Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,3,Mod(401,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1200.401");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.l (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: | \(32.6976317232\) |
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: | \( x^{12} - 4x^{10} + 30x^{8} - 216x^{6} + 1080x^{4} - 5184x^{2} + 46656 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{18}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 401.12 | ||
Root | \(-1.05281 - 2.21170i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.401 |
Dual form | 1200.3.l.y.401.11 |
$q$-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 \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(577\) | \(751\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 2.84952 | + | 0.938195i | 0.949841 | + | 0.312732i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.81219 | −0.973170 | −0.486585 | − | 0.873633i | \(-0.661758\pi\) | ||||
−0.486585 | + | 0.873633i | \(0.661758\pi\) | |||||||
\(8\) | 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 | ||||||||
\(13\) | −16.2362 | −1.24894 | −0.624471 | − | 0.781048i | \(-0.714685\pi\) | ||||
−0.624471 | + | 0.781048i | \(0.714685\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.11928i | − | 0.242311i | −0.992634 | − | 0.121155i | \(-0.961340\pi\) | ||
0.992634 | − | 0.121155i | \(-0.0386599\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.86469 | 0.413931 | 0.206965 | − | 0.978348i | \(-0.433641\pi\) | ||||
0.206965 | + | 0.978348i | \(0.433641\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −19.4115 | − | 6.39117i | −0.924357 | − | 0.304341i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 19.5246i | 0.848895i | 0.905453 | + | 0.424447i | \(0.139532\pi\) | ||||
−0.905453 | + | 0.424447i | \(0.860468\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 15.6130 | + | 22.0280i | 0.578259 | + | 0.815853i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 55.8878i | 1.92717i | 0.267408 | + | 0.963583i | \(0.413833\pi\) | ||||
−0.267408 | + | 0.963583i | \(0.586167\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −43.4375 | −1.40121 | −0.700604 | − | 0.713550i | \(-0.747086\pi\) | ||||
−0.700604 | + | 0.713550i | \(0.747086\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.06442 | − | 21.4563i | 0.214073 | − | 0.650192i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −31.5824 | −0.853579 | −0.426790 | − | 0.904351i | \(-0.640356\pi\) | ||||
−0.426790 | + | 0.904351i | \(0.640356\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | −51.2914 | −1.19282 | −0.596412 | − | 0.802678i | \(-0.703408\pi\) | ||||
−0.596412 | + | 0.802678i | \(0.703408\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 61.7596i | − | 1.31403i | −0.753875 | − | 0.657017i | \(-0.771818\pi\) | ||
0.753875 | − | 0.657017i | \(-0.228182\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.59407 | −0.0529401 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.86469 | − | 11.7380i | 0.0757782 | − | 0.230157i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 82.7111i | 1.56059i | 0.625414 | + | 0.780293i | \(0.284930\pi\) | ||||
−0.625414 | + | 0.780293i | \(0.715070\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 22.4106 | + | 7.37861i | 0.393169 | + | 0.129449i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 97.6026i | − | 1.65428i | −0.561994 | − | 0.827141i | \(-0.689966\pi\) | ||
0.561994 | − | 0.827141i | \(-0.310034\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.13531 | 0.0677920 | 0.0338960 | − | 0.999425i | \(-0.489209\pi\) | ||||
0.0338960 | + | 0.999425i | \(0.489209\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −49.3174 | − | 36.4236i | −0.782816 | − | 0.578152i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −63.1940 | −0.943194 | −0.471597 | − | 0.881814i | \(-0.656322\pi\) | ||||
−0.471597 | + | 0.881814i | \(0.656322\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | −78.5111 | −1.07549 | −0.537747 | − | 0.843106i | \(-0.680724\pi\) | ||||
−0.537747 | + | 0.843106i | \(0.680724\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 51.2944i | 0.666161i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −51.0103 | −0.645699 | −0.322850 | − | 0.946450i | \(-0.604641\pi\) | ||||
−0.322850 | + | 0.946450i | \(0.604641\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 23.8230 | + | 77.4175i | 0.294111 | + | 0.955771i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 2.72011i | − | 0.0327725i | −0.999866 | − | 0.0163862i | \(-0.994784\pi\) | ||
0.999866 | − | 0.0163862i | \(-0.00521613\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −52.4337 | + | 159.254i | −0.602686 | + | 1.83050i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 70.4279i | − | 0.791325i | −0.918396 | − | 0.395662i | \(-0.870515\pi\) | ||
0.918396 | − | 0.395662i | \(-0.129485\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 110.604 | 1.21543 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −123.776 | − | 40.7528i | −1.33093 | − | 0.438203i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.44364 | 0.0355015 | 0.0177507 | − | 0.999842i | \(-0.494349\pi\) | ||||
0.0177507 | + | 0.999842i | \(0.494349\pi\) | |||||||
\(98\) | 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 | ||||||||
\(103\) | −90.5470 | −0.879097 | −0.439548 | − | 0.898219i | \(-0.644862\pi\) | ||||
−0.439548 | + | 0.898219i | \(0.644862\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 65.3836i | − | 0.611062i | −0.952182 | − | 0.305531i | \(-0.901166\pi\) | ||
0.952182 | − | 0.305531i | \(-0.0988339\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 170.469 | 1.56394 | 0.781968 | − | 0.623319i | \(-0.214216\pi\) | ||||
0.781968 | + | 0.623319i | \(0.214216\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −89.9949 | − | 29.6305i | −0.810765 | − | 0.266941i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 55.4137i | 0.490387i | 0.969474 | + | 0.245193i | \(0.0788514\pi\) | ||||
−0.969474 | + | 0.245193i | \(0.921149\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −117.544 | − | 86.8123i | −1.00465 | − | 0.741985i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 28.0613i | 0.235809i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 64.3022 | 0.531423 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −48.1751 | + | 146.319i | −0.391668 | + | 1.18959i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 74.9923 | 0.590491 | 0.295245 | − | 0.955421i | \(-0.404599\pi\) | ||||
0.295245 | + | 0.955421i | \(0.404599\pi\) | |||||||
\(128\) | 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 | ||||||||
\(133\) | −53.5758 | −0.402825 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 114.292i | 0.834248i | 0.908850 | + | 0.417124i | \(0.136962\pi\) | ||||
−0.908850 | + | 0.417124i | \(0.863038\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 230.156 | 1.65580 | 0.827899 | − | 0.560878i | \(-0.189536\pi\) | ||||
0.827899 | + | 0.560878i | \(0.189536\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 57.9426 | − | 175.986i | 0.410940 | − | 1.24812i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 122.256i | 0.854934i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.39185 | − | 2.43374i | −0.0502847 | − | 0.0165561i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 9.12446i | − | 0.0612380i | −0.999531 | − | 0.0306190i | \(-0.990252\pi\) | ||
0.999531 | − | 0.0306190i | \(-0.00974785\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 163.010 | 1.07954 | 0.539769 | − | 0.841813i | \(-0.318512\pi\) | ||||
0.539769 | + | 0.841813i | \(0.318512\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 22.0250 | − | 29.8218i | 0.143955 | − | 0.194914i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −122.529 | −0.780442 | −0.390221 | − | 0.920721i | \(-0.627601\pi\) | ||||
−0.390221 | + | 0.920721i | \(0.627601\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −77.5991 | + | 235.687i | −0.488045 | + | 1.48231i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 133.005i | − | 0.826119i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −66.6959 | −0.409177 | −0.204589 | − | 0.978848i | \(-0.565586\pi\) | ||||
−0.204589 | + | 0.978848i | \(0.565586\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 163.583i | − | 0.979539i | −0.871852 | − | 0.489769i | \(-0.837081\pi\) | ||
0.871852 | − | 0.489769i | \(-0.162919\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 94.6153 | 0.559854 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 56.9370 | + | 42.0511i | 0.332965 | + | 0.245913i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 34.7133i | − | 0.200655i | −0.994954 | − | 0.100327i | \(-0.968011\pi\) | ||
0.994954 | − | 0.100327i | \(-0.0319890\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 91.5704 | − | 278.121i | 0.517347 | − | 1.57131i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 273.448i | 1.52764i | 0.645429 | + | 0.763820i | \(0.276679\pi\) | ||||
−0.645429 | + | 0.763820i | \(0.723321\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −40.8749 | −0.225828 | −0.112914 | − | 0.993605i | \(-0.536019\pi\) | ||||
−0.112914 | + | 0.993605i | \(0.536019\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.7837 | + | 3.87973i | 0.0643916 | + | 0.0212007i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −31.0173 | −0.165868 | ||||||||
\(188\) | 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 | ||||||||
\(193\) | −141.259 | −0.731912 | −0.365956 | − | 0.930632i | \(-0.619258\pi\) | ||||
−0.365956 | + | 0.930632i | \(0.619258\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 232.643i | 1.18093i | 0.807064 | + | 0.590464i | \(0.201055\pi\) | ||||
−0.807064 | + | 0.590464i | \(0.798945\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 85.3744 | 0.429017 | 0.214509 | − | 0.976722i | \(-0.431185\pi\) | ||||
0.214509 | + | 0.976722i | \(0.431185\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −180.073 | − | 59.2883i | −0.895885 | − | 0.294967i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 380.719i | − | 1.87546i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −104.394 | + | 141.350i | −0.504321 | + | 0.682849i | ||||
\(208\) | 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 | ||||||||
\(213\) | −37.8175 | + | 114.861i | −0.177547 | + | 0.539252i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 295.904 | 1.36361 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −223.719 | − | 73.6587i | −1.02155 | − | 0.336341i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 66.8816i | 0.302632i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 30.2924 | 0.135840 | 0.0679201 | − | 0.997691i | \(-0.478364\pi\) | ||||
0.0679201 | + | 0.997691i | \(0.478364\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 239.380i | 1.05454i | 0.849698 | + | 0.527269i | \(0.176784\pi\) | ||||
−0.849698 | + | 0.527269i | \(0.823216\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −284.959 | −1.24436 | −0.622180 | − | 0.782874i | \(-0.713753\pi\) | ||||
−0.622180 | + | 0.782874i | \(0.713753\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −48.1242 | + | 146.165i | −0.208330 | + | 0.632747i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 93.8635i | 0.402848i | 0.979504 | + | 0.201424i | \(0.0645569\pi\) | ||||
−0.979504 | + | 0.201424i | \(0.935443\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −145.355 | − | 47.8576i | −0.613312 | − | 0.201931i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 238.326i | 0.997181i | 0.866838 | + | 0.498590i | \(0.166149\pi\) | ||||
−0.866838 | + | 0.498590i | \(0.833851\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 44.2919 | 0.183784 | 0.0918919 | − | 0.995769i | \(-0.470709\pi\) | ||||
0.0918919 | + | 0.995769i | \(0.470709\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.74848 | + | 242.954i | −0.0195411 | + | 0.999809i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −127.693 | −0.516975 | ||||||||
\(248\) | 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 | ||||||||
\(253\) | 147.016 | 0.581092 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 169.330i | 0.658870i | 0.944178 | + | 0.329435i | \(0.106858\pi\) | ||||
−0.944178 | + | 0.329435i | \(0.893142\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 215.146 | 0.830678 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −298.822 | + | 404.604i | −1.14491 | + | 1.55021i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 91.1958i | − | 0.346752i | −0.984856 | − | 0.173376i | \(-0.944532\pi\) | ||
0.984856 | − | 0.173376i | \(-0.0554676\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 66.0751 | − | 200.686i | 0.247472 | − | 0.751633i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 325.164i | − | 1.20879i | −0.796686 | − | 0.604393i | \(-0.793416\pi\) | ||
0.796686 | − | 0.604393i | \(-0.206584\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 132.719 | 0.489738 | 0.244869 | − | 0.969556i | \(-0.421255\pi\) | ||||
0.244869 | + | 0.969556i | \(0.421255\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 315.170 | + | 103.768i | 1.15447 | + | 0.380104i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −254.199 | −0.917687 | −0.458844 | − | 0.888517i | \(-0.651736\pi\) | ||||
−0.458844 | + | 0.888517i | \(0.651736\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | 109.674 | 0.387541 | 0.193770 | − | 0.981047i | \(-0.437928\pi\) | ||||
0.193770 | + | 0.981047i | \(0.437928\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 349.797i | − | 1.21881i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 272.032 | 0.941286 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.81275 | + | 3.23081i | 0.0337208 | + | 0.0111024i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 178.388i | − | 0.608832i | −0.952539 | − | 0.304416i | \(-0.901539\pi\) | ||
0.952539 | − | 0.304416i | \(-0.0984614\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 165.867 | − | 117.563i | 0.558474 | − | 0.395834i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 317.006i | − | 1.06022i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 349.407 | 1.16082 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 46.2011 | − | 140.324i | 0.152479 | − | 0.463115i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 289.046 | 0.941518 | 0.470759 | − | 0.882262i | \(-0.343980\pi\) | ||||
0.470759 | + | 0.882262i | \(0.343980\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | 563.702 | 1.80096 | 0.900482 | − | 0.434894i | \(-0.143214\pi\) | ||||
0.900482 | + | 0.434894i | \(0.143214\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 139.938i | 0.441445i | 0.975337 | + | 0.220722i | \(0.0708415\pi\) | ||||
−0.975337 | + | 0.220722i | \(0.929158\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 420.824 | 1.31920 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 61.3426 | − | 186.312i | 0.191098 | − | 0.580412i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 32.3968i | − | 0.100300i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 485.756 | + | 159.933i | 1.48549 | + | 0.489092i | ||||
\(328\) | 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 | ||||||||
\(333\) | −228.644 | − | 168.866i | −0.686617 | − | 0.507104i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 347.492 | 1.03113 | 0.515566 | − | 0.856850i | \(-0.327582\pi\) | ||||
0.515566 | + | 0.856850i | \(0.327582\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −51.9889 | + | 157.903i | −0.153359 | + | 0.465790i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 327.075i | 0.959165i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 351.469 | 1.02469 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 273.321i | 0.787670i | 0.919181 | + | 0.393835i | \(0.128852\pi\) | ||||
−0.919181 | + | 0.393835i | \(0.871148\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 550.853 | 1.57838 | 0.789188 | − | 0.614152i | \(-0.210502\pi\) | ||||
0.789188 | + | 0.614152i | \(0.210502\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −253.496 | − | 357.652i | −0.722212 | − | 1.01895i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 643.177i | − | 1.82203i | −0.412373 | − | 0.911015i | \(-0.635300\pi\) | ||
0.412373 | − | 0.911015i | \(-0.364700\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −26.3270 | + | 79.9614i | −0.0737451 | + | 0.223982i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 465.873i | − | 1.29770i | −0.760918 | − | 0.648849i | \(-0.775251\pi\) | ||
0.760918 | − | 0.648849i | \(-0.224749\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −299.147 | −0.828661 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 183.231 | + | 60.3280i | 0.504767 | + | 0.166193i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −44.7168 | −0.121844 | −0.0609221 | − | 0.998143i | \(-0.519404\pi\) | ||||
−0.0609221 | + | 0.998143i | \(0.519404\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −274.552 | + | 371.743i | −0.744044 | + | 1.00743i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 563.443i | − | 1.51872i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −275.158 | −0.737688 | −0.368844 | − | 0.929491i | \(-0.620246\pi\) | ||||
−0.368844 | + | 0.929491i | \(0.620246\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 907.408i | − | 2.40692i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −505.072 | −1.33264 | −0.666322 | − | 0.745664i | \(-0.732132\pi\) | ||||
−0.666322 | + | 0.745664i | \(0.732132\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 213.692 | + | 70.3575i | 0.560873 | + | 0.184665i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 193.577i | 0.505422i | 0.967542 | + | 0.252711i | \(0.0813222\pi\) | ||||
−0.967542 | + | 0.252711i | \(0.918678\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −371.328 | − | 274.246i | −0.959505 | − | 0.708646i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 280.077i | 0.719993i | 0.932954 | + | 0.359996i | \(0.117222\pi\) | ||||
−0.932954 | + | 0.359996i | \(0.882778\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 80.4272 | 0.205696 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 94.8975 | − | 288.226i | 0.241469 | − | 0.733401i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −468.421 | −1.17990 | −0.589951 | − | 0.807439i | \(-0.700853\pi\) | ||||
−0.589951 | + | 0.807439i | \(0.700853\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 705.261 | 1.75003 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 237.809i | 0.584298i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 202.697 | 0.495592 | 0.247796 | − | 0.968812i | \(-0.420294\pi\) | ||||
0.247796 | + | 0.968812i | \(0.420294\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −107.228 | + | 325.678i | −0.260896 | + | 0.792403i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 664.888i | 1.60990i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 655.835 | + | 215.931i | 1.57274 | + | 0.517820i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 76.6340i | 0.182897i | 0.995810 | + | 0.0914487i | \(0.0291497\pi\) | ||||
−0.995810 | + | 0.0914487i | \(0.970850\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −183.991 | −0.437033 | −0.218516 | − | 0.975833i | \(-0.570122\pi\) | ||||
−0.218516 | + | 0.975833i | \(0.570122\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 330.218 | − | 447.114i | 0.780657 | − | 1.05701i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −28.1705 | −0.0659731 | ||||||||
\(428\) | 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 | ||||||||
\(433\) | 399.351 | 0.922288 | 0.461144 | − | 0.887325i | \(-0.347439\pi\) | ||||
0.461144 | + | 0.887325i | \(0.347439\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 153.555i | 0.351384i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 140.833 | 0.320804 | 0.160402 | − | 0.987052i | \(-0.448721\pi\) | ||||
0.160402 | + | 0.987052i | \(0.448721\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.7799 | − | 13.8700i | −0.0425849 | − | 0.0314513i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 211.416i | 0.477237i | 0.971113 | + | 0.238618i | \(0.0766945\pi\) | ||||
−0.971113 | + | 0.238618i | \(0.923306\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.56052 | − | 26.0004i | 0.0191511 | − | 0.0581664i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 455.166i | 1.01373i | 0.862025 | + | 0.506866i | \(0.169196\pi\) | ||||
−0.862025 | + | 0.506866i | \(0.830804\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 386.645 | 0.857307 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 464.502 | + | 152.935i | 1.02539 | + | 0.337606i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 555.776 | 1.21614 | 0.608070 | − | 0.793883i | \(-0.291944\pi\) | ||||
0.608070 | + | 0.793883i | \(0.291944\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | −360.832 | −0.779336 | −0.389668 | − | 0.920955i | \(-0.627410\pi\) | ||||
−0.389668 | + | 0.920955i | \(0.627410\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 496.306i | − | 1.06275i | −0.847135 | − | 0.531377i | \(-0.821675\pi\) | ||
0.847135 | − | 0.531377i | \(-0.178325\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 430.490 | 0.917888 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −349.151 | − | 114.957i | −0.741296 | − | 0.244069i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 386.214i | 0.816520i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −442.241 | + | 598.793i | −0.927131 | + | 1.25533i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 286.032i | − | 0.597145i | −0.954387 | − | 0.298572i | \(-0.903490\pi\) | ||
0.954387 | − | 0.298572i | \(-0.0965105\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 512.780 | 1.06607 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 124.785 | − | 379.002i | 0.258354 | − | 0.784682i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.3276 | −0.0704880 | −0.0352440 | − | 0.999379i | \(-0.511221\pi\) | ||||
−0.0352440 | + | 0.999379i | \(0.511221\pi\) | |||||||
\(488\) | 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 | ||||||||
\(493\) | 230.218 | 0.466973 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 274.591i | − | 0.552496i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −72.9046 | −0.146101 | −0.0730507 | − | 0.997328i | \(-0.523273\pi\) | ||||
−0.0730507 | + | 0.997328i | \(0.523273\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 153.473 | − | 466.134i | 0.306333 | − | 0.930407i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 228.404i | 0.454083i | 0.973885 | + | 0.227041i | \(0.0729052\pi\) | ||||
−0.973885 | + | 0.227041i | \(0.927095\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 269.609 | + | 88.7677i | 0.531773 | + | 0.175084i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 99.1735i | − | 0.194840i | −0.995243 | − | 0.0974199i | \(-0.968941\pi\) | ||
0.995243 | − | 0.0974199i | \(-0.0310590\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 534.832 | 1.04664 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 122.791 | + | 173.244i | 0.239359 | + | 0.337707i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −465.037 | −0.899492 | ||||||||
\(518\) | 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 | ||||||||
\(523\) | −821.405 | −1.57056 | −0.785282 | − | 0.619138i | \(-0.787482\pi\) | ||||
−0.785282 | + | 0.619138i | \(0.787482\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 178.931i | 0.339528i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 147.791 | 0.279377 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 521.864 | − | 706.602i | 0.982795 | − | 1.33070i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 833.710i | − | 1.56418i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −256.547 | + | 779.196i | −0.477742 | + | 1.45102i | ||||
\(538\) | 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 | ||||||||
\(543\) | −116.474 | − | 38.3487i | −0.214501 | − | 0.0706237i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 485.492 | 0.887553 | 0.443777 | − | 0.896137i | \(-0.353638\pi\) | ||||
0.443777 | + | 0.896137i | \(0.353638\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 29.9379 | + | 22.1108i | 0.0545317 | + | 0.0402746i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 439.540i | 0.797714i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 347.492 | 0.628375 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 995.191i | − | 1.78670i | −0.449363 | − | 0.893349i | \(-0.648349\pi\) | ||
0.449363 | − | 0.893349i | \(-0.351651\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 832.780 | 1.48977 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −88.3847 | − | 29.1003i | −0.157548 | − | 0.0518722i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 486.571i | − | 0.864248i | −0.901814 | − | 0.432124i | \(-0.857764\pi\) | ||
0.901814 | − | 0.432124i | \(-0.142236\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −162.287 | − | 527.383i | −0.286220 | − | 0.930128i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 737.704i | − | 1.29649i | −0.761431 | − | 0.648246i | \(-0.775503\pi\) | ||
0.761431 | − | 0.648246i | \(-0.224497\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −805.843 | −1.41128 | −0.705642 | − | 0.708569i | \(-0.749341\pi\) | ||||
−0.705642 | + | 0.708569i | \(0.749341\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 38.0846 | − | 115.672i | 0.0664652 | − | 0.201871i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 690.512 | 1.19673 | 0.598364 | − | 0.801225i | \(-0.295818\pi\) | ||||
0.598364 | + | 0.801225i | \(0.295818\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −402.521 | − | 132.529i | −0.695201 | − | 0.228892i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.5299i | 0.0318932i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 622.798 | 1.06826 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 670.611i | 1.14244i | 0.820798 | + | 0.571219i | \(0.193529\pi\) | ||||
−0.820798 | + | 0.571219i | \(0.806471\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −341.622 | −0.580004 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −218.265 | + | 662.922i | −0.369314 | + | 1.12170i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 214.249i | 0.361296i | 0.983548 | + | 0.180648i | \(0.0578195\pi\) | ||||
−0.983548 | + | 0.180648i | \(0.942181\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 243.276 | + | 80.0979i | 0.407498 | + | 0.134167i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 303.315i | − | 0.506368i | −0.967418 | − | 0.253184i | \(-0.918522\pi\) | ||
0.967418 | − | 0.253184i | \(-0.0814779\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 66.0555 | 0.109909 | 0.0549546 | − | 0.998489i | \(-0.482499\pi\) | ||||
0.0549546 | + | 0.998489i | \(0.482499\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −457.498 | − | 337.887i | −0.758703 | − | 0.560343i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 178.972 | 0.294847 | 0.147423 | − | 0.989073i | \(-0.452902\pi\) | ||||
0.147423 | + | 0.989073i | \(0.452902\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 357.188 | − | 1084.87i | 0.586516 | − | 1.78139i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1002.74i | 1.64115i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −728.201 | −1.18793 | −0.593965 | − | 0.804491i | \(-0.702438\pi\) | ||||
−0.593965 | + | 0.804491i | \(0.702438\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 198.426i | − | 0.321598i | −0.986987 | − | 0.160799i | \(-0.948593\pi\) | ||
0.986987 | − | 0.160799i | \(-0.0514071\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.1752 | 0.0277468 | 0.0138734 | − | 0.999904i | \(-0.495584\pi\) | ||||
0.0138734 | + | 0.999904i | \(0.495584\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −430.088 | + | 304.837i | −0.692574 | + | 0.490881i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 479.768i | 0.770094i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 55.5595 | − | 168.747i | 0.0886116 | − | 0.269135i | ||||
\(628\) | 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 | ||||||||
\(633\) | −810.781 | − | 266.947i | −1.28085 | − | 0.421717i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 42.1179 | 0.0661191 | ||||||||
\(638\) | 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 | ||||||||
\(643\) | 701.008 | 1.09021 | 0.545107 | − | 0.838367i | \(-0.316489\pi\) | ||||
0.545107 | + | 0.838367i | \(0.316489\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 114.266i | 0.176609i | 0.996094 | + | 0.0883046i | \(0.0281449\pi\) | ||||
−0.996094 | + | 0.0883046i | \(0.971855\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −734.928 | −1.13240 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 843.187 | + | 277.616i | 1.29522 | + | 0.426446i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 240.882i | 0.368884i | 0.982843 | + | 0.184442i | \(0.0590479\pi\) | ||||
−0.982843 | + | 0.184442i | \(0.940952\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −568.387 | − | 419.785i | −0.865125 | − | 0.638942i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1218.15i | 1.84848i | 0.381807 | + | 0.924242i | \(0.375302\pi\) | ||||
−0.381807 | + | 0.924242i | \(0.624698\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1075.32 | −1.62681 | −0.813404 | − | 0.581699i | \(-0.802388\pi\) | ||||
−0.813404 | + | 0.581699i | \(0.802388\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −62.7480 | + | 190.581i | −0.0946425 | + | 0.287452i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1091.19 | −1.63596 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 86.3189 | + | 28.4202i | 0.129027 | + | 0.0424816i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 31.1381i | − | 0.0464054i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −356.367 | −0.529521 | −0.264760 | − | 0.964314i | \(-0.585293\pi\) | ||||
−0.264760 | + | 0.964314i | \(0.585293\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 79.8649i | 0.117969i | 0.998259 | + | 0.0589844i | \(0.0187862\pi\) | ||||
−0.998259 | + | 0.0589844i | \(0.981214\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −23.4588 | −0.0345490 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −224.585 | + | 682.120i | −0.329788 | + | 1.00164i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1270.41i | 1.86004i | 0.367507 | + | 0.930021i | \(0.380211\pi\) | ||||
−0.367507 | + | 0.930021i | \(0.619789\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −811.996 | − | 267.347i | −1.18195 | − | 0.389151i | ||||
\(688\) | 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 | ||||||||
\(693\) | −274.262 | + | 371.350i | −0.395760 | + | 0.535858i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 211.520 | 0.303472 | ||||||||
\(698\) | 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 | ||||||||
\(703\) | −248.386 | −0.353323 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 335.464i | 0.474489i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −659.081 | −0.929592 | −0.464796 | − | 0.885418i | \(-0.653872\pi\) | ||||
−0.464796 | + | 0.885418i | \(0.653872\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −369.293 | − | 272.743i | −0.519399 | − | 0.383604i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 848.099i | − | 1.18948i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −223.597 | + | 679.116i | −0.311850 | + | 0.947164i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 471.213i | 0.655373i | 0.944787 | + | 0.327686i | \(0.106269\pi\) | ||||
−0.944787 | + | 0.327686i | \(0.893731\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 616.823 | 0.855511 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 126.211 | + | 41.5545i | 0.174566 | + | 0.0574750i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 640.411 | 0.880895 | 0.440447 | − | 0.897778i | \(-0.354820\pi\) | ||||
0.440447 | + | 0.897778i | \(0.354820\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −241.469 | + | 687.847i | −0.331233 | + | 0.943549i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 211.284i | 0.289034i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −619.831 | −0.845608 | −0.422804 | − | 0.906221i | \(-0.638954\pi\) | ||||
−0.422804 | + | 0.906221i | \(0.638954\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 475.838i | 0.645642i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −135.992 | −0.184022 | −0.0920111 | − | 0.995758i | \(-0.529330\pi\) | ||||
−0.0920111 | + | 0.995758i | \(0.529330\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −363.864 | − | 119.801i | −0.491045 | − | 0.161675i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 986.468i | − | 1.32768i | −0.747874 | − | 0.663841i | \(-0.768925\pi\) | ||
0.747874 | − | 0.663841i | \(-0.231075\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.5440 | − | 19.6925i | 0.0194698 | − | 0.0263621i | ||||
\(748\) | 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 | ||||||||
\(753\) | −274.978 | + | 835.175i | −0.365177 | + | 1.10913i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1143.91 | −1.51111 | −0.755556 | − | 0.655084i | \(-0.772633\pi\) | ||||
−0.755556 | + | 0.655084i | \(0.772633\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | −1161.27 | −1.52198 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1584.70i | 2.06610i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 61.7841 | 0.0803434 | 0.0401717 | − | 0.999193i | \(-0.487210\pi\) | ||||
0.0401717 | + | 0.999193i | \(0.487210\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −158.864 | + | 482.509i | −0.206050 | + | 0.625822i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 444.408i | 0.574913i | 0.957794 | + | 0.287457i | \(0.0928097\pi\) | ||||
−0.957794 | + | 0.287457i | \(0.907190\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 613.063 | + | 201.849i | 0.789012 | + | 0.259779i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 403.842i | 0.518410i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 303.517 | 0.388626 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1231.10 | + | 872.576i | −1.57229 | + | 1.11440i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 206.738 | 0.262691 | 0.131346 | − | 0.991337i | \(-0.458070\pi\) | ||||
0.131346 | + | 0.991337i | \(0.458070\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 85.5595 | − | 259.865i | 0.108440 | − | 0.329360i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 377.489i | − | 0.477230i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −67.1419 | −0.0846682 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 235.281i | 0.295208i | 0.989047 | + | 0.147604i | \(0.0471562\pi\) | ||||
−0.989047 | + | 0.147604i | \(0.952844\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −254.405 | −0.318404 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 376.565 | − | 509.868i | 0.470119 | − | 0.636540i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 591.172i | 0.736205i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 305.067 | − | 926.561i | 0.378026 | − | 1.14816i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 56.7919i | 0.0702001i | 0.999384 | + | 0.0351000i | \(0.0111750\pi\) | ||||
−0.999384 | + | 0.0351000i | \(0.988825\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −743.889 | −0.917249 | −0.458625 | − | 0.888630i | \(-0.651658\pi\) | ||||
−0.458625 | + | 0.888630i | \(0.651658\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 378.186 | + | 124.516i | 0.465174 | + | 0.153157i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −403.391 | −0.493747 | ||||||||
\(818\) | 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 | ||||||||
\(823\) | −1059.68 | −1.28758 | −0.643789 | − | 0.765203i | \(-0.722639\pi\) | ||||
−0.643789 | + | 0.765203i | \(0.722639\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 834.408i | − | 1.00896i | −0.863424 | − | 0.504479i | \(-0.831685\pi\) | ||
0.863424 | − | 0.504479i | \(-0.168315\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.3660 | −0.0233607 | −0.0116803 | − | 0.999932i | \(-0.503718\pi\) | ||||
−0.0116803 | + | 0.999932i | \(0.503718\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −724.347 | − | 238.489i | −0.871658 | − | 0.286990i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.6857i | 0.0128279i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −678.189 | − | 956.842i | −0.810262 | − | 1.14318i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1565.62i | 1.86605i | 0.359808 | + | 0.933026i | \(0.382842\pi\) | ||||
−0.359808 | + | 0.933026i | \(0.617158\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2282.45 | −2.71397 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −18.3406 | + | 55.7048i | −0.0217563 | + | 0.0660792i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −438.039 | −0.517165 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 312.519 | + | 102.896i | 0.368102 | + | 0.121196i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 616.634i | − | 0.724599i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.9266 | −0.0245329 | −0.0122665 | − | 0.999925i | \(-0.503905\pi\) | ||||
−0.0122665 | + | 0.999925i | \(0.503905\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 236.110i | − | 0.275508i | −0.990466 | − | 0.137754i | \(-0.956012\pi\) | ||
0.990466 | − | 0.137754i | \(-0.0439884\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −997.970 | −1.16178 | −0.580891 | − | 0.813982i | \(-0.697296\pi\) | ||||
−0.580891 | + | 0.813982i | \(0.697296\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 328.178 | − | 996.756i | 0.381159 | − | 1.15767i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1147.63i | − | 1.32982i | −0.746924 | − | 0.664909i | \(-0.768470\pi\) | ||
0.746924 | − | 0.664909i | \(-0.231530\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 775.161 | + | 255.219i | 0.894072 | + | 0.294370i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 384.097i | 0.441999i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1026.03 | 1.17799 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 24.9305 | + | 18.4125i | 0.0285573 | + | 0.0210911i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 166.283 | 0.189604 | 0.0948022 | − | 0.995496i | \(-0.469778\pi\) | ||||
0.0948022 | + | 0.995496i | \(0.469778\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | −262.830 | −0.297656 | −0.148828 | − | 0.988863i | \(-0.547550\pi\) | ||||
−0.148828 | + | 0.988863i | \(0.547550\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 406.164i | − | 0.457908i | −0.973437 | − | 0.228954i | \(-0.926469\pi\) | ||
0.973437 | − | 0.228954i | \(-0.0735306\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −510.862 | −0.574648 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 582.938 | − | 179.382i | 0.654251 | − | 0.201327i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 485.720i | − | 0.543920i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 297.413 | − | 903.316i | 0.331564 | − | 1.00704i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 2427.63i | − | 2.70036i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 340.710 | 0.378146 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 995.644 | + | 327.812i | 1.10260 | + | 0.363026i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1284.19 | −1.41587 | −0.707934 | − | 0.706278i | \(-0.750373\pi\) | ||||
−0.707934 | + | 0.706278i | \(0.750373\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | −20.4819 | −0.0224336 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 689.046i | 0.751413i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 210.284 | 0.228818 | 0.114409 | − | 0.993434i | \(-0.463503\pi\) | ||||
0.114409 | + | 0.993434i | \(0.463503\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 823.644 | + | 271.182i | 0.894293 | + | 0.294443i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 654.462i | − | 0.709060i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −655.522 | − | 484.139i | −0.707143 | − | 0.522264i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1095.27i | 1.17898i | 0.807777 | + | 0.589488i | \(0.200670\pi\) | ||||
−0.807777 | + | 0.589488i | \(0.799330\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.4015 | −0.0219136 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −315.291 | + | 957.614i | −0.337932 | + | 1.02638i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −567.824 | −0.606002 | −0.303001 | − | 0.952990i | \(-0.597989\pi\) | ||||
−0.303001 | + | 0.952990i | \(0.597989\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | −1002.56 | −1.06316 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 568.400i | − | 0.600211i | −0.953906 | − | 0.300105i | \(-0.902978\pi\) | ||
0.953906 | − | 0.300105i | \(-0.0970219\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1274.72 | 1.34323 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −131.289 | + | 398.757i | −0.138054 | + | 0.419303i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1118.37i | 1.17353i | 0.809758 | + | 0.586765i | \(0.199599\pi\) | ||||
−0.809758 | + | 0.586765i | \(0.800401\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1199.15 | + | 394.815i | 1.25303 | + | 0.412555i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 778.578i | − | 0.811865i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 925.814 | 0.963386 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 349.594 | − | 473.350i | 0.363026 | − | 0.491537i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −759.775 | −0.785704 | −0.392852 | − | 0.919602i | \(-0.628511\pi\) | ||||
−0.392852 | + | 0.919602i | \(0.628511\pi\) | |||||||
\(968\) | 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 | ||||||||
\(973\) | −1567.87 | −1.61137 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 897.030i | 0.918147i | 0.888398 | + | 0.459074i | \(0.151819\pi\) | ||||
−0.888398 | + | 0.459074i | \(0.848181\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −530.308 | −0.541683 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1234.12 | + | 911.467i | 1.25803 | + | 0.929121i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 377.542i | 0.384071i | 0.981388 | + | 0.192035i | \(0.0615088\pi\) | ||||
−0.981388 | + | 0.192035i | \(0.938491\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −394.716 | + | 1198.85i | −0.399915 | + | 1.21464i | ||||
\(988\) | 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 | ||||||||
\(993\) | 41.3511 | + | 13.6147i | 0.0416426 | + | 0.0137107i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1018.21 | 1.02127 | 0.510635 | − | 0.859797i | \(-0.329410\pi\) | ||||
0.510635 | + | 0.859797i | \(0.329410\pi\) | |||||||
\(998\) | 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 | 1200.3.l.y.401.12 | 12 | ||
3.2 | odd | 2 | inner | 1200.3.l.y.401.11 | 12 | ||
4.3 | odd | 2 | 600.3.l.g.401.1 | 12 | |||
5.2 | odd | 4 | 240.3.c.e.209.7 | 12 | |||
5.3 | odd | 4 | 240.3.c.e.209.6 | 12 | |||
5.4 | even | 2 | inner | 1200.3.l.y.401.1 | 12 | ||
12.11 | even | 2 | 600.3.l.g.401.2 | 12 | |||
15.2 | even | 4 | 240.3.c.e.209.5 | 12 | |||
15.8 | even | 4 | 240.3.c.e.209.8 | 12 | |||
15.14 | odd | 2 | inner | 1200.3.l.y.401.2 | 12 | ||
20.3 | even | 4 | 120.3.c.a.89.7 | yes | 12 | ||
20.7 | even | 4 | 120.3.c.a.89.6 | yes | 12 | ||
20.19 | odd | 2 | 600.3.l.g.401.12 | 12 | |||
40.3 | even | 4 | 960.3.c.k.449.6 | 12 | |||
40.13 | odd | 4 | 960.3.c.j.449.7 | 12 | |||
40.27 | even | 4 | 960.3.c.k.449.7 | 12 | |||
40.37 | odd | 4 | 960.3.c.j.449.6 | 12 | |||
60.23 | odd | 4 | 120.3.c.a.89.5 | ✓ | 12 | ||
60.47 | odd | 4 | 120.3.c.a.89.8 | yes | 12 | ||
60.59 | even | 2 | 600.3.l.g.401.11 | 12 | |||
120.53 | even | 4 | 960.3.c.j.449.5 | 12 | |||
120.77 | even | 4 | 960.3.c.j.449.8 | 12 | |||
120.83 | odd | 4 | 960.3.c.k.449.8 | 12 | |||
120.107 | odd | 4 | 960.3.c.k.449.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.3.c.a.89.5 | ✓ | 12 | 60.23 | odd | 4 | ||
120.3.c.a.89.6 | yes | 12 | 20.7 | even | 4 | ||
120.3.c.a.89.7 | yes | 12 | 20.3 | even | 4 | ||
120.3.c.a.89.8 | yes | 12 | 60.47 | odd | 4 | ||
240.3.c.e.209.5 | 12 | 15.2 | even | 4 | |||
240.3.c.e.209.6 | 12 | 5.3 | odd | 4 | |||
240.3.c.e.209.7 | 12 | 5.2 | odd | 4 | |||
240.3.c.e.209.8 | 12 | 15.8 | even | 4 | |||
600.3.l.g.401.1 | 12 | 4.3 | odd | 2 | |||
600.3.l.g.401.2 | 12 | 12.11 | even | 2 | |||
600.3.l.g.401.11 | 12 | 60.59 | even | 2 | |||
600.3.l.g.401.12 | 12 | 20.19 | odd | 2 | |||
960.3.c.j.449.5 | 12 | 120.53 | even | 4 | |||
960.3.c.j.449.6 | 12 | 40.37 | odd | 4 | |||
960.3.c.j.449.7 | 12 | 40.13 | odd | 4 | |||
960.3.c.j.449.8 | 12 | 120.77 | even | 4 | |||
960.3.c.k.449.5 | 12 | 120.107 | odd | 4 | |||
960.3.c.k.449.6 | 12 | 40.3 | even | 4 | |||
960.3.c.k.449.7 | 12 | 40.27 | even | 4 | |||
960.3.c.k.449.8 | 12 | 120.83 | odd | 4 | |||
1200.3.l.y.401.1 | 12 | 5.4 | even | 2 | inner | ||
1200.3.l.y.401.2 | 12 | 15.14 | odd | 2 | inner | ||
1200.3.l.y.401.11 | 12 | 3.2 | odd | 2 | inner | ||
1200.3.l.y.401.12 | 12 | 1.1 | even | 1 | trivial |