Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,2,Mod(321,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1280.321");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.l (of order \(4\), 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: | \(10.2208514587\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 321.2 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1280.321 |
Dual form | 1280.2.l.a.961.2 |
$q$-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 \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.658919 | − | 0.658919i | −0.380427 | − | 0.380427i | 0.490829 | − | 0.871256i | \(-0.336694\pi\) |
−0.871256 | + | 0.490829i | \(0.836694\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.707107 | + | 0.707107i | −0.316228 | + | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.34607i | 0.886729i | 0.896341 | + | 0.443365i | \(0.146215\pi\) | ||||
−0.896341 | + | 0.443365i | \(0.853785\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 2.13165i | − | 0.710551i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.19980 | − | 1.19980i | 0.361754 | − | 0.361754i | −0.502705 | − | 0.864458i | \(-0.667662\pi\) |
0.864458 | + | 0.502705i | \(0.167662\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.51764 | − | 1.51764i | −0.420917 | − | 0.420917i | 0.464602 | − | 0.885519i | \(-0.346197\pi\) |
−0.885519 | + | 0.464602i | \(0.846197\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.931852 | 0.240603 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.11099 | 0.269454 | 0.134727 | − | 0.990883i | \(-0.456984\pi\) | ||||
0.134727 | + | 0.990883i | \(0.456984\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.53225 | − | 1.53225i | −0.351522 | − | 0.351522i | 0.509153 | − | 0.860676i | \(-0.329959\pi\) |
−0.860676 | + | 0.509153i | \(0.829959\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.54587 | − | 1.54587i | 0.337336 | − | 0.337336i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.83548i | 1.00827i | 0.863626 | + | 0.504133i | \(0.168188\pi\) | ||||
−0.863626 | + | 0.504133i | \(0.831812\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.38134 | + | 3.38134i | −0.650739 | + | 0.650739i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.49938 | − | 5.49938i | −1.02121 | − | 1.02121i | −0.999770 | − | 0.0214387i | \(-0.993175\pi\) |
−0.0214387 | − | 0.999770i | \(-0.506825\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.29253 | 1.13017 | 0.565086 | − | 0.825032i | \(-0.308843\pi\) | ||||
0.565086 | + | 0.825032i | \(0.308843\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.58114 | −0.275242 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.65892 | − | 1.65892i | −0.280408 | − | 0.280408i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.59575 | − | 4.59575i | 0.755537 | − | 0.755537i | −0.219969 | − | 0.975507i | \(-0.570596\pi\) |
0.975507 | + | 0.219969i | \(0.0705958\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.00000i | 0.320256i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10.0599i | − | 1.57109i | −0.618807 | − | 0.785543i | \(-0.712384\pi\) | ||
0.618807 | − | 0.785543i | \(-0.287616\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.14128 | − | 5.14128i | 0.784038 | − | 0.784038i | −0.196472 | − | 0.980510i | \(-0.562948\pi\) |
0.980510 | + | 0.196472i | \(0.0629483\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.50731 | + | 1.50731i | 0.224696 | + | 0.224696i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.44584 | 0.940223 | 0.470111 | − | 0.882607i | \(-0.344214\pi\) | ||||
0.470111 | + | 0.882607i | \(0.344214\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.49598 | 0.213711 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.732051 | − | 0.732051i | −0.102508 | − | 0.102508i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.02823 | − | 5.02823i | 0.690680 | − | 0.690680i | −0.271701 | − | 0.962382i | \(-0.587586\pi\) |
0.962382 | + | 0.271701i | \(0.0875863\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.69677i | 0.228793i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.01926i | 0.267457i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.46170 | + | 1.46170i | −0.190297 | + | 0.190297i | −0.795824 | − | 0.605528i | \(-0.792962\pi\) |
0.605528 | + | 0.795824i | \(0.292962\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.752715 | − | 0.752715i | −0.0963753 | − | 0.0963753i | 0.657275 | − | 0.753651i | \(-0.271709\pi\) |
−0.753651 | + | 0.657275i | \(0.771709\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.00100 | 0.630066 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.14626 | 0.266211 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.2975 | − | 11.2975i | −1.38021 | − | 1.38021i | −0.844230 | − | 0.535980i | \(-0.819942\pi\) |
−0.535980 | − | 0.844230i | \(-0.680058\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.18618 | − | 3.18618i | 0.383572 | − | 0.383572i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 0.399602i | − | 0.0474240i | −0.999719 | − | 0.0237120i | \(-0.992452\pi\) | ||
0.999719 | − | 0.0237120i | \(-0.00754847\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.02406i | − | 0.705063i | −0.935800 | − | 0.352532i | \(-0.885321\pi\) | ||
0.935800 | − | 0.352532i | \(-0.114679\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.658919 | + | 0.658919i | −0.0760854 | + | 0.0760854i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.81481 | + | 2.81481i | 0.320777 | + | 0.320777i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.8637 | −1.78481 | −0.892403 | − | 0.451239i | \(-0.850982\pi\) | ||||
−0.892403 | + | 0.451239i | \(0.850982\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.93890 | −0.215433 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.312853 | + | 0.312853i | 0.0343401 | + | 0.0343401i | 0.724068 | − | 0.689728i | \(-0.242270\pi\) |
−0.689728 | + | 0.724068i | \(0.742270\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.785587 | + | 0.785587i | −0.0852089 | + | 0.0852089i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.24728i | 0.776990i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 16.5558i | − | 1.75491i | −0.479655 | − | 0.877457i | \(-0.659238\pi\) | ||
0.479655 | − | 0.877457i | \(-0.340762\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.56048 | − | 3.56048i | 0.373240 | − | 0.373240i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.14626 | − | 4.14626i | −0.429948 | − | 0.429948i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.16693 | 0.222322 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.14502 | 0.928536 | 0.464268 | − | 0.885695i | \(-0.346317\pi\) | ||||
0.464268 | + | 0.885695i | \(0.346317\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.55756 | − | 2.55756i | −0.257044 | − | 0.257044i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.96472 | − | 1.96472i | 0.195497 | − | 0.195497i | −0.602569 | − | 0.798067i | \(-0.705856\pi\) |
0.798067 | + | 0.602569i | \(0.205856\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 4.52885i | − | 0.446241i | −0.974791 | − | 0.223120i | \(-0.928376\pi\) | ||
0.974791 | − | 0.223120i | \(-0.0716243\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.18618i | 0.213350i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.87574 | + | 2.87574i | −0.278008 | + | 0.278008i | −0.832313 | − | 0.554305i | \(-0.812984\pi\) |
0.554305 | + | 0.832313i | \(0.312984\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.74202 | − | 2.74202i | −0.262638 | − | 0.262638i | 0.563487 | − | 0.826125i | \(-0.309459\pi\) |
−0.826125 | + | 0.563487i | \(0.809459\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.05646 | −0.574853 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.3923 | −1.35391 | −0.676957 | − | 0.736022i | \(-0.736702\pi\) | ||||
−0.676957 | + | 0.736022i | \(0.736702\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.41920 | − | 3.41920i | −0.318842 | − | 0.318842i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.23508 | + | 3.23508i | −0.299083 | + | 0.299083i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.60645i | 0.238933i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.12096i | 0.738269i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.62863 | + | 6.62863i | −0.597683 | + | 0.597683i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.707107 | + | 0.707107i | 0.0632456 | + | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.2611 | 1.62041 | 0.810204 | − | 0.586148i | \(-0.199356\pi\) | ||||
0.810204 | + | 0.586148i | \(0.199356\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.77537 | −0.596538 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.61401 | − | 4.61401i | −0.403128 | − | 0.403128i | 0.476206 | − | 0.879334i | \(-0.342012\pi\) |
−0.879334 | + | 0.476206i | \(0.842012\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.59476 | − | 3.59476i | 0.311705 | − | 0.311705i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 4.78194i | − | 0.411564i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.4195i | 1.23194i | 0.787768 | + | 0.615972i | \(0.211237\pi\) | ||||
−0.787768 | + | 0.615972i | \(0.788763\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.9160 | − | 11.9160i | 1.01070 | − | 1.01070i | 0.0107594 | − | 0.999942i | \(-0.496575\pi\) |
0.999942 | − | 0.0107594i | \(-0.00342490\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.24728 | − | 4.24728i | −0.357686 | − | 0.357686i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.64173 | −0.304537 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.77729 | 0.645869 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.985728 | − | 0.985728i | −0.0813015 | − | 0.0813015i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.47407 | + | 9.47407i | −0.776146 | + | 0.776146i | −0.979173 | − | 0.203027i | \(-0.934922\pi\) |
0.203027 | + | 0.979173i | \(0.434922\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.7062i | 0.871260i | 0.900126 | + | 0.435630i | \(0.143474\pi\) | ||||
−0.900126 | + | 0.435630i | \(0.856526\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.36824i | − | 0.191461i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.44949 | + | 4.44949i | −0.357392 | + | 0.357392i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.4986 | + | 16.4986i | 1.31674 | + | 1.31674i | 0.916344 | + | 0.400391i | \(0.131126\pi\) |
0.400391 | + | 0.916344i | \(0.368874\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.62639 | −0.525507 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.3443 | −0.894059 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.8152 | + | 10.8152i | 0.847108 | + | 0.847108i | 0.989771 | − | 0.142663i | \(-0.0455666\pi\) |
−0.142663 | + | 0.989771i | \(0.545567\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.11804 | − | 1.11804i | 0.0870390 | − | 0.0870390i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 13.9413i | − | 1.07881i | −0.842046 | − | 0.539405i | \(-0.818649\pi\) | ||
0.842046 | − | 0.539405i | \(-0.181351\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 8.39355i | − | 0.645658i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.26622 | + | 3.26622i | −0.249774 | + | 0.249774i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.73205 | − | 2.73205i | −0.207714 | − | 0.207714i | 0.595581 | − | 0.803295i | \(-0.296922\pi\) |
−0.803295 | + | 0.595581i | \(0.796922\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.34607 | 0.177346 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.92628 | 0.144788 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.7656 | + | 17.7656i | 1.32786 | + | 1.32786i | 0.907231 | + | 0.420632i | \(0.138192\pi\) |
0.420632 | + | 0.907231i | \(0.361808\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.24213 | − | 2.24213i | 0.166656 | − | 0.166656i | −0.618852 | − | 0.785508i | \(-0.712402\pi\) |
0.785508 | + | 0.618852i | \(0.212402\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.991956i | 0.0733275i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.49938i | 0.477844i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.33296 | − | 1.33296i | 0.0974760 | − | 0.0974760i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.93285 | − | 7.93285i | −0.577030 | − | 0.577030i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.60164 | 0.188248 | 0.0941241 | − | 0.995560i | \(-0.469995\pi\) | ||||
0.0941241 | + | 0.995560i | \(0.469995\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.0452 | 1.22694 | 0.613472 | − | 0.789717i | \(-0.289772\pi\) | ||||
0.613472 | + | 0.789717i | \(0.289772\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.41421 | − | 1.41421i | −0.101274 | − | 0.101274i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.0535 | + | 10.0535i | −0.716285 | + | 0.716285i | −0.967842 | − | 0.251558i | \(-0.919057\pi\) |
0.251558 | + | 0.967842i | \(0.419057\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 10.7287i | − | 0.760534i | −0.924877 | − | 0.380267i | \(-0.875832\pi\) | ||
0.924877 | − | 0.380267i | \(-0.124168\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.8883i | 1.05014i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.9019 | − | 12.9019i | 0.905536 | − | 0.905536i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.11339 | + | 7.11339i | 0.496821 | + | 0.496821i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.3076 | 0.716424 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.67679 | −0.254329 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.7350 | + | 17.7350i | 1.22093 | + | 1.22093i | 0.967303 | + | 0.253622i | \(0.0816221\pi\) |
0.253622 | + | 0.967303i | \(0.418378\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.263305 | + | 0.263305i | −0.0180414 | + | 0.0180414i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.27087i | 0.495869i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.7627i | 1.00216i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.96937 | + | 3.96937i | −0.268225 | + | 0.268225i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.68608 | − | 1.68608i | −0.113418 | − | 0.113418i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.2124 | −1.21960 | −0.609798 | − | 0.792557i | \(-0.708749\pi\) | ||||
−0.609798 | + | 0.792557i | \(0.708749\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.13165 | −0.142110 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.98797 | − | 8.98797i | −0.596552 | − | 0.596552i | 0.342841 | − | 0.939393i | \(-0.388611\pi\) |
−0.939393 | + | 0.342841i | \(0.888611\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.60645 | − | 1.60645i | 0.106157 | − | 0.106157i | −0.652033 | − | 0.758190i | \(-0.726084\pi\) |
0.758190 | + | 0.652033i | \(0.226084\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 3.70946i | − | 0.244065i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.287369i | 0.0188262i | 0.999956 | + | 0.00941309i | \(0.00299632\pi\) | ||||
−0.999956 | + | 0.00941309i | \(0.997004\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.55790 | + | 4.55790i | −0.297324 | + | 0.297324i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.4529 | + | 10.4529i | 0.678988 | + | 0.678988i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.5274 | −1.13375 | −0.566875 | − | 0.823804i | \(-0.691848\pi\) | ||||
−0.566875 | + | 0.823804i | \(0.691848\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.39371 | 0.540687 | 0.270343 | − | 0.962764i | \(-0.412863\pi\) | ||||
0.270343 | + | 0.962764i | \(0.412863\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.4216 | + | 11.4216i | 0.732696 | + | 0.732696i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.05782 | + | 1.05782i | −0.0675814 | + | 0.0675814i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.65080i | 0.295923i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 0.412290i | − | 0.0261278i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.83548 | + | 9.83548i | −0.620810 | + | 0.620810i | −0.945738 | − | 0.324929i | \(-0.894660\pi\) |
0.324929 | + | 0.945738i | \(0.394660\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.80161 | + | 5.80161i | 0.364744 | + | 0.364744i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.03528 | 0.0648315 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.2054 | 1.13562 | 0.567811 | − | 0.823159i | \(-0.307791\pi\) | ||||
0.567811 | + | 0.823159i | \(0.307791\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.7819 | + | 10.7819i | 0.669957 | + | 0.669957i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.7228 | + | 11.7228i | −0.725621 | + | 0.725621i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 22.5174i | − | 1.38848i | −0.719742 | − | 0.694242i | \(-0.755740\pi\) | ||
0.719742 | − | 0.694242i | \(-0.244260\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.11099i | 0.436825i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.9089 | + | 10.9089i | −0.667617 | + | 0.667617i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.0745 | − | 15.0745i | −0.919107 | − | 0.919107i | 0.0778580 | − | 0.996964i | \(-0.475192\pi\) |
−0.996964 | + | 0.0778580i | \(0.975192\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.6848 | −1.86397 | −0.931985 | − | 0.362496i | \(-0.881925\pi\) | ||||
−0.931985 | + | 0.362496i | \(0.881925\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.69213 | −0.283981 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.19980 | − | 1.19980i | −0.0723507 | − | 0.0723507i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.85425 | + | 6.85425i | −0.411832 | + | 0.411832i | −0.882376 | − | 0.470544i | \(-0.844058\pi\) |
0.470544 | + | 0.882376i | \(0.344058\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 13.4135i | − | 0.803044i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.44433i | 0.145817i | 0.997339 | + | 0.0729083i | \(0.0232280\pi\) | ||||
−0.997339 | + | 0.0729083i | \(0.976772\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.29171 | + | 2.29171i | −0.136228 | + | 0.136228i | −0.771932 | − | 0.635705i | \(-0.780710\pi\) |
0.635705 | + | 0.771932i | \(0.280710\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.42783 | − | 1.42783i | −0.0845773 | − | 0.0845773i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 23.6011 | 1.39313 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.7657 | −0.927394 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.02582 | − | 6.02582i | −0.353240 | − | 0.353240i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.9043 | + | 17.9043i | −1.04598 | + | 1.04598i | −0.0470899 | + | 0.998891i | \(0.514995\pi\) |
−0.998891 | + | 0.0470899i | \(0.985005\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 2.06715i | − | 0.120354i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.11387i | 0.470815i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.33850 | − | 7.33850i | 0.424397 | − | 0.424397i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.0618 | + | 12.0618i | 0.695229 | + | 0.695229i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.58919 | −0.148745 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.06450 | 0.0609531 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.15125 | + | 7.15125i | 0.408143 | + | 0.408143i | 0.881091 | − | 0.472947i | \(-0.156810\pi\) |
−0.472947 | + | 0.881091i | \(0.656810\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.98414 | + | 2.98414i | −0.169762 | + | 0.169762i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 23.2114i | − | 1.31620i | −0.752930 | − | 0.658100i | \(-0.771360\pi\) | ||
0.752930 | − | 0.658100i | \(-0.228640\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.10686i | 0.288657i | 0.989530 | + | 0.144328i | \(0.0461022\pi\) | ||||
−0.989530 | + | 0.144328i | \(0.953898\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.53624 | + | 3.53624i | −0.199244 | + | 0.199244i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.6162 | + | 20.6162i | 1.15792 | + | 1.15792i | 0.984922 | + | 0.172997i | \(0.0553451\pi\) |
0.172997 | + | 0.984922i | \(0.444655\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.1963 | −0.738852 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.78975 | 0.211523 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.70231 | − | 1.70231i | −0.0947192 | − | 0.0947192i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.51764 | + | 1.51764i | −0.0841834 | + | 0.0841834i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.61353i | 0.199829i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.1224i | 0.833723i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.1686 | − | 10.1686i | 0.558917 | − | 0.558917i | −0.370082 | − | 0.928999i | \(-0.620670\pi\) |
0.928999 | + | 0.370082i | \(0.120670\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.79655 | − | 9.79655i | −0.536848 | − | 0.536848i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.9771 | 0.872922 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.9542 | 0.760133 | 0.380067 | − | 0.924959i | \(-0.375901\pi\) | ||||
0.380067 | + | 0.924959i | \(0.375901\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.48336 | + | 9.48336i | 0.515065 | + | 0.515065i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.54978 | − | 7.54978i | 0.408844 | − | 0.408844i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.9321i | 1.07623i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.50595i | 0.242592i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.1208 | + | 20.1208i | −1.08014 | + | 1.08014i | −0.0836444 | + | 0.996496i | \(0.526656\pi\) |
−0.996496 | + | 0.0836444i | \(0.973344\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.33386 | + | 3.33386i | 0.178457 | + | 0.178457i | 0.790683 | − | 0.612226i | \(-0.209726\pi\) |
−0.612226 | + | 0.790683i | \(0.709726\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.2633 | 0.547815 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −35.7352 | −1.90199 | −0.950997 | − | 0.309199i | \(-0.899939\pi\) | ||||
−0.950997 | + | 0.309199i | \(0.899939\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.282561 | + | 0.282561i | 0.0149968 | + | 0.0149968i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.71744 | − | 1.71744i | 0.0908965 | − | 0.0908965i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 11.2159i | − | 0.591954i | −0.955195 | − | 0.295977i | \(-0.904355\pi\) | ||
0.955195 | − | 0.295977i | \(-0.0956451\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 14.3044i | − | 0.752864i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.35105 | − | 5.35105i | 0.280857 | − | 0.280857i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.25966 | + | 4.25966i | 0.222961 | + | 0.222961i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.2867 | −0.693561 | −0.346781 | − | 0.937946i | \(-0.612725\pi\) | ||||
−0.346781 | + | 0.937946i | \(0.612725\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −21.4441 | −1.11634 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.7966 | + | 11.7966i | 0.612446 | + | 0.612446i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.58166 | + | 2.58166i | −0.133673 | + | 0.133673i | −0.770778 | − | 0.637104i | \(-0.780132\pi\) |
0.637104 | + | 0.770778i | \(0.280132\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 0.931852i | − | 0.0481206i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.6921i | 0.859688i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.2025 | − | 19.2025i | 0.986365 | − | 0.986365i | −0.0135436 | − | 0.999908i | \(-0.504311\pi\) |
0.999908 | + | 0.0135436i | \(0.00431118\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.0326 | − | 12.0326i | −0.616447 | − | 0.616447i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.5286 | −0.997867 | −0.498933 | − | 0.866640i | \(-0.666275\pi\) | ||||
−0.498933 | + | 0.866640i | \(0.666275\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.98074 | −0.202877 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.9594 | − | 10.9594i | −0.557099 | − | 0.557099i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.67412 | − | 5.67412i | 0.287689 | − | 0.287689i | −0.548477 | − | 0.836166i | \(-0.684792\pi\) |
0.836166 | + | 0.548477i | \(0.184792\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.37216i | 0.271682i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.08052i | 0.306722i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.2173 | − | 11.2173i | 0.564405 | − | 0.564405i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.8102 | + | 13.8102i | 0.693112 | + | 0.693112i | 0.962916 | − | 0.269803i | \(-0.0869586\pi\) |
−0.269803 | + | 0.962916i | \(0.586959\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.73731 | −0.237162 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.06126 | 0.202810 | 0.101405 | − | 0.994845i | \(-0.467666\pi\) | ||||
0.101405 | + | 0.994845i | \(0.467666\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.54978 | − | 9.54978i | −0.475708 | − | 0.475708i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.37101 | − | 1.37101i | 0.0681260 | − | 0.0681260i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 11.0280i | − | 0.546637i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 15.6651i | − | 0.774587i | −0.921956 | − | 0.387294i | \(-0.873410\pi\) | ||
0.921956 | − | 0.387294i | \(-0.126590\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.50130 | − | 9.50130i | 0.468665 | − | 0.468665i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.42924 | − | 3.42924i | −0.168742 | − | 0.168742i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.442442 | −0.0217186 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.7033 | −0.768996 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.6081 | + | 12.6081i | 0.615947 | + | 0.615947i | 0.944489 | − | 0.328542i | \(-0.106557\pi\) |
−0.328542 | + | 0.944489i | \(0.606557\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.77589 | + | 5.77589i | −0.281499 | + | 0.281499i | −0.833707 | − | 0.552207i | \(-0.813786\pi\) |
0.552207 | + | 0.833707i | \(0.313786\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 13.7403i | − | 0.668076i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 1.11099i | − | 0.0538908i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.76592 | − | 1.76592i | 0.0854588 | − | 0.0854588i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.39960 | + | 2.39960i | 0.115854 | + | 0.115854i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.928203 | 0.0447100 | 0.0223550 | − | 0.999750i | \(-0.492884\pi\) | ||||
0.0223550 | + | 0.999750i | \(0.492884\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.3730 | 1.17129 | 0.585647 | − | 0.810566i | \(-0.300841\pi\) | ||||
0.585647 | + | 0.810566i | \(0.300841\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.12460 | − | 5.12460i | −0.245706 | − | 0.245706i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.40916 | − | 7.40916i | 0.354428 | − | 0.354428i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.1832i | 1.20193i | 0.799276 | + | 0.600964i | \(0.205216\pi\) | ||||
−0.799276 | + | 0.600964i | \(0.794784\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 3.18891i | − | 0.151853i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.38152 | + | 8.38152i | −0.398218 | + | 0.398218i | −0.877604 | − | 0.479386i | \(-0.840859\pi\) |
0.479386 | + | 0.877604i | \(0.340859\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.7067 | + | 11.7067i | 0.554953 | + | 0.554953i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.4853 | 0.590534 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.60607 | 0.311760 | 0.155880 | − | 0.987776i | \(-0.450179\pi\) | ||||
0.155880 | + | 0.987776i | \(0.450179\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.0698 | − | 12.0698i | −0.568346 | − | 0.568346i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.05453 | − | 7.05453i | 0.331451 | − | 0.331451i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.03528i | 0.236057i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 36.6201i | 1.71302i | 0.516133 | + | 0.856508i | \(0.327371\pi\) | ||||
−0.516133 | + | 0.856508i | \(0.672629\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.75663 | + | 3.75663i | −0.175344 | + | 0.175344i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.96472 | + | 5.96472i | 0.277805 | + | 0.277805i | 0.832232 | − | 0.554427i | \(-0.187063\pi\) |
−0.554427 | + | 0.832232i | \(0.687063\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.8749 | −0.644820 | −0.322410 | − | 0.946600i | \(-0.604493\pi\) | ||||
−0.322410 | + | 0.946600i | \(0.604493\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.86370 | 0.271923 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.8755 | − | 19.8755i | −0.919729 | − | 0.919729i | 0.0772800 | − | 0.997009i | \(-0.475376\pi\) |
−0.997009 | + | 0.0772800i | \(0.975376\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26.5047 | − | 26.5047i | 1.22387 | − | 1.22387i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 21.7425i | − | 1.00184i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 12.3370i | − | 0.567257i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.53225 | + | 1.53225i | −0.0703044 | + | 0.0703044i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.7184 | − | 10.7184i | −0.490763 | − | 0.490763i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.5931 | 0.712467 | 0.356233 | − | 0.934397i | \(-0.384061\pi\) | ||||
0.356233 | + | 0.934397i | \(0.384061\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.9494 | −0.636037 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.47500 | + | 7.47500i | 0.340124 | + | 0.340124i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.46651 | + | 6.46651i | −0.293629 | + | 0.293629i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.1319i | 0.640378i | 0.947354 | + | 0.320189i | \(0.103746\pi\) | ||||
−0.947354 | + | 0.320189i | \(0.896254\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 14.2526i | − | 0.644525i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.7841 | + | 23.7841i | −1.07336 | + | 1.07336i | −0.0762760 | + | 0.997087i | \(0.524303\pi\) |
−0.997087 | + | 0.0762760i | \(0.975697\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.10974 | − | 6.10974i | −0.275169 | − | 0.275169i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.61693 | 0.162569 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.937492 | 0.0420522 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.91119 | + | 1.91119i | 0.0855565 | + | 0.0855565i | 0.748590 | − | 0.663033i | \(-0.230731\pi\) |
−0.663033 | + | 0.748590i | \(0.730731\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.18618 | + | 9.18618i | −0.410408 | + | 0.410408i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.9343i | 0.933414i | 0.884412 | + | 0.466707i | \(0.154560\pi\) | ||||
−0.884412 | + | 0.466707i | \(0.845440\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.77854i | 0.123643i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.53067 | + | 5.53067i | −0.245625 | + | 0.245625i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.2127 | − | 17.2127i | −0.762939 | − | 0.762939i | 0.213914 | − | 0.976853i | \(-0.431379\pi\) |
−0.976853 | + | 0.213914i | \(0.931379\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.1328 | 0.625200 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.3621 | 0.457499 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.20238 | + | 3.20238i | 0.141114 | + | 0.141114i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.73373 | − | 7.73373i | 0.340129 | − | 0.340129i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.60040i | 0.158040i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 30.0588i | − | 1.31690i | −0.752625 | − | 0.658449i | \(-0.771213\pi\) | ||
0.752625 | − | 0.658449i | \(-0.228787\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.17948 | − | 6.17948i | 0.270210 | − | 0.270210i | −0.558975 | − | 0.829185i | \(-0.688805\pi\) |
0.829185 | + | 0.558975i | \(0.188805\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.54587 | − | 1.54587i | −0.0674671 | − | 0.0674671i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.99093 | 0.304529 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.381822 | −0.0166009 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.11583 | + | 3.11583i | 0.135216 | + | 0.135216i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.2672 | + | 15.2672i | −0.661297 | + | 0.661297i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 4.06690i | − | 0.175828i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 23.4122i | − | 1.01031i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.79488 | − | 1.79488i | 0.0773108 | − | 0.0773108i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.3198 | + | 11.3198i | 0.486675 | + | 0.486675i | 0.907255 | − | 0.420581i | \(-0.138174\pi\) |
−0.420581 | + | 0.907255i | \(0.638174\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.95476 | −0.126801 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.87780 | 0.166107 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.87965 | − | 5.87965i | −0.251396 | − | 0.251396i | 0.570147 | − | 0.821543i | \(-0.306886\pi\) |
−0.821543 | + | 0.570147i | \(0.806886\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.60453 | + | 1.60453i | −0.0684795 | + | 0.0684795i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.8528i | 0.717955i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 37.2173i | − | 1.58264i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.28256 | − | 4.28256i | 0.181785 | − | 0.181785i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.0900 | − | 21.0900i | −0.893611 | − | 0.893611i | 0.101250 | − | 0.994861i | \(-0.467716\pi\) |
−0.994861 | + | 0.101250i | \(0.967716\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.6052 | −0.660030 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.75663 | −0.0741650 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.9169 | − | 29.9169i | −1.26084 | − | 1.26084i | −0.950684 | − | 0.310161i | \(-0.899617\pi\) |
−0.310161 | − | 0.950684i | \(-0.600383\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.1769 | − | 10.1769i | 0.428145 | − | 0.428145i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 4.54879i | − | 0.191031i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.80990i | 0.201641i | 0.994905 | + | 0.100821i | \(0.0321469\pi\) | ||||
−0.994905 | + | 0.100821i | \(0.967853\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.6639 | − | 22.6639i | 0.948455 | − | 0.948455i | −0.0502803 | − | 0.998735i | \(-0.516011\pi\) |
0.998735 | + | 0.0502803i | \(0.0160115\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.71427 | − | 1.71427i | −0.0716147 | − | 0.0716147i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.83548 | 0.201653 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 45.5463 | 1.89612 | 0.948059 | − | 0.318094i | \(-0.103043\pi\) | ||||
0.948059 | + | 0.318094i | \(0.103043\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.2314 | − | 11.2314i | −0.466762 | − | 0.466762i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.733974 | + | 0.733974i | −0.0304504 | + | 0.0304504i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 12.0657i | − | 0.499712i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 4.57509i | − | 0.189157i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.27826 | + | 9.27826i | −0.382955 | + | 0.382955i | −0.872166 | − | 0.489211i | \(-0.837285\pi\) |
0.489211 | + | 0.872166i | \(0.337285\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.64173 | − | 9.64173i | −0.397280 | − | 0.397280i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.2489 | 0.544988 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.32677 | −0.136614 | −0.0683071 | − | 0.997664i | \(-0.521760\pi\) | ||||
−0.0683071 | + | 0.997664i | \(0.521760\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.84304 | − | 1.84304i | −0.0755572 | − | 0.0755572i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.06931 | + | 7.06931i | −0.289328 | + | 0.289328i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.52640i | 0.307520i | 0.988108 | + | 0.153760i | \(0.0491383\pi\) | ||||
−0.988108 | + | 0.153760i | \(0.950862\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 9.03188i | − | 0.368418i | −0.982887 | − | 0.184209i | \(-0.941028\pi\) | ||
0.982887 | − | 0.184209i | \(-0.0589723\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −24.0824 | + | 24.0824i | −0.980710 | + | 0.980710i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.74238 | − | 5.74238i | −0.233461 | − | 0.233461i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.7031 | 0.475014 | 0.237507 | − | 0.971386i | \(-0.423670\pi\) | ||||
0.237507 | + | 0.971386i | \(0.423670\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −17.0026 | −0.688980 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.78245 | − | 9.78245i | −0.395756 | − | 0.395756i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.2477 | − | 19.2477i | 0.777408 | − | 0.777408i | −0.201981 | − | 0.979389i | \(-0.564738\pi\) |
0.979389 | + | 0.201981i | \(0.0647381\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 9.37429i | − | 0.378008i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 13.5963i | − | 0.547365i | −0.961820 | − | 0.273683i | \(-0.911758\pi\) | ||
0.961820 | − | 0.273683i | \(-0.0882418\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.50303 | + | 1.50303i | −0.0604117 | + | 0.0604117i | −0.736667 | − | 0.676255i | \(-0.763602\pi\) |
0.676255 | + | 0.736667i | \(0.263602\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.3504 | − | 16.3504i | −0.656119 | − | 0.656119i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 38.8411 | 1.55613 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.42271 | + | 2.42271i | 0.0967535 | + | 0.0967535i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.10583 | − | 5.10583i | 0.203583 | − | 0.203583i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.1399i | 1.08042i | 0.841530 | + | 0.540210i | \(0.181655\pi\) | ||||
−0.841530 | + | 0.540210i | \(0.818345\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 23.3718i | − | 0.928946i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.9125 | + | 12.9125i | −0.512418 | + | 0.512418i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.27035 | − | 2.27035i | −0.0899547 | − | 0.0899547i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.851812 | −0.0336972 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.5635 | 1.08869 | 0.544346 | − | 0.838861i | \(-0.316778\pi\) | ||||
0.544346 | + | 0.838861i | \(0.316778\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.1493 | + | 23.1493i | 0.912918 | + | 0.912918i | 0.996501 | − | 0.0835832i | \(-0.0266364\pi\) |
−0.0835832 | + | 0.996501i | \(0.526636\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.79091 | − | 4.79091i | 0.188642 | − | 0.188642i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.4410i | 1.11813i | 0.829123 | + | 0.559066i | \(0.188840\pi\) | ||||
−0.829123 | + | 0.559066i | \(0.811160\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.50749i | 0.137681i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.72741 | − | 9.72741i | 0.381247 | − | 0.381247i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.957676 | − | 0.957676i | −0.0374767 | − | 0.0374767i | 0.688120 | − | 0.725597i | \(-0.258436\pi\) |
−0.725597 | + | 0.688120i | \(0.758436\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.52520 | 0.254961 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.8412 | −0.500983 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.917240 | + | 0.917240i | 0.0357306 | + | 0.0357306i | 0.724746 | − | 0.689016i | \(-0.241957\pi\) |
−0.689016 | + | 0.724746i | \(0.741957\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.7481 | − | 11.7481i | 0.456947 | − | 0.456947i | −0.440705 | − | 0.897652i | \(-0.645272\pi\) |
0.897652 | + | 0.440705i | \(0.145272\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.22198i | 0.0862944i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.08376i | 0.197140i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.5921 | − | 26.5921i | 1.02965 | − | 1.02965i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.0005 | + | 12.0005i | 0.463967 | + | 0.463967i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.80622 | −0.0697282 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.48817 | 0.288648 | 0.144324 | − | 0.989531i | \(-0.453899\pi\) | ||||
0.144324 | + | 0.989531i | \(0.453899\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.38134 | + | 3.38134i | 0.130148 | + | 0.130148i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.3721 | − | 19.3721i | 0.744528 | − | 0.744528i | −0.228917 | − | 0.973446i | \(-0.573519\pi\) |
0.973446 | + | 0.228917i | \(0.0735186\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.4548i | 0.823360i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.8447i | 0.453889i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.4723 | − | 14.4723i | 0.553765 | − | 0.553765i | −0.373760 | − | 0.927525i | \(-0.621932\pi\) |
0.927525 | + | 0.373760i | \(0.121932\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.1962 | − | 10.1962i | −0.389575 | − | 0.389575i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.11704 | −0.0807701 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.2621 | −0.581438 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.3482 | − | 18.3482i | −0.697999 | − | 0.697999i | 0.265979 | − | 0.963979i | \(-0.414305\pi\) |
−0.963979 | + | 0.265979i | \(0.914305\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.00020 | − | 6.00020i | 0.227929 | − | 0.227929i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.8518i | 0.639224i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 11.1764i | − | 0.423336i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.189353 | − | 0.189353i | 0.00716198 | − | 0.00716198i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.9630 | − | 12.9630i | −0.489604 | − | 0.489604i | 0.418577 | − | 0.908181i | \(-0.362529\pi\) |
−0.908181 | + | 0.418577i | \(0.862529\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.0837 | −0.531176 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.00657 | 0.226220 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.60937 | + | 4.60937i | 0.173353 | + | 0.173353i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.10583 | − | 6.10583i | 0.229309 | − | 0.229309i | −0.583095 | − | 0.812404i | \(-0.698158\pi\) |
0.812404 | + | 0.583095i | \(0.198158\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 33.8159i | 1.26820i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 30.4274i | 1.13951i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.57509 | − | 2.57509i | 0.0963029 | − | 0.0963029i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.5491 | + | 11.5491i | 0.431309 | + | 0.431309i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 49.9396 | 1.86243 | 0.931216 | − | 0.364467i | \(-0.118749\pi\) | ||||
0.931216 | + | 0.364467i | \(0.118749\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.6250 | 0.395695 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.53077 | − | 5.53077i | −0.205692 | − | 0.205692i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.49938 | + | 5.49938i | −0.204242 | + | 0.204242i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.41214i | 0.311989i | 0.987758 | + | 0.155994i | \(0.0498582\pi\) | ||||
−0.987758 | + | 0.155994i | \(0.950142\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 9.23511i | − | 0.342041i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.71190 | − | 5.71190i | 0.211262 | − | 0.211262i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.6663 | − | 10.6663i | −0.393969 | − | 0.393969i | 0.482130 | − | 0.876099i | \(-0.339863\pi\) |
−0.876099 | + | 0.482130i | \(0.839863\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.39403 | 0.0514196 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −27.1095 | −0.998592 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.63735 | − | 8.63735i | −0.317730 | − | 0.317730i | 0.530165 | − | 0.847895i | \(-0.322130\pi\) |
−0.847895 | + | 0.530165i | \(0.822130\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.06450 | − | 3.06450i | 0.112577 | − | 0.112577i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.1561i | 0.372592i | 0.982494 | + | 0.186296i | \(0.0596484\pi\) | ||||
−0.982494 | + | 0.186296i | \(0.940352\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 13.3984i | − | 0.490878i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.666895 | − | 0.666895i | 0.0244004 | − | 0.0244004i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.74666 | − | 6.74666i | −0.246518 | − | 0.246518i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.3700 | −0.889272 | −0.444636 | − | 0.895711i | \(-0.646667\pi\) | ||||
−0.444636 | + | 0.895711i | \(0.646667\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.9616 | 0.472345 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.57045 | − | 7.57045i | −0.275517 | − | 0.275517i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.98325 | + | 8.98325i | −0.326502 | + | 0.326502i | −0.851255 | − | 0.524753i | \(-0.824158\pi\) |
0.524753 | + | 0.851255i | \(0.324158\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 7.64557i | − | 0.277517i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.00929i | 0.145337i | 0.997356 | + | 0.0726683i | \(0.0231514\pi\) | ||||
−0.997356 | + | 0.0726683i | \(0.976849\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.43295 | − | 6.43295i | 0.232889 | − | 0.232889i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.67460 | + | 1.67460i | 0.0605453 | + | 0.0605453i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.43666 | 0.160198 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 46.6663 | 1.68283 | 0.841414 | − | 0.540391i | \(-0.181724\pi\) | ||||
0.841414 | + | 0.540391i | \(0.181724\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.9959 | − | 11.9959i | −0.432021 | − | 0.432021i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.8133 | − | 15.8133i | 0.568766 | − | 0.568766i | −0.363017 | − | 0.931783i | \(-0.618253\pi\) |
0.931783 | + | 0.363017i | \(0.118253\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 6.29253i | − | 0.226034i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 14.2088i | − | 0.509739i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.4142 | + | 15.4142i | −0.552272 | + | 0.552272i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.479442 | − | 0.479442i | −0.0171558 | − | 0.0171558i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 37.1905 | 1.32908 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −23.3326 | −0.832777 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.1108 | − | 20.1108i | −0.716873 | − | 0.716873i | 0.251091 | − | 0.967964i | \(-0.419211\pi\) |
−0.967964 | + | 0.251091i | \(0.919211\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.8372 | + | 14.8372i | −0.528217 | + | 0.528217i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 33.7653i | − | 1.20056i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.28470i | 0.0811320i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.68556 | − | 4.68556i | 0.166180 | − | 0.166180i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.79415 | − | 2.79415i | −0.0989738 | − | 0.0989738i | 0.655886 | − | 0.754860i | \(-0.272295\pi\) |
−0.754860 | + | 0.655886i | \(0.772295\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.16125 | 0.253347 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −35.2913 | −1.24696 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.22768 | − | 7.22768i | −0.255059 | − | 0.255059i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.02166 | − | 8.02166i | 0.282726 | − | 0.282726i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 19.8657i | 0.699306i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 39.9600i | − | 1.40492i | −0.711723 | − | 0.702460i | \(-0.752085\pi\) | ||
0.711723 | − | 0.702460i | \(-0.247915\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.8685 | + | 29.8685i | −1.04883 | + | 1.04883i | −0.0500814 | + | 0.998745i | \(0.515948\pi\) |
−0.998745 | + | 0.0500814i | \(0.984052\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.2188 | + | 20.2188i | 0.709105 | + | 0.709105i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15.2949 | −0.535758 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.7555 | −0.551214 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.58970 | − | 7.58970i | −0.265206 | − | 0.265206i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.2658 | − | 11.2658i | 0.393180 | − | 0.393180i | −0.482640 | − | 0.875819i | \(-0.660322\pi\) |
0.875819 | + | 0.482640i | \(0.160322\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.8670i | 0.413657i | 0.978377 | + | 0.206828i | \(0.0663142\pi\) | ||||
−0.978377 | + | 0.206828i | \(0.933686\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.58114i | 0.0550483i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.5457 | − | 13.5457i | 0.471030 | − | 0.471030i | −0.431218 | − | 0.902248i | \(-0.641916\pi\) |
0.902248 | + | 0.431218i | \(0.141916\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.3975 | + | 10.3975i | 0.361119 | + | 0.361119i | 0.864225 | − | 0.503106i | \(-0.167809\pi\) |
−0.503106 | + | 0.864225i | \(0.667809\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.03279 | 0.313344 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.66201 | 0.0575854 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.85799 | + | 9.85799i | 0.341150 | + | 0.341150i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −21.2772 | + | 21.2772i | −0.735447 | + | 0.735447i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 2.89168i | − | 0.0998320i | −0.998753 | − | 0.0499160i | \(-0.984105\pi\) | ||
0.998753 | − | 0.0499160i | \(-0.0158954\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31.4863i | 1.08573i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.61061 | − | 1.61061i | 0.0554725 | − | 0.0554725i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.93514 | + | 5.93514i | 0.204175 | + | 0.204175i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.0523 | −0.654645 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.02010 | 0.103650 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 22.2227 | + | 22.2227i | 0.761783 | + | 0.761783i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.6325 | − | 13.6325i | 0.466769 | − | 0.466769i | −0.434097 | − | 0.900866i | \(-0.642932\pi\) |
0.900866 | + | 0.434097i | \(0.142932\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 4.61914i | − | 0.157971i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 37.4062i | − | 1.27777i | −0.769302 | − | 0.638886i | \(-0.779396\pi\) | ||
0.769302 | − | 0.638886i | \(-0.220604\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.8754 | − | 13.8754i | 0.473422 | − | 0.473422i | −0.429598 | − | 0.903020i | \(-0.641345\pi\) |
0.903020 | + | 0.429598i | \(0.141345\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.5512 | − | 15.5512i | −0.529983 | − | 0.529983i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −47.5152 | −1.61744 | −0.808718 | − | 0.588196i | \(-0.799838\pi\) | ||||
−0.808718 | + | 0.588196i | \(0.799838\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.86370 | 0.131370 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.3883 | + | 10.3883i | 0.352806 | + | 0.352806i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19.0333 | + | 19.0333i | −0.645660 | + | 0.645660i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34.2911i | 1.16191i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 19.4940i | − | 0.659772i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.65892 | + | 1.65892i | −0.0560817 | + | 0.0560817i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.0217 | − | 22.0217i | −0.743620 | − | 0.743620i | 0.229653 | − | 0.973273i | \(-0.426241\pi\) |
−0.973273 | + | 0.229653i | \(0.926241\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 23.5950 | 0.795838 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.8379 | −0.668355 | −0.334178 | − | 0.942510i | \(-0.608459\pi\) | ||||
−0.334178 | + | 0.942510i | \(0.608459\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.7398 | − | 10.7398i | −0.361423 | − | 0.361423i | 0.502914 | − | 0.864337i | \(-0.332261\pi\) |
−0.864337 | + | 0.502914i | \(0.832261\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.36209 | + | 1.36209i | −0.0457860 | + | 0.0457860i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 57.5726i | − | 1.93310i | −0.256478 | − | 0.966550i | \(-0.582562\pi\) | ||
0.256478 | − | 0.966550i | \(-0.417438\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 42.8416i | 1.43686i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.32629 | + | 2.32629i | −0.0779338 | + | 0.0779338i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.87664 | − | 9.87664i | −0.330509 | − | 0.330509i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.1244 | −0.839815 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.67095 | −0.322904 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −34.6050 | − | 34.6050i | −1.15414 | − | 1.15414i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.58630 | − | 5.58630i | 0.186107 | − | 0.186107i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 15.8955i | − | 0.528968i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.17084i | 0.105402i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.73175 | + | 3.73175i | −0.123911 | + | 0.123911i | −0.766343 | − | 0.642432i | \(-0.777925\pi\) |
0.642432 | + | 0.766343i | \(0.277925\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.18811 | − | 4.18811i | −0.138911 | − | 0.138911i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.9590 | −0.396219 | −0.198110 | − | 0.980180i | \(-0.563480\pi\) | ||||
−0.198110 | + | 0.980180i | \(0.563480\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.750724 | 0.0248453 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.701419 | − | 0.701419i | −0.0231882 | − | 0.0231882i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.8248 | − | 10.8248i | 0.357466 | − | 0.357466i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 53.6932i | − | 1.77118i | −0.464472 | − | 0.885588i | \(-0.653756\pi\) | ||
0.464472 | − | 0.885588i | \(-0.346244\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 9.42418i | − | 0.310537i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.606451 | + | 0.606451i | −0.0199616 | + | 0.0199616i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.59575 | − | 4.59575i | −0.151107 | − | 0.151107i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.65393 | −0.317077 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.25033 | 0.237876 | 0.118938 | − | 0.992902i | \(-0.462051\pi\) | ||||
0.118938 | + | 0.992902i | \(0.462051\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.29221 | − | 2.29221i | −0.0751242 | − | 0.0751242i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.2945 | + | 15.2945i | −0.500718 | + | 0.500718i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.88510i | 0.0616493i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 31.3398i | − | 1.02383i | −0.859037 | − | 0.511913i | \(-0.828937\pi\) | ||
0.859037 | − | 0.511913i | \(-0.171063\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.36500 | − | 3.36500i | 0.109813 | − | 0.109813i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.5972 | + | 25.5972i | 0.834444 | + | 0.834444i | 0.988121 | − | 0.153677i | \(-0.0491117\pi\) |
−0.153677 | + | 0.988121i | \(0.549112\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 48.6442 | 1.58407 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.2187 | 0.364946 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 37.1739 | + | 37.1739i | 1.20799 | + | 1.20799i | 0.971678 | + | 0.236310i | \(0.0759382\pi\) |
0.236310 | + | 0.971678i | \(0.424062\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.14235 | + | 9.14235i | −0.296773 | + | 0.296773i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 27.1688i | − | 0.881007i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.0538i | 1.07072i | 0.844625 | + | 0.535358i | \(0.179823\pi\) | ||||
−0.844625 | + | 0.535358i | \(0.820177\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.83964 | + | 1.83964i | −0.0595293 | + | 0.0595293i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.69530 | + | 8.69530i | 0.281079 | + | 0.281079i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −33.8292 | −1.09240 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.59592 | 0.277288 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.13007 | + | 6.13007i | 0.197539 | + | 0.197539i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.0528 | + | 12.0528i | −0.387994 | + | 0.387994i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 19.8952i | − | 0.639785i | −0.947454 | − | 0.319893i | \(-0.896353\pi\) | ||
0.947454 | − | 0.319893i | \(-0.103647\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.24337i | 0.0720674i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36.6690 | + | 36.6690i | −1.17676 | + | 1.17676i | −0.196201 | + | 0.980564i | \(0.562860\pi\) |
−0.980564 | + | 0.196201i | \(0.937140\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 27.9557 | + | 27.9557i | 0.896219 | + | 0.896219i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.00000 | 0.0640513 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.8822 | 0.476124 | 0.238062 | − | 0.971250i | \(-0.423488\pi\) | ||||
0.238062 | + | 0.971250i | \(0.423488\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.8637 | − | 19.8637i | −0.634847 | − | 0.634847i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.84503 | + | 5.84503i | −0.186617 | + | 0.186617i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 39.9254i | 1.27342i | 0.771102 | + | 0.636711i | \(0.219706\pi\) | ||||
−0.771102 | + | 0.636711i | \(0.780294\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 14.2178i | − | 0.453018i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.96441 | − | 9.96441i | 0.317171 | − | 0.317171i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.8605 | + | 24.8605i | 0.790519 | + | 0.790519i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.22646 | 0.0707257 | 0.0353629 | − | 0.999375i | \(-0.488741\pi\) | ||||
0.0353629 | + | 0.999375i | \(0.488741\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.4006 | −0.425254 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.58630 | + | 7.58630i | 0.240502 | + | 0.240502i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.9730 | − | 17.9730i | 0.569211 | − | 0.569211i | −0.362696 | − | 0.931907i | \(-0.618144\pi\) |
0.931907 | + | 0.362696i | \(0.118144\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 31.0796i | 0.983316i |
(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 | 1280.2.l.a.321.2 | ✓ | 8 | |
4.3 | odd | 2 | 1280.2.l.f.321.3 | yes | 8 | ||
8.3 | odd | 2 | 1280.2.l.d.321.2 | yes | 8 | ||
8.5 | even | 2 | 1280.2.l.g.321.3 | yes | 8 | ||
16.3 | odd | 4 | 1280.2.l.d.961.2 | yes | 8 | ||
16.5 | even | 4 | inner | 1280.2.l.a.961.2 | yes | 8 | |
16.11 | odd | 4 | 1280.2.l.f.961.3 | yes | 8 | ||
16.13 | even | 4 | 1280.2.l.g.961.3 | yes | 8 | ||
32.5 | even | 8 | 5120.2.a.a.1.4 | 4 | |||
32.11 | odd | 8 | 5120.2.a.b.1.4 | 4 | |||
32.21 | even | 8 | 5120.2.a.r.1.1 | 4 | |||
32.27 | odd | 8 | 5120.2.a.q.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1280.2.l.a.321.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
1280.2.l.a.961.2 | yes | 8 | 16.5 | even | 4 | inner | |
1280.2.l.d.321.2 | yes | 8 | 8.3 | odd | 2 | ||
1280.2.l.d.961.2 | yes | 8 | 16.3 | odd | 4 | ||
1280.2.l.f.321.3 | yes | 8 | 4.3 | odd | 2 | ||
1280.2.l.f.961.3 | yes | 8 | 16.11 | odd | 4 | ||
1280.2.l.g.321.3 | yes | 8 | 8.5 | even | 2 | ||
1280.2.l.g.961.3 | yes | 8 | 16.13 | even | 4 | ||
5120.2.a.a.1.4 | 4 | 32.5 | even | 8 | |||
5120.2.a.b.1.4 | 4 | 32.11 | odd | 8 | |||
5120.2.a.q.1.1 | 4 | 32.27 | odd | 8 | |||
5120.2.a.r.1.1 | 4 | 32.21 | even | 8 |