Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,2,Mod(451,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, 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("1350.451");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.e (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: | \(10.7798042729\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 450) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 901.1 | ||
Root | \(-1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.901 |
Dual form | 1350.2.e.k.451.1 |
$q$-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 \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.22474 | − | 3.85337i | −0.840875 | − | 1.45644i | −0.889156 | − | 0.457604i | \(-0.848708\pi\) |
0.0482818 | − | 0.998834i | \(-0.484625\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.44949 | + | 4.24264i | 0.738549 | + | 1.27920i | 0.953149 | + | 0.302502i | \(0.0978220\pi\) |
−0.214600 | + | 0.976702i | \(0.568845\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.22474 | + | 3.85337i | −0.617033 | + | 1.06873i | 0.372991 | + | 0.927835i | \(0.378332\pi\) |
−0.990024 | + | 0.140898i | \(0.955001\pi\) | |||||||
\(14\) | −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 | \(0.297513\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.55051 | 0.585127 | 0.292564 | − | 0.956246i | \(-0.405492\pi\) | ||||
0.292564 | + | 0.956246i | \(0.405492\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 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 | \(0.0844671\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.44949 | 0.872617 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.44949 | 0.840875 | ||||||||
\(29\) | 1.22474 | + | 2.12132i | 0.227429 | + | 0.393919i | 0.957046 | − | 0.289938i | \(-0.0936346\pi\) |
−0.729616 | + | 0.683857i | \(0.760301\pi\) | |||||||
\(30\) | 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 | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.44949 | − | 4.24264i | −0.420084 | − | 0.727607i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.34847 | 0.550485 | 0.275242 | − | 0.961375i | \(-0.411242\pi\) | ||||
0.275242 | + | 0.961375i | \(0.411242\pi\) | |||||||
\(38\) | −1.27526 | − | 2.20881i | −0.206874 | − | 0.358316i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.50000 | − | 7.79423i | 0.702782 | − | 1.21725i | −0.264704 | − | 0.964330i | \(-0.585274\pi\) |
0.967486 | − | 0.252924i | \(-0.0813924\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.72474 | − | 6.45145i | −0.568018 | − | 0.983836i | −0.996762 | − | 0.0804103i | \(-0.974377\pi\) |
0.428744 | − | 0.903426i | \(-0.358956\pi\) | |||||||
\(44\) | −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 | \(0.858921\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.39898 | + | 11.0834i | −0.914140 | + | 1.58334i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.22474 | − | 3.85337i | −0.308517 | − | 0.534366i | ||||
\(53\) | 8.44949 | 1.16063 | 0.580313 | − | 0.814393i | \(-0.302930\pi\) | ||||
0.580313 | + | 0.814393i | \(0.302930\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.22474 | − | 3.85337i | −0.297294 | − | 0.514928i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.22474 | − | 2.12132i | 0.160817 | − | 0.278543i | ||||
\(59\) | −0.275255 | + | 0.476756i | −0.0358352 | + | 0.0620683i | −0.883387 | − | 0.468645i | \(-0.844742\pi\) |
0.847552 | + | 0.530713i | \(0.178076\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.17423 | − | 12.4261i | 0.876472 | − | 1.51809i | 0.0212861 | − | 0.999773i | \(-0.493224\pi\) |
0.855186 | − | 0.518321i | \(-0.173443\pi\) | |||||||
\(68\) | −2.44949 | + | 4.24264i | −0.297044 | + | 0.514496i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.34847 | 0.160034 | 0.0800169 | − | 0.996794i | \(-0.474503\pi\) | ||||
0.0800169 | + | 0.996794i | \(0.474503\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.00000 | −0.117041 | −0.0585206 | − | 0.998286i | \(-0.518638\pi\) | ||||
−0.0585206 | + | 0.998286i | \(0.518638\pi\) | |||||||
\(74\) | −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 | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 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 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −9.00000 | −0.993884 | ||||||||
\(83\) | −0.275255 | − | 0.476756i | −0.0302132 | − | 0.0523308i | 0.850523 | − | 0.525937i | \(-0.176285\pi\) |
−0.880737 | + | 0.473606i | \(0.842952\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.72474 | + | 6.45145i | −0.401650 | + | 0.695677i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.44949 | + | 4.24264i | 0.261116 | + | 0.452267i | ||||
\(89\) | 9.00000 | 0.953998 | 0.476999 | − | 0.878904i | \(-0.341725\pi\) | ||||
0.476999 | + | 0.878904i | \(0.341725\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.7980 | 2.07539 | ||||||||
\(92\) | 1.22474 | + | 2.12132i | 0.127688 | + | 0.221163i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.550510 | + | 0.953512i | −0.0567808 | + | 0.0983472i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.39898 | + | 9.35131i | 0.548183 | + | 0.949481i | 0.998399 | + | 0.0565616i | \(0.0180137\pi\) |
−0.450216 | + | 0.892920i | \(0.648653\pi\) | |||||||
\(98\) | 12.7980 | 1.29279 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.77526 | + | 3.07483i | 0.176644 | + | 0.305957i | 0.940729 | − | 0.339159i | \(-0.110142\pi\) |
−0.764085 | + | 0.645116i | \(0.776809\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.34847 | − | 10.9959i | 0.625533 | − | 1.08346i | −0.362904 | − | 0.931826i | \(-0.618215\pi\) |
0.988437 | − | 0.151629i | \(-0.0484519\pi\) | |||||||
\(104\) | −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 | \(0.236236\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.4495 | 1.00088 | 0.500440 | − | 0.865771i | \(-0.333172\pi\) | ||||
0.500440 | + | 0.865771i | \(0.333172\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −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 | \(0.939860\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.44949 | −0.227429 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 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 | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.224745 | + | 0.389270i | 0.0201827 | + | 0.0349574i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.3485 | −1.00701 | −0.503507 | − | 0.863991i | \(-0.667957\pi\) | ||||
−0.503507 | + | 0.863991i | \(0.667957\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.89898 | − | 13.6814i | 0.690137 | − | 1.19535i | −0.281656 | − | 0.959516i | \(-0.590884\pi\) |
0.971793 | − | 0.235837i | \(-0.0757831\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −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 | \(0.792428\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 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 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.674235 | − | 1.16781i | −0.0565805 | − | 0.0980003i | ||||
\(143\) | −21.7980 | −1.82284 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.500000 | + | 0.866025i | 0.0413803 | + | 0.0716728i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.67423 | + | 2.89986i | −0.137621 | + | 0.238367i | ||||
\(149\) | −3.00000 | + | 5.19615i | −0.245770 | + | 0.425685i | −0.962348 | − | 0.271821i | \(-0.912374\pi\) |
0.716578 | + | 0.697507i | \(0.245707\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −21.7980 | −1.75653 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.101021 | − | 0.174973i | 0.00806231 | − | 0.0139643i | −0.861966 | − | 0.506966i | \(-0.830767\pi\) |
0.870028 | + | 0.493002i | \(0.164100\pi\) | |||||||
\(158\) | 6.34847 | − | 10.9959i | 0.505057 | − | 0.874785i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.8990 | −0.858960 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.55051 | 0.199771 | 0.0998857 | − | 0.994999i | \(-0.468152\pi\) | ||||
0.0998857 | + | 0.994999i | \(0.468152\pi\) | |||||||
\(164\) | 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 | \(0.892751\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.39898 | − | 5.88721i | −0.261460 | − | 0.452862i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.44949 | 0.568018 | ||||||||
\(173\) | −4.89898 | − | 8.48528i | −0.372463 | − | 0.645124i | 0.617481 | − | 0.786586i | \(-0.288153\pi\) |
−0.989944 | + | 0.141462i | \(0.954820\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.44949 | − | 4.24264i | 0.184637 | − | 0.319801i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.50000 | − | 7.79423i | −0.337289 | − | 0.584202i | ||||
\(179\) | 15.2474 | 1.13965 | 0.569824 | − | 0.821767i | \(-0.307011\pi\) | ||||
0.569824 | + | 0.821767i | \(0.307011\pi\) | |||||||
\(180\) | 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 | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.22474 | − | 2.12132i | 0.0902894 | − | 0.156386i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.0000 | + | 20.7846i | 0.877527 | + | 1.51992i | ||||
\(188\) | 1.10102 | 0.0803002 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.44949 | − | 9.43879i | −0.394311 | − | 0.682967i | 0.598702 | − | 0.800972i | \(-0.295683\pi\) |
−0.993013 | + | 0.118005i | \(0.962350\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.0000 | + | 17.3205i | −0.719816 | + | 1.24676i | 0.241257 | + | 0.970461i | \(0.422440\pi\) |
−0.961073 | + | 0.276296i | \(0.910893\pi\) | |||||||
\(194\) | 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 | \(0.831909\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.79796 | 0.411006 | 0.205503 | − | 0.978656i | \(-0.434117\pi\) | ||||
0.205503 | + | 0.978656i | \(0.434117\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.77526 | − | 3.07483i | 0.124907 | − | 0.216344i | ||||
\(203\) | 5.44949 | − | 9.43879i | 0.382479 | − | 0.662473i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −12.6969 | −0.884638 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 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 | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.62372 | − | 13.2047i | −0.521147 | − | 0.902653i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.00000 | −0.135769 | ||||||||
\(218\) | −5.22474 | − | 9.04952i | −0.353864 | − | 0.612911i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.8990 | + | 18.8776i | −0.733145 | + | 1.26984i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.898979 | + | 1.55708i | 0.0602001 | + | 0.104270i | 0.894555 | − | 0.446958i | \(-0.147493\pi\) |
−0.834355 | + | 0.551228i | \(0.814159\pi\) | |||||||
\(224\) | 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 | \(0.443431\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 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 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.22474 | + | 2.12132i | 0.0804084 | + | 0.139272i | ||||
\(233\) | −5.69694 | −0.373219 | −0.186609 | − | 0.982434i | \(-0.559750\pi\) | ||||
−0.186609 | + | 0.982434i | \(0.559750\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.275255 | − | 0.476756i | −0.0179176 | − | 0.0310342i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −10.8990 | + | 18.8776i | −0.706476 | + | 1.22365i | ||||
\(239\) | 4.77526 | − | 8.27098i | 0.308886 | − | 0.535006i | −0.669233 | − | 0.743052i | \(-0.733377\pi\) |
0.978119 | + | 0.208047i | \(0.0667107\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.00000 | 0.512148 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.67423 | + | 9.82806i | −0.361043 | + | 0.625345i | ||||
\(248\) | 0.224745 | − | 0.389270i | 0.0142713 | − | 0.0247186i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.44949 | 0.343969 | 0.171984 | − | 0.985100i | \(-0.444982\pi\) | ||||
0.171984 | + | 0.985100i | \(0.444982\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 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 | \(0.0986616\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.44949 | − | 12.9029i | −0.462889 | − | 0.801747i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −15.7980 | −0.976001 | ||||||||
\(263\) | 7.77526 | + | 13.4671i | 0.479443 | + | 0.830419i | 0.999722 | − | 0.0235770i | \(-0.00750547\pi\) |
−0.520279 | + | 0.853996i | \(0.674172\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5.67423 | + | 9.82806i | −0.347910 | + | 0.602597i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.17423 | + | 12.4261i | 0.438236 | + | 0.759047i | ||||
\(269\) | −9.55051 | −0.582305 | −0.291152 | − | 0.956677i | \(-0.594039\pi\) | ||||
−0.291152 | + | 0.956677i | \(0.594039\pi\) | |||||||
\(270\) | 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 | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.50000 | − | 2.59808i | 0.0906183 | − | 0.156956i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.22474 | + | 5.58542i | 0.193756 | + | 0.335595i | 0.946492 | − | 0.322727i | \(-0.104600\pi\) |
−0.752736 | + | 0.658323i | \(0.771266\pi\) | |||||||
\(278\) | −4.00000 | −0.239904 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.4495 | + | 25.0273i | 0.861984 | + | 1.49300i | 0.870011 | + | 0.493033i | \(0.164112\pi\) |
−0.00802643 | + | 0.999968i | \(0.502555\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.62372 | + | 9.74058i | −0.334296 | + | 0.579017i | −0.983349 | − | 0.181726i | \(-0.941832\pi\) |
0.649054 | + | 0.760743i | \(0.275165\pi\) | |||||||
\(284\) | −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 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.00000 | 0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 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 | \(0.861076\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.34847 | 0.194626 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 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 | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.27526 | − | 2.20881i | −0.0731409 | − | 0.126684i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.69694 | −0.382214 | −0.191107 | − | 0.981569i | \(-0.561208\pi\) | ||||
−0.191107 | + | 0.981569i | \(0.561208\pi\) | |||||||
\(308\) | 10.8990 | + | 18.8776i | 0.621027 | + | 1.07565i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.44949 | + | 9.43879i | −0.309012 | + | 0.535225i | −0.978147 | − | 0.207917i | \(-0.933332\pi\) |
0.669134 | + | 0.743141i | \(0.266665\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.94949 | − | 3.37662i | −0.110192 | − | 0.190858i | 0.805656 | − | 0.592384i | \(-0.201813\pi\) |
−0.915847 | + | 0.401526i | \(0.868480\pi\) | |||||||
\(314\) | −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 | \(0.993248\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.00000 | + | 10.3923i | −0.335936 | + | 0.581857i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.44949 | + | 9.43879i | 0.303688 | + | 0.526003i | ||||
\(323\) | 12.4949 | 0.695235 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.27526 | − | 2.20881i | −0.0706298 | − | 0.122334i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 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 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 19.5959 | 1.07224 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.55051 | − | 9.61377i | 0.302356 | − | 0.523695i | −0.674313 | − | 0.738445i | \(-0.735560\pi\) |
0.976669 | + | 0.214750i | \(0.0688937\pi\) | |||||||
\(338\) | −3.39898 | + | 5.88721i | −0.184880 | + | 0.320222i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.20204 | 0.119247 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 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 | \(0.0622790\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −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 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −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 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.50000 | + | 7.79423i | −0.238500 | + | 0.413093i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.62372 | − | 13.2047i | −0.402926 | − | 0.697889i | ||||
\(359\) | 33.7980 | 1.78379 | 0.891894 | − | 0.452244i | \(-0.149377\pi\) | ||||
0.891894 | + | 0.452244i | \(0.149377\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.4949 | −0.657626 | ||||||||
\(362\) | 0.898979 | + | 1.55708i | 0.0472493 | + | 0.0818382i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9.89898 | + | 17.1455i | −0.518848 | + | 0.898670i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.34847 | − | 14.4600i | −0.435787 | − | 0.754804i | 0.561573 | − | 0.827427i | \(-0.310196\pi\) |
−0.997359 | + | 0.0726228i | \(0.976863\pi\) | |||||||
\(368\) | −2.44949 | −0.127688 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.7980 | − | 32.5590i | −0.975941 | − | 1.69038i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.79796 | + | 13.5065i | −0.403763 | + | 0.699338i | −0.994177 | − | 0.107763i | \(-0.965631\pi\) |
0.590414 | + | 0.807101i | \(0.298965\pi\) | |||||||
\(374\) | 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 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.898979 | 0.0461775 | 0.0230887 | − | 0.999733i | \(-0.492650\pi\) | ||||
0.0230887 | + | 0.999733i | \(0.492650\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −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 | \(-0.0695147\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 20.0000 | 1.01797 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10.7980 | −0.548183 | ||||||||
\(389\) | −6.79796 | − | 11.7744i | −0.344670 | − | 0.596986i | 0.640624 | − | 0.767855i | \(-0.278676\pi\) |
−0.985294 | + | 0.170869i | \(0.945343\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.00000 | − | 10.3923i | 0.303433 | − | 0.525561i | ||||
\(392\) | −6.39898 | + | 11.0834i | −0.323197 | + | 0.559794i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.1237 | + | 20.9989i | 0.610784 | + | 1.05791i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.5959 | 1.08387 | 0.541934 | − | 0.840421i | \(-0.317692\pi\) | ||||
0.541934 | + | 0.840421i | \(0.317692\pi\) | |||||||
\(398\) | −2.89898 | − | 5.02118i | −0.145313 | − | 0.251689i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.65153 | − | 8.05669i | 0.232286 | − | 0.402332i | −0.726194 | − | 0.687490i | \(-0.758713\pi\) |
0.958481 | + | 0.285158i | \(0.0920460\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 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 | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −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 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.34847 | + | 10.9959i | 0.312767 | + | 0.541728i | ||||
\(413\) | 2.44949 | 0.120532 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.22474 | − | 3.85337i | −0.109077 | − | 0.188927i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.24745 | − | 10.8209i | 0.305573 | − | 0.529267i | ||||
\(419\) | 4.07321 | − | 7.05501i | 0.198990 | − | 0.344660i | −0.749212 | − | 0.662331i | \(-0.769567\pi\) |
0.948201 | + | 0.317671i | \(0.102901\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.44949 | 0.410343 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.7980 | + | 30.8270i | −0.861304 | + | 1.49182i | ||||
\(428\) | −7.62372 | + | 13.2047i | −0.368507 | + | 0.638272i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.6515 | −0.513066 | −0.256533 | − | 0.966535i | \(-0.582580\pi\) | ||||
−0.256533 | + | 0.966535i | \(0.582580\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.5959 | −1.42229 | −0.711145 | − | 0.703046i | \(-0.751823\pi\) | ||||
−0.711145 | + | 0.703046i | \(0.751823\pi\) | |||||||
\(434\) | 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 | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 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 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 21.7980 | 1.03682 | ||||||||
\(443\) | 13.8990 | + | 24.0737i | 0.660360 | + | 1.14378i | 0.980521 | + | 0.196415i | \(0.0629298\pi\) |
−0.320161 | + | 0.947363i | \(0.603737\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.898979 | − | 1.55708i | 0.0425679 | − | 0.0737298i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.22474 | − | 3.85337i | −0.105109 | − | 0.182055i | ||||
\(449\) | −10.5959 | −0.500052 | −0.250026 | − | 0.968239i | \(-0.580439\pi\) | ||||
−0.250026 | + | 0.968239i | \(0.580439\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 44.0908 | 2.07616 | ||||||||
\(452\) | −6.94949 | − | 12.0369i | −0.326877 | − | 0.566167i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.1742 | − | 24.5505i | 0.665230 | − | 1.15221i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.84847 | + | 13.5939i | 0.367136 | + | 0.635898i | 0.989116 | − | 0.147135i | \(-0.0470051\pi\) |
−0.621981 | + | 0.783033i | \(0.713672\pi\) | |||||||
\(458\) | −21.1464 | −0.988108 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.67423 | + | 16.7563i | 0.450574 | + | 0.780417i | 0.998422 | − | 0.0561610i | \(-0.0178860\pi\) |
−0.547848 | + | 0.836578i | \(0.684553\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.67423 | + | 8.09601i | −0.217230 | + | 0.376254i | −0.953960 | − | 0.299933i | \(-0.903036\pi\) |
0.736730 | + | 0.676187i | \(0.236369\pi\) | |||||||
\(464\) | 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 | \(0.532080\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −63.8434 | −2.94801 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.275255 | + | 0.476756i | −0.0126696 | + | 0.0219445i | ||||
\(473\) | 18.2474 | − | 31.6055i | 0.839019 | − | 1.45322i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 21.7980 | 0.999108 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.55051 | −0.436830 | ||||||||
\(479\) | −12.1237 | − | 20.9989i | −0.553947 | − | 0.959465i | −0.997985 | − | 0.0634563i | \(-0.979788\pi\) |
0.444038 | − | 0.896008i | \(-0.353546\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.44949 | + | 12.9029i | −0.339667 | + | 0.588321i | ||||
\(482\) | 11.3990 | − | 19.7436i | 0.519209 | − | 0.899297i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.50000 | − | 11.2583i | −0.295455 | − | 0.511742i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.5505 | −0.885918 | −0.442959 | − | 0.896542i | \(-0.646071\pi\) | ||||
−0.442959 | + | 0.896542i | \(0.646071\pi\) | |||||||
\(488\) | −4.00000 | − | 6.92820i | −0.181071 | − | 0.313625i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.37628 | + | 2.38378i | −0.0621105 | + | 0.107578i | −0.895409 | − | 0.445245i | \(-0.853116\pi\) |
0.833298 | + | 0.552824i | \(0.186450\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 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 | 0 | ||||||||
\(499\) | −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 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.72474 | − | 4.71940i | −0.121611 | − | 0.210637i | ||||
\(503\) | −26.4495 | −1.17932 | −0.589662 | − | 0.807650i | \(-0.700739\pi\) | ||||
−0.589662 | + | 0.807650i | \(0.700739\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6.00000 | − | 10.3923i | −0.266733 | − | 0.461994i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 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 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.79796 | −0.299845 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.69694 | − | 4.67123i | 0.118611 | − | 0.205441i | ||||
\(518\) | −7.44949 | + | 12.9029i | −0.327312 | + | 0.566921i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.3939 | −1.28777 | −0.643885 | − | 0.765123i | \(-0.722678\pi\) | ||||
−0.643885 | + | 0.765123i | \(0.722678\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.65153 | −0.247124 | −0.123562 | − | 0.992337i | \(-0.539432\pi\) | ||||
−0.123562 | + | 0.992337i | \(0.539432\pi\) | |||||||
\(524\) | 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 | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.50000 | + | 14.7224i | 0.369565 | + | 0.640106i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 11.3485 | 0.492019 | ||||||||
\(533\) | 20.0227 | + | 34.6803i | 0.867280 | + | 1.50217i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 7.17423 | − | 12.4261i | 0.309880 | − | 0.536727i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 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 | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.44949 | + | 4.24264i | −0.105021 | + | 0.181902i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.1742 | − | 26.2825i | −0.648803 | − | 1.12376i | −0.983409 | − | 0.181402i | \(-0.941936\pi\) |
0.334606 | − | 0.942358i | \(-0.391397\pi\) | |||||||
\(548\) | −3.00000 | −0.128154 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.12372 | + | 5.41045i | 0.133075 | + | 0.230493i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 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 | 0 | ||||||||
\(559\) | 33.1464 | 1.40194 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 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 | \(-0.0506897\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 11.2474 | 0.472766 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.34847 | 0.0565805 | ||||||||
\(569\) | 7.10102 | + | 12.2993i | 0.297690 | + | 0.515615i | 0.975607 | − | 0.219524i | \(-0.0704504\pi\) |
−0.677917 | + | 0.735139i | \(0.737117\pi\) | |||||||
\(570\) | 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 | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 20.0227 | + | 34.6803i | 0.835732 | + | 1.44753i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.3939 | −0.765747 | −0.382874 | − | 0.923801i | \(-0.625066\pi\) | ||||
−0.382874 | + | 0.923801i | \(0.625066\pi\) | |||||||
\(578\) | −3.50000 | − | 6.06218i | −0.145581 | − | 0.252153i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.22474 | + | 2.12132i | −0.0508110 | + | 0.0880072i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 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 | \(0.815608\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.573214 | − | 0.992836i | 0.0236189 | − | 0.0409091i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.67423 | − | 2.89986i | −0.0688106 | − | 0.119183i | ||||
\(593\) | −1.89898 | −0.0779817 | −0.0389909 | − | 0.999240i | \(-0.512414\pi\) | ||||
−0.0389909 | + | 0.999240i | \(0.512414\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.00000 | − | 5.19615i | −0.122885 | − | 0.212843i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.44949 | − | 9.43879i | 0.222846 | − | 0.385981i | ||||
\(599\) | −18.6742 | + | 32.3447i | −0.763009 | + | 1.32157i | 0.178285 | + | 0.983979i | \(0.442945\pi\) |
−0.941293 | + | 0.337591i | \(0.890388\pi\) | |||||||
\(600\) | 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 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 20.0000 | 0.813788 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.67423 | − | 9.82806i | 0.230310 | − | 0.398909i | −0.727589 | − | 0.686013i | \(-0.759359\pi\) |
0.957899 | + | 0.287104i | \(0.0926926\pi\) | |||||||
\(608\) | −1.27526 | + | 2.20881i | −0.0517184 | + | 0.0895789i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.89898 | 0.198191 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.0454 | −1.29430 | −0.647151 | − | 0.762362i | \(-0.724040\pi\) | ||||
−0.647151 | + | 0.762362i | \(0.724040\pi\) | |||||||
\(614\) | 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 | \(0.260235\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −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 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.8990 | 0.437009 | ||||||||
\(623\) | −20.0227 | − | 34.6803i | −0.802193 | − | 1.38944i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.94949 | + | 3.37662i | −0.0779173 | + | 0.134957i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 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 | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.57321 | + | 14.8492i | −0.340486 | + | 0.589739i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −28.4722 | − | 49.3153i | −1.12811 | − | 1.95394i | ||||
\(638\) | 12.0000 | 0.475085 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.1969 | + | 38.4462i | 0.876726 | + | 1.51853i | 0.854912 | + | 0.518773i | \(0.173611\pi\) |
0.0218141 | + | 0.999762i | \(0.493056\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.1742 | − | 28.0146i | 0.637850 | − | 1.10479i | −0.348054 | − | 0.937474i | \(-0.613157\pi\) |
0.985904 | − | 0.167313i | \(-0.0535092\pi\) | |||||||
\(644\) | 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 | \(0.498452\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.69694 | −0.105864 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −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 | \(0.205675\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −9.00000 | −0.351391 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.89898 | 0.190982 | ||||||||
\(659\) | 22.0732 | + | 38.2319i | 0.859850 | + | 1.48930i | 0.872071 | + | 0.489379i | \(0.162777\pi\) |
−0.0122208 | + | 0.999925i | \(0.503890\pi\) | |||||||
\(660\) | 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 | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.275255 | − | 0.476756i | −0.0106820 | − | 0.0185017i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.00000 | 0.232321 | ||||||||
\(668\) | −9.79796 | − | 16.9706i | −0.379094 | − | 0.656611i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.5959 | − | 33.9411i | 0.756492 | − | 1.31028i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.34847 | + | 5.79972i | 0.129074 | + | 0.223563i | 0.923318 | − | 0.384036i | \(-0.125466\pi\) |
−0.794244 | + | 0.607599i | \(0.792133\pi\) | |||||||
\(674\) | −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 | \(0.574146\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.0227 | − | 41.6085i | 0.921907 | − | 1.59679i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.10102 | − | 1.90702i | −0.0421603 | − | 0.0730237i | ||||
\(683\) | 11.9444 | 0.457039 | 0.228520 | − | 0.973539i | \(-0.426611\pi\) | ||||
0.228520 | + | 0.973539i | \(0.426611\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −12.8990 | − | 22.3417i | −0.492485 | − | 0.853010i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −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 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.0000 | −0.455514 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.0454 | − | 38.1838i | 0.835029 | − | 1.44631i | ||||
\(698\) | −7.00000 | + | 12.1244i | −0.264954 | + | 0.458914i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.2020 | −0.536404 | −0.268202 | − | 0.963363i | \(-0.586429\pi\) | ||||
−0.268202 | + | 0.963363i | \(0.586429\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 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 | 0 | ||||||||
\(709\) | 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 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.00000 | 0.337289 | ||||||||
\(713\) | −0.550510 | − | 0.953512i | −0.0206168 | − | 0.0357093i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.62372 | + | 13.2047i | −0.284912 | + | 0.493482i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −16.8990 | − | 29.2699i | −0.630664 | − | 1.09234i | ||||
\(719\) | −52.0454 | −1.94097 | −0.970483 | − | 0.241169i | \(-0.922469\pi\) | ||||
−0.970483 | + | 0.241169i | \(0.922469\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −56.4949 | −2.10398 | ||||||||
\(722\) | 6.24745 | + | 10.8209i | 0.232506 | + | 0.402712i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.898979 | − | 1.55708i | 0.0334103 | − | 0.0578684i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.00000 | + | 13.8564i | 0.296704 | + | 0.513906i | 0.975380 | − | 0.220532i | \(-0.0707793\pi\) |
−0.678676 | + | 0.734438i | \(0.737446\pi\) | |||||||
\(728\) | 19.7980 | 0.733761 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.2474 | − | 31.6055i | −0.674906 | − | 1.16897i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.0000 | + | 22.5167i | −0.480166 | + | 0.831672i | −0.999741 | − | 0.0227529i | \(-0.992757\pi\) |
0.519575 | + | 0.854425i | \(0.326090\pi\) | |||||||
\(734\) | −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 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −41.0454 | −1.50988 | −0.754940 | − | 0.655794i | \(-0.772334\pi\) | ||||
−0.754940 | + | 0.655794i | \(0.772334\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −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 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 15.5959 | 0.571007 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −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 | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.44949 | + | 9.43879i | 0.198459 | + | 0.343741i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.04541 | 0.219724 | 0.109862 | − | 0.993947i | \(-0.464959\pi\) | ||||
0.109862 | + | 0.993947i | \(0.464959\pi\) | |||||||
\(758\) | −0.449490 | − | 0.778539i | −0.0163262 | − | 0.0282778i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.05051 | − | 3.55159i | 0.0743309 | − | 0.128745i | −0.826464 | − | 0.562989i | \(-0.809651\pi\) |
0.900795 | + | 0.434244i | \(0.142985\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −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 | 0 | ||||||||
\(769\) | −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 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −10.0000 | − | 17.3205i | −0.359908 | − | 0.623379i | ||||
\(773\) | 49.5959 | 1.78384 | 0.891921 | − | 0.452192i | \(-0.149358\pi\) | ||||
0.891921 | + | 0.452192i | \(0.149358\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5.39898 | + | 9.35131i | 0.193812 | + | 0.335692i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −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 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 12.7980 | 0.457070 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.65153 | + | 4.59259i | −0.0945169 | + | 0.163708i | −0.909407 | − | 0.415908i | \(-0.863464\pi\) |
0.814890 | + | 0.579616i | \(0.196797\pi\) | |||||||
\(788\) | 12.1237 | − | 20.9989i | 0.431890 | − | 0.748055i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 61.8434 | 2.19890 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 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 | \(0.199153\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.69694 | − | 4.67123i | −0.0954108 | − | 0.165256i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.30306 | −0.328503 | ||||||||
\(803\) | −2.44949 | − | 4.24264i | −0.0864406 | − | 0.149720i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.00000 | − | 1.73205i | 0.0352235 | − | 0.0610089i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.77526 | + | 3.07483i | 0.0624533 | + | 0.108172i | ||||
\(809\) | 35.6969 | 1.25504 | 0.627519 | − | 0.778601i | \(-0.284071\pi\) | ||||
0.627519 | + | 0.778601i | \(0.284071\pi\) | |||||||
\(810\) | 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 | 0 | ||||||||
\(814\) | 8.20204 | − | 14.2064i | 0.287481 | − | 0.497932i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.50000 | − | 16.4545i | −0.332363 | − | 0.575669i | ||||
\(818\) | 9.89898 | 0.346110 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.5959 | − | 44.3334i | −0.893304 | − | 1.54725i | −0.835890 | − | 0.548897i | \(-0.815048\pi\) |
−0.0574136 | − | 0.998350i | \(-0.518285\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.4495 | − | 23.2952i | 0.468820 | − | 0.812020i | −0.530545 | − | 0.847657i | \(-0.678013\pi\) |
0.999365 | + | 0.0356371i | \(0.0113461\pi\) | |||||||
\(824\) | 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 | \(0.600997\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.7423 | 0.928800 | 0.464400 | − | 0.885626i | \(-0.346270\pi\) | ||||
0.464400 | + | 0.885626i | \(0.346270\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.22474 | + | 3.85337i | −0.0771292 | + | 0.133592i | ||||
\(833\) | −31.3485 | + | 54.2971i | −1.08616 | + | 1.88128i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −12.4949 | −0.432145 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8.14643 | −0.281414 | ||||||||
\(839\) | 11.3258 | + | 19.6168i | 0.391009 | + | 0.677247i | 0.992583 | − | 0.121570i | \(-0.0387928\pi\) |
−0.601574 | + | 0.798817i | \(0.705460\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.5000 | − | 19.9186i | 0.396552 | − | 0.686848i | ||||
\(842\) | −9.02270 | + | 15.6278i | −0.310943 | + | 0.538569i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.724745 | − | 1.25529i | −0.0249467 | − | 0.0432090i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 57.8434 | 1.98752 | ||||||||
\(848\) | −4.22474 | − | 7.31747i | −0.145078 | − | 0.251283i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.10102 | − | 7.10318i | 0.140581 | − | 0.243494i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.0000 | + | 39.8372i | 0.787505 | + | 1.36400i | 0.927491 | + | 0.373845i | \(0.121961\pi\) |
−0.139986 | + | 0.990153i | \(0.544706\pi\) | |||||||
\(854\) | 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 | \(-0.406826\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 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 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.32577 | + | 9.22450i | 0.181396 | + | 0.314188i | ||||
\(863\) | −19.8434 | −0.675476 | −0.337738 | − | 0.941240i | \(-0.609662\pi\) | ||||
−0.337738 | + | 0.941240i | \(0.609662\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 14.7980 | + | 25.6308i | 0.502855 | + | 0.870971i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 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 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.24745 | −0.211323 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.10102 | − | 10.5673i | 0.206017 | − | 0.356832i | −0.744439 | − | 0.667690i | \(-0.767283\pi\) |
0.950456 | + | 0.310858i | \(0.100617\pi\) | |||||||
\(878\) | 5.67423 | − | 9.82806i | 0.191496 | − | 0.331681i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.30306 | −0.313428 | −0.156714 | − | 0.987644i | \(-0.550090\pi\) | ||||
−0.156714 | + | 0.987644i | \(0.550090\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.2020 | 0.949074 | 0.474537 | − | 0.880235i | \(-0.342615\pi\) | ||||
0.474537 | + | 0.880235i | \(0.342615\pi\) | |||||||
\(884\) | −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 | \(-0.201048\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 25.2474 | + | 43.7299i | 0.846772 | + | 1.46665i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.79796 | −0.0602001 | ||||||||
\(893\) | −1.40408 | − | 2.43194i | −0.0469858 | − | 0.0813818i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.22474 | + | 3.85337i | −0.0743235 | + | 0.128732i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 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 | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.94949 | + | 12.0369i | −0.231137 | + | 0.400340i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.8258 | − | 18.7508i | −0.359464 | − | 0.622609i | 0.628408 | − | 0.777884i | \(-0.283707\pi\) |
−0.987871 | + | 0.155275i | \(0.950374\pi\) | |||||||
\(908\) | −28.3485 | −0.940777 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.67423 | + | 6.36396i | 0.121733 | + | 0.210847i | 0.920451 | − | 0.390858i | \(-0.127822\pi\) |
−0.798718 | + | 0.601705i | \(0.794488\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 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 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.3485 | −0.374351 | −0.187176 | − | 0.982326i | \(-0.559933\pi\) | ||||
−0.187176 | + | 0.982326i | \(0.559933\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9.67423 | − | 16.7563i | 0.318604 | − | 0.551838i | ||||
\(923\) | −3.00000 | + | 5.19615i | −0.0987462 | + | 0.171033i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9.34847 | 0.307210 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.44949 | −0.0804084 | ||||||||
\(929\) | 13.5959 | + | 23.5488i | 0.446068 | + | 0.772612i | 0.998126 | − | 0.0611938i | \(-0.0194908\pi\) |
−0.552058 | + | 0.833806i | \(0.686157\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.3207 | + | 28.2682i | −0.534888 | + | 0.926453i | ||||
\(932\) | 2.84847 | − | 4.93369i | 0.0933047 | − | 0.161609i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.17423 | + | 3.76588i | 0.0711431 | + | 0.123224i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.7980 | 0.875451 | 0.437726 | − | 0.899109i | \(-0.355784\pi\) | ||||
0.437726 | + | 0.899109i | \(0.355784\pi\) | |||||||
\(938\) | 31.9217 | + | 55.2900i | 1.04228 | + | 1.80528i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.8207 | + | 25.6701i | −0.483140 | + | 0.836823i | −0.999813 | − | 0.0193603i | \(-0.993837\pi\) |
0.516673 | + | 0.856183i | \(0.327170\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −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 | \(0.875589\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.22474 | − | 3.85337i | 0.0722183 | − | 0.125086i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −10.8990 | − | 18.8776i | −0.353238 | − | 0.611826i | ||||
\(953\) | −21.7980 | −0.706105 | −0.353053 | − | 0.935603i | \(-0.614856\pi\) | ||||
−0.353053 | + | 0.935603i | \(0.614856\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4.77526 | + | 8.27098i | 0.154443 | + | 0.267503i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −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 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −22.7980 | −0.734273 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.0000 | + | 27.7128i | −0.514525 | + | 0.891184i | 0.485333 | + | 0.874330i | \(0.338699\pi\) |
−0.999858 | + | 0.0168544i | \(0.994635\pi\) | |||||||
\(968\) | −6.50000 | + | 11.2583i | −0.208918 | + | 0.361856i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.8434 | −0.733079 | −0.366539 | − | 0.930403i | \(-0.619457\pi\) | ||||
−0.366539 | + | 0.930403i | \(0.619457\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −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 | \(0.212653\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.0454 | + | 38.1838i | 0.704574 | + | 1.22036i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.75255 | 0.0878374 | ||||||||
\(983\) | −11.4495 | − | 19.8311i | −0.365182 | − | 0.632514i | 0.623623 | − | 0.781725i | \(-0.285660\pi\) |
−0.988805 | + | 0.149211i | \(0.952327\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.00000 | − | 10.3923i | 0.191079 | − | 0.330958i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −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 | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.00000 | + | 5.19615i | −0.0951542 | + | 0.164812i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.0227 | − | 31.2162i | −0.570785 | − | 0.988628i | −0.996486 | − | 0.0837642i | \(-0.973306\pi\) |
0.425701 | − | 0.904864i | \(-0.360028\pi\) | |||||||
\(998\) | 6.34847 | 0.200957 | ||||||||
\(999\) | 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 | 1350.2.e.k.901.1 | 4 | ||
3.2 | odd | 2 | 450.2.e.m.301.2 | yes | 4 | ||
5.2 | odd | 4 | 1350.2.j.g.199.4 | 8 | |||
5.3 | odd | 4 | 1350.2.j.g.199.1 | 8 | |||
5.4 | even | 2 | 1350.2.e.n.901.2 | 4 | |||
9.2 | odd | 6 | 450.2.e.m.151.1 | yes | 4 | ||
9.4 | even | 3 | 4050.2.a.by.1.2 | 2 | |||
9.5 | odd | 6 | 4050.2.a.br.1.2 | 2 | |||
9.7 | even | 3 | inner | 1350.2.e.k.451.1 | 4 | ||
15.2 | even | 4 | 450.2.j.f.49.2 | 8 | |||
15.8 | even | 4 | 450.2.j.f.49.3 | 8 | |||
15.14 | odd | 2 | 450.2.e.l.301.1 | yes | 4 | ||
45.2 | even | 12 | 450.2.j.f.349.3 | 8 | |||
45.4 | even | 6 | 4050.2.a.bl.1.1 | 2 | |||
45.7 | odd | 12 | 1350.2.j.g.1099.1 | 8 | |||
45.13 | odd | 12 | 4050.2.c.w.649.1 | 4 | |||
45.14 | odd | 6 | 4050.2.a.bu.1.1 | 2 | |||
45.22 | odd | 12 | 4050.2.c.w.649.4 | 4 | |||
45.23 | even | 12 | 4050.2.c.y.649.3 | 4 | |||
45.29 | odd | 6 | 450.2.e.l.151.2 | ✓ | 4 | ||
45.32 | even | 12 | 4050.2.c.y.649.2 | 4 | |||
45.34 | even | 6 | 1350.2.e.n.451.2 | 4 | |||
45.38 | even | 12 | 450.2.j.f.349.2 | 8 | |||
45.43 | odd | 12 | 1350.2.j.g.1099.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.2.e.l.151.2 | ✓ | 4 | 45.29 | odd | 6 | ||
450.2.e.l.301.1 | yes | 4 | 15.14 | odd | 2 | ||
450.2.e.m.151.1 | yes | 4 | 9.2 | odd | 6 | ||
450.2.e.m.301.2 | yes | 4 | 3.2 | odd | 2 | ||
450.2.j.f.49.2 | 8 | 15.2 | even | 4 | |||
450.2.j.f.49.3 | 8 | 15.8 | even | 4 | |||
450.2.j.f.349.2 | 8 | 45.38 | even | 12 | |||
450.2.j.f.349.3 | 8 | 45.2 | even | 12 | |||
1350.2.e.k.451.1 | 4 | 9.7 | even | 3 | inner | ||
1350.2.e.k.901.1 | 4 | 1.1 | even | 1 | trivial | ||
1350.2.e.n.451.2 | 4 | 45.34 | even | 6 | |||
1350.2.e.n.901.2 | 4 | 5.4 | even | 2 | |||
1350.2.j.g.199.1 | 8 | 5.3 | odd | 4 | |||
1350.2.j.g.199.4 | 8 | 5.2 | odd | 4 | |||
1350.2.j.g.1099.1 | 8 | 45.7 | odd | 12 | |||
1350.2.j.g.1099.4 | 8 | 45.43 | odd | 12 | |||
4050.2.a.bl.1.1 | 2 | 45.4 | even | 6 | |||
4050.2.a.br.1.2 | 2 | 9.5 | odd | 6 | |||
4050.2.a.bu.1.1 | 2 | 45.14 | odd | 6 | |||
4050.2.a.by.1.2 | 2 | 9.4 | even | 3 | |||
4050.2.c.w.649.1 | 4 | 45.13 | odd | 12 | |||
4050.2.c.w.649.4 | 4 | 45.22 | odd | 12 | |||
4050.2.c.y.649.2 | 4 | 45.32 | even | 12 | |||
4050.2.c.y.649.3 | 4 | 45.23 | even | 12 |