Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, 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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.74359 | −1.94001 | −0.970004 | − | 0.243088i | \(-0.921840\pi\) | ||||
−0.970004 | + | 0.243088i | \(0.921840\pi\) | |||||||
\(3\) | −0.0877195 | −0.0506449 | −0.0253224 | − | 0.999679i | \(-0.508061\pi\) | ||||
−0.0253224 | + | 0.999679i | \(0.508061\pi\) | |||||||
\(4\) | 5.52727 | 2.76363 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.240666 | 0.0982515 | ||||||||
\(7\) | −1.38863 | −0.524854 | −0.262427 | − | 0.964952i | \(-0.584523\pi\) | ||||
−0.262427 | + | 0.964952i | \(0.584523\pi\) | |||||||
\(8\) | −9.67736 | −3.42146 | ||||||||
\(9\) | −2.99231 | −0.997435 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.68686 | −0.508609 | −0.254304 | − | 0.967124i | \(-0.581847\pi\) | ||||
−0.254304 | + | 0.967124i | \(0.581847\pi\) | |||||||
\(12\) | −0.484849 | −0.139964 | ||||||||
\(13\) | −1.34511 | −0.373065 | −0.186533 | − | 0.982449i | \(-0.559725\pi\) | ||||
−0.186533 | + | 0.982449i | \(0.559725\pi\) | |||||||
\(14\) | 3.80984 | 1.01822 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 15.4962 | 3.87404 | ||||||||
\(17\) | −3.06688 | −0.743826 | −0.371913 | − | 0.928267i | \(-0.621298\pi\) | ||||
−0.371913 | + | 0.928267i | \(0.621298\pi\) | |||||||
\(18\) | 8.20965 | 1.93503 | ||||||||
\(19\) | 8.07490 | 1.85251 | 0.926255 | − | 0.376898i | \(-0.123009\pi\) | ||||
0.926255 | + | 0.376898i | \(0.123009\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.121810 | 0.0265812 | ||||||||
\(22\) | 4.62806 | 0.986706 | ||||||||
\(23\) | −2.18428 | −0.455453 | −0.227727 | − | 0.973725i | \(-0.573129\pi\) | ||||
−0.227727 | + | 0.973725i | \(0.573129\pi\) | |||||||
\(24\) | 0.848894 | 0.173280 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.69042 | 0.723750 | ||||||||
\(27\) | 0.525642 | 0.101160 | ||||||||
\(28\) | −7.67535 | −1.45051 | ||||||||
\(29\) | −8.72354 | −1.61992 | −0.809961 | − | 0.586484i | \(-0.800512\pi\) | ||||
−0.809961 | + | 0.586484i | \(0.800512\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.09750 | 1.27475 | 0.637375 | − | 0.770554i | \(-0.280020\pi\) | ||||
0.637375 | + | 0.770554i | \(0.280020\pi\) | |||||||
\(32\) | −23.1603 | −4.09420 | ||||||||
\(33\) | 0.147971 | 0.0257584 | ||||||||
\(34\) | 8.41424 | 1.44303 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −16.5393 | −2.75655 | ||||||||
\(37\) | −0.976988 | −0.160616 | −0.0803079 | − | 0.996770i | \(-0.525590\pi\) | ||||
−0.0803079 | + | 0.996770i | \(0.525590\pi\) | |||||||
\(38\) | −22.1542 | −3.59388 | ||||||||
\(39\) | 0.117992 | 0.0188939 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.27244 | 0.511070 | 0.255535 | − | 0.966800i | \(-0.417748\pi\) | ||||
0.255535 | + | 0.966800i | \(0.417748\pi\) | |||||||
\(42\) | −0.334197 | −0.0515677 | ||||||||
\(43\) | 8.18683 | 1.24848 | 0.624240 | − | 0.781233i | \(-0.285409\pi\) | ||||
0.624240 | + | 0.781233i | \(0.285409\pi\) | |||||||
\(44\) | −9.32375 | −1.40561 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.99275 | 0.883583 | ||||||||
\(47\) | 8.16516 | 1.19101 | 0.595505 | − | 0.803351i | \(-0.296952\pi\) | ||||
0.595505 | + | 0.803351i | \(0.296952\pi\) | |||||||
\(48\) | −1.35931 | −0.196200 | ||||||||
\(49\) | −5.07170 | −0.724528 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.269025 | 0.0376710 | ||||||||
\(52\) | −7.43476 | −1.03102 | ||||||||
\(53\) | −2.61978 | −0.359854 | −0.179927 | − | 0.983680i | \(-0.557586\pi\) | ||||
−0.179927 | + | 0.983680i | \(0.557586\pi\) | |||||||
\(54\) | −1.44214 | −0.196251 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 13.4383 | 1.79577 | ||||||||
\(57\) | −0.708326 | −0.0938201 | ||||||||
\(58\) | 23.9338 | 3.14266 | ||||||||
\(59\) | 2.45879 | 0.320107 | 0.160054 | − | 0.987108i | \(-0.448833\pi\) | ||||
0.160054 | + | 0.987108i | \(0.448833\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.69058 | −0.472531 | −0.236265 | − | 0.971689i | \(-0.575923\pi\) | ||||
−0.236265 | + | 0.971689i | \(0.575923\pi\) | |||||||
\(62\) | −19.4726 | −2.47302 | ||||||||
\(63\) | 4.15522 | 0.523508 | ||||||||
\(64\) | 32.5500 | 4.06875 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.405971 | −0.0499716 | ||||||||
\(67\) | 5.99654 | 0.732594 | 0.366297 | − | 0.930498i | \(-0.380625\pi\) | ||||
0.366297 | + | 0.930498i | \(0.380625\pi\) | |||||||
\(68\) | −16.9514 | −2.05566 | ||||||||
\(69\) | 0.191604 | 0.0230664 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.10030 | 1.08001 | 0.540003 | − | 0.841663i | \(-0.318423\pi\) | ||||
0.540003 | + | 0.841663i | \(0.318423\pi\) | |||||||
\(72\) | 28.9576 | 3.41269 | ||||||||
\(73\) | 4.03560 | 0.472331 | 0.236165 | − | 0.971713i | \(-0.424109\pi\) | ||||
0.236165 | + | 0.971713i | \(0.424109\pi\) | |||||||
\(74\) | 2.68045 | 0.311596 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 44.6321 | 5.11966 | ||||||||
\(77\) | 2.34244 | 0.266946 | ||||||||
\(78\) | −0.323721 | −0.0366542 | ||||||||
\(79\) | −0.0889430 | −0.0100069 | −0.00500344 | − | 0.999987i | \(-0.501593\pi\) | ||||
−0.00500344 | + | 0.999987i | \(0.501593\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.93081 | 0.992312 | ||||||||
\(82\) | −8.97823 | −0.991480 | ||||||||
\(83\) | 10.5321 | 1.15604 | 0.578022 | − | 0.816021i | \(-0.303825\pi\) | ||||
0.578022 | + | 0.816021i | \(0.303825\pi\) | |||||||
\(84\) | 0.673278 | 0.0734607 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −22.4613 | −2.42206 | ||||||||
\(87\) | 0.765225 | 0.0820407 | ||||||||
\(88\) | 16.3244 | 1.74019 | ||||||||
\(89\) | 0.520962 | 0.0552219 | 0.0276110 | − | 0.999619i | \(-0.491210\pi\) | ||||
0.0276110 | + | 0.999619i | \(0.491210\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.86786 | 0.195805 | ||||||||
\(92\) | −12.0731 | −1.25871 | ||||||||
\(93\) | −0.622590 | −0.0645595 | ||||||||
\(94\) | −22.4018 | −2.31057 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.03161 | 0.207350 | ||||||||
\(97\) | −13.5274 | −1.37350 | −0.686748 | − | 0.726896i | \(-0.740962\pi\) | ||||
−0.686748 | + | 0.726896i | \(0.740962\pi\) | |||||||
\(98\) | 13.9146 | 1.40559 | ||||||||
\(99\) | 5.04761 | 0.507304 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.6091 | 1.15514 | 0.577572 | − | 0.816340i | \(-0.304000\pi\) | ||||
0.577572 | + | 0.816340i | \(0.304000\pi\) | |||||||
\(102\) | −0.738093 | −0.0730821 | ||||||||
\(103\) | −4.00226 | −0.394354 | −0.197177 | − | 0.980368i | \(-0.563177\pi\) | ||||
−0.197177 | + | 0.980368i | \(0.563177\pi\) | |||||||
\(104\) | 13.0171 | 1.27643 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.18759 | 0.698121 | ||||||||
\(107\) | −16.4448 | −1.58978 | −0.794890 | − | 0.606753i | \(-0.792472\pi\) | ||||
−0.794890 | + | 0.606753i | \(0.792472\pi\) | |||||||
\(108\) | 2.90536 | 0.279569 | ||||||||
\(109\) | 16.3031 | 1.56155 | 0.780775 | − | 0.624812i | \(-0.214825\pi\) | ||||
0.780775 | + | 0.624812i | \(0.214825\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.0857009 | 0.00813437 | ||||||||
\(112\) | −21.5185 | −2.03331 | ||||||||
\(113\) | 3.75354 | 0.353103 | 0.176552 | − | 0.984291i | \(-0.443506\pi\) | ||||
0.176552 | + | 0.984291i | \(0.443506\pi\) | |||||||
\(114\) | 1.94335 | 0.182012 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −48.2174 | −4.47687 | ||||||||
\(117\) | 4.02497 | 0.372109 | ||||||||
\(118\) | −6.74591 | −0.621011 | ||||||||
\(119\) | 4.25877 | 0.390401 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.15449 | −0.741317 | ||||||||
\(122\) | 10.1254 | 0.916714 | ||||||||
\(123\) | −0.287057 | −0.0258831 | ||||||||
\(124\) | 39.2298 | 3.52294 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −11.4002 | −1.01561 | ||||||||
\(127\) | 12.7182 | 1.12856 | 0.564278 | − | 0.825585i | \(-0.309155\pi\) | ||||
0.564278 | + | 0.825585i | \(0.309155\pi\) | |||||||
\(128\) | −42.9831 | −3.79921 | ||||||||
\(129\) | −0.718145 | −0.0632291 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.42086 | 0.560993 | 0.280497 | − | 0.959855i | \(-0.409501\pi\) | ||||
0.280497 | + | 0.959855i | \(0.409501\pi\) | |||||||
\(132\) | 0.817875 | 0.0711869 | ||||||||
\(133\) | −11.2131 | −0.972298 | ||||||||
\(134\) | −16.4520 | −1.42124 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 29.6793 | 2.54498 | ||||||||
\(137\) | −23.0808 | −1.97193 | −0.985964 | − | 0.166957i | \(-0.946606\pi\) | ||||
−0.985964 | + | 0.166957i | \(0.946606\pi\) | |||||||
\(138\) | −0.525681 | −0.0447490 | ||||||||
\(139\) | −3.88549 | −0.329563 | −0.164781 | − | 0.986330i | \(-0.552692\pi\) | ||||
−0.164781 | + | 0.986330i | \(0.552692\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.716244 | −0.0603186 | ||||||||
\(142\) | −24.9675 | −2.09522 | ||||||||
\(143\) | 2.26901 | 0.189744 | ||||||||
\(144\) | −46.3692 | −3.86410 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −11.0720 | −0.916326 | ||||||||
\(147\) | 0.444887 | 0.0366936 | ||||||||
\(148\) | −5.40008 | −0.443883 | ||||||||
\(149\) | −11.7040 | −0.958828 | −0.479414 | − | 0.877589i | \(-0.659151\pi\) | ||||
−0.479414 | + | 0.877589i | \(0.659151\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.8733 | −1.21037 | −0.605184 | − | 0.796085i | \(-0.706901\pi\) | ||||
−0.605184 | + | 0.796085i | \(0.706901\pi\) | |||||||
\(152\) | −78.1438 | −6.33830 | ||||||||
\(153\) | 9.17703 | 0.741919 | ||||||||
\(154\) | −6.42668 | −0.517877 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.652174 | 0.0522157 | ||||||||
\(157\) | −21.8491 | −1.74375 | −0.871873 | − | 0.489732i | \(-0.837095\pi\) | ||||
−0.871873 | + | 0.489732i | \(0.837095\pi\) | |||||||
\(158\) | 0.244023 | 0.0194134 | ||||||||
\(159\) | 0.229806 | 0.0182248 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.03316 | 0.239047 | ||||||||
\(162\) | −24.5024 | −1.92509 | ||||||||
\(163\) | 6.68221 | 0.523391 | 0.261695 | − | 0.965150i | \(-0.415718\pi\) | ||||
0.261695 | + | 0.965150i | \(0.415718\pi\) | |||||||
\(164\) | 18.0877 | 1.41241 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −28.8956 | −2.24274 | ||||||||
\(167\) | 7.44352 | 0.575997 | 0.287999 | − | 0.957631i | \(-0.407010\pi\) | ||||
0.287999 | + | 0.957631i | \(0.407010\pi\) | |||||||
\(168\) | −1.17880 | −0.0909466 | ||||||||
\(169\) | −11.1907 | −0.860822 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −24.1626 | −1.84776 | ||||||||
\(172\) | 45.2508 | 3.45034 | ||||||||
\(173\) | 6.18003 | 0.469859 | 0.234930 | − | 0.972012i | \(-0.424514\pi\) | ||||
0.234930 | + | 0.972012i | \(0.424514\pi\) | |||||||
\(174\) | −2.09946 | −0.159160 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −26.1399 | −1.97037 | ||||||||
\(177\) | −0.215684 | −0.0162118 | ||||||||
\(178\) | −1.42931 | −0.107131 | ||||||||
\(179\) | 11.7335 | 0.877002 | 0.438501 | − | 0.898731i | \(-0.355510\pi\) | ||||
0.438501 | + | 0.898731i | \(0.355510\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.7826 | −1.39610 | −0.698049 | − | 0.716050i | \(-0.745948\pi\) | ||||
−0.698049 | + | 0.716050i | \(0.745948\pi\) | |||||||
\(182\) | −5.12464 | −0.379863 | ||||||||
\(183\) | 0.323736 | 0.0239313 | ||||||||
\(184\) | 21.1380 | 1.55832 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.70813 | 0.125246 | ||||||||
\(187\) | 5.17340 | 0.378317 | ||||||||
\(188\) | 45.1310 | 3.29152 | ||||||||
\(189\) | −0.729924 | −0.0530942 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.1789 | −0.736523 | −0.368261 | − | 0.929722i | \(-0.620047\pi\) | ||||
−0.368261 | + | 0.929722i | \(0.620047\pi\) | |||||||
\(192\) | −2.85527 | −0.206061 | ||||||||
\(193\) | −2.40830 | −0.173354 | −0.0866768 | − | 0.996236i | \(-0.527625\pi\) | ||||
−0.0866768 | + | 0.996236i | \(0.527625\pi\) | |||||||
\(194\) | 37.1135 | 2.66459 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −28.0326 | −2.00233 | ||||||||
\(197\) | 2.10597 | 0.150044 | 0.0750220 | − | 0.997182i | \(-0.476097\pi\) | ||||
0.0750220 | + | 0.997182i | \(0.476097\pi\) | |||||||
\(198\) | −13.8486 | −0.984175 | ||||||||
\(199\) | −7.70654 | −0.546302 | −0.273151 | − | 0.961971i | \(-0.588066\pi\) | ||||
−0.273151 | + | 0.961971i | \(0.588066\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.526013 | −0.0371021 | ||||||||
\(202\) | −31.8505 | −2.24099 | ||||||||
\(203\) | 12.1138 | 0.850223 | ||||||||
\(204\) | 1.48697 | 0.104109 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 10.9805 | 0.765051 | ||||||||
\(207\) | 6.53602 | 0.454285 | ||||||||
\(208\) | −20.8440 | −1.44527 | ||||||||
\(209\) | −13.6213 | −0.942203 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.1242 | −1.11004 | −0.555019 | − | 0.831838i | \(-0.687289\pi\) | ||||
−0.555019 | + | 0.831838i | \(0.687289\pi\) | |||||||
\(212\) | −14.4802 | −0.994506 | ||||||||
\(213\) | −0.798274 | −0.0546968 | ||||||||
\(214\) | 45.1178 | 3.08419 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.08683 | −0.346115 | ||||||||
\(217\) | −9.85584 | −0.669058 | ||||||||
\(218\) | −44.7289 | −3.02942 | ||||||||
\(219\) | −0.354001 | −0.0239211 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.12527 | 0.277496 | ||||||||
\(222\) | −0.235128 | −0.0157808 | ||||||||
\(223\) | 22.9109 | 1.53423 | 0.767115 | − | 0.641509i | \(-0.221691\pi\) | ||||
0.767115 | + | 0.641509i | \(0.221691\pi\) | |||||||
\(224\) | 32.1612 | 2.14886 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.2982 | −0.685024 | ||||||||
\(227\) | 4.59387 | 0.304906 | 0.152453 | − | 0.988311i | \(-0.451283\pi\) | ||||
0.152453 | + | 0.988311i | \(0.451283\pi\) | |||||||
\(228\) | −3.91511 | −0.259284 | ||||||||
\(229\) | −6.48905 | −0.428808 | −0.214404 | − | 0.976745i | \(-0.568781\pi\) | ||||
−0.214404 | + | 0.976745i | \(0.568781\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.205478 | −0.0135194 | ||||||||
\(232\) | 84.4209 | 5.54250 | ||||||||
\(233\) | 23.7129 | 1.55348 | 0.776740 | − | 0.629821i | \(-0.216872\pi\) | ||||
0.776740 | + | 0.629821i | \(0.216872\pi\) | |||||||
\(234\) | −11.0429 | −0.721894 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 13.5904 | 0.884660 | ||||||||
\(237\) | 0.00780204 | 0.000506797 0 | ||||||||
\(238\) | −11.6843 | −0.757380 | ||||||||
\(239\) | 16.1211 | 1.04279 | 0.521395 | − | 0.853316i | \(-0.325412\pi\) | ||||
0.521395 | + | 0.853316i | \(0.325412\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −0.0644157 | ||||||||
\(242\) | 22.3725 | 1.43816 | ||||||||
\(243\) | −2.36033 | −0.151415 | ||||||||
\(244\) | −20.3988 | −1.30590 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.787566 | 0.0502134 | ||||||||
\(247\) | −10.8616 | −0.691107 | ||||||||
\(248\) | −68.6851 | −4.36151 | ||||||||
\(249\) | −0.923868 | −0.0585477 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.6940 | −0.927475 | −0.463737 | − | 0.885973i | \(-0.653492\pi\) | ||||
−0.463737 | + | 0.885973i | \(0.653492\pi\) | |||||||
\(252\) | 22.9670 | 1.44678 | ||||||||
\(253\) | 3.68458 | 0.231648 | ||||||||
\(254\) | −34.8934 | −2.18941 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 52.8280 | 3.30175 | ||||||||
\(257\) | −23.6089 | −1.47269 | −0.736343 | − | 0.676609i | \(-0.763449\pi\) | ||||
−0.736343 | + | 0.676609i | \(0.763449\pi\) | |||||||
\(258\) | 1.97029 | 0.122665 | ||||||||
\(259\) | 1.35668 | 0.0842999 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 26.1035 | 1.61577 | ||||||||
\(262\) | −17.6162 | −1.08833 | ||||||||
\(263\) | −18.7533 | −1.15638 | −0.578189 | − | 0.815903i | \(-0.696240\pi\) | ||||
−0.578189 | + | 0.815903i | \(0.696240\pi\) | |||||||
\(264\) | −1.43197 | −0.0881316 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 30.7641 | 1.88627 | ||||||||
\(267\) | −0.0456986 | −0.00279671 | ||||||||
\(268\) | 33.1445 | 2.02462 | ||||||||
\(269\) | −23.4769 | −1.43141 | −0.715705 | − | 0.698402i | \(-0.753895\pi\) | ||||
−0.715705 | + | 0.698402i | \(0.753895\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.41297 | 0.0858319 | 0.0429159 | − | 0.999079i | \(-0.486335\pi\) | ||||
0.0429159 | + | 0.999079i | \(0.486335\pi\) | |||||||
\(272\) | −47.5248 | −2.88161 | ||||||||
\(273\) | −0.163848 | −0.00991652 | ||||||||
\(274\) | 63.3243 | 3.82556 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.05904 | 0.0637470 | ||||||||
\(277\) | 30.7273 | 1.84622 | 0.923112 | − | 0.384530i | \(-0.125637\pi\) | ||||
0.923112 | + | 0.384530i | \(0.125637\pi\) | |||||||
\(278\) | 10.6602 | 0.639355 | ||||||||
\(279\) | −21.2379 | −1.27148 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.71354 | 0.221532 | 0.110766 | − | 0.993847i | \(-0.464670\pi\) | ||||
0.110766 | + | 0.993847i | \(0.464670\pi\) | |||||||
\(282\) | 1.96508 | 0.117019 | ||||||||
\(283\) | 13.2718 | 0.788924 | 0.394462 | − | 0.918912i | \(-0.370931\pi\) | ||||
0.394462 | + | 0.918912i | \(0.370931\pi\) | |||||||
\(284\) | 50.2998 | 2.98474 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.22523 | −0.368106 | ||||||||
\(287\) | −4.54423 | −0.268237 | ||||||||
\(288\) | 69.3027 | 4.08370 | ||||||||
\(289\) | −7.59428 | −0.446722 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.18661 | 0.0695605 | ||||||||
\(292\) | 22.3058 | 1.30535 | ||||||||
\(293\) | −22.8056 | −1.33232 | −0.666158 | − | 0.745810i | \(-0.732062\pi\) | ||||
−0.666158 | + | 0.745810i | \(0.732062\pi\) | |||||||
\(294\) | −1.22058 | −0.0711860 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9.45467 | 0.549542 | ||||||||
\(297\) | −0.886687 | −0.0514508 | ||||||||
\(298\) | 32.1109 | 1.86014 | ||||||||
\(299\) | 2.93809 | 0.169914 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.3685 | −0.655270 | ||||||||
\(302\) | 40.8061 | 2.34813 | ||||||||
\(303\) | −1.01834 | −0.0585022 | ||||||||
\(304\) | 125.130 | 7.17669 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −25.1780 | −1.43933 | ||||||||
\(307\) | 7.76735 | 0.443306 | 0.221653 | − | 0.975126i | \(-0.428855\pi\) | ||||
0.221653 | + | 0.975126i | \(0.428855\pi\) | |||||||
\(308\) | 12.9473 | 0.737740 | ||||||||
\(309\) | 0.351076 | 0.0199720 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.90820 | 0.221614 | 0.110807 | − | 0.993842i | \(-0.464657\pi\) | ||||
0.110807 | + | 0.993842i | \(0.464657\pi\) | |||||||
\(312\) | −1.14185 | −0.0646447 | ||||||||
\(313\) | 18.9001 | 1.06830 | 0.534148 | − | 0.845391i | \(-0.320633\pi\) | ||||
0.534148 | + | 0.845391i | \(0.320633\pi\) | |||||||
\(314\) | 59.9448 | 3.38288 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.491612 | −0.0276553 | ||||||||
\(317\) | −13.1540 | −0.738801 | −0.369400 | − | 0.929270i | \(-0.620437\pi\) | ||||
−0.369400 | + | 0.929270i | \(0.620437\pi\) | |||||||
\(318\) | −0.630492 | −0.0353562 | ||||||||
\(319\) | 14.7154 | 0.823907 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.44253 | 0.0805142 | ||||||||
\(322\) | −8.32174 | −0.463752 | ||||||||
\(323\) | −24.7647 | −1.37795 | ||||||||
\(324\) | 49.3630 | 2.74239 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −18.3332 | −1.01538 | ||||||||
\(327\) | −1.43010 | −0.0790845 | ||||||||
\(328\) | −31.6686 | −1.74861 | ||||||||
\(329\) | −11.3384 | −0.625107 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.8857 | −0.983089 | −0.491544 | − | 0.870852i | \(-0.663567\pi\) | ||||
−0.491544 | + | 0.870852i | \(0.663567\pi\) | |||||||
\(332\) | 58.2136 | 3.19488 | ||||||||
\(333\) | 2.92345 | 0.160204 | ||||||||
\(334\) | −20.4219 | −1.11744 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.88759 | 0.102977 | ||||||||
\(337\) | 18.4814 | 1.00675 | 0.503374 | − | 0.864069i | \(-0.332092\pi\) | ||||
0.503374 | + | 0.864069i | \(0.332092\pi\) | |||||||
\(338\) | 30.7026 | 1.67000 | ||||||||
\(339\) | −0.329259 | −0.0178829 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.9725 | −0.648349 | ||||||||
\(342\) | 66.2921 | 3.58467 | ||||||||
\(343\) | 16.7632 | 0.905126 | ||||||||
\(344\) | −79.2269 | −4.27163 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.9554 | −0.911531 | ||||||||
\(347\) | 12.4603 | 0.668906 | 0.334453 | − | 0.942412i | \(-0.391448\pi\) | ||||
0.334453 | + | 0.942412i | \(0.391448\pi\) | |||||||
\(348\) | 4.22960 | 0.226731 | ||||||||
\(349\) | −25.0759 | −1.34228 | −0.671140 | − | 0.741331i | \(-0.734195\pi\) | ||||
−0.671140 | + | 0.741331i | \(0.734195\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.707045 | −0.0377392 | ||||||||
\(352\) | 39.0683 | 2.08235 | ||||||||
\(353\) | −24.0369 | −1.27935 | −0.639677 | − | 0.768644i | \(-0.720932\pi\) | ||||
−0.639677 | + | 0.768644i | \(0.720932\pi\) | |||||||
\(354\) | 0.591748 | 0.0314510 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.87950 | 0.152613 | ||||||||
\(357\) | −0.373577 | −0.0197718 | ||||||||
\(358\) | −32.1918 | −1.70139 | ||||||||
\(359\) | −25.8489 | −1.36425 | −0.682127 | − | 0.731234i | \(-0.738945\pi\) | ||||
−0.682127 | + | 0.731234i | \(0.738945\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 46.2040 | 2.43179 | ||||||||
\(362\) | 51.5316 | 2.70844 | ||||||||
\(363\) | 0.715307 | 0.0375439 | ||||||||
\(364\) | 10.3242 | 0.541133 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.888198 | −0.0464269 | ||||||||
\(367\) | 13.7562 | 0.718068 | 0.359034 | − | 0.933324i | \(-0.383106\pi\) | ||||
0.359034 | + | 0.933324i | \(0.383106\pi\) | |||||||
\(368\) | −33.8479 | −1.76444 | ||||||||
\(369\) | −9.79215 | −0.509759 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.63792 | 0.188871 | ||||||||
\(372\) | −3.44122 | −0.178419 | ||||||||
\(373\) | −4.09173 | −0.211862 | −0.105931 | − | 0.994373i | \(-0.533782\pi\) | ||||
−0.105931 | + | 0.994373i | \(0.533782\pi\) | |||||||
\(374\) | −14.1937 | −0.733938 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −79.0172 | −4.07500 | ||||||||
\(377\) | 11.7341 | 0.604337 | ||||||||
\(378\) | 2.00261 | 0.103003 | ||||||||
\(379\) | −33.6065 | −1.72625 | −0.863124 | − | 0.504992i | \(-0.831495\pi\) | ||||
−0.863124 | + | 0.504992i | \(0.831495\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.11563 | −0.0571556 | ||||||||
\(382\) | 27.9268 | 1.42886 | ||||||||
\(383\) | 20.9590 | 1.07096 | 0.535478 | − | 0.844549i | \(-0.320132\pi\) | ||||
0.535478 | + | 0.844549i | \(0.320132\pi\) | |||||||
\(384\) | 3.77046 | 0.192410 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.60739 | 0.336307 | ||||||||
\(387\) | −24.4975 | −1.24528 | ||||||||
\(388\) | −74.7694 | −3.79584 | ||||||||
\(389\) | 6.32158 | 0.320517 | 0.160258 | − | 0.987075i | \(-0.448767\pi\) | ||||
0.160258 | + | 0.987075i | \(0.448767\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.69890 | 0.338778 | ||||||||
\(392\) | 49.0806 | 2.47895 | ||||||||
\(393\) | −0.563235 | −0.0284114 | ||||||||
\(394\) | −5.77790 | −0.291087 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 27.8995 | 1.40200 | ||||||||
\(397\) | −3.36213 | −0.168741 | −0.0843703 | − | 0.996434i | \(-0.526888\pi\) | ||||
−0.0843703 | + | 0.996434i | \(0.526888\pi\) | |||||||
\(398\) | 21.1436 | 1.05983 | ||||||||
\(399\) | 0.983606 | 0.0492419 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.5665 | −1.07698 | −0.538490 | − | 0.842632i | \(-0.681005\pi\) | ||||
−0.538490 | + | 0.842632i | \(0.681005\pi\) | |||||||
\(402\) | 1.44316 | 0.0719785 | ||||||||
\(403\) | −9.54690 | −0.475565 | ||||||||
\(404\) | 64.1664 | 3.19240 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −33.2353 | −1.64944 | ||||||||
\(407\) | 1.64805 | 0.0816907 | ||||||||
\(408\) | −2.60345 | −0.128890 | ||||||||
\(409\) | 9.59465 | 0.474425 | 0.237212 | − | 0.971458i | \(-0.423766\pi\) | ||||
0.237212 | + | 0.971458i | \(0.423766\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.02464 | 0.0998681 | ||||||||
\(412\) | −22.1216 | −1.08985 | ||||||||
\(413\) | −3.41436 | −0.168010 | ||||||||
\(414\) | −17.9321 | −0.881317 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 31.1531 | 1.52741 | ||||||||
\(417\) | 0.340833 | 0.0166907 | ||||||||
\(418\) | 37.3711 | 1.82788 | ||||||||
\(419\) | 10.9416 | 0.534534 | 0.267267 | − | 0.963623i | \(-0.413879\pi\) | ||||
0.267267 | + | 0.963623i | \(0.413879\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.843741 | −0.0411214 | −0.0205607 | − | 0.999789i | \(-0.506545\pi\) | ||||
−0.0205607 | + | 0.999789i | \(0.506545\pi\) | |||||||
\(422\) | 44.2382 | 2.15348 | ||||||||
\(423\) | −24.4326 | −1.18796 | ||||||||
\(424\) | 25.3526 | 1.23123 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.19013 | 0.106112 | ||||||||
\(427\) | 5.12487 | 0.248010 | ||||||||
\(428\) | −90.8949 | −4.39357 | ||||||||
\(429\) | −0.199037 | −0.00960958 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.19126 | −0.442727 | −0.221364 | − | 0.975191i | \(-0.571051\pi\) | ||||
−0.221364 | + | 0.975191i | \(0.571051\pi\) | |||||||
\(432\) | 8.14543 | 0.391897 | ||||||||
\(433\) | 34.5448 | 1.66012 | 0.830059 | − | 0.557676i | \(-0.188307\pi\) | ||||
0.830059 | + | 0.557676i | \(0.188307\pi\) | |||||||
\(434\) | 27.0403 | 1.29798 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 90.1114 | 4.31555 | ||||||||
\(437\) | −17.6378 | −0.843731 | ||||||||
\(438\) | 0.971231 | 0.0464072 | ||||||||
\(439\) | −34.4428 | −1.64387 | −0.821934 | − | 0.569583i | \(-0.807105\pi\) | ||||
−0.821934 | + | 0.569583i | \(0.807105\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.1761 | 0.722670 | ||||||||
\(442\) | −11.3180 | −0.538345 | ||||||||
\(443\) | 2.65568 | 0.126175 | 0.0630875 | − | 0.998008i | \(-0.479905\pi\) | ||||
0.0630875 | + | 0.998008i | \(0.479905\pi\) | |||||||
\(444\) | 0.473692 | 0.0224804 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −62.8582 | −2.97642 | ||||||||
\(447\) | 1.02667 | 0.0485597 | ||||||||
\(448\) | −45.2000 | −2.13550 | ||||||||
\(449\) | 2.75802 | 0.130159 | 0.0650794 | − | 0.997880i | \(-0.479270\pi\) | ||||
0.0650794 | + | 0.997880i | \(0.479270\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.52017 | −0.259935 | ||||||||
\(452\) | 20.7468 | 0.975848 | ||||||||
\(453\) | 1.30467 | 0.0612990 | ||||||||
\(454\) | −12.6037 | −0.591521 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.85473 | 0.321002 | ||||||||
\(457\) | −8.49913 | −0.397572 | −0.198786 | − | 0.980043i | \(-0.563700\pi\) | ||||
−0.198786 | + | 0.980043i | \(0.563700\pi\) | |||||||
\(458\) | 17.8033 | 0.831892 | ||||||||
\(459\) | −1.61208 | −0.0752454 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.3259 | −1.50557 | −0.752783 | − | 0.658269i | \(-0.771289\pi\) | ||||
−0.752783 | + | 0.658269i | \(0.771289\pi\) | |||||||
\(462\) | 0.563745 | 0.0262278 | ||||||||
\(463\) | −30.8997 | −1.43603 | −0.718016 | − | 0.696026i | \(-0.754950\pi\) | ||||
−0.718016 | + | 0.696026i | \(0.754950\pi\) | |||||||
\(464\) | −135.181 | −6.27564 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −65.0583 | −3.01377 | ||||||||
\(467\) | −0.328063 | −0.0151810 | −0.00759048 | − | 0.999971i | \(-0.502416\pi\) | ||||
−0.00759048 | + | 0.999971i | \(0.502416\pi\) | |||||||
\(468\) | 22.2471 | 1.02837 | ||||||||
\(469\) | −8.32700 | −0.384505 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.91659 | 0.0883118 | ||||||||
\(472\) | −23.7946 | −1.09524 | ||||||||
\(473\) | −13.8101 | −0.634988 | ||||||||
\(474\) | −0.0214056 | −0.000983190 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 23.5393 | 1.07892 | ||||||||
\(477\) | 7.83918 | 0.358931 | ||||||||
\(478\) | −44.2297 | −2.02302 | ||||||||
\(479\) | 25.2532 | 1.15385 | 0.576924 | − | 0.816798i | \(-0.304253\pi\) | ||||
0.576924 | + | 0.816798i | \(0.304253\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.31415 | 0.0599202 | ||||||||
\(482\) | 2.74359 | 0.124967 | ||||||||
\(483\) | −0.266067 | −0.0121065 | ||||||||
\(484\) | −45.0720 | −2.04873 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 6.47578 | 0.293747 | ||||||||
\(487\) | −39.4297 | −1.78673 | −0.893365 | − | 0.449333i | \(-0.851662\pi\) | ||||
−0.893365 | + | 0.449333i | \(0.851662\pi\) | |||||||
\(488\) | 35.7151 | 1.61675 | ||||||||
\(489\) | −0.586160 | −0.0265071 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.0485 | 0.543739 | 0.271870 | − | 0.962334i | \(-0.412358\pi\) | ||||
0.271870 | + | 0.962334i | \(0.412358\pi\) | |||||||
\(492\) | −1.58664 | −0.0715313 | ||||||||
\(493\) | 26.7540 | 1.20494 | ||||||||
\(494\) | 29.7997 | 1.34075 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 109.984 | 4.93843 | ||||||||
\(497\) | −12.6370 | −0.566846 | ||||||||
\(498\) | 2.53471 | 0.113583 | ||||||||
\(499\) | −14.5964 | −0.653426 | −0.326713 | − | 0.945124i | \(-0.605941\pi\) | ||||
−0.326713 | + | 0.945124i | \(0.605941\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.652942 | −0.0291713 | ||||||||
\(502\) | 40.3142 | 1.79931 | ||||||||
\(503\) | −33.6921 | −1.50226 | −0.751129 | − | 0.660156i | \(-0.770490\pi\) | ||||
−0.751129 | + | 0.660156i | \(0.770490\pi\) | |||||||
\(504\) | −40.2115 | −1.79116 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −10.1090 | −0.449398 | ||||||||
\(507\) | 0.981642 | 0.0435962 | ||||||||
\(508\) | 70.2968 | 3.11891 | ||||||||
\(509\) | −2.82042 | −0.125013 | −0.0625066 | − | 0.998045i | \(-0.519909\pi\) | ||||
−0.0625066 | + | 0.998045i | \(0.519909\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.60397 | −0.247905 | ||||||||
\(512\) | −58.9718 | −2.60621 | ||||||||
\(513\) | 4.24451 | 0.187400 | ||||||||
\(514\) | 64.7732 | 2.85702 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3.96938 | −0.174742 | ||||||||
\(517\) | −13.7735 | −0.605759 | ||||||||
\(518\) | −3.72217 | −0.163543 | ||||||||
\(519\) | −0.542109 | −0.0237960 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.3228 | 1.45990 | 0.729948 | − | 0.683502i | \(-0.239544\pi\) | ||||
0.729948 | + | 0.683502i | \(0.239544\pi\) | |||||||
\(522\) | −71.6172 | −3.13460 | ||||||||
\(523\) | 34.1620 | 1.49380 | 0.746900 | − | 0.664936i | \(-0.231541\pi\) | ||||
0.746900 | + | 0.664936i | \(0.231541\pi\) | |||||||
\(524\) | 35.4898 | 1.55038 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 51.4513 | 2.24338 | ||||||||
\(527\) | −21.7672 | −0.948192 | ||||||||
\(528\) | 2.29298 | 0.0997892 | ||||||||
\(529\) | −18.2289 | −0.792562 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.35746 | −0.319286 | ||||||||
\(532\) | −61.9777 | −2.68707 | ||||||||
\(533\) | −4.40178 | −0.190662 | ||||||||
\(534\) | 0.125378 | 0.00542563 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −58.0307 | −2.50654 | ||||||||
\(537\) | −1.02926 | −0.0444157 | ||||||||
\(538\) | 64.4109 | 2.77695 | ||||||||
\(539\) | 8.55527 | 0.368501 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.1983 | 0.997372 | 0.498686 | − | 0.866783i | \(-0.333816\pi\) | ||||
0.498686 | + | 0.866783i | \(0.333816\pi\) | |||||||
\(542\) | −3.87661 | −0.166515 | ||||||||
\(543\) | 1.64760 | 0.0707052 | ||||||||
\(544\) | 71.0298 | 3.04538 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.449531 | 0.0192381 | ||||||||
\(547\) | −0.251587 | −0.0107571 | −0.00537854 | − | 0.999986i | \(-0.501712\pi\) | ||||
−0.00537854 | + | 0.999986i | \(0.501712\pi\) | |||||||
\(548\) | −127.574 | −5.44969 | ||||||||
\(549\) | 11.0434 | 0.471319 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −70.4418 | −3.00092 | ||||||||
\(552\) | −1.85422 | −0.0789208 | ||||||||
\(553\) | 0.123509 | 0.00525215 | ||||||||
\(554\) | −84.3030 | −3.58169 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −21.4761 | −0.910791 | ||||||||
\(557\) | 5.86433 | 0.248480 | 0.124240 | − | 0.992252i | \(-0.460351\pi\) | ||||
0.124240 | + | 0.992252i | \(0.460351\pi\) | |||||||
\(558\) | 58.2680 | 2.46668 | ||||||||
\(559\) | −11.0122 | −0.465765 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.453808 | −0.0191598 | ||||||||
\(562\) | −10.1884 | −0.429773 | ||||||||
\(563\) | 2.00215 | 0.0843807 | 0.0421904 | − | 0.999110i | \(-0.486566\pi\) | ||||
0.0421904 | + | 0.999110i | \(0.486566\pi\) | |||||||
\(564\) | −3.95887 | −0.166699 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −36.4122 | −1.53052 | ||||||||
\(567\) | −12.4016 | −0.520819 | ||||||||
\(568\) | −88.0669 | −3.69521 | ||||||||
\(569\) | 40.0230 | 1.67785 | 0.838926 | − | 0.544246i | \(-0.183184\pi\) | ||||
0.838926 | + | 0.544246i | \(0.183184\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.3124 | −0.515260 | −0.257630 | − | 0.966244i | \(-0.582942\pi\) | ||||
−0.257630 | + | 0.966244i | \(0.582942\pi\) | |||||||
\(572\) | 12.5414 | 0.524384 | ||||||||
\(573\) | 0.892892 | 0.0373011 | ||||||||
\(574\) | 12.4675 | 0.520382 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −97.3995 | −4.05831 | ||||||||
\(577\) | −21.4137 | −0.891464 | −0.445732 | − | 0.895166i | \(-0.647057\pi\) | ||||
−0.445732 | + | 0.895166i | \(0.647057\pi\) | |||||||
\(578\) | 20.8356 | 0.866645 | ||||||||
\(579\) | 0.211255 | 0.00877947 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.6252 | −0.606755 | ||||||||
\(582\) | −3.25558 | −0.134948 | ||||||||
\(583\) | 4.41922 | 0.183025 | ||||||||
\(584\) | −39.0539 | −1.61606 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 62.5691 | 2.58471 | ||||||||
\(587\) | −6.14344 | −0.253567 | −0.126783 | − | 0.991930i | \(-0.540465\pi\) | ||||
−0.126783 | + | 0.991930i | \(0.540465\pi\) | |||||||
\(588\) | 2.45901 | 0.101408 | ||||||||
\(589\) | 57.3116 | 2.36149 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.184734 | −0.00759896 | ||||||||
\(592\) | −15.1396 | −0.622232 | ||||||||
\(593\) | 40.7560 | 1.67365 | 0.836825 | − | 0.547471i | \(-0.184409\pi\) | ||||
0.836825 | + | 0.547471i | \(0.184409\pi\) | |||||||
\(594\) | 2.43270 | 0.0998150 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −64.6911 | −2.64985 | ||||||||
\(597\) | 0.676014 | 0.0276674 | ||||||||
\(598\) | −8.06089 | −0.329634 | ||||||||
\(599\) | 34.7912 | 1.42153 | 0.710766 | − | 0.703429i | \(-0.248349\pi\) | ||||
0.710766 | + | 0.703429i | \(0.248349\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.9358 | −1.26190 | −0.630950 | − | 0.775824i | \(-0.717335\pi\) | ||||
−0.630950 | + | 0.775824i | \(0.717335\pi\) | |||||||
\(602\) | 31.1905 | 1.27123 | ||||||||
\(603\) | −17.9435 | −0.730715 | ||||||||
\(604\) | −82.2085 | −3.34502 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.79391 | 0.113495 | ||||||||
\(607\) | −38.0624 | −1.54491 | −0.772453 | − | 0.635071i | \(-0.780971\pi\) | ||||
−0.772453 | + | 0.635071i | \(0.780971\pi\) | |||||||
\(608\) | −187.017 | −7.58455 | ||||||||
\(609\) | −1.06262 | −0.0430594 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.9830 | −0.444325 | ||||||||
\(612\) | 50.7239 | 2.05039 | ||||||||
\(613\) | 26.3263 | 1.06331 | 0.531655 | − | 0.846961i | \(-0.321570\pi\) | ||||
0.531655 | + | 0.846961i | \(0.321570\pi\) | |||||||
\(614\) | −21.3104 | −0.860017 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −22.6686 | −0.913345 | ||||||||
\(617\) | −37.6152 | −1.51433 | −0.757166 | − | 0.653222i | \(-0.773417\pi\) | ||||
−0.757166 | + | 0.653222i | \(0.773417\pi\) | |||||||
\(618\) | −0.963208 | −0.0387459 | ||||||||
\(619\) | 23.5018 | 0.944616 | 0.472308 | − | 0.881433i | \(-0.343421\pi\) | ||||
0.472308 | + | 0.881433i | \(0.343421\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.14815 | −0.0460736 | ||||||||
\(622\) | −10.7225 | −0.429932 | ||||||||
\(623\) | −0.723426 | −0.0289835 | ||||||||
\(624\) | 1.82842 | 0.0731955 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −51.8540 | −2.07250 | ||||||||
\(627\) | 1.19485 | 0.0477177 | ||||||||
\(628\) | −120.766 | −4.81908 | ||||||||
\(629\) | 2.99630 | 0.119470 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.8128 | 0.430451 | 0.215225 | − | 0.976564i | \(-0.430951\pi\) | ||||
0.215225 | + | 0.976564i | \(0.430951\pi\) | |||||||
\(632\) | 0.860734 | 0.0342382 | ||||||||
\(633\) | 1.41441 | 0.0562177 | ||||||||
\(634\) | 36.0891 | 1.43328 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.27020 | 0.0503666 | ||||||||
\(637\) | 6.82197 | 0.270296 | ||||||||
\(638\) | −40.3731 | −1.59839 | ||||||||
\(639\) | −27.2309 | −1.07724 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 33.1211 | 1.30820 | 0.654101 | − | 0.756407i | \(-0.273047\pi\) | ||||
0.654101 | + | 0.756407i | \(0.273047\pi\) | |||||||
\(642\) | −3.95771 | −0.156198 | ||||||||
\(643\) | −15.2022 | −0.599516 | −0.299758 | − | 0.954015i | \(-0.596906\pi\) | ||||
−0.299758 | + | 0.954015i | \(0.596906\pi\) | |||||||
\(644\) | 16.7651 | 0.660637 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 67.9441 | 2.67323 | ||||||||
\(647\) | −3.61671 | −0.142188 | −0.0710938 | − | 0.997470i | \(-0.522649\pi\) | ||||
−0.0710938 | + | 0.997470i | \(0.522649\pi\) | |||||||
\(648\) | −86.4267 | −3.39516 | ||||||||
\(649\) | −4.14765 | −0.162810 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.864549 | 0.0338843 | ||||||||
\(652\) | 36.9344 | 1.44646 | ||||||||
\(653\) | 6.11369 | 0.239247 | 0.119624 | − | 0.992819i | \(-0.461831\pi\) | ||||
0.119624 | + | 0.992819i | \(0.461831\pi\) | |||||||
\(654\) | 3.92359 | 0.153425 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 50.7103 | 1.97990 | ||||||||
\(657\) | −12.0757 | −0.471120 | ||||||||
\(658\) | 31.1079 | 1.21271 | ||||||||
\(659\) | −7.30750 | −0.284660 | −0.142330 | − | 0.989819i | \(-0.545459\pi\) | ||||
−0.142330 | + | 0.989819i | \(0.545459\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.9475 | −1.04814 | −0.524068 | − | 0.851677i | \(-0.675586\pi\) | ||||
−0.524068 | + | 0.851677i | \(0.675586\pi\) | |||||||
\(662\) | 49.0711 | 1.90720 | ||||||||
\(663\) | −0.361867 | −0.0140537 | ||||||||
\(664\) | −101.923 | −3.95537 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.02073 | −0.310797 | ||||||||
\(667\) | 19.0546 | 0.737798 | ||||||||
\(668\) | 41.1423 | 1.59184 | ||||||||
\(669\) | −2.00974 | −0.0777009 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.22552 | 0.240333 | ||||||||
\(672\) | −2.82116 | −0.108829 | ||||||||
\(673\) | −8.91441 | −0.343625 | −0.171813 | − | 0.985130i | \(-0.554962\pi\) | ||||
−0.171813 | + | 0.985130i | \(0.554962\pi\) | |||||||
\(674\) | −50.7054 | −1.95310 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −61.8539 | −2.37900 | ||||||||
\(677\) | −16.2141 | −0.623158 | −0.311579 | − | 0.950220i | \(-0.600858\pi\) | ||||
−0.311579 | + | 0.950220i | \(0.600858\pi\) | |||||||
\(678\) | 0.903350 | 0.0346929 | ||||||||
\(679\) | 18.7846 | 0.720885 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.402972 | −0.0154419 | ||||||||
\(682\) | 32.8477 | 1.25780 | ||||||||
\(683\) | 1.03326 | 0.0395366 | 0.0197683 | − | 0.999805i | \(-0.493707\pi\) | ||||
0.0197683 | + | 0.999805i | \(0.493707\pi\) | |||||||
\(684\) | −133.553 | −5.10653 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −45.9912 | −1.75595 | ||||||||
\(687\) | 0.569216 | 0.0217169 | ||||||||
\(688\) | 126.864 | 4.83666 | ||||||||
\(689\) | 3.52388 | 0.134249 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.6967 | 0.939505 | 0.469753 | − | 0.882798i | \(-0.344343\pi\) | ||||
0.469753 | + | 0.882798i | \(0.344343\pi\) | |||||||
\(692\) | 34.1587 | 1.29852 | ||||||||
\(693\) | −7.00929 | −0.266261 | ||||||||
\(694\) | −34.1860 | −1.29768 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7.40536 | −0.280699 | ||||||||
\(697\) | −10.0362 | −0.380147 | ||||||||
\(698\) | 68.7978 | 2.60404 | ||||||||
\(699\) | −2.08008 | −0.0786758 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.9544 | −0.753668 | −0.376834 | − | 0.926281i | \(-0.622987\pi\) | ||||
−0.376834 | + | 0.926281i | \(0.622987\pi\) | |||||||
\(702\) | 1.93984 | 0.0732145 | ||||||||
\(703\) | −7.88908 | −0.297542 | ||||||||
\(704\) | −54.9075 | −2.06940 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 65.9473 | 2.48196 | ||||||||
\(707\) | −16.1207 | −0.606283 | ||||||||
\(708\) | −1.19214 | −0.0448035 | ||||||||
\(709\) | 35.3959 | 1.32932 | 0.664660 | − | 0.747146i | \(-0.268577\pi\) | ||||
0.664660 | + | 0.747146i | \(0.268577\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.266145 | 0.00998121 | ||||||||
\(712\) | −5.04154 | −0.188940 | ||||||||
\(713\) | −15.5029 | −0.580589 | ||||||||
\(714\) | 1.02494 | 0.0383574 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 64.8541 | 2.42371 | ||||||||
\(717\) | −1.41414 | −0.0528120 | ||||||||
\(718\) | 70.9187 | 2.64666 | ||||||||
\(719\) | 17.5408 | 0.654161 | 0.327080 | − | 0.944997i | \(-0.393935\pi\) | ||||
0.327080 | + | 0.944997i | \(0.393935\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.55767 | 0.206979 | ||||||||
\(722\) | −126.765 | −4.71770 | ||||||||
\(723\) | 0.0877195 | 0.00326232 | ||||||||
\(724\) | −103.816 | −3.85830 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.96251 | −0.0728355 | ||||||||
\(727\) | −33.7229 | −1.25071 | −0.625357 | − | 0.780339i | \(-0.715047\pi\) | ||||
−0.625357 | + | 0.780339i | \(0.715047\pi\) | |||||||
\(728\) | −18.0760 | −0.669940 | ||||||||
\(729\) | −26.5854 | −0.984643 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.1080 | −0.928652 | ||||||||
\(732\) | 1.78938 | 0.0661372 | ||||||||
\(733\) | 1.47790 | 0.0545876 | 0.0272938 | − | 0.999627i | \(-0.491311\pi\) | ||||
0.0272938 | + | 0.999627i | \(0.491311\pi\) | |||||||
\(734\) | −37.7414 | −1.39306 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 50.5885 | 1.86472 | ||||||||
\(737\) | −10.1154 | −0.372604 | ||||||||
\(738\) | 26.8656 | 0.988937 | ||||||||
\(739\) | −0.339380 | −0.0124843 | −0.00624214 | − | 0.999981i | \(-0.501987\pi\) | ||||
−0.00624214 | + | 0.999981i | \(0.501987\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.952774 | 0.0350010 | ||||||||
\(742\) | −9.98094 | −0.366412 | ||||||||
\(743\) | −18.6620 | −0.684643 | −0.342322 | − | 0.939583i | \(-0.611213\pi\) | ||||
−0.342322 | + | 0.939583i | \(0.611213\pi\) | |||||||
\(744\) | 6.02503 | 0.220888 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 11.2260 | 0.411014 | ||||||||
\(747\) | −31.5152 | −1.15308 | ||||||||
\(748\) | 28.5948 | 1.04553 | ||||||||
\(749\) | 22.8358 | 0.834403 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.0954 | 0.696803 | 0.348401 | − | 0.937345i | \(-0.386725\pi\) | ||||
0.348401 | + | 0.937345i | \(0.386725\pi\) | |||||||
\(752\) | 126.529 | 4.61402 | ||||||||
\(753\) | 1.28895 | 0.0469718 | ||||||||
\(754\) | −32.1935 | −1.17242 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.03449 | −0.146733 | ||||||||
\(757\) | 6.62264 | 0.240704 | 0.120352 | − | 0.992731i | \(-0.461598\pi\) | ||||
0.120352 | + | 0.992731i | \(0.461598\pi\) | |||||||
\(758\) | 92.2022 | 3.34894 | ||||||||
\(759\) | −0.323210 | −0.0117318 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.3808 | −1.31880 | −0.659401 | − | 0.751791i | \(-0.729190\pi\) | ||||
−0.659401 | + | 0.751791i | \(0.729190\pi\) | |||||||
\(762\) | 3.06083 | 0.110882 | ||||||||
\(763\) | −22.6390 | −0.819586 | ||||||||
\(764\) | −56.2618 | −2.03548 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −57.5029 | −2.07766 | ||||||||
\(767\) | −3.30734 | −0.119421 | ||||||||
\(768\) | −4.63404 | −0.167217 | ||||||||
\(769\) | −45.9984 | −1.65875 | −0.829373 | − | 0.558696i | \(-0.811302\pi\) | ||||
−0.829373 | + | 0.558696i | \(0.811302\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.07097 | 0.0745840 | ||||||||
\(772\) | −13.3113 | −0.479086 | ||||||||
\(773\) | −23.3465 | −0.839714 | −0.419857 | − | 0.907590i | \(-0.637920\pi\) | ||||
−0.419857 | + | 0.907590i | \(0.637920\pi\) | |||||||
\(774\) | 67.2110 | 2.41585 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 130.909 | 4.69937 | ||||||||
\(777\) | −0.119007 | −0.00426936 | ||||||||
\(778\) | −17.3438 | −0.621806 | ||||||||
\(779\) | 26.4247 | 0.946761 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.3510 | −0.549301 | ||||||||
\(782\) | −18.3790 | −0.657233 | ||||||||
\(783\) | −4.58546 | −0.163871 | ||||||||
\(784\) | −78.5918 | −2.80685 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.54528 | 0.0551184 | ||||||||
\(787\) | −10.6585 | −0.379933 | −0.189967 | − | 0.981791i | \(-0.560838\pi\) | ||||
−0.189967 | + | 0.981791i | \(0.560838\pi\) | |||||||
\(788\) | 11.6402 | 0.414667 | ||||||||
\(789\) | 1.64503 | 0.0585646 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.21229 | −0.185328 | ||||||||
\(792\) | −48.8476 | −1.73572 | ||||||||
\(793\) | 4.96423 | 0.176285 | ||||||||
\(794\) | 9.22430 | 0.327358 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −42.5961 | −1.50978 | ||||||||
\(797\) | −18.7371 | −0.663703 | −0.331852 | − | 0.943332i | \(-0.607673\pi\) | ||||
−0.331852 | + | 0.943332i | \(0.607673\pi\) | |||||||
\(798\) | −2.69861 | −0.0955297 | ||||||||
\(799\) | −25.0415 | −0.885905 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.55888 | −0.0550803 | ||||||||
\(802\) | 59.1696 | 2.08935 | ||||||||
\(803\) | −6.80751 | −0.240232 | ||||||||
\(804\) | −2.90742 | −0.102537 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 26.1927 | 0.922600 | ||||||||
\(807\) | 2.05938 | 0.0724936 | ||||||||
\(808\) | −112.345 | −3.95229 | ||||||||
\(809\) | −34.8006 | −1.22352 | −0.611762 | − | 0.791042i | \(-0.709539\pi\) | ||||
−0.611762 | + | 0.791042i | \(0.709539\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.12783 | 0.250292 | 0.125146 | − | 0.992138i | \(-0.460060\pi\) | ||||
0.125146 | + | 0.992138i | \(0.460060\pi\) | |||||||
\(812\) | 66.9563 | 2.34970 | ||||||||
\(813\) | −0.123945 | −0.00434694 | ||||||||
\(814\) | −4.52156 | −0.158481 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.16885 | 0.145939 | ||||||||
\(817\) | 66.1078 | 2.31282 | ||||||||
\(818\) | −26.3237 | −0.920388 | ||||||||
\(819\) | −5.58921 | −0.195303 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.3699 | −1.02502 | −0.512508 | − | 0.858682i | \(-0.671284\pi\) | ||||
−0.512508 | + | 0.858682i | \(0.671284\pi\) | |||||||
\(822\) | −5.55477 | −0.193745 | ||||||||
\(823\) | 4.23749 | 0.147710 | 0.0738548 | − | 0.997269i | \(-0.476470\pi\) | ||||
0.0738548 | + | 0.997269i | \(0.476470\pi\) | |||||||
\(824\) | 38.7313 | 1.34927 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.36760 | 0.325940 | ||||||||
\(827\) | −10.2062 | −0.354904 | −0.177452 | − | 0.984129i | \(-0.556785\pi\) | ||||
−0.177452 | + | 0.984129i | \(0.556785\pi\) | |||||||
\(828\) | 36.1263 | 1.25548 | ||||||||
\(829\) | −52.2071 | −1.81323 | −0.906614 | − | 0.421962i | \(-0.861342\pi\) | ||||
−0.906614 | + | 0.421962i | \(0.861342\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.69538 | −0.0935018 | ||||||||
\(832\) | −43.7832 | −1.51791 | ||||||||
\(833\) | 15.5543 | 0.538923 | ||||||||
\(834\) | −0.935105 | −0.0323801 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −75.2884 | −2.60390 | ||||||||
\(837\) | 3.73075 | 0.128953 | ||||||||
\(838\) | −30.0193 | −1.03700 | ||||||||
\(839\) | −54.1448 | −1.86929 | −0.934644 | − | 0.355586i | \(-0.884281\pi\) | ||||
−0.934644 | + | 0.355586i | \(0.884281\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 47.1002 | 1.62415 | ||||||||
\(842\) | 2.31488 | 0.0797759 | ||||||||
\(843\) | −0.325750 | −0.0112194 | ||||||||
\(844\) | −89.1229 | −3.06774 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 67.0331 | 2.30465 | ||||||||
\(847\) | 11.3236 | 0.389083 | ||||||||
\(848\) | −40.5965 | −1.39409 | ||||||||
\(849\) | −1.16419 | −0.0399550 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.13401 | 0.0731530 | ||||||||
\(852\) | −4.41227 | −0.151162 | ||||||||
\(853\) | 15.4892 | 0.530340 | 0.265170 | − | 0.964202i | \(-0.414572\pi\) | ||||
0.265170 | + | 0.964202i | \(0.414572\pi\) | |||||||
\(854\) | −14.0605 | −0.481141 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 159.142 | 5.43938 | ||||||||
\(857\) | −32.9960 | −1.12712 | −0.563561 | − | 0.826075i | \(-0.690569\pi\) | ||||
−0.563561 | + | 0.826075i | \(0.690569\pi\) | |||||||
\(858\) | 0.546074 | 0.0186427 | ||||||||
\(859\) | 22.7095 | 0.774837 | 0.387418 | − | 0.921904i | \(-0.373367\pi\) | ||||
0.387418 | + | 0.921904i | \(0.373367\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.398617 | 0.0135848 | ||||||||
\(862\) | 25.2170 | 0.858895 | ||||||||
\(863\) | −6.11570 | −0.208181 | −0.104090 | − | 0.994568i | \(-0.533193\pi\) | ||||
−0.104090 | + | 0.994568i | \(0.533193\pi\) | |||||||
\(864\) | −12.1740 | −0.414169 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −94.7767 | −3.22064 | ||||||||
\(867\) | 0.666166 | 0.0226242 | ||||||||
\(868\) | −54.4758 | −1.84903 | ||||||||
\(869\) | 0.150035 | 0.00508958 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.06599 | −0.273305 | ||||||||
\(872\) | −157.771 | −5.34279 | ||||||||
\(873\) | 40.4780 | 1.36997 | ||||||||
\(874\) | 48.3909 | 1.63685 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.95666 | −0.0661093 | ||||||||
\(877\) | −32.6597 | −1.10284 | −0.551420 | − | 0.834228i | \(-0.685914\pi\) | ||||
−0.551420 | + | 0.834228i | \(0.685914\pi\) | |||||||
\(878\) | 94.4969 | 3.18912 | ||||||||
\(879\) | 2.00049 | 0.0674750 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.6175 | 1.50320 | 0.751600 | − | 0.659619i | \(-0.229282\pi\) | ||||
0.751600 | + | 0.659619i | \(0.229282\pi\) | |||||||
\(882\) | −41.6368 | −1.40199 | ||||||||
\(883\) | −19.5029 | −0.656324 | −0.328162 | − | 0.944621i | \(-0.606429\pi\) | ||||
−0.328162 | + | 0.944621i | \(0.606429\pi\) | |||||||
\(884\) | 22.8015 | 0.766897 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.28608 | −0.244781 | ||||||||
\(887\) | 9.73987 | 0.327033 | 0.163516 | − | 0.986541i | \(-0.447716\pi\) | ||||
0.163516 | + | 0.986541i | \(0.447716\pi\) | |||||||
\(888\) | −0.829359 | −0.0278315 | ||||||||
\(889\) | −17.6609 | −0.592327 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.0651 | −0.504699 | ||||||||
\(892\) | 126.635 | 4.24005 | ||||||||
\(893\) | 65.9329 | 2.20636 | ||||||||
\(894\) | −2.81675 | −0.0942063 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 59.6878 | 1.99403 | ||||||||
\(897\) | −0.257727 | −0.00860527 | ||||||||
\(898\) | −7.56686 | −0.252509 | ||||||||
\(899\) | −61.9154 | −2.06499 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.03454 | 0.267669 | ||||||||
\(902\) | 15.1451 | 0.504275 | ||||||||
\(903\) | 0.997240 | 0.0331861 | ||||||||
\(904\) | −36.3244 | −1.20813 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.57949 | −0.118921 | ||||||||
\(907\) | −7.48693 | −0.248599 | −0.124300 | − | 0.992245i | \(-0.539668\pi\) | ||||
−0.124300 | + | 0.992245i | \(0.539668\pi\) | |||||||
\(908\) | 25.3916 | 0.842649 | ||||||||
\(909\) | −34.7379 | −1.15218 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.5726 | 0.648470 | 0.324235 | − | 0.945977i | \(-0.394893\pi\) | ||||
0.324235 | + | 0.945977i | \(0.394893\pi\) | |||||||
\(912\) | −10.9763 | −0.363463 | ||||||||
\(913\) | −17.7662 | −0.587975 | ||||||||
\(914\) | 23.3181 | 0.771294 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −35.8667 | −1.18507 | ||||||||
\(917\) | −8.91623 | −0.294440 | ||||||||
\(918\) | 4.42288 | 0.145977 | ||||||||
\(919\) | 3.51244 | 0.115865 | 0.0579323 | − | 0.998321i | \(-0.481549\pi\) | ||||
0.0579323 | + | 0.998321i | \(0.481549\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.681348 | −0.0224512 | ||||||||
\(922\) | 88.6888 | 2.92081 | ||||||||
\(923\) | −12.2409 | −0.402913 | ||||||||
\(924\) | −1.13573 | −0.0373627 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 84.7761 | 2.78592 | ||||||||
\(927\) | 11.9760 | 0.393343 | ||||||||
\(928\) | 202.040 | 6.63229 | ||||||||
\(929\) | −13.2440 | −0.434521 | −0.217261 | − | 0.976114i | \(-0.569712\pi\) | ||||
−0.217261 | + | 0.976114i | \(0.569712\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −40.9534 | −1.34219 | ||||||||
\(932\) | 131.067 | 4.29325 | ||||||||
\(933\) | −0.342825 | −0.0112236 | ||||||||
\(934\) | 0.900070 | 0.0294512 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −38.9511 | −1.27316 | ||||||||
\(937\) | 19.4083 | 0.634042 | 0.317021 | − | 0.948419i | \(-0.397317\pi\) | ||||
0.317021 | + | 0.948419i | \(0.397317\pi\) | |||||||
\(938\) | 22.8458 | 0.745943 | ||||||||
\(939\) | −1.65791 | −0.0541037 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −40.5608 | −1.32224 | −0.661122 | − | 0.750279i | \(-0.729919\pi\) | ||||
−0.661122 | + | 0.750279i | \(0.729919\pi\) | |||||||
\(942\) | −5.25833 | −0.171326 | ||||||||
\(943\) | −7.14792 | −0.232768 | ||||||||
\(944\) | 38.1018 | 1.24011 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 37.8891 | 1.23188 | ||||||||
\(947\) | −58.6415 | −1.90559 | −0.952797 | − | 0.303609i | \(-0.901808\pi\) | ||||
−0.952797 | + | 0.303609i | \(0.901808\pi\) | |||||||
\(948\) | 0.0431239 | 0.00140060 | ||||||||
\(949\) | −5.42831 | −0.176210 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.15386 | 0.0374165 | ||||||||
\(952\) | −41.2136 | −1.33574 | ||||||||
\(953\) | −26.5555 | −0.860217 | −0.430109 | − | 0.902777i | \(-0.641525\pi\) | ||||
−0.430109 | + | 0.902777i | \(0.641525\pi\) | |||||||
\(954\) | −21.5075 | −0.696330 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 89.1058 | 2.88189 | ||||||||
\(957\) | −1.29083 | −0.0417266 | ||||||||
\(958\) | −69.2843 | −2.23847 | ||||||||
\(959\) | 32.0508 | 1.03498 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.3746 | 0.624986 | ||||||||
\(962\) | −3.60549 | −0.116246 | ||||||||
\(963\) | 49.2079 | 1.58570 | ||||||||
\(964\) | −5.52727 | −0.178021 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.729979 | 0.0234867 | ||||||||
\(967\) | 58.4290 | 1.87895 | 0.939474 | − | 0.342619i | \(-0.111314\pi\) | ||||
0.939474 | + | 0.342619i | \(0.111314\pi\) | |||||||
\(968\) | 78.9139 | 2.53639 | ||||||||
\(969\) | 2.17235 | 0.0697859 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.4483 | 0.977134 | 0.488567 | − | 0.872526i | \(-0.337520\pi\) | ||||
0.488567 | + | 0.872526i | \(0.337520\pi\) | |||||||
\(972\) | −13.0462 | −0.418457 | ||||||||
\(973\) | 5.39552 | 0.172973 | ||||||||
\(974\) | 108.179 | 3.46627 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −57.1898 | −1.83060 | ||||||||
\(977\) | −4.89196 | −0.156508 | −0.0782539 | − | 0.996933i | \(-0.524934\pi\) | ||||
−0.0782539 | + | 0.996933i | \(0.524934\pi\) | |||||||
\(978\) | 1.60818 | 0.0514239 | ||||||||
\(979\) | −0.878793 | −0.0280864 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −48.7837 | −1.55754 | ||||||||
\(982\) | −33.0560 | −1.05486 | ||||||||
\(983\) | 10.1994 | 0.325310 | 0.162655 | − | 0.986683i | \(-0.447994\pi\) | ||||
0.162655 | + | 0.986683i | \(0.447994\pi\) | |||||||
\(984\) | 2.77796 | 0.0885580 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −73.4020 | −2.33759 | ||||||||
\(987\) | 0.994600 | 0.0316585 | ||||||||
\(988\) | −60.0350 | −1.90997 | ||||||||
\(989\) | −17.8823 | −0.568624 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 61.2312 | 1.94507 | 0.972536 | − | 0.232753i | \(-0.0747734\pi\) | ||||
0.972536 | + | 0.232753i | \(0.0747734\pi\) | |||||||
\(992\) | −164.380 | −5.21908 | ||||||||
\(993\) | 1.56893 | 0.0497884 | ||||||||
\(994\) | 34.6707 | 1.09969 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −5.10647 | −0.161805 | ||||||||
\(997\) | −19.4529 | −0.616081 | −0.308040 | − | 0.951373i | \(-0.599673\pi\) | ||||
−0.308040 | + | 0.951373i | \(0.599673\pi\) | |||||||
\(998\) | 40.0466 | 1.26765 | ||||||||
\(999\) | −0.513546 | −0.0162479 |
(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 | 6025.2.a.l.1.2 | ✓ | 40 | |
5.4 | even | 2 | 6025.2.a.o.1.39 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6025.2.a.l.1.2 | ✓ | 40 | 1.1 | even | 1 | trivial | |
6025.2.a.o.1.39 | yes | 40 | 5.4 | even | 2 |