Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [538,2,Mod(1,538)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(538, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("538.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 538 = 2 \cdot 269 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 538.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: | \(4.29595162874\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 538.1 |
$q$-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 | ||||||||
\(3\) | 2.30278 | 1.32951 | 0.664754 | − | 0.747062i | \(-0.268536\pi\) | ||||
0.664754 | + | 0.747062i | \(0.268536\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.30278 | −0.582619 | −0.291309 | − | 0.956629i | \(-0.594091\pi\) | ||||
−0.291309 | + | 0.956629i | \(0.594091\pi\) | |||||||
\(6\) | 2.30278 | 0.940104 | ||||||||
\(7\) | −1.00000 | −0.377964 | −0.188982 | − | 0.981981i | \(-0.560519\pi\) | ||||
−0.188982 | + | 0.981981i | \(0.560519\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.30278 | 0.767592 | ||||||||
\(10\) | −1.30278 | −0.411974 | ||||||||
\(11\) | 3.00000 | 0.904534 | 0.452267 | − | 0.891883i | \(-0.350615\pi\) | ||||
0.452267 | + | 0.891883i | \(0.350615\pi\) | |||||||
\(12\) | 2.30278 | 0.664754 | ||||||||
\(13\) | 5.00000 | 1.38675 | 0.693375 | − | 0.720577i | \(-0.256123\pi\) | ||||
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −3.00000 | −0.774597 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.60555 | −1.35955 | −0.679773 | − | 0.733423i | \(-0.737922\pi\) | ||||
−0.679773 | + | 0.733423i | \(0.737922\pi\) | |||||||
\(18\) | 2.30278 | 0.542769 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | −1.30278 | −0.291309 | ||||||||
\(21\) | −2.30278 | −0.502507 | ||||||||
\(22\) | 3.00000 | 0.639602 | ||||||||
\(23\) | 8.21110 | 1.71213 | 0.856067 | − | 0.516865i | \(-0.172901\pi\) | ||||
0.856067 | + | 0.516865i | \(0.172901\pi\) | |||||||
\(24\) | 2.30278 | 0.470052 | ||||||||
\(25\) | −3.30278 | −0.660555 | ||||||||
\(26\) | 5.00000 | 0.980581 | ||||||||
\(27\) | −1.60555 | −0.308988 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 4.69722 | 0.872253 | 0.436126 | − | 0.899885i | \(-0.356350\pi\) | ||||
0.436126 | + | 0.899885i | \(0.356350\pi\) | |||||||
\(30\) | −3.00000 | −0.547723 | ||||||||
\(31\) | −9.60555 | −1.72521 | −0.862604 | − | 0.505880i | \(-0.831168\pi\) | ||||
−0.862604 | + | 0.505880i | \(0.831168\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 6.90833 | 1.20259 | ||||||||
\(34\) | −5.60555 | −0.961344 | ||||||||
\(35\) | 1.30278 | 0.220209 | ||||||||
\(36\) | 2.30278 | 0.383796 | ||||||||
\(37\) | −3.60555 | −0.592749 | −0.296374 | − | 0.955072i | \(-0.595778\pi\) | ||||
−0.296374 | + | 0.955072i | \(0.595778\pi\) | |||||||
\(38\) | 2.00000 | 0.324443 | ||||||||
\(39\) | 11.5139 | 1.84370 | ||||||||
\(40\) | −1.30278 | −0.205987 | ||||||||
\(41\) | −8.60555 | −1.34396 | −0.671981 | − | 0.740569i | \(-0.734556\pi\) | ||||
−0.671981 | + | 0.740569i | \(0.734556\pi\) | |||||||
\(42\) | −2.30278 | −0.355326 | ||||||||
\(43\) | −12.2111 | −1.86218 | −0.931088 | − | 0.364795i | \(-0.881139\pi\) | ||||
−0.931088 | + | 0.364795i | \(0.881139\pi\) | |||||||
\(44\) | 3.00000 | 0.452267 | ||||||||
\(45\) | −3.00000 | −0.447214 | ||||||||
\(46\) | 8.21110 | 1.21066 | ||||||||
\(47\) | −9.90833 | −1.44528 | −0.722639 | − | 0.691226i | \(-0.757071\pi\) | ||||
−0.722639 | + | 0.691226i | \(0.757071\pi\) | |||||||
\(48\) | 2.30278 | 0.332377 | ||||||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | −3.30278 | −0.467083 | ||||||||
\(51\) | −12.9083 | −1.80753 | ||||||||
\(52\) | 5.00000 | 0.693375 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | −1.60555 | −0.218488 | ||||||||
\(55\) | −3.90833 | −0.526999 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 4.60555 | 0.610020 | ||||||||
\(58\) | 4.69722 | 0.616776 | ||||||||
\(59\) | 6.51388 | 0.848035 | 0.424017 | − | 0.905654i | \(-0.360620\pi\) | ||||
0.424017 | + | 0.905654i | \(0.360620\pi\) | |||||||
\(60\) | −3.00000 | −0.387298 | ||||||||
\(61\) | −1.00000 | −0.128037 | −0.0640184 | − | 0.997949i | \(-0.520392\pi\) | ||||
−0.0640184 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(62\) | −9.60555 | −1.21991 | ||||||||
\(63\) | −2.30278 | −0.290122 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.51388 | −0.807947 | ||||||||
\(66\) | 6.90833 | 0.850356 | ||||||||
\(67\) | 16.2111 | 1.98050 | 0.990251 | − | 0.139297i | \(-0.0444842\pi\) | ||||
0.990251 | + | 0.139297i | \(0.0444842\pi\) | |||||||
\(68\) | −5.60555 | −0.679773 | ||||||||
\(69\) | 18.9083 | 2.27630 | ||||||||
\(70\) | 1.30278 | 0.155711 | ||||||||
\(71\) | 7.81665 | 0.927666 | 0.463833 | − | 0.885923i | \(-0.346474\pi\) | ||||
0.463833 | + | 0.885923i | \(0.346474\pi\) | |||||||
\(72\) | 2.30278 | 0.271385 | ||||||||
\(73\) | −3.60555 | −0.421998 | −0.210999 | − | 0.977486i | \(-0.567672\pi\) | ||||
−0.210999 | + | 0.977486i | \(0.567672\pi\) | |||||||
\(74\) | −3.60555 | −0.419137 | ||||||||
\(75\) | −7.60555 | −0.878213 | ||||||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | −3.00000 | −0.341882 | ||||||||
\(78\) | 11.5139 | 1.30369 | ||||||||
\(79\) | −2.69722 | −0.303461 | −0.151731 | − | 0.988422i | \(-0.548485\pi\) | ||||
−0.151731 | + | 0.988422i | \(0.548485\pi\) | |||||||
\(80\) | −1.30278 | −0.145655 | ||||||||
\(81\) | −10.6056 | −1.17839 | ||||||||
\(82\) | −8.60555 | −0.950324 | ||||||||
\(83\) | 8.60555 | 0.944582 | 0.472291 | − | 0.881443i | \(-0.343427\pi\) | ||||
0.472291 | + | 0.881443i | \(0.343427\pi\) | |||||||
\(84\) | −2.30278 | −0.251253 | ||||||||
\(85\) | 7.30278 | 0.792097 | ||||||||
\(86\) | −12.2111 | −1.31676 | ||||||||
\(87\) | 10.8167 | 1.15967 | ||||||||
\(88\) | 3.00000 | 0.319801 | ||||||||
\(89\) | −7.30278 | −0.774093 | −0.387046 | − | 0.922060i | \(-0.626505\pi\) | ||||
−0.387046 | + | 0.922060i | \(0.626505\pi\) | |||||||
\(90\) | −3.00000 | −0.316228 | ||||||||
\(91\) | −5.00000 | −0.524142 | ||||||||
\(92\) | 8.21110 | 0.856067 | ||||||||
\(93\) | −22.1194 | −2.29368 | ||||||||
\(94\) | −9.90833 | −1.02197 | ||||||||
\(95\) | −2.60555 | −0.267324 | ||||||||
\(96\) | 2.30278 | 0.235026 | ||||||||
\(97\) | 4.60555 | 0.467623 | 0.233811 | − | 0.972282i | \(-0.424880\pi\) | ||||
0.233811 | + | 0.972282i | \(0.424880\pi\) | |||||||
\(98\) | −6.00000 | −0.606092 | ||||||||
\(99\) | 6.90833 | 0.694313 | ||||||||
\(100\) | −3.30278 | −0.330278 | ||||||||
\(101\) | 6.90833 | 0.687404 | 0.343702 | − | 0.939079i | \(-0.388319\pi\) | ||||
0.343702 | + | 0.939079i | \(0.388319\pi\) | |||||||
\(102\) | −12.9083 | −1.27811 | ||||||||
\(103\) | 11.1194 | 1.09563 | 0.547815 | − | 0.836600i | \(-0.315460\pi\) | ||||
0.547815 | + | 0.836600i | \(0.315460\pi\) | |||||||
\(104\) | 5.00000 | 0.490290 | ||||||||
\(105\) | 3.00000 | 0.292770 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.21110 | 0.213755 | 0.106878 | − | 0.994272i | \(-0.465915\pi\) | ||||
0.106878 | + | 0.994272i | \(0.465915\pi\) | |||||||
\(108\) | −1.60555 | −0.154494 | ||||||||
\(109\) | 18.8167 | 1.80231 | 0.901154 | − | 0.433499i | \(-0.142721\pi\) | ||||
0.901154 | + | 0.433499i | \(0.142721\pi\) | |||||||
\(110\) | −3.90833 | −0.372644 | ||||||||
\(111\) | −8.30278 | −0.788065 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 0.908327 | 0.0854482 | 0.0427241 | − | 0.999087i | \(-0.486396\pi\) | ||||
0.0427241 | + | 0.999087i | \(0.486396\pi\) | |||||||
\(114\) | 4.60555 | 0.431349 | ||||||||
\(115\) | −10.6972 | −0.997521 | ||||||||
\(116\) | 4.69722 | 0.436126 | ||||||||
\(117\) | 11.5139 | 1.06446 | ||||||||
\(118\) | 6.51388 | 0.599651 | ||||||||
\(119\) | 5.60555 | 0.513860 | ||||||||
\(120\) | −3.00000 | −0.273861 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | −1.00000 | −0.0905357 | ||||||||
\(123\) | −19.8167 | −1.78681 | ||||||||
\(124\) | −9.60555 | −0.862604 | ||||||||
\(125\) | 10.8167 | 0.967471 | ||||||||
\(126\) | −2.30278 | −0.205148 | ||||||||
\(127\) | 0.302776 | 0.0268670 | 0.0134335 | − | 0.999910i | \(-0.495724\pi\) | ||||
0.0134335 | + | 0.999910i | \(0.495724\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −28.1194 | −2.47578 | ||||||||
\(130\) | −6.51388 | −0.571305 | ||||||||
\(131\) | 20.6056 | 1.80032 | 0.900158 | − | 0.435564i | \(-0.143451\pi\) | ||||
0.900158 | + | 0.435564i | \(0.143451\pi\) | |||||||
\(132\) | 6.90833 | 0.601293 | ||||||||
\(133\) | −2.00000 | −0.173422 | ||||||||
\(134\) | 16.2111 | 1.40043 | ||||||||
\(135\) | 2.09167 | 0.180023 | ||||||||
\(136\) | −5.60555 | −0.480672 | ||||||||
\(137\) | 8.09167 | 0.691318 | 0.345659 | − | 0.938360i | \(-0.387655\pi\) | ||||
0.345659 | + | 0.938360i | \(0.387655\pi\) | |||||||
\(138\) | 18.9083 | 1.60958 | ||||||||
\(139\) | −22.5139 | −1.90960 | −0.954801 | − | 0.297245i | \(-0.903932\pi\) | ||||
−0.954801 | + | 0.297245i | \(0.903932\pi\) | |||||||
\(140\) | 1.30278 | 0.110105 | ||||||||
\(141\) | −22.8167 | −1.92151 | ||||||||
\(142\) | 7.81665 | 0.655959 | ||||||||
\(143\) | 15.0000 | 1.25436 | ||||||||
\(144\) | 2.30278 | 0.191898 | ||||||||
\(145\) | −6.11943 | −0.508191 | ||||||||
\(146\) | −3.60555 | −0.298398 | ||||||||
\(147\) | −13.8167 | −1.13958 | ||||||||
\(148\) | −3.60555 | −0.296374 | ||||||||
\(149\) | 7.69722 | 0.630581 | 0.315291 | − | 0.948995i | \(-0.397898\pi\) | ||||
0.315291 | + | 0.948995i | \(0.397898\pi\) | |||||||
\(150\) | −7.60555 | −0.620991 | ||||||||
\(151\) | −15.6056 | −1.26996 | −0.634981 | − | 0.772528i | \(-0.718992\pi\) | ||||
−0.634981 | + | 0.772528i | \(0.718992\pi\) | |||||||
\(152\) | 2.00000 | 0.162221 | ||||||||
\(153\) | −12.9083 | −1.04358 | ||||||||
\(154\) | −3.00000 | −0.241747 | ||||||||
\(155\) | 12.5139 | 1.00514 | ||||||||
\(156\) | 11.5139 | 0.921848 | ||||||||
\(157\) | 10.6056 | 0.846415 | 0.423208 | − | 0.906033i | \(-0.360904\pi\) | ||||
0.423208 | + | 0.906033i | \(0.360904\pi\) | |||||||
\(158\) | −2.69722 | −0.214580 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.30278 | −0.102993 | ||||||||
\(161\) | −8.21110 | −0.647126 | ||||||||
\(162\) | −10.6056 | −0.833251 | ||||||||
\(163\) | −8.69722 | −0.681219 | −0.340610 | − | 0.940205i | \(-0.610633\pi\) | ||||
−0.340610 | + | 0.940205i | \(0.610633\pi\) | |||||||
\(164\) | −8.60555 | −0.671981 | ||||||||
\(165\) | −9.00000 | −0.700649 | ||||||||
\(166\) | 8.60555 | 0.667920 | ||||||||
\(167\) | −20.3305 | −1.57322 | −0.786612 | − | 0.617448i | \(-0.788167\pi\) | ||||
−0.786612 | + | 0.617448i | \(0.788167\pi\) | |||||||
\(168\) | −2.30278 | −0.177663 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 7.30278 | 0.560097 | ||||||||
\(171\) | 4.60555 | 0.352195 | ||||||||
\(172\) | −12.2111 | −0.931088 | ||||||||
\(173\) | 7.42221 | 0.564300 | 0.282150 | − | 0.959370i | \(-0.408952\pi\) | ||||
0.282150 | + | 0.959370i | \(0.408952\pi\) | |||||||
\(174\) | 10.8167 | 0.820008 | ||||||||
\(175\) | 3.30278 | 0.249666 | ||||||||
\(176\) | 3.00000 | 0.226134 | ||||||||
\(177\) | 15.0000 | 1.12747 | ||||||||
\(178\) | −7.30278 | −0.547366 | ||||||||
\(179\) | −24.6333 | −1.84118 | −0.920590 | − | 0.390531i | \(-0.872292\pi\) | ||||
−0.920590 | + | 0.390531i | \(0.872292\pi\) | |||||||
\(180\) | −3.00000 | −0.223607 | ||||||||
\(181\) | 13.2111 | 0.981974 | 0.490987 | − | 0.871167i | \(-0.336636\pi\) | ||||
0.490987 | + | 0.871167i | \(0.336636\pi\) | |||||||
\(182\) | −5.00000 | −0.370625 | ||||||||
\(183\) | −2.30278 | −0.170226 | ||||||||
\(184\) | 8.21110 | 0.605331 | ||||||||
\(185\) | 4.69722 | 0.345347 | ||||||||
\(186\) | −22.1194 | −1.62188 | ||||||||
\(187\) | −16.8167 | −1.22976 | ||||||||
\(188\) | −9.90833 | −0.722639 | ||||||||
\(189\) | 1.60555 | 0.116787 | ||||||||
\(190\) | −2.60555 | −0.189027 | ||||||||
\(191\) | 0.788897 | 0.0570826 | 0.0285413 | − | 0.999593i | \(-0.490914\pi\) | ||||
0.0285413 | + | 0.999593i | \(0.490914\pi\) | |||||||
\(192\) | 2.30278 | 0.166189 | ||||||||
\(193\) | −14.0278 | −1.00974 | −0.504870 | − | 0.863195i | \(-0.668460\pi\) | ||||
−0.504870 | + | 0.863195i | \(0.668460\pi\) | |||||||
\(194\) | 4.60555 | 0.330659 | ||||||||
\(195\) | −15.0000 | −1.07417 | ||||||||
\(196\) | −6.00000 | −0.428571 | ||||||||
\(197\) | 14.0917 | 1.00399 | 0.501995 | − | 0.864870i | \(-0.332600\pi\) | ||||
0.501995 | + | 0.864870i | \(0.332600\pi\) | |||||||
\(198\) | 6.90833 | 0.490953 | ||||||||
\(199\) | −3.09167 | −0.219163 | −0.109581 | − | 0.993978i | \(-0.534951\pi\) | ||||
−0.109581 | + | 0.993978i | \(0.534951\pi\) | |||||||
\(200\) | −3.30278 | −0.233542 | ||||||||
\(201\) | 37.3305 | 2.63309 | ||||||||
\(202\) | 6.90833 | 0.486068 | ||||||||
\(203\) | −4.69722 | −0.329681 | ||||||||
\(204\) | −12.9083 | −0.903764 | ||||||||
\(205\) | 11.2111 | 0.783017 | ||||||||
\(206\) | 11.1194 | 0.774727 | ||||||||
\(207\) | 18.9083 | 1.31422 | ||||||||
\(208\) | 5.00000 | 0.346688 | ||||||||
\(209\) | 6.00000 | 0.415029 | ||||||||
\(210\) | 3.00000 | 0.207020 | ||||||||
\(211\) | −1.11943 | −0.0770647 | −0.0385324 | − | 0.999257i | \(-0.512268\pi\) | ||||
−0.0385324 | + | 0.999257i | \(0.512268\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 18.0000 | 1.23334 | ||||||||
\(214\) | 2.21110 | 0.151148 | ||||||||
\(215\) | 15.9083 | 1.08494 | ||||||||
\(216\) | −1.60555 | −0.109244 | ||||||||
\(217\) | 9.60555 | 0.652067 | ||||||||
\(218\) | 18.8167 | 1.27442 | ||||||||
\(219\) | −8.30278 | −0.561050 | ||||||||
\(220\) | −3.90833 | −0.263499 | ||||||||
\(221\) | −28.0278 | −1.88535 | ||||||||
\(222\) | −8.30278 | −0.557246 | ||||||||
\(223\) | −13.9083 | −0.931370 | −0.465685 | − | 0.884950i | \(-0.654192\pi\) | ||||
−0.465685 | + | 0.884950i | \(0.654192\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −7.60555 | −0.507037 | ||||||||
\(226\) | 0.908327 | 0.0604210 | ||||||||
\(227\) | −8.72498 | −0.579097 | −0.289549 | − | 0.957163i | \(-0.593505\pi\) | ||||
−0.289549 | + | 0.957163i | \(0.593505\pi\) | |||||||
\(228\) | 4.60555 | 0.305010 | ||||||||
\(229\) | 6.02776 | 0.398325 | 0.199163 | − | 0.979966i | \(-0.436178\pi\) | ||||
0.199163 | + | 0.979966i | \(0.436178\pi\) | |||||||
\(230\) | −10.6972 | −0.705354 | ||||||||
\(231\) | −6.90833 | −0.454535 | ||||||||
\(232\) | 4.69722 | 0.308388 | ||||||||
\(233\) | 16.8167 | 1.10170 | 0.550848 | − | 0.834606i | \(-0.314304\pi\) | ||||
0.550848 | + | 0.834606i | \(0.314304\pi\) | |||||||
\(234\) | 11.5139 | 0.752686 | ||||||||
\(235\) | 12.9083 | 0.842046 | ||||||||
\(236\) | 6.51388 | 0.424017 | ||||||||
\(237\) | −6.21110 | −0.403454 | ||||||||
\(238\) | 5.60555 | 0.363354 | ||||||||
\(239\) | 0.908327 | 0.0587548 | 0.0293774 | − | 0.999568i | \(-0.490648\pi\) | ||||
0.0293774 | + | 0.999568i | \(0.490648\pi\) | |||||||
\(240\) | −3.00000 | −0.193649 | ||||||||
\(241\) | 18.0278 | 1.16127 | 0.580635 | − | 0.814164i | \(-0.302804\pi\) | ||||
0.580635 | + | 0.814164i | \(0.302804\pi\) | |||||||
\(242\) | −2.00000 | −0.128565 | ||||||||
\(243\) | −19.6056 | −1.25770 | ||||||||
\(244\) | −1.00000 | −0.0640184 | ||||||||
\(245\) | 7.81665 | 0.499388 | ||||||||
\(246\) | −19.8167 | −1.26346 | ||||||||
\(247\) | 10.0000 | 0.636285 | ||||||||
\(248\) | −9.60555 | −0.609953 | ||||||||
\(249\) | 19.8167 | 1.25583 | ||||||||
\(250\) | 10.8167 | 0.684105 | ||||||||
\(251\) | −11.7250 | −0.740074 | −0.370037 | − | 0.929017i | \(-0.620655\pi\) | ||||
−0.370037 | + | 0.929017i | \(0.620655\pi\) | |||||||
\(252\) | −2.30278 | −0.145061 | ||||||||
\(253\) | 24.6333 | 1.54868 | ||||||||
\(254\) | 0.302776 | 0.0189978 | ||||||||
\(255\) | 16.8167 | 1.05310 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.00000 | −0.187135 | −0.0935674 | − | 0.995613i | \(-0.529827\pi\) | ||||
−0.0935674 | + | 0.995613i | \(0.529827\pi\) | |||||||
\(258\) | −28.1194 | −1.75064 | ||||||||
\(259\) | 3.60555 | 0.224038 | ||||||||
\(260\) | −6.51388 | −0.403974 | ||||||||
\(261\) | 10.8167 | 0.669534 | ||||||||
\(262\) | 20.6056 | 1.27302 | ||||||||
\(263\) | 21.5139 | 1.32660 | 0.663301 | − | 0.748352i | \(-0.269155\pi\) | ||||
0.663301 | + | 0.748352i | \(0.269155\pi\) | |||||||
\(264\) | 6.90833 | 0.425178 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.00000 | −0.122628 | ||||||||
\(267\) | −16.8167 | −1.02916 | ||||||||
\(268\) | 16.2111 | 0.990251 | ||||||||
\(269\) | −1.00000 | −0.0609711 | ||||||||
\(270\) | 2.09167 | 0.127295 | ||||||||
\(271\) | 11.0000 | 0.668202 | 0.334101 | − | 0.942537i | \(-0.391567\pi\) | ||||
0.334101 | + | 0.942537i | \(0.391567\pi\) | |||||||
\(272\) | −5.60555 | −0.339886 | ||||||||
\(273\) | −11.5139 | −0.696852 | ||||||||
\(274\) | 8.09167 | 0.488836 | ||||||||
\(275\) | −9.90833 | −0.597495 | ||||||||
\(276\) | 18.9083 | 1.13815 | ||||||||
\(277\) | −16.1194 | −0.968523 | −0.484261 | − | 0.874923i | \(-0.660912\pi\) | ||||
−0.484261 | + | 0.874923i | \(0.660912\pi\) | |||||||
\(278\) | −22.5139 | −1.35029 | ||||||||
\(279\) | −22.1194 | −1.32426 | ||||||||
\(280\) | 1.30278 | 0.0778557 | ||||||||
\(281\) | 10.8167 | 0.645267 | 0.322634 | − | 0.946524i | \(-0.395432\pi\) | ||||
0.322634 | + | 0.946524i | \(0.395432\pi\) | |||||||
\(282\) | −22.8167 | −1.35871 | ||||||||
\(283\) | −13.0000 | −0.772770 | −0.386385 | − | 0.922338i | \(-0.626276\pi\) | ||||
−0.386385 | + | 0.922338i | \(0.626276\pi\) | |||||||
\(284\) | 7.81665 | 0.463833 | ||||||||
\(285\) | −6.00000 | −0.355409 | ||||||||
\(286\) | 15.0000 | 0.886969 | ||||||||
\(287\) | 8.60555 | 0.507970 | ||||||||
\(288\) | 2.30278 | 0.135692 | ||||||||
\(289\) | 14.4222 | 0.848365 | ||||||||
\(290\) | −6.11943 | −0.359345 | ||||||||
\(291\) | 10.6056 | 0.621708 | ||||||||
\(292\) | −3.60555 | −0.210999 | ||||||||
\(293\) | 6.00000 | 0.350524 | 0.175262 | − | 0.984522i | \(-0.443923\pi\) | ||||
0.175262 | + | 0.984522i | \(0.443923\pi\) | |||||||
\(294\) | −13.8167 | −0.805804 | ||||||||
\(295\) | −8.48612 | −0.494081 | ||||||||
\(296\) | −3.60555 | −0.209568 | ||||||||
\(297\) | −4.81665 | −0.279491 | ||||||||
\(298\) | 7.69722 | 0.445888 | ||||||||
\(299\) | 41.0555 | 2.37430 | ||||||||
\(300\) | −7.60555 | −0.439107 | ||||||||
\(301\) | 12.2111 | 0.703836 | ||||||||
\(302\) | −15.6056 | −0.897999 | ||||||||
\(303\) | 15.9083 | 0.913910 | ||||||||
\(304\) | 2.00000 | 0.114708 | ||||||||
\(305\) | 1.30278 | 0.0745967 | ||||||||
\(306\) | −12.9083 | −0.737920 | ||||||||
\(307\) | 15.4222 | 0.880192 | 0.440096 | − | 0.897951i | \(-0.354944\pi\) | ||||
0.440096 | + | 0.897951i | \(0.354944\pi\) | |||||||
\(308\) | −3.00000 | −0.170941 | ||||||||
\(309\) | 25.6056 | 1.45665 | ||||||||
\(310\) | 12.5139 | 0.710741 | ||||||||
\(311\) | 13.8167 | 0.783471 | 0.391735 | − | 0.920078i | \(-0.371875\pi\) | ||||
0.391735 | + | 0.920078i | \(0.371875\pi\) | |||||||
\(312\) | 11.5139 | 0.651845 | ||||||||
\(313\) | −17.3028 | −0.978011 | −0.489005 | − | 0.872281i | \(-0.662640\pi\) | ||||
−0.489005 | + | 0.872281i | \(0.662640\pi\) | |||||||
\(314\) | 10.6056 | 0.598506 | ||||||||
\(315\) | 3.00000 | 0.169031 | ||||||||
\(316\) | −2.69722 | −0.151731 | ||||||||
\(317\) | 24.3944 | 1.37013 | 0.685064 | − | 0.728483i | \(-0.259774\pi\) | ||||
0.685064 | + | 0.728483i | \(0.259774\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.0917 | 0.788982 | ||||||||
\(320\) | −1.30278 | −0.0728274 | ||||||||
\(321\) | 5.09167 | 0.284189 | ||||||||
\(322\) | −8.21110 | −0.457587 | ||||||||
\(323\) | −11.2111 | −0.623802 | ||||||||
\(324\) | −10.6056 | −0.589197 | ||||||||
\(325\) | −16.5139 | −0.916025 | ||||||||
\(326\) | −8.69722 | −0.481695 | ||||||||
\(327\) | 43.3305 | 2.39618 | ||||||||
\(328\) | −8.60555 | −0.475162 | ||||||||
\(329\) | 9.90833 | 0.546264 | ||||||||
\(330\) | −9.00000 | −0.495434 | ||||||||
\(331\) | −1.00000 | −0.0549650 | −0.0274825 | − | 0.999622i | \(-0.508749\pi\) | ||||
−0.0274825 | + | 0.999622i | \(0.508749\pi\) | |||||||
\(332\) | 8.60555 | 0.472291 | ||||||||
\(333\) | −8.30278 | −0.454989 | ||||||||
\(334\) | −20.3305 | −1.11244 | ||||||||
\(335\) | −21.1194 | −1.15388 | ||||||||
\(336\) | −2.30278 | −0.125627 | ||||||||
\(337\) | −23.5416 | −1.28239 | −0.641197 | − | 0.767376i | \(-0.721562\pi\) | ||||
−0.641197 | + | 0.767376i | \(0.721562\pi\) | |||||||
\(338\) | 12.0000 | 0.652714 | ||||||||
\(339\) | 2.09167 | 0.113604 | ||||||||
\(340\) | 7.30278 | 0.396049 | ||||||||
\(341\) | −28.8167 | −1.56051 | ||||||||
\(342\) | 4.60555 | 0.249040 | ||||||||
\(343\) | 13.0000 | 0.701934 | ||||||||
\(344\) | −12.2111 | −0.658379 | ||||||||
\(345\) | −24.6333 | −1.32621 | ||||||||
\(346\) | 7.42221 | 0.399020 | ||||||||
\(347\) | 7.18335 | 0.385622 | 0.192811 | − | 0.981236i | \(-0.438240\pi\) | ||||
0.192811 | + | 0.981236i | \(0.438240\pi\) | |||||||
\(348\) | 10.8167 | 0.579834 | ||||||||
\(349\) | −8.30278 | −0.444437 | −0.222219 | − | 0.974997i | \(-0.571330\pi\) | ||||
−0.222219 | + | 0.974997i | \(0.571330\pi\) | |||||||
\(350\) | 3.30278 | 0.176541 | ||||||||
\(351\) | −8.02776 | −0.428490 | ||||||||
\(352\) | 3.00000 | 0.159901 | ||||||||
\(353\) | 11.3305 | 0.603063 | 0.301532 | − | 0.953456i | \(-0.402502\pi\) | ||||
0.301532 | + | 0.953456i | \(0.402502\pi\) | |||||||
\(354\) | 15.0000 | 0.797241 | ||||||||
\(355\) | −10.1833 | −0.540476 | ||||||||
\(356\) | −7.30278 | −0.387046 | ||||||||
\(357\) | 12.9083 | 0.683181 | ||||||||
\(358\) | −24.6333 | −1.30191 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | −3.00000 | −0.158114 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 13.2111 | 0.694360 | ||||||||
\(363\) | −4.60555 | −0.241729 | ||||||||
\(364\) | −5.00000 | −0.262071 | ||||||||
\(365\) | 4.69722 | 0.245864 | ||||||||
\(366\) | −2.30278 | −0.120368 | ||||||||
\(367\) | −22.9083 | −1.19580 | −0.597902 | − | 0.801569i | \(-0.703999\pi\) | ||||
−0.597902 | + | 0.801569i | \(0.703999\pi\) | |||||||
\(368\) | 8.21110 | 0.428033 | ||||||||
\(369\) | −19.8167 | −1.03161 | ||||||||
\(370\) | 4.69722 | 0.244197 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −22.1194 | −1.14684 | ||||||||
\(373\) | 20.7889 | 1.07641 | 0.538204 | − | 0.842815i | \(-0.319103\pi\) | ||||
0.538204 | + | 0.842815i | \(0.319103\pi\) | |||||||
\(374\) | −16.8167 | −0.869568 | ||||||||
\(375\) | 24.9083 | 1.28626 | ||||||||
\(376\) | −9.90833 | −0.510983 | ||||||||
\(377\) | 23.4861 | 1.20960 | ||||||||
\(378\) | 1.60555 | 0.0825806 | ||||||||
\(379\) | 4.72498 | 0.242706 | 0.121353 | − | 0.992609i | \(-0.461277\pi\) | ||||
0.121353 | + | 0.992609i | \(0.461277\pi\) | |||||||
\(380\) | −2.60555 | −0.133662 | ||||||||
\(381\) | 0.697224 | 0.0357199 | ||||||||
\(382\) | 0.788897 | 0.0403635 | ||||||||
\(383\) | −21.5139 | −1.09931 | −0.549654 | − | 0.835392i | \(-0.685240\pi\) | ||||
−0.549654 | + | 0.835392i | \(0.685240\pi\) | |||||||
\(384\) | 2.30278 | 0.117513 | ||||||||
\(385\) | 3.90833 | 0.199187 | ||||||||
\(386\) | −14.0278 | −0.713994 | ||||||||
\(387\) | −28.1194 | −1.42939 | ||||||||
\(388\) | 4.60555 | 0.233811 | ||||||||
\(389\) | −17.2111 | −0.872638 | −0.436319 | − | 0.899792i | \(-0.643718\pi\) | ||||
−0.436319 | + | 0.899792i | \(0.643718\pi\) | |||||||
\(390\) | −15.0000 | −0.759555 | ||||||||
\(391\) | −46.0278 | −2.32772 | ||||||||
\(392\) | −6.00000 | −0.303046 | ||||||||
\(393\) | 47.4500 | 2.39353 | ||||||||
\(394\) | 14.0917 | 0.709928 | ||||||||
\(395\) | 3.51388 | 0.176802 | ||||||||
\(396\) | 6.90833 | 0.347156 | ||||||||
\(397\) | 2.51388 | 0.126168 | 0.0630840 | − | 0.998008i | \(-0.479906\pi\) | ||||
0.0630840 | + | 0.998008i | \(0.479906\pi\) | |||||||
\(398\) | −3.09167 | −0.154972 | ||||||||
\(399\) | −4.60555 | −0.230566 | ||||||||
\(400\) | −3.30278 | −0.165139 | ||||||||
\(401\) | 39.1194 | 1.95353 | 0.976766 | − | 0.214311i | \(-0.0687505\pi\) | ||||
0.976766 | + | 0.214311i | \(0.0687505\pi\) | |||||||
\(402\) | 37.3305 | 1.86188 | ||||||||
\(403\) | −48.0278 | −2.39243 | ||||||||
\(404\) | 6.90833 | 0.343702 | ||||||||
\(405\) | 13.8167 | 0.686555 | ||||||||
\(406\) | −4.69722 | −0.233119 | ||||||||
\(407\) | −10.8167 | −0.536162 | ||||||||
\(408\) | −12.9083 | −0.639057 | ||||||||
\(409\) | −27.6056 | −1.36501 | −0.682503 | − | 0.730882i | \(-0.739109\pi\) | ||||
−0.682503 | + | 0.730882i | \(0.739109\pi\) | |||||||
\(410\) | 11.2111 | 0.553677 | ||||||||
\(411\) | 18.6333 | 0.919113 | ||||||||
\(412\) | 11.1194 | 0.547815 | ||||||||
\(413\) | −6.51388 | −0.320527 | ||||||||
\(414\) | 18.9083 | 0.929294 | ||||||||
\(415\) | −11.2111 | −0.550331 | ||||||||
\(416\) | 5.00000 | 0.245145 | ||||||||
\(417\) | −51.8444 | −2.53883 | ||||||||
\(418\) | 6.00000 | 0.293470 | ||||||||
\(419\) | 27.9083 | 1.36341 | 0.681705 | − | 0.731627i | \(-0.261239\pi\) | ||||
0.681705 | + | 0.731627i | \(0.261239\pi\) | |||||||
\(420\) | 3.00000 | 0.146385 | ||||||||
\(421\) | 21.4222 | 1.04405 | 0.522027 | − | 0.852929i | \(-0.325176\pi\) | ||||
0.522027 | + | 0.852929i | \(0.325176\pi\) | |||||||
\(422\) | −1.11943 | −0.0544930 | ||||||||
\(423\) | −22.8167 | −1.10938 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 18.5139 | 0.898055 | ||||||||
\(426\) | 18.0000 | 0.872103 | ||||||||
\(427\) | 1.00000 | 0.0483934 | ||||||||
\(428\) | 2.21110 | 0.106878 | ||||||||
\(429\) | 34.5416 | 1.66769 | ||||||||
\(430\) | 15.9083 | 0.767168 | ||||||||
\(431\) | −23.6056 | −1.13704 | −0.568520 | − | 0.822670i | \(-0.692484\pi\) | ||||
−0.568520 | + | 0.822670i | \(0.692484\pi\) | |||||||
\(432\) | −1.60555 | −0.0772471 | ||||||||
\(433\) | 23.9083 | 1.14896 | 0.574480 | − | 0.818518i | \(-0.305204\pi\) | ||||
0.574480 | + | 0.818518i | \(0.305204\pi\) | |||||||
\(434\) | 9.60555 | 0.461081 | ||||||||
\(435\) | −14.0917 | −0.675644 | ||||||||
\(436\) | 18.8167 | 0.901154 | ||||||||
\(437\) | 16.4222 | 0.785581 | ||||||||
\(438\) | −8.30278 | −0.396722 | ||||||||
\(439\) | −18.3305 | −0.874869 | −0.437434 | − | 0.899250i | \(-0.644113\pi\) | ||||
−0.437434 | + | 0.899250i | \(0.644113\pi\) | |||||||
\(440\) | −3.90833 | −0.186322 | ||||||||
\(441\) | −13.8167 | −0.657936 | ||||||||
\(442\) | −28.0278 | −1.33314 | ||||||||
\(443\) | 16.4222 | 0.780243 | 0.390121 | − | 0.920763i | \(-0.372433\pi\) | ||||
0.390121 | + | 0.920763i | \(0.372433\pi\) | |||||||
\(444\) | −8.30278 | −0.394032 | ||||||||
\(445\) | 9.51388 | 0.451001 | ||||||||
\(446\) | −13.9083 | −0.658578 | ||||||||
\(447\) | 17.7250 | 0.838363 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 5.09167 | 0.240291 | 0.120145 | − | 0.992756i | \(-0.461664\pi\) | ||||
0.120145 | + | 0.992756i | \(0.461664\pi\) | |||||||
\(450\) | −7.60555 | −0.358529 | ||||||||
\(451\) | −25.8167 | −1.21566 | ||||||||
\(452\) | 0.908327 | 0.0427241 | ||||||||
\(453\) | −35.9361 | −1.68842 | ||||||||
\(454\) | −8.72498 | −0.409484 | ||||||||
\(455\) | 6.51388 | 0.305375 | ||||||||
\(456\) | 4.60555 | 0.215675 | ||||||||
\(457\) | 10.7250 | 0.501693 | 0.250847 | − | 0.968027i | \(-0.419291\pi\) | ||||
0.250847 | + | 0.968027i | \(0.419291\pi\) | |||||||
\(458\) | 6.02776 | 0.281659 | ||||||||
\(459\) | 9.00000 | 0.420084 | ||||||||
\(460\) | −10.6972 | −0.498761 | ||||||||
\(461\) | 13.0278 | 0.606763 | 0.303382 | − | 0.952869i | \(-0.401884\pi\) | ||||
0.303382 | + | 0.952869i | \(0.401884\pi\) | |||||||
\(462\) | −6.90833 | −0.321404 | ||||||||
\(463\) | 35.9083 | 1.66880 | 0.834401 | − | 0.551158i | \(-0.185814\pi\) | ||||
0.834401 | + | 0.551158i | \(0.185814\pi\) | |||||||
\(464\) | 4.69722 | 0.218063 | ||||||||
\(465\) | 28.8167 | 1.33634 | ||||||||
\(466\) | 16.8167 | 0.779016 | ||||||||
\(467\) | 4.42221 | 0.204635 | 0.102318 | − | 0.994752i | \(-0.467374\pi\) | ||||
0.102318 | + | 0.994752i | \(0.467374\pi\) | |||||||
\(468\) | 11.5139 | 0.532229 | ||||||||
\(469\) | −16.2111 | −0.748559 | ||||||||
\(470\) | 12.9083 | 0.595417 | ||||||||
\(471\) | 24.4222 | 1.12532 | ||||||||
\(472\) | 6.51388 | 0.299826 | ||||||||
\(473\) | −36.6333 | −1.68440 | ||||||||
\(474\) | −6.21110 | −0.285285 | ||||||||
\(475\) | −6.60555 | −0.303083 | ||||||||
\(476\) | 5.60555 | 0.256930 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.908327 | 0.0415459 | ||||||||
\(479\) | 9.78890 | 0.447266 | 0.223633 | − | 0.974673i | \(-0.428208\pi\) | ||||
0.223633 | + | 0.974673i | \(0.428208\pi\) | |||||||
\(480\) | −3.00000 | −0.136931 | ||||||||
\(481\) | −18.0278 | −0.821995 | ||||||||
\(482\) | 18.0278 | 0.821142 | ||||||||
\(483\) | −18.9083 | −0.860359 | ||||||||
\(484\) | −2.00000 | −0.0909091 | ||||||||
\(485\) | −6.00000 | −0.272446 | ||||||||
\(486\) | −19.6056 | −0.889326 | ||||||||
\(487\) | −38.4222 | −1.74108 | −0.870538 | − | 0.492101i | \(-0.836229\pi\) | ||||
−0.870538 | + | 0.492101i | \(0.836229\pi\) | |||||||
\(488\) | −1.00000 | −0.0452679 | ||||||||
\(489\) | −20.0278 | −0.905686 | ||||||||
\(490\) | 7.81665 | 0.353120 | ||||||||
\(491\) | −37.8167 | −1.70664 | −0.853321 | − | 0.521386i | \(-0.825415\pi\) | ||||
−0.853321 | + | 0.521386i | \(0.825415\pi\) | |||||||
\(492\) | −19.8167 | −0.893404 | ||||||||
\(493\) | −26.3305 | −1.18587 | ||||||||
\(494\) | 10.0000 | 0.449921 | ||||||||
\(495\) | −9.00000 | −0.404520 | ||||||||
\(496\) | −9.60555 | −0.431302 | ||||||||
\(497\) | −7.81665 | −0.350625 | ||||||||
\(498\) | 19.8167 | 0.888005 | ||||||||
\(499\) | 35.2389 | 1.57751 | 0.788754 | − | 0.614709i | \(-0.210727\pi\) | ||||
0.788754 | + | 0.614709i | \(0.210727\pi\) | |||||||
\(500\) | 10.8167 | 0.483735 | ||||||||
\(501\) | −46.8167 | −2.09161 | ||||||||
\(502\) | −11.7250 | −0.523312 | ||||||||
\(503\) | −33.6333 | −1.49964 | −0.749818 | − | 0.661645i | \(-0.769859\pi\) | ||||
−0.749818 | + | 0.661645i | \(0.769859\pi\) | |||||||
\(504\) | −2.30278 | −0.102574 | ||||||||
\(505\) | −9.00000 | −0.400495 | ||||||||
\(506\) | 24.6333 | 1.09508 | ||||||||
\(507\) | 27.6333 | 1.22724 | ||||||||
\(508\) | 0.302776 | 0.0134335 | ||||||||
\(509\) | 28.9361 | 1.28257 | 0.641285 | − | 0.767303i | \(-0.278402\pi\) | ||||
0.641285 | + | 0.767303i | \(0.278402\pi\) | |||||||
\(510\) | 16.8167 | 0.744654 | ||||||||
\(511\) | 3.60555 | 0.159500 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −3.21110 | −0.141774 | ||||||||
\(514\) | −3.00000 | −0.132324 | ||||||||
\(515\) | −14.4861 | −0.638335 | ||||||||
\(516\) | −28.1194 | −1.23789 | ||||||||
\(517\) | −29.7250 | −1.30730 | ||||||||
\(518\) | 3.60555 | 0.158419 | ||||||||
\(519\) | 17.0917 | 0.750241 | ||||||||
\(520\) | −6.51388 | −0.285652 | ||||||||
\(521\) | 6.63331 | 0.290610 | 0.145305 | − | 0.989387i | \(-0.453584\pi\) | ||||
0.145305 | + | 0.989387i | \(0.453584\pi\) | |||||||
\(522\) | 10.8167 | 0.473432 | ||||||||
\(523\) | −23.3028 | −1.01896 | −0.509480 | − | 0.860483i | \(-0.670162\pi\) | ||||
−0.509480 | + | 0.860483i | \(0.670162\pi\) | |||||||
\(524\) | 20.6056 | 0.900158 | ||||||||
\(525\) | 7.60555 | 0.331933 | ||||||||
\(526\) | 21.5139 | 0.938050 | ||||||||
\(527\) | 53.8444 | 2.34550 | ||||||||
\(528\) | 6.90833 | 0.300646 | ||||||||
\(529\) | 44.4222 | 1.93140 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.0000 | 0.650945 | ||||||||
\(532\) | −2.00000 | −0.0867110 | ||||||||
\(533\) | −43.0278 | −1.86374 | ||||||||
\(534\) | −16.8167 | −0.727728 | ||||||||
\(535\) | −2.88057 | −0.124538 | ||||||||
\(536\) | 16.2111 | 0.700213 | ||||||||
\(537\) | −56.7250 | −2.44786 | ||||||||
\(538\) | −1.00000 | −0.0431131 | ||||||||
\(539\) | −18.0000 | −0.775315 | ||||||||
\(540\) | 2.09167 | 0.0900113 | ||||||||
\(541\) | −20.4222 | −0.878019 | −0.439010 | − | 0.898482i | \(-0.644671\pi\) | ||||
−0.439010 | + | 0.898482i | \(0.644671\pi\) | |||||||
\(542\) | 11.0000 | 0.472490 | ||||||||
\(543\) | 30.4222 | 1.30554 | ||||||||
\(544\) | −5.60555 | −0.240336 | ||||||||
\(545\) | −24.5139 | −1.05006 | ||||||||
\(546\) | −11.5139 | −0.492748 | ||||||||
\(547\) | 39.9361 | 1.70754 | 0.853772 | − | 0.520647i | \(-0.174309\pi\) | ||||
0.853772 | + | 0.520647i | \(0.174309\pi\) | |||||||
\(548\) | 8.09167 | 0.345659 | ||||||||
\(549\) | −2.30278 | −0.0982801 | ||||||||
\(550\) | −9.90833 | −0.422492 | ||||||||
\(551\) | 9.39445 | 0.400217 | ||||||||
\(552\) | 18.9083 | 0.804792 | ||||||||
\(553\) | 2.69722 | 0.114698 | ||||||||
\(554\) | −16.1194 | −0.684849 | ||||||||
\(555\) | 10.8167 | 0.459141 | ||||||||
\(556\) | −22.5139 | −0.954801 | ||||||||
\(557\) | −12.2389 | −0.518577 | −0.259289 | − | 0.965800i | \(-0.583488\pi\) | ||||
−0.259289 | + | 0.965800i | \(0.583488\pi\) | |||||||
\(558\) | −22.1194 | −0.936390 | ||||||||
\(559\) | −61.0555 | −2.58237 | ||||||||
\(560\) | 1.30278 | 0.0550523 | ||||||||
\(561\) | −38.7250 | −1.63497 | ||||||||
\(562\) | 10.8167 | 0.456273 | ||||||||
\(563\) | −0.633308 | −0.0266907 | −0.0133454 | − | 0.999911i | \(-0.504248\pi\) | ||||
−0.0133454 | + | 0.999911i | \(0.504248\pi\) | |||||||
\(564\) | −22.8167 | −0.960754 | ||||||||
\(565\) | −1.18335 | −0.0497837 | ||||||||
\(566\) | −13.0000 | −0.546431 | ||||||||
\(567\) | 10.6056 | 0.445391 | ||||||||
\(568\) | 7.81665 | 0.327980 | ||||||||
\(569\) | −20.0917 | −0.842287 | −0.421143 | − | 0.906994i | \(-0.638371\pi\) | ||||
−0.421143 | + | 0.906994i | \(0.638371\pi\) | |||||||
\(570\) | −6.00000 | −0.251312 | ||||||||
\(571\) | −30.8444 | −1.29080 | −0.645399 | − | 0.763845i | \(-0.723309\pi\) | ||||
−0.645399 | + | 0.763845i | \(0.723309\pi\) | |||||||
\(572\) | 15.0000 | 0.627182 | ||||||||
\(573\) | 1.81665 | 0.0758918 | ||||||||
\(574\) | 8.60555 | 0.359189 | ||||||||
\(575\) | −27.1194 | −1.13096 | ||||||||
\(576\) | 2.30278 | 0.0959490 | ||||||||
\(577\) | −40.6333 | −1.69159 | −0.845793 | − | 0.533511i | \(-0.820872\pi\) | ||||
−0.845793 | + | 0.533511i | \(0.820872\pi\) | |||||||
\(578\) | 14.4222 | 0.599885 | ||||||||
\(579\) | −32.3028 | −1.34246 | ||||||||
\(580\) | −6.11943 | −0.254095 | ||||||||
\(581\) | −8.60555 | −0.357018 | ||||||||
\(582\) | 10.6056 | 0.439614 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −3.60555 | −0.149199 | ||||||||
\(585\) | −15.0000 | −0.620174 | ||||||||
\(586\) | 6.00000 | 0.247858 | ||||||||
\(587\) | 19.3028 | 0.796711 | 0.398355 | − | 0.917231i | \(-0.369581\pi\) | ||||
0.398355 | + | 0.917231i | \(0.369581\pi\) | |||||||
\(588\) | −13.8167 | −0.569789 | ||||||||
\(589\) | −19.2111 | −0.791580 | ||||||||
\(590\) | −8.48612 | −0.349368 | ||||||||
\(591\) | 32.4500 | 1.33481 | ||||||||
\(592\) | −3.60555 | −0.148187 | ||||||||
\(593\) | −15.6333 | −0.641983 | −0.320991 | − | 0.947082i | \(-0.604016\pi\) | ||||
−0.320991 | + | 0.947082i | \(0.604016\pi\) | |||||||
\(594\) | −4.81665 | −0.197630 | ||||||||
\(595\) | −7.30278 | −0.299385 | ||||||||
\(596\) | 7.69722 | 0.315291 | ||||||||
\(597\) | −7.11943 | −0.291379 | ||||||||
\(598\) | 41.0555 | 1.67888 | ||||||||
\(599\) | −19.8167 | −0.809687 | −0.404843 | − | 0.914386i | \(-0.632674\pi\) | ||||
−0.404843 | + | 0.914386i | \(0.632674\pi\) | |||||||
\(600\) | −7.60555 | −0.310495 | ||||||||
\(601\) | 34.3305 | 1.40037 | 0.700186 | − | 0.713961i | \(-0.253100\pi\) | ||||
0.700186 | + | 0.713961i | \(0.253100\pi\) | |||||||
\(602\) | 12.2111 | 0.497687 | ||||||||
\(603\) | 37.3305 | 1.52022 | ||||||||
\(604\) | −15.6056 | −0.634981 | ||||||||
\(605\) | 2.60555 | 0.105931 | ||||||||
\(606\) | 15.9083 | 0.646232 | ||||||||
\(607\) | 33.5416 | 1.36141 | 0.680706 | − | 0.732556i | \(-0.261673\pi\) | ||||
0.680706 | + | 0.732556i | \(0.261673\pi\) | |||||||
\(608\) | 2.00000 | 0.0811107 | ||||||||
\(609\) | −10.8167 | −0.438313 | ||||||||
\(610\) | 1.30278 | 0.0527478 | ||||||||
\(611\) | −49.5416 | −2.00424 | ||||||||
\(612\) | −12.9083 | −0.521788 | ||||||||
\(613\) | −36.2111 | −1.46255 | −0.731276 | − | 0.682081i | \(-0.761075\pi\) | ||||
−0.731276 | + | 0.682081i | \(0.761075\pi\) | |||||||
\(614\) | 15.4222 | 0.622390 | ||||||||
\(615\) | 25.8167 | 1.04103 | ||||||||
\(616\) | −3.00000 | −0.120873 | ||||||||
\(617\) | 28.9361 | 1.16492 | 0.582461 | − | 0.812858i | \(-0.302090\pi\) | ||||
0.582461 | + | 0.812858i | \(0.302090\pi\) | |||||||
\(618\) | 25.6056 | 1.03001 | ||||||||
\(619\) | 19.2111 | 0.772159 | 0.386080 | − | 0.922465i | \(-0.373829\pi\) | ||||
0.386080 | + | 0.922465i | \(0.373829\pi\) | |||||||
\(620\) | 12.5139 | 0.502569 | ||||||||
\(621\) | −13.1833 | −0.529029 | ||||||||
\(622\) | 13.8167 | 0.553997 | ||||||||
\(623\) | 7.30278 | 0.292580 | ||||||||
\(624\) | 11.5139 | 0.460924 | ||||||||
\(625\) | 2.42221 | 0.0968882 | ||||||||
\(626\) | −17.3028 | −0.691558 | ||||||||
\(627\) | 13.8167 | 0.551784 | ||||||||
\(628\) | 10.6056 | 0.423208 | ||||||||
\(629\) | 20.2111 | 0.805869 | ||||||||
\(630\) | 3.00000 | 0.119523 | ||||||||
\(631\) | 8.11943 | 0.323229 | 0.161615 | − | 0.986854i | \(-0.448330\pi\) | ||||
0.161615 | + | 0.986854i | \(0.448330\pi\) | |||||||
\(632\) | −2.69722 | −0.107290 | ||||||||
\(633\) | −2.57779 | −0.102458 | ||||||||
\(634\) | 24.3944 | 0.968827 | ||||||||
\(635\) | −0.394449 | −0.0156532 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −30.0000 | −1.18864 | ||||||||
\(638\) | 14.0917 | 0.557895 | ||||||||
\(639\) | 18.0000 | 0.712069 | ||||||||
\(640\) | −1.30278 | −0.0514967 | ||||||||
\(641\) | 33.2389 | 1.31286 | 0.656428 | − | 0.754389i | \(-0.272067\pi\) | ||||
0.656428 | + | 0.754389i | \(0.272067\pi\) | |||||||
\(642\) | 5.09167 | 0.200952 | ||||||||
\(643\) | 24.5416 | 0.967828 | 0.483914 | − | 0.875116i | \(-0.339215\pi\) | ||||
0.483914 | + | 0.875116i | \(0.339215\pi\) | |||||||
\(644\) | −8.21110 | −0.323563 | ||||||||
\(645\) | 36.6333 | 1.44244 | ||||||||
\(646\) | −11.2111 | −0.441095 | ||||||||
\(647\) | −6.63331 | −0.260782 | −0.130391 | − | 0.991463i | \(-0.541623\pi\) | ||||
−0.130391 | + | 0.991463i | \(0.541623\pi\) | |||||||
\(648\) | −10.6056 | −0.416625 | ||||||||
\(649\) | 19.5416 | 0.767076 | ||||||||
\(650\) | −16.5139 | −0.647728 | ||||||||
\(651\) | 22.1194 | 0.866929 | ||||||||
\(652\) | −8.69722 | −0.340610 | ||||||||
\(653\) | −15.2389 | −0.596343 | −0.298171 | − | 0.954512i | \(-0.596377\pi\) | ||||
−0.298171 | + | 0.954512i | \(0.596377\pi\) | |||||||
\(654\) | 43.3305 | 1.69436 | ||||||||
\(655\) | −26.8444 | −1.04890 | ||||||||
\(656\) | −8.60555 | −0.335990 | ||||||||
\(657\) | −8.30278 | −0.323922 | ||||||||
\(658\) | 9.90833 | 0.386267 | ||||||||
\(659\) | −28.9361 | −1.12719 | −0.563595 | − | 0.826051i | \(-0.690582\pi\) | ||||
−0.563595 | + | 0.826051i | \(0.690582\pi\) | |||||||
\(660\) | −9.00000 | −0.350325 | ||||||||
\(661\) | 25.7250 | 1.00059 | 0.500293 | − | 0.865856i | \(-0.333226\pi\) | ||||
0.500293 | + | 0.865856i | \(0.333226\pi\) | |||||||
\(662\) | −1.00000 | −0.0388661 | ||||||||
\(663\) | −64.5416 | −2.50659 | ||||||||
\(664\) | 8.60555 | 0.333960 | ||||||||
\(665\) | 2.60555 | 0.101039 | ||||||||
\(666\) | −8.30278 | −0.321726 | ||||||||
\(667\) | 38.5694 | 1.49341 | ||||||||
\(668\) | −20.3305 | −0.786612 | ||||||||
\(669\) | −32.0278 | −1.23826 | ||||||||
\(670\) | −21.1194 | −0.815915 | ||||||||
\(671\) | −3.00000 | −0.115814 | ||||||||
\(672\) | −2.30278 | −0.0888315 | ||||||||
\(673\) | 24.8167 | 0.956612 | 0.478306 | − | 0.878193i | \(-0.341251\pi\) | ||||
0.478306 | + | 0.878193i | \(0.341251\pi\) | |||||||
\(674\) | −23.5416 | −0.906790 | ||||||||
\(675\) | 5.30278 | 0.204104 | ||||||||
\(676\) | 12.0000 | 0.461538 | ||||||||
\(677\) | 19.3028 | 0.741866 | 0.370933 | − | 0.928660i | \(-0.379038\pi\) | ||||
0.370933 | + | 0.928660i | \(0.379038\pi\) | |||||||
\(678\) | 2.09167 | 0.0803302 | ||||||||
\(679\) | −4.60555 | −0.176745 | ||||||||
\(680\) | 7.30278 | 0.280049 | ||||||||
\(681\) | −20.0917 | −0.769915 | ||||||||
\(682\) | −28.8167 | −1.10345 | ||||||||
\(683\) | 3.39445 | 0.129885 | 0.0649425 | − | 0.997889i | \(-0.479314\pi\) | ||||
0.0649425 | + | 0.997889i | \(0.479314\pi\) | |||||||
\(684\) | 4.60555 | 0.176098 | ||||||||
\(685\) | −10.5416 | −0.402775 | ||||||||
\(686\) | 13.0000 | 0.496342 | ||||||||
\(687\) | 13.8806 | 0.529577 | ||||||||
\(688\) | −12.2111 | −0.465544 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −24.6333 | −0.937774 | ||||||||
\(691\) | −33.4500 | −1.27250 | −0.636248 | − | 0.771484i | \(-0.719515\pi\) | ||||
−0.636248 | + | 0.771484i | \(0.719515\pi\) | |||||||
\(692\) | 7.42221 | 0.282150 | ||||||||
\(693\) | −6.90833 | −0.262426 | ||||||||
\(694\) | 7.18335 | 0.272676 | ||||||||
\(695\) | 29.3305 | 1.11257 | ||||||||
\(696\) | 10.8167 | 0.410004 | ||||||||
\(697\) | 48.2389 | 1.82718 | ||||||||
\(698\) | −8.30278 | −0.314265 | ||||||||
\(699\) | 38.7250 | 1.46471 | ||||||||
\(700\) | 3.30278 | 0.124833 | ||||||||
\(701\) | −5.09167 | −0.192310 | −0.0961549 | − | 0.995366i | \(-0.530654\pi\) | ||||
−0.0961549 | + | 0.995366i | \(0.530654\pi\) | |||||||
\(702\) | −8.02776 | −0.302988 | ||||||||
\(703\) | −7.21110 | −0.271972 | ||||||||
\(704\) | 3.00000 | 0.113067 | ||||||||
\(705\) | 29.7250 | 1.11951 | ||||||||
\(706\) | 11.3305 | 0.426430 | ||||||||
\(707\) | −6.90833 | −0.259814 | ||||||||
\(708\) | 15.0000 | 0.563735 | ||||||||
\(709\) | 32.6333 | 1.22557 | 0.612785 | − | 0.790250i | \(-0.290049\pi\) | ||||
0.612785 | + | 0.790250i | \(0.290049\pi\) | |||||||
\(710\) | −10.1833 | −0.382174 | ||||||||
\(711\) | −6.21110 | −0.232935 | ||||||||
\(712\) | −7.30278 | −0.273683 | ||||||||
\(713\) | −78.8722 | −2.95379 | ||||||||
\(714\) | 12.9083 | 0.483082 | ||||||||
\(715\) | −19.5416 | −0.730816 | ||||||||
\(716\) | −24.6333 | −0.920590 | ||||||||
\(717\) | 2.09167 | 0.0781150 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.1833 | 0.379775 | 0.189887 | − | 0.981806i | \(-0.439188\pi\) | ||||
0.189887 | + | 0.981806i | \(0.439188\pi\) | |||||||
\(720\) | −3.00000 | −0.111803 | ||||||||
\(721\) | −11.1194 | −0.414109 | ||||||||
\(722\) | −15.0000 | −0.558242 | ||||||||
\(723\) | 41.5139 | 1.54392 | ||||||||
\(724\) | 13.2111 | 0.490987 | ||||||||
\(725\) | −15.5139 | −0.576171 | ||||||||
\(726\) | −4.60555 | −0.170928 | ||||||||
\(727\) | −5.42221 | −0.201098 | −0.100549 | − | 0.994932i | \(-0.532060\pi\) | ||||
−0.100549 | + | 0.994932i | \(0.532060\pi\) | |||||||
\(728\) | −5.00000 | −0.185312 | ||||||||
\(729\) | −13.3305 | −0.493723 | ||||||||
\(730\) | 4.69722 | 0.173852 | ||||||||
\(731\) | 68.4500 | 2.53171 | ||||||||
\(732\) | −2.30278 | −0.0851130 | ||||||||
\(733\) | 5.00000 | 0.184679 | 0.0923396 | − | 0.995728i | \(-0.470565\pi\) | ||||
0.0923396 | + | 0.995728i | \(0.470565\pi\) | |||||||
\(734\) | −22.9083 | −0.845562 | ||||||||
\(735\) | 18.0000 | 0.663940 | ||||||||
\(736\) | 8.21110 | 0.302665 | ||||||||
\(737\) | 48.6333 | 1.79143 | ||||||||
\(738\) | −19.8167 | −0.729461 | ||||||||
\(739\) | −23.3028 | −0.857206 | −0.428603 | − | 0.903493i | \(-0.640994\pi\) | ||||
−0.428603 | + | 0.903493i | \(0.640994\pi\) | |||||||
\(740\) | 4.69722 | 0.172673 | ||||||||
\(741\) | 23.0278 | 0.845946 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.5416 | −0.826972 | −0.413486 | − | 0.910510i | \(-0.635689\pi\) | ||||
−0.413486 | + | 0.910510i | \(0.635689\pi\) | |||||||
\(744\) | −22.1194 | −0.810938 | ||||||||
\(745\) | −10.0278 | −0.367389 | ||||||||
\(746\) | 20.7889 | 0.761136 | ||||||||
\(747\) | 19.8167 | 0.725053 | ||||||||
\(748\) | −16.8167 | −0.614878 | ||||||||
\(749\) | −2.21110 | −0.0807919 | ||||||||
\(750\) | 24.9083 | 0.909524 | ||||||||
\(751\) | −23.5416 | −0.859046 | −0.429523 | − | 0.903056i | \(-0.641318\pi\) | ||||
−0.429523 | + | 0.903056i | \(0.641318\pi\) | |||||||
\(752\) | −9.90833 | −0.361320 | ||||||||
\(753\) | −27.0000 | −0.983935 | ||||||||
\(754\) | 23.4861 | 0.855314 | ||||||||
\(755\) | 20.3305 | 0.739904 | ||||||||
\(756\) | 1.60555 | 0.0583933 | ||||||||
\(757\) | −6.84441 | −0.248764 | −0.124382 | − | 0.992234i | \(-0.539695\pi\) | ||||
−0.124382 | + | 0.992234i | \(0.539695\pi\) | |||||||
\(758\) | 4.72498 | 0.171619 | ||||||||
\(759\) | 56.7250 | 2.05899 | ||||||||
\(760\) | −2.60555 | −0.0945133 | ||||||||
\(761\) | −30.0000 | −1.08750 | −0.543750 | − | 0.839248i | \(-0.682996\pi\) | ||||
−0.543750 | + | 0.839248i | \(0.682996\pi\) | |||||||
\(762\) | 0.697224 | 0.0252578 | ||||||||
\(763\) | −18.8167 | −0.681209 | ||||||||
\(764\) | 0.788897 | 0.0285413 | ||||||||
\(765\) | 16.8167 | 0.608007 | ||||||||
\(766\) | −21.5139 | −0.777328 | ||||||||
\(767\) | 32.5694 | 1.17601 | ||||||||
\(768\) | 2.30278 | 0.0830943 | ||||||||
\(769\) | −38.1472 | −1.37562 | −0.687811 | − | 0.725889i | \(-0.741428\pi\) | ||||
−0.687811 | + | 0.725889i | \(0.741428\pi\) | |||||||
\(770\) | 3.90833 | 0.140846 | ||||||||
\(771\) | −6.90833 | −0.248797 | ||||||||
\(772\) | −14.0278 | −0.504870 | ||||||||
\(773\) | 23.4500 | 0.843436 | 0.421718 | − | 0.906727i | \(-0.361427\pi\) | ||||
0.421718 | + | 0.906727i | \(0.361427\pi\) | |||||||
\(774\) | −28.1194 | −1.01073 | ||||||||
\(775\) | 31.7250 | 1.13959 | ||||||||
\(776\) | 4.60555 | 0.165330 | ||||||||
\(777\) | 8.30278 | 0.297860 | ||||||||
\(778\) | −17.2111 | −0.617048 | ||||||||
\(779\) | −17.2111 | −0.616652 | ||||||||
\(780\) | −15.0000 | −0.537086 | ||||||||
\(781\) | 23.4500 | 0.839106 | ||||||||
\(782\) | −46.0278 | −1.64595 | ||||||||
\(783\) | −7.54163 | −0.269516 | ||||||||
\(784\) | −6.00000 | −0.214286 | ||||||||
\(785\) | −13.8167 | −0.493138 | ||||||||
\(786\) | 47.4500 | 1.69248 | ||||||||
\(787\) | −3.84441 | −0.137038 | −0.0685192 | − | 0.997650i | \(-0.521827\pi\) | ||||
−0.0685192 | + | 0.997650i | \(0.521827\pi\) | |||||||
\(788\) | 14.0917 | 0.501995 | ||||||||
\(789\) | 49.5416 | 1.76373 | ||||||||
\(790\) | 3.51388 | 0.125018 | ||||||||
\(791\) | −0.908327 | −0.0322964 | ||||||||
\(792\) | 6.90833 | 0.245477 | ||||||||
\(793\) | −5.00000 | −0.177555 | ||||||||
\(794\) | 2.51388 | 0.0892142 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.09167 | −0.109581 | ||||||||
\(797\) | −4.54163 | −0.160873 | −0.0804365 | − | 0.996760i | \(-0.525631\pi\) | ||||
−0.0804365 | + | 0.996760i | \(0.525631\pi\) | |||||||
\(798\) | −4.60555 | −0.163035 | ||||||||
\(799\) | 55.5416 | 1.96492 | ||||||||
\(800\) | −3.30278 | −0.116771 | ||||||||
\(801\) | −16.8167 | −0.594187 | ||||||||
\(802\) | 39.1194 | 1.38136 | ||||||||
\(803\) | −10.8167 | −0.381711 | ||||||||
\(804\) | 37.3305 | 1.31655 | ||||||||
\(805\) | 10.6972 | 0.377028 | ||||||||
\(806\) | −48.0278 | −1.69171 | ||||||||
\(807\) | −2.30278 | −0.0810615 | ||||||||
\(808\) | 6.90833 | 0.243034 | ||||||||
\(809\) | 26.8444 | 0.943799 | 0.471900 | − | 0.881652i | \(-0.343568\pi\) | ||||
0.471900 | + | 0.881652i | \(0.343568\pi\) | |||||||
\(810\) | 13.8167 | 0.485468 | ||||||||
\(811\) | −8.18335 | −0.287356 | −0.143678 | − | 0.989624i | \(-0.545893\pi\) | ||||
−0.143678 | + | 0.989624i | \(0.545893\pi\) | |||||||
\(812\) | −4.69722 | −0.164840 | ||||||||
\(813\) | 25.3305 | 0.888381 | ||||||||
\(814\) | −10.8167 | −0.379124 | ||||||||
\(815\) | 11.3305 | 0.396891 | ||||||||
\(816\) | −12.9083 | −0.451882 | ||||||||
\(817\) | −24.4222 | −0.854425 | ||||||||
\(818\) | −27.6056 | −0.965205 | ||||||||
\(819\) | −11.5139 | −0.402327 | ||||||||
\(820\) | 11.2111 | 0.391509 | ||||||||
\(821\) | −6.00000 | −0.209401 | −0.104701 | − | 0.994504i | \(-0.533388\pi\) | ||||
−0.104701 | + | 0.994504i | \(0.533388\pi\) | |||||||
\(822\) | 18.6333 | 0.649911 | ||||||||
\(823\) | 1.60555 | 0.0559660 | 0.0279830 | − | 0.999608i | \(-0.491092\pi\) | ||||
0.0279830 | + | 0.999608i | \(0.491092\pi\) | |||||||
\(824\) | 11.1194 | 0.387364 | ||||||||
\(825\) | −22.8167 | −0.794374 | ||||||||
\(826\) | −6.51388 | −0.226647 | ||||||||
\(827\) | −12.9083 | −0.448867 | −0.224433 | − | 0.974489i | \(-0.572053\pi\) | ||||
−0.224433 | + | 0.974489i | \(0.572053\pi\) | |||||||
\(828\) | 18.9083 | 0.657110 | ||||||||
\(829\) | −20.9361 | −0.727140 | −0.363570 | − | 0.931567i | \(-0.618442\pi\) | ||||
−0.363570 | + | 0.931567i | \(0.618442\pi\) | |||||||
\(830\) | −11.2111 | −0.389143 | ||||||||
\(831\) | −37.1194 | −1.28766 | ||||||||
\(832\) | 5.00000 | 0.173344 | ||||||||
\(833\) | 33.6333 | 1.16533 | ||||||||
\(834\) | −51.8444 | −1.79523 | ||||||||
\(835\) | 26.4861 | 0.916590 | ||||||||
\(836\) | 6.00000 | 0.207514 | ||||||||
\(837\) | 15.4222 | 0.533069 | ||||||||
\(838\) | 27.9083 | 0.964077 | ||||||||
\(839\) | 5.72498 | 0.197648 | 0.0988241 | − | 0.995105i | \(-0.468492\pi\) | ||||
0.0988241 | + | 0.995105i | \(0.468492\pi\) | |||||||
\(840\) | 3.00000 | 0.103510 | ||||||||
\(841\) | −6.93608 | −0.239175 | ||||||||
\(842\) | 21.4222 | 0.738258 | ||||||||
\(843\) | 24.9083 | 0.857888 | ||||||||
\(844\) | −1.11943 | −0.0385324 | ||||||||
\(845\) | −15.6333 | −0.537802 | ||||||||
\(846\) | −22.8167 | −0.784453 | ||||||||
\(847\) | 2.00000 | 0.0687208 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −29.9361 | −1.02740 | ||||||||
\(850\) | 18.5139 | 0.635021 | ||||||||
\(851\) | −29.6056 | −1.01487 | ||||||||
\(852\) | 18.0000 | 0.616670 | ||||||||
\(853\) | −11.6972 | −0.400505 | −0.200253 | − | 0.979744i | \(-0.564176\pi\) | ||||
−0.200253 | + | 0.979744i | \(0.564176\pi\) | |||||||
\(854\) | 1.00000 | 0.0342193 | ||||||||
\(855\) | −6.00000 | −0.205196 | ||||||||
\(856\) | 2.21110 | 0.0755739 | ||||||||
\(857\) | −11.4500 | −0.391123 | −0.195562 | − | 0.980691i | \(-0.562653\pi\) | ||||
−0.195562 | + | 0.980691i | \(0.562653\pi\) | |||||||
\(858\) | 34.5416 | 1.17923 | ||||||||
\(859\) | −11.3028 | −0.385646 | −0.192823 | − | 0.981234i | \(-0.561764\pi\) | ||||
−0.192823 | + | 0.981234i | \(0.561764\pi\) | |||||||
\(860\) | 15.9083 | 0.542469 | ||||||||
\(861\) | 19.8167 | 0.675350 | ||||||||
\(862\) | −23.6056 | −0.804008 | ||||||||
\(863\) | 30.7527 | 1.04684 | 0.523418 | − | 0.852076i | \(-0.324657\pi\) | ||||
0.523418 | + | 0.852076i | \(0.324657\pi\) | |||||||
\(864\) | −1.60555 | −0.0546220 | ||||||||
\(865\) | −9.66947 | −0.328772 | ||||||||
\(866\) | 23.9083 | 0.812438 | ||||||||
\(867\) | 33.2111 | 1.12791 | ||||||||
\(868\) | 9.60555 | 0.326034 | ||||||||
\(869\) | −8.09167 | −0.274491 | ||||||||
\(870\) | −14.0917 | −0.477752 | ||||||||
\(871\) | 81.0555 | 2.74646 | ||||||||
\(872\) | 18.8167 | 0.637212 | ||||||||
\(873\) | 10.6056 | 0.358944 | ||||||||
\(874\) | 16.4222 | 0.555489 | ||||||||
\(875\) | −10.8167 | −0.365670 | ||||||||
\(876\) | −8.30278 | −0.280525 | ||||||||
\(877\) | 24.5416 | 0.828712 | 0.414356 | − | 0.910115i | \(-0.364007\pi\) | ||||
0.414356 | + | 0.910115i | \(0.364007\pi\) | |||||||
\(878\) | −18.3305 | −0.618625 | ||||||||
\(879\) | 13.8167 | 0.466024 | ||||||||
\(880\) | −3.90833 | −0.131750 | ||||||||
\(881\) | −39.7527 | −1.33930 | −0.669652 | − | 0.742675i | \(-0.733557\pi\) | ||||
−0.669652 | + | 0.742675i | \(0.733557\pi\) | |||||||
\(882\) | −13.8167 | −0.465231 | ||||||||
\(883\) | 41.2389 | 1.38780 | 0.693899 | − | 0.720072i | \(-0.255891\pi\) | ||||
0.693899 | + | 0.720072i | \(0.255891\pi\) | |||||||
\(884\) | −28.0278 | −0.942675 | ||||||||
\(885\) | −19.5416 | −0.656885 | ||||||||
\(886\) | 16.4222 | 0.551715 | ||||||||
\(887\) | 56.4500 | 1.89540 | 0.947702 | − | 0.319156i | \(-0.103399\pi\) | ||||
0.947702 | + | 0.319156i | \(0.103399\pi\) | |||||||
\(888\) | −8.30278 | −0.278623 | ||||||||
\(889\) | −0.302776 | −0.0101548 | ||||||||
\(890\) | 9.51388 | 0.318906 | ||||||||
\(891\) | −31.8167 | −1.06590 | ||||||||
\(892\) | −13.9083 | −0.465685 | ||||||||
\(893\) | −19.8167 | −0.663139 | ||||||||
\(894\) | 17.7250 | 0.592812 | ||||||||
\(895\) | 32.0917 | 1.07271 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 94.5416 | 3.15665 | ||||||||
\(898\) | 5.09167 | 0.169911 | ||||||||
\(899\) | −45.1194 | −1.50482 | ||||||||
\(900\) | −7.60555 | −0.253518 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −25.8167 | −0.859601 | ||||||||
\(903\) | 28.1194 | 0.935756 | ||||||||
\(904\) | 0.908327 | 0.0302105 | ||||||||
\(905\) | −17.2111 | −0.572116 | ||||||||
\(906\) | −35.9361 | −1.19390 | ||||||||
\(907\) | 10.2111 | 0.339054 | 0.169527 | − | 0.985526i | \(-0.445776\pi\) | ||||
0.169527 | + | 0.985526i | \(0.445776\pi\) | |||||||
\(908\) | −8.72498 | −0.289549 | ||||||||
\(909\) | 15.9083 | 0.527646 | ||||||||
\(910\) | 6.51388 | 0.215933 | ||||||||
\(911\) | −42.3583 | −1.40339 | −0.701696 | − | 0.712476i | \(-0.747574\pi\) | ||||
−0.701696 | + | 0.712476i | \(0.747574\pi\) | |||||||
\(912\) | 4.60555 | 0.152505 | ||||||||
\(913\) | 25.8167 | 0.854407 | ||||||||
\(914\) | 10.7250 | 0.354751 | ||||||||
\(915\) | 3.00000 | 0.0991769 | ||||||||
\(916\) | 6.02776 | 0.199163 | ||||||||
\(917\) | −20.6056 | −0.680455 | ||||||||
\(918\) | 9.00000 | 0.297044 | ||||||||
\(919\) | 12.1833 | 0.401892 | 0.200946 | − | 0.979602i | \(-0.435599\pi\) | ||||
0.200946 | + | 0.979602i | \(0.435599\pi\) | |||||||
\(920\) | −10.6972 | −0.352677 | ||||||||
\(921\) | 35.5139 | 1.17022 | ||||||||
\(922\) | 13.0278 | 0.429046 | ||||||||
\(923\) | 39.0833 | 1.28644 | ||||||||
\(924\) | −6.90833 | −0.227267 | ||||||||
\(925\) | 11.9083 | 0.391543 | ||||||||
\(926\) | 35.9083 | 1.18002 | ||||||||
\(927\) | 25.6056 | 0.840997 | ||||||||
\(928\) | 4.69722 | 0.154194 | ||||||||
\(929\) | 31.0278 | 1.01799 | 0.508994 | − | 0.860770i | \(-0.330018\pi\) | ||||
0.508994 | + | 0.860770i | \(0.330018\pi\) | |||||||
\(930\) | 28.8167 | 0.944935 | ||||||||
\(931\) | −12.0000 | −0.393284 | ||||||||
\(932\) | 16.8167 | 0.550848 | ||||||||
\(933\) | 31.8167 | 1.04163 | ||||||||
\(934\) | 4.42221 | 0.144699 | ||||||||
\(935\) | 21.9083 | 0.716479 | ||||||||
\(936\) | 11.5139 | 0.376343 | ||||||||
\(937\) | −2.06392 | −0.0674252 | −0.0337126 | − | 0.999432i | \(-0.510733\pi\) | ||||
−0.0337126 | + | 0.999432i | \(0.510733\pi\) | |||||||
\(938\) | −16.2111 | −0.529311 | ||||||||
\(939\) | −39.8444 | −1.30027 | ||||||||
\(940\) | 12.9083 | 0.421023 | ||||||||
\(941\) | −48.3583 | −1.57644 | −0.788218 | − | 0.615397i | \(-0.788996\pi\) | ||||
−0.788218 | + | 0.615397i | \(0.788996\pi\) | |||||||
\(942\) | 24.4222 | 0.795718 | ||||||||
\(943\) | −70.6611 | −2.30104 | ||||||||
\(944\) | 6.51388 | 0.212009 | ||||||||
\(945\) | −2.09167 | −0.0680421 | ||||||||
\(946\) | −36.6333 | −1.19105 | ||||||||
\(947\) | 23.8806 | 0.776014 | 0.388007 | − | 0.921656i | \(-0.373164\pi\) | ||||
0.388007 | + | 0.921656i | \(0.373164\pi\) | |||||||
\(948\) | −6.21110 | −0.201727 | ||||||||
\(949\) | −18.0278 | −0.585206 | ||||||||
\(950\) | −6.60555 | −0.214312 | ||||||||
\(951\) | 56.1749 | 1.82160 | ||||||||
\(952\) | 5.60555 | 0.181677 | ||||||||
\(953\) | 22.4222 | 0.726326 | 0.363163 | − | 0.931726i | \(-0.381697\pi\) | ||||
0.363163 | + | 0.931726i | \(0.381697\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.02776 | −0.0332574 | ||||||||
\(956\) | 0.908327 | 0.0293774 | ||||||||
\(957\) | 32.4500 | 1.04896 | ||||||||
\(958\) | 9.78890 | 0.316265 | ||||||||
\(959\) | −8.09167 | −0.261294 | ||||||||
\(960\) | −3.00000 | −0.0968246 | ||||||||
\(961\) | 61.2666 | 1.97634 | ||||||||
\(962\) | −18.0278 | −0.581238 | ||||||||
\(963\) | 5.09167 | 0.164077 | ||||||||
\(964\) | 18.0278 | 0.580635 | ||||||||
\(965\) | 18.2750 | 0.588294 | ||||||||
\(966\) | −18.9083 | −0.608365 | ||||||||
\(967\) | 45.9361 | 1.47720 | 0.738602 | − | 0.674141i | \(-0.235486\pi\) | ||||
0.738602 | + | 0.674141i | \(0.235486\pi\) | |||||||
\(968\) | −2.00000 | −0.0642824 | ||||||||
\(969\) | −25.8167 | −0.829350 | ||||||||
\(970\) | −6.00000 | −0.192648 | ||||||||
\(971\) | −10.1833 | −0.326799 | −0.163400 | − | 0.986560i | \(-0.552246\pi\) | ||||
−0.163400 | + | 0.986560i | \(0.552246\pi\) | |||||||
\(972\) | −19.6056 | −0.628848 | ||||||||
\(973\) | 22.5139 | 0.721762 | ||||||||
\(974\) | −38.4222 | −1.23113 | ||||||||
\(975\) | −38.0278 | −1.21786 | ||||||||
\(976\) | −1.00000 | −0.0320092 | ||||||||
\(977\) | 25.5416 | 0.817149 | 0.408575 | − | 0.912725i | \(-0.366026\pi\) | ||||
0.408575 | + | 0.912725i | \(0.366026\pi\) | |||||||
\(978\) | −20.0278 | −0.640417 | ||||||||
\(979\) | −21.9083 | −0.700193 | ||||||||
\(980\) | 7.81665 | 0.249694 | ||||||||
\(981\) | 43.3305 | 1.38344 | ||||||||
\(982\) | −37.8167 | −1.20678 | ||||||||
\(983\) | 34.9361 | 1.11429 | 0.557144 | − | 0.830416i | \(-0.311897\pi\) | ||||
0.557144 | + | 0.830416i | \(0.311897\pi\) | |||||||
\(984\) | −19.8167 | −0.631732 | ||||||||
\(985\) | −18.3583 | −0.584944 | ||||||||
\(986\) | −26.3305 | −0.838535 | ||||||||
\(987\) | 22.8167 | 0.726262 | ||||||||
\(988\) | 10.0000 | 0.318142 | ||||||||
\(989\) | −100.267 | −3.18829 | ||||||||
\(990\) | −9.00000 | −0.286039 | ||||||||
\(991\) | −17.5416 | −0.557228 | −0.278614 | − | 0.960403i | \(-0.589875\pi\) | ||||
−0.278614 | + | 0.960403i | \(0.589875\pi\) | |||||||
\(992\) | −9.60555 | −0.304977 | ||||||||
\(993\) | −2.30278 | −0.0730764 | ||||||||
\(994\) | −7.81665 | −0.247929 | ||||||||
\(995\) | 4.02776 | 0.127688 | ||||||||
\(996\) | 19.8167 | 0.627915 | ||||||||
\(997\) | −25.7889 | −0.816743 | −0.408371 | − | 0.912816i | \(-0.633903\pi\) | ||||
−0.408371 | + | 0.912816i | \(0.633903\pi\) | |||||||
\(998\) | 35.2389 | 1.11547 | ||||||||
\(999\) | 5.78890 | 0.183153 |
(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 | 538.2.a.b.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 4842.2.a.d.1.2 | 2 | |||
4.3 | odd | 2 | 4304.2.a.c.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
538.2.a.b.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
4304.2.a.c.1.1 | 2 | 4.3 | odd | 2 | |||
4842.2.a.d.1.2 | 2 | 3.2 | odd | 2 |