Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3525,2,Mod(1,3525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3525, 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("3525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3525 = 3 \cdot 5^{2} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3525.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: | \(28.1472667125\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 7x^{6} + 24x^{5} + 8x^{4} - 47x^{3} + 8x^{2} + 13x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-0.237165\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.237165 | 0.167701 | 0.0838505 | − | 0.996478i | \(-0.473278\pi\) | ||||
0.0838505 | + | 0.996478i | \(0.473278\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.94375 | −0.971876 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.237165 | 0.0968222 | ||||||||
\(7\) | 1.64667 | 0.622384 | 0.311192 | − | 0.950347i | \(-0.399272\pi\) | ||||
0.311192 | + | 0.950347i | \(0.399272\pi\) | |||||||
\(8\) | −0.935320 | −0.330686 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.84292 | 1.76171 | 0.880853 | − | 0.473389i | \(-0.156970\pi\) | ||||
0.880853 | + | 0.473389i | \(0.156970\pi\) | |||||||
\(12\) | −1.94375 | −0.561113 | ||||||||
\(13\) | −4.61379 | −1.27963 | −0.639817 | − | 0.768527i | \(-0.720990\pi\) | ||||
−0.639817 | + | 0.768527i | \(0.720990\pi\) | |||||||
\(14\) | 0.390533 | 0.104374 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.66568 | 0.916420 | ||||||||
\(17\) | −5.67621 | −1.37668 | −0.688342 | − | 0.725387i | \(-0.741661\pi\) | ||||
−0.688342 | + | 0.725387i | \(0.741661\pi\) | |||||||
\(18\) | 0.237165 | 0.0559003 | ||||||||
\(19\) | −6.71365 | −1.54022 | −0.770108 | − | 0.637913i | \(-0.779798\pi\) | ||||
−0.770108 | + | 0.637913i | \(0.779798\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.64667 | 0.359334 | ||||||||
\(22\) | 1.38574 | 0.295440 | ||||||||
\(23\) | −6.07976 | −1.26772 | −0.633859 | − | 0.773449i | \(-0.718530\pi\) | ||||
−0.633859 | + | 0.773449i | \(0.718530\pi\) | |||||||
\(24\) | −0.935320 | −0.190921 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.09423 | −0.214596 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −3.20073 | −0.604880 | ||||||||
\(29\) | 3.23476 | 0.600680 | 0.300340 | − | 0.953832i | \(-0.402900\pi\) | ||||
0.300340 | + | 0.953832i | \(0.402900\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.81968 | −1.22485 | −0.612425 | − | 0.790528i | \(-0.709806\pi\) | ||||
−0.612425 | + | 0.790528i | \(0.709806\pi\) | |||||||
\(32\) | 2.74001 | 0.484370 | ||||||||
\(33\) | 5.84292 | 1.01712 | ||||||||
\(34\) | −1.34620 | −0.230871 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.94375 | −0.323959 | ||||||||
\(37\) | 5.84115 | 0.960278 | 0.480139 | − | 0.877192i | \(-0.340586\pi\) | ||||
0.480139 | + | 0.877192i | \(0.340586\pi\) | |||||||
\(38\) | −1.59224 | −0.258296 | ||||||||
\(39\) | −4.61379 | −0.738797 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.60067 | −0.406157 | −0.203078 | − | 0.979162i | \(-0.565095\pi\) | ||||
−0.203078 | + | 0.979162i | \(0.565095\pi\) | |||||||
\(42\) | 0.390533 | 0.0602606 | ||||||||
\(43\) | 0.899167 | 0.137122 | 0.0685609 | − | 0.997647i | \(-0.478159\pi\) | ||||
0.0685609 | + | 0.997647i | \(0.478159\pi\) | |||||||
\(44\) | −11.3572 | −1.71216 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.44191 | −0.212597 | ||||||||
\(47\) | −1.00000 | −0.145865 | ||||||||
\(48\) | 3.66568 | 0.529095 | ||||||||
\(49\) | −4.28847 | −0.612638 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.67621 | −0.794829 | ||||||||
\(52\) | 8.96806 | 1.24365 | ||||||||
\(53\) | 4.11309 | 0.564977 | 0.282488 | − | 0.959271i | \(-0.408840\pi\) | ||||
0.282488 | + | 0.959271i | \(0.408840\pi\) | |||||||
\(54\) | 0.237165 | 0.0322741 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.54017 | −0.205814 | ||||||||
\(57\) | −6.71365 | −0.889244 | ||||||||
\(58\) | 0.767172 | 0.100735 | ||||||||
\(59\) | 6.93952 | 0.903449 | 0.451724 | − | 0.892158i | \(-0.350809\pi\) | ||||
0.451724 | + | 0.892158i | \(0.350809\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.54592 | −0.838119 | −0.419060 | − | 0.907959i | \(-0.637640\pi\) | ||||
−0.419060 | + | 0.907959i | \(0.637640\pi\) | |||||||
\(62\) | −1.61739 | −0.205409 | ||||||||
\(63\) | 1.64667 | 0.207461 | ||||||||
\(64\) | −6.68153 | −0.835191 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.38574 | 0.170572 | ||||||||
\(67\) | −9.16921 | −1.12020 | −0.560099 | − | 0.828426i | \(-0.689237\pi\) | ||||
−0.560099 | + | 0.828426i | \(0.689237\pi\) | |||||||
\(68\) | 11.0332 | 1.33797 | ||||||||
\(69\) | −6.07976 | −0.731917 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.98175 | 0.472546 | 0.236273 | − | 0.971687i | \(-0.424074\pi\) | ||||
0.236273 | + | 0.971687i | \(0.424074\pi\) | |||||||
\(72\) | −0.935320 | −0.110229 | ||||||||
\(73\) | −12.2218 | −1.43045 | −0.715226 | − | 0.698893i | \(-0.753676\pi\) | ||||
−0.715226 | + | 0.698893i | \(0.753676\pi\) | |||||||
\(74\) | 1.38532 | 0.161040 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 13.0497 | 1.49690 | ||||||||
\(77\) | 9.62138 | 1.09646 | ||||||||
\(78\) | −1.09423 | −0.123897 | ||||||||
\(79\) | 15.1032 | 1.69924 | 0.849621 | − | 0.527394i | \(-0.176831\pi\) | ||||
0.849621 | + | 0.527394i | \(0.176831\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.616789 | −0.0681129 | ||||||||
\(83\) | −14.5712 | −1.59940 | −0.799700 | − | 0.600400i | \(-0.795008\pi\) | ||||
−0.799700 | + | 0.600400i | \(0.795008\pi\) | |||||||
\(84\) | −3.20073 | −0.349228 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.213251 | 0.0229955 | ||||||||
\(87\) | 3.23476 | 0.346803 | ||||||||
\(88\) | −5.46500 | −0.582571 | ||||||||
\(89\) | −7.03976 | −0.746213 | −0.373106 | − | 0.927789i | \(-0.621707\pi\) | ||||
−0.373106 | + | 0.927789i | \(0.621707\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.59740 | −0.796424 | ||||||||
\(92\) | 11.8175 | 1.23206 | ||||||||
\(93\) | −6.81968 | −0.707168 | ||||||||
\(94\) | −0.237165 | −0.0244617 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.74001 | 0.279651 | ||||||||
\(97\) | 8.59813 | 0.873008 | 0.436504 | − | 0.899702i | \(-0.356217\pi\) | ||||
0.436504 | + | 0.899702i | \(0.356217\pi\) | |||||||
\(98\) | −1.01707 | −0.102740 | ||||||||
\(99\) | 5.84292 | 0.587236 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.31500 | 0.727870 | 0.363935 | − | 0.931424i | \(-0.381433\pi\) | ||||
0.363935 | + | 0.931424i | \(0.381433\pi\) | |||||||
\(102\) | −1.34620 | −0.133294 | ||||||||
\(103\) | −0.918971 | −0.0905489 | −0.0452744 | − | 0.998975i | \(-0.514416\pi\) | ||||
−0.0452744 | + | 0.998975i | \(0.514416\pi\) | |||||||
\(104\) | 4.31537 | 0.423157 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.975482 | 0.0947472 | ||||||||
\(107\) | −9.87708 | −0.954853 | −0.477427 | − | 0.878672i | \(-0.658430\pi\) | ||||
−0.477427 | + | 0.878672i | \(0.658430\pi\) | |||||||
\(108\) | −1.94375 | −0.187038 | ||||||||
\(109\) | −19.0166 | −1.82146 | −0.910729 | − | 0.413004i | \(-0.864479\pi\) | ||||
−0.910729 | + | 0.413004i | \(0.864479\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.84115 | 0.554417 | ||||||||
\(112\) | 6.03618 | 0.570365 | ||||||||
\(113\) | 4.31060 | 0.405507 | 0.202753 | − | 0.979230i | \(-0.435011\pi\) | ||||
0.202753 | + | 0.979230i | \(0.435011\pi\) | |||||||
\(114\) | −1.59224 | −0.149127 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.28758 | −0.583787 | ||||||||
\(117\) | −4.61379 | −0.426545 | ||||||||
\(118\) | 1.64581 | 0.151509 | ||||||||
\(119\) | −9.34687 | −0.856826 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.1397 | 2.10361 | ||||||||
\(122\) | −1.55246 | −0.140553 | ||||||||
\(123\) | −2.60067 | −0.234495 | ||||||||
\(124\) | 13.2558 | 1.19040 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.390533 | 0.0347915 | ||||||||
\(127\) | 1.55525 | 0.138006 | 0.0690031 | − | 0.997616i | \(-0.478018\pi\) | ||||
0.0690031 | + | 0.997616i | \(0.478018\pi\) | |||||||
\(128\) | −7.06465 | −0.624433 | ||||||||
\(129\) | 0.899167 | 0.0791673 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.5392 | 1.35767 | 0.678833 | − | 0.734292i | \(-0.262486\pi\) | ||||
0.678833 | + | 0.734292i | \(0.262486\pi\) | |||||||
\(132\) | −11.3572 | −0.988517 | ||||||||
\(133\) | −11.0552 | −0.958606 | ||||||||
\(134\) | −2.17462 | −0.187858 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.30908 | 0.455250 | ||||||||
\(137\) | −12.4815 | −1.06637 | −0.533183 | − | 0.846000i | \(-0.679004\pi\) | ||||
−0.533183 | + | 0.846000i | \(0.679004\pi\) | |||||||
\(138\) | −1.44191 | −0.122743 | ||||||||
\(139\) | 4.67413 | 0.396454 | 0.198227 | − | 0.980156i | \(-0.436482\pi\) | ||||
0.198227 | + | 0.980156i | \(0.436482\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.00000 | −0.0842152 | ||||||||
\(142\) | 0.944331 | 0.0792465 | ||||||||
\(143\) | −26.9580 | −2.25434 | ||||||||
\(144\) | 3.66568 | 0.305473 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.89858 | −0.239888 | ||||||||
\(147\) | −4.28847 | −0.353707 | ||||||||
\(148\) | −11.3537 | −0.933272 | ||||||||
\(149\) | −20.0538 | −1.64287 | −0.821435 | − | 0.570302i | \(-0.806826\pi\) | ||||
−0.821435 | + | 0.570302i | \(0.806826\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.3513 | −1.41203 | −0.706013 | − | 0.708198i | \(-0.749508\pi\) | ||||
−0.706013 | + | 0.708198i | \(0.749508\pi\) | |||||||
\(152\) | 6.27941 | 0.509328 | ||||||||
\(153\) | −5.67621 | −0.458895 | ||||||||
\(154\) | 2.28186 | 0.183877 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 8.96806 | 0.718019 | ||||||||
\(157\) | −9.02606 | −0.720358 | −0.360179 | − | 0.932883i | \(-0.617284\pi\) | ||||
−0.360179 | + | 0.932883i | \(0.617284\pi\) | |||||||
\(158\) | 3.58195 | 0.284965 | ||||||||
\(159\) | 4.11309 | 0.326189 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.0114 | −0.789007 | ||||||||
\(162\) | 0.237165 | 0.0186334 | ||||||||
\(163\) | −0.183786 | −0.0143952 | −0.00719760 | − | 0.999974i | \(-0.502291\pi\) | ||||
−0.00719760 | + | 0.999974i | \(0.502291\pi\) | |||||||
\(164\) | 5.05506 | 0.394734 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.45579 | −0.268221 | ||||||||
\(167\) | −16.7897 | −1.29923 | −0.649615 | − | 0.760264i | \(-0.725070\pi\) | ||||
−0.649615 | + | 0.760264i | \(0.725070\pi\) | |||||||
\(168\) | −1.54017 | −0.118827 | ||||||||
\(169\) | 8.28702 | 0.637463 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.71365 | −0.513406 | ||||||||
\(172\) | −1.74776 | −0.133265 | ||||||||
\(173\) | 9.26133 | 0.704126 | 0.352063 | − | 0.935976i | \(-0.385480\pi\) | ||||
0.352063 | + | 0.935976i | \(0.385480\pi\) | |||||||
\(174\) | 0.767172 | 0.0581592 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 21.4183 | 1.61446 | ||||||||
\(177\) | 6.93952 | 0.521606 | ||||||||
\(178\) | −1.66958 | −0.125141 | ||||||||
\(179\) | −0.495946 | −0.0370688 | −0.0185344 | − | 0.999828i | \(-0.505900\pi\) | ||||
−0.0185344 | + | 0.999828i | \(0.505900\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.8611 | −0.807296 | −0.403648 | − | 0.914914i | \(-0.632258\pi\) | ||||
−0.403648 | + | 0.914914i | \(0.632258\pi\) | |||||||
\(182\) | −1.80184 | −0.133561 | ||||||||
\(183\) | −6.54592 | −0.483888 | ||||||||
\(184\) | 5.68652 | 0.419216 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.61739 | −0.118593 | ||||||||
\(187\) | −33.1657 | −2.42531 | ||||||||
\(188\) | 1.94375 | 0.141763 | ||||||||
\(189\) | 1.64667 | 0.119778 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.78821 | −0.563535 | −0.281767 | − | 0.959483i | \(-0.590921\pi\) | ||||
−0.281767 | + | 0.959483i | \(0.590921\pi\) | |||||||
\(192\) | −6.68153 | −0.482198 | ||||||||
\(193\) | 9.91584 | 0.713758 | 0.356879 | − | 0.934151i | \(-0.383841\pi\) | ||||
0.356879 | + | 0.934151i | \(0.383841\pi\) | |||||||
\(194\) | 2.03918 | 0.146404 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.33572 | 0.595408 | ||||||||
\(197\) | −23.4872 | −1.67339 | −0.836697 | − | 0.547666i | \(-0.815516\pi\) | ||||
−0.836697 | + | 0.547666i | \(0.815516\pi\) | |||||||
\(198\) | 1.38574 | 0.0984800 | ||||||||
\(199\) | 14.0706 | 0.997438 | 0.498719 | − | 0.866764i | \(-0.333804\pi\) | ||||
0.498719 | + | 0.866764i | \(0.333804\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.16921 | −0.646746 | ||||||||
\(202\) | 1.73486 | 0.122064 | ||||||||
\(203\) | 5.32660 | 0.373854 | ||||||||
\(204\) | 11.0332 | 0.772475 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.217948 | −0.0151851 | ||||||||
\(207\) | −6.07976 | −0.422572 | ||||||||
\(208\) | −16.9127 | −1.17268 | ||||||||
\(209\) | −39.2273 | −2.71341 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.55801 | 0.313787 | 0.156893 | − | 0.987616i | \(-0.449852\pi\) | ||||
0.156893 | + | 0.987616i | \(0.449852\pi\) | |||||||
\(212\) | −7.99483 | −0.549087 | ||||||||
\(213\) | 3.98175 | 0.272825 | ||||||||
\(214\) | −2.34250 | −0.160130 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.935320 | −0.0636405 | ||||||||
\(217\) | −11.2298 | −0.762328 | ||||||||
\(218\) | −4.51007 | −0.305460 | ||||||||
\(219\) | −12.2218 | −0.825872 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 26.1888 | 1.76165 | ||||||||
\(222\) | 1.38532 | 0.0929763 | ||||||||
\(223\) | −8.38549 | −0.561534 | −0.280767 | − | 0.959776i | \(-0.590589\pi\) | ||||
−0.280767 | + | 0.959776i | \(0.590589\pi\) | |||||||
\(224\) | 4.51191 | 0.301464 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.02232 | 0.0680039 | ||||||||
\(227\) | 1.27015 | 0.0843025 | 0.0421513 | − | 0.999111i | \(-0.486579\pi\) | ||||
0.0421513 | + | 0.999111i | \(0.486579\pi\) | |||||||
\(228\) | 13.0497 | 0.864236 | ||||||||
\(229\) | −5.99457 | −0.396133 | −0.198066 | − | 0.980189i | \(-0.563466\pi\) | ||||
−0.198066 | + | 0.980189i | \(0.563466\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.62138 | 0.633041 | ||||||||
\(232\) | −3.02554 | −0.198636 | ||||||||
\(233\) | 9.99821 | 0.655005 | 0.327502 | − | 0.944850i | \(-0.393793\pi\) | ||||
0.327502 | + | 0.944850i | \(0.393793\pi\) | |||||||
\(234\) | −1.09423 | −0.0715320 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −13.4887 | −0.878041 | ||||||||
\(237\) | 15.1032 | 0.981058 | ||||||||
\(238\) | −2.21675 | −0.143691 | ||||||||
\(239\) | −7.43603 | −0.480997 | −0.240498 | − | 0.970650i | \(-0.577311\pi\) | ||||
−0.240498 | + | 0.970650i | \(0.577311\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.976110 | −0.0628768 | −0.0314384 | − | 0.999506i | \(-0.510009\pi\) | ||||
−0.0314384 | + | 0.999506i | \(0.510009\pi\) | |||||||
\(242\) | 5.48793 | 0.352778 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 12.7237 | 0.814548 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.616789 | −0.0393250 | ||||||||
\(247\) | 30.9753 | 1.97091 | ||||||||
\(248\) | 6.37859 | 0.405041 | ||||||||
\(249\) | −14.5712 | −0.923414 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.5387 | 1.42263 | 0.711314 | − | 0.702874i | \(-0.248100\pi\) | ||||
0.711314 | + | 0.702874i | \(0.248100\pi\) | |||||||
\(252\) | −3.20073 | −0.201627 | ||||||||
\(253\) | −35.5235 | −2.23335 | ||||||||
\(254\) | 0.368851 | 0.0231438 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.6876 | 0.730473 | ||||||||
\(257\) | −7.60490 | −0.474380 | −0.237190 | − | 0.971463i | \(-0.576226\pi\) | ||||
−0.237190 | + | 0.971463i | \(0.576226\pi\) | |||||||
\(258\) | 0.213251 | 0.0132764 | ||||||||
\(259\) | 9.61846 | 0.597662 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.23476 | 0.200227 | ||||||||
\(262\) | 3.68536 | 0.227682 | ||||||||
\(263\) | 20.4512 | 1.26108 | 0.630538 | − | 0.776158i | \(-0.282834\pi\) | ||||
0.630538 | + | 0.776158i | \(0.282834\pi\) | |||||||
\(264\) | −5.46500 | −0.336348 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.62190 | −0.160759 | ||||||||
\(267\) | −7.03976 | −0.430826 | ||||||||
\(268\) | 17.8227 | 1.08869 | ||||||||
\(269\) | −4.79575 | −0.292402 | −0.146201 | − | 0.989255i | \(-0.546705\pi\) | ||||
−0.146201 | + | 0.989255i | \(0.546705\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.8394 | −0.658444 | −0.329222 | − | 0.944253i | \(-0.606786\pi\) | ||||
−0.329222 | + | 0.944253i | \(0.606786\pi\) | |||||||
\(272\) | −20.8072 | −1.26162 | ||||||||
\(273\) | −7.59740 | −0.459816 | ||||||||
\(274\) | −2.96018 | −0.178831 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 11.8175 | 0.711333 | ||||||||
\(277\) | 28.9500 | 1.73944 | 0.869719 | − | 0.493548i | \(-0.164300\pi\) | ||||
0.869719 | + | 0.493548i | \(0.164300\pi\) | |||||||
\(278\) | 1.10854 | 0.0664858 | ||||||||
\(279\) | −6.81968 | −0.408284 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.7906 | −1.47888 | −0.739441 | − | 0.673222i | \(-0.764910\pi\) | ||||
−0.739441 | + | 0.673222i | \(0.764910\pi\) | |||||||
\(282\) | −0.237165 | −0.0141230 | ||||||||
\(283\) | −8.99344 | −0.534604 | −0.267302 | − | 0.963613i | \(-0.586132\pi\) | ||||
−0.267302 | + | 0.963613i | \(0.586132\pi\) | |||||||
\(284\) | −7.73953 | −0.459257 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.39349 | −0.378055 | ||||||||
\(287\) | −4.28246 | −0.252786 | ||||||||
\(288\) | 2.74001 | 0.161457 | ||||||||
\(289\) | 15.2194 | 0.895258 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.59813 | 0.504031 | ||||||||
\(292\) | 23.7561 | 1.39022 | ||||||||
\(293\) | 0.665090 | 0.0388550 | 0.0194275 | − | 0.999811i | \(-0.493816\pi\) | ||||
0.0194275 | + | 0.999811i | \(0.493816\pi\) | |||||||
\(294\) | −1.01707 | −0.0593170 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.46334 | −0.317550 | ||||||||
\(297\) | 5.84292 | 0.339041 | ||||||||
\(298\) | −4.75606 | −0.275511 | ||||||||
\(299\) | 28.0507 | 1.62221 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.48064 | 0.0853424 | ||||||||
\(302\) | −4.11512 | −0.236798 | ||||||||
\(303\) | 7.31500 | 0.420236 | ||||||||
\(304\) | −24.6101 | −1.41149 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.34620 | −0.0769571 | ||||||||
\(307\) | 0.814634 | 0.0464936 | 0.0232468 | − | 0.999730i | \(-0.492600\pi\) | ||||
0.0232468 | + | 0.999730i | \(0.492600\pi\) | |||||||
\(308\) | −18.7016 | −1.06562 | ||||||||
\(309\) | −0.918971 | −0.0522784 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.78222 | 0.271175 | 0.135587 | − | 0.990765i | \(-0.456708\pi\) | ||||
0.135587 | + | 0.990765i | \(0.456708\pi\) | |||||||
\(312\) | 4.31537 | 0.244310 | ||||||||
\(313\) | 6.26198 | 0.353948 | 0.176974 | − | 0.984216i | \(-0.443369\pi\) | ||||
0.176974 | + | 0.984216i | \(0.443369\pi\) | |||||||
\(314\) | −2.14067 | −0.120805 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −29.3569 | −1.65145 | ||||||||
\(317\) | −15.8462 | −0.890011 | −0.445005 | − | 0.895528i | \(-0.646798\pi\) | ||||
−0.445005 | + | 0.895528i | \(0.646798\pi\) | |||||||
\(318\) | 0.975482 | 0.0547023 | ||||||||
\(319\) | 18.9005 | 1.05822 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.87708 | −0.551285 | ||||||||
\(322\) | −2.37435 | −0.132317 | ||||||||
\(323\) | 38.1081 | 2.12039 | ||||||||
\(324\) | −1.94375 | −0.107986 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.0435875 | −0.00241409 | ||||||||
\(327\) | −19.0166 | −1.05162 | ||||||||
\(328\) | 2.43246 | 0.134310 | ||||||||
\(329\) | −1.64667 | −0.0907841 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.2797 | 1.71929 | 0.859643 | − | 0.510895i | \(-0.170686\pi\) | ||||
0.859643 | + | 0.510895i | \(0.170686\pi\) | |||||||
\(332\) | 28.3229 | 1.55442 | ||||||||
\(333\) | 5.84115 | 0.320093 | ||||||||
\(334\) | −3.98194 | −0.217882 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 6.03618 | 0.329301 | ||||||||
\(337\) | −18.1866 | −0.990689 | −0.495344 | − | 0.868697i | \(-0.664958\pi\) | ||||
−0.495344 | + | 0.868697i | \(0.664958\pi\) | |||||||
\(338\) | 1.96539 | 0.106903 | ||||||||
\(339\) | 4.31060 | 0.234120 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −39.8468 | −2.15783 | ||||||||
\(342\) | −1.59224 | −0.0860986 | ||||||||
\(343\) | −18.5884 | −1.00368 | ||||||||
\(344\) | −0.841010 | −0.0453442 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.19646 | 0.118083 | ||||||||
\(347\) | 16.2998 | 0.875021 | 0.437511 | − | 0.899213i | \(-0.355860\pi\) | ||||
0.437511 | + | 0.899213i | \(0.355860\pi\) | |||||||
\(348\) | −6.28758 | −0.337049 | ||||||||
\(349\) | 26.4685 | 1.41683 | 0.708413 | − | 0.705798i | \(-0.249411\pi\) | ||||
0.708413 | + | 0.705798i | \(0.249411\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.61379 | −0.246266 | ||||||||
\(352\) | 16.0097 | 0.853318 | ||||||||
\(353\) | −30.7241 | −1.63528 | −0.817638 | − | 0.575732i | \(-0.804717\pi\) | ||||
−0.817638 | + | 0.575732i | \(0.804717\pi\) | |||||||
\(354\) | 1.64581 | 0.0874739 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 13.6835 | 0.725226 | ||||||||
\(357\) | −9.34687 | −0.494689 | ||||||||
\(358\) | −0.117621 | −0.00621647 | ||||||||
\(359\) | −24.6709 | −1.30208 | −0.651041 | − | 0.759043i | \(-0.725667\pi\) | ||||
−0.651041 | + | 0.759043i | \(0.725667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.0731 | 1.37227 | ||||||||
\(362\) | −2.57586 | −0.135384 | ||||||||
\(363\) | 23.1397 | 1.21452 | ||||||||
\(364\) | 14.7675 | 0.774026 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.55246 | −0.0811486 | ||||||||
\(367\) | −0.973102 | −0.0507955 | −0.0253977 | − | 0.999677i | \(-0.508085\pi\) | ||||
−0.0253977 | + | 0.999677i | \(0.508085\pi\) | |||||||
\(368\) | −22.2864 | −1.16176 | ||||||||
\(369\) | −2.60067 | −0.135386 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.77292 | 0.351633 | ||||||||
\(372\) | 13.2558 | 0.687280 | ||||||||
\(373\) | 8.61972 | 0.446312 | 0.223156 | − | 0.974783i | \(-0.428364\pi\) | ||||
0.223156 | + | 0.974783i | \(0.428364\pi\) | |||||||
\(374\) | −7.86573 | −0.406727 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.935320 | 0.0482355 | ||||||||
\(377\) | −14.9245 | −0.768651 | ||||||||
\(378\) | 0.390533 | 0.0200869 | ||||||||
\(379\) | 5.44944 | 0.279919 | 0.139960 | − | 0.990157i | \(-0.455303\pi\) | ||||
0.139960 | + | 0.990157i | \(0.455303\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.55525 | 0.0796779 | ||||||||
\(382\) | −1.84709 | −0.0945054 | ||||||||
\(383\) | −6.45312 | −0.329739 | −0.164869 | − | 0.986315i | \(-0.552720\pi\) | ||||
−0.164869 | + | 0.986315i | \(0.552720\pi\) | |||||||
\(384\) | −7.06465 | −0.360516 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.35169 | 0.119698 | ||||||||
\(387\) | 0.899167 | 0.0457072 | ||||||||
\(388\) | −16.7126 | −0.848456 | ||||||||
\(389\) | 22.5677 | 1.14423 | 0.572113 | − | 0.820175i | \(-0.306124\pi\) | ||||
0.572113 | + | 0.820175i | \(0.306124\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 34.5100 | 1.74525 | ||||||||
\(392\) | 4.01109 | 0.202591 | ||||||||
\(393\) | 15.5392 | 0.783849 | ||||||||
\(394\) | −5.57034 | −0.280630 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −11.3572 | −0.570720 | ||||||||
\(397\) | −0.566161 | −0.0284148 | −0.0142074 | − | 0.999899i | \(-0.504523\pi\) | ||||
−0.0142074 | + | 0.999899i | \(0.504523\pi\) | |||||||
\(398\) | 3.33705 | 0.167271 | ||||||||
\(399\) | −11.0552 | −0.553452 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.5606 | −1.17656 | −0.588280 | − | 0.808658i | \(-0.700195\pi\) | ||||
−0.588280 | + | 0.808658i | \(0.700195\pi\) | |||||||
\(402\) | −2.17462 | −0.108460 | ||||||||
\(403\) | 31.4645 | 1.56736 | ||||||||
\(404\) | −14.2185 | −0.707399 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.26328 | 0.0626957 | ||||||||
\(407\) | 34.1293 | 1.69173 | ||||||||
\(408\) | 5.30908 | 0.262838 | ||||||||
\(409\) | 37.8278 | 1.87046 | 0.935232 | − | 0.354036i | \(-0.115191\pi\) | ||||
0.935232 | + | 0.354036i | \(0.115191\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.4815 | −0.615667 | ||||||||
\(412\) | 1.78625 | 0.0880023 | ||||||||
\(413\) | 11.4271 | 0.562292 | ||||||||
\(414\) | −1.44191 | −0.0708658 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −12.6418 | −0.619817 | ||||||||
\(417\) | 4.67413 | 0.228893 | ||||||||
\(418\) | −9.30335 | −0.455042 | ||||||||
\(419\) | 11.1859 | 0.546465 | 0.273233 | − | 0.961948i | \(-0.411907\pi\) | ||||
0.273233 | + | 0.961948i | \(0.411907\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 39.0593 | 1.90363 | 0.951817 | − | 0.306668i | \(-0.0992141\pi\) | ||||
0.951817 | + | 0.306668i | \(0.0992141\pi\) | |||||||
\(422\) | 1.08100 | 0.0526223 | ||||||||
\(423\) | −1.00000 | −0.0486217 | ||||||||
\(424\) | −3.84706 | −0.186830 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.944331 | 0.0457530 | ||||||||
\(427\) | −10.7790 | −0.521632 | ||||||||
\(428\) | 19.1986 | 0.928000 | ||||||||
\(429\) | −26.9580 | −1.30154 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.6413 | 1.57228 | 0.786139 | − | 0.618049i | \(-0.212077\pi\) | ||||
0.786139 | + | 0.618049i | \(0.212077\pi\) | |||||||
\(432\) | 3.66568 | 0.176365 | ||||||||
\(433\) | −24.6811 | −1.18610 | −0.593050 | − | 0.805166i | \(-0.702076\pi\) | ||||
−0.593050 | + | 0.805166i | \(0.702076\pi\) | |||||||
\(434\) | −2.66331 | −0.127843 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 36.9635 | 1.77023 | ||||||||
\(437\) | 40.8174 | 1.95256 | ||||||||
\(438\) | −2.89858 | −0.138500 | ||||||||
\(439\) | 30.1029 | 1.43673 | 0.718366 | − | 0.695665i | \(-0.244890\pi\) | ||||
0.718366 | + | 0.695665i | \(0.244890\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.28847 | −0.204213 | ||||||||
\(442\) | 6.21107 | 0.295431 | ||||||||
\(443\) | 38.1560 | 1.81285 | 0.906424 | − | 0.422370i | \(-0.138802\pi\) | ||||
0.906424 | + | 0.422370i | \(0.138802\pi\) | |||||||
\(444\) | −11.3537 | −0.538825 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.98874 | −0.0941698 | ||||||||
\(447\) | −20.0538 | −0.948511 | ||||||||
\(448\) | −11.0023 | −0.519809 | ||||||||
\(449\) | 0.588803 | 0.0277873 | 0.0138937 | − | 0.999903i | \(-0.495577\pi\) | ||||
0.0138937 | + | 0.999903i | \(0.495577\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.1955 | −0.715529 | ||||||||
\(452\) | −8.37874 | −0.394103 | ||||||||
\(453\) | −17.3513 | −0.815234 | ||||||||
\(454\) | 0.301234 | 0.0141376 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.27941 | 0.294060 | ||||||||
\(457\) | −36.8925 | −1.72576 | −0.862879 | − | 0.505411i | \(-0.831341\pi\) | ||||
−0.862879 | + | 0.505411i | \(0.831341\pi\) | |||||||
\(458\) | −1.42170 | −0.0664318 | ||||||||
\(459\) | −5.67621 | −0.264943 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.63431 | 0.169267 | 0.0846333 | − | 0.996412i | \(-0.473028\pi\) | ||||
0.0846333 | + | 0.996412i | \(0.473028\pi\) | |||||||
\(462\) | 2.28186 | 0.106162 | ||||||||
\(463\) | −1.66199 | −0.0772393 | −0.0386197 | − | 0.999254i | \(-0.512296\pi\) | ||||
−0.0386197 | + | 0.999254i | \(0.512296\pi\) | |||||||
\(464\) | 11.8576 | 0.550475 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.37123 | 0.109845 | ||||||||
\(467\) | −27.7300 | −1.28319 | −0.641596 | − | 0.767043i | \(-0.721727\pi\) | ||||
−0.641596 | + | 0.767043i | \(0.721727\pi\) | |||||||
\(468\) | 8.96806 | 0.414549 | ||||||||
\(469\) | −15.0987 | −0.697193 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.02606 | −0.415899 | ||||||||
\(472\) | −6.49068 | −0.298758 | ||||||||
\(473\) | 5.25376 | 0.241568 | ||||||||
\(474\) | 3.58195 | 0.164524 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 18.1680 | 0.832729 | ||||||||
\(477\) | 4.11309 | 0.188326 | ||||||||
\(478\) | −1.76357 | −0.0806637 | ||||||||
\(479\) | 31.8914 | 1.45716 | 0.728578 | − | 0.684962i | \(-0.240181\pi\) | ||||
0.728578 | + | 0.684962i | \(0.240181\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.9498 | −1.22880 | ||||||||
\(482\) | −0.231499 | −0.0105445 | ||||||||
\(483\) | −10.0114 | −0.455533 | ||||||||
\(484\) | −44.9779 | −2.04445 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.237165 | 0.0107580 | ||||||||
\(487\) | 7.31388 | 0.331424 | 0.165712 | − | 0.986174i | \(-0.447008\pi\) | ||||
0.165712 | + | 0.986174i | \(0.447008\pi\) | |||||||
\(488\) | 6.12253 | 0.277154 | ||||||||
\(489\) | −0.183786 | −0.00831107 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.89156 | 0.265882 | 0.132941 | − | 0.991124i | \(-0.457558\pi\) | ||||
0.132941 | + | 0.991124i | \(0.457558\pi\) | |||||||
\(492\) | 5.05506 | 0.227900 | ||||||||
\(493\) | −18.3612 | −0.826946 | ||||||||
\(494\) | 7.34627 | 0.330524 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −24.9988 | −1.12248 | ||||||||
\(497\) | 6.55664 | 0.294105 | ||||||||
\(498\) | −3.45579 | −0.154857 | ||||||||
\(499\) | −23.8545 | −1.06787 | −0.533936 | − | 0.845525i | \(-0.679288\pi\) | ||||
−0.533936 | + | 0.845525i | \(0.679288\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.7897 | −0.750110 | ||||||||
\(502\) | 5.34539 | 0.238576 | ||||||||
\(503\) | −33.9274 | −1.51275 | −0.756373 | − | 0.654140i | \(-0.773031\pi\) | ||||
−0.756373 | + | 0.654140i | \(0.773031\pi\) | |||||||
\(504\) | −1.54017 | −0.0686045 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.42494 | −0.374534 | ||||||||
\(507\) | 8.28702 | 0.368039 | ||||||||
\(508\) | −3.02302 | −0.134125 | ||||||||
\(509\) | 2.48551 | 0.110168 | 0.0550842 | − | 0.998482i | \(-0.482457\pi\) | ||||
0.0550842 | + | 0.998482i | \(0.482457\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20.1253 | −0.890291 | ||||||||
\(512\) | 16.9012 | 0.746934 | ||||||||
\(513\) | −6.71365 | −0.296415 | ||||||||
\(514\) | −1.80362 | −0.0795541 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.74776 | −0.0769408 | ||||||||
\(517\) | −5.84292 | −0.256971 | ||||||||
\(518\) | 2.28116 | 0.100229 | ||||||||
\(519\) | 9.26133 | 0.406527 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.2373 | −0.492315 | −0.246158 | − | 0.969230i | \(-0.579168\pi\) | ||||
−0.246158 | + | 0.969230i | \(0.579168\pi\) | |||||||
\(522\) | 0.767172 | 0.0335782 | ||||||||
\(523\) | 38.2596 | 1.67298 | 0.836489 | − | 0.547984i | \(-0.184605\pi\) | ||||
0.836489 | + | 0.547984i | \(0.184605\pi\) | |||||||
\(524\) | −30.2044 | −1.31948 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.85031 | 0.211484 | ||||||||
\(527\) | 38.7099 | 1.68623 | ||||||||
\(528\) | 21.4183 | 0.932111 | ||||||||
\(529\) | 13.9634 | 0.607106 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.93952 | 0.301150 | ||||||||
\(532\) | 21.4886 | 0.931647 | ||||||||
\(533\) | 11.9989 | 0.519732 | ||||||||
\(534\) | −1.66958 | −0.0722500 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.57615 | 0.370433 | ||||||||
\(537\) | −0.495946 | −0.0214017 | ||||||||
\(538\) | −1.13739 | −0.0490362 | ||||||||
\(539\) | −25.0572 | −1.07929 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 45.3760 | 1.95087 | 0.975434 | − | 0.220294i | \(-0.0707017\pi\) | ||||
0.975434 | + | 0.220294i | \(0.0707017\pi\) | |||||||
\(542\) | −2.57072 | −0.110422 | ||||||||
\(543\) | −10.8611 | −0.466093 | ||||||||
\(544\) | −15.5529 | −0.666825 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.80184 | −0.0771115 | ||||||||
\(547\) | 33.9643 | 1.45221 | 0.726104 | − | 0.687585i | \(-0.241329\pi\) | ||||
0.726104 | + | 0.687585i | \(0.241329\pi\) | |||||||
\(548\) | 24.2610 | 1.03638 | ||||||||
\(549\) | −6.54592 | −0.279373 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.7170 | −0.925177 | ||||||||
\(552\) | 5.68652 | 0.242034 | ||||||||
\(553\) | 24.8700 | 1.05758 | ||||||||
\(554\) | 6.86593 | 0.291705 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.08535 | −0.385305 | ||||||||
\(557\) | 27.9359 | 1.18368 | 0.591841 | − | 0.806055i | \(-0.298401\pi\) | ||||
0.591841 | + | 0.806055i | \(0.298401\pi\) | |||||||
\(558\) | −1.61739 | −0.0684696 | ||||||||
\(559\) | −4.14857 | −0.175466 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −33.1657 | −1.40025 | ||||||||
\(562\) | −5.87946 | −0.248010 | ||||||||
\(563\) | −40.1590 | −1.69250 | −0.846250 | − | 0.532787i | \(-0.821145\pi\) | ||||
−0.846250 | + | 0.532787i | \(0.821145\pi\) | |||||||
\(564\) | 1.94375 | 0.0818468 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.13293 | −0.0896537 | ||||||||
\(567\) | 1.64667 | 0.0691538 | ||||||||
\(568\) | −3.72421 | −0.156264 | ||||||||
\(569\) | 19.4727 | 0.816336 | 0.408168 | − | 0.912907i | \(-0.366168\pi\) | ||||
0.408168 | + | 0.912907i | \(0.366168\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.7006 | −0.447807 | −0.223904 | − | 0.974611i | \(-0.571880\pi\) | ||||
−0.223904 | + | 0.974611i | \(0.571880\pi\) | |||||||
\(572\) | 52.3997 | 2.19094 | ||||||||
\(573\) | −7.78821 | −0.325357 | ||||||||
\(574\) | −1.01565 | −0.0423924 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6.68153 | −0.278397 | ||||||||
\(577\) | 5.73302 | 0.238669 | 0.119334 | − | 0.992854i | \(-0.461924\pi\) | ||||
0.119334 | + | 0.992854i | \(0.461924\pi\) | |||||||
\(578\) | 3.60951 | 0.150136 | ||||||||
\(579\) | 9.91584 | 0.412088 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −23.9940 | −0.995441 | ||||||||
\(582\) | 2.03918 | 0.0845266 | ||||||||
\(583\) | 24.0325 | 0.995323 | ||||||||
\(584\) | 11.4313 | 0.473030 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.157736 | 0.00651602 | ||||||||
\(587\) | 16.3376 | 0.674323 | 0.337162 | − | 0.941447i | \(-0.390533\pi\) | ||||
0.337162 | + | 0.941447i | \(0.390533\pi\) | |||||||
\(588\) | 8.33572 | 0.343759 | ||||||||
\(589\) | 45.7849 | 1.88654 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −23.4872 | −0.966134 | ||||||||
\(592\) | 21.4118 | 0.880018 | ||||||||
\(593\) | −11.9853 | −0.492178 | −0.246089 | − | 0.969247i | \(-0.579146\pi\) | ||||
−0.246089 | + | 0.969247i | \(0.579146\pi\) | |||||||
\(594\) | 1.38574 | 0.0568575 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 38.9796 | 1.59667 | ||||||||
\(597\) | 14.0706 | 0.575871 | ||||||||
\(598\) | 6.65265 | 0.272047 | ||||||||
\(599\) | 23.8481 | 0.974408 | 0.487204 | − | 0.873288i | \(-0.338017\pi\) | ||||
0.487204 | + | 0.873288i | \(0.338017\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.4995 | −1.52964 | −0.764819 | − | 0.644246i | \(-0.777171\pi\) | ||||
−0.764819 | + | 0.644246i | \(0.777171\pi\) | |||||||
\(602\) | 0.351155 | 0.0143120 | ||||||||
\(603\) | −9.16921 | −0.373399 | ||||||||
\(604\) | 33.7266 | 1.37232 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.73486 | 0.0704740 | ||||||||
\(607\) | −40.9079 | −1.66040 | −0.830200 | − | 0.557466i | \(-0.811774\pi\) | ||||
−0.830200 | + | 0.557466i | \(0.811774\pi\) | |||||||
\(608\) | −18.3955 | −0.746035 | ||||||||
\(609\) | 5.32660 | 0.215845 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.61379 | 0.186654 | ||||||||
\(612\) | 11.0332 | 0.445989 | ||||||||
\(613\) | −32.7377 | −1.32226 | −0.661132 | − | 0.750269i | \(-0.729924\pi\) | ||||
−0.661132 | + | 0.750269i | \(0.729924\pi\) | |||||||
\(614\) | 0.193203 | 0.00779702 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.99908 | −0.362583 | ||||||||
\(617\) | −43.3902 | −1.74682 | −0.873412 | − | 0.486983i | \(-0.838097\pi\) | ||||
−0.873412 | + | 0.486983i | \(0.838097\pi\) | |||||||
\(618\) | −0.217948 | −0.00876714 | ||||||||
\(619\) | 1.51113 | 0.0607376 | 0.0303688 | − | 0.999539i | \(-0.490332\pi\) | ||||
0.0303688 | + | 0.999539i | \(0.490332\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.07976 | −0.243972 | ||||||||
\(622\) | 1.13417 | 0.0454763 | ||||||||
\(623\) | −11.5922 | −0.464431 | ||||||||
\(624\) | −16.9127 | −0.677048 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.48512 | 0.0593575 | ||||||||
\(627\) | −39.2273 | −1.56659 | ||||||||
\(628\) | 17.5444 | 0.700099 | ||||||||
\(629\) | −33.1556 | −1.32200 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.0838 | 1.75495 | 0.877475 | − | 0.479623i | \(-0.159227\pi\) | ||||
0.877475 | + | 0.479623i | \(0.159227\pi\) | |||||||
\(632\) | −14.1263 | −0.561915 | ||||||||
\(633\) | 4.55801 | 0.181165 | ||||||||
\(634\) | −3.75816 | −0.149256 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −7.99483 | −0.317016 | ||||||||
\(637\) | 19.7861 | 0.783952 | ||||||||
\(638\) | 4.48253 | 0.177465 | ||||||||
\(639\) | 3.98175 | 0.157515 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −41.9622 | −1.65741 | −0.828705 | − | 0.559686i | \(-0.810922\pi\) | ||||
−0.828705 | + | 0.559686i | \(0.810922\pi\) | |||||||
\(642\) | −2.34250 | −0.0924511 | ||||||||
\(643\) | 38.3467 | 1.51225 | 0.756124 | − | 0.654428i | \(-0.227091\pi\) | ||||
0.756124 | + | 0.654428i | \(0.227091\pi\) | |||||||
\(644\) | 19.4596 | 0.766817 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.03791 | 0.355592 | ||||||||
\(647\) | −20.6208 | −0.810687 | −0.405343 | − | 0.914164i | \(-0.632848\pi\) | ||||
−0.405343 | + | 0.914164i | \(0.632848\pi\) | |||||||
\(648\) | −0.935320 | −0.0367429 | ||||||||
\(649\) | 40.5471 | 1.59161 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.2298 | −0.440130 | ||||||||
\(652\) | 0.357234 | 0.0139904 | ||||||||
\(653\) | −2.96171 | −0.115901 | −0.0579504 | − | 0.998319i | \(-0.518457\pi\) | ||||
−0.0579504 | + | 0.998319i | \(0.518457\pi\) | |||||||
\(654\) | −4.51007 | −0.176358 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −9.53323 | −0.372210 | ||||||||
\(657\) | −12.2218 | −0.476818 | ||||||||
\(658\) | −0.390533 | −0.0152246 | ||||||||
\(659\) | −34.5759 | −1.34689 | −0.673444 | − | 0.739238i | \(-0.735186\pi\) | ||||
−0.673444 | + | 0.739238i | \(0.735186\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.31049 | 0.0898675 | 0.0449338 | − | 0.998990i | \(-0.485692\pi\) | ||||
0.0449338 | + | 0.998990i | \(0.485692\pi\) | |||||||
\(662\) | 7.41845 | 0.288326 | ||||||||
\(663\) | 26.1888 | 1.01709 | ||||||||
\(664\) | 13.6288 | 0.528899 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.38532 | 0.0536799 | ||||||||
\(667\) | −19.6666 | −0.761492 | ||||||||
\(668\) | 32.6351 | 1.26269 | ||||||||
\(669\) | −8.38549 | −0.324202 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −38.2473 | −1.47652 | ||||||||
\(672\) | 4.51191 | 0.174051 | ||||||||
\(673\) | 45.8261 | 1.76647 | 0.883233 | − | 0.468935i | \(-0.155362\pi\) | ||||
0.883233 | + | 0.468935i | \(0.155362\pi\) | |||||||
\(674\) | −4.31323 | −0.166140 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −16.1079 | −0.619535 | ||||||||
\(677\) | 6.48999 | 0.249431 | 0.124715 | − | 0.992193i | \(-0.460198\pi\) | ||||
0.124715 | + | 0.992193i | \(0.460198\pi\) | |||||||
\(678\) | 1.02232 | 0.0392621 | ||||||||
\(679\) | 14.1583 | 0.543346 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.27015 | 0.0486721 | ||||||||
\(682\) | −9.45028 | −0.361870 | ||||||||
\(683\) | −12.3351 | −0.471990 | −0.235995 | − | 0.971754i | \(-0.575835\pi\) | ||||
−0.235995 | + | 0.971754i | \(0.575835\pi\) | |||||||
\(684\) | 13.0497 | 0.498967 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4.40852 | −0.168318 | ||||||||
\(687\) | −5.99457 | −0.228707 | ||||||||
\(688\) | 3.29606 | 0.125661 | ||||||||
\(689\) | −18.9769 | −0.722963 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.5415 | 0.477100 | 0.238550 | − | 0.971130i | \(-0.423328\pi\) | ||||
0.238550 | + | 0.971130i | \(0.423328\pi\) | |||||||
\(692\) | −18.0017 | −0.684323 | ||||||||
\(693\) | 9.62138 | 0.365486 | ||||||||
\(694\) | 3.86575 | 0.146742 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.02554 | −0.114683 | ||||||||
\(697\) | 14.7620 | 0.559149 | ||||||||
\(698\) | 6.27740 | 0.237603 | ||||||||
\(699\) | 9.99821 | 0.378167 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.4761 | −1.15107 | −0.575534 | − | 0.817778i | \(-0.695206\pi\) | ||||
−0.575534 | + | 0.817778i | \(0.695206\pi\) | |||||||
\(702\) | −1.09423 | −0.0412990 | ||||||||
\(703\) | −39.2154 | −1.47904 | ||||||||
\(704\) | −39.0396 | −1.47136 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.28667 | −0.274238 | ||||||||
\(707\) | 12.0454 | 0.453015 | ||||||||
\(708\) | −13.4887 | −0.506937 | ||||||||
\(709\) | 35.8380 | 1.34593 | 0.672963 | − | 0.739676i | \(-0.265021\pi\) | ||||
0.672963 | + | 0.739676i | \(0.265021\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.1032 | 0.566414 | ||||||||
\(712\) | 6.58443 | 0.246762 | ||||||||
\(713\) | 41.4620 | 1.55276 | ||||||||
\(714\) | −2.21675 | −0.0829598 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.963997 | 0.0360263 | ||||||||
\(717\) | −7.43603 | −0.277704 | ||||||||
\(718\) | −5.85108 | −0.218360 | ||||||||
\(719\) | 33.7554 | 1.25886 | 0.629432 | − | 0.777056i | \(-0.283288\pi\) | ||||
0.629432 | + | 0.777056i | \(0.283288\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.51324 | −0.0563562 | ||||||||
\(722\) | 6.18362 | 0.230131 | ||||||||
\(723\) | −0.976110 | −0.0363019 | ||||||||
\(724\) | 21.1112 | 0.784592 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.48793 | 0.203676 | ||||||||
\(727\) | 37.1839 | 1.37907 | 0.689537 | − | 0.724250i | \(-0.257814\pi\) | ||||
0.689537 | + | 0.724250i | \(0.257814\pi\) | |||||||
\(728\) | 7.10600 | 0.263366 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.10386 | −0.188773 | ||||||||
\(732\) | 12.7237 | 0.470280 | ||||||||
\(733\) | 24.2578 | 0.895982 | 0.447991 | − | 0.894038i | \(-0.352140\pi\) | ||||
0.447991 | + | 0.894038i | \(0.352140\pi\) | |||||||
\(734\) | −0.230786 | −0.00851846 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −16.6586 | −0.614044 | ||||||||
\(737\) | −53.5750 | −1.97346 | ||||||||
\(738\) | −0.616789 | −0.0227043 | ||||||||
\(739\) | −20.9387 | −0.770241 | −0.385120 | − | 0.922866i | \(-0.625840\pi\) | ||||
−0.385120 | + | 0.922866i | \(0.625840\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 30.9753 | 1.13791 | ||||||||
\(742\) | 1.60630 | 0.0589691 | ||||||||
\(743\) | −6.39891 | −0.234753 | −0.117377 | − | 0.993087i | \(-0.537448\pi\) | ||||
−0.117377 | + | 0.993087i | \(0.537448\pi\) | |||||||
\(744\) | 6.37859 | 0.233850 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.04430 | 0.0748470 | ||||||||
\(747\) | −14.5712 | −0.533133 | ||||||||
\(748\) | 64.4658 | 2.35710 | ||||||||
\(749\) | −16.2643 | −0.594286 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.7017 | −0.937868 | −0.468934 | − | 0.883233i | \(-0.655362\pi\) | ||||
−0.468934 | + | 0.883233i | \(0.655362\pi\) | |||||||
\(752\) | −3.66568 | −0.133674 | ||||||||
\(753\) | 22.5387 | 0.821355 | ||||||||
\(754\) | −3.53957 | −0.128903 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.20073 | −0.116409 | ||||||||
\(757\) | 37.9646 | 1.37985 | 0.689923 | − | 0.723882i | \(-0.257644\pi\) | ||||
0.689923 | + | 0.723882i | \(0.257644\pi\) | |||||||
\(758\) | 1.29242 | 0.0469427 | ||||||||
\(759\) | −35.5235 | −1.28942 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.6250 | −0.928906 | −0.464453 | − | 0.885598i | \(-0.653749\pi\) | ||||
−0.464453 | + | 0.885598i | \(0.653749\pi\) | |||||||
\(762\) | 0.368851 | 0.0133621 | ||||||||
\(763\) | −31.3141 | −1.13365 | ||||||||
\(764\) | 15.1383 | 0.547686 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.53045 | −0.0552976 | ||||||||
\(767\) | −32.0175 | −1.15608 | ||||||||
\(768\) | 11.6876 | 0.421739 | ||||||||
\(769\) | 13.0484 | 0.470538 | 0.235269 | − | 0.971930i | \(-0.424403\pi\) | ||||
0.235269 | + | 0.971930i | \(0.424403\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.60490 | −0.273884 | ||||||||
\(772\) | −19.2739 | −0.693684 | ||||||||
\(773\) | 6.21192 | 0.223427 | 0.111714 | − | 0.993740i | \(-0.464366\pi\) | ||||
0.111714 | + | 0.993740i | \(0.464366\pi\) | |||||||
\(774\) | 0.213251 | 0.00766515 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.04201 | −0.288691 | ||||||||
\(777\) | 9.61846 | 0.345060 | ||||||||
\(778\) | 5.35226 | 0.191888 | ||||||||
\(779\) | 17.4600 | 0.625569 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 23.2650 | 0.832488 | ||||||||
\(782\) | 8.18456 | 0.292679 | ||||||||
\(783\) | 3.23476 | 0.115601 | ||||||||
\(784\) | −15.7201 | −0.561434 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.68536 | 0.131452 | ||||||||
\(787\) | −42.2577 | −1.50633 | −0.753163 | − | 0.657834i | \(-0.771473\pi\) | ||||
−0.753163 | + | 0.657834i | \(0.771473\pi\) | |||||||
\(788\) | 45.6533 | 1.62633 | ||||||||
\(789\) | 20.4512 | 0.728083 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.09815 | 0.252381 | ||||||||
\(792\) | −5.46500 | −0.194190 | ||||||||
\(793\) | 30.2015 | 1.07249 | ||||||||
\(794\) | −0.134274 | −0.00476520 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −27.3498 | −0.969386 | ||||||||
\(797\) | −17.4501 | −0.618113 | −0.309056 | − | 0.951044i | \(-0.600013\pi\) | ||||
−0.309056 | + | 0.951044i | \(0.600013\pi\) | |||||||
\(798\) | −2.62190 | −0.0928144 | ||||||||
\(799\) | 5.67621 | 0.200810 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.03976 | −0.248738 | ||||||||
\(802\) | −5.58775 | −0.197310 | ||||||||
\(803\) | −71.4110 | −2.52004 | ||||||||
\(804\) | 17.8227 | 0.628557 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.46229 | 0.262848 | ||||||||
\(807\) | −4.79575 | −0.168818 | ||||||||
\(808\) | −6.84187 | −0.240696 | ||||||||
\(809\) | 7.23858 | 0.254495 | 0.127247 | − | 0.991871i | \(-0.459386\pi\) | ||||
0.127247 | + | 0.991871i | \(0.459386\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −53.0051 | −1.86126 | −0.930630 | − | 0.365960i | \(-0.880741\pi\) | ||||
−0.930630 | + | 0.365960i | \(0.880741\pi\) | |||||||
\(812\) | −10.3536 | −0.363340 | ||||||||
\(813\) | −10.8394 | −0.380153 | ||||||||
\(814\) | 8.09429 | 0.283705 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −20.8072 | −0.728397 | ||||||||
\(817\) | −6.03669 | −0.211197 | ||||||||
\(818\) | 8.97143 | 0.313679 | ||||||||
\(819\) | −7.59740 | −0.265475 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.7613 | −1.00378 | −0.501889 | − | 0.864932i | \(-0.667361\pi\) | ||||
−0.501889 | + | 0.864932i | \(0.667361\pi\) | |||||||
\(822\) | −2.96018 | −0.103248 | ||||||||
\(823\) | 1.52418 | 0.0531296 | 0.0265648 | − | 0.999647i | \(-0.491543\pi\) | ||||
0.0265648 | + | 0.999647i | \(0.491543\pi\) | |||||||
\(824\) | 0.859532 | 0.0299432 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.71012 | 0.0942970 | ||||||||
\(827\) | −38.7593 | −1.34779 | −0.673897 | − | 0.738825i | \(-0.735381\pi\) | ||||
−0.673897 | + | 0.738825i | \(0.735381\pi\) | |||||||
\(828\) | 11.8175 | 0.410688 | ||||||||
\(829\) | 30.8699 | 1.07216 | 0.536079 | − | 0.844168i | \(-0.319905\pi\) | ||||
0.536079 | + | 0.844168i | \(0.319905\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 28.9500 | 1.00426 | ||||||||
\(832\) | 30.8271 | 1.06874 | ||||||||
\(833\) | 24.3422 | 0.843409 | ||||||||
\(834\) | 1.10854 | 0.0383856 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 76.2482 | 2.63710 | ||||||||
\(837\) | −6.81968 | −0.235723 | ||||||||
\(838\) | 2.65290 | 0.0916428 | ||||||||
\(839\) | −36.9782 | −1.27663 | −0.638314 | − | 0.769776i | \(-0.720368\pi\) | ||||
−0.638314 | + | 0.769776i | \(0.720368\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.5363 | −0.639183 | ||||||||
\(842\) | 9.26350 | 0.319241 | ||||||||
\(843\) | −24.7906 | −0.853833 | ||||||||
\(844\) | −8.85965 | −0.304962 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.237165 | −0.00815390 | ||||||||
\(847\) | 38.1036 | 1.30925 | ||||||||
\(848\) | 15.0773 | 0.517756 | ||||||||
\(849\) | −8.99344 | −0.308654 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −35.5127 | −1.21736 | ||||||||
\(852\) | −7.73953 | −0.265152 | ||||||||
\(853\) | −2.71422 | −0.0929333 | −0.0464666 | − | 0.998920i | \(-0.514796\pi\) | ||||
−0.0464666 | + | 0.998920i | \(0.514796\pi\) | |||||||
\(854\) | −2.55640 | −0.0874783 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.23824 | 0.315756 | ||||||||
\(857\) | −35.9293 | −1.22732 | −0.613660 | − | 0.789570i | \(-0.710304\pi\) | ||||
−0.613660 | + | 0.789570i | \(0.710304\pi\) | |||||||
\(858\) | −6.39349 | −0.218270 | ||||||||
\(859\) | −11.5320 | −0.393465 | −0.196733 | − | 0.980457i | \(-0.563033\pi\) | ||||
−0.196733 | + | 0.980457i | \(0.563033\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.28246 | −0.145946 | ||||||||
\(862\) | 7.74139 | 0.263673 | ||||||||
\(863\) | 29.5087 | 1.00449 | 0.502244 | − | 0.864726i | \(-0.332508\pi\) | ||||
0.502244 | + | 0.864726i | \(0.332508\pi\) | |||||||
\(864\) | 2.74001 | 0.0932171 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5.85350 | −0.198910 | ||||||||
\(867\) | 15.2194 | 0.516877 | ||||||||
\(868\) | 21.8279 | 0.740888 | ||||||||
\(869\) | 88.2468 | 2.99357 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 42.3048 | 1.43344 | ||||||||
\(872\) | 17.7866 | 0.602330 | ||||||||
\(873\) | 8.59813 | 0.291003 | ||||||||
\(874\) | 9.68045 | 0.327446 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 23.7561 | 0.802646 | ||||||||
\(877\) | 10.2327 | 0.345535 | 0.172767 | − | 0.984963i | \(-0.444729\pi\) | ||||
0.172767 | + | 0.984963i | \(0.444729\pi\) | |||||||
\(878\) | 7.13935 | 0.240941 | ||||||||
\(879\) | 0.665090 | 0.0224329 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.3238 | 0.415198 | 0.207599 | − | 0.978214i | \(-0.433435\pi\) | ||||
0.207599 | + | 0.978214i | \(0.433435\pi\) | |||||||
\(882\) | −1.01707 | −0.0342467 | ||||||||
\(883\) | 38.2214 | 1.28625 | 0.643127 | − | 0.765760i | \(-0.277637\pi\) | ||||
0.643127 | + | 0.765760i | \(0.277637\pi\) | |||||||
\(884\) | −50.9046 | −1.71211 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.04928 | 0.304016 | ||||||||
\(887\) | −1.00570 | −0.0337683 | −0.0168841 | − | 0.999857i | \(-0.505375\pi\) | ||||
−0.0168841 | + | 0.999857i | \(0.505375\pi\) | |||||||
\(888\) | −5.46334 | −0.183338 | ||||||||
\(889\) | 2.56099 | 0.0858928 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.84292 | 0.195745 | ||||||||
\(892\) | 16.2993 | 0.545741 | ||||||||
\(893\) | 6.71365 | 0.224664 | ||||||||
\(894\) | −4.75606 | −0.159066 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −11.6332 | −0.388637 | ||||||||
\(897\) | 28.0507 | 0.936586 | ||||||||
\(898\) | 0.139644 | 0.00465997 | ||||||||
\(899\) | −22.0600 | −0.735743 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23.3468 | −0.777794 | ||||||||
\(902\) | −3.60385 | −0.119995 | ||||||||
\(903\) | 1.48064 | 0.0492725 | ||||||||
\(904\) | −4.03179 | −0.134095 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.11512 | −0.136716 | ||||||||
\(907\) | 23.2637 | 0.772457 | 0.386229 | − | 0.922403i | \(-0.373778\pi\) | ||||
0.386229 | + | 0.922403i | \(0.373778\pi\) | |||||||
\(908\) | −2.46885 | −0.0819316 | ||||||||
\(909\) | 7.31500 | 0.242623 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.3133 | −1.56756 | −0.783779 | − | 0.621039i | \(-0.786711\pi\) | ||||
−0.783779 | + | 0.621039i | \(0.786711\pi\) | |||||||
\(912\) | −24.6101 | −0.814921 | ||||||||
\(913\) | −85.1385 | −2.81767 | ||||||||
\(914\) | −8.74961 | −0.289411 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 11.6520 | 0.384992 | ||||||||
\(917\) | 25.5880 | 0.844990 | ||||||||
\(918\) | −1.34620 | −0.0444312 | ||||||||
\(919\) | −5.25122 | −0.173222 | −0.0866108 | − | 0.996242i | \(-0.527604\pi\) | ||||
−0.0866108 | + | 0.996242i | \(0.527604\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.814634 | 0.0268431 | ||||||||
\(922\) | 0.861931 | 0.0283862 | ||||||||
\(923\) | −18.3709 | −0.604686 | ||||||||
\(924\) | −18.7016 | −0.615237 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −0.394166 | −0.0129531 | ||||||||
\(927\) | −0.918971 | −0.0301830 | ||||||||
\(928\) | 8.86328 | 0.290952 | ||||||||
\(929\) | 7.19607 | 0.236095 | 0.118048 | − | 0.993008i | \(-0.462336\pi\) | ||||
0.118048 | + | 0.993008i | \(0.462336\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 28.7913 | 0.943595 | ||||||||
\(932\) | −19.4341 | −0.636584 | ||||||||
\(933\) | 4.78222 | 0.156563 | ||||||||
\(934\) | −6.57659 | −0.215193 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.31537 | 0.141052 | ||||||||
\(937\) | −6.75704 | −0.220743 | −0.110371 | − | 0.993890i | \(-0.535204\pi\) | ||||
−0.110371 | + | 0.993890i | \(0.535204\pi\) | |||||||
\(938\) | −3.58088 | −0.116920 | ||||||||
\(939\) | 6.26198 | 0.204352 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.8864 | 0.648278 | 0.324139 | − | 0.946010i | \(-0.394925\pi\) | ||||
0.324139 | + | 0.946010i | \(0.394925\pi\) | |||||||
\(942\) | −2.14067 | −0.0697467 | ||||||||
\(943\) | 15.8115 | 0.514892 | ||||||||
\(944\) | 25.4381 | 0.827939 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.24601 | 0.0405113 | ||||||||
\(947\) | −57.2087 | −1.85903 | −0.929516 | − | 0.368782i | \(-0.879775\pi\) | ||||
−0.929516 | + | 0.368782i | \(0.879775\pi\) | |||||||
\(948\) | −29.3569 | −0.953467 | ||||||||
\(949\) | 56.3887 | 1.83046 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.8462 | −0.513848 | ||||||||
\(952\) | 8.74232 | 0.283340 | ||||||||
\(953\) | 11.8906 | 0.385174 | 0.192587 | − | 0.981280i | \(-0.438312\pi\) | ||||
0.192587 | + | 0.981280i | \(0.438312\pi\) | |||||||
\(954\) | 0.975482 | 0.0315824 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 14.4538 | 0.467469 | ||||||||
\(957\) | 18.9005 | 0.610965 | ||||||||
\(958\) | 7.56353 | 0.244367 | ||||||||
\(959\) | −20.5530 | −0.663690 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.5080 | 0.500259 | ||||||||
\(962\) | −6.39155 | −0.206072 | ||||||||
\(963\) | −9.87708 | −0.318284 | ||||||||
\(964\) | 1.89732 | 0.0611085 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.37435 | −0.0763934 | ||||||||
\(967\) | 16.0866 | 0.517311 | 0.258656 | − | 0.965970i | \(-0.416721\pi\) | ||||
0.258656 | + | 0.965970i | \(0.416721\pi\) | |||||||
\(968\) | −21.6430 | −0.695634 | ||||||||
\(969\) | 38.1081 | 1.22421 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.8713 | 0.605608 | 0.302804 | − | 0.953053i | \(-0.402077\pi\) | ||||
0.302804 | + | 0.953053i | \(0.402077\pi\) | |||||||
\(972\) | −1.94375 | −0.0623459 | ||||||||
\(973\) | 7.69676 | 0.246747 | ||||||||
\(974\) | 1.73460 | 0.0555801 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −23.9953 | −0.768069 | ||||||||
\(977\) | 20.3542 | 0.651190 | 0.325595 | − | 0.945509i | \(-0.394435\pi\) | ||||
0.325595 | + | 0.945509i | \(0.394435\pi\) | |||||||
\(978\) | −0.0435875 | −0.00139378 | ||||||||
\(979\) | −41.1327 | −1.31461 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19.0166 | −0.607153 | ||||||||
\(982\) | 1.39727 | 0.0445888 | ||||||||
\(983\) | 19.6706 | 0.627396 | 0.313698 | − | 0.949523i | \(-0.398432\pi\) | ||||
0.313698 | + | 0.949523i | \(0.398432\pi\) | |||||||
\(984\) | 2.43246 | 0.0775441 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.35463 | −0.138680 | ||||||||
\(987\) | −1.64667 | −0.0524142 | ||||||||
\(988\) | −60.2084 | −1.91548 | ||||||||
\(989\) | −5.46672 | −0.173832 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.493118 | 0.0156644 | 0.00783221 | − | 0.999969i | \(-0.497507\pi\) | ||||
0.00783221 | + | 0.999969i | \(0.497507\pi\) | |||||||
\(992\) | −18.6860 | −0.593281 | ||||||||
\(993\) | 31.2797 | 0.992630 | ||||||||
\(994\) | 1.55500 | 0.0493218 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 28.3229 | 0.897444 | ||||||||
\(997\) | 23.3345 | 0.739010 | 0.369505 | − | 0.929229i | \(-0.379527\pi\) | ||||
0.369505 | + | 0.929229i | \(0.379527\pi\) | |||||||
\(998\) | −5.65744 | −0.179083 | ||||||||
\(999\) | 5.84115 | 0.184806 |
(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 | 3525.2.a.bd.1.5 | ✓ | 8 | |
5.4 | even | 2 | 3525.2.a.be.1.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3525.2.a.bd.1.5 | ✓ | 8 | 1.1 | even | 1 | trivial | |
3525.2.a.be.1.4 | yes | 8 | 5.4 | even | 2 |