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: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 33x^{8} + 53x^{7} + 356x^{6} - 433x^{5} - 1296x^{4} + 1135x^{3} + 930x^{2} - 186x - 104 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.313984\) 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 | ||||||||
\(5\) | 0.313984 | 0.140418 | 0.0702089 | − | 0.997532i | \(-0.477633\pi\) | ||||
0.0702089 | + | 0.997532i | \(0.477633\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 2.10092 | 0.794073 | 0.397036 | − | 0.917803i | \(-0.370039\pi\) | ||||
0.397036 | + | 0.917803i | \(0.370039\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.313984 | −0.0992903 | ||||||||
\(11\) | −0.847786 | −0.255617 | −0.127809 | − | 0.991799i | \(-0.540794\pi\) | ||||
−0.127809 | + | 0.991799i | \(0.540794\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −6.84610 | −1.89877 | −0.949384 | − | 0.314119i | \(-0.898291\pi\) | ||||
−0.949384 | + | 0.314119i | \(0.898291\pi\) | |||||||
\(14\) | −2.10092 | −0.561494 | ||||||||
\(15\) | 0.313984 | 0.0810702 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 7.75129 | 1.77827 | 0.889134 | − | 0.457646i | \(-0.151307\pi\) | ||||
0.889134 | + | 0.457646i | \(0.151307\pi\) | |||||||
\(20\) | 0.313984 | 0.0702089 | ||||||||
\(21\) | 2.10092 | 0.458458 | ||||||||
\(22\) | 0.847786 | 0.180749 | ||||||||
\(23\) | −5.38960 | −1.12381 | −0.561904 | − | 0.827202i | \(-0.689931\pi\) | ||||
−0.561904 | + | 0.827202i | \(0.689931\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −4.90141 | −0.980283 | ||||||||
\(26\) | 6.84610 | 1.34263 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.10092 | 0.397036 | ||||||||
\(29\) | −3.96402 | −0.736099 | −0.368050 | − | 0.929806i | \(-0.619974\pi\) | ||||
−0.368050 | + | 0.929806i | \(0.619974\pi\) | |||||||
\(30\) | −0.313984 | −0.0573253 | ||||||||
\(31\) | 1.75978 | 0.316066 | 0.158033 | − | 0.987434i | \(-0.449485\pi\) | ||||
0.158033 | + | 0.987434i | \(0.449485\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.847786 | −0.147581 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | 0.659654 | 0.111502 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 3.06470 | 0.503833 | 0.251916 | − | 0.967749i | \(-0.418939\pi\) | ||||
0.251916 | + | 0.967749i | \(0.418939\pi\) | |||||||
\(38\) | −7.75129 | −1.25743 | ||||||||
\(39\) | −6.84610 | −1.09625 | ||||||||
\(40\) | −0.313984 | −0.0496452 | ||||||||
\(41\) | 4.08035 | 0.637244 | 0.318622 | − | 0.947882i | \(-0.396780\pi\) | ||||
0.318622 | + | 0.947882i | \(0.396780\pi\) | |||||||
\(42\) | −2.10092 | −0.324179 | ||||||||
\(43\) | 0.863891 | 0.131742 | 0.0658711 | − | 0.997828i | \(-0.479017\pi\) | ||||
0.0658711 | + | 0.997828i | \(0.479017\pi\) | |||||||
\(44\) | −0.847786 | −0.127809 | ||||||||
\(45\) | 0.313984 | 0.0468059 | ||||||||
\(46\) | 5.38960 | 0.794653 | ||||||||
\(47\) | −8.06572 | −1.17651 | −0.588253 | − | 0.808677i | \(-0.700184\pi\) | ||||
−0.588253 | + | 0.808677i | \(0.700184\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −2.58614 | −0.369448 | ||||||||
\(50\) | 4.90141 | 0.693165 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −6.84610 | −0.949384 | ||||||||
\(53\) | −10.2118 | −1.40269 | −0.701347 | − | 0.712820i | \(-0.747418\pi\) | ||||
−0.701347 | + | 0.712820i | \(0.747418\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −0.266191 | −0.0358932 | ||||||||
\(56\) | −2.10092 | −0.280747 | ||||||||
\(57\) | 7.75129 | 1.02668 | ||||||||
\(58\) | 3.96402 | 0.520501 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0.313984 | 0.0405351 | ||||||||
\(61\) | 7.82924 | 1.00243 | 0.501216 | − | 0.865322i | \(-0.332886\pi\) | ||||
0.501216 | + | 0.865322i | \(0.332886\pi\) | |||||||
\(62\) | −1.75978 | −0.223492 | ||||||||
\(63\) | 2.10092 | 0.264691 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.14956 | −0.266621 | ||||||||
\(66\) | 0.847786 | 0.104355 | ||||||||
\(67\) | −6.38895 | −0.780535 | −0.390268 | − | 0.920702i | \(-0.627617\pi\) | ||||
−0.390268 | + | 0.920702i | \(0.627617\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | −5.38960 | −0.648831 | ||||||||
\(70\) | −0.659654 | −0.0788437 | ||||||||
\(71\) | 11.4183 | 1.35510 | 0.677550 | − | 0.735477i | \(-0.263042\pi\) | ||||
0.677550 | + | 0.735477i | \(0.263042\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −9.05018 | −1.05924 | −0.529622 | − | 0.848234i | \(-0.677666\pi\) | ||||
−0.529622 | + | 0.848234i | \(0.677666\pi\) | |||||||
\(74\) | −3.06470 | −0.356264 | ||||||||
\(75\) | −4.90141 | −0.565967 | ||||||||
\(76\) | 7.75129 | 0.889134 | ||||||||
\(77\) | −1.78113 | −0.202979 | ||||||||
\(78\) | 6.84610 | 0.775168 | ||||||||
\(79\) | 7.33532 | 0.825288 | 0.412644 | − | 0.910892i | \(-0.364605\pi\) | ||||
0.412644 | + | 0.910892i | \(0.364605\pi\) | |||||||
\(80\) | 0.313984 | 0.0351044 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.08035 | −0.450599 | ||||||||
\(83\) | −0.416311 | −0.0456960 | −0.0228480 | − | 0.999739i | \(-0.507273\pi\) | ||||
−0.0228480 | + | 0.999739i | \(0.507273\pi\) | |||||||
\(84\) | 2.10092 | 0.229229 | ||||||||
\(85\) | −0.313984 | −0.0340563 | ||||||||
\(86\) | −0.863891 | −0.0931558 | ||||||||
\(87\) | −3.96402 | −0.424987 | ||||||||
\(88\) | 0.847786 | 0.0903743 | ||||||||
\(89\) | −13.6489 | −1.44678 | −0.723391 | − | 0.690438i | \(-0.757418\pi\) | ||||
−0.723391 | + | 0.690438i | \(0.757418\pi\) | |||||||
\(90\) | −0.313984 | −0.0330968 | ||||||||
\(91\) | −14.3831 | −1.50776 | ||||||||
\(92\) | −5.38960 | −0.561904 | ||||||||
\(93\) | 1.75978 | 0.182481 | ||||||||
\(94\) | 8.06572 | 0.831915 | ||||||||
\(95\) | 2.43378 | 0.249700 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −2.22173 | −0.225583 | −0.112791 | − | 0.993619i | \(-0.535979\pi\) | ||||
−0.112791 | + | 0.993619i | \(0.535979\pi\) | |||||||
\(98\) | 2.58614 | 0.261239 | ||||||||
\(99\) | −0.847786 | −0.0852057 | ||||||||
\(100\) | −4.90141 | −0.490141 | ||||||||
\(101\) | −4.27600 | −0.425478 | −0.212739 | − | 0.977109i | \(-0.568238\pi\) | ||||
−0.212739 | + | 0.977109i | \(0.568238\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | −15.1099 | −1.48883 | −0.744413 | − | 0.667720i | \(-0.767270\pi\) | ||||
−0.744413 | + | 0.667720i | \(0.767270\pi\) | |||||||
\(104\) | 6.84610 | 0.671316 | ||||||||
\(105\) | 0.659654 | 0.0643757 | ||||||||
\(106\) | 10.2118 | 0.991854 | ||||||||
\(107\) | 14.9644 | 1.44666 | 0.723332 | − | 0.690500i | \(-0.242609\pi\) | ||||
0.723332 | + | 0.690500i | \(0.242609\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −12.5270 | −1.19987 | −0.599936 | − | 0.800048i | \(-0.704807\pi\) | ||||
−0.599936 | + | 0.800048i | \(0.704807\pi\) | |||||||
\(110\) | 0.266191 | 0.0253803 | ||||||||
\(111\) | 3.06470 | 0.290888 | ||||||||
\(112\) | 2.10092 | 0.198518 | ||||||||
\(113\) | 6.13747 | 0.577365 | 0.288682 | − | 0.957425i | \(-0.406783\pi\) | ||||
0.288682 | + | 0.957425i | \(0.406783\pi\) | |||||||
\(114\) | −7.75129 | −0.725975 | ||||||||
\(115\) | −1.69225 | −0.157803 | ||||||||
\(116\) | −3.96402 | −0.368050 | ||||||||
\(117\) | −6.84610 | −0.632922 | ||||||||
\(118\) | −1.00000 | −0.0920575 | ||||||||
\(119\) | −2.10092 | −0.192591 | ||||||||
\(120\) | −0.313984 | −0.0286626 | ||||||||
\(121\) | −10.2813 | −0.934660 | ||||||||
\(122\) | −7.82924 | −0.708826 | ||||||||
\(123\) | 4.08035 | 0.367913 | ||||||||
\(124\) | 1.75978 | 0.158033 | ||||||||
\(125\) | −3.10888 | −0.278067 | ||||||||
\(126\) | −2.10092 | −0.187165 | ||||||||
\(127\) | −17.4017 | −1.54415 | −0.772075 | − | 0.635532i | \(-0.780781\pi\) | ||||
−0.772075 | + | 0.635532i | \(0.780781\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0.863891 | 0.0760614 | ||||||||
\(130\) | 2.14956 | 0.188529 | ||||||||
\(131\) | −19.2845 | −1.68490 | −0.842448 | − | 0.538778i | \(-0.818886\pi\) | ||||
−0.842448 | + | 0.538778i | \(0.818886\pi\) | |||||||
\(132\) | −0.847786 | −0.0737903 | ||||||||
\(133\) | 16.2848 | 1.41207 | ||||||||
\(134\) | 6.38895 | 0.551922 | ||||||||
\(135\) | 0.313984 | 0.0270234 | ||||||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | −12.4313 | −1.06208 | −0.531039 | − | 0.847347i | \(-0.678198\pi\) | ||||
−0.531039 | + | 0.847347i | \(0.678198\pi\) | |||||||
\(138\) | 5.38960 | 0.458793 | ||||||||
\(139\) | 20.6438 | 1.75098 | 0.875492 | − | 0.483232i | \(-0.160537\pi\) | ||||
0.875492 | + | 0.483232i | \(0.160537\pi\) | |||||||
\(140\) | 0.659654 | 0.0557509 | ||||||||
\(141\) | −8.06572 | −0.679256 | ||||||||
\(142\) | −11.4183 | −0.958200 | ||||||||
\(143\) | 5.80403 | 0.485357 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −1.24464 | −0.103361 | ||||||||
\(146\) | 9.05018 | 0.748998 | ||||||||
\(147\) | −2.58614 | −0.213301 | ||||||||
\(148\) | 3.06470 | 0.251916 | ||||||||
\(149\) | −21.1802 | −1.73515 | −0.867574 | − | 0.497308i | \(-0.834322\pi\) | ||||
−0.867574 | + | 0.497308i | \(0.834322\pi\) | |||||||
\(150\) | 4.90141 | 0.400199 | ||||||||
\(151\) | 19.1223 | 1.55615 | 0.778076 | − | 0.628170i | \(-0.216196\pi\) | ||||
0.778076 | + | 0.628170i | \(0.216196\pi\) | |||||||
\(152\) | −7.75129 | −0.628713 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 1.78113 | 0.143527 | ||||||||
\(155\) | 0.552542 | 0.0443812 | ||||||||
\(156\) | −6.84610 | −0.548127 | ||||||||
\(157\) | −16.5189 | −1.31835 | −0.659176 | − | 0.751989i | \(-0.729095\pi\) | ||||
−0.659176 | + | 0.751989i | \(0.729095\pi\) | |||||||
\(158\) | −7.33532 | −0.583567 | ||||||||
\(159\) | −10.2118 | −0.809846 | ||||||||
\(160\) | −0.313984 | −0.0248226 | ||||||||
\(161\) | −11.3231 | −0.892386 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −3.73417 | −0.292482 | −0.146241 | − | 0.989249i | \(-0.546718\pi\) | ||||
−0.146241 | + | 0.989249i | \(0.546718\pi\) | |||||||
\(164\) | 4.08035 | 0.318622 | ||||||||
\(165\) | −0.266191 | −0.0207229 | ||||||||
\(166\) | 0.416311 | 0.0323120 | ||||||||
\(167\) | −6.56448 | −0.507974 | −0.253987 | − | 0.967208i | \(-0.581742\pi\) | ||||
−0.253987 | + | 0.967208i | \(0.581742\pi\) | |||||||
\(168\) | −2.10092 | −0.162089 | ||||||||
\(169\) | 33.8691 | 2.60532 | ||||||||
\(170\) | 0.313984 | 0.0240814 | ||||||||
\(171\) | 7.75129 | 0.592756 | ||||||||
\(172\) | 0.863891 | 0.0658711 | ||||||||
\(173\) | 0.502200 | 0.0381815 | 0.0190908 | − | 0.999818i | \(-0.493923\pi\) | ||||
0.0190908 | + | 0.999818i | \(0.493923\pi\) | |||||||
\(174\) | 3.96402 | 0.300511 | ||||||||
\(175\) | −10.2975 | −0.778416 | ||||||||
\(176\) | −0.847786 | −0.0639043 | ||||||||
\(177\) | 1.00000 | 0.0751646 | ||||||||
\(178\) | 13.6489 | 1.02303 | ||||||||
\(179\) | −9.83124 | −0.734822 | −0.367411 | − | 0.930059i | \(-0.619756\pi\) | ||||
−0.367411 | + | 0.930059i | \(0.619756\pi\) | |||||||
\(180\) | 0.313984 | 0.0234030 | ||||||||
\(181\) | −5.83704 | −0.433864 | −0.216932 | − | 0.976187i | \(-0.569605\pi\) | ||||
−0.216932 | + | 0.976187i | \(0.569605\pi\) | |||||||
\(182\) | 14.3831 | 1.06615 | ||||||||
\(183\) | 7.82924 | 0.578754 | ||||||||
\(184\) | 5.38960 | 0.397326 | ||||||||
\(185\) | 0.962264 | 0.0707471 | ||||||||
\(186\) | −1.75978 | −0.129033 | ||||||||
\(187\) | 0.847786 | 0.0619962 | ||||||||
\(188\) | −8.06572 | −0.588253 | ||||||||
\(189\) | 2.10092 | 0.152819 | ||||||||
\(190\) | −2.43378 | −0.176565 | ||||||||
\(191\) | 15.5630 | 1.12610 | 0.563050 | − | 0.826423i | \(-0.309628\pi\) | ||||
0.563050 | + | 0.826423i | \(0.309628\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −1.10959 | −0.0798701 | −0.0399350 | − | 0.999202i | \(-0.512715\pi\) | ||||
−0.0399350 | + | 0.999202i | \(0.512715\pi\) | |||||||
\(194\) | 2.22173 | 0.159511 | ||||||||
\(195\) | −2.14956 | −0.153933 | ||||||||
\(196\) | −2.58614 | −0.184724 | ||||||||
\(197\) | −21.1479 | −1.50672 | −0.753361 | − | 0.657607i | \(-0.771569\pi\) | ||||
−0.753361 | + | 0.657607i | \(0.771569\pi\) | |||||||
\(198\) | 0.847786 | 0.0602495 | ||||||||
\(199\) | 7.69680 | 0.545612 | 0.272806 | − | 0.962069i | \(-0.412048\pi\) | ||||
0.272806 | + | 0.962069i | \(0.412048\pi\) | |||||||
\(200\) | 4.90141 | 0.346582 | ||||||||
\(201\) | −6.38895 | −0.450642 | ||||||||
\(202\) | 4.27600 | 0.300858 | ||||||||
\(203\) | −8.32808 | −0.584516 | ||||||||
\(204\) | −1.00000 | −0.0700140 | ||||||||
\(205\) | 1.28116 | 0.0894803 | ||||||||
\(206\) | 15.1099 | 1.05276 | ||||||||
\(207\) | −5.38960 | −0.374603 | ||||||||
\(208\) | −6.84610 | −0.474692 | ||||||||
\(209\) | −6.57144 | −0.454556 | ||||||||
\(210\) | −0.659654 | −0.0455205 | ||||||||
\(211\) | 26.6228 | 1.83279 | 0.916394 | − | 0.400278i | \(-0.131087\pi\) | ||||
0.916394 | + | 0.400278i | \(0.131087\pi\) | |||||||
\(212\) | −10.2118 | −0.701347 | ||||||||
\(213\) | 11.4183 | 0.782367 | ||||||||
\(214\) | −14.9644 | −1.02295 | ||||||||
\(215\) | 0.271248 | 0.0184989 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 3.69715 | 0.250979 | ||||||||
\(218\) | 12.5270 | 0.848438 | ||||||||
\(219\) | −9.05018 | −0.611555 | ||||||||
\(220\) | −0.266191 | −0.0179466 | ||||||||
\(221\) | 6.84610 | 0.460519 | ||||||||
\(222\) | −3.06470 | −0.205689 | ||||||||
\(223\) | 20.4920 | 1.37225 | 0.686124 | − | 0.727485i | \(-0.259311\pi\) | ||||
0.686124 | + | 0.727485i | \(0.259311\pi\) | |||||||
\(224\) | −2.10092 | −0.140374 | ||||||||
\(225\) | −4.90141 | −0.326761 | ||||||||
\(226\) | −6.13747 | −0.408259 | ||||||||
\(227\) | 8.46757 | 0.562012 | 0.281006 | − | 0.959706i | \(-0.409332\pi\) | ||||
0.281006 | + | 0.959706i | \(0.409332\pi\) | |||||||
\(228\) | 7.75129 | 0.513342 | ||||||||
\(229\) | 11.5494 | 0.763205 | 0.381603 | − | 0.924326i | \(-0.375372\pi\) | ||||
0.381603 | + | 0.924326i | \(0.375372\pi\) | |||||||
\(230\) | 1.69225 | 0.111583 | ||||||||
\(231\) | −1.78113 | −0.117190 | ||||||||
\(232\) | 3.96402 | 0.260250 | ||||||||
\(233\) | 0.514865 | 0.0337300 | 0.0168650 | − | 0.999858i | \(-0.494631\pi\) | ||||
0.0168650 | + | 0.999858i | \(0.494631\pi\) | |||||||
\(234\) | 6.84610 | 0.447544 | ||||||||
\(235\) | −2.53250 | −0.165202 | ||||||||
\(236\) | 1.00000 | 0.0650945 | ||||||||
\(237\) | 7.33532 | 0.476480 | ||||||||
\(238\) | 2.10092 | 0.136182 | ||||||||
\(239\) | −28.4503 | −1.84030 | −0.920149 | − | 0.391569i | \(-0.871933\pi\) | ||||
−0.920149 | + | 0.391569i | \(0.871933\pi\) | |||||||
\(240\) | 0.313984 | 0.0202676 | ||||||||
\(241\) | 7.96535 | 0.513093 | 0.256547 | − | 0.966532i | \(-0.417415\pi\) | ||||
0.256547 | + | 0.966532i | \(0.417415\pi\) | |||||||
\(242\) | 10.2813 | 0.660904 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 7.82924 | 0.501216 | ||||||||
\(245\) | −0.812005 | −0.0518771 | ||||||||
\(246\) | −4.08035 | −0.260154 | ||||||||
\(247\) | −53.0662 | −3.37652 | ||||||||
\(248\) | −1.75978 | −0.111746 | ||||||||
\(249\) | −0.416311 | −0.0263826 | ||||||||
\(250\) | 3.10888 | 0.196623 | ||||||||
\(251\) | 23.3659 | 1.47484 | 0.737422 | − | 0.675432i | \(-0.236043\pi\) | ||||
0.737422 | + | 0.675432i | \(0.236043\pi\) | |||||||
\(252\) | 2.10092 | 0.132345 | ||||||||
\(253\) | 4.56922 | 0.287265 | ||||||||
\(254\) | 17.4017 | 1.09188 | ||||||||
\(255\) | −0.313984 | −0.0196624 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −17.2084 | −1.07343 | −0.536716 | − | 0.843763i | \(-0.680335\pi\) | ||||
−0.536716 | + | 0.843763i | \(0.680335\pi\) | |||||||
\(258\) | −0.863891 | −0.0537835 | ||||||||
\(259\) | 6.43868 | 0.400080 | ||||||||
\(260\) | −2.14956 | −0.133310 | ||||||||
\(261\) | −3.96402 | −0.245366 | ||||||||
\(262\) | 19.2845 | 1.19140 | ||||||||
\(263\) | 22.8845 | 1.41112 | 0.705561 | − | 0.708649i | \(-0.250695\pi\) | ||||
0.705561 | + | 0.708649i | \(0.250695\pi\) | |||||||
\(264\) | 0.847786 | 0.0521776 | ||||||||
\(265\) | −3.20633 | −0.196963 | ||||||||
\(266\) | −16.2848 | −0.998488 | ||||||||
\(267\) | −13.6489 | −0.835300 | ||||||||
\(268\) | −6.38895 | −0.390268 | ||||||||
\(269\) | −14.5179 | −0.885171 | −0.442586 | − | 0.896726i | \(-0.645939\pi\) | ||||
−0.442586 | + | 0.896726i | \(0.645939\pi\) | |||||||
\(270\) | −0.313984 | −0.0191084 | ||||||||
\(271\) | 20.9878 | 1.27492 | 0.637458 | − | 0.770485i | \(-0.279986\pi\) | ||||
0.637458 | + | 0.770485i | \(0.279986\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | −14.3831 | −0.870505 | ||||||||
\(274\) | 12.4313 | 0.751003 | ||||||||
\(275\) | 4.15535 | 0.250577 | ||||||||
\(276\) | −5.38960 | −0.324416 | ||||||||
\(277\) | −21.6987 | −1.30375 | −0.651873 | − | 0.758328i | \(-0.726017\pi\) | ||||
−0.651873 | + | 0.758328i | \(0.726017\pi\) | |||||||
\(278\) | −20.6438 | −1.23813 | ||||||||
\(279\) | 1.75978 | 0.105355 | ||||||||
\(280\) | −0.659654 | −0.0394219 | ||||||||
\(281\) | −7.10977 | −0.424133 | −0.212067 | − | 0.977255i | \(-0.568019\pi\) | ||||
−0.212067 | + | 0.977255i | \(0.568019\pi\) | |||||||
\(282\) | 8.06572 | 0.480306 | ||||||||
\(283\) | 16.3119 | 0.969640 | 0.484820 | − | 0.874614i | \(-0.338885\pi\) | ||||
0.484820 | + | 0.874614i | \(0.338885\pi\) | |||||||
\(284\) | 11.4183 | 0.677550 | ||||||||
\(285\) | 2.43378 | 0.144165 | ||||||||
\(286\) | −5.80403 | −0.343199 | ||||||||
\(287\) | 8.57249 | 0.506018 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 1.24464 | 0.0730875 | ||||||||
\(291\) | −2.22173 | −0.130240 | ||||||||
\(292\) | −9.05018 | −0.529622 | ||||||||
\(293\) | −9.86065 | −0.576065 | −0.288033 | − | 0.957621i | \(-0.593001\pi\) | ||||
−0.288033 | + | 0.957621i | \(0.593001\pi\) | |||||||
\(294\) | 2.58614 | 0.150827 | ||||||||
\(295\) | 0.313984 | 0.0182808 | ||||||||
\(296\) | −3.06470 | −0.178132 | ||||||||
\(297\) | −0.847786 | −0.0491935 | ||||||||
\(298\) | 21.1802 | 1.22693 | ||||||||
\(299\) | 36.8977 | 2.13385 | ||||||||
\(300\) | −4.90141 | −0.282983 | ||||||||
\(301\) | 1.81497 | 0.104613 | ||||||||
\(302\) | −19.1223 | −1.10037 | ||||||||
\(303\) | −4.27600 | −0.245650 | ||||||||
\(304\) | 7.75129 | 0.444567 | ||||||||
\(305\) | 2.45825 | 0.140759 | ||||||||
\(306\) | 1.00000 | 0.0571662 | ||||||||
\(307\) | −26.5184 | −1.51349 | −0.756744 | − | 0.653711i | \(-0.773211\pi\) | ||||
−0.756744 | + | 0.653711i | \(0.773211\pi\) | |||||||
\(308\) | −1.78113 | −0.101489 | ||||||||
\(309\) | −15.1099 | −0.859574 | ||||||||
\(310\) | −0.552542 | −0.0313823 | ||||||||
\(311\) | 13.4756 | 0.764130 | 0.382065 | − | 0.924136i | \(-0.375213\pi\) | ||||
0.382065 | + | 0.924136i | \(0.375213\pi\) | |||||||
\(312\) | 6.84610 | 0.387584 | ||||||||
\(313\) | −9.63155 | −0.544408 | −0.272204 | − | 0.962240i | \(-0.587752\pi\) | ||||
−0.272204 | + | 0.962240i | \(0.587752\pi\) | |||||||
\(314\) | 16.5189 | 0.932216 | ||||||||
\(315\) | 0.659654 | 0.0371673 | ||||||||
\(316\) | 7.33532 | 0.412644 | ||||||||
\(317\) | −19.5266 | −1.09672 | −0.548361 | − | 0.836242i | \(-0.684748\pi\) | ||||
−0.548361 | + | 0.836242i | \(0.684748\pi\) | |||||||
\(318\) | 10.2118 | 0.572647 | ||||||||
\(319\) | 3.36064 | 0.188160 | ||||||||
\(320\) | 0.313984 | 0.0175522 | ||||||||
\(321\) | 14.9644 | 0.835232 | ||||||||
\(322\) | 11.3231 | 0.631012 | ||||||||
\(323\) | −7.75129 | −0.431294 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 33.5556 | 1.86133 | ||||||||
\(326\) | 3.73417 | 0.206816 | ||||||||
\(327\) | −12.5270 | −0.692747 | ||||||||
\(328\) | −4.08035 | −0.225300 | ||||||||
\(329\) | −16.9454 | −0.934231 | ||||||||
\(330\) | 0.266191 | 0.0146533 | ||||||||
\(331\) | −18.6116 | −1.02299 | −0.511494 | − | 0.859287i | \(-0.670908\pi\) | ||||
−0.511494 | + | 0.859287i | \(0.670908\pi\) | |||||||
\(332\) | −0.416311 | −0.0228480 | ||||||||
\(333\) | 3.06470 | 0.167944 | ||||||||
\(334\) | 6.56448 | 0.359192 | ||||||||
\(335\) | −2.00603 | −0.109601 | ||||||||
\(336\) | 2.10092 | 0.114615 | ||||||||
\(337\) | 12.8151 | 0.698084 | 0.349042 | − | 0.937107i | \(-0.386507\pi\) | ||||
0.349042 | + | 0.937107i | \(0.386507\pi\) | |||||||
\(338\) | −33.8691 | −1.84224 | ||||||||
\(339\) | 6.13747 | 0.333342 | ||||||||
\(340\) | −0.313984 | −0.0170282 | ||||||||
\(341\) | −1.49192 | −0.0807918 | ||||||||
\(342\) | −7.75129 | −0.419142 | ||||||||
\(343\) | −20.1397 | −1.08744 | ||||||||
\(344\) | −0.863891 | −0.0465779 | ||||||||
\(345\) | −1.69225 | −0.0911074 | ||||||||
\(346\) | −0.502200 | −0.0269984 | ||||||||
\(347\) | −13.0323 | −0.699610 | −0.349805 | − | 0.936823i | \(-0.613752\pi\) | ||||
−0.349805 | + | 0.936823i | \(0.613752\pi\) | |||||||
\(348\) | −3.96402 | −0.212494 | ||||||||
\(349\) | −3.18606 | −0.170546 | −0.0852729 | − | 0.996358i | \(-0.527176\pi\) | ||||
−0.0852729 | + | 0.996358i | \(0.527176\pi\) | |||||||
\(350\) | 10.2975 | 0.550423 | ||||||||
\(351\) | −6.84610 | −0.365418 | ||||||||
\(352\) | 0.847786 | 0.0451871 | ||||||||
\(353\) | 12.9841 | 0.691075 | 0.345538 | − | 0.938405i | \(-0.387697\pi\) | ||||
0.345538 | + | 0.938405i | \(0.387697\pi\) | |||||||
\(354\) | −1.00000 | −0.0531494 | ||||||||
\(355\) | 3.58515 | 0.190280 | ||||||||
\(356\) | −13.6489 | −0.723391 | ||||||||
\(357\) | −2.10092 | −0.111192 | ||||||||
\(358\) | 9.83124 | 0.519597 | ||||||||
\(359\) | 10.0009 | 0.527827 | 0.263913 | − | 0.964546i | \(-0.414987\pi\) | ||||
0.263913 | + | 0.964546i | \(0.414987\pi\) | |||||||
\(360\) | −0.313984 | −0.0165484 | ||||||||
\(361\) | 41.0826 | 2.16224 | ||||||||
\(362\) | 5.83704 | 0.306788 | ||||||||
\(363\) | −10.2813 | −0.539626 | ||||||||
\(364\) | −14.3831 | −0.753880 | ||||||||
\(365\) | −2.84161 | −0.148737 | ||||||||
\(366\) | −7.82924 | −0.409241 | ||||||||
\(367\) | 19.6011 | 1.02317 | 0.511583 | − | 0.859234i | \(-0.329059\pi\) | ||||
0.511583 | + | 0.859234i | \(0.329059\pi\) | |||||||
\(368\) | −5.38960 | −0.280952 | ||||||||
\(369\) | 4.08035 | 0.212415 | ||||||||
\(370\) | −0.962264 | −0.0500257 | ||||||||
\(371\) | −21.4541 | −1.11384 | ||||||||
\(372\) | 1.75978 | 0.0912403 | ||||||||
\(373\) | 38.5365 | 1.99534 | 0.997671 | − | 0.0682033i | \(-0.0217266\pi\) | ||||
0.997671 | + | 0.0682033i | \(0.0217266\pi\) | |||||||
\(374\) | −0.847786 | −0.0438380 | ||||||||
\(375\) | −3.10888 | −0.160542 | ||||||||
\(376\) | 8.06572 | 0.415958 | ||||||||
\(377\) | 27.1381 | 1.39768 | ||||||||
\(378\) | −2.10092 | −0.108060 | ||||||||
\(379\) | −20.4575 | −1.05083 | −0.525415 | − | 0.850846i | \(-0.676090\pi\) | ||||
−0.525415 | + | 0.850846i | \(0.676090\pi\) | |||||||
\(380\) | 2.43378 | 0.124850 | ||||||||
\(381\) | −17.4017 | −0.891515 | ||||||||
\(382\) | −15.5630 | −0.796274 | ||||||||
\(383\) | −30.2752 | −1.54699 | −0.773494 | − | 0.633804i | \(-0.781493\pi\) | ||||
−0.773494 | + | 0.633804i | \(0.781493\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −0.559245 | −0.0285018 | ||||||||
\(386\) | 1.10959 | 0.0564767 | ||||||||
\(387\) | 0.863891 | 0.0439141 | ||||||||
\(388\) | −2.22173 | −0.112791 | ||||||||
\(389\) | −22.4006 | −1.13575 | −0.567877 | − | 0.823113i | \(-0.692235\pi\) | ||||
−0.567877 | + | 0.823113i | \(0.692235\pi\) | |||||||
\(390\) | 2.14956 | 0.108847 | ||||||||
\(391\) | 5.38960 | 0.272564 | ||||||||
\(392\) | 2.58614 | 0.130620 | ||||||||
\(393\) | −19.2845 | −0.972775 | ||||||||
\(394\) | 21.1479 | 1.06541 | ||||||||
\(395\) | 2.30317 | 0.115885 | ||||||||
\(396\) | −0.847786 | −0.0426028 | ||||||||
\(397\) | −19.3679 | −0.972047 | −0.486024 | − | 0.873946i | \(-0.661553\pi\) | ||||
−0.486024 | + | 0.873946i | \(0.661553\pi\) | |||||||
\(398\) | −7.69680 | −0.385806 | ||||||||
\(399\) | 16.2848 | 0.815262 | ||||||||
\(400\) | −4.90141 | −0.245071 | ||||||||
\(401\) | 14.5880 | 0.728490 | 0.364245 | − | 0.931303i | \(-0.381327\pi\) | ||||
0.364245 | + | 0.931303i | \(0.381327\pi\) | |||||||
\(402\) | 6.38895 | 0.318652 | ||||||||
\(403\) | −12.0476 | −0.600135 | ||||||||
\(404\) | −4.27600 | −0.212739 | ||||||||
\(405\) | 0.313984 | 0.0156020 | ||||||||
\(406\) | 8.32808 | 0.413316 | ||||||||
\(407\) | −2.59821 | −0.128788 | ||||||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | −15.7198 | −0.777292 | −0.388646 | − | 0.921387i | \(-0.627057\pi\) | ||||
−0.388646 | + | 0.921387i | \(0.627057\pi\) | |||||||
\(410\) | −1.28116 | −0.0632721 | ||||||||
\(411\) | −12.4313 | −0.613191 | ||||||||
\(412\) | −15.1099 | −0.744413 | ||||||||
\(413\) | 2.10092 | 0.103379 | ||||||||
\(414\) | 5.38960 | 0.264884 | ||||||||
\(415\) | −0.130715 | −0.00641654 | ||||||||
\(416\) | 6.84610 | 0.335658 | ||||||||
\(417\) | 20.6438 | 1.01093 | ||||||||
\(418\) | 6.57144 | 0.321419 | ||||||||
\(419\) | 10.3992 | 0.508033 | 0.254016 | − | 0.967200i | \(-0.418248\pi\) | ||||
0.254016 | + | 0.967200i | \(0.418248\pi\) | |||||||
\(420\) | 0.659654 | 0.0321878 | ||||||||
\(421\) | 1.46278 | 0.0712914 | 0.0356457 | − | 0.999364i | \(-0.488651\pi\) | ||||
0.0356457 | + | 0.999364i | \(0.488651\pi\) | |||||||
\(422\) | −26.6228 | −1.29598 | ||||||||
\(423\) | −8.06572 | −0.392169 | ||||||||
\(424\) | 10.2118 | 0.495927 | ||||||||
\(425\) | 4.90141 | 0.237754 | ||||||||
\(426\) | −11.4183 | −0.553217 | ||||||||
\(427\) | 16.4486 | 0.796004 | ||||||||
\(428\) | 14.9644 | 0.723332 | ||||||||
\(429\) | 5.80403 | 0.280221 | ||||||||
\(430\) | −0.271248 | −0.0130807 | ||||||||
\(431\) | −8.94044 | −0.430646 | −0.215323 | − | 0.976543i | \(-0.569080\pi\) | ||||
−0.215323 | + | 0.976543i | \(0.569080\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −1.52494 | −0.0732839 | −0.0366419 | − | 0.999328i | \(-0.511666\pi\) | ||||
−0.0366419 | + | 0.999328i | \(0.511666\pi\) | |||||||
\(434\) | −3.69715 | −0.177469 | ||||||||
\(435\) | −1.24464 | −0.0596757 | ||||||||
\(436\) | −12.5270 | −0.599936 | ||||||||
\(437\) | −41.7764 | −1.99843 | ||||||||
\(438\) | 9.05018 | 0.432434 | ||||||||
\(439\) | −33.9597 | −1.62081 | −0.810403 | − | 0.585873i | \(-0.800752\pi\) | ||||
−0.810403 | + | 0.585873i | \(0.800752\pi\) | |||||||
\(440\) | 0.266191 | 0.0126901 | ||||||||
\(441\) | −2.58614 | −0.123149 | ||||||||
\(442\) | −6.84610 | −0.325636 | ||||||||
\(443\) | 28.1430 | 1.33712 | 0.668558 | − | 0.743660i | \(-0.266912\pi\) | ||||
0.668558 | + | 0.743660i | \(0.266912\pi\) | |||||||
\(444\) | 3.06470 | 0.145444 | ||||||||
\(445\) | −4.28554 | −0.203154 | ||||||||
\(446\) | −20.4920 | −0.970326 | ||||||||
\(447\) | −21.1802 | −1.00179 | ||||||||
\(448\) | 2.10092 | 0.0992591 | ||||||||
\(449\) | −23.7418 | −1.12045 | −0.560223 | − | 0.828342i | \(-0.689285\pi\) | ||||
−0.560223 | + | 0.828342i | \(0.689285\pi\) | |||||||
\(450\) | 4.90141 | 0.231055 | ||||||||
\(451\) | −3.45926 | −0.162890 | ||||||||
\(452\) | 6.13747 | 0.288682 | ||||||||
\(453\) | 19.1223 | 0.898445 | ||||||||
\(454\) | −8.46757 | −0.397403 | ||||||||
\(455\) | −4.51606 | −0.211716 | ||||||||
\(456\) | −7.75129 | −0.362988 | ||||||||
\(457\) | 28.6991 | 1.34249 | 0.671244 | − | 0.741236i | \(-0.265760\pi\) | ||||
0.671244 | + | 0.741236i | \(0.265760\pi\) | |||||||
\(458\) | −11.5494 | −0.539668 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −1.69225 | −0.0789013 | ||||||||
\(461\) | −17.6993 | −0.824338 | −0.412169 | − | 0.911107i | \(-0.635229\pi\) | ||||
−0.412169 | + | 0.911107i | \(0.635229\pi\) | |||||||
\(462\) | 1.78113 | 0.0828656 | ||||||||
\(463\) | −11.4644 | −0.532794 | −0.266397 | − | 0.963863i | \(-0.585833\pi\) | ||||
−0.266397 | + | 0.963863i | \(0.585833\pi\) | |||||||
\(464\) | −3.96402 | −0.184025 | ||||||||
\(465\) | 0.552542 | 0.0256235 | ||||||||
\(466\) | −0.514865 | −0.0238507 | ||||||||
\(467\) | −9.50755 | −0.439957 | −0.219978 | − | 0.975505i | \(-0.570599\pi\) | ||||
−0.219978 | + | 0.975505i | \(0.570599\pi\) | |||||||
\(468\) | −6.84610 | −0.316461 | ||||||||
\(469\) | −13.4227 | −0.619802 | ||||||||
\(470\) | 2.53250 | 0.116816 | ||||||||
\(471\) | −16.5189 | −0.761151 | ||||||||
\(472\) | −1.00000 | −0.0460287 | ||||||||
\(473\) | −0.732395 | −0.0336755 | ||||||||
\(474\) | −7.33532 | −0.336922 | ||||||||
\(475\) | −37.9923 | −1.74321 | ||||||||
\(476\) | −2.10092 | −0.0962955 | ||||||||
\(477\) | −10.2118 | −0.467565 | ||||||||
\(478\) | 28.4503 | 1.30129 | ||||||||
\(479\) | 7.89050 | 0.360526 | 0.180263 | − | 0.983618i | \(-0.442305\pi\) | ||||
0.180263 | + | 0.983618i | \(0.442305\pi\) | |||||||
\(480\) | −0.313984 | −0.0143313 | ||||||||
\(481\) | −20.9812 | −0.956661 | ||||||||
\(482\) | −7.96535 | −0.362812 | ||||||||
\(483\) | −11.3231 | −0.515219 | ||||||||
\(484\) | −10.2813 | −0.467330 | ||||||||
\(485\) | −0.697588 | −0.0316758 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 29.3249 | 1.32884 | 0.664419 | − | 0.747360i | \(-0.268679\pi\) | ||||
0.664419 | + | 0.747360i | \(0.268679\pi\) | |||||||
\(488\) | −7.82924 | −0.354413 | ||||||||
\(489\) | −3.73417 | −0.168865 | ||||||||
\(490\) | 0.812005 | 0.0366827 | ||||||||
\(491\) | 0.731272 | 0.0330018 | 0.0165009 | − | 0.999864i | \(-0.494747\pi\) | ||||
0.0165009 | + | 0.999864i | \(0.494747\pi\) | |||||||
\(492\) | 4.08035 | 0.183956 | ||||||||
\(493\) | 3.96402 | 0.178530 | ||||||||
\(494\) | 53.0662 | 2.38756 | ||||||||
\(495\) | −0.266191 | −0.0119644 | ||||||||
\(496\) | 1.75978 | 0.0790164 | ||||||||
\(497\) | 23.9889 | 1.07605 | ||||||||
\(498\) | 0.416311 | 0.0186553 | ||||||||
\(499\) | 39.9939 | 1.79037 | 0.895186 | − | 0.445693i | \(-0.147043\pi\) | ||||
0.895186 | + | 0.445693i | \(0.147043\pi\) | |||||||
\(500\) | −3.10888 | −0.139033 | ||||||||
\(501\) | −6.56448 | −0.293279 | ||||||||
\(502\) | −23.3659 | −1.04287 | ||||||||
\(503\) | 32.2843 | 1.43948 | 0.719742 | − | 0.694242i | \(-0.244260\pi\) | ||||
0.719742 | + | 0.694242i | \(0.244260\pi\) | |||||||
\(504\) | −2.10092 | −0.0935824 | ||||||||
\(505\) | −1.34259 | −0.0597446 | ||||||||
\(506\) | −4.56922 | −0.203127 | ||||||||
\(507\) | 33.8691 | 1.50418 | ||||||||
\(508\) | −17.4017 | −0.772075 | ||||||||
\(509\) | −2.70844 | −0.120050 | −0.0600248 | − | 0.998197i | \(-0.519118\pi\) | ||||
−0.0600248 | + | 0.998197i | \(0.519118\pi\) | |||||||
\(510\) | 0.313984 | 0.0139034 | ||||||||
\(511\) | −19.0137 | −0.841116 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 7.75129 | 0.342228 | ||||||||
\(514\) | 17.2084 | 0.759031 | ||||||||
\(515\) | −4.74427 | −0.209057 | ||||||||
\(516\) | 0.863891 | 0.0380307 | ||||||||
\(517\) | 6.83800 | 0.300735 | ||||||||
\(518\) | −6.43868 | −0.282899 | ||||||||
\(519\) | 0.502200 | 0.0220441 | ||||||||
\(520\) | 2.14956 | 0.0942646 | ||||||||
\(521\) | −9.80592 | −0.429605 | −0.214802 | − | 0.976658i | \(-0.568911\pi\) | ||||
−0.214802 | + | 0.976658i | \(0.568911\pi\) | |||||||
\(522\) | 3.96402 | 0.173500 | ||||||||
\(523\) | −19.8161 | −0.866499 | −0.433249 | − | 0.901274i | \(-0.642633\pi\) | ||||
−0.433249 | + | 0.901274i | \(0.642633\pi\) | |||||||
\(524\) | −19.2845 | −0.842448 | ||||||||
\(525\) | −10.2975 | −0.449419 | ||||||||
\(526\) | −22.8845 | −0.997814 | ||||||||
\(527\) | −1.75978 | −0.0766572 | ||||||||
\(528\) | −0.847786 | −0.0368951 | ||||||||
\(529\) | 6.04777 | 0.262946 | ||||||||
\(530\) | 3.20633 | 0.139274 | ||||||||
\(531\) | 1.00000 | 0.0433963 | ||||||||
\(532\) | 16.2848 | 0.706037 | ||||||||
\(533\) | −27.9345 | −1.20998 | ||||||||
\(534\) | 13.6489 | 0.590646 | ||||||||
\(535\) | 4.69858 | 0.203137 | ||||||||
\(536\) | 6.38895 | 0.275961 | ||||||||
\(537\) | −9.83124 | −0.424250 | ||||||||
\(538\) | 14.5179 | 0.625911 | ||||||||
\(539\) | 2.19249 | 0.0944373 | ||||||||
\(540\) | 0.313984 | 0.0135117 | ||||||||
\(541\) | 4.12466 | 0.177333 | 0.0886664 | − | 0.996061i | \(-0.471739\pi\) | ||||
0.0886664 | + | 0.996061i | \(0.471739\pi\) | |||||||
\(542\) | −20.9878 | −0.901502 | ||||||||
\(543\) | −5.83704 | −0.250492 | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | −3.93329 | −0.168483 | ||||||||
\(546\) | 14.3831 | 0.615540 | ||||||||
\(547\) | −2.56799 | −0.109799 | −0.0548997 | − | 0.998492i | \(-0.517484\pi\) | ||||
−0.0548997 | + | 0.998492i | \(0.517484\pi\) | |||||||
\(548\) | −12.4313 | −0.531039 | ||||||||
\(549\) | 7.82924 | 0.334144 | ||||||||
\(550\) | −4.15535 | −0.177185 | ||||||||
\(551\) | −30.7263 | −1.30898 | ||||||||
\(552\) | 5.38960 | 0.229397 | ||||||||
\(553\) | 15.4109 | 0.655339 | ||||||||
\(554\) | 21.6987 | 0.921888 | ||||||||
\(555\) | 0.962264 | 0.0408458 | ||||||||
\(556\) | 20.6438 | 0.875492 | ||||||||
\(557\) | 3.15332 | 0.133610 | 0.0668052 | − | 0.997766i | \(-0.478719\pi\) | ||||
0.0668052 | + | 0.997766i | \(0.478719\pi\) | |||||||
\(558\) | −1.75978 | −0.0744974 | ||||||||
\(559\) | −5.91429 | −0.250148 | ||||||||
\(560\) | 0.659654 | 0.0278755 | ||||||||
\(561\) | 0.847786 | 0.0357935 | ||||||||
\(562\) | 7.10977 | 0.299907 | ||||||||
\(563\) | −15.6236 | −0.658457 | −0.329229 | − | 0.944250i | \(-0.606789\pi\) | ||||
−0.329229 | + | 0.944250i | \(0.606789\pi\) | |||||||
\(564\) | −8.06572 | −0.339628 | ||||||||
\(565\) | 1.92707 | 0.0810722 | ||||||||
\(566\) | −16.3119 | −0.685639 | ||||||||
\(567\) | 2.10092 | 0.0882303 | ||||||||
\(568\) | −11.4183 | −0.479100 | ||||||||
\(569\) | −6.69051 | −0.280481 | −0.140240 | − | 0.990117i | \(-0.544788\pi\) | ||||
−0.140240 | + | 0.990117i | \(0.544788\pi\) | |||||||
\(570\) | −2.43378 | −0.101940 | ||||||||
\(571\) | −44.1225 | −1.84647 | −0.923234 | − | 0.384237i | \(-0.874465\pi\) | ||||
−0.923234 | + | 0.384237i | \(0.874465\pi\) | |||||||
\(572\) | 5.80403 | 0.242679 | ||||||||
\(573\) | 15.5630 | 0.650155 | ||||||||
\(574\) | −8.57249 | −0.357809 | ||||||||
\(575\) | 26.4167 | 1.10165 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 20.4682 | 0.852103 | 0.426052 | − | 0.904699i | \(-0.359904\pi\) | ||||
0.426052 | + | 0.904699i | \(0.359904\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | −1.10959 | −0.0461130 | ||||||||
\(580\) | −1.24464 | −0.0516807 | ||||||||
\(581\) | −0.874635 | −0.0362860 | ||||||||
\(582\) | 2.22173 | 0.0920938 | ||||||||
\(583\) | 8.65739 | 0.358552 | ||||||||
\(584\) | 9.05018 | 0.374499 | ||||||||
\(585\) | −2.14956 | −0.0888735 | ||||||||
\(586\) | 9.86065 | 0.407340 | ||||||||
\(587\) | −29.1919 | −1.20488 | −0.602440 | − | 0.798164i | \(-0.705805\pi\) | ||||
−0.602440 | + | 0.798164i | \(0.705805\pi\) | |||||||
\(588\) | −2.58614 | −0.106651 | ||||||||
\(589\) | 13.6406 | 0.562050 | ||||||||
\(590\) | −0.313984 | −0.0129265 | ||||||||
\(591\) | −21.1479 | −0.869907 | ||||||||
\(592\) | 3.06470 | 0.125958 | ||||||||
\(593\) | −23.0992 | −0.948568 | −0.474284 | − | 0.880372i | \(-0.657293\pi\) | ||||
−0.474284 | + | 0.880372i | \(0.657293\pi\) | |||||||
\(594\) | 0.847786 | 0.0347851 | ||||||||
\(595\) | −0.659654 | −0.0270432 | ||||||||
\(596\) | −21.1802 | −0.867574 | ||||||||
\(597\) | 7.69680 | 0.315009 | ||||||||
\(598\) | −36.8977 | −1.50886 | ||||||||
\(599\) | −38.8922 | −1.58909 | −0.794545 | − | 0.607205i | \(-0.792291\pi\) | ||||
−0.794545 | + | 0.607205i | \(0.792291\pi\) | |||||||
\(600\) | 4.90141 | 0.200099 | ||||||||
\(601\) | 25.1438 | 1.02564 | 0.512818 | − | 0.858498i | \(-0.328602\pi\) | ||||
0.512818 | + | 0.858498i | \(0.328602\pi\) | |||||||
\(602\) | −1.81497 | −0.0739725 | ||||||||
\(603\) | −6.38895 | −0.260178 | ||||||||
\(604\) | 19.1223 | 0.778076 | ||||||||
\(605\) | −3.22815 | −0.131243 | ||||||||
\(606\) | 4.27600 | 0.173701 | ||||||||
\(607\) | −27.7869 | −1.12784 | −0.563918 | − | 0.825831i | \(-0.690707\pi\) | ||||
−0.563918 | + | 0.825831i | \(0.690707\pi\) | |||||||
\(608\) | −7.75129 | −0.314356 | ||||||||
\(609\) | −8.32808 | −0.337471 | ||||||||
\(610\) | −2.45825 | −0.0995318 | ||||||||
\(611\) | 55.2187 | 2.23391 | ||||||||
\(612\) | −1.00000 | −0.0404226 | ||||||||
\(613\) | 6.59027 | 0.266178 | 0.133089 | − | 0.991104i | \(-0.457510\pi\) | ||||
0.133089 | + | 0.991104i | \(0.457510\pi\) | |||||||
\(614\) | 26.5184 | 1.07020 | ||||||||
\(615\) | 1.28116 | 0.0516615 | ||||||||
\(616\) | 1.78113 | 0.0717637 | ||||||||
\(617\) | 37.1523 | 1.49570 | 0.747848 | − | 0.663870i | \(-0.231087\pi\) | ||||
0.747848 | + | 0.663870i | \(0.231087\pi\) | |||||||
\(618\) | 15.1099 | 0.607810 | ||||||||
\(619\) | −7.71680 | −0.310164 | −0.155082 | − | 0.987902i | \(-0.549564\pi\) | ||||
−0.155082 | + | 0.987902i | \(0.549564\pi\) | |||||||
\(620\) | 0.552542 | 0.0221906 | ||||||||
\(621\) | −5.38960 | −0.216277 | ||||||||
\(622\) | −13.4756 | −0.540321 | ||||||||
\(623\) | −28.6753 | −1.14885 | ||||||||
\(624\) | −6.84610 | −0.274063 | ||||||||
\(625\) | 23.5309 | 0.941237 | ||||||||
\(626\) | 9.63155 | 0.384954 | ||||||||
\(627\) | −6.57144 | −0.262438 | ||||||||
\(628\) | −16.5189 | −0.659176 | ||||||||
\(629\) | −3.06470 | −0.122197 | ||||||||
\(630\) | −0.659654 | −0.0262812 | ||||||||
\(631\) | −30.5736 | −1.21712 | −0.608559 | − | 0.793509i | \(-0.708252\pi\) | ||||
−0.608559 | + | 0.793509i | \(0.708252\pi\) | |||||||
\(632\) | −7.33532 | −0.291783 | ||||||||
\(633\) | 26.6228 | 1.05816 | ||||||||
\(634\) | 19.5266 | 0.775500 | ||||||||
\(635\) | −5.46384 | −0.216826 | ||||||||
\(636\) | −10.2118 | −0.404923 | ||||||||
\(637\) | 17.7050 | 0.701497 | ||||||||
\(638\) | −3.36064 | −0.133049 | ||||||||
\(639\) | 11.4183 | 0.451700 | ||||||||
\(640\) | −0.313984 | −0.0124113 | ||||||||
\(641\) | −15.0331 | −0.593773 | −0.296887 | − | 0.954913i | \(-0.595948\pi\) | ||||
−0.296887 | + | 0.954913i | \(0.595948\pi\) | |||||||
\(642\) | −14.9644 | −0.590598 | ||||||||
\(643\) | 36.2393 | 1.42914 | 0.714569 | − | 0.699565i | \(-0.246623\pi\) | ||||
0.714569 | + | 0.699565i | \(0.246623\pi\) | |||||||
\(644\) | −11.3231 | −0.446193 | ||||||||
\(645\) | 0.271248 | 0.0106804 | ||||||||
\(646\) | 7.75129 | 0.304971 | ||||||||
\(647\) | −27.5268 | −1.08219 | −0.541096 | − | 0.840961i | \(-0.681990\pi\) | ||||
−0.541096 | + | 0.840961i | \(0.681990\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −0.847786 | −0.0332785 | ||||||||
\(650\) | −33.5556 | −1.31616 | ||||||||
\(651\) | 3.69715 | 0.144903 | ||||||||
\(652\) | −3.73417 | −0.146241 | ||||||||
\(653\) | 2.88900 | 0.113055 | 0.0565277 | − | 0.998401i | \(-0.481997\pi\) | ||||
0.0565277 | + | 0.998401i | \(0.481997\pi\) | |||||||
\(654\) | 12.5270 | 0.489846 | ||||||||
\(655\) | −6.05502 | −0.236589 | ||||||||
\(656\) | 4.08035 | 0.159311 | ||||||||
\(657\) | −9.05018 | −0.353081 | ||||||||
\(658\) | 16.9454 | 0.660601 | ||||||||
\(659\) | 12.2383 | 0.476737 | 0.238368 | − | 0.971175i | \(-0.423387\pi\) | ||||
0.238368 | + | 0.971175i | \(0.423387\pi\) | |||||||
\(660\) | −0.266191 | −0.0103615 | ||||||||
\(661\) | 36.3610 | 1.41428 | 0.707140 | − | 0.707074i | \(-0.249985\pi\) | ||||
0.707140 | + | 0.707074i | \(0.249985\pi\) | |||||||
\(662\) | 18.6116 | 0.723362 | ||||||||
\(663\) | 6.84610 | 0.265881 | ||||||||
\(664\) | 0.416311 | 0.0161560 | ||||||||
\(665\) | 5.11317 | 0.198280 | ||||||||
\(666\) | −3.06470 | −0.118755 | ||||||||
\(667\) | 21.3645 | 0.827235 | ||||||||
\(668\) | −6.56448 | −0.253987 | ||||||||
\(669\) | 20.4920 | 0.792268 | ||||||||
\(670\) | 2.00603 | 0.0774996 | ||||||||
\(671\) | −6.63752 | −0.256239 | ||||||||
\(672\) | −2.10092 | −0.0810447 | ||||||||
\(673\) | 9.15795 | 0.353013 | 0.176506 | − | 0.984299i | \(-0.443520\pi\) | ||||
0.176506 | + | 0.984299i | \(0.443520\pi\) | |||||||
\(674\) | −12.8151 | −0.493620 | ||||||||
\(675\) | −4.90141 | −0.188656 | ||||||||
\(676\) | 33.8691 | 1.30266 | ||||||||
\(677\) | 45.3330 | 1.74229 | 0.871145 | − | 0.491025i | \(-0.163378\pi\) | ||||
0.871145 | + | 0.491025i | \(0.163378\pi\) | |||||||
\(678\) | −6.13747 | −0.235708 | ||||||||
\(679\) | −4.66768 | −0.179129 | ||||||||
\(680\) | 0.313984 | 0.0120407 | ||||||||
\(681\) | 8.46757 | 0.324478 | ||||||||
\(682\) | 1.49192 | 0.0571284 | ||||||||
\(683\) | 33.9416 | 1.29874 | 0.649369 | − | 0.760474i | \(-0.275033\pi\) | ||||
0.649369 | + | 0.760474i | \(0.275033\pi\) | |||||||
\(684\) | 7.75129 | 0.296378 | ||||||||
\(685\) | −3.90323 | −0.149135 | ||||||||
\(686\) | 20.1397 | 0.768937 | ||||||||
\(687\) | 11.5494 | 0.440637 | ||||||||
\(688\) | 0.863891 | 0.0329355 | ||||||||
\(689\) | 69.9108 | 2.66339 | ||||||||
\(690\) | 1.69225 | 0.0644227 | ||||||||
\(691\) | −12.8355 | −0.488285 | −0.244142 | − | 0.969739i | \(-0.578506\pi\) | ||||
−0.244142 | + | 0.969739i | \(0.578506\pi\) | |||||||
\(692\) | 0.502200 | 0.0190908 | ||||||||
\(693\) | −1.78113 | −0.0676595 | ||||||||
\(694\) | 13.0323 | 0.494699 | ||||||||
\(695\) | 6.48182 | 0.245869 | ||||||||
\(696\) | 3.96402 | 0.150256 | ||||||||
\(697\) | −4.08035 | −0.154554 | ||||||||
\(698\) | 3.18606 | 0.120594 | ||||||||
\(699\) | 0.514865 | 0.0194740 | ||||||||
\(700\) | −10.2975 | −0.389208 | ||||||||
\(701\) | 18.9973 | 0.717520 | 0.358760 | − | 0.933430i | \(-0.383200\pi\) | ||||
0.358760 | + | 0.933430i | \(0.383200\pi\) | |||||||
\(702\) | 6.84610 | 0.258389 | ||||||||
\(703\) | 23.7554 | 0.895950 | ||||||||
\(704\) | −0.847786 | −0.0319521 | ||||||||
\(705\) | −2.53250 | −0.0953796 | ||||||||
\(706\) | −12.9841 | −0.488664 | ||||||||
\(707\) | −8.98353 | −0.337860 | ||||||||
\(708\) | 1.00000 | 0.0375823 | ||||||||
\(709\) | 24.6962 | 0.927484 | 0.463742 | − | 0.885970i | \(-0.346507\pi\) | ||||
0.463742 | + | 0.885970i | \(0.346507\pi\) | |||||||
\(710\) | −3.58515 | −0.134548 | ||||||||
\(711\) | 7.33532 | 0.275096 | ||||||||
\(712\) | 13.6489 | 0.511515 | ||||||||
\(713\) | −9.48450 | −0.355197 | ||||||||
\(714\) | 2.10092 | 0.0786249 | ||||||||
\(715\) | 1.82237 | 0.0681528 | ||||||||
\(716\) | −9.83124 | −0.367411 | ||||||||
\(717\) | −28.4503 | −1.06250 | ||||||||
\(718\) | −10.0009 | −0.373230 | ||||||||
\(719\) | −52.8158 | −1.96970 | −0.984849 | − | 0.173416i | \(-0.944519\pi\) | ||||
−0.984849 | + | 0.173416i | \(0.944519\pi\) | |||||||
\(720\) | 0.313984 | 0.0117015 | ||||||||
\(721\) | −31.7447 | −1.18224 | ||||||||
\(722\) | −41.0826 | −1.52893 | ||||||||
\(723\) | 7.96535 | 0.296235 | ||||||||
\(724\) | −5.83704 | −0.216932 | ||||||||
\(725\) | 19.4293 | 0.721586 | ||||||||
\(726\) | 10.2813 | 0.381573 | ||||||||
\(727\) | 38.9838 | 1.44583 | 0.722914 | − | 0.690938i | \(-0.242802\pi\) | ||||
0.722914 | + | 0.690938i | \(0.242802\pi\) | |||||||
\(728\) | 14.3831 | 0.533073 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.84161 | 0.105173 | ||||||||
\(731\) | −0.863891 | −0.0319522 | ||||||||
\(732\) | 7.82924 | 0.289377 | ||||||||
\(733\) | −35.5586 | −1.31339 | −0.656693 | − | 0.754158i | \(-0.728045\pi\) | ||||
−0.656693 | + | 0.754158i | \(0.728045\pi\) | |||||||
\(734\) | −19.6011 | −0.723488 | ||||||||
\(735\) | −0.812005 | −0.0299513 | ||||||||
\(736\) | 5.38960 | 0.198663 | ||||||||
\(737\) | 5.41646 | 0.199518 | ||||||||
\(738\) | −4.08035 | −0.150200 | ||||||||
\(739\) | 14.3912 | 0.529389 | 0.264694 | − | 0.964332i | \(-0.414729\pi\) | ||||
0.264694 | + | 0.964332i | \(0.414729\pi\) | |||||||
\(740\) | 0.962264 | 0.0353735 | ||||||||
\(741\) | −53.0662 | −1.94943 | ||||||||
\(742\) | 21.4541 | 0.787605 | ||||||||
\(743\) | −36.1816 | −1.32737 | −0.663687 | − | 0.748010i | \(-0.731009\pi\) | ||||
−0.663687 | + | 0.748010i | \(0.731009\pi\) | |||||||
\(744\) | −1.75978 | −0.0645166 | ||||||||
\(745\) | −6.65023 | −0.243645 | ||||||||
\(746\) | −38.5365 | −1.41092 | ||||||||
\(747\) | −0.416311 | −0.0152320 | ||||||||
\(748\) | 0.847786 | 0.0309981 | ||||||||
\(749\) | 31.4390 | 1.14876 | ||||||||
\(750\) | 3.10888 | 0.113520 | ||||||||
\(751\) | −45.3318 | −1.65418 | −0.827090 | − | 0.562070i | \(-0.810005\pi\) | ||||
−0.827090 | + | 0.562070i | \(0.810005\pi\) | |||||||
\(752\) | −8.06572 | −0.294126 | ||||||||
\(753\) | 23.3659 | 0.851502 | ||||||||
\(754\) | −27.1381 | −0.988310 | ||||||||
\(755\) | 6.00409 | 0.218511 | ||||||||
\(756\) | 2.10092 | 0.0764097 | ||||||||
\(757\) | −33.2244 | −1.20756 | −0.603781 | − | 0.797150i | \(-0.706340\pi\) | ||||
−0.603781 | + | 0.797150i | \(0.706340\pi\) | |||||||
\(758\) | 20.4575 | 0.743049 | ||||||||
\(759\) | 4.56922 | 0.165852 | ||||||||
\(760\) | −2.43378 | −0.0882825 | ||||||||
\(761\) | −2.29216 | −0.0830906 | −0.0415453 | − | 0.999137i | \(-0.513228\pi\) | ||||
−0.0415453 | + | 0.999137i | \(0.513228\pi\) | |||||||
\(762\) | 17.4017 | 0.630396 | ||||||||
\(763\) | −26.3183 | −0.952786 | ||||||||
\(764\) | 15.5630 | 0.563050 | ||||||||
\(765\) | −0.313984 | −0.0113521 | ||||||||
\(766\) | 30.2752 | 1.09389 | ||||||||
\(767\) | −6.84610 | −0.247198 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −29.0977 | −1.04929 | −0.524644 | − | 0.851322i | \(-0.675802\pi\) | ||||
−0.524644 | + | 0.851322i | \(0.675802\pi\) | |||||||
\(770\) | 0.559245 | 0.0201538 | ||||||||
\(771\) | −17.2084 | −0.619746 | ||||||||
\(772\) | −1.10959 | −0.0399350 | ||||||||
\(773\) | −20.9442 | −0.753310 | −0.376655 | − | 0.926354i | \(-0.622926\pi\) | ||||
−0.376655 | + | 0.926354i | \(0.622926\pi\) | |||||||
\(774\) | −0.863891 | −0.0310519 | ||||||||
\(775\) | −8.62541 | −0.309834 | ||||||||
\(776\) | 2.22173 | 0.0797556 | ||||||||
\(777\) | 6.43868 | 0.230986 | ||||||||
\(778\) | 22.4006 | 0.803100 | ||||||||
\(779\) | 31.6280 | 1.13319 | ||||||||
\(780\) | −2.14956 | −0.0769667 | ||||||||
\(781\) | −9.68025 | −0.346387 | ||||||||
\(782\) | −5.38960 | −0.192732 | ||||||||
\(783\) | −3.96402 | −0.141662 | ||||||||
\(784\) | −2.58614 | −0.0923621 | ||||||||
\(785\) | −5.18667 | −0.185120 | ||||||||
\(786\) | 19.2845 | 0.687856 | ||||||||
\(787\) | −13.6835 | −0.487763 | −0.243881 | − | 0.969805i | \(-0.578421\pi\) | ||||
−0.243881 | + | 0.969805i | \(0.578421\pi\) | |||||||
\(788\) | −21.1479 | −0.753361 | ||||||||
\(789\) | 22.8845 | 0.814712 | ||||||||
\(790\) | −2.30317 | −0.0819431 | ||||||||
\(791\) | 12.8943 | 0.458470 | ||||||||
\(792\) | 0.847786 | 0.0301248 | ||||||||
\(793\) | −53.5998 | −1.90338 | ||||||||
\(794\) | 19.3679 | 0.687341 | ||||||||
\(795\) | −3.20633 | −0.113717 | ||||||||
\(796\) | 7.69680 | 0.272806 | ||||||||
\(797\) | 5.80094 | 0.205480 | 0.102740 | − | 0.994708i | \(-0.467239\pi\) | ||||
0.102740 | + | 0.994708i | \(0.467239\pi\) | |||||||
\(798\) | −16.2848 | −0.576477 | ||||||||
\(799\) | 8.06572 | 0.285345 | ||||||||
\(800\) | 4.90141 | 0.173291 | ||||||||
\(801\) | −13.6489 | −0.482261 | ||||||||
\(802\) | −14.5880 | −0.515120 | ||||||||
\(803\) | 7.67261 | 0.270761 | ||||||||
\(804\) | −6.38895 | −0.225321 | ||||||||
\(805\) | −3.55527 | −0.125307 | ||||||||
\(806\) | 12.0476 | 0.424360 | ||||||||
\(807\) | −14.5179 | −0.511054 | ||||||||
\(808\) | 4.27600 | 0.150429 | ||||||||
\(809\) | 17.3000 | 0.608237 | 0.304119 | − | 0.952634i | \(-0.401638\pi\) | ||||
0.304119 | + | 0.952634i | \(0.401638\pi\) | |||||||
\(810\) | −0.313984 | −0.0110323 | ||||||||
\(811\) | −7.82370 | −0.274727 | −0.137364 | − | 0.990521i | \(-0.543863\pi\) | ||||
−0.137364 | + | 0.990521i | \(0.543863\pi\) | |||||||
\(812\) | −8.32808 | −0.292258 | ||||||||
\(813\) | 20.9878 | 0.736073 | ||||||||
\(814\) | 2.59821 | 0.0910670 | ||||||||
\(815\) | −1.17247 | −0.0410697 | ||||||||
\(816\) | −1.00000 | −0.0350070 | ||||||||
\(817\) | 6.69628 | 0.234273 | ||||||||
\(818\) | 15.7198 | 0.549628 | ||||||||
\(819\) | −14.3831 | −0.502586 | ||||||||
\(820\) | 1.28116 | 0.0447402 | ||||||||
\(821\) | 19.9952 | 0.697838 | 0.348919 | − | 0.937153i | \(-0.386549\pi\) | ||||
0.348919 | + | 0.937153i | \(0.386549\pi\) | |||||||
\(822\) | 12.4313 | 0.433592 | ||||||||
\(823\) | 41.1031 | 1.43276 | 0.716382 | − | 0.697709i | \(-0.245797\pi\) | ||||
0.716382 | + | 0.697709i | \(0.245797\pi\) | |||||||
\(824\) | 15.1099 | 0.526379 | ||||||||
\(825\) | 4.15535 | 0.144671 | ||||||||
\(826\) | −2.10092 | −0.0731003 | ||||||||
\(827\) | 37.8778 | 1.31714 | 0.658570 | − | 0.752519i | \(-0.271162\pi\) | ||||
0.658570 | + | 0.752519i | \(0.271162\pi\) | |||||||
\(828\) | −5.38960 | −0.187301 | ||||||||
\(829\) | −7.40449 | −0.257168 | −0.128584 | − | 0.991699i | \(-0.541043\pi\) | ||||
−0.128584 | + | 0.991699i | \(0.541043\pi\) | |||||||
\(830\) | 0.130715 | 0.00453718 | ||||||||
\(831\) | −21.6987 | −0.752718 | ||||||||
\(832\) | −6.84610 | −0.237346 | ||||||||
\(833\) | 2.58614 | 0.0896044 | ||||||||
\(834\) | −20.6438 | −0.714836 | ||||||||
\(835\) | −2.06114 | −0.0713286 | ||||||||
\(836\) | −6.57144 | −0.227278 | ||||||||
\(837\) | 1.75978 | 0.0608269 | ||||||||
\(838\) | −10.3992 | −0.359233 | ||||||||
\(839\) | 11.1425 | 0.384680 | 0.192340 | − | 0.981328i | \(-0.438392\pi\) | ||||
0.192340 | + | 0.981328i | \(0.438392\pi\) | |||||||
\(840\) | −0.659654 | −0.0227602 | ||||||||
\(841\) | −13.2866 | −0.458158 | ||||||||
\(842\) | −1.46278 | −0.0504107 | ||||||||
\(843\) | −7.10977 | −0.244873 | ||||||||
\(844\) | 26.6228 | 0.916394 | ||||||||
\(845\) | 10.6343 | 0.365833 | ||||||||
\(846\) | 8.06572 | 0.277305 | ||||||||
\(847\) | −21.6001 | −0.742188 | ||||||||
\(848\) | −10.2118 | −0.350673 | ||||||||
\(849\) | 16.3119 | 0.559822 | ||||||||
\(850\) | −4.90141 | −0.168117 | ||||||||
\(851\) | −16.5175 | −0.566212 | ||||||||
\(852\) | 11.4183 | 0.391184 | ||||||||
\(853\) | 8.32368 | 0.284997 | 0.142499 | − | 0.989795i | \(-0.454486\pi\) | ||||
0.142499 | + | 0.989795i | \(0.454486\pi\) | |||||||
\(854\) | −16.4486 | −0.562860 | ||||||||
\(855\) | 2.43378 | 0.0832335 | ||||||||
\(856\) | −14.9644 | −0.511473 | ||||||||
\(857\) | −42.4814 | −1.45114 | −0.725568 | − | 0.688150i | \(-0.758423\pi\) | ||||
−0.725568 | + | 0.688150i | \(0.758423\pi\) | |||||||
\(858\) | −5.80403 | −0.198146 | ||||||||
\(859\) | 9.00887 | 0.307379 | 0.153689 | − | 0.988119i | \(-0.450885\pi\) | ||||
0.153689 | + | 0.988119i | \(0.450885\pi\) | |||||||
\(860\) | 0.271248 | 0.00924947 | ||||||||
\(861\) | 8.57249 | 0.292150 | ||||||||
\(862\) | 8.94044 | 0.304513 | ||||||||
\(863\) | −2.81180 | −0.0957149 | −0.0478574 | − | 0.998854i | \(-0.515239\pi\) | ||||
−0.0478574 | + | 0.998854i | \(0.515239\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0.157682 | 0.00536136 | ||||||||
\(866\) | 1.52494 | 0.0518195 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 3.69715 | 0.125490 | ||||||||
\(869\) | −6.21878 | −0.210958 | ||||||||
\(870\) | 1.24464 | 0.0421971 | ||||||||
\(871\) | 43.7394 | 1.48205 | ||||||||
\(872\) | 12.5270 | 0.424219 | ||||||||
\(873\) | −2.22173 | −0.0751943 | ||||||||
\(874\) | 41.7764 | 1.41311 | ||||||||
\(875\) | −6.53151 | −0.220805 | ||||||||
\(876\) | −9.05018 | −0.305777 | ||||||||
\(877\) | −17.9219 | −0.605180 | −0.302590 | − | 0.953121i | \(-0.597851\pi\) | ||||
−0.302590 | + | 0.953121i | \(0.597851\pi\) | |||||||
\(878\) | 33.9597 | 1.14608 | ||||||||
\(879\) | −9.86065 | −0.332591 | ||||||||
\(880\) | −0.266191 | −0.00897329 | ||||||||
\(881\) | 53.5071 | 1.80270 | 0.901350 | − | 0.433091i | \(-0.142577\pi\) | ||||
0.901350 | + | 0.433091i | \(0.142577\pi\) | |||||||
\(882\) | 2.58614 | 0.0870798 | ||||||||
\(883\) | −0.645428 | −0.0217204 | −0.0108602 | − | 0.999941i | \(-0.503457\pi\) | ||||
−0.0108602 | + | 0.999941i | \(0.503457\pi\) | |||||||
\(884\) | 6.84610 | 0.230259 | ||||||||
\(885\) | 0.313984 | 0.0105544 | ||||||||
\(886\) | −28.1430 | −0.945483 | ||||||||
\(887\) | 55.3586 | 1.85876 | 0.929379 | − | 0.369126i | \(-0.120343\pi\) | ||||
0.929379 | + | 0.369126i | \(0.120343\pi\) | |||||||
\(888\) | −3.06470 | −0.102844 | ||||||||
\(889\) | −36.5595 | −1.22617 | ||||||||
\(890\) | 4.28554 | 0.143652 | ||||||||
\(891\) | −0.847786 | −0.0284019 | ||||||||
\(892\) | 20.4920 | 0.686124 | ||||||||
\(893\) | −62.5197 | −2.09214 | ||||||||
\(894\) | 21.1802 | 0.708371 | ||||||||
\(895\) | −3.08685 | −0.103182 | ||||||||
\(896\) | −2.10092 | −0.0701868 | ||||||||
\(897\) | 36.8977 | 1.23198 | ||||||||
\(898\) | 23.7418 | 0.792275 | ||||||||
\(899\) | −6.97579 | −0.232656 | ||||||||
\(900\) | −4.90141 | −0.163380 | ||||||||
\(901\) | 10.2118 | 0.340203 | ||||||||
\(902\) | 3.45926 | 0.115181 | ||||||||
\(903\) | 1.81497 | 0.0603983 | ||||||||
\(904\) | −6.13747 | −0.204129 | ||||||||
\(905\) | −1.83274 | −0.0609222 | ||||||||
\(906\) | −19.1223 | −0.635296 | ||||||||
\(907\) | 46.6071 | 1.54756 | 0.773782 | − | 0.633452i | \(-0.218362\pi\) | ||||
0.773782 | + | 0.633452i | \(0.218362\pi\) | |||||||
\(908\) | 8.46757 | 0.281006 | ||||||||
\(909\) | −4.27600 | −0.141826 | ||||||||
\(910\) | 4.51606 | 0.149706 | ||||||||
\(911\) | 2.80799 | 0.0930328 | 0.0465164 | − | 0.998918i | \(-0.485188\pi\) | ||||
0.0465164 | + | 0.998918i | \(0.485188\pi\) | |||||||
\(912\) | 7.75129 | 0.256671 | ||||||||
\(913\) | 0.352942 | 0.0116807 | ||||||||
\(914\) | −28.6991 | −0.949283 | ||||||||
\(915\) | 2.45825 | 0.0812674 | ||||||||
\(916\) | 11.5494 | 0.381603 | ||||||||
\(917\) | −40.5152 | −1.33793 | ||||||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | −56.7154 | −1.87087 | −0.935435 | − | 0.353500i | \(-0.884992\pi\) | ||||
−0.935435 | + | 0.353500i | \(0.884992\pi\) | |||||||
\(920\) | 1.69225 | 0.0557917 | ||||||||
\(921\) | −26.5184 | −0.873813 | ||||||||
\(922\) | 17.6993 | 0.582895 | ||||||||
\(923\) | −78.1707 | −2.57302 | ||||||||
\(924\) | −1.78113 | −0.0585948 | ||||||||
\(925\) | −15.0213 | −0.493899 | ||||||||
\(926\) | 11.4644 | 0.376742 | ||||||||
\(927\) | −15.1099 | −0.496275 | ||||||||
\(928\) | 3.96402 | 0.130125 | ||||||||
\(929\) | −55.5629 | −1.82296 | −0.911480 | − | 0.411344i | \(-0.865059\pi\) | ||||
−0.911480 | + | 0.411344i | \(0.865059\pi\) | |||||||
\(930\) | −0.552542 | −0.0181186 | ||||||||
\(931\) | −20.0459 | −0.656979 | ||||||||
\(932\) | 0.514865 | 0.0168650 | ||||||||
\(933\) | 13.4756 | 0.441170 | ||||||||
\(934\) | 9.50755 | 0.311096 | ||||||||
\(935\) | 0.266191 | 0.00870537 | ||||||||
\(936\) | 6.84610 | 0.223772 | ||||||||
\(937\) | −29.2649 | −0.956044 | −0.478022 | − | 0.878348i | \(-0.658646\pi\) | ||||
−0.478022 | + | 0.878348i | \(0.658646\pi\) | |||||||
\(938\) | 13.4227 | 0.438266 | ||||||||
\(939\) | −9.63155 | −0.314314 | ||||||||
\(940\) | −2.53250 | −0.0826011 | ||||||||
\(941\) | −52.3904 | −1.70788 | −0.853939 | − | 0.520373i | \(-0.825793\pi\) | ||||
−0.853939 | + | 0.520373i | \(0.825793\pi\) | |||||||
\(942\) | 16.5189 | 0.538215 | ||||||||
\(943\) | −21.9914 | −0.716140 | ||||||||
\(944\) | 1.00000 | 0.0325472 | ||||||||
\(945\) | 0.659654 | 0.0214586 | ||||||||
\(946\) | 0.732395 | 0.0238122 | ||||||||
\(947\) | 49.6228 | 1.61252 | 0.806262 | − | 0.591558i | \(-0.201487\pi\) | ||||
0.806262 | + | 0.591558i | \(0.201487\pi\) | |||||||
\(948\) | 7.33532 | 0.238240 | ||||||||
\(949\) | 61.9585 | 2.01126 | ||||||||
\(950\) | 37.9923 | 1.23263 | ||||||||
\(951\) | −19.5266 | −0.633193 | ||||||||
\(952\) | 2.10092 | 0.0680912 | ||||||||
\(953\) | 31.3574 | 1.01577 | 0.507883 | − | 0.861426i | \(-0.330428\pi\) | ||||
0.507883 | + | 0.861426i | \(0.330428\pi\) | |||||||
\(954\) | 10.2118 | 0.330618 | ||||||||
\(955\) | 4.88653 | 0.158125 | ||||||||
\(956\) | −28.4503 | −0.920149 | ||||||||
\(957\) | 3.36064 | 0.108634 | ||||||||
\(958\) | −7.89050 | −0.254931 | ||||||||
\(959\) | −26.1172 | −0.843368 | ||||||||
\(960\) | 0.313984 | 0.0101338 | ||||||||
\(961\) | −27.9032 | −0.900103 | ||||||||
\(962\) | 20.9812 | 0.676462 | ||||||||
\(963\) | 14.9644 | 0.482222 | ||||||||
\(964\) | 7.96535 | 0.256547 | ||||||||
\(965\) | −0.348393 | −0.0112152 | ||||||||
\(966\) | 11.3231 | 0.364315 | ||||||||
\(967\) | −58.7412 | −1.88899 | −0.944495 | − | 0.328525i | \(-0.893449\pi\) | ||||
−0.944495 | + | 0.328525i | \(0.893449\pi\) | |||||||
\(968\) | 10.2813 | 0.330452 | ||||||||
\(969\) | −7.75129 | −0.249007 | ||||||||
\(970\) | 0.697588 | 0.0223982 | ||||||||
\(971\) | −43.7603 | −1.40433 | −0.702167 | − | 0.712012i | \(-0.747784\pi\) | ||||
−0.702167 | + | 0.712012i | \(0.747784\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 43.3710 | 1.39041 | ||||||||
\(974\) | −29.3249 | −0.939630 | ||||||||
\(975\) | 33.5556 | 1.07464 | ||||||||
\(976\) | 7.82924 | 0.250608 | ||||||||
\(977\) | −26.2814 | −0.840818 | −0.420409 | − | 0.907335i | \(-0.638113\pi\) | ||||
−0.420409 | + | 0.907335i | \(0.638113\pi\) | |||||||
\(978\) | 3.73417 | 0.119405 | ||||||||
\(979\) | 11.5714 | 0.369822 | ||||||||
\(980\) | −0.812005 | −0.0259386 | ||||||||
\(981\) | −12.5270 | −0.399958 | ||||||||
\(982\) | −0.731272 | −0.0233358 | ||||||||
\(983\) | 33.6563 | 1.07347 | 0.536734 | − | 0.843751i | \(-0.319658\pi\) | ||||
0.536734 | + | 0.843751i | \(0.319658\pi\) | |||||||
\(984\) | −4.08035 | −0.130077 | ||||||||
\(985\) | −6.64008 | −0.211571 | ||||||||
\(986\) | −3.96402 | −0.126240 | ||||||||
\(987\) | −16.9454 | −0.539379 | ||||||||
\(988\) | −53.0662 | −1.68826 | ||||||||
\(989\) | −4.65603 | −0.148053 | ||||||||
\(990\) | 0.266191 | 0.00846010 | ||||||||
\(991\) | 10.9954 | 0.349281 | 0.174640 | − | 0.984632i | \(-0.444124\pi\) | ||||
0.174640 | + | 0.984632i | \(0.444124\pi\) | |||||||
\(992\) | −1.75978 | −0.0558730 | ||||||||
\(993\) | −18.6116 | −0.590623 | ||||||||
\(994\) | −23.9889 | −0.760881 | ||||||||
\(995\) | 2.41667 | 0.0766136 | ||||||||
\(996\) | −0.416311 | −0.0131913 | ||||||||
\(997\) | −38.9527 | −1.23365 | −0.616823 | − | 0.787102i | \(-0.711581\pi\) | ||||
−0.616823 | + | 0.787102i | \(0.711581\pi\) | |||||||
\(998\) | −39.9939 | −1.26598 | ||||||||
\(999\) | 3.06470 | 0.0969627 |
(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.y.1.6 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.y.1.6 | ✓ | 10 | 1.1 | even | 1 | trivial |