Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,2,Mod(151,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.e (of order \(3\), degree \(2\), 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: | \(3.59326809096\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 301.1 | ||
Root | \(-1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.301 |
Dual form | 450.2.e.l.151.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 1.00000 | − | 1.41421i | 0.577350 | − | 0.816497i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.72474 | − | 0.158919i | −0.704124 | − | 0.0648783i | ||||
\(7\) | 2.22474 | + | 3.85337i | 0.840875 | + | 1.45644i | 0.889156 | + | 0.457604i | \(0.151292\pi\) |
−0.0482818 | + | 0.998834i | \(0.515375\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.00000 | − | 2.82843i | −0.333333 | − | 0.942809i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.44949 | − | 4.24264i | −0.738549 | − | 1.27920i | −0.953149 | − | 0.302502i | \(-0.902178\pi\) |
0.214600 | − | 0.976702i | \(-0.431155\pi\) | |||||||
\(12\) | 0.724745 | + | 1.57313i | 0.209216 | + | 0.454124i | ||||
\(13\) | 2.22474 | − | 3.85337i | 0.617033 | − | 1.06873i | −0.372991 | − | 0.927835i | \(-0.621668\pi\) |
0.990024 | − | 0.140898i | \(-0.0449989\pi\) | |||||||
\(14\) | 2.22474 | − | 3.85337i | 0.594588 | − | 1.02986i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 4.89898 | 1.18818 | 0.594089 | − | 0.804400i | \(-0.297513\pi\) | ||||
0.594089 | + | 0.804400i | \(0.297513\pi\) | |||||||
\(18\) | −1.94949 | + | 2.28024i | −0.459499 | + | 0.537457i | ||||
\(19\) | 2.55051 | 0.585127 | 0.292564 | − | 0.956246i | \(-0.405492\pi\) | ||||
0.292564 | + | 0.956246i | \(0.405492\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.67423 | + | 0.707107i | 1.67466 | + | 0.154303i | ||||
\(22\) | −2.44949 | + | 4.24264i | −0.522233 | + | 0.904534i | ||||
\(23\) | 1.22474 | − | 2.12132i | 0.255377 | − | 0.442326i | −0.709621 | − | 0.704584i | \(-0.751134\pi\) |
0.964998 | + | 0.262258i | \(0.0844671\pi\) | |||||||
\(24\) | 1.00000 | − | 1.41421i | 0.204124 | − | 0.288675i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.44949 | −0.872617 | ||||||||
\(27\) | −5.00000 | − | 1.41421i | −0.962250 | − | 0.272166i | ||||
\(28\) | −4.44949 | −0.840875 | ||||||||
\(29\) | −1.22474 | − | 2.12132i | −0.227429 | − | 0.393919i | 0.729616 | − | 0.683857i | \(-0.239699\pi\) |
−0.957046 | + | 0.289938i | \(0.906365\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.224745 | − | 0.389270i | 0.0403654 | − | 0.0699149i | −0.845137 | − | 0.534550i | \(-0.820481\pi\) |
0.885502 | + | 0.464635i | \(0.153814\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −8.44949 | − | 0.778539i | −1.47087 | − | 0.135526i | ||||
\(34\) | −2.44949 | − | 4.24264i | −0.420084 | − | 0.727607i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.94949 | + | 0.548188i | 0.491582 | + | 0.0913647i | ||||
\(37\) | −3.34847 | −0.550485 | −0.275242 | − | 0.961375i | \(-0.588758\pi\) | ||||
−0.275242 | + | 0.961375i | \(0.588758\pi\) | |||||||
\(38\) | −1.27526 | − | 2.20881i | −0.206874 | − | 0.358316i | ||||
\(39\) | −3.22474 | − | 6.99964i | −0.516372 | − | 1.12084i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.50000 | + | 7.79423i | −0.702782 | + | 1.21725i | 0.264704 | + | 0.964330i | \(0.414726\pi\) |
−0.967486 | + | 0.252924i | \(0.918608\pi\) | |||||||
\(42\) | −3.22474 | − | 6.99964i | −0.497589 | − | 1.08007i | ||||
\(43\) | 3.72474 | + | 6.45145i | 0.568018 | + | 0.983836i | 0.996762 | + | 0.0804103i | \(0.0256230\pi\) |
−0.428744 | + | 0.903426i | \(0.641044\pi\) | |||||||
\(44\) | 4.89898 | 0.738549 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.44949 | −0.361158 | ||||||||
\(47\) | −0.550510 | − | 0.953512i | −0.0803002 | − | 0.139084i | 0.823079 | − | 0.567927i | \(-0.192255\pi\) |
−0.903379 | + | 0.428843i | \(0.858921\pi\) | |||||||
\(48\) | −1.72474 | − | 0.158919i | −0.248945 | − | 0.0229379i | ||||
\(49\) | −6.39898 | + | 11.0834i | −0.914140 | + | 1.58334i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.89898 | − | 6.92820i | 0.685994 | − | 0.970143i | ||||
\(52\) | 2.22474 | + | 3.85337i | 0.308517 | + | 0.534366i | ||||
\(53\) | 8.44949 | 1.16063 | 0.580313 | − | 0.814393i | \(-0.302930\pi\) | ||||
0.580313 | + | 0.814393i | \(0.302930\pi\) | |||||||
\(54\) | 1.27526 | + | 5.03723i | 0.173540 | + | 0.685481i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.22474 | + | 3.85337i | 0.297294 | + | 0.514928i | ||||
\(57\) | 2.55051 | − | 3.60697i | 0.337823 | − | 0.477754i | ||||
\(58\) | −1.22474 | + | 2.12132i | −0.160817 | + | 0.278543i | ||||
\(59\) | 0.275255 | − | 0.476756i | 0.0358352 | − | 0.0620683i | −0.847552 | − | 0.530713i | \(-0.821924\pi\) |
0.883387 | + | 0.468645i | \(0.155258\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00000 | − | 6.92820i | −0.512148 | − | 0.887066i | −0.999901 | − | 0.0140840i | \(-0.995517\pi\) |
0.487753 | − | 0.872982i | \(-0.337817\pi\) | |||||||
\(62\) | −0.449490 | −0.0570853 | ||||||||
\(63\) | 8.67423 | − | 10.1459i | 1.09285 | − | 1.27826i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.55051 | + | 7.70674i | 0.437038 | + | 0.948634i | ||||
\(67\) | −7.17423 | + | 12.4261i | −0.876472 | + | 1.51809i | −0.0212861 | + | 0.999773i | \(0.506776\pi\) |
−0.855186 | + | 0.518321i | \(0.826557\pi\) | |||||||
\(68\) | −2.44949 | + | 4.24264i | −0.297044 | + | 0.514496i | ||||
\(69\) | −1.77526 | − | 3.85337i | −0.213716 | − | 0.463891i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.34847 | −0.160034 | −0.0800169 | − | 0.996794i | \(-0.525497\pi\) | ||||
−0.0800169 | + | 0.996794i | \(0.525497\pi\) | |||||||
\(72\) | −1.00000 | − | 2.82843i | −0.117851 | − | 0.333333i | ||||
\(73\) | 1.00000 | 0.117041 | 0.0585206 | − | 0.998286i | \(-0.481362\pi\) | ||||
0.0585206 | + | 0.998286i | \(0.481362\pi\) | |||||||
\(74\) | 1.67423 | + | 2.89986i | 0.194626 | + | 0.337102i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.27526 | + | 2.20881i | −0.146282 | + | 0.253368i | ||||
\(77\) | 10.8990 | − | 18.8776i | 1.24205 | − | 2.15130i | ||||
\(78\) | −4.44949 | + | 6.29253i | −0.503806 | + | 0.712489i | ||||
\(79\) | 6.34847 | + | 10.9959i | 0.714259 | + | 1.23713i | 0.963245 | + | 0.268625i | \(0.0865693\pi\) |
−0.248986 | + | 0.968507i | \(0.580097\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | + | 5.65685i | −0.777778 | + | 0.628539i | ||||
\(82\) | 9.00000 | 0.993884 | ||||||||
\(83\) | −0.275255 | − | 0.476756i | −0.0302132 | − | 0.0523308i | 0.850523 | − | 0.525937i | \(-0.176285\pi\) |
−0.880737 | + | 0.473606i | \(0.842952\pi\) | |||||||
\(84\) | −4.44949 | + | 6.29253i | −0.485479 | + | 0.686571i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.72474 | − | 6.45145i | 0.401650 | − | 0.695677i | ||||
\(87\) | −4.22474 | − | 0.389270i | −0.452940 | − | 0.0417341i | ||||
\(88\) | −2.44949 | − | 4.24264i | −0.261116 | − | 0.452267i | ||||
\(89\) | −9.00000 | −0.953998 | −0.476999 | − | 0.878904i | \(-0.658275\pi\) | ||||
−0.476999 | + | 0.878904i | \(0.658275\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.7980 | 2.07539 | ||||||||
\(92\) | 1.22474 | + | 2.12132i | 0.127688 | + | 0.221163i | ||||
\(93\) | −0.325765 | − | 0.707107i | −0.0337803 | − | 0.0733236i | ||||
\(94\) | −0.550510 | + | 0.953512i | −0.0567808 | + | 0.0983472i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.724745 | + | 1.57313i | 0.0739690 | + | 0.160557i | ||||
\(97\) | −5.39898 | − | 9.35131i | −0.548183 | − | 0.949481i | −0.998399 | − | 0.0565616i | \(-0.981986\pi\) |
0.450216 | − | 0.892920i | \(-0.351347\pi\) | |||||||
\(98\) | 12.7980 | 1.29279 | ||||||||
\(99\) | −9.55051 | + | 11.1708i | −0.959862 | + | 1.12271i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.77526 | − | 3.07483i | −0.176644 | − | 0.305957i | 0.764085 | − | 0.645116i | \(-0.223191\pi\) |
−0.940729 | + | 0.339159i | \(0.889858\pi\) | |||||||
\(102\) | −8.44949 | − | 0.778539i | −0.836624 | − | 0.0770869i | ||||
\(103\) | −6.34847 | + | 10.9959i | −0.625533 | + | 1.08346i | 0.362904 | + | 0.931826i | \(0.381785\pi\) |
−0.988437 | + | 0.151629i | \(0.951548\pi\) | |||||||
\(104\) | 2.22474 | − | 3.85337i | 0.218154 | − | 0.377854i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.22474 | − | 7.31747i | −0.410343 | − | 0.710736i | ||||
\(107\) | 15.2474 | 1.47403 | 0.737013 | − | 0.675878i | \(-0.236236\pi\) | ||||
0.737013 | + | 0.675878i | \(0.236236\pi\) | |||||||
\(108\) | 3.72474 | − | 3.62302i | 0.358414 | − | 0.348625i | ||||
\(109\) | 10.4495 | 1.00088 | 0.500440 | − | 0.865771i | \(-0.333172\pi\) | ||||
0.500440 | + | 0.865771i | \(0.333172\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.34847 | + | 4.73545i | −0.317823 | + | 0.449469i | ||||
\(112\) | 2.22474 | − | 3.85337i | 0.210219 | − | 0.364109i | ||||
\(113\) | −6.94949 | + | 12.0369i | −0.653753 | + | 1.13233i | 0.328452 | + | 0.944521i | \(0.393473\pi\) |
−0.982205 | + | 0.187813i | \(0.939860\pi\) | |||||||
\(114\) | −4.39898 | − | 0.405324i | −0.412002 | − | 0.0379620i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.44949 | 0.227429 | ||||||||
\(117\) | −13.1237 | − | 2.43916i | −1.21329 | − | 0.225500i | ||||
\(118\) | −0.550510 | −0.0506786 | ||||||||
\(119\) | 10.8990 | + | 18.8776i | 0.999108 | + | 1.73051i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.50000 | + | 11.2583i | −0.590909 | + | 1.02348i | ||||
\(122\) | −4.00000 | + | 6.92820i | −0.362143 | + | 0.627250i | ||||
\(123\) | 6.52270 | + | 14.1582i | 0.588132 | + | 1.27660i | ||||
\(124\) | 0.224745 | + | 0.389270i | 0.0201827 | + | 0.0349574i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −13.1237 | − | 2.43916i | −1.16915 | − | 0.217297i | ||||
\(127\) | 11.3485 | 1.00701 | 0.503507 | − | 0.863991i | \(-0.332043\pi\) | ||||
0.503507 | + | 0.863991i | \(0.332043\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 12.8485 | + | 1.18386i | 1.13124 | + | 0.104233i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.89898 | + | 13.6814i | −0.690137 | + | 1.19535i | 0.281656 | + | 0.959516i | \(0.409116\pi\) |
−0.971793 | + | 0.235837i | \(0.924217\pi\) | |||||||
\(132\) | 4.89898 | − | 6.92820i | 0.426401 | − | 0.603023i | ||||
\(133\) | 5.67423 | + | 9.82806i | 0.492019 | + | 0.852201i | ||||
\(134\) | 14.3485 | 1.23952 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.89898 | 0.420084 | ||||||||
\(137\) | 1.50000 | + | 2.59808i | 0.128154 | + | 0.221969i | 0.922961 | − | 0.384893i | \(-0.125762\pi\) |
−0.794808 | + | 0.606861i | \(0.792428\pi\) | |||||||
\(138\) | −2.44949 | + | 3.46410i | −0.208514 | + | 0.294884i | ||||
\(139\) | 2.00000 | − | 3.46410i | 0.169638 | − | 0.293821i | −0.768655 | − | 0.639664i | \(-0.779074\pi\) |
0.938293 | + | 0.345843i | \(0.112407\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.89898 | − | 0.174973i | −0.159923 | − | 0.0147354i | ||||
\(142\) | 0.674235 | + | 1.16781i | 0.0565805 | + | 0.0980003i | ||||
\(143\) | −21.7980 | −1.82284 | ||||||||
\(144\) | −1.94949 | + | 2.28024i | −0.162457 | + | 0.190020i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.500000 | − | 0.866025i | −0.0413803 | − | 0.0716728i | ||||
\(147\) | 9.27526 | + | 20.1329i | 0.765010 | + | 1.66053i | ||||
\(148\) | 1.67423 | − | 2.89986i | 0.137621 | − | 0.238367i | ||||
\(149\) | 3.00000 | − | 5.19615i | 0.245770 | − | 0.425685i | −0.716578 | − | 0.697507i | \(-0.754293\pi\) |
0.962348 | + | 0.271821i | \(0.0876260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.0000 | − | 17.3205i | −0.813788 | − | 1.40952i | −0.910195 | − | 0.414181i | \(-0.864068\pi\) |
0.0964061 | − | 0.995342i | \(-0.469265\pi\) | |||||||
\(152\) | 2.55051 | 0.206874 | ||||||||
\(153\) | −4.89898 | − | 13.8564i | −0.396059 | − | 1.12022i | ||||
\(154\) | −21.7980 | −1.75653 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 7.67423 | + | 0.707107i | 0.614431 | + | 0.0566139i | ||||
\(157\) | −0.101021 | + | 0.174973i | −0.00806231 | + | 0.0139643i | −0.870028 | − | 0.493002i | \(-0.835900\pi\) |
0.861966 | + | 0.506966i | \(0.169233\pi\) | |||||||
\(158\) | 6.34847 | − | 10.9959i | 0.505057 | − | 0.874785i | ||||
\(159\) | 8.44949 | − | 11.9494i | 0.670088 | − | 0.947648i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.8990 | 0.858960 | ||||||||
\(162\) | 8.39898 | + | 3.23375i | 0.659886 | + | 0.254067i | ||||
\(163\) | −2.55051 | −0.199771 | −0.0998857 | − | 0.994999i | \(-0.531848\pi\) | ||||
−0.0998857 | + | 0.994999i | \(0.531848\pi\) | |||||||
\(164\) | −4.50000 | − | 7.79423i | −0.351391 | − | 0.608627i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.275255 | + | 0.476756i | −0.0213639 | + | 0.0370034i | ||||
\(167\) | −9.79796 | + | 16.9706i | −0.758189 | + | 1.31322i | 0.185584 | + | 0.982628i | \(0.440582\pi\) |
−0.943773 | + | 0.330593i | \(0.892751\pi\) | |||||||
\(168\) | 7.67423 | + | 0.707107i | 0.592080 | + | 0.0545545i | ||||
\(169\) | −3.39898 | − | 5.88721i | −0.261460 | − | 0.452862i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.55051 | − | 7.21393i | −0.195042 | − | 0.551663i | ||||
\(172\) | −7.44949 | −0.568018 | ||||||||
\(173\) | −4.89898 | − | 8.48528i | −0.372463 | − | 0.645124i | 0.617481 | − | 0.786586i | \(-0.288153\pi\) |
−0.989944 | + | 0.141462i | \(0.954820\pi\) | |||||||
\(174\) | 1.77526 | + | 3.85337i | 0.134582 | + | 0.292123i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.44949 | + | 4.24264i | −0.184637 | + | 0.319801i | ||||
\(177\) | −0.398979 | − | 0.866025i | −0.0299891 | − | 0.0650945i | ||||
\(178\) | 4.50000 | + | 7.79423i | 0.337289 | + | 0.584202i | ||||
\(179\) | −15.2474 | −1.13965 | −0.569824 | − | 0.821767i | \(-0.692989\pi\) | ||||
−0.569824 | + | 0.821767i | \(0.692989\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.79796 | −0.133641 | −0.0668206 | − | 0.997765i | \(-0.521286\pi\) | ||||
−0.0668206 | + | 0.997765i | \(0.521286\pi\) | |||||||
\(182\) | −9.89898 | − | 17.1455i | −0.733761 | − | 1.27091i | ||||
\(183\) | −13.7980 | − | 1.27135i | −1.01997 | − | 0.0939808i | ||||
\(184\) | 1.22474 | − | 2.12132i | 0.0902894 | − | 0.156386i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.449490 | + | 0.635674i | −0.0329582 | + | 0.0466099i | ||||
\(187\) | −12.0000 | − | 20.7846i | −0.877527 | − | 1.51992i | ||||
\(188\) | 1.10102 | 0.0803002 | ||||||||
\(189\) | −5.67423 | − | 22.4131i | −0.412740 | − | 1.63031i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.44949 | + | 9.43879i | 0.394311 | + | 0.682967i | 0.993013 | − | 0.118005i | \(-0.0376499\pi\) |
−0.598702 | + | 0.800972i | \(0.704317\pi\) | |||||||
\(192\) | 1.00000 | − | 1.41421i | 0.0721688 | − | 0.102062i | ||||
\(193\) | 10.0000 | − | 17.3205i | 0.719816 | − | 1.24676i | −0.241257 | − | 0.970461i | \(-0.577560\pi\) |
0.961073 | − | 0.276296i | \(-0.0891071\pi\) | |||||||
\(194\) | −5.39898 | + | 9.35131i | −0.387624 | + | 0.671385i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.39898 | − | 11.0834i | −0.457070 | − | 0.791668i | ||||
\(197\) | −24.2474 | −1.72756 | −0.863780 | − | 0.503870i | \(-0.831909\pi\) | ||||
−0.863780 | + | 0.503870i | \(0.831909\pi\) | |||||||
\(198\) | 14.4495 | + | 2.68556i | 1.02688 | + | 0.190855i | ||||
\(199\) | 5.79796 | 0.411006 | 0.205503 | − | 0.978656i | \(-0.434117\pi\) | ||||
0.205503 | + | 0.978656i | \(0.434117\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.3990 | + | 22.5720i | 0.733487 | + | 1.59211i | ||||
\(202\) | −1.77526 | + | 3.07483i | −0.124907 | + | 0.216344i | ||||
\(203\) | 5.44949 | − | 9.43879i | 0.382479 | − | 0.662473i | ||||
\(204\) | 3.55051 | + | 7.70674i | 0.248585 | + | 0.539580i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 12.6969 | 0.884638 | ||||||||
\(207\) | −7.22474 | − | 1.34278i | −0.502154 | − | 0.0933298i | ||||
\(208\) | −4.44949 | −0.308517 | ||||||||
\(209\) | −6.24745 | − | 10.8209i | −0.432145 | − | 0.748497i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.724745 | + | 1.25529i | −0.0498935 | + | 0.0864181i | −0.889894 | − | 0.456168i | \(-0.849222\pi\) |
0.840000 | + | 0.542586i | \(0.182555\pi\) | |||||||
\(212\) | −4.22474 | + | 7.31747i | −0.290157 | + | 0.502566i | ||||
\(213\) | −1.34847 | + | 1.90702i | −0.0923956 | + | 0.130667i | ||||
\(214\) | −7.62372 | − | 13.2047i | −0.521147 | − | 0.902653i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.00000 | − | 1.41421i | −0.340207 | − | 0.0962250i | ||||
\(217\) | 2.00000 | 0.135769 | ||||||||
\(218\) | −5.22474 | − | 9.04952i | −0.353864 | − | 0.612911i | ||||
\(219\) | 1.00000 | − | 1.41421i | 0.0675737 | − | 0.0955637i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.8990 | − | 18.8776i | 0.733145 | − | 1.26984i | ||||
\(222\) | 5.77526 | + | 0.532134i | 0.387610 | + | 0.0357145i | ||||
\(223\) | −0.898979 | − | 1.55708i | −0.0602001 | − | 0.104270i | 0.834355 | − | 0.551228i | \(-0.185841\pi\) |
−0.894555 | + | 0.446958i | \(0.852507\pi\) | |||||||
\(224\) | −4.44949 | −0.297294 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.8990 | 0.924546 | ||||||||
\(227\) | 14.1742 | + | 24.5505i | 0.940777 | + | 1.62947i | 0.763994 | + | 0.645224i | \(0.223236\pi\) |
0.176783 | + | 0.984250i | \(0.443431\pi\) | |||||||
\(228\) | 1.84847 | + | 4.01229i | 0.122418 | + | 0.265720i | ||||
\(229\) | 10.5732 | − | 18.3133i | 0.698698 | − | 1.21018i | −0.270221 | − | 0.962798i | \(-0.587097\pi\) |
0.968918 | − | 0.247381i | \(-0.0795701\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.7980 | − | 34.2911i | −1.03943 | − | 2.25619i | ||||
\(232\) | −1.22474 | − | 2.12132i | −0.0804084 | − | 0.139272i | ||||
\(233\) | −5.69694 | −0.373219 | −0.186609 | − | 0.982434i | \(-0.559750\pi\) | ||||
−0.186609 | + | 0.982434i | \(0.559750\pi\) | |||||||
\(234\) | 4.44949 | + | 12.5851i | 0.290872 | + | 0.822711i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.275255 | + | 0.476756i | 0.0179176 | + | 0.0310342i | ||||
\(237\) | 21.8990 | + | 2.01778i | 1.42249 | + | 0.131069i | ||||
\(238\) | 10.8990 | − | 18.8776i | 0.706476 | − | 1.22365i | ||||
\(239\) | −4.77526 | + | 8.27098i | −0.308886 | + | 0.535006i | −0.978119 | − | 0.208047i | \(-0.933289\pi\) |
0.669233 | + | 0.743052i | \(0.266623\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.3990 | + | 19.7436i | 0.734273 | + | 1.27180i | 0.955042 | + | 0.296472i | \(0.0958100\pi\) |
−0.220769 | + | 0.975326i | \(0.570857\pi\) | |||||||
\(242\) | 13.0000 | 0.835672 | ||||||||
\(243\) | 1.00000 | + | 15.5563i | 0.0641500 | + | 0.997940i | ||||
\(244\) | 8.00000 | 0.512148 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.00000 | − | 12.7279i | 0.573819 | − | 0.811503i | ||||
\(247\) | 5.67423 | − | 9.82806i | 0.361043 | − | 0.625345i | ||||
\(248\) | 0.224745 | − | 0.389270i | 0.0142713 | − | 0.0247186i | ||||
\(249\) | −0.949490 | − | 0.0874863i | −0.0601715 | − | 0.00554422i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.44949 | −0.343969 | −0.171984 | − | 0.985100i | \(-0.555018\pi\) | ||||
−0.171984 | + | 0.985100i | \(0.555018\pi\) | |||||||
\(252\) | 4.44949 | + | 12.5851i | 0.280292 | + | 0.792784i | ||||
\(253\) | −12.0000 | −0.754434 | ||||||||
\(254\) | −5.67423 | − | 9.82806i | −0.356033 | − | 0.616667i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 3.39898 | − | 5.88721i | 0.212023 | − | 0.367234i | −0.740325 | − | 0.672249i | \(-0.765328\pi\) |
0.952347 | + | 0.305016i | \(0.0986616\pi\) | |||||||
\(258\) | −5.39898 | − | 11.7190i | −0.336126 | − | 0.729595i | ||||
\(259\) | −7.44949 | − | 12.9029i | −0.462889 | − | 0.801747i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.77526 | + | 5.58542i | −0.295581 | + | 0.345729i | ||||
\(262\) | 15.7980 | 0.976001 | ||||||||
\(263\) | 7.77526 | + | 13.4671i | 0.479443 | + | 0.830419i | 0.999722 | − | 0.0235770i | \(-0.00750547\pi\) |
−0.520279 | + | 0.853996i | \(0.674172\pi\) | |||||||
\(264\) | −8.44949 | − | 0.778539i | −0.520030 | − | 0.0479158i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.67423 | − | 9.82806i | 0.347910 | − | 0.602597i | ||||
\(267\) | −9.00000 | + | 12.7279i | −0.550791 | + | 0.778936i | ||||
\(268\) | −7.17423 | − | 12.4261i | −0.438236 | − | 0.759047i | ||||
\(269\) | 9.55051 | 0.582305 | 0.291152 | − | 0.956677i | \(-0.405961\pi\) | ||||
0.291152 | + | 0.956677i | \(0.405961\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.651531 | 0.0395777 | 0.0197888 | − | 0.999804i | \(-0.493701\pi\) | ||||
0.0197888 | + | 0.999804i | \(0.493701\pi\) | |||||||
\(272\) | −2.44949 | − | 4.24264i | −0.148522 | − | 0.257248i | ||||
\(273\) | 19.7980 | − | 27.9985i | 1.19823 | − | 1.69455i | ||||
\(274\) | 1.50000 | − | 2.59808i | 0.0906183 | − | 0.156956i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.22474 | + | 0.389270i | 0.254300 | + | 0.0234313i | ||||
\(277\) | −3.22474 | − | 5.58542i | −0.193756 | − | 0.335595i | 0.752736 | − | 0.658323i | \(-0.228734\pi\) |
−0.946492 | + | 0.322727i | \(0.895400\pi\) | |||||||
\(278\) | −4.00000 | −0.239904 | ||||||||
\(279\) | −1.32577 | − | 0.246405i | −0.0793715 | − | 0.0147519i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.4495 | − | 25.0273i | −0.861984 | − | 1.49300i | −0.870011 | − | 0.493033i | \(-0.835888\pi\) |
0.00802643 | − | 0.999968i | \(-0.497445\pi\) | |||||||
\(282\) | 0.797959 | + | 1.73205i | 0.0475178 | + | 0.103142i | ||||
\(283\) | 5.62372 | − | 9.74058i | 0.334296 | − | 0.579017i | −0.649054 | − | 0.760743i | \(-0.724835\pi\) |
0.983349 | + | 0.181726i | \(0.0581682\pi\) | |||||||
\(284\) | 0.674235 | − | 1.16781i | 0.0400085 | − | 0.0692967i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.8990 | + | 18.8776i | 0.644470 | + | 1.11626i | ||||
\(287\) | −40.0454 | −2.36381 | ||||||||
\(288\) | 2.94949 | + | 0.548188i | 0.173800 | + | 0.0323023i | ||||
\(289\) | 7.00000 | 0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.6237 | − | 1.71600i | −1.09174 | − | 0.100594i | ||||
\(292\) | −0.500000 | + | 0.866025i | −0.0292603 | + | 0.0506803i | ||||
\(293\) | −14.0227 | + | 24.2880i | −0.819215 | + | 1.41892i | 0.0870462 | + | 0.996204i | \(0.472257\pi\) |
−0.906261 | + | 0.422718i | \(0.861076\pi\) | |||||||
\(294\) | 12.7980 | − | 18.0990i | 0.746392 | − | 1.05556i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.34847 | −0.194626 | ||||||||
\(297\) | 6.24745 | + | 24.6773i | 0.362514 | + | 1.43192i | ||||
\(298\) | −6.00000 | −0.347571 | ||||||||
\(299\) | −5.44949 | − | 9.43879i | −0.315152 | − | 0.545859i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.5732 | + | 28.7056i | −0.955264 | + | 1.65457i | ||||
\(302\) | −10.0000 | + | 17.3205i | −0.575435 | + | 0.996683i | ||||
\(303\) | −6.12372 | − | 0.564242i | −0.351799 | − | 0.0324149i | ||||
\(304\) | −1.27526 | − | 2.20881i | −0.0731409 | − | 0.126684i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −9.55051 | + | 11.1708i | −0.545966 | + | 0.638595i | ||||
\(307\) | 6.69694 | 0.382214 | 0.191107 | − | 0.981569i | \(-0.438792\pi\) | ||||
0.191107 | + | 0.981569i | \(0.438792\pi\) | |||||||
\(308\) | 10.8990 | + | 18.8776i | 0.621027 | + | 1.07565i | ||||
\(309\) | 9.20204 | + | 19.9740i | 0.523486 | + | 1.13628i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.44949 | − | 9.43879i | 0.309012 | − | 0.535225i | −0.669134 | − | 0.743141i | \(-0.733335\pi\) |
0.978147 | + | 0.207917i | \(0.0666683\pi\) | |||||||
\(312\) | −3.22474 | − | 6.99964i | −0.182565 | − | 0.396276i | ||||
\(313\) | 1.94949 | + | 3.37662i | 0.110192 | + | 0.190858i | 0.915847 | − | 0.401526i | \(-0.131520\pi\) |
−0.805656 | + | 0.592384i | \(0.798187\pi\) | |||||||
\(314\) | 0.202041 | 0.0114018 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.6969 | −0.714259 | ||||||||
\(317\) | −8.57321 | − | 14.8492i | −0.481520 | − | 0.834017i | 0.518255 | − | 0.855226i | \(-0.326582\pi\) |
−0.999775 | + | 0.0212094i | \(0.993248\pi\) | |||||||
\(318\) | −14.5732 | − | 1.34278i | −0.817225 | − | 0.0752994i | ||||
\(319\) | −6.00000 | + | 10.3923i | −0.335936 | + | 0.581857i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.2474 | − | 21.5631i | 0.851030 | − | 1.20354i | ||||
\(322\) | −5.44949 | − | 9.43879i | −0.303688 | − | 0.526003i | ||||
\(323\) | 12.4949 | 0.695235 | ||||||||
\(324\) | −1.39898 | − | 8.89060i | −0.0777211 | − | 0.493922i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.27526 | + | 2.20881i | 0.0706298 | + | 0.122334i | ||||
\(327\) | 10.4495 | − | 14.7778i | 0.577858 | − | 0.817215i | ||||
\(328\) | −4.50000 | + | 7.79423i | −0.248471 | + | 0.430364i | ||||
\(329\) | 2.44949 | − | 4.24264i | 0.135045 | − | 0.233904i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.17423 | + | 7.22999i | 0.229437 | + | 0.397396i | 0.957641 | − | 0.287964i | \(-0.0929783\pi\) |
−0.728205 | + | 0.685360i | \(0.759645\pi\) | |||||||
\(332\) | 0.550510 | 0.0302132 | ||||||||
\(333\) | 3.34847 | + | 9.47090i | 0.183495 | + | 0.519002i | ||||
\(334\) | 19.5959 | 1.07224 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.22474 | − | 6.99964i | −0.175924 | − | 0.381861i | ||||
\(337\) | −5.55051 | + | 9.61377i | −0.302356 | + | 0.523695i | −0.976669 | − | 0.214750i | \(-0.931106\pi\) |
0.674313 | + | 0.738445i | \(0.264440\pi\) | |||||||
\(338\) | −3.39898 | + | 5.88721i | −0.184880 | + | 0.320222i | ||||
\(339\) | 10.0732 | + | 21.8649i | 0.547102 | + | 1.18754i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.20204 | −0.119247 | ||||||||
\(342\) | −4.97219 | + | 5.81577i | −0.268865 | + | 0.314481i | ||||
\(343\) | −25.7980 | −1.39296 | ||||||||
\(344\) | 3.72474 | + | 6.45145i | 0.200825 | + | 0.347839i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.89898 | + | 8.48528i | −0.263371 | + | 0.456172i | ||||
\(347\) | 6.00000 | − | 10.3923i | 0.322097 | − | 0.557888i | −0.658824 | − | 0.752297i | \(-0.728946\pi\) |
0.980921 | + | 0.194409i | \(0.0622790\pi\) | |||||||
\(348\) | 2.44949 | − | 3.46410i | 0.131306 | − | 0.185695i | ||||
\(349\) | −7.00000 | − | 12.1244i | −0.374701 | − | 0.649002i | 0.615581 | − | 0.788074i | \(-0.288921\pi\) |
−0.990282 | + | 0.139072i | \(0.955588\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.5732 | + | 16.1206i | −0.884613 | + | 0.860454i | ||||
\(352\) | 4.89898 | 0.261116 | ||||||||
\(353\) | −4.50000 | − | 7.79423i | −0.239511 | − | 0.414845i | 0.721063 | − | 0.692869i | \(-0.243654\pi\) |
−0.960574 | + | 0.278024i | \(0.910320\pi\) | |||||||
\(354\) | −0.550510 | + | 0.778539i | −0.0292593 | + | 0.0413789i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.50000 | − | 7.79423i | 0.238500 | − | 0.413093i | ||||
\(357\) | 37.5959 | + | 3.46410i | 1.98979 | + | 0.183340i | ||||
\(358\) | 7.62372 | + | 13.2047i | 0.402926 | + | 0.697889i | ||||
\(359\) | −33.7980 | −1.78379 | −0.891894 | − | 0.452244i | \(-0.850623\pi\) | ||||
−0.891894 | + | 0.452244i | \(0.850623\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.4949 | −0.657626 | ||||||||
\(362\) | 0.898979 | + | 1.55708i | 0.0472493 | + | 0.0818382i | ||||
\(363\) | 9.42168 | + | 20.4507i | 0.494510 | + | 1.07338i | ||||
\(364\) | −9.89898 | + | 17.1455i | −0.518848 | + | 0.898670i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5.79796 | + | 12.5851i | 0.303064 | + | 0.657831i | ||||
\(367\) | 8.34847 | + | 14.4600i | 0.435787 | + | 0.754804i | 0.997359 | − | 0.0726228i | \(-0.0231369\pi\) |
−0.561573 | + | 0.827427i | \(0.689804\pi\) | |||||||
\(368\) | −2.44949 | −0.127688 | ||||||||
\(369\) | 26.5454 | + | 4.93369i | 1.38190 | + | 0.256838i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.7980 | + | 32.5590i | 0.975941 | + | 1.69038i | ||||
\(372\) | 0.775255 | + | 0.0714323i | 0.0401951 | + | 0.00370359i | ||||
\(373\) | 7.79796 | − | 13.5065i | 0.403763 | − | 0.699338i | −0.590414 | − | 0.807101i | \(-0.701035\pi\) |
0.994177 | + | 0.107763i | \(0.0343687\pi\) | |||||||
\(374\) | −12.0000 | + | 20.7846i | −0.620505 | + | 1.07475i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.550510 | − | 0.953512i | −0.0283904 | − | 0.0491736i | ||||
\(377\) | −10.8990 | −0.561326 | ||||||||
\(378\) | −16.5732 | + | 16.1206i | −0.852434 | + | 0.829154i | ||||
\(379\) | 0.898979 | 0.0461775 | 0.0230887 | − | 0.999733i | \(-0.492650\pi\) | ||||
0.0230887 | + | 0.999733i | \(0.492650\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.3485 | − | 16.0492i | 0.581400 | − | 0.822223i | ||||
\(382\) | 5.44949 | − | 9.43879i | 0.278820 | − | 0.482931i | ||||
\(383\) | 13.2247 | − | 22.9059i | 0.675753 | − | 1.17044i | −0.300495 | − | 0.953783i | \(-0.597152\pi\) |
0.976248 | − | 0.216655i | \(-0.0695147\pi\) | |||||||
\(384\) | −1.72474 | − | 0.158919i | −0.0880155 | − | 0.00810978i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −20.0000 | −1.01797 | ||||||||
\(387\) | 14.5227 | − | 16.9866i | 0.738231 | − | 0.863478i | ||||
\(388\) | 10.7980 | 0.548183 | ||||||||
\(389\) | 6.79796 | + | 11.7744i | 0.344670 | + | 0.596986i | 0.985294 | − | 0.170869i | \(-0.0546574\pi\) |
−0.640624 | + | 0.767855i | \(0.721324\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.00000 | − | 10.3923i | 0.303433 | − | 0.525561i | ||||
\(392\) | −6.39898 | + | 11.0834i | −0.323197 | + | 0.559794i | ||||
\(393\) | 11.4495 | + | 24.8523i | 0.577550 | + | 1.25363i | ||||
\(394\) | 12.1237 | + | 20.9989i | 0.610784 | + | 1.05791i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4.89898 | − | 13.8564i | −0.246183 | − | 0.696311i | ||||
\(397\) | −21.5959 | −1.08387 | −0.541934 | − | 0.840421i | \(-0.682308\pi\) | ||||
−0.541934 | + | 0.840421i | \(0.682308\pi\) | |||||||
\(398\) | −2.89898 | − | 5.02118i | −0.145313 | − | 0.251689i | ||||
\(399\) | 19.5732 | + | 1.80348i | 0.979886 | + | 0.0902871i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.65153 | + | 8.05669i | −0.232286 | + | 0.402332i | −0.958481 | − | 0.285158i | \(-0.907954\pi\) |
0.726194 | + | 0.687490i | \(0.241287\pi\) | |||||||
\(402\) | 14.3485 | − | 20.2918i | 0.715637 | − | 1.01206i | ||||
\(403\) | −1.00000 | − | 1.73205i | −0.0498135 | − | 0.0862796i | ||||
\(404\) | 3.55051 | 0.176644 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.8990 | −0.540907 | ||||||||
\(407\) | 8.20204 | + | 14.2064i | 0.406560 | + | 0.704183i | ||||
\(408\) | 4.89898 | − | 6.92820i | 0.242536 | − | 0.342997i | ||||
\(409\) | −4.94949 | + | 8.57277i | −0.244737 | + | 0.423896i | −0.962058 | − | 0.272847i | \(-0.912035\pi\) |
0.717321 | + | 0.696743i | \(0.245368\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.17423 | + | 0.476756i | 0.255226 | + | 0.0235166i | ||||
\(412\) | −6.34847 | − | 10.9959i | −0.312767 | − | 0.541728i | ||||
\(413\) | 2.44949 | 0.120532 | ||||||||
\(414\) | 2.44949 | + | 6.92820i | 0.120386 | + | 0.340503i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.22474 | + | 3.85337i | 0.109077 | + | 0.188927i | ||||
\(417\) | −2.89898 | − | 6.29253i | −0.141964 | − | 0.308146i | ||||
\(418\) | −6.24745 | + | 10.8209i | −0.305573 | + | 0.529267i | ||||
\(419\) | −4.07321 | + | 7.05501i | −0.198990 | + | 0.344660i | −0.948201 | − | 0.317671i | \(-0.897099\pi\) |
0.749212 | + | 0.662331i | \(0.230433\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.02270 | − | 15.6278i | −0.439740 | − | 0.761651i | 0.557929 | − | 0.829888i | \(-0.311596\pi\) |
−0.997669 | + | 0.0682369i | \(0.978263\pi\) | |||||||
\(422\) | 1.44949 | 0.0705601 | ||||||||
\(423\) | −2.14643 | + | 2.51059i | −0.104363 | + | 0.122069i | ||||
\(424\) | 8.44949 | 0.410343 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.32577 | + | 0.214297i | 0.112684 | + | 0.0103827i | ||||
\(427\) | 17.7980 | − | 30.8270i | 0.861304 | − | 1.49182i | ||||
\(428\) | −7.62372 | + | 13.2047i | −0.368507 | + | 0.638272i | ||||
\(429\) | −21.7980 | + | 30.8270i | −1.05242 | + | 1.48834i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.6515 | 0.513066 | 0.256533 | − | 0.966535i | \(-0.417420\pi\) | ||||
0.256533 | + | 0.966535i | \(0.417420\pi\) | |||||||
\(432\) | 1.27526 | + | 5.03723i | 0.0613557 | + | 0.242354i | ||||
\(433\) | 29.5959 | 1.42229 | 0.711145 | − | 0.703046i | \(-0.248177\pi\) | ||||
0.711145 | + | 0.703046i | \(0.248177\pi\) | |||||||
\(434\) | −1.00000 | − | 1.73205i | −0.0480015 | − | 0.0831411i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.22474 | + | 9.04952i | −0.250220 | + | 0.433394i | ||||
\(437\) | 3.12372 | − | 5.41045i | 0.149428 | − | 0.258817i | ||||
\(438\) | −1.72474 | − | 0.158919i | −0.0824115 | − | 0.00759343i | ||||
\(439\) | 5.67423 | + | 9.82806i | 0.270816 | + | 0.469068i | 0.969071 | − | 0.246782i | \(-0.0793730\pi\) |
−0.698255 | + | 0.715849i | \(0.746040\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 37.7474 | + | 7.01569i | 1.79750 | + | 0.334080i | ||||
\(442\) | −21.7980 | −1.03682 | ||||||||
\(443\) | 13.8990 | + | 24.0737i | 0.660360 | + | 1.14378i | 0.980521 | + | 0.196415i | \(0.0629298\pi\) |
−0.320161 | + | 0.947363i | \(0.603737\pi\) | |||||||
\(444\) | −2.42679 | − | 5.26758i | −0.115170 | − | 0.249989i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.898979 | + | 1.55708i | −0.0425679 | + | 0.0737298i | ||||
\(447\) | −4.34847 | − | 9.43879i | −0.205676 | − | 0.446440i | ||||
\(448\) | 2.22474 | + | 3.85337i | 0.105109 | + | 0.182055i | ||||
\(449\) | 10.5959 | 0.500052 | 0.250026 | − | 0.968239i | \(-0.419561\pi\) | ||||
0.250026 | + | 0.968239i | \(0.419561\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 44.0908 | 2.07616 | ||||||||
\(452\) | −6.94949 | − | 12.0369i | −0.326877 | − | 0.566167i | ||||
\(453\) | −34.4949 | − | 3.17837i | −1.62071 | − | 0.149333i | ||||
\(454\) | 14.1742 | − | 24.5505i | 0.665230 | − | 1.15221i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.55051 | − | 3.60697i | 0.119439 | − | 0.168912i | ||||
\(457\) | −7.84847 | − | 13.5939i | −0.367136 | − | 0.635898i | 0.621981 | − | 0.783033i | \(-0.286328\pi\) |
−0.989116 | + | 0.147135i | \(0.952995\pi\) | |||||||
\(458\) | −21.1464 | −0.988108 | ||||||||
\(459\) | −24.4949 | − | 6.92820i | −1.14332 | − | 0.323381i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.67423 | − | 16.7563i | −0.450574 | − | 0.780417i | 0.547848 | − | 0.836578i | \(-0.315447\pi\) |
−0.998422 | + | 0.0561610i | \(0.982114\pi\) | |||||||
\(462\) | −21.7980 | + | 30.8270i | −1.01413 | + | 1.43420i | ||||
\(463\) | 4.67423 | − | 8.09601i | 0.217230 | − | 0.376254i | −0.736730 | − | 0.676187i | \(-0.763631\pi\) |
0.953960 | + | 0.299933i | \(0.0969645\pi\) | |||||||
\(464\) | −1.22474 | + | 2.12132i | −0.0568574 | + | 0.0984798i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.84847 | + | 4.93369i | 0.131953 | + | 0.228549i | ||||
\(467\) | −4.34847 | −0.201223 | −0.100612 | − | 0.994926i | \(-0.532080\pi\) | ||||
−0.100612 | + | 0.994926i | \(0.532080\pi\) | |||||||
\(468\) | 8.67423 | − | 10.1459i | 0.400967 | − | 0.468994i | ||||
\(469\) | −63.8434 | −2.94801 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.146428 | + | 0.317837i | 0.00674706 | + | 0.0146452i | ||||
\(472\) | 0.275255 | − | 0.476756i | 0.0126696 | − | 0.0219445i | ||||
\(473\) | 18.2474 | − | 31.6055i | 0.839019 | − | 1.45322i | ||||
\(474\) | −9.20204 | − | 19.9740i | −0.422664 | − | 0.917434i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −21.7980 | −0.999108 | ||||||||
\(477\) | −8.44949 | − | 23.8988i | −0.386876 | − | 1.09425i | ||||
\(478\) | 9.55051 | 0.436830 | ||||||||
\(479\) | 12.1237 | + | 20.9989i | 0.553947 | + | 0.959465i | 0.997985 | + | 0.0634563i | \(0.0202124\pi\) |
−0.444038 | + | 0.896008i | \(0.646454\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.44949 | + | 12.9029i | −0.339667 | + | 0.588321i | ||||
\(482\) | 11.3990 | − | 19.7436i | 0.519209 | − | 0.899297i | ||||
\(483\) | 10.8990 | − | 15.4135i | 0.495921 | − | 0.701338i | ||||
\(484\) | −6.50000 | − | 11.2583i | −0.295455 | − | 0.511742i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 12.9722 | − | 8.64420i | 0.588431 | − | 0.392109i | ||||
\(487\) | 19.5505 | 0.885918 | 0.442959 | − | 0.896542i | \(-0.353929\pi\) | ||||
0.442959 | + | 0.896542i | \(0.353929\pi\) | |||||||
\(488\) | −4.00000 | − | 6.92820i | −0.181071 | − | 0.313625i | ||||
\(489\) | −2.55051 | + | 3.60697i | −0.115338 | + | 0.163113i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.37628 | − | 2.38378i | 0.0621105 | − | 0.107578i | −0.833298 | − | 0.552824i | \(-0.813550\pi\) |
0.895409 | + | 0.445245i | \(0.146884\pi\) | |||||||
\(492\) | −15.5227 | − | 1.43027i | −0.699818 | − | 0.0644814i | ||||
\(493\) | −6.00000 | − | 10.3923i | −0.270226 | − | 0.468046i | ||||
\(494\) | −11.3485 | −0.510592 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.449490 | −0.0201827 | ||||||||
\(497\) | −3.00000 | − | 5.19615i | −0.134568 | − | 0.233079i | ||||
\(498\) | 0.398979 | + | 0.866025i | 0.0178787 | + | 0.0388075i | ||||
\(499\) | −3.17423 | + | 5.49794i | −0.142098 | + | 0.246121i | −0.928287 | − | 0.371866i | \(-0.878718\pi\) |
0.786188 | + | 0.617987i | \(0.212052\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.2020 | + | 30.8270i | 0.634500 | + | 1.37725i | ||||
\(502\) | 2.72474 | + | 4.71940i | 0.121611 | + | 0.210637i | ||||
\(503\) | −26.4495 | −1.17932 | −0.589662 | − | 0.807650i | \(-0.700739\pi\) | ||||
−0.589662 | + | 0.807650i | \(0.700739\pi\) | |||||||
\(504\) | 8.67423 | − | 10.1459i | 0.386381 | − | 0.451934i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.00000 | + | 10.3923i | 0.266733 | + | 0.461994i | ||||
\(507\) | −11.7247 | − | 1.08032i | −0.520714 | − | 0.0479788i | ||||
\(508\) | −5.67423 | + | 9.82806i | −0.251753 | + | 0.436050i | ||||
\(509\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.22474 | + | 3.85337i | 0.0984169 | + | 0.170463i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −12.7526 | − | 3.60697i | −0.563039 | − | 0.159251i | ||||
\(514\) | −6.79796 | −0.299845 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −7.44949 | + | 10.5352i | −0.327945 | + | 0.463785i | ||||
\(517\) | −2.69694 | + | 4.67123i | −0.118611 | + | 0.205441i | ||||
\(518\) | −7.44949 | + | 12.9029i | −0.327312 | + | 0.566921i | ||||
\(519\) | −16.8990 | − | 1.55708i | −0.741783 | − | 0.0683481i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.3939 | 1.28777 | 0.643885 | − | 0.765123i | \(-0.277322\pi\) | ||||
0.643885 | + | 0.765123i | \(0.277322\pi\) | |||||||
\(522\) | 7.22474 | + | 1.34278i | 0.316218 | + | 0.0587719i | ||||
\(523\) | 5.65153 | 0.247124 | 0.123562 | − | 0.992337i | \(-0.460568\pi\) | ||||
0.123562 | + | 0.992337i | \(0.460568\pi\) | |||||||
\(524\) | −7.89898 | − | 13.6814i | −0.345069 | − | 0.597676i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.77526 | − | 13.4671i | 0.339017 | − | 0.587195i | ||||
\(527\) | 1.10102 | − | 1.90702i | 0.0479612 | − | 0.0830712i | ||||
\(528\) | 3.55051 | + | 7.70674i | 0.154516 | + | 0.335393i | ||||
\(529\) | 8.50000 | + | 14.7224i | 0.369565 | + | 0.640106i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.62372 | − | 0.301783i | −0.0704636 | − | 0.0130963i | ||||
\(532\) | −11.3485 | −0.492019 | ||||||||
\(533\) | 20.0227 | + | 34.6803i | 0.867280 | + | 1.50217i | ||||
\(534\) | 15.5227 | + | 1.43027i | 0.671733 | + | 0.0618937i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.17423 | + | 12.4261i | −0.309880 | + | 0.536727i | ||||
\(537\) | −15.2474 | + | 21.5631i | −0.657976 | + | 0.930519i | ||||
\(538\) | −4.77526 | − | 8.27098i | −0.205876 | − | 0.356587i | ||||
\(539\) | 62.6969 | 2.70055 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.2020 | −0.782567 | −0.391283 | − | 0.920270i | \(-0.627969\pi\) | ||||
−0.391283 | + | 0.920270i | \(0.627969\pi\) | |||||||
\(542\) | −0.325765 | − | 0.564242i | −0.0139928 | − | 0.0242363i | ||||
\(543\) | −1.79796 | + | 2.54270i | −0.0771578 | + | 0.109118i | ||||
\(544\) | −2.44949 | + | 4.24264i | −0.105021 | + | 0.181902i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −34.1464 | − | 3.14626i | −1.46133 | − | 0.134648i | ||||
\(547\) | 15.1742 | + | 26.2825i | 0.648803 | + | 1.12376i | 0.983409 | + | 0.181402i | \(0.0580636\pi\) |
−0.334606 | + | 0.942358i | \(0.608603\pi\) | |||||||
\(548\) | −3.00000 | −0.128154 | ||||||||
\(549\) | −15.5959 | + | 18.2419i | −0.665618 | + | 0.778546i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.12372 | − | 5.41045i | −0.133075 | − | 0.230493i | ||||
\(552\) | −1.77526 | − | 3.85337i | −0.0755599 | − | 0.164010i | ||||
\(553\) | −28.2474 | + | 48.9260i | −1.20120 | + | 2.08055i | ||||
\(554\) | −3.22474 | + | 5.58542i | −0.137006 | + | 0.237302i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.00000 | + | 3.46410i | 0.0848189 | + | 0.146911i | ||||
\(557\) | 17.3939 | 0.737002 | 0.368501 | − | 0.929627i | \(-0.379871\pi\) | ||||
0.368501 | + | 0.929627i | \(0.379871\pi\) | |||||||
\(558\) | 0.449490 | + | 1.27135i | 0.0190284 | + | 0.0538205i | ||||
\(559\) | 33.1464 | 1.40194 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −41.3939 | − | 3.81405i | −1.74765 | − | 0.161029i | ||||
\(562\) | −14.4495 | + | 25.0273i | −0.609515 | + | 1.05571i | ||||
\(563\) | 14.9722 | − | 25.9326i | 0.631003 | − | 1.09293i | −0.356344 | − | 0.934355i | \(-0.615977\pi\) |
0.987347 | − | 0.158574i | \(-0.0506897\pi\) | |||||||
\(564\) | 1.10102 | − | 1.55708i | 0.0463613 | − | 0.0655648i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −11.2474 | −0.472766 | ||||||||
\(567\) | −37.3712 | − | 14.3885i | −1.56944 | − | 0.604262i | ||||
\(568\) | −1.34847 | −0.0565805 | ||||||||
\(569\) | −7.10102 | − | 12.2993i | −0.297690 | − | 0.515615i | 0.677917 | − | 0.735139i | \(-0.262883\pi\) |
−0.975607 | + | 0.219524i | \(0.929550\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.9722 | − | 24.2005i | 0.584718 | − | 1.01276i | −0.410192 | − | 0.911999i | \(-0.634538\pi\) |
0.994911 | − | 0.100762i | \(-0.0321282\pi\) | |||||||
\(572\) | 10.8990 | − | 18.8776i | 0.455709 | − | 0.789312i | ||||
\(573\) | 18.7980 | + | 1.73205i | 0.785296 | + | 0.0723575i | ||||
\(574\) | 20.0227 | + | 34.6803i | 0.835732 | + | 1.44753i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.00000 | − | 2.82843i | −0.0416667 | − | 0.117851i | ||||
\(577\) | 18.3939 | 0.765747 | 0.382874 | − | 0.923801i | \(-0.374934\pi\) | ||||
0.382874 | + | 0.923801i | \(0.374934\pi\) | |||||||
\(578\) | −3.50000 | − | 6.06218i | −0.145581 | − | 0.252153i | ||||
\(579\) | −14.4949 | − | 31.4626i | −0.602387 | − | 1.30754i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.22474 | − | 2.12132i | 0.0508110 | − | 0.0880072i | ||||
\(582\) | 7.82577 | + | 16.9866i | 0.324388 | + | 0.704118i | ||||
\(583\) | −20.6969 | − | 35.8481i | −0.857180 | − | 1.48468i | ||||
\(584\) | 1.00000 | 0.0413803 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 28.0454 | 1.15855 | ||||||||
\(587\) | 1.34847 | + | 2.33562i | 0.0556573 | + | 0.0964012i | 0.892512 | − | 0.451024i | \(-0.148941\pi\) |
−0.836854 | + | 0.547426i | \(0.815608\pi\) | |||||||
\(588\) | −22.0732 | − | 2.03383i | −0.910284 | − | 0.0838739i | ||||
\(589\) | 0.573214 | − | 0.992836i | 0.0236189 | − | 0.0409091i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.2474 | + | 34.2911i | −0.997407 | + | 1.41055i | ||||
\(592\) | 1.67423 | + | 2.89986i | 0.0688106 | + | 0.119183i | ||||
\(593\) | −1.89898 | −0.0779817 | −0.0389909 | − | 0.999240i | \(-0.512414\pi\) | ||||
−0.0389909 | + | 0.999240i | \(0.512414\pi\) | |||||||
\(594\) | 18.2474 | − | 17.7491i | 0.748702 | − | 0.728254i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.00000 | + | 5.19615i | 0.122885 | + | 0.212843i | ||||
\(597\) | 5.79796 | − | 8.19955i | 0.237295 | − | 0.335585i | ||||
\(598\) | −5.44949 | + | 9.43879i | −0.222846 | + | 0.385981i | ||||
\(599\) | 18.6742 | − | 32.3447i | 0.763009 | − | 1.32157i | −0.178285 | − | 0.983979i | \(-0.557055\pi\) |
0.941293 | − | 0.337591i | \(-0.109612\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.2474 | − | 28.1414i | −0.662747 | − | 1.14791i | −0.979891 | − | 0.199534i | \(-0.936057\pi\) |
0.317144 | − | 0.948378i | \(-0.397276\pi\) | |||||||
\(602\) | 33.1464 | 1.35095 | ||||||||
\(603\) | 42.3207 | + | 7.86566i | 1.72343 | + | 0.320314i | ||||
\(604\) | 20.0000 | 0.813788 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.57321 | + | 5.58542i | 0.104530 | + | 0.226892i | ||||
\(607\) | −5.67423 | + | 9.82806i | −0.230310 | + | 0.398909i | −0.957899 | − | 0.287104i | \(-0.907307\pi\) |
0.727589 | + | 0.686013i | \(0.240641\pi\) | |||||||
\(608\) | −1.27526 | + | 2.20881i | −0.0517184 | + | 0.0895789i | ||||
\(609\) | −7.89898 | − | 17.1455i | −0.320083 | − | 0.694772i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.89898 | −0.198191 | ||||||||
\(612\) | 14.4495 | + | 2.68556i | 0.584086 | + | 0.108557i | ||||
\(613\) | 32.0454 | 1.29430 | 0.647151 | − | 0.762362i | \(-0.275960\pi\) | ||||
0.647151 | + | 0.762362i | \(0.275960\pi\) | |||||||
\(614\) | −3.34847 | − | 5.79972i | −0.135133 | − | 0.234058i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.8990 | − | 18.8776i | 0.439132 | − | 0.760600i | ||||
\(617\) | −7.19694 | + | 12.4655i | −0.289738 | + | 0.501841i | −0.973747 | − | 0.227633i | \(-0.926901\pi\) |
0.684009 | + | 0.729473i | \(0.260235\pi\) | |||||||
\(618\) | 12.6969 | − | 17.9562i | 0.510746 | − | 0.722304i | ||||
\(619\) | −20.8712 | − | 36.1499i | −0.838883 | − | 1.45299i | −0.890829 | − | 0.454339i | \(-0.849876\pi\) |
0.0519458 | − | 0.998650i | \(-0.483458\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.12372 | + | 8.87455i | −0.366122 | + | 0.356123i | ||||
\(622\) | −10.8990 | −0.437009 | ||||||||
\(623\) | −20.0227 | − | 34.6803i | −0.802193 | − | 1.38944i | ||||
\(624\) | −4.44949 | + | 6.29253i | −0.178122 | + | 0.251903i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.94949 | − | 3.37662i | 0.0779173 | − | 0.134957i | ||||
\(627\) | −21.5505 | − | 1.98567i | −0.860644 | − | 0.0793001i | ||||
\(628\) | −0.101021 | − | 0.174973i | −0.00403116 | − | 0.00698217i | ||||
\(629\) | −16.4041 | −0.654074 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.7980 | −1.02700 | −0.513500 | − | 0.858089i | \(-0.671651\pi\) | ||||
−0.513500 | + | 0.858089i | \(0.671651\pi\) | |||||||
\(632\) | 6.34847 | + | 10.9959i | 0.252529 | + | 0.437392i | ||||
\(633\) | 1.05051 | + | 2.28024i | 0.0417540 | + | 0.0906314i | ||||
\(634\) | −8.57321 | + | 14.8492i | −0.340486 | + | 0.589739i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6.12372 | + | 13.2922i | 0.242821 | + | 0.527069i | ||||
\(637\) | 28.4722 | + | 49.3153i | 1.12811 | + | 1.95394i | ||||
\(638\) | 12.0000 | 0.475085 | ||||||||
\(639\) | 1.34847 | + | 3.81405i | 0.0533446 | + | 0.150881i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.1969 | − | 38.4462i | −0.876726 | − | 1.51853i | −0.854912 | − | 0.518773i | \(-0.826389\pi\) |
−0.0218141 | − | 0.999762i | \(-0.506944\pi\) | |||||||
\(642\) | −26.2980 | − | 2.42310i | −1.03790 | − | 0.0956323i | ||||
\(643\) | −16.1742 | + | 28.0146i | −0.637850 | + | 1.10479i | 0.348054 | + | 0.937474i | \(0.386843\pi\) |
−0.985904 | + | 0.167313i | \(0.946491\pi\) | |||||||
\(644\) | −5.44949 | + | 9.43879i | −0.214740 | + | 0.371941i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.24745 | − | 10.8209i | −0.245803 | − | 0.425743i | ||||
\(647\) | 0.247449 | 0.00972821 | 0.00486411 | − | 0.999988i | \(-0.498452\pi\) | ||||
0.00486411 | + | 0.999988i | \(0.498452\pi\) | |||||||
\(648\) | −7.00000 | + | 5.65685i | −0.274986 | + | 0.222222i | ||||
\(649\) | −2.69694 | −0.105864 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.00000 | − | 2.82843i | 0.0783862 | − | 0.110855i | ||||
\(652\) | 1.27526 | − | 2.20881i | 0.0499428 | − | 0.0865035i | ||||
\(653\) | −3.12372 | + | 5.41045i | −0.122241 | + | 0.211727i | −0.920651 | − | 0.390387i | \(-0.872341\pi\) |
0.798410 | + | 0.602114i | \(0.205675\pi\) | |||||||
\(654\) | −18.0227 | − | 1.66062i | −0.704743 | − | 0.0649353i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.00000 | 0.351391 | ||||||||
\(657\) | −1.00000 | − | 2.82843i | −0.0390137 | − | 0.110347i | ||||
\(658\) | −4.89898 | −0.190982 | ||||||||
\(659\) | −22.0732 | − | 38.2319i | −0.859850 | − | 1.48930i | −0.872071 | − | 0.489379i | \(-0.837223\pi\) |
0.0122208 | − | 0.999925i | \(-0.496110\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.6969 | − | 44.5084i | 0.999495 | − | 1.73118i | 0.472230 | − | 0.881475i | \(-0.343449\pi\) |
0.527265 | − | 0.849701i | \(-0.323218\pi\) | |||||||
\(662\) | 4.17423 | − | 7.22999i | 0.162236 | − | 0.281001i | ||||
\(663\) | −15.7980 | − | 34.2911i | −0.613542 | − | 1.33175i | ||||
\(664\) | −0.275255 | − | 0.476756i | −0.0106820 | − | 0.0185017i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.52781 | − | 7.63531i | 0.252947 | − | 0.295862i | ||||
\(667\) | −6.00000 | −0.232321 | ||||||||
\(668\) | −9.79796 | − | 16.9706i | −0.379094 | − | 0.656611i | ||||
\(669\) | −3.10102 | − | 0.285729i | −0.119892 | − | 0.0110469i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.5959 | + | 33.9411i | −0.756492 | + | 1.31028i | ||||
\(672\) | −4.44949 | + | 6.29253i | −0.171643 | + | 0.242740i | ||||
\(673\) | −3.34847 | − | 5.79972i | −0.129074 | − | 0.223563i | 0.794244 | − | 0.607599i | \(-0.207867\pi\) |
−0.923318 | + | 0.384036i | \(0.874534\pi\) | |||||||
\(674\) | 11.1010 | 0.427595 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.79796 | 0.261460 | ||||||||
\(677\) | 18.9217 | + | 32.7733i | 0.727219 | + | 1.25958i | 0.958054 | + | 0.286588i | \(0.0925210\pi\) |
−0.230835 | + | 0.972993i | \(0.574146\pi\) | |||||||
\(678\) | 13.8990 | − | 19.6561i | 0.533787 | − | 0.754889i | ||||
\(679\) | 24.0227 | − | 41.6085i | 0.921907 | − | 1.59679i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 48.8939 | + | 4.50510i | 1.87362 | + | 0.172636i | ||||
\(682\) | 1.10102 | + | 1.90702i | 0.0421603 | + | 0.0730237i | ||||
\(683\) | 11.9444 | 0.457039 | 0.228520 | − | 0.973539i | \(-0.426611\pi\) | ||||
0.228520 | + | 0.973539i | \(0.426611\pi\) | |||||||
\(684\) | 7.52270 | + | 1.39816i | 0.287638 | + | 0.0534600i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 12.8990 | + | 22.3417i | 0.492485 | + | 0.853010i | ||||
\(687\) | −15.3258 | − | 33.2661i | −0.584714 | − | 1.26918i | ||||
\(688\) | 3.72474 | − | 6.45145i | 0.142005 | − | 0.245959i | ||||
\(689\) | 18.7980 | − | 32.5590i | 0.716145 | − | 1.24040i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.52270 | + | 4.36945i | 0.0959682 | + | 0.166222i | 0.910012 | − | 0.414581i | \(-0.136072\pi\) |
−0.814044 | + | 0.580803i | \(0.802739\pi\) | |||||||
\(692\) | 9.79796 | 0.372463 | ||||||||
\(693\) | −64.2929 | − | 11.9494i | −2.44228 | − | 0.453920i | ||||
\(694\) | −12.0000 | −0.455514 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.22474 | − | 0.389270i | −0.160139 | − | 0.0147552i | ||||
\(697\) | −22.0454 | + | 38.1838i | −0.835029 | + | 1.44631i | ||||
\(698\) | −7.00000 | + | 12.1244i | −0.264954 | + | 0.458914i | ||||
\(699\) | −5.69694 | + | 8.05669i | −0.215478 | + | 0.304732i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.2020 | 0.536404 | 0.268202 | − | 0.963363i | \(-0.413571\pi\) | ||||
0.268202 | + | 0.963363i | \(0.413571\pi\) | |||||||
\(702\) | 22.2474 | + | 6.29253i | 0.839676 | + | 0.237496i | ||||
\(703\) | −8.54031 | −0.322104 | ||||||||
\(704\) | −2.44949 | − | 4.24264i | −0.0923186 | − | 0.159901i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.50000 | + | 7.79423i | −0.169360 | + | 0.293340i | ||||
\(707\) | 7.89898 | − | 13.6814i | 0.297072 | − | 0.514543i | ||||
\(708\) | 0.949490 | + | 0.0874863i | 0.0356840 | + | 0.00328794i | ||||
\(709\) | 0.224745 | + | 0.389270i | 0.00844047 | + | 0.0146193i | 0.870215 | − | 0.492673i | \(-0.163980\pi\) |
−0.861774 | + | 0.507292i | \(0.830647\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 24.7526 | − | 28.9521i | 0.928293 | − | 1.08579i | ||||
\(712\) | −9.00000 | −0.337289 | ||||||||
\(713\) | −0.550510 | − | 0.953512i | −0.0206168 | − | 0.0357093i | ||||
\(714\) | −15.7980 | − | 34.2911i | −0.591224 | − | 1.28331i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.62372 | − | 13.2047i | 0.284912 | − | 0.493482i | ||||
\(717\) | 6.92168 | + | 15.0242i | 0.258495 | + | 0.561090i | ||||
\(718\) | 16.8990 | + | 29.2699i | 0.630664 | + | 1.09234i | ||||
\(719\) | 52.0454 | 1.94097 | 0.970483 | − | 0.241169i | \(-0.0775309\pi\) | ||||
0.970483 | + | 0.241169i | \(0.0775309\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −56.4949 | −2.10398 | ||||||||
\(722\) | 6.24745 | + | 10.8209i | 0.232506 | + | 0.402712i | ||||
\(723\) | 39.3207 | + | 3.62302i | 1.46235 | + | 0.134742i | ||||
\(724\) | 0.898979 | − | 1.55708i | 0.0334103 | − | 0.0578684i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 13.0000 | − | 18.3848i | 0.482475 | − | 0.682323i | ||||
\(727\) | −8.00000 | − | 13.8564i | −0.296704 | − | 0.513906i | 0.678676 | − | 0.734438i | \(-0.262554\pi\) |
−0.975380 | + | 0.220532i | \(0.929221\pi\) | |||||||
\(728\) | 19.7980 | 0.733761 | ||||||||
\(729\) | 23.0000 | + | 14.1421i | 0.851852 | + | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.2474 | + | 31.6055i | 0.674906 | + | 1.16897i | ||||
\(732\) | 8.00000 | − | 11.3137i | 0.295689 | − | 0.418167i | ||||
\(733\) | 13.0000 | − | 22.5167i | 0.480166 | − | 0.831672i | −0.519575 | − | 0.854425i | \(-0.673910\pi\) |
0.999741 | + | 0.0227529i | \(0.00724310\pi\) | |||||||
\(734\) | 8.34847 | − | 14.4600i | 0.308148 | − | 0.533727i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.22474 | + | 2.12132i | 0.0451447 | + | 0.0781929i | ||||
\(737\) | 70.2929 | 2.58927 | ||||||||
\(738\) | −9.00000 | − | 25.4558i | −0.331295 | − | 0.937043i | ||||
\(739\) | −41.0454 | −1.50988 | −0.754940 | − | 0.655794i | \(-0.772334\pi\) | ||||
−0.754940 | + | 0.655794i | \(0.772334\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.22474 | − | 17.8526i | −0.302144 | − | 0.655833i | ||||
\(742\) | 18.7980 | − | 32.5590i | 0.690095 | − | 1.19528i | ||||
\(743\) | 17.3258 | − | 30.0091i | 0.635621 | − | 1.10093i | −0.350763 | − | 0.936464i | \(-0.614078\pi\) |
0.986383 | − | 0.164463i | \(-0.0525891\pi\) | |||||||
\(744\) | −0.325765 | − | 0.707107i | −0.0119431 | − | 0.0259238i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −15.5959 | −0.571007 | ||||||||
\(747\) | −1.07321 | + | 1.25529i | −0.0392669 | + | 0.0459288i | ||||
\(748\) | 24.0000 | 0.877527 | ||||||||
\(749\) | 33.9217 | + | 58.7541i | 1.23947 | + | 2.14683i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.0227 | − | 43.3406i | 0.913091 | − | 1.58152i | 0.103420 | − | 0.994638i | \(-0.467022\pi\) |
0.809672 | − | 0.586883i | \(-0.199645\pi\) | |||||||
\(752\) | −0.550510 | + | 0.953512i | −0.0200750 | + | 0.0347710i | ||||
\(753\) | −5.44949 | + | 7.70674i | −0.198590 | + | 0.280849i | ||||
\(754\) | 5.44949 | + | 9.43879i | 0.198459 | + | 0.343741i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 22.2474 | + | 6.29253i | 0.809132 | + | 0.228857i | ||||
\(757\) | −6.04541 | −0.219724 | −0.109862 | − | 0.993947i | \(-0.535041\pi\) | ||||
−0.109862 | + | 0.993947i | \(0.535041\pi\) | |||||||
\(758\) | −0.449490 | − | 0.778539i | −0.0163262 | − | 0.0282778i | ||||
\(759\) | −12.0000 | + | 16.9706i | −0.435572 | + | 0.615992i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.05051 | + | 3.55159i | −0.0743309 | + | 0.128745i | −0.900795 | − | 0.434244i | \(-0.857015\pi\) |
0.826464 | + | 0.562989i | \(0.190349\pi\) | |||||||
\(762\) | −19.5732 | − | 1.80348i | −0.709063 | − | 0.0653333i | ||||
\(763\) | 23.2474 | + | 40.2658i | 0.841614 | + | 1.45772i | ||||
\(764\) | −10.8990 | −0.394311 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −26.4495 | −0.955659 | ||||||||
\(767\) | −1.22474 | − | 2.12132i | −0.0442230 | − | 0.0765964i | ||||
\(768\) | 0.724745 | + | 1.57313i | 0.0261520 | + | 0.0567655i | ||||
\(769\) | −25.0959 | + | 43.4674i | −0.904982 | + | 1.56747i | −0.0840405 | + | 0.996462i | \(0.526783\pi\) |
−0.820941 | + | 0.571012i | \(0.806551\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.92679 | − | 10.6941i | −0.177434 | − | 0.385138i | ||||
\(772\) | 10.0000 | + | 17.3205i | 0.359908 | + | 0.623379i | ||||
\(773\) | 49.5959 | 1.78384 | 0.891921 | − | 0.452192i | \(-0.149358\pi\) | ||||
0.891921 | + | 0.452192i | \(0.149358\pi\) | |||||||
\(774\) | −21.9722 | − | 4.08372i | −0.789774 | − | 0.146786i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.39898 | − | 9.35131i | −0.193812 | − | 0.335692i | ||||
\(777\) | −25.6969 | − | 2.36773i | −0.921873 | − | 0.0849417i | ||||
\(778\) | 6.79796 | − | 11.7744i | 0.243719 | − | 0.422133i | ||||
\(779\) | −11.4773 | + | 19.8793i | −0.411217 | + | 0.712248i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.30306 | + | 5.72107i | 0.118193 | + | 0.204716i | ||||
\(782\) | −12.0000 | −0.429119 | ||||||||
\(783\) | 3.12372 | + | 12.3387i | 0.111633 | + | 0.440947i | ||||
\(784\) | 12.7980 | 0.457070 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 15.7980 | − | 22.3417i | 0.563495 | − | 0.796902i | ||||
\(787\) | 2.65153 | − | 4.59259i | 0.0945169 | − | 0.163708i | −0.814890 | − | 0.579616i | \(-0.803203\pi\) |
0.909407 | + | 0.415908i | \(0.136536\pi\) | |||||||
\(788\) | 12.1237 | − | 20.9989i | 0.431890 | − | 0.748055i | ||||
\(789\) | 26.8207 | + | 2.47127i | 0.954841 | + | 0.0879794i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −61.8434 | −2.19890 | ||||||||
\(792\) | −9.55051 | + | 11.1708i | −0.339363 | + | 0.396939i | ||||
\(793\) | −35.5959 | −1.26405 | ||||||||
\(794\) | 10.7980 | + | 18.7026i | 0.383205 | + | 0.663731i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.89898 | + | 5.02118i | −0.102752 | + | 0.177971i | ||||
\(797\) | −2.87628 | + | 4.98186i | −0.101883 | + | 0.176466i | −0.912460 | − | 0.409165i | \(-0.865820\pi\) |
0.810577 | + | 0.585631i | \(0.199153\pi\) | |||||||
\(798\) | −8.22474 | − | 17.8526i | −0.291153 | − | 0.631977i | ||||
\(799\) | −2.69694 | − | 4.67123i | −0.0954108 | − | 0.165256i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.00000 | + | 25.4558i | 0.317999 | + | 0.899438i | ||||
\(802\) | 9.30306 | 0.328503 | ||||||||
\(803\) | −2.44949 | − | 4.24264i | −0.0864406 | − | 0.149720i | ||||
\(804\) | −24.7474 | − | 2.28024i | −0.872775 | − | 0.0804178i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.00000 | + | 1.73205i | −0.0352235 | + | 0.0610089i | ||||
\(807\) | 9.55051 | − | 13.5065i | 0.336194 | − | 0.475450i | ||||
\(808\) | −1.77526 | − | 3.07483i | −0.0624533 | − | 0.108172i | ||||
\(809\) | −35.6969 | −1.25504 | −0.627519 | − | 0.778601i | \(-0.715929\pi\) | ||||
−0.627519 | + | 0.778601i | \(0.715929\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.4495 | −1.17457 | −0.587285 | − | 0.809380i | \(-0.699803\pi\) | ||||
−0.587285 | + | 0.809380i | \(0.699803\pi\) | |||||||
\(812\) | 5.44949 | + | 9.43879i | 0.191240 | + | 0.331237i | ||||
\(813\) | 0.651531 | − | 0.921404i | 0.0228502 | − | 0.0323150i | ||||
\(814\) | 8.20204 | − | 14.2064i | 0.287481 | − | 0.497932i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −8.44949 | − | 0.778539i | −0.295791 | − | 0.0272543i | ||||
\(817\) | 9.50000 | + | 16.4545i | 0.332363 | + | 0.575669i | ||||
\(818\) | 9.89898 | 0.346110 | ||||||||
\(819\) | −19.7980 | − | 55.9971i | −0.691797 | − | 1.95670i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.5959 | + | 44.3334i | 0.893304 | + | 1.54725i | 0.835890 | + | 0.548897i | \(0.184952\pi\) |
0.0574136 | + | 0.998350i | \(0.481715\pi\) | |||||||
\(822\) | −2.17423 | − | 4.71940i | −0.0758351 | − | 0.164608i | ||||
\(823\) | −13.4495 | + | 23.2952i | −0.468820 | + | 0.812020i | −0.999365 | − | 0.0356371i | \(-0.988654\pi\) |
0.530545 | + | 0.847657i | \(0.321987\pi\) | |||||||
\(824\) | −6.34847 | + | 10.9959i | −0.221159 | + | 0.383059i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.22474 | − | 2.12132i | −0.0426143 | − | 0.0738102i | ||||
\(827\) | −17.9444 | −0.623987 | −0.311994 | − | 0.950084i | \(-0.600997\pi\) | ||||
−0.311994 | + | 0.950084i | \(0.600997\pi\) | |||||||
\(828\) | 4.77526 | − | 5.58542i | 0.165952 | − | 0.194107i | ||||
\(829\) | 26.7423 | 0.928800 | 0.464400 | − | 0.885626i | \(-0.346270\pi\) | ||||
0.464400 | + | 0.885626i | \(0.346270\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.1237 | − | 1.02494i | −0.385878 | − | 0.0355549i | ||||
\(832\) | 2.22474 | − | 3.85337i | 0.0771292 | − | 0.133592i | ||||
\(833\) | −31.3485 | + | 54.2971i | −1.08616 | + | 1.88128i | ||||
\(834\) | −4.00000 | + | 5.65685i | −0.138509 | + | 0.195881i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 12.4949 | 0.432145 | ||||||||
\(837\) | −1.67423 | + | 1.62851i | −0.0578700 | + | 0.0562896i | ||||
\(838\) | 8.14643 | 0.281414 | ||||||||
\(839\) | −11.3258 | − | 19.6168i | −0.391009 | − | 0.677247i | 0.601574 | − | 0.798817i | \(-0.294540\pi\) |
−0.992583 | + | 0.121570i | \(0.961207\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.5000 | − | 19.9186i | 0.396552 | − | 0.686848i | ||||
\(842\) | −9.02270 | + | 15.6278i | −0.310943 | + | 0.538569i | ||||
\(843\) | −49.8434 | − | 4.59259i | −1.71670 | − | 0.158177i | ||||
\(844\) | −0.724745 | − | 1.25529i | −0.0249467 | − | 0.0432090i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.24745 | + | 0.603566i | 0.111650 | + | 0.0207510i | ||||
\(847\) | −57.8434 | −1.98752 | ||||||||
\(848\) | −4.22474 | − | 7.31747i | −0.145078 | − | 0.251283i | ||||
\(849\) | −8.15153 | − | 17.6937i | −0.279760 | − | 0.607247i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.10102 | + | 7.10318i | −0.140581 | + | 0.243494i | ||||
\(852\) | −0.977296 | − | 2.12132i | −0.0334816 | − | 0.0726752i | ||||
\(853\) | −23.0000 | − | 39.8372i | −0.787505 | − | 1.36400i | −0.927491 | − | 0.373845i | \(-0.878039\pi\) |
0.139986 | − | 0.990153i | \(-0.455294\pi\) | |||||||
\(854\) | −35.5959 | −1.21807 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.2474 | 0.521147 | ||||||||
\(857\) | −20.0505 | − | 34.7285i | −0.684912 | − | 1.18630i | −0.973464 | − | 0.228839i | \(-0.926507\pi\) |
0.288552 | − | 0.957464i | \(-0.406826\pi\) | |||||||
\(858\) | 37.5959 | + | 3.46410i | 1.28350 | + | 0.118262i | ||||
\(859\) | 2.82577 | − | 4.89437i | 0.0964139 | − | 0.166994i | −0.813784 | − | 0.581168i | \(-0.802596\pi\) |
0.910198 | + | 0.414174i | \(0.135929\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −40.0454 | + | 56.6328i | −1.36474 | + | 1.93004i | ||||
\(862\) | −5.32577 | − | 9.22450i | −0.181396 | − | 0.314188i | ||||
\(863\) | −19.8434 | −0.675476 | −0.337738 | − | 0.941240i | \(-0.609662\pi\) | ||||
−0.337738 | + | 0.941240i | \(0.609662\pi\) | |||||||
\(864\) | 3.72474 | − | 3.62302i | 0.126718 | − | 0.123258i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −14.7980 | − | 25.6308i | −0.502855 | − | 0.870971i | ||||
\(867\) | 7.00000 | − | 9.89949i | 0.237732 | − | 0.336204i | ||||
\(868\) | −1.00000 | + | 1.73205i | −0.0339422 | + | 0.0587896i | ||||
\(869\) | 31.1010 | − | 53.8685i | 1.05503 | − | 1.82737i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.9217 | + | 55.2900i | 1.08162 | + | 1.87343i | ||||
\(872\) | 10.4495 | 0.353864 | ||||||||
\(873\) | −21.0505 | + | 24.6219i | −0.712452 | + | 0.833326i | ||||
\(874\) | −6.24745 | −0.211323 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.724745 | + | 1.57313i | 0.0244869 | + | 0.0531512i | ||||
\(877\) | −6.10102 | + | 10.5673i | −0.206017 | + | 0.356832i | −0.950456 | − | 0.310858i | \(-0.899383\pi\) |
0.744439 | + | 0.667690i | \(0.232717\pi\) | |||||||
\(878\) | 5.67423 | − | 9.82806i | 0.191496 | − | 0.331681i | ||||
\(879\) | 20.3258 | + | 44.1191i | 0.685571 | + | 1.48810i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.30306 | 0.313428 | 0.156714 | − | 0.987644i | \(-0.449910\pi\) | ||||
0.156714 | + | 0.987644i | \(0.449910\pi\) | |||||||
\(882\) | −12.7980 | − | 36.1981i | −0.430930 | − | 1.21885i | ||||
\(883\) | −28.2020 | −0.949074 | −0.474537 | − | 0.880235i | \(-0.657385\pi\) | ||||
−0.474537 | + | 0.880235i | \(0.657385\pi\) | |||||||
\(884\) | 10.8990 | + | 18.8776i | 0.366572 | + | 0.634922i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.8990 | − | 24.0737i | 0.466945 | − | 0.808773i | ||||
\(887\) | 27.2474 | − | 47.1940i | 0.914880 | − | 1.58462i | 0.107803 | − | 0.994172i | \(-0.465619\pi\) |
0.807077 | − | 0.590446i | \(-0.201048\pi\) | |||||||
\(888\) | −3.34847 | + | 4.73545i | −0.112367 | + | 0.158911i | ||||
\(889\) | 25.2474 | + | 43.7299i | 0.846772 | + | 1.46665i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 41.1464 | + | 15.8421i | 1.37846 | + | 0.530730i | ||||
\(892\) | 1.79796 | 0.0602001 | ||||||||
\(893\) | −1.40408 | − | 2.43194i | −0.0469858 | − | 0.0813818i | ||||
\(894\) | −6.00000 | + | 8.48528i | −0.200670 | + | 0.283790i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.22474 | − | 3.85337i | 0.0743235 | − | 0.128732i | ||||
\(897\) | −18.7980 | − | 1.73205i | −0.627646 | − | 0.0578315i | ||||
\(898\) | −5.29796 | − | 9.17633i | −0.176795 | − | 0.306218i | ||||
\(899\) | −1.10102 | −0.0367211 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 41.3939 | 1.37903 | ||||||||
\(902\) | −22.0454 | − | 38.1838i | −0.734032 | − | 1.27138i | ||||
\(903\) | 24.0227 | + | 52.1437i | 0.799426 | + | 1.73523i | ||||
\(904\) | −6.94949 | + | 12.0369i | −0.231137 | + | 0.400340i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 14.4949 | + | 31.4626i | 0.481561 | + | 1.04528i | ||||
\(907\) | 10.8258 | + | 18.7508i | 0.359464 | + | 0.622609i | 0.987871 | − | 0.155275i | \(-0.0496263\pi\) |
−0.628408 | + | 0.777884i | \(0.716293\pi\) | |||||||
\(908\) | −28.3485 | −0.940777 | ||||||||
\(909\) | −6.92168 | + | 8.09601i | −0.229578 | + | 0.268528i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.67423 | − | 6.36396i | −0.121733 | − | 0.210847i | 0.798718 | − | 0.601705i | \(-0.205512\pi\) |
−0.920451 | + | 0.390858i | \(0.872178\pi\) | |||||||
\(912\) | −4.39898 | − | 0.405324i | −0.145665 | − | 0.0134216i | ||||
\(913\) | −1.34847 | + | 2.33562i | −0.0446278 | + | 0.0772976i | ||||
\(914\) | −7.84847 | + | 13.5939i | −0.259604 | + | 0.449648i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.5732 | + | 18.3133i | 0.349349 | + | 0.605090i | ||||
\(917\) | −70.2929 | −2.32127 | ||||||||
\(918\) | 6.24745 | + | 24.6773i | 0.206197 | + | 0.814472i | ||||
\(919\) | −11.3485 | −0.374351 | −0.187176 | − | 0.982326i | \(-0.559933\pi\) | ||||
−0.187176 | + | 0.982326i | \(0.559933\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.69694 | − | 9.47090i | 0.220672 | − | 0.312077i | ||||
\(922\) | −9.67423 | + | 16.7563i | −0.318604 | + | 0.551838i | ||||
\(923\) | −3.00000 | + | 5.19615i | −0.0987462 | + | 0.171033i | ||||
\(924\) | 37.5959 | + | 3.46410i | 1.23681 | + | 0.113961i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −9.34847 | −0.307210 | ||||||||
\(927\) | 37.4495 | + | 6.96031i | 1.23000 | + | 0.228607i | ||||
\(928\) | 2.44949 | 0.0804084 | ||||||||
\(929\) | −13.5959 | − | 23.5488i | −0.446068 | − | 0.772612i | 0.552058 | − | 0.833806i | \(-0.313843\pi\) |
−0.998126 | + | 0.0611938i | \(0.980509\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.3207 | + | 28.2682i | −0.534888 | + | 0.926453i | ||||
\(932\) | 2.84847 | − | 4.93369i | 0.0933047 | − | 0.161609i | ||||
\(933\) | −7.89898 | − | 17.1455i | −0.258601 | − | 0.561320i | ||||
\(934\) | 2.17423 | + | 3.76588i | 0.0711431 | + | 0.123224i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −13.1237 | − | 2.43916i | −0.428962 | − | 0.0797264i | ||||
\(937\) | −26.7980 | −0.875451 | −0.437726 | − | 0.899109i | \(-0.644216\pi\) | ||||
−0.437726 | + | 0.899109i | \(0.644216\pi\) | |||||||
\(938\) | 31.9217 | + | 55.2900i | 1.04228 | + | 1.80528i | ||||
\(939\) | 6.72474 | + | 0.619620i | 0.219454 | + | 0.0202205i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.8207 | − | 25.6701i | 0.483140 | − | 0.836823i | −0.516673 | − | 0.856183i | \(-0.672830\pi\) |
0.999813 | + | 0.0193603i | \(0.00616295\pi\) | |||||||
\(942\) | 0.202041 | − | 0.285729i | 0.00658285 | − | 0.00930956i | ||||
\(943\) | 11.0227 | + | 19.0919i | 0.358949 | + | 0.621717i | ||||
\(944\) | −0.550510 | −0.0179176 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −36.4949 | −1.18655 | ||||||||
\(947\) | −4.07321 | − | 7.05501i | −0.132362 | − | 0.229257i | 0.792225 | − | 0.610229i | \(-0.208923\pi\) |
−0.924587 | + | 0.380972i | \(0.875589\pi\) | |||||||
\(948\) | −12.6969 | + | 17.9562i | −0.412377 | + | 0.583190i | ||||
\(949\) | 2.22474 | − | 3.85337i | 0.0722183 | − | 0.125086i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −29.5732 | − | 2.72489i | −0.958977 | − | 0.0883605i | ||||
\(952\) | 10.8990 | + | 18.8776i | 0.353238 | + | 0.611826i | ||||
\(953\) | −21.7980 | −0.706105 | −0.353053 | − | 0.935603i | \(-0.614856\pi\) | ||||
−0.353053 | + | 0.935603i | \(0.614856\pi\) | |||||||
\(954\) | −16.4722 | + | 19.2669i | −0.533307 | + | 0.623787i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −4.77526 | − | 8.27098i | −0.154443 | − | 0.267503i | ||||
\(957\) | 8.69694 | + | 18.8776i | 0.281132 | + | 0.610226i | ||||
\(958\) | 12.1237 | − | 20.9989i | 0.391700 | − | 0.678444i | ||||
\(959\) | −6.67423 | + | 11.5601i | −0.215522 | + | 0.373296i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.3990 | + | 26.6718i | 0.496741 | + | 0.860381i | ||||
\(962\) | 14.8990 | 0.480362 | ||||||||
\(963\) | −15.2474 | − | 43.1263i | −0.491342 | − | 1.38973i | ||||
\(964\) | −22.7980 | −0.734273 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −18.7980 | − | 1.73205i | −0.604814 | − | 0.0557278i | ||||
\(967\) | 16.0000 | − | 27.7128i | 0.514525 | − | 0.891184i | −0.485333 | − | 0.874330i | \(-0.661301\pi\) |
0.999858 | − | 0.0168544i | \(-0.00536518\pi\) | |||||||
\(968\) | −6.50000 | + | 11.2583i | −0.208918 | + | 0.361856i | ||||
\(969\) | 12.4949 | − | 17.6705i | 0.401394 | − | 0.567657i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.8434 | 0.733079 | 0.366539 | − | 0.930403i | \(-0.380543\pi\) | ||||
0.366539 | + | 0.930403i | \(0.380543\pi\) | |||||||
\(972\) | −13.9722 | − | 6.91215i | −0.448158 | − | 0.221707i | ||||
\(973\) | 17.7980 | 0.570576 | ||||||||
\(974\) | −9.77526 | − | 16.9312i | −0.313219 | − | 0.542512i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.00000 | + | 6.92820i | −0.128037 | + | 0.221766i | ||||
\(977\) | −4.50000 | + | 7.79423i | −0.143968 | + | 0.249359i | −0.928987 | − | 0.370111i | \(-0.879319\pi\) |
0.785020 | + | 0.619471i | \(0.212653\pi\) | |||||||
\(978\) | 4.39898 | + | 0.405324i | 0.140664 | + | 0.0129608i | ||||
\(979\) | 22.0454 | + | 38.1838i | 0.704574 | + | 1.22036i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.4495 | − | 29.5556i | −0.333627 | − | 0.943638i | ||||
\(982\) | −2.75255 | −0.0878374 | ||||||||
\(983\) | −11.4495 | − | 19.8311i | −0.365182 | − | 0.632514i | 0.623623 | − | 0.781725i | \(-0.285660\pi\) |
−0.988805 | + | 0.149211i | \(0.952327\pi\) | |||||||
\(984\) | 6.52270 | + | 14.1582i | 0.207936 | + | 0.451347i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −6.00000 | + | 10.3923i | −0.191079 | + | 0.330958i | ||||
\(987\) | −3.55051 | − | 7.70674i | −0.113014 | − | 0.245308i | ||||
\(988\) | 5.67423 | + | 9.82806i | 0.180521 | + | 0.312672i | ||||
\(989\) | 18.2474 | 0.580235 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0000 | −0.508257 | −0.254128 | − | 0.967170i | \(-0.581789\pi\) | ||||
−0.254128 | + | 0.967170i | \(0.581789\pi\) | |||||||
\(992\) | 0.224745 | + | 0.389270i | 0.00713566 | + | 0.0123593i | ||||
\(993\) | 14.3990 | + | 1.32673i | 0.456938 | + | 0.0421024i | ||||
\(994\) | −3.00000 | + | 5.19615i | −0.0951542 | + | 0.164812i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.550510 | − | 0.778539i | 0.0174436 | − | 0.0246690i | ||||
\(997\) | 18.0227 | + | 31.2162i | 0.570785 | + | 0.988628i | 0.996486 | + | 0.0837642i | \(0.0266943\pi\) |
−0.425701 | + | 0.904864i | \(0.639972\pi\) | |||||||
\(998\) | 6.34847 | 0.200957 | ||||||||
\(999\) | 16.7423 | + | 4.73545i | 0.529704 | + | 0.149823i |
(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 | 450.2.e.l.301.1 | yes | 4 | |
3.2 | odd | 2 | 1350.2.e.n.901.2 | 4 | |||
5.2 | odd | 4 | 450.2.j.f.49.3 | 8 | |||
5.3 | odd | 4 | 450.2.j.f.49.2 | 8 | |||
5.4 | even | 2 | 450.2.e.m.301.2 | yes | 4 | ||
9.2 | odd | 6 | 1350.2.e.n.451.2 | 4 | |||
9.4 | even | 3 | 4050.2.a.bu.1.1 | 2 | |||
9.5 | odd | 6 | 4050.2.a.bl.1.1 | 2 | |||
9.7 | even | 3 | inner | 450.2.e.l.151.2 | ✓ | 4 | |
15.2 | even | 4 | 1350.2.j.g.199.1 | 8 | |||
15.8 | even | 4 | 1350.2.j.g.199.4 | 8 | |||
15.14 | odd | 2 | 1350.2.e.k.901.1 | 4 | |||
45.2 | even | 12 | 1350.2.j.g.1099.4 | 8 | |||
45.4 | even | 6 | 4050.2.a.br.1.2 | 2 | |||
45.7 | odd | 12 | 450.2.j.f.349.2 | 8 | |||
45.13 | odd | 12 | 4050.2.c.y.649.2 | 4 | |||
45.14 | odd | 6 | 4050.2.a.by.1.2 | 2 | |||
45.22 | odd | 12 | 4050.2.c.y.649.3 | 4 | |||
45.23 | even | 12 | 4050.2.c.w.649.4 | 4 | |||
45.29 | odd | 6 | 1350.2.e.k.451.1 | 4 | |||
45.32 | even | 12 | 4050.2.c.w.649.1 | 4 | |||
45.34 | even | 6 | 450.2.e.m.151.1 | yes | 4 | ||
45.38 | even | 12 | 1350.2.j.g.1099.1 | 8 | |||
45.43 | odd | 12 | 450.2.j.f.349.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.2.e.l.151.2 | ✓ | 4 | 9.7 | even | 3 | inner | |
450.2.e.l.301.1 | yes | 4 | 1.1 | even | 1 | trivial | |
450.2.e.m.151.1 | yes | 4 | 45.34 | even | 6 | ||
450.2.e.m.301.2 | yes | 4 | 5.4 | even | 2 | ||
450.2.j.f.49.2 | 8 | 5.3 | odd | 4 | |||
450.2.j.f.49.3 | 8 | 5.2 | odd | 4 | |||
450.2.j.f.349.2 | 8 | 45.7 | odd | 12 | |||
450.2.j.f.349.3 | 8 | 45.43 | odd | 12 | |||
1350.2.e.k.451.1 | 4 | 45.29 | odd | 6 | |||
1350.2.e.k.901.1 | 4 | 15.14 | odd | 2 | |||
1350.2.e.n.451.2 | 4 | 9.2 | odd | 6 | |||
1350.2.e.n.901.2 | 4 | 3.2 | odd | 2 | |||
1350.2.j.g.199.1 | 8 | 15.2 | even | 4 | |||
1350.2.j.g.199.4 | 8 | 15.8 | even | 4 | |||
1350.2.j.g.1099.1 | 8 | 45.38 | even | 12 | |||
1350.2.j.g.1099.4 | 8 | 45.2 | even | 12 | |||
4050.2.a.bl.1.1 | 2 | 9.5 | odd | 6 | |||
4050.2.a.br.1.2 | 2 | 45.4 | even | 6 | |||
4050.2.a.bu.1.1 | 2 | 9.4 | even | 3 | |||
4050.2.a.by.1.2 | 2 | 45.14 | odd | 6 | |||
4050.2.c.w.649.1 | 4 | 45.32 | even | 12 | |||
4050.2.c.w.649.4 | 4 | 45.23 | even | 12 | |||
4050.2.c.y.649.2 | 4 | 45.13 | odd | 12 | |||
4050.2.c.y.649.3 | 4 | 45.22 | odd | 12 |