Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(37,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.m (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 108x^{16} + 1318x^{12} + 4652x^{8} + 5057x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 493.9 | ||
Root | \(-0.922947 - 0.922947i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.493 |
Dual form | 570.2.m.b.37.9 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 1.42113 | + | 1.72638i | 0.635550 | + | 0.772060i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 3.40461 | − | 3.40461i | 1.28682 | − | 1.28682i | 0.350114 | − | 0.936707i | \(-0.386143\pi\) |
0.936707 | − | 0.350114i | \(-0.113857\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | −0.215841 | + | 2.22563i | −0.0682548 | + | 0.703805i | ||||
\(11\) | 3.94163 | 1.18845 | 0.594223 | − | 0.804300i | \(-0.297460\pi\) | ||||
0.594223 | + | 0.804300i | \(0.297460\pi\) | |||||||
\(12\) | −0.707107 | − | 0.707107i | −0.204124 | − | 0.204124i | ||||
\(13\) | 4.03748 | − | 4.03748i | 1.11979 | − | 1.11979i | 0.128023 | − | 0.991771i | \(-0.459137\pi\) |
0.991771 | − | 0.128023i | \(-0.0408632\pi\) | |||||||
\(14\) | 4.81484 | 1.28682 | ||||||||
\(15\) | −2.22563 | − | 0.215841i | −0.574654 | − | 0.0557298i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −3.90683 | + | 3.90683i | −0.947544 | + | 0.947544i | −0.998691 | − | 0.0511467i | \(-0.983712\pi\) |
0.0511467 | + | 0.998691i | \(0.483712\pi\) | |||||||
\(18\) | 0.707107 | − | 0.707107i | 0.166667 | − | 0.166667i | ||||
\(19\) | −3.49740 | − | 2.60158i | −0.802358 | − | 0.596844i | ||||
\(20\) | −1.72638 | + | 1.42113i | −0.386030 | + | 0.317775i | ||||
\(21\) | 4.81484i | 1.05068i | ||||||||
\(22\) | 2.78715 | + | 2.78715i | 0.594223 | + | 0.594223i | ||||
\(23\) | 0.537022 | + | 0.537022i | 0.111977 | + | 0.111977i | 0.760875 | − | 0.648898i | \(-0.224770\pi\) |
−0.648898 | + | 0.760875i | \(0.724770\pi\) | |||||||
\(24\) | − | 1.00000i | − | 0.204124i | ||||||
\(25\) | −0.960761 | + | 4.90683i | −0.192152 | + | 0.981365i | ||||
\(26\) | 5.70985 | 1.11979 | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 3.40461 | + | 3.40461i | 0.643411 | + | 0.643411i | ||||
\(29\) | −6.28455 | −1.16701 | −0.583506 | − | 0.812109i | \(-0.698319\pi\) | ||||
−0.583506 | + | 0.812109i | \(0.698319\pi\) | |||||||
\(30\) | −1.42113 | − | 1.72638i | −0.259462 | − | 0.315192i | ||||
\(31\) | 7.00112i | 1.25744i | 0.777633 | + | 0.628719i | \(0.216420\pi\) | ||||
−0.777633 | + | 0.628719i | \(0.783580\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | −2.78715 | + | 2.78715i | −0.485181 | + | 0.485181i | ||||
\(34\) | −5.52509 | −0.947544 | ||||||||
\(35\) | 10.7160 | + | 1.03924i | 1.81134 | + | 0.175663i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.05593 | + | 1.05593i | 0.173594 | + | 0.173594i | 0.788556 | − | 0.614963i | \(-0.210829\pi\) |
−0.614963 | + | 0.788556i | \(0.710829\pi\) | |||||||
\(38\) | −0.633437 | − | 4.31263i | −0.102757 | − | 0.699601i | ||||
\(39\) | 5.70985i | 0.914308i | ||||||||
\(40\) | −2.22563 | − | 0.215841i | −0.351902 | − | 0.0341274i | ||||
\(41\) | − | 3.03704i | − | 0.474306i | −0.971472 | − | 0.237153i | \(-0.923786\pi\) | ||
0.971472 | − | 0.237153i | \(-0.0762142\pi\) | |||||||
\(42\) | −3.40461 | + | 3.40461i | −0.525342 | + | 0.525342i | ||||
\(43\) | −5.70094 | − | 5.70094i | −0.869386 | − | 0.869386i | 0.123018 | − | 0.992404i | \(-0.460743\pi\) |
−0.992404 | + | 0.123018i | \(0.960743\pi\) | |||||||
\(44\) | 3.94163i | 0.594223i | ||||||||
\(45\) | 1.72638 | − | 1.42113i | 0.257353 | − | 0.211850i | ||||
\(46\) | 0.759463i | 0.111977i | ||||||||
\(47\) | −2.04815 | + | 2.04815i | −0.298753 | + | 0.298753i | −0.840525 | − | 0.541772i | \(-0.817754\pi\) |
0.541772 | + | 0.840525i | \(0.317754\pi\) | |||||||
\(48\) | 0.707107 | − | 0.707107i | 0.102062 | − | 0.102062i | ||||
\(49\) | − | 16.1827i | − | 2.31182i | ||||||
\(50\) | −4.14901 | + | 2.79029i | −0.586759 | + | 0.394606i | ||||
\(51\) | − | 5.52509i | − | 0.773667i | ||||||
\(52\) | 4.03748 | + | 4.03748i | 0.559897 | + | 0.559897i | ||||
\(53\) | −4.39576 | + | 4.39576i | −0.603804 | + | 0.603804i | −0.941320 | − | 0.337516i | \(-0.890413\pi\) |
0.337516 | + | 0.941320i | \(0.390413\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | 5.60158 | + | 6.80474i | 0.755317 | + | 0.917551i | ||||
\(56\) | 4.81484i | 0.643411i | ||||||||
\(57\) | 4.31263 | − | 0.633437i | 0.571221 | − | 0.0839007i | ||||
\(58\) | −4.44385 | − | 4.44385i | −0.583506 | − | 0.583506i | ||||
\(59\) | 2.32680 | 0.302923 | 0.151462 | − | 0.988463i | \(-0.451602\pi\) | ||||
0.151462 | + | 0.988463i | \(0.451602\pi\) | |||||||
\(60\) | 0.215841 | − | 2.22563i | 0.0278649 | − | 0.287327i | ||||
\(61\) | −9.32341 | −1.19374 | −0.596870 | − | 0.802338i | \(-0.703589\pi\) | ||||
−0.596870 | + | 0.802338i | \(0.703589\pi\) | |||||||
\(62\) | −4.95054 | + | 4.95054i | −0.628719 | + | 0.628719i | ||||
\(63\) | −3.40461 | − | 3.40461i | −0.428940 | − | 0.428940i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 12.7080 | + | 1.23242i | 1.57623 | + | 0.152863i | ||||
\(66\) | −3.94163 | −0.485181 | ||||||||
\(67\) | 7.35838 | + | 7.35838i | 0.898969 | + | 0.898969i | 0.995345 | − | 0.0963756i | \(-0.0307250\pi\) |
−0.0963756 | + | 0.995345i | \(0.530725\pi\) | |||||||
\(68\) | −3.90683 | − | 3.90683i | −0.473772 | − | 0.473772i | ||||
\(69\) | −0.759463 | −0.0914286 | ||||||||
\(70\) | 6.84253 | + | 8.31224i | 0.817839 | + | 0.993503i | ||||
\(71\) | − | 9.62969i | − | 1.14283i | −0.820660 | − | 0.571417i | \(-0.806394\pi\) | ||
0.820660 | − | 0.571417i | \(-0.193606\pi\) | |||||||
\(72\) | 0.707107 | + | 0.707107i | 0.0833333 | + | 0.0833333i | ||||
\(73\) | 4.47808 | + | 4.47808i | 0.524119 | + | 0.524119i | 0.918813 | − | 0.394694i | \(-0.129149\pi\) |
−0.394694 | + | 0.918813i | \(0.629149\pi\) | |||||||
\(74\) | 1.49331i | 0.173594i | ||||||||
\(75\) | −2.79029 | − | 4.14901i | −0.322195 | − | 0.479086i | ||||
\(76\) | 2.60158 | − | 3.49740i | 0.298422 | − | 0.401179i | ||||
\(77\) | 13.4197 | − | 13.4197i | 1.52932 | − | 1.52932i | ||||
\(78\) | −4.03748 | + | 4.03748i | −0.457154 | + | 0.457154i | ||||
\(79\) | −0.991285 | −0.111528 | −0.0557642 | − | 0.998444i | \(-0.517759\pi\) | ||||
−0.0557642 | + | 0.998444i | \(0.517759\pi\) | |||||||
\(80\) | −1.42113 | − | 1.72638i | −0.158888 | − | 0.193015i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 2.14751 | − | 2.14751i | 0.237153 | − | 0.237153i | ||||
\(83\) | 6.64529 | + | 6.64529i | 0.729416 | + | 0.729416i | 0.970503 | − | 0.241088i | \(-0.0775041\pi\) |
−0.241088 | + | 0.970503i | \(0.577504\pi\) | |||||||
\(84\) | −4.81484 | −0.525342 | ||||||||
\(85\) | −12.2968 | − | 1.19254i | −1.33377 | − | 0.129349i | ||||
\(86\) | − | 8.06235i | − | 0.869386i | ||||||
\(87\) | 4.44385 | − | 4.44385i | 0.476430 | − | 0.476430i | ||||
\(88\) | −2.78715 | + | 2.78715i | −0.297112 | + | 0.297112i | ||||
\(89\) | −7.09242 | −0.751795 | −0.375897 | − | 0.926661i | \(-0.622666\pi\) | ||||
−0.375897 | + | 0.926661i | \(0.622666\pi\) | |||||||
\(90\) | 2.22563 | + | 0.215841i | 0.234602 | + | 0.0227516i | ||||
\(91\) | − | 27.4920i | − | 2.88195i | ||||||
\(92\) | −0.537022 | + | 0.537022i | −0.0559884 | + | 0.0559884i | ||||
\(93\) | −4.95054 | − | 4.95054i | −0.513347 | − | 0.513347i | ||||
\(94\) | −2.89652 | −0.298753 | ||||||||
\(95\) | −0.478953 | − | 9.73502i | −0.0491396 | − | 0.998792i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −7.11482 | − | 7.11482i | −0.722401 | − | 0.722401i | 0.246693 | − | 0.969094i | \(-0.420656\pi\) |
−0.969094 | + | 0.246693i | \(0.920656\pi\) | |||||||
\(98\) | 11.4429 | − | 11.4429i | 1.15591 | − | 1.15591i | ||||
\(99\) | − | 3.94163i | − | 0.396149i | ||||||
\(100\) | −4.90683 | − | 0.960761i | −0.490683 | − | 0.0960761i | ||||
\(101\) | −8.97139 | −0.892686 | −0.446343 | − | 0.894862i | \(-0.647274\pi\) | ||||
−0.446343 | + | 0.894862i | \(0.647274\pi\) | |||||||
\(102\) | 3.90683 | − | 3.90683i | 0.386833 | − | 0.386833i | ||||
\(103\) | 0.231982 | − | 0.231982i | 0.0228578 | − | 0.0228578i | −0.695585 | − | 0.718443i | \(-0.744855\pi\) |
0.718443 | + | 0.695585i | \(0.244855\pi\) | |||||||
\(104\) | 5.70985i | 0.559897i | ||||||||
\(105\) | −8.31224 | + | 6.84253i | −0.811191 | + | 0.667763i | ||||
\(106\) | −6.21654 | −0.603804 | ||||||||
\(107\) | 11.8222 | + | 11.8222i | 1.14290 | + | 1.14290i | 0.987917 | + | 0.154981i | \(0.0495316\pi\) |
0.154981 | + | 0.987917i | \(0.450468\pi\) | |||||||
\(108\) | −0.707107 | + | 0.707107i | −0.0680414 | + | 0.0680414i | ||||
\(109\) | −11.4774 | −1.09934 | −0.549670 | − | 0.835382i | \(-0.685246\pi\) | ||||
−0.549670 | + | 0.835382i | \(0.685246\pi\) | |||||||
\(110\) | −0.850764 | + | 8.77260i | −0.0811172 | + | 0.836434i | ||||
\(111\) | −1.49331 | −0.141739 | ||||||||
\(112\) | −3.40461 | + | 3.40461i | −0.321705 | + | 0.321705i | ||||
\(113\) | 11.2993 | − | 11.2993i | 1.06294 | − | 1.06294i | 0.0650630 | − | 0.997881i | \(-0.479275\pi\) |
0.997881 | − | 0.0650630i | \(-0.0207248\pi\) | |||||||
\(114\) | 3.49740 | + | 2.60158i | 0.327561 | + | 0.243660i | ||||
\(115\) | −0.163923 | + | 1.69028i | −0.0152859 | + | 0.157620i | ||||
\(116\) | − | 6.28455i | − | 0.583506i | ||||||
\(117\) | −4.03748 | − | 4.03748i | −0.373265 | − | 0.373265i | ||||
\(118\) | 1.64529 | + | 1.64529i | 0.151462 | + | 0.151462i | ||||
\(119\) | 26.6024i | 2.43864i | ||||||||
\(120\) | 1.72638 | − | 1.42113i | 0.157596 | − | 0.129731i | ||||
\(121\) | 4.53645 | 0.412404 | ||||||||
\(122\) | −6.59265 | − | 6.59265i | −0.596870 | − | 0.596870i | ||||
\(123\) | 2.14751 | + | 2.14751i | 0.193635 | + | 0.193635i | ||||
\(124\) | −7.00112 | −0.628719 | ||||||||
\(125\) | −9.83640 | + | 5.31462i | −0.879795 | + | 0.475354i | ||||
\(126\) | − | 4.81484i | − | 0.428940i | ||||||
\(127\) | 2.01606 | + | 2.01606i | 0.178896 | + | 0.178896i | 0.790875 | − | 0.611978i | \(-0.209626\pi\) |
−0.611978 | + | 0.790875i | \(0.709626\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 8.06235 | 0.709851 | ||||||||
\(130\) | 8.11446 | + | 9.85736i | 0.711685 | + | 0.864548i | ||||
\(131\) | −10.6608 | −0.931438 | −0.465719 | − | 0.884933i | \(-0.654204\pi\) | ||||
−0.465719 | + | 0.884933i | \(0.654204\pi\) | |||||||
\(132\) | −2.78715 | − | 2.78715i | −0.242591 | − | 0.242591i | ||||
\(133\) | −20.7646 | + | 3.04990i | −1.80052 | + | 0.264460i | ||||
\(134\) | 10.4063i | 0.898969i | ||||||||
\(135\) | −0.215841 | + | 2.22563i | −0.0185766 | + | 0.191551i | ||||
\(136\) | − | 5.52509i | − | 0.473772i | ||||||
\(137\) | 1.03924 | − | 1.03924i | 0.0887882 | − | 0.0887882i | −0.661318 | − | 0.750106i | \(-0.730002\pi\) |
0.750106 | + | 0.661318i | \(0.230002\pi\) | |||||||
\(138\) | −0.537022 | − | 0.537022i | −0.0457143 | − | 0.0457143i | ||||
\(139\) | − | 8.61936i | − | 0.731084i | −0.930795 | − | 0.365542i | \(-0.880884\pi\) | ||
0.930795 | − | 0.365542i | \(-0.119116\pi\) | |||||||
\(140\) | −1.03924 | + | 10.7160i | −0.0878317 | + | 0.905671i | ||||
\(141\) | − | 2.89652i | − | 0.243931i | ||||||
\(142\) | 6.80922 | − | 6.80922i | 0.571417 | − | 0.571417i | ||||
\(143\) | 15.9142 | − | 15.9142i | 1.33082 | − | 1.33082i | ||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | −8.93118 | − | 10.8495i | −0.741694 | − | 0.901002i | ||||
\(146\) | 6.33296i | 0.524119i | ||||||||
\(147\) | 11.4429 | + | 11.4429i | 0.943795 | + | 0.943795i | ||||
\(148\) | −1.05593 | + | 1.05593i | −0.0867968 | + | 0.0867968i | ||||
\(149\) | − | 4.87509i | − | 0.399383i | −0.979859 | − | 0.199691i | \(-0.936006\pi\) | ||
0.979859 | − | 0.199691i | \(-0.0639940\pi\) | |||||||
\(150\) | 0.960761 | − | 4.90683i | 0.0784458 | − | 0.400641i | ||||
\(151\) | − | 10.0048i | − | 0.814177i | −0.913389 | − | 0.407089i | \(-0.866544\pi\) | ||
0.913389 | − | 0.407089i | \(-0.133456\pi\) | |||||||
\(152\) | 4.31263 | − | 0.633437i | 0.349800 | − | 0.0513785i | ||||
\(153\) | 3.90683 | + | 3.90683i | 0.315848 | + | 0.315848i | ||||
\(154\) | 18.9783 | 1.52932 | ||||||||
\(155\) | −12.0866 | + | 9.94952i | −0.970817 | + | 0.799165i | ||||
\(156\) | −5.70985 | −0.457154 | ||||||||
\(157\) | −7.71934 | + | 7.71934i | −0.616070 | + | 0.616070i | −0.944521 | − | 0.328451i | \(-0.893473\pi\) |
0.328451 | + | 0.944521i | \(0.393473\pi\) | |||||||
\(158\) | −0.700945 | − | 0.700945i | −0.0557642 | − | 0.0557642i | ||||
\(159\) | − | 6.21654i | − | 0.493004i | ||||||
\(160\) | 0.215841 | − | 2.22563i | 0.0170637 | − | 0.175951i | ||||
\(161\) | 3.65670 | 0.288188 | ||||||||
\(162\) | −0.707107 | − | 0.707107i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | −2.46610 | − | 2.46610i | −0.193160 | − | 0.193160i | 0.603900 | − | 0.797060i | \(-0.293613\pi\) |
−0.797060 | + | 0.603900i | \(0.793613\pi\) | |||||||
\(164\) | 3.03704 | 0.237153 | ||||||||
\(165\) | −8.77260 | − | 0.850764i | −0.682946 | − | 0.0662319i | ||||
\(166\) | 9.39786i | 0.729416i | ||||||||
\(167\) | 12.6049 | + | 12.6049i | 0.975397 | + | 0.975397i | 0.999705 | − | 0.0243076i | \(-0.00773810\pi\) |
−0.0243076 | + | 0.999705i | \(0.507738\pi\) | |||||||
\(168\) | −3.40461 | − | 3.40461i | −0.262671 | − | 0.262671i | ||||
\(169\) | − | 19.6024i | − | 1.50788i | ||||||
\(170\) | −7.85188 | − | 9.53839i | −0.602212 | − | 0.731561i | ||||
\(171\) | −2.60158 | + | 3.49740i | −0.198948 | + | 0.267453i | ||||
\(172\) | 5.70094 | − | 5.70094i | 0.434693 | − | 0.434693i | ||||
\(173\) | 10.8629 | − | 10.8629i | 0.825892 | − | 0.825892i | −0.161054 | − | 0.986946i | \(-0.551489\pi\) |
0.986946 | + | 0.161054i | \(0.0514893\pi\) | |||||||
\(174\) | 6.28455 | 0.476430 | ||||||||
\(175\) | 13.4348 | + | 19.9768i | 1.01558 | + | 1.51011i | ||||
\(176\) | −3.94163 | −0.297112 | ||||||||
\(177\) | −1.64529 | + | 1.64529i | −0.123668 | + | 0.123668i | ||||
\(178\) | −5.01510 | − | 5.01510i | −0.375897 | − | 0.375897i | ||||
\(179\) | 12.4563 | 0.931024 | 0.465512 | − | 0.885042i | \(-0.345870\pi\) | ||||
0.465512 | + | 0.885042i | \(0.345870\pi\) | |||||||
\(180\) | 1.42113 | + | 1.72638i | 0.105925 | + | 0.128677i | ||||
\(181\) | − | 11.5778i | − | 0.860572i | −0.902693 | − | 0.430286i | \(-0.858413\pi\) | ||
0.902693 | − | 0.430286i | \(-0.141587\pi\) | |||||||
\(182\) | 19.4398 | − | 19.4398i | 1.44097 | − | 1.44097i | ||||
\(183\) | 6.59265 | − | 6.59265i | 0.487343 | − | 0.487343i | ||||
\(184\) | −0.759463 | −0.0559884 | ||||||||
\(185\) | −0.322317 | + | 3.32355i | −0.0236972 | + | 0.244352i | ||||
\(186\) | − | 7.00112i | − | 0.513347i | ||||||
\(187\) | −15.3993 | + | 15.3993i | −1.12611 | + | 1.12611i | ||||
\(188\) | −2.04815 | − | 2.04815i | −0.149377 | − | 0.149377i | ||||
\(189\) | 4.81484 | 0.350228 | ||||||||
\(190\) | 6.54503 | − | 7.22237i | 0.474826 | − | 0.523966i | ||||
\(191\) | 7.59311 | 0.549418 | 0.274709 | − | 0.961527i | \(-0.411418\pi\) | ||||
0.274709 | + | 0.961527i | \(0.411418\pi\) | |||||||
\(192\) | 0.707107 | + | 0.707107i | 0.0510310 | + | 0.0510310i | ||||
\(193\) | 9.61547 | − | 9.61547i | 0.692137 | − | 0.692137i | −0.270565 | − | 0.962702i | \(-0.587211\pi\) |
0.962702 | + | 0.270565i | \(0.0872105\pi\) | |||||||
\(194\) | − | 10.0619i | − | 0.722401i | ||||||
\(195\) | −9.85736 | + | 8.11446i | −0.705901 | + | 0.581089i | ||||
\(196\) | 16.1827 | 1.15591 | ||||||||
\(197\) | −9.66171 | + | 9.66171i | −0.688368 | + | 0.688368i | −0.961871 | − | 0.273503i | \(-0.911818\pi\) |
0.273503 | + | 0.961871i | \(0.411818\pi\) | |||||||
\(198\) | 2.78715 | − | 2.78715i | 0.198074 | − | 0.198074i | ||||
\(199\) | 23.6158i | 1.67408i | 0.547142 | + | 0.837040i | \(0.315716\pi\) | ||||
−0.547142 | + | 0.837040i | \(0.684284\pi\) | |||||||
\(200\) | −2.79029 | − | 4.14901i | −0.197303 | − | 0.293379i | ||||
\(201\) | −10.4063 | −0.734005 | ||||||||
\(202\) | −6.34373 | − | 6.34373i | −0.446343 | − | 0.446343i | ||||
\(203\) | −21.3964 | + | 21.3964i | −1.50173 | + | 1.50173i | ||||
\(204\) | 5.52509 | 0.386833 | ||||||||
\(205\) | 5.24308 | − | 4.31604i | 0.366192 | − | 0.301445i | ||||
\(206\) | 0.328072 | 0.0228578 | ||||||||
\(207\) | 0.537022 | − | 0.537022i | 0.0373256 | − | 0.0373256i | ||||
\(208\) | −4.03748 | + | 4.03748i | −0.279949 | + | 0.279949i | ||||
\(209\) | −13.7854 | − | 10.2545i | −0.953559 | − | 0.709316i | ||||
\(210\) | −10.7160 | − | 1.03924i | −0.739477 | − | 0.0717143i | ||||
\(211\) | 16.4846i | 1.13485i | 0.823427 | + | 0.567423i | \(0.192059\pi\) | ||||
−0.823427 | + | 0.567423i | \(0.807941\pi\) | |||||||
\(212\) | −4.39576 | − | 4.39576i | −0.301902 | − | 0.301902i | ||||
\(213\) | 6.80922 | + | 6.80922i | 0.466560 | + | 0.466560i | ||||
\(214\) | 16.7192i | 1.14290i | ||||||||
\(215\) | 1.74018 | − | 17.9438i | 0.118680 | − | 1.22376i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 23.8361 | + | 23.8361i | 1.61810 | + | 1.61810i | ||||
\(218\) | −8.11578 | − | 8.11578i | −0.549670 | − | 0.549670i | ||||
\(219\) | −6.33296 | −0.427942 | ||||||||
\(220\) | −6.80474 | + | 5.60158i | −0.458776 | + | 0.377659i | ||||
\(221\) | 31.5474i | 2.12211i | ||||||||
\(222\) | −1.05593 | − | 1.05593i | −0.0708693 | − | 0.0708693i | ||||
\(223\) | 4.91506 | − | 4.91506i | 0.329137 | − | 0.329137i | −0.523122 | − | 0.852258i | \(-0.675233\pi\) |
0.852258 | + | 0.523122i | \(0.175233\pi\) | |||||||
\(224\) | −4.81484 | −0.321705 | ||||||||
\(225\) | 4.90683 | + | 0.960761i | 0.327122 | + | 0.0640507i | ||||
\(226\) | 15.9796 | 1.06294 | ||||||||
\(227\) | −13.9125 | − | 13.9125i | −0.923408 | − | 0.923408i | 0.0738603 | − | 0.997269i | \(-0.476468\pi\) |
−0.997269 | + | 0.0738603i | \(0.976468\pi\) | |||||||
\(228\) | 0.633437 | + | 4.31263i | 0.0419504 | + | 0.285611i | ||||
\(229\) | 16.4303i | 1.08574i | 0.839816 | + | 0.542872i | \(0.182663\pi\) | ||||
−0.839816 | + | 0.542872i | \(0.817337\pi\) | |||||||
\(230\) | −1.31112 | + | 1.07930i | −0.0864527 | + | 0.0711668i | ||||
\(231\) | 18.9783i | 1.24868i | ||||||||
\(232\) | 4.44385 | − | 4.44385i | 0.291753 | − | 0.291753i | ||||
\(233\) | 0.870707 | + | 0.870707i | 0.0570419 | + | 0.0570419i | 0.735052 | − | 0.678010i | \(-0.237158\pi\) |
−0.678010 | + | 0.735052i | \(0.737158\pi\) | |||||||
\(234\) | − | 5.70985i | − | 0.373265i | ||||||
\(235\) | −6.44657 | − | 0.625186i | −0.420528 | − | 0.0407827i | ||||
\(236\) | 2.32680i | 0.151462i | ||||||||
\(237\) | 0.700945 | − | 0.700945i | 0.0455312 | − | 0.0455312i | ||||
\(238\) | −18.8108 | + | 18.8108i | −1.21932 | + | 1.21932i | ||||
\(239\) | − | 8.48625i | − | 0.548930i | −0.961597 | − | 0.274465i | \(-0.911499\pi\) | ||
0.961597 | − | 0.274465i | \(-0.0885007\pi\) | |||||||
\(240\) | 2.22563 | + | 0.215841i | 0.143664 | + | 0.0139325i | ||||
\(241\) | − | 2.53645i | − | 0.163387i | −0.996657 | − | 0.0816937i | \(-0.973967\pi\) | ||
0.996657 | − | 0.0816937i | \(-0.0260329\pi\) | |||||||
\(242\) | 3.20775 | + | 3.20775i | 0.206202 | + | 0.206202i | ||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | − | 9.32341i | − | 0.596870i | ||||||
\(245\) | 27.9375 | − | 22.9978i | 1.78486 | − | 1.46928i | ||||
\(246\) | 3.03704i | 0.193635i | ||||||||
\(247\) | −24.6245 | + | 3.61683i | −1.56682 | + | 0.230133i | ||||
\(248\) | −4.95054 | − | 4.95054i | −0.314360 | − | 0.314360i | ||||
\(249\) | −9.39786 | −0.595565 | ||||||||
\(250\) | −10.7134 | − | 3.19739i | −0.677574 | − | 0.202221i | ||||
\(251\) | −15.7046 | −0.991268 | −0.495634 | − | 0.868531i | \(-0.665064\pi\) | ||||
−0.495634 | + | 0.868531i | \(0.665064\pi\) | |||||||
\(252\) | 3.40461 | − | 3.40461i | 0.214470 | − | 0.214470i | ||||
\(253\) | 2.11674 | + | 2.11674i | 0.133078 | + | 0.133078i | ||||
\(254\) | 2.85114i | 0.178896i | ||||||||
\(255\) | 9.53839 | − | 7.85188i | 0.597317 | − | 0.491704i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.53833 | − | 9.53833i | −0.594985 | − | 0.594985i | 0.343989 | − | 0.938974i | \(-0.388222\pi\) |
−0.938974 | + | 0.343989i | \(0.888222\pi\) | |||||||
\(258\) | 5.70094 | + | 5.70094i | 0.354925 | + | 0.354925i | ||||
\(259\) | 7.19005 | 0.446768 | ||||||||
\(260\) | −1.23242 | + | 12.7080i | −0.0764313 | + | 0.788117i | ||||
\(261\) | 6.28455i | 0.389004i | ||||||||
\(262\) | −7.53832 | − | 7.53832i | −0.465719 | − | 0.465719i | ||||
\(263\) | −1.34136 | − | 1.34136i | −0.0827120 | − | 0.0827120i | 0.664540 | − | 0.747252i | \(-0.268627\pi\) |
−0.747252 | + | 0.664540i | \(0.768627\pi\) | |||||||
\(264\) | − | 3.94163i | − | 0.242591i | ||||||
\(265\) | −13.8357 | − | 1.34178i | −0.849921 | − | 0.0824251i | ||||
\(266\) | −16.8394 | − | 12.5262i | −1.03249 | − | 0.768031i | ||||
\(267\) | 5.01510 | − | 5.01510i | 0.306919 | − | 0.306919i | ||||
\(268\) | −7.35838 | + | 7.35838i | −0.449485 | + | 0.449485i | ||||
\(269\) | 1.78351 | 0.108742 | 0.0543712 | − | 0.998521i | \(-0.482685\pi\) | ||||
0.0543712 | + | 0.998521i | \(0.482685\pi\) | |||||||
\(270\) | −1.72638 | + | 1.42113i | −0.105064 | + | 0.0864874i | ||||
\(271\) | 30.0221 | 1.82371 | 0.911857 | − | 0.410507i | \(-0.134648\pi\) | ||||
0.911857 | + | 0.410507i | \(0.134648\pi\) | |||||||
\(272\) | 3.90683 | − | 3.90683i | 0.236886 | − | 0.236886i | ||||
\(273\) | 19.4398 | + | 19.4398i | 1.17655 | + | 1.17655i | ||||
\(274\) | 1.46971 | 0.0887882 | ||||||||
\(275\) | −3.78697 | + | 19.3409i | −0.228363 | + | 1.16630i | ||||
\(276\) | − | 0.759463i | − | 0.0457143i | ||||||
\(277\) | 14.5286 | − | 14.5286i | 0.872936 | − | 0.872936i | −0.119855 | − | 0.992791i | \(-0.538243\pi\) |
0.992791 | + | 0.119855i | \(0.0382430\pi\) | |||||||
\(278\) | 6.09481 | − | 6.09481i | 0.365542 | − | 0.365542i | ||||
\(279\) | 7.00112 | 0.419146 | ||||||||
\(280\) | −8.31224 | + | 6.84253i | −0.496751 | + | 0.408920i | ||||
\(281\) | 12.3316i | 0.735640i | 0.929897 | + | 0.367820i | \(0.119896\pi\) | ||||
−0.929897 | + | 0.367820i | \(0.880104\pi\) | |||||||
\(282\) | 2.04815 | − | 2.04815i | 0.121965 | − | 0.121965i | ||||
\(283\) | −6.86004 | − | 6.86004i | −0.407787 | − | 0.407787i | 0.473179 | − | 0.880966i | \(-0.343106\pi\) |
−0.880966 | + | 0.473179i | \(0.843106\pi\) | |||||||
\(284\) | 9.62969 | 0.571417 | ||||||||
\(285\) | 7.22237 | + | 6.54503i | 0.427816 | + | 0.387694i | ||||
\(286\) | 22.5061 | 1.33082 | ||||||||
\(287\) | −10.3399 | − | 10.3399i | −0.610347 | − | 0.610347i | ||||
\(288\) | −0.707107 | + | 0.707107i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | − | 13.5266i | − | 0.795681i | ||||||
\(290\) | 1.35646 | − | 13.9871i | 0.0796541 | − | 0.821348i | ||||
\(291\) | 10.0619 | 0.589838 | ||||||||
\(292\) | −4.47808 | + | 4.47808i | −0.262060 | + | 0.262060i | ||||
\(293\) | −18.7006 | + | 18.7006i | −1.09250 | + | 1.09250i | −0.0972386 | + | 0.995261i | \(0.531001\pi\) |
−0.995261 | + | 0.0972386i | \(0.968999\pi\) | |||||||
\(294\) | 16.1827i | 0.943795i | ||||||||
\(295\) | 3.30669 | + | 4.01693i | 0.192523 | + | 0.233875i | ||||
\(296\) | −1.49331 | −0.0867968 | ||||||||
\(297\) | 2.78715 | + | 2.78715i | 0.161727 | + | 0.161727i | ||||
\(298\) | 3.44721 | − | 3.44721i | 0.199691 | − | 0.199691i | ||||
\(299\) | 4.33642 | 0.250782 | ||||||||
\(300\) | 4.14901 | − | 2.79029i | 0.239543 | − | 0.161097i | ||||
\(301\) | −38.8190 | −2.23749 | ||||||||
\(302\) | 7.07444 | − | 7.07444i | 0.407089 | − | 0.407089i | ||||
\(303\) | 6.34373 | − | 6.34373i | 0.364438 | − | 0.364438i | ||||
\(304\) | 3.49740 | + | 2.60158i | 0.200589 | + | 0.149211i | ||||
\(305\) | −13.2498 | − | 16.0957i | −0.758682 | − | 0.921639i | ||||
\(306\) | 5.52509i | 0.315848i | ||||||||
\(307\) | 12.1946 | + | 12.1946i | 0.695981 | + | 0.695981i | 0.963541 | − | 0.267560i | \(-0.0862173\pi\) |
−0.267560 | + | 0.963541i | \(0.586217\pi\) | |||||||
\(308\) | 13.4197 | + | 13.4197i | 0.764659 | + | 0.764659i | ||||
\(309\) | 0.328072i | 0.0186633i | ||||||||
\(310\) | −15.5819 | − | 1.51113i | −0.884991 | − | 0.0858262i | ||||
\(311\) | −3.15000 | −0.178620 | −0.0893102 | − | 0.996004i | \(-0.528466\pi\) | ||||
−0.0893102 | + | 0.996004i | \(0.528466\pi\) | |||||||
\(312\) | −4.03748 | − | 4.03748i | −0.228577 | − | 0.228577i | ||||
\(313\) | −0.351586 | − | 0.351586i | −0.0198728 | − | 0.0198728i | 0.697101 | − | 0.716973i | \(-0.254473\pi\) |
−0.716973 | + | 0.697101i | \(0.754473\pi\) | |||||||
\(314\) | −10.9168 | −0.616070 | ||||||||
\(315\) | 1.03924 | − | 10.7160i | 0.0585545 | − | 0.603781i | ||||
\(316\) | − | 0.991285i | − | 0.0557642i | ||||||
\(317\) | −6.49068 | − | 6.49068i | −0.364553 | − | 0.364553i | 0.500933 | − | 0.865486i | \(-0.332990\pi\) |
−0.865486 | + | 0.500933i | \(0.832990\pi\) | |||||||
\(318\) | 4.39576 | − | 4.39576i | 0.246502 | − | 0.246502i | ||||
\(319\) | −24.7714 | −1.38693 | ||||||||
\(320\) | 1.72638 | − | 1.42113i | 0.0965075 | − | 0.0794438i | ||||
\(321\) | −16.7192 | −0.933173 | ||||||||
\(322\) | 2.58567 | + | 2.58567i | 0.144094 | + | 0.144094i | ||||
\(323\) | 23.8276 | − | 3.49979i | 1.32581 | − | 0.194734i | ||||
\(324\) | − | 1.00000i | − | 0.0555556i | ||||||
\(325\) | 15.9321 | + | 23.6902i | 0.883756 | + | 1.31410i | ||||
\(326\) | − | 3.48759i | − | 0.193160i | ||||||
\(327\) | 8.11578 | − | 8.11578i | 0.448803 | − | 0.448803i | ||||
\(328\) | 2.14751 | + | 2.14751i | 0.118576 | + | 0.118576i | ||||
\(329\) | 13.9463i | 0.768883i | ||||||||
\(330\) | −5.60158 | − | 6.80474i | −0.308357 | − | 0.374589i | ||||
\(331\) | − | 27.0350i | − | 1.48598i | −0.669304 | − | 0.742988i | \(-0.733408\pi\) | ||
0.669304 | − | 0.742988i | \(-0.266592\pi\) | |||||||
\(332\) | −6.64529 | + | 6.64529i | −0.364708 | + | 0.364708i | ||||
\(333\) | 1.05593 | − | 1.05593i | 0.0578645 | − | 0.0578645i | ||||
\(334\) | 17.8260i | 0.975397i | ||||||||
\(335\) | −2.24611 | + | 23.1606i | −0.122718 | + | 1.26540i | ||||
\(336\) | − | 4.81484i | − | 0.262671i | ||||||
\(337\) | 24.0565 | + | 24.0565i | 1.31044 | + | 1.31044i | 0.921090 | + | 0.389349i | \(0.127300\pi\) |
0.389349 | + | 0.921090i | \(0.372700\pi\) | |||||||
\(338\) | 13.8610 | − | 13.8610i | 0.753939 | − | 0.753939i | ||||
\(339\) | 15.9796i | 0.867890i | ||||||||
\(340\) | 1.19254 | − | 12.2968i | 0.0646745 | − | 0.666886i | ||||
\(341\) | 27.5958i | 1.49440i | ||||||||
\(342\) | −4.31263 | + | 0.633437i | −0.233200 | + | 0.0342523i | ||||
\(343\) | −31.2636 | − | 31.2636i | −1.68807 | − | 1.68807i | ||||
\(344\) | 8.06235 | 0.434693 | ||||||||
\(345\) | −1.07930 | − | 1.31112i | −0.0581075 | − | 0.0705883i | ||||
\(346\) | 15.3625 | 0.825892 | ||||||||
\(347\) | 8.63756 | − | 8.63756i | 0.463689 | − | 0.463689i | −0.436174 | − | 0.899862i | \(-0.643667\pi\) |
0.899862 | + | 0.436174i | \(0.143667\pi\) | |||||||
\(348\) | 4.44385 | + | 4.44385i | 0.238215 | + | 0.238215i | ||||
\(349\) | 5.73255i | 0.306856i | 0.988160 | + | 0.153428i | \(0.0490313\pi\) | ||||
−0.988160 | + | 0.153428i | \(0.950969\pi\) | |||||||
\(350\) | −4.62591 | + | 23.6256i | −0.247266 | + | 1.26284i | ||||
\(351\) | 5.70985 | 0.304769 | ||||||||
\(352\) | −2.78715 | − | 2.78715i | −0.148556 | − | 0.148556i | ||||
\(353\) | −1.17731 | − | 1.17731i | −0.0626617 | − | 0.0626617i | 0.675082 | − | 0.737743i | \(-0.264108\pi\) |
−0.737743 | + | 0.675082i | \(0.764108\pi\) | |||||||
\(354\) | −2.32680 | −0.123668 | ||||||||
\(355\) | 16.6245 | − | 13.6851i | 0.882336 | − | 0.726328i | ||||
\(356\) | − | 7.09242i | − | 0.375897i | ||||||
\(357\) | −18.8108 | − | 18.8108i | −0.995571 | − | 0.995571i | ||||
\(358\) | 8.80790 | + | 8.80790i | 0.465512 | + | 0.465512i | ||||
\(359\) | − | 30.2918i | − | 1.59874i | −0.600838 | − | 0.799371i | \(-0.705166\pi\) | ||
0.600838 | − | 0.799371i | \(-0.294834\pi\) | |||||||
\(360\) | −0.215841 | + | 2.22563i | −0.0113758 | + | 0.117301i | ||||
\(361\) | 5.46355 | + | 18.1975i | 0.287555 | + | 0.957764i | ||||
\(362\) | 8.18675 | − | 8.18675i | 0.430286 | − | 0.430286i | ||||
\(363\) | −3.20775 | + | 3.20775i | −0.168363 | + | 0.168363i | ||||
\(364\) | 27.4920 | 1.44097 | ||||||||
\(365\) | −1.36691 | + | 14.0948i | −0.0715473 | + | 0.737755i | ||||
\(366\) | 9.32341 | 0.487343 | ||||||||
\(367\) | 21.4259 | − | 21.4259i | 1.11842 | − | 1.11842i | 0.126452 | − | 0.991973i | \(-0.459641\pi\) |
0.991973 | − | 0.126452i | \(-0.0403590\pi\) | |||||||
\(368\) | −0.537022 | − | 0.537022i | −0.0279942 | − | 0.0279942i | ||||
\(369\) | −3.03704 | −0.158102 | ||||||||
\(370\) | −2.57802 | + | 2.12219i | −0.134025 | + | 0.110327i | ||||
\(371\) | 29.9317i | 1.55398i | ||||||||
\(372\) | 4.95054 | − | 4.95054i | 0.256673 | − | 0.256673i | ||||
\(373\) | −8.80310 | + | 8.80310i | −0.455807 | + | 0.455807i | −0.897276 | − | 0.441469i | \(-0.854457\pi\) |
0.441469 | + | 0.897276i | \(0.354457\pi\) | |||||||
\(374\) | −21.7778 | −1.12611 | ||||||||
\(375\) | 3.19739 | − | 10.7134i | 0.165112 | − | 0.553237i | ||||
\(376\) | − | 2.89652i | − | 0.149377i | ||||||
\(377\) | −25.3737 | + | 25.3737i | −1.30681 | + | 1.30681i | ||||
\(378\) | 3.40461 | + | 3.40461i | 0.175114 | + | 0.175114i | ||||
\(379\) | −25.6560 | −1.31786 | −0.658929 | − | 0.752205i | \(-0.728990\pi\) | ||||
−0.658929 | + | 0.752205i | \(0.728990\pi\) | |||||||
\(380\) | 9.73502 | − | 0.478953i | 0.499396 | − | 0.0245698i | ||||
\(381\) | −2.85114 | −0.146068 | ||||||||
\(382\) | 5.36914 | + | 5.36914i | 0.274709 | + | 0.274709i | ||||
\(383\) | −8.22807 | + | 8.22807i | −0.420435 | + | 0.420435i | −0.885353 | − | 0.464919i | \(-0.846084\pi\) |
0.464919 | + | 0.885353i | \(0.346084\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | 42.2387 | + | 4.09629i | 2.15268 | + | 0.208767i | ||||
\(386\) | 13.5983 | 0.692137 | ||||||||
\(387\) | −5.70094 | + | 5.70094i | −0.289795 | + | 0.289795i | ||||
\(388\) | 7.11482 | − | 7.11482i | 0.361200 | − | 0.361200i | ||||
\(389\) | 32.4669i | 1.64614i | 0.567940 | + | 0.823070i | \(0.307740\pi\) | ||||
−0.567940 | + | 0.823070i | \(0.692260\pi\) | |||||||
\(390\) | −12.7080 | − | 1.23242i | −0.643495 | − | 0.0624059i | ||||
\(391\) | −4.19610 | −0.212206 | ||||||||
\(392\) | 11.4429 | + | 11.4429i | 0.577954 | + | 0.577954i | ||||
\(393\) | 7.53832 | − | 7.53832i | 0.380258 | − | 0.380258i | ||||
\(394\) | −13.6637 | −0.688368 | ||||||||
\(395\) | −1.40875 | − | 1.71133i | −0.0708818 | − | 0.0861065i | ||||
\(396\) | 3.94163 | 0.198074 | ||||||||
\(397\) | 19.6595 | − | 19.6595i | 0.986681 | − | 0.986681i | −0.0132315 | − | 0.999912i | \(-0.504212\pi\) |
0.999912 | + | 0.0132315i | \(0.00421184\pi\) | |||||||
\(398\) | −16.6989 | + | 16.6989i | −0.837040 | + | 0.837040i | ||||
\(399\) | 12.5262 | − | 16.8394i | 0.627095 | − | 0.843025i | ||||
\(400\) | 0.960761 | − | 4.90683i | 0.0480381 | − | 0.245341i | ||||
\(401\) | − | 7.83053i | − | 0.391038i | −0.980700 | − | 0.195519i | \(-0.937361\pi\) | ||
0.980700 | − | 0.195519i | \(-0.0626391\pi\) | |||||||
\(402\) | −7.35838 | − | 7.35838i | −0.367003 | − | 0.367003i | ||||
\(403\) | 28.2668 | + | 28.2668i | 1.40807 | + | 1.40807i | ||||
\(404\) | − | 8.97139i | − | 0.446343i | ||||||
\(405\) | −1.42113 | − | 1.72638i | −0.0706167 | − | 0.0857844i | ||||
\(406\) | −30.2591 | −1.50173 | ||||||||
\(407\) | 4.16208 | + | 4.16208i | 0.206307 | + | 0.206307i | ||||
\(408\) | 3.90683 | + | 3.90683i | 0.193417 | + | 0.193417i | ||||
\(409\) | 29.4446 | 1.45594 | 0.727970 | − | 0.685609i | \(-0.240464\pi\) | ||||
0.727970 | + | 0.685609i | \(0.240464\pi\) | |||||||
\(410\) | 6.75931 | + | 0.655516i | 0.333819 | + | 0.0323736i | ||||
\(411\) | 1.46971i | 0.0724952i | ||||||||
\(412\) | 0.231982 | + | 0.231982i | 0.0114289 | + | 0.0114289i | ||||
\(413\) | 7.92183 | − | 7.92183i | 0.389808 | − | 0.389808i | ||||
\(414\) | 0.759463 | 0.0373256 | ||||||||
\(415\) | −2.02844 | + | 20.9161i | −0.0995723 | + | 1.02673i | ||||
\(416\) | −5.70985 | −0.279949 | ||||||||
\(417\) | 6.09481 | + | 6.09481i | 0.298464 | + | 0.298464i | ||||
\(418\) | −2.49677 | − | 16.9988i | −0.122121 | − | 0.831438i | ||||
\(419\) | 1.77581i | 0.0867538i | 0.999059 | + | 0.0433769i | \(0.0138116\pi\) | ||||
−0.999059 | + | 0.0433769i | \(0.986188\pi\) | |||||||
\(420\) | −6.84253 | − | 8.31224i | −0.333881 | − | 0.405596i | ||||
\(421\) | − | 18.2662i | − | 0.890238i | −0.895471 | − | 0.445119i | \(-0.853161\pi\) | ||
0.895471 | − | 0.445119i | \(-0.146839\pi\) | |||||||
\(422\) | −11.6564 | + | 11.6564i | −0.567423 | + | 0.567423i | ||||
\(423\) | 2.04815 | + | 2.04815i | 0.0995843 | + | 0.0995843i | ||||
\(424\) | − | 6.21654i | − | 0.301902i | ||||||
\(425\) | −15.4166 | − | 22.9236i | −0.747814 | − | 1.11196i | ||||
\(426\) | 9.62969i | 0.466560i | ||||||||
\(427\) | −31.7426 | + | 31.7426i | −1.53613 | + | 1.53613i | ||||
\(428\) | −11.8222 | + | 11.8222i | −0.571449 | + | 0.571449i | ||||
\(429\) | 22.5061i | 1.08661i | ||||||||
\(430\) | 13.9187 | − | 11.4577i | 0.671218 | − | 0.552538i | ||||
\(431\) | − | 23.1683i | − | 1.11598i | −0.829849 | − | 0.557988i | \(-0.811573\pi\) | ||
0.829849 | − | 0.557988i | \(-0.188427\pi\) | |||||||
\(432\) | −0.707107 | − | 0.707107i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | −17.1100 | + | 17.1100i | −0.822256 | + | 0.822256i | −0.986431 | − | 0.164175i | \(-0.947504\pi\) |
0.164175 | + | 0.986431i | \(0.447504\pi\) | |||||||
\(434\) | 33.7093i | 1.61810i | ||||||||
\(435\) | 13.9871 | + | 1.35646i | 0.670628 | + | 0.0650373i | ||||
\(436\) | − | 11.4774i | − | 0.549670i | ||||||
\(437\) | −0.481072 | − | 3.27528i | −0.0230128 | − | 0.156678i | ||||
\(438\) | −4.47808 | − | 4.47808i | −0.213971 | − | 0.213971i | ||||
\(439\) | −13.6373 | −0.650872 | −0.325436 | − | 0.945564i | \(-0.605511\pi\) | ||||
−0.325436 | + | 0.945564i | \(0.605511\pi\) | |||||||
\(440\) | −8.77260 | − | 0.850764i | −0.418217 | − | 0.0405586i | ||||
\(441\) | −16.1827 | −0.770606 | ||||||||
\(442\) | −22.3074 | + | 22.3074i | −1.06105 | + | 1.06105i | ||||
\(443\) | −0.0905461 | − | 0.0905461i | −0.00430198 | − | 0.00430198i | 0.704953 | − | 0.709254i | \(-0.250968\pi\) |
−0.709254 | + | 0.704953i | \(0.750968\pi\) | |||||||
\(444\) | − | 1.49331i | − | 0.0708693i | ||||||
\(445\) | −10.0793 | − | 12.2442i | −0.477803 | − | 0.580431i | ||||
\(446\) | 6.95094 | 0.329137 | ||||||||
\(447\) | 3.44721 | + | 3.44721i | 0.163047 | + | 0.163047i | ||||
\(448\) | −3.40461 | − | 3.40461i | −0.160853 | − | 0.160853i | ||||
\(449\) | −1.35350 | −0.0638754 | −0.0319377 | − | 0.999490i | \(-0.510168\pi\) | ||||
−0.0319377 | + | 0.999490i | \(0.510168\pi\) | |||||||
\(450\) | 2.79029 | + | 4.14901i | 0.131535 | + | 0.195586i | ||||
\(451\) | − | 11.9709i | − | 0.563687i | ||||||
\(452\) | 11.2993 | + | 11.2993i | 0.531472 | + | 0.531472i | ||||
\(453\) | 7.07444 | + | 7.07444i | 0.332386 | + | 0.332386i | ||||
\(454\) | − | 19.6753i | − | 0.923408i | ||||||
\(455\) | 47.4617 | − | 39.0699i | 2.22504 | − | 1.83162i | ||||
\(456\) | −2.60158 | + | 3.49740i | −0.121830 | + | 0.163781i | ||||
\(457\) | 11.4431 | − | 11.4431i | 0.535286 | − | 0.535286i | −0.386855 | − | 0.922141i | \(-0.626438\pi\) |
0.922141 | + | 0.386855i | \(0.126438\pi\) | |||||||
\(458\) | −11.6180 | + | 11.6180i | −0.542872 | + | 0.542872i | ||||
\(459\) | −5.52509 | −0.257889 | ||||||||
\(460\) | −1.69028 | − | 0.163923i | −0.0788098 | − | 0.00764295i | ||||
\(461\) | −32.5009 | −1.51372 | −0.756859 | − | 0.653578i | \(-0.773267\pi\) | ||||
−0.756859 | + | 0.653578i | \(0.773267\pi\) | |||||||
\(462\) | −13.4197 | + | 13.4197i | −0.624341 | + | 0.624341i | ||||
\(463\) | 10.2521 | + | 10.2521i | 0.476455 | + | 0.476455i | 0.903996 | − | 0.427541i | \(-0.140620\pi\) |
−0.427541 | + | 0.903996i | \(0.640620\pi\) | |||||||
\(464\) | 6.28455 | 0.291753 | ||||||||
\(465\) | 1.51113 | − | 15.5819i | 0.0700768 | − | 0.722592i | ||||
\(466\) | 1.23137i | 0.0570419i | ||||||||
\(467\) | −12.5702 | + | 12.5702i | −0.581682 | + | 0.581682i | −0.935365 | − | 0.353684i | \(-0.884929\pi\) |
0.353684 | + | 0.935365i | \(0.384929\pi\) | |||||||
\(468\) | 4.03748 | − | 4.03748i | 0.186632 | − | 0.186632i | ||||
\(469\) | 50.1048 | 2.31363 | ||||||||
\(470\) | −4.11634 | − | 5.00048i | −0.189872 | − | 0.230655i | ||||
\(471\) | − | 10.9168i | − | 0.503019i | ||||||
\(472\) | −1.64529 | + | 1.64529i | −0.0757308 | + | 0.0757308i | ||||
\(473\) | −22.4710 | − | 22.4710i | −1.03322 | − | 1.03322i | ||||
\(474\) | 0.991285 | 0.0455312 | ||||||||
\(475\) | 16.1257 | − | 14.6616i | 0.739896 | − | 0.672721i | ||||
\(476\) | −26.6024 | −1.21932 | ||||||||
\(477\) | 4.39576 | + | 4.39576i | 0.201268 | + | 0.201268i | ||||
\(478\) | 6.00068 | − | 6.00068i | 0.274465 | − | 0.274465i | ||||
\(479\) | − | 34.8202i | − | 1.59098i | −0.605969 | − | 0.795488i | \(-0.707214\pi\) | ||
0.605969 | − | 0.795488i | \(-0.292786\pi\) | |||||||
\(480\) | 1.42113 | + | 1.72638i | 0.0648656 | + | 0.0787980i | ||||
\(481\) | 8.52657 | 0.388778 | ||||||||
\(482\) | 1.79354 | − | 1.79354i | 0.0816937 | − | 0.0816937i | ||||
\(483\) | −2.58567 | + | 2.58567i | −0.117652 | + | 0.117652i | ||||
\(484\) | 4.53645i | 0.206202i | ||||||||
\(485\) | 2.17176 | − | 22.3940i | 0.0986147 | − | 1.01686i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −19.1447 | − | 19.1447i | −0.867529 | − | 0.867529i | 0.124669 | − | 0.992198i | \(-0.460213\pi\) |
−0.992198 | + | 0.124669i | \(0.960213\pi\) | |||||||
\(488\) | 6.59265 | − | 6.59265i | 0.298435 | − | 0.298435i | ||||
\(489\) | 3.48759 | 0.157714 | ||||||||
\(490\) | 36.0167 | + | 3.49289i | 1.62707 | + | 0.157793i | ||||
\(491\) | −5.10573 | −0.230418 | −0.115209 | − | 0.993341i | \(-0.536754\pi\) | ||||
−0.115209 | + | 0.993341i | \(0.536754\pi\) | |||||||
\(492\) | −2.14751 | + | 2.14751i | −0.0968173 | + | 0.0968173i | ||||
\(493\) | 24.5526 | − | 24.5526i | 1.10580 | − | 1.10580i | ||||
\(494\) | −19.9696 | − | 14.8546i | −0.898475 | − | 0.668342i | ||||
\(495\) | 6.80474 | − | 5.60158i | 0.305850 | − | 0.251772i | ||||
\(496\) | − | 7.00112i | − | 0.314360i | ||||||
\(497\) | −32.7853 | − | 32.7853i | −1.47062 | − | 1.47062i | ||||
\(498\) | −6.64529 | − | 6.64529i | −0.297783 | − | 0.297783i | ||||
\(499\) | 14.3736i | 0.643450i | 0.946833 | + | 0.321725i | \(0.104263\pi\) | ||||
−0.946833 | + | 0.321725i | \(0.895737\pi\) | |||||||
\(500\) | −5.31462 | − | 9.83640i | −0.237677 | − | 0.439897i | ||||
\(501\) | −17.8260 | −0.796408 | ||||||||
\(502\) | −11.1049 | − | 11.1049i | −0.495634 | − | 0.495634i | ||||
\(503\) | 5.66795 | + | 5.66795i | 0.252721 | + | 0.252721i | 0.822085 | − | 0.569364i | \(-0.192811\pi\) |
−0.569364 | + | 0.822085i | \(0.692811\pi\) | |||||||
\(504\) | 4.81484 | 0.214470 | ||||||||
\(505\) | −12.7495 | − | 15.4880i | −0.567347 | − | 0.689207i | ||||
\(506\) | 2.99352i | 0.133078i | ||||||||
\(507\) | 13.8610 | + | 13.8610i | 0.615589 | + | 0.615589i | ||||
\(508\) | −2.01606 | + | 2.01606i | −0.0894481 | + | 0.0894481i | ||||
\(509\) | −38.1688 | −1.69180 | −0.845900 | − | 0.533341i | \(-0.820936\pi\) | ||||
−0.845900 | + | 0.533341i | \(0.820936\pi\) | |||||||
\(510\) | 12.2968 | + | 1.19254i | 0.544510 | + | 0.0528065i | ||||
\(511\) | 30.4922 | 1.34890 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −0.633437 | − | 4.31263i | −0.0279669 | − | 0.190407i | ||||
\(514\) | − | 13.4892i | − | 0.594985i | ||||||
\(515\) | 0.730165 | + | 0.0708112i | 0.0321749 | + | 0.00312031i | ||||
\(516\) | 8.06235i | 0.354925i | ||||||||
\(517\) | −8.07304 | + | 8.07304i | −0.355052 | + | 0.355052i | ||||
\(518\) | 5.08413 | + | 5.08413i | 0.223384 | + | 0.223384i | ||||
\(519\) | 15.3625i | 0.674338i | ||||||||
\(520\) | −9.85736 | + | 8.11446i | −0.432274 | + | 0.355843i | ||||
\(521\) | 18.9469i | 0.830078i | 0.909804 | + | 0.415039i | \(0.136232\pi\) | ||||
−0.909804 | + | 0.415039i | \(0.863768\pi\) | |||||||
\(522\) | −4.44385 | + | 4.44385i | −0.194502 | + | 0.194502i | ||||
\(523\) | 2.96461 | − | 2.96461i | 0.129633 | − | 0.129633i | −0.639313 | − | 0.768946i | \(-0.720781\pi\) |
0.768946 | + | 0.639313i | \(0.220781\pi\) | |||||||
\(524\) | − | 10.6608i | − | 0.465719i | ||||||
\(525\) | −23.6256 | − | 4.62591i | −1.03111 | − | 0.201891i | ||||
\(526\) | − | 1.89697i | − | 0.0827120i | ||||||
\(527\) | −27.3522 | − | 27.3522i | −1.19148 | − | 1.19148i | ||||
\(528\) | 2.78715 | − | 2.78715i | 0.121295 | − | 0.121295i | ||||
\(529\) | − | 22.4232i | − | 0.974922i | ||||||
\(530\) | −8.83454 | − | 10.7321i | −0.383748 | − | 0.466173i | ||||
\(531\) | − | 2.32680i | − | 0.100974i | ||||||
\(532\) | −3.04990 | − | 20.7646i | −0.132230 | − | 0.900261i | ||||
\(533\) | −12.2620 | − | 12.2620i | −0.531125 | − | 0.531125i | ||||
\(534\) | 7.09242 | 0.306919 | ||||||||
\(535\) | −3.60867 | + | 37.2106i | −0.156017 | + | 1.60875i | ||||
\(536\) | −10.4063 | −0.449485 | ||||||||
\(537\) | −8.80790 | + | 8.80790i | −0.380089 | + | 0.380089i | ||||
\(538\) | 1.26113 | + | 1.26113i | 0.0543712 | + | 0.0543712i | ||||
\(539\) | − | 63.7863i | − | 2.74747i | ||||||
\(540\) | −2.22563 | − | 0.215841i | −0.0957757 | − | 0.00928830i | ||||
\(541\) | 32.1389 | 1.38176 | 0.690879 | − | 0.722970i | \(-0.257224\pi\) | ||||
0.690879 | + | 0.722970i | \(0.257224\pi\) | |||||||
\(542\) | 21.2289 | + | 21.2289i | 0.911857 | + | 0.911857i | ||||
\(543\) | 8.18675 | + | 8.18675i | 0.351327 | + | 0.351327i | ||||
\(544\) | 5.52509 | 0.236886 | ||||||||
\(545\) | −16.3110 | − | 19.8144i | −0.698685 | − | 0.848756i | ||||
\(546\) | 27.4920i | 1.17655i | ||||||||
\(547\) | −2.88206 | − | 2.88206i | −0.123228 | − | 0.123228i | 0.642803 | − | 0.766031i | \(-0.277771\pi\) |
−0.766031 | + | 0.642803i | \(0.777771\pi\) | |||||||
\(548\) | 1.03924 | + | 1.03924i | 0.0443941 | + | 0.0443941i | ||||
\(549\) | 9.32341i | 0.397914i | ||||||||
\(550\) | −16.3539 | + | 10.9983i | −0.697331 | + | 0.468969i | ||||
\(551\) | 21.9796 | + | 16.3498i | 0.936361 | + | 0.696523i | ||||
\(552\) | 0.537022 | − | 0.537022i | 0.0228572 | − | 0.0228572i | ||||
\(553\) | −3.37494 | + | 3.37494i | −0.143517 | + | 0.143517i | ||||
\(554\) | 20.5465 | 0.872936 | ||||||||
\(555\) | −2.12219 | − | 2.57802i | −0.0900820 | − | 0.109431i | ||||
\(556\) | 8.61936 | 0.365542 | ||||||||
\(557\) | 11.6948 | − | 11.6948i | 0.495523 | − | 0.495523i | −0.414518 | − | 0.910041i | \(-0.636050\pi\) |
0.910041 | + | 0.414518i | \(0.136050\pi\) | |||||||
\(558\) | 4.95054 | + | 4.95054i | 0.209573 | + | 0.209573i | ||||
\(559\) | −46.0349 | −1.94707 | ||||||||
\(560\) | −10.7160 | − | 1.03924i | −0.452835 | − | 0.0439159i | ||||
\(561\) | − | 21.7778i | − | 0.919461i | ||||||
\(562\) | −8.71974 | + | 8.71974i | −0.367820 | + | 0.367820i | ||||
\(563\) | 15.5373 | − | 15.5373i | 0.654819 | − | 0.654819i | −0.299331 | − | 0.954149i | \(-0.596763\pi\) |
0.954149 | + | 0.299331i | \(0.0967634\pi\) | |||||||
\(564\) | 2.89652 | 0.121965 | ||||||||
\(565\) | 35.5645 | + | 3.44904i | 1.49621 | + | 0.145102i | ||||
\(566\) | − | 9.70157i | − | 0.407787i | ||||||
\(567\) | −3.40461 | + | 3.40461i | −0.142980 | + | 0.142980i | ||||
\(568\) | 6.80922 | + | 6.80922i | 0.285708 | + | 0.285708i | ||||
\(569\) | −13.6985 | −0.574272 | −0.287136 | − | 0.957890i | \(-0.592703\pi\) | ||||
−0.287136 | + | 0.957890i | \(0.592703\pi\) | |||||||
\(570\) | 0.478953 | + | 9.73502i | 0.0200611 | + | 0.407755i | ||||
\(571\) | 17.7058 | 0.740964 | 0.370482 | − | 0.928840i | \(-0.379193\pi\) | ||||
0.370482 | + | 0.928840i | \(0.379193\pi\) | |||||||
\(572\) | 15.9142 | + | 15.9142i | 0.665408 | + | 0.665408i | ||||
\(573\) | −5.36914 | + | 5.36914i | −0.224299 | + | 0.224299i | ||||
\(574\) | − | 14.6229i | − | 0.610347i | ||||||
\(575\) | −3.15102 | + | 2.11912i | −0.131407 | + | 0.0883735i | ||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | −23.4215 | + | 23.4215i | −0.975050 | + | 0.975050i | −0.999696 | − | 0.0246459i | \(-0.992154\pi\) |
0.0246459 | + | 0.999696i | \(0.492154\pi\) | |||||||
\(578\) | 9.56473 | − | 9.56473i | 0.397840 | − | 0.397840i | ||||
\(579\) | 13.5983i | 0.565127i | ||||||||
\(580\) | 10.8495 | − | 8.93118i | 0.450501 | − | 0.370847i | ||||
\(581\) | 45.2492 | 1.87726 | ||||||||
\(582\) | 7.11482 | + | 7.11482i | 0.294919 | + | 0.294919i | ||||
\(583\) | −17.3265 | + | 17.3265i | −0.717589 | + | 0.717589i | ||||
\(584\) | −6.33296 | −0.262060 | ||||||||
\(585\) | 1.23242 | − | 12.7080i | 0.0509542 | − | 0.525411i | ||||
\(586\) | −26.4466 | −1.09250 | ||||||||
\(587\) | −19.2886 | + | 19.2886i | −0.796126 | + | 0.796126i | −0.982482 | − | 0.186356i | \(-0.940332\pi\) |
0.186356 | + | 0.982482i | \(0.440332\pi\) | |||||||
\(588\) | −11.4429 | + | 11.4429i | −0.471898 | + | 0.471898i | ||||
\(589\) | 18.2140 | − | 24.4857i | 0.750494 | − | 1.00891i | ||||
\(590\) | −0.502217 | + | 5.17858i | −0.0206760 | + | 0.213199i | ||||
\(591\) | − | 13.6637i | − | 0.562050i | ||||||
\(592\) | −1.05593 | − | 1.05593i | −0.0433984 | − | 0.0433984i | ||||
\(593\) | 25.4634 | + | 25.4634i | 1.04566 | + | 1.04566i | 0.998907 | + | 0.0467490i | \(0.0148861\pi\) |
0.0467490 | + | 0.998907i | \(0.485114\pi\) | |||||||
\(594\) | 3.94163i | 0.161727i | ||||||||
\(595\) | −45.9258 | + | 37.8056i | −1.88278 | + | 1.54988i | ||||
\(596\) | 4.87509 | 0.199691 | ||||||||
\(597\) | −16.6989 | − | 16.6989i | −0.683440 | − | 0.683440i | ||||
\(598\) | 3.06631 | + | 3.06631i | 0.125391 | + | 0.125391i | ||||
\(599\) | 44.5540 | 1.82043 | 0.910213 | − | 0.414140i | \(-0.135918\pi\) | ||||
0.910213 | + | 0.414140i | \(0.135918\pi\) | |||||||
\(600\) | 4.90683 | + | 0.960761i | 0.200320 | + | 0.0392229i | ||||
\(601\) | 21.3945i | 0.872700i | 0.899777 | + | 0.436350i | \(0.143729\pi\) | ||||
−0.899777 | + | 0.436350i | \(0.856271\pi\) | |||||||
\(602\) | −27.4492 | − | 27.4492i | −1.11874 | − | 1.11874i | ||||
\(603\) | 7.35838 | − | 7.35838i | 0.299656 | − | 0.299656i | ||||
\(604\) | 10.0048 | 0.407089 | ||||||||
\(605\) | 6.44689 | + | 7.83162i | 0.262104 | + | 0.318401i | ||||
\(606\) | 8.97139 | 0.364438 | ||||||||
\(607\) | 3.46614 | + | 3.46614i | 0.140686 | + | 0.140686i | 0.773942 | − | 0.633256i | \(-0.218282\pi\) |
−0.633256 | + | 0.773942i | \(0.718282\pi\) | |||||||
\(608\) | 0.633437 | + | 4.31263i | 0.0256893 | + | 0.174900i | ||||
\(609\) | − | 30.2591i | − | 1.22616i | ||||||
\(610\) | 2.01237 | − | 20.7504i | 0.0814785 | − | 0.840160i | ||||
\(611\) | 16.5387i | 0.669084i | ||||||||
\(612\) | −3.90683 | + | 3.90683i | −0.157924 | + | 0.157924i | ||||
\(613\) | 6.23977 | + | 6.23977i | 0.252022 | + | 0.252022i | 0.821799 | − | 0.569777i | \(-0.192970\pi\) |
−0.569777 | + | 0.821799i | \(0.692970\pi\) | |||||||
\(614\) | 17.2457i | 0.695981i | ||||||||
\(615\) | −0.655516 | + | 6.75931i | −0.0264330 | + | 0.272562i | ||||
\(616\) | 18.9783i | 0.764659i | ||||||||
\(617\) | −9.37481 | + | 9.37481i | −0.377416 | + | 0.377416i | −0.870169 | − | 0.492753i | \(-0.835991\pi\) |
0.492753 | + | 0.870169i | \(0.335991\pi\) | |||||||
\(618\) | −0.231982 | + | 0.231982i | −0.00933167 | + | 0.00933167i | ||||
\(619\) | − | 35.9982i | − | 1.44689i | −0.690383 | − | 0.723444i | \(-0.742558\pi\) | ||
0.690383 | − | 0.723444i | \(-0.257442\pi\) | |||||||
\(620\) | −9.94952 | − | 12.0866i | −0.399582 | − | 0.485409i | ||||
\(621\) | 0.759463i | 0.0304762i | ||||||||
\(622\) | −2.22739 | − | 2.22739i | −0.0893102 | − | 0.0893102i | ||||
\(623\) | −24.1469 | + | 24.1469i | −0.967426 | + | 0.967426i | ||||
\(624\) | − | 5.70985i | − | 0.228577i | ||||||
\(625\) | −23.1539 | − | 9.42858i | −0.926155 | − | 0.377143i | ||||
\(626\) | − | 0.497217i | − | 0.0198728i | ||||||
\(627\) | 16.9988 | − | 2.49677i | 0.678866 | − | 0.0997115i | ||||
\(628\) | −7.71934 | − | 7.71934i | −0.308035 | − | 0.308035i | ||||
\(629\) | −8.25066 | −0.328975 | ||||||||
\(630\) | 8.31224 | − | 6.84253i | 0.331168 | − | 0.272613i | ||||
\(631\) | −4.26094 | −0.169626 | −0.0848128 | − | 0.996397i | \(-0.527029\pi\) | ||||
−0.0848128 | + | 0.996397i | \(0.527029\pi\) | |||||||
\(632\) | 0.700945 | − | 0.700945i | 0.0278821 | − | 0.0278821i | ||||
\(633\) | −11.6564 | − | 11.6564i | −0.463299 | − | 0.463299i | ||||
\(634\) | − | 9.17921i | − | 0.364553i | ||||||
\(635\) | −0.615391 | + | 6.34556i | −0.0244210 | + | 0.251816i | ||||
\(636\) | 6.21654 | 0.246502 | ||||||||
\(637\) | −65.3373 | − | 65.3373i | −2.58876 | − | 2.58876i | ||||
\(638\) | −17.5160 | − | 17.5160i | −0.693465 | − | 0.693465i | ||||
\(639\) | −9.62969 | −0.380945 | ||||||||
\(640\) | 2.22563 | + | 0.215841i | 0.0879756 | + | 0.00853185i | ||||
\(641\) | 23.3013i | 0.920345i | 0.887829 | + | 0.460173i | \(0.152213\pi\) | ||||
−0.887829 | + | 0.460173i | \(0.847787\pi\) | |||||||
\(642\) | −11.8222 | − | 11.8222i | −0.466586 | − | 0.466586i | ||||
\(643\) | −25.8173 | − | 25.8173i | −1.01814 | − | 1.01814i | −0.999832 | − | 0.0183043i | \(-0.994173\pi\) |
−0.0183043 | − | 0.999832i | \(-0.505827\pi\) | |||||||
\(644\) | 3.65670i | 0.144094i | ||||||||
\(645\) | 11.4577 | + | 13.9187i | 0.451146 | + | 0.548047i | ||||
\(646\) | 19.3234 | + | 14.3740i | 0.760269 | + | 0.565536i | ||||
\(647\) | 17.2171 | − | 17.2171i | 0.676875 | − | 0.676875i | −0.282417 | − | 0.959292i | \(-0.591136\pi\) |
0.959292 | + | 0.282417i | \(0.0911362\pi\) | |||||||
\(648\) | 0.707107 | − | 0.707107i | 0.0277778 | − | 0.0277778i | ||||
\(649\) | 9.17137 | 0.360008 | ||||||||
\(650\) | −5.48581 | + | 28.0173i | −0.215171 | + | 1.09893i | ||||
\(651\) | −33.7093 | −1.32117 | ||||||||
\(652\) | 2.46610 | − | 2.46610i | 0.0965799 | − | 0.0965799i | ||||
\(653\) | 8.16718 | + | 8.16718i | 0.319606 | + | 0.319606i | 0.848616 | − | 0.529010i | \(-0.177436\pi\) |
−0.529010 | + | 0.848616i | \(0.677436\pi\) | |||||||
\(654\) | 11.4774 | 0.448803 | ||||||||
\(655\) | −15.1504 | − | 18.4046i | −0.591975 | − | 0.719126i | ||||
\(656\) | 3.03704i | 0.118576i | ||||||||
\(657\) | 4.47808 | − | 4.47808i | 0.174706 | − | 0.174706i | ||||
\(658\) | −9.86151 | + | 9.86151i | −0.384442 | + | 0.384442i | ||||
\(659\) | 49.4565 | 1.92655 | 0.963275 | − | 0.268517i | \(-0.0865335\pi\) | ||||
0.963275 | + | 0.268517i | \(0.0865335\pi\) | |||||||
\(660\) | 0.850764 | − | 8.77260i | 0.0331159 | − | 0.341473i | ||||
\(661\) | 42.8869i | 1.66811i | 0.551683 | + | 0.834054i | \(0.313986\pi\) | ||||
−0.551683 | + | 0.834054i | \(0.686014\pi\) | |||||||
\(662\) | 19.1166 | − | 19.1166i | 0.742988 | − | 0.742988i | ||||
\(663\) | −22.3074 | − | 22.3074i | −0.866348 | − | 0.866348i | ||||
\(664\) | −9.39786 | −0.364708 | ||||||||
\(665\) | −34.7746 | − | 31.5133i | −1.34850 | − | 1.22203i | ||||
\(666\) | 1.49331 | 0.0578645 | ||||||||
\(667\) | −3.37494 | − | 3.37494i | −0.130678 | − | 0.130678i | ||||
\(668\) | −12.6049 | + | 12.6049i | −0.487698 | + | 0.487698i | ||||
\(669\) | 6.95094i | 0.268739i | ||||||||
\(670\) | −17.9652 | + | 14.7888i | −0.694058 | + | 0.571340i | ||||
\(671\) | −36.7494 | −1.41870 | ||||||||
\(672\) | 3.40461 | − | 3.40461i | 0.131336 | − | 0.131336i | ||||
\(673\) | 18.4285 | − | 18.4285i | 0.710368 | − | 0.710368i | −0.256244 | − | 0.966612i | \(-0.582485\pi\) |
0.966612 | + | 0.256244i | \(0.0824852\pi\) | |||||||
\(674\) | 34.0210i | 1.31044i | ||||||||
\(675\) | −4.14901 | + | 2.79029i | −0.159695 | + | 0.107398i | ||||
\(676\) | 19.6024 | 0.753939 | ||||||||
\(677\) | −16.5124 | − | 16.5124i | −0.634623 | − | 0.634623i | 0.314601 | − | 0.949224i | \(-0.398129\pi\) |
−0.949224 | + | 0.314601i | \(0.898129\pi\) | |||||||
\(678\) | −11.2993 | + | 11.2993i | −0.433945 | + | 0.433945i | ||||
\(679\) | −48.4464 | −1.85920 | ||||||||
\(680\) | 9.53839 | − | 7.85188i | 0.365780 | − | 0.301106i | ||||
\(681\) | 19.6753 | 0.753960 | ||||||||
\(682\) | −19.5132 | + | 19.5132i | −0.747199 | + | 0.747199i | ||||
\(683\) | 0.431737 | − | 0.431737i | 0.0165200 | − | 0.0165200i | −0.698799 | − | 0.715319i | \(-0.746282\pi\) |
0.715319 | + | 0.698799i | \(0.246282\pi\) | |||||||
\(684\) | −3.49740 | − | 2.60158i | −0.133726 | − | 0.0994739i | ||||
\(685\) | 3.27102 | + | 0.317222i | 0.124979 | + | 0.0121204i | ||||
\(686\) | − | 44.2133i | − | 1.68807i | ||||||
\(687\) | −11.6180 | − | 11.6180i | −0.443253 | − | 0.443253i | ||||
\(688\) | 5.70094 | + | 5.70094i | 0.217346 | + | 0.217346i | ||||
\(689\) | 35.4956i | 1.35227i | ||||||||
\(690\) | 0.163923 | − | 1.69028i | 0.00624044 | − | 0.0643479i | ||||
\(691\) | 9.51319 | 0.361899 | 0.180949 | − | 0.983492i | \(-0.442083\pi\) | ||||
0.180949 | + | 0.983492i | \(0.442083\pi\) | |||||||
\(692\) | 10.8629 | + | 10.8629i | 0.412946 | + | 0.412946i | ||||
\(693\) | −13.4197 | − | 13.4197i | −0.509772 | − | 0.509772i | ||||
\(694\) | 12.2154 | 0.463689 | ||||||||
\(695\) | 14.8803 | − | 12.2493i | 0.564441 | − | 0.464641i | ||||
\(696\) | 6.28455i | 0.238215i | ||||||||
\(697\) | 11.8652 | + | 11.8652i | 0.449426 | + | 0.449426i | ||||
\(698\) | −4.05352 | + | 4.05352i | −0.153428 | + | 0.153428i | ||||
\(699\) | −1.23137 | −0.0465745 | ||||||||
\(700\) | −19.9768 | + | 13.4348i | −0.755053 | + | 0.507788i | ||||
\(701\) | 30.1150 | 1.13743 | 0.568715 | − | 0.822535i | \(-0.307441\pi\) | ||||
0.568715 | + | 0.822535i | \(0.307441\pi\) | |||||||
\(702\) | 4.03748 | + | 4.03748i | 0.152385 | + | 0.152385i | ||||
\(703\) | −0.945917 | − | 6.44008i | −0.0356759 | − | 0.242892i | ||||
\(704\) | − | 3.94163i | − | 0.148556i | ||||||
\(705\) | 5.00048 | − | 4.11634i | 0.188329 | − | 0.155030i | ||||
\(706\) | − | 1.66496i | − | 0.0626617i | ||||||
\(707\) | −30.5441 | + | 30.5441i | −1.14873 | + | 1.14873i | ||||
\(708\) | −1.64529 | − | 1.64529i | −0.0618339 | − | 0.0618339i | ||||
\(709\) | − | 15.3806i | − | 0.577632i | −0.957385 | − | 0.288816i | \(-0.906738\pi\) | ||
0.957385 | − | 0.288816i | \(-0.0932616\pi\) | |||||||
\(710\) | 21.4321 | + | 2.07848i | 0.804332 | + | 0.0780039i | ||||
\(711\) | 0.991285i | 0.0371761i | ||||||||
\(712\) | 5.01510 | − | 5.01510i | 0.187949 | − | 0.187949i | ||||
\(713\) | −3.75975 | + | 3.75975i | −0.140804 | + | 0.140804i | ||||
\(714\) | − | 26.6024i | − | 0.995571i | ||||||
\(715\) | 50.0902 | + | 4.85774i | 1.87327 | + | 0.181669i | ||||
\(716\) | 12.4563i | 0.465512i | ||||||||
\(717\) | 6.00068 | + | 6.00068i | 0.224100 | + | 0.224100i | ||||
\(718\) | 21.4196 | − | 21.4196i | 0.799371 | − | 0.799371i | ||||
\(719\) | 8.69928i | 0.324428i | 0.986756 | + | 0.162214i | \(0.0518636\pi\) | ||||
−0.986756 | + | 0.162214i | \(0.948136\pi\) | |||||||
\(720\) | −1.72638 | + | 1.42113i | −0.0643383 | + | 0.0529625i | ||||
\(721\) | − | 1.57961i | − | 0.0588279i | ||||||
\(722\) | −9.00427 | + | 16.7309i | −0.335104 | + | 0.622660i | ||||
\(723\) | 1.79354 | + | 1.79354i | 0.0667026 | + | 0.0667026i | ||||
\(724\) | 11.5778 | 0.430286 | ||||||||
\(725\) | 6.03795 | − | 30.8372i | 0.224244 | − | 1.14526i | ||||
\(726\) | −4.53645 | −0.168363 | ||||||||
\(727\) | −8.12640 | + | 8.12640i | −0.301391 | + | 0.301391i | −0.841558 | − | 0.540167i | \(-0.818361\pi\) |
0.540167 | + | 0.841558i | \(0.318361\pi\) | |||||||
\(728\) | 19.4398 | + | 19.4398i | 0.720487 | + | 0.720487i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | −10.9331 | + | 8.99997i | −0.404651 | + | 0.333104i | ||||
\(731\) | 44.5452 | 1.64756 | ||||||||
\(732\) | 6.59265 | + | 6.59265i | 0.243671 | + | 0.243671i | ||||
\(733\) | 3.98915 | + | 3.98915i | 0.147343 | + | 0.147343i | 0.776930 | − | 0.629587i | \(-0.216776\pi\) |
−0.629587 | + | 0.776930i | \(0.716776\pi\) | |||||||
\(734\) | 30.3008 | 1.11842 | ||||||||
\(735\) | −3.49289 | + | 36.0167i | −0.128837 | + | 1.32850i | ||||
\(736\) | − | 0.759463i | − | 0.0279942i | ||||||
\(737\) | 29.0040 | + | 29.0040i | 1.06838 | + | 1.06838i | ||||
\(738\) | −2.14751 | − | 2.14751i | −0.0790510 | − | 0.0790510i | ||||
\(739\) | − | 10.1757i | − | 0.374317i | −0.982330 | − | 0.187159i | \(-0.940072\pi\) | ||
0.982330 | − | 0.187159i | \(-0.0599279\pi\) | |||||||
\(740\) | −3.32355 | − | 0.322317i | −0.122176 | − | 0.0118486i | ||||
\(741\) | 14.8546 | − | 19.9696i | 0.545699 | − | 0.733602i | ||||
\(742\) | −21.1649 | + | 21.1649i | −0.776988 | + | 0.776988i | ||||
\(743\) | −12.6705 | + | 12.6705i | −0.464836 | + | 0.464836i | −0.900237 | − | 0.435401i | \(-0.856607\pi\) |
0.435401 | + | 0.900237i | \(0.356607\pi\) | |||||||
\(744\) | 7.00112 | 0.256673 | ||||||||
\(745\) | 8.41625 | − | 6.92815i | 0.308347 | − | 0.253828i | ||||
\(746\) | −12.4495 | −0.455807 | ||||||||
\(747\) | 6.64529 | − | 6.64529i | 0.243139 | − | 0.243139i | ||||
\(748\) | −15.3993 | − | 15.3993i | −0.563053 | − | 0.563053i | ||||
\(749\) | 80.5001 | 2.94141 | ||||||||
\(750\) | 9.83640 | − | 5.31462i | 0.359175 | − | 0.194062i | ||||
\(751\) | − | 23.7459i | − | 0.866500i | −0.901274 | − | 0.433250i | \(-0.857367\pi\) | ||
0.901274 | − | 0.433250i | \(-0.142633\pi\) | |||||||
\(752\) | 2.04815 | − | 2.04815i | 0.0746883 | − | 0.0746883i | ||||
\(753\) | 11.1049 | − | 11.1049i | 0.404684 | − | 0.404684i | ||||
\(754\) | −35.8839 | −1.30681 | ||||||||
\(755\) | 17.2720 | − | 14.2181i | 0.628593 | − | 0.517450i | ||||
\(756\) | 4.81484i | 0.175114i | ||||||||
\(757\) | 33.7824 | − | 33.7824i | 1.22784 | − | 1.22784i | 0.263062 | − | 0.964779i | \(-0.415268\pi\) |
0.964779 | − | 0.263062i | \(-0.0847322\pi\) | |||||||
\(758\) | −18.1415 | − | 18.1415i | −0.658929 | − | 0.658929i | ||||
\(759\) | −2.99352 | −0.108658 | ||||||||
\(760\) | 7.22237 | + | 6.54503i | 0.261983 | + | 0.237413i | ||||
\(761\) | −20.8359 | −0.755301 | −0.377650 | − | 0.925948i | \(-0.623268\pi\) | ||||
−0.377650 | + | 0.925948i | \(0.623268\pi\) | |||||||
\(762\) | −2.01606 | − | 2.01606i | −0.0730340 | − | 0.0730340i | ||||
\(763\) | −39.0762 | + | 39.0762i | −1.41465 | + | 1.41465i | ||||
\(764\) | 7.59311i | 0.274709i | ||||||||
\(765\) | −1.19254 | + | 12.2968i | −0.0431163 | + | 0.444591i | ||||
\(766\) | −11.6363 | −0.420435 | ||||||||
\(767\) | 9.39439 | − | 9.39439i | 0.339212 | − | 0.339212i | ||||
\(768\) | −0.707107 | + | 0.707107i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | 45.2621i | 1.63219i | 0.577916 | + | 0.816096i | \(0.303866\pi\) | ||||
−0.577916 | + | 0.816096i | \(0.696134\pi\) | |||||||
\(770\) | 26.9707 | + | 32.7638i | 0.971958 | + | 1.18072i | ||||
\(771\) | 13.4892 | 0.485803 | ||||||||
\(772\) | 9.61547 | + | 9.61547i | 0.346068 | + | 0.346068i | ||||
\(773\) | 14.8984 | − | 14.8984i | 0.535857 | − | 0.535857i | −0.386452 | − | 0.922309i | \(-0.626300\pi\) |
0.922309 | + | 0.386452i | \(0.126300\pi\) | |||||||
\(774\) | −8.06235 | −0.289795 | ||||||||
\(775\) | −34.3533 | − | 6.72640i | −1.23401 | − | 0.241620i | ||||
\(776\) | 10.0619 | 0.361200 | ||||||||
\(777\) | −5.08413 | + | 5.08413i | −0.182392 | + | 0.182392i | ||||
\(778\) | −22.9576 | + | 22.9576i | −0.823070 | + | 0.823070i | ||||
\(779\) | −7.90110 | + | 10.6217i | −0.283086 | + | 0.380563i | ||||
\(780\) | −8.11446 | − | 9.85736i | −0.290544 | − | 0.352950i | ||||
\(781\) | − | 37.9567i | − | 1.35820i | ||||||
\(782\) | −2.96709 | − | 2.96709i | −0.106103 | − | 0.106103i | ||||
\(783\) | −4.44385 | − | 4.44385i | −0.158810 | − | 0.158810i | ||||
\(784\) | 16.1827i | 0.577954i | ||||||||
\(785\) | −24.2967 | − | 2.35629i | −0.867186 | − | 0.0840995i | ||||
\(786\) | 10.6608 | 0.380258 | ||||||||
\(787\) | 11.1825 | + | 11.1825i | 0.398613 | + | 0.398613i | 0.877744 | − | 0.479131i | \(-0.159048\pi\) |
−0.479131 | + | 0.877744i | \(0.659048\pi\) | |||||||
\(788\) | −9.66171 | − | 9.66171i | −0.344184 | − | 0.344184i | ||||
\(789\) | 1.89697 | 0.0675341 | ||||||||
\(790\) | 0.213960 | − | 2.20623i | 0.00761234 | − | 0.0784942i | ||||
\(791\) | − | 76.9391i | − | 2.73564i | ||||||
\(792\) | 2.78715 | + | 2.78715i | 0.0990372 | + | 0.0990372i | ||||
\(793\) | −37.6430 | + | 37.6430i | −1.33674 | + | 1.33674i | ||||
\(794\) | 27.8027 | 0.986681 | ||||||||
\(795\) | 10.7321 | − | 8.83454i | 0.380629 | − | 0.313329i | ||||
\(796\) | −23.6158 | −0.837040 | ||||||||
\(797\) | 10.8613 | + | 10.8613i | 0.384727 | + | 0.384727i | 0.872802 | − | 0.488075i | \(-0.162301\pi\) |
−0.488075 | + | 0.872802i | \(0.662301\pi\) | |||||||
\(798\) | 20.7646 | − | 3.04990i | 0.735060 | − | 0.107965i | ||||
\(799\) | − | 16.0035i | − | 0.566163i | ||||||
\(800\) | 4.14901 | − | 2.79029i | 0.146690 | − | 0.0986516i | ||||
\(801\) | 7.09242i | 0.250598i | ||||||||
\(802\) | 5.53702 | − | 5.53702i | 0.195519 | − | 0.195519i | ||||
\(803\) | 17.6509 | + | 17.6509i | 0.622887 | + | 0.622887i | ||||
\(804\) | − | 10.4063i | − | 0.367003i | ||||||
\(805\) | 5.19665 | + | 6.31284i | 0.183158 | + | 0.222498i | ||||
\(806\) | 39.9754i | 1.40807i | ||||||||
\(807\) | −1.26113 | + | 1.26113i | −0.0443939 | + | 0.0443939i | ||||
\(808\) | 6.34373 | − | 6.34373i | 0.223172 | − | 0.223172i | ||||
\(809\) | 3.35669i | 0.118015i | 0.998258 | + | 0.0590074i | \(0.0187936\pi\) | ||||
−0.998258 | + | 0.0590074i | \(0.981206\pi\) | |||||||
\(810\) | 0.215841 | − | 2.22563i | 0.00758387 | − | 0.0782005i | ||||
\(811\) | 29.8224i | 1.04721i | 0.851962 | + | 0.523604i | \(0.175413\pi\) | ||||
−0.851962 | + | 0.523604i | \(0.824587\pi\) | |||||||
\(812\) | −21.3964 | − | 21.3964i | −0.750867 | − | 0.750867i | ||||
\(813\) | −21.2289 | + | 21.2289i | −0.744528 | + | 0.744528i | ||||
\(814\) | 5.88607i | 0.206307i | ||||||||
\(815\) | 0.752764 | − | 7.76207i | 0.0263682 | − | 0.271894i | ||||
\(816\) | 5.52509i | 0.193417i | ||||||||
\(817\) | 5.10699 | + | 34.7699i | 0.178671 | + | 1.21645i | ||||
\(818\) | 20.8205 | + | 20.8205i | 0.727970 | + | 0.727970i | ||||
\(819\) | −27.4920 | −0.960650 | ||||||||
\(820\) | 4.31604 | + | 5.24308i | 0.150723 | + | 0.183096i | ||||
\(821\) | 4.78881 | 0.167131 | 0.0835654 | − | 0.996502i | \(-0.473369\pi\) | ||||
0.0835654 | + | 0.996502i | \(0.473369\pi\) | |||||||
\(822\) | −1.03924 | + | 1.03924i | −0.0362476 | + | 0.0362476i | ||||
\(823\) | 34.2808 | + | 34.2808i | 1.19495 | + | 1.19495i | 0.975659 | + | 0.219295i | \(0.0703758\pi\) |
0.219295 | + | 0.975659i | \(0.429624\pi\) | |||||||
\(824\) | 0.328072i | 0.0114289i | ||||||||
\(825\) | −10.9983 | − | 16.3539i | −0.382911 | − | 0.569368i | ||||
\(826\) | 11.2032 | 0.389808 | ||||||||
\(827\) | 31.0384 | + | 31.0384i | 1.07931 | + | 1.07931i | 0.996571 | + | 0.0827407i | \(0.0263673\pi\) |
0.0827407 | + | 0.996571i | \(0.473633\pi\) | |||||||
\(828\) | 0.537022 | + | 0.537022i | 0.0186628 | + | 0.0186628i | ||||
\(829\) | −46.7381 | −1.62328 | −0.811641 | − | 0.584156i | \(-0.801426\pi\) | ||||
−0.811641 | + | 0.584156i | \(0.801426\pi\) | |||||||
\(830\) | −16.2243 | + | 13.3556i | −0.563152 | + | 0.463580i | ||||
\(831\) | 20.5465i | 0.712749i | ||||||||
\(832\) | −4.03748 | − | 4.03748i | −0.139974 | − | 0.139974i | ||||
\(833\) | 63.2231 | + | 63.2231i | 2.19055 | + | 2.19055i | ||||
\(834\) | 8.61936i | 0.298464i | ||||||||
\(835\) | −3.84758 | + | 39.6741i | −0.133151 | + | 1.37298i | ||||
\(836\) | 10.2545 | − | 13.7854i | 0.354658 | − | 0.476779i | ||||
\(837\) | −4.95054 | + | 4.95054i | −0.171116 | + | 0.171116i | ||||
\(838\) | −1.25568 | + | 1.25568i | −0.0433769 | + | 0.0433769i | ||||
\(839\) | 0.139898 | 0.00482982 | 0.00241491 | − | 0.999997i | \(-0.499231\pi\) | ||||
0.00241491 | + | 0.999997i | \(0.499231\pi\) | |||||||
\(840\) | 1.03924 | − | 10.7160i | 0.0358571 | − | 0.369739i | ||||
\(841\) | 10.4956 | 0.361916 | ||||||||
\(842\) | 12.9161 | − | 12.9161i | 0.445119 | − | 0.445119i | ||||
\(843\) | −8.71974 | − | 8.71974i | −0.300324 | − | 0.300324i | ||||
\(844\) | −16.4846 | −0.567423 | ||||||||
\(845\) | 33.8412 | − | 27.8577i | 1.16417 | − | 0.958332i | ||||
\(846\) | 2.89652i | 0.0995843i | ||||||||
\(847\) | 15.4448 | − | 15.4448i | 0.530690 | − | 0.530690i | ||||
\(848\) | 4.39576 | − | 4.39576i | 0.150951 | − | 0.150951i | ||||
\(849\) | 9.70157 | 0.332957 | ||||||||
\(850\) | 5.30829 | − | 27.1106i | 0.182073 | − | 0.929887i | ||||
\(851\) | 1.13411i | 0.0388769i | ||||||||
\(852\) | −6.80922 | + | 6.80922i | −0.233280 | + | 0.233280i | ||||
\(853\) | 6.40830 | + | 6.40830i | 0.219416 | + | 0.219416i | 0.808252 | − | 0.588836i | \(-0.200414\pi\) |
−0.588836 | + | 0.808252i | \(0.700414\pi\) | |||||||
\(854\) | −44.8908 | −1.53613 | ||||||||
\(855\) | −9.73502 | + | 0.478953i | −0.332931 | + | 0.0163799i | ||||
\(856\) | −16.7192 | −0.571449 | ||||||||
\(857\) | 27.2039 | + | 27.2039i | 0.929268 | + | 0.929268i | 0.997659 | − | 0.0683904i | \(-0.0217863\pi\) |
−0.0683904 | + | 0.997659i | \(0.521786\pi\) | |||||||
\(858\) | −15.9142 | + | 15.9142i | −0.543303 | + | 0.543303i | ||||
\(859\) | 41.5961i | 1.41924i | 0.704585 | + | 0.709620i | \(0.251133\pi\) | ||||
−0.704585 | + | 0.709620i | \(0.748867\pi\) | |||||||
\(860\) | 17.9438 | + | 1.74018i | 0.611878 | + | 0.0593398i | ||||
\(861\) | 14.6229 | 0.498346 | ||||||||
\(862\) | 16.3824 | − | 16.3824i | 0.557988 | − | 0.557988i | ||||
\(863\) | −33.1532 | + | 33.1532i | −1.12855 | + | 1.12855i | −0.138134 | + | 0.990414i | \(0.544110\pi\) |
−0.990414 | + | 0.138134i | \(0.955890\pi\) | |||||||
\(864\) | − | 1.00000i | − | 0.0340207i | ||||||
\(865\) | 34.1911 | + | 3.31585i | 1.16253 | + | 0.112742i | ||||
\(866\) | −24.1972 | −0.822256 | ||||||||
\(867\) | 9.56473 | + | 9.56473i | 0.324835 | + | 0.324835i | ||||
\(868\) | −23.8361 | + | 23.8361i | −0.809049 | + | 0.809049i | ||||
\(869\) | −3.90728 | −0.132545 | ||||||||
\(870\) | 8.93118 | + | 10.8495i | 0.302795 | + | 0.367833i | ||||
\(871\) | 59.4186 | 2.01332 | ||||||||
\(872\) | 8.11578 | − | 8.11578i | 0.274835 | − | 0.274835i | ||||
\(873\) | −7.11482 | + | 7.11482i | −0.240800 | + | 0.240800i | ||||
\(874\) | 1.97580 | − | 2.65614i | 0.0668326 | − | 0.0898454i | ||||
\(875\) | −15.3949 | + | 51.5833i | −0.520443 | + | 1.74383i | ||||
\(876\) | − | 6.33296i | − | 0.213971i | ||||||
\(877\) | 9.83547 | + | 9.83547i | 0.332120 | + | 0.332120i | 0.853391 | − | 0.521271i | \(-0.174542\pi\) |
−0.521271 | + | 0.853391i | \(0.674542\pi\) | |||||||
\(878\) | −9.64302 | − | 9.64302i | −0.325436 | − | 0.325436i | ||||
\(879\) | − | 26.4466i | − | 0.892022i | ||||||
\(880\) | −5.60158 | − | 6.80474i | −0.188829 | − | 0.229388i | ||||
\(881\) | 36.2626 | 1.22172 | 0.610859 | − | 0.791739i | \(-0.290824\pi\) | ||||
0.610859 | + | 0.791739i | \(0.290824\pi\) | |||||||
\(882\) | −11.4429 | − | 11.4429i | −0.385303 | − | 0.385303i | ||||
\(883\) | −12.5406 | − | 12.5406i | −0.422026 | − | 0.422026i | 0.463875 | − | 0.885901i | \(-0.346459\pi\) |
−0.885901 | + | 0.463875i | \(0.846459\pi\) | |||||||
\(884\) | −31.5474 | −1.06105 | ||||||||
\(885\) | −5.17858 | − | 0.502217i | −0.174076 | − | 0.0168818i | ||||
\(886\) | − | 0.128052i | − | 0.00430198i | ||||||
\(887\) | −27.4178 | − | 27.4178i | −0.920598 | − | 0.920598i | 0.0764734 | − | 0.997072i | \(-0.475634\pi\) |
−0.997072 | + | 0.0764734i | \(0.975634\pi\) | |||||||
\(888\) | 1.05593 | − | 1.05593i | 0.0354346 | − | 0.0354346i | ||||
\(889\) | 13.7278 | 0.460415 | ||||||||
\(890\) | 1.53083 | − | 15.7851i | 0.0513136 | − | 0.529117i | ||||
\(891\) | −3.94163 | −0.132050 | ||||||||
\(892\) | 4.91506 | + | 4.91506i | 0.164568 | + | 0.164568i | ||||
\(893\) | 12.4916 | − | 1.83476i | 0.418016 | − | 0.0613979i | ||||
\(894\) | 4.87509i | 0.163047i | ||||||||
\(895\) | 17.7020 | + | 21.5042i | 0.591713 | + | 0.718806i | ||||
\(896\) | − | 4.81484i | − | 0.160853i | ||||||
\(897\) | −3.06631 | + | 3.06631i | −0.102381 | + | 0.102381i | ||||
\(898\) | −0.957066 | − | 0.957066i | −0.0319377 | − | 0.0319377i | ||||
\(899\) | − | 43.9989i | − | 1.46744i | ||||||
\(900\) | −0.960761 | + | 4.90683i | −0.0320254 | + | 0.163561i | ||||
\(901\) | − | 34.3469i | − | 1.14426i | ||||||
\(902\) | 8.46469 | − | 8.46469i | 0.281843 | − | 0.281843i | ||||
\(903\) | 27.4492 | − | 27.4492i | 0.913451 | − | 0.913451i | ||||
\(904\) | 15.9796i | 0.531472i | ||||||||
\(905\) | 19.9877 | − | 16.4536i | 0.664413 | − | 0.546937i | ||||
\(906\) | 10.0048i | 0.332386i | ||||||||
\(907\) | 24.2538 | + | 24.2538i | 0.805333 | + | 0.805333i | 0.983924 | − | 0.178590i | \(-0.0571537\pi\) |
−0.178590 | + | 0.983924i | \(0.557154\pi\) | |||||||
\(908\) | 13.9125 | − | 13.9125i | 0.461704 | − | 0.461704i | ||||
\(909\) | 8.97139i | 0.297562i | ||||||||
\(910\) | 61.1870 | + | 5.93390i | 2.02833 | + | 0.196707i | ||||
\(911\) | − | 22.2288i | − | 0.736474i | −0.929732 | − | 0.368237i | \(-0.879961\pi\) | ||
0.929732 | − | 0.368237i | \(-0.120039\pi\) | |||||||
\(912\) | −4.31263 | + | 0.633437i | −0.142805 | + | 0.0209752i | ||||
\(913\) | 26.1933 | + | 26.1933i | 0.866871 | + | 0.866871i | ||||
\(914\) | 16.1830 | 0.535286 | ||||||||
\(915\) | 20.7504 | + | 2.01237i | 0.685988 | + | 0.0665269i | ||||
\(916\) | −16.4303 | −0.542872 | ||||||||
\(917\) | −36.2958 | + | 36.2958i | −1.19859 | + | 1.19859i | ||||
\(918\) | −3.90683 | − | 3.90683i | −0.128944 | − | 0.128944i | ||||
\(919\) | − | 17.3806i | − | 0.573334i | −0.958030 | − | 0.286667i | \(-0.907453\pi\) | ||
0.958030 | − | 0.286667i | \(-0.0925474\pi\) | |||||||
\(920\) | −1.07930 | − | 1.31112i | −0.0355834 | − | 0.0432264i | ||||
\(921\) | −17.2457 | −0.568266 | ||||||||
\(922\) | −22.9816 | − | 22.9816i | −0.756859 | − | 0.756859i | ||||
\(923\) | −38.8796 | − | 38.8796i | −1.27974 | − | 1.27974i | ||||
\(924\) | −18.9783 | −0.624341 | ||||||||
\(925\) | −6.19575 | + | 4.16676i | −0.203715 | + | 0.137002i | ||||
\(926\) | 14.4986i | 0.476455i | ||||||||
\(927\) | −0.231982 | − | 0.231982i | −0.00761928 | − | 0.00761928i | ||||
\(928\) | 4.44385 | + | 4.44385i | 0.145876 | + | 0.145876i | ||||
\(929\) | 54.5348i | 1.78923i | 0.446840 | + | 0.894614i | \(0.352549\pi\) | ||||
−0.446840 | + | 0.894614i | \(0.647451\pi\) | |||||||
\(930\) | 12.0866 | − | 9.94952i | 0.396334 | − | 0.326258i | ||||
\(931\) | −42.1006 | + | 56.5974i | −1.37979 | + | 1.85490i | ||||
\(932\) | −0.870707 | + | 0.870707i | −0.0285210 | + | 0.0285210i | ||||
\(933\) | 2.22739 | − | 2.22739i | 0.0729215 | − | 0.0729215i | ||||
\(934\) | −17.7770 | −0.581682 | ||||||||
\(935\) | −48.4693 | − | 4.70054i | −1.58512 | − | 0.153724i | ||||
\(936\) | 5.70985 | 0.186632 | ||||||||
\(937\) | 8.93268 | − | 8.93268i | 0.291818 | − | 0.291818i | −0.545980 | − | 0.837798i | \(-0.683843\pi\) |
0.837798 | + | 0.545980i | \(0.183843\pi\) | |||||||
\(938\) | 35.4295 | + | 35.4295i | 1.15681 | + | 1.15681i | ||||
\(939\) | 0.497217 | 0.0162261 | ||||||||
\(940\) | 0.625186 | − | 6.44657i | 0.0203913 | − | 0.210264i | ||||
\(941\) | 49.0347i | 1.59849i | 0.601008 | + | 0.799243i | \(0.294766\pi\) | ||||
−0.601008 | + | 0.799243i | \(0.705234\pi\) | |||||||
\(942\) | 7.71934 | − | 7.71934i | 0.251510 | − | 0.251510i | ||||
\(943\) | 1.63096 | − | 1.63096i | 0.0531112 | − | 0.0531112i | ||||
\(944\) | −2.32680 | −0.0757308 | ||||||||
\(945\) | 6.84253 | + | 8.31224i | 0.222588 | + | 0.270397i | ||||
\(946\) | − | 31.7788i | − | 1.03322i | ||||||
\(947\) | 6.55014 | − | 6.55014i | 0.212851 | − | 0.212851i | −0.592626 | − | 0.805477i | \(-0.701909\pi\) |
0.805477 | + | 0.592626i | \(0.201909\pi\) | |||||||
\(948\) | 0.700945 | + | 0.700945i | 0.0227656 | + | 0.0227656i | ||||
\(949\) | 36.1603 | 1.17381 | ||||||||
\(950\) | 21.7699 | + | 1.03524i | 0.706309 | + | 0.0335877i | ||||
\(951\) | 9.17921 | 0.297656 | ||||||||
\(952\) | −18.8108 | − | 18.8108i | −0.609660 | − | 0.609660i | ||||
\(953\) | 4.38061 | − | 4.38061i | 0.141902 | − | 0.141902i | −0.632587 | − | 0.774489i | \(-0.718007\pi\) |
0.774489 | + | 0.632587i | \(0.218007\pi\) | |||||||
\(954\) | 6.21654i | 0.201268i | ||||||||
\(955\) | 10.7908 | + | 13.1086i | 0.349183 | + | 0.424184i | ||||
\(956\) | 8.48625 | 0.274465 | ||||||||
\(957\) | 17.5160 | − | 17.5160i | 0.566212 | − | 0.566212i | ||||
\(958\) | 24.6216 | − | 24.6216i | 0.795488 | − | 0.795488i | ||||
\(959\) | − | 7.07640i | − | 0.228509i | ||||||
\(960\) | −0.215841 | + | 2.22563i | −0.00696623 | + | 0.0718318i | ||||
\(961\) | −18.0157 | −0.581150 | ||||||||
\(962\) | 6.02920 | + | 6.02920i | 0.194389 | + | 0.194389i | ||||
\(963\) | 11.8222 | − | 11.8222i | 0.380966 | − | 0.380966i | ||||
\(964\) | 2.53645 | 0.0816937 | ||||||||
\(965\) | 30.2648 | + | 2.93507i | 0.974258 | + | 0.0944833i | ||||
\(966\) | −3.65670 | −0.117652 | ||||||||
\(967\) | 22.3225 | − | 22.3225i | 0.717843 | − | 0.717843i | −0.250320 | − | 0.968163i | \(-0.580536\pi\) |
0.968163 | + | 0.250320i | \(0.0805358\pi\) | |||||||
\(968\) | −3.20775 | + | 3.20775i | −0.103101 | + | 0.103101i | ||||
\(969\) | −14.3740 | + | 19.3234i | −0.461758 | + | 0.620757i | ||||
\(970\) | 17.3706 | − | 14.2993i | 0.557737 | − | 0.459122i | ||||
\(971\) | 19.2624i | 0.618159i | 0.951036 | + | 0.309079i | \(0.100021\pi\) | ||||
−0.951036 | + | 0.309079i | \(0.899979\pi\) | |||||||
\(972\) | 0.707107 | + | 0.707107i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | −29.3455 | − | 29.3455i | −0.940775 | − | 0.940775i | ||||
\(974\) | − | 27.0747i | − | 0.867529i | ||||||
\(975\) | −28.0173 | − | 5.48581i | −0.897270 | − | 0.175686i | ||||
\(976\) | 9.32341 | 0.298435 | ||||||||
\(977\) | −36.7340 | − | 36.7340i | −1.17523 | − | 1.17523i | −0.980946 | − | 0.194280i | \(-0.937763\pi\) |
−0.194280 | − | 0.980946i | \(-0.562237\pi\) | |||||||
\(978\) | 2.46610 | + | 2.46610i | 0.0788571 | + | 0.0788571i | ||||
\(979\) | −27.9557 | −0.893468 | ||||||||
\(980\) | 22.9978 | + | 27.9375i | 0.734638 | + | 0.892430i | ||||
\(981\) | 11.4774i | 0.366446i | ||||||||
\(982\) | −3.61029 | − | 3.61029i | −0.115209 | − | 0.115209i | ||||
\(983\) | −34.6585 | + | 34.6585i | −1.10543 | + | 1.10543i | −0.111692 | + | 0.993743i | \(0.535627\pi\) |
−0.993743 | + | 0.111692i | \(0.964373\pi\) | |||||||
\(984\) | −3.03704 | −0.0968173 | ||||||||
\(985\) | −30.4103 | − | 2.94918i | −0.968954 | − | 0.0939688i | ||||
\(986\) | 34.7227 | 1.10580 | ||||||||
\(987\) | −9.86151 | − | 9.86151i | −0.313895 | − | 0.313895i | ||||
\(988\) | −3.61683 | − | 24.6245i | −0.115067 | − | 0.783409i | ||||
\(989\) | − | 6.12306i | − | 0.194702i | ||||||
\(990\) | 8.77260 | + | 0.850764i | 0.278811 | + | 0.0270391i | ||||
\(991\) | 8.29436i | 0.263479i | 0.991284 | + | 0.131740i | \(0.0420562\pi\) | ||||
−0.991284 | + | 0.131740i | \(0.957944\pi\) | |||||||
\(992\) | 4.95054 | − | 4.95054i | 0.157180 | − | 0.157180i | ||||
\(993\) | 19.1166 | + | 19.1166i | 0.606648 | + | 0.606648i | ||||
\(994\) | − | 46.3654i | − | 1.47062i | ||||||
\(995\) | −40.7698 | + | 33.5612i | −1.29249 | + | 1.06396i | ||||
\(996\) | − | 9.39786i | − | 0.297783i | ||||||
\(997\) | −41.2771 | + | 41.2771i | −1.30726 | + | 1.30726i | −0.383873 | + | 0.923386i | \(0.625410\pi\) |
−0.923386 | + | 0.383873i | \(0.874590\pi\) | |||||||
\(998\) | −10.1637 | + | 10.1637i | −0.321725 | + | 0.321725i | ||||
\(999\) | 1.49331i | 0.0472462i |
(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 | 570.2.m.b.493.9 | yes | 20 | |
3.2 | odd | 2 | 1710.2.p.c.1063.2 | 20 | |||
5.2 | odd | 4 | inner | 570.2.m.b.37.4 | ✓ | 20 | |
15.2 | even | 4 | 1710.2.p.c.37.7 | 20 | |||
19.18 | odd | 2 | inner | 570.2.m.b.493.4 | yes | 20 | |
57.56 | even | 2 | 1710.2.p.c.1063.7 | 20 | |||
95.37 | even | 4 | inner | 570.2.m.b.37.9 | yes | 20 | |
285.227 | odd | 4 | 1710.2.p.c.37.2 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.m.b.37.4 | ✓ | 20 | 5.2 | odd | 4 | inner | |
570.2.m.b.37.9 | yes | 20 | 95.37 | even | 4 | inner | |
570.2.m.b.493.4 | yes | 20 | 19.18 | odd | 2 | inner | |
570.2.m.b.493.9 | yes | 20 | 1.1 | even | 1 | trivial | |
1710.2.p.c.37.2 | 20 | 285.227 | odd | 4 | |||
1710.2.p.c.37.7 | 20 | 15.2 | even | 4 | |||
1710.2.p.c.1063.2 | 20 | 3.2 | odd | 2 | |||
1710.2.p.c.1063.7 | 20 | 57.56 | even | 2 |