Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(2305,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.2305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.q (of order \(3\), 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: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2881.8 | ||
Character | \(\chi\) | \(=\) | 3024.2881 |
Dual form | 3024.2.q.k.2305.8 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(5\) | 0.841578 | − | 1.45766i | 0.376365 | − | 0.651883i | −0.614165 | − | 0.789177i | \(-0.710507\pi\) |
0.990530 | + | 0.137294i | \(0.0438405\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.65502 | + | 2.06419i | −0.625540 | + | 0.780192i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.622490 | − | 1.07818i | −0.187688 | − | 0.325085i | 0.756791 | − | 0.653657i | \(-0.226766\pi\) |
−0.944479 | + | 0.328572i | \(0.893433\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.96039 | + | 3.39550i | 0.543715 | + | 0.941743i | 0.998687 | + | 0.0512366i | \(0.0163162\pi\) |
−0.454971 | + | 0.890506i | \(0.650350\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.62691 | − | 2.81788i | 0.394582 | − | 0.683437i | −0.598465 | − | 0.801149i | \(-0.704223\pi\) |
0.993048 | + | 0.117712i | \(0.0375559\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.36192 | − | 4.09097i | −0.541863 | − | 0.938534i | −0.998797 | − | 0.0490333i | \(-0.984386\pi\) |
0.456935 | − | 0.889500i | \(-0.348947\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.199068 | − | 0.344795i | 0.0415085 | − | 0.0718948i | −0.844525 | − | 0.535516i | \(-0.820117\pi\) |
0.886033 | + | 0.463622i | \(0.153450\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.08349 | + | 1.87667i | 0.216699 | + | 0.375333i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.19896 | − | 5.54076i | 0.594032 | − | 1.02889i | −0.399651 | − | 0.916667i | \(-0.630869\pi\) |
0.993683 | − | 0.112226i | \(-0.0357979\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.578367 | 0.103878 | 0.0519389 | − | 0.998650i | \(-0.483460\pi\) | ||||
0.0519389 | + | 0.998650i | \(0.483460\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.61605 | + | 4.14963i | 0.273163 | + | 0.701416i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.72146 | + | 4.71371i | 0.447405 | + | 0.774928i | 0.998216 | − | 0.0597015i | \(-0.0190149\pi\) |
−0.550811 | + | 0.834630i | \(0.685682\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.20216 | − | 7.27836i | −0.656267 | − | 1.13669i | −0.981574 | − | 0.191080i | \(-0.938801\pi\) |
0.325307 | − | 0.945608i | \(-0.394532\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.46299 | + | 4.26603i | −0.375603 | + | 0.650563i | −0.990417 | − | 0.138109i | \(-0.955898\pi\) |
0.614814 | + | 0.788672i | \(0.289231\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.425190 | −0.0620203 | −0.0310101 | − | 0.999519i | \(-0.509872\pi\) | ||||
−0.0310101 | + | 0.999519i | \(0.509872\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.52179 | − | 6.83258i | −0.217399 | − | 0.976083i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.466315 | − | 0.807681i | 0.0640533 | − | 0.110944i | −0.832220 | − | 0.554445i | \(-0.812931\pi\) |
0.896274 | + | 0.443501i | \(0.146264\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.09550 | −0.282557 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.05054 | 0.787713 | 0.393856 | − | 0.919172i | \(-0.371141\pi\) | ||||
0.393856 | + | 0.919172i | \(0.371141\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.2092 | 1.30715 | 0.653575 | − | 0.756862i | \(-0.273268\pi\) | ||||
0.653575 | + | 0.756862i | \(0.273268\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.59930 | 0.818542 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.41952 | 1.15078 | 0.575389 | − | 0.817880i | \(-0.304851\pi\) | ||||
0.575389 | + | 0.817880i | \(0.304851\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.46617 | 1.00475 | 0.502375 | − | 0.864650i | \(-0.332460\pi\) | ||||
0.502375 | + | 0.864650i | \(0.332460\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.82340 | − | 11.8185i | 0.798619 | − | 1.38325i | −0.121897 | − | 0.992543i | \(-0.538898\pi\) |
0.920516 | − | 0.390705i | \(-0.127769\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.25582 | + | 0.499480i | 0.371035 | + | 0.0569211i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.53340 | 0.622556 | 0.311278 | − | 0.950319i | \(-0.399243\pi\) | ||||
0.311278 | + | 0.950319i | \(0.399243\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.03669 | + | 13.9199i | −0.882141 | + | 1.52791i | −0.0331848 | + | 0.999449i | \(0.510565\pi\) |
−0.848956 | + | 0.528463i | \(0.822768\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.73833 | − | 4.74293i | −0.297014 | − | 0.514444i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.03776 | + | 10.4577i | 0.640001 | + | 1.10851i | 0.985432 | + | 0.170070i | \(0.0543993\pi\) |
−0.345431 | + | 0.938444i | \(0.612267\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.2535 | − | 1.57300i | −1.07486 | − | 0.164895i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.95097 | −0.815753 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.86046 | + | 10.1506i | −0.595040 | + | 1.03064i | 0.398501 | + | 0.917168i | \(0.369530\pi\) |
−0.993541 | + | 0.113472i | \(0.963803\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.70302 | + | 4.68177i | 0.268961 | + | 0.465854i | 0.968594 | − | 0.248649i | \(-0.0799865\pi\) |
−0.699633 | + | 0.714502i | \(0.746653\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.31018 | − | 12.6616i | 0.720294 | − | 1.24759i | −0.240588 | − | 0.970627i | \(-0.577340\pi\) |
0.960882 | − | 0.276958i | \(-0.0893263\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.40209 | − | 5.89259i | −0.328892 | − | 0.569658i | 0.653400 | − | 0.757013i | \(-0.273342\pi\) |
−0.982292 | + | 0.187354i | \(0.940009\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.37636 | − | 14.5083i | 0.802310 | − | 1.38964i | −0.115783 | − | 0.993275i | \(-0.536938\pi\) |
0.918092 | − | 0.396367i | \(-0.129729\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.77154 | − | 11.7287i | −0.637013 | − | 1.10334i | −0.986085 | − | 0.166243i | \(-0.946836\pi\) |
0.349072 | − | 0.937096i | \(-0.386497\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.335062 | − | 0.580344i | −0.0312447 | − | 0.0541174i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.12409 | + | 8.02191i | 0.286385 | + | 0.735367i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.72501 | − | 8.18396i | 0.429547 | − | 0.743996i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0632 | 1.07896 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.5904 | −0.939748 | −0.469874 | − | 0.882734i | \(-0.655701\pi\) | ||||
−0.469874 | + | 0.882734i | \(0.655701\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.1819 | − | 19.3676i | 0.976968 | − | 1.69216i | 0.303685 | − | 0.952772i | \(-0.401783\pi\) |
0.673282 | − | 0.739385i | \(-0.264884\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.3536 | + | 1.89519i | 1.07119 | + | 0.164333i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.97700 | + | 15.5486i | 0.766957 | + | 1.32841i | 0.939206 | + | 0.343354i | \(0.111563\pi\) |
−0.172249 | + | 0.985053i | \(0.555104\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.570825 | − | 0.988699i | −0.0484168 | − | 0.0838603i | 0.840801 | − | 0.541344i | \(-0.182084\pi\) |
−0.889218 | + | 0.457483i | \(0.848751\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.44065 | − | 4.22733i | 0.204098 | − | 0.353507i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.38434 | − | 9.32596i | −0.447145 | − | 0.774479i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.82916 | − | 15.2925i | 0.723313 | − | 1.25281i | −0.236352 | − | 0.971667i | \(-0.575952\pi\) |
0.959665 | − | 0.281147i | \(-0.0907148\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.61769 | − | 13.1942i | −0.619919 | − | 1.07373i | −0.989500 | − | 0.144532i | \(-0.953832\pi\) |
0.369581 | − | 0.929198i | \(-0.379501\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.486741 | − | 0.843060i | 0.0390960 | − | 0.0677162i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.6288 | −1.08769 | −0.543847 | − | 0.839184i | \(-0.683033\pi\) | ||||
−0.543847 | + | 0.839184i | \(0.683033\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.382263 | + | 0.981559i | 0.0301265 | + | 0.0773577i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.04726 | + | 7.01005i | 0.317006 | + | 0.549070i | 0.979862 | − | 0.199677i | \(-0.0639893\pi\) |
−0.662856 | + | 0.748747i | \(0.730656\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.07739 | − | 3.59814i | −0.160753 | − | 0.278433i | 0.774386 | − | 0.632714i | \(-0.218059\pi\) |
−0.935139 | + | 0.354281i | \(0.884726\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.18629 | + | 2.05471i | −0.0912529 | + | 0.158055i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.8346 | −1.05183 | −0.525913 | − | 0.850539i | \(-0.676276\pi\) | ||||
−0.525913 | + | 0.850539i | \(0.676276\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.66701 | − | 0.869385i | −0.428386 | − | 0.0657193i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.71167 | + | 8.16084i | −0.352166 | + | 0.609970i | −0.986629 | − | 0.162984i | \(-0.947888\pi\) |
0.634462 | + | 0.772954i | \(0.281222\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.32133 | 0.0982136 | 0.0491068 | − | 0.998794i | \(-0.484363\pi\) | ||||
0.0491068 | + | 0.998794i | \(0.484363\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.16128 | 0.673551 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.05093 | −0.296233 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.2854 | 1.17837 | 0.589186 | − | 0.807997i | \(-0.299449\pi\) | ||||
0.589186 | + | 0.807997i | \(0.299449\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.56155 | 0.184384 | 0.0921921 | − | 0.995741i | \(-0.470613\pi\) | ||||
0.0921921 | + | 0.995741i | \(0.470613\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.6916 | −1.54546 | −0.772730 | − | 0.634735i | \(-0.781109\pi\) | ||||
−0.772730 | + | 0.634735i | \(0.781109\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.59684 | − | 9.69402i | 0.396750 | − | 0.687191i | −0.596573 | − | 0.802559i | \(-0.703471\pi\) |
0.993323 | + | 0.115368i | \(0.0368047\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.14285 | + | 15.7734i | 0.431143 | + | 1.10707i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.1458 | −0.987985 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.94055 | + | 5.09318i | −0.203402 | + | 0.352303i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.1807 | + | 24.5616i | 0.976237 | + | 1.69089i | 0.675793 | + | 0.737092i | \(0.263801\pi\) |
0.300444 | + | 0.953799i | \(0.402865\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.14560 | + | 7.18039i | 0.282728 | + | 0.489699i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.957211 | + | 1.19386i | −0.0649797 | + | 0.0810446i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.7575 | 0.858162 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.6962 | − | 21.9905i | 0.850202 | − | 1.47259i | −0.0308242 | − | 0.999525i | \(-0.509813\pi\) |
0.881026 | − | 0.473068i | \(-0.156853\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.31430 | − | 4.00849i | −0.153606 | − | 0.266053i | 0.778945 | − | 0.627092i | \(-0.215755\pi\) |
−0.932550 | + | 0.361040i | \(0.882422\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.16296 | + | 2.01431i | −0.0768506 | + | 0.133109i | −0.901890 | − | 0.431967i | \(-0.857820\pi\) |
0.825039 | + | 0.565076i | \(0.191153\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.37989 | + | 11.0503i | 0.417960 | + | 0.723929i | 0.995734 | − | 0.0922683i | \(-0.0294117\pi\) |
−0.577774 | + | 0.816197i | \(0.696078\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.357830 | + | 0.619780i | −0.0233423 | + | 0.0404300i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.0492 | − | 19.1378i | −0.714714 | − | 1.23792i | −0.963070 | − | 0.269252i | \(-0.913223\pi\) |
0.248355 | − | 0.968669i | \(-0.420110\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0088 | − | 17.3358i | −0.644726 | − | 1.11670i | −0.984365 | − | 0.176142i | \(-0.943638\pi\) |
0.339639 | − | 0.940556i | \(-0.389695\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.2403 | − | 3.53190i | −0.718114 | − | 0.225645i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.26060 | − | 16.0398i | 0.589238 | − | 1.02059i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.12390 | −0.134059 | −0.0670297 | − | 0.997751i | \(-0.521352\pi\) | ||||
−0.0670297 | + | 0.997751i | \(0.521352\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.495671 | −0.0311625 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.38150 | + | 11.0531i | −0.398067 | + | 0.689472i | −0.993487 | − | 0.113942i | \(-0.963652\pi\) |
0.595420 | + | 0.803414i | \(0.296986\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.2341 | − | 2.18367i | −0.884463 | − | 0.135687i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.53432 | + | 9.58572i | 0.341261 | + | 0.591081i | 0.984667 | − | 0.174444i | \(-0.0558127\pi\) |
−0.643406 | + | 0.765525i | \(0.722479\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.784881 | − | 1.35945i | −0.0482148 | − | 0.0835105i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.77479 | − | 3.07403i | 0.108211 | − | 0.187427i | −0.806835 | − | 0.590777i | \(-0.798821\pi\) |
0.915046 | + | 0.403351i | \(0.132154\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.687666 | + | 1.19107i | 0.0417727 | + | 0.0723525i | 0.886156 | − | 0.463387i | \(-0.153366\pi\) |
−0.844383 | + | 0.535740i | \(0.820033\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.34893 | − | 2.33641i | 0.0813434 | − | 0.140891i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.5809 | + | 25.2548i | 0.876079 | + | 1.51741i | 0.855609 | + | 0.517622i | \(0.173183\pi\) |
0.0204692 | + | 0.999790i | \(0.493484\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.29603 | + | 10.9050i | −0.375590 | + | 0.650540i | −0.990415 | − | 0.138123i | \(-0.955893\pi\) |
0.614826 | + | 0.788663i | \(0.289226\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.46056 | 0.562372 | 0.281186 | − | 0.959653i | \(-0.409272\pi\) | ||||
0.281186 | + | 0.959653i | \(0.409272\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.9786 | + | 3.37178i | 1.29736 | + | 0.199030i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.20636 | + | 5.55358i | 0.188609 | + | 0.326681i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.32726 | + | 14.4232i | 0.486484 | + | 0.842614i | 0.999879 | − | 0.0155376i | \(-0.00494598\pi\) |
−0.513396 | + | 0.858152i | \(0.671613\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.09200 | − | 8.81960i | 0.296468 | − | 0.513497i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.56100 | 0.0902752 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.72960 | − | 12.1445i | −0.272610 | − | 0.699996i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.59181 | − | 14.8815i | 0.491966 | − | 0.852110i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.55966 | 0.545599 | 0.272799 | − | 0.962071i | \(-0.412051\pi\) | ||||
0.272799 | + | 0.962071i | \(0.412051\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.3702 | 1.49532 | 0.747658 | − | 0.664084i | \(-0.231178\pi\) | ||||
0.747658 | + | 0.664084i | \(0.231178\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.7018 | −0.717949 | −0.358975 | − | 0.933347i | \(-0.616874\pi\) | ||||
−0.358975 | + | 0.933347i | \(0.616874\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.0331536 | −0.00186209 | −0.000931047 | − | 1.00000i | \(-0.500296\pi\) | ||||
−0.000931047 | 1.00000i | \(0.500296\pi\) | ||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.96528 | −0.445970 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.3705 | −0.855238 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.24815 | + | 7.35801i | −0.235645 | + | 0.408149i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.703699 | − | 0.877674i | 0.0387962 | − | 0.0483877i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.85388 | 0.266793 | 0.133397 | − | 0.991063i | \(-0.457412\pi\) | ||||
0.133397 | + | 0.991063i | \(0.457412\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.92726 | − | 13.7304i | 0.433112 | − | 0.750173i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.32200 | − | 7.48592i | −0.235434 | − | 0.407784i | 0.723965 | − | 0.689837i | \(-0.242318\pi\) |
−0.959399 | + | 0.282053i | \(0.908985\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.360028 | − | 0.623586i | −0.0194966 | − | 0.0337691i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.6224 | + | 8.16680i | 0.897524 | + | 0.440966i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.2232 | −1.24669 | −0.623344 | − | 0.781948i | \(-0.714226\pi\) | ||||
−0.623344 | + | 0.781948i | \(0.714226\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.76025 | + | 6.51295i | −0.201282 | + | 0.348630i | −0.948942 | − | 0.315452i | \(-0.897844\pi\) |
0.747660 | + | 0.664082i | \(0.231177\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.459528 | − | 0.795925i | −0.0244582 | − | 0.0423628i | 0.853537 | − | 0.521032i | \(-0.174453\pi\) |
−0.877995 | + | 0.478669i | \(0.841119\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.12495 | − | 12.3408i | 0.378153 | − | 0.654980i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.24300 | + | 14.2773i | 0.435049 | + | 0.753527i | 0.997300 | − | 0.0734398i | \(-0.0233977\pi\) |
−0.562251 | + | 0.826967i | \(0.690064\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.65737 | + | 2.87066i | −0.0872302 | + | 0.151087i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.4848 | − | 19.8923i | −0.601144 | − | 1.04121i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.33921 | − | 10.9798i | −0.330904 | − | 0.573143i | 0.651785 | − | 0.758404i | \(-0.274020\pi\) |
−0.982689 | + | 0.185261i | \(0.940687\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.895448 | + | 2.29930i | 0.0464894 | + | 0.119373i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.3410 | + | 19.6433i | −0.587217 | + | 1.01709i | 0.407378 | + | 0.913259i | \(0.366443\pi\) |
−0.994595 | + | 0.103830i | \(0.966890\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 25.0849 | 1.29194 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.0925 | −0.980717 | −0.490358 | − | 0.871521i | \(-0.663134\pi\) | ||||
−0.490358 | + | 0.871521i | \(0.663134\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.03963 | − | 5.26479i | 0.155318 | − | 0.269018i | −0.777857 | − | 0.628441i | \(-0.783693\pi\) |
0.933175 | + | 0.359423i | \(0.117027\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.46809 | − | 4.32551i | 0.176750 | − | 0.220448i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.315781 | − | 0.546948i | −0.0160107 | − | 0.0277314i | 0.857909 | − | 0.513802i | \(-0.171763\pi\) |
−0.873920 | + | 0.486070i | \(0.838430\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.647728 | − | 1.12190i | −0.0327570 | − | 0.0567368i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.65679 | − | 8.06579i | 0.234308 | − | 0.405834i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.1830 | − | 31.4939i | −0.912578 | − | 1.58063i | −0.810408 | − | 0.585865i | \(-0.800755\pi\) |
−0.102170 | − | 0.994767i | \(-0.532579\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.8069 | + | 27.3783i | −0.789357 | + | 1.36721i | 0.137004 | + | 0.990571i | \(0.456253\pi\) |
−0.926361 | + | 0.376636i | \(0.877081\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.13383 | + | 1.96385i | 0.0564800 | + | 0.0978262i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.38816 | − | 5.86847i | 0.167945 | − | 0.290889i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.1812 | 0.997896 | 0.498948 | − | 0.866632i | \(-0.333720\pi\) | ||||
0.498948 | + | 0.866632i | \(0.333720\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.0138 | + | 12.4895i | −0.492746 | + | 0.614567i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.5270 | + | 23.4294i | 0.664014 | + | 1.15011i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.4159 | − | 21.5049i | −0.606555 | − | 1.05058i | −0.991804 | − | 0.127772i | \(-0.959217\pi\) |
0.385248 | − | 0.922813i | \(-0.374116\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.71841 | + | 9.90458i | −0.278698 | + | 0.482720i | −0.971062 | − | 0.238829i | \(-0.923236\pi\) |
0.692363 | + | 0.721549i | \(0.256570\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.05096 | 0.342022 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.8964 | + | 21.0737i | −0.817675 | + | 1.01983i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.80157 | − | 4.85246i | 0.134947 | − | 0.233735i | −0.790630 | − | 0.612294i | \(-0.790247\pi\) |
0.925577 | + | 0.378559i | \(0.123580\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.22555 | −0.203067 | −0.101534 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101534 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.88073 | −0.0899676 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 35.4631 | 1.69256 | 0.846281 | − | 0.532737i | \(-0.178836\pi\) | ||||
0.846281 | + | 0.532737i | \(0.178836\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.9315 | −1.08951 | −0.544755 | − | 0.838595i | \(-0.683377\pi\) | ||||
−0.544755 | + | 0.838595i | \(0.683377\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 20.3250 | 0.963496 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.4850 | −0.966747 | −0.483373 | − | 0.875414i | \(-0.660589\pi\) | ||||
−0.483373 | + | 0.875414i | \(0.660589\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.23161 | + | 9.06141i | −0.246347 | + | 0.426685i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.9220 | + | 13.6222i | −0.512031 | + | 0.638620i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.4535 | 0.722886 | 0.361443 | − | 0.932394i | \(-0.382284\pi\) | ||||
0.361443 | + | 0.932394i | \(0.382284\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.0815 | + | 24.3898i | −0.655839 | + | 1.13595i | 0.325844 | + | 0.945424i | \(0.394352\pi\) |
−0.981683 | + | 0.190523i | \(0.938982\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.3193 | + | 26.5338i | 0.711948 | + | 1.23313i | 0.964125 | + | 0.265449i | \(0.0855202\pi\) |
−0.252177 | + | 0.967681i | \(0.581146\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.61798 | − | 11.4627i | −0.306244 | − | 0.530429i | 0.671294 | − | 0.741191i | \(-0.265739\pi\) |
−0.977537 | + | 0.210762i | \(0.932406\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.5895 | + | 19.4437i | −0.719857 | + | 0.897827i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.13275 | 0.281984 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.11826 | − | 8.86508i | 0.234842 | − | 0.406758i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.04358 | − | 12.1998i | −0.321829 | − | 0.557425i | 0.659036 | − | 0.752111i | \(-0.270964\pi\) |
−0.980866 | + | 0.194687i | \(0.937631\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.6703 | + | 18.4814i | −0.486522 | + | 0.842681i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.86407 | + | 17.0851i | 0.447904 | + | 0.775793i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.45654 | + | 5.98690i | −0.156631 | + | 0.271292i | −0.933652 | − | 0.358183i | \(-0.883397\pi\) |
0.777021 | + | 0.629475i | \(0.216730\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.3481 | − | 26.5837i | −0.692651 | − | 1.19971i | −0.970966 | − | 0.239217i | \(-0.923109\pi\) |
0.278315 | − | 0.960490i | \(-0.410224\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.4088 | − | 18.0286i | −0.468789 | − | 0.811966i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.0117 | + | 17.4758i | −0.628511 | + | 0.783898i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.0186 | + | 19.0847i | −0.493259 | + | 0.854350i | −0.999970 | − | 0.00776631i | \(-0.997528\pi\) |
0.506711 | + | 0.862116i | \(0.330861\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 38.9653 | 1.73737 | 0.868687 | − | 0.495361i | \(-0.164964\pi\) | ||||
0.868687 | + | 0.495361i | \(0.164964\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.09922 | 0.404910 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.1471 | + | 24.5034i | −0.627058 | + | 1.08610i | 0.361082 | + | 0.932534i | \(0.382408\pi\) |
−0.988139 | + | 0.153561i | \(0.950926\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.1027 | + | 33.6447i | 0.579631 | + | 1.48835i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.3042 | − | 21.3115i | −0.542187 | − | 0.939095i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.264676 | + | 0.458433i | 0.0116405 | + | 0.0201619i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.98150 | − | 10.3603i | 0.262054 | − | 0.453892i | −0.704733 | − | 0.709472i | \(-0.748933\pi\) |
0.966788 | + | 0.255581i | \(0.0822667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.15056 | + | 5.45693i | 0.137764 | + | 0.238615i | 0.926650 | − | 0.375925i | \(-0.122675\pi\) |
−0.788886 | + | 0.614540i | \(0.789342\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.940948 | − | 1.62977i | 0.0409884 | − | 0.0709939i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4207 | + | 19.7813i | 0.496554 | + | 0.860057i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.4758 | − | 28.5369i | 0.713645 | − | 1.23607i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.4525 | −0.495135 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.41948 | + | 5.89399i | −0.276507 | + | 0.253872i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.88191 | + | 17.1160i | 0.424857 | + | 0.735873i | 0.996407 | − | 0.0846937i | \(-0.0269912\pi\) |
−0.571550 | + | 0.820567i | \(0.693658\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.0987 | − | 24.4197i | −0.603923 | − | 1.04602i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.6125 | + | 37.4340i | −0.924085 | + | 1.60056i | −0.131059 | + | 0.991375i | \(0.541838\pi\) |
−0.793026 | + | 0.609188i | \(0.791496\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −30.2228 | −1.28753 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.15791 | + | 11.4220i | −0.389434 | + | 0.485713i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.0838 | − | 24.3938i | 0.596748 | − | 1.03360i | −0.396550 | − | 0.918013i | \(-0.629793\pi\) |
0.993298 | − | 0.115584i | \(-0.0368740\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.3137 | −0.816884 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.6944 | 1.08289 | 0.541445 | − | 0.840736i | \(-0.317878\pi\) | ||||
0.541445 | + | 0.840736i | \(0.317878\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.7951 | −0.958998 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −35.4881 | −1.48774 | −0.743870 | − | 0.668324i | \(-0.767012\pi\) | ||||
−0.743870 | + | 0.668324i | \(0.767012\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.6824 | −0.907378 | −0.453689 | − | 0.891160i | \(-0.649892\pi\) | ||||
−0.453689 | + | 0.891160i | \(0.649892\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.862754 | 0.0359793 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.60727 | + | 13.1762i | −0.316695 | + | 0.548531i | −0.979796 | − | 0.199998i | \(-0.935906\pi\) |
0.663102 | + | 0.748529i | \(0.269240\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.4326 | − | 39.6271i | −0.640251 | − | 1.64401i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.16111 | −0.0480881 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.1924 | + | 33.2423i | −0.792157 | + | 1.37206i | 0.132472 | + | 0.991187i | \(0.457708\pi\) |
−0.924629 | + | 0.380869i | \(0.875625\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.36606 | − | 2.36608i | −0.0562875 | − | 0.0974928i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.25559 | + | 16.0311i | 0.380081 | + | 0.658320i | 0.991074 | − | 0.133316i | \(-0.0425626\pi\) |
−0.610992 | + | 0.791637i | \(0.709229\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.3223 | + | 2.19721i | 0.587159 | + | 0.0900770i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.6825 | −0.885924 | −0.442962 | − | 0.896540i | \(-0.646072\pi\) | ||||
−0.442962 | + | 0.896540i | \(0.646072\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.95776 | − | 6.85505i | 0.161441 | − | 0.279623i | −0.773945 | − | 0.633253i | \(-0.781719\pi\) |
0.935386 | + | 0.353630i | \(0.115053\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.95293 | − | 13.7749i | −0.323333 | − | 0.560029i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.9623 | − | 31.1117i | 0.729068 | − | 1.26278i | −0.228209 | − | 0.973612i | \(-0.573287\pi\) |
0.957277 | − | 0.289171i | \(-0.0933797\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.833539 | − | 1.44373i | −0.0337214 | − | 0.0584072i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.60252 | + | 2.77565i | −0.0647253 | + | 0.112108i | −0.896572 | − | 0.442898i | \(-0.853950\pi\) |
0.831847 | + | 0.555005i | \(0.187284\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.9357 | − | 27.6015i | −0.641549 | − | 1.11120i | −0.985087 | − | 0.172056i | \(-0.944959\pi\) |
0.343538 | − | 0.939139i | \(-0.388374\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.4863 | − | 18.1628i | −0.421480 | − | 0.730024i | 0.574605 | − | 0.818431i | \(-0.305156\pi\) |
−0.996084 | + | 0.0884070i | \(0.971822\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −31.5793 | − | 4.84464i | −1.26520 | − | 0.194096i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.73462 | − | 8.20060i | 0.189385 | − | 0.328024i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 17.7102 | 0.706153 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.4435 | −1.05270 | −0.526349 | − | 0.850268i | \(-0.676440\pi\) | ||||
−0.526349 | + | 0.850268i | \(0.676440\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.91266 | + | 15.4372i | −0.353688 | + | 0.612606i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.2167 | − | 18.5618i | 0.801016 | − | 0.735445i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.9809 | − | 24.2157i | −0.552213 | − | 0.956461i | −0.998115 | − | 0.0613792i | \(-0.980450\pi\) |
0.445901 | − | 0.895082i | \(-0.352883\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.12936 | + | 10.6164i | 0.241718 | + | 0.418669i | 0.961204 | − | 0.275839i | \(-0.0889556\pi\) |
−0.719485 | + | 0.694508i | \(0.755622\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.49923 | − | 7.79290i | 0.176883 | − | 0.306371i | −0.763928 | − | 0.645301i | \(-0.776732\pi\) |
0.940811 | + | 0.338931i | \(0.110065\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.76640 | − | 6.52360i | −0.147844 | − | 0.256074i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.3950 | + | 19.7368i | −0.445922 | + | 0.772359i | −0.998116 | − | 0.0613562i | \(-0.980457\pi\) |
0.552194 | + | 0.833716i | \(0.313791\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.8209 | − | 32.5987i | −0.735393 | − | 1.27374i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.3311 | + | 33.4824i | −0.753033 | + | 1.30429i | 0.193314 | + | 0.981137i | \(0.438076\pi\) |
−0.946347 | + | 0.323154i | \(0.895257\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.5080 | −0.447609 | −0.223804 | − | 0.974634i | \(-0.571848\pi\) | ||||
−0.223804 | + | 0.974634i | \(0.571848\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.1590 | − | 16.4124i | 0.510286 | − | 0.636444i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.27362 | − | 2.20597i | −0.0493147 | − | 0.0854156i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.35511 | − | 11.0074i | −0.245336 | − | 0.424935i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.6642 | + | 18.4709i | −0.411075 | + | 0.712002i | −0.995008 | − | 0.0997997i | \(-0.968180\pi\) |
0.583933 | + | 0.811802i | \(0.301513\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27.7599 | −1.06690 | −0.533449 | − | 0.845832i | \(-0.679104\pi\) | ||||
−0.533449 | + | 0.845832i | \(0.679104\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.2536 | − | 28.8966i | −0.431875 | − | 1.10895i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.66854 | + | 15.0143i | −0.331692 | + | 0.574508i | −0.982844 | − | 0.184440i | \(-0.940953\pi\) |
0.651151 | + | 0.758948i | \(0.274286\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 30.2194 | 1.15462 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.65664 | 0.139307 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.6046 | −1.50663 | −0.753315 | − | 0.657660i | \(-0.771547\pi\) | ||||
−0.753315 | + | 0.657660i | \(0.771547\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.92158 | −0.0728895 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −27.3461 | −1.03581 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.28469 | −0.275139 | −0.137570 | − | 0.990492i | \(-0.543929\pi\) | ||||
−0.137570 | + | 0.990492i | \(0.543929\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.8558 | − | 22.2668i | 0.484864 | − | 0.839809i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.1377 | − | 2.16888i | −0.531701 | − | 0.0815691i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.0108 | 0.451075 | 0.225538 | − | 0.974234i | \(-0.427586\pi\) | ||||
0.225538 | + | 0.974234i | \(0.427586\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.115134 | − | 0.199418i | 0.00431181 | − | 0.00746827i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.10800 | − | 7.11526i | −0.153630 | − | 0.266096i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.15819 | − | 3.73809i | −0.0804868 | − | 0.139407i | 0.822972 | − | 0.568081i | \(-0.192314\pi\) |
−0.903459 | + | 0.428674i | \(0.858981\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.0375 | + | 36.0449i | 0.522783 | + | 1.34238i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.8642 | 0.514903 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.2483 | + | 17.7506i | −0.380090 | + | 0.658334i | −0.991075 | − | 0.133308i | \(-0.957440\pi\) |
0.610985 | + | 0.791642i | \(0.290774\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.01411 | + | 13.8808i | 0.296413 | + | 0.513402i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.6661 | + | 21.9383i | −0.467833 | + | 0.810310i | −0.999324 | − | 0.0367533i | \(-0.988298\pi\) |
0.531491 | + | 0.847064i | \(0.321632\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.86356 | − | 10.1560i | −0.215987 | − | 0.374100i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.63391 | − | 11.4903i | 0.244032 | − | 0.422676i | −0.717827 | − | 0.696222i | \(-0.754863\pi\) |
0.961859 | + | 0.273545i | \(0.0881964\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.6116 | + | 39.1644i | 0.829538 | + | 1.43680i | 0.898401 | + | 0.439176i | \(0.144730\pi\) |
−0.0688624 | + | 0.997626i | \(0.521937\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.8608 | − | 25.7397i | −0.544459 | − | 0.943031i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.7940 | + | 2.72981i | 0.650178 | + | 0.0997449i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.1898 | + | 24.5775i | −0.517795 | + | 0.896847i | 0.481992 | + | 0.876176i | \(0.339914\pi\) |
−0.999786 | + | 0.0206709i | \(0.993420\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −25.6435 | −0.933263 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.08483 | 0.184811 | 0.0924056 | − | 0.995721i | \(-0.470544\pi\) | ||||
0.0924056 | + | 0.995721i | \(0.470544\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.8612 | − | 32.6686i | 0.683720 | − | 1.18424i | −0.290118 | − | 0.956991i | \(-0.593694\pi\) |
0.973837 | − | 0.227246i | \(-0.0729722\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.0848 | + | 41.3020i | 0.582310 | + | 1.49523i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.8614 | + | 20.5446i | 0.428292 | + | 0.741823i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.8729 | + | 20.5644i | 0.428147 | + | 0.741572i | 0.996709 | − | 0.0810688i | \(-0.0258333\pi\) |
−0.568562 | + | 0.822641i | \(0.692500\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.5347 | + | 33.8351i | −0.702614 | + | 1.21696i | 0.264932 | + | 0.964267i | \(0.414650\pi\) |
−0.967546 | + | 0.252696i | \(0.918683\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.626657 | + | 1.08540i | 0.0225102 | + | 0.0389888i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −19.8504 | + | 34.3819i | −0.711214 | + | 1.23186i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.27011 | − | 9.12810i | −0.188579 | − | 0.326629i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.4697 | + | 19.8661i | −0.409370 | + | 0.709050i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.80915 | −0.135782 | −0.0678908 | − | 0.997693i | \(-0.521627\pi\) | ||||
−0.0678908 | + | 0.997693i | \(0.521627\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 35.4173 | + | 5.43342i | 1.25929 | + | 0.193190i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.0140 | + | 34.6653i | 0.710718 | + | 1.23100i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.8239 | + | 18.7476i | 0.383404 | + | 0.664075i | 0.991546 | − | 0.129753i | \(-0.0414184\pi\) |
−0.608143 | + | 0.793828i | \(0.708085\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.691743 | + | 1.19813i | −0.0244721 | + | 0.0423870i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.9900 | −0.599564 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.75248 | + | 0.268851i | 0.0617667 | + | 0.00947574i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.5128 | − | 32.0652i | 0.650877 | − | 1.12735i | −0.332034 | − | 0.943268i | \(-0.607735\pi\) |
0.982910 | − | 0.184084i | \(-0.0589319\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.37416 | −0.188712 | −0.0943561 | − | 0.995539i | \(-0.530079\pi\) | ||||
−0.0943561 | + | 0.995539i | \(0.530079\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.6243 | 0.477239 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.2696 | 0.814101 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.22239 | −0.0775619 | −0.0387809 | − | 0.999248i | \(-0.512347\pi\) | ||||
−0.0387809 | + | 0.999248i | \(0.512347\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.1073 | −1.29348 | −0.646740 | − | 0.762710i | \(-0.723868\pi\) | ||||
−0.646740 | + | 0.762710i | \(0.723868\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.4790 | 0.677351 | 0.338676 | − | 0.940903i | \(-0.390021\pi\) | ||||
0.338676 | + | 0.940903i | \(0.390021\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.137129 | − | 0.237514i | 0.00476267 | − | 0.00824919i | −0.863634 | − | 0.504119i | \(-0.831817\pi\) |
0.868397 | + | 0.495870i | \(0.165151\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21.7292 | − | 6.82772i | −0.752873 | − | 0.236566i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.99314 | −0.242007 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.0711 | − | 36.4962i | 0.727455 | − | 1.25999i | −0.230501 | − | 0.973072i | \(-0.574036\pi\) |
0.957956 | − | 0.286917i | \(-0.0926303\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.96666 | − | 10.3346i | −0.205747 | − | 0.356364i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.99671 | + | 3.45840i | 0.0686888 | + | 0.118973i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.07328 | + | 23.2980i | 0.311762 | + | 0.800528i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.16702 | 0.0742844 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.3086 | − | 38.6397i | 0.763833 | − | 1.32300i | −0.177029 | − | 0.984206i | \(-0.556649\pi\) |
0.940862 | − | 0.338791i | \(-0.110018\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.66614 | − | 6.34993i | −0.125233 | − | 0.216910i | 0.796591 | − | 0.604518i | \(-0.206634\pi\) |
−0.921824 | + | 0.387609i | \(0.873301\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.35073 | + | 2.33953i | −0.0460863 | + | 0.0798238i | −0.888148 | − | 0.459557i | \(-0.848008\pi\) |
0.842062 | + | 0.539381i | \(0.181342\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.40188 | + | 12.8204i | 0.251963 | + | 0.436413i | 0.964066 | − | 0.265662i | \(-0.0855905\pi\) |
−0.712103 | + | 0.702075i | \(0.752257\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.6429 | + | 20.1661i | −0.395870 | + | 0.685668i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.44449 | − | 5.96603i | −0.116846 | − | 0.202384i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.4660 | + | 31.9840i | 0.625695 | + | 1.08374i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −19.9648 | + | 24.9007i | −0.674934 | + | 0.841797i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.54807 | − | 9.60954i | 0.187345 | − | 0.324491i | −0.757019 | − | 0.653393i | \(-0.773345\pi\) |
0.944364 | + | 0.328902i | \(0.106678\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.0536 | −0.507168 | −0.253584 | − | 0.967313i | \(-0.581609\pi\) | ||||
−0.253584 | + | 0.967313i | \(0.581609\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.39418 | −0.0805704 | −0.0402852 | − | 0.999188i | \(-0.512827\pi\) | ||||
−0.0402852 | + | 0.999188i | \(0.512827\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.46697 | − | 4.27292i | 0.0828328 | − | 0.143471i | −0.821633 | − | 0.570017i | \(-0.806937\pi\) |
0.904466 | + | 0.426546i | \(0.140270\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.5274 | − | 21.8607i | 0.587850 | − | 0.733184i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.00427 | + | 1.73944i | 0.0336065 | + | 0.0582081i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.93047 | + | 13.7360i | 0.265086 | + | 0.459143i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.85017 | − | 3.20459i | 0.0617067 | − | 0.106879i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.51730 | − | 2.62804i | −0.0505486 | − | 0.0875527i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.11200 | − | 1.92604i | 0.0369642 | − | 0.0640238i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.69815 | − | 2.94129i | −0.0563863 | − | 0.0976639i | 0.836454 | − | 0.548036i | \(-0.184624\pi\) |
−0.892841 | + | 0.450373i | \(0.851291\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.65142 | − | 8.05649i | 0.154108 | − | 0.266924i | −0.778626 | − | 0.627489i | \(-0.784083\pi\) |
0.932734 | + | 0.360565i | \(0.117416\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.0110 | 0.662268 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.4722 | + | 55.1355i | 0.709076 | + | 1.82073i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.92656 | − | 15.4613i | −0.294460 | − | 0.510020i | 0.680399 | − | 0.732842i | \(-0.261806\pi\) |
−0.974859 | + | 0.222822i | \(0.928473\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.5970 | + | 28.7469i | 0.546298 | + | 0.946216i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.89737 | + | 10.2145i | −0.193904 | + | 0.335852i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 47.2861 | 1.55141 | 0.775703 | − | 0.631098i | \(-0.217395\pi\) | ||||
0.775703 | + | 0.631098i | \(0.217395\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.3575 | + | 22.3637i | −0.798286 | + | 0.732939i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.40917 | + | 5.90486i | −0.111492 | + | 0.193110i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.2493 | 0.694183 | 0.347092 | − | 0.937831i | \(-0.387169\pi\) | ||||
0.347092 | + | 0.937831i | \(0.387169\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 60.0810 | 1.95858 | 0.979292 | − | 0.202455i | \(-0.0648920\pi\) | ||||
0.979292 | + | 0.202455i | \(0.0648920\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.34606 | −0.108963 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.66935 | 0.119238 | 0.0596189 | − | 0.998221i | \(-0.481011\pi\) | ||||
0.0596189 | + | 0.998221i | \(0.481011\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 53.5062 | 1.73688 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.837421 | −0.0271267 | −0.0135634 | − | 0.999908i | \(-0.504317\pi\) | ||||
−0.0135634 | + | 0.999908i | \(0.504317\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.7055 | − | 23.7385i | 0.443498 | − | 0.768161i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −46.9525 | − | 7.20306i | −1.51618 | − | 0.232599i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6655 | −0.989209 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.15574 | − | 3.73386i | 0.0693958 | − | 0.120197i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.8856 | − | 37.9070i | −0.703795 | − | 1.21901i | −0.967125 | − | 0.254302i | \(-0.918154\pi\) |
0.263330 | − | 0.964706i | \(-0.415179\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.3059 | − | 35.1709i | −0.651648 | − | 1.12869i | −0.982723 | − | 0.185083i | \(-0.940745\pi\) |
0.331075 | − | 0.943605i | \(-0.392589\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.98560 | + | 0.458025i | 0.0957138 | + | 0.0146836i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −57.4959 | −1.83946 | −0.919728 | − | 0.392556i | \(-0.871591\pi\) | ||||
−0.919728 | + | 0.392556i | \(0.871591\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.51689 | − | 13.0196i | 0.240241 | − | 0.416109i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.72971 | + | 11.6562i | 0.214644 | + | 0.371775i | 0.953162 | − | 0.302459i | \(-0.0978075\pi\) |
−0.738518 | + | 0.674234i | \(0.764474\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.2551 | + | 31.6188i | −0.581657 | + | 1.00746i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.980604 | + | 1.69846i | 0.0311814 | + | 0.0540078i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.7821 | − | 30.7995i | 0.564867 | − | 0.978379i | −0.432195 | − | 0.901780i | \(-0.642261\pi\) |
0.997062 | − | 0.0765983i | \(-0.0244059\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.42036 | − | 16.3165i | −0.298645 | − | 0.517269i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.3644 | − | 28.3440i | −0.518267 | − | 0.897665i | −0.999775 | − | 0.0212228i | \(-0.993244\pi\) |
0.481508 | − | 0.876442i | \(-0.340089\pi\) | |||||||
\(998\) | 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 | 3024.2.q.k.2881.8 | 22 | ||
3.2 | odd | 2 | 1008.2.q.k.529.11 | 22 | |||
4.3 | odd | 2 | 1512.2.q.c.1369.8 | 22 | |||
7.2 | even | 3 | 3024.2.t.l.289.4 | 22 | |||
9.4 | even | 3 | 3024.2.t.l.1873.4 | 22 | |||
9.5 | odd | 6 | 1008.2.t.k.193.6 | 22 | |||
12.11 | even | 2 | 504.2.q.d.25.1 | ✓ | 22 | ||
21.2 | odd | 6 | 1008.2.t.k.961.6 | 22 | |||
28.23 | odd | 6 | 1512.2.t.d.289.4 | 22 | |||
36.23 | even | 6 | 504.2.t.d.193.6 | yes | 22 | ||
36.31 | odd | 6 | 1512.2.t.d.361.4 | 22 | |||
63.23 | odd | 6 | 1008.2.q.k.625.11 | 22 | |||
63.58 | even | 3 | inner | 3024.2.q.k.2305.8 | 22 | ||
84.23 | even | 6 | 504.2.t.d.457.6 | yes | 22 | ||
252.23 | even | 6 | 504.2.q.d.121.1 | yes | 22 | ||
252.247 | odd | 6 | 1512.2.q.c.793.8 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.d.25.1 | ✓ | 22 | 12.11 | even | 2 | ||
504.2.q.d.121.1 | yes | 22 | 252.23 | even | 6 | ||
504.2.t.d.193.6 | yes | 22 | 36.23 | even | 6 | ||
504.2.t.d.457.6 | yes | 22 | 84.23 | even | 6 | ||
1008.2.q.k.529.11 | 22 | 3.2 | odd | 2 | |||
1008.2.q.k.625.11 | 22 | 63.23 | odd | 6 | |||
1008.2.t.k.193.6 | 22 | 9.5 | odd | 6 | |||
1008.2.t.k.961.6 | 22 | 21.2 | odd | 6 | |||
1512.2.q.c.793.8 | 22 | 252.247 | odd | 6 | |||
1512.2.q.c.1369.8 | 22 | 4.3 | odd | 2 | |||
1512.2.t.d.289.4 | 22 | 28.23 | odd | 6 | |||
1512.2.t.d.361.4 | 22 | 36.31 | odd | 6 | |||
3024.2.q.k.2305.8 | 22 | 63.58 | even | 3 | inner | ||
3024.2.q.k.2881.8 | 22 | 1.1 | even | 1 | trivial | ||
3024.2.t.l.289.4 | 22 | 7.2 | even | 3 | |||
3024.2.t.l.1873.4 | 22 | 9.4 | even | 3 |