Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1500,2,Mod(301,1500)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1500, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1500.301");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1500.m (of order \(5\), degree \(4\), not 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: | \(11.9775603032\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{5})\) |
Twist minimal: | no (minimal twist has level 300) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 601.1 | ||
Character | \(\chi\) | \(=\) | 1500.601 |
Dual form | 1500.2.m.c.901.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times\).
\(n\) | \(751\) | \(877\) | \(1001\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.809017 | − | 0.587785i | −0.467086 | − | 0.339358i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.13266 | −1.56200 | −0.780999 | − | 0.624532i | \(-0.785290\pi\) | ||||
−0.780999 | + | 0.624532i | \(0.785290\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.309017 | + | 0.951057i | 0.103006 | + | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.16386 | + | 3.58198i | −0.350916 | + | 1.08001i | 0.607424 | + | 0.794378i | \(0.292203\pi\) |
−0.958340 | + | 0.285630i | \(0.907797\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.215899 | − | 0.664470i | −0.0598797 | − | 0.184291i | 0.916642 | − | 0.399709i | \(-0.130889\pi\) |
−0.976522 | + | 0.215418i | \(0.930889\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.28173 | − | 3.11086i | 1.03847 | − | 0.754494i | 0.0684847 | − | 0.997652i | \(-0.478184\pi\) |
0.969987 | + | 0.243159i | \(0.0781836\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.63966 | + | 3.37091i | −1.06441 | + | 0.773340i | −0.974899 | − | 0.222646i | \(-0.928531\pi\) |
−0.0895120 | + | 0.995986i | \(0.528531\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.34339 | + | 2.42912i | 0.729588 | + | 0.530077i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.68924 | − | 5.19894i | 0.352231 | − | 1.08405i | −0.605367 | − | 0.795946i | \(-0.706974\pi\) |
0.957598 | − | 0.288108i | \(-0.0930263\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.309017 | − | 0.951057i | 0.0594703 | − | 0.183031i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.68284 | + | 4.12883i | 1.05528 | + | 0.766704i | 0.973209 | − | 0.229923i | \(-0.0738474\pi\) |
0.0820685 | + | 0.996627i | \(0.473847\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.16460 | − | 5.93193i | 1.46641 | − | 1.06541i | 0.484769 | − | 0.874642i | \(-0.338904\pi\) |
0.981636 | − | 0.190764i | \(-0.0610964\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.04701 | − | 2.21379i | 0.530417 | − | 0.385371i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.78763 | + | 5.50175i | 0.293884 | + | 0.904482i | 0.983594 | + | 0.180396i | \(0.0577381\pi\) |
−0.689710 | + | 0.724086i | \(0.742262\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.215899 | + | 0.664470i | −0.0345716 | + | 0.106400i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.03813 | − | 6.27271i | −0.318302 | − | 0.979633i | −0.974374 | − | 0.224935i | \(-0.927783\pi\) |
0.656072 | − | 0.754698i | \(-0.272217\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.79668 | 0.731488 | 0.365744 | − | 0.930716i | \(-0.380815\pi\) | ||||
0.365744 | + | 0.930716i | \(0.380815\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.82626 | − | 5.68611i | −1.14158 | − | 0.829405i | −0.154239 | − | 0.988033i | \(-0.549293\pi\) |
−0.987338 | + | 0.158629i | \(0.949293\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.0789 | 1.43984 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.29251 | −0.741099 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.74773 | + | 1.99634i | 0.377429 | + | 0.274219i | 0.760285 | − | 0.649590i | \(-0.225059\pi\) |
−0.382856 | + | 0.923808i | \(0.625059\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.73494 | 0.759611 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.230309 | + | 0.708820i | 0.0299837 | + | 0.0922804i | 0.964928 | − | 0.262513i | \(-0.0845512\pi\) |
−0.934945 | + | 0.354793i | \(0.884551\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.64886 | − | 11.2300i | 0.467188 | − | 1.43786i | −0.389021 | − | 0.921229i | \(-0.627187\pi\) |
0.856210 | − | 0.516629i | \(-0.172813\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.27706 | − | 3.93039i | −0.160895 | − | 0.495183i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.88133 | − | 2.81995i | 0.474180 | − | 0.344512i | −0.324888 | − | 0.945752i | \(-0.605327\pi\) |
0.799068 | + | 0.601241i | \(0.205327\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.42248 | + | 3.21312i | −0.532405 | + | 0.386815i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.54239 | + | 1.84715i | 0.301726 | + | 0.219217i | 0.728338 | − | 0.685218i | \(-0.240293\pi\) |
−0.426612 | + | 0.904435i | \(0.640293\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.32110 | − | 10.2213i | 0.388706 | − | 1.19631i | −0.545051 | − | 0.838403i | \(-0.683490\pi\) |
0.933756 | − | 0.357910i | \(-0.116510\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.80982 | − | 14.8031i | 0.548130 | − | 1.68697i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.38222 | + | 5.36349i | 0.830564 | + | 0.603440i | 0.919719 | − | 0.392578i | \(-0.128417\pi\) |
−0.0891546 | + | 0.996018i | \(0.528417\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.82889 | + | 4.96148i | −0.749569 | + | 0.544593i | −0.895693 | − | 0.444673i | \(-0.853320\pi\) |
0.146125 | + | 0.989266i | \(0.453320\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.17065 | − | 6.68058i | −0.232718 | − | 0.716234i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.04690 | + | 3.22202i | −0.110971 | + | 0.341533i | −0.991085 | − | 0.133228i | \(-0.957466\pi\) |
0.880114 | + | 0.474761i | \(0.157466\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.892239 | + | 2.74603i | 0.0935321 | + | 0.287862i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.0920 | −1.04649 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.44215 | − | 6.13358i | −0.857170 | − | 0.622771i | 0.0699435 | − | 0.997551i | \(-0.477718\pi\) |
−0.927114 | + | 0.374780i | \(0.877718\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.76632 | −0.378529 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.10799 | 0.707272 | 0.353636 | − | 0.935383i | \(-0.384945\pi\) | ||||
0.353636 | + | 0.935383i | \(0.384945\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.87733 | + | 7.17630i | 0.973243 | + | 0.707102i | 0.956188 | − | 0.292752i | \(-0.0945712\pi\) |
0.0170543 | + | 0.999855i | \(0.494571\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.04303 | 0.390855 | 0.195427 | − | 0.980718i | \(-0.437391\pi\) | ||||
0.195427 | + | 0.980718i | \(0.437391\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.239122 | − | 0.735942i | −0.0229037 | − | 0.0704904i | 0.938951 | − | 0.344050i | \(-0.111799\pi\) |
−0.961855 | + | 0.273560i | \(0.911799\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.78763 | − | 5.50175i | 0.169674 | − | 0.522203i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.352104 | + | 1.08366i | 0.0331231 | + | 0.101943i | 0.966251 | − | 0.257602i | \(-0.0829322\pi\) |
−0.933128 | + | 0.359544i | \(0.882932\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.565232 | − | 0.410665i | 0.0522557 | − | 0.0379660i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −17.6949 | + | 12.8561i | −1.62209 | + | 1.17852i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.57684 | − | 1.87218i | −0.234258 | − | 0.170198i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.03813 | + | 6.27271i | −0.183772 | + | 0.565591i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.166210 | + | 0.511543i | −0.0147488 | + | 0.0453921i | −0.958160 | − | 0.286233i | \(-0.907597\pi\) |
0.943411 | + | 0.331625i | \(0.107597\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.88060 | − | 2.81942i | −0.341668 | − | 0.248236i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.43855 | − | 3.95134i | 0.475169 | − | 0.345230i | −0.324284 | − | 0.945960i | \(-0.605123\pi\) |
0.799452 | + | 0.600730i | \(0.205123\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.1741 | − | 13.9308i | 1.66261 | − | 1.20796i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.0566672 | − | 0.174404i | −0.00484140 | − | 0.0149003i | 0.948607 | − | 0.316458i | \(-0.102494\pi\) |
−0.953448 | + | 0.301557i | \(0.902494\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.54014 | − | 7.81775i | 0.215452 | − | 0.663093i | −0.783669 | − | 0.621178i | \(-0.786654\pi\) |
0.999121 | − | 0.0419144i | \(-0.0133457\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.98937 | + | 9.20032i | 0.251750 | + | 0.774807i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.63140 | 0.220048 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.15398 | − | 5.92421i | −0.672529 | − | 0.488621i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.53790 | 0.453682 | 0.226841 | − | 0.973932i | \(-0.427160\pi\) | ||||
0.226841 | + | 0.973932i | \(0.427160\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.8736 | 1.04764 | 0.523821 | − | 0.851828i | \(-0.324506\pi\) | ||||
0.523821 | + | 0.851828i | \(0.324506\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.28173 | + | 3.11086i | 0.346157 | + | 0.251498i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.6395 | 1.16836 | 0.584179 | − | 0.811625i | \(-0.301417\pi\) | ||||
0.584179 | + | 0.811625i | \(0.301417\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.04954 | − | 3.23015i | −0.0832338 | − | 0.256167i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.98105 | + | 21.4855i | −0.550184 | + | 1.69329i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.37334 | + | 4.22672i | 0.107569 | + | 0.331062i | 0.990325 | − | 0.138769i | \(-0.0443146\pi\) |
−0.882756 | + | 0.469832i | \(0.844315\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.2267 | + | 13.9690i | −1.48780 | + | 1.08095i | −0.512869 | + | 0.858467i | \(0.671417\pi\) |
−0.974936 | + | 0.222487i | \(0.928583\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.1223 | − | 7.35429i | 0.778639 | − | 0.565715i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.63966 | − | 3.37091i | −0.354804 | − | 0.257780i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.66207 | − | 14.3484i | 0.354451 | − | 1.09089i | −0.601877 | − | 0.798589i | \(-0.705580\pi\) |
0.956327 | − | 0.292298i | \(-0.0944198\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.230309 | − | 0.708820i | 0.0173111 | − | 0.0532781i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.5238 | − | 9.82561i | −1.01082 | − | 0.734401i | −0.0464356 | − | 0.998921i | \(-0.514786\pi\) |
−0.964380 | + | 0.264521i | \(0.914786\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.40755 | + | 6.10844i | −0.624928 | + | 0.454037i | −0.854639 | − | 0.519222i | \(-0.826222\pi\) |
0.229711 | + | 0.973259i | \(0.426222\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.55283 | + | 6.94054i | −0.706166 | + | 0.513059i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.15971 | + | 18.9576i | 0.450443 | + | 1.38632i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.27706 | + | 3.93039i | −0.0928926 | + | 0.285894i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.10485 | − | 18.7888i | −0.441732 | − | 1.35951i | −0.886029 | − | 0.463631i | \(-0.846546\pi\) |
0.444297 | − | 0.895880i | \(-0.353454\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.23549 | 0.160914 | 0.0804571 | − | 0.996758i | \(-0.474362\pi\) | ||||
0.0804571 | + | 0.996758i | \(0.474362\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.4106 | + | 13.3761i | 1.31170 | + | 0.953008i | 0.999996 | + | 0.00282909i | \(0.000900528\pi\) |
0.311706 | + | 0.950178i | \(0.399099\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.8171 | 1.61746 | 0.808731 | − | 0.588179i | \(-0.200155\pi\) | ||||
0.808731 | + | 0.588179i | \(0.200155\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.79759 | −0.338396 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −23.4853 | − | 17.0630i | −1.64834 | − | 1.19759i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.46649 | 0.379947 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.67464 | − | 20.5424i | −0.461695 | − | 1.42095i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.21019 | − | 19.1130i | 0.427527 | − | 1.31579i | −0.473027 | − | 0.881048i | \(-0.656839\pi\) |
0.900554 | − | 0.434745i | \(-0.143161\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.971105 | − | 2.98875i | −0.0665390 | − | 0.204786i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −33.7415 | + | 24.5146i | −2.29052 | + | 1.66416i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.69476 | + | 6.31711i | −0.587537 | + | 0.426871i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.99149 | − | 2.17345i | −0.201230 | − | 0.146202i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.14665 | + | 12.7621i | −0.277680 | + | 0.854612i | 0.710817 | + | 0.703377i | \(0.248325\pi\) |
−0.988498 | + | 0.151236i | \(0.951675\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.71411 | − | 17.5862i | 0.379259 | − | 1.16724i | −0.561301 | − | 0.827612i | \(-0.689699\pi\) |
0.940560 | − | 0.339628i | \(-0.110301\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.7050 | + | 11.4104i | 1.03782 | + | 0.754017i | 0.969858 | − | 0.243671i | \(-0.0783516\pi\) |
0.0679579 | + | 0.997688i | \(0.478352\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.5923 | + | 9.14882i | −0.828511 | + | 0.601948i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.85646 | + | 7.16114i | −0.645718 | + | 0.469142i | −0.861810 | − | 0.507231i | \(-0.830669\pi\) |
0.216092 | + | 0.976373i | \(0.430669\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.81976 | − | 8.67832i | −0.183163 | − | 0.563717i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.39823 | − | 4.30330i | 0.0904438 | − | 0.278357i | −0.895596 | − | 0.444869i | \(-0.853250\pi\) |
0.986040 | + | 0.166512i | \(0.0532503\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.78479 | + | 8.57071i | 0.179384 | + | 0.552088i | 0.999807 | − | 0.0196702i | \(-0.00626163\pi\) |
−0.820422 | + | 0.571758i | \(0.806262\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.24157 | + | 2.35514i | 0.206256 | + | 0.149854i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.44098 | 0.534925 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.16965 | 0.200066 | 0.100033 | − | 0.994984i | \(-0.468105\pi\) | ||||
0.100033 | + | 0.994984i | \(0.468105\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.6565 | + | 12.1016i | 1.04718 | + | 0.760824i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.25241 | −0.202880 | −0.101440 | − | 0.994842i | \(-0.532345\pi\) | ||||
−0.101440 | + | 0.994842i | \(0.532345\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.38766 | − | 22.7369i | −0.459047 | − | 1.41280i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.17065 | + | 6.68058i | −0.134360 | + | 0.413518i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.41774 | + | 10.5187i | 0.210747 | + | 0.648612i | 0.999428 | + | 0.0338097i | \(0.0107640\pi\) |
−0.788682 | + | 0.614802i | \(0.789236\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.74081 | − | 1.99132i | 0.167735 | − | 0.121867i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −20.0279 | + | 14.5511i | −1.22112 | + | 0.887197i | −0.996193 | − | 0.0871780i | \(-0.972215\pi\) |
−0.224929 | + | 0.974375i | \(0.572215\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.202420 | − | 0.147067i | −0.0122962 | − | 0.00893369i | 0.581620 | − | 0.813460i | \(-0.302419\pi\) |
−0.593916 | + | 0.804527i | \(0.702419\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.892239 | − | 2.74603i | 0.0540008 | − | 0.166197i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.74121 | + | 8.43658i | −0.164703 | + | 0.506905i | −0.999014 | − | 0.0443894i | \(-0.985866\pi\) |
0.834311 | + | 0.551294i | \(0.185866\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.16460 | + | 5.93193i | 0.488802 | + | 0.355135i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.9683 | + | 11.6016i | −0.952588 | + | 0.692096i | −0.951418 | − | 0.307904i | \(-0.900373\pi\) |
−0.00117050 | + | 0.999999i | \(0.500373\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.3919 | + | 15.5421i | −1.27162 | + | 0.923882i | −0.999266 | − | 0.0383159i | \(-0.987801\pi\) |
−0.272349 | + | 0.962198i | \(0.587801\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.42289 | + | 25.9230i | 0.497187 | + | 1.53019i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.40247 | − | 10.4717i | 0.200145 | − | 0.615983i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.22461 | + | 9.92434i | 0.189030 | + | 0.581775i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.1882 | −1.12099 | −0.560494 | − | 0.828158i | \(-0.689389\pi\) | ||||
−0.560494 | + | 0.828158i | \(0.689389\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.04701 | + | 2.21379i | 0.176806 | + | 0.128457i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.81925 | −0.220873 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19.8231 | −1.14258 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.75049 | − | 4.17797i | −0.330357 | − | 0.240018i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.26979 | 0.529055 | 0.264527 | − | 0.964378i | \(-0.414784\pi\) | ||||
0.264527 | + | 0.964378i | \(0.414784\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.77281 | − | 11.6115i | −0.214627 | − | 0.660555i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.69255 | + | 23.6752i | −0.436204 | + | 1.34250i | 0.455643 | + | 0.890163i | \(0.349409\pi\) |
−0.891847 | + | 0.452336i | \(0.850591\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.86866 | − | 5.75115i | −0.105623 | − | 0.325074i | 0.884253 | − | 0.467008i | \(-0.154668\pi\) |
−0.989876 | + | 0.141934i | \(0.954668\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.6389 | − | 8.45614i | 0.653705 | − | 0.474944i | −0.210827 | − | 0.977523i | \(-0.567616\pi\) |
0.864531 | + | 0.502579i | \(0.167616\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −21.4034 | + | 15.5505i | −1.19836 | + | 0.870659i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.27088 | − | 2.37644i | −0.182563 | − | 0.132640i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.37934 | + | 28.8666i | −0.521881 | + | 1.60618i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.239122 | + | 0.735942i | −0.0132235 | + | 0.0406977i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 32.3433 | + | 23.4988i | 1.78314 | + | 1.29553i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.863126 | + | 0.627098i | −0.0474417 | + | 0.0344684i | −0.611253 | − | 0.791435i | \(-0.709334\pi\) |
0.563812 | + | 0.825903i | \(0.309334\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.68007 | + | 3.40027i | −0.256466 | + | 0.186334i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.51226 | − | 13.8873i | −0.245799 | − | 0.756490i | −0.995504 | − | 0.0947186i | \(-0.969805\pi\) |
0.749705 | − | 0.661772i | \(-0.230195\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.352104 | − | 1.08366i | 0.0191236 | − | 0.0588565i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.7456 | + | 36.1493i | 0.636062 | + | 1.95760i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.7239 | −0.687029 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.0618 | − | 9.48995i | −0.701194 | − | 0.509447i | 0.179127 | − | 0.983826i | \(-0.442673\pi\) |
−0.880321 | + | 0.474379i | \(0.842673\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.2622 | −1.19167 | −0.595834 | − | 0.803108i | \(-0.703178\pi\) | ||||
−0.595834 | + | 0.803108i | \(0.703178\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.698665 | −0.0372920 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.70991 | + | 5.60158i | 0.410357 | + | 0.298142i | 0.773746 | − | 0.633496i | \(-0.218381\pi\) |
−0.363389 | + | 0.931637i | \(0.618381\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 21.8721 | 1.15760 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.18753 | − | 15.9656i | −0.273788 | − | 0.842632i | −0.989538 | − | 0.144275i | \(-0.953915\pi\) |
0.715750 | − | 0.698357i | \(-0.246085\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.29210 | − | 13.2097i | 0.225900 | − | 0.695248i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.984264 | + | 3.02925i | 0.0516604 | + | 0.158995i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.2741 | + | 19.0893i | −1.37150 | + | 0.996452i | −0.373880 | + | 0.927477i | \(0.621973\pi\) |
−0.997618 | + | 0.0689751i | \(0.978027\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.33589 | − | 3.87675i | 0.277775 | − | 0.201815i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.3554 | − | 8.25020i | −0.589544 | − | 0.428329i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.41623 | + | 13.5918i | −0.228664 | + | 0.703755i | 0.769235 | + | 0.638966i | \(0.220637\pi\) |
−0.997899 | + | 0.0647890i | \(0.979363\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.51656 | − | 4.66749i | 0.0781068 | − | 0.240388i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.60155 | + | 1.89014i | 0.133633 | + | 0.0970897i | 0.652593 | − | 0.757708i | \(-0.273681\pi\) |
−0.518961 | + | 0.854798i | \(0.673681\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.435145 | − | 0.316151i | 0.0222931 | − | 0.0161969i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.99929 | − | 7.26491i | 0.510940 | − | 0.371220i | −0.302240 | − | 0.953232i | \(-0.597734\pi\) |
0.813180 | + | 0.582012i | \(0.197734\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.48226 | + | 4.56192i | 0.0753474 | + | 0.231895i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.14594 | − | 21.9930i | 0.362314 | − | 1.11509i | −0.589332 | − | 0.807891i | \(-0.700609\pi\) |
0.951646 | − | 0.307196i | \(-0.0993908\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.94031 | − | 27.5154i | −0.452131 | − | 1.39152i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.72242 | −0.339101 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.72179 | − | 1.25095i | −0.0864140 | − | 0.0627834i | 0.543739 | − | 0.839254i | \(-0.317008\pi\) |
−0.630153 | + | 0.776471i | \(0.717008\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −23.7005 | −1.18651 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −33.8250 | −1.68914 | −0.844569 | − | 0.535447i | \(-0.820143\pi\) | ||||
−0.844569 | + | 0.535447i | \(0.820143\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.70432 | − | 4.14443i | −0.284153 | − | 0.206449i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.7877 | −1.07998 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.7434 | − | 33.0647i | −0.531226 | − | 1.63495i | −0.751665 | − | 0.659545i | \(-0.770749\pi\) |
0.220439 | − | 0.975401i | \(-0.429251\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.0566672 | + | 0.174404i | −0.00279518 | + | 0.00860269i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.951790 | − | 2.92931i | −0.0468345 | − | 0.144142i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.65017 | + | 4.83163i | −0.325660 | + | 0.236606i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.49925 | − | 3.99544i | 0.268656 | − | 0.195190i | −0.445298 | − | 0.895382i | \(-0.646902\pi\) |
0.713954 | + | 0.700192i | \(0.246902\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.75730 | + | 6.36255i | 0.426805 | + | 0.310092i | 0.780370 | − | 0.625318i | \(-0.215031\pi\) |
−0.353565 | + | 0.935410i | \(0.615031\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.98937 | − | 9.20032i | 0.145348 | − | 0.447335i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.0795 | + | 46.4099i | −0.729747 | + | 2.24593i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.12884 | − | 1.54670i | −0.102782 | − | 0.0746752i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.40317 | − | 6.10526i | 0.404767 | − | 0.294080i | −0.366713 | − | 0.930334i | \(-0.619517\pi\) |
0.771480 | + | 0.636254i | \(0.219517\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.6714 | − | 9.20630i | 0.608948 | − | 0.442427i | −0.240096 | − | 0.970749i | \(-0.577179\pi\) |
0.849044 | + | 0.528323i | \(0.177179\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.68768 | + | 29.8156i | 0.463425 | + | 1.42627i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.80071 | − | 20.9304i | 0.324580 | − | 0.998955i | −0.647050 | − | 0.762448i | \(-0.723997\pi\) |
0.971630 | − | 0.236507i | \(-0.0760026\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.11454 | + | 9.58558i | 0.148312 | + | 0.456456i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.4447 | 1.39896 | 0.699480 | − | 0.714652i | \(-0.253415\pi\) | ||||
0.699480 | + | 0.714652i | \(0.253415\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.48025 | − | 3.25509i | −0.211909 | − | 0.153961i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.3445 | 1.29047 | 0.645234 | − | 0.763985i | \(-0.276760\pi\) | ||||
0.645234 | + | 0.763985i | \(0.276760\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.8408 | 1.16971 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.4150 | − | 7.56693i | −0.489339 | − | 0.355526i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.6394 | 1.57359 | 0.786793 | − | 0.617217i | \(-0.211740\pi\) | ||||
0.786793 | + | 0.617217i | \(0.211740\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.63547 | − | 5.03347i | −0.0763374 | − | 0.234942i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.86199 | − | 24.1967i | 0.366169 | − | 1.12695i | −0.583076 | − | 0.812417i | \(-0.698151\pi\) |
0.949246 | − | 0.314536i | \(-0.101849\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.42308 | + | 7.45749i | 0.112610 | + | 0.346579i | 0.991441 | − | 0.130555i | \(-0.0416758\pi\) |
−0.878831 | + | 0.477134i | \(0.841676\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.73792 | − | 6.34847i | 0.404343 | − | 0.293772i | −0.366965 | − | 0.930235i | \(-0.619603\pi\) |
0.771307 | + | 0.636463i | \(0.219603\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.0402 | + | 11.6539i | −0.740668 | + | 0.538127i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.8436 | − | 8.60487i | −0.545724 | − | 0.396491i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.58265 | + | 17.1816i | −0.256691 | + | 0.790012i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.04954 | + | 3.23015i | −0.0480551 | + | 0.147898i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.3447 | − | 13.3282i | −0.838191 | − | 0.608981i | 0.0836740 | − | 0.996493i | \(-0.473335\pi\) |
−0.921865 | + | 0.387512i | \(0.873335\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.26980 | − | 2.37565i | 0.149090 | − | 0.108320i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 18.2766 | − | 13.2787i | 0.831615 | − | 0.604204i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.54072 | + | 4.74184i | 0.0698166 | + | 0.214873i | 0.979877 | − | 0.199602i | \(-0.0639650\pi\) |
−0.910060 | + | 0.414476i | \(0.863965\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.37334 | − | 4.22672i | 0.0621048 | − | 0.191139i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.17443 | − | 25.1583i | −0.368907 | − | 1.13538i | −0.947498 | − | 0.319761i | \(-0.896397\pi\) |
0.578592 | − | 0.815617i | \(-0.303603\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 37.1766 | 1.67435 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.5068 | − | 7.63365i | −0.471295 | − | 0.342416i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 38.0875 | 1.70503 | 0.852516 | − | 0.522702i | \(-0.175076\pi\) | ||||
0.852516 | + | 0.522702i | \(0.175076\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 23.7655 | 1.06176 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.90603 | + | 1.38481i | 0.0849856 | + | 0.0617456i | 0.629467 | − | 0.777027i | \(-0.283273\pi\) |
−0.544481 | + | 0.838773i | \(0.683273\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.5119 | −0.555672 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.02282 | − | 27.7694i | −0.399929 | − | 1.23086i | −0.925056 | − | 0.379832i | \(-0.875982\pi\) |
0.525126 | − | 0.851024i | \(-0.324018\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.7250 | + | 42.2412i | −0.607158 | + | 1.86864i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.77219 | + | 5.45425i | 0.0782442 | + | 0.240811i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 29.4762 | − | 21.4157i | 1.29636 | − | 0.941862i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.2055 | + | 8.86778i | −0.535760 | + | 0.389252i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.4787 | + | 25.0503i | 1.51054 | + | 1.09747i | 0.965937 | + | 0.258779i | \(0.0833200\pi\) |
0.544604 | + | 0.838693i | \(0.316680\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.38893 | − | 19.6631i | 0.279368 | − | 0.859808i | −0.708662 | − | 0.705548i | \(-0.750701\pi\) |
0.988030 | − | 0.154259i | \(-0.0492992\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.5052 | − | 50.7978i | 0.718978 | − | 2.21279i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.56809 | − | 4.04545i | −0.242091 | − | 0.175889i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.602958 | + | 0.438075i | −0.0261661 | + | 0.0190108i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.72800 | + | 2.70855i | −0.161478 | + | 0.117320i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.16563 | + | 15.8982i | 0.222913 | + | 0.686057i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11.7304 | + | 36.1023i | −0.505262 | + | 1.55504i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.69426 | + | 11.3698i | 0.158829 | + | 0.488824i | 0.998529 | − | 0.0542264i | \(-0.0172693\pi\) |
−0.839700 | + | 0.543050i | \(0.817269\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.3923 | 0.445976 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.5220 | − | 15.6366i | −0.920214 | − | 0.668575i | 0.0233630 | − | 0.999727i | \(-0.492563\pi\) |
−0.943577 | + | 0.331152i | \(0.892563\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.8079 | 0.503951 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −40.2844 | −1.71617 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −30.5082 | − | 22.1655i | −1.29734 | − | 0.942573i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −28.3420 | −1.20089 | −0.600444 | − | 0.799667i | \(-0.705010\pi\) | ||||
−0.600444 | + | 0.799667i | \(0.705010\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.03560 | − | 3.18725i | −0.0438013 | − | 0.134806i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.15971 | − | 18.9576i | 0.260063 | − | 0.800393i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.25342 | + | 3.85764i | 0.0528255 | + | 0.162580i | 0.973989 | − | 0.226596i | \(-0.0727597\pi\) |
−0.921163 | + | 0.389176i | \(0.872760\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.34339 | − | 2.42912i | 0.140409 | − | 0.102013i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.59124 | + | 1.15610i | −0.0667081 | + | 0.0484663i | −0.620640 | − | 0.784096i | \(-0.713127\pi\) |
0.553931 | + | 0.832562i | \(0.313127\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.17273 | − | 3.03167i | −0.174623 | − | 0.126871i | 0.497040 | − | 0.867727i | \(-0.334420\pi\) |
−0.671664 | + | 0.740856i | \(0.734420\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.10485 | + | 18.7888i | −0.255034 | + | 0.784914i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.9338 | − | 36.7286i | 0.496812 | − | 1.52903i | −0.317301 | − | 0.948325i | \(-0.602776\pi\) |
0.814113 | − | 0.580706i | \(-0.197224\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.80855 | − | 1.31399i | −0.0751608 | − | 0.0546075i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 28.2215 | − | 20.5041i | 1.17083 | − | 0.850654i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.3488 | + | 7.51885i | −0.428604 | + | 0.311399i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.39659 | + | 25.8420i | 0.346564 | + | 1.06662i | 0.960741 | + | 0.277447i | \(0.0894882\pi\) |
−0.614177 | + | 0.789168i | \(0.710512\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.8850 | + | 55.0443i | −0.736937 | + | 2.26806i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.03223 | − | 21.6430i | −0.289267 | − | 0.890273i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −30.3486 | −1.24627 | −0.623135 | − | 0.782114i | \(-0.714141\pi\) | ||||
−0.623135 | + | 0.782114i | \(0.714141\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.4594 | − | 13.4116i | −0.755494 | − | 0.548899i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.9205 | −1.09994 | −0.549971 | − | 0.835184i | \(-0.685361\pi\) | ||||
−0.549971 | + | 0.835184i | \(0.685361\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.9133 | −0.689910 | −0.344955 | − | 0.938619i | \(-0.612106\pi\) | ||||
−0.344955 | + | 0.938619i | \(0.612106\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.88133 | + | 2.81995i | 0.158060 | + | 0.114837i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.9715 | 0.770028 | 0.385014 | − | 0.922911i | \(-0.374197\pi\) | ||||
0.385014 | + | 0.922911i | \(0.374197\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.97057 | + | 27.6086i | 0.363506 | + | 1.11876i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.08857 | + | 6.42795i | −0.0844944 | + | 0.260047i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.68666 | + | 5.19102i | 0.0681237 | + | 0.209663i | 0.979323 | − | 0.202302i | \(-0.0648424\pi\) |
−0.911199 | + | 0.411966i | \(0.864842\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.62485 | + | 6.99287i | −0.387482 | + | 0.281522i | −0.764423 | − | 0.644715i | \(-0.776976\pi\) |
0.376941 | + | 0.926237i | \(0.376976\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.6888 | − | 7.76586i | 0.429619 | − | 0.312136i | −0.351878 | − | 0.936046i | \(-0.614457\pi\) |
0.781496 | + | 0.623910i | \(0.214457\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.42248 | − | 3.21312i | −0.177468 | − | 0.128938i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.32647 | − | 13.3155i | 0.173336 | − | 0.533475i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.67464 | + | 20.5424i | −0.266560 | + | 0.820386i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24.7693 | + | 17.9959i | 0.987616 | + | 0.717545i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.39932 | − | 6.82900i | 0.374181 | − | 0.271858i | −0.384762 | − | 0.923016i | \(-0.625716\pi\) |
0.758943 | + | 0.651158i | \(0.225716\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.2585 | + | 11.8125i | −0.646217 | + | 0.469504i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.17602 | − | 6.69711i | −0.0862172 | − | 0.265349i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.971105 | + | 2.98875i | −0.0384163 | + | 0.118233i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.7784 | − | 33.1725i | −0.425721 | − | 1.31023i | −0.902303 | − | 0.431103i | \(-0.858124\pi\) |
0.476582 | − | 0.879130i | \(-0.341876\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.90629 | −0.114613 | −0.0573065 | − | 0.998357i | \(-0.518251\pi\) | ||||
−0.0573065 | + | 0.998357i | \(0.518251\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.82163 | + | 7.13583i | 0.386128 | + | 0.280538i | 0.763867 | − | 0.645374i | \(-0.223298\pi\) |
−0.377739 | + | 0.925912i | \(0.623298\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.80702 | −0.110185 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 41.7068 | 1.63462 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.1143 | + | 15.3404i | 0.826266 | + | 0.600318i | 0.918500 | − | 0.395420i | \(-0.129401\pi\) |
−0.0922343 | + | 0.995737i | \(0.529401\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.7473 | 0.419293 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.59035 | + | 20.2830i | 0.256724 | + | 0.790114i | 0.993485 | + | 0.113962i | \(0.0363541\pi\) |
−0.736761 | + | 0.676153i | \(0.763646\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.79161 | + | 30.1355i | −0.380850 | + | 1.17213i | 0.558597 | + | 0.829439i | \(0.311340\pi\) |
−0.939447 | + | 0.342695i | \(0.888660\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.14265 | + | 3.51671i | 0.0443768 | + | 0.136578i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.0652 | − | 22.5702i | 1.20285 | − | 0.873922i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.8561 | − | 7.88740i | 0.419720 | − | 0.304945i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 35.9790 | + | 26.1403i | 1.38895 | + | 1.00913i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.613635 | + | 1.88857i | −0.0236539 | + | 0.0727992i | −0.962187 | − | 0.272391i | \(-0.912186\pi\) |
0.938533 | + | 0.345190i | \(0.112186\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.1864 | − | 37.5057i | 0.468360 | − | 1.44146i | −0.386348 | − | 0.922353i | \(-0.626264\pi\) |
0.854708 | − | 0.519110i | \(-0.173736\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 34.8885 | + | 25.3480i | 1.33890 | + | 0.972767i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.9597 | + | 10.8689i | −0.573259 | + | 0.416497i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.94805 | − | 7.22768i | 0.380651 | − | 0.276559i | −0.380962 | − | 0.924590i | \(-0.624407\pi\) |
0.761614 | + | 0.648031i | \(0.224407\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.99878 | − | 18.4623i | −0.228868 | − | 0.704382i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.733276 | − | 2.25679i | 0.0279356 | − | 0.0859769i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.85334 | + | 14.9371i | 0.184630 | + | 0.568232i | 0.999942 | − | 0.0107896i | \(-0.00343451\pi\) |
−0.815312 | + | 0.579022i | \(0.803435\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15.5649 | 0.591262 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.2402 | − | 20.5177i | −1.06967 | − | 0.777164i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.1833 | 0.460813 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.4222 | −0.997953 | −0.498976 | − | 0.866616i | \(-0.666291\pi\) | ||||
−0.498976 | + | 0.866616i | \(0.666291\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −26.8399 | − | 19.5003i | −1.01229 | − | 0.735469i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −29.3749 | −1.10476 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.0638 | + | 46.3616i | 0.565733 | + | 1.74115i | 0.665763 | + | 0.746163i | \(0.268106\pi\) |
−0.100030 | + | 0.994984i | \(0.531894\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.81976 | + | 8.67832i | −0.105749 | + | 0.325462i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.0478 | − | 52.4677i | −0.638445 | − | 1.96493i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.66061 | + | 2.65959i | −0.136708 | + | 0.0993241i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27.7117 | − | 20.1337i | 1.03347 | − | 0.750861i | 0.0644713 | − | 0.997920i | \(-0.479464\pi\) |
0.969001 | + | 0.247058i | \(0.0794639\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −40.8197 | − | 29.6572i | −1.52020 | − | 1.10449i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.78479 | − | 8.57071i | 0.103568 | − | 0.318748i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.60134 | − | 20.3168i | 0.244830 | − | 0.753510i | −0.750834 | − | 0.660491i | \(-0.770348\pi\) |
0.995664 | − | 0.0930190i | \(-0.0296517\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.809017 | − | 0.587785i | −0.0299636 | − | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.5381 | − | 14.9218i | 0.759629 | − | 0.551903i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.3083 | − | 18.3875i | 0.934782 | − | 0.679159i | −0.0123772 | − | 0.999923i | \(-0.503940\pi\) |
0.947159 | + | 0.320765i | \(0.103940\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.58370 | + | 17.1849i | 0.205678 | + | 0.633013i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.406330 | − | 1.25056i | 0.0149471 | − | 0.0460025i | −0.943305 | − | 0.331928i | \(-0.892301\pi\) |
0.958252 | + | 0.285925i | \(0.0923009\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.23817 | − | 3.81070i | −0.0454853 | − | 0.139989i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.76431 | −0.321531 | −0.160766 | − | 0.986993i | \(-0.551396\pi\) | ||||
−0.160766 | + | 0.986993i | \(0.551396\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.82889 | − | 4.96148i | −0.249856 | − | 0.181531i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.7085 | −0.610515 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 44.6570 | 1.62956 | 0.814779 | − | 0.579772i | \(-0.196858\pi\) | ||||
0.814779 | + | 0.579772i | \(0.196858\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.56430 | − | 1.86307i | −0.0934482 | − | 0.0678941i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.70729 | −0.280126 | −0.140063 | − | 0.990143i | \(-0.544731\pi\) | ||||
−0.140063 | + | 0.990143i | \(0.544731\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.36221 | − | 19.5809i | −0.230934 | − | 0.710740i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.2344 | − | 37.6537i | 0.443498 | − | 1.36495i | −0.440625 | − | 0.897691i | \(-0.645243\pi\) |
0.884123 | − | 0.467254i | \(-0.154757\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.988210 | + | 3.04140i | 0.0357756 | + | 0.110106i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.421266 | − | 0.306068i | 0.0152110 | − | 0.0110515i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.7336 | + | 17.2435i | −0.855855 | + | 0.621815i | −0.926754 | − | 0.375668i | \(-0.877413\pi\) |
0.0708991 | + | 0.997483i | \(0.477413\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.63126 | + | 1.91172i | 0.0947624 | + | 0.0688489i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.37142 | − | 10.3762i | 0.121262 | − | 0.373205i | −0.871940 | − | 0.489613i | \(-0.837138\pi\) |
0.993201 | + | 0.116408i | \(0.0371381\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.38766 | + | 22.7369i | −0.265031 | + | 0.815681i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 30.6010 | + | 22.2329i | 1.09639 | + | 0.796577i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.57543 | + | 6.95696i | −0.342636 | + | 0.248940i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.68284 | − | 4.12883i | 0.203088 | − | 0.147552i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.6522 | − | 35.8619i | −0.415358 | − | 1.27834i | −0.911931 | − | 0.410344i | \(-0.865409\pi\) |
0.496573 | − | 0.867995i | \(-0.334591\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.41774 | − | 10.5187i | 0.121675 | − | 0.374476i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.45512 | − | 4.47841i | −0.0517383 | − | 0.159234i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.24980 | −0.292959 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 39.8369 | + | 28.9432i | 1.41110 | + | 1.02522i | 0.993162 | + | 0.116745i | \(0.0372461\pi\) |
0.417935 | + | 0.908477i | \(0.362754\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −51.1986 | −1.81128 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.38783 | −0.119703 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32.7472 | + | 23.7922i | 1.15562 | + | 0.839610i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.7558 | 0.871447 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.33675 | + | 25.6579i | 0.293105 | + | 0.902083i | 0.983852 | + | 0.178987i | \(0.0572819\pi\) |
−0.690747 | + | 0.723097i | \(0.742718\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.52546 | − | 7.77257i | 0.0886809 | − | 0.272932i | −0.896875 | − | 0.442285i | \(-0.854168\pi\) |
0.985555 | + | 0.169353i | \(0.0541679\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.0773177 | + | 0.237960i | 0.00271165 | + | 0.00834561i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.2550 | + | 16.1692i | −0.778604 | + | 0.565689i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.33591 | + | 1.69714i | −0.0816234 | + | 0.0593029i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35.4256 | + | 25.7382i | 1.23636 | + | 0.898269i | 0.997350 | − | 0.0727478i | \(-0.0231768\pi\) |
0.239011 | + | 0.971017i | \(0.423177\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.08540 | − | 15.6512i | 0.177266 | − | 0.545568i | −0.822464 | − | 0.568817i | \(-0.807401\pi\) |
0.999730 | + | 0.0232493i | \(0.00740114\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.24174 | + | 3.82167i | −0.0431794 | + | 0.132893i | −0.970322 | − | 0.241816i | \(-0.922257\pi\) |
0.927143 | + | 0.374708i | \(0.122257\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.3103 | − | 22.0217i | −1.05272 | − | 0.764847i | −0.0799935 | − | 0.996795i | \(-0.525490\pi\) |
−0.972728 | + | 0.231948i | \(0.925490\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.17658 | − | 5.21409i | 0.248953 | − | 0.180875i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 43.1550 | − | 31.3539i | 1.49523 | − | 1.08635i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.11860 | − | 9.59806i | −0.107795 | − | 0.331758i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.58335 | + | 11.0284i | −0.123711 | + | 0.380743i | −0.993664 | − | 0.112391i | \(-0.964149\pi\) |
0.869953 | + | 0.493135i | \(0.164149\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.28600 | + | 19.3463i | 0.216759 | + | 0.667114i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.7379 | 0.679809 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.6492 | + | 7.73709i | 0.365910 | + | 0.265849i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 26.4418 | 0.907481 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 31.6230 | 1.08402 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.06950 | − | 0.777036i | −0.0366189 | − | 0.0266052i | 0.569325 | − | 0.822112i | \(-0.307205\pi\) |
−0.605944 | + | 0.795507i | \(0.707205\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.5623 | −0.531598 | −0.265799 | − | 0.964028i | \(-0.585636\pi\) | ||||
−0.265799 | + | 0.964028i | \(0.585636\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.46169 | − | 26.0424i | −0.288709 | − | 0.888556i | −0.985262 | − | 0.171050i | \(-0.945284\pi\) |
0.696553 | − | 0.717505i | \(-0.254716\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.42289 | − | 25.9230i | 0.287051 | − | 0.883453i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.89760 | − | 30.4617i | −0.336918 | − | 1.03693i | −0.965769 | − | 0.259402i | \(-0.916475\pi\) |
0.628851 | − | 0.777526i | \(-0.283525\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.90777 | + | 6.47188i | −0.302524 | + | 0.219796i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −27.8038 | + | 20.2006i | −0.943178 | + | 0.685259i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.71175 | − | 1.97020i | −0.0918842 | − | 0.0667578i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.22461 | − | 9.92434i | 0.109137 | − | 0.335888i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.32606 | − | 4.08119i | 0.0447778 | − | 0.137812i | −0.926168 | − | 0.377111i | \(-0.876918\pi\) |
0.970946 | + | 0.239299i | \(0.0769176\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15.5236 | + | 11.2786i | 0.523598 | + | 0.380416i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.7520 | − | 31.7877i | 1.47404 | − | 1.07095i | 0.494625 | − | 0.869106i | \(-0.335305\pi\) |
0.979417 | − | 0.201848i | \(-0.0646947\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.6474 | + | 18.6340i | −0.863105 | + | 0.627083i | −0.928728 | − | 0.370762i | \(-0.879097\pi\) |
0.0656228 | + | 0.997845i | \(0.479097\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.66252 | + | 5.11670i | 0.0558218 | + | 0.171802i | 0.975080 | − | 0.221853i | \(-0.0712105\pi\) |
−0.919258 | + | 0.393655i | \(0.871211\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.686891 | − | 2.11403i | 0.0230376 | − | 0.0709024i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.16386 | − | 3.58198i | −0.0389906 | − | 0.120001i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 55.4786 | 1.85652 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.08984 | + | 2.24490i | 0.103167 | + | 0.0749550i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 70.8900 | 2.36432 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.9753 | 0.598846 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 16.0372 | + | 11.6517i | 0.533684 | + | 0.387744i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45.7593 | 1.51941 | 0.759706 | − | 0.650266i | \(-0.225343\pi\) | ||||
0.759706 | + | 0.650266i | \(0.225343\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.19649 | + | 6.76010i | 0.0728530 | + | 0.224219i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.669870 | − | 2.06165i | 0.0221938 | − | 0.0683054i | −0.939346 | − | 0.342970i | \(-0.888567\pi\) |
0.961540 | + | 0.274665i | \(0.0885669\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.82408 | − | 30.2354i | −0.325130 | − | 1.00065i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −22.4757 | + | 16.3295i | −0.742213 | + | 0.539249i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.9053 | − | 11.5559i | 0.524666 | − | 0.381192i | −0.293693 | − | 0.955900i | \(-0.594884\pi\) |
0.818359 | + | 0.574708i | \(0.194884\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.49942 | − | 5.44865i | −0.247114 | − | 0.179539i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.678477 | − | 2.08814i | 0.0223324 | − | 0.0687319i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.77281 | + | 11.6115i | −0.123915 | + | 0.381372i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −35.2728 | − | 25.6272i | −1.15726 | − | 0.840800i | −0.167832 | − | 0.985816i | \(-0.553677\pi\) |
−0.989429 | + | 0.145016i | \(0.953677\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −46.7626 | + | 33.9750i | −1.53258 | + | 1.11349i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 20.1393 | − | 14.6321i | 0.659333 | − | 0.479033i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.0014 | − | 40.0143i | −0.424738 | − | 1.30721i | −0.903245 | − | 0.429126i | \(-0.858822\pi\) |
0.478506 | − | 0.878084i | \(-0.341178\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.86866 | + | 5.75115i | −0.0609815 | + | 0.187682i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.1162 | + | 46.5228i | 0.492773 | + | 1.51660i | 0.820399 | + | 0.571792i | \(0.193752\pi\) |
−0.327625 | + | 0.944808i | \(0.606248\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −36.0544 | −1.17409 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.75486 | − | 4.18115i | −0.187008 | − | 0.135869i | 0.490342 | − | 0.871530i | \(-0.336872\pi\) |
−0.677350 | + | 0.735661i | \(0.736872\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.50878 | −0.243745 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.3864 | −0.466512 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.9903 | − | 13.0707i | −0.582762 | − | 0.423402i | 0.256957 | − | 0.966423i | \(-0.417280\pi\) |
−0.839719 | + | 0.543021i | \(0.817280\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 26.4560 | 0.855202 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.234186 | + | 0.720751i | 0.00756226 | + | 0.0232743i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.8934 | − | 67.3809i | 0.706238 | − | 2.17358i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.24937 | + | 3.84515i | 0.0402603 | + | 0.123908i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.2576 | − | 8.17914i | 0.362021 | − | 0.263023i | −0.391874 | − | 0.920019i | \(-0.628173\pi\) |
0.753894 | + | 0.656996i | \(0.228173\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 24.5554 | − | 17.8406i | 0.788834 | − | 0.573122i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.6548 | − | 14.2801i | −0.630754 | − | 0.458270i | 0.225907 | − | 0.974149i | \(-0.427465\pi\) |
−0.856661 | + | 0.515879i | \(0.827465\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.4975 | + | 32.3081i | −0.336535 | + | 1.03575i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14.3172 | + | 44.0637i | −0.458047 | + | 1.40972i | 0.409473 | + | 0.912322i | \(0.365713\pi\) |
−0.867520 | + | 0.497402i | \(0.834287\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.3228 | − | 7.49993i | −0.329917 | − | 0.239699i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.626030 | − | 0.454837i | 0.0199876 | − | 0.0145218i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.2168 | − | 24.1334i | 1.05945 | − | 0.769736i | 0.0854644 | − | 0.996341i | \(-0.472763\pi\) |
0.973987 | + | 0.226605i | \(0.0727626\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.3540 | − | 38.0218i | −0.393233 | − | 1.21025i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.10275 | − | 24.9377i | 0.257652 | − | 0.792972i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.26579 | + | 19.2841i | 0.199039 | + | 0.612580i | 0.999906 | + | 0.0137370i | \(0.00437276\pi\) |
−0.800866 | + | 0.598843i | \(0.795627\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.06688 | 0.0338565 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.7104 | − | 14.3204i | −0.624234 | − | 0.453533i | 0.230164 | − | 0.973152i | \(-0.426074\pi\) |
−0.854398 | + | 0.519619i | \(0.826074\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.78488 | 0.183026 |
(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 | 1500.2.m.c.601.1 | 24 | ||
5.2 | odd | 4 | 1500.2.o.c.649.2 | 24 | |||
5.3 | odd | 4 | 300.2.o.a.229.5 | yes | 24 | ||
5.4 | even | 2 | 1500.2.m.d.601.6 | 24 | |||
15.8 | even | 4 | 900.2.w.c.829.3 | 24 | |||
25.6 | even | 5 | inner | 1500.2.m.c.901.1 | 24 | ||
25.8 | odd | 20 | 1500.2.o.c.349.2 | 24 | |||
25.9 | even | 10 | 7500.2.a.m.1.12 | 12 | |||
25.12 | odd | 20 | 7500.2.d.g.1249.1 | 24 | |||
25.13 | odd | 20 | 7500.2.d.g.1249.24 | 24 | |||
25.16 | even | 5 | 7500.2.a.n.1.1 | 12 | |||
25.17 | odd | 20 | 300.2.o.a.169.5 | ✓ | 24 | ||
25.19 | even | 10 | 1500.2.m.d.901.6 | 24 | |||
75.17 | even | 20 | 900.2.w.c.469.3 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.o.a.169.5 | ✓ | 24 | 25.17 | odd | 20 | ||
300.2.o.a.229.5 | yes | 24 | 5.3 | odd | 4 | ||
900.2.w.c.469.3 | 24 | 75.17 | even | 20 | |||
900.2.w.c.829.3 | 24 | 15.8 | even | 4 | |||
1500.2.m.c.601.1 | 24 | 1.1 | even | 1 | trivial | ||
1500.2.m.c.901.1 | 24 | 25.6 | even | 5 | inner | ||
1500.2.m.d.601.6 | 24 | 5.4 | even | 2 | |||
1500.2.m.d.901.6 | 24 | 25.19 | even | 10 | |||
1500.2.o.c.349.2 | 24 | 25.8 | odd | 20 | |||
1500.2.o.c.649.2 | 24 | 5.2 | odd | 4 | |||
7500.2.a.m.1.12 | 12 | 25.9 | even | 10 | |||
7500.2.a.n.1.1 | 12 | 25.16 | even | 5 | |||
7500.2.d.g.1249.1 | 24 | 25.12 | odd | 20 | |||
7500.2.d.g.1249.24 | 24 | 25.13 | odd | 20 |