Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2009,2,Mod(1,2009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2009, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2009 = 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2009.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: | \(16.0419457661\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.257.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.713538\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.49086 | 1.76131 | 0.880653 | − | 0.473761i | \(-0.157104\pi\) | ||||
0.880653 | + | 0.473761i | \(0.157104\pi\) | |||||||
\(3\) | 1.49086 | 0.860751 | 0.430375 | − | 0.902650i | \(-0.358381\pi\) | ||||
0.430375 | + | 0.902650i | \(0.358381\pi\) | |||||||
\(4\) | 4.20440 | 2.10220 | ||||||||
\(5\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(6\) | 3.71354 | 1.51605 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 5.49086 | 1.94131 | ||||||||
\(9\) | −0.777326 | −0.259109 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.42708 | −1.03330 | −0.516651 | − | 0.856196i | \(-0.672822\pi\) | ||||
−0.516651 | + | 0.856196i | \(0.672822\pi\) | |||||||
\(12\) | 6.26819 | 1.80947 | ||||||||
\(13\) | 6.26819 | 1.73848 | 0.869241 | − | 0.494388i | \(-0.164608\pi\) | ||||
0.869241 | + | 0.494388i | \(0.164608\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.26819 | 1.31705 | ||||||||
\(17\) | 5.20440 | 1.26225 | 0.631126 | − | 0.775680i | \(-0.282593\pi\) | ||||
0.631126 | + | 0.775680i | \(0.282593\pi\) | |||||||
\(18\) | −1.93621 | −0.456370 | ||||||||
\(19\) | 2.22267 | 0.509916 | 0.254958 | − | 0.966952i | \(-0.417938\pi\) | ||||
0.254958 | + | 0.966952i | \(0.417938\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.53638 | −1.81996 | ||||||||
\(23\) | 2.91794 | 0.608432 | 0.304216 | − | 0.952603i | \(-0.401605\pi\) | ||||
0.304216 | + | 0.952603i | \(0.401605\pi\) | |||||||
\(24\) | 8.18613 | 1.67099 | ||||||||
\(25\) | −5.00000 | −1.00000 | ||||||||
\(26\) | 15.6132 | 3.06200 | ||||||||
\(27\) | −5.63148 | −1.08378 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.98173 | 0.925084 | 0.462542 | − | 0.886597i | \(-0.346938\pi\) | ||||
0.462542 | + | 0.886597i | \(0.346938\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.854152 | 0.153410 | 0.0767051 | − | 0.997054i | \(-0.475560\pi\) | ||||
0.0767051 | + | 0.997054i | \(0.475560\pi\) | |||||||
\(32\) | 2.14061 | 0.378411 | ||||||||
\(33\) | −5.10930 | −0.889415 | ||||||||
\(34\) | 12.9635 | 2.22321 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.26819 | −0.544698 | ||||||||
\(37\) | 0.268189 | 0.0440900 | 0.0220450 | − | 0.999757i | \(-0.492982\pi\) | ||||
0.0220450 | + | 0.999757i | \(0.492982\pi\) | |||||||
\(38\) | 5.53638 | 0.898119 | ||||||||
\(39\) | 9.34502 | 1.49640 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.20440 | −0.488667 | −0.244333 | − | 0.969691i | \(-0.578569\pi\) | ||||
−0.244333 | + | 0.969691i | \(0.578569\pi\) | |||||||
\(44\) | −14.4088 | −2.17221 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.26819 | 1.07164 | ||||||||
\(47\) | −4.14061 | −0.603971 | −0.301985 | − | 0.953313i | \(-0.597649\pi\) | ||||
−0.301985 | + | 0.953313i | \(0.597649\pi\) | |||||||
\(48\) | 7.85415 | 1.13365 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −12.4543 | −1.76131 | ||||||||
\(51\) | 7.75905 | 1.08648 | ||||||||
\(52\) | 26.3540 | 3.65464 | ||||||||
\(53\) | −3.42708 | −0.470745 | −0.235373 | − | 0.971905i | \(-0.575631\pi\) | ||||
−0.235373 | + | 0.971905i | \(0.575631\pi\) | |||||||
\(54\) | −14.0272 | −1.90887 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.31370 | 0.438911 | ||||||||
\(58\) | 12.4088 | 1.62936 | ||||||||
\(59\) | 2.12758 | 0.276987 | 0.138493 | − | 0.990363i | \(-0.455774\pi\) | ||||
0.138493 | + | 0.990363i | \(0.455774\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.2447 | −1.82384 | −0.911922 | − | 0.410363i | \(-0.865402\pi\) | ||||
−0.911922 | + | 0.410363i | \(0.865402\pi\) | |||||||
\(62\) | 2.12758 | 0.270202 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.20440 | −0.650550 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −12.7266 | −1.56653 | ||||||||
\(67\) | 6.12758 | 0.748602 | 0.374301 | − | 0.927307i | \(-0.377883\pi\) | ||||
0.374301 | + | 0.927307i | \(0.377883\pi\) | |||||||
\(68\) | 21.8814 | 2.65351 | ||||||||
\(69\) | 4.35025 | 0.523709 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.55465 | −0.896572 | −0.448286 | − | 0.893890i | \(-0.647965\pi\) | ||||
−0.448286 | + | 0.893890i | \(0.647965\pi\) | |||||||
\(72\) | −4.26819 | −0.503011 | ||||||||
\(73\) | −12.5364 | −1.46727 | −0.733636 | − | 0.679543i | \(-0.762178\pi\) | ||||
−0.733636 | + | 0.679543i | \(0.762178\pi\) | |||||||
\(74\) | 0.668023 | 0.0776561 | ||||||||
\(75\) | −7.45432 | −0.860751 | ||||||||
\(76\) | 9.34502 | 1.07195 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 23.2772 | 2.63562 | ||||||||
\(79\) | −6.00000 | −0.675053 | −0.337526 | − | 0.941316i | \(-0.609590\pi\) | ||||
−0.337526 | + | 0.941316i | \(0.609590\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.06379 | −0.673754 | ||||||||
\(82\) | −2.49086 | −0.275070 | ||||||||
\(83\) | 10.4088 | 1.14251 | 0.571257 | − | 0.820771i | \(-0.306456\pi\) | ||||
0.571257 | + | 0.820771i | \(0.306456\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −7.98173 | −0.860692 | ||||||||
\(87\) | 7.42708 | 0.796266 | ||||||||
\(88\) | −18.8176 | −2.00596 | ||||||||
\(89\) | 6.26819 | 0.664427 | 0.332213 | − | 0.943204i | \(-0.392205\pi\) | ||||
0.332213 | + | 0.943204i | \(0.392205\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 12.2682 | 1.27905 | ||||||||
\(93\) | 1.27342 | 0.132048 | ||||||||
\(94\) | −10.3137 | −1.06378 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.19136 | 0.325717 | ||||||||
\(97\) | 8.06379 | 0.818754 | 0.409377 | − | 0.912365i | \(-0.365746\pi\) | ||||
0.409377 | + | 0.912365i | \(0.365746\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.66395 | 0.267737 | ||||||||
\(100\) | −21.0220 | −2.10220 | ||||||||
\(101\) | −12.7538 | −1.26905 | −0.634526 | − | 0.772901i | \(-0.718805\pi\) | ||||
−0.634526 | + | 0.772901i | \(0.718805\pi\) | |||||||
\(102\) | 19.3267 | 1.91363 | ||||||||
\(103\) | −13.3905 | −1.31941 | −0.659704 | − | 0.751525i | \(-0.729318\pi\) | ||||
−0.659704 | + | 0.751525i | \(0.729318\pi\) | |||||||
\(104\) | 34.4178 | 3.37494 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.53638 | −0.829126 | ||||||||
\(107\) | 9.61320 | 0.929344 | 0.464672 | − | 0.885483i | \(-0.346172\pi\) | ||||
0.464672 | + | 0.885483i | \(0.346172\pi\) | |||||||
\(108\) | −23.6770 | −2.27832 | ||||||||
\(109\) | −8.53638 | −0.817637 | −0.408818 | − | 0.912616i | \(-0.634059\pi\) | ||||
−0.408818 | + | 0.912616i | \(0.634059\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.399834 | 0.0379505 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.4726 | −1.54961 | −0.774805 | − | 0.632200i | \(-0.782152\pi\) | ||||
−0.774805 | + | 0.632200i | \(0.782152\pi\) | |||||||
\(114\) | 8.25399 | 0.773057 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 20.9452 | 1.94471 | ||||||||
\(117\) | −4.87242 | −0.450456 | ||||||||
\(118\) | 5.29950 | 0.487859 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.744849 | 0.0677135 | ||||||||
\(122\) | −35.4816 | −3.21235 | ||||||||
\(123\) | −1.49086 | −0.134427 | ||||||||
\(124\) | 3.59120 | 0.322499 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.14061 | 0.544891 | 0.272446 | − | 0.962171i | \(-0.412167\pi\) | ||||
0.272446 | + | 0.962171i | \(0.412167\pi\) | |||||||
\(128\) | −17.2447 | −1.52423 | ||||||||
\(129\) | −4.77733 | −0.420620 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.59120 | 0.313764 | 0.156882 | − | 0.987617i | \(-0.449856\pi\) | ||||
0.156882 | + | 0.987617i | \(0.449856\pi\) | |||||||
\(132\) | −21.4816 | −1.86973 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 15.2630 | 1.31852 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 28.5767 | 2.45043 | ||||||||
\(137\) | −16.8176 | −1.43683 | −0.718413 | − | 0.695617i | \(-0.755131\pi\) | ||||
−0.718413 | + | 0.695617i | \(0.755131\pi\) | |||||||
\(138\) | 10.8359 | 0.922411 | ||||||||
\(139\) | 17.8359 | 1.51282 | 0.756410 | − | 0.654098i | \(-0.226952\pi\) | ||||
0.756410 | + | 0.654098i | \(0.226952\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.17309 | −0.519868 | ||||||||
\(142\) | −18.8176 | −1.57914 | ||||||||
\(143\) | −21.4816 | −1.79638 | ||||||||
\(144\) | −4.09510 | −0.341258 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −31.2264 | −2.58432 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.12758 | 0.0926861 | ||||||||
\(149\) | −14.9452 | −1.22436 | −0.612178 | − | 0.790720i | \(-0.709707\pi\) | ||||
−0.612178 | + | 0.790720i | \(0.709707\pi\) | |||||||
\(150\) | −18.5677 | −1.51605 | ||||||||
\(151\) | −4.94518 | −0.402433 | −0.201217 | − | 0.979547i | \(-0.564490\pi\) | ||||
−0.201217 | + | 0.979547i | \(0.564490\pi\) | |||||||
\(152\) | 12.2044 | 0.989908 | ||||||||
\(153\) | −4.04551 | −0.327061 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 39.2902 | 3.14573 | ||||||||
\(157\) | 9.45955 | 0.754954 | 0.377477 | − | 0.926019i | \(-0.376792\pi\) | ||||
0.377477 | + | 0.926019i | \(0.376792\pi\) | |||||||
\(158\) | −14.9452 | −1.18897 | ||||||||
\(159\) | −5.10930 | −0.405194 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −15.1041 | −1.18669 | ||||||||
\(163\) | 4.19136 | 0.328293 | 0.164146 | − | 0.986436i | \(-0.447513\pi\) | ||||
0.164146 | + | 0.986436i | \(0.447513\pi\) | |||||||
\(164\) | −4.20440 | −0.328309 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 25.9269 | 2.01232 | ||||||||
\(167\) | 10.9232 | 0.845261 | 0.422630 | − | 0.906302i | \(-0.361107\pi\) | ||||
0.422630 | + | 0.906302i | \(0.361107\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 26.2902 | 2.02232 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.72774 | −0.132124 | ||||||||
\(172\) | −13.4726 | −1.02728 | ||||||||
\(173\) | −3.59120 | −0.273034 | −0.136517 | − | 0.990638i | \(-0.543591\pi\) | ||||
−0.136517 | + | 0.990638i | \(0.543591\pi\) | |||||||
\(174\) | 18.4998 | 1.40247 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −18.0545 | −1.36091 | ||||||||
\(177\) | 3.17192 | 0.238416 | ||||||||
\(178\) | 15.6132 | 1.17026 | ||||||||
\(179\) | −24.9086 | −1.86176 | −0.930879 | − | 0.365327i | \(-0.880957\pi\) | ||||
−0.930879 | + | 0.365327i | \(0.880957\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.06379 | 0.599377 | 0.299688 | − | 0.954037i | \(-0.403117\pi\) | ||||
0.299688 | + | 0.954037i | \(0.403117\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −21.2369 | −1.56988 | ||||||||
\(184\) | 16.0220 | 1.18116 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.17192 | 0.232577 | ||||||||
\(187\) | −17.8359 | −1.30429 | ||||||||
\(188\) | −17.4088 | −1.26967 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.6640 | 1.63991 | 0.819953 | − | 0.572431i | \(-0.193999\pi\) | ||||
0.819953 | + | 0.572431i | \(0.193999\pi\) | |||||||
\(192\) | −7.75905 | −0.559961 | ||||||||
\(193\) | 12.9452 | 0.931815 | 0.465907 | − | 0.884834i | \(-0.345728\pi\) | ||||
0.465907 | + | 0.884834i | \(0.345728\pi\) | |||||||
\(194\) | 20.0858 | 1.44208 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.8866 | 1.34562 | 0.672808 | − | 0.739817i | \(-0.265088\pi\) | ||||
0.672808 | + | 0.739817i | \(0.265088\pi\) | |||||||
\(198\) | 6.63555 | 0.471568 | ||||||||
\(199\) | 23.2499 | 1.64814 | 0.824071 | − | 0.566486i | \(-0.191697\pi\) | ||||
0.824071 | + | 0.566486i | \(0.191697\pi\) | |||||||
\(200\) | −27.4543 | −1.94131 | ||||||||
\(201\) | 9.13538 | 0.644360 | ||||||||
\(202\) | −31.7680 | −2.23519 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 32.6222 | 2.28401 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −33.3540 | −2.32388 | ||||||||
\(207\) | −2.26819 | −0.157650 | ||||||||
\(208\) | 33.0220 | 2.28966 | ||||||||
\(209\) | −7.61727 | −0.526898 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 28.5364 | 1.96453 | 0.982263 | − | 0.187510i | \(-0.0600418\pi\) | ||||
0.982263 | + | 0.187510i | \(0.0600418\pi\) | |||||||
\(212\) | −14.4088 | −0.989601 | ||||||||
\(213\) | −11.2630 | −0.771725 | ||||||||
\(214\) | 23.9452 | 1.63686 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −30.9217 | −2.10395 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −21.2630 | −1.44011 | ||||||||
\(219\) | −18.6900 | −1.26296 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 32.6222 | 2.19440 | ||||||||
\(222\) | 0.995931 | 0.0668425 | ||||||||
\(223\) | 5.29950 | 0.354881 | 0.177440 | − | 0.984132i | \(-0.443218\pi\) | ||||
0.177440 | + | 0.984132i | \(0.443218\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.88663 | 0.259109 | ||||||||
\(226\) | −41.0310 | −2.72934 | ||||||||
\(227\) | 25.0728 | 1.66414 | 0.832069 | − | 0.554673i | \(-0.187156\pi\) | ||||
0.832069 | + | 0.554673i | \(0.187156\pi\) | |||||||
\(228\) | 13.9321 | 0.922679 | ||||||||
\(229\) | −17.0090 | −1.12398 | −0.561992 | − | 0.827143i | \(-0.689965\pi\) | ||||
−0.561992 | + | 0.827143i | \(0.689965\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 27.3540 | 1.79588 | ||||||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | −12.1365 | −0.793391 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 8.94518 | 0.582282 | ||||||||
\(237\) | −8.94518 | −0.581052 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.26295 | −0.599171 | −0.299585 | − | 0.954069i | \(-0.596848\pi\) | ||||
−0.299585 | + | 0.954069i | \(0.596848\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.29950 | 0.341371 | 0.170685 | − | 0.985326i | \(-0.445402\pi\) | ||||
0.170685 | + | 0.985326i | \(0.445402\pi\) | |||||||
\(242\) | 1.85532 | 0.119264 | ||||||||
\(243\) | 7.85415 | 0.503844 | ||||||||
\(244\) | −59.8904 | −3.83409 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.71354 | −0.236767 | ||||||||
\(247\) | 13.9321 | 0.886481 | ||||||||
\(248\) | 4.69003 | 0.297817 | ||||||||
\(249\) | 15.5181 | 0.983420 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.84635 | −0.495257 | −0.247629 | − | 0.968855i | \(-0.579651\pi\) | ||||
−0.247629 | + | 0.968855i | \(0.579651\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.0000 | −0.628695 | ||||||||
\(254\) | 15.2954 | 0.959721 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32.5453 | −2.03408 | ||||||||
\(257\) | −19.9362 | −1.24359 | −0.621793 | − | 0.783181i | \(-0.713596\pi\) | ||||
−0.621793 | + | 0.783181i | \(0.713596\pi\) | |||||||
\(258\) | −11.8997 | −0.740841 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.87242 | −0.239697 | ||||||||
\(262\) | 8.94518 | 0.552635 | ||||||||
\(263\) | 27.7993 | 1.71418 | 0.857090 | − | 0.515166i | \(-0.172270\pi\) | ||||
0.857090 | + | 0.515166i | \(0.172270\pi\) | |||||||
\(264\) | −28.0545 | −1.72663 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.34502 | 0.571906 | ||||||||
\(268\) | 25.7628 | 1.57371 | ||||||||
\(269\) | −31.8904 | −1.94439 | −0.972195 | − | 0.234173i | \(-0.924762\pi\) | ||||
−0.972195 | + | 0.234173i | \(0.924762\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.6900 | 1.13534 | 0.567669 | − | 0.823257i | \(-0.307845\pi\) | ||||
0.567669 | + | 0.823257i | \(0.307845\pi\) | |||||||
\(272\) | 27.4178 | 1.66245 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −41.8904 | −2.53069 | ||||||||
\(275\) | 17.1354 | 1.03330 | ||||||||
\(276\) | 18.2902 | 1.10094 | ||||||||
\(277\) | 20.3450 | 1.22241 | 0.611207 | − | 0.791471i | \(-0.290684\pi\) | ||||
0.611207 | + | 0.791471i | \(0.290684\pi\) | |||||||
\(278\) | 44.4267 | 2.66454 | ||||||||
\(279\) | −0.663954 | −0.0397499 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.9635 | 1.31023 | 0.655115 | − | 0.755529i | \(-0.272620\pi\) | ||||
0.655115 | + | 0.755529i | \(0.272620\pi\) | |||||||
\(282\) | −15.3763 | −0.915647 | ||||||||
\(283\) | 20.5729 | 1.22293 | 0.611467 | − | 0.791270i | \(-0.290580\pi\) | ||||
0.611467 | + | 0.791270i | \(0.290580\pi\) | |||||||
\(284\) | −31.7628 | −1.88477 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −53.5076 | −3.16397 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.66395 | −0.0980494 | ||||||||
\(289\) | 10.0858 | 0.593282 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.0220 | 0.704743 | ||||||||
\(292\) | −52.7080 | −3.08450 | ||||||||
\(293\) | −11.0728 | −0.646877 | −0.323439 | − | 0.946249i | \(-0.604839\pi\) | ||||
−0.323439 | + | 0.946249i | \(0.604839\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.47259 | 0.0855926 | ||||||||
\(297\) | 19.2995 | 1.11987 | ||||||||
\(298\) | −37.2264 | −2.15647 | ||||||||
\(299\) | 18.2902 | 1.05775 | ||||||||
\(300\) | −31.3409 | −1.80947 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −12.3178 | −0.708808 | ||||||||
\(303\) | −19.0142 | −1.09234 | ||||||||
\(304\) | 11.7095 | 0.671584 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −10.0768 | −0.576054 | ||||||||
\(307\) | −12.5364 | −0.715489 | −0.357744 | − | 0.933820i | \(-0.616454\pi\) | ||||
−0.357744 | + | 0.933820i | \(0.616454\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.9635 | −1.13568 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.5584 | −1.39258 | −0.696289 | − | 0.717761i | \(-0.745167\pi\) | ||||
−0.696289 | + | 0.717761i | \(0.745167\pi\) | |||||||
\(312\) | 51.3122 | 2.90498 | ||||||||
\(313\) | 13.9049 | 0.785951 | 0.392976 | − | 0.919549i | \(-0.371446\pi\) | ||||
0.392976 | + | 0.919549i | \(0.371446\pi\) | |||||||
\(314\) | 23.5625 | 1.32971 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −25.2264 | −1.41910 | ||||||||
\(317\) | −5.14585 | −0.289020 | −0.144510 | − | 0.989503i | \(-0.546161\pi\) | ||||
−0.144510 | + | 0.989503i | \(0.546161\pi\) | |||||||
\(318\) | −12.7266 | −0.713671 | ||||||||
\(319\) | −17.0728 | −0.955891 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.3320 | 0.799933 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.5677 | 0.643643 | ||||||||
\(324\) | −25.4946 | −1.41637 | ||||||||
\(325\) | −31.3409 | −1.73848 | ||||||||
\(326\) | 10.4401 | 0.578224 | ||||||||
\(327\) | −12.7266 | −0.703781 | ||||||||
\(328\) | −5.49086 | −0.303182 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.8176 | −1.47403 | −0.737014 | − | 0.675877i | \(-0.763765\pi\) | ||||
−0.737014 | + | 0.675877i | \(0.763765\pi\) | |||||||
\(332\) | 43.7628 | 2.40180 | ||||||||
\(333\) | −0.208470 | −0.0114241 | ||||||||
\(334\) | 27.2081 | 1.48876 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.34502 | 0.236688 | 0.118344 | − | 0.992973i | \(-0.462241\pi\) | ||||
0.118344 | + | 0.992973i | \(0.462241\pi\) | |||||||
\(338\) | 65.4853 | 3.56193 | ||||||||
\(339\) | −24.5584 | −1.33383 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.92724 | −0.158519 | ||||||||
\(342\) | −4.30357 | −0.232710 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −17.5949 | −0.948655 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.94518 | −0.480896 | ||||||||
\(347\) | −21.3174 | −1.14438 | −0.572190 | − | 0.820121i | \(-0.693906\pi\) | ||||
−0.572190 | + | 0.820121i | \(0.693906\pi\) | |||||||
\(348\) | 31.2264 | 1.67391 | ||||||||
\(349\) | 34.8721 | 1.86666 | 0.933330 | − | 0.359019i | \(-0.116889\pi\) | ||||
0.933330 | + | 0.359019i | \(0.116889\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −35.2992 | −1.88413 | ||||||||
\(352\) | −7.33605 | −0.391013 | ||||||||
\(353\) | 15.0988 | 0.803630 | 0.401815 | − | 0.915721i | \(-0.368380\pi\) | ||||
0.401815 | + | 0.915721i | \(0.368380\pi\) | |||||||
\(354\) | 7.90083 | 0.419924 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 26.3540 | 1.39676 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −62.0440 | −3.27913 | ||||||||
\(359\) | −29.2499 | −1.54375 | −0.771876 | − | 0.635773i | \(-0.780681\pi\) | ||||
−0.771876 | + | 0.635773i | \(0.780681\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.0597 | −0.739985 | ||||||||
\(362\) | 20.0858 | 1.05569 | ||||||||
\(363\) | 1.11047 | 0.0582845 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −52.8982 | −2.76503 | ||||||||
\(367\) | 21.4271 | 1.11848 | 0.559242 | − | 0.829004i | \(-0.311092\pi\) | ||||
0.559242 | + | 0.829004i | \(0.311092\pi\) | |||||||
\(368\) | 15.3723 | 0.801334 | ||||||||
\(369\) | 0.777326 | 0.0404660 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 5.35398 | 0.277591 | ||||||||
\(373\) | 31.8944 | 1.65143 | 0.825716 | − | 0.564087i | \(-0.190772\pi\) | ||||
0.825716 | + | 0.564087i | \(0.190772\pi\) | |||||||
\(374\) | −44.4267 | −2.29725 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −22.7355 | −1.17250 | ||||||||
\(377\) | 31.2264 | 1.60824 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.24618 | 0.166745 | 0.0833726 | − | 0.996518i | \(-0.473431\pi\) | ||||
0.0833726 | + | 0.996518i | \(0.473431\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.15482 | 0.469016 | ||||||||
\(382\) | 56.4528 | 2.88838 | ||||||||
\(383\) | −11.6550 | −0.595542 | −0.297771 | − | 0.954637i | \(-0.596243\pi\) | ||||
−0.297771 | + | 0.954637i | \(0.596243\pi\) | |||||||
\(384\) | −25.7095 | −1.31198 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 32.2447 | 1.64121 | ||||||||
\(387\) | 2.49086 | 0.126618 | ||||||||
\(388\) | 33.9034 | 1.72118 | ||||||||
\(389\) | 18.7941 | 0.952899 | 0.476449 | − | 0.879202i | \(-0.341924\pi\) | ||||
0.476449 | + | 0.879202i | \(0.341924\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.1861 | 0.767996 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.35398 | 0.270073 | ||||||||
\(394\) | 47.0440 | 2.37004 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 11.2003 | 0.562838 | ||||||||
\(397\) | −18.7445 | −0.940760 | −0.470380 | − | 0.882464i | \(-0.655883\pi\) | ||||
−0.470380 | + | 0.882464i | \(0.655883\pi\) | |||||||
\(398\) | 57.9124 | 2.90288 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −26.3409 | −1.31705 | ||||||||
\(401\) | −15.6848 | −0.783261 | −0.391631 | − | 0.920123i | \(-0.628089\pi\) | ||||
−0.391631 | + | 0.920123i | \(0.628089\pi\) | |||||||
\(402\) | 22.7550 | 1.13492 | ||||||||
\(403\) | 5.35398 | 0.266701 | ||||||||
\(404\) | −53.6222 | −2.66780 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.919105 | −0.0455583 | ||||||||
\(408\) | 42.6039 | 2.10921 | ||||||||
\(409\) | 29.5181 | 1.45958 | 0.729788 | − | 0.683673i | \(-0.239619\pi\) | ||||
0.729788 | + | 0.683673i | \(0.239619\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −25.0728 | −1.23675 | ||||||||
\(412\) | −56.2992 | −2.77366 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −5.64975 | −0.277670 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 13.4178 | 0.657860 | ||||||||
\(417\) | 26.5909 | 1.30216 | ||||||||
\(418\) | −18.9736 | −0.928029 | ||||||||
\(419\) | 19.3540 | 0.945504 | 0.472752 | − | 0.881196i | \(-0.343261\pi\) | ||||
0.472752 | + | 0.881196i | \(0.343261\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.2552 | 0.987176 | 0.493588 | − | 0.869696i | \(-0.335685\pi\) | ||||
0.493588 | + | 0.869696i | \(0.335685\pi\) | |||||||
\(422\) | 71.0802 | 3.46013 | ||||||||
\(423\) | 3.21861 | 0.156494 | ||||||||
\(424\) | −18.8176 | −0.913864 | ||||||||
\(425\) | −26.0220 | −1.26225 | ||||||||
\(426\) | −28.0545 | −1.35924 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 40.4178 | 1.95367 | ||||||||
\(429\) | −32.0261 | −1.54623 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.5259 | −0.892362 | −0.446181 | − | 0.894943i | \(-0.647216\pi\) | ||||
−0.446181 | + | 0.894943i | \(0.647216\pi\) | |||||||
\(432\) | −29.6677 | −1.42739 | ||||||||
\(433\) | −7.18239 | −0.345164 | −0.172582 | − | 0.984995i | \(-0.555211\pi\) | ||||
−0.172582 | + | 0.984995i | \(0.555211\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −35.8904 | −1.71884 | ||||||||
\(437\) | 6.48563 | 0.310250 | ||||||||
\(438\) | −46.5543 | −2.22445 | ||||||||
\(439\) | 2.70980 | 0.129332 | 0.0646659 | − | 0.997907i | \(-0.479402\pi\) | ||||
0.0646659 | + | 0.997907i | \(0.479402\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 81.2574 | 3.86502 | ||||||||
\(443\) | 31.4946 | 1.49635 | 0.748177 | − | 0.663499i | \(-0.230930\pi\) | ||||
0.748177 | + | 0.663499i | \(0.230930\pi\) | |||||||
\(444\) | 1.68106 | 0.0797796 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 13.2003 | 0.625054 | ||||||||
\(447\) | −22.2812 | −1.05387 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.4726 | −0.777390 | −0.388695 | − | 0.921367i | \(-0.627074\pi\) | ||||
−0.388695 | + | 0.921367i | \(0.627074\pi\) | |||||||
\(450\) | 9.68106 | 0.456370 | ||||||||
\(451\) | 3.42708 | 0.161375 | ||||||||
\(452\) | −69.2574 | −3.25759 | ||||||||
\(453\) | −7.37259 | −0.346395 | ||||||||
\(454\) | 62.4528 | 2.93106 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 18.1951 | 0.852064 | ||||||||
\(457\) | −7.76279 | −0.363128 | −0.181564 | − | 0.983379i | \(-0.558116\pi\) | ||||
−0.181564 | + | 0.983379i | \(0.558116\pi\) | |||||||
\(458\) | −42.3670 | −1.97968 | ||||||||
\(459\) | −29.3085 | −1.36800 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.2812 | −1.03774 | −0.518870 | − | 0.854853i | \(-0.673647\pi\) | ||||
−0.518870 | + | 0.854853i | \(0.673647\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.0988 | −0.608754 | −0.304377 | − | 0.952552i | \(-0.598448\pi\) | ||||
−0.304377 | + | 0.952552i | \(0.598448\pi\) | |||||||
\(464\) | 26.2447 | 1.21838 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.9452 | −0.692322 | ||||||||
\(467\) | 15.0988 | 0.698691 | 0.349345 | − | 0.936994i | \(-0.386404\pi\) | ||||
0.349345 | + | 0.936994i | \(0.386404\pi\) | |||||||
\(468\) | −20.4856 | −0.946949 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.1029 | 0.649827 | ||||||||
\(472\) | 11.6822 | 0.537718 | ||||||||
\(473\) | 10.9817 | 0.504940 | ||||||||
\(474\) | −22.2812 | −1.02341 | ||||||||
\(475\) | −11.1134 | −0.509916 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.66395 | 0.121974 | ||||||||
\(478\) | −23.0728 | −1.05532 | ||||||||
\(479\) | 2.70980 | 0.123814 | 0.0619070 | − | 0.998082i | \(-0.480282\pi\) | ||||
0.0619070 | + | 0.998082i | \(0.480282\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.68106 | 0.0766498 | ||||||||
\(482\) | 13.2003 | 0.601259 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.13164 | 0.142347 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 19.5636 | 0.887424 | ||||||||
\(487\) | −24.5845 | −1.11403 | −0.557014 | − | 0.830503i | \(-0.688053\pi\) | ||||
−0.557014 | + | 0.830503i | \(0.688053\pi\) | |||||||
\(488\) | −78.2156 | −3.54065 | ||||||||
\(489\) | 6.24875 | 0.282578 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.95449 | 0.223593 | 0.111796 | − | 0.993731i | \(-0.464340\pi\) | ||||
0.111796 | + | 0.993731i | \(0.464340\pi\) | |||||||
\(492\) | −6.26819 | −0.282592 | ||||||||
\(493\) | 25.9269 | 1.16769 | ||||||||
\(494\) | 34.7031 | 1.56136 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.49983 | 0.202048 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 38.6535 | 1.73210 | ||||||||
\(499\) | −25.3540 | −1.13500 | −0.567500 | − | 0.823373i | \(-0.692089\pi\) | ||||
−0.567500 | + | 0.823373i | \(0.692089\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.2850 | 0.727558 | ||||||||
\(502\) | −19.5442 | −0.872300 | ||||||||
\(503\) | 18.1078 | 0.807387 | 0.403694 | − | 0.914894i | \(-0.367726\pi\) | ||||
0.403694 | + | 0.914894i | \(0.367726\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −24.9086 | −1.10732 | ||||||||
\(507\) | 39.1951 | 1.74072 | ||||||||
\(508\) | 25.8176 | 1.14547 | ||||||||
\(509\) | −38.5233 | −1.70752 | −0.853759 | − | 0.520669i | \(-0.825683\pi\) | ||||
−0.853759 | + | 0.520669i | \(0.825683\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −46.5767 | −2.05842 | ||||||||
\(513\) | −12.5169 | −0.552636 | ||||||||
\(514\) | −49.6584 | −2.19034 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −20.0858 | −0.884228 | ||||||||
\(517\) | 14.1902 | 0.624084 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.35398 | −0.235014 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.3670 | −1.54946 | −0.774729 | − | 0.632294i | \(-0.782114\pi\) | ||||
−0.774729 | + | 0.632294i | \(0.782114\pi\) | |||||||
\(522\) | −9.64568 | −0.422180 | ||||||||
\(523\) | 6.38273 | 0.279097 | 0.139549 | − | 0.990215i | \(-0.455435\pi\) | ||||
0.139549 | + | 0.990215i | \(0.455435\pi\) | |||||||
\(524\) | 15.0988 | 0.659596 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 69.2443 | 3.01920 | ||||||||
\(527\) | 4.44535 | 0.193642 | ||||||||
\(528\) | −26.9168 | −1.17140 | ||||||||
\(529\) | −14.4856 | −0.629810 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.65382 | −0.0717696 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.26819 | −0.271505 | ||||||||
\(534\) | 23.2772 | 1.00730 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 33.6457 | 1.45327 | ||||||||
\(537\) | −37.1354 | −1.60251 | ||||||||
\(538\) | −79.4345 | −3.42467 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.55839 | −0.109994 | −0.0549968 | − | 0.998487i | \(-0.517515\pi\) | ||||
−0.0549968 | + | 0.998487i | \(0.517515\pi\) | |||||||
\(542\) | 46.5543 | 1.99968 | ||||||||
\(543\) | 12.0220 | 0.515914 | ||||||||
\(544\) | 11.1406 | 0.477650 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.81761 | 0.377014 | 0.188507 | − | 0.982072i | \(-0.439635\pi\) | ||||
0.188507 | + | 0.982072i | \(0.439635\pi\) | |||||||
\(548\) | −70.7080 | −3.02049 | ||||||||
\(549\) | 11.0728 | 0.472574 | ||||||||
\(550\) | 42.6819 | 1.81996 | ||||||||
\(551\) | 11.0728 | 0.471715 | ||||||||
\(552\) | 23.8866 | 1.01668 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 50.6767 | 2.15304 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 74.9892 | 3.18025 | ||||||||
\(557\) | 35.8904 | 1.52072 | 0.760362 | − | 0.649500i | \(-0.225022\pi\) | ||||
0.760362 | + | 0.649500i | \(0.225022\pi\) | |||||||
\(558\) | −1.65382 | −0.0700117 | ||||||||
\(559\) | −20.0858 | −0.849539 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −26.5909 | −1.12267 | ||||||||
\(562\) | 54.7080 | 2.30772 | ||||||||
\(563\) | 12.6509 | 0.533173 | 0.266586 | − | 0.963811i | \(-0.414104\pi\) | ||||
0.266586 | + | 0.963811i | \(0.414104\pi\) | |||||||
\(564\) | −25.9542 | −1.09287 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 51.2443 | 2.15396 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −41.4816 | −1.74053 | ||||||||
\(569\) | −18.9306 | −0.793614 | −0.396807 | − | 0.917902i | \(-0.629882\pi\) | ||||
−0.396807 | + | 0.917902i | \(0.629882\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.7889 | −1.24663 | −0.623313 | − | 0.781973i | \(-0.714214\pi\) | ||||
−0.623313 | + | 0.781973i | \(0.714214\pi\) | |||||||
\(572\) | −90.3171 | −3.77635 | ||||||||
\(573\) | 33.7889 | 1.41155 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.5897 | −0.608432 | ||||||||
\(576\) | 4.04551 | 0.168563 | ||||||||
\(577\) | −0.826910 | −0.0344247 | −0.0172123 | − | 0.999852i | \(-0.505479\pi\) | ||||
−0.0172123 | + | 0.999852i | \(0.505479\pi\) | |||||||
\(578\) | 25.1223 | 1.04495 | ||||||||
\(579\) | 19.2995 | 0.802060 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 29.9452 | 1.24127 | ||||||||
\(583\) | 11.7448 | 0.486422 | ||||||||
\(584\) | −68.8355 | −2.84844 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −27.5807 | −1.13935 | ||||||||
\(587\) | −34.9672 | −1.44325 | −0.721625 | − | 0.692284i | \(-0.756605\pi\) | ||||
−0.721625 | + | 0.692284i | \(0.756605\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.89850 | 0.0782264 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 28.1574 | 1.15824 | ||||||||
\(592\) | 1.41287 | 0.0580687 | ||||||||
\(593\) | 28.1846 | 1.15740 | 0.578702 | − | 0.815539i | \(-0.303559\pi\) | ||||
0.578702 | + | 0.815539i | \(0.303559\pi\) | |||||||
\(594\) | 48.0724 | 1.97244 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −62.8355 | −2.57384 | ||||||||
\(597\) | 34.6625 | 1.41864 | ||||||||
\(598\) | 45.5584 | 1.86302 | ||||||||
\(599\) | 8.99477 | 0.367516 | 0.183758 | − | 0.982971i | \(-0.441174\pi\) | ||||
0.183758 | + | 0.982971i | \(0.441174\pi\) | |||||||
\(600\) | −40.9306 | −1.67099 | ||||||||
\(601\) | 22.7956 | 0.929852 | 0.464926 | − | 0.885350i | \(-0.346081\pi\) | ||||
0.464926 | + | 0.885350i | \(0.346081\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.76312 | −0.193969 | ||||||||
\(604\) | −20.7915 | −0.845995 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −47.3618 | −1.92394 | ||||||||
\(607\) | 38.4088 | 1.55897 | 0.779483 | − | 0.626424i | \(-0.215482\pi\) | ||||
0.779483 | + | 0.626424i | \(0.215482\pi\) | |||||||
\(608\) | 4.75789 | 0.192958 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −25.9542 | −1.04999 | ||||||||
\(612\) | −17.0090 | −0.687547 | ||||||||
\(613\) | −21.2902 | −0.859903 | −0.429951 | − | 0.902852i | \(-0.641469\pi\) | ||||
−0.429951 | + | 0.902852i | \(0.641469\pi\) | |||||||
\(614\) | −31.2264 | −1.26020 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.8579 | 0.718931 | 0.359466 | − | 0.933158i | \(-0.382959\pi\) | ||||
0.359466 | + | 0.933158i | \(0.382959\pi\) | |||||||
\(618\) | −49.7262 | −2.00028 | ||||||||
\(619\) | −15.9530 | −0.641205 | −0.320602 | − | 0.947214i | \(-0.603885\pi\) | ||||
−0.320602 | + | 0.947214i | \(0.603885\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.4323 | −0.659406 | ||||||||
\(622\) | −61.1716 | −2.45276 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 49.2313 | 1.97083 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 34.6352 | 1.38430 | ||||||||
\(627\) | −11.3563 | −0.453528 | ||||||||
\(628\) | 39.7718 | 1.58707 | ||||||||
\(629\) | 1.39576 | 0.0556528 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.2134 | −1.08335 | −0.541674 | − | 0.840589i | \(-0.682209\pi\) | ||||
−0.541674 | + | 0.840589i | \(0.682209\pi\) | |||||||
\(632\) | −32.9452 | −1.31049 | ||||||||
\(633\) | 42.5438 | 1.69097 | ||||||||
\(634\) | −12.8176 | −0.509052 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −21.4816 | −0.851799 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −42.5259 | −1.68362 | ||||||||
\(639\) | 5.87242 | 0.232310 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.5468 | −0.495571 | −0.247785 | − | 0.968815i | \(-0.579703\pi\) | ||||
−0.247785 | + | 0.968815i | \(0.579703\pi\) | |||||||
\(642\) | 35.6990 | 1.40893 | ||||||||
\(643\) | 17.7758 | 0.701010 | 0.350505 | − | 0.936561i | \(-0.386010\pi\) | ||||
0.350505 | + | 0.936561i | \(0.386010\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 28.8135 | 1.13365 | ||||||||
\(647\) | −11.4375 | −0.449656 | −0.224828 | − | 0.974398i | \(-0.572182\pi\) | ||||
−0.224828 | + | 0.974398i | \(0.572182\pi\) | |||||||
\(648\) | −33.2954 | −1.30797 | ||||||||
\(649\) | −7.29136 | −0.286211 | ||||||||
\(650\) | −78.0660 | −3.06200 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.6222 | 0.690138 | ||||||||
\(653\) | 4.82808 | 0.188937 | 0.0944686 | − | 0.995528i | \(-0.469885\pi\) | ||||
0.0944686 | + | 0.995528i | \(0.469885\pi\) | |||||||
\(654\) | −31.7002 | −1.23957 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5.26819 | −0.205688 | ||||||||
\(657\) | 9.74485 | 0.380183 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.2186 | −1.41088 | −0.705438 | − | 0.708771i | \(-0.749250\pi\) | ||||
−0.705438 | + | 0.708771i | \(0.749250\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.3100 | 0.906653 | 0.453326 | − | 0.891345i | \(-0.350237\pi\) | ||||
0.453326 | + | 0.891345i | \(0.350237\pi\) | |||||||
\(662\) | −66.7990 | −2.59622 | ||||||||
\(663\) | 48.6352 | 1.88884 | ||||||||
\(664\) | 57.1533 | 2.21798 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.519271 | −0.0201214 | ||||||||
\(667\) | 14.5364 | 0.562851 | ||||||||
\(668\) | 45.9254 | 1.77691 | ||||||||
\(669\) | 7.90083 | 0.305464 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 48.8176 | 1.88458 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.4088 | −1.40346 | −0.701728 | − | 0.712445i | \(-0.747588\pi\) | ||||
−0.701728 | + | 0.712445i | \(0.747588\pi\) | |||||||
\(674\) | 10.8228 | 0.416880 | ||||||||
\(675\) | 28.1574 | 1.08378 | ||||||||
\(676\) | 110.535 | 4.25133 | ||||||||
\(677\) | 0.663954 | 0.0255178 | 0.0127589 | − | 0.999919i | \(-0.495939\pi\) | ||||
0.0127589 | + | 0.999919i | \(0.495939\pi\) | |||||||
\(678\) | −61.1716 | −2.34928 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 37.3801 | 1.43241 | ||||||||
\(682\) | −7.29136 | −0.279201 | ||||||||
\(683\) | −24.0000 | −0.918334 | −0.459167 | − | 0.888350i | \(-0.651852\pi\) | ||||
−0.459167 | + | 0.888350i | \(0.651852\pi\) | |||||||
\(684\) | −7.26412 | −0.277751 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −25.3581 | −0.967470 | ||||||||
\(688\) | −16.8814 | −0.643597 | ||||||||
\(689\) | −21.4816 | −0.818382 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 42.8486 | 1.63004 | 0.815018 | − | 0.579435i | \(-0.196727\pi\) | ||||
0.815018 | + | 0.579435i | \(0.196727\pi\) | |||||||
\(692\) | −15.0988 | −0.573972 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −53.0988 | −2.01560 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 40.7811 | 1.54580 | ||||||||
\(697\) | −5.20440 | −0.197131 | ||||||||
\(698\) | 86.8616 | 3.28776 | ||||||||
\(699\) | −8.94518 | −0.338338 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.596431 | 0.0225269 | 0.0112635 | − | 0.999937i | \(-0.496415\pi\) | ||||
0.0112635 | + | 0.999937i | \(0.496415\pi\) | |||||||
\(702\) | −87.9254 | −3.31853 | ||||||||
\(703\) | 0.596097 | 0.0224822 | ||||||||
\(704\) | 17.8359 | 0.672215 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 37.6091 | 1.41544 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 13.3360 | 0.501199 | ||||||||
\(709\) | 42.4528 | 1.59435 | 0.797175 | − | 0.603749i | \(-0.206327\pi\) | ||||
0.797175 | + | 0.603749i | \(0.206327\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.66395 | 0.174912 | ||||||||
\(712\) | 34.4178 | 1.28986 | ||||||||
\(713\) | 2.49236 | 0.0933397 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −104.726 | −3.91379 | ||||||||
\(717\) | −13.8098 | −0.515737 | ||||||||
\(718\) | −72.8576 | −2.71902 | ||||||||
\(719\) | 7.18239 | 0.267858 | 0.133929 | − | 0.990991i | \(-0.457241\pi\) | ||||
0.133929 | + | 0.990991i | \(0.457241\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −35.0208 | −1.30334 | ||||||||
\(723\) | 7.90083 | 0.293835 | ||||||||
\(724\) | 33.9034 | 1.26001 | ||||||||
\(725\) | −24.9086 | −0.925084 | ||||||||
\(726\) | 2.76603 | 0.102657 | ||||||||
\(727\) | −24.5584 | −0.910820 | −0.455410 | − | 0.890282i | \(-0.650507\pi\) | ||||
−0.455410 | + | 0.890282i | \(0.650507\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9008 | 1.10744 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.6770 | −0.616821 | ||||||||
\(732\) | −89.2884 | −3.30019 | ||||||||
\(733\) | 49.0623 | 1.81216 | 0.906078 | − | 0.423110i | \(-0.139061\pi\) | ||||
0.906078 | + | 0.423110i | \(0.139061\pi\) | |||||||
\(734\) | 53.3719 | 1.96999 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.24618 | 0.230237 | ||||||||
\(737\) | −20.9997 | −0.773533 | ||||||||
\(738\) | 1.93621 | 0.0712730 | ||||||||
\(739\) | 17.8855 | 0.657927 | 0.328964 | − | 0.944343i | \(-0.393301\pi\) | ||||
0.328964 | + | 0.944343i | \(0.393301\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 20.7709 | 0.763039 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 47.4305 | 1.74006 | 0.870028 | − | 0.493003i | \(-0.164101\pi\) | ||||
0.870028 | + | 0.493003i | \(0.164101\pi\) | |||||||
\(744\) | 6.99220 | 0.256346 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 79.4447 | 2.90868 | ||||||||
\(747\) | −8.09103 | −0.296035 | ||||||||
\(748\) | −74.9892 | −2.74188 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.74485 | −0.0636704 | −0.0318352 | − | 0.999493i | \(-0.510135\pi\) | ||||
−0.0318352 | + | 0.999493i | \(0.510135\pi\) | |||||||
\(752\) | −21.8135 | −0.795458 | ||||||||
\(753\) | −11.6978 | −0.426293 | ||||||||
\(754\) | 77.7807 | 2.83261 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.6640 | −0.969118 | −0.484559 | − | 0.874759i | \(-0.661020\pi\) | ||||
−0.484559 | + | 0.874759i | \(0.661020\pi\) | |||||||
\(758\) | 8.08580 | 0.293689 | ||||||||
\(759\) | −14.9086 | −0.541149 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.2992 | 0.518344 | 0.259172 | − | 0.965831i | \(-0.416550\pi\) | ||||
0.259172 | + | 0.965831i | \(0.416550\pi\) | |||||||
\(762\) | 22.8034 | 0.826080 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 95.2884 | 3.44741 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −29.0310 | −1.04893 | ||||||||
\(767\) | 13.3360 | 0.481537 | ||||||||
\(768\) | −48.5207 | −1.75084 | ||||||||
\(769\) | −43.7628 | −1.57813 | −0.789063 | − | 0.614312i | \(-0.789434\pi\) | ||||
−0.789063 | + | 0.614312i | \(0.789434\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −29.7222 | −1.07042 | ||||||||
\(772\) | 54.4267 | 1.95886 | ||||||||
\(773\) | 14.5845 | 0.524567 | 0.262283 | − | 0.964991i | \(-0.415524\pi\) | ||||
0.262283 | + | 0.964991i | \(0.415524\pi\) | |||||||
\(774\) | 6.20440 | 0.223013 | ||||||||
\(775\) | −4.27076 | −0.153410 | ||||||||
\(776\) | 44.2772 | 1.58946 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 46.8135 | 1.67835 | ||||||||
\(779\) | −2.22267 | −0.0796356 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.8904 | 0.926430 | ||||||||
\(782\) | 37.8266 | 1.35268 | ||||||||
\(783\) | −28.0545 | −1.00259 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 13.3360 | 0.475681 | ||||||||
\(787\) | 20.5729 | 0.733346 | 0.366673 | − | 0.930350i | \(-0.380497\pi\) | ||||
0.366673 | + | 0.930350i | \(0.380497\pi\) | |||||||
\(788\) | 79.4070 | 2.82876 | ||||||||
\(789\) | 41.4450 | 1.47548 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 14.6274 | 0.519762 | ||||||||
\(793\) | −89.2884 | −3.17072 | ||||||||
\(794\) | −46.6900 | −1.65697 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 97.7520 | 3.46473 | ||||||||
\(797\) | −35.9164 | −1.27223 | −0.636113 | − | 0.771596i | \(-0.719459\pi\) | ||||
−0.636113 | + | 0.771596i | \(0.719459\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.5494 | −0.762364 | ||||||||
\(800\) | −10.7031 | −0.378411 | ||||||||
\(801\) | −4.87242 | −0.172159 | ||||||||
\(802\) | −39.0687 | −1.37956 | ||||||||
\(803\) | 42.9631 | 1.51614 | ||||||||
\(804\) | 38.4088 | 1.35457 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 13.3360 | 0.469742 | ||||||||
\(807\) | −47.5442 | −1.67363 | ||||||||
\(808\) | −70.0295 | −2.46363 | ||||||||
\(809\) | 15.4375 | 0.542755 | 0.271378 | − | 0.962473i | \(-0.412521\pi\) | ||||
0.271378 | + | 0.962473i | \(0.412521\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.7889 | −1.18649 | −0.593244 | − | 0.805023i | \(-0.702153\pi\) | ||||
−0.593244 | + | 0.805023i | \(0.702153\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.8643 | 0.977243 | ||||||||
\(814\) | −2.28937 | −0.0802422 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 40.8762 | 1.43095 | ||||||||
\(817\) | −7.12234 | −0.249179 | ||||||||
\(818\) | 73.5256 | 2.57076 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.08463 | 0.142555 | 0.0712773 | − | 0.997457i | \(-0.477292\pi\) | ||||
0.0712773 | + | 0.997457i | \(0.477292\pi\) | |||||||
\(822\) | −62.4528 | −2.17829 | ||||||||
\(823\) | 8.69003 | 0.302915 | 0.151458 | − | 0.988464i | \(-0.451603\pi\) | ||||
0.151458 | + | 0.988464i | \(0.451603\pi\) | |||||||
\(824\) | −73.5256 | −2.56138 | ||||||||
\(825\) | 25.5465 | 0.889415 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.81761 | −0.167525 | −0.0837623 | − | 0.996486i | \(-0.526694\pi\) | ||||
−0.0837623 | + | 0.996486i | \(0.526694\pi\) | |||||||
\(828\) | −9.53638 | −0.331412 | ||||||||
\(829\) | −12.4819 | −0.433514 | −0.216757 | − | 0.976226i | \(-0.569548\pi\) | ||||
−0.216757 | + | 0.976226i | \(0.569548\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 30.3316 | 1.05219 | ||||||||
\(832\) | −32.6222 | −1.13097 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 66.2342 | 2.29350 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −32.0261 | −1.10765 | ||||||||
\(837\) | −4.81014 | −0.166263 | ||||||||
\(838\) | 48.2081 | 1.66532 | ||||||||
\(839\) | −29.5453 | −1.02002 | −0.510009 | − | 0.860169i | \(-0.670358\pi\) | ||||
−0.510009 | + | 0.860169i | \(0.670358\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.18239 | −0.144220 | ||||||||
\(842\) | 50.4528 | 1.73872 | ||||||||
\(843\) | 32.7445 | 1.12778 | ||||||||
\(844\) | 119.978 | 4.12983 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8.01711 | 0.275634 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −18.0545 | −0.619994 | ||||||||
\(849\) | 30.6714 | 1.05264 | ||||||||
\(850\) | −64.8173 | −2.22321 | ||||||||
\(851\) | 0.782560 | 0.0268258 | ||||||||
\(852\) | −47.3540 | −1.62232 | ||||||||
\(853\) | 16.0731 | 0.550332 | 0.275166 | − | 0.961397i | \(-0.411267\pi\) | ||||
0.275166 | + | 0.961397i | \(0.411267\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 52.7848 | 1.80415 | ||||||||
\(857\) | 9.74485 | 0.332878 | 0.166439 | − | 0.986052i | \(-0.446773\pi\) | ||||
0.166439 | + | 0.986052i | \(0.446773\pi\) | |||||||
\(858\) | −79.7726 | −2.72339 | ||||||||
\(859\) | −50.8251 | −1.73413 | −0.867065 | − | 0.498196i | \(-0.833996\pi\) | ||||
−0.867065 | + | 0.498196i | \(0.833996\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −46.1455 | −1.57172 | ||||||||
\(863\) | 3.74485 | 0.127476 | 0.0637381 | − | 0.997967i | \(-0.479698\pi\) | ||||
0.0637381 | + | 0.997967i | \(0.479698\pi\) | |||||||
\(864\) | −12.0548 | −0.410113 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −17.8904 | −0.607939 | ||||||||
\(867\) | 15.0365 | 0.510668 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.5625 | 0.697534 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.4088 | 1.30143 | ||||||||
\(872\) | −46.8721 | −1.58729 | ||||||||
\(873\) | −6.26819 | −0.212146 | ||||||||
\(874\) | 16.1548 | 0.546445 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −78.5804 | −2.65499 | ||||||||
\(877\) | 12.9075 | 0.435854 | 0.217927 | − | 0.975965i | \(-0.430070\pi\) | ||||
0.217927 | + | 0.975965i | \(0.430070\pi\) | |||||||
\(878\) | 6.74975 | 0.227793 | ||||||||
\(879\) | −16.5080 | −0.556800 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.3279 | −0.516410 | −0.258205 | − | 0.966090i | \(-0.583131\pi\) | ||||
−0.258205 | + | 0.966090i | \(0.583131\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.5103 | 0.824837 | 0.412419 | − | 0.910994i | \(-0.364684\pi\) | ||||
0.412419 | + | 0.910994i | \(0.364684\pi\) | |||||||
\(884\) | 137.157 | 4.61308 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 78.4487 | 2.63554 | ||||||||
\(887\) | 58.3122 | 1.95793 | 0.978966 | − | 0.204023i | \(-0.0654017\pi\) | ||||
0.978966 | + | 0.204023i | \(0.0654017\pi\) | |||||||
\(888\) | 2.19543 | 0.0736739 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 20.7811 | 0.696192 | ||||||||
\(892\) | 22.2812 | 0.746031 | ||||||||
\(893\) | −9.20324 | −0.307975 | ||||||||
\(894\) | −55.4995 | −1.85618 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 27.2682 | 0.910458 | ||||||||
\(898\) | −41.0310 | −1.36922 | ||||||||
\(899\) | 4.25515 | 0.141917 | ||||||||
\(900\) | 16.3409 | 0.544698 | ||||||||
\(901\) | −17.8359 | −0.594199 | ||||||||
\(902\) | 8.53638 | 0.284230 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −90.4487 | −3.00828 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −18.3641 | −0.610107 | ||||||||
\(907\) | 27.4946 | 0.912943 | 0.456472 | − | 0.889738i | \(-0.349113\pi\) | ||||
0.456472 | + | 0.889738i | \(0.349113\pi\) | |||||||
\(908\) | 105.416 | 3.49835 | ||||||||
\(909\) | 9.91387 | 0.328822 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.8318 | 0.922109 | 0.461055 | − | 0.887372i | \(-0.347471\pi\) | ||||
0.461055 | + | 0.887372i | \(0.347471\pi\) | |||||||
\(912\) | 17.4572 | 0.578066 | ||||||||
\(913\) | −35.6718 | −1.18056 | ||||||||
\(914\) | −19.3360 | −0.639580 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −71.5125 | −2.36284 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −73.0034 | −2.40947 | ||||||||
\(919\) | 19.5076 | 0.643498 | 0.321749 | − | 0.946825i | \(-0.395729\pi\) | ||||
0.321749 | + | 0.946825i | \(0.395729\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −18.6900 | −0.615857 | ||||||||
\(922\) | −55.4995 | −1.82778 | ||||||||
\(923\) | −47.3540 | −1.55868 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.34095 | −0.0440900 | ||||||||
\(926\) | −32.6274 | −1.07220 | ||||||||
\(927\) | 10.4088 | 0.341870 | ||||||||
\(928\) | 10.6640 | 0.350061 | ||||||||
\(929\) | 0.881394 | 0.0289176 | 0.0144588 | − | 0.999895i | \(-0.495397\pi\) | ||||
0.0144588 | + | 0.999895i | \(0.495397\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −25.2264 | −0.826319 | ||||||||
\(933\) | −36.6132 | −1.19866 | ||||||||
\(934\) | 37.6091 | 1.23061 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −26.7538 | −0.874476 | ||||||||
\(937\) | −8.20557 | −0.268064 | −0.134032 | − | 0.990977i | \(-0.542793\pi\) | ||||
−0.134032 | + | 0.990977i | \(0.542793\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20.7303 | 0.676508 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.30997 | 0.303496 | 0.151748 | − | 0.988419i | \(-0.451510\pi\) | ||||
0.151748 | + | 0.988419i | \(0.451510\pi\) | |||||||
\(942\) | 35.1284 | 1.14455 | ||||||||
\(943\) | −2.91794 | −0.0950212 | ||||||||
\(944\) | 11.2085 | 0.364805 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 27.3540 | 0.889355 | ||||||||
\(947\) | 10.1548 | 0.329987 | 0.164994 | − | 0.986295i | \(-0.447240\pi\) | ||||
0.164994 | + | 0.986295i | \(0.447240\pi\) | |||||||
\(948\) | −37.6091 | −1.22149 | ||||||||
\(949\) | −78.5804 | −2.55083 | ||||||||
\(950\) | −27.6819 | −0.898119 | ||||||||
\(951\) | −7.67176 | −0.248774 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.75755 | −0.154112 | −0.0770561 | − | 0.997027i | \(-0.524552\pi\) | ||||
−0.0770561 | + | 0.997027i | \(0.524552\pi\) | |||||||
\(954\) | 6.63555 | 0.214834 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −38.9452 | −1.25958 | ||||||||
\(957\) | −25.4532 | −0.822784 | ||||||||
\(958\) | 6.74975 | 0.218075 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.2704 | −0.976465 | ||||||||
\(962\) | 4.18729 | 0.135004 | ||||||||
\(963\) | −7.47259 | −0.240801 | ||||||||
\(964\) | 22.2812 | 0.717630 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.9892 | 1.12518 | 0.562588 | − | 0.826737i | \(-0.309806\pi\) | ||||
0.562588 | + | 0.826737i | \(0.309806\pi\) | |||||||
\(968\) | 4.08986 | 0.131453 | ||||||||
\(969\) | 17.2458 | 0.554016 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.96719 | −0.223588 | −0.111794 | − | 0.993731i | \(-0.535660\pi\) | ||||
−0.111794 | + | 0.993731i | \(0.535660\pi\) | |||||||
\(972\) | 33.0220 | 1.05918 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −61.2365 | −1.96215 | ||||||||
\(975\) | −46.7251 | −1.49640 | ||||||||
\(976\) | −75.0437 | −2.40209 | ||||||||
\(977\) | 33.1533 | 1.06067 | 0.530334 | − | 0.847789i | \(-0.322066\pi\) | ||||
0.530334 | + | 0.847789i | \(0.322066\pi\) | |||||||
\(978\) | 15.5648 | 0.497707 | ||||||||
\(979\) | −21.4816 | −0.686554 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.63555 | 0.211857 | ||||||||
\(982\) | 12.3409 | 0.393815 | ||||||||
\(983\) | 18.0261 | 0.574943 | 0.287471 | − | 0.957789i | \(-0.407185\pi\) | ||||
0.287471 | + | 0.957789i | \(0.407185\pi\) | |||||||
\(984\) | −8.18613 | −0.260964 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 64.5804 | 2.05666 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 58.5763 | 1.86356 | ||||||||
\(989\) | −9.35025 | −0.297321 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.0620 | 1.52674 | 0.763369 | − | 0.645962i | \(-0.223544\pi\) | ||||
0.763369 | + | 0.645962i | \(0.223544\pi\) | |||||||
\(992\) | 1.82841 | 0.0580520 | ||||||||
\(993\) | −39.9814 | −1.26877 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 65.2443 | 2.06735 | ||||||||
\(997\) | −59.8631 | −1.89588 | −0.947942 | − | 0.318443i | \(-0.896840\pi\) | ||||
−0.947942 | + | 0.318443i | \(0.896840\pi\) | |||||||
\(998\) | −63.1533 | −1.99908 | ||||||||
\(999\) | −1.51030 | −0.0477838 |
(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 | 2009.2.a.h.1.3 | ✓ | 3 | |
7.6 | odd | 2 | 2009.2.a.i.1.3 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2009.2.a.h.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
2009.2.a.i.1.3 | yes | 3 | 7.6 | odd | 2 |