Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(170,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.170");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.e (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: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 11x^{14} + 85x^{12} + 334x^{10} + 952x^{8} + 1050x^{6} + 853x^{4} + 93x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 508.4 | ||
Root | \(-0.166188 + 0.287846i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.508 |
Dual form | 1183.2.e.i.170.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(1016\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.166188 | − | 0.287846i | −0.117512 | − | 0.203538i | 0.801269 | − | 0.598304i | \(-0.204159\pi\) |
−0.918781 | + | 0.394767i | \(0.870825\pi\) | |||||||
\(3\) | −0.729919 | + | 1.26426i | −0.421419 | + | 0.729919i | −0.996079 | − | 0.0884737i | \(-0.971801\pi\) |
0.574660 | + | 0.818392i | \(0.305134\pi\) | |||||||
\(4\) | 0.944763 | − | 1.63638i | 0.472382 | − | 0.818189i | ||||
\(5\) | −0.722811 | − | 1.25195i | −0.323251 | − | 0.559887i | 0.657906 | − | 0.753100i | \(-0.271442\pi\) |
−0.981157 | + | 0.193213i | \(0.938109\pi\) | |||||||
\(6\) | 0.485214 | 0.198088 | ||||||||
\(7\) | −1.36920 | + | 2.26391i | −0.517510 | + | 0.855677i | ||||
\(8\) | −1.29278 | −0.457068 | ||||||||
\(9\) | 0.434437 | + | 0.752468i | 0.144812 | + | 0.250823i | ||||
\(10\) | −0.240245 | + | 0.416116i | −0.0759720 | + | 0.131587i | ||||
\(11\) | 2.97758 | − | 5.15732i | 0.897774 | − | 1.55499i | 0.0674405 | − | 0.997723i | \(-0.478517\pi\) |
0.830333 | − | 0.557267i | \(-0.188150\pi\) | |||||||
\(12\) | 1.37920 | + | 2.38885i | 0.398141 | + | 0.689600i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.879201 | + | 0.0178849i | 0.234976 | + | 0.00477994i | ||||
\(15\) | 2.11037 | 0.544896 | ||||||||
\(16\) | −1.67468 | − | 2.90063i | −0.418670 | − | 0.725159i | ||||
\(17\) | −2.16436 | + | 3.74877i | −0.524933 | + | 0.909211i | 0.474645 | + | 0.880177i | \(0.342576\pi\) |
−0.999578 | + | 0.0290341i | \(0.990757\pi\) | |||||||
\(18\) | 0.144396 | − | 0.250102i | 0.0340345 | − | 0.0589496i | ||||
\(19\) | −0.978767 | − | 1.69527i | −0.224545 | − | 0.388923i | 0.731638 | − | 0.681693i | \(-0.238756\pi\) |
−0.956183 | + | 0.292771i | \(0.905423\pi\) | |||||||
\(20\) | −2.73154 | −0.610791 | ||||||||
\(21\) | −1.86276 | − | 3.38349i | −0.406486 | − | 0.738339i | ||||
\(22\) | −1.97935 | −0.421998 | ||||||||
\(23\) | 0.270081 | + | 0.467795i | 0.0563158 | + | 0.0975419i | 0.892809 | − | 0.450436i | \(-0.148731\pi\) |
−0.836493 | + | 0.547977i | \(0.815398\pi\) | |||||||
\(24\) | 0.943626 | − | 1.63441i | 0.192617 | − | 0.333622i | ||||
\(25\) | 1.45509 | − | 2.52029i | 0.291018 | − | 0.504058i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.64793 | −1.08694 | ||||||||
\(28\) | 2.41104 | + | 4.37939i | 0.455644 | + | 0.827627i | ||||
\(29\) | 7.15857 | 1.32931 | 0.664656 | − | 0.747149i | \(-0.268578\pi\) | ||||
0.664656 | + | 0.747149i | \(0.268578\pi\) | |||||||
\(30\) | −0.350718 | − | 0.607461i | −0.0640320 | − | 0.110907i | ||||
\(31\) | 3.05400 | − | 5.28968i | 0.548514 | − | 0.950055i | −0.449862 | − | 0.893098i | \(-0.648527\pi\) |
0.998377 | − | 0.0569568i | \(-0.0181397\pi\) | |||||||
\(32\) | −1.84941 | + | 3.20327i | −0.326932 | + | 0.566263i | ||||
\(33\) | 4.34678 | + | 7.52885i | 0.756678 | + | 1.31060i | ||||
\(34\) | 1.43876 | 0.246745 | ||||||||
\(35\) | 3.82396 | + | 0.0777879i | 0.646368 | + | 0.0131486i | ||||
\(36\) | 1.64176 | 0.273627 | ||||||||
\(37\) | −4.01441 | − | 6.95316i | −0.659964 | − | 1.14309i | −0.980624 | − | 0.195897i | \(-0.937238\pi\) |
0.320660 | − | 0.947194i | \(-0.396095\pi\) | |||||||
\(38\) | −0.325318 | + | 0.563467i | −0.0527736 | + | 0.0914065i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.934437 | + | 1.61849i | 0.147748 | + | 0.255906i | ||||
\(41\) | −7.55362 | −1.17968 | −0.589839 | − | 0.807521i | \(-0.700809\pi\) | ||||
−0.589839 | + | 0.807521i | \(0.700809\pi\) | |||||||
\(42\) | −0.664356 | + | 1.09848i | −0.102512 | + | 0.169499i | ||||
\(43\) | 4.24839 | 0.647873 | 0.323936 | − | 0.946079i | \(-0.394994\pi\) | ||||
0.323936 | + | 0.946079i | \(0.394994\pi\) | |||||||
\(44\) | −5.62622 | − | 9.74489i | −0.848184 | − | 1.46910i | ||||
\(45\) | 0.628032 | − | 1.08778i | 0.0936215 | − | 0.162157i | ||||
\(46\) | 0.0897684 | − | 0.155483i | 0.0132356 | − | 0.0229248i | ||||
\(47\) | −3.13042 | − | 5.42204i | −0.456618 | − | 0.790886i | 0.542161 | − | 0.840274i | \(-0.317606\pi\) |
−0.998780 | + | 0.0493882i | \(0.984273\pi\) | |||||||
\(48\) | 4.88953 | 0.705742 | ||||||||
\(49\) | −3.25057 | − | 6.19950i | −0.464367 | − | 0.885643i | ||||
\(50\) | −0.967272 | −0.136793 | ||||||||
\(51\) | −3.15961 | − | 5.47260i | −0.442434 | − | 0.766317i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.38953 | − | 2.40673i | 0.190866 | − | 0.330590i | −0.754671 | − | 0.656103i | \(-0.772204\pi\) |
0.945538 | + | 0.325513i | \(0.105537\pi\) | |||||||
\(54\) | 0.938616 | + | 1.62573i | 0.127729 | + | 0.221234i | ||||
\(55\) | −8.60891 | −1.16082 | ||||||||
\(56\) | 1.77008 | − | 2.92674i | 0.236537 | − | 0.391103i | ||||
\(57\) | 2.85768 | 0.378509 | ||||||||
\(58\) | −1.18967 | − | 2.06056i | −0.156211 | − | 0.270565i | ||||
\(59\) | 0.425576 | − | 0.737119i | 0.0554053 | − | 0.0959647i | −0.836993 | − | 0.547214i | \(-0.815688\pi\) |
0.892398 | + | 0.451250i | \(0.149022\pi\) | |||||||
\(60\) | 1.99380 | − | 3.45337i | 0.257399 | − | 0.445828i | ||||
\(61\) | −3.38953 | − | 5.87083i | −0.433984 | − | 0.751683i | 0.563228 | − | 0.826302i | \(-0.309559\pi\) |
−0.997212 | + | 0.0746187i | \(0.976226\pi\) | |||||||
\(62\) | −2.03015 | −0.257829 | ||||||||
\(63\) | −2.29835 | − | 0.0467536i | −0.289565 | − | 0.00589039i | ||||
\(64\) | −5.46933 | −0.683667 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.44476 | − | 2.50240i | 0.177838 | − | 0.308025i | ||||
\(67\) | 0.493553 | − | 0.854859i | 0.0602971 | − | 0.104438i | −0.834301 | − | 0.551309i | \(-0.814129\pi\) |
0.894598 | + | 0.446871i | \(0.147462\pi\) | |||||||
\(68\) | 4.08961 | + | 7.08341i | 0.495938 | + | 0.858990i | ||||
\(69\) | −0.788550 | −0.0949302 | ||||||||
\(70\) | −0.613105 | − | 1.11364i | −0.0732801 | − | 0.133105i | ||||
\(71\) | 3.76223 | 0.446494 | 0.223247 | − | 0.974762i | \(-0.428334\pi\) | ||||
0.223247 | + | 0.974762i | \(0.428334\pi\) | |||||||
\(72\) | −0.561633 | − | 0.972777i | −0.0661891 | − | 0.114643i | ||||
\(73\) | 4.56760 | − | 7.91131i | 0.534597 | − | 0.925949i | −0.464586 | − | 0.885528i | \(-0.653797\pi\) |
0.999183 | − | 0.0404208i | \(-0.0128699\pi\) | |||||||
\(74\) | −1.33429 | + | 2.31106i | −0.155108 | + | 0.268655i | ||||
\(75\) | 2.12419 | + | 3.67921i | 0.245281 | + | 0.424839i | ||||
\(76\) | −3.69881 | −0.424283 | ||||||||
\(77\) | 7.59879 | + | 13.8024i | 0.865963 | + | 1.57293i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.0655625 | + | 0.113558i | 0.00737636 | + | 0.0127762i | 0.869690 | − | 0.493598i | \(-0.164319\pi\) |
−0.862314 | + | 0.506375i | \(0.830985\pi\) | |||||||
\(80\) | −2.42096 | + | 4.19322i | −0.270671 | + | 0.468816i | ||||
\(81\) | 2.81922 | − | 4.88303i | 0.313246 | − | 0.542558i | ||||
\(82\) | 1.25532 | + | 2.17428i | 0.138627 | + | 0.240109i | ||||
\(83\) | 2.66812 | 0.292865 | 0.146432 | − | 0.989221i | \(-0.453221\pi\) | ||||
0.146432 | + | 0.989221i | \(0.453221\pi\) | |||||||
\(84\) | −7.29653 | − | 0.148428i | −0.796117 | − | 0.0161948i | ||||
\(85\) | 6.25768 | 0.678741 | ||||||||
\(86\) | −0.706030 | − | 1.22288i | −0.0761331 | − | 0.131866i | ||||
\(87\) | −5.22517 | + | 9.05026i | −0.560197 | + | 0.970290i | ||||
\(88\) | −3.84936 | + | 6.66729i | −0.410344 | + | 0.710736i | ||||
\(89\) | −4.85869 | − | 8.41550i | −0.515021 | − | 0.892042i | −0.999848 | − | 0.0174319i | \(-0.994451\pi\) |
0.484828 | − | 0.874610i | \(-0.338882\pi\) | |||||||
\(90\) | −0.417485 | −0.0440068 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.02065 | 0.106410 | ||||||||
\(93\) | 4.45834 | + | 7.72207i | 0.462308 | + | 0.800742i | ||||
\(94\) | −1.04047 | + | 1.80215i | −0.107317 | + | 0.185878i | ||||
\(95\) | −1.41493 | + | 2.45072i | −0.145168 | + | 0.251439i | ||||
\(96\) | −2.69983 | − | 4.67625i | −0.275550 | − | 0.477267i | ||||
\(97\) | 6.58319 | 0.668422 | 0.334211 | − | 0.942498i | \(-0.391530\pi\) | ||||
0.334211 | + | 0.942498i | \(0.391530\pi\) | |||||||
\(98\) | −1.24429 | + | 1.96594i | −0.125693 | + | 0.198590i | ||||
\(99\) | 5.17429 | 0.520036 | ||||||||
\(100\) | −2.74943 | − | 4.76215i | −0.274943 | − | 0.476215i | ||||
\(101\) | 0.0354144 | − | 0.0613396i | 0.00352387 | − | 0.00610352i | −0.864258 | − | 0.503049i | \(-0.832212\pi\) |
0.867782 | + | 0.496945i | \(0.165545\pi\) | |||||||
\(102\) | −1.05018 | + | 1.81896i | −0.103983 | + | 0.180104i | ||||
\(103\) | −3.16910 | − | 5.48905i | −0.312261 | − | 0.540852i | 0.666590 | − | 0.745424i | \(-0.267753\pi\) |
−0.978852 | + | 0.204572i | \(0.934420\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.88953 | + | 4.77769i | −0.281989 | + | 0.466255i | ||||
\(106\) | −0.923689 | −0.0897166 | ||||||||
\(107\) | −3.87476 | − | 6.71129i | −0.374588 | − | 0.648805i | 0.615678 | − | 0.787998i | \(-0.288882\pi\) |
−0.990265 | + | 0.139193i | \(0.955549\pi\) | |||||||
\(108\) | −5.33596 | + | 9.24215i | −0.513453 | + | 0.889326i | ||||
\(109\) | 0.0167811 | − | 0.0290658i | 0.00160734 | − | 0.00278400i | −0.865221 | − | 0.501391i | \(-0.832822\pi\) |
0.866828 | + | 0.498607i | \(0.166155\pi\) | |||||||
\(110\) | 1.43069 | + | 2.47804i | 0.136411 | + | 0.236271i | ||||
\(111\) | 11.7208 | 1.11249 | ||||||||
\(112\) | 8.85975 | + | 0.180227i | 0.837168 | + | 0.0170298i | ||||
\(113\) | −9.19987 | −0.865451 | −0.432725 | − | 0.901526i | \(-0.642448\pi\) | ||||
−0.432725 | + | 0.901526i | \(0.642448\pi\) | |||||||
\(114\) | −0.474911 | − | 0.822571i | −0.0444795 | − | 0.0770408i | ||||
\(115\) | 0.390435 | − | 0.676254i | 0.0364083 | − | 0.0630610i | ||||
\(116\) | 6.76315 | − | 11.7141i | 0.627943 | − | 1.08763i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.282902 | −0.0260432 | ||||||||
\(119\) | −5.52344 | − | 10.0327i | −0.506333 | − | 0.919699i | ||||
\(120\) | −2.72825 | −0.249054 | ||||||||
\(121\) | −12.2320 | − | 21.1864i | −1.11200 | − | 1.92603i | ||||
\(122\) | −1.12660 | + | 1.95132i | −0.101997 | + | 0.176664i | ||||
\(123\) | 5.51353 | − | 9.54971i | 0.497138 | − | 0.861068i | ||||
\(124\) | −5.77061 | − | 9.99499i | −0.518216 | − | 0.897577i | ||||
\(125\) | −11.4351 | −1.02279 | ||||||||
\(126\) | 0.368500 | + | 0.669340i | 0.0328286 | + | 0.0596296i | ||||
\(127\) | 14.3952 | 1.27737 | 0.638683 | − | 0.769470i | \(-0.279480\pi\) | ||||
0.638683 | + | 0.769470i | \(0.279480\pi\) | |||||||
\(128\) | 4.60775 | + | 7.98085i | 0.407271 | + | 0.705414i | ||||
\(129\) | −3.10098 | + | 5.37105i | −0.273026 | + | 0.472895i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.73414 | + | 8.19978i | 0.413624 | + | 0.716418i | 0.995283 | − | 0.0970151i | \(-0.0309295\pi\) |
−0.581659 | + | 0.813433i | \(0.697596\pi\) | |||||||
\(132\) | 16.4267 | 1.42976 | ||||||||
\(133\) | 5.17808 | + | 0.105334i | 0.448996 | + | 0.00913357i | ||||
\(134\) | −0.328090 | −0.0283426 | ||||||||
\(135\) | 4.08238 | + | 7.07090i | 0.351356 | + | 0.608566i | ||||
\(136\) | 2.79804 | − | 4.84635i | 0.239930 | − | 0.415571i | ||||
\(137\) | −8.30313 | + | 14.3814i | −0.709384 | + | 1.22869i | 0.255702 | + | 0.966756i | \(0.417693\pi\) |
−0.965086 | + | 0.261934i | \(0.915640\pi\) | |||||||
\(138\) | 0.131047 | + | 0.226980i | 0.0111555 | + | 0.0193219i | ||||
\(139\) | 18.4778 | 1.56726 | 0.783632 | − | 0.621225i | \(-0.213365\pi\) | ||||
0.783632 | + | 0.621225i | \(0.213365\pi\) | |||||||
\(140\) | 3.74003 | − | 6.18396i | 0.316090 | − | 0.522640i | ||||
\(141\) | 9.13980 | 0.769710 | ||||||||
\(142\) | −0.625236 | − | 1.08294i | −0.0524687 | − | 0.0908784i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.45509 | − | 2.52029i | 0.121257 | − | 0.210024i | ||||
\(145\) | −5.17429 | − | 8.96213i | −0.429701 | − | 0.744264i | ||||
\(146\) | −3.03631 | −0.251287 | ||||||||
\(147\) | 10.2104 | + | 0.415577i | 0.842140 | + | 0.0342762i | ||||
\(148\) | −15.1707 | −1.24702 | ||||||||
\(149\) | 1.54040 | + | 2.66805i | 0.126195 | + | 0.218575i | 0.922199 | − | 0.386715i | \(-0.126390\pi\) |
−0.796005 | + | 0.605290i | \(0.793057\pi\) | |||||||
\(150\) | 0.706030 | − | 1.22288i | 0.0576471 | − | 0.0998477i | ||||
\(151\) | −1.27442 | + | 2.20737i | −0.103711 | + | 0.179633i | −0.913211 | − | 0.407487i | \(-0.866405\pi\) |
0.809500 | + | 0.587120i | \(0.199738\pi\) | |||||||
\(152\) | 1.26533 | + | 2.19162i | 0.102632 | + | 0.177764i | ||||
\(153\) | −3.76111 | −0.304068 | ||||||||
\(154\) | 2.71013 | − | 4.48106i | 0.218388 | − | 0.361095i | ||||
\(155\) | −8.82985 | −0.709231 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.70452 | − | 8.14847i | 0.375461 | − | 0.650318i | −0.614935 | − | 0.788578i | \(-0.710818\pi\) |
0.990396 | + | 0.138260i | \(0.0441509\pi\) | |||||||
\(158\) | 0.0217914 | − | 0.0377438i | 0.00173363 | − | 0.00300273i | ||||
\(159\) | 2.02848 | + | 3.51344i | 0.160869 | + | 0.278634i | ||||
\(160\) | 5.34708 | 0.422724 | ||||||||
\(161\) | −1.42884 | − | 0.0290658i | −0.112608 | − | 0.00229070i | ||||
\(162\) | −1.87408 | −0.147241 | ||||||||
\(163\) | −0.347578 | − | 0.602023i | −0.0272244 | − | 0.0471541i | 0.852092 | − | 0.523392i | \(-0.175334\pi\) |
−0.879317 | + | 0.476238i | \(0.842000\pi\) | |||||||
\(164\) | −7.13638 | + | 12.3606i | −0.557258 | + | 0.965199i | ||||
\(165\) | 6.28380 | − | 10.8839i | 0.489193 | − | 0.847308i | ||||
\(166\) | −0.443409 | − | 0.768007i | −0.0344152 | − | 0.0596089i | ||||
\(167\) | 13.9840 | 1.08211 | 0.541056 | − | 0.840986i | \(-0.318025\pi\) | ||||
0.541056 | + | 0.840986i | \(0.318025\pi\) | |||||||
\(168\) | 2.40814 | + | 4.37412i | 0.185792 | + | 0.337471i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −1.03995 | − | 1.80125i | −0.0797605 | − | 0.138149i | ||||
\(171\) | 0.850426 | − | 1.47298i | 0.0650337 | − | 0.112642i | ||||
\(172\) | 4.01372 | − | 6.95197i | 0.306043 | − | 0.530083i | ||||
\(173\) | 2.71824 | + | 4.70813i | 0.206664 | + | 0.357952i | 0.950662 | − | 0.310230i | \(-0.100406\pi\) |
−0.743998 | + | 0.668182i | \(0.767073\pi\) | |||||||
\(174\) | 3.47344 | 0.263321 | ||||||||
\(175\) | 3.71339 | + | 6.74497i | 0.280706 | + | 0.509872i | ||||
\(176\) | −19.9460 | −1.50349 | ||||||||
\(177\) | 0.621272 | + | 1.07607i | 0.0466976 | + | 0.0808827i | ||||
\(178\) | −1.61491 | + | 2.79711i | −0.121043 | + | 0.209652i | ||||
\(179\) | −2.67912 | + | 4.64037i | −0.200247 | + | 0.346838i | −0.948608 | − | 0.316454i | \(-0.897508\pi\) |
0.748361 | + | 0.663292i | \(0.230841\pi\) | |||||||
\(180\) | −1.18668 | − | 2.05540i | −0.0884502 | − | 0.153200i | ||||
\(181\) | 7.54016 | 0.560456 | 0.280228 | − | 0.959933i | \(-0.409590\pi\) | ||||
0.280228 | + | 0.959933i | \(0.409590\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.89632 | 0.731557 | ||||||||
\(184\) | −0.349157 | − | 0.604757i | −0.0257402 | − | 0.0445833i | ||||
\(185\) | −5.80331 | + | 10.0516i | −0.426668 | + | 0.739011i | ||||
\(186\) | 1.48184 | − | 2.56663i | 0.108654 | − | 0.188194i | ||||
\(187\) | 12.8891 | + | 22.3245i | 0.942543 | + | 1.63253i | ||||
\(188\) | −11.8300 | −0.862793 | ||||||||
\(189\) | 7.73316 | − | 12.7864i | 0.562504 | − | 0.930074i | ||||
\(190\) | 0.940574 | 0.0682364 | ||||||||
\(191\) | −6.77316 | − | 11.7315i | −0.490089 | − | 0.848859i | 0.509846 | − | 0.860266i | \(-0.329702\pi\) |
−0.999935 | + | 0.0114067i | \(0.996369\pi\) | |||||||
\(192\) | 3.99217 | − | 6.91464i | 0.288110 | − | 0.499021i | ||||
\(193\) | −9.27812 | + | 16.0702i | −0.667853 | + | 1.15676i | 0.310650 | + | 0.950524i | \(0.399453\pi\) |
−0.978503 | + | 0.206232i | \(0.933880\pi\) | |||||||
\(194\) | −1.09405 | − | 1.89494i | −0.0785479 | − | 0.136049i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −13.2157 | − | 0.537898i | −0.943982 | − | 0.0384213i | ||||
\(197\) | −2.66812 | −0.190096 | −0.0950480 | − | 0.995473i | \(-0.530300\pi\) | ||||
−0.0950480 | + | 0.995473i | \(0.530300\pi\) | |||||||
\(198\) | −0.859903 | − | 1.48940i | −0.0611106 | − | 0.105847i | ||||
\(199\) | −10.0999 | + | 17.4936i | −0.715965 | + | 1.24009i | 0.246621 | + | 0.969112i | \(0.420680\pi\) |
−0.962586 | + | 0.270976i | \(0.912654\pi\) | |||||||
\(200\) | −1.88111 | + | 3.25819i | −0.133015 | + | 0.230389i | ||||
\(201\) | 0.720507 | + | 1.24795i | 0.0508206 | + | 0.0880239i | ||||
\(202\) | −0.0235418 | −0.00165639 | ||||||||
\(203\) | −9.80152 | + | 16.2063i | −0.687932 | + | 1.13746i | ||||
\(204\) | −11.9403 | −0.835990 | ||||||||
\(205\) | 5.45984 | + | 9.45672i | 0.381332 | + | 0.660486i | ||||
\(206\) | −1.05333 | + | 1.82443i | −0.0733891 | + | 0.127114i | ||||
\(207\) | −0.234667 | + | 0.406455i | −0.0163105 | + | 0.0282506i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.6574 | −0.806361 | ||||||||
\(210\) | 1.85544 | + | 0.0377438i | 0.128038 | + | 0.00260457i | ||||
\(211\) | 13.1268 | 0.903683 | 0.451842 | − | 0.892098i | \(-0.350767\pi\) | ||||
0.451842 | + | 0.892098i | \(0.350767\pi\) | |||||||
\(212\) | −2.62555 | − | 4.54758i | −0.180323 | − | 0.312329i | ||||
\(213\) | −2.74612 | + | 4.75642i | −0.188161 | + | 0.325905i | ||||
\(214\) | −1.28788 | + | 2.23067i | −0.0880374 | + | 0.152485i | ||||
\(215\) | −3.07078 | − | 5.31875i | −0.209425 | − | 0.362736i | ||||
\(216\) | 7.30155 | 0.496807 | ||||||||
\(217\) | 7.79382 | + | 14.1566i | 0.529079 | + | 0.961014i | ||||
\(218\) | −0.0111553 | −0.000755530 | ||||||||
\(219\) | 6.66795 | + | 11.5492i | 0.450578 | + | 0.780424i | ||||
\(220\) | −8.13338 | + | 14.0874i | −0.548352 | + | 0.949774i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1.94785 | − | 3.37377i | −0.130731 | − | 0.226433i | ||||
\(223\) | −2.22334 | −0.148886 | −0.0744428 | − | 0.997225i | \(-0.523718\pi\) | ||||
−0.0744428 | + | 0.997225i | \(0.523718\pi\) | |||||||
\(224\) | −4.71969 | − | 8.57281i | −0.315348 | − | 0.572795i | ||||
\(225\) | 2.52858 | 0.168572 | ||||||||
\(226\) | 1.52890 | + | 2.64814i | 0.101701 | + | 0.176152i | ||||
\(227\) | −13.5523 | + | 23.4732i | −0.899495 | + | 1.55797i | −0.0713539 | + | 0.997451i | \(0.522732\pi\) |
−0.828141 | + | 0.560520i | \(0.810601\pi\) | |||||||
\(228\) | 2.69983 | − | 4.67625i | 0.178801 | − | 0.309692i | ||||
\(229\) | 9.49437 | + | 16.4447i | 0.627406 | + | 1.08670i | 0.988070 | + | 0.154003i | \(0.0492166\pi\) |
−0.360665 | + | 0.932696i | \(0.617450\pi\) | |||||||
\(230\) | −0.259542 | −0.0171137 | ||||||||
\(231\) | −22.9962 | − | 0.467795i | −1.51304 | − | 0.0307786i | ||||
\(232\) | −9.25447 | −0.607586 | ||||||||
\(233\) | −10.8700 | − | 18.8274i | −0.712118 | − | 1.23343i | −0.964060 | − | 0.265683i | \(-0.914403\pi\) |
0.251942 | − | 0.967742i | \(-0.418931\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.52540 | + | 7.83822i | −0.295205 | + | 0.511309i | ||||
\(236\) | −0.804137 | − | 1.39281i | −0.0523449 | − | 0.0906639i | ||||
\(237\) | −0.191421 | −0.0124342 | ||||||||
\(238\) | −1.96995 | + | 3.25722i | −0.127693 | + | 0.211134i | ||||
\(239\) | 19.9695 | 1.29172 | 0.645861 | − | 0.763455i | \(-0.276499\pi\) | ||||
0.645861 | + | 0.763455i | \(0.276499\pi\) | |||||||
\(240\) | −3.53420 | − | 6.12142i | −0.228132 | − | 0.395136i | ||||
\(241\) | −1.61524 | + | 2.79768i | −0.104047 | + | 0.180214i | −0.913348 | − | 0.407179i | \(-0.866513\pi\) |
0.809302 | + | 0.587393i | \(0.199846\pi\) | |||||||
\(242\) | −4.06560 | + | 7.04183i | −0.261347 | + | 0.452666i | ||||
\(243\) | −4.35630 | − | 7.54533i | −0.279456 | − | 0.484033i | ||||
\(244\) | −12.8092 | −0.820025 | ||||||||
\(245\) | −5.41188 | + | 8.55060i | −0.345753 | + | 0.546278i | ||||
\(246\) | −3.66512 | −0.233680 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −3.94816 | + | 6.83841i | −0.250708 | + | 0.434239i | ||||
\(249\) | −1.94751 | + | 3.37319i | −0.123419 | + | 0.213767i | ||||
\(250\) | 1.90038 | + | 3.29155i | 0.120190 | + | 0.208176i | ||||
\(251\) | 12.4916 | 0.788466 | 0.394233 | − | 0.919011i | \(-0.371010\pi\) | ||||
0.394233 | + | 0.919011i | \(0.371010\pi\) | |||||||
\(252\) | −2.24790 | + | 3.71680i | −0.141605 | + | 0.234136i | ||||
\(253\) | 3.21675 | 0.202236 | ||||||||
\(254\) | −2.39230 | − | 4.14359i | −0.150106 | − | 0.259992i | ||||
\(255\) | −4.56760 | + | 7.91131i | −0.286034 | + | 0.495425i | ||||
\(256\) | −3.93783 | + | 6.82052i | −0.246114 | + | 0.426283i | ||||
\(257\) | −2.91379 | − | 5.04682i | −0.181757 | − | 0.314812i | 0.760722 | − | 0.649078i | \(-0.224845\pi\) |
−0.942479 | + | 0.334266i | \(0.891512\pi\) | |||||||
\(258\) | 2.06138 | 0.128336 | ||||||||
\(259\) | 21.2378 | + | 0.432025i | 1.31966 | + | 0.0268447i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.10995 | + | 5.38659i | 0.192501 | + | 0.333422i | ||||
\(262\) | 1.57351 | − | 2.72540i | 0.0972119 | − | 0.168376i | ||||
\(263\) | −8.75736 | + | 15.1682i | −0.540002 | + | 0.935311i | 0.458901 | + | 0.888487i | \(0.348243\pi\) |
−0.998903 | + | 0.0468234i | \(0.985090\pi\) | |||||||
\(264\) | −5.61945 | − | 9.73316i | −0.345853 | − | 0.599035i | ||||
\(265\) | −4.01746 | −0.246791 | ||||||||
\(266\) | −0.830213 | − | 1.50799i | −0.0509036 | − | 0.0924609i | ||||
\(267\) | 14.1858 | 0.868157 | ||||||||
\(268\) | −0.932581 | − | 1.61528i | −0.0569665 | − | 0.0986688i | ||||
\(269\) | −11.1644 | + | 19.3372i | −0.680703 | + | 1.17901i | 0.294064 | + | 0.955786i | \(0.404992\pi\) |
−0.974767 | + | 0.223226i | \(0.928341\pi\) | |||||||
\(270\) | 1.35688 | − | 2.35019i | 0.0825773 | − | 0.143028i | ||||
\(271\) | 13.1847 | + | 22.8366i | 0.800916 | + | 1.38723i | 0.919014 | + | 0.394225i | \(0.128987\pi\) |
−0.118098 | + | 0.993002i | \(0.537680\pi\) | |||||||
\(272\) | 14.4984 | 0.879097 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.51951 | 0.333446 | ||||||||
\(275\) | −8.66529 | − | 15.0087i | −0.522536 | − | 0.905060i | ||||
\(276\) | −0.744993 | + | 1.29037i | −0.0448433 | + | 0.0776709i | ||||
\(277\) | 4.68809 | − | 8.12001i | 0.281680 | − | 0.487884i | −0.690119 | − | 0.723696i | \(-0.742442\pi\) |
0.971799 | + | 0.235812i | \(0.0757750\pi\) | |||||||
\(278\) | −3.07078 | − | 5.31875i | −0.184173 | − | 0.318997i | ||||
\(279\) | 5.30709 | 0.317727 | ||||||||
\(280\) | −4.94356 | − | 0.100563i | −0.295434 | − | 0.00600978i | ||||
\(281\) | −17.7754 | −1.06039 | −0.530195 | − | 0.847876i | \(-0.677881\pi\) | ||||
−0.530195 | + | 0.847876i | \(0.677881\pi\) | |||||||
\(282\) | −1.51892 | − | 2.63085i | −0.0904505 | − | 0.156665i | ||||
\(283\) | 4.80331 | − | 8.31958i | 0.285527 | − | 0.494548i | −0.687210 | − | 0.726459i | \(-0.741165\pi\) |
0.972737 | + | 0.231911i | \(0.0744979\pi\) | |||||||
\(284\) | 3.55442 | − | 6.15643i | 0.210916 | − | 0.365317i | ||||
\(285\) | −2.06556 | − | 3.57766i | −0.122353 | − | 0.211922i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.3424 | − | 17.1007i | 0.610494 | − | 1.00942i | ||||
\(288\) | −3.21380 | −0.189375 | ||||||||
\(289\) | −0.868875 | − | 1.50494i | −0.0511103 | − | 0.0885256i | ||||
\(290\) | −1.71981 | + | 2.97879i | −0.100990 | + | 0.174921i | ||||
\(291\) | −4.80519 | + | 8.32284i | −0.281685 | + | 0.487894i | ||||
\(292\) | −8.63060 | − | 14.9486i | −0.505067 | − | 0.874803i | ||||
\(293\) | −11.6338 | −0.679654 | −0.339827 | − | 0.940488i | \(-0.610369\pi\) | ||||
−0.339827 | + | 0.940488i | \(0.610369\pi\) | |||||||
\(294\) | −1.57722 | − | 3.00808i | −0.0919855 | − | 0.175435i | ||||
\(295\) | −1.23044 | −0.0716392 | ||||||||
\(296\) | 5.18976 | + | 8.98892i | 0.301648 | + | 0.522470i | ||||
\(297\) | −16.8172 | + | 29.1282i | −0.975830 | + | 1.69019i | ||||
\(298\) | 0.511991 | − | 0.886795i | 0.0296588 | − | 0.0513706i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 8.02744 | 0.463464 | ||||||||
\(301\) | −5.81690 | + | 9.61796i | −0.335281 | + | 0.554370i | ||||
\(302\) | 0.847174 | 0.0487494 | ||||||||
\(303\) | 0.0516993 | + | 0.0895459i | 0.00297005 | + | 0.00514427i | ||||
\(304\) | −3.27825 | + | 5.67809i | −0.188020 | + | 0.325661i | ||||
\(305\) | −4.89997 | + | 8.48700i | −0.280572 | + | 0.485964i | ||||
\(306\) | 0.625050 | + | 1.08262i | 0.0357317 | + | 0.0618892i | ||||
\(307\) | 13.8280 | 0.789204 | 0.394602 | − | 0.918852i | \(-0.370882\pi\) | ||||
0.394602 | + | 0.918852i | \(0.370882\pi\) | |||||||
\(308\) | 29.7650 | + | 0.605485i | 1.69602 | + | 0.0345007i | ||||
\(309\) | 9.25275 | 0.526371 | ||||||||
\(310\) | 1.46741 | + | 2.54163i | 0.0833435 | + | 0.144355i | ||||
\(311\) | −15.3572 | + | 26.5994i | −0.870827 | + | 1.50832i | −0.00968369 | + | 0.999953i | \(0.503082\pi\) |
−0.861143 | + | 0.508363i | \(0.830251\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.54334 | − | 9.60135i | −0.313328 | − | 0.542701i | 0.665752 | − | 0.746173i | \(-0.268111\pi\) |
−0.979081 | + | 0.203472i | \(0.934777\pi\) | |||||||
\(314\) | −3.12733 | −0.176486 | ||||||||
\(315\) | 1.60274 | + | 2.91120i | 0.0903042 | + | 0.164028i | ||||
\(316\) | 0.247764 | 0.0139378 | ||||||||
\(317\) | 11.9417 | + | 20.6836i | 0.670712 | + | 1.16171i | 0.977703 | + | 0.209994i | \(0.0673445\pi\) |
−0.306991 | + | 0.951712i | \(0.599322\pi\) | |||||||
\(318\) | 0.674218 | − | 1.16778i | 0.0378083 | − | 0.0654858i | ||||
\(319\) | 21.3152 | − | 36.9190i | 1.19342 | − | 2.06707i | ||||
\(320\) | 3.95329 | + | 6.84731i | 0.220996 | + | 0.382776i | ||||
\(321\) | 11.3130 | 0.631433 | ||||||||
\(322\) | 0.229089 | + | 0.416116i | 0.0127666 | + | 0.0231892i | ||||
\(323\) | 8.47360 | 0.471484 | ||||||||
\(324\) | −5.32698 | − | 9.22661i | −0.295944 | − | 0.512589i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.115526 | + | 0.200098i | −0.00639842 | + | 0.0110824i | ||||
\(327\) | 0.0244977 | + | 0.0424313i | 0.00135473 | + | 0.00234646i | ||||
\(328\) | 9.76519 | 0.539192 | ||||||||
\(329\) | 16.5612 | + | 0.336891i | 0.913048 | + | 0.0185734i | ||||
\(330\) | −4.17716 | −0.229945 | ||||||||
\(331\) | 9.16200 | + | 15.8690i | 0.503589 | + | 0.872241i | 0.999991 | + | 0.00414903i | \(0.00132068\pi\) |
−0.496403 | + | 0.868092i | \(0.665346\pi\) | |||||||
\(332\) | 2.52075 | − | 4.36606i | 0.138344 | − | 0.239619i | ||||
\(333\) | 3.48802 | − | 6.04142i | 0.191142 | − | 0.331068i | ||||
\(334\) | −2.32396 | − | 4.02522i | −0.127162 | − | 0.220250i | ||||
\(335\) | −1.42698 | −0.0779643 | ||||||||
\(336\) | −6.69475 | + | 11.0694i | −0.365229 | + | 0.603888i | ||||
\(337\) | −7.21762 | −0.393169 | −0.196584 | − | 0.980487i | \(-0.562985\pi\) | ||||
−0.196584 | + | 0.980487i | \(0.562985\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.71516 | − | 11.6310i | 0.364717 | − | 0.631709i | ||||
\(340\) | 5.91203 | − | 10.2399i | 0.320625 | − | 0.555338i | ||||
\(341\) | −18.1870 | − | 31.5009i | −0.984884 | − | 1.70587i | ||||
\(342\) | −0.565321 | −0.0305691 | ||||||||
\(343\) | 18.4858 | + | 1.12937i | 0.998139 | + | 0.0609804i | ||||
\(344\) | −5.49224 | −0.296122 | ||||||||
\(345\) | 0.569972 | + | 0.987221i | 0.0306863 | + | 0.0531502i | ||||
\(346\) | 0.903476 | − | 1.56487i | 0.0485712 | − | 0.0841277i | ||||
\(347\) | 10.5391 | − | 18.2543i | 0.565770 | − | 0.979942i | −0.431208 | − | 0.902253i | \(-0.641912\pi\) |
0.996978 | − | 0.0776892i | \(-0.0247542\pi\) | |||||||
\(348\) | 9.87310 | + | 17.1007i | 0.529254 | + | 0.916694i | ||||
\(349\) | −30.7629 | −1.64670 | −0.823350 | − | 0.567534i | \(-0.807898\pi\) | ||||
−0.823350 | + | 0.567534i | \(0.807898\pi\) | |||||||
\(350\) | 1.32439 | − | 2.18982i | 0.0707917 | − | 0.117051i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 11.0135 | + | 19.0760i | 0.587022 | + | 1.01675i | ||||
\(353\) | −3.06086 | + | 5.30157i | −0.162913 | + | 0.282174i | −0.935912 | − | 0.352233i | \(-0.885422\pi\) |
0.772999 | + | 0.634407i | \(0.218756\pi\) | |||||||
\(354\) | 0.206495 | − | 0.357660i | 0.0109751 | − | 0.0190094i | ||||
\(355\) | −2.71938 | − | 4.71010i | −0.144330 | − | 0.249986i | ||||
\(356\) | −18.3613 | −0.973145 | ||||||||
\(357\) | 16.7156 | + | 0.340033i | 0.884684 | + | 0.0179964i | ||||
\(358\) | 1.78095 | 0.0941259 | ||||||||
\(359\) | 9.71433 | + | 16.8257i | 0.512703 | + | 0.888028i | 0.999891 | + | 0.0147308i | \(0.00468913\pi\) |
−0.487189 | + | 0.873297i | \(0.661978\pi\) | |||||||
\(360\) | −0.811909 | + | 1.40627i | −0.0427914 | + | 0.0741168i | ||||
\(361\) | 7.58403 | − | 13.1359i | 0.399160 | − | 0.691365i | ||||
\(362\) | −1.25308 | − | 2.17040i | −0.0658605 | − | 0.114074i | ||||
\(363\) | 35.7133 | 1.87446 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.2060 | −0.691235 | ||||||||
\(366\) | −1.64465 | − | 2.84861i | −0.0859670 | − | 0.148899i | ||||
\(367\) | 2.70234 | − | 4.68058i | 0.141061 | − | 0.244324i | −0.786836 | − | 0.617163i | \(-0.788282\pi\) |
0.927896 | + | 0.372838i | \(0.121615\pi\) | |||||||
\(368\) | 0.904601 | − | 1.56681i | 0.0471556 | − | 0.0816758i | ||||
\(369\) | −3.28158 | − | 5.68385i | −0.170832 | − | 0.295890i | ||||
\(370\) | 3.85776 | 0.200555 | ||||||||
\(371\) | 3.54608 | + | 6.44106i | 0.184103 | + | 0.334403i | ||||
\(372\) | 16.8483 | 0.873544 | ||||||||
\(373\) | −8.12533 | − | 14.0735i | −0.420714 | − | 0.728698i | 0.575296 | − | 0.817946i | \(-0.304887\pi\) |
−0.996009 | + | 0.0892478i | \(0.971554\pi\) | |||||||
\(374\) | 4.28401 | − | 7.42013i | 0.221521 | − | 0.383686i | ||||
\(375\) | 8.34671 | − | 14.4569i | 0.431022 | − | 0.746553i | ||||
\(376\) | 4.04695 | + | 7.00952i | 0.208706 | + | 0.361489i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −4.96566 | − | 0.101013i | −0.255406 | − | 0.00519553i | ||||
\(379\) | 25.1730 | 1.29305 | 0.646525 | − | 0.762893i | \(-0.276222\pi\) | ||||
0.646525 | + | 0.762893i | \(0.276222\pi\) | |||||||
\(380\) | 2.67354 | + | 4.63071i | 0.137150 | + | 0.237550i | ||||
\(381\) | −10.5073 | + | 18.1992i | −0.538306 | + | 0.932373i | ||||
\(382\) | −2.25123 | + | 3.89925i | −0.115183 | + | 0.199503i | ||||
\(383\) | −1.90719 | − | 3.30335i | −0.0974529 | − | 0.168793i | 0.813177 | − | 0.582017i | \(-0.197736\pi\) |
−0.910630 | + | 0.413223i | \(0.864403\pi\) | |||||||
\(384\) | −13.4531 | −0.686527 | ||||||||
\(385\) | 11.7873 | − | 19.4898i | 0.600738 | − | 0.993291i | ||||
\(386\) | 6.16764 | 0.313924 | ||||||||
\(387\) | 1.84566 | + | 3.19677i | 0.0938201 | + | 0.162501i | ||||
\(388\) | 6.21956 | − | 10.7726i | 0.315750 | − | 0.546895i | ||||
\(389\) | 1.43548 | − | 2.48632i | 0.0727817 | − | 0.126062i | −0.827338 | − | 0.561705i | \(-0.810146\pi\) |
0.900119 | + | 0.435643i | \(0.143479\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.33821 | −0.118248 | ||||||||
\(392\) | 4.20228 | + | 8.01461i | 0.212247 | + | 0.404799i | ||||
\(393\) | −13.8222 | −0.697236 | ||||||||
\(394\) | 0.443409 | + | 0.768007i | 0.0223386 | + | 0.0386917i | ||||
\(395\) | 0.0947786 | − | 0.164161i | 0.00476883 | − | 0.00825986i | ||||
\(396\) | 4.88848 | − | 8.46709i | 0.245655 | − | 0.425487i | ||||
\(397\) | 9.55919 | + | 16.5570i | 0.479762 | + | 0.830972i | 0.999731 | − | 0.0232131i | \(-0.00738963\pi\) |
−0.519968 | + | 0.854185i | \(0.674056\pi\) | |||||||
\(398\) | 6.71394 | 0.336539 | ||||||||
\(399\) | −3.91274 | + | 6.46953i | −0.195882 | + | 0.323882i | ||||
\(400\) | −9.74725 | −0.487362 | ||||||||
\(401\) | −1.49912 | − | 2.59655i | −0.0748625 | − | 0.129666i | 0.826164 | − | 0.563430i | \(-0.190518\pi\) |
−0.901026 | + | 0.433764i | \(0.857185\pi\) | |||||||
\(402\) | 0.239479 | − | 0.414789i | 0.0119441 | − | 0.0206878i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −0.0669165 | − | 0.115903i | −0.00332922 | − | 0.00576638i | ||||
\(405\) | −8.15104 | −0.405028 | ||||||||
\(406\) | 6.29382 | + | 0.128030i | 0.312357 | + | 0.00635403i | ||||
\(407\) | −47.8129 | −2.37000 | ||||||||
\(408\) | 4.08469 | + | 7.07489i | 0.202222 | + | 0.350259i | ||||
\(409\) | 17.0403 | − | 29.5146i | 0.842587 | − | 1.45940i | −0.0451127 | − | 0.998982i | \(-0.514365\pi\) |
0.887700 | − | 0.460422i | \(-0.152302\pi\) | |||||||
\(410\) | 1.81472 | − | 3.14318i | 0.0896224 | − | 0.155231i | ||||
\(411\) | −12.1212 | − | 20.9946i | −0.597896 | − | 1.03559i | ||||
\(412\) | −11.9762 | −0.590026 | ||||||||
\(413\) | 1.08607 | + | 1.97273i | 0.0534421 | + | 0.0970717i | ||||
\(414\) | 0.155995 | 0.00766674 | ||||||||
\(415\) | −1.92855 | − | 3.34034i | −0.0946687 | − | 0.163971i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.4873 | + | 23.3606i | −0.660475 | + | 1.14398i | ||||
\(418\) | 1.93732 | + | 3.35554i | 0.0947574 | + | 0.164125i | ||||
\(419\) | 34.7759 | 1.69891 | 0.849457 | − | 0.527657i | \(-0.176929\pi\) | ||||
0.849457 | + | 0.527657i | \(0.176929\pi\) | |||||||
\(420\) | 5.08819 | + | 9.24215i | 0.248278 | + | 0.450971i | ||||
\(421\) | −24.1400 | −1.17651 | −0.588257 | − | 0.808674i | \(-0.700186\pi\) | ||||
−0.588257 | + | 0.808674i | \(0.700186\pi\) | |||||||
\(422\) | −2.18151 | − | 3.77848i | −0.106194 | − | 0.183933i | ||||
\(423\) | 2.71994 | − | 4.71108i | 0.132248 | − | 0.229060i | ||||
\(424\) | −1.79636 | + | 3.11138i | −0.0872388 | + | 0.151102i | ||||
\(425\) | 6.29866 | + | 10.9096i | 0.305530 | + | 0.529193i | ||||
\(426\) | 1.82549 | 0.0884451 | ||||||||
\(427\) | 17.9320 | + | 0.364776i | 0.867789 | + | 0.0176528i | ||||
\(428\) | −14.6429 | −0.707793 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.02065 | + | 1.76782i | −0.0492202 | + | 0.0852519i | ||||
\(431\) | 2.38238 | − | 4.12641i | 0.114755 | − | 0.198762i | −0.802927 | − | 0.596078i | \(-0.796725\pi\) |
0.917682 | + | 0.397316i | \(0.130058\pi\) | |||||||
\(432\) | 9.45848 | + | 16.3826i | 0.455071 | + | 0.788207i | ||||
\(433\) | 22.0231 | 1.05836 | 0.529181 | − | 0.848509i | \(-0.322499\pi\) | ||||
0.529181 | + | 0.848509i | \(0.322499\pi\) | |||||||
\(434\) | 2.77968 | − | 4.59607i | 0.133429 | − | 0.220618i | ||||
\(435\) | 15.1072 | 0.724337 | ||||||||
\(436\) | −0.0317084 | − | 0.0549206i | −0.00151856 | − | 0.00263022i | ||||
\(437\) | 0.528693 | − | 0.915724i | 0.0252908 | − | 0.0438050i | ||||
\(438\) | 2.21626 | − | 3.83868i | 0.105897 | − | 0.183419i | ||||
\(439\) | −1.71620 | − | 2.97254i | −0.0819097 | − | 0.141872i | 0.822161 | − | 0.569256i | \(-0.192769\pi\) |
−0.904070 | + | 0.427384i | \(0.859435\pi\) | |||||||
\(440\) | 11.1294 | 0.530576 | ||||||||
\(441\) | 3.25275 | − | 5.13924i | 0.154893 | − | 0.244726i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.35297 | + | 7.53957i | 0.206816 | + | 0.358216i | 0.950710 | − | 0.310082i | \(-0.100357\pi\) |
−0.743894 | + | 0.668298i | \(0.767023\pi\) | |||||||
\(444\) | 11.0733 | − | 19.1796i | 0.525518 | − | 0.910223i | ||||
\(445\) | −7.02383 | + | 12.1656i | −0.332962 | + | 0.576706i | ||||
\(446\) | 0.369491 | + | 0.639977i | 0.0174959 | + | 0.0303038i | ||||
\(447\) | −4.49747 | −0.212723 | ||||||||
\(448\) | 7.48862 | − | 12.3821i | 0.353804 | − | 0.584998i | ||||
\(449\) | −17.6120 | −0.831159 | −0.415580 | − | 0.909557i | \(-0.636421\pi\) | ||||
−0.415580 | + | 0.909557i | \(0.636421\pi\) | |||||||
\(450\) | −0.420219 | − | 0.727841i | −0.0198093 | − | 0.0343107i | ||||
\(451\) | −22.4915 | + | 38.9564i | −1.05908 | + | 1.83439i | ||||
\(452\) | −8.69170 | + | 15.0545i | −0.408823 | + | 0.708102i | ||||
\(453\) | −1.86045 | − | 3.22240i | −0.0874116 | − | 0.151401i | ||||
\(454\) | 9.00887 | 0.422807 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.69436 | −0.173004 | ||||||||
\(457\) | −4.53634 | − | 7.85717i | −0.212201 | − | 0.367543i | 0.740202 | − | 0.672384i | \(-0.234730\pi\) |
−0.952403 | + | 0.304842i | \(0.901396\pi\) | |||||||
\(458\) | 3.15570 | − | 5.46583i | 0.147456 | − | 0.255401i | ||||
\(459\) | 12.2241 | − | 21.1728i | 0.570573 | − | 0.988262i | ||||
\(460\) | −0.737738 | − | 1.27780i | −0.0343972 | − | 0.0595777i | ||||
\(461\) | −6.58319 | −0.306610 | −0.153305 | − | 0.988179i | \(-0.548992\pi\) | ||||
−0.153305 | + | 0.988179i | \(0.548992\pi\) | |||||||
\(462\) | 3.68704 | + | 6.69711i | 0.171537 | + | 0.311578i | ||||
\(463\) | −3.47344 | −0.161424 | −0.0807121 | − | 0.996737i | \(-0.525719\pi\) | ||||
−0.0807121 | + | 0.996737i | \(0.525719\pi\) | |||||||
\(464\) | −11.9883 | − | 20.7644i | −0.556544 | − | 0.963962i | ||||
\(465\) | 6.44507 | − | 11.1632i | 0.298883 | − | 0.517681i | ||||
\(466\) | −3.61293 | + | 6.25777i | −0.167366 | + | 0.289886i | ||||
\(467\) | −14.8927 | − | 25.7949i | −0.689152 | − | 1.19365i | −0.972112 | − | 0.234515i | \(-0.924650\pi\) |
0.282960 | − | 0.959132i | \(-0.408684\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.25955 | + | 2.28783i | 0.0581606 | + | 0.105642i | ||||
\(470\) | 3.00826 | 0.138761 | ||||||||
\(471\) | 6.86783 | + | 11.8954i | 0.316453 | + | 0.548113i | ||||
\(472\) | −0.550177 | + | 0.952935i | −0.0253240 | + | 0.0438624i | ||||
\(473\) | 12.6499 | − | 21.9103i | 0.581643 | − | 1.00744i | ||||
\(474\) | 0.0318119 | + | 0.0550998i | 0.00146117 | + | 0.00253082i | ||||
\(475\) | −5.69677 | −0.261386 | ||||||||
\(476\) | −21.6357 | − | 0.440118i | −0.991671 | − | 0.0201728i | ||||
\(477\) | 2.41465 | 0.110559 | ||||||||
\(478\) | −3.31869 | − | 5.74814i | −0.151793 | − | 0.262914i | ||||
\(479\) | 17.5927 | − | 30.4715i | 0.803833 | − | 1.39228i | −0.113243 | − | 0.993567i | \(-0.536124\pi\) |
0.917076 | − | 0.398712i | \(-0.130543\pi\) | |||||||
\(480\) | −3.90294 | + | 6.76008i | −0.178144 | + | 0.308554i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 1.07373 | 0.0489072 | ||||||||
\(483\) | 1.07968 | − | 1.78520i | 0.0491273 | − | 0.0812296i | ||||
\(484\) | −46.2252 | −2.10115 | ||||||||
\(485\) | −4.75840 | − | 8.24179i | −0.216068 | − | 0.374241i | ||||
\(486\) | −1.44793 | + | 2.50788i | −0.0656792 | + | 0.113760i | ||||
\(487\) | −0.900769 | + | 1.56018i | −0.0408178 | + | 0.0706984i | −0.885713 | − | 0.464234i | \(-0.846330\pi\) |
0.844895 | + | 0.534933i | \(0.179663\pi\) | |||||||
\(488\) | 4.38192 | + | 7.58971i | 0.198360 | + | 0.343570i | ||||
\(489\) | 1.01482 | 0.0458916 | ||||||||
\(490\) | 3.36064 | + | 0.136782i | 0.151818 | + | 0.00617920i | ||||
\(491\) | −8.19322 | −0.369755 | −0.184877 | − | 0.982762i | \(-0.559189\pi\) | ||||
−0.184877 | + | 0.982762i | \(0.559189\pi\) | |||||||
\(492\) | −10.4180 | − | 18.0444i | −0.469678 | − | 0.813506i | ||||
\(493\) | −15.4937 | + | 26.8358i | −0.697800 | + | 1.20863i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.74003 | − | 6.47792i | −0.168102 | − | 0.291161i | ||||
\(496\) | −20.4579 | −0.918587 | ||||||||
\(497\) | −5.15125 | + | 8.51734i | −0.231065 | + | 0.382055i | ||||
\(498\) | 1.29461 | 0.0580129 | ||||||||
\(499\) | −18.2582 | − | 31.6242i | −0.817350 | − | 1.41569i | −0.907628 | − | 0.419775i | \(-0.862109\pi\) |
0.0902781 | − | 0.995917i | \(-0.471224\pi\) | |||||||
\(500\) | −10.8035 | + | 18.7122i | −0.483147 | + | 0.836834i | ||||
\(501\) | −10.2072 | + | 17.6793i | −0.456022 | + | 0.789854i | ||||
\(502\) | −2.07596 | − | 3.59566i | −0.0926545 | − | 0.160482i | ||||
\(503\) | −3.02972 | −0.135089 | −0.0675443 | − | 0.997716i | \(-0.521516\pi\) | ||||
−0.0675443 | + | 0.997716i | \(0.521516\pi\) | |||||||
\(504\) | 2.97127 | + | 0.0604422i | 0.132351 | + | 0.00269231i | ||||
\(505\) | −0.102392 | −0.00455637 | ||||||||
\(506\) | −0.534585 | − | 0.925928i | −0.0237652 | − | 0.0411625i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.6000 | − | 23.5559i | 0.603404 | − | 1.04513i | ||||
\(509\) | 14.6724 | + | 25.4133i | 0.650341 | + | 1.12642i | 0.983040 | + | 0.183391i | \(0.0587074\pi\) |
−0.332699 | + | 0.943033i | \(0.607959\pi\) | |||||||
\(510\) | 3.03631 | 0.134450 | ||||||||
\(511\) | 11.6565 | + | 21.1728i | 0.515654 | + | 0.936630i | ||||
\(512\) | 21.0487 | 0.930229 | ||||||||
\(513\) | 5.52800 | + | 9.57479i | 0.244067 | + | 0.422737i | ||||
\(514\) | −0.968471 | + | 1.67744i | −0.0427174 | + | 0.0739887i | ||||
\(515\) | −4.58133 | + | 7.93509i | −0.201877 | + | 0.349662i | ||||
\(516\) | 5.85938 | + | 10.1487i | 0.257945 | + | 0.446773i | ||||
\(517\) | −37.2843 | −1.63976 | ||||||||
\(518\) | −3.40511 | − | 6.18502i | −0.149612 | − | 0.271754i | ||||
\(519\) | −7.93637 | −0.348368 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.8419 | − | 25.7069i | 0.650236 | − | 1.12624i | −0.332830 | − | 0.942987i | \(-0.608003\pi\) |
0.983066 | − | 0.183254i | \(-0.0586632\pi\) | |||||||
\(522\) | 1.03367 | − | 1.79037i | 0.0452425 | − | 0.0783624i | ||||
\(523\) | −10.2864 | − | 17.8165i | −0.449791 | − | 0.779062i | 0.548581 | − | 0.836098i | \(-0.315168\pi\) |
−0.998372 | + | 0.0570361i | \(0.981835\pi\) | |||||||
\(524\) | 17.8906 | 0.781553 | ||||||||
\(525\) | −11.2379 | − | 0.228603i | −0.490460 | − | 0.00997704i | ||||
\(526\) | 5.82146 | 0.253828 | ||||||||
\(527\) | 13.2199 | + | 22.8975i | 0.575867 | + | 0.997431i | ||||
\(528\) | 14.5590 | − | 25.2168i | 0.633597 | − | 1.09742i | ||||
\(529\) | 11.3541 | − | 19.6659i | 0.493657 | − | 0.855039i | ||||
\(530\) | 0.667652 | + | 1.15641i | 0.0290010 | + | 0.0502311i | ||||
\(531\) | 0.739544 | 0.0320935 | ||||||||
\(532\) | 5.06442 | − | 8.37377i | 0.219571 | − | 0.363049i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −2.35751 | − | 4.08332i | −0.102019 | − | 0.176703i | ||||
\(535\) | −5.60144 | + | 9.70198i | −0.242171 | + | 0.419453i | ||||
\(536\) | −0.638057 | + | 1.10515i | −0.0275599 | + | 0.0477351i | ||||
\(537\) | −3.91108 | − | 6.77419i | −0.168775 | − | 0.292328i | ||||
\(538\) | 7.42151 | 0.319964 | ||||||||
\(539\) | −41.6516 | − | 1.69527i | −1.79406 | − | 0.0730206i | ||||
\(540\) | 15.4275 | 0.663896 | ||||||||
\(541\) | −17.0334 | − | 29.5027i | −0.732324 | − | 1.26842i | −0.955888 | − | 0.293732i | \(-0.905103\pi\) |
0.223564 | − | 0.974689i | \(-0.428231\pi\) | |||||||
\(542\) | 4.38228 | − | 7.59034i | 0.188235 | − | 0.326033i | ||||
\(543\) | −5.50371 | + | 9.53270i | −0.236187 | + | 0.409087i | ||||
\(544\) | −8.00555 | − | 13.8660i | −0.343235 | − | 0.594500i | ||||
\(545\) | −0.0485183 | −0.00207830 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.850931 | −0.0363832 | −0.0181916 | − | 0.999835i | \(-0.505791\pi\) | ||||
−0.0181916 | + | 0.999835i | \(0.505791\pi\) | |||||||
\(548\) | 15.6890 | + | 27.1741i | 0.670200 | + | 1.16082i | ||||
\(549\) | 2.94507 | − | 5.10102i | 0.125693 | − | 0.217706i | ||||
\(550\) | −2.88013 | + | 4.98853i | −0.122809 | + | 0.212712i | ||||
\(551\) | −7.00657 | − | 12.1357i | −0.298490 | − | 0.516999i | ||||
\(552\) | 1.01942 | 0.0433895 | ||||||||
\(553\) | −0.346853 | − | 0.00705575i | −0.0147497 | − | 0.000300041i | ||||
\(554\) | −3.11641 | −0.132404 | ||||||||
\(555\) | −8.47189 | − | 14.6737i | −0.359612 | − | 0.622866i | ||||
\(556\) | 17.4571 | − | 30.2366i | 0.740347 | − | 1.28232i | ||||
\(557\) | 8.86404 | − | 15.3530i | 0.375581 | − | 0.650526i | −0.614833 | − | 0.788658i | \(-0.710776\pi\) |
0.990414 | + | 0.138132i | \(0.0441098\pi\) | |||||||
\(558\) | −0.881972 | − | 1.52762i | −0.0373369 | − | 0.0646694i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −6.17829 | − | 11.2222i | −0.261080 | − | 0.474224i | ||||
\(561\) | −37.6319 | −1.58882 | ||||||||
\(562\) | 2.95405 | + | 5.11656i | 0.124609 | + | 0.215829i | ||||
\(563\) | 12.0903 | − | 20.9410i | 0.509545 | − | 0.882558i | −0.490394 | − | 0.871501i | \(-0.663147\pi\) |
0.999939 | − | 0.0110571i | \(-0.00351966\pi\) | |||||||
\(564\) | 8.63495 | − | 14.9562i | 0.363597 | − | 0.629768i | ||||
\(565\) | 6.64976 | + | 11.5177i | 0.279758 | + | 0.484555i | ||||
\(566\) | −3.19301 | −0.134212 | ||||||||
\(567\) | 7.19465 | + | 13.0683i | 0.302147 | + | 0.548817i | ||||
\(568\) | −4.86375 | −0.204078 | ||||||||
\(569\) | 21.3874 | + | 37.0441i | 0.896608 | + | 1.55297i | 0.831802 | + | 0.555073i | \(0.187310\pi\) |
0.0648066 | + | 0.997898i | \(0.479357\pi\) | |||||||
\(570\) | −0.686542 | + | 1.18913i | −0.0287561 | + | 0.0498070i | ||||
\(571\) | −3.68140 | + | 6.37637i | −0.154062 | + | 0.266843i | −0.932717 | − | 0.360609i | \(-0.882569\pi\) |
0.778655 | + | 0.627452i | \(0.215902\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.7754 | 0.826131 | ||||||||
\(574\) | −6.64115 | − | 0.135096i | −0.277196 | − | 0.00563878i | ||||
\(575\) | 1.57197 | 0.0655557 | ||||||||
\(576\) | −2.37608 | − | 4.11550i | −0.0990035 | − | 0.171479i | ||||
\(577\) | 4.09696 | − | 7.09615i | 0.170559 | − | 0.295417i | −0.768057 | − | 0.640382i | \(-0.778776\pi\) |
0.938615 | + | 0.344965i | \(0.112109\pi\) | |||||||
\(578\) | −0.288793 | + | 0.500204i | −0.0120122 | + | 0.0208057i | ||||
\(579\) | −13.5445 | − | 23.4598i | −0.562892 | − | 0.974957i | ||||
\(580\) | −19.5539 | −0.811932 | ||||||||
\(581\) | −3.65320 | + | 6.04039i | −0.151560 | + | 0.250598i | ||||
\(582\) | 3.19426 | 0.132406 | ||||||||
\(583\) | −8.27485 | − | 14.3325i | −0.342709 | − | 0.593590i | ||||
\(584\) | −5.90491 | + | 10.2276i | −0.244347 | + | 0.423221i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.93339 | + | 3.34874i | 0.0798678 | + | 0.138335i | ||||
\(587\) | 39.1141 | 1.61441 | 0.807205 | − | 0.590271i | \(-0.200979\pi\) | ||||
0.807205 | + | 0.590271i | \(0.200979\pi\) | |||||||
\(588\) | 10.3265 | − | 16.3155i | 0.425856 | − | 0.672838i | ||||
\(589\) | −11.9566 | −0.492664 | ||||||||
\(590\) | 0.204485 | + | 0.354178i | 0.00841849 | + | 0.0145813i | ||||
\(591\) | 1.94751 | − | 3.37319i | 0.0801100 | − | 0.138755i | ||||
\(592\) | −13.4457 | + | 23.2886i | −0.552615 | + | 0.957158i | ||||
\(593\) | 0.606691 | + | 1.05082i | 0.0249138 | + | 0.0431520i | 0.878213 | − | 0.478269i | \(-0.158736\pi\) |
−0.853300 | + | 0.521421i | \(0.825402\pi\) | |||||||
\(594\) | 11.1792 | 0.458689 | ||||||||
\(595\) | −8.56803 | + | 14.1668i | −0.351255 | + | 0.580783i | ||||
\(596\) | 5.82125 | 0.238448 | ||||||||
\(597\) | −14.7443 | − | 25.5378i | −0.603442 | − | 1.04519i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.3319 | + | 28.2877i | −0.667303 | + | 1.15580i | 0.311352 | + | 0.950295i | \(0.399218\pi\) |
−0.978655 | + | 0.205508i | \(0.934115\pi\) | |||||||
\(600\) | −2.74612 | − | 4.75642i | −0.112110 | − | 0.194180i | ||||
\(601\) | 2.50114 | 0.102024 | 0.0510118 | − | 0.998698i | \(-0.483755\pi\) | ||||
0.0510118 | + | 0.998698i | \(0.483755\pi\) | |||||||
\(602\) | 3.73519 | + | 0.0759819i | 0.152235 | + | 0.00309679i | ||||
\(603\) | 0.857671 | 0.0349271 | ||||||||
\(604\) | 2.40806 | + | 4.17088i | 0.0979825 | + | 0.169711i | ||||
\(605\) | −17.6828 | + | 30.6275i | −0.718907 | + | 1.24518i | ||||
\(606\) | 0.0171836 | − | 0.0297628i | 0.000698035 | − | 0.00120903i | ||||
\(607\) | −6.32282 | − | 10.9515i | −0.256635 | − | 0.444506i | 0.708703 | − | 0.705507i | \(-0.249281\pi\) |
−0.965338 | + | 0.261001i | \(0.915947\pi\) | |||||||
\(608\) | 7.24055 | 0.293643 | ||||||||
\(609\) | −13.3347 | − | 24.2209i | −0.540347 | − | 0.981482i | ||||
\(610\) | 3.25726 | 0.131883 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −3.55336 | + | 6.15460i | −0.143636 | + | 0.248785i | ||||
\(613\) | −10.0140 | + | 17.3448i | −0.404462 | + | 0.700548i | −0.994259 | − | 0.107003i | \(-0.965874\pi\) |
0.589797 | + | 0.807552i | \(0.299208\pi\) | |||||||
\(614\) | −2.29804 | − | 3.98032i | −0.0927413 | − | 0.160633i | ||||
\(615\) | −15.9409 | −0.642801 | ||||||||
\(616\) | −9.82359 | − | 17.8435i | −0.395804 | − | 0.718934i | ||||
\(617\) | −45.2926 | −1.82341 | −0.911705 | − | 0.410846i | \(-0.865233\pi\) | ||||
−0.911705 | + | 0.410846i | \(0.865233\pi\) | |||||||
\(618\) | −1.53769 | − | 2.66336i | −0.0618551 | − | 0.107136i | ||||
\(619\) | 2.21658 | − | 3.83922i | 0.0890917 | − | 0.154311i | −0.818036 | − | 0.575167i | \(-0.804937\pi\) |
0.907127 | + | 0.420856i | \(0.138270\pi\) | |||||||
\(620\) | −8.34212 | + | 14.4490i | −0.335028 | + | 0.580285i | ||||
\(621\) | −1.52540 | − | 2.64207i | −0.0612122 | − | 0.106023i | ||||
\(622\) | 10.2087 | 0.409332 | ||||||||
\(623\) | 25.7045 | + | 0.522886i | 1.02983 | + | 0.0209490i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.989985 | + | 1.71471i | 0.0395994 | + | 0.0685882i | ||||
\(626\) | −1.84247 | + | 3.19125i | −0.0736400 | + | 0.127548i | ||||
\(627\) | 8.50897 | − | 14.7380i | 0.339816 | − | 0.588578i | ||||
\(628\) | −8.88931 | − | 15.3967i | −0.354722 | − | 0.614397i | ||||
\(629\) | 34.7544 | 1.38575 | ||||||||
\(630\) | 0.571621 | − | 0.945148i | 0.0227739 | − | 0.0376556i | ||||
\(631\) | 19.7358 | 0.785672 | 0.392836 | − | 0.919609i | \(-0.371494\pi\) | ||||
0.392836 | + | 0.919609i | \(0.371494\pi\) | |||||||
\(632\) | −0.0847581 | − | 0.146805i | −0.00337150 | − | 0.00583961i | ||||
\(633\) | −9.58147 | + | 16.5956i | −0.380829 | + | 0.659615i | ||||
\(634\) | 3.96912 | − | 6.87472i | 0.157634 | − | 0.273030i | ||||
\(635\) | −10.4050 | − | 18.0220i | −0.412909 | − | 0.715180i | ||||
\(636\) | 7.66574 | 0.303967 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −14.1693 | −0.560968 | ||||||||
\(639\) | 1.63445 | + | 2.83096i | 0.0646580 | + | 0.111991i | ||||
\(640\) | 6.66106 | − | 11.5373i | 0.263302 | − | 0.456052i | ||||
\(641\) | −19.8213 | + | 34.3314i | −0.782893 | + | 1.35601i | 0.147357 | + | 0.989083i | \(0.452923\pi\) |
−0.930250 | + | 0.366926i | \(0.880410\pi\) | |||||||
\(642\) | −1.88009 | − | 3.25641i | −0.0742012 | − | 0.128520i | ||||
\(643\) | −20.8300 | −0.821453 | −0.410727 | − | 0.911759i | \(-0.634725\pi\) | ||||
−0.410727 | + | 0.911759i | \(0.634725\pi\) | |||||||
\(644\) | −1.39748 | + | 2.31066i | −0.0550684 | + | 0.0910529i | ||||
\(645\) | 8.96568 | 0.353023 | ||||||||
\(646\) | −1.40821 | − | 2.43909i | −0.0554052 | − | 0.0959646i | ||||
\(647\) | 7.87206 | − | 13.6348i | 0.309482 | − | 0.536039i | −0.668767 | − | 0.743472i | \(-0.733178\pi\) |
0.978249 | + | 0.207433i | \(0.0665109\pi\) | |||||||
\(648\) | −3.64463 | + | 6.31269i | −0.143175 | + | 0.247986i | ||||
\(649\) | −2.53437 | − | 4.38966i | −0.0994828 | − | 0.172309i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −23.5864 | − | 0.479800i | −0.924426 | − | 0.0188049i | ||||
\(652\) | −1.31352 | −0.0514413 | ||||||||
\(653\) | 13.5132 | + | 23.4055i | 0.528812 | + | 0.915930i | 0.999436 | + | 0.0335954i | \(0.0106958\pi\) |
−0.470623 | + | 0.882334i | \(0.655971\pi\) | |||||||
\(654\) | 0.00814244 | − | 0.0141031i | 0.000318395 | − | 0.000551476i | ||||
\(655\) | 6.84378 | − | 11.8538i | 0.267409 | − | 0.463165i | ||||
\(656\) | 12.6499 | + | 21.9103i | 0.493896 | + | 0.855453i | ||||
\(657\) | 7.93734 | 0.309665 | ||||||||
\(658\) | −2.65529 | − | 4.82305i | −0.103514 | − | 0.188022i | ||||
\(659\) | −6.79491 | −0.264692 | −0.132346 | − | 0.991204i | \(-0.542251\pi\) | ||||
−0.132346 | + | 0.991204i | \(0.542251\pi\) | |||||||
\(660\) | −11.8734 | − | 20.5653i | −0.462172 | − | 0.800505i | ||||
\(661\) | 3.60263 | − | 6.23994i | 0.140126 | − | 0.242705i | −0.787418 | − | 0.616420i | \(-0.788583\pi\) |
0.927544 | + | 0.373714i | \(0.121916\pi\) | |||||||
\(662\) | 3.04522 | − | 5.27448i | 0.118356 | − | 0.204998i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.44930 | −0.133859 | ||||||||
\(665\) | −3.61090 | − | 6.55880i | −0.140025 | − | 0.254339i | ||||
\(666\) | −2.31866 | −0.0898463 | ||||||||
\(667\) | 1.93339 | + | 3.34874i | 0.0748613 | + | 0.129664i | ||||
\(668\) | 13.2115 | − | 22.8831i | 0.511170 | − | 0.885372i | ||||
\(669\) | 1.62285 | − | 2.81087i | 0.0627432 | − | 0.108674i | ||||
\(670\) | 0.237147 | + | 0.410750i | 0.00916178 | + | 0.0158687i | ||||
\(671\) | −40.3703 | −1.55848 | ||||||||
\(672\) | 14.2832 | + | 0.290552i | 0.550987 | + | 0.0112083i | ||||
\(673\) | 8.32130 | 0.320763 | 0.160381 | − | 0.987055i | \(-0.448728\pi\) | ||||
0.160381 | + | 0.987055i | \(0.448728\pi\) | |||||||
\(674\) | 1.19948 | + | 2.07756i | 0.0462022 | + | 0.0800246i | ||||
\(675\) | −8.21824 | + | 14.2344i | −0.316320 | + | 0.547883i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.9978 | + | 25.9770i | 0.576413 | + | 0.998376i | 0.995887 | + | 0.0906086i | \(0.0288812\pi\) |
−0.419474 | + | 0.907767i | \(0.637785\pi\) | |||||||
\(678\) | −4.46391 | −0.171435 | ||||||||
\(679\) | −9.01372 | + | 14.9037i | −0.345915 | + | 0.571953i | ||||
\(680\) | −8.08982 | −0.310231 | ||||||||
\(681\) | −19.7841 | − | 34.2671i | −0.758128 | − | 1.31312i | ||||
\(682\) | −6.04493 | + | 10.4701i | −0.231472 | + | 0.400922i | ||||
\(683\) | −18.0420 | + | 31.2496i | −0.690356 | + | 1.19573i | 0.281365 | + | 0.959601i | \(0.409213\pi\) |
−0.971721 | + | 0.236132i | \(0.924120\pi\) | |||||||
\(684\) | −1.60690 | − | 2.78324i | −0.0614415 | − | 0.106420i | ||||
\(685\) | 24.0064 | 0.917236 | ||||||||
\(686\) | −2.74703 | − | 5.50874i | −0.104882 | − | 0.210325i | ||||
\(687\) | −27.7205 | −1.05760 | ||||||||
\(688\) | −7.11470 | − | 12.3230i | −0.271245 | − | 0.469811i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0.189445 | − | 0.328128i | 0.00721204 | − | 0.0124916i | ||||
\(691\) | −12.8838 | − | 22.3155i | −0.490124 | − | 0.848920i | 0.509811 | − | 0.860286i | \(-0.329715\pi\) |
−0.999935 | + | 0.0113665i | \(0.996382\pi\) | |||||||
\(692\) | 10.2724 | 0.390497 | ||||||||
\(693\) | −7.08465 | + | 11.7141i | −0.269123 | + | 0.444983i | ||||
\(694\) | −7.00589 | −0.265940 | ||||||||
\(695\) | −13.3559 | − | 23.1332i | −0.506620 | − | 0.877491i | ||||
\(696\) | 6.75501 | − | 11.7000i | 0.256048 | − | 0.443488i | ||||
\(697\) | 16.3487 | − | 28.3168i | 0.619252 | − | 1.07258i | ||||
\(698\) | 5.11242 | + | 8.85496i | 0.193508 | + | 0.335165i | ||||
\(699\) | 31.7369 | 1.20040 | ||||||||
\(700\) | 14.5456 | + | 0.295890i | 0.549772 | + | 0.0111836i | ||||
\(701\) | 41.7872 | 1.57828 | 0.789141 | − | 0.614213i | \(-0.210526\pi\) | ||||
0.789141 | + | 0.614213i | \(0.210526\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.85834 | + | 13.6110i | −0.296383 | + | 0.513350i | ||||
\(704\) | −16.2854 | + | 28.2071i | −0.613778 | + | 1.06310i | ||||
\(705\) | −6.60635 | − | 11.4425i | −0.248809 | − | 0.430951i | ||||
\(706\) | 2.03471 | 0.0765774 | ||||||||
\(707\) | 0.0903778 | + | 0.164161i | 0.00339901 | + | 0.00617393i | ||||
\(708\) | 2.34782 | 0.0882364 | ||||||||
\(709\) | 0.171924 | + | 0.297781i | 0.00645673 | + | 0.0111834i | 0.869236 | − | 0.494398i | \(-0.164611\pi\) |
−0.862779 | + | 0.505581i | \(0.831278\pi\) | |||||||
\(710\) | −0.903855 | + | 1.56552i | −0.0339211 | + | 0.0587530i | ||||
\(711\) | −0.0569657 | + | 0.0986674i | −0.00213638 | + | 0.00370032i | ||||
\(712\) | 6.28124 | + | 10.8794i | 0.235399 | + | 0.407724i | ||||
\(713\) | 3.29931 | 0.123560 | ||||||||
\(714\) | −2.68005 | − | 4.86802i | −0.100298 | − | 0.182181i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.06227 | + | 8.76810i | 0.189186 | + | 0.327679i | ||||
\(717\) | −14.5761 | + | 25.2466i | −0.544356 | + | 0.942852i | ||||
\(718\) | 3.22881 | − | 5.59246i | 0.120498 | − | 0.208709i | ||||
\(719\) | −4.39005 | − | 7.60379i | −0.163721 | − | 0.283574i | 0.772479 | − | 0.635040i | \(-0.219016\pi\) |
−0.936200 | + | 0.351467i | \(0.885683\pi\) | |||||||
\(720\) | −4.20702 | −0.156786 | ||||||||
\(721\) | 16.7659 | + | 0.341055i | 0.624393 | + | 0.0127015i | ||||
\(722\) | −5.04149 | −0.187625 | ||||||||
\(723\) | −2.35799 | − | 4.08416i | −0.0876946 | − | 0.151891i | ||||
\(724\) | 7.12367 | − | 12.3386i | 0.264749 | − | 0.458559i | ||||
\(725\) | 10.4164 | − | 18.0416i | 0.386854 | − | 0.670050i | ||||
\(726\) | −5.93512 | − | 10.2799i | −0.220273 | − | 0.381524i | ||||
\(727\) | −17.3658 | −0.644064 | −0.322032 | − | 0.946729i | \(-0.604366\pi\) | ||||
−0.322032 | + | 0.946729i | \(0.604366\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.6343 | 1.09757 | ||||||||
\(730\) | 2.19468 | + | 3.80130i | 0.0812288 | + | 0.140692i | ||||
\(731\) | −9.19502 | + | 15.9262i | −0.340090 | + | 0.589053i | ||||
\(732\) | 9.34968 | − | 16.1941i | 0.345574 | − | 0.598552i | ||||
\(733\) | −4.52947 | − | 7.84528i | −0.167300 | − | 0.289772i | 0.770170 | − | 0.637839i | \(-0.220172\pi\) |
−0.937470 | + | 0.348067i | \(0.886838\pi\) | |||||||
\(734\) | −1.79638 | −0.0663056 | ||||||||
\(735\) | −6.85991 | − | 13.0833i | −0.253032 | − | 0.482583i | ||||
\(736\) | −1.99796 | −0.0736458 | ||||||||
\(737\) | −2.93919 | − | 5.09082i | −0.108266 | − | 0.187523i | ||||
\(738\) | −1.09071 | + | 1.88917i | −0.0401498 | + | 0.0695414i | ||||
\(739\) | −3.53921 | + | 6.13010i | −0.130192 | + | 0.225499i | −0.923751 | − | 0.382995i | \(-0.874893\pi\) |
0.793558 | + | 0.608494i | \(0.208226\pi\) | |||||||
\(740\) | 10.9655 | + | 18.9928i | 0.403100 | + | 0.698190i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.26472 | − | 2.09115i | 0.0464292 | − | 0.0767685i | ||||
\(743\) | 14.6779 | 0.538479 | 0.269240 | − | 0.963073i | \(-0.413228\pi\) | ||||
0.269240 | + | 0.963073i | \(0.413228\pi\) | |||||||
\(744\) | −5.76367 | − | 9.98297i | −0.211306 | − | 0.365993i | ||||
\(745\) | 2.22684 | − | 3.85699i | 0.0815849 | − | 0.141309i | ||||
\(746\) | −2.70066 | + | 4.67768i | −0.0988782 | + | 0.171262i | ||||
\(747\) | 1.15913 | + | 2.00768i | 0.0424105 | + | 0.0734571i | ||||
\(748\) | 48.7085 | 1.78096 | ||||||||
\(749\) | 20.4991 | + | 0.416997i | 0.749020 | + | 0.0152367i | ||||
\(750\) | −5.54848 | −0.202602 | ||||||||
\(751\) | 15.8556 | + | 27.4628i | 0.578580 | + | 1.00213i | 0.995643 | + | 0.0932523i | \(0.0297263\pi\) |
−0.417062 | + | 0.908878i | \(0.636940\pi\) | |||||||
\(752\) | −10.4849 | + | 18.1604i | −0.382345 | + | 0.662241i | ||||
\(753\) | −9.11788 | + | 15.7926i | −0.332274 | + | 0.575516i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.68467 | 0.134099 | ||||||||
\(756\) | −13.6174 | − | 24.7345i | −0.495259 | − | 0.899585i | ||||
\(757\) | 15.5317 | 0.564510 | 0.282255 | − | 0.959339i | \(-0.408918\pi\) | ||||
0.282255 | + | 0.959339i | \(0.408918\pi\) | |||||||
\(758\) | −4.18344 | − | 7.24593i | −0.151949 | − | 0.263184i | ||||
\(759\) | −2.34797 | + | 4.06680i | −0.0852259 | + | 0.147616i | ||||
\(760\) | 1.82919 | − | 3.16825i | 0.0663518 | − | 0.114925i | ||||
\(761\) | 0.125185 | + | 0.216826i | 0.00453794 | + | 0.00785993i | 0.868285 | − | 0.496065i | \(-0.165222\pi\) |
−0.863748 | + | 0.503925i | \(0.831889\pi\) | |||||||
\(762\) | 6.98474 | 0.253030 | ||||||||
\(763\) | 0.0428255 | + | 0.0777879i | 0.00155039 | + | 0.00281611i | ||||
\(764\) | −25.5961 | −0.926036 | ||||||||
\(765\) | 2.71857 | + | 4.70870i | 0.0982901 | + | 0.170243i | ||||
\(766\) | −0.633903 | + | 1.09795i | −0.0229039 | + | 0.0396706i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −5.74859 | − | 9.95686i | −0.207435 | − | 0.359287i | ||||
\(769\) | 24.0146 | 0.865988 | 0.432994 | − | 0.901397i | \(-0.357457\pi\) | ||||
0.432994 | + | 0.901397i | \(0.357457\pi\) | |||||||
\(770\) | −7.56896 | − | 0.153969i | −0.272766 | − | 0.00554867i | ||||
\(771\) | 8.50731 | 0.306383 | ||||||||
\(772\) | 17.5312 | + | 30.3650i | 0.630963 | + | 1.09286i | ||||
\(773\) | 15.2531 | − | 26.4192i | 0.548616 | − | 0.950231i | −0.449753 | − | 0.893153i | \(-0.648488\pi\) |
0.998370 | − | 0.0570784i | \(-0.0181785\pi\) | |||||||
\(774\) | 0.613451 | − | 1.06253i | 0.0220501 | − | 0.0381918i | ||||
\(775\) | −8.88768 | − | 15.3939i | −0.319255 | − | 0.552966i | ||||
\(776\) | −8.51064 | −0.305514 | ||||||||
\(777\) | −16.0481 | + | 26.5347i | −0.575722 | + | 0.951928i | ||||
\(778\) | −0.954237 | −0.0342110 | ||||||||
\(779\) | 7.39323 | + | 12.8055i | 0.264890 | + | 0.458803i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.2023 | − | 19.4030i | 0.400851 | − | 0.694294i | ||||
\(782\) | 0.388582 | + | 0.673043i | 0.0138956 | + | 0.0240680i | ||||
\(783\) | −40.4311 | −1.44489 | ||||||||
\(784\) | −12.5388 | + | 19.8109i | −0.447815 | + | 0.707532i | ||||
\(785\) | −13.6019 | −0.485473 | ||||||||
\(786\) | 2.29707 | + | 3.97865i | 0.0819339 | + | 0.141914i | ||||
\(787\) | 9.92461 | − | 17.1899i | 0.353774 | − | 0.612755i | −0.633133 | − | 0.774043i | \(-0.718231\pi\) |
0.986907 | + | 0.161288i | \(0.0515648\pi\) | |||||||
\(788\) | −2.52075 | + | 4.36606i | −0.0897978 | + | 0.155534i | ||||
\(789\) | −12.7843 | − | 22.1431i | −0.455134 | − | 0.788315i | ||||
\(790\) | −0.0630042 | −0.00224159 | ||||||||
\(791\) | 12.5965 | − | 20.8277i | 0.447879 | − | 0.740547i | ||||
\(792\) | −6.68923 | −0.237691 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 3.17724 | − | 5.50314i | 0.112756 | − | 0.195299i | ||||
\(795\) | 2.93242 | − | 5.07910i | 0.104002 | − | 0.180137i | ||||
\(796\) | 19.0841 | + | 33.0546i | 0.676418 | + | 1.17159i | ||||
\(797\) | 52.2894 | 1.85219 | 0.926093 | − | 0.377296i | \(-0.123146\pi\) | ||||
0.926093 | + | 0.377296i | \(0.123146\pi\) | |||||||
\(798\) | 2.51248 | + | 0.0511093i | 0.0889407 | + | 0.00180925i | ||||
\(799\) | 27.1014 | 0.958777 | ||||||||
\(800\) | 5.38210 | + | 9.32207i | 0.190286 | + | 0.329585i | ||||
\(801\) | 4.22160 | − | 7.31202i | 0.149163 | − | 0.258358i | ||||
\(802\) | −0.498271 | + | 0.863031i | −0.0175946 | + | 0.0304747i | ||||
\(803\) | −27.2008 | − | 47.1131i | −0.959894 | − | 1.66259i | ||||
\(804\) | 2.72283 | 0.0960269 | ||||||||
\(805\) | 0.996393 | + | 1.80984i | 0.0351182 | + | 0.0637884i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.2981 | − | 28.2292i | −0.573722 | − | 0.993715i | ||||
\(808\) | −0.0457832 | + | 0.0792988i | −0.00161065 | + | 0.00278972i | ||||
\(809\) | 1.18230 | − | 2.04780i | 0.0415674 | − | 0.0719969i | −0.844493 | − | 0.535566i | \(-0.820098\pi\) |
0.886061 | + | 0.463569i | \(0.153432\pi\) | |||||||
\(810\) | 1.35460 | + | 2.34624i | 0.0475959 | + | 0.0824385i | ||||
\(811\) | −23.6646 | −0.830978 | −0.415489 | − | 0.909598i | \(-0.636390\pi\) | ||||
−0.415489 | + | 0.909598i | \(0.636390\pi\) | |||||||
\(812\) | 17.2596 | + | 31.3502i | 0.605693 | + | 1.10017i | ||||
\(813\) | −38.4952 | −1.35008 | ||||||||
\(814\) | 7.94591 | + | 13.7627i | 0.278504 | + | 0.482383i | ||||
\(815\) | −0.502467 | + | 0.870298i | −0.0176006 | + | 0.0304852i | ||||
\(816\) | −10.5827 | + | 18.3297i | −0.370468 | + | 0.641669i | ||||
\(817\) | −4.15818 | − | 7.20218i | −0.145476 | − | 0.251972i | ||||
\(818\) | −11.3275 | −0.396058 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 20.6330 | 0.720536 | ||||||||
\(821\) | −1.78877 | − | 3.09823i | −0.0624284 | − | 0.108129i | 0.833122 | − | 0.553089i | \(-0.186551\pi\) |
−0.895550 | + | 0.444960i | \(0.853218\pi\) | |||||||
\(822\) | −4.02879 | + | 6.97808i | −0.140520 | + | 0.243388i | ||||
\(823\) | 14.9711 | − | 25.9307i | 0.521859 | − | 0.903887i | −0.477817 | − | 0.878459i | \(-0.658572\pi\) |
0.999677 | − | 0.0254278i | \(-0.00809478\pi\) | |||||||
\(824\) | 4.09696 | + | 7.09615i | 0.142725 | + | 0.247206i | ||||
\(825\) | 25.2998 | 0.880827 | ||||||||
\(826\) | 0.387350 | − | 0.640464i | 0.0134776 | − | 0.0222846i | ||||
\(827\) | 9.32620 | 0.324304 | 0.162152 | − | 0.986766i | \(-0.448157\pi\) | ||||
0.162152 | + | 0.986766i | \(0.448157\pi\) | |||||||
\(828\) | 0.443409 | + | 0.768007i | 0.0154095 | + | 0.0266901i | ||||
\(829\) | −19.1134 | + | 33.1054i | −0.663836 | + | 1.14980i | 0.315763 | + | 0.948838i | \(0.397739\pi\) |
−0.979599 | + | 0.200960i | \(0.935594\pi\) | |||||||
\(830\) | −0.641002 | + | 1.11025i | −0.0222495 | + | 0.0385373i | ||||
\(831\) | 6.84385 | + | 11.8539i | 0.237411 | + | 0.411207i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 30.2759 | + | 1.23227i | 1.04900 | + | 0.0426956i | ||||
\(834\) | 8.96568 | 0.310456 | ||||||||
\(835\) | −10.1078 | − | 17.5072i | −0.349794 | − | 0.605860i | ||||
\(836\) | −11.0135 | + | 19.0760i | −0.380910 | + | 0.659756i | ||||
\(837\) | −17.2488 | + | 29.8757i | −0.596205 | + | 1.03266i | ||||
\(838\) | −5.77933 | − | 10.0101i | −0.199644 | − | 0.345793i | ||||
\(839\) | 23.4981 | 0.811244 | 0.405622 | − | 0.914041i | \(-0.367055\pi\) | ||||
0.405622 | + | 0.914041i | \(0.367055\pi\) | |||||||
\(840\) | 3.73553 | − | 6.17652i | 0.128888 | − | 0.213110i | ||||
\(841\) | 22.2451 | 0.767071 | ||||||||
\(842\) | 4.01178 | + | 6.94860i | 0.138255 | + | 0.239465i | ||||
\(843\) | 12.9746 | − | 22.4726i | 0.446868 | − | 0.773998i | ||||
\(844\) | 12.4017 | − | 21.4803i | 0.426883 | − | 0.739384i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.80808 | −0.0621632 | ||||||||
\(847\) | 64.7121 | + | 1.31639i | 2.22353 | + | 0.0452316i | ||||
\(848\) | −9.30806 | −0.319640 | ||||||||
\(849\) | 7.01205 | + | 12.1452i | 0.240653 | + | 0.416823i | ||||
\(850\) | 2.09352 | − | 3.62608i | 0.0718072 | − | 0.124374i | ||||
\(851\) | 2.16843 | − | 3.75584i | 0.0743329 | − | 0.128748i | ||||
\(852\) | 5.18887 | + | 8.98738i | 0.177768 | + | 0.307903i | ||||
\(853\) | 40.9295 | 1.40140 | 0.700700 | − | 0.713456i | \(-0.252871\pi\) | ||||
0.700700 | + | 0.713456i | \(0.252871\pi\) | |||||||
\(854\) | −2.87508 | − | 5.22226i | −0.0983830 | − | 0.178702i | ||||
\(855\) | −2.45879 | −0.0840888 | ||||||||
\(856\) | 5.00923 | + | 8.67624i | 0.171212 | + | 0.296548i | ||||
\(857\) | 5.83099 | − | 10.0996i | 0.199183 | − | 0.344995i | −0.749081 | − | 0.662479i | \(-0.769505\pi\) |
0.948264 | + | 0.317484i | \(0.102838\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.1388 | − | 24.4891i | −0.482410 | − | 0.835559i | 0.517386 | − | 0.855752i | \(-0.326905\pi\) |
−0.999796 | + | 0.0201934i | \(0.993572\pi\) | |||||||
\(860\) | −11.6046 | −0.395715 | ||||||||
\(861\) | 14.0705 | + | 25.5576i | 0.479523 | + | 0.871001i | ||||
\(862\) | −1.58369 | −0.0539407 | ||||||||
\(863\) | −5.72212 | − | 9.91101i | −0.194783 | − | 0.337375i | 0.752046 | − | 0.659110i | \(-0.229067\pi\) |
−0.946829 | + | 0.321736i | \(0.895734\pi\) | |||||||
\(864\) | 10.4453 | − | 18.0918i | 0.355357 | − | 0.615496i | ||||
\(865\) | 3.92954 | − | 6.80617i | 0.133609 | − | 0.231417i | ||||
\(866\) | −3.65996 | − | 6.33924i | −0.124371 | − | 0.215416i | ||||
\(867\) | 2.53683 | 0.0861553 | ||||||||
\(868\) | 30.5289 | + | 0.621025i | 1.03622 | + | 0.0210790i | ||||
\(869\) | 0.780871 | 0.0264892 | ||||||||
\(870\) | −2.51064 | − | 4.34855i | −0.0851186 | − | 0.147430i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −0.0216944 | + | 0.0375757i | −0.000734664 | + | 0.00127248i | ||||
\(873\) | 2.85998 | + | 4.95364i | 0.0967958 | + | 0.167655i | ||||
\(874\) | −0.351449 | −0.0118879 | ||||||||
\(875\) | 15.6570 | − | 25.8881i | 0.529303 | − | 0.875177i | ||||
\(876\) | 25.1985 | 0.851380 | ||||||||
\(877\) | −28.1743 | − | 48.7993i | −0.951378 | − | 1.64783i | −0.742447 | − | 0.669904i | \(-0.766335\pi\) |
−0.208930 | − | 0.977930i | \(-0.566998\pi\) | |||||||
\(878\) | −0.570422 | + | 0.988000i | −0.0192508 | + | 0.0333434i | ||||
\(879\) | 8.49173 | − | 14.7081i | 0.286419 | − | 0.496092i | ||||
\(880\) | 14.4172 | + | 24.9713i | 0.486003 | + | 0.841782i | ||||
\(881\) | −1.16418 | −0.0392221 | −0.0196111 | − | 0.999808i | \(-0.506243\pi\) | ||||
−0.0196111 | + | 0.999808i | \(0.506243\pi\) | |||||||
\(882\) | −2.01988 | − | 0.0822115i | −0.0680128 | − | 0.00276821i | ||||
\(883\) | −12.1881 | −0.410162 | −0.205081 | − | 0.978745i | \(-0.565746\pi\) | ||||
−0.205081 | + | 0.978745i | \(0.565746\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.898123 | − | 1.55560i | 0.0301901 | − | 0.0522908i | ||||
\(886\) | 1.44682 | − | 2.50597i | 0.0486069 | − | 0.0841896i | ||||
\(887\) | −15.3320 | − | 26.5559i | −0.514799 | − | 0.891659i | −0.999853 | − | 0.0171740i | \(-0.994533\pi\) |
0.485053 | − | 0.874485i | \(-0.338800\pi\) | |||||||
\(888\) | −15.1524 | −0.508481 | ||||||||
\(889\) | −19.7099 | + | 32.5894i | −0.661049 | + | 1.09301i | ||||
\(890\) | 4.66910 | 0.156509 | ||||||||
\(891\) | −16.7889 | − | 29.0792i | −0.562449 | − | 0.974190i | ||||
\(892\) | −2.10053 | + | 3.63822i | −0.0703308 | + | 0.121817i | ||||
\(893\) | −6.12790 | + | 10.6138i | −0.205062 | + | 0.355178i | ||||
\(894\) | 0.747424 | + | 1.29458i | 0.0249976 | + | 0.0432971i | ||||
\(895\) | 7.74598 | 0.258920 | ||||||||
\(896\) | −24.3769 | − | 0.495879i | −0.814374 | − | 0.0165662i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.92689 | + | 5.06952i | 0.0976716 | + | 0.169172i | ||||
\(899\) | 21.8622 | − | 37.8665i | 0.729147 | − | 1.26292i | ||||
\(900\) | 2.38891 | − | 4.13771i | 0.0796303 | − | 0.137924i | ||||
\(901\) | 6.01486 | + | 10.4180i | 0.200384 | + | 0.347075i | ||||
\(902\) | 14.9512 | 0.497822 | ||||||||
\(903\) | −7.91370 | − | 14.3744i | −0.263352 | − | 0.478350i | ||||
\(904\) | 11.8934 | 0.395570 | ||||||||
\(905\) | −5.45011 | − | 9.43987i | −0.181168 | − | 0.313792i | ||||
\(906\) | −0.618368 | + | 1.07105i | −0.0205439 | + | 0.0355831i | ||||
\(907\) | 5.82396 | − | 10.0874i | 0.193382 | − | 0.334947i | −0.752987 | − | 0.658035i | \(-0.771388\pi\) |
0.946369 | + | 0.323088i | \(0.104721\pi\) | |||||||
\(908\) | 25.6074 | + | 44.3532i | 0.849810 | + | 1.47191i | ||||
\(909\) | 0.0615414 | 0.00204120 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.5833 | −0.880743 | −0.440371 | − | 0.897816i | \(-0.645153\pi\) | ||||
−0.440371 | + | 0.897816i | \(0.645153\pi\) | |||||||
\(912\) | −4.78571 | − | 8.28909i | −0.158471 | − | 0.274479i | ||||
\(913\) | 7.94455 | − | 13.7604i | 0.262926 | − | 0.455402i | ||||
\(914\) | −1.50777 | + | 2.61153i | −0.0498725 | + | 0.0863817i | ||||
\(915\) | −7.15316 | − | 12.3896i | −0.236476 | − | 0.409589i | ||||
\(916\) | 35.8797 | 1.18550 | ||||||||
\(917\) | −25.0455 | − | 0.509482i | −0.827077 | − | 0.0168246i | ||||
\(918\) | −8.12600 | −0.268198 | ||||||||
\(919\) | 22.8540 | + | 39.5842i | 0.753883 | + | 1.30576i | 0.945928 | + | 0.324377i | \(0.105155\pi\) |
−0.192045 | + | 0.981386i | \(0.561512\pi\) | |||||||
\(920\) | −0.504748 | + | 0.874250i | −0.0166411 | + | 0.0288232i | ||||
\(921\) | −10.0933 | + | 17.4821i | −0.332585 | + | 0.576055i | ||||
\(922\) | 1.09405 | + | 1.89494i | 0.0360305 | + | 0.0624066i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −22.4915 | + | 37.1886i | −0.739916 | + | 1.22342i | ||||
\(925\) | −23.3653 | −0.768246 | ||||||||
\(926\) | 0.577242 | + | 0.999813i | 0.0189694 | + | 0.0328559i | ||||
\(927\) | 2.75356 | − | 4.76930i | 0.0904386 | − | 0.156644i | ||||
\(928\) | −13.2391 | + | 22.9308i | −0.434595 | + | 0.752740i | ||||
\(929\) | −5.53257 | − | 9.58268i | −0.181518 | − | 0.314398i | 0.760880 | − | 0.648893i | \(-0.224768\pi\) |
−0.942398 | + | 0.334495i | \(0.891434\pi\) | |||||||
\(930\) | −4.28437 | −0.140490 | ||||||||
\(931\) | −7.32830 | + | 11.5785i | −0.240175 | + | 0.379469i | ||||
\(932\) | −41.0784 | −1.34557 | ||||||||
\(933\) | −22.4190 | − | 38.8309i | −0.733965 | − | 1.27127i | ||||
\(934\) | −4.94997 | + | 8.57360i | −0.161968 | + | 0.280537i | ||||
\(935\) | 18.6327 | − | 32.2729i | 0.609356 | − | 1.05544i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −57.6584 | −1.88362 | −0.941808 | − | 0.336150i | \(-0.890875\pi\) | ||||
−0.941808 | + | 0.336150i | \(0.890875\pi\) | |||||||
\(938\) | 0.449221 | − | 0.742765i | 0.0146676 | − | 0.0242521i | ||||
\(939\) | 16.1848 | 0.528170 | ||||||||
\(940\) | 8.55086 | + | 14.8105i | 0.278898 | + | 0.483066i | ||||
\(941\) | −8.48723 | + | 14.7003i | −0.276676 | + | 0.479216i | −0.970557 | − | 0.240874i | \(-0.922566\pi\) |
0.693881 | + | 0.720090i | \(0.255899\pi\) | |||||||
\(942\) | 2.28270 | − | 3.95375i | 0.0743743 | − | 0.128820i | ||||
\(943\) | −2.04009 | − | 3.53354i | −0.0664345 | − | 0.115068i | ||||
\(944\) | −2.85082 | −0.0927862 | ||||||||
\(945\) | −21.5975 | − | 0.439340i | −0.702566 | − | 0.0142917i | ||||
\(946\) | −8.40904 | −0.273401 | ||||||||
\(947\) | −8.34808 | − | 14.4593i | −0.271276 | − | 0.469864i | 0.697913 | − | 0.716183i | \(-0.254112\pi\) |
−0.969189 | + | 0.246319i | \(0.920779\pi\) | |||||||
\(948\) | −0.180848 | + | 0.313238i | −0.00587366 | + | 0.0101735i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.946733 | + | 1.63979i | 0.0307161 | + | 0.0532018i | ||||
\(951\) | −34.8658 | −1.13060 | ||||||||
\(952\) | 7.14062 | + | 12.9702i | 0.231429 | + | 0.420365i | ||||
\(953\) | −18.2473 | −0.591089 | −0.295545 | − | 0.955329i | \(-0.595501\pi\) | ||||
−0.295545 | + | 0.955329i | \(0.595501\pi\) | |||||||
\(954\) | −0.401285 | − | 0.695046i | −0.0129921 | − | 0.0225029i | ||||
\(955\) | −9.79143 | + | 16.9593i | −0.316843 | + | 0.548789i | ||||
\(956\) | 18.8665 | − | 32.6777i | 0.610186 | − | 1.05687i | ||||
\(957\) | 31.1167 | + | 53.8957i | 1.00586 | + | 1.74220i | ||||
\(958\) | −11.6948 | −0.377841 | ||||||||
\(959\) | −21.1896 | − | 38.4886i | −0.684248 | − | 1.24286i | ||||
\(960\) | −11.5423 | −0.372527 | ||||||||
\(961\) | −3.15382 | − | 5.46257i | −0.101736 | − | 0.176212i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.36669 | − | 5.83127i | 0.108490 | − | 0.187910i | ||||
\(964\) | 3.05204 | + | 5.28629i | 0.0982996 | + | 0.170260i | ||||
\(965\) | 26.8253 | 0.863537 | ||||||||
\(966\) | −0.693293 | − | 0.0141031i | −0.0223063 | − | 0.000453760i | ||||
\(967\) | 29.5845 | 0.951374 | 0.475687 | − | 0.879615i | \(-0.342199\pi\) | ||||
0.475687 | + | 0.879615i | \(0.342199\pi\) | |||||||
\(968\) | 15.8133 | + | 27.3894i | 0.508258 | + | 0.880328i | ||||
\(969\) | −6.18504 | + | 10.7128i | −0.198692 | + | 0.344145i | ||||
\(970\) | −1.58158 | + | 2.73937i | −0.0507813 | + | 0.0879558i | ||||
\(971\) | −7.56504 | − | 13.1030i | −0.242774 | − | 0.420497i | 0.718730 | − | 0.695290i | \(-0.244724\pi\) |
−0.961503 | + | 0.274793i | \(0.911391\pi\) | |||||||
\(972\) | −16.4627 | −0.528040 | ||||||||
\(973\) | −25.2998 | + | 41.8320i | −0.811075 | + | 1.34107i | ||||
\(974\) | 0.598787 | 0.0191864 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.3528 | + | 19.6636i | −0.363393 | + | 0.629415i | ||||
\(977\) | 16.2318 | − | 28.1143i | 0.519301 | − | 0.899457i | −0.480447 | − | 0.877024i | \(-0.659526\pi\) |
0.999748 | − | 0.0224327i | \(-0.00714115\pi\) | |||||||
\(978\) | −0.168650 | − | 0.292110i | −0.00539283 | − | 0.00934065i | ||||
\(979\) | −57.8686 | −1.84949 | ||||||||
\(980\) | 8.87906 | + | 16.9342i | 0.283631 | + | 0.540943i | ||||
\(981\) | 0.0291614 | 0.000931052 | ||||||||
\(982\) | 1.36161 | + | 2.35838i | 0.0434508 | + | 0.0752590i | ||||
\(983\) | −22.1473 | + | 38.3602i | −0.706388 | + | 1.22350i | 0.259800 | + | 0.965662i | \(0.416343\pi\) |
−0.966188 | + | 0.257838i | \(0.916990\pi\) | |||||||
\(984\) | −7.12779 | + | 12.3457i | −0.227226 | + | 0.393567i | ||||
\(985\) | 1.92855 | + | 3.34034i | 0.0614487 | + | 0.106432i | ||||
\(986\) | 10.2994 | 0.328001 | ||||||||
\(987\) | −12.5142 | + | 20.6917i | −0.398333 | + | 0.658624i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.14741 | + | 1.98737i | 0.0364855 | + | 0.0631948i | ||||
\(990\) | −1.24309 | + | 2.15310i | −0.0395081 | + | 0.0684301i | ||||
\(991\) | 4.26058 | − | 7.37955i | 0.135342 | − | 0.234419i | −0.790386 | − | 0.612609i | \(-0.790120\pi\) |
0.925728 | + | 0.378190i | \(0.123453\pi\) | |||||||
\(992\) | 11.2962 | + | 19.5655i | 0.358654 | + | 0.621206i | ||||
\(993\) | −26.7500 | −0.848887 | ||||||||
\(994\) | 3.30775 | + | 0.0672870i | 0.104916 | + | 0.00213422i | ||||
\(995\) | 29.2014 | 0.925746 | ||||||||
\(996\) | 3.67988 | + | 6.37374i | 0.116601 | + | 0.201960i | ||||
\(997\) | 3.38953 | − | 5.87083i | 0.107347 | − | 0.185931i | −0.807347 | − | 0.590076i | \(-0.799098\pi\) |
0.914695 | + | 0.404145i | \(0.132431\pi\) | |||||||
\(998\) | −6.06858 | + | 10.5111i | −0.192098 | + | 0.332723i | ||||
\(999\) | 22.6731 | + | 39.2709i | 0.717344 | + | 1.24248i |
(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 | 1183.2.e.i.508.4 | 16 | ||
7.2 | even | 3 | inner | 1183.2.e.i.170.4 | 16 | ||
7.3 | odd | 6 | 8281.2.a.cj.1.5 | 8 | |||
7.4 | even | 3 | 8281.2.a.ck.1.5 | 8 | |||
13.5 | odd | 4 | 91.2.r.a.25.4 | ✓ | 16 | ||
13.8 | odd | 4 | 91.2.r.a.25.5 | yes | 16 | ||
13.12 | even | 2 | inner | 1183.2.e.i.508.5 | 16 | ||
39.5 | even | 4 | 819.2.dl.e.298.5 | 16 | |||
39.8 | even | 4 | 819.2.dl.e.298.4 | 16 | |||
91.5 | even | 12 | 637.2.r.f.324.5 | 16 | |||
91.18 | odd | 12 | 637.2.c.f.246.4 | 8 | |||
91.25 | even | 6 | 8281.2.a.ck.1.4 | 8 | |||
91.31 | even | 12 | 637.2.c.e.246.4 | 8 | |||
91.34 | even | 4 | 637.2.r.f.116.5 | 16 | |||
91.38 | odd | 6 | 8281.2.a.cj.1.4 | 8 | |||
91.44 | odd | 12 | 91.2.r.a.51.5 | yes | 16 | ||
91.47 | even | 12 | 637.2.r.f.324.4 | 16 | |||
91.51 | even | 6 | inner | 1183.2.e.i.170.5 | 16 | ||
91.60 | odd | 12 | 637.2.c.f.246.5 | 8 | |||
91.73 | even | 12 | 637.2.c.e.246.5 | 8 | |||
91.83 | even | 4 | 637.2.r.f.116.4 | 16 | |||
91.86 | odd | 12 | 91.2.r.a.51.4 | yes | 16 | ||
273.44 | even | 12 | 819.2.dl.e.415.4 | 16 | |||
273.86 | even | 12 | 819.2.dl.e.415.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.r.a.25.4 | ✓ | 16 | 13.5 | odd | 4 | ||
91.2.r.a.25.5 | yes | 16 | 13.8 | odd | 4 | ||
91.2.r.a.51.4 | yes | 16 | 91.86 | odd | 12 | ||
91.2.r.a.51.5 | yes | 16 | 91.44 | odd | 12 | ||
637.2.c.e.246.4 | 8 | 91.31 | even | 12 | |||
637.2.c.e.246.5 | 8 | 91.73 | even | 12 | |||
637.2.c.f.246.4 | 8 | 91.18 | odd | 12 | |||
637.2.c.f.246.5 | 8 | 91.60 | odd | 12 | |||
637.2.r.f.116.4 | 16 | 91.83 | even | 4 | |||
637.2.r.f.116.5 | 16 | 91.34 | even | 4 | |||
637.2.r.f.324.4 | 16 | 91.47 | even | 12 | |||
637.2.r.f.324.5 | 16 | 91.5 | even | 12 | |||
819.2.dl.e.298.4 | 16 | 39.8 | even | 4 | |||
819.2.dl.e.298.5 | 16 | 39.5 | even | 4 | |||
819.2.dl.e.415.4 | 16 | 273.44 | even | 12 | |||
819.2.dl.e.415.5 | 16 | 273.86 | even | 12 | |||
1183.2.e.i.170.4 | 16 | 7.2 | even | 3 | inner | ||
1183.2.e.i.170.5 | 16 | 91.51 | even | 6 | inner | ||
1183.2.e.i.508.4 | 16 | 1.1 | even | 1 | trivial | ||
1183.2.e.i.508.5 | 16 | 13.12 | even | 2 | inner | ||
8281.2.a.cj.1.4 | 8 | 91.38 | odd | 6 | |||
8281.2.a.cj.1.5 | 8 | 7.3 | odd | 6 | |||
8281.2.a.ck.1.4 | 8 | 91.25 | even | 6 | |||
8281.2.a.ck.1.5 | 8 | 7.4 | even | 3 |