Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,4,Mod(41,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.41");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.x (of order \(6\), degree \(2\), 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: | \(14.8684813214\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 209.18 | ||
Character | \(\chi\) | \(=\) | 252.209 |
Dual form | 252.4.x.a.41.18 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 4.07854 | − | 3.21955i | 0.784916 | − | 0.619603i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.330097 | − | 0.571745i | −0.0295248 | − | 0.0511384i | 0.850885 | − | 0.525351i | \(-0.176066\pi\) |
−0.880410 | + | 0.474213i | \(0.842733\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.762896 | + | 18.5045i | −0.0411925 | + | 0.999151i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.26899 | − | 26.2621i | 0.232185 | − | 0.972672i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 21.4150 | + | 12.3640i | 0.586989 | + | 0.338898i | 0.763906 | − | 0.645328i | \(-0.223279\pi\) |
−0.176917 | + | 0.984226i | \(0.556612\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 43.5283 | − | 25.1311i | 0.928659 | − | 0.536162i | 0.0422718 | − | 0.999106i | \(-0.486540\pi\) |
0.886387 | + | 0.462945i | \(0.153207\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.18708 | − | 1.26912i | −0.0548600 | − | 0.0218457i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 67.5530 | 0.963765 | 0.481882 | − | 0.876236i | \(-0.339953\pi\) | ||||
0.481882 | + | 0.876236i | \(0.339953\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 62.9647i | 0.760268i | 0.924932 | + | 0.380134i | \(0.124122\pi\) | ||||
−0.924932 | + | 0.380134i | \(0.875878\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 56.4648 | + | 77.9277i | 0.586744 | + | 0.809772i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 135.811 | − | 78.4107i | 1.23124 | − | 0.710859i | 0.263954 | − | 0.964535i | \(-0.414973\pi\) |
0.967289 | + | 0.253676i | \(0.0816398\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 62.2821 | − | 107.876i | 0.498257 | − | 0.863006i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −58.9839 | − | 127.295i | −0.420424 | − | 0.907328i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −129.859 | − | 74.9743i | −0.831527 | − | 0.480082i | 0.0228484 | − | 0.999739i | \(-0.492727\pi\) |
−0.854375 | + | 0.519657i | \(0.826060\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −139.518 | + | 80.5507i | −0.808327 | + | 0.466688i | −0.846375 | − | 0.532588i | \(-0.821220\pi\) |
0.0380475 | + | 0.999276i | \(0.487886\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 127.149 | − | 18.5198i | 0.670719 | − | 0.0976934i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10.8317 | − | 5.67211i | 0.0523112 | − | 0.0273932i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −16.2664 | −0.0722753 | −0.0361377 | − | 0.999347i | \(-0.511505\pi\) | ||||
−0.0361377 | + | 0.999347i | \(0.511505\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 96.6211 | − | 242.639i | 0.396712 | − | 0.996241i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 134.901 | + | 233.655i | 0.513853 | + | 0.890019i | 0.999871 | + | 0.0160703i | \(0.00511554\pi\) |
−0.486018 | + | 0.873949i | \(0.661551\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 188.088 | − | 325.779i | 0.667051 | − | 1.15537i | −0.311673 | − | 0.950189i | \(-0.600889\pi\) |
0.978725 | − | 0.205178i | \(-0.0657772\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −17.0846 | + | 5.08479i | −0.0565961 | + | 0.0168444i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 31.3735 | − | 54.3405i | 0.0973679 | − | 0.168646i | −0.813226 | − | 0.581947i | \(-0.802291\pi\) |
0.910594 | + | 0.413301i | \(0.135624\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −341.836 | − | 28.2341i | −0.996606 | − | 0.0823151i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 275.518 | − | 217.490i | 0.756474 | − | 0.597151i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 136.820i | 0.354597i | 0.984157 | + | 0.177299i | \(0.0567358\pi\) | ||||
−0.984157 | + | 0.177299i | \(0.943264\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 16.3253i | − | 0.0400236i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 202.718 | + | 256.804i | 0.471064 | + | 0.596746i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 358.829 | + | 621.509i | 0.791788 | + | 1.37142i | 0.924859 | + | 0.380311i | \(0.124183\pi\) |
−0.133070 | + | 0.991107i | \(0.542484\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −23.9682 | − | 13.8380i | −0.0503083 | − | 0.0290455i | 0.474635 | − | 0.880183i | \(-0.342580\pi\) |
−0.524943 | + | 0.851137i | \(0.675913\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 481.186 | + | 136.040i | 0.962282 | + | 0.272055i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −28.7371 | − | 16.5914i | −0.0548369 | − | 0.0316601i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −163.773 | − | 283.664i | −0.298628 | − | 0.517239i | 0.677194 | − | 0.735804i | \(-0.263196\pi\) |
−0.975822 | + | 0.218565i | \(0.929862\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 301.465 | − | 757.052i | 0.525972 | − | 1.32085i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 246.304i | 0.411703i | 0.978583 | + | 0.205852i | \(0.0659965\pi\) | ||||
−0.978583 | + | 0.205852i | \(0.934004\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 261.253i | 0.418868i | 0.977823 | + | 0.209434i | \(0.0671622\pi\) | ||||
−0.977823 | + | 0.209434i | \(0.932838\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −93.2913 | − | 640.496i | −0.143631 | − | 0.986108i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −245.127 | + | 386.843i | −0.362790 | + | 0.572531i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −391.980 | + | 678.930i | −0.558244 | + | 0.966906i | 0.439400 | + | 0.898292i | \(0.355191\pi\) |
−0.997643 | + | 0.0686145i | \(0.978142\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −650.399 | − | 329.274i | −0.892180 | − | 0.451679i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 599.424 | − | 1038.23i | 0.792715 | − | 1.37302i | −0.131565 | − | 0.991308i | \(-0.542000\pi\) |
0.924280 | − | 0.381715i | \(-0.124666\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −22.2990 | − | 38.6231i | −0.0284550 | − | 0.0492854i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −771.020 | + | 112.303i | −0.950139 | + | 0.138392i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 968.771 | 1.15381 | 0.576907 | − | 0.816810i | \(-0.304259\pi\) | ||||
0.576907 | + | 0.816810i | \(0.304259\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 431.831 | + | 824.643i | 0.497453 | + | 0.949957i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −309.692 | + | 777.714i | −0.345307 | + | 0.867152i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 35.9997 | − | 20.7845i | 0.0388789 | − | 0.0224467i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1106.79 | − | 639.005i | −1.15853 | − | 0.668878i | −0.207579 | − | 0.978218i | \(-0.566558\pi\) |
−0.950951 | + | 0.309340i | \(0.899892\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 458.955 | − | 484.895i | 0.465927 | − | 0.492260i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −285.125 | + | 493.852i | −0.280901 | + | 0.486535i | −0.971607 | − | 0.236601i | \(-0.923967\pi\) |
0.690706 | + | 0.723136i | \(0.257300\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1559.24 | + | 900.228i | −1.49162 | + | 0.861186i | −0.999954 | − | 0.00959990i | \(-0.996944\pi\) |
−0.491663 | + | 0.870785i | \(0.663611\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 25.9159 | − | 58.0072i | 0.0240870 | − | 0.0539135i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2038.95i | 1.84218i | 0.389350 | + | 0.921090i | \(0.372700\pi\) | ||||
−0.389350 | + | 0.921090i | \(0.627300\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1189.58 | −1.04533 | −0.522666 | − | 0.852538i | \(-0.675062\pi\) | ||||
−0.522666 | + | 0.852538i | \(0.675062\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −66.3434 | + | 52.3706i | −0.0567300 | + | 0.0447820i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −646.454 | + | 373.230i | −0.538171 | + | 0.310713i | −0.744337 | − | 0.667804i | \(-0.767234\pi\) |
0.206167 | + | 0.978517i | \(0.433901\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −89.6618 | − | 51.7663i | −0.0727044 | − | 0.0419759i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −387.117 | − | 1300.69i | −0.305889 | − | 1.02777i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −51.5359 | + | 1250.04i | −0.0396999 | + | 0.962947i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −359.764 | − | 623.130i | −0.270296 | − | 0.468167i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1302.46 | + | 518.652i | 0.954789 | + | 0.380205i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −164.761 | −0.117893 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1832.75 | −1.28055 | −0.640277 | − | 0.768144i | \(-0.721180\pi\) | ||||
−0.640277 | + | 0.768144i | \(0.721180\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −281.735 | − | 1934.26i | −0.192289 | − | 1.32017i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 235.639 | + | 408.138i | 0.157159 | + | 0.272208i | 0.933843 | − | 0.357683i | \(-0.116433\pi\) |
−0.776684 | + | 0.629890i | \(0.783100\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1165.13 | − | 48.0355i | −0.759622 | − | 0.0313173i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −53.3096 | + | 75.7433i | −0.0339864 | + | 0.0482885i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2271.58 | − | 1311.50i | −1.41660 | − | 0.817874i | −0.420601 | − | 0.907246i | \(-0.638181\pi\) |
−0.995998 | + | 0.0893720i | \(0.971514\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −164.415 | + | 94.9252i | −0.100328 | + | 0.0579241i | −0.549324 | − | 0.835609i | \(-0.685115\pi\) |
0.448997 | + | 0.893533i | \(0.351781\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −46.9938 | − | 322.638i | −0.0280680 | − | 0.192702i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1242.88 | 0.726817 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 98.9953i | 0.0566973i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1485.09 | + | 985.404i | −0.833255 | + | 0.552890i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −383.974 | + | 221.687i | −0.211117 | + | 0.121888i | −0.601830 | − | 0.798624i | \(-0.705562\pi\) |
0.390714 | + | 0.920512i | \(0.372228\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 943.459 | − | 1634.12i | 0.508461 | − | 0.880680i | −0.491491 | − | 0.870883i | \(-0.663548\pi\) |
0.999952 | − | 0.00979739i | \(-0.00311865\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 423.489 | − | 1774.09i | 0.223772 | − | 0.937427i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 92.1089 | + | 53.1791i | 0.0477314 | + | 0.0275577i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2133.22 | + | 1231.62i | −1.08439 | + | 0.626075i | −0.932078 | − | 0.362257i | \(-0.882006\pi\) |
−0.152316 | + | 0.988332i | \(0.548673\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 440.498 | + | 558.025i | 0.219709 | + | 0.278329i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1347.34 | + | 2572.94i | 0.659537 | + | 1.25948i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2514.36 | 1.20822 | 0.604111 | − | 0.796900i | \(-0.293528\pi\) | ||||
0.604111 | + | 0.796900i | \(0.293528\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −52.5600 | − | 66.5832i | −0.0247987 | − | 0.0314151i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1415.81 | + | 2452.25i | 0.656038 | + | 1.13629i | 0.981632 | + | 0.190782i | \(0.0611024\pi\) |
−0.325594 | + | 0.945510i | \(0.605564\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 164.640 | − | 285.164i | 0.0749385 | − | 0.129797i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1653.59 | + | 394.725i | 0.739491 | + | 0.176523i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 667.439 | − | 1156.04i | 0.293320 | − | 0.508046i | −0.681272 | − | 0.732030i | \(-0.738573\pi\) |
0.974593 | + | 0.223984i | \(0.0719064\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1948.68 | + | 1234.80i | 0.841749 | + | 0.533383i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3464.48 | + | 1379.58i | 1.47122 | + | 0.585853i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 1431.23i | − | 0.597626i | −0.954312 | − | 0.298813i | \(-0.903409\pi\) | ||
0.954312 | − | 0.298813i | \(-0.0965907\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 262.769i | 0.107909i | 0.998543 | + | 0.0539543i | \(0.0171825\pi\) | ||||
−0.998543 | + | 0.0539543i | \(0.982817\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −142.307 | + | 20.7278i | −0.0574845 | + | 0.00837289i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.36951 | + | 9.30026i | 0.00213391 | + | 0.00369605i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1446.65 | + | 835.223i | 0.565719 | + | 0.326618i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2400.53 | − | 994.358i | 0.923876 | − | 0.382693i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −97.8990 | − | 56.5220i | −0.0370876 | − | 0.0214125i | 0.481342 | − | 0.876533i | \(-0.340150\pi\) |
−0.518429 | + | 0.855121i | \(0.673483\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2091.54 | − | 3622.65i | −0.780063 | − | 1.35111i | −0.931905 | − | 0.362704i | \(-0.881854\pi\) |
0.151842 | − | 0.988405i | \(-0.451480\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −170.622 | + | 24.8520i | −0.0626591 | + | 0.00912659i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 314.320i | − | 0.113677i | −0.998383 | − | 0.0568385i | \(-0.981898\pi\) | ||
0.998383 | − | 0.0568385i | \(-0.0181020\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1407.97i | 0.501550i | 0.968045 | + | 0.250775i | \(0.0806855\pi\) | ||||
−0.968045 | + | 0.250775i | \(0.919314\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1581.23 | − | 629.658i | −0.554881 | − | 0.220958i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1486.43 | − | 2345.79i | 0.513927 | − | 0.811045i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 89.0607 | − | 154.258i | 0.0303428 | − | 0.0525552i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1207.83 | − | 4058.25i | −0.405556 | − | 1.36265i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −778.494 | + | 1348.39i | −0.257653 | + | 0.446269i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −73.9358 | − | 128.061i | −0.0241230 | − | 0.0417822i | 0.853712 | − | 0.520746i | \(-0.174346\pi\) |
−0.877835 | + | 0.478963i | \(0.841013\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 792.989 | + | 1004.56i | 0.255093 | + | 0.323152i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −248.350 | −0.0787782 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1384.12 | − | 2643.16i | −0.432995 | − | 0.826865i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 841.118 | + | 1065.53i | 0.259532 | + | 0.328776i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2940.46 | − | 1697.68i | 0.895009 | − | 0.516734i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2005.48 | + | 1157.86i | 0.602228 | + | 0.347696i | 0.769917 | − | 0.638143i | \(-0.220297\pi\) |
−0.167690 | + | 0.985840i | \(0.553631\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2442.60 | − | 2311.93i | −0.723734 | − | 0.685017i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2233.35 | − | 3868.27i | 0.653006 | − | 1.13104i | −0.329384 | − | 0.944196i | \(-0.606841\pi\) |
0.982390 | − | 0.186843i | \(-0.0598257\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1016.15 | − | 586.677i | 0.293229 | − | 0.169296i | −0.346168 | − | 0.938172i | \(-0.612517\pi\) |
0.639397 | + | 0.768877i | \(0.279184\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 245.699 | + | 2366.95i | 0.0699819 | + | 0.674174i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1751.08i | 0.492347i | 0.969226 | + | 0.246173i | \(0.0791733\pi\) | ||||
−0.969226 | + | 0.246173i | \(0.920827\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −41.4252 | −0.0114991 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 587.141 | + | 4031.04i | 0.160924 | + | 1.10483i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5007.40 | − | 2891.03i | 1.35524 | − | 0.782447i | 0.366261 | − | 0.930512i | \(-0.380638\pi\) |
0.988978 | + | 0.148065i | \(0.0473045\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −230.468 | − | 133.061i | −0.0616005 | − | 0.0355651i | 0.468883 | − | 0.883260i | \(-0.344656\pi\) |
−0.530484 | + | 0.847695i | \(0.677990\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3712.80 | + | 751.035i | −0.980148 | + | 0.198267i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 96.6964 | + | 204.763i | 0.0252151 | + | 0.0533952i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1582.37 | + | 2740.74i | 0.407626 | + | 0.706029i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −897.867 | − | 6164.35i | −0.228514 | − | 1.56887i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7212.14 | −1.81365 | −0.906826 | − | 0.421506i | \(-0.861502\pi\) | ||||
−0.906826 | + | 0.421506i | \(0.861502\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3877.87 | 0.963635 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −215.297 | − | 85.7329i | −0.0528721 | − | 0.0210541i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2752.31 | + | 4767.14i | 0.668033 | + | 1.15707i | 0.978453 | + | 0.206468i | \(0.0661968\pi\) |
−0.310421 | + | 0.950599i | \(0.600470\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.4096 | − | 301.003i | 0.00297720 | − | 0.0722140i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2783.07 | + | 2940.37i | −0.660030 | + | 0.697335i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4088.19 | − | 2360.32i | −0.958511 | − | 0.553396i | −0.0627964 | − | 0.998026i | \(-0.520002\pi\) |
−0.895714 | + | 0.444630i | \(0.853335\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 78.2261 | − | 45.1639i | 0.0181336 | − | 0.0104694i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3951.17 | − | 3119.01i | 0.905647 | − | 0.714907i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3595.18 | −0.814877 | −0.407439 | − | 0.913233i | \(-0.633578\pi\) | ||||
−0.407439 | + | 0.913233i | \(0.633578\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3673.66i | 0.823466i | 0.911305 | + | 0.411733i | \(0.135076\pi\) | ||||
−0.911305 | + | 0.411733i | \(0.864924\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4416.22 | + | 1973.04i | 0.979054 | + | 0.437413i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2667.55 | − | 1540.11i | 0.584942 | − | 0.337716i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 880.297 | − | 1524.72i | 0.190946 | − | 0.330727i | −0.754618 | − | 0.656164i | \(-0.772178\pi\) |
0.945564 | + | 0.325437i | \(0.105511\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1240.80 | + | 4169.01i | 0.266253 | + | 0.894595i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6960.95 | − | 4018.91i | −1.47778 | − | 0.853195i | −0.478093 | − | 0.878309i | \(-0.658672\pi\) |
−0.999685 | + | 0.0251141i | \(0.992005\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6519.11 | − | 3763.81i | 1.36933 | − | 0.790584i | 0.378488 | − | 0.925606i | \(-0.376444\pi\) |
0.990843 | + | 0.135022i | \(0.0431106\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 79.9098 | − | 200.673i | 0.0166086 | − | 0.0417083i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4426.59 | + | 2318.02i | −0.910430 | + | 0.476754i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −349.597 | −0.0711575 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6571.40 | + | 957.156i | −1.32379 | + | 0.192816i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 105.807 | + | 183.262i | 0.0210965 | + | 0.0365403i | 0.876381 | − | 0.481619i | \(-0.159951\pi\) |
−0.855284 | + | 0.518159i | \(0.826618\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 236.897 | − | 410.317i | 0.0467548 | − | 0.0809816i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 310.724 | − | 3455.29i | 0.0607072 | − | 0.675072i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3941.08 | − | 6826.16i | 0.762270 | − | 1.32029i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5884.89 | + | 3729.02i | 1.12691 | + | 0.714078i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 427.085 | + | 2932.17i | 0.0809748 | + | 0.555937i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 18.2716i | 0.00343025i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2701.00i | − | 0.502131i | −0.967970 | − | 0.251065i | \(-0.919219\pi\) | ||
0.967970 | − | 0.251065i | \(-0.0807809\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3461.10 | + | 8691.67i | −0.637201 | + | 1.60017i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3234.86 | − | 5602.95i | −0.589815 | − | 1.02159i | −0.994256 | − | 0.107025i | \(-0.965867\pi\) |
0.404442 | − | 0.914564i | \(-0.367466\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1476.26 | + | 852.319i | 0.266592 | + | 0.153917i | 0.627338 | − | 0.778747i | \(-0.284145\pi\) |
−0.360746 | + | 0.932664i | \(0.617478\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −81.0579 | − | 320.022i | −0.0144987 | − | 0.0572419i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1247.17 | + | 720.056i | 0.220972 | + | 0.127578i | 0.606400 | − | 0.795159i | \(-0.292613\pi\) |
−0.385428 | + | 0.922738i | \(0.625946\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1853.96 | − | 3211.16i | −0.325398 | − | 0.563606i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6564.52 | + | 8315.96i | 1.14142 | + | 1.44596i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4253.45i | 0.732719i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 6260.86i | − | 1.06858i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4851.75 | + | 3829.91i | −0.820497 | + | 0.647690i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 981.610 | + | 622.008i | 0.164492 | + | 0.104232i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5661.53 | + | 9806.05i | −0.940138 | + | 1.62837i | −0.174932 | + | 0.984580i | \(0.555971\pi\) |
−0.765205 | + | 0.643786i | \(0.777363\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −101.974 | + | 427.191i | −0.0167812 | + | 0.0703002i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −108.122 | + | 187.273i | −0.0176339 | + | 0.0305428i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1069.77 | − | 1852.89i | −0.172920 | − | 0.299505i | 0.766520 | − | 0.642221i | \(-0.221987\pi\) |
−0.939439 | + | 0.342715i | \(0.888653\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1434.96 | + | 3603.53i | −0.229900 | + | 0.577335i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3983.71 | −0.632639 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 783.244 | − | 6303.98i | 0.123298 | − | 0.992370i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −532.354 | + | 77.5399i | −0.0830752 | + | 0.0121003i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3237.97 | − | 1869.44i | 0.500931 | − | 0.289213i | −0.228167 | − | 0.973622i | \(-0.573273\pi\) |
0.729098 | + | 0.684409i | \(0.239940\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5644.28 | − | 3258.72i | −0.865705 | − | 0.499815i | 0.000213394 | − | 1.00000i | \(-0.499932\pi\) |
−0.865919 | + | 0.500185i | \(0.833265\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5766.51 | − | 4058.58i | −0.876905 | − | 0.617183i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1772.88 | + | 3070.72i | −0.267312 | + | 0.462998i | −0.968167 | − | 0.250306i | \(-0.919469\pi\) |
0.700855 | + | 0.713304i | \(0.252802\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 140.823 | − | 81.3044i | 0.0210539 | − | 0.0121555i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3814.36 | + | 5264.25i | 0.565483 | + | 0.780430i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6414.84i | 0.943071i | 0.881847 | + | 0.471535i | \(0.156300\pi\) | ||||
−0.881847 | + | 0.471535i | \(0.843700\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2894.45 | 0.421993 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3473.51 | − | 1383.18i | −0.502237 | − | 0.199995i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 149.370 | − | 86.2390i | 0.0214203 | − | 0.0123670i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6771.55 | + | 3909.55i | 0.963139 | + | 0.556068i | 0.897138 | − | 0.441751i | \(-0.145643\pi\) |
0.0660011 | + | 0.997820i | \(0.478976\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6981.97 | − | 2078.00i | 0.985005 | − | 0.293161i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2531.79 | − | 104.379i | −0.354296 | − | 0.0146068i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5548.13 | + | 9609.65i | 0.770165 | + | 1.33396i | 0.937472 | + | 0.348060i | \(0.113159\pi\) |
−0.167307 | + | 0.985905i | \(0.553507\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −671.984 | + | 530.456i | −0.0925363 | + | 0.0730470i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7536.74 | −1.02961 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5192.03 | −0.703686 | −0.351843 | − | 0.936059i | \(-0.614445\pi\) | ||||
−0.351843 | + | 0.936059i | \(0.614445\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7474.95 | + | 5900.63i | −1.00513 | + | 0.793435i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6875.13 | − | 11908.1i | −0.917240 | − | 1.58871i | −0.803588 | − | 0.595186i | \(-0.797078\pi\) |
−0.113652 | − | 0.993521i | \(-0.536255\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 302.091 | + | 12.4545i | 0.0399896 | + | 0.00164867i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7376.52 | − | 6981.91i | −0.968913 | − | 0.917081i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8425.29 | − | 4864.34i | −1.09815 | − | 0.634016i | −0.162413 | − | 0.986723i | \(-0.551928\pi\) |
−0.935734 | + | 0.352707i | \(0.885261\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9174.45 | − | 5296.87i | 1.18663 | − | 0.685101i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2275.08 | + | 905.958i | 0.292017 | + | 0.116284i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 517.567 | 0.0659281 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9192.44i | 1.16210i | 0.813866 | + | 0.581052i | \(0.197359\pi\) | ||||
−0.813866 | + | 0.581052i | \(0.802641\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4906.69 | + | 3555.29i | −0.615644 | + | 0.446083i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7796.50 | − | 4501.31i | 0.970919 | − | 0.560560i | 0.0714027 | − | 0.997448i | \(-0.477252\pi\) |
0.899516 | + | 0.436887i | \(0.143919\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4048.65 | + | 7012.46i | −0.500440 | + | 0.866788i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 26.4341 | + | 480.555i | 0.00324326 | + | 0.0589604i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −348.346 | − | 201.118i | −0.0424248 | − | 0.0244940i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4580.39 | + | 2644.49i | −0.553755 | + | 0.319711i | −0.750635 | − | 0.660717i | \(-0.770252\pi\) |
0.196880 | + | 0.980428i | \(0.436919\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13487.2 | + | 1964.47i | −1.61867 | + | 0.235767i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11774.5 | + | 6165.81i | −1.40287 | + | 0.734624i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −791.473 | −0.0936190 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −364.958 | + | 916.500i | −0.0428587 | + | 0.107629i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2805.44 | − | 4859.17i | −0.327100 | − | 0.566554i | 0.654835 | − | 0.755772i | \(-0.272738\pi\) |
−0.981935 | + | 0.189218i | \(0.939405\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −641.365 | + | 1110.88i | −0.0742475 | + | 0.128600i | −0.900759 | − | 0.434320i | \(-0.856989\pi\) |
0.826511 | + | 0.562920i | \(0.190322\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1230.42 | − | 1164.59i | −0.141430 | − | 0.133864i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4207.34 | − | 7287.32i | 0.480202 | − | 0.831734i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 274.351 | − | 432.963i | 0.0310932 | − | 0.0490692i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5069.13 | − | 4001.51i | 0.570490 | − | 0.450338i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 7183.17i | − | 0.802787i | −0.915906 | − | 0.401393i | \(-0.868526\pi\) | ||
0.915906 | − | 0.401393i | \(-0.131474\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 15271.9i | − | 1.69497i | −0.530820 | − | 0.847485i | \(-0.678116\pi\) | ||
0.530820 | − | 0.847485i | \(-0.321884\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 318.720 | + | 403.756i | 0.0351298 | + | 0.0445026i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4937.10 | + | 8551.31i | 0.540443 | + | 0.936075i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5050.88 | + | 2916.13i | 0.549123 | + | 0.317037i | 0.748768 | − | 0.662832i | \(-0.230646\pi\) |
−0.199645 | + | 0.979868i | \(0.563979\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2884.45 | + | 8800.34i | −0.311463 | + | 0.950258i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2636.52 | + | 1522.20i | 0.282765 | + | 0.163255i | 0.634675 | − | 0.772780i | \(-0.281134\pi\) |
−0.351909 | + | 0.936034i | \(0.614467\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −319.788 | − | 553.890i | −0.0340661 | − | 0.0590043i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −852.319 | + | 2140.38i | −0.0901864 | + | 0.226480i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 1445.89i | − | 0.151973i | −0.997109 | − | 0.0759863i | \(-0.975789\pi\) | ||
0.997109 | − | 0.0759863i | \(-0.0242105\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6671.64i | 0.696575i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1413.19 | − | 9702.33i | −0.146573 | − | 1.00630i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 328.939 | − | 519.110i | 0.0338921 | − | 0.0534862i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8001.23 | − | 13858.5i | 0.818998 | − | 1.41855i | −0.0874239 | − | 0.996171i | \(-0.527863\pi\) |
0.906422 | − | 0.422374i | \(-0.138803\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3984.54 | − | 8599.12i | −0.405190 | − | 0.874450i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6375.19 | + | 11042.2i | −0.644083 | + | 1.11559i | 0.340429 | + | 0.940270i | \(0.389428\pi\) |
−0.984512 | + | 0.175315i | \(0.943906\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3779.86 | + | 6546.91i | 0.379406 | + | 0.657151i | 0.990976 | − | 0.134040i | \(-0.0427949\pi\) |
−0.611570 | + | 0.791191i | \(0.709462\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 546.883 | − | 79.6561i | 0.0545399 | − | 0.00794401i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15808.4 | 1.56643 | 0.783217 | − | 0.621749i | \(-0.213577\pi\) | ||||
0.783217 | + | 0.621749i | \(0.213577\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5374.01 | − | 2814.14i | 0.529102 | − | 0.277068i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4735.19 | + | 11891.2i | −0.463240 | + | 1.16331i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8055.84 | − | 4651.04i | 0.783103 | − | 0.452125i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6792.36 | + | 3921.57i | 0.656115 | + | 0.378808i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3593.18 | + | 857.723i | 0.344907 | + | 0.0823321i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4236.78 | − | 7338.32i | 0.404141 | − | 0.699992i | −0.590080 | − | 0.807345i | \(-0.700904\pi\) |
0.994221 | + | 0.107352i | \(0.0342372\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −708.050 | + | 408.793i | −0.0671191 | + | 0.0387512i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13778.9 | + | 6156.02i | 1.29806 | + | 0.579935i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 843.735i | 0.0789939i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5933.46 | −0.552096 | −0.276048 | − | 0.961144i | \(-0.589025\pi\) | ||||
−0.276048 | + | 0.961144i | \(0.589025\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10254.9 | − | 8095.12i | 0.948352 | − | 0.748618i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 232.094 | − | 133.999i | 0.0213325 | − | 0.0123163i | −0.489296 | − | 0.872118i | \(-0.662746\pi\) |
0.510628 | + | 0.859802i | \(0.329413\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8772.38 | − | 5064.74i | −0.801396 | − | 0.462686i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −428.736 | − | 102.343i | −0.0389298 | − | 0.00929287i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4557.75 | − | 187.905i | −0.411354 | − | 0.0169591i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5365.31 | − | 9292.98i | −0.481331 | − | 0.833689i | 0.518440 | − | 0.855114i | \(-0.326513\pi\) |
−0.999770 | + | 0.0214248i | \(0.993180\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13669.6 | + | 5443.34i | 1.21898 | + | 0.485410i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1490.98 | 0.132166 | 0.0660830 | − | 0.997814i | \(-0.478950\pi\) | ||||
0.0660830 | + | 0.997814i | \(0.478950\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 376.476 | 0.0331742 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −246.611 | − | 1693.12i | −0.0216023 | − | 0.148312i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5918.88 | + | 10251.8i | 0.515422 | + | 0.892736i | 0.999840 | + | 0.0178998i | \(0.00569800\pi\) |
−0.484418 | + | 0.874837i | \(0.660969\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4834.37 | − | 199.309i | −0.418513 | − | 0.0172543i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8015.06 | − | 3713.90i | 0.689812 | − | 0.319635i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1029.40 | + | 594.326i | 0.0880794 | + | 0.0508526i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1343.73 | − | 775.802i | 0.114308 | − | 0.0659956i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −999.746 | − | 6863.80i | −0.0845549 | − | 0.580515i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5868.12 | 0.493449 | 0.246724 | − | 0.969086i | \(-0.420646\pi\) | ||||
0.246724 | + | 0.969086i | \(0.420646\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20680.0i | 1.72901i | 0.502622 | + | 0.864507i | \(0.332369\pi\) | ||||
−0.502622 | + | 0.864507i | \(0.667631\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 11923.3 | − | 1237.68i | 0.991187 | − | 0.102889i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9424.84 | + | 5441.44i | −0.779037 | + | 0.449777i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6212.96 | − | 10761.2i | 0.510640 | − | 0.884455i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18571.7 | − | 5527.37i | 1.51778 | − | 0.451728i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11744.0 | + | 6780.40i | 0.954388 | + | 0.551016i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1165.76 | − | 673.053i | 0.0942062 | − | 0.0543900i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4607.91 | − | 5837.33i | −0.370291 | − | 0.469086i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6971.35 | − | 4831.09i | −0.557100 | − | 0.386066i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7401.95 | 0.588234 | 0.294117 | − | 0.955769i | \(-0.404974\pi\) | ||||
0.294117 | + | 0.955769i | \(0.404974\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 845.997 | + | 1071.71i | 0.0668604 | + | 0.0846991i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 392.677 | + | 680.137i | 0.0308632 | + | 0.0534566i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5185.72 | − | 8981.93i | 0.405348 | − | 0.702083i | −0.589014 | − | 0.808123i | \(-0.700484\pi\) |
0.994362 | + | 0.106040i | \(0.0338171\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −513.672 | + | 542.705i | −0.0399326 | + | 0.0421896i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4720.73 | − | 8176.55i | 0.364991 | − | 0.632183i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12264.2 | − | 7771.37i | −0.943090 | − | 0.597599i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 51.8424 | + | 20.6441i | 0.00396502 | + | 0.00157891i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23317.1i | 1.77375i | 0.462014 | + | 0.886873i | \(0.347127\pi\) | ||||
−0.462014 | + | 0.886873i | \(0.652873\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 18907.4i | − | 1.43059i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8589.26 | − | 1251.07i | 0.646415 | − | 0.0941535i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4168.16 | + | 7219.47i | 0.312020 | + | 0.540434i | 0.978799 | − | 0.204821i | \(-0.0656611\pi\) |
−0.666780 | + | 0.745255i | \(0.732328\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 426.785 | + | 246.405i | 0.0317788 | + | 0.0183475i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6589.26 | − | 11784.1i | 0.488047 | − | 0.872817i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19760.4 | − | 11408.7i | −1.45589 | − | 0.840556i | −0.457080 | − | 0.889425i | \(-0.651105\pi\) |
−0.998805 | + | 0.0488697i | \(0.984438\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4072.82 | + | 7054.34i | 0.298498 | + | 0.517014i | 0.975793 | − | 0.218698i | \(-0.0701810\pi\) |
−0.677295 | + | 0.735712i | \(0.736848\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −581.261 | + | 84.6634i | −0.0423779 | + | 0.00617254i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 19534.3i | − | 1.41676i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19823.7i | 1.43028i | 0.698982 | + | 0.715140i | \(0.253637\pi\) | ||||
−0.698982 | + | 0.715140i | \(0.746363\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −20193.7 | − | 8041.31i | −1.44943 | − | 0.577177i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18754.7 | + | 11884.1i | 1.33920 | + | 0.848600i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1691.64 | + | 2930.00i | −0.120172 | + | 0.208145i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −615.878 | + | 650.687i | −0.0435272 | + | 0.0459873i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 349.569 | − | 605.472i | 0.0245797 | − | 0.0425732i | −0.853474 | − | 0.521136i | \(-0.825509\pi\) |
0.878054 | + | 0.478562i | \(0.158842\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5071.84 | − | 8784.69i | −0.354808 | − | 0.614545i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1011.97 | − | 1281.97i | −0.0704345 | − | 0.0892268i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22770.8 | 1.57687 | 0.788434 | − | 0.615119i | \(-0.210892\pi\) | ||||
0.788434 | + | 0.615119i | \(0.210892\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 731.714 | − | 383.168i | 0.0504157 | − | 0.0264006i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4533.04 | + | 5742.47i | 0.310762 | + | 0.393675i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1737.23 | + | 1002.99i | −0.118500 | + | 0.0684159i | −0.558078 | − | 0.829788i | \(-0.688461\pi\) |
0.439579 | + | 0.898204i | \(0.355128\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12437.9 | − | 7181.05i | −0.844184 | − | 0.487390i | 0.0145004 | − | 0.999895i | \(-0.495384\pi\) |
−0.858684 | + | 0.512505i | \(0.828718\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8476.31 | + | 2522.75i | −0.572441 | + | 0.170372i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −237.514 | + | 411.387i | −0.0159609 | + | 0.0276450i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13864.4 | + | 8004.64i | −0.927085 | + | 0.535253i | −0.885888 | − | 0.463898i | \(-0.846450\pi\) |
−0.0411965 | + | 0.999151i | \(0.513117\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1489.90 | − | 14353.1i | −0.0991362 | − | 0.955033i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 3153.79i | − | 0.208820i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 721.073 | 0.0475104 | 0.0237552 | − | 0.999718i | \(-0.492438\pi\) | ||||
0.0237552 | + | 0.999718i | \(0.492438\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −133.403 | − | 915.882i | −0.00874685 | − | 0.0600519i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7798.16 | + | 4502.27i | −0.508820 | + | 0.293767i | −0.732349 | − | 0.680930i | \(-0.761576\pi\) |
0.223528 | + | 0.974697i | \(0.428242\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9685.79 | + | 5592.09i | 0.628925 | + | 0.363110i | 0.780336 | − | 0.625361i | \(-0.215048\pi\) |
−0.151411 | + | 0.988471i | \(0.548382\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −17991.9 | − | 12663.1i | −1.16263 | − | 0.818279i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −739.072 | + | 17926.7i | −0.0475285 | + | 1.15284i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7730.87 | − | 13390.3i | −0.494776 | − | 0.856977i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1166.09 | + | 8005.87i | 0.0742732 | + | 0.509926i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1098.85 | −0.0696564 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8969.76 | 0.565897 | 0.282948 | − | 0.959135i | \(-0.408688\pi\) | ||||
0.282948 | + | 0.959135i | \(0.408688\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −713.847 | − | 284.260i | −0.0448229 | − | 0.0178489i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 604.986 | + | 1047.87i | 0.0378081 | + | 0.0654855i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15589.1 | + | 7361.72i | −0.969642 | + | 0.457899i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6468.48 | + | 1544.08i | 0.400452 | + | 0.0955913i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1495.77 | − | 863.586i | −0.0921678 | − | 0.0532131i | 0.453208 | − | 0.891405i | \(-0.350280\pi\) |
−0.545375 | + | 0.838192i | \(0.683613\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15392.5 | + | 8886.86i | −0.944045 | + | 0.545045i | −0.891226 | − | 0.453560i | \(-0.850154\pi\) |
−0.0528189 | + | 0.998604i | \(0.516821\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1012.90 | + | 799.575i | −0.0618342 | + | 0.0488112i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7518.12 | −0.456828 | −0.228414 | − | 0.973564i | \(-0.573354\pi\) | ||||
−0.228414 | + | 0.973564i | \(0.573354\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17746.2i | 1.07334i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14155.0 | − | 6324.03i | −0.852192 | − | 0.380735i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5483.68 | − | 3166.00i | 0.328626 | − | 0.189732i | −0.326605 | − | 0.945161i | \(-0.605905\pi\) |
0.655231 | + | 0.755429i | \(0.272571\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 155.567 | − | 269.451i | 0.00928018 | − | 0.0160737i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6861.07 | + | 1637.80i | 0.407421 | + | 0.0972549i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5478.28 | + | 3162.89i | 0.323829 | + | 0.186963i | 0.653098 | − | 0.757273i | \(-0.273469\pi\) |
−0.329269 | + | 0.944236i | \(0.606802\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18882.2 | + | 10901.7i | −1.11110 | + | 0.641491i | −0.939113 | − | 0.343608i | \(-0.888351\pi\) |
−0.171983 | + | 0.985100i | \(0.555017\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6527.04 | − | 16391.0i | 0.382337 | − | 0.960142i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 357.143 | + | 682.015i | 0.0208262 | + | 0.0397705i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23515.1 | −1.36508 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11907.2 | − | 1734.35i | 0.688132 | − | 0.100230i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −342.186 | − | 592.684i | −0.0196870 | − | 0.0340988i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12150.3 | + | 21044.9i | −0.695926 | + | 1.20538i | 0.273942 | + | 0.961746i | \(0.411672\pi\) |
−0.969868 | + | 0.243632i | \(0.921661\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −17405.6 | − | 1565.23i | −0.992508 | − | 0.0892532i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15606.5 | − | 27031.3i | 0.885979 | − | 1.53456i | 0.0413922 | − | 0.999143i | \(-0.486821\pi\) |
0.844587 | − | 0.535418i | \(-0.179846\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12668.9 | − | 19993.1i | 0.716033 | − | 1.12999i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3345.29 | − | 22967.3i | −0.188241 | − | 1.29237i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32330.6i | 1.81127i | 0.424063 | + | 0.905633i | \(0.360603\pi\) | ||||
−0.424063 | + | 0.905633i | \(0.639397\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1731.69i | 0.0965902i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2255.59 | − | 5664.35i | 0.125264 | − | 0.314568i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3438.43 | + | 5955.53i | 0.190121 | + | 0.329300i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10098.5 | + | 5830.40i | 0.555958 | + | 0.320982i | 0.751521 | − | 0.659709i | \(-0.229320\pi\) |
−0.195564 | + | 0.980691i | \(0.562654\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8622.62 | + | 8862.68i | 0.472650 | + | 0.485809i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 108.546 | + | 62.6691i | 0.00592430 | + | 0.00342040i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9112.95 | + | 15784.1i | 0.495233 | + | 0.857769i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5637.68 | + | 7141.84i | 0.305060 | + | 0.386451i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35502.0i | 1.91283i | 0.292015 | + | 0.956414i | \(0.405674\pi\) | ||||
−0.292015 | + | 0.956414i | \(0.594326\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1024.21i | − | 0.0549486i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −168.954 | + | 133.370i | −0.00902580 | + | 0.00712485i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8920.98 | − | 5652.87i | −0.474551 | − | 0.300705i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6912.86 | − | 11973.4i | 0.366175 | − | 0.634233i | −0.622789 | − | 0.782390i | \(-0.714001\pi\) |
0.988964 | + | 0.148156i | \(0.0473339\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15372.8 | + | 14550.4i | 0.810867 | + | 0.767489i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12632.1 | + | 21879.4i | −0.663498 | + | 1.14921i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −410.271 | − | 710.610i | −0.0214591 | − | 0.0371683i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11115.1 | − | 27912.8i | 0.578941 | − | 1.45386i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 35196.0 | 1.82558 | 0.912788 | − | 0.408434i | \(-0.133925\pi\) | ||||
0.912788 | + | 0.408434i | \(0.133925\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15468.8 | − | 29539.8i | −0.799011 | − | 1.52583i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1368.37 | + | 199.309i | −0.0703874 | + | 0.0102523i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −16175.8 | + | 9339.11i | −0.828627 | + | 0.478408i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27427.8 | − | 15835.4i | −1.39923 | − | 0.807846i | −0.404918 | − | 0.914353i | \(-0.632700\pi\) |
−0.994312 | + | 0.106507i | \(0.966033\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12724.8 | + | 15016.7i | −0.646487 | + | 0.762925i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12705.9 | − | 22007.3i | 0.642881 | − | 1.11350i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33629.6 | + | 19416.1i | −1.69460 | + | 0.978375i | −0.743878 | + | 0.668315i | \(0.767016\pi\) |
−0.950717 | + | 0.310060i | \(0.899651\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1053.63 | + | 523.816i | 0.0528756 | + | 0.0262874i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 8099.56i | − | 0.404818i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −63.2905 | −0.00315044 | −0.00157522 | − | 0.999999i | \(-0.500501\pi\) | ||||
−0.00157522 | + | 0.999999i | \(0.500501\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15277.7 | + | 6083.72i | 0.757410 | + | 0.301607i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17506.0 | + | 10107.1i | −0.864376 | + | 0.499048i | −0.865475 | − | 0.500952i | \(-0.832983\pi\) |
0.00109946 | + | 0.999999i | \(0.499650\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 253.497 | + | 146.357i | 0.0124663 | + | 0.00719745i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −23508.4 | − | 22250.8i | −1.15144 | − | 1.08985i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −37729.9 | − | 1555.51i | −1.84062 | − | 0.0758840i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2887.55 | + | 5001.39i | 0.140304 | + | 0.243014i | 0.927611 | − | 0.373547i | \(-0.121859\pi\) |
−0.787307 | + | 0.616561i | \(0.788525\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −29415.0 | + | 23219.9i | −1.42356 | + | 1.12374i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1245.73 | −0.0600488 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10392.0 | −0.498949 | −0.249474 | − | 0.968381i | \(-0.580258\pi\) | ||||
−0.249474 | + | 0.968381i | \(0.580258\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15816.1 | − | 12485.0i | 0.756372 | − | 0.597071i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4343.28 | + | 7522.79i | 0.206891 | + | 0.358345i | 0.950733 | − | 0.310009i | \(-0.100332\pi\) |
−0.743843 | + | 0.668355i | \(0.766999\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 907.526 | − | 22012.6i | 0.0430598 | − | 1.04444i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1154.12 | + | 343.493i | −0.0545453 | + | 0.0162340i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 31238.4 | + | 18035.5i | 1.47060 | + | 0.849053i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24932.6 | − | 14394.8i | 1.16917 | − | 0.675021i | 0.215687 | − | 0.976463i | \(-0.430801\pi\) |
0.953485 | + | 0.301441i | \(0.0974677\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26573.5 | + | 10581.8i | 1.24127 | + | 0.494285i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12521.5 | 0.582622 | 0.291311 | − | 0.956628i | \(-0.405909\pi\) | ||||
0.291311 | + | 0.956628i | \(0.405909\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20067.4i | 0.930121i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −918.481 | − | 1267.61i | −0.0424071 | − | 0.0585266i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14712.0 | + | 8493.98i | −0.676653 | + | 0.390666i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3045.30 | + | 5274.62i | −0.139526 | + | 0.241665i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1884.21 | + | 20952.7i | −0.0859976 | + | 0.956305i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1408.34 | + | 813.107i | 0.0640330 | + | 0.0369695i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15973.1 | + | 9222.08i | −0.723482 | + | 0.417702i | −0.816033 | − | 0.578006i | \(-0.803831\pi\) |
0.0925512 | + | 0.995708i | \(0.470498\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24273.0 | + | 3535.48i | −1.09524 | + | 0.159526i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6413.28 | − | 12247.1i | −0.288281 | − | 0.550513i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1391.06 | −0.0622924 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 173.641 | − | 436.056i | 0.00774643 | − | 0.0194532i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4810.14 | + | 8331.41i | 0.213782 | + | 0.370281i | 0.952895 | − | 0.303300i | \(-0.0980886\pi\) |
−0.739113 | + | 0.673581i | \(0.764755\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2119.37 | − | 3670.86i | 0.0938398 | − | 0.162535i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6073.22 | − | 25442.0i | 0.267898 | − | 1.12228i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3230.13 | + | 5594.75i | −0.141954 | + | 0.245871i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1026.31 | − | 1619.66i | 0.0449352 | − | 0.0709136i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14663.1 | + | 11574.9i | −0.639610 | + | 0.504900i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 18955.4i | − | 0.823776i | −0.911234 | − | 0.411888i | \(-0.864869\pi\) | ||
0.911234 | − | 0.411888i | \(-0.135131\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16233.0i | 0.702857i | 0.936215 | + | 0.351428i | \(0.114304\pi\) | ||||
−0.936215 | + | 0.351428i | \(0.885696\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11827.5 | + | 14983.2i | 0.510222 | + | 0.646351i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −829.984 | − | 1437.58i | −0.0356725 | − | 0.0617866i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20512.5 | + | 11842.9i | 0.878388 | + | 0.507138i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 24364.0 | − | 6171.13i | 1.03950 | − | 0.263293i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15840.8 | + | 9145.67i | 0.673382 | + | 0.388777i | 0.797357 | − | 0.603508i | \(-0.206231\pi\) |
−0.123975 | + | 0.992285i | \(0.539564\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9144.29 | + | 15838.4i | 0.387302 | + | 0.670827i | 0.992086 | − | 0.125563i | \(-0.0400737\pi\) |
−0.604783 | + | 0.796390i | \(0.706740\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5921.24 | − | 14869.7i | 0.249880 | − | 0.627511i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 26216.6i | − | 1.10234i | −0.834392 | − | 0.551172i | \(-0.814181\pi\) | ||
0.834392 | − | 0.551172i | \(-0.185819\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 7768.92i | − | 0.325483i | −0.986669 | − | 0.162742i | \(-0.947966\pi\) | ||
0.986669 | − | 0.162742i | \(-0.0520337\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1318.58 | − | 9052.79i | −0.0550435 | − | 0.377904i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −23092.0 | − | 1907.30i | −0.960494 | − | 0.0793324i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 934.708 | − | 1618.96i | 0.0387388 | − | 0.0670976i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 18483.0 | + | 13008.7i | 0.763279 | + | 0.537210i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22208.7 | + | 38466.7i | −0.913863 | + | 1.58286i | −0.105304 | + | 0.994440i | \(0.533582\pi\) |
−0.808558 | + | 0.588416i | \(0.799752\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −952.198 | − | 1649.26i | −0.0390421 | − | 0.0676229i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −41329.6 | + | 6019.85i | −1.68857 | + | 0.245949i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −217.389 | −0.00885017 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11805.2 | − | 6181.89i | 0.478903 | − | 0.250782i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14470.7 | − | 36339.4i | 0.584961 | − | 1.46898i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2209.17 | + | 1275.46i | −0.0889885 | + | 0.0513775i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1982.58 | − | 1144.64i | −0.0795806 | − | 0.0459459i | 0.459682 | − | 0.888084i | \(-0.347964\pi\) |
−0.539262 | + | 0.842138i | \(0.681297\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −320.162 | − | 1075.73i | −0.0128062 | − | 0.0430282i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10021.5 | − | 17357.7i | 0.399448 | − | 0.691864i | −0.594210 | − | 0.804310i | \(-0.702535\pi\) |
0.993658 | + | 0.112446i | \(0.0358685\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2786.72 | − | 1608.91i | 0.110689 | − | 0.0639062i | −0.443634 | − | 0.896208i | \(-0.646311\pi\) |
0.554322 | + | 0.832302i | \(0.312977\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10591.1 | + | 23705.8i | −0.419213 | + | 0.938317i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 30086.4i | − | 1.18674i | −0.804931 | − | 0.593368i | \(-0.797798\pi\) | ||
0.804931 | − | 0.593368i | \(-0.202202\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −881.279 | −0.0346409 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1425.84 | + | 1125.54i | −0.0558526 | + | 0.0440894i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16788.6 | + | 9692.87i | −0.655365 | + | 0.378375i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14257.5 | − | 8231.59i | −0.554648 | − | 0.320226i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −23720.1 | + | 25060.7i | −0.919592 | + | 0.971566i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 125.695 | − | 3048.82i | 0.00485632 | − | 0.117793i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13897.7 | − | 24071.6i | −0.535112 | − | 0.926841i | −0.999158 | − | 0.0410299i | \(-0.986936\pi\) |
0.464046 | − | 0.885811i | \(-0.346397\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1021.56 | + | 406.793i | 0.0391995 | + | 0.0156096i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43478.8 | −1.66270 | −0.831349 | − | 0.555751i | \(-0.812431\pi\) | ||||
−0.831349 | + | 0.555751i | \(0.812431\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18034.0 | 0.687308 | 0.343654 | − | 0.939096i | \(-0.388335\pi\) | ||||
0.343654 | + | 0.939096i | \(0.388335\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −354.844 | − | 2436.20i | −0.0134779 | − | 0.0925331i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4520.21 | − | 7829.24i | −0.171109 | − | 0.296370i | 0.767699 | − | 0.640811i | \(-0.221402\pi\) |
−0.938808 | + | 0.344441i | \(0.888068\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1398.20 | − | 33914.2i | 0.0527493 | − | 1.27947i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9857.19 | − | 15092.9i | −0.370627 | − | 0.567489i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3421.53 | + | 1975.42i | 0.128216 | + | 0.0740257i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −818.298 | + | 472.445i | −0.0305617 | + | 0.0176448i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5903.29 | − | 40529.3i | −0.219738 | − | 1.50862i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 24156.9 | 0.896194 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9242.59i | 0.341748i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 36007.6 | − | 3737.73i | 1.32697 | − | 0.137745i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 150.237 | − | 86.7392i | 0.00551827 | − | 0.00318598i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20675.3 | + | 35810.7i | −0.756905 | + | 1.31100i | 0.187516 | + | 0.982261i | \(0.439956\pi\) |
−0.944422 | + | 0.328737i | \(0.893377\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11182.2 | + | 10584.0i | 0.408018 | + | 0.386191i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36143.5 | + | 20867.5i | 1.31448 | + | 0.758913i | 0.982834 | − | 0.184493i | \(-0.0590642\pi\) |
0.331642 | + | 0.943405i | \(0.392398\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25673.4 | − | 14822.5i | 0.930630 | − | 0.537299i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 58.8262 | + | 74.5214i | 0.00212539 | + | 0.00269246i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7732.18 | + | 4049.02i | −0.278450 | + | 0.145813i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4424.74 | −0.158824 | −0.0794118 | − | 0.996842i | \(-0.525304\pi\) | ||||
−0.0794118 | + | 0.996842i | \(0.525304\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8696.00 | − | 11016.1i | −0.311122 | − | 0.394130i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6189.89 | + | 10721.2i | 0.220740 | + | 0.382332i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1013.11 | + | 1754.75i | −0.0360117 | + | 0.0623740i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13867.0 | + | 46592.5i | 0.491320 | + | 1.65081i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16928.2 | − | 29320.5i | 0.597843 | − | 1.03550i | −0.395295 | − | 0.918554i | \(-0.629358\pi\) |
0.993139 | − | 0.116941i | \(-0.0373089\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1777.75 | − | 21523.6i | 0.0625815 | − | 0.757688i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −31232.5 | − | 12437.1i | −1.09593 | − | 0.436410i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 1102.82i | − | 0.0385733i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 26589.0i | − | 0.927026i | −0.886090 | − | 0.463513i | \(-0.846589\pi\) | ||
0.886090 | − | 0.463513i | \(-0.153411\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8765.07 | − | 1276.68i | 0.304619 | − | 0.0443692i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19164.6 | − | 33194.1i | −0.663919 | − | 1.14994i | −0.979577 | − | 0.201069i | \(-0.935558\pi\) |
0.315658 | − | 0.948873i | \(-0.397775\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36642.1 | + | 21155.3i | 1.26536 | + | 0.730553i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1360.93 | − | 1044.25i | −0.0468475 | − | 0.0359466i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27807.6 | + | 16054.7i | 0.954196 | + | 0.550906i | 0.894382 | − | 0.447304i | \(-0.147616\pi\) |
0.0598145 | + | 0.998210i | \(0.480949\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6565.57 | + | 11371.9i | 0.224581 | + | 0.388986i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7404.91 | − | 1078.56i | 0.252493 | − | 0.0367768i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 40510.3i | − | 1.37697i | −0.725249 | − | 0.688487i | \(-0.758275\pi\) | ||
0.725249 | − | 0.688487i | \(-0.241725\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 74.6311i | 0.00252880i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −17899.9 | − | 7127.91i | −0.604622 | − | 0.240766i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 26001.6 | − | 41034.0i | 0.875533 | − | 1.38171i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1918.68 | + | 3323.26i | −0.0644048 | + | 0.111552i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 53547.3 | + | 12782.2i | 1.79184 | + | 0.427726i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1380.82 | + | 2391.65i | −0.0460624 | + | 0.0797824i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2453.20 | − | 4249.08i | −0.0815820 | − | 0.141304i | 0.822348 | − | 0.568985i | \(-0.192664\pi\) |
−0.903930 | + | 0.427681i | \(0.859331\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13694.2 | + | 17347.9i | 0.453995 | + | 0.575123i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41704.4 | 1.37833 | 0.689165 | − | 0.724604i | \(-0.257977\pi\) | ||||
0.689165 | + | 0.724604i | \(0.257977\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1631.12 | − | 3114.85i | −0.0537422 | − | 0.102628i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −20157.1 | − | 25535.2i | −0.662098 | − | 0.838748i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39726.6 | − | 22936.2i | 1.30089 | − | 0.751067i | 0.320330 | − | 0.947306i | \(-0.396206\pi\) |
0.980556 | + | 0.196239i | \(0.0628727\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20746.3 | + | 11977.9i | 0.677276 | + | 0.391026i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7457.47 | + | 31240.9i | −0.242710 | + | 1.01676i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29949.7 | + | 51874.3i | −0.971766 | + | 1.68315i | −0.281546 | + | 0.959548i | \(0.590847\pi\) |
−0.690219 | + | 0.723600i | \(0.742486\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −179.711 | + | 103.756i | −0.00581326 | + | 0.00335629i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6006.12 | − | 623.459i | 0.193695 | − | 0.0201063i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 58992.5i | − | 1.89672i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37752.2 | 1.21013 | 0.605065 | − | 0.796176i | \(-0.293147\pi\) | ||||
0.605065 | + | 0.796176i | \(0.293147\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8480.31 | + | 58222.0i | 0.271012 | + | 1.86064i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 805.002 | − | 464.768i | 0.0256485 | − | 0.0148082i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42235.3 | + | 24384.6i | 1.34163 | + | 0.774591i | 0.987047 | − | 0.160433i | \(-0.0512889\pi\) |
0.354585 | + | 0.935024i | \(0.384622\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 959.459 | + | 2070.63i | 0.0303863 | + | 0.0655774i |
(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 | 252.4.x.a.209.18 | yes | 48 | |
3.2 | odd | 2 | 756.4.x.a.629.13 | 48 | |||
7.6 | odd | 2 | inner | 252.4.x.a.209.7 | yes | 48 | |
9.2 | odd | 6 | 2268.4.f.a.1133.23 | 48 | |||
9.4 | even | 3 | 756.4.x.a.125.12 | 48 | |||
9.5 | odd | 6 | inner | 252.4.x.a.41.7 | ✓ | 48 | |
9.7 | even | 3 | 2268.4.f.a.1133.26 | 48 | |||
21.20 | even | 2 | 756.4.x.a.629.12 | 48 | |||
63.13 | odd | 6 | 756.4.x.a.125.13 | 48 | |||
63.20 | even | 6 | 2268.4.f.a.1133.25 | 48 | |||
63.34 | odd | 6 | 2268.4.f.a.1133.24 | 48 | |||
63.41 | even | 6 | inner | 252.4.x.a.41.18 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.x.a.41.7 | ✓ | 48 | 9.5 | odd | 6 | inner | |
252.4.x.a.41.18 | yes | 48 | 63.41 | even | 6 | inner | |
252.4.x.a.209.7 | yes | 48 | 7.6 | odd | 2 | inner | |
252.4.x.a.209.18 | yes | 48 | 1.1 | even | 1 | trivial | |
756.4.x.a.125.12 | 48 | 9.4 | even | 3 | |||
756.4.x.a.125.13 | 48 | 63.13 | odd | 6 | |||
756.4.x.a.629.12 | 48 | 21.20 | even | 2 | |||
756.4.x.a.629.13 | 48 | 3.2 | odd | 2 | |||
2268.4.f.a.1133.23 | 48 | 9.2 | odd | 6 | |||
2268.4.f.a.1133.24 | 48 | 63.34 | odd | 6 | |||
2268.4.f.a.1133.25 | 48 | 63.20 | even | 6 | |||
2268.4.f.a.1133.26 | 48 | 9.7 | even | 3 |