Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8619,2,Mod(1,8619)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8619, 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("8619.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8619 = 3 \cdot 13^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8619.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: | \(68.8230615021\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 8619.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0929476 | 0.0657239 | 0.0328620 | − | 0.999460i | \(-0.489538\pi\) | ||||
0.0328620 | + | 0.999460i | \(0.489538\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.99136 | −0.995680 | ||||||||
\(5\) | −3.17289 | −1.41896 | −0.709481 | − | 0.704725i | \(-0.751070\pi\) | ||||
−0.709481 | + | 0.704725i | \(0.751070\pi\) | |||||||
\(6\) | 0.0929476 | 0.0379457 | ||||||||
\(7\) | 0.513856 | 0.194219 | 0.0971097 | − | 0.995274i | \(-0.469040\pi\) | ||||
0.0971097 | + | 0.995274i | \(0.469040\pi\) | |||||||
\(8\) | −0.370988 | −0.131164 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.294913 | −0.0932597 | ||||||||
\(11\) | −0.710085 | −0.214099 | −0.107049 | − | 0.994254i | \(-0.534140\pi\) | ||||
−0.107049 | + | 0.994254i | \(0.534140\pi\) | |||||||
\(12\) | −1.99136 | −0.574856 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.0477617 | 0.0127649 | ||||||||
\(15\) | −3.17289 | −0.819238 | ||||||||
\(16\) | 3.94824 | 0.987060 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0.0929476 | 0.0219080 | ||||||||
\(19\) | −6.95069 | −1.59460 | −0.797299 | − | 0.603585i | \(-0.793738\pi\) | ||||
−0.797299 | + | 0.603585i | \(0.793738\pi\) | |||||||
\(20\) | 6.31838 | 1.41283 | ||||||||
\(21\) | 0.513856 | 0.112133 | ||||||||
\(22\) | −0.0660007 | −0.0140714 | ||||||||
\(23\) | 4.94547 | 1.03120 | 0.515601 | − | 0.856829i | \(-0.327569\pi\) | ||||
0.515601 | + | 0.856829i | \(0.327569\pi\) | |||||||
\(24\) | −0.370988 | −0.0757275 | ||||||||
\(25\) | 5.06726 | 1.01345 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.02327 | −0.193381 | ||||||||
\(29\) | 1.24548 | 0.231279 | 0.115640 | − | 0.993291i | \(-0.463108\pi\) | ||||
0.115640 | + | 0.993291i | \(0.463108\pi\) | |||||||
\(30\) | −0.294913 | −0.0538435 | ||||||||
\(31\) | 10.7371 | 1.92845 | 0.964224 | − | 0.265089i | \(-0.0854014\pi\) | ||||
0.964224 | + | 0.265089i | \(0.0854014\pi\) | |||||||
\(32\) | 1.10895 | 0.196037 | ||||||||
\(33\) | −0.710085 | −0.123610 | ||||||||
\(34\) | −0.0929476 | −0.0159404 | ||||||||
\(35\) | −1.63041 | −0.275590 | ||||||||
\(36\) | −1.99136 | −0.331893 | ||||||||
\(37\) | −0.627020 | −0.103081 | −0.0515407 | − | 0.998671i | \(-0.516413\pi\) | ||||
−0.0515407 | + | 0.998671i | \(0.516413\pi\) | |||||||
\(38\) | −0.646050 | −0.104803 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.17710 | 0.186117 | ||||||||
\(41\) | −12.4034 | −1.93708 | −0.968539 | − | 0.248861i | \(-0.919944\pi\) | ||||
−0.968539 | + | 0.248861i | \(0.919944\pi\) | |||||||
\(42\) | 0.0477617 | 0.00736980 | ||||||||
\(43\) | 5.88517 | 0.897480 | 0.448740 | − | 0.893662i | \(-0.351873\pi\) | ||||
0.448740 | + | 0.893662i | \(0.351873\pi\) | |||||||
\(44\) | 1.41404 | 0.213174 | ||||||||
\(45\) | −3.17289 | −0.472987 | ||||||||
\(46\) | 0.459669 | 0.0677746 | ||||||||
\(47\) | 7.60138 | 1.10878 | 0.554388 | − | 0.832258i | \(-0.312952\pi\) | ||||
0.554388 | + | 0.832258i | \(0.312952\pi\) | |||||||
\(48\) | 3.94824 | 0.569879 | ||||||||
\(49\) | −6.73595 | −0.962279 | ||||||||
\(50\) | 0.470990 | 0.0666080 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.78204 | 0.244782 | 0.122391 | − | 0.992482i | \(-0.460944\pi\) | ||||
0.122391 | + | 0.992482i | \(0.460944\pi\) | |||||||
\(54\) | 0.0929476 | 0.0126486 | ||||||||
\(55\) | 2.25302 | 0.303798 | ||||||||
\(56\) | −0.190634 | −0.0254746 | ||||||||
\(57\) | −6.95069 | −0.920641 | ||||||||
\(58\) | 0.115764 | 0.0152006 | ||||||||
\(59\) | −7.25662 | −0.944731 | −0.472365 | − | 0.881403i | \(-0.656600\pi\) | ||||
−0.472365 | + | 0.881403i | \(0.656600\pi\) | |||||||
\(60\) | 6.31838 | 0.815699 | ||||||||
\(61\) | 3.22157 | 0.412480 | 0.206240 | − | 0.978501i | \(-0.433877\pi\) | ||||
0.206240 | + | 0.978501i | \(0.433877\pi\) | |||||||
\(62\) | 0.997992 | 0.126745 | ||||||||
\(63\) | 0.513856 | 0.0647398 | ||||||||
\(64\) | −7.79340 | −0.974175 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.0660007 | −0.00812413 | ||||||||
\(67\) | −14.5650 | −1.77940 | −0.889699 | − | 0.456548i | \(-0.849086\pi\) | ||||
−0.889699 | + | 0.456548i | \(0.849086\pi\) | |||||||
\(68\) | 1.99136 | 0.241488 | ||||||||
\(69\) | 4.94547 | 0.595364 | ||||||||
\(70\) | −0.151543 | −0.0181129 | ||||||||
\(71\) | 10.3399 | 1.22712 | 0.613562 | − | 0.789647i | \(-0.289736\pi\) | ||||
0.613562 | + | 0.789647i | \(0.289736\pi\) | |||||||
\(72\) | −0.370988 | −0.0437213 | ||||||||
\(73\) | 13.4443 | 1.57354 | 0.786770 | − | 0.617246i | \(-0.211752\pi\) | ||||
0.786770 | + | 0.617246i | \(0.211752\pi\) | |||||||
\(74\) | −0.0582800 | −0.00677491 | ||||||||
\(75\) | 5.06726 | 0.585117 | ||||||||
\(76\) | 13.8413 | 1.58771 | ||||||||
\(77\) | −0.364882 | −0.0415821 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.66207 | 0.974559 | 0.487279 | − | 0.873246i | \(-0.337989\pi\) | ||||
0.487279 | + | 0.873246i | \(0.337989\pi\) | |||||||
\(80\) | −12.5273 | −1.40060 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.15286 | −0.127312 | ||||||||
\(83\) | −8.16003 | −0.895680 | −0.447840 | − | 0.894114i | \(-0.647807\pi\) | ||||
−0.447840 | + | 0.894114i | \(0.647807\pi\) | |||||||
\(84\) | −1.02327 | −0.111648 | ||||||||
\(85\) | 3.17289 | 0.344149 | ||||||||
\(86\) | 0.547013 | 0.0589859 | ||||||||
\(87\) | 1.24548 | 0.133529 | ||||||||
\(88\) | 0.263433 | 0.0280820 | ||||||||
\(89\) | 13.5553 | 1.43686 | 0.718430 | − | 0.695600i | \(-0.244861\pi\) | ||||
0.718430 | + | 0.695600i | \(0.244861\pi\) | |||||||
\(90\) | −0.294913 | −0.0310866 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −9.84821 | −1.02675 | ||||||||
\(93\) | 10.7371 | 1.11339 | ||||||||
\(94\) | 0.706531 | 0.0728731 | ||||||||
\(95\) | 22.0538 | 2.26267 | ||||||||
\(96\) | 1.10895 | 0.113182 | ||||||||
\(97\) | −4.22630 | −0.429115 | −0.214558 | − | 0.976711i | \(-0.568831\pi\) | ||||
−0.214558 | + | 0.976711i | \(0.568831\pi\) | |||||||
\(98\) | −0.626091 | −0.0632447 | ||||||||
\(99\) | −0.710085 | −0.0713662 | ||||||||
\(100\) | −10.0907 | −1.00907 | ||||||||
\(101\) | 3.01091 | 0.299597 | 0.149799 | − | 0.988717i | \(-0.452137\pi\) | ||||
0.149799 | + | 0.988717i | \(0.452137\pi\) | |||||||
\(102\) | −0.0929476 | −0.00920319 | ||||||||
\(103\) | 6.96909 | 0.686685 | 0.343342 | − | 0.939210i | \(-0.388441\pi\) | ||||
0.343342 | + | 0.939210i | \(0.388441\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.63041 | −0.159112 | ||||||||
\(106\) | 0.165636 | 0.0160880 | ||||||||
\(107\) | 2.53170 | 0.244749 | 0.122375 | − | 0.992484i | \(-0.460949\pi\) | ||||
0.122375 | + | 0.992484i | \(0.460949\pi\) | |||||||
\(108\) | −1.99136 | −0.191619 | ||||||||
\(109\) | 10.4929 | 1.00504 | 0.502519 | − | 0.864566i | \(-0.332407\pi\) | ||||
0.502519 | + | 0.864566i | \(0.332407\pi\) | |||||||
\(110\) | 0.209413 | 0.0199668 | ||||||||
\(111\) | −0.627020 | −0.0595141 | ||||||||
\(112\) | 2.02883 | 0.191706 | ||||||||
\(113\) | 1.70521 | 0.160412 | 0.0802061 | − | 0.996778i | \(-0.474442\pi\) | ||||
0.0802061 | + | 0.996778i | \(0.474442\pi\) | |||||||
\(114\) | −0.646050 | −0.0605081 | ||||||||
\(115\) | −15.6914 | −1.46323 | ||||||||
\(116\) | −2.48019 | −0.230280 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.674485 | −0.0620914 | ||||||||
\(119\) | −0.513856 | −0.0471051 | ||||||||
\(120\) | 1.17710 | 0.107454 | ||||||||
\(121\) | −10.4958 | −0.954162 | ||||||||
\(122\) | 0.299437 | 0.0271098 | ||||||||
\(123\) | −12.4034 | −1.11837 | ||||||||
\(124\) | −21.3815 | −1.92012 | ||||||||
\(125\) | −0.213406 | −0.0190876 | ||||||||
\(126\) | 0.0477617 | 0.00425495 | ||||||||
\(127\) | 14.1095 | 1.25202 | 0.626008 | − | 0.779817i | \(-0.284688\pi\) | ||||
0.626008 | + | 0.779817i | \(0.284688\pi\) | |||||||
\(128\) | −2.94229 | −0.260064 | ||||||||
\(129\) | 5.88517 | 0.518161 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.6923 | −1.63315 | −0.816576 | − | 0.577238i | \(-0.804130\pi\) | ||||
−0.816576 | + | 0.577238i | \(0.804130\pi\) | |||||||
\(132\) | 1.41404 | 0.123076 | ||||||||
\(133\) | −3.57166 | −0.309702 | ||||||||
\(134\) | −1.35378 | −0.116949 | ||||||||
\(135\) | −3.17289 | −0.273079 | ||||||||
\(136\) | 0.370988 | 0.0318119 | ||||||||
\(137\) | 3.84179 | 0.328226 | 0.164113 | − | 0.986442i | \(-0.447524\pi\) | ||||
0.164113 | + | 0.986442i | \(0.447524\pi\) | |||||||
\(138\) | 0.459669 | 0.0391297 | ||||||||
\(139\) | −5.43821 | −0.461263 | −0.230631 | − | 0.973041i | \(-0.574079\pi\) | ||||
−0.230631 | + | 0.973041i | \(0.574079\pi\) | |||||||
\(140\) | 3.24674 | 0.274400 | ||||||||
\(141\) | 7.60138 | 0.640152 | ||||||||
\(142\) | 0.961072 | 0.0806514 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.94824 | 0.329020 | ||||||||
\(145\) | −3.95177 | −0.328176 | ||||||||
\(146\) | 1.24962 | 0.103419 | ||||||||
\(147\) | −6.73595 | −0.555572 | ||||||||
\(148\) | 1.24862 | 0.102636 | ||||||||
\(149\) | −10.1984 | −0.835485 | −0.417743 | − | 0.908565i | \(-0.637179\pi\) | ||||
−0.417743 | + | 0.908565i | \(0.637179\pi\) | |||||||
\(150\) | 0.470990 | 0.0384562 | ||||||||
\(151\) | −10.1235 | −0.823842 | −0.411921 | − | 0.911220i | \(-0.635142\pi\) | ||||
−0.411921 | + | 0.911220i | \(0.635142\pi\) | |||||||
\(152\) | 2.57862 | 0.209154 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −0.0339149 | −0.00273294 | ||||||||
\(155\) | −34.0678 | −2.73639 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.68481 | −0.294080 | −0.147040 | − | 0.989131i | \(-0.546975\pi\) | ||||
−0.147040 | + | 0.989131i | \(0.546975\pi\) | |||||||
\(158\) | 0.805119 | 0.0640518 | ||||||||
\(159\) | 1.78204 | 0.141325 | ||||||||
\(160\) | −3.51860 | −0.278169 | ||||||||
\(161\) | 2.54126 | 0.200279 | ||||||||
\(162\) | 0.0929476 | 0.00730266 | ||||||||
\(163\) | −5.63774 | −0.441582 | −0.220791 | − | 0.975321i | \(-0.570864\pi\) | ||||
−0.220791 | + | 0.975321i | \(0.570864\pi\) | |||||||
\(164\) | 24.6996 | 1.92871 | ||||||||
\(165\) | 2.25302 | 0.175398 | ||||||||
\(166\) | −0.758456 | −0.0588676 | ||||||||
\(167\) | −11.7187 | −0.906822 | −0.453411 | − | 0.891302i | \(-0.649793\pi\) | ||||
−0.453411 | + | 0.891302i | \(0.649793\pi\) | |||||||
\(168\) | −0.190634 | −0.0147078 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0.294913 | 0.0226188 | ||||||||
\(171\) | −6.95069 | −0.531532 | ||||||||
\(172\) | −11.7195 | −0.893604 | ||||||||
\(173\) | −5.94056 | −0.451653 | −0.225826 | − | 0.974168i | \(-0.572508\pi\) | ||||
−0.225826 | + | 0.974168i | \(0.572508\pi\) | |||||||
\(174\) | 0.115764 | 0.00877606 | ||||||||
\(175\) | 2.60384 | 0.196832 | ||||||||
\(176\) | −2.80358 | −0.211328 | ||||||||
\(177\) | −7.25662 | −0.545441 | ||||||||
\(178\) | 1.25993 | 0.0944360 | ||||||||
\(179\) | −1.17793 | −0.0880424 | −0.0440212 | − | 0.999031i | \(-0.514017\pi\) | ||||
−0.0440212 | + | 0.999031i | \(0.514017\pi\) | |||||||
\(180\) | 6.31838 | 0.470944 | ||||||||
\(181\) | 8.71950 | 0.648115 | 0.324058 | − | 0.946037i | \(-0.394953\pi\) | ||||
0.324058 | + | 0.946037i | \(0.394953\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.22157 | 0.238145 | ||||||||
\(184\) | −1.83471 | −0.135256 | ||||||||
\(185\) | 1.98947 | 0.146269 | ||||||||
\(186\) | 0.997992 | 0.0731763 | ||||||||
\(187\) | 0.710085 | 0.0519265 | ||||||||
\(188\) | −15.1371 | −1.10399 | ||||||||
\(189\) | 0.513856 | 0.0373776 | ||||||||
\(190\) | 2.04985 | 0.148712 | ||||||||
\(191\) | −23.1293 | −1.67358 | −0.836789 | − | 0.547525i | \(-0.815570\pi\) | ||||
−0.836789 | + | 0.547525i | \(0.815570\pi\) | |||||||
\(192\) | −7.79340 | −0.562440 | ||||||||
\(193\) | −12.9444 | −0.931755 | −0.465878 | − | 0.884849i | \(-0.654261\pi\) | ||||
−0.465878 | + | 0.884849i | \(0.654261\pi\) | |||||||
\(194\) | −0.392824 | −0.0282031 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.4137 | 0.958122 | ||||||||
\(197\) | −23.2525 | −1.65667 | −0.828336 | − | 0.560232i | \(-0.810712\pi\) | ||||
−0.828336 | + | 0.560232i | \(0.810712\pi\) | |||||||
\(198\) | −0.0660007 | −0.00469047 | ||||||||
\(199\) | −14.7511 | −1.04568 | −0.522840 | − | 0.852431i | \(-0.675128\pi\) | ||||
−0.522840 | + | 0.852431i | \(0.675128\pi\) | |||||||
\(200\) | −1.87989 | −0.132928 | ||||||||
\(201\) | −14.5650 | −1.02734 | ||||||||
\(202\) | 0.279857 | 0.0196907 | ||||||||
\(203\) | 0.639996 | 0.0449189 | ||||||||
\(204\) | 1.99136 | 0.139423 | ||||||||
\(205\) | 39.3545 | 2.74864 | ||||||||
\(206\) | 0.647760 | 0.0451316 | ||||||||
\(207\) | 4.94547 | 0.343734 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.93558 | 0.341401 | ||||||||
\(210\) | −0.151543 | −0.0104575 | ||||||||
\(211\) | 23.0352 | 1.58581 | 0.792903 | − | 0.609347i | \(-0.208568\pi\) | ||||
0.792903 | + | 0.609347i | \(0.208568\pi\) | |||||||
\(212\) | −3.54868 | −0.243724 | ||||||||
\(213\) | 10.3399 | 0.708480 | ||||||||
\(214\) | 0.235316 | 0.0160859 | ||||||||
\(215\) | −18.6730 | −1.27349 | ||||||||
\(216\) | −0.370988 | −0.0252425 | ||||||||
\(217\) | 5.51735 | 0.374542 | ||||||||
\(218\) | 0.975290 | 0.0660550 | ||||||||
\(219\) | 13.4443 | 0.908484 | ||||||||
\(220\) | −4.48658 | −0.302485 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −0.0582800 | −0.00391150 | ||||||||
\(223\) | −6.97643 | −0.467177 | −0.233588 | − | 0.972336i | \(-0.575047\pi\) | ||||
−0.233588 | + | 0.972336i | \(0.575047\pi\) | |||||||
\(224\) | 0.569844 | 0.0380743 | ||||||||
\(225\) | 5.06726 | 0.337817 | ||||||||
\(226\) | 0.158495 | 0.0105429 | ||||||||
\(227\) | −5.98914 | −0.397513 | −0.198757 | − | 0.980049i | \(-0.563690\pi\) | ||||
−0.198757 | + | 0.980049i | \(0.563690\pi\) | |||||||
\(228\) | 13.8413 | 0.916664 | ||||||||
\(229\) | −29.1165 | −1.92408 | −0.962038 | − | 0.272917i | \(-0.912011\pi\) | ||||
−0.962038 | + | 0.272917i | \(0.912011\pi\) | |||||||
\(230\) | −1.45848 | −0.0961695 | ||||||||
\(231\) | −0.364882 | −0.0240075 | ||||||||
\(232\) | −0.462056 | −0.0303355 | ||||||||
\(233\) | 17.8894 | 1.17197 | 0.585987 | − | 0.810321i | \(-0.300707\pi\) | ||||
0.585987 | + | 0.810321i | \(0.300707\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.1184 | −1.57331 | ||||||||
\(236\) | 14.4505 | 0.940650 | ||||||||
\(237\) | 8.66207 | 0.562662 | ||||||||
\(238\) | −0.0477617 | −0.00309593 | ||||||||
\(239\) | −11.1361 | −0.720333 | −0.360167 | − | 0.932888i | \(-0.617280\pi\) | ||||
−0.360167 | + | 0.932888i | \(0.617280\pi\) | |||||||
\(240\) | −12.5273 | −0.808637 | ||||||||
\(241\) | −7.27606 | −0.468692 | −0.234346 | − | 0.972153i | \(-0.575295\pi\) | ||||
−0.234346 | + | 0.972153i | \(0.575295\pi\) | |||||||
\(242\) | −0.975558 | −0.0627112 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −6.41530 | −0.410698 | ||||||||
\(245\) | 21.3725 | 1.36544 | ||||||||
\(246\) | −1.15286 | −0.0735038 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −3.98335 | −0.252943 | ||||||||
\(249\) | −8.16003 | −0.517121 | ||||||||
\(250\) | −0.0198356 | −0.00125451 | ||||||||
\(251\) | −11.1151 | −0.701578 | −0.350789 | − | 0.936455i | \(-0.614087\pi\) | ||||
−0.350789 | + | 0.936455i | \(0.614087\pi\) | |||||||
\(252\) | −1.02327 | −0.0644602 | ||||||||
\(253\) | −3.51170 | −0.220779 | ||||||||
\(254\) | 1.31144 | 0.0822874 | ||||||||
\(255\) | 3.17289 | 0.198694 | ||||||||
\(256\) | 15.3133 | 0.957083 | ||||||||
\(257\) | −19.5951 | −1.22231 | −0.611153 | − | 0.791512i | \(-0.709294\pi\) | ||||
−0.611153 | + | 0.791512i | \(0.709294\pi\) | |||||||
\(258\) | 0.547013 | 0.0340555 | ||||||||
\(259\) | −0.322198 | −0.0200204 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.24548 | 0.0770931 | ||||||||
\(262\) | −1.73740 | −0.107337 | ||||||||
\(263\) | −17.8319 | −1.09956 | −0.549782 | − | 0.835308i | \(-0.685289\pi\) | ||||
−0.549782 | + | 0.835308i | \(0.685289\pi\) | |||||||
\(264\) | 0.263433 | 0.0162132 | ||||||||
\(265\) | −5.65422 | −0.347336 | ||||||||
\(266\) | −0.331977 | −0.0203548 | ||||||||
\(267\) | 13.5553 | 0.829571 | ||||||||
\(268\) | 29.0042 | 1.77171 | ||||||||
\(269\) | 16.6026 | 1.01228 | 0.506139 | − | 0.862452i | \(-0.331072\pi\) | ||||
0.506139 | + | 0.862452i | \(0.331072\pi\) | |||||||
\(270\) | −0.294913 | −0.0179478 | ||||||||
\(271\) | 7.22773 | 0.439053 | 0.219527 | − | 0.975607i | \(-0.429549\pi\) | ||||
0.219527 | + | 0.975607i | \(0.429549\pi\) | |||||||
\(272\) | −3.94824 | −0.239397 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.357085 | 0.0215723 | ||||||||
\(275\) | −3.59818 | −0.216979 | ||||||||
\(276\) | −9.84821 | −0.592792 | ||||||||
\(277\) | −25.4209 | −1.52740 | −0.763698 | − | 0.645574i | \(-0.776618\pi\) | ||||
−0.763698 | + | 0.645574i | \(0.776618\pi\) | |||||||
\(278\) | −0.505469 | −0.0303160 | ||||||||
\(279\) | 10.7371 | 0.642816 | ||||||||
\(280\) | 0.604863 | 0.0361475 | ||||||||
\(281\) | −15.4198 | −0.919870 | −0.459935 | − | 0.887953i | \(-0.652127\pi\) | ||||
−0.459935 | + | 0.887953i | \(0.652127\pi\) | |||||||
\(282\) | 0.706531 | 0.0420733 | ||||||||
\(283\) | 11.1880 | 0.665056 | 0.332528 | − | 0.943093i | \(-0.392098\pi\) | ||||
0.332528 | + | 0.943093i | \(0.392098\pi\) | |||||||
\(284\) | −20.5905 | −1.22182 | ||||||||
\(285\) | 22.0538 | 1.30635 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.37354 | −0.376218 | ||||||||
\(288\) | 1.10895 | 0.0653458 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −0.367307 | −0.0215690 | ||||||||
\(291\) | −4.22630 | −0.247750 | ||||||||
\(292\) | −26.7725 | −1.56674 | ||||||||
\(293\) | −15.1237 | −0.883536 | −0.441768 | − | 0.897129i | \(-0.645649\pi\) | ||||
−0.441768 | + | 0.897129i | \(0.645649\pi\) | |||||||
\(294\) | −0.626091 | −0.0365144 | ||||||||
\(295\) | 23.0245 | 1.34054 | ||||||||
\(296\) | 0.232617 | 0.0135206 | ||||||||
\(297\) | −0.710085 | −0.0412033 | ||||||||
\(298\) | −0.947917 | −0.0549114 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −10.0907 | −0.582589 | ||||||||
\(301\) | 3.02413 | 0.174308 | ||||||||
\(302\) | −0.940960 | −0.0541461 | ||||||||
\(303\) | 3.01091 | 0.172972 | ||||||||
\(304\) | −27.4430 | −1.57396 | ||||||||
\(305\) | −10.2217 | −0.585293 | ||||||||
\(306\) | −0.0929476 | −0.00531346 | ||||||||
\(307\) | −15.3277 | −0.874796 | −0.437398 | − | 0.899268i | \(-0.644100\pi\) | ||||
−0.437398 | + | 0.899268i | \(0.644100\pi\) | |||||||
\(308\) | 0.726611 | 0.0414025 | ||||||||
\(309\) | 6.96909 | 0.396458 | ||||||||
\(310\) | −3.16652 | −0.179846 | ||||||||
\(311\) | −20.4430 | −1.15921 | −0.579607 | − | 0.814896i | \(-0.696794\pi\) | ||||
−0.579607 | + | 0.814896i | \(0.696794\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.3682 | 1.37737 | 0.688687 | − | 0.725059i | \(-0.258187\pi\) | ||||
0.688687 | + | 0.725059i | \(0.258187\pi\) | |||||||
\(314\) | −0.342494 | −0.0193281 | ||||||||
\(315\) | −1.63041 | −0.0918633 | ||||||||
\(316\) | −17.2493 | −0.970349 | ||||||||
\(317\) | −13.9897 | −0.785740 | −0.392870 | − | 0.919594i | \(-0.628518\pi\) | ||||
−0.392870 | + | 0.919594i | \(0.628518\pi\) | |||||||
\(318\) | 0.165636 | 0.00928842 | ||||||||
\(319\) | −0.884394 | −0.0495166 | ||||||||
\(320\) | 24.7276 | 1.38232 | ||||||||
\(321\) | 2.53170 | 0.141306 | ||||||||
\(322\) | 0.236204 | 0.0131631 | ||||||||
\(323\) | 6.95069 | 0.386747 | ||||||||
\(324\) | −1.99136 | −0.110631 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.524014 | −0.0290225 | ||||||||
\(327\) | 10.4929 | 0.580259 | ||||||||
\(328\) | 4.60149 | 0.254075 | ||||||||
\(329\) | 3.90602 | 0.215346 | ||||||||
\(330\) | 0.209413 | 0.0115278 | ||||||||
\(331\) | 27.7717 | 1.52647 | 0.763235 | − | 0.646121i | \(-0.223610\pi\) | ||||
0.763235 | + | 0.646121i | \(0.223610\pi\) | |||||||
\(332\) | 16.2496 | 0.891811 | ||||||||
\(333\) | −0.627020 | −0.0343605 | ||||||||
\(334\) | −1.08923 | −0.0595999 | ||||||||
\(335\) | 46.2132 | 2.52490 | ||||||||
\(336\) | 2.02883 | 0.110682 | ||||||||
\(337\) | −3.77643 | −0.205715 | −0.102858 | − | 0.994696i | \(-0.532799\pi\) | ||||
−0.102858 | + | 0.994696i | \(0.532799\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.70521 | 0.0926140 | ||||||||
\(340\) | −6.31838 | −0.342662 | ||||||||
\(341\) | −7.62428 | −0.412878 | ||||||||
\(342\) | −0.646050 | −0.0349344 | ||||||||
\(343\) | −7.05831 | −0.381113 | ||||||||
\(344\) | −2.18333 | −0.117717 | ||||||||
\(345\) | −15.6914 | −0.844799 | ||||||||
\(346\) | −0.552161 | −0.0296844 | ||||||||
\(347\) | −28.3039 | −1.51943 | −0.759717 | − | 0.650254i | \(-0.774663\pi\) | ||||
−0.759717 | + | 0.650254i | \(0.774663\pi\) | |||||||
\(348\) | −2.48019 | −0.132952 | ||||||||
\(349\) | 13.8054 | 0.738984 | 0.369492 | − | 0.929234i | \(-0.379532\pi\) | ||||
0.369492 | + | 0.929234i | \(0.379532\pi\) | |||||||
\(350\) | 0.242021 | 0.0129366 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.787452 | −0.0419713 | ||||||||
\(353\) | 25.0835 | 1.33506 | 0.667530 | − | 0.744583i | \(-0.267352\pi\) | ||||
0.667530 | + | 0.744583i | \(0.267352\pi\) | |||||||
\(354\) | −0.674485 | −0.0358485 | ||||||||
\(355\) | −32.8075 | −1.74124 | ||||||||
\(356\) | −26.9935 | −1.43065 | ||||||||
\(357\) | −0.513856 | −0.0271962 | ||||||||
\(358\) | −0.109486 | −0.00578649 | ||||||||
\(359\) | 5.58828 | 0.294938 | 0.147469 | − | 0.989067i | \(-0.452887\pi\) | ||||
0.147469 | + | 0.989067i | \(0.452887\pi\) | |||||||
\(360\) | 1.17710 | 0.0620389 | ||||||||
\(361\) | 29.3121 | 1.54274 | ||||||||
\(362\) | 0.810457 | 0.0425967 | ||||||||
\(363\) | −10.4958 | −0.550886 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −42.6574 | −2.23279 | ||||||||
\(366\) | 0.299437 | 0.0156518 | ||||||||
\(367\) | 9.20267 | 0.480375 | 0.240188 | − | 0.970726i | \(-0.422791\pi\) | ||||
0.240188 | + | 0.970726i | \(0.422791\pi\) | |||||||
\(368\) | 19.5259 | 1.01786 | ||||||||
\(369\) | −12.4034 | −0.645693 | ||||||||
\(370\) | 0.184916 | 0.00961334 | ||||||||
\(371\) | 0.915712 | 0.0475414 | ||||||||
\(372\) | −21.3815 | −1.10858 | ||||||||
\(373\) | 3.11861 | 0.161475 | 0.0807377 | − | 0.996735i | \(-0.474272\pi\) | ||||
0.0807377 | + | 0.996735i | \(0.474272\pi\) | |||||||
\(374\) | 0.0660007 | 0.00341282 | ||||||||
\(375\) | −0.213406 | −0.0110202 | ||||||||
\(376\) | −2.82002 | −0.145431 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.0477617 | 0.00245660 | ||||||||
\(379\) | 4.80123 | 0.246622 | 0.123311 | − | 0.992368i | \(-0.460649\pi\) | ||||
0.123311 | + | 0.992368i | \(0.460649\pi\) | |||||||
\(380\) | −43.9171 | −2.25290 | ||||||||
\(381\) | 14.1095 | 0.722852 | ||||||||
\(382\) | −2.14982 | −0.109994 | ||||||||
\(383\) | 16.6011 | 0.848275 | 0.424137 | − | 0.905598i | \(-0.360577\pi\) | ||||
0.424137 | + | 0.905598i | \(0.360577\pi\) | |||||||
\(384\) | −2.94229 | −0.150148 | ||||||||
\(385\) | 1.15773 | 0.0590034 | ||||||||
\(386\) | −1.20315 | −0.0612386 | ||||||||
\(387\) | 5.88517 | 0.299160 | ||||||||
\(388\) | 8.41608 | 0.427262 | ||||||||
\(389\) | 28.4377 | 1.44185 | 0.720925 | − | 0.693013i | \(-0.243717\pi\) | ||||
0.720925 | + | 0.693013i | \(0.243717\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.94547 | −0.250103 | ||||||||
\(392\) | 2.49895 | 0.126216 | ||||||||
\(393\) | −18.6923 | −0.942900 | ||||||||
\(394\) | −2.16126 | −0.108883 | ||||||||
\(395\) | −27.4838 | −1.38286 | ||||||||
\(396\) | 1.41404 | 0.0710579 | ||||||||
\(397\) | −10.4611 | −0.525028 | −0.262514 | − | 0.964928i | \(-0.584552\pi\) | ||||
−0.262514 | + | 0.964928i | \(0.584552\pi\) | |||||||
\(398\) | −1.37108 | −0.0687262 | ||||||||
\(399\) | −3.57166 | −0.178806 | ||||||||
\(400\) | 20.0068 | 1.00034 | ||||||||
\(401\) | −1.88450 | −0.0941075 | −0.0470538 | − | 0.998892i | \(-0.514983\pi\) | ||||
−0.0470538 | + | 0.998892i | \(0.514983\pi\) | |||||||
\(402\) | −1.35378 | −0.0675205 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −5.99581 | −0.298303 | ||||||||
\(405\) | −3.17289 | −0.157662 | ||||||||
\(406\) | 0.0594862 | 0.00295225 | ||||||||
\(407\) | 0.445237 | 0.0220696 | ||||||||
\(408\) | 0.370988 | 0.0183666 | ||||||||
\(409\) | −2.08512 | −0.103103 | −0.0515513 | − | 0.998670i | \(-0.516417\pi\) | ||||
−0.0515513 | + | 0.998670i | \(0.516417\pi\) | |||||||
\(410\) | 3.65791 | 0.180651 | ||||||||
\(411\) | 3.84179 | 0.189501 | ||||||||
\(412\) | −13.8780 | −0.683719 | ||||||||
\(413\) | −3.72886 | −0.183485 | ||||||||
\(414\) | 0.459669 | 0.0225915 | ||||||||
\(415\) | 25.8909 | 1.27094 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.43821 | −0.266310 | ||||||||
\(418\) | 0.458750 | 0.0224382 | ||||||||
\(419\) | −25.6130 | −1.25128 | −0.625638 | − | 0.780114i | \(-0.715161\pi\) | ||||
−0.625638 | + | 0.780114i | \(0.715161\pi\) | |||||||
\(420\) | 3.24674 | 0.158425 | ||||||||
\(421\) | 16.6900 | 0.813419 | 0.406710 | − | 0.913558i | \(-0.366676\pi\) | ||||
0.406710 | + | 0.913558i | \(0.366676\pi\) | |||||||
\(422\) | 2.14107 | 0.104225 | ||||||||
\(423\) | 7.60138 | 0.369592 | ||||||||
\(424\) | −0.661114 | −0.0321065 | ||||||||
\(425\) | −5.06726 | −0.245798 | ||||||||
\(426\) | 0.961072 | 0.0465641 | ||||||||
\(427\) | 1.65542 | 0.0801116 | ||||||||
\(428\) | −5.04154 | −0.243692 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.73561 | −0.0836987 | ||||||||
\(431\) | 15.6532 | 0.753986 | 0.376993 | − | 0.926216i | \(-0.376958\pi\) | ||||
0.376993 | + | 0.926216i | \(0.376958\pi\) | |||||||
\(432\) | 3.94824 | 0.189960 | ||||||||
\(433\) | −11.0119 | −0.529201 | −0.264600 | − | 0.964358i | \(-0.585240\pi\) | ||||
−0.264600 | + | 0.964358i | \(0.585240\pi\) | |||||||
\(434\) | 0.512825 | 0.0246164 | ||||||||
\(435\) | −3.95177 | −0.189473 | ||||||||
\(436\) | −20.8951 | −1.00070 | ||||||||
\(437\) | −34.3744 | −1.64435 | ||||||||
\(438\) | 1.24962 | 0.0597091 | ||||||||
\(439\) | 31.6240 | 1.50933 | 0.754666 | − | 0.656110i | \(-0.227799\pi\) | ||||
0.754666 | + | 0.656110i | \(0.227799\pi\) | |||||||
\(440\) | −0.835844 | −0.0398473 | ||||||||
\(441\) | −6.73595 | −0.320760 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −32.6966 | −1.55346 | −0.776730 | − | 0.629833i | \(-0.783123\pi\) | ||||
−0.776730 | + | 0.629833i | \(0.783123\pi\) | |||||||
\(444\) | 1.24862 | 0.0592570 | ||||||||
\(445\) | −43.0095 | −2.03885 | ||||||||
\(446\) | −0.648443 | −0.0307047 | ||||||||
\(447\) | −10.1984 | −0.482368 | ||||||||
\(448\) | −4.00469 | −0.189204 | ||||||||
\(449\) | −16.9612 | −0.800449 | −0.400224 | − | 0.916417i | \(-0.631068\pi\) | ||||
−0.400224 | + | 0.916417i | \(0.631068\pi\) | |||||||
\(450\) | 0.470990 | 0.0222027 | ||||||||
\(451\) | 8.80743 | 0.414726 | ||||||||
\(452\) | −3.39568 | −0.159719 | ||||||||
\(453\) | −10.1235 | −0.475646 | ||||||||
\(454\) | −0.556677 | −0.0261261 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.57862 | 0.120755 | ||||||||
\(457\) | −12.3211 | −0.576358 | −0.288179 | − | 0.957577i | \(-0.593050\pi\) | ||||
−0.288179 | + | 0.957577i | \(0.593050\pi\) | |||||||
\(458\) | −2.70631 | −0.126458 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 31.2473 | 1.45691 | ||||||||
\(461\) | −1.57749 | −0.0734712 | −0.0367356 | − | 0.999325i | \(-0.511696\pi\) | ||||
−0.0367356 | + | 0.999325i | \(0.511696\pi\) | |||||||
\(462\) | −0.0339149 | −0.00157786 | ||||||||
\(463\) | 7.79713 | 0.362363 | 0.181182 | − | 0.983450i | \(-0.442008\pi\) | ||||
0.181182 | + | 0.983450i | \(0.442008\pi\) | |||||||
\(464\) | 4.91744 | 0.228286 | ||||||||
\(465\) | −34.0678 | −1.57986 | ||||||||
\(466\) | 1.66278 | 0.0770267 | ||||||||
\(467\) | −25.8165 | −1.19464 | −0.597322 | − | 0.802002i | \(-0.703768\pi\) | ||||
−0.597322 | + | 0.802002i | \(0.703768\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.48432 | −0.345594 | ||||||||
\(470\) | −2.24175 | −0.103404 | ||||||||
\(471\) | −3.68481 | −0.169787 | ||||||||
\(472\) | 2.69211 | 0.123915 | ||||||||
\(473\) | −4.17897 | −0.192149 | ||||||||
\(474\) | 0.805119 | 0.0369803 | ||||||||
\(475\) | −35.2209 | −1.61605 | ||||||||
\(476\) | 1.02327 | 0.0469017 | ||||||||
\(477\) | 1.78204 | 0.0815939 | ||||||||
\(478\) | −1.03507 | −0.0473431 | ||||||||
\(479\) | 4.11443 | 0.187993 | 0.0939965 | − | 0.995573i | \(-0.470036\pi\) | ||||
0.0939965 | + | 0.995573i | \(0.470036\pi\) | |||||||
\(480\) | −3.51860 | −0.160601 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −0.676292 | −0.0308043 | ||||||||
\(483\) | 2.54126 | 0.115631 | ||||||||
\(484\) | 20.9009 | 0.950040 | ||||||||
\(485\) | 13.4096 | 0.608898 | ||||||||
\(486\) | 0.0929476 | 0.00421619 | ||||||||
\(487\) | −33.9931 | −1.54037 | −0.770187 | − | 0.637818i | \(-0.779837\pi\) | ||||
−0.770187 | + | 0.637818i | \(0.779837\pi\) | |||||||
\(488\) | −1.19516 | −0.0541024 | ||||||||
\(489\) | −5.63774 | −0.254947 | ||||||||
\(490\) | 1.98652 | 0.0897418 | ||||||||
\(491\) | −4.01426 | −0.181161 | −0.0905805 | − | 0.995889i | \(-0.528872\pi\) | ||||
−0.0905805 | + | 0.995889i | \(0.528872\pi\) | |||||||
\(492\) | 24.6996 | 1.11354 | ||||||||
\(493\) | −1.24548 | −0.0560935 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.25302 | 0.101266 | ||||||||
\(496\) | 42.3928 | 1.90349 | ||||||||
\(497\) | 5.31324 | 0.238331 | ||||||||
\(498\) | −0.758456 | −0.0339872 | ||||||||
\(499\) | 10.8779 | 0.486960 | 0.243480 | − | 0.969906i | \(-0.421711\pi\) | ||||
0.243480 | + | 0.969906i | \(0.421711\pi\) | |||||||
\(500\) | 0.424969 | 0.0190052 | ||||||||
\(501\) | −11.7187 | −0.523554 | ||||||||
\(502\) | −1.03312 | −0.0461104 | ||||||||
\(503\) | 33.8098 | 1.50751 | 0.753753 | − | 0.657158i | \(-0.228242\pi\) | ||||
0.753753 | + | 0.657158i | \(0.228242\pi\) | |||||||
\(504\) | −0.190634 | −0.00849153 | ||||||||
\(505\) | −9.55331 | −0.425117 | ||||||||
\(506\) | −0.326404 | −0.0145104 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −28.0971 | −1.24661 | ||||||||
\(509\) | −29.3839 | −1.30242 | −0.651210 | − | 0.758898i | \(-0.725738\pi\) | ||||
−0.651210 | + | 0.758898i | \(0.725738\pi\) | |||||||
\(510\) | 0.294913 | 0.0130590 | ||||||||
\(511\) | 6.90846 | 0.305612 | ||||||||
\(512\) | 7.30791 | 0.322967 | ||||||||
\(513\) | −6.95069 | −0.306880 | ||||||||
\(514\) | −1.82132 | −0.0803348 | ||||||||
\(515\) | −22.1122 | −0.974379 | ||||||||
\(516\) | −11.7195 | −0.515922 | ||||||||
\(517\) | −5.39763 | −0.237387 | ||||||||
\(518\) | −0.0299476 | −0.00131582 | ||||||||
\(519\) | −5.94056 | −0.260762 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.8780 | 0.958494 | 0.479247 | − | 0.877680i | \(-0.340910\pi\) | ||||
0.479247 | + | 0.877680i | \(0.340910\pi\) | |||||||
\(522\) | 0.115764 | 0.00506686 | ||||||||
\(523\) | −29.7241 | −1.29975 | −0.649873 | − | 0.760043i | \(-0.725178\pi\) | ||||
−0.649873 | + | 0.760043i | \(0.725178\pi\) | |||||||
\(524\) | 37.2231 | 1.62610 | ||||||||
\(525\) | 2.60384 | 0.113641 | ||||||||
\(526\) | −1.65744 | −0.0722677 | ||||||||
\(527\) | −10.7371 | −0.467717 | ||||||||
\(528\) | −2.80358 | −0.122010 | ||||||||
\(529\) | 1.45764 | 0.0633756 | ||||||||
\(530\) | −0.525546 | −0.0228283 | ||||||||
\(531\) | −7.25662 | −0.314910 | ||||||||
\(532\) | 7.11246 | 0.308364 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 1.25993 | 0.0545226 | ||||||||
\(535\) | −8.03283 | −0.347290 | ||||||||
\(536\) | 5.40343 | 0.233393 | ||||||||
\(537\) | −1.17793 | −0.0508313 | ||||||||
\(538\) | 1.54317 | 0.0665309 | ||||||||
\(539\) | 4.78310 | 0.206023 | ||||||||
\(540\) | 6.31838 | 0.271900 | ||||||||
\(541\) | −32.2930 | −1.38838 | −0.694192 | − | 0.719790i | \(-0.744238\pi\) | ||||
−0.694192 | + | 0.719790i | \(0.744238\pi\) | |||||||
\(542\) | 0.671800 | 0.0288563 | ||||||||
\(543\) | 8.71950 | 0.374190 | ||||||||
\(544\) | −1.10895 | −0.0475460 | ||||||||
\(545\) | −33.2929 | −1.42611 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.7225 | 0.886031 | 0.443015 | − | 0.896514i | \(-0.353909\pi\) | ||||
0.443015 | + | 0.896514i | \(0.353909\pi\) | |||||||
\(548\) | −7.65039 | −0.326808 | ||||||||
\(549\) | 3.22157 | 0.137493 | ||||||||
\(550\) | −0.334443 | −0.0142607 | ||||||||
\(551\) | −8.65692 | −0.368797 | ||||||||
\(552\) | −1.83471 | −0.0780903 | ||||||||
\(553\) | 4.45106 | 0.189278 | ||||||||
\(554\) | −2.36282 | −0.100386 | ||||||||
\(555\) | 1.98947 | 0.0844482 | ||||||||
\(556\) | 10.8294 | 0.459271 | ||||||||
\(557\) | 21.9183 | 0.928710 | 0.464355 | − | 0.885649i | \(-0.346286\pi\) | ||||
0.464355 | + | 0.885649i | \(0.346286\pi\) | |||||||
\(558\) | 0.997992 | 0.0422484 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −6.43726 | −0.272024 | ||||||||
\(561\) | 0.710085 | 0.0299798 | ||||||||
\(562\) | −1.43324 | −0.0604574 | ||||||||
\(563\) | −31.1228 | −1.31167 | −0.655835 | − | 0.754904i | \(-0.727683\pi\) | ||||
−0.655835 | + | 0.754904i | \(0.727683\pi\) | |||||||
\(564\) | −15.1371 | −0.637387 | ||||||||
\(565\) | −5.41044 | −0.227619 | ||||||||
\(566\) | 1.03990 | 0.0437101 | ||||||||
\(567\) | 0.513856 | 0.0215799 | ||||||||
\(568\) | −3.83599 | −0.160954 | ||||||||
\(569\) | 25.3193 | 1.06144 | 0.530719 | − | 0.847548i | \(-0.321922\pi\) | ||||
0.530719 | + | 0.847548i | \(0.321922\pi\) | |||||||
\(570\) | 2.04985 | 0.0858587 | ||||||||
\(571\) | −42.8079 | −1.79145 | −0.895727 | − | 0.444604i | \(-0.853345\pi\) | ||||
−0.895727 | + | 0.444604i | \(0.853345\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −23.1293 | −0.966241 | ||||||||
\(574\) | −0.592406 | −0.0247265 | ||||||||
\(575\) | 25.0600 | 1.04507 | ||||||||
\(576\) | −7.79340 | −0.324725 | ||||||||
\(577\) | −10.9462 | −0.455695 | −0.227847 | − | 0.973697i | \(-0.573169\pi\) | ||||
−0.227847 | + | 0.973697i | \(0.573169\pi\) | |||||||
\(578\) | 0.0929476 | 0.00386611 | ||||||||
\(579\) | −12.9444 | −0.537949 | ||||||||
\(580\) | 7.86939 | 0.326759 | ||||||||
\(581\) | −4.19309 | −0.173959 | ||||||||
\(582\) | −0.392824 | −0.0162831 | ||||||||
\(583\) | −1.26540 | −0.0524074 | ||||||||
\(584\) | −4.98768 | −0.206392 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.40571 | −0.0580694 | ||||||||
\(587\) | −46.0068 | −1.89890 | −0.949452 | − | 0.313912i | \(-0.898360\pi\) | ||||
−0.949452 | + | 0.313912i | \(0.898360\pi\) | |||||||
\(588\) | 13.4137 | 0.553172 | ||||||||
\(589\) | −74.6305 | −3.07510 | ||||||||
\(590\) | 2.14007 | 0.0881053 | ||||||||
\(591\) | −23.2525 | −0.956480 | ||||||||
\(592\) | −2.47562 | −0.101748 | ||||||||
\(593\) | −22.8488 | −0.938287 | −0.469144 | − | 0.883122i | \(-0.655437\pi\) | ||||
−0.469144 | + | 0.883122i | \(0.655437\pi\) | |||||||
\(594\) | −0.0660007 | −0.00270804 | ||||||||
\(595\) | 1.63041 | 0.0668404 | ||||||||
\(596\) | 20.3087 | 0.831876 | ||||||||
\(597\) | −14.7511 | −0.603724 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.4170 | 1.16109 | 0.580543 | − | 0.814229i | \(-0.302840\pi\) | ||||
0.580543 | + | 0.814229i | \(0.302840\pi\) | |||||||
\(600\) | −1.87989 | −0.0767462 | ||||||||
\(601\) | −18.1852 | −0.741788 | −0.370894 | − | 0.928675i | \(-0.620949\pi\) | ||||
−0.370894 | + | 0.928675i | \(0.620949\pi\) | |||||||
\(602\) | 0.281086 | 0.0114562 | ||||||||
\(603\) | −14.5650 | −0.593132 | ||||||||
\(604\) | 20.1596 | 0.820284 | ||||||||
\(605\) | 33.3020 | 1.35392 | ||||||||
\(606\) | 0.279857 | 0.0113684 | ||||||||
\(607\) | 33.4550 | 1.35790 | 0.678949 | − | 0.734185i | \(-0.262436\pi\) | ||||
0.678949 | + | 0.734185i | \(0.262436\pi\) | |||||||
\(608\) | −7.70800 | −0.312601 | ||||||||
\(609\) | 0.639996 | 0.0259340 | ||||||||
\(610\) | −0.950083 | −0.0384677 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1.99136 | 0.0804960 | ||||||||
\(613\) | 17.9017 | 0.723042 | 0.361521 | − | 0.932364i | \(-0.382258\pi\) | ||||
0.361521 | + | 0.932364i | \(0.382258\pi\) | |||||||
\(614\) | −1.42467 | −0.0574950 | ||||||||
\(615\) | 39.3545 | 1.58693 | ||||||||
\(616\) | 0.135367 | 0.00545407 | ||||||||
\(617\) | 10.8918 | 0.438487 | 0.219244 | − | 0.975670i | \(-0.429641\pi\) | ||||
0.219244 | + | 0.975670i | \(0.429641\pi\) | |||||||
\(618\) | 0.647760 | 0.0260567 | ||||||||
\(619\) | 7.88332 | 0.316858 | 0.158429 | − | 0.987370i | \(-0.449357\pi\) | ||||
0.158429 | + | 0.987370i | \(0.449357\pi\) | |||||||
\(620\) | 67.8413 | 2.72457 | ||||||||
\(621\) | 4.94547 | 0.198455 | ||||||||
\(622\) | −1.90013 | −0.0761881 | ||||||||
\(623\) | 6.96548 | 0.279066 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.6592 | −0.986367 | ||||||||
\(626\) | 2.26497 | 0.0905264 | ||||||||
\(627\) | 4.93558 | 0.197108 | ||||||||
\(628\) | 7.33778 | 0.292809 | ||||||||
\(629\) | 0.627020 | 0.0250009 | ||||||||
\(630\) | −0.151543 | −0.00603762 | ||||||||
\(631\) | −30.4418 | −1.21187 | −0.605934 | − | 0.795515i | \(-0.707201\pi\) | ||||
−0.605934 | + | 0.795515i | \(0.707201\pi\) | |||||||
\(632\) | −3.21352 | −0.127827 | ||||||||
\(633\) | 23.0352 | 0.915566 | ||||||||
\(634\) | −1.30031 | −0.0516419 | ||||||||
\(635\) | −44.7680 | −1.77656 | ||||||||
\(636\) | −3.54868 | −0.140714 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.0822024 | −0.00325442 | ||||||||
\(639\) | 10.3399 | 0.409041 | ||||||||
\(640\) | 9.33557 | 0.369021 | ||||||||
\(641\) | −8.97288 | −0.354407 | −0.177204 | − | 0.984174i | \(-0.556705\pi\) | ||||
−0.177204 | + | 0.984174i | \(0.556705\pi\) | |||||||
\(642\) | 0.235316 | 0.00928718 | ||||||||
\(643\) | 36.6642 | 1.44590 | 0.722948 | − | 0.690903i | \(-0.242787\pi\) | ||||
0.722948 | + | 0.690903i | \(0.242787\pi\) | |||||||
\(644\) | −5.06057 | −0.199414 | ||||||||
\(645\) | −18.6730 | −0.735250 | ||||||||
\(646\) | 0.646050 | 0.0254185 | ||||||||
\(647\) | −12.7489 | −0.501212 | −0.250606 | − | 0.968089i | \(-0.580630\pi\) | ||||
−0.250606 | + | 0.968089i | \(0.580630\pi\) | |||||||
\(648\) | −0.370988 | −0.0145738 | ||||||||
\(649\) | 5.15281 | 0.202266 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.51735 | 0.216242 | ||||||||
\(652\) | 11.2268 | 0.439674 | ||||||||
\(653\) | 29.2046 | 1.14286 | 0.571432 | − | 0.820649i | \(-0.306388\pi\) | ||||
0.571432 | + | 0.820649i | \(0.306388\pi\) | |||||||
\(654\) | 0.975290 | 0.0381369 | ||||||||
\(655\) | 59.3086 | 2.31738 | ||||||||
\(656\) | −48.9714 | −1.91201 | ||||||||
\(657\) | 13.4443 | 0.524513 | ||||||||
\(658\) | 0.363055 | 0.0141534 | ||||||||
\(659\) | 14.0648 | 0.547886 | 0.273943 | − | 0.961746i | \(-0.411672\pi\) | ||||
0.273943 | + | 0.961746i | \(0.411672\pi\) | |||||||
\(660\) | −4.48658 | −0.174640 | ||||||||
\(661\) | −9.35689 | −0.363941 | −0.181971 | − | 0.983304i | \(-0.558248\pi\) | ||||
−0.181971 | + | 0.983304i | \(0.558248\pi\) | |||||||
\(662\) | 2.58131 | 0.100326 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.02727 | 0.117481 | ||||||||
\(665\) | 11.3325 | 0.439455 | ||||||||
\(666\) | −0.0582800 | −0.00225830 | ||||||||
\(667\) | 6.15946 | 0.238495 | ||||||||
\(668\) | 23.3362 | 0.902905 | ||||||||
\(669\) | −6.97643 | −0.269725 | ||||||||
\(670\) | 4.29541 | 0.165946 | ||||||||
\(671\) | −2.28759 | −0.0883113 | ||||||||
\(672\) | 0.569844 | 0.0219822 | ||||||||
\(673\) | −35.1658 | −1.35554 | −0.677771 | − | 0.735273i | \(-0.737054\pi\) | ||||
−0.677771 | + | 0.735273i | \(0.737054\pi\) | |||||||
\(674\) | −0.351010 | −0.0135204 | ||||||||
\(675\) | 5.06726 | 0.195039 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.3276 | 0.781254 | 0.390627 | − | 0.920549i | \(-0.372258\pi\) | ||||
0.390627 | + | 0.920549i | \(0.372258\pi\) | |||||||
\(678\) | 0.158495 | 0.00608696 | ||||||||
\(679\) | −2.17171 | −0.0833426 | ||||||||
\(680\) | −1.17710 | −0.0451399 | ||||||||
\(681\) | −5.98914 | −0.229504 | ||||||||
\(682\) | −0.708659 | −0.0271360 | ||||||||
\(683\) | −17.9018 | −0.684992 | −0.342496 | − | 0.939519i | \(-0.611272\pi\) | ||||
−0.342496 | + | 0.939519i | \(0.611272\pi\) | |||||||
\(684\) | 13.8413 | 0.529236 | ||||||||
\(685\) | −12.1896 | −0.465740 | ||||||||
\(686\) | −0.656053 | −0.0250482 | ||||||||
\(687\) | −29.1165 | −1.11087 | ||||||||
\(688\) | 23.2361 | 0.885867 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −1.45848 | −0.0555235 | ||||||||
\(691\) | −25.5137 | −0.970585 | −0.485293 | − | 0.874352i | \(-0.661287\pi\) | ||||
−0.485293 | + | 0.874352i | \(0.661287\pi\) | |||||||
\(692\) | 11.8298 | 0.449702 | ||||||||
\(693\) | −0.364882 | −0.0138607 | ||||||||
\(694\) | −2.63078 | −0.0998632 | ||||||||
\(695\) | 17.2549 | 0.654514 | ||||||||
\(696\) | −0.462056 | −0.0175142 | ||||||||
\(697\) | 12.4034 | 0.469811 | ||||||||
\(698\) | 1.28317 | 0.0485689 | ||||||||
\(699\) | 17.8894 | 0.676639 | ||||||||
\(700\) | −5.18519 | −0.195982 | ||||||||
\(701\) | −0.249197 | −0.00941203 | −0.00470602 | − | 0.999989i | \(-0.501498\pi\) | ||||
−0.00470602 | + | 0.999989i | \(0.501498\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.35822 | 0.164373 | ||||||||
\(704\) | 5.53398 | 0.208570 | ||||||||
\(705\) | −24.1184 | −0.908351 | ||||||||
\(706\) | 2.33145 | 0.0877454 | ||||||||
\(707\) | 1.54718 | 0.0581876 | ||||||||
\(708\) | 14.4505 | 0.543085 | ||||||||
\(709\) | −16.0650 | −0.603333 | −0.301666 | − | 0.953414i | \(-0.597543\pi\) | ||||
−0.301666 | + | 0.953414i | \(0.597543\pi\) | |||||||
\(710\) | −3.04938 | −0.114441 | ||||||||
\(711\) | 8.66207 | 0.324853 | ||||||||
\(712\) | −5.02885 | −0.188464 | ||||||||
\(713\) | 53.1002 | 1.98862 | ||||||||
\(714\) | −0.0477617 | −0.00178744 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.34568 | 0.0876621 | ||||||||
\(717\) | −11.1361 | −0.415885 | ||||||||
\(718\) | 0.519417 | 0.0193845 | ||||||||
\(719\) | 16.9451 | 0.631946 | 0.315973 | − | 0.948768i | \(-0.397669\pi\) | ||||
0.315973 | + | 0.948768i | \(0.397669\pi\) | |||||||
\(720\) | −12.5273 | −0.466867 | ||||||||
\(721\) | 3.58111 | 0.133368 | ||||||||
\(722\) | 2.72449 | 0.101395 | ||||||||
\(723\) | −7.27606 | −0.270599 | ||||||||
\(724\) | −17.3637 | −0.645316 | ||||||||
\(725\) | 6.31115 | 0.234390 | ||||||||
\(726\) | −0.975558 | −0.0362064 | ||||||||
\(727\) | −28.4184 | −1.05398 | −0.526990 | − | 0.849872i | \(-0.676679\pi\) | ||||
−0.526990 | + | 0.849872i | \(0.676679\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −3.96491 | −0.146748 | ||||||||
\(731\) | −5.88517 | −0.217671 | ||||||||
\(732\) | −6.41530 | −0.237116 | ||||||||
\(733\) | −5.39218 | −0.199165 | −0.0995823 | − | 0.995029i | \(-0.531751\pi\) | ||||
−0.0995823 | + | 0.995029i | \(0.531751\pi\) | |||||||
\(734\) | 0.855367 | 0.0315722 | ||||||||
\(735\) | 21.3725 | 0.788335 | ||||||||
\(736\) | 5.48430 | 0.202154 | ||||||||
\(737\) | 10.3424 | 0.380967 | ||||||||
\(738\) | −1.15286 | −0.0424375 | ||||||||
\(739\) | 27.7119 | 1.01940 | 0.509699 | − | 0.860353i | \(-0.329757\pi\) | ||||
0.509699 | + | 0.860353i | \(0.329757\pi\) | |||||||
\(740\) | −3.96175 | −0.145637 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.0851132 | 0.00312461 | ||||||||
\(743\) | −34.0737 | −1.25004 | −0.625022 | − | 0.780607i | \(-0.714910\pi\) | ||||
−0.625022 | + | 0.780607i | \(0.714910\pi\) | |||||||
\(744\) | −3.98335 | −0.146037 | ||||||||
\(745\) | 32.3584 | 1.18552 | ||||||||
\(746\) | 0.289867 | 0.0106128 | ||||||||
\(747\) | −8.16003 | −0.298560 | ||||||||
\(748\) | −1.41404 | −0.0517022 | ||||||||
\(749\) | 1.30093 | 0.0475350 | ||||||||
\(750\) | −0.0198356 | −0.000724294 0 | ||||||||
\(751\) | −13.3233 | −0.486176 | −0.243088 | − | 0.970004i | \(-0.578160\pi\) | ||||
−0.243088 | + | 0.970004i | \(0.578160\pi\) | |||||||
\(752\) | 30.0121 | 1.09443 | ||||||||
\(753\) | −11.1151 | −0.405056 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 32.1209 | 1.16900 | ||||||||
\(756\) | −1.02327 | −0.0372161 | ||||||||
\(757\) | 23.0125 | 0.836404 | 0.418202 | − | 0.908354i | \(-0.362660\pi\) | ||||
0.418202 | + | 0.908354i | \(0.362660\pi\) | |||||||
\(758\) | 0.446263 | 0.0162090 | ||||||||
\(759\) | −3.51170 | −0.127467 | ||||||||
\(760\) | −8.18169 | −0.296781 | ||||||||
\(761\) | 20.2044 | 0.732409 | 0.366205 | − | 0.930534i | \(-0.380657\pi\) | ||||
0.366205 | + | 0.930534i | \(0.380657\pi\) | |||||||
\(762\) | 1.31144 | 0.0475086 | ||||||||
\(763\) | 5.39184 | 0.195198 | ||||||||
\(764\) | 46.0588 | 1.66635 | ||||||||
\(765\) | 3.17289 | 0.114716 | ||||||||
\(766\) | 1.54303 | 0.0557519 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 15.3133 | 0.552572 | ||||||||
\(769\) | −9.05451 | −0.326514 | −0.163257 | − | 0.986584i | \(-0.552200\pi\) | ||||
−0.163257 | + | 0.986584i | \(0.552200\pi\) | |||||||
\(770\) | 0.107608 | 0.00387794 | ||||||||
\(771\) | −19.5951 | −0.705699 | ||||||||
\(772\) | 25.7769 | 0.927730 | ||||||||
\(773\) | −45.1643 | −1.62445 | −0.812224 | − | 0.583346i | \(-0.801743\pi\) | ||||
−0.812224 | + | 0.583346i | \(0.801743\pi\) | |||||||
\(774\) | 0.547013 | 0.0196620 | ||||||||
\(775\) | 54.4079 | 1.95439 | ||||||||
\(776\) | 1.56790 | 0.0562845 | ||||||||
\(777\) | −0.322198 | −0.0115588 | ||||||||
\(778\) | 2.64322 | 0.0947641 | ||||||||
\(779\) | 86.2119 | 3.08886 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.34223 | −0.262726 | ||||||||
\(782\) | −0.459669 | −0.0164377 | ||||||||
\(783\) | 1.24548 | 0.0445097 | ||||||||
\(784\) | −26.5951 | −0.949827 | ||||||||
\(785\) | 11.6915 | 0.417288 | ||||||||
\(786\) | −1.73740 | −0.0619711 | ||||||||
\(787\) | 22.0025 | 0.784306 | 0.392153 | − | 0.919900i | \(-0.371730\pi\) | ||||
0.392153 | + | 0.919900i | \(0.371730\pi\) | |||||||
\(788\) | 46.3041 | 1.64952 | ||||||||
\(789\) | −17.8319 | −0.634834 | ||||||||
\(790\) | −2.55456 | −0.0908871 | ||||||||
\(791\) | 0.876231 | 0.0311552 | ||||||||
\(792\) | 0.263433 | 0.00936067 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −0.972336 | −0.0345069 | ||||||||
\(795\) | −5.65422 | −0.200534 | ||||||||
\(796\) | 29.3748 | 1.04116 | ||||||||
\(797\) | 31.7813 | 1.12575 | 0.562876 | − | 0.826542i | \(-0.309695\pi\) | ||||
0.562876 | + | 0.826542i | \(0.309695\pi\) | |||||||
\(798\) | −0.331977 | −0.0117519 | ||||||||
\(799\) | −7.60138 | −0.268918 | ||||||||
\(800\) | 5.61936 | 0.198674 | ||||||||
\(801\) | 13.5553 | 0.478953 | ||||||||
\(802\) | −0.175160 | −0.00618511 | ||||||||
\(803\) | −9.54662 | −0.336893 | ||||||||
\(804\) | 29.0042 | 1.02290 | ||||||||
\(805\) | −8.06315 | −0.284189 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.6026 | 0.584439 | ||||||||
\(808\) | −1.11701 | −0.0392963 | ||||||||
\(809\) | −14.7642 | −0.519081 | −0.259540 | − | 0.965732i | \(-0.583571\pi\) | ||||
−0.259540 | + | 0.965732i | \(0.583571\pi\) | |||||||
\(810\) | −0.294913 | −0.0103622 | ||||||||
\(811\) | −0.413947 | −0.0145357 | −0.00726783 | − | 0.999974i | \(-0.502313\pi\) | ||||
−0.00726783 | + | 0.999974i | \(0.502313\pi\) | |||||||
\(812\) | −1.27446 | −0.0447249 | ||||||||
\(813\) | 7.22773 | 0.253487 | ||||||||
\(814\) | 0.0413838 | 0.00145050 | ||||||||
\(815\) | 17.8879 | 0.626587 | ||||||||
\(816\) | −3.94824 | −0.138216 | ||||||||
\(817\) | −40.9060 | −1.43112 | ||||||||
\(818\) | −0.193807 | −0.00677631 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −78.3691 | −2.73677 | ||||||||
\(821\) | 4.53178 | 0.158160 | 0.0790801 | − | 0.996868i | \(-0.474802\pi\) | ||||
0.0790801 | + | 0.996868i | \(0.474802\pi\) | |||||||
\(822\) | 0.357085 | 0.0124548 | ||||||||
\(823\) | −0.721512 | −0.0251503 | −0.0125752 | − | 0.999921i | \(-0.504003\pi\) | ||||
−0.0125752 | + | 0.999921i | \(0.504003\pi\) | |||||||
\(824\) | −2.58545 | −0.0900683 | ||||||||
\(825\) | −3.59818 | −0.125273 | ||||||||
\(826\) | −0.346589 | −0.0120594 | ||||||||
\(827\) | −11.2099 | −0.389806 | −0.194903 | − | 0.980823i | \(-0.562439\pi\) | ||||
−0.194903 | + | 0.980823i | \(0.562439\pi\) | |||||||
\(828\) | −9.84821 | −0.342249 | ||||||||
\(829\) | 10.3215 | 0.358482 | 0.179241 | − | 0.983805i | \(-0.442636\pi\) | ||||
0.179241 | + | 0.983805i | \(0.442636\pi\) | |||||||
\(830\) | 2.40650 | 0.0835309 | ||||||||
\(831\) | −25.4209 | −0.881842 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.73595 | 0.233387 | ||||||||
\(834\) | −0.505469 | −0.0175030 | ||||||||
\(835\) | 37.1823 | 1.28675 | ||||||||
\(836\) | −9.82852 | −0.339926 | ||||||||
\(837\) | 10.7371 | 0.371130 | ||||||||
\(838\) | −2.38066 | −0.0822387 | ||||||||
\(839\) | −45.6743 | −1.57685 | −0.788427 | − | 0.615129i | \(-0.789104\pi\) | ||||
−0.788427 | + | 0.615129i | \(0.789104\pi\) | |||||||
\(840\) | 0.604863 | 0.0208697 | ||||||||
\(841\) | −27.4488 | −0.946510 | ||||||||
\(842\) | 1.55129 | 0.0534611 | ||||||||
\(843\) | −15.4198 | −0.531087 | ||||||||
\(844\) | −45.8713 | −1.57896 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.706531 | 0.0242910 | ||||||||
\(847\) | −5.39332 | −0.185317 | ||||||||
\(848\) | 7.03591 | 0.241614 | ||||||||
\(849\) | 11.1880 | 0.383970 | ||||||||
\(850\) | −0.470990 | −0.0161548 | ||||||||
\(851\) | −3.10091 | −0.106298 | ||||||||
\(852\) | −20.5905 | −0.705420 | ||||||||
\(853\) | 33.4854 | 1.14652 | 0.573260 | − | 0.819374i | \(-0.305679\pi\) | ||||
0.573260 | + | 0.819374i | \(0.305679\pi\) | |||||||
\(854\) | 0.153868 | 0.00526525 | ||||||||
\(855\) | 22.0538 | 0.754224 | ||||||||
\(856\) | −0.939231 | −0.0321022 | ||||||||
\(857\) | −35.4841 | −1.21211 | −0.606056 | − | 0.795422i | \(-0.707249\pi\) | ||||
−0.606056 | + | 0.795422i | \(0.707249\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.0729 | −1.36727 | −0.683634 | − | 0.729825i | \(-0.739602\pi\) | ||||
−0.683634 | + | 0.729825i | \(0.739602\pi\) | |||||||
\(860\) | 37.1847 | 1.26799 | ||||||||
\(861\) | −6.37354 | −0.217210 | ||||||||
\(862\) | 1.45492 | 0.0495549 | ||||||||
\(863\) | −27.3341 | −0.930463 | −0.465232 | − | 0.885189i | \(-0.654029\pi\) | ||||
−0.465232 | + | 0.885189i | \(0.654029\pi\) | |||||||
\(864\) | 1.10895 | 0.0377274 | ||||||||
\(865\) | 18.8488 | 0.640878 | ||||||||
\(866\) | −1.02353 | −0.0347811 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −10.9870 | −0.372924 | ||||||||
\(869\) | −6.15080 | −0.208652 | ||||||||
\(870\) | −0.367307 | −0.0124529 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −3.89274 | −0.131825 | ||||||||
\(873\) | −4.22630 | −0.143038 | ||||||||
\(874\) | −3.19502 | −0.108073 | ||||||||
\(875\) | −0.109660 | −0.00370719 | ||||||||
\(876\) | −26.7725 | −0.904560 | ||||||||
\(877\) | 53.6867 | 1.81287 | 0.906435 | − | 0.422345i | \(-0.138793\pi\) | ||||
0.906435 | + | 0.422345i | \(0.138793\pi\) | |||||||
\(878\) | 2.93938 | 0.0991992 | ||||||||
\(879\) | −15.1237 | −0.510110 | ||||||||
\(880\) | 8.89548 | 0.299867 | ||||||||
\(881\) | 0.887871 | 0.0299131 | 0.0149566 | − | 0.999888i | \(-0.495239\pi\) | ||||
0.0149566 | + | 0.999888i | \(0.495239\pi\) | |||||||
\(882\) | −0.626091 | −0.0210816 | ||||||||
\(883\) | 16.3629 | 0.550656 | 0.275328 | − | 0.961350i | \(-0.411214\pi\) | ||||
0.275328 | + | 0.961350i | \(0.411214\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 23.0245 | 0.773959 | ||||||||
\(886\) | −3.03907 | −0.102099 | ||||||||
\(887\) | −19.3307 | −0.649063 | −0.324531 | − | 0.945875i | \(-0.605207\pi\) | ||||
−0.324531 | + | 0.945875i | \(0.605207\pi\) | |||||||
\(888\) | 0.232617 | 0.00780610 | ||||||||
\(889\) | 7.25026 | 0.243166 | ||||||||
\(890\) | −3.99764 | −0.134001 | ||||||||
\(891\) | −0.710085 | −0.0237887 | ||||||||
\(892\) | 13.8926 | 0.465159 | ||||||||
\(893\) | −52.8348 | −1.76805 | ||||||||
\(894\) | −0.947917 | −0.0317031 | ||||||||
\(895\) | 3.73744 | 0.124929 | ||||||||
\(896\) | −1.51191 | −0.0505095 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.57650 | −0.0526086 | ||||||||
\(899\) | 13.3729 | 0.446010 | ||||||||
\(900\) | −10.0907 | −0.336358 | ||||||||
\(901\) | −1.78204 | −0.0593683 | ||||||||
\(902\) | 0.818630 | 0.0272574 | ||||||||
\(903\) | 3.02413 | 0.100637 | ||||||||
\(904\) | −0.632610 | −0.0210403 | ||||||||
\(905\) | −27.6661 | −0.919651 | ||||||||
\(906\) | −0.940960 | −0.0312613 | ||||||||
\(907\) | −52.2898 | −1.73625 | −0.868127 | − | 0.496342i | \(-0.834676\pi\) | ||||
−0.868127 | + | 0.496342i | \(0.834676\pi\) | |||||||
\(908\) | 11.9265 | 0.395796 | ||||||||
\(909\) | 3.01091 | 0.0998657 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.4555 | 0.644588 | 0.322294 | − | 0.946640i | \(-0.395546\pi\) | ||||
0.322294 | + | 0.946640i | \(0.395546\pi\) | |||||||
\(912\) | −27.4430 | −0.908728 | ||||||||
\(913\) | 5.79432 | 0.191764 | ||||||||
\(914\) | −1.14522 | −0.0378805 | ||||||||
\(915\) | −10.2217 | −0.337919 | ||||||||
\(916\) | 57.9815 | 1.91576 | ||||||||
\(917\) | −9.60515 | −0.317190 | ||||||||
\(918\) | −0.0929476 | −0.00306773 | ||||||||
\(919\) | 16.9897 | 0.560437 | 0.280219 | − | 0.959936i | \(-0.409593\pi\) | ||||
0.280219 | + | 0.959936i | \(0.409593\pi\) | |||||||
\(920\) | 5.82133 | 0.191924 | ||||||||
\(921\) | −15.3277 | −0.505064 | ||||||||
\(922\) | −0.146624 | −0.00482881 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0.726611 | 0.0239037 | ||||||||
\(925\) | −3.17727 | −0.104468 | ||||||||
\(926\) | 0.724725 | 0.0238159 | ||||||||
\(927\) | 6.96909 | 0.228895 | ||||||||
\(928\) | 1.38118 | 0.0453394 | ||||||||
\(929\) | −52.0044 | −1.70621 | −0.853104 | − | 0.521741i | \(-0.825283\pi\) | ||||
−0.853104 | + | 0.521741i | \(0.825283\pi\) | |||||||
\(930\) | −3.16652 | −0.103834 | ||||||||
\(931\) | 46.8195 | 1.53445 | ||||||||
\(932\) | −35.6242 | −1.16691 | ||||||||
\(933\) | −20.4430 | −0.669273 | ||||||||
\(934\) | −2.39958 | −0.0785166 | ||||||||
\(935\) | −2.25302 | −0.0736818 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 57.9027 | 1.89160 | 0.945800 | − | 0.324751i | \(-0.105280\pi\) | ||||
0.945800 | + | 0.324751i | \(0.105280\pi\) | |||||||
\(938\) | −0.695650 | −0.0227138 | ||||||||
\(939\) | 24.3682 | 0.795228 | ||||||||
\(940\) | 48.0284 | 1.56651 | ||||||||
\(941\) | −19.9637 | −0.650799 | −0.325400 | − | 0.945577i | \(-0.605499\pi\) | ||||
−0.325400 | + | 0.945577i | \(0.605499\pi\) | |||||||
\(942\) | −0.342494 | −0.0111591 | ||||||||
\(943\) | −61.3404 | −1.99752 | ||||||||
\(944\) | −28.6509 | −0.932506 | ||||||||
\(945\) | −1.63041 | −0.0530373 | ||||||||
\(946\) | −0.388426 | −0.0126288 | ||||||||
\(947\) | 1.44437 | 0.0469356 | 0.0234678 | − | 0.999725i | \(-0.492529\pi\) | ||||
0.0234678 | + | 0.999725i | \(0.492529\pi\) | |||||||
\(948\) | −17.2493 | −0.560231 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −3.27370 | −0.106213 | ||||||||
\(951\) | −13.9897 | −0.453647 | ||||||||
\(952\) | 0.190634 | 0.00617850 | ||||||||
\(953\) | −29.2363 | −0.947057 | −0.473528 | − | 0.880779i | \(-0.657020\pi\) | ||||
−0.473528 | + | 0.880779i | \(0.657020\pi\) | |||||||
\(954\) | 0.165636 | 0.00536267 | ||||||||
\(955\) | 73.3869 | 2.37474 | ||||||||
\(956\) | 22.1760 | 0.717222 | ||||||||
\(957\) | −0.884394 | −0.0285884 | ||||||||
\(958\) | 0.382426 | 0.0123556 | ||||||||
\(959\) | 1.97413 | 0.0637479 | ||||||||
\(960\) | 24.7276 | 0.798081 | ||||||||
\(961\) | 84.2862 | 2.71891 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.53170 | 0.0815830 | ||||||||
\(964\) | 14.4893 | 0.466667 | ||||||||
\(965\) | 41.0711 | 1.32212 | ||||||||
\(966\) | 0.236204 | 0.00759974 | ||||||||
\(967\) | 18.3197 | 0.589122 | 0.294561 | − | 0.955633i | \(-0.404827\pi\) | ||||
0.294561 | + | 0.955633i | \(0.404827\pi\) | |||||||
\(968\) | 3.89380 | 0.125152 | ||||||||
\(969\) | 6.95069 | 0.223288 | ||||||||
\(970\) | 1.24639 | 0.0400192 | ||||||||
\(971\) | 13.8769 | 0.445331 | 0.222665 | − | 0.974895i | \(-0.428524\pi\) | ||||
0.222665 | + | 0.974895i | \(0.428524\pi\) | |||||||
\(972\) | −1.99136 | −0.0638729 | ||||||||
\(973\) | −2.79446 | −0.0895863 | ||||||||
\(974\) | −3.15958 | −0.101239 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.7195 | 0.407142 | ||||||||
\(977\) | −3.63021 | −0.116141 | −0.0580704 | − | 0.998312i | \(-0.518495\pi\) | ||||
−0.0580704 | + | 0.998312i | \(0.518495\pi\) | |||||||
\(978\) | −0.524014 | −0.0167561 | ||||||||
\(979\) | −9.62541 | −0.307630 | ||||||||
\(980\) | −42.5603 | −1.35954 | ||||||||
\(981\) | 10.4929 | 0.335012 | ||||||||
\(982\) | −0.373116 | −0.0119066 | ||||||||
\(983\) | −24.5856 | −0.784160 | −0.392080 | − | 0.919931i | \(-0.628244\pi\) | ||||
−0.392080 | + | 0.919931i | \(0.628244\pi\) | |||||||
\(984\) | 4.60149 | 0.146690 | ||||||||
\(985\) | 73.7777 | 2.35075 | ||||||||
\(986\) | −0.115764 | −0.00368668 | ||||||||
\(987\) | 3.90602 | 0.124330 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 29.1049 | 0.925483 | ||||||||
\(990\) | 0.209413 | 0.00665559 | ||||||||
\(991\) | −21.1201 | −0.670903 | −0.335451 | − | 0.942058i | \(-0.608889\pi\) | ||||
−0.335451 | + | 0.942058i | \(0.608889\pi\) | |||||||
\(992\) | 11.9070 | 0.378048 | ||||||||
\(993\) | 27.7717 | 0.881308 | ||||||||
\(994\) | 0.493853 | 0.0156641 | ||||||||
\(995\) | 46.8038 | 1.48378 | ||||||||
\(996\) | 16.2496 | 0.514887 | ||||||||
\(997\) | 33.6508 | 1.06573 | 0.532866 | − | 0.846200i | \(-0.321115\pi\) | ||||
0.532866 | + | 0.846200i | \(0.321115\pi\) | |||||||
\(998\) | 1.01107 | 0.0320049 | ||||||||
\(999\) | −0.627020 | −0.0198380 |
(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 | 8619.2.a.bp.1.14 | ✓ | 21 | |
13.12 | even | 2 | 8619.2.a.bq.1.8 | yes | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8619.2.a.bp.1.14 | ✓ | 21 | 1.1 | even | 1 | trivial | |
8619.2.a.bq.1.8 | yes | 21 | 13.12 | even | 2 |