Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, 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("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(47.9341963334\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.473233 | −0.334626 | −0.167313 | − | 0.985904i | \(-0.553509\pi\) | ||||
−0.167313 | + | 0.985904i | \(0.553509\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.77605 | −0.888025 | ||||||||
\(5\) | 1.04483 | 0.467260 | 0.233630 | − | 0.972326i | \(-0.424940\pi\) | ||||
0.233630 | + | 0.972326i | \(0.424940\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.83278 | 1.44866 | 0.724328 | − | 0.689456i | \(-0.242150\pi\) | ||||
0.724328 | + | 0.689456i | \(0.242150\pi\) | |||||||
\(8\) | 1.78695 | 0.631783 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.494446 | −0.156357 | ||||||||
\(11\) | −2.56396 | −0.773063 | −0.386531 | − | 0.922276i | \(-0.626327\pi\) | ||||
−0.386531 | + | 0.922276i | \(0.626327\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.32837 | 0.645774 | 0.322887 | − | 0.946437i | \(-0.395347\pi\) | ||||
0.322887 | + | 0.946437i | \(0.395347\pi\) | |||||||
\(14\) | −1.81380 | −0.484758 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.70646 | 0.676614 | ||||||||
\(17\) | −6.35999 | −1.54253 | −0.771263 | − | 0.636517i | \(-0.780374\pi\) | ||||
−0.771263 | + | 0.636517i | \(0.780374\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.47559 | 1.71502 | 0.857509 | − | 0.514469i | \(-0.172011\pi\) | ||||
0.857509 | + | 0.514469i | \(0.172011\pi\) | |||||||
\(20\) | −1.85566 | −0.414939 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.21335 | 0.258687 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.90834 | −0.781668 | ||||||||
\(26\) | −1.10186 | −0.216093 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −6.80721 | −1.28644 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.99906 | 1.61628 | 0.808139 | − | 0.588991i | \(-0.200475\pi\) | ||||
0.808139 | + | 0.588991i | \(0.200475\pi\) | |||||||
\(32\) | −4.85469 | −0.858196 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.00976 | 0.516169 | ||||||||
\(35\) | 4.00459 | 0.676899 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.17971 | −0.851539 | −0.425769 | − | 0.904832i | \(-0.639996\pi\) | ||||
−0.425769 | + | 0.904832i | \(0.639996\pi\) | |||||||
\(38\) | −3.53770 | −0.573890 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.86705 | 0.295207 | ||||||||
\(41\) | −0.118500 | −0.0185066 | −0.00925330 | − | 0.999957i | \(-0.502945\pi\) | ||||
−0.00925330 | + | 0.999957i | \(0.502945\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.97677 | −0.453953 | −0.226976 | − | 0.973900i | \(-0.572884\pi\) | ||||
−0.226976 | + | 0.973900i | \(0.572884\pi\) | |||||||
\(44\) | 4.55372 | 0.686499 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.473233 | −0.0697744 | ||||||||
\(47\) | 10.7617 | 1.56975 | 0.784875 | − | 0.619654i | \(-0.212727\pi\) | ||||
0.784875 | + | 0.619654i | \(0.212727\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.69021 | 1.09860 | ||||||||
\(50\) | 1.84956 | 0.261567 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.13531 | −0.573464 | ||||||||
\(53\) | 5.29192 | 0.726901 | 0.363451 | − | 0.931613i | \(-0.381599\pi\) | ||||
0.363451 | + | 0.931613i | \(0.381599\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.67889 | −0.361221 | ||||||||
\(56\) | 6.84899 | 0.915235 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.473233 | 0.0621385 | ||||||||
\(59\) | 9.96740 | 1.29764 | 0.648822 | − | 0.760940i | \(-0.275262\pi\) | ||||
0.648822 | + | 0.760940i | \(0.275262\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.51664 | 0.450260 | 0.225130 | − | 0.974329i | \(-0.427719\pi\) | ||||
0.225130 | + | 0.974329i | \(0.427719\pi\) | |||||||
\(62\) | −4.25865 | −0.540849 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.11551 | −0.389439 | ||||||||
\(65\) | 2.43274 | 0.301745 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.1207 | 1.72512 | 0.862561 | − | 0.505952i | \(-0.168859\pi\) | ||||
0.862561 | + | 0.505952i | \(0.168859\pi\) | |||||||
\(68\) | 11.2957 | 1.36980 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.89510 | −0.226508 | ||||||||
\(71\) | −10.5253 | −1.24912 | −0.624560 | − | 0.780977i | \(-0.714722\pi\) | ||||
−0.624560 | + | 0.780977i | \(0.714722\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.05985 | −0.358129 | −0.179064 | − | 0.983837i | \(-0.557307\pi\) | ||||
−0.179064 | + | 0.983837i | \(0.557307\pi\) | |||||||
\(74\) | 2.45121 | 0.284947 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −13.2770 | −1.52298 | ||||||||
\(77\) | −9.82709 | −1.11990 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.286819 | −0.0322696 | −0.0161348 | − | 0.999870i | \(-0.505136\pi\) | ||||
−0.0161348 | + | 0.999870i | \(0.505136\pi\) | |||||||
\(80\) | 2.82777 | 0.316155 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.0560781 | 0.00619279 | ||||||||
\(83\) | −4.82285 | −0.529376 | −0.264688 | − | 0.964334i | \(-0.585269\pi\) | ||||
−0.264688 | + | 0.964334i | \(0.585269\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.64508 | −0.720760 | ||||||||
\(86\) | 1.40870 | 0.151904 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.58167 | −0.488408 | ||||||||
\(89\) | 1.13200 | 0.119992 | 0.0599961 | − | 0.998199i | \(-0.480891\pi\) | ||||
0.0599961 | + | 0.998199i | \(0.480891\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.92414 | 0.935504 | ||||||||
\(92\) | −1.77605 | −0.185166 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.09277 | −0.525279 | ||||||||
\(95\) | 7.81069 | 0.801360 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.76909 | −0.281158 | −0.140579 | − | 0.990069i | \(-0.544896\pi\) | ||||
−0.140579 | + | 0.990069i | \(0.544896\pi\) | |||||||
\(98\) | −3.63926 | −0.367621 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.94141 | 0.694141 | ||||||||
\(101\) | 7.62918 | 0.759132 | 0.379566 | − | 0.925165i | \(-0.376073\pi\) | ||||
0.379566 | + | 0.925165i | \(0.376073\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.31505 | −0.129575 | −0.0647877 | − | 0.997899i | \(-0.520637\pi\) | ||||
−0.0647877 | + | 0.997899i | \(0.520637\pi\) | |||||||
\(104\) | 4.16069 | 0.407989 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.50431 | −0.243240 | ||||||||
\(107\) | 3.09134 | 0.298852 | 0.149426 | − | 0.988773i | \(-0.452258\pi\) | ||||
0.149426 | + | 0.988773i | \(0.452258\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.6005 | −1.01534 | −0.507672 | − | 0.861551i | \(-0.669494\pi\) | ||||
−0.507672 | + | 0.861551i | \(0.669494\pi\) | |||||||
\(110\) | 1.26774 | 0.120874 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.3733 | 0.980181 | ||||||||
\(113\) | −2.36263 | −0.222257 | −0.111129 | − | 0.993806i | \(-0.535447\pi\) | ||||
−0.111129 | + | 0.993806i | \(0.535447\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.04483 | 0.0974304 | ||||||||
\(116\) | 1.77605 | 0.164902 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.71690 | −0.434226 | ||||||||
\(119\) | −24.3765 | −2.23459 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.42611 | −0.402374 | ||||||||
\(122\) | −1.66419 | −0.150669 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −15.9828 | −1.43530 | ||||||||
\(125\) | −9.30766 | −0.832502 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.1438 | 1.25506 | 0.627528 | − | 0.778594i | \(-0.284067\pi\) | ||||
0.627528 | + | 0.778594i | \(0.284067\pi\) | |||||||
\(128\) | 11.1837 | 0.988512 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.15125 | −0.100972 | ||||||||
\(131\) | −17.7401 | −1.54996 | −0.774979 | − | 0.631986i | \(-0.782240\pi\) | ||||
−0.774979 | + | 0.631986i | \(0.782240\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 28.6523 | 2.48447 | ||||||||
\(134\) | −6.68240 | −0.577271 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −11.3650 | −0.974541 | ||||||||
\(137\) | −8.12457 | −0.694129 | −0.347064 | − | 0.937841i | \(-0.612821\pi\) | ||||
−0.347064 | + | 0.937841i | \(0.612821\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.00074 | 0.254519 | 0.127260 | − | 0.991869i | \(-0.459382\pi\) | ||||
0.127260 | + | 0.991869i | \(0.459382\pi\) | |||||||
\(140\) | −7.11235 | −0.601103 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.98091 | 0.417989 | ||||||||
\(143\) | −5.96985 | −0.499224 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.04483 | −0.0867680 | ||||||||
\(146\) | 1.44802 | 0.119839 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.19942 | 0.756188 | ||||||||
\(149\) | −15.2424 | −1.24870 | −0.624352 | − | 0.781143i | \(-0.714637\pi\) | ||||
−0.624352 | + | 0.781143i | \(0.714637\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.08563 | 0.576620 | 0.288310 | − | 0.957537i | \(-0.406907\pi\) | ||||
0.288310 | + | 0.957537i | \(0.406907\pi\) | |||||||
\(152\) | 13.3585 | 1.08352 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.65051 | 0.374748 | ||||||||
\(155\) | 9.40244 | 0.755222 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.33644 | −0.106659 | −0.0533297 | − | 0.998577i | \(-0.516983\pi\) | ||||
−0.0533297 | + | 0.998577i | \(0.516983\pi\) | |||||||
\(158\) | 0.135732 | 0.0107983 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.07230 | −0.401001 | ||||||||
\(161\) | 3.83278 | 0.302065 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.55986 | 0.748786 | 0.374393 | − | 0.927270i | \(-0.377851\pi\) | ||||
0.374393 | + | 0.927270i | \(0.377851\pi\) | |||||||
\(164\) | 0.210462 | 0.0164343 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.28233 | 0.177143 | ||||||||
\(167\) | 12.1300 | 0.938648 | 0.469324 | − | 0.883026i | \(-0.344498\pi\) | ||||
0.469324 | + | 0.883026i | \(0.344498\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.57868 | −0.582975 | ||||||||
\(170\) | 3.14467 | 0.241185 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.28689 | 0.403121 | ||||||||
\(173\) | 23.8506 | 1.81333 | 0.906664 | − | 0.421853i | \(-0.138620\pi\) | ||||
0.906664 | + | 0.421853i | \(0.138620\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.9798 | −1.13237 | ||||||||
\(176\) | −6.93924 | −0.523065 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.535702 | −0.0401525 | ||||||||
\(179\) | 20.3159 | 1.51848 | 0.759240 | − | 0.650811i | \(-0.225571\pi\) | ||||
0.759240 | + | 0.650811i | \(0.225571\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.6061 | 1.15999 | 0.579997 | − | 0.814619i | \(-0.303054\pi\) | ||||
0.579997 | + | 0.814619i | \(0.303054\pi\) | |||||||
\(182\) | −4.22320 | −0.313044 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.78695 | 0.131736 | ||||||||
\(185\) | −5.41189 | −0.397890 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.3068 | 1.19247 | ||||||||
\(188\) | −19.1133 | −1.39398 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.69627 | −0.268156 | ||||||||
\(191\) | 19.5710 | 1.41611 | 0.708055 | − | 0.706157i | \(-0.249573\pi\) | ||||
0.708055 | + | 0.706157i | \(0.249573\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.09645 | 0.366850 | 0.183425 | − | 0.983034i | \(-0.441282\pi\) | ||||
0.183425 | + | 0.983034i | \(0.441282\pi\) | |||||||
\(194\) | 1.31042 | 0.0940829 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −13.6582 | −0.975586 | ||||||||
\(197\) | −23.2485 | −1.65639 | −0.828195 | − | 0.560440i | \(-0.810632\pi\) | ||||
−0.828195 | + | 0.560440i | \(0.810632\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.2684 | 1.72034 | 0.860170 | − | 0.510007i | \(-0.170357\pi\) | ||||
0.860170 | + | 0.510007i | \(0.170357\pi\) | |||||||
\(200\) | −6.98402 | −0.493844 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.61038 | −0.254025 | ||||||||
\(203\) | −3.83278 | −0.269009 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.123812 | −0.00864739 | ||||||||
\(206\) | 0.622324 | 0.0433594 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.30164 | 0.436940 | ||||||||
\(209\) | −19.1671 | −1.32582 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.0565 | −0.898847 | −0.449423 | − | 0.893319i | \(-0.648371\pi\) | ||||
−0.449423 | + | 0.893319i | \(0.648371\pi\) | |||||||
\(212\) | −9.39872 | −0.645507 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.46293 | −0.100004 | ||||||||
\(215\) | −3.11020 | −0.212114 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 34.4914 | 2.34143 | ||||||||
\(218\) | 5.01651 | 0.339761 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.75784 | 0.320774 | ||||||||
\(221\) | −14.8084 | −0.996123 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.0983 | 1.41285 | 0.706424 | − | 0.707789i | \(-0.250307\pi\) | ||||
0.706424 | + | 0.707789i | \(0.250307\pi\) | |||||||
\(224\) | −18.6070 | −1.24323 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.11807 | 0.0743731 | ||||||||
\(227\) | −28.6355 | −1.90060 | −0.950301 | − | 0.311333i | \(-0.899225\pi\) | ||||
−0.950301 | + | 0.311333i | \(0.899225\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.5257 | −1.75287 | −0.876433 | − | 0.481524i | \(-0.840084\pi\) | ||||
−0.876433 | + | 0.481524i | \(0.840084\pi\) | |||||||
\(230\) | −0.494446 | −0.0326028 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.78695 | −0.117319 | ||||||||
\(233\) | 2.34122 | 0.153378 | 0.0766892 | − | 0.997055i | \(-0.475565\pi\) | ||||
0.0766892 | + | 0.997055i | \(0.475565\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.2441 | 0.733481 | ||||||||
\(236\) | −17.7026 | −1.15234 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 11.5357 | 0.747751 | ||||||||
\(239\) | −3.07650 | −0.199002 | −0.0995011 | − | 0.995037i | \(-0.531725\pi\) | ||||
−0.0995011 | + | 0.995037i | \(0.531725\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.8645 | −1.27958 | −0.639791 | − | 0.768549i | \(-0.720979\pi\) | ||||
−0.639791 | + | 0.768549i | \(0.720979\pi\) | |||||||
\(242\) | 2.09458 | 0.134645 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.24573 | −0.399842 | ||||||||
\(245\) | 8.03493 | 0.513333 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.4060 | 1.10751 | ||||||||
\(248\) | 16.0809 | 1.02114 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.40469 | 0.278577 | ||||||||
\(251\) | 12.3435 | 0.779116 | 0.389558 | − | 0.921002i | \(-0.372628\pi\) | ||||
0.389558 | + | 0.921002i | \(0.372628\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.56396 | −0.161195 | ||||||||
\(254\) | −6.69329 | −0.419975 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.938515 | 0.0586572 | ||||||||
\(257\) | −0.764367 | −0.0476799 | −0.0238399 | − | 0.999716i | \(-0.507589\pi\) | ||||
−0.0238399 | + | 0.999716i | \(0.507589\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.8527 | −1.23359 | ||||||||
\(260\) | −4.32067 | −0.267957 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.39520 | 0.518657 | ||||||||
\(263\) | 12.4337 | 0.766693 | 0.383346 | − | 0.923605i | \(-0.374772\pi\) | ||||
0.383346 | + | 0.923605i | \(0.374772\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.52913 | 0.339652 | ||||||||
\(266\) | −13.5592 | −0.831369 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −25.0791 | −1.53195 | ||||||||
\(269\) | −17.2895 | −1.05416 | −0.527080 | − | 0.849816i | \(-0.676713\pi\) | ||||
−0.527080 | + | 0.849816i | \(0.676713\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.2849 | 0.746254 | 0.373127 | − | 0.927780i | \(-0.378286\pi\) | ||||
0.373127 | + | 0.927780i | \(0.378286\pi\) | |||||||
\(272\) | −17.2130 | −1.04369 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.84481 | 0.232274 | ||||||||
\(275\) | 10.0208 | 0.604279 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.0877 | 1.44729 | 0.723645 | − | 0.690172i | \(-0.242465\pi\) | ||||
0.723645 | + | 0.690172i | \(0.242465\pi\) | |||||||
\(278\) | −1.42005 | −0.0851688 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7.15600 | 0.427653 | ||||||||
\(281\) | 25.8168 | 1.54010 | 0.770050 | − | 0.637983i | \(-0.220231\pi\) | ||||
0.770050 | + | 0.637983i | \(0.220231\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.67500 | −0.0995687 | −0.0497843 | − | 0.998760i | \(-0.515853\pi\) | ||||
−0.0497843 | + | 0.998760i | \(0.515853\pi\) | |||||||
\(284\) | 18.6934 | 1.10925 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.82513 | 0.167053 | ||||||||
\(287\) | −0.454185 | −0.0268097 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 23.4495 | 1.37938 | ||||||||
\(290\) | 0.494446 | 0.0290349 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.43445 | 0.318027 | ||||||||
\(293\) | 3.20666 | 0.187335 | 0.0936674 | − | 0.995604i | \(-0.470141\pi\) | ||||
0.0936674 | + | 0.995604i | \(0.470141\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.4142 | 0.606337 | ||||||||
\(296\) | −9.25589 | −0.537987 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.21319 | 0.417849 | ||||||||
\(299\) | 2.32837 | 0.134653 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.4093 | −0.657621 | ||||||||
\(302\) | −3.35315 | −0.192952 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 20.2324 | 1.16041 | ||||||||
\(305\) | 3.67427 | 0.210388 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.2790 | −0.586655 | −0.293328 | − | 0.956012i | \(-0.594763\pi\) | ||||
−0.293328 | + | 0.956012i | \(0.594763\pi\) | |||||||
\(308\) | 17.4534 | 0.994501 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.44955 | −0.252717 | ||||||||
\(311\) | 8.33747 | 0.472775 | 0.236387 | − | 0.971659i | \(-0.424037\pi\) | ||||
0.236387 | + | 0.971659i | \(0.424037\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.141232 | −0.00798291 | −0.00399146 | − | 0.999992i | \(-0.501271\pi\) | ||||
−0.00399146 | + | 0.999992i | \(0.501271\pi\) | |||||||
\(314\) | 0.632447 | 0.0356911 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.509404 | 0.0286562 | ||||||||
\(317\) | 7.06189 | 0.396635 | 0.198318 | − | 0.980138i | \(-0.436452\pi\) | ||||
0.198318 | + | 0.980138i | \(0.436452\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.56396 | 0.143554 | ||||||||
\(320\) | −3.25517 | −0.181969 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.81380 | −0.101079 | ||||||||
\(323\) | −47.5447 | −2.64546 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.10007 | −0.504781 | ||||||||
\(326\) | −4.52404 | −0.250563 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.211754 | −0.0116922 | ||||||||
\(329\) | 41.2471 | 2.27403 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.4463 | 1.39866 | 0.699329 | − | 0.714800i | \(-0.253482\pi\) | ||||
0.699329 | + | 0.714800i | \(0.253482\pi\) | |||||||
\(332\) | 8.56562 | 0.470099 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.74032 | −0.314096 | ||||||||
\(335\) | 14.7537 | 0.806081 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.8723 | −0.864617 | −0.432308 | − | 0.901726i | \(-0.642301\pi\) | ||||
−0.432308 | + | 0.901726i | \(0.642301\pi\) | |||||||
\(338\) | 3.58648 | 0.195079 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 11.8020 | 0.640053 | ||||||||
\(341\) | −23.0732 | −1.24948 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.64543 | 0.142840 | ||||||||
\(344\) | −5.31934 | −0.286800 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.2869 | −0.606787 | ||||||||
\(347\) | 3.77366 | 0.202581 | 0.101290 | − | 0.994857i | \(-0.467703\pi\) | ||||
0.101290 | + | 0.994857i | \(0.467703\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.83978 | −0.473183 | −0.236591 | − | 0.971609i | \(-0.576030\pi\) | ||||
−0.236591 | + | 0.971609i | \(0.576030\pi\) | |||||||
\(350\) | 7.08894 | 0.378920 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 12.4472 | 0.663439 | ||||||||
\(353\) | 26.2225 | 1.39568 | 0.697840 | − | 0.716253i | \(-0.254144\pi\) | ||||
0.697840 | + | 0.716253i | \(0.254144\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.9971 | −0.583664 | ||||||||
\(356\) | −2.01050 | −0.106556 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.61414 | −0.508123 | ||||||||
\(359\) | 17.3443 | 0.915398 | 0.457699 | − | 0.889107i | \(-0.348674\pi\) | ||||
0.457699 | + | 0.889107i | \(0.348674\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 36.8845 | 1.94129 | ||||||||
\(362\) | −7.38533 | −0.388164 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −15.8497 | −0.830751 | ||||||||
\(365\) | −3.19701 | −0.167339 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.0965 | −0.527032 | −0.263516 | − | 0.964655i | \(-0.584882\pi\) | ||||
−0.263516 | + | 0.964655i | \(0.584882\pi\) | |||||||
\(368\) | 2.70646 | 0.141084 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.56108 | 0.133144 | ||||||||
\(371\) | 20.2828 | 1.05303 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.0445 | −0.675421 | −0.337710 | − | 0.941250i | \(-0.609652\pi\) | ||||
−0.337710 | + | 0.941250i | \(0.609652\pi\) | |||||||
\(374\) | −7.71690 | −0.399031 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 19.2306 | 0.991741 | ||||||||
\(377\) | −2.32837 | −0.119917 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.81802 | 0.401585 | 0.200792 | − | 0.979634i | \(-0.435648\pi\) | ||||
0.200792 | + | 0.979634i | \(0.435648\pi\) | |||||||
\(380\) | −13.8722 | −0.711628 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9.26166 | −0.473868 | ||||||||
\(383\) | 3.73452 | 0.190825 | 0.0954126 | − | 0.995438i | \(-0.469583\pi\) | ||||
0.0954126 | + | 0.995438i | \(0.469583\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.2676 | −0.523285 | ||||||||
\(386\) | −2.41181 | −0.122758 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.91804 | 0.249675 | ||||||||
\(389\) | 22.7578 | 1.15387 | 0.576933 | − | 0.816792i | \(-0.304249\pi\) | ||||
0.576933 | + | 0.816792i | \(0.304249\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.35999 | −0.321639 | ||||||||
\(392\) | 13.7420 | 0.694078 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11.0020 | 0.554272 | ||||||||
\(395\) | −0.299675 | −0.0150783 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.6267 | 0.734093 | 0.367046 | − | 0.930203i | \(-0.380369\pi\) | ||||
0.367046 | + | 0.930203i | \(0.380369\pi\) | |||||||
\(398\) | −11.4846 | −0.575671 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10.5778 | −0.528888 | ||||||||
\(401\) | −28.2873 | −1.41260 | −0.706301 | − | 0.707912i | \(-0.749637\pi\) | ||||
−0.706301 | + | 0.707912i | \(0.749637\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.9532 | 1.04375 | ||||||||
\(404\) | −13.5498 | −0.674128 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.81380 | 0.0900173 | ||||||||
\(407\) | 13.2806 | 0.658293 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.9885 | −0.790581 | −0.395291 | − | 0.918556i | \(-0.629356\pi\) | ||||
−0.395291 | + | 0.918556i | \(0.629356\pi\) | |||||||
\(410\) | 0.0585918 | 0.00289364 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.33559 | 0.115066 | ||||||||
\(413\) | 38.2028 | 1.87984 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.03903 | −0.247356 | ||||||||
\(416\) | −11.3035 | −0.554201 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 9.07051 | 0.443653 | ||||||||
\(419\) | 20.1167 | 0.982766 | 0.491383 | − | 0.870943i | \(-0.336491\pi\) | ||||
0.491383 | + | 0.870943i | \(0.336491\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.27858 | 0.305999 | 0.153000 | − | 0.988226i | \(-0.451107\pi\) | ||||
0.153000 | + | 0.988226i | \(0.451107\pi\) | |||||||
\(422\) | 6.17877 | 0.300778 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.45641 | 0.459244 | ||||||||
\(425\) | 24.8570 | 1.20574 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.4785 | 0.652271 | ||||||||
\(428\) | −5.49038 | −0.265388 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.47185 | 0.0709789 | ||||||||
\(431\) | −12.1897 | −0.587159 | −0.293579 | − | 0.955935i | \(-0.594847\pi\) | ||||
−0.293579 | + | 0.955935i | \(0.594847\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.3379 | 1.21766 | 0.608830 | − | 0.793301i | \(-0.291639\pi\) | ||||
0.608830 | + | 0.793301i | \(0.291639\pi\) | |||||||
\(434\) | −16.3225 | −0.783504 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.8270 | 0.901651 | ||||||||
\(437\) | 7.47559 | 0.357606 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.21937 | 0.153652 | 0.0768260 | − | 0.997045i | \(-0.475521\pi\) | ||||
0.0768260 | + | 0.997045i | \(0.475521\pi\) | |||||||
\(440\) | −4.78705 | −0.228213 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.00784 | 0.333329 | ||||||||
\(443\) | −20.6170 | −0.979541 | −0.489771 | − | 0.871851i | \(-0.662919\pi\) | ||||
−0.489771 | + | 0.871851i | \(0.662919\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.18275 | 0.0560675 | ||||||||
\(446\) | −9.98442 | −0.472776 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −11.9411 | −0.564163 | ||||||||
\(449\) | 32.3690 | 1.52759 | 0.763793 | − | 0.645461i | \(-0.223335\pi\) | ||||
0.763793 | + | 0.645461i | \(0.223335\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.303829 | 0.0143068 | ||||||||
\(452\) | 4.19614 | 0.197370 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.5512 | 0.635991 | ||||||||
\(455\) | 9.32417 | 0.437124 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.711685 | 0.0332912 | 0.0166456 | − | 0.999861i | \(-0.494701\pi\) | ||||
0.0166456 | + | 0.999861i | \(0.494701\pi\) | |||||||
\(458\) | 12.5528 | 0.586555 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.85566 | −0.0865207 | ||||||||
\(461\) | −13.5927 | −0.633076 | −0.316538 | − | 0.948580i | \(-0.602520\pi\) | ||||
−0.316538 | + | 0.948580i | \(0.602520\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.6700 | 1.84362 | 0.921811 | − | 0.387640i | \(-0.126710\pi\) | ||||
0.921811 | + | 0.387640i | \(0.126710\pi\) | |||||||
\(464\) | −2.70646 | −0.125644 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.10794 | −0.0513244 | ||||||||
\(467\) | −3.81127 | −0.176365 | −0.0881824 | − | 0.996104i | \(-0.528106\pi\) | ||||
−0.0881824 | + | 0.996104i | \(0.528106\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 54.1217 | 2.49911 | ||||||||
\(470\) | −5.32106 | −0.245442 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 17.8113 | 0.819829 | ||||||||
\(473\) | 7.63231 | 0.350934 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −29.2172 | −1.34058 | ||||||||
\(476\) | 43.2938 | 1.98437 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.45590 | 0.0665914 | ||||||||
\(479\) | −24.6634 | −1.12690 | −0.563450 | − | 0.826150i | \(-0.690526\pi\) | ||||
−0.563450 | + | 0.826150i | \(0.690526\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.0603 | −0.549902 | ||||||||
\(482\) | 9.40051 | 0.428182 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.86100 | 0.357318 | ||||||||
\(485\) | −2.89321 | −0.131374 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.2115 | 1.32370 | 0.661850 | − | 0.749636i | \(-0.269771\pi\) | ||||
0.661850 | + | 0.749636i | \(0.269771\pi\) | |||||||
\(488\) | 6.28407 | 0.284466 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.80239 | −0.171775 | ||||||||
\(491\) | −7.93069 | −0.357907 | −0.178953 | − | 0.983858i | \(-0.557271\pi\) | ||||
−0.178953 | + | 0.983858i | \(0.557271\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.35999 | 0.286440 | ||||||||
\(494\) | −8.23708 | −0.370604 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 24.3556 | 1.09360 | ||||||||
\(497\) | −40.3411 | −1.80954 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.4840 | 1.63325 | 0.816623 | − | 0.577171i | \(-0.195843\pi\) | ||||
0.816623 | + | 0.577171i | \(0.195843\pi\) | |||||||
\(500\) | 16.5309 | 0.739283 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.84136 | −0.260713 | ||||||||
\(503\) | −26.4478 | −1.17925 | −0.589624 | − | 0.807678i | \(-0.700724\pi\) | ||||
−0.589624 | + | 0.807678i | \(0.700724\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.97116 | 0.354712 | ||||||||
\(506\) | 1.21335 | 0.0539400 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −25.1200 | −1.11452 | ||||||||
\(509\) | 34.7697 | 1.54114 | 0.770571 | − | 0.637354i | \(-0.219971\pi\) | ||||
0.770571 | + | 0.637354i | \(0.219971\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.7278 | −0.518805 | ||||||||
\(512\) | −22.8116 | −1.00814 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.361724 | 0.0159549 | ||||||||
\(515\) | −1.37399 | −0.0605454 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27.5925 | −1.21352 | ||||||||
\(518\) | 9.39495 | 0.412790 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.34719 | 0.190637 | ||||||||
\(521\) | 18.9963 | 0.832244 | 0.416122 | − | 0.909309i | \(-0.363389\pi\) | ||||
0.416122 | + | 0.909309i | \(0.363389\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.84802 | 0.211989 | 0.105995 | − | 0.994367i | \(-0.466197\pi\) | ||||
0.105995 | + | 0.994367i | \(0.466197\pi\) | |||||||
\(524\) | 31.5073 | 1.37640 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.88402 | −0.256556 | ||||||||
\(527\) | −57.2340 | −2.49315 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −2.61657 | −0.113656 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −50.8880 | −2.20627 | ||||||||
\(533\) | −0.275912 | −0.0119511 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.22991 | 0.139641 | ||||||||
\(536\) | 25.2331 | 1.08990 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.18197 | 0.352750 | ||||||||
\(539\) | −19.7174 | −0.849288 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.52437 | 0.366491 | 0.183246 | − | 0.983067i | \(-0.441340\pi\) | ||||
0.183246 | + | 0.983067i | \(0.441340\pi\) | |||||||
\(542\) | −5.81361 | −0.249716 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 30.8758 | 1.32379 | ||||||||
\(545\) | −11.0757 | −0.474429 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.4348 | 1.72887 | 0.864433 | − | 0.502748i | \(-0.167678\pi\) | ||||
0.864433 | + | 0.502748i | \(0.167678\pi\) | |||||||
\(548\) | 14.4296 | 0.616404 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.74219 | −0.202207 | ||||||||
\(551\) | −7.47559 | −0.318471 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.09931 | −0.0467475 | ||||||||
\(554\) | −11.3991 | −0.484301 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.32946 | −0.226019 | ||||||||
\(557\) | 0.156519 | 0.00663191 | 0.00331595 | − | 0.999995i | \(-0.498944\pi\) | ||||
0.00331595 | + | 0.999995i | \(0.498944\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.93102 | −0.293151 | ||||||||
\(560\) | 10.8382 | 0.457999 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.2174 | −0.515358 | ||||||||
\(563\) | 9.14136 | 0.385262 | 0.192631 | − | 0.981271i | \(-0.438298\pi\) | ||||
0.192631 | + | 0.981271i | \(0.438298\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.46853 | −0.103852 | ||||||||
\(566\) | 0.792667 | 0.0333183 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −18.8082 | −0.789173 | ||||||||
\(569\) | 43.2851 | 1.81461 | 0.907304 | − | 0.420476i | \(-0.138137\pi\) | ||||
0.907304 | + | 0.420476i | \(0.138137\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.9946 | 1.12969 | 0.564844 | − | 0.825198i | \(-0.308937\pi\) | ||||
0.564844 | + | 0.825198i | \(0.308937\pi\) | |||||||
\(572\) | 10.6028 | 0.443324 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.214935 | 0.00897122 | ||||||||
\(575\) | −3.90834 | −0.162989 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.2683 | 0.635626 | 0.317813 | − | 0.948153i | \(-0.397052\pi\) | ||||
0.317813 | + | 0.948153i | \(0.397052\pi\) | |||||||
\(578\) | −11.0971 | −0.461578 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.85566 | 0.0770522 | ||||||||
\(581\) | −18.4849 | −0.766884 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.5683 | −0.561940 | ||||||||
\(584\) | −5.46781 | −0.226260 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.51750 | −0.0626872 | ||||||||
\(587\) | 13.8956 | 0.573534 | 0.286767 | − | 0.958000i | \(-0.407419\pi\) | ||||
0.286767 | + | 0.958000i | \(0.407419\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 67.2733 | 2.77195 | ||||||||
\(590\) | −4.92834 | −0.202896 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −14.0187 | −0.576163 | ||||||||
\(593\) | −37.4682 | −1.53864 | −0.769318 | − | 0.638866i | \(-0.779404\pi\) | ||||
−0.769318 | + | 0.638866i | \(0.779404\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −25.4691 | −1.04413 | ||||||||
\(596\) | 27.0712 | 1.10888 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.10186 | −0.0450585 | ||||||||
\(599\) | −38.3625 | −1.56745 | −0.783725 | − | 0.621108i | \(-0.786683\pi\) | ||||
−0.783725 | + | 0.621108i | \(0.786683\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −40.5272 | −1.65314 | −0.826570 | − | 0.562834i | \(-0.809711\pi\) | ||||
−0.826570 | + | 0.562834i | \(0.809711\pi\) | |||||||
\(602\) | 5.39926 | 0.220057 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −12.5844 | −0.512054 | ||||||||
\(605\) | −4.62451 | −0.188013 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.348810 | 0.0141578 | 0.00707888 | − | 0.999975i | \(-0.497747\pi\) | ||||
0.00707888 | + | 0.999975i | \(0.497747\pi\) | |||||||
\(608\) | −36.2917 | −1.47182 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.73879 | −0.0704015 | ||||||||
\(611\) | 25.0572 | 1.01370 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.9753 | −0.483679 | −0.241839 | − | 0.970316i | \(-0.577751\pi\) | ||||
−0.241839 | + | 0.970316i | \(0.577751\pi\) | |||||||
\(614\) | 4.86438 | 0.196310 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −17.5605 | −0.707534 | ||||||||
\(617\) | 4.83441 | 0.194626 | 0.0973131 | − | 0.995254i | \(-0.468975\pi\) | ||||
0.0973131 | + | 0.995254i | \(0.468975\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.0325 | −0.403239 | −0.201620 | − | 0.979464i | \(-0.564621\pi\) | ||||
−0.201620 | + | 0.979464i | \(0.564621\pi\) | |||||||
\(620\) | −16.6992 | −0.670657 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.94557 | −0.158203 | ||||||||
\(623\) | 4.33872 | 0.173827 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.81683 | 0.392673 | ||||||||
\(626\) | 0.0668357 | 0.00267129 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.37358 | 0.0947163 | ||||||||
\(629\) | 32.9429 | 1.31352 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.9638 | 0.476271 | 0.238136 | − | 0.971232i | \(-0.423464\pi\) | ||||
0.238136 | + | 0.971232i | \(0.423464\pi\) | |||||||
\(632\) | −0.512531 | −0.0203874 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.34192 | −0.132724 | ||||||||
\(635\) | 14.7778 | 0.586437 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.9057 | 0.709449 | ||||||||
\(638\) | −1.21335 | −0.0480370 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 11.6851 | 0.461892 | ||||||||
\(641\) | 34.0018 | 1.34299 | 0.671494 | − | 0.741010i | \(-0.265653\pi\) | ||||
0.671494 | + | 0.741010i | \(0.265653\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.25288 | −0.167717 | −0.0838587 | − | 0.996478i | \(-0.526724\pi\) | ||||
−0.0838587 | + | 0.996478i | \(0.526724\pi\) | |||||||
\(644\) | −6.80721 | −0.268242 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 22.4997 | 0.885240 | ||||||||
\(647\) | 46.7915 | 1.83956 | 0.919781 | − | 0.392431i | \(-0.128366\pi\) | ||||
0.919781 | + | 0.392431i | \(0.128366\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25.5560 | −1.00316 | ||||||||
\(650\) | 4.30645 | 0.168913 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −16.9788 | −0.664941 | ||||||||
\(653\) | −36.0850 | −1.41212 | −0.706058 | − | 0.708154i | \(-0.749528\pi\) | ||||
−0.706058 | + | 0.708154i | \(0.749528\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.5353 | −0.724234 | ||||||||
\(656\) | −0.320715 | −0.0125218 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −19.5195 | −0.760949 | ||||||||
\(659\) | 2.53082 | 0.0985867 | 0.0492934 | − | 0.998784i | \(-0.484303\pi\) | ||||
0.0492934 | + | 0.998784i | \(0.484303\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.0031 | −0.505763 | −0.252882 | − | 0.967497i | \(-0.581378\pi\) | ||||
−0.252882 | + | 0.967497i | \(0.581378\pi\) | |||||||
\(662\) | −12.0421 | −0.468028 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.61819 | −0.334451 | ||||||||
\(665\) | 29.9367 | 1.16089 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | −21.5435 | −0.833543 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.98194 | −0.269736 | ||||||||
\(671\) | −9.01652 | −0.348079 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.1647 | −1.39405 | −0.697023 | − | 0.717049i | \(-0.745493\pi\) | ||||
−0.697023 | + | 0.717049i | \(0.745493\pi\) | |||||||
\(674\) | 7.51128 | 0.289324 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.4601 | 0.517697 | ||||||||
\(677\) | 15.7179 | 0.604089 | 0.302044 | − | 0.953294i | \(-0.402331\pi\) | ||||
0.302044 | + | 0.953294i | \(0.402331\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.6133 | −0.407301 | ||||||||
\(680\) | −11.8744 | −0.455364 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10.9190 | 0.418110 | ||||||||
\(683\) | 39.2207 | 1.50074 | 0.750370 | − | 0.661018i | \(-0.229875\pi\) | ||||
0.750370 | + | 0.661018i | \(0.229875\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.48875 | −0.324339 | ||||||||
\(686\) | −1.25191 | −0.0477980 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −8.05649 | −0.307151 | ||||||||
\(689\) | 12.3216 | 0.469414 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −48.3185 | −1.83812 | −0.919060 | − | 0.394117i | \(-0.871050\pi\) | ||||
−0.919060 | + | 0.394117i | \(0.871050\pi\) | |||||||
\(692\) | −42.3599 | −1.61028 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.78582 | −0.0677888 | ||||||||
\(695\) | 3.13524 | 0.118927 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.753660 | 0.0285469 | ||||||||
\(698\) | 4.18328 | 0.158339 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 26.6049 | 1.00557 | ||||||||
\(701\) | −25.3649 | −0.958019 | −0.479010 | − | 0.877810i | \(-0.659004\pi\) | ||||
−0.479010 | + | 0.877810i | \(0.659004\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −38.7214 | −1.46040 | ||||||||
\(704\) | 7.98805 | 0.301061 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.4093 | −0.467031 | ||||||||
\(707\) | 29.2410 | 1.09972 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.1340 | 0.793703 | 0.396852 | − | 0.917883i | \(-0.370103\pi\) | ||||
0.396852 | + | 0.917883i | \(0.370103\pi\) | |||||||
\(710\) | 5.20418 | 0.195309 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.02284 | 0.0758090 | ||||||||
\(713\) | 8.99906 | 0.337017 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.23745 | −0.233267 | ||||||||
\(716\) | −36.0820 | −1.34845 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.20790 | −0.306316 | ||||||||
\(719\) | −41.6848 | −1.55458 | −0.777291 | − | 0.629142i | \(-0.783407\pi\) | ||||
−0.777291 | + | 0.629142i | \(0.783407\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.04029 | −0.187710 | ||||||||
\(722\) | −17.4550 | −0.649606 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −27.7173 | −1.03010 | ||||||||
\(725\) | 3.90834 | 0.145152 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.1346 | 0.375870 | 0.187935 | − | 0.982181i | \(-0.439821\pi\) | ||||
0.187935 | + | 0.982181i | \(0.439821\pi\) | |||||||
\(728\) | 15.9470 | 0.591036 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.51293 | 0.0559961 | ||||||||
\(731\) | 18.9322 | 0.700233 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −41.3568 | −1.52755 | −0.763775 | − | 0.645483i | \(-0.776656\pi\) | ||||
−0.763775 | + | 0.645483i | \(0.776656\pi\) | |||||||
\(734\) | 4.77798 | 0.176359 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.85469 | −0.178946 | ||||||||
\(737\) | −36.2050 | −1.33363 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.4713 | 1.15769 | 0.578845 | − | 0.815438i | \(-0.303504\pi\) | ||||
0.578845 | + | 0.815438i | \(0.303504\pi\) | |||||||
\(740\) | 9.61179 | 0.353336 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.59848 | −0.352371 | ||||||||
\(743\) | −10.4909 | −0.384873 | −0.192436 | − | 0.981309i | \(-0.561639\pi\) | ||||
−0.192436 | + | 0.981309i | \(0.561639\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.9256 | −0.583469 | ||||||||
\(746\) | 6.17311 | 0.226014 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −28.9616 | −1.05894 | ||||||||
\(749\) | 11.8484 | 0.432933 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.4188 | −1.18298 | −0.591489 | − | 0.806313i | \(-0.701460\pi\) | ||||
−0.591489 | + | 0.806313i | \(0.701460\pi\) | |||||||
\(752\) | 29.1260 | 1.06211 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.10186 | 0.0401275 | ||||||||
\(755\) | 7.40324 | 0.269432 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −46.3828 | −1.68581 | −0.842906 | − | 0.538061i | \(-0.819157\pi\) | ||||
−0.842906 | + | 0.538061i | \(0.819157\pi\) | |||||||
\(758\) | −3.69975 | −0.134381 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 13.9573 | 0.506285 | ||||||||
\(761\) | −12.2143 | −0.442768 | −0.221384 | − | 0.975187i | \(-0.571057\pi\) | ||||
−0.221384 | + | 0.975187i | \(0.571057\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −40.6294 | −1.47088 | ||||||||
\(764\) | −34.7591 | −1.25754 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.76730 | −0.0638551 | ||||||||
\(767\) | 23.2078 | 0.837985 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.07966 | −0.0749946 | −0.0374973 | − | 0.999297i | \(-0.511939\pi\) | ||||
−0.0374973 | + | 0.999297i | \(0.511939\pi\) | |||||||
\(770\) | 4.85896 | 0.175105 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9.05155 | −0.325772 | ||||||||
\(773\) | 6.91282 | 0.248637 | 0.124318 | − | 0.992242i | \(-0.460326\pi\) | ||||
0.124318 | + | 0.992242i | \(0.460326\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −35.1714 | −1.26339 | ||||||||
\(776\) | −4.94822 | −0.177631 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10.7697 | −0.386114 | ||||||||
\(779\) | −0.885858 | −0.0317392 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 26.9864 | 0.965649 | ||||||||
\(782\) | 3.00976 | 0.107629 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 20.8132 | 0.743329 | ||||||||
\(785\) | −1.39635 | −0.0498377 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.8364 | −0.457570 | −0.228785 | − | 0.973477i | \(-0.573475\pi\) | ||||
−0.228785 | + | 0.973477i | \(0.573475\pi\) | |||||||
\(788\) | 41.2906 | 1.47092 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.141816 | 0.00504559 | ||||||||
\(791\) | −9.05543 | −0.321974 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.18805 | 0.290766 | ||||||||
\(794\) | −6.92183 | −0.245647 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −43.1019 | −1.52771 | ||||||||
\(797\) | 20.2940 | 0.718849 | 0.359425 | − | 0.933174i | \(-0.382973\pi\) | ||||
0.359425 | + | 0.933174i | \(0.382973\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −68.4441 | −2.42138 | ||||||||
\(800\) | 18.9738 | 0.670824 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 13.3865 | 0.472694 | ||||||||
\(803\) | 7.84534 | 0.276856 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.00459 | 0.141143 | ||||||||
\(806\) | −9.91573 | −0.349267 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 13.6330 | 0.479606 | ||||||||
\(809\) | 34.7953 | 1.22334 | 0.611669 | − | 0.791114i | \(-0.290498\pi\) | ||||
0.611669 | + | 0.791114i | \(0.290498\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.1603 | 0.813268 | 0.406634 | − | 0.913591i | \(-0.366702\pi\) | ||||
0.406634 | + | 0.913591i | \(0.366702\pi\) | |||||||
\(812\) | 6.80721 | 0.238886 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.28480 | −0.220282 | ||||||||
\(815\) | 9.98838 | 0.349878 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.2531 | −0.778537 | ||||||||
\(818\) | 7.56629 | 0.264549 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.219896 | 0.00767910 | ||||||||
\(821\) | −49.5815 | −1.73041 | −0.865203 | − | 0.501422i | \(-0.832810\pi\) | ||||
−0.865203 | + | 0.501422i | \(0.832810\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.0778 | −0.874159 | −0.437079 | − | 0.899423i | \(-0.643987\pi\) | ||||
−0.437079 | + | 0.899423i | \(0.643987\pi\) | |||||||
\(824\) | −2.34993 | −0.0818636 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18.0788 | −0.629044 | ||||||||
\(827\) | −35.7445 | −1.24296 | −0.621480 | − | 0.783430i | \(-0.713468\pi\) | ||||
−0.621480 | + | 0.783430i | \(0.713468\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 43.5954 | 1.51413 | 0.757066 | − | 0.653339i | \(-0.226632\pi\) | ||||
0.757066 | + | 0.653339i | \(0.226632\pi\) | |||||||
\(830\) | 2.38464 | 0.0827719 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −7.25408 | −0.251490 | ||||||||
\(833\) | −48.9097 | −1.69462 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.6737 | 0.438593 | ||||||||
\(836\) | 34.0418 | 1.17736 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9.51990 | −0.328859 | ||||||||
\(839\) | 18.4127 | 0.635679 | 0.317839 | − | 0.948145i | \(-0.397043\pi\) | ||||
0.317839 | + | 0.948145i | \(0.397043\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −2.97123 | −0.102395 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 23.1890 | 0.798199 | ||||||||
\(845\) | −7.91840 | −0.272401 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.9643 | −0.582901 | ||||||||
\(848\) | 14.3224 | 0.491832 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −11.7632 | −0.403473 | ||||||||
\(851\) | −5.17971 | −0.177558 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.4481 | −0.631651 | −0.315826 | − | 0.948817i | \(-0.602281\pi\) | ||||
−0.315826 | + | 0.948817i | \(0.602281\pi\) | |||||||
\(854\) | −6.37848 | −0.218267 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.52408 | 0.188809 | ||||||||
\(857\) | −2.81664 | −0.0962147 | −0.0481074 | − | 0.998842i | \(-0.515319\pi\) | ||||
−0.0481074 | + | 0.998842i | \(0.515319\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −45.9546 | −1.56795 | −0.783975 | − | 0.620793i | \(-0.786811\pi\) | ||||
−0.783975 | + | 0.620793i | \(0.786811\pi\) | |||||||
\(860\) | 5.52387 | 0.188363 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.76859 | 0.196479 | ||||||||
\(863\) | 18.0449 | 0.614254 | 0.307127 | − | 0.951669i | \(-0.400632\pi\) | ||||
0.307127 | + | 0.951669i | \(0.400632\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.9197 | 0.847296 | ||||||||
\(866\) | −11.9907 | −0.407461 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −61.2585 | −2.07925 | ||||||||
\(869\) | 0.735391 | 0.0249464 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.8783 | 1.11404 | ||||||||
\(872\) | −18.9426 | −0.641477 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.53770 | −0.119664 | ||||||||
\(875\) | −35.6742 | −1.20601 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.0156 | 1.08109 | 0.540545 | − | 0.841315i | \(-0.318218\pi\) | ||||
0.540545 | + | 0.841315i | \(0.318218\pi\) | |||||||
\(878\) | −1.52351 | −0.0514160 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −7.25030 | −0.244407 | ||||||||
\(881\) | −48.5137 | −1.63447 | −0.817234 | − | 0.576306i | \(-0.804494\pi\) | ||||
−0.817234 | + | 0.576306i | \(0.804494\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.9176 | 0.468364 | 0.234182 | − | 0.972193i | \(-0.424759\pi\) | ||||
0.234182 | + | 0.972193i | \(0.424759\pi\) | |||||||
\(884\) | 26.3005 | 0.884583 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.75662 | 0.327780 | ||||||||
\(887\) | −56.2498 | −1.88868 | −0.944341 | − | 0.328968i | \(-0.893299\pi\) | ||||
−0.944341 | + | 0.328968i | \(0.893299\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 54.2099 | 1.81814 | ||||||||
\(890\) | −0.559714 | −0.0187617 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −37.4717 | −1.25464 | ||||||||
\(893\) | 80.4498 | 2.69215 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.2265 | 0.709525 | ||||||||
\(896\) | 42.8648 | 1.43201 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15.3181 | −0.511170 | ||||||||
\(899\) | −8.99906 | −0.300135 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33.6566 | −1.12126 | ||||||||
\(902\) | −0.143782 | −0.00478742 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.22190 | −0.140418 | ||||||||
\(905\) | 16.3057 | 0.542019 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.0052 | 0.797080 | 0.398540 | − | 0.917151i | \(-0.369517\pi\) | ||||
0.398540 | + | 0.917151i | \(0.369517\pi\) | |||||||
\(908\) | 50.8580 | 1.68778 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.41250 | −0.146273 | ||||||||
\(911\) | −27.2733 | −0.903605 | −0.451803 | − | 0.892118i | \(-0.649219\pi\) | ||||
−0.451803 | + | 0.892118i | \(0.649219\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.3656 | 0.409241 | ||||||||
\(914\) | −0.336793 | −0.0111401 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 47.1109 | 1.55659 | ||||||||
\(917\) | −67.9939 | −2.24536 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −54.4520 | −1.79621 | −0.898103 | − | 0.439784i | \(-0.855055\pi\) | ||||
−0.898103 | + | 0.439784i | \(0.855055\pi\) | |||||||
\(920\) | 1.86705 | 0.0615549 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.43252 | 0.211844 | ||||||||
\(923\) | −24.5068 | −0.806650 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.2441 | 0.665621 | ||||||||
\(926\) | −18.7732 | −0.616924 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.85469 | 0.159363 | ||||||||
\(929\) | 28.7869 | 0.944468 | 0.472234 | − | 0.881473i | \(-0.343448\pi\) | ||||
0.472234 | + | 0.881473i | \(0.343448\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 57.4889 | 1.88412 | ||||||||
\(932\) | −4.15812 | −0.136204 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.80362 | 0.0590163 | ||||||||
\(935\) | 17.0377 | 0.557193 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.2809 | −0.335863 | −0.167932 | − | 0.985799i | \(-0.553709\pi\) | ||||
−0.167932 | + | 0.985799i | \(0.553709\pi\) | |||||||
\(938\) | −25.6122 | −0.836267 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −19.9700 | −0.651350 | ||||||||
\(941\) | 5.08436 | 0.165745 | 0.0828726 | − | 0.996560i | \(-0.473591\pi\) | ||||
0.0828726 | + | 0.996560i | \(0.473591\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.118500 | −0.00385889 | ||||||||
\(944\) | 26.9763 | 0.878005 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.61186 | −0.117432 | ||||||||
\(947\) | −33.5032 | −1.08871 | −0.544354 | − | 0.838856i | \(-0.683225\pi\) | ||||
−0.544354 | + | 0.838856i | \(0.683225\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.12448 | −0.231270 | ||||||||
\(950\) | 13.8265 | 0.448592 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −43.5596 | −1.41177 | ||||||||
\(953\) | 51.6427 | 1.67287 | 0.836435 | − | 0.548065i | \(-0.184636\pi\) | ||||
0.836435 | + | 0.548065i | \(0.184636\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.4483 | 0.661692 | ||||||||
\(956\) | 5.46402 | 0.176719 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 11.6715 | 0.377090 | ||||||||
\(959\) | −31.1397 | −1.00555 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 49.9831 | 1.61236 | ||||||||
\(962\) | 5.70733 | 0.184012 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 35.2803 | 1.13630 | ||||||||
\(965\) | 5.32490 | 0.171414 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.0050 | −0.964897 | −0.482448 | − | 0.875924i | \(-0.660252\pi\) | ||||
−0.482448 | + | 0.875924i | \(0.660252\pi\) | |||||||
\(968\) | −7.90925 | −0.254213 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.36916 | 0.0439612 | ||||||||
\(971\) | 22.9615 | 0.736869 | 0.368434 | − | 0.929654i | \(-0.379894\pi\) | ||||
0.368434 | + | 0.929654i | \(0.379894\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.5012 | 0.368710 | ||||||||
\(974\) | −13.8239 | −0.442945 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.51764 | 0.304652 | ||||||||
\(977\) | 39.9218 | 1.27721 | 0.638606 | − | 0.769534i | \(-0.279512\pi\) | ||||
0.638606 | + | 0.769534i | \(0.279512\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.90241 | −0.0927615 | ||||||||
\(980\) | −14.2704 | −0.455852 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.75306 | 0.119765 | ||||||||
\(983\) | 16.8911 | 0.538742 | 0.269371 | − | 0.963036i | \(-0.413184\pi\) | ||||
0.269371 | + | 0.963036i | \(0.413184\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.2907 | −0.773965 | ||||||||
\(986\) | −3.00976 | −0.0958503 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −30.9139 | −0.983501 | ||||||||
\(989\) | −2.97677 | −0.0946557 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.1299 | −1.17947 | −0.589734 | − | 0.807597i | \(-0.700768\pi\) | ||||
−0.589734 | + | 0.807597i | \(0.700768\pi\) | |||||||
\(992\) | −43.6876 | −1.38708 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 19.0907 | 0.605521 | ||||||||
\(995\) | 25.3562 | 0.803846 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.6652 | 0.464452 | 0.232226 | − | 0.972662i | \(-0.425399\pi\) | ||||
0.232226 | + | 0.972662i | \(0.425399\pi\) | |||||||
\(998\) | −17.2654 | −0.546527 | ||||||||
\(999\) | 0 | 0 |
(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 | 6003.2.a.v.1.14 | ✓ | 30 | |
3.2 | odd | 2 | 6003.2.a.w.1.17 | yes | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6003.2.a.v.1.14 | ✓ | 30 | 1.1 | even | 1 | trivial | |
6003.2.a.w.1.17 | yes | 30 | 3.2 | odd | 2 |