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 | 170.6 | ||
Root | \(0.536527 + 0.929293i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.170 |
Dual form | 1183.2.e.i.508.6 |
$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(1016\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.536527 | − | 0.929293i | 0.379382 | − | 0.657109i | −0.611590 | − | 0.791175i | \(-0.709470\pi\) |
0.990972 | + | 0.134065i | \(0.0428032\pi\) | |||||||
\(3\) | 1.21570 | + | 2.10566i | 0.701886 | + | 1.21570i | 0.967804 | + | 0.251707i | \(0.0809918\pi\) |
−0.265918 | + | 0.963996i | \(0.585675\pi\) | |||||||
\(4\) | 0.424277 | + | 0.734868i | 0.212138 | + | 0.367434i | ||||
\(5\) | −0.312716 | + | 0.541640i | −0.139851 | + | 0.242229i | −0.927440 | − | 0.373972i | \(-0.877996\pi\) |
0.787589 | + | 0.616201i | \(0.211329\pi\) | |||||||
\(6\) | 2.60903 | 1.06513 | ||||||||
\(7\) | 1.21561 | − | 2.34996i | 0.459458 | − | 0.888200i | ||||
\(8\) | 3.05665 | 1.08069 | ||||||||
\(9\) | −1.45586 | + | 2.52163i | −0.485288 | + | 0.840544i | ||||
\(10\) | 0.335561 | + | 0.581209i | 0.106114 | + | 0.183795i | ||||
\(11\) | 0.354260 | + | 0.613597i | 0.106814 | + | 0.185006i | 0.914478 | − | 0.404636i | \(-0.132602\pi\) |
−0.807664 | + | 0.589643i | \(0.799269\pi\) | |||||||
\(12\) | −1.03159 | + | 1.78676i | −0.297794 | + | 0.515794i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.53159 | − | 2.39047i | −0.409334 | − | 0.638881i | ||||
\(15\) | −1.52068 | −0.392637 | ||||||||
\(16\) | 0.791426 | − | 1.37079i | 0.197856 | − | 0.342697i | ||||
\(17\) | 1.67157 | + | 2.89524i | 0.405414 | + | 0.702199i | 0.994370 | − | 0.105967i | \(-0.0337939\pi\) |
−0.588955 | + | 0.808166i | \(0.700461\pi\) | |||||||
\(18\) | 1.56222 | + | 2.70585i | 0.368219 | + | 0.637775i | ||||
\(19\) | 2.60138 | − | 4.50573i | 0.596798 | − | 1.03368i | −0.396492 | − | 0.918038i | \(-0.629773\pi\) |
0.993290 | − | 0.115646i | \(-0.0368939\pi\) | |||||||
\(20\) | −0.530712 | −0.118671 | ||||||||
\(21\) | 6.42602 | − | 0.297185i | 1.40227 | − | 0.0648510i | ||||
\(22\) | 0.760282 | 0.162093 | ||||||||
\(23\) | 2.21570 | − | 3.83771i | 0.462006 | − | 0.800218i | −0.537055 | − | 0.843547i | \(-0.680463\pi\) |
0.999061 | + | 0.0433296i | \(0.0137966\pi\) | |||||||
\(24\) | 3.71598 | + | 6.43627i | 0.758522 | + | 1.31380i | ||||
\(25\) | 2.30442 | + | 3.99137i | 0.460883 | + | 0.798274i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.214623 | 0.0413042 | ||||||||
\(28\) | 2.24266 | − | 0.103717i | 0.423824 | − | 0.0196006i | ||||
\(29\) | −6.59711 | −1.22505 | −0.612526 | − | 0.790450i | \(-0.709847\pi\) | ||||
−0.612526 | + | 0.790450i | \(0.709847\pi\) | |||||||
\(30\) | −0.815886 | + | 1.41316i | −0.148960 | + | 0.258006i | ||||
\(31\) | 2.19530 | + | 3.80238i | 0.394288 | + | 0.682927i | 0.993010 | − | 0.118030i | \(-0.0376579\pi\) |
−0.598722 | + | 0.800957i | \(0.704325\pi\) | |||||||
\(32\) | 2.20741 | + | 3.82335i | 0.390219 | + | 0.675879i | ||||
\(33\) | −0.861351 | + | 1.49190i | −0.149942 | + | 0.259707i | ||||
\(34\) | 3.58737 | 0.615228 | ||||||||
\(35\) | 0.892689 | + | 1.39329i | 0.150892 | + | 0.235509i | ||||
\(36\) | −2.47076 | −0.411793 | ||||||||
\(37\) | −0.211704 | + | 0.366683i | −0.0348040 | + | 0.0602823i | −0.882903 | − | 0.469556i | \(-0.844414\pi\) |
0.848099 | + | 0.529838i | \(0.177747\pi\) | |||||||
\(38\) | −2.79143 | − | 4.83489i | −0.452829 | − | 0.784323i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.955864 | + | 1.65561i | −0.151135 | + | 0.261774i | ||||
\(41\) | −5.01604 | −0.783374 | −0.391687 | − | 0.920099i | \(-0.628108\pi\) | ||||
−0.391687 | + | 0.920099i | \(0.628108\pi\) | |||||||
\(42\) | 3.17157 | − | 6.13111i | 0.489383 | − | 0.946050i | ||||
\(43\) | −11.2059 | −1.70889 | −0.854445 | − | 0.519542i | \(-0.826103\pi\) | ||||
−0.854445 | + | 0.519542i | \(0.826103\pi\) | |||||||
\(44\) | −0.300609 | + | 0.520670i | −0.0453185 | + | 0.0784939i | ||||
\(45\) | −0.910544 | − | 1.57711i | −0.135736 | − | 0.235101i | ||||
\(46\) | −2.37757 | − | 4.11807i | −0.350554 | − | 0.607177i | ||||
\(47\) | −4.03635 | + | 6.99116i | −0.588762 | + | 1.01977i | 0.405633 | + | 0.914036i | \(0.367051\pi\) |
−0.994395 | + | 0.105729i | \(0.966282\pi\) | |||||||
\(48\) | 3.84855 | 0.555491 | ||||||||
\(49\) | −4.04458 | − | 5.71326i | −0.577797 | − | 0.816180i | ||||
\(50\) | 4.94553 | 0.699404 | ||||||||
\(51\) | −4.06426 | + | 7.03950i | −0.569110 | + | 0.985727i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.348553 | + | 0.603712i | 0.0478774 | + | 0.0829262i | 0.888971 | − | 0.457964i | \(-0.151421\pi\) |
−0.841094 | + | 0.540890i | \(0.818088\pi\) | |||||||
\(54\) | 0.115151 | − | 0.199447i | 0.0156701 | − | 0.0271414i | ||||
\(55\) | −0.443132 | −0.0597519 | ||||||||
\(56\) | 3.71570 | − | 7.18300i | 0.496532 | − | 0.959869i | ||||
\(57\) | 12.6500 | 1.67554 | ||||||||
\(58\) | −3.53953 | + | 6.13065i | −0.464763 | + | 0.804993i | ||||
\(59\) | −4.93159 | − | 8.54177i | −0.642039 | − | 1.11204i | −0.984977 | − | 0.172686i | \(-0.944756\pi\) |
0.342938 | − | 0.939358i | \(-0.388578\pi\) | |||||||
\(60\) | −0.645188 | − | 1.11750i | −0.0832934 | − | 0.144268i | ||||
\(61\) | −2.34855 | + | 4.06781i | −0.300701 | + | 0.520830i | −0.976295 | − | 0.216444i | \(-0.930554\pi\) |
0.675594 | + | 0.737274i | \(0.263887\pi\) | |||||||
\(62\) | 4.71136 | 0.598344 | ||||||||
\(63\) | 4.15596 | + | 6.48654i | 0.523601 | + | 0.817227i | ||||
\(64\) | 7.90305 | 0.987881 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.924277 | + | 1.60089i | 0.113771 | + | 0.197056i | ||||
\(67\) | −5.21041 | − | 9.02470i | −0.636553 | − | 1.10254i | −0.986184 | − | 0.165655i | \(-0.947026\pi\) |
0.349631 | − | 0.936888i | \(-0.386307\pi\) | |||||||
\(68\) | −1.41841 | + | 2.45676i | −0.172008 | + | 0.297926i | ||||
\(69\) | 10.7745 | 1.29710 | ||||||||
\(70\) | 1.77373 | − | 0.0820297i | 0.212001 | − | 0.00980443i | ||||
\(71\) | −14.0876 | −1.67189 | −0.835946 | − | 0.548812i | \(-0.815080\pi\) | ||||
−0.835946 | + | 0.548812i | \(0.815080\pi\) | |||||||
\(72\) | −4.45007 | + | 7.70775i | −0.524446 | + | 0.908368i | ||||
\(73\) | 2.54191 | + | 4.40273i | 0.297509 | + | 0.515300i | 0.975565 | − | 0.219710i | \(-0.0705110\pi\) |
−0.678057 | + | 0.735010i | \(0.737178\pi\) | |||||||
\(74\) | 0.227170 | + | 0.393471i | 0.0264080 | + | 0.0457400i | ||||
\(75\) | −5.60297 | + | 9.70463i | −0.646975 | + | 1.12059i | ||||
\(76\) | 4.41482 | 0.506415 | ||||||||
\(77\) | 1.87257 | − | 0.0866008i | 0.213399 | − | 0.00986908i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.95586 | − | 3.38766i | 0.220052 | − | 0.381141i | −0.734772 | − | 0.678315i | \(-0.762711\pi\) |
0.954823 | + | 0.297174i | \(0.0960440\pi\) | |||||||
\(80\) | 0.494983 | + | 0.857336i | 0.0553408 | + | 0.0958530i | ||||
\(81\) | 4.62851 | + | 8.01682i | 0.514279 | + | 0.890757i | ||||
\(82\) | −2.69124 | + | 4.66137i | −0.297198 | + | 0.514762i | ||||
\(83\) | 10.2035 | 1.11998 | 0.559990 | − | 0.828499i | \(-0.310805\pi\) | ||||
0.559990 | + | 0.828499i | \(0.310805\pi\) | |||||||
\(84\) | 2.94480 | + | 4.59619i | 0.321304 | + | 0.501486i | ||||
\(85\) | −2.09090 | −0.226790 | ||||||||
\(86\) | −6.01230 | + | 10.4136i | −0.648323 | + | 1.12293i | ||||
\(87\) | −8.02012 | − | 13.8913i | −0.859847 | − | 1.48930i | ||||
\(88\) | 1.08285 | + | 1.87555i | 0.115432 | + | 0.199935i | ||||
\(89\) | 6.68955 | − | 11.5866i | 0.709090 | − | 1.22818i | −0.256104 | − | 0.966649i | \(-0.582439\pi\) |
0.965195 | − | 0.261532i | \(-0.0842276\pi\) | |||||||
\(90\) | −1.95413 | −0.205983 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.76028 | 0.392036 | ||||||||
\(93\) | −5.33767 | + | 9.24512i | −0.553491 | + | 0.958674i | ||||
\(94\) | 4.33122 | + | 7.50190i | 0.446731 | + | 0.773761i | ||||
\(95\) | 1.62699 | + | 2.81802i | 0.166925 | + | 0.289123i | ||||
\(96\) | −5.36711 | + | 9.29610i | −0.547778 | + | 0.948780i | ||||
\(97\) | −0.202023 | −0.0205123 | −0.0102562 | − | 0.999947i | \(-0.503265\pi\) | ||||
−0.0102562 | + | 0.999947i | \(0.503265\pi\) | |||||||
\(98\) | −7.47932 | + | 0.693276i | −0.755526 | + | 0.0700315i | ||||
\(99\) | −2.06302 | −0.207341 | ||||||||
\(100\) | −1.95542 | + | 3.38689i | −0.195542 | + | 0.338689i | ||||
\(101\) | 8.66723 | + | 15.0121i | 0.862421 | + | 1.49376i | 0.869585 | + | 0.493783i | \(0.164386\pi\) |
−0.00716374 | + | 0.999974i | \(0.502280\pi\) | |||||||
\(102\) | 4.36117 | + | 7.55377i | 0.431820 | + | 0.747934i | ||||
\(103\) | 5.40739 | − | 9.36587i | 0.532806 | − | 0.922847i | −0.466460 | − | 0.884542i | \(-0.654471\pi\) |
0.999266 | − | 0.0383047i | \(-0.0121957\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.84855 | + | 3.57353i | −0.180400 | + | 0.348740i | ||||
\(106\) | 0.748033 | 0.0726554 | ||||||||
\(107\) | 3.05839 | − | 5.29729i | 0.295666 | − | 0.512108i | −0.679474 | − | 0.733700i | \(-0.737792\pi\) |
0.975140 | + | 0.221592i | \(0.0711252\pi\) | |||||||
\(108\) | 0.0910594 | + | 0.157720i | 0.00876220 | + | 0.0151766i | ||||
\(109\) | −5.69958 | − | 9.87196i | −0.545921 | − | 0.945563i | −0.998548 | − | 0.0538629i | \(-0.982847\pi\) |
0.452628 | − | 0.891700i | \(-0.350487\pi\) | |||||||
\(110\) | −0.237752 | + | 0.411799i | −0.0226688 | + | 0.0392635i | ||||
\(111\) | −1.02948 | −0.0977137 | ||||||||
\(112\) | −2.25923 | − | 3.52616i | −0.213477 | − | 0.333191i | ||||
\(113\) | −0.923456 | −0.0868714 | −0.0434357 | − | 0.999056i | \(-0.513830\pi\) | ||||
−0.0434357 | + | 0.999056i | \(0.513830\pi\) | |||||||
\(114\) | 6.78709 | − | 11.7556i | 0.635669 | − | 1.10101i | ||||
\(115\) | 1.38577 | + | 2.40023i | 0.129224 | + | 0.223822i | ||||
\(116\) | −2.79900 | − | 4.84801i | −0.259880 | − | 0.450126i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.5837 | −0.974312 | ||||||||
\(119\) | 8.83566 | − | 0.408623i | 0.809963 | − | 0.0374584i | ||||
\(120\) | −4.64819 | −0.424319 | ||||||||
\(121\) | 5.24900 | − | 9.09153i | 0.477182 | − | 0.826503i | ||||
\(122\) | 2.52013 | + | 4.36499i | 0.228162 | + | 0.395187i | ||||
\(123\) | −6.09801 | − | 10.5621i | −0.549839 | − | 0.952349i | ||||
\(124\) | −1.86283 | + | 3.22652i | −0.167287 | + | 0.289750i | ||||
\(125\) | −6.00967 | −0.537521 | ||||||||
\(126\) | 8.25768 | − | 0.381893i | 0.735652 | − | 0.0340218i | ||||
\(127\) | −8.50972 | −0.755116 | −0.377558 | − | 0.925986i | \(-0.623236\pi\) | ||||
−0.377558 | + | 0.925986i | \(0.623236\pi\) | |||||||
\(128\) | −0.174618 | + | 0.302447i | −0.0154342 | + | 0.0267328i | ||||
\(129\) | −13.6231 | − | 23.5959i | −1.19945 | − | 2.07750i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.50152 | − | 6.06482i | 0.305930 | − | 0.529885i | −0.671538 | − | 0.740970i | \(-0.734366\pi\) |
0.977468 | + | 0.211084i | \(0.0676995\pi\) | |||||||
\(132\) | −1.46180 | −0.127234 | ||||||||
\(133\) | −7.42599 | − | 11.5903i | −0.643915 | − | 1.00501i | ||||
\(134\) | −11.1821 | −0.965988 | ||||||||
\(135\) | −0.0671160 | + | 0.116248i | −0.00577642 | + | 0.0100051i | ||||
\(136\) | 5.10940 | + | 8.84974i | 0.438128 | + | 0.758859i | ||||
\(137\) | 3.10847 | + | 5.38403i | 0.265575 | + | 0.459989i | 0.967714 | − | 0.252051i | \(-0.0811050\pi\) |
−0.702139 | + | 0.712040i | \(0.747772\pi\) | |||||||
\(138\) | 5.78084 | − | 10.0127i | 0.492097 | − | 0.852338i | ||||
\(139\) | 6.53140 | 0.553986 | 0.276993 | − | 0.960872i | \(-0.410662\pi\) | ||||
0.276993 | + | 0.960872i | \(0.410662\pi\) | |||||||
\(140\) | −0.645140 | + | 1.24715i | −0.0545242 | + | 0.105403i | ||||
\(141\) | −19.6280 | −1.65297 | ||||||||
\(142\) | −7.55839 | + | 13.0915i | −0.634286 | + | 1.09862i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.30442 | + | 3.99137i | 0.192035 | + | 0.332614i | ||||
\(145\) | 2.06302 | − | 3.57326i | 0.171325 | − | 0.296743i | ||||
\(146\) | 5.45523 | 0.451478 | ||||||||
\(147\) | 7.11317 | − | 15.4621i | 0.586685 | − | 1.27529i | ||||
\(148\) | −0.359285 | −0.0295330 | ||||||||
\(149\) | 1.84869 | − | 3.20203i | 0.151451 | − | 0.262320i | −0.780310 | − | 0.625393i | \(-0.784939\pi\) |
0.931761 | + | 0.363072i | \(0.118272\pi\) | |||||||
\(150\) | 6.01230 | + | 10.4136i | 0.490902 | + | 0.850267i | ||||
\(151\) | 2.43887 | + | 4.22425i | 0.198473 | + | 0.343764i | 0.948033 | − | 0.318171i | \(-0.103069\pi\) |
−0.749561 | + | 0.661935i | \(0.769735\pi\) | |||||||
\(152\) | 7.95152 | − | 13.7724i | 0.644954 | − | 1.11709i | ||||
\(153\) | −9.73430 | −0.786971 | ||||||||
\(154\) | 0.924207 | − | 1.78663i | 0.0744747 | − | 0.143971i | ||||
\(155\) | −2.74603 | −0.220566 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.75984 | + | 8.24428i | 0.379876 | + | 0.657965i | 0.991044 | − | 0.133536i | \(-0.0426332\pi\) |
−0.611168 | + | 0.791501i | \(0.709300\pi\) | |||||||
\(158\) | −2.09875 | − | 3.63514i | −0.166968 | − | 0.289196i | ||||
\(159\) | −0.847473 | + | 1.46787i | −0.0672090 | + | 0.116409i | ||||
\(160\) | −2.76117 | −0.218290 | ||||||||
\(161\) | −6.32501 | − | 9.87196i | −0.498481 | − | 0.778020i | ||||
\(162\) | 9.93329 | 0.780433 | ||||||||
\(163\) | 11.8544 | − | 20.5325i | 0.928511 | − | 1.60823i | 0.142696 | − | 0.989767i | \(-0.454423\pi\) |
0.785815 | − | 0.618461i | \(-0.212244\pi\) | |||||||
\(164\) | −2.12819 | − | 3.68613i | −0.166184 | − | 0.287838i | ||||
\(165\) | −0.538716 | − | 0.933084i | −0.0419390 | − | 0.0726405i | ||||
\(166\) | 5.47446 | − | 9.48204i | 0.424901 | − | 0.735949i | ||||
\(167\) | 1.13193 | 0.0875914 | 0.0437957 | − | 0.999041i | \(-0.486055\pi\) | ||||
0.0437957 | + | 0.999041i | \(0.486055\pi\) | |||||||
\(168\) | 19.6421 | − | 0.908391i | 1.51542 | − | 0.0700839i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −1.12183 | + | 1.94306i | −0.0860402 | + | 0.149026i | ||||
\(171\) | 7.57452 | + | 13.1195i | 0.579238 | + | 1.00327i | ||||
\(172\) | −4.75442 | − | 8.23489i | −0.362521 | − | 0.627905i | ||||
\(173\) | −5.99458 | + | 10.3829i | −0.455760 | + | 0.789399i | −0.998732 | − | 0.0503522i | \(-0.983966\pi\) |
0.542972 | + | 0.839751i | \(0.317299\pi\) | |||||||
\(174\) | −17.2121 | −1.30484 | ||||||||
\(175\) | 12.1808 | − | 0.563327i | 0.920783 | − | 0.0425835i | ||||
\(176\) | 1.12148 | 0.0845350 | ||||||||
\(177\) | 11.9907 | − | 20.7685i | 0.901276 | − | 1.56106i | ||||
\(178\) | −7.17825 | − | 12.4331i | −0.538033 | − | 0.931900i | ||||
\(179\) | −4.73538 | − | 8.20192i | −0.353939 | − | 0.613040i | 0.632997 | − | 0.774154i | \(-0.281825\pi\) |
−0.986936 | + | 0.161114i | \(0.948491\pi\) | |||||||
\(180\) | 0.772645 | − | 1.33826i | 0.0575896 | − | 0.0997480i | ||||
\(181\) | 11.4314 | 0.849690 | 0.424845 | − | 0.905266i | \(-0.360329\pi\) | ||||
0.424845 | + | 0.905266i | \(0.360329\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.4206 | −0.844233 | ||||||||
\(184\) | 6.77264 | − | 11.7305i | 0.499285 | − | 0.864788i | ||||
\(185\) | −0.132407 | − | 0.229335i | −0.00973473 | − | 0.0168611i | ||||
\(186\) | 5.72761 | + | 9.92052i | 0.419969 | + | 0.727408i | ||||
\(187\) | −1.18434 | + | 2.05134i | −0.0866075 | + | 0.150009i | ||||
\(188\) | −6.85011 | −0.499595 | ||||||||
\(189\) | 0.260898 | − | 0.504354i | 0.0189775 | − | 0.0366864i | ||||
\(190\) | 3.49169 | 0.253314 | ||||||||
\(191\) | −7.84377 | + | 13.5858i | −0.567555 | + | 0.983034i | 0.429252 | + | 0.903185i | \(0.358777\pi\) |
−0.996807 | + | 0.0798496i | \(0.974556\pi\) | |||||||
\(192\) | 9.60776 | + | 16.6411i | 0.693380 | + | 1.20097i | ||||
\(193\) | −11.5036 | − | 19.9248i | −0.828045 | − | 1.43422i | −0.899570 | − | 0.436776i | \(-0.856120\pi\) |
0.0715256 | − | 0.997439i | \(-0.477213\pi\) | |||||||
\(194\) | −0.108391 | + | 0.187739i | −0.00778202 | + | 0.0134788i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.48248 | − | 5.39624i | 0.177320 | − | 0.385446i | ||||
\(197\) | −10.2035 | −0.726970 | −0.363485 | − | 0.931600i | \(-0.618413\pi\) | ||||
−0.363485 | + | 0.931600i | \(0.618413\pi\) | |||||||
\(198\) | −1.10687 | + | 1.91715i | −0.0786616 | + | 0.136246i | ||||
\(199\) | −5.96173 | − | 10.3260i | −0.422616 | − | 0.731992i | 0.573579 | − | 0.819150i | \(-0.305555\pi\) |
−0.996194 | + | 0.0871586i | \(0.972221\pi\) | |||||||
\(200\) | 7.04381 | + | 12.2002i | 0.498072 | + | 0.862687i | ||||
\(201\) | 12.6686 | − | 21.9427i | 0.893576 | − | 1.54772i | ||||
\(202\) | 18.6008 | 1.30875 | ||||||||
\(203\) | −8.01952 | + | 15.5029i | −0.562860 | + | 1.08809i | ||||
\(204\) | −6.89747 | −0.482920 | ||||||||
\(205\) | 1.56860 | − | 2.71689i | 0.109555 | − | 0.189756i | ||||
\(206\) | −5.80243 | − | 10.0501i | −0.404274 | − | 0.700223i | ||||
\(207\) | 6.45152 | + | 11.1744i | 0.448412 | + | 0.776672i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.68627 | 0.254984 | ||||||||
\(210\) | 2.32905 | + | 3.63514i | 0.160720 | + | 0.250849i | ||||
\(211\) | −15.5893 | −1.07321 | −0.536606 | − | 0.843833i | \(-0.680294\pi\) | ||||
−0.536606 | + | 0.843833i | \(0.680294\pi\) | |||||||
\(212\) | −0.295766 | + | 0.512281i | −0.0203133 | + | 0.0351836i | ||||
\(213\) | −17.1263 | − | 29.6637i | −1.17348 | − | 2.03252i | ||||
\(214\) | −3.28182 | − | 5.68428i | −0.224341 | − | 0.388570i | ||||
\(215\) | 3.50428 | − | 6.06959i | 0.238990 | − | 0.413942i | ||||
\(216\) | 0.656028 | 0.0446370 | ||||||||
\(217\) | 11.6041 | − | 0.536653i | 0.787734 | − | 0.0364304i | ||||
\(218\) | −12.2319 | −0.828451 | ||||||||
\(219\) | −6.18042 | + | 10.7048i | −0.417634 | + | 0.723364i | ||||
\(220\) | −0.188010 | − | 0.325643i | −0.0126757 | − | 0.0219549i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −0.552343 | + | 0.956687i | −0.0370709 | + | 0.0642086i | ||||
\(223\) | 6.76662 | 0.453126 | 0.226563 | − | 0.973996i | \(-0.427251\pi\) | ||||
0.226563 | + | 0.973996i | \(0.427251\pi\) | |||||||
\(224\) | 11.6680 | − | 0.539613i | 0.779604 | − | 0.0360544i | ||||
\(225\) | −13.4197 | −0.894645 | ||||||||
\(226\) | −0.495459 | + | 0.858161i | −0.0329575 | + | 0.0570840i | ||||
\(227\) | 8.41225 | + | 14.5704i | 0.558340 | + | 0.967074i | 0.997635 | + | 0.0687311i | \(0.0218950\pi\) |
−0.439295 | + | 0.898343i | \(0.644772\pi\) | |||||||
\(228\) | 5.36711 | + | 9.29610i | 0.355445 | + | 0.615650i | ||||
\(229\) | 5.51286 | − | 9.54855i | 0.364300 | − | 0.630986i | −0.624364 | − | 0.781134i | \(-0.714642\pi\) |
0.988664 | + | 0.150148i | \(0.0479750\pi\) | |||||||
\(230\) | 2.97402 | 0.196101 | ||||||||
\(231\) | 2.45884 | + | 3.83771i | 0.161780 | + | 0.252503i | ||||
\(232\) | −20.1651 | −1.32390 | ||||||||
\(233\) | −8.67743 | + | 15.0298i | −0.568477 | + | 0.984632i | 0.428239 | + | 0.903665i | \(0.359134\pi\) |
−0.996717 | + | 0.0809664i | \(0.974199\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.52446 | − | 4.37249i | −0.164678 | − | 0.285230i | ||||
\(236\) | 4.18472 | − | 7.24814i | 0.272402 | − | 0.471814i | ||||
\(237\) | 9.51100 | 0.617806 | ||||||||
\(238\) | 4.36084 | − | 8.43015i | 0.282671 | − | 0.546445i | ||||
\(239\) | −19.7223 | −1.27573 | −0.637865 | − | 0.770148i | \(-0.720182\pi\) | ||||
−0.637865 | + | 0.770148i | \(0.720182\pi\) | |||||||
\(240\) | −1.20350 | + | 2.08453i | −0.0776858 | + | 0.134556i | ||||
\(241\) | 1.39206 | + | 2.41112i | 0.0896706 | + | 0.155314i | 0.907372 | − | 0.420329i | \(-0.138085\pi\) |
−0.817701 | + | 0.575643i | \(0.804752\pi\) | |||||||
\(242\) | −5.63246 | − | 9.75571i | −0.362069 | − | 0.627121i | ||||
\(243\) | −10.9318 | + | 18.9345i | −0.701278 | + | 1.21465i | ||||
\(244\) | −3.98574 | −0.255161 | ||||||||
\(245\) | 4.35934 | − | 0.404077i | 0.278508 | − | 0.0258155i | ||||
\(246\) | −13.0870 | −0.834397 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 6.71028 | + | 11.6226i | 0.426103 | + | 0.738033i | ||||
\(249\) | 12.4044 | + | 21.4851i | 0.786098 | + | 1.36156i | ||||
\(250\) | −3.22435 | + | 5.58475i | −0.203926 | + | 0.353210i | ||||
\(251\) | 23.5608 | 1.48714 | 0.743572 | − | 0.668655i | \(-0.233130\pi\) | ||||
0.743572 | + | 0.668655i | \(0.233130\pi\) | |||||||
\(252\) | −3.00348 | + | 5.80617i | −0.189201 | + | 0.365754i | ||||
\(253\) | 3.13974 | 0.197394 | ||||||||
\(254\) | −4.56570 | + | 7.90803i | −0.286478 | + | 0.496194i | ||||
\(255\) | −2.54191 | − | 4.40273i | −0.159181 | − | 0.275709i | ||||
\(256\) | 8.09042 | + | 14.0130i | 0.505651 | + | 0.875814i | ||||
\(257\) | 1.71615 | − | 2.97245i | 0.107050 | − | 0.185417i | −0.807524 | − | 0.589835i | \(-0.799193\pi\) |
0.914574 | + | 0.404419i | \(0.132526\pi\) | |||||||
\(258\) | −29.2367 | −1.82019 | ||||||||
\(259\) | 0.604338 | + | 0.943239i | 0.0375517 | + | 0.0586100i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.60450 | − | 16.6355i | 0.594503 | − | 1.02971i | ||||
\(262\) | −3.75733 | − | 6.50788i | −0.232128 | − | 0.402058i | ||||
\(263\) | 10.7245 | + | 18.5754i | 0.661303 | + | 1.14541i | 0.980273 | + | 0.197646i | \(0.0633298\pi\) |
−0.318970 | + | 0.947765i | \(0.603337\pi\) | |||||||
\(264\) | −2.63285 | + | 4.56023i | −0.162041 | + | 0.280663i | ||||
\(265\) | −0.435992 | −0.0267828 | ||||||||
\(266\) | −14.7551 | + | 0.682378i | −0.904691 | + | 0.0418393i | ||||
\(267\) | 32.5300 | 1.99080 | ||||||||
\(268\) | 4.42131 | − | 7.65794i | 0.270075 | − | 0.467783i | ||||
\(269\) | −7.32843 | − | 12.6932i | −0.446822 | − | 0.773919i | 0.551355 | − | 0.834271i | \(-0.314111\pi\) |
−0.998177 | + | 0.0603517i | \(0.980778\pi\) | |||||||
\(270\) | 0.0720191 | + | 0.124741i | 0.00438294 | + | 0.00759148i | ||||
\(271\) | −1.02183 | + | 1.76986i | −0.0620717 | + | 0.107511i | −0.895391 | − | 0.445280i | \(-0.853104\pi\) |
0.833320 | + | 0.552792i | \(0.186437\pi\) | |||||||
\(272\) | 5.29168 | 0.320856 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.67112 | 0.403017 | ||||||||
\(275\) | −1.63273 | + | 2.82797i | −0.0984572 | + | 0.170533i | ||||
\(276\) | 4.57138 | + | 7.91787i | 0.275165 | + | 0.476600i | ||||
\(277\) | 2.71678 | + | 4.70560i | 0.163236 | + | 0.282732i | 0.936027 | − | 0.351927i | \(-0.114474\pi\) |
−0.772792 | + | 0.634660i | \(0.781140\pi\) | |||||||
\(278\) | 3.50428 | − | 6.06959i | 0.210173 | − | 0.364030i | ||||
\(279\) | −12.7843 | −0.765373 | ||||||||
\(280\) | 2.72864 | + | 4.25881i | 0.163067 | + | 0.254513i | ||||
\(281\) | −20.2356 | −1.20715 | −0.603577 | − | 0.797305i | \(-0.706258\pi\) | ||||
−0.603577 | + | 0.797305i | \(0.706258\pi\) | |||||||
\(282\) | −10.5310 | + | 18.2401i | −0.627109 | + | 1.08618i | ||||
\(283\) | −0.867593 | − | 1.50272i | −0.0515731 | − | 0.0893272i | 0.839086 | − | 0.543998i | \(-0.183090\pi\) |
−0.890659 | + | 0.454671i | \(0.849757\pi\) | |||||||
\(284\) | −5.97704 | − | 10.3525i | −0.354672 | − | 0.614310i | ||||
\(285\) | −3.95586 | + | 6.85176i | −0.234325 | + | 0.405863i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.09755 | + | 11.7875i | −0.359927 | + | 0.695792i | ||||
\(288\) | −12.8548 | −0.757474 | ||||||||
\(289\) | 2.91173 | − | 5.04326i | 0.171278 | − | 0.296662i | ||||
\(290\) | −2.21373 | − | 3.83430i | −0.129995 | − | 0.225158i | ||||
\(291\) | −0.245600 | − | 0.425392i | −0.0143973 | − | 0.0249369i | ||||
\(292\) | −2.15695 | + | 3.73595i | −0.126226 | + | 0.218630i | ||||
\(293\) | −27.2441 | −1.59162 | −0.795810 | − | 0.605547i | \(-0.792954\pi\) | ||||
−0.795810 | + | 0.605547i | \(0.792954\pi\) | |||||||
\(294\) | −10.5524 | − | 14.9061i | −0.615430 | − | 0.869340i | ||||
\(295\) | 6.16875 | 0.359159 | ||||||||
\(296\) | −0.647107 | + | 1.12082i | −0.0376123 | + | 0.0651465i | ||||
\(297\) | 0.0760324 | + | 0.131692i | 0.00441185 | + | 0.00764154i | ||||
\(298\) | −1.98375 | − | 3.43595i | −0.114915 | − | 0.199039i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −9.50884 | −0.548993 | ||||||||
\(301\) | −13.6221 | + | 26.3335i | −0.785163 | + | 1.51784i | ||||
\(302\) | 5.23409 | 0.301188 | ||||||||
\(303\) | −21.0735 | + | 36.5004i | −1.21064 | + | 2.09690i | ||||
\(304\) | −4.11760 | − | 7.13190i | −0.236161 | − | 0.409042i | ||||
\(305\) | −1.46886 | − | 2.54414i | −0.0841067 | − | 0.145677i | ||||
\(306\) | −5.22272 | + | 9.04601i | −0.298563 | + | 0.517126i | ||||
\(307\) | −12.7138 | −0.725612 | −0.362806 | − | 0.931865i | \(-0.618181\pi\) | ||||
−0.362806 | + | 0.931865i | \(0.618181\pi\) | |||||||
\(308\) | 0.858127 | + | 1.33935i | 0.0488963 | + | 0.0763165i | ||||
\(309\) | 26.2951 | 1.49588 | ||||||||
\(310\) | −1.47332 | + | 2.55186i | −0.0836788 | + | 0.144936i | ||||
\(311\) | −4.80939 | − | 8.33011i | −0.272716 | − | 0.472357i | 0.696841 | − | 0.717226i | \(-0.254588\pi\) |
−0.969556 | + | 0.244869i | \(0.921255\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.51273 | − | 7.81628i | 0.255075 | − | 0.441802i | −0.709841 | − | 0.704362i | \(-0.751233\pi\) |
0.964916 | + | 0.262559i | \(0.0845666\pi\) | |||||||
\(314\) | 10.2151 | 0.576473 | ||||||||
\(315\) | −4.81300 | + | 0.222587i | −0.271182 | + | 0.0125414i | ||||
\(316\) | 3.31931 | 0.186726 | ||||||||
\(317\) | 12.3131 | − | 21.3269i | 0.691572 | − | 1.19784i | −0.279750 | − | 0.960073i | \(-0.590252\pi\) |
0.971323 | − | 0.237766i | \(-0.0764150\pi\) | |||||||
\(318\) | 0.909386 | + | 1.57510i | 0.0509958 | + | 0.0883273i | ||||
\(319\) | −2.33709 | − | 4.04797i | −0.130852 | − | 0.226643i | ||||
\(320\) | −2.47141 | + | 4.28061i | −0.138156 | + | 0.239293i | ||||
\(321\) | 14.8724 | 0.830095 | ||||||||
\(322\) | −12.5675 | + | 0.581209i | −0.700359 | + | 0.0323895i | ||||
\(323\) | 17.3935 | 0.967802 | ||||||||
\(324\) | −3.92754 | + | 6.80269i | −0.218196 | + | 0.377927i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −12.7205 | − | 22.0325i | −0.704521 | − | 1.22027i | ||||
\(327\) | 13.8580 | − | 24.0027i | 0.766348 | − | 1.32735i | ||||
\(328\) | −15.3323 | −0.846584 | ||||||||
\(329\) | 11.5223 | + | 17.9838i | 0.635244 | + | 0.991477i | ||||
\(330\) | −1.15614 | −0.0636436 | ||||||||
\(331\) | 6.58591 | − | 11.4071i | 0.361994 | − | 0.626993i | −0.626295 | − | 0.779586i | \(-0.715429\pi\) |
0.988289 | + | 0.152594i | \(0.0487626\pi\) | |||||||
\(332\) | 4.32911 | + | 7.49823i | 0.237591 | + | 0.411519i | ||||
\(333\) | −0.616426 | − | 1.06768i | −0.0337799 | − | 0.0585085i | ||||
\(334\) | 0.607311 | − | 1.05189i | 0.0332306 | − | 0.0575571i | ||||
\(335\) | 6.51752 | 0.356090 | ||||||||
\(336\) | 4.67834 | − | 9.04393i | 0.255225 | − | 0.493387i | ||||
\(337\) | −17.0307 | −0.927720 | −0.463860 | − | 0.885909i | \(-0.653536\pi\) | ||||
−0.463860 | + | 0.885909i | \(0.653536\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.12265 | − | 1.94448i | −0.0609738 | − | 0.105610i | ||||
\(340\) | −0.887121 | − | 1.53654i | −0.0481109 | − | 0.0833305i | ||||
\(341\) | −1.55542 | + | 2.69406i | −0.0842306 | + | 0.145892i | ||||
\(342\) | 16.2558 | 0.879010 | ||||||||
\(343\) | −18.3425 | + | 2.55948i | −0.990405 | + | 0.138199i | ||||
\(344\) | −34.2527 | −1.84678 | ||||||||
\(345\) | −3.36937 | + | 5.83592i | −0.181401 | + | 0.314195i | ||||
\(346\) | 6.43251 | + | 11.1414i | 0.345814 | + | 0.598968i | ||||
\(347\) | −0.229959 | − | 0.398300i | −0.0123448 | − | 0.0213819i | 0.859787 | − | 0.510653i | \(-0.170596\pi\) |
−0.872132 | + | 0.489271i | \(0.837263\pi\) | |||||||
\(348\) | 6.80550 | − | 11.7875i | 0.364813 | − | 0.631875i | ||||
\(349\) | 6.87822 | 0.368183 | 0.184091 | − | 0.982909i | \(-0.441066\pi\) | ||||
0.184091 | + | 0.982909i | \(0.441066\pi\) | |||||||
\(350\) | 6.01184 | − | 11.6218i | 0.321347 | − | 0.621210i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.56400 | + | 2.70892i | −0.0833613 | + | 0.144386i | ||||
\(353\) | 0.766631 | + | 1.32784i | 0.0408036 | + | 0.0706740i | 0.885706 | − | 0.464247i | \(-0.153675\pi\) |
−0.844902 | + | 0.534921i | \(0.820342\pi\) | |||||||
\(354\) | −12.8667 | − | 22.2857i | −0.683856 | − | 1.18447i | ||||
\(355\) | 4.40542 | − | 7.63041i | 0.233815 | − | 0.404980i | ||||
\(356\) | 11.3529 | 0.601701 | ||||||||
\(357\) | 11.6019 | + | 18.1081i | 0.614040 | + | 0.958383i | ||||
\(358\) | −10.1626 | −0.537112 | ||||||||
\(359\) | −13.6034 | + | 23.5617i | −0.717959 | + | 1.24354i | 0.243848 | + | 0.969813i | \(0.421590\pi\) |
−0.961807 | + | 0.273728i | \(0.911743\pi\) | |||||||
\(360\) | −2.78322 | − | 4.82068i | −0.146688 | − | 0.254072i | ||||
\(361\) | −4.03438 | − | 6.98774i | −0.212336 | − | 0.367776i | ||||
\(362\) | 6.13326 | − | 10.6231i | 0.322357 | − | 0.558339i | ||||
\(363\) | 25.5249 | 1.33971 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.17959 | −0.166427 | ||||||||
\(366\) | −6.12745 | + | 10.6131i | −0.320287 | + | 0.554753i | ||||
\(367\) | −13.4907 | − | 23.3666i | −0.704208 | − | 1.21972i | −0.966977 | − | 0.254865i | \(-0.917969\pi\) |
0.262769 | − | 0.964859i | \(-0.415364\pi\) | |||||||
\(368\) | −3.50713 | − | 6.07452i | −0.182822 | − | 0.316656i | ||||
\(369\) | 7.30267 | − | 12.6486i | 0.380162 | − | 0.658460i | ||||
\(370\) | −0.284159 | −0.0147727 | ||||||||
\(371\) | 1.84240 | − | 0.0852056i | 0.0956526 | − | 0.00442365i | ||||
\(372\) | −9.05859 | −0.469666 | ||||||||
\(373\) | −1.98619 | + | 3.44018i | −0.102841 | + | 0.178126i | −0.912854 | − | 0.408286i | \(-0.866127\pi\) |
0.810013 | + | 0.586412i | \(0.199460\pi\) | |||||||
\(374\) | 1.27086 | + | 2.20120i | 0.0657147 | + | 0.113821i | ||||
\(375\) | −7.30597 | − | 12.6543i | −0.377279 | − | 0.653466i | ||||
\(376\) | −12.3377 | + | 21.3695i | −0.636269 | + | 1.10205i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.328714 | − | 0.513050i | −0.0169072 | − | 0.0263885i | ||||
\(379\) | 11.4059 | 0.585884 | 0.292942 | − | 0.956130i | \(-0.405366\pi\) | ||||
0.292942 | + | 0.956130i | \(0.405366\pi\) | |||||||
\(380\) | −1.38058 | + | 2.39124i | −0.0708225 | + | 0.122668i | ||||
\(381\) | −10.3453 | − | 17.9186i | −0.530005 | − | 0.917996i | ||||
\(382\) | 8.41680 | + | 14.5783i | 0.430641 | + | 0.745892i | ||||
\(383\) | −11.8960 | + | 20.6044i | −0.607856 | + | 1.05284i | 0.383737 | + | 0.923442i | \(0.374637\pi\) |
−0.991593 | + | 0.129395i | \(0.958696\pi\) | |||||||
\(384\) | −0.849134 | −0.0433322 | ||||||||
\(385\) | −0.538676 | + | 1.04134i | −0.0274535 | + | 0.0530716i | ||||
\(386\) | −24.6879 | −1.25658 | ||||||||
\(387\) | 16.3143 | − | 28.2573i | 0.829304 | − | 1.43640i | ||||
\(388\) | −0.0857137 | − | 0.148460i | −0.00435145 | − | 0.00753694i | ||||
\(389\) | 14.2055 | + | 24.6046i | 0.720247 | + | 1.24751i | 0.960901 | + | 0.276894i | \(0.0893051\pi\) |
−0.240653 | + | 0.970611i | \(0.577362\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.8148 | 0.749216 | ||||||||
\(392\) | −12.3629 | − | 17.4635i | −0.624420 | − | 0.882038i | ||||
\(393\) | 17.0272 | 0.858911 | ||||||||
\(394\) | −5.47446 | + | 9.48204i | −0.275799 | + | 0.477698i | ||||
\(395\) | 1.22326 | + | 2.11875i | 0.0615489 | + | 0.106606i | ||||
\(396\) | −0.875291 | − | 1.51605i | −0.0439850 | − | 0.0761843i | ||||
\(397\) | −4.92956 | + | 8.53825i | −0.247408 | + | 0.428522i | −0.962806 | − | 0.270195i | \(-0.912912\pi\) |
0.715398 | + | 0.698717i | \(0.246245\pi\) | |||||||
\(398\) | −12.7945 | −0.641332 | ||||||||
\(399\) | 15.3775 | − | 29.7270i | 0.769838 | − | 1.48821i | ||||
\(400\) | 7.29510 | 0.364755 | ||||||||
\(401\) | 6.30971 | − | 10.9287i | 0.315092 | − | 0.545756i | −0.664365 | − | 0.747408i | \(-0.731298\pi\) |
0.979457 | + | 0.201653i | \(0.0646313\pi\) | |||||||
\(402\) | −13.5941 | − | 23.5457i | −0.678013 | − | 1.17435i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −7.35460 | + | 12.7385i | −0.365905 | + | 0.633766i | ||||
\(405\) | −5.78964 | −0.287689 | ||||||||
\(406\) | 10.1041 | + | 15.7702i | 0.501456 | + | 0.782663i | ||||
\(407\) | −0.299994 | −0.0148701 | ||||||||
\(408\) | −12.4230 | + | 21.5173i | −0.615031 | + | 1.06527i | ||||
\(409\) | −9.02867 | − | 15.6381i | −0.446439 | − | 0.773255i | 0.551712 | − | 0.834035i | \(-0.313975\pi\) |
−0.998151 | + | 0.0607793i | \(0.980641\pi\) | |||||||
\(410\) | −1.68319 | − | 2.91537i | −0.0831268 | − | 0.143980i | ||||
\(411\) | −7.55795 | + | 13.0908i | −0.372806 | + | 0.645720i | ||||
\(412\) | 9.17691 | 0.452114 | ||||||||
\(413\) | −26.0677 | + | 1.20555i | −1.28271 | + | 0.0593214i | ||||
\(414\) | 13.8457 | 0.680478 | ||||||||
\(415\) | −3.19080 | + | 5.52663i | −0.156630 | + | 0.271291i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.94024 | + | 13.7529i | 0.388835 | + | 0.673483i | ||||
\(418\) | 1.97778 | − | 3.42562i | 0.0967366 | − | 0.167553i | ||||
\(419\) | 14.2805 | 0.697647 | 0.348823 | − | 0.937188i | \(-0.386581\pi\) | ||||
0.348823 | + | 0.937188i | \(0.386581\pi\) | |||||||
\(420\) | −3.41037 | + | 0.157720i | −0.166409 | + | 0.00769593i | ||||
\(421\) | −4.27439 | −0.208321 | −0.104160 | − | 0.994561i | \(-0.533216\pi\) | ||||
−0.104160 | + | 0.994561i | \(0.533216\pi\) | |||||||
\(422\) | −8.36410 | + | 14.4870i | −0.407158 | + | 0.705218i | ||||
\(423\) | −11.7527 | − | 20.3564i | −0.571438 | − | 0.989760i | ||||
\(424\) | 1.06541 | + | 1.84534i | 0.0517407 | + | 0.0896175i | ||||
\(425\) | −7.70398 | + | 13.3437i | −0.373698 | + | 0.647263i | ||||
\(426\) | −36.7550 | −1.78079 | ||||||||
\(427\) | 6.70425 | + | 10.4639i | 0.324441 | + | 0.506382i | ||||
\(428\) | 5.19042 | 0.250888 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.76028 | − | 6.51300i | −0.181337 | − | 0.314085i | ||||
\(431\) | 7.30335 | + | 12.6498i | 0.351790 | + | 0.609318i | 0.986563 | − | 0.163381i | \(-0.0522398\pi\) |
−0.634773 | + | 0.772698i | \(0.718906\pi\) | |||||||
\(432\) | 0.169858 | − | 0.294203i | 0.00817230 | − | 0.0141548i | ||||
\(433\) | −28.0099 | −1.34607 | −0.673035 | − | 0.739611i | \(-0.735009\pi\) | ||||
−0.673035 | + | 0.739611i | \(0.735009\pi\) | |||||||
\(434\) | 5.72718 | − | 11.0715i | 0.274914 | − | 0.531449i | ||||
\(435\) | 10.0321 | 0.481001 | ||||||||
\(436\) | 4.83640 | − | 8.37688i | 0.231621 | − | 0.401180i | ||||
\(437\) | −11.5278 | − | 19.9667i | −0.551448 | − | 0.955137i | ||||
\(438\) | 6.63193 | + | 11.4868i | 0.316886 | + | 0.548863i | ||||
\(439\) | −8.53872 | + | 14.7895i | −0.407531 | + | 0.705864i | −0.994612 | − | 0.103664i | \(-0.966943\pi\) |
0.587082 | + | 0.809528i | \(0.300277\pi\) | |||||||
\(440\) | −1.35450 | −0.0645733 | ||||||||
\(441\) | 20.2951 | − | 1.88120i | 0.966433 | − | 0.0895810i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.90783 | + | 11.9647i | −0.328201 | + | 0.568461i | −0.982155 | − | 0.188073i | \(-0.939776\pi\) |
0.653954 | + | 0.756534i | \(0.273109\pi\) | |||||||
\(444\) | −0.436783 | − | 0.756531i | −0.0207288 | − | 0.0359034i | ||||
\(445\) | 4.18386 | + | 7.24665i | 0.198334 | + | 0.343524i | ||||
\(446\) | 3.63048 | − | 6.28817i | 0.171908 | − | 0.297754i | ||||
\(447\) | 8.98984 | 0.425205 | ||||||||
\(448\) | 9.60703 | − | 18.5718i | 0.453890 | − | 0.877436i | ||||
\(449\) | −32.6410 | −1.54042 | −0.770211 | − | 0.637789i | \(-0.779849\pi\) | ||||
−0.770211 | + | 0.637789i | \(0.779849\pi\) | |||||||
\(450\) | −7.20003 | + | 12.4708i | −0.339412 | + | 0.587880i | ||||
\(451\) | −1.77698 | − | 3.07783i | −0.0836749 | − | 0.144929i | ||||
\(452\) | −0.391801 | − | 0.678619i | −0.0184287 | − | 0.0319195i | ||||
\(453\) | −5.92988 | + | 10.2709i | −0.278610 | + | 0.482567i | ||||
\(454\) | 18.0536 | 0.847298 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 38.6667 | 1.81074 | ||||||||
\(457\) | −1.58517 | + | 2.74559i | −0.0741511 | + | 0.128433i | −0.900717 | − | 0.434407i | \(-0.856958\pi\) |
0.826566 | + | 0.562840i | \(0.190291\pi\) | |||||||
\(458\) | −5.91560 | − | 10.2461i | −0.276418 | − | 0.478769i | ||||
\(459\) | 0.358756 | + | 0.621384i | 0.0167453 | + | 0.0290037i | ||||
\(460\) | −1.17590 | + | 2.03672i | −0.0548266 | + | 0.0949625i | ||||
\(461\) | 0.202023 | 0.00940915 | 0.00470458 | − | 0.999989i | \(-0.498502\pi\) | ||||
0.00470458 | + | 0.999989i | \(0.498502\pi\) | |||||||
\(462\) | 4.88559 | − | 0.225944i | 0.227298 | − | 0.0105119i | ||||
\(463\) | 17.2121 | 0.799912 | 0.399956 | − | 0.916534i | \(-0.369025\pi\) | ||||
0.399956 | + | 0.916534i | \(0.369025\pi\) | |||||||
\(464\) | −5.22112 | + | 9.04325i | −0.242384 | + | 0.419822i | ||||
\(465\) | −3.33835 | − | 5.78219i | −0.154812 | − | 0.268143i | ||||
\(466\) | 9.31136 | + | 16.1277i | 0.431340 | + | 0.747103i | ||||
\(467\) | 0.0955845 | − | 0.165557i | 0.00442312 | − | 0.00766108i | −0.863805 | − | 0.503826i | \(-0.831925\pi\) |
0.868228 | + | 0.496165i | \(0.165259\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −27.5415 | + | 1.27371i | −1.27175 | + | 0.0588146i | ||||
\(470\) | −5.41777 | −0.249903 | ||||||||
\(471\) | −11.5731 | + | 20.0452i | −0.533260 | + | 0.923633i | ||||
\(472\) | −15.0742 | − | 26.1092i | −0.693845 | − | 1.20177i | ||||
\(473\) | −3.96982 | − | 6.87593i | −0.182533 | − | 0.316156i | ||||
\(474\) | 5.10291 | − | 8.83850i | 0.234384 | − | 0.405966i | ||||
\(475\) | 23.9787 | 1.10022 | ||||||||
\(476\) | 4.04905 | + | 6.31968i | 0.185588 | + | 0.289662i | ||||
\(477\) | −2.02978 | −0.0929374 | ||||||||
\(478\) | −10.5816 | + | 18.3278i | −0.483989 | + | 0.838294i | ||||
\(479\) | 10.7392 | + | 18.6009i | 0.490688 | + | 0.849897i | 0.999943 | − | 0.0107189i | \(-0.00341199\pi\) |
−0.509254 | + | 0.860616i | \(0.670079\pi\) | |||||||
\(480\) | −3.35676 | − | 5.81408i | −0.153214 | − | 0.265375i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 2.98752 | 0.136078 | ||||||||
\(483\) | 13.0976 | − | 25.3197i | 0.595964 | − | 1.15209i | ||||
\(484\) | 8.90811 | 0.404914 | ||||||||
\(485\) | 0.0631758 | − | 0.109424i | 0.00286867 | − | 0.00496868i | ||||
\(486\) | 11.7305 | + | 20.3178i | 0.532105 | + | 0.921633i | ||||
\(487\) | 9.52422 | + | 16.4964i | 0.431584 | + | 0.747525i | 0.997010 | − | 0.0772740i | \(-0.0246216\pi\) |
−0.565426 | + | 0.824799i | \(0.691288\pi\) | |||||||
\(488\) | −7.17871 | + | 12.4339i | −0.324965 | + | 0.562856i | ||||
\(489\) | 57.6458 | 2.60684 | ||||||||
\(490\) | 1.96340 | − | 4.26790i | 0.0886973 | − | 0.192804i | ||||
\(491\) | 35.7559 | 1.61364 | 0.806821 | − | 0.590796i | \(-0.201186\pi\) | ||||
0.806821 | + | 0.590796i | \(0.201186\pi\) | |||||||
\(492\) | 5.17448 | − | 8.96247i | 0.233284 | − | 0.404059i | ||||
\(493\) | −11.0275 | − | 19.1002i | −0.496654 | − | 0.860230i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.645140 | − | 1.11741i | 0.0289969 | − | 0.0502240i | ||||
\(496\) | 6.94968 | 0.312050 | ||||||||
\(497\) | −17.1251 | + | 33.1053i | −0.768164 | + | 1.48497i | ||||
\(498\) | 26.6213 | 1.19293 | ||||||||
\(499\) | 8.84457 | − | 15.3192i | 0.395937 | − | 0.685784i | −0.597283 | − | 0.802031i | \(-0.703753\pi\) |
0.993220 | + | 0.116247i | \(0.0370864\pi\) | |||||||
\(500\) | −2.54976 | − | 4.41632i | −0.114029 | − | 0.197504i | ||||
\(501\) | 1.37609 | + | 2.38346i | 0.0614792 | + | 0.106485i | ||||
\(502\) | 12.6410 | − | 21.8949i | 0.564196 | − | 0.977217i | ||||
\(503\) | 11.3305 | 0.505203 | 0.252601 | − | 0.967570i | \(-0.418714\pi\) | ||||
0.252601 | + | 0.967570i | \(0.418714\pi\) | |||||||
\(504\) | 12.7033 | + | 19.8271i | 0.565851 | + | 0.883169i | ||||
\(505\) | −10.8415 | −0.482441 | ||||||||
\(506\) | 1.68456 | − | 2.91774i | 0.0748878 | − | 0.129709i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.61048 | − | 6.25353i | −0.160189 | − | 0.277455i | ||||
\(509\) | −9.67569 | + | 16.7588i | −0.428868 | + | 0.742821i | −0.996773 | − | 0.0802734i | \(-0.974421\pi\) |
0.567905 | + | 0.823094i | \(0.307754\pi\) | |||||||
\(510\) | −5.45523 | −0.241562 | ||||||||
\(511\) | 13.4362 | − | 0.621384i | 0.594382 | − | 0.0274884i | ||||
\(512\) | 16.6645 | 0.736472 | ||||||||
\(513\) | 0.558316 | − | 0.967032i | 0.0246502 | − | 0.0426955i | ||||
\(514\) | −1.84152 | − | 3.18961i | −0.0812259 | − | 0.140687i | ||||
\(515\) | 3.38195 | + | 5.85772i | 0.149027 | + | 0.258122i | ||||
\(516\) | 11.5599 | − | 20.0224i | 0.508897 | − | 0.881435i | ||||
\(517\) | −5.71967 | −0.251551 | ||||||||
\(518\) | 1.20079 | − | 0.0555330i | 0.0527597 | − | 0.00243998i | ||||
\(519\) | −29.1505 | −1.27957 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.85550 | + | 6.67791i | 0.168912 | + | 0.292565i | 0.938038 | − | 0.346533i | \(-0.112641\pi\) |
−0.769125 | + | 0.639098i | \(0.779308\pi\) | |||||||
\(522\) | −10.3062 | − | 17.8508i | −0.451088 | − | 0.781307i | ||||
\(523\) | 17.5251 | − | 30.3543i | 0.766317 | − | 1.32730i | −0.173230 | − | 0.984881i | \(-0.555420\pi\) |
0.939547 | − | 0.342419i | \(-0.111246\pi\) | |||||||
\(524\) | 5.94246 | 0.259597 | ||||||||
\(525\) | 15.9944 | + | 24.9638i | 0.698054 | + | 1.08951i | ||||
\(526\) | 23.0160 | 1.00355 | ||||||||
\(527\) | −7.33919 | + | 12.7119i | −0.319700 | + | 0.553737i | ||||
\(528\) | 1.36339 | + | 2.36146i | 0.0593339 | + | 0.102769i | ||||
\(529\) | 1.68133 | + | 2.91214i | 0.0731011 | + | 0.126615i | ||||
\(530\) | −0.233922 | + | 0.405165i | −0.0101609 | + | 0.0175992i | ||||
\(531\) | 28.7189 | 1.24630 | ||||||||
\(532\) | 5.36671 | − | 10.3746i | 0.232676 | − | 0.449797i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 17.4532 | − | 30.2299i | 0.755275 | − | 1.30818i | ||||
\(535\) | 1.91282 | + | 3.31309i | 0.0826982 | + | 0.143238i | ||||
\(536\) | −15.9264 | − | 27.5854i | −0.687917 | − | 1.19151i | ||||
\(537\) | 11.5136 | − | 19.9422i | 0.496849 | − | 0.860568i | ||||
\(538\) | −15.7276 | −0.678066 | ||||||||
\(539\) | 2.07281 | − | 4.50573i | 0.0892821 | − | 0.194075i | ||||
\(540\) | −0.113903 | −0.00490160 | ||||||||
\(541\) | 6.06674 | − | 10.5079i | 0.260829 | − | 0.451770i | −0.705633 | − | 0.708577i | \(-0.749337\pi\) |
0.966463 | + | 0.256807i | \(0.0826706\pi\) | |||||||
\(542\) | 1.09648 | + | 1.89916i | 0.0470978 | + | 0.0815758i | ||||
\(543\) | 13.8972 | + | 24.0706i | 0.596385 | + | 1.03297i | ||||
\(544\) | −7.37967 | + | 12.7820i | −0.316401 | + | 0.548022i | ||||
\(545\) | 7.12940 | 0.305390 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.12546 | −0.219149 | −0.109575 | − | 0.993979i | \(-0.534949\pi\) | ||||
−0.109575 | + | 0.993979i | \(0.534949\pi\) | |||||||
\(548\) | −2.63770 | + | 4.56864i | −0.112677 | + | 0.195162i | ||||
\(549\) | −6.83835 | − | 11.8444i | −0.291854 | − | 0.505505i | ||||
\(550\) | 1.75201 | + | 3.03457i | 0.0747058 | + | 0.129394i | ||||
\(551\) | −17.1616 | + | 29.7248i | −0.731109 | + | 1.26632i | ||||
\(552\) | 32.9340 | 1.40177 | ||||||||
\(553\) | −5.58327 | − | 8.71427i | −0.237425 | − | 0.370568i | ||||
\(554\) | 5.83051 | 0.247715 | ||||||||
\(555\) | 0.321934 | − | 0.557606i | 0.0136653 | − | 0.0236691i | ||||
\(556\) | 2.77112 | + | 4.79972i | 0.117522 | + | 0.203554i | ||||
\(557\) | 18.7793 | + | 32.5267i | 0.795705 | + | 1.37820i | 0.922391 | + | 0.386258i | \(0.126233\pi\) |
−0.126686 | + | 0.991943i | \(0.540434\pi\) | |||||||
\(558\) | −6.85911 | + | 11.8803i | −0.290369 | + | 0.502934i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 2.61641 | − | 0.121001i | 0.110563 | − | 0.00511323i | ||||
\(561\) | −5.75922 | −0.243154 | ||||||||
\(562\) | −10.8569 | + | 18.8048i | −0.457973 | + | 0.793232i | ||||
\(563\) | −14.3504 | − | 24.8557i | −0.604799 | − | 1.04754i | −0.992083 | − | 0.125583i | \(-0.959920\pi\) |
0.387284 | − | 0.921960i | \(-0.373413\pi\) | |||||||
\(564\) | −8.32769 | − | 14.4240i | −0.350659 | − | 0.607359i | ||||
\(565\) | 0.288779 | − | 0.500180i | 0.0121490 | − | 0.0210428i | ||||
\(566\) | −1.86195 | −0.0782636 | ||||||||
\(567\) | 24.4656 | − | 1.13146i | 1.02746 | − | 0.0475170i | ||||
\(568\) | −43.0610 | −1.80680 | ||||||||
\(569\) | −8.97417 | + | 15.5437i | −0.376217 | + | 0.651627i | −0.990508 | − | 0.137452i | \(-0.956109\pi\) |
0.614291 | + | 0.789079i | \(0.289442\pi\) | |||||||
\(570\) | 4.24486 | + | 7.35231i | 0.177798 | + | 0.307955i | ||||
\(571\) | −8.91370 | − | 15.4390i | −0.373027 | − | 0.646101i | 0.617003 | − | 0.786961i | \(-0.288347\pi\) |
−0.990030 | + | 0.140860i | \(0.955013\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −38.1428 | −1.59344 | ||||||||
\(574\) | 7.68250 | + | 11.9907i | 0.320662 | + | 0.500483i | ||||
\(575\) | 20.4236 | 0.851724 | ||||||||
\(576\) | −11.5058 | + | 19.9286i | −0.479407 | + | 0.830357i | ||||
\(577\) | 16.5285 | + | 28.6282i | 0.688091 | + | 1.19181i | 0.972455 | + | 0.233092i | \(0.0748844\pi\) |
−0.284363 | + | 0.958717i | \(0.591782\pi\) | |||||||
\(578\) | −3.12445 | − | 5.41170i | −0.129960 | − | 0.225097i | ||||
\(579\) | 27.9698 | − | 48.4451i | 1.16239 | − | 2.01331i | ||||
\(580\) | 3.50117 | 0.145378 | ||||||||
\(581\) | 12.4035 | − | 23.9778i | 0.514584 | − | 0.994766i | ||||
\(582\) | −0.527085 | −0.0218484 | ||||||||
\(583\) | −0.246957 | + | 0.427742i | −0.0102279 | + | 0.0177153i | ||||
\(584\) | 7.76975 | + | 13.4576i | 0.321515 | + | 0.556880i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.6172 | + | 25.3178i | −0.603832 | + | 1.04587i | ||||
\(587\) | −14.7295 | −0.607953 | −0.303976 | − | 0.952680i | \(-0.598314\pi\) | ||||
−0.303976 | + | 0.952680i | \(0.598314\pi\) | |||||||
\(588\) | 14.3806 | − | 1.33297i | 0.593045 | − | 0.0549708i | ||||
\(589\) | 22.8433 | 0.941241 | ||||||||
\(590\) | 3.30970 | − | 5.73258i | 0.136258 | − | 0.236006i | ||||
\(591\) | −12.4044 | − | 21.4851i | −0.510250 | − | 0.883779i | ||||
\(592\) | 0.335097 | + | 0.580404i | 0.0137724 | + | 0.0238545i | ||||
\(593\) | −4.60494 | + | 7.97598i | −0.189102 | + | 0.327534i | −0.944951 | − | 0.327212i | \(-0.893891\pi\) |
0.755849 | + | 0.654746i | \(0.227224\pi\) | |||||||
\(594\) | 0.163174 | 0.00669510 | ||||||||
\(595\) | −2.54172 | + | 4.91353i | −0.104201 | + | 0.201435i | ||||
\(596\) | 3.13743 | 0.128514 | ||||||||
\(597\) | 14.4954 | − | 25.1067i | 0.593256 | − | 1.02755i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.28727 | + | 9.15782i | 0.216032 | + | 0.374178i | 0.953591 | − | 0.301104i | \(-0.0973551\pi\) |
−0.737559 | + | 0.675282i | \(0.764022\pi\) | |||||||
\(600\) | −17.1263 | + | 29.6637i | −0.699180 | + | 1.21102i | ||||
\(601\) | 4.08916 | 0.166800 | 0.0834001 | − | 0.996516i | \(-0.473422\pi\) | ||||
0.0834001 | + | 0.996516i | \(0.473422\pi\) | |||||||
\(602\) | 17.1629 | + | 26.7875i | 0.699507 | + | 1.09178i | ||||
\(603\) | 30.3426 | 1.23565 | ||||||||
\(604\) | −2.06951 | + | 3.58450i | −0.0842072 | + | 0.145851i | ||||
\(605\) | 3.28289 | + | 5.68613i | 0.133469 | + | 0.231174i | ||||
\(606\) | 22.6131 | + | 39.1670i | 0.918593 | + | 1.59105i | ||||
\(607\) | −1.80353 | + | 3.12380i | −0.0732030 | + | 0.126791i | −0.900303 | − | 0.435263i | \(-0.856655\pi\) |
0.827100 | + | 0.562054i | \(0.189989\pi\) | |||||||
\(608\) | 22.9693 | 0.931527 | ||||||||
\(609\) | −42.3932 | + | 1.96056i | −1.71786 | + | 0.0794459i | ||||
\(610\) | −3.15233 | −0.127634 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −4.13003 | − | 7.15343i | −0.166947 | − | 0.289160i | ||||
\(613\) | −19.2422 | − | 33.3285i | −0.777186 | − | 1.34613i | −0.933557 | − | 0.358428i | \(-0.883313\pi\) |
0.156371 | − | 0.987698i | \(-0.450020\pi\) | |||||||
\(614\) | −6.82128 | + | 11.8148i | −0.275284 | + | 0.476806i | ||||
\(615\) | 7.62778 | 0.307582 | ||||||||
\(616\) | 5.72379 | − | 0.264709i | 0.230618 | − | 0.0106654i | ||||
\(617\) | 3.09503 | 0.124601 | 0.0623007 | − | 0.998057i | \(-0.480156\pi\) | ||||
0.0623007 | + | 0.998057i | \(0.480156\pi\) | |||||||
\(618\) | 14.1080 | − | 24.4359i | 0.567509 | − | 0.982954i | ||||
\(619\) | 6.13462 | + | 10.6255i | 0.246571 | + | 0.427074i | 0.962572 | − | 0.271025i | \(-0.0873627\pi\) |
−0.716001 | + | 0.698099i | \(0.754029\pi\) | |||||||
\(620\) | −1.16507 | − | 2.01797i | −0.0467905 | − | 0.0810435i | ||||
\(621\) | 0.475540 | − | 0.823660i | 0.0190828 | − | 0.0330523i | ||||
\(622\) | −10.3215 | −0.413854 | ||||||||
\(623\) | −19.0962 | − | 29.8050i | −0.765073 | − | 1.19411i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.64277 | + | 16.7018i | −0.385711 | + | 0.668071i | ||||
\(626\) | −4.84241 | − | 8.38730i | −0.193542 | − | 0.335224i | ||||
\(627\) | 4.48140 | + | 7.76202i | 0.178970 | + | 0.309985i | ||||
\(628\) | −4.03897 | + | 6.99571i | −0.161173 | + | 0.279159i | ||||
\(629\) | −1.41551 | −0.0564402 | ||||||||
\(630\) | −2.37546 | + | 4.59211i | −0.0946406 | + | 0.182954i | ||||
\(631\) | 5.31780 | 0.211698 | 0.105849 | − | 0.994382i | \(-0.466244\pi\) | ||||
0.105849 | + | 0.994382i | \(0.466244\pi\) | |||||||
\(632\) | 5.97840 | − | 10.3549i | 0.237808 | − | 0.411896i | ||||
\(633\) | −18.9520 | − | 32.8258i | −0.753273 | − | 1.30471i | ||||
\(634\) | −13.2126 | − | 22.8849i | −0.524740 | − | 0.908877i | ||||
\(635\) | 2.66113 | − | 4.60921i | 0.105604 | − | 0.182911i | ||||
\(636\) | −1.43825 | −0.0570304 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.01566 | −0.198572 | ||||||||
\(639\) | 20.5097 | − | 35.5238i | 0.811349 | − | 1.40530i | ||||
\(640\) | −0.109212 | − | 0.189160i | −0.00431697 | − | 0.00747721i | ||||
\(641\) | −6.09521 | − | 10.5572i | −0.240746 | − | 0.416985i | 0.720181 | − | 0.693787i | \(-0.244059\pi\) |
−0.960927 | + | 0.276801i | \(0.910726\pi\) | |||||||
\(642\) | 7.97944 | − | 13.8208i | 0.314923 | − | 0.545463i | ||||
\(643\) | 18.9733 | 0.748235 | 0.374117 | − | 0.927381i | \(-0.377946\pi\) | ||||
0.374117 | + | 0.927381i | \(0.377946\pi\) | |||||||
\(644\) | 4.57104 | − | 8.83649i | 0.180124 | − | 0.348207i | ||||
\(645\) | 17.0406 | 0.670974 | ||||||||
\(646\) | 9.33211 | − | 16.1637i | 0.367167 | − | 0.635952i | ||||
\(647\) | −9.85587 | − | 17.0709i | −0.387474 | − | 0.671125i | 0.604635 | − | 0.796503i | \(-0.293319\pi\) |
−0.992109 | + | 0.125378i | \(0.959986\pi\) | |||||||
\(648\) | 14.1478 | + | 24.5046i | 0.555776 | + | 0.962633i | ||||
\(649\) | 3.49414 | − | 6.05202i | 0.137157 | − | 0.237563i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.2371 | + | 23.7818i | 0.597188 | + | 0.932080i | ||||
\(652\) | 20.1182 | 0.787891 | ||||||||
\(653\) | 10.1986 | − | 17.6645i | 0.399103 | − | 0.691267i | −0.594512 | − | 0.804087i | \(-0.702655\pi\) |
0.993616 | + | 0.112819i | \(0.0359882\pi\) | |||||||
\(654\) | −14.8704 | − | 25.7563i | −0.581478 | − | 1.00715i | ||||
\(655\) | 2.18996 | + | 3.79313i | 0.0855690 | + | 0.148210i | ||||
\(656\) | −3.96982 | + | 6.87593i | −0.154996 | + | 0.268460i | ||||
\(657\) | −14.8027 | −0.577510 | ||||||||
\(658\) | 22.8942 | − | 1.05879i | 0.892509 | − | 0.0412759i | ||||
\(659\) | 32.6628 | 1.27236 | 0.636181 | − | 0.771540i | \(-0.280513\pi\) | ||||
0.636181 | + | 0.771540i | \(0.280513\pi\) | |||||||
\(660\) | 0.457129 | − | 0.791771i | 0.0177937 | − | 0.0308196i | ||||
\(661\) | −4.86846 | − | 8.43242i | −0.189361 | − | 0.327983i | 0.755676 | − | 0.654945i | \(-0.227308\pi\) |
−0.945037 | + | 0.326962i | \(0.893975\pi\) | |||||||
\(662\) | −7.06704 | − | 12.2405i | −0.274668 | − | 0.475740i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 31.1886 | 1.21035 | ||||||||
\(665\) | 8.60002 | − | 0.397725i | 0.333494 | − | 0.0154231i | ||||
\(666\) | −1.32292 | −0.0512620 | ||||||||
\(667\) | −14.6172 | + | 25.3178i | −0.565981 | + | 0.980308i | ||||
\(668\) | 0.480251 | + | 0.831819i | 0.0185815 | + | 0.0321841i | ||||
\(669\) | 8.22620 | + | 14.2482i | 0.318043 | + | 0.550867i | ||||
\(670\) | 3.49683 | − | 6.05668i | 0.135094 | − | 0.233990i | ||||
\(671\) | −3.32800 | −0.128476 | ||||||||
\(672\) | 15.3211 | + | 23.9129i | 0.591025 | + | 0.922461i | ||||
\(673\) | 39.4512 | 1.52073 | 0.760367 | − | 0.649494i | \(-0.225019\pi\) | ||||
0.760367 | + | 0.649494i | \(0.225019\pi\) | |||||||
\(674\) | −9.13742 | + | 15.8265i | −0.351960 | + | 0.609613i | ||||
\(675\) | 0.494581 | + | 0.856639i | 0.0190364 | + | 0.0329720i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.3169 | − | 42.1182i | 0.934576 | − | 1.61873i | 0.159187 | − | 0.987248i | \(-0.449113\pi\) |
0.775389 | − | 0.631484i | \(-0.217554\pi\) | |||||||
\(678\) | −2.40932 | −0.0925296 | ||||||||
\(679\) | −0.245582 | + | 0.474745i | −0.00942455 | + | 0.0182191i | ||||
\(680\) | −6.39117 | −0.245090 | ||||||||
\(681\) | −20.4536 | + | 35.4266i | −0.783783 | + | 1.35755i | ||||
\(682\) | 1.66905 | + | 2.89088i | 0.0639112 | + | 0.110697i | ||||
\(683\) | 2.85387 | + | 4.94304i | 0.109200 | + | 0.189140i | 0.915446 | − | 0.402440i | \(-0.131838\pi\) |
−0.806246 | + | 0.591580i | \(0.798504\pi\) | |||||||
\(684\) | −6.42738 | + | 11.1326i | −0.245757 | + | 0.425664i | ||||
\(685\) | −3.88828 | −0.148563 | ||||||||
\(686\) | −7.46278 | + | 18.4188i | −0.284930 | + | 0.703234i | ||||
\(687\) | 26.8080 | 1.02279 | ||||||||
\(688\) | −8.86867 | + | 15.3610i | −0.338115 | + | 0.585632i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 3.61552 | + | 6.26226i | 0.137640 | + | 0.238400i | ||||
\(691\) | −20.8866 | + | 36.1766i | −0.794563 | + | 1.37622i | 0.128553 | + | 0.991703i | \(0.458967\pi\) |
−0.923116 | + | 0.384521i | \(0.874367\pi\) | |||||||
\(692\) | −10.1734 | −0.386736 | ||||||||
\(693\) | −2.50783 | + | 4.84801i | −0.0952646 | + | 0.184161i | ||||
\(694\) | −0.493517 | −0.0187336 | ||||||||
\(695\) | −2.04247 | + | 3.53767i | −0.0774754 | + | 0.134191i | ||||
\(696\) | −24.5147 | − | 42.4608i | −0.929228 | − | 1.60947i | ||||
\(697\) | −8.38464 | − | 14.5226i | −0.317591 | − | 0.550084i | ||||
\(698\) | 3.69035 | − | 6.39188i | 0.139682 | − | 0.241936i | ||||
\(699\) | −42.1967 | −1.59603 | ||||||||
\(700\) | 5.58200 | + | 8.71229i | 0.210980 | + | 0.329294i | ||||
\(701\) | −22.4361 | −0.847399 | −0.423700 | − | 0.905803i | \(-0.639269\pi\) | ||||
−0.423700 | + | 0.905803i | \(0.639269\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.10145 | + | 1.90776i | 0.0415419 | + | 0.0719527i | ||||
\(704\) | 2.79974 | + | 4.84929i | 0.105519 | + | 0.182764i | ||||
\(705\) | 6.13798 | − | 10.6313i | 0.231170 | − | 0.400398i | ||||
\(706\) | 1.64527 | 0.0619207 | ||||||||
\(707\) | 45.8137 | − | 2.11875i | 1.72300 | − | 0.0796837i | ||||
\(708\) | 20.3495 | 0.764780 | ||||||||
\(709\) | −14.3734 | + | 24.8955i | −0.539804 | + | 0.934969i | 0.459110 | + | 0.888380i | \(0.348168\pi\) |
−0.998914 | + | 0.0465891i | \(0.985165\pi\) | |||||||
\(710\) | −4.72726 | − | 8.18785i | −0.177411 | − | 0.307285i | ||||
\(711\) | 5.69495 | + | 9.86394i | 0.213577 | + | 0.369927i | ||||
\(712\) | 20.4476 | − | 35.4163i | 0.766307 | − | 1.32728i | ||||
\(713\) | 19.4566 | 0.728654 | ||||||||
\(714\) | 23.0525 | − | 1.06611i | 0.862718 | − | 0.0398982i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.01822 | − | 6.95976i | 0.150168 | − | 0.260098i | ||||
\(717\) | −23.9765 | − | 41.5284i | −0.895417 | − | 1.55091i | ||||
\(718\) | 14.5972 | + | 25.2830i | 0.544762 | + | 0.943555i | ||||
\(719\) | 2.10450 | − | 3.64509i | 0.0784844 | − | 0.135939i | −0.824112 | − | 0.566427i | \(-0.808325\pi\) |
0.902596 | + | 0.430488i | \(0.141659\pi\) | |||||||
\(720\) | −2.88251 | −0.107425 | ||||||||
\(721\) | −15.4361 | − | 24.0924i | −0.574870 | − | 0.897247i | ||||
\(722\) | −8.65821 | −0.322225 | ||||||||
\(723\) | −3.38467 | + | 5.86242i | −0.125877 | + | 0.218026i | ||||
\(724\) | 4.85008 | + | 8.40058i | 0.180252 | + | 0.312205i | ||||
\(725\) | −15.2025 | − | 26.3315i | −0.564606 | − | 0.977927i | ||||
\(726\) | 13.6948 | − | 23.7201i | 0.508262 | − | 0.880335i | ||||
\(727\) | 43.4680 | 1.61214 | 0.806070 | − | 0.591820i | \(-0.201591\pi\) | ||||
0.806070 | + | 0.591820i | \(0.201591\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.3884 | −0.940312 | ||||||||
\(730\) | −1.70594 | + | 2.95477i | −0.0631396 | + | 0.109361i | ||||
\(731\) | −18.7315 | − | 32.4439i | −0.692809 | − | 1.19998i | ||||
\(732\) | −4.84548 | − | 8.39261i | −0.179094 | − | 0.310200i | ||||
\(733\) | −4.54710 | + | 7.87581i | −0.167951 | + | 0.290900i | −0.937699 | − | 0.347448i | \(-0.887048\pi\) |
0.769748 | + | 0.638348i | \(0.220382\pi\) | |||||||
\(734\) | −28.9525 | −1.06866 | ||||||||
\(735\) | 6.15050 | + | 8.68803i | 0.226865 | + | 0.320463i | ||||
\(736\) | 19.5639 | 0.721133 | ||||||||
\(737\) | 3.69169 | − | 6.39419i | 0.135985 | − | 0.235533i | ||||
\(738\) | −7.83617 | − | 13.5726i | −0.288453 | − | 0.499616i | ||||
\(739\) | −4.80433 | − | 8.32135i | −0.176730 | − | 0.306106i | 0.764028 | − | 0.645183i | \(-0.223219\pi\) |
−0.940759 | + | 0.339077i | \(0.889885\pi\) | |||||||
\(740\) | 0.112354 | − | 0.194603i | 0.00413022 | − | 0.00715375i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.909317 | − | 1.75784i | 0.0333821 | − | 0.0645325i | ||||
\(743\) | 32.1771 | 1.18046 | 0.590231 | − | 0.807234i | \(-0.299036\pi\) | ||||
0.590231 | + | 0.807234i | \(0.299036\pi\) | |||||||
\(744\) | −16.3154 | + | 28.2591i | −0.598152 | + | 1.03603i | ||||
\(745\) | 1.15623 | + | 2.00265i | 0.0423610 | + | 0.0733714i | ||||
\(746\) | 2.13129 | + | 3.69150i | 0.0780320 | + | 0.135155i | ||||
\(747\) | −14.8549 | + | 25.7295i | −0.543513 | + | 0.941392i | ||||
\(748\) | −2.00995 | −0.0734911 | ||||||||
\(749\) | −8.73058 | − | 13.6265i | −0.319008 | − | 0.497903i | ||||
\(750\) | −15.6794 | −0.572531 | ||||||||
\(751\) | −3.89892 | + | 6.75313i | −0.142274 | + | 0.246425i | −0.928352 | − | 0.371701i | \(-0.878775\pi\) |
0.786079 | + | 0.618126i | \(0.212108\pi\) | |||||||
\(752\) | 6.38894 | + | 11.0660i | 0.232981 | + | 0.403534i | ||||
\(753\) | 28.6429 | + | 49.6110i | 1.04381 | + | 1.80793i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.05070 | −0.111026 | ||||||||
\(756\) | 0.481327 | − | 0.0222599i | 0.0175057 | − | 0.000809586i | ||||
\(757\) | 17.9970 | 0.654110 | 0.327055 | − | 0.945005i | \(-0.393944\pi\) | ||||
0.327055 | + | 0.945005i | \(0.393944\pi\) | |||||||
\(758\) | 6.11960 | − | 10.5995i | 0.222274 | − | 0.384990i | ||||
\(759\) | 3.81699 | + | 6.61123i | 0.138548 | + | 0.239972i | ||||
\(760\) | 4.97314 | + | 8.61373i | 0.180395 | + | 0.312453i | ||||
\(761\) | −20.3395 | + | 35.2290i | −0.737306 | + | 1.27705i | 0.216398 | + | 0.976305i | \(0.430569\pi\) |
−0.953704 | + | 0.300746i | \(0.902764\pi\) | |||||||
\(762\) | −22.2021 | −0.804299 | ||||||||
\(763\) | −30.1271 | + | 1.39329i | −1.09068 | + | 0.0504406i | ||||
\(764\) | −13.3117 | −0.481601 | ||||||||
\(765\) | 3.04407 | − | 5.27248i | 0.110059 | − | 0.190627i | ||||
\(766\) | 12.7650 | + | 22.1097i | 0.461220 | + | 0.798856i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −19.6711 | + | 34.0713i | −0.709819 | + | 1.22944i | ||||
\(769\) | −39.3098 | −1.41755 | −0.708774 | − | 0.705435i | \(-0.750752\pi\) | ||||
−0.708774 | + | 0.705435i | \(0.750752\pi\) | |||||||
\(770\) | 0.678695 | + | 1.05929i | 0.0244585 | + | 0.0381743i | ||||
\(771\) | 8.34529 | 0.300548 | ||||||||
\(772\) | 9.76138 | − | 16.9072i | 0.351320 | − | 0.608504i | ||||
\(773\) | 6.73679 | + | 11.6685i | 0.242306 | + | 0.419685i | 0.961371 | − | 0.275257i | \(-0.0887630\pi\) |
−0.719065 | + | 0.694943i | \(0.755430\pi\) | |||||||
\(774\) | −17.5062 | − | 30.3216i | −0.629247 | − | 1.08989i | ||||
\(775\) | −10.1178 | + | 17.5245i | −0.363442 | + | 0.629500i | ||||
\(776\) | −0.617515 | −0.0221675 | ||||||||
\(777\) | −1.25144 | + | 2.41923i | −0.0448953 | + | 0.0867893i | ||||
\(778\) | 30.4866 | 1.09300 | ||||||||
\(779\) | −13.0486 | + | 22.6009i | −0.467516 | + | 0.809761i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.99068 | − | 8.64412i | −0.178581 | − | 0.309311i | ||||
\(782\) | 7.94854 | − | 13.7673i | 0.284239 | − | 0.492316i | ||||
\(783\) | −1.41589 | −0.0505998 | ||||||||
\(784\) | −11.0327 | + | 1.02264i | −0.394024 | + | 0.0365230i | ||||
\(785\) | −5.95391 | −0.212504 | ||||||||
\(786\) | 9.13558 | − | 15.8233i | 0.325855 | − | 0.564398i | ||||
\(787\) | 19.9145 | + | 34.4930i | 0.709877 | + | 1.22954i | 0.964903 | + | 0.262608i | \(0.0845827\pi\) |
−0.255026 | + | 0.966934i | \(0.582084\pi\) | |||||||
\(788\) | −4.32911 | − | 7.49823i | −0.154218 | − | 0.267114i | ||||
\(789\) | −26.0757 | + | 45.1644i | −0.928319 | + | 1.60790i | ||||
\(790\) | 2.62525 | 0.0934022 | ||||||||
\(791\) | −1.12256 | + | 2.17008i | −0.0399137 | + | 0.0771592i | ||||
\(792\) | −6.30594 | −0.224072 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 5.28969 | + | 9.16201i | 0.187724 | + | 0.325148i | ||||
\(795\) | −0.530037 | − | 0.918051i | −0.0187985 | − | 0.0325599i | ||||
\(796\) | 5.05884 | − | 8.76217i | 0.179306 | − | 0.310567i | ||||
\(797\) | −21.2530 | −0.752821 | −0.376410 | − | 0.926453i | \(-0.622842\pi\) | ||||
−0.376410 | + | 0.926453i | \(0.622842\pi\) | |||||||
\(798\) | −19.3746 | − | 30.2396i | −0.685854 | − | 1.07047i | ||||
\(799\) | −26.9881 | −0.954770 | ||||||||
\(800\) | −10.1736 | + | 17.6212i | −0.359691 | + | 0.623003i | ||||
\(801\) | 19.4781 | + | 33.7371i | 0.688226 | + | 1.19204i | ||||
\(802\) | −6.77067 | − | 11.7271i | −0.239081 | − | 0.414100i | ||||
\(803\) | −1.80100 | + | 3.11942i | −0.0635559 | + | 0.110082i | ||||
\(804\) | 21.5000 | 0.758246 | ||||||||
\(805\) | 7.32498 | − | 0.338759i | 0.258172 | − | 0.0119397i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17.8184 | − | 30.8624i | 0.627237 | − | 1.08641i | ||||
\(808\) | 26.4927 | + | 45.8867i | 0.932010 | + | 1.61429i | ||||
\(809\) | −10.7088 | − | 18.5481i | −0.376500 | − | 0.652117i | 0.614050 | − | 0.789267i | \(-0.289539\pi\) |
−0.990550 | + | 0.137150i | \(0.956206\pi\) | |||||||
\(810\) | −3.10630 | + | 5.38027i | −0.109144 | + | 0.189043i | ||||
\(811\) | 11.0116 | 0.386669 | 0.193335 | − | 0.981133i | \(-0.438070\pi\) | ||||
0.193335 | + | 0.981133i | \(0.438070\pi\) | |||||||
\(812\) | −14.7951 | + | 0.684230i | −0.519206 | + | 0.0240118i | ||||
\(813\) | −4.96896 | −0.174269 | ||||||||
\(814\) | −0.160955 | + | 0.278782i | −0.00564147 | + | 0.00977131i | ||||
\(815\) | 7.41414 | + | 12.8417i | 0.259706 | + | 0.449824i | ||||
\(816\) | 6.43311 | + | 11.1425i | 0.225204 | + | 0.390065i | ||||
\(817\) | −29.1509 | + | 50.4909i | −1.01986 | + | 1.76645i | ||||
\(818\) | −19.3765 | −0.677484 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.66207 | 0.0929636 | ||||||||
\(821\) | −19.3342 | + | 33.4879i | −0.674769 | + | 1.16873i | 0.301767 | + | 0.953382i | \(0.402424\pi\) |
−0.976536 | + | 0.215353i | \(0.930910\pi\) | |||||||
\(822\) | 8.11010 | + | 14.0471i | 0.282872 | + | 0.489949i | ||||
\(823\) | 10.2283 | + | 17.7160i | 0.356537 | + | 0.617540i | 0.987380 | − | 0.158371i | \(-0.0506241\pi\) |
−0.630843 | + | 0.775911i | \(0.717291\pi\) | |||||||
\(824\) | 16.5285 | − | 28.6282i | 0.575798 | − | 0.997312i | ||||
\(825\) | −7.93965 | −0.276423 | ||||||||
\(826\) | −12.8657 | + | 24.8713i | −0.447655 | + | 0.865384i | ||||
\(827\) | −27.3451 | −0.950881 | −0.475440 | − | 0.879748i | \(-0.657711\pi\) | ||||
−0.475440 | + | 0.879748i | \(0.657711\pi\) | |||||||
\(828\) | −5.47446 | + | 9.48204i | −0.190251 | + | 0.329524i | ||||
\(829\) | 12.5043 | + | 21.6581i | 0.434292 | + | 0.752217i | 0.997238 | − | 0.0742776i | \(-0.0236651\pi\) |
−0.562945 | + | 0.826494i | \(0.690332\pi\) | |||||||
\(830\) | 3.42390 | + | 5.93037i | 0.118845 | + | 0.205846i | ||||
\(831\) | −6.60560 | + | 11.4412i | −0.229146 | + | 0.396892i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.78048 | − | 21.2601i | 0.338873 | − | 0.736620i | ||||
\(834\) | 17.0406 | 0.590069 | ||||||||
\(835\) | −0.353972 | + | 0.613098i | −0.0122497 | + | 0.0212171i | ||||
\(836\) | 1.56400 | + | 2.70892i | 0.0540920 | + | 0.0936900i | ||||
\(837\) | 0.471162 | + | 0.816077i | 0.0162857 | + | 0.0282077i | ||||
\(838\) | 7.66187 | − | 13.2707i | 0.264675 | − | 0.458430i | ||||
\(839\) | −8.76981 | −0.302768 | −0.151384 | − | 0.988475i | \(-0.548373\pi\) | ||||
−0.151384 | + | 0.988475i | \(0.548373\pi\) | |||||||
\(840\) | −5.65039 | + | 10.9230i | −0.194957 | + | 0.376880i | ||||
\(841\) | 14.5218 | 0.500753 | ||||||||
\(842\) | −2.29333 | + | 3.97216i | −0.0790332 | + | 0.136890i | ||||
\(843\) | −24.6004 | − | 42.6092i | −0.847284 | − | 1.46754i | ||||
\(844\) | −6.61418 | − | 11.4561i | −0.227669 | − | 0.394335i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −25.2227 | −0.867174 | ||||||||
\(847\) | −14.9840 | − | 23.3867i | −0.514855 | − | 0.803576i | ||||
\(848\) | 1.10342 | 0.0378914 | ||||||||
\(849\) | 2.10947 | − | 3.65371i | 0.0723968 | − | 0.125395i | ||||
\(850\) | 8.26679 | + | 14.3185i | 0.283549 | + | 0.491120i | ||||
\(851\) | 0.938148 | + | 1.62492i | 0.0321593 | + | 0.0557015i | ||||
\(852\) | 14.5326 | − | 25.1712i | 0.497879 | − | 0.862352i | ||||
\(853\) | −19.8232 | −0.678734 | −0.339367 | − | 0.940654i | \(-0.610213\pi\) | ||||
−0.339367 | + | 0.940654i | \(0.610213\pi\) | |||||||
\(854\) | 13.3210 | − | 0.616058i | 0.455836 | − | 0.0210811i | ||||
\(855\) | −9.47469 | −0.324028 | ||||||||
\(856\) | 9.34845 | − | 16.1920i | 0.319523 | − | 0.553431i | ||||
\(857\) | 1.33518 | + | 2.31261i | 0.0456090 | + | 0.0789972i | 0.887929 | − | 0.459981i | \(-0.152144\pi\) |
−0.842320 | + | 0.538978i | \(0.818810\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.4798 | − | 33.7401i | 0.664644 | − | 1.15120i | −0.314738 | − | 0.949179i | \(-0.601917\pi\) |
0.979382 | − | 0.202018i | \(-0.0647500\pi\) | |||||||
\(860\) | 5.94713 | 0.202795 | ||||||||
\(861\) | −32.2332 | + | 1.49069i | −1.09850 | + | 0.0508026i | ||||
\(862\) | 15.6738 | 0.533851 | ||||||||
\(863\) | −12.3988 | + | 21.4754i | −0.422060 | + | 0.731030i | −0.996141 | − | 0.0877689i | \(-0.972026\pi\) |
0.574081 | + | 0.818799i | \(0.305360\pi\) | |||||||
\(864\) | 0.473761 | + | 0.820578i | 0.0161177 | + | 0.0279166i | ||||
\(865\) | −3.74920 | − | 6.49381i | −0.127477 | − | 0.220796i | ||||
\(866\) | −15.0281 | + | 26.0294i | −0.510675 | + | 0.884514i | ||||
\(867\) | 14.1592 | 0.480871 | ||||||||
\(868\) | 5.31770 | + | 8.29976i | 0.180494 | + | 0.281712i | ||||
\(869\) | 2.77154 | 0.0940181 | ||||||||
\(870\) | 5.38249 | − | 9.32274i | 0.182483 | − | 0.316070i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −17.4216 | − | 30.1752i | −0.589971 | − | 1.02186i | ||||
\(873\) | 0.294118 | − | 0.509428i | 0.00995439 | − | 0.0172415i | ||||
\(874\) | −24.7399 | −0.836839 | ||||||||
\(875\) | −7.30542 | + | 14.1225i | −0.246968 | + | 0.477426i | ||||
\(876\) | −10.4888 | −0.354385 | ||||||||
\(877\) | 0.989201 | − | 1.71335i | 0.0334029 | − | 0.0578556i | −0.848841 | − | 0.528649i | \(-0.822699\pi\) |
0.882244 | + | 0.470793i | \(0.156032\pi\) | |||||||
\(878\) | 9.16251 | + | 15.8699i | 0.309220 | + | 0.535584i | ||||
\(879\) | −33.1208 | − | 57.3668i | −1.11714 | − | 1.93494i | ||||
\(880\) | −0.350706 | + | 0.607440i | −0.0118223 | + | 0.0204768i | ||||
\(881\) | 17.1466 | 0.577683 | 0.288841 | − | 0.957377i | \(-0.406730\pi\) | ||||
0.288841 | + | 0.957377i | \(0.406730\pi\) | |||||||
\(882\) | 9.14069 | − | 19.8694i | 0.307783 | − | 0.669038i | ||||
\(883\) | −10.2168 | −0.343822 | −0.171911 | − | 0.985112i | \(-0.554994\pi\) | ||||
−0.171911 | + | 0.985112i | \(0.554994\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.49936 | + | 12.9893i | 0.252088 | + | 0.436630i | ||||
\(886\) | 7.41248 | + | 12.8388i | 0.249027 | + | 0.431328i | ||||
\(887\) | −25.4965 | + | 44.1613i | −0.856090 | + | 1.48279i | 0.0195395 | + | 0.999809i | \(0.493780\pi\) |
−0.875630 | + | 0.482983i | \(0.839553\pi\) | |||||||
\(888\) | −3.14676 | −0.105598 | ||||||||
\(889\) | −10.3445 | + | 19.9975i | −0.346944 | + | 0.670694i | ||||
\(890\) | 8.97901 | 0.300977 | ||||||||
\(891\) | −3.27940 | + | 5.68008i | −0.109864 | + | 0.190290i | ||||
\(892\) | 2.87092 | + | 4.97258i | 0.0961255 | + | 0.166494i | ||||
\(893\) | 21.0002 | + | 36.3733i | 0.702743 | + | 1.21719i | ||||
\(894\) | 4.82329 | − | 8.35419i | 0.161315 | − | 0.279406i | ||||
\(895\) | 5.92331 | 0.197995 | ||||||||
\(896\) | 0.498470 | + | 0.778003i | 0.0166527 | + | 0.0259913i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −17.5128 | + | 30.3330i | −0.584409 | + | 1.01223i | ||||
\(899\) | −14.4827 | − | 25.0847i | −0.483024 | − | 0.836621i | ||||
\(900\) | −5.69365 | − | 9.86170i | −0.189788 | − | 0.328723i | ||||
\(901\) | −1.16526 | + | 2.01829i | −0.0388204 | + | 0.0672389i | ||||
\(902\) | −3.81360 | −0.126979 | ||||||||
\(903\) | −72.0097 | + | 3.33024i | −2.39633 | + | 0.110823i | ||||
\(904\) | −2.82268 | −0.0938811 | ||||||||
\(905\) | −3.57478 | + | 6.19170i | −0.118830 | + | 0.205819i | ||||
\(906\) | 6.36309 | + | 11.0212i | 0.211400 | + | 0.366155i | ||||
\(907\) | 2.89269 | + | 5.01028i | 0.0960501 | + | 0.166364i | 0.910046 | − | 0.414506i | \(-0.136046\pi\) |
−0.813996 | + | 0.580870i | \(0.802712\pi\) | |||||||
\(908\) | −7.13824 | + | 12.3638i | −0.236891 | + | 0.410307i | ||||
\(909\) | −50.4732 | −1.67409 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.70706 | −0.0565573 | −0.0282787 | − | 0.999600i | \(-0.509003\pi\) | ||||
−0.0282787 | + | 0.999600i | \(0.509003\pi\) | |||||||
\(912\) | 10.0116 | − | 17.3405i | 0.331516 | − | 0.574202i | ||||
\(913\) | 3.61470 | + | 6.26084i | 0.119629 | + | 0.207204i | ||||
\(914\) | 1.70097 | + | 2.94617i | 0.0562632 | + | 0.0974507i | ||||
\(915\) | 3.57139 | − | 6.18583i | 0.118067 | − | 0.204497i | ||||
\(916\) | 9.35590 | 0.309128 | ||||||||
\(917\) | −9.99556 | − | 15.6009i | −0.330082 | − | 0.515187i | ||||
\(918\) | 0.769931 | 0.0254115 | ||||||||
\(919\) | −18.6025 | + | 32.2205i | −0.613640 | + | 1.06286i | 0.376982 | + | 0.926221i | \(0.376962\pi\) |
−0.990622 | + | 0.136634i | \(0.956371\pi\) | |||||||
\(920\) | 4.23582 | + | 7.33666i | 0.139651 | + | 0.241882i | ||||
\(921\) | −15.4561 | − | 26.7708i | −0.509297 | − | 0.882128i | ||||
\(922\) | 0.108391 | − | 0.187739i | 0.00356967 | − | 0.00618284i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −1.77698 | + | 3.43517i | −0.0584585 | + | 0.113009i | ||||
\(925\) | −1.95142 | −0.0641623 | ||||||||
\(926\) | 9.23474 | − | 15.9950i | 0.303472 | − | 0.525630i | ||||
\(927\) | 15.7449 | + | 27.2709i | 0.517129 | + | 0.895693i | ||||
\(928\) | −14.5625 | − | 25.2230i | −0.478038 | − | 0.827987i | ||||
\(929\) | −9.95229 | + | 17.2379i | −0.326524 | + | 0.565556i | −0.981820 | − | 0.189816i | \(-0.939211\pi\) |
0.655296 | + | 0.755373i | \(0.272544\pi\) | |||||||
\(930\) | −7.16447 | −0.234932 | ||||||||
\(931\) | −36.2639 | + | 3.36139i | −1.18850 | + | 0.110165i | ||||
\(932\) | −14.7265 | −0.482383 | ||||||||
\(933\) | 11.6936 | − | 20.2539i | 0.382831 | − | 0.663082i | ||||
\(934\) | −0.102567 | − | 0.177652i | −0.00335611 | − | 0.00581295i | ||||
\(935\) | −0.740724 | − | 1.28297i | −0.0242243 | − | 0.0419577i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.16949 | 0.234217 | 0.117109 | − | 0.993119i | \(-0.462637\pi\) | ||||
0.117109 | + | 0.993119i | \(0.462637\pi\) | |||||||
\(938\) | −13.5931 | + | 26.2775i | −0.443831 | + | 0.857990i | ||||
\(939\) | 21.9446 | 0.716134 | ||||||||
\(940\) | 2.14214 | − | 3.71029i | 0.0698688 | − | 0.121016i | ||||
\(941\) | −1.53036 | − | 2.65066i | −0.0498883 | − | 0.0864091i | 0.840003 | − | 0.542582i | \(-0.182553\pi\) |
−0.889891 | + | 0.456173i | \(0.849220\pi\) | |||||||
\(942\) | 12.4186 | + | 21.5096i | 0.404619 | + | 0.700820i | ||||
\(943\) | −11.1140 | + | 19.2501i | −0.361923 | + | 0.626869i | ||||
\(944\) | −15.6120 | −0.508126 | ||||||||
\(945\) | 0.191591 | + | 0.299032i | 0.00623247 | + | 0.00972752i | ||||
\(946\) | −8.51968 | −0.276999 | ||||||||
\(947\) | 22.1028 | − | 38.2832i | 0.718244 | − | 1.24404i | −0.243451 | − | 0.969913i | \(-0.578279\pi\) |
0.961695 | − | 0.274122i | \(-0.0883872\pi\) | |||||||
\(948\) | 4.03529 | + | 6.98933i | 0.131060 | + | 0.227003i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 12.8652 | − | 22.2832i | 0.417403 | − | 0.722963i | ||||
\(951\) | 59.8762 | 1.94162 | ||||||||
\(952\) | 27.0075 | − | 1.24902i | 0.875320 | − | 0.0404810i | ||||
\(953\) | −13.7002 | −0.443791 | −0.221896 | − | 0.975070i | \(-0.571224\pi\) | ||||
−0.221896 | + | 0.975070i | \(0.571224\pi\) | |||||||
\(954\) | −1.08903 | + | 1.88626i | −0.0352588 | + | 0.0610700i | ||||
\(955\) | −4.90574 | − | 8.49700i | −0.158746 | − | 0.274956i | ||||
\(956\) | −8.36771 | − | 14.4933i | −0.270631 | − | 0.468747i | ||||
\(957\) | 5.68242 | − | 9.84225i | 0.183687 | − | 0.318155i | ||||
\(958\) | 23.0476 | 0.744634 | ||||||||
\(959\) | 16.4309 | − | 0.759882i | 0.530582 | − | 0.0245379i | ||||
\(960\) | −12.0180 | −0.387879 | ||||||||
\(961\) | 5.86129 | − | 10.1520i | 0.189074 | − | 0.327485i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.90521 | + | 15.4243i | 0.286966 | + | 0.497040i | ||||
\(964\) | −1.18124 | + | 2.04597i | −0.0380451 | + | 0.0658961i | ||||
\(965\) | 14.3894 | 0.463211 | ||||||||
\(966\) | −16.5022 | − | 25.7563i | −0.530948 | − | 0.828694i | ||||
\(967\) | −43.9429 | −1.41311 | −0.706554 | − | 0.707659i | \(-0.749751\pi\) | ||||
−0.706554 | + | 0.707659i | \(0.749751\pi\) | |||||||
\(968\) | 16.0444 | − | 27.7897i | 0.515686 | − | 0.893194i | ||||
\(969\) | 21.1454 | + | 36.6248i | 0.679287 | + | 1.17656i | ||||
\(970\) | −0.0677912 | − | 0.117418i | −0.00217664 | − | 0.00377006i | ||||
\(971\) | 10.6585 | − | 18.4611i | 0.342049 | − | 0.592446i | −0.642764 | − | 0.766064i | \(-0.722212\pi\) |
0.984813 | + | 0.173618i | \(0.0555458\pi\) | |||||||
\(972\) | −18.5525 | −0.595072 | ||||||||
\(973\) | 7.93965 | − | 15.3485i | 0.254533 | − | 0.492050i | ||||
\(974\) | 20.4400 | 0.654941 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.71741 | + | 6.43874i | 0.118991 | + | 0.206099i | ||||
\(977\) | 8.22330 | + | 14.2432i | 0.263087 | + | 0.455679i | 0.967061 | − | 0.254547i | \(-0.0819262\pi\) |
−0.703974 | + | 0.710226i | \(0.748593\pi\) | |||||||
\(978\) | 30.9286 | − | 53.5699i | 0.988987 | − | 1.71298i | ||||
\(979\) | 9.47937 | 0.302962 | ||||||||
\(980\) | 2.14651 | + | 3.03210i | 0.0685677 | + | 0.0968568i | ||||
\(981\) | 33.1913 | 1.05972 | ||||||||
\(982\) | 19.1840 | − | 33.2277i | 0.612187 | − | 1.06034i | ||||
\(983\) | −5.85521 | − | 10.1415i | −0.186752 | − | 0.323464i | 0.757413 | − | 0.652936i | \(-0.226463\pi\) |
−0.944166 | + | 0.329471i | \(0.893129\pi\) | |||||||
\(984\) | −18.6395 | − | 32.2846i | −0.594206 | − | 1.02919i | ||||
\(985\) | 3.19080 | − | 5.52663i | 0.101667 | − | 0.176093i | ||||
\(986\) | −23.6662 | −0.753687 | ||||||||
\(987\) | −23.8600 | + | 46.1249i | −0.759472 | + | 1.46817i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −24.8290 | + | 43.0051i | −0.789517 | + | 1.36748i | ||||
\(990\) | −0.692270 | − | 1.19905i | −0.0220018 | − | 0.0381082i | ||||
\(991\) | 15.6873 | + | 27.1713i | 0.498325 | + | 0.863124i | 0.999998 | − | 0.00193305i | \(-0.000615311\pi\) |
−0.501673 | + | 0.865057i | \(0.667282\pi\) | |||||||
\(992\) | −9.69187 | + | 16.7868i | −0.307717 | + | 0.532982i | ||||
\(993\) | 32.0260 | 1.01632 | ||||||||
\(994\) | 21.5764 | + | 33.6761i | 0.684362 | + | 1.06814i | ||||
\(995\) | 7.45731 | 0.236413 | ||||||||
\(996\) | −10.5258 | + | 18.2312i | −0.333523 | + | 0.577679i | ||||
\(997\) | 2.34855 | + | 4.06781i | 0.0743794 | + | 0.128829i | 0.900816 | − | 0.434201i | \(-0.142969\pi\) |
−0.826437 | + | 0.563029i | \(0.809636\pi\) | |||||||
\(998\) | −9.49071 | − | 16.4384i | −0.300423 | − | 0.520348i | ||||
\(999\) | −0.0454366 | + | 0.0786985i | −0.00143755 | + | 0.00248991i |
(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.170.6 | 16 | ||
7.2 | even | 3 | 8281.2.a.ck.1.3 | 8 | |||
7.4 | even | 3 | inner | 1183.2.e.i.508.6 | 16 | ||
7.5 | odd | 6 | 8281.2.a.cj.1.3 | 8 | |||
13.5 | odd | 4 | 91.2.r.a.51.3 | yes | 16 | ||
13.8 | odd | 4 | 91.2.r.a.51.6 | yes | 16 | ||
13.12 | even | 2 | inner | 1183.2.e.i.170.3 | 16 | ||
39.5 | even | 4 | 819.2.dl.e.415.6 | 16 | |||
39.8 | even | 4 | 819.2.dl.e.415.3 | 16 | |||
91.5 | even | 12 | 637.2.c.e.246.6 | 8 | |||
91.12 | odd | 6 | 8281.2.a.cj.1.6 | 8 | |||
91.18 | odd | 12 | 91.2.r.a.25.6 | yes | 16 | ||
91.25 | even | 6 | inner | 1183.2.e.i.508.3 | 16 | ||
91.31 | even | 12 | 637.2.r.f.116.6 | 16 | |||
91.34 | even | 4 | 637.2.r.f.324.6 | 16 | |||
91.44 | odd | 12 | 637.2.c.f.246.6 | 8 | |||
91.47 | even | 12 | 637.2.c.e.246.3 | 8 | |||
91.51 | even | 6 | 8281.2.a.ck.1.6 | 8 | |||
91.60 | odd | 12 | 91.2.r.a.25.3 | ✓ | 16 | ||
91.73 | even | 12 | 637.2.r.f.116.3 | 16 | |||
91.83 | even | 4 | 637.2.r.f.324.3 | 16 | |||
91.86 | odd | 12 | 637.2.c.f.246.3 | 8 | |||
273.200 | even | 12 | 819.2.dl.e.298.3 | 16 | |||
273.242 | even | 12 | 819.2.dl.e.298.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.r.a.25.3 | ✓ | 16 | 91.60 | odd | 12 | ||
91.2.r.a.25.6 | yes | 16 | 91.18 | odd | 12 | ||
91.2.r.a.51.3 | yes | 16 | 13.5 | odd | 4 | ||
91.2.r.a.51.6 | yes | 16 | 13.8 | odd | 4 | ||
637.2.c.e.246.3 | 8 | 91.47 | even | 12 | |||
637.2.c.e.246.6 | 8 | 91.5 | even | 12 | |||
637.2.c.f.246.3 | 8 | 91.86 | odd | 12 | |||
637.2.c.f.246.6 | 8 | 91.44 | odd | 12 | |||
637.2.r.f.116.3 | 16 | 91.73 | even | 12 | |||
637.2.r.f.116.6 | 16 | 91.31 | even | 12 | |||
637.2.r.f.324.3 | 16 | 91.83 | even | 4 | |||
637.2.r.f.324.6 | 16 | 91.34 | even | 4 | |||
819.2.dl.e.298.3 | 16 | 273.200 | even | 12 | |||
819.2.dl.e.298.6 | 16 | 273.242 | even | 12 | |||
819.2.dl.e.415.3 | 16 | 39.8 | even | 4 | |||
819.2.dl.e.415.6 | 16 | 39.5 | even | 4 | |||
1183.2.e.i.170.3 | 16 | 13.12 | even | 2 | inner | ||
1183.2.e.i.170.6 | 16 | 1.1 | even | 1 | trivial | ||
1183.2.e.i.508.3 | 16 | 91.25 | even | 6 | inner | ||
1183.2.e.i.508.6 | 16 | 7.4 | even | 3 | inner | ||
8281.2.a.cj.1.3 | 8 | 7.5 | odd | 6 | |||
8281.2.a.cj.1.6 | 8 | 91.12 | odd | 6 | |||
8281.2.a.ck.1.3 | 8 | 7.2 | even | 3 | |||
8281.2.a.ck.1.6 | 8 | 91.51 | even | 6 |