Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6018,2,Mod(1,6018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6018, 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("6018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6018.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.0539719364\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 21x^{7} + 42x^{6} + 121x^{5} - 127x^{4} - 141x^{3} + 27x^{2} + 26x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.460972\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6018.1 |
$q$-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 | ||||||||
\(5\) | 0.539028 | 0.241060 | 0.120530 | − | 0.992710i | \(-0.461541\pi\) | ||||
0.120530 | + | 0.992710i | \(0.461541\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0.211506 | 0.0799418 | 0.0399709 | − | 0.999201i | \(-0.487273\pi\) | ||||
0.0399709 | + | 0.999201i | \(0.487273\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.539028 | −0.170455 | ||||||||
\(11\) | −0.438866 | −0.132323 | −0.0661615 | − | 0.997809i | \(-0.521075\pi\) | ||||
−0.0661615 | + | 0.997809i | \(0.521075\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −2.12175 | −0.588468 | −0.294234 | − | 0.955733i | \(-0.595064\pi\) | ||||
−0.294234 | + | 0.955733i | \(0.595064\pi\) | |||||||
\(14\) | −0.211506 | −0.0565274 | ||||||||
\(15\) | −0.539028 | −0.139176 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 1.46680 | 0.336507 | 0.168254 | − | 0.985744i | \(-0.446187\pi\) | ||||
0.168254 | + | 0.985744i | \(0.446187\pi\) | |||||||
\(20\) | 0.539028 | 0.120530 | ||||||||
\(21\) | −0.211506 | −0.0461544 | ||||||||
\(22\) | 0.438866 | 0.0935665 | ||||||||
\(23\) | 5.56633 | 1.16066 | 0.580330 | − | 0.814381i | \(-0.302924\pi\) | ||||
0.580330 | + | 0.814381i | \(0.302924\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.70945 | −0.941890 | ||||||||
\(26\) | 2.12175 | 0.416110 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.211506 | 0.0399709 | ||||||||
\(29\) | −4.54548 | −0.844074 | −0.422037 | − | 0.906578i | \(-0.638685\pi\) | ||||
−0.422037 | + | 0.906578i | \(0.638685\pi\) | |||||||
\(30\) | 0.539028 | 0.0984125 | ||||||||
\(31\) | 4.41902 | 0.793679 | 0.396839 | − | 0.917888i | \(-0.370107\pi\) | ||||
0.396839 | + | 0.917888i | \(0.370107\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.438866 | 0.0763967 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | 0.114008 | 0.0192708 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 6.05133 | 0.994832 | 0.497416 | − | 0.867512i | \(-0.334282\pi\) | ||||
0.497416 | + | 0.867512i | \(0.334282\pi\) | |||||||
\(38\) | −1.46680 | −0.237946 | ||||||||
\(39\) | 2.12175 | 0.339752 | ||||||||
\(40\) | −0.539028 | −0.0852277 | ||||||||
\(41\) | 3.13941 | 0.490293 | 0.245146 | − | 0.969486i | \(-0.421164\pi\) | ||||
0.245146 | + | 0.969486i | \(0.421164\pi\) | |||||||
\(42\) | 0.211506 | 0.0326361 | ||||||||
\(43\) | −12.5429 | −1.91277 | −0.956385 | − | 0.292110i | \(-0.905643\pi\) | ||||
−0.956385 | + | 0.292110i | \(0.905643\pi\) | |||||||
\(44\) | −0.438866 | −0.0661615 | ||||||||
\(45\) | 0.539028 | 0.0803535 | ||||||||
\(46\) | −5.56633 | −0.820711 | ||||||||
\(47\) | −3.68645 | −0.537724 | −0.268862 | − | 0.963179i | \(-0.586648\pi\) | ||||
−0.268862 | + | 0.963179i | \(0.586648\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.95527 | −0.993609 | ||||||||
\(50\) | 4.70945 | 0.666017 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −2.12175 | −0.294234 | ||||||||
\(53\) | 3.44950 | 0.473826 | 0.236913 | − | 0.971531i | \(-0.423864\pi\) | ||||
0.236913 | + | 0.971531i | \(0.423864\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −0.236561 | −0.0318978 | ||||||||
\(56\) | −0.211506 | −0.0282637 | ||||||||
\(57\) | −1.46680 | −0.194282 | ||||||||
\(58\) | 4.54548 | 0.596851 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | −0.539028 | −0.0695882 | ||||||||
\(61\) | 7.40497 | 0.948109 | 0.474055 | − | 0.880495i | \(-0.342790\pi\) | ||||
0.474055 | + | 0.880495i | \(0.342790\pi\) | |||||||
\(62\) | −4.41902 | −0.561216 | ||||||||
\(63\) | 0.211506 | 0.0266473 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.14368 | −0.141856 | ||||||||
\(66\) | −0.438866 | −0.0540206 | ||||||||
\(67\) | −5.96072 | −0.728217 | −0.364109 | − | 0.931356i | \(-0.618626\pi\) | ||||
−0.364109 | + | 0.931356i | \(0.618626\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | −5.56633 | −0.670107 | ||||||||
\(70\) | −0.114008 | −0.0136265 | ||||||||
\(71\) | 16.5135 | 1.95979 | 0.979893 | − | 0.199524i | \(-0.0639394\pi\) | ||||
0.979893 | + | 0.199524i | \(0.0639394\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 15.6717 | 1.83423 | 0.917117 | − | 0.398617i | \(-0.130510\pi\) | ||||
0.917117 | + | 0.398617i | \(0.130510\pi\) | |||||||
\(74\) | −6.05133 | −0.703452 | ||||||||
\(75\) | 4.70945 | 0.543800 | ||||||||
\(76\) | 1.46680 | 0.168254 | ||||||||
\(77\) | −0.0928228 | −0.0105781 | ||||||||
\(78\) | −2.12175 | −0.240241 | ||||||||
\(79\) | −1.40882 | −0.158505 | −0.0792525 | − | 0.996855i | \(-0.525253\pi\) | ||||
−0.0792525 | + | 0.996855i | \(0.525253\pi\) | |||||||
\(80\) | 0.539028 | 0.0602651 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.13941 | −0.346689 | ||||||||
\(83\) | −5.92017 | −0.649824 | −0.324912 | − | 0.945744i | \(-0.605335\pi\) | ||||
−0.324912 | + | 0.945744i | \(0.605335\pi\) | |||||||
\(84\) | −0.211506 | −0.0230772 | ||||||||
\(85\) | −0.539028 | −0.0584658 | ||||||||
\(86\) | 12.5429 | 1.35253 | ||||||||
\(87\) | 4.54548 | 0.487327 | ||||||||
\(88\) | 0.438866 | 0.0467832 | ||||||||
\(89\) | −16.8839 | −1.78969 | −0.894844 | − | 0.446378i | \(-0.852714\pi\) | ||||
−0.894844 | + | 0.446378i | \(0.852714\pi\) | |||||||
\(90\) | −0.539028 | −0.0568185 | ||||||||
\(91\) | −0.448764 | −0.0470432 | ||||||||
\(92\) | 5.56633 | 0.580330 | ||||||||
\(93\) | −4.41902 | −0.458231 | ||||||||
\(94\) | 3.68645 | 0.380229 | ||||||||
\(95\) | 0.790646 | 0.0811185 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −12.8379 | −1.30349 | −0.651744 | − | 0.758439i | \(-0.725962\pi\) | ||||
−0.651744 | + | 0.758439i | \(0.725962\pi\) | |||||||
\(98\) | 6.95527 | 0.702588 | ||||||||
\(99\) | −0.438866 | −0.0441077 | ||||||||
\(100\) | −4.70945 | −0.470945 | ||||||||
\(101\) | 7.75113 | 0.771266 | 0.385633 | − | 0.922652i | \(-0.373983\pi\) | ||||
0.385633 | + | 0.922652i | \(0.373983\pi\) | |||||||
\(102\) | −1.00000 | −0.0990148 | ||||||||
\(103\) | −16.0367 | −1.58015 | −0.790073 | − | 0.613013i | \(-0.789957\pi\) | ||||
−0.790073 | + | 0.613013i | \(0.789957\pi\) | |||||||
\(104\) | 2.12175 | 0.208055 | ||||||||
\(105\) | −0.114008 | −0.0111260 | ||||||||
\(106\) | −3.44950 | −0.335045 | ||||||||
\(107\) | −1.24872 | −0.120718 | −0.0603591 | − | 0.998177i | \(-0.519225\pi\) | ||||
−0.0603591 | + | 0.998177i | \(0.519225\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −6.85017 | −0.656128 | −0.328064 | − | 0.944656i | \(-0.606396\pi\) | ||||
−0.328064 | + | 0.944656i | \(0.606396\pi\) | |||||||
\(110\) | 0.236561 | 0.0225552 | ||||||||
\(111\) | −6.05133 | −0.574366 | ||||||||
\(112\) | 0.211506 | 0.0199855 | ||||||||
\(113\) | −9.66703 | −0.909397 | −0.454699 | − | 0.890645i | \(-0.650253\pi\) | ||||
−0.454699 | + | 0.890645i | \(0.650253\pi\) | |||||||
\(114\) | 1.46680 | 0.137378 | ||||||||
\(115\) | 3.00041 | 0.279789 | ||||||||
\(116\) | −4.54548 | −0.422037 | ||||||||
\(117\) | −2.12175 | −0.196156 | ||||||||
\(118\) | 1.00000 | 0.0920575 | ||||||||
\(119\) | −0.211506 | −0.0193887 | ||||||||
\(120\) | 0.539028 | 0.0492063 | ||||||||
\(121\) | −10.8074 | −0.982491 | ||||||||
\(122\) | −7.40497 | −0.670414 | ||||||||
\(123\) | −3.13941 | −0.283071 | ||||||||
\(124\) | 4.41902 | 0.396839 | ||||||||
\(125\) | −5.23366 | −0.468113 | ||||||||
\(126\) | −0.211506 | −0.0188425 | ||||||||
\(127\) | 6.20893 | 0.550954 | 0.275477 | − | 0.961308i | \(-0.411164\pi\) | ||||
0.275477 | + | 0.961308i | \(0.411164\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 12.5429 | 1.10434 | ||||||||
\(130\) | 1.14368 | 0.100308 | ||||||||
\(131\) | 12.9595 | 1.13228 | 0.566139 | − | 0.824310i | \(-0.308437\pi\) | ||||
0.566139 | + | 0.824310i | \(0.308437\pi\) | |||||||
\(132\) | 0.438866 | 0.0381983 | ||||||||
\(133\) | 0.310237 | 0.0269010 | ||||||||
\(134\) | 5.96072 | 0.514928 | ||||||||
\(135\) | −0.539028 | −0.0463921 | ||||||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | −1.07309 | −0.0916802 | −0.0458401 | − | 0.998949i | \(-0.514596\pi\) | ||||
−0.0458401 | + | 0.998949i | \(0.514596\pi\) | |||||||
\(138\) | 5.56633 | 0.473838 | ||||||||
\(139\) | −22.5370 | −1.91157 | −0.955783 | − | 0.294071i | \(-0.904990\pi\) | ||||
−0.955783 | + | 0.294071i | \(0.904990\pi\) | |||||||
\(140\) | 0.114008 | 0.00963541 | ||||||||
\(141\) | 3.68645 | 0.310455 | ||||||||
\(142\) | −16.5135 | −1.38578 | ||||||||
\(143\) | 0.931164 | 0.0778678 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −2.45014 | −0.203473 | ||||||||
\(146\) | −15.6717 | −1.29700 | ||||||||
\(147\) | 6.95527 | 0.573661 | ||||||||
\(148\) | 6.05133 | 0.497416 | ||||||||
\(149\) | 5.69941 | 0.466914 | 0.233457 | − | 0.972367i | \(-0.424996\pi\) | ||||
0.233457 | + | 0.972367i | \(0.424996\pi\) | |||||||
\(150\) | −4.70945 | −0.384525 | ||||||||
\(151\) | −8.91010 | −0.725094 | −0.362547 | − | 0.931966i | \(-0.618093\pi\) | ||||
−0.362547 | + | 0.931966i | \(0.618093\pi\) | |||||||
\(152\) | −1.46680 | −0.118973 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 0.0928228 | 0.00747988 | ||||||||
\(155\) | 2.38197 | 0.191325 | ||||||||
\(156\) | 2.12175 | 0.169876 | ||||||||
\(157\) | 13.2021 | 1.05364 | 0.526820 | − | 0.849977i | \(-0.323384\pi\) | ||||
0.526820 | + | 0.849977i | \(0.323384\pi\) | |||||||
\(158\) | 1.40882 | 0.112080 | ||||||||
\(159\) | −3.44950 | −0.273563 | ||||||||
\(160\) | −0.539028 | −0.0426139 | ||||||||
\(161\) | 1.17731 | 0.0927853 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 9.32418 | 0.730326 | 0.365163 | − | 0.930944i | \(-0.381013\pi\) | ||||
0.365163 | + | 0.930944i | \(0.381013\pi\) | |||||||
\(164\) | 3.13941 | 0.245146 | ||||||||
\(165\) | 0.236561 | 0.0184162 | ||||||||
\(166\) | 5.92017 | 0.459495 | ||||||||
\(167\) | −1.79156 | −0.138635 | −0.0693174 | − | 0.997595i | \(-0.522082\pi\) | ||||
−0.0693174 | + | 0.997595i | \(0.522082\pi\) | |||||||
\(168\) | 0.211506 | 0.0163181 | ||||||||
\(169\) | −8.49817 | −0.653705 | ||||||||
\(170\) | 0.539028 | 0.0413415 | ||||||||
\(171\) | 1.46680 | 0.112169 | ||||||||
\(172\) | −12.5429 | −0.956385 | ||||||||
\(173\) | 17.3103 | 1.31608 | 0.658041 | − | 0.752982i | \(-0.271386\pi\) | ||||
0.658041 | + | 0.752982i | \(0.271386\pi\) | |||||||
\(174\) | −4.54548 | −0.344592 | ||||||||
\(175\) | −0.996078 | −0.0752964 | ||||||||
\(176\) | −0.438866 | −0.0330807 | ||||||||
\(177\) | 1.00000 | 0.0751646 | ||||||||
\(178\) | 16.8839 | 1.26550 | ||||||||
\(179\) | 13.2098 | 0.987344 | 0.493672 | − | 0.869648i | \(-0.335654\pi\) | ||||
0.493672 | + | 0.869648i | \(0.335654\pi\) | |||||||
\(180\) | 0.539028 | 0.0401767 | ||||||||
\(181\) | 10.1745 | 0.756263 | 0.378131 | − | 0.925752i | \(-0.376567\pi\) | ||||
0.378131 | + | 0.925752i | \(0.376567\pi\) | |||||||
\(182\) | 0.448764 | 0.0332646 | ||||||||
\(183\) | −7.40497 | −0.547391 | ||||||||
\(184\) | −5.56633 | −0.410355 | ||||||||
\(185\) | 3.26183 | 0.239815 | ||||||||
\(186\) | 4.41902 | 0.324018 | ||||||||
\(187\) | 0.438866 | 0.0320930 | ||||||||
\(188\) | −3.68645 | −0.268862 | ||||||||
\(189\) | −0.211506 | −0.0153848 | ||||||||
\(190\) | −0.790646 | −0.0573595 | ||||||||
\(191\) | −6.41217 | −0.463968 | −0.231984 | − | 0.972720i | \(-0.574522\pi\) | ||||
−0.231984 | + | 0.972720i | \(0.574522\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −7.78514 | −0.560387 | −0.280193 | − | 0.959944i | \(-0.590399\pi\) | ||||
−0.280193 | + | 0.959944i | \(0.590399\pi\) | |||||||
\(194\) | 12.8379 | 0.921705 | ||||||||
\(195\) | 1.14368 | 0.0819008 | ||||||||
\(196\) | −6.95527 | −0.496805 | ||||||||
\(197\) | 3.71958 | 0.265009 | 0.132504 | − | 0.991182i | \(-0.457698\pi\) | ||||
0.132504 | + | 0.991182i | \(0.457698\pi\) | |||||||
\(198\) | 0.438866 | 0.0311888 | ||||||||
\(199\) | 13.4826 | 0.955757 | 0.477879 | − | 0.878426i | \(-0.341406\pi\) | ||||
0.477879 | + | 0.878426i | \(0.341406\pi\) | |||||||
\(200\) | 4.70945 | 0.333008 | ||||||||
\(201\) | 5.96072 | 0.420437 | ||||||||
\(202\) | −7.75113 | −0.545367 | ||||||||
\(203\) | −0.961397 | −0.0674769 | ||||||||
\(204\) | 1.00000 | 0.0700140 | ||||||||
\(205\) | 1.69223 | 0.118190 | ||||||||
\(206\) | 16.0367 | 1.11733 | ||||||||
\(207\) | 5.56633 | 0.386887 | ||||||||
\(208\) | −2.12175 | −0.147117 | ||||||||
\(209\) | −0.643728 | −0.0445276 | ||||||||
\(210\) | 0.114008 | 0.00786728 | ||||||||
\(211\) | 17.8998 | 1.23227 | 0.616136 | − | 0.787639i | \(-0.288697\pi\) | ||||
0.616136 | + | 0.787639i | \(0.288697\pi\) | |||||||
\(212\) | 3.44950 | 0.236913 | ||||||||
\(213\) | −16.5135 | −1.13148 | ||||||||
\(214\) | 1.24872 | 0.0853607 | ||||||||
\(215\) | −6.76095 | −0.461093 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0.934649 | 0.0634481 | ||||||||
\(218\) | 6.85017 | 0.463952 | ||||||||
\(219\) | −15.6717 | −1.05900 | ||||||||
\(220\) | −0.236561 | −0.0159489 | ||||||||
\(221\) | 2.12175 | 0.142724 | ||||||||
\(222\) | 6.05133 | 0.406138 | ||||||||
\(223\) | −16.7755 | −1.12337 | −0.561684 | − | 0.827352i | \(-0.689846\pi\) | ||||
−0.561684 | + | 0.827352i | \(0.689846\pi\) | |||||||
\(224\) | −0.211506 | −0.0141319 | ||||||||
\(225\) | −4.70945 | −0.313963 | ||||||||
\(226\) | 9.66703 | 0.643041 | ||||||||
\(227\) | −17.1186 | −1.13620 | −0.568100 | − | 0.822960i | \(-0.692321\pi\) | ||||
−0.568100 | + | 0.822960i | \(0.692321\pi\) | |||||||
\(228\) | −1.46680 | −0.0971412 | ||||||||
\(229\) | −13.1200 | −0.866993 | −0.433496 | − | 0.901155i | \(-0.642720\pi\) | ||||
−0.433496 | + | 0.901155i | \(0.642720\pi\) | |||||||
\(230\) | −3.00041 | −0.197841 | ||||||||
\(231\) | 0.0928228 | 0.00610729 | ||||||||
\(232\) | 4.54548 | 0.298425 | ||||||||
\(233\) | −4.42173 | −0.289677 | −0.144839 | − | 0.989455i | \(-0.546266\pi\) | ||||
−0.144839 | + | 0.989455i | \(0.546266\pi\) | |||||||
\(234\) | 2.12175 | 0.138703 | ||||||||
\(235\) | −1.98710 | −0.129624 | ||||||||
\(236\) | −1.00000 | −0.0650945 | ||||||||
\(237\) | 1.40882 | 0.0915129 | ||||||||
\(238\) | 0.211506 | 0.0137099 | ||||||||
\(239\) | −2.99710 | −0.193866 | −0.0969331 | − | 0.995291i | \(-0.530903\pi\) | ||||
−0.0969331 | + | 0.995291i | \(0.530903\pi\) | |||||||
\(240\) | −0.539028 | −0.0347941 | ||||||||
\(241\) | −9.85479 | −0.634803 | −0.317401 | − | 0.948291i | \(-0.602810\pi\) | ||||
−0.317401 | + | 0.948291i | \(0.602810\pi\) | |||||||
\(242\) | 10.8074 | 0.694726 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 7.40497 | 0.474055 | ||||||||
\(245\) | −3.74908 | −0.239520 | ||||||||
\(246\) | 3.13941 | 0.200161 | ||||||||
\(247\) | −3.11219 | −0.198024 | ||||||||
\(248\) | −4.41902 | −0.280608 | ||||||||
\(249\) | 5.92017 | 0.375176 | ||||||||
\(250\) | 5.23366 | 0.331006 | ||||||||
\(251\) | 4.23635 | 0.267396 | 0.133698 | − | 0.991022i | \(-0.457315\pi\) | ||||
0.133698 | + | 0.991022i | \(0.457315\pi\) | |||||||
\(252\) | 0.211506 | 0.0133236 | ||||||||
\(253\) | −2.44287 | −0.153582 | ||||||||
\(254\) | −6.20893 | −0.389583 | ||||||||
\(255\) | 0.539028 | 0.0337552 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −21.3977 | −1.33475 | −0.667377 | − | 0.744720i | \(-0.732583\pi\) | ||||
−0.667377 | + | 0.744720i | \(0.732583\pi\) | |||||||
\(258\) | −12.5429 | −0.780885 | ||||||||
\(259\) | 1.27989 | 0.0795287 | ||||||||
\(260\) | −1.14368 | −0.0709282 | ||||||||
\(261\) | −4.54548 | −0.281358 | ||||||||
\(262\) | −12.9595 | −0.800641 | ||||||||
\(263\) | 18.4208 | 1.13588 | 0.567938 | − | 0.823071i | \(-0.307741\pi\) | ||||
0.567938 | + | 0.823071i | \(0.307741\pi\) | |||||||
\(264\) | −0.438866 | −0.0270103 | ||||||||
\(265\) | 1.85938 | 0.114221 | ||||||||
\(266\) | −0.310237 | −0.0190219 | ||||||||
\(267\) | 16.8839 | 1.03328 | ||||||||
\(268\) | −5.96072 | −0.364109 | ||||||||
\(269\) | 15.2337 | 0.928817 | 0.464409 | − | 0.885621i | \(-0.346267\pi\) | ||||
0.464409 | + | 0.885621i | \(0.346267\pi\) | |||||||
\(270\) | 0.539028 | 0.0328042 | ||||||||
\(271\) | 11.5622 | 0.702353 | 0.351177 | − | 0.936309i | \(-0.385782\pi\) | ||||
0.351177 | + | 0.936309i | \(0.385782\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | 0.448764 | 0.0271604 | ||||||||
\(274\) | 1.07309 | 0.0648277 | ||||||||
\(275\) | 2.06682 | 0.124634 | ||||||||
\(276\) | −5.56633 | −0.335054 | ||||||||
\(277\) | −3.45542 | −0.207616 | −0.103808 | − | 0.994597i | \(-0.533103\pi\) | ||||
−0.103808 | + | 0.994597i | \(0.533103\pi\) | |||||||
\(278\) | 22.5370 | 1.35168 | ||||||||
\(279\) | 4.41902 | 0.264560 | ||||||||
\(280\) | −0.114008 | −0.00681326 | ||||||||
\(281\) | −20.8551 | −1.24411 | −0.622055 | − | 0.782973i | \(-0.713702\pi\) | ||||
−0.622055 | + | 0.782973i | \(0.713702\pi\) | |||||||
\(282\) | −3.68645 | −0.219525 | ||||||||
\(283\) | −23.9561 | −1.42404 | −0.712021 | − | 0.702158i | \(-0.752220\pi\) | ||||
−0.712021 | + | 0.702158i | \(0.752220\pi\) | |||||||
\(284\) | 16.5135 | 0.979893 | ||||||||
\(285\) | −0.790646 | −0.0468338 | ||||||||
\(286\) | −0.931164 | −0.0550609 | ||||||||
\(287\) | 0.664004 | 0.0391949 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 2.45014 | 0.143877 | ||||||||
\(291\) | 12.8379 | 0.752569 | ||||||||
\(292\) | 15.6717 | 0.917117 | ||||||||
\(293\) | 13.9518 | 0.815074 | 0.407537 | − | 0.913189i | \(-0.366388\pi\) | ||||
0.407537 | + | 0.913189i | \(0.366388\pi\) | |||||||
\(294\) | −6.95527 | −0.405639 | ||||||||
\(295\) | −0.539028 | −0.0313834 | ||||||||
\(296\) | −6.05133 | −0.351726 | ||||||||
\(297\) | 0.438866 | 0.0254656 | ||||||||
\(298\) | −5.69941 | −0.330158 | ||||||||
\(299\) | −11.8104 | −0.683011 | ||||||||
\(300\) | 4.70945 | 0.271900 | ||||||||
\(301\) | −2.65289 | −0.152910 | ||||||||
\(302\) | 8.91010 | 0.512719 | ||||||||
\(303\) | −7.75113 | −0.445291 | ||||||||
\(304\) | 1.46680 | 0.0841268 | ||||||||
\(305\) | 3.99148 | 0.228552 | ||||||||
\(306\) | 1.00000 | 0.0571662 | ||||||||
\(307\) | −26.2365 | −1.49740 | −0.748698 | − | 0.662911i | \(-0.769321\pi\) | ||||
−0.748698 | + | 0.662911i | \(0.769321\pi\) | |||||||
\(308\) | −0.0928228 | −0.00528907 | ||||||||
\(309\) | 16.0367 | 0.912297 | ||||||||
\(310\) | −2.38197 | −0.135287 | ||||||||
\(311\) | −18.3831 | −1.04241 | −0.521205 | − | 0.853432i | \(-0.674517\pi\) | ||||
−0.521205 | + | 0.853432i | \(0.674517\pi\) | |||||||
\(312\) | −2.12175 | −0.120121 | ||||||||
\(313\) | −33.8390 | −1.91269 | −0.956345 | − | 0.292239i | \(-0.905600\pi\) | ||||
−0.956345 | + | 0.292239i | \(0.905600\pi\) | |||||||
\(314\) | −13.2021 | −0.745036 | ||||||||
\(315\) | 0.114008 | 0.00642361 | ||||||||
\(316\) | −1.40882 | −0.0792525 | ||||||||
\(317\) | 6.55955 | 0.368421 | 0.184211 | − | 0.982887i | \(-0.441027\pi\) | ||||
0.184211 | + | 0.982887i | \(0.441027\pi\) | |||||||
\(318\) | 3.44950 | 0.193439 | ||||||||
\(319\) | 1.99485 | 0.111690 | ||||||||
\(320\) | 0.539028 | 0.0301326 | ||||||||
\(321\) | 1.24872 | 0.0696967 | ||||||||
\(322\) | −1.17731 | −0.0656091 | ||||||||
\(323\) | −1.46680 | −0.0816149 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 9.99228 | 0.554272 | ||||||||
\(326\) | −9.32418 | −0.516419 | ||||||||
\(327\) | 6.85017 | 0.378816 | ||||||||
\(328\) | −3.13941 | −0.173345 | ||||||||
\(329\) | −0.779708 | −0.0429867 | ||||||||
\(330\) | −0.236561 | −0.0130222 | ||||||||
\(331\) | 6.13447 | 0.337181 | 0.168590 | − | 0.985686i | \(-0.446078\pi\) | ||||
0.168590 | + | 0.985686i | \(0.446078\pi\) | |||||||
\(332\) | −5.92017 | −0.324912 | ||||||||
\(333\) | 6.05133 | 0.331611 | ||||||||
\(334\) | 1.79156 | 0.0980296 | ||||||||
\(335\) | −3.21299 | −0.175544 | ||||||||
\(336\) | −0.211506 | −0.0115386 | ||||||||
\(337\) | −0.735362 | −0.0400577 | −0.0200289 | − | 0.999799i | \(-0.506376\pi\) | ||||
−0.0200289 | + | 0.999799i | \(0.506376\pi\) | |||||||
\(338\) | 8.49817 | 0.462240 | ||||||||
\(339\) | 9.66703 | 0.525041 | ||||||||
\(340\) | −0.539028 | −0.0292329 | ||||||||
\(341\) | −1.93935 | −0.105022 | ||||||||
\(342\) | −1.46680 | −0.0793155 | ||||||||
\(343\) | −2.95163 | −0.159373 | ||||||||
\(344\) | 12.5429 | 0.676266 | ||||||||
\(345\) | −3.00041 | −0.161536 | ||||||||
\(346\) | −17.3103 | −0.930610 | ||||||||
\(347\) | −22.3832 | −1.20159 | −0.600796 | − | 0.799403i | \(-0.705149\pi\) | ||||
−0.600796 | + | 0.799403i | \(0.705149\pi\) | |||||||
\(348\) | 4.54548 | 0.243663 | ||||||||
\(349\) | 23.9783 | 1.28353 | 0.641765 | − | 0.766901i | \(-0.278202\pi\) | ||||
0.641765 | + | 0.766901i | \(0.278202\pi\) | |||||||
\(350\) | 0.996078 | 0.0532426 | ||||||||
\(351\) | 2.12175 | 0.113251 | ||||||||
\(352\) | 0.438866 | 0.0233916 | ||||||||
\(353\) | 33.9101 | 1.80485 | 0.902425 | − | 0.430847i | \(-0.141785\pi\) | ||||
0.902425 | + | 0.430847i | \(0.141785\pi\) | |||||||
\(354\) | −1.00000 | −0.0531494 | ||||||||
\(355\) | 8.90121 | 0.472427 | ||||||||
\(356\) | −16.8839 | −0.894844 | ||||||||
\(357\) | 0.211506 | 0.0111941 | ||||||||
\(358\) | −13.2098 | −0.698157 | ||||||||
\(359\) | −4.45057 | −0.234892 | −0.117446 | − | 0.993079i | \(-0.537471\pi\) | ||||
−0.117446 | + | 0.993079i | \(0.537471\pi\) | |||||||
\(360\) | −0.539028 | −0.0284092 | ||||||||
\(361\) | −16.8485 | −0.886763 | ||||||||
\(362\) | −10.1745 | −0.534759 | ||||||||
\(363\) | 10.8074 | 0.567241 | ||||||||
\(364\) | −0.448764 | −0.0235216 | ||||||||
\(365\) | 8.44748 | 0.442161 | ||||||||
\(366\) | 7.40497 | 0.387064 | ||||||||
\(367\) | −34.7031 | −1.81149 | −0.905744 | − | 0.423825i | \(-0.860687\pi\) | ||||
−0.905744 | + | 0.423825i | \(0.860687\pi\) | |||||||
\(368\) | 5.56633 | 0.290165 | ||||||||
\(369\) | 3.13941 | 0.163431 | ||||||||
\(370\) | −3.26183 | −0.169575 | ||||||||
\(371\) | 0.729591 | 0.0378785 | ||||||||
\(372\) | −4.41902 | −0.229115 | ||||||||
\(373\) | −20.2021 | −1.04602 | −0.523012 | − | 0.852325i | \(-0.675192\pi\) | ||||
−0.523012 | + | 0.852325i | \(0.675192\pi\) | |||||||
\(374\) | −0.438866 | −0.0226932 | ||||||||
\(375\) | 5.23366 | 0.270265 | ||||||||
\(376\) | 3.68645 | 0.190114 | ||||||||
\(377\) | 9.64438 | 0.496711 | ||||||||
\(378\) | 0.211506 | 0.0108787 | ||||||||
\(379\) | −23.6280 | −1.21369 | −0.606844 | − | 0.794821i | \(-0.707565\pi\) | ||||
−0.606844 | + | 0.794821i | \(0.707565\pi\) | |||||||
\(380\) | 0.790646 | 0.0405593 | ||||||||
\(381\) | −6.20893 | −0.318093 | ||||||||
\(382\) | 6.41217 | 0.328075 | ||||||||
\(383\) | 6.51425 | 0.332863 | 0.166431 | − | 0.986053i | \(-0.446776\pi\) | ||||
0.166431 | + | 0.986053i | \(0.446776\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −0.0500341 | −0.00254997 | ||||||||
\(386\) | 7.78514 | 0.396253 | ||||||||
\(387\) | −12.5429 | −0.637590 | ||||||||
\(388\) | −12.8379 | −0.651744 | ||||||||
\(389\) | 36.1981 | 1.83531 | 0.917657 | − | 0.397372i | \(-0.130078\pi\) | ||||
0.917657 | + | 0.397372i | \(0.130078\pi\) | |||||||
\(390\) | −1.14368 | −0.0579126 | ||||||||
\(391\) | −5.56633 | −0.281501 | ||||||||
\(392\) | 6.95527 | 0.351294 | ||||||||
\(393\) | −12.9595 | −0.653721 | ||||||||
\(394\) | −3.71958 | −0.187390 | ||||||||
\(395\) | −0.759394 | −0.0382093 | ||||||||
\(396\) | −0.438866 | −0.0220538 | ||||||||
\(397\) | 0.608826 | 0.0305561 | 0.0152781 | − | 0.999883i | \(-0.495137\pi\) | ||||
0.0152781 | + | 0.999883i | \(0.495137\pi\) | |||||||
\(398\) | −13.4826 | −0.675823 | ||||||||
\(399\) | −0.310237 | −0.0155313 | ||||||||
\(400\) | −4.70945 | −0.235472 | ||||||||
\(401\) | 1.93078 | 0.0964187 | 0.0482094 | − | 0.998837i | \(-0.484649\pi\) | ||||
0.0482094 | + | 0.998837i | \(0.484649\pi\) | |||||||
\(402\) | −5.96072 | −0.297294 | ||||||||
\(403\) | −9.37605 | −0.467054 | ||||||||
\(404\) | 7.75113 | 0.385633 | ||||||||
\(405\) | 0.539028 | 0.0267845 | ||||||||
\(406\) | 0.961397 | 0.0477134 | ||||||||
\(407\) | −2.65572 | −0.131639 | ||||||||
\(408\) | −1.00000 | −0.0495074 | ||||||||
\(409\) | 4.42657 | 0.218880 | 0.109440 | − | 0.993993i | \(-0.465094\pi\) | ||||
0.109440 | + | 0.993993i | \(0.465094\pi\) | |||||||
\(410\) | −1.69223 | −0.0835731 | ||||||||
\(411\) | 1.07309 | 0.0529316 | ||||||||
\(412\) | −16.0367 | −0.790073 | ||||||||
\(413\) | −0.211506 | −0.0104075 | ||||||||
\(414\) | −5.56633 | −0.273570 | ||||||||
\(415\) | −3.19114 | −0.156647 | ||||||||
\(416\) | 2.12175 | 0.104027 | ||||||||
\(417\) | 22.5370 | 1.10364 | ||||||||
\(418\) | 0.643728 | 0.0314858 | ||||||||
\(419\) | 0.140900 | 0.00688343 | 0.00344172 | − | 0.999994i | \(-0.498904\pi\) | ||||
0.00344172 | + | 0.999994i | \(0.498904\pi\) | |||||||
\(420\) | −0.114008 | −0.00556301 | ||||||||
\(421\) | 0.179517 | 0.00874910 | 0.00437455 | − | 0.999990i | \(-0.498608\pi\) | ||||
0.00437455 | + | 0.999990i | \(0.498608\pi\) | |||||||
\(422\) | −17.8998 | −0.871348 | ||||||||
\(423\) | −3.68645 | −0.179241 | ||||||||
\(424\) | −3.44950 | −0.167523 | ||||||||
\(425\) | 4.70945 | 0.228442 | ||||||||
\(426\) | 16.5135 | 0.800079 | ||||||||
\(427\) | 1.56620 | 0.0757936 | ||||||||
\(428\) | −1.24872 | −0.0603591 | ||||||||
\(429\) | −0.931164 | −0.0449570 | ||||||||
\(430\) | 6.76095 | 0.326042 | ||||||||
\(431\) | −10.1503 | −0.488922 | −0.244461 | − | 0.969659i | \(-0.578611\pi\) | ||||
−0.244461 | + | 0.969659i | \(0.578611\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 11.9389 | 0.573748 | 0.286874 | − | 0.957968i | \(-0.407384\pi\) | ||||
0.286874 | + | 0.957968i | \(0.407384\pi\) | |||||||
\(434\) | −0.934649 | −0.0448646 | ||||||||
\(435\) | 2.45014 | 0.117475 | ||||||||
\(436\) | −6.85017 | −0.328064 | ||||||||
\(437\) | 8.16469 | 0.390570 | ||||||||
\(438\) | 15.6717 | 0.748823 | ||||||||
\(439\) | −29.0640 | −1.38715 | −0.693575 | − | 0.720385i | \(-0.743965\pi\) | ||||
−0.693575 | + | 0.720385i | \(0.743965\pi\) | |||||||
\(440\) | 0.236561 | 0.0112776 | ||||||||
\(441\) | −6.95527 | −0.331203 | ||||||||
\(442\) | −2.12175 | −0.100921 | ||||||||
\(443\) | −24.1041 | −1.14522 | −0.572611 | − | 0.819827i | \(-0.694070\pi\) | ||||
−0.572611 | + | 0.819827i | \(0.694070\pi\) | |||||||
\(444\) | −6.05133 | −0.287183 | ||||||||
\(445\) | −9.10088 | −0.431423 | ||||||||
\(446\) | 16.7755 | 0.794341 | ||||||||
\(447\) | −5.69941 | −0.269573 | ||||||||
\(448\) | 0.211506 | 0.00999273 | ||||||||
\(449\) | −0.949278 | −0.0447992 | −0.0223996 | − | 0.999749i | \(-0.507131\pi\) | ||||
−0.0223996 | + | 0.999749i | \(0.507131\pi\) | |||||||
\(450\) | 4.70945 | 0.222006 | ||||||||
\(451\) | −1.37778 | −0.0648770 | ||||||||
\(452\) | −9.66703 | −0.454699 | ||||||||
\(453\) | 8.91010 | 0.418633 | ||||||||
\(454\) | 17.1186 | 0.803414 | ||||||||
\(455\) | −0.241896 | −0.0113403 | ||||||||
\(456\) | 1.46680 | 0.0686892 | ||||||||
\(457\) | −6.77458 | −0.316901 | −0.158451 | − | 0.987367i | \(-0.550650\pi\) | ||||
−0.158451 | + | 0.987367i | \(0.550650\pi\) | |||||||
\(458\) | 13.1200 | 0.613056 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 3.00041 | 0.139895 | ||||||||
\(461\) | −20.6995 | −0.964073 | −0.482037 | − | 0.876151i | \(-0.660103\pi\) | ||||
−0.482037 | + | 0.876151i | \(0.660103\pi\) | |||||||
\(462\) | −0.0928228 | −0.00431851 | ||||||||
\(463\) | −27.0311 | −1.25624 | −0.628120 | − | 0.778116i | \(-0.716175\pi\) | ||||
−0.628120 | + | 0.778116i | \(0.716175\pi\) | |||||||
\(464\) | −4.54548 | −0.211019 | ||||||||
\(465\) | −2.38197 | −0.110461 | ||||||||
\(466\) | 4.42173 | 0.204833 | ||||||||
\(467\) | −30.7402 | −1.42249 | −0.711244 | − | 0.702946i | \(-0.751868\pi\) | ||||
−0.711244 | + | 0.702946i | \(0.751868\pi\) | |||||||
\(468\) | −2.12175 | −0.0980780 | ||||||||
\(469\) | −1.26073 | −0.0582150 | ||||||||
\(470\) | 1.98710 | 0.0916581 | ||||||||
\(471\) | −13.2021 | −0.608319 | ||||||||
\(472\) | 1.00000 | 0.0460287 | ||||||||
\(473\) | 5.50463 | 0.253103 | ||||||||
\(474\) | −1.40882 | −0.0647094 | ||||||||
\(475\) | −6.90782 | −0.316953 | ||||||||
\(476\) | −0.211506 | −0.00969437 | ||||||||
\(477\) | 3.44950 | 0.157942 | ||||||||
\(478\) | 2.99710 | 0.137084 | ||||||||
\(479\) | −40.0644 | −1.83059 | −0.915296 | − | 0.402783i | \(-0.868043\pi\) | ||||
−0.915296 | + | 0.402783i | \(0.868043\pi\) | |||||||
\(480\) | 0.539028 | 0.0246031 | ||||||||
\(481\) | −12.8394 | −0.585427 | ||||||||
\(482\) | 9.85479 | 0.448873 | ||||||||
\(483\) | −1.17731 | −0.0535696 | ||||||||
\(484\) | −10.8074 | −0.491245 | ||||||||
\(485\) | −6.91996 | −0.314219 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 2.55945 | 0.115980 | 0.0579899 | − | 0.998317i | \(-0.481531\pi\) | ||||
0.0579899 | + | 0.998317i | \(0.481531\pi\) | |||||||
\(488\) | −7.40497 | −0.335207 | ||||||||
\(489\) | −9.32418 | −0.421654 | ||||||||
\(490\) | 3.74908 | 0.169366 | ||||||||
\(491\) | −16.3895 | −0.739647 | −0.369824 | − | 0.929102i | \(-0.620582\pi\) | ||||
−0.369824 | + | 0.929102i | \(0.620582\pi\) | |||||||
\(492\) | −3.13941 | −0.141535 | ||||||||
\(493\) | 4.54548 | 0.204718 | ||||||||
\(494\) | 3.11219 | 0.140024 | ||||||||
\(495\) | −0.236561 | −0.0106326 | ||||||||
\(496\) | 4.41902 | 0.198420 | ||||||||
\(497\) | 3.49270 | 0.156669 | ||||||||
\(498\) | −5.92017 | −0.265289 | ||||||||
\(499\) | −41.1581 | −1.84249 | −0.921244 | − | 0.388986i | \(-0.872826\pi\) | ||||
−0.921244 | + | 0.388986i | \(0.872826\pi\) | |||||||
\(500\) | −5.23366 | −0.234056 | ||||||||
\(501\) | 1.79156 | 0.0800408 | ||||||||
\(502\) | −4.23635 | −0.189078 | ||||||||
\(503\) | −25.8571 | −1.15291 | −0.576454 | − | 0.817129i | \(-0.695564\pi\) | ||||
−0.576454 | + | 0.817129i | \(0.695564\pi\) | |||||||
\(504\) | −0.211506 | −0.00942124 | ||||||||
\(505\) | 4.17807 | 0.185922 | ||||||||
\(506\) | 2.44287 | 0.108599 | ||||||||
\(507\) | 8.49817 | 0.377417 | ||||||||
\(508\) | 6.20893 | 0.275477 | ||||||||
\(509\) | −28.5132 | −1.26383 | −0.631914 | − | 0.775039i | \(-0.717730\pi\) | ||||
−0.631914 | + | 0.775039i | \(0.717730\pi\) | |||||||
\(510\) | −0.539028 | −0.0238685 | ||||||||
\(511\) | 3.31466 | 0.146632 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.46680 | −0.0647608 | ||||||||
\(514\) | 21.3977 | 0.943814 | ||||||||
\(515\) | −8.64424 | −0.380911 | ||||||||
\(516\) | 12.5429 | 0.552169 | ||||||||
\(517\) | 1.61786 | 0.0711533 | ||||||||
\(518\) | −1.27989 | −0.0562353 | ||||||||
\(519\) | −17.3103 | −0.759840 | ||||||||
\(520\) | 1.14368 | 0.0501538 | ||||||||
\(521\) | 13.5418 | 0.593276 | 0.296638 | − | 0.954990i | \(-0.404135\pi\) | ||||
0.296638 | + | 0.954990i | \(0.404135\pi\) | |||||||
\(522\) | 4.54548 | 0.198950 | ||||||||
\(523\) | 11.0886 | 0.484872 | 0.242436 | − | 0.970167i | \(-0.422054\pi\) | ||||
0.242436 | + | 0.970167i | \(0.422054\pi\) | |||||||
\(524\) | 12.9595 | 0.566139 | ||||||||
\(525\) | 0.996078 | 0.0434724 | ||||||||
\(526\) | −18.4208 | −0.803186 | ||||||||
\(527\) | −4.41902 | −0.192495 | ||||||||
\(528\) | 0.438866 | 0.0190992 | ||||||||
\(529\) | 7.98403 | 0.347132 | ||||||||
\(530\) | −1.85938 | −0.0807662 | ||||||||
\(531\) | −1.00000 | −0.0433963 | ||||||||
\(532\) | 0.310237 | 0.0134505 | ||||||||
\(533\) | −6.66104 | −0.288522 | ||||||||
\(534\) | −16.8839 | −0.730637 | ||||||||
\(535\) | −0.673094 | −0.0291004 | ||||||||
\(536\) | 5.96072 | 0.257464 | ||||||||
\(537\) | −13.2098 | −0.570043 | ||||||||
\(538\) | −15.2337 | −0.656773 | ||||||||
\(539\) | 3.05243 | 0.131477 | ||||||||
\(540\) | −0.539028 | −0.0231961 | ||||||||
\(541\) | −31.9945 | −1.37555 | −0.687776 | − | 0.725923i | \(-0.741413\pi\) | ||||
−0.687776 | + | 0.725923i | \(0.741413\pi\) | |||||||
\(542\) | −11.5622 | −0.496639 | ||||||||
\(543\) | −10.1745 | −0.436629 | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | −3.69243 | −0.158166 | ||||||||
\(546\) | −0.448764 | −0.0192053 | ||||||||
\(547\) | 26.2785 | 1.12359 | 0.561793 | − | 0.827278i | \(-0.310112\pi\) | ||||
0.561793 | + | 0.827278i | \(0.310112\pi\) | |||||||
\(548\) | −1.07309 | −0.0458401 | ||||||||
\(549\) | 7.40497 | 0.316036 | ||||||||
\(550\) | −2.06682 | −0.0881293 | ||||||||
\(551\) | −6.66731 | −0.284037 | ||||||||
\(552\) | 5.56633 | 0.236919 | ||||||||
\(553\) | −0.297975 | −0.0126712 | ||||||||
\(554\) | 3.45542 | 0.146807 | ||||||||
\(555\) | −3.26183 | −0.138457 | ||||||||
\(556\) | −22.5370 | −0.955783 | ||||||||
\(557\) | 33.2841 | 1.41029 | 0.705147 | − | 0.709061i | \(-0.250881\pi\) | ||||
0.705147 | + | 0.709061i | \(0.250881\pi\) | |||||||
\(558\) | −4.41902 | −0.187072 | ||||||||
\(559\) | 26.6128 | 1.12560 | ||||||||
\(560\) | 0.114008 | 0.00481770 | ||||||||
\(561\) | −0.438866 | −0.0185289 | ||||||||
\(562\) | 20.8551 | 0.879719 | ||||||||
\(563\) | −3.32705 | −0.140218 | −0.0701092 | − | 0.997539i | \(-0.522335\pi\) | ||||
−0.0701092 | + | 0.997539i | \(0.522335\pi\) | |||||||
\(564\) | 3.68645 | 0.155228 | ||||||||
\(565\) | −5.21079 | −0.219220 | ||||||||
\(566\) | 23.9561 | 1.00695 | ||||||||
\(567\) | 0.211506 | 0.00888243 | ||||||||
\(568\) | −16.5135 | −0.692889 | ||||||||
\(569\) | 18.1936 | 0.762713 | 0.381357 | − | 0.924428i | \(-0.375457\pi\) | ||||
0.381357 | + | 0.924428i | \(0.375457\pi\) | |||||||
\(570\) | 0.790646 | 0.0331165 | ||||||||
\(571\) | −16.3061 | −0.682389 | −0.341194 | − | 0.939993i | \(-0.610831\pi\) | ||||
−0.341194 | + | 0.939993i | \(0.610831\pi\) | |||||||
\(572\) | 0.931164 | 0.0389339 | ||||||||
\(573\) | 6.41217 | 0.267872 | ||||||||
\(574\) | −0.664004 | −0.0277150 | ||||||||
\(575\) | −26.2144 | −1.09321 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 29.3488 | 1.22181 | 0.610904 | − | 0.791705i | \(-0.290806\pi\) | ||||
0.610904 | + | 0.791705i | \(0.290806\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | 7.78514 | 0.323539 | ||||||||
\(580\) | −2.45014 | −0.101736 | ||||||||
\(581\) | −1.25215 | −0.0519481 | ||||||||
\(582\) | −12.8379 | −0.532147 | ||||||||
\(583\) | −1.51387 | −0.0626980 | ||||||||
\(584\) | −15.6717 | −0.648500 | ||||||||
\(585\) | −1.14368 | −0.0472855 | ||||||||
\(586\) | −13.9518 | −0.576344 | ||||||||
\(587\) | −28.6575 | −1.18282 | −0.591411 | − | 0.806371i | \(-0.701429\pi\) | ||||
−0.591411 | + | 0.806371i | \(0.701429\pi\) | |||||||
\(588\) | 6.95527 | 0.286830 | ||||||||
\(589\) | 6.48181 | 0.267078 | ||||||||
\(590\) | 0.539028 | 0.0221914 | ||||||||
\(591\) | −3.71958 | −0.153003 | ||||||||
\(592\) | 6.05133 | 0.248708 | ||||||||
\(593\) | 1.68840 | 0.0693341 | 0.0346671 | − | 0.999399i | \(-0.488963\pi\) | ||||
0.0346671 | + | 0.999399i | \(0.488963\pi\) | |||||||
\(594\) | −0.438866 | −0.0180069 | ||||||||
\(595\) | −0.114008 | −0.00467386 | ||||||||
\(596\) | 5.69941 | 0.233457 | ||||||||
\(597\) | −13.4826 | −0.551807 | ||||||||
\(598\) | 11.8104 | 0.482962 | ||||||||
\(599\) | 40.8972 | 1.67101 | 0.835506 | − | 0.549481i | \(-0.185174\pi\) | ||||
0.835506 | + | 0.549481i | \(0.185174\pi\) | |||||||
\(600\) | −4.70945 | −0.192262 | ||||||||
\(601\) | 41.8343 | 1.70646 | 0.853228 | − | 0.521538i | \(-0.174642\pi\) | ||||
0.853228 | + | 0.521538i | \(0.174642\pi\) | |||||||
\(602\) | 2.65289 | 0.108124 | ||||||||
\(603\) | −5.96072 | −0.242739 | ||||||||
\(604\) | −8.91010 | −0.362547 | ||||||||
\(605\) | −5.82549 | −0.236840 | ||||||||
\(606\) | 7.75113 | 0.314868 | ||||||||
\(607\) | −39.5868 | −1.60678 | −0.803389 | − | 0.595454i | \(-0.796972\pi\) | ||||
−0.803389 | + | 0.595454i | \(0.796972\pi\) | |||||||
\(608\) | −1.46680 | −0.0594866 | ||||||||
\(609\) | 0.961397 | 0.0389578 | ||||||||
\(610\) | −3.99148 | −0.161610 | ||||||||
\(611\) | 7.82174 | 0.316434 | ||||||||
\(612\) | −1.00000 | −0.0404226 | ||||||||
\(613\) | −27.6076 | −1.11506 | −0.557530 | − | 0.830157i | \(-0.688251\pi\) | ||||
−0.557530 | + | 0.830157i | \(0.688251\pi\) | |||||||
\(614\) | 26.2365 | 1.05882 | ||||||||
\(615\) | −1.69223 | −0.0682372 | ||||||||
\(616\) | 0.0928228 | 0.00373994 | ||||||||
\(617\) | −35.0611 | −1.41151 | −0.705754 | − | 0.708457i | \(-0.749391\pi\) | ||||
−0.705754 | + | 0.708457i | \(0.749391\pi\) | |||||||
\(618\) | −16.0367 | −0.645092 | ||||||||
\(619\) | 33.6253 | 1.35151 | 0.675757 | − | 0.737124i | \(-0.263817\pi\) | ||||
0.675757 | + | 0.737124i | \(0.263817\pi\) | |||||||
\(620\) | 2.38197 | 0.0956623 | ||||||||
\(621\) | −5.56633 | −0.223369 | ||||||||
\(622\) | 18.3831 | 0.737095 | ||||||||
\(623\) | −3.57105 | −0.143071 | ||||||||
\(624\) | 2.12175 | 0.0849380 | ||||||||
\(625\) | 20.7262 | 0.829046 | ||||||||
\(626\) | 33.8390 | 1.35248 | ||||||||
\(627\) | 0.643728 | 0.0257080 | ||||||||
\(628\) | 13.2021 | 0.526820 | ||||||||
\(629\) | −6.05133 | −0.241282 | ||||||||
\(630\) | −0.114008 | −0.00454218 | ||||||||
\(631\) | −32.4730 | −1.29273 | −0.646365 | − | 0.763029i | \(-0.723712\pi\) | ||||
−0.646365 | + | 0.763029i | \(0.723712\pi\) | |||||||
\(632\) | 1.40882 | 0.0560400 | ||||||||
\(633\) | −17.8998 | −0.711453 | ||||||||
\(634\) | −6.55955 | −0.260513 | ||||||||
\(635\) | 3.34679 | 0.132813 | ||||||||
\(636\) | −3.44950 | −0.136782 | ||||||||
\(637\) | 14.7573 | 0.584707 | ||||||||
\(638\) | −1.99485 | −0.0789771 | ||||||||
\(639\) | 16.5135 | 0.653262 | ||||||||
\(640\) | −0.539028 | −0.0213069 | ||||||||
\(641\) | 7.90895 | 0.312385 | 0.156192 | − | 0.987727i | \(-0.450078\pi\) | ||||
0.156192 | + | 0.987727i | \(0.450078\pi\) | |||||||
\(642\) | −1.24872 | −0.0492830 | ||||||||
\(643\) | 7.82653 | 0.308648 | 0.154324 | − | 0.988020i | \(-0.450680\pi\) | ||||
0.154324 | + | 0.988020i | \(0.450680\pi\) | |||||||
\(644\) | 1.17731 | 0.0463927 | ||||||||
\(645\) | 6.76095 | 0.266212 | ||||||||
\(646\) | 1.46680 | 0.0577105 | ||||||||
\(647\) | −30.0438 | −1.18115 | −0.590573 | − | 0.806985i | \(-0.701098\pi\) | ||||
−0.590573 | + | 0.806985i | \(0.701098\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 0.438866 | 0.0172270 | ||||||||
\(650\) | −9.99228 | −0.391929 | ||||||||
\(651\) | −0.934649 | −0.0366318 | ||||||||
\(652\) | 9.32418 | 0.365163 | ||||||||
\(653\) | −34.1931 | −1.33808 | −0.669040 | − | 0.743226i | \(-0.733295\pi\) | ||||
−0.669040 | + | 0.743226i | \(0.733295\pi\) | |||||||
\(654\) | −6.85017 | −0.267863 | ||||||||
\(655\) | 6.98553 | 0.272947 | ||||||||
\(656\) | 3.13941 | 0.122573 | ||||||||
\(657\) | 15.6717 | 0.611412 | ||||||||
\(658\) | 0.779708 | 0.0303962 | ||||||||
\(659\) | 29.3351 | 1.14273 | 0.571367 | − | 0.820695i | \(-0.306413\pi\) | ||||
0.571367 | + | 0.820695i | \(0.306413\pi\) | |||||||
\(660\) | 0.236561 | 0.00920811 | ||||||||
\(661\) | −23.2967 | −0.906138 | −0.453069 | − | 0.891475i | \(-0.649671\pi\) | ||||
−0.453069 | + | 0.891475i | \(0.649671\pi\) | |||||||
\(662\) | −6.13447 | −0.238423 | ||||||||
\(663\) | −2.12175 | −0.0824020 | ||||||||
\(664\) | 5.92017 | 0.229747 | ||||||||
\(665\) | 0.167227 | 0.00648477 | ||||||||
\(666\) | −6.05133 | −0.234484 | ||||||||
\(667\) | −25.3016 | −0.979684 | ||||||||
\(668\) | −1.79156 | −0.0693174 | ||||||||
\(669\) | 16.7755 | 0.648576 | ||||||||
\(670\) | 3.21299 | 0.124129 | ||||||||
\(671\) | −3.24979 | −0.125457 | ||||||||
\(672\) | 0.211506 | 0.00815903 | ||||||||
\(673\) | 9.70042 | 0.373924 | 0.186962 | − | 0.982367i | \(-0.440136\pi\) | ||||
0.186962 | + | 0.982367i | \(0.440136\pi\) | |||||||
\(674\) | 0.735362 | 0.0283251 | ||||||||
\(675\) | 4.70945 | 0.181267 | ||||||||
\(676\) | −8.49817 | −0.326853 | ||||||||
\(677\) | 37.3161 | 1.43417 | 0.717087 | − | 0.696984i | \(-0.245475\pi\) | ||||
0.717087 | + | 0.696984i | \(0.245475\pi\) | |||||||
\(678\) | −9.66703 | −0.371260 | ||||||||
\(679\) | −2.71529 | −0.104203 | ||||||||
\(680\) | 0.539028 | 0.0206708 | ||||||||
\(681\) | 17.1186 | 0.655985 | ||||||||
\(682\) | 1.93935 | 0.0742617 | ||||||||
\(683\) | 22.6132 | 0.865272 | 0.432636 | − | 0.901569i | \(-0.357584\pi\) | ||||
0.432636 | + | 0.901569i | \(0.357584\pi\) | |||||||
\(684\) | 1.46680 | 0.0560845 | ||||||||
\(685\) | −0.578425 | −0.0221005 | ||||||||
\(686\) | 2.95163 | 0.112694 | ||||||||
\(687\) | 13.1200 | 0.500558 | ||||||||
\(688\) | −12.5429 | −0.478192 | ||||||||
\(689\) | −7.31899 | −0.278831 | ||||||||
\(690\) | 3.00041 | 0.114223 | ||||||||
\(691\) | −41.2023 | −1.56741 | −0.783705 | − | 0.621133i | \(-0.786673\pi\) | ||||
−0.783705 | + | 0.621133i | \(0.786673\pi\) | |||||||
\(692\) | 17.3103 | 0.658041 | ||||||||
\(693\) | −0.0928228 | −0.00352605 | ||||||||
\(694\) | 22.3832 | 0.849653 | ||||||||
\(695\) | −12.1481 | −0.460803 | ||||||||
\(696\) | −4.54548 | −0.172296 | ||||||||
\(697\) | −3.13941 | −0.118913 | ||||||||
\(698\) | −23.9783 | −0.907593 | ||||||||
\(699\) | 4.42173 | 0.167245 | ||||||||
\(700\) | −0.996078 | −0.0376482 | ||||||||
\(701\) | −7.54376 | −0.284924 | −0.142462 | − | 0.989800i | \(-0.545502\pi\) | ||||
−0.142462 | + | 0.989800i | \(0.545502\pi\) | |||||||
\(702\) | −2.12175 | −0.0800803 | ||||||||
\(703\) | 8.87608 | 0.334768 | ||||||||
\(704\) | −0.438866 | −0.0165404 | ||||||||
\(705\) | 1.98710 | 0.0748385 | ||||||||
\(706\) | −33.9101 | −1.27622 | ||||||||
\(707\) | 1.63941 | 0.0616564 | ||||||||
\(708\) | 1.00000 | 0.0375823 | ||||||||
\(709\) | −6.73497 | −0.252937 | −0.126469 | − | 0.991971i | \(-0.540364\pi\) | ||||
−0.126469 | + | 0.991971i | \(0.540364\pi\) | |||||||
\(710\) | −8.90121 | −0.334056 | ||||||||
\(711\) | −1.40882 | −0.0528350 | ||||||||
\(712\) | 16.8839 | 0.632751 | ||||||||
\(713\) | 24.5977 | 0.921191 | ||||||||
\(714\) | −0.211506 | −0.00791542 | ||||||||
\(715\) | 0.501923 | 0.0187709 | ||||||||
\(716\) | 13.2098 | 0.493672 | ||||||||
\(717\) | 2.99710 | 0.111929 | ||||||||
\(718\) | 4.45057 | 0.166094 | ||||||||
\(719\) | 23.4588 | 0.874864 | 0.437432 | − | 0.899251i | \(-0.355888\pi\) | ||||
0.437432 | + | 0.899251i | \(0.355888\pi\) | |||||||
\(720\) | 0.539028 | 0.0200884 | ||||||||
\(721\) | −3.39187 | −0.126320 | ||||||||
\(722\) | 16.8485 | 0.627036 | ||||||||
\(723\) | 9.85479 | 0.366503 | ||||||||
\(724\) | 10.1745 | 0.378131 | ||||||||
\(725\) | 21.4067 | 0.795025 | ||||||||
\(726\) | −10.8074 | −0.401100 | ||||||||
\(727\) | 13.5103 | 0.501071 | 0.250535 | − | 0.968107i | \(-0.419393\pi\) | ||||
0.250535 | + | 0.968107i | \(0.419393\pi\) | |||||||
\(728\) | 0.448764 | 0.0166323 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −8.44748 | −0.312655 | ||||||||
\(731\) | 12.5429 | 0.463915 | ||||||||
\(732\) | −7.40497 | −0.273696 | ||||||||
\(733\) | 13.7655 | 0.508441 | 0.254221 | − | 0.967146i | \(-0.418181\pi\) | ||||
0.254221 | + | 0.967146i | \(0.418181\pi\) | |||||||
\(734\) | 34.7031 | 1.28092 | ||||||||
\(735\) | 3.74908 | 0.138287 | ||||||||
\(736\) | −5.56633 | −0.205178 | ||||||||
\(737\) | 2.61595 | 0.0963599 | ||||||||
\(738\) | −3.13941 | −0.115563 | ||||||||
\(739\) | −28.4909 | −1.04805 | −0.524027 | − | 0.851702i | \(-0.675571\pi\) | ||||
−0.524027 | + | 0.851702i | \(0.675571\pi\) | |||||||
\(740\) | 3.26183 | 0.119907 | ||||||||
\(741\) | 3.11219 | 0.114329 | ||||||||
\(742\) | −0.729591 | −0.0267841 | ||||||||
\(743\) | −10.3317 | −0.379032 | −0.189516 | − | 0.981878i | \(-0.560692\pi\) | ||||
−0.189516 | + | 0.981878i | \(0.560692\pi\) | |||||||
\(744\) | 4.41902 | 0.162009 | ||||||||
\(745\) | 3.07214 | 0.112554 | ||||||||
\(746\) | 20.2021 | 0.739650 | ||||||||
\(747\) | −5.92017 | −0.216608 | ||||||||
\(748\) | 0.438866 | 0.0160465 | ||||||||
\(749\) | −0.264112 | −0.00965043 | ||||||||
\(750\) | −5.23366 | −0.191106 | ||||||||
\(751\) | 0.744006 | 0.0271491 | 0.0135746 | − | 0.999908i | \(-0.495679\pi\) | ||||
0.0135746 | + | 0.999908i | \(0.495679\pi\) | |||||||
\(752\) | −3.68645 | −0.134431 | ||||||||
\(753\) | −4.23635 | −0.154381 | ||||||||
\(754\) | −9.64438 | −0.351228 | ||||||||
\(755\) | −4.80279 | −0.174791 | ||||||||
\(756\) | −0.211506 | −0.00769241 | ||||||||
\(757\) | 12.1056 | 0.439985 | 0.219992 | − | 0.975502i | \(-0.429397\pi\) | ||||
0.219992 | + | 0.975502i | \(0.429397\pi\) | |||||||
\(758\) | 23.6280 | 0.858207 | ||||||||
\(759\) | 2.44287 | 0.0886706 | ||||||||
\(760\) | −0.790646 | −0.0286797 | ||||||||
\(761\) | 12.5077 | 0.453404 | 0.226702 | − | 0.973964i | \(-0.427206\pi\) | ||||
0.226702 | + | 0.973964i | \(0.427206\pi\) | |||||||
\(762\) | 6.20893 | 0.224926 | ||||||||
\(763\) | −1.44885 | −0.0524521 | ||||||||
\(764\) | −6.41217 | −0.231984 | ||||||||
\(765\) | −0.539028 | −0.0194886 | ||||||||
\(766\) | −6.51425 | −0.235369 | ||||||||
\(767\) | 2.12175 | 0.0766120 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −26.8112 | −0.966838 | −0.483419 | − | 0.875389i | \(-0.660605\pi\) | ||||
−0.483419 | + | 0.875389i | \(0.660605\pi\) | |||||||
\(770\) | 0.0500341 | 0.00180310 | ||||||||
\(771\) | 21.3977 | 0.770621 | ||||||||
\(772\) | −7.78514 | −0.280193 | ||||||||
\(773\) | 8.97768 | 0.322905 | 0.161452 | − | 0.986881i | \(-0.448382\pi\) | ||||
0.161452 | + | 0.986881i | \(0.448382\pi\) | |||||||
\(774\) | 12.5429 | 0.450844 | ||||||||
\(775\) | −20.8111 | −0.747558 | ||||||||
\(776\) | 12.8379 | 0.460853 | ||||||||
\(777\) | −1.27989 | −0.0459159 | ||||||||
\(778\) | −36.1981 | −1.29776 | ||||||||
\(779\) | 4.60488 | 0.164987 | ||||||||
\(780\) | 1.14368 | 0.0409504 | ||||||||
\(781\) | −7.24719 | −0.259325 | ||||||||
\(782\) | 5.56633 | 0.199052 | ||||||||
\(783\) | 4.54548 | 0.162442 | ||||||||
\(784\) | −6.95527 | −0.248402 | ||||||||
\(785\) | 7.11628 | 0.253991 | ||||||||
\(786\) | 12.9595 | 0.462250 | ||||||||
\(787\) | −52.0718 | −1.85616 | −0.928080 | − | 0.372382i | \(-0.878541\pi\) | ||||
−0.928080 | + | 0.372382i | \(0.878541\pi\) | |||||||
\(788\) | 3.71958 | 0.132504 | ||||||||
\(789\) | −18.4208 | −0.655798 | ||||||||
\(790\) | 0.759394 | 0.0270180 | ||||||||
\(791\) | −2.04464 | −0.0726989 | ||||||||
\(792\) | 0.438866 | 0.0155944 | ||||||||
\(793\) | −15.7115 | −0.557932 | ||||||||
\(794\) | −0.608826 | −0.0216064 | ||||||||
\(795\) | −1.85938 | −0.0659453 | ||||||||
\(796\) | 13.4826 | 0.477879 | ||||||||
\(797\) | −38.8981 | −1.37784 | −0.688920 | − | 0.724837i | \(-0.741915\pi\) | ||||
−0.688920 | + | 0.724837i | \(0.741915\pi\) | |||||||
\(798\) | 0.310237 | 0.0109823 | ||||||||
\(799\) | 3.68645 | 0.130417 | ||||||||
\(800\) | 4.70945 | 0.166504 | ||||||||
\(801\) | −16.8839 | −0.596563 | ||||||||
\(802\) | −1.93078 | −0.0681783 | ||||||||
\(803\) | −6.87777 | −0.242711 | ||||||||
\(804\) | 5.96072 | 0.210218 | ||||||||
\(805\) | 0.634605 | 0.0223669 | ||||||||
\(806\) | 9.37605 | 0.330257 | ||||||||
\(807\) | −15.2337 | −0.536253 | ||||||||
\(808\) | −7.75113 | −0.272684 | ||||||||
\(809\) | −40.9085 | −1.43827 | −0.719133 | − | 0.694873i | \(-0.755461\pi\) | ||||
−0.719133 | + | 0.694873i | \(0.755461\pi\) | |||||||
\(810\) | −0.539028 | −0.0189395 | ||||||||
\(811\) | −47.4225 | −1.66523 | −0.832614 | − | 0.553854i | \(-0.813157\pi\) | ||||
−0.832614 | + | 0.553854i | \(0.813157\pi\) | |||||||
\(812\) | −0.961397 | −0.0337384 | ||||||||
\(813\) | −11.5622 | −0.405504 | ||||||||
\(814\) | 2.65572 | 0.0930829 | ||||||||
\(815\) | 5.02599 | 0.176053 | ||||||||
\(816\) | 1.00000 | 0.0350070 | ||||||||
\(817\) | −18.3979 | −0.643660 | ||||||||
\(818\) | −4.42657 | −0.154772 | ||||||||
\(819\) | −0.448764 | −0.0156811 | ||||||||
\(820\) | 1.69223 | 0.0590951 | ||||||||
\(821\) | 34.2865 | 1.19661 | 0.598303 | − | 0.801270i | \(-0.295842\pi\) | ||||
0.598303 | + | 0.801270i | \(0.295842\pi\) | |||||||
\(822\) | −1.07309 | −0.0374283 | ||||||||
\(823\) | −8.78439 | −0.306205 | −0.153102 | − | 0.988210i | \(-0.548926\pi\) | ||||
−0.153102 | + | 0.988210i | \(0.548926\pi\) | |||||||
\(824\) | 16.0367 | 0.558666 | ||||||||
\(825\) | −2.06682 | −0.0719573 | ||||||||
\(826\) | 0.211506 | 0.00735924 | ||||||||
\(827\) | −49.5039 | −1.72142 | −0.860710 | − | 0.509096i | \(-0.829980\pi\) | ||||
−0.860710 | + | 0.509096i | \(0.829980\pi\) | |||||||
\(828\) | 5.56633 | 0.193443 | ||||||||
\(829\) | −24.8680 | −0.863700 | −0.431850 | − | 0.901946i | \(-0.642139\pi\) | ||||
−0.431850 | + | 0.901946i | \(0.642139\pi\) | |||||||
\(830\) | 3.19114 | 0.110766 | ||||||||
\(831\) | 3.45542 | 0.119867 | ||||||||
\(832\) | −2.12175 | −0.0735585 | ||||||||
\(833\) | 6.95527 | 0.240986 | ||||||||
\(834\) | −22.5370 | −0.780394 | ||||||||
\(835\) | −0.965698 | −0.0334194 | ||||||||
\(836\) | −0.643728 | −0.0222638 | ||||||||
\(837\) | −4.41902 | −0.152744 | ||||||||
\(838\) | −0.140900 | −0.00486732 | ||||||||
\(839\) | −18.0088 | −0.621731 | −0.310866 | − | 0.950454i | \(-0.600619\pi\) | ||||
−0.310866 | + | 0.950454i | \(0.600619\pi\) | |||||||
\(840\) | 0.114008 | 0.00393364 | ||||||||
\(841\) | −8.33861 | −0.287538 | ||||||||
\(842\) | −0.179517 | −0.00618655 | ||||||||
\(843\) | 20.8551 | 0.718287 | ||||||||
\(844\) | 17.8998 | 0.616136 | ||||||||
\(845\) | −4.58075 | −0.157583 | ||||||||
\(846\) | 3.68645 | 0.126743 | ||||||||
\(847\) | −2.28583 | −0.0785421 | ||||||||
\(848\) | 3.44950 | 0.118456 | ||||||||
\(849\) | 23.9561 | 0.822171 | ||||||||
\(850\) | −4.70945 | −0.161533 | ||||||||
\(851\) | 33.6837 | 1.15466 | ||||||||
\(852\) | −16.5135 | −0.565742 | ||||||||
\(853\) | −50.3682 | −1.72457 | −0.862287 | − | 0.506420i | \(-0.830969\pi\) | ||||
−0.862287 | + | 0.506420i | \(0.830969\pi\) | |||||||
\(854\) | −1.56620 | −0.0535942 | ||||||||
\(855\) | 0.790646 | 0.0270395 | ||||||||
\(856\) | 1.24872 | 0.0426803 | ||||||||
\(857\) | −41.6692 | −1.42339 | −0.711696 | − | 0.702487i | \(-0.752073\pi\) | ||||
−0.711696 | + | 0.702487i | \(0.752073\pi\) | |||||||
\(858\) | 0.931164 | 0.0317894 | ||||||||
\(859\) | 44.2210 | 1.50880 | 0.754401 | − | 0.656414i | \(-0.227928\pi\) | ||||
0.754401 | + | 0.656414i | \(0.227928\pi\) | |||||||
\(860\) | −6.76095 | −0.230547 | ||||||||
\(861\) | −0.664004 | −0.0226292 | ||||||||
\(862\) | 10.1503 | 0.345720 | ||||||||
\(863\) | 6.25889 | 0.213055 | 0.106527 | − | 0.994310i | \(-0.466027\pi\) | ||||
0.106527 | + | 0.994310i | \(0.466027\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 9.33075 | 0.317255 | ||||||||
\(866\) | −11.9389 | −0.405701 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 0.934649 | 0.0317241 | ||||||||
\(869\) | 0.618284 | 0.0209738 | ||||||||
\(870\) | −2.45014 | −0.0830675 | ||||||||
\(871\) | 12.6472 | 0.428533 | ||||||||
\(872\) | 6.85017 | 0.231976 | ||||||||
\(873\) | −12.8379 | −0.434496 | ||||||||
\(874\) | −8.16469 | −0.276175 | ||||||||
\(875\) | −1.10695 | −0.0374218 | ||||||||
\(876\) | −15.6717 | −0.529498 | ||||||||
\(877\) | 23.7244 | 0.801117 | 0.400558 | − | 0.916271i | \(-0.368816\pi\) | ||||
0.400558 | + | 0.916271i | \(0.368816\pi\) | |||||||
\(878\) | 29.0640 | 0.980863 | ||||||||
\(879\) | −13.9518 | −0.470583 | ||||||||
\(880\) | −0.236561 | −0.00797446 | ||||||||
\(881\) | 36.7669 | 1.23871 | 0.619354 | − | 0.785112i | \(-0.287395\pi\) | ||||
0.619354 | + | 0.785112i | \(0.287395\pi\) | |||||||
\(882\) | 6.95527 | 0.234196 | ||||||||
\(883\) | 48.5757 | 1.63470 | 0.817351 | − | 0.576140i | \(-0.195442\pi\) | ||||
0.817351 | + | 0.576140i | \(0.195442\pi\) | |||||||
\(884\) | 2.12175 | 0.0713622 | ||||||||
\(885\) | 0.539028 | 0.0181192 | ||||||||
\(886\) | 24.1041 | 0.809795 | ||||||||
\(887\) | −33.0801 | −1.11072 | −0.555360 | − | 0.831610i | \(-0.687420\pi\) | ||||
−0.555360 | + | 0.831610i | \(0.687420\pi\) | |||||||
\(888\) | 6.05133 | 0.203069 | ||||||||
\(889\) | 1.31323 | 0.0440443 | ||||||||
\(890\) | 9.10088 | 0.305062 | ||||||||
\(891\) | −0.438866 | −0.0147026 | ||||||||
\(892\) | −16.7755 | −0.561684 | ||||||||
\(893\) | −5.40729 | −0.180948 | ||||||||
\(894\) | 5.69941 | 0.190617 | ||||||||
\(895\) | 7.12042 | 0.238010 | ||||||||
\(896\) | −0.211506 | −0.00706593 | ||||||||
\(897\) | 11.8104 | 0.394337 | ||||||||
\(898\) | 0.949278 | 0.0316778 | ||||||||
\(899\) | −20.0865 | −0.669924 | ||||||||
\(900\) | −4.70945 | −0.156982 | ||||||||
\(901\) | −3.44950 | −0.114920 | ||||||||
\(902\) | 1.37778 | 0.0458750 | ||||||||
\(903\) | 2.65289 | 0.0882828 | ||||||||
\(904\) | 9.66703 | 0.321520 | ||||||||
\(905\) | 5.48432 | 0.182305 | ||||||||
\(906\) | −8.91010 | −0.296018 | ||||||||
\(907\) | −32.8325 | −1.09018 | −0.545092 | − | 0.838376i | \(-0.683505\pi\) | ||||
−0.545092 | + | 0.838376i | \(0.683505\pi\) | |||||||
\(908\) | −17.1186 | −0.568100 | ||||||||
\(909\) | 7.75113 | 0.257089 | ||||||||
\(910\) | 0.241896 | 0.00801877 | ||||||||
\(911\) | 34.0063 | 1.12668 | 0.563340 | − | 0.826225i | \(-0.309516\pi\) | ||||
0.563340 | + | 0.826225i | \(0.309516\pi\) | |||||||
\(912\) | −1.46680 | −0.0485706 | ||||||||
\(913\) | 2.59816 | 0.0859866 | ||||||||
\(914\) | 6.77458 | 0.224083 | ||||||||
\(915\) | −3.99148 | −0.131954 | ||||||||
\(916\) | −13.1200 | −0.433496 | ||||||||
\(917\) | 2.74102 | 0.0905164 | ||||||||
\(918\) | −1.00000 | −0.0330049 | ||||||||
\(919\) | 22.6974 | 0.748719 | 0.374360 | − | 0.927284i | \(-0.377863\pi\) | ||||
0.374360 | + | 0.927284i | \(0.377863\pi\) | |||||||
\(920\) | −3.00041 | −0.0989204 | ||||||||
\(921\) | 26.2365 | 0.864522 | ||||||||
\(922\) | 20.6995 | 0.681703 | ||||||||
\(923\) | −35.0374 | −1.15327 | ||||||||
\(924\) | 0.0928228 | 0.00305365 | ||||||||
\(925\) | −28.4984 | −0.937022 | ||||||||
\(926\) | 27.0311 | 0.888296 | ||||||||
\(927\) | −16.0367 | −0.526715 | ||||||||
\(928\) | 4.54548 | 0.149213 | ||||||||
\(929\) | −7.52463 | −0.246875 | −0.123438 | − | 0.992352i | \(-0.539392\pi\) | ||||
−0.123438 | + | 0.992352i | \(0.539392\pi\) | |||||||
\(930\) | 2.38197 | 0.0781079 | ||||||||
\(931\) | −10.2020 | −0.334357 | ||||||||
\(932\) | −4.42173 | −0.144839 | ||||||||
\(933\) | 18.3831 | 0.601836 | ||||||||
\(934\) | 30.7402 | 1.00585 | ||||||||
\(935\) | 0.236561 | 0.00773636 | ||||||||
\(936\) | 2.12175 | 0.0693516 | ||||||||
\(937\) | 41.2745 | 1.34838 | 0.674190 | − | 0.738558i | \(-0.264493\pi\) | ||||
0.674190 | + | 0.738558i | \(0.264493\pi\) | |||||||
\(938\) | 1.26073 | 0.0411643 | ||||||||
\(939\) | 33.8390 | 1.10429 | ||||||||
\(940\) | −1.98710 | −0.0648121 | ||||||||
\(941\) | 37.5672 | 1.22466 | 0.612328 | − | 0.790603i | \(-0.290233\pi\) | ||||
0.612328 | + | 0.790603i | \(0.290233\pi\) | |||||||
\(942\) | 13.2021 | 0.430147 | ||||||||
\(943\) | 17.4750 | 0.569063 | ||||||||
\(944\) | −1.00000 | −0.0325472 | ||||||||
\(945\) | −0.114008 | −0.00370867 | ||||||||
\(946\) | −5.50463 | −0.178971 | ||||||||
\(947\) | 44.8040 | 1.45593 | 0.727967 | − | 0.685612i | \(-0.240465\pi\) | ||||
0.727967 | + | 0.685612i | \(0.240465\pi\) | |||||||
\(948\) | 1.40882 | 0.0457564 | ||||||||
\(949\) | −33.2515 | −1.07939 | ||||||||
\(950\) | 6.90782 | 0.224119 | ||||||||
\(951\) | −6.55955 | −0.212708 | ||||||||
\(952\) | 0.211506 | 0.00685496 | ||||||||
\(953\) | −17.8320 | −0.577636 | −0.288818 | − | 0.957384i | \(-0.593262\pi\) | ||||
−0.288818 | + | 0.957384i | \(0.593262\pi\) | |||||||
\(954\) | −3.44950 | −0.111682 | ||||||||
\(955\) | −3.45634 | −0.111844 | ||||||||
\(956\) | −2.99710 | −0.0969331 | ||||||||
\(957\) | −1.99485 | −0.0644845 | ||||||||
\(958\) | 40.0644 | 1.29442 | ||||||||
\(959\) | −0.226965 | −0.00732909 | ||||||||
\(960\) | −0.539028 | −0.0173970 | ||||||||
\(961\) | −11.4723 | −0.370074 | ||||||||
\(962\) | 12.8394 | 0.413959 | ||||||||
\(963\) | −1.24872 | −0.0402394 | ||||||||
\(964\) | −9.85479 | −0.317401 | ||||||||
\(965\) | −4.19641 | −0.135087 | ||||||||
\(966\) | 1.17731 | 0.0378794 | ||||||||
\(967\) | −48.0470 | −1.54509 | −0.772544 | − | 0.634961i | \(-0.781016\pi\) | ||||
−0.772544 | + | 0.634961i | \(0.781016\pi\) | |||||||
\(968\) | 10.8074 | 0.347363 | ||||||||
\(969\) | 1.46680 | 0.0471204 | ||||||||
\(970\) | 6.91996 | 0.222187 | ||||||||
\(971\) | 44.8342 | 1.43880 | 0.719399 | − | 0.694597i | \(-0.244417\pi\) | ||||
0.719399 | + | 0.694597i | \(0.244417\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −4.76672 | −0.152814 | ||||||||
\(974\) | −2.55945 | −0.0820102 | ||||||||
\(975\) | −9.99228 | −0.320009 | ||||||||
\(976\) | 7.40497 | 0.237027 | ||||||||
\(977\) | 13.9821 | 0.447328 | 0.223664 | − | 0.974666i | \(-0.428198\pi\) | ||||
0.223664 | + | 0.974666i | \(0.428198\pi\) | |||||||
\(978\) | 9.32418 | 0.298154 | ||||||||
\(979\) | 7.40976 | 0.236817 | ||||||||
\(980\) | −3.74908 | −0.119760 | ||||||||
\(981\) | −6.85017 | −0.218709 | ||||||||
\(982\) | 16.3895 | 0.523009 | ||||||||
\(983\) | 45.6759 | 1.45684 | 0.728418 | − | 0.685133i | \(-0.240256\pi\) | ||||
0.728418 | + | 0.685133i | \(0.240256\pi\) | |||||||
\(984\) | 3.13941 | 0.100081 | ||||||||
\(985\) | 2.00495 | 0.0638832 | ||||||||
\(986\) | −4.54548 | −0.144758 | ||||||||
\(987\) | 0.779708 | 0.0248184 | ||||||||
\(988\) | −3.11219 | −0.0990118 | ||||||||
\(989\) | −69.8177 | −2.22008 | ||||||||
\(990\) | 0.236561 | 0.00751839 | ||||||||
\(991\) | 46.7111 | 1.48383 | 0.741914 | − | 0.670495i | \(-0.233918\pi\) | ||||
0.741914 | + | 0.670495i | \(0.233918\pi\) | |||||||
\(992\) | −4.41902 | −0.140304 | ||||||||
\(993\) | −6.13447 | −0.194671 | ||||||||
\(994\) | −3.49270 | −0.110782 | ||||||||
\(995\) | 7.26750 | 0.230395 | ||||||||
\(996\) | 5.92017 | 0.187588 | ||||||||
\(997\) | 39.5453 | 1.25241 | 0.626206 | − | 0.779657i | \(-0.284607\pi\) | ||||
0.626206 | + | 0.779657i | \(0.284607\pi\) | |||||||
\(998\) | 41.1581 | 1.30284 | ||||||||
\(999\) | −6.05133 | −0.191455 |
(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 | 6018.2.a.v.1.4 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.v.1.4 | ✓ | 9 | 1.1 | even | 1 | trivial |