Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4026,2,Mod(1,4026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4026, 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("4026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4026.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: | \(32.1477718538\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.9176805.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 12x^{3} + 7x^{2} + 30x - 20 \) |
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 | 1.1 | ||
Root | \(3.32361\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4026.1 |
$q$-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 | ||||||||
\(5\) | −3.32361 | −1.48637 | −0.743183 | − | 0.669089i | \(-0.766685\pi\) | ||||
−0.743183 | + | 0.669089i | \(0.766685\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −3.91566 | −1.47998 | −0.739990 | − | 0.672618i | \(-0.765170\pi\) | ||||
−0.739990 | + | 0.672618i | \(0.765170\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.32361 | 1.05102 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −2.77487 | −0.769609 | −0.384805 | − | 0.922998i | \(-0.625731\pi\) | ||||
−0.384805 | + | 0.922998i | \(0.625731\pi\) | |||||||
\(14\) | 3.91566 | 1.04650 | ||||||||
\(15\) | −3.32361 | −0.858153 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.807136 | 0.195759 | 0.0978797 | − | 0.995198i | \(-0.468794\pi\) | ||||
0.0978797 | + | 0.995198i | \(0.468794\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −7.13386 | −1.63662 | −0.818310 | − | 0.574777i | \(-0.805089\pi\) | ||||
−0.818310 | + | 0.574777i | \(0.805089\pi\) | |||||||
\(20\) | −3.32361 | −0.743183 | ||||||||
\(21\) | −3.91566 | −0.854467 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −5.96773 | −1.24436 | −0.622179 | − | 0.782875i | \(-0.713752\pi\) | ||||
−0.622179 | + | 0.782875i | \(0.713752\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 6.04641 | 1.20928 | ||||||||
\(26\) | 2.77487 | 0.544196 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −3.91566 | −0.739990 | ||||||||
\(29\) | −8.37002 | −1.55427 | −0.777137 | − | 0.629331i | \(-0.783329\pi\) | ||||
−0.777137 | + | 0.629331i | \(0.783329\pi\) | |||||||
\(30\) | 3.32361 | 0.606806 | ||||||||
\(31\) | −0.644116 | −0.115687 | −0.0578433 | − | 0.998326i | \(-0.518422\pi\) | ||||
−0.0578433 | + | 0.998326i | \(0.518422\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −0.807136 | −0.138423 | ||||||||
\(35\) | 13.0141 | 2.19979 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −8.31795 | −1.36746 | −0.683732 | − | 0.729734i | \(-0.739644\pi\) | ||||
−0.683732 | + | 0.729734i | \(0.739644\pi\) | |||||||
\(38\) | 7.13386 | 1.15727 | ||||||||
\(39\) | −2.77487 | −0.444334 | ||||||||
\(40\) | 3.32361 | 0.525510 | ||||||||
\(41\) | 9.01414 | 1.40777 | 0.703886 | − | 0.710313i | \(-0.251447\pi\) | ||||
0.703886 | + | 0.710313i | \(0.251447\pi\) | |||||||
\(42\) | 3.91566 | 0.604199 | ||||||||
\(43\) | 10.4023 | 1.58633 | 0.793167 | − | 0.609004i | \(-0.208431\pi\) | ||||
0.793167 | + | 0.609004i | \(0.208431\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | −3.32361 | −0.495455 | ||||||||
\(46\) | 5.96773 | 0.879894 | ||||||||
\(47\) | −2.49766 | −0.364321 | −0.182161 | − | 0.983269i | \(-0.558309\pi\) | ||||
−0.182161 | + | 0.983269i | \(0.558309\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 8.33239 | 1.19034 | ||||||||
\(50\) | −6.04641 | −0.855091 | ||||||||
\(51\) | 0.807136 | 0.113022 | ||||||||
\(52\) | −2.77487 | −0.384805 | ||||||||
\(53\) | 0.130750 | 0.0179599 | 0.00897997 | − | 0.999960i | \(-0.497142\pi\) | ||||
0.00897997 | + | 0.999960i | \(0.497142\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 3.32361 | 0.448156 | ||||||||
\(56\) | 3.91566 | 0.523252 | ||||||||
\(57\) | −7.13386 | −0.944903 | ||||||||
\(58\) | 8.37002 | 1.09904 | ||||||||
\(59\) | −14.3533 | −1.86865 | −0.934323 | − | 0.356429i | \(-0.883994\pi\) | ||||
−0.934323 | + | 0.356429i | \(0.883994\pi\) | |||||||
\(60\) | −3.32361 | −0.429077 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | 0.644116 | 0.0818028 | ||||||||
\(63\) | −3.91566 | −0.493327 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 9.22258 | 1.14392 | ||||||||
\(66\) | 1.00000 | 0.123091 | ||||||||
\(67\) | 11.9931 | 1.46519 | 0.732593 | − | 0.680667i | \(-0.238310\pi\) | ||||
0.732593 | + | 0.680667i | \(0.238310\pi\) | |||||||
\(68\) | 0.807136 | 0.0978797 | ||||||||
\(69\) | −5.96773 | −0.718430 | ||||||||
\(70\) | −13.0141 | −1.55549 | ||||||||
\(71\) | −12.0031 | −1.42451 | −0.712254 | − | 0.701922i | \(-0.752325\pi\) | ||||
−0.712254 | + | 0.701922i | \(0.752325\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 9.98430 | 1.16857 | 0.584287 | − | 0.811547i | \(-0.301374\pi\) | ||||
0.584287 | + | 0.811547i | \(0.301374\pi\) | |||||||
\(74\) | 8.31795 | 0.966942 | ||||||||
\(75\) | 6.04641 | 0.698179 | ||||||||
\(76\) | −7.13386 | −0.818310 | ||||||||
\(77\) | 3.91566 | 0.446231 | ||||||||
\(78\) | 2.77487 | 0.314192 | ||||||||
\(79\) | 16.7103 | 1.88006 | 0.940029 | − | 0.341094i | \(-0.110797\pi\) | ||||
0.940029 | + | 0.341094i | \(0.110797\pi\) | |||||||
\(80\) | −3.32361 | −0.371591 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −9.01414 | −0.995445 | ||||||||
\(83\) | 3.25047 | 0.356786 | 0.178393 | − | 0.983959i | \(-0.442910\pi\) | ||||
0.178393 | + | 0.983959i | \(0.442910\pi\) | |||||||
\(84\) | −3.91566 | −0.427233 | ||||||||
\(85\) | −2.68261 | −0.290970 | ||||||||
\(86\) | −10.4023 | −1.12171 | ||||||||
\(87\) | −8.37002 | −0.897361 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −14.1282 | −1.49759 | −0.748793 | − | 0.662804i | \(-0.769366\pi\) | ||||
−0.748793 | + | 0.662804i | \(0.769366\pi\) | |||||||
\(90\) | 3.32361 | 0.350340 | ||||||||
\(91\) | 10.8654 | 1.13901 | ||||||||
\(92\) | −5.96773 | −0.622179 | ||||||||
\(93\) | −0.644116 | −0.0667917 | ||||||||
\(94\) | 2.49766 | 0.257614 | ||||||||
\(95\) | 23.7102 | 2.43262 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −12.4575 | −1.26487 | −0.632433 | − | 0.774615i | \(-0.717943\pi\) | ||||
−0.632433 | + | 0.774615i | \(0.717943\pi\) | |||||||
\(98\) | −8.33239 | −0.841698 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 6.04641 | 0.604641 | ||||||||
\(101\) | −3.04203 | −0.302693 | −0.151347 | − | 0.988481i | \(-0.548361\pi\) | ||||
−0.151347 | + | 0.988481i | \(0.548361\pi\) | |||||||
\(102\) | −0.807136 | −0.0799184 | ||||||||
\(103\) | −12.4252 | −1.22429 | −0.612146 | − | 0.790745i | \(-0.709694\pi\) | ||||
−0.612146 | + | 0.790745i | \(0.709694\pi\) | |||||||
\(104\) | 2.77487 | 0.272098 | ||||||||
\(105\) | 13.0141 | 1.27005 | ||||||||
\(106\) | −0.130750 | −0.0126996 | ||||||||
\(107\) | −0.406685 | −0.0393157 | −0.0196579 | − | 0.999807i | \(-0.506258\pi\) | ||||
−0.0196579 | + | 0.999807i | \(0.506258\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −3.50077 | −0.335313 | −0.167657 | − | 0.985845i | \(-0.553620\pi\) | ||||
−0.167657 | + | 0.985845i | \(0.553620\pi\) | |||||||
\(110\) | −3.32361 | −0.316894 | ||||||||
\(111\) | −8.31795 | −0.789505 | ||||||||
\(112\) | −3.91566 | −0.369995 | ||||||||
\(113\) | −16.9353 | −1.59314 | −0.796571 | − | 0.604545i | \(-0.793355\pi\) | ||||
−0.796571 | + | 0.604545i | \(0.793355\pi\) | |||||||
\(114\) | 7.13386 | 0.668147 | ||||||||
\(115\) | 19.8344 | 1.84957 | ||||||||
\(116\) | −8.37002 | −0.777137 | ||||||||
\(117\) | −2.77487 | −0.256536 | ||||||||
\(118\) | 14.3533 | 1.32133 | ||||||||
\(119\) | −3.16047 | −0.289720 | ||||||||
\(120\) | 3.32361 | 0.303403 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.00000 | 0.0905357 | ||||||||
\(123\) | 9.01414 | 0.812778 | ||||||||
\(124\) | −0.644116 | −0.0578433 | ||||||||
\(125\) | −3.47786 | −0.311069 | ||||||||
\(126\) | 3.91566 | 0.348835 | ||||||||
\(127\) | 0.0833558 | 0.00739663 | 0.00369831 | − | 0.999993i | \(-0.498823\pi\) | ||||
0.00369831 | + | 0.999993i | \(0.498823\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 10.4023 | 0.915871 | ||||||||
\(130\) | −9.22258 | −0.808874 | ||||||||
\(131\) | 18.1194 | 1.58310 | 0.791551 | − | 0.611103i | \(-0.209274\pi\) | ||||
0.791551 | + | 0.611103i | \(0.209274\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | 27.9338 | 2.42217 | ||||||||
\(134\) | −11.9931 | −1.03604 | ||||||||
\(135\) | −3.32361 | −0.286051 | ||||||||
\(136\) | −0.807136 | −0.0692114 | ||||||||
\(137\) | −10.0875 | −0.861829 | −0.430915 | − | 0.902393i | \(-0.641809\pi\) | ||||
−0.430915 | + | 0.902393i | \(0.641809\pi\) | |||||||
\(138\) | 5.96773 | 0.508007 | ||||||||
\(139\) | −2.57409 | −0.218331 | −0.109166 | − | 0.994024i | \(-0.534818\pi\) | ||||
−0.109166 | + | 0.994024i | \(0.534818\pi\) | |||||||
\(140\) | 13.0141 | 1.09990 | ||||||||
\(141\) | −2.49766 | −0.210341 | ||||||||
\(142\) | 12.0031 | 1.00728 | ||||||||
\(143\) | 2.77487 | 0.232046 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 27.8187 | 2.31022 | ||||||||
\(146\) | −9.98430 | −0.826306 | ||||||||
\(147\) | 8.33239 | 0.687244 | ||||||||
\(148\) | −8.31795 | −0.683732 | ||||||||
\(149\) | 19.3798 | 1.58765 | 0.793827 | − | 0.608144i | \(-0.208086\pi\) | ||||
0.793827 | + | 0.608144i | \(0.208086\pi\) | |||||||
\(150\) | −6.04641 | −0.493687 | ||||||||
\(151\) | 11.6305 | 0.946480 | 0.473240 | − | 0.880934i | \(-0.343084\pi\) | ||||
0.473240 | + | 0.880934i | \(0.343084\pi\) | |||||||
\(152\) | 7.13386 | 0.578633 | ||||||||
\(153\) | 0.807136 | 0.0652531 | ||||||||
\(154\) | −3.91566 | −0.315533 | ||||||||
\(155\) | 2.14079 | 0.171953 | ||||||||
\(156\) | −2.77487 | −0.222167 | ||||||||
\(157\) | 12.0906 | 0.964932 | 0.482466 | − | 0.875915i | \(-0.339741\pi\) | ||||
0.482466 | + | 0.875915i | \(0.339741\pi\) | |||||||
\(158\) | −16.7103 | −1.32940 | ||||||||
\(159\) | 0.130750 | 0.0103692 | ||||||||
\(160\) | 3.32361 | 0.262755 | ||||||||
\(161\) | 23.3676 | 1.84162 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 23.4030 | 1.83306 | 0.916531 | − | 0.399963i | \(-0.130977\pi\) | ||||
0.916531 | + | 0.399963i | \(0.130977\pi\) | |||||||
\(164\) | 9.01414 | 0.703886 | ||||||||
\(165\) | 3.32361 | 0.258743 | ||||||||
\(166\) | −3.25047 | −0.252286 | ||||||||
\(167\) | 9.58638 | 0.741817 | 0.370908 | − | 0.928669i | \(-0.379046\pi\) | ||||
0.370908 | + | 0.928669i | \(0.379046\pi\) | |||||||
\(168\) | 3.91566 | 0.302100 | ||||||||
\(169\) | −5.30012 | −0.407701 | ||||||||
\(170\) | 2.68261 | 0.205747 | ||||||||
\(171\) | −7.13386 | −0.545540 | ||||||||
\(172\) | 10.4023 | 0.793167 | ||||||||
\(173\) | −12.3525 | −0.939141 | −0.469571 | − | 0.882895i | \(-0.655591\pi\) | ||||
−0.469571 | + | 0.882895i | \(0.655591\pi\) | |||||||
\(174\) | 8.37002 | 0.634530 | ||||||||
\(175\) | −23.6757 | −1.78971 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | −14.3533 | −1.07886 | ||||||||
\(178\) | 14.1282 | 1.05895 | ||||||||
\(179\) | −4.78053 | −0.357313 | −0.178657 | − | 0.983911i | \(-0.557175\pi\) | ||||
−0.178657 | + | 0.983911i | \(0.557175\pi\) | |||||||
\(180\) | −3.32361 | −0.247728 | ||||||||
\(181\) | 22.0037 | 1.63552 | 0.817760 | − | 0.575559i | \(-0.195216\pi\) | ||||
0.817760 | + | 0.575559i | \(0.195216\pi\) | |||||||
\(182\) | −10.8654 | −0.805399 | ||||||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | 5.96773 | 0.439947 | ||||||||
\(185\) | 27.6457 | 2.03255 | ||||||||
\(186\) | 0.644116 | 0.0472289 | ||||||||
\(187\) | −0.807136 | −0.0590237 | ||||||||
\(188\) | −2.49766 | −0.182161 | ||||||||
\(189\) | −3.91566 | −0.284822 | ||||||||
\(190\) | −23.7102 | −1.72012 | ||||||||
\(191\) | −7.89570 | −0.571313 | −0.285656 | − | 0.958332i | \(-0.592212\pi\) | ||||
−0.285656 | + | 0.958332i | \(0.592212\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −8.24919 | −0.593790 | −0.296895 | − | 0.954910i | \(-0.595951\pi\) | ||||
−0.296895 | + | 0.954910i | \(0.595951\pi\) | |||||||
\(194\) | 12.4575 | 0.894395 | ||||||||
\(195\) | 9.22258 | 0.660443 | ||||||||
\(196\) | 8.33239 | 0.595170 | ||||||||
\(197\) | −3.26843 | −0.232866 | −0.116433 | − | 0.993199i | \(-0.537146\pi\) | ||||
−0.116433 | + | 0.993199i | \(0.537146\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | 12.1108 | 0.858510 | 0.429255 | − | 0.903183i | \(-0.358776\pi\) | ||||
0.429255 | + | 0.903183i | \(0.358776\pi\) | |||||||
\(200\) | −6.04641 | −0.427546 | ||||||||
\(201\) | 11.9931 | 0.845926 | ||||||||
\(202\) | 3.04203 | 0.214036 | ||||||||
\(203\) | 32.7742 | 2.30030 | ||||||||
\(204\) | 0.807136 | 0.0565109 | ||||||||
\(205\) | −29.9595 | −2.09246 | ||||||||
\(206\) | 12.4252 | 0.865705 | ||||||||
\(207\) | −5.96773 | −0.414786 | ||||||||
\(208\) | −2.77487 | −0.192402 | ||||||||
\(209\) | 7.13386 | 0.493460 | ||||||||
\(210\) | −13.0141 | −0.898061 | ||||||||
\(211\) | 1.11333 | 0.0766446 | 0.0383223 | − | 0.999265i | \(-0.487799\pi\) | ||||
0.0383223 | + | 0.999265i | \(0.487799\pi\) | |||||||
\(212\) | 0.130750 | 0.00897997 | ||||||||
\(213\) | −12.0031 | −0.822440 | ||||||||
\(214\) | 0.406685 | 0.0278004 | ||||||||
\(215\) | −34.5732 | −2.35787 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 2.52214 | 0.171214 | ||||||||
\(218\) | 3.50077 | 0.237102 | ||||||||
\(219\) | 9.98430 | 0.674676 | ||||||||
\(220\) | 3.32361 | 0.224078 | ||||||||
\(221\) | −2.23970 | −0.150658 | ||||||||
\(222\) | 8.31795 | 0.558264 | ||||||||
\(223\) | −23.2289 | −1.55552 | −0.777762 | − | 0.628559i | \(-0.783645\pi\) | ||||
−0.777762 | + | 0.628559i | \(0.783645\pi\) | |||||||
\(224\) | 3.91566 | 0.261626 | ||||||||
\(225\) | 6.04641 | 0.403094 | ||||||||
\(226\) | 16.9353 | 1.12652 | ||||||||
\(227\) | 11.1327 | 0.738904 | 0.369452 | − | 0.929250i | \(-0.379545\pi\) | ||||
0.369452 | + | 0.929250i | \(0.379545\pi\) | |||||||
\(228\) | −7.13386 | −0.472452 | ||||||||
\(229\) | 13.8435 | 0.914804 | 0.457402 | − | 0.889260i | \(-0.348780\pi\) | ||||
0.457402 | + | 0.889260i | \(0.348780\pi\) | |||||||
\(230\) | −19.8344 | −1.30784 | ||||||||
\(231\) | 3.91566 | 0.257631 | ||||||||
\(232\) | 8.37002 | 0.549519 | ||||||||
\(233\) | −23.9928 | −1.57182 | −0.785909 | − | 0.618342i | \(-0.787805\pi\) | ||||
−0.785909 | + | 0.618342i | \(0.787805\pi\) | |||||||
\(234\) | 2.77487 | 0.181399 | ||||||||
\(235\) | 8.30126 | 0.541515 | ||||||||
\(236\) | −14.3533 | −0.934323 | ||||||||
\(237\) | 16.7103 | 1.08545 | ||||||||
\(238\) | 3.16047 | 0.204863 | ||||||||
\(239\) | −18.2856 | −1.18279 | −0.591397 | − | 0.806380i | \(-0.701423\pi\) | ||||
−0.591397 | + | 0.806380i | \(0.701423\pi\) | |||||||
\(240\) | −3.32361 | −0.214538 | ||||||||
\(241\) | −15.7631 | −1.01539 | −0.507696 | − | 0.861536i | \(-0.669503\pi\) | ||||
−0.507696 | + | 0.861536i | \(0.669503\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −1.00000 | −0.0640184 | ||||||||
\(245\) | −27.6936 | −1.76928 | ||||||||
\(246\) | −9.01414 | −0.574721 | ||||||||
\(247\) | 19.7955 | 1.25956 | ||||||||
\(248\) | 0.644116 | 0.0409014 | ||||||||
\(249\) | 3.25047 | 0.205990 | ||||||||
\(250\) | 3.47786 | 0.219959 | ||||||||
\(251\) | 13.6086 | 0.858968 | 0.429484 | − | 0.903074i | \(-0.358695\pi\) | ||||
0.429484 | + | 0.903074i | \(0.358695\pi\) | |||||||
\(252\) | −3.91566 | −0.246663 | ||||||||
\(253\) | 5.96773 | 0.375188 | ||||||||
\(254\) | −0.0833558 | −0.00523021 | ||||||||
\(255\) | −2.68261 | −0.167992 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 22.9018 | 1.42857 | 0.714287 | − | 0.699852i | \(-0.246751\pi\) | ||||
0.714287 | + | 0.699852i | \(0.246751\pi\) | |||||||
\(258\) | −10.4023 | −0.647619 | ||||||||
\(259\) | 32.5703 | 2.02382 | ||||||||
\(260\) | 9.22258 | 0.571960 | ||||||||
\(261\) | −8.37002 | −0.518091 | ||||||||
\(262\) | −18.1194 | −1.11942 | ||||||||
\(263\) | −19.2813 | −1.18894 | −0.594468 | − | 0.804120i | \(-0.702637\pi\) | ||||
−0.594468 | + | 0.804120i | \(0.702637\pi\) | |||||||
\(264\) | 1.00000 | 0.0615457 | ||||||||
\(265\) | −0.434564 | −0.0266950 | ||||||||
\(266\) | −27.9338 | −1.71273 | ||||||||
\(267\) | −14.1282 | −0.864632 | ||||||||
\(268\) | 11.9931 | 0.732593 | ||||||||
\(269\) | 30.4439 | 1.85620 | 0.928099 | − | 0.372334i | \(-0.121443\pi\) | ||||
0.928099 | + | 0.372334i | \(0.121443\pi\) | |||||||
\(270\) | 3.32361 | 0.202269 | ||||||||
\(271\) | 14.8369 | 0.901275 | 0.450637 | − | 0.892707i | \(-0.351197\pi\) | ||||
0.450637 | + | 0.892707i | \(0.351197\pi\) | |||||||
\(272\) | 0.807136 | 0.0489398 | ||||||||
\(273\) | 10.8654 | 0.657606 | ||||||||
\(274\) | 10.0875 | 0.609405 | ||||||||
\(275\) | −6.04641 | −0.364612 | ||||||||
\(276\) | −5.96773 | −0.359215 | ||||||||
\(277\) | −20.0794 | −1.20645 | −0.603226 | − | 0.797570i | \(-0.706118\pi\) | ||||
−0.603226 | + | 0.797570i | \(0.706118\pi\) | |||||||
\(278\) | 2.57409 | 0.154383 | ||||||||
\(279\) | −0.644116 | −0.0385622 | ||||||||
\(280\) | −13.0141 | −0.777744 | ||||||||
\(281\) | 9.91566 | 0.591519 | 0.295759 | − | 0.955262i | \(-0.404427\pi\) | ||||
0.295759 | + | 0.955262i | \(0.404427\pi\) | |||||||
\(282\) | 2.49766 | 0.148734 | ||||||||
\(283\) | 22.2578 | 1.32309 | 0.661544 | − | 0.749906i | \(-0.269901\pi\) | ||||
0.661544 | + | 0.749906i | \(0.269901\pi\) | |||||||
\(284\) | −12.0031 | −0.712254 | ||||||||
\(285\) | 23.7102 | 1.40447 | ||||||||
\(286\) | −2.77487 | −0.164081 | ||||||||
\(287\) | −35.2963 | −2.08347 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −16.3485 | −0.961678 | ||||||||
\(290\) | −27.8187 | −1.63357 | ||||||||
\(291\) | −12.4575 | −0.730270 | ||||||||
\(292\) | 9.98430 | 0.584287 | ||||||||
\(293\) | 0.943253 | 0.0551054 | 0.0275527 | − | 0.999620i | \(-0.491229\pi\) | ||||
0.0275527 | + | 0.999620i | \(0.491229\pi\) | |||||||
\(294\) | −8.33239 | −0.485955 | ||||||||
\(295\) | 47.7049 | 2.77749 | ||||||||
\(296\) | 8.31795 | 0.483471 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −19.3798 | −1.12264 | ||||||||
\(299\) | 16.5597 | 0.957669 | ||||||||
\(300\) | 6.04641 | 0.349090 | ||||||||
\(301\) | −40.7318 | −2.34774 | ||||||||
\(302\) | −11.6305 | −0.669262 | ||||||||
\(303\) | −3.04203 | −0.174760 | ||||||||
\(304\) | −7.13386 | −0.409155 | ||||||||
\(305\) | 3.32361 | 0.190310 | ||||||||
\(306\) | −0.807136 | −0.0461409 | ||||||||
\(307\) | 18.0430 | 1.02977 | 0.514884 | − | 0.857260i | \(-0.327835\pi\) | ||||
0.514884 | + | 0.857260i | \(0.327835\pi\) | |||||||
\(308\) | 3.91566 | 0.223115 | ||||||||
\(309\) | −12.4252 | −0.706845 | ||||||||
\(310\) | −2.14079 | −0.121589 | ||||||||
\(311\) | 15.0514 | 0.853485 | 0.426742 | − | 0.904373i | \(-0.359661\pi\) | ||||
0.426742 | + | 0.904373i | \(0.359661\pi\) | |||||||
\(312\) | 2.77487 | 0.157096 | ||||||||
\(313\) | 13.1048 | 0.740729 | 0.370364 | − | 0.928887i | \(-0.379233\pi\) | ||||
0.370364 | + | 0.928887i | \(0.379233\pi\) | |||||||
\(314\) | −12.0906 | −0.682310 | ||||||||
\(315\) | 13.0141 | 0.733264 | ||||||||
\(316\) | 16.7103 | 0.940029 | ||||||||
\(317\) | −3.78844 | −0.212780 | −0.106390 | − | 0.994324i | \(-0.533929\pi\) | ||||
−0.106390 | + | 0.994324i | \(0.533929\pi\) | |||||||
\(318\) | −0.130750 | −0.00733211 | ||||||||
\(319\) | 8.37002 | 0.468631 | ||||||||
\(320\) | −3.32361 | −0.185796 | ||||||||
\(321\) | −0.406685 | −0.0226990 | ||||||||
\(322\) | −23.3676 | −1.30223 | ||||||||
\(323\) | −5.75800 | −0.320384 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −16.7780 | −0.930675 | ||||||||
\(326\) | −23.4030 | −1.29617 | ||||||||
\(327\) | −3.50077 | −0.193593 | ||||||||
\(328\) | −9.01414 | −0.497723 | ||||||||
\(329\) | 9.77999 | 0.539188 | ||||||||
\(330\) | −3.32361 | −0.182959 | ||||||||
\(331\) | −33.4307 | −1.83752 | −0.918760 | − | 0.394817i | \(-0.870808\pi\) | ||||
−0.918760 | + | 0.394817i | \(0.870808\pi\) | |||||||
\(332\) | 3.25047 | 0.178393 | ||||||||
\(333\) | −8.31795 | −0.455821 | ||||||||
\(334\) | −9.58638 | −0.524544 | ||||||||
\(335\) | −39.8603 | −2.17780 | ||||||||
\(336\) | −3.91566 | −0.213617 | ||||||||
\(337\) | −6.57265 | −0.358035 | −0.179017 | − | 0.983846i | \(-0.557292\pi\) | ||||
−0.179017 | + | 0.983846i | \(0.557292\pi\) | |||||||
\(338\) | 5.30012 | 0.288288 | ||||||||
\(339\) | −16.9353 | −0.919801 | ||||||||
\(340\) | −2.68261 | −0.145485 | ||||||||
\(341\) | 0.644116 | 0.0348808 | ||||||||
\(342\) | 7.13386 | 0.385755 | ||||||||
\(343\) | −5.21717 | −0.281701 | ||||||||
\(344\) | −10.4023 | −0.560854 | ||||||||
\(345\) | 19.8344 | 1.06785 | ||||||||
\(346\) | 12.3525 | 0.664073 | ||||||||
\(347\) | −13.6625 | −0.733442 | −0.366721 | − | 0.930331i | \(-0.619520\pi\) | ||||
−0.366721 | + | 0.930331i | \(0.619520\pi\) | |||||||
\(348\) | −8.37002 | −0.448680 | ||||||||
\(349\) | 15.5871 | 0.834359 | 0.417180 | − | 0.908824i | \(-0.363019\pi\) | ||||
0.417180 | + | 0.908824i | \(0.363019\pi\) | |||||||
\(350\) | 23.6757 | 1.26552 | ||||||||
\(351\) | −2.77487 | −0.148111 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −27.3100 | −1.45357 | −0.726783 | − | 0.686867i | \(-0.758986\pi\) | ||||
−0.726783 | + | 0.686867i | \(0.758986\pi\) | |||||||
\(354\) | 14.3533 | 0.762871 | ||||||||
\(355\) | 39.8937 | 2.11734 | ||||||||
\(356\) | −14.1282 | −0.748793 | ||||||||
\(357\) | −3.16047 | −0.167270 | ||||||||
\(358\) | 4.78053 | 0.252659 | ||||||||
\(359\) | 2.41656 | 0.127541 | 0.0637705 | − | 0.997965i | \(-0.479687\pi\) | ||||
0.0637705 | + | 0.997965i | \(0.479687\pi\) | |||||||
\(360\) | 3.32361 | 0.175170 | ||||||||
\(361\) | 31.8920 | 1.67853 | ||||||||
\(362\) | −22.0037 | −1.15649 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 10.8654 | 0.569503 | ||||||||
\(365\) | −33.1839 | −1.73693 | ||||||||
\(366\) | 1.00000 | 0.0522708 | ||||||||
\(367\) | −19.6890 | −1.02776 | −0.513878 | − | 0.857864i | \(-0.671791\pi\) | ||||
−0.513878 | + | 0.857864i | \(0.671791\pi\) | |||||||
\(368\) | −5.96773 | −0.311089 | ||||||||
\(369\) | 9.01414 | 0.469257 | ||||||||
\(370\) | −27.6457 | −1.43723 | ||||||||
\(371\) | −0.511974 | −0.0265804 | ||||||||
\(372\) | −0.644116 | −0.0333959 | ||||||||
\(373\) | −3.71020 | −0.192107 | −0.0960535 | − | 0.995376i | \(-0.530622\pi\) | ||||
−0.0960535 | + | 0.995376i | \(0.530622\pi\) | |||||||
\(374\) | 0.807136 | 0.0417360 | ||||||||
\(375\) | −3.47786 | −0.179596 | ||||||||
\(376\) | 2.49766 | 0.128807 | ||||||||
\(377\) | 23.2257 | 1.19618 | ||||||||
\(378\) | 3.91566 | 0.201400 | ||||||||
\(379\) | 2.53813 | 0.130375 | 0.0651875 | − | 0.997873i | \(-0.479235\pi\) | ||||
0.0651875 | + | 0.997873i | \(0.479235\pi\) | |||||||
\(380\) | 23.7102 | 1.21631 | ||||||||
\(381\) | 0.0833558 | 0.00427044 | ||||||||
\(382\) | 7.89570 | 0.403979 | ||||||||
\(383\) | −31.5793 | −1.61363 | −0.806813 | − | 0.590807i | \(-0.798809\pi\) | ||||
−0.806813 | + | 0.590807i | \(0.798809\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −13.0141 | −0.663262 | ||||||||
\(386\) | 8.24919 | 0.419873 | ||||||||
\(387\) | 10.4023 | 0.528778 | ||||||||
\(388\) | −12.4575 | −0.632433 | ||||||||
\(389\) | −4.45252 | −0.225752 | −0.112876 | − | 0.993609i | \(-0.536006\pi\) | ||||
−0.112876 | + | 0.993609i | \(0.536006\pi\) | |||||||
\(390\) | −9.22258 | −0.467004 | ||||||||
\(391\) | −4.81677 | −0.243595 | ||||||||
\(392\) | −8.33239 | −0.420849 | ||||||||
\(393\) | 18.1194 | 0.914004 | ||||||||
\(394\) | 3.26843 | 0.164661 | ||||||||
\(395\) | −55.5387 | −2.79445 | ||||||||
\(396\) | −1.00000 | −0.0502519 | ||||||||
\(397\) | −24.1293 | −1.21102 | −0.605508 | − | 0.795839i | \(-0.707030\pi\) | ||||
−0.605508 | + | 0.795839i | \(0.707030\pi\) | |||||||
\(398\) | −12.1108 | −0.607058 | ||||||||
\(399\) | 27.9338 | 1.39844 | ||||||||
\(400\) | 6.04641 | 0.302320 | ||||||||
\(401\) | 20.9175 | 1.04457 | 0.522285 | − | 0.852771i | \(-0.325080\pi\) | ||||
0.522285 | + | 0.852771i | \(0.325080\pi\) | |||||||
\(402\) | −11.9931 | −0.598160 | ||||||||
\(403\) | 1.78734 | 0.0890335 | ||||||||
\(404\) | −3.04203 | −0.151347 | ||||||||
\(405\) | −3.32361 | −0.165152 | ||||||||
\(406\) | −32.7742 | −1.62655 | ||||||||
\(407\) | 8.31795 | 0.412306 | ||||||||
\(408\) | −0.807136 | −0.0399592 | ||||||||
\(409\) | −31.6698 | −1.56597 | −0.782987 | − | 0.622039i | \(-0.786305\pi\) | ||||
−0.782987 | + | 0.622039i | \(0.786305\pi\) | |||||||
\(410\) | 29.9595 | 1.47960 | ||||||||
\(411\) | −10.0875 | −0.497577 | ||||||||
\(412\) | −12.4252 | −0.612146 | ||||||||
\(413\) | 56.2028 | 2.76556 | ||||||||
\(414\) | 5.96773 | 0.293298 | ||||||||
\(415\) | −10.8033 | −0.530314 | ||||||||
\(416\) | 2.77487 | 0.136049 | ||||||||
\(417\) | −2.57409 | −0.126054 | ||||||||
\(418\) | −7.13386 | −0.348929 | ||||||||
\(419\) | 14.9639 | 0.731035 | 0.365517 | − | 0.930804i | \(-0.380892\pi\) | ||||
0.365517 | + | 0.930804i | \(0.380892\pi\) | |||||||
\(420\) | 13.0141 | 0.635025 | ||||||||
\(421\) | 23.1925 | 1.13033 | 0.565166 | − | 0.824977i | \(-0.308812\pi\) | ||||
0.565166 | + | 0.824977i | \(0.308812\pi\) | |||||||
\(422\) | −1.11333 | −0.0541959 | ||||||||
\(423\) | −2.49766 | −0.121440 | ||||||||
\(424\) | −0.130750 | −0.00634980 | ||||||||
\(425\) | 4.88028 | 0.236728 | ||||||||
\(426\) | 12.0031 | 0.581553 | ||||||||
\(427\) | 3.91566 | 0.189492 | ||||||||
\(428\) | −0.406685 | −0.0196579 | ||||||||
\(429\) | 2.77487 | 0.133972 | ||||||||
\(430\) | 34.5732 | 1.66727 | ||||||||
\(431\) | 31.4330 | 1.51407 | 0.757037 | − | 0.653372i | \(-0.226646\pi\) | ||||
0.757037 | + | 0.653372i | \(0.226646\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −23.8895 | −1.14806 | −0.574028 | − | 0.818836i | \(-0.694620\pi\) | ||||
−0.574028 | + | 0.818836i | \(0.694620\pi\) | |||||||
\(434\) | −2.52214 | −0.121067 | ||||||||
\(435\) | 27.8187 | 1.33381 | ||||||||
\(436\) | −3.50077 | −0.167657 | ||||||||
\(437\) | 42.5730 | 2.03654 | ||||||||
\(438\) | −9.98430 | −0.477068 | ||||||||
\(439\) | −24.3409 | −1.16173 | −0.580863 | − | 0.814001i | \(-0.697285\pi\) | ||||
−0.580863 | + | 0.814001i | \(0.697285\pi\) | |||||||
\(440\) | −3.32361 | −0.158447 | ||||||||
\(441\) | 8.33239 | 0.396780 | ||||||||
\(442\) | 2.23970 | 0.106531 | ||||||||
\(443\) | −24.7483 | −1.17583 | −0.587913 | − | 0.808924i | \(-0.700050\pi\) | ||||
−0.587913 | + | 0.808924i | \(0.700050\pi\) | |||||||
\(444\) | −8.31795 | −0.394753 | ||||||||
\(445\) | 46.9567 | 2.22596 | ||||||||
\(446\) | 23.2289 | 1.09992 | ||||||||
\(447\) | 19.3798 | 0.916632 | ||||||||
\(448\) | −3.91566 | −0.184998 | ||||||||
\(449\) | 6.44772 | 0.304287 | 0.152143 | − | 0.988358i | \(-0.451382\pi\) | ||||
0.152143 | + | 0.988358i | \(0.451382\pi\) | |||||||
\(450\) | −6.04641 | −0.285030 | ||||||||
\(451\) | −9.01414 | −0.424459 | ||||||||
\(452\) | −16.9353 | −0.796571 | ||||||||
\(453\) | 11.6305 | 0.546450 | ||||||||
\(454\) | −11.1327 | −0.522484 | ||||||||
\(455\) | −36.1125 | −1.69298 | ||||||||
\(456\) | 7.13386 | 0.334074 | ||||||||
\(457\) | −8.49877 | −0.397556 | −0.198778 | − | 0.980045i | \(-0.563697\pi\) | ||||
−0.198778 | + | 0.980045i | \(0.563697\pi\) | |||||||
\(458\) | −13.8435 | −0.646864 | ||||||||
\(459\) | 0.807136 | 0.0376739 | ||||||||
\(460\) | 19.8344 | 0.924785 | ||||||||
\(461\) | 3.36904 | 0.156912 | 0.0784559 | − | 0.996918i | \(-0.475001\pi\) | ||||
0.0784559 | + | 0.996918i | \(0.475001\pi\) | |||||||
\(462\) | −3.91566 | −0.182173 | ||||||||
\(463\) | 7.77444 | 0.361309 | 0.180655 | − | 0.983547i | \(-0.442178\pi\) | ||||
0.180655 | + | 0.983547i | \(0.442178\pi\) | |||||||
\(464\) | −8.37002 | −0.388569 | ||||||||
\(465\) | 2.14079 | 0.0992769 | ||||||||
\(466\) | 23.9928 | 1.11144 | ||||||||
\(467\) | 5.06904 | 0.234567 | 0.117284 | − | 0.993098i | \(-0.462581\pi\) | ||||
0.117284 | + | 0.993098i | \(0.462581\pi\) | |||||||
\(468\) | −2.77487 | −0.128268 | ||||||||
\(469\) | −46.9608 | −2.16845 | ||||||||
\(470\) | −8.30126 | −0.382909 | ||||||||
\(471\) | 12.0906 | 0.557104 | ||||||||
\(472\) | 14.3533 | 0.660666 | ||||||||
\(473\) | −10.4023 | −0.478298 | ||||||||
\(474\) | −16.7103 | −0.767531 | ||||||||
\(475\) | −43.1343 | −1.97914 | ||||||||
\(476\) | −3.16047 | −0.144860 | ||||||||
\(477\) | 0.130750 | 0.00598665 | ||||||||
\(478\) | 18.2856 | 0.836362 | ||||||||
\(479\) | 2.62190 | 0.119798 | 0.0598988 | − | 0.998204i | \(-0.480922\pi\) | ||||
0.0598988 | + | 0.998204i | \(0.480922\pi\) | |||||||
\(480\) | 3.32361 | 0.151702 | ||||||||
\(481\) | 23.0812 | 1.05241 | ||||||||
\(482\) | 15.7631 | 0.717991 | ||||||||
\(483\) | 23.3676 | 1.06326 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 41.4038 | 1.88005 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 5.61653 | 0.254509 | 0.127255 | − | 0.991870i | \(-0.459383\pi\) | ||||
0.127255 | + | 0.991870i | \(0.459383\pi\) | |||||||
\(488\) | 1.00000 | 0.0452679 | ||||||||
\(489\) | 23.4030 | 1.05832 | ||||||||
\(490\) | 27.6936 | 1.25107 | ||||||||
\(491\) | −12.3413 | −0.556956 | −0.278478 | − | 0.960443i | \(-0.589830\pi\) | ||||
−0.278478 | + | 0.960443i | \(0.589830\pi\) | |||||||
\(492\) | 9.01414 | 0.406389 | ||||||||
\(493\) | −6.75575 | −0.304264 | ||||||||
\(494\) | −19.7955 | −0.890642 | ||||||||
\(495\) | 3.32361 | 0.149385 | ||||||||
\(496\) | −0.644116 | −0.0289217 | ||||||||
\(497\) | 47.0001 | 2.10824 | ||||||||
\(498\) | −3.25047 | −0.145657 | ||||||||
\(499\) | −22.5628 | −1.01005 | −0.505024 | − | 0.863105i | \(-0.668516\pi\) | ||||
−0.505024 | + | 0.863105i | \(0.668516\pi\) | |||||||
\(500\) | −3.47786 | −0.155535 | ||||||||
\(501\) | 9.58638 | 0.428288 | ||||||||
\(502\) | −13.6086 | −0.607382 | ||||||||
\(503\) | 4.85240 | 0.216358 | 0.108179 | − | 0.994131i | \(-0.465498\pi\) | ||||
0.108179 | + | 0.994131i | \(0.465498\pi\) | |||||||
\(504\) | 3.91566 | 0.174417 | ||||||||
\(505\) | 10.1105 | 0.449913 | ||||||||
\(506\) | −5.96773 | −0.265298 | ||||||||
\(507\) | −5.30012 | −0.235386 | ||||||||
\(508\) | 0.0833558 | 0.00369831 | ||||||||
\(509\) | 11.4961 | 0.509556 | 0.254778 | − | 0.967000i | \(-0.417998\pi\) | ||||
0.254778 | + | 0.967000i | \(0.417998\pi\) | |||||||
\(510\) | 2.68261 | 0.118788 | ||||||||
\(511\) | −39.0951 | −1.72947 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −7.13386 | −0.314968 | ||||||||
\(514\) | −22.9018 | −1.01015 | ||||||||
\(515\) | 41.2966 | 1.81975 | ||||||||
\(516\) | 10.4023 | 0.457935 | ||||||||
\(517\) | 2.49766 | 0.109847 | ||||||||
\(518\) | −32.5703 | −1.43106 | ||||||||
\(519\) | −12.3525 | −0.542214 | ||||||||
\(520\) | −9.22258 | −0.404437 | ||||||||
\(521\) | 31.6025 | 1.38453 | 0.692265 | − | 0.721644i | \(-0.256613\pi\) | ||||
0.692265 | + | 0.721644i | \(0.256613\pi\) | |||||||
\(522\) | 8.37002 | 0.366346 | ||||||||
\(523\) | −19.5926 | −0.856725 | −0.428362 | − | 0.903607i | \(-0.640909\pi\) | ||||
−0.428362 | + | 0.903607i | \(0.640909\pi\) | |||||||
\(524\) | 18.1194 | 0.791551 | ||||||||
\(525\) | −23.6757 | −1.03329 | ||||||||
\(526\) | 19.2813 | 0.840704 | ||||||||
\(527\) | −0.519889 | −0.0226467 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | 12.6138 | 0.548426 | ||||||||
\(530\) | 0.434564 | 0.0188762 | ||||||||
\(531\) | −14.3533 | −0.622882 | ||||||||
\(532\) | 27.9338 | 1.21108 | ||||||||
\(533\) | −25.0130 | −1.08343 | ||||||||
\(534\) | 14.1282 | 0.611387 | ||||||||
\(535\) | 1.35166 | 0.0584376 | ||||||||
\(536\) | −11.9931 | −0.518022 | ||||||||
\(537\) | −4.78053 | −0.206295 | ||||||||
\(538\) | −30.4439 | −1.31253 | ||||||||
\(539\) | −8.33239 | −0.358901 | ||||||||
\(540\) | −3.32361 | −0.143026 | ||||||||
\(541\) | 26.2198 | 1.12728 | 0.563638 | − | 0.826022i | \(-0.309401\pi\) | ||||
0.563638 | + | 0.826022i | \(0.309401\pi\) | |||||||
\(542\) | −14.8369 | −0.637298 | ||||||||
\(543\) | 22.0037 | 0.944268 | ||||||||
\(544\) | −0.807136 | −0.0346057 | ||||||||
\(545\) | 11.6352 | 0.498398 | ||||||||
\(546\) | −10.8654 | −0.464998 | ||||||||
\(547\) | 1.24847 | 0.0533807 | 0.0266903 | − | 0.999644i | \(-0.491503\pi\) | ||||
0.0266903 | + | 0.999644i | \(0.491503\pi\) | |||||||
\(548\) | −10.0875 | −0.430915 | ||||||||
\(549\) | −1.00000 | −0.0426790 | ||||||||
\(550\) | 6.04641 | 0.257820 | ||||||||
\(551\) | 59.7106 | 2.54376 | ||||||||
\(552\) | 5.96773 | 0.254003 | ||||||||
\(553\) | −65.4319 | −2.78245 | ||||||||
\(554\) | 20.0794 | 0.853090 | ||||||||
\(555\) | 27.6457 | 1.17349 | ||||||||
\(556\) | −2.57409 | −0.109166 | ||||||||
\(557\) | 17.4996 | 0.741483 | 0.370741 | − | 0.928736i | \(-0.379104\pi\) | ||||
0.370741 | + | 0.928736i | \(0.379104\pi\) | |||||||
\(558\) | 0.644116 | 0.0272676 | ||||||||
\(559\) | −28.8650 | −1.22086 | ||||||||
\(560\) | 13.0141 | 0.549948 | ||||||||
\(561\) | −0.807136 | −0.0340773 | ||||||||
\(562\) | −9.91566 | −0.418267 | ||||||||
\(563\) | 7.44473 | 0.313758 | 0.156879 | − | 0.987618i | \(-0.449857\pi\) | ||||
0.156879 | + | 0.987618i | \(0.449857\pi\) | |||||||
\(564\) | −2.49766 | −0.105171 | ||||||||
\(565\) | 56.2865 | 2.36799 | ||||||||
\(566\) | −22.2578 | −0.935565 | ||||||||
\(567\) | −3.91566 | −0.164442 | ||||||||
\(568\) | 12.0031 | 0.503639 | ||||||||
\(569\) | 17.4883 | 0.733148 | 0.366574 | − | 0.930389i | \(-0.380531\pi\) | ||||
0.366574 | + | 0.930389i | \(0.380531\pi\) | |||||||
\(570\) | −23.7102 | −0.993111 | ||||||||
\(571\) | 36.6687 | 1.53454 | 0.767270 | − | 0.641325i | \(-0.221615\pi\) | ||||
0.767270 | + | 0.641325i | \(0.221615\pi\) | |||||||
\(572\) | 2.77487 | 0.116023 | ||||||||
\(573\) | −7.89570 | −0.329847 | ||||||||
\(574\) | 35.2963 | 1.47324 | ||||||||
\(575\) | −36.0833 | −1.50478 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 23.6678 | 0.985301 | 0.492651 | − | 0.870227i | \(-0.336028\pi\) | ||||
0.492651 | + | 0.870227i | \(0.336028\pi\) | |||||||
\(578\) | 16.3485 | 0.680009 | ||||||||
\(579\) | −8.24919 | −0.342825 | ||||||||
\(580\) | 27.8187 | 1.15511 | ||||||||
\(581\) | −12.7277 | −0.528036 | ||||||||
\(582\) | 12.4575 | 0.516379 | ||||||||
\(583\) | −0.130750 | −0.00541513 | ||||||||
\(584\) | −9.98430 | −0.413153 | ||||||||
\(585\) | 9.22258 | 0.381307 | ||||||||
\(586\) | −0.943253 | −0.0389654 | ||||||||
\(587\) | −40.3512 | −1.66547 | −0.832736 | − | 0.553670i | \(-0.813227\pi\) | ||||
−0.832736 | + | 0.553670i | \(0.813227\pi\) | |||||||
\(588\) | 8.33239 | 0.343622 | ||||||||
\(589\) | 4.59503 | 0.189335 | ||||||||
\(590\) | −47.7049 | −1.96398 | ||||||||
\(591\) | −3.26843 | −0.134445 | ||||||||
\(592\) | −8.31795 | −0.341866 | ||||||||
\(593\) | −20.4508 | −0.839816 | −0.419908 | − | 0.907567i | \(-0.637938\pi\) | ||||
−0.419908 | + | 0.907567i | \(0.637938\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | 10.5042 | 0.430630 | ||||||||
\(596\) | 19.3798 | 0.793827 | ||||||||
\(597\) | 12.1108 | 0.495661 | ||||||||
\(598\) | −16.5597 | −0.677175 | ||||||||
\(599\) | 8.00213 | 0.326958 | 0.163479 | − | 0.986547i | \(-0.447728\pi\) | ||||
0.163479 | + | 0.986547i | \(0.447728\pi\) | |||||||
\(600\) | −6.04641 | −0.246844 | ||||||||
\(601\) | −38.6988 | −1.57856 | −0.789279 | − | 0.614035i | \(-0.789546\pi\) | ||||
−0.789279 | + | 0.614035i | \(0.789546\pi\) | |||||||
\(602\) | 40.7318 | 1.66011 | ||||||||
\(603\) | 11.9931 | 0.488396 | ||||||||
\(604\) | 11.6305 | 0.473240 | ||||||||
\(605\) | −3.32361 | −0.135124 | ||||||||
\(606\) | 3.04203 | 0.123574 | ||||||||
\(607\) | 16.4545 | 0.667867 | 0.333934 | − | 0.942597i | \(-0.391624\pi\) | ||||
0.333934 | + | 0.942597i | \(0.391624\pi\) | |||||||
\(608\) | 7.13386 | 0.289316 | ||||||||
\(609\) | 32.7742 | 1.32808 | ||||||||
\(610\) | −3.32361 | −0.134569 | ||||||||
\(611\) | 6.93068 | 0.280385 | ||||||||
\(612\) | 0.807136 | 0.0326266 | ||||||||
\(613\) | −22.9397 | −0.926527 | −0.463263 | − | 0.886221i | \(-0.653322\pi\) | ||||
−0.463263 | + | 0.886221i | \(0.653322\pi\) | |||||||
\(614\) | −18.0430 | −0.728156 | ||||||||
\(615\) | −29.9595 | −1.20808 | ||||||||
\(616\) | −3.91566 | −0.157766 | ||||||||
\(617\) | −47.6198 | −1.91710 | −0.958550 | − | 0.284924i | \(-0.908032\pi\) | ||||
−0.958550 | + | 0.284924i | \(0.908032\pi\) | |||||||
\(618\) | 12.4252 | 0.499815 | ||||||||
\(619\) | −13.7119 | −0.551127 | −0.275563 | − | 0.961283i | \(-0.588864\pi\) | ||||
−0.275563 | + | 0.961283i | \(0.588864\pi\) | |||||||
\(620\) | 2.14079 | 0.0859763 | ||||||||
\(621\) | −5.96773 | −0.239477 | ||||||||
\(622\) | −15.0514 | −0.603505 | ||||||||
\(623\) | 55.3212 | 2.21640 | ||||||||
\(624\) | −2.77487 | −0.111084 | ||||||||
\(625\) | −18.6730 | −0.746919 | ||||||||
\(626\) | −13.1048 | −0.523774 | ||||||||
\(627\) | 7.13386 | 0.284899 | ||||||||
\(628\) | 12.0906 | 0.482466 | ||||||||
\(629\) | −6.71372 | −0.267694 | ||||||||
\(630\) | −13.0141 | −0.518496 | ||||||||
\(631\) | −29.2950 | −1.16622 | −0.583108 | − | 0.812394i | \(-0.698164\pi\) | ||||
−0.583108 | + | 0.812394i | \(0.698164\pi\) | |||||||
\(632\) | −16.7103 | −0.664701 | ||||||||
\(633\) | 1.11333 | 0.0442508 | ||||||||
\(634\) | 3.78844 | 0.150458 | ||||||||
\(635\) | −0.277042 | −0.0109941 | ||||||||
\(636\) | 0.130750 | 0.00518459 | ||||||||
\(637\) | −23.1213 | −0.916098 | ||||||||
\(638\) | −8.37002 | −0.331372 | ||||||||
\(639\) | −12.0031 | −0.474836 | ||||||||
\(640\) | 3.32361 | 0.131377 | ||||||||
\(641\) | 35.9524 | 1.42004 | 0.710018 | − | 0.704184i | \(-0.248687\pi\) | ||||
0.710018 | + | 0.704184i | \(0.248687\pi\) | |||||||
\(642\) | 0.406685 | 0.0160506 | ||||||||
\(643\) | −5.34924 | −0.210954 | −0.105477 | − | 0.994422i | \(-0.533637\pi\) | ||||
−0.105477 | + | 0.994422i | \(0.533637\pi\) | |||||||
\(644\) | 23.3676 | 0.920812 | ||||||||
\(645\) | −34.5732 | −1.36132 | ||||||||
\(646\) | 5.75800 | 0.226545 | ||||||||
\(647\) | −18.3927 | −0.723091 | −0.361546 | − | 0.932354i | \(-0.617751\pi\) | ||||
−0.361546 | + | 0.932354i | \(0.617751\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 14.3533 | 0.563418 | ||||||||
\(650\) | 16.7780 | 0.658086 | ||||||||
\(651\) | 2.52214 | 0.0988504 | ||||||||
\(652\) | 23.4030 | 0.916531 | ||||||||
\(653\) | 5.98049 | 0.234035 | 0.117017 | − | 0.993130i | \(-0.462667\pi\) | ||||
0.117017 | + | 0.993130i | \(0.462667\pi\) | |||||||
\(654\) | 3.50077 | 0.136891 | ||||||||
\(655\) | −60.2220 | −2.35307 | ||||||||
\(656\) | 9.01414 | 0.351943 | ||||||||
\(657\) | 9.98430 | 0.389524 | ||||||||
\(658\) | −9.77999 | −0.381264 | ||||||||
\(659\) | −36.7362 | −1.43104 | −0.715520 | − | 0.698592i | \(-0.753810\pi\) | ||||
−0.715520 | + | 0.698592i | \(0.753810\pi\) | |||||||
\(660\) | 3.32361 | 0.129371 | ||||||||
\(661\) | 8.44202 | 0.328357 | 0.164178 | − | 0.986431i | \(-0.447503\pi\) | ||||
0.164178 | + | 0.986431i | \(0.447503\pi\) | |||||||
\(662\) | 33.4307 | 1.29932 | ||||||||
\(663\) | −2.23970 | −0.0869826 | ||||||||
\(664\) | −3.25047 | −0.126143 | ||||||||
\(665\) | −92.8411 | −3.60022 | ||||||||
\(666\) | 8.31795 | 0.322314 | ||||||||
\(667\) | 49.9500 | 1.93407 | ||||||||
\(668\) | 9.58638 | 0.370908 | ||||||||
\(669\) | −23.2289 | −0.898083 | ||||||||
\(670\) | 39.8603 | 1.53994 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | 3.91566 | 0.151050 | ||||||||
\(673\) | −20.7868 | −0.801270 | −0.400635 | − | 0.916238i | \(-0.631211\pi\) | ||||
−0.400635 | + | 0.916238i | \(0.631211\pi\) | |||||||
\(674\) | 6.57265 | 0.253169 | ||||||||
\(675\) | 6.04641 | 0.232726 | ||||||||
\(676\) | −5.30012 | −0.203851 | ||||||||
\(677\) | −23.0018 | −0.884032 | −0.442016 | − | 0.897007i | \(-0.645737\pi\) | ||||
−0.442016 | + | 0.897007i | \(0.645737\pi\) | |||||||
\(678\) | 16.9353 | 0.650398 | ||||||||
\(679\) | 48.7792 | 1.87198 | ||||||||
\(680\) | 2.68261 | 0.102873 | ||||||||
\(681\) | 11.1327 | 0.426607 | ||||||||
\(682\) | −0.644116 | −0.0246645 | ||||||||
\(683\) | −1.35728 | −0.0519349 | −0.0259675 | − | 0.999663i | \(-0.508267\pi\) | ||||
−0.0259675 | + | 0.999663i | \(0.508267\pi\) | |||||||
\(684\) | −7.13386 | −0.272770 | ||||||||
\(685\) | 33.5268 | 1.28099 | ||||||||
\(686\) | 5.21717 | 0.199193 | ||||||||
\(687\) | 13.8435 | 0.528163 | ||||||||
\(688\) | 10.4023 | 0.396584 | ||||||||
\(689\) | −0.362815 | −0.0138221 | ||||||||
\(690\) | −19.8344 | −0.755084 | ||||||||
\(691\) | 29.7747 | 1.13268 | 0.566342 | − | 0.824170i | \(-0.308358\pi\) | ||||
0.566342 | + | 0.824170i | \(0.308358\pi\) | |||||||
\(692\) | −12.3525 | −0.469571 | ||||||||
\(693\) | 3.91566 | 0.148744 | ||||||||
\(694\) | 13.6625 | 0.518622 | ||||||||
\(695\) | 8.55527 | 0.324520 | ||||||||
\(696\) | 8.37002 | 0.317265 | ||||||||
\(697\) | 7.27564 | 0.275585 | ||||||||
\(698\) | −15.5871 | −0.589981 | ||||||||
\(699\) | −23.9928 | −0.907490 | ||||||||
\(700\) | −23.6757 | −0.894857 | ||||||||
\(701\) | −36.3283 | −1.37210 | −0.686050 | − | 0.727554i | \(-0.740657\pi\) | ||||
−0.686050 | + | 0.727554i | \(0.740657\pi\) | |||||||
\(702\) | 2.77487 | 0.104731 | ||||||||
\(703\) | 59.3391 | 2.23802 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 8.30126 | 0.312644 | ||||||||
\(706\) | 27.3100 | 1.02783 | ||||||||
\(707\) | 11.9115 | 0.447980 | ||||||||
\(708\) | −14.3533 | −0.539431 | ||||||||
\(709\) | 0.0400134 | 0.00150274 | 0.000751368 | − | 1.00000i | \(-0.499761\pi\) | ||||
0.000751368 | 1.00000i | \(0.499761\pi\) | ||||||||
\(710\) | −39.8937 | −1.49718 | ||||||||
\(711\) | 16.7103 | 0.626686 | ||||||||
\(712\) | 14.1282 | 0.529477 | ||||||||
\(713\) | 3.84391 | 0.143956 | ||||||||
\(714\) | 3.16047 | 0.118278 | ||||||||
\(715\) | −9.22258 | −0.344905 | ||||||||
\(716\) | −4.78053 | −0.178657 | ||||||||
\(717\) | −18.2856 | −0.682887 | ||||||||
\(718\) | −2.41656 | −0.0901850 | ||||||||
\(719\) | 41.6522 | 1.55336 | 0.776682 | − | 0.629893i | \(-0.216901\pi\) | ||||
0.776682 | + | 0.629893i | \(0.216901\pi\) | |||||||
\(720\) | −3.32361 | −0.123864 | ||||||||
\(721\) | 48.6529 | 1.81193 | ||||||||
\(722\) | −31.8920 | −1.18690 | ||||||||
\(723\) | −15.7631 | −0.586237 | ||||||||
\(724\) | 22.0037 | 0.817760 | ||||||||
\(725\) | −50.6086 | −1.87956 | ||||||||
\(726\) | −1.00000 | −0.0371135 | ||||||||
\(727\) | −8.83076 | −0.327515 | −0.163757 | − | 0.986501i | \(-0.552361\pi\) | ||||
−0.163757 | + | 0.986501i | \(0.552361\pi\) | |||||||
\(728\) | −10.8654 | −0.402700 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 33.1839 | 1.22819 | ||||||||
\(731\) | 8.39607 | 0.310540 | ||||||||
\(732\) | −1.00000 | −0.0369611 | ||||||||
\(733\) | −5.35801 | −0.197903 | −0.0989513 | − | 0.995092i | \(-0.531549\pi\) | ||||
−0.0989513 | + | 0.995092i | \(0.531549\pi\) | |||||||
\(734\) | 19.6890 | 0.726733 | ||||||||
\(735\) | −27.6936 | −1.02150 | ||||||||
\(736\) | 5.96773 | 0.219973 | ||||||||
\(737\) | −11.9931 | −0.441770 | ||||||||
\(738\) | −9.01414 | −0.331815 | ||||||||
\(739\) | 16.4781 | 0.606158 | 0.303079 | − | 0.952965i | \(-0.401985\pi\) | ||||
0.303079 | + | 0.952965i | \(0.401985\pi\) | |||||||
\(740\) | 27.6457 | 1.01627 | ||||||||
\(741\) | 19.7955 | 0.727206 | ||||||||
\(742\) | 0.511974 | 0.0187951 | ||||||||
\(743\) | −30.8241 | −1.13083 | −0.565413 | − | 0.824808i | \(-0.691283\pi\) | ||||
−0.565413 | + | 0.824808i | \(0.691283\pi\) | |||||||
\(744\) | 0.644116 | 0.0236144 | ||||||||
\(745\) | −64.4109 | −2.35983 | ||||||||
\(746\) | 3.71020 | 0.135840 | ||||||||
\(747\) | 3.25047 | 0.118929 | ||||||||
\(748\) | −0.807136 | −0.0295118 | ||||||||
\(749\) | 1.59244 | 0.0581865 | ||||||||
\(750\) | 3.47786 | 0.126994 | ||||||||
\(751\) | −0.0567469 | −0.00207072 | −0.00103536 | − | 0.999999i | \(-0.500330\pi\) | ||||
−0.00103536 | + | 0.999999i | \(0.500330\pi\) | |||||||
\(752\) | −2.49766 | −0.0910804 | ||||||||
\(753\) | 13.6086 | 0.495925 | ||||||||
\(754\) | −23.2257 | −0.845830 | ||||||||
\(755\) | −38.6554 | −1.40681 | ||||||||
\(756\) | −3.91566 | −0.142411 | ||||||||
\(757\) | 51.8773 | 1.88551 | 0.942756 | − | 0.333484i | \(-0.108224\pi\) | ||||
0.942756 | + | 0.333484i | \(0.108224\pi\) | |||||||
\(758\) | −2.53813 | −0.0921891 | ||||||||
\(759\) | 5.96773 | 0.216615 | ||||||||
\(760\) | −23.7102 | −0.860059 | ||||||||
\(761\) | −10.5467 | −0.382319 | −0.191160 | − | 0.981559i | \(-0.561225\pi\) | ||||
−0.191160 | + | 0.981559i | \(0.561225\pi\) | |||||||
\(762\) | −0.0833558 | −0.00301966 | ||||||||
\(763\) | 13.7078 | 0.496257 | ||||||||
\(764\) | −7.89570 | −0.285656 | ||||||||
\(765\) | −2.68261 | −0.0969900 | ||||||||
\(766\) | 31.5793 | 1.14101 | ||||||||
\(767\) | 39.8286 | 1.43813 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 22.2267 | 0.801514 | 0.400757 | − | 0.916184i | \(-0.368747\pi\) | ||||
0.400757 | + | 0.916184i | \(0.368747\pi\) | |||||||
\(770\) | 13.0141 | 0.468997 | ||||||||
\(771\) | 22.9018 | 0.824788 | ||||||||
\(772\) | −8.24919 | −0.296895 | ||||||||
\(773\) | 21.0215 | 0.756090 | 0.378045 | − | 0.925787i | \(-0.376596\pi\) | ||||
0.378045 | + | 0.925787i | \(0.376596\pi\) | |||||||
\(774\) | −10.4023 | −0.373903 | ||||||||
\(775\) | −3.89459 | −0.139898 | ||||||||
\(776\) | 12.4575 | 0.447197 | ||||||||
\(777\) | 32.5703 | 1.16845 | ||||||||
\(778\) | 4.45252 | 0.159631 | ||||||||
\(779\) | −64.3056 | −2.30399 | ||||||||
\(780\) | 9.22258 | 0.330221 | ||||||||
\(781\) | 12.0031 | 0.429505 | ||||||||
\(782\) | 4.81677 | 0.172247 | ||||||||
\(783\) | −8.37002 | −0.299120 | ||||||||
\(784\) | 8.33239 | 0.297585 | ||||||||
\(785\) | −40.1844 | −1.43424 | ||||||||
\(786\) | −18.1194 | −0.646299 | ||||||||
\(787\) | −5.60095 | −0.199652 | −0.0998261 | − | 0.995005i | \(-0.531829\pi\) | ||||
−0.0998261 | + | 0.995005i | \(0.531829\pi\) | |||||||
\(788\) | −3.26843 | −0.116433 | ||||||||
\(789\) | −19.2813 | −0.686432 | ||||||||
\(790\) | 55.5387 | 1.97598 | ||||||||
\(791\) | 66.3130 | 2.35782 | ||||||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | 2.77487 | 0.0985384 | ||||||||
\(794\) | 24.1293 | 0.856317 | ||||||||
\(795\) | −0.434564 | −0.0154124 | ||||||||
\(796\) | 12.1108 | 0.429255 | ||||||||
\(797\) | −6.58795 | −0.233357 | −0.116679 | − | 0.993170i | \(-0.537225\pi\) | ||||
−0.116679 | + | 0.993170i | \(0.537225\pi\) | |||||||
\(798\) | −27.9338 | −0.988845 | ||||||||
\(799\) | −2.01595 | −0.0713193 | ||||||||
\(800\) | −6.04641 | −0.213773 | ||||||||
\(801\) | −14.1282 | −0.499195 | ||||||||
\(802\) | −20.9175 | −0.738622 | ||||||||
\(803\) | −9.98430 | −0.352338 | ||||||||
\(804\) | 11.9931 | 0.422963 | ||||||||
\(805\) | −77.6649 | −2.73733 | ||||||||
\(806\) | −1.78734 | −0.0629562 | ||||||||
\(807\) | 30.4439 | 1.07168 | ||||||||
\(808\) | 3.04203 | 0.107018 | ||||||||
\(809\) | −25.7442 | −0.905116 | −0.452558 | − | 0.891735i | \(-0.649488\pi\) | ||||
−0.452558 | + | 0.891735i | \(0.649488\pi\) | |||||||
\(810\) | 3.32361 | 0.116780 | ||||||||
\(811\) | 39.4129 | 1.38397 | 0.691987 | − | 0.721910i | \(-0.256736\pi\) | ||||
0.691987 | + | 0.721910i | \(0.256736\pi\) | |||||||
\(812\) | 32.7742 | 1.15015 | ||||||||
\(813\) | 14.8369 | 0.520351 | ||||||||
\(814\) | −8.31795 | −0.291544 | ||||||||
\(815\) | −77.7825 | −2.72460 | ||||||||
\(816\) | 0.807136 | 0.0282554 | ||||||||
\(817\) | −74.2085 | −2.59623 | ||||||||
\(818\) | 31.6698 | 1.10731 | ||||||||
\(819\) | 10.8654 | 0.379669 | ||||||||
\(820\) | −29.9595 | −1.04623 | ||||||||
\(821\) | 21.0603 | 0.735009 | 0.367505 | − | 0.930022i | \(-0.380212\pi\) | ||||
0.367505 | + | 0.930022i | \(0.380212\pi\) | |||||||
\(822\) | 10.0875 | 0.351840 | ||||||||
\(823\) | 17.3989 | 0.606487 | 0.303244 | − | 0.952913i | \(-0.401930\pi\) | ||||
0.303244 | + | 0.952913i | \(0.401930\pi\) | |||||||
\(824\) | 12.4252 | 0.432853 | ||||||||
\(825\) | −6.04641 | −0.210509 | ||||||||
\(826\) | −56.2028 | −1.95554 | ||||||||
\(827\) | −15.2596 | −0.530630 | −0.265315 | − | 0.964162i | \(-0.585476\pi\) | ||||
−0.265315 | + | 0.964162i | \(0.585476\pi\) | |||||||
\(828\) | −5.96773 | −0.207393 | ||||||||
\(829\) | −35.3149 | −1.22654 | −0.613268 | − | 0.789875i | \(-0.710145\pi\) | ||||
−0.613268 | + | 0.789875i | \(0.710145\pi\) | |||||||
\(830\) | 10.8033 | 0.374989 | ||||||||
\(831\) | −20.0794 | −0.696545 | ||||||||
\(832\) | −2.77487 | −0.0962012 | ||||||||
\(833\) | 6.72537 | 0.233020 | ||||||||
\(834\) | 2.57409 | 0.0891333 | ||||||||
\(835\) | −31.8614 | −1.10261 | ||||||||
\(836\) | 7.13386 | 0.246730 | ||||||||
\(837\) | −0.644116 | −0.0222639 | ||||||||
\(838\) | −14.9639 | −0.516920 | ||||||||
\(839\) | −55.9965 | −1.93321 | −0.966606 | − | 0.256266i | \(-0.917508\pi\) | ||||
−0.966606 | + | 0.256266i | \(0.917508\pi\) | |||||||
\(840\) | −13.0141 | −0.449030 | ||||||||
\(841\) | 41.0573 | 1.41577 | ||||||||
\(842\) | −23.1925 | −0.799265 | ||||||||
\(843\) | 9.91566 | 0.341513 | ||||||||
\(844\) | 1.11333 | 0.0383223 | ||||||||
\(845\) | 17.6155 | 0.605993 | ||||||||
\(846\) | 2.49766 | 0.0858714 | ||||||||
\(847\) | −3.91566 | −0.134544 | ||||||||
\(848\) | 0.130750 | 0.00448998 | ||||||||
\(849\) | 22.2578 | 0.763886 | ||||||||
\(850\) | −4.88028 | −0.167392 | ||||||||
\(851\) | 49.6393 | 1.70161 | ||||||||
\(852\) | −12.0031 | −0.411220 | ||||||||
\(853\) | −54.4324 | −1.86373 | −0.931865 | − | 0.362805i | \(-0.881819\pi\) | ||||
−0.931865 | + | 0.362805i | \(0.881819\pi\) | |||||||
\(854\) | −3.91566 | −0.133991 | ||||||||
\(855\) | 23.7102 | 0.810872 | ||||||||
\(856\) | 0.406685 | 0.0139002 | ||||||||
\(857\) | −18.1084 | −0.618570 | −0.309285 | − | 0.950969i | \(-0.600090\pi\) | ||||
−0.309285 | + | 0.950969i | \(0.600090\pi\) | |||||||
\(858\) | −2.77487 | −0.0947324 | ||||||||
\(859\) | 17.1123 | 0.583865 | 0.291932 | − | 0.956439i | \(-0.405702\pi\) | ||||
0.291932 | + | 0.956439i | \(0.405702\pi\) | |||||||
\(860\) | −34.5732 | −1.17894 | ||||||||
\(861\) | −35.2963 | −1.20289 | ||||||||
\(862\) | −31.4330 | −1.07061 | ||||||||
\(863\) | 22.4227 | 0.763276 | 0.381638 | − | 0.924312i | \(-0.375360\pi\) | ||||
0.381638 | + | 0.924312i | \(0.375360\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 41.0549 | 1.39591 | ||||||||
\(866\) | 23.8895 | 0.811798 | ||||||||
\(867\) | −16.3485 | −0.555225 | ||||||||
\(868\) | 2.52214 | 0.0856070 | ||||||||
\(869\) | −16.7103 | −0.566859 | ||||||||
\(870\) | −27.8187 | −0.943143 | ||||||||
\(871\) | −33.2792 | −1.12762 | ||||||||
\(872\) | 3.50077 | 0.118551 | ||||||||
\(873\) | −12.4575 | −0.421622 | ||||||||
\(874\) | −42.5730 | −1.44005 | ||||||||
\(875\) | 13.6181 | 0.460376 | ||||||||
\(876\) | 9.98430 | 0.337338 | ||||||||
\(877\) | −12.6452 | −0.426999 | −0.213499 | − | 0.976943i | \(-0.568486\pi\) | ||||
−0.213499 | + | 0.976943i | \(0.568486\pi\) | |||||||
\(878\) | 24.3409 | 0.821464 | ||||||||
\(879\) | 0.943253 | 0.0318151 | ||||||||
\(880\) | 3.32361 | 0.112039 | ||||||||
\(881\) | −19.8657 | −0.669292 | −0.334646 | − | 0.942344i | \(-0.608617\pi\) | ||||
−0.334646 | + | 0.942344i | \(0.608617\pi\) | |||||||
\(882\) | −8.33239 | −0.280566 | ||||||||
\(883\) | −37.4856 | −1.26149 | −0.630746 | − | 0.775990i | \(-0.717251\pi\) | ||||
−0.630746 | + | 0.775990i | \(0.717251\pi\) | |||||||
\(884\) | −2.23970 | −0.0753291 | ||||||||
\(885\) | 47.7049 | 1.60358 | ||||||||
\(886\) | 24.7483 | 0.831434 | ||||||||
\(887\) | 46.3574 | 1.55653 | 0.778265 | − | 0.627936i | \(-0.216100\pi\) | ||||
0.778265 | + | 0.627936i | \(0.216100\pi\) | |||||||
\(888\) | 8.31795 | 0.279132 | ||||||||
\(889\) | −0.326393 | −0.0109469 | ||||||||
\(890\) | −46.9567 | −1.57399 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −23.2289 | −0.777762 | ||||||||
\(893\) | 17.8180 | 0.596256 | ||||||||
\(894\) | −19.3798 | −0.648157 | ||||||||
\(895\) | 15.8886 | 0.531098 | ||||||||
\(896\) | 3.91566 | 0.130813 | ||||||||
\(897\) | 16.5597 | 0.552911 | ||||||||
\(898\) | −6.44772 | −0.215163 | ||||||||
\(899\) | 5.39127 | 0.179809 | ||||||||
\(900\) | 6.04641 | 0.201547 | ||||||||
\(901\) | 0.105533 | 0.00351583 | ||||||||
\(902\) | 9.01414 | 0.300138 | ||||||||
\(903\) | −40.7318 | −1.35547 | ||||||||
\(904\) | 16.9353 | 0.563261 | ||||||||
\(905\) | −73.1317 | −2.43098 | ||||||||
\(906\) | −11.6305 | −0.386399 | ||||||||
\(907\) | 32.1322 | 1.06693 | 0.533466 | − | 0.845822i | \(-0.320889\pi\) | ||||
0.533466 | + | 0.845822i | \(0.320889\pi\) | |||||||
\(908\) | 11.1327 | 0.369452 | ||||||||
\(909\) | −3.04203 | −0.100898 | ||||||||
\(910\) | 36.1125 | 1.19712 | ||||||||
\(911\) | 18.0275 | 0.597276 | 0.298638 | − | 0.954366i | \(-0.403468\pi\) | ||||
0.298638 | + | 0.954366i | \(0.403468\pi\) | |||||||
\(912\) | −7.13386 | −0.236226 | ||||||||
\(913\) | −3.25047 | −0.107575 | ||||||||
\(914\) | 8.49877 | 0.281114 | ||||||||
\(915\) | 3.32361 | 0.109875 | ||||||||
\(916\) | 13.8435 | 0.457402 | ||||||||
\(917\) | −70.9495 | −2.34296 | ||||||||
\(918\) | −0.807136 | −0.0266395 | ||||||||
\(919\) | 2.88312 | 0.0951052 | 0.0475526 | − | 0.998869i | \(-0.484858\pi\) | ||||
0.0475526 | + | 0.998869i | \(0.484858\pi\) | |||||||
\(920\) | −19.8344 | −0.653922 | ||||||||
\(921\) | 18.0430 | 0.594537 | ||||||||
\(922\) | −3.36904 | −0.110953 | ||||||||
\(923\) | 33.3070 | 1.09631 | ||||||||
\(924\) | 3.91566 | 0.128816 | ||||||||
\(925\) | −50.2937 | −1.65365 | ||||||||
\(926\) | −7.77444 | −0.255484 | ||||||||
\(927\) | −12.4252 | −0.408097 | ||||||||
\(928\) | 8.37002 | 0.274759 | ||||||||
\(929\) | −36.0073 | −1.18136 | −0.590681 | − | 0.806905i | \(-0.701141\pi\) | ||||
−0.590681 | + | 0.806905i | \(0.701141\pi\) | |||||||
\(930\) | −2.14079 | −0.0701994 | ||||||||
\(931\) | −59.4421 | −1.94814 | ||||||||
\(932\) | −23.9928 | −0.785909 | ||||||||
\(933\) | 15.0514 | 0.492760 | ||||||||
\(934\) | −5.06904 | −0.165864 | ||||||||
\(935\) | 2.68261 | 0.0877307 | ||||||||
\(936\) | 2.77487 | 0.0906993 | ||||||||
\(937\) | −47.6008 | −1.55505 | −0.777525 | − | 0.628851i | \(-0.783525\pi\) | ||||
−0.777525 | + | 0.628851i | \(0.783525\pi\) | |||||||
\(938\) | 46.9608 | 1.53332 | ||||||||
\(939\) | 13.1048 | 0.427660 | ||||||||
\(940\) | 8.30126 | 0.270757 | ||||||||
\(941\) | 19.2111 | 0.626264 | 0.313132 | − | 0.949710i | \(-0.398622\pi\) | ||||
0.313132 | + | 0.949710i | \(0.398622\pi\) | |||||||
\(942\) | −12.0906 | −0.393932 | ||||||||
\(943\) | −53.7939 | −1.75177 | ||||||||
\(944\) | −14.3533 | −0.467161 | ||||||||
\(945\) | 13.0141 | 0.423350 | ||||||||
\(946\) | 10.4023 | 0.338208 | ||||||||
\(947\) | −25.5746 | −0.831063 | −0.415531 | − | 0.909579i | \(-0.636404\pi\) | ||||
−0.415531 | + | 0.909579i | \(0.636404\pi\) | |||||||
\(948\) | 16.7103 | 0.542726 | ||||||||
\(949\) | −27.7051 | −0.899345 | ||||||||
\(950\) | 43.1343 | 1.39946 | ||||||||
\(951\) | −3.78844 | −0.122849 | ||||||||
\(952\) | 3.16047 | 0.102431 | ||||||||
\(953\) | −24.8695 | −0.805603 | −0.402801 | − | 0.915287i | \(-0.631963\pi\) | ||||
−0.402801 | + | 0.915287i | \(0.631963\pi\) | |||||||
\(954\) | −0.130750 | −0.00423320 | ||||||||
\(955\) | 26.2422 | 0.849179 | ||||||||
\(956\) | −18.2856 | −0.591397 | ||||||||
\(957\) | 8.37002 | 0.270564 | ||||||||
\(958\) | −2.62190 | −0.0847097 | ||||||||
\(959\) | 39.4990 | 1.27549 | ||||||||
\(960\) | −3.32361 | −0.107269 | ||||||||
\(961\) | −30.5851 | −0.986617 | ||||||||
\(962\) | −23.0812 | −0.744168 | ||||||||
\(963\) | −0.406685 | −0.0131052 | ||||||||
\(964\) | −15.7631 | −0.507696 | ||||||||
\(965\) | 27.4171 | 0.882589 | ||||||||
\(966\) | −23.3676 | −0.751840 | ||||||||
\(967\) | 13.5029 | 0.434223 | 0.217111 | − | 0.976147i | \(-0.430336\pi\) | ||||
0.217111 | + | 0.976147i | \(0.430336\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −5.75800 | −0.184974 | ||||||||
\(970\) | −41.4038 | −1.32940 | ||||||||
\(971\) | 44.2459 | 1.41992 | 0.709959 | − | 0.704243i | \(-0.248713\pi\) | ||||
0.709959 | + | 0.704243i | \(0.248713\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 10.0792 | 0.323126 | ||||||||
\(974\) | −5.61653 | −0.179965 | ||||||||
\(975\) | −16.7780 | −0.537325 | ||||||||
\(976\) | −1.00000 | −0.0320092 | ||||||||
\(977\) | 20.0638 | 0.641898 | 0.320949 | − | 0.947096i | \(-0.395998\pi\) | ||||
0.320949 | + | 0.947096i | \(0.395998\pi\) | |||||||
\(978\) | −23.4030 | −0.748345 | ||||||||
\(979\) | 14.1282 | 0.451539 | ||||||||
\(980\) | −27.6936 | −0.884641 | ||||||||
\(981\) | −3.50077 | −0.111771 | ||||||||
\(982\) | 12.3413 | 0.393828 | ||||||||
\(983\) | −4.55400 | −0.145250 | −0.0726251 | − | 0.997359i | \(-0.523138\pi\) | ||||
−0.0726251 | + | 0.997359i | \(0.523138\pi\) | |||||||
\(984\) | −9.01414 | −0.287360 | ||||||||
\(985\) | 10.8630 | 0.346124 | ||||||||
\(986\) | 6.75575 | 0.215147 | ||||||||
\(987\) | 9.77999 | 0.311301 | ||||||||
\(988\) | 19.7955 | 0.629779 | ||||||||
\(989\) | −62.0781 | −1.97397 | ||||||||
\(990\) | −3.32361 | −0.105631 | ||||||||
\(991\) | −24.7967 | −0.787692 | −0.393846 | − | 0.919176i | \(-0.628856\pi\) | ||||
−0.393846 | + | 0.919176i | \(0.628856\pi\) | |||||||
\(992\) | 0.644116 | 0.0204507 | ||||||||
\(993\) | −33.4307 | −1.06089 | ||||||||
\(994\) | −47.0001 | −1.49075 | ||||||||
\(995\) | −40.2515 | −1.27606 | ||||||||
\(996\) | 3.25047 | 0.102995 | ||||||||
\(997\) | −27.5577 | −0.872761 | −0.436381 | − | 0.899762i | \(-0.643740\pi\) | ||||
−0.436381 | + | 0.899762i | \(0.643740\pi\) | |||||||
\(998\) | 22.5628 | 0.714212 | ||||||||
\(999\) | −8.31795 | −0.263168 |
(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 | 4026.2.a.u.1.1 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4026.2.a.u.1.1 | ✓ | 5 | 1.1 | even | 1 | trivial |