Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,2,Mod(1249,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1875.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.b (of order \(2\), degree \(1\), not 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: | \(14.9719503790\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.324000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 9x^{6} + 26x^{4} + 24x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.2 | ||
Root | \(-1.95630i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1249 |
Dual form | 1875.2.b.d.1249.7 |
$q$-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 \(\left(\mathbb{Z}/1875\mathbb{Z}\right)^\times\).
\(n\) | \(626\) | \(1252\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.82709i | − 1.29195i | −0.763359 | − | 0.645974i | \(-0.776451\pi\) | ||||
0.763359 | − | 0.645974i | \(-0.223549\pi\) | |||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | −1.33826 | −0.669131 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.82709 | −0.745907 | ||||||||
\(7\) | 1.44512i | 0.546206i | 0.961985 | + | 0.273103i | \(0.0880500\pi\) | ||||
−0.961985 | + | 0.273103i | \(0.911950\pi\) | |||||||
\(8\) | − 1.20906i | − 0.427466i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.12920 | −0.641979 | −0.320990 | − | 0.947083i | \(-0.604015\pi\) | ||||
−0.320990 | + | 0.947083i | \(0.604015\pi\) | |||||||
\(12\) | 1.33826i | 0.386323i | ||||||||
\(13\) | 5.70353i | 1.58188i | 0.611897 | + | 0.790938i | \(0.290407\pi\) | ||||
−0.611897 | + | 0.790938i | \(0.709593\pi\) | |||||||
\(14\) | 2.64037 | 0.705670 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.88558 | −1.22139 | ||||||||
\(17\) | 4.15622i | 1.00803i | 0.863695 | + | 0.504015i | \(0.168144\pi\) | ||||
−0.863695 | + | 0.504015i | \(0.831856\pi\) | |||||||
\(18\) | 1.82709i | 0.430649i | ||||||||
\(19\) | −1.70353 | −0.390817 | −0.195409 | − | 0.980722i | \(-0.562603\pi\) | ||||
−0.195409 | + | 0.980722i | \(0.562603\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.44512 | 0.315352 | ||||||||
\(22\) | 3.89025i | 0.829404i | ||||||||
\(23\) | 0.323478i | 0.0674497i | 0.999431 | + | 0.0337249i | \(0.0107370\pi\) | ||||
−0.999431 | + | 0.0337249i | \(0.989263\pi\) | |||||||
\(24\) | −1.20906 | −0.246798 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 10.4209 | 2.04370 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | − 1.93395i | − 0.365483i | ||||||||
\(29\) | 8.74724 | 1.62432 | 0.812161 | − | 0.583434i | \(-0.198291\pi\) | ||||
0.812161 | + | 0.583434i | \(0.198291\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.45991 | −1.51944 | −0.759722 | − | 0.650248i | \(-0.774665\pi\) | ||||
−0.759722 | + | 0.650248i | \(0.774665\pi\) | |||||||
\(32\) | 6.50828i | 1.15051i | ||||||||
\(33\) | 2.12920i | 0.370647i | ||||||||
\(34\) | 7.59378 | 1.30232 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.33826 | 0.223044 | ||||||||
\(37\) | 1.75170i | 0.287978i | 0.989579 | + | 0.143989i | \(0.0459931\pi\) | ||||
−0.989579 | + | 0.143989i | \(0.954007\pi\) | |||||||
\(38\) | 3.11251i | 0.504916i | ||||||||
\(39\) | 5.70353 | 0.913296 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.87802 | −1.07417 | −0.537083 | − | 0.843529i | \(-0.680474\pi\) | ||||
−0.537083 | + | 0.843529i | \(0.680474\pi\) | |||||||
\(42\) | − 2.64037i | − 0.407419i | ||||||||
\(43\) | 11.1411i | 1.69900i | 0.527587 | + | 0.849501i | \(0.323097\pi\) | ||||
−0.527587 | + | 0.849501i | \(0.676903\pi\) | |||||||
\(44\) | 2.84943 | 0.429568 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.591023 | 0.0871416 | ||||||||
\(47\) | 12.5982i | 1.83764i | 0.394673 | + | 0.918822i | \(0.370858\pi\) | ||||
−0.394673 | + | 0.918822i | \(0.629142\pi\) | |||||||
\(48\) | 4.88558i | 0.705173i | ||||||||
\(49\) | 4.91161 | 0.701659 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.15622 | 0.581987 | ||||||||
\(52\) | − 7.63282i | − 1.05848i | ||||||||
\(53\) | − 8.34451i | − 1.14621i | −0.819483 | − | 0.573103i | \(-0.805739\pi\) | ||||
0.819483 | − | 0.573103i | \(-0.194261\pi\) | |||||||
\(54\) | 1.82709 | 0.248636 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.74724 | 0.233485 | ||||||||
\(57\) | 1.70353i | 0.225639i | ||||||||
\(58\) | − 15.9820i | − 2.09854i | ||||||||
\(59\) | 2.12474 | 0.276617 | 0.138309 | − | 0.990389i | \(-0.455833\pi\) | ||||
0.138309 | + | 0.990389i | \(0.455833\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.38952 | −0.690058 | −0.345029 | − | 0.938592i | \(-0.612131\pi\) | ||||
−0.345029 | + | 0.938592i | \(0.612131\pi\) | |||||||
\(62\) | 15.4570i | 1.96304i | ||||||||
\(63\) | − 1.44512i | − 0.182069i | ||||||||
\(64\) | 2.12007 | 0.265008 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.89025 | 0.478857 | ||||||||
\(67\) | − 7.13078i | − 0.871164i | −0.900149 | − | 0.435582i | \(-0.856543\pi\) | ||||
0.900149 | − | 0.435582i | \(-0.143457\pi\) | |||||||
\(68\) | − 5.56210i | − 0.674504i | ||||||||
\(69\) | 0.323478 | 0.0389421 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.67461 | 0.317418 | 0.158709 | − | 0.987325i | \(-0.449267\pi\) | ||||
0.158709 | + | 0.987325i | \(0.449267\pi\) | |||||||
\(72\) | 1.20906i | 0.142489i | ||||||||
\(73\) | − 6.28253i | − 0.735315i | −0.929961 | − | 0.367657i | \(-0.880160\pi\) | ||||
0.929961 | − | 0.367657i | \(-0.119840\pi\) | |||||||
\(74\) | 3.20052 | 0.372053 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.27977 | 0.261508 | ||||||||
\(77\) | − 3.07697i | − 0.350653i | ||||||||
\(78\) | − 10.4209i | − 1.17993i | ||||||||
\(79\) | −8.37092 | −0.941802 | −0.470901 | − | 0.882186i | \(-0.656071\pi\) | ||||
−0.470901 | + | 0.882186i | \(0.656071\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 12.5668i | 1.38777i | ||||||||
\(83\) | 14.5872i | 1.60115i | 0.599230 | + | 0.800577i | \(0.295473\pi\) | ||||
−0.599230 | + | 0.800577i | \(0.704527\pi\) | |||||||
\(84\) | −1.93395 | −0.211012 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 20.3558 | 2.19502 | ||||||||
\(87\) | − 8.74724i | − 0.937802i | ||||||||
\(88\) | 2.57433i | 0.274424i | ||||||||
\(89\) | −2.68119 | −0.284206 | −0.142103 | − | 0.989852i | \(-0.545386\pi\) | ||||
−0.142103 | + | 0.989852i | \(0.545386\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.24232 | −0.864030 | ||||||||
\(92\) | − 0.432897i | − 0.0451327i | ||||||||
\(93\) | 8.45991i | 0.877252i | ||||||||
\(94\) | 23.0181 | 2.37414 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 6.50828 | 0.664249 | ||||||||
\(97\) | 8.55105i | 0.868228i | 0.900858 | + | 0.434114i | \(0.142939\pi\) | ||||
−0.900858 | + | 0.434114i | \(0.857061\pi\) | |||||||
\(98\) | − 8.97397i | − 0.906507i | ||||||||
\(99\) | 2.12920 | 0.213993 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.85377 | 0.980487 | 0.490243 | − | 0.871586i | \(-0.336908\pi\) | ||||
0.490243 | + | 0.871586i | \(0.336908\pi\) | |||||||
\(102\) | − 7.59378i | − 0.751897i | ||||||||
\(103\) | 16.1279i | 1.58913i | 0.607180 | + | 0.794564i | \(0.292301\pi\) | ||||
−0.607180 | + | 0.794564i | \(0.707699\pi\) | |||||||
\(104\) | 6.89590 | 0.676198 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −15.2462 | −1.48084 | ||||||||
\(107\) | − 1.81198i | − 0.175170i | −0.996157 | − | 0.0875852i | \(-0.972085\pi\) | ||||
0.996157 | − | 0.0875852i | \(-0.0279150\pi\) | |||||||
\(108\) | − 1.33826i | − 0.128774i | ||||||||
\(109\) | 18.4646 | 1.76859 | 0.884293 | − | 0.466933i | \(-0.154641\pi\) | ||||
0.884293 | + | 0.466933i | \(0.154641\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.75170 | 0.166264 | ||||||||
\(112\) | − 7.06027i | − 0.667133i | ||||||||
\(113\) | − 13.3653i | − 1.25730i | −0.777689 | − | 0.628650i | \(-0.783608\pi\) | ||||
0.777689 | − | 0.628650i | \(-0.216392\pi\) | |||||||
\(114\) | 3.11251 | 0.291513 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −11.7061 | −1.08688 | ||||||||
\(117\) | − 5.70353i | − 0.527292i | ||||||||
\(118\) | − 3.88209i | − 0.357375i | ||||||||
\(119\) | −6.00625 | −0.550592 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.46649 | −0.587863 | ||||||||
\(122\) | 9.84715i | 0.891519i | ||||||||
\(123\) | 6.87802i | 0.620170i | ||||||||
\(124\) | 11.3216 | 1.01671 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.64037 | −0.235223 | ||||||||
\(127\) | 1.01381i | 0.0899608i | 0.998988 | + | 0.0449804i | \(0.0143225\pi\) | ||||
−0.998988 | + | 0.0449804i | \(0.985677\pi\) | |||||||
\(128\) | 9.14301i | 0.808136i | ||||||||
\(129\) | 11.1411 | 0.980919 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.08550 | 0.182211 | 0.0911055 | − | 0.995841i | \(-0.470960\pi\) | ||||
0.0911055 | + | 0.995841i | \(0.470960\pi\) | |||||||
\(132\) | − 2.84943i | − 0.248011i | ||||||||
\(133\) | − 2.46182i | − 0.213467i | ||||||||
\(134\) | −13.0286 | −1.12550 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.02510 | 0.430899 | ||||||||
\(137\) | − 16.9365i | − 1.44698i | −0.690333 | − | 0.723492i | \(-0.742536\pi\) | ||||
0.690333 | − | 0.723492i | \(-0.257464\pi\) | |||||||
\(138\) | − 0.591023i | − 0.0503112i | ||||||||
\(139\) | −14.8883 | −1.26281 | −0.631406 | − | 0.775452i | \(-0.717522\pi\) | ||||
−0.631406 | + | 0.775452i | \(0.717522\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.5982 | 1.06096 | ||||||||
\(142\) | − 4.88676i | − 0.410088i | ||||||||
\(143\) | − 12.1440i | − 1.01553i | ||||||||
\(144\) | 4.88558 | 0.407132 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −11.4788 | −0.949989 | ||||||||
\(147\) | − 4.91161i | − 0.405103i | ||||||||
\(148\) | − 2.34424i | − 0.192695i | ||||||||
\(149\) | 4.70991 | 0.385851 | 0.192925 | − | 0.981213i | \(-0.438202\pi\) | ||||
0.192925 | + | 0.981213i | \(0.438202\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.63091 | −0.783752 | −0.391876 | − | 0.920018i | \(-0.628174\pi\) | ||||
−0.391876 | + | 0.920018i | \(0.628174\pi\) | |||||||
\(152\) | 2.05967i | 0.167061i | ||||||||
\(153\) | − 4.15622i | − 0.336010i | ||||||||
\(154\) | −5.62190 | −0.453025 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.63282 | −0.611114 | ||||||||
\(157\) | − 18.5557i | − 1.48091i | −0.672107 | − | 0.740454i | \(-0.734611\pi\) | ||||
0.672107 | − | 0.740454i | \(-0.265389\pi\) | |||||||
\(158\) | 15.2944i | 1.21676i | ||||||||
\(159\) | −8.34451 | −0.661763 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.467465 | −0.0368414 | ||||||||
\(162\) | − 1.82709i | − 0.143550i | ||||||||
\(163\) | 0.451705i | 0.0353803i | 0.999844 | + | 0.0176902i | \(0.00563124\pi\) | ||||
−0.999844 | + | 0.0176902i | \(0.994369\pi\) | |||||||
\(164\) | 9.20459 | 0.718758 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 26.6521 | 2.06861 | ||||||||
\(167\) | − 4.72648i | − 0.365746i | −0.983137 | − | 0.182873i | \(-0.941460\pi\) | ||||
0.983137 | − | 0.182873i | \(-0.0585397\pi\) | |||||||
\(168\) | − 1.74724i | − 0.134802i | ||||||||
\(169\) | −19.5303 | −1.50233 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.70353 | 0.130272 | ||||||||
\(172\) | − 14.9097i | − 1.13685i | ||||||||
\(173\) | 2.29489i | 0.174477i | 0.996187 | + | 0.0872385i | \(0.0278042\pi\) | ||||
−0.996187 | + | 0.0872385i | \(0.972196\pi\) | |||||||
\(174\) | −15.9820 | −1.21159 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 10.4024 | 0.784110 | ||||||||
\(177\) | − 2.12474i | − 0.159705i | ||||||||
\(178\) | 4.89878i | 0.367179i | ||||||||
\(179\) | −2.68757 | −0.200878 | −0.100439 | − | 0.994943i | \(-0.532025\pi\) | ||||
−0.100439 | + | 0.994943i | \(0.532025\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.9088 | −1.77712 | −0.888562 | − | 0.458756i | \(-0.848295\pi\) | ||||
−0.888562 | + | 0.458756i | \(0.848295\pi\) | |||||||
\(182\) | 15.0595i | 1.11628i | ||||||||
\(183\) | 5.38952i | 0.398405i | ||||||||
\(184\) | 0.391103 | 0.0288325 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 15.4570 | 1.13336 | ||||||||
\(187\) | − 8.84943i | − 0.647135i | ||||||||
\(188\) | − 16.8597i | − 1.22962i | ||||||||
\(189\) | −1.44512 | −0.105117 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.91824 | −0.283514 | −0.141757 | − | 0.989902i | \(-0.545275\pi\) | ||||
−0.141757 | + | 0.989902i | \(0.545275\pi\) | |||||||
\(192\) | − 2.12007i | − 0.153003i | ||||||||
\(193\) | − 8.54752i | − 0.615264i | −0.951505 | − | 0.307632i | \(-0.900463\pi\) | ||||
0.951505 | − | 0.307632i | \(-0.0995366\pi\) | |||||||
\(194\) | 15.6236 | 1.12171 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.57302 | −0.469502 | ||||||||
\(197\) | − 2.45235i | − 0.174723i | −0.996177 | − | 0.0873614i | \(-0.972157\pi\) | ||||
0.996177 | − | 0.0873614i | \(-0.0278435\pi\) | |||||||
\(198\) | − 3.89025i | − 0.276468i | ||||||||
\(199\) | 10.4345 | 0.739680 | 0.369840 | − | 0.929095i | \(-0.379412\pi\) | ||||
0.369840 | + | 0.929095i | \(0.379412\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.13078 | −0.502967 | ||||||||
\(202\) | − 18.0037i | − 1.26674i | ||||||||
\(203\) | 12.6409i | 0.887214i | ||||||||
\(204\) | −5.56210 | −0.389425 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 29.4671 | 2.05307 | ||||||||
\(207\) | − 0.323478i | − 0.0224832i | ||||||||
\(208\) | − 27.8651i | − 1.93209i | ||||||||
\(209\) | 3.62717 | 0.250897 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.2618 | 1.32604 | 0.663018 | − | 0.748604i | \(-0.269275\pi\) | ||||
0.663018 | + | 0.748604i | \(0.269275\pi\) | |||||||
\(212\) | 11.1671i | 0.766962i | ||||||||
\(213\) | − 2.67461i | − 0.183261i | ||||||||
\(214\) | −3.31065 | −0.226311 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.20906 | 0.0822659 | ||||||||
\(217\) | − 12.2256i | − 0.829929i | ||||||||
\(218\) | − 33.7365i | − 2.28492i | ||||||||
\(219\) | −6.28253 | −0.424534 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.7051 | −1.59458 | ||||||||
\(222\) | − 3.20052i | − 0.214805i | ||||||||
\(223\) | 7.61706i | 0.510076i | 0.966931 | + | 0.255038i | \(0.0820880\pi\) | ||||
−0.966931 | + | 0.255038i | \(0.917912\pi\) | |||||||
\(224\) | −9.40528 | −0.628417 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −24.4196 | −1.62437 | ||||||||
\(227\) | 1.31803i | 0.0874810i | 0.999043 | + | 0.0437405i | \(0.0139275\pi\) | ||||
−0.999043 | + | 0.0437405i | \(0.986073\pi\) | |||||||
\(228\) | − 2.27977i | − 0.150982i | ||||||||
\(229\) | −1.12632 | −0.0744292 | −0.0372146 | − | 0.999307i | \(-0.511849\pi\) | ||||
−0.0372146 | + | 0.999307i | \(0.511849\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.07697 | −0.202450 | ||||||||
\(232\) | − 10.5759i | − 0.694342i | ||||||||
\(233\) | 26.6071i | 1.74309i | 0.490319 | + | 0.871543i | \(0.336880\pi\) | ||||
−0.490319 | + | 0.871543i | \(0.663120\pi\) | |||||||
\(234\) | −10.4209 | −0.681234 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.84345 | −0.185093 | ||||||||
\(237\) | 8.37092i | 0.543750i | ||||||||
\(238\) | 10.9740i | 0.711337i | ||||||||
\(239\) | 24.8692 | 1.60865 | 0.804326 | − | 0.594188i | \(-0.202527\pi\) | ||||
0.804326 | + | 0.594188i | \(0.202527\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.3532 | −0.795743 | −0.397871 | − | 0.917441i | \(-0.630251\pi\) | ||||
−0.397871 | + | 0.917441i | \(0.630251\pi\) | |||||||
\(242\) | 11.8149i | 0.759488i | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 7.21259 | 0.461739 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 12.5668 | 0.801228 | ||||||||
\(247\) | − 9.71616i | − 0.618224i | ||||||||
\(248\) | 10.2285i | 0.649511i | ||||||||
\(249\) | 14.5872 | 0.924426 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −29.0986 | −1.83669 | −0.918343 | − | 0.395786i | \(-0.870472\pi\) | ||||
−0.918343 | + | 0.395786i | \(0.870472\pi\) | |||||||
\(252\) | 1.93395i | 0.121828i | ||||||||
\(253\) | − 0.688750i | − 0.0433013i | ||||||||
\(254\) | 1.85232 | 0.116225 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.9452 | 1.30908 | ||||||||
\(257\) | 12.0500i | 0.751656i | 0.926690 | + | 0.375828i | \(0.122642\pi\) | ||||
−0.926690 | + | 0.375828i | \(0.877358\pi\) | |||||||
\(258\) | − 20.3558i | − 1.26730i | ||||||||
\(259\) | −2.53143 | −0.157296 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.74724 | −0.541440 | ||||||||
\(262\) | − 3.81040i | − 0.235407i | ||||||||
\(263\) | − 1.02892i | − 0.0634460i | −0.999497 | − | 0.0317230i | \(-0.989901\pi\) | ||||
0.999497 | − | 0.0317230i | \(-0.0100994\pi\) | |||||||
\(264\) | 2.57433 | 0.158439 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.49797 | −0.275788 | ||||||||
\(267\) | 2.68119i | 0.164086i | ||||||||
\(268\) | 9.54285i | 0.582922i | ||||||||
\(269\) | −23.9072 | −1.45765 | −0.728824 | − | 0.684701i | \(-0.759933\pi\) | ||||
−0.728824 | + | 0.684701i | \(0.759933\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.72214 | 0.226104 | 0.113052 | − | 0.993589i | \(-0.463937\pi\) | ||||
0.113052 | + | 0.993589i | \(0.463937\pi\) | |||||||
\(272\) | − 20.3055i | − 1.23120i | ||||||||
\(273\) | 8.24232i | 0.498848i | ||||||||
\(274\) | −30.9445 | −1.86943 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.432897 | −0.0260574 | ||||||||
\(277\) | 17.5802i | 1.05629i | 0.849153 | + | 0.528147i | \(0.177113\pi\) | ||||
−0.849153 | + | 0.528147i | \(0.822887\pi\) | |||||||
\(278\) | 27.2024i | 1.63149i | ||||||||
\(279\) | 8.45991 | 0.506481 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.2536 | 0.790644 | 0.395322 | − | 0.918543i | \(-0.370633\pi\) | ||||
0.395322 | + | 0.918543i | \(0.370633\pi\) | |||||||
\(282\) | − 23.0181i | − 1.37071i | ||||||||
\(283\) | 12.0996i | 0.719249i | 0.933097 | + | 0.359624i | \(0.117095\pi\) | ||||
−0.933097 | + | 0.359624i | \(0.882905\pi\) | |||||||
\(284\) | −3.57933 | −0.212394 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −22.1882 | −1.31201 | ||||||||
\(287\) | − 9.93960i | − 0.586716i | ||||||||
\(288\) | − 6.50828i | − 0.383504i | ||||||||
\(289\) | −0.274126 | −0.0161251 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.55105 | 0.501272 | ||||||||
\(292\) | 8.40767i | 0.492022i | ||||||||
\(293\) | 3.61673i | 0.211291i | 0.994404 | + | 0.105646i | \(0.0336910\pi\) | ||||
−0.994404 | + | 0.105646i | \(0.966309\pi\) | |||||||
\(294\) | −8.97397 | −0.523372 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.11791 | 0.123101 | ||||||||
\(297\) | − 2.12920i | − 0.123549i | ||||||||
\(298\) | − 8.60543i | − 0.498499i | ||||||||
\(299\) | −1.84497 | −0.106697 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.1003 | −0.928005 | ||||||||
\(302\) | 17.5965i | 1.01257i | ||||||||
\(303\) | − 9.85377i | − 0.566084i | ||||||||
\(304\) | 8.32275 | 0.477342 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −7.59378 | −0.434108 | ||||||||
\(307\) | − 14.8273i | − 0.846238i | −0.906074 | − | 0.423119i | \(-0.860935\pi\) | ||||
0.906074 | − | 0.423119i | \(-0.139065\pi\) | |||||||
\(308\) | 4.11778i | 0.234633i | ||||||||
\(309\) | 16.1279 | 0.917484 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.61579 | −0.375147 | −0.187574 | − | 0.982251i | \(-0.560062\pi\) | ||||
−0.187574 | + | 0.982251i | \(0.560062\pi\) | |||||||
\(312\) | − 6.89590i | − 0.390403i | ||||||||
\(313\) | − 7.17823i | − 0.405737i | −0.979206 | − | 0.202869i | \(-0.934974\pi\) | ||||
0.979206 | − | 0.202869i | \(-0.0650264\pi\) | |||||||
\(314\) | −33.9030 | −1.91326 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.2025 | 0.630189 | ||||||||
\(317\) | 9.75255i | 0.547758i | 0.961764 | + | 0.273879i | \(0.0883068\pi\) | ||||
−0.961764 | + | 0.273879i | \(0.911693\pi\) | |||||||
\(318\) | 15.2462i | 0.854963i | ||||||||
\(319\) | −18.6247 | −1.04278 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.81198 | −0.101135 | ||||||||
\(322\) | 0.854102i | 0.0475972i | ||||||||
\(323\) | − 7.08025i | − 0.393956i | ||||||||
\(324\) | −1.33826 | −0.0743478 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.825307 | 0.0457095 | ||||||||
\(327\) | − 18.4646i | − 1.02109i | ||||||||
\(328\) | 8.31592i | 0.459170i | ||||||||
\(329\) | −18.2060 | −1.00373 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.68822 | 0.367618 | 0.183809 | − | 0.982962i | \(-0.441157\pi\) | ||||
0.183809 | + | 0.982962i | \(0.441157\pi\) | |||||||
\(332\) | − 19.5215i | − 1.07138i | ||||||||
\(333\) | − 1.75170i | − 0.0959928i | ||||||||
\(334\) | −8.63570 | −0.472525 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −7.06027 | −0.385169 | ||||||||
\(337\) | 20.8191i | 1.13409i | 0.823687 | + | 0.567045i | \(0.191914\pi\) | ||||
−0.823687 | + | 0.567045i | \(0.808086\pi\) | |||||||
\(338\) | 35.6836i | 1.94093i | ||||||||
\(339\) | −13.3653 | −0.725902 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.0129 | 0.975452 | ||||||||
\(342\) | − 3.11251i | − 0.168305i | ||||||||
\(343\) | 17.2138i | 0.929456i | ||||||||
\(344\) | 13.4702 | 0.726266 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.19297 | 0.225415 | ||||||||
\(347\) | 30.9907i | 1.66367i | 0.555023 | + | 0.831835i | \(0.312709\pi\) | ||||
−0.555023 | + | 0.831835i | \(0.687291\pi\) | |||||||
\(348\) | 11.7061i | 0.627512i | ||||||||
\(349\) | 7.45484 | 0.399048 | 0.199524 | − | 0.979893i | \(-0.436060\pi\) | ||||
0.199524 | + | 0.979893i | \(0.436060\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.70353 | −0.304432 | ||||||||
\(352\) | − 13.8575i | − 0.738605i | ||||||||
\(353\) | − 3.68948i | − 0.196371i | −0.995168 | − | 0.0981856i | \(-0.968696\pi\) | ||||
0.995168 | − | 0.0981856i | \(-0.0313039\pi\) | |||||||
\(354\) | −3.88209 | −0.206331 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.58814 | 0.190171 | ||||||||
\(357\) | 6.00625i | 0.317884i | ||||||||
\(358\) | 4.91043i | 0.259524i | ||||||||
\(359\) | 9.92989 | 0.524079 | 0.262040 | − | 0.965057i | \(-0.415605\pi\) | ||||
0.262040 | + | 0.965057i | \(0.415605\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.0980 | −0.847262 | ||||||||
\(362\) | 43.6835i | 2.29595i | ||||||||
\(363\) | 6.46649i | 0.339403i | ||||||||
\(364\) | 11.0304 | 0.578149 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 9.84715 | 0.514719 | ||||||||
\(367\) | 12.5507i | 0.655142i | 0.944826 | + | 0.327571i | \(0.106230\pi\) | ||||
−0.944826 | + | 0.327571i | \(0.893770\pi\) | |||||||
\(368\) | − 1.58038i | − 0.0823828i | ||||||||
\(369\) | 6.87802 | 0.358056 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.0589 | 0.626065 | ||||||||
\(372\) | − 11.3216i | − 0.586996i | ||||||||
\(373\) | 14.8576i | 0.769299i | 0.923063 | + | 0.384650i | \(0.125678\pi\) | ||||
−0.923063 | + | 0.384650i | \(0.874322\pi\) | |||||||
\(374\) | −16.1687 | −0.836064 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 15.2320 | 0.785530 | ||||||||
\(377\) | 49.8902i | 2.56947i | ||||||||
\(378\) | 2.64037i | 0.135806i | ||||||||
\(379\) | −11.2957 | −0.580223 | −0.290112 | − | 0.956993i | \(-0.593692\pi\) | ||||
−0.290112 | + | 0.956993i | \(0.593692\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.01381 | 0.0519389 | ||||||||
\(382\) | 7.15898i | 0.366285i | ||||||||
\(383\) | − 3.04968i | − 0.155831i | −0.996960 | − | 0.0779157i | \(-0.975173\pi\) | ||||
0.996960 | − | 0.0779157i | \(-0.0248265\pi\) | |||||||
\(384\) | 9.14301 | 0.466577 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −15.6171 | −0.794889 | ||||||||
\(387\) | − 11.1411i | − 0.566334i | ||||||||
\(388\) | − 11.4435i | − 0.580958i | ||||||||
\(389\) | 21.3939 | 1.08472 | 0.542358 | − | 0.840148i | \(-0.317532\pi\) | ||||
0.542358 | + | 0.840148i | \(0.317532\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.34444 | −0.0679914 | ||||||||
\(392\) | − 5.93842i | − 0.299936i | ||||||||
\(393\) | − 2.08550i | − 0.105200i | ||||||||
\(394\) | −4.48067 | −0.225733 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.84943 | −0.143189 | ||||||||
\(397\) | − 34.4305i | − 1.72802i | −0.503476 | − | 0.864009i | \(-0.667946\pi\) | ||||
0.503476 | − | 0.864009i | \(-0.332054\pi\) | |||||||
\(398\) | − 19.0647i | − 0.955629i | ||||||||
\(399\) | −2.46182 | −0.123245 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 36.2976 | 1.81262 | 0.906309 | − | 0.422616i | \(-0.138888\pi\) | ||||
0.906309 | + | 0.422616i | \(0.138888\pi\) | |||||||
\(402\) | 13.0286i | 0.649807i | ||||||||
\(403\) | − 48.2514i | − 2.40357i | ||||||||
\(404\) | −13.1869 | −0.656074 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 23.0960 | 1.14623 | ||||||||
\(407\) | − 3.72974i | − 0.184876i | ||||||||
\(408\) | − 5.02510i | − 0.248780i | ||||||||
\(409\) | −24.9896 | −1.23566 | −0.617828 | − | 0.786313i | \(-0.711987\pi\) | ||||
−0.617828 | + | 0.786313i | \(0.711987\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.9365 | −0.835416 | ||||||||
\(412\) | − 21.5833i | − 1.06333i | ||||||||
\(413\) | 3.07051i | 0.151090i | ||||||||
\(414\) | −0.591023 | −0.0290472 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −37.1202 | −1.81997 | ||||||||
\(417\) | 14.8883i | 0.729085i | ||||||||
\(418\) | − 6.62717i | − 0.324146i | ||||||||
\(419\) | −2.70313 | −0.132057 | −0.0660284 | − | 0.997818i | \(-0.521033\pi\) | ||||
−0.0660284 | + | 0.997818i | \(0.521033\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.6496 | 1.29882 | 0.649411 | − | 0.760438i | \(-0.275016\pi\) | ||||
0.649411 | + | 0.760438i | \(0.275016\pi\) | |||||||
\(422\) | − 35.1930i | − 1.71317i | ||||||||
\(423\) | − 12.5982i | − 0.612548i | ||||||||
\(424\) | −10.0890 | −0.489965 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.88676 | −0.236764 | ||||||||
\(427\) | − 7.78853i | − 0.376914i | ||||||||
\(428\) | 2.42490i | 0.117212i | ||||||||
\(429\) | −12.1440 | −0.586317 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.6242 | 1.61962 | 0.809811 | − | 0.586691i | \(-0.199570\pi\) | ||||
0.809811 | + | 0.586691i | \(0.199570\pi\) | |||||||
\(432\) | − 4.88558i | − 0.235058i | ||||||||
\(433\) | 5.34260i | 0.256749i | 0.991726 | + | 0.128375i | \(0.0409760\pi\) | ||||
−0.991726 | + | 0.128375i | \(0.959024\pi\) | |||||||
\(434\) | −22.3373 | −1.07223 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −24.7104 | −1.18341 | ||||||||
\(437\) | − 0.551055i | − 0.0263605i | ||||||||
\(438\) | 11.4788i | 0.548476i | ||||||||
\(439\) | −26.9690 | −1.28716 | −0.643580 | − | 0.765379i | \(-0.722552\pi\) | ||||
−0.643580 | + | 0.765379i | \(0.722552\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.91161 | −0.233886 | ||||||||
\(442\) | 43.3114i | 2.06011i | ||||||||
\(443\) | 16.8670i | 0.801374i | 0.916215 | + | 0.400687i | \(0.131229\pi\) | ||||
−0.916215 | + | 0.400687i | \(0.868771\pi\) | |||||||
\(444\) | −2.34424 | −0.111253 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 13.9171 | 0.658992 | ||||||||
\(447\) | − 4.70991i | − 0.222771i | ||||||||
\(448\) | 3.06376i | 0.144749i | ||||||||
\(449\) | −21.5942 | −1.01909 | −0.509546 | − | 0.860443i | \(-0.670187\pi\) | ||||
−0.509546 | + | 0.860443i | \(0.670187\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.6447 | 0.689593 | ||||||||
\(452\) | 17.8862i | 0.841297i | ||||||||
\(453\) | 9.63091i | 0.452500i | ||||||||
\(454\) | 2.40817 | 0.113021 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.05967 | 0.0964528 | ||||||||
\(457\) | 5.60699i | 0.262284i | 0.991364 | + | 0.131142i | \(0.0418644\pi\) | ||||
−0.991364 | + | 0.131142i | \(0.958136\pi\) | |||||||
\(458\) | 2.05788i | 0.0961587i | ||||||||
\(459\) | −4.15622 | −0.193996 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.54504 | −0.444557 | −0.222278 | − | 0.974983i | \(-0.571349\pi\) | ||||
−0.222278 | + | 0.974983i | \(0.571349\pi\) | |||||||
\(462\) | 5.62190i | 0.261554i | ||||||||
\(463\) | − 23.5262i | − 1.09336i | −0.837343 | − | 0.546678i | \(-0.815892\pi\) | ||||
0.837343 | − | 0.546678i | \(-0.184108\pi\) | |||||||
\(464\) | −42.7353 | −1.98394 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 48.6135 | 2.25198 | ||||||||
\(467\) | 36.5834i | 1.69288i | 0.532486 | + | 0.846439i | \(0.321258\pi\) | ||||
−0.532486 | + | 0.846439i | \(0.678742\pi\) | |||||||
\(468\) | 7.63282i | 0.352827i | ||||||||
\(469\) | 10.3049 | 0.475835 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.5557 | −0.855003 | ||||||||
\(472\) | − 2.56893i | − 0.118245i | ||||||||
\(473\) | − 23.7217i | − 1.09072i | ||||||||
\(474\) | 15.2944 | 0.702496 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 8.03793 | 0.368418 | ||||||||
\(477\) | 8.34451i | 0.382069i | ||||||||
\(478\) | − 45.4382i | − 2.07830i | ||||||||
\(479\) | −29.2750 | −1.33761 | −0.668804 | − | 0.743439i | \(-0.733193\pi\) | ||||
−0.668804 | + | 0.743439i | \(0.733193\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.99091 | −0.455546 | ||||||||
\(482\) | 22.5705i | 1.02806i | ||||||||
\(483\) | 0.467465i | 0.0212704i | ||||||||
\(484\) | 8.65385 | 0.393357 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.82709 | −0.0828785 | ||||||||
\(487\) | 21.2869i | 0.964600i | 0.876006 | + | 0.482300i | \(0.160199\pi\) | ||||
−0.876006 | + | 0.482300i | \(0.839801\pi\) | |||||||
\(488\) | 6.51624i | 0.294976i | ||||||||
\(489\) | 0.451705 | 0.0204268 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.1940 | −1.49803 | −0.749013 | − | 0.662556i | \(-0.769472\pi\) | ||||
−0.749013 | + | 0.662556i | \(0.769472\pi\) | |||||||
\(492\) | − 9.20459i | − 0.414975i | ||||||||
\(493\) | 36.3554i | 1.63737i | ||||||||
\(494\) | −17.7523 | −0.798714 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 41.3316 | 1.85584 | ||||||||
\(497\) | 3.86515i | 0.173376i | ||||||||
\(498\) | − 26.6521i | − 1.19431i | ||||||||
\(499\) | −4.72872 | −0.211686 | −0.105843 | − | 0.994383i | \(-0.533754\pi\) | ||||
−0.105843 | + | 0.994383i | \(0.533754\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.72648 | −0.211163 | ||||||||
\(502\) | 53.1657i | 2.37290i | ||||||||
\(503\) | − 0.400444i | − 0.0178549i | −0.999960 | − | 0.00892745i | \(-0.997158\pi\) | ||||
0.999960 | − | 0.00892745i | \(-0.00284173\pi\) | |||||||
\(504\) | −1.74724 | −0.0778282 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.25841 | −0.0559431 | ||||||||
\(507\) | 19.5303i | 0.867371i | ||||||||
\(508\) | − 1.35674i | − 0.0601956i | ||||||||
\(509\) | 27.6104 | 1.22381 | 0.611904 | − | 0.790932i | \(-0.290404\pi\) | ||||
0.611904 | + | 0.790932i | \(0.290404\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.07905 | 0.401633 | ||||||||
\(512\) | − 19.9828i | − 0.883126i | ||||||||
\(513\) | − 1.70353i | − 0.0752128i | ||||||||
\(514\) | 22.0164 | 0.971100 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −14.9097 | −0.656363 | ||||||||
\(517\) | − 26.8242i | − 1.17973i | ||||||||
\(518\) | 4.62516i | 0.203218i | ||||||||
\(519\) | 2.29489 | 0.100734 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.7374 | −1.25901 | −0.629505 | − | 0.776996i | \(-0.716742\pi\) | ||||
−0.629505 | + | 0.776996i | \(0.716742\pi\) | |||||||
\(522\) | 15.9820i | 0.699513i | ||||||||
\(523\) | 18.0660i | 0.789969i | 0.918688 | + | 0.394985i | \(0.129250\pi\) | ||||
−0.918688 | + | 0.394985i | \(0.870750\pi\) | |||||||
\(524\) | −2.79094 | −0.121923 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.87993 | −0.0819690 | ||||||||
\(527\) | − 35.1612i | − 1.53165i | ||||||||
\(528\) | − 10.4024i | − 0.452706i | ||||||||
\(529\) | 22.8954 | 0.995451 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.12474 | −0.0922058 | ||||||||
\(532\) | 3.29456i | 0.142837i | ||||||||
\(533\) | − 39.2290i | − 1.69920i | ||||||||
\(534\) | 4.89878 | 0.211991 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8.62152 | −0.372393 | ||||||||
\(537\) | 2.68757i | 0.115977i | ||||||||
\(538\) | 43.6807i | 1.88321i | ||||||||
\(539\) | −10.4578 | −0.450451 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.26032 | −0.226159 | −0.113079 | − | 0.993586i | \(-0.536071\pi\) | ||||
−0.113079 | + | 0.993586i | \(0.536071\pi\) | |||||||
\(542\) | − 6.80068i | − 0.292114i | ||||||||
\(543\) | 23.9088i | 1.02602i | ||||||||
\(544\) | −27.0498 | −1.15975 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 15.0595 | 0.644486 | ||||||||
\(547\) | 36.7888i | 1.57297i | 0.617607 | + | 0.786487i | \(0.288102\pi\) | ||||
−0.617607 | + | 0.786487i | \(0.711898\pi\) | |||||||
\(548\) | 22.6655i | 0.968221i | ||||||||
\(549\) | 5.38952 | 0.230019 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.9012 | −0.634813 | ||||||||
\(552\) | − 0.391103i | − 0.0166464i | ||||||||
\(553\) | − 12.0970i | − 0.514418i | ||||||||
\(554\) | 32.1207 | 1.36468 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 19.9245 | 0.844986 | ||||||||
\(557\) | − 23.3475i | − 0.989266i | −0.869102 | − | 0.494633i | \(-0.835302\pi\) | ||||
0.869102 | − | 0.494633i | \(-0.164698\pi\) | |||||||
\(558\) | − 15.4570i | − 0.654348i | ||||||||
\(559\) | −63.5436 | −2.68761 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.84943 | −0.373623 | ||||||||
\(562\) | − 24.2156i | − 1.02147i | ||||||||
\(563\) | − 29.2369i | − 1.23219i | −0.787672 | − | 0.616095i | \(-0.788714\pi\) | ||||
0.787672 | − | 0.616095i | \(-0.211286\pi\) | |||||||
\(564\) | −16.8597 | −0.709923 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 22.1071 | 0.929232 | ||||||||
\(567\) | 1.44512i | 0.0606895i | ||||||||
\(568\) | − 3.23376i | − 0.135685i | ||||||||
\(569\) | 20.2530 | 0.849051 | 0.424526 | − | 0.905416i | \(-0.360441\pi\) | ||||
0.424526 | + | 0.905416i | \(0.360441\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.57564 | −0.191484 | −0.0957422 | − | 0.995406i | \(-0.530522\pi\) | ||||
−0.0957422 | + | 0.995406i | \(0.530522\pi\) | |||||||
\(572\) | 16.2518i | 0.679523i | ||||||||
\(573\) | 3.91824i | 0.163687i | ||||||||
\(574\) | −18.1606 | −0.758007 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.12007 | −0.0883361 | ||||||||
\(577\) | 31.3502i | 1.30513i | 0.757734 | + | 0.652564i | \(0.226306\pi\) | ||||
−0.757734 | + | 0.652564i | \(0.773694\pi\) | |||||||
\(578\) | 0.500853i | 0.0208327i | ||||||||
\(579\) | −8.54752 | −0.355223 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.0803 | −0.874559 | ||||||||
\(582\) | − 15.6236i | − 0.647617i | ||||||||
\(583\) | 17.7672i | 0.735841i | ||||||||
\(584\) | −7.59594 | −0.314322 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.60809 | 0.272978 | ||||||||
\(587\) | 4.67218i | 0.192842i | 0.995341 | + | 0.0964208i | \(0.0307395\pi\) | ||||
−0.995341 | + | 0.0964208i | \(0.969261\pi\) | |||||||
\(588\) | 6.57302i | 0.271067i | ||||||||
\(589\) | 14.4117 | 0.593825 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.45235 | −0.100876 | ||||||||
\(592\) | − 8.55809i | − 0.351735i | ||||||||
\(593\) | − 7.37978i | − 0.303051i | −0.988453 | − | 0.151526i | \(-0.951581\pi\) | ||||
0.988453 | − | 0.151526i | \(-0.0484186\pi\) | |||||||
\(594\) | −3.89025 | −0.159619 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.30309 | −0.258185 | ||||||||
\(597\) | − 10.4345i | − 0.427055i | ||||||||
\(598\) | 3.37092i | 0.137847i | ||||||||
\(599\) | 46.7505 | 1.91018 | 0.955088 | − | 0.296323i | \(-0.0957605\pi\) | ||||
0.955088 | + | 0.296323i | \(0.0957605\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.3225 | 1.31846 | 0.659230 | − | 0.751941i | \(-0.270882\pi\) | ||||
0.659230 | + | 0.751941i | \(0.270882\pi\) | |||||||
\(602\) | 29.4167i | 1.19893i | ||||||||
\(603\) | 7.13078i | 0.290388i | ||||||||
\(604\) | 12.8887 | 0.524433 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −18.0037 | −0.731352 | ||||||||
\(607\) | 14.0891i | 0.571858i | 0.958251 | + | 0.285929i | \(0.0923021\pi\) | ||||
−0.958251 | + | 0.285929i | \(0.907698\pi\) | |||||||
\(608\) | − 11.0871i | − 0.449640i | ||||||||
\(609\) | 12.6409 | 0.512233 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −71.8545 | −2.90692 | ||||||||
\(612\) | 5.56210i | 0.224835i | ||||||||
\(613\) | − 12.2959i | − 0.496625i | −0.968680 | − | 0.248313i | \(-0.920124\pi\) | ||||
0.968680 | − | 0.248313i | \(-0.0798760\pi\) | |||||||
\(614\) | −27.0908 | −1.09330 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.72023 | −0.149892 | ||||||||
\(617\) | 1.96969i | 0.0792969i | 0.999214 | + | 0.0396485i | \(0.0126238\pi\) | ||||
−0.999214 | + | 0.0396485i | \(0.987376\pi\) | |||||||
\(618\) | − 29.4671i | − 1.18534i | ||||||||
\(619\) | −14.9714 | −0.601749 | −0.300875 | − | 0.953664i | \(-0.597279\pi\) | ||||
−0.300875 | + | 0.953664i | \(0.597279\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.323478 | −0.0129807 | ||||||||
\(622\) | 12.0877i | 0.484671i | ||||||||
\(623\) | − 3.87466i | − 0.155235i | ||||||||
\(624\) | −27.8651 | −1.11550 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −13.1153 | −0.524192 | ||||||||
\(627\) | − 3.62717i | − 0.144855i | ||||||||
\(628\) | 24.8324i | 0.990921i | ||||||||
\(629\) | −7.28046 | −0.290291 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.0729 | 0.719472 | 0.359736 | − | 0.933054i | \(-0.382867\pi\) | ||||
0.359736 | + | 0.933054i | \(0.382867\pi\) | |||||||
\(632\) | 10.1209i | 0.402588i | ||||||||
\(633\) | − 19.2618i | − 0.765587i | ||||||||
\(634\) | 17.8188 | 0.707675 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 11.1671 | 0.442806 | ||||||||
\(637\) | 28.0136i | 1.10994i | ||||||||
\(638\) | 34.0289i | 1.34722i | ||||||||
\(639\) | −2.67461 | −0.105806 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.2381 | 0.483374 | 0.241687 | − | 0.970354i | \(-0.422299\pi\) | ||||
0.241687 | + | 0.970354i | \(0.422299\pi\) | |||||||
\(642\) | 3.31065i | 0.130661i | ||||||||
\(643\) | − 16.4453i | − 0.648540i | −0.945964 | − | 0.324270i | \(-0.894881\pi\) | ||||
0.945964 | − | 0.324270i | \(-0.105119\pi\) | |||||||
\(644\) | 0.625591 | 0.0246517 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.9363 | −0.508971 | ||||||||
\(647\) | − 17.3991i | − 0.684028i | −0.939695 | − | 0.342014i | \(-0.888891\pi\) | ||||
0.939695 | − | 0.342014i | \(-0.111109\pi\) | |||||||
\(648\) | − 1.20906i | − 0.0474962i | ||||||||
\(649\) | −4.52400 | −0.177583 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.2256 | −0.479160 | ||||||||
\(652\) | − 0.604500i | − 0.0236740i | ||||||||
\(653\) | − 28.4645i | − 1.11390i | −0.830546 | − | 0.556950i | \(-0.811971\pi\) | ||||
0.830546 | − | 0.556950i | \(-0.188029\pi\) | |||||||
\(654\) | −33.7365 | −1.31920 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 33.6031 | 1.31198 | ||||||||
\(657\) | 6.28253i | 0.245105i | ||||||||
\(658\) | 33.2641i | 1.29677i | ||||||||
\(659\) | 1.51333 | 0.0589509 | 0.0294754 | − | 0.999566i | \(-0.490616\pi\) | ||||
0.0294754 | + | 0.999566i | \(0.490616\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.7842 | 1.04179 | 0.520893 | − | 0.853622i | \(-0.325599\pi\) | ||||
0.520893 | + | 0.853622i | \(0.325599\pi\) | |||||||
\(662\) | − 12.2200i | − 0.474943i | ||||||||
\(663\) | 23.7051i | 0.920630i | ||||||||
\(664\) | 17.6368 | 0.684439 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.20052 | −0.124018 | ||||||||
\(667\) | 2.82954i | 0.109560i | ||||||||
\(668\) | 6.32526i | 0.244732i | ||||||||
\(669\) | 7.61706 | 0.294492 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.4754 | 0.443003 | ||||||||
\(672\) | 9.40528i | 0.362817i | ||||||||
\(673\) | 9.31141i | 0.358929i | 0.983764 | + | 0.179464i | \(0.0574364\pi\) | ||||
−0.983764 | + | 0.179464i | \(0.942564\pi\) | |||||||
\(674\) | 38.0385 | 1.46519 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 26.1366 | 1.00526 | ||||||||
\(677\) | − 24.7854i | − 0.952579i | −0.879288 | − | 0.476290i | \(-0.841981\pi\) | ||||
0.879288 | − | 0.476290i | \(-0.158019\pi\) | |||||||
\(678\) | 24.4196i | 0.937828i | ||||||||
\(679\) | −12.3573 | −0.474231 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.31803 | 0.0505072 | ||||||||
\(682\) | − 32.9112i | − 1.26023i | ||||||||
\(683\) | − 37.3864i | − 1.43055i | −0.698842 | − | 0.715276i | \(-0.746301\pi\) | ||||
0.698842 | − | 0.715276i | \(-0.253699\pi\) | |||||||
\(684\) | −2.27977 | −0.0871693 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 31.4511 | 1.20081 | ||||||||
\(687\) | 1.12632i | 0.0429717i | ||||||||
\(688\) | − 54.4307i | − 2.07515i | ||||||||
\(689\) | 47.5932 | 1.81316 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.8909 | −1.25123 | −0.625615 | − | 0.780132i | \(-0.715152\pi\) | ||||
−0.625615 | + | 0.780132i | \(0.715152\pi\) | |||||||
\(692\) | − 3.07116i | − 0.116748i | ||||||||
\(693\) | 3.07697i | 0.116884i | ||||||||
\(694\) | 56.6229 | 2.14938 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −10.5759 | −0.400879 | ||||||||
\(697\) | − 28.5865i | − 1.08279i | ||||||||
\(698\) | − 13.6207i | − 0.515550i | ||||||||
\(699\) | 26.6071 | 1.00637 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.3336 | −1.59892 | −0.799459 | − | 0.600721i | \(-0.794880\pi\) | ||||
−0.799459 | + | 0.600721i | \(0.794880\pi\) | |||||||
\(702\) | 10.4209i | 0.393311i | ||||||||
\(703\) | − 2.98409i | − 0.112547i | ||||||||
\(704\) | −4.51406 | −0.170130 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.74101 | −0.253701 | ||||||||
\(707\) | 14.2399i | 0.535548i | ||||||||
\(708\) | 2.84345i | 0.106864i | ||||||||
\(709\) | −18.3593 | −0.689498 | −0.344749 | − | 0.938695i | \(-0.612036\pi\) | ||||
−0.344749 | + | 0.938695i | \(0.612036\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.37092 | 0.313934 | ||||||||
\(712\) | 3.24171i | 0.121488i | ||||||||
\(713\) | − 2.73659i | − 0.102486i | ||||||||
\(714\) | 10.9740 | 0.410690 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.59667 | 0.134414 | ||||||||
\(717\) | − 24.8692i | − 0.928756i | ||||||||
\(718\) | − 18.1428i | − 0.677084i | ||||||||
\(719\) | 19.2706 | 0.718671 | 0.359336 | − | 0.933208i | \(-0.383003\pi\) | ||||
0.359336 | + | 0.933208i | \(0.383003\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.3068 | −0.867992 | ||||||||
\(722\) | 29.4125i | 1.09462i | ||||||||
\(723\) | 12.3532i | 0.459422i | ||||||||
\(724\) | 31.9962 | 1.18913 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 11.8149 | 0.438491 | ||||||||
\(727\) | − 17.4238i | − 0.646214i | −0.946362 | − | 0.323107i | \(-0.895273\pi\) | ||||
0.946362 | − | 0.323107i | \(-0.104727\pi\) | |||||||
\(728\) | 9.96543i | 0.369343i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −46.3048 | −1.71265 | ||||||||
\(732\) | − 7.21259i | − 0.266585i | ||||||||
\(733\) | 24.2010i | 0.893883i | 0.894563 | + | 0.446942i | \(0.147487\pi\) | ||||
−0.894563 | + | 0.446942i | \(0.852513\pi\) | |||||||
\(734\) | 22.9313 | 0.846410 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.10528 | −0.0776018 | ||||||||
\(737\) | 15.1829i | 0.559269i | ||||||||
\(738\) | − 12.5668i | − 0.462589i | ||||||||
\(739\) | 38.5798 | 1.41918 | 0.709591 | − | 0.704613i | \(-0.248880\pi\) | ||||
0.709591 | + | 0.704613i | \(0.248880\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.71616 | −0.356932 | ||||||||
\(742\) | − 22.0326i | − 0.808844i | ||||||||
\(743\) | − 33.8580i | − 1.24213i | −0.783759 | − | 0.621065i | \(-0.786700\pi\) | ||||
0.783759 | − | 0.621065i | \(-0.213300\pi\) | |||||||
\(744\) | 10.2285 | 0.374995 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 27.1462 | 0.993895 | ||||||||
\(747\) | − 14.5872i | − 0.533718i | ||||||||
\(748\) | 11.8429i | 0.433018i | ||||||||
\(749\) | 2.61853 | 0.0956791 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −45.9138 | −1.67542 | −0.837710 | − | 0.546115i | \(-0.816106\pi\) | ||||
−0.837710 | + | 0.546115i | \(0.816106\pi\) | |||||||
\(752\) | − 61.5497i | − 2.24449i | ||||||||
\(753\) | 29.0986i | 1.06041i | ||||||||
\(754\) | 91.1539 | 3.31963 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.93395 | 0.0703372 | ||||||||
\(757\) | − 10.3561i | − 0.376400i | −0.982131 | − | 0.188200i | \(-0.939735\pi\) | ||||
0.982131 | − | 0.188200i | \(-0.0602653\pi\) | |||||||
\(758\) | 20.6383i | 0.749618i | ||||||||
\(759\) | −0.688750 | −0.0250000 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 49.2652 | 1.78586 | 0.892931 | − | 0.450193i | \(-0.148645\pi\) | ||||
0.892931 | + | 0.450193i | \(0.148645\pi\) | |||||||
\(762\) | − 1.85232i | − 0.0671024i | ||||||||
\(763\) | 26.6836i | 0.966012i | ||||||||
\(764\) | 5.24362 | 0.189708 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.57205 | −0.201326 | ||||||||
\(767\) | 12.1185i | 0.437574i | ||||||||
\(768\) | − 20.9452i | − 0.755797i | ||||||||
\(769\) | 1.26208 | 0.0455116 | 0.0227558 | − | 0.999741i | \(-0.492756\pi\) | ||||
0.0227558 | + | 0.999741i | \(0.492756\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.0500 | 0.433969 | ||||||||
\(772\) | 11.4388i | 0.411692i | ||||||||
\(773\) | − 26.9903i | − 0.970772i | −0.874300 | − | 0.485386i | \(-0.838679\pi\) | ||||
0.874300 | − | 0.485386i | \(-0.161321\pi\) | |||||||
\(774\) | −20.3558 | −0.731674 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 10.3387 | 0.371138 | ||||||||
\(777\) | 2.53143i | 0.0908146i | ||||||||
\(778\) | − 39.0887i | − 1.40140i | ||||||||
\(779\) | 11.7169 | 0.419803 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.69480 | −0.203776 | ||||||||
\(782\) | 2.45642i | 0.0878413i | ||||||||
\(783\) | 8.74724i | 0.312601i | ||||||||
\(784\) | −23.9961 | −0.857003 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.81040 | −0.135912 | ||||||||
\(787\) | − 7.62303i | − 0.271732i | −0.990727 | − | 0.135866i | \(-0.956618\pi\) | ||||
0.990727 | − | 0.135866i | \(-0.0433816\pi\) | |||||||
\(788\) | 3.28189i | 0.116912i | ||||||||
\(789\) | −1.02892 | −0.0366306 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.3145 | 0.686744 | ||||||||
\(792\) | − 2.57433i | − 0.0914748i | ||||||||
\(793\) | − 30.7393i | − 1.09159i | ||||||||
\(794\) | −62.9077 | −2.23251 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −13.9641 | −0.494943 | ||||||||
\(797\) | − 4.98266i | − 0.176495i | −0.996099 | − | 0.0882474i | \(-0.971873\pi\) | ||||
0.996099 | − | 0.0882474i | \(-0.0281266\pi\) | |||||||
\(798\) | 4.49797i | 0.159226i | ||||||||
\(799\) | −52.3610 | −1.85240 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.68119 | 0.0947353 | ||||||||
\(802\) | − 66.3191i | − 2.34181i | ||||||||
\(803\) | 13.3768i | 0.472057i | ||||||||
\(804\) | 9.54285 | 0.336550 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −88.1596 | −3.10529 | ||||||||
\(807\) | 23.9072i | 0.841574i | ||||||||
\(808\) | − 11.9138i | − 0.419125i | ||||||||
\(809\) | −5.74271 | −0.201903 | −0.100952 | − | 0.994891i | \(-0.532189\pi\) | ||||
−0.100952 | + | 0.994891i | \(0.532189\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.8021 | 1.36253 | 0.681264 | − | 0.732038i | \(-0.261431\pi\) | ||||
0.681264 | + | 0.732038i | \(0.261431\pi\) | |||||||
\(812\) | − 16.9168i | − 0.593662i | ||||||||
\(813\) | − 3.72214i | − 0.130541i | ||||||||
\(814\) | −6.81457 | −0.238851 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −20.3055 | −0.710835 | ||||||||
\(817\) | − 18.9792i | − 0.664000i | ||||||||
\(818\) | 45.6583i | 1.59640i | ||||||||
\(819\) | 8.24232 | 0.288010 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −41.8919 | −1.46204 | −0.731019 | − | 0.682357i | \(-0.760955\pi\) | ||||
−0.731019 | + | 0.682357i | \(0.760955\pi\) | |||||||
\(822\) | 30.9445i | 1.07931i | ||||||||
\(823\) | − 29.2212i | − 1.01859i | −0.860593 | − | 0.509294i | \(-0.829907\pi\) | ||||
0.860593 | − | 0.509294i | \(-0.170093\pi\) | |||||||
\(824\) | 19.4995 | 0.679299 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.61010 | 0.195200 | ||||||||
\(827\) | − 7.41934i | − 0.257996i | −0.991645 | − | 0.128998i | \(-0.958824\pi\) | ||||
0.991645 | − | 0.128998i | \(-0.0411760\pi\) | |||||||
\(828\) | 0.432897i | 0.0150442i | ||||||||
\(829\) | −29.7586 | −1.03356 | −0.516779 | − | 0.856119i | \(-0.672869\pi\) | ||||
−0.516779 | + | 0.856119i | \(0.672869\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.5802 | 0.609852 | ||||||||
\(832\) | 12.0919i | 0.419210i | ||||||||
\(833\) | 20.4137i | 0.707294i | ||||||||
\(834\) | 27.2024 | 0.941940 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.85410 | −0.167883 | ||||||||
\(837\) | − 8.45991i | − 0.292417i | ||||||||
\(838\) | 4.93887i | 0.170610i | ||||||||
\(839\) | −29.5793 | −1.02119 | −0.510595 | − | 0.859821i | \(-0.670575\pi\) | ||||
−0.510595 | + | 0.859821i | \(0.670575\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 47.5142 | 1.63842 | ||||||||
\(842\) | − 48.6912i | − 1.67801i | ||||||||
\(843\) | − 13.2536i | − 0.456479i | ||||||||
\(844\) | −25.7773 | −0.887291 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −23.0181 | −0.791380 | ||||||||
\(847\) | − 9.34488i | − 0.321094i | ||||||||
\(848\) | 40.7678i | 1.39997i | ||||||||
\(849\) | 12.0996 | 0.415258 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.566637 | −0.0194241 | ||||||||
\(852\) | 3.57933i | 0.122626i | ||||||||
\(853\) | 37.5298i | 1.28499i | 0.766288 | + | 0.642497i | \(0.222102\pi\) | ||||
−0.766288 | + | 0.642497i | \(0.777898\pi\) | |||||||
\(854\) | −14.2304 | −0.486953 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.19078 | −0.0748794 | ||||||||
\(857\) | − 49.4333i | − 1.68861i | −0.535864 | − | 0.844305i | \(-0.680014\pi\) | ||||
0.535864 | − | 0.844305i | \(-0.319986\pi\) | |||||||
\(858\) | 22.1882i | 0.757492i | ||||||||
\(859\) | −2.82651 | −0.0964394 | −0.0482197 | − | 0.998837i | \(-0.515355\pi\) | ||||
−0.0482197 | + | 0.998837i | \(0.515355\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.93960 | −0.338741 | ||||||||
\(862\) | − 61.4345i | − 2.09247i | ||||||||
\(863\) | − 33.3977i | − 1.13687i | −0.822727 | − | 0.568436i | \(-0.807549\pi\) | ||||
0.822727 | − | 0.568436i | \(-0.192451\pi\) | |||||||
\(864\) | −6.50828 | −0.221416 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 9.76142 | 0.331707 | ||||||||
\(867\) | 0.274126i | 0.00930980i | ||||||||
\(868\) | 16.3611i | 0.555331i | ||||||||
\(869\) | 17.8234 | 0.604617 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 40.6707 | 1.37807 | ||||||||
\(872\) | − 22.3247i | − 0.756011i | ||||||||
\(873\) | − 8.55105i | − 0.289409i | ||||||||
\(874\) | −1.00683 | −0.0340564 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.40767 | 0.284069 | ||||||||
\(877\) | − 9.28115i | − 0.313402i | −0.987646 | − | 0.156701i | \(-0.949914\pi\) | ||||
0.987646 | − | 0.156701i | \(-0.0500859\pi\) | |||||||
\(878\) | 49.2748i | 1.66294i | ||||||||
\(879\) | 3.61673 | 0.121989 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.58736 | 0.221934 | 0.110967 | − | 0.993824i | \(-0.464605\pi\) | ||||
0.110967 | + | 0.993824i | \(0.464605\pi\) | |||||||
\(882\) | 8.97397i | 0.302169i | ||||||||
\(883\) | − 4.18883i | − 0.140965i | −0.997513 | − | 0.0704827i | \(-0.977546\pi\) | ||||
0.997513 | − | 0.0704827i | \(-0.0224540\pi\) | |||||||
\(884\) | 31.7236 | 1.06698 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 30.8175 | 1.03533 | ||||||||
\(887\) | − 26.8716i | − 0.902260i | −0.892458 | − | 0.451130i | \(-0.851021\pi\) | ||||
0.892458 | − | 0.451130i | \(-0.148979\pi\) | |||||||
\(888\) | − 2.11791i | − 0.0710724i | ||||||||
\(889\) | −1.46508 | −0.0491371 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.12920 | −0.0713310 | ||||||||
\(892\) | − 10.1936i | − 0.341307i | ||||||||
\(893\) | − 21.4615i | − 0.718183i | ||||||||
\(894\) | −8.60543 | −0.287809 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −13.2128 | −0.441408 | ||||||||
\(897\) | 1.84497i | 0.0616016i | ||||||||
\(898\) | 39.4545i | 1.31661i | ||||||||
\(899\) | −74.0008 | −2.46807 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.6816 | 1.15541 | ||||||||
\(902\) | − 26.7572i | − 0.890918i | ||||||||
\(903\) | 16.1003i | 0.535784i | ||||||||
\(904\) | −16.1594 | −0.537453 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 17.5965 | 0.584606 | ||||||||
\(907\) | 39.1821i | 1.30102i | 0.759497 | + | 0.650511i | \(0.225445\pi\) | ||||
−0.759497 | + | 0.650511i | \(0.774555\pi\) | |||||||
\(908\) | − 1.76387i | − 0.0585362i | ||||||||
\(909\) | −9.85377 | −0.326829 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.2926 | 1.79880 | 0.899398 | − | 0.437132i | \(-0.144006\pi\) | ||||
0.899398 | + | 0.437132i | \(0.144006\pi\) | |||||||
\(912\) | − 8.32275i | − 0.275594i | ||||||||
\(913\) | − 31.0591i | − 1.02791i | ||||||||
\(914\) | 10.2445 | 0.338857 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.50731 | 0.0498028 | ||||||||
\(917\) | 3.01381i | 0.0995247i | ||||||||
\(918\) | 7.59378i | 0.250632i | ||||||||
\(919\) | 28.0959 | 0.926798 | 0.463399 | − | 0.886150i | \(-0.346630\pi\) | ||||
0.463399 | + | 0.886150i | \(0.346630\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.8273 | −0.488576 | ||||||||
\(922\) | 17.4396i | 0.574344i | ||||||||
\(923\) | 15.2547i | 0.502116i | ||||||||
\(924\) | 4.11778 | 0.135465 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −42.9846 | −1.41256 | ||||||||
\(927\) | − 16.1279i | − 0.529710i | ||||||||
\(928\) | 56.9295i | 1.86880i | ||||||||
\(929\) | 31.3772 | 1.02945 | 0.514727 | − | 0.857354i | \(-0.327893\pi\) | ||||
0.514727 | + | 0.857354i | \(0.327893\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.36710 | −0.274221 | ||||||||
\(932\) | − 35.6072i | − 1.16635i | ||||||||
\(933\) | 6.61579i | 0.216591i | ||||||||
\(934\) | 66.8412 | 2.18711 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.89590 | −0.225399 | ||||||||
\(937\) | 49.7286i | 1.62456i | 0.583266 | + | 0.812281i | \(0.301774\pi\) | ||||
−0.583266 | + | 0.812281i | \(0.698226\pi\) | |||||||
\(938\) | − 18.8279i | − 0.614754i | ||||||||
\(939\) | −7.17823 | −0.234253 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.49598 | −0.146565 | −0.0732824 | − | 0.997311i | \(-0.523347\pi\) | ||||
−0.0732824 | + | 0.997311i | \(0.523347\pi\) | |||||||
\(942\) | 33.9030i | 1.10462i | ||||||||
\(943\) | − 2.22489i | − 0.0724523i | ||||||||
\(944\) | −10.3806 | −0.337859 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −43.3417 | −1.40916 | ||||||||
\(947\) | 28.8993i | 0.939101i | 0.882906 | + | 0.469551i | \(0.155584\pi\) | ||||
−0.882906 | + | 0.469551i | \(0.844416\pi\) | |||||||
\(948\) | − 11.2025i | − 0.363840i | ||||||||
\(949\) | 35.8326 | 1.16318 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.75255 | 0.316248 | ||||||||
\(952\) | 7.26190i | 0.235359i | ||||||||
\(953\) | − 46.1922i | − 1.49631i | −0.663523 | − | 0.748156i | \(-0.730940\pi\) | ||||
0.663523 | − | 0.748156i | \(-0.269060\pi\) | |||||||
\(954\) | 15.2462 | 0.493613 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −33.2814 | −1.07640 | ||||||||
\(957\) | 18.6247i | 0.602050i | ||||||||
\(958\) | 53.4880i | 1.72812i | ||||||||
\(959\) | 24.4754 | 0.790351 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 40.5701 | 1.30871 | ||||||||
\(962\) | 18.2543i | 0.588542i | ||||||||
\(963\) | 1.81198i | 0.0583901i | ||||||||
\(964\) | 16.5319 | 0.532456 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.854102 | 0.0274803 | ||||||||
\(967\) | − 8.41820i | − 0.270711i | −0.990797 | − | 0.135356i | \(-0.956782\pi\) | ||||
0.990797 | − | 0.135356i | \(-0.0432177\pi\) | |||||||
\(968\) | 7.81835i | 0.251291i | ||||||||
\(969\) | −7.08025 | −0.227450 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.4421 | 0.848567 | 0.424284 | − | 0.905529i | \(-0.360526\pi\) | ||||
0.424284 | + | 0.905529i | \(0.360526\pi\) | |||||||
\(972\) | 1.33826i | 0.0429247i | ||||||||
\(973\) | − 21.5155i | − 0.689756i | ||||||||
\(974\) | 38.8931 | 1.24621 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 26.3309 | 0.842833 | ||||||||
\(977\) | − 39.8235i | − 1.27407i | −0.770836 | − | 0.637034i | \(-0.780161\pi\) | ||||
0.770836 | − | 0.637034i | \(-0.219839\pi\) | |||||||
\(978\) | − 0.825307i | − 0.0263904i | ||||||||
\(979\) | 5.70881 | 0.182454 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.4646 | −0.589529 | ||||||||
\(982\) | 60.6485i | 1.93537i | ||||||||
\(983\) | − 24.1179i | − 0.769242i | −0.923075 | − | 0.384621i | \(-0.874332\pi\) | ||||
0.923075 | − | 0.384621i | \(-0.125668\pi\) | |||||||
\(984\) | 8.31592 | 0.265102 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 66.4246 | 2.11539 | ||||||||
\(987\) | 18.2060i | 0.579505i | ||||||||
\(988\) | 13.0028i | 0.413673i | ||||||||
\(989\) | −3.60390 | −0.114597 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.4044 | −0.330506 | −0.165253 | − | 0.986251i | \(-0.552844\pi\) | ||||
−0.165253 | + | 0.986251i | \(0.552844\pi\) | |||||||
\(992\) | − 55.0595i | − 1.74814i | ||||||||
\(993\) | − 6.68822i | − 0.212244i | ||||||||
\(994\) | 7.06198 | 0.223992 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −19.5215 | −0.618562 | ||||||||
\(997\) | 13.3642i | 0.423249i | 0.977351 | + | 0.211624i | \(0.0678754\pi\) | ||||
−0.977351 | + | 0.211624i | \(0.932125\pi\) | |||||||
\(998\) | 8.63980i | 0.273488i | ||||||||
\(999\) | −1.75170 | −0.0554215 |
(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 | 1875.2.b.d.1249.2 | 8 | ||
5.2 | odd | 4 | 1875.2.a.g.1.4 | yes | 4 | ||
5.3 | odd | 4 | 1875.2.a.f.1.1 | ✓ | 4 | ||
5.4 | even | 2 | inner | 1875.2.b.d.1249.7 | 8 | ||
15.2 | even | 4 | 5625.2.a.j.1.1 | 4 | |||
15.8 | even | 4 | 5625.2.a.m.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1875.2.a.f.1.1 | ✓ | 4 | 5.3 | odd | 4 | ||
1875.2.a.g.1.4 | yes | 4 | 5.2 | odd | 4 | ||
1875.2.b.d.1249.2 | 8 | 1.1 | even | 1 | trivial | ||
1875.2.b.d.1249.7 | 8 | 5.4 | even | 2 | inner | ||
5625.2.a.j.1.1 | 4 | 15.2 | even | 4 | |||
5625.2.a.m.1.4 | 4 | 15.8 | even | 4 |