Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8670,2,Mod(1,8670)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8670, 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("8670.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8670 = 2 \cdot 3 \cdot 5 \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8670.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: | \(69.2302985525\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{18})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.87939\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8670.1 |
$q$-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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −3.87939 | −1.46627 | −0.733135 | − | 0.680083i | \(-0.761944\pi\) | ||||
−0.733135 | + | 0.680083i | \(0.761944\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 1.53209 | 0.461942 | 0.230971 | − | 0.972961i | \(-0.425810\pi\) | ||||
0.230971 | + | 0.972961i | \(0.425810\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 4.10607 | 1.13882 | 0.569409 | − | 0.822054i | \(-0.307172\pi\) | ||||
0.569409 | + | 0.822054i | \(0.307172\pi\) | |||||||
\(14\) | −3.87939 | −1.03681 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 1.00000 | 0.229416 | 0.114708 | − | 0.993399i | \(-0.463407\pi\) | ||||
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −3.87939 | −0.846551 | ||||||||
\(22\) | 1.53209 | 0.326642 | ||||||||
\(23\) | −9.41147 | −1.96243 | −0.981214 | − | 0.192922i | \(-0.938203\pi\) | ||||
−0.981214 | + | 0.192922i | \(0.938203\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.10607 | 0.805266 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −3.87939 | −0.733135 | ||||||||
\(29\) | −5.75877 | −1.06938 | −0.534688 | − | 0.845049i | \(-0.679571\pi\) | ||||
−0.534688 | + | 0.845049i | \(0.679571\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | −6.45336 | −1.15906 | −0.579529 | − | 0.814952i | \(-0.696764\pi\) | ||||
−0.579529 | + | 0.814952i | \(0.696764\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.53209 | 0.266702 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.87939 | 0.655736 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −0.305407 | −0.0502086 | −0.0251043 | − | 0.999685i | \(-0.507992\pi\) | ||||
−0.0251043 | + | 0.999685i | \(0.507992\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 4.10607 | 0.657497 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 11.5817 | 1.80876 | 0.904380 | − | 0.426727i | \(-0.140334\pi\) | ||||
0.904380 | + | 0.426727i | \(0.140334\pi\) | |||||||
\(42\) | −3.87939 | −0.598602 | ||||||||
\(43\) | −12.5817 | −1.91869 | −0.959347 | − | 0.282229i | \(-0.908926\pi\) | ||||
−0.959347 | + | 0.282229i | \(0.908926\pi\) | |||||||
\(44\) | 1.53209 | 0.230971 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −9.41147 | −1.38765 | ||||||||
\(47\) | 5.63816 | 0.822410 | 0.411205 | − | 0.911543i | \(-0.365108\pi\) | ||||
0.411205 | + | 0.911543i | \(0.365108\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 8.04963 | 1.14995 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.10607 | 0.569409 | ||||||||
\(53\) | 4.22668 | 0.580579 | 0.290290 | − | 0.956939i | \(-0.406248\pi\) | ||||
0.290290 | + | 0.956939i | \(0.406248\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −1.53209 | −0.206587 | ||||||||
\(56\) | −3.87939 | −0.518405 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | −5.75877 | −0.756164 | ||||||||
\(59\) | −13.0496 | −1.69892 | −0.849459 | − | 0.527655i | \(-0.823071\pi\) | ||||
−0.849459 | + | 0.527655i | \(0.823071\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | −4.61081 | −0.590354 | −0.295177 | − | 0.955443i | \(-0.595379\pi\) | ||||
−0.295177 | + | 0.955443i | \(0.595379\pi\) | |||||||
\(62\) | −6.45336 | −0.819578 | ||||||||
\(63\) | −3.87939 | −0.488757 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.10607 | −0.509295 | ||||||||
\(66\) | 1.53209 | 0.188587 | ||||||||
\(67\) | −4.08378 | −0.498913 | −0.249456 | − | 0.968386i | \(-0.580252\pi\) | ||||
−0.249456 | + | 0.968386i | \(0.580252\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.41147 | −1.13301 | ||||||||
\(70\) | 3.87939 | 0.463675 | ||||||||
\(71\) | −14.2567 | −1.69196 | −0.845980 | − | 0.533214i | \(-0.820984\pi\) | ||||
−0.845980 | + | 0.533214i | \(0.820984\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 15.4047 | 1.80298 | 0.901490 | − | 0.432800i | \(-0.142474\pi\) | ||||
0.901490 | + | 0.432800i | \(0.142474\pi\) | |||||||
\(74\) | −0.305407 | −0.0355029 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −5.94356 | −0.677332 | ||||||||
\(78\) | 4.10607 | 0.464921 | ||||||||
\(79\) | 7.19253 | 0.809223 | 0.404612 | − | 0.914489i | \(-0.367407\pi\) | ||||
0.404612 | + | 0.914489i | \(0.367407\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 11.5817 | 1.27899 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | −3.87939 | −0.423276 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −12.5817 | −1.35672 | ||||||||
\(87\) | −5.75877 | −0.617405 | ||||||||
\(88\) | 1.53209 | 0.163321 | ||||||||
\(89\) | 6.24897 | 0.662390 | 0.331195 | − | 0.943562i | \(-0.392548\pi\) | ||||
0.331195 | + | 0.943562i | \(0.392548\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | −15.9290 | −1.66981 | ||||||||
\(92\) | −9.41147 | −0.981214 | ||||||||
\(93\) | −6.45336 | −0.669183 | ||||||||
\(94\) | 5.63816 | 0.581531 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −2.24123 | −0.227562 | −0.113781 | − | 0.993506i | \(-0.536296\pi\) | ||||
−0.113781 | + | 0.993506i | \(0.536296\pi\) | |||||||
\(98\) | 8.04963 | 0.813135 | ||||||||
\(99\) | 1.53209 | 0.153981 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 11.5175 | 1.14604 | 0.573019 | − | 0.819542i | \(-0.305772\pi\) | ||||
0.573019 | + | 0.819542i | \(0.305772\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.69459 | −0.758171 | −0.379085 | − | 0.925362i | \(-0.623761\pi\) | ||||
−0.379085 | + | 0.925362i | \(0.623761\pi\) | |||||||
\(104\) | 4.10607 | 0.402633 | ||||||||
\(105\) | 3.87939 | 0.378589 | ||||||||
\(106\) | 4.22668 | 0.410532 | ||||||||
\(107\) | −0.694593 | −0.0671488 | −0.0335744 | − | 0.999436i | \(-0.510689\pi\) | ||||
−0.0335744 | + | 0.999436i | \(0.510689\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −12.1284 | −1.16169 | −0.580843 | − | 0.814016i | \(-0.697277\pi\) | ||||
−0.580843 | + | 0.814016i | \(0.697277\pi\) | |||||||
\(110\) | −1.53209 | −0.146079 | ||||||||
\(111\) | −0.305407 | −0.0289880 | ||||||||
\(112\) | −3.87939 | −0.366567 | ||||||||
\(113\) | 3.43376 | 0.323021 | 0.161511 | − | 0.986871i | \(-0.448363\pi\) | ||||
0.161511 | + | 0.986871i | \(0.448363\pi\) | |||||||
\(114\) | 1.00000 | 0.0936586 | ||||||||
\(115\) | 9.41147 | 0.877624 | ||||||||
\(116\) | −5.75877 | −0.534688 | ||||||||
\(117\) | 4.10607 | 0.379606 | ||||||||
\(118\) | −13.0496 | −1.20132 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | −8.65270 | −0.786609 | ||||||||
\(122\) | −4.61081 | −0.417444 | ||||||||
\(123\) | 11.5817 | 1.04429 | ||||||||
\(124\) | −6.45336 | −0.579529 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −3.87939 | −0.345603 | ||||||||
\(127\) | −7.34049 | −0.651363 | −0.325682 | − | 0.945480i | \(-0.605594\pi\) | ||||
−0.325682 | + | 0.945480i | \(0.605594\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −12.5817 | −1.10776 | ||||||||
\(130\) | −4.10607 | −0.360126 | ||||||||
\(131\) | −12.4757 | −1.09000 | −0.545001 | − | 0.838435i | \(-0.683471\pi\) | ||||
−0.545001 | + | 0.838435i | \(0.683471\pi\) | |||||||
\(132\) | 1.53209 | 0.133351 | ||||||||
\(133\) | −3.87939 | −0.336385 | ||||||||
\(134\) | −4.08378 | −0.352785 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.45336 | −0.551348 | −0.275674 | − | 0.961251i | \(-0.588901\pi\) | ||||
−0.275674 | + | 0.961251i | \(0.588901\pi\) | |||||||
\(138\) | −9.41147 | −0.801158 | ||||||||
\(139\) | −11.6108 | −0.984816 | −0.492408 | − | 0.870364i | \(-0.663883\pi\) | ||||
−0.492408 | + | 0.870364i | \(0.663883\pi\) | |||||||
\(140\) | 3.87939 | 0.327868 | ||||||||
\(141\) | 5.63816 | 0.474818 | ||||||||
\(142\) | −14.2567 | −1.19640 | ||||||||
\(143\) | 6.29086 | 0.526068 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 5.75877 | 0.478240 | ||||||||
\(146\) | 15.4047 | 1.27490 | ||||||||
\(147\) | 8.04963 | 0.663922 | ||||||||
\(148\) | −0.305407 | −0.0251043 | ||||||||
\(149\) | −19.9317 | −1.63287 | −0.816434 | − | 0.577438i | \(-0.804052\pi\) | ||||
−0.816434 | + | 0.577438i | \(0.804052\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | −22.8229 | −1.85731 | −0.928653 | − | 0.370951i | \(-0.879032\pi\) | ||||
−0.928653 | + | 0.370951i | \(0.879032\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5.94356 | −0.478946 | ||||||||
\(155\) | 6.45336 | 0.518347 | ||||||||
\(156\) | 4.10607 | 0.328748 | ||||||||
\(157\) | −0.573978 | −0.0458084 | −0.0229042 | − | 0.999738i | \(-0.507291\pi\) | ||||
−0.0229042 | + | 0.999738i | \(0.507291\pi\) | |||||||
\(158\) | 7.19253 | 0.572207 | ||||||||
\(159\) | 4.22668 | 0.335198 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 36.5107 | 2.87745 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 13.4338 | 1.05221 | 0.526107 | − | 0.850419i | \(-0.323651\pi\) | ||||
0.526107 | + | 0.850419i | \(0.323651\pi\) | |||||||
\(164\) | 11.5817 | 0.904380 | ||||||||
\(165\) | −1.53209 | −0.119273 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.01455 | −0.620184 | −0.310092 | − | 0.950706i | \(-0.600360\pi\) | ||||
−0.310092 | + | 0.950706i | \(0.600360\pi\) | |||||||
\(168\) | −3.87939 | −0.299301 | ||||||||
\(169\) | 3.85978 | 0.296907 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | −12.5817 | −0.959347 | ||||||||
\(173\) | 4.43107 | 0.336888 | 0.168444 | − | 0.985711i | \(-0.446126\pi\) | ||||
0.168444 | + | 0.985711i | \(0.446126\pi\) | |||||||
\(174\) | −5.75877 | −0.436571 | ||||||||
\(175\) | −3.87939 | −0.293254 | ||||||||
\(176\) | 1.53209 | 0.115486 | ||||||||
\(177\) | −13.0496 | −0.980870 | ||||||||
\(178\) | 6.24897 | 0.468380 | ||||||||
\(179\) | 4.95811 | 0.370587 | 0.185293 | − | 0.982683i | \(-0.440676\pi\) | ||||
0.185293 | + | 0.982683i | \(0.440676\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | −4.28581 | −0.318562 | −0.159281 | − | 0.987233i | \(-0.550918\pi\) | ||||
−0.159281 | + | 0.987233i | \(0.550918\pi\) | |||||||
\(182\) | −15.9290 | −1.18074 | ||||||||
\(183\) | −4.61081 | −0.340841 | ||||||||
\(184\) | −9.41147 | −0.693823 | ||||||||
\(185\) | 0.305407 | 0.0224540 | ||||||||
\(186\) | −6.45336 | −0.473184 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 5.63816 | 0.411205 | ||||||||
\(189\) | −3.87939 | −0.282184 | ||||||||
\(190\) | −1.00000 | −0.0725476 | ||||||||
\(191\) | 10.0155 | 0.724695 | 0.362347 | − | 0.932043i | \(-0.381975\pi\) | ||||
0.362347 | + | 0.932043i | \(0.381975\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 12.6108 | 0.907746 | 0.453873 | − | 0.891066i | \(-0.350042\pi\) | ||||
0.453873 | + | 0.891066i | \(0.350042\pi\) | |||||||
\(194\) | −2.24123 | −0.160911 | ||||||||
\(195\) | −4.10607 | −0.294042 | ||||||||
\(196\) | 8.04963 | 0.574974 | ||||||||
\(197\) | −2.55169 | −0.181800 | −0.0909002 | − | 0.995860i | \(-0.528974\pi\) | ||||
−0.0909002 | + | 0.995860i | \(0.528974\pi\) | |||||||
\(198\) | 1.53209 | 0.108881 | ||||||||
\(199\) | 16.0993 | 1.14125 | 0.570623 | − | 0.821212i | \(-0.306702\pi\) | ||||
0.570623 | + | 0.821212i | \(0.306702\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −4.08378 | −0.288048 | ||||||||
\(202\) | 11.5175 | 0.810371 | ||||||||
\(203\) | 22.3405 | 1.56799 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.5817 | −0.808902 | ||||||||
\(206\) | −7.69459 | −0.536108 | ||||||||
\(207\) | −9.41147 | −0.654143 | ||||||||
\(208\) | 4.10607 | 0.284705 | ||||||||
\(209\) | 1.53209 | 0.105977 | ||||||||
\(210\) | 3.87939 | 0.267703 | ||||||||
\(211\) | −20.2199 | −1.39199 | −0.695997 | − | 0.718045i | \(-0.745037\pi\) | ||||
−0.695997 | + | 0.718045i | \(0.745037\pi\) | |||||||
\(212\) | 4.22668 | 0.290290 | ||||||||
\(213\) | −14.2567 | −0.976854 | ||||||||
\(214\) | −0.694593 | −0.0474814 | ||||||||
\(215\) | 12.5817 | 0.858066 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 25.0351 | 1.69949 | ||||||||
\(218\) | −12.1284 | −0.821436 | ||||||||
\(219\) | 15.4047 | 1.04095 | ||||||||
\(220\) | −1.53209 | −0.103293 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −0.305407 | −0.0204976 | ||||||||
\(223\) | 2.47565 | 0.165782 | 0.0828910 | − | 0.996559i | \(-0.473585\pi\) | ||||
0.0828910 | + | 0.996559i | \(0.473585\pi\) | |||||||
\(224\) | −3.87939 | −0.259202 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 3.43376 | 0.228411 | ||||||||
\(227\) | −10.1284 | −0.672243 | −0.336121 | − | 0.941819i | \(-0.609115\pi\) | ||||
−0.336121 | + | 0.941819i | \(0.609115\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | −11.5621 | −0.764046 | −0.382023 | − | 0.924153i | \(-0.624773\pi\) | ||||
−0.382023 | + | 0.924153i | \(0.624773\pi\) | |||||||
\(230\) | 9.41147 | 0.620574 | ||||||||
\(231\) | −5.94356 | −0.391058 | ||||||||
\(232\) | −5.75877 | −0.378082 | ||||||||
\(233\) | −4.65539 | −0.304985 | −0.152492 | − | 0.988305i | \(-0.548730\pi\) | ||||
−0.152492 | + | 0.988305i | \(0.548730\pi\) | |||||||
\(234\) | 4.10607 | 0.268422 | ||||||||
\(235\) | −5.63816 | −0.367793 | ||||||||
\(236\) | −13.0496 | −0.849459 | ||||||||
\(237\) | 7.19253 | 0.467205 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.4534 | −1.19365 | −0.596824 | − | 0.802372i | \(-0.703571\pi\) | ||||
−0.596824 | + | 0.802372i | \(0.703571\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | 27.0428 | 1.74198 | 0.870991 | − | 0.491300i | \(-0.163478\pi\) | ||||
0.870991 | + | 0.491300i | \(0.163478\pi\) | |||||||
\(242\) | −8.65270 | −0.556217 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −4.61081 | −0.295177 | ||||||||
\(245\) | −8.04963 | −0.514272 | ||||||||
\(246\) | 11.5817 | 0.738423 | ||||||||
\(247\) | 4.10607 | 0.261263 | ||||||||
\(248\) | −6.45336 | −0.409789 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 27.7989 | 1.75465 | 0.877326 | − | 0.479895i | \(-0.159325\pi\) | ||||
0.877326 | + | 0.479895i | \(0.159325\pi\) | |||||||
\(252\) | −3.87939 | −0.244378 | ||||||||
\(253\) | −14.4192 | −0.906528 | ||||||||
\(254\) | −7.34049 | −0.460583 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −8.99050 | −0.560812 | −0.280406 | − | 0.959881i | \(-0.590469\pi\) | ||||
−0.280406 | + | 0.959881i | \(0.590469\pi\) | |||||||
\(258\) | −12.5817 | −0.783304 | ||||||||
\(259\) | 1.18479 | 0.0736194 | ||||||||
\(260\) | −4.10607 | −0.254647 | ||||||||
\(261\) | −5.75877 | −0.356459 | ||||||||
\(262\) | −12.4757 | −0.770748 | ||||||||
\(263\) | 2.37639 | 0.146535 | 0.0732673 | − | 0.997312i | \(-0.476657\pi\) | ||||
0.0732673 | + | 0.997312i | \(0.476657\pi\) | |||||||
\(264\) | 1.53209 | 0.0942936 | ||||||||
\(265\) | −4.22668 | −0.259643 | ||||||||
\(266\) | −3.87939 | −0.237860 | ||||||||
\(267\) | 6.24897 | 0.382431 | ||||||||
\(268\) | −4.08378 | −0.249456 | ||||||||
\(269\) | −24.7493 | −1.50899 | −0.754495 | − | 0.656306i | \(-0.772118\pi\) | ||||
−0.754495 | + | 0.656306i | \(0.772118\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | −12.6209 | −0.766666 | −0.383333 | − | 0.923610i | \(-0.625224\pi\) | ||||
−0.383333 | + | 0.923610i | \(0.625224\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −15.9290 | −0.964068 | ||||||||
\(274\) | −6.45336 | −0.389862 | ||||||||
\(275\) | 1.53209 | 0.0923884 | ||||||||
\(276\) | −9.41147 | −0.566504 | ||||||||
\(277\) | −10.1898 | −0.612248 | −0.306124 | − | 0.951992i | \(-0.599032\pi\) | ||||
−0.306124 | + | 0.951992i | \(0.599032\pi\) | |||||||
\(278\) | −11.6108 | −0.696370 | ||||||||
\(279\) | −6.45336 | −0.386353 | ||||||||
\(280\) | 3.87939 | 0.231838 | ||||||||
\(281\) | −27.2226 | −1.62396 | −0.811981 | − | 0.583684i | \(-0.801611\pi\) | ||||
−0.811981 | + | 0.583684i | \(0.801611\pi\) | |||||||
\(282\) | 5.63816 | 0.335747 | ||||||||
\(283\) | 10.6554 | 0.633397 | 0.316699 | − | 0.948526i | \(-0.397426\pi\) | ||||
0.316699 | + | 0.948526i | \(0.397426\pi\) | |||||||
\(284\) | −14.2567 | −0.845980 | ||||||||
\(285\) | −1.00000 | −0.0592349 | ||||||||
\(286\) | 6.29086 | 0.371986 | ||||||||
\(287\) | −44.9299 | −2.65213 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 5.75877 | 0.338167 | ||||||||
\(291\) | −2.24123 | −0.131383 | ||||||||
\(292\) | 15.4047 | 0.901490 | ||||||||
\(293\) | 3.12330 | 0.182465 | 0.0912327 | − | 0.995830i | \(-0.470919\pi\) | ||||
0.0912327 | + | 0.995830i | \(0.470919\pi\) | |||||||
\(294\) | 8.04963 | 0.469464 | ||||||||
\(295\) | 13.0496 | 0.759779 | ||||||||
\(296\) | −0.305407 | −0.0177514 | ||||||||
\(297\) | 1.53209 | 0.0889008 | ||||||||
\(298\) | −19.9317 | −1.15461 | ||||||||
\(299\) | −38.6441 | −2.23485 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 48.8093 | 2.81332 | ||||||||
\(302\) | −22.8229 | −1.31331 | ||||||||
\(303\) | 11.5175 | 0.661665 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 4.61081 | 0.264014 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.9864 | −1.59727 | −0.798634 | − | 0.601817i | \(-0.794443\pi\) | ||||
−0.798634 | + | 0.601817i | \(0.794443\pi\) | |||||||
\(308\) | −5.94356 | −0.338666 | ||||||||
\(309\) | −7.69459 | −0.437730 | ||||||||
\(310\) | 6.45336 | 0.366526 | ||||||||
\(311\) | −6.98040 | −0.395822 | −0.197911 | − | 0.980220i | \(-0.563416\pi\) | ||||
−0.197911 | + | 0.980220i | \(0.563416\pi\) | |||||||
\(312\) | 4.10607 | 0.232460 | ||||||||
\(313\) | −27.8188 | −1.57241 | −0.786207 | − | 0.617964i | \(-0.787958\pi\) | ||||
−0.786207 | + | 0.617964i | \(0.787958\pi\) | |||||||
\(314\) | −0.573978 | −0.0323914 | ||||||||
\(315\) | 3.87939 | 0.218579 | ||||||||
\(316\) | 7.19253 | 0.404612 | ||||||||
\(317\) | 2.27631 | 0.127850 | 0.0639252 | − | 0.997955i | \(-0.479638\pi\) | ||||
0.0639252 | + | 0.997955i | \(0.479638\pi\) | |||||||
\(318\) | 4.22668 | 0.237021 | ||||||||
\(319\) | −8.82295 | −0.493990 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −0.694593 | −0.0387684 | ||||||||
\(322\) | 36.5107 | 2.03466 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 4.10607 | 0.227764 | ||||||||
\(326\) | 13.4338 | 0.744027 | ||||||||
\(327\) | −12.1284 | −0.670700 | ||||||||
\(328\) | 11.5817 | 0.639493 | ||||||||
\(329\) | −21.8726 | −1.20587 | ||||||||
\(330\) | −1.53209 | −0.0843387 | ||||||||
\(331\) | −9.20027 | −0.505693 | −0.252846 | − | 0.967506i | \(-0.581367\pi\) | ||||
−0.252846 | + | 0.967506i | \(0.581367\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.305407 | −0.0167362 | ||||||||
\(334\) | −8.01455 | −0.438537 | ||||||||
\(335\) | 4.08378 | 0.223121 | ||||||||
\(336\) | −3.87939 | −0.211638 | ||||||||
\(337\) | 16.9513 | 0.923396 | 0.461698 | − | 0.887037i | \(-0.347240\pi\) | ||||
0.461698 | + | 0.887037i | \(0.347240\pi\) | |||||||
\(338\) | 3.85978 | 0.209945 | ||||||||
\(339\) | 3.43376 | 0.186496 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.88713 | −0.535418 | ||||||||
\(342\) | 1.00000 | 0.0540738 | ||||||||
\(343\) | −4.07192 | −0.219863 | ||||||||
\(344\) | −12.5817 | −0.678361 | ||||||||
\(345\) | 9.41147 | 0.506697 | ||||||||
\(346\) | 4.43107 | 0.238216 | ||||||||
\(347\) | −24.9067 | −1.33706 | −0.668532 | − | 0.743684i | \(-0.733077\pi\) | ||||
−0.668532 | + | 0.743684i | \(0.733077\pi\) | |||||||
\(348\) | −5.75877 | −0.308703 | ||||||||
\(349\) | 9.77425 | 0.523204 | 0.261602 | − | 0.965176i | \(-0.415749\pi\) | ||||
0.261602 | + | 0.965176i | \(0.415749\pi\) | |||||||
\(350\) | −3.87939 | −0.207362 | ||||||||
\(351\) | 4.10607 | 0.219166 | ||||||||
\(352\) | 1.53209 | 0.0816606 | ||||||||
\(353\) | 11.3601 | 0.604637 | 0.302318 | − | 0.953207i | \(-0.402239\pi\) | ||||
0.302318 | + | 0.953207i | \(0.402239\pi\) | |||||||
\(354\) | −13.0496 | −0.693580 | ||||||||
\(355\) | 14.2567 | 0.756668 | ||||||||
\(356\) | 6.24897 | 0.331195 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.95811 | 0.262044 | ||||||||
\(359\) | 11.3892 | 0.601098 | 0.300549 | − | 0.953766i | \(-0.402830\pi\) | ||||
0.300549 | + | 0.953766i | \(0.402830\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | −4.28581 | −0.225257 | ||||||||
\(363\) | −8.65270 | −0.454149 | ||||||||
\(364\) | −15.9290 | −0.834907 | ||||||||
\(365\) | −15.4047 | −0.806317 | ||||||||
\(366\) | −4.61081 | −0.241011 | ||||||||
\(367\) | 23.0651 | 1.20399 | 0.601995 | − | 0.798500i | \(-0.294373\pi\) | ||||
0.601995 | + | 0.798500i | \(0.294373\pi\) | |||||||
\(368\) | −9.41147 | −0.490607 | ||||||||
\(369\) | 11.5817 | 0.602920 | ||||||||
\(370\) | 0.305407 | 0.0158774 | ||||||||
\(371\) | −16.3969 | −0.851286 | ||||||||
\(372\) | −6.45336 | −0.334591 | ||||||||
\(373\) | 13.0719 | 0.676838 | 0.338419 | − | 0.940995i | \(-0.390108\pi\) | ||||
0.338419 | + | 0.940995i | \(0.390108\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 5.63816 | 0.290766 | ||||||||
\(377\) | −23.6459 | −1.21783 | ||||||||
\(378\) | −3.87939 | −0.199534 | ||||||||
\(379\) | −14.1284 | −0.725725 | −0.362862 | − | 0.931843i | \(-0.618201\pi\) | ||||
−0.362862 | + | 0.931843i | \(0.618201\pi\) | |||||||
\(380\) | −1.00000 | −0.0512989 | ||||||||
\(381\) | −7.34049 | −0.376065 | ||||||||
\(382\) | 10.0155 | 0.512437 | ||||||||
\(383\) | 1.72369 | 0.0880764 | 0.0440382 | − | 0.999030i | \(-0.485978\pi\) | ||||
0.0440382 | + | 0.999030i | \(0.485978\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 5.94356 | 0.302912 | ||||||||
\(386\) | 12.6108 | 0.641874 | ||||||||
\(387\) | −12.5817 | −0.639565 | ||||||||
\(388\) | −2.24123 | −0.113781 | ||||||||
\(389\) | −7.06418 | −0.358168 | −0.179084 | − | 0.983834i | \(-0.557313\pi\) | ||||
−0.179084 | + | 0.983834i | \(0.557313\pi\) | |||||||
\(390\) | −4.10607 | −0.207919 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 8.04963 | 0.406568 | ||||||||
\(393\) | −12.4757 | −0.629313 | ||||||||
\(394\) | −2.55169 | −0.128552 | ||||||||
\(395\) | −7.19253 | −0.361896 | ||||||||
\(396\) | 1.53209 | 0.0769904 | ||||||||
\(397\) | −30.7033 | −1.54095 | −0.770476 | − | 0.637469i | \(-0.779982\pi\) | ||||
−0.770476 | + | 0.637469i | \(0.779982\pi\) | |||||||
\(398\) | 16.0993 | 0.806983 | ||||||||
\(399\) | −3.87939 | −0.194212 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −8.97596 | −0.448238 | −0.224119 | − | 0.974562i | \(-0.571950\pi\) | ||||
−0.224119 | + | 0.974562i | \(0.571950\pi\) | |||||||
\(402\) | −4.08378 | −0.203680 | ||||||||
\(403\) | −26.4979 | −1.31996 | ||||||||
\(404\) | 11.5175 | 0.573019 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 22.3405 | 1.10874 | ||||||||
\(407\) | −0.467911 | −0.0231935 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.4311 | 0.515783 | 0.257892 | − | 0.966174i | \(-0.416972\pi\) | ||||
0.257892 | + | 0.966174i | \(0.416972\pi\) | |||||||
\(410\) | −11.5817 | −0.571980 | ||||||||
\(411\) | −6.45336 | −0.318321 | ||||||||
\(412\) | −7.69459 | −0.379085 | ||||||||
\(413\) | 50.6245 | 2.49107 | ||||||||
\(414\) | −9.41147 | −0.462549 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.10607 | 0.201316 | ||||||||
\(417\) | −11.6108 | −0.568584 | ||||||||
\(418\) | 1.53209 | 0.0749369 | ||||||||
\(419\) | 1.86484 | 0.0911033 | 0.0455516 | − | 0.998962i | \(-0.485495\pi\) | ||||
0.0455516 | + | 0.998962i | \(0.485495\pi\) | |||||||
\(420\) | 3.87939 | 0.189295 | ||||||||
\(421\) | 3.84255 | 0.187274 | 0.0936372 | − | 0.995606i | \(-0.470151\pi\) | ||||
0.0936372 | + | 0.995606i | \(0.470151\pi\) | |||||||
\(422\) | −20.2199 | −0.984288 | ||||||||
\(423\) | 5.63816 | 0.274137 | ||||||||
\(424\) | 4.22668 | 0.205266 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −14.2567 | −0.690740 | ||||||||
\(427\) | 17.8871 | 0.865619 | ||||||||
\(428\) | −0.694593 | −0.0335744 | ||||||||
\(429\) | 6.29086 | 0.303726 | ||||||||
\(430\) | 12.5817 | 0.606744 | ||||||||
\(431\) | 17.9608 | 0.865141 | 0.432571 | − | 0.901600i | \(-0.357607\pi\) | ||||
0.432571 | + | 0.901600i | \(0.357607\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 0.723689 | 0.0347783 | 0.0173891 | − | 0.999849i | \(-0.494465\pi\) | ||||
0.0173891 | + | 0.999849i | \(0.494465\pi\) | |||||||
\(434\) | 25.0351 | 1.20172 | ||||||||
\(435\) | 5.75877 | 0.276112 | ||||||||
\(436\) | −12.1284 | −0.580843 | ||||||||
\(437\) | −9.41147 | −0.450212 | ||||||||
\(438\) | 15.4047 | 0.736063 | ||||||||
\(439\) | −29.5722 | −1.41141 | −0.705703 | − | 0.708508i | \(-0.749369\pi\) | ||||
−0.705703 | + | 0.708508i | \(0.749369\pi\) | |||||||
\(440\) | −1.53209 | −0.0730395 | ||||||||
\(441\) | 8.04963 | 0.383316 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.3851 | 1.15857 | 0.579285 | − | 0.815125i | \(-0.303332\pi\) | ||||
0.579285 | + | 0.815125i | \(0.303332\pi\) | |||||||
\(444\) | −0.305407 | −0.0144940 | ||||||||
\(445\) | −6.24897 | −0.296230 | ||||||||
\(446\) | 2.47565 | 0.117226 | ||||||||
\(447\) | −19.9317 | −0.942737 | ||||||||
\(448\) | −3.87939 | −0.183284 | ||||||||
\(449\) | −12.3851 | −0.584487 | −0.292244 | − | 0.956344i | \(-0.594402\pi\) | ||||
−0.292244 | + | 0.956344i | \(0.594402\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 17.7442 | 0.835543 | ||||||||
\(452\) | 3.43376 | 0.161511 | ||||||||
\(453\) | −22.8229 | −1.07232 | ||||||||
\(454\) | −10.1284 | −0.475347 | ||||||||
\(455\) | 15.9290 | 0.746764 | ||||||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | 18.3797 | 0.859766 | 0.429883 | − | 0.902885i | \(-0.358555\pi\) | ||||
0.429883 | + | 0.902885i | \(0.358555\pi\) | |||||||
\(458\) | −11.5621 | −0.540262 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9.41147 | 0.438812 | ||||||||
\(461\) | −11.9263 | −0.555464 | −0.277732 | − | 0.960659i | \(-0.589583\pi\) | ||||
−0.277732 | + | 0.960659i | \(0.589583\pi\) | |||||||
\(462\) | −5.94356 | −0.276520 | ||||||||
\(463\) | 30.5996 | 1.42208 | 0.711041 | − | 0.703150i | \(-0.248224\pi\) | ||||
0.711041 | + | 0.703150i | \(0.248224\pi\) | |||||||
\(464\) | −5.75877 | −0.267344 | ||||||||
\(465\) | 6.45336 | 0.299268 | ||||||||
\(466\) | −4.65539 | −0.215657 | ||||||||
\(467\) | 14.8075 | 0.685208 | 0.342604 | − | 0.939480i | \(-0.388691\pi\) | ||||
0.342604 | + | 0.939480i | \(0.388691\pi\) | |||||||
\(468\) | 4.10607 | 0.189803 | ||||||||
\(469\) | 15.8425 | 0.731541 | ||||||||
\(470\) | −5.63816 | −0.260069 | ||||||||
\(471\) | −0.573978 | −0.0264475 | ||||||||
\(472\) | −13.0496 | −0.600658 | ||||||||
\(473\) | −19.2763 | −0.886326 | ||||||||
\(474\) | 7.19253 | 0.330364 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.22668 | 0.193526 | ||||||||
\(478\) | −18.4534 | −0.844037 | ||||||||
\(479\) | 28.8093 | 1.31633 | 0.658166 | − | 0.752873i | \(-0.271332\pi\) | ||||
0.658166 | + | 0.752873i | \(0.271332\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | −1.25402 | −0.0571785 | ||||||||
\(482\) | 27.0428 | 1.23177 | ||||||||
\(483\) | 36.5107 | 1.66130 | ||||||||
\(484\) | −8.65270 | −0.393305 | ||||||||
\(485\) | 2.24123 | 0.101769 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −17.8229 | −0.807635 | −0.403817 | − | 0.914840i | \(-0.632317\pi\) | ||||
−0.403817 | + | 0.914840i | \(0.632317\pi\) | |||||||
\(488\) | −4.61081 | −0.208722 | ||||||||
\(489\) | 13.4338 | 0.607496 | ||||||||
\(490\) | −8.04963 | −0.363645 | ||||||||
\(491\) | −10.8699 | −0.490551 | −0.245276 | − | 0.969453i | \(-0.578878\pi\) | ||||
−0.245276 | + | 0.969453i | \(0.578878\pi\) | |||||||
\(492\) | 11.5817 | 0.522144 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 4.10607 | 0.184741 | ||||||||
\(495\) | −1.53209 | −0.0688623 | ||||||||
\(496\) | −6.45336 | −0.289765 | ||||||||
\(497\) | 55.3073 | 2.48087 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.0719 | −1.03284 | −0.516420 | − | 0.856335i | \(-0.672736\pi\) | ||||
−0.516420 | + | 0.856335i | \(0.672736\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −8.01455 | −0.358064 | ||||||||
\(502\) | 27.7989 | 1.24073 | ||||||||
\(503\) | 27.1465 | 1.21040 | 0.605202 | − | 0.796072i | \(-0.293092\pi\) | ||||
0.605202 | + | 0.796072i | \(0.293092\pi\) | |||||||
\(504\) | −3.87939 | −0.172802 | ||||||||
\(505\) | −11.5175 | −0.512524 | ||||||||
\(506\) | −14.4192 | −0.641012 | ||||||||
\(507\) | 3.85978 | 0.171419 | ||||||||
\(508\) | −7.34049 | −0.325682 | ||||||||
\(509\) | 20.6946 | 0.917272 | 0.458636 | − | 0.888624i | \(-0.348338\pi\) | ||||
0.458636 | + | 0.888624i | \(0.348338\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −59.7606 | −2.64365 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | −8.99050 | −0.396554 | ||||||||
\(515\) | 7.69459 | 0.339064 | ||||||||
\(516\) | −12.5817 | −0.553879 | ||||||||
\(517\) | 8.63816 | 0.379906 | ||||||||
\(518\) | 1.18479 | 0.0520568 | ||||||||
\(519\) | 4.43107 | 0.194503 | ||||||||
\(520\) | −4.10607 | −0.180063 | ||||||||
\(521\) | 1.49256 | 0.0653904 | 0.0326952 | − | 0.999465i | \(-0.489591\pi\) | ||||
0.0326952 | + | 0.999465i | \(0.489591\pi\) | |||||||
\(522\) | −5.75877 | −0.252055 | ||||||||
\(523\) | 36.5134 | 1.59662 | 0.798310 | − | 0.602246i | \(-0.205728\pi\) | ||||
0.798310 | + | 0.602246i | \(0.205728\pi\) | |||||||
\(524\) | −12.4757 | −0.545001 | ||||||||
\(525\) | −3.87939 | −0.169310 | ||||||||
\(526\) | 2.37639 | 0.103616 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 1.53209 | 0.0666756 | ||||||||
\(529\) | 65.5758 | 2.85112 | ||||||||
\(530\) | −4.22668 | −0.183595 | ||||||||
\(531\) | −13.0496 | −0.566306 | ||||||||
\(532\) | −3.87939 | −0.168193 | ||||||||
\(533\) | 47.5553 | 2.05985 | ||||||||
\(534\) | 6.24897 | 0.270419 | ||||||||
\(535\) | 0.694593 | 0.0300299 | ||||||||
\(536\) | −4.08378 | −0.176392 | ||||||||
\(537\) | 4.95811 | 0.213958 | ||||||||
\(538\) | −24.7493 | −1.06702 | ||||||||
\(539\) | 12.3327 | 0.531209 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | 5.23173 | 0.224930 | 0.112465 | − | 0.993656i | \(-0.464125\pi\) | ||||
0.112465 | + | 0.993656i | \(0.464125\pi\) | |||||||
\(542\) | −12.6209 | −0.542115 | ||||||||
\(543\) | −4.28581 | −0.183922 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.1284 | 0.519522 | ||||||||
\(546\) | −15.9290 | −0.681699 | ||||||||
\(547\) | −9.63579 | −0.411997 | −0.205998 | − | 0.978552i | \(-0.566044\pi\) | ||||
−0.205998 | + | 0.978552i | \(0.566044\pi\) | |||||||
\(548\) | −6.45336 | −0.275674 | ||||||||
\(549\) | −4.61081 | −0.196785 | ||||||||
\(550\) | 1.53209 | 0.0653285 | ||||||||
\(551\) | −5.75877 | −0.245332 | ||||||||
\(552\) | −9.41147 | −0.400579 | ||||||||
\(553\) | −27.9026 | −1.18654 | ||||||||
\(554\) | −10.1898 | −0.432925 | ||||||||
\(555\) | 0.305407 | 0.0129638 | ||||||||
\(556\) | −11.6108 | −0.492408 | ||||||||
\(557\) | −26.5895 | −1.12663 | −0.563316 | − | 0.826242i | \(-0.690475\pi\) | ||||
−0.563316 | + | 0.826242i | \(0.690475\pi\) | |||||||
\(558\) | −6.45336 | −0.273193 | ||||||||
\(559\) | −51.6614 | −2.18504 | ||||||||
\(560\) | 3.87939 | 0.163934 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −27.2226 | −1.14831 | ||||||||
\(563\) | 27.9263 | 1.17695 | 0.588477 | − | 0.808514i | \(-0.299728\pi\) | ||||
0.588477 | + | 0.808514i | \(0.299728\pi\) | |||||||
\(564\) | 5.63816 | 0.237409 | ||||||||
\(565\) | −3.43376 | −0.144459 | ||||||||
\(566\) | 10.6554 | 0.447880 | ||||||||
\(567\) | −3.87939 | −0.162919 | ||||||||
\(568\) | −14.2567 | −0.598198 | ||||||||
\(569\) | 17.6209 | 0.738707 | 0.369354 | − | 0.929289i | \(-0.379579\pi\) | ||||
0.369354 | + | 0.929289i | \(0.379579\pi\) | |||||||
\(570\) | −1.00000 | −0.0418854 | ||||||||
\(571\) | −5.97771 | −0.250159 | −0.125080 | − | 0.992147i | \(-0.539919\pi\) | ||||
−0.125080 | + | 0.992147i | \(0.539919\pi\) | |||||||
\(572\) | 6.29086 | 0.263034 | ||||||||
\(573\) | 10.0155 | 0.418403 | ||||||||
\(574\) | −44.9299 | −1.87534 | ||||||||
\(575\) | −9.41147 | −0.392486 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −7.75877 | −0.323002 | −0.161501 | − | 0.986873i | \(-0.551633\pi\) | ||||
−0.161501 | + | 0.986873i | \(0.551633\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.6108 | 0.524088 | ||||||||
\(580\) | 5.75877 | 0.239120 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2.24123 | −0.0929020 | ||||||||
\(583\) | 6.47565 | 0.268194 | ||||||||
\(584\) | 15.4047 | 0.637450 | ||||||||
\(585\) | −4.10607 | −0.169765 | ||||||||
\(586\) | 3.12330 | 0.129022 | ||||||||
\(587\) | 29.6013 | 1.22178 | 0.610889 | − | 0.791717i | \(-0.290812\pi\) | ||||
0.610889 | + | 0.791717i | \(0.290812\pi\) | |||||||
\(588\) | 8.04963 | 0.331961 | ||||||||
\(589\) | −6.45336 | −0.265906 | ||||||||
\(590\) | 13.0496 | 0.537245 | ||||||||
\(591\) | −2.55169 | −0.104962 | ||||||||
\(592\) | −0.305407 | −0.0125522 | ||||||||
\(593\) | −43.2336 | −1.77539 | −0.887696 | − | 0.460431i | \(-0.847695\pi\) | ||||
−0.887696 | + | 0.460431i | \(0.847695\pi\) | |||||||
\(594\) | 1.53209 | 0.0628624 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −19.9317 | −0.816434 | ||||||||
\(597\) | 16.0993 | 0.658899 | ||||||||
\(598\) | −38.6441 | −1.58028 | ||||||||
\(599\) | 27.3209 | 1.11630 | 0.558151 | − | 0.829740i | \(-0.311511\pi\) | ||||
0.558151 | + | 0.829740i | \(0.311511\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | 31.6604 | 1.29146 | 0.645728 | − | 0.763567i | \(-0.276554\pi\) | ||||
0.645728 | + | 0.763567i | \(0.276554\pi\) | |||||||
\(602\) | 48.8093 | 1.98932 | ||||||||
\(603\) | −4.08378 | −0.166304 | ||||||||
\(604\) | −22.8229 | −0.928653 | ||||||||
\(605\) | 8.65270 | 0.351782 | ||||||||
\(606\) | 11.5175 | 0.467868 | ||||||||
\(607\) | −10.9135 | −0.442967 | −0.221483 | − | 0.975164i | \(-0.571090\pi\) | ||||
−0.221483 | + | 0.975164i | \(0.571090\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 22.3405 | 0.905282 | ||||||||
\(610\) | 4.61081 | 0.186686 | ||||||||
\(611\) | 23.1506 | 0.936575 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.243594 | −0.00983865 | −0.00491933 | − | 0.999988i | \(-0.501566\pi\) | ||||
−0.00491933 | + | 0.999988i | \(0.501566\pi\) | |||||||
\(614\) | −27.9864 | −1.12944 | ||||||||
\(615\) | −11.5817 | −0.467020 | ||||||||
\(616\) | −5.94356 | −0.239473 | ||||||||
\(617\) | 24.1830 | 0.973572 | 0.486786 | − | 0.873521i | \(-0.338169\pi\) | ||||
0.486786 | + | 0.873521i | \(0.338169\pi\) | |||||||
\(618\) | −7.69459 | −0.309522 | ||||||||
\(619\) | −31.3286 | −1.25920 | −0.629602 | − | 0.776918i | \(-0.716782\pi\) | ||||
−0.629602 | + | 0.776918i | \(0.716782\pi\) | |||||||
\(620\) | 6.45336 | 0.259173 | ||||||||
\(621\) | −9.41147 | −0.377669 | ||||||||
\(622\) | −6.98040 | −0.279889 | ||||||||
\(623\) | −24.2422 | −0.971242 | ||||||||
\(624\) | 4.10607 | 0.164374 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −27.8188 | −1.11186 | ||||||||
\(627\) | 1.53209 | 0.0611857 | ||||||||
\(628\) | −0.573978 | −0.0229042 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 3.87939 | 0.154558 | ||||||||
\(631\) | −22.1967 | −0.883635 | −0.441817 | − | 0.897105i | \(-0.645666\pi\) | ||||
−0.441817 | + | 0.897105i | \(0.645666\pi\) | |||||||
\(632\) | 7.19253 | 0.286104 | ||||||||
\(633\) | −20.2199 | −0.803668 | ||||||||
\(634\) | 2.27631 | 0.0904039 | ||||||||
\(635\) | 7.34049 | 0.291298 | ||||||||
\(636\) | 4.22668 | 0.167599 | ||||||||
\(637\) | 33.0523 | 1.30958 | ||||||||
\(638\) | −8.82295 | −0.349304 | ||||||||
\(639\) | −14.2567 | −0.563987 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 39.1557 | 1.54656 | 0.773279 | − | 0.634067i | \(-0.218615\pi\) | ||||
0.773279 | + | 0.634067i | \(0.218615\pi\) | |||||||
\(642\) | −0.694593 | −0.0274134 | ||||||||
\(643\) | 17.3054 | 0.682459 | 0.341229 | − | 0.939980i | \(-0.389157\pi\) | ||||
0.341229 | + | 0.939980i | \(0.389157\pi\) | |||||||
\(644\) | 36.5107 | 1.43872 | ||||||||
\(645\) | 12.5817 | 0.495405 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 31.1388 | 1.22419 | 0.612096 | − | 0.790783i | \(-0.290327\pi\) | ||||
0.612096 | + | 0.790783i | \(0.290327\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −19.9932 | −0.784801 | ||||||||
\(650\) | 4.10607 | 0.161053 | ||||||||
\(651\) | 25.0351 | 0.981202 | ||||||||
\(652\) | 13.4338 | 0.526107 | ||||||||
\(653\) | −1.27395 | −0.0498534 | −0.0249267 | − | 0.999689i | \(-0.507935\pi\) | ||||
−0.0249267 | + | 0.999689i | \(0.507935\pi\) | |||||||
\(654\) | −12.1284 | −0.474256 | ||||||||
\(655\) | 12.4757 | 0.487464 | ||||||||
\(656\) | 11.5817 | 0.452190 | ||||||||
\(657\) | 15.4047 | 0.600993 | ||||||||
\(658\) | −21.8726 | −0.852682 | ||||||||
\(659\) | 26.5466 | 1.03411 | 0.517055 | − | 0.855952i | \(-0.327028\pi\) | ||||
0.517055 | + | 0.855952i | \(0.327028\pi\) | |||||||
\(660\) | −1.53209 | −0.0596365 | ||||||||
\(661\) | −14.2412 | −0.553920 | −0.276960 | − | 0.960882i | \(-0.589327\pi\) | ||||
−0.276960 | + | 0.960882i | \(0.589327\pi\) | |||||||
\(662\) | −9.20027 | −0.357579 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.87939 | 0.150436 | ||||||||
\(666\) | −0.305407 | −0.0118343 | ||||||||
\(667\) | 54.1985 | 2.09858 | ||||||||
\(668\) | −8.01455 | −0.310092 | ||||||||
\(669\) | 2.47565 | 0.0957142 | ||||||||
\(670\) | 4.08378 | 0.157770 | ||||||||
\(671\) | −7.06418 | −0.272710 | ||||||||
\(672\) | −3.87939 | −0.149651 | ||||||||
\(673\) | 50.5134 | 1.94715 | 0.973575 | − | 0.228369i | \(-0.0733392\pi\) | ||||
0.973575 | + | 0.228369i | \(0.0733392\pi\) | |||||||
\(674\) | 16.9513 | 0.652940 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 3.85978 | 0.148453 | ||||||||
\(677\) | 19.4962 | 0.749299 | 0.374650 | − | 0.927166i | \(-0.377763\pi\) | ||||
0.374650 | + | 0.927166i | \(0.377763\pi\) | |||||||
\(678\) | 3.43376 | 0.131873 | ||||||||
\(679\) | 8.69459 | 0.333668 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.1284 | −0.388119 | ||||||||
\(682\) | −9.88713 | −0.378598 | ||||||||
\(683\) | 42.9905 | 1.64499 | 0.822493 | − | 0.568775i | \(-0.192583\pi\) | ||||
0.822493 | + | 0.568775i | \(0.192583\pi\) | |||||||
\(684\) | 1.00000 | 0.0382360 | ||||||||
\(685\) | 6.45336 | 0.246570 | ||||||||
\(686\) | −4.07192 | −0.155467 | ||||||||
\(687\) | −11.5621 | −0.441122 | ||||||||
\(688\) | −12.5817 | −0.479674 | ||||||||
\(689\) | 17.3550 | 0.661174 | ||||||||
\(690\) | 9.41147 | 0.358289 | ||||||||
\(691\) | −19.9385 | −0.758497 | −0.379248 | − | 0.925295i | \(-0.623817\pi\) | ||||
−0.379248 | + | 0.925295i | \(0.623817\pi\) | |||||||
\(692\) | 4.43107 | 0.168444 | ||||||||
\(693\) | −5.94356 | −0.225777 | ||||||||
\(694\) | −24.9067 | −0.945446 | ||||||||
\(695\) | 11.6108 | 0.440423 | ||||||||
\(696\) | −5.75877 | −0.218286 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 9.77425 | 0.369961 | ||||||||
\(699\) | −4.65539 | −0.176083 | ||||||||
\(700\) | −3.87939 | −0.146627 | ||||||||
\(701\) | 4.30129 | 0.162457 | 0.0812287 | − | 0.996695i | \(-0.474116\pi\) | ||||
0.0812287 | + | 0.996695i | \(0.474116\pi\) | |||||||
\(702\) | 4.10607 | 0.154974 | ||||||||
\(703\) | −0.305407 | −0.0115187 | ||||||||
\(704\) | 1.53209 | 0.0577428 | ||||||||
\(705\) | −5.63816 | −0.212345 | ||||||||
\(706\) | 11.3601 | 0.427543 | ||||||||
\(707\) | −44.6810 | −1.68040 | ||||||||
\(708\) | −13.0496 | −0.490435 | ||||||||
\(709\) | 41.6032 | 1.56244 | 0.781220 | − | 0.624256i | \(-0.214598\pi\) | ||||
0.781220 | + | 0.624256i | \(0.214598\pi\) | |||||||
\(710\) | 14.2567 | 0.535045 | ||||||||
\(711\) | 7.19253 | 0.269741 | ||||||||
\(712\) | 6.24897 | 0.234190 | ||||||||
\(713\) | 60.7357 | 2.27457 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.29086 | −0.235265 | ||||||||
\(716\) | 4.95811 | 0.185293 | ||||||||
\(717\) | −18.4534 | −0.689153 | ||||||||
\(718\) | 11.3892 | 0.425041 | ||||||||
\(719\) | 45.0060 | 1.67844 | 0.839220 | − | 0.543792i | \(-0.183012\pi\) | ||||
0.839220 | + | 0.543792i | \(0.183012\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | 29.8503 | 1.11168 | ||||||||
\(722\) | −18.0000 | −0.669891 | ||||||||
\(723\) | 27.0428 | 1.00573 | ||||||||
\(724\) | −4.28581 | −0.159281 | ||||||||
\(725\) | −5.75877 | −0.213875 | ||||||||
\(726\) | −8.65270 | −0.321132 | ||||||||
\(727\) | 49.5553 | 1.83790 | 0.918952 | − | 0.394369i | \(-0.129037\pi\) | ||||
0.918952 | + | 0.394369i | \(0.129037\pi\) | |||||||
\(728\) | −15.9290 | −0.590369 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −15.4047 | −0.570152 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −4.61081 | −0.170421 | ||||||||
\(733\) | 39.7648 | 1.46874 | 0.734372 | − | 0.678747i | \(-0.237477\pi\) | ||||
0.734372 | + | 0.678747i | \(0.237477\pi\) | |||||||
\(734\) | 23.0651 | 0.851349 | ||||||||
\(735\) | −8.04963 | −0.296915 | ||||||||
\(736\) | −9.41147 | −0.346912 | ||||||||
\(737\) | −6.25671 | −0.230469 | ||||||||
\(738\) | 11.5817 | 0.426329 | ||||||||
\(739\) | −23.9617 | −0.881447 | −0.440723 | − | 0.897643i | \(-0.645278\pi\) | ||||
−0.440723 | + | 0.897643i | \(0.645278\pi\) | |||||||
\(740\) | 0.305407 | 0.0112270 | ||||||||
\(741\) | 4.10607 | 0.150840 | ||||||||
\(742\) | −16.3969 | −0.601950 | ||||||||
\(743\) | −54.0556 | −1.98311 | −0.991554 | − | 0.129694i | \(-0.958601\pi\) | ||||
−0.991554 | + | 0.129694i | \(0.958601\pi\) | |||||||
\(744\) | −6.45336 | −0.236592 | ||||||||
\(745\) | 19.9317 | 0.730241 | ||||||||
\(746\) | 13.0719 | 0.478597 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.69459 | 0.0984583 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | −49.0351 | −1.78932 | −0.894658 | − | 0.446752i | \(-0.852581\pi\) | ||||
−0.894658 | + | 0.446752i | \(0.852581\pi\) | |||||||
\(752\) | 5.63816 | 0.205602 | ||||||||
\(753\) | 27.7989 | 1.01305 | ||||||||
\(754\) | −23.6459 | −0.861133 | ||||||||
\(755\) | 22.8229 | 0.830612 | ||||||||
\(756\) | −3.87939 | −0.141092 | ||||||||
\(757\) | −1.52198 | −0.0553174 | −0.0276587 | − | 0.999617i | \(-0.508805\pi\) | ||||
−0.0276587 | + | 0.999617i | \(0.508805\pi\) | |||||||
\(758\) | −14.1284 | −0.513165 | ||||||||
\(759\) | −14.4192 | −0.523384 | ||||||||
\(760\) | −1.00000 | −0.0362738 | ||||||||
\(761\) | −20.6186 | −0.747422 | −0.373711 | − | 0.927545i | \(-0.621915\pi\) | ||||
−0.373711 | + | 0.927545i | \(0.621915\pi\) | |||||||
\(762\) | −7.34049 | −0.265918 | ||||||||
\(763\) | 47.0506 | 1.70334 | ||||||||
\(764\) | 10.0155 | 0.362347 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.72369 | 0.0622794 | ||||||||
\(767\) | −53.5827 | −1.93476 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −43.0428 | −1.55216 | −0.776082 | − | 0.630632i | \(-0.782796\pi\) | ||||
−0.776082 | + | 0.630632i | \(0.782796\pi\) | |||||||
\(770\) | 5.94356 | 0.214191 | ||||||||
\(771\) | −8.99050 | −0.323785 | ||||||||
\(772\) | 12.6108 | 0.453873 | ||||||||
\(773\) | −19.9222 | −0.716552 | −0.358276 | − | 0.933616i | \(-0.616635\pi\) | ||||
−0.358276 | + | 0.933616i | \(0.616635\pi\) | |||||||
\(774\) | −12.5817 | −0.452241 | ||||||||
\(775\) | −6.45336 | −0.231812 | ||||||||
\(776\) | −2.24123 | −0.0804555 | ||||||||
\(777\) | 1.18479 | 0.0425042 | ||||||||
\(778\) | −7.06418 | −0.253263 | ||||||||
\(779\) | 11.5817 | 0.414958 | ||||||||
\(780\) | −4.10607 | −0.147021 | ||||||||
\(781\) | −21.8425 | −0.781588 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.75877 | −0.205802 | ||||||||
\(784\) | 8.04963 | 0.287487 | ||||||||
\(785\) | 0.573978 | 0.0204862 | ||||||||
\(786\) | −12.4757 | −0.444992 | ||||||||
\(787\) | 55.0215 | 1.96130 | 0.980652 | − | 0.195760i | \(-0.0627175\pi\) | ||||
0.980652 | + | 0.195760i | \(0.0627175\pi\) | |||||||
\(788\) | −2.55169 | −0.0909002 | ||||||||
\(789\) | 2.37639 | 0.0846018 | ||||||||
\(790\) | −7.19253 | −0.255899 | ||||||||
\(791\) | −13.3209 | −0.473636 | ||||||||
\(792\) | 1.53209 | 0.0544404 | ||||||||
\(793\) | −18.9323 | −0.672306 | ||||||||
\(794\) | −30.7033 | −1.08962 | ||||||||
\(795\) | −4.22668 | −0.149905 | ||||||||
\(796\) | 16.0993 | 0.570623 | ||||||||
\(797\) | −9.75641 | −0.345590 | −0.172795 | − | 0.984958i | \(-0.555280\pi\) | ||||
−0.172795 | + | 0.984958i | \(0.555280\pi\) | |||||||
\(798\) | −3.87939 | −0.137329 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 6.24897 | 0.220797 | ||||||||
\(802\) | −8.97596 | −0.316952 | ||||||||
\(803\) | 23.6013 | 0.832872 | ||||||||
\(804\) | −4.08378 | −0.144024 | ||||||||
\(805\) | −36.5107 | −1.28683 | ||||||||
\(806\) | −26.4979 | −0.933350 | ||||||||
\(807\) | −24.7493 | −0.871216 | ||||||||
\(808\) | 11.5175 | 0.405186 | ||||||||
\(809\) | 4.12237 | 0.144935 | 0.0724674 | − | 0.997371i | \(-0.476913\pi\) | ||||
0.0724674 | + | 0.997371i | \(0.476913\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 50.9353 | 1.78858 | 0.894291 | − | 0.447487i | \(-0.147681\pi\) | ||||
0.894291 | + | 0.447487i | \(0.147681\pi\) | |||||||
\(812\) | 22.3405 | 0.783997 | ||||||||
\(813\) | −12.6209 | −0.442635 | ||||||||
\(814\) | −0.467911 | −0.0164003 | ||||||||
\(815\) | −13.4338 | −0.470564 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.5817 | −0.440179 | ||||||||
\(818\) | 10.4311 | 0.364714 | ||||||||
\(819\) | −15.9290 | −0.556605 | ||||||||
\(820\) | −11.5817 | −0.404451 | ||||||||
\(821\) | −10.2276 | −0.356946 | −0.178473 | − | 0.983945i | \(-0.557116\pi\) | ||||
−0.178473 | + | 0.983945i | \(0.557116\pi\) | |||||||
\(822\) | −6.45336 | −0.225087 | ||||||||
\(823\) | 3.26083 | 0.113665 | 0.0568327 | − | 0.998384i | \(-0.481900\pi\) | ||||
0.0568327 | + | 0.998384i | \(0.481900\pi\) | |||||||
\(824\) | −7.69459 | −0.268054 | ||||||||
\(825\) | 1.53209 | 0.0533405 | ||||||||
\(826\) | 50.6245 | 1.76145 | ||||||||
\(827\) | 45.0351 | 1.56602 | 0.783012 | − | 0.622007i | \(-0.213683\pi\) | ||||
0.783012 | + | 0.622007i | \(0.213683\pi\) | |||||||
\(828\) | −9.41147 | −0.327071 | ||||||||
\(829\) | −12.5763 | −0.436794 | −0.218397 | − | 0.975860i | \(-0.570083\pi\) | ||||
−0.218397 | + | 0.975860i | \(0.570083\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.1898 | −0.353482 | ||||||||
\(832\) | 4.10607 | 0.142352 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −11.6108 | −0.402050 | ||||||||
\(835\) | 8.01455 | 0.277355 | ||||||||
\(836\) | 1.53209 | 0.0529884 | ||||||||
\(837\) | −6.45336 | −0.223061 | ||||||||
\(838\) | 1.86484 | 0.0644197 | ||||||||
\(839\) | 5.45748 | 0.188413 | 0.0942066 | − | 0.995553i | \(-0.469969\pi\) | ||||
0.0942066 | + | 0.995553i | \(0.469969\pi\) | |||||||
\(840\) | 3.87939 | 0.133852 | ||||||||
\(841\) | 4.16344 | 0.143567 | ||||||||
\(842\) | 3.84255 | 0.132423 | ||||||||
\(843\) | −27.2226 | −0.937595 | ||||||||
\(844\) | −20.2199 | −0.695997 | ||||||||
\(845\) | −3.85978 | −0.132781 | ||||||||
\(846\) | 5.63816 | 0.193844 | ||||||||
\(847\) | 33.5672 | 1.15338 | ||||||||
\(848\) | 4.22668 | 0.145145 | ||||||||
\(849\) | 10.6554 | 0.365692 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.87433 | 0.0985309 | ||||||||
\(852\) | −14.2567 | −0.488427 | ||||||||
\(853\) | 17.1179 | 0.586107 | 0.293053 | − | 0.956096i | \(-0.405329\pi\) | ||||
0.293053 | + | 0.956096i | \(0.405329\pi\) | |||||||
\(854\) | 17.8871 | 0.612085 | ||||||||
\(855\) | −1.00000 | −0.0341993 | ||||||||
\(856\) | −0.694593 | −0.0237407 | ||||||||
\(857\) | −52.1931 | −1.78288 | −0.891442 | − | 0.453135i | \(-0.850306\pi\) | ||||
−0.891442 | + | 0.453135i | \(0.850306\pi\) | |||||||
\(858\) | 6.29086 | 0.214766 | ||||||||
\(859\) | 49.7701 | 1.69814 | 0.849068 | − | 0.528284i | \(-0.177164\pi\) | ||||
0.849068 | + | 0.528284i | \(0.177164\pi\) | |||||||
\(860\) | 12.5817 | 0.429033 | ||||||||
\(861\) | −44.9299 | −1.53121 | ||||||||
\(862\) | 17.9608 | 0.611747 | ||||||||
\(863\) | 12.8922 | 0.438855 | 0.219427 | − | 0.975629i | \(-0.429581\pi\) | ||||
0.219427 | + | 0.975629i | \(0.429581\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −4.43107 | −0.150661 | ||||||||
\(866\) | 0.723689 | 0.0245919 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 25.0351 | 0.849746 | ||||||||
\(869\) | 11.0196 | 0.373814 | ||||||||
\(870\) | 5.75877 | 0.195241 | ||||||||
\(871\) | −16.7683 | −0.568171 | ||||||||
\(872\) | −12.1284 | −0.410718 | ||||||||
\(873\) | −2.24123 | −0.0758541 | ||||||||
\(874\) | −9.41147 | −0.318348 | ||||||||
\(875\) | 3.87939 | 0.131147 | ||||||||
\(876\) | 15.4047 | 0.520475 | ||||||||
\(877\) | −52.4529 | −1.77121 | −0.885604 | − | 0.464442i | \(-0.846255\pi\) | ||||
−0.885604 | + | 0.464442i | \(0.846255\pi\) | |||||||
\(878\) | −29.5722 | −0.998014 | ||||||||
\(879\) | 3.12330 | 0.105346 | ||||||||
\(880\) | −1.53209 | −0.0516467 | ||||||||
\(881\) | 35.4816 | 1.19541 | 0.597703 | − | 0.801717i | \(-0.296080\pi\) | ||||
0.597703 | + | 0.801717i | \(0.296080\pi\) | |||||||
\(882\) | 8.04963 | 0.271045 | ||||||||
\(883\) | −50.6709 | −1.70521 | −0.852605 | − | 0.522555i | \(-0.824979\pi\) | ||||
−0.852605 | + | 0.522555i | \(0.824979\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.0496 | 0.438659 | ||||||||
\(886\) | 24.3851 | 0.819232 | ||||||||
\(887\) | 12.7897 | 0.429437 | 0.214719 | − | 0.976676i | \(-0.431117\pi\) | ||||
0.214719 | + | 0.976676i | \(0.431117\pi\) | |||||||
\(888\) | −0.305407 | −0.0102488 | ||||||||
\(889\) | 28.4766 | 0.955074 | ||||||||
\(890\) | −6.24897 | −0.209466 | ||||||||
\(891\) | 1.53209 | 0.0513269 | ||||||||
\(892\) | 2.47565 | 0.0828910 | ||||||||
\(893\) | 5.63816 | 0.188674 | ||||||||
\(894\) | −19.9317 | −0.666616 | ||||||||
\(895\) | −4.95811 | −0.165731 | ||||||||
\(896\) | −3.87939 | −0.129601 | ||||||||
\(897\) | −38.6441 | −1.29029 | ||||||||
\(898\) | −12.3851 | −0.413295 | ||||||||
\(899\) | 37.1634 | 1.23947 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 17.7442 | 0.590818 | ||||||||
\(903\) | 48.8093 | 1.62427 | ||||||||
\(904\) | 3.43376 | 0.114205 | ||||||||
\(905\) | 4.28581 | 0.142465 | ||||||||
\(906\) | −22.8229 | −0.758242 | ||||||||
\(907\) | −12.8830 | −0.427773 | −0.213887 | − | 0.976858i | \(-0.568612\pi\) | ||||
−0.213887 | + | 0.976858i | \(0.568612\pi\) | |||||||
\(908\) | −10.1284 | −0.336121 | ||||||||
\(909\) | 11.5175 | 0.382013 | ||||||||
\(910\) | 15.9290 | 0.528042 | ||||||||
\(911\) | −19.2026 | −0.636212 | −0.318106 | − | 0.948055i | \(-0.603047\pi\) | ||||
−0.318106 | + | 0.948055i | \(0.603047\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 18.3797 | 0.607946 | ||||||||
\(915\) | 4.61081 | 0.152429 | ||||||||
\(916\) | −11.5621 | −0.382023 | ||||||||
\(917\) | 48.3979 | 1.59824 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 56.6709 | 1.86940 | 0.934700 | − | 0.355438i | \(-0.115668\pi\) | ||||
0.934700 | + | 0.355438i | \(0.115668\pi\) | |||||||
\(920\) | 9.41147 | 0.310287 | ||||||||
\(921\) | −27.9864 | −0.922183 | ||||||||
\(922\) | −11.9263 | −0.392773 | ||||||||
\(923\) | −58.5390 | −1.92683 | ||||||||
\(924\) | −5.94356 | −0.195529 | ||||||||
\(925\) | −0.305407 | −0.0100417 | ||||||||
\(926\) | 30.5996 | 1.00556 | ||||||||
\(927\) | −7.69459 | −0.252724 | ||||||||
\(928\) | −5.75877 | −0.189041 | ||||||||
\(929\) | 31.8716 | 1.04567 | 0.522837 | − | 0.852432i | \(-0.324874\pi\) | ||||
0.522837 | + | 0.852432i | \(0.324874\pi\) | |||||||
\(930\) | 6.45336 | 0.211614 | ||||||||
\(931\) | 8.04963 | 0.263816 | ||||||||
\(932\) | −4.65539 | −0.152492 | ||||||||
\(933\) | −6.98040 | −0.228528 | ||||||||
\(934\) | 14.8075 | 0.484515 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.10607 | 0.134211 | ||||||||
\(937\) | −44.8093 | −1.46386 | −0.731929 | − | 0.681381i | \(-0.761380\pi\) | ||||
−0.731929 | + | 0.681381i | \(0.761380\pi\) | |||||||
\(938\) | 15.8425 | 0.517278 | ||||||||
\(939\) | −27.8188 | −0.907833 | ||||||||
\(940\) | −5.63816 | −0.183896 | ||||||||
\(941\) | −24.4688 | −0.797662 | −0.398831 | − | 0.917025i | \(-0.630584\pi\) | ||||
−0.398831 | + | 0.917025i | \(0.630584\pi\) | |||||||
\(942\) | −0.573978 | −0.0187012 | ||||||||
\(943\) | −109.001 | −3.54956 | ||||||||
\(944\) | −13.0496 | −0.424729 | ||||||||
\(945\) | 3.87939 | 0.126196 | ||||||||
\(946\) | −19.2763 | −0.626727 | ||||||||
\(947\) | 38.7837 | 1.26030 | 0.630151 | − | 0.776472i | \(-0.282993\pi\) | ||||
0.630151 | + | 0.776472i | \(0.282993\pi\) | |||||||
\(948\) | 7.19253 | 0.233603 | ||||||||
\(949\) | 63.2526 | 2.05327 | ||||||||
\(950\) | 1.00000 | 0.0324443 | ||||||||
\(951\) | 2.27631 | 0.0738145 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.1581 | −0.750163 | −0.375082 | − | 0.926992i | \(-0.622385\pi\) | ||||
−0.375082 | + | 0.926992i | \(0.622385\pi\) | |||||||
\(954\) | 4.22668 | 0.136844 | ||||||||
\(955\) | −10.0155 | −0.324093 | ||||||||
\(956\) | −18.4534 | −0.596824 | ||||||||
\(957\) | −8.82295 | −0.285205 | ||||||||
\(958\) | 28.8093 | 0.930787 | ||||||||
\(959\) | 25.0351 | 0.808425 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | 10.6459 | 0.343416 | ||||||||
\(962\) | −1.25402 | −0.0404313 | ||||||||
\(963\) | −0.694593 | −0.0223829 | ||||||||
\(964\) | 27.0428 | 0.870991 | ||||||||
\(965\) | −12.6108 | −0.405956 | ||||||||
\(966\) | 36.5107 | 1.17471 | ||||||||
\(967\) | −15.3987 | −0.495188 | −0.247594 | − | 0.968864i | \(-0.579640\pi\) | ||||
−0.247594 | + | 0.968864i | \(0.579640\pi\) | |||||||
\(968\) | −8.65270 | −0.278108 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.24123 | 0.0719615 | ||||||||
\(971\) | −21.2276 | −0.681227 | −0.340613 | − | 0.940203i | \(-0.610635\pi\) | ||||
−0.340613 | + | 0.940203i | \(0.610635\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 45.0428 | 1.44401 | ||||||||
\(974\) | −17.8229 | −0.571084 | ||||||||
\(975\) | 4.10607 | 0.131499 | ||||||||
\(976\) | −4.61081 | −0.147589 | ||||||||
\(977\) | 29.5431 | 0.945168 | 0.472584 | − | 0.881286i | \(-0.343321\pi\) | ||||
0.472584 | + | 0.881286i | \(0.343321\pi\) | |||||||
\(978\) | 13.4338 | 0.429564 | ||||||||
\(979\) | 9.57398 | 0.305986 | ||||||||
\(980\) | −8.04963 | −0.257136 | ||||||||
\(981\) | −12.1284 | −0.387229 | ||||||||
\(982\) | −10.8699 | −0.346872 | ||||||||
\(983\) | 6.03920 | 0.192621 | 0.0963103 | − | 0.995351i | \(-0.469296\pi\) | ||||
0.0963103 | + | 0.995351i | \(0.469296\pi\) | |||||||
\(984\) | 11.5817 | 0.369212 | ||||||||
\(985\) | 2.55169 | 0.0813036 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −21.8726 | −0.696212 | ||||||||
\(988\) | 4.10607 | 0.130631 | ||||||||
\(989\) | 118.413 | 3.76530 | ||||||||
\(990\) | −1.53209 | −0.0486930 | ||||||||
\(991\) | −52.0464 | −1.65331 | −0.826655 | − | 0.562709i | \(-0.809759\pi\) | ||||
−0.826655 | + | 0.562709i | \(0.809759\pi\) | |||||||
\(992\) | −6.45336 | −0.204894 | ||||||||
\(993\) | −9.20027 | −0.291962 | ||||||||
\(994\) | 55.3073 | 1.75424 | ||||||||
\(995\) | −16.0993 | −0.510381 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35.3645 | 1.12001 | 0.560003 | − | 0.828491i | \(-0.310800\pi\) | ||||
0.560003 | + | 0.828491i | \(0.310800\pi\) | |||||||
\(998\) | −23.0719 | −0.730329 | ||||||||
\(999\) | −0.305407 | −0.00966266 |
(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 | 8670.2.a.br.1.1 | yes | 3 | |
17.16 | even | 2 | 8670.2.a.bq.1.3 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8670.2.a.bq.1.3 | ✓ | 3 | 17.16 | even | 2 | ||
8670.2.a.br.1.1 | yes | 3 | 1.1 | even | 1 | trivial |