Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [855,2,Mod(514,855)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(855, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("855.514");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 855 = 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 855.c (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: | \(6.82720937282\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.16516096.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 9x^{4} + 13x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 514.5 | ||
Root | \(2.68667i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 855.514 |
Dual form | 855.2.c.d.514.2 |
$q$-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 \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).
\(n\) | \(172\) | \(191\) | \(496\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.82254i | 1.28873i | 0.764719 | + | 0.644364i | \(0.222878\pi\) | ||||
−0.764719 | + | 0.644364i | \(0.777122\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.32164 | −0.660819 | ||||||||
\(5\) | −1.94827 | − | 1.09737i | −0.871295 | − | 0.490760i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.45033i | − | 0.548172i | −0.961705 | − | 0.274086i | \(-0.911625\pi\) | ||
0.961705 | − | 0.274086i | \(-0.0883754\pi\) | |||||||
\(8\) | 1.23634i | 0.437112i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.00000 | − | 3.55080i | 0.632456 | − | 1.12286i | ||||
\(11\) | 3.89655 | 1.17485 | 0.587427 | − | 0.809277i | \(-0.300141\pi\) | ||||
0.587427 | + | 0.809277i | \(0.300141\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.05888i | 0.848380i | 0.905573 | + | 0.424190i | \(0.139441\pi\) | ||||
−0.905573 | + | 0.424190i | \(0.860559\pi\) | |||||||
\(14\) | 2.64327 | 0.706445 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.89655 | −1.22414 | ||||||||
\(17\) | 3.92301i | 0.951469i | 0.879589 | + | 0.475735i | \(0.157818\pi\) | ||||
−0.879589 | + | 0.475735i | \(0.842182\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 2.57491 | + | 1.45033i | 0.575768 | + | 0.324303i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.10160i | 1.51407i | ||||||||
\(23\) | 5.37334i | 1.12042i | 0.828351 | + | 0.560209i | \(0.189279\pi\) | ||||
−0.828351 | + | 0.560209i | \(0.810721\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.59155 | + | 4.27596i | 0.518310 | + | 0.855193i | ||||
\(26\) | −5.57491 | −1.09333 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.91681i | 0.362242i | ||||||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.43637 | −1.51522 | −0.757609 | − | 0.652709i | \(-0.773632\pi\) | ||||
−0.757609 | + | 0.652709i | \(0.773632\pi\) | |||||||
\(32\) | − | 6.45146i | − | 1.14047i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.14982 | −1.22618 | ||||||||
\(35\) | −1.59155 | + | 2.82564i | −0.269021 | + | 0.477620i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.95953i | 0.979741i | 0.871795 | + | 0.489871i | \(0.162956\pi\) | ||||
−0.871795 | + | 0.489871i | \(0.837044\pi\) | |||||||
\(38\) | 1.82254i | 0.295654i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.35673 | − | 2.40873i | 0.214517 | − | 0.380854i | ||||
\(41\) | −10.4364 | −1.62989 | −0.814944 | − | 0.579540i | \(-0.803232\pi\) | ||||
−0.814944 | + | 0.579540i | \(0.803232\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.45033i | − | 0.221173i | −0.993867 | − | 0.110586i | \(-0.964727\pi\) | ||
0.993867 | − | 0.110586i | \(-0.0352729\pi\) | |||||||
\(44\) | −5.14982 | −0.776365 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.79310 | −1.44391 | ||||||||
\(47\) | 4.90686i | 0.715739i | 0.933772 | + | 0.357869i | \(0.116497\pi\) | ||||
−0.933772 | + | 0.357869i | \(0.883503\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.89655 | 0.699507 | ||||||||
\(50\) | −7.79310 | + | 4.72319i | −1.10211 | + | 0.667960i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 4.04272i | − | 0.560625i | ||||||
\(53\) | 4.23127i | 0.581209i | 0.956843 | + | 0.290605i | \(0.0938564\pi\) | ||||
−0.956843 | + | 0.290605i | \(0.906144\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.59155 | − | 4.27596i | −1.02364 | − | 0.576571i | ||||
\(56\) | 1.79310 | 0.239613 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10.9352i | 1.43586i | ||||||||
\(59\) | 3.35673 | 0.437008 | 0.218504 | − | 0.975836i | \(-0.429882\pi\) | ||||
0.218504 | + | 0.975836i | \(0.429882\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.3329 | 1.32300 | 0.661498 | − | 0.749947i | \(-0.269921\pi\) | ||||
0.661498 | + | 0.749947i | \(0.269921\pi\) | |||||||
\(62\) | − | 15.3756i | − | 1.95270i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.96491 | 0.245614 | ||||||||
\(65\) | 3.35673 | − | 5.95953i | 0.416351 | − | 0.739189i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.84404i | 1.20264i | 0.799008 | + | 0.601320i | \(0.205358\pi\) | ||||
−0.799008 | + | 0.601320i | \(0.794642\pi\) | |||||||
\(68\) | − | 5.18479i | − | 0.628749i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.14982 | − | 2.90066i | −0.615522 | − | 0.346695i | ||||
\(71\) | −8.64327 | −1.02577 | −0.512884 | − | 0.858458i | \(-0.671423\pi\) | ||||
−0.512884 | + | 0.858458i | \(0.671423\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 2.43418i | − | 0.284899i | −0.989802 | − | 0.142449i | \(-0.954502\pi\) | ||
0.989802 | − | 0.142449i | \(-0.0454978\pi\) | |||||||
\(74\) | −10.8615 | −1.26262 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.32164 | −0.151602 | ||||||||
\(77\) | − | 5.65127i | − | 0.644022i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.4364 | 1.39920 | 0.699601 | − | 0.714534i | \(-0.253361\pi\) | ||||
0.699601 | + | 0.714534i | \(0.253361\pi\) | |||||||
\(80\) | 9.53982 | + | 5.37334i | 1.06658 | + | 0.600757i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 19.0207i | − | 2.10048i | ||||||
\(83\) | − | 12.6635i | − | 1.39000i | −0.719011 | − | 0.694999i | \(-0.755405\pi\) | ||
0.719011 | − | 0.694999i | \(-0.244595\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.30500 | − | 7.64310i | 0.466943 | − | 0.829011i | ||||
\(86\) | 2.64327 | 0.285032 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.81746i | 0.513543i | ||||||||
\(89\) | 12.3662 | 1.31081 | 0.655407 | − | 0.755276i | \(-0.272497\pi\) | ||||
0.655407 | + | 0.755276i | \(0.272497\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.43637 | 0.465058 | ||||||||
\(92\) | − | 7.10160i | − | 0.740393i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.94292 | −0.922392 | ||||||||
\(95\) | −1.94827 | − | 1.09737i | −0.199889 | − | 0.112588i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.05888i | − | 0.310582i | −0.987869 | − | 0.155291i | \(-0.950369\pi\) | ||
0.987869 | − | 0.155291i | \(-0.0496315\pi\) | |||||||
\(98\) | 8.92414i | 0.901474i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.42509 | − | 5.65127i | −0.342509 | − | 0.565127i | ||||
\(101\) | −3.35673 | −0.334007 | −0.167003 | − | 0.985956i | \(-0.553409\pi\) | ||||
−0.167003 | + | 0.985956i | \(0.553409\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.0611i | 1.28695i | 0.765466 | + | 0.643476i | \(0.222508\pi\) | ||||
−0.765466 | + | 0.643476i | \(0.777492\pi\) | |||||||
\(104\) | −3.78181 | −0.370837 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.71164 | −0.749020 | ||||||||
\(107\) | − | 5.77099i | − | 0.557903i | −0.960305 | − | 0.278951i | \(-0.910013\pi\) | ||
0.960305 | − | 0.278951i | \(-0.0899868\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.64327 | −0.636310 | −0.318155 | − | 0.948039i | \(-0.603063\pi\) | ||||
−0.318155 | + | 0.948039i | \(0.603063\pi\) | |||||||
\(110\) | 7.79310 | − | 13.8359i | 0.743043 | − | 1.31920i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.10160i | 0.671038i | ||||||||
\(113\) | 9.41606i | 0.885789i | 0.896574 | + | 0.442894i | \(0.146048\pi\) | ||||
−0.896574 | + | 0.442894i | \(0.853952\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.89655 | − | 10.4687i | 0.549856 | − | 0.976215i | ||||
\(116\) | −7.92982 | −0.736266 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.11775i | 0.563185i | ||||||||
\(119\) | 5.68965 | 0.521569 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.18310 | 0.380282 | ||||||||
\(122\) | 18.8321i | 1.70498i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 11.1498 | 1.00128 | ||||||||
\(125\) | −0.356726 | − | 11.1746i | −0.0319065 | − | 0.999491i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 11.0934i | − | 0.984383i | −0.870487 | − | 0.492192i | \(-0.836196\pi\) | ||
0.870487 | − | 0.492192i | \(-0.163804\pi\) | |||||||
\(128\) | − | 9.32179i | − | 0.823938i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 10.8615 | + | 6.11775i | 0.952613 | + | 0.536562i | ||||
\(131\) | −4.61000 | −0.402778 | −0.201389 | − | 0.979511i | \(-0.564545\pi\) | ||||
−0.201389 | + | 0.979511i | \(0.564545\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 1.45033i | − | 0.125759i | ||||||
\(134\) | −17.9411 | −1.54988 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.85018 | −0.415899 | ||||||||
\(137\) | − | 13.1808i | − | 1.12612i | −0.826417 | − | 0.563058i | \(-0.809625\pi\) | ||
0.826417 | − | 0.563058i | \(-0.190375\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.18310 | −0.100349 | −0.0501745 | − | 0.998740i | \(-0.515978\pi\) | ||||
−0.0501745 | + | 0.998740i | \(0.515978\pi\) | |||||||
\(140\) | 2.10345 | − | 3.73447i | 0.177774 | − | 0.315620i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 15.7527i | − | 1.32194i | ||||||
\(143\) | 11.9191i | 0.996722i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.6896 | − | 6.58423i | −0.970772 | − | 0.546791i | ||||
\(146\) | 4.43637 | 0.367157 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 7.87634i | − | 0.647431i | ||||||
\(149\) | 5.46018 | 0.447315 | 0.223658 | − | 0.974668i | \(-0.428200\pi\) | ||||
0.223658 | + | 0.974668i | \(0.428200\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.07965 | −0.413376 | −0.206688 | − | 0.978407i | \(-0.566268\pi\) | ||||
−0.206688 | + | 0.978407i | \(0.566268\pi\) | |||||||
\(152\) | 1.23634i | 0.100280i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 10.2996 | 0.829969 | ||||||||
\(155\) | 16.4364 | + | 9.25784i | 1.32020 | + | 0.743608i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 6.11775i | − | 0.488250i | −0.969744 | − | 0.244125i | \(-0.921499\pi\) | ||
0.969744 | − | 0.244125i | \(-0.0785007\pi\) | |||||||
\(158\) | 22.6657i | 1.80319i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −7.07965 | + | 12.5692i | −0.559695 | + | 0.993683i | ||||
\(161\) | 7.79310 | 0.614182 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 16.4365i | − | 1.28740i | −0.765277 | − | 0.643701i | \(-0.777398\pi\) | ||
0.765277 | − | 0.643701i | \(-0.222602\pi\) | |||||||
\(164\) | 13.7931 | 1.07706 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 23.0796 | 1.79133 | ||||||||
\(167\) | − | 3.80329i | − | 0.294308i | −0.989114 | − | 0.147154i | \(-0.952989\pi\) | ||
0.989114 | − | 0.147154i | \(-0.0470112\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.64327 | 0.280252 | ||||||||
\(170\) | 13.9298 | + | 7.84602i | 1.06837 | + | 0.601762i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.91681i | 0.146155i | ||||||||
\(173\) | 11.3838i | 0.865491i | 0.901516 | + | 0.432746i | \(0.142455\pi\) | ||||
−0.901516 | + | 0.432746i | \(0.857545\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.20155 | − | 3.75860i | 0.468793 | − | 0.284123i | ||||
\(176\) | −19.0796 | −1.43818 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 22.5378i | 1.68928i | ||||||||
\(179\) | 10.0702 | 0.752680 | 0.376340 | − | 0.926482i | \(-0.377182\pi\) | ||||
0.376340 | + | 0.926482i | \(0.377182\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.573097 | 0.0425980 | 0.0212990 | − | 0.999773i | \(-0.493220\pi\) | ||||
0.0212990 | + | 0.999773i | \(0.493220\pi\) | |||||||
\(182\) | 8.08545i | 0.599333i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.64327 | −0.489749 | ||||||||
\(185\) | 6.53982 | − | 11.6108i | 0.480817 | − | 0.853643i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.2862i | 1.11784i | ||||||||
\(188\) | − | 6.48509i | − | 0.472973i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.00000 | − | 3.55080i | 0.145095 | − | 0.257602i | ||||
\(191\) | 3.18310 | 0.230321 | 0.115160 | − | 0.993347i | \(-0.463262\pi\) | ||||
0.115160 | + | 0.993347i | \(0.463262\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.05888i | 0.220183i | 0.993921 | + | 0.110091i | \(0.0351143\pi\) | ||||
−0.993921 | + | 0.110091i | \(0.964886\pi\) | |||||||
\(194\) | 5.57491 | 0.400255 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.47146 | −0.462247 | ||||||||
\(197\) | 21.4933i | 1.53134i | 0.643235 | + | 0.765669i | \(0.277592\pi\) | ||||
−0.643235 | + | 0.765669i | \(0.722408\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.81690 | 0.341461 | 0.170731 | − | 0.985318i | \(-0.445387\pi\) | ||||
0.170731 | + | 0.985318i | \(0.445387\pi\) | |||||||
\(200\) | −5.28655 | + | 3.20404i | −0.373815 | + | 0.226560i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 6.11775i | − | 0.430444i | ||||||
\(203\) | − | 8.70197i | − | 0.610758i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.3329 | + | 11.4526i | 1.42011 | + | 0.799883i | ||||
\(206\) | −23.8044 | −1.65853 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 14.9779i | − | 1.03853i | ||||||
\(209\) | 3.89655 | 0.269530 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.5066 | 0.723301 | 0.361650 | − | 0.932314i | \(-0.382213\pi\) | ||||
0.361650 | + | 0.932314i | \(0.382213\pi\) | |||||||
\(212\) | − | 5.59220i | − | 0.384074i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 10.5178 | 0.718984 | ||||||||
\(215\) | −1.59155 | + | 2.82564i | −0.108543 | + | 0.192707i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.2355i | 0.830600i | ||||||||
\(218\) | − | 12.1076i | − | 0.820031i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 10.0333 | + | 5.65127i | 0.676443 | + | 0.381009i | ||||
\(221\) | −12.0000 | −0.807207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 16.8947i | − | 1.13136i | −0.824626 | − | 0.565678i | \(-0.808615\pi\) | ||
0.824626 | − | 0.565678i | \(-0.191385\pi\) | |||||||
\(224\) | −9.35673 | −0.625173 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −17.1611 | −1.14154 | ||||||||
\(227\) | 17.1342i | 1.13724i | 0.822602 | + | 0.568618i | \(0.192522\pi\) | ||||
−0.822602 | + | 0.568618i | \(0.807478\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.0464 | −1.65511 | −0.827555 | − | 0.561384i | \(-0.810269\pi\) | ||||
−0.827555 | + | 0.561384i | \(0.810269\pi\) | |||||||
\(230\) | 19.0796 | + | 10.7467i | 1.25807 | + | 0.708615i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.41804i | 0.487018i | ||||||||
\(233\) | − | 19.2986i | − | 1.26429i | −0.774849 | − | 0.632147i | \(-0.782174\pi\) | ||
0.774849 | − | 0.632147i | \(-0.217826\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.38465 | − | 9.55991i | 0.351256 | − | 0.623620i | ||||
\(236\) | −4.43637 | −0.288783 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 10.3696i | 0.672161i | ||||||||
\(239\) | 18.7693 | 1.21408 | 0.607042 | − | 0.794669i | \(-0.292356\pi\) | ||||
0.607042 | + | 0.794669i | \(0.292356\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.4364 | −0.929929 | −0.464964 | − | 0.885329i | \(-0.653933\pi\) | ||||
−0.464964 | + | 0.885329i | \(0.653933\pi\) | |||||||
\(242\) | 7.62385i | 0.490079i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −13.6564 | −0.874260 | ||||||||
\(245\) | −9.53982 | − | 5.37334i | −0.609477 | − | 0.343290i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.05888i | 0.194632i | ||||||||
\(248\) | − | 10.4302i | − | 0.662320i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 20.3662 | − | 0.650145i | 1.28807 | − | 0.0411188i | ||||
\(251\) | 10.9762 | 0.692811 | 0.346406 | − | 0.938085i | \(-0.387402\pi\) | ||||
0.346406 | + | 0.938085i | \(0.387402\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.9375i | 1.31633i | ||||||||
\(254\) | 20.2182 | 1.26860 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.9191 | 1.30745 | ||||||||
\(257\) | − | 17.6392i | − | 1.10030i | −0.835066 | − | 0.550150i | \(-0.814570\pi\) | ||
0.835066 | − | 0.550150i | \(-0.185430\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.64327 | 0.537067 | ||||||||
\(260\) | −4.43637 | + | 7.87634i | −0.275132 | + | 0.488470i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 8.40189i | − | 0.519071i | ||||||
\(263\) | 1.68976i | 0.104195i | 0.998642 | + | 0.0520975i | \(0.0165907\pi\) | ||||
−0.998642 | + | 0.0520975i | \(0.983409\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.64327 | − | 8.24367i | 0.285234 | − | 0.506405i | ||||
\(266\) | 2.64327 | 0.162070 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 13.0102i | − | 0.794727i | ||||||
\(269\) | −27.1022 | −1.65245 | −0.826226 | − | 0.563339i | \(-0.809516\pi\) | ||||
−0.826226 | + | 0.563339i | \(0.809516\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.9524 | 1.45500 | 0.727502 | − | 0.686105i | \(-0.240681\pi\) | ||||
0.727502 | + | 0.686105i | \(0.240681\pi\) | |||||||
\(272\) | − | 19.2092i | − | 1.16473i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 24.0226 | 1.45126 | ||||||||
\(275\) | 10.0981 | + | 16.6615i | 0.608938 | + | 1.00473i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 8.23549i | − | 0.494822i | −0.968911 | − | 0.247411i | \(-0.920420\pi\) | ||
0.968911 | − | 0.247411i | \(-0.0795799\pi\) | |||||||
\(278\) | − | 2.15624i | − | 0.129323i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.49345 | − | 1.96770i | −0.208774 | − | 0.117592i | ||||
\(281\) | 10.4364 | 0.622582 | 0.311291 | − | 0.950315i | \(-0.399239\pi\) | ||||
0.311291 | + | 0.950315i | \(0.399239\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 10.4687i | − | 0.622302i | −0.950361 | − | 0.311151i | \(-0.899286\pi\) | ||
0.950361 | − | 0.311151i | \(-0.100714\pi\) | |||||||
\(284\) | 11.4233 | 0.677847 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −21.7229 | −1.28450 | ||||||||
\(287\) | 15.1362i | 0.893459i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.61000 | 0.0947059 | ||||||||
\(290\) | 12.0000 | − | 21.3048i | 0.704664 | − | 1.25106i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.21710i | 0.188266i | ||||||||
\(293\) | 16.4668i | 0.961999i | 0.876721 | + | 0.481000i | \(0.159726\pi\) | ||||
−0.876721 | + | 0.481000i | \(0.840274\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.53982 | − | 3.68358i | −0.380763 | − | 0.214466i | ||||
\(296\) | −7.36801 | −0.428257 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.95137i | 0.576467i | ||||||||
\(299\) | −16.4364 | −0.950540 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.10345 | −0.121241 | ||||||||
\(302\) | − | 9.25784i | − | 0.532729i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.89655 | −0.280836 | ||||||||
\(305\) | −20.1314 | − | 11.3391i | −1.15272 | − | 0.649273i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7.87634i | − | 0.449526i | −0.974413 | − | 0.224763i | \(-0.927839\pi\) | ||
0.974413 | − | 0.224763i | \(-0.0721609\pi\) | |||||||
\(308\) | 7.46893i | 0.425582i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −16.8727 | + | 29.9559i | −0.958308 | + | 1.70138i | ||||
\(311\) | −3.89655 | −0.220953 | −0.110477 | − | 0.993879i | \(-0.535238\pi\) | ||||
−0.110477 | + | 0.993879i | \(0.535238\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.76901i | 0.439130i | 0.975598 | + | 0.219565i | \(0.0704638\pi\) | ||||
−0.975598 | + | 0.219565i | \(0.929536\pi\) | |||||||
\(314\) | 11.1498 | 0.629221 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.4364 | −0.924618 | ||||||||
\(317\) | 19.0510i | 1.07001i | 0.844849 | + | 0.535005i | \(0.179690\pi\) | ||||
−0.844849 | + | 0.535005i | \(0.820310\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23.3793 | 1.30899 | ||||||||
\(320\) | −3.82819 | − | 2.15624i | −0.214002 | − | 0.120537i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 14.2032i | 0.791514i | ||||||||
\(323\) | 3.92301i | 0.218282i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.0796 | + | 7.92723i | −0.725528 | + | 0.439724i | ||||
\(326\) | 29.9560 | 1.65911 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 12.9029i | − | 0.712444i | ||||||
\(329\) | 7.11655 | 0.392348 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.00000 | 0.439720 | 0.219860 | − | 0.975531i | \(-0.429440\pi\) | ||||
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(332\) | 16.7365i | 0.918536i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.93164 | 0.379282 | ||||||||
\(335\) | 10.8026 | − | 19.1789i | 0.590207 | − | 1.04785i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.89249i | 0.375458i | 0.982221 | + | 0.187729i | \(0.0601127\pi\) | ||||
−0.982221 | + | 0.187729i | \(0.939887\pi\) | |||||||
\(338\) | 6.64000i | 0.361168i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.68965 | + | 10.1014i | −0.308565 | + | 0.547826i | ||||
\(341\) | −32.8727 | −1.78016 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 17.2539i | − | 0.931623i | ||||||
\(344\) | 1.79310 | 0.0966774 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −20.7473 | −1.11538 | ||||||||
\(347\) | − | 30.5503i | − | 1.64002i | −0.572346 | − | 0.820012i | \(-0.693967\pi\) | ||
0.572346 | − | 0.820012i | \(-0.306033\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.7693 | −0.897640 | −0.448820 | − | 0.893622i | \(-0.648156\pi\) | ||||
−0.448820 | + | 0.893622i | \(0.648156\pi\) | |||||||
\(350\) | 6.85018 | + | 11.3025i | 0.366157 | + | 0.604147i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 25.1384i | − | 1.33988i | ||||||
\(353\) | − | 29.0999i | − | 1.54883i | −0.632676 | − | 0.774417i | \(-0.718044\pi\) | ||
0.632676 | − | 0.774417i | \(-0.281956\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.8395 | + | 9.48489i | 0.893746 | + | 0.503406i | ||||
\(356\) | −16.3436 | −0.866210 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 18.3533i | 0.970000i | ||||||||
\(359\) | −11.6896 | −0.616956 | −0.308478 | − | 0.951231i | \(-0.599820\pi\) | ||||
−0.308478 | + | 0.951231i | \(0.599820\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 1.04449i | 0.0548972i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.86328 | −0.307319 | ||||||||
\(365\) | −2.67120 | + | 4.74244i | −0.139817 | + | 0.248231i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.20095i | 0.219288i | 0.993971 | + | 0.109644i | \(0.0349710\pi\) | ||||
−0.993971 | + | 0.109644i | \(0.965029\pi\) | |||||||
\(368\) | − | 26.3108i | − | 1.37155i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 21.1611 | + | 11.9191i | 1.10011 | + | 0.619643i | ||||
\(371\) | 6.13672 | 0.318603 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 16.9456i | − | 0.877412i | −0.898631 | − | 0.438706i | \(-0.855437\pi\) | ||
0.898631 | − | 0.438706i | \(-0.144563\pi\) | |||||||
\(374\) | −27.8596 | −1.44059 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.06655 | −0.312858 | ||||||||
\(377\) | 18.3533i | 0.945241i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.3662 | −0.532476 | −0.266238 | − | 0.963907i | \(-0.585781\pi\) | ||||
−0.266238 | + | 0.963907i | \(0.585781\pi\) | |||||||
\(380\) | 2.57491 | + | 1.45033i | 0.132090 | + | 0.0744002i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.80131i | 0.296821i | ||||||||
\(383\) | − | 20.5907i | − | 1.05214i | −0.850442 | − | 0.526068i | \(-0.823666\pi\) | ||
0.850442 | − | 0.526068i | \(-0.176334\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.20155 | + | 11.0102i | −0.316060 | + | 0.561133i | ||||
\(386\) | −5.57491 | −0.283756 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.04272i | 0.205238i | ||||||||
\(389\) | 8.10345 | 0.410861 | 0.205431 | − | 0.978672i | \(-0.434141\pi\) | ||||
0.205431 | + | 0.978672i | \(0.434141\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.0796 | −1.06604 | ||||||||
\(392\) | 6.05380i | 0.305763i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −39.1724 | −1.97348 | ||||||||
\(395\) | −24.2295 | − | 13.6473i | −1.21912 | − | 0.686672i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 3.46891i | − | 0.174100i | −0.996204 | − | 0.0870499i | \(-0.972256\pi\) | ||
0.996204 | − | 0.0870499i | \(-0.0277440\pi\) | |||||||
\(398\) | 8.77898i | 0.440050i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12.6896 | − | 20.9375i | −0.634482 | − | 1.04687i | ||||
\(401\) | 15.9524 | 0.796625 | 0.398312 | − | 0.917250i | \(-0.369596\pi\) | ||||
0.398312 | + | 0.917250i | \(0.369596\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 25.8058i | − | 1.28548i | ||||||
\(404\) | 4.43637 | 0.220718 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 15.8596 | 0.787101 | ||||||||
\(407\) | 23.2216i | 1.15105i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.92982 | 0.194317 | 0.0971586 | − | 0.995269i | \(-0.469025\pi\) | ||||
0.0971586 | + | 0.995269i | \(0.469025\pi\) | |||||||
\(410\) | −20.8727 | + | 37.0575i | −1.03083 | + | 1.83014i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 17.2621i | − | 0.850442i | ||||||
\(413\) | − | 4.86835i | − | 0.239556i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.8965 | + | 24.6719i | −0.682155 | + | 1.21110i | ||||
\(416\) | 19.7342 | 0.967549 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.10160i | 0.347351i | ||||||||
\(419\) | −34.2996 | −1.67565 | −0.837824 | − | 0.545941i | \(-0.816172\pi\) | ||||
−0.837824 | + | 0.545941i | \(0.816172\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.0891 | −1.27151 | −0.635753 | − | 0.771893i | \(-0.719310\pi\) | ||||
−0.635753 | + | 0.771893i | \(0.719310\pi\) | |||||||
\(422\) | 19.1486i | 0.932138i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.23129 | −0.254054 | ||||||||
\(425\) | −16.7746 | + | 10.1667i | −0.813690 | + | 0.493156i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 14.9861i | − | 0.725229i | ||||||
\(428\) | 7.62715i | 0.368672i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.14982 | − | 2.90066i | −0.248347 | − | 0.139882i | ||||
\(431\) | −10.2996 | −0.496117 | −0.248058 | − | 0.968745i | \(-0.579792\pi\) | ||||
−0.248058 | + | 0.968745i | \(0.579792\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 36.2319i | − | 1.74119i | −0.491999 | − | 0.870596i | \(-0.663734\pi\) | ||
0.491999 | − | 0.870596i | \(-0.336266\pi\) | |||||||
\(434\) | −22.2996 | −1.07042 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.78000 | 0.420486 | ||||||||
\(437\) | 5.37334i | 0.257042i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.0891 | 1.14971 | 0.574855 | − | 0.818255i | \(-0.305058\pi\) | ||||
0.574855 | + | 0.818255i | \(0.305058\pi\) | |||||||
\(440\) | 5.28655 | − | 9.38574i | 0.252026 | − | 0.447448i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 21.8704i | − | 1.04027i | ||||||
\(443\) | 5.52337i | 0.262423i | 0.991354 | + | 0.131212i | \(0.0418868\pi\) | ||||
−0.991354 | + | 0.131212i | \(0.958113\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.0927 | − | 13.5703i | −1.14211 | − | 0.643295i | ||||
\(446\) | 30.7913 | 1.45801 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 2.84977i | − | 0.134639i | ||||||
\(449\) | 7.92982 | 0.374231 | 0.187116 | − | 0.982338i | \(-0.440086\pi\) | ||||
0.187116 | + | 0.982338i | \(0.440086\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −40.6658 | −1.91488 | ||||||||
\(452\) | − | 12.4446i | − | 0.585346i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −31.2277 | −1.46559 | ||||||||
\(455\) | −8.64327 | − | 4.86835i | −0.405203 | − | 0.228232i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.6534i | 1.05968i | 0.848098 | + | 0.529840i | \(0.177748\pi\) | ||||
−0.848098 | + | 0.529840i | \(0.822252\pi\) | |||||||
\(458\) | − | 45.6479i | − | 2.13299i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.79310 | + | 13.8359i | −0.363355 | + | 0.645101i | ||||
\(461\) | −13.3900 | −0.623634 | −0.311817 | − | 0.950142i | \(-0.600938\pi\) | ||||
−0.311817 | + | 0.950142i | \(0.600938\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 16.9029i | − | 0.785546i | −0.919635 | − | 0.392773i | \(-0.871516\pi\) | ||
0.919635 | − | 0.392773i | \(-0.128484\pi\) | |||||||
\(464\) | −29.3793 | −1.36390 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 35.1724 | 1.62933 | ||||||||
\(467\) | − | 22.2501i | − | 1.02961i | −0.857306 | − | 0.514807i | \(-0.827864\pi\) | ||
0.857306 | − | 0.514807i | \(-0.172136\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.2771 | 0.659254 | ||||||||
\(470\) | 17.4233 | + | 9.81371i | 0.803676 | + | 0.452673i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.15006i | 0.191022i | ||||||||
\(473\) | − | 5.65127i | − | 0.259846i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.59155 | + | 4.27596i | 0.118908 | + | 0.196195i | ||||
\(476\) | −7.51965 | −0.344663 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 34.2077i | 1.56462i | ||||||||
\(479\) | 0.366196 | 0.0167319 | 0.00836597 | − | 0.999965i | \(-0.497337\pi\) | ||||
0.00836597 | + | 0.999965i | \(0.497337\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.2295 | −0.831192 | ||||||||
\(482\) | − | 26.3108i | − | 1.19842i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.52854 | −0.251297 | ||||||||
\(485\) | −3.35673 | + | 5.95953i | −0.152421 | + | 0.270608i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.8461i | 1.21651i | 0.793740 | + | 0.608257i | \(0.208131\pi\) | ||||
−0.793740 | + | 0.608257i | \(0.791869\pi\) | |||||||
\(488\) | 12.7750i | 0.578298i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 9.79310 | − | 17.3867i | 0.442407 | − | 0.785450i | ||||
\(491\) | 23.7266 | 1.07076 | 0.535382 | − | 0.844610i | \(-0.320168\pi\) | ||||
0.535382 | + | 0.844610i | \(0.320168\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.5381i | 1.06010i | ||||||||
\(494\) | −5.57491 | −0.250827 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 41.3091 | 1.85483 | ||||||||
\(497\) | 12.5356i | 0.562298i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.81690 | −0.305166 | −0.152583 | − | 0.988291i | \(-0.548759\pi\) | ||||
−0.152583 | + | 0.988291i | \(0.548759\pi\) | |||||||
\(500\) | 0.471462 | + | 14.7688i | 0.0210844 | + | 0.660482i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 20.0045i | 0.892845i | ||||||||
\(503\) | 23.4102i | 1.04381i | 0.853004 | + | 0.521904i | \(0.174778\pi\) | ||||
−0.853004 | + | 0.521904i | \(0.825222\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.53982 | + | 3.68358i | 0.291018 | + | 0.163917i | ||||
\(506\) | −38.1593 | −1.69639 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14.6615i | 0.650499i | ||||||||
\(509\) | 16.9204 | 0.749981 | 0.374991 | − | 0.927029i | \(-0.377646\pi\) | ||||
0.374991 | + | 0.927029i | \(0.377646\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.53035 | −0.156174 | ||||||||
\(512\) | 19.4823i | 0.861003i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 32.1480 | 1.41799 | ||||||||
\(515\) | 14.3329 | − | 25.4467i | 0.631584 | − | 1.12131i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.1198i | 0.840888i | ||||||||
\(518\) | 15.7527i | 0.692133i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.36801 | + | 4.15006i | 0.323109 | + | 0.181992i | ||||
\(521\) | 3.49345 | 0.153051 | 0.0765254 | − | 0.997068i | \(-0.475617\pi\) | ||||
0.0765254 | + | 0.997068i | \(0.475617\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 14.9271i | − | 0.652714i | −0.945247 | − | 0.326357i | \(-0.894179\pi\) | ||
0.945247 | − | 0.326357i | \(-0.105821\pi\) | |||||||
\(524\) | 6.09275 | 0.266163 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.07965 | −0.134279 | ||||||||
\(527\) | − | 33.0960i | − | 1.44168i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.87275 | −0.255337 | ||||||||
\(530\) | 15.0244 | + | 8.46253i | 0.652618 | + | 0.367589i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.91681i | 0.0831041i | ||||||||
\(533\) | − | 31.9236i | − | 1.38276i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.33292 | + | 11.2435i | −0.273796 | + | 0.486098i | ||||
\(536\) | −12.1706 | −0.525689 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 49.3948i | − | 2.12956i | ||||||
\(539\) | 19.0796 | 0.821819 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.6991 | −0.545978 | −0.272989 | − | 0.962017i | \(-0.588012\pi\) | ||||
−0.272989 | + | 0.962017i | \(0.588012\pi\) | |||||||
\(542\) | 43.6541i | 1.87510i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 25.3091 | 1.08512 | ||||||||
\(545\) | 12.9429 | + | 7.29014i | 0.554414 | + | 0.312275i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.8162i | 1.36036i | 0.733043 | + | 0.680182i | \(0.238099\pi\) | ||||
−0.733043 | + | 0.680182i | \(0.761901\pi\) | |||||||
\(548\) | 17.4203i | 0.744158i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −30.3662 | + | 18.4041i | −1.29482 | + | 0.784756i | ||||
\(551\) | 6.00000 | 0.255609 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 18.0368i | − | 0.767003i | ||||||
\(554\) | 15.0095 | 0.637691 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.56363 | 0.0663125 | ||||||||
\(557\) | − | 9.64731i | − | 0.408770i | −0.978891 | − | 0.204385i | \(-0.934481\pi\) | ||
0.978891 | − | 0.204385i | \(-0.0655194\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.43637 | 0.187639 | ||||||||
\(560\) | 7.79310 | − | 13.8359i | 0.329319 | − | 0.584672i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 19.0207i | 0.802338i | ||||||||
\(563\) | 4.28216i | 0.180471i | 0.995920 | + | 0.0902357i | \(0.0287620\pi\) | ||||
−0.995920 | + | 0.0902357i | \(0.971238\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.3329 | − | 18.3451i | 0.434709 | − | 0.771783i | ||||
\(566\) | 19.0796 | 0.801977 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 10.6860i | − | 0.448376i | ||||||
\(569\) | 42.2295 | 1.77035 | 0.885176 | − | 0.465257i | \(-0.154038\pi\) | ||||
0.885176 | + | 0.465257i | \(0.154038\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.2200 | −0.804332 | −0.402166 | − | 0.915567i | \(-0.631743\pi\) | ||||
−0.402166 | + | 0.915567i | \(0.631743\pi\) | |||||||
\(572\) | − | 15.7527i | − | 0.658653i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −27.5862 | −1.15143 | ||||||||
\(575\) | −22.9762 | + | 13.9253i | −0.958174 | + | 0.580724i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.7919i | 1.69819i | 0.528239 | + | 0.849096i | \(0.322852\pi\) | ||||
−0.528239 | + | 0.849096i | \(0.677148\pi\) | |||||||
\(578\) | 2.93428i | 0.122050i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 15.4495 | + | 8.70197i | 0.641504 | + | 0.361329i | ||||
\(581\) | −18.3662 | −0.761958 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.4873i | 0.682836i | ||||||||
\(584\) | 3.00947 | 0.124533 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −30.0113 | −1.23975 | ||||||||
\(587\) | − | 31.8851i | − | 1.31604i | −0.753001 | − | 0.658019i | \(-0.771395\pi\) | ||
0.753001 | − | 0.658019i | \(-0.228605\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.43637 | −0.347615 | ||||||||
\(590\) | 6.71345 | − | 11.9191i | 0.276388 | − | 0.490700i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 29.1811i | − | 1.19934i | ||||||
\(593\) | 38.8973i | 1.59732i | 0.601783 | + | 0.798660i | \(0.294457\pi\) | ||||
−0.601783 | + | 0.798660i | \(0.705543\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.0850 | − | 6.24366i | −0.454441 | − | 0.255965i | ||||
\(596\) | −7.21637 | −0.295594 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 29.9559i | − | 1.22499i | ||||||
\(599\) | 28.1629 | 1.15071 | 0.575353 | − | 0.817905i | \(-0.304865\pi\) | ||||
0.575353 | + | 0.817905i | \(0.304865\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.56363 | −0.226945 | −0.113473 | − | 0.993541i | \(-0.536197\pi\) | ||||
−0.113473 | + | 0.993541i | \(0.536197\pi\) | |||||||
\(602\) | − | 3.83361i | − | 0.156246i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.71345 | 0.273166 | ||||||||
\(605\) | −8.14982 | − | 4.59042i | −0.331337 | − | 0.186627i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 33.9986i | − | 1.37996i | −0.723828 | − | 0.689980i | \(-0.757619\pi\) | ||
0.723828 | − | 0.689980i | \(-0.242381\pi\) | |||||||
\(608\) | − | 6.45146i | − | 0.261641i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 20.6658 | − | 36.6902i | 0.836736 | − | 1.48554i | ||||
\(611\) | −15.0095 | −0.607218 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.5703i | 0.709659i | 0.934931 | + | 0.354830i | \(0.115461\pi\) | ||||
−0.934931 | + | 0.354830i | \(0.884539\pi\) | |||||||
\(614\) | 14.3549 | 0.579317 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.98690 | 0.281510 | ||||||||
\(617\) | − | 13.0791i | − | 0.526544i | −0.964722 | − | 0.263272i | \(-0.915198\pi\) | ||
0.964722 | − | 0.263272i | \(-0.0848016\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.9393 | 0.761234 | 0.380617 | − | 0.924733i | \(-0.375712\pi\) | ||||
0.380617 | + | 0.924733i | \(0.375712\pi\) | |||||||
\(620\) | −21.7229 | − | 12.2355i | −0.872414 | − | 0.491390i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 7.10160i | − | 0.284748i | ||||||
\(623\) | − | 17.9350i | − | 0.718552i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.5677 | + | 22.1627i | −0.462710 | + | 0.886510i | ||||
\(626\) | −14.1593 | −0.565919 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.08545i | 0.322645i | ||||||||
\(629\) | −23.3793 | −0.932194 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.6896 | 1.26154 | 0.630772 | − | 0.775968i | \(-0.282738\pi\) | ||||
0.630772 | + | 0.775968i | \(0.282738\pi\) | |||||||
\(632\) | 15.3756i | 0.611608i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −34.7211 | −1.37895 | ||||||||
\(635\) | −12.1736 | + | 21.6131i | −0.483096 | + | 0.857688i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.9779i | 0.593448i | ||||||||
\(638\) | 42.6096i | 1.68693i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −10.2295 | + | 18.1614i | −0.404355 | + | 0.717893i | ||||
\(641\) | −47.9750 | −1.89490 | −0.947449 | − | 0.319908i | \(-0.896348\pi\) | ||||
−0.947449 | + | 0.319908i | \(0.896348\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 0.200927i | − | 0.00792378i | −0.999992 | − | 0.00396189i | \(-0.998739\pi\) | ||
0.999992 | − | 0.00396189i | \(-0.00126111\pi\) | |||||||
\(644\) | −10.2996 | −0.405863 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.14982 | −0.281306 | ||||||||
\(647\) | 1.58798i | 0.0624299i | 0.999513 | + | 0.0312150i | \(0.00993765\pi\) | ||||
−0.999513 | + | 0.0312150i | \(0.990062\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.0796 | 0.513421 | ||||||||
\(650\) | −14.4477 | − | 23.8381i | −0.566684 | − | 0.935008i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 21.7230i | 0.850739i | ||||||||
\(653\) | 33.5624i | 1.31340i | 0.754152 | + | 0.656700i | \(0.228048\pi\) | ||||
−0.754152 | + | 0.656700i | \(0.771952\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.98155 | + | 5.05889i | 0.350938 | + | 0.197667i | ||||
\(656\) | 51.1022 | 1.99521 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12.9702i | 0.505630i | ||||||||
\(659\) | 15.3567 | 0.598213 | 0.299107 | − | 0.954220i | \(-0.403311\pi\) | ||||
0.299107 | + | 0.954220i | \(0.403311\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.8026 | 0.497962 | 0.248981 | − | 0.968508i | \(-0.419904\pi\) | ||||
0.248981 | + | 0.968508i | \(0.419904\pi\) | |||||||
\(662\) | 14.5803i | 0.566679i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15.6564 | 0.607585 | ||||||||
\(665\) | −1.59155 | + | 2.82564i | −0.0617176 | + | 0.109573i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 32.2400i | 1.24834i | ||||||||
\(668\) | 5.02657i | 0.194484i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 34.9542 | + | 19.6881i | 1.35040 | + | 0.760617i | ||||
\(671\) | 40.2627 | 1.55433 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.82545i | 0.301649i | 0.988561 | + | 0.150824i | \(0.0481928\pi\) | ||||
−0.988561 | + | 0.150824i | \(0.951807\pi\) | |||||||
\(674\) | −12.5618 | −0.483863 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.81509 | −0.185196 | ||||||||
\(677\) | 21.6516i | 0.832137i | 0.909333 | + | 0.416069i | \(0.136592\pi\) | ||||
−0.909333 | + | 0.416069i | \(0.863408\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.43637 | −0.170252 | ||||||||
\(680\) | 9.44947 | + | 5.32245i | 0.362371 | + | 0.204107i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 59.9118i | − | 2.29414i | ||||||
\(683\) | − | 6.38751i | − | 0.244411i | −0.992505 | − | 0.122206i | \(-0.961003\pi\) | ||
0.992505 | − | 0.122206i | \(-0.0389967\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.4643 | + | 25.6799i | −0.552652 | + | 0.981179i | ||||
\(686\) | 31.4458 | 1.20061 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.10160i | 0.270746i | ||||||||
\(689\) | −12.9429 | −0.493086 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.4958 | 1.69270 | 0.846351 | − | 0.532626i | \(-0.178795\pi\) | ||||
0.846351 | + | 0.532626i | \(0.178795\pi\) | |||||||
\(692\) | − | 15.0452i | − | 0.571933i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 55.6789 | 2.11354 | ||||||||
\(695\) | 2.30500 | + | 1.29830i | 0.0874336 | + | 0.0492473i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 40.9420i | − | 1.55079i | ||||||
\(698\) | − | 30.5626i | − | 1.15681i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.19620 | + | 4.96750i | −0.309787 | + | 0.187754i | ||||
\(701\) | −17.5160 | −0.661571 | −0.330785 | − | 0.943706i | \(-0.607314\pi\) | ||||
−0.330785 | + | 0.943706i | \(0.607314\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.95953i | 0.224768i | ||||||||
\(704\) | 7.65638 | 0.288560 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 53.0357 | 1.99602 | ||||||||
\(707\) | 4.86835i | 0.183093i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.4269 | −0.429146 | −0.214573 | − | 0.976708i | \(-0.568836\pi\) | ||||
−0.214573 | + | 0.976708i | \(0.568836\pi\) | |||||||
\(710\) | −17.2865 | + | 30.6905i | −0.648753 | + | 1.15180i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15.2888i | 0.572973i | ||||||||
\(713\) | − | 45.3315i | − | 1.69768i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.0796 | − | 23.2216i | 0.489151 | − | 0.868439i | ||||
\(716\) | −13.3091 | −0.497385 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 21.3048i | − | 0.795088i | ||||||
\(719\) | 15.8965 | 0.592841 | 0.296421 | − | 0.955057i | \(-0.404207\pi\) | ||||
0.296421 | + | 0.955057i | \(0.404207\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.9429 | 0.705471 | ||||||||
\(722\) | 1.82254i | 0.0678278i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.757427 | −0.0281495 | ||||||||
\(725\) | 15.5493 | + | 25.6558i | 0.577486 | + | 0.952832i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 41.9905i | − | 1.55734i | −0.627434 | − | 0.778670i | \(-0.715895\pi\) | ||
0.627434 | − | 0.778670i | \(-0.284105\pi\) | |||||||
\(728\) | 5.48487i | 0.203283i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.64327 | − | 4.86835i | −0.319902 | − | 0.180186i | ||||
\(731\) | 5.68965 | 0.210439 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 0.632884i | − | 0.0233761i | −0.999932 | − | 0.0116881i | \(-0.996279\pi\) | ||
0.999932 | − | 0.0116881i | \(-0.00372051\pi\) | |||||||
\(734\) | −7.65638 | −0.282602 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 34.6658 | 1.27780 | ||||||||
\(737\) | 38.3578i | 1.41293i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.5493 | 1.08699 | 0.543494 | − | 0.839413i | \(-0.317101\pi\) | ||||
0.543494 | + | 0.839413i | \(0.317101\pi\) | |||||||
\(740\) | −8.64327 | + | 15.3453i | −0.317733 | + | 0.564103i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.1844i | 0.410592i | ||||||||
\(743\) | 31.3374i | 1.14966i | 0.818274 | + | 0.574829i | \(0.194931\pi\) | ||||
−0.818274 | + | 0.574829i | \(0.805069\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.6379 | − | 5.99184i | −0.389743 | − | 0.219524i | ||||
\(746\) | 30.8840 | 1.13074 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 20.2028i | − | 0.738688i | ||||||
\(749\) | −8.36983 | −0.305827 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.0131 | 0.912741 | 0.456371 | − | 0.889790i | \(-0.349149\pi\) | ||||
0.456371 | + | 0.889790i | \(0.349149\pi\) | |||||||
\(752\) | − | 24.0267i | − | 0.876163i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −33.4495 | −1.21816 | ||||||||
\(755\) | 9.89655 | + | 5.57426i | 0.360172 | + | 0.202868i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.0900i | 1.16633i | 0.812354 | + | 0.583165i | \(0.198186\pi\) | ||||
−0.812354 | + | 0.583165i | \(0.801814\pi\) | |||||||
\(758\) | − | 18.8928i | − | 0.686216i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.35673 | − | 2.40873i | 0.0492136 | − | 0.0873739i | ||||
\(761\) | 40.4922 | 1.46784 | 0.733921 | − | 0.679235i | \(-0.237688\pi\) | ||||
0.733921 | + | 0.679235i | \(0.237688\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.63492i | 0.348808i | ||||||||
\(764\) | −4.20690 | −0.152200 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 37.5273 | 1.35592 | ||||||||
\(767\) | 10.2678i | 0.370749i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.09398 | −0.111572 | −0.0557859 | − | 0.998443i | \(-0.517766\pi\) | ||||
−0.0557859 | + | 0.998443i | \(0.517766\pi\) | |||||||
\(770\) | −20.0665 | − | 11.3025i | −0.723148 | − | 0.407316i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 4.04272i | − | 0.145501i | ||||||
\(773\) | 1.96350i | 0.0706220i | 0.999376 | + | 0.0353110i | \(0.0112422\pi\) | ||||
−0.999376 | + | 0.0353110i | \(0.988758\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.8633 | − | 36.0736i | −0.785352 | − | 1.29580i | ||||
\(776\) | 3.78181 | 0.135759 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 14.7688i | 0.529488i | ||||||||
\(779\) | −10.4364 | −0.373922 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −33.6789 | −1.20513 | ||||||||
\(782\) | − | 38.4184i | − | 1.37384i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −23.9762 | −0.856293 | ||||||||
\(785\) | −6.71345 | + | 11.9191i | −0.239613 | + | 0.425410i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.107331i | 0.00382595i | 0.999998 | + | 0.00191297i | \(0.000608919\pi\) | ||||
−0.999998 | + | 0.00191297i | \(0.999391\pi\) | |||||||
\(788\) | − | 28.4064i | − | 1.01194i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 24.8727 | − | 44.1591i | 0.884933 | − | 1.57111i | ||||
\(791\) | 13.6564 | 0.485565 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31.6071i | 1.12240i | ||||||||
\(794\) | 6.32222 | 0.224367 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.36620 | −0.225644 | ||||||||
\(797\) | − | 8.32068i | − | 0.294734i | −0.989082 | − | 0.147367i | \(-0.952920\pi\) | ||
0.989082 | − | 0.147367i | \(-0.0470798\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19.2496 | −0.681003 | ||||||||
\(800\) | 27.5862 | − | 16.7193i | 0.975319 | − | 0.591115i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 29.0738i | 1.02663i | ||||||||
\(803\) | − | 9.48489i | − | 0.334714i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.1831 | − | 8.55193i | −0.535134 | − | 0.301416i | ||||
\(806\) | 47.0320 | 1.65663 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 4.15006i | − | 0.145998i | ||||||
\(809\) | −27.6231 | −0.971177 | −0.485588 | − | 0.874188i | \(-0.661395\pi\) | ||||
−0.485588 | + | 0.874188i | \(0.661395\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.0095 | 0.807972 | 0.403986 | − | 0.914765i | \(-0.367624\pi\) | ||||
0.403986 | + | 0.914765i | \(0.367624\pi\) | |||||||
\(812\) | 11.5008i | 0.403600i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −42.3222 | −1.48339 | ||||||||
\(815\) | −18.0369 | + | 32.0227i | −0.631805 | + | 1.12171i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1.45033i | − | 0.0507405i | ||||||
\(818\) | 7.16224i | 0.250422i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −26.8727 | − | 15.1362i | −0.938437 | − | 0.528578i | ||||
\(821\) | −31.1355 | −1.08664 | −0.543318 | − | 0.839527i | \(-0.682832\pi\) | ||||
−0.543318 | + | 0.839527i | \(0.682832\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.4201i | 0.711800i | 0.934524 | + | 0.355900i | \(0.115826\pi\) | ||||
−0.934524 | + | 0.355900i | \(0.884174\pi\) | |||||||
\(824\) | −16.1480 | −0.562543 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.87275 | 0.308722 | ||||||||
\(827\) | − | 0.902638i | − | 0.0313878i | −0.999877 | − | 0.0156939i | \(-0.995004\pi\) | ||
0.999877 | − | 0.0156939i | \(-0.00499573\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.4971 | 0.468773 | 0.234386 | − | 0.972143i | \(-0.424692\pi\) | ||||
0.234386 | + | 0.972143i | \(0.424692\pi\) | |||||||
\(830\) | −44.9655 | − | 25.3270i | −1.56078 | − | 0.879112i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.01042i | 0.208374i | ||||||||
\(833\) | 19.2092i | 0.665560i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.17363 | + | 7.40986i | −0.144434 | + | 0.256429i | ||||
\(836\) | −5.14982 | −0.178110 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 62.5123i | − | 2.15945i | ||||||
\(839\) | 33.1022 | 1.14282 | 0.571408 | − | 0.820666i | \(-0.306397\pi\) | ||||
0.571408 | + | 0.820666i | \(0.306397\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | − | 47.5484i | − | 1.63862i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13.8858 | −0.477971 | ||||||||
\(845\) | −7.09810 | − | 3.99803i | −0.244182 | − | 0.137536i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 6.06686i | − | 0.208460i | ||||||
\(848\) | − | 20.7186i | − | 0.711480i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −18.5291 | − | 30.5724i | −0.635544 | − | 1.04862i | ||||
\(851\) | −32.0226 | −1.09772 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 50.9097i | 1.74312i | 0.490293 | + | 0.871558i | \(0.336890\pi\) | ||||
−0.490293 | + | 0.871558i | \(0.663110\pi\) | |||||||
\(854\) | 27.3128 | 0.934623 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.13491 | 0.243866 | ||||||||
\(857\) | 21.2333i | 0.725317i | 0.931922 | + | 0.362659i | \(0.118131\pi\) | ||||
−0.931922 | + | 0.362659i | \(0.881869\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.4827 | −1.00594 | −0.502969 | − | 0.864304i | \(-0.667759\pi\) | ||||
−0.502969 | + | 0.864304i | \(0.667759\pi\) | |||||||
\(860\) | 2.10345 | − | 3.73447i | 0.0717271 | − | 0.127344i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 18.7715i | − | 0.639359i | ||||||
\(863\) | − | 25.7755i | − | 0.877408i | −0.898632 | − | 0.438704i | \(-0.855438\pi\) | ||
0.898632 | − | 0.438704i | \(-0.144562\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.4922 | − | 22.1787i | 0.424748 | − | 0.754098i | ||||
\(866\) | 66.0339 | 2.24392 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 16.1709i | − | 0.548876i | ||||||
\(869\) | 48.4589 | 1.64386 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.1117 | −1.02030 | ||||||||
\(872\) | − | 8.21335i | − | 0.278139i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −9.79310 | −0.331257 | ||||||||
\(875\) | −16.2069 | + | 0.517369i | −0.547893 | + | 0.0174903i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 54.2687i | − | 1.83252i | −0.400581 | − | 0.916261i | \(-0.631192\pi\) | ||
0.400581 | − | 0.916261i | \(-0.368808\pi\) | |||||||
\(878\) | 43.9033i | 1.48166i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 37.1724 | + | 20.9375i | 1.25308 | + | 0.705802i | ||||
\(881\) | 28.4922 | 0.959927 | 0.479964 | − | 0.877288i | \(-0.340650\pi\) | ||||
0.479964 | + | 0.877288i | \(0.340650\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.5264i | 1.36382i | 0.731435 | + | 0.681911i | \(0.238851\pi\) | ||||
−0.731435 | + | 0.681911i | \(0.761149\pi\) | |||||||
\(884\) | 15.8596 | 0.533418 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.0665 | −0.338192 | ||||||||
\(887\) | − | 11.4705i | − | 0.385142i | −0.981283 | − | 0.192571i | \(-0.938317\pi\) | ||
0.981283 | − | 0.192571i | \(-0.0616826\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.0891 | −0.539612 | ||||||||
\(890\) | 24.7324 | − | 43.9099i | 0.829032 | − | 1.47186i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 22.3287i | 0.747621i | ||||||||
\(893\) | 4.90686i | 0.164202i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.6195 | − | 11.0507i | −0.655807 | − | 0.369385i | ||||
\(896\) | −13.5197 | −0.451660 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 14.4524i | 0.482282i | ||||||||
\(899\) | −50.6182 | −1.68821 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.5993 | −0.553003 | ||||||||
\(902\) | − | 74.1150i | − | 2.46776i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11.6415 | −0.387189 | ||||||||
\(905\) | −1.11655 | − | 0.628901i | −0.0371154 | − | 0.0209054i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.1000i | 1.59714i | 0.601905 | + | 0.798568i | \(0.294409\pi\) | ||||
−0.601905 | + | 0.798568i | \(0.705591\pi\) | |||||||
\(908\) | − | 22.6452i | − | 0.751506i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 8.87275 | − | 15.7527i | 0.294129 | − | 0.522196i | ||||
\(911\) | 12.8062 | 0.424288 | 0.212144 | − | 0.977238i | \(-0.431955\pi\) | ||||
0.212144 | + | 0.977238i | \(0.431955\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 49.3439i | − | 1.63304i | ||||||
\(914\) | −41.2865 | −1.36564 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 33.1022 | 1.09373 | ||||||||
\(917\) | 6.68601i | 0.220792i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.7135 | 1.27704 | 0.638519 | − | 0.769606i | \(-0.279547\pi\) | ||||
0.638519 | + | 0.769606i | \(0.279547\pi\) | |||||||
\(920\) | 12.9429 | + | 7.29014i | 0.426716 | + | 0.240349i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 24.4038i | − | 0.803695i | ||||||
\(923\) | − | 26.4387i | − | 0.870241i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.4827 | + | 15.4444i | −0.837868 | + | 0.507809i | ||||
\(926\) | 30.8062 | 1.01235 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 38.7087i | − | 1.27068i | ||||||
\(929\) | −36.0189 | −1.18174 | −0.590872 | − | 0.806766i | \(-0.701216\pi\) | ||||
−0.590872 | + | 0.806766i | \(0.701216\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.89655 | 0.160478 | ||||||||
\(932\) | 25.5058i | 0.835469i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 40.5517 | 1.32689 | ||||||||
\(935\) | 16.7746 | − | 29.7817i | 0.548590 | − | 0.973966i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 45.2421i | − | 1.47799i | −0.673709 | − | 0.738997i | \(-0.735300\pi\) | ||
0.673709 | − | 0.738997i | \(-0.264700\pi\) | |||||||
\(938\) | 26.0205i | 0.849599i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.11655 | + | 12.6347i | −0.232116 | + | 0.412099i | ||||
\(941\) | 11.7455 | 0.382892 | 0.191446 | − | 0.981503i | \(-0.438682\pi\) | ||||
0.191446 | + | 0.981503i | \(0.438682\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 56.0781i | − | 1.82616i | ||||||
\(944\) | −16.4364 | −0.534958 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.2996 | 0.334870 | ||||||||
\(947\) | 13.7752i | 0.447635i | 0.974631 | + | 0.223817i | \(0.0718519\pi\) | ||||
−0.974631 | + | 0.223817i | \(0.928148\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.44584 | 0.241702 | ||||||||
\(950\) | −7.79310 | + | 4.72319i | −0.252842 | + | 0.153241i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.03434i | 0.227984i | ||||||||
\(953\) | 9.01421i | 0.291999i | 0.989285 | + | 0.145999i | \(0.0466398\pi\) | ||||
−0.989285 | + | 0.145999i | \(0.953360\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.20155 | − | 3.49304i | −0.200677 | − | 0.113032i | ||||
\(956\) | −24.8062 | −0.802290 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.667406i | 0.0215629i | ||||||||
\(959\) | −19.1166 | −0.617306 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 40.1724 | 1.29588 | ||||||||
\(962\) | − | 33.2239i | − | 1.07118i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 19.0796 | 0.614514 | ||||||||
\(965\) | 3.35673 | − | 5.95953i | 0.108057 | − | 0.191844i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.3232i | 0.975129i | 0.873087 | + | 0.487564i | \(0.162115\pi\) | ||||
−0.873087 | + | 0.487564i | \(0.837885\pi\) | |||||||
\(968\) | 5.17173i | 0.166226i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −10.8615 | − | 6.11775i | −0.348740 | − | 0.196429i | ||||
\(971\) | 31.5636 | 1.01292 | 0.506462 | − | 0.862262i | \(-0.330953\pi\) | ||||
0.506462 | + | 0.862262i | \(0.330953\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.71588i | 0.0550086i | ||||||||
\(974\) | −48.9280 | −1.56775 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −50.5957 | −1.61953 | ||||||||
\(977\) | − | 43.1285i | − | 1.37980i | −0.723903 | − | 0.689902i | \(-0.757654\pi\) | ||
0.723903 | − | 0.689902i | \(-0.242346\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 48.1855 | 1.54002 | ||||||||
\(980\) | 12.6082 | + | 7.10160i | 0.402754 | + | 0.226852i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 43.2425i | 1.37992i | ||||||||
\(983\) | 7.81570i | 0.249282i | 0.992202 | + | 0.124641i | \(0.0397779\pi\) | ||||
−0.992202 | + | 0.124641i | \(0.960222\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.5862 | − | 41.8749i | 0.751519 | − | 1.33425i | ||||
\(986\) | −42.8989 | −1.36618 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 4.04272i | − | 0.128616i | ||||||
\(989\) | 7.79310 | 0.247806 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.5197 | −0.747126 | −0.373563 | − | 0.927605i | \(-0.621864\pi\) | ||||
−0.373563 | + | 0.927605i | \(0.621864\pi\) | |||||||
\(992\) | 54.4269i | 1.72806i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −22.8465 | −0.724648 | ||||||||
\(995\) | −9.38465 | − | 5.28593i | −0.297513 | − | 0.167575i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 33.6395i | − | 1.06537i | −0.846313 | − | 0.532686i | \(-0.821183\pi\) | ||
0.846313 | − | 0.532686i | \(-0.178817\pi\) | |||||||
\(998\) | − | 12.4240i | − | 0.393276i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 855.2.c.d.514.5 | 6 | ||
3.2 | odd | 2 | 95.2.b.b.39.2 | ✓ | 6 | ||
5.2 | odd | 4 | 4275.2.a.br.1.2 | 6 | |||
5.3 | odd | 4 | 4275.2.a.br.1.5 | 6 | |||
5.4 | even | 2 | inner | 855.2.c.d.514.2 | 6 | ||
12.11 | even | 2 | 1520.2.d.h.609.2 | 6 | |||
15.2 | even | 4 | 475.2.a.j.1.5 | 6 | |||
15.8 | even | 4 | 475.2.a.j.1.2 | 6 | |||
15.14 | odd | 2 | 95.2.b.b.39.5 | yes | 6 | ||
57.56 | even | 2 | 1805.2.b.e.1084.5 | 6 | |||
60.23 | odd | 4 | 7600.2.a.ck.1.5 | 6 | |||
60.47 | odd | 4 | 7600.2.a.ck.1.2 | 6 | |||
60.59 | even | 2 | 1520.2.d.h.609.5 | 6 | |||
285.113 | odd | 4 | 9025.2.a.bx.1.5 | 6 | |||
285.227 | odd | 4 | 9025.2.a.bx.1.2 | 6 | |||
285.284 | even | 2 | 1805.2.b.e.1084.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.b.b.39.2 | ✓ | 6 | 3.2 | odd | 2 | ||
95.2.b.b.39.5 | yes | 6 | 15.14 | odd | 2 | ||
475.2.a.j.1.2 | 6 | 15.8 | even | 4 | |||
475.2.a.j.1.5 | 6 | 15.2 | even | 4 | |||
855.2.c.d.514.2 | 6 | 5.4 | even | 2 | inner | ||
855.2.c.d.514.5 | 6 | 1.1 | even | 1 | trivial | ||
1520.2.d.h.609.2 | 6 | 12.11 | even | 2 | |||
1520.2.d.h.609.5 | 6 | 60.59 | even | 2 | |||
1805.2.b.e.1084.2 | 6 | 285.284 | even | 2 | |||
1805.2.b.e.1084.5 | 6 | 57.56 | even | 2 | |||
4275.2.a.br.1.2 | 6 | 5.2 | odd | 4 | |||
4275.2.a.br.1.5 | 6 | 5.3 | odd | 4 | |||
7600.2.a.ck.1.2 | 6 | 60.47 | odd | 4 | |||
7600.2.a.ck.1.5 | 6 | 60.23 | odd | 4 | |||
9025.2.a.bx.1.2 | 6 | 285.227 | odd | 4 | |||
9025.2.a.bx.1.5 | 6 | 285.113 | odd | 4 |