Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(1,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, 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("1323.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.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: | \(10.5642081874\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.321.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 189) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.46050\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.46050 | 1.03273 | 0.516366 | − | 0.856368i | \(-0.327284\pi\) | ||||
0.516366 | + | 0.856368i | \(0.327284\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.133074 | 0.0665372 | ||||||||
\(5\) | −0.593579 | −0.265457 | −0.132728 | − | 0.991152i | \(-0.542374\pi\) | ||||
−0.132728 | + | 0.991152i | \(0.542374\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.72665 | −0.964018 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.866926 | −0.274146 | ||||||||
\(11\) | −4.46050 | −1.34489 | −0.672446 | − | 0.740146i | \(-0.734756\pi\) | ||||
−0.672446 | + | 0.740146i | \(0.734756\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.51459 | 1.25212 | 0.626061 | − | 0.779774i | \(-0.284666\pi\) | ||||
0.626061 | + | 0.779774i | \(0.284666\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.24844 | −1.06211 | ||||||||
\(17\) | −0.273346 | −0.0662962 | −0.0331481 | − | 0.999450i | \(-0.510553\pi\) | ||||
−0.0331481 | + | 0.999450i | \(0.510553\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.86693 | −0.657718 | −0.328859 | − | 0.944379i | \(-0.606664\pi\) | ||||
−0.328859 | + | 0.944379i | \(0.606664\pi\) | |||||||
\(20\) | −0.0789903 | −0.0176628 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.51459 | −1.38892 | ||||||||
\(23\) | −5.05408 | −1.05385 | −0.526925 | − | 0.849912i | \(-0.676655\pi\) | ||||
−0.526925 | + | 0.849912i | \(0.676655\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.64766 | −0.929533 | ||||||||
\(26\) | 6.59358 | 1.29311 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.352336 | −0.0654272 | −0.0327136 | − | 0.999465i | \(-0.510415\pi\) | ||||
−0.0327136 | + | 0.999465i | \(0.510415\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.51459 | −0.451634 | −0.225817 | − | 0.974170i | \(-0.572505\pi\) | ||||
−0.225817 | + | 0.974170i | \(0.572505\pi\) | |||||||
\(32\) | −0.751560 | −0.132858 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.399223 | −0.0684663 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.64766 | −1.09287 | −0.546435 | − | 0.837502i | \(-0.684015\pi\) | ||||
−0.546435 | + | 0.837502i | \(0.684015\pi\) | |||||||
\(38\) | −4.18716 | −0.679247 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.61849 | 0.255905 | ||||||||
\(41\) | −10.8961 | −1.70169 | −0.850843 | − | 0.525420i | \(-0.823908\pi\) | ||||
−0.850843 | + | 0.525420i | \(0.823908\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.38151 | 0.515676 | 0.257838 | − | 0.966188i | \(-0.416990\pi\) | ||||
0.257838 | + | 0.966188i | \(0.416990\pi\) | |||||||
\(44\) | −0.593579 | −0.0894855 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.38151 | −1.08834 | ||||||||
\(47\) | 12.4356 | 1.81392 | 0.906959 | − | 0.421218i | \(-0.138397\pi\) | ||||
0.906959 | + | 0.421218i | \(0.138397\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −6.78794 | −0.959959 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.600777 | 0.0833127 | ||||||||
\(53\) | −11.3274 | −1.55594 | −0.777971 | − | 0.628300i | \(-0.783751\pi\) | ||||
−0.777971 | + | 0.628300i | \(0.783751\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.64766 | 0.357011 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.514589 | −0.0675689 | ||||||||
\(59\) | −8.05408 | −1.04855 | −0.524276 | − | 0.851548i | \(-0.675664\pi\) | ||||
−0.524276 | + | 0.851548i | \(0.675664\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.73385 | 0.350034 | 0.175017 | − | 0.984565i | \(-0.444002\pi\) | ||||
0.175017 | + | 0.984565i | \(0.444002\pi\) | |||||||
\(62\) | −3.67257 | −0.466417 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.39922 | 0.924903 | ||||||||
\(65\) | −2.67977 | −0.332384 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.86693 | 0.716759 | 0.358380 | − | 0.933576i | \(-0.383329\pi\) | ||||
0.358380 | + | 0.933576i | \(0.383329\pi\) | |||||||
\(68\) | −0.0363754 | −0.00441117 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.60078 | −0.308655 | −0.154328 | − | 0.988020i | \(-0.549321\pi\) | ||||
−0.154328 | + | 0.988020i | \(0.549321\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.1154 | −1.30096 | −0.650478 | − | 0.759525i | \(-0.725431\pi\) | ||||
−0.650478 | + | 0.759525i | \(0.725431\pi\) | |||||||
\(74\) | −9.70895 | −1.12864 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.381515 | −0.0437627 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.1623 | 1.25585 | 0.627926 | − | 0.778273i | \(-0.283904\pi\) | ||||
0.627926 | + | 0.778273i | \(0.283904\pi\) | |||||||
\(80\) | 2.52179 | 0.281944 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −15.9138 | −1.75739 | ||||||||
\(83\) | 16.5438 | 1.81591 | 0.907957 | − | 0.419063i | \(-0.137641\pi\) | ||||
0.907957 | + | 0.419063i | \(0.137641\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.162253 | 0.0175988 | ||||||||
\(86\) | 4.93872 | 0.532556 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 12.1623 | 1.29650 | ||||||||
\(89\) | −5.37432 | −0.569677 | −0.284838 | − | 0.958576i | \(-0.591940\pi\) | ||||
−0.284838 | + | 0.958576i | \(0.591940\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.672570 | −0.0701202 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 18.1623 | 1.87329 | ||||||||
\(95\) | 1.70175 | 0.174596 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.26615 | 0.230093 | 0.115046 | − | 0.993360i | \(-0.463298\pi\) | ||||
0.115046 | + | 0.993360i | \(0.463298\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.618485 | −0.0618485 | ||||||||
\(101\) | 9.35661 | 0.931017 | 0.465509 | − | 0.885043i | \(-0.345871\pi\) | ||||
0.465509 | + | 0.885043i | \(0.345871\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.7630 | 1.55318 | 0.776589 | − | 0.630008i | \(-0.216948\pi\) | ||||
0.776589 | + | 0.630008i | \(0.216948\pi\) | |||||||
\(104\) | −12.3097 | −1.20707 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −16.5438 | −1.60687 | ||||||||
\(107\) | −1.02491 | −0.0990814 | −0.0495407 | − | 0.998772i | \(-0.515776\pi\) | ||||
−0.0495407 | + | 0.998772i | \(0.515776\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.29533 | 0.124070 | 0.0620349 | − | 0.998074i | \(-0.480241\pi\) | ||||
0.0620349 | + | 0.998074i | \(0.480241\pi\) | |||||||
\(110\) | 3.86693 | 0.368697 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.2953 | −1.34479 | −0.672396 | − | 0.740192i | \(-0.734735\pi\) | ||||
−0.672396 | + | 0.740192i | \(0.734735\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.00000 | 0.279751 | ||||||||
\(116\) | −0.0468870 | −0.00435335 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.7630 | −1.08287 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.89610 | 0.808737 | ||||||||
\(122\) | 3.99280 | 0.361491 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.334628 | −0.0300504 | ||||||||
\(125\) | 5.72665 | 0.512207 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.3346 | 1.09452 | 0.547261 | − | 0.836962i | \(-0.315671\pi\) | ||||
0.547261 | + | 0.836962i | \(0.315671\pi\) | |||||||
\(128\) | 12.3097 | 1.08804 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.91381 | −0.343264 | ||||||||
\(131\) | −3.19436 | −0.279092 | −0.139546 | − | 0.990216i | \(-0.544564\pi\) | ||||
−0.139546 | + | 0.990216i | \(0.544564\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.56867 | 0.740221 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.745320 | 0.0639107 | ||||||||
\(137\) | −10.1082 | −0.863599 | −0.431800 | − | 0.901970i | \(-0.642121\pi\) | ||||
−0.431800 | + | 0.901970i | \(0.642121\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.0761 | −1.53319 | −0.766596 | − | 0.642130i | \(-0.778051\pi\) | ||||
−0.766596 | + | 0.642130i | \(0.778051\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.79845 | −0.318759 | ||||||||
\(143\) | −20.1373 | −1.68397 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.209140 | 0.0173681 | ||||||||
\(146\) | −16.2340 | −1.34354 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.884634 | −0.0727165 | ||||||||
\(149\) | −14.0541 | −1.15136 | −0.575678 | − | 0.817677i | \(-0.695262\pi\) | ||||
−0.575678 | + | 0.817677i | \(0.695262\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.381515 | 0.0310472 | 0.0155236 | − | 0.999880i | \(-0.495058\pi\) | ||||
0.0155236 | + | 0.999880i | \(0.495058\pi\) | |||||||
\(152\) | 7.81711 | 0.634052 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.49261 | 0.119889 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.51459 | 0.599729 | 0.299865 | − | 0.953982i | \(-0.403058\pi\) | ||||
0.299865 | + | 0.953982i | \(0.403058\pi\) | |||||||
\(158\) | 16.3025 | 1.29696 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.446110 | 0.0352681 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.1914 | 1.18988 | 0.594942 | − | 0.803768i | \(-0.297175\pi\) | ||||
0.594942 | + | 0.803768i | \(0.297175\pi\) | |||||||
\(164\) | −1.44999 | −0.113225 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 24.1623 | 1.87535 | ||||||||
\(167\) | 8.95311 | 0.692813 | 0.346406 | − | 0.938085i | \(-0.387402\pi\) | ||||
0.346406 | + | 0.938085i | \(0.387402\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.38151 | 0.567809 | ||||||||
\(170\) | 0.236971 | 0.0181748 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.449993 | 0.0343117 | ||||||||
\(173\) | −10.4605 | −0.795297 | −0.397649 | − | 0.917538i | \(-0.630174\pi\) | ||||
−0.397649 | + | 0.917538i | \(0.630174\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 18.9502 | 1.42842 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.84922 | −0.588324 | ||||||||
\(179\) | 8.96790 | 0.670292 | 0.335146 | − | 0.942166i | \(-0.391214\pi\) | ||||
0.335146 | + | 0.942166i | \(0.391214\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.04689 | −0.375132 | −0.187566 | − | 0.982252i | \(-0.560060\pi\) | ||||
−0.187566 | + | 0.982252i | \(0.560060\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 13.7807 | 1.01593 | ||||||||
\(185\) | 3.94592 | 0.290109 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.21926 | 0.0891613 | ||||||||
\(188\) | 1.65486 | 0.120693 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.48541 | 0.180311 | ||||||||
\(191\) | −12.1301 | −0.877707 | −0.438853 | − | 0.898559i | \(-0.644615\pi\) | ||||
−0.438853 | + | 0.898559i | \(0.644615\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.1623 | 1.23537 | 0.617683 | − | 0.786427i | \(-0.288071\pi\) | ||||
0.617683 | + | 0.786427i | \(0.288071\pi\) | |||||||
\(194\) | 3.30972 | 0.237624 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.751560 | −0.0535464 | −0.0267732 | − | 0.999642i | \(-0.508523\pi\) | ||||
−0.0267732 | + | 0.999642i | \(0.508523\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.2953 | −0.729816 | −0.364908 | − | 0.931044i | \(-0.618900\pi\) | ||||
−0.364908 | + | 0.931044i | \(0.618900\pi\) | |||||||
\(200\) | 12.6726 | 0.896086 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 13.6654 | 0.961492 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.46770 | 0.451724 | ||||||||
\(206\) | 23.0220 | 1.60402 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −19.1800 | −1.32989 | ||||||||
\(209\) | 12.7879 | 0.884560 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.1154 | −1.10943 | −0.554714 | − | 0.832041i | \(-0.687172\pi\) | ||||
−0.554714 | + | 0.832041i | \(0.687172\pi\) | |||||||
\(212\) | −1.50739 | −0.103528 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.49688 | −0.102325 | ||||||||
\(215\) | −2.00720 | −0.136890 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.89183 | 0.128131 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.352336 | 0.0237545 | ||||||||
\(221\) | −1.23405 | −0.0830109 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.95311 | 0.465615 | 0.232807 | − | 0.972523i | \(-0.425209\pi\) | ||||
0.232807 | + | 0.972523i | \(0.425209\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −20.8784 | −1.38881 | ||||||||
\(227\) | −5.29105 | −0.351180 | −0.175590 | − | 0.984463i | \(-0.556183\pi\) | ||||
−0.175590 | + | 0.984463i | \(0.556183\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.7237 | −0.774726 | −0.387363 | − | 0.921927i | \(-0.626614\pi\) | ||||
−0.387363 | + | 0.921927i | \(0.626614\pi\) | |||||||
\(230\) | 4.38151 | 0.288909 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.960699 | 0.0630730 | ||||||||
\(233\) | 3.87120 | 0.253611 | 0.126805 | − | 0.991928i | \(-0.459528\pi\) | ||||
0.126805 | + | 0.991928i | \(0.459528\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.38151 | −0.481517 | ||||||||
\(236\) | −1.07179 | −0.0697678 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.3992 | 0.802039 | 0.401020 | − | 0.916069i | \(-0.368656\pi\) | ||||
0.401020 | + | 0.916069i | \(0.368656\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.5615 | 1.06682 | 0.533409 | − | 0.845857i | \(-0.320911\pi\) | ||||
0.533409 | + | 0.845857i | \(0.320911\pi\) | |||||||
\(242\) | 12.9928 | 0.835209 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.363806 | 0.0232903 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.9430 | −0.823543 | ||||||||
\(248\) | 6.85641 | 0.435383 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 8.36381 | 0.528974 | ||||||||
\(251\) | −1.84922 | −0.116722 | −0.0583608 | − | 0.998296i | \(-0.518587\pi\) | ||||
−0.0583608 | + | 0.998296i | \(0.518587\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.5438 | 1.41731 | ||||||||
\(254\) | 18.0148 | 1.13035 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.17996 | 0.198748 | ||||||||
\(257\) | −26.8420 | −1.67436 | −0.837180 | − | 0.546928i | \(-0.815797\pi\) | ||||
−0.837180 | + | 0.546928i | \(0.815797\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.356609 | −0.0221159 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.66537 | −0.288228 | ||||||||
\(263\) | 20.2848 | 1.25082 | 0.625408 | − | 0.780298i | \(-0.284933\pi\) | ||||
0.625408 | + | 0.780298i | \(0.284933\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.72373 | 0.413035 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.780738 | 0.0476912 | ||||||||
\(269\) | 8.72665 | 0.532073 | 0.266037 | − | 0.963963i | \(-0.414286\pi\) | ||||
0.266037 | + | 0.963963i | \(0.414286\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.1914 | −1.46952 | −0.734762 | − | 0.678325i | \(-0.762706\pi\) | ||||
−0.734762 | + | 0.678325i | \(0.762706\pi\) | |||||||
\(272\) | 1.16129 | 0.0704138 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.7630 | −0.891867 | ||||||||
\(275\) | 20.7309 | 1.25012 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.11537 | −0.427521 | −0.213760 | − | 0.976886i | \(-0.568571\pi\) | ||||
−0.213760 | + | 0.976886i | \(0.568571\pi\) | |||||||
\(278\) | −26.4002 | −1.58338 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.89610 | 0.471042 | 0.235521 | − | 0.971869i | \(-0.424320\pi\) | ||||
0.235521 | + | 0.971869i | \(0.424320\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.20914 | −0.131320 | −0.0656599 | − | 0.997842i | \(-0.520915\pi\) | ||||
−0.0656599 | + | 0.997842i | \(0.520915\pi\) | |||||||
\(284\) | −0.346097 | −0.0205371 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −29.4107 | −1.73909 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9253 | −0.995605 | ||||||||
\(290\) | 0.305449 | 0.0179366 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.47917 | −0.0865620 | ||||||||
\(293\) | 19.1914 | 1.12118 | 0.560588 | − | 0.828095i | \(-0.310575\pi\) | ||||
0.560588 | + | 0.828095i | \(0.310575\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.78074 | 0.278345 | ||||||||
\(296\) | 18.1259 | 1.05355 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −20.5261 | −1.18904 | ||||||||
\(299\) | −22.8171 | −1.31955 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.557204 | 0.0320635 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 12.1800 | 0.698569 | ||||||||
\(305\) | −1.62276 | −0.0929188 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.9138 | 0.794103 | 0.397052 | − | 0.917796i | \(-0.370033\pi\) | ||||
0.397052 | + | 0.917796i | \(0.370033\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.17996 | 0.123813 | ||||||||
\(311\) | −10.6549 | −0.604182 | −0.302091 | − | 0.953279i | \(-0.597685\pi\) | ||||
−0.302091 | + | 0.953279i | \(0.597685\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.5615 | 0.936110 | 0.468055 | − | 0.883699i | \(-0.344955\pi\) | ||||
0.468055 | + | 0.883699i | \(0.344955\pi\) | |||||||
\(314\) | 10.9751 | 0.619360 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.48541 | 0.0835609 | ||||||||
\(317\) | −26.6372 | −1.49609 | −0.748046 | − | 0.663647i | \(-0.769008\pi\) | ||||
−0.748046 | + | 0.663647i | \(0.769008\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.57160 | 0.0879926 | ||||||||
\(320\) | −4.39203 | −0.245522 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.783663 | 0.0436042 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.9823 | −1.16389 | ||||||||
\(326\) | 22.1872 | 1.22883 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 29.7099 | 1.64045 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.3068 | −1.28106 | −0.640529 | − | 0.767934i | \(-0.721285\pi\) | ||||
−0.640529 | + | 0.767934i | \(0.721285\pi\) | |||||||
\(332\) | 2.20155 | 0.120826 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 13.0761 | 0.715490 | ||||||||
\(335\) | −3.48249 | −0.190269 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.2383 | −1.26587 | −0.632936 | − | 0.774204i | \(-0.718150\pi\) | ||||
−0.632936 | + | 0.774204i | \(0.718150\pi\) | |||||||
\(338\) | 10.7807 | 0.586395 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.0215917 | 0.00117097 | ||||||||
\(341\) | 11.2163 | 0.607399 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −9.22022 | −0.497121 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.2776 | −0.821330 | ||||||||
\(347\) | −17.1373 | −0.919981 | −0.459990 | − | 0.887924i | \(-0.652147\pi\) | ||||
−0.459990 | + | 0.887924i | \(0.652147\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.5146 | 1.04459 | 0.522296 | − | 0.852764i | \(-0.325076\pi\) | ||||
0.522296 | + | 0.852764i | \(0.325076\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.35234 | 0.178680 | ||||||||
\(353\) | 16.0613 | 0.854856 | 0.427428 | − | 0.904049i | \(-0.359420\pi\) | ||||
0.427428 | + | 0.904049i | \(0.359420\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.54377 | 0.0819347 | ||||||||
\(356\) | −0.715184 | −0.0379047 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.0977 | 0.692233 | ||||||||
\(359\) | −13.8640 | −0.731714 | −0.365857 | − | 0.930671i | \(-0.619224\pi\) | ||||
−0.365857 | + | 0.930671i | \(0.619224\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.7807 | −0.567407 | ||||||||
\(362\) | −7.37100 | −0.387411 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.59785 | 0.345347 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.2953 | −1.32041 | −0.660203 | − | 0.751088i | \(-0.729530\pi\) | ||||
−0.660203 | + | 0.751088i | \(0.729530\pi\) | |||||||
\(368\) | 21.4720 | 1.11930 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.76303 | 0.299606 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.00000 | 0.103556 | 0.0517780 | − | 0.998659i | \(-0.483511\pi\) | ||||
0.0517780 | + | 0.998659i | \(0.483511\pi\) | |||||||
\(374\) | 1.78074 | 0.0920798 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −33.9076 | −1.74865 | ||||||||
\(377\) | −1.59065 | −0.0819229 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.8099 | −0.966200 | −0.483100 | − | 0.875565i | \(-0.660489\pi\) | ||||
−0.483100 | + | 0.875565i | \(0.660489\pi\) | |||||||
\(380\) | 0.226459 | 0.0116171 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −17.7161 | −0.906437 | ||||||||
\(383\) | 35.1416 | 1.79565 | 0.897826 | − | 0.440350i | \(-0.145145\pi\) | ||||
0.897826 | + | 0.440350i | \(0.145145\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 25.0656 | 1.27580 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.301567 | 0.0153097 | ||||||||
\(389\) | 8.37859 | 0.424811 | 0.212406 | − | 0.977182i | \(-0.431870\pi\) | ||||
0.212406 | + | 0.977182i | \(0.431870\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.38151 | 0.0698662 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.09766 | −0.0552992 | ||||||||
\(395\) | −6.62568 | −0.333374 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.24844 | 0.464166 | 0.232083 | − | 0.972696i | \(-0.425446\pi\) | ||||
0.232083 | + | 0.972696i | \(0.425446\pi\) | |||||||
\(398\) | −15.0364 | −0.753705 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19.7453 | 0.987266 | ||||||||
\(401\) | 0.147469 | 0.00736425 | 0.00368212 | − | 0.999993i | \(-0.498828\pi\) | ||||
0.00368212 | + | 0.999993i | \(0.498828\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.3523 | −0.565500 | ||||||||
\(404\) | 1.24513 | 0.0619473 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 29.6519 | 1.46979 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.92528 | 0.194093 | 0.0970463 | − | 0.995280i | \(-0.469060\pi\) | ||||
0.0970463 | + | 0.995280i | \(0.469060\pi\) | |||||||
\(410\) | 9.44611 | 0.466510 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.09766 | 0.103344 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.82004 | −0.482047 | ||||||||
\(416\) | −3.39298 | −0.166355 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 18.6768 | 0.913514 | ||||||||
\(419\) | 21.0000 | 1.02592 | 0.512959 | − | 0.858413i | \(-0.328549\pi\) | ||||
0.512959 | + | 0.858413i | \(0.328549\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.6883 | −1.20323 | −0.601617 | − | 0.798784i | \(-0.705477\pi\) | ||||
−0.601617 | + | 0.798784i | \(0.705477\pi\) | |||||||
\(422\) | −23.5366 | −1.14574 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 30.8860 | 1.49996 | ||||||||
\(425\) | 1.27042 | 0.0616245 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.136389 | −0.00659260 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.93152 | −0.141371 | ||||||||
\(431\) | 5.47490 | 0.263717 | 0.131858 | − | 0.991269i | \(-0.457906\pi\) | ||||
0.131858 | + | 0.991269i | \(0.457906\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.6300 | −1.13558 | −0.567792 | − | 0.823172i | \(-0.692202\pi\) | ||||
−0.567792 | + | 0.823172i | \(0.692202\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.172375 | 0.00825526 | ||||||||
\(437\) | 14.4897 | 0.693136 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.26615 | 0.251340 | 0.125670 | − | 0.992072i | \(-0.459892\pi\) | ||||
0.125670 | + | 0.992072i | \(0.459892\pi\) | |||||||
\(440\) | −7.21926 | −0.344165 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.80233 | −0.0857281 | ||||||||
\(443\) | −6.03638 | −0.286797 | −0.143398 | − | 0.989665i | \(-0.545803\pi\) | ||||
−0.143398 | + | 0.989665i | \(0.545803\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.19008 | 0.151224 | ||||||||
\(446\) | 10.1551 | 0.480856 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.1445 | −1.04507 | −0.522533 | − | 0.852619i | \(-0.675013\pi\) | ||||
−0.522533 | + | 0.852619i | \(0.675013\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 48.6021 | 2.28858 | ||||||||
\(452\) | −1.90234 | −0.0894787 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7.72761 | −0.362675 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.33463 | −0.249543 | −0.124772 | − | 0.992185i | \(-0.539820\pi\) | ||||
−0.124772 | + | 0.992185i | \(0.539820\pi\) | |||||||
\(458\) | −17.1226 | −0.800085 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.399223 | 0.0186139 | ||||||||
\(461\) | −29.6946 | −1.38301 | −0.691507 | − | 0.722370i | \(-0.743053\pi\) | ||||
−0.691507 | + | 0.722370i | \(0.743053\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.5907 | 0.863981 | 0.431990 | − | 0.901878i | \(-0.357811\pi\) | ||||
0.431990 | + | 0.901878i | \(0.357811\pi\) | |||||||
\(464\) | 1.49688 | 0.0694909 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.65390 | 0.261912 | ||||||||
\(467\) | −24.6126 | −1.13894 | −0.569468 | − | 0.822013i | \(-0.692851\pi\) | ||||
−0.569468 | + | 0.822013i | \(0.692851\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −10.7807 | −0.497278 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 21.9607 | 1.01082 | ||||||||
\(473\) | −15.0833 | −0.693529 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.3245 | 0.611370 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.1091 | 0.828292 | ||||||||
\(479\) | 0.356609 | 0.0162939 | 0.00814693 | − | 0.999967i | \(-0.497407\pi\) | ||||
0.00814693 | + | 0.999967i | \(0.497407\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −30.0115 | −1.36841 | ||||||||
\(482\) | 24.1881 | 1.10174 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.18384 | 0.0538111 | ||||||||
\(485\) | −1.34514 | −0.0610796 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.8784 | −0.583576 | −0.291788 | − | 0.956483i | \(-0.594250\pi\) | ||||
−0.291788 | + | 0.956483i | \(0.594250\pi\) | |||||||
\(488\) | −7.45427 | −0.337439 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.55389 | 0.250644 | 0.125322 | − | 0.992116i | \(-0.460004\pi\) | ||||
0.125322 | + | 0.992116i | \(0.460004\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.0963098 | 0.00433758 | ||||||||
\(494\) | −18.9033 | −0.850500 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.6831 | 0.479685 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.1154 | −1.25862 | −0.629308 | − | 0.777156i | \(-0.716662\pi\) | ||||
−0.629308 | + | 0.777156i | \(0.716662\pi\) | |||||||
\(500\) | 0.762071 | 0.0340809 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.70079 | −0.120542 | ||||||||
\(503\) | −16.9430 | −0.755451 | −0.377725 | − | 0.925918i | \(-0.623294\pi\) | ||||
−0.377725 | + | 0.925918i | \(0.623294\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.55389 | −0.247145 | ||||||||
\(506\) | 32.9253 | 1.46371 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.64142 | 0.0728264 | ||||||||
\(509\) | 22.3025 | 0.988542 | 0.494271 | − | 0.869308i | \(-0.335435\pi\) | ||||
0.494271 | + | 0.869308i | \(0.335435\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −19.9751 | −0.882783 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −39.2029 | −1.72917 | ||||||||
\(515\) | −9.35661 | −0.412301 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −55.4690 | −2.43953 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.30680 | 0.320424 | ||||||||
\(521\) | −12.3609 | −0.541540 | −0.270770 | − | 0.962644i | \(-0.587278\pi\) | ||||
−0.270770 | + | 0.962644i | \(0.587278\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.19143 | −0.270732 | −0.135366 | − | 0.990796i | \(-0.543221\pi\) | ||||
−0.135366 | + | 0.990796i | \(0.543221\pi\) | |||||||
\(524\) | −0.425087 | −0.0185700 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 29.6261 | 1.29176 | ||||||||
\(527\) | 0.687353 | 0.0299416 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.54377 | 0.110599 | ||||||||
\(530\) | 9.82004 | 0.426555 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −49.1914 | −2.13072 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.608363 | 0.0263018 | ||||||||
\(536\) | −15.9971 | −0.690968 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12.7453 | 0.549490 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.8200 | 1.15308 | 0.576542 | − | 0.817068i | \(-0.304402\pi\) | ||||
0.576542 | + | 0.817068i | \(0.304402\pi\) | |||||||
\(542\) | −35.3317 | −1.51763 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.205436 | 0.00880800 | ||||||||
\(545\) | −0.768879 | −0.0329352 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.6591 | −0.626779 | −0.313390 | − | 0.949625i | \(-0.601465\pi\) | ||||
−0.313390 | + | 0.949625i | \(0.601465\pi\) | |||||||
\(548\) | −1.34514 | −0.0574615 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 30.2776 | 1.29104 | ||||||||
\(551\) | 1.01012 | 0.0430327 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −10.3920 | −0.441515 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.40546 | −0.102014 | ||||||||
\(557\) | −23.6798 | −1.00334 | −0.501672 | − | 0.865058i | \(-0.667282\pi\) | ||||
−0.501672 | + | 0.865058i | \(0.667282\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.2661 | 0.645689 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11.5323 | 0.486461 | ||||||||
\(563\) | 16.3858 | 0.690579 | 0.345289 | − | 0.938496i | \(-0.387781\pi\) | ||||
0.345289 | + | 0.938496i | \(0.387781\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.48541 | 0.356984 | ||||||||
\(566\) | −3.22646 | −0.135618 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.09142 | 0.297549 | ||||||||
\(569\) | −15.7879 | −0.661865 | −0.330932 | − | 0.943654i | \(-0.607363\pi\) | ||||
−0.330932 | + | 0.943654i | \(0.607363\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.38151 | 0.267058 | 0.133529 | − | 0.991045i | \(-0.457369\pi\) | ||||
0.133529 | + | 0.991045i | \(0.457369\pi\) | |||||||
\(572\) | −2.67977 | −0.112047 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 23.4897 | 0.979587 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 37.0406 | 1.54202 | 0.771011 | − | 0.636822i | \(-0.219751\pi\) | ||||
0.771011 | + | 0.636822i | \(0.219751\pi\) | |||||||
\(578\) | −24.7195 | −1.02819 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.0278311 | 0.00115563 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 50.5261 | 2.09258 | ||||||||
\(584\) | 30.3078 | 1.25414 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 28.0292 | 1.15787 | ||||||||
\(587\) | 12.0938 | 0.499163 | 0.249582 | − | 0.968354i | \(-0.419707\pi\) | ||||
0.249582 | + | 0.968354i | \(0.419707\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.20914 | 0.297047 | ||||||||
\(590\) | 6.98229 | 0.287456 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 28.2422 | 1.16075 | ||||||||
\(593\) | −16.5290 | −0.678764 | −0.339382 | − | 0.940649i | \(-0.610218\pi\) | ||||
−0.339382 | + | 0.940649i | \(0.610218\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.87024 | −0.0766080 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −33.3245 | −1.36274 | ||||||||
\(599\) | −8.74825 | −0.357444 | −0.178722 | − | 0.983900i | \(-0.557196\pi\) | ||||
−0.178722 | + | 0.983900i | \(0.557196\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.92393 | 0.241642 | 0.120821 | − | 0.992674i | \(-0.461447\pi\) | ||||
0.120821 | + | 0.992674i | \(0.461447\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.0507699 | 0.00206580 | ||||||||
\(605\) | −5.28054 | −0.214685 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.741438 | 0.0300940 | 0.0150470 | − | 0.999887i | \(-0.495210\pi\) | ||||
0.0150470 | + | 0.999887i | \(0.495210\pi\) | |||||||
\(608\) | 2.15467 | 0.0873833 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.37005 | −0.0959603 | ||||||||
\(611\) | 56.1416 | 2.27125 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.50700 | 0.182036 | 0.0910181 | − | 0.995849i | \(-0.470988\pi\) | ||||
0.0910181 | + | 0.995849i | \(0.470988\pi\) | |||||||
\(614\) | 20.3212 | 0.820097 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.2016 | −0.692508 | −0.346254 | − | 0.938141i | \(-0.612547\pi\) | ||||
−0.346254 | + | 0.938141i | \(0.612547\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.48541 | −0.180284 | −0.0901419 | − | 0.995929i | \(-0.528732\pi\) | ||||
−0.0901419 | + | 0.995929i | \(0.528732\pi\) | |||||||
\(620\) | 0.198628 | 0.00797709 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −15.5615 | −0.623958 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.8391 | 0.793564 | ||||||||
\(626\) | 24.1881 | 0.966752 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.00000 | 0.0399043 | ||||||||
\(629\) | 1.81711 | 0.0724531 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.3068 | −0.688973 | −0.344486 | − | 0.938791i | \(-0.611947\pi\) | ||||
−0.344486 | + | 0.938791i | \(0.611947\pi\) | |||||||
\(632\) | −30.4356 | −1.21066 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −38.9037 | −1.54506 | ||||||||
\(635\) | −7.32158 | −0.290548 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.29533 | 0.0908729 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −7.30680 | −0.288826 | ||||||||
\(641\) | 43.3216 | 1.71110 | 0.855550 | − | 0.517721i | \(-0.173219\pi\) | ||||
0.855550 | + | 0.517721i | \(0.173219\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.9823 | −1.18239 | −0.591193 | − | 0.806530i | \(-0.701343\pi\) | ||||
−0.591193 | + | 0.806530i | \(0.701343\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.14454 | 0.0450315 | ||||||||
\(647\) | −14.1694 | −0.557059 | −0.278529 | − | 0.960428i | \(-0.589847\pi\) | ||||
−0.278529 | + | 0.960428i | \(0.589847\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 35.9253 | 1.41019 | ||||||||
\(650\) | −30.6447 | −1.20199 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.02159 | 0.0791716 | ||||||||
\(653\) | −28.3963 | −1.11123 | −0.555617 | − | 0.831439i | \(-0.687518\pi\) | ||||
−0.555617 | + | 0.831439i | \(0.687518\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.89610 | 0.0740869 | ||||||||
\(656\) | 46.2914 | 1.80738 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.39922 | 0.366142 | 0.183071 | − | 0.983100i | \(-0.441396\pi\) | ||||
0.183071 | + | 0.983100i | \(0.441396\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.7161 | 0.494601 | 0.247300 | − | 0.968939i | \(-0.420457\pi\) | ||||
0.247300 | + | 0.968939i | \(0.420457\pi\) | |||||||
\(662\) | −34.0397 | −1.32299 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −45.1091 | −1.75057 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.78074 | 0.0689505 | ||||||||
\(668\) | 1.19143 | 0.0460978 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.08619 | −0.196497 | ||||||||
\(671\) | −12.1944 | −0.470758 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.7922 | 1.37969 | 0.689844 | − | 0.723958i | \(-0.257679\pi\) | ||||
0.689844 | + | 0.723958i | \(0.257679\pi\) | |||||||
\(674\) | −33.9397 | −1.30731 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.982291 | 0.0377804 | ||||||||
\(677\) | 10.8918 | 0.418607 | 0.209304 | − | 0.977851i | \(-0.432880\pi\) | ||||
0.209304 | + | 0.977851i | \(0.432880\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.442407 | −0.0169655 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 16.3815 | 0.627281 | ||||||||
\(683\) | −35.0157 | −1.33984 | −0.669920 | − | 0.742433i | \(-0.733672\pi\) | ||||
−0.669920 | + | 0.742433i | \(0.733672\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.00000 | 0.229248 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −14.3662 | −0.547705 | ||||||||
\(689\) | −51.1387 | −1.94823 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.42082 | −0.320343 | −0.160171 | − | 0.987089i | \(-0.551205\pi\) | ||||
−0.160171 | + | 0.987089i | \(0.551205\pi\) | |||||||
\(692\) | −1.39203 | −0.0529169 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −25.0292 | −0.950095 | ||||||||
\(695\) | 10.7296 | 0.406996 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.97841 | 0.112815 | ||||||||
\(698\) | 28.5012 | 1.07878 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.7453 | −1.61447 | −0.807234 | − | 0.590231i | \(-0.799037\pi\) | ||||
−0.807234 | + | 0.590231i | \(0.799037\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.0584 | 0.718800 | ||||||||
\(704\) | −33.0043 | −1.24390 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 23.4576 | 0.882838 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.0862 | −0.904576 | −0.452288 | − | 0.891872i | \(-0.649392\pi\) | ||||
−0.452288 | + | 0.891872i | \(0.649392\pi\) | |||||||
\(710\) | 2.25468 | 0.0846166 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 14.6539 | 0.549178 | ||||||||
\(713\) | 12.7089 | 0.475954 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.9531 | 0.447021 | ||||||||
\(716\) | 1.19340 | 0.0445994 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −20.2484 | −0.755665 | ||||||||
\(719\) | 42.1023 | 1.57015 | 0.785076 | − | 0.619400i | \(-0.212624\pi\) | ||||
0.785076 | + | 0.619400i | \(0.212624\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −15.7453 | −0.585980 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.671612 | −0.0249603 | ||||||||
\(725\) | 1.63754 | 0.0608168 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.0698 | −1.33776 | −0.668878 | − | 0.743372i | \(-0.733225\pi\) | ||||
−0.668878 | + | 0.743372i | \(0.733225\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 9.63619 | 0.356652 | ||||||||
\(731\) | −0.924324 | −0.0341874 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.1331 | −1.26073 | −0.630367 | − | 0.776297i | \(-0.717096\pi\) | ||||
−0.630367 | + | 0.776297i | \(0.717096\pi\) | |||||||
\(734\) | −36.9439 | −1.36363 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.79845 | 0.140013 | ||||||||
\(737\) | −26.1694 | −0.963964 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.8961 | 0.805461 | 0.402731 | − | 0.915319i | \(-0.368061\pi\) | ||||
0.402731 | + | 0.915319i | \(0.368061\pi\) | |||||||
\(740\) | 0.525101 | 0.0193031 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.2852 | 1.03768 | 0.518842 | − | 0.854870i | \(-0.326363\pi\) | ||||
0.518842 | + | 0.854870i | \(0.326363\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.34221 | 0.305635 | ||||||||
\(746\) | 2.92101 | 0.106946 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.162253 | 0.00593254 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.4969 | −0.528999 | −0.264499 | − | 0.964386i | \(-0.585207\pi\) | ||||
−0.264499 | + | 0.964386i | \(0.585207\pi\) | |||||||
\(752\) | −52.8319 | −1.92658 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.32316 | −0.0846044 | ||||||||
\(755\) | −0.226459 | −0.00824169 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.9646 | −1.41619 | −0.708096 | − | 0.706116i | \(-0.750446\pi\) | ||||
−0.708096 | + | 0.706116i | \(0.750446\pi\) | |||||||
\(758\) | −27.4720 | −0.997827 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.64008 | −0.168313 | ||||||||
\(761\) | 1.25564 | 0.0455168 | 0.0227584 | − | 0.999741i | \(-0.492755\pi\) | ||||
0.0227584 | + | 0.999741i | \(0.492755\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1.61421 | −0.0584002 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 51.3245 | 1.85443 | ||||||||
\(767\) | −36.3609 | −1.31292 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.6883 | 0.998466 | 0.499233 | − | 0.866468i | \(-0.333615\pi\) | ||||
0.499233 | + | 0.866468i | \(0.333615\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.28386 | 0.0821978 | ||||||||
\(773\) | −7.91089 | −0.284535 | −0.142267 | − | 0.989828i | \(-0.545439\pi\) | ||||
−0.142267 | + | 0.989828i | \(0.545439\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.6870 | 0.419808 | ||||||||
\(776\) | −6.17900 | −0.221813 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12.2370 | 0.438717 | ||||||||
\(779\) | 31.2383 | 1.11923 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.6008 | 0.415108 | ||||||||
\(782\) | 2.01771 | 0.0721531 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.46050 | −0.159202 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.6693 | −1.12889 | −0.564444 | − | 0.825472i | \(-0.690909\pi\) | ||||
−0.564444 | + | 0.825472i | \(0.690909\pi\) | |||||||
\(788\) | −0.100013 | −0.00356283 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −9.67684 | −0.344287 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.3422 | 0.438285 | ||||||||
\(794\) | 13.5074 | 0.479359 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.37005 | −0.0485600 | ||||||||
\(797\) | −33.7922 | −1.19698 | −0.598491 | − | 0.801130i | \(-0.704233\pi\) | ||||
−0.598491 | + | 0.801130i | \(0.704233\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.39922 | −0.120256 | ||||||||
\(800\) | 3.49300 | 0.123496 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.215379 | 0.00760530 | ||||||||
\(803\) | 49.5801 | 1.74965 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −16.5801 | −0.584011 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −25.5122 | −0.897517 | ||||||||
\(809\) | 36.7601 | 1.29242 | 0.646208 | − | 0.763161i | \(-0.276354\pi\) | ||||
0.646208 | + | 0.763161i | \(0.276354\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.54377 | −0.124438 | −0.0622192 | − | 0.998063i | \(-0.519818\pi\) | ||||
−0.0622192 | + | 0.998063i | \(0.519818\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 43.3068 | 1.51790 | ||||||||
\(815\) | −9.01732 | −0.315863 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.69455 | −0.339169 | ||||||||
\(818\) | 5.73289 | 0.200446 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.860686 | 0.0300565 | ||||||||
\(821\) | 20.8636 | 0.728145 | 0.364073 | − | 0.931371i | \(-0.381386\pi\) | ||||
0.364073 | + | 0.931371i | \(0.381386\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 45.4006 | 1.58256 | 0.791282 | − | 0.611451i | \(-0.209414\pi\) | ||||
0.791282 | + | 0.611451i | \(0.209414\pi\) | |||||||
\(824\) | −42.9803 | −1.49729 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.34221 | −0.185767 | −0.0928835 | − | 0.995677i | \(-0.529608\pi\) | ||||
−0.0928835 | + | 0.995677i | \(0.529608\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.9037 | −0.587089 | −0.293545 | − | 0.955945i | \(-0.594835\pi\) | ||||
−0.293545 | + | 0.955945i | \(0.594835\pi\) | |||||||
\(830\) | −14.3422 | −0.497826 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 33.4045 | 1.15809 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.31438 | −0.183912 | ||||||||
\(836\) | 1.70175 | 0.0588562 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 30.6706 | 1.05950 | ||||||||
\(839\) | 9.83909 | 0.339683 | 0.169842 | − | 0.985471i | \(-0.445674\pi\) | ||||
0.169842 | + | 0.985471i | \(0.445674\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8759 | −0.995719 | ||||||||
\(842\) | −36.0574 | −1.24262 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.14454 | −0.0738182 | ||||||||
\(845\) | −4.38151 | −0.150729 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 48.1239 | 1.65258 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.85546 | 0.0636416 | ||||||||
\(851\) | 33.5979 | 1.15172 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 55.4868 | 1.89983 | 0.949915 | − | 0.312508i | \(-0.101169\pi\) | ||||
0.949915 | + | 0.312508i | \(0.101169\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.79456 | 0.0955162 | ||||||||
\(857\) | 56.3465 | 1.92476 | 0.962380 | − | 0.271708i | \(-0.0875886\pi\) | ||||
0.962380 | + | 0.271708i | \(0.0875886\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.9253 | −1.49871 | −0.749356 | − | 0.662168i | \(-0.769637\pi\) | ||||
−0.749356 | + | 0.662168i | \(0.769637\pi\) | |||||||
\(860\) | −0.267107 | −0.00910826 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.99612 | 0.272349 | ||||||||
\(863\) | 11.3274 | 0.385590 | 0.192795 | − | 0.981239i | \(-0.438245\pi\) | ||||
0.192795 | + | 0.981239i | \(0.438245\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.20914 | 0.211117 | ||||||||
\(866\) | −34.5117 | −1.17275 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −49.7893 | −1.68899 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26.4868 | 0.897470 | ||||||||
\(872\) | −3.53191 | −0.119606 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 21.1623 | 0.715824 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −46.4615 | −1.56889 | −0.784446 | − | 0.620197i | \(-0.787053\pi\) | ||||
−0.784446 | + | 0.620197i | \(0.787053\pi\) | |||||||
\(878\) | 7.69124 | 0.259567 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −11.2484 | −0.379185 | ||||||||
\(881\) | −21.6578 | −0.729669 | −0.364835 | − | 0.931072i | \(-0.618874\pi\) | ||||
−0.364835 | + | 0.931072i | \(0.618874\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.4868 | 0.386560 | 0.193280 | − | 0.981144i | \(-0.438087\pi\) | ||||
0.193280 | + | 0.981144i | \(0.438087\pi\) | |||||||
\(884\) | −0.164220 | −0.00552332 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.81616 | −0.296185 | ||||||||
\(887\) | −17.8420 | −0.599076 | −0.299538 | − | 0.954084i | \(-0.596833\pi\) | ||||
−0.299538 | + | 0.954084i | \(0.596833\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 4.65913 | 0.156174 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.925282 | 0.0309807 | ||||||||
\(893\) | −35.6519 | −1.19305 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.32316 | −0.177934 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −32.3422 | −1.07927 | ||||||||
\(899\) | 0.885981 | 0.0295491 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.09631 | 0.103153 | ||||||||
\(902\) | 70.9836 | 2.36350 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 38.9784 | 1.29640 | ||||||||
\(905\) | 2.99573 | 0.0995814 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −51.8506 | −1.72167 | −0.860835 | − | 0.508884i | \(-0.830058\pi\) | ||||
−0.860835 | + | 0.508884i | \(0.830058\pi\) | |||||||
\(908\) | −0.704104 | −0.0233665 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.48676 | −0.214916 | −0.107458 | − | 0.994210i | \(-0.534271\pi\) | ||||
−0.107458 | + | 0.994210i | \(0.534271\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −73.7936 | −2.44221 | ||||||||
\(914\) | −7.79125 | −0.257712 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.56013 | −0.0515481 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.6844 | −0.385434 | −0.192717 | − | 0.981254i | \(-0.561730\pi\) | ||||
−0.192717 | + | 0.981254i | \(0.561730\pi\) | |||||||
\(920\) | −8.17996 | −0.269685 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −43.3690 | −1.42828 | ||||||||
\(923\) | −11.7414 | −0.386474 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30.8961 | 1.01586 | ||||||||
\(926\) | 27.1517 | 0.892262 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.264802 | 0.00869255 | ||||||||
\(929\) | −1.46050 | −0.0479176 | −0.0239588 | − | 0.999713i | \(-0.507627\pi\) | ||||
−0.0239588 | + | 0.999713i | \(0.507627\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.515158 | 0.0168745 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −35.9469 | −1.17622 | ||||||||
\(935\) | −0.723729 | −0.0236685 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.87451 | −0.322586 | −0.161293 | − | 0.986907i | \(-0.551566\pi\) | ||||
−0.161293 | + | 0.986907i | \(0.551566\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.982291 | −0.0320388 | ||||||||
\(941\) | 54.1944 | 1.76669 | 0.883343 | − | 0.468728i | \(-0.155287\pi\) | ||||
0.883343 | + | 0.468728i | \(0.155287\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 55.0698 | 1.79332 | ||||||||
\(944\) | 34.2173 | 1.11368 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −22.0292 | −0.716230 | ||||||||
\(947\) | 54.8903 | 1.78369 | 0.891847 | − | 0.452338i | \(-0.149410\pi\) | ||||
0.891847 | + | 0.452338i | \(0.149410\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −50.1813 | −1.62895 | ||||||||
\(950\) | 19.4605 | 0.631382 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.0406 | 0.875932 | 0.437966 | − | 0.898991i | \(-0.355699\pi\) | ||||
0.437966 | + | 0.898991i | \(0.355699\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.20021 | 0.232993 | ||||||||
\(956\) | 1.65002 | 0.0533655 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.520829 | 0.0168272 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.6768 | −0.796027 | ||||||||
\(962\) | −43.8319 | −1.41320 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.20391 | 0.0709832 | ||||||||
\(965\) | −10.1872 | −0.327936 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.5146 | −0.434600 | −0.217300 | − | 0.976105i | \(-0.569725\pi\) | ||||
−0.217300 | + | 0.976105i | \(0.569725\pi\) | |||||||
\(968\) | −24.2566 | −0.779636 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.96458 | −0.0630789 | ||||||||
\(971\) | 12.9311 | 0.414980 | 0.207490 | − | 0.978237i | \(-0.433471\pi\) | ||||
0.207490 | + | 0.978237i | \(0.433471\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −18.8090 | −0.602678 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.6146 | −0.371774 | ||||||||
\(977\) | 36.5979 | 1.17087 | 0.585435 | − | 0.810720i | \(-0.300924\pi\) | ||||
0.585435 | + | 0.810720i | \(0.300924\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.9722 | 0.766154 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8.11148 | 0.258848 | ||||||||
\(983\) | −17.2379 | −0.549805 | −0.274902 | − | 0.961472i | \(-0.588646\pi\) | ||||
−0.274902 | + | 0.961472i | \(0.588646\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.446110 | 0.0142143 | ||||||||
\(986\) | 0.140661 | 0.00447956 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.72238 | −0.0547963 | ||||||||
\(989\) | −17.0905 | −0.543445 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.3422 | −0.487361 | −0.243681 | − | 0.969856i | \(-0.578355\pi\) | ||||
−0.243681 | + | 0.969856i | \(0.578355\pi\) | |||||||
\(992\) | 1.88986 | 0.0600032 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.11109 | 0.193735 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.1154 | 1.08044 | 0.540222 | − | 0.841522i | \(-0.318340\pi\) | ||||
0.540222 | + | 0.841522i | \(0.318340\pi\) | |||||||
\(998\) | −41.0626 | −1.29981 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1323.2.a.y.1.3 | 3 | ||
3.2 | odd | 2 | 1323.2.a.z.1.1 | 3 | |||
7.3 | odd | 6 | 189.2.e.f.163.1 | yes | 6 | ||
7.5 | odd | 6 | 189.2.e.f.109.1 | yes | 6 | ||
7.6 | odd | 2 | 1323.2.a.x.1.3 | 3 | |||
21.5 | even | 6 | 189.2.e.e.109.3 | ✓ | 6 | ||
21.17 | even | 6 | 189.2.e.e.163.3 | yes | 6 | ||
21.20 | even | 2 | 1323.2.a.ba.1.1 | 3 | |||
63.5 | even | 6 | 567.2.h.i.298.1 | 6 | |||
63.31 | odd | 6 | 567.2.g.i.541.1 | 6 | |||
63.38 | even | 6 | 567.2.h.i.352.1 | 6 | |||
63.40 | odd | 6 | 567.2.h.h.298.3 | 6 | |||
63.47 | even | 6 | 567.2.g.h.109.3 | 6 | |||
63.52 | odd | 6 | 567.2.h.h.352.3 | 6 | |||
63.59 | even | 6 | 567.2.g.h.541.3 | 6 | |||
63.61 | odd | 6 | 567.2.g.i.109.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.2.e.e.109.3 | ✓ | 6 | 21.5 | even | 6 | ||
189.2.e.e.163.3 | yes | 6 | 21.17 | even | 6 | ||
189.2.e.f.109.1 | yes | 6 | 7.5 | odd | 6 | ||
189.2.e.f.163.1 | yes | 6 | 7.3 | odd | 6 | ||
567.2.g.h.109.3 | 6 | 63.47 | even | 6 | |||
567.2.g.h.541.3 | 6 | 63.59 | even | 6 | |||
567.2.g.i.109.1 | 6 | 63.61 | odd | 6 | |||
567.2.g.i.541.1 | 6 | 63.31 | odd | 6 | |||
567.2.h.h.298.3 | 6 | 63.40 | odd | 6 | |||
567.2.h.h.352.3 | 6 | 63.52 | odd | 6 | |||
567.2.h.i.298.1 | 6 | 63.5 | even | 6 | |||
567.2.h.i.352.1 | 6 | 63.38 | even | 6 | |||
1323.2.a.x.1.3 | 3 | 7.6 | odd | 2 | |||
1323.2.a.y.1.3 | 3 | 1.1 | even | 1 | trivial | ||
1323.2.a.z.1.1 | 3 | 3.2 | odd | 2 | |||
1323.2.a.ba.1.1 | 3 | 21.20 | even | 2 |