Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(543,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.543");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.o (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: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.49787136.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 320) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 543.2 | ||
Root | \(0.228425 + 1.39564i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.543 |
Dual form | 1600.2.o.l.607.2 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.456850 | − | 0.456850i | −0.263763 | − | 0.263763i | 0.562818 | − | 0.826581i | \(-0.309717\pi\) |
−0.826581 | + | 0.562818i | \(0.809717\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.79129 | + | 2.79129i | 1.05501 | + | 1.05501i | 0.998396 | + | 0.0566113i | \(0.0180296\pi\) |
0.0566113 | + | 0.998396i | \(0.481970\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 2.58258i | − | 0.860859i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.37780 | −1.31996 | −0.659979 | − | 0.751284i | \(-0.729435\pi\) | ||||
−0.659979 | + | 0.751284i | \(0.729435\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.73205 | + | 1.73205i | −0.480384 | + | 0.480384i | −0.905254 | − | 0.424870i | \(-0.860320\pi\) |
0.424870 | + | 0.905254i | \(0.360320\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.00000 | + | 3.00000i | −0.727607 | + | 0.727607i | −0.970143 | − | 0.242536i | \(-0.922021\pi\) |
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.46410i | 0.794719i | 0.917663 | + | 0.397360i | \(0.130073\pi\) | ||||
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 2.55040i | − | 0.556543i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.791288 | − | 0.791288i | 0.164995 | − | 0.164995i | −0.619780 | − | 0.784775i | \(-0.712778\pi\) |
0.784775 | + | 0.619780i | \(0.212778\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.55040 | + | 2.55040i | −0.490825 | + | 0.490825i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.29150 | −0.982607 | −0.491304 | − | 0.870988i | \(-0.663479\pi\) | ||||
−0.491304 | + | 0.870988i | \(0.663479\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.58258i | − | 0.284239i | −0.989850 | − | 0.142119i | \(-0.954608\pi\) | ||
0.989850 | − | 0.142119i | \(-0.0453917\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.00000 | + | 2.00000i | 0.348155 | + | 0.348155i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.19615 | − | 5.19615i | −0.854242 | − | 0.854242i | 0.136410 | − | 0.990652i | \(-0.456443\pi\) |
−0.990652 | + | 0.136410i | \(0.956443\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.58258 | 0.253415 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.58258 | −1.18420 | −0.592100 | − | 0.805865i | \(-0.701701\pi\) | ||||
−0.592100 | + | 0.805865i | \(0.701701\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.29875 | + | 8.29875i | 1.26555 | + | 1.26555i | 0.948364 | + | 0.317184i | \(0.102737\pi\) |
0.317184 | + | 0.948364i | \(0.397263\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.791288 | − | 0.791288i | −0.115421 | − | 0.115421i | 0.647037 | − | 0.762458i | \(-0.276008\pi\) |
−0.762458 | + | 0.647037i | \(0.776008\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.58258i | 1.22608i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.74110 | 0.383831 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.64575 | + | 2.64575i | −0.363422 | + | 0.363422i | −0.865071 | − | 0.501649i | \(-0.832727\pi\) |
0.501649 | + | 0.865071i | \(0.332727\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.58258 | − | 1.58258i | 0.209617 | − | 0.209617i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 5.29150i | − | 0.688895i | −0.938806 | − | 0.344447i | \(-0.888066\pi\) | ||
0.938806 | − | 0.344447i | \(-0.111934\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 9.66930i | − | 1.23803i | −0.785380 | − | 0.619014i | \(-0.787532\pi\) | ||
0.785380 | − | 0.619014i | \(-0.212468\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.20871 | − | 7.20871i | 0.908212 | − | 0.908212i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.29875 | + | 8.29875i | −1.01385 | + | 1.01385i | −0.0139515 | + | 0.999903i | \(0.504441\pi\) |
−0.999903 | + | 0.0139515i | \(0.995559\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.723000 | −0.0870390 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.5826i | 1.61196i | 0.591946 | + | 0.805978i | \(0.298360\pi\) | ||||
−0.591946 | + | 0.805978i | \(0.701640\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.582576 | − | 0.582576i | −0.0681853 | − | 0.0681853i | 0.672192 | − | 0.740377i | \(-0.265353\pi\) |
−0.740377 | + | 0.672192i | \(0.765353\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.2197 | − | 12.2197i | −1.39256 | − | 1.39256i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.0000 | 1.35011 | 0.675053 | − | 0.737769i | \(-0.264121\pi\) | ||||
0.675053 | + | 0.737769i | \(0.264121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.41742 | −0.601936 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.83465 | − | 4.83465i | −0.530672 | − | 0.530672i | 0.390100 | − | 0.920772i | \(-0.372440\pi\) |
−0.920772 | + | 0.390100i | \(0.872440\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.41742 | + | 2.41742i | 0.259175 | + | 0.259175i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.16515i | 0.335505i | 0.985829 | + | 0.167753i | \(0.0536510\pi\) | ||||
−0.985829 | + | 0.167753i | \(0.946349\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.66930 | −1.01362 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.723000 | + | 0.723000i | −0.0749716 | + | 0.0749716i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.582576 | + | 0.582576i | −0.0591516 | + | 0.0591516i | −0.736064 | − | 0.676912i | \(-0.763318\pi\) |
0.676912 | + | 0.736064i | \(0.263318\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.3060i | 1.13630i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.65480i | 0.363666i | 0.983329 | + | 0.181833i | \(0.0582031\pi\) | ||||
−0.983329 | + | 0.181833i | \(0.941797\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.3739 | + | 10.3739i | −1.02217 | + | 1.02217i | −0.0224185 | + | 0.999749i | \(0.507137\pi\) |
−0.999749 | + | 0.0224185i | \(0.992863\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.29875 | + | 8.29875i | −0.802271 | + | 0.802271i | −0.983450 | − | 0.181179i | \(-0.942009\pi\) |
0.181179 | + | 0.983450i | \(0.442009\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.20520 | 0.594351 | 0.297175 | − | 0.954823i | \(-0.403955\pi\) | ||||
0.297175 | + | 0.954823i | \(0.403955\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.74773i | 0.450634i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.58258 | + | 4.58258i | 0.431092 | + | 0.431092i | 0.889000 | − | 0.457907i | \(-0.151401\pi\) |
−0.457907 | + | 0.889000i | \(0.651401\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.47315 | + | 4.47315i | 0.413543 | + | 0.413543i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −16.7477 | −1.53526 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.16515 | 0.742286 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.46410 | + | 3.46410i | 0.312348 | + | 0.312348i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.20871 | − | 1.20871i | −0.107256 | − | 0.107256i | 0.651442 | − | 0.758698i | \(-0.274164\pi\) |
−0.758698 | + | 0.651442i | \(0.774164\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 7.58258i | − | 0.667609i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.3060 | −0.987810 | −0.493905 | − | 0.869516i | \(-0.664431\pi\) | ||||
−0.493905 | + | 0.869516i | \(0.664431\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.66930 | + | 9.66930i | −0.838435 | + | 0.838435i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.1652 | + | 12.1652i | −1.03934 | + | 1.03934i | −0.0401452 | + | 0.999194i | \(0.512782\pi\) |
−0.999194 | + | 0.0401452i | \(0.987218\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.94630i | 0.758816i | 0.925230 | + | 0.379408i | \(0.123872\pi\) | ||||
−0.925230 | + | 0.379408i | \(0.876128\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.723000i | 0.0608876i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.58258 | − | 7.58258i | 0.634087 | − | 0.634087i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.92095 | − | 3.92095i | 0.323395 | − | 0.323395i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.37780 | −0.358644 | −0.179322 | − | 0.983790i | \(-0.557390\pi\) | ||||
−0.179322 | + | 0.983790i | \(0.557390\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 12.7477i | − | 1.03740i | −0.854958 | − | 0.518698i | \(-0.826417\pi\) | ||
0.854958 | − | 0.518698i | \(-0.173583\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.74773 | + | 7.74773i | 0.626367 | + | 0.626367i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.4014 | + | 11.4014i | 0.909927 | + | 0.909927i | 0.996266 | − | 0.0863386i | \(-0.0275167\pi\) |
−0.0863386 | + | 0.996266i | \(0.527517\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.41742 | 0.191714 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.41742 | 0.348142 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.29875 | + | 8.29875i | 0.650009 | + | 0.650009i | 0.952995 | − | 0.302986i | \(-0.0979837\pi\) |
−0.302986 | + | 0.952995i | \(0.597984\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.2087 | + | 11.2087i | 0.867356 | + | 0.867356i | 0.992179 | − | 0.124823i | \(-0.0398363\pi\) |
−0.124823 | + | 0.992179i | \(0.539836\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000i | 0.538462i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.94630 | 0.684141 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.66025 | − | 8.66025i | 0.658427 | − | 0.658427i | −0.296581 | − | 0.955008i | \(-0.595846\pi\) |
0.955008 | + | 0.296581i | \(0.0958464\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.41742 | + | 2.41742i | −0.181705 | + | 0.181705i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 8.56490i | − | 0.640171i | −0.947389 | − | 0.320085i | \(-0.896288\pi\) | ||
0.947389 | − | 0.320085i | \(-0.103712\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.92820i | − | 0.514969i | −0.966282 | − | 0.257485i | \(-0.917106\pi\) | ||
0.966282 | − | 0.257485i | \(-0.0828937\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.41742 | + | 4.41742i | −0.326545 | + | 0.326545i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.1334 | − | 13.1334i | 0.960410 | − | 0.960410i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −14.2378 | −1.03565 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 13.5826i | − | 0.982801i | −0.870934 | − | 0.491400i | \(-0.836485\pi\) | ||
0.870934 | − | 0.491400i | \(-0.163515\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.1652 | − | 14.1652i | −1.01963 | − | 1.01963i | −0.999803 | − | 0.0198265i | \(-0.993689\pi\) |
−0.0198265 | − | 0.999803i | \(-0.506311\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.64575 | − | 2.64575i | −0.188502 | − | 0.188502i | 0.606546 | − | 0.795048i | \(-0.292554\pi\) |
−0.795048 | + | 0.606546i | \(0.792554\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.00000 | −0.283552 | −0.141776 | − | 0.989899i | \(-0.545281\pi\) | ||||
−0.141776 | + | 0.989899i | \(0.545281\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.58258 | 0.534834 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −14.7701 | − | 14.7701i | −1.03666 | − | 1.03666i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.04356 | − | 2.04356i | −0.142037 | − | 0.142037i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 15.1652i | − | 1.04900i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.65120 | 0.526731 | 0.263365 | − | 0.964696i | \(-0.415168\pi\) | ||||
0.263365 | + | 0.964696i | \(0.415168\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.20520 | − | 6.20520i | 0.425174 | − | 0.425174i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.41742 | − | 4.41742i | 0.299874 | − | 0.299874i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.532300i | 0.0359695i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 10.3923i | − | 0.699062i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.3739 | − | 12.3739i | 0.828615 | − | 0.828615i | −0.158710 | − | 0.987325i | \(-0.550734\pi\) |
0.987325 | + | 0.158710i | \(0.0507335\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.66205 | − | 6.66205i | 0.442176 | − | 0.442176i | −0.450567 | − | 0.892743i | \(-0.648778\pi\) |
0.892743 | + | 0.450567i | \(0.148778\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.46410 | 0.228914 | 0.114457 | − | 0.993428i | \(-0.463487\pi\) | ||||
0.114457 | + | 0.993428i | \(0.463487\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.1652i | 0.734613i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.16515 | − | 6.16515i | −0.403892 | − | 0.403892i | 0.475710 | − | 0.879602i | \(-0.342191\pi\) |
−0.879602 | + | 0.475710i | \(0.842191\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.48220 | − | 5.48220i | −0.356107 | − | 0.356107i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.16515 | 0.204737 | 0.102368 | − | 0.994747i | \(-0.467358\pi\) | ||||
0.102368 | + | 0.994747i | \(0.467358\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.7477 | −0.692322 | −0.346161 | − | 0.938175i | \(-0.612515\pi\) | ||||
−0.346161 | + | 0.938175i | \(0.612515\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.1262 | + | 10.1262i | 0.649593 | + | 0.649593i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.00000 | − | 6.00000i | −0.381771 | − | 0.381771i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.41742i | 0.279943i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.2342 | 1.15093 | 0.575467 | − | 0.817825i | \(-0.304821\pi\) | ||||
0.575467 | + | 0.817825i | \(0.304821\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.46410 | + | 3.46410i | −0.217786 | + | 0.217786i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.7477 | − | 19.7477i | 1.23183 | − | 1.23183i | 0.268569 | − | 0.963260i | \(-0.413449\pi\) |
0.963260 | − | 0.268569i | \(-0.0865507\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 29.0079i | − | 1.80246i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.6657i | 0.845886i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.7913 | + | 18.7913i | −1.15872 | + | 1.15872i | −0.173969 | + | 0.984751i | \(0.555659\pi\) |
−0.984751 | + | 0.173969i | \(0.944341\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.44600 | − | 1.44600i | 0.0884938 | − | 0.0884938i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.7164 | 1.44602 | 0.723008 | − | 0.690840i | \(-0.242759\pi\) | ||||
0.723008 | + | 0.690840i | \(0.242759\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 8.74773i | − | 0.531387i | −0.964058 | − | 0.265693i | \(-0.914399\pi\) | ||
0.964058 | − | 0.265693i | \(-0.0856008\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.41742 | + | 4.41742i | 0.267355 | + | 0.267355i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.91915 | + | 5.91915i | 0.355647 | + | 0.355647i | 0.862206 | − | 0.506558i | \(-0.169083\pi\) |
−0.506558 | + | 0.862206i | \(0.669083\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.08712 | −0.244690 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.7477 | −0.641156 | −0.320578 | − | 0.947222i | \(-0.603877\pi\) | ||||
−0.320578 | + | 0.947222i | \(0.603877\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.2451 | − | 17.2451i | −1.02511 | − | 1.02511i | −0.999676 | − | 0.0254359i | \(-0.991903\pi\) |
−0.0254359 | − | 0.999676i | \(-0.508097\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −21.1652 | − | 21.1652i | −1.24934 | − | 1.24934i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 1.00000i | − | 0.0588235i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.532300 | 0.0312040 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.4304 | − | 23.4304i | 1.36882 | − | 1.36882i | 0.506685 | − | 0.862131i | \(-0.330871\pi\) |
0.862131 | − | 0.506685i | \(-0.169129\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.1652 | − | 11.1652i | 0.647868 | − | 0.647868i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.74110i | 0.158522i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 46.3284i | 2.67033i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.66970 | − | 1.66970i | 0.0959216 | − | 0.0959216i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.37055 | + | 1.37055i | −0.0782215 | + | 0.0782215i | −0.745135 | − | 0.666914i | \(-0.767615\pi\) |
0.666914 | + | 0.745135i | \(0.267615\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.47860 | 0.539219 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.4174i | 0.590718i | 0.955386 | + | 0.295359i | \(0.0954392\pi\) | ||||
−0.955386 | + | 0.295359i | \(0.904561\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.58258 | − | 2.58258i | −0.145976 | − | 0.145976i | 0.630342 | − | 0.776318i | \(-0.282915\pi\) |
−0.776318 | + | 0.630342i | \(0.782915\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.6066 | + | 17.6066i | 0.988883 | + | 0.988883i | 0.999939 | − | 0.0110560i | \(-0.00351931\pi\) |
−0.0110560 | + | 0.999939i | \(0.503519\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23.1652 | 1.29700 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.58258 | 0.423218 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.3923 | − | 10.3923i | −0.578243 | − | 0.578243i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.83485 | − | 2.83485i | −0.156767 | − | 0.156767i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 4.41742i | − | 0.243540i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.20520 | 0.341069 | 0.170534 | − | 0.985352i | \(-0.445451\pi\) | ||||
0.170534 | + | 0.985352i | \(0.445451\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −13.4195 | + | 13.4195i | −0.735382 | + | 0.735382i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.00000 | + | 1.00000i | −0.0544735 | + | 0.0544735i | −0.733819 | − | 0.679345i | \(-0.762264\pi\) |
0.679345 | + | 0.733819i | \(0.262264\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 4.18710i | − | 0.227412i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.92820i | 0.375183i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.41742 | + | 4.41742i | −0.238518 | + | 0.238518i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.92095 | + | 3.92095i | −0.210488 | + | 0.210488i | −0.804475 | − | 0.593987i | \(-0.797553\pi\) |
0.593987 | + | 0.804475i | \(0.297553\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.3923 | −0.556287 | −0.278144 | − | 0.960539i | \(-0.589719\pi\) | ||||
−0.278144 | + | 0.960539i | \(0.589719\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 8.83485i | − | 0.471569i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.83485 | − | 5.83485i | −0.310558 | − | 0.310558i | 0.534568 | − | 0.845126i | \(-0.320474\pi\) |
−0.845126 | + | 0.534568i | \(0.820474\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.65120 | + | 7.65120i | 0.404945 | + | 0.404945i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.83485 | −0.466285 | −0.233143 | − | 0.972443i | \(-0.574901\pi\) | ||||
−0.233143 | + | 0.972443i | \(0.574901\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.00000 | 0.368421 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.73025 | − | 3.73025i | −0.195787 | − | 0.195787i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.5390 | − | 15.5390i | −0.811130 | − | 0.811130i | 0.173673 | − | 0.984803i | \(-0.444436\pi\) |
−0.984803 | + | 0.173673i | \(0.944436\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 19.5826i | 1.01943i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.7701 | −0.766826 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.19615 | + | 5.19615i | −0.269047 | + | 0.269047i | −0.828716 | − | 0.559669i | \(-0.810928\pi\) |
0.559669 | + | 0.828716i | \(0.310928\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.16515 | − | 9.16515i | 0.472029 | − | 0.472029i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.3923i | 0.533817i | 0.963722 | + | 0.266908i | \(0.0860021\pi\) | ||||
−0.963722 | + | 0.266908i | \(0.913998\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.10440i | 0.0565802i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.62614 | + | 3.62614i | −0.185287 | + | 0.185287i | −0.793655 | − | 0.608368i | \(-0.791824\pi\) |
0.608368 | + | 0.793655i | \(0.291824\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 21.4322 | − | 21.4322i | 1.08946 | − | 1.08946i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.2632 | 1.53441 | 0.767203 | − | 0.641404i | \(-0.221648\pi\) | ||||
0.767203 | + | 0.641404i | \(0.221648\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.74773i | 0.240103i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.16515 | + | 5.16515i | 0.260547 | + | 0.260547i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.93725 | + | 7.93725i | 0.398359 | + | 0.398359i | 0.877654 | − | 0.479295i | \(-0.159107\pi\) |
−0.479295 | + | 0.877654i | \(0.659107\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.83485 | 0.442296 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.3303 | 0.615746 | 0.307873 | − | 0.951427i | \(-0.400383\pi\) | ||||
0.307873 | + | 0.951427i | \(0.400383\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.74110 | + | 2.74110i | 0.136544 | + | 0.136544i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 22.7477 | + | 22.7477i | 1.12756 | + | 1.12756i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 25.5826i | − | 1.26498i | −0.774570 | − | 0.632488i | \(-0.782034\pi\) | ||
0.774570 | − | 0.632488i | \(-0.217966\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.1153 | 0.548278 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.7701 | − | 14.7701i | 0.726789 | − | 0.726789i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.08712 | − | 4.08712i | 0.200147 | − | 0.200147i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.190700i | 0.00931632i | 0.999989 | + | 0.00465816i | \(0.00148274\pi\) | ||||
−0.999989 | + | 0.00465816i | \(0.998517\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 2.74110i | − | 0.133593i | −0.997767 | − | 0.0667966i | \(-0.978722\pi\) | ||
0.997767 | − | 0.0667966i | \(-0.0212778\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.04356 | + | 2.04356i | −0.0993613 | + | 0.0993613i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 26.9898 | − | 26.9898i | 1.30613 | − | 1.30613i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.92820 | −0.334497 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 16.7477i | − | 0.806710i | −0.915044 | − | 0.403355i | \(-0.867844\pi\) | ||
0.915044 | − | 0.403355i | \(-0.132156\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.5826 | + | 14.5826i | 0.700794 | + | 0.700794i | 0.964581 | − | 0.263787i | \(-0.0849716\pi\) |
−0.263787 | + | 0.964581i | \(0.584972\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.74110 | + | 2.74110i | 0.131125 | + | 0.131125i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −29.4955 | −1.40774 | −0.703871 | − | 0.710328i | \(-0.748547\pi\) | ||||
−0.703871 | + | 0.710328i | \(0.748547\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 22.1652 | 1.05548 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.17985 | − | 1.17985i | −0.0560564 | − | 0.0560564i | 0.678523 | − | 0.734579i | \(-0.262620\pi\) |
−0.734579 | + | 0.678523i | \(0.762620\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.00000 | + | 2.00000i | 0.0945968 | + | 0.0945968i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 10.4174i | − | 0.491629i | −0.969317 | − | 0.245814i | \(-0.920945\pi\) | ||
0.969317 | − | 0.245814i | \(-0.0790553\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 33.1950 | 1.56309 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.82380 | + | 5.82380i | −0.273626 | + | 0.273626i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.41742 | + | 3.41742i | −0.159860 | + | 0.159860i | −0.782505 | − | 0.622644i | \(-0.786058\pi\) |
0.622644 | + | 0.782505i | \(0.286058\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 15.3024i | − | 0.714255i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 17.5112i | − | 0.815578i | −0.913076 | − | 0.407789i | \(-0.866300\pi\) | ||
0.913076 | − | 0.407789i | \(-0.133700\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.7913 | − | 16.7913i | 0.780357 | − | 0.780357i | −0.199534 | − | 0.979891i | \(-0.563943\pi\) |
0.979891 | + | 0.199534i | \(0.0639427\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.57575 | + | 7.57575i | −0.350564 | + | 0.350564i | −0.860319 | − | 0.509755i | \(-0.829736\pi\) |
0.509755 | + | 0.860319i | \(0.329736\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −46.3284 | −2.13925 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 10.4174i | − | 0.480010i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −36.3303 | − | 36.3303i | −1.67047 | − | 1.67047i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.83285 | + | 6.83285i | 0.312855 | + | 0.312855i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.4955 | −0.982152 | −0.491076 | − | 0.871117i | \(-0.663396\pi\) | ||||
−0.491076 | + | 0.871117i | \(0.663396\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.0000 | 0.820729 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.01810 | − | 2.01810i | −0.0918268 | − | 0.0918268i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.373864 | − | 0.373864i | −0.0169414 | − | 0.0169414i | 0.698585 | − | 0.715527i | \(-0.253813\pi\) |
−0.715527 | + | 0.698585i | \(0.753813\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 7.58258i | − | 0.342896i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.86001 | 0.444976 | 0.222488 | − | 0.974935i | \(-0.428582\pi\) | ||||
0.222488 | + | 0.974935i | \(0.428582\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.8745 | − | 15.8745i | 0.714952 | − | 0.714952i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −37.9129 | + | 37.9129i | −1.70063 | + | 1.70063i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.2487i | 1.08552i | 0.839887 | + | 0.542761i | \(0.182621\pi\) | ||||
−0.839887 | + | 0.542761i | \(0.817379\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 10.2414i | − | 0.457552i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.5390 | + | 17.5390i | −0.782026 | + | 0.782026i | −0.980172 | − | 0.198146i | \(-0.936508\pi\) |
0.198146 | + | 0.980172i | \(0.436508\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.19795 | − | 3.19795i | 0.142026 | − | 0.142026i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 38.4865 | 1.70588 | 0.852942 | − | 0.522005i | \(-0.174816\pi\) | ||||
0.852942 | + | 0.522005i | \(0.174816\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 3.25227i | − | 0.143872i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.83485 | − | 8.83485i | −0.390068 | − | 0.390068i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.46410 | + | 3.46410i | 0.152351 | + | 0.152351i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.91288 | −0.347337 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.1652 | −1.45299 | −0.726496 | − | 0.687171i | \(-0.758852\pi\) | ||||
−0.726496 | + | 0.687171i | \(0.758852\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.9500 | + | 15.9500i | 0.697443 | + | 0.697443i | 0.963858 | − | 0.266415i | \(-0.0858393\pi\) |
−0.266415 | + | 0.963858i | \(0.585839\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.74773 | + | 4.74773i | 0.206814 | + | 0.206814i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.7477i | 0.945553i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.6657 | −0.593041 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.1334 | − | 13.1334i | 0.568871 | − | 0.568871i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.91288 | + | 3.91288i | −0.168853 | + | 0.168853i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 37.5728i | − | 1.61838i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.16515 | + | 3.16515i | −0.135830 | + | 0.135830i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.647551 | + | 0.647551i | −0.0276873 | + | 0.0276873i | −0.720815 | − | 0.693128i | \(-0.756232\pi\) |
0.693128 | + | 0.720815i | \(0.256232\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −24.9717 | −1.06577 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 18.3303i | − | 0.780897i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 33.4955 | + | 33.4955i | 1.42437 | + | 1.42437i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.2970 | − | 10.2970i | −0.436296 | − | 0.436296i | 0.454467 | − | 0.890763i | \(-0.349830\pi\) |
−0.890763 | + | 0.454467i | \(0.849830\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28.7477 | −1.21590 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.0000 | −0.506640 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.3133 | − | 14.3133i | −0.603232 | − | 0.603232i | 0.337937 | − | 0.941169i | \(-0.390271\pi\) |
−0.941169 | + | 0.337937i | \(0.890271\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −15.1216 | − | 15.1216i | −0.635047 | − | 0.635047i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 4.74773i | − | 0.199035i | −0.995036 | − | 0.0995175i | \(-0.968270\pi\) | ||
0.995036 | − | 0.0995175i | \(-0.0317299\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.4002 | −1.64885 | −0.824424 | − | 0.565973i | \(-0.808501\pi\) | ||||
−0.824424 | + | 0.565973i | \(0.808501\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.20520 | + | 6.20520i | −0.259226 | + | 0.259226i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.7477 | − | 11.7477i | 0.489064 | − | 0.489064i | −0.418947 | − | 0.908011i | \(-0.637601\pi\) |
0.908011 | + | 0.418947i | \(0.137601\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.9427i | 0.537881i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 26.9898i | − | 1.11973i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.5826 | − | 11.5826i | 0.479701 | − | 0.479701i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.3604 | + | 28.3604i | −1.17056 | + | 1.17056i | −0.188481 | + | 0.982077i | \(0.560356\pi\) |
−0.982077 | + | 0.188481i | \(0.939644\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.48220 | 0.225890 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.41742i | 0.0994395i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.165151 | − | 0.165151i | −0.00678195 | − | 0.00678195i | 0.703708 | − | 0.710490i | \(-0.251526\pi\) |
−0.710490 | + | 0.703708i | \(0.751526\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.82740 | + | 1.82740i | 0.0747905 | + | 0.0747905i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 42.3303 | 1.72957 | 0.864785 | − | 0.502143i | \(-0.167455\pi\) | ||||
0.864785 | + | 0.502143i | \(0.167455\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.74773 | −0.112082 | −0.0560411 | − | 0.998428i | \(-0.517848\pi\) | ||||
−0.0560411 | + | 0.998428i | \(0.517848\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 21.4322 | + | 21.4322i | 0.872785 | + | 0.872785i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.37386 | + | 6.37386i | 0.258707 | + | 0.258707i | 0.824528 | − | 0.565821i | \(-0.191441\pi\) |
−0.565821 | + | 0.824528i | \(0.691441\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 13.4955i | 0.546863i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.74110 | 0.110893 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.66025 | + | 8.66025i | −0.349784 | + | 0.349784i | −0.860029 | − | 0.510245i | \(-0.829555\pi\) |
0.510245 | + | 0.860029i | \(0.329555\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.00000 | + | 3.00000i | −0.120775 | + | 0.120775i | −0.764911 | − | 0.644136i | \(-0.777217\pi\) |
0.644136 | + | 0.764911i | \(0.277217\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.7309i | 1.19499i | 0.801874 | + | 0.597493i | \(0.203836\pi\) | ||||
−0.801874 | + | 0.597493i | \(0.796164\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.03620i | 0.161967i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.83485 | + | 8.83485i | −0.353961 | + | 0.353961i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.92820 | + | 6.92820i | −0.276686 | + | 0.276686i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 31.1769 | 1.24310 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 47.0780i | 1.87415i | 0.349132 | + | 0.937073i | \(0.386476\pi\) | ||||
−0.349132 | + | 0.937073i | \(0.613524\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.49545 | − | 3.49545i | −0.138932 | − | 0.138932i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.8655 | − | 14.8655i | −0.588991 | − | 0.588991i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 35.0780 | 1.38767 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.9129 | 1.02350 | 0.511749 | − | 0.859135i | \(-0.328998\pi\) | ||||
0.511749 | + | 0.859135i | \(0.328998\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.6911 | − | 18.6911i | −0.737103 | − | 0.737103i | 0.234913 | − | 0.972016i | \(-0.424519\pi\) |
−0.972016 | + | 0.234913i | \(0.924519\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.460985 | + | 0.460985i | 0.0181232 | + | 0.0181232i | 0.716110 | − | 0.697987i | \(-0.245921\pi\) |
−0.697987 | + | 0.716110i | \(0.745921\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23.1652i | 0.909312i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.03620 | −0.158191 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.4014 | + | 11.4014i | −0.446170 | + | 0.446170i | −0.894079 | − | 0.447909i | \(-0.852169\pi\) |
0.447909 | + | 0.894079i | \(0.352169\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.50455 | + | 1.50455i | −0.0586979 | + | 0.0586979i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.84550i | 0.149800i | 0.997191 | + | 0.0748998i | \(0.0238637\pi\) | ||||
−0.997191 | + | 0.0748998i | \(0.976136\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.4183i | 1.61099i | 0.592605 | + | 0.805493i | \(0.298099\pi\) | ||||
−0.592605 | + | 0.805493i | \(0.701901\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.74773 | + | 4.74773i | −0.184386 | + | 0.184386i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.18710 | + | 4.18710i | −0.162125 | + | 0.162125i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.3060 | −0.437115 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 42.3303i | 1.63414i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.5826 | + | 18.5826i | 0.716306 | + | 0.716306i | 0.967847 | − | 0.251541i | \(-0.0809373\pi\) |
−0.251541 | + | 0.967847i | \(0.580937\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.3296 | − | 18.3296i | −0.704462 | − | 0.704462i | 0.260903 | − | 0.965365i | \(-0.415980\pi\) |
−0.965365 | + | 0.260903i | \(0.915980\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.25227 | −0.124811 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.08712 | −0.233259 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.85275 | + | 6.85275i | 0.262213 | + | 0.262213i | 0.825953 | − | 0.563739i | \(-0.190638\pi\) |
−0.563739 | + | 0.825953i | \(0.690638\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.58258 | − | 1.58258i | −0.0603790 | − | 0.0603790i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 9.16515i | − | 0.349164i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.4720 | 1.23529 | 0.617647 | − | 0.786456i | \(-0.288086\pi\) | ||||
0.617647 | + | 0.786456i | \(0.288086\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −31.5583 | + | 31.5583i | −1.19880 | + | 1.19880i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.7477 | − | 22.7477i | 0.861632 | − | 0.861632i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.63310i | 0.213063i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.8709i | 0.750514i | 0.926921 | + | 0.375257i | \(0.122446\pi\) | ||||
−0.926921 | + | 0.375257i | \(0.877554\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.0000 | − | 18.0000i | 0.678883 | − | 0.678883i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.2016 | + | 10.2016i | −0.383671 | + | 0.383671i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.91010 | 0.184403 | 0.0922014 | − | 0.995740i | \(-0.470610\pi\) | ||||
0.0922014 | + | 0.995740i | \(0.470610\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 30.9909i | − | 1.16225i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.25227 | − | 1.25227i | −0.0468980 | − | 0.0468980i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.44600 | − | 1.44600i | −0.0540019 | − | 0.0540019i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 39.8258 | 1.48525 | 0.742625 | − | 0.669707i | \(-0.233580\pi\) | ||||
0.742625 | + | 0.669707i | \(0.233580\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −57.9129 | −2.15679 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.91010 | + | 4.91010i | 0.182609 | + | 0.182609i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.95644 | + | 5.95644i | 0.220912 | + | 0.220912i | 0.808882 | − | 0.587970i | \(-0.200073\pi\) |
−0.587970 | + | 0.808882i | \(0.700073\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.00000i | 0.259259i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −49.7925 | −1.84164 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.6066 | + | 17.6066i | −0.650313 | + | 0.650313i | −0.953068 | − | 0.302755i | \(-0.902094\pi\) |
0.302755 | + | 0.953068i | \(0.402094\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 36.3303 | − | 36.3303i | 1.33824 | − | 1.33824i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 2.01810i | − | 0.0742371i | −0.999311 | − | 0.0371185i | \(-0.988182\pi\) | ||
0.999311 | − | 0.0371185i | \(-0.0118179\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.48220i | 0.201394i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.2087 | − | 17.2087i | 0.631326 | − | 0.631326i | −0.317074 | − | 0.948401i | \(-0.602700\pi\) |
0.948401 | + | 0.317074i | \(0.102700\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.4859 | + | 12.4859i | −0.456834 | + | 0.456834i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −46.3284 | −1.69280 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.0780i | 0.842129i | 0.907031 | + | 0.421065i | \(0.138343\pi\) | ||||
−0.907031 | + | 0.421065i | \(0.861657\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.33030 | − | 8.33030i | −0.303573 | − | 0.303573i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.3477 | − | 20.3477i | −0.739548 | − | 0.739548i | 0.232942 | − | 0.972491i | \(-0.425165\pi\) |
−0.972491 | + | 0.232942i | \(0.925165\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.16515 | 0.114888 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.00000 | 0.217500 | 0.108750 | − | 0.994069i | \(-0.465315\pi\) | ||||
0.108750 | + | 0.994069i | \(0.465315\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.3205 | + | 17.3205i | 0.627044 | + | 0.627044i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.16515 | + | 9.16515i | 0.330934 | + | 0.330934i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 37.4955i | − | 1.35212i | −0.736846 | − | 0.676060i | \(-0.763686\pi\) | ||
0.736846 | − | 0.676060i | \(-0.236314\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.0435 | −0.649821 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.286051 | + | 0.286051i | −0.0102885 | + | 0.0102885i | −0.712232 | − | 0.701944i | \(-0.752316\pi\) |
0.701944 | + | 0.712232i | \(0.252316\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13.2523 | + | 13.2523i | −0.475423 | + | 0.475423i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 26.2668i | − | 0.941106i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 59.4618i | − | 2.12771i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 13.4955 | − | 13.4955i | 0.482288 | − | 0.482288i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.7092 | + | 20.7092i | −0.738202 | + | 0.738202i | −0.972230 | − | 0.234028i | \(-0.924809\pi\) |
0.234028 | + | 0.972230i | \(0.424809\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 17.1696 | 0.611254 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 25.5826i | 0.909612i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.7477 | + | 16.7477i | 0.594729 | + | 0.594729i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −34.9271 | − | 34.9271i | −1.23718 | − | 1.23718i | −0.961149 | − | 0.276032i | \(-0.910981\pi\) |
−0.276032 | − | 0.961149i | \(-0.589019\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.74773 | 0.167963 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.17424 | 0.288823 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.55040 | + | 2.55040i | 0.0900017 | + | 0.0900017i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.8348 | − | 10.8348i | −0.381405 | − | 0.381405i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30.3303i | 1.06636i | 0.846003 | + | 0.533178i | \(0.179003\pi\) | ||||
−0.846003 | + | 0.533178i | \(0.820997\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.16900 | −0.0761639 | −0.0380820 | − | 0.999275i | \(-0.512125\pi\) | ||||
−0.0380820 | + | 0.999275i | \(0.512125\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.99640 | + | 3.99640i | −0.140160 | + | 0.140160i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28.7477 | + | 28.7477i | −1.00576 | + | 1.00576i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 24.9717i | 0.872582i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 54.8933i | − | 1.91579i | −0.287118 | − | 0.957895i | \(-0.592697\pi\) | ||
0.287118 | − | 0.957895i | \(-0.407303\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.20871 | + | 3.20871i | −0.111849 | + | 0.111849i | −0.760816 | − | 0.648967i | \(-0.775201\pi\) |
0.648967 | + | 0.760816i | \(0.275201\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.1226 | + | 14.1226i | −0.491089 | + | 0.491089i | −0.908649 | − | 0.417560i | \(-0.862885\pi\) |
0.417560 | + | 0.908649i | \(0.362885\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.65120 | −0.265737 | −0.132869 | − | 0.991134i | \(-0.542419\pi\) | ||||
−0.132869 | + | 0.991134i | \(0.542419\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 5.40833i | − | 0.187613i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −25.7477 | − | 25.7477i | −0.892106 | − | 0.892106i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.03620 | + | 4.03620i | 0.139512 | + | 0.139512i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.3303 | −1.04712 | −0.523559 | − | 0.851989i | \(-0.675396\pi\) | ||||
−0.523559 | + | 0.851989i | \(0.675396\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.00000 | −0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.91010 | + | 4.91010i | 0.169113 | + | 0.169113i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.7913 | + | 22.7913i | 0.783118 | + | 0.783118i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.7568i | 0.540773i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.22330 | −0.281891 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.9452 | − | 36.9452i | 1.26498 | − | 1.26498i | 0.316329 | − | 0.948650i | \(-0.397550\pi\) |
0.948650 | − | 0.316329i | \(-0.102450\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −39.3303 | + | 39.3303i | −1.34350 | + | 1.34350i | −0.450947 | + | 0.892551i | \(0.648914\pi\) |
−0.892551 | + | 0.450947i | \(0.851086\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.01810i | 0.0688567i | 0.999407 | + | 0.0344284i | \(0.0109611\pi\) | ||||
−0.999407 | + | 0.0344284i | \(0.989039\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 19.3386i | 0.659058i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.7042 | + | 32.7042i | −1.11326 | + | 1.11326i | −0.120556 | + | 0.992706i | \(0.538468\pi\) |
−0.992706 | + | 0.120556i | \(0.961532\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.456850 | + | 0.456850i | −0.0155154 | + | 0.0155154i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −52.5336 | −1.78208 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 28.7477i | − | 0.974080i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.50455 | + | 1.50455i | 0.0509212 | + | 0.0509212i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.7756 | + | 19.7756i | 0.667773 | + | 0.667773i | 0.957200 | − | 0.289427i | \(-0.0934647\pi\) |
−0.289427 | + | 0.957200i | \(0.593465\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −21.4083 | −0.722085 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −55.5826 | −1.87262 | −0.936312 | − | 0.351169i | \(-0.885784\pi\) | ||||
−0.936312 | + | 0.351169i | \(0.885784\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.1552 | + | 22.1552i | 0.745581 | + | 0.745581i | 0.973646 | − | 0.228065i | \(-0.0732400\pi\) |
−0.228065 | + | 0.973646i | \(0.573240\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.9564 | + | 21.9564i | 0.737225 | + | 0.737225i | 0.972040 | − | 0.234815i | \(-0.0754484\pi\) |
−0.234815 | + | 0.972040i | \(0.575448\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 6.74773i | − | 0.226312i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23.7164 | 0.794530 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.74110 | − | 2.74110i | 0.0917275 | − | 0.0917275i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.25227 | − | 1.25227i | 0.0418122 | − | 0.0418122i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.37420i | 0.279295i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 15.8745i | − | 0.528857i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 21.1652 | − | 21.1652i | 0.704332 | − | 0.704332i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.0399 | − | 11.0399i | 0.366572 | − | 0.366572i | −0.499653 | − | 0.866226i | \(-0.666539\pi\) |
0.866226 | + | 0.499653i | \(0.166539\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.43880 | 0.313065 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 49.5826i | − | 1.64274i | −0.570393 | − | 0.821372i | \(-0.693209\pi\) | ||
0.570393 | − | 0.821372i | \(-0.306791\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.1652 | + | 21.1652i | 0.700464 | + | 0.700464i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −31.5583 | − | 31.5583i | −1.04215 | − | 1.04215i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.3303 | 1.39635 | 0.698174 | − | 0.715928i | \(-0.253996\pi\) | ||||
0.698174 | + | 0.715928i | \(0.253996\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.25227 | 0.0412638 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −23.5257 | − | 23.5257i | −0.774358 | − | 0.774358i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 26.7913 | + | 26.7913i | 0.879941 | + | 0.879941i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 19.9129i | − | 0.653320i | −0.945142 | − | 0.326660i | \(-0.894077\pi\) | ||
0.945142 | − | 0.326660i | \(-0.105923\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −29.7309 | −0.974391 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.75920 | − | 4.75920i | 0.155809 | − | 0.155809i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.1652 | + | 34.1652i | −1.11613 | + | 1.11613i | −0.123822 | + | 0.992304i | \(0.539515\pi\) |
−0.992304 | + | 0.123822i | \(0.960485\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.35970i | 0.0770059i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 24.4394i | − | 0.796702i | −0.917233 | − | 0.398351i | \(-0.869583\pi\) | ||
0.917233 | − | 0.398351i | \(-0.130417\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.00000 | + | 6.00000i | −0.195387 | + | 0.195387i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.6947 | − | 14.6947i | 0.477512 | − | 0.477512i | −0.426823 | − | 0.904335i | \(-0.640367\pi\) |
0.904335 | + | 0.426823i | \(0.140367\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.01810 | 0.0655103 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 16.0871i | − | 0.521661i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.9129 | + | 10.9129i | 0.353503 | + | 0.353503i | 0.861411 | − | 0.507908i | \(-0.169581\pi\) |
−0.507908 | + | 0.861411i | \(0.669581\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.5830 | − | 10.5830i | −0.342100 | − | 0.342100i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −67.9129 | −2.19302 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.4955 | 0.919208 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 21.4322 | + | 21.4322i | 0.690642 | + | 0.690642i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.79129 | − | 8.79129i | −0.282709 | − | 0.282709i | 0.551480 | − | 0.834188i | \(-0.314063\pi\) |
−0.834188 | + | 0.551480i | \(0.814063\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.49545i | 0.305038i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37.5728 | −1.20577 | −0.602885 | − | 0.797828i | \(-0.705982\pi\) | ||||
−0.602885 | + | 0.797828i | \(0.705982\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.9717 | + | 24.9717i | −0.800556 | + | 0.800556i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28.5826 | + | 28.5826i | −0.914438 | + | 0.914438i | −0.996618 | − | 0.0821799i | \(-0.973812\pi\) |
0.0821799 | + | 0.996618i | \(0.473812\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 13.8564i | − | 0.442853i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 16.0254i | − | 0.511652i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.7042 | − | 26.7042i | 0.851731 | − | 0.851731i | −0.138616 | − | 0.990346i | \(-0.544265\pi\) |
0.990346 | + | 0.138616i | \(0.0442653\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.01810 | + | 2.01810i | −0.0642369 | + | 0.0642369i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.1334 | 0.417618 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.25227i | 0.103312i | 0.998665 | + | 0.0516559i | \(0.0164499\pi\) | ||||
−0.998665 | + | 0.0516559i | \(0.983550\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.83485 | − | 2.83485i | −0.0899612 | − | 0.0899612i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.6066 | + | 17.6066i | 0.557605 | + | 0.557605i | 0.928625 | − | 0.371020i | \(-0.120992\pi\) |
−0.371020 | + | 0.928625i | \(0.620992\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 26.5045 | 0.838567 |
(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 | 1600.2.o.l.543.2 | 8 | ||
4.3 | odd | 2 | 1600.2.o.e.543.3 | 8 | |||
5.2 | odd | 4 | 1600.2.o.e.607.2 | 8 | |||
5.3 | odd | 4 | 320.2.o.f.287.3 | yes | 8 | ||
5.4 | even | 2 | 320.2.o.e.223.3 | yes | 8 | ||
8.3 | odd | 2 | 1600.2.o.e.543.2 | 8 | |||
8.5 | even | 2 | inner | 1600.2.o.l.543.3 | 8 | ||
20.3 | even | 4 | 320.2.o.e.287.2 | yes | 8 | ||
20.7 | even | 4 | inner | 1600.2.o.l.607.3 | 8 | ||
20.19 | odd | 2 | 320.2.o.f.223.2 | yes | 8 | ||
40.3 | even | 4 | 320.2.o.e.287.3 | yes | 8 | ||
40.13 | odd | 4 | 320.2.o.f.287.2 | yes | 8 | ||
40.19 | odd | 2 | 320.2.o.f.223.3 | yes | 8 | ||
40.27 | even | 4 | inner | 1600.2.o.l.607.2 | 8 | ||
40.29 | even | 2 | 320.2.o.e.223.2 | ✓ | 8 | ||
40.37 | odd | 4 | 1600.2.o.e.607.3 | 8 | |||
80.3 | even | 4 | 1280.2.n.p.767.2 | 8 | |||
80.13 | odd | 4 | 1280.2.n.n.767.3 | 8 | |||
80.19 | odd | 4 | 1280.2.n.n.1023.3 | 8 | |||
80.29 | even | 4 | 1280.2.n.p.1023.2 | 8 | |||
80.43 | even | 4 | 1280.2.n.p.767.3 | 8 | |||
80.53 | odd | 4 | 1280.2.n.n.767.2 | 8 | |||
80.59 | odd | 4 | 1280.2.n.n.1023.2 | 8 | |||
80.69 | even | 4 | 1280.2.n.p.1023.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
320.2.o.e.223.2 | ✓ | 8 | 40.29 | even | 2 | ||
320.2.o.e.223.3 | yes | 8 | 5.4 | even | 2 | ||
320.2.o.e.287.2 | yes | 8 | 20.3 | even | 4 | ||
320.2.o.e.287.3 | yes | 8 | 40.3 | even | 4 | ||
320.2.o.f.223.2 | yes | 8 | 20.19 | odd | 2 | ||
320.2.o.f.223.3 | yes | 8 | 40.19 | odd | 2 | ||
320.2.o.f.287.2 | yes | 8 | 40.13 | odd | 4 | ||
320.2.o.f.287.3 | yes | 8 | 5.3 | odd | 4 | ||
1280.2.n.n.767.2 | 8 | 80.53 | odd | 4 | |||
1280.2.n.n.767.3 | 8 | 80.13 | odd | 4 | |||
1280.2.n.n.1023.2 | 8 | 80.59 | odd | 4 | |||
1280.2.n.n.1023.3 | 8 | 80.19 | odd | 4 | |||
1280.2.n.p.767.2 | 8 | 80.3 | even | 4 | |||
1280.2.n.p.767.3 | 8 | 80.43 | even | 4 | |||
1280.2.n.p.1023.2 | 8 | 80.29 | even | 4 | |||
1280.2.n.p.1023.3 | 8 | 80.69 | even | 4 | |||
1600.2.o.e.543.2 | 8 | 8.3 | odd | 2 | |||
1600.2.o.e.543.3 | 8 | 4.3 | odd | 2 | |||
1600.2.o.e.607.2 | 8 | 5.2 | odd | 4 | |||
1600.2.o.e.607.3 | 8 | 40.37 | odd | 4 | |||
1600.2.o.l.543.2 | 8 | 1.1 | even | 1 | trivial | ||
1600.2.o.l.543.3 | 8 | 8.5 | even | 2 | inner | ||
1600.2.o.l.607.2 | 8 | 40.27 | even | 4 | inner | ||
1600.2.o.l.607.3 | 8 | 20.7 | even | 4 | inner |