Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(201,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.201");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.1715763840\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + 15 x^{10} - 16 x^{9} + 79 x^{8} - 65 x^{7} + 298 x^{6} + 13 x^{5} + 233 x^{4} + \cdots + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 201.4 | ||
Root | \(-0.126563 + 0.219213i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.201 |
Dual form | 1900.2.i.f.501.4 |
$q$-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 \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) | \(951\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.626563 | − | 1.08524i | 0.361746 | − | 0.626563i | −0.626502 | − | 0.779420i | \(-0.715514\pi\) |
0.988248 | + | 0.152857i | \(0.0488473\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.18534 | −0.825980 | −0.412990 | − | 0.910736i | \(-0.635516\pi\) | ||||
−0.412990 | + | 0.910736i | \(0.635516\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.714838 | + | 1.23814i | 0.238279 | + | 0.412712i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.12964 | 0.642109 | 0.321055 | − | 0.947061i | \(-0.395963\pi\) | ||||
0.321055 | + | 0.947061i | \(0.395963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.58011 | − | 4.46889i | −0.715595 | − | 1.23945i | −0.962730 | − | 0.270465i | \(-0.912822\pi\) |
0.247135 | − | 0.968981i | \(-0.420511\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.31355 | + | 2.27514i | −0.318583 | + | 0.551801i | −0.980193 | − | 0.198047i | \(-0.936540\pi\) |
0.661610 | + | 0.749848i | \(0.269874\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.80353 | − | 3.33770i | 0.643174 | − | 0.765720i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.36925 | + | 2.37161i | −0.298795 | + | 0.517528i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.27261 | − | 2.20422i | −0.265357 | − | 0.459611i | 0.702300 | − | 0.711881i | \(-0.252156\pi\) |
−0.967657 | + | 0.252269i | \(0.918823\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.55094 | 1.06828 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.08011 | − | 5.33491i | −0.571963 | − | 0.990668i | −0.996364 | − | 0.0851943i | \(-0.972849\pi\) |
0.424402 | − | 0.905474i | \(-0.360484\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.05063 | −0.188699 | −0.0943493 | − | 0.995539i | \(-0.530077\pi\) | ||||
−0.0943493 | + | 0.995539i | \(0.530077\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.33435 | − | 2.31116i | 0.232281 | − | 0.402322i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.25927 | −0.371422 | −0.185711 | − | 0.982604i | \(-0.559459\pi\) | ||||
−0.185711 | + | 0.982604i | \(0.559459\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.46641 | −1.03545 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.02728 | − | 8.70750i | 0.785129 | − | 1.35988i | −0.143794 | − | 0.989608i | \(-0.545930\pi\) |
0.928922 | − | 0.370275i | \(-0.120736\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.840080 | + | 1.45506i | −0.128111 | + | 0.221895i | −0.922945 | − | 0.384933i | \(-0.874225\pi\) |
0.794834 | + | 0.606827i | \(0.207558\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.24455 | − | 5.61972i | −0.473266 | − | 0.819720i | 0.526266 | − | 0.850320i | \(-0.323592\pi\) |
−0.999532 | + | 0.0305997i | \(0.990258\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.22430 | −0.317757 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.64604 | + | 2.85103i | 0.230492 | + | 0.399224i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.63184 | − | 6.29053i | −0.498871 | − | 0.864071i | 0.501128 | − | 0.865373i | \(-0.332919\pi\) |
−0.999999 | + | 0.00130277i | \(0.999585\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.86561 | − | 5.13378i | −0.247106 | − | 0.679985i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.53663 | − | 6.12563i | 0.460430 | − | 0.797489i | −0.538552 | − | 0.842592i | \(-0.681028\pi\) |
0.998982 | + | 0.0451035i | \(0.0143618\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.41986 | + | 9.38748i | 0.693943 | + | 1.20194i | 0.970536 | + | 0.240957i | \(0.0774612\pi\) |
−0.276593 | + | 0.960987i | \(0.589205\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.56216 | − | 2.70574i | −0.196814 | − | 0.340892i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.41877 | + | 2.45739i | 0.173331 | + | 0.300218i | 0.939582 | − | 0.342323i | \(-0.111214\pi\) |
−0.766251 | + | 0.642541i | \(0.777880\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.18947 | −0.383967 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.11236 | + | 5.39076i | −0.369369 | + | 0.639766i | −0.989467 | − | 0.144759i | \(-0.953759\pi\) |
0.620098 | + | 0.784524i | \(0.287093\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.78260 | − | 13.4799i | 0.910885 | − | 1.57770i | 0.0980678 | − | 0.995180i | \(-0.468734\pi\) |
0.812817 | − | 0.582519i | \(-0.197933\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.65397 | −0.530370 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.80671 | − | 4.86136i | 0.315779 | − | 0.546946i | −0.663823 | − | 0.747889i | \(-0.731067\pi\) |
0.979603 | + | 0.200943i | \(0.0644007\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.33350 | − | 2.30969i | 0.148167 | − | 0.256632i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.55136 | −0.828869 | −0.414435 | − | 0.910079i | \(-0.636021\pi\) | ||||
−0.414435 | + | 0.910079i | \(0.636021\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.71954 | −0.827621 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.73341 | − | 13.3947i | −0.819740 | − | 1.41983i | −0.905874 | − | 0.423548i | \(-0.860784\pi\) |
0.0861333 | − | 0.996284i | \(-0.472549\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.63842 | + | 9.76603i | 0.591067 | + | 1.02376i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.658285 | + | 1.14018i | −0.0682610 | + | 0.118232i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.63073 | − | 11.4848i | 0.673248 | − | 1.16610i | −0.303729 | − | 0.952758i | \(-0.598232\pi\) |
0.976978 | − | 0.213342i | \(-0.0684348\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.52234 | + | 2.63678i | 0.153001 | + | 0.265006i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.08748 | + | 3.61562i | 0.207712 | + | 0.359767i | 0.950993 | − | 0.309211i | \(-0.100065\pi\) |
−0.743282 | + | 0.668979i | \(0.766732\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.8667 | −1.56340 | −0.781699 | − | 0.623656i | \(-0.785646\pi\) | ||||
−0.781699 | + | 0.623656i | \(0.785646\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.02114 | −0.388739 | −0.194369 | − | 0.980928i | \(-0.562266\pi\) | ||||
−0.194369 | + | 0.980928i | \(0.562266\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.21086 | + | 3.82932i | −0.211762 | + | 0.366783i | −0.952266 | − | 0.305269i | \(-0.901254\pi\) |
0.740504 | + | 0.672052i | \(0.234587\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.41558 | + | 2.45185i | −0.134361 | + | 0.232719i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.04226 | 0.568408 | 0.284204 | − | 0.958764i | \(-0.408271\pi\) | ||||
0.284204 | + | 0.958764i | \(0.408271\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.68873 | − | 6.38906i | 0.341023 | − | 0.590669i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.87055 | − | 4.97194i | 0.263143 | − | 0.455777i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.46465 | −0.587695 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.29981 | − | 10.9116i | −0.568035 | − | 0.983865i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.88488 | + | 6.72881i | 0.344727 | + | 0.597085i | 0.985304 | − | 0.170809i | \(-0.0546380\pi\) |
−0.640577 | + | 0.767894i | \(0.721305\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.05273 | + | 1.82338i | 0.0926874 | + | 0.160539i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.18596 | + | 14.1785i | −0.715211 | + | 1.23878i | 0.247667 | + | 0.968845i | \(0.420336\pi\) |
−0.962878 | + | 0.269937i | \(0.912997\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.12666 | + | 7.29399i | −0.531249 | + | 0.632470i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.255662 | − | 0.442820i | −0.0218427 | − | 0.0378326i | 0.854897 | − | 0.518797i | \(-0.173620\pi\) |
−0.876740 | + | 0.480964i | \(0.840287\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.83289 | + | 6.63877i | 0.325102 | + | 0.563093i | 0.981533 | − | 0.191293i | \(-0.0612681\pi\) |
−0.656431 | + | 0.754386i | \(0.727935\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.13165 | −0.684808 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.49470 | − | 9.51710i | −0.459490 | − | 0.795860i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.39366 | + | 2.41390i | −0.114947 | + | 0.199095i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.96176 | + | 12.0581i | −0.570330 | + | 0.987840i | 0.426202 | + | 0.904628i | \(0.359851\pi\) |
−0.996532 | + | 0.0832122i | \(0.973482\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.617238 | 0.0502301 | 0.0251151 | − | 0.999685i | \(-0.492005\pi\) | ||||
0.0251151 | + | 0.999685i | \(0.492005\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.75590 | −0.303647 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.52408 | − | 16.4962i | 0.760104 | − | 1.31654i | −0.182692 | − | 0.983170i | \(-0.558481\pi\) |
0.942796 | − | 0.333369i | \(-0.108185\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.10230 | −0.721859 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.78107 | + | 4.81696i | 0.219179 | + | 0.379630i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.523410 | −0.0409967 | −0.0204983 | − | 0.999790i | \(-0.506525\pi\) | ||||
−0.0204983 | + | 0.999790i | \(0.506525\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.4720 | + | 18.1381i | 0.810349 | + | 1.40357i | 0.912620 | + | 0.408810i | \(0.134056\pi\) |
−0.102270 | + | 0.994757i | \(0.532611\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.81397 | + | 11.8021i | −0.524151 | + | 0.907857i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.13659 | + | 1.08524i | 0.469277 | + | 0.0829903i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.896215 | − | 1.55229i | 0.0681380 | − | 0.118018i | −0.829944 | − | 0.557847i | \(-0.811628\pi\) |
0.898082 | + | 0.439829i | \(0.144961\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.43185 | − | 7.67618i | −0.333118 | − | 0.576977i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 26.6492 | 1.99186 | 0.995928 | − | 0.0901537i | \(-0.0287358\pi\) | ||||
0.995928 | + | 0.0901537i | \(0.0287358\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.21515 | − | 9.03290i | −0.387639 | − | 0.671410i | 0.604492 | − | 0.796611i | \(-0.293376\pi\) |
−0.992131 | + | 0.125200i | \(0.960043\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.5835 | 1.00412 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.79738 | + | 4.84521i | −0.204565 | + | 0.354317i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −12.1307 | −0.882377 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.07372 | 0.367122 | 0.183561 | − | 0.983008i | \(-0.441238\pi\) | ||||
0.183561 | + | 0.983008i | \(0.441238\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.25345 | + | 5.63515i | −0.234189 | + | 0.405627i | −0.959037 | − | 0.283282i | \(-0.908577\pi\) |
0.724848 | + | 0.688909i | \(0.241910\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.78955 | −0.483735 | −0.241868 | − | 0.970309i | \(-0.577760\pi\) | ||||
−0.241868 | + | 0.970309i | \(0.577760\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.90024 | − | 11.9516i | −0.489145 | − | 0.847224i | 0.510777 | − | 0.859713i | \(-0.329358\pi\) |
−0.999922 | + | 0.0124890i | \(0.996025\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.55581 | 0.250807 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.73109 | + | 11.6586i | 0.472430 | + | 0.818272i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.81941 | − | 3.15132i | 0.126458 | − | 0.219032i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.97050 | − | 7.10808i | 0.412988 | − | 0.491676i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.06131 | + | 3.57030i | −0.141907 | + | 0.245789i | −0.928215 | − | 0.372045i | \(-0.878657\pi\) |
0.786308 | + | 0.617835i | \(0.211990\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.90018 | + | 6.75530i | 0.267236 | + | 0.462866i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.29598 | 0.155861 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.75258 | − | 16.8920i | −0.659018 | − | 1.14145i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.5564 | 0.911904 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.53146 | − | 4.38462i | 0.169519 | − | 0.293616i | −0.768732 | − | 0.639571i | \(-0.779112\pi\) |
0.938251 | + | 0.345956i | \(0.112445\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.05466 | 0.335489 | 0.167745 | − | 0.985830i | \(-0.446352\pi\) | ||||
0.167745 | + | 0.985830i | \(0.446352\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.01317 | 0.0669523 | 0.0334761 | − | 0.999440i | \(-0.489342\pi\) | ||||
0.0334761 | + | 0.999440i | \(0.489342\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.91601 | + | 5.05067i | −0.191859 | + | 0.332310i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.73375 | − | 9.93114i | 0.375630 | − | 0.650611i | −0.614791 | − | 0.788690i | \(-0.710760\pi\) |
0.990421 | + | 0.138079i | \(0.0440929\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.51716 | − | 6.09190i | −0.228464 | − | 0.395711i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.0027 | 1.16450 | 0.582250 | − | 0.813010i | \(-0.302172\pi\) | ||||
0.582250 | + | 0.813010i | \(0.302172\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.52915 | − | 2.64856i | −0.0985012 | − | 0.170609i | 0.812563 | − | 0.582873i | \(-0.198071\pi\) |
−0.911064 | + | 0.412264i | \(0.864738\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.65537 | + | 11.5274i | 0.426942 | + | 0.739485i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −22.1492 | − | 3.91703i | −1.40932 | − | 0.249234i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.73140 | + | 8.19503i | −0.299840 | + | 0.519339i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.789341 | − | 1.36718i | −0.0498228 | − | 0.0862956i | 0.840038 | − | 0.542527i | \(-0.182532\pi\) |
−0.889861 | + | 0.456231i | \(0.849199\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.71019 | − | 4.69418i | −0.170388 | − | 0.295121i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.07800 | + | 12.2595i | 0.441513 | + | 0.764724i | 0.997802 | − | 0.0662654i | \(-0.0211084\pi\) |
−0.556289 | + | 0.830989i | \(0.687775\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.93727 | 0.306787 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.40356 | − | 7.62719i | 0.272574 | − | 0.472112i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.04170 | + | 15.6607i | −0.557535 | + | 0.965679i | 0.440166 | + | 0.897916i | \(0.354919\pi\) |
−0.997701 | + | 0.0677628i | \(0.978414\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −19.3819 | −1.18615 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.29767 | − | 5.71172i | 0.201062 | − | 0.348250i | −0.747809 | − | 0.663914i | \(-0.768894\pi\) |
0.948871 | + | 0.315664i | \(0.102227\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.4587 | − | 21.5791i | 0.756811 | − | 1.31084i | −0.187657 | − | 0.982235i | \(-0.560089\pi\) |
0.944469 | − | 0.328601i | \(-0.106577\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 14.1313 | 0.855265 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.5130 | 1.05226 | 0.526128 | − | 0.850406i | \(-0.323643\pi\) | ||||
0.526128 | + | 0.850406i | \(0.323643\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.751029 | − | 1.30082i | −0.0449630 | − | 0.0778781i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.43050 | − | 14.6021i | −0.502922 | − | 0.871086i | −0.999994 | − | 0.00337702i | \(-0.998925\pi\) |
0.497073 | − | 0.867709i | \(-0.334408\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.90656 | + | 3.30226i | −0.113333 | + | 0.196299i | −0.917112 | − | 0.398629i | \(-0.869486\pi\) |
0.803779 | + | 0.594928i | \(0.202819\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.9863 | + | 19.0288i | −0.648501 | + | 1.12324i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.04917 | + | 8.74542i | 0.297010 | + | 0.514437i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.30913 | − | 14.3918i | −0.487090 | − | 0.843665i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.6667 | −0.739996 | −0.369998 | − | 0.929033i | \(-0.620642\pi\) | ||||
−0.369998 | + | 0.929033i | \(0.620642\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.8215 | 0.685952 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.56694 | + | 11.3743i | −0.379776 | + | 0.657791i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.83586 | − | 3.17980i | 0.105817 | − | 0.183281i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.23174 | 0.300556 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.64480 | − | 13.2412i | 0.436312 | − | 0.755714i | −0.561090 | − | 0.827755i | \(-0.689618\pi\) |
0.997402 | + | 0.0720410i | \(0.0229512\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.94152 | + | 17.2192i | −0.565553 | + | 0.979567i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.9152 | −1.58292 | −0.791462 | − | 0.611218i | \(-0.790680\pi\) | ||||
−0.791462 | + | 0.611218i | \(0.790680\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.95539 | + | 3.38684i | 0.110525 | + | 0.191436i | 0.915982 | − | 0.401219i | \(-0.131413\pi\) |
−0.805457 | + | 0.592654i | \(0.798080\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.70175 | + | 8.14366i | 0.264076 | + | 0.457394i | 0.967321 | − | 0.253554i | \(-0.0815996\pi\) |
−0.703245 | + | 0.710948i | \(0.748266\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.55952 | − | 11.3614i | −0.367263 | − | 0.636118i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.51950 | + | 4.36390i | −0.140625 | + | 0.243569i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.91113 | + | 10.7626i | 0.217621 | + | 0.598849i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.77049 | + | 4.79863i | 0.153208 | + | 0.265365i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.09043 | + | 12.2810i | 0.390908 | + | 0.677073i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.46413 | 0.0804757 | 0.0402379 | − | 0.999190i | \(-0.487188\pi\) | ||||
0.0402379 | + | 0.999190i | \(0.487188\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.61501 | − | 2.79729i | −0.0885022 | − | 0.153290i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.6121 | − | 27.0410i | 0.850447 | − | 1.47302i | −0.0303589 | − | 0.999539i | \(-0.509665\pi\) |
0.880806 | − | 0.473478i | \(-0.157002\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.78585 | − | 6.55729i | 0.205619 | − | 0.356143i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.23746 | −0.121165 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1582 | 1.08844 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.1197 | + | 26.1882i | −0.811670 | + | 1.40585i | 0.100024 | + | 0.994985i | \(0.468108\pi\) |
−0.911694 | + | 0.410869i | \(0.865225\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.1752 | 0.919367 | 0.459683 | − | 0.888083i | \(-0.347963\pi\) | ||||
0.459683 | + | 0.888083i | \(0.347963\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −14.3221 | − | 24.8065i | −0.764455 | − | 1.32407i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.6712 | 0.567970 | 0.283985 | − | 0.958829i | \(-0.408343\pi\) | ||||
0.283985 | + | 0.958829i | \(0.408343\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.59716 | − | 6.23047i | −0.190382 | − | 0.329751i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.751774 | + | 1.30211i | −0.0396771 | + | 0.0687228i | −0.885182 | − | 0.465245i | \(-0.845966\pi\) |
0.845505 | + | 0.533968i | \(0.179300\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.28043 | − | 18.7147i | −0.172654 | − | 0.984982i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.05051 | + | 7.01569i | −0.212597 | + | 0.368228i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.9857 | + | 31.1522i | 0.938846 | + | 1.62613i | 0.767628 | + | 0.640896i | \(0.221437\pi\) |
0.171218 | + | 0.985233i | \(0.445230\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.3747 | 0.748320 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.93679 | + | 13.7469i | 0.412058 | + | 0.713705i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.0175 | 0.932911 | 0.466455 | − | 0.884545i | \(-0.345531\pi\) | ||||
0.466455 | + | 0.884545i | \(0.345531\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.8941 | + | 27.5294i | −0.818587 | + | 1.41783i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.1538 | −0.727032 | −0.363516 | − | 0.931588i | \(-0.618424\pi\) | ||||
−0.363516 | + | 0.931588i | \(0.618424\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.73649 | 0.498815 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.80446 | + | 15.2498i | −0.449887 | + | 0.779227i | −0.998378 | − | 0.0569291i | \(-0.981869\pi\) |
0.548491 | + | 0.836156i | \(0.315202\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.40208 | −0.122105 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.72023 | + | 9.90774i | 0.290027 | + | 0.502342i | 0.973816 | − | 0.227338i | \(-0.0730023\pi\) |
−0.683789 | + | 0.729680i | \(0.739669\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.68653 | 0.338152 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.2580 | + | 17.7674i | 0.517450 | + | 0.896249i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.97852 | + | 15.5513i | −0.450619 | + | 0.780495i | −0.998425 | − | 0.0561107i | \(-0.982130\pi\) |
0.547806 | + | 0.836606i | \(0.315463\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.07699 | + | 11.2190i | 0.204105 | + | 0.561654i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.69150 | + | 8.12592i | −0.234282 | + | 0.405789i | −0.959064 | − | 0.283190i | \(-0.908607\pi\) |
0.724782 | + | 0.688979i | \(0.241941\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.71074 | + | 4.69514i | 0.135032 | + | 0.233882i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.81143 | −0.238494 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.4232 | + | 33.6420i | 0.960415 | + | 1.66349i | 0.721459 | + | 0.692457i | \(0.243472\pi\) |
0.238956 | + | 0.971030i | \(0.423195\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.640753 | −0.0316060 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.72874 | + | 13.3866i | −0.380306 | + | 0.658710i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.60620 | 0.470418 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 40.0512 | 1.95663 | 0.978314 | − | 0.207128i | \(-0.0664118\pi\) | ||||
0.978314 | + | 0.207128i | \(0.0664118\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.7255 | − | 32.4336i | 0.912627 | − | 1.58072i | 0.102289 | − | 0.994755i | \(-0.467383\pi\) |
0.810339 | − | 0.585962i | \(-0.199283\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.63865 | − | 8.03438i | 0.225539 | − | 0.390645i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.8442 | − | 20.5148i | −0.573183 | − | 0.992782i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13.7711 | −0.664875 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.38909 | + | 12.7983i | 0.355920 | + | 0.616472i | 0.987275 | − | 0.159022i | \(-0.0508342\pi\) |
−0.631355 | + | 0.775494i | \(0.717501\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.84501 | + | 8.39180i | 0.232836 | + | 0.403284i | 0.958642 | − | 0.284616i | \(-0.0918661\pi\) |
−0.725805 | + | 0.687900i | \(0.758533\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.9248 | − | 1.93202i | −0.522604 | − | 0.0924211i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.80499 | + | 4.85838i | −0.133875 | + | 0.231878i | −0.925167 | − | 0.379560i | \(-0.876075\pi\) |
0.791292 | + | 0.611438i | \(0.209409\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.59001 | − | 2.75398i | −0.0757149 | − | 0.131142i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.68171 | + | 4.64485i | 0.127412 | + | 0.220684i | 0.922673 | − | 0.385583i | \(-0.126000\pi\) |
−0.795261 | + | 0.606267i | \(0.792666\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.72396 | + | 15.1103i | 0.412629 | + | 0.714695i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.14784 | 0.290134 | 0.145067 | − | 0.989422i | \(-0.453660\pi\) | ||||
0.145067 | + | 0.989422i | \(0.453660\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.7063 | − | 18.5438i | 0.504138 | − | 0.873193i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.386738 | − | 0.669851i | 0.0181706 | − | 0.0314723i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.6775 | 1.48181 | 0.740906 | − | 0.671608i | \(-0.234396\pi\) | ||||
0.740906 | + | 0.671608i | \(0.234396\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.29144 | + | 12.6291i | −0.340335 | + | 0.589478i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.34077 | − | 7.51844i | 0.202170 | − | 0.350169i | −0.747057 | − | 0.664760i | \(-0.768534\pi\) |
0.949227 | + | 0.314591i | \(0.101867\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.258854 | 0.0120300 | 0.00601499 | − | 0.999982i | \(-0.498085\pi\) | ||||
0.00601499 | + | 0.999982i | \(0.498085\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.8060 | 1.05534 | 0.527668 | − | 0.849451i | \(-0.323066\pi\) | ||||
0.527668 | + | 0.849451i | \(0.323066\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.10050 | − | 5.37023i | −0.143168 | − | 0.247974i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.9349 | − | 20.6718i | −0.549930 | − | 0.952506i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.78907 | + | 3.09875i | −0.0822613 | + | 0.142481i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.19235 | − | 8.99342i | 0.237741 | − | 0.411780i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.10389 | − | 5.37609i | −0.141820 | − | 0.245640i | 0.786362 | − | 0.617766i | \(-0.211962\pi\) |
−0.928182 | + | 0.372126i | \(0.878629\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.82918 | + | 10.0964i | 0.265788 | + | 0.460358i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.97007 | 0.317149 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.5698 | −0.977420 | −0.488710 | − | 0.872446i | \(-0.662532\pi\) | ||||
−0.488710 | + | 0.872446i | \(0.662532\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.327950 | + | 0.568025i | −0.0148304 | + | 0.0256870i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.2548 | + | 31.6182i | −0.823828 | + | 1.42691i | 0.0789841 | + | 0.996876i | \(0.474832\pi\) |
−0.902812 | + | 0.430036i | \(0.858501\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.1835 | 0.728870 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.80155 | − | 11.7806i | 0.305091 | − | 0.528434i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.5178 | + | 32.0737i | −0.828969 | + | 1.43582i | 0.0698794 | + | 0.997555i | \(0.477739\pi\) |
−0.898848 | + | 0.438260i | \(0.855595\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 26.2455 | 1.17256 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.0971 | + | 29.6130i | 0.762321 | + | 1.32038i | 0.941651 | + | 0.336590i | \(0.109274\pi\) |
−0.179330 | + | 0.983789i | \(0.557393\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.53876 | + | 14.7896i | 0.379220 | + | 0.656827i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.0016 | − | 29.4476i | −0.753581 | − | 1.30524i | −0.946077 | − | 0.323943i | \(-0.894991\pi\) |
0.192495 | − | 0.981298i | \(-0.438342\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.0076 | + | 29.4581i | −0.752373 | + | 1.30315i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 15.5622 | − | 18.5274i | 0.687089 | − | 0.818003i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.90970 | − | 11.9680i | −0.303888 | − | 0.526350i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.12307 | − | 1.94522i | −0.0492973 | − | 0.0853855i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.6165 | −1.47277 | −0.736383 | − | 0.676565i | \(-0.763468\pi\) | ||||
−0.736383 | + | 0.676565i | \(0.763468\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.6947 | + | 20.2557i | 0.511372 | + | 0.885722i | 0.999913 | + | 0.0131810i | \(0.00419577\pi\) |
−0.488541 | + | 0.872541i | \(0.662471\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.38005 | − | 2.39032i | 0.0601161 | − | 0.104124i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.26095 | − | 14.3084i | 0.359172 | − | 0.622103i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.1125 | 0.438844 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −51.8838 | −2.24734 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.6974 | − | 28.9208i | 0.720546 | − | 1.24802i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.73695 | −0.204035 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.0050 | − | 31.1856i | −0.774097 | − | 1.34077i | −0.935301 | − | 0.353854i | \(-0.884871\pi\) |
0.161204 | − | 0.986921i | \(-0.448462\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.0705 | −0.560908 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.61701 | − | 11.4610i | −0.282923 | − | 0.490037i | 0.689180 | − | 0.724590i | \(-0.257971\pi\) |
−0.972103 | + | 0.234553i | \(0.924637\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.74865 | + | 13.4211i | −0.330704 | + | 0.572797i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −26.4415 | − | 4.67611i | −1.12645 | − | 0.199209i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.13361 | + | 10.6237i | −0.260827 | + | 0.451766i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.03385 | + | 15.6471i | 0.382776 | + | 0.662988i | 0.991458 | − | 0.130427i | \(-0.0416347\pi\) |
−0.608682 | + | 0.793415i | \(0.708301\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.67001 | 0.366702 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.50547 | + | 6.07166i | 0.148001 | + | 0.256346i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −24.4686 | −1.03123 | −0.515613 | − | 0.856821i | \(-0.672436\pi\) | ||||
−0.515613 | + | 0.856821i | \(0.672436\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.91415 | + | 5.04745i | −0.122383 | + | 0.211973i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.4580 | −0.773801 | −0.386900 | − | 0.922122i | \(-0.626454\pi\) | ||||
−0.386900 | + | 0.922122i | \(0.626454\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.5131 | −0.816598 | −0.408299 | − | 0.912848i | \(-0.633878\pi\) | ||||
−0.408299 | + | 0.912848i | \(0.633878\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.17901 | − | 5.50620i | 0.132805 | − | 0.230025i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.03750 | −0.209714 | −0.104857 | − | 0.994487i | \(-0.533438\pi\) | ||||
−0.104857 | + | 0.994487i | \(0.533438\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.07699 | + | 7.06155i | 0.169434 | + | 0.293468i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.5023 | 0.684630 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.73449 | − | 13.3965i | −0.320330 | − | 0.554828i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.8436 | + | 25.7099i | −0.612662 | + | 1.06116i | 0.378128 | + | 0.925754i | \(0.376568\pi\) |
−0.990790 | + | 0.135409i | \(0.956765\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.94547 | + | 3.50668i | −0.121366 | + | 0.144490i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.25408 | + | 7.36828i | −0.174989 | + | 0.303091i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.2178 | + | 29.8222i | 0.707052 | + | 1.22465i | 0.965946 | + | 0.258744i | \(0.0833085\pi\) |
−0.258894 | + | 0.965906i | \(0.583358\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −17.2937 | −0.707786 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.909784 | − | 1.57579i | −0.0371728 | − | 0.0643851i | 0.846840 | − | 0.531847i | \(-0.178502\pi\) |
−0.884013 | + | 0.467462i | \(0.845169\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.14106 | −0.372872 | −0.186436 | − | 0.982467i | \(-0.559694\pi\) | ||||
−0.186436 | + | 0.982467i | \(0.559694\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.02839 | + | 3.51327i | −0.0826023 | + | 0.143071i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.7363 | 1.12578 | 0.562890 | − | 0.826532i | \(-0.309689\pi\) | ||||
0.562890 | + | 0.826532i | \(0.309689\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 16.8698 | 0.683599 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.7426 | + | 28.9990i | −0.677333 | + | 1.17317i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.1937 | − | 19.3881i | 0.452109 | − | 0.783076i | −0.546407 | − | 0.837519i | \(-0.684005\pi\) |
0.998517 | + | 0.0544430i | \(0.0173383\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.8234 | − | 37.7993i | −0.878578 | − | 1.52174i | −0.852902 | − | 0.522071i | \(-0.825160\pi\) |
−0.0256759 | − | 0.999670i | \(-0.508174\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.7258 | 1.11440 | 0.557198 | − | 0.830380i | \(-0.311876\pi\) | ||||
0.557198 | + | 0.830380i | \(0.311876\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.06416 | − | 12.2355i | −0.283475 | − | 0.490993i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.9001 | + | 29.2719i | 0.677089 | + | 1.17275i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.97307 | − | 10.9331i | −0.158669 | − | 0.436625i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.96767 | − | 5.14015i | 0.118329 | − | 0.204951i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.83973 | − | 10.1147i | −0.232476 | − | 0.402660i | 0.726060 | − | 0.687631i | \(-0.241349\pi\) |
−0.958536 | + | 0.284971i | \(0.908016\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.58308 | + | 4.47403i | 0.102668 | + | 0.177827i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.73894 | + | 9.94014i | 0.227385 | + | 0.393843i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.89932 | −0.352052 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.87218 | + | 17.0991i | −0.389928 | + | 0.675374i | −0.992439 | − | 0.122736i | \(-0.960833\pi\) |
0.602512 | + | 0.798110i | \(0.294167\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.48677 | + | 16.4316i | −0.374122 | + | 0.647998i | −0.990195 | − | 0.139691i | \(-0.955389\pi\) |
0.616073 | + | 0.787689i | \(0.288722\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.83157 | −0.268577 | −0.134288 | − | 0.990942i | \(-0.542875\pi\) | ||||
−0.134288 | + | 0.990942i | \(0.542875\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.53174 | − | 13.0454i | 0.295647 | − | 0.512075i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.43858 | − | 2.49169i | 0.0563822 | − | 0.0976569i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.7904 | −0.735325 | −0.367663 | − | 0.929959i | \(-0.619842\pi\) | ||||
−0.367663 | + | 0.929959i | \(0.619842\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 22.2532 | 0.868180 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.7289 | − | 30.7073i | −0.690619 | − | 1.19619i | −0.971635 | − | 0.236485i | \(-0.924005\pi\) |
0.281016 | − | 0.959703i | \(-0.409329\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.8550 | + | 20.5335i | 0.461108 | + | 0.798662i | 0.999016 | − | 0.0443412i | \(-0.0141189\pi\) |
−0.537909 | + | 0.843003i | \(0.680786\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.49396 | − | 14.7120i | 0.329878 | − | 0.571365i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.83954 | + | 13.5785i | −0.303548 | + | 0.525761i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.17224 | − | 5.49448i | −0.122646 | − | 0.212429i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.5423 | + | 19.9919i | 0.445587 | + | 0.771779i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.76230 | −0.106479 | −0.0532394 | − | 0.998582i | \(-0.516955\pi\) | ||||
−0.0532394 | + | 0.998582i | \(0.516955\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.0981 | −0.657132 | −0.328566 | − | 0.944481i | \(-0.606565\pi\) | ||||
−0.328566 | + | 0.944481i | \(0.606565\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.4904 | + | 25.0981i | −0.556090 | + | 0.963175i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.16706 | − | 5.48551i | 0.121362 | − | 0.210205i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.4864 | 0.669098 | 0.334549 | − | 0.942378i | \(-0.391416\pi\) | ||||
0.334549 | + | 0.942378i | \(0.391416\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.634816 | − | 1.09953i | 0.0242197 | − | 0.0419498i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18.7411 | + | 32.4605i | −0.713979 | + | 1.23665i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.2781 | 0.771416 | 0.385708 | − | 0.922621i | \(-0.373957\pi\) | ||||
0.385708 | + | 0.922621i | \(0.373957\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.32684 | − | 5.76225i | −0.126376 | − | 0.218890i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.2072 | + | 22.8755i | 0.500257 | + | 0.866470i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.18511 | − | 12.4450i | −0.271766 | − | 0.470712i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.2078 | − | 41.9292i | 0.914317 | − | 1.58364i | 0.106418 | − | 0.994322i | \(-0.466062\pi\) |
0.807899 | − | 0.589321i | \(-0.200605\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.33394 | + | 7.54077i | −0.238889 | + | 0.284405i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.56184 | − | 7.90134i | −0.171566 | − | 0.297161i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.60392 | + | 16.6345i | 0.360683 | + | 0.624721i | 0.988073 | − | 0.153984i | \(-0.0492104\pi\) |
−0.627391 | + | 0.778705i | \(0.715877\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.02537 | 0.300975 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.33704 | + | 2.31582i | 0.0500724 | + | 0.0867280i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.2799 | − | 19.5373i | 0.421254 | − | 0.729633i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.0395 | − | 43.3698i | 0.933817 | − | 1.61742i | 0.157088 | − | 0.987585i | \(-0.449789\pi\) |
0.776729 | − | 0.629835i | \(-0.216877\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 34.6742 | 1.29133 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.83243 | −0.142530 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.2320 | − | 38.5070i | 0.824540 | − | 1.42815i | −0.0777303 | − | 0.996974i | \(-0.524767\pi\) |
0.902270 | − | 0.431171i | \(-0.141899\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.6810 | 0.914112 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.20697 | − | 3.82259i | −0.0816279 | − | 0.141384i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −40.6973 | −1.50319 | −0.751594 | − | 0.659626i | \(-0.770715\pi\) | ||||
−0.751594 | + | 0.659626i | \(0.770715\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.02147 | + | 5.23335i | 0.111297 | + | 0.192773i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.0899 | + | 34.7967i | −0.739019 | + | 1.28002i | 0.213919 | + | 0.976851i | \(0.431377\pi\) |
−0.952938 | + | 0.303167i | \(0.901956\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.1288 | + | 21.5829i | −0.665978 | + | 0.792868i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.7584 | − | 25.5623i | 0.541432 | − | 0.937788i | −0.457390 | − | 0.889266i | \(-0.651216\pi\) |
0.998822 | − | 0.0485220i | \(-0.0154511\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.39800 | − | 9.34961i | −0.197502 | − | 0.342084i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.78756 | 0.321090 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.886284 | − | 1.53509i | −0.0323410 | − | 0.0560162i | 0.849402 | − | 0.527747i | \(-0.176963\pi\) |
−0.881743 | + | 0.471730i | \(0.843630\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.97829 | −0.0720928 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.33238 | + | 9.23595i | −0.193809 | + | 0.335686i | −0.946509 | − | 0.322677i | \(-0.895417\pi\) |
0.752701 | + | 0.658363i | \(0.228751\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.79241 | −0.246549 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.5852 | −0.963713 | −0.481856 | − | 0.876250i | \(-0.660037\pi\) | ||||
−0.481856 | + | 0.876250i | \(0.660037\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.83148 | − | 8.36837i | 0.174911 | − | 0.302955i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −36.4997 | −1.31793 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.28351 | − | 5.68721i | −0.118406 | − | 0.205086i | 0.800730 | − | 0.599026i | \(-0.204445\pi\) |
−0.919136 | + | 0.393940i | \(0.871112\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.7392 | 0.638863 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.8126 | + | 18.7279i | 0.388902 | + | 0.673597i | 0.992302 | − | 0.123841i | \(-0.0395213\pi\) |
−0.603400 | + | 0.797438i | \(0.706188\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.09351 | − | 5.35812i | 0.110979 | − | 0.192222i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14.9689 | − | 41.1913i | −0.536315 | − | 1.47583i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.62819 | + | 11.4804i | −0.237175 | + | 0.410800i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −17.0975 | − | 29.6138i | −0.611016 | − | 1.05831i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −46.4649 | −1.65630 | −0.828148 | − | 0.560509i | \(-0.810605\pi\) | ||||
−0.828148 | + | 0.560509i | \(0.810605\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.3304 | + | 19.6248i | 0.403372 | + | 0.698662i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.2044 | −0.469494 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.9677 | − | 48.4415i | 0.993163 | − | 1.72021i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36.8012 | 1.30357 | 0.651783 | − | 0.758405i | \(-0.274021\pi\) | ||||
0.651783 | + | 0.758405i | \(0.274021\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.0475 | 0.603097 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.0563 | − | 19.1500i | 0.390654 | − | 0.676633i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.5741 | − | 28.7072i | 0.584888 | − | 1.01306i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.13239 | − | 7.15751i | −0.145467 | − | 0.251956i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.18674 | −0.0417234 | −0.0208617 | − | 0.999782i | \(-0.506641\pi\) | ||||
−0.0208617 | + | 0.999782i | \(0.506641\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.3332 | + | 40.4144i | 0.819341 | + | 1.41914i | 0.906168 | + | 0.422917i | \(0.138994\pi\) |
−0.0868272 | + | 0.996223i | \(0.527673\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15.6123 | − | 27.0413i | −0.547547 | − | 0.948380i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.50136 | + | 6.88324i | 0.0875116 | + | 0.240814i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.06111 | + | 13.9623i | −0.281678 | + | 0.487881i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23.4760 | + | 40.6617i | 0.819319 | + | 1.41910i | 0.906185 | + | 0.422882i | \(0.138981\pi\) |
−0.0868660 | + | 0.996220i | \(0.527685\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.5603 | − | 28.6833i | −0.577257 | − | 0.999838i | −0.995792 | − | 0.0916375i | \(-0.970790\pi\) |
0.418536 | − | 0.908200i | \(-0.362543\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.36751 | + | 11.0288i | 0.221420 | + | 0.383511i | 0.955239 | − | 0.295834i | \(-0.0955975\pi\) |
−0.733819 | + | 0.679345i | \(0.762264\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.1725 | −0.735352 | −0.367676 | − | 0.929954i | \(-0.619846\pi\) | ||||
−0.367676 | + | 0.929954i | \(0.619846\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.9730 | − | 19.0058i | 0.380649 | − | 0.659304i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.92173 | − | 5.06058i | 0.101232 | − | 0.175339i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.83198 | −0.201583 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.20388 | − | 9.01338i | 0.179658 | − | 0.311177i | −0.762106 | − | 0.647453i | \(-0.775834\pi\) |
0.941763 | + | 0.336276i | \(0.109168\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.47419 | + | 7.74953i | −0.154283 | + | 0.267225i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −21.1290 | −0.727720 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.1274 | 0.485425 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.38916 | + | 4.13815i | 0.0819959 | + | 0.142021i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.87516 | + | 4.97993i | 0.0985594 | + | 0.170710i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.2168 | − | 21.1602i | 0.418296 | − | 0.724511i | −0.577472 | − | 0.816411i | \(-0.695961\pi\) |
0.995768 | + | 0.0918999i | \(0.0292940\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.9649 | + | 44.9725i | −0.886944 | + | 1.53623i | −0.0434759 | + | 0.999054i | \(0.513843\pi\) |
−0.843469 | + | 0.537178i | \(0.819490\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.7960 | − | 49.8761i | −0.982505 | − | 1.70175i | −0.652536 | − | 0.757758i | \(-0.726295\pi\) |
−0.329970 | − | 0.943992i | \(-0.607039\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.7672 | + | 23.8455i | 0.469185 | + | 0.812653i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −44.2381 | −1.50588 | −0.752941 | − | 0.658089i | \(-0.771365\pi\) | ||||
−0.752941 | + | 0.658089i | \(0.771365\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12.6545 | 0.429769 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.97727 | − | 10.3529i | 0.202765 | − | 0.351199i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.32120 | − | 12.6807i | 0.248069 | − | 0.429669i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18.9596 | 0.641684 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.601541 | − | 1.04190i | 0.0203126 | − | 0.0351825i | −0.855690 | − | 0.517488i | \(-0.826867\pi\) |
0.876003 | + | 0.482306i | \(0.160201\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.93648 | + | 13.7464i | −0.267691 | + | 0.463654i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.5743 | −1.33329 | −0.666646 | − | 0.745374i | \(-0.732271\pi\) | ||||
−0.666646 | + | 0.745374i | \(0.732271\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.7178 | − | 28.9561i | −0.562598 | − | 0.974449i | −0.997269 | − | 0.0738592i | \(-0.976468\pi\) |
0.434670 | − | 0.900590i | \(-0.356865\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.7869 | + | 32.5399i | 0.630803 | + | 1.09258i | 0.987388 | + | 0.158319i | \(0.0506076\pi\) |
−0.356585 | + | 0.934263i | \(0.616059\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.48978 | − | 14.7047i | −0.284738 | − | 0.493181i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.83987 | − | 4.91880i | 0.0951392 | − | 0.164786i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −27.8531 | − | 4.92574i | −0.932068 | − | 0.164834i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.22920 | + | 14.2534i | 0.274765 | + | 0.475907i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.23606 | + | 5.60501i | 0.107929 | + | 0.186938i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.0824 | 0.635727 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.30056 | − | 3.98469i | −0.0765579 | − | 0.132602i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.2915 | − | 28.2178i | 0.540951 | − | 0.936955i | −0.457898 | − | 0.889005i | \(-0.651398\pi\) |
0.998850 | − | 0.0479506i | \(-0.0152690\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.98442 | + | 5.16916i | −0.0989868 | + | 0.171450i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.37691 | 0.111882 | 0.0559410 | − | 0.998434i | \(-0.482184\pi\) | ||||
0.0559410 | + | 0.998434i | \(0.482184\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.0816 | −0.532225 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.8891 | − | 30.9848i | 0.590750 | − | 1.02321i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.8096 | 0.488523 | 0.244262 | − | 0.969709i | \(-0.421454\pi\) | ||||
0.244262 | + | 0.969709i | \(0.421454\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.57989 | − | 16.5929i | −0.315668 | − | 0.546753i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 32.1209 | 1.05727 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.3422 | − | 19.6452i | −0.372525 | − | 0.645233i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.5943 | − | 44.3307i | 0.839723 | − | 1.45444i | −0.0504032 | − | 0.998729i | \(-0.516051\pi\) |
0.890126 | − | 0.455714i | \(-0.150616\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.23589 | + | 7.42403i | −0.204373 | + | 0.243313i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −17.4906 | + | 30.2946i | −0.572617 | + | 0.991802i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.296297 | − | 0.513202i | −0.00967961 | − | 0.0167656i | 0.861145 | − | 0.508359i | \(-0.169748\pi\) |
−0.870825 | + | 0.491594i | \(0.836414\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.90071 | 0.159929 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.0480 | + | 31.2601i | 0.588348 | + | 1.01905i | 0.994449 | + | 0.105220i | \(0.0335548\pi\) |
−0.406101 | + | 0.913828i | \(0.633112\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −25.5910 | −0.833357 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.4620 | + | 30.2450i | −0.567438 | + | 0.982831i | 0.429381 | + | 0.903124i | \(0.358732\pi\) |
−0.996818 | + | 0.0797073i | \(0.974601\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −80.3200 | −2.60730 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.7838 | 0.382115 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.8329 | − | 25.6914i | 0.480485 | − | 0.832225i | −0.519264 | − | 0.854614i | \(-0.673794\pi\) |
0.999749 | + | 0.0223888i | \(0.00712716\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16.4398 | −0.531424 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.558708 | + | 0.967710i | 0.0180416 | + | 0.0312490i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.8962 | −0.964393 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.87447 | − | 4.97872i | −0.0926284 | − | 0.160437i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.5515 | − | 23.4719i | 0.435788 | − | 0.754807i | −0.561572 | − | 0.827428i | \(-0.689803\pi\) |
0.997360 | + | 0.0726212i | \(0.0231364\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.1306 | + | 2.49896i | 0.453941 | + | 0.0802781i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.4010 | − | 40.5316i | 0.750973 | − | 1.30072i | −0.196379 | − | 0.980528i | \(-0.562918\pi\) |
0.947352 | − | 0.320195i | \(-0.103748\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.37617 | − | 14.5080i | −0.268528 | − | 0.465104i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −42.0640 | −1.34575 | −0.672874 | − | 0.739757i | \(-0.734940\pi\) | ||||
−0.672874 | + | 0.739757i | \(0.734940\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.4694 | − | 28.5258i | −0.526363 | − | 0.911687i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.32163 | −0.201834 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.61466 | − | 14.9210i | 0.274765 | − | 0.475907i | −0.695311 | − | 0.718709i | \(-0.744733\pi\) |
0.970076 | + | 0.242802i | \(0.0780666\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 17.7704 | 0.565638 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.27637 | 0.135981 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.75314 | − | 6.50063i | 0.119223 | − | 0.206499i | −0.800237 | − | 0.599684i | \(-0.795293\pi\) |
0.919460 | + | 0.393184i | \(0.128626\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.917368 | − | 1.58893i | 0.0291118 | − | 0.0504231i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.5433 | − | 51.1705i | −0.935646 | − | 1.62059i | −0.773478 | − | 0.633823i | \(-0.781485\pi\) |
−0.162167 | − | 0.986763i | \(-0.551848\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −12.5411 | −0.396782 |
(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 | 1900.2.i.f.201.4 | yes | 12 | |
5.2 | odd | 4 | 1900.2.s.e.49.5 | 24 | |||
5.3 | odd | 4 | 1900.2.s.e.49.8 | 24 | |||
5.4 | even | 2 | 1900.2.i.e.201.3 | ✓ | 12 | ||
19.7 | even | 3 | inner | 1900.2.i.f.501.4 | yes | 12 | |
95.7 | odd | 12 | 1900.2.s.e.349.8 | 24 | |||
95.64 | even | 6 | 1900.2.i.e.501.3 | yes | 12 | ||
95.83 | odd | 12 | 1900.2.s.e.349.5 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1900.2.i.e.201.3 | ✓ | 12 | 5.4 | even | 2 | ||
1900.2.i.e.501.3 | yes | 12 | 95.64 | even | 6 | ||
1900.2.i.f.201.4 | yes | 12 | 1.1 | even | 1 | trivial | |
1900.2.i.f.501.4 | yes | 12 | 19.7 | even | 3 | inner | |
1900.2.s.e.49.5 | 24 | 5.2 | odd | 4 | |||
1900.2.s.e.49.8 | 24 | 5.3 | odd | 4 | |||
1900.2.s.e.349.5 | 24 | 95.83 | odd | 12 | |||
1900.2.s.e.349.8 | 24 | 95.7 | odd | 12 |