Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,2,Mod(31,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.bb (of order \(6\), 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: | \(10.7318940317\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 15x^{10} + 84x^{8} - 187x^{6} + 141x^{4} + 108x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.2 | ||
Root | \(-1.51496 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.31 |
Dual form | 1344.2.bb.e.607.2 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.727452 | − | 1.25998i | −0.325326 | − | 0.563482i | 0.656252 | − | 0.754542i | \(-0.272141\pi\) |
−0.981578 | + | 0.191060i | \(0.938808\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.51496 | + | 2.16908i | −0.572600 | + | 0.819835i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.12100 | − | 1.94163i | 0.337994 | − | 0.585423i | −0.646061 | − | 0.763285i | \(-0.723585\pi\) |
0.984055 | + | 0.177863i | \(0.0569183\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.88325 | 1.35437 | 0.677185 | − | 0.735812i | \(-0.263199\pi\) | ||||
0.677185 | + | 0.735812i | \(0.263199\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.45490i | 0.375655i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.12398 | − | 2.38098i | −1.00021 | − | 0.577473i | −0.0919016 | − | 0.995768i | \(-0.529295\pi\) |
−0.908311 | + | 0.418295i | \(0.862628\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.393958 | − | 0.227452i | 0.0903803 | − | 0.0521811i | −0.454129 | − | 0.890936i | \(-0.650049\pi\) |
0.544509 | + | 0.838755i | \(0.316716\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.39653 | − | 1.12100i | 0.522966 | − | 0.244622i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.62298 | + | 2.66908i | −0.963958 | + | 0.556541i | −0.897389 | − | 0.441240i | \(-0.854539\pi\) |
−0.0665691 | + | 0.997782i | \(0.521205\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.44163 | − | 2.49697i | 0.288325 | − | 0.499394i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.22210i | 0.226939i | 0.993541 | + | 0.113469i | \(0.0361964\pi\) | ||||
−0.993541 | + | 0.113469i | \(0.963804\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.217093 | − | 0.376017i | 0.0389911 | − | 0.0675346i | −0.845871 | − | 0.533387i | \(-0.820919\pi\) |
0.884862 | + | 0.465852i | \(0.154252\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.94163 | + | 1.12100i | −0.337994 | + | 0.195141i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.83506 | + | 0.330921i | 0.648244 | + | 0.0559358i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.80634 | − | 2.77494i | 0.790157 | − | 0.456198i | −0.0498606 | − | 0.998756i | \(-0.515878\pi\) |
0.840018 | + | 0.542559i | \(0.182544\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.22902 | − | 2.44163i | −0.677185 | − | 0.390973i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.05983i | − | 0.946386i | −0.880959 | − | 0.473193i | \(-0.843101\pi\) | ||
0.880959 | − | 0.473193i | \(-0.156899\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.27191 | −0.803959 | −0.401980 | − | 0.915649i | \(-0.631678\pi\) | ||||
−0.401980 | + | 0.915649i | \(0.631678\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.727452 | − | 1.25998i | 0.108442 | − | 0.187827i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.59307 | − | 2.75927i | −0.232373 | − | 0.402481i | 0.726133 | − | 0.687554i | \(-0.241316\pi\) |
−0.958506 | + | 0.285073i | \(0.907982\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.40981 | − | 6.57212i | −0.344258 | − | 0.938875i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.38098 | + | 4.12398i | 0.333404 | + | 0.577473i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.06561 | − | 5.23403i | −1.24526 | − | 0.718950i | −0.275098 | − | 0.961416i | \(-0.588710\pi\) |
−0.970160 | + | 0.242467i | \(0.922044\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.26189 | −0.439833 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.454904 | −0.0602535 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.82976 | − | 4.52051i | −1.01935 | − | 0.588521i | −0.105433 | − | 0.994426i | \(-0.533623\pi\) |
−0.913915 | + | 0.405906i | \(0.866956\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.45490 | − | 4.25202i | −0.314318 | − | 0.544415i | 0.664974 | − | 0.746866i | \(-0.268443\pi\) |
−0.979292 | + | 0.202451i | \(0.935109\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.63596 | − | 0.227452i | −0.332099 | − | 0.0286563i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.55233 | − | 6.15282i | −0.440613 | − | 0.763164i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.12601 | − | 3.68236i | 0.259733 | − | 0.449871i | −0.706437 | − | 0.707776i | \(-0.749699\pi\) |
0.966170 | + | 0.257904i | \(0.0830320\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.33816 | 0.642639 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.3382i | 1.34559i | 0.739828 | + | 0.672796i | \(0.234907\pi\) | ||||
−0.739828 | + | 0.672796i | \(0.765093\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.6896 | − | 6.74899i | −1.36816 | − | 0.789910i | −0.377470 | − | 0.926022i | \(-0.623206\pi\) |
−0.990693 | + | 0.136112i | \(0.956539\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.49697 | + | 1.44163i | −0.288325 | + | 0.166465i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.51328 | + | 5.37302i | 0.286415 | + | 0.612312i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.5289 | + | 6.07889i | −1.18460 | + | 0.683928i | −0.957074 | − | 0.289844i | \(-0.906397\pi\) |
−0.227525 | + | 0.973772i | \(0.573063\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 15.0410i | − | 1.65097i | −0.564426 | − | 0.825484i | \(-0.690902\pi\) | ||
0.564426 | − | 0.825484i | \(-0.309098\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.92820i | 0.751469i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.611052 | − | 1.05837i | 0.0655116 | − | 0.113469i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.7665 | − | 7.94810i | 1.45925 | − | 0.842497i | 0.460273 | − | 0.887778i | \(-0.347752\pi\) |
0.998974 | + | 0.0452810i | \(0.0144183\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.39792 | + | 10.5922i | −0.775513 | + | 1.11036i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.376017 | + | 0.217093i | −0.0389911 | + | 0.0225115i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.573172 | − | 0.330921i | −0.0588062 | − | 0.0339518i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.7460i | 1.09109i | 0.838080 | + | 0.545547i | \(0.183678\pi\) | ||||
−0.838080 | + | 0.545547i | \(0.816322\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.24200 | 0.225329 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.0901918 | − | 0.156217i | 0.00897442 | − | 0.0155442i | −0.861503 | − | 0.507752i | \(-0.830477\pi\) |
0.870478 | + | 0.492208i | \(0.163810\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.12601 | + | 3.68236i | 0.209482 | + | 0.362833i | 0.951551 | − | 0.307490i | \(-0.0994889\pi\) |
−0.742070 | + | 0.670323i | \(0.766156\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.15580 | − | 2.20412i | −0.307975 | − | 0.215100i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.71803 | − | 16.8321i | −0.939477 | − | 1.62722i | −0.766449 | − | 0.642305i | \(-0.777978\pi\) |
−0.173029 | − | 0.984917i | \(-0.555355\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.57285 | + | 5.52689i | 0.916912 | + | 0.529380i | 0.882649 | − | 0.470033i | \(-0.155758\pi\) |
0.0342637 | + | 0.999413i | \(0.489091\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.54988 | −0.526772 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.06758 | −0.758934 | −0.379467 | − | 0.925205i | \(-0.623893\pi\) | ||||
−0.379467 | + | 0.925205i | \(0.623893\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.72599 | + | 3.88325i | 0.627202 | + | 0.362115i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.44163 | + | 4.22902i | 0.225728 | + | 0.390973i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.4122 | − | 5.33816i | 1.04615 | − | 0.489348i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.98672 | + | 5.17316i | 0.271520 | + | 0.470287i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.02991 | + | 5.24797i | −0.273198 | + | 0.473193i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.4694 | −1.02585 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1.24797i | − | 0.110739i | −0.998466 | − | 0.0553696i | \(-0.982366\pi\) | ||
0.998466 | − | 0.0553696i | \(-0.0176337\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.56561 | + | 2.63596i | 0.401980 | + | 0.232083i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.73662 | − | 2.73469i | 0.413840 | − | 0.238931i | −0.278598 | − | 0.960408i | \(-0.589870\pi\) |
0.692439 | + | 0.721477i | \(0.256536\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.103469 | + | 1.19911i | −0.00897189 | + | 0.103976i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.25998 | + | 0.727452i | −0.108442 | + | 0.0626091i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.54510 | + | 7.87234i | −0.388314 | + | 0.672579i | −0.992223 | − | 0.124474i | \(-0.960276\pi\) |
0.603909 | + | 0.797053i | \(0.293609\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 6.63529i | − | 0.562798i | −0.959591 | − | 0.281399i | \(-0.909202\pi\) | ||
0.959591 | − | 0.281399i | \(-0.0907984\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.18613i | 0.268321i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.47412 | − | 9.48146i | 0.457769 | − | 0.792879i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.53983 | − | 0.889022i | 0.127876 | − | 0.0738293i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.19911 | + | 6.89653i | −0.0989007 | + | 0.568816i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.75203 | − | 2.16624i | 0.307379 | − | 0.177465i | −0.338374 | − | 0.941012i | \(-0.609877\pi\) |
0.645753 | + | 0.763547i | \(0.276544\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.0073 | − | 10.3965i | −1.46541 | − | 0.846058i | −0.466162 | − | 0.884699i | \(-0.654364\pi\) |
−0.999253 | + | 0.0386418i | \(0.987697\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 4.76197i | − | 0.384982i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.631700 | −0.0507394 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.88325 | − | 15.3862i | 0.708961 | − | 1.22796i | −0.256282 | − | 0.966602i | \(-0.582498\pi\) |
0.965243 | − | 0.261354i | \(-0.0841691\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.23403 | + | 9.06561i | 0.415086 | + | 0.718950i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.21417 | − | 14.0712i | 0.0956904 | − | 1.10896i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.02991 | + | 5.24797i | 0.237321 | + | 0.411052i | 0.959945 | − | 0.280189i | \(-0.0903973\pi\) |
−0.722623 | + | 0.691242i | \(0.757064\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.82488 | + | 1.63095i | 0.219917 | + | 0.126969i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.2659 | 0.794396 | 0.397198 | − | 0.917733i | \(-0.369983\pi\) | ||||
0.397198 | + | 0.917733i | \(0.369983\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.8462 | 0.834321 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.393958 | + | 0.227452i | 0.0301268 | + | 0.0173937i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.66908 | − | 15.0153i | −0.659098 | − | 1.14159i | −0.980850 | − | 0.194767i | \(-0.937605\pi\) |
0.321752 | − | 0.946824i | \(-0.395728\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.23212 | + | 6.90981i | 0.244326 | + | 0.522332i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.52051 | + | 7.82976i | 0.339783 | + | 0.588521i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.41090 | − | 9.37195i | 0.404429 | − | 0.700492i | −0.589825 | − | 0.807531i | \(-0.700803\pi\) |
0.994255 | + | 0.107038i | \(0.0341368\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.88325 | −0.362969 | −0.181485 | − | 0.983394i | \(-0.558090\pi\) | ||||
−0.181485 | + | 0.983394i | \(0.558090\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.90981i | 0.362943i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.99276 | − | 4.03727i | −0.514118 | − | 0.296826i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.24596 | + | 5.33816i | −0.676132 | + | 0.390365i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.16908 | + | 1.51496i | 0.157777 | + | 0.110197i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.7127 | − | 7.91705i | 0.992218 | − | 0.572857i | 0.0862814 | − | 0.996271i | \(-0.472502\pi\) |
0.905937 | + | 0.423414i | \(0.139168\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.92835 | + | 15.4644i | −0.642677 | + | 1.11315i | 0.342156 | + | 0.939643i | \(0.388843\pi\) |
−0.984833 | + | 0.173506i | \(0.944491\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.10467i | 0.508776i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.6902i | 0.832890i | 0.909161 | + | 0.416445i | \(0.136724\pi\) | ||||
−0.909161 | + | 0.416445i | \(0.863276\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.68015 | − | 16.7665i | 0.686207 | − | 1.18855i | −0.286848 | − | 0.957976i | \(-0.592608\pi\) |
0.973056 | − | 0.230570i | \(-0.0740591\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.68236 | + | 2.12601i | −0.259733 | + | 0.149957i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.65084 | − | 1.85144i | −0.186052 | − | 0.129945i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.63529 | + | 4.40824i | −0.533272 | + | 0.307885i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.62298 | − | 2.66908i | −0.321319 | − | 0.185514i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1.01989i | − | 0.0705475i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.6635 | 1.56022 | 0.780109 | − | 0.625643i | \(-0.215163\pi\) | ||||
0.780109 | + | 0.625643i | \(0.215163\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.66908 | − | 9.81913i | 0.388439 | − | 0.672796i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.83506 | + | 6.64252i | 0.261549 | + | 0.453016i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.486723 | + | 1.04054i | 0.0330409 | + | 0.0706366i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.74899 | + | 11.6896i | 0.456054 | + | 0.789910i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.1385 | − | 11.6269i | −1.35466 | − | 0.782113i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.39367 | 0.361187 | 0.180593 | − | 0.983558i | \(-0.442198\pi\) | ||||
0.180593 | + | 0.983558i | \(0.442198\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.88325 | 0.192217 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 25.5212 | + | 14.7347i | 1.69390 | + | 0.977976i | 0.951311 | + | 0.308232i | \(0.0997373\pi\) |
0.742592 | + | 0.669744i | \(0.233596\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.01328 | + | 10.4153i | 0.397369 | + | 0.688262i | 0.993400 | − | 0.114698i | \(-0.0365901\pi\) |
−0.596032 | + | 0.802961i | \(0.703257\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.509947 | − | 5.90981i | 0.0335520 | − | 0.388837i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.0072 | + | 19.0651i | 0.721108 | + | 1.24900i | 0.960556 | + | 0.278087i | \(0.0897002\pi\) |
−0.239448 | + | 0.970909i | \(0.576966\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.31776 | + | 4.01447i | −0.151194 | + | 0.261875i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.1578 | 0.789732 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.0000i | 1.16432i | 0.813073 | + | 0.582162i | \(0.197793\pi\) | ||||
−0.813073 | + | 0.582162i | \(0.802207\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.32081 | + | 4.22667i | 0.471575 | + | 0.272264i | 0.716899 | − | 0.697177i | \(-0.245561\pi\) |
−0.245324 | + | 0.969441i | \(0.578894\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.52775 | + | 7.81723i | −0.417043 | + | 0.499424i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.92380 | − | 1.11071i | 0.122408 | − | 0.0706725i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.52051 | + | 13.0259i | −0.476593 | + | 0.825484i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.54510i | 0.286884i | 0.989659 | + | 0.143442i | \(0.0458170\pi\) | ||||
−0.989659 | + | 0.143442i | \(0.954183\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.9681i | 0.752430i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.46410 | − | 6.00000i | 0.216930 | − | 0.375735i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.24073 | − | 5.33514i | 0.576421 | − | 0.332797i | −0.183289 | − | 0.983059i | \(-0.558674\pi\) |
0.759710 | + | 0.650262i | \(0.225341\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.26233 | + | 14.6292i | −0.0784375 | + | 0.909017i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.05837 | + | 0.611052i | −0.0655116 | + | 0.0378232i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.01868 | − | 5.20694i | −0.556116 | − | 0.321074i | 0.195469 | − | 0.980710i | \(-0.437377\pi\) |
−0.751585 | + | 0.659636i | \(0.770710\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.2300i | 0.935573i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.8962 | −0.972831 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.27979 | + | 12.6090i | −0.443856 | + | 0.768782i | −0.997972 | − | 0.0636581i | \(-0.979723\pi\) |
0.554115 | + | 0.832440i | \(0.313057\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.93883 | − | 8.55431i | −0.300013 | − | 0.519637i | 0.676126 | − | 0.736786i | \(-0.263658\pi\) |
−0.976138 | + | 0.217149i | \(0.930324\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.7029 | − | 5.47412i | 0.708290 | − | 0.331309i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.23212 | − | 5.59820i | −0.194904 | − | 0.337584i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.4416 | − | 8.91523i | −0.927797 | − | 0.535664i | −0.0416832 | − | 0.999131i | \(-0.513272\pi\) |
−0.886114 | + | 0.463467i | \(0.846605\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.434187 | 0.0259941 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.6537 | 1.64968 | 0.824841 | − | 0.565365i | \(-0.191265\pi\) | ||||
0.824841 | + | 0.565365i | \(0.191265\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.08002 | − | 1.20090i | −0.123644 | − | 0.0713860i | 0.436902 | − | 0.899509i | \(-0.356076\pi\) |
−0.560546 | + | 0.828123i | \(0.689409\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.330921 | + | 0.573172i | 0.0196021 | + | 0.0339518i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.1442 | + | 9.18038i | 0.775881 | + | 0.541901i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.83816 | + | 4.91583i | 0.166950 | + | 0.289167i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.37302 | − | 9.30634i | 0.314972 | − | 0.545547i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.7931 | −0.747379 | −0.373689 | − | 0.927554i | \(-0.621907\pi\) | ||||
−0.373689 | + | 0.927554i | \(0.621907\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.1538i | 0.765846i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.94163 | − | 1.12100i | −0.112665 | − | 0.0650470i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −22.5752 | + | 13.0338i | −1.30556 | + | 0.753764i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.98672 | − | 11.4352i | 0.460347 | − | 0.659114i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.156217 | + | 0.0901918i | −0.00897442 | + | 0.00518138i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.57165 | + | 6.18628i | −0.204512 | + | 0.354225i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.7173i | 1.18240i | 0.806525 | + | 0.591201i | \(0.201346\pi\) | ||||
−0.806525 | + | 0.591201i | \(0.798654\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 4.25202i | − | 0.241889i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.51391 | − | 13.0145i | 0.426075 | − | 0.737983i | −0.570445 | − | 0.821336i | \(-0.693229\pi\) |
0.996520 | + | 0.0833524i | \(0.0265627\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.11268 | + | 4.68386i | −0.458556 | + | 0.264747i | −0.711437 | − | 0.702750i | \(-0.751955\pi\) |
0.252881 | + | 0.967497i | \(0.418622\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.63095 | + | 3.48672i | 0.0918934 | + | 0.196455i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.8023 | + | 11.4328i | −1.11221 | + | 0.642133i | −0.939400 | − | 0.342823i | \(-0.888617\pi\) |
−0.172806 | + | 0.984956i | \(0.555284\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.37287 | + | 1.36998i | 0.132855 | + | 0.0767040i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.4361i | 1.08481i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.16624 | −0.120533 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.03983 | − | 12.1933i | 0.390500 | − | 0.676365i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.52689 | − | 9.57285i | −0.305637 | − | 0.529380i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.39850 | + | 0.724692i | 0.463024 | + | 0.0399536i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.671929 | − | 1.16381i | −0.0369325 | − | 0.0639690i | 0.846968 | − | 0.531643i | \(-0.178425\pi\) |
−0.883901 | + | 0.467674i | \(0.845092\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.80634 | + | 2.77494i | 0.263386 | + | 0.152066i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.18628 | −0.337993 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 31.2624 | 1.70297 | 0.851487 | − | 0.524376i | \(-0.175701\pi\) | ||||
0.851487 | + | 0.524376i | \(0.175701\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.98673 | + | 4.03379i | 0.379467 | + | 0.219085i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.486723 | − | 0.843029i | −0.0263575 | − | 0.0456526i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.9062 | + | 4.72942i | 0.966845 | + | 0.255365i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.88325 | − | 6.72599i | −0.209067 | − | 0.362115i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.51125 | − | 11.2778i | 0.349542 | − | 0.605425i | −0.636626 | − | 0.771173i | \(-0.719670\pi\) |
0.986168 | + | 0.165748i | \(0.0530038\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.18038 | 0.223771 | 0.111885 | − | 0.993721i | \(-0.464311\pi\) | ||||
0.111885 | + | 0.993721i | \(0.464311\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 4.88325i | − | 0.260649i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.7737 | − | 17.7672i | −1.63792 | − | 0.945654i | −0.981548 | − | 0.191218i | \(-0.938756\pi\) |
−0.656374 | − | 0.754436i | \(-0.727911\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.2859 | − | 8.24797i | 0.758217 | − | 0.437757i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −12.5523 | − | 1.08312i | −0.664340 | − | 0.0573247i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.8059 | − | 9.70287i | 0.886980 | − | 0.512098i | 0.0140263 | − | 0.999902i | \(-0.495535\pi\) |
0.872953 | + | 0.487804i | \(0.162202\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.39653 | + | 16.2753i | −0.494554 | + | 0.856593i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 5.97345i | − | 0.313525i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.6383i | 1.02791i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.8813 | − | 27.5072i | 0.828998 | − | 1.43587i | −0.0698276 | − | 0.997559i | \(-0.522245\pi\) |
0.898825 | − | 0.438307i | \(-0.144422\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.24797 | − | 3.02991i | 0.273198 | − | 0.157731i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 25.0870 | − | 11.7347i | 1.30245 | − | 0.609235i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.28780 | + | 1.32086i | −0.118458 | + | 0.0683916i | −0.558058 | − | 0.829802i | \(-0.688453\pi\) |
0.439600 | + | 0.898193i | \(0.355120\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.93277 | + | 5.73469i | 0.512926 | + | 0.296138i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.96784i | 0.307360i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.1361 | −1.54799 | −0.773994 | − | 0.633193i | \(-0.781744\pi\) | ||||
−0.773994 | + | 0.633193i | \(0.781744\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.623983 | + | 1.08077i | −0.0319676 | + | 0.0553696i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.36109 | − | 2.35748i | −0.0695484 | − | 0.120461i | 0.829154 | − | 0.559020i | \(-0.188822\pi\) |
−0.898703 | + | 0.438559i | \(0.855489\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.94163 | − | 7.07530i | 0.251849 | − | 0.360591i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.63596 | − | 4.56561i | −0.133993 | − | 0.232083i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.5113 | − | 7.22341i | −0.634348 | − | 0.366241i | 0.148086 | − | 0.988975i | \(-0.452689\pi\) |
−0.782434 | + | 0.622733i | \(0.786022\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.4201 | 1.28555 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.46938 | −0.275894 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.3186 | + | 8.84420i | 0.770762 | + | 0.445000i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.8208 | + | 32.5986i | 0.944590 | + | 1.63608i | 0.756571 | + | 0.653912i | \(0.226873\pi\) |
0.188019 | + | 0.982165i | \(0.439793\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.689160 | − | 0.986723i | 0.0345012 | − | 0.0493979i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.3044 | + | 17.8477i | 0.514576 | + | 0.891271i | 0.999857 | + | 0.0169129i | \(0.00538381\pi\) |
−0.485281 | + | 0.874358i | \(0.661283\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.06012 | − | 1.83619i | 0.0528085 | − | 0.0914669i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.45490 | 0.0722948 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 12.4428i | − | 0.616768i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.3833 | − | 10.0362i | −0.859547 | − | 0.496259i | 0.00431383 | − | 0.999991i | \(-0.498627\pi\) |
−0.863860 | + | 0.503731i | \(0.831960\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.87234 | − | 4.54510i | 0.388314 | − | 0.224193i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 21.6671 | − | 10.1350i | 1.06617 | − | 0.498710i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.9515 | + | 10.9416i | −0.930290 | + | 0.537103i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.31764 | + | 5.74633i | −0.162466 | + | 0.281399i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 1.76651i | − | 0.0862996i | −0.999069 | − | 0.0431498i | \(-0.986261\pi\) | ||
0.999069 | − | 0.0431498i | \(-0.0137393\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 1.37832i | − | 0.0671752i | −0.999436 | − | 0.0335876i | \(-0.989307\pi\) | ||
0.999436 | − | 0.0335876i | \(-0.0106933\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.59307 | − | 2.75927i | 0.0774575 | − | 0.134160i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.8905 | + | 6.86498i | −0.576774 | + | 0.333000i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.9420 | + | 1.11675i | 0.626309 | + | 0.0540431i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.48146 | + | 5.47412i | −0.457769 | + | 0.264293i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.29917 | − | 4.21417i | −0.351588 | − | 0.202990i | 0.313796 | − | 0.949490i | \(-0.398399\pi\) |
−0.665385 | + | 0.746501i | \(0.731732\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.6298i | 0.751118i | 0.926798 | + | 0.375559i | \(0.122549\pi\) | ||||
−0.926798 | + | 0.375559i | \(0.877451\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.77804 | −0.0852507 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.21417 | + | 2.10301i | −0.0580819 | + | 0.100601i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.2912 | + | 17.8249i | 0.491172 | + | 0.850735i | 0.999948 | − | 0.0101637i | \(-0.00323525\pi\) |
−0.508776 | + | 0.860899i | \(0.669902\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.48672 | − | 5.37302i | 0.213653 | − | 0.255858i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.8644 | − | 18.8176i | −0.516182 | − | 0.894053i | −0.999824 | − | 0.0187871i | \(-0.994020\pi\) |
0.483642 | − | 0.875266i | \(-0.339314\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20.0289 | − | 11.5637i | −0.949463 | − | 0.548173i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.33248 | −0.204919 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.74390 | −0.318264 | −0.159132 | − | 0.987257i | \(-0.550870\pi\) | ||||
−0.159132 | + | 0.987257i | \(0.550870\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.7659 | − | 6.79306i | −0.554036 | − | 0.319873i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.3965 | + | 18.0073i | 0.488472 | + | 0.846058i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 18.7276 | + | 1.61597i | 0.877963 | + | 0.0757579i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.6312 | − | 25.3420i | −0.684420 | − | 1.18545i | −0.973619 | − | 0.228181i | \(-0.926722\pi\) |
0.289199 | − | 0.957269i | \(-0.406611\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.38098 | + | 4.12398i | −0.111135 | + | 0.192491i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.0821 | 0.842165 | 0.421083 | − | 0.907022i | \(-0.361650\pi\) | ||||
0.421083 | + | 0.907022i | \(0.361650\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.13122i | 0.331416i | 0.986175 | + | 0.165708i | \(0.0529909\pi\) | ||||
−0.986175 | + | 0.165708i | \(0.947009\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.547068 | + | 0.315850i | 0.0253697 | + | 0.0146472i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −29.4574 | + | 17.0072i | −1.36313 | + | 0.787001i | −0.990039 | − | 0.140795i | \(-0.955034\pi\) |
−0.373087 | + | 0.927796i | \(0.621701\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.76651 | + | 10.1901i | 0.220097 | + | 0.470535i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.3862 | + | 8.88325i | −0.708961 | + | 0.409319i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.90981 | + | 10.2361i | −0.271733 | + | 0.470656i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1.31160i | − | 0.0601805i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 10.4681i | − | 0.479300i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.51125 | − | 11.2778i | 0.297507 | − | 0.515296i | −0.678058 | − | 0.735008i | \(-0.737178\pi\) |
0.975565 | + | 0.219712i | \(0.0705117\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.4706 | − | 13.5507i | 1.07017 | − | 0.617861i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.08708 | + | 11.5789i | −0.367975 | + | 0.526858i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.5398 | − | 7.81723i | 0.614812 | − | 0.354962i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.9551 | − | 17.8719i | −1.40271 | − | 0.809855i | −0.408040 | − | 0.912964i | \(-0.633788\pi\) |
−0.994670 | + | 0.103109i | \(0.967121\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 6.05983i | − | 0.274035i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.11037 | −0.140369 | −0.0701845 | − | 0.997534i | \(-0.522359\pi\) | ||||
−0.0701845 | + | 0.997534i | \(0.522359\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.90981 | − | 5.03994i | 0.131051 | − | 0.226987i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.63095 | − | 2.82488i | −0.0733056 | − | 0.126969i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −24.5934 | − | 17.1768i | −1.10316 | − | 0.770486i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.28223 | + | 3.95293i | 0.102166 | + | 0.176958i | 0.912577 | − | 0.408905i | \(-0.134089\pi\) |
−0.810411 | + | 0.585862i | \(0.800756\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.89049 | − | 5.13293i | −0.397198 | − | 0.229322i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −42.8922 | −1.91247 | −0.956233 | − | 0.292605i | \(-0.905478\pi\) | ||||
−0.956233 | + | 0.292605i | \(0.905478\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.262441 | −0.0116785 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.39306 | − | 5.42309i | −0.417160 | − | 0.240848i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.1292 | − | 27.9367i | −0.714916 | − | 1.23827i | −0.962992 | − | 0.269531i | \(-0.913131\pi\) |
0.248075 | − | 0.968741i | \(-0.420202\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 32.3483 | − | 15.1312i | 1.43101 | − | 0.669366i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.227452 | − | 0.393958i | −0.0100423 | − | 0.0173937i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.09314 | − | 5.35748i | 0.136300 | − | 0.236079i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.14330 | −0.314162 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.3382i | 0.761061i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.1457 | + | 5.85762i | 0.444491 | + | 0.256627i | 0.705501 | − | 0.708709i | \(-0.250722\pi\) |
−0.261010 | + | 0.965336i | \(0.584055\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.38335 | + | 4.84013i | −0.366578 | + | 0.211644i | −0.671963 | − | 0.740585i | \(-0.734548\pi\) |
0.305384 | + | 0.952229i | \(0.401215\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.655802 | − | 7.60013i | 0.0286215 | − | 0.331697i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.79058 | + | 1.03379i | −0.0779989 | + | 0.0450327i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.74797 | − | 4.75962i | 0.119477 | − | 0.206940i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 9.04103i | − | 0.392347i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 29.5917i | − | 1.28176i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.1388 | + | 24.4891i | −0.611274 | + | 1.05876i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.37195 | + | 5.41090i | −0.404429 | + | 0.233497i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15.4620 | − | 2.68840i | −0.665996 | − | 0.115797i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −39.5728 | + | 22.8474i | −1.70137 | + | 0.982286i | −0.756991 | + | 0.653425i | \(0.773332\pi\) |
−0.944378 | + | 0.328861i | \(0.893335\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.22902 | + | 2.44163i | 0.181485 | + | 0.104780i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 16.0822i | − | 0.688885i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.35237 | −0.228851 | −0.114425 | − | 0.993432i | \(-0.536503\pi\) | ||||
−0.114425 | + | 0.993432i | \(0.536503\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.45490 | − | 4.25202i | 0.104773 | − | 0.181472i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.277970 | + | 0.481458i | 0.0118419 | + | 0.0205108i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.76531 | − | 32.0474i | 0.117593 | − | 1.36279i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.03727 | + | 6.99276i | 0.171373 | + | 0.296826i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 37.8538 | + | 21.8549i | 1.60392 | + | 0.926023i | 0.990693 | + | 0.136114i | \(0.0434615\pi\) |
0.613225 | + | 0.789908i | \(0.289872\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.7441 | −1.08886 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.6763 | 0.450754 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.5646 | + | 14.1824i | 1.03527 | + | 0.597715i | 0.918491 | − | 0.395443i | \(-0.129409\pi\) |
0.116782 | + | 0.993158i | \(0.462742\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.86878 | + | 10.1650i | 0.246901 | + | 0.427646i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.12100 | − | 2.39653i | −0.0470775 | − | 0.100645i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.7931 | + | 27.3544i | 0.662080 | + | 1.14676i | 0.980068 | + | 0.198661i | \(0.0636593\pi\) |
−0.317989 | + | 0.948095i | \(0.603007\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.9578 | − | 25.9077i | 0.625966 | − | 1.08420i | −0.362388 | − | 0.932027i | \(-0.618038\pi\) |
0.988353 | − | 0.152177i | \(-0.0486283\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.8341 | −0.661479 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15.3913i | 0.641860i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.50000 | + | 0.866025i | 0.0624458 | + | 0.0360531i | 0.530898 | − | 0.847436i | \(-0.321855\pi\) |
−0.468452 | + | 0.883489i | \(0.655188\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.4644 | − | 8.92835i | 0.642677 | − | 0.371050i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 32.6252 | + | 22.7865i | 1.35352 | + | 0.945344i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.3251 | + | 11.7347i | −0.841779 | + | 0.486001i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.55233 | − | 6.15282i | 0.146871 | − | 0.254388i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.6498i | 0.728484i | 0.931304 | + | 0.364242i | \(0.118672\pi\) | ||||
−0.931304 | + | 0.364242i | \(0.881328\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 0.197513i | − | 0.00813840i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.84508 | − | 10.1240i | 0.240435 | − | 0.416445i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.74390 | + | 2.16154i | −0.153744 | + | 0.0887639i | −0.574898 | − | 0.818225i | \(-0.694958\pi\) |
0.421155 | + | 0.906989i | \(0.361625\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15.0278 | − | 10.4959i | −0.616081 | − | 0.430291i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −16.7665 | + | 9.68015i | −0.686207 | + | 0.396182i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.3643 | − | 15.2214i | −1.07721 | − | 0.621930i | −0.147071 | − | 0.989126i | \(-0.546985\pi\) |
−0.930144 | + | 0.367196i | \(0.880318\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 28.8795i | − | 1.17802i | −0.808126 | − | 0.589010i | \(-0.799518\pi\) | ||
0.808126 | − | 0.589010i | \(-0.200482\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.25202 | 0.173156 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.34540 | − | 7.52645i | 0.176665 | − | 0.305994i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.49903 | + | 12.9887i | 0.304376 | + | 0.527195i | 0.977122 | − | 0.212679i | \(-0.0682187\pi\) |
−0.672746 | + | 0.739873i | \(0.734885\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.36998 | + | 2.92881i | 0.0555143 | + | 0.118681i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.77935 | − | 13.4742i | −0.314719 | − | 0.545109i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.37919 | + | 4.83773i | 0.338432 | + | 0.195394i | 0.659579 | − | 0.751636i | \(-0.270735\pi\) |
−0.321146 | + | 0.947030i | \(0.604068\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.81647 | 0.355514 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.1191 | 1.41384 | 0.706922 | − | 0.707292i | \(-0.250083\pi\) | ||||
0.706922 | + | 0.707292i | \(0.250083\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.7483 | + | 16.0205i | 1.11530 | + | 0.643919i | 0.940197 | − | 0.340631i | \(-0.110641\pi\) |
0.175103 | + | 0.984550i | \(0.443974\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.66908 | + | 4.62298i | 0.107106 | + | 0.185514i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.61562 | + | 41.9017i | −0.144857 | + | 1.67876i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.13529 | + | 1.96638i | 0.0454115 | + | 0.0786550i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.509947 | + | 0.883254i | −0.0203653 | + | 0.0352738i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −26.4283 | −1.05377 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.64976i | − | 0.0656760i | −0.999461 | − | 0.0328380i | \(-0.989545\pi\) | ||
0.999461 | − | 0.0328380i | \(-0.0104545\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −19.6272 | − | 11.3317i | −0.780109 | − | 0.450396i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.57242 | + | 0.907836i | −0.0623995 | + | 0.0360264i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.7677 | − | 32.0934i | −0.466253 | − | 1.27159i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.81913 | + | 5.66908i | −0.388439 | + | 0.224265i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.12398 | − | 7.14295i | 0.162888 | − | 0.282129i | −0.773016 | − | 0.634387i | \(-0.781253\pi\) |
0.935903 | + | 0.352258i | \(0.114586\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 17.6272i | − | 0.695147i | −0.937653 | − | 0.347574i | \(-0.887006\pi\) | ||
0.937653 | − | 0.347574i | \(-0.112994\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 7.67013i | − | 0.302011i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.9820 | + | 31.1457i | −0.706944 | + | 1.22446i | 0.259041 | + | 0.965866i | \(0.416594\pi\) |
−0.965985 | + | 0.258597i | \(0.916740\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.5543 | + | 10.1350i | −0.689067 | + | 0.397833i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.0987567 | − | 1.14450i | 0.00387058 | − | 0.0448564i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 38.9480 | − | 22.4866i | 1.52415 | − | 0.879969i | 0.524561 | − | 0.851373i | \(-0.324230\pi\) |
0.999591 | − | 0.0285964i | \(-0.00910374\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.89133 | − | 3.97871i | −0.269267 | − | 0.155461i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 13.4980i | − | 0.526606i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.6981 | −1.00106 | −0.500528 | − | 0.865720i | \(-0.666861\pi\) | ||||
−0.500528 | + | 0.865720i | \(0.666861\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.2983 | − | 26.4975i | 0.595036 | − | 1.03063i | −0.398506 | − | 0.917166i | \(-0.630471\pi\) |
0.993542 | − | 0.113467i | \(-0.0361955\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.6269 | + | 20.1385i | 0.451553 | + | 0.782113i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.58612 | − | 0.741924i | 0.0615073 | − | 0.0287706i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.26189 | − | 5.64976i | −0.126301 | − | 0.218760i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.67105 | − | 2.69683i | −0.180593 | − | 0.104266i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.0078 | −0.424951 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.2624 | −0.511230 | −0.255615 | − | 0.966779i | \(-0.582278\pi\) | ||||
−0.255615 | + | 0.966779i | \(0.582278\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.49697 | − | 1.44163i | −0.0961085 | − | 0.0554883i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.2532 | + | 19.4912i | 0.432497 | + | 0.749106i | 0.997088 | − | 0.0762645i | \(-0.0242993\pi\) |
−0.564591 | + | 0.825371i | \(0.690966\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −23.3090 | − | 16.2798i | −0.894517 | − | 0.624761i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.7347 | − | 25.5212i | −0.564635 | − | 0.977976i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.99600 | + | 17.3136i | −0.382486 | + | 0.662486i | −0.991417 | − | 0.130738i | \(-0.958265\pi\) |
0.608931 | + | 0.793223i | \(0.291599\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.2254 | 0.505315 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 12.0266i | − | 0.458842i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −44.2697 | − | 25.5591i | −1.68654 | − | 0.973725i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.6864 | − | 19.4489i | 1.28149 | − | 0.739870i | 0.304371 | − | 0.952554i | \(-0.401554\pi\) |
0.977121 | + | 0.212684i | \(0.0682205\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.39653 | + | 4.86307i | −0.129024 | + | 0.184733i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.36036 | + | 4.82685i | −0.317126 | + | 0.183093i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.4283 | + | 24.9906i | −0.546513 | + | 0.946588i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 22.0145i | − | 0.832664i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.8005i | 0.559009i | 0.960144 | + | 0.279504i | \(0.0901701\pi\) | ||||
−0.960144 | + | 0.279504i | \(0.909830\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.26233 | − | 2.18642i | 0.0476098 | − | 0.0824625i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.01447 | − | 2.31776i | 0.151194 | − | 0.0872918i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.202210 | + | 0.432295i | 0.00760488 | + | 0.0162581i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.7810 | − | 17.1941i | 1.11845 | − | 0.645736i | 0.177444 | − | 0.984131i | \(-0.443217\pi\) |
0.941004 | + | 0.338394i | \(0.109884\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.5289 | − | 6.07889i | −0.394866 | − | 0.227976i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.31776i | 0.0868007i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.9286 | −0.595698 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.00000 | − | 15.5885i | 0.336111 | − | 0.582162i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.41826 | − | 11.1167i | −0.239361 | − | 0.414585i | 0.721170 | − | 0.692758i | \(-0.243604\pi\) |
−0.960531 | + | 0.278173i | \(0.910271\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.2081 | − | 0.967130i | −0.417413 | − | 0.0360178i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.22667 | − | 7.32081i | −0.157192 | − | 0.272264i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.05156 | + | 1.76182i | 0.113332 | + | 0.0654323i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.04981 | −0.150199 | −0.0750995 | − | 0.997176i | \(-0.523927\pi\) | ||||
−0.0750995 | + | 0.997176i | \(0.523927\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.7413 | + | 12.5523i | 0.804130 | + | 0.464265i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.5237 | − | 45.9404i | −0.979675 | − | 1.69685i | −0.663556 | − | 0.748127i | \(-0.730954\pi\) |
−0.316119 | − | 0.948720i | \(-0.602380\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.56181 | − | 3.50604i | 0.352693 | − | 0.129322i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.76651 | − | 8.25583i | −0.175577 | − | 0.304108i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.68044 | − | 8.10676i | 0.172173 | − | 0.298212i | −0.767006 | − | 0.641639i | \(-0.778255\pi\) |
0.939179 | + | 0.343427i | \(0.111588\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.22141 | −0.0816056 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.5249i | 1.11985i | 0.828544 | + | 0.559925i | \(0.189170\pi\) | ||||
−0.828544 | + | 0.559925i | \(0.810830\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.45885 | − | 3.15167i | −0.199997 | − | 0.115468i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.0259 | − | 7.52051i | 0.476593 | − | 0.275161i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 51.2326 | + | 4.42077i | 1.87200 | + | 0.161531i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.57948 | + | 4.37602i | −0.276579 | + | 0.159683i | −0.631874 | − | 0.775071i | \(-0.717714\pi\) |
0.355295 | + | 0.934754i | \(0.384381\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.27255 | − | 3.93617i | 0.0828163 | − | 0.143442i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 30.2519i | 1.10098i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 9.22089i | − | 0.335139i | −0.985860 | − | 0.167569i | \(-0.946408\pi\) | ||
0.985860 | − | 0.167569i | \(-0.0535919\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.98407 | − | 10.3647i | 0.217208 | − | 0.376215i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.4661 | − | 14.7029i | 0.923145 | − | 0.532978i | 0.0385079 | − | 0.999258i | \(-0.487740\pi\) |
0.884637 | + | 0.466280i | \(0.154406\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −26.4907 | + | 12.3913i | −0.959028 | + | 0.448594i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.00000 | + | 3.46410i | −0.216930 | + | 0.125245i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −38.2347 | − | 22.0748i | −1.38058 | − | 0.797076i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 23.9316i | − | 0.862995i | −0.902114 | − | 0.431497i | \(-0.857985\pi\) | ||
0.902114 | − | 0.431497i | \(-0.142015\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.6703 | −0.384281 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.26244 | − | 16.0430i | 0.333147 | − | 0.577027i | −0.649980 | − | 0.759951i | \(-0.725223\pi\) |
0.983127 | + | 0.182924i | \(0.0585562\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.625935 | − | 1.08415i | −0.0224843 | − | 0.0389439i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.40784 | − | 12.0381i | 0.301629 | − | 0.431866i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.37832 | − | 2.38732i | −0.0493835 | − | 0.0855347i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.0145 | + | 12.7101i | 0.787740 | + | 0.454802i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.22210 | 0.0436744 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −25.8486 | −0.922575 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.5839 | − | 10.7294i | −0.662445 | − | 0.382463i | 0.130763 | − | 0.991414i | \(-0.458257\pi\) |
−0.793208 | + | 0.608951i | \(0.791591\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.20694 | + | 9.01868i | 0.185372 | + | 0.321074i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.2220 | − | 17.4992i | 0.434566 | − | 0.622201i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.9879 | − | 20.7637i | −0.425704 | − | 0.737340i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.61502 | − | 13.1896i | 0.270077 | − | 0.467787i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.5982 | −0.517095 | −0.258547 | − | 0.965999i | \(-0.583244\pi\) | ||||
−0.258547 | + | 0.965999i | \(0.583244\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.1722i | 0.536756i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.7665 | + | 7.94810i | 0.486416 | + | 0.280832i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −26.2080 | + | 15.1312i | −0.924862 | + | 0.533969i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −18.6127 | + | 8.70625i | −0.656011 | + | 0.306855i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.6090 | − | 7.27979i | 0.443856 | − | 0.256261i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.75927 | + | 4.77920i | −0.0970108 | + | 0.168028i | −0.910446 | − | 0.413628i | \(-0.864261\pi\) |
0.813435 | + | 0.581655i | \(0.197595\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 12.7294i | − | 0.446991i | −0.974705 | − | 0.223495i | \(-0.928253\pi\) | ||
0.974705 | − | 0.223495i | \(-0.0717467\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.87766i | 0.346425i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.40824 | − | 7.63529i | 0.154414 | − | 0.267452i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.07691 | + | 1.19911i | −0.0726620 | + | 0.0419515i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.8720 | − | 1.11071i | −0.449786 | − | 0.0388112i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.9489 | − | 23.0645i | 1.39422 | − | 0.804956i | 0.400445 | − | 0.916321i | \(-0.368855\pi\) |
0.993780 | + | 0.111364i | \(0.0355221\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33.2073 | + | 19.1722i | 1.15753 | + | 0.668303i | 0.950712 | − | 0.310076i | \(-0.100354\pi\) |
0.206822 | + | 0.978379i | \(0.433688\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.46425i | 0.225056i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 53.9162 | 1.87485 | 0.937424 | − | 0.348189i | \(-0.113203\pi\) | ||||
0.937424 | + | 0.348189i | \(0.113203\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.9376 | + | 20.6765i | −0.414609 | + | 0.718123i | −0.995387 | − | 0.0959384i | \(-0.969415\pi\) |
0.580779 | + | 0.814061i | \(0.302748\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.91523 | + | 15.4416i | 0.309266 | + | 0.535664i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.71011 | + | 32.8410i | −0.197844 | + | 1.13787i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.46792 | − | 12.9348i | −0.258438 | − | 0.447628i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.376017 | − | 0.217093i | −0.0129970 | − | 0.00750385i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.77654 | −0.130380 | −0.0651902 | − | 0.997873i | \(-0.520765\pi\) | ||||
−0.0651902 | + | 0.997873i | \(0.520765\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.5065 | 0.948499 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −23.9488 | − | 13.8269i | −0.824841 | − | 0.476222i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.89007 | − | 13.6660i | −0.271427 | − | 0.470125i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.7457 | − | 1.35867i | −0.541030 | − | 0.0466845i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.20090 | + | 2.08002i | 0.0412147 | + | 0.0713860i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.8131 | + | 25.6570i | −0.507786 | + | 0.879511i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.469379 | −0.0160712 | −0.00803561 | − | 0.999968i | \(-0.502558\pi\) | ||||
−0.00803561 | + | 0.999968i | \(0.502558\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 0.661842i | − | 0.0226345i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.262441 | + | 0.151520i | 0.00896481 | + | 0.00517584i | 0.504476 | − | 0.863426i | \(-0.331686\pi\) |
−0.495511 | + | 0.868602i | \(0.665019\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48.0078 | − | 27.7173i | 1.63801 | − | 0.945704i | 0.656488 | − | 0.754336i | \(-0.272041\pi\) |
0.981518 | − | 0.191367i | \(-0.0612922\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.79306 | − | 14.5226i | −0.231507 | − | 0.494928i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23.9154 | + | 13.8075i | −0.814088 | + | 0.470014i | −0.848374 | − | 0.529398i | \(-0.822418\pi\) |
0.0342854 | + | 0.999412i | \(0.489084\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.6127 | + | 21.8458i | −0.428844 | + | 0.742779i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 5.67632i | − | 0.192778i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 27.2577i | 0.924654i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.3818 | − | 17.9819i | 0.351775 | − | 0.609293i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.30634 | + | 5.37302i | −0.314972 | + | 0.181849i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 17.3756 | − | 24.8780i | 0.587403 | − | 0.841030i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.0371 | + | 16.7646i | −0.980513 | + | 0.566099i | −0.902425 | − | 0.430847i | \(-0.858215\pi\) |
−0.0780878 | + | 0.996946i | \(0.524881\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.0791 | + | 6.39653i | 0.373689 | + | 0.215750i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 23.6583i | − | 0.797069i | −0.917153 | − | 0.398534i | \(-0.869519\pi\) | ||
0.917153 | − | 0.398534i | \(-0.130481\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −55.3953 | −1.86420 | −0.932100 | − | 0.362200i | \(-0.882026\pi\) | ||||
−0.932100 | + | 0.362200i | \(0.882026\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.57691 | − | 11.3916i | 0.221081 | − | 0.382923i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.5936 | − | 25.2769i | −0.490006 | − | 0.848716i | 0.509928 | − | 0.860217i | \(-0.329672\pi\) |
−0.999934 | + | 0.0115016i | \(0.996339\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.70694 | + | 1.89062i | 0.0907878 | + | 0.0634092i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.12100 | + | 1.94163i | 0.0375549 | + | 0.0650470i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.25520 | − | 0.724692i | −0.0420038 | − | 0.0242509i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.7447 | −0.526286 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 26.0676 | 0.870371 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.459532 | + | 0.265311i | 0.0153262 | + | 0.00884861i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.9243 | + | 43.1701i | 0.830348 | + | 1.43821i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.6343 | + | 5.90981i | −0.420443 | + | 0.196666i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.55233 | + | 6.15282i | 0.118084 | + | 0.204527i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.1678 | − | 45.3240i | 0.868888 | − | 1.50496i | 0.00575389 | − | 0.999983i | \(-0.498168\pi\) |
0.863134 | − | 0.504975i | \(-0.168498\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.180384 | 0.00598295 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.6458i | 0.650895i | 0.945560 | + | 0.325447i | \(0.105515\pi\) | ||||
−0.945560 | + | 0.325447i | \(0.894485\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −29.2041 | − | 16.8610i | −0.966514 | − | 0.558017i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.18628 | − | 3.57165i | 0.204512 | − | 0.118075i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.24402 | + | 14.4170i | −0.0410812 | + | 0.476093i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.3560 | − | 10.0205i | 0.572523 | − | 0.330546i | −0.185633 | − | 0.982619i | \(-0.559434\pi\) |
0.758156 | + | 0.652073i | \(0.226100\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.3587 | − | 17.9417i | 0.341330 | − | 0.591201i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 55.3671i | 1.82243i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 16.0017i | − | 0.526133i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.12601 | + | 3.68236i | −0.0698273 | + | 0.120944i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.66513 | − | 4.42547i | 0.251485 | − | 0.145195i | −0.368959 | − | 0.929446i | \(-0.620286\pi\) |
0.620444 | + | 0.784251i | \(0.286952\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.44421 | − | 2.04103i | −0.0801057 | − | 0.0668920i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.0145 | + | 7.51391i | −0.426075 | + | 0.245994i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.4520 | + | 7.76651i | 0.439927 | + | 0.253992i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 15.7400i | − | 0.514203i | −0.966384 | − | 0.257101i | \(-0.917233\pi\) | ||
0.966384 | − | 0.257101i | \(-0.0827674\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.36771 | 0.305704 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.7009 | + | 28.9268i | −0.544434 | + | 0.942987i | 0.454209 | + | 0.890895i | \(0.349922\pi\) |
−0.998642 | + | 0.0520915i | \(0.983411\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.1742 | + | 28.0145i | 0.526703 | + | 0.912277i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.330921 | − | 3.83506i | 0.0107649 | − | 0.124755i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.69759 | + | 2.94031i | 0.0551642 | + | 0.0955471i | 0.892289 | − | 0.451465i | \(-0.149098\pi\) |
−0.837125 | + | 0.547012i | \(0.815765\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −57.0833 | − | 32.9570i | −1.85300 | − | 1.06983i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.8657 | 0.741471 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.2319 | −0.687770 | −0.343885 | − | 0.939012i | \(-0.611743\pi\) | ||||
−0.343885 | + | 0.939012i | \(0.611743\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.9507 | − | 11.5185i | −0.645589 | − | 0.372731i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.36998 | − | 2.37287i | −0.0442851 | − | 0.0767040i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.1901 | − | 21.7849i | −0.329055 | − | 0.703472i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.4057 | + | 26.6835i | 0.496959 | + | 0.860759i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.71803 | − | 16.8321i | 0.313159 | − | 0.542407i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25.9798 | 0.836319 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 5.37524i | − | 0.172856i | −0.996258 | − | 0.0864281i | \(-0.972455\pi\) | ||
0.996258 | − | 0.0864281i | \(-0.0275453\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.87602 | + | 1.08312i | 0.0602663 | + | 0.0347948i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.39495 | + | 3.11477i | −0.173132 | + | 0.0999578i | −0.584062 | − | 0.811709i | \(-0.698537\pi\) |
0.410930 | + | 0.911667i | \(0.365204\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.3925 | + | 10.0522i | 0.461401 | + | 0.322258i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.1933 | + | 7.03983i | −0.390500 | + | 0.225455i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.4959 | + | 33.7679i | −0.623730 | + | 1.08033i | 0.365055 | + | 0.930986i | \(0.381050\pi\) |
−0.988785 | + | 0.149346i | \(0.952283\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 35.6392i | − | 1.13903i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.0538i | 0.352920i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.7373 | + | 25.5258i | −0.470047 | + | 0.814146i | −0.999413 | − | 0.0342476i | \(-0.989097\pi\) |
0.529366 | + | 0.848394i | \(0.322430\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.7294 | − | 8.50404i | 0.469318 | − | 0.270961i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.91097 | − | 4.82685i | −0.219979 | − | 0.153640i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.3719 | − | 14.0712i | 0.774983 | − | 0.447437i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.35404 | − | 0.781758i | −0.0430126 | − | 0.0248334i | 0.478339 | − | 0.878175i | \(-0.341239\pi\) |
−0.521352 | + | 0.853342i | \(0.674572\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.34386i | 0.0426460i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −28.1674 | −0.892966 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.2757 | + | 35.1186i | −0.642138 | + | 1.11222i | 0.342816 | + | 0.939403i | \(0.388619\pi\) |
−0.984955 | + | 0.172814i | \(0.944714\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.77494 | − | 4.80634i | −0.0877953 | − | 0.152066i |
(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 | 1344.2.bb.e.31.2 | ✓ | 12 | |
4.3 | odd | 2 | inner | 1344.2.bb.e.31.5 | yes | 12 | |
7.5 | odd | 6 | 1344.2.bb.h.607.2 | yes | 12 | ||
8.3 | odd | 2 | 1344.2.bb.h.31.2 | yes | 12 | ||
8.5 | even | 2 | 1344.2.bb.h.31.5 | yes | 12 | ||
28.19 | even | 6 | 1344.2.bb.h.607.5 | yes | 12 | ||
56.5 | odd | 6 | inner | 1344.2.bb.e.607.5 | yes | 12 | |
56.19 | even | 6 | inner | 1344.2.bb.e.607.2 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.2.bb.e.31.2 | ✓ | 12 | 1.1 | even | 1 | trivial | |
1344.2.bb.e.31.5 | yes | 12 | 4.3 | odd | 2 | inner | |
1344.2.bb.e.607.2 | yes | 12 | 56.19 | even | 6 | inner | |
1344.2.bb.e.607.5 | yes | 12 | 56.5 | odd | 6 | inner | |
1344.2.bb.h.31.2 | yes | 12 | 8.3 | odd | 2 | ||
1344.2.bb.h.31.5 | yes | 12 | 8.5 | even | 2 | ||
1344.2.bb.h.607.2 | yes | 12 | 7.5 | odd | 6 | ||
1344.2.bb.h.607.5 | yes | 12 | 28.19 | even | 6 |