Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - x^{14} - 35 x^{13} + 32 x^{12} + 477 x^{11} - 392 x^{10} - 3236 x^{9} + 2330 x^{8} + 11690 x^{7} - 7119 x^{6} - 22246 x^{5} + 11137 x^{4} + 20034 x^{3} - 8392 x^{2} + \cdots + 2560 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(0.619952\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.619952 | −0.357929 | −0.178965 | − | 0.983856i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983856i | \(0.557275\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.29231 | −0.577940 | −0.288970 | − | 0.957338i | \(-0.593313\pi\) | ||||
−0.288970 | + | 0.957338i | \(0.593313\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.61566 | −0.871887 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.801172 | 0.206862 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.20824 | −1.50572 | −0.752859 | − | 0.658181i | \(-0.771326\pi\) | ||||
−0.752859 | + | 0.658181i | \(0.771326\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.57687 | −1.73825 | −0.869127 | − | 0.494589i | \(-0.835318\pi\) | ||||
−0.869127 | + | 0.494589i | \(0.835318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.619952 | 0.135285 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.07849 | −0.433395 | −0.216697 | − | 0.976239i | \(-0.569528\pi\) | ||||
−0.216697 | + | 0.976239i | \(0.569528\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.32993 | −0.665985 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.48144 | 0.670003 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.36889 | 0.811283 | 0.405641 | − | 0.914032i | \(-0.367048\pi\) | ||||
0.405641 | + | 0.914032i | \(0.367048\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.32165 | −1.67422 | −0.837109 | − | 0.547036i | \(-0.815756\pi\) | ||||
−0.837109 | + | 0.547036i | \(0.815756\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.619952 | 0.107920 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.29231 | 0.218441 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.40784 | −1.05344 | −0.526721 | − | 0.850038i | \(-0.676579\pi\) | ||||
−0.526721 | + | 0.850038i | \(0.676579\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.619952 | −0.0992717 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.4066 | −1.93758 | −0.968790 | − | 0.247884i | \(-0.920265\pi\) | ||||
−0.968790 | + | 0.247884i | \(0.920265\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.61081 | 1.46564 | 0.732818 | − | 0.680425i | \(-0.238205\pi\) | ||||
0.732818 | + | 0.680425i | \(0.238205\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.38025 | 0.503898 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.59201 | −0.961544 | −0.480772 | − | 0.876846i | \(-0.659644\pi\) | ||||
−0.480772 | + | 0.876846i | \(0.659644\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.84881 | 0.538941 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.49683 | 1.16713 | 0.583565 | − | 0.812066i | \(-0.301657\pi\) | ||||
0.583565 | + | 0.812066i | \(0.301657\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.29231 | 0.174255 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.69729 | 0.622172 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.3403 | 1.34620 | 0.673098 | − | 0.739553i | \(-0.264963\pi\) | ||||
0.673098 | + | 0.739553i | \(0.264963\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.17828 | −0.150864 | −0.0754319 | − | 0.997151i | \(-0.524034\pi\) | ||||
−0.0754319 | + | 0.997151i | \(0.524034\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.61566 | 0.329542 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.29231 | −0.160292 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.17214 | −0.143200 | −0.0715999 | − | 0.997433i | \(-0.522810\pi\) | ||||
−0.0715999 | + | 0.997433i | \(0.522810\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.28856 | 0.155125 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.9076 | −1.65053 | −0.825263 | − | 0.564749i | \(-0.808973\pi\) | ||||
−0.825263 | + | 0.564749i | \(0.808973\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.0315 | 1.40818 | 0.704090 | − | 0.710111i | \(-0.251355\pi\) | ||||
0.704090 | + | 0.710111i | \(0.251355\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.06439 | 0.238376 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.4620 | 1.28958 | 0.644789 | − | 0.764361i | \(-0.276945\pi\) | ||||
0.644789 | + | 0.764361i | \(0.276945\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.68866 | 0.632073 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.04207 | −0.333911 | −0.166955 | − | 0.985964i | \(-0.553394\pi\) | ||||
−0.166955 | + | 0.985964i | \(0.553394\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.02299 | 0.870215 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.70850 | −0.290382 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.94288 | −0.205945 | −0.102973 | − | 0.994684i | \(-0.532835\pi\) | ||||
−0.102973 | + | 0.994684i | \(0.532835\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.77897 | 0.599252 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.79169 | 1.00461 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.4101 | −1.66619 | −0.833095 | − | 0.553130i | \(-0.813433\pi\) | ||||
−0.833095 | + | 0.553130i | \(0.813433\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.61566 | 0.262884 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.57255 | 0.156475 | 0.0782373 | − | 0.996935i | \(-0.475071\pi\) | ||||
0.0782373 | + | 0.996935i | \(0.475071\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.8754 | −1.85985 | −0.929925 | − | 0.367749i | \(-0.880128\pi\) | ||||
−0.929925 | + | 0.367749i | \(0.880128\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.801172 | −0.0781863 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.75305 | −0.942863 | −0.471432 | − | 0.881903i | \(-0.656263\pi\) | ||||
−0.471432 | + | 0.881903i | \(0.656263\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.17646 | −0.687380 | −0.343690 | − | 0.939083i | \(-0.611677\pi\) | ||||
−0.343690 | + | 0.939083i | \(0.611677\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.97255 | 0.377058 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.7361 | 1.66847 | 0.834234 | − | 0.551411i | \(-0.185910\pi\) | ||||
0.834234 | + | 0.551411i | \(0.185910\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.68606 | 0.250476 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.61566 | −0.241818 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.20824 | 0.569108 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.69147 | 0.693516 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.7649 | 0.962840 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.9800 | −1.50673 | −0.753363 | − | 0.657604i | \(-0.771570\pi\) | ||||
−0.753363 | + | 0.657604i | \(0.771570\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.95824 | −0.524594 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.80885 | −0.158040 | −0.0790200 | − | 0.996873i | \(-0.525179\pi\) | ||||
−0.0790200 | + | 0.996873i | \(0.525179\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.57687 | 0.656998 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.49911 | −0.387222 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.48116 | −0.211979 | −0.105990 | − | 0.994367i | \(-0.533801\pi\) | ||||
−0.105990 | + | 0.994367i | \(0.533801\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.3192 | 1.21454 | 0.607270 | − | 0.794495i | \(-0.292264\pi\) | ||||
0.607270 | + | 0.794495i | \(0.292264\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.08673 | 0.344165 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.64598 | −0.468873 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.619952 | −0.0511328 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −24.0105 | −1.96702 | −0.983509 | − | 0.180862i | \(-0.942111\pi\) | ||||
−0.983509 | + | 0.180862i | \(0.942111\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.4303 | 1.49984 | 0.749918 | − | 0.661531i | \(-0.230093\pi\) | ||||
0.749918 | + | 0.661531i | \(0.230093\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 16.2386 | 1.31282 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.0465 | 0.967597 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.83286 | −0.704939 | −0.352469 | − | 0.935823i | \(-0.614658\pi\) | ||||
−0.352469 | + | 0.935823i | \(0.614658\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.26763 | −0.417750 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.07849 | 0.163808 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.3803 | −1.04802 | −0.524012 | − | 0.851711i | \(-0.675565\pi\) | ||||
−0.524012 | + | 0.851711i | \(0.675565\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.801172 | −0.0623711 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.34806 | −0.491227 | −0.245614 | − | 0.969368i | \(-0.578989\pi\) | ||||
−0.245614 | + | 0.969368i | \(0.578989\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 19.8185 | 1.51556 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.41887 | −0.411989 | −0.205994 | − | 0.978553i | \(-0.566043\pi\) | ||||
−0.205994 | + | 0.978553i | \(0.566043\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.32993 | 0.251719 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.41050 | −0.481843 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.09721 | −0.0820093 | −0.0410046 | − | 0.999159i | \(-0.513056\pi\) | ||||
−0.0410046 | + | 0.999159i | \(0.513056\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.0611 | 1.34247 | 0.671236 | − | 0.741243i | \(-0.265764\pi\) | ||||
0.671236 | + | 0.741243i | \(0.265764\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.730479 | 0.0539986 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.28094 | 0.608827 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.20824 | 0.453991 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.48144 | −0.253237 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.6107 | 1.27426 | 0.637131 | − | 0.770755i | \(-0.280121\pi\) | ||||
0.637131 | + | 0.770755i | \(0.280121\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.44303 | 0.319816 | 0.159908 | − | 0.987132i | \(-0.448880\pi\) | ||||
0.159908 | + | 0.987132i | \(0.448880\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.801172 | 0.0573731 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.87740 | −0.347500 | −0.173750 | − | 0.984790i | \(-0.555588\pi\) | ||||
−0.173750 | + | 0.984790i | \(0.555588\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.9307 | 0.845744 | 0.422872 | − | 0.906189i | \(-0.361022\pi\) | ||||
0.422872 | + | 0.906189i | \(0.361022\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.726671 | 0.0512554 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.36889 | −0.306636 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.0332 | 1.11980 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.43662 | 0.377871 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.57687 | 0.524103 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.9152 | −1.64639 | −0.823195 | − | 0.567758i | \(-0.807811\pi\) | ||||
−0.823195 | + | 0.567758i | \(0.807811\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.62202 | 0.590771 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.4202 | −0.847049 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.32165 | 0.632795 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.45894 | −0.504028 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.20824 | −0.417611 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.23055 | −0.350263 | −0.175132 | − | 0.984545i | \(-0.556035\pi\) | ||||
−0.175132 | + | 0.984545i | \(0.556035\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.70996 | 0.580664 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.6686 | 0.907214 | 0.453607 | − | 0.891202i | \(-0.350137\pi\) | ||||
0.453607 | + | 0.891202i | \(0.350137\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.3511 | −1.21267 | −0.606336 | − | 0.795209i | \(-0.707361\pi\) | ||||
−0.606336 | + | 0.795209i | \(0.707361\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.619952 | −0.0407898 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.2260 | 1.06300 | 0.531500 | − | 0.847058i | \(-0.321628\pi\) | ||||
0.531500 | + | 0.847058i | \(0.321628\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.51895 | 0.555715 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.10589 | −0.461577 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.47650 | 0.354245 | 0.177123 | − | 0.984189i | \(-0.443321\pi\) | ||||
0.177123 | + | 0.984189i | \(0.443321\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.1742 | 1.36395 | 0.681976 | − | 0.731375i | \(-0.261121\pi\) | ||||
0.681976 | + | 0.731375i | \(0.261121\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.9710 | −0.896240 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.29231 | −0.0825629 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.57687 | −0.482105 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.88594 | 0.119517 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.5021 | 0.662888 | 0.331444 | − | 0.943475i | \(-0.392464\pi\) | ||||
0.331444 | + | 0.943475i | \(0.392464\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.07849 | 0.130673 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.97386 | −0.311475 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.2850 | −1.07821 | −0.539106 | − | 0.842238i | \(-0.681238\pi\) | ||||
−0.539106 | + | 0.842238i | \(0.681238\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.40784 | 0.398164 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.4275 | −0.707347 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.2976 | −0.634979 | −0.317489 | − | 0.948262i | \(-0.602840\pi\) | ||||
−0.317489 | + | 0.948262i | \(0.602840\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.9806 | −0.674531 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.20449 | 0.0737138 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.0830 | 0.614770 | 0.307385 | − | 0.951585i | \(-0.400546\pi\) | ||||
0.307385 | + | 0.951585i | \(0.400546\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.32823 | 0.0806841 | 0.0403421 | − | 0.999186i | \(-0.487155\pi\) | ||||
0.0403421 | + | 0.999186i | \(0.487155\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.619952 | 0.0375212 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.32993 | 0.200802 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.3437 | 1.46267 | 0.731335 | − | 0.682018i | \(-0.238897\pi\) | ||||
0.731335 | + | 0.682018i | \(0.238897\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 24.3823 | 1.45973 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.36292 | 0.439235 | 0.219617 | − | 0.975586i | \(-0.429519\pi\) | ||||
0.219617 | + | 0.975586i | \(0.429519\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.8568 | −1.29925 | −0.649626 | − | 0.760254i | \(-0.725074\pi\) | ||||
−0.649626 | + | 0.760254i | \(0.725074\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.07037 | −0.359578 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.4066 | 0.732336 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.5422 | 1.26719 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.1735 | 0.596378 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.47001 | 0.0858792 | 0.0429396 | − | 0.999078i | \(-0.486328\pi\) | ||||
0.0429396 | + | 0.999078i | \(0.486328\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.3629 | −0.778020 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.48144 | −0.202014 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.07849 | −0.120202 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.61081 | −0.553958 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.974905 | −0.0560068 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.52271 | 0.0871902 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.3314 | −0.817938 | −0.408969 | − | 0.912548i | \(-0.634112\pi\) | ||||
−0.408969 | + | 0.912548i | \(0.634112\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.7018 | 0.665695 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.8291 | −1.12440 | −0.562201 | − | 0.827000i | \(-0.690045\pi\) | ||||
−0.562201 | + | 0.827000i | \(0.690045\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.2120 | 1.65116 | 0.825580 | − | 0.564285i | \(-0.190848\pi\) | ||||
0.825580 | + | 0.564285i | \(0.190848\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.38025 | −0.190456 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.747824 | 0.0420020 | 0.0210010 | − | 0.999779i | \(-0.493315\pi\) | ||||
0.0210010 | + | 0.999779i | \(0.493315\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.36889 | −0.244611 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.04642 | 0.337478 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 47.0390 | 2.61732 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.32993 | −0.184711 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.44906 | 0.246033 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.59201 | 0.363430 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.67424 | −0.531744 | −0.265872 | − | 0.964008i | \(-0.585660\pi\) | ||||
−0.265872 | + | 0.964008i | \(0.585660\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 16.7607 | 0.918483 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.51477 | 0.0827609 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.06916 | −0.112714 | −0.0563572 | − | 0.998411i | \(-0.517949\pi\) | ||||
−0.0563572 | + | 0.998411i | \(0.517949\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.9955 | −0.597193 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.32165 | 0.504796 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.66523 | −0.0896527 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.4310 | −0.721013 | −0.360506 | − | 0.932757i | \(-0.617396\pi\) | ||||
−0.360506 | + | 0.932757i | \(0.617396\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.515138 | −0.0275747 | −0.0137874 | − | 0.999905i | \(-0.504389\pi\) | ||||
−0.0137874 | + | 0.999905i | \(0.504389\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.48144 | 0.185825 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −29.2092 | −1.55465 | −0.777324 | − | 0.629101i | \(-0.783423\pi\) | ||||
−0.777324 | + | 0.629101i | \(0.783423\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.9729 | 0.953905 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.84881 | −0.203700 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.3605 | −0.546807 | −0.273403 | − | 0.961899i | \(-0.588149\pi\) | ||||
−0.273403 | + | 0.961899i | \(0.588149\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 38.4090 | 2.02153 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.619952 | −0.0325390 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.5484 | −0.813843 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.4510 | −1.22413 | −0.612067 | − | 0.790806i | \(-0.709662\pi\) | ||||
−0.612067 | + | 0.790806i | \(0.709662\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 32.4513 | 1.68935 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.49683 | −0.441134 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.83239 | 0.509102 | 0.254551 | − | 0.967059i | \(-0.418072\pi\) | ||||
0.254551 | + | 0.967059i | \(0.418072\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.67370 | −0.344628 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.36889 | 0.225009 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.3709 | −0.635452 | −0.317726 | − | 0.948183i | \(-0.602919\pi\) | ||||
−0.317726 | + | 0.948183i | \(0.602919\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.5267 | 0.539302 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 30.8124 | 1.57444 | 0.787221 | − | 0.616671i | \(-0.211519\pi\) | ||||
0.787221 | + | 0.616671i | \(0.211519\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.29231 | −0.0658624 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −25.1386 | −1.27787 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.3490 | −0.626118 | −0.313059 | − | 0.949734i | \(-0.601354\pi\) | ||||
−0.313059 | + | 0.949734i | \(0.601354\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.9037 | 0.652570 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.12140 | 0.0565671 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.8125 | −0.745298 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.6331 | 1.43705 | 0.718526 | − | 0.695500i | \(-0.244817\pi\) | ||||
0.718526 | + | 0.695500i | \(0.244817\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.69729 | −0.235159 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 35.5777 | 1.77666 | 0.888332 | − | 0.459201i | \(-0.151864\pi\) | ||||
0.888332 | + | 0.459201i | \(0.151864\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.32165 | −0.464344 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.35153 | −0.365300 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.40784 | 0.317625 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 37.0587 | 1.83244 | 0.916219 | − | 0.400679i | \(-0.131226\pi\) | ||||
0.916219 | + | 0.400679i | \(0.131226\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.53820 | 0.0758737 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.3403 | −0.508814 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.93131 | 0.192981 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.87723 | −0.434720 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.1674 | −0.692121 | −0.346061 | − | 0.938212i | \(-0.612481\pi\) | ||||
−0.346061 | + | 0.938212i | \(0.612481\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.61952 | −0.176405 | −0.0882023 | − | 0.996103i | \(-0.528112\pi\) | ||||
−0.0882023 | + | 0.996103i | \(0.528112\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 17.2425 | 0.838358 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 20.6730 | 1.00279 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.17828 | 0.0570211 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.619952 | 0.0299315 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.79753 | −0.375594 | −0.187797 | − | 0.982208i | \(-0.560135\pi\) | ||||
−0.187797 | + | 0.982208i | \(0.560135\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.6345 | −0.943572 | −0.471786 | − | 0.881713i | \(-0.656391\pi\) | ||||
−0.471786 | + | 0.881713i | \(0.656391\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.50023 | 0.167823 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.7484 | 0.753350 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.1122 | 0.959901 | 0.479951 | − | 0.877295i | \(-0.340655\pi\) | ||||
0.479951 | + | 0.877295i | \(0.340655\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.61566 | −0.124555 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.7559 | 1.36623 | 0.683117 | − | 0.730309i | \(-0.260624\pi\) | ||||
0.683117 | + | 0.730309i | \(0.260624\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.51081 | 0.119024 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.8854 | 0.704053 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 34.9243 | 1.64818 | 0.824090 | − | 0.566459i | \(-0.191687\pi\) | ||||
0.824090 | + | 0.566459i | \(0.191687\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.4066 | 0.584202 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.4259 | −0.536835 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.29231 | 0.0605846 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.7566 | 0.549951 | 0.274976 | − | 0.961451i | \(-0.411330\pi\) | ||||
0.274976 | + | 0.961451i | \(0.411330\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −21.6136 | −1.00884 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.1726 | 1.17241 | 0.586203 | − | 0.810164i | \(-0.300622\pi\) | ||||
0.586203 | + | 0.810164i | \(0.300622\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.2344 | 0.615056 | 0.307528 | − | 0.951539i | \(-0.400498\pi\) | ||||
0.307528 | + | 0.951539i | \(0.400498\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.46824 | −0.346331 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.0162 | 0.741139 | 0.370570 | − | 0.928805i | \(-0.379162\pi\) | ||||
0.370570 | + | 0.928805i | \(0.379162\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.17214 | 0.0541245 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.47595 | 0.252318 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.61081 | −0.441906 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 25.2304 | 1.15765 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −22.2248 | −1.01760 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.90965 | 0.178636 | 0.0893181 | − | 0.996003i | \(-0.471531\pi\) | ||||
0.0893181 | + | 0.996003i | \(0.471531\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.40784 | −0.292172 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.28856 | −0.0586316 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.2070 | 0.962958 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.7629 | 0.850228 | 0.425114 | − | 0.905140i | \(-0.360234\pi\) | ||||
0.425114 | + | 0.905140i | \(0.360234\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.29513 | 0.375119 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.9958 | 0.676750 | 0.338375 | − | 0.941011i | \(-0.390123\pi\) | ||||
0.338375 | + | 0.941011i | \(0.390123\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27.1231 | −1.22156 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.38025 | −0.151931 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.9076 | 0.623840 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −40.7120 | −1.82252 | −0.911260 | − | 0.411831i | \(-0.864889\pi\) | ||||
−0.911260 | + | 0.411831i | \(0.864889\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.93549 | 0.175825 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.90482 | −0.263283 | −0.131641 | − | 0.991297i | \(-0.542025\pi\) | ||||
−0.131641 | + | 0.991297i | \(0.542025\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.03223 | −0.0904329 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.619952 | −0.0275330 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.1013 | 0.536380 | 0.268190 | − | 0.963366i | \(-0.413574\pi\) | ||||
0.268190 | + | 0.963366i | \(0.413574\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.0315 | −0.532242 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −26.3784 | −1.16464 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.3929 | 1.07488 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.59201 | 0.289916 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.35944 | 0.147463 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.7226 | 1.38979 | 0.694896 | − | 0.719110i | \(-0.255450\pi\) | ||||
0.694896 | + | 0.719110i | \(0.255450\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.7025 | −1.51744 | −0.758718 | − | 0.651419i | \(-0.774174\pi\) | ||||
−0.758718 | + | 0.651419i | \(0.774174\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.06439 | −0.0900975 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 57.8710 | 2.52090 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.6799 | −0.812169 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −27.0468 | −1.17373 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.4066 | −0.537388 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.6040 | 0.544918 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.680217 | 0.0293535 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.7064 | −0.761258 | −0.380629 | − | 0.924728i | \(-0.624293\pi\) | ||||
−0.380629 | + | 0.924728i | \(0.624293\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.1970 | −0.480510 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.27423 | 0.397264 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.21418 | 0.0946713 | 0.0473356 | − | 0.998879i | \(-0.484927\pi\) | ||||
0.0473356 | + | 0.998879i | \(0.484927\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.08199 | 0.131536 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −33.1025 | −1.41022 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.4620 | −0.487414 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.13378 | −0.217917 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.770744 | 0.0326575 | 0.0163287 | − | 0.999867i | \(-0.494802\pi\) | ||||
0.0163287 | + | 0.999867i | \(0.494802\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.61081 | 0.406494 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.84881 | −0.162497 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.6229 | −0.658426 | −0.329213 | − | 0.944256i | \(-0.606783\pi\) | ||||
−0.329213 | + | 0.944256i | \(0.606783\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.9205 | −0.964274 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.68866 | −0.238901 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −31.2760 | −1.31116 | −0.655580 | − | 0.755126i | \(-0.727576\pi\) | ||||
−0.655580 | + | 0.755126i | \(0.727576\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −45.5926 | −1.90799 | −0.953996 | − | 0.299820i | \(-0.903073\pi\) | ||||
−0.953996 | + | 0.299820i | \(0.903073\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.9178 | −0.456096 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.92121 | 0.288634 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.1204 | 0.587838 | 0.293919 | − | 0.955830i | \(-0.405040\pi\) | ||||
0.293919 | + | 0.955830i | \(0.405040\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.75446 | −0.114472 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.04207 | 0.126206 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.49683 | −0.351903 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.38025 | 0.139756 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 34.8879 | 1.43998 | 0.719989 | − | 0.693986i | \(-0.244147\pi\) | ||||
0.719989 | + | 0.693986i | \(0.244147\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 70.6289 | 2.91021 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.02375 | 0.124380 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.5512 | −0.802871 | −0.401436 | − | 0.915887i | \(-0.631489\pi\) | ||||
−0.401436 | + | 0.915887i | \(0.631489\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.02299 | −0.328910 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.39645 | −0.302717 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.8081 | −0.768477 | −0.384238 | − | 0.923234i | \(-0.625536\pi\) | ||||
−0.384238 | + | 0.923234i | \(0.625536\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −48.7858 | −1.99001 | −0.995006 | − | 0.0998129i | \(-0.968176\pi\) | ||||
−0.995006 | + | 0.0998129i | \(0.968176\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.06592 | 0.124854 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.29231 | −0.0525400 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −34.8493 | −1.41449 | −0.707245 | − | 0.706969i | \(-0.750062\pi\) | ||||
−0.707245 | + | 0.706969i | \(0.750062\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.70850 | 0.109754 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.59201 | −0.266684 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.56338 | 0.143924 | 0.0719618 | − | 0.997407i | \(-0.477074\pi\) | ||||
0.0719618 | + | 0.997407i | \(0.477074\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.93978 | −0.400811 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.35703 | −0.296183 | −0.148091 | − | 0.988974i | \(-0.547313\pi\) | ||||
−0.148091 | + | 0.988974i | \(0.547313\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −38.9999 | −1.56754 | −0.783770 | − | 0.621051i | \(-0.786706\pi\) | ||||
−0.783770 | + | 0.621051i | \(0.786706\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.23612 | −0.290376 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.94288 | 0.0778400 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.73805 | 0.109522 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.69729 | −0.187592 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 39.7814 | 1.58619 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.6259 | −1.33863 | −0.669313 | − | 0.742981i | \(-0.733411\pi\) | ||||
−0.669313 | + | 0.742981i | \(0.733411\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.8263 | 0.589291 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21.9434 | 0.870798 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 36.3775 | 1.43907 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.2385 | −1.03636 | −0.518179 | − | 0.855272i | \(-0.673390\pi\) | ||||
−0.518179 | + | 0.855272i | \(0.673390\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −36.2912 | −1.43119 | −0.715593 | − | 0.698517i | \(-0.753843\pi\) | ||||
−0.715593 | + | 0.698517i | \(0.753843\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.69991 | 0.303184 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.2318 | 1.03128 | 0.515638 | − | 0.856806i | \(-0.327555\pi\) | ||||
0.515638 | + | 0.856806i | \(0.327555\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.3403 | −0.405893 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.77897 | −0.226496 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.4011 | −0.954890 | −0.477445 | − | 0.878662i | \(-0.658437\pi\) | ||||
−0.477445 | + | 0.878662i | \(0.658437\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.33760 | 0.0913376 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −31.4703 | −1.22777 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 42.4192 | 1.65242 | 0.826209 | − | 0.563364i | \(-0.190493\pi\) | ||||
0.826209 | + | 0.563364i | \(0.190493\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.6437 | −1.19190 | −0.595950 | − | 0.803021i | \(-0.703224\pi\) | ||||
−0.595950 | + | 0.803021i | \(0.703224\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.84881 | 0.149475 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.79169 | −0.379705 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.08069 | −0.351606 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.24269 | 0.125370 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.17828 | 0.0454871 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.7296 | −1.57001 | −0.785006 | − | 0.619488i | \(-0.787340\pi\) | ||||
−0.785006 | + | 0.619488i | \(0.787340\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −11.5929 | −0.446212 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 44.3760 | 1.70551 | 0.852754 | − | 0.522313i | \(-0.174931\pi\) | ||||
0.852754 | + | 0.522313i | \(0.174931\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.4101 | 0.629761 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.47385 | −0.324718 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.0658 | 0.538213 | 0.269107 | − | 0.963110i | \(-0.413272\pi\) | ||||
0.269107 | + | 0.963110i | \(0.413272\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.20643 | 0.122511 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.3768 | 0.434051 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.49683 | 0.323704 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.9219 | −0.681782 | −0.340891 | − | 0.940103i | \(-0.610729\pi\) | ||||
−0.340891 | + | 0.940103i | \(0.610729\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.61566 | −0.0993607 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.5049 | −0.701932 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 77.0229 | 2.91745 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.0593 | −0.380479 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.6269 | 1.49669 | 0.748343 | − | 0.663312i | \(-0.230850\pi\) | ||||
0.748343 | + | 0.663312i | \(0.230850\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 48.5514 | 1.83115 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.28134 | −0.198907 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.57255 | −0.0591418 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.2174 | 0.421278 | 0.210639 | − | 0.977564i | \(-0.432446\pi\) | ||||
0.210639 | + | 0.977564i | \(0.432446\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −29.9807 | −1.12436 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.3749 | 0.725597 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.29231 | 0.0483298 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.39516 | −0.126795 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.80817 | −0.0674333 | −0.0337166 | − | 0.999431i | \(-0.510734\pi\) | ||||
−0.0337166 | + | 0.999431i | \(0.510734\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.8754 | 0.702957 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.1270 | −0.488198 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −14.5481 | −0.540303 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.6656 | −1.06315 | −0.531573 | − | 0.847012i | \(-0.678399\pi\) | ||||
−0.531573 | + | 0.847012i | \(0.678399\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.40462 | −0.311282 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −59.6662 | −2.20683 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32.3537 | 1.19501 | 0.597505 | − | 0.801865i | \(-0.296159\pi\) | ||||
0.597505 | + | 0.801865i | \(0.296159\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.801172 | 0.0295517 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.17214 | 0.0431764 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.88480 | −0.179690 | −0.0898452 | − | 0.995956i | \(-0.528637\pi\) | ||||
−0.0898452 | + | 0.995956i | \(0.528637\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.69729 | 0.172559 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.2509 | 1.32992 | 0.664958 | − | 0.746881i | \(-0.268449\pi\) | ||||
0.664958 | + | 0.746881i | \(0.268449\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 31.0291 | 1.13682 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.95703 | 0.291133 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.75305 | 0.356369 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.2303 | −0.446289 | −0.223144 | − | 0.974785i | \(-0.571632\pi\) | ||||
−0.223144 | + | 0.974785i | \(0.571632\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.51081 | −0.237267 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −23.8177 | −0.866815 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.6868 | 1.29706 | 0.648529 | − | 0.761190i | \(-0.275384\pi\) | ||||
0.648529 | + | 0.761190i | \(0.275384\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.28856 | −0.0467718 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −50.8042 | −1.84165 | −0.920825 | − | 0.389977i | \(-0.872483\pi\) | ||||
−0.920825 | + | 0.389977i | \(0.872483\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.17646 | 0.259805 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −20.9854 | −0.758729 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.3403 | 0.373367 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.95698 | −0.286936 | −0.143468 | − | 0.989655i | \(-0.545825\pi\) | ||||
−0.143468 | + | 0.989655i | \(0.545825\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.7159 | 0.385924 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 39.3667 | 1.41592 | 0.707960 | − | 0.706252i | \(-0.249616\pi\) | ||||
0.707960 | + | 0.706252i | \(0.249616\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 31.0404 | 1.11500 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.97255 | −0.142515 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 94.0029 | 3.36800 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.9076 | 0.497652 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 15.2100 | 0.543562 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.4148 | 0.407412 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.7885 | −0.634090 | −0.317045 | − | 0.948410i | \(-0.602691\pi\) | ||||
−0.317045 | + | 0.948410i | \(0.602691\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.38403 | 0.227277 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.7361 | −0.630621 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.17828 | −0.0418421 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.80742 | 0.241434 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.10907 | −0.216394 | −0.108197 | − | 0.994129i | \(-0.534508\pi\) | ||||
−0.108197 | + | 0.994129i | \(0.534508\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 40.9248 | 1.44782 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.08192 | 0.179561 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.0315 | −0.424582 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.68606 | −0.0946710 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.25096 | −0.220044 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.33308 | 0.222659 | 0.111330 | − | 0.993784i | \(-0.464489\pi\) | ||||
0.111330 | + | 0.993784i | \(0.464489\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.4720 | −1.10513 | −0.552565 | − | 0.833470i | \(-0.686351\pi\) | ||||
−0.552565 | + | 0.833470i | \(0.686351\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.823437 | −0.0288792 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.2915 | 0.605695 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −72.8199 | −2.54765 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.61566 | 0.0913986 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.3983 | 0.397804 | 0.198902 | − | 0.980019i | \(-0.436262\pi\) | ||||
0.198902 | + | 0.980019i | \(0.436262\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.64642 | −0.301395 | −0.150698 | − | 0.988580i | \(-0.548152\pi\) | ||||
−0.150698 | + | 0.988580i | \(0.548152\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.06439 | −0.0718730 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.7132 | −0.998456 | −0.499228 | − | 0.866471i | \(-0.666383\pi\) | ||||
−0.499228 | + | 0.866471i | \(0.666383\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.5172 | 0.677860 | 0.338930 | − | 0.940812i | \(-0.389935\pi\) | ||||
0.338930 | + | 0.940812i | \(0.389935\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.0919 | −0.523533 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.20824 | −0.215103 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.20367 | 0.283900 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −32.4527 | −1.12173 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −38.0423 | −1.31337 | −0.656683 | − | 0.754167i | \(-0.728041\pi\) | ||||
−0.656683 | + | 0.754167i | \(0.728041\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.91278 | −0.341820 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.56465 | −0.157215 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.29231 | −0.0444569 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.5502 | 0.465040 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.3186 | 0.456556 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.9466 | −0.409045 | −0.204523 | − | 0.978862i | \(-0.565564\pi\) | ||||
−0.204523 | + | 0.978862i | \(0.565564\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −25.6117 | −0.875903 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.2108 | 0.451272 | 0.225636 | − | 0.974212i | \(-0.427554\pi\) | ||||
0.225636 | + | 0.974212i | \(0.427554\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.9509 | −0.407759 | −0.203879 | − | 0.978996i | \(-0.565355\pi\) | ||||
−0.203879 | + | 0.978996i | \(0.565355\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.69147 | −0.262125 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.2473 | −0.450943 | −0.225472 | − | 0.974250i | \(-0.572392\pi\) | ||||
−0.225472 | + | 0.974250i | \(0.572392\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.00287 | 0.238105 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.3551 | −0.453564 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.4620 | −0.388822 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.17214 | −0.0397165 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 42.9232 | 1.45273 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.7649 | −0.363919 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.2730 | 0.617034 | 0.308517 | − | 0.951219i | \(-0.400167\pi\) | ||||
0.308517 | + | 0.951219i | \(0.400167\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.911338 | −0.0307387 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.5003 | −0.488529 | −0.244265 | − | 0.969709i | \(-0.578547\pi\) | ||||
−0.244265 | + | 0.969709i | \(0.578547\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.8291 | 0.599998 | 0.299999 | − | 0.953940i | \(-0.403014\pi\) | ||||
0.299999 | + | 0.953940i | \(0.403014\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.28437 | 0.278476 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.8407 | 0.766917 | 0.383458 | − | 0.923558i | \(-0.374733\pi\) | ||||
0.383458 | + | 0.923558i | \(0.374733\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.9800 | 0.569489 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.68866 | −0.190577 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 49.9469 | 1.67141 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.41794 | 0.0473964 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.28856 | 0.0430238 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −40.7253 | −1.35826 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −52.7504 | −1.75737 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.95824 | 0.198278 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −23.3406 | −0.775869 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.8704 | 1.09144 | 0.545722 | − | 0.837966i | \(-0.316255\pi\) | ||||
0.545722 | + | 0.837966i | \(0.316255\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.11326 | −0.136428 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.22055 | 0.172964 | 0.0864822 | − | 0.996253i | \(-0.472437\pi\) | ||||
0.0864822 | + | 0.996253i | \(0.472437\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.04207 | 0.100678 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.944008 | −0.0312079 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.80885 | 0.0597335 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.5120 | 0.874549 | 0.437274 | − | 0.899328i | \(-0.355944\pi\) | ||||
0.437274 | + | 0.899328i | \(0.355944\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.88479 | 0.292764 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.9076 | −0.457773 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.3376 | 0.701578 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 49.3717 | 1.62158 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.34919 | 0.0442653 | 0.0221327 | − | 0.999755i | \(-0.492954\pi\) | ||||
0.0221327 | + | 0.999755i | \(0.492954\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.57687 | −0.248322 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.2931 | 0.402457 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.02299 | −0.262380 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.61167 | 0.281331 | 0.140666 | − | 0.990057i | \(-0.455076\pi\) | ||||
0.140666 | + | 0.990057i | \(0.455076\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −18.1100 | −0.590999 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40.6016 | 1.32358 | 0.661788 | − | 0.749691i | \(-0.269798\pi\) | ||||
0.661788 | + | 0.749691i | \(0.269798\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.7869 | 0.839736 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.49911 | 0.146356 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.77733 | 0.0902511 | 0.0451255 | − | 0.998981i | \(-0.485631\pi\) | ||||
0.0451255 | + | 0.998981i | \(0.485631\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.0315 | 0.390559 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.463615 | −0.0150337 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.7363 | 0.963252 | 0.481626 | − | 0.876377i | \(-0.340046\pi\) | ||||
0.481626 | + | 0.876377i | \(0.340046\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22.7585 | −0.736447 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.70850 | 0.0875534 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.48116 | 0.0801207 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 55.8931 | 1.80300 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 25.5107 | 0.822070 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.74178 | −0.184835 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.1425 | 0.872843 | 0.436421 | − | 0.899742i | \(-0.356246\pi\) | ||||
0.436421 | + | 0.899742i | \(0.356246\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −29.1619 | −0.936816 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.5397 | 0.755423 | 0.377712 | − | 0.925923i | \(-0.376711\pi\) | ||||
0.377712 | + | 0.925923i | \(0.376711\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.3192 | −0.459053 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.06439 | 0.0661135 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.1425 | 0.708402 | 0.354201 | − | 0.935169i | \(-0.384753\pi\) | ||||
0.354201 | + | 0.935169i | \(0.384753\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.94288 | 0.0620948 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.7712 | 0.599317 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.7248 | −0.597229 | −0.298615 | − | 0.954374i | \(-0.596525\pi\) | ||||
−0.298615 | + | 0.954374i | \(0.596525\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.30312 | 0.200834 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.08673 | −0.130082 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19.9760 | −0.635198 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.4591 | −0.776968 | −0.388484 | − | 0.921456i | \(-0.627001\pi\) | ||||
−0.388484 | + | 0.921456i | \(0.627001\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.99756 | 0.190327 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.4182 | −0.488790 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 53.9538 | 1.70873 | 0.854366 | − | 0.519671i | \(-0.173945\pi\) | ||||
0.854366 | + | 0.519671i | \(0.173945\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −22.3085 | −0.705810 |
(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 | 8008.2.a.z.1.7 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.z.1.7 | ✓ | 15 | 1.1 | even | 1 | trivial |