Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5610,2,Mod(1,5610)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5610, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("5610.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5610.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: | \(44.7960755339\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 8 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5610.1 |
$q$-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 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 2.37228 | 0.896638 | 0.448319 | − | 0.893874i | \(-0.352023\pi\) | ||||
0.448319 | + | 0.893874i | \(0.352023\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −4.00000 | −1.10940 | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | −2.37228 | −0.634019 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 4.00000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −2.37228 | −0.517674 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −1.62772 | −0.339403 | −0.169701 | − | 0.985496i | \(-0.554280\pi\) | ||||
−0.169701 | + | 0.985496i | \(0.554280\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.00000 | 0.784465 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.37228 | 0.448319 | ||||||||
\(29\) | −6.37228 | −1.18330 | −0.591651 | − | 0.806194i | \(-0.701524\pi\) | ||||
−0.591651 | + | 0.806194i | \(0.701524\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | −9.11684 | −1.63743 | −0.818717 | − | 0.574198i | \(-0.805314\pi\) | ||||
−0.818717 | + | 0.574198i | \(0.805314\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | 2.37228 | 0.400989 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 8.74456 | 1.43760 | 0.718799 | − | 0.695218i | \(-0.244692\pi\) | ||||
0.718799 | + | 0.695218i | \(0.244692\pi\) | |||||||
\(38\) | −4.00000 | −0.648886 | ||||||||
\(39\) | 4.00000 | 0.640513 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 10.7446 | 1.67802 | 0.839009 | − | 0.544117i | \(-0.183135\pi\) | ||||
0.839009 | + | 0.544117i | \(0.183135\pi\) | |||||||
\(42\) | 2.37228 | 0.366051 | ||||||||
\(43\) | −10.3723 | −1.58176 | −0.790879 | − | 0.611973i | \(-0.790376\pi\) | ||||
−0.790879 | + | 0.611973i | \(0.790376\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 1.62772 | 0.239994 | ||||||||
\(47\) | 10.7446 | 1.56726 | 0.783628 | − | 0.621231i | \(-0.213367\pi\) | ||||
0.783628 | + | 0.621231i | \(0.213367\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −1.37228 | −0.196040 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −4.00000 | −0.554700 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | −2.37228 | −0.317009 | ||||||||
\(57\) | −4.00000 | −0.529813 | ||||||||
\(58\) | 6.37228 | 0.836722 | ||||||||
\(59\) | 12.7446 | 1.65920 | 0.829600 | − | 0.558358i | \(-0.188568\pi\) | ||||
0.829600 | + | 0.558358i | \(0.188568\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | 11.4891 | 1.47103 | 0.735516 | − | 0.677507i | \(-0.236940\pi\) | ||||
0.735516 | + | 0.677507i | \(0.236940\pi\) | |||||||
\(62\) | 9.11684 | 1.15784 | ||||||||
\(63\) | 2.37228 | 0.298879 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.00000 | −0.496139 | ||||||||
\(66\) | 1.00000 | 0.123091 | ||||||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | 1.00000 | 0.121268 | ||||||||
\(69\) | 1.62772 | 0.195954 | ||||||||
\(70\) | −2.37228 | −0.283542 | ||||||||
\(71\) | 4.74456 | 0.563076 | 0.281538 | − | 0.959550i | \(-0.409155\pi\) | ||||
0.281538 | + | 0.959550i | \(0.409155\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −6.00000 | −0.702247 | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | −8.74456 | −1.01653 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 4.00000 | 0.458831 | ||||||||
\(77\) | 2.37228 | 0.270347 | ||||||||
\(78\) | −4.00000 | −0.452911 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −10.7446 | −1.18654 | ||||||||
\(83\) | −13.4891 | −1.48062 | −0.740312 | − | 0.672264i | \(-0.765322\pi\) | ||||
−0.740312 | + | 0.672264i | \(0.765322\pi\) | |||||||
\(84\) | −2.37228 | −0.258837 | ||||||||
\(85\) | 1.00000 | 0.108465 | ||||||||
\(86\) | 10.3723 | 1.11847 | ||||||||
\(87\) | 6.37228 | 0.683180 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −2.74456 | −0.290923 | −0.145462 | − | 0.989364i | \(-0.546467\pi\) | ||||
−0.145462 | + | 0.989364i | \(0.546467\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | −9.48913 | −0.994731 | ||||||||
\(92\) | −1.62772 | −0.169701 | ||||||||
\(93\) | 9.11684 | 0.945373 | ||||||||
\(94\) | −10.7446 | −1.10822 | ||||||||
\(95\) | 4.00000 | 0.410391 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −17.8614 | −1.81355 | −0.906776 | − | 0.421614i | \(-0.861464\pi\) | ||||
−0.906776 | + | 0.421614i | \(0.861464\pi\) | |||||||
\(98\) | 1.37228 | 0.138621 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 2.00000 | 0.199007 | 0.0995037 | − | 0.995037i | \(-0.468274\pi\) | ||||
0.0995037 | + | 0.995037i | \(0.468274\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | 18.3723 | 1.81027 | 0.905137 | − | 0.425119i | \(-0.139768\pi\) | ||||
0.905137 | + | 0.425119i | \(0.139768\pi\) | |||||||
\(104\) | 4.00000 | 0.392232 | ||||||||
\(105\) | −2.37228 | −0.231511 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.3723 | 1.00273 | 0.501363 | − | 0.865237i | \(-0.332832\pi\) | ||||
0.501363 | + | 0.865237i | \(0.332832\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 16.2337 | 1.55491 | 0.777453 | − | 0.628941i | \(-0.216511\pi\) | ||||
0.777453 | + | 0.628941i | \(0.216511\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | −8.74456 | −0.829997 | ||||||||
\(112\) | 2.37228 | 0.224160 | ||||||||
\(113\) | 7.48913 | 0.704518 | 0.352259 | − | 0.935903i | \(-0.385414\pi\) | ||||
0.352259 | + | 0.935903i | \(0.385414\pi\) | |||||||
\(114\) | 4.00000 | 0.374634 | ||||||||
\(115\) | −1.62772 | −0.151786 | ||||||||
\(116\) | −6.37228 | −0.591651 | ||||||||
\(117\) | −4.00000 | −0.369800 | ||||||||
\(118\) | −12.7446 | −1.17323 | ||||||||
\(119\) | 2.37228 | 0.217467 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −11.4891 | −1.04018 | ||||||||
\(123\) | −10.7446 | −0.968805 | ||||||||
\(124\) | −9.11684 | −0.818717 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −2.37228 | −0.211340 | ||||||||
\(127\) | −11.4891 | −1.01950 | −0.509748 | − | 0.860324i | \(-0.670261\pi\) | ||||
−0.509748 | + | 0.860324i | \(0.670261\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 10.3723 | 0.913228 | ||||||||
\(130\) | 4.00000 | 0.350823 | ||||||||
\(131\) | 8.00000 | 0.698963 | 0.349482 | − | 0.936943i | \(-0.386358\pi\) | ||||
0.349482 | + | 0.936943i | \(0.386358\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | 9.48913 | 0.822812 | ||||||||
\(134\) | −4.00000 | −0.345547 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | 1.11684 | 0.0954184 | 0.0477092 | − | 0.998861i | \(-0.484808\pi\) | ||||
0.0477092 | + | 0.998861i | \(0.484808\pi\) | |||||||
\(138\) | −1.62772 | −0.138561 | ||||||||
\(139\) | 1.62772 | 0.138061 | 0.0690306 | − | 0.997615i | \(-0.478009\pi\) | ||||
0.0690306 | + | 0.997615i | \(0.478009\pi\) | |||||||
\(140\) | 2.37228 | 0.200494 | ||||||||
\(141\) | −10.7446 | −0.904855 | ||||||||
\(142\) | −4.74456 | −0.398155 | ||||||||
\(143\) | −4.00000 | −0.334497 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −6.37228 | −0.529189 | ||||||||
\(146\) | 6.00000 | 0.496564 | ||||||||
\(147\) | 1.37228 | 0.113184 | ||||||||
\(148\) | 8.74456 | 0.718799 | ||||||||
\(149\) | 14.7446 | 1.20792 | 0.603961 | − | 0.797014i | \(-0.293588\pi\) | ||||
0.603961 | + | 0.797014i | \(0.293588\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | 16.2337 | 1.32108 | 0.660539 | − | 0.750791i | \(-0.270328\pi\) | ||||
0.660539 | + | 0.750791i | \(0.270328\pi\) | |||||||
\(152\) | −4.00000 | −0.324443 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −2.37228 | −0.191164 | ||||||||
\(155\) | −9.11684 | −0.732283 | ||||||||
\(156\) | 4.00000 | 0.320256 | ||||||||
\(157\) | 10.0000 | 0.798087 | 0.399043 | − | 0.916932i | \(-0.369342\pi\) | ||||
0.399043 | + | 0.916932i | \(0.369342\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −3.86141 | −0.304321 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −7.86141 | −0.615753 | −0.307876 | − | 0.951426i | \(-0.599618\pi\) | ||||
−0.307876 | + | 0.951426i | \(0.599618\pi\) | |||||||
\(164\) | 10.7446 | 0.839009 | ||||||||
\(165\) | −1.00000 | −0.0778499 | ||||||||
\(166\) | 13.4891 | 1.04696 | ||||||||
\(167\) | 19.4891 | 1.50811 | 0.754057 | − | 0.656809i | \(-0.228094\pi\) | ||||
0.754057 | + | 0.656809i | \(0.228094\pi\) | |||||||
\(168\) | 2.37228 | 0.183025 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | −1.00000 | −0.0766965 | ||||||||
\(171\) | 4.00000 | 0.305888 | ||||||||
\(172\) | −10.3723 | −0.790879 | ||||||||
\(173\) | −14.2337 | −1.08217 | −0.541084 | − | 0.840969i | \(-0.681986\pi\) | ||||
−0.541084 | + | 0.840969i | \(0.681986\pi\) | |||||||
\(174\) | −6.37228 | −0.483081 | ||||||||
\(175\) | 2.37228 | 0.179328 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −12.7446 | −0.957940 | ||||||||
\(178\) | 2.74456 | 0.205714 | ||||||||
\(179\) | −0.744563 | −0.0556512 | −0.0278256 | − | 0.999613i | \(-0.508858\pi\) | ||||
−0.0278256 | + | 0.999613i | \(0.508858\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | −14.3723 | −1.06828 | −0.534142 | − | 0.845395i | \(-0.679365\pi\) | ||||
−0.534142 | + | 0.845395i | \(0.679365\pi\) | |||||||
\(182\) | 9.48913 | 0.703381 | ||||||||
\(183\) | −11.4891 | −0.849301 | ||||||||
\(184\) | 1.62772 | 0.119997 | ||||||||
\(185\) | 8.74456 | 0.642913 | ||||||||
\(186\) | −9.11684 | −0.668479 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | 10.7446 | 0.783628 | ||||||||
\(189\) | −2.37228 | −0.172558 | ||||||||
\(190\) | −4.00000 | −0.290191 | ||||||||
\(191\) | 7.62772 | 0.551922 | 0.275961 | − | 0.961169i | \(-0.411004\pi\) | ||||
0.275961 | + | 0.961169i | \(0.411004\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −3.48913 | −0.251153 | −0.125576 | − | 0.992084i | \(-0.540078\pi\) | ||||
−0.125576 | + | 0.992084i | \(0.540078\pi\) | |||||||
\(194\) | 17.8614 | 1.28237 | ||||||||
\(195\) | 4.00000 | 0.286446 | ||||||||
\(196\) | −1.37228 | −0.0980201 | ||||||||
\(197\) | −13.4891 | −0.961060 | −0.480530 | − | 0.876978i | \(-0.659556\pi\) | ||||
−0.480530 | + | 0.876978i | \(0.659556\pi\) | |||||||
\(198\) | −1.00000 | −0.0710669 | ||||||||
\(199\) | −14.7446 | −1.04521 | −0.522607 | − | 0.852574i | \(-0.675041\pi\) | ||||
−0.522607 | + | 0.852574i | \(0.675041\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −4.00000 | −0.282138 | ||||||||
\(202\) | −2.00000 | −0.140720 | ||||||||
\(203\) | −15.1168 | −1.06099 | ||||||||
\(204\) | −1.00000 | −0.0700140 | ||||||||
\(205\) | 10.7446 | 0.750433 | ||||||||
\(206\) | −18.3723 | −1.28006 | ||||||||
\(207\) | −1.62772 | −0.113134 | ||||||||
\(208\) | −4.00000 | −0.277350 | ||||||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 2.37228 | 0.163703 | ||||||||
\(211\) | −9.62772 | −0.662799 | −0.331400 | − | 0.943490i | \(-0.607521\pi\) | ||||
−0.331400 | + | 0.943490i | \(0.607521\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.74456 | −0.325092 | ||||||||
\(214\) | −10.3723 | −0.709035 | ||||||||
\(215\) | −10.3723 | −0.707384 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −21.6277 | −1.46819 | ||||||||
\(218\) | −16.2337 | −1.09948 | ||||||||
\(219\) | 6.00000 | 0.405442 | ||||||||
\(220\) | 1.00000 | 0.0674200 | ||||||||
\(221\) | −4.00000 | −0.269069 | ||||||||
\(222\) | 8.74456 | 0.586897 | ||||||||
\(223\) | −3.11684 | −0.208719 | −0.104360 | − | 0.994540i | \(-0.533279\pi\) | ||||
−0.104360 | + | 0.994540i | \(0.533279\pi\) | |||||||
\(224\) | −2.37228 | −0.158505 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −7.48913 | −0.498169 | ||||||||
\(227\) | 23.8614 | 1.58374 | 0.791869 | − | 0.610692i | \(-0.209108\pi\) | ||||
0.791869 | + | 0.610692i | \(0.209108\pi\) | |||||||
\(228\) | −4.00000 | −0.264906 | ||||||||
\(229\) | −1.25544 | −0.0829616 | −0.0414808 | − | 0.999139i | \(-0.513208\pi\) | ||||
−0.0414808 | + | 0.999139i | \(0.513208\pi\) | |||||||
\(230\) | 1.62772 | 0.107329 | ||||||||
\(231\) | −2.37228 | −0.156085 | ||||||||
\(232\) | 6.37228 | 0.418361 | ||||||||
\(233\) | −1.11684 | −0.0731669 | −0.0365834 | − | 0.999331i | \(-0.511647\pi\) | ||||
−0.0365834 | + | 0.999331i | \(0.511647\pi\) | |||||||
\(234\) | 4.00000 | 0.261488 | ||||||||
\(235\) | 10.7446 | 0.700898 | ||||||||
\(236\) | 12.7446 | 0.829600 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.37228 | −0.153772 | ||||||||
\(239\) | −30.2337 | −1.95565 | −0.977827 | − | 0.209413i | \(-0.932845\pi\) | ||||
−0.977827 | + | 0.209413i | \(0.932845\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | 22.6060 | 1.45618 | 0.728089 | − | 0.685482i | \(-0.240409\pi\) | ||||
0.728089 | + | 0.685482i | \(0.240409\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 11.4891 | 0.735516 | ||||||||
\(245\) | −1.37228 | −0.0876718 | ||||||||
\(246\) | 10.7446 | 0.685048 | ||||||||
\(247\) | −16.0000 | −1.01806 | ||||||||
\(248\) | 9.11684 | 0.578920 | ||||||||
\(249\) | 13.4891 | 0.854839 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 2.37228 | 0.149440 | ||||||||
\(253\) | −1.62772 | −0.102334 | ||||||||
\(254\) | 11.4891 | 0.720892 | ||||||||
\(255\) | −1.00000 | −0.0626224 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.11684 | −0.568693 | −0.284347 | − | 0.958722i | \(-0.591777\pi\) | ||||
−0.284347 | + | 0.958722i | \(0.591777\pi\) | |||||||
\(258\) | −10.3723 | −0.645750 | ||||||||
\(259\) | 20.7446 | 1.28900 | ||||||||
\(260\) | −4.00000 | −0.248069 | ||||||||
\(261\) | −6.37228 | −0.394434 | ||||||||
\(262\) | −8.00000 | −0.494242 | ||||||||
\(263\) | −19.1168 | −1.17880 | −0.589398 | − | 0.807843i | \(-0.700635\pi\) | ||||
−0.589398 | + | 0.807843i | \(0.700635\pi\) | |||||||
\(264\) | 1.00000 | 0.0615457 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −9.48913 | −0.581816 | ||||||||
\(267\) | 2.74456 | 0.167965 | ||||||||
\(268\) | 4.00000 | 0.244339 | ||||||||
\(269\) | 14.0000 | 0.853595 | 0.426798 | − | 0.904347i | \(-0.359642\pi\) | ||||
0.426798 | + | 0.904347i | \(0.359642\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | −7.62772 | −0.463351 | −0.231675 | − | 0.972793i | \(-0.574421\pi\) | ||||
−0.231675 | + | 0.972793i | \(0.574421\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | 9.48913 | 0.574308 | ||||||||
\(274\) | −1.11684 | −0.0674710 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 1.62772 | 0.0979772 | ||||||||
\(277\) | 15.4891 | 0.930651 | 0.465326 | − | 0.885140i | \(-0.345937\pi\) | ||||
0.465326 | + | 0.885140i | \(0.345937\pi\) | |||||||
\(278\) | −1.62772 | −0.0976241 | ||||||||
\(279\) | −9.11684 | −0.545811 | ||||||||
\(280\) | −2.37228 | −0.141771 | ||||||||
\(281\) | 13.8614 | 0.826902 | 0.413451 | − | 0.910526i | \(-0.364323\pi\) | ||||
0.413451 | + | 0.910526i | \(0.364323\pi\) | |||||||
\(282\) | 10.7446 | 0.639829 | ||||||||
\(283\) | −24.7446 | −1.47091 | −0.735456 | − | 0.677573i | \(-0.763032\pi\) | ||||
−0.735456 | + | 0.677573i | \(0.763032\pi\) | |||||||
\(284\) | 4.74456 | 0.281538 | ||||||||
\(285\) | −4.00000 | −0.236940 | ||||||||
\(286\) | 4.00000 | 0.236525 | ||||||||
\(287\) | 25.4891 | 1.50458 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 6.37228 | 0.374193 | ||||||||
\(291\) | 17.8614 | 1.04705 | ||||||||
\(292\) | −6.00000 | −0.351123 | ||||||||
\(293\) | 2.88316 | 0.168436 | 0.0842179 | − | 0.996447i | \(-0.473161\pi\) | ||||
0.0842179 | + | 0.996447i | \(0.473161\pi\) | |||||||
\(294\) | −1.37228 | −0.0800331 | ||||||||
\(295\) | 12.7446 | 0.742017 | ||||||||
\(296\) | −8.74456 | −0.508267 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −14.7446 | −0.854130 | ||||||||
\(299\) | 6.51087 | 0.376534 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | −24.6060 | −1.41826 | ||||||||
\(302\) | −16.2337 | −0.934144 | ||||||||
\(303\) | −2.00000 | −0.114897 | ||||||||
\(304\) | 4.00000 | 0.229416 | ||||||||
\(305\) | 11.4891 | 0.657865 | ||||||||
\(306\) | −1.00000 | −0.0571662 | ||||||||
\(307\) | −12.0000 | −0.684876 | −0.342438 | − | 0.939540i | \(-0.611253\pi\) | ||||
−0.342438 | + | 0.939540i | \(0.611253\pi\) | |||||||
\(308\) | 2.37228 | 0.135173 | ||||||||
\(309\) | −18.3723 | −1.04516 | ||||||||
\(310\) | 9.11684 | 0.517802 | ||||||||
\(311\) | 10.5109 | 0.596017 | 0.298009 | − | 0.954563i | \(-0.403678\pi\) | ||||
0.298009 | + | 0.954563i | \(0.403678\pi\) | |||||||
\(312\) | −4.00000 | −0.226455 | ||||||||
\(313\) | 4.37228 | 0.247136 | 0.123568 | − | 0.992336i | \(-0.460566\pi\) | ||||
0.123568 | + | 0.992336i | \(0.460566\pi\) | |||||||
\(314\) | −10.0000 | −0.564333 | ||||||||
\(315\) | 2.37228 | 0.133663 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.11684 | −0.0627282 | −0.0313641 | − | 0.999508i | \(-0.509985\pi\) | ||||
−0.0313641 | + | 0.999508i | \(0.509985\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.37228 | −0.356779 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −10.3723 | −0.578924 | ||||||||
\(322\) | 3.86141 | 0.215188 | ||||||||
\(323\) | 4.00000 | 0.222566 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −4.00000 | −0.221880 | ||||||||
\(326\) | 7.86141 | 0.435403 | ||||||||
\(327\) | −16.2337 | −0.897725 | ||||||||
\(328\) | −10.7446 | −0.593269 | ||||||||
\(329\) | 25.4891 | 1.40526 | ||||||||
\(330\) | 1.00000 | 0.0550482 | ||||||||
\(331\) | 27.1168 | 1.49048 | 0.745238 | − | 0.666798i | \(-0.232336\pi\) | ||||
0.745238 | + | 0.666798i | \(0.232336\pi\) | |||||||
\(332\) | −13.4891 | −0.740312 | ||||||||
\(333\) | 8.74456 | 0.479199 | ||||||||
\(334\) | −19.4891 | −1.06640 | ||||||||
\(335\) | 4.00000 | 0.218543 | ||||||||
\(336\) | −2.37228 | −0.129419 | ||||||||
\(337\) | −11.4891 | −0.625853 | −0.312926 | − | 0.949777i | \(-0.601309\pi\) | ||||
−0.312926 | + | 0.949777i | \(0.601309\pi\) | |||||||
\(338\) | −3.00000 | −0.163178 | ||||||||
\(339\) | −7.48913 | −0.406753 | ||||||||
\(340\) | 1.00000 | 0.0542326 | ||||||||
\(341\) | −9.11684 | −0.493705 | ||||||||
\(342\) | −4.00000 | −0.216295 | ||||||||
\(343\) | −19.8614 | −1.07242 | ||||||||
\(344\) | 10.3723 | 0.559236 | ||||||||
\(345\) | 1.62772 | 0.0876334 | ||||||||
\(346\) | 14.2337 | 0.765208 | ||||||||
\(347\) | 17.4891 | 0.938865 | 0.469433 | − | 0.882968i | \(-0.344458\pi\) | ||||
0.469433 | + | 0.882968i | \(0.344458\pi\) | |||||||
\(348\) | 6.37228 | 0.341590 | ||||||||
\(349\) | −30.2337 | −1.61837 | −0.809186 | − | 0.587552i | \(-0.800092\pi\) | ||||
−0.809186 | + | 0.587552i | \(0.800092\pi\) | |||||||
\(350\) | −2.37228 | −0.126804 | ||||||||
\(351\) | 4.00000 | 0.213504 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 19.6277 | 1.04468 | 0.522339 | − | 0.852738i | \(-0.325060\pi\) | ||||
0.522339 | + | 0.852738i | \(0.325060\pi\) | |||||||
\(354\) | 12.7446 | 0.677366 | ||||||||
\(355\) | 4.74456 | 0.251815 | ||||||||
\(356\) | −2.74456 | −0.145462 | ||||||||
\(357\) | −2.37228 | −0.125554 | ||||||||
\(358\) | 0.744563 | 0.0393514 | ||||||||
\(359\) | 24.7446 | 1.30597 | 0.652984 | − | 0.757372i | \(-0.273517\pi\) | ||||
0.652984 | + | 0.757372i | \(0.273517\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 14.3723 | 0.755390 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | −9.48913 | −0.497365 | ||||||||
\(365\) | −6.00000 | −0.314054 | ||||||||
\(366\) | 11.4891 | 0.600546 | ||||||||
\(367\) | 0.510875 | 0.0266674 | 0.0133337 | − | 0.999911i | \(-0.495756\pi\) | ||||
0.0133337 | + | 0.999911i | \(0.495756\pi\) | |||||||
\(368\) | −1.62772 | −0.0848507 | ||||||||
\(369\) | 10.7446 | 0.559340 | ||||||||
\(370\) | −8.74456 | −0.454608 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 9.11684 | 0.472686 | ||||||||
\(373\) | 35.7228 | 1.84966 | 0.924829 | − | 0.380384i | \(-0.124208\pi\) | ||||
0.924829 | + | 0.380384i | \(0.124208\pi\) | |||||||
\(374\) | −1.00000 | −0.0517088 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −10.7446 | −0.554109 | ||||||||
\(377\) | 25.4891 | 1.31276 | ||||||||
\(378\) | 2.37228 | 0.122017 | ||||||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 4.00000 | 0.205196 | ||||||||
\(381\) | 11.4891 | 0.588606 | ||||||||
\(382\) | −7.62772 | −0.390268 | ||||||||
\(383\) | −2.74456 | −0.140241 | −0.0701203 | − | 0.997539i | \(-0.522338\pi\) | ||||
−0.0701203 | + | 0.997539i | \(0.522338\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 2.37228 | 0.120903 | ||||||||
\(386\) | 3.48913 | 0.177592 | ||||||||
\(387\) | −10.3723 | −0.527253 | ||||||||
\(388\) | −17.8614 | −0.906776 | ||||||||
\(389\) | 20.7446 | 1.05179 | 0.525896 | − | 0.850549i | \(-0.323730\pi\) | ||||
0.525896 | + | 0.850549i | \(0.323730\pi\) | |||||||
\(390\) | −4.00000 | −0.202548 | ||||||||
\(391\) | −1.62772 | −0.0823173 | ||||||||
\(392\) | 1.37228 | 0.0693107 | ||||||||
\(393\) | −8.00000 | −0.403547 | ||||||||
\(394\) | 13.4891 | 0.679572 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.00000 | 0.0502519 | ||||||||
\(397\) | 22.2337 | 1.11588 | 0.557938 | − | 0.829882i | \(-0.311593\pi\) | ||||
0.557938 | + | 0.829882i | \(0.311593\pi\) | |||||||
\(398\) | 14.7446 | 0.739078 | ||||||||
\(399\) | −9.48913 | −0.475050 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 29.8614 | 1.49121 | 0.745604 | − | 0.666390i | \(-0.232161\pi\) | ||||
0.745604 | + | 0.666390i | \(0.232161\pi\) | |||||||
\(402\) | 4.00000 | 0.199502 | ||||||||
\(403\) | 36.4674 | 1.81657 | ||||||||
\(404\) | 2.00000 | 0.0995037 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 15.1168 | 0.750236 | ||||||||
\(407\) | 8.74456 | 0.433452 | ||||||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | 12.2337 | 0.604917 | 0.302458 | − | 0.953163i | \(-0.402193\pi\) | ||||
0.302458 | + | 0.953163i | \(0.402193\pi\) | |||||||
\(410\) | −10.7446 | −0.530636 | ||||||||
\(411\) | −1.11684 | −0.0550899 | ||||||||
\(412\) | 18.3723 | 0.905137 | ||||||||
\(413\) | 30.2337 | 1.48770 | ||||||||
\(414\) | 1.62772 | 0.0799980 | ||||||||
\(415\) | −13.4891 | −0.662155 | ||||||||
\(416\) | 4.00000 | 0.196116 | ||||||||
\(417\) | −1.62772 | −0.0797097 | ||||||||
\(418\) | −4.00000 | −0.195646 | ||||||||
\(419\) | 38.3723 | 1.87461 | 0.937304 | − | 0.348512i | \(-0.113313\pi\) | ||||
0.937304 | + | 0.348512i | \(0.113313\pi\) | |||||||
\(420\) | −2.37228 | −0.115755 | ||||||||
\(421\) | −25.2554 | −1.23087 | −0.615437 | − | 0.788186i | \(-0.711021\pi\) | ||||
−0.615437 | + | 0.788186i | \(0.711021\pi\) | |||||||
\(422\) | 9.62772 | 0.468670 | ||||||||
\(423\) | 10.7446 | 0.522419 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.00000 | 0.0485071 | ||||||||
\(426\) | 4.74456 | 0.229875 | ||||||||
\(427\) | 27.2554 | 1.31898 | ||||||||
\(428\) | 10.3723 | 0.501363 | ||||||||
\(429\) | 4.00000 | 0.193122 | ||||||||
\(430\) | 10.3723 | 0.500196 | ||||||||
\(431\) | −17.8614 | −0.860354 | −0.430177 | − | 0.902745i | \(-0.641549\pi\) | ||||
−0.430177 | + | 0.902745i | \(0.641549\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 18.7446 | 0.900806 | 0.450403 | − | 0.892825i | \(-0.351280\pi\) | ||||
0.450403 | + | 0.892825i | \(0.351280\pi\) | |||||||
\(434\) | 21.6277 | 1.03816 | ||||||||
\(435\) | 6.37228 | 0.305528 | ||||||||
\(436\) | 16.2337 | 0.777453 | ||||||||
\(437\) | −6.51087 | −0.311457 | ||||||||
\(438\) | −6.00000 | −0.286691 | ||||||||
\(439\) | 32.7446 | 1.56281 | 0.781406 | − | 0.624023i | \(-0.214503\pi\) | ||||
0.781406 | + | 0.624023i | \(0.214503\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | −1.37228 | −0.0653467 | ||||||||
\(442\) | 4.00000 | 0.190261 | ||||||||
\(443\) | 10.3723 | 0.492802 | 0.246401 | − | 0.969168i | \(-0.420752\pi\) | ||||
0.246401 | + | 0.969168i | \(0.420752\pi\) | |||||||
\(444\) | −8.74456 | −0.414999 | ||||||||
\(445\) | −2.74456 | −0.130105 | ||||||||
\(446\) | 3.11684 | 0.147587 | ||||||||
\(447\) | −14.7446 | −0.697394 | ||||||||
\(448\) | 2.37228 | 0.112080 | ||||||||
\(449\) | −1.86141 | −0.0878452 | −0.0439226 | − | 0.999035i | \(-0.513985\pi\) | ||||
−0.0439226 | + | 0.999035i | \(0.513985\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | 10.7446 | 0.505942 | ||||||||
\(452\) | 7.48913 | 0.352259 | ||||||||
\(453\) | −16.2337 | −0.762725 | ||||||||
\(454\) | −23.8614 | −1.11987 | ||||||||
\(455\) | −9.48913 | −0.444857 | ||||||||
\(456\) | 4.00000 | 0.187317 | ||||||||
\(457\) | −16.9783 | −0.794209 | −0.397105 | − | 0.917773i | \(-0.629985\pi\) | ||||
−0.397105 | + | 0.917773i | \(0.629985\pi\) | |||||||
\(458\) | 1.25544 | 0.0586627 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −1.62772 | −0.0758928 | ||||||||
\(461\) | 23.4891 | 1.09400 | 0.546999 | − | 0.837133i | \(-0.315770\pi\) | ||||
0.546999 | + | 0.837133i | \(0.315770\pi\) | |||||||
\(462\) | 2.37228 | 0.110369 | ||||||||
\(463\) | 8.00000 | 0.371792 | 0.185896 | − | 0.982569i | \(-0.440481\pi\) | ||||
0.185896 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(464\) | −6.37228 | −0.295826 | ||||||||
\(465\) | 9.11684 | 0.422784 | ||||||||
\(466\) | 1.11684 | 0.0517368 | ||||||||
\(467\) | 30.9783 | 1.43350 | 0.716751 | − | 0.697329i | \(-0.245628\pi\) | ||||
0.716751 | + | 0.697329i | \(0.245628\pi\) | |||||||
\(468\) | −4.00000 | −0.184900 | ||||||||
\(469\) | 9.48913 | 0.438167 | ||||||||
\(470\) | −10.7446 | −0.495610 | ||||||||
\(471\) | −10.0000 | −0.460776 | ||||||||
\(472\) | −12.7446 | −0.586616 | ||||||||
\(473\) | −10.3723 | −0.476918 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | 2.37228 | 0.108733 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 30.2337 | 1.38286 | ||||||||
\(479\) | −33.1168 | −1.51315 | −0.756574 | − | 0.653909i | \(-0.773128\pi\) | ||||
−0.756574 | + | 0.653909i | \(0.773128\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | −34.9783 | −1.59487 | ||||||||
\(482\) | −22.6060 | −1.02967 | ||||||||
\(483\) | 3.86141 | 0.175700 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −17.8614 | −0.811045 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 7.48913 | 0.339365 | 0.169682 | − | 0.985499i | \(-0.445726\pi\) | ||||
0.169682 | + | 0.985499i | \(0.445726\pi\) | |||||||
\(488\) | −11.4891 | −0.520088 | ||||||||
\(489\) | 7.86141 | 0.355505 | ||||||||
\(490\) | 1.37228 | 0.0619934 | ||||||||
\(491\) | 18.5109 | 0.835384 | 0.417692 | − | 0.908589i | \(-0.362839\pi\) | ||||
0.417692 | + | 0.908589i | \(0.362839\pi\) | |||||||
\(492\) | −10.7446 | −0.484402 | ||||||||
\(493\) | −6.37228 | −0.286993 | ||||||||
\(494\) | 16.0000 | 0.719874 | ||||||||
\(495\) | 1.00000 | 0.0449467 | ||||||||
\(496\) | −9.11684 | −0.409358 | ||||||||
\(497\) | 11.2554 | 0.504875 | ||||||||
\(498\) | −13.4891 | −0.604462 | ||||||||
\(499\) | 36.0000 | 1.61158 | 0.805791 | − | 0.592200i | \(-0.201741\pi\) | ||||
0.805791 | + | 0.592200i | \(0.201741\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −19.4891 | −0.870710 | ||||||||
\(502\) | −12.0000 | −0.535586 | ||||||||
\(503\) | 33.7228 | 1.50363 | 0.751813 | − | 0.659376i | \(-0.229180\pi\) | ||||
0.751813 | + | 0.659376i | \(0.229180\pi\) | |||||||
\(504\) | −2.37228 | −0.105670 | ||||||||
\(505\) | 2.00000 | 0.0889988 | ||||||||
\(506\) | 1.62772 | 0.0723609 | ||||||||
\(507\) | −3.00000 | −0.133235 | ||||||||
\(508\) | −11.4891 | −0.509748 | ||||||||
\(509\) | 20.7446 | 0.919487 | 0.459743 | − | 0.888052i | \(-0.347941\pi\) | ||||
0.459743 | + | 0.888052i | \(0.347941\pi\) | |||||||
\(510\) | 1.00000 | 0.0442807 | ||||||||
\(511\) | −14.2337 | −0.629661 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −4.00000 | −0.176604 | ||||||||
\(514\) | 9.11684 | 0.402127 | ||||||||
\(515\) | 18.3723 | 0.809579 | ||||||||
\(516\) | 10.3723 | 0.456614 | ||||||||
\(517\) | 10.7446 | 0.472545 | ||||||||
\(518\) | −20.7446 | −0.911464 | ||||||||
\(519\) | 14.2337 | 0.624790 | ||||||||
\(520\) | 4.00000 | 0.175412 | ||||||||
\(521\) | 2.00000 | 0.0876216 | 0.0438108 | − | 0.999040i | \(-0.486050\pi\) | ||||
0.0438108 | + | 0.999040i | \(0.486050\pi\) | |||||||
\(522\) | 6.37228 | 0.278907 | ||||||||
\(523\) | 3.11684 | 0.136290 | 0.0681450 | − | 0.997675i | \(-0.478292\pi\) | ||||
0.0681450 | + | 0.997675i | \(0.478292\pi\) | |||||||
\(524\) | 8.00000 | 0.349482 | ||||||||
\(525\) | −2.37228 | −0.103535 | ||||||||
\(526\) | 19.1168 | 0.833534 | ||||||||
\(527\) | −9.11684 | −0.397136 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | −20.3505 | −0.884806 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.7446 | 0.553067 | ||||||||
\(532\) | 9.48913 | 0.411406 | ||||||||
\(533\) | −42.9783 | −1.86159 | ||||||||
\(534\) | −2.74456 | −0.118769 | ||||||||
\(535\) | 10.3723 | 0.448433 | ||||||||
\(536\) | −4.00000 | −0.172774 | ||||||||
\(537\) | 0.744563 | 0.0321302 | ||||||||
\(538\) | −14.0000 | −0.603583 | ||||||||
\(539\) | −1.37228 | −0.0591083 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | −32.2337 | −1.38583 | −0.692917 | − | 0.721017i | \(-0.743675\pi\) | ||||
−0.692917 | + | 0.721017i | \(0.743675\pi\) | |||||||
\(542\) | 7.62772 | 0.327639 | ||||||||
\(543\) | 14.3723 | 0.616774 | ||||||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | 16.2337 | 0.695375 | ||||||||
\(546\) | −9.48913 | −0.406097 | ||||||||
\(547\) | 16.7446 | 0.715946 | 0.357973 | − | 0.933732i | \(-0.383468\pi\) | ||||
0.357973 | + | 0.933732i | \(0.383468\pi\) | |||||||
\(548\) | 1.11684 | 0.0477092 | ||||||||
\(549\) | 11.4891 | 0.490344 | ||||||||
\(550\) | −1.00000 | −0.0426401 | ||||||||
\(551\) | −25.4891 | −1.08587 | ||||||||
\(552\) | −1.62772 | −0.0692803 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −15.4891 | −0.658070 | ||||||||
\(555\) | −8.74456 | −0.371186 | ||||||||
\(556\) | 1.62772 | 0.0690306 | ||||||||
\(557\) | −29.8614 | −1.26527 | −0.632634 | − | 0.774451i | \(-0.718026\pi\) | ||||
−0.632634 | + | 0.774451i | \(0.718026\pi\) | |||||||
\(558\) | 9.11684 | 0.385947 | ||||||||
\(559\) | 41.4891 | 1.75480 | ||||||||
\(560\) | 2.37228 | 0.100247 | ||||||||
\(561\) | −1.00000 | −0.0422200 | ||||||||
\(562\) | −13.8614 | −0.584708 | ||||||||
\(563\) | 10.5109 | 0.442981 | 0.221490 | − | 0.975163i | \(-0.428908\pi\) | ||||
0.221490 | + | 0.975163i | \(0.428908\pi\) | |||||||
\(564\) | −10.7446 | −0.452428 | ||||||||
\(565\) | 7.48913 | 0.315070 | ||||||||
\(566\) | 24.7446 | 1.04009 | ||||||||
\(567\) | 2.37228 | 0.0996265 | ||||||||
\(568\) | −4.74456 | −0.199077 | ||||||||
\(569\) | 6.00000 | 0.251533 | 0.125767 | − | 0.992060i | \(-0.459861\pi\) | ||||
0.125767 | + | 0.992060i | \(0.459861\pi\) | |||||||
\(570\) | 4.00000 | 0.167542 | ||||||||
\(571\) | 4.00000 | 0.167395 | 0.0836974 | − | 0.996491i | \(-0.473327\pi\) | ||||
0.0836974 | + | 0.996491i | \(0.473327\pi\) | |||||||
\(572\) | −4.00000 | −0.167248 | ||||||||
\(573\) | −7.62772 | −0.318653 | ||||||||
\(574\) | −25.4891 | −1.06390 | ||||||||
\(575\) | −1.62772 | −0.0678806 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −30.4674 | −1.26837 | −0.634187 | − | 0.773180i | \(-0.718665\pi\) | ||||
−0.634187 | + | 0.773180i | \(0.718665\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | 3.48913 | 0.145003 | ||||||||
\(580\) | −6.37228 | −0.264595 | ||||||||
\(581\) | −32.0000 | −1.32758 | ||||||||
\(582\) | −17.8614 | −0.740379 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 6.00000 | 0.248282 | ||||||||
\(585\) | −4.00000 | −0.165380 | ||||||||
\(586\) | −2.88316 | −0.119102 | ||||||||
\(587\) | −29.3505 | −1.21143 | −0.605713 | − | 0.795683i | \(-0.707112\pi\) | ||||
−0.605713 | + | 0.795683i | \(0.707112\pi\) | |||||||
\(588\) | 1.37228 | 0.0565919 | ||||||||
\(589\) | −36.4674 | −1.50261 | ||||||||
\(590\) | −12.7446 | −0.524685 | ||||||||
\(591\) | 13.4891 | 0.554868 | ||||||||
\(592\) | 8.74456 | 0.359399 | ||||||||
\(593\) | −4.97825 | −0.204432 | −0.102216 | − | 0.994762i | \(-0.532593\pi\) | ||||
−0.102216 | + | 0.994762i | \(0.532593\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | 2.37228 | 0.0972541 | ||||||||
\(596\) | 14.7446 | 0.603961 | ||||||||
\(597\) | 14.7446 | 0.603455 | ||||||||
\(598\) | −6.51087 | −0.266249 | ||||||||
\(599\) | 26.8832 | 1.09842 | 0.549208 | − | 0.835686i | \(-0.314929\pi\) | ||||
0.549208 | + | 0.835686i | \(0.314929\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | −8.97825 | −0.366230 | −0.183115 | − | 0.983091i | \(-0.558618\pi\) | ||||
−0.183115 | + | 0.983091i | \(0.558618\pi\) | |||||||
\(602\) | 24.6060 | 1.00286 | ||||||||
\(603\) | 4.00000 | 0.162893 | ||||||||
\(604\) | 16.2337 | 0.660539 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 2.00000 | 0.0812444 | ||||||||
\(607\) | 8.00000 | 0.324710 | 0.162355 | − | 0.986732i | \(-0.448091\pi\) | ||||
0.162355 | + | 0.986732i | \(0.448091\pi\) | |||||||
\(608\) | −4.00000 | −0.162221 | ||||||||
\(609\) | 15.1168 | 0.612565 | ||||||||
\(610\) | −11.4891 | −0.465181 | ||||||||
\(611\) | −42.9783 | −1.73871 | ||||||||
\(612\) | 1.00000 | 0.0404226 | ||||||||
\(613\) | −16.7446 | −0.676307 | −0.338153 | − | 0.941091i | \(-0.609802\pi\) | ||||
−0.338153 | + | 0.941091i | \(0.609802\pi\) | |||||||
\(614\) | 12.0000 | 0.484281 | ||||||||
\(615\) | −10.7446 | −0.433263 | ||||||||
\(616\) | −2.37228 | −0.0955819 | ||||||||
\(617\) | −42.4674 | −1.70967 | −0.854836 | − | 0.518898i | \(-0.826342\pi\) | ||||
−0.854836 | + | 0.518898i | \(0.826342\pi\) | |||||||
\(618\) | 18.3723 | 0.739042 | ||||||||
\(619\) | 18.2337 | 0.732874 | 0.366437 | − | 0.930443i | \(-0.380578\pi\) | ||||
0.366437 | + | 0.930443i | \(0.380578\pi\) | |||||||
\(620\) | −9.11684 | −0.366141 | ||||||||
\(621\) | 1.62772 | 0.0653181 | ||||||||
\(622\) | −10.5109 | −0.421448 | ||||||||
\(623\) | −6.51087 | −0.260853 | ||||||||
\(624\) | 4.00000 | 0.160128 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −4.37228 | −0.174752 | ||||||||
\(627\) | −4.00000 | −0.159745 | ||||||||
\(628\) | 10.0000 | 0.399043 | ||||||||
\(629\) | 8.74456 | 0.348669 | ||||||||
\(630\) | −2.37228 | −0.0945140 | ||||||||
\(631\) | 34.2337 | 1.36282 | 0.681411 | − | 0.731901i | \(-0.261367\pi\) | ||||
0.681411 | + | 0.731901i | \(0.261367\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.62772 | 0.382667 | ||||||||
\(634\) | 1.11684 | 0.0443555 | ||||||||
\(635\) | −11.4891 | −0.455932 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.48913 | 0.217487 | ||||||||
\(638\) | 6.37228 | 0.252281 | ||||||||
\(639\) | 4.74456 | 0.187692 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −18.8832 | −0.745840 | −0.372920 | − | 0.927864i | \(-0.621643\pi\) | ||||
−0.372920 | + | 0.927864i | \(0.621643\pi\) | |||||||
\(642\) | 10.3723 | 0.409361 | ||||||||
\(643\) | 10.3723 | 0.409043 | 0.204521 | − | 0.978862i | \(-0.434436\pi\) | ||||
0.204521 | + | 0.978862i | \(0.434436\pi\) | |||||||
\(644\) | −3.86141 | −0.152161 | ||||||||
\(645\) | 10.3723 | 0.408408 | ||||||||
\(646\) | −4.00000 | −0.157378 | ||||||||
\(647\) | −32.9783 | −1.29651 | −0.648254 | − | 0.761424i | \(-0.724501\pi\) | ||||
−0.648254 | + | 0.761424i | \(0.724501\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 12.7446 | 0.500268 | ||||||||
\(650\) | 4.00000 | 0.156893 | ||||||||
\(651\) | 21.6277 | 0.847657 | ||||||||
\(652\) | −7.86141 | −0.307876 | ||||||||
\(653\) | 28.3723 | 1.11029 | 0.555147 | − | 0.831753i | \(-0.312662\pi\) | ||||
0.555147 | + | 0.831753i | \(0.312662\pi\) | |||||||
\(654\) | 16.2337 | 0.634787 | ||||||||
\(655\) | 8.00000 | 0.312586 | ||||||||
\(656\) | 10.7446 | 0.419505 | ||||||||
\(657\) | −6.00000 | −0.234082 | ||||||||
\(658\) | −25.4891 | −0.993670 | ||||||||
\(659\) | 14.3723 | 0.559865 | 0.279932 | − | 0.960020i | \(-0.409688\pi\) | ||||
0.279932 | + | 0.960020i | \(0.409688\pi\) | |||||||
\(660\) | −1.00000 | −0.0389249 | ||||||||
\(661\) | 17.2554 | 0.671159 | 0.335579 | − | 0.942012i | \(-0.391068\pi\) | ||||
0.335579 | + | 0.942012i | \(0.391068\pi\) | |||||||
\(662\) | −27.1168 | −1.05393 | ||||||||
\(663\) | 4.00000 | 0.155347 | ||||||||
\(664\) | 13.4891 | 0.523480 | ||||||||
\(665\) | 9.48913 | 0.367972 | ||||||||
\(666\) | −8.74456 | −0.338845 | ||||||||
\(667\) | 10.3723 | 0.401616 | ||||||||
\(668\) | 19.4891 | 0.754057 | ||||||||
\(669\) | 3.11684 | 0.120504 | ||||||||
\(670\) | −4.00000 | −0.154533 | ||||||||
\(671\) | 11.4891 | 0.443533 | ||||||||
\(672\) | 2.37228 | 0.0915127 | ||||||||
\(673\) | −24.2337 | −0.934140 | −0.467070 | − | 0.884220i | \(-0.654690\pi\) | ||||
−0.467070 | + | 0.884220i | \(0.654690\pi\) | |||||||
\(674\) | 11.4891 | 0.442545 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 3.00000 | 0.115385 | ||||||||
\(677\) | −23.2554 | −0.893779 | −0.446890 | − | 0.894589i | \(-0.647468\pi\) | ||||
−0.446890 | + | 0.894589i | \(0.647468\pi\) | |||||||
\(678\) | 7.48913 | 0.287618 | ||||||||
\(679\) | −42.3723 | −1.62610 | ||||||||
\(680\) | −1.00000 | −0.0383482 | ||||||||
\(681\) | −23.8614 | −0.914371 | ||||||||
\(682\) | 9.11684 | 0.349102 | ||||||||
\(683\) | 46.9783 | 1.79757 | 0.898786 | − | 0.438387i | \(-0.144450\pi\) | ||||
0.898786 | + | 0.438387i | \(0.144450\pi\) | |||||||
\(684\) | 4.00000 | 0.152944 | ||||||||
\(685\) | 1.11684 | 0.0426724 | ||||||||
\(686\) | 19.8614 | 0.758312 | ||||||||
\(687\) | 1.25544 | 0.0478979 | ||||||||
\(688\) | −10.3723 | −0.395440 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −1.62772 | −0.0619662 | ||||||||
\(691\) | 8.00000 | 0.304334 | 0.152167 | − | 0.988355i | \(-0.451375\pi\) | ||||
0.152167 | + | 0.988355i | \(0.451375\pi\) | |||||||
\(692\) | −14.2337 | −0.541084 | ||||||||
\(693\) | 2.37228 | 0.0901155 | ||||||||
\(694\) | −17.4891 | −0.663878 | ||||||||
\(695\) | 1.62772 | 0.0617429 | ||||||||
\(696\) | −6.37228 | −0.241541 | ||||||||
\(697\) | 10.7446 | 0.406979 | ||||||||
\(698\) | 30.2337 | 1.14436 | ||||||||
\(699\) | 1.11684 | 0.0422429 | ||||||||
\(700\) | 2.37228 | 0.0896638 | ||||||||
\(701\) | 6.00000 | 0.226617 | 0.113308 | − | 0.993560i | \(-0.463855\pi\) | ||||
0.113308 | + | 0.993560i | \(0.463855\pi\) | |||||||
\(702\) | −4.00000 | −0.150970 | ||||||||
\(703\) | 34.9783 | 1.31923 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | −10.7446 | −0.404664 | ||||||||
\(706\) | −19.6277 | −0.738699 | ||||||||
\(707\) | 4.74456 | 0.178438 | ||||||||
\(708\) | −12.7446 | −0.478970 | ||||||||
\(709\) | −11.2554 | −0.422707 | −0.211353 | − | 0.977410i | \(-0.567787\pi\) | ||||
−0.211353 | + | 0.977410i | \(0.567787\pi\) | |||||||
\(710\) | −4.74456 | −0.178060 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.74456 | 0.102857 | ||||||||
\(713\) | 14.8397 | 0.555750 | ||||||||
\(714\) | 2.37228 | 0.0887804 | ||||||||
\(715\) | −4.00000 | −0.149592 | ||||||||
\(716\) | −0.744563 | −0.0278256 | ||||||||
\(717\) | 30.2337 | 1.12910 | ||||||||
\(718\) | −24.7446 | −0.923459 | ||||||||
\(719\) | −22.2337 | −0.829177 | −0.414588 | − | 0.910009i | \(-0.636074\pi\) | ||||
−0.414588 | + | 0.910009i | \(0.636074\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | 43.5842 | 1.62316 | ||||||||
\(722\) | 3.00000 | 0.111648 | ||||||||
\(723\) | −22.6060 | −0.840725 | ||||||||
\(724\) | −14.3723 | −0.534142 | ||||||||
\(725\) | −6.37228 | −0.236661 | ||||||||
\(726\) | 1.00000 | 0.0371135 | ||||||||
\(727\) | −11.1168 | −0.412301 | −0.206150 | − | 0.978520i | \(-0.566094\pi\) | ||||
−0.206150 | + | 0.978520i | \(0.566094\pi\) | |||||||
\(728\) | 9.48913 | 0.351690 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 6.00000 | 0.222070 | ||||||||
\(731\) | −10.3723 | −0.383633 | ||||||||
\(732\) | −11.4891 | −0.424650 | ||||||||
\(733\) | −13.4891 | −0.498232 | −0.249116 | − | 0.968474i | \(-0.580140\pi\) | ||||
−0.249116 | + | 0.968474i | \(0.580140\pi\) | |||||||
\(734\) | −0.510875 | −0.0188567 | ||||||||
\(735\) | 1.37228 | 0.0506174 | ||||||||
\(736\) | 1.62772 | 0.0599985 | ||||||||
\(737\) | 4.00000 | 0.147342 | ||||||||
\(738\) | −10.7446 | −0.395513 | ||||||||
\(739\) | 1.76631 | 0.0649748 | 0.0324874 | − | 0.999472i | \(-0.489657\pi\) | ||||
0.0324874 | + | 0.999472i | \(0.489657\pi\) | |||||||
\(740\) | 8.74456 | 0.321457 | ||||||||
\(741\) | 16.0000 | 0.587775 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.2119 | 1.29180 | 0.645900 | − | 0.763422i | \(-0.276482\pi\) | ||||
0.645900 | + | 0.763422i | \(0.276482\pi\) | |||||||
\(744\) | −9.11684 | −0.334240 | ||||||||
\(745\) | 14.7446 | 0.540199 | ||||||||
\(746\) | −35.7228 | −1.30791 | ||||||||
\(747\) | −13.4891 | −0.493541 | ||||||||
\(748\) | 1.00000 | 0.0365636 | ||||||||
\(749\) | 24.6060 | 0.899083 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | 17.1168 | 0.624603 | 0.312301 | − | 0.949983i | \(-0.398900\pi\) | ||||
0.312301 | + | 0.949983i | \(0.398900\pi\) | |||||||
\(752\) | 10.7446 | 0.391814 | ||||||||
\(753\) | −12.0000 | −0.437304 | ||||||||
\(754\) | −25.4891 | −0.928259 | ||||||||
\(755\) | 16.2337 | 0.590804 | ||||||||
\(756\) | −2.37228 | −0.0862790 | ||||||||
\(757\) | −20.3723 | −0.740443 | −0.370222 | − | 0.928943i | \(-0.620718\pi\) | ||||
−0.370222 | + | 0.928943i | \(0.620718\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.62772 | 0.0590824 | ||||||||
\(760\) | −4.00000 | −0.145095 | ||||||||
\(761\) | 24.0951 | 0.873446 | 0.436723 | − | 0.899596i | \(-0.356139\pi\) | ||||
0.436723 | + | 0.899596i | \(0.356139\pi\) | |||||||
\(762\) | −11.4891 | −0.416207 | ||||||||
\(763\) | 38.5109 | 1.39419 | ||||||||
\(764\) | 7.62772 | 0.275961 | ||||||||
\(765\) | 1.00000 | 0.0361551 | ||||||||
\(766\) | 2.74456 | 0.0991651 | ||||||||
\(767\) | −50.9783 | −1.84072 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −20.9783 | −0.756495 | −0.378248 | − | 0.925704i | \(-0.623473\pi\) | ||||
−0.378248 | + | 0.925704i | \(0.623473\pi\) | |||||||
\(770\) | −2.37228 | −0.0854911 | ||||||||
\(771\) | 9.11684 | 0.328335 | ||||||||
\(772\) | −3.48913 | −0.125576 | ||||||||
\(773\) | −10.5109 | −0.378050 | −0.189025 | − | 0.981972i | \(-0.560533\pi\) | ||||
−0.189025 | + | 0.981972i | \(0.560533\pi\) | |||||||
\(774\) | 10.3723 | 0.372824 | ||||||||
\(775\) | −9.11684 | −0.327487 | ||||||||
\(776\) | 17.8614 | 0.641187 | ||||||||
\(777\) | −20.7446 | −0.744207 | ||||||||
\(778\) | −20.7446 | −0.743729 | ||||||||
\(779\) | 42.9783 | 1.53986 | ||||||||
\(780\) | 4.00000 | 0.143223 | ||||||||
\(781\) | 4.74456 | 0.169774 | ||||||||
\(782\) | 1.62772 | 0.0582071 | ||||||||
\(783\) | 6.37228 | 0.227727 | ||||||||
\(784\) | −1.37228 | −0.0490100 | ||||||||
\(785\) | 10.0000 | 0.356915 | ||||||||
\(786\) | 8.00000 | 0.285351 | ||||||||
\(787\) | 13.4891 | 0.480835 | 0.240418 | − | 0.970670i | \(-0.422716\pi\) | ||||
0.240418 | + | 0.970670i | \(0.422716\pi\) | |||||||
\(788\) | −13.4891 | −0.480530 | ||||||||
\(789\) | 19.1168 | 0.680578 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.7663 | 0.631697 | ||||||||
\(792\) | −1.00000 | −0.0355335 | ||||||||
\(793\) | −45.9565 | −1.63196 | ||||||||
\(794\) | −22.2337 | −0.789044 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14.7446 | −0.522607 | ||||||||
\(797\) | 17.4891 | 0.619497 | 0.309748 | − | 0.950819i | \(-0.399755\pi\) | ||||
0.309748 | + | 0.950819i | \(0.399755\pi\) | |||||||
\(798\) | 9.48913 | 0.335911 | ||||||||
\(799\) | 10.7446 | 0.380115 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −2.74456 | −0.0969744 | ||||||||
\(802\) | −29.8614 | −1.05444 | ||||||||
\(803\) | −6.00000 | −0.211735 | ||||||||
\(804\) | −4.00000 | −0.141069 | ||||||||
\(805\) | −3.86141 | −0.136097 | ||||||||
\(806\) | −36.4674 | −1.28451 | ||||||||
\(807\) | −14.0000 | −0.492823 | ||||||||
\(808\) | −2.00000 | −0.0703598 | ||||||||
\(809\) | −4.97825 | −0.175026 | −0.0875130 | − | 0.996163i | \(-0.527892\pi\) | ||||
−0.0875130 | + | 0.996163i | \(0.527892\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 13.4891 | 0.473667 | 0.236834 | − | 0.971550i | \(-0.423890\pi\) | ||||
0.236834 | + | 0.971550i | \(0.423890\pi\) | |||||||
\(812\) | −15.1168 | −0.530497 | ||||||||
\(813\) | 7.62772 | 0.267516 | ||||||||
\(814\) | −8.74456 | −0.306497 | ||||||||
\(815\) | −7.86141 | −0.275373 | ||||||||
\(816\) | −1.00000 | −0.0350070 | ||||||||
\(817\) | −41.4891 | −1.45152 | ||||||||
\(818\) | −12.2337 | −0.427741 | ||||||||
\(819\) | −9.48913 | −0.331577 | ||||||||
\(820\) | 10.7446 | 0.375216 | ||||||||
\(821\) | −21.6277 | −0.754813 | −0.377406 | − | 0.926048i | \(-0.623184\pi\) | ||||
−0.377406 | + | 0.926048i | \(0.623184\pi\) | |||||||
\(822\) | 1.11684 | 0.0389544 | ||||||||
\(823\) | 10.0000 | 0.348578 | 0.174289 | − | 0.984695i | \(-0.444237\pi\) | ||||
0.174289 | + | 0.984695i | \(0.444237\pi\) | |||||||
\(824\) | −18.3723 | −0.640029 | ||||||||
\(825\) | −1.00000 | −0.0348155 | ||||||||
\(826\) | −30.2337 | −1.05196 | ||||||||
\(827\) | −50.8397 | −1.76787 | −0.883934 | − | 0.467612i | \(-0.845115\pi\) | ||||
−0.883934 | + | 0.467612i | \(0.845115\pi\) | |||||||
\(828\) | −1.62772 | −0.0565671 | ||||||||
\(829\) | −20.9783 | −0.728605 | −0.364302 | − | 0.931281i | \(-0.618693\pi\) | ||||
−0.364302 | + | 0.931281i | \(0.618693\pi\) | |||||||
\(830\) | 13.4891 | 0.468214 | ||||||||
\(831\) | −15.4891 | −0.537312 | ||||||||
\(832\) | −4.00000 | −0.138675 | ||||||||
\(833\) | −1.37228 | −0.0475467 | ||||||||
\(834\) | 1.62772 | 0.0563633 | ||||||||
\(835\) | 19.4891 | 0.674449 | ||||||||
\(836\) | 4.00000 | 0.138343 | ||||||||
\(837\) | 9.11684 | 0.315124 | ||||||||
\(838\) | −38.3723 | −1.32555 | ||||||||
\(839\) | 43.7228 | 1.50948 | 0.754740 | − | 0.656025i | \(-0.227763\pi\) | ||||
0.754740 | + | 0.656025i | \(0.227763\pi\) | |||||||
\(840\) | 2.37228 | 0.0818515 | ||||||||
\(841\) | 11.6060 | 0.400206 | ||||||||
\(842\) | 25.2554 | 0.870360 | ||||||||
\(843\) | −13.8614 | −0.477412 | ||||||||
\(844\) | −9.62772 | −0.331400 | ||||||||
\(845\) | 3.00000 | 0.103203 | ||||||||
\(846\) | −10.7446 | −0.369406 | ||||||||
\(847\) | 2.37228 | 0.0815126 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 24.7446 | 0.849231 | ||||||||
\(850\) | −1.00000 | −0.0342997 | ||||||||
\(851\) | −14.2337 | −0.487925 | ||||||||
\(852\) | −4.74456 | −0.162546 | ||||||||
\(853\) | 13.1168 | 0.449112 | 0.224556 | − | 0.974461i | \(-0.427907\pi\) | ||||
0.224556 | + | 0.974461i | \(0.427907\pi\) | |||||||
\(854\) | −27.2554 | −0.932662 | ||||||||
\(855\) | 4.00000 | 0.136797 | ||||||||
\(856\) | −10.3723 | −0.354517 | ||||||||
\(857\) | −9.86141 | −0.336859 | −0.168430 | − | 0.985714i | \(-0.553870\pi\) | ||||
−0.168430 | + | 0.985714i | \(0.553870\pi\) | |||||||
\(858\) | −4.00000 | −0.136558 | ||||||||
\(859\) | 34.8397 | 1.18871 | 0.594357 | − | 0.804201i | \(-0.297407\pi\) | ||||
0.594357 | + | 0.804201i | \(0.297407\pi\) | |||||||
\(860\) | −10.3723 | −0.353692 | ||||||||
\(861\) | −25.4891 | −0.868667 | ||||||||
\(862\) | 17.8614 | 0.608362 | ||||||||
\(863\) | −37.7228 | −1.28410 | −0.642050 | − | 0.766663i | \(-0.721916\pi\) | ||||
−0.642050 | + | 0.766663i | \(0.721916\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −14.2337 | −0.483960 | ||||||||
\(866\) | −18.7446 | −0.636966 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −21.6277 | −0.734093 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −6.37228 | −0.216041 | ||||||||
\(871\) | −16.0000 | −0.542139 | ||||||||
\(872\) | −16.2337 | −0.549742 | ||||||||
\(873\) | −17.8614 | −0.604517 | ||||||||
\(874\) | 6.51087 | 0.220234 | ||||||||
\(875\) | 2.37228 | 0.0801977 | ||||||||
\(876\) | 6.00000 | 0.202721 | ||||||||
\(877\) | −24.3723 | −0.822993 | −0.411497 | − | 0.911411i | \(-0.634994\pi\) | ||||
−0.411497 | + | 0.911411i | \(0.634994\pi\) | |||||||
\(878\) | −32.7446 | −1.10508 | ||||||||
\(879\) | −2.88316 | −0.0972464 | ||||||||
\(880\) | 1.00000 | 0.0337100 | ||||||||
\(881\) | −29.1168 | −0.980971 | −0.490486 | − | 0.871449i | \(-0.663181\pi\) | ||||
−0.490486 | + | 0.871449i | \(0.663181\pi\) | |||||||
\(882\) | 1.37228 | 0.0462071 | ||||||||
\(883\) | −21.4891 | −0.723167 | −0.361583 | − | 0.932340i | \(-0.617764\pi\) | ||||
−0.361583 | + | 0.932340i | \(0.617764\pi\) | |||||||
\(884\) | −4.00000 | −0.134535 | ||||||||
\(885\) | −12.7446 | −0.428404 | ||||||||
\(886\) | −10.3723 | −0.348464 | ||||||||
\(887\) | 45.7228 | 1.53522 | 0.767611 | − | 0.640916i | \(-0.221445\pi\) | ||||
0.767611 | + | 0.640916i | \(0.221445\pi\) | |||||||
\(888\) | 8.74456 | 0.293448 | ||||||||
\(889\) | −27.2554 | −0.914118 | ||||||||
\(890\) | 2.74456 | 0.0919979 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | −3.11684 | −0.104360 | ||||||||
\(893\) | 42.9783 | 1.43821 | ||||||||
\(894\) | 14.7446 | 0.493132 | ||||||||
\(895\) | −0.744563 | −0.0248880 | ||||||||
\(896\) | −2.37228 | −0.0792524 | ||||||||
\(897\) | −6.51087 | −0.217392 | ||||||||
\(898\) | 1.86141 | 0.0621159 | ||||||||
\(899\) | 58.0951 | 1.93758 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −10.7446 | −0.357755 | ||||||||
\(903\) | 24.6060 | 0.818835 | ||||||||
\(904\) | −7.48913 | −0.249085 | ||||||||
\(905\) | −14.3723 | −0.477751 | ||||||||
\(906\) | 16.2337 | 0.539328 | ||||||||
\(907\) | 47.8614 | 1.58921 | 0.794606 | − | 0.607125i | \(-0.207677\pi\) | ||||
0.794606 | + | 0.607125i | \(0.207677\pi\) | |||||||
\(908\) | 23.8614 | 0.791869 | ||||||||
\(909\) | 2.00000 | 0.0663358 | ||||||||
\(910\) | 9.48913 | 0.314561 | ||||||||
\(911\) | 28.4674 | 0.943166 | 0.471583 | − | 0.881822i | \(-0.343683\pi\) | ||||
0.471583 | + | 0.881822i | \(0.343683\pi\) | |||||||
\(912\) | −4.00000 | −0.132453 | ||||||||
\(913\) | −13.4891 | −0.446425 | ||||||||
\(914\) | 16.9783 | 0.561591 | ||||||||
\(915\) | −11.4891 | −0.379819 | ||||||||
\(916\) | −1.25544 | −0.0414808 | ||||||||
\(917\) | 18.9783 | 0.626717 | ||||||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | 45.1168 | 1.48827 | 0.744134 | − | 0.668031i | \(-0.232863\pi\) | ||||
0.744134 | + | 0.668031i | \(0.232863\pi\) | |||||||
\(920\) | 1.62772 | 0.0536643 | ||||||||
\(921\) | 12.0000 | 0.395413 | ||||||||
\(922\) | −23.4891 | −0.773573 | ||||||||
\(923\) | −18.9783 | −0.624677 | ||||||||
\(924\) | −2.37228 | −0.0780423 | ||||||||
\(925\) | 8.74456 | 0.287519 | ||||||||
\(926\) | −8.00000 | −0.262896 | ||||||||
\(927\) | 18.3723 | 0.603425 | ||||||||
\(928\) | 6.37228 | 0.209180 | ||||||||
\(929\) | 19.6277 | 0.643965 | 0.321982 | − | 0.946746i | \(-0.395651\pi\) | ||||
0.321982 | + | 0.946746i | \(0.395651\pi\) | |||||||
\(930\) | −9.11684 | −0.298953 | ||||||||
\(931\) | −5.48913 | −0.179899 | ||||||||
\(932\) | −1.11684 | −0.0365834 | ||||||||
\(933\) | −10.5109 | −0.344111 | ||||||||
\(934\) | −30.9783 | −1.01364 | ||||||||
\(935\) | 1.00000 | 0.0327035 | ||||||||
\(936\) | 4.00000 | 0.130744 | ||||||||
\(937\) | 34.4674 | 1.12600 | 0.563000 | − | 0.826457i | \(-0.309647\pi\) | ||||
0.563000 | + | 0.826457i | \(0.309647\pi\) | |||||||
\(938\) | −9.48913 | −0.309831 | ||||||||
\(939\) | −4.37228 | −0.142684 | ||||||||
\(940\) | 10.7446 | 0.350449 | ||||||||
\(941\) | −3.25544 | −0.106124 | −0.0530621 | − | 0.998591i | \(-0.516898\pi\) | ||||
−0.0530621 | + | 0.998591i | \(0.516898\pi\) | |||||||
\(942\) | 10.0000 | 0.325818 | ||||||||
\(943\) | −17.4891 | −0.569524 | ||||||||
\(944\) | 12.7446 | 0.414800 | ||||||||
\(945\) | −2.37228 | −0.0771703 | ||||||||
\(946\) | 10.3723 | 0.337232 | ||||||||
\(947\) | −23.2554 | −0.755700 | −0.377850 | − | 0.925867i | \(-0.623337\pi\) | ||||
−0.377850 | + | 0.925867i | \(0.623337\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.0000 | 0.779073 | ||||||||
\(950\) | −4.00000 | −0.129777 | ||||||||
\(951\) | 1.11684 | 0.0362161 | ||||||||
\(952\) | −2.37228 | −0.0768861 | ||||||||
\(953\) | −52.9783 | −1.71613 | −0.858067 | − | 0.513538i | \(-0.828335\pi\) | ||||
−0.858067 | + | 0.513538i | \(0.828335\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.62772 | 0.246827 | ||||||||
\(956\) | −30.2337 | −0.977827 | ||||||||
\(957\) | 6.37228 | 0.205987 | ||||||||
\(958\) | 33.1168 | 1.06996 | ||||||||
\(959\) | 2.64947 | 0.0855558 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | 52.1168 | 1.68119 | ||||||||
\(962\) | 34.9783 | 1.12774 | ||||||||
\(963\) | 10.3723 | 0.334242 | ||||||||
\(964\) | 22.6060 | 0.728089 | ||||||||
\(965\) | −3.48913 | −0.112319 | ||||||||
\(966\) | −3.86141 | −0.124239 | ||||||||
\(967\) | −42.4674 | −1.36566 | −0.682829 | − | 0.730578i | \(-0.739251\pi\) | ||||
−0.682829 | + | 0.730578i | \(0.739251\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −4.00000 | −0.128499 | ||||||||
\(970\) | 17.8614 | 0.573495 | ||||||||
\(971\) | −20.4674 | −0.656829 | −0.328415 | − | 0.944534i | \(-0.606514\pi\) | ||||
−0.328415 | + | 0.944534i | \(0.606514\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 3.86141 | 0.123791 | ||||||||
\(974\) | −7.48913 | −0.239967 | ||||||||
\(975\) | 4.00000 | 0.128103 | ||||||||
\(976\) | 11.4891 | 0.367758 | ||||||||
\(977\) | 11.4891 | 0.367570 | 0.183785 | − | 0.982966i | \(-0.441165\pi\) | ||||
0.183785 | + | 0.982966i | \(0.441165\pi\) | |||||||
\(978\) | −7.86141 | −0.251380 | ||||||||
\(979\) | −2.74456 | −0.0877166 | ||||||||
\(980\) | −1.37228 | −0.0438359 | ||||||||
\(981\) | 16.2337 | 0.518302 | ||||||||
\(982\) | −18.5109 | −0.590706 | ||||||||
\(983\) | −23.1168 | −0.737313 | −0.368656 | − | 0.929566i | \(-0.620182\pi\) | ||||
−0.368656 | + | 0.929566i | \(0.620182\pi\) | |||||||
\(984\) | 10.7446 | 0.342524 | ||||||||
\(985\) | −13.4891 | −0.429799 | ||||||||
\(986\) | 6.37228 | 0.202935 | ||||||||
\(987\) | −25.4891 | −0.811328 | ||||||||
\(988\) | −16.0000 | −0.509028 | ||||||||
\(989\) | 16.8832 | 0.536853 | ||||||||
\(990\) | −1.00000 | −0.0317821 | ||||||||
\(991\) | 7.62772 | 0.242302 | 0.121151 | − | 0.992634i | \(-0.461341\pi\) | ||||
0.121151 | + | 0.992634i | \(0.461341\pi\) | |||||||
\(992\) | 9.11684 | 0.289460 | ||||||||
\(993\) | −27.1168 | −0.860527 | ||||||||
\(994\) | −11.2554 | −0.357001 | ||||||||
\(995\) | −14.7446 | −0.467434 | ||||||||
\(996\) | 13.4891 | 0.427419 | ||||||||
\(997\) | 6.88316 | 0.217992 | 0.108996 | − | 0.994042i | \(-0.465236\pi\) | ||||
0.108996 | + | 0.994042i | \(0.465236\pi\) | |||||||
\(998\) | −36.0000 | −1.13956 | ||||||||
\(999\) | −8.74456 | −0.276666 |
(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 | 5610.2.a.bq.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5610.2.a.bq.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial |