Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(1065,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1148.1065");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.d (of order \(2\), degree \(1\), 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: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 39 x^{18} + 531 x^{16} + 3488 x^{14} + 12661 x^{12} + 27027 x^{10} + 34540 x^{8} + 25909 x^{6} + 10677 x^{4} + 2092 x^{2} + 144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1065.19 | ||
Root | \(-1.52399i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1148.1065 |
Dual form | 1148.2.d.a.1065.2 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 2.64112i | 1.52485i | 0.647075 | + | 0.762427i | \(0.275992\pi\) | ||||
−0.647075 | + | 0.762427i | \(0.724008\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.508610 | 0.227457 | 0.113729 | − | 0.993512i | \(-0.463721\pi\) | ||||
0.113729 | + | 0.993512i | \(0.463721\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.97553 | −1.32518 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.38158i | − | 0.416561i | −0.978069 | − | 0.208280i | \(-0.933213\pi\) | ||
0.978069 | − | 0.208280i | \(-0.0667867\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.62949i | 0.729291i | 0.931146 | + | 0.364645i | \(0.118810\pi\) | ||||
−0.931146 | + | 0.364645i | \(0.881190\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.34330i | 0.346839i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.63814i | 0.882380i | 0.897414 | + | 0.441190i | \(0.145443\pi\) | ||||
−0.897414 | + | 0.441190i | \(0.854557\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0724145i | 0.0166130i | 0.999966 | + | 0.00830652i | \(0.00264408\pi\) | ||||
−0.999966 | + | 0.00830652i | \(0.997356\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.64112 | −0.576340 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.11469 | −0.649457 | −0.324729 | − | 0.945807i | \(-0.605273\pi\) | ||||
−0.324729 | + | 0.945807i | \(0.605273\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.74132 | −0.948263 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 2.57650i | − | 0.495847i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.90463i | 1.09646i | 0.836327 | + | 0.548231i | \(0.184699\pi\) | ||||
−0.836327 | + | 0.548231i | \(0.815301\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.48761 | −0.446789 | −0.223394 | − | 0.974728i | \(-0.571714\pi\) | ||||
−0.223394 | + | 0.974728i | \(0.571714\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.64891 | 0.635194 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.508610i | 0.0859708i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.477276 | −0.0784637 | −0.0392319 | − | 0.999230i | \(-0.512491\pi\) | ||||
−0.0392319 | + | 0.999230i | \(0.512491\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.94482 | −1.11206 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.803934 | + | 6.35246i | −0.125553 | + | 0.992087i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.169419 | −0.0258362 | −0.0129181 | − | 0.999917i | \(-0.504112\pi\) | ||||
−0.0129181 | + | 0.999917i | \(0.504112\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.02199 | −0.301421 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 7.87970i | − | 1.14937i | −0.818374 | − | 0.574686i | \(-0.805124\pi\) | ||
0.818374 | − | 0.574686i | \(-0.194876\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.60879 | −1.34550 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1.97267i | − | 0.270966i | −0.990780 | − | 0.135483i | \(-0.956741\pi\) | ||
0.990780 | − | 0.135483i | \(-0.0432587\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.702683i | − | 0.0947498i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.191256 | −0.0253324 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.22422 | −0.549947 | −0.274974 | − | 0.961452i | \(-0.588669\pi\) | ||||
−0.274974 | + | 0.961452i | \(0.588669\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.4481 | 1.33775 | 0.668873 | − | 0.743377i | \(-0.266777\pi\) | ||||
0.668873 | + | 0.743377i | \(0.266777\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 3.97553i | − | 0.500870i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.33739i | 0.165882i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 8.77120i | − | 1.07157i | −0.844354 | − | 0.535786i | \(-0.820015\pi\) | ||
0.844354 | − | 0.535786i | \(-0.179985\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 8.22627i | − | 0.990327i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.853928i | 0.101343i | 0.998715 | + | 0.0506713i | \(0.0161361\pi\) | ||||
−0.998715 | + | 0.0506713i | \(0.983864\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.17800 | 0.723081 | 0.361540 | − | 0.932356i | \(-0.382251\pi\) | ||||
0.361540 | + | 0.932356i | \(0.382251\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 12.5224i | − | 1.44596i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.38158 | 0.157445 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1.30234i | − | 0.146525i | −0.997313 | − | 0.0732624i | \(-0.976659\pi\) | ||
0.997313 | − | 0.0732624i | \(-0.0233411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.12175 | −0.569083 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.00782 | 0.549680 | 0.274840 | − | 0.961490i | \(-0.411375\pi\) | ||||
0.274840 | + | 0.961490i | \(0.411375\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.85040i | 0.200704i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −15.5949 | −1.67194 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.89431i | 0.730796i | 0.930851 | + | 0.365398i | \(0.119067\pi\) | ||||
−0.930851 | + | 0.365398i | \(0.880933\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.62949 | −0.275646 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 6.57009i | − | 0.681287i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.0368307i | 0.00377876i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 9.36862i | − | 0.951239i | −0.879651 | − | 0.475620i | \(-0.842224\pi\) | ||
0.879651 | − | 0.475620i | \(-0.157776\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.49250i | 0.552017i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.89885i | 0.984972i | 0.870320 | + | 0.492486i | \(0.163912\pi\) | ||||
−0.870320 | + | 0.492486i | \(0.836088\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.792482 | −0.0780856 | −0.0390428 | − | 0.999238i | \(-0.512431\pi\) | ||||
−0.0390428 | + | 0.999238i | \(0.512431\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.34330 | −0.131093 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.0102 | −1.35442 | −0.677209 | − | 0.735791i | \(-0.736811\pi\) | ||||
−0.677209 | + | 0.735791i | \(0.736811\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.0323i | 1.05670i | 0.849026 | + | 0.528351i | \(0.177190\pi\) | ||||
−0.849026 | + | 0.528351i | \(0.822810\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 1.26055i | − | 0.119646i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.22227 | −0.114982 | −0.0574909 | − | 0.998346i | \(-0.518310\pi\) | ||||
−0.0574909 | + | 0.998346i | \(0.518310\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.58416 | −0.147724 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 10.4536i | − | 0.966439i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.63814 | −0.333508 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.09125 | 0.826477 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −16.7776 | − | 2.12329i | −1.51279 | − | 0.191451i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.95453 | −0.443147 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.17280 | 0.370276 | 0.185138 | − | 0.982713i | \(-0.440727\pi\) | ||||
0.185138 | + | 0.982713i | \(0.440727\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 0.447458i | − | 0.0393965i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.5869 | 0.924980 | 0.462490 | − | 0.886624i | \(-0.346956\pi\) | ||||
0.462490 | + | 0.886624i | \(0.346956\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0724145 | −0.00627914 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 1.31043i | − | 0.112784i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.05390i | 0.773527i | 0.922179 | + | 0.386764i | \(0.126407\pi\) | ||||
−0.922179 | + | 0.386764i | \(0.873593\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.99820 | −0.423942 | −0.211971 | − | 0.977276i | \(-0.567988\pi\) | ||||
−0.211971 | + | 0.977276i | \(0.567988\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 20.8113 | 1.75262 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.63285 | 0.303794 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.00315i | 0.249398i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 2.64112i | − | 0.217836i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 1.83394i | − | 0.150242i | −0.997174 | − | 0.0751210i | \(-0.976066\pi\) | ||
0.997174 | − | 0.0751210i | \(-0.0239343\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.2271i | 1.32054i | 0.751026 | + | 0.660272i | \(0.229559\pi\) | ||||
−0.751026 | + | 0.660272i | \(0.770441\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 14.4636i | − | 1.16931i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.26522 | −0.101625 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.55114i | 0.203603i | 0.994805 | + | 0.101801i | \(0.0324606\pi\) | ||||
−0.994805 | + | 0.101801i | \(0.967539\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.21005 | 0.413184 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 3.11469i | − | 0.245472i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.52310 | 0.667581 | 0.333790 | − | 0.942647i | \(-0.391672\pi\) | ||||
0.333790 | + | 0.942647i | \(0.391672\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.85587 | 0.144480 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 6.36055i | − | 0.492194i | −0.969245 | − | 0.246097i | \(-0.920852\pi\) | ||
0.969245 | − | 0.246097i | \(-0.0791482\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.08576 | 0.468135 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 0.287886i | − | 0.0220152i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.0590 | 0.840804 | 0.420402 | − | 0.907338i | \(-0.361889\pi\) | ||||
0.420402 | + | 0.907338i | \(0.361889\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 4.74132i | − | 0.358410i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 11.1567i | − | 0.838589i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 2.28487i | − | 0.170779i | −0.996348 | − | 0.0853895i | \(-0.972787\pi\) | ||
0.996348 | − | 0.0853895i | \(-0.0272135\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.46071i | 0.182903i | 0.995810 | + | 0.0914515i | \(0.0291506\pi\) | ||||
−0.995810 | + | 0.0914515i | \(0.970849\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 27.5948i | 2.03987i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.242747 | −0.0178471 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.02637 | 0.367565 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.57650 | 0.187413 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.76820i | 0.489730i | 0.969557 | + | 0.244865i | \(0.0787437\pi\) | ||||
−0.969557 | + | 0.244865i | \(0.921256\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.6140i | 0.907979i | 0.891007 | + | 0.453989i | \(0.150000\pi\) | ||||
−0.891007 | + | 0.453989i | \(0.850000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.53220 | −0.252946 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.9937 | 0.783265 | 0.391633 | − | 0.920122i | \(-0.371910\pi\) | ||||
0.391633 | + | 0.920122i | \(0.371910\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.0421i | 1.56252i | 0.624206 | + | 0.781260i | \(0.285423\pi\) | ||||
−0.624206 | + | 0.781260i | \(0.714577\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 23.1658 | 1.63399 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.90463 | −0.414424 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.408889 | + | 3.23092i | −0.0285580 | + | 0.225657i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.3825 | 0.860646 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.100046 | 0.00692034 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 1.59811i | − | 0.110018i | −0.998486 | − | 0.0550092i | \(-0.982481\pi\) | ||
0.998486 | − | 0.0550092i | \(-0.0175188\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.25533 | −0.154533 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.0861684 | −0.00587664 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 2.48761i | − | 0.168870i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.3169i | 1.10259i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.56648 | −0.643511 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 28.1669 | 1.88620 | 0.943098 | − | 0.332515i | \(-0.107897\pi\) | ||||
0.943098 | + | 0.332515i | \(0.107897\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 18.8492 | 1.25662 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 11.3800i | − | 0.755320i | −0.925944 | − | 0.377660i | \(-0.876729\pi\) | ||
0.925944 | − | 0.377660i | \(-0.123271\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.55923i | 0.499528i | 0.968307 | + | 0.249764i | \(0.0803530\pi\) | ||||
−0.968307 | + | 0.249764i | \(0.919647\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.64891i | 0.240081i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 4.36747i | − | 0.286122i | −0.989714 | − | 0.143061i | \(-0.954305\pi\) | ||
0.989714 | − | 0.143061i | \(-0.0456945\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 4.00769i | − | 0.261433i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.43964 | 0.223429 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.4430i | 1.64577i | 0.568208 | + | 0.822885i | \(0.307637\pi\) | ||||
−0.568208 | + | 0.822885i | \(0.692363\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.8105 | 1.27611 | 0.638053 | − | 0.769993i | \(-0.279740\pi\) | ||||
0.638053 | + | 0.769993i | \(0.279740\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 21.2567i | − | 1.36361i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.508610 | −0.0324939 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.190414 | −0.0121157 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.2263i | 0.838181i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.0327888 | −0.00206961 | −0.00103480 | − | 0.999999i | \(-0.500329\pi\) | ||||
−0.00103480 | + | 0.999999i | \(0.500329\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.30318i | 0.270538i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.88712 | −0.306044 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 12.6386i | − | 0.788371i | −0.919031 | − | 0.394186i | \(-0.871027\pi\) | ||
0.919031 | − | 0.394186i | \(-0.128973\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 0.477276i | − | 0.0296565i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 23.4740i | − | 1.45301i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.3942i | 0.825922i | 0.910749 | + | 0.412961i | \(0.135505\pi\) | ||||
−0.910749 | + | 0.412961i | \(0.864495\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.00332i | − | 0.0616333i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.2087 | −1.11436 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −27.8300 | −1.69683 | −0.848413 | − | 0.529335i | \(-0.822442\pi\) | ||||
−0.848413 | + | 0.529335i | \(0.822442\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.756271 | −0.0459402 | −0.0229701 | − | 0.999736i | \(-0.507312\pi\) | ||||
−0.0229701 | + | 0.999736i | \(0.507312\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 6.94482i | − | 0.420320i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.55049i | 0.395009i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.35529 | −0.502021 | −0.251010 | − | 0.967984i | \(-0.580763\pi\) | ||||
−0.251010 | + | 0.967984i | \(0.580763\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.88958 | 0.592074 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.9049i | 1.06812i | 0.845447 | + | 0.534060i | \(0.179334\pi\) | ||||
−0.845447 | + | 0.534060i | \(0.820666\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.2783 | 1.62153 | 0.810763 | − | 0.585374i | \(-0.199052\pi\) | ||||
0.810763 | + | 0.585374i | \(0.199052\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.0972745 | −0.00576205 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.35246 | − | 0.803934i | −0.374974 | − | 0.0474547i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.76391 | 0.221406 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 24.7437 | 1.45050 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 19.1720i | − | 1.12004i | −0.828479 | − | 0.560021i | \(-0.810793\pi\) | ||
0.828479 | − | 0.560021i | \(-0.189207\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.14848 | −0.125089 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.55963 | −0.206551 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 8.19005i | − | 0.473643i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 0.169419i | − | 0.00976518i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −26.1441 | −1.50194 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.31402 | 0.304280 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.2272 | 1.15443 | 0.577213 | − | 0.816594i | \(-0.304140\pi\) | ||||
0.577213 | + | 0.816594i | \(0.304140\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 2.09304i | − | 0.119069i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.34846i | 0.189874i | 0.995483 | + | 0.0949368i | \(0.0302649\pi\) | ||||
−0.995483 | + | 0.0949368i | \(0.969735\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.29250i | 0.129580i | 0.997899 | + | 0.0647899i | \(0.0206377\pi\) | ||||
−0.997899 | + | 0.0647899i | \(0.979362\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 2.02199i | − | 0.113926i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.09588i | 0.0615507i | 0.999526 | + | 0.0307754i | \(0.00979765\pi\) | ||||
−0.999526 | + | 0.0307754i | \(0.990202\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.15770 | 0.456743 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 37.0027i | − | 2.06529i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.263454 | −0.0146590 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 12.4673i | − | 0.691560i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −29.1377 | −1.61132 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.87970 | 0.434422 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 29.3385i | − | 1.61259i | −0.591515 | − | 0.806294i | \(-0.701470\pi\) | ||
0.591515 | − | 0.806294i | \(-0.298530\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.89743 | 0.103978 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 4.46112i | − | 0.243737i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.155119 | 0.00844988 | 0.00422494 | − | 0.999991i | \(-0.498655\pi\) | ||||
0.00422494 | + | 0.999991i | \(0.498655\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 3.22817i | − | 0.175330i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.43683i | 0.186115i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 4.18396i | − | 0.225257i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 16.6077i | − | 0.891550i | −0.895145 | − | 0.445775i | \(-0.852928\pi\) | ||
0.895145 | − | 0.445775i | \(-0.147072\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.3856 | −1.25180 | −0.625900 | − | 0.779903i | \(-0.715268\pi\) | ||||
−0.625900 | + | 0.779903i | \(0.715268\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.77489 | 0.361617 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.1859 | 0.808262 | 0.404131 | − | 0.914701i | \(-0.367574\pi\) | ||||
0.404131 | + | 0.914701i | \(0.367574\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.434316i | 0.0230511i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 9.60879i | − | 0.508551i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.88726 | −0.363495 | −0.181748 | − | 0.983345i | \(-0.558175\pi\) | ||||
−0.181748 | + | 0.983345i | \(0.558175\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9948 | 0.999724 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 24.0111i | 1.26026i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.14219 | 0.164470 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.5256 | 0.549430 | 0.274715 | − | 0.961526i | \(-0.411416\pi\) | ||||
0.274715 | + | 0.961526i | \(0.411416\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.19606 | − | 25.2544i | 0.166380 | − | 1.31469i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.97267 | 0.102416 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.8894 | 1.08161 | 0.540807 | − | 0.841147i | \(-0.318119\pi\) | ||||
0.540807 | + | 0.841147i | \(0.318119\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 13.0855i | − | 0.675734i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.5262 | −0.799640 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.4170 | −0.689183 | −0.344592 | − | 0.938753i | \(-0.611983\pi\) | ||||
−0.344592 | + | 0.938753i | \(0.611983\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.0209i | 0.564617i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 4.10325i | − | 0.209666i | −0.994490 | − | 0.104833i | \(-0.966569\pi\) | ||
0.994490 | − | 0.104833i | \(-0.0334309\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.702683 | 0.0358121 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.673532 | 0.0342376 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.82685 | −0.143327 | −0.0716636 | − | 0.997429i | \(-0.522831\pi\) | ||||
−0.0716636 | + | 0.997429i | \(0.522831\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 11.3317i | − | 0.573068i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 27.9613i | 1.41046i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 0.662383i | − | 0.0333281i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 13.6818i | − | 0.686670i | −0.939213 | − | 0.343335i | \(-0.888443\pi\) | ||
0.939213 | − | 0.343335i | \(-0.111557\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 0.191256i | − | 0.00957476i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.0564 | 1.45101 | 0.725503 | − | 0.688219i | \(-0.241607\pi\) | ||||
0.725503 | + | 0.688219i | \(0.241607\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 6.54117i | − | 0.325839i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.60497 | −0.129442 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.659393i | 0.0326849i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.6631 | 1.31840 | 0.659202 | − | 0.751966i | \(-0.270894\pi\) | ||||
0.659202 | + | 0.751966i | \(0.270894\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −23.9125 | −1.17952 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 4.22422i | − | 0.207860i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.54703 | 0.125029 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 13.2009i | − | 0.646449i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.54721 | −0.417559 | −0.208779 | − | 0.977963i | \(-0.566949\pi\) | ||||
−0.208779 | + | 0.977963i | \(0.566949\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.69195i | 0.277409i | 0.990334 | + | 0.138704i | \(0.0442938\pi\) | ||||
−0.990334 | + | 0.138704i | \(0.955706\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 31.3260i | 1.52312i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 17.2496i | − | 0.836728i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.4481i | 0.505620i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.59480i | 0.463241i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.8902 | −0.861740 | −0.430870 | − | 0.902414i | \(-0.641793\pi\) | ||||
−0.430870 | + | 0.902414i | \(0.641793\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.3887 | −0.595364 | −0.297682 | − | 0.954665i | \(-0.596214\pi\) | ||||
−0.297682 | + | 0.954665i | \(0.596214\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.93170 | −0.380296 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 0.225549i | − | 0.0107895i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 14.4192i | − | 0.688192i | −0.938934 | − | 0.344096i | \(-0.888185\pi\) | ||
0.938934 | − | 0.344096i | \(-0.111815\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.97553 | 0.189311 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.41166 | −0.304627 | −0.152314 | − | 0.988332i | \(-0.548672\pi\) | ||||
−0.152314 | + | 0.988332i | \(0.548672\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.50652i | 0.166225i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.84366 | 0.229097 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.48174 | 0.117120 | 0.0585602 | − | 0.998284i | \(-0.481349\pi\) | ||||
0.0585602 | + | 0.998284i | \(0.481349\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.77640 | + | 1.11070i | 0.413265 | + | 0.0523006i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −42.8578 | −2.01364 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.33739 | −0.0626977 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 26.4456i | − | 1.23707i | −0.785756 | − | 0.618537i | \(-0.787726\pi\) | ||
0.785756 | − | 0.618537i | \(-0.212274\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.37367 | 0.437525 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.4793 | −1.14012 | −0.570058 | − | 0.821605i | \(-0.693079\pi\) | ||||
−0.570058 | + | 0.821605i | \(0.693079\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.5271i | 1.37224i | 0.727489 | + | 0.686119i | \(0.240687\pi\) | ||||
−0.727489 | + | 0.686119i | \(0.759313\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 3.34161i | − | 0.154964i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −38.5304 | −1.78297 | −0.891487 | − | 0.453047i | \(-0.850337\pi\) | ||||
−0.891487 | + | 0.453047i | \(0.850337\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.77120 | 0.405016 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.73787 | −0.310465 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.234066i | 0.0107624i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 0.343340i | − | 0.0157535i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.84239i | 0.359079i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.8626i | 0.953235i | 0.879111 | + | 0.476618i | \(0.158137\pi\) | ||||
−0.879111 | + | 0.476618i | \(0.841863\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 1.25500i | − | 0.0572229i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.22627 | 0.374308 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 4.76497i | − | 0.216366i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.7296 | 1.30186 | 0.650931 | − | 0.759137i | \(-0.274379\pi\) | ||||
0.650931 | + | 0.759137i | \(0.274379\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 22.5106i | 1.01796i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.6652 | −1.47416 | −0.737079 | − | 0.675806i | \(-0.763796\pi\) | ||||
−0.737079 | + | 0.675806i | \(0.763796\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21.4819 | −0.967496 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.79354i | 0.125560i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.853928 | −0.0383039 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 14.7265i | − | 0.659250i | −0.944112 | − | 0.329625i | \(-0.893078\pi\) | ||
0.944112 | − | 0.329625i | \(-0.106922\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.7990 | 0.750524 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.5002i | 0.646532i | 0.946308 | + | 0.323266i | \(0.104781\pi\) | ||||
−0.946308 | + | 0.323266i | \(0.895219\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.03465i | 0.224039i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16.0732i | 0.713837i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.2537i | 0.809080i | 0.914520 | + | 0.404540i | \(0.132568\pi\) | ||||
−0.914520 | + | 0.404540i | \(0.867432\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.17800i | 0.273299i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.186576 | 0.00823753 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.403064 | −0.0177611 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.8864 | −0.478784 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 29.2083i | 1.28210i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.597365i | 0.0261710i | 0.999914 | + | 0.0130855i | \(0.00416537\pi\) | ||||
−0.999914 | + | 0.0130855i | \(0.995835\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.8032 | −1.04084 | −0.520421 | − | 0.853910i | \(-0.674225\pi\) | ||||
−0.520421 | + | 0.853910i | \(0.674225\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12.5224 | 0.546522 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 9.05030i | − | 0.394237i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.2987 | −0.578206 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 16.7935 | 0.728777 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.7037 | − | 2.11394i | −0.723520 | − | 0.0915649i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.12573 | −0.308072 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.03462 | 0.260413 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.38158i | 0.0595087i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.9049 | 0.554823 | 0.277411 | − | 0.960751i | \(-0.410523\pi\) | ||||
0.277411 | + | 0.960751i | \(0.410523\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.49903 | −0.278900 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.61114i | 0.240355i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.0350i | 0.728366i | 0.931327 | + | 0.364183i | \(0.118652\pi\) | ||||
−0.931327 | + | 0.364183i | \(0.881348\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −41.5369 | −1.77275 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.427581 | −0.0182156 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.30234 | 0.0553812 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 0.641126i | − | 0.0272143i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.89705i | 0.376980i | 0.982075 | + | 0.188490i | \(0.0603593\pi\) | ||||
−0.982075 | + | 0.188490i | \(0.939641\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 0.445488i | − | 0.0188421i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.2753i | 0.560482i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 23.0993i | − | 0.973521i | −0.873536 | − | 0.486760i | \(-0.838178\pi\) | ||
0.873536 | − | 0.486760i | \(-0.161822\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.621660 | −0.0261534 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 5.12175i | − | 0.215093i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 42.3708 | 1.77628 | 0.888139 | − | 0.459575i | \(-0.151998\pi\) | ||||
0.888139 | + | 0.459575i | \(0.151998\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 22.8718i | − | 0.957156i | −0.878045 | − | 0.478578i | \(-0.841152\pi\) | ||
0.878045 | − | 0.478578i | \(-0.158848\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.8757 | −0.746766 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14.7677 | 0.615856 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.4374i | 0.517775i | 0.965908 | + | 0.258887i | \(0.0833558\pi\) | ||||
−0.965908 | + | 0.258887i | \(0.916644\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −33.3152 | −1.38453 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.00782i | 0.207760i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.72539 | −0.112874 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 5.31682i | − | 0.219824i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.01267i | 0.0830716i | 0.999137 | + | 0.0415358i | \(0.0132251\pi\) | ||||
−0.999137 | + | 0.0415358i | \(0.986775\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 0.180139i | − | 0.00742251i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 29.0356i | 1.19436i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.6460i | 0.683568i | 0.939778 | + | 0.341784i | \(0.111031\pi\) | ||||
−0.939778 | + | 0.341784i | \(0.888969\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.85040 | −0.0758588 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −58.2158 | −2.38261 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.2512 | −0.704866 | −0.352433 | − | 0.935837i | \(-0.614646\pi\) | ||||
−0.352433 | + | 0.935837i | \(0.614646\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 1.49145i | − | 0.0608376i | −0.999537 | − | 0.0304188i | \(-0.990316\pi\) | ||
0.999537 | − | 0.0304188i | \(-0.00968409\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 34.8702i | 1.42002i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.62390 | 0.187988 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.38778 | 0.137506 | 0.0687529 | − | 0.997634i | \(-0.478098\pi\) | ||||
0.0687529 | + | 0.997634i | \(0.478098\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 15.5949i | − | 0.631936i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.7196 | 0.838227 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.3851 | 0.661789 | 0.330894 | − | 0.943668i | \(-0.392650\pi\) | ||||
0.330894 | + | 0.943668i | \(0.392650\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.53326 | − | 1.07993i | −0.344094 | − | 0.0435468i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −32.3742 | −1.30334 | −0.651668 | − | 0.758505i | \(-0.725930\pi\) | ||||
−0.651668 | + | 0.758505i | \(0.725930\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.7849 | 1.47851 | 0.739255 | − | 0.673426i | \(-0.235178\pi\) | ||||
0.739255 | + | 0.673426i | \(0.235178\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.02498i | 0.322031i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.89431 | −0.276215 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.1867 | 0.847466 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.264234i | 0.0105525i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.73640i | − | 0.0692348i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.1438 | −0.961149 | −0.480575 | − | 0.876954i | \(-0.659572\pi\) | ||||
−0.480575 | + | 0.876954i | \(0.659572\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.22080 | 0.167762 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.12233 | 0.0842220 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 2.62949i | − | 0.104184i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 3.39482i | − | 0.134297i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.9449i | 0.945765i | 0.881125 | + | 0.472883i | \(0.156787\pi\) | ||||
−0.881125 | + | 0.472883i | \(0.843213\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 30.1202i | − | 1.18783i | −0.804529 | − | 0.593913i | \(-0.797582\pi\) | ||
0.804529 | − | 0.593913i | \(-0.202418\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 0.227581i | − | 0.00896101i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.5113 | 1.00295 | 0.501477 | − | 0.865171i | \(-0.332790\pi\) | ||||
0.501477 | + | 0.865171i | \(0.332790\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.83609i | 0.229086i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.57009 | 0.257502 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 48.7156i | 1.90639i | 0.302356 | + | 0.953195i | \(0.402227\pi\) | ||||
−0.302356 | + | 0.953195i | \(0.597773\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.38459 | 0.210394 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −24.5609 | −0.958210 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 25.5196i | − | 0.994102i | −0.867721 | − | 0.497051i | \(-0.834416\pi\) | ||
0.867721 | − | 0.497051i | \(-0.165584\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.94107 | 0.347767 | 0.173884 | − | 0.984766i | \(-0.444368\pi\) | ||||
0.173884 | + | 0.984766i | \(0.444368\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 25.2663i | − | 0.981260i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.0368307 | −0.00142824 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 18.3911i | − | 0.712105i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 74.3923i | 2.87617i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 14.4349i | − | 0.557253i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 38.1905i | − | 1.47214i | −0.676907 | − | 0.736068i | \(-0.736680\pi\) | ||
0.676907 | − | 0.736068i | \(-0.263320\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12.2160i | 0.470194i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.4119 | −0.976658 | −0.488329 | − | 0.872660i | \(-0.662393\pi\) | ||||
−0.488329 | + | 0.872660i | \(0.662393\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.36862 | 0.359535 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 30.0561 | 1.15175 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 14.5602i | − | 0.557132i | −0.960417 | − | 0.278566i | \(-0.910141\pi\) | ||
0.960417 | − | 0.278566i | \(-0.0898591\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.60491i | 0.175944i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19.9648 | −0.761706 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.18711 | 0.197613 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.1979i | 0.502072i | 0.967978 | + | 0.251036i | \(0.0807712\pi\) | ||||
−0.967978 | + | 0.251036i | \(0.919229\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.49250 | −0.208643 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.54214 | −0.0964287 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23.1111 | − | 2.92483i | −0.875397 | − | 0.110786i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.5350 | 0.436294 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.5136 | −0.774787 | −0.387393 | − | 0.921914i | \(-0.626624\pi\) | ||||
−0.387393 | + | 0.921914i | \(0.626624\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.0345617i | − | 0.00130352i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.5848 | 0.398647 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.89885 | −0.372284 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.5794i | 0.397319i | 0.980069 | + | 0.198659i | \(0.0636588\pi\) | ||||
−0.980069 | + | 0.198659i | \(0.936341\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.17750i | 0.194171i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.74814 | 0.290170 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.84770 | 0.0691001 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −67.1980 | −2.50956 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 12.9033i | − | 0.481211i | −0.970623 | − | 0.240605i | \(-0.922654\pi\) | ||
0.970623 | − | 0.240605i | \(-0.0773460\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 0.792482i | − | 0.0295136i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 52.3219i | 1.94587i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 27.9957i | − | 1.03974i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 12.9443i | − | 0.480078i | −0.970763 | − | 0.240039i | \(-0.922840\pi\) | ||
0.970763 | − | 0.240039i | \(-0.0771603\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 40.7762 | 1.51023 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 0.616372i | − | 0.0227974i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.2751 | −0.564197 | −0.282099 | − | 0.959385i | \(-0.591031\pi\) | ||||
−0.282099 | + | 0.959385i | \(0.591031\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 1.34330i | − | 0.0495484i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.1181 | −0.446375 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.9475 | 0.549852 | 0.274926 | − | 0.961465i | \(-0.411347\pi\) | ||||
0.274926 | + | 0.961465i | \(0.411347\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 0.502906i | − | 0.0184747i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.8721 | −0.765723 | −0.382861 | − | 0.923806i | \(-0.625061\pi\) | ||||
−0.382861 | + | 0.923806i | \(0.625061\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 0.932759i | − | 0.0341736i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −19.9088 | −0.728423 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 14.0102i | − | 0.511922i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 46.1750i | − | 1.68495i | −0.538736 | − | 0.842475i | \(-0.681098\pi\) | ||
0.538736 | − | 0.842475i | \(-0.318902\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 0.0865991i | − | 0.00315585i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.25328i | 0.300367i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.19901i | 0.188961i | 0.995527 | + | 0.0944806i | \(0.0301190\pi\) | ||||
−0.995527 | + | 0.0944806i | \(0.969881\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.3652 | −0.412531 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.4753 | −0.887227 | −0.443614 | − | 0.896218i | \(-0.646304\pi\) | ||||
−0.443614 | + | 0.896218i | \(0.646304\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.0323 | −0.399396 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 7.35631i | − | 0.265968i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 11.1076i | − | 0.401071i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42.7224 | −1.54061 | −0.770305 | − | 0.637676i | \(-0.779896\pi\) | ||||
−0.770305 | + | 0.637676i | \(0.779896\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 33.3800 | 1.20215 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 51.4835i | − | 1.85173i | −0.377852 | − | 0.925866i | \(-0.623337\pi\) | ||
0.377852 | − | 0.925866i | \(-0.376663\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.7946 | 0.423673 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.26055 | 0.0452218 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.460010 | − | 0.0582165i | −0.0164816 | − | 0.00208582i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.17977 | 0.0422154 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 15.2133 | 0.543678 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.29753i | 0.0463110i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.6859 | 1.05819 | 0.529094 | − | 0.848563i | \(-0.322532\pi\) | ||||
0.529094 | + | 0.848563i | \(0.322532\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −35.3757 | −1.25941 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1.22227i | − | 0.0434590i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.4733i | 0.975606i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.64988 | 0.0939817 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.71982 | −0.202606 | −0.101303 | − | 0.994856i | \(-0.532301\pi\) | ||||
−0.101303 | + | 0.994856i | \(0.532301\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28.6675 | 1.01418 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 27.4086i | − | 0.968434i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 8.53538i | − | 0.301207i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 1.58416i | − | 0.0558343i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 73.5025i | − | 2.58741i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 20.5245i | − | 0.721602i | −0.932643 | − | 0.360801i | \(-0.882503\pi\) | ||
0.932643 | − | 0.360801i | \(-0.117497\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.70155 | 0.200208 | 0.100104 | − | 0.994977i | \(-0.468082\pi\) | ||||
0.100104 | + | 0.994977i | \(0.468082\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 1.99740i | − | 0.0700520i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.33493 | 0.151846 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 0.0122684i | − | 0.000429218i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.4536 | 0.365280 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.40505 | −0.328239 | −0.164119 | − | 0.986440i | \(-0.552478\pi\) | ||||
−0.164119 | + | 0.986440i | \(0.552478\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.4682i | 0.399757i | 0.979821 | + | 0.199879i | \(0.0640548\pi\) | ||||
−0.979821 | + | 0.199879i | \(0.935945\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −17.3006 | −0.602331 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 28.8800i | − | 1.00426i | −0.864793 | − | 0.502129i | \(-0.832550\pi\) | ||
0.864793 | − | 0.502129i | \(-0.167450\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.9681 | −0.971372 | −0.485686 | − | 0.874133i | \(-0.661430\pi\) | ||||
−0.485686 | + | 0.874133i | \(0.661430\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 22.0674i | − | 0.765508i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 3.63814i | − | 0.126054i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 3.23504i | − | 0.111953i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.40933i | 0.221539i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 38.2678i | − | 1.32115i | −0.750760 | − | 0.660575i | \(-0.770313\pi\) | ||
0.750760 | − | 0.660575i | \(-0.229687\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.86468 | −0.202230 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −47.2892 | −1.62873 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.09528 | 0.106481 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.09125i | 0.312379i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 72.0454i | 2.47259i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.48657 | 0.0509588 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.3437 | 0.936229 | 0.468115 | − | 0.883668i | \(-0.344933\pi\) | ||||
0.468115 | + | 0.883668i | \(0.344933\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 0.146422i | − | 0.00500752i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 47.3742 | 1.61827 | 0.809137 | − | 0.587620i | \(-0.199935\pi\) | ||||
0.809137 | + | 0.587620i | \(0.199935\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.4481 | 1.72127 | 0.860634 | − | 0.509224i | \(-0.170067\pi\) | ||||
0.860634 | + | 0.509224i | \(0.170067\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.12329 | − | 16.7776i | 0.0723615 | − | 0.571780i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20.9609 | −0.713516 | −0.356758 | − | 0.934197i | \(-0.616118\pi\) | ||||
−0.356758 | + | 0.934197i | \(0.616118\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.62474 | 0.191247 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.94095i | 0.337612i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.79928 | −0.0610365 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.0638 | 0.781488 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 37.2452i | 1.26056i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 4.95453i | − | 0.167494i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.05263 | 0.271918 | 0.135959 | − | 0.990714i | \(-0.456588\pi\) | ||||
0.135959 | + | 0.990714i | \(0.456588\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 50.6357 | 1.70790 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.47471 | −0.184448 | −0.0922239 | − | 0.995738i | \(-0.529398\pi\) | ||||
−0.0922239 | + | 0.995738i | \(0.529398\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 27.4554i | − | 0.923948i | −0.886894 | − | 0.461974i | \(-0.847141\pi\) | ||
0.886894 | − | 0.461974i | \(-0.152859\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 5.67441i | − | 0.190743i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 35.2825i | 1.18467i | 0.805691 | + | 0.592336i | \(0.201794\pi\) | ||||
−0.805691 | + | 0.592336i | \(0.798206\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.17280i | 0.139951i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.07608i | 0.237058i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.570605 | 0.0190946 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1.16211i | − | 0.0388449i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 21.6309 | 0.722236 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 14.6884i | − | 0.489887i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.17684 | 0.239095 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.447458 | 0.0148905 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.25154i | 0.0416026i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.7572 | −0.954866 | −0.477433 | − | 0.878668i | \(-0.658433\pi\) | ||||
−0.477433 | + | 0.878668i | \(0.658433\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 39.3532i | − | 1.30526i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.8242 | 0.789330 | 0.394665 | − | 0.918825i | \(-0.370861\pi\) | ||||
0.394665 | + | 0.918825i | \(0.370861\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 6.91869i | − | 0.228975i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 14.0350i | 0.463982i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.5869i | 0.349610i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 34.1087i | − | 1.12514i | −0.826749 | − | 0.562570i | \(-0.809813\pi\) | ||
0.826749 | − | 0.562570i | \(-0.190187\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 53.4225i | 1.76033i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.24540 | −0.0739082 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.26292 | 0.0744043 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.15054 | 0.103477 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 5.84282i | − | 0.191697i | −0.995396 | − | 0.0958484i | \(-0.969444\pi\) | ||
0.995396 | − | 0.0958484i | \(-0.0305564\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 0.0724145i | − | 0.00237329i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.84369 | −0.289529 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.55646 | 0.0836053 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 8.90391i | − | 0.290878i | −0.989367 | − | 0.145439i | \(-0.953541\pi\) | ||
0.989367 | − | 0.145439i | \(-0.0464595\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.05478 | −0.197590 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 47.0369 | 1.53336 | 0.766679 | − | 0.642030i | \(-0.221908\pi\) | ||||
0.766679 | + | 0.642030i | \(0.221908\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.50400 | − | 19.7859i | 0.0815415 | − | 0.644318i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.31043 | 0.0426284 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36.1207 | 1.17377 | 0.586883 | − | 0.809672i | \(-0.300355\pi\) | ||||
0.586883 | + | 0.809672i | \(0.300355\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.2450i | 0.527336i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.89435 | −0.0938558 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −50.8702 | −1.64785 | −0.823923 | − | 0.566702i | \(-0.808219\pi\) | ||||
−0.823923 | + | 0.566702i | \(0.808219\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.44238i | 0.111393i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 21.5455i | 0.696467i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.05390 | −0.292366 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.8118 | −0.800380 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 55.6980 | 1.79484 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.41563i | 0.206526i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 46.9253i | − | 1.50902i | −0.656291 | − | 0.754508i | \(-0.727875\pi\) | ||
0.656291 | − | 0.754508i | \(-0.272125\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 0.695816i | − | 0.0223528i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.92337i | 0.0617238i | 0.999524 | + | 0.0308619i | \(0.00982521\pi\) | ||||
−0.999524 | + | 0.0308619i | \(0.990175\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 4.99820i | − | 0.160235i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 32.9276 | 1.05453 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.0040i | 0.703971i | 0.936006 | + | 0.351985i | \(0.114493\pi\) | ||||
−0.936006 | + | 0.351985i | \(0.885507\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.52502 | 0.304421 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 43.8593i | − | 1.40032i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29.6426 | 0.945453 | 0.472727 | − | 0.881209i | \(-0.343270\pi\) | ||||
0.472727 | + | 0.881209i | \(0.343270\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.59148 | 0.178159 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 20.8113i | 0.662430i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.527688 | 0.0167795 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 9.45715i | − | 0.300416i | −0.988654 | − | 0.150208i | \(-0.952006\pi\) | ||
0.988654 | − | 0.150208i | \(-0.0479944\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 77.4865 | 2.45896 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.2108i | 0.355407i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44.0949i | 1.39650i | 0.715854 | + | 0.698250i | \(0.246038\pi\) | ||||
−0.715854 | + | 0.698250i | \(0.753962\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.22970i | 0.0389060i |
(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 | 1148.2.d.a.1065.19 | yes | 20 | |
41.40 | even | 2 | inner | 1148.2.d.a.1065.2 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.d.a.1065.2 | ✓ | 20 | 41.40 | even | 2 | inner | |
1148.2.d.a.1065.19 | yes | 20 | 1.1 | even | 1 | trivial |