Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,2,Mod(449,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1792.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.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: | \(14.3091920422\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} - 180 x^{7} + 358 x^{6} - 336 x^{5} + 390 x^{4} - 344 x^{3} + 164 x^{2} - 40 x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1345.7 | ||
Root | \(-0.709944 - 0.925217i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.1345 |
Dual form | 1792.2.m.h.449.7 |
$q$-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 \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | 0 | ||||||||
\(3\) | 2.04137 | + | 2.04137i | 1.17858 | + | 1.17858i | 0.980105 | + | 0.198478i | \(0.0635997\pi\) |
0.198478 | + | 0.980105i | \(0.436400\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.701647 | + | 0.701647i | −0.313786 | + | 0.313786i | −0.846375 | − | 0.532588i | \(-0.821219\pi\) |
0.532588 | + | 0.846375i | \(0.321219\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.33435i | 1.77812i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.41989 | + | 2.41989i | −0.729624 | + | 0.729624i | −0.970545 | − | 0.240921i | \(-0.922551\pi\) |
0.240921 | + | 0.970545i | \(0.422551\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.96098 | − | 1.96098i | −0.543879 | − | 0.543879i | 0.380784 | − | 0.924664i | \(-0.375654\pi\) |
−0.924664 | + | 0.380784i | \(0.875654\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.86464 | −0.739646 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.93050 | −1.68089 | −0.840447 | − | 0.541894i | \(-0.817707\pi\) | ||||
−0.840447 | + | 0.541894i | \(0.817707\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.38948 | + | 1.38948i | 0.318770 | + | 0.318770i | 0.848294 | − | 0.529525i | \(-0.177630\pi\) |
−0.529525 | + | 0.848294i | \(0.677630\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.04137 | − | 2.04137i | 0.445463 | − | 0.445463i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.05612i | − | 0.428730i | −0.976754 | − | 0.214365i | \(-0.931232\pi\) | ||
0.976754 | − | 0.214365i | \(-0.0687682\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.01538i | 0.803076i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.76526 | + | 4.76526i | −0.917074 | + | 0.917074i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.34414 | + | 5.34414i | 0.992381 | + | 0.992381i | 0.999971 | − | 0.00758978i | \(-0.00241593\pi\) |
−0.00758978 | + | 0.999971i | \(0.502416\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.23708 | −0.940607 | −0.470304 | − | 0.882505i | \(-0.655856\pi\) | ||||
−0.470304 | + | 0.882505i | \(0.655856\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9.87975 | −1.71984 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.701647 | + | 0.701647i | 0.118600 | + | 0.118600i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.58401 | + | 6.58401i | −1.08240 | + | 1.08240i | −0.0861191 | + | 0.996285i | \(0.527447\pi\) |
−0.996285 | + | 0.0861191i | \(0.972553\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 8.00617i | − | 1.28201i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.949797i | 0.148333i | 0.997246 | + | 0.0741667i | \(0.0236297\pi\) | ||||
−0.997246 | + | 0.0741667i | \(0.976370\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.95343 | + | 5.95343i | −0.907889 | + | 0.907889i | −0.996102 | − | 0.0882122i | \(-0.971885\pi\) |
0.0882122 | + | 0.996102i | \(0.471885\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.74283 | − | 3.74283i | −0.557948 | − | 0.557948i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.64785 | −0.677959 | −0.338980 | − | 0.940794i | \(-0.610082\pi\) | ||||
−0.338980 | + | 0.940794i | \(0.610082\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −14.1477 | − | 14.1477i | −1.98107 | − | 1.98107i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.24791 | − | 7.24791i | 0.995577 | − | 0.995577i | −0.00441361 | − | 0.999990i | \(-0.501405\pi\) |
0.999990 | + | 0.00441361i | \(0.00140490\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.39582i | − | 0.457892i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.67289i | 0.751393i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.58048 | − | 8.58048i | 1.11708 | − | 1.11708i | 0.124916 | − | 0.992167i | \(-0.460134\pi\) |
0.992167 | − | 0.124916i | \(-0.0398661\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.81502 | + | 2.81502i | 0.360427 | + | 0.360427i | 0.863970 | − | 0.503543i | \(-0.167970\pi\) |
−0.503543 | + | 0.863970i | \(0.667970\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.33435 | 0.672065 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.75184 | 0.341324 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.07198 | + | 9.07198i | 1.10832 | + | 1.10832i | 0.993372 | + | 0.114947i | \(0.0366699\pi\) |
0.114947 | + | 0.993372i | \(0.463330\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.19729 | − | 4.19729i | 0.505294 | − | 0.505294i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.60510i | − | 0.427847i | −0.976850 | − | 0.213923i | \(-0.931376\pi\) | ||
0.976850 | − | 0.213923i | \(-0.0686243\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.53179i | 0.764488i | 0.924061 | + | 0.382244i | \(0.124849\pi\) | ||||
−0.924061 | + | 0.382244i | \(0.875151\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.19686 | + | 8.19686i | −0.946492 | + | 0.946492i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.41989 | + | 2.41989i | 0.275772 | + | 0.275772i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.7819 | −1.55059 | −0.775293 | − | 0.631602i | \(-0.782398\pi\) | ||||
−0.775293 | + | 0.631602i | \(0.782398\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.45223 | −0.383581 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.49372 | − | 4.49372i | −0.493250 | − | 0.493250i | 0.416079 | − | 0.909329i | \(-0.363404\pi\) |
−0.909329 | + | 0.416079i | \(0.863404\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.86277 | − | 4.86277i | 0.527441 | − | 0.527441i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 21.8187i | 2.33921i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.428825i | 0.0454554i | 0.999742 | + | 0.0227277i | \(0.00723508\pi\) | ||||
−0.999742 | + | 0.0227277i | \(0.992765\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.96098 | + | 1.96098i | −0.205567 | + | 0.205567i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.6908 | − | 10.6908i | −1.10858 | − | 1.10858i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.94986 | −0.200051 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.6339 | 1.48584 | 0.742922 | − | 0.669378i | \(-0.233439\pi\) | ||||
0.742922 | + | 0.669378i | \(0.233439\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.9085 | − | 12.9085i | −1.29736 | − | 1.29736i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.2007 | − | 11.2007i | 1.11451 | − | 1.11451i | 0.121978 | − | 0.992533i | \(-0.461076\pi\) |
0.992533 | − | 0.121978i | \(-0.0389237\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.4673i | 1.81964i | 0.415005 | + | 0.909819i | \(0.363780\pi\) | ||||
−0.415005 | + | 0.909819i | \(0.636220\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.86464i | 0.279560i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.146171 | + | 0.146171i | −0.0141309 | + | 0.0141309i | −0.714137 | − | 0.700006i | \(-0.753181\pi\) |
0.700006 | + | 0.714137i | \(0.253181\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.309414 | − | 0.309414i | −0.0296365 | − | 0.0296365i | 0.692133 | − | 0.721770i | \(-0.256671\pi\) |
−0.721770 | + | 0.692133i | \(0.756671\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −26.8807 | −2.55141 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.7193 | 1.57282 | 0.786409 | − | 0.617706i | \(-0.211938\pi\) | ||||
0.786409 | + | 0.617706i | \(0.211938\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.44267 | + | 1.44267i | 0.134530 | + | 0.134530i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.4606 | − | 10.4606i | 0.967081 | − | 0.967081i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.93050i | 0.635318i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 0.711717i | − | 0.0647016i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.93888 | + | 1.93888i | −0.174823 | + | 0.174823i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.32562 | − | 6.32562i | −0.565781 | − | 0.565781i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.91639 | 0.436259 | 0.218130 | − | 0.975920i | \(-0.430004\pi\) | ||||
0.218130 | + | 0.975920i | \(0.430004\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −24.3063 | −2.14005 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.10403 | + | 1.10403i | 0.0964592 | + | 0.0964592i | 0.753690 | − | 0.657230i | \(-0.228272\pi\) |
−0.657230 | + | 0.753690i | \(0.728272\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.38948 | − | 1.38948i | 0.120484 | − | 0.120484i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 6.68706i | − | 0.575531i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 0.184924i | − | 0.0157991i | −0.999969 | − | 0.00789957i | \(-0.997485\pi\) | ||
0.999969 | − | 0.00789957i | \(-0.00251454\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.08707 | − | 4.08707i | 0.346661 | − | 0.346661i | −0.512203 | − | 0.858864i | \(-0.671171\pi\) |
0.858864 | + | 0.512203i | \(0.171171\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.48797 | − | 9.48797i | −0.799031 | − | 0.799031i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.49073 | 0.793654 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.49940 | −0.622791 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.04137 | − | 2.04137i | −0.168369 | − | 0.168369i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.37041 | + | 5.37041i | −0.439961 | + | 0.439961i | −0.891999 | − | 0.452038i | \(-0.850697\pi\) |
0.452038 | + | 0.891999i | \(0.350697\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.4266i | 0.929880i | 0.885342 | + | 0.464940i | \(0.153924\pi\) | ||||
−0.885342 | + | 0.464940i | \(0.846076\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 36.9697i | − | 2.98882i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.67458 | − | 3.67458i | 0.295150 | − | 0.295150i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.41825 | + | 9.41825i | 0.751658 | + | 0.751658i | 0.974789 | − | 0.223131i | \(-0.0716276\pi\) |
−0.223131 | + | 0.974789i | \(0.571628\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 29.5913 | 2.34674 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.05612 | −0.162045 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.4770 | − | 12.4770i | −0.977270 | − | 0.977270i | 0.0224770 | − | 0.999747i | \(-0.492845\pi\) |
−0.999747 | + | 0.0224770i | \(0.992845\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.93210 | − | 6.93210i | 0.539664 | − | 0.539664i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 16.0783i | − | 1.24418i | −0.782947 | − | 0.622088i | \(-0.786284\pi\) | ||
0.782947 | − | 0.622088i | \(-0.213716\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 5.30908i | − | 0.408391i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.41200 | + | 7.41200i | −0.566809 | + | 0.566809i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.4256 | + | 14.4256i | 1.09676 | + | 1.09676i | 0.994787 | + | 0.101973i | \(0.0325154\pi\) |
0.101973 | + | 0.994787i | \(0.467485\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.01538 | 0.303534 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 35.0318 | 2.63315 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.32674 | − | 3.32674i | −0.248652 | − | 0.248652i | 0.571765 | − | 0.820417i | \(-0.306259\pi\) |
−0.820417 | + | 0.571765i | \(0.806259\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.2899 | − | 10.2899i | 0.764846 | − | 0.764846i | −0.212348 | − | 0.977194i | \(-0.568111\pi\) |
0.977194 | + | 0.212348i | \(0.0681112\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.4930i | 0.849586i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 9.23930i | − | 0.679287i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.7710 | − | 16.7710i | 1.22642 | − | 1.22642i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.76526 | + | 4.76526i | 0.346622 | + | 0.346622i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −26.6094 | −1.92539 | −0.962693 | − | 0.270595i | \(-0.912780\pi\) | ||||
−0.962693 | + | 0.270595i | \(0.912780\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −25.2624 | −1.81843 | −0.909215 | − | 0.416327i | \(-0.863317\pi\) | ||||
−0.909215 | + | 0.416327i | \(0.863317\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.61751 | + | 5.61751i | 0.402278 | + | 0.402278i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.96551 | + | 6.96551i | −0.496272 | + | 0.496272i | −0.910275 | − | 0.414003i | \(-0.864130\pi\) |
0.414003 | + | 0.910275i | \(0.364130\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 15.2541i | − | 1.08133i | −0.841238 | − | 0.540666i | \(-0.818172\pi\) | ||
0.841238 | − | 0.540666i | \(-0.181828\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 37.0385i | 2.61249i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.34414 | − | 5.34414i | 0.375085 | − | 0.375085i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.666423 | − | 0.666423i | −0.0465450 | − | 0.0465450i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.9680 | 0.762332 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.72480 | −0.465164 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.46973 | − | 2.46973i | −0.170023 | − | 0.170023i | 0.616966 | − | 0.786990i | \(-0.288361\pi\) |
−0.786990 | + | 0.616966i | \(0.788361\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.35933 | − | 7.35933i | 0.504253 | − | 0.504253i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 8.35442i | − | 0.569767i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.23708i | 0.355516i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.3338 | + | 13.3338i | −0.901013 | + | 0.901013i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.5906 | + | 13.5906i | 0.914203 | + | 0.914203i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.2245 | −0.818610 | −0.409305 | − | 0.912398i | \(-0.634229\pi\) | ||||
−0.409305 | + | 0.912398i | \(0.634229\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −21.4194 | −1.42796 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.6687 | + | 10.6687i | 0.708107 | + | 0.708107i | 0.966137 | − | 0.258030i | \(-0.0830733\pi\) |
−0.258030 | + | 0.966137i | \(0.583073\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.75289 | + | 6.75289i | −0.446244 | + | 0.446244i | −0.894104 | − | 0.447860i | \(-0.852186\pi\) |
0.447860 | + | 0.894104i | \(0.352186\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.87975i | 0.650040i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.42241i | 0.486258i | 0.969994 | + | 0.243129i | \(0.0781739\pi\) | ||||
−0.969994 | + | 0.243129i | \(0.921826\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.26115 | − | 3.26115i | 0.212734 | − | 0.212734i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −28.1339 | − | 28.1339i | −1.82749 | − | 1.82749i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.44262 | −0.222685 | −0.111342 | − | 0.993782i | \(-0.535515\pi\) | ||||
−0.111342 | + | 0.993782i | \(0.535515\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.0386 | 1.48404 | 0.742022 | − | 0.670376i | \(-0.233867\pi\) | ||||
0.742022 | + | 0.670376i | \(0.233867\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.24852 | + | 7.24852i | 0.464993 | + | 0.464993i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.701647 | − | 0.701647i | 0.0448266 | − | 0.0448266i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 5.44952i | − | 0.346744i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 18.3466i | − | 1.16267i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0833 | − | 12.0833i | 0.762690 | − | 0.762690i | −0.214118 | − | 0.976808i | \(-0.568688\pi\) |
0.976808 | + | 0.214118i | \(0.0686876\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.97557 | + | 4.97557i | 0.312812 | + | 0.312812i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 19.8534 | 1.24327 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.15842 | 0.134638 | 0.0673191 | − | 0.997731i | \(-0.478555\pi\) | ||||
0.0673191 | + | 0.997731i | \(0.478555\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.58401 | + | 6.58401i | 0.409110 | + | 0.409110i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −28.5075 | + | 28.5075i | −1.76457 | + | 1.76457i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.124319i | 0.00766581i | 0.999993 | + | 0.00383290i | \(0.00122005\pi\) | ||||
−0.999993 | + | 0.00383290i | \(0.998780\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.1710i | 0.624797i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.875390 | + | 0.875390i | −0.0535730 | + | 0.0535730i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.93651 | + | 7.93651i | 0.483897 | + | 0.483897i | 0.906374 | − | 0.422476i | \(-0.138839\pi\) |
−0.422476 | + | 0.906374i | \(0.638839\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.326600 | −0.0198395 | −0.00991976 | − | 0.999951i | \(-0.503158\pi\) | ||||
−0.00991976 | + | 0.999951i | \(0.503158\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.00617 | −0.484556 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.71677 | − | 9.71677i | −0.585944 | − | 0.585944i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.9992 | + | 14.9992i | −0.901214 | + | 0.901214i | −0.995541 | − | 0.0943269i | \(-0.969930\pi\) |
0.0943269 | + | 0.995541i | \(0.469930\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 27.9364i | − | 1.67251i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.8495i | 1.66136i | 0.556750 | + | 0.830680i | \(0.312048\pi\) | ||||
−0.556750 | + | 0.830680i | \(0.687952\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.4548 | + | 16.4548i | −0.978134 | + | 0.978134i | −0.999766 | − | 0.0216317i | \(-0.993114\pi\) |
0.0216317 | + | 0.999766i | \(0.493114\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.98037 | − | 3.98037i | −0.235777 | − | 0.235777i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.949797 | 0.0560648 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 31.0318 | 1.82540 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 29.8731 | + | 29.8731i | 1.75119 | + | 1.75119i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −20.0525 | + | 20.0525i | −1.17148 | + | 1.17148i | −0.189624 | + | 0.981857i | \(0.560727\pi\) |
−0.981857 | + | 0.189624i | \(0.939273\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.0409i | 0.701051i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 23.0628i | − | 1.33824i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.03201 | + | 4.03201i | −0.233177 | + | 0.233177i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.95343 | + | 5.95343i | 0.343150 | + | 0.343150i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 45.7294 | 2.62709 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.95031 | −0.226194 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.8054 | + | 18.8054i | 1.07328 | + | 1.07328i | 0.997093 | + | 0.0761901i | \(0.0242756\pi\) |
0.0761901 | + | 0.997093i | \(0.475724\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −37.6985 | + | 37.6985i | −2.14460 | + | 2.14460i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 5.25843i | − | 0.298178i | −0.988824 | − | 0.149089i | \(-0.952366\pi\) | ||
0.988824 | − | 0.149089i | \(-0.0476341\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 7.82442i | − | 0.442262i | −0.975244 | − | 0.221131i | \(-0.929025\pi\) | ||
0.975244 | − | 0.221131i | \(-0.0709749\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.74283 | + | 3.74283i | −0.210885 | + | 0.210885i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.0890 | + | 18.0890i | 1.01598 | + | 1.01598i | 0.999870 | + | 0.0161108i | \(0.00512846\pi\) |
0.0161108 | + | 0.999870i | \(0.494872\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −25.8644 | −1.44813 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.596777 | −0.0333089 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.62983 | − | 9.62983i | −0.535818 | − | 0.535818i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.87410 | − | 7.87410i | 0.436777 | − | 0.436777i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 1.26325i | − | 0.0698581i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.64785i | 0.256244i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.702951 | + | 0.702951i | −0.0386377 | + | 0.0386377i | −0.726162 | − | 0.687524i | \(-0.758698\pi\) |
0.687524 | + | 0.726162i | \(0.258698\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −35.1214 | − | 35.1214i | −1.92464 | − | 1.92464i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.7307 | −0.695551 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.4691 | 0.733710 | 0.366855 | − | 0.930278i | \(-0.380434\pi\) | ||||
0.366855 | + | 0.930278i | \(0.380434\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 34.1302 | + | 34.1302i | 1.85370 | + | 1.85370i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.6731 | − | 12.6731i | 0.686289 | − | 0.686289i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.89003i | 0.317109i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.54293 | − | 2.54293i | 0.136512 | − | 0.136512i | −0.635549 | − | 0.772061i | \(-0.719226\pi\) |
0.772061 | + | 0.635549i | \(0.219226\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.81167 | − | 1.81167i | −0.0969765 | − | 0.0969765i | 0.656954 | − | 0.753931i | \(-0.271845\pi\) |
−0.753931 | + | 0.656954i | \(0.771845\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.6892 | 0.997556 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.72060 | −0.251252 | −0.125626 | − | 0.992078i | \(-0.540094\pi\) | ||||
−0.125626 | + | 0.992078i | \(0.540094\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.52951 | + | 2.52951i | 0.134252 | + | 0.134252i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −14.1477 | + | 14.1477i | −0.748775 | + | 0.748775i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 16.9233i | − | 0.893177i | −0.894739 | − | 0.446589i | \(-0.852639\pi\) | ||
0.894739 | − | 0.446589i | \(-0.147361\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 15.1387i | − | 0.796772i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.45287 | − | 1.45287i | 0.0762562 | − | 0.0762562i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.58301 | − | 4.58301i | −0.239886 | − | 0.239886i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.8872 | 1.03810 | 0.519051 | − | 0.854743i | \(-0.326286\pi\) | ||||
0.519051 | + | 0.854743i | \(0.326286\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.06655 | −0.263754 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.24791 | − | 7.24791i | −0.376293 | − | 0.376293i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.84947 | + | 6.84947i | −0.354652 | + | 0.354652i | −0.861837 | − | 0.507185i | \(-0.830686\pi\) |
0.507185 | + | 0.861837i | \(0.330686\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 25.8258i | − | 1.33364i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 20.9595i | − | 1.07947i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.9445 | − | 11.9445i | 0.613548 | − | 0.613548i | −0.330320 | − | 0.943869i | \(-0.607157\pi\) |
0.943869 | + | 0.330320i | \(0.107157\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.0362 | + | 10.0362i | 0.514168 | + | 0.514168i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.7947 | 1.26695 | 0.633476 | − | 0.773763i | \(-0.281628\pi\) | ||||
0.633476 | + | 0.773763i | \(0.281628\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.39582 | −0.173067 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −31.7577 | − | 31.7577i | −1.61433 | − | 1.61433i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.18643 | + | 2.18643i | −0.110857 | + | 0.110857i | −0.760359 | − | 0.649503i | \(-0.774977\pi\) |
0.649503 | + | 0.760359i | \(0.274977\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.2499i | 0.720649i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.50744i | 0.227370i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.67004 | − | 9.67004i | 0.486553 | − | 0.486553i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.272216 | + | 0.272216i | 0.0136621 | + | 0.0136621i | 0.713905 | − | 0.700243i | \(-0.246925\pi\) |
−0.700243 | + | 0.713905i | \(0.746925\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.67289 | 0.284000 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.6370 | −0.730937 | −0.365468 | − | 0.930824i | \(-0.619091\pi\) | ||||
−0.365468 | + | 0.930824i | \(0.619091\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.2698 | + | 10.2698i | 0.511577 | + | 0.511577i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.42225 | − | 2.42225i | 0.120362 | − | 0.120362i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 31.8651i | − | 1.57950i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.20342i | 0.257292i | 0.991691 | + | 0.128646i | \(0.0410632\pi\) | ||||
−0.991691 | + | 0.128646i | \(0.958937\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.377498 | − | 0.377498i | 0.0186206 | − | 0.0186206i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.58048 | − | 8.58048i | −0.422218 | − | 0.422218i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.30601 | 0.309550 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.6864 | 0.817138 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.91249 | + | 9.91249i | 0.484257 | + | 0.484257i | 0.906488 | − | 0.422231i | \(-0.138753\pi\) |
−0.422231 | + | 0.906488i | \(0.638753\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.87543 | − | 5.87543i | 0.286351 | − | 0.286351i | −0.549285 | − | 0.835635i | \(-0.685100\pi\) |
0.835635 | + | 0.549285i | \(0.185100\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 24.7933i | − | 1.20549i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 27.8286i | − | 1.34989i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.81502 | − | 2.81502i | 0.136229 | − | 0.136229i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 19.3740 | + | 19.3740i | 0.935388 | + | 0.935388i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.4777 | −0.890039 | −0.445019 | − | 0.895521i | \(-0.646803\pi\) | ||||
−0.445019 | + | 0.895521i | \(0.646803\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.69984 | 0.418088 | 0.209044 | − | 0.977906i | \(-0.432965\pi\) | ||||
0.209044 | + | 0.977906i | \(0.432965\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −15.3090 | − | 15.3090i | −0.734011 | − | 0.734011i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.85694 | − | 2.85694i | 0.136666 | − | 0.136666i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.08886i | 0.0996959i | 0.998757 | + | 0.0498479i | \(0.0158737\pi\) | ||||
−0.998757 | + | 0.0498479i | \(0.984126\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 5.33435i | − | 0.254017i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.57395 | − | 1.57395i | 0.0747808 | − | 0.0747808i | −0.668727 | − | 0.743508i | \(-0.733161\pi\) |
0.743508 | + | 0.668727i | \(0.233161\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.300884 | − | 0.300884i | −0.0142633 | − | 0.0142633i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −21.9260 | −1.03706 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.6235 | −1.06767 | −0.533835 | − | 0.845589i | \(-0.679250\pi\) | ||||
−0.533835 | + | 0.845589i | \(0.679250\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.29840 | − | 2.29840i | −0.108228 | − | 0.108228i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −23.3258 | + | 23.3258i | −1.09594 | + | 1.09594i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 2.75184i | − | 0.129008i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.9357i | 1.07289i | 0.843937 | + | 0.536443i | \(0.180232\pi\) | ||||
−0.843937 | + | 0.536443i | \(0.819768\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 33.0256 | − | 33.0256i | 1.54150 | − | 1.54150i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.77472 | + | 9.77472i | 0.455254 | + | 0.455254i | 0.897094 | − | 0.441840i | \(-0.145674\pi\) |
−0.441840 | + | 0.897094i | \(0.645674\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.4440 | 1.04306 | 0.521531 | − | 0.853233i | \(-0.325361\pi\) | ||||
0.521531 | + | 0.853233i | \(0.325361\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 15.0023 | 0.695717 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.55804 | + | 1.55804i | 0.0720976 | + | 0.0720976i | 0.742236 | − | 0.670138i | \(-0.233765\pi\) |
−0.670138 | + | 0.742236i | \(0.733765\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.07198 | − | 9.07198i | 0.418905 | − | 0.418905i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 38.4522i | 1.77178i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 28.8133i | − | 1.32484i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.57931 | + | 5.57931i | −0.255996 | + | 0.255996i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 38.6629 | + | 38.6629i | 1.77025 | + | 1.77025i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −36.0952 | −1.64923 | −0.824615 | − | 0.565694i | \(-0.808608\pi\) | ||||
−0.824615 | + | 0.565694i | \(0.808608\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.8223 | 1.17739 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.19729 | − | 4.19729i | −0.190983 | − | 0.190983i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.2678 | + | 10.2678i | −0.466237 | + | 0.466237i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 40.4748i | 1.83409i | 0.398785 | + | 0.917044i | \(0.369432\pi\) | ||||
−0.398785 | + | 0.917044i | \(0.630568\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 50.9400i | − | 2.30359i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.1284 | − | 27.1284i | 1.22429 | − | 1.22429i | 0.258192 | − | 0.966094i | \(-0.416873\pi\) |
0.966094 | − | 0.258192i | \(-0.0831266\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −37.0375 | − | 37.0375i | −1.66809 | − | 1.66809i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 18.1145 | 0.814185 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.60510 | −0.161711 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.38687 | + | 1.38687i | 0.0620847 | + | 0.0620847i | 0.737467 | − | 0.675383i | \(-0.236022\pi\) |
−0.675383 | + | 0.737467i | \(0.736022\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 32.8217 | − | 32.8217i | 1.46637 | − | 1.46637i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 16.6445i | − | 0.742140i | −0.928605 | − | 0.371070i | \(-0.878991\pi\) | ||
0.928605 | − | 0.371070i | \(-0.121009\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.7179i | 0.699436i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.8378 | − | 10.8378i | 0.481322 | − | 0.481322i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.4276 | + | 17.4276i | 0.772463 | + | 0.772463i | 0.978536 | − | 0.206074i | \(-0.0660686\pi\) |
−0.206074 | + | 0.978536i | \(0.566069\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.53179 | 0.288949 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −13.2425 | −0.584671 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.9575 | − | 12.9575i | −0.570978 | − | 0.570978i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.2473 | − | 11.2473i | 0.494655 | − | 0.494655i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 58.8960i | 2.58525i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.69192i | 0.117935i | 0.998260 | + | 0.0589676i | \(0.0187809\pi\) | ||||
−0.998260 | + | 0.0589676i | \(0.981219\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.9962 | + | 10.9962i | −0.480830 | + | 0.480830i | −0.905397 | − | 0.424566i | \(-0.860427\pi\) |
0.424566 | + | 0.905397i | \(0.360427\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.19686 | + | 8.19686i | 0.357740 | + | 0.357740i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 36.2956 | 1.58106 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.7724 | 0.816191 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 45.7713 | + | 45.7713i | 1.98630 | + | 1.98630i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.86254 | − | 1.86254i | 0.0806755 | − | 0.0806755i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 0.205121i | − | 0.00886816i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 13.5822i | − | 0.586115i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.41989 | − | 2.41989i | 0.104232 | − | 0.104232i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.46720 | − | 6.46720i | −0.278047 | − | 0.278047i | 0.554282 | − | 0.832329i | \(-0.312993\pi\) |
−0.832329 | + | 0.554282i | \(0.812993\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 42.0111 | 1.80287 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.434199 | 0.0185990 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.5089 | + | 20.5089i | 0.876896 | + | 0.876896i | 0.993212 | − | 0.116316i | \(-0.0371085\pi\) |
−0.116316 | + | 0.993212i | \(0.537109\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −15.0163 | + | 15.0163i | −0.640881 | + | 0.640881i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.8512i | 0.632682i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.7819i | 0.586066i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 18.8608 | − | 18.8608i | 0.800596 | − | 0.800596i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.0551 | + | 11.0551i | 0.468421 | + | 0.468421i | 0.901403 | − | 0.432981i | \(-0.142538\pi\) |
−0.432981 | + | 0.901403i | \(0.642538\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.3492 | 0.987565 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 68.4716 | 2.89087 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.3790 | − | 15.3790i | −0.648147 | − | 0.648147i | 0.304398 | − | 0.952545i | \(-0.401545\pi\) |
−0.952545 | + | 0.304398i | \(0.901545\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.7310 | + | 11.7310i | −0.493529 | + | 0.493529i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.45223i | 0.144980i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 9.21322i | − | 0.386238i | −0.981175 | − | 0.193119i | \(-0.938140\pi\) | ||
0.981175 | − | 0.193119i | \(-0.0618604\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.3471 | + | 10.3471i | −0.433014 | + | 0.433014i | −0.889653 | − | 0.456638i | \(-0.849053\pi\) |
0.456638 | + | 0.889653i | \(0.349053\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −54.3195 | − | 54.3195i | −2.26923 | − | 2.26923i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.25609 | 0.344303 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.75852 | 0.114839 | 0.0574193 | − | 0.998350i | \(-0.481713\pi\) | ||||
0.0574193 | + | 0.998350i | \(0.481713\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −51.5699 | − | 51.5699i | −2.14317 | − | 2.14317i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.49372 | + | 4.49372i | −0.186431 | + | 0.186431i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 35.0783i | 1.45279i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 14.6793i | 0.606913i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.18689 | − | 4.18689i | 0.172812 | − | 0.172812i | −0.615402 | − | 0.788213i | \(-0.711006\pi\) |
0.788213 | + | 0.615402i | \(0.211006\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.27684 | − | 7.27684i | −0.299837 | − | 0.299837i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −28.4383 | −1.16980 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.11656 | −0.127982 | −0.0639908 | − | 0.997950i | \(-0.520383\pi\) | ||||
−0.0639908 | + | 0.997950i | \(0.520383\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.86277 | − | 4.86277i | −0.199354 | − | 0.199354i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 31.1391 | − | 31.1391i | 1.27444 | − | 1.27444i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 5.12382i | − | 0.209354i | −0.994506 | − | 0.104677i | \(-0.966619\pi\) | ||
0.994506 | − | 0.104677i | \(-0.0333808\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 28.1920i | − | 1.14997i | −0.818162 | − | 0.574987i | \(-0.805007\pi\) | ||
0.818162 | − | 0.574987i | \(-0.194993\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −48.3931 | + | 48.3931i | −1.97072 | + | 1.97072i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.499374 | + | 0.499374i | 0.0203025 | + | 0.0203025i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −40.0403 | −1.62518 | −0.812592 | − | 0.582832i | \(-0.801944\pi\) | ||||
−0.812592 | + | 0.582832i | \(0.801944\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 21.8187 | 0.884137 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.11437 | + | 9.11437i | 0.368728 | + | 0.368728i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.6820 | − | 12.6820i | 0.512222 | − | 0.512222i | −0.402985 | − | 0.915207i | \(-0.632027\pi\) |
0.915207 | + | 0.402985i | \(0.132027\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 2.72083i | − | 0.109714i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 35.2965i | − | 1.42098i | −0.703706 | − | 0.710491i | \(-0.748473\pi\) | ||
0.703706 | − | 0.710491i | \(-0.251527\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.40966 | − | 6.40966i | 0.257626 | − | 0.257626i | −0.566462 | − | 0.824088i | \(-0.691688\pi\) |
0.824088 | + | 0.566462i | \(0.191688\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.79793 | + | 9.79793i | 0.393177 | + | 0.393177i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.428825 | 0.0171805 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.2002 | −0.448008 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −13.7278 | − | 13.7278i | −0.548234 | − | 0.548234i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 45.6305 | − | 45.6305i | 1.81941 | − | 1.81941i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 8.85344i | − | 0.352450i | −0.984350 | − | 0.176225i | \(-0.943611\pi\) | ||
0.984350 | − | 0.176225i | \(-0.0563886\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 10.0832i | − | 0.400773i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.44957 | + | 3.44957i | −0.136892 | + | 0.136892i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.96098 | + | 1.96098i | 0.0776970 | + | 0.0776970i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 19.2309 | 0.760761 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.523959 | −0.0206951 | −0.0103476 | − | 0.999946i | \(-0.503294\pi\) | ||||
−0.0103476 | + | 0.999946i | \(0.503294\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.52914 | + | 7.52914i | 0.296920 | + | 0.296920i | 0.839806 | − | 0.542886i | \(-0.182668\pi\) |
−0.542886 | + | 0.839806i | \(0.682668\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17.0544 | − | 17.0544i | 0.671517 | − | 0.671517i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.9059i | 0.703955i | 0.936009 | + | 0.351977i | \(0.114491\pi\) | ||||
−0.936009 | + | 0.351977i | \(0.885509\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 41.5276i | 1.63010i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.6908 | + | 10.6908i | −0.419005 | + | 0.419005i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.60327 | − | 7.60327i | −0.297539 | − | 0.297539i | 0.542510 | − | 0.840049i | \(-0.317474\pi\) |
−0.840049 | + | 0.542510i | \(0.817474\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.54927 | −0.0605351 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −34.8428 | −1.35935 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.7271 | − | 12.7271i | −0.495776 | − | 0.495776i | 0.414344 | − | 0.910120i | \(-0.364011\pi\) |
−0.910120 | + | 0.414344i | \(0.864011\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.3267 | + | 22.3267i | −0.868410 | + | 0.868410i | −0.992296 | − | 0.123887i | \(-0.960464\pi\) |
0.123887 | + | 0.992296i | \(0.460464\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 55.4868i | 2.15493i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.94986i | 0.0756122i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.9882 | − | 10.9882i | 0.425464 | − | 0.425464i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −24.9546 | − | 24.9546i | −0.964800 | − | 0.964800i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.6241 | −0.525952 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.7030 | −1.14497 | −0.572483 | − | 0.819917i | \(-0.694020\pi\) | ||||
−0.572483 | + | 0.819917i | \(0.694020\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −19.1343 | − | 19.1343i | −0.736481 | − | 0.736481i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.03778 | + | 1.03778i | −0.0398853 | + | 0.0398853i | −0.726768 | − | 0.686883i | \(-0.758979\pi\) |
0.686883 | + | 0.726768i | \(0.258979\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 14.6339i | − | 0.561596i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 43.5575i | 1.66913i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.91035 | + | 5.91035i | −0.226153 | + | 0.226153i | −0.811084 | − | 0.584930i | \(-0.801122\pi\) |
0.584930 | + | 0.811084i | \(0.301122\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.129752 | + | 0.129752i | 0.00495755 | + | 0.00495755i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −27.5702 | −1.05187 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −28.4261 | −1.08295 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.31513 | − | 6.31513i | −0.240239 | − | 0.240239i | 0.576710 | − | 0.816949i | \(-0.304336\pi\) |
−0.816949 | + | 0.576710i | \(0.804336\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12.9085 | + | 12.9085i | −0.490354 | + | 0.490354i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.73537i | 0.217555i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 6.58257i | − | 0.249333i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15.1519 | + | 15.1519i | −0.573096 | + | 0.573096i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.3526 | + | 35.3526i | 1.33525 | + | 1.33525i | 0.900601 | + | 0.434647i | \(0.143127\pi\) |
0.434647 | + | 0.900601i | \(0.356873\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.2968 | −0.690075 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13.3144 | 0.501450 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.2007 | − | 11.2007i | −0.421245 | − | 0.421245i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.6099 | − | 25.6099i | 0.961801 | − | 0.961801i | −0.0374956 | − | 0.999297i | \(-0.511938\pi\) |
0.999297 | + | 0.0374956i | \(0.0119380\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 73.5175i | − | 2.75712i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.7680i | 0.403267i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.65914 | + | 6.65914i | −0.249038 | + | 0.249038i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.02764 | − | 7.02764i | −0.262452 | − | 0.262452i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.8390 | 0.478816 | 0.239408 | − | 0.970919i | \(-0.423047\pi\) | ||||
0.239408 | + | 0.970919i | \(0.423047\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.4673 | 0.687759 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 47.0301 | + | 47.0301i | 1.74907 | + | 1.74907i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −21.4588 | + | 21.4588i | −0.796958 | + | 0.796958i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 50.1537i | − | 1.86010i | −0.367436 | − | 0.930049i | \(-0.619764\pi\) | ||
0.367436 | − | 0.930049i | \(-0.380236\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 39.9504i | 1.47965i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 41.2602 | − | 41.2602i | 1.52607 | − | 1.52607i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.4286 | − | 21.4286i | −0.791485 | − | 0.791485i | 0.190250 | − | 0.981736i | \(-0.439070\pi\) |
−0.981736 | + | 0.190250i | \(0.939070\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.86464 | 0.105664 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −43.9064 | −1.61731 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.36694 | − | 2.36694i | −0.0870693 | − | 0.0870693i | 0.662231 | − | 0.749300i | \(-0.269610\pi\) |
−0.749300 | + | 0.662231i | \(0.769610\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.1245 | − | 11.1245i | 0.408667 | − | 0.408667i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 4.56306i | − | 0.167403i | −0.996491 | − | 0.0837013i | \(-0.973326\pi\) | ||
0.996491 | − | 0.0837013i | \(-0.0266742\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 7.53627i | − | 0.276108i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 23.9711 | − | 23.9711i | 0.877055 | − | 0.877055i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.146171 | + | 0.146171i | 0.00534097 | + | 0.00534097i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.04590 | −0.220618 | −0.110309 | − | 0.993897i | \(-0.535184\pi\) | ||||
−0.110309 | + | 0.993897i | \(0.535184\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 49.3328 | 1.79779 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.01741 | − | 8.01741i | −0.291784 | − | 0.291784i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.0992 | + | 25.0992i | −0.912244 | + | 0.912244i | −0.996449 | − | 0.0842043i | \(-0.973165\pi\) |
0.0842043 | + | 0.996449i | \(0.473165\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.3139i | 0.737349i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 16.2508i | − | 0.589089i | −0.955638 | − | 0.294545i | \(-0.904832\pi\) | ||
0.955638 | − | 0.294545i | \(-0.0951680\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.309414 | + | 0.309414i | −0.0112015 | + | 0.0112015i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 25.9397 | + | 25.9397i | 0.937852 | + | 0.937852i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −33.6524 | −1.21512 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.6812 | −0.673660 | −0.336830 | − | 0.941565i | \(-0.609355\pi\) | ||||
−0.336830 | + | 0.941565i | \(0.609355\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.40612 | + | 4.40612i | 0.158682 | + | 0.158682i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.6288 | + | 10.6288i | −0.382293 | + | 0.382293i | −0.871928 | − | 0.489635i | \(-0.837130\pi\) |
0.489635 | + | 0.871928i | \(0.337130\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 21.0289i | − | 0.755380i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 26.8807i | 0.964341i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.31973 | + | 1.31973i | −0.0472842 | + | 0.0472842i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.72394 | + | 8.72394i | 0.312167 | + | 0.312167i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −50.9324 | −1.82018 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13.2166 | −0.471720 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.1899 | − | 17.1899i | −0.612755 | − | 0.612755i | 0.330908 | − | 0.943663i | \(-0.392645\pi\) |
−0.943663 | + | 0.330908i | \(0.892645\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.253780 | + | 0.253780i | −0.00903479 | + | 0.00903479i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 16.7193i | − | 0.594470i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 11.0404i | − | 0.392058i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −20.7626 | + | 20.7626i | −0.736375 | + | 0.736375i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19.5801 | + | 19.5801i | 0.693561 | + | 0.693561i | 0.963014 | − | 0.269453i | \(-0.0868427\pi\) |
−0.269453 | + | 0.963014i | \(0.586843\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32.2120 | 1.13958 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.28750 | −0.0808250 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.8062 | − | 15.8062i | −0.557789 | − | 0.557789i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.44267 | − | 1.44267i | 0.0508474 | − | 0.0508474i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 32.4026i | 1.14063i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 52.7688i | − | 1.85525i | −0.373511 | − | 0.927626i | \(-0.621846\pi\) | ||
0.373511 | − | 0.927626i | \(-0.378154\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.0534 | − | 10.0534i | 0.353024 | − | 0.353024i | −0.508210 | − | 0.861233i | \(-0.669693\pi\) |
0.861233 | + | 0.508210i | \(0.169693\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.666709 | − | 0.666709i | −0.0233825 | − | 0.0233825i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.5088 | 0.613308 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.5444 | −0.578815 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10.4606 | − | 10.4606i | −0.365522 | − | 0.365522i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.10780 | + | 4.10780i | −0.143363 | + | 0.143363i | −0.775146 | − | 0.631782i | \(-0.782324\pi\) |
0.631782 | + | 0.775146i | \(0.282324\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 23.4496i | − | 0.817403i | −0.912668 | − | 0.408702i | \(-0.865982\pi\) | ||
0.912668 | − | 0.408702i | \(-0.134018\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 39.6710i | − | 1.38117i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.3518 | + | 33.3518i | −1.15976 | + | 1.15976i | −0.175228 | + | 0.984528i | \(0.556066\pi\) |
−0.984528 | + | 0.175228i | \(0.943934\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.5208 | − | 21.5208i | −0.747449 | − | 0.747449i | 0.226550 | − | 0.973999i | \(-0.427255\pi\) |
−0.973999 | + | 0.226550i | \(0.927255\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −61.2377 | −2.12431 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.93050 | 0.240128 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.2813 | + | 11.2813i | 0.390406 | + | 0.390406i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 24.9560 | − | 24.9560i | 0.862607 | − | 0.862607i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 36.6874i | − | 1.26659i | −0.773911 | − | 0.633295i | \(-0.781702\pi\) | ||
0.773911 | − | 0.633295i | \(-0.218298\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.1196i | 0.969642i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −56.8510 | + | 56.8510i | −1.95805 | + | 1.95805i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.72510 | + | 3.72510i | 0.128147 | + | 0.128147i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.711717 | −0.0244549 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −67.1804 | −2.30562 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.5375 | + | 13.5375i | 0.464059 | + | 0.464059i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.01880 | − | 6.01880i | 0.206080 | − | 0.206080i | −0.596519 | − | 0.802599i | \(-0.703450\pi\) |
0.802599 | + | 0.596519i | \(0.203450\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 10.4012i | − | 0.355714i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 54.0539i | 1.84645i | 0.384266 | + | 0.923223i | \(0.374455\pi\) | ||||
−0.384266 | + | 0.923223i | \(0.625545\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.1054 | + | 20.1054i | −0.685986 | + | 0.685986i | −0.961342 | − | 0.275356i | \(-0.911204\pi\) |
0.275356 | + | 0.961342i | \(0.411204\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.93888 | + | 1.93888i | 0.0660770 | + | 0.0660770i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.1553 | 0.379732 | 0.189866 | − | 0.981810i | \(-0.439195\pi\) | ||||
0.189866 | + | 0.981810i | \(0.439195\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.2434 | −0.688296 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 63.3473 | + | 63.3473i | 2.15139 | + | 2.15139i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 33.3507 | − | 33.3507i | 1.13134 | − | 1.13134i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 35.5800i | − | 1.20558i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 78.0621i | 2.64200i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.32562 | + | 6.32562i | −0.213845 | + | 0.213845i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.1457 | + | 23.1457i | 0.781575 | + | 0.781575i | 0.980097 | − | 0.198522i | \(-0.0636140\pi\) |
−0.198522 | + | 0.980097i | \(0.563614\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −81.8691 | −2.76138 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.2981 | −0.751244 | −0.375622 | − | 0.926773i | \(-0.622571\pi\) | ||||
−0.375622 | + | 0.926773i | \(0.622571\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.3610 | − | 20.3610i | −0.685203 | − | 0.685203i | 0.275965 | − | 0.961168i | \(-0.411003\pi\) |
−0.961168 | + | 0.275965i | \(0.911003\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −24.5800 | + | 24.5800i | −0.826247 | + | 0.826247i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 40.1793i | − | 1.34909i | −0.738234 | − | 0.674544i | \(-0.764340\pi\) | ||
0.738234 | − | 0.674544i | \(-0.235660\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 4.91639i | − | 0.164891i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.35400 | − | 8.35400i | 0.279870 | − | 0.279870i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.45812 | − | 6.45812i | −0.216113 | − | 0.216113i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.66840 | 0.156047 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.4616 | −0.549638 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −27.9877 | − | 27.9877i | −0.933441 | − | 0.933441i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −50.2316 | + | 50.2316i | −1.67346 | + | 1.67346i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 24.3063i | 0.808861i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.4398i | 0.479996i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38.4478 | + | 38.4478i | −1.27664 | + | 1.27664i | −0.334102 | + | 0.942537i | \(0.608433\pi\) |
−0.942537 | + | 0.334102i | \(0.891567\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 59.7484 | + | 59.7484i | 1.98173 | + | 1.98173i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.5940 | 0.947362 | 0.473681 | − | 0.880697i | \(-0.342925\pi\) | ||||
0.473681 | + | 0.880697i | \(0.342925\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.7486 | 0.719773 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.06403 | − | 8.06403i | −0.266589 | − | 0.266589i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.10403 | − | 1.10403i | 0.0364581 | − | 0.0364581i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.6386i | 0.482881i | 0.970416 | + | 0.241441i | \(0.0776199\pi\) | ||||
−0.970416 | + | 0.241441i | \(0.922380\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 76.7776i | 2.52991i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.06954 | + | 7.06954i | −0.232697 | + | 0.232697i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −26.4373 | − | 26.4373i | −0.869253 | − | 0.869253i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −98.5111 | −3.23553 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 48.8608 | 1.60307 | 0.801535 | − | 0.597948i | \(-0.204017\pi\) | ||||
0.801535 | + | 0.597948i | \(0.204017\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.38948 | − | 1.38948i | −0.0455385 | − | 0.0455385i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.7344 | − | 10.7344i | 0.351428 | − | 0.351428i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 23.5347i | 0.769667i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.4306i | 1.68016i | 0.542460 | + | 0.840081i | \(0.317493\pi\) | ||||
−0.542460 | + | 0.840081i | \(0.682507\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.9725 | − | 15.9725i | 0.521243 | − | 0.521243i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.2233 | − | 26.2233i | −0.854856 | − | 0.854856i | 0.135871 | − | 0.990727i | \(-0.456617\pi\) |
−0.990727 | + | 0.135871i | \(0.956617\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.95289 | 0.0635950 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.68706 | −0.217530 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.60278 | − | 8.60278i | −0.279553 | − | 0.279553i | 0.553378 | − | 0.832930i | \(-0.313339\pi\) |
−0.832930 | + | 0.553378i | \(0.813339\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.8087 | − | 12.8087i | 0.415789 | − | 0.415789i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 73.8526i | 2.39484i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.1027i | 0.845549i | 0.906235 | + | 0.422775i | \(0.138944\pi\) | ||||
−0.906235 | + | 0.422775i | \(0.861056\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.6704 | − | 18.6704i | 0.604160 | − | 0.604160i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −52.7988 | − | 52.7988i | −1.70674 | − | 1.70674i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.184924 | −0.00597152 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.57299 | −0.115258 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.779727 | − | 0.779727i | −0.0251264 | − | 0.0251264i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.7253 | − | 17.7253i | 0.570598 | − | 0.570598i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.74115i | 0.281097i | 0.990074 | + | 0.140548i | \(0.0448865\pi\) | ||||
−0.990074 | + | 0.140548i | \(0.955113\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 39.3160i | − | 1.26301i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29.8601 | + | 29.8601i | −0.958255 | + | 0.958255i | −0.999163 | − | 0.0409077i | \(-0.986975\pi\) |
0.0409077 | + | 0.999163i | \(0.486975\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.08707 | − | 4.08707i | −0.131026 | − | 0.131026i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 32.1478 | 1.02955 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24.3299 | −0.778383 | −0.389191 | − | 0.921157i | \(-0.627245\pi\) | ||||
−0.389191 | + | 0.921157i | \(0.627245\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.03771 | − | 1.03771i | −0.0331653 | − | 0.0331653i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.65052 | − | 1.65052i | 0.0526971 | − | 0.0526971i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 36.0892i | − | 1.15107i | −0.817778 | − | 0.575534i | \(-0.804794\pi\) | ||
0.817778 | − | 0.575534i | \(-0.195206\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 9.77466i | − | 0.311447i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9.48797 | + | 9.48797i | −0.302005 | + | 0.302005i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.2409 | + | 12.2409i | 0.389239 | + | 0.389239i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.3921 | 1.41016 | 0.705080 | − | 0.709127i | \(-0.250911\pi\) | ||||
0.705080 | + | 0.709127i | \(0.250911\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.86996 | −0.0910754 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.7030 | + | 10.7030i | 0.339307 | + | 0.339307i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.44245 | − | 1.44245i | 0.0456830 | − | 0.0456830i | −0.683896 | − | 0.729579i | \(-0.739716\pi\) |
0.729579 | + | 0.683896i | \(0.239716\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 62.7490i | − | 1.98529i |
(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 | 1792.2.m.h.1345.7 | yes | 16 | |
4.3 | odd | 2 | 1792.2.m.f.1345.2 | yes | 16 | ||
8.3 | odd | 2 | 1792.2.m.g.1345.7 | yes | 16 | ||
8.5 | even | 2 | 1792.2.m.e.1345.2 | yes | 16 | ||
16.3 | odd | 4 | 1792.2.m.g.449.7 | yes | 16 | ||
16.5 | even | 4 | inner | 1792.2.m.h.449.7 | yes | 16 | |
16.11 | odd | 4 | 1792.2.m.f.449.2 | yes | 16 | ||
16.13 | even | 4 | 1792.2.m.e.449.2 | ✓ | 16 | ||
32.5 | even | 8 | 7168.2.a.bb.1.1 | 8 | |||
32.11 | odd | 8 | 7168.2.a.be.1.1 | 8 | |||
32.21 | even | 8 | 7168.2.a.bf.1.8 | 8 | |||
32.27 | odd | 8 | 7168.2.a.ba.1.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1792.2.m.e.449.2 | ✓ | 16 | 16.13 | even | 4 | ||
1792.2.m.e.1345.2 | yes | 16 | 8.5 | even | 2 | ||
1792.2.m.f.449.2 | yes | 16 | 16.11 | odd | 4 | ||
1792.2.m.f.1345.2 | yes | 16 | 4.3 | odd | 2 | ||
1792.2.m.g.449.7 | yes | 16 | 16.3 | odd | 4 | ||
1792.2.m.g.1345.7 | yes | 16 | 8.3 | odd | 2 | ||
1792.2.m.h.449.7 | yes | 16 | 16.5 | even | 4 | inner | |
1792.2.m.h.1345.7 | yes | 16 | 1.1 | even | 1 | trivial | |
7168.2.a.ba.1.8 | 8 | 32.27 | odd | 8 | |||
7168.2.a.bb.1.1 | 8 | 32.5 | even | 8 | |||
7168.2.a.be.1.1 | 8 | 32.11 | odd | 8 | |||
7168.2.a.bf.1.8 | 8 | 32.21 | even | 8 |