 13.3747 | 1.04759 | 0.523795 | − | 0.851845i | \(-0.324516\pi\) | ||||
0.523795 | + | 0.851845i | \(0.324516\pi\) | |||||||
\(164\) | −23.8620 | −1.86331 | ||||||||
\(165\) | −0.575266 | −0.0447844 | ||||||||
\(166\) | 21.2761 | 1.65135 | ||||||||
\(167\) | 2.92099 | 0.226033 | 0.113017 | − | 0.993593i | \(-0.463949\pi\) | ||||
0.113017 | + | 0.993593i | \(0.463949\pi\) | |||||||
\(168\) | 3.09225 | 0.238572 | ||||||||
\(169\) | −12.3586 | −0.950664 | ||||||||
\(170\) | 2.73612 | 0.209851 | ||||||||
\(171\) | 22.8986 | 1.75110 | ||||||||
\(172\) | −39.9080 | −3.04296 | ||||||||
\(173\) | 11.8602 | 0.901711 | 0.450856 | − | 0.892597i | \(-0.351119\pi\) | ||||
0.450856 | + | 0.892597i | \(0.351119\pi\) | |||||||
\(174\) | 7.84676 | 0.594861 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 33.5600 | 2.52968 | ||||||||
\(177\) | 0.442540 | 0.0332634 | ||||||||
\(178\) | −15.6455 | −1.17268 | ||||||||
\(179\) | −6.68431 | −0.499609 | −0.249805 | − | 0.968296i | \(-0.580366\pi\) | ||||
−0.249805 | + | 0.968296i | \(0.580366\pi\) | |||||||
\(180\) | 16.6853 | 1.24365 | ||||||||
\(181\) | 16.3937 | 1.21854 | 0.609268 | − | 0.792965i | \(-0.291463\pi\) | ||||
0.609268 | + | 0.792965i | \(0.291463\pi\) | |||||||
\(182\) | 2.22683 | 0.165063 | ||||||||
\(183\) | 2.40569 | 0.177834 | ||||||||
\(184\) | −40.9638 | −3.01989 | ||||||||
\(185\) | −9.35326 | −0.687665 | ||||||||
\(186\) | 1.99826 | 0.146520 | ||||||||
\(187\) | 1.89936 | 0.138895 | ||||||||
\(188\) | −48.7248 | −3.55362 | ||||||||
\(189\) | 1.76173 | 0.128147 | ||||||||
\(190\) | −21.8711 | −1.58670 | ||||||||
\(191\) | 10.8073 | 0.781986 | 0.390993 | − | 0.920394i | \(-0.372132\pi\) | ||||
0.390993 | + | 0.920394i | \(0.372132\pi\) | |||||||
\(192\) | 12.5031 | 0.902336 | ||||||||
\(193\) | 3.27495 | 0.235736 | 0.117868 | − | 0.993029i | \(-0.462394\pi\) | ||||
0.117868 | + | 0.993029i | \(0.462394\pi\) | |||||||
\(194\) | −52.1590 | −3.74480 | ||||||||
\(195\) | −0.238682 | −0.0170924 | ||||||||
\(196\) | 5.73146 | 0.409390 | ||||||||
\(197\) | −3.98985 | −0.284265 | −0.142132 | − | 0.989848i | \(-0.545396\pi\) | ||||
−0.142132 | + | 0.989848i | \(0.545396\pi\) | |||||||
\(198\) | 15.6244 | 1.11038 | ||||||||
\(199\) | 9.65928 | 0.684728 | 0.342364 | − | 0.939567i | \(-0.388772\pi\) | ||||
0.342364 | + | 0.939567i | \(0.388772\pi\) | |||||||
\(200\) | −10.3755 | −0.733660 | ||||||||
\(201\) | −3.95679 | −0.279091 | ||||||||
\(202\) | 41.9567 | 2.95207 | ||||||||
\(203\) | 9.46879 | 0.664579 | ||||||||
\(204\) | 1.68087 | 0.117685 | ||||||||
\(205\) | 4.16333 | 0.290780 | ||||||||
\(206\) | −9.81960 | −0.684164 | ||||||||
\(207\) | −11.4937 | −0.798865 | ||||||||
\(208\) | 13.9243 | 0.965477 | ||||||||
\(209\) | −15.1825 | −1.05020 | ||||||||
\(210\) | −0.828697 | −0.0571855 | ||||||||
\(211\) | −20.8322 | −1.43415 | −0.717075 | − | 0.696996i | \(-0.754519\pi\) | ||||
−0.717075 | + | 0.696996i | \(0.754519\pi\) | |||||||
\(212\) | 32.2867 | 2.21746 | ||||||||
\(213\) | −1.06157 | −0.0727374 | ||||||||
\(214\) | 54.5846 | 3.73133 | ||||||||
\(215\) | 6.96297 | 0.474871 | ||||||||
\(216\) | 18.2788 | 1.24372 | ||||||||
\(217\) | 2.41133 | 0.163692 | ||||||||
\(218\) | −3.48815 | −0.236247 | ||||||||
\(219\) | 4.08624 | 0.276123 | ||||||||
\(220\) | −11.0629 | −0.745861 | ||||||||
\(221\) | 0.788061 | 0.0530107 | ||||||||
\(222\) | −7.75102 | −0.520214 | ||||||||
\(223\) | 5.42935 | 0.363576 | 0.181788 | − | 0.983338i | \(-0.441812\pi\) | ||||
0.181788 | + | 0.983338i | \(0.441812\pi\) | |||||||
\(224\) | 27.5937 | 1.84368 | ||||||||
\(225\) | −2.91118 | −0.194078 | ||||||||
\(226\) | 14.3259 | 0.952945 | ||||||||
\(227\) | 7.57562 | 0.502812 | 0.251406 | − | 0.967882i | \(-0.419107\pi\) | ||||
0.251406 | + | 0.967882i | \(0.419107\pi\) | |||||||
\(228\) | −13.4360 | −0.889823 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | 10.9779 | 0.723864 | ||||||||
\(231\) | −0.575266 | −0.0378497 | ||||||||
\(232\) | 98.2437 | 6.45001 | ||||||||
\(233\) | −22.7454 | −1.49010 | −0.745050 | − | 0.667008i | \(-0.767575\pi\) | ||||
−0.745050 | + | 0.667008i | \(0.767575\pi\) | |||||||
\(234\) | 6.48268 | 0.423786 | ||||||||
\(235\) | 8.50129 | 0.554563 | ||||||||
\(236\) | 8.51046 | 0.553984 | ||||||||
\(237\) | −1.33294 | −0.0865835 | ||||||||
\(238\) | 2.73612 | 0.177356 | ||||||||
\(239\) | 9.30016 | 0.601578 | 0.300789 | − | 0.953691i | \(-0.402750\pi\) | ||||
0.300789 | + | 0.953691i | \(0.402750\pi\) | |||||||
\(240\) | −5.18183 | −0.334486 | ||||||||
\(241\) | 0.572380 | 0.0368703 | 0.0184351 | − | 0.999830i | \(-0.494132\pi\) | ||||
0.0184351 | + | 0.999830i | \(0.494132\pi\) | |||||||
\(242\) | 20.2266 | 1.30021 | ||||||||
\(243\) | 7.73158 | 0.495981 | ||||||||
\(244\) | 46.2637 | 2.96173 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 3.45014 | 0.219973 | ||||||||
\(247\) | −6.29936 | −0.400818 | ||||||||
\(248\) | 25.0188 | 1.58870 | ||||||||
\(249\) | −2.28048 | −0.144520 | ||||||||
\(250\) | 2.78055 | 0.175857 | ||||||||
\(251\) | −14.2096 | −0.896903 | −0.448451 | − | 0.893807i | \(-0.648024\pi\) | ||||
−0.448451 | + | 0.893807i | \(0.648024\pi\) | |||||||
\(252\) | 16.6853 | 1.05107 | ||||||||
\(253\) | 7.62069 | 0.479108 | ||||||||
\(254\) | −39.1687 | −2.45766 | ||||||||
\(255\) | −0.293271 | −0.0183653 | ||||||||
\(256\) | 86.9958 | 5.43724 | ||||||||
\(257\) | 6.65911 | 0.415384 | 0.207692 | − | 0.978194i | \(-0.433405\pi\) | ||||
0.207692 | + | 0.978194i | \(0.433405\pi\) | |||||||
\(258\) | 5.77020 | 0.359237 | ||||||||
\(259\) | −9.35326 | −0.581183 | ||||||||
\(260\) | −4.59009 | −0.284665 | ||||||||
\(261\) | 27.5653 | 1.70625 | ||||||||
\(262\) | 55.2263 | 3.41189 | ||||||||
\(263\) | 26.6547 | 1.64360 | 0.821799 | − | 0.569777i | \(-0.192970\pi\) | ||||
0.821799 | + | 0.569777i | \(0.192970\pi\) | |||||||
\(264\) | −5.96869 | −0.367347 | ||||||||
\(265\) | −5.63325 | −0.346048 | ||||||||
\(266\) | −21.8711 | −1.34101 | ||||||||
\(267\) | 1.67696 | 0.102629 | ||||||||
\(268\) | −76.0929 | −4.64811 | ||||||||
\(269\) | −5.50963 | −0.335928 | −0.167964 | − | 0.985793i | \(-0.553719\pi\) | ||||
−0.167964 | + | 0.985793i | \(0.553719\pi\) | |||||||
\(270\) | −4.89857 | −0.298118 | ||||||||
\(271\) | 19.3282 | 1.17411 | 0.587053 | − | 0.809549i | \(-0.300288\pi\) | ||||
0.587053 | + | 0.809549i | \(0.300288\pi\) | |||||||
\(272\) | 17.1089 | 1.03738 | ||||||||
\(273\) | −0.238682 | −0.0144457 | ||||||||
\(274\) | −41.1155 | −2.48388 | ||||||||
\(275\) | 1.93021 | 0.116396 | ||||||||
\(276\) | 6.74405 | 0.405944 | ||||||||
\(277\) | 9.36540 | 0.562712 | 0.281356 | − | 0.959603i | \(-0.409216\pi\) | ||||
0.281356 | + | 0.959603i | \(0.409216\pi\) | |||||||
\(278\) | 61.0359 | 3.66069 | ||||||||
\(279\) | 7.01981 | 0.420265 | ||||||||
\(280\) | −10.3755 | −0.620056 | ||||||||
\(281\) | 27.6185 | 1.64758 | 0.823792 | − | 0.566892i | \(-0.191854\pi\) | ||||
0.823792 | + | 0.566892i | \(0.191854\pi\) | |||||||
\(282\) | 7.04500 | 0.419523 | ||||||||
\(283\) | 26.9369 | 1.60123 | 0.800617 | − | 0.599176i | \(-0.204505\pi\) | ||||
0.800617 | + | 0.599176i | \(0.204505\pi\) | |||||||
\(284\) | −20.4149 | −1.21140 | ||||||||
\(285\) | 2.34426 | 0.138862 | ||||||||
\(286\) | −4.29824 | −0.254160 | ||||||||
\(287\) | 4.16333 | 0.245754 | ||||||||
\(288\) | 80.3300 | 4.73349 | ||||||||
\(289\) | −16.0317 | −0.943041 | ||||||||
\(290\) | −26.3285 | −1.54606 | ||||||||
\(291\) | 5.59066 | 0.327730 | ||||||||
\(292\) | 78.5823 | 4.59868 | ||||||||
\(293\) | −14.5291 | −0.848797 | −0.424398 | − | 0.905476i | \(-0.639514\pi\) | ||||
−0.424398 | + | 0.905476i | \(0.639514\pi\) | |||||||
\(294\) | −0.828697 | −0.0483306 | ||||||||
\(295\) | −1.48487 | −0.0864523 | ||||||||
\(296\) | −97.0449 | −5.64062 | ||||||||
\(297\) | −3.40050 | −0.197317 | ||||||||
\(298\) | −37.0804 | −2.14801 | ||||||||
\(299\) | 3.16188 | 0.182856 | ||||||||
\(300\) | 1.70817 | 0.0986211 | ||||||||
\(301\) | 6.96297 | 0.401339 | ||||||||
\(302\) | 4.25319 | 0.244744 | ||||||||
\(303\) | −4.49714 | −0.258354 | ||||||||
\(304\) | −136.760 | −7.84372 | ||||||||
\(305\) | −8.07188 | −0.462195 | ||||||||
\(306\) | 7.96533 | 0.455347 | ||||||||
\(307\) | 32.6927 | 1.86587 | 0.932935 | − | 0.360044i | \(-0.117238\pi\) | ||||
0.932935 | + | 0.360044i | \(0.117238\pi\) | |||||||
\(308\) | −11.0629 | −0.630368 | ||||||||
\(309\) | 1.05251 | 0.0598754 | ||||||||
\(310\) | −6.70483 | −0.380808 | ||||||||
\(311\) | −26.4579 | −1.50029 | −0.750145 | − | 0.661274i | \(-0.770016\pi\) | ||||
−0.750145 | + | 0.661274i | \(0.770016\pi\) | |||||||
\(312\) | −2.47646 | −0.140202 | ||||||||
\(313\) | 31.1423 | 1.76027 | 0.880135 | − | 0.474724i | \(-0.157452\pi\) | ||||
0.880135 | + | 0.474724i | \(0.157452\pi\) | |||||||
\(314\) | 38.1652 | 2.15378 | ||||||||
\(315\) | −2.91118 | −0.164026 | ||||||||
\(316\) | −25.6336 | −1.44200 | ||||||||
\(317\) | −14.3876 | −0.808085 | −0.404043 | − | 0.914740i | \(-0.632395\pi\) | ||||
−0.404043 | + | 0.914740i | \(0.632395\pi\) | |||||||
\(318\) | −4.66825 | −0.261783 | ||||||||
\(319\) | −18.2767 | −1.02330 | ||||||||
\(320\) | −41.9521 | −2.34519 | ||||||||
\(321\) | −5.85066 | −0.326552 | ||||||||
\(322\) | 10.9779 | 0.611777 | ||||||||
\(323\) | −7.74007 | −0.430669 | ||||||||
\(324\) | 47.0466 | 2.61370 | ||||||||
\(325\) | 0.800858 | 0.0444236 | ||||||||
\(326\) | −37.1891 | −2.05971 | ||||||||
\(327\) | 0.373877 | 0.0206754 | ||||||||
\(328\) | 43.1967 | 2.38514 | ||||||||
\(329\) | 8.50129 | 0.468691 | ||||||||
\(330\) | 1.59956 | 0.0880527 | ||||||||
\(331\) | 2.76125 | 0.151772 | 0.0758859 | − | 0.997117i | \(-0.475822\pi\) | ||||
0.0758859 | + | 0.997117i | \(0.475822\pi\) | |||||||
\(332\) | −43.8558 | −2.40690 | ||||||||
\(333\) | −27.2290 | −1.49214 | ||||||||
\(334\) | −8.12197 | −0.444414 | ||||||||
\(335\) | 13.2763 | 0.725364 | ||||||||
\(336\) | −5.18183 | −0.282692 | ||||||||
\(337\) | −31.0714 | −1.69257 | −0.846284 | − | 0.532732i | \(-0.821165\pi\) | ||||
−0.846284 | + | 0.532732i | \(0.821165\pi\) | |||||||
\(338\) | 34.3638 | 1.86914 | ||||||||
\(339\) | −1.53552 | −0.0833981 | ||||||||
\(340\) | −5.63988 | −0.305865 | ||||||||
\(341\) | −4.65437 | −0.252048 | ||||||||
\(342\) | −63.6707 | −3.44292 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 72.2445 | 3.89516 | ||||||||
\(345\) | −1.17667 | −0.0633498 | ||||||||
\(346\) | −32.9778 | −1.77290 | ||||||||
\(347\) | −29.2759 | −1.57161 | −0.785806 | − | 0.618473i | \(-0.787752\pi\) | ||||
−0.785806 | + | 0.618473i | \(0.787752\pi\) | |||||||
\(348\) | −16.1743 | −0.867033 | ||||||||
\(349\) | 10.6770 | 0.571528 | 0.285764 | − | 0.958300i | \(-0.407753\pi\) | ||||
0.285764 | + | 0.958300i | \(0.407753\pi\) | |||||||
\(350\) | 2.78055 | 0.148627 | ||||||||
\(351\) | −1.41089 | −0.0753080 | ||||||||
\(352\) | −53.2615 | −2.83885 | ||||||||
\(353\) | −9.63726 | −0.512940 | −0.256470 | − | 0.966552i | \(-0.582559\pi\) | ||||
−0.256470 | + | 0.966552i | \(0.582559\pi\) | |||||||
\(354\) | −1.23051 | −0.0654006 | ||||||||
\(355\) | 3.56191 | 0.189046 | ||||||||
\(356\) | 32.2496 | 1.70922 | ||||||||
\(357\) | −0.293271 | −0.0155216 | ||||||||
\(358\) | 18.5861 | 0.982304 | ||||||||
\(359\) | 19.4085 | 1.02434 | 0.512171 | − | 0.858883i | \(-0.328841\pi\) | ||||
0.512171 | + | 0.858883i | \(0.328841\pi\) | |||||||
\(360\) | −30.2050 | −1.59194 | ||||||||
\(361\) | 42.8702 | 2.25632 | ||||||||
\(362\) | −45.5836 | −2.39582 | ||||||||
\(363\) | −2.16798 | −0.113790 | ||||||||
\(364\) | −4.59009 | −0.240586 | ||||||||
\(365\) | −13.7107 | −0.717650 | ||||||||
\(366\) | −6.68915 | −0.349647 | ||||||||
\(367\) | 12.5807 | 0.656709 | 0.328354 | − | 0.944555i | \(-0.393506\pi\) | ||||
0.328354 | + | 0.944555i | \(0.393506\pi\) | |||||||
\(368\) | 68.6449 | 3.57836 | ||||||||
\(369\) | 12.1202 | 0.630952 | ||||||||
\(370\) | 26.0072 | 1.35205 | ||||||||
\(371\) | −5.63325 | −0.292464 | ||||||||
\(372\) | −4.11896 | −0.213558 | ||||||||
\(373\) | −27.3935 | −1.41838 | −0.709192 | − | 0.705016i | \(-0.750940\pi\) | ||||
−0.709192 | + | 0.705016i | \(0.750940\pi\) | |||||||
\(374\) | −5.28128 | −0.273088 | ||||||||
\(375\) | −0.298033 | −0.0153904 | ||||||||
\(376\) | 88.2053 | 4.54884 | ||||||||
\(377\) | −7.58316 | −0.390553 | ||||||||
\(378\) | −4.89857 | −0.251955 | ||||||||
\(379\) | −19.5606 | −1.00476 | −0.502381 | − | 0.864646i | \(-0.667542\pi\) | ||||
−0.502381 | + | 0.864646i | \(0.667542\pi\) | |||||||
\(380\) | 45.0823 | 2.31267 | ||||||||
\(381\) | 4.19830 | 0.215085 | ||||||||
\(382\) | −30.0501 | −1.53750 | ||||||||
\(383\) | 22.0264 | 1.12549 | 0.562747 | − | 0.826629i | \(-0.309744\pi\) | ||||
0.562747 | + | 0.826629i | \(0.309744\pi\) | |||||||
\(384\) | −18.3179 | −0.934783 | ||||||||
\(385\) | 1.93021 | 0.0983725 | ||||||||
\(386\) | −9.10616 | −0.463491 | ||||||||
\(387\) | 20.2704 | 1.03040 | ||||||||
\(388\) | 107.514 | 5.45818 | ||||||||
\(389\) | −39.1240 | −1.98367 | −0.991833 | − | 0.127546i | \(-0.959290\pi\) | ||||
−0.991833 | + | 0.127546i | \(0.959290\pi\) | |||||||
\(390\) | 0.663669 | 0.0336062 | ||||||||
\(391\) | 3.88503 | 0.196474 | ||||||||
\(392\) | −10.3755 | −0.524043 | ||||||||
\(393\) | −5.91943 | −0.298596 | ||||||||
\(394\) | 11.0940 | 0.558906 | ||||||||
\(395\) | 4.47244 | 0.225033 | ||||||||
\(396\) | −32.2061 | −1.61842 | ||||||||
\(397\) | 2.21011 | 0.110922 | 0.0554611 | − | 0.998461i | \(-0.482337\pi\) | ||||
0.0554611 | + | 0.998461i | \(0.482337\pi\) | |||||||
\(398\) | −26.8581 | −1.34628 | ||||||||
\(399\) | 2.34426 | 0.117360 | ||||||||
\(400\) | 17.3867 | 0.869337 | ||||||||
\(401\) | −7.74623 | −0.386828 | −0.193414 | − | 0.981117i | \(-0.561956\pi\) | ||||
−0.193414 | + | 0.981117i | \(0.561956\pi\) | |||||||
\(402\) | 11.0021 | 0.548733 | ||||||||
\(403\) | −1.93113 | −0.0961966 | ||||||||
\(404\) | −86.4841 | −4.30275 | ||||||||
\(405\) | −8.20847 | −0.407882 | ||||||||
\(406\) | −26.3285 | −1.30666 | ||||||||
\(407\) | 18.0537 | 0.894890 | ||||||||
\(408\) | −3.04284 | −0.150643 | ||||||||
\(409\) | 0.843997 | 0.0417329 | 0.0208665 | − | 0.999782i | \(-0.493358\pi\) | ||||
0.0208665 | + | 0.999782i | \(0.493358\pi\) | |||||||
\(410\) | −11.5764 | −0.571715 | ||||||||
\(411\) | 4.40697 | 0.217380 | ||||||||
\(412\) | 20.2408 | 0.997194 | ||||||||
\(413\) | −1.48487 | −0.0730656 | ||||||||
\(414\) | 31.9587 | 1.57069 | ||||||||
\(415\) | 7.65176 | 0.375610 | ||||||||
\(416\) | −22.0986 | −1.08347 | ||||||||
\(417\) | −6.54214 | −0.320370 | ||||||||
\(418\) | 42.2158 | 2.06484 | ||||||||
\(419\) | 13.5588 | 0.662391 | 0.331196 | − | 0.943562i | \(-0.392548\pi\) | ||||
0.331196 | + | 0.943562i | \(0.392548\pi\) | |||||||
\(420\) | 1.70817 | 0.0833500 | ||||||||
\(421\) | 34.5469 | 1.68371 | 0.841855 | − | 0.539703i | \(-0.181464\pi\) | ||||
0.841855 | + | 0.539703i | \(0.181464\pi\) | |||||||
\(422\) | 57.9251 | 2.81975 | ||||||||
\(423\) | 24.7488 | 1.20333 | ||||||||
\(424\) | −58.4479 | −2.83848 | ||||||||
\(425\) | 0.984021 | 0.0477320 | ||||||||
\(426\) | 2.95174 | 0.143012 | ||||||||
\(427\) | −8.07188 | −0.390626 | ||||||||
\(428\) | −112.514 | −5.43855 | ||||||||
\(429\) | 0.460707 | 0.0222431 | ||||||||
\(430\) | −19.3609 | −0.933666 | ||||||||
\(431\) | −16.4036 | −0.790134 | −0.395067 | − | 0.918652i | \(-0.629279\pi\) | ||||
−0.395067 | + | 0.918652i | \(0.629279\pi\) | |||||||
\(432\) | −30.6307 | −1.47372 | ||||||||
\(433\) | 7.60672 | 0.365555 | 0.182778 | − | 0.983154i | \(-0.441491\pi\) | ||||
0.182778 | + | 0.983154i | \(0.441491\pi\) | |||||||
\(434\) | −6.70483 | −0.321842 | ||||||||
\(435\) | 2.82202 | 0.135305 | ||||||||
\(436\) | 7.19001 | 0.344339 | ||||||||
\(437\) | −31.0549 | −1.48556 | ||||||||
\(438\) | −11.3620 | −0.542898 | ||||||||
\(439\) | −18.1859 | −0.867964 | −0.433982 | − | 0.900921i | \(-0.642892\pi\) | ||||
−0.433982 | + | 0.900921i | \(0.642892\pi\) | |||||||
\(440\) | 20.0269 | 0.954745 | ||||||||
\(441\) | −2.91118 | −0.138627 | ||||||||
\(442\) | −2.19124 | −0.104227 | ||||||||
\(443\) | −11.7409 | −0.557826 | −0.278913 | − | 0.960316i | \(-0.589974\pi\) | ||||
−0.278913 | + | 0.960316i | \(0.589974\pi\) | |||||||
\(444\) | 15.9769 | 0.758232 | ||||||||
\(445\) | −5.62676 | −0.266734 | ||||||||
\(446\) | −15.0966 | −0.714843 | ||||||||
\(447\) | 3.97447 | 0.187986 | ||||||||
\(448\) | −41.9521 | −1.98205 | ||||||||
\(449\) | −7.45839 | −0.351983 | −0.175992 | − | 0.984392i | \(-0.556313\pi\) | ||||
−0.175992 | + | 0.984392i | \(0.556313\pi\) | |||||||
\(450\) | 8.09467 | 0.381587 | ||||||||
\(451\) | −8.03609 | −0.378405 | ||||||||
\(452\) | −29.5295 | −1.38895 | ||||||||
\(453\) | −0.455879 | −0.0214191 | ||||||||
\(454\) | −21.0644 | −0.988602 | ||||||||
\(455\) | 0.800858 | 0.0375448 | ||||||||
\(456\) | 24.3229 | 1.13902 | ||||||||
\(457\) | −21.8356 | −1.02143 | −0.510714 | − | 0.859751i | \(-0.670619\pi\) | ||||
−0.510714 | + | 0.859751i | \(0.670619\pi\) | |||||||
\(458\) | −2.78055 | −0.129927 | ||||||||
\(459\) | −1.73358 | −0.0809164 | ||||||||
\(460\) | −22.6285 | −1.05506 | ||||||||
\(461\) | 15.6388 | 0.728371 | 0.364185 | − | 0.931327i | \(-0.381347\pi\) | ||||
0.364185 | + | 0.931327i | \(0.381347\pi\) | |||||||
\(462\) | 1.59956 | 0.0744181 | ||||||||
\(463\) | 29.1462 | 1.35454 | 0.677269 | − | 0.735736i | \(-0.263164\pi\) | ||||
0.677269 | + | 0.735736i | \(0.263164\pi\) | |||||||
\(464\) | −164.631 | −7.64282 | ||||||||
\(465\) | 0.718657 | 0.0333269 | ||||||||
\(466\) | 63.2447 | 2.92976 | ||||||||
\(467\) | −3.70976 | −0.171667 | −0.0858337 | − | 0.996309i | \(-0.527355\pi\) | ||||
−0.0858337 | + | 0.996309i | \(0.527355\pi\) | |||||||
\(468\) | −13.3626 | −0.617684 | ||||||||
\(469\) | 13.2763 | 0.613045 | ||||||||
\(470\) | −23.6383 | −1.09035 | ||||||||
\(471\) | −4.09073 | −0.188491 | ||||||||
\(472\) | −15.4063 | −0.709131 | ||||||||
\(473\) | −13.4400 | −0.617971 | ||||||||
\(474\) | 3.70630 | 0.170236 | ||||||||
\(475\) | −7.86576 | −0.360906 | ||||||||
\(476\) | −5.63988 | −0.258503 | ||||||||
\(477\) | −16.3994 | −0.750876 | ||||||||
\(478\) | −25.8596 | −1.18279 | ||||||||
\(479\) | −28.0449 | −1.28140 | −0.640701 | − | 0.767790i | \(-0.721356\pi\) | ||||
−0.640701 | + | 0.767790i | \(0.721356\pi\) | |||||||
\(480\) | 8.22384 | 0.375365 | ||||||||
\(481\) | 7.49063 | 0.341543 | ||||||||
\(482\) | −1.59153 | −0.0724923 | ||||||||
\(483\) | −1.17667 | −0.0535404 | ||||||||
\(484\) | −41.6924 | −1.89511 | ||||||||
\(485\) | −18.7585 | −0.851780 | ||||||||
\(486\) | −21.4981 | −0.975172 | ||||||||
\(487\) | −21.3870 | −0.969139 | −0.484569 | − | 0.874753i | \(-0.661024\pi\) | ||||
−0.484569 | + | 0.874753i | \(0.661024\pi\) | |||||||
\(488\) | −83.7500 | −3.79118 | ||||||||
\(489\) | 3.98612 | 0.180258 | ||||||||
\(490\) | 2.78055 | 0.125612 | ||||||||
\(491\) | 13.6251 | 0.614892 | 0.307446 | − | 0.951566i | \(-0.400526\pi\) | ||||
0.307446 | + | 0.951566i | \(0.400526\pi\) | |||||||
\(492\) | −7.11167 | −0.320619 | ||||||||
\(493\) | −9.31749 | −0.419639 | ||||||||
\(494\) | 17.5157 | 0.788068 | ||||||||
\(495\) | 5.61917 | 0.252563 | ||||||||
\(496\) | −41.9252 | −1.88250 | ||||||||
\(497\) | 3.56191 | 0.159773 | ||||||||
\(498\) | 6.34100 | 0.284147 | ||||||||
\(499\) | 9.29854 | 0.416260 | 0.208130 | − | 0.978101i | \(-0.433262\pi\) | ||||
0.208130 | + | 0.978101i | \(0.433262\pi\) | |||||||
\(500\) | −5.73146 | −0.256319 | ||||||||
\(501\) | 0.870553 | 0.0388935 | ||||||||
\(502\) | 39.5105 | 1.76344 | ||||||||
\(503\) | −11.1887 | −0.498879 | −0.249439 | − | 0.968390i | \(-0.580246\pi\) | ||||
−0.249439 | + | 0.968390i | \(0.580246\pi\) | |||||||
\(504\) | −30.2050 | −1.34544 | ||||||||
\(505\) | 15.0894 | 0.671468 | ||||||||
\(506\) | −21.1897 | −0.941997 | ||||||||
\(507\) | −3.68328 | −0.163580 | ||||||||
\(508\) | 80.7372 | 3.58213 | ||||||||
\(509\) | 42.8827 | 1.90074 | 0.950371 | − | 0.311118i | \(-0.100704\pi\) | ||||
0.950371 | + | 0.311118i | \(0.100704\pi\) | |||||||
\(510\) | 0.815455 | 0.0361090 | ||||||||
\(511\) | −13.7107 | −0.606525 | ||||||||
\(512\) | −118.971 | −5.25782 | ||||||||
\(513\) | 13.8573 | 0.611816 | ||||||||
\(514\) | −18.5160 | −0.816705 | ||||||||
\(515\) | −3.53153 | −0.155618 | ||||||||
\(516\) | −11.8939 | −0.523601 | ||||||||
\(517\) | −16.4093 | −0.721678 | ||||||||
\(518\) | 26.0072 | 1.14269 | ||||||||
\(519\) | 3.53472 | 0.155157 | ||||||||
\(520\) | 8.30932 | 0.364388 | ||||||||
\(521\) | 19.0920 | 0.836434 | 0.418217 | − | 0.908347i | \(-0.362655\pi\) | ||||
0.418217 | + | 0.908347i | \(0.362655\pi\) | |||||||
\(522\) | −76.6468 | −3.35474 | ||||||||
\(523\) | 0.946269 | 0.0413775 | 0.0206887 | − | 0.999786i | \(-0.493414\pi\) | ||||
0.0206887 | + | 0.999786i | \(0.493414\pi\) | |||||||
\(524\) | −113.836 | −4.97296 | ||||||||
\(525\) | −0.298033 | −0.0130072 | ||||||||
\(526\) | −74.1147 | −3.23156 | ||||||||
\(527\) | −2.37280 | −0.103361 | ||||||||
\(528\) | 10.0020 | 0.435281 | ||||||||
\(529\) | −7.41237 | −0.322277 | ||||||||
\(530\) | 15.6635 | 0.680380 | ||||||||
\(531\) | −4.32271 | −0.187590 | ||||||||
\(532\) | 45.0823 | 1.95457 | ||||||||
\(533\) | −3.33424 | −0.144422 | ||||||||
\(534\) | −4.66288 | −0.201783 | ||||||||
\(535\) | 19.6309 | 0.848717 | ||||||||
\(536\) | 137.749 | 5.94985 | ||||||||
\(537\) | −1.99215 | −0.0859676 | ||||||||
\(538\) | 15.3198 | 0.660484 | ||||||||
\(539\) | 1.93021 | 0.0831399 | ||||||||
\(540\) | 10.0973 | 0.434518 | ||||||||
\(541\) | 6.05878 | 0.260487 | 0.130244 | − | 0.991482i | \(-0.458424\pi\) | ||||
0.130244 | + | 0.991482i | \(0.458424\pi\) | |||||||
\(542\) | −53.7431 | −2.30846 | ||||||||
\(543\) | 4.88588 | 0.209673 | ||||||||
\(544\) | −27.1527 | −1.16416 | ||||||||
\(545\) | −1.25448 | −0.0537360 | ||||||||
\(546\) | 0.663669 | 0.0284024 | ||||||||
\(547\) | 22.3395 | 0.955167 | 0.477584 | − | 0.878586i | \(-0.341513\pi\) | ||||
0.477584 | + | 0.878586i | \(0.341513\pi\) | |||||||
\(548\) | 84.7501 | 3.62035 | ||||||||
\(549\) | −23.4987 | −1.00290 | ||||||||
\(550\) | −5.36704 | −0.228851 | ||||||||
\(551\) | 74.4793 | 3.17292 | ||||||||
\(552\) | −12.2086 | −0.519632 | ||||||||
\(553\) | 4.47244 | 0.190187 | ||||||||
\(554\) | −26.0410 | −1.10637 | ||||||||
\(555\) | −2.78758 | −0.118326 | ||||||||
\(556\) | −125.811 | −5.33560 | ||||||||
\(557\) | −28.3183 | −1.19988 | −0.599942 | − | 0.800044i | \(-0.704810\pi\) | ||||
−0.599942 | + | 0.800044i | \(0.704810\pi\) | |||||||
\(558\) | −19.5189 | −0.826302 | ||||||||
\(559\) | −5.57635 | −0.235855 | ||||||||
\(560\) | 17.3867 | 0.734724 | ||||||||
\(561\) | 0.566074 | 0.0238997 | ||||||||
\(562\) | −76.7948 | −3.23939 | ||||||||
\(563\) | 34.7133 | 1.46299 | 0.731495 | − | 0.681847i | \(-0.238823\pi\) | ||||
0.731495 | + | 0.681847i | \(0.238823\pi\) | |||||||
\(564\) | −14.5216 | −0.611471 | ||||||||
\(565\) | 5.15218 | 0.216754 | ||||||||
\(566\) | −74.8995 | −3.14826 | ||||||||
\(567\) | −8.20847 | −0.344724 | ||||||||
\(568\) | 36.9566 | 1.55067 | ||||||||
\(569\) | 32.8004 | 1.37506 | 0.687532 | − | 0.726154i | \(-0.258694\pi\) | ||||
0.687532 | + | 0.726154i | \(0.258694\pi\) | |||||||
\(570\) | −6.51833 | −0.273023 | ||||||||
\(571\) | 28.7894 | 1.20480 | 0.602398 | − | 0.798196i | \(-0.294212\pi\) | ||||
0.602398 | + | 0.798196i | \(0.294212\pi\) | |||||||
\(572\) | 8.85982 | 0.370448 | ||||||||
\(573\) | 3.22092 | 0.134556 | ||||||||
\(574\) | −11.5764 | −0.483188 | ||||||||
\(575\) | 3.94812 | 0.164648 | ||||||||
\(576\) | −122.130 | −5.08875 | ||||||||
\(577\) | 18.8693 | 0.785540 | 0.392770 | − | 0.919637i | \(-0.371517\pi\) | ||||
0.392770 | + | 0.919637i | \(0.371517\pi\) | |||||||
\(578\) | 44.5770 | 1.85416 | ||||||||
\(579\) | 0.976044 | 0.0405630 | ||||||||
\(580\) | 54.2700 | 2.25344 | ||||||||
\(581\) | 7.65176 | 0.317449 | ||||||||
\(582\) | −15.5451 | −0.644366 | ||||||||
\(583\) | 10.8733 | 0.450327 | ||||||||
\(584\) | −142.256 | −5.88658 | ||||||||
\(585\) | 2.33144 | 0.0963931 | ||||||||
\(586\) | 40.3988 | 1.66886 | ||||||||
\(587\) | −20.2809 | −0.837081 | −0.418540 | − | 0.908198i | \(-0.637458\pi\) | ||||
−0.418540 | + | 0.908198i | \(0.637458\pi\) | |||||||
\(588\) | 1.70817 | 0.0704436 | ||||||||
\(589\) | 18.9669 | 0.781519 | ||||||||
\(590\) | 4.12875 | 0.169978 | ||||||||
\(591\) | −1.18911 | −0.0489134 | ||||||||
\(592\) | 162.623 | 6.68375 | ||||||||
\(593\) | 41.7801 | 1.71570 | 0.857852 | − | 0.513897i | \(-0.171799\pi\) | ||||
0.857852 | + | 0.513897i | \(0.171799\pi\) | |||||||
\(594\) | 9.45526 | 0.387954 | ||||||||
\(595\) | 0.984021 | 0.0403409 | ||||||||
\(596\) | 76.4328 | 3.13081 | ||||||||
\(597\) | 2.87879 | 0.117821 | ||||||||
\(598\) | −8.79177 | −0.359522 | ||||||||
\(599\) | 12.7717 | 0.521836 | 0.260918 | − | 0.965361i | \(-0.415975\pi\) | ||||
0.260918 | + | 0.965361i | \(0.415975\pi\) | |||||||
\(600\) | −3.09225 | −0.126241 | ||||||||
\(601\) | 20.7937 | 0.848192 | 0.424096 | − | 0.905617i | \(-0.360592\pi\) | ||||
0.424096 | + | 0.905617i | \(0.360592\pi\) | |||||||
\(602\) | −19.3609 | −0.789091 | ||||||||
\(603\) | 38.6498 | 1.57394 | ||||||||
\(604\) | −8.76698 | −0.356723 | ||||||||
\(605\) | 7.27430 | 0.295742 | ||||||||
\(606\) | 12.5045 | 0.507961 | ||||||||
\(607\) | −30.7120 | −1.24656 | −0.623280 | − | 0.781999i | \(-0.714200\pi\) | ||||
−0.623280 | + | 0.781999i | \(0.714200\pi\) | |||||||
\(608\) | 217.045 | 8.80234 | ||||||||
\(609\) | 2.82202 | 0.114354 | ||||||||
\(610\) | 22.4443 | 0.908742 | ||||||||
\(611\) | −6.80833 | −0.275435 | ||||||||
\(612\) | −16.4187 | −0.663686 | ||||||||
\(613\) | −31.8057 | −1.28462 | −0.642310 | − | 0.766445i | \(-0.722024\pi\) | ||||
−0.642310 | + | 0.766445i | \(0.722024\pi\) | |||||||
\(614\) | −90.9037 | −3.66857 | ||||||||
\(615\) | 1.24081 | 0.0500344 | ||||||||
\(616\) | 20.0269 | 0.806907 | ||||||||
\(617\) | 13.5320 | 0.544778 | 0.272389 | − | 0.962187i | \(-0.412186\pi\) | ||||
0.272389 | + | 0.962187i | \(0.412186\pi\) | |||||||
\(618\) | −2.92657 | −0.117724 | ||||||||
\(619\) | 6.94027 | 0.278953 | 0.139477 | − | 0.990225i | \(-0.455458\pi\) | ||||
0.139477 | + | 0.990225i | \(0.455458\pi\) | |||||||
\(620\) | 13.8204 | 0.555043 | ||||||||
\(621\) | −6.95551 | −0.279115 | ||||||||
\(622\) | 73.5675 | 2.94979 | ||||||||
\(623\) | −5.62676 | −0.225432 | ||||||||
\(624\) | 4.14991 | 0.166129 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −86.5929 | −3.46095 | ||||||||
\(627\) | −4.52491 | −0.180707 | ||||||||
\(628\) | −78.6687 | −3.13922 | ||||||||
\(629\) | 9.20380 | 0.366980 | ||||||||
\(630\) | 8.09467 | 0.322499 | ||||||||
\(631\) | 16.5062 | 0.657102 | 0.328551 | − | 0.944486i | \(-0.393440\pi\) | ||||
0.328551 | + | 0.944486i | \(0.393440\pi\) | |||||||
\(632\) | 46.4039 | 1.84585 | ||||||||
\(633\) | −6.20870 | −0.246774 | ||||||||
\(634\) | 40.0053 | 1.58881 | ||||||||
\(635\) | −14.0867 | −0.559012 | ||||||||
\(636\) | 9.62253 | 0.381558 | ||||||||
\(637\) | 0.800858 | 0.0317312 | ||||||||
\(638\) | 50.8194 | 2.01196 | ||||||||
\(639\) | 10.3693 | 0.410205 | ||||||||
\(640\) | 61.4626 | 2.42952 | ||||||||
\(641\) | 2.48703 | 0.0982320 | 0.0491160 | − | 0.998793i | \(-0.484360\pi\) | ||||
0.0491160 | + | 0.998793i | \(0.484360\pi\) | |||||||
\(642\) | 16.2680 | 0.642049 | ||||||||
\(643\) | −40.9647 | −1.61549 | −0.807745 | − | 0.589532i | \(-0.799312\pi\) | ||||
−0.807745 | + | 0.589532i | \(0.799312\pi\) | |||||||
\(644\) | −22.6285 | −0.891687 | ||||||||
\(645\) | 2.07520 | 0.0817109 | ||||||||
\(646\) | 21.5217 | 0.846758 | ||||||||
\(647\) | −15.3833 | −0.604780 | −0.302390 | − | 0.953184i | \(-0.597785\pi\) | ||||
−0.302390 | + | 0.953184i | \(0.597785\pi\) | |||||||
\(648\) | −85.1672 | −3.34568 | ||||||||
\(649\) | 2.86610 | 0.112504 | ||||||||
\(650\) | −2.22683 | −0.0873433 | ||||||||
\(651\) | 0.718657 | 0.0281664 | ||||||||
\(652\) | 76.6567 | 3.00211 | ||||||||
\(653\) | 31.0434 | 1.21482 | 0.607411 | − | 0.794388i | \(-0.292208\pi\) | ||||
0.607411 | + | 0.794388i | \(0.292208\pi\) | |||||||
\(654\) | −1.03958 | −0.0406510 | ||||||||
\(655\) | 19.8616 | 0.776059 | ||||||||
\(656\) | −72.3868 | −2.82623 | ||||||||
\(657\) | −39.9142 | −1.55720 | ||||||||
\(658\) | −23.6383 | −0.921516 | ||||||||
\(659\) | 45.5061 | 1.77266 | 0.886332 | − | 0.463049i | \(-0.153245\pi\) | ||||
0.886332 | + | 0.463049i | \(0.153245\pi\) | |||||||
\(660\) | −3.29712 | −0.128340 | ||||||||
\(661\) | 34.7740 | 1.35255 | 0.676276 | − | 0.736648i | \(-0.263592\pi\) | ||||
0.676276 | + | 0.736648i | \(0.263592\pi\) | |||||||
\(662\) | −7.67779 | −0.298406 | ||||||||
\(663\) | 0.234868 | 0.00912154 | ||||||||
\(664\) | 79.3910 | 3.08097 | ||||||||
\(665\) | −7.86576 | −0.305021 | ||||||||
\(666\) | 75.7116 | 2.93376 | ||||||||
\(667\) | −37.3839 | −1.44751 | ||||||||
\(668\) | 16.7416 | 0.647750 | ||||||||
\(669\) | 1.61813 | 0.0625604 | ||||||||
\(670\) | −36.9155 | −1.42617 | ||||||||
\(671\) | 15.5804 | 0.601475 | ||||||||
\(672\) | 8.22384 | 0.317241 | ||||||||
\(673\) | 33.1060 | 1.27614 | 0.638072 | − | 0.769977i | \(-0.279732\pi\) | ||||
0.638072 | + | 0.769977i | \(0.279732\pi\) | |||||||
\(674\) | 86.3957 | 3.32784 | ||||||||
\(675\) | −1.76173 | −0.0678089 | ||||||||
\(676\) | −70.8330 | −2.72435 | ||||||||
\(677\) | 2.59983 | 0.0999196 | 0.0499598 | − | 0.998751i | \(-0.484091\pi\) | ||||
0.0499598 | + | 0.998751i | \(0.484091\pi\) | |||||||
\(678\) | 4.26960 | 0.163973 | ||||||||
\(679\) | −18.7585 | −0.719886 | ||||||||
\(680\) | 10.2097 | 0.391525 | ||||||||
\(681\) | 2.25779 | 0.0865187 | ||||||||
\(682\) | 12.9417 | 0.495563 | ||||||||
\(683\) | −6.29909 | −0.241028 | −0.120514 | − | 0.992712i | \(-0.538454\pi\) | ||||
−0.120514 | + | 0.992712i | \(0.538454\pi\) | |||||||
\(684\) | 131.243 | 5.01818 | ||||||||
\(685\) | −14.7868 | −0.564975 | ||||||||
\(686\) | 2.78055 | 0.106162 | ||||||||
\(687\) | 0.298033 | 0.0113707 | ||||||||
\(688\) | −121.063 | −4.61550 | ||||||||
\(689\) | 4.51143 | 0.171872 | ||||||||
\(690\) | 3.27179 | 0.124555 | ||||||||
\(691\) | 6.69528 | 0.254701 | 0.127350 | − | 0.991858i | \(-0.459353\pi\) | ||||
0.127350 | + | 0.991858i | \(0.459353\pi\) | |||||||
\(692\) | 67.9761 | 2.58406 | ||||||||
\(693\) | 5.61917 | 0.213455 | ||||||||
\(694\) | 81.4031 | 3.09002 | ||||||||
\(695\) | 21.9510 | 0.832650 | ||||||||
\(696\) | 29.2799 | 1.10985 | ||||||||
\(697\) | −4.09680 | −0.155178 | ||||||||
\(698\) | −29.6880 | −1.12371 | ||||||||
\(699\) | −6.77889 | −0.256401 | ||||||||
\(700\) | −5.73146 | −0.216629 | ||||||||
\(701\) | 19.6673 | 0.742823 | 0.371411 | − | 0.928468i | \(-0.378874\pi\) | ||||
0.371411 | + | 0.928468i | \(0.378874\pi\) | |||||||
\(702\) | 3.92306 | 0.148066 | ||||||||
\(703\) | −73.5705 | −2.77476 | ||||||||
\(704\) | 80.9763 | 3.05191 | ||||||||
\(705\) | 2.53367 | 0.0954235 | ||||||||
\(706\) | 26.7969 | 1.00851 | ||||||||
\(707\) | 15.0894 | 0.567494 | ||||||||
\(708\) | 2.53640 | 0.0953239 | ||||||||
\(709\) | −15.2843 | −0.574015 | −0.287007 | − | 0.957928i | \(-0.592660\pi\) | ||||
−0.287007 | + | 0.957928i | \(0.592660\pi\) | |||||||
\(710\) | −9.90406 | −0.371693 | ||||||||
\(711\) | 13.0201 | 0.488290 | ||||||||
\(712\) | −58.3806 | −2.18791 | ||||||||
\(713\) | −9.52022 | −0.356535 | ||||||||
\(714\) | 0.815455 | 0.0305176 | ||||||||
\(715\) | −1.54582 | −0.0578105 | ||||||||
\(716\) | −38.3109 | −1.43175 | ||||||||
\(717\) | 2.77176 | 0.103513 | ||||||||
\(718\) | −53.9664 | −2.01401 | ||||||||
\(719\) | −35.5503 | −1.32580 | −0.662902 | − | 0.748706i | \(-0.730675\pi\) | ||||
−0.662902 | + | 0.748706i | \(0.730675\pi\) | |||||||
\(720\) | 50.6159 | 1.88634 | ||||||||
\(721\) | −3.53153 | −0.131521 | ||||||||
\(722\) | −119.203 | −4.43626 | ||||||||
\(723\) | 0.170589 | 0.00634425 | ||||||||
\(724\) | 93.9600 | 3.49200 | ||||||||
\(725\) | −9.46879 | −0.351662 | ||||||||
\(726\) | 6.02819 | 0.223727 | ||||||||
\(727\) | −13.6884 | −0.507675 | −0.253837 | − | 0.967247i | \(-0.581693\pi\) | ||||
−0.253837 | + | 0.967247i | \(0.581693\pi\) | |||||||
\(728\) | 8.30932 | 0.307964 | ||||||||
\(729\) | −22.3212 | −0.826709 | ||||||||
\(730\) | 38.1233 | 1.41101 | ||||||||
\(731\) | −6.85171 | −0.253420 | ||||||||
\(732\) | 13.7881 | 0.509624 | ||||||||
\(733\) | 48.7271 | 1.79978 | 0.899889 | − | 0.436120i | \(-0.143648\pi\) | ||||
0.899889 | + | 0.436120i | \(0.143648\pi\) | |||||||
\(734\) | −34.9814 | −1.29119 | ||||||||
\(735\) | −0.298033 | −0.0109931 | ||||||||
\(736\) | −108.943 | −4.01569 | ||||||||
\(737\) | −25.6261 | −0.943949 | ||||||||
\(738\) | −33.7008 | −1.24054 | ||||||||
\(739\) | 20.4498 | 0.752258 | 0.376129 | − | 0.926567i | \(-0.377255\pi\) | ||||
0.376129 | + | 0.926567i | \(0.377255\pi\) | |||||||
\(740\) | −53.6079 | −1.97066 | ||||||||
\(741\) | −1.87742 | −0.0689687 | ||||||||
\(742\) | 15.6635 | 0.575026 | ||||||||
\(743\) | 28.5780 | 1.04842 | 0.524212 | − | 0.851588i | \(-0.324360\pi\) | ||||
0.524212 | + | 0.851588i | \(0.324360\pi\) | |||||||
\(744\) | 7.45644 | 0.273366 | ||||||||
\(745\) | −13.3356 | −0.488580 | ||||||||
\(746\) | 76.1691 | 2.78875 | ||||||||
\(747\) | 22.2756 | 0.815023 | ||||||||
\(748\) | 10.8861 | 0.398036 | ||||||||
\(749\) | 19.6309 | 0.717296 | ||||||||
\(750\) | 0.828697 | 0.0302597 | ||||||||
\(751\) | −3.69614 | −0.134874 | −0.0674370 | − | 0.997724i | \(-0.521482\pi\) | ||||
−0.0674370 | + | 0.997724i | \(0.521482\pi\) | |||||||
\(752\) | −147.810 | −5.39007 | ||||||||
\(753\) | −4.23494 | −0.154330 | ||||||||
\(754\) | 21.0854 | 0.767884 | ||||||||
\(755\) | 1.52962 | 0.0556687 | ||||||||
\(756\) | 10.0973 | 0.367234 | ||||||||
\(757\) | −35.7776 | −1.30036 | −0.650179 | − | 0.759781i | \(-0.725306\pi\) | ||||
−0.650179 | + | 0.759781i | \(0.725306\pi\) | |||||||
\(758\) | 54.3893 | 1.97551 | ||||||||
\(759\) | 2.27122 | 0.0824400 | ||||||||
\(760\) | −81.6114 | −2.96035 | ||||||||
\(761\) | 13.1374 | 0.476231 | 0.238116 | − | 0.971237i | \(-0.423470\pi\) | ||||
0.238116 | + | 0.971237i | \(0.423470\pi\) | |||||||
\(762\) | −11.6736 | −0.422889 | ||||||||
\(763\) | −1.25448 | −0.0454152 | ||||||||
\(764\) | 61.9414 | 2.24096 | ||||||||
\(765\) | 2.86466 | 0.103572 | ||||||||
\(766\) | −61.2454 | −2.21289 | ||||||||
\(767\) | 1.18917 | 0.0429384 | ||||||||
\(768\) | 25.9277 | 0.935584 | ||||||||
\(769\) | 46.7354 | 1.68532 | 0.842661 | − | 0.538444i | \(-0.180988\pi\) | ||||
0.842661 | + | 0.538444i | \(0.180988\pi\) | |||||||
\(770\) | −5.36704 | −0.193415 | ||||||||
\(771\) | 1.98464 | 0.0714749 | ||||||||
\(772\) | 18.7702 | 0.675556 | ||||||||
\(773\) | −36.9751 | −1.32990 | −0.664950 | − | 0.746888i | \(-0.731547\pi\) | ||||
−0.664950 | + | 0.746888i | \(0.731547\pi\) | |||||||
\(774\) | −56.3630 | −2.02593 | ||||||||
\(775\) | −2.41133 | −0.0866175 | ||||||||
\(776\) | −194.629 | −6.98679 | ||||||||
\(777\) | −2.78758 | −0.100004 | ||||||||
\(778\) | 108.786 | 3.90018 | ||||||||
\(779\) | 32.7478 | 1.17331 | ||||||||
\(780\) | −1.36800 | −0.0489822 | ||||||||
\(781\) | −6.87522 | −0.246015 | ||||||||
\(782\) | −10.8025 | −0.386297 | ||||||||
\(783\) | 16.6814 | 0.596146 | ||||||||
\(784\) | 17.3867 | 0.620955 | ||||||||
\(785\) | 13.7258 | 0.489893 | ||||||||
\(786\) | 16.4593 | 0.587083 | ||||||||
\(787\) | 31.8596 | 1.13567 | 0.567836 | − | 0.823142i | \(-0.307781\pi\) | ||||
0.567836 | + | 0.823142i | \(0.307781\pi\) | |||||||
\(788\) | −22.8677 | −0.814627 | ||||||||
\(789\) | 7.94399 | 0.282814 | ||||||||
\(790\) | −12.4358 | −0.442447 | ||||||||
\(791\) | 5.15218 | 0.183190 | ||||||||
\(792\) | 58.3019 | 2.07167 | ||||||||
\(793\) | 6.46443 | 0.229559 | ||||||||
\(794\) | −6.14532 | −0.218089 | ||||||||
\(795\) | −1.67890 | −0.0595443 | ||||||||
\(796\) | 55.3618 | 1.96225 | ||||||||
\(797\) | 0.294649 | 0.0104370 | 0.00521850 | − | 0.999986i | \(-0.498339\pi\) | ||||
0.00521850 | + | 0.999986i | \(0.498339\pi\) | |||||||
\(798\) | −6.51833 | −0.230746 | ||||||||
\(799\) | −8.36545 | −0.295948 | ||||||||
\(800\) | −27.5937 | −0.975583 | ||||||||
\(801\) | −16.3805 | −0.578777 | ||||||||
\(802\) | 21.5388 | 0.760561 | ||||||||
\(803\) | 26.4645 | 0.933911 | ||||||||
\(804\) | −22.6782 | −0.799799 | ||||||||
\(805\) | 3.94812 | 0.139153 | ||||||||
\(806\) | 5.36961 | 0.189137 | ||||||||
\(807\) | −1.64205 | −0.0578031 | ||||||||
\(808\) | 156.560 | 5.50776 | ||||||||
\(809\) | −47.6044 | −1.67368 | −0.836841 | − | 0.547446i | \(-0.815600\pi\) | ||||
−0.836841 | + | 0.547446i | \(0.815600\pi\) | |||||||
\(810\) | 22.8241 | 0.801956 | ||||||||
\(811\) | −23.3322 | −0.819305 | −0.409652 | − | 0.912242i | \(-0.634350\pi\) | ||||
−0.409652 | + | 0.912242i | \(0.634350\pi\) | |||||||
\(812\) | 54.2700 | 1.90450 | ||||||||
\(813\) | 5.76045 | 0.202028 | ||||||||
\(814\) | −50.1993 | −1.75948 | ||||||||
\(815\) | −13.3747 | −0.468496 | ||||||||
\(816\) | 5.09903 | 0.178502 | ||||||||
\(817\) | 54.7691 | 1.91613 | ||||||||
\(818\) | −2.34678 | −0.0820531 | ||||||||
\(819\) | 2.33144 | 0.0814671 | ||||||||
\(820\) | 23.8620 | 0.833296 | ||||||||
\(821\) | 28.6336 | 0.999320 | 0.499660 | − | 0.866222i | \(-0.333458\pi\) | ||||
0.499660 | + | 0.866222i | \(0.333458\pi\) | |||||||
\(822\) | −12.2538 | −0.427400 | ||||||||
\(823\) | 47.1786 | 1.64454 | 0.822271 | − | 0.569096i | \(-0.192707\pi\) | ||||
0.822271 | + | 0.569096i | \(0.192707\pi\) | |||||||
\(824\) | −36.6415 | −1.27647 | ||||||||
\(825\) | 0.575266 | 0.0200282 | ||||||||
\(826\) | 4.12875 | 0.143658 | ||||||||
\(827\) | −33.4694 | −1.16384 | −0.581922 | − | 0.813244i | \(-0.697699\pi\) | ||||
−0.581922 | + | 0.813244i | \(0.697699\pi\) | |||||||
\(828\) | −65.8755 | −2.28933 | ||||||||
\(829\) | 11.2550 | 0.390902 | 0.195451 | − | 0.980713i | \(-0.437383\pi\) | ||||
0.195451 | + | 0.980713i | \(0.437383\pi\) | |||||||
\(830\) | −21.2761 | −0.738505 | ||||||||
\(831\) | 2.79120 | 0.0968257 | ||||||||
\(832\) | 33.5977 | 1.16479 | ||||||||
\(833\) | 0.984021 | 0.0340943 | ||||||||
\(834\) | 18.1908 | 0.629894 | ||||||||
\(835\) | −2.92099 | −0.101085 | ||||||||
\(836\) | −87.0182 | −3.00959 | ||||||||
\(837\) | 4.24811 | 0.146836 | ||||||||
\(838\) | −37.7010 | −1.30236 | ||||||||
\(839\) | 22.1711 | 0.765431 | 0.382715 | − | 0.923866i | \(-0.374989\pi\) | ||||
0.382715 | + | 0.923866i | \(0.374989\pi\) | |||||||
\(840\) | −3.09225 | −0.106693 | ||||||||
\(841\) | 60.6581 | 2.09166 | ||||||||
\(842\) | −96.0593 | −3.31042 | ||||||||
\(843\) | 8.23125 | 0.283499 | ||||||||
\(844\) | −119.399 | −4.10989 | ||||||||
\(845\) | 12.3586 | 0.425150 | ||||||||
\(846\) | −68.8152 | −2.36591 | ||||||||
\(847\) | 7.27430 | 0.249948 | ||||||||
\(848\) | 97.9438 | 3.36340 | ||||||||
\(849\) | 8.02811 | 0.275524 | ||||||||
\(850\) | −2.73612 | −0.0938481 | ||||||||
\(851\) | 36.9278 | 1.26587 | ||||||||
\(852\) | −6.08433 | −0.208446 | ||||||||
\(853\) | −13.6775 | −0.468309 | −0.234155 | − | 0.972199i | \(-0.575232\pi\) | ||||
−0.234155 | + | 0.972199i | \(0.575232\pi\) | |||||||
\(854\) | 22.4443 | 0.768027 | ||||||||
\(855\) | −22.8986 | −0.783116 | ||||||||
\(856\) | 203.681 | 6.96166 | ||||||||
\(857\) | 42.9241 | 1.46626 | 0.733130 | − | 0.680088i | \(-0.238059\pi\) | ||||
0.733130 | + | 0.680088i | \(0.238059\pi\) | |||||||
\(858\) | −1.28102 | −0.0437332 | ||||||||
\(859\) | −37.0842 | −1.26530 | −0.632649 | − | 0.774439i | \(-0.718032\pi\) | ||||
−0.632649 | + | 0.774439i | \(0.718032\pi\) | |||||||
\(860\) | 39.9080 | 1.36085 | ||||||||
\(861\) | 1.24081 | 0.0422868 | ||||||||
\(862\) | 45.6111 | 1.55352 | ||||||||
\(863\) | 19.8413 | 0.675406 | 0.337703 | − | 0.941253i | \(-0.390350\pi\) | ||||
0.337703 | + | 0.941253i | \(0.390350\pi\) | |||||||
\(864\) | 48.6125 | 1.65383 | ||||||||
\(865\) | −11.8602 | −0.403258 | ||||||||
\(866\) | −21.1509 | −0.718735 | ||||||||
\(867\) | −4.77798 | −0.162269 | ||||||||
\(868\) | 13.8204 | 0.469097 | ||||||||
\(869\) | −8.63273 | −0.292845 | ||||||||
\(870\) | −7.84676 | −0.266030 | ||||||||
\(871\) | −10.6325 | −0.360267 | ||||||||
\(872\) | −13.0159 | −0.440774 | ||||||||
\(873\) | −54.6093 | −1.84825 | ||||||||
\(874\) | 86.3499 | 2.92083 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 23.4201 | 0.791294 | ||||||||
\(877\) | 30.8011 | 1.04008 | 0.520040 | − | 0.854142i | \(-0.325917\pi\) | ||||
0.520040 | + | 0.854142i | \(0.325917\pi\) | |||||||
\(878\) | 50.5667 | 1.70654 | ||||||||
\(879\) | −4.33015 | −0.146052 | ||||||||
\(880\) | −33.5600 | −1.13131 | ||||||||
\(881\) | −3.35327 | −0.112974 | −0.0564872 | − | 0.998403i | \(-0.517990\pi\) | ||||
−0.0564872 | + | 0.998403i | \(0.517990\pi\) | |||||||
\(882\) | 8.09467 | 0.272562 | ||||||||
\(883\) | −19.9101 | −0.670027 | −0.335014 | − | 0.942213i | \(-0.608741\pi\) | ||||
−0.335014 | + | 0.942213i | \(0.608741\pi\) | |||||||
\(884\) | 4.51674 | 0.151914 | ||||||||
\(885\) | −0.442540 | −0.0148758 | ||||||||
\(886\) | 32.6461 | 1.09677 | ||||||||
\(887\) | 38.0937 | 1.27906 | 0.639530 | − | 0.768766i | \(-0.279129\pi\) | ||||
0.639530 | + | 0.768766i | \(0.279129\pi\) | |||||||
\(888\) | −28.9226 | −0.970580 | ||||||||
\(889\) | −14.0867 | −0.472452 | ||||||||
\(890\) | 15.6455 | 0.524438 | ||||||||
\(891\) | 15.8441 | 0.530796 | ||||||||
\(892\) | 31.1181 | 1.04191 | ||||||||
\(893\) | 66.8691 | 2.23769 | ||||||||
\(894\) | −11.0512 | −0.369608 | ||||||||
\(895\) | 6.68431 | 0.223432 | ||||||||
\(896\) | 61.4626 | 2.05332 | ||||||||
\(897\) | 0.942347 | 0.0314640 | ||||||||
\(898\) | 20.7384 | 0.692051 | ||||||||
\(899\) | 22.8324 | 0.761503 | ||||||||
\(900\) | −16.6853 | −0.556177 | ||||||||
\(901\) | 5.54323 | 0.184672 | ||||||||
\(902\) | 22.3448 | 0.743999 | ||||||||
\(903\) | 2.07520 | 0.0690583 | ||||||||
\(904\) | 53.4566 | 1.77794 | ||||||||
\(905\) | −16.3937 | −0.544946 | ||||||||
\(906\) | 1.26759 | 0.0421130 | ||||||||
\(907\) | 21.5946 | 0.717037 | 0.358518 | − | 0.933523i | \(-0.383282\pi\) | ||||
0.358518 | + | 0.933523i | \(0.383282\pi\) | |||||||
\(908\) | 43.4194 | 1.44092 | ||||||||
\(909\) | 43.9278 | 1.45699 | ||||||||
\(910\) | −2.22683 | −0.0738186 | ||||||||
\(911\) | 43.0329 | 1.42574 | 0.712872 | − | 0.701294i | \(-0.247394\pi\) | ||||
0.712872 | + | 0.701294i | \(0.247394\pi\) | |||||||
\(912\) | −40.7590 | −1.34967 | ||||||||
\(913\) | −14.7695 | −0.488799 | ||||||||
\(914\) | 60.7151 | 2.00828 | ||||||||
\(915\) | −2.40569 | −0.0795297 | ||||||||
\(916\) | 5.73146 | 0.189373 | ||||||||
\(917\) | 19.8616 | 0.655889 | ||||||||
\(918\) | 4.82030 | 0.159094 | ||||||||
\(919\) | −3.59329 | −0.118532 | −0.0592658 | − | 0.998242i | \(-0.518876\pi\) | ||||
−0.0592658 | + | 0.998242i | \(0.518876\pi\) | |||||||
\(920\) | 40.9638 | 1.35054 | ||||||||
\(921\) | 9.74352 | 0.321060 | ||||||||
\(922\) | −43.4844 | −1.43208 | ||||||||
\(923\) | −2.85258 | −0.0938938 | ||||||||
\(924\) | −3.29712 | −0.108467 | ||||||||
\(925\) | 9.35326 | 0.307533 | ||||||||
\(926\) | −81.0424 | −2.66322 | ||||||||
\(927\) | −10.2809 | −0.337669 | ||||||||
\(928\) | 261.279 | 8.57689 | ||||||||
\(929\) | 6.21078 | 0.203769 | 0.101885 | − | 0.994796i | \(-0.467513\pi\) | ||||
0.101885 | + | 0.994796i | \(0.467513\pi\) | |||||||
\(930\) | −1.99826 | −0.0655256 | ||||||||
\(931\) | −7.86576 | −0.257790 | ||||||||
\(932\) | −130.364 | −4.27023 | ||||||||
\(933\) | −7.88534 | −0.258154 | ||||||||
\(934\) | 10.3152 | 0.337523 | ||||||||
\(935\) | −1.89936 | −0.0621158 | ||||||||
\(936\) | 24.1899 | 0.790671 | ||||||||
\(937\) | −32.9998 | −1.07806 | −0.539028 | − | 0.842288i | \(-0.681208\pi\) | ||||
−0.539028 | + | 0.842288i | \(0.681208\pi\) | |||||||
\(938\) | −36.9155 | −1.20534 | ||||||||
\(939\) | 9.28146 | 0.302889 | ||||||||
\(940\) | 48.7248 | 1.58923 | ||||||||
\(941\) | −22.3146 | −0.727436 | −0.363718 | − | 0.931509i | \(-0.618493\pi\) | ||||
−0.363718 | + | 0.931509i | \(0.618493\pi\) | |||||||
\(942\) | 11.3745 | 0.370601 | ||||||||
\(943\) | −16.4373 | −0.535273 | ||||||||
\(944\) | 25.8170 | 0.840272 | ||||||||
\(945\) | −1.76173 | −0.0573090 | ||||||||
\(946\) | 37.3706 | 1.21502 | ||||||||
\(947\) | 35.2445 | 1.14529 | 0.572646 | − | 0.819802i | \(-0.305917\pi\) | ||||
0.572646 | + | 0.819802i | \(0.305917\pi\) | |||||||
\(948\) | −7.63967 | −0.248125 | ||||||||
\(949\) | 10.9803 | 0.356436 | ||||||||
\(950\) | 21.8711 | 0.709594 | ||||||||
\(951\) | −4.28797 | −0.139047 | ||||||||
\(952\) | 10.2097 | 0.330899 | ||||||||
\(953\) | −25.9978 | −0.842150 | −0.421075 | − | 0.907026i | \(-0.638347\pi\) | ||||
−0.421075 | + | 0.907026i | \(0.638347\pi\) | |||||||
\(954\) | 45.5993 | 1.47633 | ||||||||
\(955\) | −10.8073 | −0.349715 | ||||||||
\(956\) | 53.3035 | 1.72396 | ||||||||
\(957\) | −5.44708 | −0.176079 | ||||||||
\(958\) | 77.9802 | 2.51943 | ||||||||
\(959\) | −14.7868 | −0.477491 | ||||||||
\(960\) | −12.5031 | −0.403537 | ||||||||
\(961\) | −25.1855 | −0.812435 | ||||||||
\(962\) | −20.8281 | −0.671524 | ||||||||
\(963\) | 57.1489 | 1.84160 | ||||||||
\(964\) | 3.28058 | 0.105660 | ||||||||
\(965\) | −3.27495 | −0.105424 | ||||||||
\(966\) | 3.27179 | 0.105268 | ||||||||
\(967\) | −27.8976 | −0.897127 | −0.448564 | − | 0.893751i | \(-0.648064\pi\) | ||||
−0.448564 | + | 0.893751i | \(0.648064\pi\) | |||||||
\(968\) | 75.4747 | 2.42585 | ||||||||
\(969\) | −2.30680 | −0.0741051 | ||||||||
\(970\) | 52.1590 | 1.67472 | ||||||||
\(971\) | 8.17443 | 0.262330 | 0.131165 | − | 0.991361i | \(-0.458128\pi\) | ||||
0.131165 | + | 0.991361i | \(0.458128\pi\) | |||||||
\(972\) | 44.3133 | 1.42135 | ||||||||
\(973\) | 21.9510 | 0.703718 | ||||||||
\(974\) | 59.4677 | 1.90547 | ||||||||
\(975\) | 0.238682 | 0.00764396 | ||||||||
\(976\) | 140.344 | 4.49229 | ||||||||
\(977\) | 54.1255 | 1.73163 | 0.865814 | − | 0.500365i | \(-0.166801\pi\) | ||||
0.865814 | + | 0.500365i | \(0.166801\pi\) | |||||||
\(978\) | −11.0836 | −0.354414 | ||||||||
\(979\) | 10.8608 | 0.347113 | ||||||||
\(980\) | −5.73146 | −0.183085 | ||||||||
\(981\) | −3.65201 | −0.116600 | ||||||||
\(982\) | −37.8853 | −1.20897 | ||||||||
\(983\) | −27.7172 | −0.884043 | −0.442021 | − | 0.897005i | \(-0.645738\pi\) | ||||
−0.442021 | + | 0.897005i | \(0.645738\pi\) | |||||||
\(984\) | 12.8741 | 0.410410 | ||||||||
\(985\) | 3.98985 | 0.127127 | ||||||||
\(986\) | 25.9078 | 0.825071 | ||||||||
\(987\) | 2.53367 | 0.0806476 | ||||||||
\(988\) | −36.1045 | −1.14864 | ||||||||
\(989\) | −27.4906 | −0.874152 | ||||||||
\(990\) | −15.6244 | −0.496576 | ||||||||
\(991\) | 24.2773 | 0.771193 | 0.385596 | − | 0.922668i | \(-0.373996\pi\) | ||||
0.385596 | + | 0.922668i | \(0.373996\pi\) | |||||||
\(992\) | 66.5374 | 2.11257 | ||||||||
\(993\) | 0.822944 | 0.0261153 | ||||||||
\(994\) | −9.90406 | −0.314138 | ||||||||
\(995\) | −9.65928 | −0.306220 | ||||||||
\(996\) | −13.0705 | −0.414155 | ||||||||
\(997\) | 32.3716 | 1.02522 | 0.512610 | − | 0.858622i | \(-0.328679\pi\) | ||||
0.512610 | + | 0.858622i | \(0.328679\pi\) | |||||||
\(998\) | −25.8551 | −0.818428 | ||||||||
\(999\) | −16.4779 | −0.521338 |
(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 | 8015.2.a.l.1.1 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.l.1.1 | ✓ | 62 | 1.1 | even | 1 | trivial |