Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5054,2,Mod(1,5054)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5054, 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("5054.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5054 = 2 \cdot 7 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5054.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: | \(40.3563931816\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5054.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.618034 | −0.356822 | −0.178411 | − | 0.983956i | \(-0.557096\pi\) | ||||
−0.178411 | + | 0.983956i | \(0.557096\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.381966 | −0.170820 | −0.0854102 | − | 0.996346i | \(-0.527220\pi\) | ||||
−0.0854102 | + | 0.996346i | \(0.527220\pi\) | |||||||
\(6\) | 0.618034 | 0.252311 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.61803 | −0.872678 | ||||||||
\(10\) | 0.381966 | 0.120788 | ||||||||
\(11\) | 1.85410 | 0.559033 | 0.279516 | − | 0.960141i | \(-0.409826\pi\) | ||||
0.279516 | + | 0.960141i | \(0.409826\pi\) | |||||||
\(12\) | −0.618034 | −0.178411 | ||||||||
\(13\) | 4.47214 | 1.24035 | 0.620174 | − | 0.784465i | \(-0.287062\pi\) | ||||
0.620174 | + | 0.784465i | \(0.287062\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0.236068 | 0.0609525 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.23607 | 1.26993 | 0.634967 | − | 0.772540i | \(-0.281014\pi\) | ||||
0.634967 | + | 0.772540i | \(0.281014\pi\) | |||||||
\(18\) | 2.61803 | 0.617077 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −0.381966 | −0.0854102 | ||||||||
\(21\) | −0.618034 | −0.134866 | ||||||||
\(22\) | −1.85410 | −0.395296 | ||||||||
\(23\) | −8.94427 | −1.86501 | −0.932505 | − | 0.361158i | \(-0.882382\pi\) | ||||
−0.932505 | + | 0.361158i | \(0.882382\pi\) | |||||||
\(24\) | 0.618034 | 0.126156 | ||||||||
\(25\) | −4.85410 | −0.970820 | ||||||||
\(26\) | −4.47214 | −0.877058 | ||||||||
\(27\) | 3.47214 | 0.668213 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 6.85410 | 1.27277 | 0.636387 | − | 0.771370i | \(-0.280428\pi\) | ||||
0.636387 | + | 0.771370i | \(0.280428\pi\) | |||||||
\(30\) | −0.236068 | −0.0430999 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.14590 | −0.199475 | ||||||||
\(34\) | −5.23607 | −0.897978 | ||||||||
\(35\) | −0.381966 | −0.0645640 | ||||||||
\(36\) | −2.61803 | −0.436339 | ||||||||
\(37\) | 1.14590 | 0.188384 | 0.0941922 | − | 0.995554i | \(-0.469973\pi\) | ||||
0.0941922 | + | 0.995554i | \(0.469973\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.76393 | −0.442583 | ||||||||
\(40\) | 0.381966 | 0.0603941 | ||||||||
\(41\) | 10.5623 | 1.64956 | 0.824778 | − | 0.565457i | \(-0.191300\pi\) | ||||
0.824778 | + | 0.565457i | \(0.191300\pi\) | |||||||
\(42\) | 0.618034 | 0.0953647 | ||||||||
\(43\) | −2.85410 | −0.435246 | −0.217623 | − | 0.976033i | \(-0.569830\pi\) | ||||
−0.217623 | + | 0.976033i | \(0.569830\pi\) | |||||||
\(44\) | 1.85410 | 0.279516 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 8.94427 | 1.31876 | ||||||||
\(47\) | −4.14590 | −0.604741 | −0.302371 | − | 0.953190i | \(-0.597778\pi\) | ||||
−0.302371 | + | 0.953190i | \(0.597778\pi\) | |||||||
\(48\) | −0.618034 | −0.0892055 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.85410 | 0.686474 | ||||||||
\(51\) | −3.23607 | −0.453140 | ||||||||
\(52\) | 4.47214 | 0.620174 | ||||||||
\(53\) | −11.8541 | −1.62829 | −0.814143 | − | 0.580664i | \(-0.802793\pi\) | ||||
−0.814143 | + | 0.580664i | \(0.802793\pi\) | |||||||
\(54\) | −3.47214 | −0.472498 | ||||||||
\(55\) | −0.708204 | −0.0954942 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.85410 | −0.899988 | ||||||||
\(59\) | 8.56231 | 1.11472 | 0.557359 | − | 0.830272i | \(-0.311815\pi\) | ||||
0.557359 | + | 0.830272i | \(0.311815\pi\) | |||||||
\(60\) | 0.236068 | 0.0304762 | ||||||||
\(61\) | 11.5623 | 1.48040 | 0.740201 | − | 0.672386i | \(-0.234730\pi\) | ||||
0.740201 | + | 0.672386i | \(0.234730\pi\) | |||||||
\(62\) | −6.00000 | −0.762001 | ||||||||
\(63\) | −2.61803 | −0.329841 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.70820 | −0.211877 | ||||||||
\(66\) | 1.14590 | 0.141050 | ||||||||
\(67\) | 0.763932 | 0.0933292 | 0.0466646 | − | 0.998911i | \(-0.485141\pi\) | ||||
0.0466646 | + | 0.998911i | \(0.485141\pi\) | |||||||
\(68\) | 5.23607 | 0.634967 | ||||||||
\(69\) | 5.52786 | 0.665477 | ||||||||
\(70\) | 0.381966 | 0.0456537 | ||||||||
\(71\) | −11.5623 | −1.37219 | −0.686097 | − | 0.727510i | \(-0.740677\pi\) | ||||
−0.686097 | + | 0.727510i | \(0.740677\pi\) | |||||||
\(72\) | 2.61803 | 0.308538 | ||||||||
\(73\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(74\) | −1.14590 | −0.133208 | ||||||||
\(75\) | 3.00000 | 0.346410 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.85410 | 0.211295 | ||||||||
\(78\) | 2.76393 | 0.312954 | ||||||||
\(79\) | −15.3262 | −1.72434 | −0.862168 | − | 0.506622i | \(-0.830894\pi\) | ||||
−0.862168 | + | 0.506622i | \(0.830894\pi\) | |||||||
\(80\) | −0.381966 | −0.0427051 | ||||||||
\(81\) | 5.70820 | 0.634245 | ||||||||
\(82\) | −10.5623 | −1.16641 | ||||||||
\(83\) | 6.76393 | 0.742438 | 0.371219 | − | 0.928545i | \(-0.378940\pi\) | ||||
0.371219 | + | 0.928545i | \(0.378940\pi\) | |||||||
\(84\) | −0.618034 | −0.0674330 | ||||||||
\(85\) | −2.00000 | −0.216930 | ||||||||
\(86\) | 2.85410 | 0.307766 | ||||||||
\(87\) | −4.23607 | −0.454154 | ||||||||
\(88\) | −1.85410 | −0.197648 | ||||||||
\(89\) | −9.85410 | −1.04453 | −0.522266 | − | 0.852782i | \(-0.674913\pi\) | ||||
−0.522266 | + | 0.852782i | \(0.674913\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 4.47214 | 0.468807 | ||||||||
\(92\) | −8.94427 | −0.932505 | ||||||||
\(93\) | −3.70820 | −0.384523 | ||||||||
\(94\) | 4.14590 | 0.427617 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.618034 | 0.0630778 | ||||||||
\(97\) | 13.8541 | 1.40667 | 0.703335 | − | 0.710858i | \(-0.251693\pi\) | ||||
0.703335 | + | 0.710858i | \(0.251693\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −4.85410 | −0.487856 | ||||||||
\(100\) | −4.85410 | −0.485410 | ||||||||
\(101\) | −14.9443 | −1.48701 | −0.743505 | − | 0.668730i | \(-0.766838\pi\) | ||||
−0.743505 | + | 0.668730i | \(0.766838\pi\) | |||||||
\(102\) | 3.23607 | 0.320418 | ||||||||
\(103\) | −8.94427 | −0.881305 | −0.440653 | − | 0.897678i | \(-0.645253\pi\) | ||||
−0.440653 | + | 0.897678i | \(0.645253\pi\) | |||||||
\(104\) | −4.47214 | −0.438529 | ||||||||
\(105\) | 0.236068 | 0.0230379 | ||||||||
\(106\) | 11.8541 | 1.15137 | ||||||||
\(107\) | 6.29180 | 0.608251 | 0.304125 | − | 0.952632i | \(-0.401636\pi\) | ||||
0.304125 | + | 0.952632i | \(0.401636\pi\) | |||||||
\(108\) | 3.47214 | 0.334106 | ||||||||
\(109\) | 4.14590 | 0.397105 | 0.198553 | − | 0.980090i | \(-0.436376\pi\) | ||||
0.198553 | + | 0.980090i | \(0.436376\pi\) | |||||||
\(110\) | 0.708204 | 0.0675246 | ||||||||
\(111\) | −0.708204 | −0.0672197 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 10.0000 | 0.940721 | 0.470360 | − | 0.882474i | \(-0.344124\pi\) | ||||
0.470360 | + | 0.882474i | \(0.344124\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.41641 | 0.318582 | ||||||||
\(116\) | 6.85410 | 0.636387 | ||||||||
\(117\) | −11.7082 | −1.08242 | ||||||||
\(118\) | −8.56231 | −0.788224 | ||||||||
\(119\) | 5.23607 | 0.479990 | ||||||||
\(120\) | −0.236068 | −0.0215500 | ||||||||
\(121\) | −7.56231 | −0.687482 | ||||||||
\(122\) | −11.5623 | −1.04680 | ||||||||
\(123\) | −6.52786 | −0.588598 | ||||||||
\(124\) | 6.00000 | 0.538816 | ||||||||
\(125\) | 3.76393 | 0.336656 | ||||||||
\(126\) | 2.61803 | 0.233233 | ||||||||
\(127\) | 10.9098 | 0.968091 | 0.484045 | − | 0.875043i | \(-0.339167\pi\) | ||||
0.484045 | + | 0.875043i | \(0.339167\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 1.76393 | 0.155306 | ||||||||
\(130\) | 1.70820 | 0.149819 | ||||||||
\(131\) | 4.47214 | 0.390732 | 0.195366 | − | 0.980730i | \(-0.437410\pi\) | ||||
0.195366 | + | 0.980730i | \(0.437410\pi\) | |||||||
\(132\) | −1.14590 | −0.0997376 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.763932 | −0.0659937 | ||||||||
\(135\) | −1.32624 | −0.114144 | ||||||||
\(136\) | −5.23607 | −0.448989 | ||||||||
\(137\) | 5.61803 | 0.479981 | 0.239991 | − | 0.970775i | \(-0.422856\pi\) | ||||
0.239991 | + | 0.970775i | \(0.422856\pi\) | |||||||
\(138\) | −5.52786 | −0.470563 | ||||||||
\(139\) | 6.00000 | 0.508913 | 0.254457 | − | 0.967084i | \(-0.418103\pi\) | ||||
0.254457 | + | 0.967084i | \(0.418103\pi\) | |||||||
\(140\) | −0.381966 | −0.0322820 | ||||||||
\(141\) | 2.56231 | 0.215785 | ||||||||
\(142\) | 11.5623 | 0.970287 | ||||||||
\(143\) | 8.29180 | 0.693395 | ||||||||
\(144\) | −2.61803 | −0.218169 | ||||||||
\(145\) | −2.61803 | −0.217416 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.618034 | −0.0509746 | ||||||||
\(148\) | 1.14590 | 0.0941922 | ||||||||
\(149\) | −12.7639 | −1.04566 | −0.522831 | − | 0.852436i | \(-0.675124\pi\) | ||||
−0.522831 | + | 0.852436i | \(0.675124\pi\) | |||||||
\(150\) | −3.00000 | −0.244949 | ||||||||
\(151\) | 20.9443 | 1.70442 | 0.852210 | − | 0.523199i | \(-0.175262\pi\) | ||||
0.852210 | + | 0.523199i | \(0.175262\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.7082 | −1.10824 | ||||||||
\(154\) | −1.85410 | −0.149408 | ||||||||
\(155\) | −2.29180 | −0.184081 | ||||||||
\(156\) | −2.76393 | −0.221292 | ||||||||
\(157\) | −3.85410 | −0.307591 | −0.153795 | − | 0.988103i | \(-0.549150\pi\) | ||||
−0.153795 | + | 0.988103i | \(0.549150\pi\) | |||||||
\(158\) | 15.3262 | 1.21929 | ||||||||
\(159\) | 7.32624 | 0.581008 | ||||||||
\(160\) | 0.381966 | 0.0301971 | ||||||||
\(161\) | −8.94427 | −0.704907 | ||||||||
\(162\) | −5.70820 | −0.448479 | ||||||||
\(163\) | 13.2705 | 1.03943 | 0.519713 | − | 0.854341i | \(-0.326039\pi\) | ||||
0.519713 | + | 0.854341i | \(0.326039\pi\) | |||||||
\(164\) | 10.5623 | 0.824778 | ||||||||
\(165\) | 0.437694 | 0.0340744 | ||||||||
\(166\) | −6.76393 | −0.524983 | ||||||||
\(167\) | −10.0000 | −0.773823 | −0.386912 | − | 0.922117i | \(-0.626458\pi\) | ||||
−0.386912 | + | 0.922117i | \(0.626458\pi\) | |||||||
\(168\) | 0.618034 | 0.0476824 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 2.00000 | 0.153393 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.85410 | −0.217623 | ||||||||
\(173\) | 18.0000 | 1.36851 | 0.684257 | − | 0.729241i | \(-0.260127\pi\) | ||||
0.684257 | + | 0.729241i | \(0.260127\pi\) | |||||||
\(174\) | 4.23607 | 0.321135 | ||||||||
\(175\) | −4.85410 | −0.366936 | ||||||||
\(176\) | 1.85410 | 0.139758 | ||||||||
\(177\) | −5.29180 | −0.397756 | ||||||||
\(178\) | 9.85410 | 0.738596 | ||||||||
\(179\) | 4.29180 | 0.320784 | 0.160392 | − | 0.987053i | \(-0.448724\pi\) | ||||
0.160392 | + | 0.987053i | \(0.448724\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | 19.4164 | 1.44321 | 0.721605 | − | 0.692305i | \(-0.243405\pi\) | ||||
0.721605 | + | 0.692305i | \(0.243405\pi\) | |||||||
\(182\) | −4.47214 | −0.331497 | ||||||||
\(183\) | −7.14590 | −0.528240 | ||||||||
\(184\) | 8.94427 | 0.659380 | ||||||||
\(185\) | −0.437694 | −0.0321799 | ||||||||
\(186\) | 3.70820 | 0.271899 | ||||||||
\(187\) | 9.70820 | 0.709934 | ||||||||
\(188\) | −4.14590 | −0.302371 | ||||||||
\(189\) | 3.47214 | 0.252561 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.94427 | −0.213040 | −0.106520 | − | 0.994311i | \(-0.533971\pi\) | ||||
−0.106520 | + | 0.994311i | \(0.533971\pi\) | |||||||
\(192\) | −0.618034 | −0.0446028 | ||||||||
\(193\) | −3.05573 | −0.219956 | −0.109978 | − | 0.993934i | \(-0.535078\pi\) | ||||
−0.109978 | + | 0.993934i | \(0.535078\pi\) | |||||||
\(194\) | −13.8541 | −0.994667 | ||||||||
\(195\) | 1.05573 | 0.0756023 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −0.763932 | −0.0544279 | −0.0272140 | − | 0.999630i | \(-0.508664\pi\) | ||||
−0.0272140 | + | 0.999630i | \(0.508664\pi\) | |||||||
\(198\) | 4.85410 | 0.344966 | ||||||||
\(199\) | −18.5623 | −1.31585 | −0.657923 | − | 0.753085i | \(-0.728565\pi\) | ||||
−0.657923 | + | 0.753085i | \(0.728565\pi\) | |||||||
\(200\) | 4.85410 | 0.343237 | ||||||||
\(201\) | −0.472136 | −0.0333019 | ||||||||
\(202\) | 14.9443 | 1.05148 | ||||||||
\(203\) | 6.85410 | 0.481064 | ||||||||
\(204\) | −3.23607 | −0.226570 | ||||||||
\(205\) | −4.03444 | −0.281778 | ||||||||
\(206\) | 8.94427 | 0.623177 | ||||||||
\(207\) | 23.4164 | 1.62755 | ||||||||
\(208\) | 4.47214 | 0.310087 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.236068 | −0.0162902 | ||||||||
\(211\) | 12.7639 | 0.878705 | 0.439353 | − | 0.898315i | \(-0.355208\pi\) | ||||
0.439353 | + | 0.898315i | \(0.355208\pi\) | |||||||
\(212\) | −11.8541 | −0.814143 | ||||||||
\(213\) | 7.14590 | 0.489629 | ||||||||
\(214\) | −6.29180 | −0.430098 | ||||||||
\(215\) | 1.09017 | 0.0743490 | ||||||||
\(216\) | −3.47214 | −0.236249 | ||||||||
\(217\) | 6.00000 | 0.407307 | ||||||||
\(218\) | −4.14590 | −0.280796 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.708204 | −0.0477471 | ||||||||
\(221\) | 23.4164 | 1.57516 | ||||||||
\(222\) | 0.708204 | 0.0475315 | ||||||||
\(223\) | −0.763932 | −0.0511567 | −0.0255783 | − | 0.999673i | \(-0.508143\pi\) | ||||
−0.0255783 | + | 0.999673i | \(0.508143\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 12.7082 | 0.847214 | ||||||||
\(226\) | −10.0000 | −0.665190 | ||||||||
\(227\) | −7.41641 | −0.492244 | −0.246122 | − | 0.969239i | \(-0.579156\pi\) | ||||
−0.246122 | + | 0.969239i | \(0.579156\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.1459 | 1.13303 | 0.566516 | − | 0.824050i | \(-0.308291\pi\) | ||||
0.566516 | + | 0.824050i | \(0.308291\pi\) | |||||||
\(230\) | −3.41641 | −0.225271 | ||||||||
\(231\) | −1.14590 | −0.0753946 | ||||||||
\(232\) | −6.85410 | −0.449994 | ||||||||
\(233\) | −7.09017 | −0.464492 | −0.232246 | − | 0.972657i | \(-0.574608\pi\) | ||||
−0.232246 | + | 0.972657i | \(0.574608\pi\) | |||||||
\(234\) | 11.7082 | 0.765389 | ||||||||
\(235\) | 1.58359 | 0.103302 | ||||||||
\(236\) | 8.56231 | 0.557359 | ||||||||
\(237\) | 9.47214 | 0.615281 | ||||||||
\(238\) | −5.23607 | −0.339404 | ||||||||
\(239\) | −8.18034 | −0.529142 | −0.264571 | − | 0.964366i | \(-0.585230\pi\) | ||||
−0.264571 | + | 0.964366i | \(0.585230\pi\) | |||||||
\(240\) | 0.236068 | 0.0152381 | ||||||||
\(241\) | −2.56231 | −0.165053 | −0.0825263 | − | 0.996589i | \(-0.526299\pi\) | ||||
−0.0825263 | + | 0.996589i | \(0.526299\pi\) | |||||||
\(242\) | 7.56231 | 0.486123 | ||||||||
\(243\) | −13.9443 | −0.894525 | ||||||||
\(244\) | 11.5623 | 0.740201 | ||||||||
\(245\) | −0.381966 | −0.0244029 | ||||||||
\(246\) | 6.52786 | 0.416201 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.00000 | −0.381000 | ||||||||
\(249\) | −4.18034 | −0.264918 | ||||||||
\(250\) | −3.76393 | −0.238052 | ||||||||
\(251\) | 26.9443 | 1.70071 | 0.850354 | − | 0.526212i | \(-0.176388\pi\) | ||||
0.850354 | + | 0.526212i | \(0.176388\pi\) | |||||||
\(252\) | −2.61803 | −0.164921 | ||||||||
\(253\) | −16.5836 | −1.04260 | ||||||||
\(254\) | −10.9098 | −0.684544 | ||||||||
\(255\) | 1.23607 | 0.0774056 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.14590 | 0.196236 | 0.0981179 | − | 0.995175i | \(-0.468718\pi\) | ||||
0.0981179 | + | 0.995175i | \(0.468718\pi\) | |||||||
\(258\) | −1.76393 | −0.109818 | ||||||||
\(259\) | 1.14590 | 0.0712026 | ||||||||
\(260\) | −1.70820 | −0.105938 | ||||||||
\(261\) | −17.9443 | −1.11072 | ||||||||
\(262\) | −4.47214 | −0.276289 | ||||||||
\(263\) | −18.6525 | −1.15016 | −0.575080 | − | 0.818097i | \(-0.695029\pi\) | ||||
−0.575080 | + | 0.818097i | \(0.695029\pi\) | |||||||
\(264\) | 1.14590 | 0.0705251 | ||||||||
\(265\) | 4.52786 | 0.278144 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.09017 | 0.372712 | ||||||||
\(268\) | 0.763932 | 0.0466646 | ||||||||
\(269\) | −31.4164 | −1.91549 | −0.957746 | − | 0.287615i | \(-0.907138\pi\) | ||||
−0.957746 | + | 0.287615i | \(0.907138\pi\) | |||||||
\(270\) | 1.32624 | 0.0807123 | ||||||||
\(271\) | 22.5623 | 1.37056 | 0.685281 | − | 0.728279i | \(-0.259679\pi\) | ||||
0.685281 | + | 0.728279i | \(0.259679\pi\) | |||||||
\(272\) | 5.23607 | 0.317483 | ||||||||
\(273\) | −2.76393 | −0.167281 | ||||||||
\(274\) | −5.61803 | −0.339398 | ||||||||
\(275\) | −9.00000 | −0.542720 | ||||||||
\(276\) | 5.52786 | 0.332738 | ||||||||
\(277\) | 1.41641 | 0.0851037 | 0.0425519 | − | 0.999094i | \(-0.486451\pi\) | ||||
0.0425519 | + | 0.999094i | \(0.486451\pi\) | |||||||
\(278\) | −6.00000 | −0.359856 | ||||||||
\(279\) | −15.7082 | −0.940426 | ||||||||
\(280\) | 0.381966 | 0.0228268 | ||||||||
\(281\) | 3.41641 | 0.203806 | 0.101903 | − | 0.994794i | \(-0.467507\pi\) | ||||
0.101903 | + | 0.994794i | \(0.467507\pi\) | |||||||
\(282\) | −2.56231 | −0.152583 | ||||||||
\(283\) | 8.00000 | 0.475551 | 0.237775 | − | 0.971320i | \(-0.423582\pi\) | ||||
0.237775 | + | 0.971320i | \(0.423582\pi\) | |||||||
\(284\) | −11.5623 | −0.686097 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.29180 | −0.490304 | ||||||||
\(287\) | 10.5623 | 0.623473 | ||||||||
\(288\) | 2.61803 | 0.154269 | ||||||||
\(289\) | 10.4164 | 0.612730 | ||||||||
\(290\) | 2.61803 | 0.153736 | ||||||||
\(291\) | −8.56231 | −0.501931 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.58359 | 0.267776 | 0.133888 | − | 0.990996i | \(-0.457254\pi\) | ||||
0.133888 | + | 0.990996i | \(0.457254\pi\) | |||||||
\(294\) | 0.618034 | 0.0360445 | ||||||||
\(295\) | −3.27051 | −0.190416 | ||||||||
\(296\) | −1.14590 | −0.0666040 | ||||||||
\(297\) | 6.43769 | 0.373553 | ||||||||
\(298\) | 12.7639 | 0.739395 | ||||||||
\(299\) | −40.0000 | −2.31326 | ||||||||
\(300\) | 3.00000 | 0.173205 | ||||||||
\(301\) | −2.85410 | −0.164508 | ||||||||
\(302\) | −20.9443 | −1.20521 | ||||||||
\(303\) | 9.23607 | 0.530598 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.41641 | −0.252883 | ||||||||
\(306\) | 13.7082 | 0.783646 | ||||||||
\(307\) | −27.9787 | −1.59683 | −0.798415 | − | 0.602108i | \(-0.794328\pi\) | ||||
−0.798415 | + | 0.602108i | \(0.794328\pi\) | |||||||
\(308\) | 1.85410 | 0.105647 | ||||||||
\(309\) | 5.52786 | 0.314469 | ||||||||
\(310\) | 2.29180 | 0.130165 | ||||||||
\(311\) | −5.67376 | −0.321730 | −0.160865 | − | 0.986976i | \(-0.551428\pi\) | ||||
−0.160865 | + | 0.986976i | \(0.551428\pi\) | |||||||
\(312\) | 2.76393 | 0.156477 | ||||||||
\(313\) | 10.0000 | 0.565233 | 0.282617 | − | 0.959233i | \(-0.408798\pi\) | ||||
0.282617 | + | 0.959233i | \(0.408798\pi\) | |||||||
\(314\) | 3.85410 | 0.217500 | ||||||||
\(315\) | 1.00000 | 0.0563436 | ||||||||
\(316\) | −15.3262 | −0.862168 | ||||||||
\(317\) | 34.6869 | 1.94821 | 0.974106 | − | 0.226093i | \(-0.0725954\pi\) | ||||
0.974106 | + | 0.226093i | \(0.0725954\pi\) | |||||||
\(318\) | −7.32624 | −0.410835 | ||||||||
\(319\) | 12.7082 | 0.711523 | ||||||||
\(320\) | −0.381966 | −0.0213525 | ||||||||
\(321\) | −3.88854 | −0.217037 | ||||||||
\(322\) | 8.94427 | 0.498445 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 5.70820 | 0.317122 | ||||||||
\(325\) | −21.7082 | −1.20415 | ||||||||
\(326\) | −13.2705 | −0.734986 | ||||||||
\(327\) | −2.56231 | −0.141696 | ||||||||
\(328\) | −10.5623 | −0.583206 | ||||||||
\(329\) | −4.14590 | −0.228571 | ||||||||
\(330\) | −0.437694 | −0.0240943 | ||||||||
\(331\) | 9.70820 | 0.533611 | 0.266806 | − | 0.963750i | \(-0.414032\pi\) | ||||
0.266806 | + | 0.963750i | \(0.414032\pi\) | |||||||
\(332\) | 6.76393 | 0.371219 | ||||||||
\(333\) | −3.00000 | −0.164399 | ||||||||
\(334\) | 10.0000 | 0.547176 | ||||||||
\(335\) | −0.291796 | −0.0159425 | ||||||||
\(336\) | −0.618034 | −0.0337165 | ||||||||
\(337\) | −3.70820 | −0.201999 | −0.100999 | − | 0.994886i | \(-0.532204\pi\) | ||||
−0.100999 | + | 0.994886i | \(0.532204\pi\) | |||||||
\(338\) | −7.00000 | −0.380750 | ||||||||
\(339\) | −6.18034 | −0.335670 | ||||||||
\(340\) | −2.00000 | −0.108465 | ||||||||
\(341\) | 11.1246 | 0.602432 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 2.85410 | 0.153883 | ||||||||
\(345\) | −2.11146 | −0.113677 | ||||||||
\(346\) | −18.0000 | −0.967686 | ||||||||
\(347\) | −8.94427 | −0.480154 | −0.240077 | − | 0.970754i | \(-0.577173\pi\) | ||||
−0.240077 | + | 0.970754i | \(0.577173\pi\) | |||||||
\(348\) | −4.23607 | −0.227077 | ||||||||
\(349\) | 36.8328 | 1.97162 | 0.985808 | − | 0.167878i | \(-0.0536916\pi\) | ||||
0.985808 | + | 0.167878i | \(0.0536916\pi\) | |||||||
\(350\) | 4.85410 | 0.259463 | ||||||||
\(351\) | 15.5279 | 0.828816 | ||||||||
\(352\) | −1.85410 | −0.0988240 | ||||||||
\(353\) | −13.4164 | −0.714083 | −0.357042 | − | 0.934088i | \(-0.616215\pi\) | ||||
−0.357042 | + | 0.934088i | \(0.616215\pi\) | |||||||
\(354\) | 5.29180 | 0.281256 | ||||||||
\(355\) | 4.41641 | 0.234399 | ||||||||
\(356\) | −9.85410 | −0.522266 | ||||||||
\(357\) | −3.23607 | −0.171271 | ||||||||
\(358\) | −4.29180 | −0.226828 | ||||||||
\(359\) | 15.7082 | 0.829047 | 0.414524 | − | 0.910039i | \(-0.363948\pi\) | ||||
0.414524 | + | 0.910039i | \(0.363948\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −19.4164 | −1.02050 | ||||||||
\(363\) | 4.67376 | 0.245309 | ||||||||
\(364\) | 4.47214 | 0.234404 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 7.14590 | 0.373522 | ||||||||
\(367\) | 27.2705 | 1.42351 | 0.711755 | − | 0.702428i | \(-0.247901\pi\) | ||||
0.711755 | + | 0.702428i | \(0.247901\pi\) | |||||||
\(368\) | −8.94427 | −0.466252 | ||||||||
\(369\) | −27.6525 | −1.43953 | ||||||||
\(370\) | 0.437694 | 0.0227546 | ||||||||
\(371\) | −11.8541 | −0.615434 | ||||||||
\(372\) | −3.70820 | −0.192261 | ||||||||
\(373\) | 12.3820 | 0.641114 | 0.320557 | − | 0.947229i | \(-0.396130\pi\) | ||||
0.320557 | + | 0.947229i | \(0.396130\pi\) | |||||||
\(374\) | −9.70820 | −0.501999 | ||||||||
\(375\) | −2.32624 | −0.120126 | ||||||||
\(376\) | 4.14590 | 0.213808 | ||||||||
\(377\) | 30.6525 | 1.57868 | ||||||||
\(378\) | −3.47214 | −0.178587 | ||||||||
\(379\) | 9.81966 | 0.504402 | 0.252201 | − | 0.967675i | \(-0.418846\pi\) | ||||
0.252201 | + | 0.967675i | \(0.418846\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.74265 | −0.345436 | ||||||||
\(382\) | 2.94427 | 0.150642 | ||||||||
\(383\) | 27.1246 | 1.38600 | 0.693001 | − | 0.720936i | \(-0.256288\pi\) | ||||
0.693001 | + | 0.720936i | \(0.256288\pi\) | |||||||
\(384\) | 0.618034 | 0.0315389 | ||||||||
\(385\) | −0.708204 | −0.0360934 | ||||||||
\(386\) | 3.05573 | 0.155532 | ||||||||
\(387\) | 7.47214 | 0.379830 | ||||||||
\(388\) | 13.8541 | 0.703335 | ||||||||
\(389\) | 25.3050 | 1.28301 | 0.641506 | − | 0.767118i | \(-0.278310\pi\) | ||||
0.641506 | + | 0.767118i | \(0.278310\pi\) | |||||||
\(390\) | −1.05573 | −0.0534589 | ||||||||
\(391\) | −46.8328 | −2.36844 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −2.76393 | −0.139422 | ||||||||
\(394\) | 0.763932 | 0.0384863 | ||||||||
\(395\) | 5.85410 | 0.294552 | ||||||||
\(396\) | −4.85410 | −0.243928 | ||||||||
\(397\) | −8.43769 | −0.423476 | −0.211738 | − | 0.977326i | \(-0.567912\pi\) | ||||
−0.211738 | + | 0.977326i | \(0.567912\pi\) | |||||||
\(398\) | 18.5623 | 0.930444 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.85410 | −0.242705 | ||||||||
\(401\) | 1.41641 | 0.0707320 | 0.0353660 | − | 0.999374i | \(-0.488740\pi\) | ||||
0.0353660 | + | 0.999374i | \(0.488740\pi\) | |||||||
\(402\) | 0.472136 | 0.0235480 | ||||||||
\(403\) | 26.8328 | 1.33664 | ||||||||
\(404\) | −14.9443 | −0.743505 | ||||||||
\(405\) | −2.18034 | −0.108342 | ||||||||
\(406\) | −6.85410 | −0.340163 | ||||||||
\(407\) | 2.12461 | 0.105313 | ||||||||
\(408\) | 3.23607 | 0.160209 | ||||||||
\(409\) | 22.7984 | 1.12731 | 0.563654 | − | 0.826011i | \(-0.309395\pi\) | ||||
0.563654 | + | 0.826011i | \(0.309395\pi\) | |||||||
\(410\) | 4.03444 | 0.199247 | ||||||||
\(411\) | −3.47214 | −0.171268 | ||||||||
\(412\) | −8.94427 | −0.440653 | ||||||||
\(413\) | 8.56231 | 0.421324 | ||||||||
\(414\) | −23.4164 | −1.15085 | ||||||||
\(415\) | −2.58359 | −0.126824 | ||||||||
\(416\) | −4.47214 | −0.219265 | ||||||||
\(417\) | −3.70820 | −0.181592 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.6525 | 0.911233 | 0.455617 | − | 0.890176i | \(-0.349419\pi\) | ||||
0.455617 | + | 0.890176i | \(0.349419\pi\) | |||||||
\(420\) | 0.236068 | 0.0115189 | ||||||||
\(421\) | 28.4721 | 1.38765 | 0.693823 | − | 0.720145i | \(-0.255925\pi\) | ||||
0.693823 | + | 0.720145i | \(0.255925\pi\) | |||||||
\(422\) | −12.7639 | −0.621338 | ||||||||
\(423\) | 10.8541 | 0.527744 | ||||||||
\(424\) | 11.8541 | 0.575686 | ||||||||
\(425\) | −25.4164 | −1.23288 | ||||||||
\(426\) | −7.14590 | −0.346220 | ||||||||
\(427\) | 11.5623 | 0.559539 | ||||||||
\(428\) | 6.29180 | 0.304125 | ||||||||
\(429\) | −5.12461 | −0.247419 | ||||||||
\(430\) | −1.09017 | −0.0525727 | ||||||||
\(431\) | 16.1459 | 0.777721 | 0.388860 | − | 0.921297i | \(-0.372869\pi\) | ||||
0.388860 | + | 0.921297i | \(0.372869\pi\) | |||||||
\(432\) | 3.47214 | 0.167053 | ||||||||
\(433\) | −5.61803 | −0.269985 | −0.134993 | − | 0.990847i | \(-0.543101\pi\) | ||||
−0.134993 | + | 0.990847i | \(0.543101\pi\) | |||||||
\(434\) | −6.00000 | −0.288009 | ||||||||
\(435\) | 1.61803 | 0.0775788 | ||||||||
\(436\) | 4.14590 | 0.198553 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.1803 | 0.963155 | 0.481578 | − | 0.876403i | \(-0.340064\pi\) | ||||
0.481578 | + | 0.876403i | \(0.340064\pi\) | |||||||
\(440\) | 0.708204 | 0.0337623 | ||||||||
\(441\) | −2.61803 | −0.124668 | ||||||||
\(442\) | −23.4164 | −1.11380 | ||||||||
\(443\) | −10.0902 | −0.479398 | −0.239699 | − | 0.970847i | \(-0.577049\pi\) | ||||
−0.239699 | + | 0.970847i | \(0.577049\pi\) | |||||||
\(444\) | −0.708204 | −0.0336099 | ||||||||
\(445\) | 3.76393 | 0.178427 | ||||||||
\(446\) | 0.763932 | 0.0361732 | ||||||||
\(447\) | 7.88854 | 0.373115 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −13.7082 | −0.646930 | −0.323465 | − | 0.946240i | \(-0.604848\pi\) | ||||
−0.323465 | + | 0.946240i | \(0.604848\pi\) | |||||||
\(450\) | −12.7082 | −0.599070 | ||||||||
\(451\) | 19.5836 | 0.922155 | ||||||||
\(452\) | 10.0000 | 0.470360 | ||||||||
\(453\) | −12.9443 | −0.608175 | ||||||||
\(454\) | 7.41641 | 0.348069 | ||||||||
\(455\) | −1.70820 | −0.0800818 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 37.8541 | 1.77074 | 0.885370 | − | 0.464887i | \(-0.153905\pi\) | ||||
0.885370 | + | 0.464887i | \(0.153905\pi\) | |||||||
\(458\) | −17.1459 | −0.801175 | ||||||||
\(459\) | 18.1803 | 0.848586 | ||||||||
\(460\) | 3.41641 | 0.159291 | ||||||||
\(461\) | −3.49342 | −0.162705 | −0.0813524 | − | 0.996685i | \(-0.525924\pi\) | ||||
−0.0813524 | + | 0.996685i | \(0.525924\pi\) | |||||||
\(462\) | 1.14590 | 0.0533120 | ||||||||
\(463\) | −12.0000 | −0.557687 | −0.278844 | − | 0.960337i | \(-0.589951\pi\) | ||||
−0.278844 | + | 0.960337i | \(0.589951\pi\) | |||||||
\(464\) | 6.85410 | 0.318194 | ||||||||
\(465\) | 1.41641 | 0.0656843 | ||||||||
\(466\) | 7.09017 | 0.328446 | ||||||||
\(467\) | 4.36068 | 0.201788 | 0.100894 | − | 0.994897i | \(-0.467830\pi\) | ||||
0.100894 | + | 0.994897i | \(0.467830\pi\) | |||||||
\(468\) | −11.7082 | −0.541212 | ||||||||
\(469\) | 0.763932 | 0.0352751 | ||||||||
\(470\) | −1.58359 | −0.0730457 | ||||||||
\(471\) | 2.38197 | 0.109755 | ||||||||
\(472\) | −8.56231 | −0.394112 | ||||||||
\(473\) | −5.29180 | −0.243317 | ||||||||
\(474\) | −9.47214 | −0.435070 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.23607 | 0.239995 | ||||||||
\(477\) | 31.0344 | 1.42097 | ||||||||
\(478\) | 8.18034 | 0.374160 | ||||||||
\(479\) | 20.6738 | 0.944608 | 0.472304 | − | 0.881436i | \(-0.343422\pi\) | ||||
0.472304 | + | 0.881436i | \(0.343422\pi\) | |||||||
\(480\) | −0.236068 | −0.0107750 | ||||||||
\(481\) | 5.12461 | 0.233662 | ||||||||
\(482\) | 2.56231 | 0.116710 | ||||||||
\(483\) | 5.52786 | 0.251527 | ||||||||
\(484\) | −7.56231 | −0.343741 | ||||||||
\(485\) | −5.29180 | −0.240288 | ||||||||
\(486\) | 13.9443 | 0.632525 | ||||||||
\(487\) | 28.0902 | 1.27289 | 0.636444 | − | 0.771323i | \(-0.280405\pi\) | ||||
0.636444 | + | 0.771323i | \(0.280405\pi\) | |||||||
\(488\) | −11.5623 | −0.523401 | ||||||||
\(489\) | −8.20163 | −0.370890 | ||||||||
\(490\) | 0.381966 | 0.0172555 | ||||||||
\(491\) | 4.36068 | 0.196795 | 0.0983974 | − | 0.995147i | \(-0.468628\pi\) | ||||
0.0983974 | + | 0.995147i | \(0.468628\pi\) | |||||||
\(492\) | −6.52786 | −0.294299 | ||||||||
\(493\) | 35.8885 | 1.61634 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.85410 | 0.0833357 | ||||||||
\(496\) | 6.00000 | 0.269408 | ||||||||
\(497\) | −11.5623 | −0.518640 | ||||||||
\(498\) | 4.18034 | 0.187326 | ||||||||
\(499\) | 41.6869 | 1.86616 | 0.933081 | − | 0.359665i | \(-0.117109\pi\) | ||||
0.933081 | + | 0.359665i | \(0.117109\pi\) | |||||||
\(500\) | 3.76393 | 0.168328 | ||||||||
\(501\) | 6.18034 | 0.276117 | ||||||||
\(502\) | −26.9443 | −1.20258 | ||||||||
\(503\) | −21.2148 | −0.945920 | −0.472960 | − | 0.881084i | \(-0.656815\pi\) | ||||
−0.472960 | + | 0.881084i | \(0.656815\pi\) | |||||||
\(504\) | 2.61803 | 0.116617 | ||||||||
\(505\) | 5.70820 | 0.254012 | ||||||||
\(506\) | 16.5836 | 0.737231 | ||||||||
\(507\) | −4.32624 | −0.192135 | ||||||||
\(508\) | 10.9098 | 0.484045 | ||||||||
\(509\) | 5.12461 | 0.227144 | 0.113572 | − | 0.993530i | \(-0.463771\pi\) | ||||
0.113572 | + | 0.993530i | \(0.463771\pi\) | |||||||
\(510\) | −1.23607 | −0.0547340 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.14590 | −0.138760 | ||||||||
\(515\) | 3.41641 | 0.150545 | ||||||||
\(516\) | 1.76393 | 0.0776528 | ||||||||
\(517\) | −7.68692 | −0.338070 | ||||||||
\(518\) | −1.14590 | −0.0503479 | ||||||||
\(519\) | −11.1246 | −0.488316 | ||||||||
\(520\) | 1.70820 | 0.0749097 | ||||||||
\(521\) | 5.41641 | 0.237297 | 0.118649 | − | 0.992936i | \(-0.462144\pi\) | ||||
0.118649 | + | 0.992936i | \(0.462144\pi\) | |||||||
\(522\) | 17.9443 | 0.785399 | ||||||||
\(523\) | 24.0000 | 1.04945 | 0.524723 | − | 0.851273i | \(-0.324169\pi\) | ||||
0.524723 | + | 0.851273i | \(0.324169\pi\) | |||||||
\(524\) | 4.47214 | 0.195366 | ||||||||
\(525\) | 3.00000 | 0.130931 | ||||||||
\(526\) | 18.6525 | 0.813287 | ||||||||
\(527\) | 31.4164 | 1.36852 | ||||||||
\(528\) | −1.14590 | −0.0498688 | ||||||||
\(529\) | 57.0000 | 2.47826 | ||||||||
\(530\) | −4.52786 | −0.196678 | ||||||||
\(531\) | −22.4164 | −0.972789 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 47.2361 | 2.04602 | ||||||||
\(534\) | −6.09017 | −0.263547 | ||||||||
\(535\) | −2.40325 | −0.103902 | ||||||||
\(536\) | −0.763932 | −0.0329968 | ||||||||
\(537\) | −2.65248 | −0.114463 | ||||||||
\(538\) | 31.4164 | 1.35446 | ||||||||
\(539\) | 1.85410 | 0.0798618 | ||||||||
\(540\) | −1.32624 | −0.0570722 | ||||||||
\(541\) | −21.1246 | −0.908218 | −0.454109 | − | 0.890946i | \(-0.650042\pi\) | ||||
−0.454109 | + | 0.890946i | \(0.650042\pi\) | |||||||
\(542\) | −22.5623 | −0.969134 | ||||||||
\(543\) | −12.0000 | −0.514969 | ||||||||
\(544\) | −5.23607 | −0.224495 | ||||||||
\(545\) | −1.58359 | −0.0678336 | ||||||||
\(546\) | 2.76393 | 0.118285 | ||||||||
\(547\) | −18.6525 | −0.797522 | −0.398761 | − | 0.917055i | \(-0.630560\pi\) | ||||
−0.398761 | + | 0.917055i | \(0.630560\pi\) | |||||||
\(548\) | 5.61803 | 0.239991 | ||||||||
\(549\) | −30.2705 | −1.29191 | ||||||||
\(550\) | 9.00000 | 0.383761 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −5.52786 | −0.235282 | ||||||||
\(553\) | −15.3262 | −0.651738 | ||||||||
\(554\) | −1.41641 | −0.0601774 | ||||||||
\(555\) | 0.270510 | 0.0114825 | ||||||||
\(556\) | 6.00000 | 0.254457 | ||||||||
\(557\) | 26.0689 | 1.10457 | 0.552287 | − | 0.833654i | \(-0.313755\pi\) | ||||
0.552287 | + | 0.833654i | \(0.313755\pi\) | |||||||
\(558\) | 15.7082 | 0.664981 | ||||||||
\(559\) | −12.7639 | −0.539857 | ||||||||
\(560\) | −0.381966 | −0.0161410 | ||||||||
\(561\) | −6.00000 | −0.253320 | ||||||||
\(562\) | −3.41641 | −0.144112 | ||||||||
\(563\) | 13.5623 | 0.571583 | 0.285792 | − | 0.958292i | \(-0.407744\pi\) | ||||
0.285792 | + | 0.958292i | \(0.407744\pi\) | |||||||
\(564\) | 2.56231 | 0.107893 | ||||||||
\(565\) | −3.81966 | −0.160694 | ||||||||
\(566\) | −8.00000 | −0.336265 | ||||||||
\(567\) | 5.70820 | 0.239722 | ||||||||
\(568\) | 11.5623 | 0.485144 | ||||||||
\(569\) | −12.2918 | −0.515299 | −0.257649 | − | 0.966238i | \(-0.582948\pi\) | ||||
−0.257649 | + | 0.966238i | \(0.582948\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −44.6869 | −1.87009 | −0.935045 | − | 0.354530i | \(-0.884641\pi\) | ||||
−0.935045 | + | 0.354530i | \(0.884641\pi\) | |||||||
\(572\) | 8.29180 | 0.346697 | ||||||||
\(573\) | 1.81966 | 0.0760174 | ||||||||
\(574\) | −10.5623 | −0.440862 | ||||||||
\(575\) | 43.4164 | 1.81059 | ||||||||
\(576\) | −2.61803 | −0.109085 | ||||||||
\(577\) | 27.1246 | 1.12921 | 0.564606 | − | 0.825360i | \(-0.309028\pi\) | ||||
0.564606 | + | 0.825360i | \(0.309028\pi\) | |||||||
\(578\) | −10.4164 | −0.433265 | ||||||||
\(579\) | 1.88854 | 0.0784852 | ||||||||
\(580\) | −2.61803 | −0.108708 | ||||||||
\(581\) | 6.76393 | 0.280615 | ||||||||
\(582\) | 8.56231 | 0.354919 | ||||||||
\(583\) | −21.9787 | −0.910265 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.47214 | 0.184900 | ||||||||
\(586\) | −4.58359 | −0.189346 | ||||||||
\(587\) | 28.4721 | 1.17517 | 0.587585 | − | 0.809162i | \(-0.300079\pi\) | ||||
0.587585 | + | 0.809162i | \(0.300079\pi\) | |||||||
\(588\) | −0.618034 | −0.0254873 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 3.27051 | 0.134645 | ||||||||
\(591\) | 0.472136 | 0.0194211 | ||||||||
\(592\) | 1.14590 | 0.0470961 | ||||||||
\(593\) | 7.52786 | 0.309132 | 0.154566 | − | 0.987982i | \(-0.450602\pi\) | ||||
0.154566 | + | 0.987982i | \(0.450602\pi\) | |||||||
\(594\) | −6.43769 | −0.264142 | ||||||||
\(595\) | −2.00000 | −0.0819920 | ||||||||
\(596\) | −12.7639 | −0.522831 | ||||||||
\(597\) | 11.4721 | 0.469523 | ||||||||
\(598\) | 40.0000 | 1.63572 | ||||||||
\(599\) | −34.9787 | −1.42919 | −0.714596 | − | 0.699538i | \(-0.753389\pi\) | ||||
−0.714596 | + | 0.699538i | \(0.753389\pi\) | |||||||
\(600\) | −3.00000 | −0.122474 | ||||||||
\(601\) | −34.3607 | −1.40160 | −0.700801 | − | 0.713357i | \(-0.747174\pi\) | ||||
−0.700801 | + | 0.713357i | \(0.747174\pi\) | |||||||
\(602\) | 2.85410 | 0.116325 | ||||||||
\(603\) | −2.00000 | −0.0814463 | ||||||||
\(604\) | 20.9443 | 0.852210 | ||||||||
\(605\) | 2.88854 | 0.117436 | ||||||||
\(606\) | −9.23607 | −0.375190 | ||||||||
\(607\) | −28.3607 | −1.15112 | −0.575562 | − | 0.817758i | \(-0.695217\pi\) | ||||
−0.575562 | + | 0.817758i | \(0.695217\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.23607 | −0.171654 | ||||||||
\(610\) | 4.41641 | 0.178815 | ||||||||
\(611\) | −18.5410 | −0.750089 | ||||||||
\(612\) | −13.7082 | −0.554121 | ||||||||
\(613\) | 25.7082 | 1.03834 | 0.519172 | − | 0.854670i | \(-0.326240\pi\) | ||||
0.519172 | + | 0.854670i | \(0.326240\pi\) | |||||||
\(614\) | 27.9787 | 1.12913 | ||||||||
\(615\) | 2.49342 | 0.100544 | ||||||||
\(616\) | −1.85410 | −0.0747039 | ||||||||
\(617\) | −30.9230 | −1.24491 | −0.622456 | − | 0.782655i | \(-0.713865\pi\) | ||||
−0.622456 | + | 0.782655i | \(0.713865\pi\) | |||||||
\(618\) | −5.52786 | −0.222363 | ||||||||
\(619\) | −8.58359 | −0.345004 | −0.172502 | − | 0.985009i | \(-0.555185\pi\) | ||||
−0.172502 | + | 0.985009i | \(0.555185\pi\) | |||||||
\(620\) | −2.29180 | −0.0920407 | ||||||||
\(621\) | −31.0557 | −1.24622 | ||||||||
\(622\) | 5.67376 | 0.227497 | ||||||||
\(623\) | −9.85410 | −0.394796 | ||||||||
\(624\) | −2.76393 | −0.110646 | ||||||||
\(625\) | 22.8328 | 0.913313 | ||||||||
\(626\) | −10.0000 | −0.399680 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.85410 | −0.153795 | ||||||||
\(629\) | 6.00000 | 0.239236 | ||||||||
\(630\) | −1.00000 | −0.0398410 | ||||||||
\(631\) | −30.8328 | −1.22744 | −0.613718 | − | 0.789526i | \(-0.710327\pi\) | ||||
−0.613718 | + | 0.789526i | \(0.710327\pi\) | |||||||
\(632\) | 15.3262 | 0.609645 | ||||||||
\(633\) | −7.88854 | −0.313541 | ||||||||
\(634\) | −34.6869 | −1.37759 | ||||||||
\(635\) | −4.16718 | −0.165370 | ||||||||
\(636\) | 7.32624 | 0.290504 | ||||||||
\(637\) | 4.47214 | 0.177192 | ||||||||
\(638\) | −12.7082 | −0.503123 | ||||||||
\(639\) | 30.2705 | 1.19748 | ||||||||
\(640\) | 0.381966 | 0.0150985 | ||||||||
\(641\) | 19.4164 | 0.766902 | 0.383451 | − | 0.923561i | \(-0.374735\pi\) | ||||
0.383451 | + | 0.923561i | \(0.374735\pi\) | |||||||
\(642\) | 3.88854 | 0.153469 | ||||||||
\(643\) | −5.41641 | −0.213602 | −0.106801 | − | 0.994280i | \(-0.534061\pi\) | ||||
−0.106801 | + | 0.994280i | \(0.534061\pi\) | |||||||
\(644\) | −8.94427 | −0.352454 | ||||||||
\(645\) | −0.673762 | −0.0265294 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.3262 | 0.602537 | 0.301268 | − | 0.953539i | \(-0.402590\pi\) | ||||
0.301268 | + | 0.953539i | \(0.402590\pi\) | |||||||
\(648\) | −5.70820 | −0.224239 | ||||||||
\(649\) | 15.8754 | 0.623163 | ||||||||
\(650\) | 21.7082 | 0.851466 | ||||||||
\(651\) | −3.70820 | −0.145336 | ||||||||
\(652\) | 13.2705 | 0.519713 | ||||||||
\(653\) | −22.4721 | −0.879403 | −0.439701 | − | 0.898144i | \(-0.644916\pi\) | ||||
−0.439701 | + | 0.898144i | \(0.644916\pi\) | |||||||
\(654\) | 2.56231 | 0.100194 | ||||||||
\(655\) | −1.70820 | −0.0667451 | ||||||||
\(656\) | 10.5623 | 0.412389 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.14590 | 0.161624 | ||||||||
\(659\) | −41.1246 | −1.60199 | −0.800994 | − | 0.598673i | \(-0.795695\pi\) | ||||
−0.800994 | + | 0.598673i | \(0.795695\pi\) | |||||||
\(660\) | 0.437694 | 0.0170372 | ||||||||
\(661\) | 26.8328 | 1.04368 | 0.521838 | − | 0.853045i | \(-0.325247\pi\) | ||||
0.521838 | + | 0.853045i | \(0.325247\pi\) | |||||||
\(662\) | −9.70820 | −0.377320 | ||||||||
\(663\) | −14.4721 | −0.562051 | ||||||||
\(664\) | −6.76393 | −0.262491 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.00000 | 0.116248 | ||||||||
\(667\) | −61.3050 | −2.37374 | ||||||||
\(668\) | −10.0000 | −0.386912 | ||||||||
\(669\) | 0.472136 | 0.0182538 | ||||||||
\(670\) | 0.291796 | 0.0112731 | ||||||||
\(671\) | 21.4377 | 0.827593 | ||||||||
\(672\) | 0.618034 | 0.0238412 | ||||||||
\(673\) | −20.9443 | −0.807342 | −0.403671 | − | 0.914904i | \(-0.632266\pi\) | ||||
−0.403671 | + | 0.914904i | \(0.632266\pi\) | |||||||
\(674\) | 3.70820 | 0.142835 | ||||||||
\(675\) | −16.8541 | −0.648715 | ||||||||
\(676\) | 7.00000 | 0.269231 | ||||||||
\(677\) | −28.2918 | −1.08734 | −0.543671 | − | 0.839298i | \(-0.682966\pi\) | ||||
−0.543671 | + | 0.839298i | \(0.682966\pi\) | |||||||
\(678\) | 6.18034 | 0.237355 | ||||||||
\(679\) | 13.8541 | 0.531672 | ||||||||
\(680\) | 2.00000 | 0.0766965 | ||||||||
\(681\) | 4.58359 | 0.175644 | ||||||||
\(682\) | −11.1246 | −0.425983 | ||||||||
\(683\) | −15.7082 | −0.601058 | −0.300529 | − | 0.953773i | \(-0.597163\pi\) | ||||
−0.300529 | + | 0.953773i | \(0.597163\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.14590 | −0.0819905 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −10.5967 | −0.404291 | ||||||||
\(688\) | −2.85410 | −0.108812 | ||||||||
\(689\) | −53.0132 | −2.01964 | ||||||||
\(690\) | 2.11146 | 0.0803818 | ||||||||
\(691\) | −46.5410 | −1.77050 | −0.885252 | − | 0.465112i | \(-0.846014\pi\) | ||||
−0.885252 | + | 0.465112i | \(0.846014\pi\) | |||||||
\(692\) | 18.0000 | 0.684257 | ||||||||
\(693\) | −4.85410 | −0.184392 | ||||||||
\(694\) | 8.94427 | 0.339520 | ||||||||
\(695\) | −2.29180 | −0.0869328 | ||||||||
\(696\) | 4.23607 | 0.160568 | ||||||||
\(697\) | 55.3050 | 2.09482 | ||||||||
\(698\) | −36.8328 | −1.39414 | ||||||||
\(699\) | 4.38197 | 0.165741 | ||||||||
\(700\) | −4.85410 | −0.183468 | ||||||||
\(701\) | −0.763932 | −0.0288533 | −0.0144267 | − | 0.999896i | \(-0.504592\pi\) | ||||
−0.0144267 | + | 0.999896i | \(0.504592\pi\) | |||||||
\(702\) | −15.5279 | −0.586061 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.85410 | 0.0698791 | ||||||||
\(705\) | −0.978714 | −0.0368605 | ||||||||
\(706\) | 13.4164 | 0.504933 | ||||||||
\(707\) | −14.9443 | −0.562037 | ||||||||
\(708\) | −5.29180 | −0.198878 | ||||||||
\(709\) | −31.1246 | −1.16891 | −0.584455 | − | 0.811426i | \(-0.698692\pi\) | ||||
−0.584455 | + | 0.811426i | \(0.698692\pi\) | |||||||
\(710\) | −4.41641 | −0.165745 | ||||||||
\(711\) | 40.1246 | 1.50479 | ||||||||
\(712\) | 9.85410 | 0.369298 | ||||||||
\(713\) | −53.6656 | −2.00979 | ||||||||
\(714\) | 3.23607 | 0.121107 | ||||||||
\(715\) | −3.16718 | −0.118446 | ||||||||
\(716\) | 4.29180 | 0.160392 | ||||||||
\(717\) | 5.05573 | 0.188810 | ||||||||
\(718\) | −15.7082 | −0.586225 | ||||||||
\(719\) | −28.3607 | −1.05767 | −0.528837 | − | 0.848723i | \(-0.677372\pi\) | ||||
−0.528837 | + | 0.848723i | \(0.677372\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | −8.94427 | −0.333102 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.58359 | 0.0588944 | ||||||||
\(724\) | 19.4164 | 0.721605 | ||||||||
\(725\) | −33.2705 | −1.23564 | ||||||||
\(726\) | −4.67376 | −0.173460 | ||||||||
\(727\) | 8.43769 | 0.312937 | 0.156468 | − | 0.987683i | \(-0.449989\pi\) | ||||
0.156468 | + | 0.987683i | \(0.449989\pi\) | |||||||
\(728\) | −4.47214 | −0.165748 | ||||||||
\(729\) | −8.50658 | −0.315058 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14.9443 | −0.552734 | ||||||||
\(732\) | −7.14590 | −0.264120 | ||||||||
\(733\) | 0.562306 | 0.0207692 | 0.0103846 | − | 0.999946i | \(-0.496694\pi\) | ||||
0.0103846 | + | 0.999946i | \(0.496694\pi\) | |||||||
\(734\) | −27.2705 | −1.00657 | ||||||||
\(735\) | 0.236068 | 0.00870750 | ||||||||
\(736\) | 8.94427 | 0.329690 | ||||||||
\(737\) | 1.41641 | 0.0521741 | ||||||||
\(738\) | 27.6525 | 1.01790 | ||||||||
\(739\) | 1.72949 | 0.0636203 | 0.0318102 | − | 0.999494i | \(-0.489873\pi\) | ||||
0.0318102 | + | 0.999494i | \(0.489873\pi\) | |||||||
\(740\) | −0.437694 | −0.0160900 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.8541 | 0.435178 | ||||||||
\(743\) | −21.9787 | −0.806321 | −0.403160 | − | 0.915129i | \(-0.632088\pi\) | ||||
−0.403160 | + | 0.915129i | \(0.632088\pi\) | |||||||
\(744\) | 3.70820 | 0.135949 | ||||||||
\(745\) | 4.87539 | 0.178620 | ||||||||
\(746\) | −12.3820 | −0.453336 | ||||||||
\(747\) | −17.7082 | −0.647909 | ||||||||
\(748\) | 9.70820 | 0.354967 | ||||||||
\(749\) | 6.29180 | 0.229897 | ||||||||
\(750\) | 2.32624 | 0.0849422 | ||||||||
\(751\) | 15.3262 | 0.559262 | 0.279631 | − | 0.960107i | \(-0.409788\pi\) | ||||
0.279631 | + | 0.960107i | \(0.409788\pi\) | |||||||
\(752\) | −4.14590 | −0.151185 | ||||||||
\(753\) | −16.6525 | −0.606850 | ||||||||
\(754\) | −30.6525 | −1.11630 | ||||||||
\(755\) | −8.00000 | −0.291150 | ||||||||
\(756\) | 3.47214 | 0.126280 | ||||||||
\(757\) | −34.2492 | −1.24481 | −0.622405 | − | 0.782696i | \(-0.713844\pi\) | ||||
−0.622405 | + | 0.782696i | \(0.713844\pi\) | |||||||
\(758\) | −9.81966 | −0.356666 | ||||||||
\(759\) | 10.2492 | 0.372023 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 53.7771 | 1.94942 | 0.974709 | − | 0.223478i | \(-0.0717411\pi\) | ||||
0.974709 | + | 0.223478i | \(0.0717411\pi\) | |||||||
\(762\) | 6.74265 | 0.244260 | ||||||||
\(763\) | 4.14590 | 0.150092 | ||||||||
\(764\) | −2.94427 | −0.106520 | ||||||||
\(765\) | 5.23607 | 0.189310 | ||||||||
\(766\) | −27.1246 | −0.980052 | ||||||||
\(767\) | 38.2918 | 1.38264 | ||||||||
\(768\) | −0.618034 | −0.0223014 | ||||||||
\(769\) | 25.7082 | 0.927062 | 0.463531 | − | 0.886081i | \(-0.346582\pi\) | ||||
0.463531 | + | 0.886081i | \(0.346582\pi\) | |||||||
\(770\) | 0.708204 | 0.0255219 | ||||||||
\(771\) | −1.94427 | −0.0700212 | ||||||||
\(772\) | −3.05573 | −0.109978 | ||||||||
\(773\) | −11.7082 | −0.421115 | −0.210557 | − | 0.977581i | \(-0.567528\pi\) | ||||
−0.210557 | + | 0.977581i | \(0.567528\pi\) | |||||||
\(774\) | −7.47214 | −0.268580 | ||||||||
\(775\) | −29.1246 | −1.04619 | ||||||||
\(776\) | −13.8541 | −0.497333 | ||||||||
\(777\) | −0.708204 | −0.0254067 | ||||||||
\(778\) | −25.3050 | −0.907226 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 1.05573 | 0.0378011 | ||||||||
\(781\) | −21.4377 | −0.767101 | ||||||||
\(782\) | 46.8328 | 1.67474 | ||||||||
\(783\) | 23.7984 | 0.850484 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 1.47214 | 0.0525428 | ||||||||
\(786\) | 2.76393 | 0.0985862 | ||||||||
\(787\) | 6.27051 | 0.223520 | 0.111760 | − | 0.993735i | \(-0.464351\pi\) | ||||
0.111760 | + | 0.993735i | \(0.464351\pi\) | |||||||
\(788\) | −0.763932 | −0.0272140 | ||||||||
\(789\) | 11.5279 | 0.410403 | ||||||||
\(790\) | −5.85410 | −0.208280 | ||||||||
\(791\) | 10.0000 | 0.355559 | ||||||||
\(792\) | 4.85410 | 0.172483 | ||||||||
\(793\) | 51.7082 | 1.83621 | ||||||||
\(794\) | 8.43769 | 0.299443 | ||||||||
\(795\) | −2.79837 | −0.0992481 | ||||||||
\(796\) | −18.5623 | −0.657923 | ||||||||
\(797\) | 8.83282 | 0.312874 | 0.156437 | − | 0.987688i | \(-0.449999\pi\) | ||||
0.156437 | + | 0.987688i | \(0.449999\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.7082 | −0.767981 | ||||||||
\(800\) | 4.85410 | 0.171618 | ||||||||
\(801\) | 25.7984 | 0.911541 | ||||||||
\(802\) | −1.41641 | −0.0500151 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −0.472136 | −0.0166510 | ||||||||
\(805\) | 3.41641 | 0.120413 | ||||||||
\(806\) | −26.8328 | −0.945146 | ||||||||
\(807\) | 19.4164 | 0.683490 | ||||||||
\(808\) | 14.9443 | 0.525738 | ||||||||
\(809\) | 13.0344 | 0.458267 | 0.229133 | − | 0.973395i | \(-0.426411\pi\) | ||||
0.229133 | + | 0.973395i | \(0.426411\pi\) | |||||||
\(810\) | 2.18034 | 0.0766093 | ||||||||
\(811\) | 48.9787 | 1.71988 | 0.859938 | − | 0.510399i | \(-0.170502\pi\) | ||||
0.859938 | + | 0.510399i | \(0.170502\pi\) | |||||||
\(812\) | 6.85410 | 0.240532 | ||||||||
\(813\) | −13.9443 | −0.489047 | ||||||||
\(814\) | −2.12461 | −0.0744676 | ||||||||
\(815\) | −5.06888 | −0.177555 | ||||||||
\(816\) | −3.23607 | −0.113285 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −22.7984 | −0.797126 | ||||||||
\(819\) | −11.7082 | −0.409118 | ||||||||
\(820\) | −4.03444 | −0.140889 | ||||||||
\(821\) | 47.1246 | 1.64466 | 0.822330 | − | 0.569011i | \(-0.192674\pi\) | ||||
0.822330 | + | 0.569011i | \(0.192674\pi\) | |||||||
\(822\) | 3.47214 | 0.121105 | ||||||||
\(823\) | −15.7082 | −0.547554 | −0.273777 | − | 0.961793i | \(-0.588273\pi\) | ||||
−0.273777 | + | 0.961793i | \(0.588273\pi\) | |||||||
\(824\) | 8.94427 | 0.311588 | ||||||||
\(825\) | 5.56231 | 0.193655 | ||||||||
\(826\) | −8.56231 | −0.297921 | ||||||||
\(827\) | 49.9574 | 1.73719 | 0.868595 | − | 0.495523i | \(-0.165023\pi\) | ||||
0.868595 | + | 0.495523i | \(0.165023\pi\) | |||||||
\(828\) | 23.4164 | 0.813776 | ||||||||
\(829\) | 5.12461 | 0.177985 | 0.0889926 | − | 0.996032i | \(-0.471635\pi\) | ||||
0.0889926 | + | 0.996032i | \(0.471635\pi\) | |||||||
\(830\) | 2.58359 | 0.0896778 | ||||||||
\(831\) | −0.875388 | −0.0303669 | ||||||||
\(832\) | 4.47214 | 0.155043 | ||||||||
\(833\) | 5.23607 | 0.181419 | ||||||||
\(834\) | 3.70820 | 0.128405 | ||||||||
\(835\) | 3.81966 | 0.132185 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 20.8328 | 0.720087 | ||||||||
\(838\) | −18.6525 | −0.644339 | ||||||||
\(839\) | 48.8328 | 1.68590 | 0.842948 | − | 0.537995i | \(-0.180818\pi\) | ||||
0.842948 | + | 0.537995i | \(0.180818\pi\) | |||||||
\(840\) | −0.236068 | −0.00814512 | ||||||||
\(841\) | 17.9787 | 0.619956 | ||||||||
\(842\) | −28.4721 | −0.981215 | ||||||||
\(843\) | −2.11146 | −0.0727224 | ||||||||
\(844\) | 12.7639 | 0.439353 | ||||||||
\(845\) | −2.67376 | −0.0919802 | ||||||||
\(846\) | −10.8541 | −0.373172 | ||||||||
\(847\) | −7.56231 | −0.259844 | ||||||||
\(848\) | −11.8541 | −0.407072 | ||||||||
\(849\) | −4.94427 | −0.169687 | ||||||||
\(850\) | 25.4164 | 0.871776 | ||||||||
\(851\) | −10.2492 | −0.351339 | ||||||||
\(852\) | 7.14590 | 0.244814 | ||||||||
\(853\) | 10.2705 | 0.351656 | 0.175828 | − | 0.984421i | \(-0.443740\pi\) | ||||
0.175828 | + | 0.984421i | \(0.443740\pi\) | |||||||
\(854\) | −11.5623 | −0.395654 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.29180 | −0.215049 | ||||||||
\(857\) | −48.2492 | −1.64816 | −0.824081 | − | 0.566472i | \(-0.808308\pi\) | ||||
−0.824081 | + | 0.566472i | \(0.808308\pi\) | |||||||
\(858\) | 5.12461 | 0.174951 | ||||||||
\(859\) | −34.0000 | −1.16007 | −0.580033 | − | 0.814593i | \(-0.696960\pi\) | ||||
−0.580033 | + | 0.814593i | \(0.696960\pi\) | |||||||
\(860\) | 1.09017 | 0.0371745 | ||||||||
\(861\) | −6.52786 | −0.222469 | ||||||||
\(862\) | −16.1459 | −0.549931 | ||||||||
\(863\) | 2.02129 | 0.0688054 | 0.0344027 | − | 0.999408i | \(-0.489047\pi\) | ||||
0.0344027 | + | 0.999408i | \(0.489047\pi\) | |||||||
\(864\) | −3.47214 | −0.118124 | ||||||||
\(865\) | −6.87539 | −0.233770 | ||||||||
\(866\) | 5.61803 | 0.190909 | ||||||||
\(867\) | −6.43769 | −0.218636 | ||||||||
\(868\) | 6.00000 | 0.203653 | ||||||||
\(869\) | −28.4164 | −0.963961 | ||||||||
\(870\) | −1.61803 | −0.0548565 | ||||||||
\(871\) | 3.41641 | 0.115761 | ||||||||
\(872\) | −4.14590 | −0.140398 | ||||||||
\(873\) | −36.2705 | −1.22757 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.76393 | 0.127244 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.3951 | 0.891300 | 0.445650 | − | 0.895207i | \(-0.352973\pi\) | ||||
0.445650 | + | 0.895207i | \(0.352973\pi\) | |||||||
\(878\) | −20.1803 | −0.681053 | ||||||||
\(879\) | −2.83282 | −0.0955485 | ||||||||
\(880\) | −0.708204 | −0.0238735 | ||||||||
\(881\) | 32.1803 | 1.08418 | 0.542092 | − | 0.840319i | \(-0.317633\pi\) | ||||
0.542092 | + | 0.840319i | \(0.317633\pi\) | |||||||
\(882\) | 2.61803 | 0.0881538 | ||||||||
\(883\) | 32.6869 | 1.10000 | 0.550001 | − | 0.835164i | \(-0.314627\pi\) | ||||
0.550001 | + | 0.835164i | \(0.314627\pi\) | |||||||
\(884\) | 23.4164 | 0.787579 | ||||||||
\(885\) | 2.02129 | 0.0679448 | ||||||||
\(886\) | 10.0902 | 0.338986 | ||||||||
\(887\) | −50.8328 | −1.70680 | −0.853399 | − | 0.521257i | \(-0.825463\pi\) | ||||
−0.853399 | + | 0.521257i | \(0.825463\pi\) | |||||||
\(888\) | 0.708204 | 0.0237658 | ||||||||
\(889\) | 10.9098 | 0.365904 | ||||||||
\(890\) | −3.76393 | −0.126167 | ||||||||
\(891\) | 10.5836 | 0.354564 | ||||||||
\(892\) | −0.763932 | −0.0255783 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −7.88854 | −0.263832 | ||||||||
\(895\) | −1.63932 | −0.0547964 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 24.7214 | 0.825422 | ||||||||
\(898\) | 13.7082 | 0.457449 | ||||||||
\(899\) | 41.1246 | 1.37158 | ||||||||
\(900\) | 12.7082 | 0.423607 | ||||||||
\(901\) | −62.0689 | −2.06781 | ||||||||
\(902\) | −19.5836 | −0.652062 | ||||||||
\(903\) | 1.76393 | 0.0587000 | ||||||||
\(904\) | −10.0000 | −0.332595 | ||||||||
\(905\) | −7.41641 | −0.246530 | ||||||||
\(906\) | 12.9443 | 0.430045 | ||||||||
\(907\) | 48.0000 | 1.59381 | 0.796907 | − | 0.604102i | \(-0.206468\pi\) | ||||
0.796907 | + | 0.604102i | \(0.206468\pi\) | |||||||
\(908\) | −7.41641 | −0.246122 | ||||||||
\(909\) | 39.1246 | 1.29768 | ||||||||
\(910\) | 1.70820 | 0.0566264 | ||||||||
\(911\) | −43.1459 | −1.42949 | −0.714744 | − | 0.699386i | \(-0.753457\pi\) | ||||
−0.714744 | + | 0.699386i | \(0.753457\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.5410 | 0.415047 | ||||||||
\(914\) | −37.8541 | −1.25210 | ||||||||
\(915\) | 2.72949 | 0.0902342 | ||||||||
\(916\) | 17.1459 | 0.566516 | ||||||||
\(917\) | 4.47214 | 0.147683 | ||||||||
\(918\) | −18.1803 | −0.600041 | ||||||||
\(919\) | −25.7082 | −0.848035 | −0.424018 | − | 0.905654i | \(-0.639381\pi\) | ||||
−0.424018 | + | 0.905654i | \(0.639381\pi\) | |||||||
\(920\) | −3.41641 | −0.112636 | ||||||||
\(921\) | 17.2918 | 0.569784 | ||||||||
\(922\) | 3.49342 | 0.115050 | ||||||||
\(923\) | −51.7082 | −1.70200 | ||||||||
\(924\) | −1.14590 | −0.0376973 | ||||||||
\(925\) | −5.56231 | −0.182887 | ||||||||
\(926\) | 12.0000 | 0.394344 | ||||||||
\(927\) | 23.4164 | 0.769096 | ||||||||
\(928\) | −6.85410 | −0.224997 | ||||||||
\(929\) | 47.2361 | 1.54977 | 0.774883 | − | 0.632105i | \(-0.217809\pi\) | ||||
0.774883 | + | 0.632105i | \(0.217809\pi\) | |||||||
\(930\) | −1.41641 | −0.0464458 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −7.09017 | −0.232246 | ||||||||
\(933\) | 3.50658 | 0.114800 | ||||||||
\(934\) | −4.36068 | −0.142686 | ||||||||
\(935\) | −3.70820 | −0.121271 | ||||||||
\(936\) | 11.7082 | 0.382695 | ||||||||
\(937\) | 0.291796 | 0.00953256 | 0.00476628 | − | 0.999989i | \(-0.498483\pi\) | ||||
0.00476628 | + | 0.999989i | \(0.498483\pi\) | |||||||
\(938\) | −0.763932 | −0.0249433 | ||||||||
\(939\) | −6.18034 | −0.201688 | ||||||||
\(940\) | 1.58359 | 0.0516511 | ||||||||
\(941\) | −20.2918 | −0.661494 | −0.330747 | − | 0.943720i | \(-0.607301\pi\) | ||||
−0.330747 | + | 0.943720i | \(0.607301\pi\) | |||||||
\(942\) | −2.38197 | −0.0776086 | ||||||||
\(943\) | −94.4721 | −3.07644 | ||||||||
\(944\) | 8.56231 | 0.278679 | ||||||||
\(945\) | −1.32624 | −0.0431425 | ||||||||
\(946\) | 5.29180 | 0.172051 | ||||||||
\(947\) | −49.8541 | −1.62004 | −0.810020 | − | 0.586402i | \(-0.800544\pi\) | ||||
−0.810020 | + | 0.586402i | \(0.800544\pi\) | |||||||
\(948\) | 9.47214 | 0.307641 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.4377 | −0.695165 | ||||||||
\(952\) | −5.23607 | −0.169702 | ||||||||
\(953\) | 15.7082 | 0.508839 | 0.254419 | − | 0.967094i | \(-0.418116\pi\) | ||||
0.254419 | + | 0.967094i | \(0.418116\pi\) | |||||||
\(954\) | −31.0344 | −1.00478 | ||||||||
\(955\) | 1.12461 | 0.0363916 | ||||||||
\(956\) | −8.18034 | −0.264571 | ||||||||
\(957\) | −7.85410 | −0.253887 | ||||||||
\(958\) | −20.6738 | −0.667939 | ||||||||
\(959\) | 5.61803 | 0.181416 | ||||||||
\(960\) | 0.236068 | 0.00761906 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | −5.12461 | −0.165224 | ||||||||
\(963\) | −16.4721 | −0.530807 | ||||||||
\(964\) | −2.56231 | −0.0825263 | ||||||||
\(965\) | 1.16718 | 0.0375730 | ||||||||
\(966\) | −5.52786 | −0.177856 | ||||||||
\(967\) | −26.2492 | −0.844118 | −0.422059 | − | 0.906568i | \(-0.638693\pi\) | ||||
−0.422059 | + | 0.906568i | \(0.638693\pi\) | |||||||
\(968\) | 7.56231 | 0.243062 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.29180 | 0.169909 | ||||||||
\(971\) | 45.2705 | 1.45280 | 0.726400 | − | 0.687272i | \(-0.241192\pi\) | ||||
0.726400 | + | 0.687272i | \(0.241192\pi\) | |||||||
\(972\) | −13.9443 | −0.447263 | ||||||||
\(973\) | 6.00000 | 0.192351 | ||||||||
\(974\) | −28.0902 | −0.900067 | ||||||||
\(975\) | 13.4164 | 0.429669 | ||||||||
\(976\) | 11.5623 | 0.370100 | ||||||||
\(977\) | 22.2918 | 0.713178 | 0.356589 | − | 0.934261i | \(-0.383940\pi\) | ||||
0.356589 | + | 0.934261i | \(0.383940\pi\) | |||||||
\(978\) | 8.20163 | 0.262259 | ||||||||
\(979\) | −18.2705 | −0.583928 | ||||||||
\(980\) | −0.381966 | −0.0122015 | ||||||||
\(981\) | −10.8541 | −0.346545 | ||||||||
\(982\) | −4.36068 | −0.139155 | ||||||||
\(983\) | −21.1246 | −0.673770 | −0.336885 | − | 0.941546i | \(-0.609373\pi\) | ||||
−0.336885 | + | 0.941546i | \(0.609373\pi\) | |||||||
\(984\) | 6.52786 | 0.208101 | ||||||||
\(985\) | 0.291796 | 0.00929740 | ||||||||
\(986\) | −35.8885 | −1.14292 | ||||||||
\(987\) | 2.56231 | 0.0815591 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25.5279 | 0.811739 | ||||||||
\(990\) | −1.85410 | −0.0589272 | ||||||||
\(991\) | −26.3951 | −0.838469 | −0.419234 | − | 0.907878i | \(-0.637701\pi\) | ||||
−0.419234 | + | 0.907878i | \(0.637701\pi\) | |||||||
\(992\) | −6.00000 | −0.190500 | ||||||||
\(993\) | −6.00000 | −0.190404 | ||||||||
\(994\) | 11.5623 | 0.366734 | ||||||||
\(995\) | 7.09017 | 0.224773 | ||||||||
\(996\) | −4.18034 | −0.132459 | ||||||||
\(997\) | −45.1459 | −1.42978 | −0.714892 | − | 0.699234i | \(-0.753524\pi\) | ||||
−0.714892 | + | 0.699234i | \(0.753524\pi\) | |||||||
\(998\) | −41.6869 | −1.31958 | ||||||||
\(999\) | 3.97871 | 0.125881 |
(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 | 5054.2.a.g.1.1 | ✓ | 2 | |
19.18 | odd | 2 | 5054.2.a.l.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5054.2.a.g.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
5054.2.a.l.1.2 | yes | 2 | 19.18 | odd | 2 |