Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,4,Mod(17,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.bc (of order \(6\), degree \(2\), 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: | \(19.8246417619\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} - x^{14} - 2 x^{13} + 9 x^{12} - 24 x^{11} + 714 x^{10} - 1940 x^{9} - 2834 x^{8} + \cdots + 43046721 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{11} \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 257.5 | ||
Root | \(-0.0204843 - 2.99993i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.257 |
Dual form | 336.4.bc.e.17.5 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | 0.0354799 | + | 5.19603i | 0.00682811 | + | 0.999977i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.27257 | − | 9.13236i | 0.471593 | − | 0.816823i | −0.527879 | − | 0.849320i | \(-0.677012\pi\) |
0.999472 | + | 0.0324964i | \(0.0103457\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −17.7029 | − | 5.44135i | −0.955865 | − | 0.293806i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −26.9975 | + | 0.368709i | −0.999907 | + | 0.0136559i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 26.6918 | − | 15.4105i | 0.731626 | − | 0.422405i | −0.0873906 | − | 0.996174i | \(-0.527853\pi\) |
0.819017 | + | 0.573770i | \(0.194519\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 19.8400i | 0.423280i | 0.977348 | + | 0.211640i | \(0.0678804\pi\) | ||||
−0.977348 | + | 0.211640i | \(0.932120\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 47.6391 | + | 27.0724i | 0.820025 | + | 0.466005i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 46.3453 | + | 80.2724i | 0.661199 | + | 1.14523i | 0.980301 | + | 0.197510i | \(0.0632854\pi\) |
−0.319102 | + | 0.947720i | \(0.603381\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 118.901 | + | 68.6474i | 1.43567 | + | 0.828884i | 0.997545 | − | 0.0700296i | \(-0.0223094\pi\) |
0.438125 | + | 0.898914i | \(0.355643\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 27.6454 | − | 92.1777i | 0.287272 | − | 0.957849i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 37.6697 | + | 21.7486i | 0.341508 | + | 0.197170i | 0.660939 | − | 0.750440i | \(-0.270158\pi\) |
−0.319431 | + | 0.947610i | \(0.603492\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.89995 | + | 11.9511i | 0.0551996 | + | 0.0956085i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.87369 | − | 140.267i | −0.0204831 | − | 0.999790i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 134.318i | 0.860079i | 0.902810 | + | 0.430039i | \(0.141500\pi\) | ||||
−0.902810 | + | 0.430039i | \(0.858500\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −144.963 | + | 83.6945i | −0.839876 | + | 0.484903i | −0.857222 | − | 0.514947i | \(-0.827812\pi\) |
0.0173460 | + | 0.999850i | \(0.494478\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 81.0206 | + | 138.145i | 0.427390 | + | 0.728725i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −143.032 | + | 132.979i | −0.690767 | + | 0.642216i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 191.747 | − | 332.115i | 0.851972 | − | 1.47566i | −0.0274532 | − | 0.999623i | \(-0.508740\pi\) |
0.879426 | − | 0.476036i | \(-0.157927\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −103.089 | + | 0.703923i | −0.423270 | + | 0.00289020i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 107.887 | 0.410954 | 0.205477 | − | 0.978662i | \(-0.434125\pi\) | ||||
0.205477 | + | 0.978662i | \(0.434125\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 285.480 | 1.01245 | 0.506225 | − | 0.862402i | \(-0.331041\pi\) | ||||
0.506225 | + | 0.862402i | \(0.331041\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −138.979 | + | 248.495i | −0.460395 | + | 0.823187i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −120.906 | + | 209.416i | −0.375234 | + | 0.649924i | −0.990362 | − | 0.138503i | \(-0.955771\pi\) |
0.615128 | + | 0.788427i | \(0.289104\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 283.783 | + | 192.655i | 0.827357 | + | 0.561677i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −415.453 | + | 243.660i | −1.14069 | + | 0.669003i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −432.694 | + | 249.816i | −1.12142 | + | 0.647451i | −0.941762 | − | 0.336279i | \(-0.890831\pi\) |
−0.179655 | + | 0.983730i | \(0.557498\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 325.013i | − | 0.796813i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −352.476 | + | 620.248i | −0.819062 | + | 1.44130i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 366.212 | + | 634.299i | 0.808081 | + | 1.39964i | 0.914191 | + | 0.405284i | \(0.132827\pi\) |
−0.106110 | + | 0.994354i | \(0.533839\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −265.207 | − | 153.117i | −0.556661 | − | 0.321388i | 0.195143 | − | 0.980775i | \(-0.437483\pi\) |
−0.751804 | + | 0.659387i | \(0.770816\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 479.939 | + | 140.376i | 0.959788 | + | 0.280725i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 181.187 | + | 104.608i | 0.345745 | + | 0.199616i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 280.049 | + | 485.060i | 0.510649 | + | 0.884470i | 0.999924 | + | 0.0123404i | \(0.00392817\pi\) |
−0.489275 | + | 0.872130i | \(0.662739\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −111.670 | + | 196.505i | −0.194833 | + | 0.342846i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 74.2161i | 0.124054i | 0.998074 | + | 0.0620270i | \(0.0197565\pi\) | ||||
−0.998074 | + | 0.0620270i | \(0.980244\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 141.409 | − | 81.6426i | 0.226722 | − | 0.130898i | −0.382337 | − | 0.924023i | \(-0.624881\pi\) |
0.609059 | + | 0.793125i | \(0.291547\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −61.8533 | + | 36.2764i | −0.0952294 | + | 0.0558512i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −556.376 | + | 127.571i | −0.823441 | + | 0.188806i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 437.160 | − | 757.183i | 0.622586 | − | 1.07835i | −0.366416 | − | 0.930451i | \(-0.619415\pi\) |
0.989002 | − | 0.147900i | \(-0.0472515\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 728.728 | − | 19.9084i | 0.999627 | − | 0.0273093i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −406.600 | −0.537712 | −0.268856 | − | 0.963180i | \(-0.586646\pi\) | ||||
−0.268856 | + | 0.963180i | \(0.586646\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 977.435 | 1.24727 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −697.922 | + | 4.76560i | −0.860059 | + | 0.00587271i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 526.091 | − | 911.216i | 0.626579 | − | 1.08527i | −0.361655 | − | 0.932312i | \(-0.617788\pi\) |
0.988233 | − | 0.152954i | \(-0.0488786\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 107.957 | − | 351.226i | 0.124362 | − | 0.404598i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −440.023 | − | 750.264i | −0.490626 | − | 0.836546i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1253.83 | − | 723.897i | 1.35410 | − | 0.781793i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 243.235i | − | 0.254606i | −0.991864 | − | 0.127303i | \(-0.959368\pi\) | ||
0.991864 | − | 0.127303i | \(-0.0406320\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −714.930 | + | 425.887i | −0.725790 | + | 0.432356i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 106.008 | + | 183.612i | 0.104438 | + | 0.180892i | 0.913508 | − | 0.406820i | \(-0.133362\pi\) |
−0.809070 | + | 0.587712i | \(0.800029\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 742.977 | + | 428.958i | 0.710754 | + | 0.410354i | 0.811340 | − | 0.584574i | \(-0.198738\pi\) |
−0.100586 | + | 0.994928i | \(0.532072\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −696.038 | − | 738.481i | −0.646918 | − | 0.686366i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1860.36 | − | 1074.08i | −1.68082 | − | 0.970424i | −0.961115 | − | 0.276148i | \(-0.910942\pi\) |
−0.719708 | − | 0.694276i | \(-0.755725\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 621.510 | + | 1076.49i | 0.546145 | + | 0.945952i | 0.998534 | + | 0.0541307i | \(0.0172388\pi\) |
−0.452388 | + | 0.891821i | \(0.649428\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1732.48 | + | 984.539i | 1.48144 | + | 0.841877i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 193.701i | − | 0.161256i | −0.996744 | − | 0.0806278i | \(-0.974307\pi\) | ||
0.996744 | − | 0.0806278i | \(-0.0256925\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 397.233 | − | 229.342i | 0.322106 | − | 0.185968i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.31521 | − | 535.631i | −0.00578027 | − | 0.423240i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −383.654 | − | 1673.23i | −0.295542 | − | 1.28895i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −190.531 | + | 330.009i | −0.143149 | + | 0.247941i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.82782 | + | 560.584i | 0.00280604 | + | 0.410944i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1463.67 | 1.04731 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1010.51 | −0.706052 | −0.353026 | − | 0.935614i | \(-0.614847\pi\) | ||||
−0.353026 | + | 0.935614i | \(0.614847\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.1288 | + | 1483.36i | 0.00691312 | + | 1.01243i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 179.314 | − | 310.581i | 0.119593 | − | 0.207142i | −0.800013 | − | 0.599982i | \(-0.795174\pi\) |
0.919607 | + | 0.392841i | \(0.128508\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1731.35 | − | 1862.24i | −1.12878 | − | 1.21411i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1296.12 | − | 713.323i | −0.826312 | − | 0.454763i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1194.04 | + | 689.378i | −0.744625 | + | 0.429909i | −0.823748 | − | 0.566956i | \(-0.808121\pi\) |
0.0791238 | + | 0.996865i | \(0.474788\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 474.488i | − | 0.289536i | −0.989466 | − | 0.144768i | \(-0.953756\pi\) | ||
0.989466 | − | 0.144768i | \(-0.0462436\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1092.42 | − | 620.803i | −0.652471 | − | 0.370787i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 305.746 | + | 529.567i | 0.178795 | + | 0.309683i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1226.64 | + | 708.203i | 0.702533 | + | 0.405607i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −990.974 | + | 1481.38i | −0.556015 | + | 0.831173i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −519.125 | − | 299.717i | −0.285426 | − | 0.164791i | 0.350451 | − | 0.936581i | \(-0.386028\pi\) |
−0.635877 | + | 0.771790i | \(0.719361\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −997.588 | − | 1727.87i | −0.537633 | − | 0.931208i | −0.999031 | − | 0.0440145i | \(-0.985985\pi\) |
0.461398 | − | 0.887193i | \(-0.347348\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1280.80 | − | 2150.06i | −0.676776 | − | 1.13609i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1765.14i | 0.914707i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −765.966 | + | 442.231i | −0.389368 | + | 0.224802i | −0.681886 | − | 0.731458i | \(-0.738840\pi\) |
0.292518 | + | 0.956260i | \(0.405507\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1313.40 | − | 2239.43i | −0.655093 | − | 1.11697i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −548.520 | − | 589.988i | −0.268506 | − | 0.288805i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −338.492 | + | 586.286i | −0.162655 | + | 0.281727i | −0.935820 | − | 0.352478i | \(-0.885339\pi\) |
0.773165 | + | 0.634205i | \(0.218672\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1688.78 | − | 11.5314i | 0.796794 | − | 0.00544072i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3718.74 | 1.72314 | 0.861571 | − | 0.507637i | \(-0.169481\pi\) | ||||
0.861571 | + | 0.507637i | \(0.169481\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1803.37 | 0.820834 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3235.34 | − | 1809.47i | −1.44686 | − | 0.809202i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1318.97 | − | 2284.52i | 0.579650 | − | 1.00398i | −0.415869 | − | 0.909425i | \(-0.636523\pi\) |
0.995519 | − | 0.0945591i | \(-0.0301441\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −57.1190 | − | 249.113i | −0.0246731 | − | 0.107607i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3282.84 | + | 1925.36i | −1.39409 | + | 0.817619i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2861.56 | + | 1652.12i | −1.19488 | + | 0.689862i | −0.959409 | − | 0.282020i | \(-0.908996\pi\) |
−0.235468 | + | 0.971882i | \(0.575662\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 417.941i | − | 0.171631i | −0.996311 | − | 0.0858157i | \(-0.972650\pi\) | ||
0.996311 | − | 0.0858157i | \(-0.0273496\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 786.193 | − | 1383.46i | 0.317580 | − | 0.558842i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2022.00 | − | 3502.20i | −0.803569 | − | 1.39182i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2474.08 | + | 1428.41i | 0.967501 | + | 0.558587i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −712.368 | + | 2498.76i | −0.274165 | + | 0.961683i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 920.494 | + | 531.447i | 0.348715 | + | 0.201331i | 0.664119 | − | 0.747627i | \(-0.268807\pi\) |
−0.315404 | + | 0.948957i | \(0.602140\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1945.03 | − | 3368.89i | −0.725420 | − | 1.25646i | −0.958801 | − | 0.284079i | \(-0.908312\pi\) |
0.233380 | − | 0.972386i | \(-0.425021\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −537.118 | + | 945.162i | −0.197250 | + | 0.347100i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3227.57i | 1.16728i | 0.812011 | + | 0.583642i | \(0.198373\pi\) | ||||
−0.812011 | + | 0.583642i | \(0.801627\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2398.78 | − | 1384.94i | 0.854497 | − | 0.493344i | −0.00766855 | − | 0.999971i | \(-0.502441\pi\) |
0.862166 | + | 0.506626i | \(0.169108\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2510.45 | + | 1472.36i | −0.880963 | + | 0.516676i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 730.874 | − | 2377.82i | 0.252696 | − | 0.822119i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 568.842 | − | 985.263i | 0.193803 | − | 0.335677i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1025.01 | − | 573.269i | −0.344169 | − | 0.192488i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4231.58 | 1.40050 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1978.76 | 0.645610 | 0.322805 | − | 0.946465i | \(-0.395374\pi\) | ||||
0.322805 | + | 0.946465i | \(0.395374\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −385.629 | + | 2.63318i | −0.124051 | + | 0.000847053i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1505.22 | − | 2607.11i | 0.477464 | − | 0.826993i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3021.68 | − | 692.838i | 0.945275 | − | 0.216741i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 429.235 | + | 731.869i | 0.132443 | + | 0.225823i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1592.61 | + | 919.492i | −0.484753 | + | 0.279872i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 2434.70i | − | 0.731120i | −0.930788 | − | 0.365560i | \(-0.880878\pi\) | ||
0.930788 | − | 0.365560i | \(-0.119122\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −190.688 | − | 320.105i | −0.0565001 | − | 0.0948458i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −165.862 | − | 287.281i | −0.0484961 | − | 0.0839977i | 0.840758 | − | 0.541411i | \(-0.182110\pi\) |
−0.889254 | + | 0.457413i | \(0.848776\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1842.29 | + | 1063.65i | 0.531624 | + | 0.306933i | 0.741677 | − | 0.670757i | \(-0.234031\pi\) |
−0.210054 | + | 0.977690i | \(0.567364\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −682.603 | − | 2886.42i | −0.194424 | − | 0.822132i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −809.394 | − | 467.304i | −0.227576 | − | 0.131391i | 0.381877 | − | 0.924213i | \(-0.375278\pi\) |
−0.609453 | + | 0.792822i | \(0.708611\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1274.97 | + | 2208.32i | 0.353915 | + | 0.613000i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3949.86 | + | 2244.63i | 1.08258 | + | 0.615209i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1923.73i | 0.520651i | 0.965521 | + | 0.260325i | \(0.0838298\pi\) | ||||
−0.965521 | + | 0.260325i | \(0.916170\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2846.13 | − | 1643.22i | 0.760729 | − | 0.439207i | −0.0688286 | − | 0.997629i | \(-0.521926\pi\) |
0.829557 | + | 0.558422i | \(0.188593\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 129.300 | + | 3785.79i | 0.0341342 | + | 0.999417i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3255.67 | − | 1575.82i | 0.848967 | − | 0.410921i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1361.97 | + | 2359.00i | −0.350850 | + | 0.607690i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.4261 | − | 2112.70i | −0.00367156 | − | 0.537700i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4303.94 | −1.08232 | −0.541160 | − | 0.840919i | \(-0.682015\pi\) | ||||
−0.541160 | + | 0.840919i | \(0.682015\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1340.63 | 0.333142 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 34.6793 | + | 5078.78i | 0.00851648 | + | 1.24724i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2345.95 | + | 4063.31i | −0.569403 | + | 0.986235i | 0.427222 | + | 0.904147i | \(0.359492\pi\) |
−0.996625 | + | 0.0820884i | \(0.973841\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5201.63 | + | 4836.03i | −1.24793 | + | 1.16022i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −49.5244 | − | 3626.26i | −0.0117451 | − | 0.859999i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −911.918 | + | 526.496i | −0.213807 | + | 0.123442i | −0.603079 | − | 0.797681i | \(-0.706060\pi\) |
0.389272 | + | 0.921123i | \(0.372726\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5268.69i | 1.22133i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4753.37 | + | 2701.25i | 1.08952 | + | 0.619154i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1327.49 | + | 2299.28i | 0.300887 | + | 0.521151i | 0.976337 | − | 0.216255i | \(-0.0693841\pi\) |
−0.675450 | + | 0.737405i | \(0.736051\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2347.45 | − | 1355.30i | −0.526189 | − | 0.303795i | 0.213274 | − | 0.976992i | \(-0.431587\pi\) |
−0.739463 | + | 0.673197i | \(0.764921\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1828.81 | + | 548.485i | 0.405438 | + | 0.121596i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 368.345 | + | 212.664i | 0.0807710 | + | 0.0466331i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −960.218 | − | 1663.15i | −0.208281 | − | 0.360754i | 0.742892 | − | 0.669411i | \(-0.233454\pi\) |
−0.951173 | + | 0.308658i | \(0.900120\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3882.78 | − | 2312.99i | 0.833176 | − | 0.496327i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5730.99i | 1.21666i | 0.793683 | + | 0.608331i | \(0.208161\pi\) | ||||
−0.793683 | + | 0.608331i | \(0.791839\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1588.75 | − | 917.265i | 0.333715 | − | 0.192670i | −0.323774 | − | 0.946134i | \(-0.604952\pi\) |
0.657489 | + | 0.753464i | \(0.271619\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3805.88 | + | 6489.24i | 0.791020 | + | 1.34873i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1909.91 | − | 587.051i | −0.392817 | − | 0.120741i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1839.27 | + | 3185.71i | −0.374368 | + | 0.648424i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1263.86 | − | 8.62995i | 0.254600 | − | 0.00173848i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1206.83 | −0.240627 | −0.120314 | − | 0.992736i | \(-0.538390\pi\) | ||||
−0.120314 | + | 0.992736i | \(0.538390\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7723.53 | 1.52434 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2238.29 | − | 3699.69i | −0.437302 | − | 0.722821i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −431.494 | + | 747.369i | −0.0834580 | + | 0.144553i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5053.82 | − | 1553.40i | −0.967765 | − | 0.297463i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −950.293 | + | 557.338i | −0.180175 | + | 0.105671i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2796.65 | + | 1614.65i | −0.525035 | + | 0.303129i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 5508.71i | − | 1.02410i | −0.858955 | − | 0.512050i | \(-0.828886\pi\) | ||
0.858955 | − | 0.512050i | \(-0.171114\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2202.52 | + | 3875.75i | −0.405491 | + | 0.713539i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2114.51 | − | 3662.44i | −0.385540 | − | 0.667775i | 0.606304 | − | 0.795233i | \(-0.292652\pi\) |
−0.991844 | + | 0.127458i | \(0.959318\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4672.64 | − | 2697.75i | −0.843813 | − | 0.487176i | 0.0147455 | − | 0.999891i | \(-0.495306\pi\) |
−0.858558 | + | 0.512716i | \(0.828640\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3812.48 | − | 3642.84i | 0.681932 | − | 0.651590i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6169.57 | − | 3562.00i | −1.09312 | − | 0.631111i | −0.158711 | − | 0.987325i | \(-0.550734\pi\) |
−0.934404 | + | 0.356214i | \(0.884067\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2069.92 | + | 3585.20i | 0.363301 | + | 0.629256i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5514.96 | − | 9704.62i | 0.958925 | − | 1.68741i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12725.9i | 2.19223i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −237.110 | + | 136.895i | −0.0404692 | + | 0.0233649i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5571.41 | + | 3267.58i | −0.942200 | + | 0.552592i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3279.89 | − | 3049.37i | 0.549624 | − | 0.510994i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 886.224 | − | 1534.99i | 0.147164 | − | 0.254896i | −0.783014 | − | 0.622004i | \(-0.786319\pi\) |
0.930178 | + | 0.367108i | \(0.119652\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5054.23 | + | 9036.97i | −0.831741 | + | 1.48716i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5906.32 | 0.963275 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7800.94 | 1.26096 | 0.630481 | − | 0.776205i | \(-0.282858\pi\) | ||||
0.630481 | + | 0.776205i | \(0.282858\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1006.48 | − | 6.87250i | 0.161252 | − | 0.00110107i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2579.56 | + | 4467.92i | −0.409650 | + | 0.709535i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3975.47 | − | 4954.72i | −0.625818 | − | 0.779969i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1205.76 | + | 2055.90i | 0.188163 | + | 0.320828i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6209.38 | + | 3584.99i | −0.960625 | + | 0.554617i | −0.896365 | − | 0.443316i | \(-0.853802\pi\) |
−0.0642596 | + | 0.997933i | \(0.520469\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 5543.44i | − | 0.850240i | −0.905137 | − | 0.425120i | \(-0.860232\pi\) | ||
0.905137 | − | 0.425120i | \(-0.139768\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2782.90 | − | 57.0142i | 0.423191 | − | 0.00867006i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.4669 | − | 26.7895i | −0.00233207 | − | 0.00403926i | 0.864857 | − | 0.502018i | \(-0.167409\pi\) |
−0.867189 | + | 0.497979i | \(0.834076\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 677.768 | + | 391.310i | 0.101330 | + | 0.0585030i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8680.56 | − | 2052.84i | 1.28690 | − | 0.304336i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5694.34 | + | 3287.63i | 0.837147 | + | 0.483327i | 0.856294 | − | 0.516489i | \(-0.172761\pi\) |
−0.0191462 | + | 0.999817i | \(0.506095\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5995.44 | + | 10384.4i | 0.874099 | + | 1.51398i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1721.50 | − | 978.296i | −0.248912 | − | 0.141452i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 1721.87i | − | 0.246922i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2095.30 | + | 1209.72i | −0.298021 | + | 0.172062i | −0.641553 | − | 0.767078i | \(-0.721710\pi\) |
0.343533 | + | 0.939141i | \(0.388376\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2912.68 | + | 39.7789i | −0.410916 | + | 0.00561195i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9019.27 | − | 2068.02i | 1.26215 | − | 0.289397i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4895.66 | + | 8479.53i | −0.679591 | + | 1.17709i | 0.295513 | + | 0.955339i | \(0.404510\pi\) |
−0.975104 | + | 0.221748i | \(0.928824\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 51.9307 | + | 7605.25i | 0.00715117 | + | 1.04729i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2664.88 | −0.364054 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12660.9 | −1.71595 | −0.857977 | − | 0.513689i | \(-0.828279\pi\) | ||||
−0.857977 | + | 0.513689i | \(0.828279\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −35.8529 | − | 5250.66i | −0.00482100 | − | 0.706035i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4549.42 | + | 7879.82i | −0.606957 | + | 1.05128i | 0.384782 | + | 0.923007i | \(0.374276\pi\) |
−0.991739 | + | 0.128272i | \(0.959057\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1768.51 | + | 5753.66i | −0.234108 | + | 0.761645i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7707.25 | + | 105.259i | −1.01236 | + | 0.0138259i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8450.00 | − | 4878.61i | 1.10137 | − | 0.635875i | 0.164787 | − | 0.986329i | \(-0.447306\pi\) |
0.936580 | + | 0.350454i | \(0.113973\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4031.78i | 0.521473i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1620.15 | + | 920.701i | 0.207954 | + | 0.118176i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4609.91 | − | 7984.61i | −0.587215 | − | 1.01709i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7069.17 | − | 4081.39i | −0.893681 | − | 0.515967i | −0.0185365 | − | 0.999828i | \(-0.505901\pi\) |
−0.875145 | + | 0.483861i | \(0.839234\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9614.82 | − | 9062.23i | 1.20637 | − | 1.13704i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8885.22 | + | 5129.88i | 1.10650 | + | 0.638838i | 0.937921 | − | 0.346850i | \(-0.112749\pi\) |
0.168579 | + | 0.985688i | \(0.446082\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1660.50 | − | 2876.08i | −0.205250 | − | 0.355503i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3660.46 | − | 6759.98i | 0.449111 | − | 0.829398i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 11819.7i | − | 1.43951i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1795.47 | + | 1036.61i | −0.217067 | + | 0.125323i | −0.604591 | − | 0.796536i | \(-0.706664\pi\) |
0.387525 | + | 0.921859i | \(0.373330\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3624.40 | − | 6179.80i | −0.434984 | − | 0.741672i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3031.57 | − | 13221.6i | −0.361196 | − | 1.57528i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2143.83 | + | 3713.22i | −0.253581 | + | 0.439216i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2465.45 | − | 16.8348i | 0.289530 | − | 0.00197699i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11576.2 | 1.34973 | 0.674863 | − | 0.737943i | \(-0.264203\pi\) | ||||
0.674863 | + | 0.737943i | \(0.264203\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1493.04 | −0.172842 | −0.0864208 | − | 0.996259i | \(-0.527543\pi\) | ||||
−0.0864208 | + | 0.996259i | \(0.527543\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3186.95 | − | 5698.28i | 0.366324 | − | 0.654988i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −639.560 | + | 1107.75i | −0.0729958 | + | 0.126432i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3861.76 | + | 4153.70i | 0.437667 | + | 0.470754i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2740.80 | + | 1607.45i | −0.308455 | + | 0.180906i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3354.19 | + | 1936.54i | −0.374862 | + | 0.216427i | −0.675580 | − | 0.737286i | \(-0.736107\pi\) |
0.300719 | + | 0.953713i | \(0.402774\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 5450.01i | − | 0.604875i | −0.953169 | − | 0.302437i | \(-0.902200\pi\) | ||
0.953169 | − | 0.302437i | \(-0.0978003\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3636.32 | + | 6398.81i | −0.400801 | + | 0.705286i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2985.98 | + | 5171.86i | 0.326862 | + | 0.566141i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2350.20 | + | 1356.89i | 0.255510 | + | 0.147519i | 0.622284 | − | 0.782791i | \(-0.286205\pi\) |
−0.366775 | + | 0.930310i | \(0.619538\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7732.47 | − | 5096.57i | −0.834950 | − | 0.550326i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9583.65 | − | 5533.13i | −1.02784 | − | 0.593424i | −0.111475 | − | 0.993767i | \(-0.535557\pi\) |
−0.916365 | + | 0.400344i | \(0.868891\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5547.70 | − | 9608.90i | −0.590980 | − | 1.02361i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1538.92 | − | 2708.03i | 0.162838 | − | 0.286544i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3599.14i | 0.378294i | 0.981949 | + | 0.189147i | \(0.0605722\pi\) | ||||
−0.981949 | + | 0.189147i | \(0.939428\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2879.70 | − | 1662.60i | 0.300665 | − | 0.173589i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8942.69 | − | 5244.81i | 0.927515 | − | 0.543979i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2638.31 | − | 2837.76i | −0.271837 | − | 0.292388i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4157.54 | + | 7201.08i | −0.425562 | + | 0.737094i | −0.996473 | − | 0.0839176i | \(-0.973257\pi\) |
0.570911 | + | 0.821012i | \(0.306590\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11126.4 | − | 6731.38i | 1.13145 | − | 0.684518i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5672.08 | −0.573048 | −0.286524 | − | 0.958073i | \(-0.592500\pi\) | ||||
−0.286524 | + | 0.958073i | \(0.592500\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6332.06 | −0.635585 | −0.317792 | − | 0.948160i | \(-0.602942\pi\) | ||||
−0.317792 | + | 0.948160i | \(0.602942\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9171.73 | + | 62.6271i | −0.914686 | + | 0.00624572i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6469.64 | − | 11205.7i | 0.641069 | − | 1.11036i | −0.344126 | − | 0.938924i | \(-0.611825\pi\) |
0.985195 | − | 0.171440i | \(-0.0548420\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2318.30 | − | 10110.8i | −0.228249 | − | 0.995466i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2325.02 | − | 3964.29i | −0.227455 | − | 0.387824i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7619.99 | − | 4399.40i | 0.740735 | − | 0.427663i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1894.66i | 0.183016i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11589.5 | − | 6903.94i | 1.11247 | − | 0.662704i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1051.99 | + | 1822.10i | 0.100348 | + | 0.173808i | 0.911828 | − | 0.410572i | \(-0.134671\pi\) |
−0.811480 | + | 0.584380i | \(0.801338\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6589.18 | + | 3804.26i | 0.624617 | + | 0.360623i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3046.13 | − | 2871.06i | 0.286964 | − | 0.270472i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2221.31 | − | 1282.47i | −0.207968 | − | 0.120070i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6295.98 | − | 10905.0i | −0.585828 | − | 1.01468i | −0.994772 | − | 0.102124i | \(-0.967436\pi\) |
0.408944 | − | 0.912559i | \(-0.365897\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3058.37 | − | 1738.01i | −0.282831 | − | 0.160727i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1372.36i | 0.126138i | 0.998009 | + | 0.0630689i | \(0.0200888\pi\) | ||||
−0.998009 | + | 0.0630689i | \(0.979911\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10782.0 | + | 6225.02i | −0.984988 | + | 0.568683i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 119.835 | + | 8774.52i | 0.0108812 | + | 0.796738i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 403.836 | − | 1313.84i | 0.0364477 | − | 0.118579i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4588.75 | + | 7947.95i | −0.411665 | + | 0.713025i | −0.995072 | − | 0.0991554i | \(-0.968386\pi\) |
0.583407 | + | 0.812180i | \(0.301719\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 131.941 | + | 19322.7i | 0.0117658 | + | 1.72310i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1025.01 | 0.0908605 | 0.0454302 | − | 0.998968i | \(-0.485534\pi\) | ||||
0.0454302 | + | 0.998968i | \(0.485534\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2235.75 | 0.197009 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 63.9835 | + | 9370.38i | 0.00560474 | + | 0.820815i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2308.88 | − | 3999.09i | 0.201059 | − | 0.348245i | −0.747811 | − | 0.663912i | \(-0.768895\pi\) |
0.948870 | + | 0.315667i | \(0.102228\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2947.59 | + | 675.851i | −0.255174 | + | 0.0585086i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9287.27 | − | 16875.1i | 0.799304 | − | 1.45235i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7834.80 | − | 4523.42i | 0.670374 | − | 0.387040i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7452.92i | 0.634002i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11917.3 | + | 6772.36i | 1.00792 | + | 0.572781i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6012.38 | − | 10413.7i | −0.505580 | − | 0.875690i | −0.999979 | − | 0.00645499i | \(-0.997945\pi\) |
0.494399 | − | 0.869235i | \(-0.335388\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2045.16 | − | 1180.78i | −0.170992 | − | 0.0987222i | 0.412062 | − | 0.911156i | \(-0.364809\pi\) |
−0.583053 | + | 0.812434i | \(0.698142\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1292.37 | − | 305.630i | 0.107436 | − | 0.0254073i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13436.7 | − | 7757.69i | −1.11065 | − | 0.641234i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5137.49 | − | 8898.40i | −0.422248 | − | 0.731355i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10120.7 | − | 16989.4i | −0.827119 | − | 1.38847i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2140.48i | 0.173949i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19617.8 | + | 11326.3i | −1.58533 | + | 0.915291i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8686.00 | − | 14810.1i | −0.698005 | − | 1.19014i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10543.6 | + | 769.067i | 0.842571 | + | 0.0614583i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1479.47 | − | 2562.52i | 0.117574 | − | 0.203644i | −0.801232 | − | 0.598354i | \(-0.795822\pi\) |
0.918806 | + | 0.394710i | \(0.129155\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2171.63 | − | 14.8285i | 0.171627 | − | 0.00117192i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13107.8 | 1.03023 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8615.33 | 0.673427 | 0.336714 | − | 0.941607i | \(-0.390685\pi\) | ||||
0.336714 | + | 0.941607i | \(0.390685\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7216.38 | + | 4036.00i | 0.560997 | + | 0.313756i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9220.61 | + | 15970.6i | −0.712906 | + | 1.23479i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11859.1 | + | 11025.6i | −0.911934 | + | 0.847839i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 18125.8 | − | 10630.6i | 1.38630 | − | 0.813054i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20665.9 | + | 11931.5i | −1.57207 | + | 0.907635i | −0.576155 | + | 0.817340i | \(0.695448\pi\) |
−0.995915 | + | 0.0902950i | \(0.971219\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5663.94i | 0.428550i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7334.29 | + | 12906.1i | −0.551968 | + | 0.971292i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5552.10 | − | 9616.52i | −0.415618 | − | 0.719872i | 0.579875 | − | 0.814705i | \(-0.303101\pi\) |
−0.995493 | + | 0.0948337i | \(0.969768\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1768.95 | − | 1021.30i | −0.131717 | − | 0.0760470i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13008.9 | − | 3612.83i | −0.963532 | − | 0.267592i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20144.7 | − | 11630.5i | −1.48420 | − | 0.856903i | −0.484361 | − | 0.874868i | \(-0.660948\pi\) |
−0.999839 | + | 0.0179647i | \(0.994281\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1521.55 | − | 2635.40i | −0.111514 | − | 0.193149i | 0.804867 | − | 0.593456i | \(-0.202237\pi\) |
−0.916381 | + | 0.400307i | \(0.868903\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2728.76 | + | 4801.77i | −0.198945 | + | 0.350082i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 600.258i | 0.0435348i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8570.32 | − | 4948.08i | 0.618349 | − | 0.357004i | −0.157877 | − | 0.987459i | \(-0.550465\pi\) |
0.776226 | + | 0.630455i | \(0.217132\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 17435.8 | − | 10226.0i | 1.25148 | − | 0.733983i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7197.98 | + | 2212.45i | 0.513980 | + | 0.157983i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7699.60 | + | 13336.1i | −0.546972 | + | 0.947384i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4930.15 | − | 2757.35i | −0.348439 | − | 0.194876i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14853.9 | 1.04444 | 0.522219 | − | 0.852812i | \(-0.325104\pi\) | ||||
0.522219 | + | 0.852812i | \(0.325104\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22981.7 | −1.60771 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16770.6 | + | 114.514i | −1.16726 | + | 0.00797034i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2072.42 | − | 3589.54i | 0.143515 | − | 0.248575i | −0.785303 | − | 0.619111i | \(-0.787493\pi\) |
0.928818 | + | 0.370537i | \(0.120826\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17303.4 | − | 5318.57i | −1.19222 | − | 0.366454i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7281.28 | + | 12415.0i | 0.499167 | + | 0.851109i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4311.66 | + | 2489.34i | −0.294107 | + | 0.169802i | −0.639792 | − | 0.768548i | \(-0.720980\pi\) |
0.345686 | + | 0.938350i | \(0.387646\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6641.45i | 0.450766i | 0.974270 | + | 0.225383i | \(0.0723633\pi\) | ||||
−0.974270 | + | 0.225383i | \(0.927637\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7739.48 | − | 12992.1i | −0.522680 | − | 0.877414i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2009.18 | + | 3480.00i | 0.135016 | + | 0.233854i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6658.36 | + | 3844.21i | 0.445230 | + | 0.257054i | 0.705814 | − | 0.708398i | \(-0.250582\pi\) |
−0.260583 | + | 0.965451i | \(0.583915\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12381.2 | + | 3713.28i | 0.823826 | + | 0.247077i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4154.82 | − | 2398.79i | −0.275100 | − | 0.158829i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4708.37 | − | 8155.14i | −0.310227 | − | 0.537330i | 0.668184 | − | 0.743996i | \(-0.267072\pi\) |
−0.978411 | + | 0.206666i | \(0.933739\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5139.64 | + | 2920.76i | 0.336992 | + | 0.191507i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9209.91i | 0.600935i | 0.953792 | + | 0.300468i | \(0.0971428\pi\) | ||||
−0.953792 | + | 0.300468i | \(0.902857\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8867.28 | − | 5119.53i | 0.575777 | − | 0.332425i | −0.183676 | − | 0.982987i | \(-0.558800\pi\) |
0.759454 | + | 0.650562i | \(0.225466\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2942.36 | − | 5346.31i | 0.190133 | − | 0.345475i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14271.6 | + | 13268.5i | −0.917782 | + | 0.853276i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6854.79 | − | 11872.8i | 0.438706 | − | 0.759862i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 150.136 | + | 21987.4i | 0.00956276 | + | 1.40047i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 35546.2 | 2.25329 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25041.7 | 1.57987 | 0.789934 | − | 0.613192i | \(-0.210115\pi\) | ||||
0.789934 | + | 0.613192i | \(0.210115\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 70.2063 | + | 10281.7i | 0.00440830 | + | 0.645595i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5328.00 | + | 9228.37i | −0.332969 | + | 0.576719i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3822.29 | + | 5630.27i | −0.237747 | + | 0.350203i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −27.3642 | − | 2003.65i | −0.00169407 | − | 0.124042i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 545.089 | − | 314.707i | 0.0335877 | − | 0.0193919i | −0.483112 | − | 0.875558i | \(-0.660494\pi\) |
0.516700 | + | 0.856167i | \(0.327160\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 11568.9i | − | 0.709538i | −0.934954 | − | 0.354769i | \(-0.884559\pi\) | ||
0.934954 | − | 0.354769i | \(-0.115441\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13600.0 | + | 7728.65i | 0.830234 | + | 0.471807i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9784.59 | + | 16947.4i | 0.594547 | + | 1.02979i | 0.993611 | + | 0.112862i | \(0.0360018\pi\) |
−0.399064 | + | 0.916923i | \(0.630665\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19549.8 | + | 11287.1i | 1.18243 | + | 0.682675i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3707.21 | + | 15676.1i | 0.223191 | + | 0.943773i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5834.29 | − | 3368.43i | −0.349638 | − | 0.201863i | 0.314888 | − | 0.949129i | \(-0.398033\pi\) |
−0.664526 | + | 0.747265i | \(0.731366\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1890.89 | − | 3275.12i | −0.112799 | − | 0.195373i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3787.59 | + | 2256.28i | −0.224913 | + | 0.133982i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3912.25i | 0.231259i | 0.993292 | + | 0.115629i | \(0.0368885\pi\) | ||||
−0.993292 | + | 0.115629i | \(0.963112\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24001.8 | − | 13857.5i | 1.41235 | − | 0.815420i | 0.416740 | − | 0.909026i | \(-0.363173\pi\) |
0.995609 | + | 0.0936057i | \(0.0298393\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4834.22 | − | 8242.61i | −0.283176 | − | 0.482830i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −26135.3 | + | 5992.54i | −1.52404 | + | 0.349445i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2921.24 | + | 5059.73i | −0.169581 | + | 0.293724i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12650.8 | − | 86.3830i | 0.731103 | − | 0.00499217i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9438.48 | −0.543023 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27462.5 | 1.57296 | 0.786479 | − | 0.617617i | \(-0.211902\pi\) | ||||
0.786479 | + | 0.617617i | \(0.211902\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1656.51 | − | 1002.18i | 0.0944578 | − | 0.0571464i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4757.18 | + | 8239.68i | −0.270064 | + | 0.467765i | −0.968878 | − | 0.247539i | \(-0.920378\pi\) |
0.698814 | + | 0.715303i | \(0.253712\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1323.53 | + | 4305.96i | −0.0748046 | + | 0.243369i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1486.83 | − | 872.014i | 0.0836646 | − | 0.0490685i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22760.4 | − | 13140.7i | 1.27511 | − | 0.736186i | 0.299166 | − | 0.954201i | \(-0.403292\pi\) |
0.975945 | + | 0.218015i | \(0.0699583\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14539.2i | 0.810969i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5461.37 | + | 9610.33i | −0.303296 | + | 0.533707i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4956.36 | − | 8584.67i | −0.274053 | − | 0.474673i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6698.34 | + | 3867.29i | 0.368765 | + | 0.212907i | 0.672919 | − | 0.739716i | \(-0.265040\pi\) |
−0.304154 | + | 0.952623i | \(0.598374\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 14973.7 | − | 3649.24i | 0.820786 | − | 0.200033i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4333.20 | − | 2501.77i | −0.236500 | − | 0.136543i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5000.05 | + | 8660.34i | 0.271722 | + | 0.470637i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2399.41 | − | 4222.22i | 0.129834 | − | 0.228468i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 16405.7i | − | 0.883929i | −0.897033 | − | 0.441964i | \(-0.854282\pi\) | ||
0.897033 | − | 0.441964i | \(-0.145718\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 45597.7 | − | 26325.9i | 2.44630 | − | 1.41237i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11429.3 | + | 6703.16i | −0.610569 | + | 0.358093i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −877.556 | − | 3827.29i | −0.0466816 | − | 0.203593i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5304.71 | − | 9188.03i | 0.280991 | − | 0.486691i | −0.690638 | − | 0.723201i | \(-0.742670\pi\) |
0.971629 | + | 0.236510i | \(0.0760035\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11523.0 | + | 20603.2i | −0.607803 | + | 1.08675i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7280.97 | −0.382432 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6448.26 | 0.337275 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9995.74 | + | 68.2536i | −0.520638 | + | 0.00355506i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10075.2 | − | 17450.8i | 0.522591 | − | 0.905153i | −0.477064 | − | 0.878869i | \(-0.658299\pi\) |
0.999654 | − | 0.0262848i | \(-0.00836768\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10818.7 | − | 11636.6i | −0.558821 | − | 0.601067i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8639.18 | + | 14730.3i | 0.444391 | + | 0.757712i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1605.25 | + | 926.790i | −0.0822309 | + | 0.0474760i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26758.5i | 1.36509i | 0.730846 | + | 0.682543i | \(0.239126\pi\) | ||||
−0.730846 | + | 0.682543i | \(0.760874\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19666.5 | + | 806.167i | −0.999161 | + | 0.0409575i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13230.7 | + | 22916.2i | 0.669431 | + | 1.15949i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7106.39 | + | 4102.88i | 0.358091 | + | 0.206744i | 0.668243 | − | 0.743943i | \(-0.267047\pi\) |
−0.310152 | + | 0.950687i | \(0.600380\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8303.54 | + | 16860.6i | 0.416709 | + | 0.846141i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14950.1 | + | 8631.42i | 0.747208 | + | 0.431401i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10324.9 | − | 17883.2i | −0.513946 | − | 0.890180i | −0.999869 | − | 0.0161788i | \(-0.994850\pi\) |
0.485923 | − | 0.874001i | \(-0.338483\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12305.8 | − | 6993.13i | −0.610072 | − | 0.346693i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 8375.29i | − | 0.413539i | −0.978390 | − | 0.206769i | \(-0.933705\pi\) | ||
0.978390 | − | 0.206769i | \(-0.0662950\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5474.25 | + | 3160.56i | −0.269210 | + | 0.155428i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10977.2 | − | 149.917i | 0.537662 | − | 0.00734294i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 27089.3 | + | 29137.2i | 1.32152 | + | 1.42143i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13298.8 | − | 23034.3i | 0.646181 | − | 1.11922i | −0.337847 | − | 0.941201i | \(-0.609699\pi\) |
0.984028 | − | 0.178016i | \(-0.0569680\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −152.703 | − | 22363.4i | −0.00739020 | − | 1.08230i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21039.4 | −1.01418 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26633.6 | −1.27875 | −0.639376 | − | 0.768894i | \(-0.720807\pi\) | ||||
−0.639376 | + | 0.768894i | \(0.720807\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 47.5655 | + | 6965.97i | 0.00227473 | + | 0.333134i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4243.87 | + | 7350.60i | −0.202155 | + | 0.350143i | −0.949223 | − | 0.314605i | \(-0.898128\pi\) |
0.747067 | + | 0.664748i | \(0.231461\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5144.96 | − | 22438.8i | −0.244116 | − | 1.06466i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −26388.3 | + | 360.389i | −1.24715 | + | 0.0170326i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12584.5 | + | 7265.67i | −0.592439 | + | 0.342045i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22673.5i | 1.06324i | 0.846984 | + | 0.531618i | \(0.178416\pi\) | ||||
−0.846984 | + | 0.531618i | \(0.821584\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21196.3 | − | 12045.5i | −0.990100 | − | 0.562656i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18141.2 | + | 31421.4i | 0.844103 | + | 1.46203i | 0.886398 | + | 0.462925i | \(0.153200\pi\) |
−0.0422941 | + | 0.999105i | \(0.513467\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2000.48 | − | 1154.98i | −0.0927217 | − | 0.0535329i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −25312.7 | − | 26856.2i | −1.16871 | − | 1.23998i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12827.9 | + | 7406.17i | 0.589994 | + | 0.340633i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1143.71 | + | 1980.96i | 0.0524009 | + | 0.0907611i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 18840.4 | − | 385.990i | 0.859898 | − | 0.0176170i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9326.77i | 0.424060i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1911.44 | − | 1103.57i | 0.0865763 | − | 0.0499849i | −0.456087 | − | 0.889935i | \(-0.650749\pi\) |
0.542663 | + | 0.839950i | \(0.317416\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2768.04 | − | 4719.67i | −0.124899 | − | 0.212959i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1054.00 | + | 3429.07i | −0.0473778 | + | 0.154139i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3037.86 | − | 5261.72i | 0.136037 | − | 0.235623i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −27376.3 | + | 186.933i | −1.22130 | + | 0.00833940i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −43496.3 | −1.93315 | −0.966574 | − | 0.256388i | \(-0.917467\pi\) | ||||
−0.966574 | + | 0.256388i | \(0.917467\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22413.7 | −0.992417 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13867.1 | + | 24794.5i | −0.611700 | + | 1.09372i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2516.31 | − | 4358.38i | 0.110584 | − | 0.191537i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8280.09 | + | 1898.54i | −0.362528 | + | 0.0831237i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11900.0 | + | 6979.26i | −0.519084 | + | 0.304438i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23156.7 | − | 13369.5i | 1.00636 | − | 0.581024i | 0.0962378 | − | 0.995358i | \(-0.469319\pi\) |
0.910125 | + | 0.414335i | \(0.135986\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43614.5i | 1.88842i | 0.329338 | + | 0.944212i | \(0.393174\pi\) | ||||
−0.329338 | + | 0.944212i | \(0.606826\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6958.89 | − | 12245.5i | 0.300195 | − | 0.528251i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3569.45 | + | 6182.47i | 0.153414 | + | 0.265721i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33943.9 | + | 19597.5i | 1.45354 | + | 0.839204i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2785.06 | + | 9522.02i | −0.118825 | + | 0.406259i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3199.70 | + | 1847.35i | 0.136017 | + | 0.0785297i | 0.566465 | − | 0.824086i | \(-0.308311\pi\) |
−0.430447 | + | 0.902616i | \(0.641644\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8733.70 | + | 15127.2i | 0.369912 | + | 0.640706i | 0.989551 | − | 0.144180i | \(-0.0460545\pi\) |
−0.619640 | + | 0.784887i | \(0.712721\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1091.94 | + | 1921.48i | −0.0460805 | + | 0.0810875i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37321.1i | 1.56926i | 0.619962 | + | 0.784632i | \(0.287148\pi\) | ||||
−0.619962 | + | 0.784632i | \(0.712852\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39701.3 | − | 22921.6i | 1.66331 | − | 0.960313i | 0.692193 | − | 0.721712i | \(-0.256645\pi\) |
0.971118 | − | 0.238601i | \(-0.0766887\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8607.69 | − | 5048.33i | 0.359323 | − | 0.210740i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2312.87 | + | 31708.6i | −0.0962020 | + | 1.31889i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19607.3 | − | 33960.9i | 0.812622 | − | 1.40750i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12156.1 | + | 20093.0i | 0.502004 | + | 0.829768i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11522.6 | −0.474141 | −0.237071 | − | 0.971492i | \(-0.576187\pi\) | ||||
−0.237071 | + | 0.971492i | \(0.576187\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6347.59 | 0.260264 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −29778.4 | + | 203.335i | −1.21663 | + | 0.00830750i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9508.41 | − | 16469.1i | 0.387100 | − | 0.670477i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5168.64 | − | 4805.36i | 0.209677 | − | 0.194940i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4822.51 | + | 8222.65i | 0.194945 | + | 0.332392i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14446.1 | − | 8340.46i | 0.581911 | − | 0.335966i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 44074.7i | − | 1.76915i | −0.466395 | − | 0.884577i | \(-0.654447\pi\) | ||
0.466395 | − | 0.884577i | \(-0.345553\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −33583.3 | + | 20005.7i | −1.34330 | + | 0.800211i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8037.61 | − | 13921.5i | −0.320373 | − | 0.554902i | 0.660192 | − | 0.751097i | \(-0.270475\pi\) |
−0.980565 | + | 0.196195i | \(0.937142\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16666.7 | − | 9622.52i | −0.662002 | − | 0.382207i | 0.131037 | − | 0.991377i | \(-0.458169\pi\) |
−0.793040 | + | 0.609170i | \(0.791503\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2982.57 | − | 9944.78i | 0.118056 | − | 0.393632i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10098.5 | + | 5830.35i | 0.398326 | + | 0.229974i | 0.685762 | − | 0.727826i | \(-0.259469\pi\) |
−0.287435 | + | 0.957800i | \(0.592803\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13908.7 | − | 24090.6i | −0.546718 | − | 0.946944i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16618.3 | − | 9443.87i | −0.650965 | − | 0.369931i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 26947.5i | − | 1.05193i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9623.61 | + | 5556.19i | −0.374378 | + | 0.216147i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 89.6830 | + | 6566.73i | 0.00347687 | + | 0.254582i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −25911.1 | − | 7964.32i | −1.00109 | − | 0.307707i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18913.9 | + | 32759.9i | −0.728254 | + | 1.26137i | 0.229367 | + | 0.973340i | \(0.426334\pi\) |
−0.957621 | + | 0.288033i | \(0.906999\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −42.8182 | − | 6270.73i | −0.00164303 | − | 0.240622i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26234.8 | 1.00326 | 0.501631 | − | 0.865082i | \(-0.332734\pi\) | ||||
0.501631 | + | 0.865082i | \(0.332734\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6803.07 | 0.259277 | 0.129639 | − | 0.991561i | \(-0.458618\pi\) | ||||
0.129639 | + | 0.991561i | \(0.458618\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 274.030 | + | 40131.7i | 0.0104084 | + | 1.52431i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6115.02 | + | 10591.5i | −0.231480 | + | 0.400934i | −0.958244 | − | 0.285953i | \(-0.907690\pi\) |
0.726764 | + | 0.686887i | \(0.241023\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17889.0 | + | 5498.56i | 0.674890 | + | 0.207442i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 19144.3 | − | 11761.5i | 0.719818 | − | 0.442227i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −28751.7 | + | 16599.8i | −1.07742 | + | 0.622051i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 34843.7i | 1.30134i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3898.66 | − | 2215.54i | −0.145120 | − | 0.0824690i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11241.7 | − | 19471.2i | −0.417055 | − | 0.722360i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −40106.7 | − | 23155.6i | −1.48296 | − | 0.856187i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7892.20 | − | 26314.9i | 0.290848 | − | 0.969774i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3816.79 | − | 2203.62i | −0.140193 | − | 0.0809402i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9920.70 | − | 17183.2i | −0.363188 | − | 0.629060i | 0.625296 | − | 0.780388i | \(-0.284978\pi\) |
−0.988484 | + | 0.151328i | \(0.951645\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2929.66 | − | 4917.98i | −0.106898 | − | 0.179449i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 48153.2i | − | 1.75125i | −0.482995 | − | 0.875623i | \(-0.660451\pi\) | ||
0.482995 | − | 0.875623i | \(-0.339549\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10852.9 | + | 6265.92i | −0.393404 | + | 0.227132i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8488.97 | − | 14474.2i | −0.306707 | − | 0.522953i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4864.35 | + | 4522.46i | −0.175175 | + | 0.162862i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11559.8 | − | 20022.1i | 0.414932 | − | 0.718683i | −0.580490 | − | 0.814268i | \(-0.697139\pi\) |
0.995421 | + | 0.0955849i | \(0.0304721\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28623.5 | − | 195.449i | 1.02408 | − | 0.00699267i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1472.45 | −0.0525095 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5292.17 | 0.188114 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −20216.7 | − | 11306.8i | −0.716291 | − | 0.400610i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16001.3 | − | 27715.1i | 0.565109 | − | 0.978797i | −0.431931 | − | 0.901907i | \(-0.642168\pi\) |
0.997040 | − | 0.0768903i | \(-0.0244991\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20516.8 | + | 42387.9i | 0.722246 | + | 1.49217i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18955.2 | − | 11117.0i | 0.665127 | − | 0.390091i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 26089.5 | − | 15062.8i | 0.912534 | − | 0.526852i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 22855.6i | − | 0.796863i | −0.917198 | − | 0.398431i | \(-0.869555\pi\) | ||
0.917198 | − | 0.398431i | \(-0.130445\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13851.8 | − | 24374.9i | 0.481403 | − | 0.847120i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27703.7 | − | 47984.2i | −0.959739 | − | 1.66232i | −0.723129 | − | 0.690713i | \(-0.757297\pi\) |
−0.236610 | − | 0.971605i | \(-0.576036\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4064.07 | + | 2346.39i | 0.140344 | + | 0.0810277i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 19063.6 | + | 19680.5i | 0.656231 | + | 0.677467i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5965.73 | − | 3444.31i | −0.204710 | − | 0.118189i | 0.394141 | − | 0.919050i | \(-0.371042\pi\) |
−0.598850 | + | 0.800861i | \(0.704376\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1619.79 | + | 2805.56i | 0.0554064 | + | 0.0959667i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18289.4 | − | 32183.7i | 0.623632 | − | 1.09740i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 50638.7i | − | 1.72125i | −0.509242 | − | 0.860623i | \(-0.670074\pi\) | ||
0.509242 | − | 0.860623i | \(-0.329926\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9706.74 | − | 5604.19i | 0.328903 | − | 0.189892i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −18555.4 | + | 10882.6i | −0.626761 | + | 0.367589i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 24889.1 | − | 5706.79i | 0.838070 | − | 0.192160i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −885.947 | + | 1534.51i | −0.0297387 | + | 0.0515090i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 50621.2 | + | 28311.6i | 1.69392 | + | 0.947380i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −41021.2 | −1.36841 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15112.3 | 0.502562 | 0.251281 | − | 0.967914i | \(-0.419148\pi\) | ||||
0.251281 | + | 0.967914i | \(0.419148\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −66124.4 | + | 451.515i | −2.19218 | + | 0.0149688i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14046.2 | − | 24328.7i | 0.464226 | − | 0.804063i | −0.534941 | − | 0.844890i | \(-0.679666\pi\) |
0.999166 | + | 0.0408272i | \(0.0129993\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2581.86 | + | 8399.80i | −0.0850674 | + | 0.276758i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −719.725 | − | 1227.17i | −0.0236407 | − | 0.0403087i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 34769.9 | − | 20074.4i | 1.13857 | − | 0.657356i | 0.192497 | − | 0.981298i | \(-0.438341\pi\) |
0.946077 | + | 0.323941i | \(0.105008\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 32429.3i | − | 1.05868i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17176.1 | − | 28833.3i | −0.559012 | − | 0.938405i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7276.53 | + | 12603.3i | 0.236099 | + | 0.408935i | 0.959591 | − | 0.281397i | \(-0.0907977\pi\) |
−0.723493 | + | 0.690332i | \(0.757464\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 29475.4 | + | 17017.6i | 0.953465 | + | 0.550483i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15961.0 | + | 16934.2i | 0.514735 | + | 0.546122i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10754.0 | + | 6208.81i | 0.345760 | + | 0.199624i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16550.0 | − | 28665.4i | −0.530503 | − | 0.918857i | −0.999367 | − | 0.0355870i | \(-0.988670\pi\) |
0.468864 | − | 0.883270i | \(-0.344663\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8007.28 | + | 4550.39i | 0.255894 | + | 0.145420i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 29208.7i | − | 0.930631i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 43647.5 | − | 25199.9i | 1.38649 | − | 0.800491i | 0.393573 | − | 0.919293i | \(-0.371239\pi\) |
0.992918 | + | 0.118803i | \(0.0379055\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −47135.7 | − | 25941.3i | −1.49280 | − | 0.821568i |
(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 | 336.4.bc.e.257.5 | 16 | ||
3.2 | odd | 2 | inner | 336.4.bc.e.257.2 | 16 | ||
4.3 | odd | 2 | 42.4.f.a.5.6 | yes | 16 | ||
7.3 | odd | 6 | inner | 336.4.bc.e.17.2 | 16 | ||
12.11 | even | 2 | 42.4.f.a.5.4 | ✓ | 16 | ||
21.17 | even | 6 | inner | 336.4.bc.e.17.5 | 16 | ||
28.3 | even | 6 | 42.4.f.a.17.4 | yes | 16 | ||
28.11 | odd | 6 | 294.4.f.a.227.1 | 16 | |||
28.19 | even | 6 | 294.4.d.a.293.2 | 16 | |||
28.23 | odd | 6 | 294.4.d.a.293.7 | 16 | |||
28.27 | even | 2 | 294.4.f.a.215.7 | 16 | |||
84.11 | even | 6 | 294.4.f.a.227.7 | 16 | |||
84.23 | even | 6 | 294.4.d.a.293.10 | 16 | |||
84.47 | odd | 6 | 294.4.d.a.293.15 | 16 | |||
84.59 | odd | 6 | 42.4.f.a.17.6 | yes | 16 | ||
84.83 | odd | 2 | 294.4.f.a.215.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.4.f.a.5.4 | ✓ | 16 | 12.11 | even | 2 | ||
42.4.f.a.5.6 | yes | 16 | 4.3 | odd | 2 | ||
42.4.f.a.17.4 | yes | 16 | 28.3 | even | 6 | ||
42.4.f.a.17.6 | yes | 16 | 84.59 | odd | 6 | ||
294.4.d.a.293.2 | 16 | 28.19 | even | 6 | |||
294.4.d.a.293.7 | 16 | 28.23 | odd | 6 | |||
294.4.d.a.293.10 | 16 | 84.23 | even | 6 | |||
294.4.d.a.293.15 | 16 | 84.47 | odd | 6 | |||
294.4.f.a.215.1 | 16 | 84.83 | odd | 2 | |||
294.4.f.a.215.7 | 16 | 28.27 | even | 2 | |||
294.4.f.a.227.1 | 16 | 28.11 | odd | 6 | |||
294.4.f.a.227.7 | 16 | 84.11 | even | 6 | |||
336.4.bc.e.17.2 | 16 | 7.3 | odd | 6 | inner | ||
336.4.bc.e.17.5 | 16 | 21.17 | even | 6 | inner | ||
336.4.bc.e.257.2 | 16 | 3.2 | odd | 2 | inner | ||
336.4.bc.e.257.5 | 16 | 1.1 | even | 1 | trivial |