Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [240,3,Mod(209,240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("240.209");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 240 = 2^{4} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 240.c (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(6.53952634465\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 34x^{10} + 305x^{8} + 616x^{6} + 305x^{4} + 34x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{15}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 209.7 | ||
Root | \(-1.38205i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 240.209 |
Dual form | 240.3.c.e.209.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(161\) | \(181\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.938195 | − | 2.84952i | 0.312732 | − | 0.949841i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.88807 | − | 1.05205i | 0.977613 | − | 0.210409i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 6.81219i | − | 0.973170i | −0.873633 | − | 0.486585i | \(-0.838242\pi\) | ||
0.873633 | − | 0.486585i | \(-0.161758\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −7.23958 | − | 5.34682i | −0.804398 | − | 0.594091i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 7.52980i | − | 0.684527i | −0.939604 | − | 0.342263i | \(-0.888806\pi\) | ||
0.939604 | − | 0.342263i | \(-0.111194\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 16.2362i | 1.24894i | 0.781048 | + | 0.624471i | \(0.214685\pi\) | ||||
−0.781048 | + | 0.624471i | \(0.785315\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.58813 | − | 14.9157i | 0.105875 | − | 0.994379i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.11928 | 0.242311 | 0.121155 | − | 0.992634i | \(-0.461340\pi\) | ||||
0.121155 | + | 0.992634i | \(0.461340\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.86469 | −0.413931 | −0.206965 | − | 0.978348i | \(-0.566359\pi\) | ||||
−0.206965 | + | 0.978348i | \(0.566359\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −19.4115 | − | 6.39117i | −0.924357 | − | 0.304341i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 19.5246 | 0.848895 | 0.424447 | − | 0.905453i | \(-0.360468\pi\) | ||||
0.424447 | + | 0.905453i | \(0.360468\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 22.7864 | − | 10.2850i | 0.911456 | − | 0.411398i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −22.0280 | + | 15.6130i | −0.815853 | + | 0.578259i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 55.8878i | − | 1.92717i | −0.267408 | − | 0.963583i | \(-0.586167\pi\) | ||
0.267408 | − | 0.963583i | \(-0.413833\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −43.4375 | −1.40121 | −0.700604 | − | 0.713550i | \(-0.747086\pi\) | ||||
−0.700604 | + | 0.713550i | \(0.747086\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −21.4563 | − | 7.06442i | −0.650192 | − | 0.214073i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.16675 | − | 33.2984i | −0.204764 | − | 0.951384i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 31.5824i | − | 0.853579i | −0.904351 | − | 0.426790i | \(-0.859644\pi\) | ||
0.904351 | − | 0.426790i | \(-0.140356\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 46.2655 | + | 15.2328i | 1.18630 | + | 0.390584i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 51.3487i | 1.25241i | 0.779659 | + | 0.626204i | \(0.215392\pi\) | ||||
−0.779659 | + | 0.626204i | \(0.784608\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 51.2914i | 1.19282i | 0.802678 | + | 0.596412i | \(0.203408\pi\) | ||||
−0.802678 | + | 0.596412i | \(0.796592\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −41.0127 | − | 18.5192i | −0.911392 | − | 0.411539i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 61.7596 | 1.31403 | 0.657017 | − | 0.753875i | \(-0.271818\pi\) | ||||
0.657017 | + | 0.753875i | \(0.271818\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.59407 | 0.0529401 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.86469 | − | 11.7380i | 0.0757782 | − | 0.230157i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 82.7111 | 1.56059 | 0.780293 | − | 0.625414i | \(-0.215070\pi\) | ||||
0.780293 | + | 0.625414i | \(0.215070\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.92170 | − | 36.8061i | −0.144031 | − | 0.669203i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.37861 | + | 22.4106i | −0.129449 | + | 0.393169i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 97.6026i | 1.65428i | 0.561994 | + | 0.827141i | \(0.310034\pi\) | ||||
−0.561994 | + | 0.827141i | \(0.689966\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.13531 | 0.0677920 | 0.0338960 | − | 0.999425i | \(-0.489209\pi\) | ||||
0.0338960 | + | 0.999425i | \(0.489209\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −36.4236 | + | 49.3174i | −0.578152 | + | 0.782816i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 17.0813 | + | 79.3638i | 0.262789 | + | 1.22098i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 63.1940i | − | 0.943194i | −0.881814 | − | 0.471597i | \(-0.843678\pi\) | ||
0.881814 | − | 0.471597i | \(-0.156322\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 18.3179 | − | 55.6358i | 0.265476 | − | 0.806316i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 40.3087i | 0.567729i | 0.958864 | + | 0.283864i | \(0.0916165\pi\) | ||||
−0.958864 | + | 0.283864i | \(0.908383\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 78.5111i | 1.07549i | 0.843106 | + | 0.537747i | \(0.180724\pi\) | ||||
−0.843106 | + | 0.537747i | \(0.819276\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.92915 | − | 74.5797i | −0.105722 | − | 0.994396i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −51.2944 | −0.666161 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 51.0103 | 0.645699 | 0.322850 | − | 0.946450i | \(-0.395359\pi\) | ||||
0.322850 | + | 0.946450i | \(0.395359\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 23.8230 | + | 77.4175i | 0.294111 | + | 0.955771i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.72011 | −0.0327725 | −0.0163862 | − | 0.999866i | \(-0.505216\pi\) | ||||
−0.0163862 | + | 0.999866i | \(0.505216\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 20.1353 | − | 4.33368i | 0.236886 | − | 0.0509844i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −159.254 | − | 52.4337i | −1.83050 | − | 0.602686i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 70.4279i | 0.791325i | 0.918396 | + | 0.395662i | \(0.129485\pi\) | ||||
−0.918396 | + | 0.395662i | \(0.870515\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 110.604 | 1.21543 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −40.7528 | + | 123.776i | −0.438203 | + | 1.33093i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −38.4431 | + | 8.27403i | −0.404664 | + | 0.0870950i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.44364i | 0.0355015i | 0.999842 | + | 0.0177507i | \(0.00565053\pi\) | ||||
−0.999842 | + | 0.0177507i | \(0.994349\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −40.2605 | + | 54.5126i | −0.406671 | + | 0.550632i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 49.2446i | − | 0.487570i | −0.969829 | − | 0.243785i | \(-0.921611\pi\) | ||
0.969829 | − | 0.243785i | \(-0.0783892\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 90.5470i | 0.879097i | 0.898219 | + | 0.439548i | \(0.144862\pi\) | ||||
−0.898219 | + | 0.439548i | \(0.855138\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −101.609 | − | 10.8186i | −0.967700 | − | 0.103034i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 65.3836 | 0.611062 | 0.305531 | − | 0.952182i | \(-0.401166\pi\) | ||||
0.305531 | + | 0.952182i | \(0.401166\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −170.469 | −1.56394 | −0.781968 | − | 0.623319i | \(-0.785784\pi\) | ||||
−0.781968 | + | 0.623319i | \(0.785784\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −89.9949 | − | 29.6305i | −0.810765 | − | 0.266941i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 55.4137 | 0.490387 | 0.245193 | − | 0.969474i | \(-0.421149\pi\) | ||||
0.245193 | + | 0.969474i | \(0.421149\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 95.4375 | − | 20.5408i | 0.829891 | − | 0.178616i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 86.8123 | − | 117.544i | 0.741985 | − | 1.00465i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 28.0613i | − | 0.235809i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 64.3022 | 0.531423 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 146.319 | + | 48.1751i | 1.18959 | + | 0.391668i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 100.561 | − | 74.2459i | 0.804489 | − | 0.593967i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 74.9923i | 0.590491i | 0.955421 | + | 0.295245i | \(0.0954014\pi\) | ||||
−0.955421 | + | 0.295245i | \(0.904599\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 146.156 | + | 48.1214i | 1.13299 | + | 0.373034i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 101.149i | − | 0.772130i | −0.922472 | − | 0.386065i | \(-0.873834\pi\) | ||
0.922472 | − | 0.386065i | \(-0.126166\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 53.5758i | 0.402825i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −91.2489 | + | 99.4919i | −0.675918 | + | 0.736977i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −114.292 | −0.834248 | −0.417124 | − | 0.908850i | \(-0.636962\pi\) | ||||
−0.417124 | + | 0.908850i | \(0.636962\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −230.156 | −1.65580 | −0.827899 | − | 0.560878i | \(-0.810464\pi\) | ||||
−0.827899 | + | 0.560878i | \(0.810464\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 57.9426 | − | 175.986i | 0.410940 | − | 1.24812i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 122.256 | 0.854934 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −58.7966 | − | 273.183i | −0.405494 | − | 1.88402i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.43374 | − | 7.39185i | 0.0165561 | − | 0.0502847i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.12446i | 0.0612380i | 0.999531 | + | 0.0306190i | \(0.00974785\pi\) | ||||
−0.999531 | + | 0.0306190i | \(0.990252\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 163.010 | 1.07954 | 0.539769 | − | 0.841813i | \(-0.318512\pi\) | ||||
0.539769 | + | 0.841813i | \(0.318512\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −29.8218 | − | 22.0250i | −0.194914 | − | 0.143955i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −212.325 | + | 45.6983i | −1.36984 | + | 0.294828i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 122.529i | − | 0.780442i | −0.920721 | − | 0.390221i | \(-0.872399\pi\) | ||
0.920721 | − | 0.390221i | \(-0.127601\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 77.5991 | − | 235.687i | 0.488045 | − | 1.48231i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 133.005i | − | 0.826119i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 66.6959i | 0.409177i | 0.978848 | + | 0.204589i | \(0.0655857\pi\) | ||||
−0.978848 | + | 0.204589i | \(0.934414\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −112.312 | − | 11.9583i | −0.680680 | − | 0.0724744i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 163.583 | 0.979539 | 0.489769 | − | 0.871852i | \(-0.337081\pi\) | ||||
0.489769 | + | 0.871852i | \(0.337081\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −94.6153 | −0.559854 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 56.9370 | + | 42.0511i | 0.332965 | + | 0.245913i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −34.7133 | −0.200655 | −0.100327 | − | 0.994954i | \(-0.531989\pi\) | ||||
−0.100327 | + | 0.994954i | \(0.531989\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −70.0631 | − | 155.225i | −0.400360 | − | 0.887001i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 278.121 | + | 91.5704i | 1.57131 | + | 0.517347i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 273.448i | − | 1.52764i | −0.645429 | − | 0.763820i | \(-0.723321\pi\) | ||
0.645429 | − | 0.763820i | \(-0.276679\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −40.8749 | −0.225828 | −0.112914 | − | 0.993605i | \(-0.536019\pi\) | ||||
−0.112914 | + | 0.993605i | \(0.536019\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.87973 | − | 11.7837i | 0.0212007 | − | 0.0643916i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −33.2262 | − | 154.377i | −0.179601 | − | 0.834471i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 31.0173i | − | 0.165868i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 106.359 | + | 150.059i | 0.562744 | + | 0.793964i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 40.5934i | − | 0.212531i | −0.994338 | − | 0.106266i | \(-0.966111\pi\) | ||
0.994338 | − | 0.106266i | \(-0.0338894\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 141.259i | 0.731912i | 0.930632 | + | 0.365956i | \(0.119258\pi\) | ||||
−0.930632 | + | 0.365956i | \(0.880742\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 242.175 | + | 25.7852i | 1.24192 | + | 0.132232i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −232.643 | −1.18093 | −0.590464 | − | 0.807064i | \(-0.701055\pi\) | ||||
−0.590464 | + | 0.807064i | \(0.701055\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −85.3744 | −0.429017 | −0.214509 | − | 0.976722i | \(-0.568815\pi\) | ||||
−0.214509 | + | 0.976722i | \(0.568815\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −180.073 | − | 59.2883i | −0.895885 | − | 0.294967i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −380.719 | −1.87546 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 54.0213 | + | 250.996i | 0.263518 | + | 1.22437i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −141.350 | − | 104.394i | −0.682849 | − | 0.504321i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 59.2195i | 0.283347i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −284.532 | −1.34849 | −0.674247 | − | 0.738506i | \(-0.735532\pi\) | ||||
−0.674247 | + | 0.738506i | \(0.735532\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 114.861 | + | 37.8175i | 0.539252 | + | 0.177547i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 53.9610 | + | 250.716i | 0.250982 | + | 1.16612i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 295.904i | 1.36361i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 223.719 | + | 73.6587i | 1.02155 | + | 0.336341i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 66.8816i | 0.302632i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 30.2924i | − | 0.135840i | −0.997691 | − | 0.0679201i | \(-0.978364\pi\) | ||
0.997691 | − | 0.0679201i | \(-0.0216363\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −219.956 | − | 47.3760i | −0.977581 | − | 0.210560i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −239.380 | −1.05454 | −0.527269 | − | 0.849698i | \(-0.676784\pi\) | ||||
−0.527269 | + | 0.849698i | \(0.676784\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 284.959 | 1.24436 | 0.622180 | − | 0.782874i | \(-0.286247\pi\) | ||||
0.622180 | + | 0.782874i | \(0.286247\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −48.1242 | + | 146.165i | −0.208330 | + | 0.632747i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 93.8635 | 0.402848 | 0.201424 | − | 0.979504i | \(-0.435443\pi\) | ||||
0.201424 | + | 0.979504i | \(0.435443\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 301.885 | − | 64.9741i | 1.28462 | − | 0.276485i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 47.8576 | − | 145.355i | 0.201931 | − | 0.613312i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 238.326i | − | 0.997181i | −0.866838 | − | 0.498590i | \(-0.833851\pi\) | ||
0.866838 | − | 0.498590i | \(-0.166149\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 44.2919 | 0.183784 | 0.0918919 | − | 0.995769i | \(-0.470709\pi\) | ||||
0.0918919 | + | 0.995769i | \(0.470709\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 242.954 | + | 4.74848i | 0.999809 | + | 0.0195411i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.6800 | − | 2.72908i | 0.0517550 | − | 0.0111391i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 127.693i | − | 0.516975i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.55200 | + | 7.75103i | −0.0102490 | + | 0.0311286i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 293.093i | 1.16770i | 0.811862 | + | 0.583850i | \(0.198454\pi\) | ||||
−0.811862 | + | 0.583850i | \(0.801546\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 147.016i | − | 0.581092i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.54194 | − | 61.4419i | 0.0256547 | − | 0.240949i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −169.330 | −0.658870 | −0.329435 | − | 0.944178i | \(-0.606858\pi\) | ||||
−0.329435 | + | 0.944178i | \(0.606858\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −215.146 | −0.830678 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −298.822 | + | 404.604i | −1.14491 | + | 1.55021i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −91.1958 | −0.346752 | −0.173376 | − | 0.984856i | \(-0.555468\pi\) | ||||
−0.173376 | + | 0.984856i | \(0.555468\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 404.297 | − | 87.0160i | 1.52565 | − | 0.328362i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 200.686 | + | 66.0751i | 0.751633 | + | 0.247472i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 325.164i | 1.20879i | 0.796686 | + | 0.604393i | \(0.206584\pi\) | ||||
−0.796686 | + | 0.604393i | \(0.793416\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 132.719 | 0.489738 | 0.244869 | − | 0.969556i | \(-0.421255\pi\) | ||||
0.244869 | + | 0.969556i | \(0.421255\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 103.768 | − | 315.170i | 0.380104 | − | 1.15447i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −77.4436 | − | 171.577i | −0.281613 | − | 0.623916i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 254.199i | − | 0.917687i | −0.888517 | − | 0.458844i | \(-0.848264\pi\) | ||
0.888517 | − | 0.458844i | \(-0.151736\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 314.469 | + | 232.252i | 1.12713 | + | 0.832446i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.5488i | 0.0695687i | 0.999395 | + | 0.0347843i | \(0.0110744\pi\) | ||||
−0.999395 | + | 0.0347843i | \(0.988926\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 109.674i | − | 0.387541i | −0.981047 | − | 0.193770i | \(-0.937928\pi\) | ||
0.981047 | − | 0.193770i | \(-0.0620717\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −12.4901 | + | 117.307i | −0.0438250 | + | 0.411604i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 349.797 | 1.21881 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −272.032 | −0.941286 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.81275 | + | 3.23081i | 0.0337208 | + | 0.0111024i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −178.388 | −0.608832 | −0.304416 | − | 0.952539i | \(-0.598461\pi\) | ||||
−0.304416 | + | 0.952539i | \(0.598461\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 102.683 | + | 477.088i | 0.348077 | + | 1.61725i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 117.563 | + | 165.867i | 0.395834 | + | 0.558474i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 317.006i | 1.06022i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 349.407 | 1.16082 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −140.324 | − | 46.2011i | −0.463115 | − | 0.152479i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 20.2137 | − | 4.35054i | 0.0662744 | − | 0.0142641i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 289.046i | 0.941518i | 0.882262 | + | 0.470759i | \(0.156020\pi\) | ||||
−0.882262 | + | 0.470759i | \(0.843980\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 258.016 | + | 84.9508i | 0.835003 | + | 0.274922i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 336.061i | 1.08058i | 0.841478 | + | 0.540291i | \(0.181686\pi\) | ||||
−0.841478 | + | 0.540291i | \(0.818314\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 563.702i | − | 1.80096i | −0.434894 | − | 0.900482i | \(-0.643214\pi\) | ||
0.434894 | − | 0.900482i | \(-0.356786\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −126.157 | + | 279.386i | −0.400497 | + | 0.886940i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −139.938 | −0.441445 | −0.220722 | − | 0.975337i | \(-0.570842\pi\) | ||||
−0.220722 | + | 0.975337i | \(0.570842\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −420.824 | −1.31920 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 61.3426 | − | 186.312i | 0.191098 | − | 0.580412i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −32.3968 | −0.100300 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 166.989 | + | 369.965i | 0.513812 | + | 1.13835i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −159.933 | + | 485.756i | −0.489092 | + | 1.48549i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 420.718i | − | 1.27878i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.5116 | 0.0438416 | 0.0219208 | − | 0.999760i | \(-0.493022\pi\) | ||||
0.0219208 | + | 0.999760i | \(0.493022\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −168.866 | + | 228.644i | −0.507104 | + | 0.686617i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −66.4831 | − | 308.896i | −0.198457 | − | 0.922079i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 347.492i | 1.03113i | 0.856850 | + | 0.515566i | \(0.172418\pi\) | ||||
−0.856850 | + | 0.515566i | \(0.827582\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 51.9889 | − | 157.903i | 0.153359 | − | 0.465790i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 327.075i | 0.959165i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 351.469i | − | 1.02469i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 31.0075 | − | 291.223i | 0.0898769 | − | 0.844124i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −273.321 | −0.787670 | −0.393835 | − | 0.919181i | \(-0.628852\pi\) | ||||
−0.393835 | + | 0.919181i | \(0.628852\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −550.853 | −1.57838 | −0.789188 | − | 0.614152i | \(-0.789498\pi\) | ||||
−0.789188 | + | 0.614152i | \(0.789498\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −253.496 | − | 357.652i | −0.722212 | − | 1.01895i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −643.177 | −1.82203 | −0.911015 | − | 0.412373i | \(-0.864700\pi\) | ||||
−0.911015 | + | 0.412373i | \(0.864700\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 42.4067 | + | 197.032i | 0.119455 | + | 0.555019i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −79.9614 | − | 26.3270i | −0.223982 | − | 0.0737451i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 465.873i | 1.29770i | 0.760918 | + | 0.648849i | \(0.224749\pi\) | ||||
−0.760918 | + | 0.648849i | \(0.775251\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −299.147 | −0.828661 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 60.3280 | − | 183.231i | 0.166193 | − | 0.504767i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 82.5974 | + | 383.767i | 0.226294 | + | 1.05142i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 44.7168i | − | 0.121844i | −0.998143 | − | 0.0609221i | \(-0.980596\pi\) | ||
0.998143 | − | 0.0609221i | \(-0.0194041\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 274.552 | − | 371.743i | 0.744044 | − | 1.00743i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 563.443i | − | 1.51872i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 275.158i | 0.737688i | 0.929491 | + | 0.368844i | \(0.120246\pi\) | ||||
−0.929491 | + | 0.368844i | \(0.879754\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −117.220 | − | 356.209i | −0.312585 | − | 0.949890i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 907.408 | 2.40692 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 505.072 | 1.33264 | 0.666322 | − | 0.745664i | \(-0.267868\pi\) | ||||
0.666322 | + | 0.745664i | \(0.267868\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 213.692 | + | 70.3575i | 0.560873 | + | 0.184665i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 193.577 | 0.505422 | 0.252711 | − | 0.967542i | \(-0.418678\pi\) | ||||
0.252711 | + | 0.967542i | \(0.418678\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −250.730 | + | 53.9642i | −0.651248 | + | 0.140167i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 274.246 | − | 371.328i | 0.708646 | − | 0.959505i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 280.077i | − | 0.719993i | −0.932954 | − | 0.359996i | \(-0.882778\pi\) | ||
0.932954 | − | 0.359996i | \(-0.117222\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 80.4272 | 0.205696 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −288.226 | − | 94.8975i | −0.733401 | − | 0.241469i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 249.342 | − | 53.6652i | 0.631244 | − | 0.135861i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 468.421i | − | 1.17990i | −0.807439 | − | 0.589951i | \(-0.799147\pi\) | ||
0.807439 | − | 0.589951i | \(-0.200853\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 152.665 | + | 50.2645i | 0.382620 | + | 0.125976i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 274.969i | − | 0.685707i | −0.939389 | − | 0.342854i | \(-0.888606\pi\) | ||
0.939389 | − | 0.342854i | \(-0.111394\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 705.261i | − | 1.75003i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 197.895 | + | 353.359i | 0.488630 | + | 0.872491i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −237.809 | −0.584298 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −202.697 | −0.495592 | −0.247796 | − | 0.968812i | \(-0.579706\pi\) | ||||
−0.247796 | + | 0.968812i | \(0.579706\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −107.228 | + | 325.678i | −0.260896 | + | 0.792403i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 664.888 | 1.60990 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.2961 | + | 2.86169i | −0.0320388 | + | 0.00689564i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −215.931 | + | 655.835i | −0.517820 | + | 1.57274i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 76.6340i | − | 0.182897i | −0.995810 | − | 0.0914487i | \(-0.970850\pi\) | ||
0.995810 | − | 0.0914487i | \(-0.0291497\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −183.991 | −0.437033 | −0.218516 | − | 0.975833i | \(-0.570122\pi\) | ||||
−0.218516 | + | 0.975833i | \(0.570122\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −447.114 | − | 330.218i | −1.05701 | − | 0.780657i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 93.8635 | − | 42.3666i | 0.220855 | − | 0.0996861i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 28.1705i | − | 0.0659731i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 114.700 | − | 348.370i | 0.267365 | − | 0.812052i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 671.408i | − | 1.55779i | −0.627153 | − | 0.778896i | \(-0.715780\pi\) | ||
0.627153 | − | 0.778896i | \(-0.284220\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 399.351i | − | 0.922288i | −0.887325 | − | 0.461144i | \(-0.847439\pi\) | ||
0.887325 | − | 0.461144i | \(-0.152561\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −833.606 | − | 88.7570i | −1.91633 | − | 0.204039i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −153.555 | −0.351384 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −140.833 | −0.320804 | −0.160402 | − | 0.987052i | \(-0.551279\pi\) | ||||
−0.160402 | + | 0.987052i | \(0.551279\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.7799 | − | 13.8700i | −0.0425849 | − | 0.0314513i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 211.416 | 0.477237 | 0.238618 | − | 0.971113i | \(-0.423306\pi\) | ||||
0.238618 | + | 0.971113i | \(0.423306\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 74.0935 | + | 344.256i | 0.166502 | + | 0.773610i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 26.0004 | + | 8.56052i | 0.0581664 | + | 0.0191511i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 455.166i | − | 1.01373i | −0.862025 | − | 0.506866i | \(-0.830804\pi\) | ||
0.862025 | − | 0.506866i | \(-0.169196\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 386.645 | 0.857307 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 152.935 | − | 464.502i | 0.337606 | − | 1.02539i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 540.641 | − | 116.361i | 1.18822 | − | 0.255738i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 555.776i | 1.21614i | 0.793883 | + | 0.608070i | \(0.208056\pi\) | ||||
−0.793883 | + | 0.608070i | \(0.791944\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −90.7396 | + | 64.3143i | −0.197690 | + | 0.140118i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 369.227i | − | 0.800927i | −0.916313 | − | 0.400463i | \(-0.868849\pi\) | ||
0.916313 | − | 0.400463i | \(-0.131151\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 360.832i | 0.779336i | 0.920955 | + | 0.389668i | \(0.127410\pi\) | ||||
−0.920955 | + | 0.389668i | \(0.872590\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −68.9842 | + | 647.900i | −0.148353 | + | 1.39333i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 496.306 | 1.06275 | 0.531377 | − | 0.847135i | \(-0.321675\pi\) | ||||
0.531377 | + | 0.847135i | \(0.321675\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −430.490 | −0.917888 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −349.151 | − | 114.957i | −0.741296 | − | 0.244069i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 386.214 | 0.816520 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −179.208 | + | 80.8880i | −0.377280 | + | 0.170290i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −598.793 | − | 442.241i | −1.25533 | − | 0.927131i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 286.032i | 0.597145i | 0.954387 | + | 0.298572i | \(0.0965105\pi\) | ||||
−0.954387 | + | 0.298572i | \(0.903490\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 512.780 | 1.06607 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −379.002 | − | 124.785i | −0.784682 | − | 0.258354i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.62288 | + | 16.8328i | 0.00746985 | + | 0.0347067i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 34.3276i | − | 0.0704880i | −0.999379 | − | 0.0352440i | \(-0.988779\pi\) | ||
0.999379 | − | 0.0352440i | \(-0.0112208\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 190.052 | + | 62.5738i | 0.388653 | + | 0.127963i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 26.4204i | − | 0.0538094i | −0.999638 | − | 0.0269047i | \(-0.991435\pi\) | ||
0.999638 | − | 0.0269047i | \(-0.00856507\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 230.218i | − | 0.466973i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −139.446 | + | 308.817i | −0.281709 | + | 0.623873i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 274.591 | 0.552496 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 72.9046 | 0.146101 | 0.0730507 | − | 0.997328i | \(-0.476727\pi\) | ||||
0.0730507 | + | 0.997328i | \(0.476727\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 153.473 | − | 466.134i | 0.306333 | − | 0.930407i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 228.404 | 0.454083 | 0.227041 | − | 0.973885i | \(-0.427095\pi\) | ||||
0.227041 | + | 0.973885i | \(0.427095\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −51.8077 | − | 240.711i | −0.102589 | − | 0.476655i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −88.7677 | + | 269.609i | −0.175084 | + | 0.531773i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 99.1735i | 0.194840i | 0.995243 | + | 0.0974199i | \(0.0310590\pi\) | ||||
−0.995243 | + | 0.0974199i | \(0.968941\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 534.832 | 1.04664 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 173.244 | − | 122.791i | 0.337707 | − | 0.239359i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 95.2597 | + | 442.600i | 0.184970 | + | 0.859417i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 465.037i | − | 0.899492i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −32.5678 | + | 98.9163i | −0.0627511 | + | 0.190590i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 691.462i | 1.32718i | 0.748095 | + | 0.663592i | \(0.230969\pi\) | ||||
−0.748095 | + | 0.663592i | \(0.769031\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 821.405i | 1.57056i | 0.619138 | + | 0.785282i | \(0.287482\pi\) | ||||
−0.619138 | + | 0.785282i | \(0.712518\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −508.051 | + | 54.0149i | −0.967716 | + | 0.102885i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −178.931 | −0.339528 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −147.791 | −0.279377 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 521.864 | − | 706.602i | 0.982795 | − | 1.33070i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −833.710 | −1.56418 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 319.599 | − | 68.7866i | 0.597382 | − | 0.128573i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −779.196 | − | 256.547i | −1.45102 | − | 0.477742i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 19.5328i | − | 0.0362389i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 446.354 | 0.825054 | 0.412527 | − | 0.910945i | \(-0.364646\pi\) | ||||
0.412527 | + | 0.910945i | \(0.364646\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −38.3487 | + | 116.474i | −0.0706237 | + | 0.214501i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −833.264 | + | 179.341i | −1.52892 | + | 0.329067i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 485.492i | 0.887553i | 0.896137 | + | 0.443777i | \(0.146362\pi\) | ||||
−0.896137 | + | 0.443777i | \(0.853638\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −29.9379 | − | 22.1108i | −0.0545317 | − | 0.0402746i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 439.540i | 0.797714i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 347.492i | − | 0.628375i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −471.074 | − | 50.1569i | −0.848782 | − | 0.0903728i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 995.191 | 1.78670 | 0.893349 | − | 0.449363i | \(-0.148349\pi\) | ||||
0.893349 | + | 0.449363i | \(0.148349\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −832.780 | −1.48977 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −88.3847 | − | 29.1003i | −0.157548 | − | 0.0518722i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −486.571 | −0.864248 | −0.432124 | − | 0.901814i | \(-0.642236\pi\) | ||||
−0.432124 | + | 0.901814i | \(0.642236\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 270.866 | − | 58.2978i | 0.479408 | − | 0.103182i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 527.383 | − | 162.287i | 0.930128 | − | 0.286220i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 737.704i | 1.29649i | 0.761431 | + | 0.648246i | \(0.224497\pi\) | ||||
−0.761431 | + | 0.648246i | \(0.775503\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −805.843 | −1.41128 | −0.705642 | − | 0.708569i | \(-0.749341\pi\) | ||||
−0.705642 | + | 0.708569i | \(0.749341\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −115.672 | − | 38.0846i | −0.201871 | − | 0.0664652i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 444.895 | − | 200.810i | 0.773730 | − | 0.349234i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 690.512i | 1.19673i | 0.801225 | + | 0.598364i | \(0.204182\pi\) | ||||
−0.801225 | + | 0.598364i | \(0.795818\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 402.521 | + | 132.529i | 0.695201 | + | 0.228892i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.5299i | 0.0318932i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 622.798i | − | 1.06826i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 300.683 | − | 665.891i | 0.513988 | − | 1.13828i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −670.611 | −1.14244 | −0.571219 | − | 0.820798i | \(-0.693529\pi\) | ||||
−0.571219 | + | 0.820798i | \(0.693529\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 341.622 | 0.580004 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −218.265 | + | 662.922i | −0.369314 | + | 1.12170i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 214.249 | 0.361296 | 0.180648 | − | 0.983548i | \(-0.442181\pi\) | ||||
0.180648 | + | 0.983548i | \(0.442181\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −29.5218 | − | 137.166i | −0.0496165 | − | 0.230530i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −80.0979 | + | 243.276i | −0.134167 | + | 0.407498i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 303.315i | 0.506368i | 0.967418 | + | 0.253184i | \(0.0814779\pi\) | ||||
−0.967418 | + | 0.253184i | \(0.918522\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 66.0555 | 0.109909 | 0.0549546 | − | 0.998489i | \(-0.482499\pi\) | ||||
0.0549546 | + | 0.998489i | \(0.482499\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −337.887 | + | 457.498i | −0.560343 | + | 0.758703i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 314.313 | − | 67.6489i | 0.519526 | − | 0.111816i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 178.972i | 0.294847i | 0.989073 | + | 0.147423i | \(0.0470980\pi\) | ||||
−0.989073 | + | 0.147423i | \(0.952902\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −357.188 | + | 1084.87i | −0.586516 | + | 1.78139i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1002.74i | 1.64115i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 728.201i | 1.18793i | 0.804491 | + | 0.593965i | \(0.202438\pi\) | ||||
−0.804491 | + | 0.593965i | \(0.797562\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 765.902 | + | 81.5483i | 1.24537 | + | 0.132599i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 198.426 | 0.321598 | 0.160799 | − | 0.986987i | \(-0.448593\pi\) | ||||
0.160799 | + | 0.986987i | \(0.448593\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.1752 | −0.0277468 | −0.0138734 | − | 0.999904i | \(-0.504416\pi\) | ||||
−0.0138734 | + | 0.999904i | \(0.504416\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −430.088 | + | 304.837i | −0.692574 | + | 0.490881i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 479.768 | 0.770094 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 413.439 | − | 468.714i | 0.661503 | − | 0.749943i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 168.747 | + | 55.5595i | 0.269135 | + | 0.0886116i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 130.097i | − | 0.206831i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 388.876 | 0.616285 | 0.308142 | − | 0.951340i | \(-0.400293\pi\) | ||||
0.308142 | + | 0.951340i | \(0.400293\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −266.947 | + | 810.781i | −0.421717 | + | 1.28085i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 78.8955 | + | 366.568i | 0.124245 | + | 0.577272i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 42.1179i | 0.0661191i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 215.524 | − | 291.818i | 0.337283 | − | 0.456680i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 180.547i | 0.281664i | 0.990034 | + | 0.140832i | \(0.0449778\pi\) | ||||
−0.990034 | + | 0.140832i | \(0.955022\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 701.008i | − | 1.09021i | −0.838367 | − | 0.545107i | \(-0.816489\pi\) | ||
0.838367 | − | 0.545107i | \(-0.183511\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 765.047 | + | 81.4573i | 1.18612 | + | 0.126290i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −114.266 | −0.176609 | −0.0883046 | − | 0.996094i | \(-0.528145\pi\) | ||||
−0.0883046 | + | 0.996094i | \(0.528145\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 734.928 | 1.13240 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 843.187 | + | 277.616i | 1.29522 | + | 0.426446i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 240.882 | 0.368884 | 0.184442 | − | 0.982843i | \(-0.440952\pi\) | ||||
0.184442 | + | 0.982843i | \(0.440952\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −106.414 | − | 494.423i | −0.162463 | − | 0.754844i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 419.785 | − | 568.387i | 0.638942 | − | 0.865125i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1218.15i | − | 1.84848i | −0.381807 | − | 0.924242i | \(-0.624698\pi\) | ||
0.381807 | − | 0.924242i | \(-0.375302\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1075.32 | −1.62681 | −0.813404 | − | 0.581699i | \(-0.802388\pi\) | ||||
−0.813404 | + | 0.581699i | \(0.802388\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 190.581 | + | 62.7480i | 0.287452 | + | 0.0946425i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 56.3642 | + | 261.882i | 0.0847583 | + | 0.393807i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1091.19i | − | 1.63596i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −86.3189 | − | 28.4202i | −0.129027 | − | 0.0424816i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 31.1381i | − | 0.0464054i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 356.367i | 0.529521i | 0.964314 | + | 0.264760i | \(0.0852928\pi\) | ||||
−0.964314 | + | 0.264760i | \(0.914707\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −341.361 | + | 582.321i | −0.505719 | + | 0.862698i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −79.8649 | −0.117969 | −0.0589844 | − | 0.998259i | \(-0.518786\pi\) | ||||
−0.0589844 | + | 0.998259i | \(0.518786\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 23.4588 | 0.0345490 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −224.585 | + | 682.120i | −0.329788 | + | 1.00164i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1270.41 | 1.86004 | 0.930021 | − | 0.367507i | \(-0.119789\pi\) | ||||
0.930021 | + | 0.367507i | \(0.119789\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −558.667 | + | 120.241i | −0.815572 | + | 0.175534i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 267.347 | − | 811.996i | 0.389151 | − | 1.18195i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1342.92i | 1.94908i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1244.39 | −1.80085 | −0.900424 | − | 0.435013i | \(-0.856744\pi\) | ||||
−0.900424 | + | 0.435013i | \(0.856744\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 371.350 | + | 274.262i | 0.535858 | + | 0.395760i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1125.02 | + | 242.135i | −1.61873 | + | 0.348395i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 211.520i | 0.303472i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 88.0623 | − | 267.466i | 0.125983 | − | 0.382641i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1034.47i | − | 1.47570i | −0.674965 | − | 0.737850i | \(-0.735841\pi\) | ||
0.674965 | − | 0.737850i | \(-0.264159\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 248.386i | 0.353323i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 98.0821 | − | 921.188i | 0.139124 | − | 1.30665i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −335.464 | −0.474489 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 659.081 | 0.929592 | 0.464796 | − | 0.885418i | \(-0.346128\pi\) | ||||
0.464796 | + | 0.885418i | \(0.346128\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −369.293 | − | 272.743i | −0.519399 | − | 0.383604i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −848.099 | −1.18948 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 597.593 | − | 128.619i | 0.835795 | − | 0.179886i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −679.116 | − | 223.597i | −0.947164 | − | 0.311850i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 471.213i | − | 0.655373i | −0.944787 | − | 0.327686i | \(-0.893731\pi\) | ||
0.944787 | − | 0.327686i | \(-0.106269\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 616.823 | 0.855511 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 41.5545 | − | 126.211i | 0.0574750 | − | 0.174566i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −574.804 | − | 1273.48i | −0.792833 | − | 1.75653i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 640.411i | 0.880895i | 0.897778 | + | 0.440447i | \(0.145180\pi\) | ||||
−0.897778 | + | 0.440447i | \(0.854820\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 241.469 | − | 687.847i | 0.331233 | − | 0.943549i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 211.284i | 0.289034i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 619.831i | 0.845608i | 0.906221 | + | 0.422804i | \(0.138954\pi\) | ||||
−0.906221 | + | 0.422804i | \(0.861046\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.11971 | − | 38.6923i | 0.00560504 | − | 0.0526426i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −475.838 | −0.645642 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 135.992 | 0.184022 | 0.0920111 | − | 0.995758i | \(-0.470670\pi\) | ||||
0.0920111 | + | 0.995758i | \(0.470670\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −363.864 | − | 119.801i | −0.491045 | − | 0.161675i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −986.468 | −1.32768 | −0.663841 | − | 0.747874i | \(-0.731075\pi\) | ||||
−0.663841 | + | 0.747874i | \(0.731075\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.59936 | + | 44.6010i | 0.0128851 | + | 0.0598671i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19.6925 | + | 14.5440i | 0.0263621 | + | 0.0194698i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 445.405i | − | 0.594667i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 551.977 | 0.734990 | 0.367495 | − | 0.930026i | \(-0.380216\pi\) | ||||
0.367495 | + | 0.930026i | \(0.380216\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 835.175 | + | 274.978i | 1.10913 | + | 0.365177i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 796.805 | − | 171.495i | 1.05537 | − | 0.227145i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1143.91i | − | 1.51111i | −0.655084 | − | 0.755556i | \(-0.727367\pi\) | ||
0.655084 | − | 0.755556i | \(-0.272633\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −418.926 | − | 137.930i | −0.551945 | − | 0.181726i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 29.3201i | − | 0.0385284i | −0.999814 | − | 0.0192642i | \(-0.993868\pi\) | ||
0.999814 | − | 0.0192642i | \(-0.00613236\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1161.27i | 1.52198i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −168.943 | − | 76.2859i | −0.220840 | − | 0.0997201i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1584.70 | −2.06610 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −61.7841 | −0.0803434 | −0.0401717 | − | 0.999193i | \(-0.512790\pi\) | ||||
−0.0401717 | + | 0.999193i | \(0.512790\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −158.864 | + | 482.509i | −0.206050 | + | 0.625822i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 444.408 | 0.574913 | 0.287457 | − | 0.957794i | \(-0.407190\pi\) | ||||
0.287457 | + | 0.957794i | \(0.407190\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −989.783 | + | 446.753i | −1.27714 | + | 0.576455i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −201.849 | + | 613.063i | −0.259779 | + | 0.789012i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 403.842i | − | 0.518410i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 303.517 | 0.388626 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 872.576 | + | 1231.10i | 1.11440 | + | 1.57229i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −128.907 | − | 598.932i | −0.164212 | − | 0.762971i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 206.738i | 0.262691i | 0.991337 | + | 0.131346i | \(0.0419298\pi\) | ||||
−0.991337 | + | 0.131346i | \(0.958070\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −85.5595 | + | 259.865i | −0.108440 | + | 0.329360i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 377.489i | − | 0.477230i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 67.1419i | 0.0846682i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 131.356 | − | 1233.69i | 0.165227 | − | 1.55181i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −235.281 | −0.295208 | −0.147604 | − | 0.989047i | \(-0.547156\pi\) | ||||
−0.147604 | + | 0.989047i | \(0.547156\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 254.405 | 0.318404 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 376.565 | − | 509.868i | 0.470119 | − | 0.636540i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 591.172 | 0.736205 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −139.928 | − | 650.138i | −0.173823 | − | 0.807625i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 926.561 | + | 305.067i | 1.14816 | + | 0.378026i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 56.7919i | − | 0.0702001i | −0.999384 | − | 0.0351000i | \(-0.988825\pi\) | ||
0.999384 | − | 0.0351000i | \(-0.0111750\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −743.889 | −0.917249 | −0.458625 | − | 0.888630i | \(-0.651658\pi\) | ||||
−0.458625 | + | 0.888630i | \(0.651658\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 124.516 | − | 378.186i | 0.153157 | − | 0.465174i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 70.1672 | + | 326.014i | 0.0860948 | + | 0.400017i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 403.391i | − | 0.493747i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −800.729 | − | 591.382i | −0.977691 | − | 0.722078i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 314.095i | 0.382576i | 0.981534 | + | 0.191288i | \(0.0612665\pi\) | ||||
−0.981534 | + | 0.191288i | \(0.938733\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1059.68i | 1.28758i | 0.765203 | + | 0.643789i | \(0.222639\pi\) | ||||
−0.765203 | + | 0.643789i | \(0.777361\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −561.570 | + | 59.7049i | −0.680691 | + | 0.0723695i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 834.408 | 1.00896 | 0.504479 | − | 0.863424i | \(-0.331685\pi\) | ||||
0.504479 | + | 0.863424i | \(0.331685\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.3660 | 0.0233607 | 0.0116803 | − | 0.999932i | \(-0.496282\pi\) | ||||
0.0116803 | + | 0.999932i | \(0.496282\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −724.347 | − | 238.489i | −0.871658 | − | 0.286990i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.6857 | 0.0128279 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 799.605 | − | 172.097i | 0.957610 | − | 0.206104i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 956.842 | − | 678.189i | 1.14318 | − | 0.810262i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1565.62i | − | 1.86605i | −0.359808 | − | 0.933026i | \(-0.617158\pi\) | ||
0.359808 | − | 0.933026i | \(-0.382842\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2282.45 | −2.71397 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 55.7048 | + | 18.3406i | 0.0660792 | + | 0.0217563i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −462.486 | + | 99.5398i | −0.547321 | + | 0.117799i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 438.039i | − | 0.517165i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −312.519 | − | 102.896i | −0.368102 | − | 0.121196i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 616.634i | − | 0.724599i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.9266i | 0.0245329i | 0.999925 | + | 0.0122665i | \(0.00390463\pi\) | ||||
−0.999925 | + | 0.0122665i | \(0.996095\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 322.552 | + | 145.648i | 0.377254 | + | 0.170349i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 236.110 | 0.275508 | 0.137754 | − | 0.990466i | \(-0.456012\pi\) | ||||
0.137754 | + | 0.990466i | \(0.456012\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 997.970 | 1.16178 | 0.580891 | − | 0.813982i | \(-0.302704\pi\) | ||||
0.580891 | + | 0.813982i | \(0.302704\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 328.178 | − | 996.756i | 0.381159 | − | 1.15767i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1147.63 | −1.32982 | −0.664909 | − | 0.746924i | \(-0.731530\pi\) | ||||
−0.664909 | + | 0.746924i | \(0.731530\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −169.681 | + | 36.5200i | −0.196163 | + | 0.0422197i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −255.219 | + | 775.161i | −0.294370 | + | 0.894072i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 384.097i | − | 0.441999i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1026.03 | 1.17799 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18.4125 | − | 24.9305i | 0.0210911 | − | 0.0285573i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −505.777 | − | 685.042i | −0.578031 | − | 0.782905i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 166.283i | 0.189604i | 0.995496 | + | 0.0948022i | \(0.0302219\pi\) | ||||
−0.995496 | + | 0.0948022i | \(0.969778\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −167.363 | + | 508.321i | −0.190401 | + | 0.578294i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 275.137i | − | 0.312301i | −0.987733 | − | 0.156150i | \(-0.950092\pi\) | ||
0.987733 | − | 0.156150i | \(-0.0499085\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 262.830i | 0.297656i | 0.988863 | + | 0.148828i | \(0.0475501\pi\) | ||||
−0.988863 | + | 0.148828i | \(0.952450\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1455.81 | + | 155.005i | 1.64498 | + | 0.175147i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 406.164 | 0.457908 | 0.228954 | − | 0.973437i | \(-0.426469\pi\) | ||||
0.228954 | + | 0.973437i | \(0.426469\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 510.862 | 0.574648 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 582.938 | − | 179.382i | 0.654251 | − | 0.201327i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −485.720 | −0.543920 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −287.680 | − | 1336.63i | −0.321430 | − | 1.49344i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 903.316 | + | 297.413i | 1.00704 | + | 0.331564i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2427.63i | 2.70036i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 340.710 | 0.378146 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 327.812 | − | 995.644i | 0.363026 | − | 1.10260i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −199.799 | + | 43.0024i | −0.220773 | + | 0.0475164i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1284.19i | − | 1.41587i | −0.706278 | − | 0.707934i | \(-0.749627\pi\) | ||
0.706278 | − | 0.707934i | \(-0.250373\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −263.302 | + | 356.510i | −0.289661 | + | 0.392201i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 353.054i | 0.387546i | 0.981046 | + | 0.193773i | \(0.0620725\pi\) | ||||
−0.981046 | + | 0.193773i | \(0.937928\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.4819i | 0.0224336i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.56740 | − | 61.6810i | 0.00717748 | − | 0.0674110i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −689.046 | −0.751413 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −210.284 | −0.228818 | −0.114409 | − | 0.993434i | \(-0.536497\pi\) | ||||
−0.114409 | + | 0.993434i | \(0.536497\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 823.644 | + | 271.182i | 0.894293 | + | 0.294443i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −654.462 | −0.709060 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −324.824 | − | 719.650i | −0.351161 | − | 0.778000i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 484.139 | − | 655.522i | 0.522264 | − | 0.707143i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1095.27i | − | 1.17898i | −0.807777 | − | 0.589488i | \(-0.799330\pi\) | ||
0.807777 | − | 0.589488i | \(-0.200670\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.4015 | −0.0219136 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 957.614 | + | 315.291i | 1.02638 | + | 0.337932i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −32.6317 | − | 151.615i | −0.0349002 | − | 0.162155i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 567.824i | − | 0.606002i | −0.952990 | − | 0.303001i | \(-0.902011\pi\) | ||
0.952990 | − | 0.303001i | \(-0.0979885\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1606.28 | − | 528.862i | −1.71063 | − | 0.563219i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 726.052i | 0.771575i | 0.922588 | + | 0.385787i | \(0.126070\pi\) | ||||
−0.922588 | + | 0.385787i | \(0.873930\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1002.56i | 1.06316i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 677.758 | + | 621.605i | 0.717204 | + | 0.657783i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 568.400 | 0.600211 | 0.300105 | − | 0.953906i | \(-0.402978\pi\) | ||||
0.300105 | + | 0.953906i | \(0.402978\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1274.72 | −1.34323 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −131.289 | + | 398.757i | −0.138054 | + | 0.419303i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1118.37 | 1.17353 | 0.586765 | − | 0.809758i | \(-0.300401\pi\) | ||||
0.586765 | + | 0.809758i | \(0.300401\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −42.7062 | − | 198.423i | −0.0447186 | − | 0.207773i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −394.815 | + | 1199.15i | −0.412555 | + | 1.25303i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 778.578i | 0.811865i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 925.814 | 0.963386 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −473.350 | − | 349.594i | −0.491537 | − | 0.363026i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 148.611 | + | 690.484i | 0.154001 | + | 0.715527i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 759.775i | − | 0.785704i | −0.919602 | − | 0.392852i | \(-0.871489\pi\) | ||
0.919602 | − | 0.392852i | \(-0.128511\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −30.3946 | + | 92.3156i | −0.0313669 | + | 0.0952689i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1342.50i | − | 1.38259i | −0.722570 | − | 0.691297i | \(-0.757040\pi\) | ||
0.722570 | − | 0.691297i | \(-0.242960\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1567.87i | 1.61137i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1210.89 | − | 128.739i | 1.24194 | − | 0.132041i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −897.030 | −0.918147 | −0.459074 | − | 0.888398i | \(-0.651819\pi\) | ||||
−0.459074 | + | 0.888398i | \(0.651819\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 530.308 | 0.541683 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1234.12 | + | 911.467i | 1.25803 | + | 0.929121i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 377.542 | 0.384071 | 0.192035 | − | 0.981388i | \(-0.438491\pi\) | ||||
0.192035 | + | 0.981388i | \(0.438491\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1137.17 | + | 244.751i | −1.15449 | + | 0.248479i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1198.85 | − | 394.716i | −1.21464 | − | 0.399915i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1001.44i | 1.01258i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 224.222 | 0.226258 | 0.113129 | − | 0.993580i | \(-0.463913\pi\) | ||||
0.113129 | + | 0.993580i | \(0.463913\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.6147 | − | 41.3511i | 0.0137107 | − | 0.0416426i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −417.316 | + | 89.8179i | −0.419413 | + | 0.0902693i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1018.21i | 1.02127i | 0.859797 | + | 0.510635i | \(0.170590\pi\) | ||||
−0.859797 | + | 0.510635i | \(0.829410\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 493.096 | + | 695.699i | 0.493590 | + | 0.696396i |
(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 | 240.3.c.e.209.7 | 12 | ||
3.2 | odd | 2 | inner | 240.3.c.e.209.5 | 12 | ||
4.3 | odd | 2 | 120.3.c.a.89.6 | yes | 12 | ||
5.2 | odd | 4 | 1200.3.l.y.401.1 | 12 | |||
5.3 | odd | 4 | 1200.3.l.y.401.12 | 12 | |||
5.4 | even | 2 | inner | 240.3.c.e.209.6 | 12 | ||
8.3 | odd | 2 | 960.3.c.k.449.7 | 12 | |||
8.5 | even | 2 | 960.3.c.j.449.6 | 12 | |||
12.11 | even | 2 | 120.3.c.a.89.8 | yes | 12 | ||
15.2 | even | 4 | 1200.3.l.y.401.2 | 12 | |||
15.8 | even | 4 | 1200.3.l.y.401.11 | 12 | |||
15.14 | odd | 2 | inner | 240.3.c.e.209.8 | 12 | ||
20.3 | even | 4 | 600.3.l.g.401.1 | 12 | |||
20.7 | even | 4 | 600.3.l.g.401.12 | 12 | |||
20.19 | odd | 2 | 120.3.c.a.89.7 | yes | 12 | ||
24.5 | odd | 2 | 960.3.c.j.449.8 | 12 | |||
24.11 | even | 2 | 960.3.c.k.449.5 | 12 | |||
40.19 | odd | 2 | 960.3.c.k.449.6 | 12 | |||
40.29 | even | 2 | 960.3.c.j.449.7 | 12 | |||
60.23 | odd | 4 | 600.3.l.g.401.2 | 12 | |||
60.47 | odd | 4 | 600.3.l.g.401.11 | 12 | |||
60.59 | even | 2 | 120.3.c.a.89.5 | ✓ | 12 | ||
120.29 | odd | 2 | 960.3.c.j.449.5 | 12 | |||
120.59 | even | 2 | 960.3.c.k.449.8 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.3.c.a.89.5 | ✓ | 12 | 60.59 | even | 2 | ||
120.3.c.a.89.6 | yes | 12 | 4.3 | odd | 2 | ||
120.3.c.a.89.7 | yes | 12 | 20.19 | odd | 2 | ||
120.3.c.a.89.8 | yes | 12 | 12.11 | even | 2 | ||
240.3.c.e.209.5 | 12 | 3.2 | odd | 2 | inner | ||
240.3.c.e.209.6 | 12 | 5.4 | even | 2 | inner | ||
240.3.c.e.209.7 | 12 | 1.1 | even | 1 | trivial | ||
240.3.c.e.209.8 | 12 | 15.14 | odd | 2 | inner | ||
600.3.l.g.401.1 | 12 | 20.3 | even | 4 | |||
600.3.l.g.401.2 | 12 | 60.23 | odd | 4 | |||
600.3.l.g.401.11 | 12 | 60.47 | odd | 4 | |||
600.3.l.g.401.12 | 12 | 20.7 | even | 4 | |||
960.3.c.j.449.5 | 12 | 120.29 | odd | 2 | |||
960.3.c.j.449.6 | 12 | 8.5 | even | 2 | |||
960.3.c.j.449.7 | 12 | 40.29 | even | 2 | |||
960.3.c.j.449.8 | 12 | 24.5 | odd | 2 | |||
960.3.c.k.449.5 | 12 | 24.11 | even | 2 | |||
960.3.c.k.449.6 | 12 | 40.19 | odd | 2 | |||
960.3.c.k.449.7 | 12 | 8.3 | odd | 2 | |||
960.3.c.k.449.8 | 12 | 120.59 | even | 2 | |||
1200.3.l.y.401.1 | 12 | 5.2 | odd | 4 | |||
1200.3.l.y.401.2 | 12 | 15.2 | even | 4 | |||
1200.3.l.y.401.11 | 12 | 15.8 | even | 4 | |||
1200.3.l.y.401.12 | 12 | 5.3 | odd | 4 |