Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,4,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2151.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.a (trivial) |
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: | yes |
Analytic conductor: | \(126.913108422\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | no (minimal twist has level 717) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.27604 | −1.51181 | −0.755903 | − | 0.654683i | \(-0.772802\pi\) | ||||
−0.755903 | + | 0.654683i | \(0.772802\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 10.2845 | 1.28556 | ||||||||
\(5\) | 1.46589 | 0.131114 | 0.0655568 | − | 0.997849i | \(-0.479118\pi\) | ||||
0.0655568 | + | 0.997849i | \(0.479118\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −24.3497 | −1.31476 | −0.657381 | − | 0.753558i | \(-0.728336\pi\) | ||||
−0.657381 | + | 0.753558i | \(0.728336\pi\) | |||||||
\(8\) | −9.76851 | −0.431711 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −6.26822 | −0.198218 | ||||||||
\(11\) | 39.8171 | 1.09139 | 0.545696 | − | 0.837983i | \(-0.316265\pi\) | ||||
0.545696 | + | 0.837983i | \(0.316265\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −56.6674 | −1.20898 | −0.604489 | − | 0.796614i | \(-0.706623\pi\) | ||||
−0.604489 | + | 0.796614i | \(0.706623\pi\) | |||||||
\(14\) | 104.120 | 1.98767 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −40.5053 | −0.632896 | ||||||||
\(17\) | −98.8941 | −1.41090 | −0.705451 | − | 0.708759i | \(-0.749256\pi\) | ||||
−0.705451 | + | 0.708759i | \(0.749256\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −20.1280 | −0.243035 | −0.121518 | − | 0.992589i | \(-0.538776\pi\) | ||||
−0.121518 | + | 0.992589i | \(0.538776\pi\) | |||||||
\(20\) | 15.0760 | 0.168554 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −170.259 | −1.64997 | ||||||||
\(23\) | −217.605 | −1.97277 | −0.986386 | − | 0.164447i | \(-0.947416\pi\) | ||||
−0.986386 | + | 0.164447i | \(0.947416\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −122.851 | −0.982809 | ||||||||
\(26\) | 242.312 | 1.82774 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −250.424 | −1.69020 | ||||||||
\(29\) | 158.291 | 1.01358 | 0.506790 | − | 0.862069i | \(-0.330832\pi\) | ||||
0.506790 | + | 0.862069i | \(0.330832\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −275.269 | −1.59483 | −0.797415 | − | 0.603431i | \(-0.793800\pi\) | ||||
−0.797415 | + | 0.603431i | \(0.793800\pi\) | |||||||
\(32\) | 251.350 | 1.38853 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 422.875 | 2.13301 | ||||||||
\(35\) | −35.6941 | −0.172383 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −341.944 | −1.51933 | −0.759665 | − | 0.650315i | \(-0.774637\pi\) | ||||
−0.759665 | + | 0.650315i | \(0.774637\pi\) | |||||||
\(38\) | 86.0679 | 0.367423 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −14.3196 | −0.0566032 | ||||||||
\(41\) | 409.072 | 1.55820 | 0.779102 | − | 0.626897i | \(-0.215675\pi\) | ||||
0.779102 | + | 0.626897i | \(0.215675\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 100.252 | 0.355541 | 0.177771 | − | 0.984072i | \(-0.443112\pi\) | ||||
0.177771 | + | 0.984072i | \(0.443112\pi\) | |||||||
\(44\) | 409.498 | 1.40305 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 930.486 | 2.98245 | ||||||||
\(47\) | −254.372 | −0.789447 | −0.394724 | − | 0.918800i | \(-0.629160\pi\) | ||||
−0.394724 | + | 0.918800i | \(0.629160\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 249.909 | 0.728598 | ||||||||
\(50\) | 525.316 | 1.48582 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −582.794 | −1.55421 | ||||||||
\(53\) | −509.753 | −1.32113 | −0.660566 | − | 0.750768i | \(-0.729684\pi\) | ||||
−0.660566 | + | 0.750768i | \(0.729684\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 58.3677 | 0.143096 | ||||||||
\(56\) | 237.861 | 0.567597 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −676.857 | −1.53234 | ||||||||
\(59\) | −808.008 | −1.78294 | −0.891472 | − | 0.453076i | \(-0.850327\pi\) | ||||
−0.891472 | + | 0.453076i | \(0.850327\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −24.1394 | −0.0506677 | −0.0253339 | − | 0.999679i | \(-0.508065\pi\) | ||||
−0.0253339 | + | 0.999679i | \(0.508065\pi\) | |||||||
\(62\) | 1177.06 | 2.41108 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −750.740 | −1.46629 | ||||||||
\(65\) | −83.0684 | −0.158513 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 242.006 | 0.441280 | 0.220640 | − | 0.975355i | \(-0.429185\pi\) | ||||
0.220640 | + | 0.975355i | \(0.429185\pi\) | |||||||
\(68\) | −1017.07 | −1.81380 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 152.629 | 0.260610 | ||||||||
\(71\) | 4.86949 | 0.00813947 | 0.00406974 | − | 0.999992i | \(-0.498705\pi\) | ||||
0.00406974 | + | 0.999992i | \(0.498705\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 45.9729 | 0.0737086 | 0.0368543 | − | 0.999321i | \(-0.488266\pi\) | ||||
0.0368543 | + | 0.999321i | \(0.488266\pi\) | |||||||
\(74\) | 1462.16 | 2.29693 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −207.006 | −0.312437 | ||||||||
\(77\) | −969.536 | −1.43492 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −208.443 | −0.296856 | −0.148428 | − | 0.988923i | \(-0.547421\pi\) | ||||
−0.148428 | + | 0.988923i | \(0.547421\pi\) | |||||||
\(80\) | −59.3765 | −0.0829812 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1749.21 | −2.35570 | ||||||||
\(83\) | 200.204 | 0.264762 | 0.132381 | − | 0.991199i | \(-0.457738\pi\) | ||||
0.132381 | + | 0.991199i | \(0.457738\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −144.968 | −0.184988 | ||||||||
\(86\) | −428.680 | −0.537509 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −388.954 | −0.471166 | ||||||||
\(89\) | 713.266 | 0.849506 | 0.424753 | − | 0.905309i | \(-0.360361\pi\) | ||||
0.424753 | + | 0.905309i | \(0.360361\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1379.84 | 1.58952 | ||||||||
\(92\) | −2237.95 | −2.53612 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1087.71 | 1.19349 | ||||||||
\(95\) | −29.5055 | −0.0318652 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1598.60 | −1.67333 | −0.836664 | − | 0.547716i | \(-0.815497\pi\) | ||||
−0.836664 | + | 0.547716i | \(0.815497\pi\) | |||||||
\(98\) | −1068.62 | −1.10150 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1263.46 | −1.26346 | ||||||||
\(101\) | 151.191 | 0.148951 | 0.0744757 | − | 0.997223i | \(-0.476272\pi\) | ||||
0.0744757 | + | 0.997223i | \(0.476272\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1815.75 | 1.73700 | 0.868501 | − | 0.495688i | \(-0.165084\pi\) | ||||
0.868501 | + | 0.495688i | \(0.165084\pi\) | |||||||
\(104\) | 553.556 | 0.521929 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2179.72 | 1.99730 | ||||||||
\(107\) | −704.181 | −0.636222 | −0.318111 | − | 0.948053i | \(-0.603048\pi\) | ||||
−0.318111 | + | 0.948053i | \(0.603048\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1508.90 | 1.32593 | 0.662966 | − | 0.748650i | \(-0.269297\pi\) | ||||
0.662966 | + | 0.748650i | \(0.269297\pi\) | |||||||
\(110\) | −249.582 | −0.216334 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 986.294 | 0.832107 | ||||||||
\(113\) | −713.075 | −0.593632 | −0.296816 | − | 0.954935i | \(-0.595925\pi\) | ||||
−0.296816 | + | 0.954935i | \(0.595925\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −318.986 | −0.258657 | ||||||||
\(116\) | 1627.94 | 1.30302 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3455.07 | 2.69547 | ||||||||
\(119\) | 2408.04 | 1.85500 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 254.403 | 0.191137 | ||||||||
\(122\) | 103.221 | 0.0765998 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2831.00 | −2.05025 | ||||||||
\(125\) | −363.324 | −0.259973 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1501.02 | −1.04877 | −0.524387 | − | 0.851480i | \(-0.675705\pi\) | ||||
−0.524387 | + | 0.851480i | \(0.675705\pi\) | |||||||
\(128\) | 1199.39 | 0.828219 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 355.203 | 0.239642 | ||||||||
\(131\) | 193.574 | 0.129104 | 0.0645522 | − | 0.997914i | \(-0.479438\pi\) | ||||
0.0645522 | + | 0.997914i | \(0.479438\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 490.111 | 0.319534 | ||||||||
\(134\) | −1034.83 | −0.667131 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 966.048 | 0.609102 | ||||||||
\(137\) | 51.7070 | 0.0322455 | 0.0161227 | − | 0.999870i | \(-0.494868\pi\) | ||||
0.0161227 | + | 0.999870i | \(0.494868\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3064.21 | −1.86981 | −0.934903 | − | 0.354902i | \(-0.884514\pi\) | ||||
−0.934903 | + | 0.354902i | \(0.884514\pi\) | |||||||
\(140\) | −367.096 | −0.221609 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −20.8221 | −0.0123053 | ||||||||
\(143\) | −2256.33 | −1.31947 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 232.038 | 0.132894 | ||||||||
\(146\) | −196.582 | −0.111433 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3516.71 | −1.95319 | ||||||||
\(149\) | −630.884 | −0.346873 | −0.173436 | − | 0.984845i | \(-0.555487\pi\) | ||||
−0.173436 | + | 0.984845i | \(0.555487\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −299.797 | −0.161571 | −0.0807853 | − | 0.996732i | \(-0.525743\pi\) | ||||
−0.0807853 | + | 0.996732i | \(0.525743\pi\) | |||||||
\(152\) | 196.620 | 0.104921 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4145.77 | 2.16932 | ||||||||
\(155\) | −403.515 | −0.209104 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3810.32 | 1.93692 | 0.968461 | − | 0.249166i | \(-0.0801564\pi\) | ||||
0.968461 | + | 0.249166i | \(0.0801564\pi\) | |||||||
\(158\) | 891.309 | 0.448789 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 368.453 | 0.182055 | ||||||||
\(161\) | 5298.62 | 2.59373 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3956.66 | −1.90129 | −0.950644 | − | 0.310284i | \(-0.899576\pi\) | ||||
−0.950644 | + | 0.310284i | \(0.899576\pi\) | |||||||
\(164\) | 4207.10 | 2.00317 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −856.079 | −0.400269 | ||||||||
\(167\) | 664.588 | 0.307948 | 0.153974 | − | 0.988075i | \(-0.450793\pi\) | ||||
0.153974 | + | 0.988075i | \(0.450793\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1014.19 | 0.461626 | ||||||||
\(170\) | 619.890 | 0.279667 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1031.04 | 0.457069 | ||||||||
\(173\) | −2287.00 | −1.00507 | −0.502536 | − | 0.864556i | \(-0.667600\pi\) | ||||
−0.502536 | + | 0.864556i | \(0.667600\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2991.39 | 1.29216 | ||||||||
\(176\) | −1612.81 | −0.690738 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3049.95 | −1.28429 | ||||||||
\(179\) | 2687.63 | 1.12225 | 0.561124 | − | 0.827731i | \(-0.310369\pi\) | ||||
0.561124 | + | 0.827731i | \(0.310369\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −445.211 | −0.182830 | −0.0914150 | − | 0.995813i | \(-0.529139\pi\) | ||||
−0.0914150 | + | 0.995813i | \(0.529139\pi\) | |||||||
\(182\) | −5900.23 | −2.40304 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2125.68 | 0.851668 | ||||||||
\(185\) | −501.253 | −0.199205 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3937.68 | −1.53985 | ||||||||
\(188\) | −2616.09 | −1.01488 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 126.166 | 0.0481741 | ||||||||
\(191\) | 146.088 | 0.0553431 | 0.0276715 | − | 0.999617i | \(-0.491191\pi\) | ||||
0.0276715 | + | 0.999617i | \(0.491191\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1155.84 | 0.431085 | 0.215543 | − | 0.976494i | \(-0.430848\pi\) | ||||
0.215543 | + | 0.976494i | \(0.430848\pi\) | |||||||
\(194\) | 6835.66 | 2.52975 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2570.19 | 0.936657 | ||||||||
\(197\) | −2980.18 | −1.07781 | −0.538906 | − | 0.842366i | \(-0.681162\pi\) | ||||
−0.538906 | + | 0.842366i | \(0.681162\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2147.13 | −0.764856 | −0.382428 | − | 0.923985i | \(-0.624912\pi\) | ||||
−0.382428 | + | 0.923985i | \(0.624912\pi\) | |||||||
\(200\) | 1200.07 | 0.424290 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −646.499 | −0.225186 | ||||||||
\(203\) | −3854.34 | −1.33262 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 599.657 | 0.204302 | ||||||||
\(206\) | −7764.21 | −2.62601 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2295.33 | 0.765157 | ||||||||
\(209\) | −801.438 | −0.265247 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2889.67 | −0.942811 | −0.471405 | − | 0.881917i | \(-0.656253\pi\) | ||||
−0.471405 | + | 0.881917i | \(0.656253\pi\) | |||||||
\(212\) | −5242.55 | −1.69839 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3011.10 | 0.961845 | ||||||||
\(215\) | 146.959 | 0.0466163 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6702.72 | 2.09682 | ||||||||
\(218\) | −6452.12 | −2.00455 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 600.281 | 0.183959 | ||||||||
\(221\) | 5604.07 | 1.70575 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3236.20 | −0.971803 | −0.485901 | − | 0.874014i | \(-0.661509\pi\) | ||||
−0.485901 | + | 0.874014i | \(0.661509\pi\) | |||||||
\(224\) | −6120.31 | −1.82558 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3049.13 | 0.897457 | ||||||||
\(227\) | 847.513 | 0.247803 | 0.123902 | − | 0.992294i | \(-0.460459\pi\) | ||||
0.123902 | + | 0.992294i | \(0.460459\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3025.55 | −0.873075 | −0.436537 | − | 0.899686i | \(-0.643795\pi\) | ||||
−0.436537 | + | 0.899686i | \(0.643795\pi\) | |||||||
\(230\) | 1363.99 | 0.391040 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1546.26 | −0.437574 | ||||||||
\(233\) | −5012.85 | −1.40945 | −0.704727 | − | 0.709478i | \(-0.748931\pi\) | ||||
−0.704727 | + | 0.709478i | \(0.748931\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −372.883 | −0.103507 | ||||||||
\(236\) | −8309.94 | −2.29208 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −10296.9 | −2.80440 | ||||||||
\(239\) | 239.000 | 0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4683.07 | −1.25171 | −0.625856 | − | 0.779938i | \(-0.715250\pi\) | ||||
−0.625856 | + | 0.779938i | \(0.715250\pi\) | |||||||
\(242\) | −1087.84 | −0.288962 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −248.261 | −0.0651364 | ||||||||
\(245\) | 366.341 | 0.0955292 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1140.60 | 0.293824 | ||||||||
\(248\) | 2688.97 | 0.688506 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1553.58 | 0.393029 | ||||||||
\(251\) | 6402.32 | 1.61000 | 0.805002 | − | 0.593272i | \(-0.202164\pi\) | ||||
0.805002 | + | 0.593272i | \(0.202164\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8664.40 | −2.15307 | ||||||||
\(254\) | 6418.42 | 1.58554 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 877.292 | 0.214183 | ||||||||
\(257\) | 1188.16 | 0.288386 | 0.144193 | − | 0.989550i | \(-0.453941\pi\) | ||||
0.144193 | + | 0.989550i | \(0.453941\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8326.24 | 1.99756 | ||||||||
\(260\) | −854.315 | −0.203778 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −827.731 | −0.195181 | ||||||||
\(263\) | −1198.30 | −0.280953 | −0.140476 | − | 0.990084i | \(-0.544863\pi\) | ||||
−0.140476 | + | 0.990084i | \(0.544863\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −747.244 | −0.173218 | ||||||||
\(266\) | −2095.73 | −0.483073 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2488.91 | 0.567292 | ||||||||
\(269\) | −5118.04 | −1.16005 | −0.580023 | − | 0.814600i | \(-0.696956\pi\) | ||||
−0.580023 | + | 0.814600i | \(0.696956\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1236.70 | 0.277211 | 0.138605 | − | 0.990348i | \(-0.455738\pi\) | ||||
0.138605 | + | 0.990348i | \(0.455738\pi\) | |||||||
\(272\) | 4005.74 | 0.892954 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −221.101 | −0.0487489 | ||||||||
\(275\) | −4891.58 | −1.07263 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2314.81 | −0.502106 | −0.251053 | − | 0.967973i | \(-0.580777\pi\) | ||||
−0.251053 | + | 0.967973i | \(0.580777\pi\) | |||||||
\(278\) | 13102.7 | 2.82679 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 348.679 | 0.0744197 | ||||||||
\(281\) | −1811.91 | −0.384659 | −0.192330 | − | 0.981330i | \(-0.561604\pi\) | ||||
−0.192330 | + | 0.981330i | \(0.561604\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4717.55 | 0.990916 | 0.495458 | − | 0.868632i | \(-0.335000\pi\) | ||||
0.495458 | + | 0.868632i | \(0.335000\pi\) | |||||||
\(284\) | 50.0802 | 0.0104638 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9648.16 | 1.99478 | ||||||||
\(287\) | −9960.80 | −2.04867 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4867.04 | 0.990645 | ||||||||
\(290\) | −992.201 | −0.200910 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 472.808 | 0.0947568 | ||||||||
\(293\) | −3604.11 | −0.718615 | −0.359308 | − | 0.933219i | \(-0.616987\pi\) | ||||
−0.359308 | + | 0.933219i | \(0.616987\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1184.45 | −0.233768 | ||||||||
\(296\) | 3340.28 | 0.655912 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2697.68 | 0.524405 | ||||||||
\(299\) | 12331.1 | 2.38504 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2441.11 | −0.467452 | ||||||||
\(302\) | 1281.94 | 0.244264 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 815.290 | 0.153816 | ||||||||
\(305\) | −35.3858 | −0.00664322 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3983.31 | 0.740520 | 0.370260 | − | 0.928928i | \(-0.379269\pi\) | ||||
0.370260 | + | 0.928928i | \(0.379269\pi\) | |||||||
\(308\) | −9971.17 | −1.84468 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1725.45 | 0.316125 | ||||||||
\(311\) | 7594.07 | 1.38463 | 0.692316 | − | 0.721595i | \(-0.256591\pi\) | ||||
0.692316 | + | 0.721595i | \(0.256591\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6738.10 | −1.21681 | −0.608403 | − | 0.793628i | \(-0.708189\pi\) | ||||
−0.608403 | + | 0.793628i | \(0.708189\pi\) | |||||||
\(314\) | −16293.1 | −2.92825 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2143.73 | −0.381626 | ||||||||
\(317\) | 10590.1 | 1.87634 | 0.938168 | − | 0.346180i | \(-0.112521\pi\) | ||||
0.938168 | + | 0.346180i | \(0.112521\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6302.68 | 1.10621 | ||||||||
\(320\) | −1100.51 | −0.192250 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −22657.1 | −3.92121 | ||||||||
\(323\) | 1990.54 | 0.342899 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6961.65 | 1.18819 | ||||||||
\(326\) | 16918.8 | 2.87438 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3996.03 | −0.672694 | ||||||||
\(329\) | 6193.90 | 1.03794 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3791.26 | −0.629567 | −0.314784 | − | 0.949163i | \(-0.601932\pi\) | ||||
−0.314784 | + | 0.949163i | \(0.601932\pi\) | |||||||
\(332\) | 2058.99 | 0.340367 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2841.80 | −0.465558 | ||||||||
\(335\) | 354.756 | 0.0578579 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9258.31 | 1.49653 | 0.748267 | − | 0.663397i | \(-0.230886\pi\) | ||||
0.748267 | + | 0.663397i | \(0.230886\pi\) | |||||||
\(338\) | −4336.72 | −0.697889 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1490.92 | −0.237814 | ||||||||
\(341\) | −10960.4 | −1.74059 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2266.73 | 0.356828 | ||||||||
\(344\) | −979.311 | −0.153491 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9779.30 | 1.51948 | ||||||||
\(347\) | 10437.4 | 1.61472 | 0.807360 | − | 0.590060i | \(-0.200896\pi\) | ||||
0.807360 | + | 0.590060i | \(0.200896\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 943.111 | 0.144652 | 0.0723261 | − | 0.997381i | \(-0.476958\pi\) | ||||
0.0723261 | + | 0.997381i | \(0.476958\pi\) | |||||||
\(350\) | −12791.3 | −1.95350 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10008.0 | 1.51543 | ||||||||
\(353\) | −10865.4 | −1.63826 | −0.819132 | − | 0.573604i | \(-0.805545\pi\) | ||||
−0.819132 | + | 0.573604i | \(0.805545\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.13816 | 0.00106720 | ||||||||
\(356\) | 7335.57 | 1.09209 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11492.4 | −1.69662 | ||||||||
\(359\) | −667.485 | −0.0981296 | −0.0490648 | − | 0.998796i | \(-0.515624\pi\) | ||||
−0.0490648 | + | 0.998796i | \(0.515624\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6453.86 | −0.940934 | ||||||||
\(362\) | 1903.74 | 0.276404 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 14190.9 | 2.04342 | ||||||||
\(365\) | 67.3915 | 0.00966420 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8566.53 | −1.21844 | −0.609222 | − | 0.792999i | \(-0.708518\pi\) | ||||
−0.609222 | + | 0.792999i | \(0.708518\pi\) | |||||||
\(368\) | 8814.16 | 1.24856 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2143.38 | 0.301159 | ||||||||
\(371\) | 12412.4 | 1.73697 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4410.94 | 0.612305 | 0.306152 | − | 0.951983i | \(-0.400958\pi\) | ||||
0.306152 | + | 0.951983i | \(0.400958\pi\) | |||||||
\(374\) | 16837.6 | 2.32795 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2484.84 | 0.340813 | ||||||||
\(377\) | −8969.92 | −1.22540 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8965.78 | −1.21515 | −0.607574 | − | 0.794263i | \(-0.707857\pi\) | ||||
−0.607574 | + | 0.794263i | \(0.707857\pi\) | |||||||
\(380\) | −303.449 | −0.0409647 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −624.676 | −0.0836680 | ||||||||
\(383\) | 11564.1 | 1.54282 | 0.771408 | − | 0.636341i | \(-0.219553\pi\) | ||||
0.771408 | + | 0.636341i | \(0.219553\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1421.24 | −0.188138 | ||||||||
\(386\) | −4942.43 | −0.651718 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −16440.7 | −2.15116 | ||||||||
\(389\) | 3853.49 | 0.502261 | 0.251131 | − | 0.967953i | \(-0.419198\pi\) | ||||
0.251131 | + | 0.967953i | \(0.419198\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21519.8 | 2.78339 | ||||||||
\(392\) | −2441.24 | −0.314544 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12743.3 | 1.62944 | ||||||||
\(395\) | −305.555 | −0.0389219 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9911.16 | 1.25296 | 0.626482 | − | 0.779436i | \(-0.284494\pi\) | ||||
0.626482 | + | 0.779436i | \(0.284494\pi\) | |||||||
\(398\) | 9181.22 | 1.15631 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4976.13 | 0.622016 | ||||||||
\(401\) | 4926.69 | 0.613534 | 0.306767 | − | 0.951785i | \(-0.400753\pi\) | ||||
0.306767 | + | 0.951785i | \(0.400753\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15598.8 | 1.92811 | ||||||||
\(404\) | 1554.92 | 0.191486 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 16481.3 | 2.01466 | ||||||||
\(407\) | −13615.2 | −1.65818 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8904.87 | 1.07657 | 0.538285 | − | 0.842763i | \(-0.319072\pi\) | ||||
0.538285 | + | 0.842763i | \(0.319072\pi\) | |||||||
\(410\) | −2564.16 | −0.308865 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 18674.0 | 2.23302 | ||||||||
\(413\) | 19674.8 | 2.34415 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 293.478 | 0.0347139 | ||||||||
\(416\) | −14243.4 | −1.67870 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3426.98 | 0.401002 | ||||||||
\(419\) | 12060.5 | 1.40620 | 0.703098 | − | 0.711093i | \(-0.251800\pi\) | ||||
0.703098 | + | 0.711093i | \(0.251800\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10986.1 | −1.27180 | −0.635902 | − | 0.771769i | \(-0.719372\pi\) | ||||
−0.635902 | + | 0.771769i | \(0.719372\pi\) | |||||||
\(422\) | 12356.3 | 1.42535 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4979.53 | 0.570347 | ||||||||
\(425\) | 12149.3 | 1.38665 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 587.787 | 0.0666160 | ||||||||
\(428\) | −7242.14 | −0.817902 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −628.400 | −0.0704748 | ||||||||
\(431\) | −13635.0 | −1.52384 | −0.761920 | − | 0.647672i | \(-0.775743\pi\) | ||||
−0.761920 | + | 0.647672i | \(0.775743\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3364.17 | −0.373375 | −0.186688 | − | 0.982419i | \(-0.559775\pi\) | ||||
−0.186688 | + | 0.982419i | \(0.559775\pi\) | |||||||
\(434\) | −28661.1 | −3.16999 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15518.3 | 1.70456 | ||||||||
\(437\) | 4379.94 | 0.479453 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5135.11 | −0.558281 | −0.279141 | − | 0.960250i | \(-0.590050\pi\) | ||||
−0.279141 | + | 0.960250i | \(0.590050\pi\) | |||||||
\(440\) | −570.166 | −0.0617763 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −23963.2 | −2.57876 | ||||||||
\(443\) | 5446.13 | 0.584093 | 0.292047 | − | 0.956404i | \(-0.405664\pi\) | ||||
0.292047 | + | 0.956404i | \(0.405664\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1045.57 | 0.111382 | ||||||||
\(446\) | 13838.1 | 1.46918 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 18280.3 | 1.92782 | ||||||||
\(449\) | 6622.05 | 0.696022 | 0.348011 | − | 0.937490i | \(-0.386857\pi\) | ||||
0.348011 | + | 0.937490i | \(0.386857\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16288.1 | 1.70061 | ||||||||
\(452\) | −7333.60 | −0.763150 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3623.99 | −0.374631 | ||||||||
\(455\) | 2022.69 | 0.208407 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7790.53 | −0.797430 | −0.398715 | − | 0.917075i | \(-0.630544\pi\) | ||||
−0.398715 | + | 0.917075i | \(0.630544\pi\) | |||||||
\(458\) | 12937.4 | 1.31992 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3280.60 | −0.332519 | ||||||||
\(461\) | −1328.81 | −0.134249 | −0.0671244 | − | 0.997745i | \(-0.521382\pi\) | ||||
−0.0671244 | + | 0.997745i | \(0.521382\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13716.6 | 1.37682 | 0.688409 | − | 0.725323i | \(-0.258310\pi\) | ||||
0.688409 | + | 0.725323i | \(0.258310\pi\) | |||||||
\(464\) | −6411.62 | −0.641491 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 21435.1 | 2.13082 | ||||||||
\(467\) | 9312.55 | 0.922770 | 0.461385 | − | 0.887200i | \(-0.347353\pi\) | ||||
0.461385 | + | 0.887200i | \(0.347353\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5892.79 | −0.580179 | ||||||||
\(470\) | 1594.46 | 0.156483 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7893.03 | 0.769717 | ||||||||
\(473\) | 3991.74 | 0.388035 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2472.74 | 0.238857 | ||||||||
\(476\) | 24765.5 | 2.38471 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1021.97 | −0.0977907 | ||||||||
\(479\) | −13199.4 | −1.25907 | −0.629536 | − | 0.776971i | \(-0.716755\pi\) | ||||
−0.629536 | + | 0.776971i | \(0.716755\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19377.1 | 1.83684 | ||||||||
\(482\) | 20025.0 | 1.89235 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2616.41 | 0.245718 | ||||||||
\(485\) | −2343.37 | −0.219396 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6626.32 | −0.616565 | −0.308282 | − | 0.951295i | \(-0.599754\pi\) | ||||
−0.308282 | + | 0.951295i | \(0.599754\pi\) | |||||||
\(488\) | 235.806 | 0.0218738 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1566.49 | −0.144422 | ||||||||
\(491\) | −636.455 | −0.0584986 | −0.0292493 | − | 0.999572i | \(-0.509312\pi\) | ||||
−0.0292493 | + | 0.999572i | \(0.509312\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15654.0 | −1.43006 | ||||||||
\(494\) | −4877.24 | −0.444206 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 11149.9 | 1.00936 | ||||||||
\(497\) | −118.571 | −0.0107015 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13771.2 | −1.23544 | −0.617719 | − | 0.786399i | \(-0.711943\pi\) | ||||
−0.617719 | + | 0.786399i | \(0.711943\pi\) | |||||||
\(500\) | −3736.59 | −0.334211 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −27376.6 | −2.43401 | ||||||||
\(503\) | −15036.3 | −1.33288 | −0.666438 | − | 0.745560i | \(-0.732182\pi\) | ||||
−0.666438 | + | 0.745560i | \(0.732182\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 221.630 | 0.0195295 | ||||||||
\(506\) | 37049.3 | 3.25502 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −15437.2 | −1.34826 | ||||||||
\(509\) | −2199.22 | −0.191510 | −0.0957551 | − | 0.995405i | \(-0.530527\pi\) | ||||
−0.0957551 | + | 0.995405i | \(0.530527\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1119.43 | −0.0969092 | ||||||||
\(512\) | −13346.4 | −1.15202 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5080.60 | −0.435984 | ||||||||
\(515\) | 2661.70 | 0.227744 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10128.4 | −0.861597 | ||||||||
\(518\) | −35603.3 | −3.01992 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 811.455 | 0.0684320 | ||||||||
\(521\) | 12525.5 | 1.05327 | 0.526634 | − | 0.850092i | \(-0.323454\pi\) | ||||
0.526634 | + | 0.850092i | \(0.323454\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6134.01 | 0.512852 | 0.256426 | − | 0.966564i | \(-0.417455\pi\) | ||||
0.256426 | + | 0.966564i | \(0.417455\pi\) | |||||||
\(524\) | 1990.81 | 0.165971 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5123.99 | 0.424747 | ||||||||
\(527\) | 27222.5 | 2.25015 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 35184.9 | 2.89183 | ||||||||
\(530\) | 3195.24 | 0.261873 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5040.53 | 0.410780 | ||||||||
\(533\) | −23181.1 | −1.88383 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1032.26 | −0.0834174 | ||||||||
\(536\) | −2364.04 | −0.190506 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 21884.9 | 1.75376 | ||||||||
\(539\) | 9950.67 | 0.795187 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8024.28 | −0.637691 | −0.318846 | − | 0.947807i | \(-0.603295\pi\) | ||||
−0.318846 | + | 0.947807i | \(0.603295\pi\) | |||||||
\(542\) | −5288.17 | −0.419089 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −24857.1 | −1.95908 | ||||||||
\(545\) | 2211.89 | 0.173848 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24001.4 | 1.87610 | 0.938049 | − | 0.346502i | \(-0.112631\pi\) | ||||
0.938049 | + | 0.346502i | \(0.112631\pi\) | |||||||
\(548\) | 531.780 | 0.0414535 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 20916.6 | 1.62161 | ||||||||
\(551\) | −3186.07 | −0.246336 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5075.52 | 0.390295 | ||||||||
\(554\) | 9898.21 | 0.759088 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −31513.8 | −2.40375 | ||||||||
\(557\) | 9564.09 | 0.727547 | 0.363773 | − | 0.931488i | \(-0.381488\pi\) | ||||
0.363773 | + | 0.931488i | \(0.381488\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5681.01 | −0.429841 | ||||||||
\(560\) | 1445.80 | 0.109101 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7747.77 | 0.581530 | ||||||||
\(563\) | −10937.5 | −0.818759 | −0.409379 | − | 0.912364i | \(-0.634255\pi\) | ||||
−0.409379 | + | 0.912364i | \(0.634255\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1045.29 | −0.0778332 | ||||||||
\(566\) | −20172.4 | −1.49807 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −47.5677 | −0.00351390 | ||||||||
\(569\) | 7816.61 | 0.575904 | 0.287952 | − | 0.957645i | \(-0.407026\pi\) | ||||
0.287952 | + | 0.957645i | \(0.407026\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9864.06 | 0.722939 | 0.361469 | − | 0.932384i | \(-0.382275\pi\) | ||||
0.361469 | + | 0.932384i | \(0.382275\pi\) | |||||||
\(572\) | −23205.2 | −1.69626 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 42592.7 | 3.09719 | ||||||||
\(575\) | 26733.0 | 1.93886 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23145.5 | 1.66995 | 0.834974 | − | 0.550290i | \(-0.185483\pi\) | ||||
0.834974 | + | 0.550290i | \(0.185483\pi\) | |||||||
\(578\) | −20811.6 | −1.49766 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2386.38 | 0.170844 | ||||||||
\(581\) | −4874.91 | −0.348099 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20296.9 | −1.44187 | ||||||||
\(584\) | −449.087 | −0.0318208 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15411.3 | 1.08641 | ||||||||
\(587\) | 17074.8 | 1.20060 | 0.600300 | − | 0.799775i | \(-0.295048\pi\) | ||||
0.600300 | + | 0.799775i | \(0.295048\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5540.60 | 0.387600 | ||||||||
\(590\) | 5064.77 | 0.353412 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 13850.5 | 0.961577 | ||||||||
\(593\) | −9165.65 | −0.634718 | −0.317359 | − | 0.948305i | \(-0.602796\pi\) | ||||
−0.317359 | + | 0.948305i | \(0.602796\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3529.94 | 0.243216 | ||||||||
\(596\) | −6488.31 | −0.445926 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −52728.2 | −3.60571 | ||||||||
\(599\) | −2460.58 | −0.167840 | −0.0839202 | − | 0.996472i | \(-0.526744\pi\) | ||||
−0.0839202 | + | 0.996472i | \(0.526744\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9682.17 | 0.657145 | 0.328572 | − | 0.944479i | \(-0.393432\pi\) | ||||
0.328572 | + | 0.944479i | \(0.393432\pi\) | |||||||
\(602\) | 10438.3 | 0.706697 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3083.26 | −0.207709 | ||||||||
\(605\) | 372.929 | 0.0250607 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25077.7 | −1.67689 | −0.838445 | − | 0.544986i | \(-0.816535\pi\) | ||||
−0.838445 | + | 0.544986i | \(0.816535\pi\) | |||||||
\(608\) | −5059.17 | −0.337461 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 151.311 | 0.0100433 | ||||||||
\(611\) | 14414.6 | 0.954424 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2294.94 | 0.151210 | 0.0756050 | − | 0.997138i | \(-0.475911\pi\) | ||||
0.0756050 | + | 0.997138i | \(0.475911\pi\) | |||||||
\(614\) | −17032.8 | −1.11952 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9470.92 | 0.619471 | ||||||||
\(617\) | −255.755 | −0.0166877 | −0.00834385 | − | 0.999965i | \(-0.502656\pi\) | ||||
−0.00834385 | + | 0.999965i | \(0.502656\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1884.06 | −0.122337 | −0.0611686 | − | 0.998127i | \(-0.519483\pi\) | ||||
−0.0611686 | + | 0.998127i | \(0.519483\pi\) | |||||||
\(620\) | −4149.94 | −0.268816 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −32472.5 | −2.09329 | ||||||||
\(623\) | −17367.8 | −1.11690 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14823.8 | 0.948723 | ||||||||
\(626\) | 28812.4 | 1.83957 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 39187.2 | 2.49003 | ||||||||
\(629\) | 33816.2 | 2.14363 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6657.49 | −0.420017 | −0.210008 | − | 0.977700i | \(-0.567349\pi\) | ||||
−0.210008 | + | 0.977700i | \(0.567349\pi\) | |||||||
\(632\) | 2036.18 | 0.128156 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −45283.6 | −2.83666 | ||||||||
\(635\) | −2200.34 | −0.137508 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14161.7 | −0.880859 | ||||||||
\(638\) | −26950.5 | −1.67238 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1758.18 | 0.108591 | ||||||||
\(641\) | −22664.8 | −1.39657 | −0.698287 | − | 0.715818i | \(-0.746054\pi\) | ||||
−0.698287 | + | 0.715818i | \(0.746054\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17131.7 | −1.05071 | −0.525356 | − | 0.850882i | \(-0.676068\pi\) | ||||
−0.525356 | + | 0.850882i | \(0.676068\pi\) | |||||||
\(644\) | 54493.5 | 3.33439 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8511.61 | −0.518397 | ||||||||
\(647\) | 3822.86 | 0.232291 | 0.116145 | − | 0.993232i | \(-0.462946\pi\) | ||||
0.116145 | + | 0.993232i | \(0.462946\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −32172.5 | −1.94589 | ||||||||
\(650\) | −29768.3 | −1.79632 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −40692.2 | −2.44422 | ||||||||
\(653\) | −1365.75 | −0.0818467 | −0.0409233 | − | 0.999162i | \(-0.513030\pi\) | ||||
−0.0409233 | + | 0.999162i | \(0.513030\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 283.760 | 0.0169273 | ||||||||
\(656\) | −16569.6 | −0.986181 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −26485.3 | −1.56916 | ||||||||
\(659\) | 26622.9 | 1.57372 | 0.786858 | − | 0.617134i | \(-0.211706\pi\) | ||||
0.786858 | + | 0.617134i | \(0.211706\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13900.8 | −0.817972 | −0.408986 | − | 0.912541i | \(-0.634118\pi\) | ||||
−0.408986 | + | 0.912541i | \(0.634118\pi\) | |||||||
\(662\) | 16211.6 | 0.951784 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1955.69 | −0.114301 | ||||||||
\(665\) | 718.450 | 0.0418952 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −34444.8 | −1.99956 | ||||||||
\(668\) | 6834.94 | 0.395886 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1516.95 | −0.0874699 | ||||||||
\(671\) | −961.160 | −0.0552983 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4959.57 | −0.284067 | −0.142034 | − | 0.989862i | \(-0.545364\pi\) | ||||
−0.142034 | + | 0.989862i | \(0.545364\pi\) | |||||||
\(674\) | −39588.8 | −2.26247 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10430.4 | 0.593448 | ||||||||
\(677\) | −6386.06 | −0.362535 | −0.181268 | − | 0.983434i | \(-0.558020\pi\) | ||||
−0.181268 | + | 0.983434i | \(0.558020\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 38925.4 | 2.20003 | ||||||||
\(680\) | 1416.12 | 0.0798616 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 46867.1 | 2.63143 | ||||||||
\(683\) | 31804.3 | 1.78178 | 0.890891 | − | 0.454217i | \(-0.150081\pi\) | ||||
0.890891 | + | 0.454217i | \(0.150081\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 75.7970 | 0.00422782 | ||||||||
\(686\) | −9692.64 | −0.539456 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4060.73 | −0.225020 | ||||||||
\(689\) | 28886.4 | 1.59722 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2521.19 | −0.138799 | −0.0693997 | − | 0.997589i | \(-0.522108\pi\) | ||||
−0.0693997 | + | 0.997589i | \(0.522108\pi\) | |||||||
\(692\) | −23520.6 | −1.29208 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −44630.6 | −2.44114 | ||||||||
\(695\) | −4491.81 | −0.245157 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −40454.8 | −2.19847 | ||||||||
\(698\) | −4032.78 | −0.218686 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 30764.9 | 1.66115 | ||||||||
\(701\) | 32083.7 | 1.72865 | 0.864325 | − | 0.502934i | \(-0.167746\pi\) | ||||
0.864325 | + | 0.502934i | \(0.167746\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6882.63 | 0.369251 | ||||||||
\(704\) | −29892.3 | −1.60030 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 46460.9 | 2.47674 | ||||||||
\(707\) | −3681.46 | −0.195836 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9806.75 | −0.519464 | −0.259732 | − | 0.965681i | \(-0.583634\pi\) | ||||
−0.259732 | + | 0.965681i | \(0.583634\pi\) | |||||||
\(710\) | −30.5230 | −0.00161339 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6967.55 | −0.366741 | ||||||||
\(713\) | 59899.9 | 3.14624 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3307.55 | −0.173000 | ||||||||
\(716\) | 27640.8 | 1.44272 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2854.19 | 0.148353 | ||||||||
\(719\) | −24234.5 | −1.25702 | −0.628508 | − | 0.777803i | \(-0.716334\pi\) | ||||
−0.628508 | + | 0.777803i | \(0.716334\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −44213.0 | −2.28374 | ||||||||
\(722\) | 27597.0 | 1.42251 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4578.76 | −0.235039 | ||||||||
\(725\) | −19446.2 | −0.996157 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27192.9 | −1.38725 | −0.693623 | − | 0.720338i | \(-0.743987\pi\) | ||||
−0.693623 | + | 0.720338i | \(0.743987\pi\) | |||||||
\(728\) | −13478.9 | −0.686212 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −288.168 | −0.0146104 | ||||||||
\(731\) | −9914.32 | −0.501634 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31910.6 | 1.60797 | 0.803986 | − | 0.594649i | \(-0.202709\pi\) | ||||
0.803986 | + | 0.594649i | \(0.202709\pi\) | |||||||
\(734\) | 36630.8 | 1.84205 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −54695.1 | −2.73925 | ||||||||
\(737\) | 9636.00 | 0.481610 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7912.59 | −0.393869 | −0.196935 | − | 0.980417i | \(-0.563099\pi\) | ||||
−0.196935 | + | 0.980417i | \(0.563099\pi\) | |||||||
\(740\) | −5155.13 | −0.256090 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −53075.6 | −2.62597 | ||||||||
\(743\) | 19460.3 | 0.960875 | 0.480437 | − | 0.877029i | \(-0.340478\pi\) | ||||
0.480437 | + | 0.877029i | \(0.340478\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −924.809 | −0.0454797 | ||||||||
\(746\) | −18861.3 | −0.925686 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −40497.0 | −1.97957 | ||||||||
\(749\) | 17146.6 | 0.836481 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3189.64 | −0.154982 | −0.0774911 | − | 0.996993i | \(-0.524691\pi\) | ||||
−0.0774911 | + | 0.996993i | \(0.524691\pi\) | |||||||
\(752\) | 10303.4 | 0.499638 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 38355.7 | 1.85256 | ||||||||
\(755\) | −439.471 | −0.0211841 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27847.0 | 1.33701 | 0.668506 | − | 0.743707i | \(-0.266934\pi\) | ||||
0.668506 | + | 0.743707i | \(0.266934\pi\) | |||||||
\(758\) | 38338.0 | 1.83707 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 288.225 | 0.0137566 | ||||||||
\(761\) | −8994.13 | −0.428432 | −0.214216 | − | 0.976786i | \(-0.568720\pi\) | ||||
−0.214216 | + | 0.976786i | \(0.568720\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −36741.3 | −1.74328 | ||||||||
\(764\) | 1502.43 | 0.0711468 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −49448.5 | −2.33244 | ||||||||
\(767\) | 45787.7 | 2.15554 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9288.68 | −0.435577 | −0.217788 | − | 0.975996i | \(-0.569884\pi\) | ||||
−0.217788 | + | 0.975996i | \(0.569884\pi\) | |||||||
\(770\) | 6077.26 | 0.284428 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11887.3 | 0.554186 | ||||||||
\(773\) | 16998.7 | 0.790946 | 0.395473 | − | 0.918478i | \(-0.370581\pi\) | ||||
0.395473 | + | 0.918478i | \(0.370581\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 33817.1 | 1.56741 | ||||||||
\(776\) | 15615.9 | 0.722395 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −16477.6 | −0.759322 | ||||||||
\(779\) | −8233.80 | −0.378699 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 193.889 | 0.00888336 | ||||||||
\(782\) | −92019.6 | −4.20795 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −10122.7 | −0.461127 | ||||||||
\(785\) | 5585.53 | 0.253957 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30289.1 | 1.37191 | 0.685954 | − | 0.727645i | \(-0.259385\pi\) | ||||
0.685954 | + | 0.727645i | \(0.259385\pi\) | |||||||
\(788\) | −30649.6 | −1.38559 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1306.56 | 0.0588424 | ||||||||
\(791\) | 17363.2 | 0.780485 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1367.92 | 0.0612561 | ||||||||
\(794\) | −42380.5 | −1.89424 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −22082.2 | −0.983268 | ||||||||
\(797\) | 12794.7 | 0.568645 | 0.284323 | − | 0.958729i | \(-0.408231\pi\) | ||||
0.284323 | + | 0.958729i | \(0.408231\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25155.9 | 1.11383 | ||||||||
\(800\) | −30878.7 | −1.36466 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −21066.7 | −0.927545 | ||||||||
\(803\) | 1830.51 | 0.0804450 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7767.22 | 0.340073 | ||||||||
\(806\) | −66700.9 | −2.91494 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1476.91 | −0.0643040 | ||||||||
\(809\) | −36851.2 | −1.60151 | −0.800753 | − | 0.598995i | \(-0.795567\pi\) | ||||
−0.800753 | + | 0.598995i | \(0.795567\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12988.3 | −0.562370 | −0.281185 | − | 0.959654i | \(-0.590727\pi\) | ||||
−0.281185 | + | 0.959654i | \(0.590727\pi\) | |||||||
\(812\) | −39639.8 | −1.71316 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 58219.1 | 2.50685 | ||||||||
\(815\) | −5800.05 | −0.249285 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2017.87 | −0.0864091 | ||||||||
\(818\) | −38077.5 | −1.62757 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6167.16 | 0.262642 | ||||||||
\(821\) | −19988.9 | −0.849717 | −0.424859 | − | 0.905260i | \(-0.639676\pi\) | ||||
−0.424859 | + | 0.905260i | \(0.639676\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7405.51 | 0.313657 | 0.156829 | − | 0.987626i | \(-0.449873\pi\) | ||||
0.156829 | + | 0.987626i | \(0.449873\pi\) | |||||||
\(824\) | −17737.2 | −0.749883 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −84130.0 | −3.54390 | ||||||||
\(827\) | 20628.9 | 0.867396 | 0.433698 | − | 0.901058i | \(-0.357208\pi\) | ||||
0.433698 | + | 0.901058i | \(0.357208\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16056.1 | 0.672678 | 0.336339 | − | 0.941741i | \(-0.390811\pi\) | ||||
0.336339 | + | 0.941741i | \(0.390811\pi\) | |||||||
\(830\) | −1254.92 | −0.0524807 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 42542.5 | 1.77271 | ||||||||
\(833\) | −24714.5 | −1.02798 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 974.216 | 0.0403762 | ||||||||
\(836\) | −8242.37 | −0.340991 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −51571.3 | −2.12590 | ||||||||
\(839\) | −41595.4 | −1.71160 | −0.855801 | − | 0.517306i | \(-0.826935\pi\) | ||||
−0.855801 | + | 0.517306i | \(0.826935\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 666.952 | 0.0273464 | ||||||||
\(842\) | 46977.0 | 1.92272 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −29718.7 | −1.21204 | ||||||||
\(845\) | 1486.70 | 0.0605255 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6194.65 | −0.251300 | ||||||||
\(848\) | 20647.7 | 0.836139 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −51950.6 | −2.09634 | ||||||||
\(851\) | 74408.6 | 2.99729 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5129.86 | 0.205912 | 0.102956 | − | 0.994686i | \(-0.467170\pi\) | ||||
0.102956 | + | 0.994686i | \(0.467170\pi\) | |||||||
\(854\) | −2513.40 | −0.100710 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6878.80 | 0.274664 | ||||||||
\(857\) | −14897.8 | −0.593815 | −0.296908 | − | 0.954906i | \(-0.595955\pi\) | ||||
−0.296908 | + | 0.954906i | \(0.595955\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1214.24 | −0.0482298 | −0.0241149 | − | 0.999709i | \(-0.507677\pi\) | ||||
−0.0241149 | + | 0.999709i | \(0.507677\pi\) | |||||||
\(860\) | 1511.39 | 0.0599280 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 58303.7 | 2.30375 | ||||||||
\(863\) | −34377.1 | −1.35598 | −0.677990 | − | 0.735071i | \(-0.737149\pi\) | ||||
−0.677990 | + | 0.735071i | \(0.737149\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3352.50 | −0.131779 | ||||||||
\(866\) | 14385.3 | 0.564471 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 68934.0 | 2.69559 | ||||||||
\(869\) | −8299.59 | −0.323987 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13713.9 | −0.533498 | ||||||||
\(872\) | −14739.7 | −0.572420 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −18728.8 | −0.724841 | ||||||||
\(875\) | 8846.83 | 0.341803 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13636.4 | 0.525050 | 0.262525 | − | 0.964925i | \(-0.415445\pi\) | ||||
0.262525 | + | 0.964925i | \(0.415445\pi\) | |||||||
\(878\) | 21957.9 | 0.844014 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2364.20 | −0.0905651 | ||||||||
\(881\) | 31632.4 | 1.20967 | 0.604837 | − | 0.796349i | \(-0.293238\pi\) | ||||
0.604837 | + | 0.796349i | \(0.293238\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8580.37 | 0.327013 | 0.163506 | − | 0.986542i | \(-0.447720\pi\) | ||||
0.163506 | + | 0.986542i | \(0.447720\pi\) | |||||||
\(884\) | 57634.9 | 2.19284 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −23287.8 | −0.883036 | ||||||||
\(887\) | −44205.6 | −1.67337 | −0.836685 | − | 0.547685i | \(-0.815509\pi\) | ||||
−0.836685 | + | 0.547685i | \(0.815509\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36549.5 | 1.37889 | ||||||||
\(890\) | −4470.91 | −0.168388 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −33282.6 | −1.24931 | ||||||||
\(893\) | 5120.00 | 0.191864 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3939.78 | 0.147142 | ||||||||
\(896\) | −29204.8 | −1.08891 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −28316.1 | −1.05225 | ||||||||
\(899\) | −43572.5 | −1.61649 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 50411.6 | 1.86399 | ||||||||
\(902\) | −69648.4 | −2.57100 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6965.68 | 0.256278 | ||||||||
\(905\) | −652.632 | −0.0239715 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8833.45 | 0.323385 | 0.161692 | − | 0.986841i | \(-0.448305\pi\) | ||||
0.161692 | + | 0.986841i | \(0.448305\pi\) | |||||||
\(908\) | 8716.22 | 0.318566 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8649.11 | −0.315072 | ||||||||
\(911\) | −30321.7 | −1.10275 | −0.551374 | − | 0.834258i | \(-0.685896\pi\) | ||||
−0.551374 | + | 0.834258i | \(0.685896\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7971.54 | 0.288959 | ||||||||
\(914\) | 33312.6 | 1.20556 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −31116.2 | −1.12239 | ||||||||
\(917\) | −4713.48 | −0.169741 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38461.2 | −1.38054 | −0.690271 | − | 0.723551i | \(-0.742509\pi\) | ||||
−0.690271 | + | 0.723551i | \(0.742509\pi\) | |||||||
\(920\) | 3116.02 | 0.111665 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5682.02 | 0.202958 | ||||||||
\(923\) | −275.941 | −0.00984044 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 42008.2 | 1.49321 | ||||||||
\(926\) | −58652.8 | −2.08148 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 39786.4 | 1.40739 | ||||||||
\(929\) | 6433.61 | 0.227212 | 0.113606 | − | 0.993526i | \(-0.463760\pi\) | ||||
0.113606 | + | 0.993526i | \(0.463760\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5030.17 | −0.177075 | ||||||||
\(932\) | −51554.6 | −1.81194 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −39820.8 | −1.39505 | ||||||||
\(935\) | −5772.22 | −0.201895 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 533.942 | 0.0186159 | 0.00930796 | − | 0.999957i | \(-0.497037\pi\) | ||||
0.00930796 | + | 0.999957i | \(0.497037\pi\) | |||||||
\(938\) | 25197.8 | 0.877118 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3834.91 | −0.133065 | ||||||||
\(941\) | −4862.87 | −0.168464 | −0.0842322 | − | 0.996446i | \(-0.526844\pi\) | ||||
−0.0842322 | + | 0.996446i | \(0.526844\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −89016.2 | −3.07398 | ||||||||
\(944\) | 32728.6 | 1.12842 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17068.8 | −0.586634 | ||||||||
\(947\) | −21694.9 | −0.744444 | −0.372222 | − | 0.928144i | \(-0.621404\pi\) | ||||
−0.372222 | + | 0.928144i | \(0.621404\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2605.17 | −0.0891120 | ||||||||
\(950\) | −10573.5 | −0.361106 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −23523.0 | −0.800824 | ||||||||
\(953\) | 25594.3 | 0.869971 | 0.434985 | − | 0.900438i | \(-0.356754\pi\) | ||||
0.434985 | + | 0.900438i | \(0.356754\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 214.149 | 0.00725623 | ||||||||
\(956\) | 2457.99 | 0.0831560 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 56441.1 | 1.90347 | ||||||||
\(959\) | −1259.05 | −0.0423951 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 45982.0 | 1.54349 | ||||||||
\(962\) | −82857.0 | −2.77694 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −48162.9 | −1.60915 | ||||||||
\(965\) | 1694.35 | 0.0565211 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46972.0 | 1.56206 | 0.781032 | − | 0.624490i | \(-0.214693\pi\) | ||||
0.781032 | + | 0.624490i | \(0.214693\pi\) | |||||||
\(968\) | −2485.14 | −0.0825160 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10020.4 | 0.331685 | ||||||||
\(971\) | −46294.7 | −1.53004 | −0.765019 | − | 0.644007i | \(-0.777271\pi\) | ||||
−0.765019 | + | 0.644007i | \(0.777271\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 74612.7 | 2.45835 | ||||||||
\(974\) | 28334.4 | 0.932127 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 977.773 | 0.0320674 | ||||||||
\(977\) | 12342.1 | 0.404154 | 0.202077 | − | 0.979370i | \(-0.435231\pi\) | ||||
0.202077 | + | 0.979370i | \(0.435231\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28400.2 | 0.927144 | ||||||||
\(980\) | 3767.62 | 0.122808 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2721.51 | 0.0884386 | ||||||||
\(983\) | −30527.1 | −0.990502 | −0.495251 | − | 0.868750i | \(-0.664924\pi\) | ||||
−0.495251 | + | 0.868750i | \(0.664924\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4368.62 | −0.141316 | ||||||||
\(986\) | 66937.1 | 2.16198 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11730.5 | 0.377729 | ||||||||
\(989\) | −21815.3 | −0.701401 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28138.6 | −0.901970 | −0.450985 | − | 0.892532i | \(-0.648927\pi\) | ||||
−0.450985 | + | 0.892532i | \(0.648927\pi\) | |||||||
\(992\) | −69188.9 | −2.21447 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 507.013 | 0.0161785 | ||||||||
\(995\) | −3147.47 | −0.100283 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29322.3 | 0.931442 | 0.465721 | − | 0.884932i | \(-0.345795\pi\) | ||||
0.465721 | + | 0.884932i | \(0.345795\pi\) | |||||||
\(998\) | 58886.2 | 1.86774 | ||||||||
\(999\) | 0 | 0 |
(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 | 2151.4.a.c.1.2 | 28 | ||
3.2 | odd | 2 | 717.4.a.a.1.27 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
717.4.a.a.1.27 | ✓ | 28 | 3.2 | odd | 2 | ||
2151.4.a.c.1.2 | 28 | 1.1 | even | 1 | trivial |