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: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 3 x^{16} - 25 x^{15} + 77 x^{14} + 247 x^{13} - 790 x^{12} - 1231 x^{11} + 4173 x^{10} + 3251 x^{9} - 12183 x^{8} - 4259 x^{7} + 19567 x^{6} + 2029 x^{5} - 16136 x^{4} + \cdots - 464 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 287) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(1.11543\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.11543 | 0.788725 | 0.394363 | − | 0.918955i | \(-0.370965\pi\) | ||||
0.394363 | + | 0.918955i | \(0.370965\pi\) | |||||||
\(3\) | −2.75409 | −1.59008 | −0.795038 | − | 0.606559i | \(-0.792549\pi\) | ||||
−0.795038 | + | 0.606559i | \(0.792549\pi\) | |||||||
\(4\) | −0.755825 | −0.377913 | ||||||||
\(5\) | −1.34462 | −0.601331 | −0.300666 | − | 0.953730i | \(-0.597209\pi\) | ||||
−0.300666 | + | 0.953730i | \(0.597209\pi\) | |||||||
\(6\) | −3.07199 | −1.25413 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.07392 | −1.08679 | ||||||||
\(9\) | 4.58503 | 1.52834 | ||||||||
\(10\) | −1.49982 | −0.474285 | ||||||||
\(11\) | −1.07728 | −0.324812 | −0.162406 | − | 0.986724i | \(-0.551925\pi\) | ||||
−0.162406 | + | 0.986724i | \(0.551925\pi\) | |||||||
\(12\) | 2.08161 | 0.600910 | ||||||||
\(13\) | −0.966204 | −0.267977 | −0.133988 | − | 0.990983i | \(-0.542778\pi\) | ||||
−0.133988 | + | 0.990983i | \(0.542778\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.70320 | 0.956163 | ||||||||
\(16\) | −1.91708 | −0.479269 | ||||||||
\(17\) | −6.52880 | −1.58347 | −0.791734 | − | 0.610866i | \(-0.790821\pi\) | ||||
−0.791734 | + | 0.610866i | \(0.790821\pi\) | |||||||
\(18\) | 5.11426 | 1.20544 | ||||||||
\(19\) | −7.07942 | −1.62413 | −0.812065 | − | 0.583566i | \(-0.801657\pi\) | ||||
−0.812065 | + | 0.583566i | \(0.801657\pi\) | |||||||
\(20\) | 1.01630 | 0.227251 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.20163 | −0.256187 | ||||||||
\(23\) | 0.898247 | 0.187297 | 0.0936487 | − | 0.995605i | \(-0.470147\pi\) | ||||
0.0936487 | + | 0.995605i | \(0.470147\pi\) | |||||||
\(24\) | 8.46586 | 1.72809 | ||||||||
\(25\) | −3.19200 | −0.638401 | ||||||||
\(26\) | −1.07773 | −0.211360 | ||||||||
\(27\) | −4.36532 | −0.840106 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.82453 | 0.524502 | 0.262251 | − | 0.965000i | \(-0.415535\pi\) | ||||
0.262251 | + | 0.965000i | \(0.415535\pi\) | |||||||
\(30\) | 4.13065 | 0.754149 | ||||||||
\(31\) | −1.38928 | −0.249523 | −0.124761 | − | 0.992187i | \(-0.539817\pi\) | ||||
−0.124761 | + | 0.992187i | \(0.539817\pi\) | |||||||
\(32\) | 4.00948 | 0.708783 | ||||||||
\(33\) | 2.96693 | 0.516476 | ||||||||
\(34\) | −7.28240 | −1.24892 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.46548 | −0.577580 | ||||||||
\(37\) | −7.12505 | −1.17135 | −0.585676 | − | 0.810545i | \(-0.699171\pi\) | ||||
−0.585676 | + | 0.810545i | \(0.699171\pi\) | |||||||
\(38\) | −7.89657 | −1.28099 | ||||||||
\(39\) | 2.66102 | 0.426103 | ||||||||
\(40\) | 4.13324 | 0.653523 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.23495 | 0.188328 | 0.0941642 | − | 0.995557i | \(-0.469982\pi\) | ||||
0.0941642 | + | 0.995557i | \(0.469982\pi\) | |||||||
\(44\) | 0.814235 | 0.122751 | ||||||||
\(45\) | −6.16511 | −0.919040 | ||||||||
\(46\) | 1.00193 | 0.147726 | ||||||||
\(47\) | 7.85310 | 1.14549 | 0.572746 | − | 0.819733i | \(-0.305878\pi\) | ||||
0.572746 | + | 0.819733i | \(0.305878\pi\) | |||||||
\(48\) | 5.27981 | 0.762075 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.56044 | −0.503523 | ||||||||
\(51\) | 17.9809 | 2.51783 | ||||||||
\(52\) | 0.730281 | 0.101272 | ||||||||
\(53\) | 6.58939 | 0.905122 | 0.452561 | − | 0.891733i | \(-0.350510\pi\) | ||||
0.452561 | + | 0.891733i | \(0.350510\pi\) | |||||||
\(54\) | −4.86919 | −0.662613 | ||||||||
\(55\) | 1.44853 | 0.195320 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 19.4974 | 2.58249 | ||||||||
\(58\) | 3.15055 | 0.413688 | ||||||||
\(59\) | 2.72107 | 0.354253 | 0.177126 | − | 0.984188i | \(-0.443320\pi\) | ||||
0.177126 | + | 0.984188i | \(0.443320\pi\) | |||||||
\(60\) | −2.79897 | −0.361346 | ||||||||
\(61\) | −11.0489 | −1.41467 | −0.707334 | − | 0.706880i | \(-0.750102\pi\) | ||||
−0.707334 | + | 0.706880i | \(0.750102\pi\) | |||||||
\(62\) | −1.54964 | −0.196805 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.30643 | 1.03830 | ||||||||
\(65\) | 1.29917 | 0.161143 | ||||||||
\(66\) | 3.30939 | 0.407357 | ||||||||
\(67\) | 2.45673 | 0.300138 | 0.150069 | − | 0.988676i | \(-0.452050\pi\) | ||||
0.150069 | + | 0.988676i | \(0.452050\pi\) | |||||||
\(68\) | 4.93463 | 0.598412 | ||||||||
\(69\) | −2.47385 | −0.297817 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.40706 | 0.285666 | 0.142833 | − | 0.989747i | \(-0.454379\pi\) | ||||
0.142833 | + | 0.989747i | \(0.454379\pi\) | |||||||
\(72\) | −14.0940 | −1.66099 | ||||||||
\(73\) | 8.12078 | 0.950465 | 0.475232 | − | 0.879860i | \(-0.342364\pi\) | ||||
0.475232 | + | 0.879860i | \(0.342364\pi\) | |||||||
\(74\) | −7.94747 | −0.923875 | ||||||||
\(75\) | 8.79108 | 1.01511 | ||||||||
\(76\) | 5.35081 | 0.613780 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.96816 | 0.336078 | ||||||||
\(79\) | −1.96133 | −0.220666 | −0.110333 | − | 0.993895i | \(-0.535192\pi\) | ||||
−0.110333 | + | 0.993895i | \(0.535192\pi\) | |||||||
\(80\) | 2.57774 | 0.288200 | ||||||||
\(81\) | −1.73260 | −0.192511 | ||||||||
\(82\) | 1.11543 | 0.123178 | ||||||||
\(83\) | −9.30225 | −1.02105 | −0.510527 | − | 0.859862i | \(-0.670550\pi\) | ||||
−0.510527 | + | 0.859862i | \(0.670550\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.77874 | 0.952188 | ||||||||
\(86\) | 1.37750 | 0.148539 | ||||||||
\(87\) | −7.77902 | −0.833999 | ||||||||
\(88\) | 3.31147 | 0.353004 | ||||||||
\(89\) | 12.7953 | 1.35629 | 0.678147 | − | 0.734926i | \(-0.262783\pi\) | ||||
0.678147 | + | 0.734926i | \(0.262783\pi\) | |||||||
\(90\) | −6.87672 | −0.724870 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.678918 | −0.0707820 | ||||||||
\(93\) | 3.82622 | 0.396760 | ||||||||
\(94\) | 8.75955 | 0.903478 | ||||||||
\(95\) | 9.51912 | 0.976641 | ||||||||
\(96\) | −11.0425 | −1.12702 | ||||||||
\(97\) | 18.4064 | 1.86888 | 0.934442 | − | 0.356117i | \(-0.115899\pi\) | ||||
0.934442 | + | 0.356117i | \(0.115899\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.93936 | −0.496424 | ||||||||
\(100\) | 2.41260 | 0.241260 | ||||||||
\(101\) | −7.26316 | −0.722711 | −0.361356 | − | 0.932428i | \(-0.617686\pi\) | ||||
−0.361356 | + | 0.932428i | \(0.617686\pi\) | |||||||
\(102\) | 20.0564 | 1.98588 | ||||||||
\(103\) | 19.0867 | 1.88066 | 0.940332 | − | 0.340257i | \(-0.110514\pi\) | ||||
0.940332 | + | 0.340257i | \(0.110514\pi\) | |||||||
\(104\) | 2.97003 | 0.291236 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.34997 | 0.713892 | ||||||||
\(107\) | −11.6695 | −1.12813 | −0.564065 | − | 0.825730i | \(-0.690763\pi\) | ||||
−0.564065 | + | 0.825730i | \(0.690763\pi\) | |||||||
\(108\) | 3.29942 | 0.317487 | ||||||||
\(109\) | 17.0444 | 1.63256 | 0.816281 | − | 0.577656i | \(-0.196032\pi\) | ||||
0.816281 | + | 0.577656i | \(0.196032\pi\) | |||||||
\(110\) | 1.61573 | 0.154053 | ||||||||
\(111\) | 19.6231 | 1.86254 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.74418 | −0.446295 | −0.223147 | − | 0.974785i | \(-0.571633\pi\) | ||||
−0.223147 | + | 0.974785i | \(0.571633\pi\) | |||||||
\(114\) | 21.7479 | 2.03688 | ||||||||
\(115\) | −1.20780 | −0.112628 | ||||||||
\(116\) | −2.13485 | −0.198216 | ||||||||
\(117\) | −4.43007 | −0.409560 | ||||||||
\(118\) | 3.03515 | 0.279408 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −11.3833 | −1.03915 | ||||||||
\(121\) | −9.83947 | −0.894497 | ||||||||
\(122\) | −12.3242 | −1.11578 | ||||||||
\(123\) | −2.75409 | −0.248328 | ||||||||
\(124\) | 1.05006 | 0.0942978 | ||||||||
\(125\) | 11.0151 | 0.985222 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.95232 | −0.883126 | −0.441563 | − | 0.897230i | \(-0.645576\pi\) | ||||
−0.441563 | + | 0.897230i | \(0.645576\pi\) | |||||||
\(128\) | 1.24625 | 0.110154 | ||||||||
\(129\) | −3.40117 | −0.299457 | ||||||||
\(130\) | 1.44913 | 0.127097 | ||||||||
\(131\) | 21.0937 | 1.84297 | 0.921484 | − | 0.388416i | \(-0.126978\pi\) | ||||
0.921484 | + | 0.388416i | \(0.126978\pi\) | |||||||
\(132\) | −2.24248 | −0.195183 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.74030 | 0.236726 | ||||||||
\(135\) | 5.86968 | 0.505182 | ||||||||
\(136\) | 20.0690 | 1.72090 | ||||||||
\(137\) | −8.00151 | −0.683616 | −0.341808 | − | 0.939770i | \(-0.611039\pi\) | ||||
−0.341808 | + | 0.939770i | \(0.611039\pi\) | |||||||
\(138\) | −2.75940 | −0.234896 | ||||||||
\(139\) | −7.13603 | −0.605270 | −0.302635 | − | 0.953107i | \(-0.597866\pi\) | ||||
−0.302635 | + | 0.953107i | \(0.597866\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −21.6282 | −1.82142 | ||||||||
\(142\) | 2.68490 | 0.225312 | ||||||||
\(143\) | 1.04087 | 0.0870420 | ||||||||
\(144\) | −8.78986 | −0.732488 | ||||||||
\(145\) | −3.79791 | −0.315400 | ||||||||
\(146\) | 9.05812 | 0.749656 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.38530 | 0.442669 | ||||||||
\(149\) | −10.9781 | −0.899361 | −0.449680 | − | 0.893190i | \(-0.648462\pi\) | ||||
−0.449680 | + | 0.893190i | \(0.648462\pi\) | |||||||
\(150\) | 9.80579 | 0.800640 | ||||||||
\(151\) | 19.8359 | 1.61422 | 0.807112 | − | 0.590399i | \(-0.201029\pi\) | ||||
0.807112 | + | 0.590399i | \(0.201029\pi\) | |||||||
\(152\) | 21.7616 | 1.76510 | ||||||||
\(153\) | −29.9348 | −2.42008 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.86806 | 0.150046 | ||||||||
\(156\) | −2.01126 | −0.161030 | ||||||||
\(157\) | −9.62144 | −0.767875 | −0.383937 | − | 0.923359i | \(-0.625432\pi\) | ||||
−0.383937 | + | 0.923359i | \(0.625432\pi\) | |||||||
\(158\) | −2.18771 | −0.174045 | ||||||||
\(159\) | −18.1478 | −1.43921 | ||||||||
\(160\) | −5.39122 | −0.426213 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.93258 | −0.151838 | ||||||||
\(163\) | 0.333705 | 0.0261378 | 0.0130689 | − | 0.999915i | \(-0.495840\pi\) | ||||
0.0130689 | + | 0.999915i | \(0.495840\pi\) | |||||||
\(164\) | −0.755825 | −0.0590200 | ||||||||
\(165\) | −3.98938 | −0.310573 | ||||||||
\(166\) | −10.3760 | −0.805332 | ||||||||
\(167\) | −16.6780 | −1.29058 | −0.645290 | − | 0.763938i | \(-0.723263\pi\) | ||||
−0.645290 | + | 0.763938i | \(0.723263\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0665 | −0.928188 | ||||||||
\(170\) | 9.79204 | 0.751015 | ||||||||
\(171\) | −32.4594 | −2.48223 | ||||||||
\(172\) | −0.933408 | −0.0711717 | ||||||||
\(173\) | −12.9458 | −0.984250 | −0.492125 | − | 0.870524i | \(-0.663780\pi\) | ||||
−0.492125 | + | 0.870524i | \(0.663780\pi\) | |||||||
\(174\) | −8.67692 | −0.657796 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.06523 | 0.155672 | ||||||||
\(177\) | −7.49408 | −0.563289 | ||||||||
\(178\) | 14.2722 | 1.06974 | ||||||||
\(179\) | 17.0658 | 1.27556 | 0.637779 | − | 0.770219i | \(-0.279853\pi\) | ||||
0.637779 | + | 0.770219i | \(0.279853\pi\) | |||||||
\(180\) | 4.65975 | 0.347317 | ||||||||
\(181\) | −0.402992 | −0.0299541 | −0.0149771 | − | 0.999888i | \(-0.504768\pi\) | ||||
−0.0149771 | + | 0.999888i | \(0.504768\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 30.4297 | 2.24943 | ||||||||
\(184\) | −2.76114 | −0.203554 | ||||||||
\(185\) | 9.58047 | 0.704370 | ||||||||
\(186\) | 4.26786 | 0.312935 | ||||||||
\(187\) | 7.03334 | 0.514329 | ||||||||
\(188\) | −5.93557 | −0.432896 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.6179 | 0.770301 | ||||||||
\(191\) | −13.6069 | −0.984559 | −0.492280 | − | 0.870437i | \(-0.663836\pi\) | ||||
−0.492280 | + | 0.870437i | \(0.663836\pi\) | |||||||
\(192\) | −22.8767 | −1.65098 | ||||||||
\(193\) | −6.39685 | −0.460456 | −0.230228 | − | 0.973137i | \(-0.573947\pi\) | ||||
−0.230228 | + | 0.973137i | \(0.573947\pi\) | |||||||
\(194\) | 20.5309 | 1.47404 | ||||||||
\(195\) | −3.57805 | −0.256229 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.8587 | −1.55737 | −0.778684 | − | 0.627416i | \(-0.784113\pi\) | ||||
−0.778684 | + | 0.627416i | \(0.784113\pi\) | |||||||
\(198\) | −5.50949 | −0.391542 | ||||||||
\(199\) | 22.1759 | 1.57201 | 0.786005 | − | 0.618220i | \(-0.212146\pi\) | ||||
0.786005 | + | 0.618220i | \(0.212146\pi\) | |||||||
\(200\) | 9.81196 | 0.693810 | ||||||||
\(201\) | −6.76607 | −0.477242 | ||||||||
\(202\) | −8.10151 | −0.570020 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −13.5904 | −0.951521 | ||||||||
\(205\) | −1.34462 | −0.0939122 | ||||||||
\(206\) | 21.2898 | 1.48333 | ||||||||
\(207\) | 4.11849 | 0.286255 | ||||||||
\(208\) | 1.85229 | 0.128433 | ||||||||
\(209\) | 7.62652 | 0.527537 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.8283 | 1.15851 | 0.579254 | − | 0.815147i | \(-0.303344\pi\) | ||||
0.579254 | + | 0.815147i | \(0.303344\pi\) | |||||||
\(212\) | −4.98043 | −0.342057 | ||||||||
\(213\) | −6.62927 | −0.454230 | ||||||||
\(214\) | −13.0164 | −0.889785 | ||||||||
\(215\) | −1.66054 | −0.113248 | ||||||||
\(216\) | 13.4186 | 0.913022 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 19.0118 | 1.28764 | ||||||||
\(219\) | −22.3654 | −1.51131 | ||||||||
\(220\) | −1.09483 | −0.0738137 | ||||||||
\(221\) | 6.30815 | 0.424332 | ||||||||
\(222\) | 21.8881 | 1.46903 | ||||||||
\(223\) | 3.85768 | 0.258329 | 0.129165 | − | 0.991623i | \(-0.458770\pi\) | ||||
0.129165 | + | 0.991623i | \(0.458770\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −14.6354 | −0.975695 | ||||||||
\(226\) | −5.29178 | −0.352004 | ||||||||
\(227\) | −28.1917 | −1.87115 | −0.935576 | − | 0.353126i | \(-0.885119\pi\) | ||||
−0.935576 | + | 0.353126i | \(0.885119\pi\) | |||||||
\(228\) | −14.7366 | −0.975956 | ||||||||
\(229\) | −15.2236 | −1.00601 | −0.503003 | − | 0.864285i | \(-0.667772\pi\) | ||||
−0.503003 | + | 0.864285i | \(0.667772\pi\) | |||||||
\(230\) | −1.34721 | −0.0888323 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.68238 | −0.570026 | ||||||||
\(233\) | −29.0175 | −1.90100 | −0.950501 | − | 0.310722i | \(-0.899429\pi\) | ||||
−0.950501 | + | 0.310722i | \(0.899429\pi\) | |||||||
\(234\) | −4.94142 | −0.323031 | ||||||||
\(235\) | −10.5594 | −0.688820 | ||||||||
\(236\) | −2.05665 | −0.133877 | ||||||||
\(237\) | 5.40168 | 0.350877 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.0381 | 1.61958 | 0.809792 | − | 0.586718i | \(-0.199580\pi\) | ||||
0.809792 | + | 0.586718i | \(0.199580\pi\) | |||||||
\(240\) | −7.09932 | −0.458259 | ||||||||
\(241\) | −1.11382 | −0.0717474 | −0.0358737 | − | 0.999356i | \(-0.511421\pi\) | ||||
−0.0358737 | + | 0.999356i | \(0.511421\pi\) | |||||||
\(242\) | −10.9752 | −0.705512 | ||||||||
\(243\) | 17.8677 | 1.14621 | ||||||||
\(244\) | 8.35104 | 0.534621 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.07199 | −0.195863 | ||||||||
\(247\) | 6.84016 | 0.435229 | ||||||||
\(248\) | 4.27054 | 0.271180 | ||||||||
\(249\) | 25.6193 | 1.62356 | ||||||||
\(250\) | 12.2865 | 0.777069 | ||||||||
\(251\) | 7.27825 | 0.459399 | 0.229700 | − | 0.973262i | \(-0.426226\pi\) | ||||
0.229700 | + | 0.973262i | \(0.426226\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.967663 | −0.0608364 | ||||||||
\(254\) | −11.1011 | −0.696544 | ||||||||
\(255\) | −24.1775 | −1.51405 | ||||||||
\(256\) | −15.2228 | −0.951423 | ||||||||
\(257\) | −8.89942 | −0.555130 | −0.277565 | − | 0.960707i | \(-0.589527\pi\) | ||||
−0.277565 | + | 0.960707i | \(0.589527\pi\) | |||||||
\(258\) | −3.79376 | −0.236189 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.981949 | −0.0608979 | ||||||||
\(261\) | 12.9506 | 0.801619 | ||||||||
\(262\) | 23.5285 | 1.45360 | ||||||||
\(263\) | −5.89870 | −0.363729 | −0.181865 | − | 0.983324i | \(-0.558213\pi\) | ||||
−0.181865 | + | 0.983324i | \(0.558213\pi\) | |||||||
\(264\) | −9.12009 | −0.561303 | ||||||||
\(265\) | −8.86021 | −0.544278 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −35.2393 | −2.15661 | ||||||||
\(268\) | −1.85686 | −0.113426 | ||||||||
\(269\) | 4.18733 | 0.255306 | 0.127653 | − | 0.991819i | \(-0.459256\pi\) | ||||
0.127653 | + | 0.991819i | \(0.459256\pi\) | |||||||
\(270\) | 6.54719 | 0.398450 | ||||||||
\(271\) | 10.0501 | 0.610499 | 0.305250 | − | 0.952272i | \(-0.401260\pi\) | ||||
0.305250 | + | 0.952272i | \(0.401260\pi\) | |||||||
\(272\) | 12.5162 | 0.758907 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.92510 | −0.539185 | ||||||||
\(275\) | 3.43868 | 0.207360 | ||||||||
\(276\) | 1.86980 | 0.112549 | ||||||||
\(277\) | −6.16607 | −0.370483 | −0.185242 | − | 0.982693i | \(-0.559307\pi\) | ||||
−0.185242 | + | 0.982693i | \(0.559307\pi\) | |||||||
\(278\) | −7.95971 | −0.477392 | ||||||||
\(279\) | −6.36991 | −0.381356 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.64050 | −0.396139 | −0.198069 | − | 0.980188i | \(-0.563467\pi\) | ||||
−0.198069 | + | 0.980188i | \(0.563467\pi\) | |||||||
\(282\) | −24.1246 | −1.43660 | ||||||||
\(283\) | 32.4418 | 1.92846 | 0.964232 | − | 0.265061i | \(-0.0853921\pi\) | ||||
0.964232 | + | 0.265061i | \(0.0853921\pi\) | |||||||
\(284\) | −1.81932 | −0.107957 | ||||||||
\(285\) | −26.2165 | −1.55293 | ||||||||
\(286\) | 1.16101 | 0.0686522 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 18.3836 | 1.08326 | ||||||||
\(289\) | 25.6253 | 1.50737 | ||||||||
\(290\) | −4.23629 | −0.248764 | ||||||||
\(291\) | −50.6928 | −2.97167 | ||||||||
\(292\) | −6.13789 | −0.359193 | ||||||||
\(293\) | 3.63051 | 0.212097 | 0.106048 | − | 0.994361i | \(-0.466180\pi\) | ||||
0.106048 | + | 0.994361i | \(0.466180\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.65880 | −0.213023 | ||||||||
\(296\) | 21.9018 | 1.27302 | ||||||||
\(297\) | 4.70267 | 0.272876 | ||||||||
\(298\) | −12.2453 | −0.709349 | ||||||||
\(299\) | −0.867889 | −0.0501913 | ||||||||
\(300\) | −6.64452 | −0.383621 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 22.1255 | 1.27318 | ||||||||
\(303\) | 20.0034 | 1.14917 | ||||||||
\(304\) | 13.5718 | 0.778396 | ||||||||
\(305\) | 14.8566 | 0.850684 | ||||||||
\(306\) | −33.3900 | −1.90878 | ||||||||
\(307\) | −0.641523 | −0.0366136 | −0.0183068 | − | 0.999832i | \(-0.505828\pi\) | ||||
−0.0183068 | + | 0.999832i | \(0.505828\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −52.5664 | −2.99040 | ||||||||
\(310\) | 2.08368 | 0.118345 | ||||||||
\(311\) | −11.8418 | −0.671485 | −0.335743 | − | 0.941954i | \(-0.608987\pi\) | ||||
−0.335743 | + | 0.941954i | \(0.608987\pi\) | |||||||
\(312\) | −8.17974 | −0.463087 | ||||||||
\(313\) | 19.7303 | 1.11522 | 0.557612 | − | 0.830102i | \(-0.311718\pi\) | ||||
0.557612 | + | 0.830102i | \(0.311718\pi\) | |||||||
\(314\) | −10.7320 | −0.605642 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.48242 | 0.0833926 | ||||||||
\(317\) | 24.5065 | 1.37642 | 0.688211 | − | 0.725510i | \(-0.258396\pi\) | ||||
0.688211 | + | 0.725510i | \(0.258396\pi\) | |||||||
\(318\) | −20.2425 | −1.13514 | ||||||||
\(319\) | −3.04281 | −0.170365 | ||||||||
\(320\) | −11.1690 | −0.624365 | ||||||||
\(321\) | 32.1388 | 1.79381 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 46.2202 | 2.57176 | ||||||||
\(324\) | 1.30954 | 0.0727522 | ||||||||
\(325\) | 3.08413 | 0.171077 | ||||||||
\(326\) | 0.372223 | 0.0206155 | ||||||||
\(327\) | −46.9420 | −2.59590 | ||||||||
\(328\) | −3.07392 | −0.169729 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.44986 | −0.244957 | ||||||||
\(331\) | 27.8301 | 1.52968 | 0.764841 | − | 0.644219i | \(-0.222817\pi\) | ||||
0.764841 | + | 0.644219i | \(0.222817\pi\) | |||||||
\(332\) | 7.03088 | 0.385869 | ||||||||
\(333\) | −32.6686 | −1.79023 | ||||||||
\(334\) | −18.6030 | −1.01791 | ||||||||
\(335\) | −3.30337 | −0.180482 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.235392 | 0.0128226 | 0.00641130 | − | 0.999979i | \(-0.497959\pi\) | ||||
0.00641130 | + | 0.999979i | \(0.497959\pi\) | |||||||
\(338\) | −13.4592 | −0.732086 | ||||||||
\(339\) | 13.0659 | 0.709643 | ||||||||
\(340\) | −6.63520 | −0.359844 | ||||||||
\(341\) | 1.49665 | 0.0810480 | ||||||||
\(342\) | −36.2060 | −1.95780 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.79614 | −0.204674 | ||||||||
\(345\) | 3.32639 | 0.179087 | ||||||||
\(346\) | −14.4401 | −0.776303 | ||||||||
\(347\) | −0.509008 | −0.0273250 | −0.0136625 | − | 0.999907i | \(-0.504349\pi\) | ||||
−0.0136625 | + | 0.999907i | \(0.504349\pi\) | |||||||
\(348\) | 5.87958 | 0.315179 | ||||||||
\(349\) | −23.8662 | −1.27753 | −0.638764 | − | 0.769403i | \(-0.720554\pi\) | ||||
−0.638764 | + | 0.769403i | \(0.720554\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.21779 | 0.225129 | ||||||||
\(352\) | −4.31933 | −0.230221 | ||||||||
\(353\) | 13.6030 | 0.724016 | 0.362008 | − | 0.932175i | \(-0.382091\pi\) | ||||
0.362008 | + | 0.932175i | \(0.382091\pi\) | |||||||
\(354\) | −8.35909 | −0.444280 | ||||||||
\(355\) | −3.23658 | −0.171780 | ||||||||
\(356\) | −9.67098 | −0.512561 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.0356 | 1.00607 | ||||||||
\(359\) | −4.84897 | −0.255919 | −0.127959 | − | 0.991779i | \(-0.540843\pi\) | ||||
−0.127959 | + | 0.991779i | \(0.540843\pi\) | |||||||
\(360\) | 18.9510 | 0.998808 | ||||||||
\(361\) | 31.1182 | 1.63780 | ||||||||
\(362\) | −0.449507 | −0.0236256 | ||||||||
\(363\) | 27.0988 | 1.42232 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.9193 | −0.571544 | ||||||||
\(366\) | 33.9421 | 1.77418 | ||||||||
\(367\) | −20.2354 | −1.05628 | −0.528139 | − | 0.849158i | \(-0.677110\pi\) | ||||
−0.528139 | + | 0.849158i | \(0.677110\pi\) | |||||||
\(368\) | −1.72201 | −0.0897659 | ||||||||
\(369\) | 4.58503 | 0.238687 | ||||||||
\(370\) | 10.6863 | 0.555555 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.89195 | −0.149941 | ||||||||
\(373\) | −14.0870 | −0.729399 | −0.364700 | − | 0.931125i | \(-0.618828\pi\) | ||||
−0.364700 | + | 0.931125i | \(0.618828\pi\) | |||||||
\(374\) | 7.84517 | 0.405664 | ||||||||
\(375\) | −30.3366 | −1.56658 | ||||||||
\(376\) | −24.1398 | −1.24491 | ||||||||
\(377\) | −2.72907 | −0.140554 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.35252 | −0.120841 | −0.0604205 | − | 0.998173i | \(-0.519244\pi\) | ||||
−0.0604205 | + | 0.998173i | \(0.519244\pi\) | |||||||
\(380\) | −7.19479 | −0.369085 | ||||||||
\(381\) | 27.4096 | 1.40424 | ||||||||
\(382\) | −15.1775 | −0.776547 | ||||||||
\(383\) | −11.8503 | −0.605524 | −0.302762 | − | 0.953066i | \(-0.597909\pi\) | ||||
−0.302762 | + | 0.953066i | \(0.597909\pi\) | |||||||
\(384\) | −3.43229 | −0.175153 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.13522 | −0.363173 | ||||||||
\(387\) | 5.66229 | 0.287830 | ||||||||
\(388\) | −13.9120 | −0.706275 | ||||||||
\(389\) | −8.23104 | −0.417330 | −0.208665 | − | 0.977987i | \(-0.566912\pi\) | ||||
−0.208665 | + | 0.977987i | \(0.566912\pi\) | |||||||
\(390\) | −3.99105 | −0.202094 | ||||||||
\(391\) | −5.86448 | −0.296579 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −58.0941 | −2.93046 | ||||||||
\(394\) | −24.3818 | −1.22834 | ||||||||
\(395\) | 2.63723 | 0.132694 | ||||||||
\(396\) | 3.73329 | 0.187605 | ||||||||
\(397\) | −7.05555 | −0.354108 | −0.177054 | − | 0.984201i | \(-0.556657\pi\) | ||||
−0.177054 | + | 0.984201i | \(0.556657\pi\) | |||||||
\(398\) | 24.7356 | 1.23988 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.11932 | 0.305966 | ||||||||
\(401\) | 32.5397 | 1.62495 | 0.812477 | − | 0.582993i | \(-0.198118\pi\) | ||||
0.812477 | + | 0.582993i | \(0.198118\pi\) | |||||||
\(402\) | −7.54705 | −0.376413 | ||||||||
\(403\) | 1.34233 | 0.0668663 | ||||||||
\(404\) | 5.48968 | 0.273122 | ||||||||
\(405\) | 2.32968 | 0.115763 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.67567 | 0.380469 | ||||||||
\(408\) | −55.2719 | −2.73637 | ||||||||
\(409\) | −4.62355 | −0.228620 | −0.114310 | − | 0.993445i | \(-0.536466\pi\) | ||||
−0.114310 | + | 0.993445i | \(0.536466\pi\) | |||||||
\(410\) | −1.49982 | −0.0740709 | ||||||||
\(411\) | 22.0369 | 1.08700 | ||||||||
\(412\) | −14.4262 | −0.710727 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.59387 | 0.225776 | ||||||||
\(415\) | 12.5080 | 0.613992 | ||||||||
\(416\) | −3.87397 | −0.189937 | ||||||||
\(417\) | 19.6533 | 0.962426 | ||||||||
\(418\) | 8.50681 | 0.416082 | ||||||||
\(419\) | −13.1741 | −0.643598 | −0.321799 | − | 0.946808i | \(-0.604288\pi\) | ||||
−0.321799 | + | 0.946808i | \(0.604288\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.1903 | 1.47139 | 0.735693 | − | 0.677316i | \(-0.236857\pi\) | ||||
0.735693 | + | 0.677316i | \(0.236857\pi\) | |||||||
\(422\) | 18.7707 | 0.913745 | ||||||||
\(423\) | 36.0067 | 1.75070 | ||||||||
\(424\) | −20.2552 | −0.983681 | ||||||||
\(425\) | 20.8400 | 1.01089 | ||||||||
\(426\) | −7.39446 | −0.358263 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 8.82008 | 0.426335 | ||||||||
\(429\) | −2.86666 | −0.138403 | ||||||||
\(430\) | −1.85221 | −0.0893214 | ||||||||
\(431\) | −5.94948 | −0.286576 | −0.143288 | − | 0.989681i | \(-0.545768\pi\) | ||||
−0.143288 | + | 0.989681i | \(0.545768\pi\) | |||||||
\(432\) | 8.36865 | 0.402637 | ||||||||
\(433\) | 27.8876 | 1.34019 | 0.670096 | − | 0.742274i | \(-0.266253\pi\) | ||||
0.670096 | + | 0.742274i | \(0.266253\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.4598 | 0.501509 | ||||||||
\(436\) | −12.8826 | −0.616966 | ||||||||
\(437\) | −6.35907 | −0.304195 | ||||||||
\(438\) | −24.9469 | −1.19201 | ||||||||
\(439\) | 25.4479 | 1.21456 | 0.607281 | − | 0.794487i | \(-0.292260\pi\) | ||||
0.607281 | + | 0.794487i | \(0.292260\pi\) | |||||||
\(440\) | −4.45266 | −0.212272 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.03628 | 0.334682 | ||||||||
\(443\) | 9.42035 | 0.447575 | 0.223787 | − | 0.974638i | \(-0.428158\pi\) | ||||
0.223787 | + | 0.974638i | \(0.428158\pi\) | |||||||
\(444\) | −14.8316 | −0.703877 | ||||||||
\(445\) | −17.2047 | −0.815582 | ||||||||
\(446\) | 4.30295 | 0.203751 | ||||||||
\(447\) | 30.2347 | 1.43005 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.2678 | −1.09808 | −0.549038 | − | 0.835798i | \(-0.685006\pi\) | ||||
−0.549038 | + | 0.835798i | \(0.685006\pi\) | |||||||
\(450\) | −16.3247 | −0.769555 | ||||||||
\(451\) | −1.07728 | −0.0507271 | ||||||||
\(452\) | 3.58577 | 0.168660 | ||||||||
\(453\) | −54.6300 | −2.56674 | ||||||||
\(454\) | −31.4458 | −1.47582 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −59.9334 | −2.80664 | ||||||||
\(457\) | 4.86796 | 0.227713 | 0.113857 | − | 0.993497i | \(-0.463680\pi\) | ||||
0.113857 | + | 0.993497i | \(0.463680\pi\) | |||||||
\(458\) | −16.9808 | −0.793462 | ||||||||
\(459\) | 28.5003 | 1.33028 | ||||||||
\(460\) | 0.912884 | 0.0425635 | ||||||||
\(461\) | 16.1888 | 0.753987 | 0.376993 | − | 0.926216i | \(-0.376958\pi\) | ||||
0.376993 | + | 0.926216i | \(0.376958\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.0971 | −0.562200 | −0.281100 | − | 0.959679i | \(-0.590699\pi\) | ||||
−0.281100 | + | 0.959679i | \(0.590699\pi\) | |||||||
\(464\) | −5.41484 | −0.251378 | ||||||||
\(465\) | −5.14480 | −0.238584 | ||||||||
\(466\) | −32.3669 | −1.49937 | ||||||||
\(467\) | 3.23514 | 0.149704 | 0.0748521 | − | 0.997195i | \(-0.476152\pi\) | ||||
0.0748521 | + | 0.997195i | \(0.476152\pi\) | |||||||
\(468\) | 3.34836 | 0.154778 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −11.7782 | −0.543290 | ||||||||
\(471\) | 26.4983 | 1.22098 | ||||||||
\(472\) | −8.36434 | −0.385000 | ||||||||
\(473\) | −1.33039 | −0.0611713 | ||||||||
\(474\) | 6.02517 | 0.276745 | ||||||||
\(475\) | 22.5975 | 1.03685 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 30.2125 | 1.38334 | ||||||||
\(478\) | 27.9282 | 1.27741 | ||||||||
\(479\) | −12.2257 | −0.558605 | −0.279303 | − | 0.960203i | \(-0.590103\pi\) | ||||
−0.279303 | + | 0.960203i | \(0.590103\pi\) | |||||||
\(480\) | 14.8479 | 0.677711 | ||||||||
\(481\) | 6.88425 | 0.313895 | ||||||||
\(482\) | −1.24238 | −0.0565890 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.43692 | 0.338042 | ||||||||
\(485\) | −24.7495 | −1.12382 | ||||||||
\(486\) | 19.9301 | 0.904047 | ||||||||
\(487\) | 3.36737 | 0.152590 | 0.0762951 | − | 0.997085i | \(-0.475691\pi\) | ||||
0.0762951 | + | 0.997085i | \(0.475691\pi\) | |||||||
\(488\) | 33.9634 | 1.53745 | ||||||||
\(489\) | −0.919055 | −0.0415611 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.58497 | −0.0715286 | −0.0357643 | − | 0.999360i | \(-0.511387\pi\) | ||||
−0.0357643 | + | 0.999360i | \(0.511387\pi\) | |||||||
\(492\) | 2.08161 | 0.0938464 | ||||||||
\(493\) | −18.4408 | −0.830532 | ||||||||
\(494\) | 7.62970 | 0.343276 | ||||||||
\(495\) | 6.64155 | 0.298515 | ||||||||
\(496\) | 2.66336 | 0.119589 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 28.5764 | 1.28054 | ||||||||
\(499\) | −27.5970 | −1.23541 | −0.617706 | − | 0.786409i | \(-0.711938\pi\) | ||||
−0.617706 | + | 0.786409i | \(0.711938\pi\) | |||||||
\(500\) | −8.32550 | −0.372328 | ||||||||
\(501\) | 45.9326 | 2.05212 | ||||||||
\(502\) | 8.11835 | 0.362340 | ||||||||
\(503\) | −0.387957 | −0.0172982 | −0.00864908 | − | 0.999963i | \(-0.502753\pi\) | ||||
−0.00864908 | + | 0.999963i | \(0.502753\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.76617 | 0.434589 | ||||||||
\(506\) | −1.07936 | −0.0479832 | ||||||||
\(507\) | 33.2321 | 1.47589 | ||||||||
\(508\) | 7.52222 | 0.333744 | ||||||||
\(509\) | −38.7667 | −1.71830 | −0.859151 | − | 0.511722i | \(-0.829008\pi\) | ||||
−0.859151 | + | 0.511722i | \(0.829008\pi\) | |||||||
\(510\) | −26.9682 | −1.19417 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −19.4724 | −0.860565 | ||||||||
\(513\) | 30.9039 | 1.36444 | ||||||||
\(514\) | −9.92664 | −0.437845 | ||||||||
\(515\) | −25.6643 | −1.13090 | ||||||||
\(516\) | 2.57069 | 0.113168 | ||||||||
\(517\) | −8.45998 | −0.372069 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 35.6539 | 1.56503 | ||||||||
\(520\) | −3.99356 | −0.175129 | ||||||||
\(521\) | −0.619049 | −0.0271210 | −0.0135605 | − | 0.999908i | \(-0.504317\pi\) | ||||
−0.0135605 | + | 0.999908i | \(0.504317\pi\) | |||||||
\(522\) | 14.4454 | 0.632257 | ||||||||
\(523\) | −1.03218 | −0.0451341 | −0.0225670 | − | 0.999745i | \(-0.507184\pi\) | ||||
−0.0225670 | + | 0.999745i | \(0.507184\pi\) | |||||||
\(524\) | −15.9432 | −0.696481 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.57956 | −0.286883 | ||||||||
\(527\) | 9.07036 | 0.395111 | ||||||||
\(528\) | −5.68783 | −0.247531 | ||||||||
\(529\) | −22.1932 | −0.964920 | ||||||||
\(530\) | −9.88290 | −0.429286 | ||||||||
\(531\) | 12.4762 | 0.541420 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.966204 | −0.0418509 | ||||||||
\(534\) | −39.3069 | −1.70097 | ||||||||
\(535\) | 15.6910 | 0.678380 | ||||||||
\(536\) | −7.55180 | −0.326188 | ||||||||
\(537\) | −47.0008 | −2.02824 | ||||||||
\(538\) | 4.67065 | 0.201366 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.43645 | −0.190915 | ||||||||
\(541\) | 38.3318 | 1.64801 | 0.824007 | − | 0.566580i | \(-0.191734\pi\) | ||||
0.824007 | + | 0.566580i | \(0.191734\pi\) | |||||||
\(542\) | 11.2101 | 0.481516 | ||||||||
\(543\) | 1.10988 | 0.0476294 | ||||||||
\(544\) | −26.1771 | −1.12233 | ||||||||
\(545\) | −22.9183 | −0.981710 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.37593 | 0.0588306 | 0.0294153 | − | 0.999567i | \(-0.490635\pi\) | ||||
0.0294153 | + | 0.999567i | \(0.490635\pi\) | |||||||
\(548\) | 6.04775 | 0.258347 | ||||||||
\(549\) | −50.6596 | −2.16210 | ||||||||
\(550\) | 3.83559 | 0.163550 | ||||||||
\(551\) | −19.9960 | −0.851860 | ||||||||
\(552\) | 7.60443 | 0.323666 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −6.87780 | −0.292210 | ||||||||
\(555\) | −26.3855 | −1.12000 | ||||||||
\(556\) | 5.39359 | 0.228739 | ||||||||
\(557\) | −14.8018 | −0.627174 | −0.313587 | − | 0.949560i | \(-0.601531\pi\) | ||||
−0.313587 | + | 0.949560i | \(0.601531\pi\) | |||||||
\(558\) | −7.10516 | −0.300785 | ||||||||
\(559\) | −1.19322 | −0.0504676 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19.3705 | −0.817823 | ||||||||
\(562\) | −7.40698 | −0.312445 | ||||||||
\(563\) | 32.7991 | 1.38232 | 0.691158 | − | 0.722704i | \(-0.257101\pi\) | ||||
0.691158 | + | 0.722704i | \(0.257101\pi\) | |||||||
\(564\) | 16.3471 | 0.688337 | ||||||||
\(565\) | 6.37910 | 0.268371 | ||||||||
\(566\) | 36.1864 | 1.52103 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.39911 | −0.310460 | ||||||||
\(569\) | 12.7274 | 0.533562 | 0.266781 | − | 0.963757i | \(-0.414040\pi\) | ||||
0.266781 | + | 0.963757i | \(0.414040\pi\) | |||||||
\(570\) | −29.2426 | −1.22484 | ||||||||
\(571\) | 25.8904 | 1.08348 | 0.541740 | − | 0.840546i | \(-0.317766\pi\) | ||||
0.541740 | + | 0.840546i | \(0.317766\pi\) | |||||||
\(572\) | −0.786717 | −0.0328943 | ||||||||
\(573\) | 37.4746 | 1.56552 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.86721 | −0.119571 | ||||||||
\(576\) | 38.0852 | 1.58688 | ||||||||
\(577\) | −15.7044 | −0.653784 | −0.326892 | − | 0.945062i | \(-0.606001\pi\) | ||||
−0.326892 | + | 0.945062i | \(0.606001\pi\) | |||||||
\(578\) | 28.5831 | 1.18890 | ||||||||
\(579\) | 17.6175 | 0.732160 | ||||||||
\(580\) | 2.87056 | 0.119193 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −56.5441 | −2.34383 | ||||||||
\(583\) | −7.09861 | −0.293994 | ||||||||
\(584\) | −24.9626 | −1.03296 | ||||||||
\(585\) | 5.95675 | 0.246281 | ||||||||
\(586\) | 4.04957 | 0.167286 | ||||||||
\(587\) | −11.2577 | −0.464653 | −0.232327 | − | 0.972638i | \(-0.574634\pi\) | ||||
−0.232327 | + | 0.972638i | \(0.574634\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.83533 | 0.405258 | ||||||||
\(590\) | −4.08112 | −0.168017 | ||||||||
\(591\) | 60.2009 | 2.47634 | ||||||||
\(592\) | 13.6593 | 0.561393 | ||||||||
\(593\) | −3.77210 | −0.154902 | −0.0774508 | − | 0.996996i | \(-0.524678\pi\) | ||||
−0.0774508 | + | 0.996996i | \(0.524678\pi\) | |||||||
\(594\) | 5.24548 | 0.215224 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.29752 | 0.339880 | ||||||||
\(597\) | −61.0746 | −2.49962 | ||||||||
\(598\) | −0.968066 | −0.0395872 | ||||||||
\(599\) | 22.1317 | 0.904278 | 0.452139 | − | 0.891947i | \(-0.350661\pi\) | ||||
0.452139 | + | 0.891947i | \(0.350661\pi\) | |||||||
\(600\) | −27.0231 | −1.10321 | ||||||||
\(601\) | 16.4817 | 0.672301 | 0.336151 | − | 0.941808i | \(-0.390875\pi\) | ||||
0.336151 | + | 0.941808i | \(0.390875\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.2642 | 0.458713 | ||||||||
\(604\) | −14.9925 | −0.610036 | ||||||||
\(605\) | 13.2303 | 0.537889 | ||||||||
\(606\) | 22.3123 | 0.906376 | ||||||||
\(607\) | 14.0566 | 0.570539 | 0.285270 | − | 0.958447i | \(-0.407917\pi\) | ||||
0.285270 | + | 0.958447i | \(0.407917\pi\) | |||||||
\(608\) | −28.3848 | −1.15116 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 16.5714 | 0.670956 | ||||||||
\(611\) | −7.58769 | −0.306965 | ||||||||
\(612\) | 22.6254 | 0.914579 | ||||||||
\(613\) | −36.8757 | −1.48939 | −0.744697 | − | 0.667403i | \(-0.767406\pi\) | ||||
−0.744697 | + | 0.667403i | \(0.767406\pi\) | |||||||
\(614\) | −0.715571 | −0.0288781 | ||||||||
\(615\) | 3.70320 | 0.149328 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.53517 | 0.303354 | 0.151677 | − | 0.988430i | \(-0.451533\pi\) | ||||
0.151677 | + | 0.988430i | \(0.451533\pi\) | |||||||
\(618\) | −58.6340 | −2.35860 | ||||||||
\(619\) | 22.5002 | 0.904358 | 0.452179 | − | 0.891927i | \(-0.350647\pi\) | ||||
0.452179 | + | 0.891927i | \(0.350647\pi\) | |||||||
\(620\) | −1.41192 | −0.0567042 | ||||||||
\(621\) | −3.92113 | −0.157350 | ||||||||
\(622\) | −13.2086 | −0.529617 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −5.10137 | −0.204218 | ||||||||
\(625\) | 1.14891 | 0.0459564 | ||||||||
\(626\) | 22.0077 | 0.879606 | ||||||||
\(627\) | −21.0041 | −0.838824 | ||||||||
\(628\) | 7.27213 | 0.290190 | ||||||||
\(629\) | 46.5181 | 1.85480 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.4663 | 1.01380 | 0.506899 | − | 0.862005i | \(-0.330792\pi\) | ||||
0.506899 | + | 0.862005i | \(0.330792\pi\) | |||||||
\(632\) | 6.02896 | 0.239819 | ||||||||
\(633\) | −46.3467 | −1.84212 | ||||||||
\(634\) | 27.3352 | 1.08562 | ||||||||
\(635\) | 13.3821 | 0.531051 | ||||||||
\(636\) | 13.7166 | 0.543897 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −3.39403 | −0.134371 | ||||||||
\(639\) | 11.0365 | 0.436595 | ||||||||
\(640\) | −1.67573 | −0.0662390 | ||||||||
\(641\) | 45.2070 | 1.78557 | 0.892785 | − | 0.450483i | \(-0.148748\pi\) | ||||
0.892785 | + | 0.450483i | \(0.148748\pi\) | |||||||
\(642\) | 35.8485 | 1.41483 | ||||||||
\(643\) | 7.05984 | 0.278413 | 0.139206 | − | 0.990263i | \(-0.455545\pi\) | ||||
0.139206 | + | 0.990263i | \(0.455545\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.57328 | 0.180073 | ||||||||
\(646\) | 51.5552 | 2.02841 | ||||||||
\(647\) | −0.683172 | −0.0268583 | −0.0134291 | − | 0.999910i | \(-0.504275\pi\) | ||||
−0.0134291 | + | 0.999910i | \(0.504275\pi\) | |||||||
\(648\) | 5.32586 | 0.209220 | ||||||||
\(649\) | −2.93135 | −0.115066 | ||||||||
\(650\) | 3.44011 | 0.134932 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.252223 | −0.00987780 | ||||||||
\(653\) | −17.1829 | −0.672419 | −0.336210 | − | 0.941787i | \(-0.609145\pi\) | ||||
−0.336210 | + | 0.941787i | \(0.609145\pi\) | |||||||
\(654\) | −52.3603 | −2.04745 | ||||||||
\(655\) | −28.3630 | −1.10823 | ||||||||
\(656\) | −1.91708 | −0.0748493 | ||||||||
\(657\) | 37.2340 | 1.45264 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.11888 | −0.277312 | −0.138656 | − | 0.990341i | \(-0.544278\pi\) | ||||
−0.138656 | + | 0.990341i | \(0.544278\pi\) | |||||||
\(660\) | 3.01528 | 0.117369 | ||||||||
\(661\) | −24.3519 | −0.947180 | −0.473590 | − | 0.880745i | \(-0.657042\pi\) | ||||
−0.473590 | + | 0.880745i | \(0.657042\pi\) | |||||||
\(662\) | 31.0424 | 1.20650 | ||||||||
\(663\) | −17.3732 | −0.674721 | ||||||||
\(664\) | 28.5944 | 1.10968 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −36.4394 | −1.41200 | ||||||||
\(667\) | 2.53713 | 0.0982379 | ||||||||
\(668\) | 12.6056 | 0.487726 | ||||||||
\(669\) | −10.6244 | −0.410763 | ||||||||
\(670\) | −3.68466 | −0.142351 | ||||||||
\(671\) | 11.9028 | 0.459501 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 45.7116 | 1.76205 | 0.881027 | − | 0.473066i | \(-0.156853\pi\) | ||||
0.881027 | + | 0.473066i | \(0.156853\pi\) | |||||||
\(674\) | 0.262562 | 0.0101135 | ||||||||
\(675\) | 13.9341 | 0.536324 | ||||||||
\(676\) | 9.12013 | 0.350774 | ||||||||
\(677\) | 22.1983 | 0.853151 | 0.426576 | − | 0.904452i | \(-0.359720\pi\) | ||||
0.426576 | + | 0.904452i | \(0.359720\pi\) | |||||||
\(678\) | 14.5740 | 0.559713 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −26.9851 | −1.03483 | ||||||||
\(681\) | 77.6427 | 2.97527 | ||||||||
\(682\) | 1.66940 | 0.0639246 | ||||||||
\(683\) | 11.3820 | 0.435522 | 0.217761 | − | 0.976002i | \(-0.430125\pi\) | ||||
0.217761 | + | 0.976002i | \(0.430125\pi\) | |||||||
\(684\) | 24.5336 | 0.938066 | ||||||||
\(685\) | 10.7590 | 0.411079 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 41.9273 | 1.59963 | ||||||||
\(688\) | −2.36750 | −0.0902601 | ||||||||
\(689\) | −6.36669 | −0.242552 | ||||||||
\(690\) | 3.71034 | 0.141250 | ||||||||
\(691\) | −38.3097 | −1.45737 | −0.728685 | − | 0.684849i | \(-0.759868\pi\) | ||||
−0.728685 | + | 0.684849i | \(0.759868\pi\) | |||||||
\(692\) | 9.78476 | 0.371961 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.567761 | −0.0215519 | ||||||||
\(695\) | 9.59523 | 0.363968 | ||||||||
\(696\) | 23.9121 | 0.906385 | ||||||||
\(697\) | −6.52880 | −0.247296 | ||||||||
\(698\) | −26.6210 | −1.00762 | ||||||||
\(699\) | 79.9170 | 3.02274 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.1871 | −1.17792 | −0.588961 | − | 0.808162i | \(-0.700463\pi\) | ||||
−0.588961 | + | 0.808162i | \(0.700463\pi\) | |||||||
\(702\) | 4.70463 | 0.177565 | ||||||||
\(703\) | 50.4413 | 1.90243 | ||||||||
\(704\) | −8.94835 | −0.337254 | ||||||||
\(705\) | 29.0816 | 1.09528 | ||||||||
\(706\) | 15.1732 | 0.571050 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 5.66421 | 0.212874 | ||||||||
\(709\) | 24.9158 | 0.935733 | 0.467867 | − | 0.883799i | \(-0.345023\pi\) | ||||
0.467867 | + | 0.883799i | \(0.345023\pi\) | |||||||
\(710\) | −3.61016 | −0.135487 | ||||||||
\(711\) | −8.99274 | −0.337254 | ||||||||
\(712\) | −39.3316 | −1.47401 | ||||||||
\(713\) | −1.24792 | −0.0467349 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.39957 | −0.0523411 | ||||||||
\(716\) | −12.8988 | −0.482050 | ||||||||
\(717\) | −68.9574 | −2.57526 | ||||||||
\(718\) | −5.40867 | −0.201850 | ||||||||
\(719\) | 41.1707 | 1.53541 | 0.767704 | − | 0.640804i | \(-0.221399\pi\) | ||||
0.767704 | + | 0.640804i | \(0.221399\pi\) | |||||||
\(720\) | 11.8190 | 0.440468 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 34.7101 | 1.29178 | ||||||||
\(723\) | 3.06756 | 0.114084 | ||||||||
\(724\) | 0.304591 | 0.0113200 | ||||||||
\(725\) | −9.01591 | −0.334843 | ||||||||
\(726\) | 30.2267 | 1.12182 | ||||||||
\(727\) | −2.84985 | −0.105695 | −0.0528475 | − | 0.998603i | \(-0.516830\pi\) | ||||
−0.0528475 | + | 0.998603i | \(0.516830\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −44.0115 | −1.63005 | ||||||||
\(730\) | −12.1797 | −0.450791 | ||||||||
\(731\) | −8.06276 | −0.298212 | ||||||||
\(732\) | −22.9996 | −0.850088 | ||||||||
\(733\) | 36.0067 | 1.32994 | 0.664968 | − | 0.746872i | \(-0.268445\pi\) | ||||
0.664968 | + | 0.746872i | \(0.268445\pi\) | |||||||
\(734\) | −22.5711 | −0.833113 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.60150 | 0.132753 | ||||||||
\(737\) | −2.64659 | −0.0974883 | ||||||||
\(738\) | 5.11426 | 0.188258 | ||||||||
\(739\) | −5.90631 | −0.217267 | −0.108634 | − | 0.994082i | \(-0.534648\pi\) | ||||
−0.108634 | + | 0.994082i | \(0.534648\pi\) | |||||||
\(740\) | −7.24116 | −0.266190 | ||||||||
\(741\) | −18.8385 | −0.692048 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −47.1256 | −1.72887 | −0.864436 | − | 0.502744i | \(-0.832324\pi\) | ||||
−0.864436 | + | 0.502744i | \(0.832324\pi\) | |||||||
\(744\) | −11.7615 | −0.431197 | ||||||||
\(745\) | 14.7613 | 0.540814 | ||||||||
\(746\) | −15.7130 | −0.575295 | ||||||||
\(747\) | −42.6511 | −1.56052 | ||||||||
\(748\) | −5.31598 | −0.194371 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −33.8383 | −1.23560 | ||||||||
\(751\) | −3.99429 | −0.145754 | −0.0728768 | − | 0.997341i | \(-0.523218\pi\) | ||||
−0.0728768 | + | 0.997341i | \(0.523218\pi\) | |||||||
\(752\) | −15.0550 | −0.548999 | ||||||||
\(753\) | −20.0450 | −0.730480 | ||||||||
\(754\) | −3.04408 | −0.110859 | ||||||||
\(755\) | −26.6717 | −0.970683 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.0523804 | 0.00190380 | 0.000951899 | − | 1.00000i | \(-0.499697\pi\) | ||||
0.000951899 | 1.00000i | \(0.499697\pi\) | ||||||||
\(758\) | −2.62407 | −0.0953104 | ||||||||
\(759\) | 2.66503 | 0.0967346 | ||||||||
\(760\) | −29.2610 | −1.06141 | ||||||||
\(761\) | 47.4215 | 1.71903 | 0.859515 | − | 0.511111i | \(-0.170766\pi\) | ||||
0.859515 | + | 0.511111i | \(0.170766\pi\) | |||||||
\(762\) | 30.5734 | 1.10756 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 10.2844 | 0.372077 | ||||||||
\(765\) | 40.2508 | 1.45527 | ||||||||
\(766\) | −13.2182 | −0.477592 | ||||||||
\(767\) | −2.62911 | −0.0949315 | ||||||||
\(768\) | 41.9249 | 1.51283 | ||||||||
\(769\) | −24.0845 | −0.868508 | −0.434254 | − | 0.900790i | \(-0.642988\pi\) | ||||
−0.434254 | + | 0.900790i | \(0.642988\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.5098 | 0.882700 | ||||||||
\(772\) | 4.83490 | 0.174012 | ||||||||
\(773\) | 25.7537 | 0.926297 | 0.463148 | − | 0.886281i | \(-0.346720\pi\) | ||||
0.463148 | + | 0.886281i | \(0.346720\pi\) | |||||||
\(774\) | 6.31587 | 0.227019 | ||||||||
\(775\) | 4.43460 | 0.159295 | ||||||||
\(776\) | −56.5797 | −2.03109 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.18111 | −0.329159 | ||||||||
\(779\) | −7.07942 | −0.253647 | ||||||||
\(780\) | 2.70438 | 0.0968323 | ||||||||
\(781\) | −2.59308 | −0.0927877 | ||||||||
\(782\) | −6.54139 | −0.233920 | ||||||||
\(783\) | −12.3300 | −0.440637 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.9372 | 0.461747 | ||||||||
\(786\) | −64.7997 | −2.31133 | ||||||||
\(787\) | −30.9026 | −1.10156 | −0.550780 | − | 0.834651i | \(-0.685670\pi\) | ||||
−0.550780 | + | 0.834651i | \(0.685670\pi\) | |||||||
\(788\) | 16.5214 | 0.588549 | ||||||||
\(789\) | 16.2456 | 0.578358 | ||||||||
\(790\) | 2.94164 | 0.104659 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 15.1832 | 0.539511 | ||||||||
\(793\) | 10.6755 | 0.379098 | ||||||||
\(794\) | −7.86994 | −0.279294 | ||||||||
\(795\) | 24.4018 | 0.865444 | ||||||||
\(796\) | −16.7611 | −0.594083 | ||||||||
\(797\) | −39.1277 | −1.38598 | −0.692988 | − | 0.720949i | \(-0.743706\pi\) | ||||
−0.692988 | + | 0.720949i | \(0.743706\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −51.2713 | −1.81385 | ||||||||
\(800\) | −12.7983 | −0.452487 | ||||||||
\(801\) | 58.6666 | 2.07288 | ||||||||
\(802\) | 36.2956 | 1.28164 | ||||||||
\(803\) | −8.74834 | −0.308722 | ||||||||
\(804\) | 5.11397 | 0.180356 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.49727 | 0.0527391 | ||||||||
\(807\) | −11.5323 | −0.405956 | ||||||||
\(808\) | 22.3264 | 0.785438 | ||||||||
\(809\) | 15.7632 | 0.554205 | 0.277102 | − | 0.960840i | \(-0.410626\pi\) | ||||
0.277102 | + | 0.960840i | \(0.410626\pi\) | |||||||
\(810\) | 2.59858 | 0.0913049 | ||||||||
\(811\) | −32.9193 | −1.15595 | −0.577976 | − | 0.816054i | \(-0.696157\pi\) | ||||
−0.577976 | + | 0.816054i | \(0.696157\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −27.6789 | −0.970740 | ||||||||
\(814\) | 8.56164 | 0.300085 | ||||||||
\(815\) | −0.448706 | −0.0157175 | ||||||||
\(816\) | −34.4708 | −1.20672 | ||||||||
\(817\) | −8.74275 | −0.305870 | ||||||||
\(818\) | −5.15722 | −0.180318 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.01630 | 0.0354906 | ||||||||
\(821\) | −41.7837 | −1.45826 | −0.729131 | − | 0.684375i | \(-0.760075\pi\) | ||||
−0.729131 | + | 0.684375i | \(0.760075\pi\) | |||||||
\(822\) | 24.5805 | 0.857345 | ||||||||
\(823\) | 35.0046 | 1.22018 | 0.610091 | − | 0.792331i | \(-0.291133\pi\) | ||||
0.610091 | + | 0.792331i | \(0.291133\pi\) | |||||||
\(824\) | −58.6708 | −2.04390 | ||||||||
\(825\) | −9.47044 | −0.329719 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.3017 | 0.566866 | 0.283433 | − | 0.958992i | \(-0.408527\pi\) | ||||
0.283433 | + | 0.958992i | \(0.408527\pi\) | |||||||
\(828\) | −3.11286 | −0.108179 | ||||||||
\(829\) | 21.1961 | 0.736171 | 0.368085 | − | 0.929792i | \(-0.380013\pi\) | ||||
0.368085 | + | 0.929792i | \(0.380013\pi\) | |||||||
\(830\) | 13.9517 | 0.484271 | ||||||||
\(831\) | 16.9819 | 0.589097 | ||||||||
\(832\) | −8.02571 | −0.278241 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 21.9218 | 0.759089 | ||||||||
\(835\) | 22.4255 | 0.776065 | ||||||||
\(836\) | −5.76431 | −0.199363 | ||||||||
\(837\) | 6.06466 | 0.209625 | ||||||||
\(838\) | −14.6948 | −0.507622 | ||||||||
\(839\) | 33.6120 | 1.16042 | 0.580208 | − | 0.814468i | \(-0.302971\pi\) | ||||
0.580208 | + | 0.814468i | \(0.302971\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.0220 | −0.724897 | ||||||||
\(842\) | 33.6750 | 1.16052 | ||||||||
\(843\) | 18.2885 | 0.629891 | ||||||||
\(844\) | −12.7193 | −0.437815 | ||||||||
\(845\) | 16.2248 | 0.558149 | ||||||||
\(846\) | 40.1628 | 1.38082 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −12.6324 | −0.433797 | ||||||||
\(849\) | −89.3477 | −3.06640 | ||||||||
\(850\) | 23.2454 | 0.797312 | ||||||||
\(851\) | −6.40006 | −0.219391 | ||||||||
\(852\) | 5.01057 | 0.171659 | ||||||||
\(853\) | −49.5839 | −1.69772 | −0.848860 | − | 0.528618i | \(-0.822711\pi\) | ||||
−0.848860 | + | 0.528618i | \(0.822711\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 43.6454 | 1.49264 | ||||||||
\(856\) | 35.8710 | 1.22605 | ||||||||
\(857\) | −40.8291 | −1.39470 | −0.697348 | − | 0.716732i | \(-0.745637\pi\) | ||||
−0.697348 | + | 0.716732i | \(0.745637\pi\) | |||||||
\(858\) | −3.19754 | −0.109162 | ||||||||
\(859\) | −5.75495 | −0.196356 | −0.0981782 | − | 0.995169i | \(-0.531302\pi\) | ||||
−0.0981782 | + | 0.995169i | \(0.531302\pi\) | |||||||
\(860\) | 1.25508 | 0.0427978 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.63621 | −0.226030 | ||||||||
\(863\) | −5.44313 | −0.185286 | −0.0926432 | − | 0.995699i | \(-0.529532\pi\) | ||||
−0.0926432 | + | 0.995699i | \(0.529532\pi\) | |||||||
\(864\) | −17.5027 | −0.595452 | ||||||||
\(865\) | 17.4071 | 0.591860 | ||||||||
\(866\) | 31.1066 | 1.05704 | ||||||||
\(867\) | −70.5744 | −2.39683 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.11290 | 0.0716751 | ||||||||
\(870\) | 11.6671 | 0.395553 | ||||||||
\(871\) | −2.37370 | −0.0804299 | ||||||||
\(872\) | −52.3932 | −1.77426 | ||||||||
\(873\) | 84.3937 | 2.85629 | ||||||||
\(874\) | −7.09307 | −0.239927 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 16.9043 | 0.571144 | ||||||||
\(877\) | −0.0377361 | −0.00127426 | −0.000637128 | − | 1.00000i | \(-0.500203\pi\) | ||||
−0.000637128 | 1.00000i | \(0.500203\pi\) | ||||||||
\(878\) | 28.3852 | 0.957956 | ||||||||
\(879\) | −9.99877 | −0.337250 | ||||||||
\(880\) | −2.77694 | −0.0936107 | ||||||||
\(881\) | 43.4095 | 1.46250 | 0.731252 | − | 0.682108i | \(-0.238936\pi\) | ||||
0.731252 | + | 0.682108i | \(0.238936\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.9703 | 1.00858 | 0.504291 | − | 0.863534i | \(-0.331754\pi\) | ||||
0.504291 | + | 0.863534i | \(0.331754\pi\) | |||||||
\(884\) | −4.76786 | −0.160361 | ||||||||
\(885\) | 10.0767 | 0.338723 | ||||||||
\(886\) | 10.5077 | 0.353013 | ||||||||
\(887\) | −19.5093 | −0.655059 | −0.327529 | − | 0.944841i | \(-0.606216\pi\) | ||||
−0.327529 | + | 0.944841i | \(0.606216\pi\) | |||||||
\(888\) | −60.3197 | −2.02420 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −19.1906 | −0.643270 | ||||||||
\(891\) | 1.86649 | 0.0625298 | ||||||||
\(892\) | −2.91573 | −0.0976259 | ||||||||
\(893\) | −55.5954 | −1.86043 | ||||||||
\(894\) | 33.7246 | 1.12792 | ||||||||
\(895\) | −22.9470 | −0.767033 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.39025 | 0.0798081 | ||||||||
\(898\) | −25.9535 | −0.866080 | ||||||||
\(899\) | −3.92407 | −0.130875 | ||||||||
\(900\) | 11.0618 | 0.368728 | ||||||||
\(901\) | −43.0208 | −1.43323 | ||||||||
\(902\) | −1.20163 | −0.0400097 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.5832 | 0.485031 | ||||||||
\(905\) | 0.541870 | 0.0180124 | ||||||||
\(906\) | −60.9357 | −2.02445 | ||||||||
\(907\) | 35.2788 | 1.17141 | 0.585707 | − | 0.810523i | \(-0.300817\pi\) | ||||
0.585707 | + | 0.810523i | \(0.300817\pi\) | |||||||
\(908\) | 21.3080 | 0.707132 | ||||||||
\(909\) | −33.3018 | −1.10455 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.2689 | 0.505882 | 0.252941 | − | 0.967482i | \(-0.418602\pi\) | ||||
0.252941 | + | 0.967482i | \(0.418602\pi\) | |||||||
\(912\) | −37.3780 | −1.23771 | ||||||||
\(913\) | 10.0211 | 0.331651 | ||||||||
\(914\) | 5.42984 | 0.179603 | ||||||||
\(915\) | −40.9163 | −1.35265 | ||||||||
\(916\) | 11.5064 | 0.380182 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 31.7900 | 1.04923 | ||||||||
\(919\) | 52.3612 | 1.72724 | 0.863619 | − | 0.504145i | \(-0.168192\pi\) | ||||
0.863619 | + | 0.504145i | \(0.168192\pi\) | |||||||
\(920\) | 3.71267 | 0.122403 | ||||||||
\(921\) | 1.76681 | 0.0582185 | ||||||||
\(922\) | 18.0574 | 0.594688 | ||||||||
\(923\) | −2.32571 | −0.0765518 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.7432 | 0.747792 | ||||||||
\(926\) | −13.4934 | −0.443421 | ||||||||
\(927\) | 87.5129 | 2.87430 | ||||||||
\(928\) | 11.3249 | 0.371758 | ||||||||
\(929\) | 46.0886 | 1.51212 | 0.756060 | − | 0.654503i | \(-0.227122\pi\) | ||||
0.756060 | + | 0.654503i | \(0.227122\pi\) | |||||||
\(930\) | −5.73864 | −0.188177 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 21.9322 | 0.718413 | ||||||||
\(933\) | 32.6133 | 1.06771 | ||||||||
\(934\) | 3.60856 | 0.118076 | ||||||||
\(935\) | −9.45716 | −0.309282 | ||||||||
\(936\) | 13.6177 | 0.445108 | ||||||||
\(937\) | −33.6725 | −1.10003 | −0.550016 | − | 0.835154i | \(-0.685378\pi\) | ||||
−0.550016 | + | 0.835154i | \(0.685378\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −54.3392 | −1.77329 | ||||||||
\(940\) | 7.98107 | 0.260314 | ||||||||
\(941\) | −9.44269 | −0.307823 | −0.153911 | − | 0.988085i | \(-0.549187\pi\) | ||||
−0.153911 | + | 0.988085i | \(0.549187\pi\) | |||||||
\(942\) | 29.5569 | 0.963017 | ||||||||
\(943\) | 0.898247 | 0.0292509 | ||||||||
\(944\) | −5.21650 | −0.169783 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.48395 | −0.0482474 | ||||||||
\(947\) | −30.4919 | −0.990853 | −0.495427 | − | 0.868650i | \(-0.664988\pi\) | ||||
−0.495427 | + | 0.868650i | \(0.664988\pi\) | |||||||
\(948\) | −4.08272 | −0.132601 | ||||||||
\(949\) | −7.84632 | −0.254702 | ||||||||
\(950\) | 25.2059 | 0.817787 | ||||||||
\(951\) | −67.4932 | −2.18862 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −60.9536 | −1.97448 | −0.987241 | − | 0.159235i | \(-0.949097\pi\) | ||||
−0.987241 | + | 0.159235i | \(0.949097\pi\) | |||||||
\(954\) | 33.6998 | 1.09107 | ||||||||
\(955\) | 18.2961 | 0.592046 | ||||||||
\(956\) | −18.9245 | −0.612061 | ||||||||
\(957\) | 8.38018 | 0.270893 | ||||||||
\(958\) | −13.6368 | −0.440586 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 30.7604 | 0.992787 | ||||||||
\(961\) | −29.0699 | −0.937738 | ||||||||
\(962\) | 7.67887 | 0.247577 | ||||||||
\(963\) | −53.5049 | −1.72417 | ||||||||
\(964\) | 0.841853 | 0.0271143 | ||||||||
\(965\) | 8.60132 | 0.276886 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.3405 | 0.429001 | 0.214501 | − | 0.976724i | \(-0.431188\pi\) | ||||
0.214501 | + | 0.976724i | \(0.431188\pi\) | |||||||
\(968\) | 30.2457 | 0.972135 | ||||||||
\(969\) | −127.295 | −4.08929 | ||||||||
\(970\) | −27.6063 | −0.886383 | ||||||||
\(971\) | 14.3391 | 0.460163 | 0.230081 | − | 0.973171i | \(-0.426101\pi\) | ||||
0.230081 | + | 0.973171i | \(0.426101\pi\) | |||||||
\(972\) | −13.5048 | −0.433168 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 3.75605 | 0.120352 | ||||||||
\(975\) | −8.49397 | −0.272025 | ||||||||
\(976\) | 21.1816 | 0.678007 | ||||||||
\(977\) | 46.5148 | 1.48814 | 0.744069 | − | 0.668102i | \(-0.232893\pi\) | ||||
0.744069 | + | 0.668102i | \(0.232893\pi\) | |||||||
\(978\) | −1.02514 | −0.0327803 | ||||||||
\(979\) | −13.7841 | −0.440541 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 78.1493 | 2.49511 | ||||||||
\(982\) | −1.76791 | −0.0564164 | ||||||||
\(983\) | −43.7876 | −1.39661 | −0.698303 | − | 0.715802i | \(-0.746061\pi\) | ||||
−0.698303 | + | 0.715802i | \(0.746061\pi\) | |||||||
\(984\) | 8.46586 | 0.269882 | ||||||||
\(985\) | 29.3916 | 0.936494 | ||||||||
\(986\) | −20.5693 | −0.655062 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.16997 | −0.164479 | ||||||||
\(989\) | 1.10929 | 0.0352734 | ||||||||
\(990\) | 7.40815 | 0.235447 | ||||||||
\(991\) | −8.16795 | −0.259463 | −0.129732 | − | 0.991549i | \(-0.541412\pi\) | ||||
−0.129732 | + | 0.991549i | \(0.541412\pi\) | |||||||
\(992\) | −5.57030 | −0.176857 | ||||||||
\(993\) | −76.6468 | −2.43231 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −29.8182 | −0.945299 | ||||||||
\(996\) | −19.3637 | −0.613562 | ||||||||
\(997\) | −44.3813 | −1.40557 | −0.702786 | − | 0.711402i | \(-0.748061\pi\) | ||||
−0.702786 | + | 0.711402i | \(0.748061\pi\) | |||||||
\(998\) | −30.7824 | −0.974401 | ||||||||
\(999\) | 31.1031 | 0.984059 |
(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.s.1.10 | 17 | ||
7.2 | even | 3 | 287.2.e.d.165.8 | ✓ | 34 | ||
7.4 | even | 3 | 287.2.e.d.247.8 | yes | 34 | ||
7.6 | odd | 2 | 2009.2.a.r.1.10 | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.2.e.d.165.8 | ✓ | 34 | 7.2 | even | 3 | ||
287.2.e.d.247.8 | yes | 34 | 7.4 | even | 3 | ||
2009.2.a.r.1.10 | 17 | 7.6 | odd | 2 | |||
2009.2.a.s.1.10 | 17 | 1.1 | even | 1 | trivial |