Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6080,2,Mod(1,6080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6080.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6080 = 2^{6} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6080.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: | \(48.5490444289\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - 2 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 380) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6080.1 |
$q$-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 | 0 | ||||||||
\(3\) | 0.585786 | 0.338204 | 0.169102 | − | 0.985599i | \(-0.445913\pi\) | ||||
0.169102 | + | 0.985599i | \(0.445913\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.82843 | −1.82497 | −0.912487 | − | 0.409106i | \(-0.865841\pi\) | ||||
−0.912487 | + | 0.409106i | \(0.865841\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.65685 | −0.885618 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.24264 | −0.621997 | −0.310998 | − | 0.950410i | \(-0.600663\pi\) | ||||
−0.310998 | + | 0.950410i | \(0.600663\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.585786 | −0.151249 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.82843 | −1.17107 | −0.585533 | − | 0.810649i | \(-0.699115\pi\) | ||||
−0.585533 | + | 0.810649i | \(0.699115\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.82843 | −0.617213 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.00000 | −1.25109 | −0.625543 | − | 0.780189i | \(-0.715123\pi\) | ||||
−0.625543 | + | 0.780189i | \(0.715123\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.31371 | −0.637723 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.4853 | −1.94707 | −0.973534 | − | 0.228543i | \(-0.926604\pi\) | ||||
−0.973534 | + | 0.228543i | \(0.926604\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.17157 | −0.210421 | −0.105210 | − | 0.994450i | \(-0.533552\pi\) | ||||
−0.105210 | + | 0.994450i | \(0.533552\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.17157 | 0.203945 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.82843 | 0.816153 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.2426 | 1.68388 | 0.841940 | − | 0.539571i | \(-0.181414\pi\) | ||||
0.841940 | + | 0.539571i | \(0.181414\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.31371 | −0.210362 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.65685 | −1.19580 | −0.597900 | − | 0.801571i | \(-0.703998\pi\) | ||||
−0.597900 | + | 0.801571i | \(0.703998\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.828427 | 0.126334 | 0.0631670 | − | 0.998003i | \(-0.479880\pi\) | ||||
0.0631670 | + | 0.998003i | \(0.479880\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.65685 | 0.396060 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.828427 | 0.120839 | 0.0604193 | − | 0.998173i | \(-0.480756\pi\) | ||||
0.0604193 | + | 0.998173i | \(0.480756\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16.3137 | 2.33053 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.82843 | −0.396059 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.07107 | 0.696565 | 0.348282 | − | 0.937390i | \(-0.386765\pi\) | ||||
0.348282 | + | 0.937390i | \(0.386765\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.585786 | 0.0775893 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.34315 | −0.305052 | −0.152526 | − | 0.988299i | \(-0.548741\pi\) | ||||
−0.152526 | + | 0.988299i | \(0.548741\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.34315 | 0.300009 | 0.150005 | − | 0.988685i | \(-0.452071\pi\) | ||||
0.150005 | + | 0.988685i | \(0.452071\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 12.8284 | 1.61623 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.24264 | 0.278165 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.585786 | 0.0715652 | 0.0357826 | − | 0.999360i | \(-0.488608\pi\) | ||||
0.0357826 | + | 0.999360i | \(0.488608\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.51472 | −0.423122 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.8284 | 1.28510 | 0.642549 | − | 0.766245i | \(-0.277877\pi\) | ||||
0.642549 | + | 0.766245i | \(0.277877\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.4853 | 1.69537 | 0.847687 | − | 0.530497i | \(-0.177995\pi\) | ||||
0.847687 | + | 0.530497i | \(0.177995\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.585786 | 0.0676408 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.65685 | −1.10050 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.65685 | −1.08648 | −0.543240 | − | 0.839577i | \(-0.682803\pi\) | ||||
−0.543240 | + | 0.839577i | \(0.682803\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.02944 | 0.669937 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.31371 | −1.02231 | −0.511156 | − | 0.859488i | \(-0.670783\pi\) | ||||
−0.511156 | + | 0.859488i | \(0.670783\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.82843 | 0.523716 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.14214 | −0.658506 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.4853 | 1.11144 | 0.555719 | − | 0.831370i | \(-0.312443\pi\) | ||||
0.555719 | + | 0.831370i | \(0.312443\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.8284 | 1.13513 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.686292 | −0.0711651 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.75736 | −0.178433 | −0.0892164 | − | 0.996012i | \(-0.528436\pi\) | ||||
−0.0892164 | + | 0.996012i | \(0.528436\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.31371 | −0.534048 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.00000 | −0.398015 | −0.199007 | − | 0.979998i | \(-0.563772\pi\) | ||||
−0.199007 | + | 0.979998i | \(0.563772\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.8995 | −1.56662 | −0.783312 | − | 0.621629i | \(-0.786471\pi\) | ||||
−0.783312 | + | 0.621629i | \(0.786471\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.82843 | 0.276026 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.58579 | −0.443325 | −0.221662 | − | 0.975123i | \(-0.571148\pi\) | ||||
−0.221662 | + | 0.975123i | \(0.571148\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.82843 | 0.845610 | 0.422805 | − | 0.906221i | \(-0.361046\pi\) | ||||
0.422805 | + | 0.906221i | \(0.361046\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.00000 | 0.569495 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.07107 | 0.477046 | 0.238523 | − | 0.971137i | \(-0.423337\pi\) | ||||
0.238523 | + | 0.971137i | \(0.423337\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.00000 | 0.559503 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.95837 | 0.550851 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 23.3137 | 2.13716 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.48528 | −0.404424 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −21.5563 | −1.91282 | −0.956408 | − | 0.292033i | \(-0.905668\pi\) | ||||
−0.956408 | + | 0.292033i | \(0.905668\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.485281 | 0.0427266 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.65685 | 0.494242 | 0.247121 | − | 0.968985i | \(-0.420516\pi\) | ||||
0.247121 | + | 0.968985i | \(0.420516\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.82843 | −0.418678 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.31371 | 0.285199 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −20.1421 | −1.72086 | −0.860429 | − | 0.509570i | \(-0.829805\pi\) | ||||
−0.860429 | + | 0.509570i | \(0.829805\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.3137 | 1.46853 | 0.734265 | − | 0.678863i | \(-0.237527\pi\) | ||||
0.734265 | + | 0.678863i | \(0.237527\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.485281 | 0.0408681 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.48528 | −0.375078 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.4853 | 0.870755 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.55635 | 0.788194 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.00000 | 0.655386 | 0.327693 | − | 0.944784i | \(-0.393729\pi\) | ||||
0.327693 | + | 0.944784i | \(0.393729\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.1421 | 1.47639 | 0.738193 | − | 0.674590i | \(-0.235679\pi\) | ||||
0.738193 | + | 0.674590i | \(0.235679\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.8284 | 1.03712 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.17157 | 0.0941030 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.17157 | −0.253119 | −0.126560 | − | 0.991959i | \(-0.540393\pi\) | ||||
−0.126560 | + | 0.991959i | \(0.540393\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.97056 | 0.235581 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 28.9706 | 2.28320 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.48528 | 0.194662 | 0.0973311 | − | 0.995252i | \(-0.468969\pi\) | ||||
0.0973311 | + | 0.995252i | \(0.468969\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.17157 | −0.0912068 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.7279 | −0.830152 | −0.415076 | − | 0.909787i | \(-0.636245\pi\) | ||||
−0.415076 | + | 0.909787i | \(0.636245\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.97056 | −0.613120 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.65685 | −0.203175 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.89949 | 0.296473 | 0.148237 | − | 0.988952i | \(-0.452640\pi\) | ||||
0.148237 | + | 0.988952i | \(0.452640\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.82843 | −0.364995 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.37258 | −0.103170 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.6569 | −1.61871 | −0.809355 | − | 0.587320i | \(-0.800183\pi\) | ||||
−0.809355 | + | 0.587320i | \(0.800183\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.0000 | 1.33793 | 0.668965 | − | 0.743294i | \(-0.266738\pi\) | ||||
0.668965 | + | 0.743294i | \(0.266738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.37258 | 0.101464 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.2426 | −0.753054 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.65685 | −0.706179 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 16.0000 | 1.16383 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.00000 | 0.289430 | 0.144715 | − | 0.989473i | \(-0.453773\pi\) | ||||
0.144715 | + | 0.989473i | \(0.453773\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.585786 | 0.0421658 | 0.0210829 | − | 0.999778i | \(-0.493289\pi\) | ||||
0.0210829 | + | 0.999778i | \(0.493289\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.31371 | 0.0940766 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.31371 | 0.378586 | 0.189293 | − | 0.981921i | \(-0.439380\pi\) | ||||
0.189293 | + | 0.981921i | \(0.439380\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.3431 | −0.733206 | −0.366603 | − | 0.930377i | \(-0.619479\pi\) | ||||
−0.366603 | + | 0.930377i | \(0.619479\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.343146 | 0.0242036 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 50.6274 | 3.55335 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.65685 | 0.534778 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.9411 | 1.10798 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.00000 | 0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.5147 | 0.792706 | 0.396353 | − | 0.918098i | \(-0.370276\pi\) | ||||
0.396353 | + | 0.918098i | \(0.370276\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.34315 | 0.434625 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.828427 | −0.0564983 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.65685 | 0.384012 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.48528 | 0.573382 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.8284 | 0.728399 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.2132 | 1.28661 | 0.643306 | − | 0.765609i | \(-0.277562\pi\) | ||||
0.643306 | + | 0.765609i | \(0.277562\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.65685 | −0.177124 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.5858 | −1.36633 | −0.683163 | − | 0.730266i | \(-0.739396\pi\) | ||||
−0.683163 | + | 0.730266i | \(0.739396\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.6569 | 1.43113 | 0.715563 | − | 0.698549i | \(-0.246170\pi\) | ||||
0.715563 | + | 0.698549i | \(0.246170\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.65685 | −0.372194 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.0000 | 0.655122 | 0.327561 | − | 0.944830i | \(-0.393773\pi\) | ||||
0.327561 | + | 0.944830i | \(0.393773\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.828427 | −0.0540406 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.65685 | −0.367452 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.3431 | 0.669042 | 0.334521 | − | 0.942388i | \(-0.391425\pi\) | ||||
0.334521 | + | 0.942388i | \(0.391425\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −30.2843 | −1.95078 | −0.975391 | − | 0.220484i | \(-0.929236\pi\) | ||||
−0.975391 | + | 0.220484i | \(0.929236\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.4731 | 0.864299 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −16.3137 | −1.04224 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.24264 | −0.142696 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.45584 | −0.345750 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.6569 | 0.862013 | 0.431006 | − | 0.902349i | \(-0.358159\pi\) | ||||
0.431006 | + | 0.902349i | \(0.358159\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.0000 | −0.754434 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.82843 | 0.177123 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.24264 | −0.139892 | −0.0699460 | − | 0.997551i | \(-0.522283\pi\) | ||||
−0.0699460 | + | 0.997551i | \(0.522283\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −49.4558 | −3.07304 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 27.8579 | 1.72436 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.65685 | 0.225491 | 0.112746 | − | 0.993624i | \(-0.464035\pi\) | ||||
0.112746 | + | 0.993624i | \(0.464035\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.07107 | −0.311513 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.14214 | 0.375893 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.4853 | 1.37095 | 0.685476 | − | 0.728095i | \(-0.259594\pi\) | ||||
0.685476 | + | 0.728095i | \(0.259594\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.6569 | 1.43705 | 0.718526 | − | 0.695500i | \(-0.244817\pi\) | ||||
0.718526 | + | 0.695500i | \(0.244817\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.34315 | 0.383905 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.00000 | 0.120605 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.8284 | −1.01112 | −0.505561 | − | 0.862791i | \(-0.668714\pi\) | ||||
−0.505561 | + | 0.862791i | \(0.668714\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.11270 | 0.186352 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.9706 | 1.13169 | 0.565844 | − | 0.824512i | \(-0.308550\pi\) | ||||
0.565844 | + | 0.824512i | \(0.308550\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.68629 | 0.159683 | 0.0798417 | − | 0.996808i | \(-0.474559\pi\) | ||||
0.0798417 | + | 0.996808i | \(0.474559\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.585786 | −0.0346990 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 36.9706 | 2.18230 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.31371 | 0.371395 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.02944 | −0.0603467 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.4142 | 1.36787 | 0.683936 | − | 0.729542i | \(-0.260267\pi\) | ||||
0.683936 | + | 0.729542i | \(0.260267\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.34315 | 0.136423 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.62742 | −0.384562 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.4558 | 0.778172 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.00000 | −0.230556 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.34315 | −0.134610 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.34315 | −0.134168 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.89949 | −0.450848 | −0.225424 | − | 0.974261i | \(-0.572377\pi\) | ||||
−0.225424 | + | 0.974261i | \(0.572377\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.31371 | −0.529838 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.0000 | −0.793867 | −0.396934 | − | 0.917847i | \(-0.629926\pi\) | ||||
−0.396934 | + | 0.917847i | \(0.629926\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.0000 | 1.01742 | 0.508710 | − | 0.860938i | \(-0.330123\pi\) | ||||
0.508710 | + | 0.860938i | \(0.330123\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −12.8284 | −0.722800 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.75736 | 0.323366 | 0.161683 | − | 0.986843i | \(-0.448308\pi\) | ||||
0.161683 | + | 0.986843i | \(0.448308\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.9706 | −1.17413 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.68629 | −0.149934 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.82843 | −0.268661 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.24264 | −0.124399 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.17157 | 0.285989 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.00000 | −0.220527 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.17157 | −0.0643955 | −0.0321977 | − | 0.999482i | \(-0.510251\pi\) | ||||
−0.0321977 | + | 0.999482i | \(0.510251\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −27.2132 | −1.49127 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.585786 | −0.0320049 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.7574 | 0.967305 | 0.483652 | − | 0.875260i | \(-0.339310\pi\) | ||||
0.483652 | + | 0.875260i | \(0.339310\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.97056 | 0.161339 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.34315 | −0.126888 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −44.9706 | −2.42818 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.51472 | 0.189226 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −22.9706 | −1.23312 | −0.616562 | − | 0.787306i | \(-0.711475\pi\) | ||||
−0.616562 | + | 0.787306i | \(0.711475\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.343146 | 0.0183682 | 0.00918409 | − | 0.999958i | \(-0.497077\pi\) | ||||
0.00918409 | + | 0.999958i | \(0.497077\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.43146 | 0.396662 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.85786 | −0.205333 | −0.102667 | − | 0.994716i | \(-0.532738\pi\) | ||||
−0.102667 | + | 0.994716i | \(0.532738\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.8284 | −0.574713 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 13.6569 | 0.722797 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.3137 | −1.12489 | −0.562447 | − | 0.826833i | \(-0.690140\pi\) | ||||
−0.562447 | + | 0.826833i | \(0.690140\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.10051 | −0.215221 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.4853 | −0.758194 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.1421 | −1.46901 | −0.734504 | − | 0.678605i | \(-0.762585\pi\) | ||||
−0.734504 | + | 0.678605i | \(0.762585\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 20.3431 | 1.05902 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.4853 | −1.27121 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.55635 | −0.494809 | −0.247405 | − | 0.968912i | \(-0.579578\pi\) | ||||
−0.247405 | + | 0.968912i | \(0.579578\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.585786 | −0.0302499 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 23.5147 | 1.21107 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.3431 | −1.14769 | −0.573845 | − | 0.818964i | \(-0.694549\pi\) | ||||
−0.573845 | + | 0.818964i | \(0.694549\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.6274 | −0.646922 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.92893 | 0.149661 | 0.0748307 | − | 0.997196i | \(-0.476158\pi\) | ||||
0.0748307 | + | 0.997196i | \(0.476158\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.65685 | 0.492159 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.20101 | −0.111884 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 28.6274 | 1.45147 | 0.725734 | − | 0.687976i | \(-0.241500\pi\) | ||||
0.725734 | + | 0.687976i | \(0.241500\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.9706 | 1.46510 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.31371 | 0.167154 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.65685 | 0.485889 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.1421 | 1.61317 | 0.806584 | − | 0.591120i | \(-0.201314\pi\) | ||||
0.806584 | + | 0.591120i | \(0.201314\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.82843 | −0.141598 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.68629 | −0.333897 | −0.166949 | − | 0.985966i | \(-0.553391\pi\) | ||||
−0.166949 | + | 0.985966i | \(0.553391\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.62742 | 0.130881 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.02944 | −0.299605 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20.4853 | 1.01542 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.51472 | 0.470473 | 0.235236 | − | 0.971938i | \(-0.424414\pi\) | ||||
0.235236 | + | 0.971938i | \(0.424414\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.7990 | −0.582001 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.3137 | 0.556711 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.31371 | 0.457192 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.1421 | 0.496663 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.65685 | −0.471768 | −0.235884 | − | 0.971781i | \(-0.575799\pi\) | ||||
−0.235884 | + | 0.971781i | \(0.575799\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.34315 | 0.406620 | 0.203310 | − | 0.979114i | \(-0.434830\pi\) | ||||
0.203310 | + | 0.979114i | \(0.434830\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.20101 | −0.107017 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.82843 | −0.234213 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.3137 | −0.547509 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.62742 | −0.126853 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.4558 | 1.61151 | 0.805756 | − | 0.592248i | \(-0.201759\pi\) | ||||
0.805756 | + | 0.592248i | \(0.201759\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.2132 | −0.731100 | −0.365550 | − | 0.930792i | \(-0.619119\pi\) | ||||
−0.365550 | + | 0.930792i | \(0.619119\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.14214 | 0.294493 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.00000 | −0.287019 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −29.6569 | −1.41544 | −0.707722 | − | 0.706491i | \(-0.750277\pi\) | ||||
−0.707722 | + | 0.706491i | \(0.750277\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −43.3431 | −2.06396 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.2843 | −1.62889 | −0.814447 | − | 0.580237i | \(-0.802960\pi\) | ||||
−0.814447 | + | 0.580237i | \(0.802960\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.4853 | −0.497050 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.68629 | 0.221654 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.5147 | −0.637799 | −0.318900 | − | 0.947789i | \(-0.603313\pi\) | ||||
−0.318900 | + | 0.947789i | \(0.603313\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.3137 | −0.721094 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.6274 | 0.499320 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.8284 | −0.507644 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.9706 | 0.887405 | 0.443703 | − | 0.896174i | \(-0.353665\pi\) | ||||
0.443703 | + | 0.896174i | \(0.353665\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 16.0000 | 0.746816 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.31371 | 0.247484 | 0.123742 | − | 0.992314i | \(-0.460510\pi\) | ||||
0.123742 | + | 0.992314i | \(0.460510\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.31371 | −0.432845 | −0.216422 | − | 0.976300i | \(-0.569439\pi\) | ||||
−0.216422 | + | 0.976300i | \(0.569439\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.686292 | 0.0318260 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.31371 | −0.430987 | −0.215494 | − | 0.976505i | \(-0.569136\pi\) | ||||
−0.215494 | + | 0.976505i | \(0.569136\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.82843 | −0.130605 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.85786 | −0.0856059 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.65685 | 0.0761822 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.4731 | −0.616890 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.0000 | −0.456912 | −0.228456 | − | 0.973554i | \(-0.573368\pi\) | ||||
−0.228456 | + | 0.973554i | \(0.573368\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.9706 | −1.04737 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 16.9706 | 0.772187 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.75736 | 0.0797976 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.3848 | 1.10498 | 0.552490 | − | 0.833520i | \(-0.313678\pi\) | ||||
0.552490 | + | 0.833520i | \(0.313678\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.45584 | 0.0658355 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −35.3137 | −1.59369 | −0.796843 | − | 0.604187i | \(-0.793498\pi\) | ||||
−0.796843 | + | 0.604187i | \(0.793498\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 50.6274 | 2.28014 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.31371 | 0.238833 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −52.2843 | −2.34527 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.9706 | 1.20737 | 0.603684 | − | 0.797224i | \(-0.293699\pi\) | ||||
0.603684 | + | 0.797224i | \(0.293699\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.28427 | −0.280761 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.97056 | 0.132451 | 0.0662254 | − | 0.997805i | \(-0.478904\pi\) | ||||
0.0662254 | + | 0.997805i | \(0.478904\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.00000 | 0.177998 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.66905 | −0.207360 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 33.7990 | 1.49811 | 0.749057 | − | 0.662506i | \(-0.230507\pi\) | ||||
0.749057 | + | 0.662506i | \(0.230507\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −69.9411 | −3.09401 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.31371 | −0.146304 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.8995 | 0.700615 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.65685 | 0.0728684 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.28427 | 0.100268 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.3431 | 1.24174 | 0.620868 | − | 0.783915i | \(-0.286780\pi\) | ||||
0.620868 | + | 0.783915i | \(0.286780\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.72792 | 0.294191 | 0.147096 | − | 0.989122i | \(-0.453007\pi\) | ||||
0.147096 | + | 0.989122i | \(0.453007\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.82843 | −0.123443 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.65685 | 0.246416 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000 | 0.565217 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.22540 | 0.270159 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.1716 | 0.743783 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.58579 | 0.198261 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.6863 | −0.547454 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 32.6274 | 1.40536 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.3137 | −0.486414 | −0.243207 | − | 0.969974i | \(-0.578199\pi\) | ||||
−0.243207 | + | 0.969974i | \(0.578199\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.5442 | 0.452493 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.82843 | −0.378168 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.3848 | −1.55570 | −0.777850 | − | 0.628450i | \(-0.783690\pi\) | ||||
−0.777850 | + | 0.628450i | \(0.783690\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.22540 | −0.265693 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.4853 | −0.446688 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 46.6274 | 1.98280 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.00000 | −0.254686 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −41.7990 | −1.77108 | −0.885540 | − | 0.464563i | \(-0.846211\pi\) | ||||
−0.885540 | + | 0.464563i | \(0.846211\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.85786 | −0.0785793 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.65685 | −0.238833 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.4142 | 0.481052 | 0.240526 | − | 0.970643i | \(-0.422680\pi\) | ||||
0.240526 | + | 0.970643i | \(0.422680\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.07107 | −0.213341 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −29.1127 | −1.22262 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.828427 | 0.0347295 | 0.0173647 | − | 0.999849i | \(-0.494472\pi\) | ||||
0.0173647 | + | 0.999849i | \(0.494472\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.6863 | 0.614602 | 0.307301 | − | 0.951612i | \(-0.400574\pi\) | ||||
0.307301 | + | 0.951612i | \(0.400574\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.34315 | 0.0978863 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.00000 | −0.250217 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.00000 | −0.249783 | −0.124892 | − | 0.992170i | \(-0.539858\pi\) | ||||
−0.124892 | + | 0.992170i | \(0.539858\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.343146 | 0.0142607 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 44.9706 | 1.86569 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.1421 | 0.420044 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.95837 | −0.246348 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.9706 | 0.617901 | 0.308951 | − | 0.951078i | \(-0.400022\pi\) | ||||
0.308951 | + | 0.951078i | \(0.400022\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.17157 | −0.0482738 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.11270 | 0.128039 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.62742 | 0.354286 | 0.177143 | − | 0.984185i | \(-0.443315\pi\) | ||||
0.177143 | + | 0.984185i | \(0.443315\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −23.3137 | −0.955769 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.05887 | −0.247973 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.68629 | −0.191477 | −0.0957383 | − | 0.995407i | \(-0.530521\pi\) | ||||
−0.0957383 | + | 0.995407i | \(0.530521\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.0000 | −0.734235 | −0.367118 | − | 0.930175i | \(-0.619655\pi\) | ||||
−0.367118 | + | 0.930175i | \(0.619655\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.55635 | −0.0633794 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.00000 | 0.284590 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.07107 | 0.205828 | 0.102914 | − | 0.994690i | \(-0.467183\pi\) | ||||
0.102914 | + | 0.994690i | \(0.467183\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 29.6569 | 1.20176 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.85786 | −0.0751611 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.5147 | −0.707413 | −0.353706 | − | 0.935356i | \(-0.615079\pi\) | ||||
−0.353706 | + | 0.935356i | \(0.615079\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.48528 | 0.180864 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.20101 | −0.249643 | −0.124822 | − | 0.992179i | \(-0.539836\pi\) | ||||
−0.124822 | + | 0.992179i | \(0.539836\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.0000 | −0.723481 | −0.361741 | − | 0.932279i | \(-0.617817\pi\) | ||||
−0.361741 | + | 0.932279i | \(0.617817\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 19.8823 | 0.797847 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −50.6274 | −2.02834 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.17157 | 0.0467881 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −49.4558 | −1.97193 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.65685 | −0.145577 | −0.0727885 | − | 0.997347i | \(-0.523190\pi\) | ||||
−0.0727885 | + | 0.997347i | \(0.523190\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.74517 | 0.268096 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21.5563 | 0.855438 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −36.5858 | −1.44958 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −28.7696 | −1.13811 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.3137 | −0.841841 | −0.420920 | − | 0.907098i | \(-0.638293\pi\) | ||||
−0.420920 | + | 0.907098i | \(0.638293\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.6274 | −0.971211 | −0.485605 | − | 0.874178i | \(-0.661401\pi\) | ||||
−0.485605 | + | 0.874178i | \(0.661401\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.485281 | −0.0191079 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.68629 | 0.262865 | 0.131433 | − | 0.991325i | \(-0.458042\pi\) | ||||
0.131433 | + | 0.991325i | \(0.458042\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.68629 | −0.183953 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.31371 | 0.129874 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.7990 | −0.539996 | −0.269998 | − | 0.962861i | \(-0.587023\pi\) | ||||
−0.269998 | + | 0.962861i | \(0.587023\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.65685 | −0.221032 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −38.4853 | −1.50145 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 34.6274 | 1.34889 | 0.674446 | − | 0.738324i | \(-0.264382\pi\) | ||||
0.674446 | + | 0.738324i | \(0.264382\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.6274 | 0.491150 | 0.245575 | − | 0.969378i | \(-0.421023\pi\) | ||||
0.245575 | + | 0.969378i | \(0.421023\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.34315 | 0.246347 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.82843 | 0.187238 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 62.9117 | 2.43595 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.2548 | 0.435137 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.68629 | 0.180912 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.2426 | 0.394825 | 0.197412 | − | 0.980321i | \(-0.436746\pi\) | ||||
0.197412 | + | 0.980321i | \(0.436746\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.31371 | −0.127545 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.5563 | −0.982210 | −0.491105 | − | 0.871100i | \(-0.663407\pi\) | ||||
−0.491105 | + | 0.871100i | \(0.663407\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.48528 | 0.325635 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.0589 | −0.462097 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.7279 | 1.48188 | 0.740941 | − | 0.671570i | \(-0.234380\pi\) | ||||
0.740941 | + | 0.671570i | \(0.234380\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.1421 | 0.769591 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.6863 | 0.484012 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.3726 | −0.433261 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.6569 | 0.595615 | 0.297807 | − | 0.954626i | \(-0.403745\pi\) | ||||
0.297807 | + | 0.954626i | \(0.403745\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 25.6569 | 0.974623 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17.3137 | −0.656746 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 36.9706 | 1.40036 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.85786 | 0.221565 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −49.6569 | −1.87551 | −0.937757 | − | 0.347293i | \(-0.887101\pi\) | ||||
−0.937757 | + | 0.347293i | \(0.887101\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.2426 | 0.386309 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.485281 | −0.0182768 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19.3137 | 0.726367 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.9706 | −0.712454 | −0.356227 | − | 0.934399i | \(-0.615937\pi\) | ||||
−0.356227 | + | 0.934399i | \(0.615937\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 25.6569 | 0.962207 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.02944 | 0.263254 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.48528 | 0.167740 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.05887 | 0.226273 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 38.2843 | 1.42776 | 0.713881 | − | 0.700267i | \(-0.246936\pi\) | ||||
0.713881 | + | 0.700267i | \(0.246936\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 76.7696 | 2.85905 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17.7401 | −0.659762 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.4853 | −0.389414 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.5147 | −1.09464 | −0.547320 | − | 0.836923i | \(-0.684352\pi\) | ||||
−0.547320 | + | 0.836923i | \(0.684352\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −10.1960 | −0.377628 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.00000 | −0.147945 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −39.6569 | −1.46476 | −0.732380 | − | 0.680896i | \(-0.761590\pi\) | ||||
−0.732380 | + | 0.680896i | \(0.761590\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.55635 | −0.352491 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.17157 | 0.0431554 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.6274 | −1.27379 | −0.636895 | − | 0.770951i | \(-0.719782\pi\) | ||||
−0.636895 | + | 0.770951i | \(0.719782\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.31371 | −0.0482603 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.0416 | 0.515137 | 0.257569 | − | 0.966260i | \(-0.417079\pi\) | ||||
0.257569 | + | 0.966260i | \(0.417079\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.00000 | −0.293097 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 24.7452 | 0.905378 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22.1421 | 0.809056 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.1421 | 0.516054 | 0.258027 | − | 0.966138i | \(-0.416928\pi\) | ||||
0.258027 | + | 0.966138i | \(0.416928\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.00000 | 0.291536 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18.1421 | −0.660260 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.6569 | −0.714441 | −0.357220 | − | 0.934020i | \(-0.616275\pi\) | ||||
−0.357220 | + | 0.934020i | \(0.616275\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.02944 | −0.255152 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.6274 | 1.11024 | 0.555121 | − | 0.831769i | \(-0.312672\pi\) | ||||
0.555121 | + | 0.831769i | \(0.312672\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −42.6274 | −1.54322 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12.8284 | −0.463813 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.25483 | 0.189741 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38.6274 | 1.39294 | 0.696470 | − | 0.717586i | \(-0.254753\pi\) | ||||
0.696470 | + | 0.717586i | \(0.254753\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.31371 | −0.0473121 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.100505 | 0.00361492 | 0.00180746 | − | 0.999998i | \(-0.499425\pi\) | ||||
0.00180746 | + | 0.999998i | \(0.499425\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.17157 | −0.0420841 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −28.9706 | −1.03931 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.65685 | −0.274335 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.6569 | 0.774943 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 34.7452 | 1.24169 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.17157 | 0.113198 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.8406 | 1.49146 | 0.745729 | − | 0.666250i | \(-0.232102\pi\) | ||||
0.745729 | + | 0.666250i | \(0.232102\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.14214 | 0.0762620 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −24.4853 | −0.870596 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.25483 | −0.186605 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.97056 | −0.105355 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.8995 | −0.421502 | −0.210751 | − | 0.977540i | \(-0.567591\pi\) | ||||
−0.210751 | + | 0.977540i | \(0.567591\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.00000 | −0.141510 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −27.8579 | −0.984309 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 28.9706 | 1.02235 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −28.9706 | −1.02108 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.1716 | 0.463661 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39.2548 | −1.38013 | −0.690063 | − | 0.723749i | \(-0.742417\pi\) | ||||
−0.690063 | + | 0.723749i | \(0.742417\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.7990 | −0.695237 | −0.347618 | − | 0.937636i | \(-0.613009\pi\) | ||||
−0.347618 | + | 0.937636i | \(0.613009\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.8579 | 0.486017 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.48528 | −0.0870556 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.828427 | 0.0289830 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −28.7696 | −1.00529 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.0000 | −0.349002 | −0.174501 | − | 0.984657i | \(-0.555831\pi\) | ||||
−0.174501 | + | 0.984657i | \(0.555831\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.1716 | −0.528848 | −0.264424 | − | 0.964407i | \(-0.585182\pi\) | ||||
−0.264424 | + | 0.964407i | \(0.585182\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.17157 | 0.0407889 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.0711 | 1.01090 | 0.505450 | − | 0.862856i | \(-0.331326\pi\) | ||||
0.505450 | + | 0.862856i | \(0.331326\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.4264 | 1.40407 | 0.702034 | − | 0.712144i | \(-0.252276\pi\) | ||||
0.702034 | + | 0.712144i | \(0.252276\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.85786 | −0.341966 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −78.7696 | −2.72920 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.7279 | 0.371255 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.88225 | 0.134190 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 43.5980 | 1.50517 | 0.752585 | − | 0.658495i | \(-0.228807\pi\) | ||||
0.752585 | + | 0.658495i | \(0.228807\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 80.9411 | 2.79107 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.1127 | 0.382742 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.97056 | 0.274196 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 33.7990 | 1.16135 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.57359 | 0.0540056 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −61.4558 | −2.10668 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42.0000 | −1.43805 | −0.719026 | − | 0.694983i | \(-0.755412\pi\) | ||||
−0.719026 | + | 0.694983i | \(0.755412\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.65685 | 0.0908625 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.2132 | −0.929585 | −0.464793 | − | 0.885420i | \(-0.653871\pi\) | ||||
−0.464793 | + | 0.885420i | \(0.653871\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.2843 | 0.828569 | 0.414284 | − | 0.910148i | \(-0.364032\pi\) | ||||
0.414284 | + | 0.910148i | \(0.364032\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 21.6569 | 0.738064 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.89949 | −0.132740 | −0.0663702 | − | 0.997795i | \(-0.521142\pi\) | ||||
−0.0663702 | + | 0.997795i | \(0.521142\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.89949 | −0.132587 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.69848 | 0.125607 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19.3137 | −0.655173 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.31371 | −0.0445133 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.66905 | 0.158023 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.82843 | 0.163231 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.0711 | 1.25180 | 0.625901 | − | 0.779903i | \(-0.284732\pi\) | ||||
0.625901 | + | 0.779903i | \(0.284732\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.7157 | 0.462620 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.2843 | 1.49198 | 0.745988 | − | 0.665960i | \(-0.231978\pi\) | ||||
0.745988 | + | 0.665960i | \(0.231978\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39.1716 | 1.31823 | 0.659114 | − | 0.752043i | \(-0.270931\pi\) | ||||
0.659114 | + | 0.752043i | \(0.270931\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.37258 | 0.0461389 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −49.0711 | −1.64765 | −0.823823 | − | 0.566848i | \(-0.808163\pi\) | ||||
−0.823823 | + | 0.566848i | \(0.808163\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 104.083 | 3.49084 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12.0589 | 0.403987 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.828427 | 0.0277223 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.6569 | 0.723909 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.88225 | 0.263181 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.2843 | 0.409703 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.4853 | −0.815723 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.34315 | −0.0779750 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.0000 | −0.598340 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.3848 | 0.676865 | 0.338433 | − | 0.940991i | \(-0.390103\pi\) | ||||
0.338433 | + | 0.940991i | \(0.390103\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.6274 | 0.352489 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.20101 | 0.139186 | 0.0695928 | − | 0.997575i | \(-0.477830\pi\) | ||||
0.0695928 | + | 0.997575i | \(0.477830\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.6274 | −0.616478 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.37258 | −0.0453762 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −27.3137 | −0.901978 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.3137 | 1.16489 | 0.582446 | − | 0.812869i | \(-0.302096\pi\) | ||||
0.582446 | + | 0.812869i | \(0.302096\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.62742 | −0.152479 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −24.2843 | −0.799327 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.2426 | 0.336776 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 42.2426 | 1.38743 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.68629 | 0.219370 | 0.109685 | − | 0.993966i | \(-0.465016\pi\) | ||||
0.109685 | + | 0.993966i | \(0.465016\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.3137 | 0.534660 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.20101 | −0.268489 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.65685 | 0.315813 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.1421 | −1.31139 | −0.655693 | − | 0.755027i | \(-0.727624\pi\) | ||||
−0.655693 | + | 0.755027i | \(0.727624\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.5442 | 0.344096 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.2843 | 0.987239 | 0.493620 | − | 0.869678i | \(-0.335674\pi\) | ||||
0.493620 | + | 0.869678i | \(0.335674\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 45.9411 | 1.49605 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −16.0000 | −0.520480 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.34315 | 0.271116 | 0.135558 | − | 0.990769i | \(-0.456717\pi\) | ||||
0.135558 | + | 0.990769i | \(0.456717\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −32.4853 | −1.05452 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.37258 | 0.109363 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.75736 | 0.186499 | 0.0932496 | − | 0.995643i | \(-0.470275\pi\) | ||||
0.0932496 | + | 0.995643i | \(0.470275\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.00000 | −0.129437 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.2843 | −0.397094 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 97.2548 | 3.14052 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.6274 | −0.955723 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.1838 | 0.392616 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.585786 | −0.0188571 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.6274 | 0.663333 | 0.331667 | − | 0.943397i | \(-0.392389\pi\) | ||||
0.331667 | + | 0.943397i | \(0.392389\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.82843 | −0.0908622 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.1127 | 1.12682 | 0.563410 | − | 0.826177i | \(-0.309489\pi\) | ||||
0.563410 | + | 0.826177i | \(0.309489\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −83.5980 | −2.68003 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.31371 | −0.0420723 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.27208 | 0.296640 | 0.148320 | − | 0.988939i | \(-0.452613\pi\) | ||||
0.148320 | + | 0.988939i | \(0.452613\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.9706 | 0.670222 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23.4558 | −0.748887 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −23.4142 | −0.746797 | −0.373399 | − | 0.927671i | \(-0.621808\pi\) | ||||
−0.373399 | + | 0.927671i | \(0.621808\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.31371 | −0.169309 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.34315 | −0.0745832 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.97056 | −0.158055 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −51.1127 | −1.62365 | −0.811824 | − | 0.583902i | \(-0.801525\pi\) | ||||
−0.811824 | + | 0.583902i | \(0.801525\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.686292 | −0.0217788 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.3431 | 0.327900 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.5147 | 0.428015 | 0.214008 | − | 0.976832i | \(-0.431348\pi\) | ||||
0.214008 | + | 0.976832i | \(0.431348\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −33.9411 | −1.07385 |
(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 | 6080.2.a.bl.1.1 | 2 | ||
4.3 | odd | 2 | 6080.2.a.y.1.2 | 2 | |||
8.3 | odd | 2 | 1520.2.a.o.1.1 | 2 | |||
8.5 | even | 2 | 380.2.a.c.1.2 | ✓ | 2 | ||
24.5 | odd | 2 | 3420.2.a.g.1.1 | 2 | |||
40.13 | odd | 4 | 1900.2.c.d.1749.2 | 4 | |||
40.19 | odd | 2 | 7600.2.a.u.1.2 | 2 | |||
40.29 | even | 2 | 1900.2.a.e.1.1 | 2 | |||
40.37 | odd | 4 | 1900.2.c.d.1749.3 | 4 | |||
152.37 | odd | 2 | 7220.2.a.m.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.a.c.1.2 | ✓ | 2 | 8.5 | even | 2 | ||
1520.2.a.o.1.1 | 2 | 8.3 | odd | 2 | |||
1900.2.a.e.1.1 | 2 | 40.29 | even | 2 | |||
1900.2.c.d.1749.2 | 4 | 40.13 | odd | 4 | |||
1900.2.c.d.1749.3 | 4 | 40.37 | odd | 4 | |||
3420.2.a.g.1.1 | 2 | 24.5 | odd | 2 | |||
6080.2.a.y.1.2 | 2 | 4.3 | odd | 2 | |||
6080.2.a.bl.1.1 | 2 | 1.1 | even | 1 | trivial | ||
7220.2.a.m.1.1 | 2 | 152.37 | odd | 2 | |||
7600.2.a.u.1.2 | 2 | 40.19 | odd | 2 |