Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,4,Mod(5,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 16]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.5");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.i (of order \(9\), degree \(6\), 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: | \(4.48414516044\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 25.5 | ||
Character | \(\chi\) | \(=\) | 76.25 |
Dual form | 76.4.i.a.73.5 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{7}{9}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 6.26044 | + | 2.27861i | 1.20482 | + | 0.438520i | 0.864905 | − | 0.501935i | \(-0.167379\pi\) |
0.339918 | + | 0.940455i | \(0.389601\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.15308 | + | 12.2107i | 0.192577 | + | 1.09216i | 0.915827 | + | 0.401573i | \(0.131536\pi\) |
−0.723250 | + | 0.690586i | \(0.757353\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.57544 | + | 7.92489i | −0.247050 | + | 0.427904i | −0.962706 | − | 0.270549i | \(-0.912795\pi\) |
0.715656 | + | 0.698453i | \(0.246128\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 13.3179 | + | 11.1750i | 0.493254 | + | 0.413889i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −7.90249 | − | 13.6875i | −0.216608 | − | 0.375176i | 0.737161 | − | 0.675717i | \(-0.236166\pi\) |
−0.953769 | + | 0.300541i | \(0.902833\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 23.5530 | − | 8.57261i | 0.502495 | − | 0.182893i | −0.0783207 | − | 0.996928i | \(-0.524956\pi\) |
0.580816 | + | 0.814035i | \(0.302734\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −14.3443 | + | 81.3505i | −0.246912 | + | 1.40031i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 23.2232 | − | 19.4866i | 0.331321 | − | 0.278011i | −0.461917 | − | 0.886923i | \(-0.652838\pi\) |
0.793238 | + | 0.608912i | \(0.208394\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 82.6404 | + | 5.43657i | 0.997843 | + | 0.0656439i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −46.7020 | + | 39.1877i | −0.485296 | + | 0.407212i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.18772 | + | 12.4072i | −0.0198335 | + | 0.112481i | −0.993117 | − | 0.117124i | \(-0.962632\pi\) |
0.973284 | + | 0.229605i | \(0.0737436\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −27.0040 | + | 9.82867i | −0.216032 | + | 0.0786294i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −32.0279 | − | 55.4739i | −0.228288 | − | 0.395406i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −78.9982 | − | 66.2873i | −0.505848 | − | 0.424457i | 0.353817 | − | 0.935315i | \(-0.384883\pi\) |
−0.859665 | + | 0.510858i | \(0.829328\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 117.534 | − | 203.576i | 0.680962 | − | 1.17946i | −0.293726 | − | 0.955890i | \(-0.594895\pi\) |
0.974688 | − | 0.223570i | \(-0.0717713\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −18.2845 | − | 103.697i | −0.0964522 | − | 0.547008i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −106.620 | − | 38.8064i | −0.514915 | − | 0.187414i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −338.196 | −1.50268 | −0.751340 | − | 0.659916i | \(-0.770592\pi\) | ||||
−0.751340 | + | 0.659916i | \(0.770592\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 166.986 | 0.685620 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −361.846 | − | 131.701i | −1.37831 | − | 0.501665i | −0.456646 | − | 0.889648i | \(-0.650949\pi\) |
−0.921666 | + | 0.387984i | \(0.873172\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −83.3298 | − | 472.587i | −0.295527 | − | 1.67602i | −0.665051 | − | 0.746798i | \(-0.731590\pi\) |
0.369524 | − | 0.929221i | \(-0.379521\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −107.780 | + | 186.681i | −0.357044 | + | 0.618418i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 412.476 | + | 346.108i | 1.28012 | + | 1.07415i | 0.993227 | + | 0.116190i | \(0.0370681\pi\) |
0.286897 | + | 0.957962i | \(0.407376\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 129.631 | + | 224.527i | 0.377932 | + | 0.654598i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 189.790 | − | 69.0779i | 0.521096 | − | 0.189664i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −93.1773 | + | 528.435i | −0.241488 | + | 1.36955i | 0.587020 | + | 0.809573i | \(0.300301\pi\) |
−0.828508 | + | 0.559977i | \(0.810810\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 150.119 | − | 125.965i | 0.368038 | − | 0.308821i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 504.978 | + | 222.341i | 1.17344 | + | 0.516663i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 305.958 | − | 256.729i | 0.675125 | − | 0.566497i | −0.239452 | − | 0.970908i | \(-0.576968\pi\) |
0.914577 | + | 0.404411i | \(0.132523\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.1610 | + | 74.6398i | −0.0276245 | + | 0.156666i | −0.995500 | − | 0.0947648i | \(-0.969790\pi\) |
0.967875 | + | 0.251431i | \(0.0809012\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −149.496 | + | 54.4120i | −0.298963 | + | 0.108814i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 155.389 | + | 269.142i | 0.296518 | + | 0.513584i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −160.604 | − | 134.763i | −0.292849 | − | 0.245730i | 0.484511 | − | 0.874785i | \(-0.338997\pi\) |
−0.777361 | + | 0.629055i | \(0.783442\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −41.9672 | + | 72.6893i | −0.0732211 | + | 0.126823i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 134.844 | + | 764.741i | 0.225396 | + | 1.27828i | 0.861928 | + | 0.507031i | \(0.169257\pi\) |
−0.636532 | + | 0.771250i | \(0.719632\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −826.398 | − | 300.784i | −1.32497 | − | 0.482249i | −0.419921 | − | 0.907561i | \(-0.637942\pi\) |
−0.905047 | + | 0.425312i | \(0.860164\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −191.453 | −0.294761 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 144.629 | 0.214052 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 539.847 | + | 196.488i | 0.768830 | + | 0.279831i | 0.696507 | − | 0.717550i | \(-0.254737\pi\) |
0.0723228 | + | 0.997381i | \(0.476959\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −155.616 | − | 882.540i | −0.213465 | − | 1.21062i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −472.093 | + | 817.688i | −0.624324 | + | 1.08136i | 0.364347 | + | 0.931263i | \(0.381292\pi\) |
−0.988671 | + | 0.150098i | \(0.952041\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 287.946 | + | 241.616i | 0.367437 | + | 0.308316i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −343.520 | − | 594.994i | −0.423325 | − | 0.733220i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 127.516 | − | 46.4121i | 0.151873 | − | 0.0552772i | −0.264965 | − | 0.964258i | \(-0.585360\pi\) |
0.416838 | + | 0.908981i | \(0.363138\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −39.8285 | + | 225.879i | −0.0458809 | + | 0.260203i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1199.69 | − | 1006.66i | 1.33765 | − | 1.12243i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 111.547 | + | 1020.80i | 0.120468 | + | 1.10244i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 525.497 | − | 440.944i | 0.550063 | − | 0.461558i | −0.324899 | − | 0.945749i | \(-0.605330\pi\) |
0.874962 | + | 0.484191i | \(0.160886\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 47.7139 | − | 270.599i | 0.0484386 | − | 0.274709i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 226.806 | − | 82.5507i | 0.223446 | − | 0.0813277i | −0.227871 | − | 0.973691i | \(-0.573176\pi\) |
0.451317 | + | 0.892364i | \(0.350954\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −336.162 | − | 582.249i | −0.321583 | − | 0.556997i | 0.659232 | − | 0.751940i | \(-0.270881\pi\) |
−0.980815 | + | 0.194942i | \(0.937548\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −579.062 | − | 485.891i | −0.538197 | − | 0.451601i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −53.3019 | + | 92.3216i | −0.0481579 | + | 0.0834119i | −0.889100 | − | 0.457714i | \(-0.848668\pi\) |
0.840942 | + | 0.541126i | \(0.182002\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 94.3891 | + | 535.307i | 0.0829435 | + | 0.470396i | 0.997781 | + | 0.0665747i | \(0.0212071\pi\) |
−0.914838 | + | 0.403821i | \(0.867682\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2117.26 | − | 770.619i | −1.81046 | − | 0.658954i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2000.81 | −1.66567 | −0.832835 | − | 0.553522i | \(-0.813284\pi\) | ||||
−0.832835 | + | 0.553522i | \(0.813284\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −156.210 | −0.126667 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 409.475 | + | 149.037i | 0.323556 | + | 0.117765i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 48.1727 | + | 273.201i | 0.0371091 | + | 0.210456i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 540.601 | − | 936.349i | 0.406162 | − | 0.703493i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1965.22 | − | 1649.01i | −1.44063 | − | 1.20883i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 596.785 | + | 1033.66i | 0.427025 | + | 0.739629i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1260.82 | − | 458.902i | 0.880944 | − | 0.320637i | 0.138353 | − | 0.990383i | \(-0.455819\pi\) |
0.742591 | + | 0.669746i | \(0.233597\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 555.162 | − | 3148.48i | 0.378909 | − | 2.14890i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −402.594 | + | 337.816i | −0.268510 | + | 0.225307i | −0.767094 | − | 0.641535i | \(-0.778298\pi\) |
0.498584 | + | 0.866841i | \(0.333854\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −421.200 | + | 630.042i | −0.274607 | + | 0.410763i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 608.417 | − | 510.522i | 0.387883 | − | 0.325472i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −441.677 | + | 2504.87i | −0.275438 | + | 1.56209i | 0.462129 | + | 0.886813i | \(0.347086\pi\) |
−0.737567 | + | 0.675274i | \(0.764025\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 666.214 | − | 242.482i | 0.406529 | − | 0.147964i | −0.130658 | − | 0.991427i | \(-0.541709\pi\) |
0.537187 | + | 0.843463i | \(0.319487\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1793.63 | + | 3106.67i | 1.07129 | + | 1.85552i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −303.465 | − | 254.638i | −0.177462 | − | 0.148908i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 639.326 | − | 1107.35i | 0.366160 | − | 0.634207i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 299.935 | + | 1701.02i | 0.168287 | + | 0.954405i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −66.1491 | − | 24.0763i | −0.0363701 | − | 0.0132376i | 0.323771 | − | 0.946135i | \(-0.395049\pi\) |
−0.360141 | + | 0.932898i | \(0.617271\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −533.022 | −0.287263 | −0.143631 | − | 0.989631i | \(-0.545878\pi\) | ||||
−0.143631 | + | 0.989631i | \(0.545878\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 527.046 | 0.278491 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2738.86 | + | 996.865i | 1.41930 | + | 0.516581i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 250.432 | + | 1420.27i | 0.127303 | + | 0.721974i | 0.979913 | + | 0.199425i | \(0.0639075\pi\) |
−0.852610 | + | 0.522548i | \(0.824981\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1787.43 | + | 3095.92i | −0.891525 | + | 1.54417i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −88.3156 | − | 74.1056i | −0.0432313 | − | 0.0362754i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 470.642 | + | 815.175i | 0.226156 | + | 0.391715i | 0.956666 | − | 0.291188i | \(-0.0940506\pi\) |
−0.730509 | + | 0.682903i | \(0.760717\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1226.84 | − | 446.533i | 0.578845 | − | 0.210682i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 252.301 | − | 1430.87i | 0.116908 | − | 0.663019i | −0.868880 | − | 0.495023i | \(-0.835159\pi\) |
0.985788 | − | 0.167995i | \(-0.0537294\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1201.74 | + | 1008.38i | −0.546993 | + | 0.458981i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1039.84 | + | 995.912i | 0.465021 | + | 0.445376i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 228.128 | − | 191.422i | 0.100256 | − | 0.0841246i | −0.591282 | − | 0.806465i | \(-0.701378\pi\) |
0.691538 | + | 0.722340i | \(0.256934\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 45.6642 | − | 258.975i | 0.0197251 | − | 0.111866i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2500.42 | − | 910.079i | 1.06183 | − | 0.386473i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 228.176 | + | 395.212i | 0.0952774 | + | 0.165025i | 0.909724 | − | 0.415213i | \(-0.136293\pi\) |
−0.814447 | + | 0.580238i | \(0.802960\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2602.24 | − | 2183.54i | −1.06864 | − | 0.896692i | −0.0737081 | − | 0.997280i | \(-0.523483\pi\) |
−0.994928 | + | 0.100588i | \(0.967928\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −252.469 | + | 437.289i | −0.101984 | + | 0.176641i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −728.163 | − | 4129.62i | −0.289382 | − | 1.64116i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −450.244 | − | 163.875i | −0.176070 | − | 0.0640842i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 586.166 | 0.225594 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2645.80 | −1.00232 | −0.501161 | − | 0.865354i | \(-0.667094\pi\) | ||||
−0.501161 | + | 0.865354i | \(0.667094\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1981.71 | + | 721.282i | 0.739100 | + | 0.269011i | 0.684012 | − | 0.729471i | \(-0.260234\pi\) |
0.0550885 | + | 0.998481i | \(0.482456\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 359.534 | + | 2039.02i | 0.132035 | + | 0.748806i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2118.61 | + | 3669.55i | −0.766219 | + | 1.32713i | 0.173381 | + | 0.984855i | \(0.444531\pi\) |
−0.939600 | + | 0.342275i | \(0.888803\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3983.16 | − | 3342.27i | −1.41889 | − | 1.19059i | −0.951932 | − | 0.306309i | \(-0.900906\pi\) |
−0.466957 | − | 0.884280i | \(-0.654650\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −698.379 | − | 1209.63i | −0.245074 | − | 0.424481i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 886.771 | − | 322.758i | 0.306597 | − | 0.111592i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 829.081 | − | 4701.95i | 0.282466 | − | 1.60195i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −167.786 | + | 140.789i | −0.0563378 | + | 0.0472730i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −578.652 | − | 1174.10i | −0.191513 | − | 0.388586i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1392.21 | + | 1168.21i | −0.454237 | + | 0.381150i | −0.841005 | − | 0.541027i | \(-0.818036\pi\) |
0.386768 | + | 0.922177i | \(0.373591\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −898.364 | + | 5094.87i | −0.288990 | + | 1.63894i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5591.20 | − | 2035.03i | 1.77357 | − | 0.645526i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1075.54 | + | 1862.89i | 0.336464 | + | 0.582772i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4488.25 | − | 3766.09i | −1.38488 | − | 1.16205i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 379.926 | − | 658.052i | 0.115641 | − | 0.200296i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −110.607 | − | 627.282i | −0.0332142 | − | 0.188367i | 0.963687 | − | 0.267036i | \(-0.0860442\pi\) |
−0.996901 | + | 0.0786685i | \(0.974933\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −469.472 | − | 170.874i | −0.139103 | − | 0.0506293i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4874.69 | 1.42531 | 0.712653 | − | 0.701516i | \(-0.247493\pi\) | ||||
0.712653 | + | 0.701516i | \(0.247493\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3195.65 | −0.922158 | −0.461079 | − | 0.887359i | \(-0.652538\pi\) | ||||
−0.461079 | + | 0.887359i | \(0.652538\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 905.443 | + | 329.554i | 0.257895 | + | 0.0938662i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −966.384 | − | 5480.63i | −0.271716 | − | 1.54098i | −0.749203 | − | 0.662340i | \(-0.769563\pi\) |
0.477487 | − | 0.878639i | \(-0.341548\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3338.14 | + | 5781.82i | −0.926621 | + | 1.60496i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2931.96 | + | 2460.21i | 0.803592 | + | 0.674294i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2643.59 | − | 4578.84i | −0.715480 | − | 1.23925i | −0.962774 | − | 0.270308i | \(-0.912875\pi\) |
0.247294 | − | 0.968941i | \(-0.420459\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6315.36 | − | 2298.60i | 1.68800 | − | 0.614382i | 0.693630 | − | 0.720332i | \(-0.256010\pi\) |
0.994372 | + | 0.105949i | \(0.0337881\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 736.421 | − | 4176.45i | 0.194409 | − | 1.10255i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2462.53 | + | 2066.31i | −0.642144 | + | 0.538823i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1993.04 | − | 580.396i | 0.513417 | − | 0.149513i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4818.71 | + | 4043.37i | −1.22640 | + | 1.02907i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −114.775 | + | 650.924i | −0.0288628 | + | 0.163689i | −0.995832 | − | 0.0912030i | \(-0.970929\pi\) |
0.966970 | + | 0.254892i | \(0.0820399\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 187.111 | − | 68.1030i | 0.0464964 | − | 0.0169233i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1252.12 | + | 2168.74i | 0.307494 | + | 0.532595i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1324.92 | − | 1111.74i | −0.321582 | − | 0.269839i | 0.467678 | − | 0.883899i | \(-0.345091\pi\) |
−0.789259 | + | 0.614060i | \(0.789535\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1547.40 | − | 2680.17i | 0.371237 | − | 0.643002i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −311.325 | − | 1765.61i | −0.0738334 | − | 0.418730i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 647.332 | + | 235.610i | 0.151773 | + | 0.0552407i | 0.416789 | − | 0.909003i | \(-0.363155\pi\) |
−0.265017 | + | 0.964244i | \(0.585377\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6653.18 | −1.54227 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 904.063 | 0.207220 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6231.45 | − | 2268.06i | −1.41241 | − | 0.514075i | −0.480573 | − | 0.876955i | \(-0.659571\pi\) |
−0.931836 | + | 0.362880i | \(0.881794\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 713.033 | + | 4043.81i | 0.159829 | + | 0.906435i | 0.954237 | + | 0.299051i | \(0.0966701\pi\) |
−0.794408 | + | 0.607384i | \(0.792219\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −764.035 | + | 1323.35i | −0.169383 | + | 0.293379i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 347.929 | + | 291.947i | 0.0762942 | + | 0.0640185i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3816.25 | + | 6609.93i | 0.827784 | + | 1.43376i | 0.899773 | + | 0.436358i | \(0.143732\pi\) |
−0.0719893 | + | 0.997405i | \(0.522935\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3840.27 | − | 1397.74i | 0.824053 | − | 0.299931i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 605.923 | − | 3436.36i | 0.128635 | − | 0.729523i | −0.850448 | − | 0.526060i | \(-0.823669\pi\) |
0.979082 | − | 0.203464i | \(-0.0652200\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 40.7950 | − | 34.2310i | 0.00856894 | − | 0.00719019i | −0.638493 | − | 0.769628i | \(-0.720442\pi\) |
0.647062 | + | 0.762437i | \(0.275997\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1627.69 | + | 6644.86i | −0.338301 | + | 1.38108i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2699.32 | − | 2265.00i | 0.555177 | − | 0.465849i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −693.543 | + | 3933.28i | −0.141165 | + | 0.800586i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4294.58 | − | 1563.10i | 0.865130 | − | 0.314882i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2814.07 | + | 4874.11i | 0.561091 | + | 0.971838i | 0.997402 | + | 0.0720418i | \(0.0229515\pi\) |
−0.436311 | + | 0.899796i | \(0.643715\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3793.60 | + | 3183.21i | 0.748718 | + | 0.628249i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −506.199 | + | 876.763i | −0.0988979 | + | 0.171296i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 54.8343 | + | 310.981i | 0.0106058 | + | 0.0601488i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4126.47 | + | 1501.91i | 0.790185 | + | 0.287604i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1608.01 | 0.304877 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −939.741 | −0.176424 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9833.35 | + | 3579.05i | 1.82808 | + | 0.665365i | 0.993411 | + | 0.114606i | \(0.0365605\pi\) |
0.834664 | + | 0.550759i | \(0.185662\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −777.800 | − | 4411.12i | −0.143196 | − | 0.812104i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2428.55 | + | 4206.37i | −0.442799 | + | 0.766950i | −0.997896 | − | 0.0648353i | \(-0.979348\pi\) |
0.555097 | + | 0.831786i | \(0.312681\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −254.377 | − | 213.447i | −0.0459368 | − | 0.0385456i | 0.619530 | − | 0.784973i | \(-0.287323\pi\) |
−0.665467 | + | 0.746427i | \(0.731768\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −986.285 | − | 1708.30i | −0.176415 | − | 0.305561i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5714.93 | − | 2080.06i | 1.01256 | − | 0.368543i | 0.218146 | − | 0.975916i | \(-0.429999\pi\) |
0.794416 | + | 0.607373i | \(0.207777\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −283.026 | + | 1605.12i | −0.0496753 | + | 0.281723i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −544.059 | + | 456.520i | −0.0945994 | + | 0.0793784i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2025.12 | − | 1484.13i | 0.348856 | − | 0.255662i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −551.770 | + | 462.990i | −0.0941745 | + | 0.0790218i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −628.841 | + | 3566.34i | −0.106346 | + | 0.603116i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4630.13 | + | 1685.23i | −0.775888 | + | 0.282400i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2721.96 | − | 4714.58i | −0.452002 | − | 0.782891i | 0.546508 | − | 0.837454i | \(-0.315957\pi\) |
−0.998510 | + | 0.0545631i | \(0.982623\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4504.05 | − | 3779.35i | −0.741203 | − | 0.621943i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1299.76 | − | 2251.24i | 0.211980 | − | 0.367160i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 299.208 | + | 1696.90i | 0.0483648 | + | 0.274290i | 0.999394 | − | 0.0348110i | \(-0.0110829\pi\) |
−0.951029 | + | 0.309101i | \(0.899972\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12526.0 | − | 4559.08i | −2.00684 | − | 0.730429i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3715.26 | −0.590007 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5511.22 | −0.867574 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −977.947 | − | 355.943i | −0.152611 | − | 0.0555460i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −568.366 | − | 3223.37i | −0.0879294 | − | 0.498672i | −0.996686 | − | 0.0813458i | \(-0.974078\pi\) |
0.908757 | − | 0.417327i | \(-0.137033\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1000.80 | − | 1733.44i | 0.153501 | − | 0.265871i | −0.779011 | − | 0.627010i | \(-0.784279\pi\) |
0.932512 | + | 0.361139i | \(0.117612\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1229.91 | − | 1032.02i | −0.187031 | − | 0.156937i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 240.987 | + | 417.402i | 0.0363355 | + | 0.0629350i | 0.883621 | − | 0.468202i | \(-0.155098\pi\) |
−0.847286 | + | 0.531137i | \(0.821765\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9047.69 | + | 3293.09i | −1.35268 | + | 0.492336i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −320.937 | + | 1820.13i | −0.0475793 | + | 0.269836i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8141.14 | − | 6831.23i | 1.19686 | − | 1.00429i | 0.197147 | − | 0.980374i | \(-0.436832\pi\) |
0.999714 | − | 0.0239119i | \(-0.00761212\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6799.89 | + | 898.561i | 0.991382 | + | 0.131005i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5517.98 | − | 4630.14i | 0.797849 | − | 0.669474i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1893.49 | − | 10738.5i | 0.271534 | − | 1.53994i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8677.98 | + | 3158.52i | −1.23430 | + | 0.449247i | −0.875067 | − | 0.484002i | \(-0.839183\pi\) |
−0.359229 | + | 0.933249i | \(0.616960\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3347.25 | − | 5797.61i | −0.472225 | − | 0.817917i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3761.46 | − | 3156.24i | −0.526375 | − | 0.441681i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2181.71 | − | 3778.84i | 0.302855 | − | 0.524560i | −0.673927 | − | 0.738798i | \(-0.735394\pi\) |
0.976781 | + | 0.214238i | \(0.0687270\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1380.82 | + | 7831.03i | 0.190148 | + | 1.07838i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2428.90 | − | 884.048i | −0.331817 | − | 0.120771i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10524.7 | −1.42644 | −0.713218 | − | 0.700942i | \(-0.752763\pi\) | ||||
−0.713218 | + | 0.700942i | \(0.752763\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8938.97 | 1.20199 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5547.15 | + | 2019.00i | 0.740069 | + | 0.269363i | 0.684421 | − | 0.729087i | \(-0.260055\pi\) |
0.0556482 | + | 0.998450i | \(0.482277\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 311.398 | + | 1766.03i | 0.0412216 | + | 0.233779i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4171.39 | − | 7225.06i | 0.547916 | − | 0.949019i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2731.85 | − | 2292.29i | −0.356067 | − | 0.298776i | 0.447154 | − | 0.894457i | \(-0.352438\pi\) |
−0.803221 | + | 0.595681i | \(0.796882\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 190.967 | + | 330.765i | 0.0246998 | + | 0.0427814i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3290.17 | + | 1197.52i | −0.422308 | + | 0.153708i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1236.93 | + | 7014.97i | −0.157561 | + | 0.893573i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1115.03 | − | 935.617i | 0.140961 | − | 0.118280i | −0.569581 | − | 0.821935i | \(-0.692894\pi\) |
0.710542 | + | 0.703655i | \(0.248450\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4072.52 | + | 2984.59i | −0.510980 | + | 0.374477i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5830.05 | − | 4891.99i | 0.726032 | − | 0.609213i | −0.203015 | − | 0.979176i | \(-0.565074\pi\) |
0.929047 | + | 0.369963i | \(0.120630\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1023.12 | − | 5802.40i | 0.126465 | − | 0.717217i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10441.4 | − | 3800.35i | 1.28108 | − | 0.466274i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2672.59 | + | 4629.06i | 0.325492 | + | 0.563769i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7178.29 | + | 6023.30i | 0.867832 | + | 0.728198i | 0.963641 | − | 0.267202i | \(-0.0860991\pi\) |
−0.0958082 | + | 0.995400i | \(0.530544\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8472.74 | + | 14675.2i | −1.01686 | + | 1.76125i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 634.660 | + | 3599.33i | 0.0756164 | + | 0.428842i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11001.0 | − | 4004.04i | −1.30125 | − | 0.473616i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4723.32 | 0.554681 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5260.54 | 0.613351 | 0.306676 | − | 0.951814i | \(-0.400783\pi\) | ||||
0.306676 | + | 0.951814i | \(0.400783\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9246.90 | − | 3365.60i | −1.07047 | − | 0.389618i | −0.254115 | − | 0.967174i | \(-0.581784\pi\) |
−0.816351 | + | 0.577556i | \(0.804007\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1625.53 | + | 9218.85i | 0.186847 | + | 1.05966i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −435.593 | + | 754.470i | −0.0497162 | + | 0.0861110i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −531.294 | − | 445.809i | −0.0602134 | − | 0.0505251i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1319.61 | − | 2285.62i | −0.148511 | − | 0.257228i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8194.59 | + | 2982.59i | −0.915823 | + | 0.333332i | −0.756575 | − | 0.653906i | \(-0.773129\pi\) |
−0.159247 | + | 0.987239i | \(0.550907\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −514.972 | + | 2920.55i | −0.0571546 | + | 0.324140i | −0.999958 | − | 0.00921057i | \(-0.997068\pi\) |
0.942803 | + | 0.333351i | \(0.108179\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6525.68 | − | 5475.69i | 0.719270 | − | 0.603539i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −248.246 | + | 1013.44i | −0.0271744 | + | 0.110937i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6639.59 | − | 5571.28i | 0.721846 | − | 0.605701i | −0.206049 | − | 0.978542i | \(-0.566061\pi\) |
0.927895 | + | 0.372841i | \(0.121616\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −782.688 | + | 4438.85i | −0.0845145 | + | 0.479305i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8523.60 | + | 3102.34i | −0.914150 | + | 0.332723i | −0.755909 | − | 0.654677i | \(-0.772805\pi\) |
−0.158241 | + | 0.987401i | \(0.550582\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 841.276 | + | 1457.13i | 0.0896187 | + | 0.155224i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −359.262 | − | 301.457i | −0.0380146 | − | 0.0318980i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3757.00 | − | 6507.31i | 0.394886 | − | 0.683962i | −0.598201 | − | 0.801346i | \(-0.704118\pi\) |
0.993087 | + | 0.117384i | \(0.0374508\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1056.82 | + | 5993.53i | 0.110341 | + | 0.625775i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3336.95 | − | 1214.55i | −0.346101 | − | 0.125970i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2843.89 | −0.293019 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15863.4 | 1.62376 | 0.811882 | − | 0.583822i | \(-0.198443\pi\) | ||||
0.811882 | + | 0.583822i | \(0.198443\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1824.79 | − | 664.168i | −0.185564 | − | 0.0675397i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3070.27 | − | 17412.3i | −0.310188 | − | 1.75916i | −0.598020 | − | 0.801481i | \(-0.704046\pi\) |
0.287833 | − | 0.957681i | \(-0.407065\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7521.42 | − | 13027.5i | 0.754968 | − | 1.30764i | −0.190422 | − | 0.981702i | \(-0.560986\pi\) |
0.945390 | − | 0.325940i | \(-0.105681\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 14875.0 | + | 12481.6i | 1.48347 | + | 1.24478i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5537.24 | + | 9590.79i | 0.548679 | + | 0.950340i | 0.998365 | + | 0.0571535i | \(0.0182024\pi\) |
−0.449686 | + | 0.893187i | \(0.648464\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1802.81 | − | 656.170i | 0.177497 | − | 0.0646037i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1668.43 | + | 9462.15i | −0.163222 | + | 0.925675i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5810.02 | + | 4875.19i | −0.564789 | + | 0.473914i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2285.06 | + | 665.436i | −0.220728 | + | 0.0642785i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7146.19 | + | 5996.37i | −0.685957 | + | 0.575586i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1248.65 | + | 7081.45i | −0.119107 | + | 0.675490i | 0.865527 | + | 0.500862i | \(0.166983\pi\) |
−0.984634 | + | 0.174628i | \(0.944128\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7965.55 | + | 2899.22i | −0.755089 | + | 0.274830i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −384.037 | − | 665.171i | −0.0361786 | − | 0.0626632i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6515.67 | + | 5467.30i | 0.610024 | + | 0.511871i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 395.052 | − | 684.249i | 0.0367587 | − | 0.0636680i | −0.847061 | − | 0.531496i | \(-0.821630\pi\) |
0.883819 | + | 0.467828i | \(0.154963\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1088.95 | + | 6175.77i | 0.100704 | + | 0.571121i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12995.0 | + | 4729.80i | 1.19441 | + | 0.434731i | 0.861272 | − | 0.508145i | \(-0.169669\pi\) |
0.333143 | + | 0.942876i | \(0.391891\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3126.30 | −0.285602 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3406.93 | 0.309354 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6677.45 | − | 2430.39i | −0.602666 | − | 0.219352i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.6955 | − | 140.055i | −0.00221548 | − | 0.0125646i | 0.983680 | − | 0.179927i | \(-0.0575861\pi\) |
−0.985895 | + | 0.167362i | \(0.946475\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4839.92 | − | 8382.99i | 0.431600 | − | 0.747554i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7413.09 | − | 6220.32i | −0.657124 | − | 0.551393i | 0.252099 | − | 0.967701i | \(-0.418879\pi\) |
−0.909223 | + | 0.416309i | \(0.863324\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1496.33 | + | 2591.73i | 0.131853 | + | 0.228377i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9821.16 | + | 3574.61i | −0.860302 | + | 0.313124i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3636.15 | + | 20621.6i | −0.316639 | + | 1.79575i | 0.246238 | + | 0.969209i | \(0.420806\pi\) |
−0.562877 | + | 0.826541i | \(0.690306\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6164.82 | − | 5172.89i | 0.533690 | − | 0.447819i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2345.21 | − | 4758.51i | −0.201839 | − | 0.409539i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6385.89 | − | 5358.40i | 0.546400 | − | 0.458484i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1477.78 | − | 8380.89i | 0.125711 | − | 0.712942i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1864.36 | − | 678.571i | 0.157681 | − | 0.0573911i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1757.60 | − | 3044.25i | −0.147796 | − | 0.255991i | 0.782616 | − | 0.622504i | \(-0.213885\pi\) |
−0.930413 | + | 0.366514i | \(0.880551\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6716.93 | + | 5636.17i | 0.561589 | + | 0.471229i | 0.878843 | − | 0.477112i | \(-0.158316\pi\) |
−0.317254 | + | 0.948341i | \(0.602761\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 875.981 | − | 1517.24i | 0.0728209 | − | 0.126129i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1237.47 | − | 7018.02i | −0.102286 | − | 0.580095i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11284.1 | + | 4107.07i | 0.927434 | + | 0.337558i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6943.67 | 0.567475 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9651.59 | −0.784347 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1242.08 | − | 452.079i | −0.100373 | − | 0.0365328i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 527.945 | + | 2994.13i | 0.0424255 | + | 0.240607i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2048.81 | − | 3548.64i | 0.163726 | − | 0.283582i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2253.01 | − | 1890.50i | −0.179047 | − | 0.150238i | 0.548860 | − | 0.835914i | \(-0.315062\pi\) |
−0.727907 | + | 0.685676i | \(0.759507\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11315.7 | − | 19599.4i | −0.894300 | − | 1.54897i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6333.25 | + | 2305.12i | −0.497774 | + | 0.181175i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1971.24 | − | 11179.5i | 0.154085 | − | 0.873857i | −0.805533 | − | 0.592550i | \(-0.798121\pi\) |
0.959618 | − | 0.281307i | \(-0.0907678\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1009.38 | + | 846.968i | −0.0784684 | + | 0.0658428i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6168.07 | − | 5907.49i | −0.476894 | − | 0.456747i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4027.18 | + | 3379.21i | −0.309680 | + | 0.259853i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4851.18 | − | 27512.4i | 0.371029 | − | 2.10421i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8365.06 | + | 3044.63i | −0.636336 | + | 0.231607i | −0.639987 | − | 0.768386i | \(-0.721060\pi\) |
0.00365087 | + | 0.999993i | \(0.498838\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6013.97 | − | 10416.5i | −0.455034 | − | 0.788142i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2445.32 | − | 2051.86i | −0.184031 | − | 0.154420i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8827.77 | + | 15290.1i | −0.660828 | + | 1.14459i | 0.319571 | + | 0.947562i | \(0.396461\pi\) |
−0.980398 | + | 0.197025i | \(0.936872\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4307.90 | − | 24431.3i | −0.320770 | − | 1.81918i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7706.04 | + | 2804.77i | 0.570764 | + | 0.207741i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12764.0 | 0.940412 | 0.470206 | − | 0.882557i | \(-0.344180\pi\) | ||||
0.470206 | + | 0.882557i | \(0.344180\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26572.6 | −1.94751 | −0.973755 | − | 0.227597i | \(-0.926913\pi\) | ||||
−0.973755 | + | 0.227597i | \(0.926913\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16563.9 | − | 6028.76i | −1.20762 | − | 0.439538i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −62.8686 | − | 356.546i | −0.00455966 | − | 0.0258591i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11865.9 | + | 20552.3i | −0.856121 | + | 1.48285i | 0.0194801 | + | 0.999810i | \(0.493799\pi\) |
−0.875601 | + | 0.483035i | \(0.839534\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10762.8 | + | 9031.09i | 0.772519 | + | 0.648220i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4320.06 | − | 7482.56i | −0.308479 | − | 0.534301i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7969.29 | − | 2900.58i | 0.566131 | − | 0.206055i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −938.213 | + | 5320.87i | −0.0663083 | + | 0.376053i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10707.0 | + | 8984.23i | −0.752853 | + | 0.631719i | −0.936256 | − | 0.351319i | \(-0.885733\pi\) |
0.183403 | + | 0.983038i | \(0.441289\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10819.9 | − | 16184.6i | 0.756917 | − | 1.13222i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21625.0 | + | 18145.5i | −1.50513 | + | 1.26295i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1694.21 | + | 9608.33i | −0.117323 | + | 0.665374i | 0.868250 | + | 0.496127i | \(0.165245\pi\) |
−0.985574 | + | 0.169248i | \(0.945866\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3232.26 | + | 1176.45i | −0.222705 | + | 0.0810581i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −17320.6 | − | 30000.2i | −1.18741 | − | 2.05666i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15432.1 | + | 12949.1i | 1.05265 | + | 0.883281i | 0.993370 | − | 0.114961i | \(-0.0366742\pi\) |
0.0592828 | + | 0.998241i | \(0.481119\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13140.4 | − | 22759.9i | 0.891862 | − | 1.54475i | 0.0542207 | − | 0.998529i | \(-0.482733\pi\) |
0.837641 | − | 0.546221i | \(-0.183934\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −632.926 | − | 3589.50i | −0.0427442 | − | 0.242414i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12597.4 | + | 4585.09i | 0.846544 | + | 0.308117i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2188.00 | 0.146307 | 0.0731533 | − | 0.997321i | \(-0.476694\pi\) | ||||
0.0731533 | + | 0.997321i | \(0.476694\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6287.02 | 0.418330 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12682.1 | + | 4615.91i | 0.839711 | + | 0.305630i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2331.96 | + | 13225.2i | 0.153649 | + | 0.871390i | 0.960010 | + | 0.279965i | \(0.0903230\pi\) |
−0.806361 | + | 0.591424i | \(0.798566\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15904.4 | − | 27547.2i | 1.04281 | − | 1.80619i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14320.4 | + | 12016.3i | 0.934389 | + | 0.784046i | 0.976600 | − | 0.215063i | \(-0.0689957\pi\) |
−0.0422109 | + | 0.999109i | \(0.513440\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13935.1 | + | 24136.3i | 0.904846 | + | 1.56724i | 0.821123 | + | 0.570751i | \(0.193348\pi\) |
0.0837230 | + | 0.996489i | \(0.473319\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 758.341 | − | 276.014i | 0.0490035 | − | 0.0178358i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −215.631 | + | 1222.91i | −0.0138669 | + | 0.0786432i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14088.6 | + | 11821.7i | −0.901668 | + | 0.756589i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −947.286 | − | 8668.94i | −0.0603364 | − | 0.552159i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7854.00 | + | 6590.29i | −0.497869 | + | 0.417762i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 386.405 | − | 2191.41i | 0.0243780 | − | 0.138255i | −0.970190 | − | 0.242347i | \(-0.922083\pi\) |
0.994568 | + | 0.104093i | \(0.0331938\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11377.8 | + | 4141.17i | −0.714417 | + | 0.260027i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8318.16 | + | 14407.5i | 0.519837 | + | 0.900383i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4977.98 | + | 4177.02i | 0.309631 | + | 0.259811i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6750.15 | + | 11691.6i | −0.417890 | + | 0.723807i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −392.851 | − | 2227.97i | −0.0242070 | − | 0.137285i | 0.970309 | − | 0.241868i | \(-0.0777602\pi\) |
−0.994516 | + | 0.104584i | \(0.966649\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19158.6 | + | 6973.16i | 1.17503 | + | 0.427674i | 0.854442 | − | 0.519546i | \(-0.173899\pi\) |
0.320583 | + | 0.947220i | \(0.396121\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 39640.5 | 2.41991 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8354.21 | 0.507632 | 0.253816 | − | 0.967252i | \(-0.418314\pi\) | ||||
0.253816 | + | 0.967252i | \(0.418314\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5931.82 | − | 2159.00i | −0.358774 | − | 0.130583i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2488.55 | + | 14113.3i | 0.149822 | + | 0.849683i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −746.125 | + | 1292.33i | −0.0447138 | + | 0.0774466i | −0.887516 | − | 0.460777i | \(-0.847571\pi\) |
0.842802 | + | 0.538223i | \(0.180904\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4991.79 | − | 4188.61i | −0.297779 | − | 0.249867i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7644.59 | − | 13240.8i | −0.453948 | − | 0.786261i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5538.44 | + | 2015.83i | −0.327385 | + | 0.119159i | −0.500484 | − | 0.865746i | \(-0.666844\pi\) |
0.173098 | + | 0.984905i | \(0.444622\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2332.97 | + | 13230.9i | −0.137280 | + | 0.778554i | 0.835965 | + | 0.548783i | \(0.184909\pi\) |
−0.973245 | + | 0.229771i | \(0.926202\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3877.95 | − | 3253.99i | 0.227160 | − | 0.190610i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8600.13 | − | 3786.63i | −0.501502 | − | 0.220811i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 995.263 | − | 835.125i | 0.0577762 | − | 0.0484800i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 736.887 | − | 4179.09i | 0.0425855 | − | 0.241514i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1125.64 | − | 409.698i | 0.0647611 | − | 0.0235711i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3402.96 | − | 5894.10i | −0.194910 | − | 0.337594i | 0.751961 | − | 0.659208i | \(-0.229108\pi\) |
−0.946871 | + | 0.321613i | \(0.895775\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1410.12 | + | 1183.23i | 0.0804080 | + | 0.0674703i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9972.07 | + | 17272.1i | −0.566112 | + | 0.980534i | 0.430834 | + | 0.902431i | \(0.358220\pi\) |
−0.996945 | + | 0.0781028i | \(0.975114\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1090.06 | + | 6182.01i | 0.0616090 | + | 0.349402i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 30517.7 | + | 11107.5i | 1.71724 | + | 0.625025i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5186.63 | 0.290572 | 0.145286 | − | 0.989390i | \(-0.453590\pi\) | ||||
0.145286 | + | 0.989390i | \(0.453590\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −31537.3 | −1.75909 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −20006.2 | − | 7281.65i | −1.11104 | − | 0.404385i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2335.45 | + | 13245.0i | 0.129135 | + | 0.732359i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13242.4 | − | 22936.5i | 0.729038 | − | 1.26273i | −0.228253 | − | 0.973602i | \(-0.573301\pi\) |
0.957290 | − | 0.289128i | \(-0.0933654\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1926.15 | + | 1616.23i | 0.105582 | + | 0.0885940i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4395.29 | + | 7612.86i | 0.239889 | + | 0.415500i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10969.6 | + | 3992.62i | −0.596132 | + | 0.216974i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6438.26 | − | 36513.2i | 0.348380 | − | 1.97576i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22689.8 | + | 19039.0i | −1.22251 | + | 1.02581i | −0.223824 | + | 0.974630i | \(0.571854\pi\) |
−0.998689 | + | 0.0511810i | \(0.983701\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27948.7 | − | 1838.63i | −1.49944 | − | 0.0986418i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −34072.8 | + | 28590.4i | −1.82022 | + | 1.52735i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −383.532 | + | 2175.12i | −0.0204020 | + | 0.115705i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24656.2 | − | 8974.11i | 1.30604 | − | 0.475359i | 0.407080 | − | 0.913392i | \(-0.366547\pi\) |
0.898959 | + | 0.438033i | \(0.144325\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4993.85 | + | 8649.60i | 0.263409 | + | 0.456238i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2268.66 | + | 1903.63i | 0.119161 | + | 0.0999883i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2455.92 | − | 4253.78i | 0.128456 | − | 0.222493i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6116.66 | − | 34689.3i | −0.318592 | − | 1.80683i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20946.6 | + | 7623.93i | 1.08648 | + | 0.395445i | 0.822314 | − | 0.569034i | \(-0.192683\pi\) |
0.264161 | + | 0.964479i | \(0.414905\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6152.35 | 0.317788 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 44774.6 | 2.30316 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2784.79 | + | 1013.58i | 0.142654 | + | 0.0519219i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −906.627 | − | 5141.74i | −0.0462516 | − | 0.262306i | 0.952910 | − | 0.303254i | \(-0.0980732\pi\) |
−0.999161 | + | 0.0409484i | \(0.986962\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2028.76 | − | 3513.91i | 0.103072 | − | 0.178525i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11144.3 | − | 9351.17i | −0.563866 | − | 0.473140i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.61916 | − | 16.6609i | −0.000484709 | − | 0.000839541i | 0.865783 | − | 0.500420i | \(-0.166821\pi\) |
−0.866268 | + | 0.499580i | \(0.833488\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −20124.8 | + | 7324.84i | −1.00995 | + | 0.367593i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −575.395 | + | 3263.23i | −0.0287584 | + | 0.163097i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7023.94 | + | 5893.79i | −0.349634 | + | 0.293378i | −0.800643 | − | 0.599141i | \(-0.795509\pi\) |
0.451009 | + | 0.892519i | \(0.351064\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13799.8 | + | 907.832i | 0.684141 | + | 0.0450068i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25389.8 | − | 21304.6i | 1.25365 | − | 1.05194i | 0.257320 | − | 0.966326i | \(-0.417161\pi\) |
0.996329 | − | 0.0856096i | \(-0.0272838\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 151.565 | − | 859.566i | 0.00745356 | − | 0.0422712i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15424.9 | + | 5614.22i | −0.755514 | + | 0.274985i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −487.759 | − | 844.824i | −0.0237948 | − | 0.0412139i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14825.3 | + | 12439.9i | 0.720348 | + | 0.604443i | 0.927481 | − | 0.373869i | \(-0.121969\pi\) |
−0.207134 | + | 0.978313i | \(0.566414\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2201.75 | + | 3813.54i | −0.106555 | + | 0.184559i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1147.64 | − | 6508.57i | −0.0553203 | − | 0.313737i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8679.37 | + | 3159.03i | 0.416720 | + | 0.151674i | 0.541866 | − | 0.840465i | \(-0.317718\pi\) |
−0.125146 | + | 0.992138i | \(0.539940\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1326.58 | 0.0634411 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18921.9 | −0.901336 | −0.450668 | − | 0.892692i | \(-0.648814\pi\) | ||||
−0.450668 | + | 0.892692i | \(0.648814\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4674.12 | − | 1701.24i | −0.221775 | − | 0.0807196i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1134.77 | + | 6435.61i | 0.0536310 | + | 0.304157i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5005.41 | − | 8669.62i | 0.235639 | − | 0.408138i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1729.72 | + | 1451.41i | 0.0811123 | + | 0.0680613i | 0.682442 | − | 0.730939i | \(-0.260918\pi\) |
−0.601330 | + | 0.799001i | \(0.705362\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5761.38 | − | 9979.00i | −0.269119 | − | 0.466128i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7074.05 | − | 2574.74i | 0.329154 | − | 0.119802i | −0.172157 | − | 0.985070i | \(-0.555074\pi\) |
0.501311 | + | 0.865267i | \(0.332851\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1173.03 | + | 6652.57i | −0.0543696 | + | 0.308345i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 15794.5 | − | 13253.1i | 0.729244 | − | 0.611909i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −29187.1 | − | 12851.0i | −1.34241 | − | 0.591060i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9401.78 | − | 7889.03i | 0.430758 | − | 0.361449i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1147.07 | + | 6505.38i | −0.0523538 | + | 0.296913i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16803.3 | + | 6115.90i | −0.763994 | + | 0.278071i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4288.31 | − | 7427.58i | −0.194234 | − | 0.336423i | 0.752415 | − | 0.658689i | \(-0.228889\pi\) |
−0.946649 | + | 0.322266i | \(0.895555\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3515.72 | + | 2950.04i | 0.158635 | + | 0.133111i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9154.59 | − | 15856.2i | 0.411504 | − | 0.712746i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 329.876 | + | 1870.82i | 0.0147720 | + | 0.0837764i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −41651.9 | − | 15160.0i | −1.85816 | − | 0.676316i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3324.77 | −0.147766 | −0.0738828 | − | 0.997267i | \(-0.523539\pi\) | ||||
−0.0738828 | + | 0.997267i | \(0.523539\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16323.5 | 0.722758 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2216.90 | + | 806.885i | 0.0977906 | + | 0.0355929i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2413.61 | + | 13688.3i | 0.106070 | + | 0.601555i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 714.731 | − | 1237.95i | 0.0312931 | − | 0.0542013i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −33843.6 | − | 28398.1i | −1.47627 | − | 1.23874i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15652.3 | − | 27110.6i | −0.680229 | − | 1.17819i | −0.974911 | − | 0.222596i | \(-0.928547\pi\) |
0.294682 | − | 0.955595i | \(-0.404786\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33322.3 | + | 12128.3i | −1.44279 | + | 0.525133i | −0.940568 | − | 0.339606i | \(-0.889706\pi\) |
−0.502223 | + | 0.864738i | \(0.667484\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4750.39 | + | 26940.8i | −0.204924 | + | 1.16218i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8940.54 | + | 7502.00i | −0.384262 | + | 0.322434i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4317.16 | − | 39507.8i | −0.184869 | − | 1.69180i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3054.63 | + | 2563.14i | −0.130326 | + | 0.109357i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7023.01 | − | 39829.5i | 0.298544 | − | 1.69313i | −0.353894 | − | 0.935286i | \(-0.615143\pi\) |
0.652438 | − | 0.757842i | \(-0.273746\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11727.4 | − | 4268.41i | 0.496707 | − | 0.180787i | −0.0815050 | − | 0.996673i | \(-0.525973\pi\) |
0.578213 | + | 0.815886i | \(0.303750\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1512.96 | + | 2620.51i | 0.0638477 | + | 0.110587i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8391.47 | − | 7041.28i | −0.352842 | − | 0.296069i | 0.449088 | − | 0.893487i | \(-0.351749\pi\) |
−0.801930 | + | 0.597418i | \(0.796193\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17615.7 | + | 30511.3i | −0.738020 | + | 1.27829i | 0.215365 | + | 0.976534i | \(0.430906\pi\) |
−0.953386 | + | 0.301755i | \(0.902428\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8829.91 | + | 50076.9i | 0.368599 | + | 2.09043i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7385.71 | + | 2688.18i | 0.307202 | + | 0.111813i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18015.2 | 0.746636 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −15057.5 | −0.621820 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22899.3 | + | 8334.68i | 0.942280 | + | 0.342962i | 0.767066 | − | 0.641569i | \(-0.221716\pi\) |
0.175214 | + | 0.984530i | \(0.443938\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2388.41 | − | 13545.3i | −0.0979296 | − | 0.555387i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11623.5 | − | 20132.5i | 0.474892 | − | 0.822538i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14900.5 | − | 12503.0i | −0.606619 | − | 0.509014i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4946.97 | + | 8568.41i | 0.200685 | + | 0.347596i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 333.394 | − | 121.345i | 0.0134771 | − | 0.00490526i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 739.877 | − | 4196.05i | 0.0298034 | − | 0.169023i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25463.0 | − | 21366.0i | 1.02208 | − | 0.857630i | 0.0321960 | − | 0.999482i | \(-0.489750\pi\) |
0.989888 | + | 0.141851i | \(0.0453055\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9921.93 | + | 14841.5i | −0.396869 | + | 0.593646i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 32182.4 | − | 27004.2i | 1.28276 | − | 1.07637i | 0.289907 | − | 0.957055i | \(-0.406376\pi\) |
0.992857 | − | 0.119311i | \(-0.0380687\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1929.88 | + | 10944.9i | −0.0766552 | + | 0.434733i | 0.922192 | + | 0.386732i | \(0.126396\pi\) |
−0.998847 | + | 0.0480010i | \(0.984715\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 22060.0 | − | 8029.18i | 0.873173 | − | 0.317809i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5088.42 | − | 8813.40i | −0.200709 | − | 0.347638i | 0.748048 | − | 0.663645i | \(-0.230991\pi\) |
−0.948757 | + | 0.316006i | \(0.897658\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2828.58 | + | 2373.46i | 0.111184 | + | 0.0932948i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13304.3 | + | 23043.7i | −0.521151 | + | 0.902661i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1576.70 | − | 8941.90i | −0.0615487 | − | 0.349060i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4937.98 | − | 1797.28i | −0.192098 | − | 0.0699178i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11926.0 | 0.462355 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10922.2 | −0.421987 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −832.509 | − | 303.008i | −0.0320545 | − | 0.0116669i | 0.325943 | − | 0.945389i | \(-0.394318\pi\) |
−0.357998 | + | 0.933722i | \(0.616540\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6511.10 | + | 36926.3i | 0.249845 | + | 1.41694i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −974.955 | + | 1688.67i | −0.0372839 | + | 0.0645775i | −0.884065 | − | 0.467364i | \(-0.845204\pi\) |
0.846781 | + | 0.531941i | \(0.178537\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9964.07 | + | 8360.84i | 0.379748 | + | 0.318646i | 0.812604 | − | 0.582817i | \(-0.198050\pi\) |
−0.432855 | + | 0.901463i | \(0.642494\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16496.3 | + | 28572.4i | 0.626573 | + | 1.08526i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4138.11 | + | 1506.15i | −0.156645 | + | 0.0570141i | −0.419153 | − | 0.907916i | \(-0.637673\pi\) |
0.262508 | + | 0.964930i | \(0.415451\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2132.07 | + | 12091.6i | −0.0804356 | + | 0.456173i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10850.0 | + | 9104.25i | −0.407957 | + | 0.342316i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 32205.6 | + | 30845.0i | 1.20685 | + | 1.15587i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4334.54 | + | 3637.11i | −0.161886 | + | 0.135838i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −365.318 | + | 2071.82i | −0.0135982 | + | 0.0771195i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −22779.5 | + | 8291.06i | −0.845093 | + | 0.307589i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8133.51 | + | 14087.7i | 0.300740 | + | 0.520897i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 22411.2 | + | 18805.3i | 0.825913 | + | 0.693023i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21059.7 | − | 36476.6i | 0.773536 | − | 1.33980i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4100.04 | + | 23252.5i | 0.150099 | + | 0.851252i | 0.963131 | + | 0.269033i | \(0.0867041\pi\) |
−0.813032 | + | 0.582219i | \(0.802185\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3943.08 | + | 1435.16i | 0.143876 | + | 0.0523667i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46961.0 | −1.70789 | −0.853944 | − | 0.520365i | \(-0.825796\pi\) | ||||
−0.853944 | + | 0.520365i | \(0.825796\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14922.8 | 0.540935 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5883.19 | − | 2141.31i | −0.212560 | − | 0.0773655i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −835.114 | − | 4736.17i | −0.0300741 | − | 0.170558i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7643.95 | + | 13239.7i | −0.274375 | + | 0.475231i | −0.969977 | − | 0.243196i | \(-0.921804\pi\) |
0.695602 | + | 0.718427i | \(0.255138\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 53405.9 | + | 44812.9i | 1.91073 | + | 1.60329i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9731.82 | + | 16856.0i | 0.347049 | + | 0.601107i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9132.67 | − | 3324.02i | 0.324627 | − | 0.118155i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2029.69 | − | 11510.9i | 0.0719134 | − | 0.407841i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32830.3 | − | 27547.9i | 1.15945 | − | 0.972893i | 0.159551 | − | 0.987190i | \(-0.448995\pi\) |
0.999898 | + | 0.0142963i | \(0.00455080\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9492.09 | + | 19259.8i | 0.334147 | + | 0.677995i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24788.5 | + | 20800.0i | −0.869817 | + | 0.729863i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1031.62 | − | 5850.63i | 0.0360831 | − | 0.204638i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18292.3 | + | 6657.86i | −0.637763 | + | 0.232127i | −0.640607 | − | 0.767869i | \(-0.721317\pi\) |
0.00284361 | + | 0.999996i | \(0.499095\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1106.15 | − | 1915.90i | −0.0384427 | − | 0.0665848i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8172.65 | − | 6857.67i | −0.283125 | − | 0.237570i | 0.490154 | − | 0.871636i | \(-0.336941\pi\) |
−0.773279 | + | 0.634065i | \(0.781385\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2425.65 | − | 4201.35i | 0.0837647 | − | 0.145085i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1262.06 | + | 7157.50i | 0.0434442 | + | 0.246385i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19411.4 | − | 7065.16i | −0.666087 | − | 0.242436i | −0.0132248 | − | 0.999913i | \(-0.504210\pi\) |
−0.652862 | + | 0.757477i | \(0.726432\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22042.7 | −0.753990 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 40517.7 | 1.38157 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33465.4 | + | 12180.4i | 1.13751 | + | 0.414021i | 0.841015 | − | 0.541012i | \(-0.181959\pi\) |
0.296499 | + | 0.955033i | \(0.404181\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5696.61 | − | 32307.1i | −0.193024 | − | 1.09469i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5429.33 | + | 9403.87i | −0.183391 | + | 0.317643i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17830.0 | − | 14961.1i | −0.600376 | − | 0.503775i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12733.2 | − | 22054.5i | −0.427417 | − | 0.740309i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1741.56 | + | 633.877i | −0.0582774 | + | 0.0212112i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4540.60 | + | 25751.0i | −0.151468 | + | 0.859020i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11682.1 | + | 9802.44i | −0.388491 | + | 0.325983i | −0.816025 | − | 0.578017i | \(-0.803827\pi\) |
0.427534 | + | 0.903999i | \(0.359382\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16059.9 | − | 4676.82i | 0.532423 | − | 0.155048i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 39659.7 | − | 33278.4i | 1.31075 | − | 1.09985i | 0.322573 | − | 0.946545i | \(-0.395452\pi\) |
0.988179 | − | 0.153307i | \(-0.0489922\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1126.58 | + | 6389.13i | −0.0371186 | + | 0.210510i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4509.30 | + | 1641.25i | −0.148116 | + | 0.0539099i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14233.2 | − | 24652.6i | −0.466080 | − | 0.807275i | 0.533169 | − | 0.846009i | \(-0.321001\pi\) |
−0.999250 | + | 0.0387336i | \(0.987668\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1642.96 | − | 1378.61i | −0.0536356 | − | 0.0450056i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4725.01 | + | 8183.95i | −0.153780 | + | 0.266354i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4070.02 | − | 23082.2i | −0.132059 | − | 0.748941i | −0.976863 | − | 0.213866i | \(-0.931394\pi\) |
0.844804 | − | 0.535075i | \(-0.179717\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −49369.3 | − | 17969.0i | −1.59699 | − | 0.581258i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −32826.6 | −1.05865 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6045.76 | 0.194382 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30107.7 | − | 10958.3i | −0.965089 | − | 0.351264i | −0.189063 | − | 0.981965i | \(-0.560545\pi\) |
−0.776026 | + | 0.630701i | \(0.782767\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6297.99 | − | 35717.7i | −0.201270 | − | 1.14146i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 32235.4 | − | 55833.4i | 1.02707 | − | 1.77893i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15963.6 | + | 13395.1i | 0.507094 | + | 0.425503i | 0.860105 | − | 0.510117i | \(-0.170398\pi\) |
−0.353011 | + | 0.935619i | \(0.614842\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10831.7 | + | 18761.1i | 0.343043 | + | 0.594168i |
(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 | 76.4.i.a.25.5 | ✓ | 30 | |
19.4 | even | 9 | 1444.4.a.j.1.3 | 15 | |||
19.15 | odd | 18 | 1444.4.a.k.1.13 | 15 | |||
19.16 | even | 9 | inner | 76.4.i.a.73.5 | yes | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.4.i.a.25.5 | ✓ | 30 | 1.1 | even | 1 | trivial | |
76.4.i.a.73.5 | yes | 30 | 19.16 | even | 9 | inner | |
1444.4.a.j.1.3 | 15 | 19.4 | even | 9 | |||
1444.4.a.k.1.13 | 15 | 19.15 | odd | 18 |