Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1357,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.1357");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.x (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8x^{14} + 8x^{12} - 8x^{10} + 212x^{8} + 248x^{6} + 368x^{4} + 32x^{2} + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1693.1 | ||
Root | \(0.919224 - 1.30296i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1693 |
Dual form | 2100.2.x.d.1357.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.16604 | + | 1.51930i | −0.818685 | + | 0.574243i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.10553 | 0.333329 | 0.166665 | − | 0.986014i | \(-0.446700\pi\) | ||||
0.166665 | + | 0.986014i | \(0.446700\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.52265 | − | 3.52265i | 0.977007 | − | 0.977007i | −0.0227347 | − | 0.999742i | \(-0.507237\pi\) |
0.999742 | + | 0.0227347i | \(0.00723730\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.23842 | + | 3.23842i | 0.785432 | + | 0.785432i | 0.980742 | − | 0.195310i | \(-0.0625713\pi\) |
−0.195310 | + | 0.980742i | \(0.562571\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.916719 | −0.210310 | −0.105155 | − | 0.994456i | \(-0.533534\pi\) | ||||
−0.105155 | + | 0.994456i | \(0.533534\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.457309 | − | 2.60593i | 0.0997931 | − | 0.568660i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.43909 | − | 4.43909i | −0.925613 | − | 0.925613i | 0.0718052 | − | 0.997419i | \(-0.477124\pi\) |
−0.997419 | + | 0.0718052i | \(0.977124\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 8.28530i | − | 1.53854i | −0.638923 | − | 0.769271i | \(-0.720620\pi\) | ||
0.638923 | − | 0.769271i | \(-0.279380\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.59362i | 0.825038i | 0.910949 | + | 0.412519i | \(0.135351\pi\) | ||||
−0.910949 | + | 0.412519i | \(0.864649\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.781726 | + | 0.781726i | −0.136081 | + | 0.136081i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.30352 | − | 2.30352i | 0.378697 | − | 0.378697i | −0.491935 | − | 0.870632i | \(-0.663710\pi\) |
0.870632 | + | 0.491935i | \(0.163710\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.98178i | 0.797723i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.15091i | 0.492090i | 0.969258 | + | 0.246045i | \(0.0791311\pi\) | ||||
−0.969258 | + | 0.246045i | \(0.920869\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.70356 | − | 2.70356i | −0.412290 | − | 0.412290i | 0.470246 | − | 0.882535i | \(-0.344165\pi\) |
−0.882535 | + | 0.470246i | \(0.844165\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.71436 | + | 4.71436i | 0.687661 | + | 0.687661i | 0.961714 | − | 0.274054i | \(-0.0883646\pi\) |
−0.274054 | + | 0.961714i | \(0.588365\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.38343 | − | 6.58174i | 0.340490 | − | 0.940248i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.57981 | −0.641302 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.41894 | + | 6.41894i | 0.881709 | + | 0.881709i | 0.993708 | − | 0.111999i | \(-0.0357254\pi\) |
−0.111999 | + | 0.993708i | \(0.535725\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.648218 | − | 0.648218i | 0.0858586 | − | 0.0858586i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.36339 | 0.568065 | 0.284032 | − | 0.958815i | \(-0.408328\pi\) | ||||
0.284032 | + | 0.958815i | \(0.408328\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.8687i | 1.39160i | 0.718237 | + | 0.695798i | \(0.244949\pi\) | ||||
−0.718237 | + | 0.695798i | \(0.755051\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.51930 | + | 2.16604i | 0.191414 | + | 0.272895i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.81101 | − | 6.81101i | 0.832098 | − | 0.832098i | −0.155706 | − | 0.987803i | \(-0.549765\pi\) |
0.987803 | + | 0.155706i | \(0.0497651\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.27782 | 0.755760 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.79796 | 0.569413 | 0.284706 | − | 0.958615i | \(-0.408104\pi\) | ||||
0.284706 | + | 0.958615i | \(0.408104\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.72950 | − | 9.72950i | 1.13875 | − | 1.13875i | 0.150077 | − | 0.988674i | \(-0.452048\pi\) |
0.988674 | − | 0.150077i | \(-0.0479522\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.39461 | + | 1.67963i | −0.272892 | + | 0.191412i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.5706i | 1.41430i | 0.707062 | + | 0.707152i | \(0.250020\pi\) | ||||
−0.707062 | + | 0.707152i | \(0.749980\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.227509 | − | 0.227509i | 0.0249724 | − | 0.0249724i | −0.694510 | − | 0.719483i | \(-0.744379\pi\) |
0.719483 | + | 0.694510i | \(0.244379\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.85859 | + | 5.85859i | 0.628107 | + | 0.628107i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.93123 | 0.946709 | 0.473354 | − | 0.880872i | \(-0.343043\pi\) | ||||
0.473354 | + | 0.880872i | \(0.343043\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.27821 | + | 12.9822i | −0.238822 | + | 1.36090i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.24818 | − | 3.24818i | −0.336820 | − | 0.336820i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.4114 | + | 12.4114i | 1.26019 | + | 1.26019i | 0.951002 | + | 0.309185i | \(0.100056\pi\) |
0.309185 | + | 0.951002i | \(0.399944\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 1.10553i | − | 0.111110i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 4.91786i | − | 0.489346i | −0.969606 | − | 0.244673i | \(-0.921319\pi\) | ||
0.969606 | − | 0.244673i | \(-0.0786806\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.91171 | + | 1.91171i | −0.188366 | + | 0.188366i | −0.794989 | − | 0.606623i | \(-0.792524\pi\) |
0.606623 | + | 0.794989i | \(0.292524\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.3426 | − | 14.3426i | 1.38655 | − | 1.38655i | 0.554095 | − | 0.832453i | \(-0.313064\pi\) |
0.832453 | − | 0.554095i | \(-0.186936\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.15963i | 0.877333i | 0.898650 | + | 0.438667i | \(0.144549\pi\) | ||||
−0.898650 | + | 0.438667i | \(0.855451\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.25767i | 0.309205i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.70424 | + | 6.70424i | 0.630682 | + | 0.630682i | 0.948239 | − | 0.317557i | \(-0.102863\pi\) |
−0.317557 | + | 0.948239i | \(0.602863\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.52265 | − | 3.52265i | −0.325669 | − | 0.325669i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.9347 | − | 2.09439i | −1.09405 | − | 0.191993i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.77781 | −0.888892 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.22803 | − | 2.22803i | −0.200895 | − | 0.200895i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.7414 | + | 14.7414i | −1.30808 | + | 1.30808i | −0.385288 | + | 0.922796i | \(0.625898\pi\) |
−0.922796 | + | 0.385288i | \(0.874102\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.82342 | 0.336633 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 0.298477i | − | 0.0260780i | −0.999915 | − | 0.0130390i | \(-0.995849\pi\) | ||
0.999915 | − | 0.0130390i | \(-0.00415056\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.98565 | − | 1.39277i | 0.172177 | − | 0.120769i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.74069 | − | 4.74069i | 0.405024 | − | 0.405024i | −0.474975 | − | 0.879999i | \(-0.657543\pi\) |
0.879999 | + | 0.474975i | \(0.157543\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.35670 | 0.199893 | 0.0999465 | − | 0.994993i | \(-0.468133\pi\) | ||||
0.0999465 | + | 0.994993i | \(0.468133\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.66712 | −0.561473 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.89438 | − | 3.89438i | 0.325665 | − | 0.325665i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.96865 | + | 6.33933i | 0.244850 | + | 0.522859i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.95242i | 0.569564i | 0.958592 | + | 0.284782i | \(0.0919213\pi\) | ||||
−0.958592 | + | 0.284782i | \(0.908079\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.15963 | −0.0943691 | −0.0471845 | − | 0.998886i | \(-0.515025\pi\) | ||||
−0.0471845 | + | 0.998886i | \(0.515025\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.23842 | − | 3.23842i | 0.261811 | − | 0.261811i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.0207600 | + | 0.0207600i | 0.00165683 | + | 0.00165683i | 0.707935 | − | 0.706278i | \(-0.249627\pi\) |
−0.706278 | + | 0.707935i | \(0.749627\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.07775 | −0.719913 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.3595 | + | 2.87090i | 1.28931 | + | 0.226259i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.58174 | − | 3.58174i | −0.280543 | − | 0.280543i | 0.552782 | − | 0.833326i | \(-0.313566\pi\) |
−0.833326 | + | 0.552782i | \(0.813566\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.41192 | − | 2.41192i | −0.186640 | − | 0.186640i | 0.607602 | − | 0.794242i | \(-0.292132\pi\) |
−0.794242 | + | 0.607602i | \(0.792132\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 11.8181i | − | 0.909085i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.916719i | 0.0701032i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.8622 | − | 10.8622i | 0.825838 | − | 0.825838i | −0.161100 | − | 0.986938i | \(-0.551504\pi\) |
0.986938 | + | 0.161100i | \(0.0515043\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.08538 | + | 3.08538i | −0.231911 | + | 0.231911i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 7.35054i | − | 0.549405i | −0.961529 | − | 0.274702i | \(-0.911421\pi\) | ||
0.961529 | − | 0.274702i | \(-0.0885793\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 23.1359i | − | 1.71968i | −0.510566 | − | 0.859839i | \(-0.670564\pi\) | ||
0.510566 | − | 0.859839i | \(-0.329436\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.68534 | − | 7.68534i | −0.568117 | − | 0.568117i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.58016 | + | 3.58016i | 0.261807 | + | 0.261807i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.60593 | − | 0.457309i | −0.189553 | − | 0.0332644i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.0326 | 1.52187 | 0.760934 | − | 0.648829i | \(-0.224741\pi\) | ||||
0.760934 | + | 0.648829i | \(0.224741\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.47813 | − | 8.47813i | −0.610269 | − | 0.610269i | 0.332747 | − | 0.943016i | \(-0.392025\pi\) |
−0.943016 | + | 0.332747i | \(0.892025\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.7407 | + | 12.7407i | −0.907736 | + | 0.907736i | −0.996089 | − | 0.0883529i | \(-0.971840\pi\) |
0.0883529 | + | 0.996089i | \(0.471840\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.7111 | 1.60995 | 0.804975 | − | 0.593309i | \(-0.202179\pi\) | ||||
0.804975 | + | 0.593309i | \(0.202179\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.63223i | 0.679405i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.5879 | + | 17.9463i | 0.883497 | + | 1.25958i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.43909 | + | 4.43909i | −0.308538 | + | 0.308538i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.01346 | −0.0701023 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.55258 | −0.175727 | −0.0878634 | − | 0.996133i | \(-0.528004\pi\) | ||||
−0.0878634 | + | 0.996133i | \(0.528004\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.39267 | + | 3.39267i | −0.232462 | + | 0.232462i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.97910 | − | 9.94994i | −0.473772 | − | 0.675446i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.7596i | 0.929787i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.8156 | 1.53474 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.4422 | + | 12.4422i | −0.833191 | + | 0.833191i | −0.987952 | − | 0.154761i | \(-0.950539\pi\) |
0.154761 | + | 0.987952i | \(0.450539\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.1465 | + | 17.1465i | 1.13806 | + | 1.13806i | 0.988798 | + | 0.149257i | \(0.0476880\pi\) |
0.149257 | + | 0.988798i | \(0.452312\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.5306 | −1.02629 | −0.513145 | − | 0.858302i | \(-0.671520\pi\) | ||||
−0.513145 | + | 0.858302i | \(0.671520\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.505568 | − | 2.88093i | 0.0332639 | − | 0.189551i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.78962 | + | 5.78962i | 0.379291 | + | 0.379291i | 0.870846 | − | 0.491556i | \(-0.163572\pi\) |
−0.491556 | + | 0.870846i | \(0.663572\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.88876 | − | 8.88876i | −0.577387 | − | 0.577387i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 14.4398i | − | 0.934031i | −0.884249 | − | 0.467015i | \(-0.845329\pi\) | ||
0.884249 | − | 0.467015i | \(-0.154671\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 10.0102i | − | 0.644815i | −0.946601 | − | 0.322407i | \(-0.895508\pi\) | ||
0.946601 | − | 0.322407i | \(-0.104492\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.22928 | + | 3.22928i | −0.205474 | + | 0.205474i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.321746i | 0.0203898i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.6809i | 1.43160i | 0.698303 | + | 0.715802i | \(0.253939\pi\) | ||||
−0.698303 | + | 0.715802i | \(0.746061\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.90753 | − | 4.90753i | −0.308534 | − | 0.308534i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.8047 | − | 11.8047i | −0.736356 | − | 0.736356i | 0.235515 | − | 0.971871i | \(-0.424322\pi\) |
−0.971871 | + | 0.235515i | \(0.924322\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.48976 | + | 8.48927i | −0.0925695 | + | 0.527497i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.28530 | −0.512847 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.48454 | + | 1.48454i | 0.0915408 | + | 0.0915408i | 0.751394 | − | 0.659853i | \(-0.229382\pi\) |
−0.659853 | + | 0.751394i | \(0.729382\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.31534 | + | 6.31534i | −0.386492 | + | 0.386492i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 30.7202 | 1.87304 | 0.936522 | − | 0.350609i | \(-0.114025\pi\) | ||||
0.936522 | + | 0.350609i | \(0.114025\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 5.29013i | − | 0.321352i | −0.987007 | − | 0.160676i | \(-0.948633\pi\) | ||
0.987007 | − | 0.160676i | \(-0.0513675\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.56883 | − | 10.7907i | −0.458087 | − | 0.653084i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.1817 | + | 11.1817i | −0.671843 | + | 0.671843i | −0.958141 | − | 0.286298i | \(-0.907575\pi\) |
0.286298 | + | 0.958141i | \(0.407575\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.59362 | 0.275013 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.00864 | 0.0601706 | 0.0300853 | − | 0.999547i | \(-0.490422\pi\) | ||||
0.0300853 | + | 0.999547i | \(0.490422\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.8457 | + | 10.8457i | −0.644708 | + | 0.644708i | −0.951709 | − | 0.307001i | \(-0.900674\pi\) |
0.307001 | + | 0.951709i | \(0.400674\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.78719 | − | 6.82499i | −0.282579 | − | 0.402867i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.97469i | 0.233805i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.5524 | −1.02894 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.8047 | − | 11.8047i | 0.689637 | − | 0.689637i | −0.272514 | − | 0.962152i | \(-0.587855\pi\) |
0.962152 | + | 0.272514i | \(0.0878552\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.781726 | + | 0.781726i | 0.0453603 | + | 0.0453603i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −31.2747 | −1.80866 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.96355 | + | 1.74848i | 0.574290 | + | 0.100781i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.47746 | + | 3.47746i | 0.199775 | + | 0.199775i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.0408 | + | 16.0408i | 0.915498 | + | 0.915498i | 0.996698 | − | 0.0812002i | \(-0.0258753\pi\) |
−0.0812002 | + | 0.996698i | \(0.525875\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 2.70356i | − | 0.153800i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 24.0259i | − | 1.36238i | −0.732105 | − | 0.681191i | \(-0.761462\pi\) | ||
0.732105 | − | 0.681191i | \(-0.238538\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.2483 | + | 17.2483i | −0.974930 | + | 0.974930i | −0.999693 | − | 0.0247630i | \(-0.992117\pi\) |
0.0247630 | + | 0.999693i | \(0.492117\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.2079 | − | 12.2079i | 0.685663 | − | 0.685663i | −0.275607 | − | 0.961270i | \(-0.588879\pi\) |
0.961270 | + | 0.275607i | \(0.0888789\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 9.15963i | − | 0.512841i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 20.2835i | 1.13211i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.96872 | − | 2.96872i | −0.165184 | − | 0.165184i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.47683 | − | 6.47683i | −0.358170 | − | 0.358170i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.3740 | − | 3.04894i | −0.957862 | − | 0.168093i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.1746 | −1.10890 | −0.554448 | − | 0.832218i | \(-0.687071\pi\) | ||||
−0.554448 | + | 0.832218i | \(0.687071\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.30352 | − | 2.30352i | −0.126232 | − | 0.126232i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.7903 | − | 22.7903i | 1.24147 | − | 1.24147i | 0.282074 | − | 0.959393i | \(-0.408978\pi\) |
0.959393 | − | 0.282074i | \(-0.0910224\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.48123 | −0.514950 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.07837i | 0.275009i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.83706 | + | 17.8774i | 0.261176 | + | 0.965291i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.9153 | − | 16.9153i | 0.908061 | − | 0.908061i | −0.0880550 | − | 0.996116i | \(-0.528065\pi\) |
0.996116 | + | 0.0880550i | \(0.0280651\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.04573 | −0.430678 | −0.215339 | − | 0.976539i | \(-0.569086\pi\) | ||||
−0.215339 | + | 0.976539i | \(0.569086\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.98178 | 0.265908 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.77285 | − | 5.77285i | 0.307258 | − | 0.307258i | −0.536587 | − | 0.843845i | \(-0.680287\pi\) |
0.843845 | + | 0.536587i | \(0.180287\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.92004 | − | 6.95813i | 0.525024 | − | 0.368263i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 33.1408i | − | 1.74911i | −0.484930 | − | 0.874553i | \(-0.661155\pi\) | ||
0.484930 | − | 0.874553i | \(-0.338845\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.1596 | −0.955770 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.91396 | − | 6.91396i | 0.362889 | − | 0.362889i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.56222 | − | 9.56222i | −0.499144 | − | 0.499144i | 0.412028 | − | 0.911171i | \(-0.364821\pi\) |
−0.911171 | + | 0.412028i | \(0.864821\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.15091 | 0.164030 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −23.6560 | − | 4.15134i | −1.22816 | − | 0.215527i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.15963 | − | 6.15963i | −0.318933 | − | 0.318933i | 0.529424 | − | 0.848357i | \(-0.322408\pi\) |
−0.848357 | + | 0.529424i | \(0.822408\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −29.1862 | − | 29.1862i | −1.50317 | − | 1.50317i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.42515i | 0.381404i | 0.981648 | + | 0.190702i | \(0.0610765\pi\) | ||||
−0.981648 | + | 0.190702i | \(0.938924\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 20.8474i | − | 1.06805i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.9659 | + | 21.9659i | −1.12240 | + | 1.12240i | −0.131026 | + | 0.991379i | \(0.541827\pi\) |
−0.991379 | + | 0.131026i | \(0.958173\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.70356 | + | 2.70356i | −0.137430 | + | 0.137430i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.95971i | 0.504977i | 0.967600 | + | 0.252489i | \(0.0812490\pi\) | ||||
−0.967600 | + | 0.252489i | \(0.918751\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 28.7512i | − | 1.45401i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.211055 | + | 0.211055i | 0.0106463 | + | 0.0106463i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.5244 | − | 13.5244i | −0.678771 | − | 0.678771i | 0.280951 | − | 0.959722i | \(-0.409350\pi\) |
−0.959722 | + | 0.280951i | \(0.909350\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.419224 | + | 2.38890i | −0.0209875 | + | 0.119595i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.39215 | 0.419084 | 0.209542 | − | 0.977800i | \(-0.432803\pi\) | ||||
0.209542 | + | 0.977800i | \(0.432803\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.1817 | + | 16.1817i | 0.806068 | + | 0.806068i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.54661 | − | 2.54661i | 0.126231 | − | 0.126231i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.7124 | 1.12305 | 0.561527 | − | 0.827458i | \(-0.310214\pi\) | ||||
0.561527 | + | 0.827458i | \(0.310214\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.70434i | 0.330701i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.45126 | + | 6.62931i | −0.465066 | + | 0.326207i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.66644 | + | 1.66644i | −0.0816060 | + | 0.0816060i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.4037 | 0.508253 | 0.254126 | − | 0.967171i | \(-0.418212\pi\) | ||||
0.254126 | + | 0.967171i | \(0.418212\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.3523 | −1.33307 | −0.666534 | − | 0.745475i | \(-0.732223\pi\) | ||||
−0.666534 | + | 0.745475i | \(0.732223\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.71436 | − | 4.71436i | 0.229220 | − | 0.229220i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.5129 | − | 23.5420i | −0.799114 | − | 1.13928i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.50749i | 0.265904i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.64217 | −0.0791008 | −0.0395504 | − | 0.999218i | \(-0.512593\pi\) | ||||
−0.0395504 | + | 0.999218i | \(0.512593\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.24765 | + | 4.24765i | −0.204129 | + | 0.204129i | −0.801767 | − | 0.597637i | \(-0.796106\pi\) |
0.597637 | + | 0.801767i | \(0.296106\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.06939 | + | 4.06939i | 0.194666 | + | 0.194666i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.4776 | −1.26371 | −0.631853 | − | 0.775089i | \(-0.717705\pi\) | ||||
−0.631853 | + | 0.775089i | \(0.717705\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.58174 | − | 2.38343i | −0.313416 | − | 0.113497i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.74453 | + | 6.74453i | 0.320442 | + | 0.320442i | 0.848937 | − | 0.528494i | \(-0.177243\pi\) |
−0.528494 | + | 0.848937i | \(0.677243\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.91610 | − | 4.91610i | −0.232524 | − | 0.232524i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.1785i | 0.763508i | 0.924264 | + | 0.381754i | \(0.124680\pi\) | ||||
−0.924264 | + | 0.381754i | \(0.875320\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.48342i | 0.164028i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.819980 | − | 0.819980i | 0.0385260 | − | 0.0385260i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.8923 | + | 17.8923i | −0.836969 | + | 0.836969i | −0.988459 | − | 0.151490i | \(-0.951593\pi\) |
0.151490 | + | 0.988459i | \(0.451593\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.57981i | 0.213767i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 33.5156i | − | 1.56098i | −0.625171 | − | 0.780488i | \(-0.714971\pi\) | ||
0.625171 | − | 0.780488i | \(-0.285029\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.5303 | − | 12.5303i | −0.582333 | − | 0.582333i | 0.353211 | − | 0.935544i | \(-0.385090\pi\) |
−0.935544 | + | 0.353211i | \(0.885090\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −26.9253 | − | 26.9253i | −1.24595 | − | 1.24595i | −0.957491 | − | 0.288462i | \(-0.906856\pi\) |
−0.288462 | − | 0.957491i | \(-0.593144\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.40491 | + | 25.1009i | −0.203400 | + | 1.15905i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.0293591 | −0.00135280 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.98886 | − | 2.98886i | −0.137428 | − | 0.137428i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.41894 | − | 6.41894i | 0.293903 | − | 0.293903i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −38.0334 | −1.73779 | −0.868896 | − | 0.494995i | \(-0.835170\pi\) | ||||
−0.868896 | + | 0.494995i | \(0.835170\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 16.2290i | − | 0.739979i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −13.5980 | + | 9.53791i | −0.618730 | + | 0.433990i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.53280 | + | 2.53280i | −0.114772 | + | 0.114772i | −0.762160 | − | 0.647388i | \(-0.775861\pi\) |
0.647388 | + | 0.762160i | \(0.275861\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.06534 | 0.229063 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.72506 | 0.393757 | 0.196878 | − | 0.980428i | \(-0.436920\pi\) | ||||
0.196878 | + | 0.980428i | \(0.436920\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.8313 | − | 26.8313i | 1.20842 | − | 1.20842i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.3925 | + | 7.28955i | −0.466169 | + | 0.326981i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 12.7452i | − | 0.570554i | −0.958445 | − | 0.285277i | \(-0.907914\pi\) | ||
0.958445 | − | 0.285277i | \(-0.0920856\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.41097 | 0.152391 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.9056 | + | 15.9056i | −0.709194 | + | 0.709194i | −0.966366 | − | 0.257172i | \(-0.917209\pi\) |
0.257172 | + | 0.966366i | \(0.417209\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.35666 | + | 8.35666i | 0.371132 | + | 0.371132i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.12085 | −0.226978 | −0.113489 | − | 0.993539i | \(-0.536203\pi\) | ||||
−0.113489 | + | 0.993539i | \(0.536203\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.29239 | + | 35.8565i | −0.278359 | + | 1.58620i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.648218 | − | 0.648218i | −0.0286195 | − | 0.0286195i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.21186 | + | 5.21186i | 0.229217 | + | 0.229217i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.3615i | 0.674294i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 34.4071i | − | 1.50740i | −0.657217 | − | 0.753702i | \(-0.728266\pi\) | ||
0.657217 | − | 0.753702i | \(-0.271734\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.25548 | − | 9.25548i | 0.404714 | − | 0.404714i | −0.475177 | − | 0.879890i | \(-0.657616\pi\) |
0.879890 | + | 0.475177i | \(0.157616\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.8760 | + | 14.8760i | −0.648011 | + | 0.648011i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.4110i | 0.713521i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 4.36339i | − | 0.189355i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.0996 | + | 11.0996i | 0.480775 | + | 0.480775i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.19761 | + | 5.19761i | 0.224294 | + | 0.224294i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.63495 | − | 7.27629i | 0.113495 | − | 0.313412i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.3304 | 0.573118 | 0.286559 | − | 0.958063i | \(-0.407489\pi\) | ||||
0.286559 | + | 0.958063i | \(0.407489\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.3595 | + | 16.3595i | 0.702055 | + | 0.702055i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.0071 | − | 10.0071i | 0.427872 | − | 0.427872i | −0.460031 | − | 0.887903i | \(-0.652162\pi\) |
0.887903 | + | 0.460031i | \(0.152162\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.8687 | 0.463865 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.59529i | 0.323570i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19.0986 | − | 27.2284i | −0.812153 | − | 1.15787i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.8441 | + | 17.8441i | −0.756078 | + | 0.756078i | −0.975606 | − | 0.219528i | \(-0.929548\pi\) |
0.219528 | + | 0.975606i | \(0.429548\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.0474 | −0.805620 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.06311 | −0.213765 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.36339 | − | 4.36339i | 0.183895 | − | 0.183895i | −0.609156 | − | 0.793051i | \(-0.708492\pi\) |
0.793051 | + | 0.609156i | \(0.208492\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.16604 | − | 1.51930i | 0.0909650 | − | 0.0638048i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 35.9854i | − | 1.50859i | −0.656537 | − | 0.754294i | \(-0.727980\pi\) | ||
0.656537 | − | 0.754294i | \(-0.272020\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.5414 | 0.734087 | 0.367043 | − | 0.930204i | \(-0.380370\pi\) | ||||
0.367043 | + | 0.930204i | \(0.380370\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.8723 | + | 14.8723i | −0.621300 | + | 0.621300i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.45573 | + | 2.45573i | 0.102234 | + | 0.102234i | 0.756374 | − | 0.654140i | \(-0.226969\pi\) |
−0.654140 | + | 0.756374i | \(0.726969\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.9899 | 0.498283 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.147138 | + | 0.838448i | −0.00610430 | + | 0.0347847i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.09631 | + | 7.09631i | 0.293899 | + | 0.293899i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.1108 | + | 24.1108i | 0.995161 | + | 0.995161i | 0.999988 | − | 0.00482767i | \(-0.00153670\pi\) |
−0.00482767 | + | 0.999988i | \(0.501537\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 4.21105i | − | 0.173513i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 18.0181i | − | 0.741164i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.8752 | + | 10.8752i | −0.446592 | + | 0.446592i | −0.894220 | − | 0.447628i | \(-0.852269\pi\) |
0.447628 | + | 0.894220i | \(0.352269\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −16.0592 | + | 16.0592i | −0.657259 | + | 0.657259i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 20.8319i | − | 0.851169i | −0.904919 | − | 0.425584i | \(-0.860069\pi\) | ||
0.904919 | − | 0.425584i | \(-0.139931\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 11.0253i | − | 0.449730i | −0.974390 | − | 0.224865i | \(-0.927806\pi\) | ||
0.974390 | − | 0.224865i | \(-0.0721940\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.81101 | − | 6.81101i | −0.277366 | − | 0.277366i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.6440 | − | 17.6440i | −0.716149 | − | 0.716149i | 0.251665 | − | 0.967814i | \(-0.419022\pi\) |
−0.967814 | + | 0.251665i | \(0.919022\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −21.5909 | − | 3.78895i | −0.874908 | − | 0.153536i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 33.2141 | 1.34370 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.97854 | + | 5.97854i | 0.241471 | + | 0.241471i | 0.817458 | − | 0.575988i | \(-0.195382\pi\) |
−0.575988 | + | 0.817458i | \(0.695382\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.90416 | − | 1.90416i | 0.0766586 | − | 0.0766586i | −0.667738 | − | 0.744396i | \(-0.732737\pi\) |
0.744396 | + | 0.667738i | \(0.232737\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 38.2048 | 1.53558 | 0.767790 | − | 0.640702i | \(-0.221357\pi\) | ||||
0.767790 | + | 0.640702i | \(0.221357\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 6.27782i | − | 0.251920i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −19.3454 | + | 13.5693i | −0.775056 | + | 0.543641i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.716623 | − | 0.716623i | 0.0286192 | − | 0.0286192i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.9195 | 0.594881 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 46.8028 | 1.86319 | 0.931595 | − | 0.363499i | \(-0.118418\pi\) | ||||
0.931595 | + | 0.363499i | \(0.118418\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.80495 | − | 1.80495i | 0.0717402 | − | 0.0717402i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.7892 | − | 31.5811i | −0.585967 | − | 1.25129i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 4.79796i | − | 0.189804i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.4235 | 0.727683 | 0.363842 | − | 0.931461i | \(-0.381465\pi\) | ||||
0.363842 | + | 0.931461i | \(0.381465\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.26164 | + | 5.26164i | −0.207499 | + | 0.207499i | −0.803204 | − | 0.595705i | \(-0.796873\pi\) |
0.595705 | + | 0.803204i | \(0.296873\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.421944 | − | 0.421944i | −0.0165883 | − | 0.0165883i | 0.698764 | − | 0.715352i | \(-0.253734\pi\) |
−0.715352 | + | 0.698764i | \(0.753734\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.82385 | 0.189352 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.9706 | + | 2.10070i | 0.469166 | + | 0.0823331i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.2593 | − | 13.2593i | −0.518877 | − | 0.518877i | 0.398355 | − | 0.917232i | \(-0.369581\pi\) |
−0.917232 | + | 0.398355i | \(0.869581\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.72950 | − | 9.72950i | −0.379584 | − | 0.379584i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.1322i | 1.48542i | 0.669614 | + | 0.742710i | \(0.266460\pi\) | ||||
−0.669614 | + | 0.742710i | \(0.733540\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 48.1006i | 1.87090i | 0.353462 | + | 0.935449i | \(0.385004\pi\) | ||||
−0.353462 | + | 0.935449i | \(0.614996\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −16.1331 | + | 16.1331i | −0.626557 | + | 0.626557i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −36.7792 | + | 36.7792i | −1.42409 | + | 1.42409i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 17.5959i | − | 0.680297i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.0157i | 0.463859i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.10360 | + | 3.10360i | 0.119635 | + | 0.119635i | 0.764390 | − | 0.644755i | \(-0.223040\pi\) |
−0.644755 | + | 0.764390i | \(0.723040\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.28037 | + | 6.28037i | 0.241374 | + | 0.241374i | 0.817418 | − | 0.576044i | \(-0.195404\pi\) |
−0.576044 | + | 0.817418i | \(0.695404\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −45.7403 | − | 8.02687i | −1.75535 | − | 0.308043i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −24.2489 | −0.929218 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.16030 | + | 7.16030i | 0.273981 | + | 0.273981i | 0.830701 | − | 0.556719i | \(-0.187940\pi\) |
−0.556719 | + | 0.830701i | \(0.687940\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.9818 | − | 10.9818i | 0.418981 | − | 0.418981i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 45.2233 | 1.72287 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.60364i | 0.0990470i | 0.998773 | + | 0.0495235i | \(0.0157703\pi\) | ||||
−0.998773 | + | 0.0495235i | \(0.984230\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.67963 | + | 2.39461i | 0.0638039 | + | 0.0909638i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.2040 | + | 10.2040i | −0.386503 | + | 0.386503i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.18776 | −0.309690 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33.1974 | −1.25385 | −0.626925 | − | 0.779080i | \(-0.715687\pi\) | ||||
−0.626925 | + | 0.779080i | \(0.715687\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.11168 | + | 2.11168i | −0.0796436 | + | 0.0796436i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.47173 | + | 10.6523i | 0.281003 | + | 0.400620i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 29.2613i | − | 1.09893i | −0.835516 | − | 0.549466i | \(-0.814831\pi\) | ||
0.835516 | − | 0.549466i | \(-0.185169\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.5706 | 0.471434 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.3915 | − | 20.3915i | 0.763666 | − | 0.763666i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.2105 | + | 10.2105i | 0.381316 | + | 0.381316i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.3340 | −0.795622 | −0.397811 | − | 0.917467i | \(-0.630230\pi\) | ||||
−0.397811 | + | 0.917467i | \(0.630230\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.23636 | − | 7.04530i | 0.0460446 | − | 0.262381i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.07829 | + | 7.07829i | 0.263245 | + | 0.263245i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.80881 | + | 5.80881i | 0.215437 | + | 0.215437i | 0.806572 | − | 0.591135i | \(-0.201320\pi\) |
−0.591135 | + | 0.806572i | \(0.701320\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 17.5105i | − | 0.647651i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.239203 | − | 0.239203i | 0.00883517 | − | 0.00883517i | −0.702675 | − | 0.711511i | \(-0.748011\pi\) |
0.711511 | + | 0.702675i | \(0.248011\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.52976 | − | 7.52976i | 0.277362 | − | 0.277362i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.4536i | 0.825968i | 0.910738 | + | 0.412984i | \(0.135513\pi\) | ||||
−0.910738 | + | 0.412984i | \(0.864487\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 4.56689i | − | 0.167769i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.25547 | + | 9.25547i | 0.339550 | + | 0.339550i | 0.856198 | − | 0.516648i | \(-0.172820\pi\) |
−0.516648 | + | 0.856198i | \(0.672820\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.227509 | − | 0.227509i | −0.00832412 | − | 0.00832412i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.27581 | + | 52.8573i | −0.338931 | + | 1.93136i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.77477 | −0.210724 | −0.105362 | − | 0.994434i | \(-0.533600\pi\) | ||||
−0.105362 | + | 0.994434i | \(0.533600\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16.0378 | − | 16.0378i | −0.584450 | − | 0.584450i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.5904 | + | 13.5904i | −0.493951 | + | 0.493951i | −0.909549 | − | 0.415598i | \(-0.863572\pi\) |
0.415598 | + | 0.909549i | \(0.363572\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.94030 | 0.251917 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.7986i | 1.29770i | 0.760918 | + | 0.648849i | \(0.224749\pi\) | ||||
−0.760918 | + | 0.648849i | \(0.775251\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.9163 | − | 19.8401i | −0.503802 | − | 0.718259i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.3707 | − | 15.3707i | 0.555003 | − | 0.555003i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.22523 | 0.332670 | 0.166335 | − | 0.986069i | \(-0.446807\pi\) | ||||
0.166335 | + | 0.986069i | \(0.446807\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.6944 | 0.601232 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.7901 | + | 13.7901i | −0.495995 | + | 0.495995i | −0.910189 | − | 0.414194i | \(-0.864064\pi\) |
0.414194 | + | 0.910189i | \(0.364064\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.94940 | − | 7.05624i | −0.177559 | − | 0.253141i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 2.88850i | − | 0.103491i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.30427 | 0.189802 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.85859 | − | 5.85859i | 0.209369 | − | 0.209369i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.5876 | + | 23.5876i | 0.840806 | + | 0.840806i | 0.988964 | − | 0.148158i | \(-0.0473343\pi\) |
−0.148158 | + | 0.988964i | \(0.547334\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.09946 | −0.0747428 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −24.7074 | − | 4.33585i | −0.878494 | − | 0.154165i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 38.2867 | + | 38.2867i | 1.35960 | + | 1.35960i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.38379 | + | 8.38379i | 0.296969 | + | 0.296969i | 0.839826 | − | 0.542856i | \(-0.182657\pi\) |
−0.542856 | + | 0.839826i | \(0.682657\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.5342i | 1.08022i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 8.93123i | − | 0.315570i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.7562 | − | 10.7562i | 0.379579 | − | 0.379579i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −21.7225 | + | 21.7225i | −0.764667 | + | 0.764667i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.45910i | 0.191932i | 0.995385 | + | 0.0959659i | \(0.0305940\pi\) | ||||
−0.995385 | + | 0.0959659i | \(0.969406\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.7871i | 0.870393i | 0.900335 | + | 0.435197i | \(0.143321\pi\) | ||||
−0.900335 | + | 0.435197i | \(0.856679\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.74069 | + | 3.74069i | 0.131192 | + | 0.131192i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.47841 | + | 2.47841i | 0.0867085 | + | 0.0867085i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.9822 | + | 2.27821i | 0.453633 | + | 0.0796072i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.6418 | 0.964706 | 0.482353 | − | 0.875977i | \(-0.339782\pi\) | ||||
0.482353 | + | 0.875977i | \(0.339782\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.76364 | − | 8.76364i | −0.305481 | − | 0.305481i | 0.537673 | − | 0.843154i | \(-0.319304\pi\) |
−0.843154 | + | 0.537673i | \(0.819304\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.39400 | − | 3.39400i | 0.118021 | − | 0.118021i | −0.645630 | − | 0.763651i | \(-0.723405\pi\) |
0.763651 | + | 0.645630i | \(0.223405\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.04845 | −0.0364140 | −0.0182070 | − | 0.999834i | \(-0.505796\pi\) | ||||
−0.0182070 | + | 0.999834i | \(0.505796\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 15.8133i | − | 0.548557i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 29.0330 | − | 13.5959i | 1.00593 | − | 0.471069i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.24818 | + | 3.24818i | −0.112273 | + | 0.112273i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 51.4166 | 1.77510 | 0.887550 | − | 0.460712i | \(-0.152406\pi\) | ||||
0.887550 | + | 0.460712i | \(0.152406\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −39.6462 | −1.36711 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.713218 | + | 0.713218i | −0.0245645 | + | 0.0245645i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.1791 | − | 14.8555i | 0.727722 | − | 0.510440i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 15.3381i | − | 0.526402i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.4511 | −0.701054 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.3132 | − | 21.3132i | 0.729750 | − | 0.729750i | −0.240820 | − | 0.970570i | \(-0.577416\pi\) |
0.970570 | + | 0.240820i | \(0.0774164\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.7450 | + | 18.7450i | 0.640317 | + | 0.640317i | 0.950633 | − | 0.310317i | \(-0.100435\pi\) |
−0.310317 | + | 0.950633i | \(0.600435\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.5452 | −1.34926 | −0.674632 | − | 0.738154i | \(-0.735698\pi\) | ||||
−0.674632 | + | 0.738154i | \(0.735698\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.21105 | + | 1.44094i | 0.279832 | + | 0.0491072i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24.4872 | − | 24.4872i | −0.833554 | − | 0.833554i | 0.154447 | − | 0.988001i | \(-0.450641\pi\) |
−0.988001 | + | 0.154447i | \(0.950641\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.81053 | − | 2.81053i | −0.0954506 | − | 0.0954506i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.8971i | 0.471428i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 47.9856i | − | 1.62593i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.4114 | − | 12.4114i | 0.420062 | − | 0.420062i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.3269 | − | 31.3269i | 1.05784 | − | 1.05784i | 0.0596143 | − | 0.998221i | \(-0.481013\pi\) |
0.998221 | − | 0.0596143i | \(-0.0189871\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.6944i | 0.563086i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 20.8419i | − | 0.702181i | −0.936341 | − | 0.351091i | \(-0.885811\pi\) | ||
0.936341 | − | 0.351091i | \(-0.114189\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.72563 | − | 9.72563i | −0.327294 | − | 0.327294i | 0.524263 | − | 0.851556i | \(-0.324341\pi\) |
−0.851556 | + | 0.524263i | \(0.824341\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.0130 | − | 19.0130i | −0.638395 | − | 0.638395i | 0.311764 | − | 0.950160i | \(-0.399080\pi\) |
−0.950160 | + | 0.311764i | \(0.899080\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.53373 | − | 54.3269i | 0.319751 | − | 1.82207i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.10553 | −0.0370366 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.32175 | − | 4.32175i | −0.144622 | − | 0.144622i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 22.1145 | − | 22.1145i | 0.738383 | − | 0.738383i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 38.0595 | 1.26936 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 41.5744i | 1.38504i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.28166 | + | 5.80893i | −0.275596 | + | 0.193309i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.5146 | − | 11.5146i | 0.382335 | − | 0.382335i | −0.489608 | − | 0.871943i | \(-0.662860\pi\) |
0.871943 | + | 0.489608i | \(0.162860\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.91786 | −0.163115 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.5480 | −1.14463 | −0.572313 | − | 0.820036i | \(-0.693954\pi\) | ||||
−0.572313 | + | 0.820036i | \(0.693954\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.251517 | − | 0.251517i | 0.00832401 | − | 0.00832401i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.453477 | + | 0.646511i | 0.0149751 | + | 0.0213497i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.6646i | 1.20945i | 0.796433 | + | 0.604727i | \(0.206718\pi\) | ||||
−0.796433 | + | 0.604727i | \(0.793282\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.6851 | −0.747501 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.9015 | − | 16.9015i | 0.556320 | − | 0.556320i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.91171 | + | 1.91171i | 0.0627887 | + | 0.0627887i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −55.6250 | −1.82500 | −0.912498 | − | 0.409081i | \(-0.865849\pi\) | ||||
−0.912498 | + | 0.409081i | \(0.865849\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.18494 | + | 6.03360i | −0.0716084 | + | 0.197743i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16.9889 | + | 16.9889i | 0.556190 | + | 0.556190i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.414213 | − | 0.414213i | −0.0135317 | − | 0.0135317i | 0.700309 | − | 0.713840i | \(-0.253046\pi\) |
−0.713840 | + | 0.700309i | \(0.753046\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 24.3928i | − | 0.796027i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.32435i | 0.238767i | 0.992848 | + | 0.119383i | \(0.0380918\pi\) | ||||
−0.992848 | + | 0.119383i | \(0.961908\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.9872 | − | 13.9872i | 0.455485 | − | 0.455485i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 32.0774 | − | 32.0774i | 1.04238 | − | 1.04238i | 0.0433144 | − | 0.999061i | \(-0.486208\pi\) |
0.999061 | − | 0.0433144i | \(-0.0137917\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 68.5472i | − | 2.22514i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.2646i | 0.559842i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.2117 | + | 28.2117i | 0.913868 | + | 0.913868i | 0.996574 | − | 0.0827063i | \(-0.0263564\pi\) |
−0.0827063 | + | 0.996574i | \(0.526356\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.47683 | + | 6.47683i | 0.209366 | + | 0.209366i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.06596 | + | 17.4710i | −0.0990050 | + | 0.564169i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.89869 | 0.319312 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.3426 | − | 14.3426i | −0.462183 | − | 0.462183i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.9303 | − | 29.9303i | 0.962495 | − | 0.962495i | −0.0368265 | − | 0.999322i | \(-0.511725\pi\) |
0.999322 | + | 0.0368265i | \(0.0117249\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.19840 | 0.134872 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.0470i | 1.15680i | 0.815752 | + | 0.578401i | \(0.196323\pi\) | ||||
−0.815752 | + | 0.578401i | \(0.803677\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.10471 | + | 3.58055i | −0.163649 | + | 0.114787i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.64977 | + | 4.64977i | −0.148759 | + | 0.148759i | −0.777564 | − | 0.628804i | \(-0.783545\pi\) |
0.628804 | + | 0.777564i | \(0.283545\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.87372 | 0.315566 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.15963 | 0.292444 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.0934 | − | 21.0934i | 0.672775 | − | 0.672775i | −0.285580 | − | 0.958355i | \(-0.592186\pi\) |
0.958355 | + | 0.285580i | \(0.0921861\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14.4412 | − | 10.1294i | 0.459669 | − | 0.322422i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.0027i | 0.763242i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.2260 | −0.674267 | −0.337134 | − | 0.941457i | \(-0.609457\pi\) | ||||
−0.337134 | + | 0.941457i | \(0.609457\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.2656 | − | 14.2656i | 0.452705 | − | 0.452705i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.71103 | + | 9.71103i | 0.307551 | + | 0.307551i | 0.843959 | − | 0.536408i | \(-0.180219\pi\) |
−0.536408 | + | 0.843959i | \(0.680219\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.25767 | 0.103068 |
(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 | 2100.2.x.d.1693.1 | 16 | ||
5.2 | odd | 4 | inner | 2100.2.x.d.1357.6 | 16 | ||
5.3 | odd | 4 | 420.2.x.a.97.1 | yes | 16 | ||
5.4 | even | 2 | 420.2.x.a.13.8 | yes | 16 | ||
7.6 | odd | 2 | inner | 2100.2.x.d.1693.6 | 16 | ||
15.8 | even | 4 | 1260.2.ba.b.937.8 | 16 | |||
15.14 | odd | 2 | 1260.2.ba.b.433.1 | 16 | |||
20.3 | even | 4 | 1680.2.cz.c.97.5 | 16 | |||
20.19 | odd | 2 | 1680.2.cz.c.433.4 | 16 | |||
35.13 | even | 4 | 420.2.x.a.97.8 | yes | 16 | ||
35.27 | even | 4 | inner | 2100.2.x.d.1357.1 | 16 | ||
35.34 | odd | 2 | 420.2.x.a.13.1 | ✓ | 16 | ||
105.83 | odd | 4 | 1260.2.ba.b.937.1 | 16 | |||
105.104 | even | 2 | 1260.2.ba.b.433.8 | 16 | |||
140.83 | odd | 4 | 1680.2.cz.c.97.4 | 16 | |||
140.139 | even | 2 | 1680.2.cz.c.433.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.x.a.13.1 | ✓ | 16 | 35.34 | odd | 2 | ||
420.2.x.a.13.8 | yes | 16 | 5.4 | even | 2 | ||
420.2.x.a.97.1 | yes | 16 | 5.3 | odd | 4 | ||
420.2.x.a.97.8 | yes | 16 | 35.13 | even | 4 | ||
1260.2.ba.b.433.1 | 16 | 15.14 | odd | 2 | |||
1260.2.ba.b.433.8 | 16 | 105.104 | even | 2 | |||
1260.2.ba.b.937.1 | 16 | 105.83 | odd | 4 | |||
1260.2.ba.b.937.8 | 16 | 15.8 | even | 4 | |||
1680.2.cz.c.97.4 | 16 | 140.83 | odd | 4 | |||
1680.2.cz.c.97.5 | 16 | 20.3 | even | 4 | |||
1680.2.cz.c.433.4 | 16 | 20.19 | odd | 2 | |||
1680.2.cz.c.433.5 | 16 | 140.139 | even | 2 | |||
2100.2.x.d.1357.1 | 16 | 35.27 | even | 4 | inner | ||
2100.2.x.d.1357.6 | 16 | 5.2 | odd | 4 | inner | ||
2100.2.x.d.1693.1 | 16 | 1.1 | even | 1 | trivial | ||
2100.2.x.d.1693.6 | 16 | 7.6 | odd | 2 | inner |