Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3525,2,Mod(1,3525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3525, 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("3525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3525 = 3 \cdot 5^{2} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3525.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: | \(28.1472667125\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 7x^{6} + 24x^{5} + 8x^{4} - 47x^{3} + 8x^{2} + 13x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.62510\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.62510 | −1.85623 | −0.928113 | − | 0.372299i | \(-0.878570\pi\) | ||||
−0.928113 | + | 0.372299i | \(0.878570\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 4.89115 | 2.44557 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.62510 | −1.07169 | ||||||||
\(7\) | −5.24764 | −1.98342 | −0.991710 | − | 0.128494i | \(-0.958986\pi\) | ||||
−0.991710 | + | 0.128494i | \(0.958986\pi\) | |||||||
\(8\) | −7.58955 | −2.68331 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.45327 | 0.739688 | 0.369844 | − | 0.929094i | \(-0.379411\pi\) | ||||
0.369844 | + | 0.929094i | \(0.379411\pi\) | |||||||
\(12\) | 4.89115 | 1.41195 | ||||||||
\(13\) | 1.47869 | 0.410115 | 0.205058 | − | 0.978750i | \(-0.434262\pi\) | ||||
0.205058 | + | 0.978750i | \(0.434262\pi\) | |||||||
\(14\) | 13.7756 | 3.68168 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 10.1410 | 2.53526 | ||||||||
\(17\) | −4.14255 | −1.00471 | −0.502357 | − | 0.864660i | \(-0.667534\pi\) | ||||
−0.502357 | + | 0.864660i | \(0.667534\pi\) | |||||||
\(18\) | −2.62510 | −0.618742 | ||||||||
\(19\) | 4.25408 | 0.975954 | 0.487977 | − | 0.872857i | \(-0.337735\pi\) | ||||
0.487977 | + | 0.872857i | \(0.337735\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.24764 | −1.14513 | ||||||||
\(22\) | −6.44007 | −1.37303 | ||||||||
\(23\) | 6.50248 | 1.35586 | 0.677931 | − | 0.735126i | \(-0.262877\pi\) | ||||
0.677931 | + | 0.735126i | \(0.262877\pi\) | |||||||
\(24\) | −7.58955 | −1.54921 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.88171 | −0.761266 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −25.6670 | −4.85060 | ||||||||
\(29\) | −8.17052 | −1.51723 | −0.758614 | − | 0.651540i | \(-0.774123\pi\) | ||||
−0.758614 | + | 0.651540i | \(0.774123\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.69350 | −1.02258 | −0.511291 | − | 0.859407i | \(-0.670833\pi\) | ||||
−0.511291 | + | 0.859407i | \(0.670833\pi\) | |||||||
\(32\) | −11.4421 | −2.02270 | ||||||||
\(33\) | 2.45327 | 0.427059 | ||||||||
\(34\) | 10.8746 | 1.86498 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.89115 | 0.815191 | ||||||||
\(37\) | 1.84684 | 0.303619 | 0.151810 | − | 0.988410i | \(-0.451490\pi\) | ||||
0.151810 | + | 0.988410i | \(0.451490\pi\) | |||||||
\(38\) | −11.1674 | −1.81159 | ||||||||
\(39\) | 1.47869 | 0.236780 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.39994 | −1.46802 | −0.734012 | − | 0.679137i | \(-0.762354\pi\) | ||||
−0.734012 | + | 0.679137i | \(0.762354\pi\) | |||||||
\(42\) | 13.7756 | 2.12562 | ||||||||
\(43\) | 4.34441 | 0.662517 | 0.331259 | − | 0.943540i | \(-0.392527\pi\) | ||||
0.331259 | + | 0.943540i | \(0.392527\pi\) | |||||||
\(44\) | 11.9993 | 1.80896 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −17.0697 | −2.51679 | ||||||||
\(47\) | −1.00000 | −0.145865 | ||||||||
\(48\) | 10.1410 | 1.46373 | ||||||||
\(49\) | 20.5377 | 2.93396 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.14255 | −0.580072 | ||||||||
\(52\) | 7.23250 | 1.00297 | ||||||||
\(53\) | 6.95955 | 0.955967 | 0.477984 | − | 0.878369i | \(-0.341368\pi\) | ||||
0.477984 | + | 0.878369i | \(0.341368\pi\) | |||||||
\(54\) | −2.62510 | −0.357231 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 39.8272 | 5.32214 | ||||||||
\(57\) | 4.25408 | 0.563467 | ||||||||
\(58\) | 21.4484 | 2.81632 | ||||||||
\(59\) | −7.70051 | −1.00252 | −0.501260 | − | 0.865297i | \(-0.667130\pi\) | ||||
−0.501260 | + | 0.865297i | \(0.667130\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.0670 | 1.54501 | 0.772507 | − | 0.635006i | \(-0.219002\pi\) | ||||
0.772507 | + | 0.635006i | \(0.219002\pi\) | |||||||
\(62\) | 14.9460 | 1.89814 | ||||||||
\(63\) | −5.24764 | −0.661140 | ||||||||
\(64\) | 9.75464 | 1.21933 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.44007 | −0.792718 | ||||||||
\(67\) | 5.84395 | 0.713952 | 0.356976 | − | 0.934113i | \(-0.383808\pi\) | ||||
0.356976 | + | 0.934113i | \(0.383808\pi\) | |||||||
\(68\) | −20.2618 | −2.45710 | ||||||||
\(69\) | 6.50248 | 0.782807 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.81951 | −0.334614 | −0.167307 | − | 0.985905i | \(-0.553507\pi\) | ||||
−0.167307 | + | 0.985905i | \(0.553507\pi\) | |||||||
\(72\) | −7.58955 | −0.894437 | ||||||||
\(73\) | −5.10213 | −0.597159 | −0.298579 | − | 0.954385i | \(-0.596513\pi\) | ||||
−0.298579 | + | 0.954385i | \(0.596513\pi\) | |||||||
\(74\) | −4.84815 | −0.563586 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 20.8074 | 2.38677 | ||||||||
\(77\) | −12.8739 | −1.46711 | ||||||||
\(78\) | −3.88171 | −0.439517 | ||||||||
\(79\) | 5.56405 | 0.626005 | 0.313002 | − | 0.949752i | \(-0.398665\pi\) | ||||
0.313002 | + | 0.949752i | \(0.398665\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 24.6758 | 2.72498 | ||||||||
\(83\) | −15.4973 | −1.70105 | −0.850523 | − | 0.525937i | \(-0.823715\pi\) | ||||
−0.850523 | + | 0.525937i | \(0.823715\pi\) | |||||||
\(84\) | −25.6670 | −2.80050 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −11.4045 | −1.22978 | ||||||||
\(87\) | −8.17052 | −0.875972 | ||||||||
\(88\) | −18.6192 | −1.98481 | ||||||||
\(89\) | −3.59698 | −0.381280 | −0.190640 | − | 0.981660i | \(-0.561056\pi\) | ||||
−0.190640 | + | 0.981660i | \(0.561056\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.75963 | −0.813431 | ||||||||
\(92\) | 31.8046 | 3.31586 | ||||||||
\(93\) | −5.69350 | −0.590388 | ||||||||
\(94\) | 2.62510 | 0.270758 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −11.4421 | −1.16781 | ||||||||
\(97\) | 3.34748 | 0.339886 | 0.169943 | − | 0.985454i | \(-0.445642\pi\) | ||||
0.169943 | + | 0.985454i | \(0.445642\pi\) | |||||||
\(98\) | −53.9135 | −5.44609 | ||||||||
\(99\) | 2.45327 | 0.246563 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.29938 | −0.129294 | −0.0646468 | − | 0.997908i | \(-0.520592\pi\) | ||||
−0.0646468 | + | 0.997908i | \(0.520592\pi\) | |||||||
\(102\) | 10.8746 | 1.07675 | ||||||||
\(103\) | 16.5846 | 1.63413 | 0.817065 | − | 0.576546i | \(-0.195600\pi\) | ||||
0.817065 | + | 0.576546i | \(0.195600\pi\) | |||||||
\(104\) | −11.2226 | −1.10047 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −18.2695 | −1.77449 | ||||||||
\(107\) | −10.0354 | −0.970163 | −0.485081 | − | 0.874469i | \(-0.661210\pi\) | ||||
−0.485081 | + | 0.874469i | \(0.661210\pi\) | |||||||
\(108\) | 4.89115 | 0.470651 | ||||||||
\(109\) | −9.16258 | −0.877616 | −0.438808 | − | 0.898581i | \(-0.644599\pi\) | ||||
−0.438808 | + | 0.898581i | \(0.644599\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.84684 | 0.175295 | ||||||||
\(112\) | −53.2165 | −5.02848 | ||||||||
\(113\) | −11.4553 | −1.07762 | −0.538810 | − | 0.842427i | \(-0.681126\pi\) | ||||
−0.538810 | + | 0.842427i | \(0.681126\pi\) | |||||||
\(114\) | −11.1674 | −1.04592 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −39.9632 | −3.71049 | ||||||||
\(117\) | 1.47869 | 0.136705 | ||||||||
\(118\) | 20.2146 | 1.86090 | ||||||||
\(119\) | 21.7386 | 1.99277 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.98148 | −0.452862 | ||||||||
\(122\) | −31.6770 | −2.86790 | ||||||||
\(123\) | −9.39994 | −0.847564 | ||||||||
\(124\) | −27.8477 | −2.50080 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 13.7756 | 1.22723 | ||||||||
\(127\) | −7.50757 | −0.666189 | −0.333095 | − | 0.942893i | \(-0.608093\pi\) | ||||
−0.333095 | + | 0.942893i | \(0.608093\pi\) | |||||||
\(128\) | −2.72267 | −0.240652 | ||||||||
\(129\) | 4.34441 | 0.382504 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.4292 | 1.08595 | 0.542974 | − | 0.839749i | \(-0.317298\pi\) | ||||
0.542974 | + | 0.839749i | \(0.317298\pi\) | |||||||
\(132\) | 11.9993 | 1.04440 | ||||||||
\(133\) | −22.3239 | −1.93573 | ||||||||
\(134\) | −15.3410 | −1.32526 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 31.4401 | 2.69596 | ||||||||
\(137\) | 12.7385 | 1.08832 | 0.544162 | − | 0.838980i | \(-0.316848\pi\) | ||||
0.544162 | + | 0.838980i | \(0.316848\pi\) | |||||||
\(138\) | −17.0697 | −1.45307 | ||||||||
\(139\) | −13.7235 | −1.16401 | −0.582005 | − | 0.813185i | \(-0.697732\pi\) | ||||
−0.582005 | + | 0.813185i | \(0.697732\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.00000 | −0.0842152 | ||||||||
\(142\) | 7.40148 | 0.621119 | ||||||||
\(143\) | 3.62762 | 0.303357 | ||||||||
\(144\) | 10.1410 | 0.845086 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 13.3936 | 1.10846 | ||||||||
\(147\) | 20.5377 | 1.69392 | ||||||||
\(148\) | 9.03319 | 0.742524 | ||||||||
\(149\) | 6.30968 | 0.516909 | 0.258455 | − | 0.966023i | \(-0.416787\pi\) | ||||
0.258455 | + | 0.966023i | \(0.416787\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.80524 | 0.635182 | 0.317591 | − | 0.948228i | \(-0.397126\pi\) | ||||
0.317591 | + | 0.948228i | \(0.397126\pi\) | |||||||
\(152\) | −32.2866 | −2.61879 | ||||||||
\(153\) | −4.14255 | −0.334905 | ||||||||
\(154\) | 33.7952 | 2.72329 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 7.23250 | 0.579063 | ||||||||
\(157\) | −21.1234 | −1.68583 | −0.842914 | − | 0.538048i | \(-0.819162\pi\) | ||||
−0.842914 | + | 0.538048i | \(0.819162\pi\) | |||||||
\(158\) | −14.6062 | −1.16201 | ||||||||
\(159\) | 6.95955 | 0.551928 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −34.1227 | −2.68924 | ||||||||
\(162\) | −2.62510 | −0.206247 | ||||||||
\(163\) | −19.5801 | −1.53363 | −0.766816 | − | 0.641867i | \(-0.778160\pi\) | ||||
−0.766816 | + | 0.641867i | \(0.778160\pi\) | |||||||
\(164\) | −45.9765 | −3.59016 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 40.6819 | 3.15753 | ||||||||
\(167\) | 2.84701 | 0.220308 | 0.110154 | − | 0.993915i | \(-0.464866\pi\) | ||||
0.110154 | + | 0.993915i | \(0.464866\pi\) | |||||||
\(168\) | 39.8272 | 3.07274 | ||||||||
\(169\) | −10.8135 | −0.831806 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.25408 | 0.325318 | ||||||||
\(172\) | 21.2492 | 1.62023 | ||||||||
\(173\) | 7.99152 | 0.607584 | 0.303792 | − | 0.952738i | \(-0.401747\pi\) | ||||
0.303792 | + | 0.952738i | \(0.401747\pi\) | |||||||
\(174\) | 21.4484 | 1.62600 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 24.8787 | 1.87530 | ||||||||
\(177\) | −7.70051 | −0.578806 | ||||||||
\(178\) | 9.44244 | 0.707741 | ||||||||
\(179\) | −11.6594 | −0.871461 | −0.435731 | − | 0.900077i | \(-0.643510\pi\) | ||||
−0.435731 | + | 0.900077i | \(0.643510\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.5331 | 1.45188 | 0.725942 | − | 0.687756i | \(-0.241404\pi\) | ||||
0.725942 | + | 0.687756i | \(0.241404\pi\) | |||||||
\(182\) | 20.3698 | 1.50991 | ||||||||
\(183\) | 12.0670 | 0.892015 | ||||||||
\(184\) | −49.3509 | −3.63820 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 14.9460 | 1.09589 | ||||||||
\(187\) | −10.1628 | −0.743175 | ||||||||
\(188\) | −4.89115 | −0.356724 | ||||||||
\(189\) | −5.24764 | −0.381709 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.1126 | −1.67237 | −0.836185 | − | 0.548447i | \(-0.815219\pi\) | ||||
−0.836185 | + | 0.548447i | \(0.815219\pi\) | |||||||
\(192\) | 9.75464 | 0.703981 | ||||||||
\(193\) | −17.2364 | −1.24070 | −0.620351 | − | 0.784324i | \(-0.713010\pi\) | ||||
−0.620351 | + | 0.784324i | \(0.713010\pi\) | |||||||
\(194\) | −8.78748 | −0.630904 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 100.453 | 7.17521 | ||||||||
\(197\) | −11.1056 | −0.791240 | −0.395620 | − | 0.918414i | \(-0.629470\pi\) | ||||
−0.395620 | + | 0.918414i | \(0.629470\pi\) | |||||||
\(198\) | −6.44007 | −0.457676 | ||||||||
\(199\) | −23.0611 | −1.63476 | −0.817380 | − | 0.576098i | \(-0.804575\pi\) | ||||
−0.817380 | + | 0.576098i | \(0.804575\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.84395 | 0.412201 | ||||||||
\(202\) | 3.41101 | 0.239998 | ||||||||
\(203\) | 42.8759 | 3.00930 | ||||||||
\(204\) | −20.2618 | −1.41861 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −43.5362 | −3.03331 | ||||||||
\(207\) | 6.50248 | 0.451954 | ||||||||
\(208\) | 14.9955 | 1.03975 | ||||||||
\(209\) | 10.4364 | 0.721901 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.09406 | 0.281847 | 0.140923 | − | 0.990021i | \(-0.454993\pi\) | ||||
0.140923 | + | 0.990021i | \(0.454993\pi\) | |||||||
\(212\) | 34.0402 | 2.33789 | ||||||||
\(213\) | −2.81951 | −0.193189 | ||||||||
\(214\) | 26.3440 | 1.80084 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −7.58955 | −0.516404 | ||||||||
\(217\) | 29.8774 | 2.02821 | ||||||||
\(218\) | 24.0527 | 1.62905 | ||||||||
\(219\) | −5.10213 | −0.344770 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.12555 | −0.412049 | ||||||||
\(222\) | −4.84815 | −0.325387 | ||||||||
\(223\) | 21.0775 | 1.41146 | 0.705728 | − | 0.708483i | \(-0.250620\pi\) | ||||
0.705728 | + | 0.708483i | \(0.250620\pi\) | |||||||
\(224\) | 60.0441 | 4.01187 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 30.0712 | 2.00031 | ||||||||
\(227\) | 1.70842 | 0.113392 | 0.0566958 | − | 0.998391i | \(-0.481943\pi\) | ||||
0.0566958 | + | 0.998391i | \(0.481943\pi\) | |||||||
\(228\) | 20.8074 | 1.37800 | ||||||||
\(229\) | 5.07837 | 0.335588 | 0.167794 | − | 0.985822i | \(-0.446336\pi\) | ||||
0.167794 | + | 0.985822i | \(0.446336\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.8739 | −0.847037 | ||||||||
\(232\) | 62.0106 | 4.07120 | ||||||||
\(233\) | −0.738739 | −0.0483964 | −0.0241982 | − | 0.999707i | \(-0.507703\pi\) | ||||
−0.0241982 | + | 0.999707i | \(0.507703\pi\) | |||||||
\(234\) | −3.88171 | −0.253755 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −37.6643 | −2.45174 | ||||||||
\(237\) | 5.56405 | 0.361424 | ||||||||
\(238\) | −57.0659 | −3.69904 | ||||||||
\(239\) | −3.36660 | −0.217767 | −0.108884 | − | 0.994055i | \(-0.534728\pi\) | ||||
−0.108884 | + | 0.994055i | \(0.534728\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.51135 | 0.419433 | 0.209716 | − | 0.977762i | \(-0.432746\pi\) | ||||
0.209716 | + | 0.977762i | \(0.432746\pi\) | |||||||
\(242\) | 13.0769 | 0.840614 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 59.0212 | 3.77845 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 24.6758 | 1.57327 | ||||||||
\(247\) | 6.29048 | 0.400253 | ||||||||
\(248\) | 43.2111 | 2.74391 | ||||||||
\(249\) | −15.4973 | −0.982100 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.7004 | 0.738524 | 0.369262 | − | 0.929325i | \(-0.379611\pi\) | ||||
0.369262 | + | 0.929325i | \(0.379611\pi\) | |||||||
\(252\) | −25.6670 | −1.61687 | ||||||||
\(253\) | 15.9523 | 1.00291 | ||||||||
\(254\) | 19.7081 | 1.23660 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.3620 | −0.772626 | ||||||||
\(257\) | −28.1645 | −1.75685 | −0.878427 | − | 0.477876i | \(-0.841407\pi\) | ||||
−0.878427 | + | 0.477876i | \(0.841407\pi\) | |||||||
\(258\) | −11.4045 | −0.710015 | ||||||||
\(259\) | −9.69157 | −0.602205 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.17052 | −0.505743 | ||||||||
\(262\) | −32.6280 | −2.01577 | ||||||||
\(263\) | 15.2487 | 0.940276 | 0.470138 | − | 0.882593i | \(-0.344204\pi\) | ||||
0.470138 | + | 0.882593i | \(0.344204\pi\) | |||||||
\(264\) | −18.6192 | −1.14593 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 58.6024 | 3.59315 | ||||||||
\(267\) | −3.59698 | −0.220132 | ||||||||
\(268\) | 28.5836 | 1.74602 | ||||||||
\(269\) | −7.75275 | −0.472693 | −0.236347 | − | 0.971669i | \(-0.575950\pi\) | ||||
−0.236347 | + | 0.971669i | \(0.575950\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.9314 | −0.907020 | −0.453510 | − | 0.891251i | \(-0.649828\pi\) | ||||
−0.453510 | + | 0.891251i | \(0.649828\pi\) | |||||||
\(272\) | −42.0097 | −2.54721 | ||||||||
\(273\) | −7.75963 | −0.469634 | ||||||||
\(274\) | −33.4398 | −2.02018 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 31.8046 | 1.91441 | ||||||||
\(277\) | 19.0645 | 1.14548 | 0.572739 | − | 0.819738i | \(-0.305881\pi\) | ||||
0.572739 | + | 0.819738i | \(0.305881\pi\) | |||||||
\(278\) | 36.0255 | 2.16067 | ||||||||
\(279\) | −5.69350 | −0.340861 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.2828 | −0.673076 | −0.336538 | − | 0.941670i | \(-0.609256\pi\) | ||||
−0.336538 | + | 0.941670i | \(0.609256\pi\) | |||||||
\(282\) | 2.62510 | 0.156322 | ||||||||
\(283\) | −16.9950 | −1.01025 | −0.505124 | − | 0.863047i | \(-0.668553\pi\) | ||||
−0.505124 | + | 0.863047i | \(0.668553\pi\) | |||||||
\(284\) | −13.7906 | −0.818323 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.52287 | −0.563099 | ||||||||
\(287\) | 49.3275 | 2.91171 | ||||||||
\(288\) | −11.4421 | −0.674234 | ||||||||
\(289\) | 0.160687 | 0.00945218 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.34748 | 0.196233 | ||||||||
\(292\) | −24.9553 | −1.46040 | ||||||||
\(293\) | −29.7556 | −1.73834 | −0.869170 | − | 0.494513i | \(-0.835346\pi\) | ||||
−0.869170 | + | 0.494513i | \(0.835346\pi\) | |||||||
\(294\) | −53.9135 | −3.14430 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −14.0167 | −0.814705 | ||||||||
\(297\) | 2.45327 | 0.142353 | ||||||||
\(298\) | −16.5635 | −0.959500 | ||||||||
\(299\) | 9.61516 | 0.556059 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.7979 | −1.31405 | ||||||||
\(302\) | −20.4895 | −1.17904 | ||||||||
\(303\) | −1.29938 | −0.0746477 | ||||||||
\(304\) | 43.1408 | 2.47430 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 10.8746 | 0.621659 | ||||||||
\(307\) | −24.4730 | −1.39675 | −0.698373 | − | 0.715734i | \(-0.746092\pi\) | ||||
−0.698373 | + | 0.715734i | \(0.746092\pi\) | |||||||
\(308\) | −62.9679 | −3.58793 | ||||||||
\(309\) | 16.5846 | 0.943465 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.26842 | −0.468859 | −0.234430 | − | 0.972133i | \(-0.575322\pi\) | ||||
−0.234430 | + | 0.972133i | \(0.575322\pi\) | |||||||
\(312\) | −11.2226 | −0.635355 | ||||||||
\(313\) | −26.7049 | −1.50945 | −0.754724 | − | 0.656043i | \(-0.772229\pi\) | ||||
−0.754724 | + | 0.656043i | \(0.772229\pi\) | |||||||
\(314\) | 55.4509 | 3.12928 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 27.2146 | 1.53094 | ||||||||
\(317\) | 12.1898 | 0.684649 | 0.342325 | − | 0.939582i | \(-0.388786\pi\) | ||||
0.342325 | + | 0.939582i | \(0.388786\pi\) | |||||||
\(318\) | −18.2695 | −1.02450 | ||||||||
\(319\) | −20.0445 | −1.12227 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.0354 | −0.560124 | ||||||||
\(322\) | 89.5754 | 4.99184 | ||||||||
\(323\) | −17.6227 | −0.980556 | ||||||||
\(324\) | 4.89115 | 0.271730 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 51.3997 | 2.84677 | ||||||||
\(327\) | −9.16258 | −0.506692 | ||||||||
\(328\) | 71.3413 | 3.93916 | ||||||||
\(329\) | 5.24764 | 0.289312 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.91572 | 0.490052 | 0.245026 | − | 0.969516i | \(-0.421203\pi\) | ||||
0.245026 | + | 0.969516i | \(0.421203\pi\) | |||||||
\(332\) | −75.7995 | −4.16004 | ||||||||
\(333\) | 1.84684 | 0.101206 | ||||||||
\(334\) | −7.47368 | −0.408942 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −53.2165 | −2.90320 | ||||||||
\(337\) | −0.427820 | −0.0233049 | −0.0116524 | − | 0.999932i | \(-0.503709\pi\) | ||||
−0.0116524 | + | 0.999932i | \(0.503709\pi\) | |||||||
\(338\) | 28.3864 | 1.54402 | ||||||||
\(339\) | −11.4553 | −0.622165 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.9677 | −0.756392 | ||||||||
\(342\) | −11.1674 | −0.603864 | ||||||||
\(343\) | −71.0410 | −3.83585 | ||||||||
\(344\) | −32.9722 | −1.77774 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −20.9785 | −1.12781 | ||||||||
\(347\) | −13.8379 | −0.742859 | −0.371430 | − | 0.928461i | \(-0.621132\pi\) | ||||
−0.371430 | + | 0.928461i | \(0.621132\pi\) | |||||||
\(348\) | −39.9632 | −2.14225 | ||||||||
\(349\) | 22.3237 | 1.19496 | 0.597479 | − | 0.801884i | \(-0.296169\pi\) | ||||
0.597479 | + | 0.801884i | \(0.296169\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.47869 | 0.0789267 | ||||||||
\(352\) | −28.0706 | −1.49617 | ||||||||
\(353\) | −20.0786 | −1.06868 | −0.534339 | − | 0.845270i | \(-0.679439\pi\) | ||||
−0.534339 | + | 0.845270i | \(0.679439\pi\) | |||||||
\(354\) | 20.2146 | 1.07439 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −17.5934 | −0.932448 | ||||||||
\(357\) | 21.7386 | 1.15053 | ||||||||
\(358\) | 30.6070 | 1.61763 | ||||||||
\(359\) | −18.8565 | −0.995208 | −0.497604 | − | 0.867404i | \(-0.665787\pi\) | ||||
−0.497604 | + | 0.867404i | \(0.665787\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.902764 | −0.0475139 | ||||||||
\(362\) | −51.2763 | −2.69502 | ||||||||
\(363\) | −4.98148 | −0.261460 | ||||||||
\(364\) | −37.9535 | −1.98931 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −31.6770 | −1.65578 | ||||||||
\(367\) | −21.5685 | −1.12587 | −0.562934 | − | 0.826502i | \(-0.690328\pi\) | ||||
−0.562934 | + | 0.826502i | \(0.690328\pi\) | |||||||
\(368\) | 65.9419 | 3.43746 | ||||||||
\(369\) | −9.39994 | −0.489341 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −36.5212 | −1.89609 | ||||||||
\(372\) | −27.8477 | −1.44384 | ||||||||
\(373\) | 8.49759 | 0.439988 | 0.219994 | − | 0.975501i | \(-0.429396\pi\) | ||||
0.219994 | + | 0.975501i | \(0.429396\pi\) | |||||||
\(374\) | 26.6783 | 1.37950 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.58955 | 0.391401 | ||||||||
\(377\) | −12.0817 | −0.622238 | ||||||||
\(378\) | 13.7756 | 0.708539 | ||||||||
\(379\) | 12.9777 | 0.666618 | 0.333309 | − | 0.942818i | \(-0.391835\pi\) | ||||
0.333309 | + | 0.942818i | \(0.391835\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.50757 | −0.384624 | ||||||||
\(382\) | 60.6729 | 3.10430 | ||||||||
\(383\) | 28.8351 | 1.47340 | 0.736701 | − | 0.676218i | \(-0.236382\pi\) | ||||
0.736701 | + | 0.676218i | \(0.236382\pi\) | |||||||
\(384\) | −2.72267 | −0.138940 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 45.2472 | 2.30302 | ||||||||
\(387\) | 4.34441 | 0.220839 | ||||||||
\(388\) | 16.3730 | 0.831215 | ||||||||
\(389\) | 21.5803 | 1.09417 | 0.547084 | − | 0.837078i | \(-0.315738\pi\) | ||||
0.547084 | + | 0.837078i | \(0.315738\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −26.9368 | −1.36225 | ||||||||
\(392\) | −155.872 | −7.87272 | ||||||||
\(393\) | 12.4292 | 0.626972 | ||||||||
\(394\) | 29.1533 | 1.46872 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 11.9993 | 0.602987 | ||||||||
\(397\) | 16.6366 | 0.834969 | 0.417484 | − | 0.908684i | \(-0.362912\pi\) | ||||
0.417484 | + | 0.908684i | \(0.362912\pi\) | |||||||
\(398\) | 60.5378 | 3.03449 | ||||||||
\(399\) | −22.3239 | −1.11759 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −33.5127 | −1.67354 | −0.836772 | − | 0.547552i | \(-0.815560\pi\) | ||||
−0.836772 | + | 0.547552i | \(0.815560\pi\) | |||||||
\(402\) | −15.3410 | −0.765137 | ||||||||
\(403\) | −8.41892 | −0.419376 | ||||||||
\(404\) | −6.35548 | −0.316197 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −112.554 | −5.58594 | ||||||||
\(407\) | 4.53080 | 0.224583 | ||||||||
\(408\) | 31.4401 | 1.55652 | ||||||||
\(409\) | −11.8817 | −0.587512 | −0.293756 | − | 0.955880i | \(-0.594905\pi\) | ||||
−0.293756 | + | 0.955880i | \(0.594905\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.7385 | 0.628344 | ||||||||
\(412\) | 81.1178 | 3.99639 | ||||||||
\(413\) | 40.4095 | 1.98842 | ||||||||
\(414\) | −17.0697 | −0.838928 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −16.9194 | −0.829540 | ||||||||
\(417\) | −13.7235 | −0.672042 | ||||||||
\(418\) | −27.3966 | −1.34001 | ||||||||
\(419\) | −2.52390 | −0.123301 | −0.0616503 | − | 0.998098i | \(-0.519636\pi\) | ||||
−0.0616503 | + | 0.998098i | \(0.519636\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.7777 | 0.720220 | 0.360110 | − | 0.932910i | \(-0.382739\pi\) | ||||
0.360110 | + | 0.932910i | \(0.382739\pi\) | |||||||
\(422\) | −10.7473 | −0.523171 | ||||||||
\(423\) | −1.00000 | −0.0486217 | ||||||||
\(424\) | −52.8198 | −2.56516 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.40148 | 0.358603 | ||||||||
\(427\) | −63.3230 | −3.06441 | ||||||||
\(428\) | −49.0848 | −2.37260 | ||||||||
\(429\) | 3.62762 | 0.175143 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.6446 | −1.37976 | −0.689880 | − | 0.723923i | \(-0.742337\pi\) | ||||
−0.689880 | + | 0.723923i | \(0.742337\pi\) | |||||||
\(432\) | 10.1410 | 0.487911 | ||||||||
\(433\) | 14.0010 | 0.672844 | 0.336422 | − | 0.941711i | \(-0.390783\pi\) | ||||
0.336422 | + | 0.941711i | \(0.390783\pi\) | |||||||
\(434\) | −78.4312 | −3.76482 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −44.8155 | −2.14627 | ||||||||
\(437\) | 27.6621 | 1.32326 | ||||||||
\(438\) | 13.3936 | 0.639971 | ||||||||
\(439\) | −23.0784 | −1.10147 | −0.550735 | − | 0.834680i | \(-0.685653\pi\) | ||||
−0.550735 | + | 0.834680i | \(0.685653\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.5377 | 0.977986 | ||||||||
\(442\) | 16.0802 | 0.764856 | ||||||||
\(443\) | −17.2342 | −0.818822 | −0.409411 | − | 0.912350i | \(-0.634266\pi\) | ||||
−0.409411 | + | 0.912350i | \(0.634266\pi\) | |||||||
\(444\) | 9.03319 | 0.428696 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −55.3306 | −2.61998 | ||||||||
\(447\) | 6.30968 | 0.298438 | ||||||||
\(448\) | −51.1888 | −2.41845 | ||||||||
\(449\) | −14.4444 | −0.681673 | −0.340837 | − | 0.940123i | \(-0.610710\pi\) | ||||
−0.340837 | + | 0.940123i | \(0.610710\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −23.0606 | −1.08588 | ||||||||
\(452\) | −56.0294 | −2.63540 | ||||||||
\(453\) | 7.80524 | 0.366722 | ||||||||
\(454\) | −4.48476 | −0.210480 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −32.2866 | −1.51196 | ||||||||
\(457\) | 29.3230 | 1.37167 | 0.685835 | − | 0.727757i | \(-0.259437\pi\) | ||||
0.685835 | + | 0.727757i | \(0.259437\pi\) | |||||||
\(458\) | −13.3312 | −0.622928 | ||||||||
\(459\) | −4.14255 | −0.193357 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.0074 | −0.466091 | −0.233045 | − | 0.972466i | \(-0.574869\pi\) | ||||
−0.233045 | + | 0.972466i | \(0.574869\pi\) | |||||||
\(462\) | 33.7952 | 1.57229 | ||||||||
\(463\) | −6.74306 | −0.313377 | −0.156688 | − | 0.987648i | \(-0.550082\pi\) | ||||
−0.156688 | + | 0.987648i | \(0.550082\pi\) | |||||||
\(464\) | −82.8576 | −3.84657 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.93926 | 0.0898347 | ||||||||
\(467\) | −22.6006 | −1.04583 | −0.522915 | − | 0.852385i | \(-0.675155\pi\) | ||||
−0.522915 | + | 0.852385i | \(0.675155\pi\) | |||||||
\(468\) | 7.23250 | 0.334322 | ||||||||
\(469\) | −30.6669 | −1.41607 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −21.1234 | −0.973313 | ||||||||
\(472\) | 58.4434 | 2.69008 | ||||||||
\(473\) | 10.6580 | 0.490056 | ||||||||
\(474\) | −14.6062 | −0.670885 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 106.327 | 4.87347 | ||||||||
\(477\) | 6.95955 | 0.318656 | ||||||||
\(478\) | 8.83765 | 0.404225 | ||||||||
\(479\) | 28.0031 | 1.27949 | 0.639747 | − | 0.768585i | \(-0.279039\pi\) | ||||
0.639747 | + | 0.768585i | \(0.279039\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.73091 | 0.124519 | ||||||||
\(482\) | −17.0929 | −0.778562 | ||||||||
\(483\) | −34.1227 | −1.55264 | ||||||||
\(484\) | −24.3652 | −1.10751 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.62510 | −0.119077 | ||||||||
\(487\) | −29.5359 | −1.33840 | −0.669200 | − | 0.743082i | \(-0.733363\pi\) | ||||
−0.669200 | + | 0.743082i | \(0.733363\pi\) | |||||||
\(488\) | −91.5828 | −4.14576 | ||||||||
\(489\) | −19.5801 | −0.885443 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.1287 | −0.457102 | −0.228551 | − | 0.973532i | \(-0.573399\pi\) | ||||
−0.228551 | + | 0.973532i | \(0.573399\pi\) | |||||||
\(492\) | −45.9765 | −2.07278 | ||||||||
\(493\) | 33.8468 | 1.52438 | ||||||||
\(494\) | −16.5131 | −0.742961 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −57.7380 | −2.59251 | ||||||||
\(497\) | 14.7957 | 0.663680 | ||||||||
\(498\) | 40.6819 | 1.82300 | ||||||||
\(499\) | −6.22375 | −0.278613 | −0.139307 | − | 0.990249i | \(-0.544487\pi\) | ||||
−0.139307 | + | 0.990249i | \(0.544487\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.84701 | 0.127195 | ||||||||
\(502\) | −30.7148 | −1.37087 | ||||||||
\(503\) | −31.8043 | −1.41809 | −0.709043 | − | 0.705166i | \(-0.750873\pi\) | ||||
−0.709043 | + | 0.705166i | \(0.750873\pi\) | |||||||
\(504\) | 39.8272 | 1.77405 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −41.8765 | −1.86164 | ||||||||
\(507\) | −10.8135 | −0.480243 | ||||||||
\(508\) | −36.7206 | −1.62921 | ||||||||
\(509\) | 13.5256 | 0.599513 | 0.299756 | − | 0.954016i | \(-0.403095\pi\) | ||||
0.299756 | + | 0.954016i | \(0.403095\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26.7741 | 1.18442 | ||||||||
\(512\) | 37.8969 | 1.67482 | ||||||||
\(513\) | 4.25408 | 0.187822 | ||||||||
\(514\) | 73.9347 | 3.26112 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 21.2492 | 0.935443 | ||||||||
\(517\) | −2.45327 | −0.107895 | ||||||||
\(518\) | 25.4413 | 1.11783 | ||||||||
\(519\) | 7.99152 | 0.350789 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.89142 | −0.301918 | −0.150959 | − | 0.988540i | \(-0.548236\pi\) | ||||
−0.150959 | + | 0.988540i | \(0.548236\pi\) | |||||||
\(522\) | 21.4484 | 0.938773 | ||||||||
\(523\) | 10.4160 | 0.455461 | 0.227730 | − | 0.973724i | \(-0.426869\pi\) | ||||
0.227730 | + | 0.973724i | \(0.426869\pi\) | |||||||
\(524\) | 60.7933 | 2.65577 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −40.0294 | −1.74537 | ||||||||
\(527\) | 23.5856 | 1.02740 | ||||||||
\(528\) | 24.8787 | 1.08270 | ||||||||
\(529\) | 19.2823 | 0.838361 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.70051 | −0.334174 | ||||||||
\(532\) | −109.189 | −4.73396 | ||||||||
\(533\) | −13.8996 | −0.602059 | ||||||||
\(534\) | 9.44244 | 0.408615 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −44.3530 | −1.91576 | ||||||||
\(537\) | −11.6594 | −0.503138 | ||||||||
\(538\) | 20.3517 | 0.877426 | ||||||||
\(539\) | 50.3845 | 2.17021 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.77543 | −0.205312 | −0.102656 | − | 0.994717i | \(-0.532734\pi\) | ||||
−0.102656 | + | 0.994717i | \(0.532734\pi\) | |||||||
\(542\) | 39.1965 | 1.68363 | ||||||||
\(543\) | 19.5331 | 0.838245 | ||||||||
\(544\) | 47.3995 | 2.03224 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 20.3698 | 0.871748 | ||||||||
\(547\) | 35.1733 | 1.50390 | 0.751950 | − | 0.659220i | \(-0.229113\pi\) | ||||
0.751950 | + | 0.659220i | \(0.229113\pi\) | |||||||
\(548\) | 62.3059 | 2.66158 | ||||||||
\(549\) | 12.0670 | 0.515005 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −34.7581 | −1.48074 | ||||||||
\(552\) | −49.3509 | −2.10052 | ||||||||
\(553\) | −29.1981 | −1.24163 | ||||||||
\(554\) | −50.0463 | −2.12626 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −67.1236 | −2.84667 | ||||||||
\(557\) | 41.5731 | 1.76151 | 0.880755 | − | 0.473573i | \(-0.157036\pi\) | ||||
0.880755 | + | 0.473573i | \(0.157036\pi\) | |||||||
\(558\) | 14.9460 | 0.632715 | ||||||||
\(559\) | 6.42405 | 0.271708 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.1628 | −0.429072 | ||||||||
\(562\) | 29.6185 | 1.24938 | ||||||||
\(563\) | 20.6694 | 0.871112 | 0.435556 | − | 0.900162i | \(-0.356552\pi\) | ||||
0.435556 | + | 0.900162i | \(0.356552\pi\) | |||||||
\(564\) | −4.89115 | −0.205954 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 44.6135 | 1.87525 | ||||||||
\(567\) | −5.24764 | −0.220380 | ||||||||
\(568\) | 21.3988 | 0.897873 | ||||||||
\(569\) | 33.7275 | 1.41393 | 0.706966 | − | 0.707248i | \(-0.250063\pi\) | ||||
0.706966 | + | 0.707248i | \(0.250063\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.88647 | 0.0789464 | 0.0394732 | − | 0.999221i | \(-0.487432\pi\) | ||||
0.0394732 | + | 0.999221i | \(0.487432\pi\) | |||||||
\(572\) | 17.7432 | 0.741882 | ||||||||
\(573\) | −23.1126 | −0.965544 | ||||||||
\(574\) | −129.490 | −5.40479 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 9.75464 | 0.406443 | ||||||||
\(577\) | −15.4800 | −0.644440 | −0.322220 | − | 0.946665i | \(-0.604429\pi\) | ||||
−0.322220 | + | 0.946665i | \(0.604429\pi\) | |||||||
\(578\) | −0.421820 | −0.0175454 | ||||||||
\(579\) | −17.2364 | −0.716320 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 81.3241 | 3.37389 | ||||||||
\(582\) | −8.78748 | −0.364253 | ||||||||
\(583\) | 17.0736 | 0.707117 | ||||||||
\(584\) | 38.7229 | 1.60236 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 78.1114 | 3.22675 | ||||||||
\(587\) | −24.5995 | −1.01533 | −0.507665 | − | 0.861554i | \(-0.669491\pi\) | ||||
−0.507665 | + | 0.861554i | \(0.669491\pi\) | |||||||
\(588\) | 100.453 | 4.14261 | ||||||||
\(589\) | −24.2206 | −0.997993 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.1056 | −0.456823 | ||||||||
\(592\) | 18.7289 | 0.769754 | ||||||||
\(593\) | 5.36195 | 0.220189 | 0.110094 | − | 0.993921i | \(-0.464885\pi\) | ||||
0.110094 | + | 0.993921i | \(0.464885\pi\) | |||||||
\(594\) | −6.44007 | −0.264239 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 30.8616 | 1.26414 | ||||||||
\(597\) | −23.0611 | −0.943830 | ||||||||
\(598\) | −25.2408 | −1.03217 | ||||||||
\(599\) | 32.0888 | 1.31111 | 0.655556 | − | 0.755147i | \(-0.272434\pi\) | ||||
0.655556 | + | 0.755147i | \(0.272434\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.4599 | 0.426668 | 0.213334 | − | 0.976979i | \(-0.431568\pi\) | ||||
0.213334 | + | 0.976979i | \(0.431568\pi\) | |||||||
\(602\) | 59.8468 | 2.43917 | ||||||||
\(603\) | 5.84395 | 0.237984 | ||||||||
\(604\) | 38.1766 | 1.55338 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.41101 | 0.138563 | ||||||||
\(607\) | −37.0898 | −1.50543 | −0.752714 | − | 0.658347i | \(-0.771256\pi\) | ||||
−0.752714 | + | 0.658347i | \(0.771256\pi\) | |||||||
\(608\) | −48.6758 | −1.97406 | ||||||||
\(609\) | 42.8759 | 1.73742 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.47869 | −0.0598214 | ||||||||
\(612\) | −20.2618 | −0.819035 | ||||||||
\(613\) | 40.3328 | 1.62903 | 0.814513 | − | 0.580145i | \(-0.197004\pi\) | ||||
0.814513 | + | 0.580145i | \(0.197004\pi\) | |||||||
\(614\) | 64.2440 | 2.59268 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 97.7068 | 3.93672 | ||||||||
\(617\) | 5.61640 | 0.226108 | 0.113054 | − | 0.993589i | \(-0.463937\pi\) | ||||
0.113054 | + | 0.993589i | \(0.463937\pi\) | |||||||
\(618\) | −43.5362 | −1.75128 | ||||||||
\(619\) | −26.8598 | −1.07959 | −0.539794 | − | 0.841797i | \(-0.681498\pi\) | ||||
−0.539794 | + | 0.841797i | \(0.681498\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.50248 | 0.260936 | ||||||||
\(622\) | 21.7054 | 0.870308 | ||||||||
\(623\) | 18.8757 | 0.756238 | ||||||||
\(624\) | 14.9955 | 0.600299 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 70.1029 | 2.80188 | ||||||||
\(627\) | 10.4364 | 0.416790 | ||||||||
\(628\) | −103.318 | −4.12282 | ||||||||
\(629\) | −7.65064 | −0.305051 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −46.1673 | −1.83789 | −0.918946 | − | 0.394384i | \(-0.870958\pi\) | ||||
−0.918946 | + | 0.394384i | \(0.870958\pi\) | |||||||
\(632\) | −42.2287 | −1.67977 | ||||||||
\(633\) | 4.09406 | 0.162724 | ||||||||
\(634\) | −31.9995 | −1.27086 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 34.0402 | 1.34978 | ||||||||
\(637\) | 30.3689 | 1.20326 | ||||||||
\(638\) | 52.6187 | 2.08320 | ||||||||
\(639\) | −2.81951 | −0.111538 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.1813 | −0.718119 | −0.359059 | − | 0.933315i | \(-0.616902\pi\) | ||||
−0.359059 | + | 0.933315i | \(0.616902\pi\) | |||||||
\(642\) | 26.3440 | 1.03972 | ||||||||
\(643\) | −23.3628 | −0.921338 | −0.460669 | − | 0.887572i | \(-0.652391\pi\) | ||||
−0.460669 | + | 0.887572i | \(0.652391\pi\) | |||||||
\(644\) | −166.899 | −6.57675 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 46.2615 | 1.82013 | ||||||||
\(647\) | 36.0372 | 1.41677 | 0.708383 | − | 0.705828i | \(-0.249425\pi\) | ||||
0.708383 | + | 0.705828i | \(0.249425\pi\) | |||||||
\(648\) | −7.58955 | −0.298146 | ||||||||
\(649\) | −18.8914 | −0.741552 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 29.8774 | 1.17099 | ||||||||
\(652\) | −95.7692 | −3.75061 | ||||||||
\(653\) | 39.5118 | 1.54622 | 0.773109 | − | 0.634274i | \(-0.218701\pi\) | ||||
0.773109 | + | 0.634274i | \(0.218701\pi\) | |||||||
\(654\) | 24.0527 | 0.940534 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −95.3251 | −3.72182 | ||||||||
\(657\) | −5.10213 | −0.199053 | ||||||||
\(658\) | −13.7756 | −0.537028 | ||||||||
\(659\) | 2.13562 | 0.0831919 | 0.0415960 | − | 0.999135i | \(-0.486756\pi\) | ||||
0.0415960 | + | 0.999135i | \(0.486756\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.344591 | 0.0134030 | 0.00670151 | − | 0.999978i | \(-0.497867\pi\) | ||||
0.00670151 | + | 0.999978i | \(0.497867\pi\) | |||||||
\(662\) | −23.4047 | −0.909648 | ||||||||
\(663\) | −6.12555 | −0.237896 | ||||||||
\(664\) | 117.617 | 4.56444 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.84815 | −0.187862 | ||||||||
\(667\) | −53.1287 | −2.05715 | ||||||||
\(668\) | 13.9251 | 0.538780 | ||||||||
\(669\) | 21.0775 | 0.814904 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.6034 | 1.14283 | ||||||||
\(672\) | 60.0441 | 2.31625 | ||||||||
\(673\) | −27.1613 | −1.04699 | −0.523495 | − | 0.852029i | \(-0.675372\pi\) | ||||
−0.523495 | + | 0.852029i | \(0.675372\pi\) | |||||||
\(674\) | 1.12307 | 0.0432591 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −52.8903 | −2.03424 | ||||||||
\(677\) | −13.1729 | −0.506275 | −0.253137 | − | 0.967430i | \(-0.581462\pi\) | ||||
−0.253137 | + | 0.967430i | \(0.581462\pi\) | |||||||
\(678\) | 30.0712 | 1.15488 | ||||||||
\(679\) | −17.5664 | −0.674136 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.70842 | 0.0654667 | ||||||||
\(682\) | 36.6665 | 1.40403 | ||||||||
\(683\) | −15.2104 | −0.582011 | −0.291006 | − | 0.956721i | \(-0.593990\pi\) | ||||
−0.291006 | + | 0.956721i | \(0.593990\pi\) | |||||||
\(684\) | 20.8074 | 0.795589 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 186.490 | 7.12021 | ||||||||
\(687\) | 5.07837 | 0.193752 | ||||||||
\(688\) | 44.0569 | 1.67965 | ||||||||
\(689\) | 10.2910 | 0.392057 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.3184 | 0.506656 | 0.253328 | − | 0.967380i | \(-0.418475\pi\) | ||||
0.253328 | + | 0.967380i | \(0.418475\pi\) | |||||||
\(692\) | 39.0877 | 1.48589 | ||||||||
\(693\) | −12.8739 | −0.489037 | ||||||||
\(694\) | 36.3260 | 1.37891 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 62.0106 | 2.35051 | ||||||||
\(697\) | 38.9397 | 1.47495 | ||||||||
\(698\) | −58.6018 | −2.21811 | ||||||||
\(699\) | −0.738739 | −0.0279417 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.9303 | −0.941604 | −0.470802 | − | 0.882239i | \(-0.656035\pi\) | ||||
−0.470802 | + | 0.882239i | \(0.656035\pi\) | |||||||
\(702\) | −3.88171 | −0.146506 | ||||||||
\(703\) | 7.85663 | 0.296318 | ||||||||
\(704\) | 23.9307 | 0.901924 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 52.7084 | 1.98371 | ||||||||
\(707\) | 6.81870 | 0.256444 | ||||||||
\(708\) | −37.6643 | −1.41551 | ||||||||
\(709\) | 17.1322 | 0.643414 | 0.321707 | − | 0.946839i | \(-0.395743\pi\) | ||||
0.321707 | + | 0.946839i | \(0.395743\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.56405 | 0.208668 | ||||||||
\(712\) | 27.2995 | 1.02309 | ||||||||
\(713\) | −37.0219 | −1.38648 | ||||||||
\(714\) | −57.0659 | −2.13564 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −57.0277 | −2.13122 | ||||||||
\(717\) | −3.36660 | −0.125728 | ||||||||
\(718\) | 49.5002 | 1.84733 | ||||||||
\(719\) | −36.7634 | −1.37104 | −0.685521 | − | 0.728053i | \(-0.740426\pi\) | ||||
−0.685521 | + | 0.728053i | \(0.740426\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −87.0300 | −3.24117 | ||||||||
\(722\) | 2.36985 | 0.0881965 | ||||||||
\(723\) | 6.51135 | 0.242160 | ||||||||
\(724\) | 95.5392 | 3.55069 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 13.0769 | 0.485329 | ||||||||
\(727\) | −46.9974 | −1.74304 | −0.871519 | − | 0.490362i | \(-0.836865\pi\) | ||||
−0.871519 | + | 0.490362i | \(0.836865\pi\) | |||||||
\(728\) | 58.8922 | 2.18269 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.9969 | −0.665641 | ||||||||
\(732\) | 59.0212 | 2.18149 | ||||||||
\(733\) | −0.790148 | −0.0291848 | −0.0145924 | − | 0.999894i | \(-0.504645\pi\) | ||||
−0.0145924 | + | 0.999894i | \(0.504645\pi\) | |||||||
\(734\) | 56.6196 | 2.08987 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −74.4022 | −2.74250 | ||||||||
\(737\) | 14.3368 | 0.528102 | ||||||||
\(738\) | 24.6758 | 0.908328 | ||||||||
\(739\) | 34.4106 | 1.26581 | 0.632907 | − | 0.774228i | \(-0.281861\pi\) | ||||
0.632907 | + | 0.774228i | \(0.281861\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.29048 | 0.231086 | ||||||||
\(742\) | 95.8717 | 3.51956 | ||||||||
\(743\) | 26.4476 | 0.970267 | 0.485133 | − | 0.874440i | \(-0.338771\pi\) | ||||
0.485133 | + | 0.874440i | \(0.338771\pi\) | |||||||
\(744\) | 43.2111 | 1.58420 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −22.3070 | −0.816718 | ||||||||
\(747\) | −15.4973 | −0.567016 | ||||||||
\(748\) | −49.7076 | −1.81749 | ||||||||
\(749\) | 52.6624 | 1.92424 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 47.6505 | 1.73879 | 0.869396 | − | 0.494117i | \(-0.164508\pi\) | ||||
0.869396 | + | 0.494117i | \(0.164508\pi\) | |||||||
\(752\) | −10.1410 | −0.369806 | ||||||||
\(753\) | 11.7004 | 0.426387 | ||||||||
\(754\) | 31.7156 | 1.15501 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −25.6670 | −0.933499 | ||||||||
\(757\) | 32.3523 | 1.17587 | 0.587933 | − | 0.808910i | \(-0.299942\pi\) | ||||
0.587933 | + | 0.808910i | \(0.299942\pi\) | |||||||
\(758\) | −34.0677 | −1.23739 | ||||||||
\(759\) | 15.9523 | 0.579033 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.25280 | −0.0816639 | −0.0408319 | − | 0.999166i | \(-0.513001\pi\) | ||||
−0.0408319 | + | 0.999166i | \(0.513001\pi\) | |||||||
\(762\) | 19.7081 | 0.713950 | ||||||||
\(763\) | 48.0819 | 1.74068 | ||||||||
\(764\) | −113.047 | −4.08991 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −75.6949 | −2.73497 | ||||||||
\(767\) | −11.3867 | −0.411149 | ||||||||
\(768\) | −12.3620 | −0.446076 | ||||||||
\(769\) | 2.40249 | 0.0866361 | 0.0433181 | − | 0.999061i | \(-0.486207\pi\) | ||||
0.0433181 | + | 0.999061i | \(0.486207\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.1645 | −1.01432 | ||||||||
\(772\) | −84.3057 | −3.03423 | ||||||||
\(773\) | −16.0770 | −0.578248 | −0.289124 | − | 0.957292i | \(-0.593364\pi\) | ||||
−0.289124 | + | 0.957292i | \(0.593364\pi\) | |||||||
\(774\) | −11.4045 | −0.409927 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −25.4059 | −0.912019 | ||||||||
\(777\) | −9.69157 | −0.347683 | ||||||||
\(778\) | −56.6506 | −2.03102 | ||||||||
\(779\) | −39.9881 | −1.43272 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.91700 | −0.247510 | ||||||||
\(782\) | 70.7119 | 2.52865 | ||||||||
\(783\) | −8.17052 | −0.291991 | ||||||||
\(784\) | 208.274 | 7.43834 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −32.6280 | −1.16380 | ||||||||
\(787\) | −18.5923 | −0.662745 | −0.331372 | − | 0.943500i | \(-0.607512\pi\) | ||||
−0.331372 | + | 0.943500i | \(0.607512\pi\) | |||||||
\(788\) | −54.3190 | −1.93504 | ||||||||
\(789\) | 15.2487 | 0.542869 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 60.1131 | 2.13738 | ||||||||
\(792\) | −18.6192 | −0.661604 | ||||||||
\(793\) | 17.8433 | 0.633634 | ||||||||
\(794\) | −43.6728 | −1.54989 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −112.795 | −3.99793 | ||||||||
\(797\) | 19.2123 | 0.680535 | 0.340267 | − | 0.940329i | \(-0.389482\pi\) | ||||
0.340267 | + | 0.940329i | \(0.389482\pi\) | |||||||
\(798\) | 58.6024 | 2.07450 | ||||||||
\(799\) | 4.14255 | 0.146553 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.59698 | −0.127093 | ||||||||
\(802\) | 87.9741 | 3.10647 | ||||||||
\(803\) | −12.5169 | −0.441711 | ||||||||
\(804\) | 28.5836 | 1.00807 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 22.1005 | 0.778457 | ||||||||
\(807\) | −7.75275 | −0.272910 | ||||||||
\(808\) | 9.86175 | 0.346935 | ||||||||
\(809\) | 15.4036 | 0.541561 | 0.270781 | − | 0.962641i | \(-0.412718\pi\) | ||||
0.270781 | + | 0.962641i | \(0.412718\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.0580 | −0.563872 | −0.281936 | − | 0.959433i | \(-0.590977\pi\) | ||||
−0.281936 | + | 0.959433i | \(0.590977\pi\) | |||||||
\(812\) | 209.713 | 7.35947 | ||||||||
\(813\) | −14.9314 | −0.523668 | ||||||||
\(814\) | −11.8938 | −0.416878 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −42.0097 | −1.47063 | ||||||||
\(817\) | 18.4815 | 0.646586 | ||||||||
\(818\) | 31.1906 | 1.09055 | ||||||||
\(819\) | −7.75963 | −0.271144 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.4199 | −0.852259 | −0.426130 | − | 0.904662i | \(-0.640123\pi\) | ||||
−0.426130 | + | 0.904662i | \(0.640123\pi\) | |||||||
\(822\) | −33.4398 | −1.16635 | ||||||||
\(823\) | −36.9868 | −1.28928 | −0.644640 | − | 0.764486i | \(-0.722993\pi\) | ||||
−0.644640 | + | 0.764486i | \(0.722993\pi\) | |||||||
\(824\) | −125.870 | −4.38488 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −106.079 | −3.69096 | ||||||||
\(827\) | −11.7608 | −0.408963 | −0.204481 | − | 0.978870i | \(-0.565551\pi\) | ||||
−0.204481 | + | 0.978870i | \(0.565551\pi\) | |||||||
\(828\) | 31.8046 | 1.10529 | ||||||||
\(829\) | 1.09175 | 0.0379182 | 0.0189591 | − | 0.999820i | \(-0.493965\pi\) | ||||
0.0189591 | + | 0.999820i | \(0.493965\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19.0645 | 0.661342 | ||||||||
\(832\) | 14.4241 | 0.500066 | ||||||||
\(833\) | −85.0784 | −2.94779 | ||||||||
\(834\) | 36.0255 | 1.24746 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 51.0460 | 1.76546 | ||||||||
\(837\) | −5.69350 | −0.196796 | ||||||||
\(838\) | 6.62549 | 0.228874 | ||||||||
\(839\) | −9.05720 | −0.312689 | −0.156345 | − | 0.987703i | \(-0.549971\pi\) | ||||
−0.156345 | + | 0.987703i | \(0.549971\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 37.7574 | 1.30198 | ||||||||
\(842\) | −38.7929 | −1.33689 | ||||||||
\(843\) | −11.2828 | −0.388601 | ||||||||
\(844\) | 20.0247 | 0.689277 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.62510 | 0.0902528 | ||||||||
\(847\) | 26.1410 | 0.898216 | ||||||||
\(848\) | 70.5770 | 2.42362 | ||||||||
\(849\) | −16.9950 | −0.583266 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.0091 | 0.411666 | ||||||||
\(852\) | −13.7906 | −0.472459 | ||||||||
\(853\) | −23.2497 | −0.796053 | −0.398027 | − | 0.917374i | \(-0.630305\pi\) | ||||
−0.398027 | + | 0.917374i | \(0.630305\pi\) | |||||||
\(854\) | 166.229 | 5.68824 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 76.1645 | 2.60325 | ||||||||
\(857\) | 22.9394 | 0.783596 | 0.391798 | − | 0.920051i | \(-0.371853\pi\) | ||||
0.391798 | + | 0.920051i | \(0.371853\pi\) | |||||||
\(858\) | −9.52287 | −0.325105 | ||||||||
\(859\) | −1.31714 | −0.0449402 | −0.0224701 | − | 0.999748i | \(-0.507153\pi\) | ||||
−0.0224701 | + | 0.999748i | \(0.507153\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 49.3275 | 1.68108 | ||||||||
\(862\) | 75.1949 | 2.56115 | ||||||||
\(863\) | −42.4780 | −1.44597 | −0.722983 | − | 0.690865i | \(-0.757230\pi\) | ||||
−0.722983 | + | 0.690865i | \(0.757230\pi\) | |||||||
\(864\) | −11.4421 | −0.389269 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −36.7539 | −1.24895 | ||||||||
\(867\) | 0.160687 | 0.00545722 | ||||||||
\(868\) | 146.135 | 4.96014 | ||||||||
\(869\) | 13.6501 | 0.463048 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.64140 | 0.292803 | ||||||||
\(872\) | 69.5399 | 2.35492 | ||||||||
\(873\) | 3.34748 | 0.113295 | ||||||||
\(874\) | −72.6158 | −2.45627 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −24.9553 | −0.843160 | ||||||||
\(877\) | −50.9867 | −1.72170 | −0.860850 | − | 0.508859i | \(-0.830068\pi\) | ||||
−0.860850 | + | 0.508859i | \(0.830068\pi\) | |||||||
\(878\) | 60.5830 | 2.04458 | ||||||||
\(879\) | −29.7556 | −1.00363 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.851944 | 0.0287027 | 0.0143514 | − | 0.999897i | \(-0.495432\pi\) | ||||
0.0143514 | + | 0.999897i | \(0.495432\pi\) | |||||||
\(882\) | −53.9135 | −1.81536 | ||||||||
\(883\) | 21.6486 | 0.728532 | 0.364266 | − | 0.931295i | \(-0.381320\pi\) | ||||
0.364266 | + | 0.931295i | \(0.381320\pi\) | |||||||
\(884\) | −29.9609 | −1.00770 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 45.2415 | 1.51992 | ||||||||
\(887\) | 20.7832 | 0.697830 | 0.348915 | − | 0.937154i | \(-0.386550\pi\) | ||||
0.348915 | + | 0.937154i | \(0.386550\pi\) | |||||||
\(888\) | −14.0167 | −0.470370 | ||||||||
\(889\) | 39.3970 | 1.32133 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.45327 | 0.0821875 | ||||||||
\(892\) | 103.093 | 3.45182 | ||||||||
\(893\) | −4.25408 | −0.142358 | ||||||||
\(894\) | −16.5635 | −0.553968 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 14.2876 | 0.477314 | ||||||||
\(897\) | 9.61516 | 0.321041 | ||||||||
\(898\) | 37.9180 | 1.26534 | ||||||||
\(899\) | 46.5189 | 1.55149 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28.8302 | −0.960475 | ||||||||
\(902\) | 60.5362 | 2.01564 | ||||||||
\(903\) | −22.7979 | −0.758667 | ||||||||
\(904\) | 86.9404 | 2.89159 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −20.4895 | −0.680719 | ||||||||
\(907\) | 31.4193 | 1.04326 | 0.521631 | − | 0.853171i | \(-0.325324\pi\) | ||||
0.521631 | + | 0.853171i | \(0.325324\pi\) | |||||||
\(908\) | 8.35612 | 0.277308 | ||||||||
\(909\) | −1.29938 | −0.0430979 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 53.0020 | 1.75603 | 0.878017 | − | 0.478630i | \(-0.158867\pi\) | ||||
0.878017 | + | 0.478630i | \(0.158867\pi\) | |||||||
\(912\) | 43.1408 | 1.42854 | ||||||||
\(913\) | −38.0189 | −1.25824 | ||||||||
\(914\) | −76.9757 | −2.54613 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 24.8391 | 0.820706 | ||||||||
\(917\) | −65.2242 | −2.15389 | ||||||||
\(918\) | 10.8746 | 0.358915 | ||||||||
\(919\) | −29.1849 | −0.962720 | −0.481360 | − | 0.876523i | \(-0.659857\pi\) | ||||
−0.481360 | + | 0.876523i | \(0.659857\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24.4730 | −0.806412 | ||||||||
\(922\) | 26.2704 | 0.865170 | ||||||||
\(923\) | −4.16918 | −0.137230 | ||||||||
\(924\) | −62.9679 | −2.07149 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 17.7012 | 0.581698 | ||||||||
\(927\) | 16.5846 | 0.544710 | ||||||||
\(928\) | 93.4881 | 3.06890 | ||||||||
\(929\) | 3.60942 | 0.118421 | 0.0592106 | − | 0.998246i | \(-0.481142\pi\) | ||||
0.0592106 | + | 0.998246i | \(0.481142\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 87.3691 | 2.86341 | ||||||||
\(932\) | −3.61328 | −0.118357 | ||||||||
\(933\) | −8.26842 | −0.270696 | ||||||||
\(934\) | 59.3287 | 1.94129 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −11.2226 | −0.366822 | ||||||||
\(937\) | −2.39765 | −0.0783279 | −0.0391640 | − | 0.999233i | \(-0.512469\pi\) | ||||
−0.0391640 | + | 0.999233i | \(0.512469\pi\) | |||||||
\(938\) | 80.5038 | 2.62854 | ||||||||
\(939\) | −26.7049 | −0.871480 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.61594 | −0.0852774 | −0.0426387 | − | 0.999091i | \(-0.513576\pi\) | ||||
−0.0426387 | + | 0.999091i | \(0.513576\pi\) | |||||||
\(942\) | 55.4509 | 1.80669 | ||||||||
\(943\) | −61.1229 | −1.99044 | ||||||||
\(944\) | −78.0911 | −2.54165 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −27.9783 | −0.909654 | ||||||||
\(947\) | −49.1337 | −1.59663 | −0.798316 | − | 0.602239i | \(-0.794276\pi\) | ||||
−0.798316 | + | 0.602239i | \(0.794276\pi\) | |||||||
\(948\) | 27.2146 | 0.883889 | ||||||||
\(949\) | −7.54447 | −0.244904 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.1898 | 0.395283 | ||||||||
\(952\) | −164.986 | −5.34723 | ||||||||
\(953\) | 52.3473 | 1.69569 | 0.847847 | − | 0.530240i | \(-0.177898\pi\) | ||||
0.847847 | + | 0.530240i | \(0.177898\pi\) | |||||||
\(954\) | −18.2695 | −0.591497 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −16.4665 | −0.532565 | ||||||||
\(957\) | −20.0445 | −0.647946 | ||||||||
\(958\) | −73.5109 | −2.37503 | ||||||||
\(959\) | −66.8471 | −2.15860 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.41592 | 0.0456750 | ||||||||
\(962\) | −7.16892 | −0.231135 | ||||||||
\(963\) | −10.0354 | −0.323388 | ||||||||
\(964\) | 31.8480 | 1.02575 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 89.5754 | 2.88204 | ||||||||
\(967\) | −34.5982 | −1.11260 | −0.556301 | − | 0.830981i | \(-0.687780\pi\) | ||||
−0.556301 | + | 0.830981i | \(0.687780\pi\) | |||||||
\(968\) | 37.8072 | 1.21517 | ||||||||
\(969\) | −17.6227 | −0.566124 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.0689 | 0.579857 | 0.289929 | − | 0.957048i | \(-0.406368\pi\) | ||||
0.289929 | + | 0.957048i | \(0.406368\pi\) | |||||||
\(972\) | 4.89115 | 0.156884 | ||||||||
\(973\) | 72.0158 | 2.30872 | ||||||||
\(974\) | 77.5348 | 2.48437 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 122.371 | 3.91701 | ||||||||
\(977\) | 4.72708 | 0.151233 | 0.0756163 | − | 0.997137i | \(-0.475908\pi\) | ||||
0.0756163 | + | 0.997137i | \(0.475908\pi\) | |||||||
\(978\) | 51.3997 | 1.64358 | ||||||||
\(979\) | −8.82436 | −0.282028 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.16258 | −0.292539 | ||||||||
\(982\) | 26.5889 | 0.848485 | ||||||||
\(983\) | 53.3395 | 1.70126 | 0.850632 | − | 0.525761i | \(-0.176219\pi\) | ||||
0.850632 | + | 0.525761i | \(0.176219\pi\) | |||||||
\(984\) | 71.3413 | 2.27428 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −88.8511 | −2.82960 | ||||||||
\(987\) | 5.24764 | 0.167034 | ||||||||
\(988\) | 30.7677 | 0.978849 | ||||||||
\(989\) | 28.2495 | 0.898282 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.8741 | −0.567791 | −0.283895 | − | 0.958855i | \(-0.591627\pi\) | ||||
−0.283895 | + | 0.958855i | \(0.591627\pi\) | |||||||
\(992\) | 65.1457 | 2.06838 | ||||||||
\(993\) | 8.91572 | 0.282932 | ||||||||
\(994\) | −38.8403 | −1.23194 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −75.7995 | −2.40180 | ||||||||
\(997\) | −26.5743 | −0.841616 | −0.420808 | − | 0.907150i | \(-0.638253\pi\) | ||||
−0.420808 | + | 0.907150i | \(0.638253\pi\) | |||||||
\(998\) | 16.3380 | 0.517169 | ||||||||
\(999\) | 1.84684 | 0.0584316 |
(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 | 3525.2.a.bd.1.1 | ✓ | 8 | |
5.4 | even | 2 | 3525.2.a.be.1.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3525.2.a.bd.1.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
3525.2.a.be.1.8 | yes | 8 | 5.4 | even | 2 |