Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,2,Mod(431,2880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2880.431");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.bl (of order \(4\), degree \(2\), 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: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.3317760000.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 17x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 720) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1871.2 | ||
Root | \(1.72286 + 1.01575i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2880.1871 |
Dual form | 2880.2.bl.a.431.2 |
$q$-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 \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.707107 | + | 0.707107i | −0.316228 | + | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.87298 | 1.08589 | 0.542943 | − | 0.839770i | \(-0.317310\pi\) | ||||
0.542943 | + | 0.839770i | \(0.317310\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.03151 | + | 2.03151i | 0.612522 | + | 0.612522i | 0.943603 | − | 0.331080i | \(-0.107413\pi\) |
−0.331080 | + | 0.943603i | \(0.607413\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.87298 | − | 3.87298i | 1.07417 | − | 1.07417i | 0.0771531 | − | 0.997019i | \(-0.475417\pi\) |
0.997019 | − | 0.0771531i | \(-0.0245830\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.41421i | 0.342997i | 0.985184 | + | 0.171499i | \(0.0548609\pi\) | ||||
−0.985184 | + | 0.171499i | \(0.945139\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.87298 | − | 5.87298i | −1.34735 | − | 1.34735i | −0.888523 | − | 0.458831i | \(-0.848268\pi\) |
−0.458831 | − | 0.888523i | \(-0.651732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.47723i | − | 1.14208i | −0.820922 | − | 0.571040i | \(-0.806540\pi\) | ||
0.820922 | − | 0.571040i | \(-0.193460\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.82843 | + | 2.82843i | 0.525226 | + | 0.525226i | 0.919145 | − | 0.393919i | \(-0.128881\pi\) |
−0.393919 | + | 0.919145i | \(0.628881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.00000i | − | 0.718421i | −0.933257 | − | 0.359211i | \(-0.883046\pi\) | ||
0.933257 | − | 0.359211i | \(-0.116954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.03151 | + | 2.03151i | −0.343387 | + | 0.343387i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | − | 1.00000i | −0.164399 | − | 0.164399i | 0.620113 | − | 0.784512i | \(-0.287087\pi\) |
−0.784512 | + | 0.620113i | \(0.787087\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.1341 | 1.73885 | 0.869426 | − | 0.494064i | \(-0.164489\pi\) | ||||
0.869426 | + | 0.494064i | \(0.164489\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.00000 | − | 6.00000i | 0.914991 | − | 0.914991i | −0.0816682 | − | 0.996660i | \(-0.526025\pi\) |
0.996660 | + | 0.0816682i | \(0.0260248\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.41421 | 0.206284 | 0.103142 | − | 0.994667i | \(-0.467110\pi\) | ||||
0.103142 | + | 0.994667i | \(0.467110\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.25403 | 0.179148 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.41421 | + | 1.41421i | −0.194257 | + | 0.194257i | −0.797533 | − | 0.603276i | \(-0.793862\pi\) |
0.603276 | + | 0.797533i | \(0.293862\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.87298 | −0.387393 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.10257 | − | 9.10257i | −1.18505 | − | 1.18505i | −0.978418 | − | 0.206636i | \(-0.933748\pi\) |
−0.206636 | − | 0.978418i | \(-0.566252\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.7460 | + | 10.7460i | −1.37588 | + | 1.37588i | −0.524421 | + | 0.851459i | \(0.675718\pi\) |
−0.851459 | + | 0.524421i | \(0.824282\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.47723i | 0.679366i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.12702 | − | 3.12702i | −0.382026 | − | 0.382026i | 0.489806 | − | 0.871832i | \(-0.337068\pi\) |
−0.871832 | + | 0.489806i | \(0.837068\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.71987i | 1.15354i | 0.816908 | + | 0.576768i | \(0.195686\pi\) | ||||
−0.816908 | + | 0.576768i | \(0.804314\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.74597i | 0.672515i | 0.941770 | + | 0.336257i | \(0.109161\pi\) | ||||
−0.941770 | + | 0.336257i | \(0.890839\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.83648 | + | 5.83648i | 0.665129 | + | 0.665129i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.74597i | 0.421454i | 0.977545 | + | 0.210727i | \(0.0675831\pi\) | ||||
−0.977545 | + | 0.210727i | \(0.932417\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.41421 | − | 1.41421i | 0.155230 | − | 0.155230i | −0.625219 | − | 0.780449i | \(-0.714990\pi\) |
0.780449 | + | 0.625219i | \(0.214990\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.00000 | − | 1.00000i | −0.108465 | − | 0.108465i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.83648 | 0.618666 | 0.309333 | − | 0.950954i | \(-0.399894\pi\) | ||||
0.309333 | + | 0.950954i | \(0.399894\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.1270 | − | 11.1270i | 1.16643 | − | 1.16643i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.30565 | 0.852142 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.4919 | 1.77604 | 0.888018 | − | 0.459808i | \(-0.152082\pi\) | ||||
0.888018 | + | 0.459808i | \(0.152082\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.23458 | + | 1.23458i | −0.122846 | + | 0.122846i | −0.765857 | − | 0.643011i | \(-0.777685\pi\) |
0.643011 | + | 0.765857i | \(0.277685\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.872983 | −0.0860176 | −0.0430088 | − | 0.999075i | \(-0.513694\pi\) | ||||
−0.0430088 | + | 0.999075i | \(0.513694\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.47723 | − | 5.47723i | −0.529503 | − | 0.529503i | 0.390921 | − | 0.920424i | \(-0.372157\pi\) |
−0.920424 | + | 0.390921i | \(0.872157\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.7460 | − | 12.7460i | 1.22084 | − | 1.22084i | 0.253509 | − | 0.967333i | \(-0.418415\pi\) |
0.967333 | − | 0.253509i | \(-0.0815848\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 12.3687i | − | 1.16355i | −0.813351 | − | 0.581773i | \(-0.802359\pi\) | ||
0.813351 | − | 0.581773i | \(-0.197641\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.87298 | + | 3.87298i | 0.361158 | + | 0.361158i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.06301i | 0.372456i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 2.74597i | − | 0.249633i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.707107 | + | 0.707107i | 0.0632456 | + | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.61895i | − | 0.587337i | −0.955907 | − | 0.293668i | \(-0.905124\pi\) | ||
0.955907 | − | 0.293668i | \(-0.0948762\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.45378 | + | 6.45378i | −0.563869 | + | 0.563869i | −0.930404 | − | 0.366535i | \(-0.880544\pi\) |
0.366535 | + | 0.930404i | \(0.380544\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.8730 | − | 16.8730i | −1.46307 | − | 1.46307i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.5563 | 1.32907 | 0.664534 | − | 0.747258i | \(-0.268630\pi\) | ||||
0.664534 | + | 0.747258i | \(0.268630\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.74597 | − | 8.74597i | 0.741823 | − | 0.741823i | −0.231105 | − | 0.972929i | \(-0.574234\pi\) |
0.972929 | + | 0.231105i | \(0.0742343\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.7360 | 1.31591 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.00000 | −0.332182 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.00806 | + | 3.00806i | −0.246430 | + | 0.246430i | −0.819504 | − | 0.573074i | \(-0.805751\pi\) |
0.573074 | + | 0.819504i | \(0.305751\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.82843 | + | 2.82843i | 0.227185 | + | 0.227185i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.74597 | + | 2.74597i | −0.219152 | + | 0.219152i | −0.808141 | − | 0.588989i | \(-0.799526\pi\) |
0.588989 | + | 0.808141i | \(0.299526\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 15.7360i | − | 1.24017i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.87298 | + | 8.87298i | 0.694986 | + | 0.694986i | 0.963325 | − | 0.268339i | \(-0.0864747\pi\) |
−0.268339 | + | 0.963325i | \(0.586475\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.66491i | 0.670511i | 0.942127 | + | 0.335255i | \(0.108823\pi\) | ||||
−0.942127 | + | 0.335255i | \(0.891177\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 17.0000i | − | 1.30769i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.3687 | + | 12.3687i | 0.940372 | + | 0.940372i | 0.998320 | − | 0.0579475i | \(-0.0184556\pi\) |
−0.0579475 | + | 0.998320i | \(0.518456\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 2.87298i | − | 0.217177i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.7514 | − | 11.7514i | 0.878339 | − | 0.878339i | −0.115024 | − | 0.993363i | \(-0.536694\pi\) |
0.993363 | + | 0.115024i | \(0.0366945\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.00000 | − | 9.00000i | −0.668965 | − | 0.668965i | 0.288512 | − | 0.957476i | \(-0.406840\pi\) |
−0.957476 | + | 0.288512i | \(0.906840\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.41421 | 0.103975 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.87298 | + | 2.87298i | −0.210093 | + | 0.210093i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.42227 | 0.319984 | 0.159992 | − | 0.987118i | \(-0.448853\pi\) | ||||
0.159992 | + | 0.987118i | \(0.448853\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.25403 | 0.450175 | 0.225088 | − | 0.974339i | \(-0.427733\pi\) | ||||
0.225088 | + | 0.974339i | \(0.427733\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.00806 | + | 3.00806i | −0.214315 | + | 0.214315i | −0.806098 | − | 0.591783i | \(-0.798424\pi\) |
0.591783 | + | 0.806098i | \(0.298424\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.7460 | 1.11620 | 0.558101 | − | 0.829773i | \(-0.311530\pi\) | ||||
0.558101 | + | 0.829773i | \(0.311530\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.12602 | + | 8.12602i | 0.570335 | + | 0.570335i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.87298 | + | 7.87298i | −0.549873 | + | 0.549873i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 23.8620i | − | 1.65057i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.7460 | − | 10.7460i | −0.739783 | − | 0.739783i | 0.232753 | − | 0.972536i | \(-0.425227\pi\) |
−0.972536 | + | 0.232753i | \(0.925227\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.48528i | 0.578691i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 11.4919i | − | 0.780123i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.47723 | + | 5.47723i | 0.368438 | + | 0.368438i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.12702i | 0.611190i | 0.952162 | + | 0.305595i | \(0.0988554\pi\) | ||||
−0.952162 | + | 0.305595i | \(0.901145\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.9625 | + | 13.9625i | −0.926724 | + | 0.926724i | −0.997493 | − | 0.0707686i | \(-0.977455\pi\) |
0.0707686 | + | 0.997493i | \(0.477455\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.4919 | + | 18.4919i | 1.22198 | + | 1.22198i | 0.966927 | + | 0.255055i | \(0.0820935\pi\) |
0.255055 | + | 0.966927i | \(0.417907\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −23.6824 | −1.55148 | −0.775742 | − | 0.631050i | \(-0.782624\pi\) | ||||
−0.775742 | + | 0.631050i | \(0.782624\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.00000 | + | 1.00000i | −0.0652328 | + | 0.0652328i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.9076 | 0.834920 | 0.417460 | − | 0.908695i | \(-0.362920\pi\) | ||||
0.417460 | + | 0.908695i | \(0.362920\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.00000 | −0.128831 | −0.0644157 | − | 0.997923i | \(-0.520518\pi\) | ||||
−0.0644157 | + | 0.997923i | \(0.520518\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.886735 | + | 0.886735i | −0.0566515 | + | 0.0566515i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −45.4919 | −2.89458 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.617292 | − | 0.617292i | −0.0389632 | − | 0.0389632i | 0.687357 | − | 0.726320i | \(-0.258771\pi\) |
−0.726320 | + | 0.687357i | \(0.758771\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.1270 | − | 11.1270i | 0.699550 | − | 0.699550i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.8539i | 1.30083i | 0.759578 | + | 0.650417i | \(0.225406\pi\) | ||||
−0.759578 | + | 0.650417i | \(0.774594\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.87298 | − | 2.87298i | −0.178518 | − | 0.178518i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.28954i | 0.141179i | 0.997505 | + | 0.0705896i | \(0.0224881\pi\) | ||||
−0.997505 | + | 0.0705896i | \(0.977512\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2.00000i | − | 0.122859i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.25070 | − | 7.25070i | −0.442083 | − | 0.442083i | 0.450629 | − | 0.892711i | \(-0.351200\pi\) |
−0.892711 | + | 0.450629i | \(0.851200\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.74597i | 0.227551i | 0.993506 | + | 0.113776i | \(0.0362945\pi\) | ||||
−0.993506 | + | 0.113776i | \(0.963705\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.03151 | − | 2.03151i | 0.122504 | − | 0.122504i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.7460 | − | 12.7460i | −0.765831 | − | 0.765831i | 0.211539 | − | 0.977370i | \(-0.432153\pi\) |
−0.977370 | + | 0.211539i | \(0.932153\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.0255 | −1.07531 | −0.537656 | − | 0.843164i | \(-0.680690\pi\) | ||||
−0.537656 | + | 0.843164i | \(0.680690\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.8730 | − | 12.8730i | 0.765219 | − | 0.765219i | −0.212041 | − | 0.977261i | \(-0.568011\pi\) |
0.977261 | + | 0.212041i | \(0.0680111\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 31.9880 | 1.88819 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.0000 | 0.882353 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.4397 | + | 19.4397i | −1.13568 | + | 1.13568i | −0.146466 | + | 0.989216i | \(0.546790\pi\) |
−0.989216 | + | 0.146466i | \(0.953210\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.8730 | 0.749494 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −21.2132 | − | 21.2132i | −1.22679 | − | 1.22679i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.2379 | − | 17.2379i | 0.993576 | − | 0.993576i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 15.1971i | − | 0.870183i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.74597 | + | 1.74597i | 0.0996476 | + | 0.0996476i | 0.755173 | − | 0.655525i | \(-0.227553\pi\) |
−0.655525 | + | 0.755173i | \(0.727553\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.0791i | 0.571535i | 0.958299 | + | 0.285767i | \(0.0922485\pi\) | ||||
−0.958299 | + | 0.285767i | \(0.907752\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 5.74597i | − | 0.324781i | −0.986727 | − | 0.162391i | \(-0.948080\pi\) | ||
0.986727 | − | 0.162391i | \(-0.0519205\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.4933 | + | 11.4933i | 0.645530 | + | 0.645530i | 0.951909 | − | 0.306379i | \(-0.0991176\pi\) |
−0.306379 | + | 0.951909i | \(0.599118\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.4919i | 0.643425i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.30565 | − | 8.30565i | 0.462139 | − | 0.462139i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.87298 | − | 3.87298i | −0.214834 | − | 0.214834i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.06301 | 0.224001 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.87298 | − | 9.87298i | 0.542668 | − | 0.542668i | −0.381642 | − | 0.924310i | \(-0.624641\pi\) |
0.924310 | + | 0.381642i | \(0.124641\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.42227 | 0.241614 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.508067 | 0.0276762 | 0.0138381 | − | 0.999904i | \(-0.495595\pi\) | ||||
0.0138381 | + | 0.999904i | \(0.495595\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.12602 | − | 8.12602i | 0.440049 | − | 0.440049i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.5081 | −0.891352 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.89144 | + | 6.89144i | 0.369952 | + | 0.369952i | 0.867460 | − | 0.497508i | \(-0.165751\pi\) |
−0.497508 | + | 0.867460i | \(0.665751\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.00000 | + | 3.00000i | −0.160586 | + | 0.160586i | −0.782826 | − | 0.622240i | \(-0.786223\pi\) |
0.622240 | + | 0.782826i | \(0.286223\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.05496i | 0.0561497i | 0.999606 | + | 0.0280748i | \(0.00893767\pi\) | ||||
−0.999606 | + | 0.0280748i | \(0.991062\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.87298 | − | 6.87298i | −0.364780 | − | 0.364780i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 13.7829i | − | 0.727432i | −0.931510 | − | 0.363716i | \(-0.881508\pi\) | ||
0.931510 | − | 0.363716i | \(-0.118492\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 49.9839i | 2.63073i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.06301 | − | 4.06301i | −0.212668 | − | 0.212668i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.1270i | 0.998422i | 0.866480 | + | 0.499211i | \(0.166377\pi\) | ||||
−0.866480 | + | 0.499211i | \(0.833623\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.06301 | + | 4.06301i | −0.210941 | + | 0.210941i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.74597 | + | 4.74597i | 0.245737 | + | 0.245737i | 0.819218 | − | 0.573482i | \(-0.194408\pi\) |
−0.573482 | + | 0.819218i | \(0.694408\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 21.9089 | 1.12837 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.7460 | + | 10.7460i | −0.551983 | + | 0.551983i | −0.927013 | − | 0.375030i | \(-0.877633\pi\) |
0.375030 | + | 0.927013i | \(0.377633\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −26.5108 | −1.35464 | −0.677319 | − | 0.735689i | \(-0.736858\pi\) | ||||
−0.677319 | + | 0.735689i | \(0.736858\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.25403 | −0.420664 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.0885 | + | 22.0885i | −1.11993 | + | 1.11993i | −0.128182 | + | 0.991751i | \(0.540914\pi\) |
−0.991751 | + | 0.128182i | \(0.959086\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.74597 | 0.391730 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.64880 | − | 2.64880i | −0.133276 | − | 0.133276i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.6190 | + | 13.6190i | −0.683516 | + | 0.683516i | −0.960791 | − | 0.277275i | \(-0.910569\pi\) |
0.277275 | + | 0.960791i | \(0.410569\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 19.2601i | − | 0.961804i | −0.876774 | − | 0.480902i | \(-0.840309\pi\) | ||
0.876774 | − | 0.480902i | \(-0.159691\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.4919 | − | 15.4919i | −0.771708 | − | 0.771708i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 4.06301i | − | 0.201396i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 0.508067i | − | 0.0251223i | −0.999921 | − | 0.0125611i | \(-0.996002\pi\) | ||
0.999921 | − | 0.0125611i | \(-0.00399844\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −26.1515 | − | 26.1515i | −1.28683 | − | 1.28683i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.00000i | 0.0981761i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.4002 | + | 14.4002i | −0.703494 | + | 0.703494i | −0.965159 | − | 0.261665i | \(-0.915729\pi\) |
0.261665 | + | 0.965159i | \(0.415729\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.00000 | − | 9.00000i | −0.438633 | − | 0.438633i | 0.452919 | − | 0.891552i | \(-0.350383\pi\) |
−0.891552 | + | 0.452919i | \(0.850383\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.41421 | 0.0685994 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −30.8730 | + | 30.8730i | −1.49405 | + | 1.49405i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.2682 | 1.07262 | 0.536310 | − | 0.844021i | \(-0.319818\pi\) | ||||
0.536310 | + | 0.844021i | \(0.319818\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 39.4919 | 1.89786 | 0.948931 | − | 0.315485i | \(-0.102167\pi\) | ||||
0.948931 | + | 0.315485i | \(0.102167\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −32.1677 | + | 32.1677i | −1.53879 | + | 1.53879i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.2540 | 0.775763 | 0.387881 | − | 0.921709i | \(-0.373207\pi\) | ||||
0.387881 | + | 0.921709i | \(0.373207\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.1515 | − | 26.1515i | −1.24250 | − | 1.24250i | −0.958962 | − | 0.283536i | \(-0.908493\pi\) |
−0.283536 | − | 0.958962i | \(-0.591507\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.12702 | + | 4.12702i | −0.195639 | + | 0.195639i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 32.5269i | − | 1.53504i | −0.641025 | − | 0.767520i | \(-0.721491\pi\) | ||
0.641025 | − | 0.767520i | \(-0.278509\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.6190 | + | 22.6190i | 1.06508 | + | 1.06508i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15.7360i | 0.737714i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.2379i | 1.27414i | 0.770808 | + | 0.637068i | \(0.219853\pi\) | ||||
−0.770808 | + | 0.637068i | \(0.780147\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.0885 | − | 22.0885i | −1.02877 | − | 1.02877i | −0.999574 | − | 0.0291916i | \(-0.990707\pi\) |
−0.0291916 | − | 0.999574i | \(-0.509293\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.3649i | 1.31823i | 0.752042 | + | 0.659115i | \(0.229069\pi\) | ||||
−0.752042 | + | 0.659115i | \(0.770931\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.46917 | + | 2.46917i | −0.114260 | + | 0.114260i | −0.761925 | − | 0.647665i | \(-0.775745\pi\) |
0.647665 | + | 0.761925i | \(0.275745\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.98387 | − | 8.98387i | −0.414836 | − | 0.414836i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 24.3781 | 1.12090 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.87298 | + | 5.87298i | −0.269471 | + | 0.269471i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.42227 | −0.202059 | −0.101029 | − | 0.994883i | \(-0.532214\pi\) | ||||
−0.101029 | + | 0.994883i | \(0.532214\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.74597 | −0.353186 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.3687 | + | 12.3687i | −0.561632 | + | 0.561632i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.6190 | −1.56873 | −0.784367 | − | 0.620297i | \(-0.787012\pi\) | ||||
−0.784367 | + | 0.620297i | \(0.787012\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.68030 | − | 4.68030i | −0.211219 | − | 0.211219i | 0.593566 | − | 0.804785i | \(-0.297720\pi\) |
−0.804785 | + | 0.593566i | \(0.797720\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.00000 | + | 4.00000i | −0.180151 | + | 0.180151i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 27.9250i | 1.25261i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.381050 | − | 0.381050i | −0.0170581 | − | 0.0170581i | 0.698526 | − | 0.715584i | \(-0.253840\pi\) |
−0.715584 | + | 0.698526i | \(0.753840\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 37.8245i | − | 1.68651i | −0.537513 | − | 0.843256i | \(-0.680636\pi\) | ||
0.537513 | − | 0.843256i | \(-0.319364\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 1.74597i | − | 0.0776945i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.1421 | − | 14.1421i | −0.626839 | − | 0.626839i | 0.320432 | − | 0.947271i | \(-0.396172\pi\) |
−0.947271 | + | 0.320432i | \(0.896172\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.5081i | 0.730274i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.617292 | − | 0.617292i | 0.0272012 | − | 0.0272012i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.87298 | + | 2.87298i | 0.126354 | + | 0.126354i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.5563 | −0.681536 | −0.340768 | − | 0.940147i | \(-0.610687\pi\) | ||||
−0.340768 | + | 0.940147i | \(0.610687\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.61895 | + | 4.61895i | −0.201973 | + | 0.201973i | −0.800845 | − | 0.598872i | \(-0.795616\pi\) |
0.598872 | + | 0.800845i | \(0.295616\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.65685 | 0.246416 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 43.1221 | − | 43.1221i | 1.86783 | − | 1.86783i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.74597 | 0.334887 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.54758 | + | 2.54758i | 0.109732 | + | 0.109732i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.7460 | + | 10.7460i | −0.462005 | + | 0.462005i | −0.899312 | − | 0.437307i | \(-0.855932\pi\) |
0.437307 | + | 0.899312i | \(0.355932\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.0255i | 0.772128i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.74597 | − | 1.74597i | −0.0746521 | − | 0.0746521i | 0.668795 | − | 0.743447i | \(-0.266810\pi\) |
−0.743447 | + | 0.668795i | \(0.766810\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 33.2226i | − | 1.41533i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.7621i | 0.457651i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.1515 | + | 26.1515i | 1.10808 | + | 1.10808i | 0.993403 | + | 0.114673i | \(0.0365821\pi\) |
0.114673 | + | 0.993403i | \(0.463418\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 46.4758i | − | 1.96572i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.2051 | + | 18.2051i | −0.767255 | + | 0.767255i | −0.977622 | − | 0.210367i | \(-0.932534\pi\) |
0.210367 | + | 0.977622i | \(0.432534\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.74597 | + | 8.74597i | 0.367946 | + | 0.367946i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.47723 | 0.229617 | 0.114809 | − | 0.993388i | \(-0.463375\pi\) | ||||
0.114809 | + | 0.993388i | \(0.463375\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.3649 | − | 31.3649i | 1.31258 | − | 1.31258i | 0.393074 | − | 0.919507i | \(-0.371412\pi\) |
0.919507 | − | 0.393074i | \(-0.128588\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.47723 | −0.228416 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.2540 | −0.676664 | −0.338332 | − | 0.941027i | \(-0.609863\pi\) | ||||
−0.338332 | + | 0.941027i | \(0.609863\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.06301 | − | 4.06301i | 0.168562 | − | 0.168562i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.74597 | −0.237974 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.0885 | + | 22.0885i | 0.911691 | + | 0.911691i | 0.996405 | − | 0.0847141i | \(-0.0269977\pi\) |
−0.0847141 | + | 0.996405i | \(0.526998\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.4919 | + | 23.4919i | −0.967968 | + | 0.967968i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.18098i | 0.377018i | 0.982071 | + | 0.188509i | \(0.0603654\pi\) | ||||
−0.982071 | + | 0.188509i | \(0.939635\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.87298 | − | 2.87298i | −0.117781 | − | 0.117781i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.5658i | 1.12631i | 0.826353 | + | 0.563153i | \(0.190412\pi\) | ||||
−0.826353 | + | 0.563153i | \(0.809588\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 16.9839i | − | 0.692786i | −0.938089 | − | 0.346393i | \(-0.887406\pi\) | ||
0.938089 | − | 0.346393i | \(-0.112594\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.94169 | + | 1.94169i | 0.0789410 | + | 0.0789410i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 42.3649i | 1.71954i | 0.510682 | + | 0.859769i | \(0.329393\pi\) | ||||
−0.510682 | + | 0.859769i | \(0.670607\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.47723 | − | 5.47723i | 0.221585 | − | 0.221585i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.61895 | + | 5.61895i | 0.226947 | + | 0.226947i | 0.811416 | − | 0.584469i | \(-0.198697\pi\) |
−0.584469 | + | 0.811416i | \(0.698697\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −42.4036 | −1.70710 | −0.853552 | − | 0.521007i | \(-0.825556\pi\) | ||||
−0.853552 | + | 0.521007i | \(0.825556\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.7460 | + | 26.7460i | −1.07501 | + | 1.07501i | −0.0780627 | + | 0.996948i | \(0.524873\pi\) |
−0.996948 | + | 0.0780627i | \(0.975127\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.7681 | 0.671800 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.41421 | − | 1.41421i | 0.0563884 | − | 0.0563884i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.0000 | −0.875806 | −0.437903 | − | 0.899022i | \(-0.644279\pi\) | ||||
−0.437903 | + | 0.899022i | \(0.644279\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.68030 | + | 4.68030i | 0.185732 | + | 0.185732i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.85685 | − | 4.85685i | 0.192435 | − | 0.192435i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 12.3687i | − | 0.488533i | −0.969708 | − | 0.244266i | \(-0.921453\pi\) | ||
0.969708 | − | 0.244266i | \(-0.0785471\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.12702 | + | 3.12702i | 0.123317 | + | 0.123317i | 0.766072 | − | 0.642755i | \(-0.222209\pi\) |
−0.642755 | + | 0.766072i | \(0.722209\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 42.7628i | 1.68118i | 0.541671 | + | 0.840591i | \(0.317792\pi\) | ||||
−0.541671 | + | 0.840591i | \(0.682208\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 36.9839i | − | 1.45174i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.5483 | + | 12.5483i | 0.491053 | + | 0.491053i | 0.908638 | − | 0.417585i | \(-0.137123\pi\) |
−0.417585 | + | 0.908638i | \(0.637123\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 9.12702i | − | 0.356622i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.3077 | − | 27.3077i | 1.06376 | − | 1.06376i | 0.0659338 | − | 0.997824i | \(-0.478997\pi\) |
0.997824 | − | 0.0659338i | \(-0.0210026\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.00000 | − | 7.00000i | −0.272268 | − | 0.272268i | 0.557744 | − | 0.830013i | \(-0.311667\pi\) |
−0.830013 | + | 0.557744i | \(0.811667\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 23.8620 | 0.925329 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.4919 | − | 15.4919i | 0.599850 | − | 0.599850i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −43.6610 | −1.68551 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.4919 | −0.597170 | −0.298585 | − | 0.954383i | \(-0.596515\pi\) | ||||
−0.298585 | + | 0.954383i | \(0.596515\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.3312 | − | 26.3312i | 1.01199 | − | 1.01199i | 0.0120619 | − | 0.999927i | \(-0.496160\pi\) |
0.999927 | − | 0.0120619i | \(-0.00383951\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 50.2540 | 1.92857 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.71987 | − | 9.71987i | −0.371920 | − | 0.371920i | 0.496256 | − | 0.868176i | \(-0.334708\pi\) |
−0.868176 | + | 0.496256i | \(0.834708\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.0000 | + | 11.0000i | −0.420288 | + | 0.420288i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.9545i | 0.417331i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.3649 | + | 29.3649i | 1.11709 | + | 1.11709i | 0.992166 | + | 0.124928i | \(0.0398701\pi\) |
0.124928 | + | 0.992166i | \(0.460130\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.3687i | 0.469170i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.7460i | 0.596421i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.53218 | + | 6.53218i | 0.246717 | + | 0.246717i | 0.819622 | − | 0.572905i | \(-0.194184\pi\) |
−0.572905 | + | 0.819622i | \(0.694184\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.7460i | 0.443008i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.54694 | + | 3.54694i | −0.133396 | + | 0.133396i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.7460 | + | 32.7460i | 1.22980 | + | 1.22980i | 0.964039 | + | 0.265762i | \(0.0856235\pi\) |
0.265762 | + | 0.964039i | \(0.414377\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −21.9089 | −0.820495 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.1270 | + | 11.1270i | −0.416127 | + | 0.416127i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −49.8339 | −1.85849 | −0.929246 | − | 0.369462i | \(-0.879542\pi\) | ||||
−0.929246 | + | 0.369462i | \(0.879542\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.50807 | −0.0934053 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.82843 | − | 2.82843i | 0.105045 | − | 0.105045i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.6028 | 1.54296 | 0.771482 | − | 0.636252i | \(-0.219516\pi\) | ||||
0.771482 | + | 0.636252i | \(0.219516\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.48528 | + | 8.48528i | 0.313839 | + | 0.313839i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.7460 | + | 18.7460i | −0.692398 | + | 0.692398i | −0.962759 | − | 0.270361i | \(-0.912857\pi\) |
0.270361 | + | 0.962759i | \(0.412857\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 12.7051i | − | 0.467999i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.381050 | + | 0.381050i | 0.0140171 | + | 0.0140171i | 0.714081 | − | 0.700063i | \(-0.246845\pi\) |
−0.700063 | + | 0.714081i | \(0.746845\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.41421i | 0.0518825i | 0.999663 | + | 0.0259412i | \(0.00825828\pi\) | ||||
−0.999663 | + | 0.0259412i | \(0.991742\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 4.25403i | − | 0.155856i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.7360 | − | 15.7360i | −0.574980 | − | 0.574980i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 17.7460i | − | 0.647560i | −0.946132 | − | 0.323780i | \(-0.895046\pi\) | ||
0.946132 | − | 0.323780i | \(-0.104954\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.65685 | + | 5.65685i | −0.205874 | + | 0.205874i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.49193 | + | 2.49193i | 0.0905709 | + | 0.0905709i | 0.750941 | − | 0.660370i | \(-0.229600\pi\) |
−0.660370 | + | 0.750941i | \(0.729600\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.9344 | −1.44762 | −0.723811 | − | 0.689998i | \(-0.757611\pi\) | ||||
−0.723811 | + | 0.689998i | \(0.757611\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 36.6190 | − | 36.6190i | 1.32570 | − | 1.32570i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −70.5082 | −2.54590 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.23790 | 0.261005 | 0.130503 | − | 0.991448i | \(-0.458341\pi\) | ||||
0.130503 | + | 0.991448i | \(0.458341\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30.9331 | − | 30.9331i | 1.11259 | − | 1.11259i | 0.119785 | − | 0.992800i | \(-0.461779\pi\) |
0.992800 | − | 0.119785i | \(-0.0382206\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.00000 | −0.143684 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −65.3903 | − | 65.3903i | −2.34285 | − | 2.34285i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.7460 | + | 19.7460i | −0.706566 | + | 0.706566i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 3.88338i | − | 0.138604i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.6190 | − | 26.6190i | −0.948863 | − | 0.948863i | 0.0498915 | − | 0.998755i | \(-0.484112\pi\) |
−0.998755 | + | 0.0498915i | \(0.984112\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 35.5350i | − | 1.26348i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 83.2379i | 2.95586i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.0966 | + | 25.0966i | 0.888967 | + | 0.888967i | 0.994424 | − | 0.105457i | \(-0.0336306\pi\) |
−0.105457 | + | 0.994424i | \(0.533631\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.00000i | 0.0707549i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.6730 | + | 11.6730i | −0.411930 | + | 0.411930i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.1270 | + | 11.1270i | 0.392176 | + | 0.392176i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.8701 | 0.944701 | 0.472350 | − | 0.881411i | \(-0.343406\pi\) | ||||
0.472350 | + | 0.881411i | \(0.343406\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.4919 | + | 24.4919i | −0.860028 | + | 0.860028i | −0.991341 | − | 0.131313i | \(-0.958081\pi\) |
0.131313 | + | 0.991341i | \(0.458081\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.5483 | −0.439548 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −70.4758 | −2.46564 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.9545 | + | 10.9545i | −0.382313 | + | 0.382313i | −0.871935 | − | 0.489622i | \(-0.837135\pi\) |
0.489622 | + | 0.871935i | \(0.337135\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.8730 | −0.518440 | −0.259220 | − | 0.965818i | \(-0.583465\pi\) | ||||
−0.259220 | + | 0.965818i | \(0.583465\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.93834 | − | 4.93834i | −0.171723 | − | 0.171723i | 0.616013 | − | 0.787736i | \(-0.288747\pi\) |
−0.787736 | + | 0.616013i | \(0.788747\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.2540 | − | 11.2540i | 0.390869 | − | 0.390869i | −0.484128 | − | 0.874997i | \(-0.660863\pi\) |
0.874997 | + | 0.484128i | \(0.160863\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.77347i | 0.0614471i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.12702 | − | 6.12702i | −0.212034 | − | 0.212034i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 44.1771i | − | 1.52516i | −0.646893 | − | 0.762581i | \(-0.723932\pi\) | ||
0.646893 | − | 0.762581i | \(-0.276068\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 13.0000i | − | 0.448276i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.0208 | + | 12.0208i | 0.413529 | + | 0.413529i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 7.88912i | − | 0.271073i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.47723 | + | 5.47723i | −0.187757 | + | 0.187757i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.6190 | − | 19.6190i | −0.671740 | − | 0.671740i | 0.286377 | − | 0.958117i | \(-0.407549\pi\) |
−0.958117 | + | 0.286377i | \(0.907549\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.88338 | 0.132654 | 0.0663269 | − | 0.997798i | \(-0.478872\pi\) | ||||
0.0663269 | + | 0.997798i | \(0.478872\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.4919 | + | 22.4919i | −0.767415 | + | 0.767415i | −0.977651 | − | 0.210236i | \(-0.932577\pi\) |
0.210236 | + | 0.977651i | \(0.432577\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −50.3728 | −1.71471 | −0.857355 | − | 0.514725i | \(-0.827894\pi\) | ||||
−0.857355 | + | 0.514725i | \(0.827894\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.4919 | −0.594744 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.60995 | + | 7.60995i | −0.258150 | + | 0.258150i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.2218 | −0.820723 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.03151 | + | 2.03151i | 0.0686774 | + | 0.0686774i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.00000 | − | 3.00000i | 0.101303 | − | 0.101303i | −0.654639 | − | 0.755942i | \(-0.727179\pi\) |
0.755942 | + | 0.654639i | \(0.227179\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41.5283i | 1.39912i | 0.714573 | + | 0.699561i | \(0.246621\pi\) | ||||
−0.714573 | + | 0.699561i | \(0.753379\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.3649 | + | 22.3649i | 0.752639 | + | 0.752639i | 0.974971 | − | 0.222332i | \(-0.0713668\pi\) |
−0.222332 | + | 0.974971i | \(0.571367\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.30565i | 0.278877i | 0.990231 | + | 0.139438i | \(0.0445297\pi\) | ||||
−0.990231 | + | 0.139438i | \(0.955470\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 19.0161i | − | 0.637781i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.30565 | − | 8.30565i | −0.277938 | − | 0.277938i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.6190i | 0.555510i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.3137 | − | 11.3137i | 0.377333 | − | 0.377333i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.00000 | − | 2.00000i | −0.0666297 | − | 0.0666297i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.7279 | 0.423090 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.0000 | + | 18.0000i | −0.597680 | + | 0.597680i | −0.939695 | − | 0.342014i | \(-0.888891\pi\) |
0.342014 | + | 0.939695i | \(0.388891\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.6274 | 0.749680 | 0.374840 | − | 0.927090i | \(-0.377698\pi\) | ||||
0.374840 | + | 0.927090i | \(0.377698\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.74597 | 0.190164 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18.5416 | + | 18.5416i | −0.612297 | + | 0.612297i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35.4919 | −1.17077 | −0.585385 | − | 0.810755i | \(-0.699057\pi\) | ||||
−0.585385 | + | 0.810755i | \(0.699057\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 37.6449 | + | 37.6449i | 1.23910 | + | 1.23910i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.00000 | + | 1.00000i | −0.0328798 | + | 0.0328798i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 31.4491i | − | 1.03181i | −0.856645 | − | 0.515906i | \(-0.827455\pi\) | ||
0.856645 | − | 0.515906i | \(-0.172545\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.36492 | − | 7.36492i | −0.241375 | − | 0.241375i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 4.06301i | − | 0.132875i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.2540i | 1.05369i | 0.849960 | + | 0.526847i | \(0.176626\pi\) | ||||
−0.849960 | + | 0.526847i | \(0.823374\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.1971 | − | 15.1971i | −0.495411 | − | 0.495411i | 0.414595 | − | 0.910006i | \(-0.363923\pi\) |
−0.910006 | + | 0.414595i | \(0.863923\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 60.9839i | − | 1.98591i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 31.8084 | − | 31.8084i | 1.03363 | − | 1.03363i | 0.0342197 | − | 0.999414i | \(-0.489105\pi\) |
0.999414 | − | 0.0342197i | \(-0.0108946\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.2540 | + | 22.2540i | 0.722396 | + | 0.722396i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.3392 | −0.950391 | −0.475195 | − | 0.879880i | \(-0.657623\pi\) | ||||
−0.475195 | + | 0.879880i | \(0.657623\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.12702 | + | 3.12702i | −0.101188 | + | 0.101188i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 44.6931 | 1.44322 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0000 | 0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.42227 | + | 4.42227i | −0.142358 | + | 0.142358i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.61895 | 0.277167 | 0.138583 | − | 0.990351i | \(-0.455745\pi\) | ||||
0.138583 | + | 0.990351i | \(0.455745\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.97790 | + | 9.97790i | 0.320206 | + | 0.320206i | 0.848846 | − | 0.528640i | \(-0.177298\pi\) |
−0.528640 | + | 0.848846i | \(0.677298\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 25.1270 | − | 25.1270i | 0.805535 | − | 0.805535i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32.5269i | 1.04063i | 0.853975 | + | 0.520314i | \(0.174185\pi\) | ||||
−0.853975 | + | 0.520314i | \(0.825815\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.8569 | + | 11.8569i | 0.378947 | + | 0.378947i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 7.78958i | − | 0.248449i | −0.992254 | − | 0.124225i | \(-0.960356\pi\) | ||
0.992254 | − | 0.124225i | \(-0.0396443\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 4.25403i | − | 0.135545i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −32.8634 | − | 32.8634i | −1.04499 | − | 1.04499i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.2379i | 0.484048i | 0.970270 | + | 0.242024i | \(0.0778112\pi\) | ||||
−0.970270 | + | 0.242024i | \(0.922189\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.1341 | + | 11.1341i | −0.352974 | + | 0.352974i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.87298 | − | 1.87298i | −0.0593180 | − | 0.0593180i | 0.676826 | − | 0.736143i | \(-0.263355\pi\) |
−0.736143 | + | 0.676826i | \(0.763355\pi\) | |||||||
\(998\) | 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.bl.a.1871.2 | 8 | ||
3.2 | odd | 2 | inner | 2880.2.bl.a.1871.4 | 8 | ||
4.3 | odd | 2 | 720.2.bl.a.251.1 | ✓ | 8 | ||
12.11 | even | 2 | 720.2.bl.a.251.3 | yes | 8 | ||
16.3 | odd | 4 | inner | 2880.2.bl.a.431.4 | 8 | ||
16.13 | even | 4 | 720.2.bl.a.611.3 | yes | 8 | ||
48.29 | odd | 4 | 720.2.bl.a.611.1 | yes | 8 | ||
48.35 | even | 4 | inner | 2880.2.bl.a.431.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
720.2.bl.a.251.1 | ✓ | 8 | 4.3 | odd | 2 | ||
720.2.bl.a.251.3 | yes | 8 | 12.11 | even | 2 | ||
720.2.bl.a.611.1 | yes | 8 | 48.29 | odd | 4 | ||
720.2.bl.a.611.3 | yes | 8 | 16.13 | even | 4 | ||
2880.2.bl.a.431.2 | 8 | 48.35 | even | 4 | inner | ||
2880.2.bl.a.431.4 | 8 | 16.3 | odd | 4 | inner | ||
2880.2.bl.a.1871.2 | 8 | 1.1 | even | 1 | trivial | ||
2880.2.bl.a.1871.4 | 8 | 3.2 | odd | 2 | inner |