Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3174,2,Mod(1,3174)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3174, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3174.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3174 = 2 \cdot 3 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3174.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(25.3445176016\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\Q(\zeta_{22})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 138) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.68251\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3174.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.194262 | −0.0868765 | −0.0434383 | − | 0.999056i | \(-0.513831\pi\) | ||||
−0.0434383 | + | 0.999056i | \(0.513831\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.95185 | 0.737730 | 0.368865 | − | 0.929483i | \(-0.379747\pi\) | ||||
0.368865 | + | 0.929483i | \(0.379747\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.194262 | −0.0614310 | ||||||||
\(11\) | 6.30195 | 1.90011 | 0.950055 | − | 0.312083i | \(-0.101027\pi\) | ||||
0.950055 | + | 0.312083i | \(0.101027\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 4.81288 | 1.33485 | 0.667426 | − | 0.744676i | \(-0.267396\pi\) | ||||
0.667426 | + | 0.744676i | \(0.267396\pi\) | |||||||
\(14\) | 1.95185 | 0.521654 | ||||||||
\(15\) | 0.194262 | 0.0501582 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.20786 | −0.778020 | −0.389010 | − | 0.921233i | \(-0.627183\pi\) | ||||
−0.389010 | + | 0.921233i | \(0.627183\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 0.859449 | 0.197171 | 0.0985855 | − | 0.995129i | \(-0.468568\pi\) | ||||
0.0985855 | + | 0.995129i | \(0.468568\pi\) | |||||||
\(20\) | −0.194262 | −0.0434383 | ||||||||
\(21\) | −1.95185 | −0.425928 | ||||||||
\(22\) | 6.30195 | 1.34358 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −4.96226 | −0.992452 | ||||||||
\(26\) | 4.81288 | 0.943883 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.95185 | 0.368865 | ||||||||
\(29\) | 5.41741 | 1.00599 | 0.502994 | − | 0.864290i | \(-0.332232\pi\) | ||||
0.502994 | + | 0.864290i | \(0.332232\pi\) | |||||||
\(30\) | 0.194262 | 0.0354672 | ||||||||
\(31\) | −1.01371 | −0.182067 | −0.0910334 | − | 0.995848i | \(-0.529017\pi\) | ||||
−0.0910334 | + | 0.995848i | \(0.529017\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −6.30195 | −1.09703 | ||||||||
\(34\) | −3.20786 | −0.550144 | ||||||||
\(35\) | −0.379170 | −0.0640914 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 6.89037 | 1.13277 | 0.566385 | − | 0.824141i | \(-0.308342\pi\) | ||||
0.566385 | + | 0.824141i | \(0.308342\pi\) | |||||||
\(38\) | 0.859449 | 0.139421 | ||||||||
\(39\) | −4.81288 | −0.770678 | ||||||||
\(40\) | −0.194262 | −0.0307155 | ||||||||
\(41\) | −0.972011 | −0.151803 | −0.0759013 | − | 0.997115i | \(-0.524183\pi\) | ||||
−0.0759013 | + | 0.997115i | \(0.524183\pi\) | |||||||
\(42\) | −1.95185 | −0.301177 | ||||||||
\(43\) | −5.14282 | −0.784273 | −0.392136 | − | 0.919907i | \(-0.628264\pi\) | ||||
−0.392136 | + | 0.919907i | \(0.628264\pi\) | |||||||
\(44\) | 6.30195 | 0.950055 | ||||||||
\(45\) | −0.194262 | −0.0289588 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.41216 | −1.08117 | −0.540587 | − | 0.841288i | \(-0.681798\pi\) | ||||
−0.540587 | + | 0.841288i | \(0.681798\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −3.19028 | −0.455755 | ||||||||
\(50\) | −4.96226 | −0.701770 | ||||||||
\(51\) | 3.20786 | 0.449190 | ||||||||
\(52\) | 4.81288 | 0.667426 | ||||||||
\(53\) | 2.00797 | 0.275815 | 0.137908 | − | 0.990445i | \(-0.455962\pi\) | ||||
0.137908 | + | 0.990445i | \(0.455962\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −1.22423 | −0.165075 | ||||||||
\(56\) | 1.95185 | 0.260827 | ||||||||
\(57\) | −0.859449 | −0.113837 | ||||||||
\(58\) | 5.41741 | 0.711341 | ||||||||
\(59\) | −8.60221 | −1.11991 | −0.559956 | − | 0.828522i | \(-0.689182\pi\) | ||||
−0.559956 | + | 0.828522i | \(0.689182\pi\) | |||||||
\(60\) | 0.194262 | 0.0250791 | ||||||||
\(61\) | 12.1201 | 1.55182 | 0.775912 | − | 0.630841i | \(-0.217290\pi\) | ||||
0.775912 | + | 0.630841i | \(0.217290\pi\) | |||||||
\(62\) | −1.01371 | −0.128741 | ||||||||
\(63\) | 1.95185 | 0.245910 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.934959 | −0.115967 | ||||||||
\(66\) | −6.30195 | −0.775716 | ||||||||
\(67\) | 7.09327 | 0.866580 | 0.433290 | − | 0.901254i | \(-0.357353\pi\) | ||||
0.433290 | + | 0.901254i | \(0.357353\pi\) | |||||||
\(68\) | −3.20786 | −0.389010 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.379170 | −0.0453194 | ||||||||
\(71\) | 1.10938 | 0.131659 | 0.0658294 | − | 0.997831i | \(-0.479031\pi\) | ||||
0.0658294 | + | 0.997831i | \(0.479031\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −13.1859 | −1.54330 | −0.771648 | − | 0.636049i | \(-0.780567\pi\) | ||||
−0.771648 | + | 0.636049i | \(0.780567\pi\) | |||||||
\(74\) | 6.89037 | 0.800989 | ||||||||
\(75\) | 4.96226 | 0.572993 | ||||||||
\(76\) | 0.859449 | 0.0985855 | ||||||||
\(77\) | 12.3005 | 1.40177 | ||||||||
\(78\) | −4.81288 | −0.544951 | ||||||||
\(79\) | 1.12979 | 0.127112 | 0.0635559 | − | 0.997978i | \(-0.479756\pi\) | ||||
0.0635559 | + | 0.997978i | \(0.479756\pi\) | |||||||
\(80\) | −0.194262 | −0.0217191 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.972011 | −0.107341 | ||||||||
\(83\) | 4.00714 | 0.439841 | 0.219920 | − | 0.975518i | \(-0.429420\pi\) | ||||
0.219920 | + | 0.975518i | \(0.429420\pi\) | |||||||
\(84\) | −1.95185 | −0.212964 | ||||||||
\(85\) | 0.623165 | 0.0675917 | ||||||||
\(86\) | −5.14282 | −0.554564 | ||||||||
\(87\) | −5.41741 | −0.580807 | ||||||||
\(88\) | 6.30195 | 0.671790 | ||||||||
\(89\) | −9.55158 | −1.01247 | −0.506233 | − | 0.862397i | \(-0.668962\pi\) | ||||
−0.506233 | + | 0.862397i | \(0.668962\pi\) | |||||||
\(90\) | −0.194262 | −0.0204770 | ||||||||
\(91\) | 9.39402 | 0.984760 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.01371 | 0.105116 | ||||||||
\(94\) | −7.41216 | −0.764506 | ||||||||
\(95\) | −0.166958 | −0.0171295 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −1.12094 | −0.113815 | −0.0569073 | − | 0.998379i | \(-0.518124\pi\) | ||||
−0.0569073 | + | 0.998379i | \(0.518124\pi\) | |||||||
\(98\) | −3.19028 | −0.322267 | ||||||||
\(99\) | 6.30195 | 0.633370 | ||||||||
\(100\) | −4.96226 | −0.496226 | ||||||||
\(101\) | 12.5714 | 1.25090 | 0.625451 | − | 0.780263i | \(-0.284915\pi\) | ||||
0.625451 | + | 0.780263i | \(0.284915\pi\) | |||||||
\(102\) | 3.20786 | 0.317626 | ||||||||
\(103\) | 19.3963 | 1.91117 | 0.955587 | − | 0.294708i | \(-0.0952223\pi\) | ||||
0.955587 | + | 0.294708i | \(0.0952223\pi\) | |||||||
\(104\) | 4.81288 | 0.471942 | ||||||||
\(105\) | 0.379170 | 0.0370032 | ||||||||
\(106\) | 2.00797 | 0.195031 | ||||||||
\(107\) | 3.07594 | 0.297363 | 0.148681 | − | 0.988885i | \(-0.452497\pi\) | ||||
0.148681 | + | 0.988885i | \(0.452497\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 1.94929 | 0.186708 | 0.0933542 | − | 0.995633i | \(-0.470241\pi\) | ||||
0.0933542 | + | 0.995633i | \(0.470241\pi\) | |||||||
\(110\) | −1.22423 | −0.116726 | ||||||||
\(111\) | −6.89037 | −0.654005 | ||||||||
\(112\) | 1.95185 | 0.184432 | ||||||||
\(113\) | −17.1492 | −1.61326 | −0.806632 | − | 0.591054i | \(-0.798712\pi\) | ||||
−0.806632 | + | 0.591054i | \(0.798712\pi\) | |||||||
\(114\) | −0.859449 | −0.0804947 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.41741 | 0.502994 | ||||||||
\(117\) | 4.81288 | 0.444951 | ||||||||
\(118\) | −8.60221 | −0.791898 | ||||||||
\(119\) | −6.26126 | −0.573969 | ||||||||
\(120\) | 0.194262 | 0.0177336 | ||||||||
\(121\) | 28.7146 | 2.61042 | ||||||||
\(122\) | 12.1201 | 1.09731 | ||||||||
\(123\) | 0.972011 | 0.0876433 | ||||||||
\(124\) | −1.01371 | −0.0910334 | ||||||||
\(125\) | 1.93529 | 0.173097 | ||||||||
\(126\) | 1.95185 | 0.173885 | ||||||||
\(127\) | −21.6118 | −1.91774 | −0.958869 | − | 0.283850i | \(-0.908388\pi\) | ||||
−0.958869 | + | 0.283850i | \(0.908388\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 5.14282 | 0.452800 | ||||||||
\(130\) | −0.934959 | −0.0820013 | ||||||||
\(131\) | −14.9571 | −1.30681 | −0.653404 | − | 0.757009i | \(-0.726660\pi\) | ||||
−0.653404 | + | 0.757009i | \(0.726660\pi\) | |||||||
\(132\) | −6.30195 | −0.548514 | ||||||||
\(133\) | 1.67751 | 0.145459 | ||||||||
\(134\) | 7.09327 | 0.612765 | ||||||||
\(135\) | 0.194262 | 0.0167194 | ||||||||
\(136\) | −3.20786 | −0.275072 | ||||||||
\(137\) | 18.1570 | 1.55126 | 0.775628 | − | 0.631190i | \(-0.217433\pi\) | ||||
0.775628 | + | 0.631190i | \(0.217433\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.36718 | −0.624876 | −0.312438 | − | 0.949938i | \(-0.601146\pi\) | ||||
−0.312438 | + | 0.949938i | \(0.601146\pi\) | |||||||
\(140\) | −0.379170 | −0.0320457 | ||||||||
\(141\) | 7.41216 | 0.624217 | ||||||||
\(142\) | 1.10938 | 0.0930969 | ||||||||
\(143\) | 30.3305 | 2.53637 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −1.05240 | −0.0873967 | ||||||||
\(146\) | −13.1859 | −1.09128 | ||||||||
\(147\) | 3.19028 | 0.263130 | ||||||||
\(148\) | 6.89037 | 0.566385 | ||||||||
\(149\) | 15.6333 | 1.28073 | 0.640365 | − | 0.768070i | \(-0.278783\pi\) | ||||
0.640365 | + | 0.768070i | \(0.278783\pi\) | |||||||
\(150\) | 4.96226 | 0.405167 | ||||||||
\(151\) | 20.7042 | 1.68488 | 0.842440 | − | 0.538790i | \(-0.181118\pi\) | ||||
0.842440 | + | 0.538790i | \(0.181118\pi\) | |||||||
\(152\) | 0.859449 | 0.0697105 | ||||||||
\(153\) | −3.20786 | −0.259340 | ||||||||
\(154\) | 12.3005 | 0.991199 | ||||||||
\(155\) | 0.196924 | 0.0158173 | ||||||||
\(156\) | −4.81288 | −0.385339 | ||||||||
\(157\) | −3.97631 | −0.317344 | −0.158672 | − | 0.987331i | \(-0.550721\pi\) | ||||
−0.158672 | + | 0.987331i | \(0.550721\pi\) | |||||||
\(158\) | 1.12979 | 0.0898816 | ||||||||
\(159\) | −2.00797 | −0.159242 | ||||||||
\(160\) | −0.194262 | −0.0153577 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 24.5129 | 1.91999 | 0.959997 | − | 0.280009i | \(-0.0903375\pi\) | ||||
0.959997 | + | 0.280009i | \(0.0903375\pi\) | |||||||
\(164\) | −0.972011 | −0.0759013 | ||||||||
\(165\) | 1.22423 | 0.0953060 | ||||||||
\(166\) | 4.00714 | 0.311015 | ||||||||
\(167\) | −1.95444 | −0.151239 | −0.0756194 | − | 0.997137i | \(-0.524093\pi\) | ||||
−0.0756194 | + | 0.997137i | \(0.524093\pi\) | |||||||
\(168\) | −1.95185 | −0.150588 | ||||||||
\(169\) | 10.1638 | 0.781832 | ||||||||
\(170\) | 0.623165 | 0.0477945 | ||||||||
\(171\) | 0.859449 | 0.0657237 | ||||||||
\(172\) | −5.14282 | −0.392136 | ||||||||
\(173\) | 6.14165 | 0.466941 | 0.233471 | − | 0.972364i | \(-0.424992\pi\) | ||||
0.233471 | + | 0.972364i | \(0.424992\pi\) | |||||||
\(174\) | −5.41741 | −0.410693 | ||||||||
\(175\) | −9.68559 | −0.732162 | ||||||||
\(176\) | 6.30195 | 0.475027 | ||||||||
\(177\) | 8.60221 | 0.646582 | ||||||||
\(178\) | −9.55158 | −0.715921 | ||||||||
\(179\) | 6.47091 | 0.483658 | 0.241829 | − | 0.970319i | \(-0.422253\pi\) | ||||
0.241829 | + | 0.970319i | \(0.422253\pi\) | |||||||
\(180\) | −0.194262 | −0.0144794 | ||||||||
\(181\) | 3.26146 | 0.242423 | 0.121211 | − | 0.992627i | \(-0.461322\pi\) | ||||
0.121211 | + | 0.992627i | \(0.461322\pi\) | |||||||
\(182\) | 9.39402 | 0.696331 | ||||||||
\(183\) | −12.1201 | −0.895946 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.33853 | −0.0984110 | ||||||||
\(186\) | 1.01371 | 0.0743285 | ||||||||
\(187\) | −20.2158 | −1.47832 | ||||||||
\(188\) | −7.41216 | −0.540587 | ||||||||
\(189\) | −1.95185 | −0.141976 | ||||||||
\(190\) | −0.166958 | −0.0121124 | ||||||||
\(191\) | −22.8536 | −1.65363 | −0.826815 | − | 0.562474i | \(-0.809850\pi\) | ||||
−0.826815 | + | 0.562474i | \(0.809850\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −16.9414 | −1.21947 | −0.609734 | − | 0.792606i | \(-0.708724\pi\) | ||||
−0.609734 | + | 0.792606i | \(0.708724\pi\) | |||||||
\(194\) | −1.12094 | −0.0804790 | ||||||||
\(195\) | 0.934959 | 0.0669538 | ||||||||
\(196\) | −3.19028 | −0.227877 | ||||||||
\(197\) | 1.25480 | 0.0894010 | 0.0447005 | − | 0.999000i | \(-0.485767\pi\) | ||||
0.0447005 | + | 0.999000i | \(0.485767\pi\) | |||||||
\(198\) | 6.30195 | 0.447860 | ||||||||
\(199\) | 24.8140 | 1.75902 | 0.879509 | − | 0.475883i | \(-0.157871\pi\) | ||||
0.879509 | + | 0.475883i | \(0.157871\pi\) | |||||||
\(200\) | −4.96226 | −0.350885 | ||||||||
\(201\) | −7.09327 | −0.500320 | ||||||||
\(202\) | 12.5714 | 0.884521 | ||||||||
\(203\) | 10.5740 | 0.742147 | ||||||||
\(204\) | 3.20786 | 0.224595 | ||||||||
\(205\) | 0.188825 | 0.0131881 | ||||||||
\(206\) | 19.3963 | 1.35140 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.81288 | 0.333713 | ||||||||
\(209\) | 5.41620 | 0.374646 | ||||||||
\(210\) | 0.379170 | 0.0261652 | ||||||||
\(211\) | 7.25827 | 0.499680 | 0.249840 | − | 0.968287i | \(-0.419622\pi\) | ||||
0.249840 | + | 0.968287i | \(0.419622\pi\) | |||||||
\(212\) | 2.00797 | 0.137908 | ||||||||
\(213\) | −1.10938 | −0.0760133 | ||||||||
\(214\) | 3.07594 | 0.210267 | ||||||||
\(215\) | 0.999053 | 0.0681349 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −1.97860 | −0.134316 | ||||||||
\(218\) | 1.94929 | 0.132023 | ||||||||
\(219\) | 13.1859 | 0.891023 | ||||||||
\(220\) | −1.22423 | −0.0825374 | ||||||||
\(221\) | −15.4390 | −1.03854 | ||||||||
\(222\) | −6.89037 | −0.462451 | ||||||||
\(223\) | 20.7342 | 1.38846 | 0.694231 | − | 0.719752i | \(-0.255745\pi\) | ||||
0.694231 | + | 0.719752i | \(0.255745\pi\) | |||||||
\(224\) | 1.95185 | 0.130413 | ||||||||
\(225\) | −4.96226 | −0.330817 | ||||||||
\(226\) | −17.1492 | −1.14075 | ||||||||
\(227\) | −21.0504 | −1.39716 | −0.698581 | − | 0.715531i | \(-0.746185\pi\) | ||||
−0.698581 | + | 0.715531i | \(0.746185\pi\) | |||||||
\(228\) | −0.859449 | −0.0569184 | ||||||||
\(229\) | −1.91595 | −0.126609 | −0.0633047 | − | 0.997994i | \(-0.520164\pi\) | ||||
−0.0633047 | + | 0.997994i | \(0.520164\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.3005 | −0.809311 | ||||||||
\(232\) | 5.41741 | 0.355670 | ||||||||
\(233\) | −14.4306 | −0.945378 | −0.472689 | − | 0.881229i | \(-0.656717\pi\) | ||||
−0.472689 | + | 0.881229i | \(0.656717\pi\) | |||||||
\(234\) | 4.81288 | 0.314628 | ||||||||
\(235\) | 1.43990 | 0.0939287 | ||||||||
\(236\) | −8.60221 | −0.559956 | ||||||||
\(237\) | −1.12979 | −0.0733880 | ||||||||
\(238\) | −6.26126 | −0.405857 | ||||||||
\(239\) | −9.81701 | −0.635010 | −0.317505 | − | 0.948257i | \(-0.602845\pi\) | ||||
−0.317505 | + | 0.948257i | \(0.602845\pi\) | |||||||
\(240\) | 0.194262 | 0.0125395 | ||||||||
\(241\) | −14.9039 | −0.960043 | −0.480022 | − | 0.877257i | \(-0.659371\pi\) | ||||
−0.480022 | + | 0.877257i | \(0.659371\pi\) | |||||||
\(242\) | 28.7146 | 1.84584 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 12.1201 | 0.775912 | ||||||||
\(245\) | 0.619750 | 0.0395944 | ||||||||
\(246\) | 0.972011 | 0.0619732 | ||||||||
\(247\) | 4.13642 | 0.263194 | ||||||||
\(248\) | −1.01371 | −0.0643703 | ||||||||
\(249\) | −4.00714 | −0.253942 | ||||||||
\(250\) | 1.93529 | 0.122398 | ||||||||
\(251\) | −2.14471 | −0.135373 | −0.0676864 | − | 0.997707i | \(-0.521562\pi\) | ||||
−0.0676864 | + | 0.997707i | \(0.521562\pi\) | |||||||
\(252\) | 1.95185 | 0.122955 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −21.6118 | −1.35604 | ||||||||
\(255\) | −0.623165 | −0.0390241 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −15.8488 | −0.988620 | −0.494310 | − | 0.869286i | \(-0.664579\pi\) | ||||
−0.494310 | + | 0.869286i | \(0.664579\pi\) | |||||||
\(258\) | 5.14282 | 0.320178 | ||||||||
\(259\) | 13.4490 | 0.835678 | ||||||||
\(260\) | −0.934959 | −0.0579837 | ||||||||
\(261\) | 5.41741 | 0.335329 | ||||||||
\(262\) | −14.9571 | −0.924053 | ||||||||
\(263\) | 0.130608 | 0.00805362 | 0.00402681 | − | 0.999992i | \(-0.498718\pi\) | ||||
0.00402681 | + | 0.999992i | \(0.498718\pi\) | |||||||
\(264\) | −6.30195 | −0.387858 | ||||||||
\(265\) | −0.390071 | −0.0239619 | ||||||||
\(266\) | 1.67751 | 0.102855 | ||||||||
\(267\) | 9.55158 | 0.584547 | ||||||||
\(268\) | 7.09327 | 0.433290 | ||||||||
\(269\) | −23.9688 | −1.46140 | −0.730702 | − | 0.682697i | \(-0.760807\pi\) | ||||
−0.730702 | + | 0.682697i | \(0.760807\pi\) | |||||||
\(270\) | 0.194262 | 0.0118224 | ||||||||
\(271\) | 3.22188 | 0.195715 | 0.0978575 | − | 0.995200i | \(-0.468801\pi\) | ||||
0.0978575 | + | 0.995200i | \(0.468801\pi\) | |||||||
\(272\) | −3.20786 | −0.194505 | ||||||||
\(273\) | −9.39402 | −0.568552 | ||||||||
\(274\) | 18.1570 | 1.09690 | ||||||||
\(275\) | −31.2719 | −1.88577 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.0026 | −0.781250 | −0.390625 | − | 0.920550i | \(-0.627741\pi\) | ||||
−0.390625 | + | 0.920550i | \(0.627741\pi\) | |||||||
\(278\) | −7.36718 | −0.441854 | ||||||||
\(279\) | −1.01371 | −0.0606889 | ||||||||
\(280\) | −0.379170 | −0.0226597 | ||||||||
\(281\) | 9.71850 | 0.579757 | 0.289878 | − | 0.957063i | \(-0.406385\pi\) | ||||
0.289878 | + | 0.957063i | \(0.406385\pi\) | |||||||
\(282\) | 7.41216 | 0.441388 | ||||||||
\(283\) | 19.9847 | 1.18797 | 0.593985 | − | 0.804476i | \(-0.297554\pi\) | ||||
0.593985 | + | 0.804476i | \(0.297554\pi\) | |||||||
\(284\) | 1.10938 | 0.0658294 | ||||||||
\(285\) | 0.166958 | 0.00988974 | ||||||||
\(286\) | 30.3305 | 1.79348 | ||||||||
\(287\) | −1.89722 | −0.111989 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −6.70963 | −0.394684 | ||||||||
\(290\) | −1.05240 | −0.0617988 | ||||||||
\(291\) | 1.12094 | 0.0657108 | ||||||||
\(292\) | −13.1859 | −0.771648 | ||||||||
\(293\) | −17.8821 | −1.04468 | −0.522341 | − | 0.852737i | \(-0.674941\pi\) | ||||
−0.522341 | + | 0.852737i | \(0.674941\pi\) | |||||||
\(294\) | 3.19028 | 0.186061 | ||||||||
\(295\) | 1.67108 | 0.0972941 | ||||||||
\(296\) | 6.89037 | 0.400494 | ||||||||
\(297\) | −6.30195 | −0.365676 | ||||||||
\(298\) | 15.6333 | 0.905613 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 4.96226 | 0.286496 | ||||||||
\(301\) | −10.0380 | −0.578581 | ||||||||
\(302\) | 20.7042 | 1.19139 | ||||||||
\(303\) | −12.5714 | −0.722209 | ||||||||
\(304\) | 0.859449 | 0.0492928 | ||||||||
\(305\) | −2.35448 | −0.134817 | ||||||||
\(306\) | −3.20786 | −0.183381 | ||||||||
\(307\) | −12.5139 | −0.714205 | −0.357102 | − | 0.934065i | \(-0.616235\pi\) | ||||
−0.357102 | + | 0.934065i | \(0.616235\pi\) | |||||||
\(308\) | 12.3005 | 0.700884 | ||||||||
\(309\) | −19.3963 | −1.10342 | ||||||||
\(310\) | 0.196924 | 0.0111845 | ||||||||
\(311\) | 5.45773 | 0.309479 | 0.154740 | − | 0.987955i | \(-0.450546\pi\) | ||||
0.154740 | + | 0.987955i | \(0.450546\pi\) | |||||||
\(312\) | −4.81288 | −0.272476 | ||||||||
\(313\) | −23.9234 | −1.35223 | −0.676114 | − | 0.736797i | \(-0.736337\pi\) | ||||
−0.676114 | + | 0.736797i | \(0.736337\pi\) | |||||||
\(314\) | −3.97631 | −0.224396 | ||||||||
\(315\) | −0.379170 | −0.0213638 | ||||||||
\(316\) | 1.12979 | 0.0635559 | ||||||||
\(317\) | −16.1225 | −0.905532 | −0.452766 | − | 0.891629i | \(-0.649563\pi\) | ||||
−0.452766 | + | 0.891629i | \(0.649563\pi\) | |||||||
\(318\) | −2.00797 | −0.112601 | ||||||||
\(319\) | 34.1402 | 1.91149 | ||||||||
\(320\) | −0.194262 | −0.0108596 | ||||||||
\(321\) | −3.07594 | −0.171682 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.75699 | −0.153403 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −23.8828 | −1.32478 | ||||||||
\(326\) | 24.5129 | 1.35764 | ||||||||
\(327\) | −1.94929 | −0.107796 | ||||||||
\(328\) | −0.972011 | −0.0536703 | ||||||||
\(329\) | −14.4674 | −0.797615 | ||||||||
\(330\) | 1.22423 | 0.0673915 | ||||||||
\(331\) | −0.517893 | −0.0284660 | −0.0142330 | − | 0.999899i | \(-0.504531\pi\) | ||||
−0.0142330 | + | 0.999899i | \(0.504531\pi\) | |||||||
\(332\) | 4.00714 | 0.219920 | ||||||||
\(333\) | 6.89037 | 0.377590 | ||||||||
\(334\) | −1.95444 | −0.106942 | ||||||||
\(335\) | −1.37795 | −0.0752855 | ||||||||
\(336\) | −1.95185 | −0.106482 | ||||||||
\(337\) | −0.530119 | −0.0288774 | −0.0144387 | − | 0.999896i | \(-0.504596\pi\) | ||||
−0.0144387 | + | 0.999896i | \(0.504596\pi\) | |||||||
\(338\) | 10.1638 | 0.552839 | ||||||||
\(339\) | 17.1492 | 0.931418 | ||||||||
\(340\) | 0.623165 | 0.0337958 | ||||||||
\(341\) | −6.38832 | −0.345947 | ||||||||
\(342\) | 0.859449 | 0.0464737 | ||||||||
\(343\) | −19.8899 | −1.07395 | ||||||||
\(344\) | −5.14282 | −0.277282 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.14165 | 0.330177 | ||||||||
\(347\) | 26.8126 | 1.43937 | 0.719687 | − | 0.694298i | \(-0.244285\pi\) | ||||
0.719687 | + | 0.694298i | \(0.244285\pi\) | |||||||
\(348\) | −5.41741 | −0.290404 | ||||||||
\(349\) | 1.45728 | 0.0780066 | 0.0390033 | − | 0.999239i | \(-0.487582\pi\) | ||||
0.0390033 | + | 0.999239i | \(0.487582\pi\) | |||||||
\(350\) | −9.68559 | −0.517716 | ||||||||
\(351\) | −4.81288 | −0.256893 | ||||||||
\(352\) | 6.30195 | 0.335895 | ||||||||
\(353\) | 22.4537 | 1.19509 | 0.597545 | − | 0.801835i | \(-0.296143\pi\) | ||||
0.597545 | + | 0.801835i | \(0.296143\pi\) | |||||||
\(354\) | 8.60221 | 0.457202 | ||||||||
\(355\) | −0.215510 | −0.0114381 | ||||||||
\(356\) | −9.55158 | −0.506233 | ||||||||
\(357\) | 6.26126 | 0.331381 | ||||||||
\(358\) | 6.47091 | 0.341998 | ||||||||
\(359\) | 0.168999 | 0.00891940 | 0.00445970 | − | 0.999990i | \(-0.498580\pi\) | ||||
0.00445970 | + | 0.999990i | \(0.498580\pi\) | |||||||
\(360\) | −0.194262 | −0.0102385 | ||||||||
\(361\) | −18.2613 | −0.961124 | ||||||||
\(362\) | 3.26146 | 0.171419 | ||||||||
\(363\) | −28.7146 | −1.50712 | ||||||||
\(364\) | 9.39402 | 0.492380 | ||||||||
\(365\) | 2.56152 | 0.134076 | ||||||||
\(366\) | −12.1201 | −0.633530 | ||||||||
\(367\) | 17.8312 | 0.930782 | 0.465391 | − | 0.885105i | \(-0.345914\pi\) | ||||
0.465391 | + | 0.885105i | \(0.345914\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.972011 | −0.0506009 | ||||||||
\(370\) | −1.33853 | −0.0695871 | ||||||||
\(371\) | 3.91925 | 0.203477 | ||||||||
\(372\) | 1.01371 | 0.0525582 | ||||||||
\(373\) | −27.3884 | −1.41812 | −0.709058 | − | 0.705150i | \(-0.750879\pi\) | ||||
−0.709058 | + | 0.705150i | \(0.750879\pi\) | |||||||
\(374\) | −20.2158 | −1.04533 | ||||||||
\(375\) | −1.93529 | −0.0999378 | ||||||||
\(376\) | −7.41216 | −0.382253 | ||||||||
\(377\) | 26.0733 | 1.34285 | ||||||||
\(378\) | −1.95185 | −0.100392 | ||||||||
\(379\) | −2.73604 | −0.140541 | −0.0702704 | − | 0.997528i | \(-0.522386\pi\) | ||||
−0.0702704 | + | 0.997528i | \(0.522386\pi\) | |||||||
\(380\) | −0.166958 | −0.00856476 | ||||||||
\(381\) | 21.6118 | 1.10721 | ||||||||
\(382\) | −22.8536 | −1.16929 | ||||||||
\(383\) | −14.4109 | −0.736362 | −0.368181 | − | 0.929754i | \(-0.620019\pi\) | ||||
−0.368181 | + | 0.929754i | \(0.620019\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −2.38951 | −0.121781 | ||||||||
\(386\) | −16.9414 | −0.862294 | ||||||||
\(387\) | −5.14282 | −0.261424 | ||||||||
\(388\) | −1.12094 | −0.0569073 | ||||||||
\(389\) | 1.08404 | 0.0549630 | 0.0274815 | − | 0.999622i | \(-0.491251\pi\) | ||||
0.0274815 | + | 0.999622i | \(0.491251\pi\) | |||||||
\(390\) | 0.934959 | 0.0473435 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −3.19028 | −0.161134 | ||||||||
\(393\) | 14.9571 | 0.754486 | ||||||||
\(394\) | 1.25480 | 0.0632161 | ||||||||
\(395\) | −0.219476 | −0.0110430 | ||||||||
\(396\) | 6.30195 | 0.316685 | ||||||||
\(397\) | −27.0241 | −1.35630 | −0.678149 | − | 0.734924i | \(-0.737218\pi\) | ||||
−0.678149 | + | 0.734924i | \(0.737218\pi\) | |||||||
\(398\) | 24.8140 | 1.24381 | ||||||||
\(399\) | −1.67751 | −0.0839807 | ||||||||
\(400\) | −4.96226 | −0.248113 | ||||||||
\(401\) | 9.27409 | 0.463126 | 0.231563 | − | 0.972820i | \(-0.425616\pi\) | ||||
0.231563 | + | 0.972820i | \(0.425616\pi\) | |||||||
\(402\) | −7.09327 | −0.353780 | ||||||||
\(403\) | −4.87884 | −0.243032 | ||||||||
\(404\) | 12.5714 | 0.625451 | ||||||||
\(405\) | −0.194262 | −0.00965294 | ||||||||
\(406\) | 10.5740 | 0.524777 | ||||||||
\(407\) | 43.4228 | 2.15239 | ||||||||
\(408\) | 3.20786 | 0.158813 | ||||||||
\(409\) | 36.7657 | 1.81795 | 0.908974 | − | 0.416852i | \(-0.136867\pi\) | ||||
0.908974 | + | 0.416852i | \(0.136867\pi\) | |||||||
\(410\) | 0.188825 | 0.00932538 | ||||||||
\(411\) | −18.1570 | −0.895619 | ||||||||
\(412\) | 19.3963 | 0.955587 | ||||||||
\(413\) | −16.7902 | −0.826193 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.778434 | −0.0382118 | ||||||||
\(416\) | 4.81288 | 0.235971 | ||||||||
\(417\) | 7.36718 | 0.360772 | ||||||||
\(418\) | 5.41620 | 0.264915 | ||||||||
\(419\) | −26.4958 | −1.29441 | −0.647203 | − | 0.762318i | \(-0.724061\pi\) | ||||
−0.647203 | + | 0.762318i | \(0.724061\pi\) | |||||||
\(420\) | 0.379170 | 0.0185016 | ||||||||
\(421\) | 9.95095 | 0.484980 | 0.242490 | − | 0.970154i | \(-0.422036\pi\) | ||||
0.242490 | + | 0.970154i | \(0.422036\pi\) | |||||||
\(422\) | 7.25827 | 0.353327 | ||||||||
\(423\) | −7.41216 | −0.360392 | ||||||||
\(424\) | 2.00797 | 0.0975155 | ||||||||
\(425\) | 15.9182 | 0.772148 | ||||||||
\(426\) | −1.10938 | −0.0537495 | ||||||||
\(427\) | 23.6567 | 1.14483 | ||||||||
\(428\) | 3.07594 | 0.148681 | ||||||||
\(429\) | −30.3305 | −1.46437 | ||||||||
\(430\) | 0.999053 | 0.0481786 | ||||||||
\(431\) | 8.77287 | 0.422575 | 0.211287 | − | 0.977424i | \(-0.432234\pi\) | ||||
0.211287 | + | 0.977424i | \(0.432234\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −7.99061 | −0.384004 | −0.192002 | − | 0.981395i | \(-0.561498\pi\) | ||||
−0.192002 | + | 0.981395i | \(0.561498\pi\) | |||||||
\(434\) | −1.97860 | −0.0949758 | ||||||||
\(435\) | 1.05240 | 0.0504585 | ||||||||
\(436\) | 1.94929 | 0.0933542 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 13.1859 | 0.630048 | ||||||||
\(439\) | −1.41063 | −0.0673257 | −0.0336628 | − | 0.999433i | \(-0.510717\pi\) | ||||
−0.0336628 | + | 0.999433i | \(0.510717\pi\) | |||||||
\(440\) | −1.22423 | −0.0583628 | ||||||||
\(441\) | −3.19028 | −0.151918 | ||||||||
\(442\) | −15.4390 | −0.734361 | ||||||||
\(443\) | 12.5935 | 0.598335 | 0.299167 | − | 0.954201i | \(-0.403291\pi\) | ||||
0.299167 | + | 0.954201i | \(0.403291\pi\) | |||||||
\(444\) | −6.89037 | −0.327002 | ||||||||
\(445\) | 1.85551 | 0.0879594 | ||||||||
\(446\) | 20.7342 | 0.981791 | ||||||||
\(447\) | −15.6333 | −0.739430 | ||||||||
\(448\) | 1.95185 | 0.0922162 | ||||||||
\(449\) | −38.3533 | −1.81000 | −0.905002 | − | 0.425407i | \(-0.860131\pi\) | ||||
−0.905002 | + | 0.425407i | \(0.860131\pi\) | |||||||
\(450\) | −4.96226 | −0.233923 | ||||||||
\(451\) | −6.12557 | −0.288442 | ||||||||
\(452\) | −17.1492 | −0.806632 | ||||||||
\(453\) | −20.7042 | −0.972766 | ||||||||
\(454\) | −21.0504 | −0.987943 | ||||||||
\(455\) | −1.82490 | −0.0855525 | ||||||||
\(456\) | −0.859449 | −0.0402474 | ||||||||
\(457\) | 26.6357 | 1.24597 | 0.622983 | − | 0.782235i | \(-0.285921\pi\) | ||||
0.622983 | + | 0.782235i | \(0.285921\pi\) | |||||||
\(458\) | −1.91595 | −0.0895264 | ||||||||
\(459\) | 3.20786 | 0.149730 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.65301 | 0.356436 | 0.178218 | − | 0.983991i | \(-0.442967\pi\) | ||||
0.178218 | + | 0.983991i | \(0.442967\pi\) | |||||||
\(462\) | −12.3005 | −0.572269 | ||||||||
\(463\) | −4.15149 | −0.192936 | −0.0964681 | − | 0.995336i | \(-0.530755\pi\) | ||||
−0.0964681 | + | 0.995336i | \(0.530755\pi\) | |||||||
\(464\) | 5.41741 | 0.251497 | ||||||||
\(465\) | −0.196924 | −0.00913214 | ||||||||
\(466\) | −14.4306 | −0.668483 | ||||||||
\(467\) | −32.1155 | −1.48613 | −0.743063 | − | 0.669221i | \(-0.766628\pi\) | ||||
−0.743063 | + | 0.669221i | \(0.766628\pi\) | |||||||
\(468\) | 4.81288 | 0.222475 | ||||||||
\(469\) | 13.8450 | 0.639302 | ||||||||
\(470\) | 1.43990 | 0.0664176 | ||||||||
\(471\) | 3.97631 | 0.183219 | ||||||||
\(472\) | −8.60221 | −0.395949 | ||||||||
\(473\) | −32.4098 | −1.49020 | ||||||||
\(474\) | −1.12979 | −0.0518932 | ||||||||
\(475\) | −4.26481 | −0.195683 | ||||||||
\(476\) | −6.26126 | −0.286984 | ||||||||
\(477\) | 2.00797 | 0.0919385 | ||||||||
\(478\) | −9.81701 | −0.449020 | ||||||||
\(479\) | 1.81509 | 0.0829337 | 0.0414668 | − | 0.999140i | \(-0.486797\pi\) | ||||
0.0414668 | + | 0.999140i | \(0.486797\pi\) | |||||||
\(480\) | 0.194262 | 0.00886680 | ||||||||
\(481\) | 33.1625 | 1.51208 | ||||||||
\(482\) | −14.9039 | −0.678853 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 28.7146 | 1.30521 | ||||||||
\(485\) | 0.217756 | 0.00988781 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −16.1873 | −0.733515 | −0.366758 | − | 0.930317i | \(-0.619532\pi\) | ||||
−0.366758 | + | 0.930317i | \(0.619532\pi\) | |||||||
\(488\) | 12.1201 | 0.548653 | ||||||||
\(489\) | −24.5129 | −1.10851 | ||||||||
\(490\) | 0.619750 | 0.0279975 | ||||||||
\(491\) | −1.42155 | −0.0641536 | −0.0320768 | − | 0.999485i | \(-0.510212\pi\) | ||||
−0.0320768 | + | 0.999485i | \(0.510212\pi\) | |||||||
\(492\) | 0.972011 | 0.0438216 | ||||||||
\(493\) | −17.3783 | −0.782679 | ||||||||
\(494\) | 4.13642 | 0.186106 | ||||||||
\(495\) | −1.22423 | −0.0550250 | ||||||||
\(496\) | −1.01371 | −0.0455167 | ||||||||
\(497\) | 2.16534 | 0.0971286 | ||||||||
\(498\) | −4.00714 | −0.179564 | ||||||||
\(499\) | 20.5750 | 0.921061 | 0.460531 | − | 0.887644i | \(-0.347659\pi\) | ||||
0.460531 | + | 0.887644i | \(0.347659\pi\) | |||||||
\(500\) | 1.93529 | 0.0865487 | ||||||||
\(501\) | 1.95444 | 0.0873177 | ||||||||
\(502\) | −2.14471 | −0.0957230 | ||||||||
\(503\) | 14.7875 | 0.659342 | 0.329671 | − | 0.944096i | \(-0.393062\pi\) | ||||
0.329671 | + | 0.944096i | \(0.393062\pi\) | |||||||
\(504\) | 1.95185 | 0.0869423 | ||||||||
\(505\) | −2.44214 | −0.108674 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.1638 | −0.451391 | ||||||||
\(508\) | −21.6118 | −0.958869 | ||||||||
\(509\) | 33.1496 | 1.46933 | 0.734666 | − | 0.678429i | \(-0.237339\pi\) | ||||
0.734666 | + | 0.678429i | \(0.237339\pi\) | |||||||
\(510\) | −0.623165 | −0.0275942 | ||||||||
\(511\) | −25.7370 | −1.13854 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.859449 | −0.0379456 | ||||||||
\(514\) | −15.8488 | −0.699060 | ||||||||
\(515\) | −3.76796 | −0.166036 | ||||||||
\(516\) | 5.14282 | 0.226400 | ||||||||
\(517\) | −46.7111 | −2.05435 | ||||||||
\(518\) | 13.4490 | 0.590913 | ||||||||
\(519\) | −6.14165 | −0.269589 | ||||||||
\(520\) | −0.934959 | −0.0410006 | ||||||||
\(521\) | −28.9660 | −1.26902 | −0.634511 | − | 0.772913i | \(-0.718799\pi\) | ||||
−0.634511 | + | 0.772913i | \(0.718799\pi\) | |||||||
\(522\) | 5.41741 | 0.237114 | ||||||||
\(523\) | 33.6692 | 1.47225 | 0.736126 | − | 0.676845i | \(-0.236653\pi\) | ||||
0.736126 | + | 0.676845i | \(0.236653\pi\) | |||||||
\(524\) | −14.9571 | −0.653404 | ||||||||
\(525\) | 9.68559 | 0.422714 | ||||||||
\(526\) | 0.130608 | 0.00569477 | ||||||||
\(527\) | 3.25182 | 0.141652 | ||||||||
\(528\) | −6.30195 | −0.274257 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | −0.390071 | −0.0169436 | ||||||||
\(531\) | −8.60221 | −0.373304 | ||||||||
\(532\) | 1.67751 | 0.0727295 | ||||||||
\(533\) | −4.67817 | −0.202634 | ||||||||
\(534\) | 9.55158 | 0.413337 | ||||||||
\(535\) | −0.597538 | −0.0258338 | ||||||||
\(536\) | 7.09327 | 0.306382 | ||||||||
\(537\) | −6.47091 | −0.279240 | ||||||||
\(538\) | −23.9688 | −1.03337 | ||||||||
\(539\) | −20.1050 | −0.865984 | ||||||||
\(540\) | 0.194262 | 0.00835970 | ||||||||
\(541\) | −40.1990 | −1.72829 | −0.864144 | − | 0.503245i | \(-0.832139\pi\) | ||||
−0.864144 | + | 0.503245i | \(0.832139\pi\) | |||||||
\(542\) | 3.22188 | 0.138391 | ||||||||
\(543\) | −3.26146 | −0.139963 | ||||||||
\(544\) | −3.20786 | −0.137536 | ||||||||
\(545\) | −0.378673 | −0.0162206 | ||||||||
\(546\) | −9.39402 | −0.402027 | ||||||||
\(547\) | 22.7001 | 0.970588 | 0.485294 | − | 0.874351i | \(-0.338713\pi\) | ||||
0.485294 | + | 0.874351i | \(0.338713\pi\) | |||||||
\(548\) | 18.1570 | 0.775628 | ||||||||
\(549\) | 12.1201 | 0.517275 | ||||||||
\(550\) | −31.2719 | −1.33344 | ||||||||
\(551\) | 4.65598 | 0.198352 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.20519 | 0.0937741 | ||||||||
\(554\) | −13.0026 | −0.552427 | ||||||||
\(555\) | 1.33853 | 0.0568176 | ||||||||
\(556\) | −7.36718 | −0.312438 | ||||||||
\(557\) | 3.95623 | 0.167631 | 0.0838154 | − | 0.996481i | \(-0.473289\pi\) | ||||
0.0838154 | + | 0.996481i | \(0.473289\pi\) | |||||||
\(558\) | −1.01371 | −0.0429136 | ||||||||
\(559\) | −24.7518 | −1.04689 | ||||||||
\(560\) | −0.379170 | −0.0160228 | ||||||||
\(561\) | 20.2158 | 0.853511 | ||||||||
\(562\) | 9.71850 | 0.409950 | ||||||||
\(563\) | −27.2143 | −1.14695 | −0.573473 | − | 0.819224i | \(-0.694404\pi\) | ||||
−0.573473 | + | 0.819224i | \(0.694404\pi\) | |||||||
\(564\) | 7.41216 | 0.312108 | ||||||||
\(565\) | 3.33144 | 0.140155 | ||||||||
\(566\) | 19.9847 | 0.840022 | ||||||||
\(567\) | 1.95185 | 0.0819700 | ||||||||
\(568\) | 1.10938 | 0.0465484 | ||||||||
\(569\) | −20.6417 | −0.865344 | −0.432672 | − | 0.901551i | \(-0.642429\pi\) | ||||
−0.432672 | + | 0.901551i | \(0.642429\pi\) | |||||||
\(570\) | 0.166958 | 0.00699310 | ||||||||
\(571\) | 30.3575 | 1.27042 | 0.635212 | − | 0.772338i | \(-0.280913\pi\) | ||||
0.635212 | + | 0.772338i | \(0.280913\pi\) | |||||||
\(572\) | 30.3305 | 1.26818 | ||||||||
\(573\) | 22.8536 | 0.954723 | ||||||||
\(574\) | −1.89722 | −0.0791884 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −14.1163 | −0.587667 | −0.293834 | − | 0.955857i | \(-0.594931\pi\) | ||||
−0.293834 | + | 0.955857i | \(0.594931\pi\) | |||||||
\(578\) | −6.70963 | −0.279084 | ||||||||
\(579\) | 16.9414 | 0.704060 | ||||||||
\(580\) | −1.05240 | −0.0436983 | ||||||||
\(581\) | 7.82134 | 0.324484 | ||||||||
\(582\) | 1.12094 | 0.0464646 | ||||||||
\(583\) | 12.6541 | 0.524079 | ||||||||
\(584\) | −13.1859 | −0.545638 | ||||||||
\(585\) | −0.934959 | −0.0386558 | ||||||||
\(586\) | −17.8821 | −0.738702 | ||||||||
\(587\) | 36.5538 | 1.50874 | 0.754369 | − | 0.656451i | \(-0.227943\pi\) | ||||
0.754369 | + | 0.656451i | \(0.227943\pi\) | |||||||
\(588\) | 3.19028 | 0.131565 | ||||||||
\(589\) | −0.871227 | −0.0358983 | ||||||||
\(590\) | 1.67108 | 0.0687973 | ||||||||
\(591\) | −1.25480 | −0.0516157 | ||||||||
\(592\) | 6.89037 | 0.283192 | ||||||||
\(593\) | 6.64351 | 0.272816 | 0.136408 | − | 0.990653i | \(-0.456444\pi\) | ||||
0.136408 | + | 0.990653i | \(0.456444\pi\) | |||||||
\(594\) | −6.30195 | −0.258572 | ||||||||
\(595\) | 1.21632 | 0.0498644 | ||||||||
\(596\) | 15.6333 | 0.640365 | ||||||||
\(597\) | −24.8140 | −1.01557 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.0099 | 1.14445 | 0.572226 | − | 0.820096i | \(-0.306080\pi\) | ||||
0.572226 | + | 0.820096i | \(0.306080\pi\) | |||||||
\(600\) | 4.96226 | 0.202584 | ||||||||
\(601\) | 17.5864 | 0.717363 | 0.358682 | − | 0.933460i | \(-0.383226\pi\) | ||||
0.358682 | + | 0.933460i | \(0.383226\pi\) | |||||||
\(602\) | −10.0380 | −0.409119 | ||||||||
\(603\) | 7.09327 | 0.288860 | ||||||||
\(604\) | 20.7042 | 0.842440 | ||||||||
\(605\) | −5.57814 | −0.226784 | ||||||||
\(606\) | −12.5714 | −0.510679 | ||||||||
\(607\) | −23.5948 | −0.957684 | −0.478842 | − | 0.877901i | \(-0.658943\pi\) | ||||
−0.478842 | + | 0.877901i | \(0.658943\pi\) | |||||||
\(608\) | 0.859449 | 0.0348552 | ||||||||
\(609\) | −10.5740 | −0.428479 | ||||||||
\(610\) | −2.35448 | −0.0953301 | ||||||||
\(611\) | −35.6738 | −1.44321 | ||||||||
\(612\) | −3.20786 | −0.129670 | ||||||||
\(613\) | 32.9938 | 1.33261 | 0.666303 | − | 0.745681i | \(-0.267876\pi\) | ||||
0.666303 | + | 0.745681i | \(0.267876\pi\) | |||||||
\(614\) | −12.5139 | −0.505019 | ||||||||
\(615\) | −0.188825 | −0.00761414 | ||||||||
\(616\) | 12.3005 | 0.495599 | ||||||||
\(617\) | −38.0582 | −1.53216 | −0.766082 | − | 0.642743i | \(-0.777796\pi\) | ||||
−0.766082 | + | 0.642743i | \(0.777796\pi\) | |||||||
\(618\) | −19.3963 | −0.780234 | ||||||||
\(619\) | −8.49110 | −0.341286 | −0.170643 | − | 0.985333i | \(-0.554584\pi\) | ||||
−0.170643 | + | 0.985333i | \(0.554584\pi\) | |||||||
\(620\) | 0.196924 | 0.00790866 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.45773 | 0.218835 | ||||||||
\(623\) | −18.6432 | −0.746926 | ||||||||
\(624\) | −4.81288 | −0.192669 | ||||||||
\(625\) | 24.4354 | 0.977414 | ||||||||
\(626\) | −23.9234 | −0.956170 | ||||||||
\(627\) | −5.41620 | −0.216302 | ||||||||
\(628\) | −3.97631 | −0.158672 | ||||||||
\(629\) | −22.1033 | −0.881318 | ||||||||
\(630\) | −0.379170 | −0.0151065 | ||||||||
\(631\) | 11.1468 | 0.443747 | 0.221874 | − | 0.975075i | \(-0.428783\pi\) | ||||
0.221874 | + | 0.975075i | \(0.428783\pi\) | |||||||
\(632\) | 1.12979 | 0.0449408 | ||||||||
\(633\) | −7.25827 | −0.288490 | ||||||||
\(634\) | −16.1225 | −0.640308 | ||||||||
\(635\) | 4.19835 | 0.166606 | ||||||||
\(636\) | −2.00797 | −0.0796210 | ||||||||
\(637\) | −15.3545 | −0.608366 | ||||||||
\(638\) | 34.1402 | 1.35163 | ||||||||
\(639\) | 1.10938 | 0.0438863 | ||||||||
\(640\) | −0.194262 | −0.00767887 | ||||||||
\(641\) | −37.8358 | −1.49442 | −0.747212 | − | 0.664586i | \(-0.768608\pi\) | ||||
−0.747212 | + | 0.664586i | \(0.768608\pi\) | |||||||
\(642\) | −3.07594 | −0.121398 | ||||||||
\(643\) | −22.3733 | −0.882317 | −0.441158 | − | 0.897429i | \(-0.645432\pi\) | ||||
−0.441158 | + | 0.897429i | \(0.645432\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.999053 | −0.0393377 | ||||||||
\(646\) | −2.75699 | −0.108472 | ||||||||
\(647\) | −10.9467 | −0.430359 | −0.215180 | − | 0.976575i | \(-0.569034\pi\) | ||||
−0.215180 | + | 0.976575i | \(0.569034\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −54.2107 | −2.12796 | ||||||||
\(650\) | −23.8828 | −0.936759 | ||||||||
\(651\) | 1.97860 | 0.0775474 | ||||||||
\(652\) | 24.5129 | 0.959997 | ||||||||
\(653\) | 5.78807 | 0.226505 | 0.113252 | − | 0.993566i | \(-0.463873\pi\) | ||||
0.113252 | + | 0.993566i | \(0.463873\pi\) | |||||||
\(654\) | −1.94929 | −0.0762234 | ||||||||
\(655\) | 2.90559 | 0.113531 | ||||||||
\(656\) | −0.972011 | −0.0379507 | ||||||||
\(657\) | −13.1859 | −0.514432 | ||||||||
\(658\) | −14.4674 | −0.563999 | ||||||||
\(659\) | −8.31443 | −0.323884 | −0.161942 | − | 0.986800i | \(-0.551776\pi\) | ||||
−0.161942 | + | 0.986800i | \(0.551776\pi\) | |||||||
\(660\) | 1.22423 | 0.0476530 | ||||||||
\(661\) | −12.1685 | −0.473301 | −0.236650 | − | 0.971595i | \(-0.576050\pi\) | ||||
−0.236650 | + | 0.971595i | \(0.576050\pi\) | |||||||
\(662\) | −0.517893 | −0.0201285 | ||||||||
\(663\) | 15.4390 | 0.599603 | ||||||||
\(664\) | 4.00714 | 0.155507 | ||||||||
\(665\) | −0.325877 | −0.0126370 | ||||||||
\(666\) | 6.89037 | 0.266996 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −1.95444 | −0.0756194 | ||||||||
\(669\) | −20.7342 | −0.801629 | ||||||||
\(670\) | −1.37795 | −0.0532349 | ||||||||
\(671\) | 76.3805 | 2.94864 | ||||||||
\(672\) | −1.95185 | −0.0752942 | ||||||||
\(673\) | 4.87132 | 0.187775 | 0.0938877 | − | 0.995583i | \(-0.470071\pi\) | ||||
0.0938877 | + | 0.995583i | \(0.470071\pi\) | |||||||
\(674\) | −0.530119 | −0.0204194 | ||||||||
\(675\) | 4.96226 | 0.190998 | ||||||||
\(676\) | 10.1638 | 0.390916 | ||||||||
\(677\) | −20.0060 | −0.768892 | −0.384446 | − | 0.923147i | \(-0.625608\pi\) | ||||
−0.384446 | + | 0.923147i | \(0.625608\pi\) | |||||||
\(678\) | 17.1492 | 0.658612 | ||||||||
\(679\) | −2.18791 | −0.0839643 | ||||||||
\(680\) | 0.623165 | 0.0238973 | ||||||||
\(681\) | 21.0504 | 0.806652 | ||||||||
\(682\) | −6.38832 | −0.244621 | ||||||||
\(683\) | −23.9883 | −0.917888 | −0.458944 | − | 0.888465i | \(-0.651772\pi\) | ||||
−0.458944 | + | 0.888465i | \(0.651772\pi\) | |||||||
\(684\) | 0.859449 | 0.0328618 | ||||||||
\(685\) | −3.52721 | −0.134768 | ||||||||
\(686\) | −19.8899 | −0.759400 | ||||||||
\(687\) | 1.91595 | 0.0730980 | ||||||||
\(688\) | −5.14282 | −0.196068 | ||||||||
\(689\) | 9.66410 | 0.368173 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.5438 | 0.629356 | 0.314678 | − | 0.949199i | \(-0.398104\pi\) | ||||
0.314678 | + | 0.949199i | \(0.398104\pi\) | |||||||
\(692\) | 6.14165 | 0.233471 | ||||||||
\(693\) | 12.3005 | 0.467256 | ||||||||
\(694\) | 26.8126 | 1.01779 | ||||||||
\(695\) | 1.43116 | 0.0542870 | ||||||||
\(696\) | −5.41741 | −0.205346 | ||||||||
\(697\) | 3.11808 | 0.118106 | ||||||||
\(698\) | 1.45728 | 0.0551590 | ||||||||
\(699\) | 14.4306 | 0.545814 | ||||||||
\(700\) | −9.68559 | −0.366081 | ||||||||
\(701\) | −15.9822 | −0.603640 | −0.301820 | − | 0.953365i | \(-0.597594\pi\) | ||||
−0.301820 | + | 0.953365i | \(0.597594\pi\) | |||||||
\(702\) | −4.81288 | −0.181650 | ||||||||
\(703\) | 5.92192 | 0.223349 | ||||||||
\(704\) | 6.30195 | 0.237514 | ||||||||
\(705\) | −1.43990 | −0.0542298 | ||||||||
\(706\) | 22.4537 | 0.845056 | ||||||||
\(707\) | 24.5375 | 0.922828 | ||||||||
\(708\) | 8.60221 | 0.323291 | ||||||||
\(709\) | 6.40478 | 0.240536 | 0.120268 | − | 0.992741i | \(-0.461625\pi\) | ||||
0.120268 | + | 0.992741i | \(0.461625\pi\) | |||||||
\(710\) | −0.215510 | −0.00808793 | ||||||||
\(711\) | 1.12979 | 0.0423706 | ||||||||
\(712\) | −9.55158 | −0.357960 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 6.26126 | 0.234322 | ||||||||
\(715\) | −5.89206 | −0.220351 | ||||||||
\(716\) | 6.47091 | 0.241829 | ||||||||
\(717\) | 9.81701 | 0.366623 | ||||||||
\(718\) | 0.168999 | 0.00630697 | ||||||||
\(719\) | −41.6971 | −1.55504 | −0.777519 | − | 0.628859i | \(-0.783522\pi\) | ||||
−0.777519 | + | 0.628859i | \(0.783522\pi\) | |||||||
\(720\) | −0.194262 | −0.00723971 | ||||||||
\(721\) | 37.8587 | 1.40993 | ||||||||
\(722\) | −18.2613 | −0.679617 | ||||||||
\(723\) | 14.9039 | 0.554281 | ||||||||
\(724\) | 3.26146 | 0.121211 | ||||||||
\(725\) | −26.8826 | −0.998395 | ||||||||
\(726\) | −28.7146 | −1.06570 | ||||||||
\(727\) | −10.0060 | −0.371101 | −0.185551 | − | 0.982635i | \(-0.559407\pi\) | ||||
−0.185551 | + | 0.982635i | \(0.559407\pi\) | |||||||
\(728\) | 9.39402 | 0.348165 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.56152 | 0.0948062 | ||||||||
\(731\) | 16.4974 | 0.610180 | ||||||||
\(732\) | −12.1201 | −0.447973 | ||||||||
\(733\) | −23.3610 | −0.862858 | −0.431429 | − | 0.902147i | \(-0.641991\pi\) | ||||
−0.431429 | + | 0.902147i | \(0.641991\pi\) | |||||||
\(734\) | 17.8312 | 0.658163 | ||||||||
\(735\) | −0.619750 | −0.0228598 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 44.7014 | 1.64660 | ||||||||
\(738\) | −0.972011 | −0.0357802 | ||||||||
\(739\) | 26.7250 | 0.983094 | 0.491547 | − | 0.870851i | \(-0.336432\pi\) | ||||
0.491547 | + | 0.870851i | \(0.336432\pi\) | |||||||
\(740\) | −1.33853 | −0.0492055 | ||||||||
\(741\) | −4.13642 | −0.151955 | ||||||||
\(742\) | 3.91925 | 0.143880 | ||||||||
\(743\) | −15.1711 | −0.556575 | −0.278288 | − | 0.960498i | \(-0.589767\pi\) | ||||
−0.278288 | + | 0.960498i | \(0.589767\pi\) | |||||||
\(744\) | 1.01371 | 0.0371642 | ||||||||
\(745\) | −3.03695 | −0.111265 | ||||||||
\(746\) | −27.3884 | −1.00276 | ||||||||
\(747\) | 4.00714 | 0.146614 | ||||||||
\(748\) | −20.2158 | −0.739162 | ||||||||
\(749\) | 6.00378 | 0.219373 | ||||||||
\(750\) | −1.93529 | −0.0706667 | ||||||||
\(751\) | 21.6684 | 0.790691 | 0.395346 | − | 0.918532i | \(-0.370625\pi\) | ||||
0.395346 | + | 0.918532i | \(0.370625\pi\) | |||||||
\(752\) | −7.41216 | −0.270294 | ||||||||
\(753\) | 2.14471 | 0.0781575 | ||||||||
\(754\) | 26.0733 | 0.949535 | ||||||||
\(755\) | −4.02203 | −0.146377 | ||||||||
\(756\) | −1.95185 | −0.0709881 | ||||||||
\(757\) | −4.05195 | −0.147271 | −0.0736354 | − | 0.997285i | \(-0.523460\pi\) | ||||
−0.0736354 | + | 0.997285i | \(0.523460\pi\) | |||||||
\(758\) | −2.73604 | −0.0993774 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.166958 | −0.00605620 | ||||||||
\(761\) | −44.2112 | −1.60266 | −0.801328 | − | 0.598225i | \(-0.795873\pi\) | ||||
−0.801328 | + | 0.598225i | \(0.795873\pi\) | |||||||
\(762\) | 21.6118 | 0.782913 | ||||||||
\(763\) | 3.80473 | 0.137740 | ||||||||
\(764\) | −22.8536 | −0.826815 | ||||||||
\(765\) | 0.623165 | 0.0225306 | ||||||||
\(766\) | −14.4109 | −0.520687 | ||||||||
\(767\) | −41.4014 | −1.49492 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 8.81046 | 0.317713 | 0.158857 | − | 0.987302i | \(-0.449219\pi\) | ||||
0.158857 | + | 0.987302i | \(0.449219\pi\) | |||||||
\(770\) | −2.38951 | −0.0861119 | ||||||||
\(771\) | 15.8488 | 0.570780 | ||||||||
\(772\) | −16.9414 | −0.609734 | ||||||||
\(773\) | −0.634119 | −0.0228077 | −0.0114038 | − | 0.999935i | \(-0.503630\pi\) | ||||
−0.0114038 | + | 0.999935i | \(0.503630\pi\) | |||||||
\(774\) | −5.14282 | −0.184855 | ||||||||
\(775\) | 5.03027 | 0.180693 | ||||||||
\(776\) | −1.12094 | −0.0402395 | ||||||||
\(777\) | −13.4490 | −0.482479 | ||||||||
\(778\) | 1.08404 | 0.0388647 | ||||||||
\(779\) | −0.835394 | −0.0299311 | ||||||||
\(780\) | 0.934959 | 0.0334769 | ||||||||
\(781\) | 6.99124 | 0.250166 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.41741 | −0.193602 | ||||||||
\(784\) | −3.19028 | −0.113939 | ||||||||
\(785\) | 0.772445 | 0.0275698 | ||||||||
\(786\) | 14.9571 | 0.533502 | ||||||||
\(787\) | 15.9809 | 0.569659 | 0.284829 | − | 0.958578i | \(-0.408063\pi\) | ||||
0.284829 | + | 0.958578i | \(0.408063\pi\) | |||||||
\(788\) | 1.25480 | 0.0447005 | ||||||||
\(789\) | −0.130608 | −0.00464976 | ||||||||
\(790\) | −0.219476 | −0.00780860 | ||||||||
\(791\) | −33.4727 | −1.19015 | ||||||||
\(792\) | 6.30195 | 0.223930 | ||||||||
\(793\) | 58.3328 | 2.07146 | ||||||||
\(794\) | −27.0241 | −0.959048 | ||||||||
\(795\) | 0.390071 | 0.0138344 | ||||||||
\(796\) | 24.8140 | 0.879509 | ||||||||
\(797\) | −40.9716 | −1.45129 | −0.725644 | − | 0.688070i | \(-0.758458\pi\) | ||||
−0.725644 | + | 0.688070i | \(0.758458\pi\) | |||||||
\(798\) | −1.67751 | −0.0593833 | ||||||||
\(799\) | 23.7772 | 0.841176 | ||||||||
\(800\) | −4.96226 | −0.175442 | ||||||||
\(801\) | −9.55158 | −0.337488 | ||||||||
\(802\) | 9.27409 | 0.327479 | ||||||||
\(803\) | −83.0971 | −2.93243 | ||||||||
\(804\) | −7.09327 | −0.250160 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.87884 | −0.171850 | ||||||||
\(807\) | 23.9688 | 0.843742 | ||||||||
\(808\) | 12.5714 | 0.442261 | ||||||||
\(809\) | −28.2257 | −0.992363 | −0.496181 | − | 0.868219i | \(-0.665265\pi\) | ||||
−0.496181 | + | 0.868219i | \(0.665265\pi\) | |||||||
\(810\) | −0.194262 | −0.00682566 | ||||||||
\(811\) | −3.61726 | −0.127019 | −0.0635096 | − | 0.997981i | \(-0.520229\pi\) | ||||
−0.0635096 | + | 0.997981i | \(0.520229\pi\) | |||||||
\(812\) | 10.5740 | 0.371073 | ||||||||
\(813\) | −3.22188 | −0.112996 | ||||||||
\(814\) | 43.4228 | 1.52197 | ||||||||
\(815\) | −4.76191 | −0.166802 | ||||||||
\(816\) | 3.20786 | 0.112298 | ||||||||
\(817\) | −4.41999 | −0.154636 | ||||||||
\(818\) | 36.7657 | 1.28548 | ||||||||
\(819\) | 9.39402 | 0.328253 | ||||||||
\(820\) | 0.188825 | 0.00659404 | ||||||||
\(821\) | 30.8947 | 1.07823 | 0.539116 | − | 0.842231i | \(-0.318758\pi\) | ||||
0.539116 | + | 0.842231i | \(0.318758\pi\) | |||||||
\(822\) | −18.1570 | −0.633298 | ||||||||
\(823\) | 4.00604 | 0.139642 | 0.0698209 | − | 0.997560i | \(-0.477757\pi\) | ||||
0.0698209 | + | 0.997560i | \(0.477757\pi\) | |||||||
\(824\) | 19.3963 | 0.675702 | ||||||||
\(825\) | 31.2719 | 1.08875 | ||||||||
\(826\) | −16.7902 | −0.584206 | ||||||||
\(827\) | −26.0104 | −0.904469 | −0.452234 | − | 0.891899i | \(-0.649373\pi\) | ||||
−0.452234 | + | 0.891899i | \(0.649373\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39.4460 | 1.37002 | 0.685008 | − | 0.728535i | \(-0.259798\pi\) | ||||
0.685008 | + | 0.728535i | \(0.259798\pi\) | |||||||
\(830\) | −0.778434 | −0.0270199 | ||||||||
\(831\) | 13.0026 | 0.451055 | ||||||||
\(832\) | 4.81288 | 0.166857 | ||||||||
\(833\) | 10.2340 | 0.354587 | ||||||||
\(834\) | 7.36718 | 0.255104 | ||||||||
\(835\) | 0.379672 | 0.0131391 | ||||||||
\(836\) | 5.41620 | 0.187323 | ||||||||
\(837\) | 1.01371 | 0.0350388 | ||||||||
\(838\) | −26.4958 | −0.915283 | ||||||||
\(839\) | 3.26103 | 0.112583 | 0.0562916 | − | 0.998414i | \(-0.482072\pi\) | ||||
0.0562916 | + | 0.998414i | \(0.482072\pi\) | |||||||
\(840\) | 0.379170 | 0.0130826 | ||||||||
\(841\) | 0.348328 | 0.0120113 | ||||||||
\(842\) | 9.95095 | 0.342932 | ||||||||
\(843\) | −9.71850 | −0.334723 | ||||||||
\(844\) | 7.25827 | 0.249840 | ||||||||
\(845\) | −1.97444 | −0.0679228 | ||||||||
\(846\) | −7.41216 | −0.254835 | ||||||||
\(847\) | 56.0465 | 1.92578 | ||||||||
\(848\) | 2.00797 | 0.0689539 | ||||||||
\(849\) | −19.9847 | −0.685875 | ||||||||
\(850\) | 15.9182 | 0.545991 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −1.10938 | −0.0380066 | ||||||||
\(853\) | −7.71650 | −0.264208 | −0.132104 | − | 0.991236i | \(-0.542173\pi\) | ||||
−0.132104 | + | 0.991236i | \(0.542173\pi\) | |||||||
\(854\) | 23.6567 | 0.809515 | ||||||||
\(855\) | −0.166958 | −0.00570984 | ||||||||
\(856\) | 3.07594 | 0.105134 | ||||||||
\(857\) | 4.63538 | 0.158342 | 0.0791708 | − | 0.996861i | \(-0.474773\pi\) | ||||
0.0791708 | + | 0.996861i | \(0.474773\pi\) | |||||||
\(858\) | −30.3305 | −1.03547 | ||||||||
\(859\) | −49.1319 | −1.67636 | −0.838179 | − | 0.545396i | \(-0.816379\pi\) | ||||
−0.838179 | + | 0.545396i | \(0.816379\pi\) | |||||||
\(860\) | 0.999053 | 0.0340674 | ||||||||
\(861\) | 1.89722 | 0.0646571 | ||||||||
\(862\) | 8.77287 | 0.298805 | ||||||||
\(863\) | −40.8058 | −1.38905 | −0.694523 | − | 0.719470i | \(-0.744385\pi\) | ||||
−0.694523 | + | 0.719470i | \(0.744385\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −1.19309 | −0.0405662 | ||||||||
\(866\) | −7.99061 | −0.271532 | ||||||||
\(867\) | 6.70963 | 0.227871 | ||||||||
\(868\) | −1.97860 | −0.0671580 | ||||||||
\(869\) | 7.11991 | 0.241526 | ||||||||
\(870\) | 1.05240 | 0.0356796 | ||||||||
\(871\) | 34.1390 | 1.15676 | ||||||||
\(872\) | 1.94929 | 0.0660114 | ||||||||
\(873\) | −1.12094 | −0.0379382 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.77739 | 0.127699 | ||||||||
\(876\) | 13.1859 | 0.445511 | ||||||||
\(877\) | 25.6472 | 0.866043 | 0.433021 | − | 0.901384i | \(-0.357447\pi\) | ||||
0.433021 | + | 0.901384i | \(0.357447\pi\) | |||||||
\(878\) | −1.41063 | −0.0476064 | ||||||||
\(879\) | 17.8821 | 0.603147 | ||||||||
\(880\) | −1.22423 | −0.0412687 | ||||||||
\(881\) | 43.0288 | 1.44968 | 0.724838 | − | 0.688919i | \(-0.241915\pi\) | ||||
0.724838 | + | 0.688919i | \(0.241915\pi\) | |||||||
\(882\) | −3.19028 | −0.107422 | ||||||||
\(883\) | −10.0370 | −0.337771 | −0.168885 | − | 0.985636i | \(-0.554017\pi\) | ||||
−0.168885 | + | 0.985636i | \(0.554017\pi\) | |||||||
\(884\) | −15.4390 | −0.519271 | ||||||||
\(885\) | −1.67108 | −0.0561728 | ||||||||
\(886\) | 12.5935 | 0.423087 | ||||||||
\(887\) | −10.5222 | −0.353300 | −0.176650 | − | 0.984274i | \(-0.556526\pi\) | ||||
−0.176650 | + | 0.984274i | \(0.556526\pi\) | |||||||
\(888\) | −6.89037 | −0.231226 | ||||||||
\(889\) | −42.1830 | −1.41477 | ||||||||
\(890\) | 1.85551 | 0.0621967 | ||||||||
\(891\) | 6.30195 | 0.211123 | ||||||||
\(892\) | 20.7342 | 0.694231 | ||||||||
\(893\) | −6.37037 | −0.213176 | ||||||||
\(894\) | −15.6333 | −0.522856 | ||||||||
\(895\) | −1.25705 | −0.0420185 | ||||||||
\(896\) | 1.95185 | 0.0652067 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −38.3533 | −1.27987 | ||||||||
\(899\) | −5.49166 | −0.183157 | ||||||||
\(900\) | −4.96226 | −0.165409 | ||||||||
\(901\) | −6.44128 | −0.214590 | ||||||||
\(902\) | −6.12557 | −0.203959 | ||||||||
\(903\) | 10.0380 | 0.334044 | ||||||||
\(904\) | −17.1492 | −0.570375 | ||||||||
\(905\) | −0.633578 | −0.0210608 | ||||||||
\(906\) | −20.7042 | −0.687850 | ||||||||
\(907\) | 39.0117 | 1.29536 | 0.647680 | − | 0.761912i | \(-0.275739\pi\) | ||||
0.647680 | + | 0.761912i | \(0.275739\pi\) | |||||||
\(908\) | −21.0504 | −0.698581 | ||||||||
\(909\) | 12.5714 | 0.416967 | ||||||||
\(910\) | −1.82490 | −0.0604948 | ||||||||
\(911\) | −22.7667 | −0.754294 | −0.377147 | − | 0.926153i | \(-0.623095\pi\) | ||||
−0.377147 | + | 0.926153i | \(0.623095\pi\) | |||||||
\(912\) | −0.859449 | −0.0284592 | ||||||||
\(913\) | 25.2528 | 0.835746 | ||||||||
\(914\) | 26.6357 | 0.881031 | ||||||||
\(915\) | 2.35448 | 0.0778367 | ||||||||
\(916\) | −1.91595 | −0.0633047 | ||||||||
\(917\) | −29.1940 | −0.964071 | ||||||||
\(918\) | 3.20786 | 0.105875 | ||||||||
\(919\) | −21.7361 | −0.717007 | −0.358504 | − | 0.933528i | \(-0.616713\pi\) | ||||
−0.358504 | + | 0.933528i | \(0.616713\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.5139 | 0.412346 | ||||||||
\(922\) | 7.65301 | 0.252039 | ||||||||
\(923\) | 5.33930 | 0.175745 | ||||||||
\(924\) | −12.3005 | −0.404655 | ||||||||
\(925\) | −34.1918 | −1.12422 | ||||||||
\(926\) | −4.15149 | −0.136426 | ||||||||
\(927\) | 19.3963 | 0.637058 | ||||||||
\(928\) | 5.41741 | 0.177835 | ||||||||
\(929\) | −40.7826 | −1.33803 | −0.669016 | − | 0.743248i | \(-0.733284\pi\) | ||||
−0.669016 | + | 0.743248i | \(0.733284\pi\) | |||||||
\(930\) | −0.196924 | −0.00645740 | ||||||||
\(931\) | −2.74189 | −0.0898617 | ||||||||
\(932\) | −14.4306 | −0.472689 | ||||||||
\(933\) | −5.45773 | −0.178678 | ||||||||
\(934\) | −32.1155 | −1.05085 | ||||||||
\(935\) | 3.92715 | 0.128432 | ||||||||
\(936\) | 4.81288 | 0.157314 | ||||||||
\(937\) | −7.22235 | −0.235944 | −0.117972 | − | 0.993017i | \(-0.537639\pi\) | ||||
−0.117972 | + | 0.993017i | \(0.537639\pi\) | |||||||
\(938\) | 13.8450 | 0.452055 | ||||||||
\(939\) | 23.9234 | 0.780710 | ||||||||
\(940\) | 1.43990 | 0.0469643 | ||||||||
\(941\) | 13.2043 | 0.430449 | 0.215225 | − | 0.976565i | \(-0.430952\pi\) | ||||
0.215225 | + | 0.976565i | \(0.430952\pi\) | |||||||
\(942\) | 3.97631 | 0.129555 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −8.60221 | −0.279978 | ||||||||
\(945\) | 0.379170 | 0.0123344 | ||||||||
\(946\) | −32.4098 | −1.05373 | ||||||||
\(947\) | 33.7912 | 1.09807 | 0.549034 | − | 0.835800i | \(-0.314996\pi\) | ||||
0.549034 | + | 0.835800i | \(0.314996\pi\) | |||||||
\(948\) | −1.12979 | −0.0366940 | ||||||||
\(949\) | −63.4623 | −2.06007 | ||||||||
\(950\) | −4.26481 | −0.138369 | ||||||||
\(951\) | 16.1225 | 0.522809 | ||||||||
\(952\) | −6.26126 | −0.202929 | ||||||||
\(953\) | −22.5608 | −0.730815 | −0.365407 | − | 0.930848i | \(-0.619070\pi\) | ||||
−0.365407 | + | 0.930848i | \(0.619070\pi\) | |||||||
\(954\) | 2.00797 | 0.0650103 | ||||||||
\(955\) | 4.43958 | 0.143662 | ||||||||
\(956\) | −9.81701 | −0.317505 | ||||||||
\(957\) | −34.1402 | −1.10360 | ||||||||
\(958\) | 1.81509 | 0.0586430 | ||||||||
\(959\) | 35.4397 | 1.14441 | ||||||||
\(960\) | 0.194262 | 0.00626977 | ||||||||
\(961\) | −29.9724 | −0.966852 | ||||||||
\(962\) | 33.1625 | 1.06920 | ||||||||
\(963\) | 3.07594 | 0.0991209 | ||||||||
\(964\) | −14.9039 | −0.480022 | ||||||||
\(965\) | 3.29107 | 0.105943 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.9309 | −0.512303 | −0.256152 | − | 0.966637i | \(-0.582455\pi\) | ||||
−0.256152 | + | 0.966637i | \(0.582455\pi\) | |||||||
\(968\) | 28.7146 | 0.922921 | ||||||||
\(969\) | 2.75699 | 0.0885673 | ||||||||
\(970\) | 0.217756 | 0.00699174 | ||||||||
\(971\) | 42.1496 | 1.35264 | 0.676322 | − | 0.736606i | \(-0.263573\pi\) | ||||
0.676322 | + | 0.736606i | \(0.263573\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −14.3796 | −0.460989 | ||||||||
\(974\) | −16.1873 | −0.518674 | ||||||||
\(975\) | 23.8828 | 0.764861 | ||||||||
\(976\) | 12.1201 | 0.387956 | ||||||||
\(977\) | −31.8104 | −1.01770 | −0.508852 | − | 0.860854i | \(-0.669930\pi\) | ||||
−0.508852 | + | 0.860854i | \(0.669930\pi\) | |||||||
\(978\) | −24.5129 | −0.783835 | ||||||||
\(979\) | −60.1936 | −1.92379 | ||||||||
\(980\) | 0.619750 | 0.0197972 | ||||||||
\(981\) | 1.94929 | 0.0622361 | ||||||||
\(982\) | −1.42155 | −0.0453634 | ||||||||
\(983\) | 19.8293 | 0.632457 | 0.316229 | − | 0.948683i | \(-0.397583\pi\) | ||||
0.316229 | + | 0.948683i | \(0.397583\pi\) | |||||||
\(984\) | 0.972011 | 0.0309866 | ||||||||
\(985\) | −0.243760 | −0.00776685 | ||||||||
\(986\) | −17.3783 | −0.553438 | ||||||||
\(987\) | 14.4674 | 0.460503 | ||||||||
\(988\) | 4.13642 | 0.131597 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −1.22423 | −0.0389085 | ||||||||
\(991\) | 6.30934 | 0.200423 | 0.100211 | − | 0.994966i | \(-0.468048\pi\) | ||||
0.100211 | + | 0.994966i | \(0.468048\pi\) | |||||||
\(992\) | −1.01371 | −0.0321852 | ||||||||
\(993\) | 0.517893 | 0.0164348 | ||||||||
\(994\) | 2.16534 | 0.0686803 | ||||||||
\(995\) | −4.82041 | −0.152817 | ||||||||
\(996\) | −4.00714 | −0.126971 | ||||||||
\(997\) | −44.5390 | −1.41056 | −0.705282 | − | 0.708927i | \(-0.749180\pi\) | ||||
−0.705282 | + | 0.708927i | \(0.749180\pi\) | |||||||
\(998\) | 20.5750 | 0.651289 | ||||||||
\(999\) | −6.89037 | −0.218002 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3174.2.a.ba.1.3 | 5 | ||
3.2 | odd | 2 | 9522.2.a.bs.1.3 | 5 | |||
23.9 | even | 11 | 138.2.e.b.127.1 | yes | 10 | ||
23.18 | even | 11 | 138.2.e.b.25.1 | ✓ | 10 | ||
23.22 | odd | 2 | 3174.2.a.bb.1.3 | 5 | |||
69.32 | odd | 22 | 414.2.i.e.127.1 | 10 | |||
69.41 | odd | 22 | 414.2.i.e.163.1 | 10 | |||
69.68 | even | 2 | 9522.2.a.br.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
138.2.e.b.25.1 | ✓ | 10 | 23.18 | even | 11 | ||
138.2.e.b.127.1 | yes | 10 | 23.9 | even | 11 | ||
414.2.i.e.127.1 | 10 | 69.32 | odd | 22 | |||
414.2.i.e.163.1 | 10 | 69.41 | odd | 22 | |||
3174.2.a.ba.1.3 | 5 | 1.1 | even | 1 | trivial | ||
3174.2.a.bb.1.3 | 5 | 23.22 | odd | 2 | |||
9522.2.a.br.1.3 | 5 | 69.68 | even | 2 | |||
9522.2.a.bs.1.3 | 5 | 3.2 | odd | 2 |