Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6018,2,Mod(1,6018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6018, 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("6018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6018.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.0539719364\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.1668357.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 11x^{3} + x^{2} + 17x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.44651\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6018.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.37256 | −0.613826 | −0.306913 | − | 0.951738i | \(-0.599296\pi\) | ||||
−0.306913 | + | 0.951738i | \(0.599296\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 2.44651 | 0.924694 | 0.462347 | − | 0.886699i | \(-0.347007\pi\) | ||||
0.462347 | + | 0.886699i | \(0.347007\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.37256 | 0.434040 | ||||||||
\(11\) | 4.53685 | 1.36791 | 0.683956 | − | 0.729524i | \(-0.260258\pi\) | ||||
0.683956 | + | 0.729524i | \(0.260258\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −3.92241 | −1.08788 | −0.543940 | − | 0.839124i | \(-0.683068\pi\) | ||||
−0.543940 | + | 0.839124i | \(0.683068\pi\) | |||||||
\(14\) | −2.44651 | −0.653858 | ||||||||
\(15\) | −1.37256 | −0.354392 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 1.28222 | 0.294161 | 0.147081 | − | 0.989125i | \(-0.453012\pi\) | ||||
0.147081 | + | 0.989125i | \(0.453012\pi\) | |||||||
\(20\) | −1.37256 | −0.306913 | ||||||||
\(21\) | 2.44651 | 0.533873 | ||||||||
\(22\) | −4.53685 | −0.967259 | ||||||||
\(23\) | 3.17888 | 0.662841 | 0.331421 | − | 0.943483i | \(-0.392472\pi\) | ||||
0.331421 | + | 0.943483i | \(0.392472\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −3.11609 | −0.623218 | ||||||||
\(26\) | 3.92241 | 0.769248 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.44651 | 0.462347 | ||||||||
\(29\) | −4.44468 | −0.825356 | −0.412678 | − | 0.910877i | \(-0.635406\pi\) | ||||
−0.412678 | + | 0.910877i | \(0.635406\pi\) | |||||||
\(30\) | 1.37256 | 0.250593 | ||||||||
\(31\) | 5.90783 | 1.06108 | 0.530539 | − | 0.847661i | \(-0.321990\pi\) | ||||
0.530539 | + | 0.847661i | \(0.321990\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.53685 | 0.789764 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | −3.35797 | −0.567601 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −1.11972 | −0.184082 | −0.0920408 | − | 0.995755i | \(-0.529339\pi\) | ||||
−0.0920408 | + | 0.995755i | \(0.529339\pi\) | |||||||
\(38\) | −1.28222 | −0.208003 | ||||||||
\(39\) | −3.92241 | −0.628088 | ||||||||
\(40\) | 1.37256 | 0.217020 | ||||||||
\(41\) | 5.71415 | 0.892400 | 0.446200 | − | 0.894933i | \(-0.352777\pi\) | ||||
0.446200 | + | 0.894933i | \(0.352777\pi\) | |||||||
\(42\) | −2.44651 | −0.377505 | ||||||||
\(43\) | −3.32679 | −0.507330 | −0.253665 | − | 0.967292i | \(-0.581636\pi\) | ||||
−0.253665 | + | 0.967292i | \(0.581636\pi\) | |||||||
\(44\) | 4.53685 | 0.683956 | ||||||||
\(45\) | −1.37256 | −0.204609 | ||||||||
\(46\) | −3.17888 | −0.468700 | ||||||||
\(47\) | 12.7605 | 1.86131 | 0.930656 | − | 0.365895i | \(-0.119237\pi\) | ||||
0.930656 | + | 0.365895i | \(0.119237\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −1.01458 | −0.144940 | ||||||||
\(50\) | 3.11609 | 0.440682 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −3.92241 | −0.543940 | ||||||||
\(53\) | 6.22101 | 0.854522 | 0.427261 | − | 0.904128i | \(-0.359479\pi\) | ||||
0.427261 | + | 0.904128i | \(0.359479\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −6.22708 | −0.839659 | ||||||||
\(56\) | −2.44651 | −0.326929 | ||||||||
\(57\) | 1.28222 | 0.169834 | ||||||||
\(58\) | 4.44468 | 0.583615 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | −1.37256 | −0.177196 | ||||||||
\(61\) | 4.28402 | 0.548512 | 0.274256 | − | 0.961657i | \(-0.411568\pi\) | ||||
0.274256 | + | 0.961657i | \(0.411568\pi\) | |||||||
\(62\) | −5.90783 | −0.750295 | ||||||||
\(63\) | 2.44651 | 0.308231 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.38373 | 0.667769 | ||||||||
\(66\) | −4.53685 | −0.558447 | ||||||||
\(67\) | −14.1086 | −1.72364 | −0.861818 | − | 0.507218i | \(-0.830674\pi\) | ||||
−0.861818 | + | 0.507218i | \(0.830674\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | 3.17888 | 0.382692 | ||||||||
\(70\) | 3.35797 | 0.401355 | ||||||||
\(71\) | −10.3817 | −1.23208 | −0.616039 | − | 0.787716i | \(-0.711264\pi\) | ||||
−0.616039 | + | 0.787716i | \(0.711264\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 11.6347 | 1.36174 | 0.680871 | − | 0.732404i | \(-0.261602\pi\) | ||||
0.680871 | + | 0.732404i | \(0.261602\pi\) | |||||||
\(74\) | 1.11972 | 0.130165 | ||||||||
\(75\) | −3.11609 | −0.359815 | ||||||||
\(76\) | 1.28222 | 0.147081 | ||||||||
\(77\) | 11.0995 | 1.26490 | ||||||||
\(78\) | 3.92241 | 0.444126 | ||||||||
\(79\) | 14.0873 | 1.58495 | 0.792473 | − | 0.609908i | \(-0.208793\pi\) | ||||
0.792473 | + | 0.609908i | \(0.208793\pi\) | |||||||
\(80\) | −1.37256 | −0.153456 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.71415 | −0.631022 | ||||||||
\(83\) | 9.20886 | 1.01080 | 0.505402 | − | 0.862884i | \(-0.331344\pi\) | ||||
0.505402 | + | 0.862884i | \(0.331344\pi\) | |||||||
\(84\) | 2.44651 | 0.266936 | ||||||||
\(85\) | 1.37256 | 0.148875 | ||||||||
\(86\) | 3.32679 | 0.358737 | ||||||||
\(87\) | −4.44468 | −0.476519 | ||||||||
\(88\) | −4.53685 | −0.483630 | ||||||||
\(89\) | 14.8009 | 1.56889 | 0.784443 | − | 0.620200i | \(-0.212949\pi\) | ||||
0.784443 | + | 0.620200i | \(0.212949\pi\) | |||||||
\(90\) | 1.37256 | 0.144680 | ||||||||
\(91\) | −9.59622 | −1.00596 | ||||||||
\(92\) | 3.17888 | 0.331421 | ||||||||
\(93\) | 5.90783 | 0.612613 | ||||||||
\(94\) | −12.7605 | −1.31615 | ||||||||
\(95\) | −1.75992 | −0.180564 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −6.25100 | −0.634692 | −0.317346 | − | 0.948310i | \(-0.602792\pi\) | ||||
−0.317346 | + | 0.948310i | \(0.602792\pi\) | |||||||
\(98\) | 1.01458 | 0.102488 | ||||||||
\(99\) | 4.53685 | 0.455970 | ||||||||
\(100\) | −3.11609 | −0.311609 | ||||||||
\(101\) | −7.31037 | −0.727409 | −0.363704 | − | 0.931514i | \(-0.618488\pi\) | ||||
−0.363704 | + | 0.931514i | \(0.618488\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | 7.63233 | 0.752035 | 0.376018 | − | 0.926612i | \(-0.377293\pi\) | ||||
0.376018 | + | 0.926612i | \(0.377293\pi\) | |||||||
\(104\) | 3.92241 | 0.384624 | ||||||||
\(105\) | −3.35797 | −0.327705 | ||||||||
\(106\) | −6.22101 | −0.604238 | ||||||||
\(107\) | −4.49082 | −0.434144 | −0.217072 | − | 0.976156i | \(-0.569651\pi\) | ||||
−0.217072 | + | 0.976156i | \(0.569651\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −4.25283 | −0.407347 | −0.203674 | − | 0.979039i | \(-0.565288\pi\) | ||||
−0.203674 | + | 0.979039i | \(0.565288\pi\) | |||||||
\(110\) | 6.22708 | 0.593728 | ||||||||
\(111\) | −1.11972 | −0.106280 | ||||||||
\(112\) | 2.44651 | 0.231174 | ||||||||
\(113\) | 9.44831 | 0.888822 | 0.444411 | − | 0.895823i | \(-0.353413\pi\) | ||||
0.444411 | + | 0.895823i | \(0.353413\pi\) | |||||||
\(114\) | −1.28222 | −0.120091 | ||||||||
\(115\) | −4.36318 | −0.406869 | ||||||||
\(116\) | −4.44468 | −0.412678 | ||||||||
\(117\) | −3.92241 | −0.362627 | ||||||||
\(118\) | 1.00000 | 0.0920575 | ||||||||
\(119\) | −2.44651 | −0.224271 | ||||||||
\(120\) | 1.37256 | 0.125297 | ||||||||
\(121\) | 9.58299 | 0.871181 | ||||||||
\(122\) | −4.28402 | −0.387857 | ||||||||
\(123\) | 5.71415 | 0.515227 | ||||||||
\(124\) | 5.90783 | 0.530539 | ||||||||
\(125\) | 11.1398 | 0.996373 | ||||||||
\(126\) | −2.44651 | −0.217953 | ||||||||
\(127\) | 0.617352 | 0.0547811 | 0.0273906 | − | 0.999625i | \(-0.491280\pi\) | ||||
0.0273906 | + | 0.999625i | \(0.491280\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −3.32679 | −0.292907 | ||||||||
\(130\) | −5.38373 | −0.472184 | ||||||||
\(131\) | −4.86386 | −0.424957 | −0.212479 | − | 0.977166i | \(-0.568154\pi\) | ||||
−0.212479 | + | 0.977166i | \(0.568154\pi\) | |||||||
\(132\) | 4.53685 | 0.394882 | ||||||||
\(133\) | 3.13696 | 0.272009 | ||||||||
\(134\) | 14.1086 | 1.21879 | ||||||||
\(135\) | −1.37256 | −0.118131 | ||||||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | 4.51260 | 0.385538 | 0.192769 | − | 0.981244i | \(-0.438253\pi\) | ||||
0.192769 | + | 0.981244i | \(0.438253\pi\) | |||||||
\(138\) | −3.17888 | −0.270604 | ||||||||
\(139\) | −10.2338 | −0.868016 | −0.434008 | − | 0.900909i | \(-0.642901\pi\) | ||||
−0.434008 | + | 0.900909i | \(0.642901\pi\) | |||||||
\(140\) | −3.35797 | −0.283801 | ||||||||
\(141\) | 12.7605 | 1.07463 | ||||||||
\(142\) | 10.3817 | 0.871210 | ||||||||
\(143\) | −17.7954 | −1.48812 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 6.10057 | 0.506624 | ||||||||
\(146\) | −11.6347 | −0.962896 | ||||||||
\(147\) | −1.01458 | −0.0836814 | ||||||||
\(148\) | −1.11972 | −0.0920408 | ||||||||
\(149\) | 15.1122 | 1.23804 | 0.619020 | − | 0.785375i | \(-0.287530\pi\) | ||||
0.619020 | + | 0.785375i | \(0.287530\pi\) | |||||||
\(150\) | 3.11609 | 0.254428 | ||||||||
\(151\) | −18.4536 | −1.50173 | −0.750865 | − | 0.660456i | \(-0.770363\pi\) | ||||
−0.750865 | + | 0.660456i | \(0.770363\pi\) | |||||||
\(152\) | −1.28222 | −0.104002 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −11.0995 | −0.894419 | ||||||||
\(155\) | −8.10882 | −0.651316 | ||||||||
\(156\) | −3.92241 | −0.314044 | ||||||||
\(157\) | −7.52286 | −0.600390 | −0.300195 | − | 0.953878i | \(-0.597052\pi\) | ||||
−0.300195 | + | 0.953878i | \(0.597052\pi\) | |||||||
\(158\) | −14.0873 | −1.12073 | ||||||||
\(159\) | 6.22101 | 0.493358 | ||||||||
\(160\) | 1.37256 | 0.108510 | ||||||||
\(161\) | 7.77715 | 0.612926 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 10.9961 | 0.861282 | 0.430641 | − | 0.902523i | \(-0.358288\pi\) | ||||
0.430641 | + | 0.902523i | \(0.358288\pi\) | |||||||
\(164\) | 5.71415 | 0.446200 | ||||||||
\(165\) | −6.22708 | −0.484777 | ||||||||
\(166\) | −9.20886 | −0.714746 | ||||||||
\(167\) | −0.349234 | −0.0270246 | −0.0135123 | − | 0.999909i | \(-0.504301\pi\) | ||||
−0.0135123 | + | 0.999909i | \(0.504301\pi\) | |||||||
\(168\) | −2.44651 | −0.188752 | ||||||||
\(169\) | 2.38530 | 0.183485 | ||||||||
\(170\) | −1.37256 | −0.105270 | ||||||||
\(171\) | 1.28222 | 0.0980537 | ||||||||
\(172\) | −3.32679 | −0.253665 | ||||||||
\(173\) | −2.38590 | −0.181397 | −0.0906983 | − | 0.995878i | \(-0.528910\pi\) | ||||
−0.0906983 | + | 0.995878i | \(0.528910\pi\) | |||||||
\(174\) | 4.44468 | 0.336950 | ||||||||
\(175\) | −7.62355 | −0.576286 | ||||||||
\(176\) | 4.53685 | 0.341978 | ||||||||
\(177\) | −1.00000 | −0.0751646 | ||||||||
\(178\) | −14.8009 | −1.10937 | ||||||||
\(179\) | −1.29654 | −0.0969081 | −0.0484541 | − | 0.998825i | \(-0.515429\pi\) | ||||
−0.0484541 | + | 0.998825i | \(0.515429\pi\) | |||||||
\(180\) | −1.37256 | −0.102304 | ||||||||
\(181\) | −7.64648 | −0.568358 | −0.284179 | − | 0.958771i | \(-0.591721\pi\) | ||||
−0.284179 | + | 0.958771i | \(0.591721\pi\) | |||||||
\(182\) | 9.59622 | 0.711319 | ||||||||
\(183\) | 4.28402 | 0.316684 | ||||||||
\(184\) | −3.17888 | −0.234350 | ||||||||
\(185\) | 1.53688 | 0.112994 | ||||||||
\(186\) | −5.90783 | −0.433183 | ||||||||
\(187\) | −4.53685 | −0.331767 | ||||||||
\(188\) | 12.7605 | 0.930656 | ||||||||
\(189\) | 2.44651 | 0.177958 | ||||||||
\(190\) | 1.75992 | 0.127678 | ||||||||
\(191\) | 14.1519 | 1.02399 | 0.511997 | − | 0.858987i | \(-0.328906\pi\) | ||||
0.511997 | + | 0.858987i | \(0.328906\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 16.3671 | 1.17813 | 0.589064 | − | 0.808086i | \(-0.299496\pi\) | ||||
0.589064 | + | 0.808086i | \(0.299496\pi\) | |||||||
\(194\) | 6.25100 | 0.448795 | ||||||||
\(195\) | 5.38373 | 0.385537 | ||||||||
\(196\) | −1.01458 | −0.0724702 | ||||||||
\(197\) | 4.28585 | 0.305354 | 0.152677 | − | 0.988276i | \(-0.451211\pi\) | ||||
0.152677 | + | 0.988276i | \(0.451211\pi\) | |||||||
\(198\) | −4.53685 | −0.322420 | ||||||||
\(199\) | −20.6226 | −1.46190 | −0.730948 | − | 0.682434i | \(-0.760922\pi\) | ||||
−0.730948 | + | 0.682434i | \(0.760922\pi\) | |||||||
\(200\) | 3.11609 | 0.220341 | ||||||||
\(201\) | −14.1086 | −0.995141 | ||||||||
\(202\) | 7.31037 | 0.514356 | ||||||||
\(203\) | −10.8739 | −0.763202 | ||||||||
\(204\) | −1.00000 | −0.0700140 | ||||||||
\(205\) | −7.84299 | −0.547778 | ||||||||
\(206\) | −7.63233 | −0.531769 | ||||||||
\(207\) | 3.17888 | 0.220947 | ||||||||
\(208\) | −3.92241 | −0.271970 | ||||||||
\(209\) | 5.81723 | 0.402386 | ||||||||
\(210\) | 3.35797 | 0.231722 | ||||||||
\(211\) | −3.27881 | −0.225722 | −0.112861 | − | 0.993611i | \(-0.536002\pi\) | ||||
−0.112861 | + | 0.993611i | \(0.536002\pi\) | |||||||
\(212\) | 6.22101 | 0.427261 | ||||||||
\(213\) | −10.3817 | −0.711340 | ||||||||
\(214\) | 4.49082 | 0.306986 | ||||||||
\(215\) | 4.56620 | 0.311412 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 14.4536 | 0.981172 | ||||||||
\(218\) | 4.25283 | 0.288038 | ||||||||
\(219\) | 11.6347 | 0.786202 | ||||||||
\(220\) | −6.22708 | −0.419829 | ||||||||
\(221\) | 3.92241 | 0.263850 | ||||||||
\(222\) | 1.11972 | 0.0751510 | ||||||||
\(223\) | 7.89786 | 0.528880 | 0.264440 | − | 0.964402i | \(-0.414813\pi\) | ||||
0.264440 | + | 0.964402i | \(0.414813\pi\) | |||||||
\(224\) | −2.44651 | −0.163464 | ||||||||
\(225\) | −3.11609 | −0.207739 | ||||||||
\(226\) | −9.44831 | −0.628492 | ||||||||
\(227\) | 3.21878 | 0.213638 | 0.106819 | − | 0.994278i | \(-0.465933\pi\) | ||||
0.106819 | + | 0.994278i | \(0.465933\pi\) | |||||||
\(228\) | 1.28222 | 0.0849170 | ||||||||
\(229\) | 8.63791 | 0.570809 | 0.285405 | − | 0.958407i | \(-0.407872\pi\) | ||||
0.285405 | + | 0.958407i | \(0.407872\pi\) | |||||||
\(230\) | 4.36318 | 0.287700 | ||||||||
\(231\) | 11.0995 | 0.730290 | ||||||||
\(232\) | 4.44468 | 0.291807 | ||||||||
\(233\) | −2.25951 | −0.148026 | −0.0740128 | − | 0.997257i | \(-0.523581\pi\) | ||||
−0.0740128 | + | 0.997257i | \(0.523581\pi\) | |||||||
\(234\) | 3.92241 | 0.256416 | ||||||||
\(235\) | −17.5145 | −1.14252 | ||||||||
\(236\) | −1.00000 | −0.0650945 | ||||||||
\(237\) | 14.0873 | 0.915068 | ||||||||
\(238\) | 2.44651 | 0.158584 | ||||||||
\(239\) | 25.9175 | 1.67647 | 0.838233 | − | 0.545312i | \(-0.183589\pi\) | ||||
0.838233 | + | 0.545312i | \(0.183589\pi\) | |||||||
\(240\) | −1.37256 | −0.0885981 | ||||||||
\(241\) | 14.0196 | 0.903084 | 0.451542 | − | 0.892250i | \(-0.350874\pi\) | ||||
0.451542 | + | 0.892250i | \(0.350874\pi\) | |||||||
\(242\) | −9.58299 | −0.616018 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 4.28402 | 0.274256 | ||||||||
\(245\) | 1.39257 | 0.0889681 | ||||||||
\(246\) | −5.71415 | −0.364321 | ||||||||
\(247\) | −5.02939 | −0.320012 | ||||||||
\(248\) | −5.90783 | −0.375147 | ||||||||
\(249\) | 9.20886 | 0.583588 | ||||||||
\(250\) | −11.1398 | −0.704542 | ||||||||
\(251\) | −10.4937 | −0.662359 | −0.331179 | − | 0.943568i | \(-0.607446\pi\) | ||||
−0.331179 | + | 0.943568i | \(0.607446\pi\) | |||||||
\(252\) | 2.44651 | 0.154116 | ||||||||
\(253\) | 14.4221 | 0.906708 | ||||||||
\(254\) | −0.617352 | −0.0387361 | ||||||||
\(255\) | 1.37256 | 0.0859528 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 25.9848 | 1.62089 | 0.810445 | − | 0.585815i | \(-0.199226\pi\) | ||||
0.810445 | + | 0.585815i | \(0.199226\pi\) | |||||||
\(258\) | 3.32679 | 0.207117 | ||||||||
\(259\) | −2.73942 | −0.170219 | ||||||||
\(260\) | 5.38373 | 0.333885 | ||||||||
\(261\) | −4.44468 | −0.275119 | ||||||||
\(262\) | 4.86386 | 0.300490 | ||||||||
\(263\) | 16.6742 | 1.02818 | 0.514088 | − | 0.857738i | \(-0.328131\pi\) | ||||
0.514088 | + | 0.857738i | \(0.328131\pi\) | |||||||
\(264\) | −4.53685 | −0.279224 | ||||||||
\(265\) | −8.53868 | −0.524527 | ||||||||
\(266\) | −3.13696 | −0.192340 | ||||||||
\(267\) | 14.8009 | 0.905797 | ||||||||
\(268\) | −14.1086 | −0.861818 | ||||||||
\(269\) | −17.1270 | −1.04425 | −0.522127 | − | 0.852868i | \(-0.674861\pi\) | ||||
−0.522127 | + | 0.852868i | \(0.674861\pi\) | |||||||
\(270\) | 1.37256 | 0.0835311 | ||||||||
\(271\) | −16.7230 | −1.01585 | −0.507925 | − | 0.861401i | \(-0.669587\pi\) | ||||
−0.507925 | + | 0.861401i | \(0.669587\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | −9.59622 | −0.580790 | ||||||||
\(274\) | −4.51260 | −0.272616 | ||||||||
\(275\) | −14.1372 | −0.852507 | ||||||||
\(276\) | 3.17888 | 0.191346 | ||||||||
\(277\) | 6.16976 | 0.370705 | 0.185353 | − | 0.982672i | \(-0.440657\pi\) | ||||
0.185353 | + | 0.982672i | \(0.440657\pi\) | |||||||
\(278\) | 10.2338 | 0.613780 | ||||||||
\(279\) | 5.90783 | 0.353692 | ||||||||
\(280\) | 3.35797 | 0.200677 | ||||||||
\(281\) | −21.8738 | −1.30488 | −0.652440 | − | 0.757840i | \(-0.726255\pi\) | ||||
−0.652440 | + | 0.757840i | \(0.726255\pi\) | |||||||
\(282\) | −12.7605 | −0.759878 | ||||||||
\(283\) | −3.51379 | −0.208873 | −0.104436 | − | 0.994532i | \(-0.533304\pi\) | ||||
−0.104436 | + | 0.994532i | \(0.533304\pi\) | |||||||
\(284\) | −10.3817 | −0.616039 | ||||||||
\(285\) | −1.75992 | −0.104248 | ||||||||
\(286\) | 17.7954 | 1.05226 | ||||||||
\(287\) | 13.9797 | 0.825197 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −6.10057 | −0.358238 | ||||||||
\(291\) | −6.25100 | −0.366440 | ||||||||
\(292\) | 11.6347 | 0.680871 | ||||||||
\(293\) | 9.89280 | 0.577944 | 0.288972 | − | 0.957338i | \(-0.406687\pi\) | ||||
0.288972 | + | 0.957338i | \(0.406687\pi\) | |||||||
\(294\) | 1.01458 | 0.0591717 | ||||||||
\(295\) | 1.37256 | 0.0799133 | ||||||||
\(296\) | 1.11972 | 0.0650827 | ||||||||
\(297\) | 4.53685 | 0.263255 | ||||||||
\(298\) | −15.1122 | −0.875426 | ||||||||
\(299\) | −12.4689 | −0.721092 | ||||||||
\(300\) | −3.11609 | −0.179908 | ||||||||
\(301\) | −8.13902 | −0.469125 | ||||||||
\(302\) | 18.4536 | 1.06188 | ||||||||
\(303\) | −7.31037 | −0.419970 | ||||||||
\(304\) | 1.28222 | 0.0735403 | ||||||||
\(305\) | −5.88005 | −0.336691 | ||||||||
\(306\) | 1.00000 | 0.0571662 | ||||||||
\(307\) | 13.8309 | 0.789370 | 0.394685 | − | 0.918817i | \(-0.370854\pi\) | ||||
0.394685 | + | 0.918817i | \(0.370854\pi\) | |||||||
\(308\) | 11.0995 | 0.632450 | ||||||||
\(309\) | 7.63233 | 0.434188 | ||||||||
\(310\) | 8.10882 | 0.460550 | ||||||||
\(311\) | 14.0500 | 0.796702 | 0.398351 | − | 0.917233i | \(-0.369583\pi\) | ||||
0.398351 | + | 0.917233i | \(0.369583\pi\) | |||||||
\(312\) | 3.92241 | 0.222063 | ||||||||
\(313\) | −6.65585 | −0.376211 | −0.188106 | − | 0.982149i | \(-0.560235\pi\) | ||||
−0.188106 | + | 0.982149i | \(0.560235\pi\) | |||||||
\(314\) | 7.52286 | 0.424540 | ||||||||
\(315\) | −3.35797 | −0.189200 | ||||||||
\(316\) | 14.0873 | 0.792473 | ||||||||
\(317\) | −8.10346 | −0.455136 | −0.227568 | − | 0.973762i | \(-0.573077\pi\) | ||||
−0.227568 | + | 0.973762i | \(0.573077\pi\) | |||||||
\(318\) | −6.22101 | −0.348857 | ||||||||
\(319\) | −20.1648 | −1.12901 | ||||||||
\(320\) | −1.37256 | −0.0767282 | ||||||||
\(321\) | −4.49082 | −0.250653 | ||||||||
\(322\) | −7.77715 | −0.433404 | ||||||||
\(323\) | −1.28222 | −0.0713446 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 12.2226 | 0.677987 | ||||||||
\(326\) | −10.9961 | −0.609018 | ||||||||
\(327\) | −4.25283 | −0.235182 | ||||||||
\(328\) | −5.71415 | −0.315511 | ||||||||
\(329\) | 31.2187 | 1.72114 | ||||||||
\(330\) | 6.22708 | 0.342789 | ||||||||
\(331\) | −6.21793 | −0.341768 | −0.170884 | − | 0.985291i | \(-0.554662\pi\) | ||||
−0.170884 | + | 0.985291i | \(0.554662\pi\) | |||||||
\(332\) | 9.20886 | 0.505402 | ||||||||
\(333\) | −1.11972 | −0.0613605 | ||||||||
\(334\) | 0.349234 | 0.0191093 | ||||||||
\(335\) | 19.3648 | 1.05801 | ||||||||
\(336\) | 2.44651 | 0.133468 | ||||||||
\(337\) | −5.56650 | −0.303226 | −0.151613 | − | 0.988440i | \(-0.548447\pi\) | ||||
−0.151613 | + | 0.988440i | \(0.548447\pi\) | |||||||
\(338\) | −2.38530 | −0.129743 | ||||||||
\(339\) | 9.44831 | 0.513162 | ||||||||
\(340\) | 1.37256 | 0.0744373 | ||||||||
\(341\) | 26.8029 | 1.45146 | ||||||||
\(342\) | −1.28222 | −0.0693344 | ||||||||
\(343\) | −19.6078 | −1.05872 | ||||||||
\(344\) | 3.32679 | 0.179368 | ||||||||
\(345\) | −4.36318 | −0.234906 | ||||||||
\(346\) | 2.38590 | 0.128267 | ||||||||
\(347\) | 24.3057 | 1.30480 | 0.652398 | − | 0.757877i | \(-0.273763\pi\) | ||||
0.652398 | + | 0.757877i | \(0.273763\pi\) | |||||||
\(348\) | −4.44468 | −0.238260 | ||||||||
\(349\) | 24.6813 | 1.32116 | 0.660579 | − | 0.750757i | \(-0.270311\pi\) | ||||
0.660579 | + | 0.750757i | \(0.270311\pi\) | |||||||
\(350\) | 7.62355 | 0.407496 | ||||||||
\(351\) | −3.92241 | −0.209363 | ||||||||
\(352\) | −4.53685 | −0.241815 | ||||||||
\(353\) | 30.3271 | 1.61415 | 0.807075 | − | 0.590449i | \(-0.201049\pi\) | ||||
0.807075 | + | 0.590449i | \(0.201049\pi\) | |||||||
\(354\) | 1.00000 | 0.0531494 | ||||||||
\(355\) | 14.2494 | 0.756281 | ||||||||
\(356\) | 14.8009 | 0.784443 | ||||||||
\(357\) | −2.44651 | −0.129483 | ||||||||
\(358\) | 1.29654 | 0.0685244 | ||||||||
\(359\) | 15.5771 | 0.822130 | 0.411065 | − | 0.911606i | \(-0.365157\pi\) | ||||
0.411065 | + | 0.911606i | \(0.365157\pi\) | |||||||
\(360\) | 1.37256 | 0.0723400 | ||||||||
\(361\) | −17.3559 | −0.913469 | ||||||||
\(362\) | 7.64648 | 0.401890 | ||||||||
\(363\) | 9.58299 | 0.502977 | ||||||||
\(364\) | −9.59622 | −0.502979 | ||||||||
\(365\) | −15.9693 | −0.835872 | ||||||||
\(366\) | −4.28402 | −0.223929 | ||||||||
\(367\) | 12.8664 | 0.671622 | 0.335811 | − | 0.941929i | \(-0.390990\pi\) | ||||
0.335811 | + | 0.941929i | \(0.390990\pi\) | |||||||
\(368\) | 3.17888 | 0.165710 | ||||||||
\(369\) | 5.71415 | 0.297467 | ||||||||
\(370\) | −1.53688 | −0.0798988 | ||||||||
\(371\) | 15.2198 | 0.790171 | ||||||||
\(372\) | 5.90783 | 0.306307 | ||||||||
\(373\) | 21.6663 | 1.12184 | 0.560919 | − | 0.827871i | \(-0.310448\pi\) | ||||
0.560919 | + | 0.827871i | \(0.310448\pi\) | |||||||
\(374\) | 4.53685 | 0.234595 | ||||||||
\(375\) | 11.1398 | 0.575256 | ||||||||
\(376\) | −12.7605 | −0.658073 | ||||||||
\(377\) | 17.4338 | 0.897889 | ||||||||
\(378\) | −2.44651 | −0.125835 | ||||||||
\(379\) | 23.2861 | 1.19613 | 0.598064 | − | 0.801448i | \(-0.295937\pi\) | ||||
0.598064 | + | 0.801448i | \(0.295937\pi\) | |||||||
\(380\) | −1.75992 | −0.0902818 | ||||||||
\(381\) | 0.617352 | 0.0316279 | ||||||||
\(382\) | −14.1519 | −0.724073 | ||||||||
\(383\) | 0.383389 | 0.0195902 | 0.00979512 | − | 0.999952i | \(-0.496882\pi\) | ||||
0.00979512 | + | 0.999952i | \(0.496882\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −15.2346 | −0.776428 | ||||||||
\(386\) | −16.3671 | −0.833063 | ||||||||
\(387\) | −3.32679 | −0.169110 | ||||||||
\(388\) | −6.25100 | −0.317346 | ||||||||
\(389\) | −3.45139 | −0.174993 | −0.0874963 | − | 0.996165i | \(-0.527887\pi\) | ||||
−0.0874963 | + | 0.996165i | \(0.527887\pi\) | |||||||
\(390\) | −5.38373 | −0.272616 | ||||||||
\(391\) | −3.17888 | −0.160763 | ||||||||
\(392\) | 1.01458 | 0.0512442 | ||||||||
\(393\) | −4.86386 | −0.245349 | ||||||||
\(394\) | −4.28585 | −0.215918 | ||||||||
\(395\) | −19.3356 | −0.972880 | ||||||||
\(396\) | 4.53685 | 0.227985 | ||||||||
\(397\) | 4.45900 | 0.223791 | 0.111895 | − | 0.993720i | \(-0.464308\pi\) | ||||
0.111895 | + | 0.993720i | \(0.464308\pi\) | |||||||
\(398\) | 20.6226 | 1.03372 | ||||||||
\(399\) | 3.13696 | 0.157045 | ||||||||
\(400\) | −3.11609 | −0.155805 | ||||||||
\(401\) | −7.81142 | −0.390084 | −0.195042 | − | 0.980795i | \(-0.562484\pi\) | ||||
−0.195042 | + | 0.980795i | \(0.562484\pi\) | |||||||
\(402\) | 14.1086 | 0.703671 | ||||||||
\(403\) | −23.1729 | −1.15433 | ||||||||
\(404\) | −7.31037 | −0.363704 | ||||||||
\(405\) | −1.37256 | −0.0682028 | ||||||||
\(406\) | 10.8739 | 0.539665 | ||||||||
\(407\) | −5.08002 | −0.251807 | ||||||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | 6.90534 | 0.341447 | 0.170724 | − | 0.985319i | \(-0.445389\pi\) | ||||
0.170724 | + | 0.985319i | \(0.445389\pi\) | |||||||
\(410\) | 7.84299 | 0.387337 | ||||||||
\(411\) | 4.51260 | 0.222590 | ||||||||
\(412\) | 7.63233 | 0.376018 | ||||||||
\(413\) | −2.44651 | −0.120385 | ||||||||
\(414\) | −3.17888 | −0.156233 | ||||||||
\(415\) | −12.6397 | −0.620457 | ||||||||
\(416\) | 3.92241 | 0.192312 | ||||||||
\(417\) | −10.2338 | −0.501149 | ||||||||
\(418\) | −5.81723 | −0.284530 | ||||||||
\(419\) | 10.4229 | 0.509192 | 0.254596 | − | 0.967048i | \(-0.418058\pi\) | ||||
0.254596 | + | 0.967048i | \(0.418058\pi\) | |||||||
\(420\) | −3.35797 | −0.163852 | ||||||||
\(421\) | −27.6947 | −1.34976 | −0.674880 | − | 0.737928i | \(-0.735804\pi\) | ||||
−0.674880 | + | 0.737928i | \(0.735804\pi\) | |||||||
\(422\) | 3.27881 | 0.159610 | ||||||||
\(423\) | 12.7605 | 0.620437 | ||||||||
\(424\) | −6.22101 | −0.302119 | ||||||||
\(425\) | 3.11609 | 0.151153 | ||||||||
\(426\) | 10.3817 | 0.502994 | ||||||||
\(427\) | 10.4809 | 0.507206 | ||||||||
\(428\) | −4.49082 | −0.217072 | ||||||||
\(429\) | −17.7954 | −0.859169 | ||||||||
\(430\) | −4.56620 | −0.220202 | ||||||||
\(431\) | 13.8370 | 0.666504 | 0.333252 | − | 0.942838i | \(-0.391854\pi\) | ||||
0.333252 | + | 0.942838i | \(0.391854\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −9.03973 | −0.434422 | −0.217211 | − | 0.976125i | \(-0.569696\pi\) | ||||
−0.217211 | + | 0.976125i | \(0.569696\pi\) | |||||||
\(434\) | −14.4536 | −0.693793 | ||||||||
\(435\) | 6.10057 | 0.292500 | ||||||||
\(436\) | −4.25283 | −0.203674 | ||||||||
\(437\) | 4.07601 | 0.194982 | ||||||||
\(438\) | −11.6347 | −0.555929 | ||||||||
\(439\) | −6.09702 | −0.290995 | −0.145497 | − | 0.989359i | \(-0.546478\pi\) | ||||
−0.145497 | + | 0.989359i | \(0.546478\pi\) | |||||||
\(440\) | 6.22708 | 0.296864 | ||||||||
\(441\) | −1.01458 | −0.0483135 | ||||||||
\(442\) | −3.92241 | −0.186570 | ||||||||
\(443\) | −21.3040 | −1.01219 | −0.506093 | − | 0.862479i | \(-0.668911\pi\) | ||||
−0.506093 | + | 0.862479i | \(0.668911\pi\) | |||||||
\(444\) | −1.11972 | −0.0531398 | ||||||||
\(445\) | −20.3150 | −0.963023 | ||||||||
\(446\) | −7.89786 | −0.373974 | ||||||||
\(447\) | 15.1122 | 0.714782 | ||||||||
\(448\) | 2.44651 | 0.115587 | ||||||||
\(449\) | 9.14428 | 0.431545 | 0.215773 | − | 0.976444i | \(-0.430773\pi\) | ||||
0.215773 | + | 0.976444i | \(0.430773\pi\) | |||||||
\(450\) | 3.11609 | 0.146894 | ||||||||
\(451\) | 25.9242 | 1.22072 | ||||||||
\(452\) | 9.44831 | 0.444411 | ||||||||
\(453\) | −18.4536 | −0.867024 | ||||||||
\(454\) | −3.21878 | −0.151065 | ||||||||
\(455\) | 13.1713 | 0.617482 | ||||||||
\(456\) | −1.28222 | −0.0600454 | ||||||||
\(457\) | 24.4679 | 1.14456 | 0.572280 | − | 0.820058i | \(-0.306059\pi\) | ||||
0.572280 | + | 0.820058i | \(0.306059\pi\) | |||||||
\(458\) | −8.63791 | −0.403623 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −4.36318 | −0.203434 | ||||||||
\(461\) | −0.986656 | −0.0459531 | −0.0229766 | − | 0.999736i | \(-0.507314\pi\) | ||||
−0.0229766 | + | 0.999736i | \(0.507314\pi\) | |||||||
\(462\) | −11.0995 | −0.516393 | ||||||||
\(463\) | 10.0240 | 0.465856 | 0.232928 | − | 0.972494i | \(-0.425169\pi\) | ||||
0.232928 | + | 0.972494i | \(0.425169\pi\) | |||||||
\(464\) | −4.44468 | −0.206339 | ||||||||
\(465\) | −8.10882 | −0.376038 | ||||||||
\(466\) | 2.25951 | 0.104670 | ||||||||
\(467\) | 8.99505 | 0.416241 | 0.208121 | − | 0.978103i | \(-0.433265\pi\) | ||||
0.208121 | + | 0.978103i | \(0.433265\pi\) | |||||||
\(468\) | −3.92241 | −0.181313 | ||||||||
\(469\) | −34.5168 | −1.59384 | ||||||||
\(470\) | 17.5145 | 0.807884 | ||||||||
\(471\) | −7.52286 | −0.346635 | ||||||||
\(472\) | 1.00000 | 0.0460287 | ||||||||
\(473\) | −15.0931 | −0.693983 | ||||||||
\(474\) | −14.0873 | −0.647051 | ||||||||
\(475\) | −3.99551 | −0.183327 | ||||||||
\(476\) | −2.44651 | −0.112136 | ||||||||
\(477\) | 6.22101 | 0.284841 | ||||||||
\(478\) | −25.9175 | −1.18544 | ||||||||
\(479\) | 25.8738 | 1.18220 | 0.591102 | − | 0.806597i | \(-0.298693\pi\) | ||||
0.591102 | + | 0.806597i | \(0.298693\pi\) | |||||||
\(480\) | 1.37256 | 0.0626483 | ||||||||
\(481\) | 4.39202 | 0.200259 | ||||||||
\(482\) | −14.0196 | −0.638577 | ||||||||
\(483\) | 7.77715 | 0.353873 | ||||||||
\(484\) | 9.58299 | 0.435591 | ||||||||
\(485\) | 8.57984 | 0.389590 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 1.84849 | 0.0837631 | 0.0418816 | − | 0.999123i | \(-0.486665\pi\) | ||||
0.0418816 | + | 0.999123i | \(0.486665\pi\) | |||||||
\(488\) | −4.28402 | −0.193928 | ||||||||
\(489\) | 10.9961 | 0.497261 | ||||||||
\(490\) | −1.39257 | −0.0629100 | ||||||||
\(491\) | −35.3045 | −1.59327 | −0.796636 | − | 0.604460i | \(-0.793389\pi\) | ||||
−0.796636 | + | 0.604460i | \(0.793389\pi\) | |||||||
\(492\) | 5.71415 | 0.257614 | ||||||||
\(493\) | 4.44468 | 0.200178 | ||||||||
\(494\) | 5.02939 | 0.226283 | ||||||||
\(495\) | −6.22708 | −0.279886 | ||||||||
\(496\) | 5.90783 | 0.265269 | ||||||||
\(497\) | −25.3989 | −1.13930 | ||||||||
\(498\) | −9.20886 | −0.412659 | ||||||||
\(499\) | −9.67804 | −0.433249 | −0.216624 | − | 0.976255i | \(-0.569505\pi\) | ||||
−0.216624 | + | 0.976255i | \(0.569505\pi\) | |||||||
\(500\) | 11.1398 | 0.498186 | ||||||||
\(501\) | −0.349234 | −0.0156026 | ||||||||
\(502\) | 10.4937 | 0.468358 | ||||||||
\(503\) | −40.2304 | −1.79378 | −0.896892 | − | 0.442249i | \(-0.854181\pi\) | ||||
−0.896892 | + | 0.442249i | \(0.854181\pi\) | |||||||
\(504\) | −2.44651 | −0.108976 | ||||||||
\(505\) | 10.0339 | 0.446502 | ||||||||
\(506\) | −14.4221 | −0.641139 | ||||||||
\(507\) | 2.38530 | 0.105935 | ||||||||
\(508\) | 0.617352 | 0.0273906 | ||||||||
\(509\) | 7.40618 | 0.328273 | 0.164137 | − | 0.986438i | \(-0.447516\pi\) | ||||
0.164137 | + | 0.986438i | \(0.447516\pi\) | |||||||
\(510\) | −1.37256 | −0.0607778 | ||||||||
\(511\) | 28.4645 | 1.25919 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.28222 | 0.0566113 | ||||||||
\(514\) | −25.9848 | −1.14614 | ||||||||
\(515\) | −10.4758 | −0.461619 | ||||||||
\(516\) | −3.32679 | −0.146454 | ||||||||
\(517\) | 57.8925 | 2.54611 | ||||||||
\(518\) | 2.73942 | 0.120363 | ||||||||
\(519\) | −2.38590 | −0.104729 | ||||||||
\(520\) | −5.38373 | −0.236092 | ||||||||
\(521\) | −36.4063 | −1.59499 | −0.797495 | − | 0.603325i | \(-0.793842\pi\) | ||||
−0.797495 | + | 0.603325i | \(0.793842\pi\) | |||||||
\(522\) | 4.44468 | 0.194538 | ||||||||
\(523\) | 18.1574 | 0.793966 | 0.396983 | − | 0.917826i | \(-0.370057\pi\) | ||||
0.396983 | + | 0.917826i | \(0.370057\pi\) | |||||||
\(524\) | −4.86386 | −0.212479 | ||||||||
\(525\) | −7.62355 | −0.332719 | ||||||||
\(526\) | −16.6742 | −0.727030 | ||||||||
\(527\) | −5.90783 | −0.257349 | ||||||||
\(528\) | 4.53685 | 0.197441 | ||||||||
\(529\) | −12.8948 | −0.560641 | ||||||||
\(530\) | 8.53868 | 0.370897 | ||||||||
\(531\) | −1.00000 | −0.0433963 | ||||||||
\(532\) | 3.13696 | 0.136005 | ||||||||
\(533\) | −22.4132 | −0.970825 | ||||||||
\(534\) | −14.8009 | −0.640495 | ||||||||
\(535\) | 6.16390 | 0.266489 | ||||||||
\(536\) | 14.1086 | 0.609397 | ||||||||
\(537\) | −1.29654 | −0.0559499 | ||||||||
\(538\) | 17.1270 | 0.738399 | ||||||||
\(539\) | −4.60301 | −0.198266 | ||||||||
\(540\) | −1.37256 | −0.0590654 | ||||||||
\(541\) | −21.7888 | −0.936774 | −0.468387 | − | 0.883523i | \(-0.655165\pi\) | ||||
−0.468387 | + | 0.883523i | \(0.655165\pi\) | |||||||
\(542\) | 16.7230 | 0.718314 | ||||||||
\(543\) | −7.64648 | −0.328142 | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | 5.83725 | 0.250040 | ||||||||
\(546\) | 9.59622 | 0.410680 | ||||||||
\(547\) | 18.3549 | 0.784799 | 0.392399 | − | 0.919795i | \(-0.371645\pi\) | ||||
0.392399 | + | 0.919795i | \(0.371645\pi\) | |||||||
\(548\) | 4.51260 | 0.192769 | ||||||||
\(549\) | 4.28402 | 0.182837 | ||||||||
\(550\) | 14.1372 | 0.602814 | ||||||||
\(551\) | −5.69905 | −0.242788 | ||||||||
\(552\) | −3.17888 | −0.135302 | ||||||||
\(553\) | 34.4647 | 1.46559 | ||||||||
\(554\) | −6.16976 | −0.262128 | ||||||||
\(555\) | 1.53688 | 0.0652371 | ||||||||
\(556\) | −10.2338 | −0.434008 | ||||||||
\(557\) | 19.9045 | 0.843382 | 0.421691 | − | 0.906740i | \(-0.361437\pi\) | ||||
0.421691 | + | 0.906740i | \(0.361437\pi\) | |||||||
\(558\) | −5.90783 | −0.250098 | ||||||||
\(559\) | 13.0490 | 0.551915 | ||||||||
\(560\) | −3.35797 | −0.141900 | ||||||||
\(561\) | −4.53685 | −0.191546 | ||||||||
\(562\) | 21.8738 | 0.922690 | ||||||||
\(563\) | 1.46278 | 0.0616487 | 0.0308244 | − | 0.999525i | \(-0.490187\pi\) | ||||
0.0308244 | + | 0.999525i | \(0.490187\pi\) | |||||||
\(564\) | 12.7605 | 0.537315 | ||||||||
\(565\) | −12.9683 | −0.545582 | ||||||||
\(566\) | 3.51379 | 0.147695 | ||||||||
\(567\) | 2.44651 | 0.102744 | ||||||||
\(568\) | 10.3817 | 0.435605 | ||||||||
\(569\) | −12.7127 | −0.532942 | −0.266471 | − | 0.963843i | \(-0.585858\pi\) | ||||
−0.266471 | + | 0.963843i | \(0.585858\pi\) | |||||||
\(570\) | 1.75992 | 0.0737148 | ||||||||
\(571\) | −10.7548 | −0.450073 | −0.225037 | − | 0.974350i | \(-0.572250\pi\) | ||||
−0.225037 | + | 0.974350i | \(0.572250\pi\) | |||||||
\(572\) | −17.7954 | −0.744062 | ||||||||
\(573\) | 14.1519 | 0.591203 | ||||||||
\(574\) | −13.9797 | −0.583502 | ||||||||
\(575\) | −9.90566 | −0.413095 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −1.00812 | −0.0419688 | −0.0209844 | − | 0.999780i | \(-0.506680\pi\) | ||||
−0.0209844 | + | 0.999780i | \(0.506680\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | 16.3671 | 0.680193 | ||||||||
\(580\) | 6.10057 | 0.253312 | ||||||||
\(581\) | 22.5296 | 0.934684 | ||||||||
\(582\) | 6.25100 | 0.259112 | ||||||||
\(583\) | 28.2238 | 1.16891 | ||||||||
\(584\) | −11.6347 | −0.481448 | ||||||||
\(585\) | 5.38373 | 0.222590 | ||||||||
\(586\) | −9.89280 | −0.408668 | ||||||||
\(587\) | −45.4167 | −1.87455 | −0.937273 | − | 0.348596i | \(-0.886658\pi\) | ||||
−0.937273 | + | 0.348596i | \(0.886658\pi\) | |||||||
\(588\) | −1.01458 | −0.0418407 | ||||||||
\(589\) | 7.57513 | 0.312128 | ||||||||
\(590\) | −1.37256 | −0.0565072 | ||||||||
\(591\) | 4.28585 | 0.176296 | ||||||||
\(592\) | −1.11972 | −0.0460204 | ||||||||
\(593\) | −10.5736 | −0.434207 | −0.217103 | − | 0.976149i | \(-0.569661\pi\) | ||||
−0.217103 | + | 0.976149i | \(0.569661\pi\) | |||||||
\(594\) | −4.53685 | −0.186149 | ||||||||
\(595\) | 3.35797 | 0.137663 | ||||||||
\(596\) | 15.1122 | 0.619020 | ||||||||
\(597\) | −20.6226 | −0.844026 | ||||||||
\(598\) | 12.4689 | 0.509889 | ||||||||
\(599\) | 25.8614 | 1.05667 | 0.528335 | − | 0.849036i | \(-0.322817\pi\) | ||||
0.528335 | + | 0.849036i | \(0.322817\pi\) | |||||||
\(600\) | 3.11609 | 0.127214 | ||||||||
\(601\) | −28.1495 | −1.14824 | −0.574122 | − | 0.818770i | \(-0.694656\pi\) | ||||
−0.574122 | + | 0.818770i | \(0.694656\pi\) | |||||||
\(602\) | 8.13902 | 0.331722 | ||||||||
\(603\) | −14.1086 | −0.574545 | ||||||||
\(604\) | −18.4536 | −0.750865 | ||||||||
\(605\) | −13.1532 | −0.534753 | ||||||||
\(606\) | 7.31037 | 0.296963 | ||||||||
\(607\) | 35.9274 | 1.45825 | 0.729124 | − | 0.684382i | \(-0.239928\pi\) | ||||
0.729124 | + | 0.684382i | \(0.239928\pi\) | |||||||
\(608\) | −1.28222 | −0.0520008 | ||||||||
\(609\) | −10.8739 | −0.440635 | ||||||||
\(610\) | 5.88005 | 0.238076 | ||||||||
\(611\) | −50.0520 | −2.02489 | ||||||||
\(612\) | −1.00000 | −0.0404226 | ||||||||
\(613\) | 18.1800 | 0.734285 | 0.367142 | − | 0.930165i | \(-0.380336\pi\) | ||||
0.367142 | + | 0.930165i | \(0.380336\pi\) | |||||||
\(614\) | −13.8309 | −0.558169 | ||||||||
\(615\) | −7.84299 | −0.316260 | ||||||||
\(616\) | −11.0995 | −0.447210 | ||||||||
\(617\) | 15.3181 | 0.616682 | 0.308341 | − | 0.951276i | \(-0.400226\pi\) | ||||
0.308341 | + | 0.951276i | \(0.400226\pi\) | |||||||
\(618\) | −7.63233 | −0.307017 | ||||||||
\(619\) | −6.33812 | −0.254750 | −0.127375 | − | 0.991855i | \(-0.540655\pi\) | ||||
−0.127375 | + | 0.991855i | \(0.540655\pi\) | |||||||
\(620\) | −8.10882 | −0.325658 | ||||||||
\(621\) | 3.17888 | 0.127564 | ||||||||
\(622\) | −14.0500 | −0.563354 | ||||||||
\(623\) | 36.2104 | 1.45074 | ||||||||
\(624\) | −3.92241 | −0.157022 | ||||||||
\(625\) | 0.290476 | 0.0116190 | ||||||||
\(626\) | 6.65585 | 0.266021 | ||||||||
\(627\) | 5.81723 | 0.232318 | ||||||||
\(628\) | −7.52286 | −0.300195 | ||||||||
\(629\) | 1.11972 | 0.0446464 | ||||||||
\(630\) | 3.35797 | 0.133785 | ||||||||
\(631\) | −8.70564 | −0.346566 | −0.173283 | − | 0.984872i | \(-0.555438\pi\) | ||||
−0.173283 | + | 0.984872i | \(0.555438\pi\) | |||||||
\(632\) | −14.0873 | −0.560363 | ||||||||
\(633\) | −3.27881 | −0.130321 | ||||||||
\(634\) | 8.10346 | 0.321829 | ||||||||
\(635\) | −0.847350 | −0.0336260 | ||||||||
\(636\) | 6.22101 | 0.246679 | ||||||||
\(637\) | 3.97961 | 0.157678 | ||||||||
\(638\) | 20.1648 | 0.798333 | ||||||||
\(639\) | −10.3817 | −0.410692 | ||||||||
\(640\) | 1.37256 | 0.0542550 | ||||||||
\(641\) | −9.56592 | −0.377831 | −0.188916 | − | 0.981993i | \(-0.560497\pi\) | ||||
−0.188916 | + | 0.981993i | \(0.560497\pi\) | |||||||
\(642\) | 4.49082 | 0.177239 | ||||||||
\(643\) | −19.2741 | −0.760098 | −0.380049 | − | 0.924966i | \(-0.624093\pi\) | ||||
−0.380049 | + | 0.924966i | \(0.624093\pi\) | |||||||
\(644\) | 7.77715 | 0.306463 | ||||||||
\(645\) | 4.56620 | 0.179794 | ||||||||
\(646\) | 1.28222 | 0.0504482 | ||||||||
\(647\) | −23.7598 | −0.934096 | −0.467048 | − | 0.884232i | \(-0.654682\pi\) | ||||
−0.467048 | + | 0.884232i | \(0.654682\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −4.53685 | −0.178087 | ||||||||
\(650\) | −12.2226 | −0.479409 | ||||||||
\(651\) | 14.4536 | 0.566480 | ||||||||
\(652\) | 10.9961 | 0.430641 | ||||||||
\(653\) | 37.2182 | 1.45646 | 0.728230 | − | 0.685333i | \(-0.240343\pi\) | ||||
0.728230 | + | 0.685333i | \(0.240343\pi\) | |||||||
\(654\) | 4.25283 | 0.166299 | ||||||||
\(655\) | 6.67591 | 0.260850 | ||||||||
\(656\) | 5.71415 | 0.223100 | ||||||||
\(657\) | 11.6347 | 0.453914 | ||||||||
\(658\) | −31.2187 | −1.21703 | ||||||||
\(659\) | 10.3196 | 0.401995 | 0.200997 | − | 0.979592i | \(-0.435582\pi\) | ||||
0.200997 | + | 0.979592i | \(0.435582\pi\) | |||||||
\(660\) | −6.22708 | −0.242389 | ||||||||
\(661\) | 5.50184 | 0.213997 | 0.106998 | − | 0.994259i | \(-0.465876\pi\) | ||||
0.106998 | + | 0.994259i | \(0.465876\pi\) | |||||||
\(662\) | 6.21793 | 0.241667 | ||||||||
\(663\) | 3.92241 | 0.152334 | ||||||||
\(664\) | −9.20886 | −0.357373 | ||||||||
\(665\) | −4.30566 | −0.166966 | ||||||||
\(666\) | 1.11972 | 0.0433885 | ||||||||
\(667\) | −14.1291 | −0.547080 | ||||||||
\(668\) | −0.349234 | −0.0135123 | ||||||||
\(669\) | 7.89786 | 0.305349 | ||||||||
\(670\) | −19.3648 | −0.748127 | ||||||||
\(671\) | 19.4359 | 0.750316 | ||||||||
\(672\) | −2.44651 | −0.0943762 | ||||||||
\(673\) | 11.7544 | 0.453100 | 0.226550 | − | 0.974000i | \(-0.427255\pi\) | ||||
0.226550 | + | 0.974000i | \(0.427255\pi\) | |||||||
\(674\) | 5.56650 | 0.214413 | ||||||||
\(675\) | −3.11609 | −0.119938 | ||||||||
\(676\) | 2.38530 | 0.0917424 | ||||||||
\(677\) | −36.9735 | −1.42101 | −0.710503 | − | 0.703694i | \(-0.751533\pi\) | ||||
−0.710503 | + | 0.703694i | \(0.751533\pi\) | |||||||
\(678\) | −9.44831 | −0.362860 | ||||||||
\(679\) | −15.2931 | −0.586896 | ||||||||
\(680\) | −1.37256 | −0.0526351 | ||||||||
\(681\) | 3.21878 | 0.123344 | ||||||||
\(682\) | −26.8029 | −1.02634 | ||||||||
\(683\) | −14.5844 | −0.558056 | −0.279028 | − | 0.960283i | \(-0.590012\pi\) | ||||
−0.279028 | + | 0.960283i | \(0.590012\pi\) | |||||||
\(684\) | 1.28222 | 0.0490269 | ||||||||
\(685\) | −6.19380 | −0.236653 | ||||||||
\(686\) | 19.6078 | 0.748628 | ||||||||
\(687\) | 8.63791 | 0.329557 | ||||||||
\(688\) | −3.32679 | −0.126833 | ||||||||
\(689\) | −24.4014 | −0.929618 | ||||||||
\(690\) | 4.36318 | 0.166104 | ||||||||
\(691\) | −16.4570 | −0.626056 | −0.313028 | − | 0.949744i | \(-0.601343\pi\) | ||||
−0.313028 | + | 0.949744i | \(0.601343\pi\) | |||||||
\(692\) | −2.38590 | −0.0906983 | ||||||||
\(693\) | 11.0995 | 0.421633 | ||||||||
\(694\) | −24.3057 | −0.922630 | ||||||||
\(695\) | 14.0464 | 0.532810 | ||||||||
\(696\) | 4.44468 | 0.168475 | ||||||||
\(697\) | −5.71415 | −0.216439 | ||||||||
\(698\) | −24.6813 | −0.934199 | ||||||||
\(699\) | −2.25951 | −0.0854626 | ||||||||
\(700\) | −7.62355 | −0.288143 | ||||||||
\(701\) | 30.3060 | 1.14464 | 0.572320 | − | 0.820030i | \(-0.306043\pi\) | ||||
0.572320 | + | 0.820030i | \(0.306043\pi\) | |||||||
\(702\) | 3.92241 | 0.148042 | ||||||||
\(703\) | −1.43573 | −0.0541497 | ||||||||
\(704\) | 4.53685 | 0.170989 | ||||||||
\(705\) | −17.5145 | −0.659635 | ||||||||
\(706\) | −30.3271 | −1.14138 | ||||||||
\(707\) | −17.8849 | −0.672631 | ||||||||
\(708\) | −1.00000 | −0.0375823 | ||||||||
\(709\) | 47.8644 | 1.79759 | 0.898793 | − | 0.438374i | \(-0.144445\pi\) | ||||
0.898793 | + | 0.438374i | \(0.144445\pi\) | |||||||
\(710\) | −14.2494 | −0.534771 | ||||||||
\(711\) | 14.0873 | 0.528315 | ||||||||
\(712\) | −14.8009 | −0.554685 | ||||||||
\(713\) | 18.7802 | 0.703326 | ||||||||
\(714\) | 2.44651 | 0.0915584 | ||||||||
\(715\) | 24.4252 | 0.913449 | ||||||||
\(716\) | −1.29654 | −0.0484541 | ||||||||
\(717\) | 25.9175 | 0.967908 | ||||||||
\(718\) | −15.5771 | −0.581334 | ||||||||
\(719\) | −21.2687 | −0.793190 | −0.396595 | − | 0.917994i | \(-0.629808\pi\) | ||||
−0.396595 | + | 0.917994i | \(0.629808\pi\) | |||||||
\(720\) | −1.37256 | −0.0511521 | ||||||||
\(721\) | 18.6726 | 0.695403 | ||||||||
\(722\) | 17.3559 | 0.645920 | ||||||||
\(723\) | 14.0196 | 0.521396 | ||||||||
\(724\) | −7.64648 | −0.284179 | ||||||||
\(725\) | 13.8500 | 0.514377 | ||||||||
\(726\) | −9.58299 | −0.355658 | ||||||||
\(727\) | 7.60032 | 0.281880 | 0.140940 | − | 0.990018i | \(-0.454987\pi\) | ||||
0.140940 | + | 0.990018i | \(0.454987\pi\) | |||||||
\(728\) | 9.59622 | 0.355660 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 15.9693 | 0.591050 | ||||||||
\(731\) | 3.32679 | 0.123046 | ||||||||
\(732\) | 4.28402 | 0.158342 | ||||||||
\(733\) | 43.2703 | 1.59823 | 0.799113 | − | 0.601181i | \(-0.205303\pi\) | ||||
0.799113 | + | 0.601181i | \(0.205303\pi\) | |||||||
\(734\) | −12.8664 | −0.474908 | ||||||||
\(735\) | 1.39257 | 0.0513658 | ||||||||
\(736\) | −3.17888 | −0.117175 | ||||||||
\(737\) | −64.0084 | −2.35778 | ||||||||
\(738\) | −5.71415 | −0.210341 | ||||||||
\(739\) | 25.2377 | 0.928384 | 0.464192 | − | 0.885735i | \(-0.346345\pi\) | ||||
0.464192 | + | 0.885735i | \(0.346345\pi\) | |||||||
\(740\) | 1.53688 | 0.0564970 | ||||||||
\(741\) | −5.02939 | −0.184759 | ||||||||
\(742\) | −15.2198 | −0.558735 | ||||||||
\(743\) | −12.6389 | −0.463675 | −0.231838 | − | 0.972755i | \(-0.574474\pi\) | ||||
−0.231838 | + | 0.972755i | \(0.574474\pi\) | |||||||
\(744\) | −5.90783 | −0.216591 | ||||||||
\(745\) | −20.7423 | −0.759940 | ||||||||
\(746\) | −21.6663 | −0.793259 | ||||||||
\(747\) | 9.20886 | 0.336935 | ||||||||
\(748\) | −4.53685 | −0.165884 | ||||||||
\(749\) | −10.9868 | −0.401450 | ||||||||
\(750\) | −11.1398 | −0.406768 | ||||||||
\(751\) | −30.5853 | −1.11607 | −0.558036 | − | 0.829817i | \(-0.688445\pi\) | ||||
−0.558036 | + | 0.829817i | \(0.688445\pi\) | |||||||
\(752\) | 12.7605 | 0.465328 | ||||||||
\(753\) | −10.4937 | −0.382413 | ||||||||
\(754\) | −17.4338 | −0.634903 | ||||||||
\(755\) | 25.3285 | 0.921800 | ||||||||
\(756\) | 2.44651 | 0.0889788 | ||||||||
\(757\) | 30.5441 | 1.11014 | 0.555072 | − | 0.831802i | \(-0.312691\pi\) | ||||
0.555072 | + | 0.831802i | \(0.312691\pi\) | |||||||
\(758\) | −23.2861 | −0.845790 | ||||||||
\(759\) | 14.4221 | 0.523488 | ||||||||
\(760\) | 1.75992 | 0.0638389 | ||||||||
\(761\) | 33.5608 | 1.21658 | 0.608289 | − | 0.793716i | \(-0.291856\pi\) | ||||
0.608289 | + | 0.793716i | \(0.291856\pi\) | |||||||
\(762\) | −0.617352 | −0.0223643 | ||||||||
\(763\) | −10.4046 | −0.376672 | ||||||||
\(764\) | 14.1519 | 0.511997 | ||||||||
\(765\) | 1.37256 | 0.0496249 | ||||||||
\(766\) | −0.383389 | −0.0138524 | ||||||||
\(767\) | 3.92241 | 0.141630 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −11.9763 | −0.431875 | −0.215938 | − | 0.976407i | \(-0.569281\pi\) | ||||
−0.215938 | + | 0.976407i | \(0.569281\pi\) | |||||||
\(770\) | 15.2346 | 0.549017 | ||||||||
\(771\) | 25.9848 | 0.935821 | ||||||||
\(772\) | 16.3671 | 0.589064 | ||||||||
\(773\) | 53.1645 | 1.91219 | 0.956097 | − | 0.293050i | \(-0.0946703\pi\) | ||||
0.956097 | + | 0.293050i | \(0.0946703\pi\) | |||||||
\(774\) | 3.32679 | 0.119579 | ||||||||
\(775\) | −18.4093 | −0.661283 | ||||||||
\(776\) | 6.25100 | 0.224398 | ||||||||
\(777\) | −2.73942 | −0.0982761 | ||||||||
\(778\) | 3.45139 | 0.123738 | ||||||||
\(779\) | 7.32679 | 0.262509 | ||||||||
\(780\) | 5.38373 | 0.192768 | ||||||||
\(781\) | −47.1001 | −1.68537 | ||||||||
\(782\) | 3.17888 | 0.113676 | ||||||||
\(783\) | −4.44468 | −0.158840 | ||||||||
\(784\) | −1.01458 | −0.0362351 | ||||||||
\(785\) | 10.3255 | 0.368535 | ||||||||
\(786\) | 4.86386 | 0.173488 | ||||||||
\(787\) | 10.3491 | 0.368905 | 0.184453 | − | 0.982841i | \(-0.440949\pi\) | ||||
0.184453 | + | 0.982841i | \(0.440949\pi\) | |||||||
\(788\) | 4.28585 | 0.152677 | ||||||||
\(789\) | 16.6742 | 0.593617 | ||||||||
\(790\) | 19.3356 | 0.687930 | ||||||||
\(791\) | 23.1154 | 0.821889 | ||||||||
\(792\) | −4.53685 | −0.161210 | ||||||||
\(793\) | −16.8037 | −0.596716 | ||||||||
\(794\) | −4.45900 | −0.158244 | ||||||||
\(795\) | −8.53868 | −0.302836 | ||||||||
\(796\) | −20.6226 | −0.730948 | ||||||||
\(797\) | −11.0883 | −0.392769 | −0.196385 | − | 0.980527i | \(-0.562920\pi\) | ||||
−0.196385 | + | 0.980527i | \(0.562920\pi\) | |||||||
\(798\) | −3.13696 | −0.111047 | ||||||||
\(799\) | −12.7605 | −0.451435 | ||||||||
\(800\) | 3.11609 | 0.110170 | ||||||||
\(801\) | 14.8009 | 0.522962 | ||||||||
\(802\) | 7.81142 | 0.275831 | ||||||||
\(803\) | 52.7850 | 1.86274 | ||||||||
\(804\) | −14.1086 | −0.497571 | ||||||||
\(805\) | −10.6746 | −0.376229 | ||||||||
\(806\) | 23.1729 | 0.816231 | ||||||||
\(807\) | −17.1270 | −0.602900 | ||||||||
\(808\) | 7.31037 | 0.257178 | ||||||||
\(809\) | 36.1007 | 1.26923 | 0.634616 | − | 0.772828i | \(-0.281158\pi\) | ||||
0.634616 | + | 0.772828i | \(0.281158\pi\) | |||||||
\(810\) | 1.37256 | 0.0482267 | ||||||||
\(811\) | −10.0801 | −0.353960 | −0.176980 | − | 0.984214i | \(-0.556633\pi\) | ||||
−0.176980 | + | 0.984214i | \(0.556633\pi\) | |||||||
\(812\) | −10.8739 | −0.381601 | ||||||||
\(813\) | −16.7230 | −0.586501 | ||||||||
\(814\) | 5.08002 | 0.178055 | ||||||||
\(815\) | −15.0928 | −0.528677 | ||||||||
\(816\) | −1.00000 | −0.0350070 | ||||||||
\(817\) | −4.26567 | −0.149237 | ||||||||
\(818\) | −6.90534 | −0.241440 | ||||||||
\(819\) | −9.59622 | −0.335319 | ||||||||
\(820\) | −7.84299 | −0.273889 | ||||||||
\(821\) | 21.5479 | 0.752025 | 0.376013 | − | 0.926614i | \(-0.377295\pi\) | ||||
0.376013 | + | 0.926614i | \(0.377295\pi\) | |||||||
\(822\) | −4.51260 | −0.157395 | ||||||||
\(823\) | −28.9849 | −1.01035 | −0.505175 | − | 0.863017i | \(-0.668572\pi\) | ||||
−0.505175 | + | 0.863017i | \(0.668572\pi\) | |||||||
\(824\) | −7.63233 | −0.265885 | ||||||||
\(825\) | −14.1372 | −0.492195 | ||||||||
\(826\) | 2.44651 | 0.0851250 | ||||||||
\(827\) | −8.30302 | −0.288724 | −0.144362 | − | 0.989525i | \(-0.546113\pi\) | ||||
−0.144362 | + | 0.989525i | \(0.546113\pi\) | |||||||
\(828\) | 3.17888 | 0.110474 | ||||||||
\(829\) | 11.8225 | 0.410611 | 0.205305 | − | 0.978698i | \(-0.434181\pi\) | ||||
0.205305 | + | 0.978698i | \(0.434181\pi\) | |||||||
\(830\) | 12.6397 | 0.438729 | ||||||||
\(831\) | 6.16976 | 0.214027 | ||||||||
\(832\) | −3.92241 | −0.135985 | ||||||||
\(833\) | 1.01458 | 0.0351532 | ||||||||
\(834\) | 10.2338 | 0.354366 | ||||||||
\(835\) | 0.479344 | 0.0165884 | ||||||||
\(836\) | 5.81723 | 0.201193 | ||||||||
\(837\) | 5.90783 | 0.204204 | ||||||||
\(838\) | −10.4229 | −0.360053 | ||||||||
\(839\) | 46.9065 | 1.61939 | 0.809696 | − | 0.586849i | \(-0.199632\pi\) | ||||
0.809696 | + | 0.586849i | \(0.199632\pi\) | |||||||
\(840\) | 3.35797 | 0.115861 | ||||||||
\(841\) | −9.24486 | −0.318788 | ||||||||
\(842\) | 27.6947 | 0.954424 | ||||||||
\(843\) | −21.8738 | −0.753373 | ||||||||
\(844\) | −3.27881 | −0.112861 | ||||||||
\(845\) | −3.27396 | −0.112628 | ||||||||
\(846\) | −12.7605 | −0.438715 | ||||||||
\(847\) | 23.4449 | 0.805576 | ||||||||
\(848\) | 6.22101 | 0.213630 | ||||||||
\(849\) | −3.51379 | −0.120593 | ||||||||
\(850\) | −3.11609 | −0.106881 | ||||||||
\(851\) | −3.55947 | −0.122017 | ||||||||
\(852\) | −10.3817 | −0.355670 | ||||||||
\(853\) | −22.8736 | −0.783176 | −0.391588 | − | 0.920141i | \(-0.628074\pi\) | ||||
−0.391588 | + | 0.920141i | \(0.628074\pi\) | |||||||
\(854\) | −10.4809 | −0.358649 | ||||||||
\(855\) | −1.75992 | −0.0601879 | ||||||||
\(856\) | 4.49082 | 0.153493 | ||||||||
\(857\) | −41.6744 | −1.42357 | −0.711785 | − | 0.702397i | \(-0.752113\pi\) | ||||
−0.711785 | + | 0.702397i | \(0.752113\pi\) | |||||||
\(858\) | 17.7954 | 0.607524 | ||||||||
\(859\) | −28.1161 | −0.959310 | −0.479655 | − | 0.877457i | \(-0.659238\pi\) | ||||
−0.479655 | + | 0.877457i | \(0.659238\pi\) | |||||||
\(860\) | 4.56620 | 0.155706 | ||||||||
\(861\) | 13.9797 | 0.476428 | ||||||||
\(862\) | −13.8370 | −0.471290 | ||||||||
\(863\) | −37.6570 | −1.28186 | −0.640930 | − | 0.767600i | \(-0.721451\pi\) | ||||
−0.640930 | + | 0.767600i | \(0.721451\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 3.27478 | 0.111346 | ||||||||
\(866\) | 9.03973 | 0.307183 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 14.4536 | 0.490586 | ||||||||
\(869\) | 63.9119 | 2.16806 | ||||||||
\(870\) | −6.10057 | −0.206829 | ||||||||
\(871\) | 55.3396 | 1.87511 | ||||||||
\(872\) | 4.25283 | 0.144019 | ||||||||
\(873\) | −6.25100 | −0.211564 | ||||||||
\(874\) | −4.07601 | −0.137873 | ||||||||
\(875\) | 27.2536 | 0.921340 | ||||||||
\(876\) | 11.6347 | 0.393101 | ||||||||
\(877\) | 20.0188 | 0.675986 | 0.337993 | − | 0.941149i | \(-0.390252\pi\) | ||||
0.337993 | + | 0.941149i | \(0.390252\pi\) | |||||||
\(878\) | 6.09702 | 0.205764 | ||||||||
\(879\) | 9.89280 | 0.333676 | ||||||||
\(880\) | −6.22708 | −0.209915 | ||||||||
\(881\) | −5.20291 | −0.175290 | −0.0876452 | − | 0.996152i | \(-0.527934\pi\) | ||||
−0.0876452 | + | 0.996152i | \(0.527934\pi\) | |||||||
\(882\) | 1.01458 | 0.0341628 | ||||||||
\(883\) | 7.60991 | 0.256094 | 0.128047 | − | 0.991768i | \(-0.459129\pi\) | ||||
0.128047 | + | 0.991768i | \(0.459129\pi\) | |||||||
\(884\) | 3.92241 | 0.131925 | ||||||||
\(885\) | 1.37256 | 0.0461380 | ||||||||
\(886\) | 21.3040 | 0.715723 | ||||||||
\(887\) | −9.66067 | −0.324374 | −0.162187 | − | 0.986760i | \(-0.551855\pi\) | ||||
−0.162187 | + | 0.986760i | \(0.551855\pi\) | |||||||
\(888\) | 1.11972 | 0.0375755 | ||||||||
\(889\) | 1.51036 | 0.0506558 | ||||||||
\(890\) | 20.3150 | 0.680960 | ||||||||
\(891\) | 4.53685 | 0.151990 | ||||||||
\(892\) | 7.89786 | 0.264440 | ||||||||
\(893\) | 16.3618 | 0.547526 | ||||||||
\(894\) | −15.1122 | −0.505427 | ||||||||
\(895\) | 1.77958 | 0.0594847 | ||||||||
\(896\) | −2.44651 | −0.0817322 | ||||||||
\(897\) | −12.4689 | −0.416323 | ||||||||
\(898\) | −9.14428 | −0.305148 | ||||||||
\(899\) | −26.2584 | −0.875766 | ||||||||
\(900\) | −3.11609 | −0.103870 | ||||||||
\(901\) | −6.22101 | −0.207252 | ||||||||
\(902\) | −25.9242 | −0.863182 | ||||||||
\(903\) | −8.13902 | −0.270850 | ||||||||
\(904\) | −9.44831 | −0.314246 | ||||||||
\(905\) | 10.4952 | 0.348873 | ||||||||
\(906\) | 18.4536 | 0.613079 | ||||||||
\(907\) | −5.93790 | −0.197165 | −0.0985824 | − | 0.995129i | \(-0.531431\pi\) | ||||
−0.0985824 | + | 0.995129i | \(0.531431\pi\) | |||||||
\(908\) | 3.21878 | 0.106819 | ||||||||
\(909\) | −7.31037 | −0.242470 | ||||||||
\(910\) | −13.1713 | −0.436626 | ||||||||
\(911\) | −5.78904 | −0.191799 | −0.0958997 | − | 0.995391i | \(-0.530573\pi\) | ||||
−0.0958997 | + | 0.995391i | \(0.530573\pi\) | |||||||
\(912\) | 1.28222 | 0.0424585 | ||||||||
\(913\) | 41.7792 | 1.38269 | ||||||||
\(914\) | −24.4679 | −0.809326 | ||||||||
\(915\) | −5.88005 | −0.194389 | ||||||||
\(916\) | 8.63791 | 0.285405 | ||||||||
\(917\) | −11.8995 | −0.392955 | ||||||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | −9.84962 | −0.324909 | −0.162454 | − | 0.986716i | \(-0.551941\pi\) | ||||
−0.162454 | + | 0.986716i | \(0.551941\pi\) | |||||||
\(920\) | 4.36318 | 0.143850 | ||||||||
\(921\) | 13.8309 | 0.455743 | ||||||||
\(922\) | 0.986656 | 0.0324938 | ||||||||
\(923\) | 40.7212 | 1.34035 | ||||||||
\(924\) | 11.0995 | 0.365145 | ||||||||
\(925\) | 3.48916 | 0.114723 | ||||||||
\(926\) | −10.0240 | −0.329410 | ||||||||
\(927\) | 7.63233 | 0.250678 | ||||||||
\(928\) | 4.44468 | 0.145904 | ||||||||
\(929\) | −26.2741 | −0.862026 | −0.431013 | − | 0.902346i | \(-0.641844\pi\) | ||||
−0.431013 | + | 0.902346i | \(0.641844\pi\) | |||||||
\(930\) | 8.10882 | 0.265899 | ||||||||
\(931\) | −1.30092 | −0.0426358 | ||||||||
\(932\) | −2.25951 | −0.0740128 | ||||||||
\(933\) | 14.0500 | 0.459976 | ||||||||
\(934\) | −8.99505 | −0.294327 | ||||||||
\(935\) | 6.22708 | 0.203647 | ||||||||
\(936\) | 3.92241 | 0.128208 | ||||||||
\(937\) | 43.4759 | 1.42029 | 0.710147 | − | 0.704053i | \(-0.248628\pi\) | ||||
0.710147 | + | 0.704053i | \(0.248628\pi\) | |||||||
\(938\) | 34.5168 | 1.12701 | ||||||||
\(939\) | −6.65585 | −0.217206 | ||||||||
\(940\) | −17.5145 | −0.571261 | ||||||||
\(941\) | −49.9516 | −1.62838 | −0.814188 | − | 0.580601i | \(-0.802818\pi\) | ||||
−0.814188 | + | 0.580601i | \(0.802818\pi\) | |||||||
\(942\) | 7.52286 | 0.245108 | ||||||||
\(943\) | 18.1646 | 0.591520 | ||||||||
\(944\) | −1.00000 | −0.0325472 | ||||||||
\(945\) | −3.35797 | −0.109235 | ||||||||
\(946\) | 15.0931 | 0.490720 | ||||||||
\(947\) | 7.25843 | 0.235867 | 0.117934 | − | 0.993021i | \(-0.462373\pi\) | ||||
0.117934 | + | 0.993021i | \(0.462373\pi\) | |||||||
\(948\) | 14.0873 | 0.457534 | ||||||||
\(949\) | −45.6362 | −1.48141 | ||||||||
\(950\) | 3.99551 | 0.129631 | ||||||||
\(951\) | −8.10346 | −0.262773 | ||||||||
\(952\) | 2.44651 | 0.0792919 | ||||||||
\(953\) | −50.4910 | −1.63556 | −0.817781 | − | 0.575529i | \(-0.804796\pi\) | ||||
−0.817781 | + | 0.575529i | \(0.804796\pi\) | |||||||
\(954\) | −6.22101 | −0.201413 | ||||||||
\(955\) | −19.4242 | −0.628554 | ||||||||
\(956\) | 25.9175 | 0.838233 | ||||||||
\(957\) | −20.1648 | −0.651836 | ||||||||
\(958\) | −25.8738 | −0.835944 | ||||||||
\(959\) | 11.0401 | 0.356504 | ||||||||
\(960\) | −1.37256 | −0.0442990 | ||||||||
\(961\) | 3.90243 | 0.125885 | ||||||||
\(962\) | −4.39202 | −0.141604 | ||||||||
\(963\) | −4.49082 | −0.144715 | ||||||||
\(964\) | 14.0196 | 0.451542 | ||||||||
\(965\) | −22.4647 | −0.723165 | ||||||||
\(966\) | −7.77715 | −0.250226 | ||||||||
\(967\) | 30.9893 | 0.996548 | 0.498274 | − | 0.867020i | \(-0.333967\pi\) | ||||
0.498274 | + | 0.867020i | \(0.333967\pi\) | |||||||
\(968\) | −9.58299 | −0.308009 | ||||||||
\(969\) | −1.28222 | −0.0411908 | ||||||||
\(970\) | −8.57984 | −0.275482 | ||||||||
\(971\) | 41.1170 | 1.31951 | 0.659754 | − | 0.751482i | \(-0.270661\pi\) | ||||
0.659754 | + | 0.751482i | \(0.270661\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −25.0370 | −0.802649 | ||||||||
\(974\) | −1.84849 | −0.0592295 | ||||||||
\(975\) | 12.2226 | 0.391436 | ||||||||
\(976\) | 4.28402 | 0.137128 | ||||||||
\(977\) | −26.5130 | −0.848228 | −0.424114 | − | 0.905609i | \(-0.639414\pi\) | ||||
−0.424114 | + | 0.905609i | \(0.639414\pi\) | |||||||
\(978\) | −10.9961 | −0.351617 | ||||||||
\(979\) | 67.1492 | 2.14610 | ||||||||
\(980\) | 1.39257 | 0.0444841 | ||||||||
\(981\) | −4.25283 | −0.135782 | ||||||||
\(982\) | 35.3045 | 1.12661 | ||||||||
\(983\) | 55.9913 | 1.78585 | 0.892923 | − | 0.450210i | \(-0.148651\pi\) | ||||
0.892923 | + | 0.450210i | \(0.148651\pi\) | |||||||
\(984\) | −5.71415 | −0.182160 | ||||||||
\(985\) | −5.88257 | −0.187434 | ||||||||
\(986\) | −4.44468 | −0.141547 | ||||||||
\(987\) | 31.2187 | 0.993703 | ||||||||
\(988\) | −5.02939 | −0.160006 | ||||||||
\(989\) | −10.5754 | −0.336279 | ||||||||
\(990\) | 6.22708 | 0.197909 | ||||||||
\(991\) | 18.0439 | 0.573182 | 0.286591 | − | 0.958053i | \(-0.407478\pi\) | ||||
0.286591 | + | 0.958053i | \(0.407478\pi\) | |||||||
\(992\) | −5.90783 | −0.187574 | ||||||||
\(993\) | −6.21793 | −0.197320 | ||||||||
\(994\) | 25.3989 | 0.805603 | ||||||||
\(995\) | 28.3056 | 0.897349 | ||||||||
\(996\) | 9.20886 | 0.291794 | ||||||||
\(997\) | −13.3287 | −0.422124 | −0.211062 | − | 0.977473i | \(-0.567692\pi\) | ||||
−0.211062 | + | 0.977473i | \(0.567692\pi\) | |||||||
\(998\) | 9.67804 | 0.306353 | ||||||||
\(999\) | −1.11972 | −0.0354265 |
(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 | 6018.2.a.p.1.2 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.p.1.2 | ✓ | 5 | 1.1 | even | 1 | trivial |