Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6762,2,Mod(1,6762)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6762, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6762.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6762.a (trivial) |
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: | yes |
Analytic conductor: | \(53.9948418468\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{41}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 966) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.70156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6762.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.70156 | 1.65539 | 0.827694 | − | 0.561179i | \(-0.189652\pi\) | ||||
0.827694 | + | 0.561179i | \(0.189652\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.70156 | −1.17054 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −5.70156 | −1.58133 | −0.790664 | − | 0.612250i | \(-0.790265\pi\) | ||||
−0.790664 | + | 0.612250i | \(0.790265\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.70156 | −0.955739 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 5.40312 | 1.23956 | 0.619781 | − | 0.784775i | \(-0.287221\pi\) | ||||
0.619781 | + | 0.784775i | \(0.287221\pi\) | |||||||
\(20\) | 3.70156 | 0.827694 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 8.70156 | 1.74031 | ||||||||
\(26\) | 5.70156 | 1.11817 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.298438 | 0.0554185 | 0.0277093 | − | 0.999616i | \(-0.491179\pi\) | ||||
0.0277093 | + | 0.999616i | \(0.491179\pi\) | |||||||
\(30\) | 3.70156 | 0.675810 | ||||||||
\(31\) | −6.00000 | −1.07763 | −0.538816 | − | 0.842424i | \(-0.681128\pi\) | ||||
−0.538816 | + | 0.842424i | \(0.681128\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 3.70156 | 0.608533 | 0.304267 | − | 0.952587i | \(-0.401589\pi\) | ||||
0.304267 | + | 0.952587i | \(0.401589\pi\) | |||||||
\(38\) | −5.40312 | −0.876502 | ||||||||
\(39\) | 5.70156 | 0.912981 | ||||||||
\(40\) | −3.70156 | −0.585268 | ||||||||
\(41\) | −7.70156 | −1.20278 | −0.601391 | − | 0.798955i | \(-0.705387\pi\) | ||||
−0.601391 | + | 0.798955i | \(0.705387\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.70156 | 0.869480 | 0.434740 | − | 0.900556i | \(-0.356840\pi\) | ||||
0.434740 | + | 0.900556i | \(0.356840\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.70156 | 0.551796 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −3.70156 | −0.539928 | −0.269964 | − | 0.962870i | \(-0.587012\pi\) | ||||
−0.269964 | + | 0.962870i | \(0.587012\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −8.70156 | −1.23059 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.70156 | −0.790664 | ||||||||
\(53\) | 9.40312 | 1.29162 | 0.645809 | − | 0.763499i | \(-0.276520\pi\) | ||||
0.645809 | + | 0.763499i | \(0.276520\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.40312 | −0.715661 | ||||||||
\(58\) | −0.298438 | −0.0391868 | ||||||||
\(59\) | 0.596876 | 0.0777066 | 0.0388533 | − | 0.999245i | \(-0.487629\pi\) | ||||
0.0388533 | + | 0.999245i | \(0.487629\pi\) | |||||||
\(60\) | −3.70156 | −0.477870 | ||||||||
\(61\) | −10.0000 | −1.28037 | −0.640184 | − | 0.768221i | \(-0.721142\pi\) | ||||
−0.640184 | + | 0.768221i | \(0.721142\pi\) | |||||||
\(62\) | 6.00000 | 0.762001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −21.1047 | −2.61771 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.40312 | 0.878589 | 0.439295 | − | 0.898343i | \(-0.355228\pi\) | ||||
0.439295 | + | 0.898343i | \(0.355228\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 5.40312 | 0.632388 | 0.316194 | − | 0.948695i | \(-0.397595\pi\) | ||||
0.316194 | + | 0.948695i | \(0.397595\pi\) | |||||||
\(74\) | −3.70156 | −0.430298 | ||||||||
\(75\) | −8.70156 | −1.00477 | ||||||||
\(76\) | 5.40312 | 0.619781 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.70156 | −0.645575 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 3.70156 | 0.413847 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 7.70156 | 0.850495 | ||||||||
\(83\) | 2.59688 | 0.285044 | 0.142522 | − | 0.989792i | \(-0.454479\pi\) | ||||
0.142522 | + | 0.989792i | \(0.454479\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.70156 | −0.614815 | ||||||||
\(87\) | −0.298438 | −0.0319959 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.4031 | 1.63273 | 0.816364 | − | 0.577538i | \(-0.195986\pi\) | ||||
0.816364 | + | 0.577538i | \(0.195986\pi\) | |||||||
\(90\) | −3.70156 | −0.390179 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 6.00000 | 0.622171 | ||||||||
\(94\) | 3.70156 | 0.381787 | ||||||||
\(95\) | 20.0000 | 2.05196 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 1.10469 | 0.112164 | 0.0560820 | − | 0.998426i | \(-0.482139\pi\) | ||||
0.0560820 | + | 0.998426i | \(0.482139\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.70156 | 0.870156 | ||||||||
\(101\) | −4.59688 | −0.457406 | −0.228703 | − | 0.973496i | \(-0.573449\pi\) | ||||
−0.228703 | + | 0.973496i | \(0.573449\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.1047 | 1.68537 | 0.842687 | − | 0.538403i | \(-0.180972\pi\) | ||||
0.842687 | + | 0.538403i | \(0.180972\pi\) | |||||||
\(104\) | 5.70156 | 0.559084 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.40312 | −0.913312 | ||||||||
\(107\) | 14.8062 | 1.43137 | 0.715687 | − | 0.698421i | \(-0.246114\pi\) | ||||
0.715687 | + | 0.698421i | \(0.246114\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 15.7016 | 1.50394 | 0.751968 | − | 0.659199i | \(-0.229105\pi\) | ||||
0.751968 | + | 0.659199i | \(0.229105\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.70156 | −0.351337 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.29844 | −0.404363 | −0.202182 | − | 0.979348i | \(-0.564803\pi\) | ||||
−0.202182 | + | 0.979348i | \(0.564803\pi\) | |||||||
\(114\) | 5.40312 | 0.506049 | ||||||||
\(115\) | −3.70156 | −0.345172 | ||||||||
\(116\) | 0.298438 | 0.0277093 | ||||||||
\(117\) | −5.70156 | −0.527110 | ||||||||
\(118\) | −0.596876 | −0.0549469 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.70156 | 0.337905 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 10.0000 | 0.905357 | ||||||||
\(123\) | 7.70156 | 0.694426 | ||||||||
\(124\) | −6.00000 | −0.538816 | ||||||||
\(125\) | 13.7016 | 1.22550 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.1047 | 1.51780 | 0.758898 | − | 0.651210i | \(-0.225738\pi\) | ||||
0.758898 | + | 0.651210i | \(0.225738\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −5.70156 | −0.501995 | ||||||||
\(130\) | 21.1047 | 1.85100 | ||||||||
\(131\) | −15.4031 | −1.34578 | −0.672889 | − | 0.739744i | \(-0.734947\pi\) | ||||
−0.672889 | + | 0.739744i | \(0.734947\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.00000 | −0.345547 | ||||||||
\(135\) | −3.70156 | −0.318580 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.895314 | 0.0764918 | 0.0382459 | − | 0.999268i | \(-0.487823\pi\) | ||||
0.0382459 | + | 0.999268i | \(0.487823\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | 21.1047 | 1.79008 | 0.895038 | − | 0.445990i | \(-0.147148\pi\) | ||||
0.895038 | + | 0.445990i | \(0.147148\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.70156 | 0.311728 | ||||||||
\(142\) | −7.40312 | −0.621256 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 1.10469 | 0.0917392 | ||||||||
\(146\) | −5.40312 | −0.447166 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.70156 | 0.304267 | ||||||||
\(149\) | −17.4031 | −1.42572 | −0.712860 | − | 0.701307i | \(-0.752600\pi\) | ||||
−0.712860 | + | 0.701307i | \(0.752600\pi\) | |||||||
\(150\) | 8.70156 | 0.710480 | ||||||||
\(151\) | 9.10469 | 0.740929 | 0.370464 | − | 0.928847i | \(-0.379199\pi\) | ||||
0.370464 | + | 0.928847i | \(0.379199\pi\) | |||||||
\(152\) | −5.40312 | −0.438251 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −22.2094 | −1.78390 | ||||||||
\(156\) | 5.70156 | 0.456490 | ||||||||
\(157\) | 13.4031 | 1.06969 | 0.534843 | − | 0.844952i | \(-0.320371\pi\) | ||||
0.534843 | + | 0.844952i | \(0.320371\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.40312 | −0.745716 | ||||||||
\(160\) | −3.70156 | −0.292634 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −12.0000 | −0.939913 | −0.469956 | − | 0.882690i | \(-0.655730\pi\) | ||||
−0.469956 | + | 0.882690i | \(0.655730\pi\) | |||||||
\(164\) | −7.70156 | −0.601391 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.59688 | −0.201557 | ||||||||
\(167\) | 21.4031 | 1.65622 | 0.828112 | − | 0.560563i | \(-0.189415\pi\) | ||||
0.828112 | + | 0.560563i | \(0.189415\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.5078 | 1.50060 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.40312 | 0.413187 | ||||||||
\(172\) | 5.70156 | 0.434740 | ||||||||
\(173\) | 3.40312 | 0.258735 | 0.129367 | − | 0.991597i | \(-0.458705\pi\) | ||||
0.129367 | + | 0.991597i | \(0.458705\pi\) | |||||||
\(174\) | 0.298438 | 0.0226245 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.596876 | −0.0448639 | ||||||||
\(178\) | −15.4031 | −1.15451 | ||||||||
\(179\) | 5.70156 | 0.426155 | 0.213077 | − | 0.977035i | \(-0.431651\pi\) | ||||
0.213077 | + | 0.977035i | \(0.431651\pi\) | |||||||
\(180\) | 3.70156 | 0.275898 | ||||||||
\(181\) | −16.8062 | −1.24920 | −0.624599 | − | 0.780945i | \(-0.714738\pi\) | ||||
−0.624599 | + | 0.780945i | \(0.714738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.0000 | 0.739221 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 13.7016 | 1.00736 | ||||||||
\(186\) | −6.00000 | −0.439941 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −3.70156 | −0.269964 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −20.0000 | −1.45095 | ||||||||
\(191\) | 22.8062 | 1.65020 | 0.825101 | − | 0.564985i | \(-0.191118\pi\) | ||||
0.825101 | + | 0.564985i | \(0.191118\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −7.10469 | −0.511407 | −0.255703 | − | 0.966755i | \(-0.582307\pi\) | ||||
−0.255703 | + | 0.966755i | \(0.582307\pi\) | |||||||
\(194\) | −1.10469 | −0.0793119 | ||||||||
\(195\) | 21.1047 | 1.51134 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.50781 | 0.463662 | 0.231831 | − | 0.972756i | \(-0.425528\pi\) | ||||
0.231831 | + | 0.972756i | \(0.425528\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.10469 | −0.0783091 | −0.0391546 | − | 0.999233i | \(-0.512466\pi\) | ||||
−0.0391546 | + | 0.999233i | \(0.512466\pi\) | |||||||
\(200\) | −8.70156 | −0.615293 | ||||||||
\(201\) | −4.00000 | −0.282138 | ||||||||
\(202\) | 4.59688 | 0.323435 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −28.5078 | −1.99107 | ||||||||
\(206\) | −17.1047 | −1.19174 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | −5.70156 | −0.395332 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | 9.40312 | 0.645809 | ||||||||
\(213\) | −7.40312 | −0.507254 | ||||||||
\(214\) | −14.8062 | −1.01213 | ||||||||
\(215\) | 21.1047 | 1.43933 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −15.7016 | −1.06344 | ||||||||
\(219\) | −5.40312 | −0.365109 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 3.70156 | 0.248433 | ||||||||
\(223\) | 20.8062 | 1.39329 | 0.696645 | − | 0.717416i | \(-0.254675\pi\) | ||||
0.696645 | + | 0.717416i | \(0.254675\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.70156 | 0.580104 | ||||||||
\(226\) | 4.29844 | 0.285928 | ||||||||
\(227\) | 26.5078 | 1.75939 | 0.879693 | − | 0.475543i | \(-0.157748\pi\) | ||||
0.879693 | + | 0.475543i | \(0.157748\pi\) | |||||||
\(228\) | −5.40312 | −0.357831 | ||||||||
\(229\) | −28.2094 | −1.86413 | −0.932064 | − | 0.362294i | \(-0.881994\pi\) | ||||
−0.932064 | + | 0.362294i | \(0.881994\pi\) | |||||||
\(230\) | 3.70156 | 0.244074 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.298438 | −0.0195934 | ||||||||
\(233\) | 28.8062 | 1.88716 | 0.943580 | − | 0.331145i | \(-0.107435\pi\) | ||||
0.943580 | + | 0.331145i | \(0.107435\pi\) | |||||||
\(234\) | 5.70156 | 0.372723 | ||||||||
\(235\) | −13.7016 | −0.893791 | ||||||||
\(236\) | 0.596876 | 0.0388533 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.8062 | −1.21648 | −0.608238 | − | 0.793755i | \(-0.708123\pi\) | ||||
−0.608238 | + | 0.793755i | \(0.708123\pi\) | |||||||
\(240\) | −3.70156 | −0.238935 | ||||||||
\(241\) | −5.10469 | −0.328822 | −0.164411 | − | 0.986392i | \(-0.552572\pi\) | ||||
−0.164411 | + | 0.986392i | \(0.552572\pi\) | |||||||
\(242\) | 11.0000 | 0.707107 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −10.0000 | −0.640184 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.70156 | −0.491034 | ||||||||
\(247\) | −30.8062 | −1.96015 | ||||||||
\(248\) | 6.00000 | 0.381000 | ||||||||
\(249\) | −2.59688 | −0.164570 | ||||||||
\(250\) | −13.7016 | −0.866563 | ||||||||
\(251\) | −13.9109 | −0.878050 | −0.439025 | − | 0.898475i | \(-0.644676\pi\) | ||||
−0.439025 | + | 0.898475i | \(0.644676\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −17.1047 | −1.07324 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −23.6125 | −1.47291 | −0.736454 | − | 0.676488i | \(-0.763501\pi\) | ||||
−0.736454 | + | 0.676488i | \(0.763501\pi\) | |||||||
\(258\) | 5.70156 | 0.354964 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −21.1047 | −1.30886 | ||||||||
\(261\) | 0.298438 | 0.0184728 | ||||||||
\(262\) | 15.4031 | 0.951608 | ||||||||
\(263\) | −16.5078 | −1.01792 | −0.508958 | − | 0.860792i | \(-0.669969\pi\) | ||||
−0.508958 | + | 0.860792i | \(0.669969\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 34.8062 | 2.13813 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.4031 | −0.942656 | ||||||||
\(268\) | 4.00000 | 0.244339 | ||||||||
\(269\) | 3.40312 | 0.207492 | 0.103746 | − | 0.994604i | \(-0.466917\pi\) | ||||
0.103746 | + | 0.994604i | \(0.466917\pi\) | |||||||
\(270\) | 3.70156 | 0.225270 | ||||||||
\(271\) | −17.4031 | −1.05716 | −0.528582 | − | 0.848882i | \(-0.677276\pi\) | ||||
−0.528582 | + | 0.848882i | \(0.677276\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.895314 | −0.0540879 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.00000 | 0.0601929 | ||||||||
\(277\) | −13.4031 | −0.805316 | −0.402658 | − | 0.915351i | \(-0.631914\pi\) | ||||
−0.402658 | + | 0.915351i | \(0.631914\pi\) | |||||||
\(278\) | −21.1047 | −1.26577 | ||||||||
\(279\) | −6.00000 | −0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.29844 | 0.256423 | 0.128212 | − | 0.991747i | \(-0.459076\pi\) | ||||
0.128212 | + | 0.991747i | \(0.459076\pi\) | |||||||
\(282\) | −3.70156 | −0.220425 | ||||||||
\(283\) | 10.0000 | 0.594438 | 0.297219 | − | 0.954809i | \(-0.403941\pi\) | ||||
0.297219 | + | 0.954809i | \(0.403941\pi\) | |||||||
\(284\) | 7.40312 | 0.439295 | ||||||||
\(285\) | −20.0000 | −1.18470 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | −1.10469 | −0.0648694 | ||||||||
\(291\) | −1.10469 | −0.0647579 | ||||||||
\(292\) | 5.40312 | 0.316194 | ||||||||
\(293\) | 3.19375 | 0.186581 | 0.0932905 | − | 0.995639i | \(-0.470261\pi\) | ||||
0.0932905 | + | 0.995639i | \(0.470261\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.20937 | 0.128635 | ||||||||
\(296\) | −3.70156 | −0.215149 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 17.4031 | 1.00814 | ||||||||
\(299\) | 5.70156 | 0.329730 | ||||||||
\(300\) | −8.70156 | −0.502385 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −9.10469 | −0.523916 | ||||||||
\(303\) | 4.59688 | 0.264084 | ||||||||
\(304\) | 5.40312 | 0.309890 | ||||||||
\(305\) | −37.0156 | −2.11951 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.10469 | −0.291340 | −0.145670 | − | 0.989333i | \(-0.546534\pi\) | ||||
−0.145670 | + | 0.989333i | \(0.546534\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.1047 | −0.973052 | ||||||||
\(310\) | 22.2094 | 1.26141 | ||||||||
\(311\) | 16.2094 | 0.919149 | 0.459575 | − | 0.888139i | \(-0.348002\pi\) | ||||
0.459575 | + | 0.888139i | \(0.348002\pi\) | |||||||
\(312\) | −5.70156 | −0.322787 | ||||||||
\(313\) | 4.59688 | 0.259831 | 0.129915 | − | 0.991525i | \(-0.458529\pi\) | ||||
0.129915 | + | 0.991525i | \(0.458529\pi\) | |||||||
\(314\) | −13.4031 | −0.756382 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.70156 | 0.432563 | 0.216281 | − | 0.976331i | \(-0.430607\pi\) | ||||
0.216281 | + | 0.976331i | \(0.430607\pi\) | |||||||
\(318\) | 9.40312 | 0.527301 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 3.70156 | 0.206924 | ||||||||
\(321\) | −14.8062 | −0.826404 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −49.6125 | −2.75201 | ||||||||
\(326\) | 12.0000 | 0.664619 | ||||||||
\(327\) | −15.7016 | −0.868298 | ||||||||
\(328\) | 7.70156 | 0.425248 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.6125 | −0.968070 | −0.484035 | − | 0.875049i | \(-0.660829\pi\) | ||||
−0.484035 | + | 0.875049i | \(0.660829\pi\) | |||||||
\(332\) | 2.59688 | 0.142522 | ||||||||
\(333\) | 3.70156 | 0.202844 | ||||||||
\(334\) | −21.4031 | −1.17113 | ||||||||
\(335\) | 14.8062 | 0.808952 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.4031 | 0.948009 | 0.474004 | − | 0.880523i | \(-0.342808\pi\) | ||||
0.474004 | + | 0.880523i | \(0.342808\pi\) | |||||||
\(338\) | −19.5078 | −1.06109 | ||||||||
\(339\) | 4.29844 | 0.233459 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −5.40312 | −0.292167 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −5.70156 | −0.307408 | ||||||||
\(345\) | 3.70156 | 0.199285 | ||||||||
\(346\) | −3.40312 | −0.182953 | ||||||||
\(347\) | 20.5078 | 1.10092 | 0.550458 | − | 0.834863i | \(-0.314453\pi\) | ||||
0.550458 | + | 0.834863i | \(0.314453\pi\) | |||||||
\(348\) | −0.298438 | −0.0159979 | ||||||||
\(349\) | −34.2094 | −1.83119 | −0.915593 | − | 0.402107i | \(-0.868278\pi\) | ||||
−0.915593 | + | 0.402107i | \(0.868278\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.70156 | 0.304327 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 33.3141 | 1.77313 | 0.886564 | − | 0.462606i | \(-0.153085\pi\) | ||||
0.886564 | + | 0.462606i | \(0.153085\pi\) | |||||||
\(354\) | 0.596876 | 0.0317236 | ||||||||
\(355\) | 27.4031 | 1.45441 | ||||||||
\(356\) | 15.4031 | 0.816364 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.70156 | −0.301337 | ||||||||
\(359\) | 9.70156 | 0.512029 | 0.256014 | − | 0.966673i | \(-0.417591\pi\) | ||||
0.256014 | + | 0.966673i | \(0.417591\pi\) | |||||||
\(360\) | −3.70156 | −0.195089 | ||||||||
\(361\) | 10.1938 | 0.536513 | ||||||||
\(362\) | 16.8062 | 0.883317 | ||||||||
\(363\) | 11.0000 | 0.577350 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 20.0000 | 1.04685 | ||||||||
\(366\) | −10.0000 | −0.522708 | ||||||||
\(367\) | −15.9109 | −0.830544 | −0.415272 | − | 0.909697i | \(-0.636314\pi\) | ||||
−0.415272 | + | 0.909697i | \(0.636314\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | −7.70156 | −0.400927 | ||||||||
\(370\) | −13.7016 | −0.712310 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 6.00000 | 0.311086 | ||||||||
\(373\) | −4.80625 | −0.248858 | −0.124429 | − | 0.992229i | \(-0.539710\pi\) | ||||
−0.124429 | + | 0.992229i | \(0.539710\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −13.7016 | −0.707546 | ||||||||
\(376\) | 3.70156 | 0.190893 | ||||||||
\(377\) | −1.70156 | −0.0876349 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.7016 | −0.909268 | −0.454634 | − | 0.890678i | \(-0.650230\pi\) | ||||
−0.454634 | + | 0.890678i | \(0.650230\pi\) | |||||||
\(380\) | 20.0000 | 1.02598 | ||||||||
\(381\) | −17.1047 | −0.876300 | ||||||||
\(382\) | −22.8062 | −1.16687 | ||||||||
\(383\) | −6.80625 | −0.347783 | −0.173892 | − | 0.984765i | \(-0.555634\pi\) | ||||
−0.173892 | + | 0.984765i | \(0.555634\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.10469 | 0.361619 | ||||||||
\(387\) | 5.70156 | 0.289827 | ||||||||
\(388\) | 1.10469 | 0.0560820 | ||||||||
\(389\) | 36.8062 | 1.86615 | 0.933075 | − | 0.359681i | \(-0.117114\pi\) | ||||
0.933075 | + | 0.359681i | \(0.117114\pi\) | |||||||
\(390\) | −21.1047 | −1.06868 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.4031 | 0.776985 | ||||||||
\(394\) | −6.50781 | −0.327859 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.20937 | −0.311639 | −0.155820 | − | 0.987786i | \(-0.549802\pi\) | ||||
−0.155820 | + | 0.987786i | \(0.549802\pi\) | |||||||
\(398\) | 1.10469 | 0.0553729 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.70156 | 0.435078 | ||||||||
\(401\) | 28.8062 | 1.43852 | 0.719258 | − | 0.694743i | \(-0.244482\pi\) | ||||
0.719258 | + | 0.694743i | \(0.244482\pi\) | |||||||
\(402\) | 4.00000 | 0.199502 | ||||||||
\(403\) | 34.2094 | 1.70409 | ||||||||
\(404\) | −4.59688 | −0.228703 | ||||||||
\(405\) | 3.70156 | 0.183932 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.2094 | 1.59265 | 0.796325 | − | 0.604868i | \(-0.206774\pi\) | ||||
0.796325 | + | 0.604868i | \(0.206774\pi\) | |||||||
\(410\) | 28.5078 | 1.40790 | ||||||||
\(411\) | −0.895314 | −0.0441626 | ||||||||
\(412\) | 17.1047 | 0.842687 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | 9.61250 | 0.471859 | ||||||||
\(416\) | 5.70156 | 0.279542 | ||||||||
\(417\) | −21.1047 | −1.03350 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.59688 | 0.126866 | 0.0634328 | − | 0.997986i | \(-0.479795\pi\) | ||||
0.0634328 | + | 0.997986i | \(0.479795\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.7016 | 0.765247 | 0.382624 | − | 0.923904i | \(-0.375021\pi\) | ||||
0.382624 | + | 0.923904i | \(0.375021\pi\) | |||||||
\(422\) | 12.0000 | 0.584151 | ||||||||
\(423\) | −3.70156 | −0.179976 | ||||||||
\(424\) | −9.40312 | −0.456656 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.40312 | 0.358683 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 14.8062 | 0.715687 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −21.1047 | −1.01776 | ||||||||
\(431\) | 5.10469 | 0.245884 | 0.122942 | − | 0.992414i | \(-0.460767\pi\) | ||||
0.122942 | + | 0.992414i | \(0.460767\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −17.1047 | −0.821999 | −0.410999 | − | 0.911636i | \(-0.634820\pi\) | ||||
−0.410999 | + | 0.911636i | \(0.634820\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.10469 | −0.0529657 | ||||||||
\(436\) | 15.7016 | 0.751968 | ||||||||
\(437\) | −5.40312 | −0.258466 | ||||||||
\(438\) | 5.40312 | 0.258171 | ||||||||
\(439\) | −3.19375 | −0.152429 | −0.0762147 | − | 0.997091i | \(-0.524283\pi\) | ||||
−0.0762147 | + | 0.997091i | \(0.524283\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.1047 | 0.812668 | 0.406334 | − | 0.913725i | \(-0.366807\pi\) | ||||
0.406334 | + | 0.913725i | \(0.366807\pi\) | |||||||
\(444\) | −3.70156 | −0.175668 | ||||||||
\(445\) | 57.0156 | 2.70280 | ||||||||
\(446\) | −20.8062 | −0.985204 | ||||||||
\(447\) | 17.4031 | 0.823140 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.6125 | 1.30311 | 0.651557 | − | 0.758600i | \(-0.274116\pi\) | ||||
0.651557 | + | 0.758600i | \(0.274116\pi\) | |||||||
\(450\) | −8.70156 | −0.410196 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −4.29844 | −0.202182 | ||||||||
\(453\) | −9.10469 | −0.427775 | ||||||||
\(454\) | −26.5078 | −1.24407 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.40312 | 0.253024 | ||||||||
\(457\) | −16.2094 | −0.758242 | −0.379121 | − | 0.925347i | \(-0.623774\pi\) | ||||
−0.379121 | + | 0.925347i | \(0.623774\pi\) | |||||||
\(458\) | 28.2094 | 1.31814 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.70156 | −0.172586 | ||||||||
\(461\) | −27.4031 | −1.27629 | −0.638145 | − | 0.769916i | \(-0.720298\pi\) | ||||
−0.638145 | + | 0.769916i | \(0.720298\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.1047 | −0.609026 | −0.304513 | − | 0.952508i | \(-0.598494\pi\) | ||||
−0.304513 | + | 0.952508i | \(0.598494\pi\) | |||||||
\(464\) | 0.298438 | 0.0138546 | ||||||||
\(465\) | 22.2094 | 1.02993 | ||||||||
\(466\) | −28.8062 | −1.33442 | ||||||||
\(467\) | 8.29844 | 0.384006 | 0.192003 | − | 0.981394i | \(-0.438502\pi\) | ||||
0.192003 | + | 0.981394i | \(0.438502\pi\) | |||||||
\(468\) | −5.70156 | −0.263555 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 13.7016 | 0.632006 | ||||||||
\(471\) | −13.4031 | −0.617583 | ||||||||
\(472\) | −0.596876 | −0.0274734 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 47.0156 | 2.15722 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.40312 | 0.430539 | ||||||||
\(478\) | 18.8062 | 0.860178 | ||||||||
\(479\) | −7.40312 | −0.338257 | −0.169129 | − | 0.985594i | \(-0.554095\pi\) | ||||
−0.169129 | + | 0.985594i | \(0.554095\pi\) | |||||||
\(480\) | 3.70156 | 0.168952 | ||||||||
\(481\) | −21.1047 | −0.962291 | ||||||||
\(482\) | 5.10469 | 0.232512 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11.0000 | −0.500000 | ||||||||
\(485\) | 4.08907 | 0.185675 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −13.1047 | −0.593830 | −0.296915 | − | 0.954904i | \(-0.595958\pi\) | ||||
−0.296915 | + | 0.954904i | \(0.595958\pi\) | |||||||
\(488\) | 10.0000 | 0.452679 | ||||||||
\(489\) | 12.0000 | 0.542659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.6125 | −0.794841 | −0.397420 | − | 0.917637i | \(-0.630095\pi\) | ||||
−0.397420 | + | 0.917637i | \(0.630095\pi\) | |||||||
\(492\) | 7.70156 | 0.347213 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 30.8062 | 1.38604 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.00000 | −0.269408 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.59688 | 0.116369 | ||||||||
\(499\) | 37.0156 | 1.65705 | 0.828523 | − | 0.559954i | \(-0.189181\pi\) | ||||
0.828523 | + | 0.559954i | \(0.189181\pi\) | |||||||
\(500\) | 13.7016 | 0.612752 | ||||||||
\(501\) | −21.4031 | −0.956221 | ||||||||
\(502\) | 13.9109 | 0.620875 | ||||||||
\(503\) | 11.4031 | 0.508440 | 0.254220 | − | 0.967146i | \(-0.418181\pi\) | ||||
0.254220 | + | 0.967146i | \(0.418181\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.0156 | −0.757185 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19.5078 | −0.866372 | ||||||||
\(508\) | 17.1047 | 0.758898 | ||||||||
\(509\) | 14.8062 | 0.656275 | 0.328138 | − | 0.944630i | \(-0.393579\pi\) | ||||
0.328138 | + | 0.944630i | \(0.393579\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −5.40312 | −0.238554 | ||||||||
\(514\) | 23.6125 | 1.04150 | ||||||||
\(515\) | 63.3141 | 2.78995 | ||||||||
\(516\) | −5.70156 | −0.250997 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.40312 | −0.149381 | ||||||||
\(520\) | 21.1047 | 0.925502 | ||||||||
\(521\) | −15.4031 | −0.674823 | −0.337412 | − | 0.941357i | \(-0.609551\pi\) | ||||
−0.337412 | + | 0.941357i | \(0.609551\pi\) | |||||||
\(522\) | −0.298438 | −0.0130623 | ||||||||
\(523\) | 38.4187 | 1.67993 | 0.839967 | − | 0.542637i | \(-0.182574\pi\) | ||||
0.839967 | + | 0.542637i | \(0.182574\pi\) | |||||||
\(524\) | −15.4031 | −0.672889 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.5078 | 0.719775 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −34.8062 | −1.51189 | ||||||||
\(531\) | 0.596876 | 0.0259022 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 43.9109 | 1.90199 | ||||||||
\(534\) | 15.4031 | 0.666558 | ||||||||
\(535\) | 54.8062 | 2.36948 | ||||||||
\(536\) | −4.00000 | −0.172774 | ||||||||
\(537\) | −5.70156 | −0.246041 | ||||||||
\(538\) | −3.40312 | −0.146719 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.70156 | −0.159290 | ||||||||
\(541\) | −20.2094 | −0.868869 | −0.434434 | − | 0.900703i | \(-0.643052\pi\) | ||||
−0.434434 | + | 0.900703i | \(0.643052\pi\) | |||||||
\(542\) | 17.4031 | 0.747528 | ||||||||
\(543\) | 16.8062 | 0.721225 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 58.1203 | 2.48960 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.2094 | −0.607549 | −0.303774 | − | 0.952744i | \(-0.598247\pi\) | ||||
−0.303774 | + | 0.952744i | \(0.598247\pi\) | |||||||
\(548\) | 0.895314 | 0.0382459 | ||||||||
\(549\) | −10.0000 | −0.426790 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.61250 | 0.0686947 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 13.4031 | 0.569444 | ||||||||
\(555\) | −13.7016 | −0.581599 | ||||||||
\(556\) | 21.1047 | 0.895038 | ||||||||
\(557\) | 21.4031 | 0.906879 | 0.453440 | − | 0.891287i | \(-0.350197\pi\) | ||||
0.453440 | + | 0.891287i | \(0.350197\pi\) | |||||||
\(558\) | 6.00000 | 0.254000 | ||||||||
\(559\) | −32.5078 | −1.37493 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.29844 | −0.181319 | ||||||||
\(563\) | −44.7172 | −1.88460 | −0.942302 | − | 0.334763i | \(-0.891344\pi\) | ||||
−0.942302 | + | 0.334763i | \(0.891344\pi\) | |||||||
\(564\) | 3.70156 | 0.155864 | ||||||||
\(565\) | −15.9109 | −0.669378 | ||||||||
\(566\) | −10.0000 | −0.420331 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.40312 | −0.310628 | ||||||||
\(569\) | 11.1047 | 0.465533 | 0.232766 | − | 0.972533i | \(-0.425222\pi\) | ||||
0.232766 | + | 0.972533i | \(0.425222\pi\) | |||||||
\(570\) | 20.0000 | 0.837708 | ||||||||
\(571\) | −12.0000 | −0.502184 | −0.251092 | − | 0.967963i | \(-0.580790\pi\) | ||||
−0.251092 | + | 0.967963i | \(0.580790\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −22.8062 | −0.952745 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.70156 | −0.362880 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 23.6125 | 0.983001 | 0.491501 | − | 0.870877i | \(-0.336449\pi\) | ||||
0.491501 | + | 0.870877i | \(0.336449\pi\) | |||||||
\(578\) | 17.0000 | 0.707107 | ||||||||
\(579\) | 7.10469 | 0.295261 | ||||||||
\(580\) | 1.10469 | 0.0458696 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.10469 | 0.0457907 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −5.40312 | −0.223583 | ||||||||
\(585\) | −21.1047 | −0.872571 | ||||||||
\(586\) | −3.19375 | −0.131933 | ||||||||
\(587\) | 1.19375 | 0.0492714 | 0.0246357 | − | 0.999696i | \(-0.492157\pi\) | ||||
0.0246357 | + | 0.999696i | \(0.492157\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −32.4187 | −1.33579 | ||||||||
\(590\) | −2.20937 | −0.0909584 | ||||||||
\(591\) | −6.50781 | −0.267696 | ||||||||
\(592\) | 3.70156 | 0.152133 | ||||||||
\(593\) | 41.9109 | 1.72108 | 0.860538 | − | 0.509386i | \(-0.170128\pi\) | ||||
0.860538 | + | 0.509386i | \(0.170128\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −17.4031 | −0.712860 | ||||||||
\(597\) | 1.10469 | 0.0452118 | ||||||||
\(598\) | −5.70156 | −0.233154 | ||||||||
\(599\) | −29.6125 | −1.20993 | −0.604967 | − | 0.796251i | \(-0.706814\pi\) | ||||
−0.604967 | + | 0.796251i | \(0.706814\pi\) | |||||||
\(600\) | 8.70156 | 0.355240 | ||||||||
\(601\) | −25.4031 | −1.03622 | −0.518108 | − | 0.855315i | \(-0.673363\pi\) | ||||
−0.518108 | + | 0.855315i | \(0.673363\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.00000 | 0.162893 | ||||||||
\(604\) | 9.10469 | 0.370464 | ||||||||
\(605\) | −40.7172 | −1.65539 | ||||||||
\(606\) | −4.59688 | −0.186735 | ||||||||
\(607\) | 2.00000 | 0.0811775 | 0.0405887 | − | 0.999176i | \(-0.487077\pi\) | ||||
0.0405887 | + | 0.999176i | \(0.487077\pi\) | |||||||
\(608\) | −5.40312 | −0.219126 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 37.0156 | 1.49872 | ||||||||
\(611\) | 21.1047 | 0.853804 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.3141 | −1.02243 | −0.511213 | − | 0.859454i | \(-0.670804\pi\) | ||||
−0.511213 | + | 0.859454i | \(0.670804\pi\) | |||||||
\(614\) | 5.10469 | 0.206008 | ||||||||
\(615\) | 28.5078 | 1.14955 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −42.0000 | −1.69086 | −0.845428 | − | 0.534089i | \(-0.820655\pi\) | ||||
−0.845428 | + | 0.534089i | \(0.820655\pi\) | |||||||
\(618\) | 17.1047 | 0.688051 | ||||||||
\(619\) | 30.0000 | 1.20580 | 0.602901 | − | 0.797816i | \(-0.294011\pi\) | ||||
0.602901 | + | 0.797816i | \(0.294011\pi\) | |||||||
\(620\) | −22.2094 | −0.891950 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | −16.2094 | −0.649937 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.70156 | 0.228245 | ||||||||
\(625\) | 7.20937 | 0.288375 | ||||||||
\(626\) | −4.59688 | −0.183728 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.4031 | 0.534843 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.19375 | 0.365997 | 0.182999 | − | 0.983113i | \(-0.441420\pi\) | ||||
0.182999 | + | 0.983113i | \(0.441420\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.0000 | 0.476957 | ||||||||
\(634\) | −7.70156 | −0.305868 | ||||||||
\(635\) | 63.3141 | 2.51254 | ||||||||
\(636\) | −9.40312 | −0.372858 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.40312 | 0.292863 | ||||||||
\(640\) | −3.70156 | −0.146317 | ||||||||
\(641\) | −11.7016 | −0.462184 | −0.231092 | − | 0.972932i | \(-0.574230\pi\) | ||||
−0.231092 | + | 0.972932i | \(0.574230\pi\) | |||||||
\(642\) | 14.8062 | 0.584356 | ||||||||
\(643\) | −3.19375 | −0.125949 | −0.0629746 | − | 0.998015i | \(-0.520059\pi\) | ||||
−0.0629746 | + | 0.998015i | \(0.520059\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −21.1047 | −0.830996 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.20937 | 0.165488 | 0.0827438 | − | 0.996571i | \(-0.473632\pi\) | ||||
0.0827438 | + | 0.996571i | \(0.473632\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 49.6125 | 1.94596 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.0000 | −0.469956 | ||||||||
\(653\) | 47.1047 | 1.84335 | 0.921674 | − | 0.387964i | \(-0.126822\pi\) | ||||
0.921674 | + | 0.387964i | \(0.126822\pi\) | |||||||
\(654\) | 15.7016 | 0.613980 | ||||||||
\(655\) | −57.0156 | −2.22778 | ||||||||
\(656\) | −7.70156 | −0.300695 | ||||||||
\(657\) | 5.40312 | 0.210796 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.6125 | 0.997721 | 0.498861 | − | 0.866682i | \(-0.333752\pi\) | ||||
0.498861 | + | 0.866682i | \(0.333752\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.8062 | 0.809269 | 0.404635 | − | 0.914478i | \(-0.367399\pi\) | ||||
0.404635 | + | 0.914478i | \(0.367399\pi\) | |||||||
\(662\) | 17.6125 | 0.684529 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.59688 | −0.100778 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.70156 | −0.143433 | ||||||||
\(667\) | −0.298438 | −0.0115556 | ||||||||
\(668\) | 21.4031 | 0.828112 | ||||||||
\(669\) | −20.8062 | −0.804416 | ||||||||
\(670\) | −14.8062 | −0.572015 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.29844 | −0.319881 | −0.159941 | − | 0.987127i | \(-0.551130\pi\) | ||||
−0.159941 | + | 0.987127i | \(0.551130\pi\) | |||||||
\(674\) | −17.4031 | −0.670343 | ||||||||
\(675\) | −8.70156 | −0.334923 | ||||||||
\(676\) | 19.5078 | 0.750300 | ||||||||
\(677\) | 3.19375 | 0.122746 | 0.0613729 | − | 0.998115i | \(-0.480452\pi\) | ||||
0.0613729 | + | 0.998115i | \(0.480452\pi\) | |||||||
\(678\) | −4.29844 | −0.165081 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.5078 | −1.01578 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.0000 | 1.37750 | 0.688751 | − | 0.724998i | \(-0.258159\pi\) | ||||
0.688751 | + | 0.724998i | \(0.258159\pi\) | |||||||
\(684\) | 5.40312 | 0.206594 | ||||||||
\(685\) | 3.31406 | 0.126624 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 28.2094 | 1.07625 | ||||||||
\(688\) | 5.70156 | 0.217370 | ||||||||
\(689\) | −53.6125 | −2.04247 | ||||||||
\(690\) | −3.70156 | −0.140916 | ||||||||
\(691\) | 41.7016 | 1.58640 | 0.793201 | − | 0.608960i | \(-0.208413\pi\) | ||||
0.793201 | + | 0.608960i | \(0.208413\pi\) | |||||||
\(692\) | 3.40312 | 0.129367 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20.5078 | −0.778466 | ||||||||
\(695\) | 78.1203 | 2.96327 | ||||||||
\(696\) | 0.298438 | 0.0113123 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 34.2094 | 1.29484 | ||||||||
\(699\) | −28.8062 | −1.08955 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.5969 | 0.551316 | 0.275658 | − | 0.961256i | \(-0.411104\pi\) | ||||
0.275658 | + | 0.961256i | \(0.411104\pi\) | |||||||
\(702\) | −5.70156 | −0.215192 | ||||||||
\(703\) | 20.0000 | 0.754314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13.7016 | 0.516031 | ||||||||
\(706\) | −33.3141 | −1.25379 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.596876 | −0.0224320 | ||||||||
\(709\) | −15.1938 | −0.570613 | −0.285307 | − | 0.958436i | \(-0.592095\pi\) | ||||
−0.285307 | + | 0.958436i | \(0.592095\pi\) | |||||||
\(710\) | −27.4031 | −1.02842 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −15.4031 | −0.577256 | ||||||||
\(713\) | 6.00000 | 0.224702 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.70156 | 0.213077 | ||||||||
\(717\) | 18.8062 | 0.702332 | ||||||||
\(718\) | −9.70156 | −0.362059 | ||||||||
\(719\) | −14.5078 | −0.541050 | −0.270525 | − | 0.962713i | \(-0.587197\pi\) | ||||
−0.270525 | + | 0.962713i | \(0.587197\pi\) | |||||||
\(720\) | 3.70156 | 0.137949 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −10.1938 | −0.379372 | ||||||||
\(723\) | 5.10469 | 0.189845 | ||||||||
\(724\) | −16.8062 | −0.624599 | ||||||||
\(725\) | 2.59688 | 0.0964455 | ||||||||
\(726\) | −11.0000 | −0.408248 | ||||||||
\(727\) | 44.0000 | 1.63187 | 0.815935 | − | 0.578144i | \(-0.196223\pi\) | ||||
0.815935 | + | 0.578144i | \(0.196223\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −20.0000 | −0.740233 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 10.0000 | 0.369611 | ||||||||
\(733\) | −31.0156 | −1.14559 | −0.572794 | − | 0.819699i | \(-0.694141\pi\) | ||||
−0.572794 | + | 0.819699i | \(0.694141\pi\) | |||||||
\(734\) | 15.9109 | 0.587283 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 7.70156 | 0.283498 | ||||||||
\(739\) | 38.2094 | 1.40555 | 0.702777 | − | 0.711410i | \(-0.251943\pi\) | ||||
0.702777 | + | 0.711410i | \(0.251943\pi\) | |||||||
\(740\) | 13.7016 | 0.503679 | ||||||||
\(741\) | 30.8062 | 1.13170 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.6125 | −0.792886 | −0.396443 | − | 0.918059i | \(-0.629755\pi\) | ||||
−0.396443 | + | 0.918059i | \(0.629755\pi\) | |||||||
\(744\) | −6.00000 | −0.219971 | ||||||||
\(745\) | −64.4187 | −2.36012 | ||||||||
\(746\) | 4.80625 | 0.175969 | ||||||||
\(747\) | 2.59688 | 0.0950147 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 13.7016 | 0.500310 | ||||||||
\(751\) | 8.00000 | 0.291924 | 0.145962 | − | 0.989290i | \(-0.453372\pi\) | ||||
0.145962 | + | 0.989290i | \(0.453372\pi\) | |||||||
\(752\) | −3.70156 | −0.134982 | ||||||||
\(753\) | 13.9109 | 0.506943 | ||||||||
\(754\) | 1.70156 | 0.0619672 | ||||||||
\(755\) | 33.7016 | 1.22653 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.19375 | 0.261461 | 0.130731 | − | 0.991418i | \(-0.458268\pi\) | ||||
0.130731 | + | 0.991418i | \(0.458268\pi\) | |||||||
\(758\) | 17.7016 | 0.642950 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −20.0000 | −0.725476 | ||||||||
\(761\) | −15.6125 | −0.565953 | −0.282976 | − | 0.959127i | \(-0.591322\pi\) | ||||
−0.282976 | + | 0.959127i | \(0.591322\pi\) | |||||||
\(762\) | 17.1047 | 0.619637 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 22.8062 | 0.825101 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.80625 | 0.245920 | ||||||||
\(767\) | −3.40312 | −0.122880 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 29.1047 | 1.04954 | 0.524771 | − | 0.851243i | \(-0.324151\pi\) | ||||
0.524771 | + | 0.851243i | \(0.324151\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.6125 | 0.850383 | ||||||||
\(772\) | −7.10469 | −0.255703 | ||||||||
\(773\) | −44.7172 | −1.60837 | −0.804183 | − | 0.594382i | \(-0.797397\pi\) | ||||
−0.804183 | + | 0.594382i | \(0.797397\pi\) | |||||||
\(774\) | −5.70156 | −0.204938 | ||||||||
\(775\) | −52.2094 | −1.87542 | ||||||||
\(776\) | −1.10469 | −0.0396559 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −36.8062 | −1.31957 | ||||||||
\(779\) | −41.6125 | −1.49092 | ||||||||
\(780\) | 21.1047 | 0.755669 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.298438 | −0.0106653 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 49.6125 | 1.77075 | ||||||||
\(786\) | −15.4031 | −0.549411 | ||||||||
\(787\) | −49.8219 | −1.77596 | −0.887979 | − | 0.459884i | \(-0.847891\pi\) | ||||
−0.887979 | + | 0.459884i | \(0.847891\pi\) | |||||||
\(788\) | 6.50781 | 0.231831 | ||||||||
\(789\) | 16.5078 | 0.587694 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 57.0156 | 2.02468 | ||||||||
\(794\) | 6.20937 | 0.220362 | ||||||||
\(795\) | −34.8062 | −1.23445 | ||||||||
\(796\) | −1.10469 | −0.0391546 | ||||||||
\(797\) | 31.7016 | 1.12293 | 0.561463 | − | 0.827502i | \(-0.310239\pi\) | ||||
0.561463 | + | 0.827502i | \(0.310239\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −8.70156 | −0.307647 | ||||||||
\(801\) | 15.4031 | 0.544243 | ||||||||
\(802\) | −28.8062 | −1.01718 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −4.00000 | −0.141069 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −34.2094 | −1.20497 | ||||||||
\(807\) | −3.40312 | −0.119796 | ||||||||
\(808\) | 4.59688 | 0.161718 | ||||||||
\(809\) | −21.4031 | −0.752494 | −0.376247 | − | 0.926519i | \(-0.622786\pi\) | ||||
−0.376247 | + | 0.926519i | \(0.622786\pi\) | |||||||
\(810\) | −3.70156 | −0.130060 | ||||||||
\(811\) | −11.3141 | −0.397290 | −0.198645 | − | 0.980071i | \(-0.563654\pi\) | ||||
−0.198645 | + | 0.980071i | \(0.563654\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.4031 | 0.610354 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −44.4187 | −1.55592 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30.8062 | 1.07777 | ||||||||
\(818\) | −32.2094 | −1.12617 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −28.5078 | −0.995536 | ||||||||
\(821\) | 6.00000 | 0.209401 | 0.104701 | − | 0.994504i | \(-0.466612\pi\) | ||||
0.104701 | + | 0.994504i | \(0.466612\pi\) | |||||||
\(822\) | 0.895314 | 0.0312276 | ||||||||
\(823\) | 46.7172 | 1.62846 | 0.814229 | − | 0.580543i | \(-0.197160\pi\) | ||||
0.814229 | + | 0.580543i | \(0.197160\pi\) | |||||||
\(824\) | −17.1047 | −0.595870 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.0156 | −1.14807 | −0.574033 | − | 0.818832i | \(-0.694622\pi\) | ||||
−0.574033 | + | 0.818832i | \(0.694622\pi\) | |||||||
\(828\) | −1.00000 | −0.0347524 | ||||||||
\(829\) | 30.2094 | 1.04921 | 0.524607 | − | 0.851344i | \(-0.324212\pi\) | ||||
0.524607 | + | 0.851344i | \(0.324212\pi\) | |||||||
\(830\) | −9.61250 | −0.333655 | ||||||||
\(831\) | 13.4031 | 0.464949 | ||||||||
\(832\) | −5.70156 | −0.197666 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 21.1047 | 0.730796 | ||||||||
\(835\) | 79.2250 | 2.74169 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.00000 | 0.207390 | ||||||||
\(838\) | −2.59688 | −0.0897076 | ||||||||
\(839\) | 19.4031 | 0.669870 | 0.334935 | − | 0.942241i | \(-0.391286\pi\) | ||||
0.334935 | + | 0.942241i | \(0.391286\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9109 | −0.996929 | ||||||||
\(842\) | −15.7016 | −0.541112 | ||||||||
\(843\) | −4.29844 | −0.148046 | ||||||||
\(844\) | −12.0000 | −0.413057 | ||||||||
\(845\) | 72.2094 | 2.48408 | ||||||||
\(846\) | 3.70156 | 0.127262 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 9.40312 | 0.322905 | ||||||||
\(849\) | −10.0000 | −0.343199 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.70156 | −0.126888 | ||||||||
\(852\) | −7.40312 | −0.253627 | ||||||||
\(853\) | −41.1047 | −1.40740 | −0.703699 | − | 0.710498i | \(-0.748470\pi\) | ||||
−0.703699 | + | 0.710498i | \(0.748470\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 20.0000 | 0.683986 | ||||||||
\(856\) | −14.8062 | −0.506067 | ||||||||
\(857\) | −2.08907 | −0.0713611 | −0.0356806 | − | 0.999363i | \(-0.511360\pi\) | ||||
−0.0356806 | + | 0.999363i | \(0.511360\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.91093 | 0.133439 | 0.0667197 | − | 0.997772i | \(-0.478747\pi\) | ||||
0.0667197 | + | 0.997772i | \(0.478747\pi\) | |||||||
\(860\) | 21.1047 | 0.719664 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.10469 | −0.173866 | ||||||||
\(863\) | −10.8062 | −0.367849 | −0.183924 | − | 0.982940i | \(-0.558880\pi\) | ||||
−0.183924 | + | 0.982940i | \(0.558880\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 12.5969 | 0.428307 | ||||||||
\(866\) | 17.1047 | 0.581241 | ||||||||
\(867\) | 17.0000 | 0.577350 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 1.10469 | 0.0374524 | ||||||||
\(871\) | −22.8062 | −0.772760 | ||||||||
\(872\) | −15.7016 | −0.531722 | ||||||||
\(873\) | 1.10469 | 0.0373880 | ||||||||
\(874\) | 5.40312 | 0.182763 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.40312 | −0.182555 | ||||||||
\(877\) | −48.2094 | −1.62791 | −0.813957 | − | 0.580925i | \(-0.802691\pi\) | ||||
−0.813957 | + | 0.580925i | \(0.802691\pi\) | |||||||
\(878\) | 3.19375 | 0.107784 | ||||||||
\(879\) | −3.19375 | −0.107723 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.2094 | 0.343963 | 0.171981 | − | 0.985100i | \(-0.444983\pi\) | ||||
0.171981 | + | 0.985100i | \(0.444983\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.5969 | 0.558529 | 0.279265 | − | 0.960214i | \(-0.409909\pi\) | ||||
0.279265 | + | 0.960214i | \(0.409909\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.20937 | −0.0742673 | ||||||||
\(886\) | −17.1047 | −0.574643 | ||||||||
\(887\) | 52.2094 | 1.75302 | 0.876510 | − | 0.481384i | \(-0.159866\pi\) | ||||
0.876510 | + | 0.481384i | \(0.159866\pi\) | |||||||
\(888\) | 3.70156 | 0.124216 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −57.0156 | −1.91117 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 20.8062 | 0.696645 | ||||||||
\(893\) | −20.0000 | −0.669274 | ||||||||
\(894\) | −17.4031 | −0.582048 | ||||||||
\(895\) | 21.1047 | 0.705452 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.70156 | −0.190370 | ||||||||
\(898\) | −27.6125 | −0.921441 | ||||||||
\(899\) | −1.79063 | −0.0597208 | ||||||||
\(900\) | 8.70156 | 0.290052 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.29844 | 0.142964 | ||||||||
\(905\) | −62.2094 | −2.06791 | ||||||||
\(906\) | 9.10469 | 0.302483 | ||||||||
\(907\) | −2.89531 | −0.0961373 | −0.0480687 | − | 0.998844i | \(-0.515307\pi\) | ||||
−0.0480687 | + | 0.998844i | \(0.515307\pi\) | |||||||
\(908\) | 26.5078 | 0.879693 | ||||||||
\(909\) | −4.59688 | −0.152469 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.70156 | 0.0563753 | 0.0281876 | − | 0.999603i | \(-0.491026\pi\) | ||||
0.0281876 | + | 0.999603i | \(0.491026\pi\) | |||||||
\(912\) | −5.40312 | −0.178915 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 16.2094 | 0.536158 | ||||||||
\(915\) | 37.0156 | 1.22370 | ||||||||
\(916\) | −28.2094 | −0.932064 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.19375 | 0.0393782 | 0.0196891 | − | 0.999806i | \(-0.493732\pi\) | ||||
0.0196891 | + | 0.999806i | \(0.493732\pi\) | |||||||
\(920\) | 3.70156 | 0.122037 | ||||||||
\(921\) | 5.10469 | 0.168205 | ||||||||
\(922\) | 27.4031 | 0.902474 | ||||||||
\(923\) | −42.2094 | −1.38934 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.2094 | 1.05904 | ||||||||
\(926\) | 13.1047 | 0.430647 | ||||||||
\(927\) | 17.1047 | 0.561792 | ||||||||
\(928\) | −0.298438 | −0.00979670 | ||||||||
\(929\) | −23.7016 | −0.777623 | −0.388812 | − | 0.921317i | \(-0.627114\pi\) | ||||
−0.388812 | + | 0.921317i | \(0.627114\pi\) | |||||||
\(930\) | −22.2094 | −0.728274 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 28.8062 | 0.943580 | ||||||||
\(933\) | −16.2094 | −0.530671 | ||||||||
\(934\) | −8.29844 | −0.271533 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.70156 | 0.186361 | ||||||||
\(937\) | −47.3141 | −1.54568 | −0.772841 | − | 0.634599i | \(-0.781165\pi\) | ||||
−0.772841 | + | 0.634599i | \(0.781165\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.59688 | −0.150013 | ||||||||
\(940\) | −13.7016 | −0.446896 | ||||||||
\(941\) | 9.31406 | 0.303630 | 0.151815 | − | 0.988409i | \(-0.451488\pi\) | ||||
0.151815 | + | 0.988409i | \(0.451488\pi\) | |||||||
\(942\) | 13.4031 | 0.436697 | ||||||||
\(943\) | 7.70156 | 0.250797 | ||||||||
\(944\) | 0.596876 | 0.0194267 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.49219 | 0.113481 | 0.0567405 | − | 0.998389i | \(-0.481929\pi\) | ||||
0.0567405 | + | 0.998389i | \(0.481929\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.8062 | −1.00001 | ||||||||
\(950\) | −47.0156 | −1.52539 | ||||||||
\(951\) | −7.70156 | −0.249740 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.8062 | −0.673980 | −0.336990 | − | 0.941508i | \(-0.609409\pi\) | ||||
−0.336990 | + | 0.941508i | \(0.609409\pi\) | |||||||
\(954\) | −9.40312 | −0.304437 | ||||||||
\(955\) | 84.4187 | 2.73173 | ||||||||
\(956\) | −18.8062 | −0.608238 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.40312 | 0.239184 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.70156 | −0.119467 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 21.1047 | 0.680442 | ||||||||
\(963\) | 14.8062 | 0.477125 | ||||||||
\(964\) | −5.10469 | −0.164411 | ||||||||
\(965\) | −26.2984 | −0.846577 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.4187 | 0.656623 | 0.328311 | − | 0.944570i | \(-0.393521\pi\) | ||||
0.328311 | + | 0.944570i | \(0.393521\pi\) | |||||||
\(968\) | 11.0000 | 0.353553 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.08907 | −0.131292 | ||||||||
\(971\) | 33.4031 | 1.07196 | 0.535979 | − | 0.844232i | \(-0.319943\pi\) | ||||
0.535979 | + | 0.844232i | \(0.319943\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 13.1047 | 0.419901 | ||||||||
\(975\) | 49.6125 | 1.58887 | ||||||||
\(976\) | −10.0000 | −0.320092 | ||||||||
\(977\) | −40.2984 | −1.28926 | −0.644631 | − | 0.764494i | \(-0.722989\pi\) | ||||
−0.644631 | + | 0.764494i | \(0.722989\pi\) | |||||||
\(978\) | −12.0000 | −0.383718 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.7016 | 0.501312 | ||||||||
\(982\) | 17.6125 | 0.562037 | ||||||||
\(983\) | 55.8219 | 1.78044 | 0.890221 | − | 0.455530i | \(-0.150550\pi\) | ||||
0.890221 | + | 0.455530i | \(0.150550\pi\) | |||||||
\(984\) | −7.70156 | −0.245517 | ||||||||
\(985\) | 24.0891 | 0.767541 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −30.8062 | −0.980077 | ||||||||
\(989\) | −5.70156 | −0.181299 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0000 | 0.635321 | 0.317660 | − | 0.948205i | \(-0.397103\pi\) | ||||
0.317660 | + | 0.948205i | \(0.397103\pi\) | |||||||
\(992\) | 6.00000 | 0.190500 | ||||||||
\(993\) | 17.6125 | 0.558916 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.08907 | −0.129632 | ||||||||
\(996\) | −2.59688 | −0.0822852 | ||||||||
\(997\) | −48.5969 | −1.53908 | −0.769539 | − | 0.638600i | \(-0.779514\pi\) | ||||
−0.769539 | + | 0.638600i | \(0.779514\pi\) | |||||||
\(998\) | −37.0156 | −1.17171 | ||||||||
\(999\) | −3.70156 | −0.117112 |
(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 | 6762.2.a.bq.1.2 | 2 | ||
7.6 | odd | 2 | 966.2.a.m.1.1 | ✓ | 2 | ||
21.20 | even | 2 | 2898.2.a.bc.1.2 | 2 | |||
28.27 | even | 2 | 7728.2.a.z.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.a.m.1.1 | ✓ | 2 | 7.6 | odd | 2 | ||
2898.2.a.bc.1.2 | 2 | 21.20 | even | 2 | |||
6762.2.a.bq.1.2 | 2 | 1.1 | even | 1 | trivial | ||
7728.2.a.z.1.1 | 2 | 28.27 | even | 2 |