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 | 1.9 | ||
Root | \(-3.46791\) 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 | ||||||||
\(5\) | 3.46791 | 1.55090 | 0.775449 | − | 0.631410i | \(-0.217524\pi\) | ||||
0.775449 | + | 0.631410i | \(0.217524\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −1.61634 | −0.610920 | −0.305460 | − | 0.952205i | \(-0.598810\pi\) | ||||
−0.305460 | + | 0.952205i | \(0.598810\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.46791 | −1.09665 | ||||||||
\(11\) | 4.46894 | 1.34744 | 0.673719 | − | 0.738988i | \(-0.264696\pi\) | ||||
0.673719 | + | 0.738988i | \(0.264696\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −4.75403 | −1.31853 | −0.659266 | − | 0.751910i | \(-0.729133\pi\) | ||||
−0.659266 | + | 0.751910i | \(0.729133\pi\) | |||||||
\(14\) | 1.61634 | 0.431986 | ||||||||
\(15\) | 3.46791 | 0.895411 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −4.47086 | −1.02569 | −0.512843 | − | 0.858483i | \(-0.671408\pi\) | ||||
−0.512843 | + | 0.858483i | \(0.671408\pi\) | |||||||
\(20\) | 3.46791 | 0.775449 | ||||||||
\(21\) | −1.61634 | −0.352715 | ||||||||
\(22\) | −4.46894 | −0.952782 | ||||||||
\(23\) | −8.14330 | −1.69800 | −0.848998 | − | 0.528396i | \(-0.822794\pi\) | ||||
−0.848998 | + | 0.528396i | \(0.822794\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 7.02642 | 1.40528 | ||||||||
\(26\) | 4.75403 | 0.932343 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.61634 | −0.305460 | ||||||||
\(29\) | 6.35448 | 1.18000 | 0.589998 | − | 0.807404i | \(-0.299128\pi\) | ||||
0.589998 | + | 0.807404i | \(0.299128\pi\) | |||||||
\(30\) | −3.46791 | −0.633151 | ||||||||
\(31\) | −10.4107 | −1.86982 | −0.934912 | − | 0.354879i | \(-0.884522\pi\) | ||||
−0.934912 | + | 0.354879i | \(0.884522\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.46894 | 0.777943 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | −5.60533 | −0.947474 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −11.5338 | −1.89615 | −0.948073 | − | 0.318054i | \(-0.896971\pi\) | ||||
−0.948073 | + | 0.318054i | \(0.896971\pi\) | |||||||
\(38\) | 4.47086 | 0.725269 | ||||||||
\(39\) | −4.75403 | −0.761255 | ||||||||
\(40\) | −3.46791 | −0.548325 | ||||||||
\(41\) | −6.83512 | −1.06747 | −0.533733 | − | 0.845653i | \(-0.679211\pi\) | ||||
−0.533733 | + | 0.845653i | \(0.679211\pi\) | |||||||
\(42\) | 1.61634 | 0.249407 | ||||||||
\(43\) | −3.54907 | −0.541228 | −0.270614 | − | 0.962688i | \(-0.587227\pi\) | ||||
−0.270614 | + | 0.962688i | \(0.587227\pi\) | |||||||
\(44\) | 4.46894 | 0.673719 | ||||||||
\(45\) | 3.46791 | 0.516966 | ||||||||
\(46\) | 8.14330 | 1.20066 | ||||||||
\(47\) | −4.44449 | −0.648295 | −0.324148 | − | 0.946007i | \(-0.605077\pi\) | ||||
−0.324148 | + | 0.946007i | \(0.605077\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −4.38744 | −0.626777 | ||||||||
\(50\) | −7.02642 | −0.993685 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −4.75403 | −0.659266 | ||||||||
\(53\) | 7.21748 | 0.991397 | 0.495698 | − | 0.868495i | \(-0.334912\pi\) | ||||
0.495698 | + | 0.868495i | \(0.334912\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 15.4979 | 2.08974 | ||||||||
\(56\) | 1.61634 | 0.215993 | ||||||||
\(57\) | −4.47086 | −0.592180 | ||||||||
\(58\) | −6.35448 | −0.834384 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 3.46791 | 0.447706 | ||||||||
\(61\) | −3.12863 | −0.400580 | −0.200290 | − | 0.979737i | \(-0.564188\pi\) | ||||
−0.200290 | + | 0.979737i | \(0.564188\pi\) | |||||||
\(62\) | 10.4107 | 1.32217 | ||||||||
\(63\) | −1.61634 | −0.203640 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −16.4866 | −2.04491 | ||||||||
\(66\) | −4.46894 | −0.550089 | ||||||||
\(67\) | −13.7911 | −1.68485 | −0.842425 | − | 0.538814i | \(-0.818873\pi\) | ||||
−0.842425 | + | 0.538814i | \(0.818873\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | −8.14330 | −0.980338 | ||||||||
\(70\) | 5.60533 | 0.669965 | ||||||||
\(71\) | −6.19584 | −0.735311 | −0.367655 | − | 0.929962i | \(-0.619839\pi\) | ||||
−0.367655 | + | 0.929962i | \(0.619839\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −6.44163 | −0.753936 | −0.376968 | − | 0.926226i | \(-0.623033\pi\) | ||||
−0.376968 | + | 0.926226i | \(0.623033\pi\) | |||||||
\(74\) | 11.5338 | 1.34078 | ||||||||
\(75\) | 7.02642 | 0.811341 | ||||||||
\(76\) | −4.47086 | −0.512843 | ||||||||
\(77\) | −7.22334 | −0.823176 | ||||||||
\(78\) | 4.75403 | 0.538288 | ||||||||
\(79\) | 1.63136 | 0.183542 | 0.0917711 | − | 0.995780i | \(-0.470747\pi\) | ||||
0.0917711 | + | 0.995780i | \(0.470747\pi\) | |||||||
\(80\) | 3.46791 | 0.387724 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.83512 | 0.754813 | ||||||||
\(83\) | 15.0535 | 1.65233 | 0.826166 | − | 0.563426i | \(-0.190517\pi\) | ||||
0.826166 | + | 0.563426i | \(0.190517\pi\) | |||||||
\(84\) | −1.61634 | −0.176357 | ||||||||
\(85\) | −3.46791 | −0.376148 | ||||||||
\(86\) | 3.54907 | 0.382706 | ||||||||
\(87\) | 6.35448 | 0.681271 | ||||||||
\(88\) | −4.46894 | −0.476391 | ||||||||
\(89\) | 11.4660 | 1.21540 | 0.607699 | − | 0.794167i | \(-0.292093\pi\) | ||||
0.607699 | + | 0.794167i | \(0.292093\pi\) | |||||||
\(90\) | −3.46791 | −0.365550 | ||||||||
\(91\) | 7.68415 | 0.805517 | ||||||||
\(92\) | −8.14330 | −0.848998 | ||||||||
\(93\) | −10.4107 | −1.07954 | ||||||||
\(94\) | 4.44449 | 0.458414 | ||||||||
\(95\) | −15.5046 | −1.59073 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 8.18102 | 0.830657 | 0.415328 | − | 0.909672i | \(-0.363667\pi\) | ||||
0.415328 | + | 0.909672i | \(0.363667\pi\) | |||||||
\(98\) | 4.38744 | 0.443198 | ||||||||
\(99\) | 4.46894 | 0.449146 | ||||||||
\(100\) | 7.02642 | 0.702642 | ||||||||
\(101\) | 1.99314 | 0.198325 | 0.0991623 | − | 0.995071i | \(-0.468384\pi\) | ||||
0.0991623 | + | 0.995071i | \(0.468384\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | −14.2936 | −1.40839 | −0.704195 | − | 0.710007i | \(-0.748692\pi\) | ||||
−0.704195 | + | 0.710007i | \(0.748692\pi\) | |||||||
\(104\) | 4.75403 | 0.466171 | ||||||||
\(105\) | −5.60533 | −0.547025 | ||||||||
\(106\) | −7.21748 | −0.701023 | ||||||||
\(107\) | 4.73424 | 0.457676 | 0.228838 | − | 0.973465i | \(-0.426507\pi\) | ||||
0.228838 | + | 0.973465i | \(0.426507\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −7.09575 | −0.679650 | −0.339825 | − | 0.940489i | \(-0.610368\pi\) | ||||
−0.339825 | + | 0.940489i | \(0.610368\pi\) | |||||||
\(110\) | −15.4979 | −1.47767 | ||||||||
\(111\) | −11.5338 | −1.09474 | ||||||||
\(112\) | −1.61634 | −0.152730 | ||||||||
\(113\) | −2.12850 | −0.200232 | −0.100116 | − | 0.994976i | \(-0.531921\pi\) | ||||
−0.100116 | + | 0.994976i | \(0.531921\pi\) | |||||||
\(114\) | 4.47086 | 0.418734 | ||||||||
\(115\) | −28.2403 | −2.63342 | ||||||||
\(116\) | 6.35448 | 0.589998 | ||||||||
\(117\) | −4.75403 | −0.439511 | ||||||||
\(118\) | −1.00000 | −0.0920575 | ||||||||
\(119\) | 1.61634 | 0.148170 | ||||||||
\(120\) | −3.46791 | −0.316576 | ||||||||
\(121\) | 8.97147 | 0.815588 | ||||||||
\(122\) | 3.12863 | 0.283253 | ||||||||
\(123\) | −6.83512 | −0.616302 | ||||||||
\(124\) | −10.4107 | −0.934912 | ||||||||
\(125\) | 7.02743 | 0.628553 | ||||||||
\(126\) | 1.61634 | 0.143995 | ||||||||
\(127\) | 4.83842 | 0.429340 | 0.214670 | − | 0.976687i | \(-0.431132\pi\) | ||||
0.214670 | + | 0.976687i | \(0.431132\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −3.54907 | −0.312478 | ||||||||
\(130\) | 16.4866 | 1.44597 | ||||||||
\(131\) | −15.6705 | −1.36914 | −0.684569 | − | 0.728948i | \(-0.740010\pi\) | ||||
−0.684569 | + | 0.728948i | \(0.740010\pi\) | |||||||
\(132\) | 4.46894 | 0.388972 | ||||||||
\(133\) | 7.22644 | 0.626612 | ||||||||
\(134\) | 13.7911 | 1.19137 | ||||||||
\(135\) | 3.46791 | 0.298470 | ||||||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | 10.1634 | 0.868319 | 0.434159 | − | 0.900836i | \(-0.357045\pi\) | ||||
0.434159 | + | 0.900836i | \(0.357045\pi\) | |||||||
\(138\) | 8.14330 | 0.693204 | ||||||||
\(139\) | −8.26128 | −0.700712 | −0.350356 | − | 0.936617i | \(-0.613939\pi\) | ||||
−0.350356 | + | 0.936617i | \(0.613939\pi\) | |||||||
\(140\) | −5.60533 | −0.473737 | ||||||||
\(141\) | −4.44449 | −0.374293 | ||||||||
\(142\) | 6.19584 | 0.519943 | ||||||||
\(143\) | −21.2455 | −1.77664 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 22.0368 | 1.83005 | ||||||||
\(146\) | 6.44163 | 0.533113 | ||||||||
\(147\) | −4.38744 | −0.361870 | ||||||||
\(148\) | −11.5338 | −0.948073 | ||||||||
\(149\) | −2.73869 | −0.224362 | −0.112181 | − | 0.993688i | \(-0.535784\pi\) | ||||
−0.112181 | + | 0.993688i | \(0.535784\pi\) | |||||||
\(150\) | −7.02642 | −0.573705 | ||||||||
\(151\) | −2.48875 | −0.202532 | −0.101266 | − | 0.994859i | \(-0.532289\pi\) | ||||
−0.101266 | + | 0.994859i | \(0.532289\pi\) | |||||||
\(152\) | 4.47086 | 0.362635 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 7.22334 | 0.582074 | ||||||||
\(155\) | −36.1035 | −2.89991 | ||||||||
\(156\) | −4.75403 | −0.380627 | ||||||||
\(157\) | 18.6301 | 1.48684 | 0.743422 | − | 0.668822i | \(-0.233201\pi\) | ||||
0.743422 | + | 0.668822i | \(0.233201\pi\) | |||||||
\(158\) | −1.63136 | −0.129784 | ||||||||
\(159\) | 7.21748 | 0.572383 | ||||||||
\(160\) | −3.46791 | −0.274163 | ||||||||
\(161\) | 13.1624 | 1.03734 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 16.2123 | 1.26985 | 0.634924 | − | 0.772575i | \(-0.281032\pi\) | ||||
0.634924 | + | 0.772575i | \(0.281032\pi\) | |||||||
\(164\) | −6.83512 | −0.533733 | ||||||||
\(165\) | 15.4979 | 1.20651 | ||||||||
\(166\) | −15.0535 | −1.16838 | ||||||||
\(167\) | 9.85713 | 0.762768 | 0.381384 | − | 0.924417i | \(-0.375448\pi\) | ||||
0.381384 | + | 0.924417i | \(0.375448\pi\) | |||||||
\(168\) | 1.61634 | 0.124704 | ||||||||
\(169\) | 9.60084 | 0.738526 | ||||||||
\(170\) | 3.46791 | 0.265977 | ||||||||
\(171\) | −4.47086 | −0.341895 | ||||||||
\(172\) | −3.54907 | −0.270614 | ||||||||
\(173\) | −7.57175 | −0.575669 | −0.287835 | − | 0.957680i | \(-0.592935\pi\) | ||||
−0.287835 | + | 0.957680i | \(0.592935\pi\) | |||||||
\(174\) | −6.35448 | −0.481732 | ||||||||
\(175\) | −11.3571 | −0.858516 | ||||||||
\(176\) | 4.46894 | 0.336859 | ||||||||
\(177\) | 1.00000 | 0.0751646 | ||||||||
\(178\) | −11.4660 | −0.859416 | ||||||||
\(179\) | 14.1115 | 1.05474 | 0.527371 | − | 0.849635i | \(-0.323178\pi\) | ||||
0.527371 | + | 0.849635i | \(0.323178\pi\) | |||||||
\(180\) | 3.46791 | 0.258483 | ||||||||
\(181\) | 24.0460 | 1.78733 | 0.893664 | − | 0.448737i | \(-0.148126\pi\) | ||||
0.893664 | + | 0.448737i | \(0.148126\pi\) | |||||||
\(182\) | −7.68415 | −0.569587 | ||||||||
\(183\) | −3.12863 | −0.231275 | ||||||||
\(184\) | 8.14330 | 0.600332 | ||||||||
\(185\) | −39.9982 | −2.94073 | ||||||||
\(186\) | 10.4107 | 0.763353 | ||||||||
\(187\) | −4.46894 | −0.326802 | ||||||||
\(188\) | −4.44449 | −0.324148 | ||||||||
\(189\) | −1.61634 | −0.117572 | ||||||||
\(190\) | 15.5046 | 1.12482 | ||||||||
\(191\) | 27.3260 | 1.97724 | 0.988621 | − | 0.150430i | \(-0.0480657\pi\) | ||||
0.988621 | + | 0.150430i | \(0.0480657\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −15.3997 | −1.10850 | −0.554248 | − | 0.832352i | \(-0.686994\pi\) | ||||
−0.554248 | + | 0.832352i | \(0.686994\pi\) | |||||||
\(194\) | −8.18102 | −0.587363 | ||||||||
\(195\) | −16.4866 | −1.18063 | ||||||||
\(196\) | −4.38744 | −0.313388 | ||||||||
\(197\) | −6.44083 | −0.458890 | −0.229445 | − | 0.973322i | \(-0.573691\pi\) | ||||
−0.229445 | + | 0.973322i | \(0.573691\pi\) | |||||||
\(198\) | −4.46894 | −0.317594 | ||||||||
\(199\) | −22.0655 | −1.56418 | −0.782092 | − | 0.623163i | \(-0.785847\pi\) | ||||
−0.782092 | + | 0.623163i | \(0.785847\pi\) | |||||||
\(200\) | −7.02642 | −0.496843 | ||||||||
\(201\) | −13.7911 | −0.972748 | ||||||||
\(202\) | −1.99314 | −0.140237 | ||||||||
\(203\) | −10.2710 | −0.720884 | ||||||||
\(204\) | −1.00000 | −0.0700140 | ||||||||
\(205\) | −23.7036 | −1.65553 | ||||||||
\(206\) | 14.2936 | 0.995882 | ||||||||
\(207\) | −8.14330 | −0.565999 | ||||||||
\(208\) | −4.75403 | −0.329633 | ||||||||
\(209\) | −19.9800 | −1.38205 | ||||||||
\(210\) | 5.60533 | 0.386805 | ||||||||
\(211\) | 12.2576 | 0.843846 | 0.421923 | − | 0.906632i | \(-0.361355\pi\) | ||||
0.421923 | + | 0.906632i | \(0.361355\pi\) | |||||||
\(212\) | 7.21748 | 0.495698 | ||||||||
\(213\) | −6.19584 | −0.424532 | ||||||||
\(214\) | −4.73424 | −0.323626 | ||||||||
\(215\) | −12.3079 | −0.839389 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 16.8273 | 1.14231 | ||||||||
\(218\) | 7.09575 | 0.480585 | ||||||||
\(219\) | −6.44163 | −0.435285 | ||||||||
\(220\) | 15.4979 | 1.04487 | ||||||||
\(221\) | 4.75403 | 0.319791 | ||||||||
\(222\) | 11.5338 | 0.774098 | ||||||||
\(223\) | 25.7757 | 1.72607 | 0.863033 | − | 0.505147i | \(-0.168562\pi\) | ||||
0.863033 | + | 0.505147i | \(0.168562\pi\) | |||||||
\(224\) | 1.61634 | 0.107996 | ||||||||
\(225\) | 7.02642 | 0.468428 | ||||||||
\(226\) | 2.12850 | 0.141586 | ||||||||
\(227\) | −18.7200 | −1.24249 | −0.621247 | − | 0.783615i | \(-0.713373\pi\) | ||||
−0.621247 | + | 0.783615i | \(0.713373\pi\) | |||||||
\(228\) | −4.47086 | −0.296090 | ||||||||
\(229\) | 16.0744 | 1.06222 | 0.531112 | − | 0.847301i | \(-0.321774\pi\) | ||||
0.531112 | + | 0.847301i | \(0.321774\pi\) | |||||||
\(230\) | 28.2403 | 1.86211 | ||||||||
\(231\) | −7.22334 | −0.475261 | ||||||||
\(232\) | −6.35448 | −0.417192 | ||||||||
\(233\) | −4.16581 | −0.272911 | −0.136455 | − | 0.990646i | \(-0.543571\pi\) | ||||
−0.136455 | + | 0.990646i | \(0.543571\pi\) | |||||||
\(234\) | 4.75403 | 0.310781 | ||||||||
\(235\) | −15.4131 | −1.00544 | ||||||||
\(236\) | 1.00000 | 0.0650945 | ||||||||
\(237\) | 1.63136 | 0.105968 | ||||||||
\(238\) | −1.61634 | −0.104772 | ||||||||
\(239\) | 14.3722 | 0.929662 | 0.464831 | − | 0.885399i | \(-0.346115\pi\) | ||||
0.464831 | + | 0.885399i | \(0.346115\pi\) | |||||||
\(240\) | 3.46791 | 0.223853 | ||||||||
\(241\) | 25.4335 | 1.63832 | 0.819158 | − | 0.573568i | \(-0.194441\pi\) | ||||
0.819158 | + | 0.573568i | \(0.194441\pi\) | |||||||
\(242\) | −8.97147 | −0.576708 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −3.12863 | −0.200290 | ||||||||
\(245\) | −15.2153 | −0.972067 | ||||||||
\(246\) | 6.83512 | 0.435791 | ||||||||
\(247\) | 21.2546 | 1.35240 | ||||||||
\(248\) | 10.4107 | 0.661083 | ||||||||
\(249\) | 15.0535 | 0.953975 | ||||||||
\(250\) | −7.02743 | −0.444454 | ||||||||
\(251\) | 19.8080 | 1.25027 | 0.625135 | − | 0.780516i | \(-0.285044\pi\) | ||||
0.625135 | + | 0.780516i | \(0.285044\pi\) | |||||||
\(252\) | −1.61634 | −0.101820 | ||||||||
\(253\) | −36.3920 | −2.28794 | ||||||||
\(254\) | −4.83842 | −0.303589 | ||||||||
\(255\) | −3.46791 | −0.217169 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.19238 | −0.199135 | −0.0995676 | − | 0.995031i | \(-0.531746\pi\) | ||||
−0.0995676 | + | 0.995031i | \(0.531746\pi\) | |||||||
\(258\) | 3.54907 | 0.220955 | ||||||||
\(259\) | 18.6426 | 1.15839 | ||||||||
\(260\) | −16.4866 | −1.02245 | ||||||||
\(261\) | 6.35448 | 0.393332 | ||||||||
\(262\) | 15.6705 | 0.968127 | ||||||||
\(263\) | −23.7811 | −1.46641 | −0.733204 | − | 0.680009i | \(-0.761976\pi\) | ||||
−0.733204 | + | 0.680009i | \(0.761976\pi\) | |||||||
\(264\) | −4.46894 | −0.275045 | ||||||||
\(265\) | 25.0296 | 1.53756 | ||||||||
\(266\) | −7.22644 | −0.443081 | ||||||||
\(267\) | 11.4660 | 0.701711 | ||||||||
\(268\) | −13.7911 | −0.842425 | ||||||||
\(269\) | 9.46182 | 0.576897 | 0.288449 | − | 0.957495i | \(-0.406861\pi\) | ||||
0.288449 | + | 0.957495i | \(0.406861\pi\) | |||||||
\(270\) | −3.46791 | −0.211050 | ||||||||
\(271\) | −9.12209 | −0.554128 | −0.277064 | − | 0.960852i | \(-0.589361\pi\) | ||||
−0.277064 | + | 0.960852i | \(0.589361\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | 7.68415 | 0.465066 | ||||||||
\(274\) | −10.1634 | −0.613994 | ||||||||
\(275\) | 31.4007 | 1.89353 | ||||||||
\(276\) | −8.14330 | −0.490169 | ||||||||
\(277\) | −28.5229 | −1.71377 | −0.856887 | − | 0.515504i | \(-0.827605\pi\) | ||||
−0.856887 | + | 0.515504i | \(0.827605\pi\) | |||||||
\(278\) | 8.26128 | 0.495479 | ||||||||
\(279\) | −10.4107 | −0.623275 | ||||||||
\(280\) | 5.60533 | 0.334983 | ||||||||
\(281\) | −2.93316 | −0.174977 | −0.0874887 | − | 0.996166i | \(-0.527884\pi\) | ||||
−0.0874887 | + | 0.996166i | \(0.527884\pi\) | |||||||
\(282\) | 4.44449 | 0.264665 | ||||||||
\(283\) | 2.59567 | 0.154297 | 0.0771483 | − | 0.997020i | \(-0.475418\pi\) | ||||
0.0771483 | + | 0.997020i | \(0.475418\pi\) | |||||||
\(284\) | −6.19584 | −0.367655 | ||||||||
\(285\) | −15.5046 | −0.918410 | ||||||||
\(286\) | 21.2455 | 1.25627 | ||||||||
\(287\) | 11.0479 | 0.652136 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −22.0368 | −1.29404 | ||||||||
\(291\) | 8.18102 | 0.479580 | ||||||||
\(292\) | −6.44163 | −0.376968 | ||||||||
\(293\) | 4.30235 | 0.251346 | 0.125673 | − | 0.992072i | \(-0.459891\pi\) | ||||
0.125673 | + | 0.992072i | \(0.459891\pi\) | |||||||
\(294\) | 4.38744 | 0.255881 | ||||||||
\(295\) | 3.46791 | 0.201910 | ||||||||
\(296\) | 11.5338 | 0.670389 | ||||||||
\(297\) | 4.46894 | 0.259314 | ||||||||
\(298\) | 2.73869 | 0.158648 | ||||||||
\(299\) | 38.7135 | 2.23886 | ||||||||
\(300\) | 7.02642 | 0.405670 | ||||||||
\(301\) | 5.73651 | 0.330647 | ||||||||
\(302\) | 2.48875 | 0.143212 | ||||||||
\(303\) | 1.99314 | 0.114503 | ||||||||
\(304\) | −4.47086 | −0.256421 | ||||||||
\(305\) | −10.8498 | −0.621259 | ||||||||
\(306\) | 1.00000 | 0.0571662 | ||||||||
\(307\) | 8.18122 | 0.466927 | 0.233463 | − | 0.972366i | \(-0.424994\pi\) | ||||
0.233463 | + | 0.972366i | \(0.424994\pi\) | |||||||
\(308\) | −7.22334 | −0.411588 | ||||||||
\(309\) | −14.2936 | −0.813134 | ||||||||
\(310\) | 36.1035 | 2.05054 | ||||||||
\(311\) | −28.1098 | −1.59396 | −0.796979 | − | 0.604006i | \(-0.793570\pi\) | ||||
−0.796979 | + | 0.604006i | \(0.793570\pi\) | |||||||
\(312\) | 4.75403 | 0.269144 | ||||||||
\(313\) | 9.95547 | 0.562716 | 0.281358 | − | 0.959603i | \(-0.409215\pi\) | ||||
0.281358 | + | 0.959603i | \(0.409215\pi\) | |||||||
\(314\) | −18.6301 | −1.05136 | ||||||||
\(315\) | −5.60533 | −0.315825 | ||||||||
\(316\) | 1.63136 | 0.0917711 | ||||||||
\(317\) | 3.36859 | 0.189199 | 0.0945995 | − | 0.995515i | \(-0.469843\pi\) | ||||
0.0945995 | + | 0.995515i | \(0.469843\pi\) | |||||||
\(318\) | −7.21748 | −0.404736 | ||||||||
\(319\) | 28.3978 | 1.58997 | ||||||||
\(320\) | 3.46791 | 0.193862 | ||||||||
\(321\) | 4.73424 | 0.264239 | ||||||||
\(322\) | −13.1624 | −0.733510 | ||||||||
\(323\) | 4.47086 | 0.248765 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −33.4038 | −1.85291 | ||||||||
\(326\) | −16.2123 | −0.897918 | ||||||||
\(327\) | −7.09575 | −0.392396 | ||||||||
\(328\) | 6.83512 | 0.377406 | ||||||||
\(329\) | 7.18381 | 0.396057 | ||||||||
\(330\) | −15.4979 | −0.853132 | ||||||||
\(331\) | 26.7813 | 1.47203 | 0.736016 | − | 0.676964i | \(-0.236705\pi\) | ||||
0.736016 | + | 0.676964i | \(0.236705\pi\) | |||||||
\(332\) | 15.0535 | 0.826166 | ||||||||
\(333\) | −11.5338 | −0.632048 | ||||||||
\(334\) | −9.85713 | −0.539358 | ||||||||
\(335\) | −47.8263 | −2.61303 | ||||||||
\(336\) | −1.61634 | −0.0881787 | ||||||||
\(337\) | −13.9894 | −0.762051 | −0.381026 | − | 0.924564i | \(-0.624429\pi\) | ||||
−0.381026 | + | 0.924564i | \(0.624429\pi\) | |||||||
\(338\) | −9.60084 | −0.522217 | ||||||||
\(339\) | −2.12850 | −0.115604 | ||||||||
\(340\) | −3.46791 | −0.188074 | ||||||||
\(341\) | −46.5250 | −2.51947 | ||||||||
\(342\) | 4.47086 | 0.241756 | ||||||||
\(343\) | 18.4060 | 0.993830 | ||||||||
\(344\) | 3.54907 | 0.191353 | ||||||||
\(345\) | −28.2403 | −1.52040 | ||||||||
\(346\) | 7.57175 | 0.407060 | ||||||||
\(347\) | −24.1939 | −1.29879 | −0.649397 | − | 0.760449i | \(-0.724979\pi\) | ||||
−0.649397 | + | 0.760449i | \(0.724979\pi\) | |||||||
\(348\) | 6.35448 | 0.340636 | ||||||||
\(349\) | −17.9313 | −0.959838 | −0.479919 | − | 0.877313i | \(-0.659334\pi\) | ||||
−0.479919 | + | 0.877313i | \(0.659334\pi\) | |||||||
\(350\) | 11.3571 | 0.607062 | ||||||||
\(351\) | −4.75403 | −0.253752 | ||||||||
\(352\) | −4.46894 | −0.238196 | ||||||||
\(353\) | 19.6448 | 1.04559 | 0.522793 | − | 0.852460i | \(-0.324890\pi\) | ||||
0.522793 | + | 0.852460i | \(0.324890\pi\) | |||||||
\(354\) | −1.00000 | −0.0531494 | ||||||||
\(355\) | −21.4866 | −1.14039 | ||||||||
\(356\) | 11.4660 | 0.607699 | ||||||||
\(357\) | 1.61634 | 0.0855459 | ||||||||
\(358\) | −14.1115 | −0.745815 | ||||||||
\(359\) | 26.0866 | 1.37680 | 0.688400 | − | 0.725331i | \(-0.258313\pi\) | ||||
0.688400 | + | 0.725331i | \(0.258313\pi\) | |||||||
\(360\) | −3.46791 | −0.182775 | ||||||||
\(361\) | 0.988588 | 0.0520309 | ||||||||
\(362\) | −24.0460 | −1.26383 | ||||||||
\(363\) | 8.97147 | 0.470880 | ||||||||
\(364\) | 7.68415 | 0.402759 | ||||||||
\(365\) | −22.3390 | −1.16928 | ||||||||
\(366\) | 3.12863 | 0.163536 | ||||||||
\(367\) | −4.27970 | −0.223398 | −0.111699 | − | 0.993742i | \(-0.535629\pi\) | ||||
−0.111699 | + | 0.993742i | \(0.535629\pi\) | |||||||
\(368\) | −8.14330 | −0.424499 | ||||||||
\(369\) | −6.83512 | −0.355822 | ||||||||
\(370\) | 39.9982 | 2.07941 | ||||||||
\(371\) | −11.6659 | −0.605664 | ||||||||
\(372\) | −10.4107 | −0.539772 | ||||||||
\(373\) | −6.48381 | −0.335719 | −0.167859 | − | 0.985811i | \(-0.553685\pi\) | ||||
−0.167859 | + | 0.985811i | \(0.553685\pi\) | |||||||
\(374\) | 4.46894 | 0.231084 | ||||||||
\(375\) | 7.02743 | 0.362895 | ||||||||
\(376\) | 4.44449 | 0.229207 | ||||||||
\(377\) | −30.2094 | −1.55586 | ||||||||
\(378\) | 1.61634 | 0.0831357 | ||||||||
\(379\) | 16.7701 | 0.861423 | 0.430712 | − | 0.902490i | \(-0.358263\pi\) | ||||
0.430712 | + | 0.902490i | \(0.358263\pi\) | |||||||
\(380\) | −15.5046 | −0.795367 | ||||||||
\(381\) | 4.83842 | 0.247880 | ||||||||
\(382\) | −27.3260 | −1.39812 | ||||||||
\(383\) | 14.5264 | 0.742264 | 0.371132 | − | 0.928580i | \(-0.378970\pi\) | ||||
0.371132 | + | 0.928580i | \(0.378970\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −25.0499 | −1.27666 | ||||||||
\(386\) | 15.3997 | 0.783824 | ||||||||
\(387\) | −3.54907 | −0.180409 | ||||||||
\(388\) | 8.18102 | 0.415328 | ||||||||
\(389\) | −7.40238 | −0.375315 | −0.187658 | − | 0.982234i | \(-0.560090\pi\) | ||||
−0.187658 | + | 0.982234i | \(0.560090\pi\) | |||||||
\(390\) | 16.4866 | 0.834830 | ||||||||
\(391\) | 8.14330 | 0.411824 | ||||||||
\(392\) | 4.38744 | 0.221599 | ||||||||
\(393\) | −15.6705 | −0.790473 | ||||||||
\(394\) | 6.44083 | 0.324484 | ||||||||
\(395\) | 5.65741 | 0.284655 | ||||||||
\(396\) | 4.46894 | 0.224573 | ||||||||
\(397\) | 23.5013 | 1.17949 | 0.589747 | − | 0.807588i | \(-0.299227\pi\) | ||||
0.589747 | + | 0.807588i | \(0.299227\pi\) | |||||||
\(398\) | 22.0655 | 1.10605 | ||||||||
\(399\) | 7.22644 | 0.361774 | ||||||||
\(400\) | 7.02642 | 0.351321 | ||||||||
\(401\) | 33.5228 | 1.67405 | 0.837025 | − | 0.547164i | \(-0.184293\pi\) | ||||
0.837025 | + | 0.547164i | \(0.184293\pi\) | |||||||
\(402\) | 13.7911 | 0.687837 | ||||||||
\(403\) | 49.4930 | 2.46542 | ||||||||
\(404\) | 1.99314 | 0.0991623 | ||||||||
\(405\) | 3.46791 | 0.172322 | ||||||||
\(406\) | 10.2710 | 0.509742 | ||||||||
\(407\) | −51.5439 | −2.55494 | ||||||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | 17.5661 | 0.868589 | 0.434295 | − | 0.900771i | \(-0.356998\pi\) | ||||
0.434295 | + | 0.900771i | \(0.356998\pi\) | |||||||
\(410\) | 23.7036 | 1.17064 | ||||||||
\(411\) | 10.1634 | 0.501324 | ||||||||
\(412\) | −14.2936 | −0.704195 | ||||||||
\(413\) | −1.61634 | −0.0795350 | ||||||||
\(414\) | 8.14330 | 0.400221 | ||||||||
\(415\) | 52.2041 | 2.56260 | ||||||||
\(416\) | 4.75403 | 0.233086 | ||||||||
\(417\) | −8.26128 | −0.404557 | ||||||||
\(418\) | 19.9800 | 0.977255 | ||||||||
\(419\) | −6.89542 | −0.336863 | −0.168432 | − | 0.985713i | \(-0.553870\pi\) | ||||
−0.168432 | + | 0.985713i | \(0.553870\pi\) | |||||||
\(420\) | −5.60533 | −0.273512 | ||||||||
\(421\) | 2.86944 | 0.139848 | 0.0699240 | − | 0.997552i | \(-0.477724\pi\) | ||||
0.0699240 | + | 0.997552i | \(0.477724\pi\) | |||||||
\(422\) | −12.2576 | −0.596689 | ||||||||
\(423\) | −4.44449 | −0.216098 | ||||||||
\(424\) | −7.21748 | −0.350512 | ||||||||
\(425\) | −7.02642 | −0.340831 | ||||||||
\(426\) | 6.19584 | 0.300189 | ||||||||
\(427\) | 5.05694 | 0.244722 | ||||||||
\(428\) | 4.73424 | 0.228838 | ||||||||
\(429\) | −21.2455 | −1.02574 | ||||||||
\(430\) | 12.3079 | 0.593538 | ||||||||
\(431\) | 30.4374 | 1.46612 | 0.733060 | − | 0.680164i | \(-0.238092\pi\) | ||||
0.733060 | + | 0.680164i | \(0.238092\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 40.5363 | 1.94805 | 0.974025 | − | 0.226442i | \(-0.0727092\pi\) | ||||
0.974025 | + | 0.226442i | \(0.0727092\pi\) | |||||||
\(434\) | −16.8273 | −0.807737 | ||||||||
\(435\) | 22.0368 | 1.05658 | ||||||||
\(436\) | −7.09575 | −0.339825 | ||||||||
\(437\) | 36.4076 | 1.74161 | ||||||||
\(438\) | 6.44163 | 0.307793 | ||||||||
\(439\) | −10.1448 | −0.484185 | −0.242093 | − | 0.970253i | \(-0.577834\pi\) | ||||
−0.242093 | + | 0.970253i | \(0.577834\pi\) | |||||||
\(440\) | −15.4979 | −0.738834 | ||||||||
\(441\) | −4.38744 | −0.208926 | ||||||||
\(442\) | −4.75403 | −0.226126 | ||||||||
\(443\) | 39.0984 | 1.85762 | 0.928811 | − | 0.370555i | \(-0.120832\pi\) | ||||
0.928811 | + | 0.370555i | \(0.120832\pi\) | |||||||
\(444\) | −11.5338 | −0.547370 | ||||||||
\(445\) | 39.7632 | 1.88496 | ||||||||
\(446\) | −25.7757 | −1.22051 | ||||||||
\(447\) | −2.73869 | −0.129535 | ||||||||
\(448\) | −1.61634 | −0.0763650 | ||||||||
\(449\) | 11.7537 | 0.554693 | 0.277347 | − | 0.960770i | \(-0.410545\pi\) | ||||
0.277347 | + | 0.960770i | \(0.410545\pi\) | |||||||
\(450\) | −7.02642 | −0.331228 | ||||||||
\(451\) | −30.5458 | −1.43834 | ||||||||
\(452\) | −2.12850 | −0.100116 | ||||||||
\(453\) | −2.48875 | −0.116932 | ||||||||
\(454\) | 18.7200 | 0.878575 | ||||||||
\(455\) | 26.6479 | 1.24927 | ||||||||
\(456\) | 4.47086 | 0.209367 | ||||||||
\(457\) | −17.9916 | −0.841609 | −0.420805 | − | 0.907151i | \(-0.638252\pi\) | ||||
−0.420805 | + | 0.907151i | \(0.638252\pi\) | |||||||
\(458\) | −16.0744 | −0.751106 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −28.2403 | −1.31671 | ||||||||
\(461\) | −5.57560 | −0.259682 | −0.129841 | − | 0.991535i | \(-0.541447\pi\) | ||||
−0.129841 | + | 0.991535i | \(0.541447\pi\) | |||||||
\(462\) | 7.22334 | 0.336060 | ||||||||
\(463\) | −29.3945 | −1.36608 | −0.683038 | − | 0.730383i | \(-0.739342\pi\) | ||||
−0.683038 | + | 0.730383i | \(0.739342\pi\) | |||||||
\(464\) | 6.35448 | 0.294999 | ||||||||
\(465\) | −36.1035 | −1.67426 | ||||||||
\(466\) | 4.16581 | 0.192977 | ||||||||
\(467\) | −15.0331 | −0.695651 | −0.347825 | − | 0.937559i | \(-0.613080\pi\) | ||||
−0.347825 | + | 0.937559i | \(0.613080\pi\) | |||||||
\(468\) | −4.75403 | −0.219755 | ||||||||
\(469\) | 22.2911 | 1.02931 | ||||||||
\(470\) | 15.4131 | 0.710953 | ||||||||
\(471\) | 18.6301 | 0.858430 | ||||||||
\(472\) | −1.00000 | −0.0460287 | ||||||||
\(473\) | −15.8606 | −0.729271 | ||||||||
\(474\) | −1.63136 | −0.0749308 | ||||||||
\(475\) | −31.4141 | −1.44138 | ||||||||
\(476\) | 1.61634 | 0.0740849 | ||||||||
\(477\) | 7.21748 | 0.330466 | ||||||||
\(478\) | −14.3722 | −0.657371 | ||||||||
\(479\) | −37.9795 | −1.73533 | −0.867663 | − | 0.497153i | \(-0.834379\pi\) | ||||
−0.867663 | + | 0.497153i | \(0.834379\pi\) | |||||||
\(480\) | −3.46791 | −0.158288 | ||||||||
\(481\) | 54.8321 | 2.50013 | ||||||||
\(482\) | −25.4335 | −1.15846 | ||||||||
\(483\) | 13.1624 | 0.598908 | ||||||||
\(484\) | 8.97147 | 0.407794 | ||||||||
\(485\) | 28.3711 | 1.28826 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −0.239403 | −0.0108484 | −0.00542420 | − | 0.999985i | \(-0.501727\pi\) | ||||
−0.00542420 | + | 0.999985i | \(0.501727\pi\) | |||||||
\(488\) | 3.12863 | 0.141626 | ||||||||
\(489\) | 16.2123 | 0.733147 | ||||||||
\(490\) | 15.2153 | 0.687355 | ||||||||
\(491\) | −16.5815 | −0.748312 | −0.374156 | − | 0.927366i | \(-0.622067\pi\) | ||||
−0.374156 | + | 0.927366i | \(0.622067\pi\) | |||||||
\(492\) | −6.83512 | −0.308151 | ||||||||
\(493\) | −6.35448 | −0.286191 | ||||||||
\(494\) | −21.2546 | −0.956291 | ||||||||
\(495\) | 15.4979 | 0.696579 | ||||||||
\(496\) | −10.4107 | −0.467456 | ||||||||
\(497\) | 10.0146 | 0.449216 | ||||||||
\(498\) | −15.0535 | −0.674562 | ||||||||
\(499\) | −10.1572 | −0.454699 | −0.227349 | − | 0.973813i | \(-0.573006\pi\) | ||||
−0.227349 | + | 0.973813i | \(0.573006\pi\) | |||||||
\(500\) | 7.02743 | 0.314276 | ||||||||
\(501\) | 9.85713 | 0.440384 | ||||||||
\(502\) | −19.8080 | −0.884075 | ||||||||
\(503\) | −30.5565 | −1.36245 | −0.681225 | − | 0.732075i | \(-0.738552\pi\) | ||||
−0.681225 | + | 0.732075i | \(0.738552\pi\) | |||||||
\(504\) | 1.61634 | 0.0719976 | ||||||||
\(505\) | 6.91203 | 0.307581 | ||||||||
\(506\) | 36.3920 | 1.61782 | ||||||||
\(507\) | 9.60084 | 0.426388 | ||||||||
\(508\) | 4.83842 | 0.214670 | ||||||||
\(509\) | 11.7305 | 0.519947 | 0.259973 | − | 0.965616i | \(-0.416286\pi\) | ||||
0.259973 | + | 0.965616i | \(0.416286\pi\) | |||||||
\(510\) | 3.46791 | 0.153562 | ||||||||
\(511\) | 10.4119 | 0.460595 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −4.47086 | −0.197393 | ||||||||
\(514\) | 3.19238 | 0.140810 | ||||||||
\(515\) | −49.5689 | −2.18427 | ||||||||
\(516\) | −3.54907 | −0.156239 | ||||||||
\(517\) | −19.8622 | −0.873537 | ||||||||
\(518\) | −18.6426 | −0.819107 | ||||||||
\(519\) | −7.57175 | −0.332363 | ||||||||
\(520\) | 16.4866 | 0.722984 | ||||||||
\(521\) | 1.94656 | 0.0852804 | 0.0426402 | − | 0.999090i | \(-0.486423\pi\) | ||||
0.0426402 | + | 0.999090i | \(0.486423\pi\) | |||||||
\(522\) | −6.35448 | −0.278128 | ||||||||
\(523\) | −31.0243 | −1.35660 | −0.678299 | − | 0.734786i | \(-0.737283\pi\) | ||||
−0.678299 | + | 0.734786i | \(0.737283\pi\) | |||||||
\(524\) | −15.6705 | −0.684569 | ||||||||
\(525\) | −11.3571 | −0.495664 | ||||||||
\(526\) | 23.7811 | 1.03691 | ||||||||
\(527\) | 10.4107 | 0.453499 | ||||||||
\(528\) | 4.46894 | 0.194486 | ||||||||
\(529\) | 43.3134 | 1.88319 | ||||||||
\(530\) | −25.0296 | −1.08722 | ||||||||
\(531\) | 1.00000 | 0.0433963 | ||||||||
\(532\) | 7.22644 | 0.313306 | ||||||||
\(533\) | 32.4944 | 1.40749 | ||||||||
\(534\) | −11.4660 | −0.496184 | ||||||||
\(535\) | 16.4179 | 0.709808 | ||||||||
\(536\) | 13.7911 | 0.595684 | ||||||||
\(537\) | 14.1115 | 0.608956 | ||||||||
\(538\) | −9.46182 | −0.407928 | ||||||||
\(539\) | −19.6072 | −0.844543 | ||||||||
\(540\) | 3.46791 | 0.149235 | ||||||||
\(541\) | −31.9444 | −1.37340 | −0.686698 | − | 0.726943i | \(-0.740941\pi\) | ||||
−0.686698 | + | 0.726943i | \(0.740941\pi\) | |||||||
\(542\) | 9.12209 | 0.391827 | ||||||||
\(543\) | 24.0460 | 1.03191 | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | −24.6074 | −1.05407 | ||||||||
\(546\) | −7.68415 | −0.328851 | ||||||||
\(547\) | 13.4088 | 0.573318 | 0.286659 | − | 0.958033i | \(-0.407455\pi\) | ||||
0.286659 | + | 0.958033i | \(0.407455\pi\) | |||||||
\(548\) | 10.1634 | 0.434159 | ||||||||
\(549\) | −3.12863 | −0.133527 | ||||||||
\(550\) | −31.4007 | −1.33893 | ||||||||
\(551\) | −28.4100 | −1.21031 | ||||||||
\(552\) | 8.14330 | 0.346602 | ||||||||
\(553\) | −2.63683 | −0.112130 | ||||||||
\(554\) | 28.5229 | 1.21182 | ||||||||
\(555\) | −39.9982 | −1.69783 | ||||||||
\(556\) | −8.26128 | −0.350356 | ||||||||
\(557\) | 25.2577 | 1.07021 | 0.535103 | − | 0.844787i | \(-0.320273\pi\) | ||||
0.535103 | + | 0.844787i | \(0.320273\pi\) | |||||||
\(558\) | 10.4107 | 0.440722 | ||||||||
\(559\) | 16.8724 | 0.713626 | ||||||||
\(560\) | −5.60533 | −0.236869 | ||||||||
\(561\) | −4.46894 | −0.188679 | ||||||||
\(562\) | 2.93316 | 0.123728 | ||||||||
\(563\) | −46.3267 | −1.95244 | −0.976218 | − | 0.216792i | \(-0.930441\pi\) | ||||
−0.976218 | + | 0.216792i | \(0.930441\pi\) | |||||||
\(564\) | −4.44449 | −0.187147 | ||||||||
\(565\) | −7.38145 | −0.310540 | ||||||||
\(566\) | −2.59567 | −0.109104 | ||||||||
\(567\) | −1.61634 | −0.0678800 | ||||||||
\(568\) | 6.19584 | 0.259972 | ||||||||
\(569\) | −19.5129 | −0.818024 | −0.409012 | − | 0.912529i | \(-0.634127\pi\) | ||||
−0.409012 | + | 0.912529i | \(0.634127\pi\) | |||||||
\(570\) | 15.5046 | 0.649414 | ||||||||
\(571\) | 3.60657 | 0.150930 | 0.0754652 | − | 0.997148i | \(-0.475956\pi\) | ||||
0.0754652 | + | 0.997148i | \(0.475956\pi\) | |||||||
\(572\) | −21.2455 | −0.888320 | ||||||||
\(573\) | 27.3260 | 1.14156 | ||||||||
\(574\) | −11.0479 | −0.461130 | ||||||||
\(575\) | −57.2182 | −2.38616 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −5.13057 | −0.213588 | −0.106794 | − | 0.994281i | \(-0.534059\pi\) | ||||
−0.106794 | + | 0.994281i | \(0.534059\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | −15.3997 | −0.639990 | ||||||||
\(580\) | 22.0368 | 0.915027 | ||||||||
\(581\) | −24.3316 | −1.00944 | ||||||||
\(582\) | −8.18102 | −0.339114 | ||||||||
\(583\) | 32.2545 | 1.33585 | ||||||||
\(584\) | 6.44163 | 0.266557 | ||||||||
\(585\) | −16.4866 | −0.681636 | ||||||||
\(586\) | −4.30235 | −0.177728 | ||||||||
\(587\) | 7.56561 | 0.312266 | 0.156133 | − | 0.987736i | \(-0.450097\pi\) | ||||
0.156133 | + | 0.987736i | \(0.450097\pi\) | |||||||
\(588\) | −4.38744 | −0.180935 | ||||||||
\(589\) | 46.5450 | 1.91785 | ||||||||
\(590\) | −3.46791 | −0.142772 | ||||||||
\(591\) | −6.44083 | −0.264940 | ||||||||
\(592\) | −11.5338 | −0.474036 | ||||||||
\(593\) | −16.4343 | −0.674876 | −0.337438 | − | 0.941348i | \(-0.609560\pi\) | ||||
−0.337438 | + | 0.941348i | \(0.609560\pi\) | |||||||
\(594\) | −4.46894 | −0.183363 | ||||||||
\(595\) | 5.60533 | 0.229796 | ||||||||
\(596\) | −2.73869 | −0.112181 | ||||||||
\(597\) | −22.0655 | −0.903082 | ||||||||
\(598\) | −38.7135 | −1.58311 | ||||||||
\(599\) | −31.8269 | −1.30041 | −0.650206 | − | 0.759758i | \(-0.725317\pi\) | ||||
−0.650206 | + | 0.759758i | \(0.725317\pi\) | |||||||
\(600\) | −7.02642 | −0.286852 | ||||||||
\(601\) | 28.2907 | 1.15400 | 0.577001 | − | 0.816744i | \(-0.304223\pi\) | ||||
0.577001 | + | 0.816744i | \(0.304223\pi\) | |||||||
\(602\) | −5.73651 | −0.233803 | ||||||||
\(603\) | −13.7911 | −0.561617 | ||||||||
\(604\) | −2.48875 | −0.101266 | ||||||||
\(605\) | 31.1123 | 1.26489 | ||||||||
\(606\) | −1.99314 | −0.0809657 | ||||||||
\(607\) | 7.17649 | 0.291285 | 0.145642 | − | 0.989337i | \(-0.453475\pi\) | ||||
0.145642 | + | 0.989337i | \(0.453475\pi\) | |||||||
\(608\) | 4.47086 | 0.181317 | ||||||||
\(609\) | −10.2710 | −0.416202 | ||||||||
\(610\) | 10.8498 | 0.439296 | ||||||||
\(611\) | 21.1292 | 0.854798 | ||||||||
\(612\) | −1.00000 | −0.0404226 | ||||||||
\(613\) | −18.8731 | −0.762279 | −0.381140 | − | 0.924517i | \(-0.624468\pi\) | ||||
−0.381140 | + | 0.924517i | \(0.624468\pi\) | |||||||
\(614\) | −8.18122 | −0.330167 | ||||||||
\(615\) | −23.7036 | −0.955821 | ||||||||
\(616\) | 7.22334 | 0.291037 | ||||||||
\(617\) | −33.3657 | −1.34325 | −0.671626 | − | 0.740891i | \(-0.734404\pi\) | ||||
−0.671626 | + | 0.740891i | \(0.734404\pi\) | |||||||
\(618\) | 14.2936 | 0.574973 | ||||||||
\(619\) | −12.0309 | −0.483564 | −0.241782 | − | 0.970331i | \(-0.577732\pi\) | ||||
−0.241782 | + | 0.970331i | \(0.577732\pi\) | |||||||
\(620\) | −36.1035 | −1.44995 | ||||||||
\(621\) | −8.14330 | −0.326779 | ||||||||
\(622\) | 28.1098 | 1.12710 | ||||||||
\(623\) | −18.5331 | −0.742511 | ||||||||
\(624\) | −4.75403 | −0.190314 | ||||||||
\(625\) | −10.7616 | −0.430462 | ||||||||
\(626\) | −9.95547 | −0.397900 | ||||||||
\(627\) | −19.9800 | −0.797925 | ||||||||
\(628\) | 18.6301 | 0.743422 | ||||||||
\(629\) | 11.5338 | 0.459883 | ||||||||
\(630\) | 5.60533 | 0.223322 | ||||||||
\(631\) | −39.5712 | −1.57530 | −0.787652 | − | 0.616121i | \(-0.788703\pi\) | ||||
−0.787652 | + | 0.616121i | \(0.788703\pi\) | |||||||
\(632\) | −1.63136 | −0.0648919 | ||||||||
\(633\) | 12.2576 | 0.487195 | ||||||||
\(634\) | −3.36859 | −0.133784 | ||||||||
\(635\) | 16.7792 | 0.665862 | ||||||||
\(636\) | 7.21748 | 0.286192 | ||||||||
\(637\) | 20.8580 | 0.826425 | ||||||||
\(638\) | −28.3978 | −1.12428 | ||||||||
\(639\) | −6.19584 | −0.245104 | ||||||||
\(640\) | −3.46791 | −0.137081 | ||||||||
\(641\) | −22.2416 | −0.878491 | −0.439245 | − | 0.898367i | \(-0.644754\pi\) | ||||
−0.439245 | + | 0.898367i | \(0.644754\pi\) | |||||||
\(642\) | −4.73424 | −0.186845 | ||||||||
\(643\) | −43.9222 | −1.73212 | −0.866062 | − | 0.499936i | \(-0.833357\pi\) | ||||
−0.866062 | + | 0.499936i | \(0.833357\pi\) | |||||||
\(644\) | 13.1624 | 0.518670 | ||||||||
\(645\) | −12.3079 | −0.484622 | ||||||||
\(646\) | −4.47086 | −0.175904 | ||||||||
\(647\) | −17.1562 | −0.674481 | −0.337241 | − | 0.941418i | \(-0.609494\pi\) | ||||
−0.337241 | + | 0.941418i | \(0.609494\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 4.46894 | 0.175421 | ||||||||
\(650\) | 33.4038 | 1.31021 | ||||||||
\(651\) | 16.8273 | 0.659515 | ||||||||
\(652\) | 16.2123 | 0.634924 | ||||||||
\(653\) | −11.5343 | −0.451371 | −0.225686 | − | 0.974200i | \(-0.572462\pi\) | ||||
−0.225686 | + | 0.974200i | \(0.572462\pi\) | |||||||
\(654\) | 7.09575 | 0.277466 | ||||||||
\(655\) | −54.3440 | −2.12339 | ||||||||
\(656\) | −6.83512 | −0.266867 | ||||||||
\(657\) | −6.44163 | −0.251312 | ||||||||
\(658\) | −7.18381 | −0.280054 | ||||||||
\(659\) | 22.1531 | 0.862962 | 0.431481 | − | 0.902122i | \(-0.357991\pi\) | ||||
0.431481 | + | 0.902122i | \(0.357991\pi\) | |||||||
\(660\) | 15.4979 | 0.603255 | ||||||||
\(661\) | −38.4517 | −1.49560 | −0.747798 | − | 0.663926i | \(-0.768889\pi\) | ||||
−0.747798 | + | 0.663926i | \(0.768889\pi\) | |||||||
\(662\) | −26.7813 | −1.04088 | ||||||||
\(663\) | 4.75403 | 0.184631 | ||||||||
\(664\) | −15.0535 | −0.584188 | ||||||||
\(665\) | 25.0607 | 0.971811 | ||||||||
\(666\) | 11.5338 | 0.446926 | ||||||||
\(667\) | −51.7464 | −2.00363 | ||||||||
\(668\) | 9.85713 | 0.381384 | ||||||||
\(669\) | 25.7757 | 0.996545 | ||||||||
\(670\) | 47.8263 | 1.84769 | ||||||||
\(671\) | −13.9817 | −0.539757 | ||||||||
\(672\) | 1.61634 | 0.0623518 | ||||||||
\(673\) | −41.2596 | −1.59044 | −0.795220 | − | 0.606320i | \(-0.792645\pi\) | ||||
−0.795220 | + | 0.606320i | \(0.792645\pi\) | |||||||
\(674\) | 13.9894 | 0.538852 | ||||||||
\(675\) | 7.02642 | 0.270447 | ||||||||
\(676\) | 9.60084 | 0.369263 | ||||||||
\(677\) | 15.2627 | 0.586595 | 0.293297 | − | 0.956021i | \(-0.405247\pi\) | ||||
0.293297 | + | 0.956021i | \(0.405247\pi\) | |||||||
\(678\) | 2.12850 | 0.0817445 | ||||||||
\(679\) | −13.2233 | −0.507465 | ||||||||
\(680\) | 3.46791 | 0.132988 | ||||||||
\(681\) | −18.7200 | −0.717354 | ||||||||
\(682\) | 46.5250 | 1.78154 | ||||||||
\(683\) | 1.15361 | 0.0441418 | 0.0220709 | − | 0.999756i | \(-0.492974\pi\) | ||||
0.0220709 | + | 0.999756i | \(0.492974\pi\) | |||||||
\(684\) | −4.47086 | −0.170948 | ||||||||
\(685\) | 35.2458 | 1.34667 | ||||||||
\(686\) | −18.4060 | −0.702744 | ||||||||
\(687\) | 16.0744 | 0.613276 | ||||||||
\(688\) | −3.54907 | −0.135307 | ||||||||
\(689\) | −34.3121 | −1.30719 | ||||||||
\(690\) | 28.2403 | 1.07509 | ||||||||
\(691\) | −38.3330 | −1.45826 | −0.729128 | − | 0.684378i | \(-0.760074\pi\) | ||||
−0.729128 | + | 0.684378i | \(0.760074\pi\) | |||||||
\(692\) | −7.57175 | −0.287835 | ||||||||
\(693\) | −7.22334 | −0.274392 | ||||||||
\(694\) | 24.1939 | 0.918386 | ||||||||
\(695\) | −28.6494 | −1.08673 | ||||||||
\(696\) | −6.35448 | −0.240866 | ||||||||
\(697\) | 6.83512 | 0.258899 | ||||||||
\(698\) | 17.9313 | 0.678708 | ||||||||
\(699\) | −4.16581 | −0.157565 | ||||||||
\(700\) | −11.3571 | −0.429258 | ||||||||
\(701\) | −29.6260 | −1.11896 | −0.559480 | − | 0.828844i | \(-0.688999\pi\) | ||||
−0.559480 | + | 0.828844i | \(0.688999\pi\) | |||||||
\(702\) | 4.75403 | 0.179429 | ||||||||
\(703\) | 51.5660 | 1.94485 | ||||||||
\(704\) | 4.46894 | 0.168430 | ||||||||
\(705\) | −15.4131 | −0.580491 | ||||||||
\(706\) | −19.6448 | −0.739340 | ||||||||
\(707\) | −3.22159 | −0.121160 | ||||||||
\(708\) | 1.00000 | 0.0375823 | ||||||||
\(709\) | −35.1146 | −1.31876 | −0.659379 | − | 0.751811i | \(-0.729181\pi\) | ||||
−0.659379 | + | 0.751811i | \(0.729181\pi\) | |||||||
\(710\) | 21.4866 | 0.806379 | ||||||||
\(711\) | 1.63136 | 0.0611807 | ||||||||
\(712\) | −11.4660 | −0.429708 | ||||||||
\(713\) | 84.7778 | 3.17495 | ||||||||
\(714\) | −1.61634 | −0.0604901 | ||||||||
\(715\) | −73.6776 | −2.75539 | ||||||||
\(716\) | 14.1115 | 0.527371 | ||||||||
\(717\) | 14.3722 | 0.536741 | ||||||||
\(718\) | −26.0866 | −0.973545 | ||||||||
\(719\) | 15.3282 | 0.571644 | 0.285822 | − | 0.958283i | \(-0.407733\pi\) | ||||
0.285822 | + | 0.958283i | \(0.407733\pi\) | |||||||
\(720\) | 3.46791 | 0.129241 | ||||||||
\(721\) | 23.1033 | 0.860413 | ||||||||
\(722\) | −0.988588 | −0.0367914 | ||||||||
\(723\) | 25.4335 | 0.945882 | ||||||||
\(724\) | 24.0460 | 0.893664 | ||||||||
\(725\) | 44.6492 | 1.65823 | ||||||||
\(726\) | −8.97147 | −0.332962 | ||||||||
\(727\) | −14.8629 | −0.551233 | −0.275617 | − | 0.961268i | \(-0.588882\pi\) | ||||
−0.275617 | + | 0.961268i | \(0.588882\pi\) | |||||||
\(728\) | −7.68415 | −0.284793 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 22.3390 | 0.826804 | ||||||||
\(731\) | 3.54907 | 0.131267 | ||||||||
\(732\) | −3.12863 | −0.115637 | ||||||||
\(733\) | −49.4269 | −1.82563 | −0.912813 | − | 0.408379i | \(-0.866094\pi\) | ||||
−0.912813 | + | 0.408379i | \(0.866094\pi\) | |||||||
\(734\) | 4.27970 | 0.157966 | ||||||||
\(735\) | −15.2153 | −0.561223 | ||||||||
\(736\) | 8.14330 | 0.300166 | ||||||||
\(737\) | −61.6316 | −2.27023 | ||||||||
\(738\) | 6.83512 | 0.251604 | ||||||||
\(739\) | −42.0135 | −1.54549 | −0.772745 | − | 0.634716i | \(-0.781117\pi\) | ||||
−0.772745 | + | 0.634716i | \(0.781117\pi\) | |||||||
\(740\) | −39.9982 | −1.47036 | ||||||||
\(741\) | 21.2546 | 0.780808 | ||||||||
\(742\) | 11.6659 | 0.428269 | ||||||||
\(743\) | −19.5197 | −0.716109 | −0.358055 | − | 0.933701i | \(-0.616560\pi\) | ||||
−0.358055 | + | 0.933701i | \(0.616560\pi\) | |||||||
\(744\) | 10.4107 | 0.381676 | ||||||||
\(745\) | −9.49752 | −0.347962 | ||||||||
\(746\) | 6.48381 | 0.237389 | ||||||||
\(747\) | 15.0535 | 0.550778 | ||||||||
\(748\) | −4.46894 | −0.163401 | ||||||||
\(749\) | −7.65215 | −0.279603 | ||||||||
\(750\) | −7.02743 | −0.256606 | ||||||||
\(751\) | −17.8153 | −0.650089 | −0.325044 | − | 0.945699i | \(-0.605379\pi\) | ||||
−0.325044 | + | 0.945699i | \(0.605379\pi\) | |||||||
\(752\) | −4.44449 | −0.162074 | ||||||||
\(753\) | 19.8080 | 0.721844 | ||||||||
\(754\) | 30.2094 | 1.10016 | ||||||||
\(755\) | −8.63078 | −0.314106 | ||||||||
\(756\) | −1.61634 | −0.0587858 | ||||||||
\(757\) | −41.0173 | −1.49080 | −0.745399 | − | 0.666618i | \(-0.767741\pi\) | ||||
−0.745399 | + | 0.666618i | \(0.767741\pi\) | |||||||
\(758\) | −16.7701 | −0.609118 | ||||||||
\(759\) | −36.3920 | −1.32094 | ||||||||
\(760\) | 15.5046 | 0.562409 | ||||||||
\(761\) | −25.2129 | −0.913967 | −0.456984 | − | 0.889475i | \(-0.651070\pi\) | ||||
−0.456984 | + | 0.889475i | \(0.651070\pi\) | |||||||
\(762\) | −4.83842 | −0.175277 | ||||||||
\(763\) | 11.4692 | 0.415212 | ||||||||
\(764\) | 27.3260 | 0.988621 | ||||||||
\(765\) | −3.46791 | −0.125383 | ||||||||
\(766\) | −14.5264 | −0.524860 | ||||||||
\(767\) | −4.75403 | −0.171658 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 23.8825 | 0.861227 | 0.430613 | − | 0.902537i | \(-0.358297\pi\) | ||||
0.430613 | + | 0.902537i | \(0.358297\pi\) | |||||||
\(770\) | 25.0499 | 0.902737 | ||||||||
\(771\) | −3.19238 | −0.114971 | ||||||||
\(772\) | −15.3997 | −0.554248 | ||||||||
\(773\) | 11.1622 | 0.401476 | 0.200738 | − | 0.979645i | \(-0.435666\pi\) | ||||
0.200738 | + | 0.979645i | \(0.435666\pi\) | |||||||
\(774\) | 3.54907 | 0.127569 | ||||||||
\(775\) | −73.1502 | −2.62763 | ||||||||
\(776\) | −8.18102 | −0.293682 | ||||||||
\(777\) | 18.6426 | 0.668798 | ||||||||
\(778\) | 7.40238 | 0.265388 | ||||||||
\(779\) | 30.5589 | 1.09488 | ||||||||
\(780\) | −16.4866 | −0.590314 | ||||||||
\(781\) | −27.6889 | −0.990785 | ||||||||
\(782\) | −8.14330 | −0.291204 | ||||||||
\(783\) | 6.35448 | 0.227090 | ||||||||
\(784\) | −4.38744 | −0.156694 | ||||||||
\(785\) | 64.6076 | 2.30594 | ||||||||
\(786\) | 15.6705 | 0.558949 | ||||||||
\(787\) | 15.2737 | 0.544450 | 0.272225 | − | 0.962234i | \(-0.412241\pi\) | ||||
0.272225 | + | 0.962234i | \(0.412241\pi\) | |||||||
\(788\) | −6.44083 | −0.229445 | ||||||||
\(789\) | −23.7811 | −0.846631 | ||||||||
\(790\) | −5.65741 | −0.201281 | ||||||||
\(791\) | 3.44038 | 0.122326 | ||||||||
\(792\) | −4.46894 | −0.158797 | ||||||||
\(793\) | 14.8736 | 0.528178 | ||||||||
\(794\) | −23.5013 | −0.834029 | ||||||||
\(795\) | 25.0296 | 0.887708 | ||||||||
\(796\) | −22.0655 | −0.782092 | ||||||||
\(797\) | −38.0890 | −1.34918 | −0.674590 | − | 0.738192i | \(-0.735680\pi\) | ||||
−0.674590 | + | 0.738192i | \(0.735680\pi\) | |||||||
\(798\) | −7.22644 | −0.255813 | ||||||||
\(799\) | 4.44449 | 0.157235 | ||||||||
\(800\) | −7.02642 | −0.248421 | ||||||||
\(801\) | 11.4660 | 0.405133 | ||||||||
\(802\) | −33.5228 | −1.18373 | ||||||||
\(803\) | −28.7873 | −1.01588 | ||||||||
\(804\) | −13.7911 | −0.486374 | ||||||||
\(805\) | 45.6459 | 1.60881 | ||||||||
\(806\) | −49.4930 | −1.74332 | ||||||||
\(807\) | 9.46182 | 0.333072 | ||||||||
\(808\) | −1.99314 | −0.0701183 | ||||||||
\(809\) | 12.6651 | 0.445282 | 0.222641 | − | 0.974901i | \(-0.428532\pi\) | ||||
0.222641 | + | 0.974901i | \(0.428532\pi\) | |||||||
\(810\) | −3.46791 | −0.121850 | ||||||||
\(811\) | 45.8034 | 1.60837 | 0.804187 | − | 0.594377i | \(-0.202601\pi\) | ||||
0.804187 | + | 0.594377i | \(0.202601\pi\) | |||||||
\(812\) | −10.2710 | −0.360442 | ||||||||
\(813\) | −9.12209 | −0.319926 | ||||||||
\(814\) | 51.5439 | 1.80661 | ||||||||
\(815\) | 56.2229 | 1.96940 | ||||||||
\(816\) | −1.00000 | −0.0350070 | ||||||||
\(817\) | 15.8674 | 0.555130 | ||||||||
\(818\) | −17.5661 | −0.614185 | ||||||||
\(819\) | 7.68415 | 0.268506 | ||||||||
\(820\) | −23.7036 | −0.827765 | ||||||||
\(821\) | 28.2967 | 0.987563 | 0.493782 | − | 0.869586i | \(-0.335614\pi\) | ||||
0.493782 | + | 0.869586i | \(0.335614\pi\) | |||||||
\(822\) | −10.1634 | −0.354490 | ||||||||
\(823\) | −49.7708 | −1.73490 | −0.867450 | − | 0.497525i | \(-0.834242\pi\) | ||||
−0.867450 | + | 0.497525i | \(0.834242\pi\) | |||||||
\(824\) | 14.2936 | 0.497941 | ||||||||
\(825\) | 31.4007 | 1.09323 | ||||||||
\(826\) | 1.61634 | 0.0562397 | ||||||||
\(827\) | 8.29893 | 0.288582 | 0.144291 | − | 0.989535i | \(-0.453910\pi\) | ||||
0.144291 | + | 0.989535i | \(0.453910\pi\) | |||||||
\(828\) | −8.14330 | −0.282999 | ||||||||
\(829\) | 18.8724 | 0.655465 | 0.327732 | − | 0.944771i | \(-0.393716\pi\) | ||||
0.327732 | + | 0.944771i | \(0.393716\pi\) | |||||||
\(830\) | −52.2041 | −1.81203 | ||||||||
\(831\) | −28.5229 | −0.989448 | ||||||||
\(832\) | −4.75403 | −0.164816 | ||||||||
\(833\) | 4.38744 | 0.152016 | ||||||||
\(834\) | 8.26128 | 0.286065 | ||||||||
\(835\) | 34.1837 | 1.18297 | ||||||||
\(836\) | −19.9800 | −0.691024 | ||||||||
\(837\) | −10.4107 | −0.359848 | ||||||||
\(838\) | 6.89542 | 0.238198 | ||||||||
\(839\) | 8.29043 | 0.286217 | 0.143109 | − | 0.989707i | \(-0.454290\pi\) | ||||
0.143109 | + | 0.989707i | \(0.454290\pi\) | |||||||
\(840\) | 5.60533 | 0.193402 | ||||||||
\(841\) | 11.3794 | 0.392392 | ||||||||
\(842\) | −2.86944 | −0.0988875 | ||||||||
\(843\) | −2.93316 | −0.101023 | ||||||||
\(844\) | 12.2576 | 0.421923 | ||||||||
\(845\) | 33.2949 | 1.14538 | ||||||||
\(846\) | 4.44449 | 0.152805 | ||||||||
\(847\) | −14.5010 | −0.498259 | ||||||||
\(848\) | 7.21748 | 0.247849 | ||||||||
\(849\) | 2.59567 | 0.0890832 | ||||||||
\(850\) | 7.02642 | 0.241004 | ||||||||
\(851\) | 93.9232 | 3.21965 | ||||||||
\(852\) | −6.19584 | −0.212266 | ||||||||
\(853\) | −20.9784 | −0.718286 | −0.359143 | − | 0.933283i | \(-0.616931\pi\) | ||||
−0.359143 | + | 0.933283i | \(0.616931\pi\) | |||||||
\(854\) | −5.05694 | −0.173045 | ||||||||
\(855\) | −15.5046 | −0.530244 | ||||||||
\(856\) | −4.73424 | −0.161813 | ||||||||
\(857\) | −18.6774 | −0.638009 | −0.319005 | − | 0.947753i | \(-0.603349\pi\) | ||||
−0.319005 | + | 0.947753i | \(0.603349\pi\) | |||||||
\(858\) | 21.2455 | 0.725310 | ||||||||
\(859\) | −6.62451 | −0.226026 | −0.113013 | − | 0.993594i | \(-0.536050\pi\) | ||||
−0.113013 | + | 0.993594i | \(0.536050\pi\) | |||||||
\(860\) | −12.3079 | −0.419695 | ||||||||
\(861\) | 11.0479 | 0.376511 | ||||||||
\(862\) | −30.4374 | −1.03670 | ||||||||
\(863\) | −23.3004 | −0.793154 | −0.396577 | − | 0.918001i | \(-0.629802\pi\) | ||||
−0.396577 | + | 0.918001i | \(0.629802\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −26.2581 | −0.892804 | ||||||||
\(866\) | −40.5363 | −1.37748 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 16.8273 | 0.571156 | ||||||||
\(869\) | 7.29045 | 0.247312 | ||||||||
\(870\) | −22.0368 | −0.747116 | ||||||||
\(871\) | 65.5633 | 2.22153 | ||||||||
\(872\) | 7.09575 | 0.240292 | ||||||||
\(873\) | 8.18102 | 0.276886 | ||||||||
\(874\) | −36.4076 | −1.23150 | ||||||||
\(875\) | −11.3587 | −0.383995 | ||||||||
\(876\) | −6.44163 | −0.217643 | ||||||||
\(877\) | 42.3728 | 1.43083 | 0.715414 | − | 0.698701i | \(-0.246238\pi\) | ||||
0.715414 | + | 0.698701i | \(0.246238\pi\) | |||||||
\(878\) | 10.1448 | 0.342371 | ||||||||
\(879\) | 4.30235 | 0.145115 | ||||||||
\(880\) | 15.4979 | 0.522434 | ||||||||
\(881\) | 22.4733 | 0.757145 | 0.378573 | − | 0.925572i | \(-0.376415\pi\) | ||||
0.378573 | + | 0.925572i | \(0.376415\pi\) | |||||||
\(882\) | 4.38744 | 0.147733 | ||||||||
\(883\) | −18.4621 | −0.621301 | −0.310650 | − | 0.950524i | \(-0.600547\pi\) | ||||
−0.310650 | + | 0.950524i | \(0.600547\pi\) | |||||||
\(884\) | 4.75403 | 0.159895 | ||||||||
\(885\) | 3.46791 | 0.116573 | ||||||||
\(886\) | −39.0984 | −1.31354 | ||||||||
\(887\) | 33.3760 | 1.12066 | 0.560328 | − | 0.828271i | \(-0.310675\pi\) | ||||
0.560328 | + | 0.828271i | \(0.310675\pi\) | |||||||
\(888\) | 11.5338 | 0.387049 | ||||||||
\(889\) | −7.82054 | −0.262292 | ||||||||
\(890\) | −39.7632 | −1.33287 | ||||||||
\(891\) | 4.46894 | 0.149715 | ||||||||
\(892\) | 25.7757 | 0.863033 | ||||||||
\(893\) | 19.8707 | 0.664947 | ||||||||
\(894\) | 2.73869 | 0.0915954 | ||||||||
\(895\) | 48.9374 | 1.63580 | ||||||||
\(896\) | 1.61634 | 0.0539982 | ||||||||
\(897\) | 38.7135 | 1.29261 | ||||||||
\(898\) | −11.7537 | −0.392228 | ||||||||
\(899\) | −66.1548 | −2.20639 | ||||||||
\(900\) | 7.02642 | 0.234214 | ||||||||
\(901\) | −7.21748 | −0.240449 | ||||||||
\(902\) | 30.5458 | 1.01706 | ||||||||
\(903\) | 5.73651 | 0.190899 | ||||||||
\(904\) | 2.12850 | 0.0707928 | ||||||||
\(905\) | 83.3895 | 2.77196 | ||||||||
\(906\) | 2.48875 | 0.0826833 | ||||||||
\(907\) | −22.0740 | −0.732955 | −0.366477 | − | 0.930427i | \(-0.619436\pi\) | ||||
−0.366477 | + | 0.930427i | \(0.619436\pi\) | |||||||
\(908\) | −18.7200 | −0.621247 | ||||||||
\(909\) | 1.99314 | 0.0661082 | ||||||||
\(910\) | −26.6479 | −0.883371 | ||||||||
\(911\) | −14.6962 | −0.486908 | −0.243454 | − | 0.969912i | \(-0.578280\pi\) | ||||
−0.243454 | + | 0.969912i | \(0.578280\pi\) | |||||||
\(912\) | −4.47086 | −0.148045 | ||||||||
\(913\) | 67.2731 | 2.22641 | ||||||||
\(914\) | 17.9916 | 0.595108 | ||||||||
\(915\) | −10.8498 | −0.358684 | ||||||||
\(916\) | 16.0744 | 0.531112 | ||||||||
\(917\) | 25.3289 | 0.836434 | ||||||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | −42.1922 | −1.39179 | −0.695896 | − | 0.718142i | \(-0.744993\pi\) | ||||
−0.695896 | + | 0.718142i | \(0.744993\pi\) | |||||||
\(920\) | 28.2403 | 0.931054 | ||||||||
\(921\) | 8.18122 | 0.269580 | ||||||||
\(922\) | 5.57560 | 0.183623 | ||||||||
\(923\) | 29.4552 | 0.969531 | ||||||||
\(924\) | −7.22334 | −0.237631 | ||||||||
\(925\) | −81.0413 | −2.66462 | ||||||||
\(926\) | 29.3945 | 0.965962 | ||||||||
\(927\) | −14.2936 | −0.469463 | ||||||||
\(928\) | −6.35448 | −0.208596 | ||||||||
\(929\) | 37.2670 | 1.22269 | 0.611345 | − | 0.791365i | \(-0.290629\pi\) | ||||
0.611345 | + | 0.791365i | \(0.290629\pi\) | |||||||
\(930\) | 36.1035 | 1.18388 | ||||||||
\(931\) | 19.6156 | 0.642876 | ||||||||
\(932\) | −4.16581 | −0.136455 | ||||||||
\(933\) | −28.1098 | −0.920273 | ||||||||
\(934\) | 15.0331 | 0.491899 | ||||||||
\(935\) | −15.4979 | −0.506836 | ||||||||
\(936\) | 4.75403 | 0.155390 | ||||||||
\(937\) | −16.7330 | −0.546644 | −0.273322 | − | 0.961923i | \(-0.588122\pi\) | ||||
−0.273322 | + | 0.961923i | \(0.588122\pi\) | |||||||
\(938\) | −22.2911 | −0.727831 | ||||||||
\(939\) | 9.95547 | 0.324884 | ||||||||
\(940\) | −15.4131 | −0.502720 | ||||||||
\(941\) | 12.2415 | 0.399061 | 0.199531 | − | 0.979892i | \(-0.436058\pi\) | ||||
0.199531 | + | 0.979892i | \(0.436058\pi\) | |||||||
\(942\) | −18.6301 | −0.607002 | ||||||||
\(943\) | 55.6604 | 1.81255 | ||||||||
\(944\) | 1.00000 | 0.0325472 | ||||||||
\(945\) | −5.60533 | −0.182342 | ||||||||
\(946\) | 15.8606 | 0.515672 | ||||||||
\(947\) | −51.3523 | −1.66873 | −0.834363 | − | 0.551215i | \(-0.814165\pi\) | ||||
−0.834363 | + | 0.551215i | \(0.814165\pi\) | |||||||
\(948\) | 1.63136 | 0.0529840 | ||||||||
\(949\) | 30.6237 | 0.994089 | ||||||||
\(950\) | 31.4141 | 1.01921 | ||||||||
\(951\) | 3.36859 | 0.109234 | ||||||||
\(952\) | −1.61634 | −0.0523860 | ||||||||
\(953\) | 0.954361 | 0.0309148 | 0.0154574 | − | 0.999881i | \(-0.495080\pi\) | ||||
0.0154574 | + | 0.999881i | \(0.495080\pi\) | |||||||
\(954\) | −7.21748 | −0.233674 | ||||||||
\(955\) | 94.7642 | 3.06650 | ||||||||
\(956\) | 14.3722 | 0.464831 | ||||||||
\(957\) | 28.3978 | 0.917971 | ||||||||
\(958\) | 37.9795 | 1.22706 | ||||||||
\(959\) | −16.4275 | −0.530473 | ||||||||
\(960\) | 3.46791 | 0.111926 | ||||||||
\(961\) | 77.3835 | 2.49624 | ||||||||
\(962\) | −54.8321 | −1.76786 | ||||||||
\(963\) | 4.73424 | 0.152559 | ||||||||
\(964\) | 25.4335 | 0.819158 | ||||||||
\(965\) | −53.4048 | −1.71916 | ||||||||
\(966\) | −13.1624 | −0.423492 | ||||||||
\(967\) | −16.5773 | −0.533090 | −0.266545 | − | 0.963822i | \(-0.585882\pi\) | ||||
−0.266545 | + | 0.963822i | \(0.585882\pi\) | |||||||
\(968\) | −8.97147 | −0.288354 | ||||||||
\(969\) | 4.47086 | 0.143625 | ||||||||
\(970\) | −28.3711 | −0.910940 | ||||||||
\(971\) | 21.6566 | 0.694994 | 0.347497 | − | 0.937681i | \(-0.387032\pi\) | ||||
0.347497 | + | 0.937681i | \(0.387032\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 13.3531 | 0.428079 | ||||||||
\(974\) | 0.239403 | 0.00767098 | ||||||||
\(975\) | −33.4038 | −1.06978 | ||||||||
\(976\) | −3.12863 | −0.100145 | ||||||||
\(977\) | 38.3897 | 1.22819 | 0.614097 | − | 0.789230i | \(-0.289520\pi\) | ||||
0.614097 | + | 0.789230i | \(0.289520\pi\) | |||||||
\(978\) | −16.2123 | −0.518413 | ||||||||
\(979\) | 51.2411 | 1.63767 | ||||||||
\(980\) | −15.2153 | −0.486033 | ||||||||
\(981\) | −7.09575 | −0.226550 | ||||||||
\(982\) | 16.5815 | 0.529136 | ||||||||
\(983\) | 0.501750 | 0.0160033 | 0.00800167 | − | 0.999968i | \(-0.497453\pi\) | ||||
0.00800167 | + | 0.999968i | \(0.497453\pi\) | |||||||
\(984\) | 6.83512 | 0.217896 | ||||||||
\(985\) | −22.3362 | −0.711692 | ||||||||
\(986\) | 6.35448 | 0.202368 | ||||||||
\(987\) | 7.18381 | 0.228663 | ||||||||
\(988\) | 21.2546 | 0.676200 | ||||||||
\(989\) | 28.9011 | 0.919003 | ||||||||
\(990\) | −15.4979 | −0.492556 | ||||||||
\(991\) | −24.5139 | −0.778711 | −0.389356 | − | 0.921088i | \(-0.627302\pi\) | ||||
−0.389356 | + | 0.921088i | \(0.627302\pi\) | |||||||
\(992\) | 10.4107 | 0.330541 | ||||||||
\(993\) | 26.7813 | 0.849878 | ||||||||
\(994\) | −10.0146 | −0.317644 | ||||||||
\(995\) | −76.5213 | −2.42589 | ||||||||
\(996\) | 15.0535 | 0.476987 | ||||||||
\(997\) | 5.89342 | 0.186647 | 0.0933233 | − | 0.995636i | \(-0.470251\pi\) | ||||
0.0933233 | + | 0.995636i | \(0.470251\pi\) | |||||||
\(998\) | 10.1572 | 0.321521 | ||||||||
\(999\) | −11.5338 | −0.364913 |
(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.1.9 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.y.1.9 | ✓ | 10 | 1.1 | even | 1 | trivial |