Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2005,2,Mod(1,2005)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2005, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2005.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2005 = 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2005.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: | \(16.0100056053\) |
Analytic rank: | \(1\) |
Dimension: | \(29\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 2005.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.77645 | −1.25614 | −0.628070 | − | 0.778157i | \(-0.716155\pi\) | ||||
−0.628070 | + | 0.778157i | \(0.716155\pi\) | |||||||
\(3\) | −3.27205 | −1.88912 | −0.944558 | − | 0.328343i | \(-0.893510\pi\) | ||||
−0.944558 | + | 0.328343i | \(0.893510\pi\) | |||||||
\(4\) | 1.15578 | 0.577889 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 5.81263 | 2.37300 | ||||||||
\(7\) | 2.00064 | 0.756172 | 0.378086 | − | 0.925770i | \(-0.376582\pi\) | ||||
0.378086 | + | 0.925770i | \(0.376582\pi\) | |||||||
\(8\) | 1.49972 | 0.530231 | ||||||||
\(9\) | 7.70629 | 2.56876 | ||||||||
\(10\) | 1.77645 | 0.561763 | ||||||||
\(11\) | −5.30313 | −1.59895 | −0.799477 | − | 0.600697i | \(-0.794890\pi\) | ||||
−0.799477 | + | 0.600697i | \(0.794890\pi\) | |||||||
\(12\) | −3.78176 | −1.09170 | ||||||||
\(13\) | 1.99088 | 0.552170 | 0.276085 | − | 0.961133i | \(-0.410963\pi\) | ||||
0.276085 | + | 0.961133i | \(0.410963\pi\) | |||||||
\(14\) | −3.55404 | −0.949858 | ||||||||
\(15\) | 3.27205 | 0.844839 | ||||||||
\(16\) | −4.97573 | −1.24393 | ||||||||
\(17\) | −2.15638 | −0.523000 | −0.261500 | − | 0.965203i | \(-0.584217\pi\) | ||||
−0.261500 | + | 0.965203i | \(0.584217\pi\) | |||||||
\(18\) | −13.6898 | −3.22673 | ||||||||
\(19\) | −5.13856 | −1.17887 | −0.589433 | − | 0.807817i | \(-0.700649\pi\) | ||||
−0.589433 | + | 0.807817i | \(0.700649\pi\) | |||||||
\(20\) | −1.15578 | −0.258440 | ||||||||
\(21\) | −6.54620 | −1.42850 | ||||||||
\(22\) | 9.42075 | 2.00851 | ||||||||
\(23\) | 2.16945 | 0.452363 | 0.226181 | − | 0.974085i | \(-0.427376\pi\) | ||||
0.226181 | + | 0.974085i | \(0.427376\pi\) | |||||||
\(24\) | −4.90715 | −1.00167 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.53670 | −0.693603 | ||||||||
\(27\) | −15.3992 | −2.96358 | ||||||||
\(28\) | 2.31230 | 0.436984 | ||||||||
\(29\) | −4.23544 | −0.786501 | −0.393251 | − | 0.919431i | \(-0.628650\pi\) | ||||
−0.393251 | + | 0.919431i | \(0.628650\pi\) | |||||||
\(30\) | −5.81263 | −1.06124 | ||||||||
\(31\) | 2.91445 | 0.523451 | 0.261725 | − | 0.965142i | \(-0.415709\pi\) | ||||
0.261725 | + | 0.965142i | \(0.415709\pi\) | |||||||
\(32\) | 5.83971 | 1.03232 | ||||||||
\(33\) | 17.3521 | 3.02061 | ||||||||
\(34\) | 3.83071 | 0.656962 | ||||||||
\(35\) | −2.00064 | −0.338170 | ||||||||
\(36\) | 8.90676 | 1.48446 | ||||||||
\(37\) | 6.02644 | 0.990740 | 0.495370 | − | 0.868682i | \(-0.335032\pi\) | ||||
0.495370 | + | 0.868682i | \(0.335032\pi\) | |||||||
\(38\) | 9.12840 | 1.48082 | ||||||||
\(39\) | −6.51424 | −1.04311 | ||||||||
\(40\) | −1.49972 | −0.237126 | ||||||||
\(41\) | 8.60000 | 1.34309 | 0.671547 | − | 0.740962i | \(-0.265630\pi\) | ||||
0.671547 | + | 0.740962i | \(0.265630\pi\) | |||||||
\(42\) | 11.6290 | 1.79439 | ||||||||
\(43\) | 3.93746 | 0.600456 | 0.300228 | − | 0.953867i | \(-0.402937\pi\) | ||||
0.300228 | + | 0.953867i | \(0.402937\pi\) | |||||||
\(44\) | −6.12924 | −0.924018 | ||||||||
\(45\) | −7.70629 | −1.14879 | ||||||||
\(46\) | −3.85393 | −0.568231 | ||||||||
\(47\) | 5.97785 | 0.871959 | 0.435980 | − | 0.899957i | \(-0.356402\pi\) | ||||
0.435980 | + | 0.899957i | \(0.356402\pi\) | |||||||
\(48\) | 16.2808 | 2.34994 | ||||||||
\(49\) | −2.99743 | −0.428204 | ||||||||
\(50\) | −1.77645 | −0.251228 | ||||||||
\(51\) | 7.05579 | 0.988008 | ||||||||
\(52\) | 2.30101 | 0.319093 | ||||||||
\(53\) | 0.642395 | 0.0882397 | 0.0441199 | − | 0.999026i | \(-0.485952\pi\) | ||||
0.0441199 | + | 0.999026i | \(0.485952\pi\) | |||||||
\(54\) | 27.3559 | 3.72267 | ||||||||
\(55\) | 5.30313 | 0.715074 | ||||||||
\(56\) | 3.00040 | 0.400946 | ||||||||
\(57\) | 16.8136 | 2.22702 | ||||||||
\(58\) | 7.52405 | 0.987956 | ||||||||
\(59\) | −7.87937 | −1.02581 | −0.512903 | − | 0.858447i | \(-0.671430\pi\) | ||||
−0.512903 | + | 0.858447i | \(0.671430\pi\) | |||||||
\(60\) | 3.78176 | 0.488223 | ||||||||
\(61\) | 4.28306 | 0.548390 | 0.274195 | − | 0.961674i | \(-0.411589\pi\) | ||||
0.274195 | + | 0.961674i | \(0.411589\pi\) | |||||||
\(62\) | −5.17738 | −0.657528 | ||||||||
\(63\) | 15.4175 | 1.94243 | ||||||||
\(64\) | −0.422489 | −0.0528111 | ||||||||
\(65\) | −1.99088 | −0.246938 | ||||||||
\(66\) | −30.8251 | −3.79431 | ||||||||
\(67\) | 1.67698 | 0.204876 | 0.102438 | − | 0.994739i | \(-0.467336\pi\) | ||||
0.102438 | + | 0.994739i | \(0.467336\pi\) | |||||||
\(68\) | −2.49230 | −0.302236 | ||||||||
\(69\) | −7.09856 | −0.854566 | ||||||||
\(70\) | 3.55404 | 0.424790 | ||||||||
\(71\) | −13.2242 | −1.56943 | −0.784713 | − | 0.619860i | \(-0.787190\pi\) | ||||
−0.784713 | + | 0.619860i | \(0.787190\pi\) | |||||||
\(72\) | 11.5573 | 1.36204 | ||||||||
\(73\) | 0.667843 | 0.0781651 | 0.0390826 | − | 0.999236i | \(-0.487556\pi\) | ||||
0.0390826 | + | 0.999236i | \(0.487556\pi\) | |||||||
\(74\) | −10.7057 | −1.24451 | ||||||||
\(75\) | −3.27205 | −0.377823 | ||||||||
\(76\) | −5.93904 | −0.681254 | ||||||||
\(77\) | −10.6097 | −1.20908 | ||||||||
\(78\) | 11.5722 | 1.31030 | ||||||||
\(79\) | 10.9897 | 1.23644 | 0.618221 | − | 0.786005i | \(-0.287854\pi\) | ||||
0.618221 | + | 0.786005i | \(0.287854\pi\) | |||||||
\(80\) | 4.97573 | 0.556304 | ||||||||
\(81\) | 27.2680 | 3.02978 | ||||||||
\(82\) | −15.2775 | −1.68712 | ||||||||
\(83\) | 1.46499 | 0.160803 | 0.0804016 | − | 0.996763i | \(-0.474380\pi\) | ||||
0.0804016 | + | 0.996763i | \(0.474380\pi\) | |||||||
\(84\) | −7.56595 | −0.825513 | ||||||||
\(85\) | 2.15638 | 0.233893 | ||||||||
\(86\) | −6.99470 | −0.754258 | ||||||||
\(87\) | 13.8586 | 1.48579 | ||||||||
\(88\) | −7.95320 | −0.847814 | ||||||||
\(89\) | 4.48277 | 0.475173 | 0.237586 | − | 0.971366i | \(-0.423644\pi\) | ||||
0.237586 | + | 0.971366i | \(0.423644\pi\) | |||||||
\(90\) | 13.6898 | 1.44304 | ||||||||
\(91\) | 3.98303 | 0.417535 | ||||||||
\(92\) | 2.50741 | 0.261415 | ||||||||
\(93\) | −9.53622 | −0.988860 | ||||||||
\(94\) | −10.6194 | −1.09530 | ||||||||
\(95\) | 5.13856 | 0.527205 | ||||||||
\(96\) | −19.1078 | −1.95018 | ||||||||
\(97\) | 10.8071 | 1.09730 | 0.548648 | − | 0.836053i | \(-0.315143\pi\) | ||||
0.548648 | + | 0.836053i | \(0.315143\pi\) | |||||||
\(98\) | 5.32478 | 0.537884 | ||||||||
\(99\) | −40.8674 | −4.10733 | ||||||||
\(100\) | 1.15578 | 0.115578 | ||||||||
\(101\) | −9.19515 | −0.914952 | −0.457476 | − | 0.889222i | \(-0.651246\pi\) | ||||
−0.457476 | + | 0.889222i | \(0.651246\pi\) | |||||||
\(102\) | −12.5343 | −1.24108 | ||||||||
\(103\) | 4.41787 | 0.435306 | 0.217653 | − | 0.976026i | \(-0.430160\pi\) | ||||
0.217653 | + | 0.976026i | \(0.430160\pi\) | |||||||
\(104\) | 2.98576 | 0.292777 | ||||||||
\(105\) | 6.54620 | 0.638843 | ||||||||
\(106\) | −1.14118 | −0.110842 | ||||||||
\(107\) | −13.3453 | −1.29014 | −0.645068 | − | 0.764126i | \(-0.723171\pi\) | ||||
−0.645068 | + | 0.764126i | \(0.723171\pi\) | |||||||
\(108\) | −17.7980 | −1.71262 | ||||||||
\(109\) | 10.9998 | 1.05359 | 0.526795 | − | 0.849992i | \(-0.323394\pi\) | ||||
0.526795 | + | 0.849992i | \(0.323394\pi\) | |||||||
\(110\) | −9.42075 | −0.898233 | ||||||||
\(111\) | −19.7188 | −1.87162 | ||||||||
\(112\) | −9.95467 | −0.940628 | ||||||||
\(113\) | −12.4778 | −1.17381 | −0.586906 | − | 0.809655i | \(-0.699654\pi\) | ||||
−0.586906 | + | 0.809655i | \(0.699654\pi\) | |||||||
\(114\) | −29.8686 | −2.79745 | ||||||||
\(115\) | −2.16945 | −0.202303 | ||||||||
\(116\) | −4.89523 | −0.454510 | ||||||||
\(117\) | 15.3423 | 1.41839 | ||||||||
\(118\) | 13.9973 | 1.28856 | ||||||||
\(119\) | −4.31416 | −0.395478 | ||||||||
\(120\) | 4.90715 | 0.447959 | ||||||||
\(121\) | 17.1232 | 1.55665 | ||||||||
\(122\) | −7.60865 | −0.688855 | ||||||||
\(123\) | −28.1396 | −2.53726 | ||||||||
\(124\) | 3.36846 | 0.302497 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −27.3885 | −2.43996 | ||||||||
\(127\) | 1.98310 | 0.175972 | 0.0879858 | − | 0.996122i | \(-0.471957\pi\) | ||||
0.0879858 | + | 0.996122i | \(0.471957\pi\) | |||||||
\(128\) | −10.9289 | −0.965986 | ||||||||
\(129\) | −12.8835 | −1.13433 | ||||||||
\(130\) | 3.53670 | 0.310189 | ||||||||
\(131\) | 20.7594 | 1.81376 | 0.906881 | − | 0.421388i | \(-0.138457\pi\) | ||||
0.906881 | + | 0.421388i | \(0.138457\pi\) | |||||||
\(132\) | 20.0552 | 1.74558 | ||||||||
\(133\) | −10.2804 | −0.891426 | ||||||||
\(134\) | −2.97908 | −0.257353 | ||||||||
\(135\) | 15.3992 | 1.32535 | ||||||||
\(136\) | −3.23397 | −0.277311 | ||||||||
\(137\) | 15.7003 | 1.34136 | 0.670682 | − | 0.741745i | \(-0.266002\pi\) | ||||
0.670682 | + | 0.741745i | \(0.266002\pi\) | |||||||
\(138\) | 12.6102 | 1.07345 | ||||||||
\(139\) | −16.8238 | −1.42698 | −0.713490 | − | 0.700665i | \(-0.752887\pi\) | ||||
−0.713490 | + | 0.700665i | \(0.752887\pi\) | |||||||
\(140\) | −2.31230 | −0.195425 | ||||||||
\(141\) | −19.5598 | −1.64723 | ||||||||
\(142\) | 23.4922 | 1.97142 | ||||||||
\(143\) | −10.5579 | −0.882894 | ||||||||
\(144\) | −38.3444 | −3.19537 | ||||||||
\(145\) | 4.23544 | 0.351734 | ||||||||
\(146\) | −1.18639 | −0.0981864 | ||||||||
\(147\) | 9.80772 | 0.808927 | ||||||||
\(148\) | 6.96522 | 0.572538 | ||||||||
\(149\) | 10.9931 | 0.900587 | 0.450293 | − | 0.892881i | \(-0.351319\pi\) | ||||
0.450293 | + | 0.892881i | \(0.351319\pi\) | |||||||
\(150\) | 5.81263 | 0.474599 | ||||||||
\(151\) | −13.5460 | −1.10236 | −0.551179 | − | 0.834387i | \(-0.685822\pi\) | ||||
−0.551179 | + | 0.834387i | \(0.685822\pi\) | |||||||
\(152\) | −7.70640 | −0.625071 | ||||||||
\(153\) | −16.6177 | −1.34346 | ||||||||
\(154\) | 18.8476 | 1.51878 | ||||||||
\(155\) | −2.91445 | −0.234094 | ||||||||
\(156\) | −7.52902 | −0.602804 | ||||||||
\(157\) | 13.2825 | 1.06006 | 0.530029 | − | 0.847979i | \(-0.322181\pi\) | ||||
0.530029 | + | 0.847979i | \(0.322181\pi\) | |||||||
\(158\) | −19.5227 | −1.55314 | ||||||||
\(159\) | −2.10195 | −0.166695 | ||||||||
\(160\) | −5.83971 | −0.461669 | ||||||||
\(161\) | 4.34030 | 0.342064 | ||||||||
\(162\) | −48.4403 | −3.80583 | ||||||||
\(163\) | −16.5031 | −1.29262 | −0.646312 | − | 0.763073i | \(-0.723689\pi\) | ||||
−0.646312 | + | 0.763073i | \(0.723689\pi\) | |||||||
\(164\) | 9.93969 | 0.776160 | ||||||||
\(165\) | −17.3521 | −1.35086 | ||||||||
\(166\) | −2.60248 | −0.201991 | ||||||||
\(167\) | 2.97244 | 0.230014 | 0.115007 | − | 0.993365i | \(-0.463311\pi\) | ||||
0.115007 | + | 0.993365i | \(0.463311\pi\) | |||||||
\(168\) | −9.81746 | −0.757433 | ||||||||
\(169\) | −9.03641 | −0.695108 | ||||||||
\(170\) | −3.83071 | −0.293802 | ||||||||
\(171\) | −39.5992 | −3.02823 | ||||||||
\(172\) | 4.55083 | 0.346997 | ||||||||
\(173\) | 3.45083 | 0.262362 | 0.131181 | − | 0.991358i | \(-0.458123\pi\) | ||||
0.131181 | + | 0.991358i | \(0.458123\pi\) | |||||||
\(174\) | −24.6190 | −1.86636 | ||||||||
\(175\) | 2.00064 | 0.151234 | ||||||||
\(176\) | 26.3870 | 1.98899 | ||||||||
\(177\) | 25.7817 | 1.93787 | ||||||||
\(178\) | −7.96342 | −0.596884 | ||||||||
\(179\) | −17.5419 | −1.31115 | −0.655573 | − | 0.755132i | \(-0.727573\pi\) | ||||
−0.655573 | + | 0.755132i | \(0.727573\pi\) | |||||||
\(180\) | −8.90676 | −0.663871 | ||||||||
\(181\) | −3.80660 | −0.282942 | −0.141471 | − | 0.989942i | \(-0.545183\pi\) | ||||
−0.141471 | + | 0.989942i | \(0.545183\pi\) | |||||||
\(182\) | −7.07567 | −0.524483 | ||||||||
\(183\) | −14.0144 | −1.03597 | ||||||||
\(184\) | 3.25357 | 0.239856 | ||||||||
\(185\) | −6.02644 | −0.443073 | ||||||||
\(186\) | 16.9406 | 1.24215 | ||||||||
\(187\) | 11.4356 | 0.836253 | ||||||||
\(188\) | 6.90907 | 0.503896 | ||||||||
\(189\) | −30.8083 | −2.24097 | ||||||||
\(190\) | −9.12840 | −0.662244 | ||||||||
\(191\) | 4.66268 | 0.337379 | 0.168690 | − | 0.985669i | \(-0.446046\pi\) | ||||
0.168690 | + | 0.985669i | \(0.446046\pi\) | |||||||
\(192\) | 1.38240 | 0.0997664 | ||||||||
\(193\) | −27.1145 | −1.95175 | −0.975873 | − | 0.218337i | \(-0.929937\pi\) | ||||
−0.975873 | + | 0.218337i | \(0.929937\pi\) | |||||||
\(194\) | −19.1983 | −1.37836 | ||||||||
\(195\) | 6.51424 | 0.466495 | ||||||||
\(196\) | −3.46436 | −0.247454 | ||||||||
\(197\) | −7.56487 | −0.538974 | −0.269487 | − | 0.963004i | \(-0.586854\pi\) | ||||
−0.269487 | + | 0.963004i | \(0.586854\pi\) | |||||||
\(198\) | 72.5990 | 5.15939 | ||||||||
\(199\) | 13.8659 | 0.982929 | 0.491464 | − | 0.870898i | \(-0.336462\pi\) | ||||
0.491464 | + | 0.870898i | \(0.336462\pi\) | |||||||
\(200\) | 1.49972 | 0.106046 | ||||||||
\(201\) | −5.48717 | −0.387035 | ||||||||
\(202\) | 16.3347 | 1.14931 | ||||||||
\(203\) | −8.47360 | −0.594730 | ||||||||
\(204\) | 8.15493 | 0.570959 | ||||||||
\(205\) | −8.60000 | −0.600650 | ||||||||
\(206\) | −7.84814 | −0.546806 | ||||||||
\(207\) | 16.7184 | 1.16201 | ||||||||
\(208\) | −9.90607 | −0.686863 | ||||||||
\(209\) | 27.2504 | 1.88495 | ||||||||
\(210\) | −11.6290 | −0.802477 | ||||||||
\(211\) | 6.11062 | 0.420673 | 0.210336 | − | 0.977629i | \(-0.432544\pi\) | ||||
0.210336 | + | 0.977629i | \(0.432544\pi\) | |||||||
\(212\) | 0.742466 | 0.0509928 | ||||||||
\(213\) | 43.2702 | 2.96483 | ||||||||
\(214\) | 23.7072 | 1.62059 | ||||||||
\(215\) | −3.93746 | −0.268532 | ||||||||
\(216\) | −23.0945 | −1.57138 | ||||||||
\(217\) | 5.83078 | 0.395819 | ||||||||
\(218\) | −19.5406 | −1.32346 | ||||||||
\(219\) | −2.18521 | −0.147663 | ||||||||
\(220\) | 6.12924 | 0.413233 | ||||||||
\(221\) | −4.29310 | −0.288785 | ||||||||
\(222\) | 35.0295 | 2.35102 | ||||||||
\(223\) | 6.53109 | 0.437354 | 0.218677 | − | 0.975797i | \(-0.429826\pi\) | ||||
0.218677 | + | 0.975797i | \(0.429826\pi\) | |||||||
\(224\) | 11.6832 | 0.780615 | ||||||||
\(225\) | 7.70629 | 0.513753 | ||||||||
\(226\) | 22.1662 | 1.47447 | ||||||||
\(227\) | 19.1455 | 1.27073 | 0.635366 | − | 0.772211i | \(-0.280849\pi\) | ||||
0.635366 | + | 0.772211i | \(0.280849\pi\) | |||||||
\(228\) | 19.4328 | 1.28697 | ||||||||
\(229\) | 19.0903 | 1.26153 | 0.630763 | − | 0.775976i | \(-0.282742\pi\) | ||||
0.630763 | + | 0.775976i | \(0.282742\pi\) | |||||||
\(230\) | 3.85393 | 0.254121 | ||||||||
\(231\) | 34.7153 | 2.28410 | ||||||||
\(232\) | −6.35197 | −0.417027 | ||||||||
\(233\) | 18.5284 | 1.21383 | 0.606917 | − | 0.794765i | \(-0.292406\pi\) | ||||
0.606917 | + | 0.794765i | \(0.292406\pi\) | |||||||
\(234\) | −27.2548 | −1.78170 | ||||||||
\(235\) | −5.97785 | −0.389952 | ||||||||
\(236\) | −9.10680 | −0.592802 | ||||||||
\(237\) | −35.9589 | −2.33578 | ||||||||
\(238\) | 7.66389 | 0.496776 | ||||||||
\(239\) | −27.3329 | −1.76802 | −0.884008 | − | 0.467472i | \(-0.845165\pi\) | ||||
−0.884008 | + | 0.467472i | \(0.845165\pi\) | |||||||
\(240\) | −16.2808 | −1.05092 | ||||||||
\(241\) | −7.61957 | −0.490820 | −0.245410 | − | 0.969419i | \(-0.578923\pi\) | ||||
−0.245410 | + | 0.969419i | \(0.578923\pi\) | |||||||
\(242\) | −30.4185 | −1.95537 | ||||||||
\(243\) | −43.0246 | −2.76003 | ||||||||
\(244\) | 4.95027 | 0.316909 | ||||||||
\(245\) | 2.99743 | 0.191499 | ||||||||
\(246\) | 49.9886 | 3.18716 | ||||||||
\(247\) | −10.2302 | −0.650935 | ||||||||
\(248\) | 4.37086 | 0.277550 | ||||||||
\(249\) | −4.79351 | −0.303776 | ||||||||
\(250\) | 1.77645 | 0.112353 | ||||||||
\(251\) | 25.2312 | 1.59258 | 0.796288 | − | 0.604918i | \(-0.206794\pi\) | ||||
0.796288 | + | 0.604918i | \(0.206794\pi\) | |||||||
\(252\) | 17.8192 | 1.12251 | ||||||||
\(253\) | −11.5049 | −0.723307 | ||||||||
\(254\) | −3.52288 | −0.221045 | ||||||||
\(255\) | −7.05579 | −0.441851 | ||||||||
\(256\) | 20.2596 | 1.26623 | ||||||||
\(257\) | −25.9750 | −1.62028 | −0.810138 | − | 0.586240i | \(-0.800608\pi\) | ||||
−0.810138 | + | 0.586240i | \(0.800608\pi\) | |||||||
\(258\) | 22.8870 | 1.42488 | ||||||||
\(259\) | 12.0568 | 0.749170 | ||||||||
\(260\) | −2.30101 | −0.142703 | ||||||||
\(261\) | −32.6395 | −2.02033 | ||||||||
\(262\) | −36.8781 | −2.27834 | ||||||||
\(263\) | −5.27279 | −0.325134 | −0.162567 | − | 0.986698i | \(-0.551977\pi\) | ||||
−0.162567 | + | 0.986698i | \(0.551977\pi\) | |||||||
\(264\) | 26.0232 | 1.60162 | ||||||||
\(265\) | −0.642395 | −0.0394620 | ||||||||
\(266\) | 18.2627 | 1.11976 | ||||||||
\(267\) | −14.6678 | −0.897657 | ||||||||
\(268\) | 1.93822 | 0.118396 | ||||||||
\(269\) | −17.4052 | −1.06121 | −0.530606 | − | 0.847618i | \(-0.678036\pi\) | ||||
−0.530606 | + | 0.847618i | \(0.678036\pi\) | |||||||
\(270\) | −27.3559 | −1.66483 | ||||||||
\(271\) | −28.6279 | −1.73902 | −0.869511 | − | 0.493913i | \(-0.835566\pi\) | ||||
−0.869511 | + | 0.493913i | \(0.835566\pi\) | |||||||
\(272\) | 10.7296 | 0.650577 | ||||||||
\(273\) | −13.0327 | −0.788773 | ||||||||
\(274\) | −27.8907 | −1.68494 | ||||||||
\(275\) | −5.30313 | −0.319791 | ||||||||
\(276\) | −8.20435 | −0.493844 | ||||||||
\(277\) | 14.2130 | 0.853979 | 0.426990 | − | 0.904257i | \(-0.359574\pi\) | ||||
0.426990 | + | 0.904257i | \(0.359574\pi\) | |||||||
\(278\) | 29.8867 | 1.79249 | ||||||||
\(279\) | 22.4596 | 1.34462 | ||||||||
\(280\) | −3.00040 | −0.179308 | ||||||||
\(281\) | −19.0089 | −1.13398 | −0.566989 | − | 0.823725i | \(-0.691892\pi\) | ||||
−0.566989 | + | 0.823725i | \(0.691892\pi\) | |||||||
\(282\) | 34.7470 | 2.06916 | ||||||||
\(283\) | 0.0513036 | 0.00304968 | 0.00152484 | − | 0.999999i | \(-0.499515\pi\) | ||||
0.00152484 | + | 0.999999i | \(0.499515\pi\) | |||||||
\(284\) | −15.2843 | −0.906954 | ||||||||
\(285\) | −16.8136 | −0.995952 | ||||||||
\(286\) | 18.7556 | 1.10904 | ||||||||
\(287\) | 17.2055 | 1.01561 | ||||||||
\(288\) | 45.0025 | 2.65180 | ||||||||
\(289\) | −12.3500 | −0.726471 | ||||||||
\(290\) | −7.52405 | −0.441827 | ||||||||
\(291\) | −35.3614 | −2.07292 | ||||||||
\(292\) | 0.771878 | 0.0451708 | ||||||||
\(293\) | −11.8644 | −0.693125 | −0.346562 | − | 0.938027i | \(-0.612651\pi\) | ||||
−0.346562 | + | 0.938027i | \(0.612651\pi\) | |||||||
\(294\) | −17.4229 | −1.01613 | ||||||||
\(295\) | 7.87937 | 0.458754 | ||||||||
\(296\) | 9.03796 | 0.525321 | ||||||||
\(297\) | 81.6639 | 4.73862 | ||||||||
\(298\) | −19.5286 | −1.13126 | ||||||||
\(299\) | 4.31912 | 0.249781 | ||||||||
\(300\) | −3.78176 | −0.218340 | ||||||||
\(301\) | 7.87745 | 0.454048 | ||||||||
\(302\) | 24.0638 | 1.38472 | ||||||||
\(303\) | 30.0870 | 1.72845 | ||||||||
\(304\) | 25.5681 | 1.46643 | ||||||||
\(305\) | −4.28306 | −0.245248 | ||||||||
\(306\) | 29.5206 | 1.68758 | ||||||||
\(307\) | −22.1034 | −1.26151 | −0.630755 | − | 0.775982i | \(-0.717255\pi\) | ||||
−0.630755 | + | 0.775982i | \(0.717255\pi\) | |||||||
\(308\) | −12.2624 | −0.698716 | ||||||||
\(309\) | −14.4555 | −0.822344 | ||||||||
\(310\) | 5.17738 | 0.294055 | ||||||||
\(311\) | −26.3510 | −1.49423 | −0.747114 | − | 0.664696i | \(-0.768561\pi\) | ||||
−0.747114 | + | 0.664696i | \(0.768561\pi\) | |||||||
\(312\) | −9.76953 | −0.553091 | ||||||||
\(313\) | −22.9371 | −1.29648 | −0.648241 | − | 0.761435i | \(-0.724495\pi\) | ||||
−0.648241 | + | 0.761435i | \(0.724495\pi\) | |||||||
\(314\) | −23.5957 | −1.33158 | ||||||||
\(315\) | −15.4175 | −0.868680 | ||||||||
\(316\) | 12.7017 | 0.714526 | ||||||||
\(317\) | 1.83582 | 0.103110 | 0.0515550 | − | 0.998670i | \(-0.483582\pi\) | ||||
0.0515550 | + | 0.998670i | \(0.483582\pi\) | |||||||
\(318\) | 3.73400 | 0.209393 | ||||||||
\(319\) | 22.4611 | 1.25758 | ||||||||
\(320\) | 0.422489 | 0.0236179 | ||||||||
\(321\) | 43.6663 | 2.43722 | ||||||||
\(322\) | −7.71034 | −0.429680 | ||||||||
\(323\) | 11.0807 | 0.616547 | ||||||||
\(324\) | 31.5158 | 1.75088 | ||||||||
\(325\) | 1.99088 | 0.110434 | ||||||||
\(326\) | 29.3170 | 1.62372 | ||||||||
\(327\) | −35.9919 | −1.99035 | ||||||||
\(328\) | 12.8976 | 0.712150 | ||||||||
\(329\) | 11.9595 | 0.659351 | ||||||||
\(330\) | 30.8251 | 1.69687 | ||||||||
\(331\) | 8.69410 | 0.477871 | 0.238936 | − | 0.971035i | \(-0.423202\pi\) | ||||
0.238936 | + | 0.971035i | \(0.423202\pi\) | |||||||
\(332\) | 1.69320 | 0.0929264 | ||||||||
\(333\) | 46.4415 | 2.54498 | ||||||||
\(334\) | −5.28039 | −0.288930 | ||||||||
\(335\) | −1.67698 | −0.0916234 | ||||||||
\(336\) | 32.5721 | 1.77696 | ||||||||
\(337\) | 4.26203 | 0.232168 | 0.116084 | − | 0.993239i | \(-0.462966\pi\) | ||||
0.116084 | + | 0.993239i | \(0.462966\pi\) | |||||||
\(338\) | 16.0527 | 0.873154 | ||||||||
\(339\) | 40.8279 | 2.21747 | ||||||||
\(340\) | 2.49230 | 0.135164 | ||||||||
\(341\) | −15.4557 | −0.836974 | ||||||||
\(342\) | 70.3461 | 3.80388 | ||||||||
\(343\) | −20.0013 | −1.07997 | ||||||||
\(344\) | 5.90508 | 0.318380 | ||||||||
\(345\) | 7.09856 | 0.382173 | ||||||||
\(346\) | −6.13023 | −0.329563 | ||||||||
\(347\) | −15.4188 | −0.827724 | −0.413862 | − | 0.910340i | \(-0.635820\pi\) | ||||
−0.413862 | + | 0.910340i | \(0.635820\pi\) | |||||||
\(348\) | 16.0174 | 0.858623 | ||||||||
\(349\) | −29.8920 | −1.60008 | −0.800041 | − | 0.599945i | \(-0.795189\pi\) | ||||
−0.800041 | + | 0.599945i | \(0.795189\pi\) | |||||||
\(350\) | −3.55404 | −0.189972 | ||||||||
\(351\) | −30.6579 | −1.63640 | ||||||||
\(352\) | −30.9687 | −1.65064 | ||||||||
\(353\) | −18.8540 | −1.00350 | −0.501749 | − | 0.865013i | \(-0.667310\pi\) | ||||
−0.501749 | + | 0.865013i | \(0.667310\pi\) | |||||||
\(354\) | −45.7998 | −2.43423 | ||||||||
\(355\) | 13.2242 | 0.701868 | ||||||||
\(356\) | 5.18109 | 0.274597 | ||||||||
\(357\) | 14.1161 | 0.747104 | ||||||||
\(358\) | 31.1624 | 1.64698 | ||||||||
\(359\) | −20.3588 | −1.07450 | −0.537249 | − | 0.843423i | \(-0.680537\pi\) | ||||
−0.537249 | + | 0.843423i | \(0.680537\pi\) | |||||||
\(360\) | −11.5573 | −0.609121 | ||||||||
\(361\) | 7.40481 | 0.389727 | ||||||||
\(362\) | 6.76223 | 0.355415 | ||||||||
\(363\) | −56.0278 | −2.94070 | ||||||||
\(364\) | 4.60350 | 0.241289 | ||||||||
\(365\) | −0.667843 | −0.0349565 | ||||||||
\(366\) | 24.8959 | 1.30133 | ||||||||
\(367\) | 7.81716 | 0.408053 | 0.204026 | − | 0.978965i | \(-0.434597\pi\) | ||||
0.204026 | + | 0.978965i | \(0.434597\pi\) | |||||||
\(368\) | −10.7946 | −0.562709 | ||||||||
\(369\) | 66.2741 | 3.45009 | ||||||||
\(370\) | 10.7057 | 0.556561 | ||||||||
\(371\) | 1.28520 | 0.0667244 | ||||||||
\(372\) | −11.0218 | −0.571451 | ||||||||
\(373\) | −16.9545 | −0.877871 | −0.438936 | − | 0.898519i | \(-0.644644\pi\) | ||||
−0.438936 | + | 0.898519i | \(0.644644\pi\) | |||||||
\(374\) | −20.3148 | −1.05045 | ||||||||
\(375\) | 3.27205 | 0.168968 | ||||||||
\(376\) | 8.96510 | 0.462339 | ||||||||
\(377\) | −8.43224 | −0.434282 | ||||||||
\(378\) | 54.7294 | 2.81498 | ||||||||
\(379\) | 33.2628 | 1.70859 | 0.854297 | − | 0.519786i | \(-0.173988\pi\) | ||||
0.854297 | + | 0.519786i | \(0.173988\pi\) | |||||||
\(380\) | 5.93904 | 0.304666 | ||||||||
\(381\) | −6.48879 | −0.332431 | ||||||||
\(382\) | −8.28301 | −0.423796 | ||||||||
\(383\) | −17.5968 | −0.899153 | −0.449576 | − | 0.893242i | \(-0.648425\pi\) | ||||
−0.449576 | + | 0.893242i | \(0.648425\pi\) | |||||||
\(384\) | 35.7598 | 1.82486 | ||||||||
\(385\) | 10.6097 | 0.540719 | ||||||||
\(386\) | 48.1676 | 2.45167 | ||||||||
\(387\) | 30.3432 | 1.54243 | ||||||||
\(388\) | 12.4906 | 0.634115 | ||||||||
\(389\) | −24.3012 | −1.23212 | −0.616061 | − | 0.787698i | \(-0.711273\pi\) | ||||
−0.616061 | + | 0.787698i | \(0.711273\pi\) | |||||||
\(390\) | −11.5722 | −0.585983 | ||||||||
\(391\) | −4.67818 | −0.236586 | ||||||||
\(392\) | −4.49530 | −0.227047 | ||||||||
\(393\) | −67.9259 | −3.42641 | ||||||||
\(394\) | 13.4386 | 0.677028 | ||||||||
\(395\) | −10.9897 | −0.552953 | ||||||||
\(396\) | −47.2337 | −2.37358 | ||||||||
\(397\) | −6.84511 | −0.343546 | −0.171773 | − | 0.985137i | \(-0.554950\pi\) | ||||
−0.171773 | + | 0.985137i | \(0.554950\pi\) | |||||||
\(398\) | −24.6321 | −1.23470 | ||||||||
\(399\) | 33.6380 | 1.68401 | ||||||||
\(400\) | −4.97573 | −0.248787 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | 9.74769 | 0.486171 | ||||||||
\(403\) | 5.80231 | 0.289034 | ||||||||
\(404\) | −10.6276 | −0.528740 | ||||||||
\(405\) | −27.2680 | −1.35496 | ||||||||
\(406\) | 15.0529 | 0.747065 | ||||||||
\(407\) | −31.9590 | −1.58415 | ||||||||
\(408\) | 10.5817 | 0.523872 | ||||||||
\(409\) | −13.8179 | −0.683253 | −0.341626 | − | 0.939836i | \(-0.610978\pi\) | ||||
−0.341626 | + | 0.939836i | \(0.610978\pi\) | |||||||
\(410\) | 15.2775 | 0.754501 | ||||||||
\(411\) | −51.3720 | −2.53399 | ||||||||
\(412\) | 5.10608 | 0.251559 | ||||||||
\(413\) | −15.7638 | −0.775686 | ||||||||
\(414\) | −29.6995 | −1.45965 | ||||||||
\(415\) | −1.46499 | −0.0719134 | ||||||||
\(416\) | 11.6261 | 0.570018 | ||||||||
\(417\) | 55.0484 | 2.69573 | ||||||||
\(418\) | −48.4091 | −2.36777 | ||||||||
\(419\) | 20.3903 | 0.996132 | 0.498066 | − | 0.867139i | \(-0.334044\pi\) | ||||
0.498066 | + | 0.867139i | \(0.334044\pi\) | |||||||
\(420\) | 7.56595 | 0.369181 | ||||||||
\(421\) | 21.0156 | 1.02424 | 0.512118 | − | 0.858915i | \(-0.328861\pi\) | ||||
0.512118 | + | 0.858915i | \(0.328861\pi\) | |||||||
\(422\) | −10.8552 | −0.528424 | ||||||||
\(423\) | 46.0670 | 2.23986 | ||||||||
\(424\) | 0.963412 | 0.0467874 | ||||||||
\(425\) | −2.15638 | −0.104600 | ||||||||
\(426\) | −76.8675 | −3.72424 | ||||||||
\(427\) | 8.56888 | 0.414677 | ||||||||
\(428\) | −15.4242 | −0.745555 | ||||||||
\(429\) | 34.5459 | 1.66789 | ||||||||
\(430\) | 6.99470 | 0.337314 | ||||||||
\(431\) | −28.6657 | −1.38078 | −0.690390 | − | 0.723438i | \(-0.742561\pi\) | ||||
−0.690390 | + | 0.723438i | \(0.742561\pi\) | |||||||
\(432\) | 76.6223 | 3.68649 | ||||||||
\(433\) | 36.1591 | 1.73770 | 0.868848 | − | 0.495078i | \(-0.164861\pi\) | ||||
0.868848 | + | 0.495078i | \(0.164861\pi\) | |||||||
\(434\) | −10.3581 | −0.497204 | ||||||||
\(435\) | −13.8586 | −0.664467 | ||||||||
\(436\) | 12.7133 | 0.608858 | ||||||||
\(437\) | −11.1479 | −0.533275 | ||||||||
\(438\) | 3.88192 | 0.185486 | ||||||||
\(439\) | 37.4419 | 1.78700 | 0.893501 | − | 0.449061i | \(-0.148241\pi\) | ||||
0.893501 | + | 0.449061i | \(0.148241\pi\) | |||||||
\(440\) | 7.95320 | 0.379154 | ||||||||
\(441\) | −23.0990 | −1.09995 | ||||||||
\(442\) | 7.62648 | 0.362755 | ||||||||
\(443\) | −20.5304 | −0.975427 | −0.487713 | − | 0.873004i | \(-0.662169\pi\) | ||||
−0.487713 | + | 0.873004i | \(0.662169\pi\) | |||||||
\(444\) | −22.7905 | −1.08159 | ||||||||
\(445\) | −4.48277 | −0.212504 | ||||||||
\(446\) | −11.6022 | −0.549378 | ||||||||
\(447\) | −35.9698 | −1.70131 | ||||||||
\(448\) | −0.845250 | −0.0399343 | ||||||||
\(449\) | 0.797432 | 0.0376332 | 0.0188166 | − | 0.999823i | \(-0.494010\pi\) | ||||
0.0188166 | + | 0.999823i | \(0.494010\pi\) | |||||||
\(450\) | −13.6898 | −0.645345 | ||||||||
\(451\) | −45.6069 | −2.14755 | ||||||||
\(452\) | −14.4215 | −0.678333 | ||||||||
\(453\) | 44.3231 | 2.08248 | ||||||||
\(454\) | −34.0110 | −1.59622 | ||||||||
\(455\) | −3.98303 | −0.186728 | ||||||||
\(456\) | 25.2157 | 1.18083 | ||||||||
\(457\) | 37.8312 | 1.76967 | 0.884834 | − | 0.465906i | \(-0.154272\pi\) | ||||
0.884834 | + | 0.465906i | \(0.154272\pi\) | |||||||
\(458\) | −33.9131 | −1.58465 | ||||||||
\(459\) | 33.2066 | 1.54995 | ||||||||
\(460\) | −2.50741 | −0.116908 | ||||||||
\(461\) | 4.50255 | 0.209705 | 0.104852 | − | 0.994488i | \(-0.466563\pi\) | ||||
0.104852 | + | 0.994488i | \(0.466563\pi\) | |||||||
\(462\) | −61.6701 | −2.86915 | ||||||||
\(463\) | −18.2279 | −0.847120 | −0.423560 | − | 0.905868i | \(-0.639220\pi\) | ||||
−0.423560 | + | 0.905868i | \(0.639220\pi\) | |||||||
\(464\) | 21.0744 | 0.978355 | ||||||||
\(465\) | 9.53622 | 0.442232 | ||||||||
\(466\) | −32.9148 | −1.52475 | ||||||||
\(467\) | 11.6686 | 0.539958 | 0.269979 | − | 0.962866i | \(-0.412983\pi\) | ||||
0.269979 | + | 0.962866i | \(0.412983\pi\) | |||||||
\(468\) | 17.7323 | 0.819674 | ||||||||
\(469\) | 3.35505 | 0.154922 | ||||||||
\(470\) | 10.6194 | 0.489834 | ||||||||
\(471\) | −43.4609 | −2.00257 | ||||||||
\(472\) | −11.8168 | −0.543914 | ||||||||
\(473\) | −20.8808 | −0.960102 | ||||||||
\(474\) | 63.8792 | 2.93407 | ||||||||
\(475\) | −5.13856 | −0.235773 | ||||||||
\(476\) | −4.98621 | −0.228542 | ||||||||
\(477\) | 4.95048 | 0.226667 | ||||||||
\(478\) | 48.5555 | 2.22088 | ||||||||
\(479\) | −0.846587 | −0.0386815 | −0.0193408 | − | 0.999813i | \(-0.506157\pi\) | ||||
−0.0193408 | + | 0.999813i | \(0.506157\pi\) | |||||||
\(480\) | 19.1078 | 0.872148 | ||||||||
\(481\) | 11.9979 | 0.547057 | ||||||||
\(482\) | 13.5358 | 0.616539 | ||||||||
\(483\) | −14.2017 | −0.646199 | ||||||||
\(484\) | 19.7906 | 0.899572 | ||||||||
\(485\) | −10.8071 | −0.490726 | ||||||||
\(486\) | 76.4311 | 3.46699 | ||||||||
\(487\) | −23.0455 | −1.04429 | −0.522145 | − | 0.852857i | \(-0.674868\pi\) | ||||
−0.522145 | + | 0.852857i | \(0.674868\pi\) | |||||||
\(488\) | 6.42339 | 0.290773 | ||||||||
\(489\) | 53.9989 | 2.44192 | ||||||||
\(490\) | −5.32478 | −0.240549 | ||||||||
\(491\) | −24.9565 | −1.12627 | −0.563136 | − | 0.826364i | \(-0.690405\pi\) | ||||
−0.563136 | + | 0.826364i | \(0.690405\pi\) | |||||||
\(492\) | −32.5231 | −1.46626 | ||||||||
\(493\) | 9.13324 | 0.411340 | ||||||||
\(494\) | 18.1735 | 0.817666 | ||||||||
\(495\) | 40.8674 | 1.83685 | ||||||||
\(496\) | −14.5015 | −0.651138 | ||||||||
\(497\) | −26.4569 | −1.18676 | ||||||||
\(498\) | 8.51543 | 0.381585 | ||||||||
\(499\) | −10.7280 | −0.480252 | −0.240126 | − | 0.970742i | \(-0.577189\pi\) | ||||
−0.240126 | + | 0.970742i | \(0.577189\pi\) | |||||||
\(500\) | −1.15578 | −0.0516880 | ||||||||
\(501\) | −9.72595 | −0.434524 | ||||||||
\(502\) | −44.8219 | −2.00050 | ||||||||
\(503\) | −7.61939 | −0.339732 | −0.169866 | − | 0.985467i | \(-0.554333\pi\) | ||||
−0.169866 | + | 0.985467i | \(0.554333\pi\) | |||||||
\(504\) | 23.1220 | 1.02993 | ||||||||
\(505\) | 9.19515 | 0.409179 | ||||||||
\(506\) | 20.4379 | 0.908575 | ||||||||
\(507\) | 29.5675 | 1.31314 | ||||||||
\(508\) | 2.29202 | 0.101692 | ||||||||
\(509\) | 19.0995 | 0.846570 | 0.423285 | − | 0.905997i | \(-0.360877\pi\) | ||||
0.423285 | + | 0.905997i | \(0.360877\pi\) | |||||||
\(510\) | 12.5343 | 0.555027 | ||||||||
\(511\) | 1.33612 | 0.0591063 | ||||||||
\(512\) | −14.1324 | −0.624571 | ||||||||
\(513\) | 79.1297 | 3.49366 | ||||||||
\(514\) | 46.1433 | 2.03529 | ||||||||
\(515\) | −4.41787 | −0.194675 | ||||||||
\(516\) | −14.8905 | −0.655518 | ||||||||
\(517\) | −31.7013 | −1.39422 | ||||||||
\(518\) | −21.4182 | −0.941063 | ||||||||
\(519\) | −11.2913 | −0.495632 | ||||||||
\(520\) | −2.98576 | −0.130934 | ||||||||
\(521\) | 30.7586 | 1.34756 | 0.673779 | − | 0.738933i | \(-0.264670\pi\) | ||||
0.673779 | + | 0.738933i | \(0.264670\pi\) | |||||||
\(522\) | 57.9825 | 2.53782 | ||||||||
\(523\) | −12.7016 | −0.555402 | −0.277701 | − | 0.960668i | \(-0.589573\pi\) | ||||
−0.277701 | + | 0.960668i | \(0.589573\pi\) | |||||||
\(524\) | 23.9933 | 1.04815 | ||||||||
\(525\) | −6.54620 | −0.285699 | ||||||||
\(526\) | 9.36684 | 0.408414 | ||||||||
\(527\) | −6.28468 | −0.273765 | ||||||||
\(528\) | −86.3393 | −3.75744 | ||||||||
\(529\) | −18.2935 | −0.795368 | ||||||||
\(530\) | 1.14118 | 0.0495698 | ||||||||
\(531\) | −60.7207 | −2.63505 | ||||||||
\(532\) | −11.8819 | −0.515145 | ||||||||
\(533\) | 17.1215 | 0.741616 | ||||||||
\(534\) | 26.0567 | 1.12758 | ||||||||
\(535\) | 13.3453 | 0.576966 | ||||||||
\(536\) | 2.51500 | 0.108632 | ||||||||
\(537\) | 57.3980 | 2.47691 | ||||||||
\(538\) | 30.9194 | 1.33303 | ||||||||
\(539\) | 15.8957 | 0.684678 | ||||||||
\(540\) | 17.7980 | 0.765906 | ||||||||
\(541\) | 31.3673 | 1.34858 | 0.674292 | − | 0.738465i | \(-0.264449\pi\) | ||||
0.674292 | + | 0.738465i | \(0.264449\pi\) | |||||||
\(542\) | 50.8561 | 2.18446 | ||||||||
\(543\) | 12.4554 | 0.534511 | ||||||||
\(544\) | −12.5927 | −0.539906 | ||||||||
\(545\) | −10.9998 | −0.471180 | ||||||||
\(546\) | 23.1519 | 0.990810 | ||||||||
\(547\) | 39.1222 | 1.67275 | 0.836373 | − | 0.548161i | \(-0.184672\pi\) | ||||
0.836373 | + | 0.548161i | \(0.184672\pi\) | |||||||
\(548\) | 18.1460 | 0.775159 | ||||||||
\(549\) | 33.0065 | 1.40868 | ||||||||
\(550\) | 9.42075 | 0.401702 | ||||||||
\(551\) | 21.7641 | 0.927180 | ||||||||
\(552\) | −10.6458 | −0.453117 | ||||||||
\(553\) | 21.9865 | 0.934962 | ||||||||
\(554\) | −25.2488 | −1.07272 | ||||||||
\(555\) | 19.7188 | 0.837016 | ||||||||
\(556\) | −19.4446 | −0.824636 | ||||||||
\(557\) | 33.2541 | 1.40902 | 0.704512 | − | 0.709692i | \(-0.251166\pi\) | ||||
0.704512 | + | 0.709692i | \(0.251166\pi\) | |||||||
\(558\) | −39.8984 | −1.68903 | ||||||||
\(559\) | 7.83899 | 0.331554 | ||||||||
\(560\) | 9.95467 | 0.420661 | ||||||||
\(561\) | −37.4178 | −1.57978 | ||||||||
\(562\) | 33.7684 | 1.42444 | ||||||||
\(563\) | 13.6925 | 0.577071 | 0.288536 | − | 0.957469i | \(-0.406832\pi\) | ||||
0.288536 | + | 0.957469i | \(0.406832\pi\) | |||||||
\(564\) | −22.6068 | −0.951918 | ||||||||
\(565\) | 12.4778 | 0.524944 | ||||||||
\(566\) | −0.0911384 | −0.00383083 | ||||||||
\(567\) | 54.5536 | 2.29103 | ||||||||
\(568\) | −19.8326 | −0.832158 | ||||||||
\(569\) | −30.4598 | −1.27694 | −0.638471 | − | 0.769646i | \(-0.720433\pi\) | ||||
−0.638471 | + | 0.769646i | \(0.720433\pi\) | |||||||
\(570\) | 29.8686 | 1.25106 | ||||||||
\(571\) | −37.1882 | −1.55628 | −0.778140 | − | 0.628091i | \(-0.783836\pi\) | ||||
−0.778140 | + | 0.628091i | \(0.783836\pi\) | |||||||
\(572\) | −12.2026 | −0.510215 | ||||||||
\(573\) | −15.2565 | −0.637349 | ||||||||
\(574\) | −30.5648 | −1.27575 | ||||||||
\(575\) | 2.16945 | 0.0904725 | ||||||||
\(576\) | −3.25582 | −0.135659 | ||||||||
\(577\) | −28.1409 | −1.17152 | −0.585761 | − | 0.810484i | \(-0.699204\pi\) | ||||
−0.585761 | + | 0.810484i | \(0.699204\pi\) | |||||||
\(578\) | 21.9392 | 0.912549 | ||||||||
\(579\) | 88.7200 | 3.68708 | ||||||||
\(580\) | 4.89523 | 0.203263 | ||||||||
\(581\) | 2.93092 | 0.121595 | ||||||||
\(582\) | 62.8178 | 2.60388 | ||||||||
\(583\) | −3.40670 | −0.141091 | ||||||||
\(584\) | 1.00158 | 0.0414455 | ||||||||
\(585\) | −15.3423 | −0.634325 | ||||||||
\(586\) | 21.0765 | 0.870662 | ||||||||
\(587\) | 4.28532 | 0.176874 | 0.0884371 | − | 0.996082i | \(-0.471813\pi\) | ||||
0.0884371 | + | 0.996082i | \(0.471813\pi\) | |||||||
\(588\) | 11.3355 | 0.467470 | ||||||||
\(589\) | −14.9761 | −0.617079 | ||||||||
\(590\) | −13.9973 | −0.576260 | ||||||||
\(591\) | 24.7526 | 1.01819 | ||||||||
\(592\) | −29.9859 | −1.23241 | ||||||||
\(593\) | 9.97721 | 0.409715 | 0.204857 | − | 0.978792i | \(-0.434327\pi\) | ||||
0.204857 | + | 0.978792i | \(0.434327\pi\) | |||||||
\(594\) | −145.072 | −5.95237 | ||||||||
\(595\) | 4.31416 | 0.176863 | ||||||||
\(596\) | 12.7055 | 0.520439 | ||||||||
\(597\) | −45.3699 | −1.85687 | ||||||||
\(598\) | −7.67270 | −0.313760 | ||||||||
\(599\) | −40.6145 | −1.65946 | −0.829732 | − | 0.558162i | \(-0.811507\pi\) | ||||
−0.829732 | + | 0.558162i | \(0.811507\pi\) | |||||||
\(600\) | −4.90715 | −0.200334 | ||||||||
\(601\) | −7.67886 | −0.313227 | −0.156614 | − | 0.987660i | \(-0.550058\pi\) | ||||
−0.156614 | + | 0.987660i | \(0.550058\pi\) | |||||||
\(602\) | −13.9939 | −0.570349 | ||||||||
\(603\) | 12.9233 | 0.526278 | ||||||||
\(604\) | −15.6562 | −0.637041 | ||||||||
\(605\) | −17.1232 | −0.696156 | ||||||||
\(606\) | −53.4480 | −2.17118 | ||||||||
\(607\) | 25.2126 | 1.02335 | 0.511675 | − | 0.859179i | \(-0.329025\pi\) | ||||
0.511675 | + | 0.859179i | \(0.329025\pi\) | |||||||
\(608\) | −30.0077 | −1.21697 | ||||||||
\(609\) | 27.7260 | 1.12351 | ||||||||
\(610\) | 7.60865 | 0.308065 | ||||||||
\(611\) | 11.9012 | 0.481470 | ||||||||
\(612\) | −19.2064 | −0.776373 | ||||||||
\(613\) | −46.8372 | −1.89174 | −0.945868 | − | 0.324553i | \(-0.894786\pi\) | ||||
−0.945868 | + | 0.324553i | \(0.894786\pi\) | |||||||
\(614\) | 39.2657 | 1.58463 | ||||||||
\(615\) | 28.1396 | 1.13470 | ||||||||
\(616\) | −15.9115 | −0.641093 | ||||||||
\(617\) | −15.3288 | −0.617113 | −0.308557 | − | 0.951206i | \(-0.599846\pi\) | ||||
−0.308557 | + | 0.951206i | \(0.599846\pi\) | |||||||
\(618\) | 25.6795 | 1.03298 | ||||||||
\(619\) | −18.0418 | −0.725161 | −0.362581 | − | 0.931952i | \(-0.618104\pi\) | ||||
−0.362581 | + | 0.931952i | \(0.618104\pi\) | |||||||
\(620\) | −3.36846 | −0.135281 | ||||||||
\(621\) | −33.4078 | −1.34061 | ||||||||
\(622\) | 46.8112 | 1.87696 | ||||||||
\(623\) | 8.96843 | 0.359312 | ||||||||
\(624\) | 32.4131 | 1.29756 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 40.7467 | 1.62856 | ||||||||
\(627\) | −89.1647 | −3.56090 | ||||||||
\(628\) | 15.3516 | 0.612596 | ||||||||
\(629\) | −12.9953 | −0.518157 | ||||||||
\(630\) | 27.3885 | 1.09118 | ||||||||
\(631\) | 10.2808 | 0.409272 | 0.204636 | − | 0.978838i | \(-0.434399\pi\) | ||||
0.204636 | + | 0.978838i | \(0.434399\pi\) | |||||||
\(632\) | 16.4815 | 0.655599 | ||||||||
\(633\) | −19.9942 | −0.794700 | ||||||||
\(634\) | −3.26125 | −0.129521 | ||||||||
\(635\) | −1.98310 | −0.0786969 | ||||||||
\(636\) | −2.42938 | −0.0963313 | ||||||||
\(637\) | −5.96751 | −0.236441 | ||||||||
\(638\) | −39.9010 | −1.57970 | ||||||||
\(639\) | −101.910 | −4.03148 | ||||||||
\(640\) | 10.9289 | 0.432002 | ||||||||
\(641\) | 47.3547 | 1.87040 | 0.935199 | − | 0.354123i | \(-0.115221\pi\) | ||||
0.935199 | + | 0.354123i | \(0.115221\pi\) | |||||||
\(642\) | −77.5711 | −3.06149 | ||||||||
\(643\) | −27.0838 | −1.06808 | −0.534040 | − | 0.845459i | \(-0.679327\pi\) | ||||
−0.534040 | + | 0.845459i | \(0.679327\pi\) | |||||||
\(644\) | 5.01643 | 0.197675 | ||||||||
\(645\) | 12.8835 | 0.507289 | ||||||||
\(646\) | −19.6843 | −0.774470 | ||||||||
\(647\) | −1.69051 | −0.0664609 | −0.0332304 | − | 0.999448i | \(-0.510580\pi\) | ||||
−0.0332304 | + | 0.999448i | \(0.510580\pi\) | |||||||
\(648\) | 40.8943 | 1.60648 | ||||||||
\(649\) | 41.7853 | 1.64022 | ||||||||
\(650\) | −3.53670 | −0.138721 | ||||||||
\(651\) | −19.0786 | −0.747748 | ||||||||
\(652\) | −19.0739 | −0.746993 | ||||||||
\(653\) | −19.3044 | −0.755440 | −0.377720 | − | 0.925920i | \(-0.623292\pi\) | ||||
−0.377720 | + | 0.925920i | \(0.623292\pi\) | |||||||
\(654\) | 63.9378 | 2.50016 | ||||||||
\(655\) | −20.7594 | −0.811139 | ||||||||
\(656\) | −42.7913 | −1.67072 | ||||||||
\(657\) | 5.14659 | 0.200788 | ||||||||
\(658\) | −21.2455 | −0.828238 | ||||||||
\(659\) | −15.3639 | −0.598494 | −0.299247 | − | 0.954176i | \(-0.596735\pi\) | ||||
−0.299247 | + | 0.954176i | \(0.596735\pi\) | |||||||
\(660\) | −20.0552 | −0.780646 | ||||||||
\(661\) | −22.5171 | −0.875815 | −0.437908 | − | 0.899020i | \(-0.644280\pi\) | ||||
−0.437908 | + | 0.899020i | \(0.644280\pi\) | |||||||
\(662\) | −15.4446 | −0.600273 | ||||||||
\(663\) | 14.0472 | 0.545549 | ||||||||
\(664\) | 2.19707 | 0.0852628 | ||||||||
\(665\) | 10.2804 | 0.398658 | ||||||||
\(666\) | −82.5010 | −3.19685 | ||||||||
\(667\) | −9.18859 | −0.355784 | ||||||||
\(668\) | 3.43548 | 0.132923 | ||||||||
\(669\) | −21.3700 | −0.826212 | ||||||||
\(670\) | 2.97908 | 0.115092 | ||||||||
\(671\) | −22.7136 | −0.876850 | ||||||||
\(672\) | −38.2279 | −1.47467 | ||||||||
\(673\) | 33.7034 | 1.29917 | 0.649585 | − | 0.760289i | \(-0.274943\pi\) | ||||
0.649585 | + | 0.760289i | \(0.274943\pi\) | |||||||
\(674\) | −7.57129 | −0.291635 | ||||||||
\(675\) | −15.3992 | −0.592715 | ||||||||
\(676\) | −10.4441 | −0.401695 | ||||||||
\(677\) | −4.38534 | −0.168542 | −0.0842711 | − | 0.996443i | \(-0.526856\pi\) | ||||
−0.0842711 | + | 0.996443i | \(0.526856\pi\) | |||||||
\(678\) | −72.5287 | −2.78545 | ||||||||
\(679\) | 21.6212 | 0.829745 | ||||||||
\(680\) | 3.23397 | 0.124017 | ||||||||
\(681\) | −62.6450 | −2.40056 | ||||||||
\(682\) | 27.4563 | 1.05136 | ||||||||
\(683\) | 27.9445 | 1.06927 | 0.534633 | − | 0.845084i | \(-0.320450\pi\) | ||||
0.534633 | + | 0.845084i | \(0.320450\pi\) | |||||||
\(684\) | −45.7679 | −1.74998 | ||||||||
\(685\) | −15.7003 | −0.599876 | ||||||||
\(686\) | 35.5313 | 1.35659 | ||||||||
\(687\) | −62.4645 | −2.38317 | ||||||||
\(688\) | −19.5917 | −0.746928 | ||||||||
\(689\) | 1.27893 | 0.0487233 | ||||||||
\(690\) | −12.6102 | −0.480063 | ||||||||
\(691\) | −5.41290 | −0.205916 | −0.102958 | − | 0.994686i | \(-0.532831\pi\) | ||||
−0.102958 | + | 0.994686i | \(0.532831\pi\) | |||||||
\(692\) | 3.98840 | 0.151616 | ||||||||
\(693\) | −81.7612 | −3.10585 | ||||||||
\(694\) | 27.3907 | 1.03974 | ||||||||
\(695\) | 16.8238 | 0.638165 | ||||||||
\(696\) | 20.7839 | 0.787813 | ||||||||
\(697\) | −18.5449 | −0.702439 | ||||||||
\(698\) | 53.1017 | 2.00993 | ||||||||
\(699\) | −60.6257 | −2.29308 | ||||||||
\(700\) | 2.31230 | 0.0873967 | ||||||||
\(701\) | −8.97974 | −0.339160 | −0.169580 | − | 0.985516i | \(-0.554241\pi\) | ||||
−0.169580 | + | 0.985516i | \(0.554241\pi\) | |||||||
\(702\) | 54.4623 | 2.05555 | ||||||||
\(703\) | −30.9672 | −1.16795 | ||||||||
\(704\) | 2.24051 | 0.0844425 | ||||||||
\(705\) | 19.5598 | 0.736665 | ||||||||
\(706\) | 33.4932 | 1.26053 | ||||||||
\(707\) | −18.3962 | −0.691861 | ||||||||
\(708\) | 29.7979 | 1.11987 | ||||||||
\(709\) | −22.4010 | −0.841286 | −0.420643 | − | 0.907226i | \(-0.638196\pi\) | ||||
−0.420643 | + | 0.907226i | \(0.638196\pi\) | |||||||
\(710\) | −23.4922 | −0.881645 | ||||||||
\(711\) | 84.6900 | 3.17612 | ||||||||
\(712\) | 6.72290 | 0.251951 | ||||||||
\(713\) | 6.32277 | 0.236790 | ||||||||
\(714\) | −25.0766 | −0.938468 | ||||||||
\(715\) | 10.5579 | 0.394842 | ||||||||
\(716\) | −20.2746 | −0.757697 | ||||||||
\(717\) | 89.4344 | 3.33999 | ||||||||
\(718\) | 36.1665 | 1.34972 | ||||||||
\(719\) | 29.8562 | 1.11345 | 0.556724 | − | 0.830697i | \(-0.312058\pi\) | ||||
0.556724 | + | 0.830697i | \(0.312058\pi\) | |||||||
\(720\) | 38.3444 | 1.42901 | ||||||||
\(721\) | 8.83859 | 0.329166 | ||||||||
\(722\) | −13.1543 | −0.489551 | ||||||||
\(723\) | 24.9316 | 0.927216 | ||||||||
\(724\) | −4.39958 | −0.163509 | ||||||||
\(725\) | −4.23544 | −0.157300 | ||||||||
\(726\) | 99.5307 | 3.69393 | ||||||||
\(727\) | −8.59321 | −0.318705 | −0.159352 | − | 0.987222i | \(-0.550941\pi\) | ||||
−0.159352 | + | 0.987222i | \(0.550941\pi\) | |||||||
\(728\) | 5.97343 | 0.221390 | ||||||||
\(729\) | 58.9745 | 2.18424 | ||||||||
\(730\) | 1.18639 | 0.0439103 | ||||||||
\(731\) | −8.49067 | −0.314039 | ||||||||
\(732\) | −16.1975 | −0.598677 | ||||||||
\(733\) | −52.2592 | −1.93024 | −0.965119 | − | 0.261812i | \(-0.915680\pi\) | ||||
−0.965119 | + | 0.261812i | \(0.915680\pi\) | |||||||
\(734\) | −13.8868 | −0.512572 | ||||||||
\(735\) | −9.80772 | −0.361763 | ||||||||
\(736\) | 12.6690 | 0.466985 | ||||||||
\(737\) | −8.89326 | −0.327588 | ||||||||
\(738\) | −117.733 | −4.33380 | ||||||||
\(739\) | −51.3512 | −1.88898 | −0.944492 | − | 0.328534i | \(-0.893445\pi\) | ||||
−0.944492 | + | 0.328534i | \(0.893445\pi\) | |||||||
\(740\) | −6.96522 | −0.256047 | ||||||||
\(741\) | 33.4738 | 1.22969 | ||||||||
\(742\) | −2.28310 | −0.0838153 | ||||||||
\(743\) | −13.9480 | −0.511704 | −0.255852 | − | 0.966716i | \(-0.582356\pi\) | ||||
−0.255852 | + | 0.966716i | \(0.582356\pi\) | |||||||
\(744\) | −14.3016 | −0.524324 | ||||||||
\(745\) | −10.9931 | −0.402755 | ||||||||
\(746\) | 30.1188 | 1.10273 | ||||||||
\(747\) | 11.2896 | 0.413065 | ||||||||
\(748\) | 13.2170 | 0.483261 | ||||||||
\(749\) | −26.6991 | −0.975564 | ||||||||
\(750\) | −5.81263 | −0.212247 | ||||||||
\(751\) | 11.9693 | 0.436764 | 0.218382 | − | 0.975863i | \(-0.429922\pi\) | ||||
0.218382 | + | 0.975863i | \(0.429922\pi\) | |||||||
\(752\) | −29.7442 | −1.08466 | ||||||||
\(753\) | −82.5575 | −3.00856 | ||||||||
\(754\) | 14.9795 | 0.545520 | ||||||||
\(755\) | 13.5460 | 0.492990 | ||||||||
\(756\) | −35.6075 | −1.29503 | ||||||||
\(757\) | 14.6995 | 0.534262 | 0.267131 | − | 0.963660i | \(-0.413924\pi\) | ||||
0.267131 | + | 0.963660i | \(0.413924\pi\) | |||||||
\(758\) | −59.0897 | −2.14623 | ||||||||
\(759\) | 37.6446 | 1.36641 | ||||||||
\(760\) | 7.70640 | 0.279540 | ||||||||
\(761\) | 47.6939 | 1.72890 | 0.864452 | − | 0.502716i | \(-0.167666\pi\) | ||||
0.864452 | + | 0.502716i | \(0.167666\pi\) | |||||||
\(762\) | 11.5270 | 0.417580 | ||||||||
\(763\) | 22.0067 | 0.796695 | ||||||||
\(764\) | 5.38902 | 0.194968 | ||||||||
\(765\) | 16.6177 | 0.600815 | ||||||||
\(766\) | 31.2598 | 1.12946 | ||||||||
\(767\) | −15.6869 | −0.566419 | ||||||||
\(768\) | −66.2904 | −2.39205 | ||||||||
\(769\) | −5.49025 | −0.197984 | −0.0989918 | − | 0.995088i | \(-0.531562\pi\) | ||||
−0.0989918 | + | 0.995088i | \(0.531562\pi\) | |||||||
\(770\) | −18.8476 | −0.679219 | ||||||||
\(771\) | 84.9914 | 3.06089 | ||||||||
\(772\) | −31.3384 | −1.12789 | ||||||||
\(773\) | −7.29402 | −0.262348 | −0.131174 | − | 0.991359i | \(-0.541875\pi\) | ||||
−0.131174 | + | 0.991359i | \(0.541875\pi\) | |||||||
\(774\) | −53.9032 | −1.93751 | ||||||||
\(775\) | 2.91445 | 0.104690 | ||||||||
\(776\) | 16.2076 | 0.581820 | ||||||||
\(777\) | −39.4503 | −1.41527 | ||||||||
\(778\) | 43.1700 | 1.54772 | ||||||||
\(779\) | −44.1916 | −1.58333 | ||||||||
\(780\) | 7.52902 | 0.269582 | ||||||||
\(781\) | 70.1297 | 2.50944 | ||||||||
\(782\) | 8.31056 | 0.297185 | ||||||||
\(783\) | 65.2223 | 2.33086 | ||||||||
\(784\) | 14.9144 | 0.532657 | ||||||||
\(785\) | −13.2825 | −0.474072 | ||||||||
\(786\) | 120.667 | 4.30405 | ||||||||
\(787\) | 54.5469 | 1.94439 | 0.972194 | − | 0.234178i | \(-0.0752397\pi\) | ||||
0.972194 | + | 0.234178i | \(0.0752397\pi\) | |||||||
\(788\) | −8.74331 | −0.311467 | ||||||||
\(789\) | 17.2528 | 0.614216 | ||||||||
\(790\) | 19.5227 | 0.694587 | ||||||||
\(791\) | −24.9636 | −0.887603 | ||||||||
\(792\) | −61.2897 | −2.17783 | ||||||||
\(793\) | 8.52705 | 0.302805 | ||||||||
\(794\) | 12.1600 | 0.431542 | ||||||||
\(795\) | 2.10195 | 0.0745483 | ||||||||
\(796\) | 16.0259 | 0.568024 | ||||||||
\(797\) | −36.7033 | −1.30010 | −0.650049 | − | 0.759893i | \(-0.725252\pi\) | ||||
−0.650049 | + | 0.759893i | \(0.725252\pi\) | |||||||
\(798\) | −59.7563 | −2.11535 | ||||||||
\(799\) | −12.8905 | −0.456035 | ||||||||
\(800\) | 5.83971 | 0.206465 | ||||||||
\(801\) | 34.5455 | 1.22061 | ||||||||
\(802\) | 1.77645 | 0.0627287 | ||||||||
\(803\) | −3.54166 | −0.124982 | ||||||||
\(804\) | −6.34195 | −0.223663 | ||||||||
\(805\) | −4.34030 | −0.152976 | ||||||||
\(806\) | −10.3075 | −0.363067 | ||||||||
\(807\) | 56.9506 | 2.00475 | ||||||||
\(808\) | −13.7901 | −0.485135 | ||||||||
\(809\) | −6.11934 | −0.215144 | −0.107572 | − | 0.994197i | \(-0.534308\pi\) | ||||
−0.107572 | + | 0.994197i | \(0.534308\pi\) | |||||||
\(810\) | 48.4403 | 1.70202 | ||||||||
\(811\) | −8.53782 | −0.299803 | −0.149902 | − | 0.988701i | \(-0.547896\pi\) | ||||
−0.149902 | + | 0.988701i | \(0.547896\pi\) | |||||||
\(812\) | −9.79360 | −0.343688 | ||||||||
\(813\) | 93.6719 | 3.28522 | ||||||||
\(814\) | 56.7735 | 1.98991 | ||||||||
\(815\) | 16.5031 | 0.578079 | ||||||||
\(816\) | −35.1077 | −1.22902 | ||||||||
\(817\) | −20.2329 | −0.707858 | ||||||||
\(818\) | 24.5469 | 0.858262 | ||||||||
\(819\) | 30.6944 | 1.07255 | ||||||||
\(820\) | −9.93969 | −0.347109 | ||||||||
\(821\) | −12.9579 | −0.452233 | −0.226117 | − | 0.974100i | \(-0.572603\pi\) | ||||
−0.226117 | + | 0.974100i | \(0.572603\pi\) | |||||||
\(822\) | 91.2598 | 3.18305 | ||||||||
\(823\) | −43.5865 | −1.51933 | −0.759665 | − | 0.650315i | \(-0.774637\pi\) | ||||
−0.759665 | + | 0.650315i | \(0.774637\pi\) | |||||||
\(824\) | 6.62557 | 0.230813 | ||||||||
\(825\) | 17.3521 | 0.604122 | ||||||||
\(826\) | 28.0036 | 0.974371 | ||||||||
\(827\) | −23.7283 | −0.825115 | −0.412557 | − | 0.910932i | \(-0.635364\pi\) | ||||
−0.412557 | + | 0.910932i | \(0.635364\pi\) | |||||||
\(828\) | 19.3228 | 0.671514 | ||||||||
\(829\) | −45.9721 | −1.59668 | −0.798338 | − | 0.602209i | \(-0.794287\pi\) | ||||
−0.798338 | + | 0.602209i | \(0.794287\pi\) | |||||||
\(830\) | 2.60248 | 0.0903333 | ||||||||
\(831\) | −46.5057 | −1.61327 | ||||||||
\(832\) | −0.841124 | −0.0291607 | ||||||||
\(833\) | 6.46361 | 0.223951 | ||||||||
\(834\) | −97.7908 | −3.38622 | ||||||||
\(835\) | −2.97244 | −0.102865 | ||||||||
\(836\) | 31.4955 | 1.08929 | ||||||||
\(837\) | −44.8802 | −1.55129 | ||||||||
\(838\) | −36.2224 | −1.25128 | ||||||||
\(839\) | −40.4736 | −1.39730 | −0.698652 | − | 0.715462i | \(-0.746216\pi\) | ||||
−0.698652 | + | 0.715462i | \(0.746216\pi\) | |||||||
\(840\) | 9.81746 | 0.338734 | ||||||||
\(841\) | −11.0611 | −0.381416 | ||||||||
\(842\) | −37.3331 | −1.28658 | ||||||||
\(843\) | 62.1981 | 2.14222 | ||||||||
\(844\) | 7.06252 | 0.243102 | ||||||||
\(845\) | 9.03641 | 0.310862 | ||||||||
\(846\) | −81.8358 | −2.81357 | ||||||||
\(847\) | 34.2574 | 1.17710 | ||||||||
\(848\) | −3.19639 | −0.109764 | ||||||||
\(849\) | −0.167868 | −0.00576121 | ||||||||
\(850\) | 3.83071 | 0.131392 | ||||||||
\(851\) | 13.0741 | 0.448174 | ||||||||
\(852\) | 50.0108 | 1.71334 | ||||||||
\(853\) | 47.1795 | 1.61539 | 0.807697 | − | 0.589597i | \(-0.200714\pi\) | ||||
0.807697 | + | 0.589597i | \(0.200714\pi\) | |||||||
\(854\) | −15.2222 | −0.520893 | ||||||||
\(855\) | 39.5992 | 1.35427 | ||||||||
\(856\) | −20.0141 | −0.684069 | ||||||||
\(857\) | −25.4135 | −0.868110 | −0.434055 | − | 0.900886i | \(-0.642918\pi\) | ||||
−0.434055 | + | 0.900886i | \(0.642918\pi\) | |||||||
\(858\) | −61.3690 | −2.09510 | ||||||||
\(859\) | −28.2965 | −0.965464 | −0.482732 | − | 0.875768i | \(-0.660356\pi\) | ||||
−0.482732 | + | 0.875768i | \(0.660356\pi\) | |||||||
\(860\) | −4.55083 | −0.155182 | ||||||||
\(861\) | −56.2973 | −1.91861 | ||||||||
\(862\) | 50.9233 | 1.73445 | ||||||||
\(863\) | 31.1687 | 1.06100 | 0.530498 | − | 0.847686i | \(-0.322005\pi\) | ||||
0.530498 | + | 0.847686i | \(0.322005\pi\) | |||||||
\(864\) | −89.9268 | −3.05937 | ||||||||
\(865\) | −3.45083 | −0.117332 | ||||||||
\(866\) | −64.2349 | −2.18279 | ||||||||
\(867\) | 40.4098 | 1.37239 | ||||||||
\(868\) | 6.73908 | 0.228739 | ||||||||
\(869\) | −58.2799 | −1.97701 | ||||||||
\(870\) | 24.6190 | 0.834664 | ||||||||
\(871\) | 3.33867 | 0.113126 | ||||||||
\(872\) | 16.4966 | 0.558646 | ||||||||
\(873\) | 83.2827 | 2.81869 | ||||||||
\(874\) | 19.8037 | 0.669868 | ||||||||
\(875\) | −2.00064 | −0.0676341 | ||||||||
\(876\) | −2.52562 | −0.0853328 | ||||||||
\(877\) | 6.10598 | 0.206184 | 0.103092 | − | 0.994672i | \(-0.467126\pi\) | ||||
0.103092 | + | 0.994672i | \(0.467126\pi\) | |||||||
\(878\) | −66.5136 | −2.24473 | ||||||||
\(879\) | 38.8208 | 1.30939 | ||||||||
\(880\) | −26.3870 | −0.889504 | ||||||||
\(881\) | 48.6591 | 1.63937 | 0.819684 | − | 0.572816i | \(-0.194149\pi\) | ||||
0.819684 | + | 0.572816i | \(0.194149\pi\) | |||||||
\(882\) | 41.0343 | 1.38170 | ||||||||
\(883\) | 50.2633 | 1.69149 | 0.845747 | − | 0.533584i | \(-0.179155\pi\) | ||||
0.845747 | + | 0.533584i | \(0.179155\pi\) | |||||||
\(884\) | −4.96187 | −0.166886 | ||||||||
\(885\) | −25.7817 | −0.866641 | ||||||||
\(886\) | 36.4712 | 1.22527 | ||||||||
\(887\) | −6.15197 | −0.206563 | −0.103281 | − | 0.994652i | \(-0.532934\pi\) | ||||
−0.103281 | + | 0.994652i | \(0.532934\pi\) | |||||||
\(888\) | −29.5726 | −0.992393 | ||||||||
\(889\) | 3.96747 | 0.133065 | ||||||||
\(890\) | 7.96342 | 0.266935 | ||||||||
\(891\) | −144.606 | −4.84448 | ||||||||
\(892\) | 7.54849 | 0.252742 | ||||||||
\(893\) | −30.7175 | −1.02792 | ||||||||
\(894\) | 63.8986 | 2.13709 | ||||||||
\(895\) | 17.5419 | 0.586362 | ||||||||
\(896\) | −21.8648 | −0.730452 | ||||||||
\(897\) | −14.1324 | −0.471865 | ||||||||
\(898\) | −1.41660 | −0.0472725 | ||||||||
\(899\) | −12.3440 | −0.411695 | ||||||||
\(900\) | 8.90676 | 0.296892 | ||||||||
\(901\) | −1.38525 | −0.0461494 | ||||||||
\(902\) | 81.0184 | 2.69762 | ||||||||
\(903\) | −25.7754 | −0.857751 | ||||||||
\(904\) | −18.7132 | −0.622391 | ||||||||
\(905\) | 3.80660 | 0.126536 | ||||||||
\(906\) | −78.7379 | −2.61589 | ||||||||
\(907\) | −33.7824 | −1.12173 | −0.560863 | − | 0.827908i | \(-0.689531\pi\) | ||||
−0.560863 | + | 0.827908i | \(0.689531\pi\) | |||||||
\(908\) | 22.1280 | 0.734342 | ||||||||
\(909\) | −70.8605 | −2.35029 | ||||||||
\(910\) | 7.07567 | 0.234556 | ||||||||
\(911\) | −22.4517 | −0.743859 | −0.371930 | − | 0.928261i | \(-0.621304\pi\) | ||||
−0.371930 | + | 0.928261i | \(0.621304\pi\) | |||||||
\(912\) | −83.6600 | −2.77026 | ||||||||
\(913\) | −7.76901 | −0.257117 | ||||||||
\(914\) | −67.2052 | −2.22295 | ||||||||
\(915\) | 14.0144 | 0.463301 | ||||||||
\(916\) | 22.0642 | 0.729022 | ||||||||
\(917\) | 41.5322 | 1.37152 | ||||||||
\(918\) | −58.9899 | −1.94696 | ||||||||
\(919\) | −40.9486 | −1.35077 | −0.675385 | − | 0.737466i | \(-0.736022\pi\) | ||||
−0.675385 | + | 0.737466i | \(0.736022\pi\) | |||||||
\(920\) | −3.25357 | −0.107267 | ||||||||
\(921\) | 72.3235 | 2.38314 | ||||||||
\(922\) | −7.99856 | −0.263419 | ||||||||
\(923\) | −26.3278 | −0.866590 | ||||||||
\(924\) | 40.1232 | 1.31996 | ||||||||
\(925\) | 6.02644 | 0.198148 | ||||||||
\(926\) | 32.3809 | 1.06410 | ||||||||
\(927\) | 34.0454 | 1.11820 | ||||||||
\(928\) | −24.7337 | −0.811924 | ||||||||
\(929\) | −25.1507 | −0.825167 | −0.412583 | − | 0.910920i | \(-0.635373\pi\) | ||||
−0.412583 | + | 0.910920i | \(0.635373\pi\) | |||||||
\(930\) | −16.9406 | −0.555505 | ||||||||
\(931\) | 15.4025 | 0.504795 | ||||||||
\(932\) | 21.4147 | 0.701462 | ||||||||
\(933\) | 86.2216 | 2.82277 | ||||||||
\(934\) | −20.7287 | −0.678263 | ||||||||
\(935\) | −11.4356 | −0.373984 | ||||||||
\(936\) | 23.0091 | 0.752076 | ||||||||
\(937\) | 11.6143 | 0.379422 | 0.189711 | − | 0.981840i | \(-0.439245\pi\) | ||||
0.189711 | + | 0.981840i | \(0.439245\pi\) | |||||||
\(938\) | −5.96008 | −0.194603 | ||||||||
\(939\) | 75.0513 | 2.44921 | ||||||||
\(940\) | −6.90907 | −0.225349 | ||||||||
\(941\) | −9.80807 | −0.319734 | −0.159867 | − | 0.987139i | \(-0.551107\pi\) | ||||
−0.159867 | + | 0.987139i | \(0.551107\pi\) | |||||||
\(942\) | 77.2062 | 2.51551 | ||||||||
\(943\) | 18.6573 | 0.607566 | ||||||||
\(944\) | 39.2056 | 1.27603 | ||||||||
\(945\) | 30.8083 | 1.00219 | ||||||||
\(946\) | 37.0938 | 1.20602 | ||||||||
\(947\) | 26.9200 | 0.874783 | 0.437391 | − | 0.899271i | \(-0.355902\pi\) | ||||
0.437391 | + | 0.899271i | \(0.355902\pi\) | |||||||
\(948\) | −41.5605 | −1.34982 | ||||||||
\(949\) | 1.32959 | 0.0431604 | ||||||||
\(950\) | 9.12840 | 0.296164 | ||||||||
\(951\) | −6.00690 | −0.194787 | ||||||||
\(952\) | −6.47002 | −0.209695 | ||||||||
\(953\) | −10.8377 | −0.351067 | −0.175534 | − | 0.984473i | \(-0.556165\pi\) | ||||
−0.175534 | + | 0.984473i | \(0.556165\pi\) | |||||||
\(954\) | −8.79429 | −0.284726 | ||||||||
\(955\) | −4.66268 | −0.150881 | ||||||||
\(956\) | −31.5907 | −1.02172 | ||||||||
\(957\) | −73.4937 | −2.37571 | ||||||||
\(958\) | 1.50392 | 0.0485894 | ||||||||
\(959\) | 31.4106 | 1.01430 | ||||||||
\(960\) | −1.38240 | −0.0446169 | ||||||||
\(961\) | −22.5060 | −0.725999 | ||||||||
\(962\) | −21.3137 | −0.687180 | ||||||||
\(963\) | −102.842 | −3.31405 | ||||||||
\(964\) | −8.80653 | −0.283639 | ||||||||
\(965\) | 27.1145 | 0.872848 | ||||||||
\(966\) | 25.2286 | 0.811716 | ||||||||
\(967\) | 47.0076 | 1.51166 | 0.755831 | − | 0.654767i | \(-0.227233\pi\) | ||||
0.755831 | + | 0.654767i | \(0.227233\pi\) | |||||||
\(968\) | 25.6799 | 0.825385 | ||||||||
\(969\) | −36.2566 | −1.16473 | ||||||||
\(970\) | 19.1983 | 0.616421 | ||||||||
\(971\) | 1.85484 | 0.0595247 | 0.0297623 | − | 0.999557i | \(-0.490525\pi\) | ||||
0.0297623 | + | 0.999557i | \(0.490525\pi\) | |||||||
\(972\) | −49.7269 | −1.59499 | ||||||||
\(973\) | −33.6585 | −1.07904 | ||||||||
\(974\) | 40.9392 | 1.31178 | ||||||||
\(975\) | −6.51424 | −0.208623 | ||||||||
\(976\) | −21.3114 | −0.682161 | ||||||||
\(977\) | 26.1144 | 0.835473 | 0.417736 | − | 0.908568i | \(-0.362824\pi\) | ||||
0.417736 | + | 0.908568i | \(0.362824\pi\) | |||||||
\(978\) | −95.9265 | −3.06739 | ||||||||
\(979\) | −23.7727 | −0.759779 | ||||||||
\(980\) | 3.46436 | 0.110665 | ||||||||
\(981\) | 84.7676 | 2.70642 | ||||||||
\(982\) | 44.3340 | 1.41476 | ||||||||
\(983\) | 24.7248 | 0.788599 | 0.394300 | − | 0.918982i | \(-0.370987\pi\) | ||||
0.394300 | + | 0.918982i | \(0.370987\pi\) | |||||||
\(984\) | −42.2015 | −1.34533 | ||||||||
\(985\) | 7.56487 | 0.241037 | ||||||||
\(986\) | −16.2247 | −0.516701 | ||||||||
\(987\) | −39.1322 | −1.24559 | ||||||||
\(988\) | −11.8239 | −0.376168 | ||||||||
\(989\) | 8.54213 | 0.271624 | ||||||||
\(990\) | −72.5990 | −2.30735 | ||||||||
\(991\) | −47.3321 | −1.50355 | −0.751777 | − | 0.659418i | \(-0.770803\pi\) | ||||
−0.751777 | + | 0.659418i | \(0.770803\pi\) | |||||||
\(992\) | 17.0195 | 0.540371 | ||||||||
\(993\) | −28.4475 | −0.902754 | ||||||||
\(994\) | 46.9995 | 1.49073 | ||||||||
\(995\) | −13.8659 | −0.439579 | ||||||||
\(996\) | −5.54023 | −0.175549 | ||||||||
\(997\) | −44.5922 | −1.41225 | −0.706124 | − | 0.708088i | \(-0.749558\pi\) | ||||
−0.706124 | + | 0.708088i | \(0.749558\pi\) | |||||||
\(998\) | 19.0578 | 0.603264 | ||||||||
\(999\) | −92.8023 | −2.93613 |
(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 | 2005.2.a.e.1.7 | ✓ | 29 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2005.2.a.e.1.7 | ✓ | 29 | 1.1 | even | 1 | trivial |