Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [260,2,Mod(61,260)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(260, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("260.61");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 260 = 2^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 260.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.07611045255\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 61.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 260.61 |
Dual form | 260.2.i.c.81.1 |
$q$-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 \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).
\(n\) | \(41\) | \(131\) | \(157\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | −0.684819 | − | 0.728714i | \(-0.740119\pi\) |
0.973494 | + | 0.228714i | \(0.0734519\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.50000 | − | 4.33013i | −0.944911 | − | 1.63663i | −0.755929 | − | 0.654654i | \(-0.772814\pi\) |
−0.188982 | − | 0.981981i | \(-0.560519\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | + | 1.73205i | 0.333333 | + | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.50000 | − | 4.33013i | 0.753778 | − | 1.30558i | −0.192201 | − | 0.981356i | \(-0.561563\pi\) |
0.945979 | − | 0.324227i | \(-0.105104\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | − | 3.46410i | −0.277350 | − | 0.960769i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.500000 | + | 0.866025i | −0.129099 | + | 0.223607i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.500000 | + | 0.866025i | 0.121268 | + | 0.210042i | 0.920268 | − | 0.391289i | \(-0.127971\pi\) |
−0.799000 | + | 0.601331i | \(0.794637\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.50000 | + | 2.59808i | 0.344124 | + | 0.596040i | 0.985194 | − | 0.171442i | \(-0.0548427\pi\) |
−0.641071 | + | 0.767482i | \(0.721509\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.00000 | −1.09109 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.50000 | + | 2.59808i | −0.312772 | + | 0.541736i | −0.978961 | − | 0.204046i | \(-0.934591\pi\) |
0.666190 | + | 0.745782i | \(0.267924\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.500000 | − | 0.866025i | 0.0928477 | − | 0.160817i | −0.815861 | − | 0.578249i | \(-0.803736\pi\) |
0.908708 | + | 0.417432i | \(0.137070\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.50000 | − | 4.33013i | −0.435194 | − | 0.753778i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.50000 | + | 4.33013i | 0.422577 | + | 0.731925i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.50000 | + | 6.06218i | −0.575396 | + | 0.996616i | 0.420602 | + | 0.907245i | \(0.361819\pi\) |
−0.995998 | + | 0.0893706i | \(0.971514\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.50000 | − | 0.866025i | −0.560449 | − | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.50000 | − | 4.33013i | 0.390434 | − | 0.676252i | −0.602072 | − | 0.798441i | \(-0.705658\pi\) |
0.992507 | + | 0.122189i | \(0.0389915\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.50000 | − | 4.33013i | −0.381246 | − | 0.660338i | 0.609994 | − | 0.792406i | \(-0.291172\pi\) |
−0.991241 | + | 0.132068i | \(0.957838\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | − | 1.73205i | −0.149071 | − | 0.258199i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.0000 | 1.75038 | 0.875190 | − | 0.483779i | \(-0.160736\pi\) | ||||
0.875190 | + | 0.483779i | \(0.160736\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.00000 | + | 15.5885i | −1.28571 | + | 2.22692i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.50000 | + | 4.33013i | −0.337100 | + | 0.583874i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.00000 | 0.397360 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.50000 | + | 9.52628i | 0.716039 | + | 1.24022i | 0.962557 | + | 0.271078i | \(0.0873801\pi\) |
−0.246518 | + | 0.969138i | \(0.579287\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.50000 | + | 11.2583i | 0.832240 | + | 1.44148i | 0.896258 | + | 0.443533i | \(0.146275\pi\) |
−0.0640184 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.00000 | − | 8.66025i | 0.629941 | − | 1.09109i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | + | 3.46410i | 0.124035 | + | 0.429669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.50000 | + | 2.59808i | −0.183254 | + | 0.317406i | −0.942987 | − | 0.332830i | \(-0.891996\pi\) |
0.759733 | + | 0.650236i | \(0.225330\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.50000 | + | 2.59808i | 0.180579 | + | 0.312772i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.50000 | − | 11.2583i | −0.771408 | − | 1.33612i | −0.936791 | − | 0.349889i | \(-0.886219\pi\) |
0.165383 | − | 0.986229i | \(-0.447114\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.00000 | −0.234082 | −0.117041 | − | 0.993127i | \(-0.537341\pi\) | ||||
−0.117041 | + | 0.993127i | \(0.537341\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.500000 | − | 0.866025i | 0.0577350 | − | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −25.0000 | −2.84901 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0000 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.500000 | − | 0.866025i | −0.0542326 | − | 0.0939336i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.500000 | − | 0.866025i | −0.0536056 | − | 0.0928477i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.50000 | + | 6.06218i | −0.370999 | + | 0.642590i | −0.989720 | − | 0.143022i | \(-0.954318\pi\) |
0.618720 | + | 0.785611i | \(0.287651\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.5000 | + | 12.9904i | −1.31036 | + | 1.36176i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.50000 | − | 2.59808i | −0.153897 | − | 0.266557i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.50000 | − | 9.52628i | −0.558440 | − | 0.967247i | −0.997627 | − | 0.0688512i | \(-0.978067\pi\) |
0.439187 | − | 0.898396i | \(-0.355267\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.0000 | 1.00504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.50000 | − | 11.2583i | 0.646774 | − | 1.12025i | −0.337115 | − | 0.941464i | \(-0.609451\pi\) |
0.983889 | − | 0.178782i | \(-0.0572157\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.00000 | 0.487950 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.50000 | − | 7.79423i | 0.435031 | − | 0.753497i | −0.562267 | − | 0.826956i | \(-0.690071\pi\) |
0.997298 | + | 0.0734594i | \(0.0234039\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.0000 | 1.72409 | 0.862044 | − | 0.506834i | \(-0.169184\pi\) | ||||
0.862044 | + | 0.506834i | \(0.169184\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.50000 | + | 6.06218i | 0.332205 | + | 0.575396i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.500000 | + | 0.866025i | 0.0470360 | + | 0.0814688i | 0.888585 | − | 0.458712i | \(-0.151689\pi\) |
−0.841549 | + | 0.540181i | \(0.818356\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.50000 | − | 2.59808i | 0.139876 | − | 0.242272i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.00000 | − | 5.19615i | 0.462250 | − | 0.480384i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.50000 | − | 4.33013i | 0.229175 | − | 0.396942i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | − | 12.1244i | −0.636364 | − | 1.10221i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.50000 | − | 4.33013i | −0.225417 | − | 0.390434i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.50000 | + | 6.06218i | −0.310575 | + | 0.537931i | −0.978487 | − | 0.206309i | \(-0.933855\pi\) |
0.667912 | + | 0.744240i | \(0.267188\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.00000 | −0.440225 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.50000 | − | 12.9904i | 0.650332 | − | 1.12641i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.00000 | −0.430331 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.50000 | − | 2.59808i | −0.128154 | − | 0.221969i | 0.794808 | − | 0.606861i | \(-0.207572\pi\) |
−0.922961 | + | 0.384893i | \(0.874238\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.50000 | − | 11.2583i | −0.551323 | − | 0.954919i | −0.998179 | − | 0.0603135i | \(-0.980790\pi\) |
0.446857 | − | 0.894606i | \(-0.352543\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | − | 10.3923i | 0.505291 | − | 0.875190i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −17.5000 | − | 4.33013i | −1.46342 | − | 0.362103i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.500000 | + | 0.866025i | −0.0415227 | + | 0.0719195i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.00000 | + | 15.5885i | 0.742307 | + | 1.28571i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.50000 | − | 9.52628i | −0.450578 | − | 0.780423i | 0.547844 | − | 0.836580i | \(-0.315449\pi\) |
−0.998422 | + | 0.0561570i | \(0.982115\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −24.0000 | −1.95309 | −0.976546 | − | 0.215308i | \(-0.930924\pi\) | ||||
−0.976546 | + | 0.215308i | \(0.930924\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.00000 | + | 1.73205i | −0.0808452 | + | 0.140028i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0000 | 0.798087 | 0.399043 | − | 0.916932i | \(-0.369342\pi\) | ||||
0.399043 | + | 0.916932i | \(0.369342\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.00000 | − | 1.73205i | 0.0793052 | − | 0.137361i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.0000 | 1.18217 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.50000 | − | 4.33013i | −0.195815 | − | 0.339162i | 0.751352 | − | 0.659901i | \(-0.229402\pi\) |
−0.947167 | + | 0.320740i | \(0.896069\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.50000 | + | 4.33013i | 0.194625 | + | 0.337100i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.50000 | − | 11.2583i | 0.502985 | − | 0.871196i | −0.497009 | − | 0.867745i | \(-0.665568\pi\) |
0.999994 | − | 0.00345033i | \(-0.00109828\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | + | 6.92820i | −0.846154 | + | 0.532939i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.00000 | + | 5.19615i | −0.229416 | + | 0.397360i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.50000 | + | 14.7224i | 0.646243 | + | 1.11933i | 0.984013 | + | 0.178097i | \(0.0569941\pi\) |
−0.337770 | + | 0.941229i | \(0.609673\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.50000 | − | 4.33013i | −0.188982 | − | 0.327327i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.0000 | 0.826811 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.50000 | + | 9.52628i | −0.411089 | + | 0.712028i | −0.995009 | − | 0.0997838i | \(-0.968185\pi\) |
0.583920 | + | 0.811811i | \(0.301518\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0000 | 0.743294 | 0.371647 | − | 0.928374i | \(-0.378793\pi\) | ||||
0.371647 | + | 0.928374i | \(0.378793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.0000 | 0.960988 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.50000 | − | 6.06218i | 0.257325 | − | 0.445700i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.00000 | 0.365636 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −12.5000 | − | 21.6506i | −0.909241 | − | 1.57485i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.50000 | + | 12.9904i | 0.542681 | + | 0.939951i | 0.998749 | + | 0.0500060i | \(0.0159241\pi\) |
−0.456068 | + | 0.889945i | \(0.650743\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.5000 | + | 19.9186i | −0.827788 | + | 1.43377i | 0.0719816 | + | 0.997406i | \(0.477068\pi\) |
−0.899770 | + | 0.436365i | \(0.856266\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.50000 | + | 0.866025i | 0.250640 | + | 0.0620174i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.5000 | + | 23.3827i | −0.961835 | + | 1.66595i | −0.243947 | + | 0.969788i | \(0.578442\pi\) |
−0.717888 | + | 0.696159i | \(0.754891\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.5000 | − | 18.1865i | −0.744325 | − | 1.28921i | −0.950509 | − | 0.310696i | \(-0.899438\pi\) |
0.206184 | − | 0.978513i | \(-0.433895\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.50000 | + | 2.59808i | 0.105802 | + | 0.183254i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.00000 | −0.350931 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.50000 | + | 4.33013i | −0.174608 | + | 0.302429i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.00000 | −0.417029 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.0000 | 1.03757 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.50000 | − | 4.33013i | 0.172107 | − | 0.298098i | −0.767049 | − | 0.641588i | \(-0.778276\pi\) |
0.939156 | + | 0.343490i | \(0.111609\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.0000 | −0.890745 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.50000 | + | 4.33013i | 0.170499 | + | 0.295312i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.00000 | + | 1.73205i | −0.0675737 | + | 0.117041i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.50000 | − | 2.59808i | 0.168168 | − | 0.174766i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.50000 | + | 16.4545i | −0.636167 | + | 1.10187i | 0.350100 | + | 0.936713i | \(0.386148\pi\) |
−0.986267 | + | 0.165161i | \(0.947186\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | + | 1.73205i | 0.0666667 | + | 0.115470i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.50000 | − | 14.7224i | −0.564165 | − | 0.977162i | −0.997127 | − | 0.0757500i | \(-0.975865\pi\) |
0.432962 | − | 0.901412i | \(-0.357468\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.0000 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.5000 | + | 21.6506i | −0.822440 | + | 1.42451i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.00000 | 0.393073 | 0.196537 | − | 0.980497i | \(-0.437031\pi\) | ||||
0.196537 | + | 0.980497i | \(0.437031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.0000 | −0.782794 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.00000 | + | 3.46410i | −0.129914 | + | 0.225018i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.00000 | −0.517477 | −0.258738 | − | 0.965947i | \(-0.583307\pi\) | ||||
−0.258738 | + | 0.965947i | \(0.583307\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.50000 | − | 9.52628i | −0.354286 | − | 0.613642i | 0.632709 | − | 0.774389i | \(-0.281943\pi\) |
−0.986996 | + | 0.160748i | \(0.948609\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.00000 | + | 13.8564i | 0.513200 | + | 0.888889i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.00000 | − | 15.5885i | 0.574989 | − | 0.995910i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.50000 | − | 7.79423i | 0.477214 | − | 0.495935i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.00000 | − | 10.3923i | 0.380235 | − | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.50000 | + | 12.9904i | 0.473396 | + | 0.819946i | 0.999536 | − | 0.0304521i | \(-0.00969471\pi\) |
−0.526140 | + | 0.850398i | \(0.676361\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.50000 | + | 12.9904i | 0.471521 | + | 0.816698i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.00000 | −0.0626224 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.50000 | + | 12.9904i | −0.467837 | + | 0.810318i | −0.999325 | − | 0.0367485i | \(-0.988300\pi\) |
0.531487 | + | 0.847066i | \(0.321633\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 35.0000 | 2.17479 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.50000 | + | 9.52628i | −0.339145 | + | 0.587416i | −0.984272 | − | 0.176659i | \(-0.943471\pi\) |
0.645128 | + | 0.764075i | \(0.276804\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.00000 | −0.122859 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.50000 | + | 6.06218i | 0.214197 | + | 0.370999i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.50000 | + | 7.79423i | 0.274370 | + | 0.475223i | 0.969976 | − | 0.243201i | \(-0.0781974\pi\) |
−0.695606 | + | 0.718423i | \(0.744864\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.50000 | + | 6.06218i | −0.212610 | + | 0.368251i | −0.952531 | − | 0.304443i | \(-0.901530\pi\) |
0.739921 | + | 0.672694i | \(0.234863\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.00000 | + | 17.3205i | 0.302614 | + | 1.04828i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.50000 | − | 4.33013i | 0.150756 | − | 0.261116i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.50000 | + | 11.2583i | 0.390547 | + | 0.676448i | 0.992522 | − | 0.122068i | \(-0.0389525\pi\) |
−0.601975 | + | 0.798515i | \(0.705619\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.0000 | 1.78965 | 0.894825 | − | 0.446417i | \(-0.147300\pi\) | ||||
0.894825 | + | 0.446417i | \(0.147300\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.5000 | + | 19.9186i | −0.683604 | + | 1.18404i | 0.290269 | + | 0.956945i | \(0.406255\pi\) |
−0.973873 | + | 0.227092i | \(0.927078\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.00000 | −0.177705 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −25.0000 | −1.47570 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.00000 | − | 13.8564i | 0.470588 | − | 0.815083i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.0000 | −0.644831 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.50000 | − | 6.06218i | −0.204472 | − | 0.354156i | 0.745492 | − | 0.666514i | \(-0.232214\pi\) |
−0.949964 | + | 0.312358i | \(0.898881\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.50000 | − | 9.52628i | −0.320222 | − | 0.554641i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.5000 | − | 21.6506i | 0.725324 | − | 1.25630i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.5000 | + | 2.59808i | 0.607231 | + | 0.150251i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.5000 | + | 21.6506i | −0.720488 | + | 1.24792i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.50000 | − | 11.2583i | −0.373415 | − | 0.646774i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.50000 | − | 11.2583i | −0.372189 | − | 0.644650i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.0000 | −0.684876 | −0.342438 | − | 0.939540i | \(-0.611253\pi\) | ||||
−0.342438 | + | 0.939540i | \(0.611253\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.00000 | 0.339140 | 0.169570 | − | 0.985518i | \(-0.445762\pi\) | ||||
0.169570 | + | 0.985518i | \(0.445762\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.00000 | + | 8.66025i | −0.281718 | + | 0.487950i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.0000 | −1.01098 | −0.505490 | − | 0.862832i | \(-0.668688\pi\) | ||||
−0.505490 | + | 0.862832i | \(0.668688\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.50000 | − | 4.33013i | −0.139973 | − | 0.242441i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.50000 | − | 7.79423i | −0.251166 | − | 0.435031i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.50000 | + | 2.59808i | −0.0834622 | + | 0.144561i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | − | 3.46410i | −0.0554700 | − | 0.192154i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.00000 | − | 15.5885i | 0.497701 | − | 0.862044i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −30.0000 | − | 51.9615i | −1.65395 | − | 2.86473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.500000 | − | 0.866025i | −0.0274825 | − | 0.0476011i | 0.851957 | − | 0.523612i | \(-0.175416\pi\) |
−0.879440 | + | 0.476011i | \(0.842082\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.0000 | −0.767195 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.50000 | − | 2.59808i | 0.0819538 | − | 0.141948i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0000 | 0.762629 | 0.381314 | − | 0.924445i | \(-0.375472\pi\) | ||||
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.00000 | 0.0543125 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 55.0000 | 2.96972 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.50000 | − | 2.59808i | −0.0807573 | − | 0.139876i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.5000 | + | 23.3827i | 0.724718 | + | 1.25525i | 0.959090 | + | 0.283101i | \(0.0913633\pi\) |
−0.234372 | + | 0.972147i | \(0.575303\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.5000 | + | 30.3109i | −0.936754 | + | 1.62250i | −0.165277 | + | 0.986247i | \(0.552852\pi\) |
−0.771477 | + | 0.636257i | \(0.780482\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.00000 | − | 17.3205i | −0.266880 | − | 0.924500i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.50000 | − | 4.33013i | 0.133062 | − | 0.230469i | −0.791794 | − | 0.610789i | \(-0.790853\pi\) |
0.924855 | + | 0.380319i | \(0.124186\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.50000 | + | 11.2583i | 0.344984 | + | 0.597530i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.50000 | − | 4.33013i | −0.132314 | − | 0.229175i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.0000 | −1.26667 | −0.633336 | − | 0.773877i | \(-0.718315\pi\) | ||||
−0.633336 | + | 0.773877i | \(0.718315\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.00000 | − | 8.66025i | 0.263158 | − | 0.455803i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.0000 | −0.734809 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.00000 | 0.104685 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.50000 | + | 2.59808i | −0.0782994 | + | 0.135618i | −0.902516 | − | 0.430656i | \(-0.858282\pi\) |
0.824217 | + | 0.566274i | \(0.191616\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.0000 | 0.520579 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.00000 | − | 8.66025i | −0.259587 | − | 0.449618i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.50000 | − | 16.4545i | −0.491891 | − | 0.851981i | 0.508065 | − | 0.861319i | \(-0.330361\pi\) |
−0.999956 | + | 0.00933789i | \(0.997028\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.500000 | + | 0.866025i | −0.0258199 | + | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.50000 | − | 0.866025i | −0.180259 | − | 0.0446026i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.5000 | − | 18.1865i | 0.539349 | − | 0.934179i | −0.459590 | − | 0.888131i | \(-0.652004\pi\) |
0.998939 | − | 0.0460485i | \(-0.0146629\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.50000 | + | 6.06218i | 0.179310 | + | 0.310575i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.50000 | + | 2.59808i | 0.0766464 | + | 0.132755i | 0.901801 | − | 0.432151i | \(-0.142245\pi\) |
−0.825155 | + | 0.564907i | \(0.808912\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 25.0000 | 1.27412 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.00000 | − | 8.66025i | 0.254164 | − | 0.440225i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.0000 | −0.507020 | −0.253510 | − | 0.967333i | \(-0.581585\pi\) | ||||
−0.253510 | + | 0.967333i | \(0.581585\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.00000 | −0.151717 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.00000 | − | 3.46410i | 0.100887 | − | 0.174741i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.00000 | 0.201262 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.50000 | + | 11.2583i | 0.326226 | + | 0.565039i | 0.981760 | − | 0.190126i | \(-0.0608897\pi\) |
−0.655534 | + | 0.755166i | \(0.727556\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.50000 | − | 12.9904i | −0.375470 | − | 0.650332i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.5000 | + | 23.3827i | −0.674158 | + | 1.16768i | 0.302556 | + | 0.953131i | \(0.402160\pi\) |
−0.976714 | + | 0.214544i | \(0.931173\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.500000 | − | 0.866025i | 0.0248452 | − | 0.0430331i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.5000 | + | 30.3109i | 0.867443 | + | 1.50245i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.50000 | − | 16.4545i | −0.469745 | − | 0.813622i | 0.529657 | − | 0.848212i | \(-0.322321\pi\) |
−0.999402 | + | 0.0345902i | \(0.988987\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.00000 | −0.147979 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 27.5000 | − | 47.6314i | 1.35319 | − | 2.34379i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.0000 | −0.589057 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.0000 | −0.636613 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.50000 | − | 14.7224i | 0.415252 | − | 0.719238i | −0.580203 | − | 0.814472i | \(-0.697027\pi\) |
0.995455 | + | 0.0952342i | \(0.0303600\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.0000 | 0.487370 | 0.243685 | − | 0.969854i | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12.0000 | + | 20.7846i | 0.583460 | + | 1.01058i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.500000 | + | 0.866025i | 0.0242536 | + | 0.0420084i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 32.5000 | − | 56.2917i | 1.57279 | − | 2.72414i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.5000 | + | 12.9904i | −0.603506 | + | 0.627182i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.5000 | − | 18.1865i | 0.505767 | − | 0.876014i | −0.494211 | − | 0.869342i | \(-0.664543\pi\) |
0.999978 | − | 0.00667224i | \(-0.00212386\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.50000 | − | 6.06218i | −0.168199 | − | 0.291330i | 0.769588 | − | 0.638541i | \(-0.220462\pi\) |
−0.937787 | + | 0.347212i | \(0.887129\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.500000 | + | 0.866025i | 0.0239732 | + | 0.0415227i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.00000 | −0.430528 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.5000 | − | 25.1147i | 0.692047 | − | 1.19866i | −0.279119 | − | 0.960257i | \(-0.590042\pi\) |
0.971166 | − | 0.238404i | \(-0.0766244\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −36.0000 | −1.71429 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.0000 | −0.950229 | −0.475114 | − | 0.879924i | \(-0.657593\pi\) | ||||
−0.475114 | + | 0.879924i | \(0.657593\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.50000 | − | 6.06218i | 0.165916 | − | 0.287375i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.0000 | −0.520282 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.5000 | + | 18.1865i | 0.495526 | + | 0.858276i | 0.999987 | − | 0.00515887i | \(-0.00164213\pi\) |
−0.504461 | + | 0.863434i | \(0.668309\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.5000 | − | 21.6506i | −0.588602 | − | 1.01949i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.0000 | + | 20.7846i | −0.563809 | + | 0.976546i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.5000 | − | 12.9904i | 0.586009 | − | 0.608998i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.50000 | + | 9.52628i | −0.257279 | + | 0.445621i | −0.965512 | − | 0.260358i | \(-0.916159\pi\) |
0.708233 | + | 0.705979i | \(0.249493\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.50000 | + | 4.33013i | 0.116690 | + | 0.202113i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.5000 | + | 28.5788i | 0.768482 | + | 1.33105i | 0.938386 | + | 0.345589i | \(0.112321\pi\) |
−0.169904 | + | 0.985461i | \(0.554346\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.00000 | −0.371792 | −0.185896 | − | 0.982569i | \(-0.559519\pi\) | ||||
−0.185896 | + | 0.982569i | \(0.559519\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.00000 | −0.370196 | −0.185098 | − | 0.982720i | \(-0.559260\pi\) | ||||
−0.185098 | + | 0.982720i | \(0.559260\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.0000 | 0.692636 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.00000 | − | 8.66025i | 0.230388 | − | 0.399043i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −25.0000 | −1.14950 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.50000 | + | 2.59808i | 0.0688247 | + | 0.119208i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.00000 | + | 3.46410i | 0.0915737 | + | 0.158610i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.50000 | + | 9.52628i | −0.251301 | + | 0.435267i | −0.963884 | − | 0.266321i | \(-0.914192\pi\) |
0.712583 | + | 0.701588i | \(0.247525\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.5000 | + | 6.06218i | 1.11710 | + | 0.276412i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.50000 | − | 12.9904i | 0.341262 | − | 0.591083i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.50000 | + | 9.52628i | 0.249742 | + | 0.432566i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.50000 | − | 14.7224i | −0.385172 | − | 0.667137i | 0.606621 | − | 0.794991i | \(-0.292524\pi\) |
−0.991793 | + | 0.127854i | \(0.959191\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.00000 | −0.226108 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.50000 | + | 12.9904i | −0.338470 | + | 0.586248i | −0.984145 | − | 0.177365i | \(-0.943243\pi\) |
0.645675 | + | 0.763612i | \(0.276576\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.00000 | 0.0450377 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.0000 | −0.449467 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −32.5000 | + | 56.2917i | −1.45782 | + | 2.52503i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.00000 | −0.179065 | −0.0895323 | − | 0.995984i | \(-0.528537\pi\) | ||||
−0.0895323 | + | 0.995984i | \(0.528537\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.50000 | − | 11.2583i | −0.290399 | − | 0.502985i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.50000 | + | 9.52628i | 0.245233 | + | 0.424756i | 0.962197 | − | 0.272354i | \(-0.0878022\pi\) |
−0.716964 | + | 0.697110i | \(0.754469\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.50000 | + | 11.2583i | −0.289246 | + | 0.500989i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.500000 | + | 12.9904i | 0.0222058 | + | 0.576923i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.50000 | + | 2.59808i | −0.0664863 | + | 0.115158i | −0.897352 | − | 0.441315i | \(-0.854512\pi\) |
0.830866 | + | 0.556473i | \(0.187846\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.00000 | + | 8.66025i | 0.221187 | + | 0.383107i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.50000 | + | 12.9904i | 0.331133 | + | 0.573539i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 30.0000 | − | 51.9615i | 1.31940 | − | 2.28527i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.0000 | 0.746217 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.0000 | 0.963837 | 0.481919 | − | 0.876216i | \(-0.339940\pi\) | ||||
0.481919 | + | 0.876216i | \(0.339940\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.5000 | − | 18.1865i | 0.459133 | − | 0.795242i | −0.539782 | − | 0.841805i | \(-0.681493\pi\) |
0.998915 | + | 0.0465630i | \(0.0148268\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.00000 | −0.218218 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | + | 12.1244i | 0.304348 | + | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.0000 | + | 19.0526i | −0.477359 | + | 0.826811i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.5000 | − | 4.33013i | −0.758009 | − | 0.187559i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.50000 | + | 7.79423i | −0.194552 | + | 0.336974i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.50000 | + | 9.52628i | 0.237343 | + | 0.411089i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 45.0000 | + | 77.9423i | 1.93829 | + | 3.35721i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.00000 | −0.0859867 | −0.0429934 | − | 0.999075i | \(-0.513689\pi\) | ||||
−0.0429934 | + | 0.999075i | \(0.513689\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.00000 | − | 8.66025i | 0.214571 | − | 0.371647i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.0000 | −0.771035 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.0000 | −0.855138 | −0.427569 | − | 0.903983i | \(-0.640630\pi\) | ||||
−0.427569 | + | 0.903983i | \(0.640630\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.0000 | + | 22.5167i | −0.554826 | + | 0.960988i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.00000 | 0.127804 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.0000 | + | 17.3205i | 0.425243 | + | 0.736543i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.50000 | − | 6.06218i | −0.148567 | − | 0.257325i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.50000 | − | 11.2583i | 0.275414 | − | 0.477031i | −0.694826 | − | 0.719178i | \(-0.744518\pi\) |
0.970239 | + | 0.242147i | \(0.0778518\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.5000 | + | 12.9904i | −0.528694 | + | 0.549435i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.50000 | − | 4.33013i | 0.105550 | − | 0.182818i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.50000 | − | 7.79423i | −0.189652 | − | 0.328488i | 0.755482 | − | 0.655169i | \(-0.227403\pi\) |
−0.945134 | + | 0.326682i | \(0.894069\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.500000 | − | 0.866025i | −0.0210352 | − | 0.0364340i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.00000 | 0.209980 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.5000 | + | 33.7750i | −0.817483 | + | 1.41592i | 0.0900490 | + | 0.995937i | \(0.471298\pi\) |
−0.907532 | + | 0.419984i | \(0.862036\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.00000 | 0.167395 | 0.0836974 | − | 0.996491i | \(-0.473327\pi\) | ||||
0.0836974 | + | 0.996491i | \(0.473327\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.0000 | 0.626634 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.50000 | + | 2.59808i | −0.0625543 | + | 0.108347i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −42.0000 | −1.74848 | −0.874241 | − | 0.485491i | \(-0.838641\pi\) | ||||
−0.874241 | + | 0.485491i | \(0.838641\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.5000 | + | 19.9186i | 0.477924 | + | 0.827788i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −30.0000 | − | 51.9615i | −1.24461 | − | 2.15573i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.00000 | − | 8.66025i | 0.207079 | − | 0.358671i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.00000 | + | 5.19615i | −0.206725 | + | 0.214834i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.50000 | + | 2.59808i | −0.0619116 | + | 0.107234i | −0.895320 | − | 0.445424i | \(-0.853053\pi\) |
0.833408 | + | 0.552658i | \(0.186386\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.5000 | + | 23.3827i | 0.555316 | + | 0.961835i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.00000 | −0.0821302 | −0.0410651 | − | 0.999156i | \(-0.513075\pi\) | ||||
−0.0410651 | + | 0.999156i | \(0.513075\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.50000 | + | 4.33013i | −0.102490 | + | 0.177518i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21.0000 | −0.859473 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −36.0000 | −1.47092 | −0.735460 | − | 0.677568i | \(-0.763034\pi\) | ||||
−0.735460 | + | 0.677568i | \(0.763034\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.50000 | − | 4.33013i | 0.101977 | − | 0.176630i | −0.810522 | − | 0.585708i | \(-0.800816\pi\) |
0.912499 | + | 0.409079i | \(0.134150\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.00000 | −0.244339 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.00000 | + | 12.1244i | 0.284590 | + | 0.492925i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.5000 | + | 26.8468i | 0.629126 | + | 1.08968i | 0.987728 | + | 0.156187i | \(0.0499202\pi\) |
−0.358602 | + | 0.933491i | \(0.616746\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.50000 | + | 4.33013i | −0.101305 | + | 0.175466i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.0000 | − | 41.5692i | −0.485468 | − | 1.68171i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.5000 | − | 21.6506i | 0.504870 | − | 0.874461i | −0.495114 | − | 0.868828i | \(-0.664874\pi\) |
0.999984 | − | 0.00563283i | \(-0.00179300\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.50000 | + | 4.33013i | 0.100810 | + | 0.174608i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.5000 | − | 23.3827i | −0.543490 | − | 0.941351i | −0.998700 | − | 0.0509678i | \(-0.983769\pi\) |
0.455211 | − | 0.890384i | \(-0.349564\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.00000 | −0.160774 | −0.0803868 | − | 0.996764i | \(-0.525616\pi\) | ||||
−0.0803868 | + | 0.996764i | \(0.525616\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.50000 | + | 12.9904i | −0.300965 | + | 0.521286i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 35.0000 | 1.40225 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.50000 | − | 12.9904i | 0.299521 | − | 0.518786i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.00000 | −0.279108 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.5000 | + | 23.3827i | 0.537427 | + | 0.930850i | 0.999042 | + | 0.0437697i | \(0.0139368\pi\) |
−0.461615 | + | 0.887080i | \(0.652730\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.50000 | − | 4.33013i | −0.0993661 | − | 0.172107i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.50000 | − | 6.06218i | 0.138893 | − | 0.240570i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 63.0000 | + | 15.5885i | 2.49615 | + | 0.617637i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.0000 | − | 22.5167i | 0.514272 | − | 0.890745i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.5000 | − | 23.3827i | −0.533218 | − | 0.923561i | −0.999247 | − | 0.0387913i | \(-0.987649\pi\) |
0.466029 | − | 0.884769i | \(-0.345684\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.50000 | − | 4.33013i | −0.0985904 | − | 0.170764i | 0.812511 | − | 0.582946i | \(-0.198100\pi\) |
−0.911101 | + | 0.412182i | \(0.864767\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.00000 | 0.196875 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.50000 | − | 7.79423i | 0.176913 | − | 0.306423i | −0.763908 | − | 0.645325i | \(-0.776722\pi\) |
0.940822 | + | 0.338902i | \(0.110055\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 55.0000 | 2.15894 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.5000 | + | 33.7750i | −0.763094 | + | 1.32172i | 0.178154 | + | 0.984003i | \(0.442987\pi\) |
−0.941248 | + | 0.337715i | \(0.890346\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.00000 | −0.156293 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.00000 | − | 3.46410i | −0.0780274 | − | 0.135147i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.50000 | − | 14.7224i | −0.331113 | − | 0.573505i | 0.651617 | − | 0.758548i | \(-0.274091\pi\) |
−0.982730 | + | 0.185043i | \(0.940757\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.50000 | + | 2.59808i | −0.0583432 | + | 0.101053i | −0.893722 | − | 0.448622i | \(-0.851915\pi\) |
0.835379 | + | 0.549675i | \(0.185248\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.00000 | − | 3.46410i | −0.0388368 | − | 0.134535i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.50000 | + | 12.9904i | −0.290838 | + | 0.503745i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.50000 | + | 2.59808i | 0.0580802 | + | 0.100598i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.50000 | + | 16.4545i | 0.367291 | + | 0.636167i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 65.0000 | 2.50930 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.50000 | + | 9.52628i | −0.212009 | + | 0.367211i | −0.952343 | − | 0.305028i | \(-0.901334\pi\) |
0.740334 | + | 0.672239i | \(0.234667\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.00000 | 0.192450 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 42.0000 | 1.61419 | 0.807096 | − | 0.590421i | \(-0.201038\pi\) | ||||
0.807096 | + | 0.590421i | \(0.201038\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.5000 | + | 47.6314i | −1.05535 | + | 1.82793i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.0000 | −0.651441 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.5000 | − | 42.4352i | −0.937466 | − | 1.62374i | −0.770176 | − | 0.637832i | \(-0.779831\pi\) |
−0.167291 | − | 0.985908i | \(-0.553502\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.50000 | + | 2.59808i | 0.0573121 | + | 0.0992674i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.00000 | − | 8.66025i | 0.190762 | − | 0.330409i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.00000 | − | 6.92820i | −0.0761939 | − | 0.263944i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.50000 | − | 4.33013i | 0.0951045 | − | 0.164726i | −0.814548 | − | 0.580097i | \(-0.803015\pi\) |
0.909652 | + | 0.415371i | \(0.136348\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −25.0000 | − | 43.3013i | −0.949671 | − | 1.64488i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.50000 | + | 11.2583i | 0.246559 | + | 0.427053i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.00000 | 0.189389 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.00000 | − | 5.19615i | 0.113470 | − | 0.196537i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.0000 | 0.982006 | 0.491003 | − | 0.871158i | \(-0.336630\pi\) | ||||
0.491003 | + | 0.871158i | \(0.336630\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.0000 | −0.792030 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.00000 | + | 10.3923i | −0.225973 | + | 0.391397i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −65.0000 | −2.44458 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.5000 | − | 19.9186i | −0.431892 | − | 0.748058i | 0.565145 | − | 0.824992i | \(-0.308820\pi\) |
−0.997036 | + | 0.0769337i | \(0.975487\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.00000 | − | 6.92820i | −0.150012 | − | 0.259828i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.5000 | + | 4.33013i | 0.654463 | + | 0.161938i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.00000 | + | 6.92820i | −0.149383 | + | 0.258738i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.5000 | − | 28.5788i | −0.615346 | − | 1.06581i | −0.990324 | − | 0.138777i | \(-0.955683\pi\) |
0.374978 | − | 0.927034i | \(-0.377650\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.0000 | −0.409094 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.500000 | − | 0.866025i | 0.0185695 | − | 0.0321634i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.00000 | −0.296704 | −0.148352 | − | 0.988935i | \(-0.547397\pi\) | ||||
−0.148352 | + | 0.988935i | \(0.547397\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.50000 | − | 4.33013i | 0.0924658 | − | 0.160156i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.0000 | −1.25582 | −0.627909 | − | 0.778287i | \(-0.716089\pi\) | ||||
−0.627909 | + | 0.778287i | \(0.716089\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.00000 | − | 15.5885i | −0.331970 | − | 0.574989i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.50000 | + | 12.9904i | 0.276266 | + | 0.478507i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.50000 | + | 12.9904i | −0.275892 | + | 0.477859i | −0.970360 | − | 0.241665i | \(-0.922307\pi\) |
0.694468 | + | 0.719524i | \(0.255640\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.00000 | − | 10.3923i | −0.110208 | − | 0.381771i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.50000 | − | 7.79423i | 0.165089 | − | 0.285943i | −0.771598 | − | 0.636111i | \(-0.780542\pi\) |
0.936687 | + | 0.350168i | \(0.113876\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.50000 | + | 9.52628i | 0.201504 | + | 0.349016i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.0000 | + | 20.7846i | 0.439057 | + | 0.760469i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −45.0000 | −1.64426 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.5000 | − | 21.6506i | 0.456131 | − | 0.790043i | −0.542621 | − | 0.839978i | \(-0.682568\pi\) |
0.998752 | + | 0.0499348i | \(0.0159013\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.0000 | 0.546630 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.0000 | 0.873449 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.50000 | − | 7.79423i | 0.163555 | − | 0.283286i | −0.772586 | − | 0.634910i | \(-0.781037\pi\) |
0.936141 | + | 0.351624i | \(0.114370\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.0000 | 0.544466 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.50000 | − | 16.4545i | −0.344375 | − | 0.596475i | 0.640865 | − | 0.767653i | \(-0.278576\pi\) |
−0.985240 | + | 0.171179i | \(0.945242\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −45.0000 | − | 77.9423i | −1.62911 | − | 2.82170i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.00000 | − | 1.73205i | 0.0361551 | − | 0.0626224i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27.5000 | − | 28.5788i | 0.992967 | − | 1.03192i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.50000 | + | 16.4545i | −0.342579 | + | 0.593364i | −0.984911 | − | 0.173063i | \(-0.944634\pi\) |
0.642332 | + | 0.766426i | \(0.277967\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.50000 | + | 12.9904i | 0.270106 | + | 0.467837i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.5000 | + | 32.0429i | 0.665399 | + | 1.15250i | 0.979177 | + | 0.203008i | \(0.0650718\pi\) |
−0.313778 | + | 0.949496i | \(0.601595\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 17.5000 | − | 30.3109i | 0.627809 | − | 1.08740i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15.0000 | 0.537431 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −65.0000 | −2.32588 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.50000 | − | 4.33013i | 0.0893427 | − | 0.154746i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.0000 | −0.356915 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.50000 | + | 9.52628i | 0.196054 | + | 0.339575i | 0.947245 | − | 0.320509i | \(-0.103854\pi\) |
−0.751192 | + | 0.660084i | \(0.770521\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.50000 | + | 9.52628i | 0.195805 | + | 0.339145i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.50000 | − | 4.33013i | 0.0888898 | − | 0.153962i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.5000 | − | 33.7750i | 1.15411 | − | 1.19939i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.00000 | + | 1.73205i | −0.0354663 | + | 0.0614295i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.5000 | − | 19.9186i | −0.407351 | − | 0.705552i | 0.587241 | − | 0.809412i | \(-0.300214\pi\) |
−0.994592 | + | 0.103860i | \(0.966881\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.00000 | + | 10.3923i | 0.212265 | + | 0.367653i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.0000 | −0.494666 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.00000 | + | 8.66025i | −0.176446 | + | 0.305614i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.0000 | −0.528681 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.00000 | 0.316815 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.5000 | − | 32.0429i | 0.650425 | − | 1.12657i | −0.332594 | − | 0.943070i | \(-0.607924\pi\) |
0.983020 | − | 0.183500i | \(-0.0587427\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.00000 | −0.280918 | −0.140459 | − | 0.990086i | \(-0.544858\pi\) | ||||
−0.140459 | + | 0.990086i | \(0.544858\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.50000 | + | 6.06218i | 0.122750 | + | 0.212610i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.50000 | + | 4.33013i | 0.0875712 | + | 0.151678i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.50000 | − | 12.9904i | 0.262392 | − | 0.454476i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −35.0000 | − | 8.66025i | −1.22300 | − | 0.302614i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.5000 | − | 21.6506i | 0.436253 | − | 0.755612i | −0.561144 | − | 0.827718i | \(-0.689639\pi\) |
0.997397 | + | 0.0721058i | \(0.0229719\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.5000 | + | 26.8468i | 0.540296 | + | 0.935820i | 0.998887 | + | 0.0471726i | \(0.0150211\pi\) |
−0.458591 | + | 0.888648i | \(0.651646\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.50000 | − | 4.33013i | −0.0870388 | − | 0.150756i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.0000 | 0.417281 | 0.208640 | − | 0.977992i | \(-0.433096\pi\) | ||||
0.208640 | + | 0.977992i | \(0.433096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.5000 | − | 21.6506i | 0.434143 | − | 0.751958i | −0.563082 | − | 0.826401i | \(-0.690385\pi\) |
0.997225 | + | 0.0744432i | \(0.0237179\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.0000 | 0.450965 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.0000 | −0.623663 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.50000 | + | 11.2583i | −0.224942 | + | 0.389611i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.5000 | + | 37.2391i | 0.742262 | + | 1.28564i | 0.951463 | + | 0.307763i | \(0.0995805\pi\) |
−0.209200 | + | 0.977873i | \(0.567086\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.0000 | + | 24.2487i | 0.482759 | + | 0.836162i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.0000 | − | 25.9808i | 0.516627 | − | 0.894825i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.0000 | − | 6.92820i | 0.378412 | − | 0.238337i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −35.0000 | + | 60.6218i | −1.20261 | + | 2.08299i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.5000 | + | 19.9186i | 0.394679 | + | 0.683604i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.5000 | − | 18.1865i | −0.359935 | − | 0.623426i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.0000 | 1.16414 | 0.582069 | − | 0.813139i | \(-0.302243\pi\) | ||||
0.582069 | + | 0.813139i | \(0.302243\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.00000 | − | 5.19615i | 0.102598 | − | 0.177705i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.0000 | −0.888143 | −0.444072 | − | 0.895991i | \(-0.646466\pi\) | ||||
−0.444072 | + | 0.895991i | \(0.646466\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.0000 | −1.22830 | −0.614152 | − | 0.789188i | \(-0.710502\pi\) | ||||
−0.614152 | + | 0.789188i | \(0.710502\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.5000 | + | 21.6506i | −0.425999 | + | 0.737852i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.0000 | 0.816970 | 0.408485 | − | 0.912765i | \(-0.366057\pi\) | ||||
0.408485 | + | 0.912765i | \(0.366057\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.50000 | − | 14.7224i | −0.289009 | − | 0.500578i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.00000 | − | 13.8564i | −0.271694 | − | 0.470588i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.0000 | + | 17.3205i | −0.339227 | + | 0.587558i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.5000 | + | 2.59808i | 0.355779 | + | 0.0880325i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.0000 | − | 19.0526i | 0.372294 | − | 0.644831i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.50000 | + | 4.33013i | 0.0845154 | + | 0.146385i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.5000 | − | 26.8468i | −0.523398 | − | 0.906552i | −0.999629 | − | 0.0272316i | \(-0.991331\pi\) |
0.476231 | − | 0.879320i | \(-0.342002\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.00000 | −0.236104 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.5000 | − | 38.9711i | 0.758044 | − | 1.31297i | −0.185802 | − | 0.982587i | \(-0.559488\pi\) |
0.943847 | − | 0.330384i | \(-0.107178\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.0000 | 0.673054 | 0.336527 | − | 0.941674i | \(-0.390748\pi\) | ||||
0.336527 | + | 0.941674i | \(0.390748\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −11.0000 | −0.369761 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15.5000 | + | 26.8468i | −0.520439 | + | 0.901427i | 0.479279 | + | 0.877663i | \(0.340898\pi\) |
−0.999718 | + | 0.0237640i | \(0.992435\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 35.0000 | 1.17386 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.50000 | + | 4.33013i | 0.0837532 | + | 0.145065i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.0000 | + | 31.1769i | 0.602347 | + | 1.04330i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.50000 | − | 9.52628i | 0.183845 | − | 0.318428i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.50000 | − | 7.79423i | 0.250418 | − | 0.260242i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.00000 | + | 1.73205i | 0.0333148 | + | 0.0577030i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.5000 | + | 21.6506i | 0.415974 | + | 0.720488i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.0000 | −0.332411 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.50000 | − | 14.7224i | 0.282238 | − | 0.488850i | −0.689698 | − | 0.724097i | \(-0.742257\pi\) |
0.971936 | + | 0.235247i | \(0.0755899\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 26.0000 | 0.862366 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.00000 | −0.265052 | −0.132526 | − | 0.991180i | \(-0.542309\pi\) | ||||
−0.132526 | + | 0.991180i | \(0.542309\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30.0000 | − | 51.9615i | 0.992855 | − | 1.71968i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −13.0000 | −0.429767 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.0000 | − | 17.3205i | −0.330229 | − | 0.571974i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.5000 | − | 42.4352i | −0.808180 | − | 1.39981i | −0.914123 | − | 0.405437i | \(-0.867119\pi\) |
0.105942 | − | 0.994372i | \(-0.466214\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.00000 | + | 10.3923i | −0.197707 | + | 0.342438i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −32.5000 | + | 33.7750i | −1.06975 | + | 1.11172i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.50000 | + | 6.06218i | −0.115079 | + | 0.199323i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.5000 | + | 38.9711i | 0.738201 | + | 1.27860i | 0.953305 | + | 0.302010i | \(0.0976578\pi\) |
−0.215104 | + | 0.976591i | \(0.569009\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −54.0000 | −1.76978 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.00000 | −0.163517 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.0000 | −0.588034 | −0.294017 | − | 0.955800i | \(-0.594992\pi\) | ||||
−0.294017 | + | 0.955800i | \(0.594992\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.00000 | − | 5.19615i | 0.0979013 | − | 0.169570i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.0000 | 0.456387 | 0.228193 | − | 0.973616i | \(-0.426718\pi\) | ||||
0.228193 | + | 0.973616i | \(0.426718\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.50000 | + | 12.9904i | 0.244234 | + | 0.423025i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 12.5000 | + | 21.6506i | 0.406625 | + | 0.704295i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.5000 | + | 26.8468i | −0.503682 | + | 0.872403i | 0.496309 | + | 0.868146i | \(0.334688\pi\) |
−0.999991 | + | 0.00425721i | \(0.998645\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.00000 | + | 6.92820i | 0.0649227 | + | 0.224899i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.00000 | + | 15.5885i | −0.291845 | + | 0.505490i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.50000 | − | 2.59808i | −0.0485898 | − | 0.0841599i | 0.840708 | − | 0.541489i | \(-0.182139\pi\) |
−0.889297 | + | 0.457329i | \(0.848806\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.50000 | − | 12.9904i | −0.242694 | − | 0.420359i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.00000 | −0.161627 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.50000 | + | 12.9904i | −0.242188 | + | 0.419481i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.0000 | 0.580042 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.5000 | − | 19.9186i | 0.370198 | − | 0.641202i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.0000 | 0.514525 | 0.257263 | − | 0.966342i | \(-0.417179\pi\) | ||||
0.257263 | + | 0.966342i | \(0.417179\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.50000 | + | 2.59808i | 0.0481869 | + | 0.0834622i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.50000 | + | 6.06218i | 0.112320 | + | 0.194545i | 0.916705 | − | 0.399564i | \(-0.130838\pi\) |
−0.804385 | + | 0.594108i | \(0.797505\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.5000 | + | 56.2917i | −1.04190 | + | 1.80463i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.50000 | − | 0.866025i | −0.112090 | − | 0.0277350i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.5000 | − | 38.9711i | 0.719839 | − | 1.24680i | −0.241225 | − | 0.970469i | \(-0.577549\pi\) |
0.961063 | − | 0.276328i | \(-0.0891176\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.5000 | + | 30.3109i | 0.559302 | + | 0.968740i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.0000 | + | 31.1769i | 0.574696 | + | 0.995402i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.0000 | −0.510321 | −0.255160 | − | 0.966899i | \(-0.582128\pi\) | ||||
−0.255160 | + | 0.966899i | \(0.582128\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.5000 | − | 23.3827i | 0.430146 | − | 0.745034i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −60.0000 | −1.90982 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.0000 | 0.476972 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.50000 | + | 2.59808i | −0.0476491 | + | 0.0825306i | −0.888866 | − | 0.458167i | \(-0.848506\pi\) |
0.841217 | + | 0.540697i | \(0.181840\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.00000 | −0.0317340 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.5000 | + | 18.1865i | 0.332872 | + | 0.576552i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.50000 | − | 6.06218i | −0.110846 | − | 0.191991i | 0.805266 | − | 0.592914i | \(-0.202023\pi\) |
−0.916112 | + | 0.400923i | \(0.868689\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −17.5000 | + | 30.3109i | −0.553675 | + | 0.958994i |
(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 | 260.2.i.c.61.1 | ✓ | 2 | |
3.2 | odd | 2 | 2340.2.q.c.1621.1 | 2 | |||
4.3 | odd | 2 | 1040.2.q.f.321.1 | 2 | |||
5.2 | odd | 4 | 1300.2.bb.c.1049.1 | 4 | |||
5.3 | odd | 4 | 1300.2.bb.c.1049.2 | 4 | |||
5.4 | even | 2 | 1300.2.i.c.1101.1 | 2 | |||
13.3 | even | 3 | inner | 260.2.i.c.81.1 | yes | 2 | |
13.4 | even | 6 | 3380.2.a.e.1.1 | 1 | |||
13.6 | odd | 12 | 3380.2.f.c.3041.2 | 2 | |||
13.7 | odd | 12 | 3380.2.f.c.3041.1 | 2 | |||
13.9 | even | 3 | 3380.2.a.d.1.1 | 1 | |||
39.29 | odd | 6 | 2340.2.q.c.2161.1 | 2 | |||
52.3 | odd | 6 | 1040.2.q.f.81.1 | 2 | |||
65.3 | odd | 12 | 1300.2.bb.c.549.1 | 4 | |||
65.29 | even | 6 | 1300.2.i.c.601.1 | 2 | |||
65.42 | odd | 12 | 1300.2.bb.c.549.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.i.c.61.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
260.2.i.c.81.1 | yes | 2 | 13.3 | even | 3 | inner | |
1040.2.q.f.81.1 | 2 | 52.3 | odd | 6 | |||
1040.2.q.f.321.1 | 2 | 4.3 | odd | 2 | |||
1300.2.i.c.601.1 | 2 | 65.29 | even | 6 | |||
1300.2.i.c.1101.1 | 2 | 5.4 | even | 2 | |||
1300.2.bb.c.549.1 | 4 | 65.3 | odd | 12 | |||
1300.2.bb.c.549.2 | 4 | 65.42 | odd | 12 | |||
1300.2.bb.c.1049.1 | 4 | 5.2 | odd | 4 | |||
1300.2.bb.c.1049.2 | 4 | 5.3 | odd | 4 | |||
2340.2.q.c.1621.1 | 2 | 3.2 | odd | 2 | |||
2340.2.q.c.2161.1 | 2 | 39.29 | odd | 6 | |||
3380.2.a.d.1.1 | 1 | 13.9 | even | 3 | |||
3380.2.a.e.1.1 | 1 | 13.4 | even | 6 | |||
3380.2.f.c.3041.1 | 2 | 13.7 | odd | 12 | |||
3380.2.f.c.3041.2 | 2 | 13.6 | odd | 12 |