Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(218,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.218");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.j (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: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 407.3 | ||
Character | \(\chi\) | \(=\) | 525.407 |
Dual form | 525.2.j.b.218.3 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.24414 | + | 1.24414i | −0.879741 | + | 0.879741i | −0.993508 | − | 0.113766i | \(-0.963709\pi\) |
0.113766 | + | 0.993508i | \(0.463709\pi\) | |||||||
\(3\) | −0.474620 | + | 1.66575i | −0.274022 | + | 0.961723i | ||||
\(4\) | − | 1.09578i | − | 0.547890i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.48194 | − | 2.66293i | −0.605000 | − | 1.08714i | ||||
\(7\) | −0.707107 | − | 0.707107i | −0.267261 | − | 0.267261i | ||||
\(8\) | −1.12498 | − | 1.12498i | −0.397740 | − | 0.397740i | ||||
\(9\) | −2.54947 | − | 1.58120i | −0.849824 | − | 0.527067i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.55221i | − | 0.468008i | −0.972236 | − | 0.234004i | \(-0.924817\pi\) | ||
0.972236 | − | 0.234004i | \(-0.0751828\pi\) | |||||||
\(12\) | 1.82530 | + | 0.520079i | 0.526919 | + | 0.150134i | ||||
\(13\) | 4.50889 | − | 4.50889i | 1.25054 | − | 1.25054i | 0.295062 | − | 0.955478i | \(-0.404660\pi\) |
0.955478 | − | 0.295062i | \(-0.0953402\pi\) | |||||||
\(14\) | 1.75948 | 0.470242 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.99083 | 1.24771 | ||||||||
\(17\) | −2.13370 | + | 2.13370i | −0.517499 | + | 0.517499i | −0.916814 | − | 0.399315i | \(-0.869248\pi\) |
0.399315 | + | 0.916814i | \(0.369248\pi\) | |||||||
\(18\) | 5.13914 | − | 1.20467i | 1.21131 | − | 0.283943i | ||||
\(19\) | − | 4.20993i | − | 0.965823i | −0.875669 | − | 0.482912i | \(-0.839579\pi\) | ||
0.875669 | − | 0.482912i | \(-0.160421\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.51347 | − | 0.842259i | 0.330267 | − | 0.183796i | ||||
\(22\) | 1.93117 | + | 1.93117i | 0.411726 | + | 0.411726i | ||||
\(23\) | −3.76050 | − | 3.76050i | −0.784119 | − | 0.784119i | 0.196404 | − | 0.980523i | \(-0.437074\pi\) |
−0.980523 | + | 0.196404i | \(0.937074\pi\) | |||||||
\(24\) | 2.40787 | − | 1.34000i | 0.491505 | − | 0.273526i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 11.2194i | 2.20030i | ||||||||
\(27\) | 3.84392 | − | 3.49632i | 0.739763 | − | 0.672868i | ||||
\(28\) | −0.774834 | + | 0.774834i | −0.146430 | + | 0.146430i | ||||
\(29\) | −2.97115 | −0.551728 | −0.275864 | − | 0.961197i | \(-0.588964\pi\) | ||||
−0.275864 | + | 0.961197i | \(0.588964\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.79770 | −1.04130 | −0.520649 | − | 0.853771i | \(-0.674310\pi\) | ||||
−0.520649 | + | 0.853771i | \(0.674310\pi\) | |||||||
\(32\) | −3.95934 | + | 3.95934i | −0.699919 | + | 0.699919i | ||||
\(33\) | 2.58559 | + | 0.736708i | 0.450094 | + | 0.128244i | ||||
\(34\) | − | 5.30926i | − | 0.910531i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.73265 | + | 2.79366i | −0.288775 | + | 0.465610i | ||||
\(37\) | 1.23123 | + | 1.23123i | 0.202414 | + | 0.202414i | 0.801033 | − | 0.598620i | \(-0.204284\pi\) |
−0.598620 | + | 0.801033i | \(0.704284\pi\) | |||||||
\(38\) | 5.23775 | + | 5.23775i | 0.849675 | + | 0.849675i | ||||
\(39\) | 5.37069 | + | 9.65070i | 0.859998 | + | 1.54535i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.68458i | − | 0.419261i | −0.977781 | − | 0.209631i | \(-0.932774\pi\) | ||
0.977781 | − | 0.209631i | \(-0.0672261\pi\) | |||||||
\(42\) | −0.835085 | + | 2.93087i | −0.128856 | + | 0.452242i | ||||
\(43\) | 2.09578 | − | 2.09578i | 0.319603 | − | 0.319603i | −0.529011 | − | 0.848615i | \(-0.677437\pi\) |
0.848615 | + | 0.529011i | \(0.177437\pi\) | |||||||
\(44\) | −1.70088 | −0.256417 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.35721 | 1.37964 | ||||||||
\(47\) | −0.0358428 | + | 0.0358428i | −0.00522821 | + | 0.00522821i | −0.709716 | − | 0.704488i | \(-0.751177\pi\) |
0.704488 | + | 0.709716i | \(0.251177\pi\) | |||||||
\(48\) | −2.36874 | + | 8.31349i | −0.341899 | + | 1.19995i | ||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.54153 | − | 4.56692i | −0.355885 | − | 0.639497i | ||||
\(52\) | −4.94075 | − | 4.94075i | −0.685158 | − | 0.685158i | ||||
\(53\) | 4.30833 | + | 4.30833i | 0.591794 | + | 0.591794i | 0.938116 | − | 0.346322i | \(-0.112569\pi\) |
−0.346322 | + | 0.938116i | \(0.612569\pi\) | |||||||
\(54\) | −0.432457 | + | 9.13231i | −0.0588500 | + | 1.24275i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.59096i | 0.212601i | ||||||||
\(57\) | 7.01270 | + | 1.99811i | 0.928855 | + | 0.264657i | ||||
\(58\) | 3.69653 | − | 3.69653i | 0.485378 | − | 0.485378i | ||||
\(59\) | 4.93760 | 0.642821 | 0.321410 | − | 0.946940i | \(-0.395843\pi\) | ||||
0.321410 | + | 0.946940i | \(0.395843\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.31687 | 0.424681 | 0.212341 | − | 0.977196i | \(-0.431891\pi\) | ||||
0.212341 | + | 0.977196i | \(0.431891\pi\) | |||||||
\(62\) | 7.21316 | − | 7.21316i | 0.916073 | − | 0.916073i | ||||
\(63\) | 0.684672 | + | 2.92083i | 0.0862606 | + | 0.367989i | ||||
\(64\) | 0.129684i | 0.0162105i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.13342 | + | 2.30028i | −0.508788 | + | 0.283145i | ||||
\(67\) | −1.71008 | − | 1.71008i | −0.208919 | − | 0.208919i | 0.594889 | − | 0.803808i | \(-0.297196\pi\) |
−0.803808 | + | 0.594889i | \(0.797196\pi\) | |||||||
\(68\) | 2.33807 | + | 2.33807i | 0.283533 | + | 0.283533i | ||||
\(69\) | 8.04889 | − | 4.47927i | 0.968972 | − | 0.539240i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.73577i | − | 0.680711i | −0.940297 | − | 0.340356i | \(-0.889453\pi\) | ||
0.940297 | − | 0.340356i | \(-0.110547\pi\) | |||||||
\(72\) | 1.08929 | + | 4.64692i | 0.128374 | + | 0.547644i | ||||
\(73\) | −7.26776 | + | 7.26776i | −0.850627 | + | 0.850627i | −0.990210 | − | 0.139583i | \(-0.955424\pi\) |
0.139583 | + | 0.990210i | \(0.455424\pi\) | |||||||
\(74\) | −3.06366 | −0.356143 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.61315 | −0.529165 | ||||||||
\(77\) | −1.09758 | + | 1.09758i | −0.125080 | + | 0.125080i | ||||
\(78\) | −18.6887 | − | 5.32495i | −2.11608 | − | 0.602931i | ||||
\(79\) | − | 3.59379i | − | 0.404333i | −0.979351 | − | 0.202166i | \(-0.935202\pi\) | ||
0.979351 | − | 0.202166i | \(-0.0647982\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.99962 | + | 8.06245i | 0.444402 | + | 0.895828i | ||||
\(82\) | 3.34000 | + | 3.34000i | 0.368841 | + | 0.368841i | ||||
\(83\) | −12.2139 | − | 12.2139i | −1.34065 | − | 1.34065i | −0.895417 | − | 0.445228i | \(-0.853123\pi\) |
−0.445228 | − | 0.895417i | \(-0.646877\pi\) | |||||||
\(84\) | −0.922931 | − | 1.65843i | −0.100700 | − | 0.180950i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.21490i | 0.562337i | ||||||||
\(87\) | 1.41016 | − | 4.94920i | 0.151185 | − | 0.530610i | ||||
\(88\) | −1.74620 | + | 1.74620i | −0.186145 | + | 0.186145i | ||||
\(89\) | 1.35643 | 0.143782 | 0.0718908 | − | 0.997413i | \(-0.477097\pi\) | ||||
0.0718908 | + | 0.997413i | \(0.477097\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.37653 | −0.668442 | ||||||||
\(92\) | −4.12069 | + | 4.12069i | −0.429611 | + | 0.429611i | ||||
\(93\) | 2.75170 | − | 9.65754i | 0.285338 | − | 1.00144i | ||||
\(94\) | − | 0.0891871i | − | 0.00919895i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.71611 | − | 8.47447i | −0.481336 | − | 0.864922i | ||||
\(97\) | −10.9812 | − | 10.9812i | −1.11497 | − | 1.11497i | −0.992468 | − | 0.122503i | \(-0.960908\pi\) |
−0.122503 | − | 0.992468i | \(-0.539092\pi\) | |||||||
\(98\) | −1.24414 | − | 1.24414i | −0.125677 | − | 0.125677i | ||||
\(99\) | −2.45435 | + | 3.95731i | −0.246671 | + | 0.397724i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 12.7033i | − | 1.26402i | −0.774958 | − | 0.632012i | \(-0.782229\pi\) | ||
0.774958 | − | 0.632012i | \(-0.217771\pi\) | |||||||
\(102\) | 8.84392 | + | 2.51988i | 0.875679 | + | 0.249505i | ||||
\(103\) | 1.46798 | − | 1.46798i | 0.144644 | − | 0.144644i | −0.631076 | − | 0.775721i | \(-0.717387\pi\) |
0.775721 | + | 0.631076i | \(0.217387\pi\) | |||||||
\(104\) | −10.1448 | −0.994779 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.7203 | −1.04125 | ||||||||
\(107\) | 13.5523 | − | 13.5523i | 1.31015 | − | 1.31015i | 0.388849 | − | 0.921302i | \(-0.372873\pi\) |
0.921302 | − | 0.388849i | \(-0.127127\pi\) | |||||||
\(108\) | −3.83120 | − | 4.21209i | −0.368658 | − | 0.405309i | ||||
\(109\) | 4.84158i | 0.463739i | 0.972747 | + | 0.231869i | \(0.0744842\pi\) | ||||
−0.972747 | + | 0.231869i | \(0.925516\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.63530 | + | 1.46656i | −0.250132 | + | 0.139200i | ||||
\(112\) | −3.52905 | − | 3.52905i | −0.333464 | − | 0.333464i | ||||
\(113\) | 10.6222 | + | 10.6222i | 0.999254 | + | 0.999254i | 1.00000 | 0.000746132i | \(-0.000237501\pi\) | |
−0.000746132 | 1.00000i | \(0.500238\pi\) | ||||||||
\(114\) | −11.2107 | + | 6.23886i | −1.04998 | + | 0.584323i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.25572i | 0.302286i | ||||||||
\(117\) | −18.6247 | + | 4.36583i | −1.72186 | + | 0.403621i | ||||
\(118\) | −6.14308 | + | 6.14308i | −0.565516 | + | 0.565516i | ||||
\(119\) | 3.01751 | 0.276615 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.59066 | 0.780969 | ||||||||
\(122\) | −4.12665 | + | 4.12665i | −0.373610 | + | 0.373610i | ||||
\(123\) | 4.47185 | + | 1.27415i | 0.403213 | + | 0.114887i | ||||
\(124\) | 6.35300i | 0.570517i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.48575 | − | 2.78209i | −0.399623 | − | 0.247849i | ||||
\(127\) | −10.1595 | − | 10.1595i | −0.901511 | − | 0.901511i | 0.0940560 | − | 0.995567i | \(-0.470017\pi\) |
−0.995567 | + | 0.0940560i | \(0.970017\pi\) | |||||||
\(128\) | −8.08003 | − | 8.08003i | −0.714180 | − | 0.714180i | ||||
\(129\) | 2.49636 | + | 4.48575i | 0.219792 | + | 0.394948i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.509374i | 0.0445042i | 0.999752 | + | 0.0222521i | \(0.00708365\pi\) | ||||
−0.999752 | + | 0.0222521i | \(0.992916\pi\) | |||||||
\(132\) | 0.807270 | − | 2.83324i | 0.0702638 | − | 0.246602i | ||||
\(133\) | −2.97687 | + | 2.97687i | −0.258127 | + | 0.258127i | ||||
\(134\) | 4.25516 | 0.367590 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.80074 | 0.411660 | ||||||||
\(137\) | 2.61947 | − | 2.61947i | 0.223797 | − | 0.223797i | −0.586298 | − | 0.810095i | \(-0.699415\pi\) |
0.810095 | + | 0.586298i | \(0.199415\pi\) | |||||||
\(138\) | −4.44112 | + | 15.5868i | −0.378053 | + | 1.32684i | ||||
\(139\) | − | 6.35379i | − | 0.538921i | −0.963011 | − | 0.269461i | \(-0.913155\pi\) | ||
0.963011 | − | 0.269461i | \(-0.0868454\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.0426936 | − | 0.0767170i | −0.00359545 | − | 0.00646074i | ||||
\(142\) | 7.13612 | + | 7.13612i | 0.598850 | + | 0.598850i | ||||
\(143\) | −6.99872 | − | 6.99872i | −0.585262 | − | 0.585262i | ||||
\(144\) | −12.7240 | − | 7.89149i | −1.06033 | − | 0.657624i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 18.0843i | − | 1.49666i | ||||||
\(147\) | −1.66575 | − | 0.474620i | −0.137389 | − | 0.0391460i | ||||
\(148\) | 1.34916 | − | 1.34916i | 0.110900 | − | 0.110900i | ||||
\(149\) | −4.27965 | −0.350602 | −0.175301 | − | 0.984515i | \(-0.556090\pi\) | ||||
−0.175301 | + | 0.984515i | \(0.556090\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.21232 | −0.424172 | −0.212086 | − | 0.977251i | \(-0.568026\pi\) | ||||
−0.212086 | + | 0.977251i | \(0.568026\pi\) | |||||||
\(152\) | −4.73607 | + | 4.73607i | −0.384146 | + | 0.384146i | ||||
\(153\) | 8.81363 | − | 2.06601i | 0.712539 | − | 0.167027i | ||||
\(154\) | − | 2.73108i | − | 0.220077i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 10.5750 | − | 5.88509i | 0.846681 | − | 0.471185i | ||||
\(157\) | 4.35999 | + | 4.35999i | 0.347965 | + | 0.347965i | 0.859351 | − | 0.511386i | \(-0.170868\pi\) |
−0.511386 | + | 0.859351i | \(0.670868\pi\) | |||||||
\(158\) | 4.47119 | + | 4.47119i | 0.355708 | + | 0.355708i | ||||
\(159\) | −9.22143 | + | 5.13179i | −0.731307 | + | 0.406978i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.31816i | 0.419129i | ||||||||
\(162\) | −15.0069 | − | 5.05474i | −1.17906 | − | 0.397138i | ||||
\(163\) | −5.34339 | + | 5.34339i | −0.418527 | + | 0.418527i | −0.884696 | − | 0.466169i | \(-0.845634\pi\) |
0.466169 | + | 0.884696i | \(0.345634\pi\) | |||||||
\(164\) | −2.94171 | −0.229709 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 30.3916 | 2.35884 | ||||||||
\(167\) | −13.8232 | + | 13.8232i | −1.06967 | + | 1.06967i | −0.0722908 | + | 0.997384i | \(0.523031\pi\) |
−0.997384 | + | 0.0722908i | \(0.976969\pi\) | |||||||
\(168\) | −2.65015 | − | 0.755101i | −0.204463 | − | 0.0582573i | ||||
\(169\) | − | 27.6601i | − | 2.12770i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.65673 | + | 10.7331i | −0.509053 | + | 0.820780i | ||||
\(172\) | −2.29651 | − | 2.29651i | −0.175108 | − | 0.175108i | ||||
\(173\) | 2.06635 | + | 2.06635i | 0.157102 | + | 0.157102i | 0.781281 | − | 0.624179i | \(-0.214567\pi\) |
−0.624179 | + | 0.781281i | \(0.714567\pi\) | |||||||
\(174\) | 4.40306 | + | 7.91195i | 0.333795 | + | 0.599803i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 7.74679i | − | 0.583936i | ||||||
\(177\) | −2.34348 | + | 8.22483i | −0.176147 | + | 0.618216i | ||||
\(178\) | −1.68759 | + | 1.68759i | −0.126491 | + | 0.126491i | ||||
\(179\) | −11.9186 | −0.890841 | −0.445420 | − | 0.895322i | \(-0.646946\pi\) | ||||
−0.445420 | + | 0.895322i | \(0.646946\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.5945 | −1.30779 | −0.653893 | − | 0.756587i | \(-0.726865\pi\) | ||||
−0.653893 | + | 0.756587i | \(0.726865\pi\) | |||||||
\(182\) | 7.93331 | − | 7.93331i | 0.588056 | − | 0.588056i | ||||
\(183\) | −1.57425 | + | 5.52508i | −0.116372 | + | 0.408426i | ||||
\(184\) | 8.46097i | 0.623751i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 8.59184 | + | 15.4389i | 0.629985 | + | 1.13203i | ||||
\(187\) | 3.31195 | + | 3.31195i | 0.242194 | + | 0.242194i | ||||
\(188\) | 0.0392758 | + | 0.0392758i | 0.00286449 | + | 0.00286449i | ||||
\(189\) | −5.19034 | − | 0.245787i | −0.377541 | − | 0.0178783i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.54023i | 0.400877i | 0.979706 | + | 0.200438i | \(0.0642366\pi\) | ||||
−0.979706 | + | 0.200438i | \(0.935763\pi\) | |||||||
\(192\) | −0.216021 | − | 0.0615505i | −0.0155900 | − | 0.00444202i | ||||
\(193\) | 13.9027 | − | 13.9027i | 1.00074 | − | 1.00074i | 0.000740397 | − | 1.00000i | \(-0.499764\pi\) |
1.00000 | 0.000740397i | \(-0.000235676\pi\) | ||||||||
\(194\) | 27.3243 | 1.96177 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.09578 | 0.0782700 | ||||||||
\(197\) | 12.7155 | − | 12.7155i | 0.905939 | − | 0.905939i | −0.0900024 | − | 0.995942i | \(-0.528687\pi\) |
0.995942 | + | 0.0900024i | \(0.0286875\pi\) | |||||||
\(198\) | −1.86989 | − | 7.97701i | −0.132888 | − | 0.566901i | ||||
\(199\) | 6.11487i | 0.433472i | 0.976230 | + | 0.216736i | \(0.0695411\pi\) | ||||
−0.976230 | + | 0.216736i | \(0.930459\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.66021 | − | 2.03693i | 0.258171 | − | 0.143674i | ||||
\(202\) | 15.8047 | + | 15.8047i | 1.11201 | + | 1.11201i | ||||
\(203\) | 2.10092 | + | 2.10092i | 0.147455 | + | 0.147455i | ||||
\(204\) | −5.00434 | + | 2.78495i | −0.350374 | + | 0.194986i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.65275i | 0.254499i | ||||||||
\(207\) | 3.64119 | + | 15.5334i | 0.253080 | + | 1.07965i | ||||
\(208\) | 22.5031 | − | 22.5031i | 1.56031 | − | 1.56031i | ||||
\(209\) | −6.53467 | −0.452013 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.4900 | 0.859849 | 0.429924 | − | 0.902865i | \(-0.358540\pi\) | ||||
0.429924 | + | 0.902865i | \(0.358540\pi\) | |||||||
\(212\) | 4.72098 | − | 4.72098i | 0.324238 | − | 0.324238i | ||||
\(213\) | 9.55439 | + | 2.72231i | 0.654656 | + | 0.186530i | ||||
\(214\) | 33.7220i | 2.30519i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −8.25761 | − | 0.391036i | −0.561859 | − | 0.0266067i | ||||
\(217\) | 4.09959 | + | 4.09959i | 0.278298 | + | 0.278298i | ||||
\(218\) | −6.02361 | − | 6.02361i | −0.407970 | − | 0.407970i | ||||
\(219\) | −8.65688 | − | 15.5557i | −0.584978 | − | 1.05116i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.2412i | 1.29431i | ||||||||
\(222\) | 1.45407 | − | 5.10330i | 0.0975910 | − | 0.342511i | ||||
\(223\) | −8.80424 | + | 8.80424i | −0.589576 | + | 0.589576i | −0.937516 | − | 0.347941i | \(-0.886881\pi\) |
0.347941 | + | 0.937516i | \(0.386881\pi\) | |||||||
\(224\) | 5.59935 | 0.374123 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −26.4311 | −1.75817 | ||||||||
\(227\) | 15.7424 | − | 15.7424i | 1.04486 | − | 1.04486i | 0.0459126 | − | 0.998945i | \(-0.485380\pi\) |
0.998945 | − | 0.0459126i | \(-0.0146196\pi\) | |||||||
\(228\) | 2.18949 | − | 7.68438i | 0.145003 | − | 0.508910i | ||||
\(229\) | 8.27446i | 0.546791i | 0.961902 | + | 0.273396i | \(0.0881468\pi\) | ||||
−0.961902 | + | 0.273396i | \(0.911853\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.30736 | − | 2.34922i | −0.0860179 | − | 0.154567i | ||||
\(232\) | 3.34247 | + | 3.34247i | 0.219444 | + | 0.219444i | ||||
\(233\) | 12.6425 | + | 12.6425i | 0.828239 | + | 0.828239i | 0.987273 | − | 0.159034i | \(-0.0508380\pi\) |
−0.159034 | + | 0.987273i | \(0.550838\pi\) | |||||||
\(234\) | 17.7401 | − | 28.6035i | 1.15971 | − | 1.86987i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 5.41052i | − | 0.352195i | ||||||
\(237\) | 5.98637 | + | 1.70568i | 0.388856 | + | 0.110796i | ||||
\(238\) | −3.75421 | + | 3.75421i | −0.243350 | + | 0.243350i | ||||
\(239\) | 25.8260 | 1.67054 | 0.835271 | − | 0.549838i | \(-0.185311\pi\) | ||||
0.835271 | + | 0.549838i | \(0.185311\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.5197 | −0.677631 | −0.338815 | − | 0.940853i | \(-0.610026\pi\) | ||||
−0.338815 | + | 0.940853i | \(0.610026\pi\) | |||||||
\(242\) | −10.6880 | + | 10.6880i | −0.687051 | + | 0.687051i | ||||
\(243\) | −15.3284 | + | 2.83578i | −0.983314 | + | 0.181915i | ||||
\(244\) | − | 3.63456i | − | 0.232679i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.14885 | + | 3.97839i | −0.455794 | + | 0.253653i | ||||
\(247\) | −18.9821 | − | 18.9821i | −1.20780 | − | 1.20780i | ||||
\(248\) | 6.52229 | + | 6.52229i | 0.414166 | + | 0.414166i | ||||
\(249\) | 26.1422 | − | 14.5483i | 1.65670 | − | 0.921964i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.94563i | 0.438405i | 0.975679 | + | 0.219202i | \(0.0703455\pi\) | ||||
−0.975679 | + | 0.219202i | \(0.929655\pi\) | |||||||
\(252\) | 3.20058 | − | 0.750250i | 0.201618 | − | 0.0472613i | ||||
\(253\) | −5.83708 | + | 5.83708i | −0.366974 | + | 0.366974i | ||||
\(254\) | 25.2798 | 1.58619 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.8460 | 1.24038 | ||||||||
\(257\) | 8.17057 | − | 8.17057i | 0.509666 | − | 0.509666i | −0.404758 | − | 0.914424i | \(-0.632644\pi\) |
0.914424 | + | 0.404758i | \(0.132644\pi\) | |||||||
\(258\) | −8.68674 | − | 2.47509i | −0.540813 | − | 0.154093i | ||||
\(259\) | − | 1.74123i | − | 0.108195i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.57485 | + | 4.69797i | 0.468872 | + | 0.290797i | ||||
\(262\) | −0.633733 | − | 0.633733i | −0.0391522 | − | 0.0391522i | ||||
\(263\) | 0.118860 | + | 0.118860i | 0.00732922 | + | 0.00732922i | 0.710762 | − | 0.703433i | \(-0.248350\pi\) |
−0.703433 | + | 0.710762i | \(0.748350\pi\) | |||||||
\(264\) | −2.07996 | − | 3.73752i | −0.128012 | − | 0.230028i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 7.40729i | − | 0.454170i | ||||||
\(267\) | −0.643790 | + | 2.25948i | −0.0393993 | + | 0.138278i | ||||
\(268\) | −1.87387 | + | 1.87387i | −0.114465 | + | 0.114465i | ||||
\(269\) | −6.60330 | −0.402610 | −0.201305 | − | 0.979529i | \(-0.564518\pi\) | ||||
−0.201305 | + | 0.979529i | \(0.564518\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.8292 | −1.44752 | −0.723759 | − | 0.690052i | \(-0.757587\pi\) | ||||
−0.723759 | + | 0.690052i | \(0.757587\pi\) | |||||||
\(272\) | −10.6489 | + | 10.6489i | −0.645687 | + | 0.645687i | ||||
\(273\) | 3.02643 | − | 10.6217i | 0.183168 | − | 0.642856i | ||||
\(274\) | 6.51800i | 0.393767i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.90829 | − | 8.81981i | −0.295444 | − | 0.530890i | ||||
\(277\) | 14.3921 | + | 14.3921i | 0.864736 | + | 0.864736i | 0.991884 | − | 0.127147i | \(-0.0405821\pi\) |
−0.127147 | + | 0.991884i | \(0.540582\pi\) | |||||||
\(278\) | 7.90501 | + | 7.90501i | 0.474111 | + | 0.474111i | ||||
\(279\) | 14.7811 | + | 9.16732i | 0.884920 | + | 0.548833i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.50698i | − | 0.0898991i | −0.998989 | − | 0.0449495i | \(-0.985687\pi\) | ||
0.998989 | − | 0.0449495i | \(-0.0143127\pi\) | |||||||
\(282\) | 0.148564 | + | 0.0423300i | 0.00884685 | + | 0.00252071i | ||||
\(283\) | −8.49114 | + | 8.49114i | −0.504746 | + | 0.504746i | −0.912909 | − | 0.408163i | \(-0.866170\pi\) |
0.408163 | + | 0.912909i | \(0.366170\pi\) | |||||||
\(284\) | −6.28515 | −0.372955 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 17.4148 | 1.02976 | ||||||||
\(287\) | −1.89828 | + | 1.89828i | −0.112052 | + | 0.112052i | ||||
\(288\) | 16.3547 | − | 3.83372i | 0.963712 | − | 0.225904i | ||||
\(289\) | 7.89463i | 0.464390i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 23.5039 | − | 13.0801i | 1.37782 | − | 0.766768i | ||||
\(292\) | 7.96387 | + | 7.96387i | 0.466050 | + | 0.466050i | ||||
\(293\) | −2.35851 | − | 2.35851i | −0.137786 | − | 0.137786i | 0.634850 | − | 0.772635i | \(-0.281062\pi\) |
−0.772635 | + | 0.634850i | \(0.781062\pi\) | |||||||
\(294\) | 2.66293 | − | 1.48194i | 0.155305 | − | 0.0864285i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 2.77022i | − | 0.161016i | ||||||
\(297\) | −5.42702 | − | 5.96656i | −0.314907 | − | 0.346215i | ||||
\(298\) | 5.32449 | − | 5.32449i | 0.308439 | − | 0.308439i | ||||
\(299\) | −33.9114 | −1.96115 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.96388 | −0.170835 | ||||||||
\(302\) | 6.48486 | − | 6.48486i | 0.373162 | − | 0.373162i | ||||
\(303\) | 21.1606 | + | 6.02923i | 1.21564 | + | 0.346370i | ||||
\(304\) | − | 21.0110i | − | 1.20506i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −8.39500 | + | 13.5358i | −0.479910 | + | 0.773791i | ||||
\(307\) | 0.793602 | + | 0.793602i | 0.0452933 | + | 0.0452933i | 0.729391 | − | 0.684097i | \(-0.239804\pi\) |
−0.684097 | + | 0.729391i | \(0.739804\pi\) | |||||||
\(308\) | 1.20270 | + | 1.20270i | 0.0685303 | + | 0.0685303i | ||||
\(309\) | 1.74856 | + | 3.14203i | 0.0994722 | + | 0.178744i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 9.91521i | − | 0.562240i | −0.959673 | − | 0.281120i | \(-0.909294\pi\) | ||
0.959673 | − | 0.281120i | \(-0.0907059\pi\) | |||||||
\(312\) | 4.81492 | − | 16.8987i | 0.272591 | − | 0.956702i | ||||
\(313\) | 9.95137 | − | 9.95137i | 0.562484 | − | 0.562484i | −0.367528 | − | 0.930012i | \(-0.619796\pi\) |
0.930012 | + | 0.367528i | \(0.119796\pi\) | |||||||
\(314\) | −10.8489 | −0.612238 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.93800 | −0.221530 | ||||||||
\(317\) | −14.9788 | + | 14.9788i | −0.841296 | + | 0.841296i | −0.989027 | − | 0.147732i | \(-0.952803\pi\) |
0.147732 | + | 0.989027i | \(0.452803\pi\) | |||||||
\(318\) | 5.08809 | − | 17.8574i | 0.285326 | − | 1.00140i | ||||
\(319\) | 4.61183i | 0.258213i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.1426 | + | 29.0070i | 0.900992 | + | 1.61901i | ||||
\(322\) | −6.61654 | − | 6.61654i | −0.368726 | − | 0.368726i | ||||
\(323\) | 8.98273 | + | 8.98273i | 0.499812 | + | 0.499812i | ||||
\(324\) | 8.83467 | − | 4.38270i | 0.490815 | − | 0.243483i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 13.2959i | − | 0.736391i | ||||||
\(327\) | −8.06487 | − | 2.29791i | −0.445989 | − | 0.127075i | ||||
\(328\) | −3.02009 | + | 3.02009i | −0.166757 | + | 0.166757i | ||||
\(329\) | 0.0506894 | 0.00279460 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.10247 | −0.170527 | −0.0852635 | − | 0.996358i | \(-0.527173\pi\) | ||||
−0.0852635 | + | 0.996358i | \(0.527173\pi\) | |||||||
\(332\) | −13.3837 | + | 13.3837i | −0.734526 | + | 0.734526i | ||||
\(333\) | −1.19217 | − | 5.08582i | −0.0653305 | − | 0.278701i | ||||
\(334\) | − | 34.3962i | − | 1.88207i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 7.55348 | − | 4.20357i | 0.412076 | − | 0.229323i | ||||
\(337\) | 23.2030 | + | 23.2030i | 1.26395 | + | 1.26395i | 0.949163 | + | 0.314784i | \(0.101932\pi\) |
0.314784 | + | 0.949163i | \(0.398068\pi\) | |||||||
\(338\) | 34.4131 | + | 34.4131i | 1.87183 | + | 1.87183i | ||||
\(339\) | −22.7355 | + | 12.6525i | −1.23482 | + | 0.687188i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.99922i | 0.487335i | ||||||||
\(342\) | −5.07157 | − | 21.6354i | −0.274239 | − | 1.16991i | ||||
\(343\) | 0.707107 | − | 0.707107i | 0.0381802 | − | 0.0381802i | ||||
\(344\) | −4.71541 | −0.254238 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.14167 | −0.276418 | ||||||||
\(347\) | −14.1837 | + | 14.1837i | −0.761423 | + | 0.761423i | −0.976580 | − | 0.215157i | \(-0.930974\pi\) |
0.215157 | + | 0.976580i | \(0.430974\pi\) | |||||||
\(348\) | −5.42323 | − | 1.54523i | −0.290716 | − | 0.0828330i | ||||
\(349\) | − | 9.27152i | − | 0.496293i | −0.968723 | − | 0.248146i | \(-0.920179\pi\) | ||
0.968723 | − | 0.248146i | \(-0.0798214\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.56726 | − | 33.0963i | 0.0836544 | − | 1.76655i | ||||
\(352\) | 6.14571 | + | 6.14571i | 0.327568 | + | 0.327568i | ||||
\(353\) | −20.2421 | − | 20.2421i | −1.07738 | − | 1.07738i | −0.996744 | − | 0.0806368i | \(-0.974305\pi\) |
−0.0806368 | − | 0.996744i | \(-0.525695\pi\) | |||||||
\(354\) | −7.31723 | − | 13.1485i | −0.388906 | − | 0.698834i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 1.48635i | − | 0.0787765i | ||||||
\(357\) | −1.43217 | + | 5.02643i | −0.0757985 | + | 0.266027i | ||||
\(358\) | 14.8285 | − | 14.8285i | 0.783710 | − | 0.783710i | ||||
\(359\) | 18.8289 | 0.993751 | 0.496876 | − | 0.867822i | \(-0.334481\pi\) | ||||
0.496876 | + | 0.867822i | \(0.334481\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.27653 | 0.0671857 | ||||||||
\(362\) | 21.8900 | − | 21.8900i | 1.15051 | − | 1.15051i | ||||
\(363\) | −4.07730 | + | 14.3099i | −0.214003 | + | 0.751076i | ||||
\(364\) | 6.98727i | 0.366233i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.91540 | − | 8.83258i | −0.256932 | − | 0.461686i | ||||
\(367\) | −0.942012 | − | 0.942012i | −0.0491726 | − | 0.0491726i | 0.682093 | − | 0.731266i | \(-0.261070\pi\) |
−0.731266 | + | 0.682093i | \(0.761070\pi\) | |||||||
\(368\) | −18.7680 | − | 18.7680i | −0.978351 | − | 0.978351i | ||||
\(369\) | −4.24486 | + | 6.84426i | −0.220978 | + | 0.356298i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 6.09289i | − | 0.316327i | ||||||
\(372\) | −10.5825 | − | 3.01526i | −0.548679 | − | 0.156334i | ||||
\(373\) | −7.39940 | + | 7.39940i | −0.383127 | + | 0.383127i | −0.872227 | − | 0.489101i | \(-0.837325\pi\) |
0.489101 | + | 0.872227i | \(0.337325\pi\) | |||||||
\(374\) | −8.24107 | −0.426135 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.0806448 | 0.00415894 | ||||||||
\(377\) | −13.3966 | + | 13.3966i | −0.689958 | + | 0.689958i | ||||
\(378\) | 6.76331 | − | 6.15172i | 0.347867 | − | 0.316411i | ||||
\(379\) | 21.9486i | 1.12743i | 0.825971 | + | 0.563713i | \(0.190627\pi\) | ||||
−0.825971 | + | 0.563713i | \(0.809373\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 21.7452 | − | 12.1013i | 1.11404 | − | 0.619970i | ||||
\(382\) | −6.89283 | − | 6.89283i | −0.352668 | − | 0.352668i | ||||
\(383\) | −19.3310 | − | 19.3310i | −0.987768 | − | 0.987768i | 0.0121580 | − | 0.999926i | \(-0.496130\pi\) |
−0.999926 | + | 0.0121580i | \(0.996130\pi\) | |||||||
\(384\) | 17.2943 | − | 9.62440i | 0.882545 | − | 0.491143i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 34.5939i | 1.76079i | ||||||||
\(387\) | −8.65698 | + | 2.02929i | −0.440059 | + | 0.103154i | ||||
\(388\) | −12.0330 | + | 12.0330i | −0.610882 | + | 0.610882i | ||||
\(389\) | −30.7961 | −1.56142 | −0.780712 | − | 0.624891i | \(-0.785144\pi\) | ||||
−0.780712 | + | 0.624891i | \(0.785144\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.0476 | 0.811562 | ||||||||
\(392\) | 1.12498 | − | 1.12498i | 0.0568200 | − | 0.0568200i | ||||
\(393\) | −0.848491 | − | 0.241759i | −0.0428007 | − | 0.0121951i | ||||
\(394\) | 31.6397i | 1.59398i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.33634 | + | 2.68943i | 0.217909 | + | 0.135149i | ||||
\(397\) | 20.8254 | + | 20.8254i | 1.04520 | + | 1.04520i | 0.998929 | + | 0.0462702i | \(0.0147335\pi\) |
0.0462702 | + | 0.998929i | \(0.485266\pi\) | |||||||
\(398\) | −7.60777 | − | 7.60777i | −0.381343 | − | 0.381343i | ||||
\(399\) | −3.54585 | − | 6.37161i | −0.177514 | − | 0.318979i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.9084i | 1.04412i | 0.852910 | + | 0.522058i | \(0.174835\pi\) | ||||
−0.852910 | + | 0.522058i | \(0.825165\pi\) | |||||||
\(402\) | −2.01958 | + | 7.08805i | −0.100728 | + | 0.353520i | ||||
\(403\) | −26.1412 | + | 26.1412i | −1.30218 | + | 1.30218i | ||||
\(404\) | −13.9200 | −0.692547 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.22768 | −0.259445 | ||||||||
\(407\) | 1.91113 | − | 1.91113i | 0.0947311 | − | 0.0947311i | ||||
\(408\) | −2.27853 | + | 7.99685i | −0.112804 | + | 0.395903i | ||||
\(409\) | 11.5773i | 0.572460i | 0.958161 | + | 0.286230i | \(0.0924022\pi\) | ||||
−0.958161 | + | 0.286230i | \(0.907598\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.12014 | + | 5.60665i | 0.153905 | + | 0.276556i | ||||
\(412\) | −1.60858 | − | 1.60858i | −0.0792493 | − | 0.0792493i | ||||
\(413\) | −3.49141 | − | 3.49141i | −0.171801 | − | 0.171801i | ||||
\(414\) | −23.8559 | − | 14.7956i | −1.17246 | − | 0.727165i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 35.7044i | 1.75055i | ||||||||
\(417\) | 10.5838 | + | 3.01563i | 0.518293 | + | 0.147676i | ||||
\(418\) | 8.13006 | − | 8.13006i | 0.397654 | − | 0.397654i | ||||
\(419\) | 0.525515 | 0.0256731 | 0.0128365 | − | 0.999918i | \(-0.495914\pi\) | ||||
0.0128365 | + | 0.999918i | \(0.495914\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.5297 | −0.756871 | −0.378435 | − | 0.925628i | \(-0.623538\pi\) | ||||
−0.378435 | + | 0.925628i | \(0.623538\pi\) | |||||||
\(422\) | −15.5394 | + | 15.5394i | −0.756445 | + | 0.756445i | ||||
\(423\) | 0.148055 | − | 0.0347056i | 0.00719868 | − | 0.00168744i | ||||
\(424\) | − | 9.69354i | − | 0.470760i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −15.2740 | + | 8.50008i | −0.740026 | + | 0.411830i | ||||
\(427\) | −2.34538 | − | 2.34538i | −0.113501 | − | 0.113501i | ||||
\(428\) | −14.8503 | − | 14.8503i | −0.717818 | − | 0.717818i | ||||
\(429\) | 14.9799 | − | 8.33641i | 0.723235 | − | 0.402486i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 23.0144i | − | 1.10856i | −0.832329 | − | 0.554282i | \(-0.812993\pi\) | ||
0.832329 | − | 0.554282i | \(-0.187007\pi\) | |||||||
\(432\) | 19.1843 | − | 17.4495i | 0.923007 | − | 0.839542i | ||||
\(433\) | 15.4001 | − | 15.4001i | 0.740081 | − | 0.740081i | −0.232513 | − | 0.972593i | \(-0.574695\pi\) |
0.972593 | + | 0.232513i | \(0.0746947\pi\) | |||||||
\(434\) | −10.2010 | −0.489661 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.30530 | 0.254078 | ||||||||
\(437\) | −15.8314 | + | 15.8314i | −0.757321 | + | 0.757321i | ||||
\(438\) | 30.1239 | + | 8.58315i | 1.43938 | + | 0.410119i | ||||
\(439\) | − | 6.04288i | − | 0.288411i | −0.989548 | − | 0.144205i | \(-0.953937\pi\) | ||
0.989548 | − | 0.144205i | \(-0.0460626\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.58120 | − | 2.54947i | 0.0752952 | − | 0.121403i | ||||
\(442\) | −23.9388 | − | 23.9388i | −1.13865 | − | 1.13865i | ||||
\(443\) | −8.64725 | − | 8.64725i | −0.410843 | − | 0.410843i | 0.471189 | − | 0.882032i | \(-0.343825\pi\) |
−0.882032 | + | 0.471189i | \(0.843825\pi\) | |||||||
\(444\) | 1.60703 | + | 2.88771i | 0.0762664 | + | 0.137045i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 21.9075i | − | 1.03735i | ||||||
\(447\) | 2.03121 | − | 7.12884i | 0.0960727 | − | 0.337183i | ||||
\(448\) | 0.0917003 | − | 0.0917003i | 0.00433243 | − | 0.00433243i | ||||
\(449\) | 20.7599 | 0.979723 | 0.489861 | − | 0.871800i | \(-0.337047\pi\) | ||||
0.489861 | + | 0.871800i | \(0.337047\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.16702 | −0.196217 | ||||||||
\(452\) | 11.6396 | − | 11.6396i | 0.547481 | − | 0.547481i | ||||
\(453\) | 2.47387 | − | 8.68243i | 0.116232 | − | 0.407936i | ||||
\(454\) | 39.1715i | 1.83841i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.64130 | − | 10.1370i | −0.264178 | − | 0.474707i | ||||
\(457\) | −17.3075 | − | 17.3075i | −0.809612 | − | 0.809612i | 0.174963 | − | 0.984575i | \(-0.444020\pi\) |
−0.984575 | + | 0.174963i | \(0.944020\pi\) | |||||||
\(458\) | −10.2946 | − | 10.2946i | −0.481035 | − | 0.481035i | ||||
\(459\) | −0.741664 | + | 15.6619i | −0.0346179 | + | 0.731035i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 4.36421i | − | 0.203262i | −0.994822 | − | 0.101631i | \(-0.967594\pi\) | ||
0.994822 | − | 0.101631i | \(-0.0324061\pi\) | |||||||
\(462\) | 4.54931 | + | 1.29622i | 0.211653 | + | 0.0603058i | ||||
\(463\) | −2.04147 | + | 2.04147i | −0.0948752 | + | 0.0948752i | −0.752951 | − | 0.658076i | \(-0.771370\pi\) |
0.658076 | + | 0.752951i | \(0.271370\pi\) | |||||||
\(464\) | −14.8285 | −0.688394 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −31.4582 | −1.45727 | ||||||||
\(467\) | −13.9629 | + | 13.9629i | −0.646128 | + | 0.646128i | −0.952055 | − | 0.305927i | \(-0.901034\pi\) |
0.305927 | + | 0.952055i | \(0.401034\pi\) | |||||||
\(468\) | 4.78399 | + | 20.4086i | 0.221140 | + | 0.943388i | ||||
\(469\) | 2.41842i | 0.111672i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.33200 | + | 5.19333i | −0.429996 | + | 0.239296i | ||||
\(472\) | −5.55469 | − | 5.55469i | −0.255675 | − | 0.255675i | ||||
\(473\) | −3.25308 | − | 3.25308i | −0.149577 | − | 0.149577i | ||||
\(474\) | −9.57001 | + | 5.32578i | −0.439565 | + | 0.244621i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 3.30653i | − | 0.151555i | ||||||
\(477\) | −4.17163 | − | 17.7963i | −0.191006 | − | 0.814836i | ||||
\(478\) | −32.1312 | + | 32.1312i | −1.46965 | + | 1.46965i | ||||
\(479\) | −16.0067 | −0.731367 | −0.365683 | − | 0.930739i | \(-0.619165\pi\) | ||||
−0.365683 | + | 0.930739i | \(0.619165\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.1030 | 0.506252 | ||||||||
\(482\) | 13.0880 | − | 13.0880i | 0.596140 | − | 0.596140i | ||||
\(483\) | −8.85874 | − | 2.52410i | −0.403087 | − | 0.114851i | ||||
\(484\) | − | 9.41347i | − | 0.427885i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 15.5425 | − | 22.5988i | 0.705024 | − | 1.02510i | ||||
\(487\) | −20.6096 | − | 20.6096i | −0.933908 | − | 0.933908i | 0.0640391 | − | 0.997947i | \(-0.479602\pi\) |
−0.997947 | + | 0.0640391i | \(0.979602\pi\) | |||||||
\(488\) | −3.73140 | − | 3.73140i | −0.168913 | − | 0.168913i | ||||
\(489\) | −6.36470 | − | 11.4369i | −0.287822 | − | 0.517192i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.8846i | 1.34867i | 0.738423 | + | 0.674337i | \(0.235571\pi\) | ||||
−0.738423 | + | 0.674337i | \(0.764429\pi\) | |||||||
\(492\) | 1.39619 | − | 4.90016i | 0.0629453 | − | 0.220916i | ||||
\(493\) | 6.33954 | − | 6.33954i | 0.285519 | − | 0.285519i | ||||
\(494\) | 47.2328 | 2.12510 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −28.9353 | −1.29923 | ||||||||
\(497\) | −4.05581 | + | 4.05581i | −0.181928 | + | 0.181928i | ||||
\(498\) | −14.4244 | + | 50.6249i | −0.646374 | + | 2.26855i | ||||
\(499\) | − | 0.940603i | − | 0.0421072i | −0.999778 | − | 0.0210536i | \(-0.993298\pi\) | ||
0.999778 | − | 0.0210536i | \(-0.00670206\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.4653 | − | 29.5869i | −0.735617 | − | 1.32185i | ||||
\(502\) | −8.64136 | − | 8.64136i | −0.385683 | − | 0.385683i | ||||
\(503\) | 23.0051 | + | 23.0051i | 1.02575 | + | 1.02575i | 0.999660 | + | 0.0260875i | \(0.00830487\pi\) |
0.0260875 | + | 0.999660i | \(0.491695\pi\) | |||||||
\(504\) | 2.51562 | − | 4.05611i | 0.112055 | − | 0.180673i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 14.5243i | − | 0.645685i | ||||||
\(507\) | 46.0749 | + | 13.1280i | 2.04626 | + | 0.583036i | ||||
\(508\) | −11.1326 | + | 11.1326i | −0.493929 | + | 0.493929i | ||||
\(509\) | 25.8128 | 1.14413 | 0.572066 | − | 0.820208i | \(-0.306142\pi\) | ||||
0.572066 | + | 0.820208i | \(0.306142\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.2782 | 0.454679 | ||||||||
\(512\) | −8.53124 | + | 8.53124i | −0.377031 | + | 0.377031i | ||||
\(513\) | −14.7193 | − | 16.1826i | −0.649871 | − | 0.714480i | ||||
\(514\) | 20.3307i | 0.896749i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.91540 | − | 2.73546i | 0.216388 | − | 0.120422i | ||||
\(517\) | 0.0556354 | + | 0.0556354i | 0.00244684 | + | 0.00244684i | ||||
\(518\) | 2.16633 | + | 2.16633i | 0.0951833 | + | 0.0951833i | ||||
\(519\) | −4.42276 | + | 2.46130i | −0.194138 | + | 0.108039i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 44.1826i | − | 1.93568i | −0.251572 | − | 0.967838i | \(-0.580948\pi\) | ||
0.251572 | − | 0.967838i | \(-0.419052\pi\) | |||||||
\(522\) | −15.2691 | + | 3.57925i | −0.668312 | + | 0.156659i | ||||
\(523\) | −13.0685 | + | 13.0685i | −0.571447 | + | 0.571447i | −0.932533 | − | 0.361086i | \(-0.882406\pi\) |
0.361086 | + | 0.932533i | \(0.382406\pi\) | |||||||
\(524\) | 0.558162 | 0.0243834 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.295757 | −0.0128956 | ||||||||
\(527\) | 12.3706 | − | 12.3706i | 0.538870 | − | 0.538870i | ||||
\(528\) | 12.9042 | + | 3.67678i | 0.561585 | + | 0.160011i | ||||
\(529\) | 5.28280i | 0.229687i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.5883 | − | 7.80733i | −0.546285 | − | 0.338809i | ||||
\(532\) | 3.26199 | + | 3.26199i | 0.141425 | + | 0.141425i | ||||
\(533\) | −12.1045 | − | 12.1045i | −0.524303 | − | 0.524303i | ||||
\(534\) | −2.01015 | − | 3.61208i | −0.0869878 | − | 0.156310i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.84760i | 0.166191i | ||||||||
\(537\) | 5.65682 | − | 19.8535i | 0.244110 | − | 0.856743i | ||||
\(538\) | 8.21544 | − | 8.21544i | 0.354193 | − | 0.354193i | ||||
\(539\) | 1.55221 | 0.0668583 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.5590 | 0.926893 | 0.463446 | − | 0.886125i | \(-0.346613\pi\) | ||||
0.463446 | + | 0.886125i | \(0.346613\pi\) | |||||||
\(542\) | 29.6469 | − | 29.6469i | 1.27344 | − | 1.27344i | ||||
\(543\) | 8.35068 | − | 29.3080i | 0.358362 | − | 1.25773i | ||||
\(544\) | − | 16.8961i | − | 0.724415i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 9.44963 | + | 16.9802i | 0.404407 | + | 0.726687i | ||||
\(547\) | 29.6665 | + | 29.6665i | 1.26845 | + | 1.26845i | 0.946891 | + | 0.321555i | \(0.104205\pi\) |
0.321555 | + | 0.946891i | \(0.395795\pi\) | |||||||
\(548\) | −2.87037 | − | 2.87037i | −0.122616 | − | 0.122616i | ||||
\(549\) | −8.45626 | − | 5.24463i | −0.360904 | − | 0.223835i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.5083i | 0.532872i | ||||||||
\(552\) | −14.0939 | − | 4.01574i | −0.599876 | − | 0.170921i | ||||
\(553\) | −2.54119 | + | 2.54119i | −0.108063 | + | 0.108063i | ||||
\(554\) | −35.8116 | −1.52149 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.96235 | −0.295269 | ||||||||
\(557\) | 19.2396 | − | 19.2396i | 0.815208 | − | 0.815208i | −0.170201 | − | 0.985409i | \(-0.554442\pi\) |
0.985409 | + | 0.170201i | \(0.0544418\pi\) | |||||||
\(558\) | −29.7952 | + | 6.98431i | −1.26133 | + | 0.295669i | ||||
\(559\) | − | 18.8993i | − | 0.799354i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.08880 | + | 3.94497i | −0.299290 | + | 0.166557i | ||||
\(562\) | 1.87490 | + | 1.87490i | 0.0790880 | + | 0.0790880i | ||||
\(563\) | −2.03574 | − | 2.03574i | −0.0857962 | − | 0.0857962i | 0.662906 | − | 0.748702i | \(-0.269323\pi\) |
−0.748702 | + | 0.662906i | \(0.769323\pi\) | |||||||
\(564\) | −0.0840650 | + | 0.0467828i | −0.00353977 | + | 0.00196991i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 21.1284i | − | 0.888092i | ||||||
\(567\) | 2.87286 | − | 8.52917i | 0.120649 | − | 0.358191i | ||||
\(568\) | −6.45262 | + | 6.45262i | −0.270746 | + | 0.270746i | ||||
\(569\) | 36.6125 | 1.53487 | 0.767437 | − | 0.641124i | \(-0.221532\pi\) | ||||
0.767437 | + | 0.641124i | \(0.221532\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.88863 | −0.413826 | −0.206913 | − | 0.978359i | \(-0.566342\pi\) | ||||
−0.206913 | + | 0.978359i | \(0.566342\pi\) | |||||||
\(572\) | −7.66906 | + | 7.66906i | −0.320659 | + | 0.320659i | ||||
\(573\) | −9.22865 | − | 2.62950i | −0.385533 | − | 0.109849i | ||||
\(574\) | − | 4.72347i | − | 0.197154i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.205056 | − | 0.330625i | 0.00854400 | − | 0.0137760i | ||||
\(577\) | −3.44953 | − | 3.44953i | −0.143606 | − | 0.143606i | 0.631649 | − | 0.775255i | \(-0.282378\pi\) |
−0.775255 | + | 0.631649i | \(0.782378\pi\) | |||||||
\(578\) | −9.82204 | − | 9.82204i | −0.408543 | − | 0.408543i | ||||
\(579\) | 16.5600 | + | 29.7570i | 0.688211 | + | 1.23666i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.2730i | 0.716605i | ||||||||
\(582\) | −12.9687 | + | 45.5156i | −0.537569 | + | 1.88668i | ||||
\(583\) | 6.68741 | − | 6.68741i | 0.276964 | − | 0.276964i | ||||
\(584\) | 16.3521 | 0.676657 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.86864 | 0.242431 | ||||||||
\(587\) | −4.70846 | + | 4.70846i | −0.194339 | + | 0.194339i | −0.797568 | − | 0.603229i | \(-0.793880\pi\) |
0.603229 | + | 0.797568i | \(0.293880\pi\) | |||||||
\(588\) | −0.520079 | + | 1.82530i | −0.0214477 | + | 0.0752741i | ||||
\(589\) | 24.4079i | 1.00571i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.1458 | + | 27.2158i | 0.623016 | + | 1.11951i | ||||
\(592\) | 6.14487 | + | 6.14487i | 0.252553 | + | 0.252553i | ||||
\(593\) | 15.2900 | + | 15.2900i | 0.627884 | + | 0.627884i | 0.947535 | − | 0.319651i | \(-0.103566\pi\) |
−0.319651 | + | 0.947535i | \(0.603566\pi\) | |||||||
\(594\) | 14.1752 | + | 0.671263i | 0.581617 | + | 0.0275422i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.68955i | 0.192092i | ||||||||
\(597\) | −10.1859 | − | 2.90224i | −0.416880 | − | 0.118781i | ||||
\(598\) | 42.1906 | − | 42.1906i | 1.72530 | − | 1.72530i | ||||
\(599\) | −9.38844 | −0.383601 | −0.191801 | − | 0.981434i | \(-0.561433\pi\) | ||||
−0.191801 | + | 0.981434i | \(0.561433\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.87361 | −0.198799 | −0.0993993 | − | 0.995048i | \(-0.531692\pi\) | ||||
−0.0993993 | + | 0.995048i | \(0.531692\pi\) | |||||||
\(602\) | 3.68749 | − | 3.68749i | 0.150291 | − | 0.150291i | ||||
\(603\) | 1.65582 | + | 7.06377i | 0.0674303 | + | 0.287659i | ||||
\(604\) | 5.71155i | 0.232400i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −33.8280 | + | 18.8255i | −1.37417 | + | 0.764734i | ||||
\(607\) | 2.56287 | + | 2.56287i | 0.104024 | + | 0.104024i | 0.757203 | − | 0.653180i | \(-0.226565\pi\) |
−0.653180 | + | 0.757203i | \(0.726565\pi\) | |||||||
\(608\) | 16.6685 | + | 16.6685i | 0.675998 | + | 0.675998i | ||||
\(609\) | −4.49675 | + | 2.50247i | −0.182217 | + | 0.101405i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.323222i | 0.0130762i | ||||||||
\(612\) | −2.26389 | − | 9.65780i | −0.0915123 | − | 0.390393i | ||||
\(613\) | −33.5166 | + | 33.5166i | −1.35372 | + | 1.35372i | −0.472264 | + | 0.881457i | \(0.656563\pi\) |
−0.881457 | + | 0.472264i | \(0.843437\pi\) | |||||||
\(614\) | −1.97471 | −0.0796927 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.46950 | 0.0994989 | ||||||||
\(617\) | 2.15297 | − | 2.15297i | 0.0866754 | − | 0.0866754i | −0.662440 | − | 0.749115i | \(-0.730479\pi\) |
0.749115 | + | 0.662440i | \(0.230479\pi\) | |||||||
\(618\) | −6.08459 | − | 1.73367i | −0.244758 | − | 0.0697384i | ||||
\(619\) | 10.1941i | 0.409737i | 0.978789 | + | 0.204869i | \(0.0656767\pi\) | ||||
−0.978789 | + | 0.204869i | \(0.934323\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −27.6030 | − | 1.30713i | −1.10767 | − | 0.0524534i | ||||
\(622\) | 12.3359 | + | 12.3359i | 0.494626 | + | 0.494626i | ||||
\(623\) | −0.959142 | − | 0.959142i | −0.0384272 | − | 0.0384272i | ||||
\(624\) | 26.8042 | + | 48.1650i | 1.07303 | + | 1.92814i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 24.7618i | 0.989682i | ||||||||
\(627\) | 3.10148 | − | 10.8852i | 0.123861 | − | 0.434711i | ||||
\(628\) | 4.77759 | − | 4.77759i | 0.190646 | − | 0.190646i | ||||
\(629\) | −5.25417 | −0.209498 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.6402 | 1.77710 | 0.888550 | − | 0.458781i | \(-0.151714\pi\) | ||||
0.888550 | + | 0.458781i | \(0.151714\pi\) | |||||||
\(632\) | −4.04293 | + | 4.04293i | −0.160819 | + | 0.160819i | ||||
\(633\) | −5.92801 | + | 20.8053i | −0.235617 | + | 0.826937i | ||||
\(634\) | − | 37.2716i | − | 1.48025i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.62332 | + | 10.1047i | 0.222979 | + | 0.400676i | ||||
\(637\) | 4.50889 | + | 4.50889i | 0.178649 | + | 0.178649i | ||||
\(638\) | −5.73777 | − | 5.73777i | −0.227161 | − | 0.227161i | ||||
\(639\) | −9.06940 | + | 14.6232i | −0.358780 | + | 0.578485i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.7329i | 0.621414i | 0.950506 | + | 0.310707i | \(0.100566\pi\) | ||||
−0.950506 | + | 0.310707i | \(0.899434\pi\) | |||||||
\(642\) | −56.1725 | − | 16.0051i | −2.21695 | − | 0.631672i | ||||
\(643\) | 11.7811 | − | 11.7811i | 0.464600 | − | 0.464600i | −0.435560 | − | 0.900160i | \(-0.643449\pi\) |
0.900160 | + | 0.435560i | \(0.143449\pi\) | |||||||
\(644\) | 5.82753 | 0.229637 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −22.3516 | −0.879411 | ||||||||
\(647\) | 10.8002 | − | 10.8002i | 0.424600 | − | 0.424600i | −0.462184 | − | 0.886784i | \(-0.652934\pi\) |
0.886784 | + | 0.462184i | \(0.152934\pi\) | |||||||
\(648\) | 4.57060 | − | 13.5696i | 0.179550 | − | 0.533063i | ||||
\(649\) | − | 7.66417i | − | 0.300845i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.77466 | + | 4.88316i | −0.343906 | + | 0.191386i | ||||
\(652\) | 5.85518 | + | 5.85518i | 0.229307 | + | 0.229307i | ||||
\(653\) | 7.88328 | + | 7.88328i | 0.308497 | + | 0.308497i | 0.844326 | − | 0.535830i | \(-0.180001\pi\) |
−0.535830 | + | 0.844326i | \(0.680001\pi\) | |||||||
\(654\) | 12.8928 | − | 7.17493i | 0.504147 | − | 0.280562i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 13.3983i | − | 0.523115i | ||||||
\(657\) | 30.0207 | − | 7.03717i | 1.17122 | − | 0.274546i | ||||
\(658\) | −0.0630648 | + | 0.0630648i | −0.00245852 | + | 0.00245852i | ||||
\(659\) | −6.73141 | −0.262219 | −0.131109 | − | 0.991368i | \(-0.541854\pi\) | ||||
−0.131109 | + | 0.991368i | \(0.541854\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.43191 | 0.172381 | 0.0861906 | − | 0.996279i | \(-0.472531\pi\) | ||||
0.0861906 | + | 0.996279i | \(0.472531\pi\) | |||||||
\(662\) | 3.85991 | − | 3.85991i | 0.150020 | − | 0.150020i | ||||
\(663\) | −32.0512 | − | 9.13228i | −1.24476 | − | 0.354668i | ||||
\(664\) | 27.4807i | 1.06646i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.81072 | + | 4.84426i | 0.302659 | + | 0.187711i | ||||
\(667\) | 11.1730 | + | 11.1730i | 0.432621 | + | 0.432621i | ||||
\(668\) | 15.1472 | + | 15.1472i | 0.586064 | + | 0.586064i | ||||
\(669\) | −10.4870 | − | 18.8444i | −0.405452 | − | 0.728565i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 5.14846i | − | 0.198754i | ||||||
\(672\) | −2.65756 | + | 9.32715i | −0.102518 | + | 0.359802i | ||||
\(673\) | 3.35642 | − | 3.35642i | 0.129381 | − | 0.129381i | −0.639451 | − | 0.768832i | \(-0.720838\pi\) |
0.768832 | + | 0.639451i | \(0.220838\pi\) | |||||||
\(674\) | −57.7356 | −2.22389 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −30.3094 | −1.16575 | ||||||||
\(677\) | −6.31136 | + | 6.31136i | −0.242565 | + | 0.242565i | −0.817911 | − | 0.575345i | \(-0.804868\pi\) |
0.575345 | + | 0.817911i | \(0.304868\pi\) | |||||||
\(678\) | 12.5447 | − | 44.0277i | 0.481777 | − | 1.69087i | ||||
\(679\) | 15.5298i | 0.595977i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.7513 | + | 33.6946i | 0.718551 | + | 1.29118i | ||||
\(682\) | −11.1963 | − | 11.1963i | −0.428729 | − | 0.428729i | ||||
\(683\) | 21.4480 | + | 21.4480i | 0.820686 | + | 0.820686i | 0.986206 | − | 0.165520i | \(-0.0529303\pi\) |
−0.165520 | + | 0.986206i | \(0.552930\pi\) | |||||||
\(684\) | 11.7611 | + | 7.29431i | 0.449697 | + | 0.278905i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.75948i | 0.0671774i | ||||||||
\(687\) | −13.7832 | − | 3.92722i | −0.525862 | − | 0.149833i | ||||
\(688\) | 10.4597 | − | 10.4597i | 0.398771 | − | 0.398771i | ||||
\(689\) | 38.8515 | 1.48012 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.7943 | 0.714968 | 0.357484 | − | 0.933919i | \(-0.383635\pi\) | ||||
0.357484 | + | 0.933919i | \(0.383635\pi\) | |||||||
\(692\) | 2.26427 | − | 2.26427i | 0.0860745 | − | 0.0860745i | ||||
\(693\) | 4.53372 | − | 1.06275i | 0.172222 | − | 0.0403706i | ||||
\(694\) | − | 35.2932i | − | 1.33971i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7.15414 | + | 3.98133i | −0.271177 | + | 0.150912i | ||||
\(697\) | 5.72810 | + | 5.72810i | 0.216967 | + | 0.216967i | ||||
\(698\) | 11.5351 | + | 11.5351i | 0.436610 | + | 0.436610i | ||||
\(699\) | −27.0597 | + | 15.0589i | −1.02349 | + | 0.569581i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 10.0310i | − | 0.378867i | −0.981894 | − | 0.189434i | \(-0.939335\pi\) | ||
0.981894 | − | 0.189434i | \(-0.0606652\pi\) | |||||||
\(702\) | 39.2266 | + | 43.1264i | 1.48051 | + | 1.62770i | ||||
\(703\) | 5.18340 | − | 5.18340i | 0.195496 | − | 0.195496i | ||||
\(704\) | 0.201296 | 0.00758663 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 50.3682 | 1.89563 | ||||||||
\(707\) | −8.98258 | + | 8.98258i | −0.337825 | + | 0.337825i | ||||
\(708\) | 9.01260 | + | 2.56794i | 0.338714 | + | 0.0965092i | ||||
\(709\) | − | 48.4192i | − | 1.81842i | −0.416335 | − | 0.909211i | \(-0.636686\pi\) | ||
0.416335 | − | 0.909211i | \(-0.363314\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.68250 | + | 9.16227i | −0.213110 | + | 0.343612i | ||||
\(712\) | −1.52596 | − | 1.52596i | −0.0571876 | − | 0.0571876i | ||||
\(713\) | 21.8023 | + | 21.8023i | 0.816502 | + | 0.816502i | ||||
\(714\) | −4.47177 | − | 8.03542i | −0.167352 | − | 0.300718i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 13.0602i | 0.488083i | ||||||||
\(717\) | −12.2575 | + | 43.0197i | −0.457765 | + | 1.60660i | ||||
\(718\) | −23.4258 | + | 23.4258i | −0.874244 | + | 0.874244i | ||||
\(719\) | 10.6931 | 0.398786 | 0.199393 | − | 0.979920i | \(-0.436103\pi\) | ||||
0.199393 | + | 0.979920i | \(0.436103\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.07604 | −0.0773157 | ||||||||
\(722\) | −1.58818 | + | 1.58818i | −0.0591060 | + | 0.0591060i | ||||
\(723\) | 4.99284 | − | 17.5232i | 0.185686 | − | 0.651693i | ||||
\(724\) | 19.2797i | 0.716523i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −12.7308 | − | 22.8763i | −0.472486 | − | 0.849020i | ||||
\(727\) | −30.9245 | − | 30.9245i | −1.14693 | − | 1.14693i | −0.987154 | − | 0.159773i | \(-0.948924\pi\) |
−0.159773 | − | 0.987154i | \(-0.551076\pi\) | |||||||
\(728\) | 7.17345 | + | 7.17345i | 0.265866 | + | 0.265866i | ||||
\(729\) | 2.55143 | − | 26.8792i | 0.0944974 | − | 0.995525i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.94354i | 0.330789i | ||||||||
\(732\) | 6.05428 | + | 1.72503i | 0.223773 | + | 0.0637590i | ||||
\(733\) | 23.0095 | − | 23.0095i | 0.849876 | − | 0.849876i | −0.140241 | − | 0.990117i | \(-0.544788\pi\) |
0.990117 | + | 0.140241i | \(0.0447879\pi\) | |||||||
\(734\) | 2.34399 | 0.0865184 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 29.7782 | 1.09764 | ||||||||
\(737\) | −2.65439 | + | 2.65439i | −0.0977759 | + | 0.0977759i | ||||
\(738\) | −3.23403 | − | 13.7964i | −0.119046 | − | 0.507854i | ||||
\(739\) | − | 31.0959i | − | 1.14388i | −0.820295 | − | 0.571941i | \(-0.806191\pi\) | ||
0.820295 | − | 0.571941i | \(-0.193809\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 40.6287 | − | 22.6102i | 1.49253 | − | 0.830606i | ||||
\(742\) | 7.58042 | + | 7.58042i | 0.278286 | + | 0.278286i | ||||
\(743\) | 4.41646 | + | 4.41646i | 0.162024 | + | 0.162024i | 0.783463 | − | 0.621439i | \(-0.213451\pi\) |
−0.621439 | + | 0.783463i | \(0.713451\pi\) | |||||||
\(744\) | −13.9601 | + | 7.76892i | −0.511803 | + | 0.284822i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 18.4118i | − | 0.674105i | ||||||
\(747\) | 11.8263 | + | 50.4514i | 0.432703 | + | 1.84592i | ||||
\(748\) | 3.62917 | − | 3.62917i | 0.132695 | − | 0.132695i | ||||
\(749\) | −19.1658 | −0.700305 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.7634 | −0.757668 | −0.378834 | − | 0.925465i | \(-0.623675\pi\) | ||||
−0.378834 | + | 0.925465i | \(0.623675\pi\) | |||||||
\(752\) | −0.178885 | + | 0.178885i | −0.00652327 | + | 0.00652327i | ||||
\(753\) | −11.5697 | − | 3.29654i | −0.421624 | − | 0.120132i | ||||
\(754\) | − | 33.3344i | − | 1.21397i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.269328 | + | 5.68747i | −0.00979536 | + | 0.206851i | ||||
\(757\) | −27.7515 | − | 27.7515i | −1.00865 | − | 1.00865i | −0.999962 | − | 0.00868333i | \(-0.997236\pi\) |
−0.00868333 | − | 0.999962i | \(-0.502764\pi\) | |||||||
\(758\) | −27.3072 | − | 27.3072i | −0.991843 | − | 0.991843i | ||||
\(759\) | −6.95274 | − | 12.4935i | −0.252369 | − | 0.453486i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 51.6155i | − | 1.87106i | −0.353246 | − | 0.935531i | \(-0.614922\pi\) | ||
0.353246 | − | 0.935531i | \(-0.385078\pi\) | |||||||
\(762\) | −11.9983 | + | 42.1099i | −0.434652 | + | 1.52548i | ||||
\(763\) | 3.42351 | − | 3.42351i | 0.123939 | − | 0.123939i | ||||
\(764\) | 6.07087 | 0.219636 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 48.1010 | 1.73796 | ||||||||
\(767\) | 22.2631 | − | 22.2631i | 0.803873 | − | 0.803873i | ||||
\(768\) | −9.41932 | + | 33.0586i | −0.339891 | + | 1.19290i | ||||
\(769\) | − | 15.3442i | − | 0.553327i | −0.960967 | − | 0.276663i | \(-0.910771\pi\) | ||
0.960967 | − | 0.276663i | \(-0.0892287\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.73225 | + | 17.4881i | 0.350498 | + | 0.629818i | ||||
\(772\) | −15.2343 | − | 15.2343i | −0.548296 | − | 0.548296i | ||||
\(773\) | 16.1229 | + | 16.1229i | 0.579900 | + | 0.579900i | 0.934876 | − | 0.354976i | \(-0.115511\pi\) |
−0.354976 | + | 0.934876i | \(0.615511\pi\) | |||||||
\(774\) | 8.24579 | − | 13.2952i | 0.296389 | − | 0.477887i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 24.7072i | 0.886937i | ||||||||
\(777\) | 2.90046 | + | 0.826421i | 0.104053 | + | 0.0296477i | ||||
\(778\) | 38.3147 | − | 38.3147i | 1.37365 | − | 1.37365i | ||||
\(779\) | −11.3019 | −0.404932 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.90311 | −0.318578 | ||||||||
\(782\) | −19.9655 | + | 19.9655i | −0.713965 | + | 0.713965i | ||||
\(783\) | −11.4208 | + | 10.3881i | −0.408148 | + | 0.371240i | ||||
\(784\) | 4.99083i | 0.178244i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.35643 | − | 0.754861i | 0.0483821 | − | 0.0269250i | ||||
\(787\) | 6.19650 | + | 6.19650i | 0.220881 | + | 0.220881i | 0.808870 | − | 0.587988i | \(-0.200080\pi\) |
−0.587988 | + | 0.808870i | \(0.700080\pi\) | |||||||
\(788\) | −13.9334 | − | 13.9334i | −0.496355 | − | 0.496355i | ||||
\(789\) | −0.254405 | + | 0.141578i | −0.00905705 | + | 0.00504032i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 15.0221i | − | 0.534124i | ||||||
\(792\) | 7.21297 | − | 1.69080i | 0.256302 | − | 0.0600798i | ||||
\(793\) | 14.9554 | − | 14.9554i | 0.531081 | − | 0.531081i | ||||
\(794\) | −51.8196 | −1.83901 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.70056 | 0.237495 | ||||||||
\(797\) | 24.6954 | − | 24.6954i | 0.874755 | − | 0.874755i | −0.118231 | − | 0.992986i | \(-0.537722\pi\) |
0.992986 | + | 0.118231i | \(0.0377223\pi\) | |||||||
\(798\) | 12.3387 | + | 3.51565i | 0.436786 | + | 0.124453i | ||||
\(799\) | − | 0.152956i | − | 0.00541119i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.45819 | − | 2.14479i | −0.122189 | − | 0.0757824i | ||||
\(802\) | −26.0130 | − | 26.0130i | −0.918552 | − | 0.918552i | ||||
\(803\) | 11.2811 | + | 11.2811i | 0.398100 | + | 0.398100i | ||||
\(804\) | −2.23203 | − | 4.01078i | −0.0787177 | − | 0.141449i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 65.0467i | − | 2.29117i | ||||||
\(807\) | 3.13406 | − | 10.9995i | 0.110324 | − | 0.387200i | ||||
\(808\) | −14.2909 | + | 14.2909i | −0.502753 | + | 0.502753i | ||||
\(809\) | 20.4064 | 0.717449 | 0.358725 | − | 0.933443i | \(-0.383212\pi\) | ||||
0.358725 | + | 0.933443i | \(0.383212\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.0632 | 0.353368 | 0.176684 | − | 0.984268i | \(-0.443463\pi\) | ||||
0.176684 | + | 0.984268i | \(0.443463\pi\) | |||||||
\(812\) | 2.30214 | − | 2.30214i | 0.0807894 | − | 0.0807894i | ||||
\(813\) | 11.3098 | − | 39.6935i | 0.396652 | − | 1.39211i | ||||
\(814\) | 4.75543i | 0.166678i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −12.6843 | − | 22.7927i | −0.444040 | − | 0.797904i | ||||
\(817\) | −8.82308 | − | 8.82308i | −0.308680 | − | 0.308680i | ||||
\(818\) | −14.4038 | − | 14.4038i | −0.503617 | − | 0.503617i | ||||
\(819\) | 16.2568 | + | 10.0826i | 0.568058 | + | 0.352313i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 55.9052i | − | 1.95110i | −0.219767 | − | 0.975552i | \(-0.570530\pi\) | ||
0.219767 | − | 0.975552i | \(-0.429470\pi\) | |||||||
\(822\) | −10.8574 | − | 3.09357i | −0.378695 | − | 0.107901i | ||||
\(823\) | 25.7909 | − | 25.7909i | 0.899015 | − | 0.899015i | −0.0963344 | − | 0.995349i | \(-0.530712\pi\) |
0.995349 | + | 0.0963344i | \(0.0307118\pi\) | |||||||
\(824\) | −3.30289 | −0.115062 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.68762 | 0.302281 | ||||||||
\(827\) | −25.9659 | + | 25.9659i | −0.902922 | + | 0.902922i | −0.995688 | − | 0.0927663i | \(-0.970429\pi\) |
0.0927663 | + | 0.995688i | \(0.470429\pi\) | |||||||
\(828\) | 17.0212 | − | 3.98995i | 0.591528 | − | 0.138660i | ||||
\(829\) | − | 12.6797i | − | 0.440385i | −0.975456 | − | 0.220193i | \(-0.929331\pi\) | ||
0.975456 | − | 0.220193i | \(-0.0706686\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −30.8044 | + | 17.1429i | −1.06859 | + | 0.594681i | ||||
\(832\) | 0.584729 | + | 0.584729i | 0.0202718 | + | 0.0202718i | ||||
\(833\) | −2.13370 | − | 2.13370i | −0.0739284 | − | 0.0739284i | ||||
\(834\) | −16.9197 | + | 9.41593i | −0.585881 | + | 0.326047i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7.16056i | 0.247653i | ||||||||
\(837\) | −22.2859 | + | 20.2706i | −0.770313 | + | 0.700656i | ||||
\(838\) | −0.653815 | + | 0.653815i | −0.0225857 | + | 0.0225857i | ||||
\(839\) | 27.2730 | 0.941569 | 0.470785 | − | 0.882248i | \(-0.343971\pi\) | ||||
0.470785 | + | 0.882248i | \(0.343971\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.1723 | −0.695596 | ||||||||
\(842\) | 19.3211 | − | 19.3211i | 0.665851 | − | 0.665851i | ||||
\(843\) | 2.51026 | + | 0.715244i | 0.0864581 | + | 0.0246343i | ||||
\(844\) | − | 13.6863i | − | 0.471103i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.141023 | + | 0.227380i | −0.00484846 | + | 0.00781749i | ||||
\(847\) | −6.07451 | − | 6.07451i | −0.208723 | − | 0.208723i | ||||
\(848\) | 21.5021 | + | 21.5021i | 0.738385 | + | 0.738385i | ||||
\(849\) | −10.1141 | − | 18.1742i | −0.347115 | − | 0.623738i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 9.26012i | − | 0.317433i | ||||||
\(852\) | 2.98306 | − | 10.4695i | 0.102198 | − | 0.358679i | ||||
\(853\) | −8.57549 | + | 8.57549i | −0.293619 | + | 0.293619i | −0.838508 | − | 0.544889i | \(-0.816572\pi\) |
0.544889 | + | 0.838508i | \(0.316572\pi\) | |||||||
\(854\) | 5.83597 | 0.199703 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −30.4921 | −1.04220 | ||||||||
\(857\) | −20.8458 | + | 20.8458i | −0.712077 | + | 0.712077i | −0.966970 | − | 0.254892i | \(-0.917960\pi\) |
0.254892 | + | 0.966970i | \(0.417960\pi\) | |||||||
\(858\) | −8.26541 | + | 29.0088i | −0.282177 | + | 0.990344i | ||||
\(859\) | 9.52782i | 0.325085i | 0.986702 | + | 0.162543i | \(0.0519695\pi\) | ||||
−0.986702 | + | 0.162543i | \(0.948031\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.26111 | − | 4.06304i | −0.0770585 | − | 0.138468i | ||||
\(862\) | 28.6332 | + | 28.6332i | 0.975249 | + | 0.975249i | ||||
\(863\) | −32.3773 | − | 32.3773i | −1.10213 | − | 1.10213i | −0.994153 | − | 0.107982i | \(-0.965561\pi\) |
−0.107982 | − | 0.994153i | \(-0.534439\pi\) | |||||||
\(864\) | −1.37625 | + | 29.0625i | −0.0468208 | + | 0.988727i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 38.3198i | 1.30216i | ||||||||
\(867\) | −13.1505 | − | 3.74695i | −0.446615 | − | 0.127253i | ||||
\(868\) | 4.49225 | − | 4.49225i | 0.152477 | − | 0.152477i | ||||
\(869\) | −5.57830 | −0.189231 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.4211 | −0.522524 | ||||||||
\(872\) | 5.44667 | − | 5.44667i | 0.184447 | − | 0.184447i | ||||
\(873\) | 10.6328 | + | 45.3597i | 0.359865 | + | 1.53519i | ||||
\(874\) | − | 39.3931i | − | 1.33249i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −17.0457 | + | 9.48604i | −0.575919 | + | 0.320503i | ||||
\(877\) | 22.3025 | + | 22.3025i | 0.753102 | + | 0.753102i | 0.975057 | − | 0.221955i | \(-0.0712439\pi\) |
−0.221955 | + | 0.975057i | \(0.571244\pi\) | |||||||
\(878\) | 7.51820 | + | 7.51820i | 0.253727 | + | 0.253727i | ||||
\(879\) | 5.04809 | − | 2.80930i | 0.170268 | − | 0.0947553i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.6927i | 1.06775i | 0.845562 | + | 0.533877i | \(0.179266\pi\) | ||||
−0.845562 | + | 0.533877i | \(0.820734\pi\) | |||||||
\(882\) | 1.20467 | + | 5.13914i | 0.0405633 | + | 0.173044i | ||||
\(883\) | 19.2435 | − | 19.2435i | 0.647595 | − | 0.647595i | −0.304816 | − | 0.952411i | \(-0.598595\pi\) |
0.952411 | + | 0.304816i | \(0.0985950\pi\) | |||||||
\(884\) | 21.0842 | 0.709137 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 21.5168 | 0.722872 | ||||||||
\(887\) | −7.26863 | + | 7.26863i | −0.244057 | + | 0.244057i | −0.818526 | − | 0.574469i | \(-0.805208\pi\) |
0.574469 | + | 0.818526i | \(0.305208\pi\) | |||||||
\(888\) | 4.61451 | + | 1.31480i | 0.154853 | + | 0.0441219i | ||||
\(889\) | 14.3677i | 0.481878i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12.5146 | − | 6.20823i | 0.419254 | − | 0.207983i | ||||
\(892\) | 9.64751 | + | 9.64751i | 0.323023 | + | 0.323023i | ||||
\(893\) | 0.150896 | + | 0.150896i | 0.00504953 | + | 0.00504953i | ||||
\(894\) | 6.34218 | + | 11.3964i | 0.212114 | + | 0.381153i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 11.4269i | 0.381745i | ||||||||
\(897\) | 16.0950 | − | 56.4880i | 0.537397 | − | 1.88608i | ||||
\(898\) | −25.8283 | + | 25.8283i | −0.861903 | + | 0.861903i | ||||
\(899\) | 17.2258 | 0.574513 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.3854 | −0.612506 | ||||||||
\(902\) | 5.18437 | − | 5.18437i | 0.172621 | − | 0.172621i | ||||
\(903\) | 1.40672 | − | 4.93710i | 0.0468126 | − | 0.164296i | ||||
\(904\) | − | 23.8995i | − | 0.794886i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 7.72434 | + | 13.8800i | 0.256624 | + | 0.461133i | ||||
\(907\) | −20.0346 | − | 20.0346i | −0.665238 | − | 0.665238i | 0.291372 | − | 0.956610i | \(-0.405888\pi\) |
−0.956610 | + | 0.291372i | \(0.905888\pi\) | |||||||
\(908\) | −17.2502 | − | 17.2502i | −0.572467 | − | 0.572467i | ||||
\(909\) | −20.0864 | + | 32.3867i | −0.666225 | + | 1.07420i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.2452i | 1.13459i | 0.823514 | + | 0.567296i | \(0.192011\pi\) | ||||
−0.823514 | + | 0.567296i | \(0.807989\pi\) | |||||||
\(912\) | 34.9992 | + | 9.97224i | 1.15894 | + | 0.330214i | ||||
\(913\) | −18.9584 | + | 18.9584i | −0.627432 | + | 0.627432i | ||||
\(914\) | 43.0661 | 1.42450 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.06698 | 0.299582 | ||||||||
\(917\) | 0.360182 | − | 0.360182i | 0.0118942 | − | 0.0118942i | ||||
\(918\) | −18.5629 | − | 20.4084i | −0.612667 | − | 0.673576i | ||||
\(919\) | − | 44.3406i | − | 1.46266i | −0.682023 | − | 0.731331i | \(-0.738900\pi\) | ||
0.682023 | − | 0.731331i | \(-0.261100\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.69861 | + | 0.945287i | −0.0559709 | + | 0.0311483i | ||||
\(922\) | 5.42970 | + | 5.42970i | 0.178818 | + | 0.178818i | ||||
\(923\) | −25.8620 | − | 25.8620i | −0.851257 | − | 0.851257i | ||||
\(924\) | −2.57423 | + | 1.43258i | −0.0846860 | + | 0.0471284i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 5.07976i | − | 0.166931i | ||||||
\(927\) | −6.06375 | + | 1.42141i | −0.199160 | + | 0.0466851i | ||||
\(928\) | 11.7638 | − | 11.7638i | 0.386165 | − | 0.386165i | ||||
\(929\) | −9.88243 | −0.324232 | −0.162116 | − | 0.986772i | \(-0.551832\pi\) | ||||
−0.162116 | + | 0.986772i | \(0.551832\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.20993 | 0.137975 | ||||||||
\(932\) | 13.8534 | − | 13.8534i | 0.453784 | − | 0.453784i | ||||
\(933\) | 16.5163 | + | 4.70596i | 0.540720 | + | 0.154066i | ||||
\(934\) | − | 34.7438i | − | 1.13685i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 25.8639 | + | 16.0409i | 0.845387 | + | 0.524315i | ||||
\(937\) | 22.4981 | + | 22.4981i | 0.734980 | + | 0.734980i | 0.971602 | − | 0.236622i | \(-0.0760403\pi\) |
−0.236622 | + | 0.971602i | \(0.576040\pi\) | |||||||
\(938\) | −3.00885 | − | 3.00885i | −0.0982426 | − | 0.0982426i | ||||
\(939\) | 11.8534 | + | 21.2996i | 0.386821 | + | 0.695088i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 56.4149i | 1.83907i | 0.393006 | + | 0.919536i | \(0.371435\pi\) | ||||
−0.393006 | + | 0.919536i | \(0.628565\pi\) | |||||||
\(942\) | 5.14910 | − | 18.0716i | 0.167767 | − | 0.588804i | ||||
\(943\) | −10.0954 | + | 10.0954i | −0.328751 | + | 0.328751i | ||||
\(944\) | 24.6427 | 0.802052 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.09460 | 0.263178 | ||||||||
\(947\) | 8.25095 | − | 8.25095i | 0.268120 | − | 0.268120i | −0.560222 | − | 0.828342i | \(-0.689284\pi\) |
0.828342 | + | 0.560222i | \(0.189284\pi\) | |||||||
\(948\) | 1.86905 | − | 6.55974i | 0.0607041 | − | 0.213051i | ||||
\(949\) | 65.5390i | 2.12749i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.8418 | − | 32.0603i | −0.578560 | − | 1.03963i | ||||
\(952\) | −3.39463 | − | 3.39463i | −0.110021 | − | 0.110021i | ||||
\(953\) | 18.3169 | + | 18.3169i | 0.593344 | + | 0.593344i | 0.938533 | − | 0.345189i | \(-0.112185\pi\) |
−0.345189 | + | 0.938533i | \(0.612185\pi\) | |||||||
\(954\) | 27.3312 | + | 16.9510i | 0.884881 | + | 0.548809i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 28.2996i | − | 0.915274i | ||||||
\(957\) | −7.68217 | − | 2.18887i | −0.248329 | − | 0.0707560i | ||||
\(958\) | 19.9147 | − | 19.9147i | 0.643414 | − | 0.643414i | ||||
\(959\) | −3.70450 | −0.119624 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.61332 | 0.0843005 | ||||||||
\(962\) | −13.8137 | + | 13.8137i | −0.445371 | + | 0.445371i | ||||
\(963\) | −55.9801 | + | 13.1223i | −1.80393 | + | 0.422861i | ||||
\(964\) | 11.5272i | 0.371267i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 14.1619 | − | 7.88119i | 0.455651 | − | 0.253573i | ||||
\(967\) | 6.55794 | + | 6.55794i | 0.210889 | + | 0.210889i | 0.804645 | − | 0.593756i | \(-0.202356\pi\) |
−0.593756 | + | 0.804645i | \(0.702356\pi\) | |||||||
\(968\) | −9.66430 | − | 9.66430i | −0.310622 | − | 0.310622i | ||||
\(969\) | −19.2264 | + | 10.6996i | −0.617641 | + | 0.343722i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.9212i | 0.446753i | 0.974732 | + | 0.223377i | \(0.0717079\pi\) | ||||
−0.974732 | + | 0.223377i | \(0.928292\pi\) | |||||||
\(972\) | 3.10739 | + | 16.7965i | 0.0996696 | + | 0.538748i | ||||
\(973\) | −4.49280 | + | 4.49280i | −0.144033 | + | 0.144033i | ||||
\(974\) | 51.2825 | 1.64320 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 16.5539 | 0.529878 | ||||||||
\(977\) | −27.2013 | + | 27.2013i | −0.870248 | + | 0.870248i | −0.992499 | − | 0.122251i | \(-0.960989\pi\) |
0.122251 | + | 0.992499i | \(0.460989\pi\) | |||||||
\(978\) | 22.1477 | + | 6.31049i | 0.708204 | + | 0.201787i | ||||
\(979\) | − | 2.10546i | − | 0.0672909i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.65550 | − | 12.3435i | 0.244421 | − | 0.394096i | ||||
\(982\) | −37.1807 | − | 37.1807i | −1.18648 | − | 1.18648i | ||||
\(983\) | 36.8517 | + | 36.8517i | 1.17539 | + | 1.17539i | 0.980907 | + | 0.194479i | \(0.0623015\pi\) |
0.194479 | + | 0.980907i | \(0.437698\pi\) | |||||||
\(984\) | −3.59734 | − | 6.46413i | −0.114679 | − | 0.206069i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 15.7746i | 0.502365i | ||||||||
\(987\) | −0.0240582 | + | 0.0844361i | −0.000765781 | + | 0.00268763i | ||||
\(988\) | −20.8002 | + | 20.8002i | −0.661742 | + | 0.661742i | ||||
\(989\) | −15.7624 | −0.501215 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.8651 | −1.32989 | −0.664945 | − | 0.746893i | \(-0.731545\pi\) | ||||
−0.664945 | + | 0.746893i | \(0.731545\pi\) | |||||||
\(992\) | 22.9551 | − | 22.9551i | 0.728824 | − | 0.728824i | ||||
\(993\) | 1.47249 | − | 5.16795i | 0.0467281 | − | 0.164000i | ||||
\(994\) | − | 10.0920i | − | 0.320099i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −15.9418 | − | 28.6461i | −0.505135 | − | 0.907687i | ||||
\(997\) | −11.4463 | − | 11.4463i | −0.362507 | − | 0.362507i | 0.502228 | − | 0.864735i | \(-0.332514\pi\) |
−0.864735 | + | 0.502228i | \(0.832514\pi\) | |||||||
\(998\) | 1.17024 | + | 1.17024i | 0.0370434 | + | 0.0370434i | ||||
\(999\) | 9.03756 | + | 0.427970i | 0.285936 | + | 0.0135404i |
(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 | 525.2.j.b.407.3 | 24 | ||
3.2 | odd | 2 | inner | 525.2.j.b.407.10 | 24 | ||
5.2 | odd | 4 | 105.2.j.a.8.3 | ✓ | 24 | ||
5.3 | odd | 4 | inner | 525.2.j.b.218.10 | 24 | ||
5.4 | even | 2 | 105.2.j.a.92.10 | yes | 24 | ||
15.2 | even | 4 | 105.2.j.a.8.10 | yes | 24 | ||
15.8 | even | 4 | inner | 525.2.j.b.218.3 | 24 | ||
15.14 | odd | 2 | 105.2.j.a.92.3 | yes | 24 | ||
35.2 | odd | 12 | 735.2.y.j.263.3 | 48 | |||
35.4 | even | 6 | 735.2.y.j.422.10 | 48 | |||
35.9 | even | 6 | 735.2.y.j.557.3 | 48 | |||
35.12 | even | 12 | 735.2.y.g.263.3 | 48 | |||
35.17 | even | 12 | 735.2.y.g.128.10 | 48 | |||
35.19 | odd | 6 | 735.2.y.g.557.3 | 48 | |||
35.24 | odd | 6 | 735.2.y.g.422.10 | 48 | |||
35.27 | even | 4 | 735.2.j.h.638.3 | 24 | |||
35.32 | odd | 12 | 735.2.y.j.128.10 | 48 | |||
35.34 | odd | 2 | 735.2.j.h.197.10 | 24 | |||
105.2 | even | 12 | 735.2.y.j.263.10 | 48 | |||
105.17 | odd | 12 | 735.2.y.g.128.3 | 48 | |||
105.32 | even | 12 | 735.2.y.j.128.3 | 48 | |||
105.44 | odd | 6 | 735.2.y.j.557.10 | 48 | |||
105.47 | odd | 12 | 735.2.y.g.263.10 | 48 | |||
105.59 | even | 6 | 735.2.y.g.422.3 | 48 | |||
105.62 | odd | 4 | 735.2.j.h.638.10 | 24 | |||
105.74 | odd | 6 | 735.2.y.j.422.3 | 48 | |||
105.89 | even | 6 | 735.2.y.g.557.10 | 48 | |||
105.104 | even | 2 | 735.2.j.h.197.3 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.j.a.8.3 | ✓ | 24 | 5.2 | odd | 4 | ||
105.2.j.a.8.10 | yes | 24 | 15.2 | even | 4 | ||
105.2.j.a.92.3 | yes | 24 | 15.14 | odd | 2 | ||
105.2.j.a.92.10 | yes | 24 | 5.4 | even | 2 | ||
525.2.j.b.218.3 | 24 | 15.8 | even | 4 | inner | ||
525.2.j.b.218.10 | 24 | 5.3 | odd | 4 | inner | ||
525.2.j.b.407.3 | 24 | 1.1 | even | 1 | trivial | ||
525.2.j.b.407.10 | 24 | 3.2 | odd | 2 | inner | ||
735.2.j.h.197.3 | 24 | 105.104 | even | 2 | |||
735.2.j.h.197.10 | 24 | 35.34 | odd | 2 | |||
735.2.j.h.638.3 | 24 | 35.27 | even | 4 | |||
735.2.j.h.638.10 | 24 | 105.62 | odd | 4 | |||
735.2.y.g.128.3 | 48 | 105.17 | odd | 12 | |||
735.2.y.g.128.10 | 48 | 35.17 | even | 12 | |||
735.2.y.g.263.3 | 48 | 35.12 | even | 12 | |||
735.2.y.g.263.10 | 48 | 105.47 | odd | 12 | |||
735.2.y.g.422.3 | 48 | 105.59 | even | 6 | |||
735.2.y.g.422.10 | 48 | 35.24 | odd | 6 | |||
735.2.y.g.557.3 | 48 | 35.19 | odd | 6 | |||
735.2.y.g.557.10 | 48 | 105.89 | even | 6 | |||
735.2.y.j.128.3 | 48 | 105.32 | even | 12 | |||
735.2.y.j.128.10 | 48 | 35.32 | odd | 12 | |||
735.2.y.j.263.3 | 48 | 35.2 | odd | 12 | |||
735.2.y.j.263.10 | 48 | 105.2 | even | 12 | |||
735.2.y.j.422.3 | 48 | 105.74 | odd | 6 | |||
735.2.y.j.422.10 | 48 | 35.4 | even | 6 | |||
735.2.y.j.557.3 | 48 | 35.9 | even | 6 | |||
735.2.y.j.557.10 | 48 | 105.44 | odd | 6 |