Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 18 x^{14} + 83 x^{13} + 112 x^{12} - 668 x^{11} - 235 x^{10} + 2648 x^{9} + \cdots - 20 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.50110\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.50110 | −1.06144 | −0.530720 | − | 0.847547i | \(-0.678079\pi\) | ||||
−0.530720 | + | 0.847547i | \(0.678079\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.253312 | 0.126656 | ||||||||
\(5\) | 2.96917 | 1.32785 | 0.663927 | − | 0.747798i | \(-0.268889\pi\) | ||||
0.663927 | + | 0.747798i | \(0.268889\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.62196 | 0.927003 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.45703 | −1.40944 | ||||||||
\(11\) | 5.03235 | 1.51731 | 0.758656 | − | 0.651492i | \(-0.225857\pi\) | ||||
0.758656 | + | 0.651492i | \(0.225857\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.28468 | 1.46571 | 0.732853 | − | 0.680387i | \(-0.238188\pi\) | ||||
0.732853 | + | 0.680387i | \(0.238188\pi\) | |||||||
\(14\) | 1.50110 | 0.401187 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.44246 | −1.11061 | ||||||||
\(17\) | −5.69847 | −1.38208 | −0.691040 | − | 0.722816i | \(-0.742847\pi\) | ||||
−0.691040 | + | 0.722816i | \(0.742847\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.97405 | 1.14113 | 0.570563 | − | 0.821254i | \(-0.306725\pi\) | ||||
0.570563 | + | 0.821254i | \(0.306725\pi\) | |||||||
\(20\) | 0.752126 | 0.168180 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.55408 | −1.61054 | ||||||||
\(23\) | −1.70002 | −0.354479 | −0.177239 | − | 0.984168i | \(-0.556717\pi\) | ||||
−0.177239 | + | 0.984168i | \(0.556717\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.81597 | 0.763194 | ||||||||
\(26\) | −7.93285 | −1.55576 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.253312 | −0.0478714 | ||||||||
\(29\) | −3.58394 | −0.665520 | −0.332760 | − | 0.943011i | \(-0.607980\pi\) | ||||
−0.332760 | + | 0.943011i | \(0.607980\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.14042 | 0.204826 | 0.102413 | − | 0.994742i | \(-0.467344\pi\) | ||||
0.102413 | + | 0.994742i | \(0.467344\pi\) | |||||||
\(32\) | 1.42467 | 0.251848 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.55399 | 1.46700 | ||||||||
\(35\) | −2.96917 | −0.501881 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.99996 | 1.31519 | 0.657593 | − | 0.753374i | \(-0.271575\pi\) | ||||
0.657593 | + | 0.753374i | \(0.271575\pi\) | |||||||
\(38\) | −7.46656 | −1.21124 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.78504 | 1.23092 | ||||||||
\(41\) | −2.27251 | −0.354907 | −0.177454 | − | 0.984129i | \(-0.556786\pi\) | ||||
−0.177454 | + | 0.984129i | \(0.556786\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.39125 | −1.27965 | −0.639827 | − | 0.768519i | \(-0.720994\pi\) | ||||
−0.639827 | + | 0.768519i | \(0.720994\pi\) | |||||||
\(44\) | 1.27475 | 0.192176 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.55191 | 0.376258 | ||||||||
\(47\) | 8.01028 | 1.16842 | 0.584210 | − | 0.811603i | \(-0.301405\pi\) | ||||
0.584210 | + | 0.811603i | \(0.301405\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −5.72816 | −0.810085 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.33867 | 0.185640 | ||||||||
\(53\) | −2.49184 | −0.342280 | −0.171140 | − | 0.985247i | \(-0.554745\pi\) | ||||
−0.171140 | + | 0.985247i | \(0.554745\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.9419 | 2.01477 | ||||||||
\(56\) | −2.62196 | −0.350374 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.37986 | 0.706410 | ||||||||
\(59\) | −5.98779 | −0.779544 | −0.389772 | − | 0.920911i | \(-0.627446\pi\) | ||||
−0.389772 | + | 0.920911i | \(0.627446\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.87074 | 1.00774 | 0.503872 | − | 0.863778i | \(-0.331908\pi\) | ||||
0.503872 | + | 0.863778i | \(0.331908\pi\) | |||||||
\(62\) | −1.71189 | −0.217411 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.74634 | 0.843292 | ||||||||
\(65\) | 15.6911 | 1.94624 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.4773 | 1.64652 | 0.823260 | − | 0.567664i | \(-0.192153\pi\) | ||||
0.823260 | + | 0.567664i | \(0.192153\pi\) | |||||||
\(68\) | −1.44349 | −0.175049 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.45703 | 0.532717 | ||||||||
\(71\) | 7.07915 | 0.840141 | 0.420071 | − | 0.907491i | \(-0.362005\pi\) | ||||
0.420071 | + | 0.907491i | \(0.362005\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.23904 | 0.730224 | 0.365112 | − | 0.930964i | \(-0.381031\pi\) | ||||
0.365112 | + | 0.930964i | \(0.381031\pi\) | |||||||
\(74\) | −12.0088 | −1.39599 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.25999 | 0.144530 | ||||||||
\(77\) | −5.03235 | −0.573490 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.41290 | 0.158964 | 0.0794819 | − | 0.996836i | \(-0.474673\pi\) | ||||
0.0794819 | + | 0.996836i | \(0.474673\pi\) | |||||||
\(80\) | −13.1904 | −1.47473 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.41128 | 0.376713 | ||||||||
\(83\) | 5.37001 | 0.589435 | 0.294718 | − | 0.955584i | \(-0.404774\pi\) | ||||
0.294718 | + | 0.955584i | \(0.404774\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16.9197 | −1.83520 | ||||||||
\(86\) | 12.5961 | 1.35828 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 13.1946 | 1.40655 | ||||||||
\(89\) | −4.94427 | −0.524091 | −0.262046 | − | 0.965056i | \(-0.584397\pi\) | ||||
−0.262046 | + | 0.965056i | \(0.584397\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.28468 | −0.553985 | ||||||||
\(92\) | −0.430635 | −0.0448968 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −12.0243 | −1.24021 | ||||||||
\(95\) | 14.7688 | 1.51525 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.90024 | 0.497544 | 0.248772 | − | 0.968562i | \(-0.419973\pi\) | ||||
0.248772 | + | 0.968562i | \(0.419973\pi\) | |||||||
\(98\) | −1.50110 | −0.151634 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.966630 | 0.0966630 | ||||||||
\(101\) | 0.367501 | 0.0365678 | 0.0182839 | − | 0.999833i | \(-0.494180\pi\) | ||||
0.0182839 | + | 0.999833i | \(0.494180\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.94858 | −0.783197 | −0.391599 | − | 0.920136i | \(-0.628078\pi\) | ||||
−0.391599 | + | 0.920136i | \(0.628078\pi\) | |||||||
\(104\) | 13.8562 | 1.35871 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.74051 | 0.363310 | ||||||||
\(107\) | −10.9611 | −1.05965 | −0.529823 | − | 0.848108i | \(-0.677742\pi\) | ||||
−0.529823 | + | 0.848108i | \(0.677742\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.7913 | 1.03362 | 0.516809 | − | 0.856101i | \(-0.327120\pi\) | ||||
0.516809 | + | 0.856101i | \(0.327120\pi\) | |||||||
\(110\) | −22.4293 | −2.13855 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.44246 | 0.419773 | ||||||||
\(113\) | −1.89200 | −0.177985 | −0.0889924 | − | 0.996032i | \(-0.528365\pi\) | ||||
−0.0889924 | + | 0.996032i | \(0.528365\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.04765 | −0.470696 | ||||||||
\(116\) | −0.907853 | −0.0842921 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.98829 | 0.827440 | ||||||||
\(119\) | 5.69847 | 0.522378 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.3246 | 1.30223 | ||||||||
\(122\) | −11.8148 | −1.06966 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.288882 | 0.0259424 | ||||||||
\(125\) | −3.51559 | −0.314444 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | −12.9763 | −1.14695 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −23.5540 | −2.06582 | ||||||||
\(131\) | 19.7242 | 1.72331 | 0.861656 | − | 0.507492i | \(-0.169428\pi\) | ||||
0.861656 | + | 0.507492i | \(0.169428\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.97405 | −0.431305 | ||||||||
\(134\) | −20.2309 | −1.74768 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −14.9411 | −1.28119 | ||||||||
\(137\) | 1.23699 | 0.105683 | 0.0528415 | − | 0.998603i | \(-0.483172\pi\) | ||||
0.0528415 | + | 0.998603i | \(0.483172\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.9060 | −1.60359 | −0.801794 | − | 0.597601i | \(-0.796121\pi\) | ||||
−0.801794 | + | 0.597601i | \(0.796121\pi\) | |||||||
\(140\) | −0.752126 | −0.0635662 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.6265 | −0.891760 | ||||||||
\(143\) | 26.5943 | 2.22393 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.6413 | −0.883713 | ||||||||
\(146\) | −9.36545 | −0.775090 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.02648 | 0.166576 | ||||||||
\(149\) | 18.6688 | 1.52940 | 0.764702 | − | 0.644384i | \(-0.222886\pi\) | ||||
0.764702 | + | 0.644384i | \(0.222886\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.9340 | 1.21531 | 0.607656 | − | 0.794201i | \(-0.292110\pi\) | ||||
0.607656 | + | 0.794201i | \(0.292110\pi\) | |||||||
\(152\) | 13.0418 | 1.05783 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.55408 | 0.608725 | ||||||||
\(155\) | 3.38611 | 0.271979 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.6259 | 0.927850 | 0.463925 | − | 0.885874i | \(-0.346441\pi\) | ||||
0.463925 | + | 0.885874i | \(0.346441\pi\) | |||||||
\(158\) | −2.12091 | −0.168731 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.23008 | 0.334417 | ||||||||
\(161\) | 1.70002 | 0.133980 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −23.6206 | −1.85011 | −0.925055 | − | 0.379833i | \(-0.875982\pi\) | ||||
−0.925055 | + | 0.379833i | \(0.875982\pi\) | |||||||
\(164\) | −0.575655 | −0.0449511 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.06094 | −0.625650 | ||||||||
\(167\) | −16.6636 | −1.28947 | −0.644735 | − | 0.764406i | \(-0.723032\pi\) | ||||
−0.644735 | + | 0.764406i | \(0.723032\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.9278 | 1.14829 | ||||||||
\(170\) | 25.3982 | 1.94796 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.12560 | −0.162076 | ||||||||
\(173\) | −4.06588 | −0.309123 | −0.154561 | − | 0.987983i | \(-0.549396\pi\) | ||||
−0.154561 | + | 0.987983i | \(0.549396\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.81597 | −0.288460 | ||||||||
\(176\) | −22.3560 | −1.68515 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.42185 | 0.556291 | ||||||||
\(179\) | −11.2678 | −0.842196 | −0.421098 | − | 0.907015i | \(-0.638355\pi\) | ||||
−0.421098 | + | 0.907015i | \(0.638355\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.9248 | −1.10935 | −0.554677 | − | 0.832066i | \(-0.687158\pi\) | ||||
−0.554677 | + | 0.832066i | \(0.687158\pi\) | |||||||
\(182\) | 7.93285 | 0.588022 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.45738 | −0.328603 | ||||||||
\(185\) | 23.7532 | 1.74637 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −28.6767 | −2.09705 | ||||||||
\(188\) | 2.02910 | 0.147987 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −22.1695 | −1.60834 | ||||||||
\(191\) | 5.10449 | 0.369348 | 0.184674 | − | 0.982800i | \(-0.440877\pi\) | ||||
0.184674 | + | 0.982800i | \(0.440877\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.4463 | 1.47176 | 0.735878 | − | 0.677114i | \(-0.236770\pi\) | ||||
0.735878 | + | 0.677114i | \(0.236770\pi\) | |||||||
\(194\) | −7.35576 | −0.528113 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.253312 | 0.0180937 | ||||||||
\(197\) | −10.8131 | −0.770405 | −0.385202 | − | 0.922832i | \(-0.625868\pi\) | ||||
−0.385202 | + | 0.922832i | \(0.625868\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.8057 | −1.04955 | −0.524774 | − | 0.851242i | \(-0.675850\pi\) | ||||
−0.524774 | + | 0.851242i | \(0.675850\pi\) | |||||||
\(200\) | 10.0053 | 0.707483 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.551658 | −0.0388145 | ||||||||
\(203\) | 3.58394 | 0.251543 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.74748 | −0.471265 | ||||||||
\(206\) | 11.9316 | 0.831317 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −23.4769 | −1.62783 | ||||||||
\(209\) | 25.0312 | 1.73144 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.296253 | −0.0203949 | −0.0101975 | − | 0.999948i | \(-0.503246\pi\) | ||||
−0.0101975 | + | 0.999948i | \(0.503246\pi\) | |||||||
\(212\) | −0.631212 | −0.0433518 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 16.4537 | 1.12475 | ||||||||
\(215\) | −24.9150 | −1.69919 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.14042 | −0.0774169 | ||||||||
\(218\) | −16.1988 | −1.09712 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.78496 | 0.255182 | ||||||||
\(221\) | −30.1145 | −2.02572 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.9296 | 0.999762 | 0.499881 | − | 0.866094i | \(-0.333377\pi\) | ||||
0.499881 | + | 0.866094i | \(0.333377\pi\) | |||||||
\(224\) | −1.42467 | −0.0951896 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.84010 | 0.188920 | ||||||||
\(227\) | 28.6612 | 1.90231 | 0.951155 | − | 0.308714i | \(-0.0998986\pi\) | ||||
0.951155 | + | 0.308714i | \(0.0998986\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.72133 | −0.444158 | −0.222079 | − | 0.975029i | \(-0.571284\pi\) | ||||
−0.222079 | + | 0.975029i | \(0.571284\pi\) | |||||||
\(230\) | 7.57704 | 0.499615 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.39694 | −0.616939 | ||||||||
\(233\) | −1.90481 | −0.124788 | −0.0623941 | − | 0.998052i | \(-0.519874\pi\) | ||||
−0.0623941 | + | 0.998052i | \(0.519874\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 23.7839 | 1.55149 | ||||||||
\(236\) | −1.51678 | −0.0987338 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.55399 | −0.554473 | ||||||||
\(239\) | 2.36861 | 0.153213 | 0.0766064 | − | 0.997061i | \(-0.475592\pi\) | ||||
0.0766064 | + | 0.997061i | \(0.475592\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.9592 | 0.770359 | 0.385180 | − | 0.922842i | \(-0.374139\pi\) | ||||
0.385180 | + | 0.922842i | \(0.374139\pi\) | |||||||
\(242\) | −21.5026 | −1.38224 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.99375 | 0.127637 | ||||||||
\(245\) | 2.96917 | 0.189693 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.2862 | 1.67255 | ||||||||
\(248\) | 2.99014 | 0.189874 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.27726 | 0.333763 | ||||||||
\(251\) | 12.9770 | 0.819101 | 0.409551 | − | 0.912287i | \(-0.365685\pi\) | ||||
0.409551 | + | 0.912287i | \(0.365685\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.55510 | −0.537854 | ||||||||
\(254\) | 1.50110 | 0.0941876 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.98607 | 0.374130 | ||||||||
\(257\) | −0.945782 | −0.0589963 | −0.0294981 | − | 0.999565i | \(-0.509391\pi\) | ||||
−0.0294981 | + | 0.999565i | \(0.509391\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.99996 | −0.497093 | ||||||||
\(260\) | 3.97474 | 0.246503 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −29.6081 | −1.82919 | ||||||||
\(263\) | −18.5648 | −1.14476 | −0.572378 | − | 0.819990i | \(-0.693979\pi\) | ||||
−0.572378 | + | 0.819990i | \(0.693979\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.39869 | −0.454498 | ||||||||
\(266\) | 7.46656 | 0.457804 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.41397 | 0.208541 | ||||||||
\(269\) | −27.9998 | −1.70718 | −0.853589 | − | 0.520947i | \(-0.825579\pi\) | ||||
−0.853589 | + | 0.520947i | \(0.825579\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.0427 | 0.731543 | 0.365772 | − | 0.930705i | \(-0.380805\pi\) | ||||
0.365772 | + | 0.930705i | \(0.380805\pi\) | |||||||
\(272\) | 25.3152 | 1.53496 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.85685 | −0.112176 | ||||||||
\(275\) | 19.2033 | 1.15800 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.97940 | −0.179015 | −0.0895074 | − | 0.995986i | \(-0.528529\pi\) | ||||
−0.0895074 | + | 0.995986i | \(0.528529\pi\) | |||||||
\(278\) | 28.3799 | 1.70211 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.78504 | −0.465245 | ||||||||
\(281\) | −18.5742 | −1.10804 | −0.554021 | − | 0.832503i | \(-0.686907\pi\) | ||||
−0.554021 | + | 0.832503i | \(0.686907\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.99311 | −0.475141 | −0.237571 | − | 0.971370i | \(-0.576351\pi\) | ||||
−0.237571 | + | 0.971370i | \(0.576351\pi\) | |||||||
\(284\) | 1.79323 | 0.106409 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −39.9209 | −2.36057 | ||||||||
\(287\) | 2.27251 | 0.134142 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.4725 | 0.910148 | ||||||||
\(290\) | 15.9737 | 0.938009 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.58042 | 0.0924872 | ||||||||
\(293\) | −10.6556 | −0.622508 | −0.311254 | − | 0.950327i | \(-0.600749\pi\) | ||||
−0.311254 | + | 0.950327i | \(0.600749\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.7788 | −1.03512 | ||||||||
\(296\) | 20.9756 | 1.21918 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −28.0237 | −1.62337 | ||||||||
\(299\) | −8.98406 | −0.519561 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.39125 | 0.483663 | ||||||||
\(302\) | −22.4175 | −1.28998 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −22.0970 | −1.26735 | ||||||||
\(305\) | 23.3696 | 1.33814 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.9512 | 1.70941 | 0.854703 | − | 0.519117i | \(-0.173739\pi\) | ||||
0.854703 | + | 0.519117i | \(0.173739\pi\) | |||||||
\(308\) | −1.27475 | −0.0726358 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.08290 | −0.288689 | ||||||||
\(311\) | −10.0081 | −0.567507 | −0.283753 | − | 0.958897i | \(-0.591580\pi\) | ||||
−0.283753 | + | 0.958897i | \(0.591580\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.1282 | −0.572482 | −0.286241 | − | 0.958158i | \(-0.592406\pi\) | ||||
−0.286241 | + | 0.958158i | \(0.592406\pi\) | |||||||
\(314\) | −17.4517 | −0.984858 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.357905 | 0.0201337 | ||||||||
\(317\) | 23.0112 | 1.29244 | 0.646220 | − | 0.763151i | \(-0.276349\pi\) | ||||
0.646220 | + | 0.763151i | \(0.276349\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.0356 | −1.00980 | ||||||||
\(320\) | 20.0310 | 1.11977 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.55191 | −0.142212 | ||||||||
\(323\) | −28.3445 | −1.57713 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.1662 | 1.11862 | ||||||||
\(326\) | 35.4570 | 1.96378 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.95844 | −0.329000 | ||||||||
\(329\) | −8.01028 | −0.441621 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.9378 | 1.09588 | 0.547941 | − | 0.836517i | \(-0.315412\pi\) | ||||
0.547941 | + | 0.836517i | \(0.315412\pi\) | |||||||
\(332\) | 1.36029 | 0.0746554 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 25.0138 | 1.36870 | ||||||||
\(335\) | 40.0165 | 2.18634 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.4694 | −1.06057 | −0.530283 | − | 0.847821i | \(-0.677914\pi\) | ||||
−0.530283 | + | 0.847821i | \(0.677914\pi\) | |||||||
\(338\) | −22.4082 | −1.21884 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.28596 | −0.232439 | ||||||||
\(341\) | 5.73901 | 0.310785 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −22.0015 | −1.18624 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.10330 | 0.328116 | ||||||||
\(347\) | 10.8161 | 0.580639 | 0.290320 | − | 0.956930i | \(-0.406238\pi\) | ||||
0.290320 | + | 0.956930i | \(0.406238\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.6549 | 0.891518 | 0.445759 | − | 0.895153i | \(-0.352934\pi\) | ||||
0.445759 | + | 0.895153i | \(0.352934\pi\) | |||||||
\(350\) | 5.72816 | 0.306183 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.16943 | 0.382132 | ||||||||
\(353\) | 34.3191 | 1.82662 | 0.913312 | − | 0.407262i | \(-0.133516\pi\) | ||||
0.913312 | + | 0.407262i | \(0.133516\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.0192 | 1.11558 | ||||||||
\(356\) | −1.25244 | −0.0663792 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 16.9141 | 0.893941 | ||||||||
\(359\) | −13.5371 | −0.714463 | −0.357232 | − | 0.934016i | \(-0.616279\pi\) | ||||
−0.357232 | + | 0.934016i | \(0.616279\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.74118 | 0.302167 | ||||||||
\(362\) | 22.4037 | 1.17751 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.33867 | −0.0701654 | ||||||||
\(365\) | 18.5248 | 0.969631 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.36464 | 0.123433 | 0.0617165 | − | 0.998094i | \(-0.480343\pi\) | ||||
0.0617165 | + | 0.998094i | \(0.480343\pi\) | |||||||
\(368\) | 7.55227 | 0.393689 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −35.6561 | −1.85367 | ||||||||
\(371\) | 2.49184 | 0.129370 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.6616 | −0.552035 | −0.276018 | − | 0.961153i | \(-0.589015\pi\) | ||||
−0.276018 | + | 0.961153i | \(0.589015\pi\) | |||||||
\(374\) | 43.0467 | 2.22589 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 21.0026 | 1.08313 | ||||||||
\(377\) | −18.9399 | −0.975457 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.1609 | 1.34379 | 0.671896 | − | 0.740645i | \(-0.265480\pi\) | ||||
0.671896 | + | 0.740645i | \(0.265480\pi\) | |||||||
\(380\) | 3.74111 | 0.191915 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.66237 | −0.392041 | ||||||||
\(383\) | 7.78799 | 0.397948 | 0.198974 | − | 0.980005i | \(-0.436239\pi\) | ||||
0.198974 | + | 0.980005i | \(0.436239\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.9419 | −0.761510 | ||||||||
\(386\) | −30.6920 | −1.56218 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.24129 | 0.0630168 | ||||||||
\(389\) | −2.64982 | −0.134351 | −0.0671757 | − | 0.997741i | \(-0.521399\pi\) | ||||
−0.0671757 | + | 0.997741i | \(0.521399\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.68751 | 0.489918 | ||||||||
\(392\) | 2.62196 | 0.132429 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 16.2317 | 0.817739 | ||||||||
\(395\) | 4.19514 | 0.211081 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.0810 | −1.45953 | −0.729767 | − | 0.683696i | \(-0.760371\pi\) | ||||
−0.729767 | + | 0.683696i | \(0.760371\pi\) | |||||||
\(398\) | 22.2249 | 1.11403 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −16.9523 | −0.847614 | ||||||||
\(401\) | −6.88884 | −0.344012 | −0.172006 | − | 0.985096i | \(-0.555025\pi\) | ||||
−0.172006 | + | 0.985096i | \(0.555025\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.02676 | 0.300214 | ||||||||
\(404\) | 0.0930924 | 0.00463152 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.37986 | −0.266998 | ||||||||
\(407\) | 40.2586 | 1.99554 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.9194 | 1.62776 | 0.813880 | − | 0.581032i | \(-0.197351\pi\) | ||||
0.813880 | + | 0.581032i | \(0.197351\pi\) | |||||||
\(410\) | 10.1287 | 0.500219 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.01347 | −0.0991965 | ||||||||
\(413\) | 5.98779 | 0.294640 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.9445 | 0.782683 | ||||||||
\(416\) | 7.52891 | 0.369135 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −37.5744 | −1.83782 | ||||||||
\(419\) | 9.10685 | 0.444899 | 0.222449 | − | 0.974944i | \(-0.428595\pi\) | ||||
0.222449 | + | 0.974944i | \(0.428595\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.5215 | −0.902685 | −0.451343 | − | 0.892351i | \(-0.649055\pi\) | ||||
−0.451343 | + | 0.892351i | \(0.649055\pi\) | |||||||
\(422\) | 0.444707 | 0.0216480 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.53350 | −0.317295 | ||||||||
\(425\) | −21.7452 | −1.05480 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.87074 | −0.380892 | ||||||||
\(428\) | −2.77657 | −0.134211 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 37.4001 | 1.80359 | ||||||||
\(431\) | 27.2836 | 1.31421 | 0.657103 | − | 0.753801i | \(-0.271782\pi\) | ||||
0.657103 | + | 0.753801i | \(0.271782\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.5517 | −1.22794 | −0.613968 | − | 0.789331i | \(-0.710427\pi\) | ||||
−0.613968 | + | 0.789331i | \(0.710427\pi\) | |||||||
\(434\) | 1.71189 | 0.0821735 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.73356 | 0.130914 | ||||||||
\(437\) | −8.45599 | −0.404505 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.2340 | −1.01344 | −0.506721 | − | 0.862110i | \(-0.669143\pi\) | ||||
−0.506721 | + | 0.862110i | \(0.669143\pi\) | |||||||
\(440\) | 39.1771 | 1.86769 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 45.2051 | 2.15019 | ||||||||
\(443\) | −12.1933 | −0.579322 | −0.289661 | − | 0.957129i | \(-0.593543\pi\) | ||||
−0.289661 | + | 0.957129i | \(0.593543\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.6804 | −0.695916 | ||||||||
\(446\) | −22.4109 | −1.06119 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.74634 | −0.318735 | ||||||||
\(449\) | −19.6586 | −0.927748 | −0.463874 | − | 0.885901i | \(-0.653541\pi\) | ||||
−0.463874 | + | 0.885901i | \(0.653541\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.4361 | −0.538505 | ||||||||
\(452\) | −0.479267 | −0.0225428 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −43.0234 | −2.01919 | ||||||||
\(455\) | −15.6911 | −0.735610 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.9369 | −1.21328 | −0.606639 | − | 0.794977i | \(-0.707483\pi\) | ||||
−0.606639 | + | 0.794977i | \(0.707483\pi\) | |||||||
\(458\) | 10.0894 | 0.471447 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.27863 | −0.0596164 | ||||||||
\(461\) | −16.5556 | −0.771073 | −0.385537 | − | 0.922693i | \(-0.625984\pi\) | ||||
−0.385537 | + | 0.922693i | \(0.625984\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.7070 | 1.00881 | 0.504404 | − | 0.863468i | \(-0.331712\pi\) | ||||
0.504404 | + | 0.863468i | \(0.331712\pi\) | |||||||
\(464\) | 15.9215 | 0.739136 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.85932 | 0.132455 | ||||||||
\(467\) | −22.5624 | −1.04406 | −0.522032 | − | 0.852926i | \(-0.674826\pi\) | ||||
−0.522032 | + | 0.852926i | \(0.674826\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.4773 | −0.622326 | ||||||||
\(470\) | −35.7021 | −1.64681 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −15.6997 | −0.722639 | ||||||||
\(473\) | −42.2277 | −1.94163 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.9808 | 0.870900 | ||||||||
\(476\) | 1.44349 | 0.0661622 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.55553 | −0.162626 | ||||||||
\(479\) | −27.0168 | −1.23443 | −0.617214 | − | 0.786795i | \(-0.711739\pi\) | ||||
−0.617214 | + | 0.786795i | \(0.711739\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 42.2772 | 1.92767 | ||||||||
\(482\) | −17.9520 | −0.817691 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.62858 | 0.164935 | ||||||||
\(485\) | 14.5496 | 0.660665 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.5223 | −0.839325 | −0.419662 | − | 0.907680i | \(-0.637851\pi\) | ||||
−0.419662 | + | 0.907680i | \(0.637851\pi\) | |||||||
\(488\) | 20.6368 | 0.934182 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.45703 | −0.201348 | ||||||||
\(491\) | 15.1509 | 0.683750 | 0.341875 | − | 0.939745i | \(-0.388938\pi\) | ||||
0.341875 | + | 0.939745i | \(0.388938\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.4229 | 0.919803 | ||||||||
\(494\) | −39.4584 | −1.77532 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.06628 | −0.227483 | ||||||||
\(497\) | −7.07915 | −0.317543 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 44.4265 | 1.98880 | 0.994401 | − | 0.105676i | \(-0.0337008\pi\) | ||||
0.994401 | + | 0.105676i | \(0.0337008\pi\) | |||||||
\(500\) | −0.890540 | −0.0398262 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −19.4798 | −0.869427 | ||||||||
\(503\) | −36.4849 | −1.62678 | −0.813390 | − | 0.581719i | \(-0.802380\pi\) | ||||
−0.813390 | + | 0.581719i | \(0.802380\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.09117 | 0.0485566 | ||||||||
\(506\) | 12.8421 | 0.570900 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.253312 | −0.0112389 | ||||||||
\(509\) | −20.1520 | −0.893222 | −0.446611 | − | 0.894728i | \(-0.647369\pi\) | ||||
−0.446611 | + | 0.894728i | \(0.647369\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.23904 | −0.275999 | ||||||||
\(512\) | 16.9669 | 0.749836 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.41972 | 0.0626210 | ||||||||
\(515\) | −23.6007 | −1.03997 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 40.3105 | 1.77286 | ||||||||
\(518\) | 12.0088 | 0.527635 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 41.1414 | 1.80417 | ||||||||
\(521\) | 18.5745 | 0.813763 | 0.406882 | − | 0.913481i | \(-0.366616\pi\) | ||||
0.406882 | + | 0.913481i | \(0.366616\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.8272 | −0.473440 | −0.236720 | − | 0.971578i | \(-0.576072\pi\) | ||||
−0.236720 | + | 0.971578i | \(0.576072\pi\) | |||||||
\(524\) | 4.99637 | 0.218268 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 27.8677 | 1.21509 | ||||||||
\(527\) | −6.49866 | −0.283086 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.1099 | −0.874345 | ||||||||
\(530\) | 11.1062 | 0.482423 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.25999 | −0.0546273 | ||||||||
\(533\) | −12.0095 | −0.520189 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −32.5453 | −1.40706 | ||||||||
\(536\) | 35.3371 | 1.52633 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 42.0306 | 1.81207 | ||||||||
\(539\) | 5.03235 | 0.216759 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.8734 | 0.897417 | 0.448709 | − | 0.893678i | \(-0.351884\pi\) | ||||
0.448709 | + | 0.893678i | \(0.351884\pi\) | |||||||
\(542\) | −18.0774 | −0.776490 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −8.11842 | −0.348074 | ||||||||
\(545\) | 32.0412 | 1.37249 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.2787 | 0.567754 | 0.283877 | − | 0.958861i | \(-0.408379\pi\) | ||||
0.283877 | + | 0.958861i | \(0.408379\pi\) | |||||||
\(548\) | 0.313343 | 0.0133854 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −28.8261 | −1.22915 | ||||||||
\(551\) | −17.8267 | −0.759442 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.41290 | −0.0600827 | ||||||||
\(554\) | 4.47239 | 0.190014 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.78912 | −0.203104 | ||||||||
\(557\) | −30.6231 | −1.29754 | −0.648772 | − | 0.760983i | \(-0.724717\pi\) | ||||
−0.648772 | + | 0.760983i | \(0.724717\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −44.3450 | −1.87559 | ||||||||
\(560\) | 13.1904 | 0.557396 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 27.8817 | 1.17612 | ||||||||
\(563\) | −44.0774 | −1.85764 | −0.928820 | − | 0.370531i | \(-0.879176\pi\) | ||||
−0.928820 | + | 0.370531i | \(0.879176\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.61768 | −0.236338 | ||||||||
\(566\) | 11.9985 | 0.504334 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 18.5613 | 0.778813 | ||||||||
\(569\) | 13.4726 | 0.564803 | 0.282401 | − | 0.959296i | \(-0.408869\pi\) | ||||
0.282401 | + | 0.959296i | \(0.408869\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.8076 | −0.452282 | −0.226141 | − | 0.974095i | \(-0.572611\pi\) | ||||
−0.226141 | + | 0.974095i | \(0.572611\pi\) | |||||||
\(572\) | 6.73666 | 0.281674 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.41128 | −0.142384 | ||||||||
\(575\) | −6.48722 | −0.270536 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.47813 | −0.103166 | −0.0515830 | − | 0.998669i | \(-0.516427\pi\) | ||||
−0.0515830 | + | 0.998669i | \(0.516427\pi\) | |||||||
\(578\) | −23.2258 | −0.966068 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.69557 | −0.111927 | ||||||||
\(581\) | −5.37001 | −0.222786 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.5398 | −0.519346 | ||||||||
\(584\) | 16.3585 | 0.676920 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.9952 | 0.660755 | ||||||||
\(587\) | 22.1676 | 0.914957 | 0.457478 | − | 0.889221i | \(-0.348753\pi\) | ||||
0.457478 | + | 0.889221i | \(0.348753\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.67252 | 0.233732 | ||||||||
\(590\) | 26.6878 | 1.09872 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −35.5395 | −1.46066 | ||||||||
\(593\) | 38.4169 | 1.57759 | 0.788797 | − | 0.614654i | \(-0.210704\pi\) | ||||
0.788797 | + | 0.614654i | \(0.210704\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.9197 | 0.693641 | ||||||||
\(596\) | 4.72902 | 0.193708 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 13.4860 | 0.551483 | ||||||||
\(599\) | −13.4735 | −0.550513 | −0.275256 | − | 0.961371i | \(-0.588763\pi\) | ||||
−0.275256 | + | 0.961371i | \(0.588763\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.1750 | 1.02691 | 0.513454 | − | 0.858117i | \(-0.328366\pi\) | ||||
0.513454 | + | 0.858117i | \(0.328366\pi\) | |||||||
\(602\) | −12.5961 | −0.513380 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.78296 | 0.153926 | ||||||||
\(605\) | 42.5321 | 1.72917 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.5557 | 1.19963 | 0.599814 | − | 0.800140i | \(-0.295241\pi\) | ||||
0.599814 | + | 0.800140i | \(0.295241\pi\) | |||||||
\(608\) | 7.08637 | 0.287390 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −35.0801 | −1.42035 | ||||||||
\(611\) | 42.3317 | 1.71256 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.7295 | 0.473752 | 0.236876 | − | 0.971540i | \(-0.423877\pi\) | ||||
0.236876 | + | 0.971540i | \(0.423877\pi\) | |||||||
\(614\) | −44.9599 | −1.81443 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −13.1946 | −0.531627 | ||||||||
\(617\) | 14.0770 | 0.566717 | 0.283359 | − | 0.959014i | \(-0.408551\pi\) | ||||
0.283359 | + | 0.959014i | \(0.408551\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.4709 | 0.903183 | 0.451591 | − | 0.892225i | \(-0.350856\pi\) | ||||
0.451591 | + | 0.892225i | \(0.350856\pi\) | |||||||
\(620\) | 0.857741 | 0.0344477 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15.0232 | 0.602375 | ||||||||
\(623\) | 4.94427 | 0.198088 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.5182 | −1.18073 | ||||||||
\(626\) | 15.2035 | 0.607655 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.94499 | 0.117518 | ||||||||
\(629\) | −45.5875 | −1.81769 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.2901 | 0.927163 | 0.463581 | − | 0.886054i | \(-0.346564\pi\) | ||||
0.463581 | + | 0.886054i | \(0.346564\pi\) | |||||||
\(632\) | 3.70457 | 0.147360 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −34.5423 | −1.37185 | ||||||||
\(635\) | −2.96917 | −0.117828 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.28468 | 0.209387 | ||||||||
\(638\) | 27.0734 | 1.07184 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −38.5288 | −1.52298 | ||||||||
\(641\) | −16.9438 | −0.669239 | −0.334620 | − | 0.942353i | \(-0.608608\pi\) | ||||
−0.334620 | + | 0.942353i | \(0.608608\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −41.7811 | −1.64768 | −0.823842 | − | 0.566819i | \(-0.808174\pi\) | ||||
−0.823842 | + | 0.566819i | \(0.808174\pi\) | |||||||
\(644\) | 0.430635 | 0.0169694 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 42.5480 | 1.67403 | ||||||||
\(647\) | 19.5797 | 0.769759 | 0.384879 | − | 0.922967i | \(-0.374243\pi\) | ||||
0.384879 | + | 0.922967i | \(0.374243\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −30.1327 | −1.18281 | ||||||||
\(650\) | −30.2715 | −1.18735 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.98338 | −0.234327 | ||||||||
\(653\) | 2.54800 | 0.0997108 | 0.0498554 | − | 0.998756i | \(-0.484124\pi\) | ||||
0.0498554 | + | 0.998756i | \(0.484124\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 58.5645 | 2.28831 | ||||||||
\(656\) | 10.0955 | 0.394165 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12.0243 | 0.468754 | ||||||||
\(659\) | 5.36661 | 0.209053 | 0.104527 | − | 0.994522i | \(-0.466667\pi\) | ||||
0.104527 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.8201 | 1.62661 | 0.813306 | − | 0.581836i | \(-0.197666\pi\) | ||||
0.813306 | + | 0.581836i | \(0.197666\pi\) | |||||||
\(662\) | −29.9287 | −1.16321 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.0800 | 0.546408 | ||||||||
\(665\) | −14.7688 | −0.572710 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.09277 | 0.235913 | ||||||||
\(668\) | −4.22109 | −0.163319 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −60.0690 | −2.32067 | ||||||||
\(671\) | 39.6083 | 1.52906 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.98792 | −0.230818 | −0.115409 | − | 0.993318i | \(-0.536818\pi\) | ||||
−0.115409 | + | 0.993318i | \(0.536818\pi\) | |||||||
\(674\) | 29.2256 | 1.12573 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.78139 | 0.145438 | ||||||||
\(677\) | 28.6767 | 1.10214 | 0.551068 | − | 0.834460i | \(-0.314221\pi\) | ||||
0.551068 | + | 0.834460i | \(0.314221\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.90024 | −0.188054 | ||||||||
\(680\) | −44.3628 | −1.70124 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.61484 | −0.329879 | ||||||||
\(683\) | 50.5969 | 1.93604 | 0.968018 | − | 0.250880i | \(-0.0807200\pi\) | ||||
0.968018 | + | 0.250880i | \(0.0807200\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.67283 | 0.140331 | ||||||||
\(686\) | 1.50110 | 0.0573124 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 37.2778 | 1.42120 | ||||||||
\(689\) | −13.1686 | −0.501682 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.4389 | 1.65249 | 0.826247 | − | 0.563309i | \(-0.190472\pi\) | ||||
0.826247 | + | 0.563309i | \(0.190472\pi\) | |||||||
\(692\) | −1.02993 | −0.0391522 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16.2361 | −0.616314 | ||||||||
\(695\) | −56.1352 | −2.12933 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.9498 | 0.490510 | ||||||||
\(698\) | −25.0008 | −0.946293 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.966630 | −0.0365352 | ||||||||
\(701\) | 47.2200 | 1.78347 | 0.891737 | − | 0.452554i | \(-0.149487\pi\) | ||||
0.891737 | + | 0.452554i | \(0.149487\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 39.7922 | 1.50079 | ||||||||
\(704\) | 33.9500 | 1.27954 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −51.5166 | −1.93885 | ||||||||
\(707\) | −0.367501 | −0.0138213 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.33102 | 0.275322 | 0.137661 | − | 0.990479i | \(-0.456041\pi\) | ||||
0.137661 | + | 0.990479i | \(0.456041\pi\) | |||||||
\(710\) | −31.5520 | −1.18413 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −12.9637 | −0.485834 | ||||||||
\(713\) | −1.93874 | −0.0726064 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 78.9631 | 2.95305 | ||||||||
\(716\) | −2.85427 | −0.106669 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 20.3207 | 0.758360 | ||||||||
\(719\) | 45.2821 | 1.68874 | 0.844368 | − | 0.535763i | \(-0.179976\pi\) | ||||
0.844368 | + | 0.535763i | \(0.179976\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.94858 | 0.296021 | ||||||||
\(722\) | −8.61811 | −0.320733 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.78064 | −0.140506 | ||||||||
\(725\) | −13.6762 | −0.507921 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.5675 | −1.05951 | −0.529754 | − | 0.848151i | \(-0.677716\pi\) | ||||
−0.529754 | + | 0.848151i | \(0.677716\pi\) | |||||||
\(728\) | −13.8562 | −0.513545 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −27.8076 | −1.02921 | ||||||||
\(731\) | 47.8172 | 1.76858 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.8036 | −0.657590 | −0.328795 | − | 0.944401i | \(-0.606643\pi\) | ||||
−0.328795 | + | 0.944401i | \(0.606643\pi\) | |||||||
\(734\) | −3.54956 | −0.131017 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.42196 | −0.0892748 | ||||||||
\(737\) | 67.8228 | 2.49828 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.0671 | 0.443897 | 0.221948 | − | 0.975058i | \(-0.428758\pi\) | ||||
0.221948 | + | 0.975058i | \(0.428758\pi\) | |||||||
\(740\) | 6.01697 | 0.221188 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.74051 | −0.137318 | ||||||||
\(743\) | −40.7391 | −1.49457 | −0.747286 | − | 0.664503i | \(-0.768644\pi\) | ||||
−0.747286 | + | 0.664503i | \(0.768644\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 55.4307 | 2.03082 | ||||||||
\(746\) | 16.0041 | 0.585952 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7.26414 | −0.265603 | ||||||||
\(749\) | 10.9611 | 0.400509 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.2733 | −0.557331 | −0.278666 | − | 0.960388i | \(-0.589892\pi\) | ||||
−0.278666 | + | 0.960388i | \(0.589892\pi\) | |||||||
\(752\) | −35.5853 | −1.29766 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 28.4308 | 1.03539 | ||||||||
\(755\) | 44.3416 | 1.61376 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.0211 | −0.364222 | −0.182111 | − | 0.983278i | \(-0.558293\pi\) | ||||
−0.182111 | + | 0.983278i | \(0.558293\pi\) | |||||||
\(758\) | −39.2702 | −1.42636 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 38.7232 | 1.40464 | ||||||||
\(761\) | −24.6930 | −0.895122 | −0.447561 | − | 0.894254i | \(-0.647707\pi\) | ||||
−0.447561 | + | 0.894254i | \(0.647707\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.7913 | −0.390671 | ||||||||
\(764\) | 1.29303 | 0.0467801 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −11.6906 | −0.422398 | ||||||||
\(767\) | −31.6435 | −1.14258 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −47.6588 | −1.71862 | −0.859310 | − | 0.511455i | \(-0.829107\pi\) | ||||
−0.859310 | + | 0.511455i | \(0.829107\pi\) | |||||||
\(770\) | 22.4293 | 0.808298 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.17928 | 0.186407 | ||||||||
\(773\) | −27.7526 | −0.998193 | −0.499097 | − | 0.866546i | \(-0.666335\pi\) | ||||
−0.499097 | + | 0.866546i | \(0.666335\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.35182 | 0.156322 | ||||||||
\(776\) | 12.8482 | 0.461224 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.97766 | 0.142606 | ||||||||
\(779\) | −11.3036 | −0.404994 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 35.6248 | 1.27476 | ||||||||
\(782\) | −14.5420 | −0.520019 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.44246 | −0.158659 | ||||||||
\(785\) | 34.5194 | 1.23205 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −45.3775 | −1.61753 | −0.808767 | − | 0.588129i | \(-0.799865\pi\) | ||||
−0.808767 | + | 0.588129i | \(0.799865\pi\) | |||||||
\(788\) | −2.73910 | −0.0975763 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.29735 | −0.224050 | ||||||||
\(791\) | 1.89200 | 0.0672720 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 41.5943 | 1.47706 | ||||||||
\(794\) | 43.6536 | 1.54921 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.75045 | −0.132931 | ||||||||
\(797\) | −0.707980 | −0.0250779 | −0.0125390 | − | 0.999921i | \(-0.503991\pi\) | ||||
−0.0125390 | + | 0.999921i | \(0.503991\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −45.6463 | −1.61485 | ||||||||
\(800\) | 5.43649 | 0.192209 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 10.3409 | 0.365148 | ||||||||
\(803\) | 31.3970 | 1.10798 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.04765 | 0.177906 | ||||||||
\(806\) | −9.04680 | −0.318660 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.963574 | 0.0338984 | ||||||||
\(809\) | 33.5412 | 1.17924 | 0.589622 | − | 0.807679i | \(-0.299277\pi\) | ||||
0.589622 | + | 0.807679i | \(0.299277\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 53.7878 | 1.88875 | 0.944373 | − | 0.328877i | \(-0.106670\pi\) | ||||
0.944373 | + | 0.328877i | \(0.106670\pi\) | |||||||
\(812\) | 0.907853 | 0.0318594 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −60.4323 | −2.11815 | ||||||||
\(815\) | −70.1337 | −2.45667 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −41.7385 | −1.46025 | ||||||||
\(818\) | −49.4155 | −1.72777 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.70922 | −0.0596884 | ||||||||
\(821\) | 56.4836 | 1.97129 | 0.985646 | − | 0.168825i | \(-0.0539973\pi\) | ||||
0.985646 | + | 0.168825i | \(0.0539973\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.1949 | 0.634233 | 0.317116 | − | 0.948387i | \(-0.397285\pi\) | ||||
0.317116 | + | 0.948387i | \(0.397285\pi\) | |||||||
\(824\) | −20.8409 | −0.726026 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.98829 | −0.312743 | ||||||||
\(827\) | −5.17250 | −0.179865 | −0.0899327 | − | 0.995948i | \(-0.528665\pi\) | ||||
−0.0899327 | + | 0.995948i | \(0.528665\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.2834 | 0.357157 | 0.178579 | − | 0.983926i | \(-0.442850\pi\) | ||||
0.178579 | + | 0.983926i | \(0.442850\pi\) | |||||||
\(830\) | −23.9343 | −0.830772 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 35.6522 | 1.23602 | ||||||||
\(833\) | −5.69847 | −0.197440 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −49.4771 | −1.71223 | ||||||||
\(836\) | 6.34069 | 0.219297 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −13.6703 | −0.472234 | ||||||||
\(839\) | 15.1684 | 0.523670 | 0.261835 | − | 0.965113i | \(-0.415672\pi\) | ||||
0.261835 | + | 0.965113i | \(0.415672\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.1554 | −0.557083 | ||||||||
\(842\) | 27.8028 | 0.958146 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.0750445 | −0.00258314 | ||||||||
\(845\) | 44.3232 | 1.52476 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.3246 | −0.492198 | ||||||||
\(848\) | 11.0699 | 0.380142 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 32.6417 | 1.11960 | ||||||||
\(851\) | −13.6001 | −0.466205 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.92663 | −0.100206 | −0.0501029 | − | 0.998744i | \(-0.515955\pi\) | ||||
−0.0501029 | + | 0.998744i | \(0.515955\pi\) | |||||||
\(854\) | 11.8148 | 0.404294 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −28.7395 | −0.982296 | ||||||||
\(857\) | 39.1115 | 1.33602 | 0.668012 | − | 0.744151i | \(-0.267146\pi\) | ||||
0.668012 | + | 0.744151i | \(0.267146\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −47.4971 | −1.62058 | −0.810290 | − | 0.586030i | \(-0.800690\pi\) | ||||
−0.810290 | + | 0.586030i | \(0.800690\pi\) | |||||||
\(860\) | −6.31127 | −0.215213 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −40.9555 | −1.39495 | ||||||||
\(863\) | −20.1050 | −0.684382 | −0.342191 | − | 0.939630i | \(-0.611169\pi\) | ||||
−0.342191 | + | 0.939630i | \(0.611169\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.0723 | −0.410470 | ||||||||
\(866\) | 38.3557 | 1.30338 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.288882 | −0.00980531 | ||||||||
\(869\) | 7.11022 | 0.241198 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 71.2234 | 2.41331 | ||||||||
\(872\) | 28.2943 | 0.958167 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 12.6933 | 0.429358 | ||||||||
\(875\) | 3.51559 | 0.118849 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −46.8020 | −1.58039 | −0.790195 | − | 0.612855i | \(-0.790021\pi\) | ||||
−0.790195 | + | 0.612855i | \(0.790021\pi\) | |||||||
\(878\) | 31.8744 | 1.07571 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −66.3788 | −2.23763 | ||||||||
\(881\) | 7.29777 | 0.245868 | 0.122934 | − | 0.992415i | \(-0.460770\pi\) | ||||
0.122934 | + | 0.992415i | \(0.460770\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.5206 | 1.73381 | 0.866904 | − | 0.498475i | \(-0.166107\pi\) | ||||
0.866904 | + | 0.498475i | \(0.166107\pi\) | |||||||
\(884\) | −7.62837 | −0.256570 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18.3034 | 0.614916 | ||||||||
\(887\) | 50.8793 | 1.70836 | 0.854180 | − | 0.519977i | \(-0.174059\pi\) | ||||
0.854180 | + | 0.519977i | \(0.174059\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | 22.0367 | 0.738673 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.78185 | 0.126626 | ||||||||
\(893\) | 39.8435 | 1.33331 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −33.4560 | −1.11831 | ||||||||
\(896\) | 12.9763 | 0.433507 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 29.5096 | 0.984749 | ||||||||
\(899\) | −4.08720 | −0.136316 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.1997 | 0.473059 | ||||||||
\(902\) | 17.1668 | 0.571591 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.96076 | −0.164992 | ||||||||
\(905\) | −44.3144 | −1.47306 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.3616 | 1.04134 | 0.520672 | − | 0.853757i | \(-0.325682\pi\) | ||||
0.520672 | + | 0.853757i | \(0.325682\pi\) | |||||||
\(908\) | 7.26022 | 0.240939 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 23.5540 | 0.780806 | ||||||||
\(911\) | 10.5764 | 0.350411 | 0.175206 | − | 0.984532i | \(-0.443941\pi\) | ||||
0.175206 | + | 0.984532i | \(0.443941\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.0238 | 0.894357 | ||||||||
\(914\) | 38.9340 | 1.28782 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.70259 | −0.0562552 | ||||||||
\(917\) | −19.7242 | −0.651351 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.5312 | 0.611289 | 0.305644 | − | 0.952146i | \(-0.401128\pi\) | ||||
0.305644 | + | 0.952146i | \(0.401128\pi\) | |||||||
\(920\) | −13.2347 | −0.436336 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 24.8517 | 0.818448 | ||||||||
\(923\) | 37.4110 | 1.23140 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30.5276 | 1.00374 | ||||||||
\(926\) | −32.5844 | −1.07079 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.10592 | −0.167610 | ||||||||
\(929\) | 8.09475 | 0.265580 | 0.132790 | − | 0.991144i | \(-0.457606\pi\) | ||||
0.132790 | + | 0.991144i | \(0.457606\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.97405 | 0.163018 | ||||||||
\(932\) | −0.482511 | −0.0158052 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 33.8685 | 1.10821 | ||||||||
\(935\) | −85.1459 | −2.78457 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −49.2094 | −1.60760 | −0.803800 | − | 0.594900i | \(-0.797192\pi\) | ||||
−0.803800 | + | 0.594900i | \(0.797192\pi\) | |||||||
\(938\) | 20.2309 | 0.660562 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.02474 | 0.196505 | ||||||||
\(941\) | −7.19836 | −0.234660 | −0.117330 | − | 0.993093i | \(-0.537433\pi\) | ||||
−0.117330 | + | 0.993093i | \(0.537433\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.86332 | 0.125807 | ||||||||
\(944\) | 26.6005 | 0.865773 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 63.3882 | 2.06093 | ||||||||
\(947\) | −28.4504 | −0.924514 | −0.462257 | − | 0.886746i | \(-0.652960\pi\) | ||||
−0.462257 | + | 0.886746i | \(0.652960\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32.9713 | 1.07029 | ||||||||
\(950\) | −28.4922 | −0.924408 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 14.9411 | 0.484245 | ||||||||
\(953\) | 35.2326 | 1.14129 | 0.570647 | − | 0.821195i | \(-0.306692\pi\) | ||||
0.570647 | + | 0.821195i | \(0.306692\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.1561 | 0.490440 | ||||||||
\(956\) | 0.599997 | 0.0194053 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 40.5550 | 1.31027 | ||||||||
\(959\) | −1.23699 | −0.0399444 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.6994 | −0.958046 | ||||||||
\(962\) | −63.4624 | −2.04611 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.02940 | 0.0975705 | ||||||||
\(965\) | 60.7085 | 1.95428 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.8331 | −0.573475 | −0.286737 | − | 0.958009i | \(-0.592571\pi\) | ||||
−0.286737 | + | 0.958009i | \(0.592571\pi\) | |||||||
\(968\) | 37.5584 | 1.20717 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −21.8405 | −0.701256 | ||||||||
\(971\) | 5.66021 | 0.181645 | 0.0908224 | − | 0.995867i | \(-0.471050\pi\) | ||||
0.0908224 | + | 0.995867i | \(0.471050\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.9060 | 0.606099 | ||||||||
\(974\) | 27.8039 | 0.890893 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −34.9654 | −1.11922 | ||||||||
\(977\) | 3.13669 | 0.100352 | 0.0501758 | − | 0.998740i | \(-0.484022\pi\) | ||||
0.0501758 | + | 0.998740i | \(0.484022\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24.8813 | −0.795209 | ||||||||
\(980\) | 0.752126 | 0.0240258 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −22.7431 | −0.725760 | ||||||||
\(983\) | 32.6268 | 1.04063 | 0.520317 | − | 0.853973i | \(-0.325814\pi\) | ||||
0.520317 | + | 0.853973i | \(0.325814\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −32.1061 | −1.02298 | ||||||||
\(986\) | −30.6570 | −0.976316 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.65862 | 0.211839 | ||||||||
\(989\) | 14.2653 | 0.453610 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.4762 | 1.03164 | 0.515821 | − | 0.856696i | \(-0.327487\pi\) | ||||
0.515821 | + | 0.856696i | \(0.327487\pi\) | |||||||
\(992\) | 1.62472 | 0.0515850 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10.6265 | 0.337053 | ||||||||
\(995\) | −43.9606 | −1.39364 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.71956 | 0.149470 | 0.0747349 | − | 0.997203i | \(-0.476189\pi\) | ||||
0.0747349 | + | 0.997203i | \(0.476189\pi\) | |||||||
\(998\) | −66.6887 | −2.11099 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8001.2.a.s.1.5 | 16 | ||
3.2 | odd | 2 | 2667.2.a.n.1.12 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.n.1.12 | ✓ | 16 | 3.2 | odd | 2 | ||
8001.2.a.s.1.5 | 16 | 1.1 | even | 1 | trivial |