Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4275,2,Mod(1,4275)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4275, 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("4275.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4275 = 3^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4275.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: | \(34.1360468641\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.621.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1425) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.66908\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4275.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.66908 | −1.88732 | −0.943662 | − | 0.330911i | \(-0.892644\pi\) | ||||
−0.943662 | + | 0.330911i | \(0.892644\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.12398 | 2.56199 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.454904 | −0.171938 | −0.0859688 | − | 0.996298i | \(-0.527399\pi\) | ||||
−0.0859688 | + | 0.996298i | \(0.527399\pi\) | |||||||
\(8\) | −8.33816 | −2.94798 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.45490 | 0.438670 | 0.219335 | − | 0.975650i | \(-0.429611\pi\) | ||||
0.219335 | + | 0.975650i | \(0.429611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.33816 | 0.925838 | 0.462919 | − | 0.886400i | \(-0.346802\pi\) | ||||
0.462919 | + | 0.886400i | \(0.346802\pi\) | |||||||
\(14\) | 1.21417 | 0.324502 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 12.0072 | 3.00181 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.88325 | −0.827913 | ||||||||
\(23\) | −6.79306 | −1.41645 | −0.708226 | − | 0.705986i | \(-0.750504\pi\) | ||||
−0.708226 | + | 0.705986i | \(0.750504\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −8.90981 | −1.74736 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.33092 | −0.440503 | ||||||||
\(29\) | −3.00000 | −0.557086 | −0.278543 | − | 0.960424i | \(-0.589851\pi\) | ||||
−0.278543 | + | 0.960424i | \(0.589851\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.79306 | 1.57928 | 0.789640 | − | 0.613570i | \(-0.210267\pi\) | ||||
0.789640 | + | 0.613570i | \(0.210267\pi\) | |||||||
\(32\) | −15.3719 | −2.71740 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.2480 | −1.68476 | −0.842378 | − | 0.538888i | \(-0.818845\pi\) | ||||
−0.842378 | + | 0.538888i | \(0.818845\pi\) | |||||||
\(38\) | −2.66908 | −0.432982 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.97345 | −0.620548 | −0.310274 | − | 0.950647i | \(-0.600421\pi\) | ||||
−0.310274 | + | 0.950647i | \(0.600421\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | 7.45490 | 1.12387 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 18.1312 | 2.67330 | ||||||||
\(47\) | 2.42835 | 0.354211 | 0.177106 | − | 0.984192i | \(-0.443327\pi\) | ||||
0.177106 | + | 0.984192i | \(0.443327\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.79306 | −0.970437 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 17.1047 | 2.37199 | ||||||||
\(53\) | 13.6763 | 1.87859 | 0.939293 | − | 0.343115i | \(-0.111482\pi\) | ||||
0.939293 | + | 0.343115i | \(0.111482\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.79306 | 0.506869 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.00724 | 1.05140 | ||||||||
\(59\) | −7.54510 | −0.982288 | −0.491144 | − | 0.871078i | \(-0.663421\pi\) | ||||
−0.491144 | + | 0.871078i | \(0.663421\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.90981 | −0.500600 | −0.250300 | − | 0.968168i | \(-0.580529\pi\) | ||||
−0.250300 | + | 0.968168i | \(0.580529\pi\) | |||||||
\(62\) | −23.4694 | −2.98061 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 17.0145 | 2.12681 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.1312 | −1.72640 | −0.863202 | − | 0.504859i | \(-0.831544\pi\) | ||||
−0.863202 | + | 0.504859i | \(0.831544\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.13122 | 1.08368 | 0.541838 | − | 0.840483i | \(-0.317729\pi\) | ||||
0.541838 | + | 0.840483i | \(0.317729\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.6763 | 1.36661 | 0.683305 | − | 0.730133i | \(-0.260542\pi\) | ||||
0.683305 | + | 0.730133i | \(0.260542\pi\) | |||||||
\(74\) | 27.3526 | 3.17968 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.12398 | 0.587761 | ||||||||
\(77\) | −0.661842 | −0.0754239 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.97345 | 1.00959 | 0.504796 | − | 0.863239i | \(-0.331568\pi\) | ||||
0.504796 | + | 0.863239i | \(0.331568\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10.6054 | 1.17118 | ||||||||
\(83\) | −4.54510 | −0.498889 | −0.249445 | − | 0.968389i | \(-0.580248\pi\) | ||||
−0.249445 | + | 0.968389i | \(0.580248\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 21.3526 | 2.30251 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −12.1312 | −1.29319 | ||||||||
\(89\) | 0.0901918 | 0.00956031 | 0.00478016 | − | 0.999989i | \(-0.498478\pi\) | ||||
0.00478016 | + | 0.999989i | \(0.498478\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.51854 | −0.159186 | ||||||||
\(92\) | −34.8075 | −3.62894 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.48146 | −0.668511 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.0145 | −1.21989 | −0.609943 | − | 0.792446i | \(-0.708807\pi\) | ||||
−0.609943 | + | 0.792446i | \(0.708807\pi\) | |||||||
\(98\) | 18.1312 | 1.83153 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.51854 | −0.549115 | −0.274558 | − | 0.961571i | \(-0.588531\pi\) | ||||
−0.274558 | + | 0.961571i | \(0.588531\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.54510 | 0.250776 | 0.125388 | − | 0.992108i | \(-0.459982\pi\) | ||||
0.125388 | + | 0.992108i | \(0.459982\pi\) | |||||||
\(104\) | −27.8341 | −2.72936 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −36.5032 | −3.54550 | ||||||||
\(107\) | −4.63529 | −0.448110 | −0.224055 | − | 0.974576i | \(-0.571930\pi\) | ||||
−0.224055 | + | 0.974576i | \(0.571930\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.24797 | −0.598447 | −0.299223 | − | 0.954183i | \(-0.596728\pi\) | ||||
−0.299223 | + | 0.954183i | \(0.596728\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.46214 | −0.516124 | ||||||||
\(113\) | −5.20694 | −0.489827 | −0.244914 | − | 0.969545i | \(-0.578760\pi\) | ||||
−0.244914 | + | 0.969545i | \(0.578760\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −15.3719 | −1.42725 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 20.1385 | 1.85390 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.88325 | −0.807569 | ||||||||
\(122\) | 10.4356 | 0.944794 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 45.0555 | 4.04610 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.6127 | 0.941723 | 0.470861 | − | 0.882207i | \(-0.343943\pi\) | ||||
0.470861 | + | 0.882207i | \(0.343943\pi\) | |||||||
\(128\) | −14.6691 | −1.29658 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.7029 | −1.89619 | −0.948094 | − | 0.317989i | \(-0.896992\pi\) | ||||
−0.948094 | + | 0.317989i | \(0.896992\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.454904 | −0.0394452 | ||||||||
\(134\) | 37.7173 | 3.25828 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 22.3155 | 1.90655 | 0.953273 | − | 0.302110i | \(-0.0976911\pi\) | ||||
0.953273 | + | 0.302110i | \(0.0976911\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.4018 | −0.882269 | −0.441134 | − | 0.897441i | \(-0.645424\pi\) | ||||
−0.441134 | + | 0.897441i | \(0.645424\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −24.3719 | −2.04525 | ||||||||
\(143\) | 4.85670 | 0.406138 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −31.1650 | −2.57923 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −52.5104 | −4.31633 | ||||||||
\(149\) | −5.15777 | −0.422541 | −0.211271 | − | 0.977428i | \(-0.567760\pi\) | ||||
−0.211271 | + | 0.977428i | \(0.567760\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.49593 | −0.691389 | −0.345695 | − | 0.938347i | \(-0.612357\pi\) | ||||
−0.345695 | + | 0.938347i | \(0.612357\pi\) | |||||||
\(152\) | −8.33816 | −0.676314 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.76651 | 0.142349 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.6498 | −1.80765 | −0.903824 | − | 0.427905i | \(-0.859252\pi\) | ||||
−0.903824 | + | 0.427905i | \(0.859252\pi\) | |||||||
\(158\) | −23.9508 | −1.90543 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.09019 | 0.243541 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.72548 | −0.291802 | −0.145901 | − | 0.989299i | \(-0.546608\pi\) | ||||
−0.145901 | + | 0.989299i | \(0.546608\pi\) | |||||||
\(164\) | −20.3599 | −1.58984 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.1312 | 0.941565 | ||||||||
\(167\) | 12.2214 | 0.945721 | 0.472861 | − | 0.881137i | \(-0.343221\pi\) | ||||
0.472861 | + | 0.881137i | \(0.343221\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.85670 | −0.142823 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −40.9919 | −3.12560 | ||||||||
\(173\) | 24.1722 | 1.83778 | 0.918891 | − | 0.394511i | \(-0.129086\pi\) | ||||
0.918891 | + | 0.394511i | \(0.129086\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 17.4694 | 1.31680 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.240729 | −0.0180434 | ||||||||
\(179\) | 6.22141 | 0.465010 | 0.232505 | − | 0.972595i | \(-0.425308\pi\) | ||||
0.232505 | + | 0.972595i | \(0.425308\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.4959 | −1.52345 | −0.761725 | − | 0.647900i | \(-0.775647\pi\) | ||||
−0.761725 | + | 0.647900i | \(0.775647\pi\) | |||||||
\(182\) | 4.05311 | 0.300436 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 56.6416 | 4.17568 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 12.4428 | 0.907486 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.793062 | −0.0573840 | −0.0286920 | − | 0.999588i | \(-0.509134\pi\) | ||||
−0.0286920 | + | 0.999588i | \(0.509134\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.8196 | 1.13872 | 0.569360 | − | 0.822088i | \(-0.307191\pi\) | ||||
0.569360 | + | 0.822088i | \(0.307191\pi\) | |||||||
\(194\) | 32.0676 | 2.30232 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −34.8075 | −2.48625 | ||||||||
\(197\) | 3.75203 | 0.267321 | 0.133661 | − | 0.991027i | \(-0.457327\pi\) | ||||
0.133661 | + | 0.991027i | \(0.457327\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.45490 | 0.457576 | 0.228788 | − | 0.973476i | \(-0.426524\pi\) | ||||
0.228788 | + | 0.973476i | \(0.426524\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 14.7294 | 1.03636 | ||||||||
\(203\) | 1.36471 | 0.0957840 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.79306 | −0.473295 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 40.0821 | 2.77919 | ||||||||
\(209\) | 1.45490 | 0.100638 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.9653 | 1.64984 | 0.824920 | − | 0.565249i | \(-0.191220\pi\) | ||||
0.824920 | + | 0.565249i | \(0.191220\pi\) | |||||||
\(212\) | 70.0772 | 4.81292 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 12.3719 | 0.845729 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.00000 | −0.271538 | ||||||||
\(218\) | 16.6763 | 1.12946 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.20694 | 0.214752 | 0.107376 | − | 0.994218i | \(-0.465755\pi\) | ||||
0.107376 | + | 0.994218i | \(0.465755\pi\) | |||||||
\(224\) | 6.99276 | 0.467224 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.8977 | 0.924463 | ||||||||
\(227\) | −9.13122 | −0.606060 | −0.303030 | − | 0.952981i | \(-0.597998\pi\) | ||||
−0.303030 | + | 0.952981i | \(0.597998\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.7400 | 1.10621 | 0.553104 | − | 0.833112i | \(-0.313443\pi\) | ||||
0.553104 | + | 0.833112i | \(0.313443\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 25.0145 | 1.64228 | ||||||||
\(233\) | −9.57165 | −0.627060 | −0.313530 | − | 0.949578i | \(-0.601512\pi\) | ||||
−0.313530 | + | 0.949578i | \(0.601512\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −38.6609 | −2.51661 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.5185 | −1.13318 | −0.566590 | − | 0.824000i | \(-0.691738\pi\) | ||||
−0.566590 | + | 0.824000i | \(0.691738\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.9098 | 1.08926 | 0.544628 | − | 0.838678i | \(-0.316671\pi\) | ||||
0.544628 | + | 0.838678i | \(0.316671\pi\) | |||||||
\(242\) | 23.7101 | 1.52414 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −20.0338 | −1.28253 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.33816 | 0.212402 | ||||||||
\(248\) | −73.3179 | −4.65569 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.6392 | 0.734662 | 0.367331 | − | 0.930090i | \(-0.380272\pi\) | ||||
0.367331 | + | 0.930090i | \(0.380272\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.88325 | −0.621355 | ||||||||
\(254\) | −28.3261 | −1.77734 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.12398 | 0.320249 | ||||||||
\(257\) | −4.76651 | −0.297327 | −0.148663 | − | 0.988888i | \(-0.547497\pi\) | ||||
−0.148663 | + | 0.988888i | \(0.547497\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.66184 | 0.289673 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 57.9267 | 3.57872 | ||||||||
\(263\) | 14.8606 | 0.916347 | 0.458173 | − | 0.888863i | \(-0.348504\pi\) | ||||
0.458173 | + | 0.888863i | \(0.348504\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.21417 | 0.0744458 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −72.4081 | −4.42303 | ||||||||
\(269\) | 21.5330 | 1.31289 | 0.656446 | − | 0.754373i | \(-0.272059\pi\) | ||||
0.656446 | + | 0.754373i | \(0.272059\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.13122 | −0.0687167 | −0.0343584 | − | 0.999410i | \(-0.510939\pi\) | ||||
−0.0343584 | + | 0.999410i | \(0.510939\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −59.5620 | −3.59827 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.2624 | 0.796863 | 0.398431 | − | 0.917198i | \(-0.369555\pi\) | ||||
0.398431 | + | 0.917198i | \(0.369555\pi\) | |||||||
\(278\) | 27.7632 | 1.66513 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.1988 | −0.847030 | −0.423515 | − | 0.905889i | \(-0.639204\pi\) | ||||
−0.423515 | + | 0.905889i | \(0.639204\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.5330 | 1.16112 | 0.580559 | − | 0.814218i | \(-0.302834\pi\) | ||||
0.580559 | + | 0.814218i | \(0.302834\pi\) | |||||||
\(284\) | 46.7882 | 2.77637 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.9629 | −0.766513 | ||||||||
\(287\) | 1.80754 | 0.106696 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 59.8292 | 3.50124 | ||||||||
\(293\) | −24.9734 | −1.45896 | −0.729482 | − | 0.684000i | \(-0.760239\pi\) | ||||
−0.729482 | + | 0.684000i | \(0.760239\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 85.4492 | 4.96663 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 13.7665 | 0.797472 | ||||||||
\(299\) | −22.6763 | −1.31141 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.63923 | 0.209762 | ||||||||
\(302\) | 22.6763 | 1.30488 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 12.0072 | 0.688662 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.4018 | −0.650735 | −0.325367 | − | 0.945588i | \(-0.605488\pi\) | ||||
−0.325367 | + | 0.945588i | \(0.605488\pi\) | |||||||
\(308\) | −3.39127 | −0.193235 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.32368 | −0.0750592 | −0.0375296 | − | 0.999296i | \(-0.511949\pi\) | ||||
−0.0375296 | + | 0.999296i | \(0.511949\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.6127 | −1.16510 | −0.582549 | − | 0.812796i | \(-0.697944\pi\) | ||||
−0.582549 | + | 0.812796i | \(0.697944\pi\) | |||||||
\(314\) | 60.4540 | 3.41162 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 45.9798 | 2.58657 | ||||||||
\(317\) | −18.1722 | −1.02066 | −0.510328 | − | 0.859980i | \(-0.670476\pi\) | ||||
−0.510328 | + | 0.859980i | \(0.670476\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.36471 | −0.244377 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.24797 | −0.459641 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9.94360 | 0.550725 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 33.1312 | 1.82937 | ||||||||
\(329\) | −1.10467 | −0.0609022 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.5225 | −1.07305 | −0.536526 | − | 0.843883i | \(-0.680264\pi\) | ||||
−0.536526 | + | 0.843883i | \(0.680264\pi\) | |||||||
\(332\) | −23.2890 | −1.27815 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −32.6199 | −1.78488 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.413875 | −0.0225452 | −0.0112726 | − | 0.999936i | \(-0.503588\pi\) | ||||
−0.0112726 | + | 0.999936i | \(0.503588\pi\) | |||||||
\(338\) | 4.95568 | 0.269553 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.7931 | 0.692783 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.27452 | 0.338792 | ||||||||
\(344\) | 66.7053 | 3.59651 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −64.5176 | −3.46849 | ||||||||
\(347\) | −30.9243 | −1.66010 | −0.830051 | − | 0.557687i | \(-0.811689\pi\) | ||||
−0.830051 | + | 0.557687i | \(0.811689\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.7665 | −0.790433 | −0.395217 | − | 0.918588i | \(-0.629330\pi\) | ||||
−0.395217 | + | 0.918588i | \(0.629330\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −22.3647 | −1.19204 | ||||||||
\(353\) | −27.5330 | −1.46543 | −0.732717 | − | 0.680533i | \(-0.761748\pi\) | ||||
−0.732717 | + | 0.680533i | \(0.761748\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.462141 | 0.0244934 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −16.6054 | −0.877625 | ||||||||
\(359\) | 3.83409 | 0.202356 | 0.101178 | − | 0.994868i | \(-0.467739\pi\) | ||||
0.101178 | + | 0.994868i | \(0.467739\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 54.7053 | 2.87524 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.78098 | −0.407834 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.2254 | −1.10795 | −0.553977 | − | 0.832532i | \(-0.686891\pi\) | ||||
−0.553977 | + | 0.832532i | \(0.686891\pi\) | |||||||
\(368\) | −81.5659 | −4.25192 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.22141 | −0.323000 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.2624 | 1.15271 | 0.576353 | − | 0.817201i | \(-0.304475\pi\) | ||||
0.576353 | + | 0.817201i | \(0.304475\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −20.2480 | −1.04421 | ||||||||
\(377\) | −10.0145 | −0.515772 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.33816 | −0.171470 | −0.0857348 | − | 0.996318i | \(-0.527324\pi\) | ||||
−0.0857348 | + | 0.996318i | \(0.527324\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.11675 | 0.108302 | ||||||||
\(383\) | 34.5370 | 1.76476 | 0.882378 | − | 0.470541i | \(-0.155941\pi\) | ||||
0.882378 | + | 0.470541i | \(0.155941\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −42.2238 | −2.14914 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −61.5620 | −3.12534 | ||||||||
\(389\) | −19.1047 | −0.968645 | −0.484323 | − | 0.874890i | \(-0.660934\pi\) | ||||
−0.484323 | + | 0.874890i | \(0.660934\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 56.6416 | 2.86083 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −10.0145 | −0.504522 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.8301 | −0.694115 | −0.347058 | − | 0.937844i | \(-0.612819\pi\) | ||||
−0.347058 | + | 0.937844i | \(0.612819\pi\) | |||||||
\(398\) | −17.2286 | −0.863594 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.79306 | −0.339229 | −0.169615 | − | 0.985510i | \(-0.554252\pi\) | ||||
−0.169615 | + | 0.985510i | \(0.554252\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 29.3526 | 1.46216 | ||||||||
\(404\) | −28.2769 | −1.40683 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.64252 | −0.180775 | ||||||||
\(407\) | −14.9098 | −0.739052 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.5104 | −0.618600 | −0.309300 | − | 0.950965i | \(-0.600095\pi\) | ||||
−0.309300 | + | 0.950965i | \(0.600095\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.0410 | 0.642485 | ||||||||
\(413\) | 3.43229 | 0.168892 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −51.3140 | −2.51588 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.88325 | −0.189936 | ||||||||
\(419\) | 2.06758 | 0.101008 | 0.0505040 | − | 0.998724i | \(-0.483917\pi\) | ||||
0.0505040 | + | 0.998724i | \(0.483917\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.51854 | −0.171483 | −0.0857416 | − | 0.996317i | \(-0.527326\pi\) | ||||
−0.0857416 | + | 0.996317i | \(0.527326\pi\) | |||||||
\(422\) | −63.9653 | −3.11378 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −114.035 | −5.53804 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.77859 | 0.0860719 | ||||||||
\(428\) | −23.7511 | −1.14805 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.4468 | −1.51474 | −0.757369 | − | 0.652987i | \(-0.773515\pi\) | ||||
−0.757369 | + | 0.652987i | \(0.773515\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.9774 | 1.00811 | 0.504055 | − | 0.863672i | \(-0.331841\pi\) | ||||
0.504055 | + | 0.863672i | \(0.331841\pi\) | |||||||
\(434\) | 10.6763 | 0.512480 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −32.0145 | −1.53322 | ||||||||
\(437\) | −6.79306 | −0.324956 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.75598 | 0.179263 | 0.0896315 | − | 0.995975i | \(-0.471431\pi\) | ||||
0.0896315 | + | 0.995975i | \(0.471431\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.0184 | −0.951104 | −0.475552 | − | 0.879688i | \(-0.657752\pi\) | ||||
−0.475552 | + | 0.879688i | \(0.657752\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8.55957 | −0.405307 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.73995 | −0.365678 | ||||||||
\(449\) | −22.4057 | −1.05739 | −0.528696 | − | 0.848811i | \(-0.677319\pi\) | ||||
−0.528696 | + | 0.848811i | \(0.677319\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.78098 | −0.272216 | ||||||||
\(452\) | −26.6803 | −1.25493 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 24.3719 | 1.14383 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.2890 | −1.60397 | −0.801986 | − | 0.597343i | \(-0.796223\pi\) | ||||
−0.801986 | + | 0.597343i | \(0.796223\pi\) | |||||||
\(458\) | −44.6803 | −2.08777 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.5104 | −0.675817 | −0.337909 | − | 0.941179i | \(-0.609719\pi\) | ||||
−0.337909 | + | 0.941179i | \(0.609719\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.8486 | −1.57308 | −0.786538 | − | 0.617542i | \(-0.788129\pi\) | ||||
−0.786538 | + | 0.617542i | \(0.788129\pi\) | |||||||
\(464\) | −36.0217 | −1.67227 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 25.5475 | 1.18346 | ||||||||
\(467\) | −9.22141 | −0.426716 | −0.213358 | − | 0.976974i | \(-0.568440\pi\) | ||||
−0.213358 | + | 0.976974i | \(0.568440\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.42835 | 0.296834 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 62.9122 | 2.89577 | ||||||||
\(473\) | −11.6392 | −0.535172 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 46.7584 | 2.13868 | ||||||||
\(479\) | −27.3035 | −1.24753 | −0.623764 | − | 0.781613i | \(-0.714397\pi\) | ||||
−0.623764 | + | 0.781613i | \(0.714397\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −34.2093 | −1.55981 | ||||||||
\(482\) | −45.1336 | −2.05578 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −45.5176 | −2.06898 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.4815 | −0.656218 | −0.328109 | − | 0.944640i | \(-0.606411\pi\) | ||||
−0.328109 | + | 0.944640i | \(0.606411\pi\) | |||||||
\(488\) | 32.6006 | 1.47576 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.2093 | 1.72436 | 0.862182 | − | 0.506599i | \(-0.169098\pi\) | ||||
0.862182 | + | 0.506599i | \(0.169098\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −8.90981 | −0.400871 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 105.580 | 4.74070 | ||||||||
\(497\) | −4.15383 | −0.186325 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 35.5740 | 1.59251 | 0.796256 | − | 0.604959i | \(-0.206811\pi\) | ||||
0.796256 | + | 0.604959i | \(0.206811\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −31.0660 | −1.38654 | ||||||||
\(503\) | −6.84223 | −0.305080 | −0.152540 | − | 0.988297i | \(-0.548745\pi\) | ||||
−0.152540 | + | 0.988297i | \(0.548745\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 26.3792 | 1.17270 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 54.3792 | 2.41269 | ||||||||
\(509\) | −25.1352 | −1.11410 | −0.557048 | − | 0.830480i | \(-0.688066\pi\) | ||||
−0.557048 | + | 0.830480i | \(0.688066\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.31160 | −0.234972 | ||||||||
\(512\) | 15.6618 | 0.692162 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 12.7222 | 0.561152 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.53302 | 0.155382 | ||||||||
\(518\) | −12.4428 | −0.546706 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.5861 | −0.463787 | −0.231893 | − | 0.972741i | \(-0.574492\pi\) | ||||
−0.231893 | + | 0.972741i | \(0.574492\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.9614 | 1.48503 | 0.742513 | − | 0.669831i | \(-0.233634\pi\) | ||||
0.742513 | + | 0.669831i | \(0.233634\pi\) | |||||||
\(524\) | −111.205 | −4.85802 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −39.6642 | −1.72944 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.1457 | 1.00633 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.33092 | −0.101058 | ||||||||
\(533\) | −13.2640 | −0.574527 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 117.828 | 5.08941 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −57.4733 | −2.47785 | ||||||||
\(539\) | −9.88325 | −0.425702 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.7318 | −1.45024 | −0.725122 | − | 0.688620i | \(-0.758217\pi\) | ||||
−0.725122 | + | 0.688620i | \(0.758217\pi\) | |||||||
\(542\) | 3.01932 | 0.129691 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.7255 | 0.886158 | 0.443079 | − | 0.896483i | \(-0.353886\pi\) | ||||
0.443079 | + | 0.896483i | \(0.353886\pi\) | |||||||
\(548\) | 114.344 | 4.88455 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.00000 | −0.127804 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.08206 | −0.173587 | ||||||||
\(554\) | −35.3985 | −1.50394 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −53.2986 | −2.26037 | ||||||||
\(557\) | −13.3237 | −0.564543 | −0.282271 | − | 0.959335i | \(-0.591088\pi\) | ||||
−0.282271 | + | 0.959335i | \(0.591088\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −26.7053 | −1.12951 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 37.8977 | 1.59862 | ||||||||
\(563\) | 11.7786 | 0.496408 | 0.248204 | − | 0.968708i | \(-0.420160\pi\) | ||||
0.248204 | + | 0.968708i | \(0.420160\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −52.1352 | −2.19140 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −76.1376 | −3.19466 | ||||||||
\(569\) | −43.2278 | −1.81220 | −0.906101 | − | 0.423062i | \(-0.860955\pi\) | ||||
−0.906101 | + | 0.423062i | \(0.860955\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.41782 | −0.143031 | −0.0715157 | − | 0.997439i | \(-0.522784\pi\) | ||||
−0.0715157 | + | 0.997439i | \(0.522784\pi\) | |||||||
\(572\) | 24.8856 | 1.04052 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.82446 | −0.201369 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.4081 | 1.34917 | 0.674584 | − | 0.738198i | \(-0.264323\pi\) | ||||
0.674584 | + | 0.738198i | \(0.264323\pi\) | |||||||
\(578\) | 45.3743 | 1.88732 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.06758 | 0.0857778 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.8977 | 0.824080 | ||||||||
\(584\) | −97.3590 | −4.02874 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 66.6561 | 2.75354 | ||||||||
\(587\) | −7.93636 | −0.327569 | −0.163784 | − | 0.986496i | \(-0.552370\pi\) | ||||
−0.163784 | + | 0.986496i | \(0.552370\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.79306 | 0.362312 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −123.050 | −5.05731 | ||||||||
\(593\) | 1.98553 | 0.0815358 | 0.0407679 | − | 0.999169i | \(-0.487020\pi\) | ||||
0.0407679 | + | 0.999169i | \(0.487020\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −26.4283 | −1.08255 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 60.5249 | 2.47505 | ||||||||
\(599\) | 21.3526 | 0.872445 | 0.436222 | − | 0.899839i | \(-0.356316\pi\) | ||||
0.436222 | + | 0.899839i | \(0.356316\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.2480 | −0.744350 | −0.372175 | − | 0.928163i | \(-0.621388\pi\) | ||||
−0.372175 | + | 0.928163i | \(0.621388\pi\) | |||||||
\(602\) | −9.71340 | −0.395889 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −43.5330 | −1.77133 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.6353 | 0.959327 | 0.479663 | − | 0.877453i | \(-0.340759\pi\) | ||||
0.479663 | + | 0.877453i | \(0.340759\pi\) | |||||||
\(608\) | −15.3719 | −0.623415 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.10622 | 0.327942 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.9122 | 1.49087 | 0.745435 | − | 0.666578i | \(-0.232242\pi\) | ||||
0.745435 | + | 0.666578i | \(0.232242\pi\) | |||||||
\(614\) | 30.4323 | 1.22815 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.51854 | 0.222348 | ||||||||
\(617\) | 14.6908 | 0.591429 | 0.295714 | − | 0.955276i | \(-0.404442\pi\) | ||||
0.295714 | + | 0.955276i | \(0.404442\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.3487 | −0.978656 | −0.489328 | − | 0.872100i | \(-0.662758\pi\) | ||||
−0.489328 | + | 0.872100i | \(0.662758\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.53302 | 0.141661 | ||||||||
\(623\) | −0.0410286 | −0.00164378 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 55.0169 | 2.19892 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −116.057 | −4.63118 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.3237 | 0.848882 | 0.424441 | − | 0.905455i | \(-0.360471\pi\) | ||||
0.424441 | + | 0.905455i | \(0.360471\pi\) | |||||||
\(632\) | −74.8220 | −2.97626 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 48.5032 | 1.92631 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.6763 | −0.898468 | ||||||||
\(638\) | 11.6498 | 0.461219 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.9919 | 1.06611 | 0.533057 | − | 0.846079i | \(-0.321043\pi\) | ||||
0.533057 | + | 0.846079i | \(0.321043\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −40.1683 | −1.58408 | −0.792042 | − | 0.610467i | \(-0.790982\pi\) | ||||
−0.792042 | + | 0.610467i | \(0.790982\pi\) | |||||||
\(644\) | 15.8341 | 0.623951 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.2890 | −0.679701 | −0.339850 | − | 0.940480i | \(-0.610376\pi\) | ||||
−0.339850 | + | 0.940480i | \(0.610376\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.9774 | −0.430900 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −19.0893 | −0.747594 | ||||||||
\(653\) | −21.6537 | −0.847375 | −0.423688 | − | 0.905808i | \(-0.639265\pi\) | ||||
−0.423688 | + | 0.905808i | \(0.639265\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −47.7101 | −1.86277 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.94844 | 0.114942 | ||||||||
\(659\) | 11.6392 | 0.453400 | 0.226700 | − | 0.973965i | \(-0.427206\pi\) | ||||
0.226700 | + | 0.973965i | \(0.427206\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.96292 | −0.193035 | −0.0965175 | − | 0.995331i | \(-0.530770\pi\) | ||||
−0.0965175 | + | 0.995331i | \(0.530770\pi\) | |||||||
\(662\) | 52.1071 | 2.02520 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 37.8977 | 1.47072 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.3792 | 0.789085 | ||||||||
\(668\) | 62.6223 | 2.42293 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.68840 | −0.219598 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.1578 | −0.507195 | −0.253597 | − | 0.967310i | \(-0.581614\pi\) | ||||
−0.253597 | + | 0.967310i | \(0.581614\pi\) | |||||||
\(674\) | 1.10467 | 0.0425502 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.51370 | −0.365912 | ||||||||
\(677\) | −13.1352 | −0.504825 | −0.252413 | − | 0.967620i | \(-0.581224\pi\) | ||||
−0.252413 | + | 0.967620i | \(0.581224\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.46543 | 0.209744 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −34.1457 | −1.30751 | ||||||||
\(683\) | 46.5370 | 1.78069 | 0.890344 | − | 0.455289i | \(-0.150464\pi\) | ||||
0.890344 | + | 0.455289i | \(0.150464\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −16.7472 | −0.639411 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −96.0579 | −3.66217 | ||||||||
\(689\) | 45.6537 | 1.73927 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.26244 | −0.162151 | −0.0810754 | − | 0.996708i | \(-0.525835\pi\) | ||||
−0.0810754 | + | 0.996708i | \(0.525835\pi\) | |||||||
\(692\) | 123.858 | 4.70838 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 82.5394 | 3.13315 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 39.4130 | 1.49180 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.4428 | 1.37643 | 0.688213 | − | 0.725508i | \(-0.258395\pi\) | ||||
0.688213 | + | 0.725508i | \(0.258395\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.2480 | −0.386509 | ||||||||
\(704\) | 24.7544 | 0.932968 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 73.4878 | 2.76575 | ||||||||
\(707\) | 2.51041 | 0.0944136 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.23349 | −0.196548 | −0.0982740 | − | 0.995159i | \(-0.531332\pi\) | ||||
−0.0982740 | + | 0.995159i | \(0.531332\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.752034 | −0.0281837 | ||||||||
\(713\) | −59.7318 | −2.23697 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 31.8784 | 1.19135 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10.2335 | −0.381911 | ||||||||
\(719\) | −50.2809 | −1.87516 | −0.937580 | − | 0.347770i | \(-0.886939\pi\) | ||||
−0.937580 | + | 0.347770i | \(0.886939\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.15777 | −0.0431178 | ||||||||
\(722\) | −2.66908 | −0.0993328 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −105.021 | −3.90307 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.81567 | 0.104427 | 0.0522137 | − | 0.998636i | \(-0.483372\pi\) | ||||
0.0522137 | + | 0.998636i | \(0.483372\pi\) | |||||||
\(728\) | 12.6618 | 0.469279 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.23349 | −0.341047 | −0.170523 | − | 0.985354i | \(-0.554546\pi\) | ||||
−0.170523 | + | 0.985354i | \(0.554546\pi\) | |||||||
\(734\) | 56.6522 | 2.09107 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 104.423 | 3.84907 | ||||||||
\(737\) | −20.5596 | −0.757322 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.1843 | −0.411422 | −0.205711 | − | 0.978613i | \(-0.565951\pi\) | ||||
−0.205711 | + | 0.978613i | \(0.565951\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 16.6054 | 0.609605 | ||||||||
\(743\) | −23.1602 | −0.849664 | −0.424832 | − | 0.905272i | \(-0.639667\pi\) | ||||
−0.424832 | + | 0.905272i | \(0.639667\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −59.4202 | −2.17553 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.10861 | 0.0770470 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.7520 | 0.428838 | 0.214419 | − | 0.976742i | \(-0.431214\pi\) | ||||
0.214419 | + | 0.976742i | \(0.431214\pi\) | |||||||
\(752\) | 29.1578 | 1.06327 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 26.7294 | 0.973428 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.6232 | −0.640526 | −0.320263 | − | 0.947329i | \(-0.603771\pi\) | ||||
−0.320263 | + | 0.947329i | \(0.603771\pi\) | |||||||
\(758\) | 8.90981 | 0.323619 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.5556 | 0.817641 | 0.408820 | − | 0.912615i | \(-0.365940\pi\) | ||||
0.408820 | + | 0.912615i | \(0.365940\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.84223 | 0.102895 | ||||||||
\(764\) | −4.06364 | −0.147017 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −92.1819 | −3.33067 | ||||||||
\(767\) | −25.1867 | −0.909440 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.8486 | −0.968184 | −0.484092 | − | 0.875017i | \(-0.660850\pi\) | ||||
−0.484092 | + | 0.875017i | \(0.660850\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 81.0594 | 2.91739 | ||||||||
\(773\) | −33.8751 | −1.21840 | −0.609202 | − | 0.793015i | \(-0.708510\pi\) | ||||
−0.609202 | + | 0.793015i | \(0.708510\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 100.179 | 3.59620 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 50.9919 | 1.82815 | ||||||||
\(779\) | −3.97345 | −0.142363 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.2850 | 0.475376 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −81.5659 | −2.91307 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.0781 | 1.07217 | 0.536084 | − | 0.844164i | \(-0.319903\pi\) | ||||
0.536084 | + | 0.844164i | \(0.319903\pi\) | |||||||
\(788\) | 19.2254 | 0.684875 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.36866 | 0.0842198 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.0516 | −0.463474 | ||||||||
\(794\) | 36.9138 | 1.31002 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 33.0748 | 1.17231 | ||||||||
\(797\) | −29.3792 | −1.04066 | −0.520332 | − | 0.853964i | \(-0.674192\pi\) | ||||
−0.520332 | + | 0.853964i | \(0.674192\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18.1312 | 0.640236 | ||||||||
\(803\) | 16.9879 | 0.599491 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −78.3445 | −2.75957 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 46.0145 | 1.61878 | ||||||||
\(809\) | 45.7358 | 1.60798 | 0.803992 | − | 0.594640i | \(-0.202705\pi\) | ||||
0.803992 | + | 0.594640i | \(0.202705\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.10227 | 0.214280 | 0.107140 | − | 0.994244i | \(-0.465831\pi\) | ||||
0.107140 | + | 0.994244i | \(0.465831\pi\) | |||||||
\(812\) | 6.99276 | 0.245398 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 39.7955 | 1.39483 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.00000 | −0.279885 | ||||||||
\(818\) | 33.3913 | 1.16750 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.2175 | 0.391492 | 0.195746 | − | 0.980655i | \(-0.437287\pi\) | ||||
0.195746 | + | 0.980655i | \(0.437287\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.6353 | −0.858732 | −0.429366 | − | 0.903131i | \(-0.641263\pi\) | ||||
−0.429366 | + | 0.903131i | \(0.641263\pi\) | |||||||
\(824\) | −21.2214 | −0.739283 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.16107 | −0.318754 | ||||||||
\(827\) | −32.6311 | −1.13469 | −0.567347 | − | 0.823479i | \(-0.692030\pi\) | ||||
−0.567347 | + | 0.823479i | \(0.692030\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.3382 | −1.15788 | −0.578941 | − | 0.815369i | \(-0.696534\pi\) | ||||
−0.578941 | + | 0.815369i | \(0.696534\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 56.7970 | 1.96908 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7.45490 | 0.257833 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.51854 | −0.190635 | ||||||||
\(839\) | −51.1312 | −1.76525 | −0.882623 | − | 0.470082i | \(-0.844224\pi\) | ||||
−0.882623 | + | 0.470082i | \(0.844224\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 9.39127 | 0.323644 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 122.798 | 4.22688 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.04103 | 0.138851 | ||||||||
\(848\) | 164.215 | 5.63916 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 69.6151 | 2.38637 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40.9122 | −1.40081 | −0.700404 | − | 0.713747i | \(-0.746997\pi\) | ||||
−0.700404 | + | 0.713747i | \(0.746997\pi\) | |||||||
\(854\) | −4.74719 | −0.162446 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 38.6498 | 1.32102 | ||||||||
\(857\) | 17.8220 | 0.608788 | 0.304394 | − | 0.952546i | \(-0.401546\pi\) | ||||
0.304394 | + | 0.952546i | \(0.401546\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.1231 | 0.481873 | 0.240937 | − | 0.970541i | \(-0.422545\pi\) | ||||
0.240937 | + | 0.970541i | \(0.422545\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 83.9339 | 2.85880 | ||||||||
\(863\) | −32.4307 | −1.10396 | −0.551978 | − | 0.833859i | \(-0.686127\pi\) | ||||
−0.551978 | + | 0.833859i | \(0.686127\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −55.9903 | −1.90263 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −20.4959 | −0.695677 | ||||||||
\(869\) | 13.0555 | 0.442878 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −47.1722 | −1.59837 | ||||||||
\(872\) | 52.0965 | 1.76421 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 18.1312 | 0.613298 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.9243 | −0.706563 | −0.353281 | − | 0.935517i | \(-0.614934\pi\) | ||||
−0.353281 | + | 0.935517i | \(0.614934\pi\) | |||||||
\(878\) | −10.0250 | −0.338327 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.3671 | 1.05678 | 0.528392 | − | 0.849000i | \(-0.322795\pi\) | ||||
0.528392 | + | 0.849000i | \(0.322795\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.635288 | −0.0213791 | −0.0106896 | − | 0.999943i | \(-0.503403\pi\) | ||||
−0.0106896 | + | 0.999943i | \(0.503403\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 53.4307 | 1.79504 | ||||||||
\(887\) | −55.0660 | −1.84894 | −0.924468 | − | 0.381259i | \(-0.875491\pi\) | ||||
−0.924468 | + | 0.381259i | \(0.875491\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.82775 | −0.161918 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 16.4323 | 0.550194 | ||||||||
\(893\) | 2.42835 | 0.0812616 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 6.67302 | 0.222930 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 59.8027 | 1.99564 | ||||||||
\(899\) | −26.3792 | −0.879795 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 15.4299 | 0.513759 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 43.4163 | 1.44400 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.49593 | 0.282103 | 0.141051 | − | 0.990002i | \(-0.454952\pi\) | ||||
0.141051 | + | 0.990002i | \(0.454952\pi\) | |||||||
\(908\) | −46.7882 | −1.55272 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −58.9798 | −1.95409 | −0.977044 | − | 0.213039i | \(-0.931664\pi\) | ||||
−0.977044 | + | 0.213039i | \(0.931664\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.61268 | −0.218848 | ||||||||
\(914\) | 91.5200 | 3.02721 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 85.7752 | 2.83409 | ||||||||
\(917\) | 9.87272 | 0.326026 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.22141 | 0.271199 | 0.135600 | − | 0.990764i | \(-0.456704\pi\) | ||||
0.135600 | + | 0.990764i | \(0.456704\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 38.7294 | 1.27549 | ||||||||
\(923\) | 30.4815 | 1.00331 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 90.3445 | 2.96890 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 46.1158 | 1.51383 | ||||||||
\(929\) | −1.76651 | −0.0579573 | −0.0289786 | − | 0.999580i | \(-0.509225\pi\) | ||||
−0.0289786 | + | 0.999580i | \(0.509225\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.79306 | −0.222634 | ||||||||
\(932\) | −49.0450 | −1.60652 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 24.6127 | 0.805351 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.20694 | 0.202772 | 0.101386 | − | 0.994847i | \(-0.467672\pi\) | ||||
0.101386 | + | 0.994847i | \(0.467672\pi\) | |||||||
\(938\) | −17.1578 | −0.560221 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.8833 | −0.517779 | −0.258890 | − | 0.965907i | \(-0.583357\pi\) | ||||
−0.258890 | + | 0.965907i | \(0.583357\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26.9919 | 0.878976 | ||||||||
\(944\) | −90.5958 | −2.94864 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 31.0660 | 1.01004 | ||||||||
\(947\) | 16.1352 | 0.524322 | 0.262161 | − | 0.965024i | \(-0.415565\pi\) | ||||
0.262161 | + | 0.965024i | \(0.415565\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 38.9774 | 1.26526 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 41.1110 | 1.33172 | 0.665858 | − | 0.746078i | \(-0.268066\pi\) | ||||
0.665858 | + | 0.746078i | \(0.268066\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −89.7647 | −2.90320 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 72.8751 | 2.35449 | ||||||||
\(959\) | −10.1514 | −0.327807 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 46.3179 | 1.49413 | ||||||||
\(962\) | 91.3074 | 2.94387 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 86.6456 | 2.79067 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.9798 | −0.996243 | −0.498121 | − | 0.867107i | \(-0.665977\pi\) | ||||
−0.498121 | + | 0.867107i | \(0.665977\pi\) | |||||||
\(968\) | 74.0700 | 2.38070 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −51.2133 | −1.64351 | −0.821756 | − | 0.569839i | \(-0.807005\pi\) | ||||
−0.821756 | + | 0.569839i | \(0.807005\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.73182 | 0.151695 | ||||||||
\(974\) | 38.6522 | 1.23850 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −46.9460 | −1.50270 | ||||||||
\(977\) | 20.2093 | 0.646554 | 0.323277 | − | 0.946304i | \(-0.395215\pi\) | ||||
0.323277 | + | 0.946304i | \(0.395215\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.131220 | 0.00419382 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −101.984 | −3.25443 | ||||||||
\(983\) | 41.1191 | 1.31150 | 0.655748 | − | 0.754979i | \(-0.272353\pi\) | ||||
0.655748 | + | 0.754979i | \(0.272353\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 17.1047 | 0.544172 | ||||||||
\(989\) | 54.3445 | 1.72805 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.4549 | 0.872134 | 0.436067 | − | 0.899914i | \(-0.356371\pi\) | ||||
0.436067 | + | 0.899914i | \(0.356371\pi\) | |||||||
\(992\) | −135.167 | −4.29154 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 11.0869 | 0.351655 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.1086 | −0.415154 | −0.207577 | − | 0.978219i | \(-0.566558\pi\) | ||||
−0.207577 | + | 0.978219i | \(0.566558\pi\) | |||||||
\(998\) | −94.9499 | −3.00559 | ||||||||
\(999\) | 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 | 4275.2.a.be.1.1 | 3 | ||
3.2 | odd | 2 | 1425.2.a.u.1.3 | ✓ | 3 | ||
5.4 | even | 2 | 4275.2.a.bh.1.3 | 3 | |||
15.2 | even | 4 | 1425.2.c.p.799.6 | 6 | |||
15.8 | even | 4 | 1425.2.c.p.799.1 | 6 | |||
15.14 | odd | 2 | 1425.2.a.v.1.1 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1425.2.a.u.1.3 | ✓ | 3 | 3.2 | odd | 2 | ||
1425.2.a.v.1.1 | yes | 3 | 15.14 | odd | 2 | ||
1425.2.c.p.799.1 | 6 | 15.8 | even | 4 | |||
1425.2.c.p.799.6 | 6 | 15.2 | even | 4 | |||
4275.2.a.be.1.1 | 3 | 1.1 | even | 1 | trivial | ||
4275.2.a.bh.1.3 | 3 | 5.4 | even | 2 |