Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3174,2,Mod(1,3174)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3174, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3174.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3174 = 2 \cdot 3 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3174.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: | \(25.3445176016\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\Q(\zeta_{22})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 138) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.830830\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3174.1 |
$q$-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 | ||||||||
\(5\) | 0.324635 | 0.145181 | 0.0725905 | − | 0.997362i | \(-0.476873\pi\) | ||||
0.0725905 | + | 0.997362i | \(0.476873\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −2.43232 | −0.919332 | −0.459666 | − | 0.888092i | \(-0.652031\pi\) | ||||
−0.459666 | + | 0.888092i | \(0.652031\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.324635 | 0.102659 | ||||||||
\(11\) | 3.40009 | 1.02517 | 0.512583 | − | 0.858638i | \(-0.328689\pi\) | ||||
0.512583 | + | 0.858638i | \(0.328689\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0.269342 | 0.0747021 | 0.0373510 | − | 0.999302i | \(-0.488108\pi\) | ||||
0.0373510 | + | 0.999302i | \(0.488108\pi\) | |||||||
\(14\) | −2.43232 | −0.650066 | ||||||||
\(15\) | −0.324635 | −0.0838203 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.84815 | 1.17585 | 0.587925 | − | 0.808916i | \(-0.299945\pi\) | ||||
0.587925 | + | 0.808916i | \(0.299945\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 4.02509 | 0.923419 | 0.461710 | − | 0.887031i | \(-0.347236\pi\) | ||||
0.461710 | + | 0.887031i | \(0.347236\pi\) | |||||||
\(20\) | 0.324635 | 0.0725905 | ||||||||
\(21\) | 2.43232 | 0.530776 | ||||||||
\(22\) | 3.40009 | 0.724901 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −4.89461 | −0.978922 | ||||||||
\(26\) | 0.269342 | 0.0528223 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.43232 | −0.459666 | ||||||||
\(29\) | 2.00935 | 0.373128 | 0.186564 | − | 0.982443i | \(-0.440265\pi\) | ||||
0.186564 | + | 0.982443i | \(0.440265\pi\) | |||||||
\(30\) | −0.324635 | −0.0592699 | ||||||||
\(31\) | −9.50557 | −1.70725 | −0.853625 | − | 0.520888i | \(-0.825601\pi\) | ||||
−0.853625 | + | 0.520888i | \(0.825601\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −3.40009 | −0.591880 | ||||||||
\(34\) | 4.84815 | 0.831451 | ||||||||
\(35\) | −0.789617 | −0.133470 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −2.01732 | −0.331645 | −0.165823 | − | 0.986156i | \(-0.553028\pi\) | ||||
−0.165823 | + | 0.986156i | \(0.553028\pi\) | |||||||
\(38\) | 4.02509 | 0.652956 | ||||||||
\(39\) | −0.269342 | −0.0431293 | ||||||||
\(40\) | 0.324635 | 0.0513293 | ||||||||
\(41\) | −2.60502 | −0.406836 | −0.203418 | − | 0.979092i | \(-0.565205\pi\) | ||||
−0.203418 | + | 0.979092i | \(0.565205\pi\) | |||||||
\(42\) | 2.43232 | 0.375316 | ||||||||
\(43\) | 3.93559 | 0.600172 | 0.300086 | − | 0.953912i | \(-0.402985\pi\) | ||||
0.300086 | + | 0.953912i | \(0.402985\pi\) | |||||||
\(44\) | 3.40009 | 0.512583 | ||||||||
\(45\) | 0.324635 | 0.0483937 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.19874 | 0.758314 | 0.379157 | − | 0.925332i | \(-0.376214\pi\) | ||||
0.379157 | + | 0.925332i | \(0.376214\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −1.08380 | −0.154829 | ||||||||
\(50\) | −4.89461 | −0.692203 | ||||||||
\(51\) | −4.84815 | −0.678877 | ||||||||
\(52\) | 0.269342 | 0.0373510 | ||||||||
\(53\) | −1.08001 | −0.148351 | −0.0741754 | − | 0.997245i | \(-0.523632\pi\) | ||||
−0.0741754 | + | 0.997245i | \(0.523632\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 1.10379 | 0.148835 | ||||||||
\(56\) | −2.43232 | −0.325033 | ||||||||
\(57\) | −4.02509 | −0.533136 | ||||||||
\(58\) | 2.00935 | 0.263841 | ||||||||
\(59\) | 9.90548 | 1.28958 | 0.644792 | − | 0.764358i | \(-0.276944\pi\) | ||||
0.644792 | + | 0.764358i | \(0.276944\pi\) | |||||||
\(60\) | −0.324635 | −0.0419102 | ||||||||
\(61\) | 4.35062 | 0.557040 | 0.278520 | − | 0.960430i | \(-0.410156\pi\) | ||||
0.278520 | + | 0.960430i | \(0.410156\pi\) | |||||||
\(62\) | −9.50557 | −1.20721 | ||||||||
\(63\) | −2.43232 | −0.306444 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.0874378 | 0.0108453 | ||||||||
\(66\) | −3.40009 | −0.418522 | ||||||||
\(67\) | 10.2730 | 1.25504 | 0.627521 | − | 0.778600i | \(-0.284070\pi\) | ||||
0.627521 | + | 0.778600i | \(0.284070\pi\) | |||||||
\(68\) | 4.84815 | 0.587925 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.789617 | −0.0943772 | ||||||||
\(71\) | 11.4304 | 1.35654 | 0.678268 | − | 0.734814i | \(-0.262731\pi\) | ||||
0.678268 | + | 0.734814i | \(0.262731\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −1.13935 | −0.133351 | −0.0666756 | − | 0.997775i | \(-0.521239\pi\) | ||||
−0.0666756 | + | 0.997775i | \(0.521239\pi\) | |||||||
\(74\) | −2.01732 | −0.234509 | ||||||||
\(75\) | 4.89461 | 0.565181 | ||||||||
\(76\) | 4.02509 | 0.461710 | ||||||||
\(77\) | −8.27012 | −0.942467 | ||||||||
\(78\) | −0.269342 | −0.0304970 | ||||||||
\(79\) | 16.0547 | 1.80629 | 0.903145 | − | 0.429335i | \(-0.141252\pi\) | ||||
0.903145 | + | 0.429335i | \(0.141252\pi\) | |||||||
\(80\) | 0.324635 | 0.0362953 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.60502 | −0.287676 | ||||||||
\(83\) | −1.05529 | −0.115833 | −0.0579167 | − | 0.998321i | \(-0.518446\pi\) | ||||
−0.0579167 | + | 0.998321i | \(0.518446\pi\) | |||||||
\(84\) | 2.43232 | 0.265388 | ||||||||
\(85\) | 1.57388 | 0.170711 | ||||||||
\(86\) | 3.93559 | 0.424385 | ||||||||
\(87\) | −2.00935 | −0.215425 | ||||||||
\(88\) | 3.40009 | 0.362451 | ||||||||
\(89\) | −2.74085 | −0.290529 | −0.145265 | − | 0.989393i | \(-0.546403\pi\) | ||||
−0.145265 | + | 0.989393i | \(0.546403\pi\) | |||||||
\(90\) | 0.324635 | 0.0342195 | ||||||||
\(91\) | −0.655127 | −0.0686760 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.50557 | 0.985681 | ||||||||
\(94\) | 5.19874 | 0.536209 | ||||||||
\(95\) | 1.30668 | 0.134063 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −13.6079 | −1.38167 | −0.690836 | − | 0.723011i | \(-0.742758\pi\) | ||||
−0.690836 | + | 0.723011i | \(0.742758\pi\) | |||||||
\(98\) | −1.08380 | −0.109481 | ||||||||
\(99\) | 3.40009 | 0.341722 | ||||||||
\(100\) | −4.89461 | −0.489461 | ||||||||
\(101\) | 15.9029 | 1.58240 | 0.791198 | − | 0.611560i | \(-0.209458\pi\) | ||||
0.791198 | + | 0.611560i | \(0.209458\pi\) | |||||||
\(102\) | −4.84815 | −0.480038 | ||||||||
\(103\) | 13.9721 | 1.37672 | 0.688358 | − | 0.725371i | \(-0.258332\pi\) | ||||
0.688358 | + | 0.725371i | \(0.258332\pi\) | |||||||
\(104\) | 0.269342 | 0.0264112 | ||||||||
\(105\) | 0.789617 | 0.0770587 | ||||||||
\(106\) | −1.08001 | −0.104900 | ||||||||
\(107\) | 10.7919 | 1.04329 | 0.521644 | − | 0.853163i | \(-0.325319\pi\) | ||||
0.521644 | + | 0.853163i | \(0.325319\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 16.3580 | 1.56681 | 0.783404 | − | 0.621513i | \(-0.213482\pi\) | ||||
0.783404 | + | 0.621513i | \(0.213482\pi\) | |||||||
\(110\) | 1.10379 | 0.105242 | ||||||||
\(111\) | 2.01732 | 0.191476 | ||||||||
\(112\) | −2.43232 | −0.229833 | ||||||||
\(113\) | 19.9598 | 1.87766 | 0.938830 | − | 0.344382i | \(-0.111911\pi\) | ||||
0.938830 | + | 0.344382i | \(0.111911\pi\) | |||||||
\(114\) | −4.02509 | −0.376984 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.00935 | 0.186564 | ||||||||
\(117\) | 0.269342 | 0.0249007 | ||||||||
\(118\) | 9.90548 | 0.911873 | ||||||||
\(119\) | −11.7923 | −1.08100 | ||||||||
\(120\) | −0.324635 | −0.0296350 | ||||||||
\(121\) | 0.560608 | 0.0509643 | ||||||||
\(122\) | 4.35062 | 0.393887 | ||||||||
\(123\) | 2.60502 | 0.234887 | ||||||||
\(124\) | −9.50557 | −0.853625 | ||||||||
\(125\) | −3.21214 | −0.287302 | ||||||||
\(126\) | −2.43232 | −0.216689 | ||||||||
\(127\) | −5.44618 | −0.483270 | −0.241635 | − | 0.970367i | \(-0.577684\pi\) | ||||
−0.241635 | + | 0.970367i | \(0.577684\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −3.93559 | −0.346509 | ||||||||
\(130\) | 0.0874378 | 0.00766881 | ||||||||
\(131\) | 15.3071 | 1.33739 | 0.668694 | − | 0.743537i | \(-0.266853\pi\) | ||||
0.668694 | + | 0.743537i | \(0.266853\pi\) | |||||||
\(132\) | −3.40009 | −0.295940 | ||||||||
\(133\) | −9.79032 | −0.848929 | ||||||||
\(134\) | 10.2730 | 0.887448 | ||||||||
\(135\) | −0.324635 | −0.0279401 | ||||||||
\(136\) | 4.84815 | 0.415725 | ||||||||
\(137\) | −17.0753 | −1.45884 | −0.729419 | − | 0.684067i | \(-0.760209\pi\) | ||||
−0.729419 | + | 0.684067i | \(0.760209\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.2779 | 1.38067 | 0.690337 | − | 0.723488i | \(-0.257462\pi\) | ||||
0.690337 | + | 0.723488i | \(0.257462\pi\) | |||||||
\(140\) | −0.789617 | −0.0667348 | ||||||||
\(141\) | −5.19874 | −0.437813 | ||||||||
\(142\) | 11.4304 | 0.959216 | ||||||||
\(143\) | 0.915787 | 0.0765820 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0.652306 | 0.0541711 | ||||||||
\(146\) | −1.13935 | −0.0942935 | ||||||||
\(147\) | 1.08380 | 0.0893907 | ||||||||
\(148\) | −2.01732 | −0.165823 | ||||||||
\(149\) | −1.63045 | −0.133571 | −0.0667857 | − | 0.997767i | \(-0.521274\pi\) | ||||
−0.0667857 | + | 0.997767i | \(0.521274\pi\) | |||||||
\(150\) | 4.89461 | 0.399643 | ||||||||
\(151\) | −11.7663 | −0.957530 | −0.478765 | − | 0.877943i | \(-0.658915\pi\) | ||||
−0.478765 | + | 0.877943i | \(0.658915\pi\) | |||||||
\(152\) | 4.02509 | 0.326478 | ||||||||
\(153\) | 4.84815 | 0.391950 | ||||||||
\(154\) | −8.27012 | −0.666425 | ||||||||
\(155\) | −3.08584 | −0.247860 | ||||||||
\(156\) | −0.269342 | −0.0215646 | ||||||||
\(157\) | 10.0065 | 0.798607 | 0.399303 | − | 0.916819i | \(-0.369252\pi\) | ||||
0.399303 | + | 0.916819i | \(0.369252\pi\) | |||||||
\(158\) | 16.0547 | 1.27724 | ||||||||
\(159\) | 1.08001 | 0.0856504 | ||||||||
\(160\) | 0.324635 | 0.0256646 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −15.9393 | −1.24846 | −0.624230 | − | 0.781241i | \(-0.714587\pi\) | ||||
−0.624230 | + | 0.781241i | \(0.714587\pi\) | |||||||
\(164\) | −2.60502 | −0.203418 | ||||||||
\(165\) | −1.10379 | −0.0859297 | ||||||||
\(166\) | −1.05529 | −0.0819066 | ||||||||
\(167\) | −9.53697 | −0.737993 | −0.368997 | − | 0.929431i | \(-0.620299\pi\) | ||||
−0.368997 | + | 0.929431i | \(0.620299\pi\) | |||||||
\(168\) | 2.43232 | 0.187658 | ||||||||
\(169\) | −12.9275 | −0.994420 | ||||||||
\(170\) | 1.57388 | 0.120711 | ||||||||
\(171\) | 4.02509 | 0.307806 | ||||||||
\(172\) | 3.93559 | 0.300086 | ||||||||
\(173\) | −24.7305 | −1.88022 | −0.940112 | − | 0.340865i | \(-0.889280\pi\) | ||||
−0.940112 | + | 0.340865i | \(0.889280\pi\) | |||||||
\(174\) | −2.00935 | −0.152329 | ||||||||
\(175\) | 11.9053 | 0.899954 | ||||||||
\(176\) | 3.40009 | 0.256291 | ||||||||
\(177\) | −9.90548 | −0.744541 | ||||||||
\(178\) | −2.74085 | −0.205435 | ||||||||
\(179\) | −26.3484 | −1.96937 | −0.984684 | − | 0.174348i | \(-0.944218\pi\) | ||||
−0.984684 | + | 0.174348i | \(0.944218\pi\) | |||||||
\(180\) | 0.324635 | 0.0241968 | ||||||||
\(181\) | −18.1768 | −1.35107 | −0.675535 | − | 0.737328i | \(-0.736087\pi\) | ||||
−0.675535 | + | 0.737328i | \(0.736087\pi\) | |||||||
\(182\) | −0.655127 | −0.0485613 | ||||||||
\(183\) | −4.35062 | −0.321607 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.654892 | −0.0481486 | ||||||||
\(186\) | 9.50557 | 0.696982 | ||||||||
\(187\) | 16.4841 | 1.20544 | ||||||||
\(188\) | 5.19874 | 0.379157 | ||||||||
\(189\) | 2.43232 | 0.176925 | ||||||||
\(190\) | 1.30668 | 0.0947969 | ||||||||
\(191\) | 7.85270 | 0.568201 | 0.284101 | − | 0.958794i | \(-0.408305\pi\) | ||||
0.284101 | + | 0.958794i | \(0.408305\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 23.5784 | 1.69721 | 0.848604 | − | 0.529028i | \(-0.177443\pi\) | ||||
0.848604 | + | 0.529028i | \(0.177443\pi\) | |||||||
\(194\) | −13.6079 | −0.976990 | ||||||||
\(195\) | −0.0874378 | −0.00626155 | ||||||||
\(196\) | −1.08380 | −0.0774146 | ||||||||
\(197\) | 9.26049 | 0.659783 | 0.329891 | − | 0.944019i | \(-0.392988\pi\) | ||||
0.329891 | + | 0.944019i | \(0.392988\pi\) | |||||||
\(198\) | 3.40009 | 0.241634 | ||||||||
\(199\) | −25.7180 | −1.82310 | −0.911552 | − | 0.411185i | \(-0.865115\pi\) | ||||
−0.911552 | + | 0.411185i | \(0.865115\pi\) | |||||||
\(200\) | −4.89461 | −0.346101 | ||||||||
\(201\) | −10.2730 | −0.724599 | ||||||||
\(202\) | 15.9029 | 1.11892 | ||||||||
\(203\) | −4.88740 | −0.343028 | ||||||||
\(204\) | −4.84815 | −0.339438 | ||||||||
\(205\) | −0.845680 | −0.0590649 | ||||||||
\(206\) | 13.9721 | 0.973485 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.269342 | 0.0186755 | ||||||||
\(209\) | 13.6857 | 0.946658 | ||||||||
\(210\) | 0.789617 | 0.0544887 | ||||||||
\(211\) | 19.6782 | 1.35470 | 0.677350 | − | 0.735660i | \(-0.263128\pi\) | ||||
0.677350 | + | 0.735660i | \(0.263128\pi\) | |||||||
\(212\) | −1.08001 | −0.0741754 | ||||||||
\(213\) | −11.4304 | −0.783197 | ||||||||
\(214\) | 10.7919 | 0.737716 | ||||||||
\(215\) | 1.27763 | 0.0871336 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 23.1206 | 1.56953 | ||||||||
\(218\) | 16.3580 | 1.10790 | ||||||||
\(219\) | 1.13935 | 0.0769903 | ||||||||
\(220\) | 1.10379 | 0.0744173 | ||||||||
\(221\) | 1.30581 | 0.0878384 | ||||||||
\(222\) | 2.01732 | 0.135394 | ||||||||
\(223\) | −4.79039 | −0.320788 | −0.160394 | − | 0.987053i | \(-0.551277\pi\) | ||||
−0.160394 | + | 0.987053i | \(0.551277\pi\) | |||||||
\(224\) | −2.43232 | −0.162516 | ||||||||
\(225\) | −4.89461 | −0.326307 | ||||||||
\(226\) | 19.9598 | 1.32771 | ||||||||
\(227\) | 6.03416 | 0.400501 | 0.200251 | − | 0.979745i | \(-0.435824\pi\) | ||||
0.200251 | + | 0.979745i | \(0.435824\pi\) | |||||||
\(228\) | −4.02509 | −0.266568 | ||||||||
\(229\) | 7.27420 | 0.480692 | 0.240346 | − | 0.970687i | \(-0.422739\pi\) | ||||
0.240346 | + | 0.970687i | \(0.422739\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.27012 | 0.544134 | ||||||||
\(232\) | 2.00935 | 0.131921 | ||||||||
\(233\) | 8.41855 | 0.551517 | 0.275759 | − | 0.961227i | \(-0.411071\pi\) | ||||
0.275759 | + | 0.961227i | \(0.411071\pi\) | |||||||
\(234\) | 0.269342 | 0.0176074 | ||||||||
\(235\) | 1.68769 | 0.110093 | ||||||||
\(236\) | 9.90548 | 0.644792 | ||||||||
\(237\) | −16.0547 | −1.04286 | ||||||||
\(238\) | −11.7923 | −0.764379 | ||||||||
\(239\) | −5.16012 | −0.333781 | −0.166890 | − | 0.985975i | \(-0.553373\pi\) | ||||
−0.166890 | + | 0.985975i | \(0.553373\pi\) | |||||||
\(240\) | −0.324635 | −0.0209551 | ||||||||
\(241\) | 15.6301 | 1.00682 | 0.503411 | − | 0.864047i | \(-0.332078\pi\) | ||||
0.503411 | + | 0.864047i | \(0.332078\pi\) | |||||||
\(242\) | 0.560608 | 0.0360372 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 4.35062 | 0.278520 | ||||||||
\(245\) | −0.351841 | −0.0224783 | ||||||||
\(246\) | 2.60502 | 0.166090 | ||||||||
\(247\) | 1.08413 | 0.0689813 | ||||||||
\(248\) | −9.50557 | −0.603604 | ||||||||
\(249\) | 1.05529 | 0.0668765 | ||||||||
\(250\) | −3.21214 | −0.203153 | ||||||||
\(251\) | −13.8839 | −0.876345 | −0.438172 | − | 0.898891i | \(-0.644374\pi\) | ||||
−0.438172 | + | 0.898891i | \(0.644374\pi\) | |||||||
\(252\) | −2.43232 | −0.153222 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −5.44618 | −0.341724 | ||||||||
\(255\) | −1.57388 | −0.0985601 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.84808 | −0.614307 | −0.307153 | − | 0.951660i | \(-0.599376\pi\) | ||||
−0.307153 | + | 0.951660i | \(0.599376\pi\) | |||||||
\(258\) | −3.93559 | −0.245019 | ||||||||
\(259\) | 4.90677 | 0.304892 | ||||||||
\(260\) | 0.0874378 | 0.00542266 | ||||||||
\(261\) | 2.00935 | 0.124376 | ||||||||
\(262\) | 15.3071 | 0.945677 | ||||||||
\(263\) | 0.229051 | 0.0141239 | 0.00706195 | − | 0.999975i | \(-0.497752\pi\) | ||||
0.00706195 | + | 0.999975i | \(0.497752\pi\) | |||||||
\(264\) | −3.40009 | −0.209261 | ||||||||
\(265\) | −0.350609 | −0.0215377 | ||||||||
\(266\) | −9.79032 | −0.600283 | ||||||||
\(267\) | 2.74085 | 0.167737 | ||||||||
\(268\) | 10.2730 | 0.627521 | ||||||||
\(269\) | −0.432758 | −0.0263857 | −0.0131928 | − | 0.999913i | \(-0.504200\pi\) | ||||
−0.0131928 | + | 0.999913i | \(0.504200\pi\) | |||||||
\(270\) | −0.324635 | −0.0197566 | ||||||||
\(271\) | −7.28255 | −0.442383 | −0.221192 | − | 0.975230i | \(-0.570995\pi\) | ||||
−0.221192 | + | 0.975230i | \(0.570995\pi\) | |||||||
\(272\) | 4.84815 | 0.293962 | ||||||||
\(273\) | 0.655127 | 0.0396501 | ||||||||
\(274\) | −17.0753 | −1.03155 | ||||||||
\(275\) | −16.6421 | −1.00356 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.9693 | −1.50026 | −0.750130 | − | 0.661291i | \(-0.770009\pi\) | ||||
−0.750130 | + | 0.661291i | \(0.770009\pi\) | |||||||
\(278\) | 16.2779 | 0.976285 | ||||||||
\(279\) | −9.50557 | −0.569083 | ||||||||
\(280\) | −0.789617 | −0.0471886 | ||||||||
\(281\) | −7.32093 | −0.436730 | −0.218365 | − | 0.975867i | \(-0.570072\pi\) | ||||
−0.218365 | + | 0.975867i | \(0.570072\pi\) | |||||||
\(282\) | −5.19874 | −0.309581 | ||||||||
\(283\) | 10.4946 | 0.623837 | 0.311918 | − | 0.950109i | \(-0.399028\pi\) | ||||
0.311918 | + | 0.950109i | \(0.399028\pi\) | |||||||
\(284\) | 11.4304 | 0.678268 | ||||||||
\(285\) | −1.30668 | −0.0774013 | ||||||||
\(286\) | 0.915787 | 0.0541516 | ||||||||
\(287\) | 6.33625 | 0.374017 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 6.50456 | 0.382621 | ||||||||
\(290\) | 0.652306 | 0.0383047 | ||||||||
\(291\) | 13.6079 | 0.797709 | ||||||||
\(292\) | −1.13935 | −0.0666756 | ||||||||
\(293\) | −16.1874 | −0.945677 | −0.472839 | − | 0.881149i | \(-0.656771\pi\) | ||||
−0.472839 | + | 0.881149i | \(0.656771\pi\) | |||||||
\(294\) | 1.08380 | 0.0632088 | ||||||||
\(295\) | 3.21566 | 0.187223 | ||||||||
\(296\) | −2.01732 | −0.117254 | ||||||||
\(297\) | −3.40009 | −0.197293 | ||||||||
\(298\) | −1.63045 | −0.0944492 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 4.89461 | 0.282591 | ||||||||
\(301\) | −9.57262 | −0.551757 | ||||||||
\(302\) | −11.7663 | −0.677076 | ||||||||
\(303\) | −15.9029 | −0.913597 | ||||||||
\(304\) | 4.02509 | 0.230855 | ||||||||
\(305\) | 1.41236 | 0.0808717 | ||||||||
\(306\) | 4.84815 | 0.277150 | ||||||||
\(307\) | 17.8501 | 1.01876 | 0.509380 | − | 0.860541i | \(-0.329875\pi\) | ||||
0.509380 | + | 0.860541i | \(0.329875\pi\) | |||||||
\(308\) | −8.27012 | −0.471234 | ||||||||
\(309\) | −13.9721 | −0.794847 | ||||||||
\(310\) | −3.08584 | −0.175264 | ||||||||
\(311\) | −14.7357 | −0.835586 | −0.417793 | − | 0.908542i | \(-0.637196\pi\) | ||||
−0.417793 | + | 0.908542i | \(0.637196\pi\) | |||||||
\(312\) | −0.269342 | −0.0152485 | ||||||||
\(313\) | −5.71682 | −0.323134 | −0.161567 | − | 0.986862i | \(-0.551655\pi\) | ||||
−0.161567 | + | 0.986862i | \(0.551655\pi\) | |||||||
\(314\) | 10.0065 | 0.564700 | ||||||||
\(315\) | −0.789617 | −0.0444899 | ||||||||
\(316\) | 16.0547 | 0.903145 | ||||||||
\(317\) | −7.00248 | −0.393298 | −0.196649 | − | 0.980474i | \(-0.563006\pi\) | ||||
−0.196649 | + | 0.980474i | \(0.563006\pi\) | |||||||
\(318\) | 1.08001 | 0.0605640 | ||||||||
\(319\) | 6.83198 | 0.382518 | ||||||||
\(320\) | 0.324635 | 0.0181476 | ||||||||
\(321\) | −10.7919 | −0.602343 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.5143 | 1.08580 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −1.31833 | −0.0731275 | ||||||||
\(326\) | −15.9393 | −0.882794 | ||||||||
\(327\) | −16.3580 | −0.904597 | ||||||||
\(328\) | −2.60502 | −0.143838 | ||||||||
\(329\) | −12.6450 | −0.697142 | ||||||||
\(330\) | −1.10379 | −0.0607615 | ||||||||
\(331\) | 19.5035 | 1.07201 | 0.536004 | − | 0.844215i | \(-0.319933\pi\) | ||||
0.536004 | + | 0.844215i | \(0.319933\pi\) | |||||||
\(332\) | −1.05529 | −0.0579167 | ||||||||
\(333\) | −2.01732 | −0.110548 | ||||||||
\(334\) | −9.53697 | −0.521840 | ||||||||
\(335\) | 3.33496 | 0.182208 | ||||||||
\(336\) | 2.43232 | 0.132694 | ||||||||
\(337\) | −20.3735 | −1.10981 | −0.554906 | − | 0.831913i | \(-0.687246\pi\) | ||||
−0.554906 | + | 0.831913i | \(0.687246\pi\) | |||||||
\(338\) | −12.9275 | −0.703161 | ||||||||
\(339\) | −19.9598 | −1.08407 | ||||||||
\(340\) | 1.57388 | 0.0853555 | ||||||||
\(341\) | −32.3198 | −1.75021 | ||||||||
\(342\) | 4.02509 | 0.217652 | ||||||||
\(343\) | 19.6624 | 1.06167 | ||||||||
\(344\) | 3.93559 | 0.212193 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −24.7305 | −1.32952 | ||||||||
\(347\) | −1.87358 | −0.100579 | −0.0502896 | − | 0.998735i | \(-0.516014\pi\) | ||||
−0.0502896 | + | 0.998735i | \(0.516014\pi\) | |||||||
\(348\) | −2.00935 | −0.107713 | ||||||||
\(349\) | 16.4616 | 0.881172 | 0.440586 | − | 0.897710i | \(-0.354771\pi\) | ||||
0.440586 | + | 0.897710i | \(0.354771\pi\) | |||||||
\(350\) | 11.9053 | 0.636364 | ||||||||
\(351\) | −0.269342 | −0.0143764 | ||||||||
\(352\) | 3.40009 | 0.181225 | ||||||||
\(353\) | −8.08237 | −0.430181 | −0.215090 | − | 0.976594i | \(-0.569005\pi\) | ||||
−0.215090 | + | 0.976594i | \(0.569005\pi\) | |||||||
\(354\) | −9.90548 | −0.526470 | ||||||||
\(355\) | 3.71070 | 0.196943 | ||||||||
\(356\) | −2.74085 | −0.145265 | ||||||||
\(357\) | 11.7923 | 0.624113 | ||||||||
\(358\) | −26.3484 | −1.39255 | ||||||||
\(359\) | 17.8120 | 0.940083 | 0.470042 | − | 0.882644i | \(-0.344239\pi\) | ||||
0.470042 | + | 0.882644i | \(0.344239\pi\) | |||||||
\(360\) | 0.324635 | 0.0171098 | ||||||||
\(361\) | −2.79864 | −0.147297 | ||||||||
\(362\) | −18.1768 | −0.955350 | ||||||||
\(363\) | −0.560608 | −0.0294243 | ||||||||
\(364\) | −0.655127 | −0.0343380 | ||||||||
\(365\) | −0.369874 | −0.0193601 | ||||||||
\(366\) | −4.35062 | −0.227411 | ||||||||
\(367\) | −4.22445 | −0.220515 | −0.110257 | − | 0.993903i | \(-0.535167\pi\) | ||||
−0.110257 | + | 0.993903i | \(0.535167\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.60502 | −0.135612 | ||||||||
\(370\) | −0.654892 | −0.0340462 | ||||||||
\(371\) | 2.62693 | 0.136384 | ||||||||
\(372\) | 9.50557 | 0.492841 | ||||||||
\(373\) | −6.77016 | −0.350545 | −0.175273 | − | 0.984520i | \(-0.556081\pi\) | ||||
−0.175273 | + | 0.984520i | \(0.556081\pi\) | |||||||
\(374\) | 16.4841 | 0.852375 | ||||||||
\(375\) | 3.21214 | 0.165874 | ||||||||
\(376\) | 5.19874 | 0.268105 | ||||||||
\(377\) | 0.541204 | 0.0278734 | ||||||||
\(378\) | 2.43232 | 0.125105 | ||||||||
\(379\) | 8.78615 | 0.451314 | 0.225657 | − | 0.974207i | \(-0.427547\pi\) | ||||
0.225657 | + | 0.974207i | \(0.427547\pi\) | |||||||
\(380\) | 1.30668 | 0.0670315 | ||||||||
\(381\) | 5.44618 | 0.279016 | ||||||||
\(382\) | 7.85270 | 0.401779 | ||||||||
\(383\) | −23.0045 | −1.17547 | −0.587737 | − | 0.809052i | \(-0.699981\pi\) | ||||
−0.587737 | + | 0.809052i | \(0.699981\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −2.68477 | −0.136828 | ||||||||
\(386\) | 23.5784 | 1.20011 | ||||||||
\(387\) | 3.93559 | 0.200057 | ||||||||
\(388\) | −13.6079 | −0.690836 | ||||||||
\(389\) | −6.52670 | −0.330917 | −0.165458 | − | 0.986217i | \(-0.552910\pi\) | ||||
−0.165458 | + | 0.986217i | \(0.552910\pi\) | |||||||
\(390\) | −0.0874378 | −0.00442759 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −1.08380 | −0.0547404 | ||||||||
\(393\) | −15.3071 | −0.772142 | ||||||||
\(394\) | 9.26049 | 0.466537 | ||||||||
\(395\) | 5.21190 | 0.262239 | ||||||||
\(396\) | 3.40009 | 0.170861 | ||||||||
\(397\) | 34.7651 | 1.74481 | 0.872404 | − | 0.488785i | \(-0.162560\pi\) | ||||
0.872404 | + | 0.488785i | \(0.162560\pi\) | |||||||
\(398\) | −25.7180 | −1.28913 | ||||||||
\(399\) | 9.79032 | 0.490129 | ||||||||
\(400\) | −4.89461 | −0.244731 | ||||||||
\(401\) | −4.23343 | −0.211408 | −0.105704 | − | 0.994398i | \(-0.533710\pi\) | ||||
−0.105704 | + | 0.994398i | \(0.533710\pi\) | |||||||
\(402\) | −10.2730 | −0.512369 | ||||||||
\(403\) | −2.56025 | −0.127535 | ||||||||
\(404\) | 15.9029 | 0.791198 | ||||||||
\(405\) | 0.324635 | 0.0161312 | ||||||||
\(406\) | −4.88740 | −0.242557 | ||||||||
\(407\) | −6.85907 | −0.339991 | ||||||||
\(408\) | −4.84815 | −0.240019 | ||||||||
\(409\) | 23.7882 | 1.17625 | 0.588126 | − | 0.808769i | \(-0.299866\pi\) | ||||
0.588126 | + | 0.808769i | \(0.299866\pi\) | |||||||
\(410\) | −0.845680 | −0.0417652 | ||||||||
\(411\) | 17.0753 | 0.842260 | ||||||||
\(412\) | 13.9721 | 0.688358 | ||||||||
\(413\) | −24.0933 | −1.18555 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.342585 | −0.0168168 | ||||||||
\(416\) | 0.269342 | 0.0132056 | ||||||||
\(417\) | −16.2779 | −0.797133 | ||||||||
\(418\) | 13.6857 | 0.669388 | ||||||||
\(419\) | 22.3001 | 1.08943 | 0.544717 | − | 0.838620i | \(-0.316637\pi\) | ||||
0.544717 | + | 0.838620i | \(0.316637\pi\) | |||||||
\(420\) | 0.789617 | 0.0385294 | ||||||||
\(421\) | −23.9034 | −1.16498 | −0.582491 | − | 0.812837i | \(-0.697922\pi\) | ||||
−0.582491 | + | 0.812837i | \(0.697922\pi\) | |||||||
\(422\) | 19.6782 | 0.957918 | ||||||||
\(423\) | 5.19874 | 0.252771 | ||||||||
\(424\) | −1.08001 | −0.0524499 | ||||||||
\(425\) | −23.7298 | −1.15107 | ||||||||
\(426\) | −11.4304 | −0.553804 | ||||||||
\(427\) | −10.5821 | −0.512105 | ||||||||
\(428\) | 10.7919 | 0.521644 | ||||||||
\(429\) | −0.915787 | −0.0442146 | ||||||||
\(430\) | 1.27763 | 0.0616127 | ||||||||
\(431\) | 10.0745 | 0.485269 | 0.242635 | − | 0.970118i | \(-0.421988\pi\) | ||||
0.242635 | + | 0.970118i | \(0.421988\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −32.9245 | −1.58225 | −0.791125 | − | 0.611655i | \(-0.790504\pi\) | ||||
−0.791125 | + | 0.611655i | \(0.790504\pi\) | |||||||
\(434\) | 23.1206 | 1.10982 | ||||||||
\(435\) | −0.652306 | −0.0312757 | ||||||||
\(436\) | 16.3580 | 0.783404 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 1.13935 | 0.0544404 | ||||||||
\(439\) | −17.6807 | −0.843852 | −0.421926 | − | 0.906630i | \(-0.638646\pi\) | ||||
−0.421926 | + | 0.906630i | \(0.638646\pi\) | |||||||
\(440\) | 1.10379 | 0.0526210 | ||||||||
\(441\) | −1.08380 | −0.0516097 | ||||||||
\(442\) | 1.30581 | 0.0621111 | ||||||||
\(443\) | −32.6096 | −1.54933 | −0.774665 | − | 0.632371i | \(-0.782082\pi\) | ||||
−0.774665 | + | 0.632371i | \(0.782082\pi\) | |||||||
\(444\) | 2.01732 | 0.0957378 | ||||||||
\(445\) | −0.889774 | −0.0421793 | ||||||||
\(446\) | −4.79039 | −0.226832 | ||||||||
\(447\) | 1.63045 | 0.0771174 | ||||||||
\(448\) | −2.43232 | −0.114916 | ||||||||
\(449\) | 35.3685 | 1.66914 | 0.834572 | − | 0.550898i | \(-0.185715\pi\) | ||||
0.834572 | + | 0.550898i | \(0.185715\pi\) | |||||||
\(450\) | −4.89461 | −0.230734 | ||||||||
\(451\) | −8.85730 | −0.417074 | ||||||||
\(452\) | 19.9598 | 0.938830 | ||||||||
\(453\) | 11.7663 | 0.552830 | ||||||||
\(454\) | 6.03416 | 0.283197 | ||||||||
\(455\) | −0.212677 | −0.00997045 | ||||||||
\(456\) | −4.02509 | −0.188492 | ||||||||
\(457\) | −8.77948 | −0.410687 | −0.205343 | − | 0.978690i | \(-0.565831\pi\) | ||||
−0.205343 | + | 0.978690i | \(0.565831\pi\) | |||||||
\(458\) | 7.27420 | 0.339901 | ||||||||
\(459\) | −4.84815 | −0.226292 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.7701 | 0.594765 | 0.297382 | − | 0.954758i | \(-0.403886\pi\) | ||||
0.297382 | + | 0.954758i | \(0.403886\pi\) | |||||||
\(462\) | 8.27012 | 0.384761 | ||||||||
\(463\) | 15.8063 | 0.734579 | 0.367290 | − | 0.930107i | \(-0.380286\pi\) | ||||
0.367290 | + | 0.930107i | \(0.380286\pi\) | |||||||
\(464\) | 2.00935 | 0.0932819 | ||||||||
\(465\) | 3.08584 | 0.143102 | ||||||||
\(466\) | 8.41855 | 0.389982 | ||||||||
\(467\) | 3.47362 | 0.160740 | 0.0803700 | − | 0.996765i | \(-0.474390\pi\) | ||||
0.0803700 | + | 0.996765i | \(0.474390\pi\) | |||||||
\(468\) | 0.269342 | 0.0124503 | ||||||||
\(469\) | −24.9872 | −1.15380 | ||||||||
\(470\) | 1.68769 | 0.0778474 | ||||||||
\(471\) | −10.0065 | −0.461076 | ||||||||
\(472\) | 9.90548 | 0.455936 | ||||||||
\(473\) | 13.3814 | 0.615275 | ||||||||
\(474\) | −16.0547 | −0.737415 | ||||||||
\(475\) | −19.7013 | −0.903956 | ||||||||
\(476\) | −11.7923 | −0.540498 | ||||||||
\(477\) | −1.08001 | −0.0494503 | ||||||||
\(478\) | −5.16012 | −0.236019 | ||||||||
\(479\) | 0.885748 | 0.0404709 | 0.0202354 | − | 0.999795i | \(-0.493558\pi\) | ||||
0.0202354 | + | 0.999795i | \(0.493558\pi\) | |||||||
\(480\) | −0.324635 | −0.0148175 | ||||||||
\(481\) | −0.543349 | −0.0247746 | ||||||||
\(482\) | 15.6301 | 0.711931 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.560608 | 0.0254822 | ||||||||
\(485\) | −4.41760 | −0.200593 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −3.28852 | −0.149017 | −0.0745085 | − | 0.997220i | \(-0.523739\pi\) | ||||
−0.0745085 | + | 0.997220i | \(0.523739\pi\) | |||||||
\(488\) | 4.35062 | 0.196943 | ||||||||
\(489\) | 15.9393 | 0.720798 | ||||||||
\(490\) | −0.351841 | −0.0158945 | ||||||||
\(491\) | 24.1044 | 1.08781 | 0.543907 | − | 0.839145i | \(-0.316944\pi\) | ||||
0.543907 | + | 0.839145i | \(0.316944\pi\) | |||||||
\(492\) | 2.60502 | 0.117443 | ||||||||
\(493\) | 9.74165 | 0.438742 | ||||||||
\(494\) | 1.08413 | 0.0487772 | ||||||||
\(495\) | 1.10379 | 0.0496116 | ||||||||
\(496\) | −9.50557 | −0.426812 | ||||||||
\(497\) | −27.8024 | −1.24711 | ||||||||
\(498\) | 1.05529 | 0.0472888 | ||||||||
\(499\) | 13.5901 | 0.608375 | 0.304187 | − | 0.952612i | \(-0.401615\pi\) | ||||
0.304187 | + | 0.952612i | \(0.401615\pi\) | |||||||
\(500\) | −3.21214 | −0.143651 | ||||||||
\(501\) | 9.53697 | 0.426081 | ||||||||
\(502\) | −13.8839 | −0.619669 | ||||||||
\(503\) | −16.4428 | −0.733149 | −0.366575 | − | 0.930389i | \(-0.619470\pi\) | ||||
−0.366575 | + | 0.930389i | \(0.619470\pi\) | |||||||
\(504\) | −2.43232 | −0.108344 | ||||||||
\(505\) | 5.16263 | 0.229734 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.9275 | 0.574128 | ||||||||
\(508\) | −5.44618 | −0.241635 | ||||||||
\(509\) | −25.3556 | −1.12387 | −0.561934 | − | 0.827182i | \(-0.689943\pi\) | ||||
−0.561934 | + | 0.827182i | \(0.689943\pi\) | |||||||
\(510\) | −1.57388 | −0.0696925 | ||||||||
\(511\) | 2.77127 | 0.122594 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −4.02509 | −0.177712 | ||||||||
\(514\) | −9.84808 | −0.434380 | ||||||||
\(515\) | 4.53584 | 0.199873 | ||||||||
\(516\) | −3.93559 | −0.173255 | ||||||||
\(517\) | 17.6762 | 0.777398 | ||||||||
\(518\) | 4.90677 | 0.215591 | ||||||||
\(519\) | 24.7305 | 1.08555 | ||||||||
\(520\) | 0.0874378 | 0.00383440 | ||||||||
\(521\) | 33.3911 | 1.46289 | 0.731445 | − | 0.681900i | \(-0.238846\pi\) | ||||
0.731445 | + | 0.681900i | \(0.238846\pi\) | |||||||
\(522\) | 2.00935 | 0.0879470 | ||||||||
\(523\) | 8.13303 | 0.355633 | 0.177816 | − | 0.984064i | \(-0.443097\pi\) | ||||
0.177816 | + | 0.984064i | \(0.443097\pi\) | |||||||
\(524\) | 15.3071 | 0.668694 | ||||||||
\(525\) | −11.9053 | −0.519589 | ||||||||
\(526\) | 0.229051 | 0.00998711 | ||||||||
\(527\) | −46.0844 | −2.00747 | ||||||||
\(528\) | −3.40009 | −0.147970 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | −0.350609 | −0.0152295 | ||||||||
\(531\) | 9.90548 | 0.429861 | ||||||||
\(532\) | −9.79032 | −0.424464 | ||||||||
\(533\) | −0.701642 | −0.0303915 | ||||||||
\(534\) | 2.74085 | 0.118608 | ||||||||
\(535\) | 3.50341 | 0.151466 | ||||||||
\(536\) | 10.2730 | 0.443724 | ||||||||
\(537\) | 26.3484 | 1.13702 | ||||||||
\(538\) | −0.432758 | −0.0186575 | ||||||||
\(539\) | −3.68503 | −0.158726 | ||||||||
\(540\) | −0.324635 | −0.0139701 | ||||||||
\(541\) | 8.92929 | 0.383900 | 0.191950 | − | 0.981405i | \(-0.438519\pi\) | ||||
0.191950 | + | 0.981405i | \(0.438519\pi\) | |||||||
\(542\) | −7.28255 | −0.312812 | ||||||||
\(543\) | 18.1768 | 0.780040 | ||||||||
\(544\) | 4.84815 | 0.207863 | ||||||||
\(545\) | 5.31036 | 0.227471 | ||||||||
\(546\) | 0.655127 | 0.0280369 | ||||||||
\(547\) | 18.3908 | 0.786335 | 0.393168 | − | 0.919467i | \(-0.371379\pi\) | ||||
0.393168 | + | 0.919467i | \(0.371379\pi\) | |||||||
\(548\) | −17.0753 | −0.729419 | ||||||||
\(549\) | 4.35062 | 0.185680 | ||||||||
\(550\) | −16.6421 | −0.709622 | ||||||||
\(551\) | 8.08783 | 0.344553 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −39.0501 | −1.66058 | ||||||||
\(554\) | −24.9693 | −1.06084 | ||||||||
\(555\) | 0.654892 | 0.0277986 | ||||||||
\(556\) | 16.2779 | 0.690337 | ||||||||
\(557\) | −15.0330 | −0.636968 | −0.318484 | − | 0.947928i | \(-0.603174\pi\) | ||||
−0.318484 | + | 0.947928i | \(0.603174\pi\) | |||||||
\(558\) | −9.50557 | −0.402403 | ||||||||
\(559\) | 1.06002 | 0.0448341 | ||||||||
\(560\) | −0.789617 | −0.0333674 | ||||||||
\(561\) | −16.4841 | −0.695961 | ||||||||
\(562\) | −7.32093 | −0.308815 | ||||||||
\(563\) | −45.8315 | −1.93157 | −0.965785 | − | 0.259346i | \(-0.916493\pi\) | ||||
−0.965785 | + | 0.259346i | \(0.916493\pi\) | |||||||
\(564\) | −5.19874 | −0.218906 | ||||||||
\(565\) | 6.47964 | 0.272601 | ||||||||
\(566\) | 10.4946 | 0.441119 | ||||||||
\(567\) | −2.43232 | −0.102148 | ||||||||
\(568\) | 11.4304 | 0.479608 | ||||||||
\(569\) | 35.3665 | 1.48264 | 0.741321 | − | 0.671150i | \(-0.234199\pi\) | ||||
0.741321 | + | 0.671150i | \(0.234199\pi\) | |||||||
\(570\) | −1.30668 | −0.0547310 | ||||||||
\(571\) | 21.0408 | 0.880528 | 0.440264 | − | 0.897868i | \(-0.354885\pi\) | ||||
0.440264 | + | 0.897868i | \(0.354885\pi\) | |||||||
\(572\) | 0.915787 | 0.0382910 | ||||||||
\(573\) | −7.85270 | −0.328051 | ||||||||
\(574\) | 6.33625 | 0.264470 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −17.0656 | −0.710452 | −0.355226 | − | 0.934780i | \(-0.615596\pi\) | ||||
−0.355226 | + | 0.934780i | \(0.615596\pi\) | |||||||
\(578\) | 6.50456 | 0.270554 | ||||||||
\(579\) | −23.5784 | −0.979884 | ||||||||
\(580\) | 0.652306 | 0.0270855 | ||||||||
\(581\) | 2.56681 | 0.106489 | ||||||||
\(582\) | 13.6079 | 0.564066 | ||||||||
\(583\) | −3.67213 | −0.152084 | ||||||||
\(584\) | −1.13935 | −0.0471467 | ||||||||
\(585\) | 0.0874378 | 0.00361511 | ||||||||
\(586\) | −16.1874 | −0.668695 | ||||||||
\(587\) | −3.20673 | −0.132356 | −0.0661780 | − | 0.997808i | \(-0.521081\pi\) | ||||
−0.0661780 | + | 0.997808i | \(0.521081\pi\) | |||||||
\(588\) | 1.08380 | 0.0446953 | ||||||||
\(589\) | −38.2608 | −1.57651 | ||||||||
\(590\) | 3.21566 | 0.132387 | ||||||||
\(591\) | −9.26049 | −0.380926 | ||||||||
\(592\) | −2.01732 | −0.0829114 | ||||||||
\(593\) | −8.15422 | −0.334854 | −0.167427 | − | 0.985884i | \(-0.553546\pi\) | ||||
−0.167427 | + | 0.985884i | \(0.553546\pi\) | |||||||
\(594\) | −3.40009 | −0.139507 | ||||||||
\(595\) | −3.82818 | −0.156940 | ||||||||
\(596\) | −1.63045 | −0.0667857 | ||||||||
\(597\) | 25.7180 | 1.05257 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −44.6481 | −1.82427 | −0.912136 | − | 0.409888i | \(-0.865568\pi\) | ||||
−0.912136 | + | 0.409888i | \(0.865568\pi\) | |||||||
\(600\) | 4.89461 | 0.199822 | ||||||||
\(601\) | −27.7579 | −1.13227 | −0.566135 | − | 0.824312i | \(-0.691562\pi\) | ||||
−0.566135 | + | 0.824312i | \(0.691562\pi\) | |||||||
\(602\) | −9.57262 | −0.390151 | ||||||||
\(603\) | 10.2730 | 0.418347 | ||||||||
\(604\) | −11.7663 | −0.478765 | ||||||||
\(605\) | 0.181993 | 0.00739906 | ||||||||
\(606\) | −15.9029 | −0.646011 | ||||||||
\(607\) | −23.5817 | −0.957153 | −0.478577 | − | 0.878046i | \(-0.658847\pi\) | ||||
−0.478577 | + | 0.878046i | \(0.658847\pi\) | |||||||
\(608\) | 4.02509 | 0.163239 | ||||||||
\(609\) | 4.88740 | 0.198047 | ||||||||
\(610\) | 1.41236 | 0.0571849 | ||||||||
\(611\) | 1.40024 | 0.0566477 | ||||||||
\(612\) | 4.84815 | 0.195975 | ||||||||
\(613\) | −32.8468 | −1.32667 | −0.663336 | − | 0.748322i | \(-0.730860\pi\) | ||||
−0.663336 | + | 0.748322i | \(0.730860\pi\) | |||||||
\(614\) | 17.8501 | 0.720373 | ||||||||
\(615\) | 0.845680 | 0.0341011 | ||||||||
\(616\) | −8.27012 | −0.333212 | ||||||||
\(617\) | −23.3881 | −0.941571 | −0.470786 | − | 0.882248i | \(-0.656029\pi\) | ||||
−0.470786 | + | 0.882248i | \(0.656029\pi\) | |||||||
\(618\) | −13.9721 | −0.562042 | ||||||||
\(619\) | −12.4486 | −0.500350 | −0.250175 | − | 0.968201i | \(-0.580488\pi\) | ||||
−0.250175 | + | 0.968201i | \(0.580488\pi\) | |||||||
\(620\) | −3.08584 | −0.123930 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −14.7357 | −0.590848 | ||||||||
\(623\) | 6.66662 | 0.267093 | ||||||||
\(624\) | −0.269342 | −0.0107823 | ||||||||
\(625\) | 23.4303 | 0.937212 | ||||||||
\(626\) | −5.71682 | −0.228490 | ||||||||
\(627\) | −13.6857 | −0.546553 | ||||||||
\(628\) | 10.0065 | 0.399303 | ||||||||
\(629\) | −9.78027 | −0.389965 | ||||||||
\(630\) | −0.789617 | −0.0314591 | ||||||||
\(631\) | 32.4757 | 1.29284 | 0.646419 | − | 0.762982i | \(-0.276266\pi\) | ||||
0.646419 | + | 0.762982i | \(0.276266\pi\) | |||||||
\(632\) | 16.0547 | 0.638620 | ||||||||
\(633\) | −19.6782 | −0.782137 | ||||||||
\(634\) | −7.00248 | −0.278104 | ||||||||
\(635\) | −1.76802 | −0.0701617 | ||||||||
\(636\) | 1.08001 | 0.0428252 | ||||||||
\(637\) | −0.291914 | −0.0115661 | ||||||||
\(638\) | 6.83198 | 0.270481 | ||||||||
\(639\) | 11.4304 | 0.452179 | ||||||||
\(640\) | 0.324635 | 0.0128323 | ||||||||
\(641\) | 3.78968 | 0.149683 | 0.0748416 | − | 0.997195i | \(-0.476155\pi\) | ||||
0.0748416 | + | 0.997195i | \(0.476155\pi\) | |||||||
\(642\) | −10.7919 | −0.425920 | ||||||||
\(643\) | 16.4223 | 0.647634 | 0.323817 | − | 0.946120i | \(-0.395034\pi\) | ||||
0.323817 | + | 0.946120i | \(0.395034\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.27763 | −0.0503066 | ||||||||
\(646\) | 19.5143 | 0.767778 | ||||||||
\(647\) | −5.18571 | −0.203871 | −0.101936 | − | 0.994791i | \(-0.532504\pi\) | ||||
−0.101936 | + | 0.994791i | \(0.532504\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 33.6795 | 1.32204 | ||||||||
\(650\) | −1.31833 | −0.0517090 | ||||||||
\(651\) | −23.1206 | −0.906168 | ||||||||
\(652\) | −15.9393 | −0.624230 | ||||||||
\(653\) | −25.7770 | −1.00873 | −0.504366 | − | 0.863490i | \(-0.668274\pi\) | ||||
−0.504366 | + | 0.863490i | \(0.668274\pi\) | |||||||
\(654\) | −16.3580 | −0.639647 | ||||||||
\(655\) | 4.96922 | 0.194164 | ||||||||
\(656\) | −2.60502 | −0.101709 | ||||||||
\(657\) | −1.13935 | −0.0444504 | ||||||||
\(658\) | −12.6450 | −0.492954 | ||||||||
\(659\) | −43.8640 | −1.70870 | −0.854349 | − | 0.519700i | \(-0.826044\pi\) | ||||
−0.854349 | + | 0.519700i | \(0.826044\pi\) | |||||||
\(660\) | −1.10379 | −0.0429649 | ||||||||
\(661\) | 9.43101 | 0.366824 | 0.183412 | − | 0.983036i | \(-0.441286\pi\) | ||||
0.183412 | + | 0.983036i | \(0.441286\pi\) | |||||||
\(662\) | 19.5035 | 0.758024 | ||||||||
\(663\) | −1.30581 | −0.0507135 | ||||||||
\(664\) | −1.05529 | −0.0409533 | ||||||||
\(665\) | −3.17828 | −0.123248 | ||||||||
\(666\) | −2.01732 | −0.0781696 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −9.53697 | −0.368997 | ||||||||
\(669\) | 4.79039 | 0.185207 | ||||||||
\(670\) | 3.33496 | 0.128841 | ||||||||
\(671\) | 14.7925 | 0.571059 | ||||||||
\(672\) | 2.43232 | 0.0938289 | ||||||||
\(673\) | −8.94031 | −0.344624 | −0.172312 | − | 0.985042i | \(-0.555124\pi\) | ||||
−0.172312 | + | 0.985042i | \(0.555124\pi\) | |||||||
\(674\) | −20.3735 | −0.784756 | ||||||||
\(675\) | 4.89461 | 0.188394 | ||||||||
\(676\) | −12.9275 | −0.497210 | ||||||||
\(677\) | −35.3761 | −1.35961 | −0.679807 | − | 0.733391i | \(-0.737937\pi\) | ||||
−0.679807 | + | 0.733391i | \(0.737937\pi\) | |||||||
\(678\) | −19.9598 | −0.766551 | ||||||||
\(679\) | 33.0988 | 1.27022 | ||||||||
\(680\) | 1.57388 | 0.0603555 | ||||||||
\(681\) | −6.03416 | −0.231229 | ||||||||
\(682\) | −32.3198 | −1.23759 | ||||||||
\(683\) | 29.2895 | 1.12073 | 0.560366 | − | 0.828245i | \(-0.310661\pi\) | ||||
0.560366 | + | 0.828245i | \(0.310661\pi\) | |||||||
\(684\) | 4.02509 | 0.153903 | ||||||||
\(685\) | −5.54322 | −0.211796 | ||||||||
\(686\) | 19.6624 | 0.750715 | ||||||||
\(687\) | −7.27420 | −0.277528 | ||||||||
\(688\) | 3.93559 | 0.150043 | ||||||||
\(689\) | −0.290892 | −0.0110821 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.9634 | −0.797487 | −0.398744 | − | 0.917062i | \(-0.630554\pi\) | ||||
−0.398744 | + | 0.917062i | \(0.630554\pi\) | |||||||
\(692\) | −24.7305 | −0.940112 | ||||||||
\(693\) | −8.27012 | −0.314156 | ||||||||
\(694\) | −1.87358 | −0.0711203 | ||||||||
\(695\) | 5.28438 | 0.200448 | ||||||||
\(696\) | −2.00935 | −0.0761644 | ||||||||
\(697\) | −12.6295 | −0.478377 | ||||||||
\(698\) | 16.4616 | 0.623083 | ||||||||
\(699\) | −8.41855 | −0.318419 | ||||||||
\(700\) | 11.9053 | 0.449977 | ||||||||
\(701\) | −32.1001 | −1.21240 | −0.606202 | − | 0.795311i | \(-0.707308\pi\) | ||||
−0.606202 | + | 0.795311i | \(0.707308\pi\) | |||||||
\(702\) | −0.269342 | −0.0101657 | ||||||||
\(703\) | −8.11990 | −0.306248 | ||||||||
\(704\) | 3.40009 | 0.128146 | ||||||||
\(705\) | −1.68769 | −0.0635622 | ||||||||
\(706\) | −8.08237 | −0.304184 | ||||||||
\(707\) | −38.6810 | −1.45475 | ||||||||
\(708\) | −9.90548 | −0.372271 | ||||||||
\(709\) | −33.7537 | −1.26765 | −0.633824 | − | 0.773477i | \(-0.718516\pi\) | ||||
−0.633824 | + | 0.773477i | \(0.718516\pi\) | |||||||
\(710\) | 3.71070 | 0.139260 | ||||||||
\(711\) | 16.0547 | 0.602097 | ||||||||
\(712\) | −2.74085 | −0.102718 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 11.7923 | 0.441315 | ||||||||
\(715\) | 0.297296 | 0.0111183 | ||||||||
\(716\) | −26.3484 | −0.984684 | ||||||||
\(717\) | 5.16012 | 0.192708 | ||||||||
\(718\) | 17.8120 | 0.664739 | ||||||||
\(719\) | −46.9884 | −1.75237 | −0.876185 | − | 0.481974i | \(-0.839920\pi\) | ||||
−0.876185 | + | 0.481974i | \(0.839920\pi\) | |||||||
\(720\) | 0.324635 | 0.0120984 | ||||||||
\(721\) | −33.9848 | −1.26566 | ||||||||
\(722\) | −2.79864 | −0.104154 | ||||||||
\(723\) | −15.6301 | −0.581289 | ||||||||
\(724\) | −18.1768 | −0.675535 | ||||||||
\(725\) | −9.83501 | −0.365263 | ||||||||
\(726\) | −0.560608 | −0.0208061 | ||||||||
\(727\) | 16.8502 | 0.624939 | 0.312470 | − | 0.949928i | \(-0.398844\pi\) | ||||
0.312470 | + | 0.949928i | \(0.398844\pi\) | |||||||
\(728\) | −0.655127 | −0.0242806 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.369874 | −0.0136896 | ||||||||
\(731\) | 19.0803 | 0.705711 | ||||||||
\(732\) | −4.35062 | −0.160804 | ||||||||
\(733\) | 10.6895 | 0.394825 | 0.197413 | − | 0.980321i | \(-0.436746\pi\) | ||||
0.197413 | + | 0.980321i | \(0.436746\pi\) | |||||||
\(734\) | −4.22445 | −0.155927 | ||||||||
\(735\) | 0.351841 | 0.0129778 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 34.9290 | 1.28663 | ||||||||
\(738\) | −2.60502 | −0.0958921 | ||||||||
\(739\) | 24.8920 | 0.915668 | 0.457834 | − | 0.889038i | \(-0.348625\pi\) | ||||
0.457834 | + | 0.889038i | \(0.348625\pi\) | |||||||
\(740\) | −0.654892 | −0.0240743 | ||||||||
\(741\) | −1.08413 | −0.0398264 | ||||||||
\(742\) | 2.62693 | 0.0964378 | ||||||||
\(743\) | 38.1691 | 1.40029 | 0.700145 | − | 0.714001i | \(-0.253119\pi\) | ||||
0.700145 | + | 0.714001i | \(0.253119\pi\) | |||||||
\(744\) | 9.50557 | 0.348491 | ||||||||
\(745\) | −0.529300 | −0.0193920 | ||||||||
\(746\) | −6.77016 | −0.247873 | ||||||||
\(747\) | −1.05529 | −0.0386111 | ||||||||
\(748\) | 16.4841 | 0.602720 | ||||||||
\(749\) | −26.2493 | −0.959128 | ||||||||
\(750\) | 3.21214 | 0.117291 | ||||||||
\(751\) | 44.2589 | 1.61503 | 0.807514 | − | 0.589848i | \(-0.200812\pi\) | ||||
0.807514 | + | 0.589848i | \(0.200812\pi\) | |||||||
\(752\) | 5.19874 | 0.189579 | ||||||||
\(753\) | 13.8839 | 0.505958 | ||||||||
\(754\) | 0.541204 | 0.0197095 | ||||||||
\(755\) | −3.81976 | −0.139015 | ||||||||
\(756\) | 2.43232 | 0.0884627 | ||||||||
\(757\) | −9.78484 | −0.355636 | −0.177818 | − | 0.984063i | \(-0.556904\pi\) | ||||
−0.177818 | + | 0.984063i | \(0.556904\pi\) | |||||||
\(758\) | 8.78615 | 0.319128 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.30668 | 0.0473984 | ||||||||
\(761\) | 23.9490 | 0.868150 | 0.434075 | − | 0.900877i | \(-0.357075\pi\) | ||||
0.434075 | + | 0.900877i | \(0.357075\pi\) | |||||||
\(762\) | 5.44618 | 0.197294 | ||||||||
\(763\) | −39.7878 | −1.44042 | ||||||||
\(764\) | 7.85270 | 0.284101 | ||||||||
\(765\) | 1.57388 | 0.0569037 | ||||||||
\(766\) | −23.0045 | −0.831186 | ||||||||
\(767\) | 2.66796 | 0.0963345 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −27.6827 | −0.998265 | −0.499132 | − | 0.866526i | \(-0.666348\pi\) | ||||
−0.499132 | + | 0.866526i | \(0.666348\pi\) | |||||||
\(770\) | −2.68477 | −0.0967523 | ||||||||
\(771\) | 9.84808 | 0.354670 | ||||||||
\(772\) | 23.5784 | 0.848604 | ||||||||
\(773\) | −33.8343 | −1.21693 | −0.608467 | − | 0.793579i | \(-0.708215\pi\) | ||||
−0.608467 | + | 0.793579i | \(0.708215\pi\) | |||||||
\(774\) | 3.93559 | 0.141462 | ||||||||
\(775\) | 46.5261 | 1.67127 | ||||||||
\(776\) | −13.6079 | −0.488495 | ||||||||
\(777\) | −4.90677 | −0.176030 | ||||||||
\(778\) | −6.52670 | −0.233993 | ||||||||
\(779\) | −10.4854 | −0.375680 | ||||||||
\(780\) | −0.0874378 | −0.00313078 | ||||||||
\(781\) | 38.8643 | 1.39067 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.00935 | −0.0718084 | ||||||||
\(784\) | −1.08380 | −0.0387073 | ||||||||
\(785\) | 3.24846 | 0.115943 | ||||||||
\(786\) | −15.3071 | −0.545987 | ||||||||
\(787\) | 24.4836 | 0.872745 | 0.436372 | − | 0.899766i | \(-0.356263\pi\) | ||||
0.436372 | + | 0.899766i | \(0.356263\pi\) | |||||||
\(788\) | 9.26049 | 0.329891 | ||||||||
\(789\) | −0.229051 | −0.00815444 | ||||||||
\(790\) | 5.21190 | 0.185431 | ||||||||
\(791\) | −48.5487 | −1.72619 | ||||||||
\(792\) | 3.40009 | 0.120817 | ||||||||
\(793\) | 1.17181 | 0.0416121 | ||||||||
\(794\) | 34.7651 | 1.23377 | ||||||||
\(795\) | 0.350609 | 0.0124348 | ||||||||
\(796\) | −25.7180 | −0.911552 | ||||||||
\(797\) | −8.69614 | −0.308033 | −0.154017 | − | 0.988068i | \(-0.549221\pi\) | ||||
−0.154017 | + | 0.988068i | \(0.549221\pi\) | |||||||
\(798\) | 9.79032 | 0.346574 | ||||||||
\(799\) | 25.2043 | 0.891663 | ||||||||
\(800\) | −4.89461 | −0.173051 | ||||||||
\(801\) | −2.74085 | −0.0968430 | ||||||||
\(802\) | −4.23343 | −0.149488 | ||||||||
\(803\) | −3.87390 | −0.136707 | ||||||||
\(804\) | −10.2730 | −0.362299 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.56025 | −0.0901809 | ||||||||
\(807\) | 0.432758 | 0.0152338 | ||||||||
\(808\) | 15.9029 | 0.559462 | ||||||||
\(809\) | 18.5536 | 0.652308 | 0.326154 | − | 0.945317i | \(-0.394247\pi\) | ||||
0.326154 | + | 0.945317i | \(0.394247\pi\) | |||||||
\(810\) | 0.324635 | 0.0114065 | ||||||||
\(811\) | −21.5690 | −0.757390 | −0.378695 | − | 0.925521i | \(-0.623627\pi\) | ||||
−0.378695 | + | 0.925521i | \(0.623627\pi\) | |||||||
\(812\) | −4.88740 | −0.171514 | ||||||||
\(813\) | 7.28255 | 0.255410 | ||||||||
\(814\) | −6.85907 | −0.240410 | ||||||||
\(815\) | −5.17444 | −0.181253 | ||||||||
\(816\) | −4.84815 | −0.169719 | ||||||||
\(817\) | 15.8411 | 0.554210 | ||||||||
\(818\) | 23.7882 | 0.831736 | ||||||||
\(819\) | −0.655127 | −0.0228920 | ||||||||
\(820\) | −0.845680 | −0.0295324 | ||||||||
\(821\) | 6.92328 | 0.241624 | 0.120812 | − | 0.992675i | \(-0.461450\pi\) | ||||
0.120812 | + | 0.992675i | \(0.461450\pi\) | |||||||
\(822\) | 17.0753 | 0.595568 | ||||||||
\(823\) | −31.3176 | −1.09166 | −0.545831 | − | 0.837895i | \(-0.683786\pi\) | ||||
−0.545831 | + | 0.837895i | \(0.683786\pi\) | |||||||
\(824\) | 13.9721 | 0.486743 | ||||||||
\(825\) | 16.6421 | 0.579404 | ||||||||
\(826\) | −24.0933 | −0.838314 | ||||||||
\(827\) | −4.77095 | −0.165902 | −0.0829511 | − | 0.996554i | \(-0.526435\pi\) | ||||
−0.0829511 | + | 0.996554i | \(0.526435\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.94168 | −0.0674372 | −0.0337186 | − | 0.999431i | \(-0.510735\pi\) | ||||
−0.0337186 | + | 0.999431i | \(0.510735\pi\) | |||||||
\(830\) | −0.342585 | −0.0118913 | ||||||||
\(831\) | 24.9693 | 0.866175 | ||||||||
\(832\) | 0.269342 | 0.00933776 | ||||||||
\(833\) | −5.25445 | −0.182056 | ||||||||
\(834\) | −16.2779 | −0.563658 | ||||||||
\(835\) | −3.09603 | −0.107143 | ||||||||
\(836\) | 13.6857 | 0.473329 | ||||||||
\(837\) | 9.50557 | 0.328560 | ||||||||
\(838\) | 22.3001 | 0.770346 | ||||||||
\(839\) | −45.8225 | −1.58197 | −0.790985 | − | 0.611836i | \(-0.790431\pi\) | ||||
−0.790985 | + | 0.611836i | \(0.790431\pi\) | |||||||
\(840\) | 0.789617 | 0.0272444 | ||||||||
\(841\) | −24.9625 | −0.860776 | ||||||||
\(842\) | −23.9034 | −0.823766 | ||||||||
\(843\) | 7.32093 | 0.252146 | ||||||||
\(844\) | 19.6782 | 0.677350 | ||||||||
\(845\) | −4.19670 | −0.144371 | ||||||||
\(846\) | 5.19874 | 0.178736 | ||||||||
\(847\) | −1.36358 | −0.0468531 | ||||||||
\(848\) | −1.08001 | −0.0370877 | ||||||||
\(849\) | −10.4946 | −0.360172 | ||||||||
\(850\) | −23.7298 | −0.813926 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −11.4304 | −0.391598 | ||||||||
\(853\) | −19.1208 | −0.654685 | −0.327342 | − | 0.944906i | \(-0.606153\pi\) | ||||
−0.327342 | + | 0.944906i | \(0.606153\pi\) | |||||||
\(854\) | −10.5821 | −0.362113 | ||||||||
\(855\) | 1.30668 | 0.0446877 | ||||||||
\(856\) | 10.7919 | 0.368858 | ||||||||
\(857\) | 9.48763 | 0.324091 | 0.162046 | − | 0.986783i | \(-0.448191\pi\) | ||||
0.162046 | + | 0.986783i | \(0.448191\pi\) | |||||||
\(858\) | −0.915787 | −0.0312645 | ||||||||
\(859\) | 39.2043 | 1.33763 | 0.668817 | − | 0.743427i | \(-0.266801\pi\) | ||||
0.668817 | + | 0.743427i | \(0.266801\pi\) | |||||||
\(860\) | 1.27763 | 0.0435668 | ||||||||
\(861\) | −6.33625 | −0.215939 | ||||||||
\(862\) | 10.0745 | 0.343137 | ||||||||
\(863\) | 12.9692 | 0.441477 | 0.220739 | − | 0.975333i | \(-0.429153\pi\) | ||||
0.220739 | + | 0.975333i | \(0.429153\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −8.02838 | −0.272973 | ||||||||
\(866\) | −32.9245 | −1.11882 | ||||||||
\(867\) | −6.50456 | −0.220907 | ||||||||
\(868\) | 23.1206 | 0.784765 | ||||||||
\(869\) | 54.5873 | 1.85175 | ||||||||
\(870\) | −0.652306 | −0.0221153 | ||||||||
\(871\) | 2.76694 | 0.0937542 | ||||||||
\(872\) | 16.3580 | 0.553950 | ||||||||
\(873\) | −13.6079 | −0.460558 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.81295 | 0.264126 | ||||||||
\(876\) | 1.13935 | 0.0384952 | ||||||||
\(877\) | 28.5809 | 0.965108 | 0.482554 | − | 0.875866i | \(-0.339709\pi\) | ||||
0.482554 | + | 0.875866i | \(0.339709\pi\) | |||||||
\(878\) | −17.6807 | −0.596694 | ||||||||
\(879\) | 16.1874 | 0.545987 | ||||||||
\(880\) | 1.10379 | 0.0372087 | ||||||||
\(881\) | 33.5556 | 1.13052 | 0.565259 | − | 0.824913i | \(-0.308776\pi\) | ||||
0.565259 | + | 0.824913i | \(0.308776\pi\) | |||||||
\(882\) | −1.08380 | −0.0364936 | ||||||||
\(883\) | 21.6186 | 0.727524 | 0.363762 | − | 0.931492i | \(-0.381492\pi\) | ||||
0.363762 | + | 0.931492i | \(0.381492\pi\) | |||||||
\(884\) | 1.30581 | 0.0439192 | ||||||||
\(885\) | −3.21566 | −0.108093 | ||||||||
\(886\) | −32.6096 | −1.09554 | ||||||||
\(887\) | −39.1158 | −1.31338 | −0.656690 | − | 0.754161i | \(-0.728044\pi\) | ||||
−0.656690 | + | 0.754161i | \(0.728044\pi\) | |||||||
\(888\) | 2.01732 | 0.0676968 | ||||||||
\(889\) | 13.2469 | 0.444285 | ||||||||
\(890\) | −0.889774 | −0.0298253 | ||||||||
\(891\) | 3.40009 | 0.113907 | ||||||||
\(892\) | −4.79039 | −0.160394 | ||||||||
\(893\) | 20.9254 | 0.700242 | ||||||||
\(894\) | 1.63045 | 0.0545303 | ||||||||
\(895\) | −8.55359 | −0.285915 | ||||||||
\(896\) | −2.43232 | −0.0812582 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 35.3685 | 1.18026 | ||||||||
\(899\) | −19.1000 | −0.637022 | ||||||||
\(900\) | −4.89461 | −0.163154 | ||||||||
\(901\) | −5.23605 | −0.174438 | ||||||||
\(902\) | −8.85730 | −0.294916 | ||||||||
\(903\) | 9.57262 | 0.318557 | ||||||||
\(904\) | 19.9598 | 0.663853 | ||||||||
\(905\) | −5.90081 | −0.196150 | ||||||||
\(906\) | 11.7663 | 0.390910 | ||||||||
\(907\) | −18.6215 | −0.618317 | −0.309158 | − | 0.951011i | \(-0.600047\pi\) | ||||
−0.309158 | + | 0.951011i | \(0.600047\pi\) | |||||||
\(908\) | 6.03416 | 0.200251 | ||||||||
\(909\) | 15.9029 | 0.527465 | ||||||||
\(910\) | −0.212677 | −0.00705018 | ||||||||
\(911\) | 16.2164 | 0.537273 | 0.268637 | − | 0.963242i | \(-0.413427\pi\) | ||||
0.268637 | + | 0.963242i | \(0.413427\pi\) | |||||||
\(912\) | −4.02509 | −0.133284 | ||||||||
\(913\) | −3.58809 | −0.118748 | ||||||||
\(914\) | −8.77948 | −0.290400 | ||||||||
\(915\) | −1.41236 | −0.0466913 | ||||||||
\(916\) | 7.27420 | 0.240346 | ||||||||
\(917\) | −37.2318 | −1.22950 | ||||||||
\(918\) | −4.84815 | −0.160013 | ||||||||
\(919\) | 7.51602 | 0.247930 | 0.123965 | − | 0.992287i | \(-0.460439\pi\) | ||||
0.123965 | + | 0.992287i | \(0.460439\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.8501 | −0.588182 | ||||||||
\(922\) | 12.7701 | 0.420562 | ||||||||
\(923\) | 3.07868 | 0.101336 | ||||||||
\(924\) | 8.27012 | 0.272067 | ||||||||
\(925\) | 9.87400 | 0.324655 | ||||||||
\(926\) | 15.8063 | 0.519426 | ||||||||
\(927\) | 13.9721 | 0.458905 | ||||||||
\(928\) | 2.00935 | 0.0659603 | ||||||||
\(929\) | 16.8540 | 0.552962 | 0.276481 | − | 0.961019i | \(-0.410832\pi\) | ||||
0.276481 | + | 0.961019i | \(0.410832\pi\) | |||||||
\(930\) | 3.08584 | 0.101189 | ||||||||
\(931\) | −4.36241 | −0.142972 | ||||||||
\(932\) | 8.41855 | 0.275759 | ||||||||
\(933\) | 14.7357 | 0.482426 | ||||||||
\(934\) | 3.47362 | 0.113660 | ||||||||
\(935\) | 5.35133 | 0.175007 | ||||||||
\(936\) | 0.269342 | 0.00880372 | ||||||||
\(937\) | −0.877608 | −0.0286702 | −0.0143351 | − | 0.999897i | \(-0.504563\pi\) | ||||
−0.0143351 | + | 0.999897i | \(0.504563\pi\) | |||||||
\(938\) | −24.9872 | −0.815859 | ||||||||
\(939\) | 5.71682 | 0.186561 | ||||||||
\(940\) | 1.68769 | 0.0550465 | ||||||||
\(941\) | 13.9836 | 0.455851 | 0.227926 | − | 0.973679i | \(-0.426806\pi\) | ||||
0.227926 | + | 0.973679i | \(0.426806\pi\) | |||||||
\(942\) | −10.0065 | −0.326030 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 9.90548 | 0.322396 | ||||||||
\(945\) | 0.789617 | 0.0256862 | ||||||||
\(946\) | 13.3814 | 0.435065 | ||||||||
\(947\) | −24.6457 | −0.800876 | −0.400438 | − | 0.916324i | \(-0.631142\pi\) | ||||
−0.400438 | + | 0.916324i | \(0.631142\pi\) | |||||||
\(948\) | −16.0547 | −0.521431 | ||||||||
\(949\) | −0.306876 | −0.00996161 | ||||||||
\(950\) | −19.7013 | −0.639193 | ||||||||
\(951\) | 7.00248 | 0.227071 | ||||||||
\(952\) | −11.7923 | −0.382190 | ||||||||
\(953\) | 56.1029 | 1.81735 | 0.908675 | − | 0.417504i | \(-0.137095\pi\) | ||||
0.908675 | + | 0.417504i | \(0.137095\pi\) | |||||||
\(954\) | −1.08001 | −0.0349666 | ||||||||
\(955\) | 2.54926 | 0.0824921 | ||||||||
\(956\) | −5.16012 | −0.166890 | ||||||||
\(957\) | −6.83198 | −0.220847 | ||||||||
\(958\) | 0.885748 | 0.0286172 | ||||||||
\(959\) | 41.5325 | 1.34116 | ||||||||
\(960\) | −0.324635 | −0.0104775 | ||||||||
\(961\) | 59.3558 | 1.91470 | ||||||||
\(962\) | −0.543349 | −0.0175183 | ||||||||
\(963\) | 10.7919 | 0.347763 | ||||||||
\(964\) | 15.6301 | 0.503411 | ||||||||
\(965\) | 7.65436 | 0.246403 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −38.0371 | −1.22319 | −0.611596 | − | 0.791170i | \(-0.709472\pi\) | ||||
−0.611596 | + | 0.791170i | \(0.709472\pi\) | |||||||
\(968\) | 0.560608 | 0.0180186 | ||||||||
\(969\) | −19.5143 | −0.626888 | ||||||||
\(970\) | −4.41760 | −0.141841 | ||||||||
\(971\) | 46.8643 | 1.50395 | 0.751974 | − | 0.659193i | \(-0.229102\pi\) | ||||
0.751974 | + | 0.659193i | \(0.229102\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −39.5932 | −1.26930 | ||||||||
\(974\) | −3.28852 | −0.105371 | ||||||||
\(975\) | 1.31833 | 0.0422202 | ||||||||
\(976\) | 4.35062 | 0.139260 | ||||||||
\(977\) | −6.32527 | −0.202363 | −0.101182 | − | 0.994868i | \(-0.532262\pi\) | ||||
−0.101182 | + | 0.994868i | \(0.532262\pi\) | |||||||
\(978\) | 15.9393 | 0.509681 | ||||||||
\(979\) | −9.31912 | −0.297840 | ||||||||
\(980\) | −0.351841 | −0.0112391 | ||||||||
\(981\) | 16.3580 | 0.522269 | ||||||||
\(982\) | 24.1044 | 0.769201 | ||||||||
\(983\) | −29.8592 | −0.952361 | −0.476181 | − | 0.879348i | \(-0.657979\pi\) | ||||
−0.476181 | + | 0.879348i | \(0.657979\pi\) | |||||||
\(984\) | 2.60502 | 0.0830450 | ||||||||
\(985\) | 3.00628 | 0.0957880 | ||||||||
\(986\) | 9.74165 | 0.310237 | ||||||||
\(987\) | 12.6450 | 0.402495 | ||||||||
\(988\) | 1.08413 | 0.0344907 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 1.10379 | 0.0350807 | ||||||||
\(991\) | 8.95060 | 0.284325 | 0.142163 | − | 0.989843i | \(-0.454594\pi\) | ||||
0.142163 | + | 0.989843i | \(0.454594\pi\) | |||||||
\(992\) | −9.50557 | −0.301802 | ||||||||
\(993\) | −19.5035 | −0.618924 | ||||||||
\(994\) | −27.8024 | −0.881838 | ||||||||
\(995\) | −8.34897 | −0.264680 | ||||||||
\(996\) | 1.05529 | 0.0334382 | ||||||||
\(997\) | 16.7521 | 0.530545 | 0.265272 | − | 0.964174i | \(-0.414538\pi\) | ||||
0.265272 | + | 0.964174i | \(0.414538\pi\) | |||||||
\(998\) | 13.5901 | 0.430186 | ||||||||
\(999\) | 2.01732 | 0.0638252 |
(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 | 3174.2.a.ba.1.4 | 5 | ||
3.2 | odd | 2 | 9522.2.a.bs.1.2 | 5 | |||
23.2 | even | 11 | 138.2.e.b.73.1 | ✓ | 10 | ||
23.12 | even | 11 | 138.2.e.b.121.1 | yes | 10 | ||
23.22 | odd | 2 | 3174.2.a.bb.1.2 | 5 | |||
69.2 | odd | 22 | 414.2.i.e.73.1 | 10 | |||
69.35 | odd | 22 | 414.2.i.e.397.1 | 10 | |||
69.68 | even | 2 | 9522.2.a.br.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
138.2.e.b.73.1 | ✓ | 10 | 23.2 | even | 11 | ||
138.2.e.b.121.1 | yes | 10 | 23.12 | even | 11 | ||
414.2.i.e.73.1 | 10 | 69.2 | odd | 22 | |||
414.2.i.e.397.1 | 10 | 69.35 | odd | 22 | |||
3174.2.a.ba.1.4 | 5 | 1.1 | even | 1 | trivial | ||
3174.2.a.bb.1.2 | 5 | 23.22 | odd | 2 | |||
9522.2.a.br.1.4 | 5 | 69.68 | even | 2 | |||
9522.2.a.bs.1.2 | 5 | 3.2 | odd | 2 |