Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [731,2,Mod(1,731)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(731, 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("731.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 731 = 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 731.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: | \(5.83706438776\) |
Analytic rank: | \(0\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 2 x^{18} - 30 x^{17} + 62 x^{16} + 365 x^{15} - 786 x^{14} - 2295 x^{13} + 5233 x^{12} + 7816 x^{11} - 19517 x^{10} - 13527 x^{9} + 40173 x^{8} + 8942 x^{7} - 41911 x^{6} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(0.614204\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 731.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.614204 | 0.434308 | 0.217154 | − | 0.976137i | \(-0.430323\pi\) | ||||
0.217154 | + | 0.976137i | \(0.430323\pi\) | |||||||
\(3\) | −2.75618 | −1.59128 | −0.795640 | − | 0.605770i | \(-0.792865\pi\) | ||||
−0.795640 | + | 0.605770i | \(0.792865\pi\) | |||||||
\(4\) | −1.62275 | −0.811377 | ||||||||
\(5\) | −1.26314 | −0.564895 | −0.282448 | − | 0.959283i | \(-0.591146\pi\) | ||||
−0.282448 | + | 0.959283i | \(0.591146\pi\) | |||||||
\(6\) | −1.69286 | −0.691106 | ||||||||
\(7\) | −3.83612 | −1.44992 | −0.724958 | − | 0.688793i | \(-0.758141\pi\) | ||||
−0.724958 | + | 0.688793i | \(0.758141\pi\) | |||||||
\(8\) | −2.22511 | −0.786695 | ||||||||
\(9\) | 4.59652 | 1.53217 | ||||||||
\(10\) | −0.775829 | −0.245339 | ||||||||
\(11\) | 1.37582 | 0.414826 | 0.207413 | − | 0.978253i | \(-0.433496\pi\) | ||||
0.207413 | + | 0.978253i | \(0.433496\pi\) | |||||||
\(12\) | 4.47260 | 1.29113 | ||||||||
\(13\) | −7.02604 | −1.94867 | −0.974337 | − | 0.225095i | \(-0.927731\pi\) | ||||
−0.974337 | + | 0.225095i | \(0.927731\pi\) | |||||||
\(14\) | −2.35616 | −0.629710 | ||||||||
\(15\) | 3.48145 | 0.898907 | ||||||||
\(16\) | 1.87883 | 0.469708 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 2.82320 | 0.665435 | ||||||||
\(19\) | −2.98388 | −0.684549 | −0.342274 | − | 0.939600i | \(-0.611197\pi\) | ||||
−0.342274 | + | 0.939600i | \(0.611197\pi\) | |||||||
\(20\) | 2.04977 | 0.458343 | ||||||||
\(21\) | 10.5730 | 2.30722 | ||||||||
\(22\) | 0.845036 | 0.180162 | ||||||||
\(23\) | 6.50242 | 1.35585 | 0.677924 | − | 0.735132i | \(-0.262880\pi\) | ||||
0.677924 | + | 0.735132i | \(0.262880\pi\) | |||||||
\(24\) | 6.13280 | 1.25185 | ||||||||
\(25\) | −3.40447 | −0.680893 | ||||||||
\(26\) | −4.31543 | −0.846325 | ||||||||
\(27\) | −4.40029 | −0.846836 | ||||||||
\(28\) | 6.22507 | 1.17643 | ||||||||
\(29\) | 9.00351 | 1.67191 | 0.835955 | − | 0.548798i | \(-0.184914\pi\) | ||||
0.835955 | + | 0.548798i | \(0.184914\pi\) | |||||||
\(30\) | 2.13832 | 0.390402 | ||||||||
\(31\) | −10.0383 | −1.80294 | −0.901469 | − | 0.432844i | \(-0.857510\pi\) | ||||
−0.901469 | + | 0.432844i | \(0.857510\pi\) | |||||||
\(32\) | 5.60421 | 0.990693 | ||||||||
\(33\) | −3.79201 | −0.660104 | ||||||||
\(34\) | 0.614204 | 0.105335 | ||||||||
\(35\) | 4.84557 | 0.819051 | ||||||||
\(36\) | −7.45901 | −1.24317 | ||||||||
\(37\) | 6.10591 | 1.00381 | 0.501903 | − | 0.864924i | \(-0.332634\pi\) | ||||
0.501903 | + | 0.864924i | \(0.332634\pi\) | |||||||
\(38\) | −1.83271 | −0.297305 | ||||||||
\(39\) | 19.3650 | 3.10089 | ||||||||
\(40\) | 2.81064 | 0.444401 | ||||||||
\(41\) | −1.48370 | −0.231715 | −0.115858 | − | 0.993266i | \(-0.536962\pi\) | ||||
−0.115858 | + | 0.993266i | \(0.536962\pi\) | |||||||
\(42\) | 6.49400 | 1.00205 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | −2.23262 | −0.336580 | ||||||||
\(45\) | −5.80607 | −0.865517 | ||||||||
\(46\) | 3.99381 | 0.588856 | ||||||||
\(47\) | 0.246738 | 0.0359904 | 0.0179952 | − | 0.999838i | \(-0.494272\pi\) | ||||
0.0179952 | + | 0.999838i | \(0.494272\pi\) | |||||||
\(48\) | −5.17840 | −0.747438 | ||||||||
\(49\) | 7.71581 | 1.10226 | ||||||||
\(50\) | −2.09104 | −0.295717 | ||||||||
\(51\) | −2.75618 | −0.385942 | ||||||||
\(52\) | 11.4015 | 1.58111 | ||||||||
\(53\) | −3.55498 | −0.488314 | −0.244157 | − | 0.969736i | \(-0.578511\pi\) | ||||
−0.244157 | + | 0.969736i | \(0.578511\pi\) | |||||||
\(54\) | −2.70268 | −0.367788 | ||||||||
\(55\) | −1.73786 | −0.234333 | ||||||||
\(56\) | 8.53579 | 1.14064 | ||||||||
\(57\) | 8.22410 | 1.08931 | ||||||||
\(58\) | 5.52999 | 0.726124 | ||||||||
\(59\) | −2.50988 | −0.326759 | −0.163379 | − | 0.986563i | \(-0.552239\pi\) | ||||
−0.163379 | + | 0.986563i | \(0.552239\pi\) | |||||||
\(60\) | −5.64954 | −0.729352 | ||||||||
\(61\) | 12.9426 | 1.65713 | 0.828565 | − | 0.559893i | \(-0.189158\pi\) | ||||
0.828565 | + | 0.559893i | \(0.189158\pi\) | |||||||
\(62\) | −6.16559 | −0.783030 | ||||||||
\(63\) | −17.6328 | −2.22152 | ||||||||
\(64\) | −0.315539 | −0.0394424 | ||||||||
\(65\) | 8.87491 | 1.10080 | ||||||||
\(66\) | −2.32907 | −0.286689 | ||||||||
\(67\) | −5.60551 | −0.684822 | −0.342411 | − | 0.939550i | \(-0.611244\pi\) | ||||
−0.342411 | + | 0.939550i | \(0.611244\pi\) | |||||||
\(68\) | −1.62275 | −0.196788 | ||||||||
\(69\) | −17.9218 | −2.15753 | ||||||||
\(70\) | 2.97617 | 0.355721 | ||||||||
\(71\) | −8.81728 | −1.04642 | −0.523209 | − | 0.852204i | \(-0.675265\pi\) | ||||
−0.523209 | + | 0.852204i | \(0.675265\pi\) | |||||||
\(72\) | −10.2278 | −1.20535 | ||||||||
\(73\) | −11.2882 | −1.32119 | −0.660593 | − | 0.750744i | \(-0.729695\pi\) | ||||
−0.660593 | + | 0.750744i | \(0.729695\pi\) | |||||||
\(74\) | 3.75028 | 0.435961 | ||||||||
\(75\) | 9.38331 | 1.08349 | ||||||||
\(76\) | 4.84210 | 0.555427 | ||||||||
\(77\) | −5.27782 | −0.601463 | ||||||||
\(78\) | 11.8941 | 1.34674 | ||||||||
\(79\) | −3.35889 | −0.377904 | −0.188952 | − | 0.981986i | \(-0.560509\pi\) | ||||
−0.188952 | + | 0.981986i | \(0.560509\pi\) | |||||||
\(80\) | −2.37324 | −0.265336 | ||||||||
\(81\) | −1.66158 | −0.184620 | ||||||||
\(82\) | −0.911296 | −0.100636 | ||||||||
\(83\) | −5.72716 | −0.628637 | −0.314319 | − | 0.949318i | \(-0.601776\pi\) | ||||
−0.314319 | + | 0.949318i | \(0.601776\pi\) | |||||||
\(84\) | −17.1574 | −1.87203 | ||||||||
\(85\) | −1.26314 | −0.137007 | ||||||||
\(86\) | −0.614204 | −0.0662313 | ||||||||
\(87\) | −24.8153 | −2.66048 | ||||||||
\(88\) | −3.06136 | −0.326342 | ||||||||
\(89\) | 12.1270 | 1.28546 | 0.642730 | − | 0.766093i | \(-0.277802\pi\) | ||||
0.642730 | + | 0.766093i | \(0.277802\pi\) | |||||||
\(90\) | −3.56611 | −0.375901 | ||||||||
\(91\) | 26.9527 | 2.82541 | ||||||||
\(92\) | −10.5518 | −1.10010 | ||||||||
\(93\) | 27.6674 | 2.86898 | ||||||||
\(94\) | 0.151547 | 0.0156309 | ||||||||
\(95\) | 3.76907 | 0.386699 | ||||||||
\(96\) | −15.4462 | −1.57647 | ||||||||
\(97\) | 0.613967 | 0.0623389 | 0.0311694 | − | 0.999514i | \(-0.490077\pi\) | ||||
0.0311694 | + | 0.999514i | \(0.490077\pi\) | |||||||
\(98\) | 4.73908 | 0.478720 | ||||||||
\(99\) | 6.32399 | 0.635585 | ||||||||
\(100\) | 5.52461 | 0.552461 | ||||||||
\(101\) | 11.8084 | 1.17498 | 0.587491 | − | 0.809231i | \(-0.300116\pi\) | ||||
0.587491 | + | 0.809231i | \(0.300116\pi\) | |||||||
\(102\) | −1.69286 | −0.167618 | ||||||||
\(103\) | −13.9161 | −1.37120 | −0.685598 | − | 0.727981i | \(-0.740459\pi\) | ||||
−0.685598 | + | 0.727981i | \(0.740459\pi\) | |||||||
\(104\) | 15.6337 | 1.53301 | ||||||||
\(105\) | −13.3553 | −1.30334 | ||||||||
\(106\) | −2.18349 | −0.212079 | ||||||||
\(107\) | −0.822787 | −0.0795418 | −0.0397709 | − | 0.999209i | \(-0.512663\pi\) | ||||
−0.0397709 | + | 0.999209i | \(0.512663\pi\) | |||||||
\(108\) | 7.14058 | 0.687103 | ||||||||
\(109\) | 10.8275 | 1.03709 | 0.518544 | − | 0.855051i | \(-0.326474\pi\) | ||||
0.518544 | + | 0.855051i | \(0.326474\pi\) | |||||||
\(110\) | −1.06740 | −0.101773 | ||||||||
\(111\) | −16.8290 | −1.59734 | ||||||||
\(112\) | −7.20743 | −0.681038 | ||||||||
\(113\) | 12.4803 | 1.17405 | 0.587024 | − | 0.809570i | \(-0.300300\pi\) | ||||
0.587024 | + | 0.809570i | \(0.300300\pi\) | |||||||
\(114\) | 5.05128 | 0.473096 | ||||||||
\(115\) | −8.21350 | −0.765913 | ||||||||
\(116\) | −14.6105 | −1.35655 | ||||||||
\(117\) | −32.2953 | −2.98570 | ||||||||
\(118\) | −1.54158 | −0.141914 | ||||||||
\(119\) | −3.83612 | −0.351656 | ||||||||
\(120\) | −7.74661 | −0.707166 | ||||||||
\(121\) | −9.10711 | −0.827919 | ||||||||
\(122\) | 7.94940 | 0.719705 | ||||||||
\(123\) | 4.08935 | 0.368724 | ||||||||
\(124\) | 16.2897 | 1.46286 | ||||||||
\(125\) | 10.6161 | 0.949529 | ||||||||
\(126\) | −10.8301 | −0.964825 | ||||||||
\(127\) | 1.03453 | 0.0917993 | 0.0458997 | − | 0.998946i | \(-0.485385\pi\) | ||||
0.0458997 | + | 0.998946i | \(0.485385\pi\) | |||||||
\(128\) | −11.4022 | −1.00782 | ||||||||
\(129\) | 2.75618 | 0.242668 | ||||||||
\(130\) | 5.45101 | 0.478085 | ||||||||
\(131\) | 18.0012 | 1.57277 | 0.786387 | − | 0.617734i | \(-0.211949\pi\) | ||||
0.786387 | + | 0.617734i | \(0.211949\pi\) | |||||||
\(132\) | 6.15350 | 0.535593 | ||||||||
\(133\) | 11.4465 | 0.992539 | ||||||||
\(134\) | −3.44293 | −0.297424 | ||||||||
\(135\) | 5.55820 | 0.478374 | ||||||||
\(136\) | −2.22511 | −0.190802 | ||||||||
\(137\) | −11.9203 | −1.01842 | −0.509211 | − | 0.860642i | \(-0.670063\pi\) | ||||
−0.509211 | + | 0.860642i | \(0.670063\pi\) | |||||||
\(138\) | −11.0077 | −0.937035 | ||||||||
\(139\) | −5.29545 | −0.449154 | −0.224577 | − | 0.974456i | \(-0.572100\pi\) | ||||
−0.224577 | + | 0.974456i | \(0.572100\pi\) | |||||||
\(140\) | −7.86317 | −0.664559 | ||||||||
\(141\) | −0.680053 | −0.0572708 | ||||||||
\(142\) | −5.41561 | −0.454468 | ||||||||
\(143\) | −9.66659 | −0.808361 | ||||||||
\(144\) | 8.63609 | 0.719675 | ||||||||
\(145\) | −11.3727 | −0.944454 | ||||||||
\(146\) | −6.93328 | −0.573802 | ||||||||
\(147\) | −21.2661 | −1.75400 | ||||||||
\(148\) | −9.90839 | −0.814464 | ||||||||
\(149\) | −3.20149 | −0.262276 | −0.131138 | − | 0.991364i | \(-0.541863\pi\) | ||||
−0.131138 | + | 0.991364i | \(0.541863\pi\) | |||||||
\(150\) | 5.76327 | 0.470569 | ||||||||
\(151\) | 6.32381 | 0.514624 | 0.257312 | − | 0.966328i | \(-0.417163\pi\) | ||||
0.257312 | + | 0.966328i | \(0.417163\pi\) | |||||||
\(152\) | 6.63946 | 0.538531 | ||||||||
\(153\) | 4.59652 | 0.371606 | ||||||||
\(154\) | −3.24166 | −0.261220 | ||||||||
\(155\) | 12.6799 | 1.01847 | ||||||||
\(156\) | −31.4247 | −2.51599 | ||||||||
\(157\) | 5.79963 | 0.462860 | 0.231430 | − | 0.972852i | \(-0.425659\pi\) | ||||
0.231430 | + | 0.972852i | \(0.425659\pi\) | |||||||
\(158\) | −2.06304 | −0.164127 | ||||||||
\(159\) | 9.79817 | 0.777045 | ||||||||
\(160\) | −7.07893 | −0.559638 | ||||||||
\(161\) | −24.9441 | −1.96587 | ||||||||
\(162\) | −1.02055 | −0.0801818 | ||||||||
\(163\) | −8.92023 | −0.698687 | −0.349343 | − | 0.936995i | \(-0.613595\pi\) | ||||
−0.349343 | + | 0.936995i | \(0.613595\pi\) | |||||||
\(164\) | 2.40768 | 0.188008 | ||||||||
\(165\) | 4.78986 | 0.372890 | ||||||||
\(166\) | −3.51765 | −0.273022 | ||||||||
\(167\) | −13.6893 | −1.05931 | −0.529654 | − | 0.848214i | \(-0.677678\pi\) | ||||
−0.529654 | + | 0.848214i | \(0.677678\pi\) | |||||||
\(168\) | −23.5262 | −1.81508 | ||||||||
\(169\) | 36.3653 | 2.79733 | ||||||||
\(170\) | −0.775829 | −0.0595034 | ||||||||
\(171\) | −13.7155 | −1.04885 | ||||||||
\(172\) | 1.62275 | 0.123734 | ||||||||
\(173\) | 12.1611 | 0.924590 | 0.462295 | − | 0.886726i | \(-0.347026\pi\) | ||||
0.462295 | + | 0.886726i | \(0.347026\pi\) | |||||||
\(174\) | −15.2416 | −1.15547 | ||||||||
\(175\) | 13.0599 | 0.987238 | ||||||||
\(176\) | 2.58494 | 0.194847 | ||||||||
\(177\) | 6.91768 | 0.519964 | ||||||||
\(178\) | 7.44845 | 0.558285 | ||||||||
\(179\) | 23.1184 | 1.72795 | 0.863976 | − | 0.503534i | \(-0.167967\pi\) | ||||
0.863976 | + | 0.503534i | \(0.167967\pi\) | |||||||
\(180\) | 9.42181 | 0.702261 | ||||||||
\(181\) | −1.14490 | −0.0850996 | −0.0425498 | − | 0.999094i | \(-0.513548\pi\) | ||||
−0.0425498 | + | 0.999094i | \(0.513548\pi\) | |||||||
\(182\) | 16.5545 | 1.22710 | ||||||||
\(183\) | −35.6721 | −2.63696 | ||||||||
\(184\) | −14.4686 | −1.06664 | ||||||||
\(185\) | −7.71265 | −0.567045 | ||||||||
\(186\) | 16.9935 | 1.24602 | ||||||||
\(187\) | 1.37582 | 0.100610 | ||||||||
\(188\) | −0.400395 | −0.0292018 | ||||||||
\(189\) | 16.8800 | 1.22784 | ||||||||
\(190\) | 2.31498 | 0.167946 | ||||||||
\(191\) | 1.64848 | 0.119280 | 0.0596398 | − | 0.998220i | \(-0.481005\pi\) | ||||
0.0596398 | + | 0.998220i | \(0.481005\pi\) | |||||||
\(192\) | 0.869682 | 0.0627639 | ||||||||
\(193\) | 16.8532 | 1.21312 | 0.606561 | − | 0.795037i | \(-0.292548\pi\) | ||||
0.606561 | + | 0.795037i | \(0.292548\pi\) | |||||||
\(194\) | 0.377101 | 0.0270743 | ||||||||
\(195\) | −24.4608 | −1.75168 | ||||||||
\(196\) | −12.5209 | −0.894347 | ||||||||
\(197\) | −5.74840 | −0.409556 | −0.204778 | − | 0.978808i | \(-0.565647\pi\) | ||||
−0.204778 | + | 0.978808i | \(0.565647\pi\) | |||||||
\(198\) | 3.88422 | 0.276040 | ||||||||
\(199\) | 7.91781 | 0.561279 | 0.280639 | − | 0.959813i | \(-0.409454\pi\) | ||||
0.280639 | + | 0.959813i | \(0.409454\pi\) | |||||||
\(200\) | 7.57531 | 0.535655 | ||||||||
\(201\) | 15.4498 | 1.08974 | ||||||||
\(202\) | 7.25278 | 0.510304 | ||||||||
\(203\) | −34.5385 | −2.42413 | ||||||||
\(204\) | 4.47260 | 0.313144 | ||||||||
\(205\) | 1.87413 | 0.130895 | ||||||||
\(206\) | −8.54733 | −0.595521 | ||||||||
\(207\) | 29.8885 | 2.07739 | ||||||||
\(208\) | −13.2008 | −0.915309 | ||||||||
\(209\) | −4.10529 | −0.283969 | ||||||||
\(210\) | −8.20286 | −0.566051 | ||||||||
\(211\) | −1.98947 | −0.136961 | −0.0684804 | − | 0.997652i | \(-0.521815\pi\) | ||||
−0.0684804 | + | 0.997652i | \(0.521815\pi\) | |||||||
\(212\) | 5.76886 | 0.396207 | ||||||||
\(213\) | 24.3020 | 1.66515 | ||||||||
\(214\) | −0.505359 | −0.0345457 | ||||||||
\(215\) | 1.26314 | 0.0861457 | ||||||||
\(216\) | 9.79113 | 0.666202 | ||||||||
\(217\) | 38.5082 | 2.61411 | ||||||||
\(218\) | 6.65030 | 0.450415 | ||||||||
\(219\) | 31.1124 | 2.10238 | ||||||||
\(220\) | 2.82012 | 0.190133 | ||||||||
\(221\) | −7.02604 | −0.472623 | ||||||||
\(222\) | −10.3364 | −0.693736 | ||||||||
\(223\) | 8.24378 | 0.552044 | 0.276022 | − | 0.961151i | \(-0.410984\pi\) | ||||
0.276022 | + | 0.961151i | \(0.410984\pi\) | |||||||
\(224\) | −21.4984 | −1.43642 | ||||||||
\(225\) | −15.6487 | −1.04325 | ||||||||
\(226\) | 7.66545 | 0.509898 | ||||||||
\(227\) | 11.1989 | 0.743297 | 0.371648 | − | 0.928374i | \(-0.378793\pi\) | ||||
0.371648 | + | 0.928374i | \(0.378793\pi\) | |||||||
\(228\) | −13.3457 | −0.883840 | ||||||||
\(229\) | 17.3516 | 1.14663 | 0.573314 | − | 0.819336i | \(-0.305658\pi\) | ||||
0.573314 | + | 0.819336i | \(0.305658\pi\) | |||||||
\(230\) | −5.04476 | −0.332642 | ||||||||
\(231\) | 14.5466 | 0.957096 | ||||||||
\(232\) | −20.0338 | −1.31528 | ||||||||
\(233\) | −19.3065 | −1.26481 | −0.632406 | − | 0.774637i | \(-0.717933\pi\) | ||||
−0.632406 | + | 0.774637i | \(0.717933\pi\) | |||||||
\(234\) | −19.8359 | −1.29672 | ||||||||
\(235\) | −0.311666 | −0.0203308 | ||||||||
\(236\) | 4.07292 | 0.265124 | ||||||||
\(237\) | 9.25769 | 0.601352 | ||||||||
\(238\) | −2.35616 | −0.152727 | ||||||||
\(239\) | −0.131800 | −0.00852545 | −0.00426273 | − | 0.999991i | \(-0.501357\pi\) | ||||
−0.00426273 | + | 0.999991i | \(0.501357\pi\) | |||||||
\(240\) | 6.54107 | 0.422224 | ||||||||
\(241\) | 12.7105 | 0.818757 | 0.409379 | − | 0.912365i | \(-0.365746\pi\) | ||||
0.409379 | + | 0.912365i | \(0.365746\pi\) | |||||||
\(242\) | −5.59363 | −0.359572 | ||||||||
\(243\) | 17.7805 | 1.14062 | ||||||||
\(244\) | −21.0026 | −1.34456 | ||||||||
\(245\) | −9.74618 | −0.622661 | ||||||||
\(246\) | 2.51169 | 0.160140 | ||||||||
\(247\) | 20.9649 | 1.33396 | ||||||||
\(248\) | 22.3364 | 1.41836 | ||||||||
\(249\) | 15.7851 | 1.00034 | ||||||||
\(250\) | 6.52043 | 0.412388 | ||||||||
\(251\) | −11.1387 | −0.703068 | −0.351534 | − | 0.936175i | \(-0.614340\pi\) | ||||
−0.351534 | + | 0.936175i | \(0.614340\pi\) | |||||||
\(252\) | 28.6137 | 1.80249 | ||||||||
\(253\) | 8.94617 | 0.562441 | ||||||||
\(254\) | 0.635410 | 0.0398692 | ||||||||
\(255\) | 3.48145 | 0.218017 | ||||||||
\(256\) | −6.37222 | −0.398263 | ||||||||
\(257\) | 24.6214 | 1.53584 | 0.767919 | − | 0.640547i | \(-0.221292\pi\) | ||||
0.767919 | + | 0.640547i | \(0.221292\pi\) | |||||||
\(258\) | 1.69286 | 0.105393 | ||||||||
\(259\) | −23.4230 | −1.45543 | ||||||||
\(260\) | −14.4018 | −0.893161 | ||||||||
\(261\) | 41.3848 | 2.56165 | ||||||||
\(262\) | 11.0564 | 0.683069 | ||||||||
\(263\) | 14.7248 | 0.907970 | 0.453985 | − | 0.891009i | \(-0.350002\pi\) | ||||
0.453985 | + | 0.891009i | \(0.350002\pi\) | |||||||
\(264\) | 8.43764 | 0.519301 | ||||||||
\(265\) | 4.49046 | 0.275847 | ||||||||
\(266\) | 7.03050 | 0.431068 | ||||||||
\(267\) | −33.4242 | −2.04553 | ||||||||
\(268\) | 9.09636 | 0.555649 | ||||||||
\(269\) | 18.0695 | 1.10172 | 0.550858 | − | 0.834599i | \(-0.314300\pi\) | ||||
0.550858 | + | 0.834599i | \(0.314300\pi\) | |||||||
\(270\) | 3.41387 | 0.207762 | ||||||||
\(271\) | −16.9413 | −1.02911 | −0.514554 | − | 0.857458i | \(-0.672042\pi\) | ||||
−0.514554 | + | 0.857458i | \(0.672042\pi\) | |||||||
\(272\) | 1.87883 | 0.113921 | ||||||||
\(273\) | −74.2865 | −4.49603 | ||||||||
\(274\) | −7.32152 | −0.442309 | ||||||||
\(275\) | −4.68394 | −0.282452 | ||||||||
\(276\) | 29.0827 | 1.75057 | ||||||||
\(277\) | −23.7585 | −1.42751 | −0.713754 | − | 0.700396i | \(-0.753007\pi\) | ||||
−0.713754 | + | 0.700396i | \(0.753007\pi\) | |||||||
\(278\) | −3.25249 | −0.195071 | ||||||||
\(279\) | −46.1414 | −2.76241 | ||||||||
\(280\) | −10.7819 | −0.644344 | ||||||||
\(281\) | −13.8505 | −0.826249 | −0.413125 | − | 0.910674i | \(-0.635563\pi\) | ||||
−0.413125 | + | 0.910674i | \(0.635563\pi\) | |||||||
\(282\) | −0.417692 | −0.0248732 | ||||||||
\(283\) | −19.2658 | −1.14524 | −0.572618 | − | 0.819823i | \(-0.694072\pi\) | ||||
−0.572618 | + | 0.819823i | \(0.694072\pi\) | |||||||
\(284\) | 14.3083 | 0.849040 | ||||||||
\(285\) | −10.3882 | −0.615346 | ||||||||
\(286\) | −5.93726 | −0.351077 | ||||||||
\(287\) | 5.69166 | 0.335968 | ||||||||
\(288\) | 25.7598 | 1.51791 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −6.98518 | −0.410184 | ||||||||
\(291\) | −1.69220 | −0.0991986 | ||||||||
\(292\) | 18.3180 | 1.07198 | ||||||||
\(293\) | −6.87426 | −0.401598 | −0.200799 | − | 0.979632i | \(-0.564354\pi\) | ||||
−0.200799 | + | 0.979632i | \(0.564354\pi\) | |||||||
\(294\) | −13.0618 | −0.761777 | ||||||||
\(295\) | 3.17034 | 0.184584 | ||||||||
\(296\) | −13.5863 | −0.789689 | ||||||||
\(297\) | −6.05401 | −0.351290 | ||||||||
\(298\) | −1.96637 | −0.113909 | ||||||||
\(299\) | −45.6863 | −2.64211 | ||||||||
\(300\) | −15.2268 | −0.879120 | ||||||||
\(301\) | 3.83612 | 0.221110 | ||||||||
\(302\) | 3.88411 | 0.223505 | ||||||||
\(303\) | −32.5461 | −1.86973 | ||||||||
\(304\) | −5.60621 | −0.321538 | ||||||||
\(305\) | −16.3484 | −0.936105 | ||||||||
\(306\) | 2.82320 | 0.161392 | ||||||||
\(307\) | 23.5940 | 1.34658 | 0.673290 | − | 0.739379i | \(-0.264881\pi\) | ||||
0.673290 | + | 0.739379i | \(0.264881\pi\) | |||||||
\(308\) | 8.56460 | 0.488013 | ||||||||
\(309\) | 38.3553 | 2.18196 | ||||||||
\(310\) | 7.78803 | 0.442330 | ||||||||
\(311\) | 34.3961 | 1.95043 | 0.975213 | − | 0.221270i | \(-0.0710201\pi\) | ||||
0.975213 | + | 0.221270i | \(0.0710201\pi\) | |||||||
\(312\) | −43.0893 | −2.43945 | ||||||||
\(313\) | −25.4996 | −1.44132 | −0.720661 | − | 0.693288i | \(-0.756162\pi\) | ||||
−0.720661 | + | 0.693288i | \(0.756162\pi\) | |||||||
\(314\) | 3.56215 | 0.201024 | ||||||||
\(315\) | 22.2728 | 1.25493 | ||||||||
\(316\) | 5.45065 | 0.306623 | ||||||||
\(317\) | 24.1380 | 1.35572 | 0.677862 | − | 0.735189i | \(-0.262907\pi\) | ||||
0.677862 | + | 0.735189i | \(0.262907\pi\) | |||||||
\(318\) | 6.01808 | 0.337477 | ||||||||
\(319\) | 12.3872 | 0.693552 | ||||||||
\(320\) | 0.398572 | 0.0222808 | ||||||||
\(321\) | 2.26775 | 0.126573 | ||||||||
\(322\) | −15.3207 | −0.853792 | ||||||||
\(323\) | −2.98388 | −0.166028 | ||||||||
\(324\) | 2.69633 | 0.149796 | ||||||||
\(325\) | 23.9199 | 1.32684 | ||||||||
\(326\) | −5.47885 | −0.303445 | ||||||||
\(327\) | −29.8426 | −1.65030 | ||||||||
\(328\) | 3.30140 | 0.182289 | ||||||||
\(329\) | −0.946516 | −0.0521831 | ||||||||
\(330\) | 2.94195 | 0.161949 | ||||||||
\(331\) | −27.4047 | −1.50630 | −0.753149 | − | 0.657850i | \(-0.771466\pi\) | ||||
−0.753149 | + | 0.657850i | \(0.771466\pi\) | |||||||
\(332\) | 9.29377 | 0.510062 | ||||||||
\(333\) | 28.0659 | 1.53800 | ||||||||
\(334\) | −8.40801 | −0.460066 | ||||||||
\(335\) | 7.08057 | 0.386853 | ||||||||
\(336\) | 19.8650 | 1.08372 | ||||||||
\(337\) | −10.8198 | −0.589391 | −0.294696 | − | 0.955591i | \(-0.595218\pi\) | ||||
−0.294696 | + | 0.955591i | \(0.595218\pi\) | |||||||
\(338\) | 22.3357 | 1.21490 | ||||||||
\(339\) | −34.3979 | −1.86824 | ||||||||
\(340\) | 2.04977 | 0.111164 | ||||||||
\(341\) | −13.8110 | −0.747905 | ||||||||
\(342\) | −8.42409 | −0.455523 | ||||||||
\(343\) | −2.74592 | −0.148266 | ||||||||
\(344\) | 2.22511 | 0.119970 | ||||||||
\(345\) | 22.6379 | 1.21878 | ||||||||
\(346\) | 7.46939 | 0.401557 | ||||||||
\(347\) | −9.49423 | −0.509677 | −0.254839 | − | 0.966984i | \(-0.582022\pi\) | ||||
−0.254839 | + | 0.966984i | \(0.582022\pi\) | |||||||
\(348\) | 40.2691 | 2.15865 | ||||||||
\(349\) | 31.1355 | 1.66665 | 0.833323 | − | 0.552786i | \(-0.186435\pi\) | ||||
0.833323 | + | 0.552786i | \(0.186435\pi\) | |||||||
\(350\) | 8.02147 | 0.428765 | ||||||||
\(351\) | 30.9166 | 1.65021 | ||||||||
\(352\) | 7.71040 | 0.410965 | ||||||||
\(353\) | −15.6254 | −0.831654 | −0.415827 | − | 0.909444i | \(-0.636508\pi\) | ||||
−0.415827 | + | 0.909444i | \(0.636508\pi\) | |||||||
\(354\) | 4.24887 | 0.225825 | ||||||||
\(355\) | 11.1375 | 0.591117 | ||||||||
\(356\) | −19.6791 | −1.04299 | ||||||||
\(357\) | 10.5730 | 0.559584 | ||||||||
\(358\) | 14.1994 | 0.750463 | ||||||||
\(359\) | 2.33909 | 0.123452 | 0.0617261 | − | 0.998093i | \(-0.480339\pi\) | ||||
0.0617261 | + | 0.998093i | \(0.480339\pi\) | |||||||
\(360\) | 12.9191 | 0.680898 | ||||||||
\(361\) | −10.0965 | −0.531393 | ||||||||
\(362\) | −0.703201 | −0.0369594 | ||||||||
\(363\) | 25.1008 | 1.31745 | ||||||||
\(364\) | −43.7376 | −2.29247 | ||||||||
\(365\) | 14.2587 | 0.746332 | ||||||||
\(366\) | −21.9100 | −1.14525 | ||||||||
\(367\) | 36.4028 | 1.90021 | 0.950105 | − | 0.311929i | \(-0.100975\pi\) | ||||
0.950105 | + | 0.311929i | \(0.100975\pi\) | |||||||
\(368\) | 12.2170 | 0.636853 | ||||||||
\(369\) | −6.81986 | −0.355028 | ||||||||
\(370\) | −4.73714 | −0.246272 | ||||||||
\(371\) | 13.6373 | 0.708015 | ||||||||
\(372\) | −44.8974 | −2.32782 | ||||||||
\(373\) | 10.0402 | 0.519864 | 0.259932 | − | 0.965627i | \(-0.416300\pi\) | ||||
0.259932 | + | 0.965627i | \(0.416300\pi\) | |||||||
\(374\) | 0.845036 | 0.0436958 | ||||||||
\(375\) | −29.2597 | −1.51097 | ||||||||
\(376\) | −0.549019 | −0.0283135 | ||||||||
\(377\) | −63.2590 | −3.25801 | ||||||||
\(378\) | 10.3678 | 0.533261 | ||||||||
\(379\) | −3.95923 | −0.203372 | −0.101686 | − | 0.994817i | \(-0.532424\pi\) | ||||
−0.101686 | + | 0.994817i | \(0.532424\pi\) | |||||||
\(380\) | −6.11627 | −0.313758 | ||||||||
\(381\) | −2.85134 | −0.146078 | ||||||||
\(382\) | 1.01250 | 0.0518041 | ||||||||
\(383\) | 18.6383 | 0.952372 | 0.476186 | − | 0.879345i | \(-0.342019\pi\) | ||||
0.476186 | + | 0.879345i | \(0.342019\pi\) | |||||||
\(384\) | 31.4266 | 1.60373 | ||||||||
\(385\) | 6.66665 | 0.339764 | ||||||||
\(386\) | 10.3513 | 0.526869 | ||||||||
\(387\) | −4.59652 | −0.233654 | ||||||||
\(388\) | −0.996317 | −0.0505803 | ||||||||
\(389\) | −17.1284 | −0.868445 | −0.434223 | − | 0.900806i | \(-0.642977\pi\) | ||||
−0.434223 | + | 0.900806i | \(0.642977\pi\) | |||||||
\(390\) | −15.0239 | −0.760767 | ||||||||
\(391\) | 6.50242 | 0.328842 | ||||||||
\(392\) | −17.1685 | −0.867141 | ||||||||
\(393\) | −49.6146 | −2.50273 | ||||||||
\(394\) | −3.53069 | −0.177874 | ||||||||
\(395\) | 4.24276 | 0.213477 | ||||||||
\(396\) | −10.2623 | −0.515699 | ||||||||
\(397\) | −17.5299 | −0.879801 | −0.439901 | − | 0.898046i | \(-0.644986\pi\) | ||||
−0.439901 | + | 0.898046i | \(0.644986\pi\) | |||||||
\(398\) | 4.86315 | 0.243768 | ||||||||
\(399\) | −31.5486 | −1.57941 | ||||||||
\(400\) | −6.39643 | −0.319821 | ||||||||
\(401\) | −31.0247 | −1.54930 | −0.774649 | − | 0.632391i | \(-0.782073\pi\) | ||||
−0.774649 | + | 0.632391i | \(0.782073\pi\) | |||||||
\(402\) | 9.48933 | 0.473285 | ||||||||
\(403\) | 70.5297 | 3.51334 | ||||||||
\(404\) | −19.1622 | −0.953353 | ||||||||
\(405\) | 2.09881 | 0.104291 | ||||||||
\(406\) | −21.2137 | −1.05282 | ||||||||
\(407\) | 8.40065 | 0.416405 | ||||||||
\(408\) | 6.13280 | 0.303619 | ||||||||
\(409\) | 21.5180 | 1.06400 | 0.531998 | − | 0.846746i | \(-0.321442\pi\) | ||||
0.531998 | + | 0.846746i | \(0.321442\pi\) | |||||||
\(410\) | 1.15110 | 0.0568487 | ||||||||
\(411\) | 32.8545 | 1.62060 | ||||||||
\(412\) | 22.5824 | 1.11256 | ||||||||
\(413\) | 9.62820 | 0.473773 | ||||||||
\(414\) | 18.3576 | 0.902229 | ||||||||
\(415\) | 7.23423 | 0.355114 | ||||||||
\(416\) | −39.3754 | −1.93054 | ||||||||
\(417\) | 14.5952 | 0.714730 | ||||||||
\(418\) | −2.52149 | −0.123330 | ||||||||
\(419\) | 4.32573 | 0.211326 | 0.105663 | − | 0.994402i | \(-0.466304\pi\) | ||||
0.105663 | + | 0.994402i | \(0.466304\pi\) | |||||||
\(420\) | 21.6723 | 1.05750 | ||||||||
\(421\) | −14.2478 | −0.694396 | −0.347198 | − | 0.937792i | \(-0.612867\pi\) | ||||
−0.347198 | + | 0.937792i | \(0.612867\pi\) | |||||||
\(422\) | −1.22194 | −0.0594832 | ||||||||
\(423\) | 1.13414 | 0.0551435 | ||||||||
\(424\) | 7.91023 | 0.384155 | ||||||||
\(425\) | −3.40447 | −0.165141 | ||||||||
\(426\) | 14.9264 | 0.723186 | ||||||||
\(427\) | −49.6493 | −2.40270 | ||||||||
\(428\) | 1.33518 | 0.0645384 | ||||||||
\(429\) | 26.6428 | 1.28633 | ||||||||
\(430\) | 0.775829 | 0.0374138 | ||||||||
\(431\) | 14.6180 | 0.704125 | 0.352063 | − | 0.935976i | \(-0.385480\pi\) | ||||
0.352063 | + | 0.935976i | \(0.385480\pi\) | |||||||
\(432\) | −8.26741 | −0.397766 | ||||||||
\(433\) | −29.6884 | −1.42673 | −0.713367 | − | 0.700791i | \(-0.752831\pi\) | ||||
−0.713367 | + | 0.700791i | \(0.752831\pi\) | |||||||
\(434\) | 23.6519 | 1.13533 | ||||||||
\(435\) | 31.3453 | 1.50289 | ||||||||
\(436\) | −17.5704 | −0.841469 | ||||||||
\(437\) | −19.4024 | −0.928145 | ||||||||
\(438\) | 19.1093 | 0.913080 | ||||||||
\(439\) | 35.7749 | 1.70744 | 0.853720 | − | 0.520732i | \(-0.174341\pi\) | ||||
0.853720 | + | 0.520732i | \(0.174341\pi\) | |||||||
\(440\) | 3.86694 | 0.184349 | ||||||||
\(441\) | 35.4658 | 1.68885 | ||||||||
\(442\) | −4.31543 | −0.205264 | ||||||||
\(443\) | 16.8157 | 0.798936 | 0.399468 | − | 0.916747i | \(-0.369195\pi\) | ||||
0.399468 | + | 0.916747i | \(0.369195\pi\) | |||||||
\(444\) | 27.3093 | 1.29604 | ||||||||
\(445\) | −15.3182 | −0.726150 | ||||||||
\(446\) | 5.06336 | 0.239757 | ||||||||
\(447\) | 8.82386 | 0.417354 | ||||||||
\(448\) | 1.21045 | 0.0571882 | ||||||||
\(449\) | −3.87481 | −0.182863 | −0.0914317 | − | 0.995811i | \(-0.529144\pi\) | ||||
−0.0914317 | + | 0.995811i | \(0.529144\pi\) | |||||||
\(450\) | −9.61149 | −0.453090 | ||||||||
\(451\) | −2.04131 | −0.0961216 | ||||||||
\(452\) | −20.2524 | −0.952594 | ||||||||
\(453\) | −17.4295 | −0.818912 | ||||||||
\(454\) | 6.87841 | 0.322820 | ||||||||
\(455\) | −34.0452 | −1.59606 | ||||||||
\(456\) | −18.2995 | −0.856955 | ||||||||
\(457\) | 3.89913 | 0.182394 | 0.0911969 | − | 0.995833i | \(-0.470931\pi\) | ||||
0.0911969 | + | 0.995833i | \(0.470931\pi\) | |||||||
\(458\) | 10.6574 | 0.497989 | ||||||||
\(459\) | −4.40029 | −0.205388 | ||||||||
\(460\) | 13.3285 | 0.621443 | ||||||||
\(461\) | 7.77268 | 0.362010 | 0.181005 | − | 0.983482i | \(-0.442065\pi\) | ||||
0.181005 | + | 0.983482i | \(0.442065\pi\) | |||||||
\(462\) | 8.93459 | 0.415675 | ||||||||
\(463\) | 3.58890 | 0.166790 | 0.0833952 | − | 0.996517i | \(-0.473424\pi\) | ||||
0.0833952 | + | 0.996517i | \(0.473424\pi\) | |||||||
\(464\) | 16.9161 | 0.785310 | ||||||||
\(465\) | −34.9480 | −1.62067 | ||||||||
\(466\) | −11.8581 | −0.549318 | ||||||||
\(467\) | 28.2210 | 1.30591 | 0.652956 | − | 0.757396i | \(-0.273529\pi\) | ||||
0.652956 | + | 0.757396i | \(0.273529\pi\) | |||||||
\(468\) | 52.4073 | 2.42253 | ||||||||
\(469\) | 21.5034 | 0.992935 | ||||||||
\(470\) | −0.191426 | −0.00882984 | ||||||||
\(471\) | −15.9848 | −0.736541 | ||||||||
\(472\) | 5.58476 | 0.257059 | ||||||||
\(473\) | −1.37582 | −0.0632604 | ||||||||
\(474\) | 5.68612 | 0.261172 | ||||||||
\(475\) | 10.1585 | 0.466105 | ||||||||
\(476\) | 6.22507 | 0.285326 | ||||||||
\(477\) | −16.3405 | −0.748182 | ||||||||
\(478\) | −0.0809523 | −0.00370267 | ||||||||
\(479\) | −30.5347 | −1.39516 | −0.697582 | − | 0.716505i | \(-0.745741\pi\) | ||||
−0.697582 | + | 0.716505i | \(0.745741\pi\) | |||||||
\(480\) | 19.5108 | 0.890541 | ||||||||
\(481\) | −42.9004 | −1.95609 | ||||||||
\(482\) | 7.80686 | 0.355593 | ||||||||
\(483\) | 68.7503 | 3.12825 | ||||||||
\(484\) | 14.7786 | 0.671754 | ||||||||
\(485\) | −0.775529 | −0.0352150 | ||||||||
\(486\) | 10.9208 | 0.495379 | ||||||||
\(487\) | 13.5108 | 0.612235 | 0.306117 | − | 0.951994i | \(-0.400970\pi\) | ||||
0.306117 | + | 0.951994i | \(0.400970\pi\) | |||||||
\(488\) | −28.7987 | −1.30366 | ||||||||
\(489\) | 24.5858 | 1.11181 | ||||||||
\(490\) | −5.98615 | −0.270427 | ||||||||
\(491\) | −14.2174 | −0.641622 | −0.320811 | − | 0.947143i | \(-0.603955\pi\) | ||||
−0.320811 | + | 0.947143i | \(0.603955\pi\) | |||||||
\(492\) | −6.63600 | −0.299174 | ||||||||
\(493\) | 9.00351 | 0.405498 | ||||||||
\(494\) | 12.8767 | 0.579351 | ||||||||
\(495\) | −7.98812 | −0.359039 | ||||||||
\(496\) | −18.8604 | −0.846855 | ||||||||
\(497\) | 33.8241 | 1.51722 | ||||||||
\(498\) | 9.69526 | 0.434455 | ||||||||
\(499\) | 1.46685 | 0.0656653 | 0.0328326 | − | 0.999461i | \(-0.489547\pi\) | ||||
0.0328326 | + | 0.999461i | \(0.489547\pi\) | |||||||
\(500\) | −17.2272 | −0.770425 | ||||||||
\(501\) | 37.7301 | 1.68565 | ||||||||
\(502\) | −6.84143 | −0.305348 | ||||||||
\(503\) | −12.2136 | −0.544579 | −0.272290 | − | 0.962215i | \(-0.587781\pi\) | ||||
−0.272290 | + | 0.962215i | \(0.587781\pi\) | |||||||
\(504\) | 39.2349 | 1.74766 | ||||||||
\(505\) | −14.9157 | −0.663742 | ||||||||
\(506\) | 5.49478 | 0.244273 | ||||||||
\(507\) | −100.229 | −4.45133 | ||||||||
\(508\) | −1.67878 | −0.0744838 | ||||||||
\(509\) | −15.6020 | −0.691546 | −0.345773 | − | 0.938318i | \(-0.612383\pi\) | ||||
−0.345773 | + | 0.938318i | \(0.612383\pi\) | |||||||
\(510\) | 2.13832 | 0.0946865 | ||||||||
\(511\) | 43.3030 | 1.91561 | ||||||||
\(512\) | 18.8906 | 0.834855 | ||||||||
\(513\) | 13.1299 | 0.579701 | ||||||||
\(514\) | 15.1225 | 0.667027 | ||||||||
\(515\) | 17.5781 | 0.774582 | ||||||||
\(516\) | −4.47260 | −0.196895 | ||||||||
\(517\) | 0.339467 | 0.0149298 | ||||||||
\(518\) | −14.3865 | −0.632107 | ||||||||
\(519\) | −33.5181 | −1.47128 | ||||||||
\(520\) | −19.7476 | −0.865992 | ||||||||
\(521\) | −43.2179 | −1.89341 | −0.946705 | − | 0.322102i | \(-0.895611\pi\) | ||||
−0.946705 | + | 0.322102i | \(0.895611\pi\) | |||||||
\(522\) | 25.4187 | 1.11255 | ||||||||
\(523\) | −11.1444 | −0.487310 | −0.243655 | − | 0.969862i | \(-0.578346\pi\) | ||||
−0.243655 | + | 0.969862i | \(0.578346\pi\) | |||||||
\(524\) | −29.2115 | −1.27611 | ||||||||
\(525\) | −35.9955 | −1.57097 | ||||||||
\(526\) | 9.04403 | 0.394339 | ||||||||
\(527\) | −10.0383 | −0.437277 | ||||||||
\(528\) | −7.12456 | −0.310057 | ||||||||
\(529\) | 19.2815 | 0.838325 | ||||||||
\(530\) | 2.75806 | 0.119802 | ||||||||
\(531\) | −11.5367 | −0.500650 | ||||||||
\(532\) | −18.5749 | −0.805323 | ||||||||
\(533\) | 10.4246 | 0.451538 | ||||||||
\(534\) | −20.5293 | −0.888388 | ||||||||
\(535\) | 1.03930 | 0.0449328 | ||||||||
\(536\) | 12.4729 | 0.538747 | ||||||||
\(537\) | −63.7185 | −2.74965 | ||||||||
\(538\) | 11.0984 | 0.478484 | ||||||||
\(539\) | 10.6156 | 0.457245 | ||||||||
\(540\) | −9.01959 | −0.388141 | ||||||||
\(541\) | −8.93756 | −0.384256 | −0.192128 | − | 0.981370i | \(-0.561539\pi\) | ||||
−0.192128 | + | 0.981370i | \(0.561539\pi\) | |||||||
\(542\) | −10.4054 | −0.446950 | ||||||||
\(543\) | 3.15554 | 0.135417 | ||||||||
\(544\) | 5.60421 | 0.240278 | ||||||||
\(545\) | −13.6767 | −0.585846 | ||||||||
\(546\) | −45.6271 | −1.95266 | ||||||||
\(547\) | 30.2438 | 1.29313 | 0.646567 | − | 0.762857i | \(-0.276204\pi\) | ||||
0.646567 | + | 0.762857i | \(0.276204\pi\) | |||||||
\(548\) | 19.3437 | 0.826324 | ||||||||
\(549\) | 59.4909 | 2.53901 | ||||||||
\(550\) | −2.87690 | −0.122671 | ||||||||
\(551\) | −26.8654 | −1.14450 | ||||||||
\(552\) | 39.8780 | 1.69732 | ||||||||
\(553\) | 12.8851 | 0.547930 | ||||||||
\(554\) | −14.5926 | −0.619978 | ||||||||
\(555\) | 21.2574 | 0.902328 | ||||||||
\(556\) | 8.59321 | 0.364433 | ||||||||
\(557\) | 13.6108 | 0.576707 | 0.288354 | − | 0.957524i | \(-0.406892\pi\) | ||||
0.288354 | + | 0.957524i | \(0.406892\pi\) | |||||||
\(558\) | −28.3402 | −1.19974 | ||||||||
\(559\) | 7.02604 | 0.297170 | ||||||||
\(560\) | 9.10403 | 0.384715 | ||||||||
\(561\) | −3.79201 | −0.160099 | ||||||||
\(562\) | −8.50701 | −0.358847 | ||||||||
\(563\) | 19.5674 | 0.824669 | 0.412335 | − | 0.911033i | \(-0.364713\pi\) | ||||
0.412335 | + | 0.911033i | \(0.364713\pi\) | |||||||
\(564\) | 1.10356 | 0.0464682 | ||||||||
\(565\) | −15.7644 | −0.663214 | ||||||||
\(566\) | −11.8332 | −0.497385 | ||||||||
\(567\) | 6.37401 | 0.267683 | ||||||||
\(568\) | 19.6194 | 0.823213 | ||||||||
\(569\) | 11.1657 | 0.468090 | 0.234045 | − | 0.972226i | \(-0.424804\pi\) | ||||
0.234045 | + | 0.972226i | \(0.424804\pi\) | |||||||
\(570\) | −6.38050 | −0.267250 | ||||||||
\(571\) | 5.03739 | 0.210808 | 0.105404 | − | 0.994429i | \(-0.466386\pi\) | ||||
0.105404 | + | 0.994429i | \(0.466386\pi\) | |||||||
\(572\) | 15.6865 | 0.655885 | ||||||||
\(573\) | −4.54350 | −0.189807 | ||||||||
\(574\) | 3.49584 | 0.145914 | ||||||||
\(575\) | −22.1373 | −0.923188 | ||||||||
\(576\) | −1.45038 | −0.0604325 | ||||||||
\(577\) | −27.1242 | −1.12919 | −0.564597 | − | 0.825366i | \(-0.690969\pi\) | ||||
−0.564597 | + | 0.825366i | \(0.690969\pi\) | |||||||
\(578\) | 0.614204 | 0.0255475 | ||||||||
\(579\) | −46.4505 | −1.93042 | ||||||||
\(580\) | 18.4551 | 0.766308 | ||||||||
\(581\) | 21.9701 | 0.911472 | ||||||||
\(582\) | −1.03936 | −0.0430828 | ||||||||
\(583\) | −4.89102 | −0.202566 | ||||||||
\(584\) | 25.1175 | 1.03937 | ||||||||
\(585\) | 40.7937 | 1.68661 | ||||||||
\(586\) | −4.22220 | −0.174417 | ||||||||
\(587\) | −30.4133 | −1.25529 | −0.627646 | − | 0.778499i | \(-0.715981\pi\) | ||||
−0.627646 | + | 0.778499i | \(0.715981\pi\) | |||||||
\(588\) | 34.5097 | 1.42316 | ||||||||
\(589\) | 29.9532 | 1.23420 | ||||||||
\(590\) | 1.94724 | 0.0801665 | ||||||||
\(591\) | 15.8436 | 0.651719 | ||||||||
\(592\) | 11.4720 | 0.471496 | ||||||||
\(593\) | 22.6475 | 0.930021 | 0.465010 | − | 0.885305i | \(-0.346051\pi\) | ||||
0.465010 | + | 0.885305i | \(0.346051\pi\) | |||||||
\(594\) | −3.71840 | −0.152568 | ||||||||
\(595\) | 4.84557 | 0.198649 | ||||||||
\(596\) | 5.19522 | 0.212805 | ||||||||
\(597\) | −21.8229 | −0.893151 | ||||||||
\(598\) | −28.0607 | −1.14749 | ||||||||
\(599\) | −27.6329 | −1.12905 | −0.564525 | − | 0.825416i | \(-0.690940\pi\) | ||||
−0.564525 | + | 0.825416i | \(0.690940\pi\) | |||||||
\(600\) | −20.8789 | −0.852378 | ||||||||
\(601\) | −0.342259 | −0.0139610 | −0.00698051 | − | 0.999976i | \(-0.502222\pi\) | ||||
−0.00698051 | + | 0.999976i | \(0.502222\pi\) | |||||||
\(602\) | 2.35616 | 0.0960299 | ||||||||
\(603\) | −25.7658 | −1.04927 | ||||||||
\(604\) | −10.2620 | −0.417554 | ||||||||
\(605\) | 11.5036 | 0.467688 | ||||||||
\(606\) | −19.9900 | −0.812037 | ||||||||
\(607\) | −33.4744 | −1.35869 | −0.679343 | − | 0.733821i | \(-0.737735\pi\) | ||||
−0.679343 | + | 0.733821i | \(0.737735\pi\) | |||||||
\(608\) | −16.7223 | −0.678178 | ||||||||
\(609\) | 95.1944 | 3.85747 | ||||||||
\(610\) | −10.0412 | −0.406558 | ||||||||
\(611\) | −1.73359 | −0.0701336 | ||||||||
\(612\) | −7.45901 | −0.301513 | ||||||||
\(613\) | 19.9080 | 0.804076 | 0.402038 | − | 0.915623i | \(-0.368302\pi\) | ||||
0.402038 | + | 0.915623i | \(0.368302\pi\) | |||||||
\(614\) | 14.4915 | 0.584830 | ||||||||
\(615\) | −5.16544 | −0.208291 | ||||||||
\(616\) | 11.7437 | 0.473168 | ||||||||
\(617\) | 22.8521 | 0.919989 | 0.459994 | − | 0.887922i | \(-0.347851\pi\) | ||||
0.459994 | + | 0.887922i | \(0.347851\pi\) | |||||||
\(618\) | 23.5580 | 0.947641 | ||||||||
\(619\) | −3.17417 | −0.127581 | −0.0637904 | − | 0.997963i | \(-0.520319\pi\) | ||||
−0.0637904 | + | 0.997963i | \(0.520319\pi\) | |||||||
\(620\) | −20.5763 | −0.826364 | ||||||||
\(621\) | −28.6125 | −1.14818 | ||||||||
\(622\) | 21.1262 | 0.847085 | ||||||||
\(623\) | −46.5206 | −1.86381 | ||||||||
\(624\) | 36.3837 | 1.45651 | ||||||||
\(625\) | 3.61271 | 0.144509 | ||||||||
\(626\) | −15.6620 | −0.625978 | ||||||||
\(627\) | 11.3149 | 0.451874 | ||||||||
\(628\) | −9.41136 | −0.375554 | ||||||||
\(629\) | 6.10591 | 0.243459 | ||||||||
\(630\) | 13.6800 | 0.545025 | ||||||||
\(631\) | −7.09662 | −0.282512 | −0.141256 | − | 0.989973i | \(-0.545114\pi\) | ||||
−0.141256 | + | 0.989973i | \(0.545114\pi\) | |||||||
\(632\) | 7.47390 | 0.297296 | ||||||||
\(633\) | 5.48334 | 0.217943 | ||||||||
\(634\) | 14.8256 | 0.588802 | ||||||||
\(635\) | −1.30676 | −0.0518570 | ||||||||
\(636\) | −15.9000 | −0.630476 | ||||||||
\(637\) | −54.2116 | −2.14794 | ||||||||
\(638\) | 7.60829 | 0.301215 | ||||||||
\(639\) | −40.5288 | −1.60329 | ||||||||
\(640\) | 14.4027 | 0.569315 | ||||||||
\(641\) | 39.4650 | 1.55877 | 0.779387 | − | 0.626543i | \(-0.215531\pi\) | ||||
0.779387 | + | 0.626543i | \(0.215531\pi\) | |||||||
\(642\) | 1.39286 | 0.0549718 | ||||||||
\(643\) | −29.0359 | −1.14506 | −0.572532 | − | 0.819883i | \(-0.694039\pi\) | ||||
−0.572532 | + | 0.819883i | \(0.694039\pi\) | |||||||
\(644\) | 40.4780 | 1.59506 | ||||||||
\(645\) | −3.48145 | −0.137082 | ||||||||
\(646\) | −1.83271 | −0.0721071 | ||||||||
\(647\) | −8.23501 | −0.323752 | −0.161876 | − | 0.986811i | \(-0.551754\pi\) | ||||
−0.161876 | + | 0.986811i | \(0.551754\pi\) | |||||||
\(648\) | 3.69719 | 0.145239 | ||||||||
\(649\) | −3.45315 | −0.135548 | ||||||||
\(650\) | 14.6917 | 0.576257 | ||||||||
\(651\) | −106.136 | −4.15978 | ||||||||
\(652\) | 14.4753 | 0.566898 | ||||||||
\(653\) | 16.5418 | 0.647330 | 0.323665 | − | 0.946172i | \(-0.395085\pi\) | ||||
0.323665 | + | 0.946172i | \(0.395085\pi\) | |||||||
\(654\) | −18.3294 | −0.716737 | ||||||||
\(655\) | −22.7382 | −0.888453 | ||||||||
\(656\) | −2.78763 | −0.108839 | ||||||||
\(657\) | −51.8865 | −2.02429 | ||||||||
\(658\) | −0.581354 | −0.0226635 | ||||||||
\(659\) | 8.48349 | 0.330470 | 0.165235 | − | 0.986254i | \(-0.447162\pi\) | ||||
0.165235 | + | 0.986254i | \(0.447162\pi\) | |||||||
\(660\) | −7.77276 | −0.302554 | ||||||||
\(661\) | 19.7339 | 0.767559 | 0.383779 | − | 0.923425i | \(-0.374622\pi\) | ||||
0.383779 | + | 0.923425i | \(0.374622\pi\) | |||||||
\(662\) | −16.8321 | −0.654198 | ||||||||
\(663\) | 19.3650 | 0.752075 | ||||||||
\(664\) | 12.7436 | 0.494546 | ||||||||
\(665\) | −14.4586 | −0.560681 | ||||||||
\(666\) | 17.2382 | 0.667967 | ||||||||
\(667\) | 58.5446 | 2.26686 | ||||||||
\(668\) | 22.2143 | 0.859497 | ||||||||
\(669\) | −22.7213 | −0.878457 | ||||||||
\(670\) | 4.34892 | 0.168013 | ||||||||
\(671\) | 17.8067 | 0.687421 | ||||||||
\(672\) | 59.2534 | 2.28575 | ||||||||
\(673\) | 19.4335 | 0.749106 | 0.374553 | − | 0.927206i | \(-0.377796\pi\) | ||||
0.374553 | + | 0.927206i | \(0.377796\pi\) | |||||||
\(674\) | −6.64556 | −0.255977 | ||||||||
\(675\) | 14.9806 | 0.576605 | ||||||||
\(676\) | −59.0119 | −2.26969 | ||||||||
\(677\) | −13.7510 | −0.528493 | −0.264247 | − | 0.964455i | \(-0.585123\pi\) | ||||
−0.264247 | + | 0.964455i | \(0.585123\pi\) | |||||||
\(678\) | −21.1273 | −0.811391 | ||||||||
\(679\) | −2.35525 | −0.0903862 | ||||||||
\(680\) | 2.81064 | 0.107783 | ||||||||
\(681\) | −30.8661 | −1.18279 | ||||||||
\(682\) | −8.48275 | −0.324821 | ||||||||
\(683\) | 40.3806 | 1.54512 | 0.772560 | − | 0.634942i | \(-0.218976\pi\) | ||||
0.772560 | + | 0.634942i | \(0.218976\pi\) | |||||||
\(684\) | 22.2568 | 0.851010 | ||||||||
\(685\) | 15.0571 | 0.575302 | ||||||||
\(686\) | −1.68656 | −0.0643931 | ||||||||
\(687\) | −47.8242 | −1.82461 | ||||||||
\(688\) | −1.87883 | −0.0716299 | ||||||||
\(689\) | 24.9775 | 0.951566 | ||||||||
\(690\) | 13.9043 | 0.529327 | ||||||||
\(691\) | −38.5069 | −1.46487 | −0.732435 | − | 0.680837i | \(-0.761616\pi\) | ||||
−0.732435 | + | 0.680837i | \(0.761616\pi\) | |||||||
\(692\) | −19.7344 | −0.750191 | ||||||||
\(693\) | −24.2596 | −0.921545 | ||||||||
\(694\) | −5.83140 | −0.221357 | ||||||||
\(695\) | 6.68892 | 0.253725 | ||||||||
\(696\) | 55.2167 | 2.09298 | ||||||||
\(697\) | −1.48370 | −0.0561992 | ||||||||
\(698\) | 19.1236 | 0.723838 | ||||||||
\(699\) | 53.2122 | 2.01267 | ||||||||
\(700\) | −21.1930 | −0.801022 | ||||||||
\(701\) | −49.7827 | −1.88027 | −0.940134 | − | 0.340806i | \(-0.889300\pi\) | ||||
−0.940134 | + | 0.340806i | \(0.889300\pi\) | |||||||
\(702\) | 18.9891 | 0.716698 | ||||||||
\(703\) | −18.2193 | −0.687154 | ||||||||
\(704\) | −0.434126 | −0.0163617 | ||||||||
\(705\) | 0.859006 | 0.0323520 | ||||||||
\(706\) | −9.59717 | −0.361194 | ||||||||
\(707\) | −45.2985 | −1.70363 | ||||||||
\(708\) | −11.2257 | −0.421887 | ||||||||
\(709\) | −2.57721 | −0.0967892 | −0.0483946 | − | 0.998828i | \(-0.515410\pi\) | ||||
−0.0483946 | + | 0.998828i | \(0.515410\pi\) | |||||||
\(710\) | 6.84070 | 0.256727 | ||||||||
\(711\) | −15.4392 | −0.579015 | ||||||||
\(712\) | −26.9839 | −1.01126 | ||||||||
\(713\) | −65.2734 | −2.44451 | ||||||||
\(714\) | 6.49400 | 0.243032 | ||||||||
\(715\) | 12.2103 | 0.456639 | ||||||||
\(716\) | −37.5155 | −1.40202 | ||||||||
\(717\) | 0.363265 | 0.0135664 | ||||||||
\(718\) | 1.43668 | 0.0536163 | ||||||||
\(719\) | −20.5368 | −0.765892 | −0.382946 | − | 0.923771i | \(-0.625090\pi\) | ||||
−0.382946 | + | 0.923771i | \(0.625090\pi\) | |||||||
\(720\) | −10.9086 | −0.406541 | ||||||||
\(721\) | 53.3839 | 1.98812 | ||||||||
\(722\) | −6.20129 | −0.230788 | ||||||||
\(723\) | −35.0325 | −1.30287 | ||||||||
\(724\) | 1.85789 | 0.0690478 | ||||||||
\(725\) | −30.6521 | −1.13839 | ||||||||
\(726\) | 15.4170 | 0.572180 | ||||||||
\(727\) | 1.84717 | 0.0685079 | 0.0342539 | − | 0.999413i | \(-0.489095\pi\) | ||||
0.0342539 | + | 0.999413i | \(0.489095\pi\) | |||||||
\(728\) | −59.9728 | −2.22274 | ||||||||
\(729\) | −44.0214 | −1.63042 | ||||||||
\(730\) | 8.75773 | 0.324138 | ||||||||
\(731\) | −1.00000 | −0.0369863 | ||||||||
\(732\) | 57.8870 | 2.13957 | ||||||||
\(733\) | −42.2608 | −1.56094 | −0.780469 | − | 0.625195i | \(-0.785019\pi\) | ||||
−0.780469 | + | 0.625195i | \(0.785019\pi\) | |||||||
\(734\) | 22.3588 | 0.825277 | ||||||||
\(735\) | 26.8622 | 0.990828 | ||||||||
\(736\) | 36.4409 | 1.34323 | ||||||||
\(737\) | −7.71219 | −0.284082 | ||||||||
\(738\) | −4.18879 | −0.154191 | ||||||||
\(739\) | −12.8553 | −0.472891 | −0.236445 | − | 0.971645i | \(-0.575982\pi\) | ||||
−0.236445 | + | 0.971645i | \(0.575982\pi\) | |||||||
\(740\) | 12.5157 | 0.460087 | ||||||||
\(741\) | −57.7829 | −2.12271 | ||||||||
\(742\) | 8.37611 | 0.307497 | ||||||||
\(743\) | 7.99183 | 0.293192 | 0.146596 | − | 0.989196i | \(-0.453168\pi\) | ||||
0.146596 | + | 0.989196i | \(0.453168\pi\) | |||||||
\(744\) | −61.5631 | −2.25701 | ||||||||
\(745\) | 4.04394 | 0.148158 | ||||||||
\(746\) | 6.16675 | 0.225781 | ||||||||
\(747\) | −26.3250 | −0.963181 | ||||||||
\(748\) | −2.23262 | −0.0816327 | ||||||||
\(749\) | 3.15631 | 0.115329 | ||||||||
\(750\) | −17.9715 | −0.656225 | ||||||||
\(751\) | 21.1542 | 0.771926 | 0.385963 | − | 0.922514i | \(-0.373869\pi\) | ||||
0.385963 | + | 0.922514i | \(0.373869\pi\) | |||||||
\(752\) | 0.463579 | 0.0169050 | ||||||||
\(753\) | 30.7002 | 1.11878 | ||||||||
\(754\) | −38.8540 | −1.41498 | ||||||||
\(755\) | −7.98789 | −0.290709 | ||||||||
\(756\) | −27.3921 | −0.996242 | ||||||||
\(757\) | 9.14310 | 0.332312 | 0.166156 | − | 0.986100i | \(-0.446865\pi\) | ||||
0.166156 | + | 0.986100i | \(0.446865\pi\) | |||||||
\(758\) | −2.43178 | −0.0883261 | ||||||||
\(759\) | −24.6573 | −0.895002 | ||||||||
\(760\) | −8.38660 | −0.304214 | ||||||||
\(761\) | 1.57450 | 0.0570757 | 0.0285378 | − | 0.999593i | \(-0.490915\pi\) | ||||
0.0285378 | + | 0.999593i | \(0.490915\pi\) | |||||||
\(762\) | −1.75130 | −0.0634431 | ||||||||
\(763\) | −41.5356 | −1.50369 | ||||||||
\(764\) | −2.67507 | −0.0967807 | ||||||||
\(765\) | −5.80607 | −0.209919 | ||||||||
\(766\) | 11.4477 | 0.413623 | ||||||||
\(767\) | 17.6345 | 0.636746 | ||||||||
\(768\) | 17.5630 | 0.633749 | ||||||||
\(769\) | −10.0371 | −0.361946 | −0.180973 | − | 0.983488i | \(-0.557925\pi\) | ||||
−0.180973 | + | 0.983488i | \(0.557925\pi\) | |||||||
\(770\) | 4.09468 | 0.147562 | ||||||||
\(771\) | −67.8609 | −2.44395 | ||||||||
\(772\) | −27.3486 | −0.984299 | ||||||||
\(773\) | −6.88424 | −0.247609 | −0.123804 | − | 0.992307i | \(-0.539510\pi\) | ||||
−0.123804 | + | 0.992307i | \(0.539510\pi\) | |||||||
\(774\) | −2.82320 | −0.101478 | ||||||||
\(775\) | 34.1752 | 1.22761 | ||||||||
\(776\) | −1.36614 | −0.0490417 | ||||||||
\(777\) | 64.5580 | 2.31600 | ||||||||
\(778\) | −10.5203 | −0.377173 | ||||||||
\(779\) | 4.42719 | 0.158621 | ||||||||
\(780\) | 39.6939 | 1.42127 | ||||||||
\(781\) | −12.1310 | −0.434082 | ||||||||
\(782\) | 3.99381 | 0.142819 | ||||||||
\(783\) | −39.6180 | −1.41583 | ||||||||
\(784\) | 14.4967 | 0.517740 | ||||||||
\(785\) | −7.32577 | −0.261468 | ||||||||
\(786\) | −30.4735 | −1.08695 | ||||||||
\(787\) | −17.3622 | −0.618894 | −0.309447 | − | 0.950917i | \(-0.600144\pi\) | ||||
−0.309447 | + | 0.950917i | \(0.600144\pi\) | |||||||
\(788\) | 9.32823 | 0.332304 | ||||||||
\(789\) | −40.5842 | −1.44483 | ||||||||
\(790\) | 2.60592 | 0.0927146 | ||||||||
\(791\) | −47.8759 | −1.70227 | ||||||||
\(792\) | −14.0716 | −0.500012 | ||||||||
\(793\) | −90.9352 | −3.22920 | ||||||||
\(794\) | −10.7669 | −0.382105 | ||||||||
\(795\) | −12.3765 | −0.438949 | ||||||||
\(796\) | −12.8486 | −0.455408 | ||||||||
\(797\) | 1.32793 | 0.0470377 | 0.0235189 | − | 0.999723i | \(-0.492513\pi\) | ||||
0.0235189 | + | 0.999723i | \(0.492513\pi\) | |||||||
\(798\) | −19.3773 | −0.685949 | ||||||||
\(799\) | 0.246738 | 0.00872896 | ||||||||
\(800\) | −19.0793 | −0.674556 | ||||||||
\(801\) | 55.7420 | 1.96955 | ||||||||
\(802\) | −19.0555 | −0.672872 | ||||||||
\(803\) | −15.5306 | −0.548063 | ||||||||
\(804\) | −25.0712 | −0.884193 | ||||||||
\(805\) | 31.5080 | 1.11051 | ||||||||
\(806\) | 43.3197 | 1.52587 | ||||||||
\(807\) | −49.8027 | −1.75314 | ||||||||
\(808\) | −26.2750 | −0.924353 | ||||||||
\(809\) | −18.5672 | −0.652789 | −0.326394 | − | 0.945234i | \(-0.605834\pi\) | ||||
−0.326394 | + | 0.945234i | \(0.605834\pi\) | |||||||
\(810\) | 1.28910 | 0.0452943 | ||||||||
\(811\) | −1.18659 | −0.0416670 | −0.0208335 | − | 0.999783i | \(-0.506632\pi\) | ||||
−0.0208335 | + | 0.999783i | \(0.506632\pi\) | |||||||
\(812\) | 56.0475 | 1.96688 | ||||||||
\(813\) | 46.6931 | 1.63760 | ||||||||
\(814\) | 5.15971 | 0.180848 | ||||||||
\(815\) | 11.2675 | 0.394685 | ||||||||
\(816\) | −5.17840 | −0.181280 | ||||||||
\(817\) | 2.98388 | 0.104393 | ||||||||
\(818\) | 13.2164 | 0.462102 | ||||||||
\(819\) | 123.889 | 4.32902 | ||||||||
\(820\) | −3.04125 | −0.106205 | ||||||||
\(821\) | −48.4440 | −1.69071 | −0.845354 | − | 0.534206i | \(-0.820611\pi\) | ||||
−0.845354 | + | 0.534206i | \(0.820611\pi\) | |||||||
\(822\) | 20.1794 | 0.703837 | ||||||||
\(823\) | 9.73575 | 0.339367 | 0.169684 | − | 0.985499i | \(-0.445725\pi\) | ||||
0.169684 | + | 0.985499i | \(0.445725\pi\) | |||||||
\(824\) | 30.9649 | 1.07871 | ||||||||
\(825\) | 12.9098 | 0.449461 | ||||||||
\(826\) | 5.91368 | 0.205763 | ||||||||
\(827\) | 54.8873 | 1.90862 | 0.954310 | − | 0.298819i | \(-0.0965926\pi\) | ||||
0.954310 | + | 0.298819i | \(0.0965926\pi\) | |||||||
\(828\) | −48.5016 | −1.68555 | ||||||||
\(829\) | 19.6707 | 0.683193 | 0.341597 | − | 0.939847i | \(-0.389032\pi\) | ||||
0.341597 | + | 0.939847i | \(0.389032\pi\) | |||||||
\(830\) | 4.44330 | 0.154229 | ||||||||
\(831\) | 65.4826 | 2.27157 | ||||||||
\(832\) | 2.21699 | 0.0768603 | ||||||||
\(833\) | 7.71581 | 0.267337 | ||||||||
\(834\) | 8.96444 | 0.310413 | ||||||||
\(835\) | 17.2915 | 0.598398 | ||||||||
\(836\) | 6.66187 | 0.230406 | ||||||||
\(837\) | 44.1715 | 1.52679 | ||||||||
\(838\) | 2.65688 | 0.0917804 | ||||||||
\(839\) | −6.89842 | −0.238160 | −0.119080 | − | 0.992885i | \(-0.537994\pi\) | ||||
−0.119080 | + | 0.992885i | \(0.537994\pi\) | |||||||
\(840\) | 29.7169 | 1.02533 | ||||||||
\(841\) | 52.0632 | 1.79528 | ||||||||
\(842\) | −8.75106 | −0.301582 | ||||||||
\(843\) | 38.1743 | 1.31479 | ||||||||
\(844\) | 3.22842 | 0.111127 | ||||||||
\(845\) | −45.9346 | −1.58020 | ||||||||
\(846\) | 0.696591 | 0.0239493 | ||||||||
\(847\) | 34.9360 | 1.20041 | ||||||||
\(848\) | −6.67922 | −0.229365 | ||||||||
\(849\) | 53.1001 | 1.82239 | ||||||||
\(850\) | −2.09104 | −0.0717220 | ||||||||
\(851\) | 39.7032 | 1.36101 | ||||||||
\(852\) | −39.4361 | −1.35106 | ||||||||
\(853\) | 22.9675 | 0.786393 | 0.393196 | − | 0.919455i | \(-0.371369\pi\) | ||||
0.393196 | + | 0.919455i | \(0.371369\pi\) | |||||||
\(854\) | −30.4948 | −1.04351 | ||||||||
\(855\) | 17.3246 | 0.592489 | ||||||||
\(856\) | 1.83079 | 0.0625752 | ||||||||
\(857\) | 13.4636 | 0.459907 | 0.229953 | − | 0.973202i | \(-0.426143\pi\) | ||||
0.229953 | + | 0.973202i | \(0.426143\pi\) | |||||||
\(858\) | 16.3641 | 0.558663 | ||||||||
\(859\) | −3.83384 | −0.130809 | −0.0654044 | − | 0.997859i | \(-0.520834\pi\) | ||||
−0.0654044 | + | 0.997859i | \(0.520834\pi\) | |||||||
\(860\) | −2.04977 | −0.0698966 | ||||||||
\(861\) | −15.6872 | −0.534619 | ||||||||
\(862\) | 8.97845 | 0.305807 | ||||||||
\(863\) | −28.1275 | −0.957470 | −0.478735 | − | 0.877960i | \(-0.658904\pi\) | ||||
−0.478735 | + | 0.877960i | \(0.658904\pi\) | |||||||
\(864\) | −24.6601 | −0.838955 | ||||||||
\(865\) | −15.3612 | −0.522297 | ||||||||
\(866\) | −18.2347 | −0.619642 | ||||||||
\(867\) | −2.75618 | −0.0936047 | ||||||||
\(868\) | −62.4894 | −2.12103 | ||||||||
\(869\) | −4.62123 | −0.156765 | ||||||||
\(870\) | 19.2524 | 0.652718 | ||||||||
\(871\) | 39.3846 | 1.33450 | ||||||||
\(872\) | −24.0924 | −0.815872 | ||||||||
\(873\) | 2.82211 | 0.0955140 | ||||||||
\(874\) | −11.9171 | −0.403101 | ||||||||
\(875\) | −40.7245 | −1.37674 | ||||||||
\(876\) | −50.4877 | −1.70582 | ||||||||
\(877\) | 22.6618 | 0.765235 | 0.382617 | − | 0.923907i | \(-0.375023\pi\) | ||||
0.382617 | + | 0.923907i | \(0.375023\pi\) | |||||||
\(878\) | 21.9731 | 0.741555 | ||||||||
\(879\) | 18.9467 | 0.639056 | ||||||||
\(880\) | −3.26516 | −0.110068 | ||||||||
\(881\) | 42.1176 | 1.41898 | 0.709488 | − | 0.704717i | \(-0.248926\pi\) | ||||
0.709488 | + | 0.704717i | \(0.248926\pi\) | |||||||
\(882\) | 21.7833 | 0.733481 | ||||||||
\(883\) | −14.4855 | −0.487476 | −0.243738 | − | 0.969841i | \(-0.578374\pi\) | ||||
−0.243738 | + | 0.969841i | \(0.578374\pi\) | |||||||
\(884\) | 11.4015 | 0.383475 | ||||||||
\(885\) | −8.73803 | −0.293726 | ||||||||
\(886\) | 10.3283 | 0.346984 | ||||||||
\(887\) | 51.5845 | 1.73204 | 0.866019 | − | 0.500010i | \(-0.166670\pi\) | ||||
0.866019 | + | 0.500010i | \(0.166670\pi\) | |||||||
\(888\) | 37.4463 | 1.25662 | ||||||||
\(889\) | −3.96856 | −0.133101 | ||||||||
\(890\) | −9.40847 | −0.315373 | ||||||||
\(891\) | −2.28603 | −0.0765850 | ||||||||
\(892\) | −13.3776 | −0.447916 | ||||||||
\(893\) | −0.736236 | −0.0246372 | ||||||||
\(894\) | 5.41965 | 0.181260 | ||||||||
\(895\) | −29.2019 | −0.976112 | ||||||||
\(896\) | 43.7403 | 1.46126 | ||||||||
\(897\) | 125.920 | 4.20433 | ||||||||
\(898\) | −2.37992 | −0.0794190 | ||||||||
\(899\) | −90.3802 | −3.01435 | ||||||||
\(900\) | 25.3940 | 0.846465 | ||||||||
\(901\) | −3.55498 | −0.118434 | ||||||||
\(902\) | −1.25378 | −0.0417464 | ||||||||
\(903\) | −10.5730 | −0.351848 | ||||||||
\(904\) | −27.7700 | −0.923617 | ||||||||
\(905\) | 1.44617 | 0.0480724 | ||||||||
\(906\) | −10.7053 | −0.355660 | ||||||||
\(907\) | −44.1493 | −1.46595 | −0.732977 | − | 0.680254i | \(-0.761870\pi\) | ||||
−0.732977 | + | 0.680254i | \(0.761870\pi\) | |||||||
\(908\) | −18.1730 | −0.603093 | ||||||||
\(909\) | 54.2776 | 1.80028 | ||||||||
\(910\) | −20.9107 | −0.693183 | ||||||||
\(911\) | 34.6750 | 1.14883 | 0.574417 | − | 0.818563i | \(-0.305229\pi\) | ||||
0.574417 | + | 0.818563i | \(0.305229\pi\) | |||||||
\(912\) | 15.4517 | 0.511658 | ||||||||
\(913\) | −7.87955 | −0.260775 | ||||||||
\(914\) | 2.39486 | 0.0792151 | ||||||||
\(915\) | 45.0590 | 1.48961 | ||||||||
\(916\) | −28.1574 | −0.930346 | ||||||||
\(917\) | −69.0549 | −2.28039 | ||||||||
\(918\) | −2.70268 | −0.0892016 | ||||||||
\(919\) | −33.2580 | −1.09708 | −0.548539 | − | 0.836125i | \(-0.684816\pi\) | ||||
−0.548539 | + | 0.836125i | \(0.684816\pi\) | |||||||
\(920\) | 18.2759 | 0.602540 | ||||||||
\(921\) | −65.0292 | −2.14278 | ||||||||
\(922\) | 4.77401 | 0.157224 | ||||||||
\(923\) | 61.9506 | 2.03913 | ||||||||
\(924\) | −23.6056 | −0.776566 | ||||||||
\(925\) | −20.7874 | −0.683484 | ||||||||
\(926\) | 2.20432 | 0.0724384 | ||||||||
\(927\) | −63.9657 | −2.10091 | ||||||||
\(928\) | 50.4575 | 1.65635 | ||||||||
\(929\) | 14.9942 | 0.491942 | 0.245971 | − | 0.969277i | \(-0.420893\pi\) | ||||
0.245971 | + | 0.969277i | \(0.420893\pi\) | |||||||
\(930\) | −21.4652 | −0.703871 | ||||||||
\(931\) | −23.0230 | −0.754550 | ||||||||
\(932\) | 31.3297 | 1.02624 | ||||||||
\(933\) | −94.8018 | −3.10367 | ||||||||
\(934\) | 17.3335 | 0.567168 | ||||||||
\(935\) | −1.73786 | −0.0568342 | ||||||||
\(936\) | 71.8607 | 2.34884 | ||||||||
\(937\) | −7.24245 | −0.236601 | −0.118300 | − | 0.992978i | \(-0.537745\pi\) | ||||
−0.118300 | + | 0.992978i | \(0.537745\pi\) | |||||||
\(938\) | 13.2075 | 0.431240 | ||||||||
\(939\) | 70.2814 | 2.29355 | ||||||||
\(940\) | 0.505756 | 0.0164960 | ||||||||
\(941\) | 13.2309 | 0.431316 | 0.215658 | − | 0.976469i | \(-0.430810\pi\) | ||||
0.215658 | + | 0.976469i | \(0.430810\pi\) | |||||||
\(942\) | −9.81793 | −0.319886 | ||||||||
\(943\) | −9.64766 | −0.314171 | ||||||||
\(944\) | −4.71565 | −0.153481 | ||||||||
\(945\) | −21.3219 | −0.693602 | ||||||||
\(946\) | −0.845036 | −0.0274745 | ||||||||
\(947\) | 26.0266 | 0.845752 | 0.422876 | − | 0.906188i | \(-0.361021\pi\) | ||||
0.422876 | + | 0.906188i | \(0.361021\pi\) | |||||||
\(948\) | −15.0230 | −0.487923 | ||||||||
\(949\) | 79.3116 | 2.57456 | ||||||||
\(950\) | 6.23940 | 0.202433 | ||||||||
\(951\) | −66.5285 | −2.15734 | ||||||||
\(952\) | 8.53579 | 0.276646 | ||||||||
\(953\) | 29.6109 | 0.959192 | 0.479596 | − | 0.877489i | \(-0.340783\pi\) | ||||
0.479596 | + | 0.877489i | \(0.340783\pi\) | |||||||
\(954\) | −10.0364 | −0.324941 | ||||||||
\(955\) | −2.08227 | −0.0673805 | ||||||||
\(956\) | 0.213879 | 0.00691735 | ||||||||
\(957\) | −34.1414 | −1.10364 | ||||||||
\(958\) | −18.7545 | −0.605931 | ||||||||
\(959\) | 45.7278 | 1.47663 | ||||||||
\(960\) | −1.09853 | −0.0354550 | ||||||||
\(961\) | 69.7681 | 2.25058 | ||||||||
\(962\) | −26.3496 | −0.849545 | ||||||||
\(963\) | −3.78196 | −0.121872 | ||||||||
\(964\) | −20.6261 | −0.664320 | ||||||||
\(965\) | −21.2881 | −0.685287 | ||||||||
\(966\) | 42.2267 | 1.35862 | ||||||||
\(967\) | 2.67336 | 0.0859694 | 0.0429847 | − | 0.999076i | \(-0.486313\pi\) | ||||
0.0429847 | + | 0.999076i | \(0.486313\pi\) | |||||||
\(968\) | 20.2643 | 0.651320 | ||||||||
\(969\) | 8.22410 | 0.264196 | ||||||||
\(970\) | −0.476333 | −0.0152941 | ||||||||
\(971\) | 34.4447 | 1.10538 | 0.552692 | − | 0.833386i | \(-0.313601\pi\) | ||||
0.552692 | + | 0.833386i | \(0.313601\pi\) | |||||||
\(972\) | −28.8533 | −0.925470 | ||||||||
\(973\) | 20.3140 | 0.651236 | ||||||||
\(974\) | 8.29842 | 0.265898 | ||||||||
\(975\) | −65.9276 | −2.11137 | ||||||||
\(976\) | 24.3170 | 0.778368 | ||||||||
\(977\) | −30.1830 | −0.965639 | −0.482819 | − | 0.875720i | \(-0.660387\pi\) | ||||
−0.482819 | + | 0.875720i | \(0.660387\pi\) | |||||||
\(978\) | 15.1007 | 0.482866 | ||||||||
\(979\) | 16.6846 | 0.533242 | ||||||||
\(980\) | 15.8156 | 0.505212 | ||||||||
\(981\) | 49.7689 | 1.58900 | ||||||||
\(982\) | −8.73238 | −0.278662 | ||||||||
\(983\) | 33.7783 | 1.07736 | 0.538680 | − | 0.842510i | \(-0.318923\pi\) | ||||
0.538680 | + | 0.842510i | \(0.318923\pi\) | |||||||
\(984\) | −9.09925 | −0.290074 | ||||||||
\(985\) | 7.26106 | 0.231356 | ||||||||
\(986\) | 5.52999 | 0.176111 | ||||||||
\(987\) | 2.60877 | 0.0830379 | ||||||||
\(988\) | −34.0208 | −1.08235 | ||||||||
\(989\) | −6.50242 | −0.206765 | ||||||||
\(990\) | −4.90634 | −0.155934 | ||||||||
\(991\) | −22.7541 | −0.722809 | −0.361404 | − | 0.932409i | \(-0.617703\pi\) | ||||
−0.361404 | + | 0.932409i | \(0.617703\pi\) | |||||||
\(992\) | −56.2569 | −1.78616 | ||||||||
\(993\) | 75.5322 | 2.39694 | ||||||||
\(994\) | 20.7749 | 0.658941 | ||||||||
\(995\) | −10.0013 | −0.317064 | ||||||||
\(996\) | −25.6153 | −0.811651 | ||||||||
\(997\) | −0.573910 | −0.0181759 | −0.00908795 | − | 0.999959i | \(-0.502893\pi\) | ||||
−0.00908795 | + | 0.999959i | \(0.502893\pi\) | |||||||
\(998\) | 0.900947 | 0.0285190 | ||||||||
\(999\) | −26.8678 | −0.850058 |
(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 | 731.2.a.e.1.11 | ✓ | 19 | |
3.2 | odd | 2 | 6579.2.a.t.1.9 | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
731.2.a.e.1.11 | ✓ | 19 | 1.1 | even | 1 | trivial | |
6579.2.a.t.1.9 | 19 | 3.2 | odd | 2 |