Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,2,Mod(1151,2880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2880.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.h (of order \(2\), degree \(1\), not 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: | \(22.9969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1440) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1151.2 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2880.1151 |
Dual form | 2880.2.h.b.1151.3 |
$q$-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 \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 1.00000i | − 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.41421i | 1.29045i | 0.763992 | + | 0.645226i | \(0.223237\pi\) | ||||
−0.763992 | + | 0.645226i | \(0.776763\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.41421 | −0.426401 | −0.213201 | − | 0.977008i | \(-0.568389\pi\) | ||||
−0.213201 | + | 0.977008i | \(0.568389\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.24264 | 1.73140 | 0.865699 | − | 0.500566i | \(-0.166875\pi\) | ||||
0.865699 | + | 0.500566i | \(0.166875\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.82843i | 1.65614i | 0.560627 | + | 0.828068i | \(0.310560\pi\) | ||||
−0.560627 | + | 0.828068i | \(0.689440\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.65685i | 1.29777i | 0.760886 | + | 0.648886i | \(0.224765\pi\) | ||||
−0.760886 | + | 0.648886i | \(0.775235\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.82843 | −1.84085 | −0.920427 | − | 0.390914i | \(-0.872159\pi\) | ||||
−0.920427 | + | 0.390914i | \(0.872159\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 2.00000i | − 0.371391i | −0.982607 | − | 0.185695i | \(-0.940546\pi\) | ||||
0.982607 | − | 0.185695i | \(-0.0594537\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 8.82843i | − 1.58563i | −0.609461 | − | 0.792816i | \(-0.708614\pi\) | ||||
0.609461 | − | 0.792816i | \(-0.291386\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.41421 | 0.577107 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.41421 | −1.21889 | −0.609445 | − | 0.792829i | \(-0.708608\pi\) | ||||
−0.609445 | + | 0.792829i | \(0.708608\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 0.242641i | − 0.0378941i | −0.999820 | − | 0.0189471i | \(-0.993969\pi\) | ||||
0.999820 | − | 0.0189471i | \(-0.00603140\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 1.17157i | − 0.178663i | −0.996002 | − | 0.0893316i | \(-0.971527\pi\) | ||||
0.996002 | − | 0.0893316i | \(-0.0284731\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.00000 | −1.16692 | −0.583460 | − | 0.812142i | \(-0.698301\pi\) | ||||
−0.583460 | + | 0.812142i | \(0.698301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.65685 | −0.665265 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 1.17157i | − 0.160928i | −0.996758 | − | 0.0804640i | \(-0.974360\pi\) | ||||
0.996758 | − | 0.0804640i | \(-0.0256402\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.41421i | 0.190693i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.58579 | 0.336641 | 0.168320 | − | 0.985732i | \(-0.446166\pi\) | ||||
0.168320 | + | 0.985732i | \(0.446166\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.82843 | 1.13036 | 0.565182 | − | 0.824966i | \(-0.308806\pi\) | ||||
0.565182 | + | 0.824966i | \(0.308806\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 6.24264i | − 0.774304i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.3137i | 1.38219i | 0.722764 | + | 0.691095i | \(0.242871\pi\) | ||||
−0.722764 | + | 0.691095i | \(0.757129\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.34315 | −0.278080 | −0.139040 | − | 0.990287i | \(-0.544402\pi\) | ||||
−0.139040 | + | 0.990287i | \(0.544402\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.82843 | −0.565125 | −0.282562 | − | 0.959249i | \(-0.591184\pi\) | ||||
−0.282562 | + | 0.959249i | \(0.591184\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 4.82843i | − 0.550250i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.4853i | 1.17969i | 0.807518 | + | 0.589843i | \(0.200810\pi\) | ||||
−0.807518 | + | 0.589843i | \(0.799190\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.82843 | −0.749517 | −0.374759 | − | 0.927122i | \(-0.622274\pi\) | ||||
−0.374759 | + | 0.927122i | \(0.622274\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.82843 | 0.740647 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.0711i | 1.59753i | 0.601643 | + | 0.798765i | \(0.294513\pi\) | ||||
−0.601643 | + | 0.798765i | \(0.705487\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 21.3137i | 2.23428i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.65685 | 0.580381 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.48528 | −0.658481 | −0.329240 | − | 0.944246i | \(-0.606793\pi\) | ||||
−0.329240 | + | 0.944246i | \(0.606793\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 16.8284i | − 1.67449i | −0.546827 | − | 0.837246i | \(-0.684165\pi\) | ||||
0.546827 | − | 0.837246i | \(-0.315835\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.24264i | 0.615106i | 0.951531 | + | 0.307553i | \(0.0995101\pi\) | ||||
−0.951531 | + | 0.307553i | \(0.900490\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.1421 | 0.980477 | 0.490239 | − | 0.871588i | \(-0.336910\pi\) | ||||
0.490239 | + | 0.871588i | \(0.336910\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.17157 | −0.303782 | −0.151891 | − | 0.988397i | \(-0.548536\pi\) | ||||
−0.151891 | + | 0.988397i | \(0.548536\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.00000i | 0.376288i | 0.982141 | + | 0.188144i | \(0.0602472\pi\) | ||||
−0.982141 | + | 0.188144i | \(0.939753\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.82843i | 0.823255i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −23.3137 | −2.13716 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.4142i | 1.36779i | 0.729580 | + | 0.683895i | \(0.239715\pi\) | ||||
−0.729580 | + | 0.683895i | \(0.760285\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.8995 | −1.21440 | −0.607202 | − | 0.794547i | \(-0.707708\pi\) | ||||
−0.607202 | + | 0.794547i | \(0.707708\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −19.3137 | −1.67471 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.65685i | 0.483298i | 0.970364 | + | 0.241649i | \(0.0776882\pi\) | ||||
−0.970364 | + | 0.241649i | \(0.922312\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 8.34315i | − 0.707656i | −0.935310 | − | 0.353828i | \(-0.884880\pi\) | ||||
0.935310 | − | 0.353828i | \(-0.115120\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.82843 | −0.738270 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00000 | −0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.82843i | 0.395560i | 0.980246 | + | 0.197780i | \(0.0633732\pi\) | ||||
−0.980246 | + | 0.197780i | \(0.936627\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.9706i | 0.892772i | 0.894841 | + | 0.446386i | \(0.147289\pi\) | ||||
−0.894841 | + | 0.446386i | \(0.852711\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.82843 | −0.709116 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.100505 | −0.00802118 | −0.00401059 | − | 0.999992i | \(-0.501277\pi\) | ||||
−0.00401059 | + | 0.999992i | \(0.501277\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 30.1421i | − 2.37553i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.48528i | 0.664619i | 0.943170 | + | 0.332309i | \(0.107828\pi\) | ||||
−0.943170 | + | 0.332309i | \(0.892172\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.4853 | 1.12090 | 0.560452 | − | 0.828187i | \(-0.310627\pi\) | ||||
0.560452 | + | 0.828187i | \(0.310627\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.9706 | 1.99774 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 0.485281i | − 0.0368953i | −0.999830 | − | 0.0184476i | \(-0.994128\pi\) | ||||
0.999830 | − | 0.0184476i | \(-0.00587240\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 3.41421i | − 0.258090i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.4142 | −1.00263 | −0.501313 | − | 0.865266i | \(-0.667149\pi\) | ||||
−0.501313 | + | 0.865266i | \(0.667149\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.8284 | 1.84548 | 0.922741 | − | 0.385420i | \(-0.125943\pi\) | ||||
0.922741 | + | 0.385420i | \(0.125943\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.41421i | 0.545104i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 9.65685i | − 0.706179i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.17157 | −0.0847720 | −0.0423860 | − | 0.999101i | \(-0.513496\pi\) | ||||
−0.0423860 | + | 0.999101i | \(0.513496\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.34315 | 0.312626 | 0.156313 | − | 0.987708i | \(-0.450039\pi\) | ||||
0.156313 | + | 0.987708i | \(0.450039\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.00000i | 0.427482i | 0.976890 | + | 0.213741i | \(0.0685649\pi\) | ||||
−0.976890 | + | 0.213741i | \(0.931435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 15.6569i | − 1.10988i | −0.831889 | − | 0.554942i | \(-0.812740\pi\) | ||||
0.831889 | − | 0.554942i | \(-0.187260\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.82843 | 0.479262 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.242641 | −0.0169468 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 8.00000i | − 0.553372i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.00000i | 0.413057i | 0.978441 | + | 0.206529i | \(0.0662166\pi\) | ||||
−0.978441 | + | 0.206529i | \(0.933783\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.17157 | −0.0799006 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 30.1421 | 2.04618 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 42.6274i | 2.86743i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 4.10051i | − 0.274590i | −0.990530 | − | 0.137295i | \(-0.956159\pi\) | ||||
0.990530 | − | 0.137295i | \(-0.0438409\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 28.2843 | 1.87729 | 0.938647 | − | 0.344881i | \(-0.112081\pi\) | ||||
0.938647 | + | 0.344881i | \(0.112081\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.65685 | −0.505979 | −0.252990 | − | 0.967469i | \(-0.581414\pi\) | ||||
−0.252990 | + | 0.967469i | \(0.581414\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.4853i | 0.817938i | 0.912548 | + | 0.408969i | \(0.134112\pi\) | ||||
−0.912548 | + | 0.408969i | \(0.865888\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.00000i | 0.521862i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.14214 | −0.397302 | −0.198651 | − | 0.980070i | \(-0.563656\pi\) | ||||
−0.198651 | + | 0.980070i | \(0.563656\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.3431 | −0.923923 | −0.461962 | − | 0.886900i | \(-0.652854\pi\) | ||||
−0.461962 | + | 0.886900i | \(0.652854\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.65685i | 0.297516i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 35.3137i | 2.24696i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.7279 | −1.30833 | −0.654167 | − | 0.756350i | \(-0.726981\pi\) | ||||
−0.654167 | + | 0.756350i | \(0.726981\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.4853 | 0.784943 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.97056i | 0.559568i | 0.960063 | + | 0.279784i | \(0.0902629\pi\) | ||||
−0.960063 | + | 0.279784i | \(0.909737\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 25.3137i | − 1.57292i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.8284 | 1.53099 | 0.765493 | − | 0.643444i | \(-0.222495\pi\) | ||||
0.765493 | + | 0.643444i | \(0.222495\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.17157 | −0.0719691 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 10.9706i | − 0.668887i | −0.942416 | − | 0.334444i | \(-0.891452\pi\) | ||||
0.942416 | − | 0.334444i | \(-0.108548\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.31371i | 0.0798021i | 0.999204 | + | 0.0399011i | \(0.0127043\pi\) | ||||
−0.999204 | + | 0.0399011i | \(0.987296\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.41421 | 0.0852803 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −32.8701 | −1.97497 | −0.987485 | − | 0.157712i | \(-0.949588\pi\) | ||||
−0.987485 | + | 0.157712i | \(0.949588\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 1.89949i | − 0.113314i | −0.998394 | − | 0.0566572i | \(-0.981956\pi\) | ||||
0.998394 | − | 0.0566572i | \(-0.0180442\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.3137i | 0.910305i | 0.890413 | + | 0.455153i | \(0.150415\pi\) | ||||
−0.890413 | + | 0.455153i | \(0.849585\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.828427 | 0.0489005 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −29.6274 | −1.74279 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 2.00000i | − 0.116841i | −0.998292 | − | 0.0584206i | \(-0.981394\pi\) | ||||
0.998292 | − | 0.0584206i | \(-0.0186065\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 2.58579i | − 0.150550i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −55.1127 | −3.18725 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000 | 0.230556 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 8.82843i | − 0.505514i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 19.3137i | − 1.10229i | −0.834409 | − | 0.551146i | \(-0.814191\pi\) | ||||
0.834409 | − | 0.551146i | \(-0.185809\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.4853 | 1.61525 | 0.807626 | − | 0.589695i | \(-0.200752\pi\) | ||||
0.807626 | + | 0.589695i | \(0.200752\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.2843 | 1.25958 | 0.629791 | − | 0.776765i | \(-0.283141\pi\) | ||||
0.629791 | + | 0.776765i | \(0.283141\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 5.31371i | − 0.298448i | −0.988803 | − | 0.149224i | \(-0.952323\pi\) | ||||
0.988803 | − | 0.149224i | \(-0.0476775\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.82843i | 0.158362i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −38.6274 | −2.14929 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.24264 | −0.346279 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 27.3137i | − 1.50585i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.68629i | 0.477442i | 0.971088 | + | 0.238721i | \(0.0767281\pi\) | ||||
−0.971088 | + | 0.238721i | \(0.923272\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.3137 | 0.618134 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.1716 | 0.608554 | 0.304277 | − | 0.952584i | \(-0.401585\pi\) | ||||
0.304277 | + | 0.952584i | \(0.401585\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.4853i | 0.676116i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.00000i | 0.431959i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.9706 | 0.696296 | 0.348148 | − | 0.937440i | \(-0.386811\pi\) | ||||
0.348148 | + | 0.937440i | \(0.386811\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.17157 | −0.169770 | −0.0848852 | − | 0.996391i | \(-0.527052\pi\) | ||||
−0.0848852 | + | 0.996391i | \(0.527052\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 32.4853i | − 1.72902i | −0.502618 | − | 0.864509i | \(-0.667630\pi\) | ||||
0.502618 | − | 0.864509i | \(-0.332370\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.34315i | 0.124361i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −31.1127 | −1.64207 | −0.821033 | − | 0.570881i | \(-0.806602\pi\) | ||||
−0.821033 | + | 0.570881i | \(0.806602\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.0000 | −0.684211 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.82843i | 0.252731i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 33.0711i | 1.72630i | 0.504951 | + | 0.863148i | \(0.331510\pi\) | ||||
−0.504951 | + | 0.863148i | \(0.668490\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.00000 | 0.207670 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.0711 | −0.883906 | −0.441953 | − | 0.897038i | \(-0.645714\pi\) | ||||
−0.441953 | + | 0.897038i | \(0.645714\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 12.4853i | − 0.643025i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 29.3137i | − 1.50574i | −0.658167 | − | 0.752872i | \(-0.728668\pi\) | ||||
0.658167 | − | 0.752872i | \(-0.271332\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.6274 | −0.747426 | −0.373713 | − | 0.927544i | \(-0.621916\pi\) | ||||
−0.373713 | + | 0.927544i | \(0.621916\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.82843 | −0.246079 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 7.65685i | − 0.388218i | −0.980980 | − | 0.194109i | \(-0.937818\pi\) | ||||
0.980980 | − | 0.194109i | \(-0.0621815\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 60.2843i | − 3.04871i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.4853 | 0.527572 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.3848 | 0.822328 | 0.411164 | − | 0.911561i | \(-0.365122\pi\) | ||||
0.411164 | + | 0.911561i | \(0.365122\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.7279i | 0.835353i | 0.908596 | + | 0.417676i | \(0.137155\pi\) | ||||
−0.908596 | + | 0.417676i | \(0.862845\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 55.1127i | − 2.74536i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.4853 | 0.519736 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.6569 | 0.576394 | 0.288197 | − | 0.957571i | \(-0.406944\pi\) | ||||
0.288197 | + | 0.957571i | \(0.406944\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.82843i | 0.434418i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.82843i | 0.335194i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 36.2426 | 1.77057 | 0.885284 | − | 0.465050i | \(-0.153964\pi\) | ||||
0.885284 | + | 0.465050i | \(0.153964\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.9411 | −1.36177 | −0.680884 | − | 0.732392i | \(-0.738404\pi\) | ||||
−0.680884 | + | 0.732392i | \(0.738404\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 6.82843i | − 0.331227i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 30.1421i | 1.45868i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.4853 | 0.601395 | 0.300697 | − | 0.953720i | \(-0.402781\pi\) | ||||
0.300697 | + | 0.953720i | \(0.402781\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.17157 | 0.344644 | 0.172322 | − | 0.985041i | \(-0.444873\pi\) | ||||
0.172322 | + | 0.985041i | \(0.444873\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 49.9411i | − 2.38901i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 4.34315i | − 0.207287i | −0.994615 | − | 0.103644i | \(-0.966950\pi\) | ||||
0.994615 | − | 0.103644i | \(-0.0330501\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.3137 | 0.727576 | 0.363788 | − | 0.931482i | \(-0.381483\pi\) | ||||
0.363788 | + | 0.931482i | \(0.381483\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.0711 | 0.714437 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.2132i | 0.812341i | 0.913797 | + | 0.406171i | \(0.133136\pi\) | ||||
−0.913797 | + | 0.406171i | \(0.866864\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.343146i | 0.0161581i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 21.3137 | 0.999202 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.1421 | 1.50355 | 0.751773 | − | 0.659422i | \(-0.229199\pi\) | ||||
0.751773 | + | 0.659422i | \(0.229199\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.7990i | 1.57418i | 0.616841 | + | 0.787088i | \(0.288412\pi\) | ||||
−0.616841 | + | 0.787088i | \(0.711588\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 20.3848i | − 0.947361i | −0.880697 | − | 0.473680i | \(-0.842925\pi\) | ||||
0.880697 | − | 0.473680i | \(-0.157075\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.7990 | 0.545992 | 0.272996 | − | 0.962015i | \(-0.411985\pi\) | ||||
0.272996 | + | 0.962015i | \(0.411985\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −38.6274 | −1.78365 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.65685i | 0.0761822i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 5.65685i | − 0.259554i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.00000 | 0.365529 | 0.182765 | − | 0.983157i | \(-0.441495\pi\) | ||||
0.182765 | + | 0.983157i | \(0.441495\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −46.2843 | −2.11038 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.48528i | 0.294481i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 6.04163i | − 0.273772i | −0.990587 | − | 0.136886i | \(-0.956291\pi\) | ||||
0.990587 | − | 0.136886i | \(-0.0437095\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.9289 | 0.583475 | 0.291737 | − | 0.956498i | \(-0.405767\pi\) | ||||
0.291737 | + | 0.956498i | \(0.405767\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.6569 | 0.615074 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 8.00000i | − 0.358849i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.9706i | 0.580642i | 0.956929 | + | 0.290321i | \(0.0937621\pi\) | ||||
−0.956929 | + | 0.290321i | \(0.906238\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.0000 | −0.713405 | −0.356702 | − | 0.934218i | \(-0.616099\pi\) | ||||
−0.356702 | + | 0.934218i | \(0.616099\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.8284 | −0.748855 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.1421i | 0.892784i | 0.894837 | + | 0.446392i | \(0.147291\pi\) | ||||
−0.894837 | + | 0.446392i | \(0.852709\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 16.4853i | − 0.729266i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.24264 | 0.275084 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.3137 | 0.497576 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.27208i | 0.318596i | 0.987231 | + | 0.159298i | \(0.0509230\pi\) | ||||
−0.987231 | + | 0.159298i | \(0.949077\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 27.7990i | − 1.21556i | −0.794104 | − | 0.607782i | \(-0.792059\pi\) | ||||
0.794104 | − | 0.607782i | \(-0.207941\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 60.2843 | 2.62602 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 54.9411 | 2.38874 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1.51472i | − 0.0656097i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 10.1421i | − 0.438483i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.58579 | 0.283670 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.14214 | 0.178084 | 0.0890422 | − | 0.996028i | \(-0.471619\pi\) | ||||
0.0890422 | + | 0.996028i | \(0.471619\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.17157i | 0.135855i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.20101i | 0.179622i | 0.995959 | + | 0.0898111i | \(0.0286263\pi\) | ||||
−0.995959 | + | 0.0898111i | \(0.971374\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.3137 | 0.481980 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −35.7990 | −1.52233 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.4853i | 0.867989i | 0.900915 | + | 0.433995i | \(0.142896\pi\) | ||||
−0.900915 | + | 0.433995i | \(0.857104\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 7.31371i | − 0.309337i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.3431 | 0.941651 | 0.470826 | − | 0.882226i | \(-0.343956\pi\) | ||||
0.470826 | + | 0.882226i | \(0.343956\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.00000 | 0.168281 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.5858i | 1.44991i | 0.688795 | + | 0.724956i | \(0.258140\pi\) | ||||
−0.688795 | + | 0.724956i | \(0.741860\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 34.6274i | − 1.44911i | −0.689216 | − | 0.724556i | \(-0.742045\pi\) | ||||
0.689216 | − | 0.724556i | \(-0.257955\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.82843 | 0.368171 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.4558 | −1.14300 | −0.571501 | − | 0.820601i | \(-0.693639\pi\) | ||||
−0.571501 | + | 0.820601i | \(0.693639\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 23.3137i | − 0.967216i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.65685i | 0.0686199i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 37.4558 | 1.54597 | 0.772984 | − | 0.634425i | \(-0.218763\pi\) | ||||
0.772984 | + | 0.634425i | \(0.218763\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 49.9411 | 2.05779 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 14.6274i | − 0.600676i | −0.953833 | − | 0.300338i | \(-0.902901\pi\) | ||||
0.953833 | − | 0.300338i | \(-0.0970995\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23.3137i | 0.955769i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.8579 | 0.566217 | 0.283108 | − | 0.959088i | \(-0.408634\pi\) | ||||
0.283108 | + | 0.959088i | \(0.408634\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 45.9411 | 1.87398 | 0.936989 | − | 0.349359i | \(-0.113601\pi\) | ||||
0.936989 | + | 0.349359i | \(0.113601\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.00000i | 0.365902i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 10.0416i | − 0.407577i | −0.979015 | − | 0.203789i | \(-0.934674\pi\) | ||||
0.979015 | − | 0.203789i | \(-0.0653255\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −49.9411 | −2.02040 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.0711 | 0.851052 | 0.425526 | − | 0.904946i | \(-0.360089\pi\) | ||||
0.425526 | + | 0.904946i | \(0.360089\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.1716i | 0.530268i | 0.964212 | + | 0.265134i | \(0.0854161\pi\) | ||||
−0.964212 | + | 0.265134i | \(0.914584\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 26.9706i | − 1.08404i | −0.840366 | − | 0.542019i | \(-0.817660\pi\) | ||||
0.840366 | − | 0.542019i | \(-0.182340\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −51.4558 | −2.06153 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 50.6274i | − 2.01865i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 16.1421i | − 0.642608i | −0.946976 | − | 0.321304i | \(-0.895879\pi\) | ||||
0.946976 | − | 0.321304i | \(-0.104121\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.4142 | 0.611694 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −29.0711 | −1.15184 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.8701i | 0.587332i | 0.955908 | + | 0.293666i | \(0.0948753\pi\) | ||||
−0.955908 | + | 0.293666i | \(0.905125\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1.17157i | − 0.0462023i | −0.999733 | − | 0.0231012i | \(-0.992646\pi\) | ||||
0.999733 | − | 0.0231012i | \(-0.00735398\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15.0294 | −0.590868 | −0.295434 | − | 0.955363i | \(-0.595464\pi\) | ||||
−0.295434 | + | 0.955363i | \(0.595464\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.65685 | −0.143544 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 30.2843i | − 1.18512i | −0.805528 | − | 0.592558i | \(-0.798118\pi\) | ||||
0.805528 | − | 0.592558i | \(-0.201882\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.8995i | 0.543098i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.04163 | −0.157440 | −0.0787198 | − | 0.996897i | \(-0.525083\pi\) | ||||
−0.0787198 | + | 0.996897i | \(0.525083\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.1421 | 1.09460 | 0.547301 | − | 0.836936i | \(-0.315655\pi\) | ||||
0.547301 | + | 0.836936i | \(0.315655\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 19.3137i | 0.748953i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.6569i | 0.683676i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.4853 | −0.481989 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −42.7696 | −1.64865 | −0.824323 | − | 0.566120i | \(-0.808444\pi\) | ||||
−0.824323 | + | 0.566120i | \(0.808444\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 6.68629i | − 0.256975i | −0.991711 | − | 0.128488i | \(-0.958988\pi\) | ||||
0.991711 | − | 0.128488i | \(-0.0410122\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 22.1421i | − 0.849737i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.7990 | −0.757587 | −0.378794 | − | 0.925481i | \(-0.623661\pi\) | ||||
−0.378794 | + | 0.925481i | \(0.623661\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.65685 | 0.216137 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 7.31371i | − 0.278630i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.6569i | 1.12820i | 0.825707 | + | 0.564100i | \(0.190777\pi\) | ||||
−0.825707 | + | 0.564100i | \(0.809223\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.34315 | −0.316474 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.65685 | 0.0627578 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 21.5147i | − 0.812600i | −0.913740 | − | 0.406300i | \(-0.866819\pi\) | ||||
0.913740 | − | 0.406300i | \(-0.133181\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 41.9411i | − 1.58184i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 57.4558 | 2.16085 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.6569 | 1.18890 | 0.594449 | − | 0.804133i | \(-0.297370\pi\) | ||||
0.594449 | + | 0.804133i | \(0.297370\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 77.9411i | 2.91892i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.82843i | 0.330164i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.7990 | −1.03673 | −0.518364 | − | 0.855160i | \(-0.673459\pi\) | ||||
−0.518364 | + | 0.855160i | \(0.673459\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.3137 | −0.793764 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.00000i | 0.0742781i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.75736i | 0.361880i | 0.983494 | + | 0.180940i | \(0.0579141\pi\) | ||||
−0.983494 | + | 0.180940i | \(0.942086\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.00000 | 0.295891 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.24264 | 0.0828338 | 0.0414169 | − | 0.999142i | \(-0.486813\pi\) | ||||
0.0414169 | + | 0.999142i | \(0.486813\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 16.0000i | − 0.589368i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 12.0000i | − 0.441427i | −0.975339 | − | 0.220714i | \(-0.929161\pi\) | ||||
0.975339 | − | 0.220714i | \(-0.0708386\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.02944 | 0.257885 | 0.128943 | − | 0.991652i | \(-0.458842\pi\) | ||||
0.128943 | + | 0.991652i | \(0.458842\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.82843 | 0.176900 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 34.6274i | 1.26526i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 21.7990i | − 0.795456i | −0.917503 | − | 0.397728i | \(-0.869799\pi\) | ||||
0.917503 | − | 0.397728i | \(-0.130201\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.9706 | 0.399260 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.41421 | 0.124092 | 0.0620459 | − | 0.998073i | \(-0.480237\pi\) | ||||
0.0620459 | + | 0.998073i | \(0.480237\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 38.8701i | − 1.40904i | −0.709685 | − | 0.704519i | \(-0.751163\pi\) | ||||
0.709685 | − | 0.704519i | \(-0.248837\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 10.8284i | − 0.392015i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16.1421 | 0.582859 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.5980 | −1.13945 | −0.569726 | − | 0.821835i | \(-0.692951\pi\) | ||||
−0.569726 | + | 0.821835i | \(0.692951\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 43.2548i | 1.55577i | 0.628408 | + | 0.777884i | \(0.283707\pi\) | ||||
−0.628408 | + | 0.777884i | \(0.716293\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.82843i | 0.317126i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.37258 | 0.0491779 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.31371 | 0.118574 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.100505i | 0.00358718i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 26.1421i | − 0.931866i | −0.884820 | − | 0.465933i | \(-0.845719\pi\) | ||||
0.884820 | − | 0.465933i | \(-0.154281\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.6569 | −0.485582 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 55.1127 | 1.95711 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.485281i | 0.0171895i | 0.999963 | + | 0.00859477i | \(0.00273584\pi\) | ||||
−0.999963 | + | 0.00859477i | \(0.997264\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 54.6274i | − 1.93258i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.82843 | 0.240970 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −30.1421 | −1.06237 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 10.1005i | − 0.355115i | −0.984110 | − | 0.177557i | \(-0.943180\pi\) | ||||
0.984110 | − | 0.177557i | \(-0.0568195\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.6274i | 0.443409i | 0.975114 | + | 0.221704i | \(0.0711620\pi\) | ||||
−0.975114 | + | 0.221704i | \(0.928838\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.48528 | 0.297226 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.62742 | 0.231864 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 5.31371i | − 0.185450i | −0.995692 | − | 0.0927249i | \(-0.970442\pi\) | ||||
0.995692 | − | 0.0927249i | \(-0.0295577\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 36.8701i | − 1.28521i | −0.766198 | − | 0.642605i | \(-0.777854\pi\) | ||||
0.766198 | − | 0.642605i | \(-0.222146\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 50.6274 | 1.76049 | 0.880244 | − | 0.474522i | \(-0.157379\pi\) | ||||
0.880244 | + | 0.474522i | \(0.157379\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.5147 | −0.469386 | −0.234693 | − | 0.972070i | \(-0.575408\pi\) | ||||
−0.234693 | + | 0.972070i | \(0.575408\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 31.7990i | − 1.10177i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 14.4853i | − 0.501284i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.4853 | −0.845326 | −0.422663 | − | 0.906287i | \(-0.638905\pi\) | ||||
−0.422663 | + | 0.906287i | \(0.638905\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.0000 | 0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 25.9706i | − 0.893415i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 30.7279i | − 1.05582i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 65.4558 | 2.24380 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −47.2132 | −1.61655 | −0.808275 | − | 0.588806i | \(-0.799598\pi\) | ||||
−0.808275 | + | 0.588806i | \(0.799598\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 48.4853i | 1.65623i | 0.560561 | + | 0.828113i | \(0.310585\pi\) | ||||
−0.560561 | + | 0.828113i | \(0.689415\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 10.0000i | − 0.341196i | −0.985341 | − | 0.170598i | \(-0.945430\pi\) | ||||
0.985341 | − | 0.170598i | \(-0.0545699\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 50.7696 | 1.72822 | 0.864108 | − | 0.503307i | \(-0.167883\pi\) | ||||
0.864108 | + | 0.503307i | \(0.167883\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.485281 | −0.0165001 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 14.8284i | − 0.503020i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 70.6274i | 2.39312i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.41421 | −0.115421 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.58579 | −0.154851 | −0.0774255 | − | 0.996998i | \(-0.524670\pi\) | ||||
−0.0774255 | + | 0.996998i | \(0.524670\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.4142i | 0.856227i | 0.903725 | + | 0.428113i | \(0.140822\pi\) | ||||
−0.903725 | + | 0.428113i | \(0.859178\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.4558i | 1.12588i | 0.826498 | + | 0.562939i | \(0.190330\pi\) | ||||
−0.826498 | + | 0.562939i | \(0.809670\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.1421 | 0.944920 | 0.472460 | − | 0.881352i | \(-0.343366\pi\) | ||||
0.472460 | + | 0.881352i | \(0.343366\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −52.6274 | −1.76507 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 45.2548i | − 1.51440i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.4142i | 0.448388i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.6569 | −0.588889 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.00000 | 0.266519 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 24.8284i | − 0.825325i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 31.1127i | − 1.03308i | −0.856263 | − | 0.516540i | \(-0.827220\pi\) | ||||
0.856263 | − | 0.516540i | \(-0.172780\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.2843 | −1.20215 | −0.601076 | − | 0.799192i | \(-0.705261\pi\) | ||||
−0.601076 | + | 0.799192i | \(0.705261\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.65685 | 0.319595 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 47.4558i | − 1.56713i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 26.4853i | − 0.873669i | −0.899542 | − | 0.436834i | \(-0.856100\pi\) | ||||
0.899542 | − | 0.436834i | \(-0.143900\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14.6274 | −0.481467 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.41421 | 0.243778 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 32.7279i | − 1.07377i | −0.843656 | − | 0.536884i | \(-0.819601\pi\) | ||||
0.843656 | − | 0.536884i | \(-0.180399\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 26.3431i | − 0.863362i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.65685 | −0.315813 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42.2843 | −1.38137 | −0.690683 | − | 0.723157i | \(-0.742690\pi\) | ||||
−0.690683 | + | 0.723157i | \(0.742690\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 46.9706i | − 1.53120i | −0.643319 | − | 0.765598i | \(-0.722443\pi\) | ||||
0.643319 | − | 0.765598i | \(-0.277557\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.14214i | 0.0697575i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −44.9706 | −1.46135 | −0.730673 | − | 0.682727i | \(-0.760794\pi\) | ||||
−0.730673 | + | 0.682727i | \(0.760794\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.1421 | −0.978455 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 2.34315i | − 0.0759019i | −0.999280 | − | 0.0379510i | \(-0.987917\pi\) | ||||
0.999280 | − | 0.0379510i | \(-0.0120831\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.17157i | 0.0379112i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.3137 | −0.623672 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −46.9411 | −1.51423 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 4.34315i | − 0.139811i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.8995i | 0.639925i | 0.947430 | + | 0.319962i | \(0.103670\pi\) | ||||
−0.947430 | + | 0.319962i | \(0.896330\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.6985 | 0.953070 | 0.476535 | − | 0.879156i | \(-0.341893\pi\) | ||||
0.476535 | + | 0.879156i | \(0.341893\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.4853 | 0.913196 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.4853i | 0.783354i | 0.920103 | + | 0.391677i | \(0.128105\pi\) | ||||
−0.920103 | + | 0.391677i | \(0.871895\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 21.3137i | − 0.681189i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −19.3137 | −0.616012 | −0.308006 | − | 0.951384i | \(-0.599662\pi\) | ||||
−0.308006 | + | 0.951384i | \(0.599662\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.00000 | 0.191176 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.3431i | 0.328893i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 0.343146i | − 0.0109004i | −0.999985 | − | 0.00545019i | \(-0.998265\pi\) | ||||
0.999985 | − | 0.00545019i | \(-0.00173486\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.6569 | −0.496356 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.2426 | 1.08448 | 0.542238 | − | 0.840225i | \(-0.317577\pi\) | ||||
0.542238 | + | 0.840225i | \(0.317577\pi\) | |||||||
\(998\) | 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 | 2880.2.h.b.1151.2 | 4 | ||
3.2 | odd | 2 | 2880.2.h.c.1151.4 | 4 | |||
4.3 | odd | 2 | 2880.2.h.c.1151.1 | 4 | |||
8.3 | odd | 2 | 1440.2.h.c.1151.3 | yes | 4 | ||
8.5 | even | 2 | 1440.2.h.b.1151.4 | yes | 4 | ||
12.11 | even | 2 | inner | 2880.2.h.b.1151.3 | 4 | ||
24.5 | odd | 2 | 1440.2.h.c.1151.2 | yes | 4 | ||
24.11 | even | 2 | 1440.2.h.b.1151.1 | ✓ | 4 | ||
40.3 | even | 4 | 7200.2.o.d.7199.1 | 4 | |||
40.13 | odd | 4 | 7200.2.o.l.7199.3 | 4 | |||
40.19 | odd | 2 | 7200.2.h.e.1151.4 | 4 | |||
40.27 | even | 4 | 7200.2.o.k.7199.4 | 4 | |||
40.29 | even | 2 | 7200.2.h.f.1151.1 | 4 | |||
40.37 | odd | 4 | 7200.2.o.c.7199.2 | 4 | |||
120.29 | odd | 2 | 7200.2.h.e.1151.1 | 4 | |||
120.53 | even | 4 | 7200.2.o.k.7199.3 | 4 | |||
120.59 | even | 2 | 7200.2.h.f.1151.4 | 4 | |||
120.77 | even | 4 | 7200.2.o.d.7199.2 | 4 | |||
120.83 | odd | 4 | 7200.2.o.c.7199.1 | 4 | |||
120.107 | odd | 4 | 7200.2.o.l.7199.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1440.2.h.b.1151.1 | ✓ | 4 | 24.11 | even | 2 | ||
1440.2.h.b.1151.4 | yes | 4 | 8.5 | even | 2 | ||
1440.2.h.c.1151.2 | yes | 4 | 24.5 | odd | 2 | ||
1440.2.h.c.1151.3 | yes | 4 | 8.3 | odd | 2 | ||
2880.2.h.b.1151.2 | 4 | 1.1 | even | 1 | trivial | ||
2880.2.h.b.1151.3 | 4 | 12.11 | even | 2 | inner | ||
2880.2.h.c.1151.1 | 4 | 4.3 | odd | 2 | |||
2880.2.h.c.1151.4 | 4 | 3.2 | odd | 2 | |||
7200.2.h.e.1151.1 | 4 | 120.29 | odd | 2 | |||
7200.2.h.e.1151.4 | 4 | 40.19 | odd | 2 | |||
7200.2.h.f.1151.1 | 4 | 40.29 | even | 2 | |||
7200.2.h.f.1151.4 | 4 | 120.59 | even | 2 | |||
7200.2.o.c.7199.1 | 4 | 120.83 | odd | 4 | |||
7200.2.o.c.7199.2 | 4 | 40.37 | odd | 4 | |||
7200.2.o.d.7199.1 | 4 | 40.3 | even | 4 | |||
7200.2.o.d.7199.2 | 4 | 120.77 | even | 4 | |||
7200.2.o.k.7199.3 | 4 | 120.53 | even | 4 | |||
7200.2.o.k.7199.4 | 4 | 40.27 | even | 4 | |||
7200.2.o.l.7199.3 | 4 | 40.13 | odd | 4 | |||
7200.2.o.l.7199.4 | 4 | 120.107 | odd | 4 |