Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(143,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.j (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: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2x^{14} + 6x^{12} - 12x^{10} + 36x^{8} - 48x^{6} + 96x^{4} - 128x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 400) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1007.6 | ||
Root | \(-0.859408 - 1.12313i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.1007 |
Dual form | 1600.2.j.c.143.3 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 1.54564i | 0.892375i | 0.894939 | + | 0.446188i | \(0.147219\pi\) | ||||
−0.894939 | + | 0.446188i | \(0.852781\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.17442 | − | 1.17442i | −0.443890 | − | 0.443890i | 0.449427 | − | 0.893317i | \(-0.351628\pi\) |
−0.893317 | + | 0.449427i | \(0.851628\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.611000 | 0.203667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.04567 | − | 2.04567i | −0.616793 | − | 0.616793i | 0.327915 | − | 0.944707i | \(-0.393654\pi\) |
−0.944707 | + | 0.327915i | \(0.893654\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.14367 | 0.594547 | 0.297273 | − | 0.954792i | \(-0.403923\pi\) | ||||
0.297273 | + | 0.954792i | \(0.403923\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.07308 | − | 2.07308i | −0.502796 | − | 0.502796i | 0.409510 | − | 0.912306i | \(-0.365700\pi\) |
−0.912306 | + | 0.409510i | \(0.865700\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.47190 | − | 4.47190i | −1.02592 | − | 1.02592i | −0.999655 | − | 0.0262700i | \(-0.991637\pi\) |
−0.0262700 | − | 0.999655i | \(-0.508363\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.81523 | − | 1.81523i | 0.396116 | − | 0.396116i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.86373 | + | 4.86373i | −1.01416 | + | 1.01416i | −0.0142597 | + | 0.999898i | \(0.504539\pi\) |
−0.999898 | + | 0.0142597i | \(0.995461\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.58130i | 1.07412i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.51757 | + | 5.51757i | −1.02459 | + | 1.02459i | −0.0248976 | + | 0.999690i | \(0.507926\pi\) |
−0.999690 | + | 0.0248976i | \(0.992074\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.72181i | − | 1.02767i | −0.857890 | − | 0.513833i | \(-0.828225\pi\) | ||
0.857890 | − | 0.513833i | \(-0.171775\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.16187 | − | 3.16187i | 0.550411 | − | 0.550411i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.0214 | −1.81191 | −0.905956 | − | 0.423373i | \(-0.860846\pi\) | ||||
−0.905956 | + | 0.423373i | \(0.860846\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.31334i | 0.530559i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 11.4241i | − | 1.78415i | −0.451885 | − | 0.892076i | \(-0.649248\pi\) | ||
0.451885 | − | 0.892076i | \(-0.350752\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.251676 | −0.0383802 | −0.0191901 | − | 0.999816i | \(-0.506109\pi\) | ||||
−0.0191901 | + | 0.999816i | \(0.506109\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.119541 | − | 0.119541i | 0.0174368 | − | 0.0174368i | −0.698335 | − | 0.715771i | \(-0.746075\pi\) |
0.715771 | + | 0.698335i | \(0.246075\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 4.24147i | − | 0.605924i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.20423 | − | 3.20423i | 0.448682 | − | 0.448682i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.69520i | 0.370214i | 0.982718 | + | 0.185107i | \(0.0592632\pi\) | ||||
−0.982718 | + | 0.185107i | \(0.940737\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.91195 | − | 6.91195i | 0.915510 | − | 0.915510i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.24990 | + | 1.24990i | −0.162724 | + | 0.162724i | −0.783772 | − | 0.621049i | \(-0.786707\pi\) |
0.621049 | + | 0.783772i | \(0.286707\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.48034 | − | 2.48034i | −0.317575 | − | 0.317575i | 0.530260 | − | 0.847835i | \(-0.322094\pi\) |
−0.847835 | + | 0.530260i | \(0.822094\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.717571 | − | 0.717571i | −0.0904055 | − | 0.0904055i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.23670 | 1.12844 | 0.564221 | − | 0.825623i | \(-0.309176\pi\) | ||||
0.564221 | + | 0.825623i | \(0.309176\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.51757 | − | 7.51757i | −0.905009 | − | 0.905009i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.85246 | 1.05059 | 0.525297 | − | 0.850919i | \(-0.323954\pi\) | ||||
0.525297 | + | 0.850919i | \(0.323954\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.85956 | − | 7.85956i | −0.919892 | − | 0.919892i | 0.0771295 | − | 0.997021i | \(-0.475424\pi\) |
−0.997021 | + | 0.0771295i | \(0.975424\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.80496i | 0.547576i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.86934 | −0.547844 | −0.273922 | − | 0.961752i | \(-0.588321\pi\) | ||||
−0.273922 | + | 0.961752i | \(0.588321\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.79368 | −0.754853 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 4.94936i | − | 0.543263i | −0.962401 | − | 0.271632i | \(-0.912437\pi\) | ||
0.962401 | − | 0.271632i | \(-0.0875632\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.52818 | − | 8.52818i | −0.914317 | − | 0.914317i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.63047 | −0.384829 | −0.192414 | − | 0.981314i | \(-0.561632\pi\) | ||||
−0.192414 | + | 0.981314i | \(0.561632\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.51757 | − | 2.51757i | −0.263913 | − | 0.263913i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.84385 | 0.917064 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.89595 | + | 9.89595i | 1.00478 | + | 1.00478i | 0.999989 | + | 0.00479337i | \(0.00152578\pi\) |
0.00479337 | + | 0.999989i | \(0.498474\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.24990 | − | 1.24990i | −0.125620 | − | 0.125620i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.29557 | − | 6.29557i | 0.626433 | − | 0.626433i | −0.320736 | − | 0.947169i | \(-0.603930\pi\) |
0.947169 | + | 0.320736i | \(0.103930\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.06642 | + | 3.06642i | −0.302143 | + | 0.302143i | −0.841852 | − | 0.539709i | \(-0.818534\pi\) |
0.539709 | + | 0.841852i | \(0.318534\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.1186i | 1.26822i | 0.773242 | + | 0.634111i | \(0.218634\pi\) | ||||
−0.773242 | + | 0.634111i | \(0.781366\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | − | 2.00000i | 0.191565 | − | 0.191565i | −0.604807 | − | 0.796372i | \(-0.706750\pi\) |
0.796372 | + | 0.604807i | \(0.206750\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 17.0351i | − | 1.61690i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.551529 | − | 0.551529i | 0.0518835 | − | 0.0518835i | −0.680689 | − | 0.732572i | \(-0.738319\pi\) |
0.732572 | + | 0.680689i | \(0.238319\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.30978 | 0.121089 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.86934i | 0.446372i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 2.63047i | − | 0.239133i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 17.6576 | 1.59213 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.39015 | − | 9.39015i | 0.833241 | − | 0.833241i | −0.154717 | − | 0.987959i | \(-0.549447\pi\) |
0.987959 | + | 0.154717i | \(0.0494467\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 0.389000i | − | 0.0342496i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.471903 | − | 0.471903i | 0.0412303 | − | 0.0412303i | −0.686191 | − | 0.727421i | \(-0.740719\pi\) |
0.727421 | + | 0.686191i | \(0.240719\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.5038i | 0.910795i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.2564 | − | 16.2564i | 1.38888 | − | 1.38888i | 0.561186 | − | 0.827690i | \(-0.310345\pi\) |
0.827690 | − | 0.561186i | \(-0.189655\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.26767 | + | 5.26767i | −0.446798 | + | 0.446798i | −0.894289 | − | 0.447491i | \(-0.852318\pi\) |
0.447491 | + | 0.894289i | \(0.352318\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.184767 | + | 0.184767i | 0.0155602 | + | 0.0155602i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.38524 | − | 4.38524i | −0.366712 | − | 0.366712i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.55577 | 0.540711 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.70234 | + | 3.70234i | 0.303308 | + | 0.303308i | 0.842306 | − | 0.538999i | \(-0.181197\pi\) |
−0.538999 | + | 0.842306i | \(0.681197\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.3133 | −0.920667 | −0.460333 | − | 0.887746i | \(-0.652270\pi\) | ||||
−0.460333 | + | 0.887746i | \(0.652270\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.26665 | − | 1.26665i | −0.102403 | − | 0.102403i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.7622i | 1.49739i | 0.662916 | + | 0.748694i | \(0.269319\pi\) | ||||
−0.662916 | + | 0.748694i | \(0.730681\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.16580 | −0.330370 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.4241 | 0.900349 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 17.9093i | − | 1.40276i | −0.712786 | − | 0.701382i | \(-0.752567\pi\) | ||
0.712786 | − | 0.701382i | \(-0.247433\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.7939 | − | 12.7939i | −0.990020 | − | 0.990020i | 0.00993072 | − | 0.999951i | \(-0.496839\pi\) |
−0.999951 | + | 0.00993072i | \(0.996839\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.40468 | −0.646514 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.73233 | − | 2.73233i | −0.208947 | − | 0.208947i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.2040 | −1.30799 | −0.653997 | − | 0.756497i | \(-0.726909\pi\) | ||||
−0.653997 | + | 0.756497i | \(0.726909\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.93190 | − | 1.93190i | −0.145210 | − | 0.145210i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.76748 | + | 3.76748i | 0.281594 | + | 0.281594i | 0.833745 | − | 0.552150i | \(-0.186193\pi\) |
−0.552150 | + | 0.833745i | \(0.686193\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.29557 | + | 4.29557i | −0.319288 | + | 0.319288i | −0.848493 | − | 0.529206i | \(-0.822490\pi\) |
0.529206 | + | 0.848493i | \(0.322490\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.83371 | − | 3.83371i | 0.283396 | − | 0.283396i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.48168i | 0.620242i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.55481 | − | 6.55481i | 0.476792 | − | 0.476792i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.8876i | 1.87316i | 0.350451 | + | 0.936581i | \(0.386028\pi\) | ||||
−0.350451 | + | 0.936581i | \(0.613972\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.1105 | + | 10.1105i | −0.727770 | + | 0.727770i | −0.970175 | − | 0.242405i | \(-0.922064\pi\) |
0.242405 | + | 0.970175i | \(0.422064\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.6118 | −1.11230 | −0.556149 | − | 0.831083i | \(-0.687722\pi\) | ||||
−0.556149 | + | 0.831083i | \(0.687722\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 25.2178i | − | 1.78764i | −0.448422 | − | 0.893822i | \(-0.648014\pi\) | ||
0.448422 | − | 0.893822i | \(-0.351986\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.2766i | 1.00699i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.9599 | 0.909608 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.97174 | + | 2.97174i | −0.206550 | + | 0.206550i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 18.2961i | 1.26557i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.84144 | − | 6.84144i | 0.470984 | − | 0.470984i | −0.431249 | − | 0.902233i | \(-0.641927\pi\) |
0.902233 | + | 0.431249i | \(0.141927\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.6827i | 0.937524i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.71982 | + | 6.71982i | −0.456171 | + | 0.456171i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.1480 | − | 12.1480i | 0.820888 | − | 0.820888i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.44400 | − | 4.44400i | −0.298936 | − | 0.298936i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.31883 | − | 1.31883i | −0.0883151 | − | 0.0883151i | 0.661569 | − | 0.749884i | \(-0.269891\pi\) |
−0.749884 | + | 0.661569i | \(0.769891\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.63692 | −0.307763 | −0.153882 | − | 0.988089i | \(-0.549177\pi\) | ||||
−0.153882 | + | 0.988089i | \(0.549177\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.7396 | + | 12.7396i | 0.841855 | + | 0.841855i | 0.989100 | − | 0.147245i | \(-0.0470407\pi\) |
−0.147245 | + | 0.989100i | \(0.547041\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.42674 | −0.488643 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.0057 | − | 12.0057i | −0.786521 | − | 0.786521i | 0.194401 | − | 0.980922i | \(-0.437724\pi\) |
−0.980922 | + | 0.194401i | \(0.937724\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 7.52625i | − | 0.488882i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.64356 | 0.170997 | 0.0854987 | − | 0.996338i | \(-0.472752\pi\) | ||||
0.0854987 | + | 0.996338i | \(0.472752\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.01568 | 0.451920 | 0.225960 | − | 0.974137i | \(-0.427448\pi\) | ||||
0.225960 | + | 0.974137i | \(0.427448\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.24333i | 0.400510i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.58628 | − | 9.58628i | −0.609961 | − | 0.609961i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.64993 | 0.484795 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.7675 | + | 15.7675i | 0.995234 | + | 0.995234i | 0.999989 | − | 0.00475439i | \(-0.00151338\pi\) |
−0.00475439 | + | 0.999989i | \(0.501513\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.8992 | 1.25105 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.27135 | + | 7.27135i | 0.453574 | + | 0.453574i | 0.896539 | − | 0.442965i | \(-0.146073\pi\) |
−0.442965 | + | 0.896539i | \(0.646073\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.9438 | + | 12.9438i | 0.804289 | + | 0.804289i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.37123 | + | 3.37123i | −0.208674 | + | 0.208674i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.32058 | + | 5.32058i | −0.328081 | + | 0.328081i | −0.851856 | − | 0.523775i | \(-0.824523\pi\) |
0.523775 | + | 0.851856i | \(0.324523\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 5.61139i | − | 0.343411i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.29766 | + | 2.29766i | −0.140091 | + | 0.140091i | −0.773674 | − | 0.633584i | \(-0.781583\pi\) |
0.633584 | + | 0.773674i | \(0.281583\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.9396i | 0.907518i | 0.891124 | + | 0.453759i | \(0.149917\pi\) | ||||
−0.891124 | + | 0.453759i | \(0.850083\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.89126 | − | 3.89126i | 0.235510 | − | 0.235510i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.2360 | −0.675104 | −0.337552 | − | 0.941307i | \(-0.609599\pi\) | ||||
−0.337552 | + | 0.941307i | \(0.609599\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 3.49602i | − | 0.209301i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.0546i | 0.898083i | 0.893511 | + | 0.449041i | \(0.148234\pi\) | ||||
−0.893511 | + | 0.449041i | \(0.851766\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.8230 | −1.11891 | −0.559455 | − | 0.828861i | \(-0.688990\pi\) | ||||
−0.559455 | + | 0.828861i | \(0.688990\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.4168 | + | 13.4168i | −0.791967 | + | 0.791967i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 8.40468i | − | 0.494393i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15.2956 | + | 15.2956i | −0.896642 | + | 0.896642i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.18256i | 0.361189i | 0.983558 | + | 0.180594i | \(0.0578021\pi\) | ||||
−0.983558 | + | 0.180594i | \(0.942198\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.4175 | − | 11.4175i | 0.662511 | − | 0.662511i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.4262 | + | 10.4262i | −0.602965 | + | 0.602965i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.295574 | + | 0.295574i | 0.0170366 | + | 0.0170366i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.73069 | + | 9.73069i | 0.559013 | + | 0.559013i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.85636 | −0.277167 | −0.138584 | − | 0.990351i | \(-0.544255\pi\) | ||||
−0.138584 | + | 0.990351i | \(0.544255\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.73957 | − | 4.73957i | −0.269625 | − | 0.269625i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.09551 | −0.118826 | −0.0594128 | − | 0.998233i | \(-0.518923\pi\) | ||||
−0.0594128 | + | 0.998233i | \(0.518923\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.6684 | + | 13.6684i | 0.772586 | + | 0.772586i | 0.978558 | − | 0.205972i | \(-0.0660355\pi\) |
−0.205972 | + | 0.978558i | \(0.566035\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.21646i | 0.349151i | 0.984644 | + | 0.174576i | \(0.0558554\pi\) | ||||
−0.984644 | + | 0.174576i | \(0.944145\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.5743 | 1.26392 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −20.2766 | −1.13173 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.5412i | 1.03166i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.09128 | + | 3.09128i | 0.170948 | + | 0.170948i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.280783 | −0.0154801 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.28922 | − | 8.28922i | −0.455617 | − | 0.455617i | 0.441597 | − | 0.897214i | \(-0.354412\pi\) |
−0.897214 | + | 0.441597i | \(0.854412\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.73409 | −0.369026 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.4175 | − | 11.4175i | −0.621951 | − | 0.621951i | 0.324079 | − | 0.946030i | \(-0.394946\pi\) |
−0.946030 | + | 0.324079i | \(0.894946\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.852465 | + | 0.852465i | 0.0462995 | + | 0.0462995i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.7049 | + | 11.7049i | −0.633857 | + | 0.633857i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.2022 | + | 13.2022i | −0.712853 | + | 0.712853i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.73654i | 0.0932226i | 0.998913 | + | 0.0466113i | \(0.0148422\pi\) | ||||
−0.998913 | + | 0.0466113i | \(0.985158\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.1087 | − | 20.1087i | 1.07640 | − | 1.07640i | 0.0795655 | − | 0.996830i | \(-0.474647\pi\) |
0.996830 | − | 0.0795655i | \(-0.0253533\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.9645i | 0.638616i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.7572 | − | 14.7572i | 0.785448 | − | 0.785448i | −0.195296 | − | 0.980744i | \(-0.562567\pi\) |
0.980744 | + | 0.195296i | \(0.0625667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.52625 | −0.398331 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.3481i | 1.33782i | 0.743343 | + | 0.668911i | \(0.233239\pi\) | ||||
−0.743343 | + | 0.668911i | \(0.766761\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.9958i | 1.10504i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.06575 | 0.213397 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.4798 | − | 19.4798i | 1.01684 | − | 1.01684i | 0.0169808 | − | 0.999856i | \(-0.494595\pi\) |
0.999856 | − | 0.0169808i | \(-0.00540540\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 6.98015i | − | 0.363372i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.16530 | − | 3.16530i | 0.164334 | − | 0.164334i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 25.4963i | − | 1.32015i | −0.751200 | − | 0.660074i | \(-0.770525\pi\) | ||
0.751200 | − | 0.660074i | \(-0.229475\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.8279 | + | 11.8279i | −0.609165 | + | 0.609165i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.82367 | − | 6.82367i | 0.350508 | − | 0.350508i | −0.509790 | − | 0.860299i | \(-0.670277\pi\) |
0.860299 | + | 0.509790i | \(0.170277\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.5138 | + | 14.5138i | 0.743564 | + | 0.743564i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.08490 | − | 2.08490i | −0.106533 | − | 0.106533i | 0.651831 | − | 0.758364i | \(-0.274001\pi\) |
−0.758364 | + | 0.651831i | \(0.774001\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.153774 | −0.00781677 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.92395 | + | 7.92395i | 0.401760 | + | 0.401760i | 0.878853 | − | 0.477093i | \(-0.158309\pi\) |
−0.477093 | + | 0.878853i | \(0.658309\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.1658 | 1.01983 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.729391 | + | 0.729391i | 0.0367929 | + | 0.0367929i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 24.1865i | − | 1.21389i | −0.794745 | − | 0.606943i | \(-0.792395\pi\) | ||
0.794745 | − | 0.606943i | \(-0.207605\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −16.2351 | −0.812771 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.9958 | 0.698918 | 0.349459 | − | 0.936952i | \(-0.386365\pi\) | ||||
0.349459 | + | 0.936952i | \(0.386365\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 12.2657i | − | 0.610996i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 22.5462 | + | 22.5462i | 1.11757 | + | 1.11757i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.4241 | 0.564888 | 0.282444 | − | 0.959284i | \(-0.408855\pi\) | ||||
0.282444 | + | 0.959284i | \(0.408855\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 25.1265 | + | 25.1265i | 1.23940 | + | 1.23940i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.93583 | 0.144463 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.14192 | − | 8.14192i | −0.398711 | − | 0.398711i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.5455 | + | 16.5455i | 0.808299 | + | 0.808299i | 0.984376 | − | 0.176077i | \(-0.0563407\pi\) |
−0.176077 | + | 0.984376i | \(0.556341\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.5900 | + | 15.5900i | −0.759808 | + | 0.759808i | −0.976287 | − | 0.216479i | \(-0.930543\pi\) |
0.216479 | + | 0.976287i | \(0.430543\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.0730395 | − | 0.0730395i | 0.00355130 | − | 0.00355130i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.82594i | 0.281937i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.77800 | − | 6.77800i | 0.327245 | − | 0.327245i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 18.4609i | − | 0.889229i | −0.895722 | − | 0.444615i | \(-0.853341\pi\) | ||
0.895722 | − | 0.444615i | \(-0.146659\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.7872 | + | 13.7872i | −0.662571 | + | 0.662571i | −0.955985 | − | 0.293414i | \(-0.905208\pi\) |
0.293414 | + | 0.955985i | \(0.405208\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 43.5003 | 2.08090 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.9049i | 0.806826i | 0.915018 | + | 0.403413i | \(0.132176\pi\) | ||||
−0.915018 | + | 0.403413i | \(0.867824\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 2.59153i | − | 0.123406i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.2979 | −0.584291 | −0.292145 | − | 0.956374i | \(-0.594369\pi\) | ||||
−0.292145 | + | 0.956374i | \(0.594369\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.72248 | + | 5.72248i | −0.270664 | + | 0.270664i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.34968i | 0.441239i | 0.975360 | + | 0.220619i | \(0.0708079\pi\) | ||||
−0.975360 | + | 0.220619i | \(0.929192\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −23.3700 | + | 23.3700i | −1.10045 | + | 1.10045i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 17.4863i | − | 0.821580i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.9127 | + | 14.9127i | −0.697586 | + | 0.697586i | −0.963889 | − | 0.266303i | \(-0.914198\pi\) |
0.266303 | + | 0.963889i | \(0.414198\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11.5705 | − | 11.5705i | 0.540064 | − | 0.540064i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.0005 | + | 18.0005i | 0.838367 | + | 0.838367i | 0.988644 | − | 0.150277i | \(-0.0480165\pi\) |
−0.150277 | + | 0.988644i | \(0.548017\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.25392 | − | 6.25392i | −0.290644 | − | 0.290644i | 0.546690 | − | 0.837335i | \(-0.315887\pi\) |
−0.837335 | + | 0.546690i | \(0.815887\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.9988 | 1.11053 | 0.555267 | − | 0.831672i | \(-0.312616\pi\) | ||||
0.555267 | + | 0.831672i | \(0.312616\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.8478 | − | 10.8478i | −0.500904 | − | 0.500904i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −28.9996 | −1.33623 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.514846 | + | 0.514846i | 0.0236727 | + | 0.0236727i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.64677i | 0.0754002i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.6618 | 1.08114 | 0.540568 | − | 0.841300i | \(-0.318209\pi\) | ||||
0.540568 | + | 0.841300i | \(0.318209\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.6263 | −1.07727 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 17.6576i | 0.803449i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.1809 | + | 21.1809i | 0.959797 | + | 0.959797i | 0.999223 | − | 0.0394255i | \(-0.0125528\pi\) |
−0.0394255 | + | 0.999223i | \(0.512553\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 27.6813 | 1.25179 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.2854 | − | 13.2854i | −0.599563 | − | 0.599563i | 0.340633 | − | 0.940196i | \(-0.389359\pi\) |
−0.940196 | + | 0.340633i | \(0.889359\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.8767 | 1.03032 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.3965 | − | 10.3965i | −0.466348 | − | 0.466348i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.8026 | − | 24.8026i | −1.11032 | − | 1.11032i | −0.993107 | − | 0.117211i | \(-0.962605\pi\) |
−0.117211 | − | 0.993107i | \(-0.537395\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.7747 | − | 19.7747i | 0.883469 | − | 0.883469i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.2205 | − | 23.2205i | 1.03535 | − | 1.03535i | 0.0359989 | − | 0.999352i | \(-0.488539\pi\) |
0.999352 | − | 0.0359989i | \(-0.0114613\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 12.9906i | − | 0.576933i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −30.5917 | + | 30.5917i | −1.35595 | + | 1.35595i | −0.477105 | + | 0.878847i | \(0.658314\pi\) |
−0.878847 | + | 0.477105i | \(0.841686\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.4609i | 0.816661i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 24.9590 | − | 24.9590i | 1.10197 | − | 1.10197i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.489083 | −0.0215098 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 26.5911i | − | 1.16722i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 13.1096i | − | 0.574342i | −0.957879 | − | 0.287171i | \(-0.907285\pi\) | ||
0.957879 | − | 0.287171i | \(-0.0927149\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.0886 | −1.35941 | −0.679706 | − | 0.733485i | \(-0.737893\pi\) | ||||
−0.679706 | + | 0.733485i | \(0.737893\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.8618 | + | 11.8618i | −0.516706 | + | 0.516706i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 24.3118i | − | 1.05703i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.763691 | + | 0.763691i | −0.0331413 | + | 0.0331413i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 24.4896i | − | 1.06076i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.82316 | + | 5.82316i | −0.251288 | + | 0.251288i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.67664 | + | 8.67664i | −0.373729 | + | 0.373729i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.926425 | − | 0.926425i | −0.0398301 | − | 0.0398301i | 0.686911 | − | 0.726741i | \(-0.258966\pi\) |
−0.726741 | + | 0.686911i | \(0.758966\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.63941 | − | 6.63941i | −0.284924 | − | 0.284924i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.1171 | −0.731875 | −0.365938 | − | 0.930639i | \(-0.619252\pi\) | ||||
−0.365938 | + | 0.930639i | \(0.619252\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.51549 | − | 1.51549i | −0.0646794 | − | 0.0646794i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 49.3481 | 2.10230 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.71866 | + | 5.71866i | 0.243182 | + | 0.243182i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 12.5797i | − | 0.533017i | −0.963833 | − | 0.266509i | \(-0.914130\pi\) | ||
0.963833 | − | 0.266509i | \(-0.0858701\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.539510 | −0.0228189 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.1096 | −0.553488 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.4227i | 0.818569i | 0.912407 | + | 0.409284i | \(0.134222\pi\) | ||||
−0.912407 | + | 0.409284i | \(0.865778\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.97865 | + | 7.97865i | 0.335072 | + | 0.335072i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.57547 | −0.233736 | −0.116868 | − | 0.993147i | \(-0.537285\pi\) | ||||
−0.116868 | + | 0.993147i | \(0.537285\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.58062 | − | 5.58062i | −0.233542 | − | 0.233542i | 0.580627 | − | 0.814169i | \(-0.302807\pi\) |
−0.814169 | + | 0.580627i | \(0.802807\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −40.0129 | −1.67156 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.7472 | + | 27.7472i | 1.15513 | + | 1.15513i | 0.985509 | + | 0.169624i | \(0.0542553\pi\) |
0.169624 | + | 0.985509i | \(0.445745\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15.6272 | − | 15.6272i | −0.649444 | − | 0.649444i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.81264 | + | 5.81264i | −0.241149 | + | 0.241149i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.51349 | − | 5.51349i | 0.228345 | − | 0.228345i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 30.8977i | − | 1.27529i | −0.770332 | − | 0.637643i | \(-0.779909\pi\) | ||
0.770332 | − | 0.637643i | \(-0.220091\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −25.5874 | + | 25.5874i | −1.05431 | + | 1.05431i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 24.1303i | − | 0.992587i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.82287 | + | 7.82287i | −0.321247 | + | 0.321247i | −0.849245 | − | 0.527998i | \(-0.822943\pi\) |
0.527998 | + | 0.849245i | \(0.322943\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 38.9777 | 1.59525 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.3316i | 0.994163i | 0.867704 | + | 0.497081i | \(0.165595\pi\) | ||||
−0.867704 | + | 0.497081i | \(0.834405\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 30.6420i | − | 1.24991i | −0.780660 | − | 0.624956i | \(-0.785117\pi\) | ||
0.780660 | − | 0.624956i | \(-0.214883\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.64362 | 0.229826 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.0615 | − | 10.0615i | 0.408386 | − | 0.408386i | −0.472790 | − | 0.881175i | \(-0.656753\pi\) |
0.881175 | + | 0.472790i | \(0.156753\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 20.0314i | 0.811712i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.256256 | − | 0.256256i | 0.0103670 | − | 0.0103670i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.66991i | 0.390564i | 0.980747 | + | 0.195282i | \(0.0625622\pi\) | ||||
−0.980747 | + | 0.195282i | \(0.937438\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.46520 | + | 4.46520i | −0.179762 | + | 0.179762i | −0.791252 | − | 0.611490i | \(-0.790570\pi\) |
0.611490 | + | 0.791252i | \(0.290570\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.32437 | − | 5.32437i | 0.214004 | − | 0.214004i | −0.591962 | − | 0.805966i | \(-0.701646\pi\) |
0.805966 | + | 0.591962i | \(0.201646\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −27.1460 | − | 27.1460i | −1.08933 | − | 1.08933i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.26370 | + | 4.26370i | 0.170822 | + | 0.170822i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −28.2791 | −1.12936 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 22.8483 | + | 22.8483i | 0.911021 | + | 0.911021i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.1303 | −0.960611 | −0.480306 | − | 0.877101i | \(-0.659474\pi\) | ||||
−0.480306 | + | 0.877101i | \(0.659474\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.5744 | + | 10.5744i | 0.420294 | + | 0.420294i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 9.09230i | − | 0.360250i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.40885 | 0.213971 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.1642 | 1.58639 | 0.793196 | − | 0.608967i | \(-0.208416\pi\) | ||||
0.793196 | + | 0.608967i | \(0.208416\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 38.2226i | − | 1.50735i | −0.657245 | − | 0.753677i | \(-0.728278\pi\) | ||
0.657245 | − | 0.753677i | \(-0.271722\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.07480 | + | 4.07480i | 0.160197 | + | 0.160197i | 0.782654 | − | 0.622457i | \(-0.213866\pi\) |
−0.622457 | + | 0.782654i | \(0.713866\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.11378 | 0.200733 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.3864 | − | 10.3864i | −0.407076 | − | 0.407076i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.5270 | −0.725016 | −0.362508 | − | 0.931981i | \(-0.618079\pi\) | ||||
−0.362508 | + | 0.931981i | \(0.618079\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.80219 | − | 4.80219i | −0.187351 | − | 0.187351i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.4021 | − | 11.4021i | −0.444163 | − | 0.444163i | 0.449245 | − | 0.893409i | \(-0.351693\pi\) |
−0.893409 | + | 0.449245i | \(0.851693\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.03893 | − | 6.03893i | 0.234887 | − | 0.234887i | −0.579842 | − | 0.814729i | \(-0.696886\pi\) |
0.814729 | + | 0.579842i | \(0.196886\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.86882 | − | 6.86882i | 0.266763 | − | 0.266763i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 53.6720i | − | 2.07819i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.03843 | − | 2.03843i | 0.0788102 | − | 0.0788102i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.1479i | 0.391756i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.5070 | + | 20.5070i | −0.790488 | + | 0.790488i | −0.981573 | − | 0.191085i | \(-0.938799\pi\) |
0.191085 | + | 0.981573i | \(0.438799\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.8942 | 0.610864 | 0.305432 | − | 0.952214i | \(-0.401199\pi\) | ||||
0.305432 | + | 0.952214i | \(0.401199\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 23.2441i | − | 0.892025i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 7.16700i | − | 0.274640i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.34149 | 0.280914 | 0.140457 | − | 0.990087i | \(-0.455143\pi\) | ||||
0.140457 | + | 0.990087i | \(0.455143\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19.6908 | + | 19.6908i | −0.751250 | + | 0.751250i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.77762i | 0.220110i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.5464 | − | 28.5464i | 1.08595 | − | 1.08595i | 0.0900145 | − | 0.995940i | \(-0.471309\pi\) |
0.995940 | − | 0.0900145i | \(-0.0286913\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.93583i | 0.111523i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23.6832 | + | 23.6832i | −0.897064 | + | 0.897064i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.5565 | − | 18.5565i | 0.701871 | − | 0.701871i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.7049 | + | 17.7049i | 0.668706 | + | 0.668706i | 0.957416 | − | 0.288710i | \(-0.0932265\pi\) |
−0.288710 | + | 0.957416i | \(0.593227\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 49.2867 | + | 49.2867i | 1.85888 | + | 1.85888i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.7873 | −0.556135 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.2225 | − | 31.2225i | −1.17259 | − | 1.17259i | −0.981591 | − | 0.190995i | \(-0.938829\pi\) |
−0.190995 | − | 0.981591i | \(-0.561171\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.97517 | −0.111577 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 27.8293 | + | 27.8293i | 1.04222 | + | 1.04222i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.08598i | 0.152594i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.7570 | −1.14704 | −0.573520 | − | 0.819191i | \(-0.694423\pi\) | ||||
−0.573520 | + | 0.819191i | \(0.694423\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.20253 | 0.268236 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.8437i | 0.403282i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.0526 | + | 20.0526i | 0.743711 | + | 0.743711i | 0.973290 | − | 0.229579i | \(-0.0737350\pi\) |
−0.229579 | + | 0.973290i | \(0.573735\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −30.0310 | −1.11226 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.521745 | + | 0.521745i | 0.0192974 | + | 0.0192974i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.69214 | 0.173308 | 0.0866540 | − | 0.996238i | \(-0.472383\pi\) | ||||
0.0866540 | + | 0.996238i | \(0.472383\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.8953 | − | 18.8953i | −0.696016 | − | 0.696016i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.45035 | − | 5.45035i | −0.200494 | − | 0.200494i | 0.599717 | − | 0.800212i | \(-0.295280\pi\) |
−0.800212 | + | 0.599717i | \(0.795280\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14.8169 | − | 14.8169i | 0.544314 | − | 0.544314i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.8916 | − | 28.8916i | 1.05993 | − | 1.05993i | 0.0618433 | − | 0.998086i | \(-0.480302\pi\) |
0.998086 | − | 0.0618433i | \(-0.0196979\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 3.02406i | − | 0.110645i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.4068 | − | 15.4068i | 0.562951 | − | 0.562951i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 34.7738i | − | 1.26892i | −0.772958 | − | 0.634458i | \(-0.781224\pi\) | ||
0.772958 | − | 0.634458i | \(-0.218776\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −24.3708 | + | 24.3708i | −0.888122 | + | 0.888122i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.0634 | −0.474796 | −0.237398 | − | 0.971412i | \(-0.576295\pi\) | ||||
−0.237398 | + | 0.971412i | \(0.576295\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 30.7570i | 1.11641i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.48332i | 0.271270i | 0.990759 | + | 0.135635i | \(0.0433074\pi\) | ||||
−0.990759 | + | 0.135635i | \(0.956693\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.69769 | −0.170068 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.67938 | + | 2.67938i | −0.0967468 | + | 0.0967468i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 21.5518i | − | 0.777179i | −0.921411 | − | 0.388589i | \(-0.872962\pi\) | ||
0.921411 | − | 0.388589i | \(-0.127038\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.2389 | + | 11.2389i | −0.404758 | + | 0.404758i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.6752i | 1.03138i | 0.856777 | + | 0.515688i | \(0.172464\pi\) | ||||
−0.856777 | + | 0.515688i | \(0.827536\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −20.0065 | + | 20.0065i | −0.717727 | + | 0.717727i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −51.0877 | + | 51.0877i | −1.83041 | + | 1.83041i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.1092 | − | 18.1092i | −0.647999 | − | 0.647999i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −30.7952 | − | 30.7952i | −1.10053 | − | 1.10053i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.9487 | −1.28143 | −0.640716 | − | 0.767778i | \(-0.721363\pi\) | ||||
−0.640716 | + | 0.767778i | \(0.721363\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.22370 | − | 8.22370i | −0.292771 | − | 0.292771i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.29546 | −0.0460611 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.31703 | − | 5.31703i | −0.188813 | − | 0.188813i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 10.7052i | − | 0.379196i | −0.981862 | − | 0.189598i | \(-0.939282\pi\) | ||
0.981862 | − | 0.189598i | \(-0.0607185\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.495636 | −0.0175343 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.21821 | −0.0783767 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32.1561i | 1.13476i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.55135 | − | 3.55135i | −0.125014 | − | 0.125014i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.3002 | −0.362137 | −0.181069 | − | 0.983470i | \(-0.557956\pi\) | ||||
−0.181069 | + | 0.983470i | \(0.557956\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.0808 | − | 27.0808i | −0.950936 | − | 0.950936i | 0.0479153 | − | 0.998851i | \(-0.484742\pi\) |
−0.998851 | + | 0.0479153i | \(0.984742\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −23.0913 | −0.809847 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.12547 | + | 1.12547i | 0.0393752 | + | 0.0393752i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.53824 | − | 1.53824i | −0.0537503 | − | 0.0537503i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.00000 | − | 6.00000i | 0.209401 | − | 0.209401i | −0.594612 | − | 0.804013i | \(-0.702694\pi\) |
0.804013 | + | 0.594612i | \(0.202694\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.4197 | − | 17.4197i | 0.607214 | − | 0.607214i | −0.335003 | − | 0.942217i | \(-0.608737\pi\) |
0.942217 | + | 0.335003i | \(0.108737\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.05415i | 0.106203i | 0.998589 | + | 0.0531016i | \(0.0169107\pi\) | ||||
−0.998589 | + | 0.0531016i | \(0.983089\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.18527 | − | 2.18527i | 0.0758976 | − | 0.0758976i | −0.668139 | − | 0.744037i | \(-0.732909\pi\) |
0.744037 | + | 0.668139i | \(0.232909\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 17.3668i | − | 0.602446i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.79290 | + | 8.79290i | −0.304656 | + | 0.304656i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 31.9351 | 1.10384 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.68627i | 0.0582167i | 0.999576 | + | 0.0291083i | \(0.00926678\pi\) | ||||
−0.999576 | + | 0.0291083i | \(0.990733\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 31.8872i | − | 1.09956i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −23.2690 | −0.801427 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.08928 | + | 3.08928i | −0.106149 | + | 0.106149i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 29.0935i | − | 0.998488i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 53.6052 | − | 53.6052i | 1.83756 | − | 1.83756i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 38.0838i | − | 1.30396i | −0.758235 | − | 0.651982i | \(-0.773938\pi\) | ||
0.758235 | − | 0.651982i | \(-0.226062\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.9027 | + | 27.9027i | −0.953138 | + | 0.953138i | −0.998950 | − | 0.0458123i | \(-0.985412\pi\) |
0.0458123 | + | 0.998950i | \(0.485412\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.51122 | − | 7.51122i | 0.256280 | − | 0.256280i | −0.567260 | − | 0.823539i | \(-0.691996\pi\) |
0.823539 | + | 0.567260i | \(0.191996\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −20.7375 | − | 20.7375i | −0.706732 | − | 0.706732i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35.6257 | − | 35.6257i | −1.21271 | − | 1.21271i | −0.970131 | − | 0.242580i | \(-0.922006\pi\) |
−0.242580 | − | 0.970131i | \(-0.577994\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12.9906 | 0.441184 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.96107 | + | 9.96107i | 0.337906 | + | 0.337906i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.8004 | 0.670912 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.04642 | + | 6.04642i | 0.204640 | + | 0.204640i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 30.6461i | − | 1.03484i | −0.855730 | − | 0.517422i | \(-0.826892\pi\) | ||
0.855730 | − | 0.517422i | \(-0.173108\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.55600 | −0.322316 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.5286 | −0.691625 | −0.345813 | − | 0.938304i | \(-0.612397\pi\) | ||||
−0.345813 | + | 0.938304i | \(0.612397\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 20.5650i | − | 0.692068i | −0.938222 | − | 0.346034i | \(-0.887528\pi\) | ||
0.938222 | − | 0.346034i | \(-0.112472\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.6473 | − | 23.6473i | −0.793997 | − | 0.793997i | 0.188144 | − | 0.982141i | \(-0.439753\pi\) |
−0.982141 | + | 0.188144i | \(0.939753\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22.0560 | −0.739735 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.8976 | + | 13.8976i | 0.465588 | + | 0.465588i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.06915 | −0.0357778 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.1152 | − | 16.1152i | −0.538071 | − | 0.538071i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 31.5705 | + | 31.5705i | 1.05293 | + | 1.05293i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.58736 | − | 5.58736i | 0.186142 | − | 0.186142i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.456851 | + | 0.456851i | −0.0152030 | + | 0.0152030i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 3.63021i | − | 0.120539i | −0.998182 | − | 0.0602696i | \(-0.980804\pi\) | ||
0.998182 | − | 0.0602696i | \(-0.0191961\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.84659 | − | 3.84659i | 0.127583 | − | 0.127583i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 44.3485i | − | 1.46933i | −0.678430 | − | 0.734665i | \(-0.737339\pi\) | ||
0.678430 | − | 0.734665i | \(-0.262661\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.1248 | + | 10.1248i | −0.335081 | + | 0.335081i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.10843 | −0.0366035 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 13.3312i | − | 0.439756i | −0.975527 | − | 0.219878i | \(-0.929434\pi\) | ||
0.975527 | − | 0.219878i | \(-0.0705660\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 7.50618i | − | 0.247337i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.9768 | 0.624628 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.87358 | + | 1.87358i | −0.0615364 | + | 0.0615364i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.5713i | 0.445260i | 0.974903 | + | 0.222630i | \(0.0714641\pi\) | ||||
−0.974903 | + | 0.222630i | \(0.928536\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.9674 | + | 18.9674i | −0.621632 | + | 0.621632i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 3.23891i | − | 0.106037i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.5066 | − | 10.5066i | 0.343235 | − | 0.343235i | −0.514347 | − | 0.857582i | \(-0.671966\pi\) |
0.857582 | + | 0.514347i | \(0.171966\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21.1265 | + | 21.1265i | −0.689437 | + | 0.689437i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.25664 | − | 4.25664i | −0.138763 | − | 0.138763i | 0.634313 | − | 0.773076i | \(-0.281283\pi\) |
−0.773076 | + | 0.634313i | \(0.781283\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 55.5640 | + | 55.5640i | 1.80941 | + | 1.80941i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27.2068 | −0.884101 | −0.442050 | − | 0.896990i | \(-0.645749\pi\) | ||||
−0.442050 | + | 0.896990i | \(0.645749\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.8483 | − | 16.8483i | −0.546919 | − | 0.546919i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.60841 | −0.311574 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.537259 | − | 0.537259i | −0.0174035 | − | 0.0174035i | 0.698351 | − | 0.715755i | \(-0.253917\pi\) |
−0.715755 | + | 0.698351i | \(0.753917\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 34.8917i | 1.12789i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −38.1837 | −1.23302 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.73907 | −0.0560990 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.01545i | 0.258294i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.89350 | + | 9.89350i | 0.318154 | + | 0.318154i | 0.848058 | − | 0.529904i | \(-0.177772\pi\) |
−0.529904 | + | 0.848058i | \(0.677772\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −28.6580 | −0.920629 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.8635 | − | 14.8635i | −0.476992 | − | 0.476992i | 0.427176 | − | 0.904168i | \(-0.359508\pi\) |
−0.904168 | + | 0.427176i | \(0.859508\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.3729 | 0.396658 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.4685 | + | 11.4685i | 0.366908 | + | 0.366908i | 0.866348 | − | 0.499440i | \(-0.166461\pi\) |
−0.499440 | + | 0.866348i | \(0.666461\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.42674 | + | 7.42674i | 0.237360 | + | 0.237360i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.22200 | − | 1.22200i | 0.0390154 | − | 0.0390154i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −34.9827 | + | 34.9827i | −1.11577 | + | 1.11577i | −0.123420 | + | 0.992355i | \(0.539386\pi\) |
−0.992355 | + | 0.123420i | \(0.960614\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 0.433989i | − | 0.0138140i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.22408 | − | 1.22408i | 0.0389236 | − | 0.0389236i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.0365i | 1.33533i | 0.744460 | + | 0.667667i | \(0.232707\pi\) | ||||
−0.744460 | + | 0.667667i | \(0.767293\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.8121 | − | 12.8121i | 0.406581 | − | 0.406581i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.7128 | 1.00435 | 0.502177 | − | 0.864765i | \(-0.332533\pi\) | ||||
0.502177 | + | 0.864765i | \(0.332533\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 61.5139i | − | 1.94621i |
(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 | 1600.2.j.c.1007.6 | 16 | ||
4.3 | odd | 2 | 400.2.j.c.307.6 | yes | 16 | ||
5.2 | odd | 4 | 1600.2.s.c.943.6 | 16 | |||
5.3 | odd | 4 | 1600.2.s.c.943.3 | 16 | |||
5.4 | even | 2 | inner | 1600.2.j.c.1007.3 | 16 | ||
16.5 | even | 4 | 400.2.s.c.107.7 | yes | 16 | ||
16.11 | odd | 4 | 1600.2.s.c.207.3 | 16 | |||
20.3 | even | 4 | 400.2.s.c.243.7 | yes | 16 | ||
20.7 | even | 4 | 400.2.s.c.243.2 | yes | 16 | ||
20.19 | odd | 2 | 400.2.j.c.307.3 | yes | 16 | ||
80.27 | even | 4 | inner | 1600.2.j.c.143.6 | 16 | ||
80.37 | odd | 4 | 400.2.j.c.43.3 | ✓ | 16 | ||
80.43 | even | 4 | inner | 1600.2.j.c.143.3 | 16 | ||
80.53 | odd | 4 | 400.2.j.c.43.6 | yes | 16 | ||
80.59 | odd | 4 | 1600.2.s.c.207.6 | 16 | |||
80.69 | even | 4 | 400.2.s.c.107.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.j.c.43.3 | ✓ | 16 | 80.37 | odd | 4 | ||
400.2.j.c.43.6 | yes | 16 | 80.53 | odd | 4 | ||
400.2.j.c.307.3 | yes | 16 | 20.19 | odd | 2 | ||
400.2.j.c.307.6 | yes | 16 | 4.3 | odd | 2 | ||
400.2.s.c.107.2 | yes | 16 | 80.69 | even | 4 | ||
400.2.s.c.107.7 | yes | 16 | 16.5 | even | 4 | ||
400.2.s.c.243.2 | yes | 16 | 20.7 | even | 4 | ||
400.2.s.c.243.7 | yes | 16 | 20.3 | even | 4 | ||
1600.2.j.c.143.3 | 16 | 80.43 | even | 4 | inner | ||
1600.2.j.c.143.6 | 16 | 80.27 | even | 4 | inner | ||
1600.2.j.c.1007.3 | 16 | 5.4 | even | 2 | inner | ||
1600.2.j.c.1007.6 | 16 | 1.1 | even | 1 | trivial | ||
1600.2.s.c.207.3 | 16 | 16.11 | odd | 4 | |||
1600.2.s.c.207.6 | 16 | 80.59 | odd | 4 | |||
1600.2.s.c.943.3 | 16 | 5.3 | odd | 4 | |||
1600.2.s.c.943.6 | 16 | 5.2 | odd | 4 |