Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 14 x^{14} + 68 x^{13} + 64 x^{12} - 456 x^{11} - 54 x^{10} + 1532 x^{9} - 400 x^{8} + \cdots - 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-0.819942\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.819942 | 0.579787 | 0.289893 | − | 0.957059i | \(-0.406380\pi\) | ||||
0.289893 | + | 0.957059i | \(0.406380\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.32769 | −0.663847 | ||||||||
\(5\) | 0.332064 | 0.148503 | 0.0742517 | − | 0.997240i | \(-0.476343\pi\) | ||||
0.0742517 | + | 0.997240i | \(0.476343\pi\) | |||||||
\(6\) | 0.819942 | 0.334740 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.72852 | −0.964677 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.272273 | 0.0861003 | ||||||||
\(11\) | 1.66451 | 0.501868 | 0.250934 | − | 0.968004i | \(-0.419262\pi\) | ||||
0.250934 | + | 0.968004i | \(0.419262\pi\) | |||||||
\(12\) | −1.32769 | −0.383272 | ||||||||
\(13\) | 0.0164518 | 0.00456290 | 0.00228145 | − | 0.999997i | \(-0.499274\pi\) | ||||
0.00228145 | + | 0.999997i | \(0.499274\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.332064 | 0.0857385 | ||||||||
\(16\) | 0.418163 | 0.104541 | ||||||||
\(17\) | 1.78787 | 0.433622 | 0.216811 | − | 0.976214i | \(-0.430435\pi\) | ||||
0.216811 | + | 0.976214i | \(0.430435\pi\) | |||||||
\(18\) | 0.819942 | 0.193262 | ||||||||
\(19\) | −2.53514 | −0.581601 | −0.290801 | − | 0.956784i | \(-0.593922\pi\) | ||||
−0.290801 | + | 0.956784i | \(0.593922\pi\) | |||||||
\(20\) | −0.440879 | −0.0985836 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.36480 | 0.290976 | ||||||||
\(23\) | −2.87658 | −0.599809 | −0.299904 | − | 0.953969i | \(-0.596955\pi\) | ||||
−0.299904 | + | 0.953969i | \(0.596955\pi\) | |||||||
\(24\) | −2.72852 | −0.556956 | ||||||||
\(25\) | −4.88973 | −0.977947 | ||||||||
\(26\) | 0.0134895 | 0.00264551 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.605814 | 0.112497 | 0.0562484 | − | 0.998417i | \(-0.482086\pi\) | ||||
0.0562484 | + | 0.998417i | \(0.482086\pi\) | |||||||
\(30\) | 0.272273 | 0.0497100 | ||||||||
\(31\) | −7.60543 | −1.36597 | −0.682987 | − | 0.730430i | \(-0.739320\pi\) | ||||
−0.682987 | + | 0.730430i | \(0.739320\pi\) | |||||||
\(32\) | 5.79990 | 1.02529 | ||||||||
\(33\) | 1.66451 | 0.289754 | ||||||||
\(34\) | 1.46595 | 0.251408 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.32769 | −0.221282 | ||||||||
\(37\) | 1.91702 | 0.315155 | 0.157578 | − | 0.987507i | \(-0.449632\pi\) | ||||
0.157578 | + | 0.987507i | \(0.449632\pi\) | |||||||
\(38\) | −2.07867 | −0.337205 | ||||||||
\(39\) | 0.0164518 | 0.00263439 | ||||||||
\(40\) | −0.906041 | −0.143258 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.8625 | −1.96151 | −0.980753 | − | 0.195251i | \(-0.937448\pi\) | ||||
−0.980753 | + | 0.195251i | \(0.937448\pi\) | |||||||
\(44\) | −2.20996 | −0.333164 | ||||||||
\(45\) | 0.332064 | 0.0495011 | ||||||||
\(46\) | −2.35863 | −0.347761 | ||||||||
\(47\) | −6.16676 | −0.899514 | −0.449757 | − | 0.893151i | \(-0.648489\pi\) | ||||
−0.449757 | + | 0.893151i | \(0.648489\pi\) | |||||||
\(48\) | 0.418163 | 0.0603566 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.00930 | −0.567001 | ||||||||
\(51\) | 1.78787 | 0.250351 | ||||||||
\(52\) | −0.0218429 | −0.00302907 | ||||||||
\(53\) | 3.84096 | 0.527596 | 0.263798 | − | 0.964578i | \(-0.415025\pi\) | ||||
0.263798 | + | 0.964578i | \(0.415025\pi\) | |||||||
\(54\) | 0.819942 | 0.111580 | ||||||||
\(55\) | 0.552722 | 0.0745291 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.53514 | −0.335788 | ||||||||
\(58\) | 0.496733 | 0.0652242 | ||||||||
\(59\) | 1.41418 | 0.184110 | 0.0920551 | − | 0.995754i | \(-0.470656\pi\) | ||||
0.0920551 | + | 0.995754i | \(0.470656\pi\) | |||||||
\(60\) | −0.440879 | −0.0569172 | ||||||||
\(61\) | −4.42492 | −0.566552 | −0.283276 | − | 0.959038i | \(-0.591421\pi\) | ||||
−0.283276 | + | 0.959038i | \(0.591421\pi\) | |||||||
\(62\) | −6.23601 | −0.791974 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.91926 | 0.489908 | ||||||||
\(65\) | 0.00546303 | 0.000677605 0 | ||||||||
\(66\) | 1.36480 | 0.167995 | ||||||||
\(67\) | 4.72149 | 0.576822 | 0.288411 | − | 0.957507i | \(-0.406873\pi\) | ||||
0.288411 | + | 0.957507i | \(0.406873\pi\) | |||||||
\(68\) | −2.37374 | −0.287858 | ||||||||
\(69\) | −2.87658 | −0.346300 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.80768 | 0.689244 | 0.344622 | − | 0.938741i | \(-0.388007\pi\) | ||||
0.344622 | + | 0.938741i | \(0.388007\pi\) | |||||||
\(72\) | −2.72852 | −0.321559 | ||||||||
\(73\) | 0.748580 | 0.0876147 | 0.0438073 | − | 0.999040i | \(-0.486051\pi\) | ||||
0.0438073 | + | 0.999040i | \(0.486051\pi\) | |||||||
\(74\) | 1.57184 | 0.182723 | ||||||||
\(75\) | −4.88973 | −0.564618 | ||||||||
\(76\) | 3.36589 | 0.386094 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.0134895 | 0.00152738 | ||||||||
\(79\) | 4.49461 | 0.505683 | 0.252842 | − | 0.967508i | \(-0.418635\pi\) | ||||
0.252842 | + | 0.967508i | \(0.418635\pi\) | |||||||
\(80\) | 0.138857 | 0.0155246 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.819942 | 0.0905475 | ||||||||
\(83\) | 11.4541 | 1.25725 | 0.628626 | − | 0.777707i | \(-0.283617\pi\) | ||||
0.628626 | + | 0.777707i | \(0.283617\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.593686 | 0.0643943 | ||||||||
\(86\) | −10.5465 | −1.13726 | ||||||||
\(87\) | 0.605814 | 0.0649501 | ||||||||
\(88\) | −4.54164 | −0.484140 | ||||||||
\(89\) | −5.00144 | −0.530152 | −0.265076 | − | 0.964228i | \(-0.585397\pi\) | ||||
−0.265076 | + | 0.964228i | \(0.585397\pi\) | |||||||
\(90\) | 0.272273 | 0.0287001 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.81922 | 0.398181 | ||||||||
\(93\) | −7.60543 | −0.788646 | ||||||||
\(94\) | −5.05638 | −0.521526 | ||||||||
\(95\) | −0.841828 | −0.0863697 | ||||||||
\(96\) | 5.79990 | 0.591950 | ||||||||
\(97\) | 6.40794 | 0.650628 | 0.325314 | − | 0.945606i | \(-0.394530\pi\) | ||||
0.325314 | + | 0.945606i | \(0.394530\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.66451 | 0.167289 | ||||||||
\(100\) | 6.49207 | 0.649207 | ||||||||
\(101\) | −17.5942 | −1.75069 | −0.875344 | − | 0.483501i | \(-0.839365\pi\) | ||||
−0.875344 | + | 0.483501i | \(0.839365\pi\) | |||||||
\(102\) | 1.46595 | 0.145150 | ||||||||
\(103\) | −4.00896 | −0.395015 | −0.197507 | − | 0.980301i | \(-0.563285\pi\) | ||||
−0.197507 | + | 0.980301i | \(0.563285\pi\) | |||||||
\(104\) | −0.0448889 | −0.00440172 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.14937 | 0.305893 | ||||||||
\(107\) | −11.8977 | −1.15019 | −0.575097 | − | 0.818085i | \(-0.695036\pi\) | ||||
−0.575097 | + | 0.818085i | \(0.695036\pi\) | |||||||
\(108\) | −1.32769 | −0.127757 | ||||||||
\(109\) | −14.1105 | −1.35154 | −0.675772 | − | 0.737110i | \(-0.736190\pi\) | ||||
−0.675772 | + | 0.737110i | \(0.736190\pi\) | |||||||
\(110\) | 0.453200 | 0.0432110 | ||||||||
\(111\) | 1.91702 | 0.181955 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.58338 | 0.337096 | 0.168548 | − | 0.985693i | \(-0.446092\pi\) | ||||
0.168548 | + | 0.985693i | \(0.446092\pi\) | |||||||
\(114\) | −2.07867 | −0.194685 | ||||||||
\(115\) | −0.955208 | −0.0890736 | ||||||||
\(116\) | −0.804336 | −0.0746807 | ||||||||
\(117\) | 0.0164518 | 0.00152097 | ||||||||
\(118\) | 1.15954 | 0.106745 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.906041 | −0.0827099 | ||||||||
\(121\) | −8.22941 | −0.748129 | ||||||||
\(122\) | −3.62818 | −0.328480 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | 10.0977 | 0.906799 | ||||||||
\(125\) | −3.28402 | −0.293732 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.6099 | −1.47389 | −0.736944 | − | 0.675954i | \(-0.763732\pi\) | ||||
−0.736944 | + | 0.675954i | \(0.763732\pi\) | |||||||
\(128\) | −8.38624 | −0.741246 | ||||||||
\(129\) | −12.8625 | −1.13248 | ||||||||
\(130\) | 0.00447937 | 0.000392867 0 | ||||||||
\(131\) | 9.60996 | 0.839626 | 0.419813 | − | 0.907611i | \(-0.362096\pi\) | ||||
0.419813 | + | 0.907611i | \(0.362096\pi\) | |||||||
\(132\) | −2.20996 | −0.192352 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.87135 | 0.334434 | ||||||||
\(135\) | 0.332064 | 0.0285795 | ||||||||
\(136\) | −4.87823 | −0.418305 | ||||||||
\(137\) | −5.93129 | −0.506744 | −0.253372 | − | 0.967369i | \(-0.581540\pi\) | ||||
−0.253372 | + | 0.967369i | \(0.581540\pi\) | |||||||
\(138\) | −2.35863 | −0.200780 | ||||||||
\(139\) | 20.3689 | 1.72767 | 0.863836 | − | 0.503773i | \(-0.168055\pi\) | ||||
0.863836 | + | 0.503773i | \(0.168055\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.16676 | −0.519335 | ||||||||
\(142\) | 4.76196 | 0.399615 | ||||||||
\(143\) | 0.0273841 | 0.00228997 | ||||||||
\(144\) | 0.418163 | 0.0348469 | ||||||||
\(145\) | 0.201169 | 0.0167062 | ||||||||
\(146\) | 0.613793 | 0.0507978 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.54521 | −0.209215 | ||||||||
\(149\) | −15.7679 | −1.29176 | −0.645878 | − | 0.763440i | \(-0.723509\pi\) | ||||
−0.645878 | + | 0.763440i | \(0.723509\pi\) | |||||||
\(150\) | −4.00930 | −0.327358 | ||||||||
\(151\) | 12.4627 | 1.01420 | 0.507102 | − | 0.861886i | \(-0.330717\pi\) | ||||
0.507102 | + | 0.861886i | \(0.330717\pi\) | |||||||
\(152\) | 6.91718 | 0.561057 | ||||||||
\(153\) | 1.78787 | 0.144541 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.52549 | −0.202852 | ||||||||
\(156\) | −0.0218429 | −0.00174883 | ||||||||
\(157\) | −14.6543 | −1.16954 | −0.584771 | − | 0.811198i | \(-0.698816\pi\) | ||||
−0.584771 | + | 0.811198i | \(0.698816\pi\) | |||||||
\(158\) | 3.68532 | 0.293188 | ||||||||
\(159\) | 3.84096 | 0.304608 | ||||||||
\(160\) | 1.92594 | 0.152259 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.819942 | 0.0644207 | ||||||||
\(163\) | −10.4822 | −0.821030 | −0.410515 | − | 0.911854i | \(-0.634651\pi\) | ||||
−0.410515 | + | 0.911854i | \(0.634651\pi\) | |||||||
\(164\) | −1.32769 | −0.103676 | ||||||||
\(165\) | 0.552722 | 0.0430294 | ||||||||
\(166\) | 9.39172 | 0.728939 | ||||||||
\(167\) | 9.45153 | 0.731381 | 0.365691 | − | 0.930736i | \(-0.380833\pi\) | ||||
0.365691 | + | 0.930736i | \(0.380833\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9997 | −0.999979 | ||||||||
\(170\) | 0.486788 | 0.0373349 | ||||||||
\(171\) | −2.53514 | −0.193867 | ||||||||
\(172\) | 17.0774 | 1.30214 | ||||||||
\(173\) | −9.52226 | −0.723964 | −0.361982 | − | 0.932185i | \(-0.617900\pi\) | ||||
−0.361982 | + | 0.932185i | \(0.617900\pi\) | |||||||
\(174\) | 0.496733 | 0.0376572 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.696035 | 0.0524656 | ||||||||
\(177\) | 1.41418 | 0.106296 | ||||||||
\(178\) | −4.10089 | −0.307375 | ||||||||
\(179\) | −22.8105 | −1.70494 | −0.852469 | − | 0.522778i | \(-0.824896\pi\) | ||||
−0.852469 | + | 0.522778i | \(0.824896\pi\) | |||||||
\(180\) | −0.440879 | −0.0328612 | ||||||||
\(181\) | −3.16124 | −0.234973 | −0.117487 | − | 0.993074i | \(-0.537484\pi\) | ||||
−0.117487 | + | 0.993074i | \(0.537484\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.42492 | −0.327099 | ||||||||
\(184\) | 7.84880 | 0.578621 | ||||||||
\(185\) | 0.636571 | 0.0468016 | ||||||||
\(186\) | −6.23601 | −0.457246 | ||||||||
\(187\) | 2.97592 | 0.217621 | ||||||||
\(188\) | 8.18757 | 0.597140 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.690250 | −0.0500760 | ||||||||
\(191\) | 5.66282 | 0.409747 | 0.204874 | − | 0.978788i | \(-0.434322\pi\) | ||||
0.204874 | + | 0.978788i | \(0.434322\pi\) | |||||||
\(192\) | 3.91926 | 0.282848 | ||||||||
\(193\) | −20.1887 | −1.45321 | −0.726606 | − | 0.687055i | \(-0.758903\pi\) | ||||
−0.726606 | + | 0.687055i | \(0.758903\pi\) | |||||||
\(194\) | 5.25414 | 0.377225 | ||||||||
\(195\) | 0.00546303 | 0.000391216 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.477679 | 0.0340332 | 0.0170166 | − | 0.999855i | \(-0.494583\pi\) | ||||
0.0170166 | + | 0.999855i | \(0.494583\pi\) | |||||||
\(198\) | 1.36480 | 0.0969921 | ||||||||
\(199\) | −3.25632 | −0.230835 | −0.115417 | − | 0.993317i | \(-0.536821\pi\) | ||||
−0.115417 | + | 0.993317i | \(0.536821\pi\) | |||||||
\(200\) | 13.3417 | 0.943402 | ||||||||
\(201\) | 4.72149 | 0.333029 | ||||||||
\(202\) | −14.4262 | −1.01503 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.37374 | −0.166195 | ||||||||
\(205\) | 0.332064 | 0.0231923 | ||||||||
\(206\) | −3.28712 | −0.229024 | ||||||||
\(207\) | −2.87658 | −0.199936 | ||||||||
\(208\) | 0.00687951 | 0.000477008 0 | ||||||||
\(209\) | −4.21976 | −0.291887 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.492222 | 0.0338860 | 0.0169430 | − | 0.999856i | \(-0.494607\pi\) | ||||
0.0169430 | + | 0.999856i | \(0.494607\pi\) | |||||||
\(212\) | −5.09962 | −0.350244 | ||||||||
\(213\) | 5.80768 | 0.397935 | ||||||||
\(214\) | −9.75543 | −0.666868 | ||||||||
\(215\) | −4.27115 | −0.291290 | ||||||||
\(216\) | −2.72852 | −0.185652 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −11.5698 | −0.783608 | ||||||||
\(219\) | 0.748580 | 0.0505844 | ||||||||
\(220\) | −0.733847 | −0.0494759 | ||||||||
\(221\) | 0.0294136 | 0.00197857 | ||||||||
\(222\) | 1.57184 | 0.105495 | ||||||||
\(223\) | 7.15813 | 0.479344 | 0.239672 | − | 0.970854i | \(-0.422960\pi\) | ||||
0.239672 | + | 0.970854i | \(0.422960\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.88973 | −0.325982 | ||||||||
\(226\) | 2.93816 | 0.195444 | ||||||||
\(227\) | −7.34618 | −0.487583 | −0.243791 | − | 0.969828i | \(-0.578391\pi\) | ||||
−0.243791 | + | 0.969828i | \(0.578391\pi\) | |||||||
\(228\) | 3.36589 | 0.222912 | ||||||||
\(229\) | −9.96063 | −0.658217 | −0.329109 | − | 0.944292i | \(-0.606748\pi\) | ||||
−0.329109 | + | 0.944292i | \(0.606748\pi\) | |||||||
\(230\) | −0.783215 | −0.0516437 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.65297 | −0.108523 | ||||||||
\(233\) | −21.3065 | −1.39583 | −0.697917 | − | 0.716179i | \(-0.745889\pi\) | ||||
−0.697917 | + | 0.716179i | \(0.745889\pi\) | |||||||
\(234\) | 0.0134895 | 0.000881835 0 | ||||||||
\(235\) | −2.04776 | −0.133581 | ||||||||
\(236\) | −1.87760 | −0.122221 | ||||||||
\(237\) | 4.49461 | 0.291956 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.7115 | −0.692868 | −0.346434 | − | 0.938074i | \(-0.612608\pi\) | ||||
−0.346434 | + | 0.938074i | \(0.612608\pi\) | |||||||
\(240\) | 0.138857 | 0.00896315 | ||||||||
\(241\) | −15.3877 | −0.991212 | −0.495606 | − | 0.868547i | \(-0.665054\pi\) | ||||
−0.495606 | + | 0.868547i | \(0.665054\pi\) | |||||||
\(242\) | −6.74764 | −0.433755 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 5.87494 | 0.376104 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.819942 | 0.0522776 | ||||||||
\(247\) | −0.0417075 | −0.00265379 | ||||||||
\(248\) | 20.7515 | 1.31772 | ||||||||
\(249\) | 11.4541 | 0.725875 | ||||||||
\(250\) | −2.69271 | −0.170302 | ||||||||
\(251\) | −3.83734 | −0.242211 | −0.121105 | − | 0.992640i | \(-0.538644\pi\) | ||||
−0.121105 | + | 0.992640i | \(0.538644\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.78809 | −0.301025 | ||||||||
\(254\) | −13.6191 | −0.854541 | ||||||||
\(255\) | 0.593686 | 0.0371780 | ||||||||
\(256\) | −14.7148 | −0.919672 | ||||||||
\(257\) | 29.6461 | 1.84927 | 0.924637 | − | 0.380850i | \(-0.124368\pi\) | ||||
0.924637 | + | 0.380850i | \(0.124368\pi\) | |||||||
\(258\) | −10.5465 | −0.656595 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.00725323 | −0.000449827 0 | ||||||||
\(261\) | 0.605814 | 0.0374990 | ||||||||
\(262\) | 7.87961 | 0.486804 | ||||||||
\(263\) | −15.0006 | −0.924976 | −0.462488 | − | 0.886625i | \(-0.653043\pi\) | ||||
−0.462488 | + | 0.886625i | \(0.653043\pi\) | |||||||
\(264\) | −4.54164 | −0.279518 | ||||||||
\(265\) | 1.27544 | 0.0783498 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.00144 | −0.306083 | ||||||||
\(268\) | −6.26870 | −0.382922 | ||||||||
\(269\) | −5.76098 | −0.351253 | −0.175627 | − | 0.984457i | \(-0.556195\pi\) | ||||
−0.175627 | + | 0.984457i | \(0.556195\pi\) | |||||||
\(270\) | 0.272273 | 0.0165700 | ||||||||
\(271\) | 5.41966 | 0.329221 | 0.164611 | − | 0.986359i | \(-0.447363\pi\) | ||||
0.164611 | + | 0.986359i | \(0.447363\pi\) | |||||||
\(272\) | 0.747619 | 0.0453311 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.86331 | −0.293803 | ||||||||
\(275\) | −8.13900 | −0.490800 | ||||||||
\(276\) | 3.81922 | 0.229890 | ||||||||
\(277\) | −20.4003 | −1.22573 | −0.612867 | − | 0.790186i | \(-0.709984\pi\) | ||||
−0.612867 | + | 0.790186i | \(0.709984\pi\) | |||||||
\(278\) | 16.7014 | 1.00168 | ||||||||
\(279\) | −7.60543 | −0.455325 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.03670 | 0.300464 | 0.150232 | − | 0.988651i | \(-0.451998\pi\) | ||||
0.150232 | + | 0.988651i | \(0.451998\pi\) | |||||||
\(282\) | −5.05638 | −0.301103 | ||||||||
\(283\) | 0.733053 | 0.0435755 | 0.0217877 | − | 0.999763i | \(-0.493064\pi\) | ||||
0.0217877 | + | 0.999763i | \(0.493064\pi\) | |||||||
\(284\) | −7.71082 | −0.457553 | ||||||||
\(285\) | −0.841828 | −0.0498656 | ||||||||
\(286\) | 0.0224534 | 0.00132769 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 5.79990 | 0.341763 | ||||||||
\(289\) | −13.8035 | −0.811972 | ||||||||
\(290\) | 0.164947 | 0.00968601 | ||||||||
\(291\) | 6.40794 | 0.375640 | ||||||||
\(292\) | −0.993886 | −0.0581628 | ||||||||
\(293\) | 9.92734 | 0.579961 | 0.289981 | − | 0.957033i | \(-0.406351\pi\) | ||||
0.289981 | + | 0.957033i | \(0.406351\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.469597 | 0.0273410 | ||||||||
\(296\) | −5.23061 | −0.304023 | ||||||||
\(297\) | 1.66451 | 0.0965845 | ||||||||
\(298\) | −12.9288 | −0.748943 | ||||||||
\(299\) | −0.0473248 | −0.00273686 | ||||||||
\(300\) | 6.49207 | 0.374820 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 10.2187 | 0.588022 | ||||||||
\(303\) | −17.5942 | −1.01076 | ||||||||
\(304\) | −1.06010 | −0.0608010 | ||||||||
\(305\) | −1.46935 | −0.0841349 | ||||||||
\(306\) | 1.46595 | 0.0838027 | ||||||||
\(307\) | 18.0797 | 1.03186 | 0.515930 | − | 0.856631i | \(-0.327446\pi\) | ||||
0.515930 | + | 0.856631i | \(0.327446\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.00896 | −0.228062 | ||||||||
\(310\) | −2.07075 | −0.117611 | ||||||||
\(311\) | 6.53524 | 0.370579 | 0.185290 | − | 0.982684i | \(-0.440678\pi\) | ||||
0.185290 | + | 0.982684i | \(0.440678\pi\) | |||||||
\(312\) | −0.0448889 | −0.00254133 | ||||||||
\(313\) | 6.62531 | 0.374485 | 0.187242 | − | 0.982314i | \(-0.440045\pi\) | ||||
0.187242 | + | 0.982314i | \(0.440045\pi\) | |||||||
\(314\) | −12.0157 | −0.678085 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.96747 | −0.335696 | ||||||||
\(317\) | 5.00888 | 0.281327 | 0.140663 | − | 0.990057i | \(-0.455077\pi\) | ||||
0.140663 | + | 0.990057i | \(0.455077\pi\) | |||||||
\(318\) | 3.14937 | 0.176608 | ||||||||
\(319\) | 1.00838 | 0.0564586 | ||||||||
\(320\) | 1.30144 | 0.0727529 | ||||||||
\(321\) | −11.8977 | −0.664065 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.53250 | −0.252195 | ||||||||
\(324\) | −1.32769 | −0.0737608 | ||||||||
\(325\) | −0.0804447 | −0.00446227 | ||||||||
\(326\) | −8.59480 | −0.476022 | ||||||||
\(327\) | −14.1105 | −0.780315 | ||||||||
\(328\) | −2.72852 | −0.150657 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.453200 | 0.0249479 | ||||||||
\(331\) | −2.06115 | −0.113291 | −0.0566456 | − | 0.998394i | \(-0.518040\pi\) | ||||
−0.0566456 | + | 0.998394i | \(0.518040\pi\) | |||||||
\(332\) | −15.2076 | −0.834624 | ||||||||
\(333\) | 1.91702 | 0.105052 | ||||||||
\(334\) | 7.74971 | 0.424045 | ||||||||
\(335\) | 1.56784 | 0.0856600 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.5592 | 0.684141 | 0.342070 | − | 0.939674i | \(-0.388872\pi\) | ||||
0.342070 | + | 0.939674i | \(0.388872\pi\) | |||||||
\(338\) | −10.6590 | −0.579775 | ||||||||
\(339\) | 3.58338 | 0.194622 | ||||||||
\(340\) | −0.788233 | −0.0427480 | ||||||||
\(341\) | −12.6593 | −0.685539 | ||||||||
\(342\) | −2.07867 | −0.112402 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 35.0954 | 1.89222 | ||||||||
\(345\) | −0.955208 | −0.0514267 | ||||||||
\(346\) | −7.80770 | −0.419745 | ||||||||
\(347\) | 11.4809 | 0.616325 | 0.308163 | − | 0.951334i | \(-0.400286\pi\) | ||||
0.308163 | + | 0.951334i | \(0.400286\pi\) | |||||||
\(348\) | −0.804336 | −0.0431169 | ||||||||
\(349\) | 15.2242 | 0.814931 | 0.407466 | − | 0.913221i | \(-0.366413\pi\) | ||||
0.407466 | + | 0.913221i | \(0.366413\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.0164518 | 0.000878130 0 | ||||||||
\(352\) | 9.65398 | 0.514559 | ||||||||
\(353\) | 20.4119 | 1.08642 | 0.543209 | − | 0.839598i | \(-0.317209\pi\) | ||||
0.543209 | + | 0.839598i | \(0.317209\pi\) | |||||||
\(354\) | 1.15954 | 0.0616291 | ||||||||
\(355\) | 1.92852 | 0.102355 | ||||||||
\(356\) | 6.64039 | 0.351940 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.7033 | −0.988501 | ||||||||
\(359\) | 30.1992 | 1.59385 | 0.796926 | − | 0.604077i | \(-0.206458\pi\) | ||||
0.796926 | + | 0.604077i | \(0.206458\pi\) | |||||||
\(360\) | −0.906041 | −0.0477526 | ||||||||
\(361\) | −12.5731 | −0.661740 | ||||||||
\(362\) | −2.59203 | −0.136234 | ||||||||
\(363\) | −8.22941 | −0.431932 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.248576 | 0.0130111 | ||||||||
\(366\) | −3.62818 | −0.189648 | ||||||||
\(367\) | 5.89363 | 0.307645 | 0.153823 | − | 0.988098i | \(-0.450842\pi\) | ||||
0.153823 | + | 0.988098i | \(0.450842\pi\) | |||||||
\(368\) | −1.20288 | −0.0627044 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | 0.521951 | 0.0271350 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 10.0977 | 0.523541 | ||||||||
\(373\) | 23.0679 | 1.19441 | 0.597206 | − | 0.802088i | \(-0.296278\pi\) | ||||
0.597206 | + | 0.802088i | \(0.296278\pi\) | |||||||
\(374\) | 2.44008 | 0.126174 | ||||||||
\(375\) | −3.28402 | −0.169586 | ||||||||
\(376\) | 16.8261 | 0.867740 | ||||||||
\(377\) | 0.00996671 | 0.000513311 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.9801 | 0.820843 | 0.410421 | − | 0.911896i | \(-0.365382\pi\) | ||||
0.410421 | + | 0.911896i | \(0.365382\pi\) | |||||||
\(380\) | 1.11769 | 0.0573363 | ||||||||
\(381\) | −16.6099 | −0.850950 | ||||||||
\(382\) | 4.64319 | 0.237566 | ||||||||
\(383\) | −28.4963 | −1.45609 | −0.728046 | − | 0.685529i | \(-0.759571\pi\) | ||||
−0.728046 | + | 0.685529i | \(0.759571\pi\) | |||||||
\(384\) | −8.38624 | −0.427959 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.5535 | −0.842553 | ||||||||
\(387\) | −12.8625 | −0.653836 | ||||||||
\(388\) | −8.50779 | −0.431918 | ||||||||
\(389\) | 4.42493 | 0.224353 | 0.112177 | − | 0.993688i | \(-0.464218\pi\) | ||||
0.112177 | + | 0.993688i | \(0.464218\pi\) | |||||||
\(390\) | 0.00447937 | 0.000226822 0 | ||||||||
\(391\) | −5.14295 | −0.260090 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.60996 | 0.484758 | ||||||||
\(394\) | 0.391669 | 0.0197320 | ||||||||
\(395\) | 1.49250 | 0.0750956 | ||||||||
\(396\) | −2.20996 | −0.111055 | ||||||||
\(397\) | 31.0599 | 1.55885 | 0.779426 | − | 0.626494i | \(-0.215511\pi\) | ||||
0.779426 | + | 0.626494i | \(0.215511\pi\) | |||||||
\(398\) | −2.67000 | −0.133835 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.04470 | −0.102235 | ||||||||
\(401\) | −2.27093 | −0.113405 | −0.0567025 | − | 0.998391i | \(-0.518059\pi\) | ||||
−0.0567025 | + | 0.998391i | \(0.518059\pi\) | |||||||
\(402\) | 3.87135 | 0.193086 | ||||||||
\(403\) | −0.125123 | −0.00623280 | ||||||||
\(404\) | 23.3597 | 1.16219 | ||||||||
\(405\) | 0.332064 | 0.0165004 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.19089 | 0.158166 | ||||||||
\(408\) | −4.87823 | −0.241508 | ||||||||
\(409\) | 5.31380 | 0.262751 | 0.131375 | − | 0.991333i | \(-0.458061\pi\) | ||||
0.131375 | + | 0.991333i | \(0.458061\pi\) | |||||||
\(410\) | 0.272273 | 0.0134466 | ||||||||
\(411\) | −5.93129 | −0.292569 | ||||||||
\(412\) | 5.32268 | 0.262229 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.35863 | −0.115920 | ||||||||
\(415\) | 3.80350 | 0.186706 | ||||||||
\(416\) | 0.0954186 | 0.00467828 | ||||||||
\(417\) | 20.3689 | 0.997472 | ||||||||
\(418\) | −3.45996 | −0.169232 | ||||||||
\(419\) | 16.3430 | 0.798410 | 0.399205 | − | 0.916862i | \(-0.369286\pi\) | ||||
0.399205 | + | 0.916862i | \(0.369286\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.54033 | −0.367493 | −0.183747 | − | 0.982974i | \(-0.558823\pi\) | ||||
−0.183747 | + | 0.982974i | \(0.558823\pi\) | |||||||
\(422\) | 0.403594 | 0.0196466 | ||||||||
\(423\) | −6.16676 | −0.299838 | ||||||||
\(424\) | −10.4801 | −0.508960 | ||||||||
\(425\) | −8.74219 | −0.424059 | ||||||||
\(426\) | 4.76196 | 0.230718 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 15.7965 | 0.763554 | ||||||||
\(429\) | 0.0273841 | 0.00132212 | ||||||||
\(430\) | −3.50210 | −0.168886 | ||||||||
\(431\) | 8.22298 | 0.396087 | 0.198044 | − | 0.980193i | \(-0.436541\pi\) | ||||
0.198044 | + | 0.980193i | \(0.436541\pi\) | |||||||
\(432\) | 0.418163 | 0.0201189 | ||||||||
\(433\) | 6.10083 | 0.293187 | 0.146594 | − | 0.989197i | \(-0.453169\pi\) | ||||
0.146594 | + | 0.989197i | \(0.453169\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.201169 | 0.00964531 | ||||||||
\(436\) | 18.7345 | 0.897220 | ||||||||
\(437\) | 7.29254 | 0.348850 | ||||||||
\(438\) | 0.613793 | 0.0293281 | ||||||||
\(439\) | −16.8750 | −0.805398 | −0.402699 | − | 0.915333i | \(-0.631928\pi\) | ||||
−0.402699 | + | 0.915333i | \(0.631928\pi\) | |||||||
\(440\) | −1.50811 | −0.0718965 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.0241174 | 0.00114715 | ||||||||
\(443\) | −24.6875 | −1.17294 | −0.586468 | − | 0.809972i | \(-0.699482\pi\) | ||||
−0.586468 | + | 0.809972i | \(0.699482\pi\) | |||||||
\(444\) | −2.54521 | −0.120790 | ||||||||
\(445\) | −1.66080 | −0.0787293 | ||||||||
\(446\) | 5.86925 | 0.277917 | ||||||||
\(447\) | −15.7679 | −0.745796 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.81494 | 0.0856523 | 0.0428262 | − | 0.999083i | \(-0.486364\pi\) | ||||
0.0428262 | + | 0.999083i | \(0.486364\pi\) | |||||||
\(450\) | −4.00930 | −0.189000 | ||||||||
\(451\) | 1.66451 | 0.0783786 | ||||||||
\(452\) | −4.75763 | −0.223780 | ||||||||
\(453\) | 12.4627 | 0.585551 | ||||||||
\(454\) | −6.02344 | −0.282694 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.91718 | 0.323927 | ||||||||
\(457\) | 28.1049 | 1.31469 | 0.657345 | − | 0.753589i | \(-0.271679\pi\) | ||||
0.657345 | + | 0.753589i | \(0.271679\pi\) | |||||||
\(458\) | −8.16714 | −0.381625 | ||||||||
\(459\) | 1.78787 | 0.0834505 | ||||||||
\(460\) | 1.26822 | 0.0591313 | ||||||||
\(461\) | 27.5428 | 1.28280 | 0.641399 | − | 0.767207i | \(-0.278354\pi\) | ||||
0.641399 | + | 0.767207i | \(0.278354\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.8028 | −1.10621 | −0.553104 | − | 0.833112i | \(-0.686557\pi\) | ||||
−0.553104 | + | 0.833112i | \(0.686557\pi\) | |||||||
\(464\) | 0.253329 | 0.0117605 | ||||||||
\(465\) | −2.52549 | −0.117117 | ||||||||
\(466\) | −17.4701 | −0.809286 | ||||||||
\(467\) | −4.10944 | −0.190162 | −0.0950811 | − | 0.995470i | \(-0.530311\pi\) | ||||
−0.0950811 | + | 0.995470i | \(0.530311\pi\) | |||||||
\(468\) | −0.0218429 | −0.00100969 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.67904 | −0.0774484 | ||||||||
\(471\) | −14.6543 | −0.675235 | ||||||||
\(472\) | −3.85861 | −0.177607 | ||||||||
\(473\) | −21.4097 | −0.984417 | ||||||||
\(474\) | 3.68532 | 0.169272 | ||||||||
\(475\) | 12.3962 | 0.568775 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.84096 | 0.175865 | ||||||||
\(478\) | −8.78279 | −0.401716 | ||||||||
\(479\) | 11.3384 | 0.518063 | 0.259031 | − | 0.965869i | \(-0.416597\pi\) | ||||
0.259031 | + | 0.965869i | \(0.416597\pi\) | |||||||
\(480\) | 1.92594 | 0.0879066 | ||||||||
\(481\) | 0.0315383 | 0.00143802 | ||||||||
\(482\) | −12.6171 | −0.574692 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.9262 | 0.496643 | ||||||||
\(485\) | 2.12784 | 0.0966204 | ||||||||
\(486\) | 0.819942 | 0.0371933 | ||||||||
\(487\) | 9.89485 | 0.448378 | 0.224189 | − | 0.974546i | \(-0.428027\pi\) | ||||
0.224189 | + | 0.974546i | \(0.428027\pi\) | |||||||
\(488\) | 12.0735 | 0.546540 | ||||||||
\(489\) | −10.4822 | −0.474022 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.2342 | 1.13880 | 0.569402 | − | 0.822059i | \(-0.307175\pi\) | ||||
0.569402 | + | 0.822059i | \(0.307175\pi\) | |||||||
\(492\) | −1.32769 | −0.0598571 | ||||||||
\(493\) | 1.08312 | 0.0487811 | ||||||||
\(494\) | −0.0341978 | −0.00153863 | ||||||||
\(495\) | 0.552722 | 0.0248430 | ||||||||
\(496\) | −3.18030 | −0.142800 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 9.39172 | 0.420853 | ||||||||
\(499\) | −1.10126 | −0.0492993 | −0.0246497 | − | 0.999696i | \(-0.507847\pi\) | ||||
−0.0246497 | + | 0.999696i | \(0.507847\pi\) | |||||||
\(500\) | 4.36018 | 0.194993 | ||||||||
\(501\) | 9.45153 | 0.422263 | ||||||||
\(502\) | −3.14640 | −0.140431 | ||||||||
\(503\) | −25.1272 | −1.12036 | −0.560182 | − | 0.828369i | \(-0.689269\pi\) | ||||
−0.560182 | + | 0.828369i | \(0.689269\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.84239 | −0.259983 | ||||||||
\(506\) | −3.92596 | −0.174530 | ||||||||
\(507\) | −12.9997 | −0.577338 | ||||||||
\(508\) | 22.0528 | 0.978437 | ||||||||
\(509\) | −7.92927 | −0.351459 | −0.175729 | − | 0.984439i | \(-0.556228\pi\) | ||||
−0.175729 | + | 0.984439i | \(0.556228\pi\) | |||||||
\(510\) | 0.486788 | 0.0215553 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 4.70723 | 0.208032 | ||||||||
\(513\) | −2.53514 | −0.111929 | ||||||||
\(514\) | 24.3081 | 1.07218 | ||||||||
\(515\) | −1.33123 | −0.0586610 | ||||||||
\(516\) | 17.0774 | 0.751791 | ||||||||
\(517\) | −10.2646 | −0.451437 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.52226 | −0.417981 | ||||||||
\(520\) | −0.0149060 | −0.000653670 0 | ||||||||
\(521\) | −14.0312 | −0.614716 | −0.307358 | − | 0.951594i | \(-0.599445\pi\) | ||||
−0.307358 | + | 0.951594i | \(0.599445\pi\) | |||||||
\(522\) | 0.496733 | 0.0217414 | ||||||||
\(523\) | 19.4953 | 0.852469 | 0.426234 | − | 0.904613i | \(-0.359840\pi\) | ||||
0.426234 | + | 0.904613i | \(0.359840\pi\) | |||||||
\(524\) | −12.7591 | −0.557384 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.2996 | −0.536289 | ||||||||
\(527\) | −13.5975 | −0.592316 | ||||||||
\(528\) | 0.696035 | 0.0302910 | ||||||||
\(529\) | −14.7253 | −0.640230 | ||||||||
\(530\) | 1.04579 | 0.0454262 | ||||||||
\(531\) | 1.41418 | 0.0613701 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.0164518 | 0.000712605 0 | ||||||||
\(534\) | −4.10089 | −0.177463 | ||||||||
\(535\) | −3.95080 | −0.170808 | ||||||||
\(536\) | −12.8827 | −0.556447 | ||||||||
\(537\) | −22.8105 | −0.984347 | ||||||||
\(538\) | −4.72367 | −0.203652 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.440879 | −0.0189724 | ||||||||
\(541\) | −13.5263 | −0.581541 | −0.290771 | − | 0.956793i | \(-0.593912\pi\) | ||||
−0.290771 | + | 0.956793i | \(0.593912\pi\) | |||||||
\(542\) | 4.44381 | 0.190878 | ||||||||
\(543\) | −3.16124 | −0.135662 | ||||||||
\(544\) | 10.3695 | 0.444587 | ||||||||
\(545\) | −4.68560 | −0.200709 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.4272 | 0.916162 | 0.458081 | − | 0.888911i | \(-0.348537\pi\) | ||||
0.458081 | + | 0.888911i | \(0.348537\pi\) | |||||||
\(548\) | 7.87494 | 0.336401 | ||||||||
\(549\) | −4.42492 | −0.188851 | ||||||||
\(550\) | −6.67351 | −0.284559 | ||||||||
\(551\) | −1.53582 | −0.0654283 | ||||||||
\(552\) | 7.84880 | 0.334067 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −16.7270 | −0.710664 | ||||||||
\(555\) | 0.636571 | 0.0270209 | ||||||||
\(556\) | −27.0437 | −1.14691 | ||||||||
\(557\) | −10.4798 | −0.444045 | −0.222022 | − | 0.975042i | \(-0.571266\pi\) | ||||
−0.222022 | + | 0.975042i | \(0.571266\pi\) | |||||||
\(558\) | −6.23601 | −0.263991 | ||||||||
\(559\) | −0.211610 | −0.00895015 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.97592 | 0.125643 | ||||||||
\(562\) | 4.12980 | 0.174205 | ||||||||
\(563\) | −31.3895 | −1.32291 | −0.661454 | − | 0.749986i | \(-0.730060\pi\) | ||||
−0.661454 | + | 0.749986i | \(0.730060\pi\) | |||||||
\(564\) | 8.18757 | 0.344759 | ||||||||
\(565\) | 1.18991 | 0.0500598 | ||||||||
\(566\) | 0.601061 | 0.0252645 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −15.8463 | −0.664898 | ||||||||
\(569\) | 6.23334 | 0.261315 | 0.130658 | − | 0.991428i | \(-0.458291\pi\) | ||||
0.130658 | + | 0.991428i | \(0.458291\pi\) | |||||||
\(570\) | −0.690250 | −0.0289114 | ||||||||
\(571\) | −23.9382 | −1.00178 | −0.500890 | − | 0.865511i | \(-0.666994\pi\) | ||||
−0.500890 | + | 0.865511i | \(0.666994\pi\) | |||||||
\(572\) | −0.0363577 | −0.00152019 | ||||||||
\(573\) | 5.66282 | 0.236568 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14.0657 | 0.586581 | ||||||||
\(576\) | 3.91926 | 0.163303 | ||||||||
\(577\) | 16.8790 | 0.702683 | 0.351341 | − | 0.936247i | \(-0.385726\pi\) | ||||
0.351341 | + | 0.936247i | \(0.385726\pi\) | |||||||
\(578\) | −11.3181 | −0.470771 | ||||||||
\(579\) | −20.1887 | −0.839012 | ||||||||
\(580\) | −0.267091 | −0.0110903 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 5.25414 | 0.217791 | ||||||||
\(583\) | 6.39331 | 0.264784 | ||||||||
\(584\) | −2.04251 | −0.0845198 | ||||||||
\(585\) | 0.00546303 | 0.000225868 0 | ||||||||
\(586\) | 8.13984 | 0.336254 | ||||||||
\(587\) | 14.5227 | 0.599416 | 0.299708 | − | 0.954031i | \(-0.403111\pi\) | ||||
0.299708 | + | 0.954031i | \(0.403111\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.2808 | 0.794453 | ||||||||
\(590\) | 0.385042 | 0.0158519 | ||||||||
\(591\) | 0.477679 | 0.0196491 | ||||||||
\(592\) | 0.801624 | 0.0329465 | ||||||||
\(593\) | −7.13395 | −0.292956 | −0.146478 | − | 0.989214i | \(-0.546794\pi\) | ||||
−0.146478 | + | 0.989214i | \(0.546794\pi\) | |||||||
\(594\) | 1.36480 | 0.0559984 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 20.9350 | 0.857529 | ||||||||
\(597\) | −3.25632 | −0.133272 | ||||||||
\(598\) | −0.0388036 | −0.00158680 | ||||||||
\(599\) | 5.13045 | 0.209624 | 0.104812 | − | 0.994492i | \(-0.466576\pi\) | ||||
0.104812 | + | 0.994492i | \(0.466576\pi\) | |||||||
\(600\) | 13.3417 | 0.544674 | ||||||||
\(601\) | 37.6827 | 1.53711 | 0.768554 | − | 0.639785i | \(-0.220977\pi\) | ||||
0.768554 | + | 0.639785i | \(0.220977\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.72149 | 0.192274 | ||||||||
\(604\) | −16.5467 | −0.673276 | ||||||||
\(605\) | −2.73269 | −0.111100 | ||||||||
\(606\) | −14.4262 | −0.586025 | ||||||||
\(607\) | −15.7766 | −0.640354 | −0.320177 | − | 0.947358i | \(-0.603742\pi\) | ||||
−0.320177 | + | 0.947358i | \(0.603742\pi\) | |||||||
\(608\) | −14.7036 | −0.596309 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.20478 | −0.0487803 | ||||||||
\(611\) | −0.101454 | −0.00410439 | ||||||||
\(612\) | −2.37374 | −0.0959528 | ||||||||
\(613\) | 28.8922 | 1.16694 | 0.583472 | − | 0.812133i | \(-0.301694\pi\) | ||||
0.583472 | + | 0.812133i | \(0.301694\pi\) | |||||||
\(614\) | 14.8243 | 0.598259 | ||||||||
\(615\) | 0.332064 | 0.0133901 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.0012 | −0.925993 | −0.462996 | − | 0.886360i | \(-0.653226\pi\) | ||||
−0.462996 | + | 0.886360i | \(0.653226\pi\) | |||||||
\(618\) | −3.28712 | −0.132227 | ||||||||
\(619\) | 13.3883 | 0.538121 | 0.269060 | − | 0.963123i | \(-0.413287\pi\) | ||||
0.269060 | + | 0.963123i | \(0.413287\pi\) | |||||||
\(620\) | 3.35307 | 0.134663 | ||||||||
\(621\) | −2.87658 | −0.115433 | ||||||||
\(622\) | 5.35852 | 0.214857 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.00687951 | 0.000275401 0 | ||||||||
\(625\) | 23.3582 | 0.934327 | ||||||||
\(626\) | 5.43237 | 0.217121 | ||||||||
\(627\) | −4.21976 | −0.168521 | ||||||||
\(628\) | 19.4565 | 0.776397 | ||||||||
\(629\) | 3.42737 | 0.136658 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.0230585 | −0.000917944 0 | −0.000458972 | − | 1.00000i | \(-0.500146\pi\) | ||||
−0.000458972 | 1.00000i | \(0.500146\pi\) | ||||||||
\(632\) | −12.2636 | −0.487821 | ||||||||
\(633\) | 0.492222 | 0.0195641 | ||||||||
\(634\) | 4.10699 | 0.163109 | ||||||||
\(635\) | −5.51554 | −0.218877 | ||||||||
\(636\) | −5.09962 | −0.202213 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.826815 | 0.0327339 | ||||||||
\(639\) | 5.80768 | 0.229748 | ||||||||
\(640\) | −2.78477 | −0.110078 | ||||||||
\(641\) | −1.14808 | −0.0453465 | −0.0226732 | − | 0.999743i | \(-0.507218\pi\) | ||||
−0.0226732 | + | 0.999743i | \(0.507218\pi\) | |||||||
\(642\) | −9.75543 | −0.385016 | ||||||||
\(643\) | 6.32451 | 0.249414 | 0.124707 | − | 0.992194i | \(-0.460201\pi\) | ||||
0.124707 | + | 0.992194i | \(0.460201\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.27115 | −0.168177 | ||||||||
\(646\) | −3.71639 | −0.146219 | ||||||||
\(647\) | 18.0069 | 0.707925 | 0.353963 | − | 0.935260i | \(-0.384834\pi\) | ||||
0.353963 | + | 0.935260i | \(0.384834\pi\) | |||||||
\(648\) | −2.72852 | −0.107186 | ||||||||
\(649\) | 2.35391 | 0.0923990 | ||||||||
\(650\) | −0.0659600 | −0.00258716 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.9172 | 0.545038 | ||||||||
\(653\) | −1.68150 | −0.0658021 | −0.0329010 | − | 0.999459i | \(-0.510475\pi\) | ||||
−0.0329010 | + | 0.999459i | \(0.510475\pi\) | |||||||
\(654\) | −11.5698 | −0.452416 | ||||||||
\(655\) | 3.19112 | 0.124687 | ||||||||
\(656\) | 0.418163 | 0.0163265 | ||||||||
\(657\) | 0.748580 | 0.0292049 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.1251 | 1.48514 | 0.742571 | − | 0.669767i | \(-0.233606\pi\) | ||||
0.742571 | + | 0.669767i | \(0.233606\pi\) | |||||||
\(660\) | −0.733847 | −0.0285649 | ||||||||
\(661\) | −7.33130 | −0.285154 | −0.142577 | − | 0.989784i | \(-0.545539\pi\) | ||||
−0.142577 | + | 0.989784i | \(0.545539\pi\) | |||||||
\(662\) | −1.69002 | −0.0656847 | ||||||||
\(663\) | 0.0294136 | 0.00114233 | ||||||||
\(664\) | −31.2528 | −1.21284 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.57184 | 0.0609076 | ||||||||
\(667\) | −1.74267 | −0.0674766 | ||||||||
\(668\) | −12.5487 | −0.485526 | ||||||||
\(669\) | 7.15813 | 0.276749 | ||||||||
\(670\) | 1.28554 | 0.0496646 | ||||||||
\(671\) | −7.36530 | −0.284334 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.6171 | 0.447806 | 0.223903 | − | 0.974611i | \(-0.428120\pi\) | ||||
0.223903 | + | 0.974611i | \(0.428120\pi\) | |||||||
\(674\) | 10.2978 | 0.396656 | ||||||||
\(675\) | −4.88973 | −0.188206 | ||||||||
\(676\) | 17.2597 | 0.663834 | ||||||||
\(677\) | 33.6999 | 1.29519 | 0.647597 | − | 0.761983i | \(-0.275774\pi\) | ||||
0.647597 | + | 0.761983i | \(0.275774\pi\) | |||||||
\(678\) | 2.93816 | 0.112839 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.61988 | −0.0621196 | ||||||||
\(681\) | −7.34618 | −0.281506 | ||||||||
\(682\) | −10.3799 | −0.397466 | ||||||||
\(683\) | 17.5803 | 0.672693 | 0.336346 | − | 0.941738i | \(-0.390809\pi\) | ||||
0.336346 | + | 0.941738i | \(0.390809\pi\) | |||||||
\(684\) | 3.36589 | 0.128698 | ||||||||
\(685\) | −1.96956 | −0.0752532 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.96063 | −0.380022 | ||||||||
\(688\) | −5.37860 | −0.205057 | ||||||||
\(689\) | 0.0631905 | 0.00240737 | ||||||||
\(690\) | −0.783215 | −0.0298165 | ||||||||
\(691\) | 8.94418 | 0.340252 | 0.170126 | − | 0.985422i | \(-0.445582\pi\) | ||||
0.170126 | + | 0.985422i | \(0.445582\pi\) | |||||||
\(692\) | 12.6427 | 0.480602 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.41365 | 0.357337 | ||||||||
\(695\) | 6.76379 | 0.256565 | ||||||||
\(696\) | −1.65297 | −0.0626558 | ||||||||
\(697\) | 1.78787 | 0.0677203 | ||||||||
\(698\) | 12.4829 | 0.472486 | ||||||||
\(699\) | −21.3065 | −0.805885 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.6138 | 1.49619 | 0.748097 | − | 0.663590i | \(-0.230968\pi\) | ||||
0.748097 | + | 0.663590i | \(0.230968\pi\) | |||||||
\(702\) | 0.0134895 | 0.000509128 0 | ||||||||
\(703\) | −4.85990 | −0.183295 | ||||||||
\(704\) | 6.52364 | 0.245869 | ||||||||
\(705\) | −2.04776 | −0.0771229 | ||||||||
\(706\) | 16.7366 | 0.629890 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.87760 | −0.0705644 | ||||||||
\(709\) | 17.1546 | 0.644256 | 0.322128 | − | 0.946696i | \(-0.395602\pi\) | ||||
0.322128 | + | 0.946696i | \(0.395602\pi\) | |||||||
\(710\) | 1.58127 | 0.0593441 | ||||||||
\(711\) | 4.49461 | 0.168561 | ||||||||
\(712\) | 13.6465 | 0.511425 | ||||||||
\(713\) | 21.8776 | 0.819324 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.00909325 | 0.000340068 0 | ||||||||
\(716\) | 30.2854 | 1.13182 | ||||||||
\(717\) | −10.7115 | −0.400028 | ||||||||
\(718\) | 24.7616 | 0.924094 | ||||||||
\(719\) | 11.0220 | 0.411053 | 0.205526 | − | 0.978652i | \(-0.434109\pi\) | ||||
0.205526 | + | 0.978652i | \(0.434109\pi\) | |||||||
\(720\) | 0.138857 | 0.00517488 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −10.3092 | −0.383668 | ||||||||
\(723\) | −15.3877 | −0.572276 | ||||||||
\(724\) | 4.19716 | 0.155986 | ||||||||
\(725\) | −2.96227 | −0.110016 | ||||||||
\(726\) | −6.74764 | −0.250429 | ||||||||
\(727\) | 25.4401 | 0.943520 | 0.471760 | − | 0.881727i | \(-0.343619\pi\) | ||||
0.471760 | + | 0.881727i | \(0.343619\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.203818 | 0.00754365 | ||||||||
\(731\) | −22.9964 | −0.850552 | ||||||||
\(732\) | 5.87494 | 0.217144 | ||||||||
\(733\) | −32.5187 | −1.20110 | −0.600552 | − | 0.799586i | \(-0.705053\pi\) | ||||
−0.600552 | + | 0.799586i | \(0.705053\pi\) | |||||||
\(734\) | 4.83244 | 0.178369 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −16.6839 | −0.614977 | ||||||||
\(737\) | 7.85896 | 0.289489 | ||||||||
\(738\) | 0.819942 | 0.0301825 | ||||||||
\(739\) | 19.0598 | 0.701126 | 0.350563 | − | 0.936539i | \(-0.385990\pi\) | ||||
0.350563 | + | 0.936539i | \(0.385990\pi\) | |||||||
\(740\) | −0.845172 | −0.0310691 | ||||||||
\(741\) | −0.0417075 | −0.00153216 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.1611 | 0.556207 | 0.278104 | − | 0.960551i | \(-0.410294\pi\) | ||||
0.278104 | + | 0.960551i | \(0.410294\pi\) | |||||||
\(744\) | 20.7515 | 0.760788 | ||||||||
\(745\) | −5.23594 | −0.191830 | ||||||||
\(746\) | 18.9144 | 0.692504 | ||||||||
\(747\) | 11.4541 | 0.419084 | ||||||||
\(748\) | −3.95111 | −0.144467 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2.69271 | −0.0983238 | ||||||||
\(751\) | −1.92281 | −0.0701645 | −0.0350822 | − | 0.999384i | \(-0.511169\pi\) | ||||
−0.0350822 | + | 0.999384i | \(0.511169\pi\) | |||||||
\(752\) | −2.57871 | −0.0940358 | ||||||||
\(753\) | −3.83734 | −0.139840 | ||||||||
\(754\) | 0.00817212 | 0.000297611 0 | ||||||||
\(755\) | 4.13842 | 0.150613 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.5738 | −0.566041 | −0.283021 | − | 0.959114i | \(-0.591336\pi\) | ||||
−0.283021 | + | 0.959114i | \(0.591336\pi\) | |||||||
\(758\) | 13.1028 | 0.475914 | ||||||||
\(759\) | −4.78809 | −0.173797 | ||||||||
\(760\) | 2.29694 | 0.0833189 | ||||||||
\(761\) | −52.7733 | −1.91303 | −0.956515 | − | 0.291683i | \(-0.905785\pi\) | ||||
−0.956515 | + | 0.291683i | \(0.905785\pi\) | |||||||
\(762\) | −13.6191 | −0.493369 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −7.51850 | −0.272010 | ||||||||
\(765\) | 0.593686 | 0.0214648 | ||||||||
\(766\) | −23.3653 | −0.844222 | ||||||||
\(767\) | 0.0232657 | 0.000840076 0 | ||||||||
\(768\) | −14.7148 | −0.530973 | ||||||||
\(769\) | 23.4101 | 0.844189 | 0.422095 | − | 0.906552i | \(-0.361295\pi\) | ||||
0.422095 | + | 0.906552i | \(0.361295\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29.6461 | 1.06768 | ||||||||
\(772\) | 26.8044 | 0.964710 | ||||||||
\(773\) | −5.06047 | −0.182012 | −0.0910062 | − | 0.995850i | \(-0.529008\pi\) | ||||
−0.0910062 | + | 0.995850i | \(0.529008\pi\) | |||||||
\(774\) | −10.5465 | −0.379085 | ||||||||
\(775\) | 37.1885 | 1.33585 | ||||||||
\(776\) | −17.4842 | −0.627646 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.62819 | 0.130077 | ||||||||
\(779\) | −2.53514 | −0.0908309 | ||||||||
\(780\) | −0.00725323 | −0.000259707 0 | ||||||||
\(781\) | 9.66692 | 0.345910 | ||||||||
\(782\) | −4.21692 | −0.150797 | ||||||||
\(783\) | 0.605814 | 0.0216500 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.86617 | −0.173681 | ||||||||
\(786\) | 7.87961 | 0.281056 | ||||||||
\(787\) | −36.6471 | −1.30633 | −0.653164 | − | 0.757216i | \(-0.726559\pi\) | ||||
−0.653164 | + | 0.757216i | \(0.726559\pi\) | |||||||
\(788\) | −0.634211 | −0.0225928 | ||||||||
\(789\) | −15.0006 | −0.534035 | ||||||||
\(790\) | 1.22376 | 0.0435395 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −4.54164 | −0.161380 | ||||||||
\(793\) | −0.0727976 | −0.00258512 | ||||||||
\(794\) | 25.4673 | 0.903802 | ||||||||
\(795\) | 1.27544 | 0.0452353 | ||||||||
\(796\) | 4.32340 | 0.153239 | ||||||||
\(797\) | −2.67790 | −0.0948562 | −0.0474281 | − | 0.998875i | \(-0.515103\pi\) | ||||
−0.0474281 | + | 0.998875i | \(0.515103\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.0253 | −0.390049 | ||||||||
\(800\) | −28.3600 | −1.00268 | ||||||||
\(801\) | −5.00144 | −0.176717 | ||||||||
\(802\) | −1.86203 | −0.0657507 | ||||||||
\(803\) | 1.24602 | 0.0439710 | ||||||||
\(804\) | −6.26870 | −0.221080 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.102593 | −0.00361370 | ||||||||
\(807\) | −5.76098 | −0.202796 | ||||||||
\(808\) | 48.0061 | 1.68885 | ||||||||
\(809\) | −26.0424 | −0.915603 | −0.457801 | − | 0.889055i | \(-0.651363\pi\) | ||||
−0.457801 | + | 0.889055i | \(0.651363\pi\) | |||||||
\(810\) | 0.272273 | 0.00956670 | ||||||||
\(811\) | −0.407542 | −0.0143108 | −0.00715538 | − | 0.999974i | \(-0.502278\pi\) | ||||
−0.00715538 | + | 0.999974i | \(0.502278\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.41966 | 0.190076 | ||||||||
\(814\) | 2.61634 | 0.0917027 | ||||||||
\(815\) | −3.48076 | −0.121926 | ||||||||
\(816\) | 0.747619 | 0.0261719 | ||||||||
\(817\) | 32.6082 | 1.14081 | ||||||||
\(818\) | 4.35701 | 0.152339 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.440879 | −0.0153962 | ||||||||
\(821\) | −38.1013 | −1.32974 | −0.664871 | − | 0.746958i | \(-0.731514\pi\) | ||||
−0.664871 | + | 0.746958i | \(0.731514\pi\) | |||||||
\(822\) | −4.86331 | −0.169628 | ||||||||
\(823\) | −3.55328 | −0.123860 | −0.0619298 | − | 0.998081i | \(-0.519725\pi\) | ||||
−0.0619298 | + | 0.998081i | \(0.519725\pi\) | |||||||
\(824\) | 10.9385 | 0.381062 | ||||||||
\(825\) | −8.13900 | −0.283364 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.3979 | 0.431118 | 0.215559 | − | 0.976491i | \(-0.430843\pi\) | ||||
0.215559 | + | 0.976491i | \(0.430843\pi\) | |||||||
\(828\) | 3.81922 | 0.132727 | ||||||||
\(829\) | 25.6106 | 0.889492 | 0.444746 | − | 0.895657i | \(-0.353294\pi\) | ||||
0.444746 | + | 0.895657i | \(0.353294\pi\) | |||||||
\(830\) | 3.11865 | 0.108250 | ||||||||
\(831\) | −20.4003 | −0.707678 | ||||||||
\(832\) | 0.0644787 | 0.00223540 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 16.7014 | 0.578321 | ||||||||
\(835\) | 3.13851 | 0.108613 | ||||||||
\(836\) | 5.60256 | 0.193768 | ||||||||
\(837\) | −7.60543 | −0.262882 | ||||||||
\(838\) | 13.4004 | 0.462908 | ||||||||
\(839\) | −20.2672 | −0.699703 | −0.349851 | − | 0.936805i | \(-0.613768\pi\) | ||||
−0.349851 | + | 0.936805i | \(0.613768\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.6330 | −0.987344 | ||||||||
\(842\) | −6.18264 | −0.213068 | ||||||||
\(843\) | 5.03670 | 0.173473 | ||||||||
\(844\) | −0.653521 | −0.0224951 | ||||||||
\(845\) | −4.31674 | −0.148500 | ||||||||
\(846\) | −5.05638 | −0.173842 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.60615 | 0.0551553 | ||||||||
\(849\) | 0.733053 | 0.0251583 | ||||||||
\(850\) | −7.16810 | −0.245864 | ||||||||
\(851\) | −5.51445 | −0.189033 | ||||||||
\(852\) | −7.71082 | −0.264168 | ||||||||
\(853\) | 17.4438 | 0.597264 | 0.298632 | − | 0.954368i | \(-0.403470\pi\) | ||||
0.298632 | + | 0.954368i | \(0.403470\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.841828 | −0.0287899 | ||||||||
\(856\) | 32.4631 | 1.10957 | ||||||||
\(857\) | 38.4532 | 1.31354 | 0.656769 | − | 0.754092i | \(-0.271923\pi\) | ||||
0.656769 | + | 0.754092i | \(0.271923\pi\) | |||||||
\(858\) | 0.0224534 | 0.000766545 0 | ||||||||
\(859\) | −1.73122 | −0.0590686 | −0.0295343 | − | 0.999564i | \(-0.509402\pi\) | ||||
−0.0295343 | + | 0.999564i | \(0.509402\pi\) | |||||||
\(860\) | 5.67079 | 0.193372 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.74237 | 0.229646 | ||||||||
\(863\) | −22.5174 | −0.766502 | −0.383251 | − | 0.923644i | \(-0.625196\pi\) | ||||
−0.383251 | + | 0.923644i | \(0.625196\pi\) | |||||||
\(864\) | 5.79990 | 0.197317 | ||||||||
\(865\) | −3.16200 | −0.107511 | ||||||||
\(866\) | 5.00233 | 0.169986 | ||||||||
\(867\) | −13.8035 | −0.468792 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.48131 | 0.253786 | ||||||||
\(870\) | 0.164947 | 0.00559222 | ||||||||
\(871\) | 0.0776769 | 0.00263198 | ||||||||
\(872\) | 38.5009 | 1.30380 | ||||||||
\(873\) | 6.40794 | 0.216876 | ||||||||
\(874\) | 5.97946 | 0.202258 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.993886 | −0.0335803 | ||||||||
\(877\) | −4.48494 | −0.151446 | −0.0757228 | − | 0.997129i | \(-0.524126\pi\) | ||||
−0.0757228 | + | 0.997129i | \(0.524126\pi\) | |||||||
\(878\) | −13.8365 | −0.466959 | ||||||||
\(879\) | 9.92734 | 0.334841 | ||||||||
\(880\) | 0.231128 | 0.00779132 | ||||||||
\(881\) | −40.1306 | −1.35203 | −0.676016 | − | 0.736887i | \(-0.736295\pi\) | ||||
−0.676016 | + | 0.736887i | \(0.736295\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.5050 | −0.521784 | −0.260892 | − | 0.965368i | \(-0.584017\pi\) | ||||
−0.260892 | + | 0.965368i | \(0.584017\pi\) | |||||||
\(884\) | −0.0390522 | −0.00131347 | ||||||||
\(885\) | 0.469597 | 0.0157853 | ||||||||
\(886\) | −20.2423 | −0.680053 | ||||||||
\(887\) | −38.3024 | −1.28607 | −0.643034 | − | 0.765838i | \(-0.722325\pi\) | ||||
−0.643034 | + | 0.765838i | \(0.722325\pi\) | |||||||
\(888\) | −5.23061 | −0.175528 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1.36176 | −0.0456462 | ||||||||
\(891\) | 1.66451 | 0.0557631 | ||||||||
\(892\) | −9.50381 | −0.318211 | ||||||||
\(893\) | 15.6336 | 0.523158 | ||||||||
\(894\) | −12.9288 | −0.432403 | ||||||||
\(895\) | −7.57454 | −0.253189 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.0473248 | −0.00158013 | ||||||||
\(898\) | 1.48815 | 0.0496601 | ||||||||
\(899\) | −4.60747 | −0.153668 | ||||||||
\(900\) | 6.49207 | 0.216402 | ||||||||
\(901\) | 6.86713 | 0.228777 | ||||||||
\(902\) | 1.36480 | 0.0454429 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.77730 | −0.325188 | ||||||||
\(905\) | −1.04973 | −0.0348943 | ||||||||
\(906\) | 10.2187 | 0.339494 | ||||||||
\(907\) | −47.6553 | −1.58237 | −0.791184 | − | 0.611578i | \(-0.790535\pi\) | ||||
−0.791184 | + | 0.611578i | \(0.790535\pi\) | |||||||
\(908\) | 9.75348 | 0.323681 | ||||||||
\(909\) | −17.5942 | −0.583562 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −49.7822 | −1.64936 | −0.824679 | − | 0.565601i | \(-0.808644\pi\) | ||||
−0.824679 | + | 0.565601i | \(0.808644\pi\) | |||||||
\(912\) | −1.06010 | −0.0351035 | ||||||||
\(913\) | 19.0655 | 0.630975 | ||||||||
\(914\) | 23.0444 | 0.762240 | ||||||||
\(915\) | −1.46935 | −0.0485753 | ||||||||
\(916\) | 13.2247 | 0.436956 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.46595 | 0.0483835 | ||||||||
\(919\) | 58.0170 | 1.91381 | 0.956903 | − | 0.290409i | \(-0.0937914\pi\) | ||||
0.956903 | + | 0.290409i | \(0.0937914\pi\) | |||||||
\(920\) | 2.60630 | 0.0859272 | ||||||||
\(921\) | 18.0797 | 0.595745 | ||||||||
\(922\) | 22.5835 | 0.743749 | ||||||||
\(923\) | 0.0955465 | 0.00314495 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.37369 | −0.308205 | ||||||||
\(926\) | −19.5169 | −0.641365 | ||||||||
\(927\) | −4.00896 | −0.131672 | ||||||||
\(928\) | 3.51366 | 0.115342 | ||||||||
\(929\) | 57.4678 | 1.88546 | 0.942728 | − | 0.333561i | \(-0.108250\pi\) | ||||
0.942728 | + | 0.333561i | \(0.108250\pi\) | |||||||
\(930\) | −2.07075 | −0.0679026 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 28.2885 | 0.926620 | ||||||||
\(933\) | 6.53524 | 0.213954 | ||||||||
\(934\) | −3.36950 | −0.110254 | ||||||||
\(935\) | 0.988194 | 0.0323174 | ||||||||
\(936\) | −0.0448889 | −0.00146724 | ||||||||
\(937\) | −3.15232 | −0.102982 | −0.0514909 | − | 0.998673i | \(-0.516397\pi\) | ||||
−0.0514909 | + | 0.998673i | \(0.516397\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.62531 | 0.216209 | ||||||||
\(940\) | 2.71879 | 0.0886773 | ||||||||
\(941\) | −6.38432 | −0.208123 | −0.104062 | − | 0.994571i | \(-0.533184\pi\) | ||||
−0.104062 | + | 0.994571i | \(0.533184\pi\) | |||||||
\(942\) | −12.0157 | −0.391493 | ||||||||
\(943\) | −2.87658 | −0.0936744 | ||||||||
\(944\) | 0.591356 | 0.0192470 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17.5547 | −0.570752 | ||||||||
\(947\) | 4.84026 | 0.157287 | 0.0786436 | − | 0.996903i | \(-0.474941\pi\) | ||||
0.0786436 | + | 0.996903i | \(0.474941\pi\) | |||||||
\(948\) | −5.96747 | −0.193814 | ||||||||
\(949\) | 0.0123155 | 0.000399777 0 | ||||||||
\(950\) | 10.1641 | 0.329768 | ||||||||
\(951\) | 5.00888 | 0.162424 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −47.9739 | −1.55403 | −0.777014 | − | 0.629484i | \(-0.783266\pi\) | ||||
−0.777014 | + | 0.629484i | \(0.783266\pi\) | |||||||
\(954\) | 3.14937 | 0.101964 | ||||||||
\(955\) | 1.88042 | 0.0608488 | ||||||||
\(956\) | 14.2216 | 0.459959 | ||||||||
\(957\) | 1.00838 | 0.0325964 | ||||||||
\(958\) | 9.29680 | 0.300366 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.30144 | 0.0420039 | ||||||||
\(961\) | 26.8425 | 0.865887 | ||||||||
\(962\) | 0.0258596 | 0.000833745 0 | ||||||||
\(963\) | −11.8977 | −0.383398 | ||||||||
\(964\) | 20.4302 | 0.658013 | ||||||||
\(965\) | −6.70392 | −0.215807 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.25867 | 0.169107 | 0.0845537 | − | 0.996419i | \(-0.473054\pi\) | ||||
0.0845537 | + | 0.996419i | \(0.473054\pi\) | |||||||
\(968\) | 22.4541 | 0.721702 | ||||||||
\(969\) | −4.53250 | −0.145605 | ||||||||
\(970\) | 1.74471 | 0.0560193 | ||||||||
\(971\) | −56.4143 | −1.81042 | −0.905210 | − | 0.424964i | \(-0.860287\pi\) | ||||
−0.905210 | + | 0.424964i | \(0.860287\pi\) | |||||||
\(972\) | −1.32769 | −0.0425858 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 8.11320 | 0.259964 | ||||||||
\(975\) | −0.0804447 | −0.00257629 | ||||||||
\(976\) | −1.85033 | −0.0592277 | ||||||||
\(977\) | 6.39439 | 0.204575 | 0.102287 | − | 0.994755i | \(-0.467384\pi\) | ||||
0.102287 | + | 0.994755i | \(0.467384\pi\) | |||||||
\(978\) | −8.59480 | −0.274832 | ||||||||
\(979\) | −8.32494 | −0.266066 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.1105 | −0.450515 | ||||||||
\(982\) | 20.6906 | 0.660264 | ||||||||
\(983\) | 25.9542 | 0.827809 | 0.413905 | − | 0.910320i | \(-0.364165\pi\) | ||||
0.413905 | + | 0.910320i | \(0.364165\pi\) | |||||||
\(984\) | −2.72852 | −0.0869820 | ||||||||
\(985\) | 0.158620 | 0.00505404 | ||||||||
\(986\) | 0.888092 | 0.0282826 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.0553749 | 0.00176171 | ||||||||
\(989\) | 36.9999 | 1.17653 | ||||||||
\(990\) | 0.453200 | 0.0144037 | ||||||||
\(991\) | 48.0216 | 1.52546 | 0.762728 | − | 0.646719i | \(-0.223859\pi\) | ||||
0.762728 | + | 0.646719i | \(0.223859\pi\) | |||||||
\(992\) | −44.1107 | −1.40052 | ||||||||
\(993\) | −2.06115 | −0.0654086 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.08131 | −0.0342797 | ||||||||
\(996\) | −15.2076 | −0.481870 | ||||||||
\(997\) | 48.7312 | 1.54333 | 0.771667 | − | 0.636027i | \(-0.219423\pi\) | ||||
0.771667 | + | 0.636027i | \(0.219423\pi\) | |||||||
\(998\) | −0.902973 | −0.0285831 | ||||||||
\(999\) | 1.91702 | 0.0606517 |
(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 | 6027.2.a.bm.1.11 | yes | 16 | |
7.6 | odd | 2 | 6027.2.a.bl.1.11 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.bl.1.11 | ✓ | 16 | 7.6 | odd | 2 | ||
6027.2.a.bm.1.11 | yes | 16 | 1.1 | even | 1 | trivial |