Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5577,2,Mod(1,5577)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5577, 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("5577.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5577 = 3 \cdot 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5577.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: | \(44.5325692073\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 7x^{5} + 21x^{4} + 13x^{3} - 33x^{2} - 7x + 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 429) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.53441\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5577.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.53441 | −1.79210 | −0.896050 | − | 0.443953i | \(-0.853576\pi\) | ||||
−0.896050 | + | 0.443953i | \(0.853576\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 4.42325 | 2.21162 | ||||||||
\(5\) | −3.70100 | −1.65514 | −0.827568 | − | 0.561366i | \(-0.810276\pi\) | ||||
−0.827568 | + | 0.561366i | \(0.810276\pi\) | |||||||
\(6\) | −2.53441 | −1.03467 | ||||||||
\(7\) | 0.957295 | 0.361823 | 0.180912 | − | 0.983499i | \(-0.442095\pi\) | ||||
0.180912 | + | 0.983499i | \(0.442095\pi\) | |||||||
\(8\) | −6.14151 | −2.17135 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 9.37985 | 2.96617 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 4.42325 | 1.27688 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −2.42618 | −0.648424 | ||||||||
\(15\) | −3.70100 | −0.955593 | ||||||||
\(16\) | 6.71863 | 1.67966 | ||||||||
\(17\) | −2.05542 | −0.498512 | −0.249256 | − | 0.968438i | \(-0.580186\pi\) | ||||
−0.249256 | + | 0.968438i | \(0.580186\pi\) | |||||||
\(18\) | −2.53441 | −0.597367 | ||||||||
\(19\) | −7.67886 | −1.76165 | −0.880825 | − | 0.473442i | \(-0.843012\pi\) | ||||
−0.880825 | + | 0.473442i | \(0.843012\pi\) | |||||||
\(20\) | −16.3704 | −3.66054 | ||||||||
\(21\) | 0.957295 | 0.208899 | ||||||||
\(22\) | 2.53441 | 0.540339 | ||||||||
\(23\) | −4.20997 | −0.877840 | −0.438920 | − | 0.898526i | \(-0.644639\pi\) | ||||
−0.438920 | + | 0.898526i | \(0.644639\pi\) | |||||||
\(24\) | −6.14151 | −1.25363 | ||||||||
\(25\) | 8.69737 | 1.73947 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.23435 | 0.800217 | ||||||||
\(29\) | 1.97786 | 0.367279 | 0.183640 | − | 0.982994i | \(-0.441212\pi\) | ||||
0.183640 | + | 0.982994i | \(0.441212\pi\) | |||||||
\(30\) | 9.37985 | 1.71252 | ||||||||
\(31\) | 10.5475 | 1.89439 | 0.947193 | − | 0.320664i | \(-0.103906\pi\) | ||||
0.947193 | + | 0.320664i | \(0.103906\pi\) | |||||||
\(32\) | −4.74476 | −0.838763 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 5.20928 | 0.893384 | ||||||||
\(35\) | −3.54294 | −0.598867 | ||||||||
\(36\) | 4.42325 | 0.737208 | ||||||||
\(37\) | 8.30741 | 1.36573 | 0.682865 | − | 0.730545i | \(-0.260734\pi\) | ||||
0.682865 | + | 0.730545i | \(0.260734\pi\) | |||||||
\(38\) | 19.4614 | 3.15705 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 22.7297 | 3.59388 | ||||||||
\(41\) | 5.23142 | 0.817011 | 0.408505 | − | 0.912756i | \(-0.366050\pi\) | ||||
0.408505 | + | 0.912756i | \(0.366050\pi\) | |||||||
\(42\) | −2.42618 | −0.374368 | ||||||||
\(43\) | 5.26116 | 0.802320 | 0.401160 | − | 0.916008i | \(-0.368607\pi\) | ||||
0.401160 | + | 0.916008i | \(0.368607\pi\) | |||||||
\(44\) | −4.42325 | −0.666830 | ||||||||
\(45\) | −3.70100 | −0.551712 | ||||||||
\(46\) | 10.6698 | 1.57318 | ||||||||
\(47\) | 1.24656 | 0.181829 | 0.0909145 | − | 0.995859i | \(-0.471021\pi\) | ||||
0.0909145 | + | 0.995859i | \(0.471021\pi\) | |||||||
\(48\) | 6.71863 | 0.969751 | ||||||||
\(49\) | −6.08359 | −0.869084 | ||||||||
\(50\) | −22.0427 | −3.11731 | ||||||||
\(51\) | −2.05542 | −0.287816 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.98297 | 0.409743 | 0.204871 | − | 0.978789i | \(-0.434322\pi\) | ||||
0.204871 | + | 0.978789i | \(0.434322\pi\) | |||||||
\(54\) | −2.53441 | −0.344890 | ||||||||
\(55\) | 3.70100 | 0.499042 | ||||||||
\(56\) | −5.87924 | −0.785646 | ||||||||
\(57\) | −7.67886 | −1.01709 | ||||||||
\(58\) | −5.01271 | −0.658202 | ||||||||
\(59\) | 12.3548 | 1.60846 | 0.804228 | − | 0.594321i | \(-0.202579\pi\) | ||||
0.804228 | + | 0.594321i | \(0.202579\pi\) | |||||||
\(60\) | −16.3704 | −2.11341 | ||||||||
\(61\) | −0.183851 | −0.0235397 | −0.0117698 | − | 0.999931i | \(-0.503747\pi\) | ||||
−0.0117698 | + | 0.999931i | \(0.503747\pi\) | |||||||
\(62\) | −26.7317 | −3.39493 | ||||||||
\(63\) | 0.957295 | 0.120608 | ||||||||
\(64\) | −1.41208 | −0.176510 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.53441 | 0.311965 | ||||||||
\(67\) | −1.40691 | −0.171881 | −0.0859407 | − | 0.996300i | \(-0.527390\pi\) | ||||
−0.0859407 | + | 0.996300i | \(0.527390\pi\) | |||||||
\(68\) | −9.09163 | −1.10252 | ||||||||
\(69\) | −4.20997 | −0.506821 | ||||||||
\(70\) | 8.97928 | 1.07323 | ||||||||
\(71\) | −12.1582 | −1.44291 | −0.721457 | − | 0.692459i | \(-0.756527\pi\) | ||||
−0.721457 | + | 0.692459i | \(0.756527\pi\) | |||||||
\(72\) | −6.14151 | −0.723784 | ||||||||
\(73\) | 3.32573 | 0.389247 | 0.194624 | − | 0.980878i | \(-0.437651\pi\) | ||||
0.194624 | + | 0.980878i | \(0.437651\pi\) | |||||||
\(74\) | −21.0544 | −2.44752 | ||||||||
\(75\) | 8.69737 | 1.00429 | ||||||||
\(76\) | −33.9655 | −3.89611 | ||||||||
\(77\) | −0.957295 | −0.109094 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.64911 | −0.410557 | −0.205279 | − | 0.978704i | \(-0.565810\pi\) | ||||
−0.205279 | + | 0.978704i | \(0.565810\pi\) | |||||||
\(80\) | −24.8656 | −2.78006 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −13.2586 | −1.46417 | ||||||||
\(83\) | −3.31957 | −0.364370 | −0.182185 | − | 0.983264i | \(-0.558317\pi\) | ||||
−0.182185 | + | 0.983264i | \(0.558317\pi\) | |||||||
\(84\) | 4.23435 | 0.462006 | ||||||||
\(85\) | 7.60710 | 0.825106 | ||||||||
\(86\) | −13.3340 | −1.43784 | ||||||||
\(87\) | 1.97786 | 0.212049 | ||||||||
\(88\) | 6.14151 | 0.654687 | ||||||||
\(89\) | −5.24302 | −0.555759 | −0.277879 | − | 0.960616i | \(-0.589632\pi\) | ||||
−0.277879 | + | 0.960616i | \(0.589632\pi\) | |||||||
\(90\) | 9.37985 | 0.988723 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −18.6217 | −1.94145 | ||||||||
\(93\) | 10.5475 | 1.09372 | ||||||||
\(94\) | −3.15929 | −0.325856 | ||||||||
\(95\) | 28.4194 | 2.91577 | ||||||||
\(96\) | −4.74476 | −0.484260 | ||||||||
\(97\) | −9.82293 | −0.997368 | −0.498684 | − | 0.866784i | \(-0.666183\pi\) | ||||
−0.498684 | + | 0.866784i | \(0.666183\pi\) | |||||||
\(98\) | 15.4183 | 1.55749 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 38.4706 | 3.84706 | ||||||||
\(101\) | −8.42338 | −0.838157 | −0.419079 | − | 0.907950i | \(-0.637647\pi\) | ||||
−0.419079 | + | 0.907950i | \(0.637647\pi\) | |||||||
\(102\) | 5.20928 | 0.515796 | ||||||||
\(103\) | −13.4029 | −1.32063 | −0.660314 | − | 0.750989i | \(-0.729577\pi\) | ||||
−0.660314 | + | 0.750989i | \(0.729577\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.54294 | −0.345756 | ||||||||
\(106\) | −7.56008 | −0.734300 | ||||||||
\(107\) | −8.05792 | −0.778988 | −0.389494 | − | 0.921029i | \(-0.627350\pi\) | ||||
−0.389494 | + | 0.921029i | \(0.627350\pi\) | |||||||
\(108\) | 4.42325 | 0.425627 | ||||||||
\(109\) | 14.3600 | 1.37544 | 0.687720 | − | 0.725976i | \(-0.258612\pi\) | ||||
0.687720 | + | 0.725976i | \(0.258612\pi\) | |||||||
\(110\) | −9.37985 | −0.894334 | ||||||||
\(111\) | 8.30741 | 0.788504 | ||||||||
\(112\) | 6.43171 | 0.607739 | ||||||||
\(113\) | 18.6675 | 1.75609 | 0.878046 | − | 0.478577i | \(-0.158847\pi\) | ||||
0.878046 | + | 0.478577i | \(0.158847\pi\) | |||||||
\(114\) | 19.4614 | 1.82273 | ||||||||
\(115\) | 15.5811 | 1.45294 | ||||||||
\(116\) | 8.74857 | 0.812284 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −31.3121 | −2.88251 | ||||||||
\(119\) | −1.96764 | −0.180373 | ||||||||
\(120\) | 22.7297 | 2.07493 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0.465954 | 0.0421855 | ||||||||
\(123\) | 5.23142 | 0.471701 | ||||||||
\(124\) | 46.6542 | 4.18967 | ||||||||
\(125\) | −13.6840 | −1.22393 | ||||||||
\(126\) | −2.42618 | −0.216141 | ||||||||
\(127\) | 6.60130 | 0.585770 | 0.292885 | − | 0.956148i | \(-0.405385\pi\) | ||||
0.292885 | + | 0.956148i | \(0.405385\pi\) | |||||||
\(128\) | 13.0683 | 1.15509 | ||||||||
\(129\) | 5.26116 | 0.463220 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.81083 | 0.507694 | 0.253847 | − | 0.967244i | \(-0.418304\pi\) | ||||
0.253847 | + | 0.967244i | \(0.418304\pi\) | |||||||
\(132\) | −4.42325 | −0.384994 | ||||||||
\(133\) | −7.35093 | −0.637406 | ||||||||
\(134\) | 3.56569 | 0.308029 | ||||||||
\(135\) | −3.70100 | −0.318531 | ||||||||
\(136\) | 12.6234 | 1.08245 | ||||||||
\(137\) | −5.64208 | −0.482035 | −0.241018 | − | 0.970521i | \(-0.577481\pi\) | ||||
−0.241018 | + | 0.970521i | \(0.577481\pi\) | |||||||
\(138\) | 10.6698 | 0.908274 | ||||||||
\(139\) | −4.46820 | −0.378987 | −0.189494 | − | 0.981882i | \(-0.560685\pi\) | ||||
−0.189494 | + | 0.981882i | \(0.560685\pi\) | |||||||
\(140\) | −15.6713 | −1.32447 | ||||||||
\(141\) | 1.24656 | 0.104979 | ||||||||
\(142\) | 30.8139 | 2.58585 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 6.71863 | 0.559886 | ||||||||
\(145\) | −7.32005 | −0.607897 | ||||||||
\(146\) | −8.42877 | −0.697570 | ||||||||
\(147\) | −6.08359 | −0.501766 | ||||||||
\(148\) | 36.7457 | 3.02048 | ||||||||
\(149\) | 7.39749 | 0.606026 | 0.303013 | − | 0.952986i | \(-0.402007\pi\) | ||||
0.303013 | + | 0.952986i | \(0.402007\pi\) | |||||||
\(150\) | −22.0427 | −1.79978 | ||||||||
\(151\) | −23.7454 | −1.93237 | −0.966187 | − | 0.257841i | \(-0.916989\pi\) | ||||
−0.966187 | + | 0.257841i | \(0.916989\pi\) | |||||||
\(152\) | 47.1598 | 3.82516 | ||||||||
\(153\) | −2.05542 | −0.166171 | ||||||||
\(154\) | 2.42618 | 0.195507 | ||||||||
\(155\) | −39.0362 | −3.13547 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.9704 | 1.03515 | 0.517576 | − | 0.855637i | \(-0.326834\pi\) | ||||
0.517576 | + | 0.855637i | \(0.326834\pi\) | |||||||
\(158\) | 9.24836 | 0.735760 | ||||||||
\(159\) | 2.98297 | 0.236565 | ||||||||
\(160\) | 17.5603 | 1.38827 | ||||||||
\(161\) | −4.03018 | −0.317623 | ||||||||
\(162\) | −2.53441 | −0.199122 | ||||||||
\(163\) | −18.6880 | −1.46376 | −0.731878 | − | 0.681436i | \(-0.761356\pi\) | ||||
−0.731878 | + | 0.681436i | \(0.761356\pi\) | |||||||
\(164\) | 23.1399 | 1.80692 | ||||||||
\(165\) | 3.70100 | 0.288122 | ||||||||
\(166\) | 8.41316 | 0.652988 | ||||||||
\(167\) | −25.0420 | −1.93781 | −0.968904 | − | 0.247437i | \(-0.920412\pi\) | ||||
−0.968904 | + | 0.247437i | \(0.920412\pi\) | |||||||
\(168\) | −5.87924 | −0.453593 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −19.2795 | −1.47867 | ||||||||
\(171\) | −7.67886 | −0.587217 | ||||||||
\(172\) | 23.2714 | 1.77443 | ||||||||
\(173\) | −3.16333 | −0.240503 | −0.120252 | − | 0.992743i | \(-0.538370\pi\) | ||||
−0.120252 | + | 0.992743i | \(0.538370\pi\) | |||||||
\(174\) | −5.01271 | −0.380013 | ||||||||
\(175\) | 8.32595 | 0.629383 | ||||||||
\(176\) | −6.71863 | −0.506436 | ||||||||
\(177\) | 12.3548 | 0.928642 | ||||||||
\(178\) | 13.2880 | 0.995976 | ||||||||
\(179\) | 1.24977 | 0.0934123 | 0.0467062 | − | 0.998909i | \(-0.485128\pi\) | ||||
0.0467062 | + | 0.998909i | \(0.485128\pi\) | |||||||
\(180\) | −16.3704 | −1.22018 | ||||||||
\(181\) | 16.0712 | 1.19456 | 0.597281 | − | 0.802032i | \(-0.296248\pi\) | ||||
0.597281 | + | 0.802032i | \(0.296248\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.183851 | −0.0135906 | ||||||||
\(184\) | 25.8556 | 1.90610 | ||||||||
\(185\) | −30.7457 | −2.26047 | ||||||||
\(186\) | −26.7317 | −1.96006 | ||||||||
\(187\) | 2.05542 | 0.150307 | ||||||||
\(188\) | 5.51383 | 0.402137 | ||||||||
\(189\) | 0.957295 | 0.0696329 | ||||||||
\(190\) | −72.0265 | −5.22535 | ||||||||
\(191\) | 15.2909 | 1.10641 | 0.553207 | − | 0.833044i | \(-0.313404\pi\) | ||||
0.553207 | + | 0.833044i | \(0.313404\pi\) | |||||||
\(192\) | −1.41208 | −0.101908 | ||||||||
\(193\) | −6.76152 | −0.486705 | −0.243353 | − | 0.969938i | \(-0.578247\pi\) | ||||
−0.243353 | + | 0.969938i | \(0.578247\pi\) | |||||||
\(194\) | 24.8954 | 1.78738 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −26.9092 | −1.92209 | ||||||||
\(197\) | 11.3320 | 0.807374 | 0.403687 | − | 0.914897i | \(-0.367728\pi\) | ||||
0.403687 | + | 0.914897i | \(0.367728\pi\) | |||||||
\(198\) | 2.53441 | 0.180113 | ||||||||
\(199\) | 21.5642 | 1.52864 | 0.764321 | − | 0.644836i | \(-0.223074\pi\) | ||||
0.764321 | + | 0.644836i | \(0.223074\pi\) | |||||||
\(200\) | −53.4150 | −3.77701 | ||||||||
\(201\) | −1.40691 | −0.0992358 | ||||||||
\(202\) | 21.3483 | 1.50206 | ||||||||
\(203\) | 1.89339 | 0.132890 | ||||||||
\(204\) | −9.09163 | −0.636541 | ||||||||
\(205\) | −19.3615 | −1.35226 | ||||||||
\(206\) | 33.9685 | 2.36670 | ||||||||
\(207\) | −4.20997 | −0.292613 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.67886 | 0.531158 | ||||||||
\(210\) | 8.97928 | 0.619629 | ||||||||
\(211\) | −23.5992 | −1.62463 | −0.812317 | − | 0.583217i | \(-0.801794\pi\) | ||||
−0.812317 | + | 0.583217i | \(0.801794\pi\) | |||||||
\(212\) | 13.1944 | 0.906197 | ||||||||
\(213\) | −12.1582 | −0.833067 | ||||||||
\(214\) | 20.4221 | 1.39603 | ||||||||
\(215\) | −19.4715 | −1.32795 | ||||||||
\(216\) | −6.14151 | −0.417877 | ||||||||
\(217\) | 10.0971 | 0.685433 | ||||||||
\(218\) | −36.3942 | −2.46493 | ||||||||
\(219\) | 3.32573 | 0.224732 | ||||||||
\(220\) | 16.3704 | 1.10369 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −21.0544 | −1.41308 | ||||||||
\(223\) | 14.7201 | 0.985730 | 0.492865 | − | 0.870106i | \(-0.335950\pi\) | ||||
0.492865 | + | 0.870106i | \(0.335950\pi\) | |||||||
\(224\) | −4.54213 | −0.303484 | ||||||||
\(225\) | 8.69737 | 0.579825 | ||||||||
\(226\) | −47.3112 | −3.14709 | ||||||||
\(227\) | −0.0358913 | −0.00238219 | −0.00119109 | − | 0.999999i | \(-0.500379\pi\) | ||||
−0.00119109 | + | 0.999999i | \(0.500379\pi\) | |||||||
\(228\) | −33.9655 | −2.24942 | ||||||||
\(229\) | −8.37257 | −0.553275 | −0.276637 | − | 0.960974i | \(-0.589220\pi\) | ||||
−0.276637 | + | 0.960974i | \(0.589220\pi\) | |||||||
\(230\) | −39.4889 | −2.60382 | ||||||||
\(231\) | −0.957295 | −0.0629854 | ||||||||
\(232\) | −12.1471 | −0.797493 | ||||||||
\(233\) | −18.0020 | −1.17935 | −0.589674 | − | 0.807641i | \(-0.700744\pi\) | ||||
−0.589674 | + | 0.807641i | \(0.700744\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.61350 | −0.300952 | ||||||||
\(236\) | 54.6483 | 3.55730 | ||||||||
\(237\) | −3.64911 | −0.237035 | ||||||||
\(238\) | 4.98682 | 0.323247 | ||||||||
\(239\) | 5.74497 | 0.371611 | 0.185806 | − | 0.982587i | \(-0.440511\pi\) | ||||
0.185806 | + | 0.982587i | \(0.440511\pi\) | |||||||
\(240\) | −24.8656 | −1.60507 | ||||||||
\(241\) | 16.1458 | 1.04004 | 0.520022 | − | 0.854153i | \(-0.325924\pi\) | ||||
0.520022 | + | 0.854153i | \(0.325924\pi\) | |||||||
\(242\) | −2.53441 | −0.162918 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −0.813218 | −0.0520609 | ||||||||
\(245\) | 22.5153 | 1.43845 | ||||||||
\(246\) | −13.2586 | −0.845336 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −64.7776 | −4.11338 | ||||||||
\(249\) | −3.31957 | −0.210369 | ||||||||
\(250\) | 34.6808 | 2.19341 | ||||||||
\(251\) | −6.83631 | −0.431504 | −0.215752 | − | 0.976448i | \(-0.569220\pi\) | ||||
−0.215752 | + | 0.976448i | \(0.569220\pi\) | |||||||
\(252\) | 4.23435 | 0.266739 | ||||||||
\(253\) | 4.20997 | 0.264679 | ||||||||
\(254\) | −16.7304 | −1.04976 | ||||||||
\(255\) | 7.60710 | 0.476375 | ||||||||
\(256\) | −30.2963 | −1.89352 | ||||||||
\(257\) | −26.8038 | −1.67197 | −0.835987 | − | 0.548749i | \(-0.815104\pi\) | ||||
−0.835987 | + | 0.548749i | \(0.815104\pi\) | |||||||
\(258\) | −13.3340 | −0.830136 | ||||||||
\(259\) | 7.95264 | 0.494153 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.97786 | 0.122426 | ||||||||
\(262\) | −14.7270 | −0.909839 | ||||||||
\(263\) | −11.9518 | −0.736980 | −0.368490 | − | 0.929632i | \(-0.620125\pi\) | ||||
−0.368490 | + | 0.929632i | \(0.620125\pi\) | |||||||
\(264\) | 6.14151 | 0.377984 | ||||||||
\(265\) | −11.0400 | −0.678180 | ||||||||
\(266\) | 18.6303 | 1.14230 | ||||||||
\(267\) | −5.24302 | −0.320868 | ||||||||
\(268\) | −6.22311 | −0.380137 | ||||||||
\(269\) | 4.59663 | 0.280261 | 0.140131 | − | 0.990133i | \(-0.455248\pi\) | ||||
0.140131 | + | 0.990133i | \(0.455248\pi\) | |||||||
\(270\) | 9.37985 | 0.570840 | ||||||||
\(271\) | −19.8969 | −1.20865 | −0.604326 | − | 0.796738i | \(-0.706557\pi\) | ||||
−0.604326 | + | 0.796738i | \(0.706557\pi\) | |||||||
\(272\) | −13.8096 | −0.837330 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.2994 | 0.863856 | ||||||||
\(275\) | −8.69737 | −0.524471 | ||||||||
\(276\) | −18.6217 | −1.12090 | ||||||||
\(277\) | −11.2319 | −0.674857 | −0.337428 | − | 0.941351i | \(-0.609557\pi\) | ||||
−0.337428 | + | 0.941351i | \(0.609557\pi\) | |||||||
\(278\) | 11.3243 | 0.679183 | ||||||||
\(279\) | 10.5475 | 0.631462 | ||||||||
\(280\) | 21.7590 | 1.30035 | ||||||||
\(281\) | 30.2946 | 1.80722 | 0.903612 | − | 0.428352i | \(-0.140906\pi\) | ||||
0.903612 | + | 0.428352i | \(0.140906\pi\) | |||||||
\(282\) | −3.15929 | −0.188133 | ||||||||
\(283\) | −15.3889 | −0.914777 | −0.457389 | − | 0.889267i | \(-0.651215\pi\) | ||||
−0.457389 | + | 0.889267i | \(0.651215\pi\) | |||||||
\(284\) | −53.7788 | −3.19118 | ||||||||
\(285\) | 28.4194 | 1.68342 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.00801 | 0.295614 | ||||||||
\(288\) | −4.74476 | −0.279588 | ||||||||
\(289\) | −12.7753 | −0.751485 | ||||||||
\(290\) | 18.5520 | 1.08941 | ||||||||
\(291\) | −9.82293 | −0.575831 | ||||||||
\(292\) | 14.7105 | 0.860869 | ||||||||
\(293\) | −6.95822 | −0.406503 | −0.203252 | − | 0.979127i | \(-0.565151\pi\) | ||||
−0.203252 | + | 0.979127i | \(0.565151\pi\) | |||||||
\(294\) | 15.4183 | 0.899215 | ||||||||
\(295\) | −45.7250 | −2.66221 | ||||||||
\(296\) | −51.0200 | −2.96548 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −18.7483 | −1.08606 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 38.4706 | 2.22110 | ||||||||
\(301\) | 5.03648 | 0.290298 | ||||||||
\(302\) | 60.1807 | 3.46301 | ||||||||
\(303\) | −8.42338 | −0.483910 | ||||||||
\(304\) | −51.5914 | −2.95897 | ||||||||
\(305\) | 0.680431 | 0.0389614 | ||||||||
\(306\) | 5.20928 | 0.297795 | ||||||||
\(307\) | 12.6233 | 0.720447 | 0.360224 | − | 0.932866i | \(-0.382700\pi\) | ||||
0.360224 | + | 0.932866i | \(0.382700\pi\) | |||||||
\(308\) | −4.23435 | −0.241275 | ||||||||
\(309\) | −13.4029 | −0.762465 | ||||||||
\(310\) | 98.9339 | 5.61907 | ||||||||
\(311\) | 2.12116 | 0.120280 | 0.0601399 | − | 0.998190i | \(-0.480845\pi\) | ||||
0.0601399 | + | 0.998190i | \(0.480845\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.5919 | 1.22045 | 0.610224 | − | 0.792229i | \(-0.291079\pi\) | ||||
0.610224 | + | 0.792229i | \(0.291079\pi\) | |||||||
\(314\) | −32.8724 | −1.85510 | ||||||||
\(315\) | −3.54294 | −0.199622 | ||||||||
\(316\) | −16.1409 | −0.907999 | ||||||||
\(317\) | −15.7684 | −0.885640 | −0.442820 | − | 0.896611i | \(-0.646022\pi\) | ||||
−0.442820 | + | 0.896611i | \(0.646022\pi\) | |||||||
\(318\) | −7.56008 | −0.423948 | ||||||||
\(319\) | −1.97786 | −0.110739 | ||||||||
\(320\) | 5.22612 | 0.292149 | ||||||||
\(321\) | −8.05792 | −0.449749 | ||||||||
\(322\) | 10.2141 | 0.569212 | ||||||||
\(323\) | 15.7833 | 0.878205 | ||||||||
\(324\) | 4.42325 | 0.245736 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 47.3631 | 2.62320 | ||||||||
\(327\) | 14.3600 | 0.794111 | ||||||||
\(328\) | −32.1288 | −1.77402 | ||||||||
\(329\) | 1.19332 | 0.0657900 | ||||||||
\(330\) | −9.37985 | −0.516344 | ||||||||
\(331\) | −11.6602 | −0.640902 | −0.320451 | − | 0.947265i | \(-0.603834\pi\) | ||||
−0.320451 | + | 0.947265i | \(0.603834\pi\) | |||||||
\(332\) | −14.6833 | −0.805850 | ||||||||
\(333\) | 8.30741 | 0.455243 | ||||||||
\(334\) | 63.4668 | 3.47275 | ||||||||
\(335\) | 5.20697 | 0.284487 | ||||||||
\(336\) | 6.43171 | 0.350879 | ||||||||
\(337\) | −7.63508 | −0.415909 | −0.207955 | − | 0.978138i | \(-0.566681\pi\) | ||||
−0.207955 | + | 0.978138i | \(0.566681\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.6675 | 1.01388 | ||||||||
\(340\) | 33.6481 | 1.82482 | ||||||||
\(341\) | −10.5475 | −0.571179 | ||||||||
\(342\) | 19.4614 | 1.05235 | ||||||||
\(343\) | −12.5248 | −0.676278 | ||||||||
\(344\) | −32.3115 | −1.74212 | ||||||||
\(345\) | 15.5811 | 0.838858 | ||||||||
\(346\) | 8.01717 | 0.431006 | ||||||||
\(347\) | −17.7823 | −0.954606 | −0.477303 | − | 0.878739i | \(-0.658386\pi\) | ||||
−0.477303 | + | 0.878739i | \(0.658386\pi\) | |||||||
\(348\) | 8.74857 | 0.468972 | ||||||||
\(349\) | −12.1663 | −0.651245 | −0.325622 | − | 0.945500i | \(-0.605574\pi\) | ||||
−0.325622 | + | 0.945500i | \(0.605574\pi\) | |||||||
\(350\) | −21.1014 | −1.12792 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.74476 | 0.252896 | ||||||||
\(353\) | 32.9025 | 1.75122 | 0.875612 | − | 0.483014i | \(-0.160458\pi\) | ||||
0.875612 | + | 0.483014i | \(0.160458\pi\) | |||||||
\(354\) | −31.3121 | −1.66422 | ||||||||
\(355\) | 44.9975 | 2.38822 | ||||||||
\(356\) | −23.1912 | −1.22913 | ||||||||
\(357\) | −1.96764 | −0.104139 | ||||||||
\(358\) | −3.16744 | −0.167404 | ||||||||
\(359\) | −7.29760 | −0.385153 | −0.192576 | − | 0.981282i | \(-0.561684\pi\) | ||||
−0.192576 | + | 0.981282i | \(0.561684\pi\) | |||||||
\(360\) | 22.7297 | 1.19796 | ||||||||
\(361\) | 39.9648 | 2.10341 | ||||||||
\(362\) | −40.7310 | −2.14078 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.3085 | −0.644257 | ||||||||
\(366\) | 0.465954 | 0.0243558 | ||||||||
\(367\) | −8.94917 | −0.467143 | −0.233571 | − | 0.972340i | \(-0.575041\pi\) | ||||
−0.233571 | + | 0.972340i | \(0.575041\pi\) | |||||||
\(368\) | −28.2852 | −1.47447 | ||||||||
\(369\) | 5.23142 | 0.272337 | ||||||||
\(370\) | 77.9222 | 4.05098 | ||||||||
\(371\) | 2.85558 | 0.148254 | ||||||||
\(372\) | 46.6542 | 2.41891 | ||||||||
\(373\) | −18.1913 | −0.941908 | −0.470954 | − | 0.882158i | \(-0.656090\pi\) | ||||
−0.470954 | + | 0.882158i | \(0.656090\pi\) | |||||||
\(374\) | −5.20928 | −0.269366 | ||||||||
\(375\) | −13.6840 | −0.706637 | ||||||||
\(376\) | −7.65574 | −0.394815 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.42618 | −0.124789 | ||||||||
\(379\) | −20.1063 | −1.03279 | −0.516396 | − | 0.856350i | \(-0.672727\pi\) | ||||
−0.516396 | + | 0.856350i | \(0.672727\pi\) | |||||||
\(380\) | 125.706 | 6.44859 | ||||||||
\(381\) | 6.60130 | 0.338195 | ||||||||
\(382\) | −38.7536 | −1.98281 | ||||||||
\(383\) | 7.99092 | 0.408317 | 0.204158 | − | 0.978938i | \(-0.434554\pi\) | ||||
0.204158 | + | 0.978938i | \(0.434554\pi\) | |||||||
\(384\) | 13.0683 | 0.666890 | ||||||||
\(385\) | 3.54294 | 0.180565 | ||||||||
\(386\) | 17.1365 | 0.872224 | ||||||||
\(387\) | 5.26116 | 0.267440 | ||||||||
\(388\) | −43.4493 | −2.20580 | ||||||||
\(389\) | 4.31617 | 0.218839 | 0.109419 | − | 0.993996i | \(-0.465101\pi\) | ||||
0.109419 | + | 0.993996i | \(0.465101\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.65326 | 0.437614 | ||||||||
\(392\) | 37.3624 | 1.88709 | ||||||||
\(393\) | 5.81083 | 0.293117 | ||||||||
\(394\) | −28.7201 | −1.44690 | ||||||||
\(395\) | 13.5054 | 0.679528 | ||||||||
\(396\) | −4.42325 | −0.222277 | ||||||||
\(397\) | −23.4560 | −1.17722 | −0.588612 | − | 0.808416i | \(-0.700325\pi\) | ||||
−0.588612 | + | 0.808416i | \(0.700325\pi\) | |||||||
\(398\) | −54.6525 | −2.73948 | ||||||||
\(399\) | −7.35093 | −0.368007 | ||||||||
\(400\) | 58.4344 | 2.92172 | ||||||||
\(401\) | 2.38235 | 0.118969 | 0.0594844 | − | 0.998229i | \(-0.481054\pi\) | ||||
0.0594844 | + | 0.998229i | \(0.481054\pi\) | |||||||
\(402\) | 3.56569 | 0.177841 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −37.2587 | −1.85369 | ||||||||
\(405\) | −3.70100 | −0.183904 | ||||||||
\(406\) | −4.79864 | −0.238153 | ||||||||
\(407\) | −8.30741 | −0.411783 | ||||||||
\(408\) | 12.6234 | 0.624951 | ||||||||
\(409\) | 10.3945 | 0.513973 | 0.256987 | − | 0.966415i | \(-0.417270\pi\) | ||||
0.256987 | + | 0.966415i | \(0.417270\pi\) | |||||||
\(410\) | 49.0700 | 2.42339 | ||||||||
\(411\) | −5.64208 | −0.278303 | ||||||||
\(412\) | −59.2844 | −2.92073 | ||||||||
\(413\) | 11.8272 | 0.581977 | ||||||||
\(414\) | 10.6698 | 0.524392 | ||||||||
\(415\) | 12.2857 | 0.603082 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.46820 | −0.218808 | ||||||||
\(418\) | −19.4614 | −0.951888 | ||||||||
\(419\) | 13.6447 | 0.666586 | 0.333293 | − | 0.942823i | \(-0.391840\pi\) | ||||
0.333293 | + | 0.942823i | \(0.391840\pi\) | |||||||
\(420\) | −15.6713 | −0.764682 | ||||||||
\(421\) | −6.41040 | −0.312424 | −0.156212 | − | 0.987724i | \(-0.549928\pi\) | ||||
−0.156212 | + | 0.987724i | \(0.549928\pi\) | |||||||
\(422\) | 59.8100 | 2.91151 | ||||||||
\(423\) | 1.24656 | 0.0606097 | ||||||||
\(424\) | −18.3200 | −0.889696 | ||||||||
\(425\) | −17.8768 | −0.867150 | ||||||||
\(426\) | 30.8139 | 1.49294 | ||||||||
\(427\) | −0.175999 | −0.00851721 | ||||||||
\(428\) | −35.6422 | −1.72283 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 49.3489 | 2.37982 | ||||||||
\(431\) | −15.8350 | −0.762747 | −0.381374 | − | 0.924421i | \(-0.624549\pi\) | ||||
−0.381374 | + | 0.924421i | \(0.624549\pi\) | |||||||
\(432\) | 6.71863 | 0.323250 | ||||||||
\(433\) | −10.6273 | −0.510716 | −0.255358 | − | 0.966847i | \(-0.582193\pi\) | ||||
−0.255358 | + | 0.966847i | \(0.582193\pi\) | |||||||
\(434\) | −25.5901 | −1.22836 | ||||||||
\(435\) | −7.32005 | −0.350970 | ||||||||
\(436\) | 63.5179 | 3.04196 | ||||||||
\(437\) | 32.3278 | 1.54645 | ||||||||
\(438\) | −8.42877 | −0.402742 | ||||||||
\(439\) | −17.2195 | −0.821841 | −0.410920 | − | 0.911671i | \(-0.634793\pi\) | ||||
−0.410920 | + | 0.911671i | \(0.634793\pi\) | |||||||
\(440\) | −22.7297 | −1.08360 | ||||||||
\(441\) | −6.08359 | −0.289695 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.1359 | −1.19424 | −0.597120 | − | 0.802152i | \(-0.703689\pi\) | ||||
−0.597120 | + | 0.802152i | \(0.703689\pi\) | |||||||
\(444\) | 36.7457 | 1.74387 | ||||||||
\(445\) | 19.4044 | 0.919857 | ||||||||
\(446\) | −37.3068 | −1.76653 | ||||||||
\(447\) | 7.39749 | 0.349889 | ||||||||
\(448\) | −1.35178 | −0.0638656 | ||||||||
\(449\) | 2.01596 | 0.0951392 | 0.0475696 | − | 0.998868i | \(-0.484852\pi\) | ||||
0.0475696 | + | 0.998868i | \(0.484852\pi\) | |||||||
\(450\) | −22.0427 | −1.03910 | ||||||||
\(451\) | −5.23142 | −0.246338 | ||||||||
\(452\) | 82.5710 | 3.88382 | ||||||||
\(453\) | −23.7454 | −1.11566 | ||||||||
\(454\) | 0.0909634 | 0.00426912 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 47.1598 | 2.20846 | ||||||||
\(457\) | −33.7659 | −1.57950 | −0.789752 | − | 0.613426i | \(-0.789791\pi\) | ||||
−0.789752 | + | 0.613426i | \(0.789791\pi\) | |||||||
\(458\) | 21.2195 | 0.991524 | ||||||||
\(459\) | −2.05542 | −0.0959388 | ||||||||
\(460\) | 68.9190 | 3.21337 | ||||||||
\(461\) | −16.7600 | −0.780589 | −0.390294 | − | 0.920690i | \(-0.627627\pi\) | ||||
−0.390294 | + | 0.920690i | \(0.627627\pi\) | |||||||
\(462\) | 2.42618 | 0.112876 | ||||||||
\(463\) | −27.5446 | −1.28011 | −0.640054 | − | 0.768330i | \(-0.721088\pi\) | ||||
−0.640054 | + | 0.768330i | \(0.721088\pi\) | |||||||
\(464\) | 13.2885 | 0.616904 | ||||||||
\(465\) | −39.0362 | −1.81026 | ||||||||
\(466\) | 45.6244 | 2.11351 | ||||||||
\(467\) | 22.9318 | 1.06116 | 0.530578 | − | 0.847636i | \(-0.321975\pi\) | ||||
0.530578 | + | 0.847636i | \(0.321975\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.34683 | −0.0621907 | ||||||||
\(470\) | 11.6925 | 0.539336 | ||||||||
\(471\) | 12.9704 | 0.597646 | ||||||||
\(472\) | −75.8770 | −3.49252 | ||||||||
\(473\) | −5.26116 | −0.241909 | ||||||||
\(474\) | 9.24836 | 0.424791 | ||||||||
\(475\) | −66.7859 | −3.06435 | ||||||||
\(476\) | −8.70337 | −0.398918 | ||||||||
\(477\) | 2.98297 | 0.136581 | ||||||||
\(478\) | −14.5601 | −0.665965 | ||||||||
\(479\) | 5.71495 | 0.261123 | 0.130561 | − | 0.991440i | \(-0.458322\pi\) | ||||
0.130561 | + | 0.991440i | \(0.458322\pi\) | |||||||
\(480\) | 17.5603 | 0.801516 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −40.9202 | −1.86386 | ||||||||
\(483\) | −4.03018 | −0.183380 | ||||||||
\(484\) | 4.42325 | 0.201057 | ||||||||
\(485\) | 36.3546 | 1.65078 | ||||||||
\(486\) | −2.53441 | −0.114963 | ||||||||
\(487\) | −10.4987 | −0.475742 | −0.237871 | − | 0.971297i | \(-0.576450\pi\) | ||||
−0.237871 | + | 0.971297i | \(0.576450\pi\) | |||||||
\(488\) | 1.12912 | 0.0511129 | ||||||||
\(489\) | −18.6880 | −0.845100 | ||||||||
\(490\) | −57.0631 | −2.57785 | ||||||||
\(491\) | 13.0458 | 0.588747 | 0.294373 | − | 0.955691i | \(-0.404889\pi\) | ||||
0.294373 | + | 0.955691i | \(0.404889\pi\) | |||||||
\(492\) | 23.1399 | 1.04323 | ||||||||
\(493\) | −4.06533 | −0.183093 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.70100 | 0.166347 | ||||||||
\(496\) | 70.8647 | 3.18192 | ||||||||
\(497\) | −11.6390 | −0.522080 | ||||||||
\(498\) | 8.41316 | 0.377003 | ||||||||
\(499\) | 38.6395 | 1.72974 | 0.864870 | − | 0.501995i | \(-0.167400\pi\) | ||||
0.864870 | + | 0.501995i | \(0.167400\pi\) | |||||||
\(500\) | −60.5276 | −2.70688 | ||||||||
\(501\) | −25.0420 | −1.11879 | ||||||||
\(502\) | 17.3260 | 0.773298 | ||||||||
\(503\) | 0.330867 | 0.0147526 | 0.00737631 | − | 0.999973i | \(-0.497652\pi\) | ||||
0.00737631 | + | 0.999973i | \(0.497652\pi\) | |||||||
\(504\) | −5.87924 | −0.261882 | ||||||||
\(505\) | 31.1749 | 1.38726 | ||||||||
\(506\) | −10.6698 | −0.474331 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 29.1992 | 1.29550 | ||||||||
\(509\) | −44.2090 | −1.95953 | −0.979764 | − | 0.200157i | \(-0.935855\pi\) | ||||
−0.979764 | + | 0.200157i | \(0.935855\pi\) | |||||||
\(510\) | −19.2795 | −0.853712 | ||||||||
\(511\) | 3.18370 | 0.140839 | ||||||||
\(512\) | 50.6468 | 2.23829 | ||||||||
\(513\) | −7.67886 | −0.339030 | ||||||||
\(514\) | 67.9318 | 2.99635 | ||||||||
\(515\) | 49.6041 | 2.18582 | ||||||||
\(516\) | 23.2714 | 1.02447 | ||||||||
\(517\) | −1.24656 | −0.0548235 | ||||||||
\(518\) | −20.1553 | −0.885571 | ||||||||
\(519\) | −3.16333 | −0.138855 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.66049 | 0.423234 | 0.211617 | − | 0.977353i | \(-0.432127\pi\) | ||||
0.211617 | + | 0.977353i | \(0.432127\pi\) | |||||||
\(522\) | −5.01271 | −0.219401 | ||||||||
\(523\) | 21.7358 | 0.950440 | 0.475220 | − | 0.879867i | \(-0.342368\pi\) | ||||
0.475220 | + | 0.879867i | \(0.342368\pi\) | |||||||
\(524\) | 25.7027 | 1.12283 | ||||||||
\(525\) | 8.32595 | 0.363374 | ||||||||
\(526\) | 30.2908 | 1.32074 | ||||||||
\(527\) | −21.6795 | −0.944375 | ||||||||
\(528\) | −6.71863 | −0.292391 | ||||||||
\(529\) | −5.27614 | −0.229398 | ||||||||
\(530\) | 27.9798 | 1.21537 | ||||||||
\(531\) | 12.3548 | 0.536152 | ||||||||
\(532\) | −32.5150 | −1.40970 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 13.2880 | 0.575027 | ||||||||
\(535\) | 29.8223 | 1.28933 | ||||||||
\(536\) | 8.64056 | 0.373215 | ||||||||
\(537\) | 1.24977 | 0.0539316 | ||||||||
\(538\) | −11.6497 | −0.502256 | ||||||||
\(539\) | 6.08359 | 0.262039 | ||||||||
\(540\) | −16.3704 | −0.704471 | ||||||||
\(541\) | −18.0139 | −0.774478 | −0.387239 | − | 0.921979i | \(-0.626571\pi\) | ||||
−0.387239 | + | 0.921979i | \(0.626571\pi\) | |||||||
\(542\) | 50.4270 | 2.16602 | ||||||||
\(543\) | 16.0712 | 0.689681 | ||||||||
\(544\) | 9.75247 | 0.418134 | ||||||||
\(545\) | −53.1464 | −2.27654 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.2740 | 0.995125 | 0.497563 | − | 0.867428i | \(-0.334228\pi\) | ||||
0.497563 | + | 0.867428i | \(0.334228\pi\) | |||||||
\(548\) | −24.9563 | −1.06608 | ||||||||
\(549\) | −0.183851 | −0.00784656 | ||||||||
\(550\) | 22.0427 | 0.939906 | ||||||||
\(551\) | −15.1877 | −0.647018 | ||||||||
\(552\) | 25.8556 | 1.10049 | ||||||||
\(553\) | −3.49328 | −0.148549 | ||||||||
\(554\) | 28.4662 | 1.20941 | ||||||||
\(555\) | −30.7457 | −1.30508 | ||||||||
\(556\) | −19.7639 | −0.838178 | ||||||||
\(557\) | −11.5996 | −0.491491 | −0.245745 | − | 0.969334i | \(-0.579033\pi\) | ||||
−0.245745 | + | 0.969334i | \(0.579033\pi\) | |||||||
\(558\) | −26.7317 | −1.13164 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −23.8037 | −1.00589 | ||||||||
\(561\) | 2.05542 | 0.0867799 | ||||||||
\(562\) | −76.7790 | −3.23873 | ||||||||
\(563\) | 26.5695 | 1.11977 | 0.559885 | − | 0.828570i | \(-0.310845\pi\) | ||||
0.559885 | + | 0.828570i | \(0.310845\pi\) | |||||||
\(564\) | 5.51383 | 0.232174 | ||||||||
\(565\) | −69.0884 | −2.90657 | ||||||||
\(566\) | 39.0019 | 1.63937 | ||||||||
\(567\) | 0.957295 | 0.0402026 | ||||||||
\(568\) | 74.6698 | 3.13308 | ||||||||
\(569\) | −22.7470 | −0.953603 | −0.476802 | − | 0.879011i | \(-0.658204\pi\) | ||||
−0.476802 | + | 0.879011i | \(0.658204\pi\) | |||||||
\(570\) | −72.0265 | −3.01686 | ||||||||
\(571\) | −29.4622 | −1.23296 | −0.616478 | − | 0.787372i | \(-0.711441\pi\) | ||||
−0.616478 | + | 0.787372i | \(0.711441\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.2909 | 0.638788 | ||||||||
\(574\) | −12.6924 | −0.529769 | ||||||||
\(575\) | −36.6157 | −1.52698 | ||||||||
\(576\) | −1.41208 | −0.0588368 | ||||||||
\(577\) | 26.6537 | 1.10961 | 0.554803 | − | 0.831981i | \(-0.312793\pi\) | ||||
0.554803 | + | 0.831981i | \(0.312793\pi\) | |||||||
\(578\) | 32.3778 | 1.34674 | ||||||||
\(579\) | −6.76152 | −0.280999 | ||||||||
\(580\) | −32.3784 | −1.34444 | ||||||||
\(581\) | −3.17781 | −0.131838 | ||||||||
\(582\) | 24.8954 | 1.03195 | ||||||||
\(583\) | −2.98297 | −0.123542 | ||||||||
\(584\) | −20.4250 | −0.845193 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.6350 | 0.728495 | ||||||||
\(587\) | −10.9203 | −0.450729 | −0.225364 | − | 0.974275i | \(-0.572357\pi\) | ||||
−0.225364 | + | 0.974275i | \(0.572357\pi\) | |||||||
\(588\) | −26.9092 | −1.10972 | ||||||||
\(589\) | −80.9927 | −3.33725 | ||||||||
\(590\) | 115.886 | 4.77095 | ||||||||
\(591\) | 11.3320 | 0.466138 | ||||||||
\(592\) | 55.8144 | 2.29396 | ||||||||
\(593\) | −19.3064 | −0.792820 | −0.396410 | − | 0.918074i | \(-0.629744\pi\) | ||||
−0.396410 | + | 0.918074i | \(0.629744\pi\) | |||||||
\(594\) | 2.53441 | 0.103988 | ||||||||
\(595\) | 7.28224 | 0.298543 | ||||||||
\(596\) | 32.7209 | 1.34030 | ||||||||
\(597\) | 21.5642 | 0.882562 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.01132 | 0.0821802 | 0.0410901 | − | 0.999155i | \(-0.486917\pi\) | ||||
0.0410901 | + | 0.999155i | \(0.486917\pi\) | |||||||
\(600\) | −53.4150 | −2.18066 | ||||||||
\(601\) | −40.1233 | −1.63667 | −0.818333 | − | 0.574745i | \(-0.805101\pi\) | ||||
−0.818333 | + | 0.574745i | \(0.805101\pi\) | |||||||
\(602\) | −12.7645 | −0.520243 | ||||||||
\(603\) | −1.40691 | −0.0572938 | ||||||||
\(604\) | −105.032 | −4.27369 | ||||||||
\(605\) | −3.70100 | −0.150467 | ||||||||
\(606\) | 21.3483 | 0.867216 | ||||||||
\(607\) | −35.4310 | −1.43810 | −0.719049 | − | 0.694959i | \(-0.755422\pi\) | ||||
−0.719049 | + | 0.694959i | \(0.755422\pi\) | |||||||
\(608\) | 36.4343 | 1.47761 | ||||||||
\(609\) | 1.89339 | 0.0767242 | ||||||||
\(610\) | −1.72449 | −0.0698227 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −9.09163 | −0.367507 | ||||||||
\(613\) | −0.644081 | −0.0260142 | −0.0130071 | − | 0.999915i | \(-0.504140\pi\) | ||||
−0.0130071 | + | 0.999915i | \(0.504140\pi\) | |||||||
\(614\) | −31.9925 | −1.29111 | ||||||||
\(615\) | −19.3615 | −0.780730 | ||||||||
\(616\) | 5.87924 | 0.236881 | ||||||||
\(617\) | −23.5775 | −0.949194 | −0.474597 | − | 0.880203i | \(-0.657406\pi\) | ||||
−0.474597 | + | 0.880203i | \(0.657406\pi\) | |||||||
\(618\) | 33.9685 | 1.36641 | ||||||||
\(619\) | 5.86810 | 0.235859 | 0.117929 | − | 0.993022i | \(-0.462374\pi\) | ||||
0.117929 | + | 0.993022i | \(0.462374\pi\) | |||||||
\(620\) | −172.667 | −6.93447 | ||||||||
\(621\) | −4.20997 | −0.168940 | ||||||||
\(622\) | −5.37589 | −0.215553 | ||||||||
\(623\) | −5.01911 | −0.201087 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.15745 | 0.286298 | ||||||||
\(626\) | −54.7229 | −2.18717 | ||||||||
\(627\) | 7.67886 | 0.306664 | ||||||||
\(628\) | 57.3714 | 2.28937 | ||||||||
\(629\) | −17.0752 | −0.680833 | ||||||||
\(630\) | 8.97928 | 0.357743 | ||||||||
\(631\) | −11.0386 | −0.439441 | −0.219721 | − | 0.975563i | \(-0.570515\pi\) | ||||
−0.219721 | + | 0.975563i | \(0.570515\pi\) | |||||||
\(632\) | 22.4111 | 0.891465 | ||||||||
\(633\) | −23.5992 | −0.937982 | ||||||||
\(634\) | 39.9636 | 1.58716 | ||||||||
\(635\) | −24.4314 | −0.969529 | ||||||||
\(636\) | 13.1944 | 0.523193 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5.01271 | 0.198455 | ||||||||
\(639\) | −12.1582 | −0.480972 | ||||||||
\(640\) | −48.3658 | −1.91183 | ||||||||
\(641\) | 11.2924 | 0.446022 | 0.223011 | − | 0.974816i | \(-0.428411\pi\) | ||||
0.223011 | + | 0.974816i | \(0.428411\pi\) | |||||||
\(642\) | 20.4221 | 0.805996 | ||||||||
\(643\) | −2.73168 | −0.107727 | −0.0538634 | − | 0.998548i | \(-0.517154\pi\) | ||||
−0.0538634 | + | 0.998548i | \(0.517154\pi\) | |||||||
\(644\) | −17.8265 | −0.702463 | ||||||||
\(645\) | −19.4715 | −0.766691 | ||||||||
\(646\) | −40.0013 | −1.57383 | ||||||||
\(647\) | −10.3135 | −0.405465 | −0.202733 | − | 0.979234i | \(-0.564982\pi\) | ||||
−0.202733 | + | 0.979234i | \(0.564982\pi\) | |||||||
\(648\) | −6.14151 | −0.241261 | ||||||||
\(649\) | −12.3548 | −0.484968 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.0971 | 0.395735 | ||||||||
\(652\) | −82.6616 | −3.23728 | ||||||||
\(653\) | −1.95601 | −0.0765446 | −0.0382723 | − | 0.999267i | \(-0.512185\pi\) | ||||
−0.0382723 | + | 0.999267i | \(0.512185\pi\) | |||||||
\(654\) | −36.3942 | −1.42313 | ||||||||
\(655\) | −21.5058 | −0.840303 | ||||||||
\(656\) | 35.1480 | 1.37230 | ||||||||
\(657\) | 3.32573 | 0.129749 | ||||||||
\(658\) | −3.02437 | −0.117902 | ||||||||
\(659\) | −21.0277 | −0.819121 | −0.409561 | − | 0.912283i | \(-0.634318\pi\) | ||||
−0.409561 | + | 0.912283i | \(0.634318\pi\) | |||||||
\(660\) | 16.3704 | 0.637218 | ||||||||
\(661\) | −25.7516 | −1.00162 | −0.500810 | − | 0.865557i | \(-0.666964\pi\) | ||||
−0.500810 | + | 0.865557i | \(0.666964\pi\) | |||||||
\(662\) | 29.5517 | 1.14856 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 20.3872 | 0.791176 | ||||||||
\(665\) | 27.2058 | 1.05499 | ||||||||
\(666\) | −21.0544 | −0.815841 | ||||||||
\(667\) | −8.32673 | −0.322412 | ||||||||
\(668\) | −110.767 | −4.28570 | ||||||||
\(669\) | 14.7201 | 0.569111 | ||||||||
\(670\) | −13.1966 | −0.509830 | ||||||||
\(671\) | 0.183851 | 0.00709748 | ||||||||
\(672\) | −4.54213 | −0.175217 | ||||||||
\(673\) | −18.2077 | −0.701856 | −0.350928 | − | 0.936403i | \(-0.614134\pi\) | ||||
−0.350928 | + | 0.936403i | \(0.614134\pi\) | |||||||
\(674\) | 19.3504 | 0.745351 | ||||||||
\(675\) | 8.69737 | 0.334762 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.3281 | −0.396941 | −0.198470 | − | 0.980107i | \(-0.563597\pi\) | ||||
−0.198470 | + | 0.980107i | \(0.563597\pi\) | |||||||
\(678\) | −47.3112 | −1.81697 | ||||||||
\(679\) | −9.40344 | −0.360871 | ||||||||
\(680\) | −46.7191 | −1.79160 | ||||||||
\(681\) | −0.0358913 | −0.00137536 | ||||||||
\(682\) | 26.7317 | 1.02361 | ||||||||
\(683\) | 33.4285 | 1.27911 | 0.639553 | − | 0.768747i | \(-0.279119\pi\) | ||||
0.639553 | + | 0.768747i | \(0.279119\pi\) | |||||||
\(684\) | −33.9655 | −1.29870 | ||||||||
\(685\) | 20.8813 | 0.797834 | ||||||||
\(686\) | 31.7431 | 1.21196 | ||||||||
\(687\) | −8.37257 | −0.319433 | ||||||||
\(688\) | 35.3478 | 1.34762 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −39.4889 | −1.50332 | ||||||||
\(691\) | 38.8290 | 1.47712 | 0.738562 | − | 0.674186i | \(-0.235505\pi\) | ||||
0.738562 | + | 0.674186i | \(0.235505\pi\) | |||||||
\(692\) | −13.9922 | −0.531903 | ||||||||
\(693\) | −0.957295 | −0.0363646 | ||||||||
\(694\) | 45.0678 | 1.71075 | ||||||||
\(695\) | 16.5368 | 0.627276 | ||||||||
\(696\) | −12.1471 | −0.460433 | ||||||||
\(697\) | −10.7528 | −0.407290 | ||||||||
\(698\) | 30.8343 | 1.16710 | ||||||||
\(699\) | −18.0020 | −0.680897 | ||||||||
\(700\) | 36.8277 | 1.39196 | ||||||||
\(701\) | 47.5275 | 1.79509 | 0.897544 | − | 0.440925i | \(-0.145350\pi\) | ||||
0.897544 | + | 0.440925i | \(0.145350\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −63.7914 | −2.40594 | ||||||||
\(704\) | 1.41208 | 0.0532199 | ||||||||
\(705\) | −4.61350 | −0.173755 | ||||||||
\(706\) | −83.3886 | −3.13837 | ||||||||
\(707\) | −8.06365 | −0.303265 | ||||||||
\(708\) | 54.6483 | 2.05381 | ||||||||
\(709\) | 28.9052 | 1.08556 | 0.542780 | − | 0.839875i | \(-0.317372\pi\) | ||||
0.542780 | + | 0.839875i | \(0.317372\pi\) | |||||||
\(710\) | −114.042 | −4.27993 | ||||||||
\(711\) | −3.64911 | −0.136852 | ||||||||
\(712\) | 32.2001 | 1.20675 | ||||||||
\(713\) | −44.4046 | −1.66297 | ||||||||
\(714\) | 4.98682 | 0.186627 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.52805 | 0.206593 | ||||||||
\(717\) | 5.74497 | 0.214550 | ||||||||
\(718\) | 18.4951 | 0.690233 | ||||||||
\(719\) | 47.9212 | 1.78716 | 0.893579 | − | 0.448906i | \(-0.148186\pi\) | ||||
0.893579 | + | 0.448906i | \(0.148186\pi\) | |||||||
\(720\) | −24.8656 | −0.926687 | ||||||||
\(721\) | −12.8305 | −0.477834 | ||||||||
\(722\) | −101.287 | −3.76953 | ||||||||
\(723\) | 16.1458 | 0.600469 | ||||||||
\(724\) | 71.0869 | 2.64192 | ||||||||
\(725\) | 17.2022 | 0.638873 | ||||||||
\(726\) | −2.53441 | −0.0940609 | ||||||||
\(727\) | 23.4347 | 0.869146 | 0.434573 | − | 0.900636i | \(-0.356899\pi\) | ||||
0.434573 | + | 0.900636i | \(0.356899\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 31.1949 | 1.15457 | ||||||||
\(731\) | −10.8139 | −0.399966 | ||||||||
\(732\) | −0.813218 | −0.0300574 | ||||||||
\(733\) | −38.8733 | −1.43582 | −0.717910 | − | 0.696136i | \(-0.754901\pi\) | ||||
−0.717910 | + | 0.696136i | \(0.754901\pi\) | |||||||
\(734\) | 22.6809 | 0.837167 | ||||||||
\(735\) | 22.5153 | 0.830491 | ||||||||
\(736\) | 19.9753 | 0.736299 | ||||||||
\(737\) | 1.40691 | 0.0518242 | ||||||||
\(738\) | −13.2586 | −0.488055 | ||||||||
\(739\) | −29.3240 | −1.07870 | −0.539350 | − | 0.842082i | \(-0.681330\pi\) | ||||
−0.539350 | + | 0.842082i | \(0.681330\pi\) | |||||||
\(740\) | −135.996 | −4.99930 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.23723 | −0.265687 | ||||||||
\(743\) | −40.8183 | −1.49748 | −0.748740 | − | 0.662864i | \(-0.769341\pi\) | ||||
−0.748740 | + | 0.662864i | \(0.769341\pi\) | |||||||
\(744\) | −64.7776 | −2.37486 | ||||||||
\(745\) | −27.3781 | −1.00305 | ||||||||
\(746\) | 46.1042 | 1.68799 | ||||||||
\(747\) | −3.31957 | −0.121457 | ||||||||
\(748\) | 9.09163 | 0.332423 | ||||||||
\(749\) | −7.71380 | −0.281856 | ||||||||
\(750\) | 34.6808 | 1.26636 | ||||||||
\(751\) | 4.36042 | 0.159114 | 0.0795570 | − | 0.996830i | \(-0.474649\pi\) | ||||
0.0795570 | + | 0.996830i | \(0.474649\pi\) | |||||||
\(752\) | 8.37515 | 0.305410 | ||||||||
\(753\) | −6.83631 | −0.249129 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 87.8817 | 3.19834 | ||||||||
\(756\) | 4.23435 | 0.154002 | ||||||||
\(757\) | 40.1387 | 1.45887 | 0.729433 | − | 0.684052i | \(-0.239784\pi\) | ||||
0.729433 | + | 0.684052i | \(0.239784\pi\) | |||||||
\(758\) | 50.9577 | 1.85087 | ||||||||
\(759\) | 4.20997 | 0.152812 | ||||||||
\(760\) | −174.538 | −6.33117 | ||||||||
\(761\) | 38.2425 | 1.38629 | 0.693144 | − | 0.720799i | \(-0.256225\pi\) | ||||
0.693144 | + | 0.720799i | \(0.256225\pi\) | |||||||
\(762\) | −16.7304 | −0.606079 | ||||||||
\(763\) | 13.7468 | 0.497667 | ||||||||
\(764\) | 67.6357 | 2.44697 | ||||||||
\(765\) | 7.60710 | 0.275035 | ||||||||
\(766\) | −20.2523 | −0.731745 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −30.2963 | −1.09323 | ||||||||
\(769\) | 35.0140 | 1.26264 | 0.631319 | − | 0.775523i | \(-0.282514\pi\) | ||||
0.631319 | + | 0.775523i | \(0.282514\pi\) | |||||||
\(770\) | −8.97928 | −0.323591 | ||||||||
\(771\) | −26.8038 | −0.965315 | ||||||||
\(772\) | −29.9079 | −1.07641 | ||||||||
\(773\) | 5.69564 | 0.204858 | 0.102429 | − | 0.994740i | \(-0.467339\pi\) | ||||
0.102429 | + | 0.994740i | \(0.467339\pi\) | |||||||
\(774\) | −13.3340 | −0.479279 | ||||||||
\(775\) | 91.7355 | 3.29524 | ||||||||
\(776\) | 60.3277 | 2.16564 | ||||||||
\(777\) | 7.95264 | 0.285299 | ||||||||
\(778\) | −10.9390 | −0.392181 | ||||||||
\(779\) | −40.1713 | −1.43929 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.1582 | 0.435055 | ||||||||
\(782\) | −21.9309 | −0.784248 | ||||||||
\(783\) | 1.97786 | 0.0706830 | ||||||||
\(784\) | −40.8734 | −1.45976 | ||||||||
\(785\) | −48.0035 | −1.71332 | ||||||||
\(786\) | −14.7270 | −0.525296 | ||||||||
\(787\) | −31.2092 | −1.11249 | −0.556244 | − | 0.831019i | \(-0.687758\pi\) | ||||
−0.556244 | + | 0.831019i | \(0.687758\pi\) | |||||||
\(788\) | 50.1244 | 1.78561 | ||||||||
\(789\) | −11.9518 | −0.425496 | ||||||||
\(790\) | −34.2282 | −1.21778 | ||||||||
\(791\) | 17.8703 | 0.635395 | ||||||||
\(792\) | 6.14151 | 0.218229 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 59.4472 | 2.10970 | ||||||||
\(795\) | −11.0400 | −0.391547 | ||||||||
\(796\) | 95.3836 | 3.38078 | ||||||||
\(797\) | −42.7214 | −1.51327 | −0.756634 | − | 0.653839i | \(-0.773157\pi\) | ||||
−0.756634 | + | 0.653839i | \(0.773157\pi\) | |||||||
\(798\) | 18.6303 | 0.659505 | ||||||||
\(799\) | −2.56220 | −0.0906440 | ||||||||
\(800\) | −41.2669 | −1.45901 | ||||||||
\(801\) | −5.24302 | −0.185253 | ||||||||
\(802\) | −6.03786 | −0.213204 | ||||||||
\(803\) | −3.32573 | −0.117362 | ||||||||
\(804\) | −6.22311 | −0.219472 | ||||||||
\(805\) | 14.9157 | 0.525709 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.59663 | 0.161809 | ||||||||
\(808\) | 51.7323 | 1.81993 | ||||||||
\(809\) | −13.3241 | −0.468449 | −0.234225 | − | 0.972182i | \(-0.575255\pi\) | ||||
−0.234225 | + | 0.972182i | \(0.575255\pi\) | |||||||
\(810\) | 9.37985 | 0.329574 | ||||||||
\(811\) | −41.9849 | −1.47429 | −0.737144 | − | 0.675735i | \(-0.763826\pi\) | ||||
−0.737144 | + | 0.675735i | \(0.763826\pi\) | |||||||
\(812\) | 8.37496 | 0.293903 | ||||||||
\(813\) | −19.8969 | −0.697815 | ||||||||
\(814\) | 21.0544 | 0.737956 | ||||||||
\(815\) | 69.1642 | 2.42272 | ||||||||
\(816\) | −13.8096 | −0.483433 | ||||||||
\(817\) | −40.3997 | −1.41341 | ||||||||
\(818\) | −26.3439 | −0.921092 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −85.6406 | −2.99070 | ||||||||
\(821\) | −10.0872 | −0.352047 | −0.176023 | − | 0.984386i | \(-0.556323\pi\) | ||||
−0.176023 | + | 0.984386i | \(0.556323\pi\) | |||||||
\(822\) | 14.2994 | 0.498748 | ||||||||
\(823\) | −1.16139 | −0.0404835 | −0.0202418 | − | 0.999795i | \(-0.506444\pi\) | ||||
−0.0202418 | + | 0.999795i | \(0.506444\pi\) | |||||||
\(824\) | 82.3142 | 2.86755 | ||||||||
\(825\) | −8.69737 | −0.302804 | ||||||||
\(826\) | −29.9749 | −1.04296 | ||||||||
\(827\) | 5.42242 | 0.188556 | 0.0942781 | − | 0.995546i | \(-0.469946\pi\) | ||||
0.0942781 | + | 0.995546i | \(0.469946\pi\) | |||||||
\(828\) | −18.6217 | −0.647151 | ||||||||
\(829\) | −16.1881 | −0.562237 | −0.281119 | − | 0.959673i | \(-0.590705\pi\) | ||||
−0.281119 | + | 0.959673i | \(0.590705\pi\) | |||||||
\(830\) | −31.1371 | −1.08078 | ||||||||
\(831\) | −11.2319 | −0.389629 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.5043 | 0.433249 | ||||||||
\(834\) | 11.3243 | 0.392127 | ||||||||
\(835\) | 92.6803 | 3.20734 | ||||||||
\(836\) | 33.9655 | 1.17472 | ||||||||
\(837\) | 10.5475 | 0.364575 | ||||||||
\(838\) | −34.5812 | −1.19459 | ||||||||
\(839\) | −13.1144 | −0.452759 | −0.226379 | − | 0.974039i | \(-0.572689\pi\) | ||||
−0.226379 | + | 0.974039i | \(0.572689\pi\) | |||||||
\(840\) | 21.7590 | 0.750758 | ||||||||
\(841\) | −25.0881 | −0.865106 | ||||||||
\(842\) | 16.2466 | 0.559895 | ||||||||
\(843\) | 30.2946 | 1.04340 | ||||||||
\(844\) | −104.385 | −3.59308 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.15929 | −0.108619 | ||||||||
\(847\) | 0.957295 | 0.0328930 | ||||||||
\(848\) | 20.0415 | 0.688227 | ||||||||
\(849\) | −15.3889 | −0.528147 | ||||||||
\(850\) | 45.3071 | 1.55402 | ||||||||
\(851\) | −34.9739 | −1.19889 | ||||||||
\(852\) | −53.7788 | −1.84243 | ||||||||
\(853\) | 8.66325 | 0.296624 | 0.148312 | − | 0.988941i | \(-0.452616\pi\) | ||||
0.148312 | + | 0.988941i | \(0.452616\pi\) | |||||||
\(854\) | 0.446055 | 0.0152637 | ||||||||
\(855\) | 28.4194 | 0.971924 | ||||||||
\(856\) | 49.4878 | 1.69146 | ||||||||
\(857\) | −28.1435 | −0.961365 | −0.480683 | − | 0.876895i | \(-0.659611\pi\) | ||||
−0.480683 | + | 0.876895i | \(0.659611\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.7375 | 0.400479 | 0.200240 | − | 0.979747i | \(-0.435828\pi\) | ||||
0.200240 | + | 0.979747i | \(0.435828\pi\) | |||||||
\(860\) | −86.1275 | −2.93692 | ||||||||
\(861\) | 5.00801 | 0.170673 | ||||||||
\(862\) | 40.1325 | 1.36692 | ||||||||
\(863\) | 14.6715 | 0.499424 | 0.249712 | − | 0.968320i | \(-0.419664\pi\) | ||||
0.249712 | + | 0.968320i | \(0.419664\pi\) | |||||||
\(864\) | −4.74476 | −0.161420 | ||||||||
\(865\) | 11.7075 | 0.398066 | ||||||||
\(866\) | 26.9340 | 0.915254 | ||||||||
\(867\) | −12.7753 | −0.433870 | ||||||||
\(868\) | 44.6618 | 1.51592 | ||||||||
\(869\) | 3.64911 | 0.123788 | ||||||||
\(870\) | 18.5520 | 0.628973 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −88.1922 | −2.98657 | ||||||||
\(873\) | −9.82293 | −0.332456 | ||||||||
\(874\) | −81.9319 | −2.77139 | ||||||||
\(875\) | −13.0996 | −0.442847 | ||||||||
\(876\) | 14.7105 | 0.497023 | ||||||||
\(877\) | 18.0884 | 0.610803 | 0.305402 | − | 0.952224i | \(-0.401209\pi\) | ||||
0.305402 | + | 0.952224i | \(0.401209\pi\) | |||||||
\(878\) | 43.6413 | 1.47282 | ||||||||
\(879\) | −6.95822 | −0.234695 | ||||||||
\(880\) | 24.8656 | 0.838220 | ||||||||
\(881\) | −31.0695 | −1.04676 | −0.523379 | − | 0.852100i | \(-0.675329\pi\) | ||||
−0.523379 | + | 0.852100i | \(0.675329\pi\) | |||||||
\(882\) | 15.4183 | 0.519162 | ||||||||
\(883\) | 34.4102 | 1.15799 | 0.578997 | − | 0.815330i | \(-0.303444\pi\) | ||||
0.578997 | + | 0.815330i | \(0.303444\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −45.7250 | −1.53703 | ||||||||
\(886\) | 63.7047 | 2.14020 | ||||||||
\(887\) | −24.0600 | −0.807857 | −0.403928 | − | 0.914791i | \(-0.632355\pi\) | ||||
−0.403928 | + | 0.914791i | \(0.632355\pi\) | |||||||
\(888\) | −51.0200 | −1.71212 | ||||||||
\(889\) | 6.31938 | 0.211945 | ||||||||
\(890\) | −49.1788 | −1.64848 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 65.1106 | 2.18006 | ||||||||
\(893\) | −9.57213 | −0.320319 | ||||||||
\(894\) | −18.7483 | −0.627036 | ||||||||
\(895\) | −4.62540 | −0.154610 | ||||||||
\(896\) | 12.5102 | 0.417938 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.10928 | −0.170499 | ||||||||
\(899\) | 20.8615 | 0.695769 | ||||||||
\(900\) | 38.4706 | 1.28235 | ||||||||
\(901\) | −6.13126 | −0.204262 | ||||||||
\(902\) | 13.2586 | 0.441462 | ||||||||
\(903\) | 5.03648 | 0.167604 | ||||||||
\(904\) | −114.647 | −3.81309 | ||||||||
\(905\) | −59.4794 | −1.97716 | ||||||||
\(906\) | 60.1807 | 1.99937 | ||||||||
\(907\) | −7.79308 | −0.258765 | −0.129382 | − | 0.991595i | \(-0.541299\pi\) | ||||
−0.129382 | + | 0.991595i | \(0.541299\pi\) | |||||||
\(908\) | −0.158756 | −0.00526851 | ||||||||
\(909\) | −8.42338 | −0.279386 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.88300 | −0.161781 | −0.0808904 | − | 0.996723i | \(-0.525776\pi\) | ||||
−0.0808904 | + | 0.996723i | \(0.525776\pi\) | |||||||
\(912\) | −51.5914 | −1.70836 | ||||||||
\(913\) | 3.31957 | 0.109862 | ||||||||
\(914\) | 85.5768 | 2.83063 | ||||||||
\(915\) | 0.680431 | 0.0224944 | ||||||||
\(916\) | −37.0339 | −1.22364 | ||||||||
\(917\) | 5.56267 | 0.183696 | ||||||||
\(918\) | 5.20928 | 0.171932 | ||||||||
\(919\) | −53.5402 | −1.76613 | −0.883065 | − | 0.469251i | \(-0.844524\pi\) | ||||
−0.883065 | + | 0.469251i | \(0.844524\pi\) | |||||||
\(920\) | −95.6914 | −3.15485 | ||||||||
\(921\) | 12.6233 | 0.415950 | ||||||||
\(922\) | 42.4766 | 1.39889 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −4.23435 | −0.139300 | ||||||||
\(925\) | 72.2526 | 2.37565 | ||||||||
\(926\) | 69.8095 | 2.29408 | ||||||||
\(927\) | −13.4029 | −0.440209 | ||||||||
\(928\) | −9.38447 | −0.308060 | ||||||||
\(929\) | 35.1499 | 1.15323 | 0.576616 | − | 0.817015i | \(-0.304373\pi\) | ||||
0.576616 | + | 0.817015i | \(0.304373\pi\) | |||||||
\(930\) | 98.9339 | 3.24417 | ||||||||
\(931\) | 46.7150 | 1.53102 | ||||||||
\(932\) | −79.6272 | −2.60828 | ||||||||
\(933\) | 2.12116 | 0.0694435 | ||||||||
\(934\) | −58.1185 | −1.90170 | ||||||||
\(935\) | −7.60710 | −0.248779 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.6307 | 0.412626 | 0.206313 | − | 0.978486i | \(-0.433854\pi\) | ||||
0.206313 | + | 0.978486i | \(0.433854\pi\) | |||||||
\(938\) | 3.41342 | 0.111452 | ||||||||
\(939\) | 21.5919 | 0.704626 | ||||||||
\(940\) | −20.4067 | −0.665592 | ||||||||
\(941\) | 39.6660 | 1.29308 | 0.646538 | − | 0.762882i | \(-0.276216\pi\) | ||||
0.646538 | + | 0.762882i | \(0.276216\pi\) | |||||||
\(942\) | −32.8724 | −1.07104 | ||||||||
\(943\) | −22.0241 | −0.717204 | ||||||||
\(944\) | 83.0072 | 2.70165 | ||||||||
\(945\) | −3.54294 | −0.115252 | ||||||||
\(946\) | 13.3340 | 0.433524 | ||||||||
\(947\) | −6.08586 | −0.197764 | −0.0988819 | − | 0.995099i | \(-0.531527\pi\) | ||||
−0.0988819 | + | 0.995099i | \(0.531527\pi\) | |||||||
\(948\) | −16.1409 | −0.524233 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 169.263 | 5.49162 | ||||||||
\(951\) | −15.7684 | −0.511324 | ||||||||
\(952\) | 12.0843 | 0.391654 | ||||||||
\(953\) | −29.8978 | −0.968484 | −0.484242 | − | 0.874934i | \(-0.660904\pi\) | ||||
−0.484242 | + | 0.874934i | \(0.660904\pi\) | |||||||
\(954\) | −7.56008 | −0.244767 | ||||||||
\(955\) | −56.5917 | −1.83127 | ||||||||
\(956\) | 25.4114 | 0.821865 | ||||||||
\(957\) | −1.97786 | −0.0639351 | ||||||||
\(958\) | −14.4840 | −0.467958 | ||||||||
\(959\) | −5.40113 | −0.174412 | ||||||||
\(960\) | 5.22612 | 0.168672 | ||||||||
\(961\) | 80.2496 | 2.58870 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.05792 | −0.259663 | ||||||||
\(964\) | 71.4170 | 2.30019 | ||||||||
\(965\) | 25.0244 | 0.805563 | ||||||||
\(966\) | 10.2141 | 0.328635 | ||||||||
\(967\) | −23.5725 | −0.758039 | −0.379020 | − | 0.925389i | \(-0.623739\pi\) | ||||
−0.379020 | + | 0.925389i | \(0.623739\pi\) | |||||||
\(968\) | −6.14151 | −0.197396 | ||||||||
\(969\) | 15.7833 | 0.507032 | ||||||||
\(970\) | −92.1377 | −2.95836 | ||||||||
\(971\) | 31.0731 | 0.997182 | 0.498591 | − | 0.866837i | \(-0.333851\pi\) | ||||
0.498591 | + | 0.866837i | \(0.333851\pi\) | |||||||
\(972\) | 4.42325 | 0.141876 | ||||||||
\(973\) | −4.27738 | −0.137126 | ||||||||
\(974\) | 26.6081 | 0.852578 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.23523 | −0.0395386 | ||||||||
\(977\) | −18.8934 | −0.604454 | −0.302227 | − | 0.953236i | \(-0.597730\pi\) | ||||
−0.302227 | + | 0.953236i | \(0.597730\pi\) | |||||||
\(978\) | 47.3631 | 1.51450 | ||||||||
\(979\) | 5.24302 | 0.167568 | ||||||||
\(980\) | 99.5909 | 3.18132 | ||||||||
\(981\) | 14.3600 | 0.458480 | ||||||||
\(982\) | −33.0633 | −1.05509 | ||||||||
\(983\) | −32.8458 | −1.04762 | −0.523809 | − | 0.851836i | \(-0.675489\pi\) | ||||
−0.523809 | + | 0.851836i | \(0.675489\pi\) | |||||||
\(984\) | −32.1288 | −1.02423 | ||||||||
\(985\) | −41.9398 | −1.33631 | ||||||||
\(986\) | 10.3032 | 0.328122 | ||||||||
\(987\) | 1.19332 | 0.0379839 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22.1493 | −0.704308 | ||||||||
\(990\) | −9.37985 | −0.298111 | ||||||||
\(991\) | −15.1204 | −0.480316 | −0.240158 | − | 0.970734i | \(-0.577199\pi\) | ||||
−0.240158 | + | 0.970734i | \(0.577199\pi\) | |||||||
\(992\) | −50.0453 | −1.58894 | ||||||||
\(993\) | −11.6602 | −0.370025 | ||||||||
\(994\) | 29.4980 | 0.935620 | ||||||||
\(995\) | −79.8088 | −2.53011 | ||||||||
\(996\) | −14.6833 | −0.465257 | ||||||||
\(997\) | −2.12151 | −0.0671889 | −0.0335945 | − | 0.999436i | \(-0.510695\pi\) | ||||
−0.0335945 | + | 0.999436i | \(0.510695\pi\) | |||||||
\(998\) | −97.9284 | −3.09987 | ||||||||
\(999\) | 8.30741 | 0.262835 |
(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 | 5577.2.a.x.1.2 | 7 | ||
13.5 | odd | 4 | 429.2.b.b.298.13 | yes | 14 | ||
13.8 | odd | 4 | 429.2.b.b.298.2 | ✓ | 14 | ||
13.12 | even | 2 | 5577.2.a.y.1.6 | 7 | |||
39.5 | even | 4 | 1287.2.b.c.298.2 | 14 | |||
39.8 | even | 4 | 1287.2.b.c.298.13 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.b.b.298.2 | ✓ | 14 | 13.8 | odd | 4 | ||
429.2.b.b.298.13 | yes | 14 | 13.5 | odd | 4 | ||
1287.2.b.c.298.2 | 14 | 39.5 | even | 4 | |||
1287.2.b.c.298.13 | 14 | 39.8 | even | 4 | |||
5577.2.a.x.1.2 | 7 | 1.1 | even | 1 | trivial | ||
5577.2.a.y.1.6 | 7 | 13.12 | even | 2 |