Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2415,2,Mod(1,2415)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2415, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2415.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2415 = 3 \cdot 5 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2415.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: | \(19.2838720881\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 16x^{8} + 30x^{7} + 83x^{6} - 137x^{5} - 164x^{4} + 208x^{3} + 108x^{2} - 83x - 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(2.42079\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2415.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.42079 | 1.71176 | 0.855878 | − | 0.517178i | \(-0.173017\pi\) | ||||
0.855878 | + | 0.517178i | \(0.173017\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 3.86022 | 1.93011 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 2.42079 | 0.988283 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 4.50319 | 1.59212 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.42079 | 0.765521 | ||||||||
\(11\) | 2.79376 | 0.842352 | 0.421176 | − | 0.906979i | \(-0.361618\pi\) | ||||
0.421176 | + | 0.906979i | \(0.361618\pi\) | |||||||
\(12\) | 3.86022 | 1.11435 | ||||||||
\(13\) | −5.96954 | −1.65565 | −0.827826 | − | 0.560985i | \(-0.810423\pi\) | ||||
−0.827826 | + | 0.560985i | \(0.810423\pi\) | |||||||
\(14\) | −2.42079 | −0.646983 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 3.18084 | 0.795210 | ||||||||
\(17\) | 4.49734 | 1.09077 | 0.545383 | − | 0.838187i | \(-0.316384\pi\) | ||||
0.545383 | + | 0.838187i | \(0.316384\pi\) | |||||||
\(18\) | 2.42079 | 0.570585 | ||||||||
\(19\) | 8.29134 | 1.90216 | 0.951082 | − | 0.308940i | \(-0.0999742\pi\) | ||||
0.951082 | + | 0.308940i | \(0.0999742\pi\) | |||||||
\(20\) | 3.86022 | 0.863171 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 6.76311 | 1.44190 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 4.50319 | 0.919210 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −14.4510 | −2.83407 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −3.86022 | −0.729512 | ||||||||
\(29\) | −0.288553 | −0.0535829 | −0.0267915 | − | 0.999641i | \(-0.508529\pi\) | ||||
−0.0267915 | + | 0.999641i | \(0.508529\pi\) | |||||||
\(30\) | 2.42079 | 0.441973 | ||||||||
\(31\) | 6.34817 | 1.14017 | 0.570083 | − | 0.821587i | \(-0.306911\pi\) | ||||
0.570083 | + | 0.821587i | \(0.306911\pi\) | |||||||
\(32\) | −1.30624 | −0.230913 | ||||||||
\(33\) | 2.79376 | 0.486332 | ||||||||
\(34\) | 10.8871 | 1.86713 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 3.86022 | 0.643369 | ||||||||
\(37\) | −11.0997 | −1.82477 | −0.912387 | − | 0.409328i | \(-0.865763\pi\) | ||||
−0.912387 | + | 0.409328i | \(0.865763\pi\) | |||||||
\(38\) | 20.0716 | 3.25604 | ||||||||
\(39\) | −5.96954 | −0.955891 | ||||||||
\(40\) | 4.50319 | 0.712017 | ||||||||
\(41\) | −8.10472 | −1.26575 | −0.632873 | − | 0.774256i | \(-0.718124\pi\) | ||||
−0.632873 | + | 0.774256i | \(0.718124\pi\) | |||||||
\(42\) | −2.42079 | −0.373536 | ||||||||
\(43\) | −0.264436 | −0.0403261 | −0.0201630 | − | 0.999797i | \(-0.506419\pi\) | ||||
−0.0201630 | + | 0.999797i | \(0.506419\pi\) | |||||||
\(44\) | 10.7845 | 1.62583 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 2.42079 | 0.356926 | ||||||||
\(47\) | 3.28997 | 0.479892 | 0.239946 | − | 0.970786i | \(-0.422870\pi\) | ||||
0.239946 | + | 0.970786i | \(0.422870\pi\) | |||||||
\(48\) | 3.18084 | 0.459115 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.42079 | 0.342351 | ||||||||
\(51\) | 4.49734 | 0.629754 | ||||||||
\(52\) | −23.0437 | −3.19559 | ||||||||
\(53\) | −4.34703 | −0.597110 | −0.298555 | − | 0.954392i | \(-0.596505\pi\) | ||||
−0.298555 | + | 0.954392i | \(0.596505\pi\) | |||||||
\(54\) | 2.42079 | 0.329428 | ||||||||
\(55\) | 2.79376 | 0.376711 | ||||||||
\(56\) | −4.50319 | −0.601764 | ||||||||
\(57\) | 8.29134 | 1.09821 | ||||||||
\(58\) | −0.698525 | −0.0917209 | ||||||||
\(59\) | 15.0558 | 1.96010 | 0.980049 | − | 0.198757i | \(-0.0636905\pi\) | ||||
0.980049 | + | 0.198757i | \(0.0636905\pi\) | |||||||
\(60\) | 3.86022 | 0.498352 | ||||||||
\(61\) | −7.31629 | −0.936755 | −0.468378 | − | 0.883528i | \(-0.655161\pi\) | ||||
−0.468378 | + | 0.883528i | \(0.655161\pi\) | |||||||
\(62\) | 15.3676 | 1.95168 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −9.52381 | −1.19048 | ||||||||
\(65\) | −5.96954 | −0.740430 | ||||||||
\(66\) | 6.76311 | 0.832482 | ||||||||
\(67\) | 2.53462 | 0.309654 | 0.154827 | − | 0.987942i | \(-0.450518\pi\) | ||||
0.154827 | + | 0.987942i | \(0.450518\pi\) | |||||||
\(68\) | 17.3607 | 2.10530 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | −2.42079 | −0.289340 | ||||||||
\(71\) | 10.2719 | 1.21905 | 0.609527 | − | 0.792765i | \(-0.291359\pi\) | ||||
0.609527 | + | 0.792765i | \(0.291359\pi\) | |||||||
\(72\) | 4.50319 | 0.530706 | ||||||||
\(73\) | −4.95971 | −0.580491 | −0.290245 | − | 0.956952i | \(-0.593737\pi\) | ||||
−0.290245 | + | 0.956952i | \(0.593737\pi\) | |||||||
\(74\) | −26.8699 | −3.12357 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 32.0064 | 3.67138 | ||||||||
\(77\) | −2.79376 | −0.318379 | ||||||||
\(78\) | −14.4510 | −1.63625 | ||||||||
\(79\) | −16.7403 | −1.88344 | −0.941718 | − | 0.336404i | \(-0.890789\pi\) | ||||
−0.941718 | + | 0.336404i | \(0.890789\pi\) | |||||||
\(80\) | 3.18084 | 0.355629 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −19.6198 | −2.16665 | ||||||||
\(83\) | 3.16745 | 0.347672 | 0.173836 | − | 0.984775i | \(-0.444384\pi\) | ||||
0.173836 | + | 0.984775i | \(0.444384\pi\) | |||||||
\(84\) | −3.86022 | −0.421184 | ||||||||
\(85\) | 4.49734 | 0.487805 | ||||||||
\(86\) | −0.640143 | −0.0690284 | ||||||||
\(87\) | −0.288553 | −0.0309361 | ||||||||
\(88\) | 12.5809 | 1.34112 | ||||||||
\(89\) | 3.44448 | 0.365114 | 0.182557 | − | 0.983195i | \(-0.441563\pi\) | ||||
0.182557 | + | 0.983195i | \(0.441563\pi\) | |||||||
\(90\) | 2.42079 | 0.255174 | ||||||||
\(91\) | 5.96954 | 0.625778 | ||||||||
\(92\) | 3.86022 | 0.402455 | ||||||||
\(93\) | 6.34817 | 0.658275 | ||||||||
\(94\) | 7.96433 | 0.821457 | ||||||||
\(95\) | 8.29134 | 0.850673 | ||||||||
\(96\) | −1.30624 | −0.133318 | ||||||||
\(97\) | −8.27346 | −0.840042 | −0.420021 | − | 0.907514i | \(-0.637977\pi\) | ||||
−0.420021 | + | 0.907514i | \(0.637977\pi\) | |||||||
\(98\) | 2.42079 | 0.244537 | ||||||||
\(99\) | 2.79376 | 0.280784 | ||||||||
\(100\) | 3.86022 | 0.386022 | ||||||||
\(101\) | −2.75695 | −0.274327 | −0.137164 | − | 0.990548i | \(-0.543799\pi\) | ||||
−0.137164 | + | 0.990548i | \(0.543799\pi\) | |||||||
\(102\) | 10.8871 | 1.07799 | ||||||||
\(103\) | −9.83291 | −0.968865 | −0.484433 | − | 0.874829i | \(-0.660974\pi\) | ||||
−0.484433 | + | 0.874829i | \(0.660974\pi\) | |||||||
\(104\) | −26.8820 | −2.63599 | ||||||||
\(105\) | −1.00000 | −0.0975900 | ||||||||
\(106\) | −10.5232 | −1.02211 | ||||||||
\(107\) | −17.4587 | −1.68779 | −0.843896 | − | 0.536507i | \(-0.819743\pi\) | ||||
−0.843896 | + | 0.536507i | \(0.819743\pi\) | |||||||
\(108\) | 3.86022 | 0.371450 | ||||||||
\(109\) | −1.08674 | −0.104091 | −0.0520456 | − | 0.998645i | \(-0.516574\pi\) | ||||
−0.0520456 | + | 0.998645i | \(0.516574\pi\) | |||||||
\(110\) | 6.76311 | 0.644837 | ||||||||
\(111\) | −11.0997 | −1.05353 | ||||||||
\(112\) | −3.18084 | −0.300561 | ||||||||
\(113\) | −14.1873 | −1.33463 | −0.667315 | − | 0.744775i | \(-0.732557\pi\) | ||||
−0.667315 | + | 0.744775i | \(0.732557\pi\) | |||||||
\(114\) | 20.0716 | 1.87987 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | −1.11388 | −0.103421 | ||||||||
\(117\) | −5.96954 | −0.551884 | ||||||||
\(118\) | 36.4469 | 3.35521 | ||||||||
\(119\) | −4.49734 | −0.412271 | ||||||||
\(120\) | 4.50319 | 0.411083 | ||||||||
\(121\) | −3.19488 | −0.290444 | ||||||||
\(122\) | −17.7112 | −1.60350 | ||||||||
\(123\) | −8.10472 | −0.730778 | ||||||||
\(124\) | 24.5053 | 2.20064 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −2.42079 | −0.215661 | ||||||||
\(127\) | −21.4471 | −1.90312 | −0.951562 | − | 0.307457i | \(-0.900522\pi\) | ||||
−0.951562 | + | 0.307457i | \(0.900522\pi\) | |||||||
\(128\) | −20.4427 | −1.80689 | ||||||||
\(129\) | −0.264436 | −0.0232823 | ||||||||
\(130\) | −14.4510 | −1.26744 | ||||||||
\(131\) | −5.79445 | −0.506264 | −0.253132 | − | 0.967432i | \(-0.581461\pi\) | ||||
−0.253132 | + | 0.967432i | \(0.581461\pi\) | |||||||
\(132\) | 10.7845 | 0.938673 | ||||||||
\(133\) | −8.29134 | −0.718950 | ||||||||
\(134\) | 6.13579 | 0.530051 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 20.2524 | 1.73663 | ||||||||
\(137\) | 6.13504 | 0.524152 | 0.262076 | − | 0.965047i | \(-0.415593\pi\) | ||||
0.262076 | + | 0.965047i | \(0.415593\pi\) | |||||||
\(138\) | 2.42079 | 0.206071 | ||||||||
\(139\) | −3.58042 | −0.303687 | −0.151843 | − | 0.988405i | \(-0.548521\pi\) | ||||
−0.151843 | + | 0.988405i | \(0.548521\pi\) | |||||||
\(140\) | −3.86022 | −0.326248 | ||||||||
\(141\) | 3.28997 | 0.277066 | ||||||||
\(142\) | 24.8662 | 2.08672 | ||||||||
\(143\) | −16.6775 | −1.39464 | ||||||||
\(144\) | 3.18084 | 0.265070 | ||||||||
\(145\) | −0.288553 | −0.0239630 | ||||||||
\(146\) | −12.0064 | −0.993658 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −42.8471 | −3.52201 | ||||||||
\(149\) | −0.559790 | −0.0458598 | −0.0229299 | − | 0.999737i | \(-0.507299\pi\) | ||||
−0.0229299 | + | 0.999737i | \(0.507299\pi\) | |||||||
\(150\) | 2.42079 | 0.197657 | ||||||||
\(151\) | 1.60558 | 0.130660 | 0.0653301 | − | 0.997864i | \(-0.479190\pi\) | ||||
0.0653301 | + | 0.997864i | \(0.479190\pi\) | |||||||
\(152\) | 37.3375 | 3.02847 | ||||||||
\(153\) | 4.49734 | 0.363589 | ||||||||
\(154\) | −6.76311 | −0.544987 | ||||||||
\(155\) | 6.34817 | 0.509897 | ||||||||
\(156\) | −23.0437 | −1.84497 | ||||||||
\(157\) | 2.55686 | 0.204059 | 0.102030 | − | 0.994781i | \(-0.467466\pi\) | ||||
0.102030 | + | 0.994781i | \(0.467466\pi\) | |||||||
\(158\) | −40.5248 | −3.22398 | ||||||||
\(159\) | −4.34703 | −0.344742 | ||||||||
\(160\) | −1.30624 | −0.103267 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 2.42079 | 0.190195 | ||||||||
\(163\) | 3.77275 | 0.295504 | 0.147752 | − | 0.989024i | \(-0.452796\pi\) | ||||
0.147752 | + | 0.989024i | \(0.452796\pi\) | |||||||
\(164\) | −31.2860 | −2.44303 | ||||||||
\(165\) | 2.79376 | 0.217494 | ||||||||
\(166\) | 7.66771 | 0.595130 | ||||||||
\(167\) | 10.5700 | 0.817933 | 0.408966 | − | 0.912549i | \(-0.365889\pi\) | ||||
0.408966 | + | 0.912549i | \(0.365889\pi\) | |||||||
\(168\) | −4.50319 | −0.347429 | ||||||||
\(169\) | 22.6354 | 1.74118 | ||||||||
\(170\) | 10.8871 | 0.835004 | ||||||||
\(171\) | 8.29134 | 0.634054 | ||||||||
\(172\) | −1.02078 | −0.0778337 | ||||||||
\(173\) | −5.38268 | −0.409237 | −0.204619 | − | 0.978842i | \(-0.565595\pi\) | ||||
−0.204619 | + | 0.978842i | \(0.565595\pi\) | |||||||
\(174\) | −0.698525 | −0.0529551 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 8.88652 | 0.669847 | ||||||||
\(177\) | 15.0558 | 1.13166 | ||||||||
\(178\) | 8.33835 | 0.624986 | ||||||||
\(179\) | 12.0616 | 0.901523 | 0.450761 | − | 0.892645i | \(-0.351153\pi\) | ||||
0.450761 | + | 0.892645i | \(0.351153\pi\) | |||||||
\(180\) | 3.86022 | 0.287724 | ||||||||
\(181\) | −4.12989 | −0.306972 | −0.153486 | − | 0.988151i | \(-0.549050\pi\) | ||||
−0.153486 | + | 0.988151i | \(0.549050\pi\) | |||||||
\(182\) | 14.4510 | 1.07118 | ||||||||
\(183\) | −7.31629 | −0.540836 | ||||||||
\(184\) | 4.50319 | 0.331980 | ||||||||
\(185\) | −11.0997 | −0.816064 | ||||||||
\(186\) | 15.3676 | 1.12681 | ||||||||
\(187\) | 12.5645 | 0.918809 | ||||||||
\(188\) | 12.7000 | 0.926243 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 20.0716 | 1.45614 | ||||||||
\(191\) | 13.4946 | 0.976437 | 0.488218 | − | 0.872722i | \(-0.337647\pi\) | ||||
0.488218 | + | 0.872722i | \(0.337647\pi\) | |||||||
\(192\) | −9.52381 | −0.687322 | ||||||||
\(193\) | 25.4725 | 1.83355 | 0.916776 | − | 0.399401i | \(-0.130782\pi\) | ||||
0.916776 | + | 0.399401i | \(0.130782\pi\) | |||||||
\(194\) | −20.0283 | −1.43795 | ||||||||
\(195\) | −5.96954 | −0.427488 | ||||||||
\(196\) | 3.86022 | 0.275730 | ||||||||
\(197\) | 8.22859 | 0.586263 | 0.293131 | − | 0.956072i | \(-0.405303\pi\) | ||||
0.293131 | + | 0.956072i | \(0.405303\pi\) | |||||||
\(198\) | 6.76311 | 0.480633 | ||||||||
\(199\) | 23.1526 | 1.64124 | 0.820621 | − | 0.571473i | \(-0.193628\pi\) | ||||
0.820621 | + | 0.571473i | \(0.193628\pi\) | |||||||
\(200\) | 4.50319 | 0.318424 | ||||||||
\(201\) | 2.53462 | 0.178779 | ||||||||
\(202\) | −6.67400 | −0.469581 | ||||||||
\(203\) | 0.288553 | 0.0202524 | ||||||||
\(204\) | 17.3607 | 1.21549 | ||||||||
\(205\) | −8.10472 | −0.566058 | ||||||||
\(206\) | −23.8034 | −1.65846 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | −18.9882 | −1.31659 | ||||||||
\(209\) | 23.1640 | 1.60229 | ||||||||
\(210\) | −2.42079 | −0.167050 | ||||||||
\(211\) | −20.3171 | −1.39869 | −0.699344 | − | 0.714785i | \(-0.746525\pi\) | ||||
−0.699344 | + | 0.714785i | \(0.746525\pi\) | |||||||
\(212\) | −16.7805 | −1.15249 | ||||||||
\(213\) | 10.2719 | 0.703821 | ||||||||
\(214\) | −42.2637 | −2.88909 | ||||||||
\(215\) | −0.264436 | −0.0180344 | ||||||||
\(216\) | 4.50319 | 0.306403 | ||||||||
\(217\) | −6.34817 | −0.430942 | ||||||||
\(218\) | −2.63078 | −0.178179 | ||||||||
\(219\) | −4.95971 | −0.335146 | ||||||||
\(220\) | 10.7845 | 0.727093 | ||||||||
\(221\) | −26.8471 | −1.80593 | ||||||||
\(222\) | −26.8699 | −1.80339 | ||||||||
\(223\) | 8.26387 | 0.553390 | 0.276695 | − | 0.960958i | \(-0.410761\pi\) | ||||
0.276695 | + | 0.960958i | \(0.410761\pi\) | |||||||
\(224\) | 1.30624 | 0.0872769 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −34.3445 | −2.28456 | ||||||||
\(227\) | 3.84124 | 0.254952 | 0.127476 | − | 0.991842i | \(-0.459312\pi\) | ||||
0.127476 | + | 0.991842i | \(0.459312\pi\) | |||||||
\(228\) | 32.0064 | 2.11967 | ||||||||
\(229\) | 4.48106 | 0.296117 | 0.148058 | − | 0.988979i | \(-0.452698\pi\) | ||||
0.148058 | + | 0.988979i | \(0.452698\pi\) | |||||||
\(230\) | 2.42079 | 0.159622 | ||||||||
\(231\) | −2.79376 | −0.183816 | ||||||||
\(232\) | −1.29941 | −0.0853103 | ||||||||
\(233\) | 8.03925 | 0.526669 | 0.263334 | − | 0.964705i | \(-0.415178\pi\) | ||||
0.263334 | + | 0.964705i | \(0.415178\pi\) | |||||||
\(234\) | −14.4510 | −0.944691 | ||||||||
\(235\) | 3.28997 | 0.214614 | ||||||||
\(236\) | 58.1186 | 3.78320 | ||||||||
\(237\) | −16.7403 | −1.08740 | ||||||||
\(238\) | −10.8871 | −0.705707 | ||||||||
\(239\) | −14.3411 | −0.927650 | −0.463825 | − | 0.885927i | \(-0.653523\pi\) | ||||
−0.463825 | + | 0.885927i | \(0.653523\pi\) | |||||||
\(240\) | 3.18084 | 0.205322 | ||||||||
\(241\) | 19.4913 | 1.25555 | 0.627774 | − | 0.778396i | \(-0.283966\pi\) | ||||
0.627774 | + | 0.778396i | \(0.283966\pi\) | |||||||
\(242\) | −7.73413 | −0.497169 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −28.2425 | −1.80804 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −19.6198 | −1.25091 | ||||||||
\(247\) | −49.4955 | −3.14932 | ||||||||
\(248\) | 28.5870 | 1.81528 | ||||||||
\(249\) | 3.16745 | 0.200729 | ||||||||
\(250\) | 2.42079 | 0.153104 | ||||||||
\(251\) | −12.2142 | −0.770956 | −0.385478 | − | 0.922717i | \(-0.625963\pi\) | ||||
−0.385478 | + | 0.922717i | \(0.625963\pi\) | |||||||
\(252\) | −3.86022 | −0.243171 | ||||||||
\(253\) | 2.79376 | 0.175642 | ||||||||
\(254\) | −51.9189 | −3.25768 | ||||||||
\(255\) | 4.49734 | 0.281635 | ||||||||
\(256\) | −30.4397 | −1.90248 | ||||||||
\(257\) | −29.3237 | −1.82916 | −0.914581 | − | 0.404403i | \(-0.867479\pi\) | ||||
−0.914581 | + | 0.404403i | \(0.867479\pi\) | |||||||
\(258\) | −0.640143 | −0.0398536 | ||||||||
\(259\) | 11.0997 | 0.689700 | ||||||||
\(260\) | −23.0437 | −1.42911 | ||||||||
\(261\) | −0.288553 | −0.0178610 | ||||||||
\(262\) | −14.0271 | −0.866600 | ||||||||
\(263\) | 4.71668 | 0.290843 | 0.145422 | − | 0.989370i | \(-0.453546\pi\) | ||||
0.145422 | + | 0.989370i | \(0.453546\pi\) | |||||||
\(264\) | 12.5809 | 0.774298 | ||||||||
\(265\) | −4.34703 | −0.267036 | ||||||||
\(266\) | −20.0716 | −1.23067 | ||||||||
\(267\) | 3.44448 | 0.210799 | ||||||||
\(268\) | 9.78420 | 0.597665 | ||||||||
\(269\) | 12.4012 | 0.756112 | 0.378056 | − | 0.925783i | \(-0.376593\pi\) | ||||
0.378056 | + | 0.925783i | \(0.376593\pi\) | |||||||
\(270\) | 2.42079 | 0.147324 | ||||||||
\(271\) | 16.9980 | 1.03255 | 0.516276 | − | 0.856422i | \(-0.327318\pi\) | ||||
0.516276 | + | 0.856422i | \(0.327318\pi\) | |||||||
\(272\) | 14.3053 | 0.867388 | ||||||||
\(273\) | 5.96954 | 0.361293 | ||||||||
\(274\) | 14.8516 | 0.897220 | ||||||||
\(275\) | 2.79376 | 0.168470 | ||||||||
\(276\) | 3.86022 | 0.232358 | ||||||||
\(277\) | 12.9327 | 0.777051 | 0.388525 | − | 0.921438i | \(-0.372985\pi\) | ||||
0.388525 | + | 0.921438i | \(0.372985\pi\) | |||||||
\(278\) | −8.66743 | −0.519838 | ||||||||
\(279\) | 6.34817 | 0.380055 | ||||||||
\(280\) | −4.50319 | −0.269117 | ||||||||
\(281\) | 3.71629 | 0.221695 | 0.110848 | − | 0.993837i | \(-0.464643\pi\) | ||||
0.110848 | + | 0.993837i | \(0.464643\pi\) | |||||||
\(282\) | 7.96433 | 0.474269 | ||||||||
\(283\) | −18.2784 | −1.08654 | −0.543269 | − | 0.839559i | \(-0.682813\pi\) | ||||
−0.543269 | + | 0.839559i | \(0.682813\pi\) | |||||||
\(284\) | 39.6519 | 2.35291 | ||||||||
\(285\) | 8.29134 | 0.491136 | ||||||||
\(286\) | −40.3727 | −2.38729 | ||||||||
\(287\) | 8.10472 | 0.478407 | ||||||||
\(288\) | −1.30624 | −0.0769710 | ||||||||
\(289\) | 3.22610 | 0.189771 | ||||||||
\(290\) | −0.698525 | −0.0410188 | ||||||||
\(291\) | −8.27346 | −0.484999 | ||||||||
\(292\) | −19.1456 | −1.12041 | ||||||||
\(293\) | −7.64958 | −0.446893 | −0.223447 | − | 0.974716i | \(-0.571731\pi\) | ||||
−0.223447 | + | 0.974716i | \(0.571731\pi\) | |||||||
\(294\) | 2.42079 | 0.141183 | ||||||||
\(295\) | 15.0558 | 0.876582 | ||||||||
\(296\) | −49.9839 | −2.90526 | ||||||||
\(297\) | 2.79376 | 0.162111 | ||||||||
\(298\) | −1.35513 | −0.0785007 | ||||||||
\(299\) | −5.96954 | −0.345227 | ||||||||
\(300\) | 3.86022 | 0.222870 | ||||||||
\(301\) | 0.264436 | 0.0152418 | ||||||||
\(302\) | 3.88677 | 0.223658 | ||||||||
\(303\) | −2.75695 | −0.158383 | ||||||||
\(304\) | 26.3734 | 1.51262 | ||||||||
\(305\) | −7.31629 | −0.418930 | ||||||||
\(306\) | 10.8871 | 0.622375 | ||||||||
\(307\) | 5.37651 | 0.306854 | 0.153427 | − | 0.988160i | \(-0.450969\pi\) | ||||
0.153427 | + | 0.988160i | \(0.450969\pi\) | |||||||
\(308\) | −10.7845 | −0.614506 | ||||||||
\(309\) | −9.83291 | −0.559374 | ||||||||
\(310\) | 15.3676 | 0.872820 | ||||||||
\(311\) | −1.60417 | −0.0909641 | −0.0454820 | − | 0.998965i | \(-0.514482\pi\) | ||||
−0.0454820 | + | 0.998965i | \(0.514482\pi\) | |||||||
\(312\) | −26.8820 | −1.52189 | ||||||||
\(313\) | 17.6416 | 0.997165 | 0.498582 | − | 0.866842i | \(-0.333854\pi\) | ||||
0.498582 | + | 0.866842i | \(0.333854\pi\) | |||||||
\(314\) | 6.18961 | 0.349300 | ||||||||
\(315\) | −1.00000 | −0.0563436 | ||||||||
\(316\) | −64.6213 | −3.63523 | ||||||||
\(317\) | −29.4338 | −1.65317 | −0.826583 | − | 0.562815i | \(-0.809718\pi\) | ||||
−0.826583 | + | 0.562815i | \(0.809718\pi\) | |||||||
\(318\) | −10.5232 | −0.590114 | ||||||||
\(319\) | −0.806148 | −0.0451356 | ||||||||
\(320\) | −9.52381 | −0.532397 | ||||||||
\(321\) | −17.4587 | −0.974447 | ||||||||
\(322\) | −2.42079 | −0.134905 | ||||||||
\(323\) | 37.2890 | 2.07481 | ||||||||
\(324\) | 3.86022 | 0.214456 | ||||||||
\(325\) | −5.96954 | −0.331130 | ||||||||
\(326\) | 9.13302 | 0.505831 | ||||||||
\(327\) | −1.08674 | −0.0600970 | ||||||||
\(328\) | −36.4971 | −2.01522 | ||||||||
\(329\) | −3.28997 | −0.181382 | ||||||||
\(330\) | 6.76311 | 0.372297 | ||||||||
\(331\) | 21.8291 | 1.19984 | 0.599918 | − | 0.800062i | \(-0.295200\pi\) | ||||
0.599918 | + | 0.800062i | \(0.295200\pi\) | |||||||
\(332\) | 12.2270 | 0.671045 | ||||||||
\(333\) | −11.0997 | −0.608258 | ||||||||
\(334\) | 25.5878 | 1.40010 | ||||||||
\(335\) | 2.53462 | 0.138481 | ||||||||
\(336\) | −3.18084 | −0.173529 | ||||||||
\(337\) | −4.31057 | −0.234812 | −0.117406 | − | 0.993084i | \(-0.537458\pi\) | ||||
−0.117406 | + | 0.993084i | \(0.537458\pi\) | |||||||
\(338\) | 54.7955 | 2.98048 | ||||||||
\(339\) | −14.1873 | −0.770549 | ||||||||
\(340\) | 17.3607 | 0.941517 | ||||||||
\(341\) | 17.7353 | 0.960420 | ||||||||
\(342\) | 20.0716 | 1.08535 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −1.19081 | −0.0642039 | ||||||||
\(345\) | 1.00000 | 0.0538382 | ||||||||
\(346\) | −13.0303 | −0.700514 | ||||||||
\(347\) | 10.9707 | 0.588937 | 0.294468 | − | 0.955661i | \(-0.404857\pi\) | ||||
0.294468 | + | 0.955661i | \(0.404857\pi\) | |||||||
\(348\) | −1.11388 | −0.0597100 | ||||||||
\(349\) | −20.1266 | −1.07735 | −0.538675 | − | 0.842514i | \(-0.681075\pi\) | ||||
−0.538675 | + | 0.842514i | \(0.681075\pi\) | |||||||
\(350\) | −2.42079 | −0.129397 | ||||||||
\(351\) | −5.96954 | −0.318630 | ||||||||
\(352\) | −3.64933 | −0.194510 | ||||||||
\(353\) | 31.7434 | 1.68953 | 0.844766 | − | 0.535136i | \(-0.179740\pi\) | ||||
0.844766 | + | 0.535136i | \(0.179740\pi\) | |||||||
\(354\) | 36.4469 | 1.93713 | ||||||||
\(355\) | 10.2719 | 0.545178 | ||||||||
\(356\) | 13.2964 | 0.704709 | ||||||||
\(357\) | −4.49734 | −0.238025 | ||||||||
\(358\) | 29.1985 | 1.54319 | ||||||||
\(359\) | −19.5016 | −1.02926 | −0.514628 | − | 0.857413i | \(-0.672070\pi\) | ||||
−0.514628 | + | 0.857413i | \(0.672070\pi\) | |||||||
\(360\) | 4.50319 | 0.237339 | ||||||||
\(361\) | 49.7463 | 2.61822 | ||||||||
\(362\) | −9.99759 | −0.525462 | ||||||||
\(363\) | −3.19488 | −0.167688 | ||||||||
\(364\) | 23.0437 | 1.20782 | ||||||||
\(365\) | −4.95971 | −0.259603 | ||||||||
\(366\) | −17.7112 | −0.925779 | ||||||||
\(367\) | −33.4821 | −1.74775 | −0.873877 | − | 0.486148i | \(-0.838402\pi\) | ||||
−0.873877 | + | 0.486148i | \(0.838402\pi\) | |||||||
\(368\) | 3.18084 | 0.165813 | ||||||||
\(369\) | −8.10472 | −0.421915 | ||||||||
\(370\) | −26.8699 | −1.39690 | ||||||||
\(371\) | 4.34703 | 0.225687 | ||||||||
\(372\) | 24.5053 | 1.27054 | ||||||||
\(373\) | 25.9151 | 1.34183 | 0.670917 | − | 0.741532i | \(-0.265901\pi\) | ||||
0.670917 | + | 0.741532i | \(0.265901\pi\) | |||||||
\(374\) | 30.4160 | 1.57278 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 14.8154 | 0.764045 | ||||||||
\(377\) | 1.72253 | 0.0887147 | ||||||||
\(378\) | −2.42079 | −0.124512 | ||||||||
\(379\) | 14.6127 | 0.750606 | 0.375303 | − | 0.926902i | \(-0.377539\pi\) | ||||
0.375303 | + | 0.926902i | \(0.377539\pi\) | |||||||
\(380\) | 32.0064 | 1.64189 | ||||||||
\(381\) | −21.4471 | −1.09877 | ||||||||
\(382\) | 32.6676 | 1.67142 | ||||||||
\(383\) | 36.0618 | 1.84267 | 0.921337 | − | 0.388765i | \(-0.127098\pi\) | ||||
0.921337 | + | 0.388765i | \(0.127098\pi\) | |||||||
\(384\) | −20.4427 | −1.04321 | ||||||||
\(385\) | −2.79376 | −0.142383 | ||||||||
\(386\) | 61.6636 | 3.13859 | ||||||||
\(387\) | −0.264436 | −0.0134420 | ||||||||
\(388\) | −31.9373 | −1.62137 | ||||||||
\(389\) | −15.7703 | −0.799587 | −0.399793 | − | 0.916605i | \(-0.630918\pi\) | ||||
−0.399793 | + | 0.916605i | \(0.630918\pi\) | |||||||
\(390\) | −14.4510 | −0.731754 | ||||||||
\(391\) | 4.49734 | 0.227440 | ||||||||
\(392\) | 4.50319 | 0.227446 | ||||||||
\(393\) | −5.79445 | −0.292292 | ||||||||
\(394\) | 19.9197 | 1.00354 | ||||||||
\(395\) | −16.7403 | −0.842298 | ||||||||
\(396\) | 10.7845 | 0.541943 | ||||||||
\(397\) | 21.5785 | 1.08299 | 0.541496 | − | 0.840703i | \(-0.317858\pi\) | ||||
0.541496 | + | 0.840703i | \(0.317858\pi\) | |||||||
\(398\) | 56.0475 | 2.80941 | ||||||||
\(399\) | −8.29134 | −0.415086 | ||||||||
\(400\) | 3.18084 | 0.159042 | ||||||||
\(401\) | −36.1057 | −1.80303 | −0.901515 | − | 0.432747i | \(-0.857544\pi\) | ||||
−0.901515 | + | 0.432747i | \(0.857544\pi\) | |||||||
\(402\) | 6.13579 | 0.306025 | ||||||||
\(403\) | −37.8957 | −1.88772 | ||||||||
\(404\) | −10.6424 | −0.529481 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0.698525 | 0.0346672 | ||||||||
\(407\) | −31.0099 | −1.53710 | ||||||||
\(408\) | 20.2524 | 1.00264 | ||||||||
\(409\) | 15.4516 | 0.764034 | 0.382017 | − | 0.924155i | \(-0.375230\pi\) | ||||
0.382017 | + | 0.924155i | \(0.375230\pi\) | |||||||
\(410\) | −19.6198 | −0.968954 | ||||||||
\(411\) | 6.13504 | 0.302619 | ||||||||
\(412\) | −37.9571 | −1.87001 | ||||||||
\(413\) | −15.0558 | −0.740847 | ||||||||
\(414\) | 2.42079 | 0.118975 | ||||||||
\(415\) | 3.16745 | 0.155484 | ||||||||
\(416\) | 7.79766 | 0.382312 | ||||||||
\(417\) | −3.58042 | −0.175334 | ||||||||
\(418\) | 56.0752 | 2.74273 | ||||||||
\(419\) | −28.0334 | −1.36952 | −0.684762 | − | 0.728767i | \(-0.740094\pi\) | ||||
−0.684762 | + | 0.728767i | \(0.740094\pi\) | |||||||
\(420\) | −3.86022 | −0.188359 | ||||||||
\(421\) | −38.2570 | −1.86453 | −0.932266 | − | 0.361773i | \(-0.882172\pi\) | ||||
−0.932266 | + | 0.361773i | \(0.882172\pi\) | |||||||
\(422\) | −49.1835 | −2.39421 | ||||||||
\(423\) | 3.28997 | 0.159964 | ||||||||
\(424\) | −19.5755 | −0.950671 | ||||||||
\(425\) | 4.49734 | 0.218153 | ||||||||
\(426\) | 24.8662 | 1.20477 | ||||||||
\(427\) | 7.31629 | 0.354060 | ||||||||
\(428\) | −67.3942 | −3.25762 | ||||||||
\(429\) | −16.6775 | −0.805197 | ||||||||
\(430\) | −0.640143 | −0.0308704 | ||||||||
\(431\) | −9.32940 | −0.449381 | −0.224691 | − | 0.974430i | \(-0.572137\pi\) | ||||
−0.224691 | + | 0.974430i | \(0.572137\pi\) | |||||||
\(432\) | 3.18084 | 0.153038 | ||||||||
\(433\) | 19.5167 | 0.937913 | 0.468956 | − | 0.883221i | \(-0.344630\pi\) | ||||
0.468956 | + | 0.883221i | \(0.344630\pi\) | |||||||
\(434\) | −15.3676 | −0.737668 | ||||||||
\(435\) | −0.288553 | −0.0138350 | ||||||||
\(436\) | −4.19507 | −0.200907 | ||||||||
\(437\) | 8.29134 | 0.396628 | ||||||||
\(438\) | −12.0064 | −0.573689 | ||||||||
\(439\) | −9.86736 | −0.470943 | −0.235472 | − | 0.971881i | \(-0.575663\pi\) | ||||
−0.235472 | + | 0.971881i | \(0.575663\pi\) | |||||||
\(440\) | 12.5809 | 0.599769 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −64.9911 | −3.09131 | ||||||||
\(443\) | −2.02873 | −0.0963878 | −0.0481939 | − | 0.998838i | \(-0.515347\pi\) | ||||
−0.0481939 | + | 0.998838i | \(0.515347\pi\) | |||||||
\(444\) | −42.8471 | −2.03343 | ||||||||
\(445\) | 3.44448 | 0.163284 | ||||||||
\(446\) | 20.0051 | 0.947268 | ||||||||
\(447\) | −0.559790 | −0.0264771 | ||||||||
\(448\) | 9.52381 | 0.449958 | ||||||||
\(449\) | 32.1591 | 1.51768 | 0.758840 | − | 0.651277i | \(-0.225766\pi\) | ||||
0.758840 | + | 0.651277i | \(0.225766\pi\) | |||||||
\(450\) | 2.42079 | 0.114117 | ||||||||
\(451\) | −22.6427 | −1.06620 | ||||||||
\(452\) | −54.7661 | −2.57598 | ||||||||
\(453\) | 1.60558 | 0.0754367 | ||||||||
\(454\) | 9.29882 | 0.436415 | ||||||||
\(455\) | 5.96954 | 0.279856 | ||||||||
\(456\) | 37.3375 | 1.74849 | ||||||||
\(457\) | −2.49748 | −0.116827 | −0.0584137 | − | 0.998292i | \(-0.518604\pi\) | ||||
−0.0584137 | + | 0.998292i | \(0.518604\pi\) | |||||||
\(458\) | 10.8477 | 0.506880 | ||||||||
\(459\) | 4.49734 | 0.209918 | ||||||||
\(460\) | 3.86022 | 0.179984 | ||||||||
\(461\) | 35.4061 | 1.64903 | 0.824513 | − | 0.565843i | \(-0.191449\pi\) | ||||
0.824513 | + | 0.565843i | \(0.191449\pi\) | |||||||
\(462\) | −6.76311 | −0.314648 | ||||||||
\(463\) | 19.0753 | 0.886502 | 0.443251 | − | 0.896397i | \(-0.353825\pi\) | ||||
0.443251 | + | 0.896397i | \(0.353825\pi\) | |||||||
\(464\) | −0.917840 | −0.0426097 | ||||||||
\(465\) | 6.34817 | 0.294389 | ||||||||
\(466\) | 19.4613 | 0.901528 | ||||||||
\(467\) | −11.1303 | −0.515049 | −0.257525 | − | 0.966272i | \(-0.582907\pi\) | ||||
−0.257525 | + | 0.966272i | \(0.582907\pi\) | |||||||
\(468\) | −23.0437 | −1.06520 | ||||||||
\(469\) | −2.53462 | −0.117038 | ||||||||
\(470\) | 7.96433 | 0.367367 | ||||||||
\(471\) | 2.55686 | 0.117814 | ||||||||
\(472\) | 67.7991 | 3.12071 | ||||||||
\(473\) | −0.738771 | −0.0339687 | ||||||||
\(474\) | −40.5248 | −1.86137 | ||||||||
\(475\) | 8.29134 | 0.380433 | ||||||||
\(476\) | −17.3607 | −0.795727 | ||||||||
\(477\) | −4.34703 | −0.199037 | ||||||||
\(478\) | −34.7168 | −1.58791 | ||||||||
\(479\) | 0.243772 | 0.0111382 | 0.00556912 | − | 0.999984i | \(-0.498227\pi\) | ||||
0.00556912 | + | 0.999984i | \(0.498227\pi\) | |||||||
\(480\) | −1.30624 | −0.0596215 | ||||||||
\(481\) | 66.2599 | 3.02119 | ||||||||
\(482\) | 47.1844 | 2.14919 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | −12.3329 | −0.560588 | ||||||||
\(485\) | −8.27346 | −0.375678 | ||||||||
\(486\) | 2.42079 | 0.109809 | ||||||||
\(487\) | −41.3260 | −1.87266 | −0.936329 | − | 0.351124i | \(-0.885799\pi\) | ||||
−0.936329 | + | 0.351124i | \(0.885799\pi\) | |||||||
\(488\) | −32.9467 | −1.49143 | ||||||||
\(489\) | 3.77275 | 0.170610 | ||||||||
\(490\) | 2.42079 | 0.109360 | ||||||||
\(491\) | −26.1570 | −1.18045 | −0.590225 | − | 0.807239i | \(-0.700961\pi\) | ||||
−0.590225 | + | 0.807239i | \(0.700961\pi\) | |||||||
\(492\) | −31.2860 | −1.41048 | ||||||||
\(493\) | −1.29772 | −0.0584464 | ||||||||
\(494\) | −119.818 | −5.39087 | ||||||||
\(495\) | 2.79376 | 0.125570 | ||||||||
\(496\) | 20.1925 | 0.906671 | ||||||||
\(497\) | −10.2719 | −0.460759 | ||||||||
\(498\) | 7.66771 | 0.343599 | ||||||||
\(499\) | 6.49734 | 0.290861 | 0.145431 | − | 0.989368i | \(-0.453543\pi\) | ||||
0.145431 | + | 0.989368i | \(0.453543\pi\) | |||||||
\(500\) | 3.86022 | 0.172634 | ||||||||
\(501\) | 10.5700 | 0.472234 | ||||||||
\(502\) | −29.5681 | −1.31969 | ||||||||
\(503\) | 15.8641 | 0.707343 | 0.353672 | − | 0.935370i | \(-0.384933\pi\) | ||||
0.353672 | + | 0.935370i | \(0.384933\pi\) | |||||||
\(504\) | −4.50319 | −0.200588 | ||||||||
\(505\) | −2.75695 | −0.122683 | ||||||||
\(506\) | 6.76311 | 0.300657 | ||||||||
\(507\) | 22.6354 | 1.00527 | ||||||||
\(508\) | −82.7905 | −3.67324 | ||||||||
\(509\) | −26.3048 | −1.16594 | −0.582969 | − | 0.812494i | \(-0.698109\pi\) | ||||
−0.582969 | + | 0.812494i | \(0.698109\pi\) | |||||||
\(510\) | 10.8871 | 0.482090 | ||||||||
\(511\) | 4.95971 | 0.219405 | ||||||||
\(512\) | −32.8028 | −1.44969 | ||||||||
\(513\) | 8.29134 | 0.366071 | ||||||||
\(514\) | −70.9865 | −3.13108 | ||||||||
\(515\) | −9.83291 | −0.433290 | ||||||||
\(516\) | −1.02078 | −0.0449373 | ||||||||
\(517\) | 9.19141 | 0.404238 | ||||||||
\(518\) | 26.8699 | 1.18060 | ||||||||
\(519\) | −5.38268 | −0.236273 | ||||||||
\(520\) | −26.8820 | −1.17885 | ||||||||
\(521\) | −6.67223 | −0.292316 | −0.146158 | − | 0.989261i | \(-0.546691\pi\) | ||||
−0.146158 | + | 0.989261i | \(0.546691\pi\) | |||||||
\(522\) | −0.698525 | −0.0305736 | ||||||||
\(523\) | 16.6224 | 0.726849 | 0.363424 | − | 0.931624i | \(-0.381607\pi\) | ||||
0.363424 | + | 0.931624i | \(0.381607\pi\) | |||||||
\(524\) | −22.3679 | −0.977144 | ||||||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | 11.4181 | 0.497852 | ||||||||
\(527\) | 28.5499 | 1.24365 | ||||||||
\(528\) | 8.88652 | 0.386736 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −10.5232 | −0.457100 | ||||||||
\(531\) | 15.0558 | 0.653366 | ||||||||
\(532\) | −32.0064 | −1.38765 | ||||||||
\(533\) | 48.3815 | 2.09563 | ||||||||
\(534\) | 8.33835 | 0.360836 | ||||||||
\(535\) | −17.4587 | −0.754803 | ||||||||
\(536\) | 11.4139 | 0.493005 | ||||||||
\(537\) | 12.0616 | 0.520494 | ||||||||
\(538\) | 30.0206 | 1.29428 | ||||||||
\(539\) | 2.79376 | 0.120336 | ||||||||
\(540\) | 3.86022 | 0.166117 | ||||||||
\(541\) | 3.08409 | 0.132595 | 0.0662977 | − | 0.997800i | \(-0.478881\pi\) | ||||
0.0662977 | + | 0.997800i | \(0.478881\pi\) | |||||||
\(542\) | 41.1485 | 1.76748 | ||||||||
\(543\) | −4.12989 | −0.177230 | ||||||||
\(544\) | −5.87462 | −0.251872 | ||||||||
\(545\) | −1.08674 | −0.0465510 | ||||||||
\(546\) | 14.4510 | 0.618445 | ||||||||
\(547\) | −2.77692 | −0.118733 | −0.0593663 | − | 0.998236i | \(-0.518908\pi\) | ||||
−0.0593663 | + | 0.998236i | \(0.518908\pi\) | |||||||
\(548\) | 23.6826 | 1.01167 | ||||||||
\(549\) | −7.31629 | −0.312252 | ||||||||
\(550\) | 6.76311 | 0.288380 | ||||||||
\(551\) | −2.39249 | −0.101923 | ||||||||
\(552\) | 4.50319 | 0.191669 | ||||||||
\(553\) | 16.7403 | 0.711872 | ||||||||
\(554\) | 31.3073 | 1.33012 | ||||||||
\(555\) | −11.0997 | −0.471155 | ||||||||
\(556\) | −13.8212 | −0.586149 | ||||||||
\(557\) | −8.98627 | −0.380761 | −0.190380 | − | 0.981710i | \(-0.560972\pi\) | ||||
−0.190380 | + | 0.981710i | \(0.560972\pi\) | |||||||
\(558\) | 15.3676 | 0.650562 | ||||||||
\(559\) | 1.57856 | 0.0667660 | ||||||||
\(560\) | −3.18084 | −0.134415 | ||||||||
\(561\) | 12.5645 | 0.530474 | ||||||||
\(562\) | 8.99636 | 0.379489 | ||||||||
\(563\) | −17.6416 | −0.743505 | −0.371752 | − | 0.928332i | \(-0.621243\pi\) | ||||
−0.371752 | + | 0.928332i | \(0.621243\pi\) | |||||||
\(564\) | 12.7000 | 0.534767 | ||||||||
\(565\) | −14.1873 | −0.596865 | ||||||||
\(566\) | −44.2481 | −1.85989 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 46.2565 | 1.94088 | ||||||||
\(569\) | 19.0859 | 0.800123 | 0.400061 | − | 0.916488i | \(-0.368989\pi\) | ||||
0.400061 | + | 0.916488i | \(0.368989\pi\) | |||||||
\(570\) | 20.0716 | 0.840706 | ||||||||
\(571\) | −22.0717 | −0.923671 | −0.461836 | − | 0.886966i | \(-0.652809\pi\) | ||||
−0.461836 | + | 0.886966i | \(0.652809\pi\) | |||||||
\(572\) | −64.3787 | −2.69181 | ||||||||
\(573\) | 13.4946 | 0.563746 | ||||||||
\(574\) | 19.6198 | 0.818915 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | −9.52381 | −0.396826 | ||||||||
\(577\) | −7.03151 | −0.292725 | −0.146363 | − | 0.989231i | \(-0.546757\pi\) | ||||
−0.146363 | + | 0.989231i | \(0.546757\pi\) | |||||||
\(578\) | 7.80971 | 0.324841 | ||||||||
\(579\) | 25.4725 | 1.05860 | ||||||||
\(580\) | −1.11388 | −0.0462512 | ||||||||
\(581\) | −3.16745 | −0.131408 | ||||||||
\(582\) | −20.0283 | −0.830199 | ||||||||
\(583\) | −12.1446 | −0.502977 | ||||||||
\(584\) | −22.3345 | −0.924210 | ||||||||
\(585\) | −5.96954 | −0.246810 | ||||||||
\(586\) | −18.5180 | −0.764972 | ||||||||
\(587\) | 40.7519 | 1.68201 | 0.841006 | − | 0.541026i | \(-0.181964\pi\) | ||||
0.841006 | + | 0.541026i | \(0.181964\pi\) | |||||||
\(588\) | 3.86022 | 0.159193 | ||||||||
\(589\) | 52.6348 | 2.16878 | ||||||||
\(590\) | 36.4469 | 1.50049 | ||||||||
\(591\) | 8.22859 | 0.338479 | ||||||||
\(592\) | −35.3063 | −1.45108 | ||||||||
\(593\) | 47.4193 | 1.94728 | 0.973638 | − | 0.228100i | \(-0.0732514\pi\) | ||||
0.973638 | + | 0.228100i | \(0.0732514\pi\) | |||||||
\(594\) | 6.76311 | 0.277494 | ||||||||
\(595\) | −4.49734 | −0.184373 | ||||||||
\(596\) | −2.16091 | −0.0885143 | ||||||||
\(597\) | 23.1526 | 0.947571 | ||||||||
\(598\) | −14.4510 | −0.590945 | ||||||||
\(599\) | −15.2730 | −0.624037 | −0.312018 | − | 0.950076i | \(-0.601005\pi\) | ||||
−0.312018 | + | 0.950076i | \(0.601005\pi\) | |||||||
\(600\) | 4.50319 | 0.183842 | ||||||||
\(601\) | −45.8805 | −1.87150 | −0.935752 | − | 0.352658i | \(-0.885278\pi\) | ||||
−0.935752 | + | 0.352658i | \(0.885278\pi\) | |||||||
\(602\) | 0.640143 | 0.0260903 | ||||||||
\(603\) | 2.53462 | 0.103218 | ||||||||
\(604\) | 6.19788 | 0.252188 | ||||||||
\(605\) | −3.19488 | −0.129890 | ||||||||
\(606\) | −6.67400 | −0.271113 | ||||||||
\(607\) | 24.4509 | 0.992431 | 0.496215 | − | 0.868199i | \(-0.334723\pi\) | ||||
0.496215 | + | 0.868199i | \(0.334723\pi\) | |||||||
\(608\) | −10.8305 | −0.439234 | ||||||||
\(609\) | 0.288553 | 0.0116927 | ||||||||
\(610\) | −17.7112 | −0.717105 | ||||||||
\(611\) | −19.6396 | −0.794534 | ||||||||
\(612\) | 17.3607 | 0.701766 | ||||||||
\(613\) | −4.18228 | −0.168921 | −0.0844604 | − | 0.996427i | \(-0.526917\pi\) | ||||
−0.0844604 | + | 0.996427i | \(0.526917\pi\) | |||||||
\(614\) | 13.0154 | 0.525259 | ||||||||
\(615\) | −8.10472 | −0.326814 | ||||||||
\(616\) | −12.5809 | −0.506897 | ||||||||
\(617\) | −2.79324 | −0.112452 | −0.0562258 | − | 0.998418i | \(-0.517907\pi\) | ||||
−0.0562258 | + | 0.998418i | \(0.517907\pi\) | |||||||
\(618\) | −23.8034 | −0.957513 | ||||||||
\(619\) | 35.0354 | 1.40819 | 0.704095 | − | 0.710106i | \(-0.251353\pi\) | ||||
0.704095 | + | 0.710106i | \(0.251353\pi\) | |||||||
\(620\) | 24.5053 | 0.984157 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | −3.88335 | −0.155708 | ||||||||
\(623\) | −3.44448 | −0.138000 | ||||||||
\(624\) | −18.9882 | −0.760134 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 42.7067 | 1.70690 | ||||||||
\(627\) | 23.1640 | 0.925083 | ||||||||
\(628\) | 9.87003 | 0.393857 | ||||||||
\(629\) | −49.9190 | −1.99040 | ||||||||
\(630\) | −2.42079 | −0.0964465 | ||||||||
\(631\) | −3.96520 | −0.157852 | −0.0789261 | − | 0.996880i | \(-0.525149\pi\) | ||||
−0.0789261 | + | 0.996880i | \(0.525149\pi\) | |||||||
\(632\) | −75.3850 | −2.99865 | ||||||||
\(633\) | −20.3171 | −0.807533 | ||||||||
\(634\) | −71.2530 | −2.82982 | ||||||||
\(635\) | −21.4471 | −0.851103 | ||||||||
\(636\) | −16.7805 | −0.665389 | ||||||||
\(637\) | −5.96954 | −0.236522 | ||||||||
\(638\) | −1.95151 | −0.0772612 | ||||||||
\(639\) | 10.2719 | 0.406351 | ||||||||
\(640\) | −20.4427 | −0.808067 | ||||||||
\(641\) | −32.2626 | −1.27430 | −0.637148 | − | 0.770742i | \(-0.719886\pi\) | ||||
−0.637148 | + | 0.770742i | \(0.719886\pi\) | |||||||
\(642\) | −42.2637 | −1.66802 | ||||||||
\(643\) | 28.1370 | 1.10961 | 0.554807 | − | 0.831979i | \(-0.312792\pi\) | ||||
0.554807 | + | 0.831979i | \(0.312792\pi\) | |||||||
\(644\) | −3.86022 | −0.152114 | ||||||||
\(645\) | −0.264436 | −0.0104122 | ||||||||
\(646\) | 90.2688 | 3.55158 | ||||||||
\(647\) | −14.6907 | −0.577549 | −0.288775 | − | 0.957397i | \(-0.593248\pi\) | ||||
−0.288775 | + | 0.957397i | \(0.593248\pi\) | |||||||
\(648\) | 4.50319 | 0.176902 | ||||||||
\(649\) | 42.0623 | 1.65109 | ||||||||
\(650\) | −14.4510 | −0.566814 | ||||||||
\(651\) | −6.34817 | −0.248804 | ||||||||
\(652\) | 14.5636 | 0.570356 | ||||||||
\(653\) | 15.4855 | 0.605994 | 0.302997 | − | 0.952992i | \(-0.402013\pi\) | ||||
0.302997 | + | 0.952992i | \(0.402013\pi\) | |||||||
\(654\) | −2.63078 | −0.102871 | ||||||||
\(655\) | −5.79445 | −0.226408 | ||||||||
\(656\) | −25.7798 | −1.00653 | ||||||||
\(657\) | −4.95971 | −0.193497 | ||||||||
\(658\) | −7.96433 | −0.310482 | ||||||||
\(659\) | −22.7662 | −0.886846 | −0.443423 | − | 0.896312i | \(-0.646236\pi\) | ||||
−0.443423 | + | 0.896312i | \(0.646236\pi\) | |||||||
\(660\) | 10.7845 | 0.419788 | ||||||||
\(661\) | −24.2449 | −0.943018 | −0.471509 | − | 0.881861i | \(-0.656291\pi\) | ||||
−0.471509 | + | 0.881861i | \(0.656291\pi\) | |||||||
\(662\) | 52.8436 | 2.05382 | ||||||||
\(663\) | −26.8471 | −1.04265 | ||||||||
\(664\) | 14.2636 | 0.553535 | ||||||||
\(665\) | −8.29134 | −0.321524 | ||||||||
\(666\) | −26.8699 | −1.04119 | ||||||||
\(667\) | −0.288553 | −0.0111728 | ||||||||
\(668\) | 40.8026 | 1.57870 | ||||||||
\(669\) | 8.26387 | 0.319500 | ||||||||
\(670\) | 6.13579 | 0.237046 | ||||||||
\(671\) | −20.4400 | −0.789077 | ||||||||
\(672\) | 1.30624 | 0.0503894 | ||||||||
\(673\) | −4.32915 | −0.166876 | −0.0834382 | − | 0.996513i | \(-0.526590\pi\) | ||||
−0.0834382 | + | 0.996513i | \(0.526590\pi\) | |||||||
\(674\) | −10.4350 | −0.401941 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 87.3775 | 3.36067 | ||||||||
\(677\) | −14.2625 | −0.548153 | −0.274076 | − | 0.961708i | \(-0.588372\pi\) | ||||
−0.274076 | + | 0.961708i | \(0.588372\pi\) | |||||||
\(678\) | −34.3445 | −1.31899 | ||||||||
\(679\) | 8.27346 | 0.317506 | ||||||||
\(680\) | 20.2524 | 0.776644 | ||||||||
\(681\) | 3.84124 | 0.147196 | ||||||||
\(682\) | 42.9334 | 1.64400 | ||||||||
\(683\) | 0.684410 | 0.0261882 | 0.0130941 | − | 0.999914i | \(-0.495832\pi\) | ||||
0.0130941 | + | 0.999914i | \(0.495832\pi\) | |||||||
\(684\) | 32.0064 | 1.22379 | ||||||||
\(685\) | 6.13504 | 0.234408 | ||||||||
\(686\) | −2.42079 | −0.0924261 | ||||||||
\(687\) | 4.48106 | 0.170963 | ||||||||
\(688\) | −0.841128 | −0.0320677 | ||||||||
\(689\) | 25.9498 | 0.988607 | ||||||||
\(690\) | 2.42079 | 0.0921578 | ||||||||
\(691\) | 29.0557 | 1.10533 | 0.552665 | − | 0.833403i | \(-0.313611\pi\) | ||||
0.552665 | + | 0.833403i | \(0.313611\pi\) | |||||||
\(692\) | −20.7783 | −0.789872 | ||||||||
\(693\) | −2.79376 | −0.106126 | ||||||||
\(694\) | 26.5577 | 1.00812 | ||||||||
\(695\) | −3.58042 | −0.135813 | ||||||||
\(696\) | −1.29941 | −0.0492539 | ||||||||
\(697\) | −36.4497 | −1.38063 | ||||||||
\(698\) | −48.7221 | −1.84416 | ||||||||
\(699\) | 8.03925 | 0.304072 | ||||||||
\(700\) | −3.86022 | −0.145902 | ||||||||
\(701\) | 34.5747 | 1.30587 | 0.652934 | − | 0.757415i | \(-0.273538\pi\) | ||||
0.652934 | + | 0.757415i | \(0.273538\pi\) | |||||||
\(702\) | −14.4510 | −0.545418 | ||||||||
\(703\) | −92.0311 | −3.47102 | ||||||||
\(704\) | −26.6073 | −1.00280 | ||||||||
\(705\) | 3.28997 | 0.123908 | ||||||||
\(706\) | 76.8441 | 2.89207 | ||||||||
\(707\) | 2.75695 | 0.103686 | ||||||||
\(708\) | 58.1186 | 2.18423 | ||||||||
\(709\) | 21.4169 | 0.804330 | 0.402165 | − | 0.915567i | \(-0.368258\pi\) | ||||
0.402165 | + | 0.915567i | \(0.368258\pi\) | |||||||
\(710\) | 24.8662 | 0.933211 | ||||||||
\(711\) | −16.7403 | −0.627812 | ||||||||
\(712\) | 15.5111 | 0.581305 | ||||||||
\(713\) | 6.34817 | 0.237741 | ||||||||
\(714\) | −10.8871 | −0.407440 | ||||||||
\(715\) | −16.6775 | −0.623703 | ||||||||
\(716\) | 46.5602 | 1.74004 | ||||||||
\(717\) | −14.3411 | −0.535579 | ||||||||
\(718\) | −47.2093 | −1.76184 | ||||||||
\(719\) | −15.4198 | −0.575062 | −0.287531 | − | 0.957771i | \(-0.592834\pi\) | ||||
−0.287531 | + | 0.957771i | \(0.592834\pi\) | |||||||
\(720\) | 3.18084 | 0.118543 | ||||||||
\(721\) | 9.83291 | 0.366197 | ||||||||
\(722\) | 120.425 | 4.48176 | ||||||||
\(723\) | 19.4913 | 0.724891 | ||||||||
\(724\) | −15.9423 | −0.592490 | ||||||||
\(725\) | −0.288553 | −0.0107166 | ||||||||
\(726\) | −7.73413 | −0.287040 | ||||||||
\(727\) | 30.5804 | 1.13416 | 0.567082 | − | 0.823661i | \(-0.308072\pi\) | ||||
0.567082 | + | 0.823661i | \(0.308072\pi\) | |||||||
\(728\) | 26.8820 | 0.996312 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −12.0064 | −0.444377 | ||||||||
\(731\) | −1.18926 | −0.0439863 | ||||||||
\(732\) | −28.2425 | −1.04387 | ||||||||
\(733\) | 25.5385 | 0.943286 | 0.471643 | − | 0.881790i | \(-0.343661\pi\) | ||||
0.471643 | + | 0.881790i | \(0.343661\pi\) | |||||||
\(734\) | −81.0532 | −2.99173 | ||||||||
\(735\) | 1.00000 | 0.0368856 | ||||||||
\(736\) | −1.30624 | −0.0481487 | ||||||||
\(737\) | 7.08114 | 0.260837 | ||||||||
\(738\) | −19.6198 | −0.722216 | ||||||||
\(739\) | 45.7218 | 1.68190 | 0.840952 | − | 0.541109i | \(-0.181996\pi\) | ||||
0.840952 | + | 0.541109i | \(0.181996\pi\) | |||||||
\(740\) | −42.8471 | −1.57509 | ||||||||
\(741\) | −49.4955 | −1.81826 | ||||||||
\(742\) | 10.5232 | 0.386320 | ||||||||
\(743\) | −23.6223 | −0.866620 | −0.433310 | − | 0.901245i | \(-0.642654\pi\) | ||||
−0.433310 | + | 0.901245i | \(0.642654\pi\) | |||||||
\(744\) | 28.5870 | 1.04805 | ||||||||
\(745\) | −0.559790 | −0.0205091 | ||||||||
\(746\) | 62.7350 | 2.29689 | ||||||||
\(747\) | 3.16745 | 0.115891 | ||||||||
\(748\) | 48.5018 | 1.77340 | ||||||||
\(749\) | 17.4587 | 0.637925 | ||||||||
\(750\) | 2.42079 | 0.0883947 | ||||||||
\(751\) | 13.9599 | 0.509404 | 0.254702 | − | 0.967020i | \(-0.418023\pi\) | ||||
0.254702 | + | 0.967020i | \(0.418023\pi\) | |||||||
\(752\) | 10.4649 | 0.381615 | ||||||||
\(753\) | −12.2142 | −0.445111 | ||||||||
\(754\) | 4.16987 | 0.151858 | ||||||||
\(755\) | 1.60558 | 0.0584330 | ||||||||
\(756\) | −3.86022 | −0.140395 | ||||||||
\(757\) | 30.8536 | 1.12139 | 0.560697 | − | 0.828021i | \(-0.310533\pi\) | ||||
0.560697 | + | 0.828021i | \(0.310533\pi\) | |||||||
\(758\) | 35.3744 | 1.28485 | ||||||||
\(759\) | 2.79376 | 0.101407 | ||||||||
\(760\) | 37.3375 | 1.35437 | ||||||||
\(761\) | −16.8438 | −0.610587 | −0.305293 | − | 0.952258i | \(-0.598755\pi\) | ||||
−0.305293 | + | 0.952258i | \(0.598755\pi\) | |||||||
\(762\) | −51.9189 | −1.88082 | ||||||||
\(763\) | 1.08674 | 0.0393428 | ||||||||
\(764\) | 52.0922 | 1.88463 | ||||||||
\(765\) | 4.49734 | 0.162602 | ||||||||
\(766\) | 87.2981 | 3.15421 | ||||||||
\(767\) | −89.8762 | −3.24524 | ||||||||
\(768\) | −30.4397 | −1.09840 | ||||||||
\(769\) | −27.9453 | −1.00773 | −0.503866 | − | 0.863782i | \(-0.668090\pi\) | ||||
−0.503866 | + | 0.863782i | \(0.668090\pi\) | |||||||
\(770\) | −6.76311 | −0.243726 | ||||||||
\(771\) | −29.3237 | −1.05607 | ||||||||
\(772\) | 98.3295 | 3.53895 | ||||||||
\(773\) | −21.6878 | −0.780055 | −0.390028 | − | 0.920803i | \(-0.627535\pi\) | ||||
−0.390028 | + | 0.920803i | \(0.627535\pi\) | |||||||
\(774\) | −0.640143 | −0.0230095 | ||||||||
\(775\) | 6.34817 | 0.228033 | ||||||||
\(776\) | −37.2570 | −1.33745 | ||||||||
\(777\) | 11.0997 | 0.398198 | ||||||||
\(778\) | −38.1766 | −1.36870 | ||||||||
\(779\) | −67.1990 | −2.40765 | ||||||||
\(780\) | −23.0437 | −0.825097 | ||||||||
\(781\) | 28.6974 | 1.02687 | ||||||||
\(782\) | 10.8871 | 0.389323 | ||||||||
\(783\) | −0.288553 | −0.0103120 | ||||||||
\(784\) | 3.18084 | 0.113601 | ||||||||
\(785\) | 2.55686 | 0.0912582 | ||||||||
\(786\) | −14.0271 | −0.500332 | ||||||||
\(787\) | 44.6257 | 1.59073 | 0.795367 | − | 0.606128i | \(-0.207278\pi\) | ||||
0.795367 | + | 0.606128i | \(0.207278\pi\) | |||||||
\(788\) | 31.7641 | 1.13155 | ||||||||
\(789\) | 4.71668 | 0.167918 | ||||||||
\(790\) | −40.5248 | −1.44181 | ||||||||
\(791\) | 14.1873 | 0.504443 | ||||||||
\(792\) | 12.5809 | 0.447041 | ||||||||
\(793\) | 43.6749 | 1.55094 | ||||||||
\(794\) | 52.2369 | 1.85382 | ||||||||
\(795\) | −4.34703 | −0.154173 | ||||||||
\(796\) | 89.3739 | 3.16777 | ||||||||
\(797\) | 7.74192 | 0.274233 | 0.137116 | − | 0.990555i | \(-0.456217\pi\) | ||||
0.137116 | + | 0.990555i | \(0.456217\pi\) | |||||||
\(798\) | −20.0716 | −0.710526 | ||||||||
\(799\) | 14.7961 | 0.523450 | ||||||||
\(800\) | −1.30624 | −0.0461826 | ||||||||
\(801\) | 3.44448 | 0.121705 | ||||||||
\(802\) | −87.4042 | −3.08635 | ||||||||
\(803\) | −13.8563 | −0.488977 | ||||||||
\(804\) | 9.78420 | 0.345062 | ||||||||
\(805\) | −1.00000 | −0.0352454 | ||||||||
\(806\) | −91.7374 | −3.23131 | ||||||||
\(807\) | 12.4012 | 0.436541 | ||||||||
\(808\) | −12.4151 | −0.436761 | ||||||||
\(809\) | −10.4539 | −0.367541 | −0.183770 | − | 0.982969i | \(-0.558830\pi\) | ||||
−0.183770 | + | 0.982969i | \(0.558830\pi\) | |||||||
\(810\) | 2.42079 | 0.0850578 | ||||||||
\(811\) | −43.6119 | −1.53142 | −0.765710 | − | 0.643186i | \(-0.777612\pi\) | ||||
−0.765710 | + | 0.643186i | \(0.777612\pi\) | |||||||
\(812\) | 1.11388 | 0.0390894 | ||||||||
\(813\) | 16.9980 | 0.596145 | ||||||||
\(814\) | −75.0683 | −2.63114 | ||||||||
\(815\) | 3.77275 | 0.132154 | ||||||||
\(816\) | 14.3053 | 0.500787 | ||||||||
\(817\) | −2.19253 | −0.0767068 | ||||||||
\(818\) | 37.4051 | 1.30784 | ||||||||
\(819\) | 5.96954 | 0.208593 | ||||||||
\(820\) | −31.2860 | −1.09255 | ||||||||
\(821\) | −7.23682 | −0.252567 | −0.126283 | − | 0.991994i | \(-0.540305\pi\) | ||||
−0.126283 | + | 0.991994i | \(0.540305\pi\) | |||||||
\(822\) | 14.8516 | 0.518010 | ||||||||
\(823\) | 50.2663 | 1.75217 | 0.876087 | − | 0.482153i | \(-0.160145\pi\) | ||||
0.876087 | + | 0.482153i | \(0.160145\pi\) | |||||||
\(824\) | −44.2795 | −1.54255 | ||||||||
\(825\) | 2.79376 | 0.0972664 | ||||||||
\(826\) | −36.4469 | −1.26815 | ||||||||
\(827\) | 46.7057 | 1.62412 | 0.812059 | − | 0.583575i | \(-0.198347\pi\) | ||||
0.812059 | + | 0.583575i | \(0.198347\pi\) | |||||||
\(828\) | 3.86022 | 0.134152 | ||||||||
\(829\) | 28.7414 | 0.998229 | 0.499115 | − | 0.866536i | \(-0.333659\pi\) | ||||
0.499115 | + | 0.866536i | \(0.333659\pi\) | |||||||
\(830\) | 7.66771 | 0.266150 | ||||||||
\(831\) | 12.9327 | 0.448630 | ||||||||
\(832\) | 56.8528 | 1.97102 | ||||||||
\(833\) | 4.49734 | 0.155824 | ||||||||
\(834\) | −8.66743 | −0.300129 | ||||||||
\(835\) | 10.5700 | 0.365791 | ||||||||
\(836\) | 89.4182 | 3.09259 | ||||||||
\(837\) | 6.34817 | 0.219425 | ||||||||
\(838\) | −67.8630 | −2.34429 | ||||||||
\(839\) | 10.0276 | 0.346193 | 0.173096 | − | 0.984905i | \(-0.444623\pi\) | ||||
0.173096 | + | 0.984905i | \(0.444623\pi\) | |||||||
\(840\) | −4.50319 | −0.155375 | ||||||||
\(841\) | −28.9167 | −0.997129 | ||||||||
\(842\) | −92.6121 | −3.19162 | ||||||||
\(843\) | 3.71629 | 0.127996 | ||||||||
\(844\) | −78.4285 | −2.69962 | ||||||||
\(845\) | 22.6354 | 0.778681 | ||||||||
\(846\) | 7.96433 | 0.273819 | ||||||||
\(847\) | 3.19488 | 0.109777 | ||||||||
\(848\) | −13.8272 | −0.474828 | ||||||||
\(849\) | −18.2784 | −0.627313 | ||||||||
\(850\) | 10.8871 | 0.373425 | ||||||||
\(851\) | −11.0997 | −0.380492 | ||||||||
\(852\) | 39.6519 | 1.35845 | ||||||||
\(853\) | 32.9784 | 1.12916 | 0.564580 | − | 0.825379i | \(-0.309038\pi\) | ||||
0.564580 | + | 0.825379i | \(0.309038\pi\) | |||||||
\(854\) | 17.7112 | 0.606065 | ||||||||
\(855\) | 8.29134 | 0.283558 | ||||||||
\(856\) | −78.6196 | −2.68716 | ||||||||
\(857\) | −27.1362 | −0.926955 | −0.463478 | − | 0.886109i | \(-0.653399\pi\) | ||||
−0.463478 | + | 0.886109i | \(0.653399\pi\) | |||||||
\(858\) | −40.3727 | −1.37830 | ||||||||
\(859\) | 6.74621 | 0.230178 | 0.115089 | − | 0.993355i | \(-0.463285\pi\) | ||||
0.115089 | + | 0.993355i | \(0.463285\pi\) | |||||||
\(860\) | −1.02078 | −0.0348083 | ||||||||
\(861\) | 8.10472 | 0.276208 | ||||||||
\(862\) | −22.5845 | −0.769231 | ||||||||
\(863\) | −4.93924 | −0.168134 | −0.0840668 | − | 0.996460i | \(-0.526791\pi\) | ||||
−0.0840668 | + | 0.996460i | \(0.526791\pi\) | |||||||
\(864\) | −1.30624 | −0.0444392 | ||||||||
\(865\) | −5.38268 | −0.183017 | ||||||||
\(866\) | 47.2458 | 1.60548 | ||||||||
\(867\) | 3.22610 | 0.109564 | ||||||||
\(868\) | −24.5053 | −0.831765 | ||||||||
\(869\) | −46.7686 | −1.58651 | ||||||||
\(870\) | −0.698525 | −0.0236822 | ||||||||
\(871\) | −15.1305 | −0.512679 | ||||||||
\(872\) | −4.89381 | −0.165725 | ||||||||
\(873\) | −8.27346 | −0.280014 | ||||||||
\(874\) | 20.0716 | 0.678931 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | −19.1456 | −0.646869 | ||||||||
\(877\) | 5.90142 | 0.199277 | 0.0996383 | − | 0.995024i | \(-0.468231\pi\) | ||||
0.0996383 | + | 0.995024i | \(0.468231\pi\) | |||||||
\(878\) | −23.8868 | −0.806140 | ||||||||
\(879\) | −7.64958 | −0.258014 | ||||||||
\(880\) | 8.88652 | 0.299564 | ||||||||
\(881\) | 24.5121 | 0.825833 | 0.412917 | − | 0.910769i | \(-0.364510\pi\) | ||||
0.412917 | + | 0.910769i | \(0.364510\pi\) | |||||||
\(882\) | 2.42079 | 0.0815122 | ||||||||
\(883\) | 19.0917 | 0.642486 | 0.321243 | − | 0.946997i | \(-0.395899\pi\) | ||||
0.321243 | + | 0.946997i | \(0.395899\pi\) | |||||||
\(884\) | −103.636 | −3.48564 | ||||||||
\(885\) | 15.0558 | 0.506095 | ||||||||
\(886\) | −4.91112 | −0.164992 | ||||||||
\(887\) | −16.6397 | −0.558705 | −0.279353 | − | 0.960189i | \(-0.590120\pi\) | ||||
−0.279353 | + | 0.960189i | \(0.590120\pi\) | |||||||
\(888\) | −49.9839 | −1.67735 | ||||||||
\(889\) | 21.4471 | 0.719313 | ||||||||
\(890\) | 8.33835 | 0.279502 | ||||||||
\(891\) | 2.79376 | 0.0935946 | ||||||||
\(892\) | 31.9003 | 1.06810 | ||||||||
\(893\) | 27.2783 | 0.912832 | ||||||||
\(894\) | −1.35513 | −0.0453224 | ||||||||
\(895\) | 12.0616 | 0.403173 | ||||||||
\(896\) | 20.4427 | 0.682941 | ||||||||
\(897\) | −5.96954 | −0.199317 | ||||||||
\(898\) | 77.8503 | 2.59790 | ||||||||
\(899\) | −1.83178 | −0.0610934 | ||||||||
\(900\) | 3.86022 | 0.128674 | ||||||||
\(901\) | −19.5501 | −0.651308 | ||||||||
\(902\) | −54.8132 | −1.82508 | ||||||||
\(903\) | 0.264436 | 0.00879987 | ||||||||
\(904\) | −63.8882 | −2.12489 | ||||||||
\(905\) | −4.12989 | −0.137282 | ||||||||
\(906\) | 3.88677 | 0.129129 | ||||||||
\(907\) | 41.6157 | 1.38183 | 0.690914 | − | 0.722937i | \(-0.257208\pi\) | ||||
0.690914 | + | 0.722937i | \(0.257208\pi\) | |||||||
\(908\) | 14.8280 | 0.492085 | ||||||||
\(909\) | −2.75695 | −0.0914424 | ||||||||
\(910\) | 14.4510 | 0.479046 | ||||||||
\(911\) | 41.6438 | 1.37972 | 0.689861 | − | 0.723942i | \(-0.257672\pi\) | ||||
0.689861 | + | 0.723942i | \(0.257672\pi\) | |||||||
\(912\) | 26.3734 | 0.873311 | ||||||||
\(913\) | 8.84910 | 0.292862 | ||||||||
\(914\) | −6.04588 | −0.199980 | ||||||||
\(915\) | −7.31629 | −0.241869 | ||||||||
\(916\) | 17.2979 | 0.571537 | ||||||||
\(917\) | 5.79445 | 0.191350 | ||||||||
\(918\) | 10.8871 | 0.359328 | ||||||||
\(919\) | 33.9080 | 1.11852 | 0.559261 | − | 0.828992i | \(-0.311085\pi\) | ||||
0.559261 | + | 0.828992i | \(0.311085\pi\) | |||||||
\(920\) | 4.50319 | 0.148466 | ||||||||
\(921\) | 5.37651 | 0.177162 | ||||||||
\(922\) | 85.7106 | 2.82273 | ||||||||
\(923\) | −61.3187 | −2.01833 | ||||||||
\(924\) | −10.7845 | −0.354785 | ||||||||
\(925\) | −11.0997 | −0.364955 | ||||||||
\(926\) | 46.1772 | 1.51748 | ||||||||
\(927\) | −9.83291 | −0.322955 | ||||||||
\(928\) | 0.376920 | 0.0123730 | ||||||||
\(929\) | 51.4642 | 1.68848 | 0.844242 | − | 0.535962i | \(-0.180051\pi\) | ||||
0.844242 | + | 0.535962i | \(0.180051\pi\) | |||||||
\(930\) | 15.3676 | 0.503923 | ||||||||
\(931\) | 8.29134 | 0.271738 | ||||||||
\(932\) | 31.0332 | 1.01653 | ||||||||
\(933\) | −1.60417 | −0.0525181 | ||||||||
\(934\) | −26.9441 | −0.881638 | ||||||||
\(935\) | 12.5645 | 0.410904 | ||||||||
\(936\) | −26.8820 | −0.878665 | ||||||||
\(937\) | −55.7423 | −1.82102 | −0.910512 | − | 0.413484i | \(-0.864312\pi\) | ||||
−0.910512 | + | 0.413484i | \(0.864312\pi\) | |||||||
\(938\) | −6.13579 | −0.200341 | ||||||||
\(939\) | 17.6416 | 0.575713 | ||||||||
\(940\) | 12.7000 | 0.414228 | ||||||||
\(941\) | 27.3939 | 0.893014 | 0.446507 | − | 0.894780i | \(-0.352668\pi\) | ||||
0.446507 | + | 0.894780i | \(0.352668\pi\) | |||||||
\(942\) | 6.18961 | 0.201668 | ||||||||
\(943\) | −8.10472 | −0.263926 | ||||||||
\(944\) | 47.8901 | 1.55869 | ||||||||
\(945\) | −1.00000 | −0.0325300 | ||||||||
\(946\) | −1.78841 | −0.0581462 | ||||||||
\(947\) | −48.6525 | −1.58099 | −0.790497 | − | 0.612466i | \(-0.790178\pi\) | ||||
−0.790497 | + | 0.612466i | \(0.790178\pi\) | |||||||
\(948\) | −64.6213 | −2.09880 | ||||||||
\(949\) | 29.6072 | 0.961090 | ||||||||
\(950\) | 20.0716 | 0.651208 | ||||||||
\(951\) | −29.4338 | −0.954456 | ||||||||
\(952\) | −20.2524 | −0.656384 | ||||||||
\(953\) | −28.4836 | −0.922676 | −0.461338 | − | 0.887224i | \(-0.652630\pi\) | ||||
−0.461338 | + | 0.887224i | \(0.652630\pi\) | |||||||
\(954\) | −10.5232 | −0.340702 | ||||||||
\(955\) | 13.4946 | 0.436676 | ||||||||
\(956\) | −55.3598 | −1.79046 | ||||||||
\(957\) | −0.806148 | −0.0260591 | ||||||||
\(958\) | 0.590121 | 0.0190659 | ||||||||
\(959\) | −6.13504 | −0.198111 | ||||||||
\(960\) | −9.52381 | −0.307380 | ||||||||
\(961\) | 9.29929 | 0.299977 | ||||||||
\(962\) | 160.401 | 5.17154 | ||||||||
\(963\) | −17.4587 | −0.562597 | ||||||||
\(964\) | 75.2408 | 2.42334 | ||||||||
\(965\) | 25.4725 | 0.819990 | ||||||||
\(966\) | −2.42079 | −0.0778876 | ||||||||
\(967\) | 37.8183 | 1.21616 | 0.608078 | − | 0.793877i | \(-0.291941\pi\) | ||||
0.608078 | + | 0.793877i | \(0.291941\pi\) | |||||||
\(968\) | −14.3872 | −0.462421 | ||||||||
\(969\) | 37.2890 | 1.19789 | ||||||||
\(970\) | −20.0283 | −0.643070 | ||||||||
\(971\) | −21.5494 | −0.691553 | −0.345776 | − | 0.938317i | \(-0.612384\pi\) | ||||
−0.345776 | + | 0.938317i | \(0.612384\pi\) | |||||||
\(972\) | 3.86022 | 0.123817 | ||||||||
\(973\) | 3.58042 | 0.114783 | ||||||||
\(974\) | −100.041 | −3.20553 | ||||||||
\(975\) | −5.96954 | −0.191178 | ||||||||
\(976\) | −23.2720 | −0.744917 | ||||||||
\(977\) | −43.8690 | −1.40349 | −0.701747 | − | 0.712426i | \(-0.747596\pi\) | ||||
−0.701747 | + | 0.712426i | \(0.747596\pi\) | |||||||
\(978\) | 9.13302 | 0.292042 | ||||||||
\(979\) | 9.62306 | 0.307554 | ||||||||
\(980\) | 3.86022 | 0.123310 | ||||||||
\(981\) | −1.08674 | −0.0346970 | ||||||||
\(982\) | −63.3206 | −2.02064 | ||||||||
\(983\) | 37.7779 | 1.20493 | 0.602464 | − | 0.798146i | \(-0.294186\pi\) | ||||
0.602464 | + | 0.798146i | \(0.294186\pi\) | |||||||
\(984\) | −36.4971 | −1.16349 | ||||||||
\(985\) | 8.22859 | 0.262185 | ||||||||
\(986\) | −3.14151 | −0.100046 | ||||||||
\(987\) | −3.28997 | −0.104721 | ||||||||
\(988\) | −191.063 | −6.07853 | ||||||||
\(989\) | −0.264436 | −0.00840857 | ||||||||
\(990\) | 6.76311 | 0.214946 | ||||||||
\(991\) | 43.5865 | 1.38457 | 0.692285 | − | 0.721624i | \(-0.256604\pi\) | ||||
0.692285 | + | 0.721624i | \(0.256604\pi\) | |||||||
\(992\) | −8.29224 | −0.263279 | ||||||||
\(993\) | 21.8291 | 0.692725 | ||||||||
\(994\) | −24.8662 | −0.788707 | ||||||||
\(995\) | 23.1526 | 0.733986 | ||||||||
\(996\) | 12.2270 | 0.387428 | ||||||||
\(997\) | 3.86893 | 0.122530 | 0.0612651 | − | 0.998122i | \(-0.480486\pi\) | ||||
0.0612651 | + | 0.998122i | \(0.480486\pi\) | |||||||
\(998\) | 15.7287 | 0.497883 | ||||||||
\(999\) | −11.0997 | −0.351178 |
(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 | 2415.2.a.v.1.9 | ✓ | 10 | |
3.2 | odd | 2 | 7245.2.a.bu.1.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2415.2.a.v.1.9 | ✓ | 10 | 1.1 | even | 1 | trivial | |
7245.2.a.bu.1.2 | 10 | 3.2 | odd | 2 |