Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3450,2,Mod(1,3450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3450, 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("3450.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3450.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: | \(27.5483886973\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.3368.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 15x + 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.723686\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3450.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −0.723686 | −0.273528 | −0.136764 | − | 0.990604i | \(-0.543670\pi\) | ||||
−0.136764 | + | 0.990604i | \(0.543670\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.51445 | 1.66267 | 0.831335 | − | 0.555771i | \(-0.187577\pi\) | ||||
0.831335 | + | 0.555771i | \(0.187577\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −4.96183 | −1.37616 | −0.688081 | − | 0.725634i | \(-0.741547\pi\) | ||||
−0.688081 | + | 0.725634i | \(0.741547\pi\) | |||||||
\(14\) | −0.723686 | −0.193413 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.23814 | −1.02790 | −0.513950 | − | 0.857820i | \(-0.671818\pi\) | ||||
−0.513950 | + | 0.857820i | \(0.671818\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 4.96183 | 1.13832 | 0.569160 | − | 0.822227i | \(-0.307268\pi\) | ||||
0.569160 | + | 0.822227i | \(0.307268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.723686 | 0.157921 | ||||||||
\(22\) | 5.51445 | 1.17569 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.96183 | −0.973094 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.723686 | −0.136764 | ||||||||
\(29\) | −1.00000 | −0.185695 | −0.0928477 | − | 0.995680i | \(-0.529597\pi\) | ||||
−0.0928477 | + | 0.995680i | \(0.529597\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −5.51445 | −0.959943 | ||||||||
\(34\) | −4.23814 | −0.726835 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 4.23814 | 0.696746 | 0.348373 | − | 0.937356i | \(-0.386734\pi\) | ||||
0.348373 | + | 0.937356i | \(0.386734\pi\) | |||||||
\(38\) | 4.96183 | 0.804914 | ||||||||
\(39\) | 4.96183 | 0.794528 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.03817 | 0.162136 | 0.0810678 | − | 0.996709i | \(-0.474167\pi\) | ||||
0.0810678 | + | 0.996709i | \(0.474167\pi\) | |||||||
\(42\) | 0.723686 | 0.111667 | ||||||||
\(43\) | 0.961825 | 0.146677 | 0.0733385 | − | 0.997307i | \(-0.476635\pi\) | ||||
0.0733385 | + | 0.997307i | \(0.476635\pi\) | |||||||
\(44\) | 5.51445 | 0.831335 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 7.96183 | 1.16135 | 0.580676 | − | 0.814135i | \(-0.302788\pi\) | ||||
0.580676 | + | 0.814135i | \(0.302788\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.47628 | −0.925183 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.23814 | 0.593458 | ||||||||
\(52\) | −4.96183 | −0.688081 | ||||||||
\(53\) | 6.47628 | 0.889585 | 0.444793 | − | 0.895634i | \(-0.353277\pi\) | ||||
0.444793 | + | 0.895634i | \(0.353277\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.723686 | −0.0967066 | ||||||||
\(57\) | −4.96183 | −0.657210 | ||||||||
\(58\) | −1.00000 | −0.131306 | ||||||||
\(59\) | −9.02891 | −1.17546 | −0.587732 | − | 0.809056i | \(-0.699979\pi\) | ||||
−0.587732 | + | 0.809056i | \(0.699979\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.44737 | 0.953538 | 0.476769 | − | 0.879029i | \(-0.341808\pi\) | ||||
0.476769 | + | 0.879029i | \(0.341808\pi\) | |||||||
\(62\) | 6.00000 | 0.762001 | ||||||||
\(63\) | −0.723686 | −0.0911759 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.51445 | −0.678782 | ||||||||
\(67\) | 11.9237 | 1.45671 | 0.728353 | − | 0.685202i | \(-0.240286\pi\) | ||||
0.728353 | + | 0.685202i | \(0.240286\pi\) | |||||||
\(68\) | −4.23814 | −0.513950 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.514453 | −0.0610544 | −0.0305272 | − | 0.999534i | \(-0.509719\pi\) | ||||
−0.0305272 | + | 0.999534i | \(0.509719\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 0.447372 | 0.0523609 | 0.0261805 | − | 0.999657i | \(-0.491666\pi\) | ||||
0.0261805 | + | 0.999657i | \(0.491666\pi\) | |||||||
\(74\) | 4.23814 | 0.492674 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.96183 | 0.569160 | ||||||||
\(77\) | −3.99073 | −0.454786 | ||||||||
\(78\) | 4.96183 | 0.561816 | ||||||||
\(79\) | −5.51445 | −0.620424 | −0.310212 | − | 0.950667i | \(-0.600400\pi\) | ||||
−0.310212 | + | 0.950667i | \(0.600400\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.03817 | 0.114647 | ||||||||
\(83\) | −6.17106 | −0.677362 | −0.338681 | − | 0.940901i | \(-0.609981\pi\) | ||||
−0.338681 | + | 0.940901i | \(0.609981\pi\) | |||||||
\(84\) | 0.723686 | 0.0789606 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.961825 | 0.103716 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | 5.51445 | 0.587843 | ||||||||
\(89\) | −2.23814 | −0.237242 | −0.118621 | − | 0.992940i | \(-0.537847\pi\) | ||||
−0.118621 | + | 0.992940i | \(0.537847\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.59080 | 0.376418 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −6.00000 | −0.622171 | ||||||||
\(94\) | 7.96183 | 0.821200 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −2.55263 | −0.259180 | −0.129590 | − | 0.991568i | \(-0.541366\pi\) | ||||
−0.129590 | + | 0.991568i | \(0.541366\pi\) | |||||||
\(98\) | −6.47628 | −0.654203 | ||||||||
\(99\) | 5.51445 | 0.554223 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.06708 | −0.106179 | −0.0530893 | − | 0.998590i | \(-0.516907\pi\) | ||||
−0.0530893 | + | 0.998590i | \(0.516907\pi\) | |||||||
\(102\) | 4.23814 | 0.419638 | ||||||||
\(103\) | 5.75259 | 0.566820 | 0.283410 | − | 0.958999i | \(-0.408534\pi\) | ||||
0.283410 | + | 0.958999i | \(0.408534\pi\) | |||||||
\(104\) | −4.96183 | −0.486547 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.47628 | 0.629032 | ||||||||
\(107\) | 15.9237 | 1.53940 | 0.769699 | − | 0.638407i | \(-0.220406\pi\) | ||||
0.769699 | + | 0.638407i | \(0.220406\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 17.2670 | 1.65388 | 0.826942 | − | 0.562288i | \(-0.190079\pi\) | ||||
0.826942 | + | 0.562288i | \(0.190079\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.23814 | −0.402266 | ||||||||
\(112\) | −0.723686 | −0.0683819 | ||||||||
\(113\) | −6.23814 | −0.586835 | −0.293417 | − | 0.955984i | \(-0.594793\pi\) | ||||
−0.293417 | + | 0.955984i | \(0.594793\pi\) | |||||||
\(114\) | −4.96183 | −0.464718 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | −4.96183 | −0.458721 | ||||||||
\(118\) | −9.02891 | −0.831178 | ||||||||
\(119\) | 3.06708 | 0.281159 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.4092 | 1.76447 | ||||||||
\(122\) | 7.44737 | 0.674253 | ||||||||
\(123\) | −1.03817 | −0.0936091 | ||||||||
\(124\) | 6.00000 | 0.538816 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.723686 | −0.0644711 | ||||||||
\(127\) | −12.9526 | −1.14935 | −0.574677 | − | 0.818380i | \(-0.694872\pi\) | ||||
−0.574677 | + | 0.818380i | \(0.694872\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −0.961825 | −0.0846840 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.5815 | 1.01188 | 0.505942 | − | 0.862568i | \(-0.331145\pi\) | ||||
0.505942 | + | 0.862568i | \(0.331145\pi\) | |||||||
\(132\) | −5.51445 | −0.479972 | ||||||||
\(133\) | −3.59080 | −0.311362 | ||||||||
\(134\) | 11.9237 | 1.03005 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.23814 | −0.363417 | ||||||||
\(137\) | 22.2381 | 1.89993 | 0.949966 | − | 0.312353i | \(-0.101117\pi\) | ||||
0.949966 | + | 0.312353i | \(0.101117\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | 18.9907 | 1.61077 | 0.805386 | − | 0.592750i | \(-0.201958\pi\) | ||||
0.805386 | + | 0.592750i | \(0.201958\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.96183 | −0.670507 | ||||||||
\(142\) | −0.514453 | −0.0431720 | ||||||||
\(143\) | −27.3618 | −2.28810 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.447372 | 0.0370248 | ||||||||
\(147\) | 6.47628 | 0.534154 | ||||||||
\(148\) | 4.23814 | 0.348373 | ||||||||
\(149\) | −5.92365 | −0.485284 | −0.242642 | − | 0.970116i | \(-0.578014\pi\) | ||||
−0.242642 | + | 0.970116i | \(0.578014\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.47628 | 0.527032 | 0.263516 | − | 0.964655i | \(-0.415118\pi\) | ||||
0.263516 | + | 0.964655i | \(0.415118\pi\) | |||||||
\(152\) | 4.96183 | 0.402457 | ||||||||
\(153\) | −4.23814 | −0.342633 | ||||||||
\(154\) | −3.99073 | −0.321582 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.96183 | 0.397264 | ||||||||
\(157\) | 9.37102 | 0.747889 | 0.373944 | − | 0.927451i | \(-0.378005\pi\) | ||||
0.373944 | + | 0.927451i | \(0.378005\pi\) | |||||||
\(158\) | −5.51445 | −0.438706 | ||||||||
\(159\) | −6.47628 | −0.513602 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.723686 | −0.0570344 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −13.9237 | −1.09058 | −0.545292 | − | 0.838246i | \(-0.683581\pi\) | ||||
−0.545292 | + | 0.838246i | \(0.683581\pi\) | |||||||
\(164\) | 1.03817 | 0.0810678 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.17106 | −0.478967 | ||||||||
\(167\) | 9.61971 | 0.744396 | 0.372198 | − | 0.928153i | \(-0.378604\pi\) | ||||
0.372198 | + | 0.928153i | \(0.378604\pi\) | |||||||
\(168\) | 0.723686 | 0.0558336 | ||||||||
\(169\) | 11.6197 | 0.893824 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.96183 | 0.379440 | ||||||||
\(172\) | 0.961825 | 0.0733385 | ||||||||
\(173\) | 1.51445 | 0.115142 | 0.0575709 | − | 0.998341i | \(-0.481664\pi\) | ||||
0.0575709 | + | 0.998341i | \(0.481664\pi\) | |||||||
\(174\) | 1.00000 | 0.0758098 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.51445 | 0.415668 | ||||||||
\(177\) | 9.02891 | 0.678654 | ||||||||
\(178\) | −2.23814 | −0.167756 | ||||||||
\(179\) | 10.4763 | 0.783034 | 0.391517 | − | 0.920171i | \(-0.371950\pi\) | ||||
0.391517 | + | 0.920171i | \(0.371950\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.7433 | −1.61617 | −0.808084 | − | 0.589067i | \(-0.799495\pi\) | ||||
−0.808084 | + | 0.589067i | \(0.799495\pi\) | |||||||
\(182\) | 3.59080 | 0.266168 | ||||||||
\(183\) | −7.44737 | −0.550526 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.00000 | −0.439941 | ||||||||
\(187\) | −23.3710 | −1.70906 | ||||||||
\(188\) | 7.96183 | 0.580676 | ||||||||
\(189\) | 0.723686 | 0.0526404 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.40920 | 0.608468 | 0.304234 | − | 0.952597i | \(-0.401600\pi\) | ||||
0.304234 | + | 0.952597i | \(0.401600\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −12.9907 | −0.935093 | −0.467547 | − | 0.883968i | \(-0.654862\pi\) | ||||
−0.467547 | + | 0.883968i | \(0.654862\pi\) | |||||||
\(194\) | −2.55263 | −0.183268 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.47628 | −0.462591 | ||||||||
\(197\) | 20.5815 | 1.46637 | 0.733187 | − | 0.680027i | \(-0.238032\pi\) | ||||
0.733187 | + | 0.680027i | \(0.238032\pi\) | |||||||
\(198\) | 5.51445 | 0.391895 | ||||||||
\(199\) | −4.64734 | −0.329441 | −0.164720 | − | 0.986340i | \(-0.552672\pi\) | ||||
−0.164720 | + | 0.986340i | \(0.552672\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.9237 | −0.841029 | ||||||||
\(202\) | −1.06708 | −0.0750796 | ||||||||
\(203\) | 0.723686 | 0.0507928 | ||||||||
\(204\) | 4.23814 | 0.296729 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.75259 | 0.400802 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | −4.96183 | −0.344041 | ||||||||
\(209\) | 27.3618 | 1.89265 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.3328 | −1.60630 | −0.803150 | − | 0.595777i | \(-0.796844\pi\) | ||||
−0.803150 | + | 0.595777i | \(0.796844\pi\) | |||||||
\(212\) | 6.47628 | 0.444793 | ||||||||
\(213\) | 0.514453 | 0.0352498 | ||||||||
\(214\) | 15.9237 | 1.08852 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −4.34212 | −0.294762 | ||||||||
\(218\) | 17.2670 | 1.16947 | ||||||||
\(219\) | −0.447372 | −0.0302306 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.0289 | 1.41456 | ||||||||
\(222\) | −4.23814 | −0.284445 | ||||||||
\(223\) | 25.2947 | 1.69386 | 0.846928 | − | 0.531707i | \(-0.178449\pi\) | ||||
0.846928 | + | 0.531707i | \(0.178449\pi\) | |||||||
\(224\) | −0.723686 | −0.0483533 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.23814 | −0.414955 | ||||||||
\(227\) | 7.13288 | 0.473426 | 0.236713 | − | 0.971580i | \(-0.423930\pi\) | ||||
0.236713 | + | 0.971580i | \(0.423930\pi\) | |||||||
\(228\) | −4.96183 | −0.328605 | ||||||||
\(229\) | −7.58154 | −0.501002 | −0.250501 | − | 0.968116i | \(-0.580595\pi\) | ||||
−0.250501 | + | 0.968116i | \(0.580595\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.99073 | 0.262571 | ||||||||
\(232\) | −1.00000 | −0.0656532 | ||||||||
\(233\) | 24.8855 | 1.63030 | 0.815151 | − | 0.579249i | \(-0.196654\pi\) | ||||
0.815151 | + | 0.579249i | \(0.196654\pi\) | |||||||
\(234\) | −4.96183 | −0.324365 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −9.02891 | −0.587732 | ||||||||
\(237\) | 5.51445 | 0.358202 | ||||||||
\(238\) | 3.06708 | 0.198809 | ||||||||
\(239\) | −18.0960 | −1.17053 | −0.585266 | − | 0.810841i | \(-0.699010\pi\) | ||||
−0.585266 | + | 0.810841i | \(0.699010\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.8762 | 1.73125 | 0.865624 | − | 0.500694i | \(-0.166922\pi\) | ||||
0.865624 | + | 0.500694i | \(0.166922\pi\) | |||||||
\(242\) | 19.4092 | 1.24767 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 7.44737 | 0.476769 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.03817 | −0.0661916 | ||||||||
\(247\) | −24.6197 | −1.56651 | ||||||||
\(248\) | 6.00000 | 0.381000 | ||||||||
\(249\) | 6.17106 | 0.391075 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.79077 | −0.554868 | −0.277434 | − | 0.960745i | \(-0.589484\pi\) | ||||
−0.277434 | + | 0.960745i | \(0.589484\pi\) | |||||||
\(252\) | −0.723686 | −0.0455879 | ||||||||
\(253\) | 5.51445 | 0.346691 | ||||||||
\(254\) | −12.9526 | −0.812716 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −10.9526 | −0.683202 | −0.341601 | − | 0.939845i | \(-0.610969\pi\) | ||||
−0.341601 | + | 0.939845i | \(0.610969\pi\) | |||||||
\(258\) | −0.961825 | −0.0598806 | ||||||||
\(259\) | −3.06708 | −0.190579 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | 11.5815 | 0.715510 | ||||||||
\(263\) | 20.8762 | 1.28728 | 0.643641 | − | 0.765327i | \(-0.277423\pi\) | ||||
0.643641 | + | 0.765327i | \(0.277423\pi\) | |||||||
\(264\) | −5.51445 | −0.339391 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.59080 | −0.220166 | ||||||||
\(267\) | 2.23814 | 0.136972 | ||||||||
\(268\) | 11.9237 | 0.728353 | ||||||||
\(269\) | 21.3618 | 1.30245 | 0.651225 | − | 0.758885i | \(-0.274256\pi\) | ||||
0.651225 | + | 0.758885i | \(0.274256\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.0289 | 0.669958 | 0.334979 | − | 0.942226i | \(-0.391271\pi\) | ||||
0.334979 | + | 0.942226i | \(0.391271\pi\) | |||||||
\(272\) | −4.23814 | −0.256975 | ||||||||
\(273\) | −3.59080 | −0.217325 | ||||||||
\(274\) | 22.2381 | 1.34346 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | −15.4381 | −0.927586 | −0.463793 | − | 0.885944i | \(-0.653512\pi\) | ||||
−0.463793 | + | 0.885944i | \(0.653512\pi\) | |||||||
\(278\) | 18.9907 | 1.13899 | ||||||||
\(279\) | 6.00000 | 0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.16179 | −0.128962 | −0.0644808 | − | 0.997919i | \(-0.520539\pi\) | ||||
−0.0644808 | + | 0.997919i | \(0.520539\pi\) | |||||||
\(282\) | −7.96183 | −0.474120 | ||||||||
\(283\) | −16.9526 | −1.00772 | −0.503862 | − | 0.863784i | \(-0.668088\pi\) | ||||
−0.503862 | + | 0.863784i | \(0.668088\pi\) | |||||||
\(284\) | −0.514453 | −0.0305272 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −27.3618 | −1.61793 | ||||||||
\(287\) | −0.751312 | −0.0443486 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 0.961825 | 0.0565780 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.55263 | 0.149638 | ||||||||
\(292\) | 0.447372 | 0.0261805 | ||||||||
\(293\) | −13.0289 | −0.761157 | −0.380578 | − | 0.924749i | \(-0.624275\pi\) | ||||
−0.380578 | + | 0.924749i | \(0.624275\pi\) | |||||||
\(294\) | 6.47628 | 0.377704 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.23814 | 0.246337 | ||||||||
\(297\) | −5.51445 | −0.319981 | ||||||||
\(298\) | −5.92365 | −0.343148 | ||||||||
\(299\) | −4.96183 | −0.286950 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.696059 | −0.0401202 | ||||||||
\(302\) | 6.47628 | 0.372668 | ||||||||
\(303\) | 1.06708 | 0.0613022 | ||||||||
\(304\) | 4.96183 | 0.284580 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4.23814 | −0.242278 | ||||||||
\(307\) | −27.0671 | −1.54480 | −0.772400 | − | 0.635136i | \(-0.780944\pi\) | ||||
−0.772400 | + | 0.635136i | \(0.780944\pi\) | |||||||
\(308\) | −3.99073 | −0.227393 | ||||||||
\(309\) | −5.75259 | −0.327254 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.4670 | −1.78433 | −0.892165 | − | 0.451709i | \(-0.850814\pi\) | ||||
−0.892165 | + | 0.451709i | \(0.850814\pi\) | |||||||
\(312\) | 4.96183 | 0.280908 | ||||||||
\(313\) | −27.2947 | −1.54279 | −0.771393 | − | 0.636359i | \(-0.780440\pi\) | ||||
−0.771393 | + | 0.636359i | \(0.780440\pi\) | |||||||
\(314\) | 9.37102 | 0.528837 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.51445 | −0.310212 | ||||||||
\(317\) | 11.0000 | 0.617822 | 0.308911 | − | 0.951091i | \(-0.400036\pi\) | ||||
0.308911 | + | 0.951091i | \(0.400036\pi\) | |||||||
\(318\) | −6.47628 | −0.363172 | ||||||||
\(319\) | −5.51445 | −0.308750 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.9237 | −0.888772 | ||||||||
\(322\) | −0.723686 | −0.0403294 | ||||||||
\(323\) | −21.0289 | −1.17008 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −13.9237 | −0.771160 | ||||||||
\(327\) | −17.2670 | −0.954870 | ||||||||
\(328\) | 1.03817 | 0.0573236 | ||||||||
\(329\) | −5.76186 | −0.317662 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.51445 | −0.467997 | −0.233998 | − | 0.972237i | \(-0.575181\pi\) | ||||
−0.233998 | + | 0.972237i | \(0.575181\pi\) | |||||||
\(332\) | −6.17106 | −0.338681 | ||||||||
\(333\) | 4.23814 | 0.232249 | ||||||||
\(334\) | 9.61971 | 0.526367 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.723686 | 0.0394803 | ||||||||
\(337\) | 1.52372 | 0.0830024 | 0.0415012 | − | 0.999138i | \(-0.486786\pi\) | ||||
0.0415012 | + | 0.999138i | \(0.486786\pi\) | |||||||
\(338\) | 11.6197 | 0.632029 | ||||||||
\(339\) | 6.23814 | 0.338809 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 33.0867 | 1.79175 | ||||||||
\(342\) | 4.96183 | 0.268305 | ||||||||
\(343\) | 9.75259 | 0.526591 | ||||||||
\(344\) | 0.961825 | 0.0518581 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.51445 | 0.0814175 | ||||||||
\(347\) | −25.5815 | −1.37329 | −0.686644 | − | 0.726993i | \(-0.740917\pi\) | ||||
−0.686644 | + | 0.726993i | \(0.740917\pi\) | |||||||
\(348\) | 1.00000 | 0.0536056 | ||||||||
\(349\) | −26.8855 | −1.43915 | −0.719573 | − | 0.694417i | \(-0.755663\pi\) | ||||
−0.719573 | + | 0.694417i | \(0.755663\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.96183 | 0.264843 | ||||||||
\(352\) | 5.51445 | 0.293921 | ||||||||
\(353\) | −10.6197 | −0.565230 | −0.282615 | − | 0.959233i | \(-0.591202\pi\) | ||||
−0.282615 | + | 0.959233i | \(0.591202\pi\) | |||||||
\(354\) | 9.02891 | 0.479881 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.23814 | −0.118621 | ||||||||
\(357\) | −3.06708 | −0.162327 | ||||||||
\(358\) | 10.4763 | 0.553689 | ||||||||
\(359\) | −5.43810 | −0.287012 | −0.143506 | − | 0.989649i | \(-0.545838\pi\) | ||||
−0.143506 | + | 0.989649i | \(0.545838\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.61971 | 0.295774 | ||||||||
\(362\) | −21.7433 | −1.14280 | ||||||||
\(363\) | −19.4092 | −1.01872 | ||||||||
\(364\) | 3.59080 | 0.188209 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −7.44737 | −0.389280 | ||||||||
\(367\) | −8.56190 | −0.446927 | −0.223464 | − | 0.974712i | \(-0.571736\pi\) | ||||
−0.223464 | + | 0.974712i | \(0.571736\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 1.03817 | 0.0540452 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.68679 | −0.243326 | ||||||||
\(372\) | −6.00000 | −0.311086 | ||||||||
\(373\) | 26.2960 | 1.36155 | 0.680776 | − | 0.732491i | \(-0.261643\pi\) | ||||
0.680776 | + | 0.732491i | \(0.261643\pi\) | |||||||
\(374\) | −23.3710 | −1.20849 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.96183 | 0.410600 | ||||||||
\(377\) | 4.96183 | 0.255547 | ||||||||
\(378\) | 0.723686 | 0.0372224 | ||||||||
\(379\) | −6.34212 | −0.325773 | −0.162886 | − | 0.986645i | \(-0.552080\pi\) | ||||
−0.162886 | + | 0.986645i | \(0.552080\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.9526 | 0.663580 | ||||||||
\(382\) | 8.40920 | 0.430252 | ||||||||
\(383\) | −35.4959 | −1.81376 | −0.906878 | − | 0.421393i | \(-0.861541\pi\) | ||||
−0.906878 | + | 0.421393i | \(0.861541\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.9907 | −0.661211 | ||||||||
\(387\) | 0.961825 | 0.0488923 | ||||||||
\(388\) | −2.55263 | −0.129590 | ||||||||
\(389\) | −9.84730 | −0.499278 | −0.249639 | − | 0.968339i | \(-0.580312\pi\) | ||||
−0.249639 | + | 0.968339i | \(0.580312\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.23814 | −0.214332 | ||||||||
\(392\) | −6.47628 | −0.327101 | ||||||||
\(393\) | −11.5815 | −0.584211 | ||||||||
\(394\) | 20.5815 | 1.03688 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.51445 | 0.277112 | ||||||||
\(397\) | 18.8762 | 0.947370 | 0.473685 | − | 0.880694i | \(-0.342924\pi\) | ||||
0.473685 | + | 0.880694i | \(0.342924\pi\) | |||||||
\(398\) | −4.64734 | −0.232950 | ||||||||
\(399\) | 3.59080 | 0.179765 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 33.5052 | 1.67317 | 0.836585 | − | 0.547838i | \(-0.184549\pi\) | ||||
0.836585 | + | 0.547838i | \(0.184549\pi\) | |||||||
\(402\) | −11.9237 | −0.594698 | ||||||||
\(403\) | −29.7710 | −1.48300 | ||||||||
\(404\) | −1.06708 | −0.0530893 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.723686 | 0.0359159 | ||||||||
\(407\) | 23.3710 | 1.15846 | ||||||||
\(408\) | 4.23814 | 0.209819 | ||||||||
\(409\) | −25.5341 | −1.26258 | −0.631290 | − | 0.775547i | \(-0.717474\pi\) | ||||
−0.631290 | + | 0.775547i | \(0.717474\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.2381 | −1.09693 | ||||||||
\(412\) | 5.75259 | 0.283410 | ||||||||
\(413\) | 6.53409 | 0.321522 | ||||||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.96183 | −0.243273 | ||||||||
\(417\) | −18.9907 | −0.929980 | ||||||||
\(418\) | 27.3618 | 1.33831 | ||||||||
\(419\) | −37.2000 | −1.81734 | −0.908669 | − | 0.417518i | \(-0.862900\pi\) | ||||
−0.908669 | + | 0.417518i | \(0.862900\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.5815 | −0.564449 | −0.282225 | − | 0.959348i | \(-0.591072\pi\) | ||||
−0.282225 | + | 0.959348i | \(0.591072\pi\) | |||||||
\(422\) | −23.3328 | −1.13583 | ||||||||
\(423\) | 7.96183 | 0.387117 | ||||||||
\(424\) | 6.47628 | 0.314516 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.514453 | 0.0249254 | ||||||||
\(427\) | −5.38956 | −0.260819 | ||||||||
\(428\) | 15.9237 | 0.769699 | ||||||||
\(429\) | 27.3618 | 1.32104 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.37102 | 0.355050 | 0.177525 | − | 0.984116i | \(-0.443191\pi\) | ||||
0.177525 | + | 0.984116i | \(0.443191\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −19.3710 | −0.930912 | −0.465456 | − | 0.885071i | \(-0.654110\pi\) | ||||
−0.465456 | + | 0.885071i | \(0.654110\pi\) | |||||||
\(434\) | −4.34212 | −0.208428 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 17.2670 | 0.826942 | ||||||||
\(437\) | 4.96183 | 0.237356 | ||||||||
\(438\) | −0.447372 | −0.0213763 | ||||||||
\(439\) | 17.5052 | 0.835477 | 0.417738 | − | 0.908567i | \(-0.362823\pi\) | ||||
0.417738 | + | 0.908567i | \(0.362823\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.47628 | −0.308394 | ||||||||
\(442\) | 21.0289 | 1.00024 | ||||||||
\(443\) | 17.3710 | 0.825322 | 0.412661 | − | 0.910885i | \(-0.364599\pi\) | ||||
0.412661 | + | 0.910885i | \(0.364599\pi\) | |||||||
\(444\) | −4.23814 | −0.201133 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 25.2947 | 1.19774 | ||||||||
\(447\) | 5.92365 | 0.280179 | ||||||||
\(448\) | −0.723686 | −0.0341909 | ||||||||
\(449\) | −16.8947 | −0.797312 | −0.398656 | − | 0.917100i | \(-0.630523\pi\) | ||||
−0.398656 | + | 0.917100i | \(0.630523\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.72497 | 0.269578 | ||||||||
\(452\) | −6.23814 | −0.293417 | ||||||||
\(453\) | −6.47628 | −0.304282 | ||||||||
\(454\) | 7.13288 | 0.334763 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.96183 | −0.232359 | ||||||||
\(457\) | −21.9237 | −1.02555 | −0.512773 | − | 0.858524i | \(-0.671382\pi\) | ||||
−0.512773 | + | 0.858524i | \(0.671382\pi\) | |||||||
\(458\) | −7.58154 | −0.354262 | ||||||||
\(459\) | 4.23814 | 0.197819 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.65788 | −0.123790 | −0.0618950 | − | 0.998083i | \(-0.519714\pi\) | ||||
−0.0618950 | + | 0.998083i | \(0.519714\pi\) | |||||||
\(462\) | 3.99073 | 0.185666 | ||||||||
\(463\) | 12.0000 | 0.557687 | 0.278844 | − | 0.960337i | \(-0.410049\pi\) | ||||
0.278844 | + | 0.960337i | \(0.410049\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 24.8855 | 1.15280 | ||||||||
\(467\) | 15.8289 | 0.732476 | 0.366238 | − | 0.930521i | \(-0.380646\pi\) | ||||
0.366238 | + | 0.930521i | \(0.380646\pi\) | |||||||
\(468\) | −4.96183 | −0.229360 | ||||||||
\(469\) | −8.62898 | −0.398449 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.37102 | −0.431794 | ||||||||
\(472\) | −9.02891 | −0.415589 | ||||||||
\(473\) | 5.30394 | 0.243875 | ||||||||
\(474\) | 5.51445 | 0.253287 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.06708 | 0.140579 | ||||||||
\(477\) | 6.47628 | 0.296528 | ||||||||
\(478\) | −18.0960 | −0.827691 | ||||||||
\(479\) | 27.5723 | 1.25981 | 0.629905 | − | 0.776673i | \(-0.283094\pi\) | ||||
0.629905 | + | 0.776673i | \(0.283094\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21.0289 | −0.958836 | ||||||||
\(482\) | 26.8762 | 1.22418 | ||||||||
\(483\) | 0.723686 | 0.0329288 | ||||||||
\(484\) | 19.4092 | 0.882236 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −16.6868 | −0.756151 | −0.378075 | − | 0.925775i | \(-0.623414\pi\) | ||||
−0.378075 | + | 0.925775i | \(0.623414\pi\) | |||||||
\(488\) | 7.44737 | 0.337127 | ||||||||
\(489\) | 13.9237 | 0.629649 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.4288 | −0.606035 | −0.303017 | − | 0.952985i | \(-0.597994\pi\) | ||||
−0.303017 | + | 0.952985i | \(0.597994\pi\) | |||||||
\(492\) | −1.03817 | −0.0468045 | ||||||||
\(493\) | 4.23814 | 0.190876 | ||||||||
\(494\) | −24.6197 | −1.10769 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.00000 | 0.269408 | ||||||||
\(497\) | 0.372303 | 0.0167001 | ||||||||
\(498\) | 6.17106 | 0.276532 | ||||||||
\(499\) | −8.99073 | −0.402480 | −0.201240 | − | 0.979542i | \(-0.564497\pi\) | ||||
−0.201240 | + | 0.979542i | \(0.564497\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.61971 | −0.429777 | ||||||||
\(502\) | −8.79077 | −0.392351 | ||||||||
\(503\) | −18.9618 | −0.845466 | −0.422733 | − | 0.906254i | \(-0.638929\pi\) | ||||
−0.422733 | + | 0.906254i | \(0.638929\pi\) | |||||||
\(504\) | −0.723686 | −0.0322355 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.51445 | 0.245147 | ||||||||
\(507\) | −11.6197 | −0.516049 | ||||||||
\(508\) | −12.9526 | −0.574677 | ||||||||
\(509\) | 26.2276 | 1.16252 | 0.581259 | − | 0.813719i | \(-0.302560\pi\) | ||||
0.581259 | + | 0.813719i | \(0.302560\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.323757 | −0.0143222 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −4.96183 | −0.219070 | ||||||||
\(514\) | −10.9526 | −0.483097 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.961825 | −0.0423420 | ||||||||
\(517\) | 43.9051 | 1.93094 | ||||||||
\(518\) | −3.06708 | −0.134760 | ||||||||
\(519\) | −1.51445 | −0.0664771 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.2381 | 1.41238 | 0.706189 | − | 0.708023i | \(-0.250413\pi\) | ||||
0.706189 | + | 0.708023i | \(0.250413\pi\) | |||||||
\(522\) | −1.00000 | −0.0437688 | ||||||||
\(523\) | −5.59080 | −0.244469 | −0.122234 | − | 0.992501i | \(-0.539006\pi\) | ||||
−0.122234 | + | 0.992501i | \(0.539006\pi\) | |||||||
\(524\) | 11.5815 | 0.505942 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.8762 | 0.910246 | ||||||||
\(527\) | −25.4288 | −1.10770 | ||||||||
\(528\) | −5.51445 | −0.239986 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.02891 | −0.391821 | ||||||||
\(532\) | −3.59080 | −0.155681 | ||||||||
\(533\) | −5.15124 | −0.223125 | ||||||||
\(534\) | 2.23814 | 0.0968538 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 11.9237 | 0.515023 | ||||||||
\(537\) | −10.4763 | −0.452085 | ||||||||
\(538\) | 21.3618 | 0.920971 | ||||||||
\(539\) | −35.7131 | −1.53827 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.6486 | 1.01673 | 0.508367 | − | 0.861141i | \(-0.330249\pi\) | ||||
0.508367 | + | 0.861141i | \(0.330249\pi\) | |||||||
\(542\) | 11.0289 | 0.473732 | ||||||||
\(543\) | 21.7433 | 0.933095 | ||||||||
\(544\) | −4.23814 | −0.181709 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.59080 | −0.153672 | ||||||||
\(547\) | −39.3328 | −1.68175 | −0.840876 | − | 0.541229i | \(-0.817959\pi\) | ||||
−0.840876 | + | 0.541229i | \(0.817959\pi\) | |||||||
\(548\) | 22.2381 | 0.949966 | ||||||||
\(549\) | 7.44737 | 0.317846 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.96183 | −0.211381 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | 3.99073 | 0.169703 | ||||||||
\(554\) | −15.4381 | −0.655902 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.9907 | 0.805386 | ||||||||
\(557\) | 34.2658 | 1.45189 | 0.725944 | − | 0.687754i | \(-0.241403\pi\) | ||||
0.725944 | + | 0.687754i | \(0.241403\pi\) | |||||||
\(558\) | 6.00000 | 0.254000 | ||||||||
\(559\) | −4.77241 | −0.201851 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 23.3710 | 0.986725 | ||||||||
\(562\) | −2.16179 | −0.0911896 | ||||||||
\(563\) | −20.5434 | −0.865799 | −0.432900 | − | 0.901442i | \(-0.642510\pi\) | ||||
−0.432900 | + | 0.901442i | \(0.642510\pi\) | |||||||
\(564\) | −7.96183 | −0.335253 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −16.9526 | −0.712569 | ||||||||
\(567\) | −0.723686 | −0.0303920 | ||||||||
\(568\) | −0.514453 | −0.0215860 | ||||||||
\(569\) | −27.4474 | −1.15065 | −0.575327 | − | 0.817924i | \(-0.695125\pi\) | ||||
−0.575327 | + | 0.817924i | \(0.695125\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.58154 | −0.233580 | −0.116790 | − | 0.993157i | \(-0.537260\pi\) | ||||
−0.116790 | + | 0.993157i | \(0.537260\pi\) | |||||||
\(572\) | −27.3618 | −1.14405 | ||||||||
\(573\) | −8.40920 | −0.351299 | ||||||||
\(574\) | −0.751312 | −0.0313592 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −4.56190 | −0.189914 | −0.0949571 | − | 0.995481i | \(-0.530271\pi\) | ||||
−0.0949571 | + | 0.995481i | \(0.530271\pi\) | |||||||
\(578\) | 0.961825 | 0.0400067 | ||||||||
\(579\) | 12.9907 | 0.539876 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.46591 | 0.185277 | ||||||||
\(582\) | 2.55263 | 0.105810 | ||||||||
\(583\) | 35.7131 | 1.47909 | ||||||||
\(584\) | 0.447372 | 0.0185124 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13.0289 | −0.538219 | ||||||||
\(587\) | 23.4474 | 0.967777 | 0.483888 | − | 0.875130i | \(-0.339224\pi\) | ||||
0.483888 | + | 0.875130i | \(0.339224\pi\) | |||||||
\(588\) | 6.47628 | 0.267077 | ||||||||
\(589\) | 29.7710 | 1.22669 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.5815 | −0.846611 | ||||||||
\(592\) | 4.23814 | 0.174186 | ||||||||
\(593\) | −14.4092 | −0.591715 | −0.295857 | − | 0.955232i | \(-0.595605\pi\) | ||||
−0.295857 | + | 0.955232i | \(0.595605\pi\) | |||||||
\(594\) | −5.51445 | −0.226261 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.92365 | −0.242642 | ||||||||
\(597\) | 4.64734 | 0.190203 | ||||||||
\(598\) | −4.96183 | −0.202904 | ||||||||
\(599\) | 27.9815 | 1.14329 | 0.571646 | − | 0.820500i | \(-0.306305\pi\) | ||||
0.571646 | + | 0.820500i | \(0.306305\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.38029 | −0.260257 | −0.130129 | − | 0.991497i | \(-0.541539\pi\) | ||||
−0.130129 | + | 0.991497i | \(0.541539\pi\) | |||||||
\(602\) | −0.696059 | −0.0283693 | ||||||||
\(603\) | 11.9237 | 0.485569 | ||||||||
\(604\) | 6.47628 | 0.263516 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.06708 | 0.0433472 | ||||||||
\(607\) | −41.6946 | −1.69233 | −0.846166 | − | 0.532920i | \(-0.821095\pi\) | ||||
−0.846166 | + | 0.532920i | \(0.821095\pi\) | |||||||
\(608\) | 4.96183 | 0.201229 | ||||||||
\(609\) | −0.723686 | −0.0293252 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −39.5052 | −1.59821 | ||||||||
\(612\) | −4.23814 | −0.171317 | ||||||||
\(613\) | 10.8486 | 0.438170 | 0.219085 | − | 0.975706i | \(-0.429693\pi\) | ||||
0.219085 | + | 0.975706i | \(0.429693\pi\) | |||||||
\(614\) | −27.0671 | −1.09234 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.99073 | −0.160791 | ||||||||
\(617\) | −17.5052 | −0.704732 | −0.352366 | − | 0.935862i | \(-0.614623\pi\) | ||||
−0.352366 | + | 0.935862i | \(0.614623\pi\) | |||||||
\(618\) | −5.75259 | −0.231403 | ||||||||
\(619\) | 22.3421 | 0.898005 | 0.449003 | − | 0.893530i | \(-0.351779\pi\) | ||||
0.449003 | + | 0.893530i | \(0.351779\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | −31.4670 | −1.26171 | ||||||||
\(623\) | 1.61971 | 0.0648923 | ||||||||
\(624\) | 4.96183 | 0.198632 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −27.2947 | −1.09091 | ||||||||
\(627\) | −27.3618 | −1.09272 | ||||||||
\(628\) | 9.37102 | 0.373944 | ||||||||
\(629\) | −17.9618 | −0.716185 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.4105 | −0.533863 | −0.266931 | − | 0.963716i | \(-0.586010\pi\) | ||||
−0.266931 | + | 0.963716i | \(0.586010\pi\) | |||||||
\(632\) | −5.51445 | −0.219353 | ||||||||
\(633\) | 23.3328 | 0.927397 | ||||||||
\(634\) | 11.0000 | 0.436866 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6.47628 | −0.256801 | ||||||||
\(637\) | 32.1342 | 1.27320 | ||||||||
\(638\) | −5.51445 | −0.218319 | ||||||||
\(639\) | −0.514453 | −0.0203515 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 35.9538 | 1.42009 | 0.710046 | − | 0.704156i | \(-0.248674\pi\) | ||||
0.710046 | + | 0.704156i | \(0.248674\pi\) | |||||||
\(642\) | −15.9237 | −0.628456 | ||||||||
\(643\) | −2.48555 | −0.0980204 | −0.0490102 | − | 0.998798i | \(-0.515607\pi\) | ||||
−0.0490102 | + | 0.998798i | \(0.515607\pi\) | |||||||
\(644\) | −0.723686 | −0.0285172 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −21.0289 | −0.827371 | ||||||||
\(647\) | −44.4381 | −1.74704 | −0.873521 | − | 0.486786i | \(-0.838169\pi\) | ||||
−0.873521 | + | 0.486786i | \(0.838169\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −49.7895 | −1.95441 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.34212 | 0.170181 | ||||||||
\(652\) | −13.9237 | −0.545292 | ||||||||
\(653\) | 21.5526 | 0.843420 | 0.421710 | − | 0.906731i | \(-0.361430\pi\) | ||||
0.421710 | + | 0.906731i | \(0.361430\pi\) | |||||||
\(654\) | −17.2670 | −0.675195 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.03817 | 0.0405339 | ||||||||
\(657\) | 0.447372 | 0.0174536 | ||||||||
\(658\) | −5.76186 | −0.224621 | ||||||||
\(659\) | −7.33413 | −0.285697 | −0.142849 | − | 0.989745i | \(-0.545626\pi\) | ||||
−0.142849 | + | 0.989745i | \(0.545626\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.1618 | −1.79549 | −0.897743 | − | 0.440520i | \(-0.854794\pi\) | ||||
−0.897743 | + | 0.440520i | \(0.854794\pi\) | |||||||
\(662\) | −8.51445 | −0.330924 | ||||||||
\(663\) | −21.0289 | −0.816695 | ||||||||
\(664\) | −6.17106 | −0.239483 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.23814 | 0.164225 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 9.61971 | 0.372198 | ||||||||
\(669\) | −25.2947 | −0.977949 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 41.0682 | 1.58542 | ||||||||
\(672\) | 0.723686 | 0.0279168 | ||||||||
\(673\) | 37.8184 | 1.45779 | 0.728896 | − | 0.684624i | \(-0.240034\pi\) | ||||
0.728896 | + | 0.684624i | \(0.240034\pi\) | |||||||
\(674\) | 1.52372 | 0.0586916 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.6197 | 0.446912 | ||||||||
\(677\) | −2.21051 | −0.0849569 | −0.0424785 | − | 0.999097i | \(-0.513525\pi\) | ||||
−0.0424785 | + | 0.999097i | \(0.513525\pi\) | |||||||
\(678\) | 6.23814 | 0.239574 | ||||||||
\(679\) | 1.84730 | 0.0708929 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.13288 | −0.273333 | ||||||||
\(682\) | 33.0867 | 1.26696 | ||||||||
\(683\) | 29.6393 | 1.13412 | 0.567059 | − | 0.823677i | \(-0.308081\pi\) | ||||
0.567059 | + | 0.823677i | \(0.308081\pi\) | |||||||
\(684\) | 4.96183 | 0.189720 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.75259 | 0.372356 | ||||||||
\(687\) | 7.58154 | 0.289254 | ||||||||
\(688\) | 0.961825 | 0.0366692 | ||||||||
\(689\) | −32.1342 | −1.22421 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −40.1512 | −1.52743 | −0.763713 | − | 0.645556i | \(-0.776626\pi\) | ||||
−0.763713 | + | 0.645556i | \(0.776626\pi\) | |||||||
\(692\) | 1.51445 | 0.0575709 | ||||||||
\(693\) | −3.99073 | −0.151595 | ||||||||
\(694\) | −25.5815 | −0.971062 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.00000 | 0.0379049 | ||||||||
\(697\) | −4.39993 | −0.166659 | ||||||||
\(698\) | −26.8855 | −1.01763 | ||||||||
\(699\) | −24.8855 | −0.941255 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −40.8762 | −1.54387 | −0.771937 | − | 0.635700i | \(-0.780712\pi\) | ||||
−0.771937 | + | 0.635700i | \(0.780712\pi\) | |||||||
\(702\) | 4.96183 | 0.187272 | ||||||||
\(703\) | 21.0289 | 0.793120 | ||||||||
\(704\) | 5.51445 | 0.207834 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.6197 | −0.399678 | ||||||||
\(707\) | 0.772232 | 0.0290428 | ||||||||
\(708\) | 9.02891 | 0.339327 | ||||||||
\(709\) | −25.0565 | −0.941018 | −0.470509 | − | 0.882395i | \(-0.655930\pi\) | ||||
−0.470509 | + | 0.882395i | \(0.655930\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.51445 | −0.206808 | ||||||||
\(712\) | −2.23814 | −0.0838778 | ||||||||
\(713\) | 6.00000 | 0.224702 | ||||||||
\(714\) | −3.06708 | −0.114783 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10.4763 | 0.391517 | ||||||||
\(717\) | 18.0960 | 0.675807 | ||||||||
\(718\) | −5.43810 | −0.202948 | ||||||||
\(719\) | −34.5145 | −1.28717 | −0.643586 | − | 0.765374i | \(-0.722554\pi\) | ||||
−0.643586 | + | 0.765374i | \(0.722554\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.16307 | −0.155041 | ||||||||
\(722\) | 5.61971 | 0.209144 | ||||||||
\(723\) | −26.8762 | −0.999537 | ||||||||
\(724\) | −21.7433 | −0.808084 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −19.4092 | −0.720343 | ||||||||
\(727\) | −37.0289 | −1.37333 | −0.686663 | − | 0.726976i | \(-0.740925\pi\) | ||||
−0.686663 | + | 0.726976i | \(0.740925\pi\) | |||||||
\(728\) | 3.59080 | 0.133084 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.07635 | −0.150769 | ||||||||
\(732\) | −7.44737 | −0.275263 | ||||||||
\(733\) | −8.02763 | −0.296507 | −0.148254 | − | 0.988949i | \(-0.547365\pi\) | ||||
−0.148254 | + | 0.988949i | \(0.547365\pi\) | |||||||
\(734\) | −8.56190 | −0.316025 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 65.7524 | 2.42202 | ||||||||
\(738\) | 1.03817 | 0.0382157 | ||||||||
\(739\) | −34.3432 | −1.26334 | −0.631668 | − | 0.775239i | \(-0.717629\pi\) | ||||
−0.631668 | + | 0.775239i | \(0.717629\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24.6197 | 0.904428 | ||||||||
\(742\) | −4.68679 | −0.172058 | ||||||||
\(743\) | 30.8855 | 1.13308 | 0.566539 | − | 0.824035i | \(-0.308282\pi\) | ||||
0.566539 | + | 0.824035i | \(0.308282\pi\) | |||||||
\(744\) | −6.00000 | −0.219971 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 26.2960 | 0.962763 | ||||||||
\(747\) | −6.17106 | −0.225787 | ||||||||
\(748\) | −23.3710 | −0.854529 | ||||||||
\(749\) | −11.5237 | −0.421068 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.0658 | 0.695721 | 0.347860 | − | 0.937546i | \(-0.386908\pi\) | ||||
0.347860 | + | 0.937546i | \(0.386908\pi\) | |||||||
\(752\) | 7.96183 | 0.290338 | ||||||||
\(753\) | 8.79077 | 0.320353 | ||||||||
\(754\) | 4.96183 | 0.180699 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.723686 | 0.0263202 | ||||||||
\(757\) | 26.1040 | 0.948765 | 0.474383 | − | 0.880319i | \(-0.342671\pi\) | ||||
0.474383 | + | 0.880319i | \(0.342671\pi\) | |||||||
\(758\) | −6.34212 | −0.230356 | ||||||||
\(759\) | −5.51445 | −0.200162 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.9433 | 0.614194 | 0.307097 | − | 0.951678i | \(-0.400642\pi\) | ||||
0.307097 | + | 0.951678i | \(0.400642\pi\) | |||||||
\(762\) | 12.9526 | 0.469222 | ||||||||
\(763\) | −12.4959 | −0.452383 | ||||||||
\(764\) | 8.40920 | 0.304234 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −35.4959 | −1.28252 | ||||||||
\(767\) | 44.7999 | 1.61763 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −41.5815 | −1.49947 | −0.749734 | − | 0.661739i | \(-0.769819\pi\) | ||||
−0.749734 | + | 0.661739i | \(0.769819\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.9526 | 0.394447 | ||||||||
\(772\) | −12.9907 | −0.467547 | ||||||||
\(773\) | −39.2183 | −1.41059 | −0.705293 | − | 0.708916i | \(-0.749184\pi\) | ||||
−0.705293 | + | 0.708916i | \(0.749184\pi\) | |||||||
\(774\) | 0.961825 | 0.0345721 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.55263 | −0.0916340 | ||||||||
\(777\) | 3.06708 | 0.110031 | ||||||||
\(778\) | −9.84730 | −0.353043 | ||||||||
\(779\) | 5.15124 | 0.184562 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.83693 | −0.101513 | ||||||||
\(782\) | −4.23814 | −0.151556 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | −6.47628 | −0.231296 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −11.5815 | −0.413100 | ||||||||
\(787\) | 17.3039 | 0.616819 | 0.308409 | − | 0.951254i | \(-0.400203\pi\) | ||||
0.308409 | + | 0.951254i | \(0.400203\pi\) | |||||||
\(788\) | 20.5815 | 0.733187 | ||||||||
\(789\) | −20.8762 | −0.743213 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.51445 | 0.160515 | ||||||||
\(792\) | 5.51445 | 0.195948 | ||||||||
\(793\) | −36.9526 | −1.31222 | ||||||||
\(794\) | 18.8762 | 0.669892 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.64734 | −0.164720 | ||||||||
\(797\) | −12.3236 | −0.436524 | −0.218262 | − | 0.975890i | \(-0.570039\pi\) | ||||
−0.218262 | + | 0.975890i | \(0.570039\pi\) | |||||||
\(798\) | 3.59080 | 0.127113 | ||||||||
\(799\) | −33.7433 | −1.19375 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.23814 | −0.0790808 | ||||||||
\(802\) | 33.5052 | 1.18311 | ||||||||
\(803\) | 2.46701 | 0.0870589 | ||||||||
\(804\) | −11.9237 | −0.420515 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −29.7710 | −1.04864 | ||||||||
\(807\) | −21.3618 | −0.751969 | ||||||||
\(808\) | −1.06708 | −0.0375398 | ||||||||
\(809\) | −21.3618 | −0.751039 | −0.375520 | − | 0.926814i | \(-0.622536\pi\) | ||||
−0.375520 | + | 0.926814i | \(0.622536\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.0104 | 1.65076 | 0.825379 | − | 0.564579i | \(-0.190962\pi\) | ||||
0.825379 | + | 0.564579i | \(0.190962\pi\) | |||||||
\(812\) | 0.723686 | 0.0253964 | ||||||||
\(813\) | −11.0289 | −0.386801 | ||||||||
\(814\) | 23.3710 | 0.819154 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.23814 | 0.148365 | ||||||||
\(817\) | 4.77241 | 0.166965 | ||||||||
\(818\) | −25.5341 | −0.892779 | ||||||||
\(819\) | 3.59080 | 0.125473 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.4855 | 1.06395 | 0.531976 | − | 0.846759i | \(-0.321449\pi\) | ||||
0.531976 | + | 0.846759i | \(0.321449\pi\) | |||||||
\(822\) | −22.2381 | −0.775644 | ||||||||
\(823\) | 6.34212 | 0.221072 | 0.110536 | − | 0.993872i | \(-0.464743\pi\) | ||||
0.110536 | + | 0.993872i | \(0.464743\pi\) | |||||||
\(824\) | 5.75259 | 0.200401 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.53409 | 0.227350 | ||||||||
\(827\) | −56.1340 | −1.95197 | −0.975985 | − | 0.217838i | \(-0.930100\pi\) | ||||
−0.975985 | + | 0.217838i | \(0.930100\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | −9.93292 | −0.344985 | −0.172492 | − | 0.985011i | \(-0.555182\pi\) | ||||
−0.172492 | + | 0.985011i | \(0.555182\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.4381 | 0.535542 | ||||||||
\(832\) | −4.96183 | −0.172020 | ||||||||
\(833\) | 27.4474 | 0.950995 | ||||||||
\(834\) | −18.9907 | −0.657595 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 27.3618 | 0.946326 | ||||||||
\(837\) | −6.00000 | −0.207390 | ||||||||
\(838\) | −37.2000 | −1.28505 | ||||||||
\(839\) | 31.7802 | 1.09718 | 0.548588 | − | 0.836093i | \(-0.315166\pi\) | ||||
0.548588 | + | 0.836093i | \(0.315166\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | −11.5815 | −0.399126 | ||||||||
\(843\) | 2.16179 | 0.0744560 | ||||||||
\(844\) | −23.3328 | −0.803150 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.96183 | 0.273733 | ||||||||
\(847\) | −14.0462 | −0.482632 | ||||||||
\(848\) | 6.47628 | 0.222396 | ||||||||
\(849\) | 16.9526 | 0.581810 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.23814 | 0.145282 | ||||||||
\(852\) | 0.514453 | 0.0176249 | ||||||||
\(853\) | 5.30394 | 0.181603 | 0.0908017 | − | 0.995869i | \(-0.471057\pi\) | ||||
0.0908017 | + | 0.995869i | \(0.471057\pi\) | |||||||
\(854\) | −5.38956 | −0.184427 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.9237 | 0.544259 | ||||||||
\(857\) | 19.6579 | 0.671501 | 0.335750 | − | 0.941951i | \(-0.391010\pi\) | ||||
0.335750 | + | 0.941951i | \(0.391010\pi\) | |||||||
\(858\) | 27.3618 | 0.934115 | ||||||||
\(859\) | 57.7524 | 1.97049 | 0.985244 | − | 0.171159i | \(-0.0547510\pi\) | ||||
0.985244 | + | 0.171159i | \(0.0547510\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.751312 | 0.0256047 | ||||||||
\(862\) | 7.37102 | 0.251058 | ||||||||
\(863\) | 27.3328 | 0.930421 | 0.465210 | − | 0.885200i | \(-0.345979\pi\) | ||||
0.465210 | + | 0.885200i | \(0.345979\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −19.3710 | −0.658254 | ||||||||
\(867\) | −0.961825 | −0.0326653 | ||||||||
\(868\) | −4.34212 | −0.147381 | ||||||||
\(869\) | −30.4092 | −1.03156 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −59.1631 | −2.00466 | ||||||||
\(872\) | 17.2670 | 0.584736 | ||||||||
\(873\) | −2.55263 | −0.0863934 | ||||||||
\(874\) | 4.96183 | 0.167836 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.447372 | −0.0151153 | ||||||||
\(877\) | −14.0000 | −0.472746 | −0.236373 | − | 0.971662i | \(-0.575959\pi\) | ||||
−0.236373 | + | 0.971662i | \(0.575959\pi\) | |||||||
\(878\) | 17.5052 | 0.590771 | ||||||||
\(879\) | 13.0289 | 0.439454 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.4474 | 0.655199 | 0.327599 | − | 0.944817i | \(-0.393760\pi\) | ||||
0.327599 | + | 0.944817i | \(0.393760\pi\) | |||||||
\(882\) | −6.47628 | −0.218068 | ||||||||
\(883\) | 34.2854 | 1.15380 | 0.576898 | − | 0.816816i | \(-0.304263\pi\) | ||||
0.576898 | + | 0.816816i | \(0.304263\pi\) | |||||||
\(884\) | 21.0289 | 0.707279 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 17.3710 | 0.583591 | ||||||||
\(887\) | 35.9433 | 1.20686 | 0.603429 | − | 0.797417i | \(-0.293801\pi\) | ||||
0.603429 | + | 0.797417i | \(0.293801\pi\) | |||||||
\(888\) | −4.23814 | −0.142223 | ||||||||
\(889\) | 9.37358 | 0.314380 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.51445 | 0.184741 | ||||||||
\(892\) | 25.2947 | 0.846928 | ||||||||
\(893\) | 39.5052 | 1.32199 | ||||||||
\(894\) | 5.92365 | 0.198117 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.723686 | −0.0241766 | ||||||||
\(897\) | 4.96183 | 0.165671 | ||||||||
\(898\) | −16.8947 | −0.563785 | ||||||||
\(899\) | −6.00000 | −0.200111 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −27.4474 | −0.914405 | ||||||||
\(902\) | 5.72497 | 0.190621 | ||||||||
\(903\) | 0.696059 | 0.0231634 | ||||||||
\(904\) | −6.23814 | −0.207477 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.47628 | −0.215160 | ||||||||
\(907\) | −34.0671 | −1.13118 | −0.565589 | − | 0.824687i | \(-0.691351\pi\) | ||||
−0.565589 | + | 0.824687i | \(0.691351\pi\) | |||||||
\(908\) | 7.13288 | 0.236713 | ||||||||
\(909\) | −1.06708 | −0.0353929 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.0671 | 0.532326 | 0.266163 | − | 0.963928i | \(-0.414244\pi\) | ||||
0.266163 | + | 0.963928i | \(0.414244\pi\) | |||||||
\(912\) | −4.96183 | −0.164302 | ||||||||
\(913\) | −34.0300 | −1.12623 | ||||||||
\(914\) | −21.9237 | −0.725170 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.58154 | −0.250501 | ||||||||
\(917\) | −8.38139 | −0.276778 | ||||||||
\(918\) | 4.23814 | 0.139879 | ||||||||
\(919\) | −19.7619 | −0.651884 | −0.325942 | − | 0.945390i | \(-0.605681\pi\) | ||||
−0.325942 | + | 0.945390i | \(0.605681\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 27.0671 | 0.891891 | ||||||||
\(922\) | −2.65788 | −0.0875328 | ||||||||
\(923\) | 2.55263 | 0.0840208 | ||||||||
\(924\) | 3.99073 | 0.131285 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 12.0000 | 0.394344 | ||||||||
\(927\) | 5.75259 | 0.188940 | ||||||||
\(928\) | −1.00000 | −0.0328266 | ||||||||
\(929\) | −6.33285 | −0.207774 | −0.103887 | − | 0.994589i | \(-0.533128\pi\) | ||||
−0.103887 | + | 0.994589i | \(0.533128\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.1342 | −1.05315 | ||||||||
\(932\) | 24.8855 | 0.815151 | ||||||||
\(933\) | 31.4670 | 1.03018 | ||||||||
\(934\) | 15.8289 | 0.517939 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.96183 | −0.162182 | ||||||||
\(937\) | −25.8473 | −0.844395 | −0.422197 | − | 0.906504i | \(-0.638741\pi\) | ||||
−0.422197 | + | 0.906504i | \(0.638741\pi\) | |||||||
\(938\) | −8.62898 | −0.281746 | ||||||||
\(939\) | 27.2947 | 0.890728 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.04744 | −0.294938 | −0.147469 | − | 0.989067i | \(-0.547113\pi\) | ||||
−0.147469 | + | 0.989067i | \(0.547113\pi\) | |||||||
\(942\) | −9.37102 | −0.305324 | ||||||||
\(943\) | 1.03817 | 0.0338076 | ||||||||
\(944\) | −9.02891 | −0.293866 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.30394 | 0.172446 | ||||||||
\(947\) | −0.971093 | −0.0315563 | −0.0157781 | − | 0.999876i | \(-0.505023\pi\) | ||||
−0.0157781 | + | 0.999876i | \(0.505023\pi\) | |||||||
\(948\) | 5.51445 | 0.179101 | ||||||||
\(949\) | −2.21978 | −0.0720571 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.0000 | −0.356699 | ||||||||
\(952\) | 3.06708 | 0.0994047 | ||||||||
\(953\) | −5.19070 | −0.168143 | −0.0840716 | − | 0.996460i | \(-0.526792\pi\) | ||||
−0.0840716 | + | 0.996460i | \(0.526792\pi\) | |||||||
\(954\) | 6.47628 | 0.209677 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −18.0960 | −0.585266 | ||||||||
\(957\) | 5.51445 | 0.178257 | ||||||||
\(958\) | 27.5723 | 0.890820 | ||||||||
\(959\) | −16.0934 | −0.519684 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | −21.0289 | −0.677999 | ||||||||
\(963\) | 15.9237 | 0.513132 | ||||||||
\(964\) | 26.8762 | 0.865624 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.723686 | 0.0232842 | ||||||||
\(967\) | −17.0289 | −0.547613 | −0.273806 | − | 0.961785i | \(-0.588283\pi\) | ||||
−0.273806 | + | 0.961785i | \(0.588283\pi\) | |||||||
\(968\) | 19.4092 | 0.623835 | ||||||||
\(969\) | 21.0289 | 0.675546 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.4683 | −0.817316 | −0.408658 | − | 0.912688i | \(-0.634003\pi\) | ||||
−0.408658 | + | 0.912688i | \(0.634003\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −13.7433 | −0.440591 | ||||||||
\(974\) | −16.6868 | −0.534679 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.44737 | 0.238385 | ||||||||
\(977\) | 23.9513 | 0.766269 | 0.383135 | − | 0.923693i | \(-0.374845\pi\) | ||||
0.383135 | + | 0.923693i | \(0.374845\pi\) | |||||||
\(978\) | 13.9237 | 0.445229 | ||||||||
\(979\) | −12.3421 | −0.394456 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.2670 | 0.551294 | ||||||||
\(982\) | −13.4288 | −0.428531 | ||||||||
\(983\) | −13.5723 | −0.432888 | −0.216444 | − | 0.976295i | \(-0.569446\pi\) | ||||
−0.216444 | + | 0.976295i | \(0.569446\pi\) | |||||||
\(984\) | −1.03817 | −0.0330958 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4.23814 | 0.134970 | ||||||||
\(987\) | 5.76186 | 0.183402 | ||||||||
\(988\) | −24.6197 | −0.783257 | ||||||||
\(989\) | 0.961825 | 0.0305843 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.9237 | 0.823492 | 0.411746 | − | 0.911299i | \(-0.364919\pi\) | ||||
0.411746 | + | 0.911299i | \(0.364919\pi\) | |||||||
\(992\) | 6.00000 | 0.190500 | ||||||||
\(993\) | 8.51445 | 0.270198 | ||||||||
\(994\) | 0.372303 | 0.0118087 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.17106 | 0.195537 | ||||||||
\(997\) | 2.06708 | 0.0654651 | 0.0327326 | − | 0.999464i | \(-0.489579\pi\) | ||||
0.0327326 | + | 0.999464i | \(0.489579\pi\) | |||||||
\(998\) | −8.99073 | −0.284597 | ||||||||
\(999\) | −4.23814 | −0.134089 |
(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 | 3450.2.a.bs.1.2 | yes | 3 | |
5.2 | odd | 4 | 3450.2.d.ba.2899.5 | 6 | |||
5.3 | odd | 4 | 3450.2.d.ba.2899.2 | 6 | |||
5.4 | even | 2 | 3450.2.a.bp.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3450.2.a.bp.1.2 | ✓ | 3 | 5.4 | even | 2 | ||
3450.2.a.bs.1.2 | yes | 3 | 1.1 | even | 1 | trivial | |
3450.2.d.ba.2899.2 | 6 | 5.3 | odd | 4 | |||
3450.2.d.ba.2899.5 | 6 | 5.2 | odd | 4 |