Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,3,Mod(65,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("144.65");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.q (of order \(6\), degree \(2\), 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: | \(3.92371580679\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 65.1 | ||
Root | \(1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.65 |
Dual form | 144.3.q.d.113.1 |
$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 3.00000 | 1.00000 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.39898 | + | 1.96240i | −0.679796 | + | 0.392480i | −0.799778 | − | 0.600296i | \(-0.795050\pi\) |
0.119982 | + | 0.992776i | \(0.461716\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.39898 | − | 11.0834i | 0.914140 | − | 1.58334i | 0.105984 | − | 0.994368i | \(-0.466201\pi\) |
0.808156 | − | 0.588969i | \(-0.200466\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 14.2980 | + | 8.25493i | 1.29981 | + | 0.750448i | 0.980372 | − | 0.197157i | \(-0.0631710\pi\) |
0.319443 | + | 0.947606i | \(0.396504\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.39898 | + | 2.42310i | 0.107614 | + | 0.186393i | 0.914803 | − | 0.403900i | \(-0.132346\pi\) |
−0.807189 | + | 0.590293i | \(0.799012\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −10.1969 | + | 5.88721i | −0.679796 | + | 0.392480i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.54270i | 0.149570i | 0.997200 | + | 0.0747852i | \(0.0238271\pi\) | ||||
−0.997200 | + | 0.0747852i | \(0.976173\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −21.5959 | −1.13663 | −0.568314 | − | 0.822812i | \(-0.692404\pi\) | ||||
−0.568314 | + | 0.822812i | \(0.692404\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 19.1969 | − | 33.2501i | 0.914140 | − | 1.58334i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.60102 | + | 1.50170i | −0.113088 | + | 0.0652913i | −0.555477 | − | 0.831532i | \(-0.687464\pi\) |
0.442389 | + | 0.896823i | \(0.354131\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.79796 | + | 8.31031i | −0.191918 | + | 0.332412i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 1.00000 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −13.1969 | − | 7.61926i | −0.455067 | − | 0.262733i | 0.254901 | − | 0.966967i | \(-0.417957\pi\) |
−0.709968 | + | 0.704234i | \(0.751290\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −13.6010 | − | 23.5577i | −0.438743 | − | 0.759924i | 0.558850 | − | 0.829269i | \(-0.311243\pi\) |
−0.997593 | + | 0.0693442i | \(0.977909\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 42.8939 | + | 24.7648i | 1.29981 | + | 0.750448i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 50.2295i | 1.43513i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.4041 | −0.281191 | −0.140596 | − | 0.990067i | \(-0.544902\pi\) | ||||
−0.140596 | + | 0.990067i | \(0.544902\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.19694 | + | 7.26931i | 0.107614 | + | 0.186393i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −34.5000 | + | 19.9186i | −0.841463 | + | 0.485819i | −0.857761 | − | 0.514048i | \(-0.828145\pi\) |
0.0162980 | + | 0.999867i | \(0.494812\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 17.0959 | − | 29.6110i | 0.397579 | − | 0.688628i | −0.595847 | − | 0.803098i | \(-0.703184\pi\) |
0.993427 | + | 0.114470i | \(0.0365170\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −30.5908 | + | 17.6616i | −0.679796 | + | 0.392480i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −58.1969 | − | 33.6000i | −1.23823 | − | 0.714894i | −0.269500 | − | 0.963000i | \(-0.586858\pi\) |
−0.968733 | + | 0.248106i | \(0.920192\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −57.3939 | − | 99.4091i | −1.17130 | − | 2.02876i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.62809i | 0.149570i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 100.680i | 1.89963i | 0.312810 | + | 0.949816i | \(0.398730\pi\) | ||||
−0.312810 | + | 0.949816i | \(0.601270\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −64.7980 | −1.17814 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −64.7878 | −1.13663 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.29796 | + | 3.05878i | −0.0897959 | + | 0.0518437i | −0.544226 | − | 0.838939i | \(-0.683176\pi\) |
0.454430 | + | 0.890783i | \(0.349843\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −20.3990 | + | 35.3321i | −0.334409 | + | 0.579214i | −0.983371 | − | 0.181607i | \(-0.941870\pi\) |
0.648962 | + | 0.760821i | \(0.275204\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 57.5908 | − | 99.7502i | 0.914140 | − | 1.58334i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.51021 | − | 5.49072i | −0.146311 | − | 0.0844726i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 54.4898 | + | 94.3791i | 0.813281 | + | 1.40864i | 0.910556 | + | 0.413386i | \(0.135654\pi\) |
−0.0972755 | + | 0.995257i | \(0.531013\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.80306 | + | 4.50510i | −0.113088 | + | 0.0652913i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 52.8829i | 0.744830i | 0.928066 | + | 0.372415i | \(0.121470\pi\) | ||||
−0.928066 | + | 0.372415i | \(0.878530\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 68.7878 | 0.942298 | 0.471149 | − | 0.882054i | \(-0.343839\pi\) | ||||
0.471149 | + | 0.882054i | \(0.343839\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −14.3939 | + | 24.9309i | −0.191918 | + | 0.332412i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 182.985 | − | 105.646i | 2.37642 | − | 1.37203i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.7929 | + | 22.1579i | −0.161935 | + | 0.280479i | −0.935563 | − | 0.353161i | \(-0.885107\pi\) |
0.773628 | + | 0.633640i | \(0.218440\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −52.0857 | − | 30.0717i | −0.627539 | − | 0.362310i | 0.152260 | − | 0.988341i | \(-0.451345\pi\) |
−0.779798 | + | 0.626031i | \(0.784678\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.98979 | − | 8.64258i | −0.0587035 | − | 0.101677i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −39.5908 | − | 22.8578i | −0.455067 | − | 0.262733i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.62809i | 0.0857089i | 0.999081 | + | 0.0428545i | \(0.0136452\pi\) | ||||
−0.999081 | + | 0.0428545i | \(0.986355\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 35.8082 | 0.393496 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −40.8031 | − | 70.6730i | −0.438743 | − | 0.759924i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 73.4041 | − | 42.3799i | 0.772675 | − | 0.446104i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 50.7020 | − | 87.8185i | 0.522701 | − | 0.905345i | −0.476950 | − | 0.878931i | \(-0.658258\pi\) |
0.999651 | − | 0.0264148i | \(-0.00840908\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 128.682 | + | 74.2944i | 1.29981 | + | 0.750448i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.19694 | − | 0.691053i | −0.0118509 | − | 0.00684211i | 0.494063 | − | 0.869426i | \(-0.335511\pi\) |
−0.505914 | + | 0.862584i | \(0.668845\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.792856 | − | 1.37327i | −0.00769763 | − | 0.0133327i | 0.862151 | − | 0.506652i | \(-0.169117\pi\) |
−0.869849 | + | 0.493319i | \(0.835784\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 150.688i | 1.43513i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 103.223i | − | 0.964702i | −0.875978 | − | 0.482351i | \(-0.839783\pi\) | ||
0.875978 | − | 0.482351i | \(-0.160217\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.4041 | 0.132148 | 0.0660738 | − | 0.997815i | \(-0.478953\pi\) | ||||
0.0660738 | + | 0.997815i | \(0.478953\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −31.2122 | −0.281191 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −92.0755 | + | 53.1598i | −0.814828 | + | 0.470441i | −0.848630 | − | 0.528988i | \(-0.822572\pi\) |
0.0338020 | + | 0.999429i | \(0.489238\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.89388 | − | 10.2085i | 0.0512511 | − | 0.0887695i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.5908 | + | 21.8079i | 0.107614 | + | 0.186393i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 28.1816 | + | 16.2707i | 0.236820 | + | 0.136728i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 75.7878 | + | 131.268i | 0.626345 | + | 1.08486i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −103.500 | + | 59.7558i | −0.841463 | + | 0.485819i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 135.782i | − | 1.08626i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 183.980 | 1.44866 | 0.724329 | − | 0.689454i | \(-0.242150\pi\) | ||||
0.724329 | + | 0.689454i | \(0.242150\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 51.2878 | − | 88.8330i | 0.397579 | − | 0.688628i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 91.6918 | − | 52.9383i | 0.699938 | − | 0.404109i | −0.107387 | − | 0.994217i | \(-0.534248\pi\) |
0.807324 | + | 0.590108i | \(0.200915\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −138.192 | + | 239.355i | −1.03904 | + | 1.79966i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −91.7724 | + | 52.9848i | −0.679796 | + | 0.392480i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −165.288 | − | 95.4289i | −1.20648 | − | 0.696562i | −0.244491 | − | 0.969651i | \(-0.578621\pi\) |
−0.961989 | + | 0.273090i | \(0.911954\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −47.4898 | − | 82.2547i | −0.341653 | − | 0.591761i | 0.643087 | − | 0.765793i | \(-0.277653\pi\) |
−0.984740 | + | 0.174033i | \(0.944320\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −174.591 | − | 100.800i | −1.23823 | − | 0.714894i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 46.1939i | 0.323034i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 59.8082 | 0.412470 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −172.182 | − | 298.227i | −1.17130 | − | 2.02876i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 79.6112 | − | 45.9636i | 0.534304 | − | 0.308480i | −0.208464 | − | 0.978030i | \(-0.566846\pi\) |
0.742767 | + | 0.669550i | \(0.233513\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.20714 | + | 14.2152i | −0.0543519 | + | 0.0941403i | −0.891921 | − | 0.452191i | \(-0.850643\pi\) |
0.837569 | + | 0.546331i | \(0.183976\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 22.8843i | 0.149570i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 92.4592 | + | 53.3813i | 0.596511 | + | 0.344396i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 105.985 | + | 183.571i | 0.675062 | + | 1.16924i | 0.976451 | + | 0.215740i | \(0.0692164\pi\) |
−0.301389 | + | 0.953501i | \(0.597450\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 302.041i | 1.89963i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 38.4374i | 0.238742i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −172.788 | −1.06005 | −0.530024 | − | 0.847983i | \(-0.677817\pi\) | ||||
−0.530024 | + | 0.847983i | \(0.677817\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −194.394 | −1.17814 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 163.197 | − | 94.2218i | 0.977227 | − | 0.564202i | 0.0757953 | − | 0.997123i | \(-0.475850\pi\) |
0.901432 | + | 0.432921i | \(0.142517\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 80.5857 | − | 139.579i | 0.476839 | − | 0.825909i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −194.363 | −1.13663 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 52.1969 | + | 30.1359i | 0.301716 | + | 0.174196i | 0.643214 | − | 0.765687i | \(-0.277601\pi\) |
−0.341497 | + | 0.939883i | \(0.610934\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 61.4041 | + | 106.355i | 0.350880 | + | 0.607743i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −15.8939 | + | 9.17633i | −0.0897959 | + | 0.0518437i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 72.7108i | 0.406205i | 0.979157 | + | 0.203103i | \(0.0651025\pi\) | ||||
−0.979157 | + | 0.203103i | \(0.934897\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −97.5959 | −0.539204 | −0.269602 | − | 0.962972i | \(-0.586892\pi\) | ||||
−0.269602 | + | 0.962972i | \(0.586892\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −61.1969 | + | 105.996i | −0.334409 | + | 0.579214i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 35.3633 | − | 20.4170i | 0.191153 | − | 0.110362i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −20.9898 | + | 36.3554i | −0.112245 | + | 0.194414i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 172.772 | − | 299.251i | 0.914140 | − | 1.58334i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −282.560 | − | 163.136i | −1.47937 | − | 0.854116i | −0.479645 | − | 0.877462i | \(-0.659235\pi\) |
−0.999727 | + | 0.0233462i | \(0.992568\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.5102 | − | 18.2042i | −0.0544570 | − | 0.0943223i | 0.837512 | − | 0.546419i | \(-0.184009\pi\) |
−0.891969 | + | 0.452097i | \(0.850676\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −28.5306 | − | 16.4722i | −0.146311 | − | 0.0844726i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 32.5413i | − | 0.165184i | −0.996583 | − | 0.0825922i | \(-0.973680\pi\) | ||
0.996583 | − | 0.0825922i | \(-0.0263199\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 62.0000 | 0.311558 | 0.155779 | − | 0.987792i | \(-0.450211\pi\) | ||||
0.155779 | + | 0.987792i | \(0.450211\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 163.469 | + | 283.137i | 0.813281 | + | 1.40864i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −168.894 | + | 97.5109i | −0.831990 | + | 0.480349i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 78.1765 | − | 135.406i | 0.381349 | − | 0.660516i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −23.4092 | + | 13.5153i | −0.113088 | + | 0.0652913i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −308.778 | − | 178.273i | −1.47740 | − | 0.852980i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −84.2980 | − | 146.008i | −0.399516 | − | 0.691983i | 0.594150 | − | 0.804354i | \(-0.297489\pi\) |
−0.993666 | + | 0.112372i | \(0.964155\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 158.649i | 0.744830i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 134.196i | 0.624169i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −348.131 | −1.60429 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 206.363 | 0.942298 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.16122 | + | 3.55718i | −0.0278788 | + | 0.0160958i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −78.1867 | + | 135.423i | −0.350613 | + | 0.607280i | −0.986357 | − | 0.164620i | \(-0.947360\pi\) |
0.635744 | + | 0.771900i | \(0.280693\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −43.1816 | + | 74.7928i | −0.191918 | + | 0.332412i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −86.6510 | − | 50.0280i | −0.381723 | − | 0.220388i | 0.296845 | − | 0.954926i | \(-0.404066\pi\) |
−0.678567 | + | 0.734538i | \(0.737399\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 104.995 | + | 181.856i | 0.458493 | + | 0.794133i | 0.998882 | − | 0.0472824i | \(-0.0150561\pi\) |
−0.540389 | + | 0.841416i | \(0.681723\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 548.954 | − | 316.939i | 2.37642 | − | 1.37203i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 307.127i | 1.31814i | 0.752081 | + | 0.659070i | \(0.229050\pi\) | ||||
−0.752081 | + | 0.659070i | \(0.770950\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 263.747 | 1.12233 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −38.3786 | + | 66.4736i | −0.161935 | + | 0.280479i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 70.3888 | − | 40.6390i | 0.294514 | − | 0.170038i | −0.345462 | − | 0.938433i | \(-0.612278\pi\) |
0.639976 | + | 0.768395i | \(0.278944\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 180.096 | − | 311.935i | 0.747286 | − | 1.29434i | −0.201833 | − | 0.979420i | \(-0.564690\pi\) |
0.949119 | − | 0.314917i | \(-0.101977\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 1.00000 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 390.161 | + | 225.260i | 1.59249 | + | 0.919427i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −30.2122 | − | 52.3291i | −0.122317 | − | 0.211859i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −156.257 | − | 90.2151i | −0.627539 | − | 0.362310i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 400.179i | − | 1.59434i | −0.603755 | − | 0.797170i | \(-0.706330\pi\) | ||
0.603755 | − | 0.797170i | \(-0.293670\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −49.5857 | −0.195991 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −14.9694 | − | 25.9277i | −0.0587035 | − | 0.101677i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 315.035 | − | 181.885i | 1.22582 | − | 0.707725i | 0.259664 | − | 0.965699i | \(-0.416388\pi\) |
0.966152 | + | 0.257974i | \(0.0830549\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −66.5755 | + | 115.312i | −0.257048 | + | 0.445221i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −118.772 | − | 68.5733i | −0.455067 | − | 0.262733i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 326.570 | + | 188.546i | 1.24171 | + | 0.716903i | 0.969443 | − | 0.245318i | \(-0.0788923\pi\) |
0.272270 | + | 0.962221i | \(0.412226\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −197.576 | − | 342.211i | −0.745568 | − | 1.29136i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 22.8843i | 0.0857089i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 170.849i | 0.635125i | 0.948237 | + | 0.317562i | \(0.102864\pi\) | ||||
−0.948237 | + | 0.317562i | \(0.897136\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 50.4041 | 0.185993 | 0.0929965 | − | 0.995666i | \(-0.470355\pi\) | ||||
0.0929965 | + | 0.995666i | \(0.470355\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 107.424 | 0.393496 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −137.202 | + | 79.2136i | −0.498917 | + | 0.288050i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.8031 | + | 22.1756i | −0.0462204 | + | 0.0800561i | −0.888210 | − | 0.459438i | \(-0.848051\pi\) |
0.841990 | + | 0.539494i | \(0.181384\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −122.409 | − | 212.019i | −0.438743 | − | 0.759924i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 290.267 | + | 167.586i | 1.03298 | + | 0.596391i | 0.917837 | − | 0.396958i | \(-0.129934\pi\) |
0.115143 | + | 0.993349i | \(0.463267\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.48979 | − | 12.9727i | −0.0264657 | − | 0.0458399i | 0.852489 | − | 0.522745i | \(-0.175092\pi\) |
−0.878955 | + | 0.476905i | \(0.841759\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 220.212 | − | 127.140i | 0.772675 | − | 0.446104i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 509.834i | 1.77643i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 282.535 | 0.977629 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 152.106 | − | 263.456i | 0.522701 | − | 0.905345i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −261.015 | + | 150.697i | −0.890837 | + | 0.514325i | −0.874216 | − | 0.485537i | \(-0.838624\pi\) |
−0.0166210 | + | 0.999862i | \(0.505291\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.0051 | − | 20.7934i | 0.0406953 | − | 0.0704863i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 386.045 | + | 222.883i | 1.29981 | + | 0.750448i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.27755 | − | 4.20169i | −0.0243396 | − | 0.0140525i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −218.793 | − | 378.960i | −0.726887 | − | 1.25900i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.59082 | − | 2.07316i | −0.0118509 | − | 0.00684211i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 160.124i | − | 0.524997i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 44.7469 | 0.145755 | 0.0728777 | − | 0.997341i | \(-0.476782\pi\) | ||||
0.0728777 | + | 0.997341i | \(0.476782\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.37857 | − | 4.11980i | −0.00769763 | − | 0.0133327i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −281.348 | + | 162.436i | −0.904656 | + | 0.522303i | −0.878708 | − | 0.477360i | \(-0.841594\pi\) |
−0.0259480 | + | 0.999663i | \(0.508260\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −156.894 | + | 271.748i | −0.501258 | + | 0.868205i | 0.498741 | + | 0.866751i | \(0.333796\pi\) |
−0.999999 | + | 0.00145368i | \(0.999537\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 452.065i | 1.43513i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −47.9847 | − | 27.7040i | −0.151371 | − | 0.0873942i | 0.422401 | − | 0.906409i | \(-0.361187\pi\) |
−0.573773 | + | 0.819015i | \(0.694521\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −125.793 | − | 217.880i | −0.394335 | − | 0.683008i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 309.669i | − | 0.964702i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 54.9119i | − | 0.170006i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −26.8490 | −0.0826123 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 43.2122 | 0.132148 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −744.802 | + | 430.012i | −2.26384 | + | 1.30703i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.70204 | − | 13.3403i | 0.0232690 | − | 0.0403031i | −0.854156 | − | 0.520016i | \(-0.825926\pi\) |
0.877425 | + | 0.479713i | \(0.159259\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −93.6367 | −0.281191 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −370.419 | − | 213.862i | −1.10573 | − | 0.638393i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −37.8837 | − | 65.6164i | −0.112414 | − | 0.194708i | 0.804329 | − | 0.594184i | \(-0.202525\pi\) |
−0.916743 | + | 0.399477i | \(0.869192\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −276.227 | + | 159.479i | −0.814828 | + | 0.470441i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 449.102i | − | 1.31701i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −841.949 | −2.45466 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 17.6816 | − | 30.6255i | 0.0512511 | − | 0.0887695i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −578.651 | + | 334.084i | −1.66758 | + | 0.962779i | −0.698646 | + | 0.715467i | \(0.746214\pi\) |
−0.968936 | + | 0.247312i | \(0.920453\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 123.015 | − | 213.069i | 0.352479 | − | 0.610512i | −0.634204 | − | 0.773166i | \(-0.718672\pi\) |
0.986683 | + | 0.162654i | \(0.0520053\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 37.7724 | + | 65.4238i | 0.107614 | + | 0.186393i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 156.510 | + | 90.3612i | 0.443372 | + | 0.255981i | 0.705027 | − | 0.709181i | \(-0.250935\pi\) |
−0.261655 | + | 0.965161i | \(0.584268\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −103.778 | − | 179.748i | −0.292331 | − | 0.506332i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 84.5449 | + | 48.8120i | 0.236820 | + | 0.136728i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 256.273i | − | 0.713852i | −0.934133 | − | 0.356926i | \(-0.883825\pi\) | ||
0.934133 | − | 0.356926i | \(-0.116175\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 105.384 | 0.291922 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 227.363 | + | 393.805i | 0.626345 | + | 1.08486i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −233.808 | + | 134.989i | −0.640570 | + | 0.369833i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 270.358 | − | 468.274i | 0.736671 | − | 1.27595i | −0.217316 | − | 0.976101i | \(-0.569730\pi\) |
0.953986 | − | 0.299850i | \(-0.0969366\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −310.500 | + | 179.267i | −0.841463 | + | 0.485819i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1115.88 | + | 644.252i | 3.00776 | + | 1.73653i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 85.9847 | + | 148.930i | 0.230522 | + | 0.399276i | 0.957962 | − | 0.286896i | \(-0.0926233\pi\) |
−0.727440 | + | 0.686171i | \(0.759290\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 407.347i | − | 1.08626i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 42.6367i | − | 0.113095i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 170.849 | 0.450789 | 0.225394 | − | 0.974268i | \(-0.427633\pi\) | ||||
0.225394 | + | 0.974268i | \(0.427633\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 551.939 | 1.44866 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 505.681 | − | 291.955i | 1.32031 | − | 0.762284i | 0.336536 | − | 0.941671i | \(-0.390745\pi\) |
0.983779 | + | 0.179386i | \(0.0574112\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −414.641 | + | 718.179i | −1.07699 | + | 1.86540i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 153.863 | − | 266.499i | 0.397579 | − | 0.688628i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −384.752 | − | 222.137i | −0.989080 | − | 0.571045i | −0.0840807 | − | 0.996459i | \(-0.526795\pi\) |
−0.904999 | + | 0.425413i | \(0.860129\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.81837 | − | 6.61361i | −0.00976565 | − | 0.0169146i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 275.076 | − | 158.815i | 0.699938 | − | 0.404109i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 100.419i | − | 0.254225i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −575.090 | −1.44859 | −0.724294 | − | 0.689491i | \(-0.757834\pi\) | ||||
−0.724294 | + | 0.689491i | \(0.757834\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −414.576 | + | 718.066i | −1.03904 | + | 1.79966i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 141.318 | − | 81.5902i | 0.352415 | − | 0.203467i | −0.313333 | − | 0.949643i | \(-0.601446\pi\) |
0.665748 | + | 0.746176i | \(0.268112\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 38.0551 | − | 65.9134i | 0.0944295 | − | 0.163557i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −275.317 | + | 158.955i | −0.679796 | + | 0.392480i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −148.757 | − | 85.8850i | −0.365497 | − | 0.211020i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 300.641 | + | 520.725i | 0.735063 | + | 1.27317i | 0.954696 | + | 0.297584i | \(0.0961808\pi\) |
−0.219633 | + | 0.975583i | \(0.570486\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −495.863 | − | 286.287i | −1.20648 | − | 0.696562i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 78.2922i | 0.189570i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 236.051 | 0.568798 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −142.469 | − | 246.764i | −0.341653 | − | 0.591761i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 158.620 | − | 91.5795i | 0.378569 | − | 0.218567i | −0.298626 | − | 0.954370i | \(-0.596528\pi\) |
0.677195 | + | 0.735803i | \(0.263195\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −83.7724 | + | 145.098i | −0.198984 | + | 0.344651i | −0.948199 | − | 0.317676i | \(-0.897098\pi\) |
0.749215 | + | 0.662327i | \(0.230431\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −523.772 | − | 302.400i | −1.23823 | − | 0.714894i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −21.1306 | − | 12.1998i | −0.0497191 | − | 0.0287053i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 261.065 | + | 452.178i | 0.611394 | + | 1.05897i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 138.582i | 0.323034i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 644.766i | − | 1.49598i | −0.663712 | − | 0.747988i | \(-0.731020\pi\) | ||
0.663712 | − | 0.747988i | \(-0.268980\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 133.514 | 0.308347 | 0.154174 | − | 0.988044i | \(-0.450729\pi\) | ||||
0.154174 | + | 0.988044i | \(0.450729\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 179.424 | 0.412470 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 56.1714 | − | 32.4306i | 0.128539 | − | 0.0742119i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −46.2276 | + | 80.0685i | −0.105302 | + | 0.182388i | −0.913862 | − | 0.406026i | \(-0.866914\pi\) |
0.808560 | + | 0.588414i | \(0.200248\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −516.545 | − | 894.682i | −1.17130 | − | 2.02876i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 150.157 | + | 86.6933i | 0.338955 | + | 0.195696i | 0.659810 | − | 0.751433i | \(-0.270637\pi\) |
−0.320855 | + | 0.947128i | \(0.603970\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.9694 | − | 25.9277i | −0.0336391 | − | 0.0582646i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 238.834 | − | 137.891i | 0.534304 | − | 0.308480i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 430.692i | − | 0.959224i | −0.877481 | − | 0.479612i | \(-0.840777\pi\) | ||
0.877481 | − | 0.479612i | \(-0.159223\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −657.706 | −1.45833 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −24.6214 | + | 42.6456i | −0.0543519 | + | 0.0941403i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −121.711 | + | 70.2700i | −0.267497 | + | 0.154440i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 262.843 | − | 455.257i | 0.575148 | − | 0.996186i | −0.420877 | − | 0.907118i | \(-0.638278\pi\) |
0.996025 | − | 0.0890687i | \(-0.0283891\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 68.6528i | 0.149570i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.54999 | + | 0.894890i | 0.00336224 | + | 0.00194119i | 0.501680 | − | 0.865053i | \(-0.332715\pi\) |
−0.498318 | + | 0.866994i | \(0.666049\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 263.166 | + | 455.817i | 0.568394 | + | 0.984487i | 0.996725 | + | 0.0808651i | \(0.0257683\pi\) |
−0.428331 | + | 0.903622i | \(0.640898\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 277.378 | + | 160.144i | 0.596511 | + | 0.344396i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 409.322i | 0.876494i | 0.898855 | + | 0.438247i | \(0.144400\pi\) | ||||
−0.898855 | + | 0.438247i | \(0.855600\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1394.72 | 2.97381 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 317.954 | + | 550.713i | 0.675062 | + | 1.16924i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 488.873 | − | 282.251i | 1.03356 | − | 0.596726i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 103.616 | − | 179.469i | 0.218140 | − | 0.377829i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 906.124i | 1.89963i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −525.207 | − | 303.228i | −1.09647 | − | 0.633045i | −0.161175 | − | 0.986926i | \(-0.551528\pi\) |
−0.935290 | + | 0.353881i | \(0.884862\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.5551 | − | 25.2102i | −0.0302601 | − | 0.0524120i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 115.312i | 0.238742i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 397.991i | 0.820600i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 275.131 | 0.564950 | 0.282475 | − | 0.959275i | \(-0.408845\pi\) | ||||
0.282475 | + | 0.959275i | \(0.408845\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −518.363 | −1.06005 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 127.469 | − | 73.5945i | 0.259612 | − | 0.149887i | −0.364546 | − | 0.931186i | \(-0.618776\pi\) |
0.624157 | + | 0.781299i | \(0.285442\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.3735 | − | 33.5558i | 0.0392971 | − | 0.0680646i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −583.182 | −1.17814 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 586.120 | + | 338.397i | 1.17932 | + | 0.680879i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 226.308 | + | 391.977i | 0.453523 | + | 0.785526i | 0.998602 | − | 0.0528594i | \(-0.0168335\pi\) |
−0.545079 | + | 0.838385i | \(0.683500\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 489.591 | − | 282.665i | 0.977227 | − | 0.564202i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 571.541i | 1.13627i | 0.822937 | + | 0.568133i | \(0.192334\pi\) | ||||
−0.822937 | + | 0.568133i | \(0.807666\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.42449 | 0.0107416 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 241.757 | − | 418.736i | 0.476839 | − | 0.825909i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 394.136 | − | 227.554i | 0.774333 | − | 0.447062i | −0.0600849 | − | 0.998193i | \(-0.519137\pi\) |
0.834418 | + | 0.551132i | \(0.185804\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 440.171 | − | 762.399i | 0.861392 | − | 1.49198i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −583.090 | −1.13663 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.38981 | + | 3.11181i | 0.0104656 | + | 0.00604234i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −554.732 | − | 960.823i | −1.07298 | − | 1.85846i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 156.591 | + | 90.4077i | 0.301716 | + | 0.174196i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 846.127i | − | 1.62404i | −0.583627 | − | 0.812022i | \(-0.698367\pi\) | ||
0.583627 | − | 0.812022i | \(-0.301633\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 487.616 | 0.932345 | 0.466172 | − | 0.884694i | \(-0.345633\pi\) | ||||
0.466172 | + | 0.884694i | \(0.345633\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 184.212 | + | 319.065i | 0.350880 | + | 0.607743i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 59.9000 | − | 34.5833i | 0.113662 | − | 0.0656229i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −259.990 | + | 450.316i | −0.491474 | + | 0.851258i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −47.6816 | + | 27.5290i | −0.0897959 | + | 0.0518437i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −96.5296 | − | 55.7314i | −0.181106 | − | 0.104562i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 202.565 | + | 350.853i | 0.378627 | + | 0.655801i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 218.132i | 0.406205i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1895.13i | − | 3.51601i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 608.302 | 1.12440 | 0.562202 | − | 0.827000i | \(-0.309955\pi\) | ||||
0.562202 | + | 0.827000i | \(0.309955\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −292.788 | −0.539204 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −48.9592 | + | 28.2666i | −0.0898334 | + | 0.0518653i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −431.671 | + | 747.677i | −0.789162 | + | 1.36687i | 0.137319 | + | 0.990527i | \(0.456151\pi\) |
−0.926481 | + | 0.376341i | \(0.877182\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −183.591 | + | 317.989i | −0.334409 | + | 0.579214i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 285.000 | + | 164.545i | 0.517241 | + | 0.298629i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 163.722 | + | 283.576i | 0.296062 | + | 0.512795i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 106.090 | − | 61.2510i | 0.191153 | − | 0.110362i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 331.526i | − | 0.595200i | −0.954691 | − | 0.297600i | \(-0.903814\pi\) | ||
0.954691 | − | 0.297600i | \(-0.0961861\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 95.6674 | 0.171140 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −62.9694 | + | 109.066i | −0.112245 | + | 0.194414i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −514.024 | + | 296.772i | −0.913010 | + | 0.527126i | −0.881398 | − | 0.472374i | \(-0.843397\pi\) |
−0.0316114 | + | 0.999500i | \(0.510064\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 208.642 | − | 361.378i | 0.369278 | − | 0.639608i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 518.317 | − | 897.752i | 0.914140 | − | 1.58334i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 889.155 | + | 513.354i | 1.56266 | + | 0.902204i | 0.996986 | + | 0.0775764i | \(0.0247182\pi\) |
0.565676 | + | 0.824627i | \(0.308615\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 191.843 | + | 332.282i | 0.335977 | + | 0.581929i | 0.983672 | − | 0.179971i | \(-0.0576002\pi\) |
−0.647695 | + | 0.761900i | \(0.724267\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −847.681 | − | 489.409i | −1.47937 | − | 0.854116i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 28.8204i | − | 0.0501224i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −777.433 | −1.34737 | −0.673685 | − | 0.739019i | \(-0.735290\pi\) | ||||
−0.673685 | + | 0.739019i | \(0.735290\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −31.5306 | − | 54.6126i | −0.0544570 | − | 0.0943223i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −666.591 | + | 384.856i | −1.14732 | + | 0.662403i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −831.110 | + | 1439.53i | −1.42557 | + | 2.46917i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −85.5918 | − | 49.4165i | −0.146311 | − | 0.0844726i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −581.520 | − | 335.741i | −0.990665 | − | 0.571961i | −0.0851921 | − | 0.996365i | \(-0.527150\pi\) |
−0.905473 | + | 0.424404i | \(0.860484\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 293.727 | + | 508.749i | 0.498687 | + | 0.863751i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 97.6240i | − | 0.165184i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 536.457i | 0.904650i | 0.891853 | + | 0.452325i | \(0.149405\pi\) | ||||
−0.891853 | + | 0.452325i | \(0.850595\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −127.718 | −0.214653 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 186.000 | 0.311558 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 735.438 | − | 424.605i | 1.22778 | − | 0.708857i | 0.261212 | − | 0.965282i | \(-0.415878\pi\) |
0.966564 | + | 0.256425i | \(0.0825446\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −330.692 | + | 572.775i | −0.550236 | + | 0.953037i | 0.448021 | + | 0.894023i | \(0.352129\pi\) |
−0.998257 | + | 0.0590138i | \(0.981204\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 490.408 | + | 849.412i | 0.813281 | + | 1.40864i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −515.202 | − | 297.452i | −0.851574 | − | 0.491656i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.9541 | − | 18.9730i | −0.0180463 | − | 0.0312570i | 0.856861 | − | 0.515547i | \(-0.172411\pi\) |
−0.874908 | + | 0.484290i | \(0.839078\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −506.682 | + | 292.533i | −0.831990 | + | 0.480349i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 188.023i | − | 0.307730i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1164.75 | −1.90008 | −0.950038 | − | 0.312133i | \(-0.898956\pi\) | ||||
−0.950038 | + | 0.312133i | \(0.898956\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 234.530 | − | 406.217i | 0.381349 | − | 0.660516i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 558.227 | − | 322.292i | 0.904743 | − | 0.522354i | 0.0260071 | − | 0.999662i | \(-0.491721\pi\) |
0.878736 | + | 0.477308i | \(0.158387\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 564.469 | − | 977.690i | 0.911905 | − | 1.57947i | 0.100535 | − | 0.994933i | \(-0.467944\pi\) |
0.811370 | − | 0.584533i | \(-0.198722\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −70.2276 | + | 40.5459i | −0.113088 | + | 0.0652913i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 84.5449 | + | 48.8120i | 0.135706 | + | 0.0783499i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 146.510 | + | 253.763i | 0.234416 | + | 0.406021i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −926.333 | − | 534.818i | −1.47740 | − | 0.852980i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 26.4544i | − | 0.0420579i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −143.212 | −0.226961 | −0.113480 | − | 0.993540i | \(-0.536200\pi\) | ||||
−0.113480 | + | 0.993540i | \(0.536200\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −252.894 | − | 438.025i | −0.399516 | − | 0.691983i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −625.343 | + | 361.042i | −0.984792 | + | 0.568570i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 160.586 | − | 278.143i | 0.252097 | − | 0.436645i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 475.946i | 0.744830i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −198.418 | − | 114.557i | −0.309545 | − | 0.178716i | 0.337178 | − | 0.941441i | \(-0.390528\pi\) |
−0.646723 | + | 0.762725i | \(0.723861\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −554.682 | − | 960.737i | −0.862646 | − | 1.49415i | −0.869365 | − | 0.494170i | \(-0.835472\pi\) |
0.00671893 | − | 0.999977i | \(-0.497861\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 402.589i | 0.624169i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1052.57i | 1.62685i | 0.581669 | + | 0.813426i | \(0.302400\pi\) | ||||
−0.581669 | + | 0.813426i | \(0.697600\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −101.000 | −0.155624 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1044.39 | −1.60429 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −795.499 | + | 459.282i | −1.21822 | + | 0.703341i | −0.964537 | − | 0.263946i | \(-0.914976\pi\) |
−0.253685 | + | 0.967287i | \(0.581643\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −207.772 | + | 359.872i | −0.317210 | + | 0.549424i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 619.090 | 0.942298 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 207.288 | + | 119.678i | 0.314549 | + | 0.181605i | 0.648960 | − | 0.760822i | \(-0.275204\pi\) |
−0.334411 | + | 0.942427i | \(0.608537\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −177.793 | − | 307.946i | −0.268976 | − | 0.465879i | 0.699622 | − | 0.714513i | \(-0.253352\pi\) |
−0.968598 | + | 0.248634i | \(0.920018\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −18.4837 | + | 10.6715i | −0.0278788 | + | 0.0160958i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 1084.75i | − | 1.63121i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 45.7673 | 0.0686167 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −234.560 | + | 406.270i | −0.350613 | + | 0.607280i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −583.328 | + | 336.784i | −0.869341 | + | 0.501914i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 291.429 | − | 504.769i | 0.433029 | − | 0.750028i | −0.564103 | − | 0.825704i | \(-0.690778\pi\) |
0.997132 | + | 0.0756758i | \(0.0241114\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −129.545 | + | 224.378i | −0.191918 | + | 0.332412i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −154.450 | − | 89.1718i | −0.228139 | − | 0.131716i | 0.381574 | − | 0.924338i | \(-0.375382\pi\) |
−0.609713 | + | 0.792622i | \(0.708715\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −648.883 | − | 1123.90i | −0.955645 | − | 1.65522i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −259.953 | − | 150.084i | −0.381723 | − | 0.220388i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 660.510i | 0.967072i | 0.875325 | + | 0.483536i | \(0.160648\pi\) | ||||
−0.875325 | + | 0.483536i | \(0.839352\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 749.080 | 1.09355 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 314.985 | + | 545.569i | 0.458493 | + | 0.794133i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −243.959 | + | 140.850i | −0.354077 | + | 0.204427i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.2571 | − | 74.9236i | 0.0626008 | − | 0.108428i | −0.833026 | − | 0.553233i | \(-0.813394\pi\) |
0.895627 | + | 0.444805i | \(0.146727\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1646.86 | − | 950.816i | 2.37642 | − | 1.37203i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 322.834 | + | 186.388i | 0.464509 | + | 0.268184i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −50.6469 | − | 87.7231i | −0.0726642 | − | 0.125858i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 921.380i | 1.31814i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1204.11i | 1.71770i | 0.512227 | + | 0.858850i | \(0.328821\pi\) | ||||
−0.512227 | + | 0.858850i | \(0.671179\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 224.686 | 0.319610 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 791.241 | 1.12233 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.3184 | + | 8.84406i | −0.0216667 | + | 0.0125093i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 401.944 | − | 696.187i | 0.566917 | − | 0.981928i | −0.429952 | − | 0.902852i | \(-0.641470\pi\) |
0.996869 | − | 0.0790766i | \(-0.0251972\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −115.136 | + | 199.421i | −0.161935 | + | 0.280479i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 70.7531 | + | 40.8493i | 0.0992329 | + | 0.0572921i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −90.6510 | − | 157.012i | −0.126785 | − | 0.219597i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 211.166 | − | 121.917i | 0.294514 | − | 0.170038i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 66.1101i | − | 0.0919474i | −0.998943 | − | 0.0459737i | \(-0.985361\pi\) | ||
0.998943 | − | 0.0459737i | \(-0.0146390\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.2939 | −0.0281469 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 540.288 | − | 935.806i | 0.747286 | − | 1.29434i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 126.637 | − | 73.1138i | 0.174671 | − | 0.100847i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 259.834 | − | 450.045i | 0.357405 | − | 0.619044i | −0.630121 | − | 0.776497i | \(-0.716995\pi\) |
0.987527 | + | 0.157453i | \(0.0503281\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 75.2918 | + | 43.4698i | 0.102998 | + | 0.0594662i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 80.1459 | + | 138.817i | 0.109340 | + | 0.189382i | 0.915503 | − | 0.402311i | \(-0.131793\pi\) |
−0.806163 | + | 0.591693i | \(0.798460\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1170.48 | + | 675.779i | 1.59249 | + | 0.919427i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1799.24i | 2.44130i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 122.849 | 0.166237 | 0.0831184 | − | 0.996540i | \(-0.473512\pi\) | ||||
0.0831184 | + | 0.996540i | \(0.473512\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −90.6367 | − | 156.987i | −0.122317 | − | 0.211859i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 585.944 | − | 338.295i | 0.788619 | − | 0.455309i | −0.0508572 | − | 0.998706i | \(-0.516195\pi\) |
0.839476 | + | 0.543397i | \(0.182862\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −180.398 | + | 312.458i | −0.242145 | + | 0.419407i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −468.771 | − | 270.645i | −0.627539 | − | 0.362310i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1144.06 | − | 660.523i | −1.52745 | − | 0.881873i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 171.430 | + | 296.925i | 0.228268 | + | 0.395373i | 0.957295 | − | 0.289113i | \(-0.0933603\pi\) |
−0.729027 | + | 0.684485i | \(0.760027\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 1200.54i | − | 1.59434i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 64.4229i | − | 0.0853283i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −452.220 | −0.597385 | −0.298692 | − | 0.954349i | \(-0.596550\pi\) | ||||
−0.298692 | + | 0.954349i | \(0.596550\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −148.757 | −0.195991 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 203.520 | − | 117.503i | 0.267438 | − | 0.154405i | −0.360285 | − | 0.932842i | \(-0.617320\pi\) |
0.627723 | + | 0.778437i | \(0.283987\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 92.1714 | − | 159.646i | 0.120801 | − | 0.209234i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −44.9082 | − | 77.7832i | −0.0587035 | − | 0.101677i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.8235 | − | 8.55834i | −0.0193266 | − | 0.0111582i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 318.439 | + | 551.552i | 0.414095 | + | 0.717233i | 0.995333 | − | 0.0965005i | \(-0.0307649\pi\) |
−0.581238 | + | 0.813733i | \(0.697432\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 945.104 | − | 545.656i | 1.22582 | − | 0.707725i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 592.885i | − | 0.766992i | −0.923543 | − | 0.383496i | \(-0.874720\pi\) | ||
0.923543 | − | 0.383496i | \(-0.125280\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 261.029 | 0.336811 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −199.727 | + | 345.936i | −0.257048 | + | 0.445221i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 745.059 | − | 430.160i | 0.956430 | − | 0.552195i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −436.545 | + | 756.118i | −0.558956 | + | 0.968141i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −356.317 | − | 205.720i | −0.455067 | − | 0.262733i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −720.480 | − | 415.969i | −0.917808 | − | 0.529897i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −666.904 | − | 1155.11i | −0.847400 | − | 1.46774i | −0.883520 | − | 0.468393i | \(-0.844833\pi\) |
0.0361199 | − | 0.999347i | \(-0.488500\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 979.711 | + | 565.637i | 1.24171 | + | 0.716903i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1360.67i | 1.72020i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −114.151 | −0.143948 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −592.727 | − | 1026.63i | −0.745568 | − | 1.29136i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 638.540 | − | 368.661i | 0.801179 | − | 0.462561i | −0.0427041 | − | 0.999088i | \(-0.513597\pi\) |
0.843883 | + | 0.536527i | \(0.180264\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 85.4347 | − | 147.977i | 0.106927 | − | 0.185203i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 68.6528i | 0.0857089i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 983.524 | + | 567.838i | 1.22481 | + | 0.707146i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −75.4296 | − | 130.648i | −0.0937014 | − | 0.162296i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 512.546i | 0.635125i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 71.6833i | 0.0886073i | 0.999018 | + | 0.0443037i | \(0.0141069\pi\) | ||||
−0.999018 | + | 0.0443037i | \(0.985893\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1086.24 | −1.33938 | −0.669692 | − | 0.742639i | \(-0.733574\pi\) | ||||
−0.669692 | + | 0.742639i | \(0.733574\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 151.212 | 0.185993 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 587.302 | − | 339.079i | 0.720616 | − | 0.416048i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −369.202 | + | 639.477i | −0.451900 | + | 0.782713i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 322.273 | 0.393496 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1232.92 | + | 711.829i | 1.50173 | + | 0.867026i | 0.999998 | + | 0.00200552i | \(0.000638377\pi\) |
0.501736 | + | 0.865021i | \(0.332695\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −217.379 | − | 376.511i | −0.264129 | − | 0.457486i | 0.703206 | − | 0.710986i | \(-0.251751\pi\) |
−0.967335 | + | 0.253501i | \(0.918418\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −411.606 | + | 237.641i | −0.498917 | + | 0.288050i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 677.821i | 0.819614i | 0.912172 | + | 0.409807i | \(0.134404\pi\) | ||||
−0.912172 | + | 0.409807i | \(0.865596\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −995.775 | −1.20118 | −0.600588 | − | 0.799558i | \(-0.705067\pi\) | ||||
−0.600588 | + | 0.799558i | \(0.705067\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −38.4092 | + | 66.5267i | −0.0462204 | + | 0.0800561i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 252.767 | − | 145.935i | 0.303442 | − | 0.175192i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −369.802 | + | 640.516i | −0.442877 | + | 0.767085i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −367.228 | − | 636.057i | −0.438743 | − | 0.759924i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1149.53 | − | 663.681i | −1.37012 | − | 0.791038i | −0.379176 | − | 0.925325i | \(-0.623793\pi\) |
−0.990943 | + | 0.134286i | \(0.957126\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −304.394 | − | 527.226i | −0.361943 | − | 0.626903i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 870.802 | + | 502.758i | 1.03298 | + | 0.596391i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 632.566i | 0.748599i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1939.86 | 2.29027 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22.4694 | − | 38.9181i | −0.0264657 | − | 0.0458399i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27.0612 | − | 15.6238i | 0.0317993 | − | 0.0183594i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 685.317 | − | 1187.00i | 0.803420 | − | 1.39156i | −0.113932 | − | 0.993489i | \(-0.536345\pi\) |
0.917352 | − | 0.398076i | \(-0.130322\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 660.637 | − | 381.419i | 0.772675 | − | 0.446104i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1038.74 | − | 599.717i | −1.21207 | − | 0.699787i | −0.248857 | − | 0.968540i | \(-0.580055\pi\) |
−0.963209 | + | 0.268753i | \(0.913388\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.1163 | + | 53.8951i | 0.0362239 | + | 0.0627416i | 0.883569 | − | 0.468301i | \(-0.155134\pi\) |
−0.847345 | + | 0.531043i | \(0.821800\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1529.50i | 1.77643i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 154.565i | − | 0.179102i | −0.995982 | − | 0.0895509i | \(-0.971457\pi\) | ||
0.995982 | − | 0.0895509i | \(-0.0285432\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −236.555 | −0.273474 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 847.604 | 0.977629 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −365.823 | + | 211.208i | −0.420971 | + | 0.243048i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −152.460 | + | 264.069i | −0.175040 | + | 0.303179i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 456.318 | − | 790.367i | 0.522701 | − | 0.905345i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1504.92 | − | 868.867i | −1.71991 | − | 0.992991i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 548.187 | + | 949.487i | 0.625070 | + | 1.08265i | 0.988527 | + | 0.151043i | \(0.0482631\pi\) |
−0.363457 | + | 0.931611i | \(0.618404\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −783.046 | + | 452.092i | −0.890837 | + | 0.514325i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1241.22i | 1.40888i | 0.709765 | + | 0.704438i | \(0.248801\pi\) | ||||
−0.709765 | + | 0.704438i | \(0.751199\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −553.555 | −0.626903 | −0.313451 | − | 0.949604i | \(-0.601485\pi\) | ||||
−0.313451 | + | 0.949604i | \(0.601485\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 36.0153 | − | 62.3803i | 0.0406953 | − | 0.0704863i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 351.905 | − | 203.173i | 0.396736 | − | 0.229056i | −0.288338 | − | 0.957529i | \(-0.593103\pi\) |
0.685075 | + | 0.728473i | \(0.259769\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1177.28 | − | 2039.11i | 1.32428 | − | 2.29371i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1158.13 | + | 668.649i | 1.29981 | + | 0.750448i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1256.82 | + | 725.623i | 1.40741 | + | 0.812568i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −142.688 | − | 247.142i | −0.159428 | − | 0.276137i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −21.8326 | − | 12.6051i | −0.0243396 | − | 0.0140525i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 414.519i | 0.461089i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −256.000 | −0.284129 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −656.379 | − | 1136.88i | −0.726887 | − | 1.25900i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 331.727 | − | 191.522i | 0.366549 | − | 0.211627i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −231.712 | + | 401.337i | −0.255471 | + | 0.442489i | −0.965023 | − | 0.262164i | \(-0.915564\pi\) |
0.709552 | + | 0.704653i | \(0.248897\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.7724 | − | 6.21947i | −0.0118509 | − | 0.00684211i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −997.489 | − | 575.900i | −1.09494 | − | 0.632163i | −0.160051 | − | 0.987109i | \(-0.551166\pi\) |
−0.934887 | + | 0.354946i | \(0.884499\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −496.480 | − | 859.928i | −0.543789 | − | 0.941871i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 480.372i | − | 0.524997i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 1355.00i | − | 1.47765i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −944.665 | −1.02793 | −0.513964 | − | 0.857812i | \(-0.671823\pi\) | ||||
−0.513964 | + | 0.857812i | \(0.671823\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 134.241 | 0.145755 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −128.141 | + | 73.9821i | −0.138831 | + | 0.0801540i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 49.9184 | − | 86.4611i | 0.0539658 | − | 0.0934715i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.13571 | − | 12.3594i | −0.00769763 | − | 0.0133327i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −912.702 | − | 526.949i | −0.982456 | − | 0.567221i | −0.0794456 | − | 0.996839i | \(-0.525315\pi\) |
−0.903011 | + | 0.429618i | \(0.858648\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1239.47 | + | 2146.83i | 1.33134 | + | 2.30594i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −844.044 | + | 487.309i | −0.904656 | + | 0.522303i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 164.762i | − | 0.176216i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 561.392 | 0.599137 | 0.299569 | − | 0.954075i | \(-0.403157\pi\) | ||||
0.299569 | + | 0.954075i | \(0.403157\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −470.682 | + | 815.244i | −0.501258 | + | 0.868205i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −98.4092 | + | 56.8166i | −0.104579 | + | 0.0603789i | −0.551377 | − | 0.834256i | \(-0.685898\pi\) |
0.446798 | + | 0.894635i | \(0.352564\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 59.8235 | − | 103.617i | 0.0634395 | − | 0.109880i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1356.20i | 1.43513i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −62.6510 | − | 36.1716i | −0.0661574 | − | 0.0381960i | 0.466556 | − | 0.884491i | \(-0.345494\pi\) |
−0.532714 | + | 0.846295i | \(0.678828\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 96.2327 | + | 166.680i | 0.101404 | + | 0.175637i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −143.954 | − | 83.1119i | −0.151371 | − | 0.0873942i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 776.447i | 0.814739i | 0.913263 | + | 0.407370i | \(0.133554\pi\) | ||||
−0.913263 | + | 0.407370i | \(0.866446\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1280.56 | 1.34090 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −377.379 | − | 653.639i | −0.394335 | − | 0.683008i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2115.35 | + | 1221.30i | −2.20578 | + | 1.27351i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 110.524 | − | 191.434i | 0.115010 | − | 0.199203i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 929.008i | − | 0.964702i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 71.4479 | + | 41.2505i | 0.0740393 | + | 0.0427466i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.3888 | + | 19.7259i | 0.0117774 | + | 0.0203991i | 0.871854 | − | 0.489766i | \(-0.162918\pi\) |
−0.860077 | + | 0.510165i | \(0.829584\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 164.736i | − | 0.170006i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1016.98i | 1.04735i | 0.851919 | + | 0.523674i | \(0.175439\pi\) | ||||
−0.851919 | + | 0.523674i | \(0.824561\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1215.54 | −1.24928 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −80.5470 | −0.0826123 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 975.802 | − | 563.380i | 0.998774 | − | 0.576642i | 0.0908886 | − | 0.995861i | \(-0.471029\pi\) |
0.907885 | + | 0.419219i | \(0.137696\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −62.9694 | + | 109.066i | −0.0643201 | + | 0.111406i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 129.637 | 0.132148 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 280.105 | + | 161.719i | 0.284949 | + | 0.164516i | 0.635662 | − | 0.771968i | \(-0.280727\pi\) |
−0.350713 | + | 0.936483i | \(0.614061\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 63.8592 | + | 110.607i | 0.0648317 | + | 0.112292i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2234.41 | + | 1290.03i | −2.26384 | + | 1.30703i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 102.692i | 0.103834i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1961.47 | −1.97929 | −0.989644 | − | 0.143547i | \(-0.954149\pi\) | ||||
−0.989644 | + | 0.143547i | \(0.954149\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 23.1061 | − | 40.0210i | 0.0232690 | − | 0.0403031i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −210.737 | + | 121.669i | −0.211796 | + | 0.122280i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −559.954 | + | 969.869i | −0.561639 | + | 0.972787i | 0.435715 | + | 0.900085i | \(0.356496\pi\) |
−0.997354 | + | 0.0727024i | \(0.976838\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −280.910 | −0.281191 |
(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 | 144.3.q.d.65.1 | 4 | ||
3.2 | odd | 2 | 432.3.q.c.305.2 | 4 | |||
4.3 | odd | 2 | 72.3.m.a.65.1 | yes | 4 | ||
8.3 | odd | 2 | 576.3.q.h.65.2 | 4 | |||
8.5 | even | 2 | 576.3.q.c.65.2 | 4 | |||
9.2 | odd | 6 | 1296.3.e.c.161.3 | 4 | |||
9.4 | even | 3 | 432.3.q.c.17.2 | 4 | |||
9.5 | odd | 6 | inner | 144.3.q.d.113.1 | 4 | ||
9.7 | even | 3 | 1296.3.e.c.161.2 | 4 | |||
12.11 | even | 2 | 216.3.m.a.89.2 | 4 | |||
24.5 | odd | 2 | 1728.3.q.f.1601.1 | 4 | |||
24.11 | even | 2 | 1728.3.q.e.1601.1 | 4 | |||
36.7 | odd | 6 | 648.3.e.b.161.2 | 4 | |||
36.11 | even | 6 | 648.3.e.b.161.3 | 4 | |||
36.23 | even | 6 | 72.3.m.a.41.1 | ✓ | 4 | ||
36.31 | odd | 6 | 216.3.m.a.17.2 | 4 | |||
72.5 | odd | 6 | 576.3.q.c.257.2 | 4 | |||
72.13 | even | 6 | 1728.3.q.f.449.1 | 4 | |||
72.59 | even | 6 | 576.3.q.h.257.2 | 4 | |||
72.67 | odd | 6 | 1728.3.q.e.449.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.3.m.a.41.1 | ✓ | 4 | 36.23 | even | 6 | ||
72.3.m.a.65.1 | yes | 4 | 4.3 | odd | 2 | ||
144.3.q.d.65.1 | 4 | 1.1 | even | 1 | trivial | ||
144.3.q.d.113.1 | 4 | 9.5 | odd | 6 | inner | ||
216.3.m.a.17.2 | 4 | 36.31 | odd | 6 | |||
216.3.m.a.89.2 | 4 | 12.11 | even | 2 | |||
432.3.q.c.17.2 | 4 | 9.4 | even | 3 | |||
432.3.q.c.305.2 | 4 | 3.2 | odd | 2 | |||
576.3.q.c.65.2 | 4 | 8.5 | even | 2 | |||
576.3.q.c.257.2 | 4 | 72.5 | odd | 6 | |||
576.3.q.h.65.2 | 4 | 8.3 | odd | 2 | |||
576.3.q.h.257.2 | 4 | 72.59 | even | 6 | |||
648.3.e.b.161.2 | 4 | 36.7 | odd | 6 | |||
648.3.e.b.161.3 | 4 | 36.11 | even | 6 | |||
1296.3.e.c.161.2 | 4 | 9.7 | even | 3 | |||
1296.3.e.c.161.3 | 4 | 9.2 | odd | 6 | |||
1728.3.q.e.449.1 | 4 | 72.67 | odd | 6 | |||
1728.3.q.e.1601.1 | 4 | 24.11 | even | 2 | |||
1728.3.q.f.449.1 | 4 | 72.13 | even | 6 | |||
1728.3.q.f.1601.1 | 4 | 24.5 | odd | 2 |