Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(89,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.bb (of order \(6\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.12745506816.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 8x^{6} + 55x^{4} - 72x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 269.3 | ||
Root | \(2.23256 + 1.28897i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.269 |
Dual form | 315.2.bb.a.89.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | − | 1.73205i | 0.500000 | − | 0.866025i | ||||
\(5\) | 1.00781 | − | 1.99607i | 0.450708 | − | 0.892672i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.32288 | + | 2.29129i | 0.500000 | + | 0.866025i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.44949 | − | 1.41421i | −0.738549 | − | 0.426401i | 0.0829925 | − | 0.996550i | \(-0.473552\pi\) |
−0.821541 | + | 0.570149i | \(0.806886\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.64575 | 0.733799 | 0.366900 | − | 0.930261i | \(-0.380419\pi\) | ||||
0.366900 | + | 0.930261i | \(0.380419\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(17\) | −3.24037 | − | 1.87083i | −0.785905 | − | 0.453743i | 0.0526138 | − | 0.998615i | \(-0.483245\pi\) |
−0.838519 | + | 0.544872i | \(0.816578\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.50000 | − | 0.866025i | 0.344124 | − | 0.198680i | −0.317970 | − | 0.948101i | \(-0.603001\pi\) |
0.662094 | + | 0.749421i | \(0.269668\pi\) | |||||||
\(20\) | −2.44949 | − | 3.74166i | −0.547723 | − | 0.836660i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.24037 | + | 5.61249i | 0.675664 | + | 1.17028i | 0.976274 | + | 0.216537i | \(0.0694763\pi\) |
−0.300610 | + | 0.953747i | \(0.597190\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.96863 | − | 4.02334i | −0.593725 | − | 0.804668i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.29150 | 1.00000 | ||||||||
\(29\) | − | 1.41421i | − | 0.262613i | −0.991342 | − | 0.131306i | \(-0.958083\pi\) | ||
0.991342 | − | 0.131306i | \(-0.0419172\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.50000 | + | 2.59808i | 0.808224 | + | 0.466628i | 0.846339 | − | 0.532645i | \(-0.178802\pi\) |
−0.0381148 | + | 0.999273i | \(0.512135\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.90679 | − | 0.331369i | 0.998430 | − | 0.0560116i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.96863 | + | 2.29129i | −0.652438 | + | 0.376685i | −0.789390 | − | 0.613892i | \(-0.789603\pi\) |
0.136951 | + | 0.990578i | \(0.456270\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.89898 | 0.765092 | 0.382546 | − | 0.923936i | \(-0.375047\pi\) | ||||
0.382546 | + | 0.923936i | \(0.375047\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.58258i | 0.698836i | 0.936967 | + | 0.349418i | \(0.113621\pi\) | ||||
−0.936967 | + | 0.349418i | \(0.886379\pi\) | |||||||
\(44\) | −4.89898 | + | 2.82843i | −0.738549 | + | 0.426401i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.24037 | − | 1.87083i | 0.472657 | − | 0.272888i | −0.244695 | − | 0.969600i | \(-0.578688\pi\) |
0.717351 | + | 0.696712i | \(0.245354\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.50000 | + | 6.06218i | −0.500000 | + | 0.866025i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.64575 | − | 4.58258i | 0.366900 | − | 0.635489i | ||||
\(53\) | −6.48074 | + | 11.2250i | −0.890198 | + | 1.54187i | −0.0505609 | + | 0.998721i | \(0.516101\pi\) |
−0.839637 | + | 0.543148i | \(0.817232\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.29150 | + | 3.46410i | −0.713506 | + | 0.467099i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.67423 | − | 6.36396i | 0.478345 | − | 0.828517i | −0.521347 | − | 0.853345i | \(-0.674570\pi\) |
0.999692 | + | 0.0248275i | \(0.00790366\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.00000 | + | 5.19615i | −1.15233 | + | 0.665299i | −0.949454 | − | 0.313905i | \(-0.898363\pi\) |
−0.202878 | + | 0.979204i | \(0.565029\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 2.66642 | − | 5.28112i | 0.330729 | − | 0.655042i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.9059 | − | 6.87386i | −1.45453 | − | 0.839776i | −0.455801 | − | 0.890082i | \(-0.650647\pi\) |
−0.998734 | + | 0.0503056i | \(0.983980\pi\) | |||||||
\(68\) | −6.48074 | + | 3.74166i | −0.785905 | + | 0.453743i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.3137i | 1.34269i | 0.741145 | + | 0.671345i | \(0.234283\pi\) | ||||
−0.741145 | + | 0.671345i | \(0.765717\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.61438 | − | 11.4564i | 0.774154 | − | 1.34087i | −0.161114 | − | 0.986936i | \(-0.551509\pi\) |
0.935269 | − | 0.353939i | \(-0.115158\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 3.46410i | − | 0.397360i | ||||||
\(77\) | − | 7.48331i | − | 0.852803i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.50000 | + | 6.06218i | 0.393781 | + | 0.682048i | 0.992945 | − | 0.118578i | \(-0.0378336\pi\) |
−0.599164 | + | 0.800626i | \(0.704500\pi\) | |||||||
\(80\) | −8.93023 | + | 0.500983i | −0.998430 | + | 0.0560116i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.9666i | 1.64280i | 0.570352 | + | 0.821401i | \(0.306807\pi\) | ||||
−0.570352 | + | 0.821401i | \(0.693193\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.00000 | + | 4.58258i | −0.759257 | + | 0.497050i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.57321 | + | 14.8492i | 0.908759 | + | 1.57402i | 0.815791 | + | 0.578347i | \(0.196302\pi\) |
0.0929683 | + | 0.995669i | \(0.470364\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.50000 | + | 6.06218i | 0.366900 | + | 0.635489i | ||||
\(92\) | 12.9615 | 1.35133 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.216932 | − | 3.86690i | −0.0222568 | − | 0.396736i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.29150 | −0.537271 | −0.268635 | − | 0.963242i | \(-0.586573\pi\) | ||||
−0.268635 | + | 0.963242i | \(0.586573\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9.93725 | + | 1.11847i | −0.993725 | + | 0.111847i | ||||
\(101\) | 4.89898 | − | 8.48528i | 0.487467 | − | 0.844317i | −0.512429 | − | 0.858729i | \(-0.671254\pi\) |
0.999896 | + | 0.0144123i | \(0.00458773\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.61438 | + | 11.4564i | 0.651734 | + | 1.12884i | 0.982702 | + | 0.185194i | \(0.0592915\pi\) |
−0.330968 | + | 0.943642i | \(0.607375\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.24037 | − | 5.61249i | −0.313258 | − | 0.542580i | 0.665807 | − | 0.746124i | \(-0.268087\pi\) |
−0.979066 | + | 0.203544i | \(0.934754\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.50000 | − | 6.06218i | 0.335239 | − | 0.580651i | −0.648292 | − | 0.761392i | \(-0.724516\pi\) |
0.983531 | + | 0.180741i | \(0.0578495\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.29150 | − | 9.16515i | 0.500000 | − | 0.866025i | ||||
\(113\) | 6.48074 | 0.609657 | 0.304828 | − | 0.952407i | \(-0.401401\pi\) | ||||
0.304828 | + | 0.952407i | \(0.401401\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.4686 | − | 0.811686i | 1.34921 | − | 0.0756901i | ||||
\(116\) | −2.44949 | − | 1.41421i | −0.227429 | − | 0.131306i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 9.89949i | − | 0.907485i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.50000 | − | 2.59808i | −0.136364 | − | 0.236189i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.00000 | − | 5.19615i | 0.808224 | − | 0.466628i | ||||
\(125\) | −11.0227 | + | 1.87083i | −0.985901 | + | 0.167332i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.7477i | 1.21991i | 0.792435 | + | 0.609957i | \(0.208813\pi\) | ||||
−0.792435 | + | 0.609957i | \(0.791187\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.57321 | − | 14.8492i | −0.749045 | − | 1.29738i | −0.948281 | − | 0.317433i | \(-0.897179\pi\) |
0.199236 | − | 0.979952i | \(-0.436154\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.96863 | + | 2.29129i | 0.344124 | + | 0.198680i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.24037 | + | 5.61249i | −0.276844 | + | 0.479507i | −0.970599 | − | 0.240704i | \(-0.922622\pi\) |
0.693755 | + | 0.720211i | \(0.255955\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 8.66025i | − | 0.734553i | −0.930112 | − | 0.367277i | \(-0.880290\pi\) | ||
0.930112 | − | 0.367277i | \(-0.119710\pi\) | |||||||
\(140\) | 5.33284 | − | 10.5622i | 0.450708 | − | 0.892672i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.48074 | − | 3.74166i | −0.541947 | − | 0.312893i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.82288 | − | 1.42526i | −0.234427 | − | 0.118362i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.16515i | 0.753371i | ||||||||
\(149\) | −12.2474 | + | 7.07107i | −1.00335 | + | 0.579284i | −0.909238 | − | 0.416277i | \(-0.863335\pi\) |
−0.0941123 | + | 0.995562i | \(0.530001\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.00000 | − | 8.66025i | 0.406894 | − | 0.704761i | −0.587646 | − | 0.809118i | \(-0.699945\pi\) |
0.994540 | + | 0.104357i | \(0.0332784\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.72111 | − | 6.36396i | 0.780818 | − | 0.511166i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.64575 | − | 4.58258i | 0.211154 | − | 0.365729i | −0.740922 | − | 0.671591i | \(-0.765611\pi\) |
0.952076 | + | 0.305862i | \(0.0989445\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.57321 | + | 14.8492i | −0.675664 | + | 1.17028i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.93725 | − | 4.58258i | 0.621694 | − | 0.358935i | −0.155834 | − | 0.987783i | \(-0.549807\pi\) |
0.777528 | + | 0.628848i | \(0.216473\pi\) | |||||||
\(164\) | 4.89898 | − | 8.48528i | 0.382546 | − | 0.662589i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 7.48331i | − | 0.579076i | −0.957166 | − | 0.289538i | \(-0.906498\pi\) | ||
0.957166 | − | 0.289538i | \(-0.0935017\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.00000 | −0.461538 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.93725 | + | 4.58258i | 0.605210 | + | 0.349418i | ||||
\(173\) | 12.9615 | − | 7.48331i | 0.985443 | − | 0.568946i | 0.0815341 | − | 0.996671i | \(-0.474018\pi\) |
0.903909 | + | 0.427725i | \(0.140685\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.29150 | − | 12.1244i | 0.400000 | − | 0.916515i | ||||
\(176\) | 11.3137i | 0.852803i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.12372 | − | 3.53553i | −0.457709 | − | 0.264258i | 0.253372 | − | 0.967369i | \(-0.418460\pi\) |
−0.711080 | + | 0.703111i | \(0.751794\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 15.5885i | − | 1.15868i | −0.815086 | − | 0.579340i | \(-0.803310\pi\) | ||
0.815086 | − | 0.579340i | \(-0.196690\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.573948 | + | 10.2309i | 0.0421975 | + | 0.752188i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.29150 | + | 9.16515i | 0.386953 | + | 0.670222i | ||||
\(188\) | − | 7.48331i | − | 0.545777i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.4722 | − | 7.77817i | 0.974814 | − | 0.562809i | 0.0741134 | − | 0.997250i | \(-0.476387\pi\) |
0.900700 | + | 0.434441i | \(0.143054\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.9059 | − | 6.87386i | −0.857004 | − | 0.494792i | 0.00600382 | − | 0.999982i | \(-0.498089\pi\) |
−0.863008 | + | 0.505190i | \(0.831422\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.00000 | + | 12.1244i | 0.500000 | + | 0.866025i | ||||
\(197\) | −19.4422 | −1.38520 | −0.692600 | − | 0.721321i | \(-0.743535\pi\) | ||||
−0.692600 | + | 0.721321i | \(0.743535\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.00000 | + | 3.46410i | 0.425329 | + | 0.245564i | 0.697355 | − | 0.716726i | \(-0.254360\pi\) |
−0.272026 | + | 0.962290i | \(0.587694\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.24037 | − | 1.87083i | 0.227429 | − | 0.131306i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.93725 | − | 9.77873i | 0.344833 | − | 0.682976i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.29150 | − | 9.16515i | −0.366900 | − | 0.635489i | ||||
\(209\) | −4.89898 | −0.338869 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.0000 | 0.963800 | 0.481900 | − | 0.876226i | \(-0.339947\pi\) | ||||
0.481900 | + | 0.876226i | \(0.339947\pi\) | |||||||
\(212\) | 12.9615 | + | 22.4499i | 0.890198 | + | 1.54187i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.14716 | + | 4.61838i | 0.623831 | + | 0.314971i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.7477i | 0.933257i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.708497 | + | 12.6293i | 0.0477669 | + | 0.851464i | ||||
\(221\) | −8.57321 | − | 4.94975i | −0.576697 | − | 0.332956i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.29150 | −0.354345 | −0.177173 | − | 0.984180i | \(-0.556695\pi\) | ||||
−0.177173 | + | 0.984180i | \(0.556695\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.9615 | − | 7.48331i | −0.860284 | − | 0.496685i | 0.00382356 | − | 0.999993i | \(-0.498783\pi\) |
−0.864107 | + | 0.503308i | \(0.832116\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.50000 | + | 0.866025i | −0.0991228 | + | 0.0572286i | −0.548742 | − | 0.835992i | \(-0.684893\pi\) |
0.449619 | + | 0.893220i | \(0.351560\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.24037 | − | 5.61249i | −0.212284 | − | 0.367686i | 0.740145 | − | 0.672447i | \(-0.234757\pi\) |
−0.952429 | + | 0.304761i | \(0.901423\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.468627 | − | 8.35347i | −0.0305699 | − | 0.544920i | ||||
\(236\) | −7.34847 | − | 12.7279i | −0.478345 | − | 0.828517i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 18.3848i | − | 1.18921i | −0.804017 | − | 0.594606i | \(-0.797308\pi\) | ||
0.804017 | − | 0.594606i | \(-0.202692\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.0000 | − | 8.66025i | −0.966235 | − | 0.557856i | −0.0681486 | − | 0.997675i | \(-0.521709\pi\) |
−0.898086 | + | 0.439819i | \(0.855043\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 20.7846i | 1.33060i | ||||||||
\(245\) | 8.57321 | + | 13.0958i | 0.547723 | + | 0.836660i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.96863 | − | 2.29129i | 0.252518 | − | 0.145791i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.0454 | 1.39149 | 0.695747 | − | 0.718287i | \(-0.255074\pi\) | ||||
0.695747 | + | 0.718287i | \(0.255074\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 18.3303i | − | 1.15242i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | −6.48074 | + | 3.74166i | −0.404257 | + | 0.233398i | −0.688319 | − | 0.725408i | \(-0.741651\pi\) |
0.284062 | + | 0.958806i | \(0.408318\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.5000 | − | 6.06218i | −0.652438 | − | 0.376685i | ||||
\(260\) | −6.48074 | − | 9.89949i | −0.401918 | − | 0.613941i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.48074 | − | 11.2250i | 0.399620 | − | 0.692161i | −0.594059 | − | 0.804421i | \(-0.702476\pi\) |
0.993679 | + | 0.112260i | \(0.0358089\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.8745 | + | 24.2487i | 0.975163 | + | 1.48959i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −23.8118 | + | 13.7477i | −1.45453 | + | 0.839776i | ||||
\(269\) | −8.57321 | + | 14.8492i | −0.522718 | + | 0.905374i | 0.476932 | + | 0.878940i | \(0.341749\pi\) |
−0.999651 | + | 0.0264343i | \(0.991585\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.0000 | + | 6.92820i | −0.728948 | + | 0.420858i | −0.818037 | − | 0.575165i | \(-0.804938\pi\) |
0.0890891 | + | 0.996024i | \(0.471604\pi\) | |||||||
\(272\) | 14.9666i | 0.907485i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.58176 | + | 14.0534i | 0.0953838 | + | 0.847452i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.96863 | + | 2.29129i | 0.238452 | + | 0.137670i | 0.614465 | − | 0.788944i | \(-0.289372\pi\) |
−0.376013 | + | 0.926614i | \(0.622705\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.2843i | 1.68730i | 0.536895 | + | 0.843649i | \(0.319597\pi\) | ||||
−0.536895 | + | 0.843649i | \(0.680403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.26013 | + | 16.0390i | −0.550458 | + | 0.953420i | 0.447784 | + | 0.894142i | \(0.352213\pi\) |
−0.998241 | + | 0.0592787i | \(0.981120\pi\) | |||||||
\(284\) | 19.5959 | + | 11.3137i | 1.16280 | + | 0.671345i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.48074 | + | 11.2250i | 0.382546 | + | 0.662589i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.50000 | − | 2.59808i | −0.0882353 | − | 0.152828i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −13.2288 | − | 22.9129i | −0.774154 | − | 1.34087i | ||||
\(293\) | − | 29.9333i | − | 1.74872i | −0.485278 | − | 0.874360i | \(-0.661282\pi\) | ||
0.485278 | − | 0.874360i | \(-0.338718\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.00000 | − | 13.7477i | −0.524000 | − | 0.800424i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.57321 | + | 14.8492i | 0.495802 | + | 0.858754i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.5000 | + | 6.06218i | −0.605210 | + | 0.349418i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.00000 | − | 3.46410i | −0.344124 | − | 0.198680i | ||||
\(305\) | 1.30159 | + | 23.2014i | 0.0745290 | + | 1.32851i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.64575 | 0.151001 | 0.0755005 | − | 0.997146i | \(-0.475945\pi\) | ||||
0.0755005 | + | 0.997146i | \(0.475945\pi\) | |||||||
\(308\) | −12.9615 | − | 7.48331i | −0.738549 | − | 0.426401i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.26013 | − | 16.0390i | −0.523413 | − | 0.906579i | −0.999629 | − | 0.0272499i | \(-0.991325\pi\) |
0.476215 | − | 0.879329i | \(-0.342008\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.0000 | 0.787562 | ||||||||
\(317\) | −9.72111 | − | 16.8375i | −0.545992 | − | 0.945686i | −0.998544 | − | 0.0539477i | \(-0.982820\pi\) |
0.452552 | − | 0.891738i | \(-0.350514\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.00000 | + | 3.46410i | −0.111979 | + | 0.193952i | ||||
\(320\) | −8.06250 | + | 15.9686i | −0.450708 | + | 0.892672i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.48074 | −0.360598 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.85425 | − | 10.6448i | −0.435675 | − | 0.590465i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.57321 | + | 4.94975i | 0.472657 | + | 0.272888i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.50000 | + | 6.06218i | 0.192377 | + | 0.333207i | 0.946038 | − | 0.324057i | \(-0.105047\pi\) |
−0.753660 | + | 0.657264i | \(0.771714\pi\) | |||||||
\(332\) | 25.9230 | + | 14.9666i | 1.42271 | + | 0.821401i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −25.7196 | + | 16.8375i | −1.40521 | + | 0.919929i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 32.0780i | − | 1.74740i | −0.486464 | − | 0.873701i | \(-0.661713\pi\) | ||
0.486464 | − | 0.873701i | \(-0.338287\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.937254 | + | 16.7069i | 0.0508297 | + | 0.906061i | ||||
\(341\) | −7.34847 | − | 12.7279i | −0.397942 | − | 0.689256i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.5203 | −1.00000 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.46410i | 0.185429i | 0.995693 | + | 0.0927146i | \(0.0295544\pi\) | ||||
−0.995693 | + | 0.0927146i | \(0.970446\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.48074 | + | 3.74166i | 0.344935 | + | 0.199148i | 0.662452 | − | 0.749104i | \(-0.269516\pi\) |
−0.317517 | + | 0.948253i | \(0.602849\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.5830 | + | 11.4021i | 1.19858 | + | 0.605161i | ||||
\(356\) | 34.2929 | 1.81752 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.4722 | − | 7.77817i | 0.711035 | − | 0.410516i | −0.100409 | − | 0.994946i | \(-0.532015\pi\) |
0.811444 | + | 0.584430i | \(0.198682\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.00000 | + | 13.8564i | −0.421053 | + | 0.729285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 14.0000 | 0.733799 | ||||||||
\(365\) | −16.2019 | − | 24.7487i | −0.848044 | − | 1.29541i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.26013 | + | 16.0390i | −0.483375 | + | 0.837230i | −0.999818 | − | 0.0190919i | \(-0.993923\pi\) |
0.516443 | + | 0.856322i | \(0.327256\pi\) | |||||||
\(368\) | 12.9615 | − | 22.4499i | 0.675664 | − | 1.17028i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −34.2929 | −1.78040 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.96863 | − | 2.29129i | 0.205488 | − | 0.118638i | −0.393725 | − | 0.919228i | \(-0.628814\pi\) |
0.599213 | + | 0.800590i | \(0.295480\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 3.74166i | − | 0.192705i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.00000 | 0.256833 | 0.128416 | − | 0.991720i | \(-0.459011\pi\) | ||||
0.128416 | + | 0.991720i | \(0.459011\pi\) | |||||||
\(380\) | −6.91460 | − | 3.49117i | −0.354712 | − | 0.179093i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.48074 | + | 3.74166i | −0.331150 | + | 0.191190i | −0.656352 | − | 0.754455i | \(-0.727901\pi\) |
0.325201 | + | 0.945645i | \(0.394568\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.9373 | − | 7.54178i | −0.761273 | − | 0.384365i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.29150 | + | 9.16515i | −0.268635 | + | 0.465290i | ||||
\(389\) | −2.44949 | − | 1.41421i | −0.124194 | − | 0.0717035i | 0.436616 | − | 0.899648i | \(-0.356177\pi\) |
−0.560810 | + | 0.827945i | \(0.689510\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 24.2487i | − | 1.22631i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.6279 | − | 0.876721i | 0.786325 | − | 0.0441126i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.5516 | + | 25.2042i | 0.730325 | + | 1.26496i | 0.956744 | + | 0.290931i | \(0.0939649\pi\) |
−0.226419 | + | 0.974030i | \(0.572702\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.00000 | + | 18.3303i | −0.400000 | + | 0.916515i | ||||
\(401\) | −4.89898 | + | 2.82843i | −0.244643 | + | 0.141245i | −0.617309 | − | 0.786721i | \(-0.711777\pi\) |
0.372666 | + | 0.927966i | \(0.378444\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.9059 | + | 6.87386i | 0.593074 | + | 0.342412i | ||||
\(404\) | −9.79796 | − | 16.9706i | −0.487467 | − | 0.844317i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.9615 | 0.642477 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.50000 | − | 2.59808i | −0.222511 | − | 0.128467i | 0.384602 | − | 0.923083i | \(-0.374339\pi\) |
−0.607112 | + | 0.794616i | \(0.707672\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 26.4575 | 1.30347 | ||||||||
\(413\) | 19.4422 | 0.956689 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 29.8745 | + | 15.0836i | 1.46648 | + | 0.740423i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.1464 | −0.837658 | −0.418829 | − | 0.908065i | \(-0.637559\pi\) | ||||
−0.418829 | + | 0.908065i | \(0.637559\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.0000 | 1.70580 | 0.852898 | − | 0.522078i | \(-0.174843\pi\) | ||||
0.852898 | + | 0.522078i | \(0.174843\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.09247 | + | 18.5909i | 0.101500 | + | 0.901791i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −23.8118 | − | 13.7477i | −1.15233 | − | 0.665299i | ||||
\(428\) | −12.9615 | −0.626517 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.12372 | − | 3.53553i | −0.294969 | − | 0.170301i | 0.345211 | − | 0.938525i | \(-0.387807\pi\) |
−0.640181 | + | 0.768224i | \(0.721141\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.2288 | −0.635733 | −0.317867 | − | 0.948135i | \(-0.602966\pi\) | ||||
−0.317867 | + | 0.948135i | \(0.602966\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.00000 | − | 12.1244i | −0.335239 | − | 0.580651i | ||||
\(437\) | 9.72111 | + | 5.61249i | 0.465024 | + | 0.268482i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.00000 | − | 5.19615i | 0.429547 | − | 0.247999i | −0.269607 | − | 0.962970i | \(-0.586894\pi\) |
0.699153 | + | 0.714972i | \(0.253560\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.4422 | − | 33.6749i | −0.923728 | − | 1.59994i | −0.793594 | − | 0.608447i | \(-0.791793\pi\) |
−0.130133 | − | 0.991496i | \(-0.541541\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 38.2804 | − | 2.14752i | 1.81466 | − | 0.101802i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −10.5830 | − | 18.3303i | −0.500000 | − | 0.866025i | ||||
\(449\) | − | 18.3848i | − | 0.867631i | −0.901002 | − | 0.433816i | \(-0.857167\pi\) | ||
0.901002 | − | 0.433816i | \(-0.142833\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.0000 | − | 6.92820i | −0.565058 | − | 0.326236i | ||||
\(452\) | 6.48074 | − | 11.2250i | 0.304828 | − | 0.527978i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15.6279 | − | 0.876721i | 0.732647 | − | 0.0411013i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.9059 | − | 6.87386i | 0.556934 | − | 0.321546i | −0.194980 | − | 0.980807i | \(-0.562464\pi\) |
0.751914 | + | 0.659261i | \(0.229131\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 13.0627 | − | 25.8721i | 0.609054 | − | 1.20629i | ||||
\(461\) | 17.1464 | 0.798589 | 0.399294 | − | 0.916823i | \(-0.369255\pi\) | ||||
0.399294 | + | 0.916823i | \(0.369255\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 4.58258i | − | 0.212970i | −0.994314 | − | 0.106485i | \(-0.966040\pi\) | ||
0.994314 | − | 0.106485i | \(-0.0339597\pi\) | |||||||
\(464\) | −4.89898 | + | 2.82843i | −0.227429 | + | 0.131306i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.24037 | − | 1.87083i | 0.149946 | − | 0.0865716i | −0.423150 | − | 0.906060i | \(-0.639076\pi\) |
0.573096 | + | 0.819488i | \(0.305742\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 36.3731i | − | 1.67955i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.48074 | − | 11.2250i | 0.297985 | − | 0.516125i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.93725 | − | 3.46410i | −0.364186 | − | 0.158944i | ||||
\(476\) | −17.1464 | − | 9.89949i | −0.785905 | − | 0.453743i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.1464 | + | 29.6985i | −0.783440 | + | 1.35696i | 0.146486 | + | 0.989213i | \(0.453204\pi\) |
−0.929926 | + | 0.367746i | \(0.880130\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.5000 | + | 6.06218i | −0.478759 | + | 0.276412i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.00000 | −0.272727 | ||||||||
\(485\) | −5.33284 | + | 10.5622i | −0.242152 | + | 0.479606i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.8431 | + | 11.4564i | 0.899178 | + | 0.519141i | 0.876933 | − | 0.480612i | \(-0.159585\pi\) |
0.0222448 | + | 0.999753i | \(0.492919\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.3137i | 0.510581i | 0.966864 | + | 0.255290i | \(0.0821710\pi\) | ||||
−0.966864 | + | 0.255290i | \(0.917829\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.64575 | + | 4.58258i | −0.119159 | + | 0.206389i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 20.7846i | − | 0.933257i | ||||||
\(497\) | −25.9230 | + | 14.9666i | −1.16280 | + | 0.671345i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.50000 | + | 11.2583i | 0.290980 | + | 0.503992i | 0.974042 | − | 0.226369i | \(-0.0726854\pi\) |
−0.683062 | + | 0.730361i | \(0.739352\pi\) | |||||||
\(500\) | −7.78233 | + | 20.9627i | −0.348037 | + | 0.937481i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.74166i | 0.166832i | 0.996515 | + | 0.0834161i | \(0.0265831\pi\) | ||||
−0.996515 | + | 0.0834161i | \(0.973417\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.0000 | − | 18.3303i | −0.533993 | − | 0.815688i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 23.8118 | + | 13.7477i | 1.05648 | + | 0.609957i | ||||
\(509\) | −8.57321 | − | 14.8492i | −0.380001 | − | 0.658181i | 0.611061 | − | 0.791584i | \(-0.290743\pi\) |
−0.991062 | + | 0.133402i | \(0.957410\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 35.0000 | 1.54831 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 29.5340 | − | 1.65685i | 1.30142 | − | 0.0730094i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.5830 | −0.465440 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.1464 | − | 29.6985i | 0.751199 | − | 1.30111i | −0.196043 | − | 0.980595i | \(-0.562809\pi\) |
0.947242 | − | 0.320519i | \(-0.103857\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.61438 | + | 11.4564i | 0.289227 | + | 0.500955i | 0.973625 | − | 0.228153i | \(-0.0732686\pi\) |
−0.684399 | + | 0.729108i | \(0.739935\pi\) | |||||||
\(524\) | −34.2929 | −1.49809 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.72111 | − | 16.8375i | −0.423458 | − | 0.733451i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.50000 | + | 16.4545i | −0.413043 | + | 0.715412i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.93725 | − | 4.58258i | 0.344124 | − | 0.198680i | ||||
\(533\) | 12.9615 | 0.561424 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.4686 | + | 0.811686i | −0.625533 | + | 0.0350922i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17.1464 | − | 9.89949i | 0.738549 | − | 0.426401i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.50000 | + | 6.06218i | 0.150477 | + | 0.260633i | 0.931403 | − | 0.363990i | \(-0.118586\pi\) |
−0.780926 | + | 0.624623i | \(0.785252\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.57321 | − | 13.0958i | −0.367236 | − | 0.560962i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.3303i | 0.783747i | 0.920019 | + | 0.391874i | \(0.128173\pi\) | ||||
−0.920019 | + | 0.391874i | \(0.871827\pi\) | |||||||
\(548\) | 6.48074 | + | 11.2250i | 0.276844 | + | 0.479507i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.22474 | − | 2.12132i | −0.0521759 | − | 0.0903713i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.26013 | + | 16.0390i | −0.393781 | + | 0.682048i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15.0000 | − | 8.66025i | −0.636142 | − | 0.367277i | ||||
\(557\) | 3.24037 | − | 5.61249i | 0.137299 | − | 0.237809i | −0.789174 | − | 0.614169i | \(-0.789491\pi\) |
0.926473 | + | 0.376360i | \(0.122825\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.1244i | 0.512806i | ||||||||
\(560\) | −12.9615 | − | 19.7990i | −0.547723 | − | 0.836660i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.2019 | + | 9.35414i | 0.682827 | + | 0.394230i | 0.800919 | − | 0.598772i | \(-0.204345\pi\) |
−0.118093 | + | 0.993003i | \(0.537678\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.53137 | − | 12.9360i | 0.274777 | − | 0.544223i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 39.1918 | − | 22.6274i | 1.64301 | − | 0.948591i | 0.663251 | − | 0.748397i | \(-0.269176\pi\) |
0.979756 | − | 0.200194i | \(-0.0641571\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.50000 | + | 14.7224i | −0.355714 | + | 0.616115i | −0.987240 | − | 0.159240i | \(-0.949096\pi\) |
0.631526 | + | 0.775355i | \(0.282429\pi\) | |||||||
\(572\) | −12.9615 | + | 7.48331i | −0.541947 | + | 0.312893i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.9615 | − | 29.6985i | 0.540531 | − | 1.23851i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.1974 | + | 29.7867i | −0.715936 | + | 1.24004i | 0.246661 | + | 0.969102i | \(0.420667\pi\) |
−0.962597 | + | 0.270936i | \(0.912667\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.29150 | + | 3.46410i | −0.219718 | + | 0.143839i | ||||
\(581\) | −34.2929 | + | 19.7990i | −1.42271 | + | 0.821401i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 31.7490 | − | 18.3303i | 1.31491 | − | 0.759164i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.1916i | 1.08104i | 0.841330 | + | 0.540522i | \(0.181773\pi\) | ||||
−0.841330 | + | 0.540522i | \(0.818227\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.00000 | 0.370839 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 15.8745 | + | 9.16515i | 0.652438 | + | 0.376685i | ||||
\(593\) | 12.9615 | − | 7.48331i | 0.532264 | − | 0.307303i | −0.209674 | − | 0.977771i | \(-0.567240\pi\) |
0.741938 | + | 0.670468i | \(0.233907\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.7601 | − | 9.97684i | −0.810086 | − | 0.409010i | ||||
\(596\) | 28.2843i | 1.15857i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.44949 | − | 1.41421i | −0.100083 | − | 0.0577832i | 0.449123 | − | 0.893470i | \(-0.351737\pi\) |
−0.549206 | + | 0.835687i | \(0.685070\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.66025i | 0.353259i | 0.984277 | + | 0.176630i | \(0.0565195\pi\) | ||||
−0.984277 | + | 0.176630i | \(0.943481\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10.0000 | − | 17.3205i | −0.406894 | − | 0.704761i | ||||
\(605\) | −6.69767 | + | 0.375737i | −0.272299 | + | 0.0152759i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.1974 | − | 29.7867i | −0.698020 | − | 1.20901i | −0.969152 | − | 0.246464i | \(-0.920731\pi\) |
0.271132 | − | 0.962542i | \(-0.412602\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.57321 | − | 4.94975i | 0.346835 | − | 0.200245i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.8745 | − | 9.16515i | −0.641165 | − | 0.370177i | 0.143898 | − | 0.989593i | \(-0.454036\pi\) |
−0.785063 | + | 0.619416i | \(0.787370\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −32.4037 | −1.30452 | −0.652262 | − | 0.757994i | \(-0.726180\pi\) | ||||
−0.652262 | + | 0.757994i | \(0.726180\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.5000 | + | 14.7224i | 1.02493 | + | 0.591744i | 0.915529 | − | 0.402253i | \(-0.131773\pi\) |
0.109403 | + | 0.993997i | \(0.465106\pi\) | |||||||
\(620\) | −1.30159 | − | 23.2014i | −0.0522732 | − | 0.931791i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −22.6826 | + | 39.2874i | −0.908759 | + | 1.57402i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.37451 | + | 23.8876i | −0.294980 | + | 0.955503i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.29150 | − | 9.16515i | −0.211154 | − | 0.365729i | ||||
\(629\) | 17.1464 | 0.683673 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.0000 | 0.557331 | 0.278666 | − | 0.960388i | \(-0.410108\pi\) | ||||
0.278666 | + | 0.960388i | \(0.410108\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 27.4415 | + | 13.8551i | 1.08898 | + | 0.549824i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.26013 | + | 16.0390i | −0.366900 | + | 0.635489i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.2702 | + | 13.4350i | 0.919116 | + | 0.530652i | 0.883353 | − | 0.468709i | \(-0.155281\pi\) |
0.0357629 | + | 0.999360i | \(0.488614\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.64575 | 0.104338 | 0.0521691 | − | 0.998638i | \(-0.483387\pi\) | ||||
0.0521691 | + | 0.998638i | \(0.483387\pi\) | |||||||
\(644\) | 17.1464 | + | 29.6985i | 0.675664 | + | 1.17028i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.9615 | − | 7.48331i | −0.509568 | − | 0.294199i | 0.223088 | − | 0.974798i | \(-0.428386\pi\) |
−0.732656 | + | 0.680599i | \(0.761720\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18.0000 | + | 10.3923i | −0.706562 | + | 0.407934i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 18.3303i | − | 0.717870i | ||||||
\(653\) | 12.9615 | + | 22.4499i | 0.507222 | + | 0.878534i | 0.999965 | + | 0.00835938i | \(0.00266090\pi\) |
−0.492743 | + | 0.870175i | \(0.664006\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −38.2804 | + | 2.14752i | −1.49574 | + | 0.0839105i | ||||
\(656\) | −9.79796 | − | 16.9706i | −0.382546 | − | 0.662589i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.2843i | 1.10180i | 0.834572 | + | 0.550899i | \(0.185715\pi\) | ||||
−0.834572 | + | 0.550899i | \(0.814285\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.50000 | − | 2.59808i | −0.175030 | − | 0.101053i | 0.409926 | − | 0.912119i | \(-0.365555\pi\) |
−0.584955 | + | 0.811065i | \(0.698888\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.57321 | − | 5.61249i | 0.332455 | − | 0.217643i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.93725 | − | 4.58258i | 0.307332 | − | 0.177438i | ||||
\(668\) | −12.9615 | − | 7.48331i | −0.501495 | − | 0.289538i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.3939 | 1.13474 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 22.9129i | − | 0.883227i | −0.897206 | − | 0.441613i | \(-0.854406\pi\) | ||
0.897206 | − | 0.441613i | \(-0.145594\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.00000 | + | 10.3923i | −0.230769 | + | 0.399704i | ||||
\(677\) | 3.24037 | − | 1.87083i | 0.124538 | − | 0.0719018i | −0.436437 | − | 0.899735i | \(-0.643760\pi\) |
0.560975 | + | 0.827833i | \(0.310427\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.00000 | − | 12.1244i | −0.268635 | − | 0.465290i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.2019 | + | 28.0624i | −0.619947 | + | 1.07378i | 0.369548 | + | 0.929212i | \(0.379512\pi\) |
−0.989495 | + | 0.144568i | \(0.953821\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.93725 | + | 12.1244i | 0.303267 | + | 0.463248i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 15.8745 | − | 9.16515i | 0.605210 | − | 0.349418i | ||||
\(689\) | −17.1464 | + | 29.6985i | −0.653227 | + | 1.13142i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −40.5000 | + | 23.3827i | −1.54069 | + | 0.889519i | −0.541897 | + | 0.840445i | \(0.682294\pi\) |
−0.998795 | + | 0.0490747i | \(0.984373\pi\) | |||||||
\(692\) | − | 29.9333i | − | 1.13789i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17.2865 | − | 8.72791i | −0.655715 | − | 0.331069i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.8745 | − | 9.16515i | −0.601290 | − | 0.347155i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −15.7085 | − | 21.2895i | −0.593725 | − | 0.804668i | ||||
\(701\) | − | 1.41421i | − | 0.0534141i | −0.999643 | − | 0.0267071i | \(-0.991498\pi\) | ||
0.999643 | − | 0.0267071i | \(-0.00850213\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.96863 | + | 6.87386i | −0.149680 | + | 0.259253i | ||||
\(704\) | 19.5959 | + | 11.3137i | 0.738549 | + | 0.426401i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 25.9230 | 0.974933 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.00000 | − | 6.92820i | −0.150223 | − | 0.260194i | 0.781086 | − | 0.624423i | \(-0.214666\pi\) |
−0.931309 | + | 0.364229i | \(0.881333\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 33.6749i | 1.26114i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.0000 | + | 9.16515i | −0.523570 | + | 0.342757i | ||||
\(716\) | −12.2474 | + | 7.07107i | −0.457709 | + | 0.264258i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.22474 | + | 2.12132i | 0.0456753 | + | 0.0791119i | 0.887959 | − | 0.459922i | \(-0.152123\pi\) |
−0.842284 | + | 0.539034i | \(0.818789\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.5000 | + | 30.3109i | −0.651734 | + | 1.12884i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −27.0000 | − | 15.5885i | −1.00345 | − | 0.579340i | ||||
\(725\) | −5.68986 | + | 4.19827i | −0.211316 | + | 0.155920i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.1033 | −1.07938 | −0.539690 | − | 0.841864i | \(-0.681459\pi\) | ||||
−0.539690 | + | 0.841864i | \(0.681459\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.57321 | − | 14.8492i | 0.317092 | − | 0.549219i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.61438 | + | 11.4564i | 0.244308 | + | 0.423153i | 0.961937 | − | 0.273272i | \(-0.0881060\pi\) |
−0.717629 | + | 0.696426i | \(0.754773\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.4422 | + | 33.6749i | 0.716163 | + | 1.24043i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.50000 | + | 14.7224i | −0.312678 | + | 0.541573i | −0.978941 | − | 0.204143i | \(-0.934559\pi\) |
0.666264 | + | 0.745716i | \(0.267893\pi\) | |||||||
\(740\) | 18.2943 | + | 9.23676i | 0.672513 | + | 0.339550i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −51.8459 | −1.90204 | −0.951021 | − | 0.309125i | \(-0.899964\pi\) | ||||
−0.951021 | + | 0.309125i | \(0.899964\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.77124 | + | 31.5731i | 0.0648933 | + | 1.15675i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 21.1660 | 0.773906 | ||||||||
\(749\) | 8.57321 | − | 14.8492i | 0.313258 | − | 0.542580i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.50000 | + | 6.06218i | 0.127717 | + | 0.221212i | 0.922792 | − | 0.385299i | \(-0.125902\pi\) |
−0.795075 | + | 0.606511i | \(0.792568\pi\) | |||||||
\(752\) | −12.9615 | − | 7.48331i | −0.472657 | − | 0.272888i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.2474 | − | 18.7083i | −0.445730 | − | 0.680864i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.57321 | − | 14.8492i | −0.310779 | − | 0.538285i | 0.667752 | − | 0.744383i | \(-0.267256\pi\) |
−0.978531 | + | 0.206099i | \(0.933923\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.5203 | 0.670478 | ||||||||
\(764\) | − | 31.1127i | − | 1.12562i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.72111 | − | 16.8375i | 0.351009 | − | 0.607965i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.9090i | 1.18673i | 0.804934 | + | 0.593364i | \(0.202200\pi\) | ||||
−0.804934 | + | 0.593364i | \(0.797800\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −23.8118 | + | 13.7477i | −0.857004 | + | 0.494792i | ||||
\(773\) | 25.9230 | + | 14.9666i | 0.932384 | + | 0.538312i | 0.887565 | − | 0.460683i | \(-0.152395\pi\) |
0.0448193 | + | 0.998995i | \(0.485729\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.90588 | − | 25.8177i | −0.104382 | − | 0.927401i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.34847 | − | 4.24264i | 0.263286 | − | 0.152008i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.0000 | − | 27.7128i | 0.572525 | − | 0.991642i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 28.0000 | 1.00000 | ||||||||
\(785\) | −6.48074 | − | 9.89949i | −0.231308 | − | 0.353328i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.4575 | − | 45.8258i | 0.943108 | − | 1.63351i | 0.183614 | − | 0.982998i | \(-0.441220\pi\) |
0.759495 | − | 0.650513i | \(-0.225446\pi\) | |||||||
\(788\) | −19.4422 | + | 33.6749i | −0.692600 | + | 1.19962i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.57321 | + | 14.8492i | 0.304828 | + | 0.527978i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23.8118 | + | 13.7477i | −0.845580 | + | 0.488196i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.0000 | − | 6.92820i | 0.425329 | − | 0.245564i | ||||
\(797\) | − | 41.1582i | − | 1.45790i | −0.684567 | − | 0.728950i | \(-0.740009\pi\) | ||
0.684567 | − | 0.728950i | \(-0.259991\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.0000 | −0.495284 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −32.4037 | + | 18.7083i | −1.14350 | + | 0.660201i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.0000 | + | 32.0780i | 0.740153 | + | 1.13060i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.1691 | − | 16.2635i | −0.990374 | − | 0.571793i | −0.0849879 | − | 0.996382i | \(-0.527085\pi\) |
−0.905386 | + | 0.424589i | \(0.860418\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 20.7846i | − | 0.729846i | −0.931038 | − | 0.364923i | \(-0.881095\pi\) | ||
0.931038 | − | 0.364923i | \(-0.118905\pi\) | |||||||
\(812\) | − | 7.48331i | − | 0.262613i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.14790 | − | 20.4617i | −0.0402091 | − | 0.716743i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.96863 | + | 6.87386i | 0.138845 | + | 0.240486i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.0000 | − | 18.3303i | −0.419058 | − | 0.640122i | ||||
\(821\) | −4.89898 | + | 2.82843i | −0.170976 | + | 0.0987128i | −0.583046 | − | 0.812439i | \(-0.698139\pi\) |
0.412070 | + | 0.911152i | \(0.364806\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.8118 | + | 13.7477i | 0.830026 | + | 0.479216i | 0.853862 | − | 0.520500i | \(-0.174255\pi\) |
−0.0238357 | + | 0.999716i | \(0.507588\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.4422 | 0.676072 | 0.338036 | − | 0.941133i | \(-0.390237\pi\) | ||||
0.338036 | + | 0.941133i | \(0.390237\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.5000 | + | 21.6506i | 1.30243 | + | 0.751958i | 0.980820 | − | 0.194915i | \(-0.0624431\pi\) |
0.321609 | + | 0.946873i | \(0.395776\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −21.1660 | −0.733799 | ||||||||
\(833\) | 22.6826 | − | 13.0958i | 0.785905 | − | 0.453743i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.9373 | − | 7.54178i | −0.516925 | − | 0.260994i | ||||
\(836\) | −4.89898 | + | 8.48528i | −0.169435 | + | 0.293470i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.2474 | −0.422829 | −0.211414 | − | 0.977397i | \(-0.567807\pi\) | ||||
−0.211414 | + | 0.977397i | \(0.567807\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.0000 | 0.931034 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 14.0000 | − | 24.2487i | 0.481900 | − | 0.834675i | ||||
\(845\) | −6.04688 | + | 11.9764i | −0.208019 | + | 0.412002i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.96863 | − | 6.87386i | 0.136364 | − | 0.236189i | ||||
\(848\) | 51.8459 | 1.78040 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.7196 | − | 14.8492i | −0.881658 | − | 0.509025i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 50.2693 | 1.72119 | 0.860594 | − | 0.509292i | \(-0.170093\pi\) | ||||
0.860594 | + | 0.509292i | \(0.170093\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.2019 | + | 9.35414i | 0.553445 | + | 0.319531i | 0.750510 | − | 0.660859i | \(-0.229808\pi\) |
−0.197065 | + | 0.980390i | \(0.563141\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.0000 | − | 6.92820i | 0.409435 | − | 0.236387i | −0.281112 | − | 0.959675i | \(-0.590703\pi\) |
0.690547 | + | 0.723288i | \(0.257370\pi\) | |||||||
\(860\) | 17.1464 | − | 11.2250i | 0.584688 | − | 0.382768i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.2019 | + | 28.0624i | 0.551517 | + | 0.955256i | 0.998165 | + | 0.0605464i | \(0.0192843\pi\) |
−0.446648 | + | 0.894710i | \(0.647382\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.87451 | − | 33.4139i | −0.0637352 | − | 1.13611i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 23.8118 | + | 13.7477i | 0.808224 | + | 0.466628i | ||||
\(869\) | − | 19.7990i | − | 0.671635i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −31.5000 | − | 18.1865i | −1.06734 | − | 0.616227i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −18.8683 | − | 22.7813i | −0.637864 | − | 0.770149i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.93725 | + | 4.58258i | −0.268022 | + | 0.154743i | −0.627988 | − | 0.778223i | \(-0.716121\pi\) |
0.359966 | + | 0.932965i | \(0.382788\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 22.5830 | + | 11.4021i | 0.761273 | + | 0.384365i | ||||
\(881\) | 29.3939 | 0.990305 | 0.495152 | − | 0.868806i | \(-0.335112\pi\) | ||||
0.495152 | + | 0.868806i | \(0.335112\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41.2432i | 1.38794i | 0.720002 | + | 0.693972i | \(0.244141\pi\) | ||||
−0.720002 | + | 0.693972i | \(0.755859\pi\) | |||||||
\(884\) | −17.1464 | + | 9.89949i | −0.576697 | + | 0.332956i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32.4037 | − | 18.7083i | 1.08801 | − | 0.628163i | 0.154964 | − | 0.987920i | \(-0.450474\pi\) |
0.933046 | + | 0.359757i | \(0.117141\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −31.5000 | + | 18.1865i | −1.05648 | + | 0.609957i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.29150 | + | 9.16515i | −0.177173 | + | 0.306872i | ||||
\(893\) | 3.24037 | − | 5.61249i | 0.108435 | − | 0.187815i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.2288 | + | 8.66025i | −0.442189 | + | 0.289480i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.67423 | − | 6.36396i | 0.122543 | − | 0.212250i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 42.0000 | − | 24.2487i | 1.39922 | − | 0.807842i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −31.1157 | − | 15.7102i | −1.03432 | − | 0.522226i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.8431 | − | 11.4564i | −0.658880 | − | 0.380405i | 0.132970 | − | 0.991120i | \(-0.457549\pi\) |
−0.791850 | + | 0.610715i | \(0.790882\pi\) | |||||||
\(908\) | −25.9230 | + | 14.9666i | −0.860284 | + | 0.496685i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.0122i | 1.35879i | 0.733771 | + | 0.679397i | \(0.237759\pi\) | ||||
−0.733771 | + | 0.679397i | \(0.762241\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.1660 | − | 36.6606i | 0.700493 | − | 1.21329i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.46410i | 0.114457i | ||||||||
\(917\) | 22.6826 | − | 39.2874i | 0.749045 | − | 1.29738i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.5000 | − | 30.3109i | −0.577272 | − | 0.999864i | −0.995791 | − | 0.0916559i | \(-0.970784\pi\) |
0.418519 | − | 0.908208i | \(-0.362549\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29.9333i | 0.985265i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.0000 | + | 9.16515i | 0.690476 | + | 0.301348i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.1244i | 0.397360i | ||||||||
\(932\) | −12.9615 | −0.424567 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 23.6272 | − | 1.32548i | 0.772691 | − | 0.0433477i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50.2693 | 1.64223 | 0.821113 | − | 0.570766i | \(-0.193354\pi\) | ||||
0.821113 | + | 0.570766i | \(0.193354\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −14.9373 | − | 7.54178i | −0.487200 | − | 0.245986i | ||||
\(941\) | 3.67423 | − | 6.36396i | 0.119777 | − | 0.207459i | −0.799902 | − | 0.600130i | \(-0.795115\pi\) |
0.919679 | + | 0.392671i | \(0.128449\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.8745 | + | 27.4955i | 0.516945 | + | 0.895375i | ||||
\(944\) | −29.3939 | −0.956689 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.4422 | − | 33.6749i | −0.631787 | − | 1.09429i | −0.987186 | − | 0.159573i | \(-0.948988\pi\) |
0.355399 | − | 0.934715i | \(-0.384345\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.5000 | − | 30.3109i | 0.568074 | − | 0.983933i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.94837 | − | 34.7304i | −0.0630477 | − | 1.12385i | ||||
\(956\) | −31.8434 | − | 18.3848i | −1.02989 | − | 0.594606i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.1464 | −0.553687 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.00000 | − | 3.46410i | −0.0645161 | − | 0.111745i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −30.0000 | + | 17.3205i | −0.966235 | + | 0.557856i | ||||
\(965\) | −25.7196 | + | 16.8375i | −0.827945 | + | 0.542017i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 4.58258i | − | 0.147366i | −0.997282 | − | 0.0736828i | \(-0.976525\pi\) | ||
0.997282 | − | 0.0736828i | \(-0.0234753\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.79796 | − | 16.9706i | −0.314431 | − | 0.544611i | 0.664885 | − | 0.746946i | \(-0.268481\pi\) |
−0.979316 | + | 0.202334i | \(0.935147\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.8431 | − | 11.4564i | 0.636142 | − | 0.367277i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 36.0000 | + | 20.7846i | 1.15233 | + | 0.665299i | ||||
\(977\) | −19.4422 | + | 33.6749i | −0.622012 | + | 1.07736i | 0.367099 | + | 0.930182i | \(0.380351\pi\) |
−0.989111 | + | 0.147174i | \(0.952982\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 48.4974i | − | 1.54998i | ||||||
\(980\) | 31.2558 | − | 1.75344i | 0.998430 | − | 0.0560116i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −42.1248 | − | 24.3208i | −1.34357 | − | 0.775712i | −0.356243 | − | 0.934393i | \(-0.615942\pi\) |
−0.987330 | + | 0.158681i | \(0.949276\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.5941 | + | 38.8081i | −0.624321 | + | 1.23653i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 9.16515i | − | 0.291582i | ||||||
\(989\) | −25.7196 | + | 14.8492i | −0.817837 | + | 0.472178i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.50000 | − | 6.06218i | 0.111181 | − | 0.192571i | −0.805066 | − | 0.593186i | \(-0.797870\pi\) |
0.916247 | + | 0.400614i | \(0.131203\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.9615 | − | 8.48528i | 0.410907 | − | 0.269002i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.32288 | + | 2.29129i | −0.0418959 | + | 0.0725658i | −0.886213 | − | 0.463278i | \(-0.846673\pi\) |
0.844317 | + | 0.535844i | \(0.180006\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 315.2.bb.a.269.3 | yes | 8 | |
3.2 | odd | 2 | inner | 315.2.bb.a.269.2 | yes | 8 | |
5.2 | odd | 4 | 1575.2.bk.d.1151.1 | 8 | |||
5.3 | odd | 4 | 1575.2.bk.d.1151.3 | 8 | |||
5.4 | even | 2 | inner | 315.2.bb.a.269.1 | yes | 8 | |
7.3 | odd | 6 | 2205.2.g.a.2204.2 | 8 | |||
7.4 | even | 3 | 2205.2.g.a.2204.8 | 8 | |||
7.5 | odd | 6 | inner | 315.2.bb.a.89.4 | yes | 8 | |
15.2 | even | 4 | 1575.2.bk.d.1151.2 | 8 | |||
15.8 | even | 4 | 1575.2.bk.d.1151.4 | 8 | |||
15.14 | odd | 2 | inner | 315.2.bb.a.269.4 | yes | 8 | |
21.5 | even | 6 | inner | 315.2.bb.a.89.1 | ✓ | 8 | |
21.11 | odd | 6 | 2205.2.g.a.2204.1 | 8 | |||
21.17 | even | 6 | 2205.2.g.a.2204.7 | 8 | |||
35.4 | even | 6 | 2205.2.g.a.2204.6 | 8 | |||
35.12 | even | 12 | 1575.2.bk.d.26.2 | 8 | |||
35.19 | odd | 6 | inner | 315.2.bb.a.89.2 | yes | 8 | |
35.24 | odd | 6 | 2205.2.g.a.2204.4 | 8 | |||
35.33 | even | 12 | 1575.2.bk.d.26.4 | 8 | |||
105.47 | odd | 12 | 1575.2.bk.d.26.1 | 8 | |||
105.59 | even | 6 | 2205.2.g.a.2204.5 | 8 | |||
105.68 | odd | 12 | 1575.2.bk.d.26.3 | 8 | |||
105.74 | odd | 6 | 2205.2.g.a.2204.3 | 8 | |||
105.89 | even | 6 | inner | 315.2.bb.a.89.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.bb.a.89.1 | ✓ | 8 | 21.5 | even | 6 | inner | |
315.2.bb.a.89.2 | yes | 8 | 35.19 | odd | 6 | inner | |
315.2.bb.a.89.3 | yes | 8 | 105.89 | even | 6 | inner | |
315.2.bb.a.89.4 | yes | 8 | 7.5 | odd | 6 | inner | |
315.2.bb.a.269.1 | yes | 8 | 5.4 | even | 2 | inner | |
315.2.bb.a.269.2 | yes | 8 | 3.2 | odd | 2 | inner | |
315.2.bb.a.269.3 | yes | 8 | 1.1 | even | 1 | trivial | |
315.2.bb.a.269.4 | yes | 8 | 15.14 | odd | 2 | inner | |
1575.2.bk.d.26.1 | 8 | 105.47 | odd | 12 | |||
1575.2.bk.d.26.2 | 8 | 35.12 | even | 12 | |||
1575.2.bk.d.26.3 | 8 | 105.68 | odd | 12 | |||
1575.2.bk.d.26.4 | 8 | 35.33 | even | 12 | |||
1575.2.bk.d.1151.1 | 8 | 5.2 | odd | 4 | |||
1575.2.bk.d.1151.2 | 8 | 15.2 | even | 4 | |||
1575.2.bk.d.1151.3 | 8 | 5.3 | odd | 4 | |||
1575.2.bk.d.1151.4 | 8 | 15.8 | even | 4 | |||
2205.2.g.a.2204.1 | 8 | 21.11 | odd | 6 | |||
2205.2.g.a.2204.2 | 8 | 7.3 | odd | 6 | |||
2205.2.g.a.2204.3 | 8 | 105.74 | odd | 6 | |||
2205.2.g.a.2204.4 | 8 | 35.24 | odd | 6 | |||
2205.2.g.a.2204.5 | 8 | 105.59 | even | 6 | |||
2205.2.g.a.2204.6 | 8 | 35.4 | even | 6 | |||
2205.2.g.a.2204.7 | 8 | 21.17 | even | 6 | |||
2205.2.g.a.2204.8 | 8 | 7.4 | even | 3 |