Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, 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("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} - 33 x^{18} + 64 x^{17} + 453 x^{16} - 846 x^{15} - 3353 x^{14} + 5985 x^{13} + \cdots - 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 2001) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Root | \(-2.80084\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.80084 | 1.98049 | 0.990247 | − | 0.139326i | \(-0.0444937\pi\) | ||||
0.990247 | + | 0.139326i | \(0.0444937\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.84471 | 2.92235 | ||||||||
\(5\) | 3.48103 | 1.55676 | 0.778381 | − | 0.627792i | \(-0.216041\pi\) | ||||
0.778381 | + | 0.627792i | \(0.216041\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.41384 | −0.534380 | −0.267190 | − | 0.963644i | \(-0.586095\pi\) | ||||
−0.267190 | + | 0.963644i | \(0.586095\pi\) | |||||||
\(8\) | 10.7684 | 3.80721 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 9.74980 | 3.08316 | ||||||||
\(11\) | 4.43439 | 1.33702 | 0.668509 | − | 0.743704i | \(-0.266933\pi\) | ||||
0.668509 | + | 0.743704i | \(0.266933\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.37735 | −0.659359 | −0.329680 | − | 0.944093i | \(-0.606941\pi\) | ||||
−0.329680 | + | 0.944093i | \(0.606941\pi\) | |||||||
\(14\) | −3.95993 | −1.05834 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 18.4712 | 4.61779 | ||||||||
\(17\) | 3.28679 | 0.797165 | 0.398582 | − | 0.917133i | \(-0.369502\pi\) | ||||
0.398582 | + | 0.917133i | \(0.369502\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.46248 | −0.794347 | −0.397173 | − | 0.917744i | \(-0.630009\pi\) | ||||
−0.397173 | + | 0.917744i | \(0.630009\pi\) | |||||||
\(20\) | 20.3456 | 4.54941 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 12.4200 | 2.64796 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.11755 | 1.42351 | ||||||||
\(26\) | −6.65859 | −1.30586 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −8.26345 | −1.56165 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.18385 | −0.751443 | −0.375721 | − | 0.926733i | \(-0.622605\pi\) | ||||
−0.375721 | + | 0.926733i | \(0.622605\pi\) | |||||||
\(32\) | 30.1980 | 5.33830 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 9.20579 | 1.57878 | ||||||||
\(35\) | −4.92160 | −0.831902 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.7653 | −1.76981 | −0.884905 | − | 0.465771i | \(-0.845777\pi\) | ||||
−0.884905 | + | 0.465771i | \(0.845777\pi\) | |||||||
\(38\) | −9.69784 | −1.57320 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 37.4851 | 5.92691 | ||||||||
\(41\) | −3.71341 | −0.579937 | −0.289968 | − | 0.957036i | \(-0.593645\pi\) | ||||
−0.289968 | + | 0.957036i | \(0.593645\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.08099 | −1.07984 | −0.539920 | − | 0.841716i | \(-0.681546\pi\) | ||||
−0.539920 | + | 0.841716i | \(0.681546\pi\) | |||||||
\(44\) | 25.9177 | 3.90724 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.80084 | −0.412961 | ||||||||
\(47\) | −1.63781 | −0.238899 | −0.119450 | − | 0.992840i | \(-0.538113\pi\) | ||||
−0.119450 | + | 0.992840i | \(0.538113\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00107 | −0.714438 | ||||||||
\(50\) | 19.9351 | 2.81925 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −13.8949 | −1.92688 | ||||||||
\(53\) | −6.97182 | −0.957653 | −0.478827 | − | 0.877910i | \(-0.658938\pi\) | ||||
−0.478827 | + | 0.877910i | \(0.658938\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.4362 | 2.08142 | ||||||||
\(56\) | −15.2248 | −2.03449 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.80084 | −0.367768 | ||||||||
\(59\) | −12.2928 | −1.60039 | −0.800195 | − | 0.599740i | \(-0.795271\pi\) | ||||
−0.800195 | + | 0.599740i | \(0.795271\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.25185 | 0.672431 | 0.336215 | − | 0.941785i | \(-0.390853\pi\) | ||||
0.336215 | + | 0.941785i | \(0.390853\pi\) | |||||||
\(62\) | −11.7183 | −1.48823 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 47.6374 | 5.95467 | ||||||||
\(65\) | −8.27563 | −1.02647 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.9828 | −1.46393 | −0.731965 | − | 0.681342i | \(-0.761397\pi\) | ||||
−0.731965 | + | 0.681342i | \(0.761397\pi\) | |||||||
\(68\) | 19.2103 | 2.32960 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −13.7846 | −1.64758 | ||||||||
\(71\) | −12.3124 | −1.46121 | −0.730604 | − | 0.682802i | \(-0.760761\pi\) | ||||
−0.730604 | + | 0.682802i | \(0.760761\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.68606 | 1.01663 | 0.508313 | − | 0.861172i | \(-0.330269\pi\) | ||||
0.508313 | + | 0.861172i | \(0.330269\pi\) | |||||||
\(74\) | −30.1520 | −3.50510 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −20.2372 | −2.32136 | ||||||||
\(77\) | −6.26950 | −0.714476 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.51988 | 1.07107 | 0.535535 | − | 0.844513i | \(-0.320110\pi\) | ||||
0.535535 | + | 0.844513i | \(0.320110\pi\) | |||||||
\(80\) | 64.2986 | 7.18881 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −10.4007 | −1.14856 | ||||||||
\(83\) | −2.12581 | −0.233338 | −0.116669 | − | 0.993171i | \(-0.537222\pi\) | ||||
−0.116669 | + | 0.993171i | \(0.537222\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.4414 | 1.24100 | ||||||||
\(86\) | −19.8327 | −2.13862 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 47.7513 | 5.09031 | ||||||||
\(89\) | 11.0119 | 1.16726 | 0.583632 | − | 0.812018i | \(-0.301631\pi\) | ||||
0.583632 | + | 0.812018i | \(0.301631\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.36119 | 0.352348 | ||||||||
\(92\) | −5.84471 | −0.609353 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.58725 | −0.473139 | ||||||||
\(95\) | −12.0530 | −1.23661 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.3407 | 1.25301 | 0.626505 | − | 0.779417i | \(-0.284485\pi\) | ||||
0.626505 | + | 0.779417i | \(0.284485\pi\) | |||||||
\(98\) | −14.0072 | −1.41494 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 41.6000 | 4.16000 | ||||||||
\(101\) | 17.4826 | 1.73959 | 0.869794 | − | 0.493416i | \(-0.164252\pi\) | ||||
0.869794 | + | 0.493416i | \(0.164252\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.0681 | −0.992040 | −0.496020 | − | 0.868311i | \(-0.665206\pi\) | ||||
−0.496020 | + | 0.868311i | \(0.665206\pi\) | |||||||
\(104\) | −25.6003 | −2.51032 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −19.5270 | −1.89663 | ||||||||
\(107\) | 8.64089 | 0.835346 | 0.417673 | − | 0.908597i | \(-0.362846\pi\) | ||||
0.417673 | + | 0.908597i | \(0.362846\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.68708 | −0.736289 | −0.368144 | − | 0.929769i | \(-0.620007\pi\) | ||||
−0.368144 | + | 0.929769i | \(0.620007\pi\) | |||||||
\(110\) | 43.2344 | 4.12224 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −26.1152 | −2.46765 | ||||||||
\(113\) | 5.51803 | 0.519092 | 0.259546 | − | 0.965731i | \(-0.416427\pi\) | ||||
0.259546 | + | 0.965731i | \(0.416427\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.48103 | −0.324607 | ||||||||
\(116\) | −5.84471 | −0.542667 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −34.4302 | −3.16956 | ||||||||
\(119\) | −4.64699 | −0.425989 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.66381 | 0.787619 | ||||||||
\(122\) | 14.7096 | 1.33174 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −24.4534 | −2.19598 | ||||||||
\(125\) | 7.37123 | 0.659303 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.7499 | 1.13137 | 0.565684 | − | 0.824622i | \(-0.308612\pi\) | ||||
0.565684 | + | 0.824622i | \(0.308612\pi\) | |||||||
\(128\) | 73.0287 | 6.45489 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −23.1787 | −2.03291 | ||||||||
\(131\) | 14.4611 | 1.26347 | 0.631735 | − | 0.775185i | \(-0.282343\pi\) | ||||
0.631735 | + | 0.775185i | \(0.282343\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.89537 | 0.424483 | ||||||||
\(134\) | −33.5619 | −2.89930 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 35.3935 | 3.03497 | ||||||||
\(137\) | −9.36729 | −0.800302 | −0.400151 | − | 0.916449i | \(-0.631042\pi\) | ||||
−0.400151 | + | 0.916449i | \(0.631042\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.17859 | −0.608880 | −0.304440 | − | 0.952532i | \(-0.598469\pi\) | ||||
−0.304440 | + | 0.952532i | \(0.598469\pi\) | |||||||
\(140\) | −28.7653 | −2.43111 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −34.4849 | −2.89391 | ||||||||
\(143\) | −10.5421 | −0.881575 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.48103 | −0.289084 | ||||||||
\(146\) | 24.3283 | 2.01342 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −62.9202 | −5.17201 | ||||||||
\(149\) | −12.0231 | −0.984974 | −0.492487 | − | 0.870320i | \(-0.663912\pi\) | ||||
−0.492487 | + | 0.870320i | \(0.663912\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.1232 | 1.14933 | 0.574665 | − | 0.818389i | \(-0.305132\pi\) | ||||
0.574665 | + | 0.818389i | \(0.305132\pi\) | |||||||
\(152\) | −37.2853 | −3.02424 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −17.5599 | −1.41501 | ||||||||
\(155\) | −14.5641 | −1.16982 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.7785 | 1.01983 | 0.509917 | − | 0.860224i | \(-0.329676\pi\) | ||||
0.509917 | + | 0.860224i | \(0.329676\pi\) | |||||||
\(158\) | 26.6637 | 2.12125 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 105.120 | 8.31046 | ||||||||
\(161\) | 1.41384 | 0.111426 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.0242 | 1.41177 | 0.705883 | − | 0.708328i | \(-0.250550\pi\) | ||||
0.705883 | + | 0.708328i | \(0.250550\pi\) | |||||||
\(164\) | −21.7038 | −1.69478 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.95405 | −0.462124 | ||||||||
\(167\) | −6.24398 | −0.483174 | −0.241587 | − | 0.970379i | \(-0.577668\pi\) | ||||
−0.241587 | + | 0.970379i | \(0.577668\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.34819 | −0.565246 | ||||||||
\(170\) | 32.0456 | 2.45778 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −41.3863 | −3.15567 | ||||||||
\(173\) | 21.4424 | 1.63024 | 0.815119 | − | 0.579293i | \(-0.196671\pi\) | ||||
0.815119 | + | 0.579293i | \(0.196671\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.0630 | −0.760694 | ||||||||
\(176\) | 81.9084 | 6.17407 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 30.8427 | 2.31176 | ||||||||
\(179\) | −19.8711 | −1.48524 | −0.742618 | − | 0.669715i | \(-0.766416\pi\) | ||||
−0.742618 | + | 0.669715i | \(0.766416\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.142040 | −0.0105578 | −0.00527889 | − | 0.999986i | \(-0.501680\pi\) | ||||
−0.00527889 | + | 0.999986i | \(0.501680\pi\) | |||||||
\(182\) | 9.41415 | 0.697823 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10.7684 | −0.793857 | ||||||||
\(185\) | −37.4744 | −2.75517 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.5749 | 1.06582 | ||||||||
\(188\) | −9.57253 | −0.698148 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −33.7584 | −2.44910 | ||||||||
\(191\) | 14.5967 | 1.05618 | 0.528091 | − | 0.849188i | \(-0.322908\pi\) | ||||
0.528091 | + | 0.849188i | \(0.322908\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.3067 | −1.24576 | −0.622881 | − | 0.782317i | \(-0.714038\pi\) | ||||
−0.622881 | + | 0.782317i | \(0.714038\pi\) | |||||||
\(194\) | 34.5644 | 2.48158 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −29.2298 | −2.08784 | ||||||||
\(197\) | −2.11009 | −0.150338 | −0.0751689 | − | 0.997171i | \(-0.523950\pi\) | ||||
−0.0751689 | + | 0.997171i | \(0.523950\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.4313 | 1.16478 | 0.582391 | − | 0.812909i | \(-0.302117\pi\) | ||||
0.582391 | + | 0.812909i | \(0.302117\pi\) | |||||||
\(200\) | 76.6446 | 5.41959 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 48.9661 | 3.44524 | ||||||||
\(203\) | 1.41384 | 0.0992318 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.9265 | −0.902824 | ||||||||
\(206\) | −28.1992 | −1.96473 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −43.9125 | −3.04478 | ||||||||
\(209\) | −15.3540 | −1.06206 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.03335 | 0.346510 | 0.173255 | − | 0.984877i | \(-0.444572\pi\) | ||||
0.173255 | + | 0.984877i | \(0.444572\pi\) | |||||||
\(212\) | −40.7482 | −2.79860 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 24.2018 | 1.65440 | ||||||||
\(215\) | −24.6491 | −1.68105 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.91528 | 0.401556 | ||||||||
\(218\) | −21.5303 | −1.45821 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 90.2202 | 6.08264 | ||||||||
\(221\) | −7.81387 | −0.525618 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.74485 | −0.317739 | −0.158869 | − | 0.987300i | \(-0.550785\pi\) | ||||
−0.158869 | + | 0.987300i | \(0.550785\pi\) | |||||||
\(224\) | −42.6950 | −2.85268 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.4551 | 1.02806 | ||||||||
\(227\) | 15.9414 | 1.05806 | 0.529032 | − | 0.848602i | \(-0.322555\pi\) | ||||
0.529032 | + | 0.848602i | \(0.322555\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.6062 | 1.62602 | 0.813012 | − | 0.582247i | \(-0.197826\pi\) | ||||
0.813012 | + | 0.582247i | \(0.197826\pi\) | |||||||
\(230\) | −9.74980 | −0.642883 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.7684 | −0.706980 | ||||||||
\(233\) | 3.43090 | 0.224765 | 0.112383 | − | 0.993665i | \(-0.464152\pi\) | ||||
0.112383 | + | 0.993665i | \(0.464152\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.70127 | −0.371910 | ||||||||
\(236\) | −71.8479 | −4.67690 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −13.0155 | −0.843668 | ||||||||
\(239\) | −5.76650 | −0.373004 | −0.186502 | − | 0.982455i | \(-0.559715\pi\) | ||||
−0.186502 | + | 0.982455i | \(0.559715\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.8383 | 1.27790 | 0.638948 | − | 0.769250i | \(-0.279370\pi\) | ||||
0.638948 | + | 0.769250i | \(0.279370\pi\) | |||||||
\(242\) | 24.2659 | 1.55987 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 30.6955 | 1.96508 | ||||||||
\(245\) | −17.4089 | −1.11221 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.23153 | 0.523760 | ||||||||
\(248\) | −45.0534 | −2.86090 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 20.6456 | 1.30574 | ||||||||
\(251\) | 1.97792 | 0.124845 | 0.0624226 | − | 0.998050i | \(-0.480117\pi\) | ||||
0.0624226 | + | 0.998050i | \(0.480117\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.43439 | −0.278788 | ||||||||
\(254\) | 35.7103 | 2.24067 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 109.267 | 6.82919 | ||||||||
\(257\) | 0.846927 | 0.0528298 | 0.0264149 | − | 0.999651i | \(-0.491591\pi\) | ||||
0.0264149 | + | 0.999651i | \(0.491591\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.2204 | 0.945751 | ||||||||
\(260\) | −48.3686 | −2.99969 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 40.5031 | 2.50229 | ||||||||
\(263\) | −0.347153 | −0.0214064 | −0.0107032 | − | 0.999943i | \(-0.503407\pi\) | ||||
−0.0107032 | + | 0.999943i | \(0.503407\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −24.2691 | −1.49084 | ||||||||
\(266\) | 13.7112 | 0.840685 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −70.0359 | −4.27812 | ||||||||
\(269\) | −22.3131 | −1.36045 | −0.680227 | − | 0.733002i | \(-0.738119\pi\) | ||||
−0.680227 | + | 0.733002i | \(0.738119\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.0578 | −1.27917 | −0.639584 | − | 0.768721i | \(-0.720893\pi\) | ||||
−0.639584 | + | 0.768721i | \(0.720893\pi\) | |||||||
\(272\) | 60.7109 | 3.68114 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −26.2363 | −1.58499 | ||||||||
\(275\) | 31.5620 | 1.90326 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.42766 | 0.145864 | 0.0729320 | − | 0.997337i | \(-0.476764\pi\) | ||||
0.0729320 | + | 0.997337i | \(0.476764\pi\) | |||||||
\(278\) | −20.1061 | −1.20588 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −52.9978 | −3.16722 | ||||||||
\(281\) | −11.6621 | −0.695703 | −0.347852 | − | 0.937550i | \(-0.613089\pi\) | ||||
−0.347852 | + | 0.937550i | \(0.613089\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.95812 | −0.473061 | −0.236530 | − | 0.971624i | \(-0.576010\pi\) | ||||
−0.236530 | + | 0.971624i | \(0.576010\pi\) | |||||||
\(284\) | −71.9621 | −4.27016 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −29.5268 | −1.74595 | ||||||||
\(287\) | 5.25015 | 0.309906 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.19698 | −0.364528 | ||||||||
\(290\) | −9.74980 | −0.572528 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 50.7675 | 2.97094 | ||||||||
\(293\) | 25.6929 | 1.50099 | 0.750497 | − | 0.660874i | \(-0.229814\pi\) | ||||
0.750497 | + | 0.660874i | \(0.229814\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −42.7917 | −2.49143 | ||||||||
\(296\) | −115.926 | −6.73803 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −33.6749 | −1.95073 | ||||||||
\(299\) | 2.37735 | 0.137486 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.0114 | 0.577045 | ||||||||
\(302\) | 39.5568 | 2.27624 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −63.9560 | −3.66813 | ||||||||
\(305\) | 18.2818 | 1.04681 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.5614 | 1.05936 | 0.529679 | − | 0.848198i | \(-0.322312\pi\) | ||||
0.529679 | + | 0.848198i | \(0.322312\pi\) | |||||||
\(308\) | −36.6434 | −2.08795 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −40.7917 | −2.31682 | ||||||||
\(311\) | −9.91454 | −0.562202 | −0.281101 | − | 0.959678i | \(-0.590700\pi\) | ||||
−0.281101 | + | 0.959678i | \(0.590700\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.3040 | 0.865032 | 0.432516 | − | 0.901626i | \(-0.357626\pi\) | ||||
0.432516 | + | 0.901626i | \(0.357626\pi\) | |||||||
\(314\) | 35.7905 | 2.01977 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 55.6409 | 3.13004 | ||||||||
\(317\) | −17.3563 | −0.974829 | −0.487414 | − | 0.873171i | \(-0.662060\pi\) | ||||
−0.487414 | + | 0.873171i | \(0.662060\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.43439 | −0.248278 | ||||||||
\(320\) | 165.827 | 9.27001 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.95993 | 0.220678 | ||||||||
\(323\) | −11.3804 | −0.633225 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.9209 | −0.938604 | ||||||||
\(326\) | 50.4830 | 2.79599 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −39.9875 | −2.20794 | ||||||||
\(329\) | 2.31560 | 0.127663 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.6184 | −1.40811 | −0.704057 | − | 0.710144i | \(-0.748630\pi\) | ||||
−0.704057 | + | 0.710144i | \(0.748630\pi\) | |||||||
\(332\) | −12.4247 | −0.681895 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −17.4884 | −0.956922 | ||||||||
\(335\) | −41.7124 | −2.27899 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.3884 | −0.892734 | −0.446367 | − | 0.894850i | \(-0.647282\pi\) | ||||
−0.446367 | + | 0.894850i | \(0.647282\pi\) | |||||||
\(338\) | −20.5811 | −1.11947 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 66.8717 | 3.62663 | ||||||||
\(341\) | −18.5528 | −1.00469 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9675 | 0.916161 | ||||||||
\(344\) | −76.2509 | −4.11117 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 60.0568 | 3.22868 | ||||||||
\(347\) | 25.0667 | 1.34565 | 0.672826 | − | 0.739800i | \(-0.265080\pi\) | ||||
0.672826 | + | 0.739800i | \(0.265080\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.4766 | 1.20315 | 0.601573 | − | 0.798818i | \(-0.294541\pi\) | ||||
0.601573 | + | 0.798818i | \(0.294541\pi\) | |||||||
\(350\) | −28.1850 | −1.50655 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 133.910 | 7.13741 | ||||||||
\(353\) | 2.42803 | 0.129231 | 0.0646156 | − | 0.997910i | \(-0.479418\pi\) | ||||
0.0646156 | + | 0.997910i | \(0.479418\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −42.8596 | −2.27475 | ||||||||
\(356\) | 64.3616 | 3.41116 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −55.6558 | −2.94150 | ||||||||
\(359\) | −36.3433 | −1.91812 | −0.959062 | − | 0.283195i | \(-0.908606\pi\) | ||||
−0.959062 | + | 0.283195i | \(0.908606\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.01126 | −0.369014 | ||||||||
\(362\) | −0.397832 | −0.0209096 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 19.6451 | 1.02969 | ||||||||
\(365\) | 30.2364 | 1.58265 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.2035 | 0.637016 | 0.318508 | − | 0.947920i | \(-0.396818\pi\) | ||||
0.318508 | + | 0.947920i | \(0.396818\pi\) | |||||||
\(368\) | −18.4712 | −0.962876 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −104.960 | −5.45660 | ||||||||
\(371\) | 9.85701 | 0.511750 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.00742 | 0.207497 | 0.103748 | − | 0.994604i | \(-0.466916\pi\) | ||||
0.103748 | + | 0.994604i | \(0.466916\pi\) | |||||||
\(374\) | 40.8220 | 2.11086 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −17.6366 | −0.909539 | ||||||||
\(377\) | 2.37735 | 0.122440 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.66384 | 0.188199 | 0.0940993 | − | 0.995563i | \(-0.470003\pi\) | ||||
0.0940993 | + | 0.995563i | \(0.470003\pi\) | |||||||
\(380\) | −70.4461 | −3.61381 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 40.8831 | 2.09176 | ||||||||
\(383\) | 12.5542 | 0.641488 | 0.320744 | − | 0.947166i | \(-0.396067\pi\) | ||||
0.320744 | + | 0.947166i | \(0.396067\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −21.8243 | −1.11227 | ||||||||
\(386\) | −48.4732 | −2.46722 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 72.1279 | 3.66174 | ||||||||
\(389\) | −18.2759 | −0.926623 | −0.463312 | − | 0.886195i | \(-0.653339\pi\) | ||||
−0.463312 | + | 0.886195i | \(0.653339\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.28679 | −0.166220 | ||||||||
\(392\) | −53.8535 | −2.72001 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.91003 | −0.297743 | ||||||||
\(395\) | 33.1389 | 1.66740 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.01959 | 0.452680 | 0.226340 | − | 0.974048i | \(-0.427324\pi\) | ||||
0.226340 | + | 0.974048i | \(0.427324\pi\) | |||||||
\(398\) | 46.0213 | 2.30684 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 131.469 | 6.57347 | ||||||||
\(401\) | −6.66076 | −0.332622 | −0.166311 | − | 0.986073i | \(-0.553186\pi\) | ||||
−0.166311 | + | 0.986073i | \(0.553186\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.94650 | 0.495470 | ||||||||
\(404\) | 102.181 | 5.08369 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.95993 | 0.196528 | ||||||||
\(407\) | −47.7377 | −2.36627 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.95276 | 0.195451 | 0.0977257 | − | 0.995213i | \(-0.468843\pi\) | ||||
0.0977257 | + | 0.995213i | \(0.468843\pi\) | |||||||
\(410\) | −36.2050 | −1.78804 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −58.8451 | −2.89909 | ||||||||
\(413\) | 17.3800 | 0.855216 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.39999 | −0.363251 | ||||||||
\(416\) | −71.7913 | −3.51986 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −43.0040 | −2.10339 | ||||||||
\(419\) | −4.41044 | −0.215464 | −0.107732 | − | 0.994180i | \(-0.534359\pi\) | ||||
−0.107732 | + | 0.994180i | \(0.534359\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.8860 | 0.725497 | 0.362748 | − | 0.931887i | \(-0.381838\pi\) | ||||
0.362748 | + | 0.931887i | \(0.381838\pi\) | |||||||
\(422\) | 14.0976 | 0.686260 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −75.0754 | −3.64598 | ||||||||
\(425\) | 23.3939 | 1.13477 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.42526 | −0.359333 | ||||||||
\(428\) | 50.5035 | 2.44118 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −69.0382 | −3.32932 | ||||||||
\(431\) | 2.60324 | 0.125393 | 0.0626967 | − | 0.998033i | \(-0.480030\pi\) | ||||
0.0626967 | + | 0.998033i | \(0.480030\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.93295 | 0.285119 | 0.142560 | − | 0.989786i | \(-0.454467\pi\) | ||||
0.142560 | + | 0.989786i | \(0.454467\pi\) | |||||||
\(434\) | 16.5678 | 0.795278 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −44.9287 | −2.15170 | ||||||||
\(437\) | 3.46248 | 0.165633 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.48828 | −0.405124 | −0.202562 | − | 0.979269i | \(-0.564927\pi\) | ||||
−0.202562 | + | 0.979269i | \(0.564927\pi\) | |||||||
\(440\) | 166.224 | 7.92440 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −21.8854 | −1.04098 | ||||||||
\(443\) | 21.2540 | 1.00981 | 0.504904 | − | 0.863176i | \(-0.331528\pi\) | ||||
0.504904 | + | 0.863176i | \(0.331528\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 38.3329 | 1.81715 | ||||||||
\(446\) | −13.2896 | −0.629279 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −67.3514 | −3.18206 | ||||||||
\(449\) | 10.8308 | 0.511139 | 0.255570 | − | 0.966791i | \(-0.417737\pi\) | ||||
0.255570 | + | 0.966791i | \(0.417737\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.4667 | −0.775386 | ||||||||
\(452\) | 32.2512 | 1.51697 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 44.6492 | 2.09549 | ||||||||
\(455\) | 11.7004 | 0.548522 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.24941 | 0.105223 | 0.0526114 | − | 0.998615i | \(-0.483246\pi\) | ||||
0.0526114 | + | 0.998615i | \(0.483246\pi\) | |||||||
\(458\) | 68.9180 | 3.22033 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −20.3456 | −0.948617 | ||||||||
\(461\) | −2.51632 | −0.117197 | −0.0585984 | − | 0.998282i | \(-0.518663\pi\) | ||||
−0.0585984 | + | 0.998282i | \(0.518663\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.2202 | −0.707341 | −0.353671 | − | 0.935370i | \(-0.615067\pi\) | ||||
−0.353671 | + | 0.935370i | \(0.615067\pi\) | |||||||
\(464\) | −18.4712 | −0.857502 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.60939 | 0.445146 | ||||||||
\(467\) | 6.08666 | 0.281657 | 0.140829 | − | 0.990034i | \(-0.455023\pi\) | ||||
0.140829 | + | 0.990034i | \(0.455023\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.9417 | 0.782295 | ||||||||
\(470\) | −15.9683 | −0.736564 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −132.374 | −6.09301 | ||||||||
\(473\) | −31.3998 | −1.44377 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −24.6443 | −1.13076 | ||||||||
\(476\) | −27.1603 | −1.24489 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −16.1510 | −0.738732 | ||||||||
\(479\) | 2.91970 | 0.133405 | 0.0667023 | − | 0.997773i | \(-0.478752\pi\) | ||||
0.0667023 | + | 0.997773i | \(0.478752\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.5930 | 1.16694 | ||||||||
\(482\) | 55.5639 | 2.53087 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 50.6374 | 2.30170 | ||||||||
\(485\) | 42.9584 | 1.95064 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.3220 | 1.60059 | 0.800297 | − | 0.599604i | \(-0.204675\pi\) | ||||
0.800297 | + | 0.599604i | \(0.204675\pi\) | |||||||
\(488\) | 56.5541 | 2.56008 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −48.7594 | −2.20273 | ||||||||
\(491\) | 5.12284 | 0.231190 | 0.115595 | − | 0.993296i | \(-0.463122\pi\) | ||||
0.115595 | + | 0.993296i | \(0.463122\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.28679 | −0.148030 | ||||||||
\(494\) | 23.0552 | 1.03730 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −77.2807 | −3.47001 | ||||||||
\(497\) | 17.4076 | 0.780840 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.30239 | 0.371666 | 0.185833 | − | 0.982581i | \(-0.440502\pi\) | ||||
0.185833 | + | 0.982581i | \(0.440502\pi\) | |||||||
\(500\) | 43.0827 | 1.92672 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.53984 | 0.247255 | ||||||||
\(503\) | 37.2320 | 1.66009 | 0.830045 | − | 0.557696i | \(-0.188314\pi\) | ||||
0.830045 | + | 0.557696i | \(0.188314\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 60.8575 | 2.70812 | ||||||||
\(506\) | −12.4200 | −0.552137 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 74.5192 | 3.30626 | ||||||||
\(509\) | 41.3069 | 1.83090 | 0.915449 | − | 0.402434i | \(-0.131836\pi\) | ||||
0.915449 | + | 0.402434i | \(0.131836\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.2807 | −0.543264 | ||||||||
\(512\) | 159.982 | 7.07027 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.37211 | 0.104629 | ||||||||
\(515\) | −35.0474 | −1.54437 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.26270 | −0.319413 | ||||||||
\(518\) | 42.6300 | 1.87305 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −89.1153 | −3.90796 | ||||||||
\(521\) | −24.8969 | −1.09075 | −0.545377 | − | 0.838191i | \(-0.683613\pi\) | ||||
−0.545377 | + | 0.838191i | \(0.683613\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.7859 | 0.471634 | 0.235817 | − | 0.971797i | \(-0.424223\pi\) | ||||
0.235817 | + | 0.971797i | \(0.424223\pi\) | |||||||
\(524\) | 84.5207 | 3.69230 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.972319 | −0.0423951 | ||||||||
\(527\) | −13.7515 | −0.599024 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −67.9738 | −2.95260 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 28.6120 | 1.24049 | ||||||||
\(533\) | 8.82808 | 0.382387 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 30.0792 | 1.30044 | ||||||||
\(536\) | −129.035 | −5.57348 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −62.4954 | −2.69437 | ||||||||
\(539\) | −22.1767 | −0.955217 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −42.3958 | −1.82274 | −0.911368 | − | 0.411592i | \(-0.864973\pi\) | ||||
−0.911368 | + | 0.411592i | \(0.864973\pi\) | |||||||
\(542\) | −58.9794 | −2.53338 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 99.2546 | 4.25550 | ||||||||
\(545\) | −26.7589 | −1.14623 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −43.7711 | −1.87151 | −0.935757 | − | 0.352644i | \(-0.885283\pi\) | ||||
−0.935757 | + | 0.352644i | \(0.885283\pi\) | |||||||
\(548\) | −54.7491 | −2.33876 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 88.4000 | 3.76939 | ||||||||
\(551\) | 3.46248 | 0.147506 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.4595 | −0.572358 | ||||||||
\(554\) | 6.79949 | 0.288883 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −41.9567 | −1.77936 | ||||||||
\(557\) | 10.4656 | 0.443443 | 0.221722 | − | 0.975110i | \(-0.428832\pi\) | ||||
0.221722 | + | 0.975110i | \(0.428832\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.8340 | 0.712002 | ||||||||
\(560\) | −90.9077 | −3.84155 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −32.6637 | −1.37784 | ||||||||
\(563\) | −30.1027 | −1.26868 | −0.634338 | − | 0.773055i | \(-0.718727\pi\) | ||||
−0.634338 | + | 0.773055i | \(0.718727\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.2084 | 0.808103 | ||||||||
\(566\) | −22.2894 | −0.936894 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −132.584 | −5.56312 | ||||||||
\(569\) | 7.93717 | 0.332744 | 0.166372 | − | 0.986063i | \(-0.446795\pi\) | ||||
0.166372 | + | 0.986063i | \(0.446795\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.1256 | 1.76290 | 0.881450 | − | 0.472277i | \(-0.156568\pi\) | ||||
0.881450 | + | 0.472277i | \(0.156568\pi\) | |||||||
\(572\) | −61.6155 | −2.57627 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 14.7048 | 0.613768 | ||||||||
\(575\) | −7.11755 | −0.296822 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.2008 | −1.00749 | −0.503745 | − | 0.863852i | \(-0.668045\pi\) | ||||
−0.503745 | + | 0.863852i | \(0.668045\pi\) | |||||||
\(578\) | −17.3568 | −0.721946 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −20.3456 | −0.844804 | ||||||||
\(581\) | 3.00554 | 0.124691 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30.9158 | −1.28040 | ||||||||
\(584\) | 93.5350 | 3.87051 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 71.9616 | 2.97271 | ||||||||
\(587\) | −1.25188 | −0.0516706 | −0.0258353 | − | 0.999666i | \(-0.508225\pi\) | ||||
−0.0258353 | + | 0.999666i | \(0.508225\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.4865 | 0.596906 | ||||||||
\(590\) | −119.853 | −4.93425 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −198.848 | −8.17262 | ||||||||
\(593\) | −16.3746 | −0.672426 | −0.336213 | − | 0.941786i | \(-0.609146\pi\) | ||||
−0.336213 | + | 0.941786i | \(0.609146\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.1763 | −0.663163 | ||||||||
\(596\) | −70.2717 | −2.87844 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.65859 | 0.272290 | ||||||||
\(599\) | 13.9988 | 0.571977 | 0.285989 | − | 0.958233i | \(-0.407678\pi\) | ||||
0.285989 | + | 0.958233i | \(0.407678\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.8577 | −0.646850 | −0.323425 | − | 0.946254i | \(-0.604834\pi\) | ||||
−0.323425 | + | 0.946254i | \(0.604834\pi\) | |||||||
\(602\) | 28.0402 | 1.14283 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 82.5460 | 3.35875 | ||||||||
\(605\) | 30.1589 | 1.22614 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −44.6641 | −1.81286 | −0.906430 | − | 0.422356i | \(-0.861203\pi\) | ||||
−0.906430 | + | 0.422356i | \(0.861203\pi\) | |||||||
\(608\) | −104.560 | −4.24046 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 51.2045 | 2.07321 | ||||||||
\(611\) | 3.89366 | 0.157521 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 41.5875 | 1.67971 | 0.839853 | − | 0.542814i | \(-0.182641\pi\) | ||||
0.839853 | + | 0.542814i | \(0.182641\pi\) | |||||||
\(614\) | 51.9876 | 2.09805 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −67.5125 | −2.72016 | ||||||||
\(617\) | 38.3035 | 1.54204 | 0.771020 | − | 0.636811i | \(-0.219747\pi\) | ||||
0.771020 | + | 0.636811i | \(0.219747\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −35.0276 | −1.40788 | −0.703939 | − | 0.710260i | \(-0.748577\pi\) | ||||
−0.703939 | + | 0.710260i | \(0.748577\pi\) | |||||||
\(620\) | −85.1229 | −3.41862 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −27.7690 | −1.11344 | ||||||||
\(623\) | −15.5691 | −0.623762 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.92828 | −0.397131 | ||||||||
\(626\) | 42.8640 | 1.71319 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 74.6865 | 2.98031 | ||||||||
\(629\) | −35.3835 | −1.41083 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.0346178 | 0.00137811 | 0.000689056 | − | 1.00000i | \(-0.499781\pi\) | ||||
0.000689056 | 1.00000i | \(0.499781\pi\) | ||||||||
\(632\) | 102.514 | 4.07778 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −48.6123 | −1.93064 | ||||||||
\(635\) | 44.3826 | 1.76127 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.8893 | 0.471071 | ||||||||
\(638\) | −12.4200 | −0.491713 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 254.215 | 10.0487 | ||||||||
\(641\) | 1.97337 | 0.0779435 | 0.0389718 | − | 0.999240i | \(-0.487592\pi\) | ||||
0.0389718 | + | 0.999240i | \(0.487592\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.6819 | −1.17054 | −0.585270 | − | 0.810838i | \(-0.699012\pi\) | ||||
−0.585270 | + | 0.810838i | \(0.699012\pi\) | |||||||
\(644\) | 8.26345 | 0.325626 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −31.8748 | −1.25410 | ||||||||
\(647\) | 8.97043 | 0.352664 | 0.176332 | − | 0.984331i | \(-0.443577\pi\) | ||||
0.176332 | + | 0.984331i | \(0.443577\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −54.5112 | −2.13975 | ||||||||
\(650\) | −47.3928 | −1.85890 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 105.346 | 4.12568 | ||||||||
\(653\) | 24.5006 | 0.958784 | 0.479392 | − | 0.877601i | \(-0.340857\pi\) | ||||
0.479392 | + | 0.877601i | \(0.340857\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 50.3394 | 1.96692 | ||||||||
\(656\) | −68.5910 | −2.67803 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.48562 | 0.252836 | ||||||||
\(659\) | 21.1494 | 0.823863 | 0.411931 | − | 0.911215i | \(-0.364854\pi\) | ||||
0.411931 | + | 0.911215i | \(0.364854\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.9812 | −1.16613 | −0.583067 | − | 0.812424i | \(-0.698147\pi\) | ||||
−0.583067 | + | 0.812424i | \(0.698147\pi\) | |||||||
\(662\) | −71.7530 | −2.78876 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −22.8915 | −0.888364 | ||||||||
\(665\) | 17.0409 | 0.660819 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | −36.4942 | −1.41200 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −116.830 | −4.51353 | ||||||||
\(671\) | 23.2888 | 0.899052 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.6843 | −0.450398 | −0.225199 | − | 0.974313i | \(-0.572303\pi\) | ||||
−0.225199 | + | 0.974313i | \(0.572303\pi\) | |||||||
\(674\) | −45.9013 | −1.76805 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −42.9480 | −1.65185 | ||||||||
\(677\) | −47.4614 | −1.82409 | −0.912046 | − | 0.410088i | \(-0.865498\pi\) | ||||
−0.912046 | + | 0.410088i | \(0.865498\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.4478 | −0.669583 | ||||||||
\(680\) | 123.206 | 4.72473 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −51.9635 | −1.98979 | ||||||||
\(683\) | −48.2425 | −1.84595 | −0.922975 | − | 0.384860i | \(-0.874250\pi\) | ||||
−0.922975 | + | 0.384860i | \(0.874250\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −32.6078 | −1.24588 | ||||||||
\(686\) | 47.5234 | 1.81445 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −130.794 | −4.98648 | ||||||||
\(689\) | 16.5745 | 0.631437 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.1961 | −0.654172 | −0.327086 | − | 0.944995i | \(-0.606067\pi\) | ||||
−0.327086 | + | 0.944995i | \(0.606067\pi\) | |||||||
\(692\) | 125.325 | 4.76413 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 70.2079 | 2.66506 | ||||||||
\(695\) | −24.9889 | −0.947881 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.2052 | −0.462305 | ||||||||
\(698\) | 62.9534 | 2.38282 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −58.8155 | −2.22302 | ||||||||
\(701\) | 27.6256 | 1.04340 | 0.521702 | − | 0.853128i | \(-0.325297\pi\) | ||||
0.521702 | + | 0.853128i | \(0.325297\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 37.2747 | 1.40584 | ||||||||
\(704\) | 211.243 | 7.96151 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.80053 | 0.255941 | ||||||||
\(707\) | −24.7176 | −0.929600 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.10255 | 0.304298 | 0.152149 | − | 0.988358i | \(-0.451381\pi\) | ||||
0.152149 | + | 0.988358i | \(0.451381\pi\) | |||||||
\(710\) | −120.043 | −4.50513 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 118.581 | 4.44402 | ||||||||
\(713\) | 4.18385 | 0.156687 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −36.6974 | −1.37240 | ||||||||
\(716\) | −116.141 | −4.34038 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −101.792 | −3.79883 | ||||||||
\(719\) | −21.9351 | −0.818041 | −0.409020 | − | 0.912525i | \(-0.634130\pi\) | ||||
−0.409020 | + | 0.912525i | \(0.634130\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.2347 | 0.530126 | ||||||||
\(722\) | −19.6374 | −0.730829 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.830184 | −0.0308536 | ||||||||
\(725\) | −7.11755 | −0.264339 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 49.7966 | 1.84685 | 0.923427 | − | 0.383773i | \(-0.125376\pi\) | ||||
0.923427 | + | 0.383773i | \(0.125376\pi\) | |||||||
\(728\) | 36.1946 | 1.34146 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 84.6873 | 3.13442 | ||||||||
\(731\) | −23.2737 | −0.860811 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.55178 | −0.205060 | −0.102530 | − | 0.994730i | \(-0.532694\pi\) | ||||
−0.102530 | + | 0.994730i | \(0.532694\pi\) | |||||||
\(734\) | 34.1799 | 1.26160 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −30.1980 | −1.11311 | ||||||||
\(737\) | −53.1363 | −1.95730 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.1640 | −1.29353 | −0.646765 | − | 0.762689i | \(-0.723879\pi\) | ||||
−0.646765 | + | 0.762689i | \(0.723879\pi\) | |||||||
\(740\) | −219.027 | −8.05159 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 27.6079 | 1.01352 | ||||||||
\(743\) | −49.3711 | −1.81125 | −0.905625 | − | 0.424079i | \(-0.860598\pi\) | ||||
−0.905625 | + | 0.424079i | \(0.860598\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −41.8529 | −1.53337 | ||||||||
\(746\) | 11.2242 | 0.410946 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 85.1862 | 3.11471 | ||||||||
\(749\) | −12.2168 | −0.446392 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.4065 | 0.963587 | 0.481793 | − | 0.876285i | \(-0.339986\pi\) | ||||
0.481793 | + | 0.876285i | \(0.339986\pi\) | |||||||
\(752\) | −30.2523 | −1.10319 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.65859 | 0.242491 | ||||||||
\(755\) | 49.1633 | 1.78923 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.0628 | 1.49245 | 0.746227 | − | 0.665692i | \(-0.231863\pi\) | ||||
0.746227 | + | 0.665692i | \(0.231863\pi\) | |||||||
\(758\) | 10.2618 | 0.372726 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −129.791 | −4.70802 | ||||||||
\(761\) | −39.5526 | −1.43378 | −0.716890 | − | 0.697187i | \(-0.754435\pi\) | ||||
−0.716890 | + | 0.697187i | \(0.754435\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.8683 | 0.393458 | ||||||||
\(764\) | 85.3135 | 3.08653 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 35.1622 | 1.27046 | ||||||||
\(767\) | 29.2244 | 1.05523 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.25396 | −0.333706 | −0.166853 | − | 0.985982i | \(-0.553361\pi\) | ||||
−0.166853 | + | 0.985982i | \(0.553361\pi\) | |||||||
\(770\) | −61.1263 | −2.20284 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −101.152 | −3.64055 | ||||||||
\(773\) | 32.8456 | 1.18137 | 0.590687 | − | 0.806901i | \(-0.298857\pi\) | ||||
0.590687 | + | 0.806901i | \(0.298857\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −29.7788 | −1.06969 | ||||||||
\(776\) | 132.890 | 4.77047 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −51.1878 | −1.83517 | ||||||||
\(779\) | 12.8576 | 0.460671 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −54.5978 | −1.95366 | ||||||||
\(782\) | −9.20579 | −0.329198 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −92.3756 | −3.29913 | ||||||||
\(785\) | 44.4822 | 1.58764 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.5920 | −0.912257 | −0.456129 | − | 0.889914i | \(-0.650764\pi\) | ||||
−0.456129 | + | 0.889914i | \(0.650764\pi\) | |||||||
\(788\) | −12.3329 | −0.439340 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 92.8169 | 3.30228 | ||||||||
\(791\) | −7.80158 | −0.277392 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.4855 | −0.443373 | ||||||||
\(794\) | 25.2624 | 0.896530 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 96.0359 | 3.40390 | ||||||||
\(797\) | 11.2097 | 0.397069 | 0.198534 | − | 0.980094i | \(-0.436382\pi\) | ||||
0.198534 | + | 0.980094i | \(0.436382\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.38315 | −0.190442 | ||||||||
\(800\) | 214.935 | 7.59912 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −18.6557 | −0.658756 | ||||||||
\(803\) | 38.5174 | 1.35925 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.92160 | 0.173464 | ||||||||
\(806\) | 27.8586 | 0.981276 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 188.260 | 6.62297 | ||||||||
\(809\) | −8.56734 | −0.301212 | −0.150606 | − | 0.988594i | \(-0.548122\pi\) | ||||
−0.150606 | + | 0.988594i | \(0.548122\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.1612 | 0.743069 | 0.371535 | − | 0.928419i | \(-0.378832\pi\) | ||||
0.371535 | + | 0.928419i | \(0.378832\pi\) | |||||||
\(812\) | 8.26345 | 0.289990 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −133.706 | −4.68638 | ||||||||
\(815\) | 62.7428 | 2.19778 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.5177 | 0.857767 | ||||||||
\(818\) | 11.0710 | 0.387090 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −75.5514 | −2.63837 | ||||||||
\(821\) | 11.7177 | 0.408950 | 0.204475 | − | 0.978872i | \(-0.434451\pi\) | ||||
0.204475 | + | 0.978872i | \(0.434451\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.38360 | −0.117945 | −0.0589724 | − | 0.998260i | \(-0.518782\pi\) | ||||
−0.0589724 | + | 0.998260i | \(0.518782\pi\) | |||||||
\(824\) | −108.417 | −3.77690 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 48.6787 | 1.69375 | ||||||||
\(827\) | −10.4103 | −0.362003 | −0.181001 | − | 0.983483i | \(-0.557934\pi\) | ||||
−0.181001 | + | 0.983483i | \(0.557934\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.8931 | −0.517259 | −0.258630 | − | 0.965977i | \(-0.583271\pi\) | ||||
−0.258630 | + | 0.965977i | \(0.583271\pi\) | |||||||
\(830\) | −20.7262 | −0.719417 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −113.251 | −3.92627 | ||||||||
\(833\) | −16.4375 | −0.569525 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.7355 | −0.752187 | ||||||||
\(836\) | −89.7394 | −3.10370 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −12.3529 | −0.426725 | ||||||||
\(839\) | 35.8545 | 1.23784 | 0.618918 | − | 0.785456i | \(-0.287571\pi\) | ||||
0.618918 | + | 0.785456i | \(0.287571\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 41.6932 | 1.43684 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 29.4184 | 1.01262 | ||||||||
\(845\) | −25.5793 | −0.879953 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.2492 | −0.420888 | ||||||||
\(848\) | −128.778 | −4.42224 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 65.5226 | 2.24741 | ||||||||
\(851\) | 10.7653 | 0.369031 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.4424 | 0.391779 | 0.195890 | − | 0.980626i | \(-0.437241\pi\) | ||||
0.195890 | + | 0.980626i | \(0.437241\pi\) | |||||||
\(854\) | −20.7970 | −0.711657 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 93.0486 | 3.18034 | ||||||||
\(857\) | 34.4455 | 1.17664 | 0.588319 | − | 0.808629i | \(-0.299790\pi\) | ||||
0.588319 | + | 0.808629i | \(0.299790\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.68062 | −0.0914617 | −0.0457308 | − | 0.998954i | \(-0.514562\pi\) | ||||
−0.0457308 | + | 0.998954i | \(0.514562\pi\) | |||||||
\(860\) | −144.067 | −4.91263 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.29125 | 0.248341 | ||||||||
\(863\) | −40.5322 | −1.37973 | −0.689866 | − | 0.723937i | \(-0.742330\pi\) | ||||
−0.689866 | + | 0.723937i | \(0.742330\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 74.6417 | 2.53789 | ||||||||
\(866\) | 16.6172 | 0.564677 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 34.5731 | 1.17349 | ||||||||
\(869\) | 42.2148 | 1.43204 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.4873 | 0.965256 | ||||||||
\(872\) | −82.7776 | −2.80320 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.69784 | 0.328034 | ||||||||
\(875\) | −10.4217 | −0.352318 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.5521 | 0.896600 | 0.448300 | − | 0.893883i | \(-0.352030\pi\) | ||||
0.448300 | + | 0.893883i | \(0.352030\pi\) | |||||||
\(878\) | −23.7743 | −0.802344 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 285.125 | 9.61157 | ||||||||
\(881\) | −2.87095 | −0.0967248 | −0.0483624 | − | 0.998830i | \(-0.515400\pi\) | ||||
−0.0483624 | + | 0.998830i | \(0.515400\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.0387 | 0.943578 | 0.471789 | − | 0.881711i | \(-0.343608\pi\) | ||||
0.471789 | + | 0.881711i | \(0.343608\pi\) | |||||||
\(884\) | −45.6698 | −1.53604 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 59.5290 | 1.99992 | ||||||||
\(887\) | −17.7793 | −0.596972 | −0.298486 | − | 0.954414i | \(-0.596482\pi\) | ||||
−0.298486 | + | 0.954414i | \(0.596482\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.0262 | −0.604580 | ||||||||
\(890\) | 107.364 | 3.59886 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −27.7323 | −0.928544 | ||||||||
\(893\) | 5.67089 | 0.189769 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −69.1718 | −2.31216 | ||||||||
\(896\) | −103.251 | −3.44936 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 30.3355 | 1.01231 | ||||||||
\(899\) | 4.18385 | 0.139539 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.9149 | −0.763407 | ||||||||
\(902\) | −46.1206 | −1.53565 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 59.4203 | 1.97629 | ||||||||
\(905\) | −0.494446 | −0.0164360 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.0328 | 1.59490 | 0.797451 | − | 0.603383i | \(-0.206181\pi\) | ||||
0.797451 | + | 0.603383i | \(0.206181\pi\) | |||||||
\(908\) | 93.1725 | 3.09204 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 32.7709 | 1.08634 | ||||||||
\(911\) | −36.9017 | −1.22261 | −0.611304 | − | 0.791396i | \(-0.709355\pi\) | ||||
−0.611304 | + | 0.791396i | \(0.709355\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.42666 | −0.311977 | ||||||||
\(914\) | 6.30023 | 0.208393 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 143.816 | 4.75181 | ||||||||
\(917\) | −20.4456 | −0.675172 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.31252 | −0.307192 | −0.153596 | − | 0.988134i | \(-0.549085\pi\) | ||||
−0.153596 | + | 0.988134i | \(0.549085\pi\) | |||||||
\(920\) | −37.4851 | −1.23585 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −7.04781 | −0.232107 | ||||||||
\(923\) | 29.2708 | 0.963460 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −76.6228 | −2.51934 | ||||||||
\(926\) | −42.6293 | −1.40088 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −30.1980 | −0.991297 | ||||||||
\(929\) | 30.7813 | 1.00990 | 0.504951 | − | 0.863148i | \(-0.331511\pi\) | ||||
0.504951 | + | 0.863148i | \(0.331511\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.3161 | 0.567512 | ||||||||
\(932\) | 20.0526 | 0.656844 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17.0478 | 0.557820 | ||||||||
\(935\) | 50.7357 | 1.65924 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.1120 | 1.31040 | 0.655202 | − | 0.755454i | \(-0.272584\pi\) | ||||
0.655202 | + | 0.755454i | \(0.272584\pi\) | |||||||
\(938\) | 47.4510 | 1.54933 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −33.3222 | −1.08685 | ||||||||
\(941\) | 47.6356 | 1.55287 | 0.776437 | − | 0.630194i | \(-0.217025\pi\) | ||||
0.776437 | + | 0.630194i | \(0.217025\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.71341 | 0.120925 | ||||||||
\(944\) | −227.063 | −7.39027 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −87.9460 | −2.85937 | ||||||||
\(947\) | −36.9283 | −1.20001 | −0.600004 | − | 0.799997i | \(-0.704834\pi\) | ||||
−0.600004 | + | 0.799997i | \(0.704834\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.6498 | −0.670322 | ||||||||
\(950\) | −69.0248 | −2.23946 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −50.0406 | −1.62183 | ||||||||
\(953\) | −9.59892 | −0.310939 | −0.155470 | − | 0.987841i | \(-0.549689\pi\) | ||||
−0.155470 | + | 0.987841i | \(0.549689\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 50.8115 | 1.64422 | ||||||||
\(956\) | −33.7035 | −1.09005 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.17762 | 0.264207 | ||||||||
\(959\) | 13.2438 | 0.427665 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.4954 | −0.435334 | ||||||||
\(962\) | 71.6819 | 2.31112 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 115.949 | 3.73446 | ||||||||
\(965\) | −60.2450 | −1.93935 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.4665 | −1.01190 | −0.505948 | − | 0.862564i | \(-0.668857\pi\) | ||||
−0.505948 | + | 0.862564i | \(0.668857\pi\) | |||||||
\(968\) | 93.2954 | 2.99863 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 120.320 | 3.86323 | ||||||||
\(971\) | −31.9428 | −1.02509 | −0.512547 | − | 0.858659i | \(-0.671298\pi\) | ||||
−0.512547 | + | 0.858659i | \(0.671298\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.1493 | 0.325373 | ||||||||
\(974\) | 98.9314 | 3.16997 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 97.0078 | 3.10515 | ||||||||
\(977\) | 18.8977 | 0.604592 | 0.302296 | − | 0.953214i | \(-0.402247\pi\) | ||||
0.302296 | + | 0.953214i | \(0.402247\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 48.8313 | 1.56065 | ||||||||
\(980\) | −101.750 | −3.25027 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 14.3482 | 0.457871 | ||||||||
\(983\) | −9.51432 | −0.303460 | −0.151730 | − | 0.988422i | \(-0.548484\pi\) | ||||
−0.151730 | + | 0.988422i | \(0.548484\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.34528 | −0.234040 | ||||||||
\(986\) | −9.20579 | −0.293172 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 48.1109 | 1.53061 | ||||||||
\(989\) | 7.08099 | 0.225162 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.2984 | 1.18482 | 0.592412 | − | 0.805635i | \(-0.298176\pi\) | ||||
0.592412 | + | 0.805635i | \(0.298176\pi\) | |||||||
\(992\) | −126.344 | −4.01143 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 48.7560 | 1.54645 | ||||||||
\(995\) | 57.1977 | 1.81329 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.35625 | −0.169634 | −0.0848171 | − | 0.996397i | \(-0.527031\pi\) | ||||
−0.0848171 | + | 0.996397i | \(0.527031\pi\) | |||||||
\(998\) | 23.2537 | 0.736082 | ||||||||
\(999\) | 0 | 0 |
(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 | 6003.2.a.s.1.20 | 20 | ||
3.2 | odd | 2 | 2001.2.a.o.1.1 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.o.1.1 | ✓ | 20 | 3.2 | odd | 2 | ||
6003.2.a.s.1.20 | 20 | 1.1 | even | 1 | trivial |