Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [19,4,Mod(1,19)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(19, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("19.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 19.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: | \(1.12103629011\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.3144.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 16x - 8 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.20905\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 19.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.96257 | −1.40098 | −0.700491 | − | 0.713661i | \(-0.747036\pi\) | ||||
−0.700491 | + | 0.713661i | \(0.747036\pi\) | |||||||
\(3\) | 6.71610 | 1.29251 | 0.646257 | − | 0.763120i | \(-0.276333\pi\) | ||||
0.646257 | + | 0.763120i | \(0.276333\pi\) | |||||||
\(4\) | 7.70200 | 0.962750 | ||||||||
\(5\) | 18.1342 | 1.62197 | 0.810986 | − | 0.585065i | \(-0.198931\pi\) | ||||
0.810986 | + | 0.585065i | \(0.198931\pi\) | |||||||
\(6\) | −26.6130 | −1.81079 | ||||||||
\(7\) | −25.8362 | −1.39502 | −0.697512 | − | 0.716573i | \(-0.745710\pi\) | ||||
−0.697512 | + | 0.716573i | \(0.745710\pi\) | |||||||
\(8\) | 1.18085 | 0.0521866 | ||||||||
\(9\) | 18.1060 | 0.670593 | ||||||||
\(10\) | −71.8581 | −2.27235 | ||||||||
\(11\) | −8.13420 | −0.222959 | −0.111480 | − | 0.993767i | \(-0.535559\pi\) | ||||
−0.111480 | + | 0.993767i | \(0.535559\pi\) | |||||||
\(12\) | 51.7274 | 1.24437 | ||||||||
\(13\) | −4.56640 | −0.0974224 | −0.0487112 | − | 0.998813i | \(-0.515511\pi\) | ||||
−0.0487112 | + | 0.998813i | \(0.515511\pi\) | |||||||
\(14\) | 102.378 | 1.95440 | ||||||||
\(15\) | 121.791 | 2.09642 | ||||||||
\(16\) | −66.2952 | −1.03586 | ||||||||
\(17\) | −62.5850 | −0.892888 | −0.446444 | − | 0.894812i | \(-0.647310\pi\) | ||||
−0.446444 | + | 0.894812i | \(0.647310\pi\) | |||||||
\(18\) | −71.7464 | −0.939488 | ||||||||
\(19\) | −19.0000 | −0.229416 | ||||||||
\(20\) | 139.670 | 1.56155 | ||||||||
\(21\) | −173.518 | −1.80309 | ||||||||
\(22\) | 32.2324 | 0.312362 | ||||||||
\(23\) | −52.7502 | −0.478225 | −0.239113 | − | 0.970992i | \(-0.576856\pi\) | ||||
−0.239113 | + | 0.970992i | \(0.576856\pi\) | |||||||
\(24\) | 7.93070 | 0.0674520 | ||||||||
\(25\) | 203.849 | 1.63079 | ||||||||
\(26\) | 18.0947 | 0.136487 | ||||||||
\(27\) | −59.7330 | −0.425764 | ||||||||
\(28\) | −198.990 | −1.34306 | ||||||||
\(29\) | 171.620 | 1.09894 | 0.549468 | − | 0.835515i | \(-0.314831\pi\) | ||||
0.549468 | + | 0.835515i | \(0.314831\pi\) | |||||||
\(30\) | −482.606 | −2.93705 | ||||||||
\(31\) | 168.749 | 0.977685 | 0.488842 | − | 0.872372i | \(-0.337419\pi\) | ||||
0.488842 | + | 0.872372i | \(0.337419\pi\) | |||||||
\(32\) | 253.253 | 1.39904 | ||||||||
\(33\) | −54.6301 | −0.288178 | ||||||||
\(34\) | 247.998 | 1.25092 | ||||||||
\(35\) | −468.519 | −2.26269 | ||||||||
\(36\) | 139.452 | 0.645613 | ||||||||
\(37\) | −147.534 | −0.655528 | −0.327764 | − | 0.944760i | \(-0.606295\pi\) | ||||
−0.327764 | + | 0.944760i | \(0.606295\pi\) | |||||||
\(38\) | 75.2889 | 0.321407 | ||||||||
\(39\) | −30.6684 | −0.125920 | ||||||||
\(40\) | 21.4138 | 0.0846453 | ||||||||
\(41\) | 308.774 | 1.17616 | 0.588078 | − | 0.808804i | \(-0.299885\pi\) | ||||
0.588078 | + | 0.808804i | \(0.299885\pi\) | |||||||
\(42\) | 687.580 | 2.52609 | ||||||||
\(43\) | −448.950 | −1.59219 | −0.796096 | − | 0.605170i | \(-0.793105\pi\) | ||||
−0.796096 | + | 0.605170i | \(0.793105\pi\) | |||||||
\(44\) | −62.6496 | −0.214654 | ||||||||
\(45\) | 328.338 | 1.08768 | ||||||||
\(46\) | 209.027 | 0.669985 | ||||||||
\(47\) | 113.335 | 0.351737 | 0.175868 | − | 0.984414i | \(-0.443727\pi\) | ||||
0.175868 | + | 0.984414i | \(0.443727\pi\) | |||||||
\(48\) | −445.245 | −1.33887 | ||||||||
\(49\) | 324.509 | 0.946091 | ||||||||
\(50\) | −807.768 | −2.28471 | ||||||||
\(51\) | −420.327 | −1.15407 | ||||||||
\(52\) | −35.1704 | −0.0937934 | ||||||||
\(53\) | 155.402 | 0.402758 | 0.201379 | − | 0.979513i | \(-0.435458\pi\) | ||||
0.201379 | + | 0.979513i | \(0.435458\pi\) | |||||||
\(54\) | 236.696 | 0.596487 | ||||||||
\(55\) | −147.507 | −0.361634 | ||||||||
\(56\) | −30.5086 | −0.0728016 | ||||||||
\(57\) | −127.606 | −0.296523 | ||||||||
\(58\) | −680.059 | −1.53959 | ||||||||
\(59\) | 182.347 | 0.402365 | 0.201183 | − | 0.979554i | \(-0.435522\pi\) | ||||
0.201183 | + | 0.979554i | \(0.435522\pi\) | |||||||
\(60\) | 938.035 | 2.01833 | ||||||||
\(61\) | 404.080 | 0.848149 | 0.424075 | − | 0.905627i | \(-0.360599\pi\) | ||||
0.424075 | + | 0.905627i | \(0.360599\pi\) | |||||||
\(62\) | −668.681 | −1.36972 | ||||||||
\(63\) | −467.790 | −0.935492 | ||||||||
\(64\) | −473.172 | −0.924164 | ||||||||
\(65\) | −82.8080 | −0.158016 | ||||||||
\(66\) | 216.476 | 0.403732 | ||||||||
\(67\) | −106.400 | −0.194013 | −0.0970064 | − | 0.995284i | \(-0.530927\pi\) | ||||
−0.0970064 | + | 0.995284i | \(0.530927\pi\) | |||||||
\(68\) | −482.030 | −0.859628 | ||||||||
\(69\) | −354.276 | −0.618113 | ||||||||
\(70\) | 1856.54 | 3.16999 | ||||||||
\(71\) | 472.079 | 0.789091 | 0.394546 | − | 0.918876i | \(-0.370902\pi\) | ||||
0.394546 | + | 0.918876i | \(0.370902\pi\) | |||||||
\(72\) | 21.3805 | 0.0349960 | ||||||||
\(73\) | 843.821 | 1.35290 | 0.676451 | − | 0.736488i | \(-0.263517\pi\) | ||||
0.676451 | + | 0.736488i | \(0.263517\pi\) | |||||||
\(74\) | 584.616 | 0.918382 | ||||||||
\(75\) | 1369.07 | 2.10782 | ||||||||
\(76\) | −146.338 | −0.220870 | ||||||||
\(77\) | 210.157 | 0.311034 | ||||||||
\(78\) | 121.526 | 0.176411 | ||||||||
\(79\) | −591.036 | −0.841731 | −0.420866 | − | 0.907123i | \(-0.638274\pi\) | ||||
−0.420866 | + | 0.907123i | \(0.638274\pi\) | |||||||
\(80\) | −1202.21 | −1.68014 | ||||||||
\(81\) | −890.035 | −1.22090 | ||||||||
\(82\) | −1223.54 | −1.64777 | ||||||||
\(83\) | 290.388 | 0.384027 | 0.192013 | − | 0.981392i | \(-0.438498\pi\) | ||||
0.192013 | + | 0.981392i | \(0.438498\pi\) | |||||||
\(84\) | −1336.44 | −1.73592 | ||||||||
\(85\) | −1134.93 | −1.44824 | ||||||||
\(86\) | 1779.00 | 2.23063 | ||||||||
\(87\) | 1152.62 | 1.42039 | ||||||||
\(88\) | −9.60526 | −0.0116355 | ||||||||
\(89\) | −964.896 | −1.14920 | −0.574600 | − | 0.818435i | \(-0.694842\pi\) | ||||
−0.574600 | + | 0.818435i | \(0.694842\pi\) | |||||||
\(90\) | −1301.06 | −1.52382 | ||||||||
\(91\) | 117.978 | 0.135907 | ||||||||
\(92\) | −406.282 | −0.460411 | ||||||||
\(93\) | 1133.34 | 1.26367 | ||||||||
\(94\) | −449.099 | −0.492777 | ||||||||
\(95\) | −344.550 | −0.372106 | ||||||||
\(96\) | 1700.87 | 1.80828 | ||||||||
\(97\) | −219.495 | −0.229756 | −0.114878 | − | 0.993380i | \(-0.536648\pi\) | ||||
−0.114878 | + | 0.993380i | \(0.536648\pi\) | |||||||
\(98\) | −1285.89 | −1.32546 | ||||||||
\(99\) | −147.278 | −0.149515 | ||||||||
\(100\) | 1570.05 | 1.57005 | ||||||||
\(101\) | 1447.94 | 1.42649 | 0.713247 | − | 0.700913i | \(-0.247224\pi\) | ||||
0.713247 | + | 0.700913i | \(0.247224\pi\) | |||||||
\(102\) | 1665.58 | 1.61683 | ||||||||
\(103\) | 883.567 | 0.845247 | 0.422623 | − | 0.906305i | \(-0.361109\pi\) | ||||
0.422623 | + | 0.906305i | \(0.361109\pi\) | |||||||
\(104\) | −5.39223 | −0.00508415 | ||||||||
\(105\) | −3146.62 | −2.92456 | ||||||||
\(106\) | −615.793 | −0.564256 | ||||||||
\(107\) | −1307.82 | −1.18160 | −0.590801 | − | 0.806817i | \(-0.701188\pi\) | ||||
−0.590801 | + | 0.806817i | \(0.701188\pi\) | |||||||
\(108\) | −460.064 | −0.409904 | ||||||||
\(109\) | 870.507 | 0.764949 | 0.382475 | − | 0.923966i | \(-0.375072\pi\) | ||||
0.382475 | + | 0.923966i | \(0.375072\pi\) | |||||||
\(110\) | 584.508 | 0.506643 | ||||||||
\(111\) | −990.856 | −0.847279 | ||||||||
\(112\) | 1712.82 | 1.44505 | ||||||||
\(113\) | −1181.41 | −0.983521 | −0.491761 | − | 0.870730i | \(-0.663646\pi\) | ||||
−0.491761 | + | 0.870730i | \(0.663646\pi\) | |||||||
\(114\) | 505.648 | 0.415423 | ||||||||
\(115\) | −956.583 | −0.775668 | ||||||||
\(116\) | 1321.82 | 1.05800 | ||||||||
\(117\) | −82.6792 | −0.0653307 | ||||||||
\(118\) | −722.564 | −0.563707 | ||||||||
\(119\) | 1616.96 | 1.24560 | ||||||||
\(120\) | 143.817 | 0.109405 | ||||||||
\(121\) | −1264.83 | −0.950289 | ||||||||
\(122\) | −1601.20 | −1.18824 | ||||||||
\(123\) | 2073.76 | 1.52020 | ||||||||
\(124\) | 1299.71 | 0.941266 | ||||||||
\(125\) | 1429.87 | 1.02313 | ||||||||
\(126\) | 1853.65 | 1.31061 | ||||||||
\(127\) | 887.509 | 0.620108 | 0.310054 | − | 0.950719i | \(-0.399653\pi\) | ||||
0.310054 | + | 0.950719i | \(0.399653\pi\) | |||||||
\(128\) | −151.044 | −0.104301 | ||||||||
\(129\) | −3015.19 | −2.05793 | ||||||||
\(130\) | 328.133 | 0.221378 | ||||||||
\(131\) | −2344.76 | −1.56384 | −0.781920 | − | 0.623379i | \(-0.785759\pi\) | ||||
−0.781920 | + | 0.623379i | \(0.785759\pi\) | |||||||
\(132\) | −420.761 | −0.277444 | ||||||||
\(133\) | 490.888 | 0.320040 | ||||||||
\(134\) | 421.619 | 0.271809 | ||||||||
\(135\) | −1083.21 | −0.690577 | ||||||||
\(136\) | −73.9034 | −0.0465968 | ||||||||
\(137\) | 2244.82 | 1.39991 | 0.699956 | − | 0.714186i | \(-0.253203\pi\) | ||||
0.699956 | + | 0.714186i | \(0.253203\pi\) | |||||||
\(138\) | 1403.84 | 0.865964 | ||||||||
\(139\) | −296.146 | −0.180711 | −0.0903554 | − | 0.995910i | \(-0.528800\pi\) | ||||
−0.0903554 | + | 0.995910i | \(0.528800\pi\) | |||||||
\(140\) | −3608.53 | −2.17840 | ||||||||
\(141\) | 761.170 | 0.454625 | ||||||||
\(142\) | −1870.65 | −1.10550 | ||||||||
\(143\) | 37.1440 | 0.0217212 | ||||||||
\(144\) | −1200.34 | −0.694642 | ||||||||
\(145\) | 3112.20 | 1.78244 | ||||||||
\(146\) | −3343.70 | −1.89539 | ||||||||
\(147\) | 2179.44 | 1.22284 | ||||||||
\(148\) | −1136.31 | −0.631109 | ||||||||
\(149\) | 1791.09 | 0.984780 | 0.492390 | − | 0.870375i | \(-0.336123\pi\) | ||||
0.492390 | + | 0.870375i | \(0.336123\pi\) | |||||||
\(150\) | −5425.05 | −2.95302 | ||||||||
\(151\) | −2352.65 | −1.26792 | −0.633960 | − | 0.773366i | \(-0.718571\pi\) | ||||
−0.633960 | + | 0.773366i | \(0.718571\pi\) | |||||||
\(152\) | −22.4361 | −0.0119724 | ||||||||
\(153\) | −1133.16 | −0.598764 | ||||||||
\(154\) | −832.762 | −0.435752 | ||||||||
\(155\) | 3060.13 | 1.58578 | ||||||||
\(156\) | −236.208 | −0.121229 | ||||||||
\(157\) | −1438.26 | −0.731118 | −0.365559 | − | 0.930788i | \(-0.619122\pi\) | ||||
−0.365559 | + | 0.930788i | \(0.619122\pi\) | |||||||
\(158\) | 2342.02 | 1.17925 | ||||||||
\(159\) | 1043.70 | 0.520570 | ||||||||
\(160\) | 4592.54 | 2.26920 | ||||||||
\(161\) | 1362.86 | 0.667135 | ||||||||
\(162\) | 3526.83 | 1.71046 | ||||||||
\(163\) | 127.493 | 0.0612640 | 0.0306320 | − | 0.999531i | \(-0.490248\pi\) | ||||
0.0306320 | + | 0.999531i | \(0.490248\pi\) | |||||||
\(164\) | 2378.18 | 1.13234 | ||||||||
\(165\) | −990.673 | −0.467417 | ||||||||
\(166\) | −1150.68 | −0.538014 | ||||||||
\(167\) | 3419.05 | 1.58428 | 0.792139 | − | 0.610341i | \(-0.208967\pi\) | ||||
0.792139 | + | 0.610341i | \(0.208967\pi\) | |||||||
\(168\) | −204.899 | −0.0940971 | ||||||||
\(169\) | −2176.15 | −0.990509 | ||||||||
\(170\) | 4497.24 | 2.02896 | ||||||||
\(171\) | −344.014 | −0.153844 | ||||||||
\(172\) | −3457.81 | −1.53288 | ||||||||
\(173\) | −362.598 | −0.159352 | −0.0796758 | − | 0.996821i | \(-0.525389\pi\) | ||||
−0.0796758 | + | 0.996821i | \(0.525389\pi\) | |||||||
\(174\) | −4567.34 | −1.98994 | ||||||||
\(175\) | −5266.69 | −2.27500 | ||||||||
\(176\) | 539.258 | 0.230955 | ||||||||
\(177\) | 1224.66 | 0.520063 | ||||||||
\(178\) | 3823.47 | 1.61001 | ||||||||
\(179\) | 2417.89 | 1.00962 | 0.504809 | − | 0.863231i | \(-0.331563\pi\) | ||||
0.504809 | + | 0.863231i | \(0.331563\pi\) | |||||||
\(180\) | 2528.86 | 1.04717 | ||||||||
\(181\) | −2444.64 | −1.00391 | −0.501957 | − | 0.864892i | \(-0.667387\pi\) | ||||
−0.501957 | + | 0.864892i | \(0.667387\pi\) | |||||||
\(182\) | −467.498 | −0.190403 | ||||||||
\(183\) | 2713.84 | 1.09624 | ||||||||
\(184\) | −62.2900 | −0.0249570 | ||||||||
\(185\) | −2675.42 | −1.06325 | ||||||||
\(186\) | −4490.93 | −1.77038 | ||||||||
\(187\) | 509.079 | 0.199078 | ||||||||
\(188\) | 872.908 | 0.338635 | ||||||||
\(189\) | 1543.27 | 0.593951 | ||||||||
\(190\) | 1365.30 | 0.521314 | ||||||||
\(191\) | −1387.66 | −0.525693 | −0.262846 | − | 0.964838i | \(-0.584661\pi\) | ||||
−0.262846 | + | 0.964838i | \(0.584661\pi\) | |||||||
\(192\) | −3177.87 | −1.19449 | ||||||||
\(193\) | −3208.03 | −1.19647 | −0.598237 | − | 0.801319i | \(-0.704132\pi\) | ||||
−0.598237 | + | 0.801319i | \(0.704132\pi\) | |||||||
\(194\) | 869.764 | 0.321884 | ||||||||
\(195\) | −556.147 | −0.204238 | ||||||||
\(196\) | 2499.37 | 0.910849 | ||||||||
\(197\) | −3445.36 | −1.24605 | −0.623025 | − | 0.782202i | \(-0.714097\pi\) | ||||
−0.623025 | + | 0.782202i | \(0.714097\pi\) | |||||||
\(198\) | 583.599 | 0.209468 | ||||||||
\(199\) | 2025.71 | 0.721602 | 0.360801 | − | 0.932643i | \(-0.382503\pi\) | ||||
0.360801 | + | 0.932643i | \(0.382503\pi\) | |||||||
\(200\) | 240.715 | 0.0851056 | ||||||||
\(201\) | −714.595 | −0.250764 | ||||||||
\(202\) | −5737.59 | −1.99849 | ||||||||
\(203\) | −4434.02 | −1.53304 | ||||||||
\(204\) | −3237.36 | −1.11108 | ||||||||
\(205\) | 5599.37 | 1.90769 | ||||||||
\(206\) | −3501.20 | −1.18418 | ||||||||
\(207\) | −955.095 | −0.320694 | ||||||||
\(208\) | 302.730 | 0.100916 | ||||||||
\(209\) | 154.550 | 0.0511504 | ||||||||
\(210\) | 12468.7 | 4.09725 | ||||||||
\(211\) | 4309.54 | 1.40607 | 0.703036 | − | 0.711155i | \(-0.251827\pi\) | ||||
0.703036 | + | 0.711155i | \(0.251827\pi\) | |||||||
\(212\) | 1196.91 | 0.387755 | ||||||||
\(213\) | 3170.53 | 1.01991 | ||||||||
\(214\) | 5182.33 | 1.65540 | ||||||||
\(215\) | −8141.35 | −2.58249 | ||||||||
\(216\) | −70.5357 | −0.0222192 | ||||||||
\(217\) | −4359.84 | −1.36389 | ||||||||
\(218\) | −3449.45 | −1.07168 | ||||||||
\(219\) | 5667.19 | 1.74864 | ||||||||
\(220\) | −1136.10 | −0.348163 | ||||||||
\(221\) | 285.788 | 0.0869873 | ||||||||
\(222\) | 3926.34 | 1.18702 | ||||||||
\(223\) | 825.648 | 0.247935 | 0.123968 | − | 0.992286i | \(-0.460438\pi\) | ||||
0.123968 | + | 0.992286i | \(0.460438\pi\) | |||||||
\(224\) | −6543.09 | −1.95169 | ||||||||
\(225\) | 3690.89 | 1.09360 | ||||||||
\(226\) | 4681.43 | 1.37790 | ||||||||
\(227\) | −1501.19 | −0.438931 | −0.219466 | − | 0.975620i | \(-0.570431\pi\) | ||||
−0.219466 | + | 0.975620i | \(0.570431\pi\) | |||||||
\(228\) | −982.821 | −0.285478 | ||||||||
\(229\) | −5250.40 | −1.51509 | −0.757547 | − | 0.652781i | \(-0.773602\pi\) | ||||
−0.757547 | + | 0.652781i | \(0.773602\pi\) | |||||||
\(230\) | 3790.53 | 1.08670 | ||||||||
\(231\) | 1411.43 | 0.402015 | ||||||||
\(232\) | 202.658 | 0.0573497 | ||||||||
\(233\) | 2139.06 | 0.601435 | 0.300717 | − | 0.953713i | \(-0.402774\pi\) | ||||
0.300717 | + | 0.953713i | \(0.402774\pi\) | |||||||
\(234\) | 327.623 | 0.0915272 | ||||||||
\(235\) | 2055.24 | 0.570508 | ||||||||
\(236\) | 1404.44 | 0.387377 | ||||||||
\(237\) | −3969.46 | −1.08795 | ||||||||
\(238\) | −6407.32 | −1.74506 | ||||||||
\(239\) | 3772.70 | 1.02107 | 0.510534 | − | 0.859857i | \(-0.329448\pi\) | ||||
0.510534 | + | 0.859857i | \(0.329448\pi\) | |||||||
\(240\) | −8074.17 | −2.17160 | ||||||||
\(241\) | 6415.39 | 1.71474 | 0.857369 | − | 0.514702i | \(-0.172097\pi\) | ||||
0.857369 | + | 0.514702i | \(0.172097\pi\) | |||||||
\(242\) | 5012.00 | 1.33134 | ||||||||
\(243\) | −4364.77 | −1.15226 | ||||||||
\(244\) | 3112.22 | 0.816555 | ||||||||
\(245\) | 5884.71 | 1.53453 | ||||||||
\(246\) | −8217.41 | −2.12977 | ||||||||
\(247\) | 86.7616 | 0.0223502 | ||||||||
\(248\) | 199.267 | 0.0510221 | ||||||||
\(249\) | 1950.27 | 0.496360 | ||||||||
\(250\) | −5665.95 | −1.43339 | ||||||||
\(251\) | −6277.31 | −1.57857 | −0.789283 | − | 0.614029i | \(-0.789548\pi\) | ||||
−0.789283 | + | 0.614029i | \(0.789548\pi\) | |||||||
\(252\) | −3602.92 | −0.900645 | ||||||||
\(253\) | 429.081 | 0.106625 | ||||||||
\(254\) | −3516.82 | −0.868760 | ||||||||
\(255\) | −7622.30 | −1.87187 | ||||||||
\(256\) | 4383.90 | 1.07029 | ||||||||
\(257\) | −3183.98 | −0.772807 | −0.386404 | − | 0.922330i | \(-0.626283\pi\) | ||||
−0.386404 | + | 0.922330i | \(0.626283\pi\) | |||||||
\(258\) | 11947.9 | 2.88312 | ||||||||
\(259\) | 3811.73 | 0.914476 | ||||||||
\(260\) | −637.787 | −0.152130 | ||||||||
\(261\) | 3107.36 | 0.736938 | ||||||||
\(262\) | 9291.31 | 2.19091 | ||||||||
\(263\) | −2624.18 | −0.615261 | −0.307630 | − | 0.951506i | \(-0.599536\pi\) | ||||
−0.307630 | + | 0.951506i | \(0.599536\pi\) | |||||||
\(264\) | −64.5099 | −0.0150391 | ||||||||
\(265\) | 2818.10 | 0.653261 | ||||||||
\(266\) | −1945.18 | −0.448371 | ||||||||
\(267\) | −6480.34 | −1.48536 | ||||||||
\(268\) | −819.495 | −0.186786 | ||||||||
\(269\) | 7444.76 | 1.68742 | 0.843708 | − | 0.536803i | \(-0.180368\pi\) | ||||
0.843708 | + | 0.536803i | \(0.180368\pi\) | |||||||
\(270\) | 4292.30 | 0.967486 | ||||||||
\(271\) | −4004.49 | −0.897621 | −0.448810 | − | 0.893627i | \(-0.648152\pi\) | ||||
−0.448810 | + | 0.893627i | \(0.648152\pi\) | |||||||
\(272\) | 4149.08 | 0.924909 | ||||||||
\(273\) | 792.355 | 0.175661 | ||||||||
\(274\) | −8895.27 | −1.96125 | ||||||||
\(275\) | −1658.15 | −0.363601 | ||||||||
\(276\) | −2728.63 | −0.595088 | ||||||||
\(277\) | −5830.66 | −1.26473 | −0.632365 | − | 0.774671i | \(-0.717916\pi\) | ||||
−0.632365 | + | 0.774671i | \(0.717916\pi\) | |||||||
\(278\) | 1173.50 | 0.253172 | ||||||||
\(279\) | 3055.37 | 0.655628 | ||||||||
\(280\) | −553.250 | −0.118082 | ||||||||
\(281\) | −7504.37 | −1.59314 | −0.796572 | − | 0.604544i | \(-0.793355\pi\) | ||||
−0.796572 | + | 0.604544i | \(0.793355\pi\) | |||||||
\(282\) | −3016.19 | −0.636921 | ||||||||
\(283\) | 5910.87 | 1.24157 | 0.620785 | − | 0.783980i | \(-0.286814\pi\) | ||||
0.620785 | + | 0.783980i | \(0.286814\pi\) | |||||||
\(284\) | 3635.95 | 0.759697 | ||||||||
\(285\) | −2314.03 | −0.480952 | ||||||||
\(286\) | −147.186 | −0.0304311 | ||||||||
\(287\) | −7977.54 | −1.64076 | ||||||||
\(288\) | 4585.40 | 0.938184 | ||||||||
\(289\) | −996.118 | −0.202752 | ||||||||
\(290\) | −12332.3 | −2.49717 | ||||||||
\(291\) | −1474.15 | −0.296962 | ||||||||
\(292\) | 6499.11 | 1.30251 | ||||||||
\(293\) | 3245.59 | 0.647131 | 0.323566 | − | 0.946206i | \(-0.395118\pi\) | ||||
0.323566 | + | 0.946206i | \(0.395118\pi\) | |||||||
\(294\) | −8636.18 | −1.71317 | ||||||||
\(295\) | 3306.72 | 0.652625 | ||||||||
\(296\) | −174.216 | −0.0342098 | ||||||||
\(297\) | 485.880 | 0.0949280 | ||||||||
\(298\) | −7097.35 | −1.37966 | ||||||||
\(299\) | 240.878 | 0.0465898 | ||||||||
\(300\) | 10544.6 | 2.02931 | ||||||||
\(301\) | 11599.2 | 2.22115 | ||||||||
\(302\) | 9322.54 | 1.77633 | ||||||||
\(303\) | 9724.54 | 1.84376 | ||||||||
\(304\) | 1259.61 | 0.237643 | ||||||||
\(305\) | 7327.66 | 1.37567 | ||||||||
\(306\) | 4490.25 | 0.838857 | ||||||||
\(307\) | 7489.14 | 1.39227 | 0.696137 | − | 0.717909i | \(-0.254901\pi\) | ||||
0.696137 | + | 0.717909i | \(0.254901\pi\) | |||||||
\(308\) | 1618.63 | 0.299448 | ||||||||
\(309\) | 5934.12 | 1.09249 | ||||||||
\(310\) | −12126.0 | −2.22165 | ||||||||
\(311\) | 2136.71 | 0.389588 | 0.194794 | − | 0.980844i | \(-0.437596\pi\) | ||||
0.194794 | + | 0.980844i | \(0.437596\pi\) | |||||||
\(312\) | −36.2147 | −0.00657133 | ||||||||
\(313\) | 2212.15 | 0.399483 | 0.199742 | − | 0.979849i | \(-0.435990\pi\) | ||||
0.199742 | + | 0.979849i | \(0.435990\pi\) | |||||||
\(314\) | 5699.21 | 1.02428 | ||||||||
\(315\) | −8483.00 | −1.51734 | ||||||||
\(316\) | −4552.16 | −0.810377 | ||||||||
\(317\) | 429.326 | 0.0760674 | 0.0380337 | − | 0.999276i | \(-0.487891\pi\) | ||||
0.0380337 | + | 0.999276i | \(0.487891\pi\) | |||||||
\(318\) | −4135.73 | −0.729309 | ||||||||
\(319\) | −1396.00 | −0.245018 | ||||||||
\(320\) | −8580.60 | −1.49897 | ||||||||
\(321\) | −8783.43 | −1.52724 | ||||||||
\(322\) | −5400.45 | −0.934644 | ||||||||
\(323\) | 1189.11 | 0.204842 | ||||||||
\(324\) | −6855.05 | −1.17542 | ||||||||
\(325\) | −930.857 | −0.158876 | ||||||||
\(326\) | −505.201 | −0.0858297 | ||||||||
\(327\) | 5846.42 | 0.988708 | ||||||||
\(328\) | 364.615 | 0.0613796 | ||||||||
\(329\) | −2928.15 | −0.490681 | ||||||||
\(330\) | 3925.62 | 0.654843 | ||||||||
\(331\) | −765.454 | −0.127109 | −0.0635546 | − | 0.997978i | \(-0.520244\pi\) | ||||
−0.0635546 | + | 0.997978i | \(0.520244\pi\) | |||||||
\(332\) | 2236.57 | 0.369722 | ||||||||
\(333\) | −2671.26 | −0.439592 | ||||||||
\(334\) | −13548.3 | −2.21954 | ||||||||
\(335\) | −1929.48 | −0.314684 | ||||||||
\(336\) | 11503.4 | 1.86775 | ||||||||
\(337\) | −3049.81 | −0.492978 | −0.246489 | − | 0.969146i | \(-0.579277\pi\) | ||||
−0.246489 | + | 0.969146i | \(0.579277\pi\) | |||||||
\(338\) | 8623.15 | 1.38768 | ||||||||
\(339\) | −7934.48 | −1.27121 | ||||||||
\(340\) | −8741.22 | −1.39429 | ||||||||
\(341\) | −1372.64 | −0.217984 | ||||||||
\(342\) | 1363.18 | 0.215533 | ||||||||
\(343\) | 477.732 | 0.0752045 | ||||||||
\(344\) | −530.142 | −0.0830912 | ||||||||
\(345\) | −6424.50 | −1.00256 | ||||||||
\(346\) | 1436.82 | 0.223249 | ||||||||
\(347\) | −5907.00 | −0.913845 | −0.456922 | − | 0.889507i | \(-0.651048\pi\) | ||||
−0.456922 | + | 0.889507i | \(0.651048\pi\) | |||||||
\(348\) | 8877.48 | 1.36748 | ||||||||
\(349\) | −12107.4 | −1.85700 | −0.928502 | − | 0.371327i | \(-0.878903\pi\) | ||||
−0.928502 | + | 0.371327i | \(0.878903\pi\) | |||||||
\(350\) | 20869.6 | 3.18723 | ||||||||
\(351\) | 272.765 | 0.0414789 | ||||||||
\(352\) | −2060.01 | −0.311929 | ||||||||
\(353\) | −2420.40 | −0.364943 | −0.182471 | − | 0.983211i | \(-0.558410\pi\) | ||||
−0.182471 | + | 0.983211i | \(0.558410\pi\) | |||||||
\(354\) | −4852.81 | −0.728599 | ||||||||
\(355\) | 8560.77 | 1.27988 | ||||||||
\(356\) | −7431.63 | −1.10639 | ||||||||
\(357\) | 10859.7 | 1.60995 | ||||||||
\(358\) | −9581.07 | −1.41446 | ||||||||
\(359\) | −1455.80 | −0.214023 | −0.107011 | − | 0.994258i | \(-0.534128\pi\) | ||||
−0.107011 | + | 0.994258i | \(0.534128\pi\) | |||||||
\(360\) | 387.717 | 0.0567625 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 9687.06 | 1.40647 | ||||||||
\(363\) | −8494.76 | −1.22826 | ||||||||
\(364\) | 908.670 | 0.130844 | ||||||||
\(365\) | 15302.0 | 2.19437 | ||||||||
\(366\) | −10753.8 | −1.53582 | ||||||||
\(367\) | 8783.80 | 1.24935 | 0.624674 | − | 0.780886i | \(-0.285232\pi\) | ||||
0.624674 | + | 0.780886i | \(0.285232\pi\) | |||||||
\(368\) | 3497.08 | 0.495375 | ||||||||
\(369\) | 5590.66 | 0.788721 | ||||||||
\(370\) | 10601.6 | 1.48959 | ||||||||
\(371\) | −4015.00 | −0.561856 | ||||||||
\(372\) | 8728.95 | 1.21660 | ||||||||
\(373\) | −9199.84 | −1.27708 | −0.638538 | − | 0.769590i | \(-0.720461\pi\) | ||||
−0.638538 | + | 0.769590i | \(0.720461\pi\) | |||||||
\(374\) | −2017.26 | −0.278904 | ||||||||
\(375\) | 9603.13 | 1.32241 | ||||||||
\(376\) | 133.832 | 0.0183560 | ||||||||
\(377\) | −783.688 | −0.107061 | ||||||||
\(378\) | −6115.34 | −0.832114 | ||||||||
\(379\) | −6161.38 | −0.835063 | −0.417531 | − | 0.908662i | \(-0.637105\pi\) | ||||
−0.417531 | + | 0.908662i | \(0.637105\pi\) | |||||||
\(380\) | −2653.72 | −0.358245 | ||||||||
\(381\) | 5960.60 | 0.801498 | ||||||||
\(382\) | 5498.70 | 0.736486 | ||||||||
\(383\) | 2630.79 | 0.350985 | 0.175492 | − | 0.984481i | \(-0.443848\pi\) | ||||
0.175492 | + | 0.984481i | \(0.443848\pi\) | |||||||
\(384\) | −1014.43 | −0.134810 | ||||||||
\(385\) | 3811.03 | 0.504488 | ||||||||
\(386\) | 12712.1 | 1.67624 | ||||||||
\(387\) | −8128.69 | −1.06771 | ||||||||
\(388\) | −1690.55 | −0.221197 | ||||||||
\(389\) | −5866.48 | −0.764633 | −0.382317 | − | 0.924031i | \(-0.624874\pi\) | ||||
−0.382317 | + | 0.924031i | \(0.624874\pi\) | |||||||
\(390\) | 2203.77 | 0.286134 | ||||||||
\(391\) | 3301.37 | 0.427001 | ||||||||
\(392\) | 383.196 | 0.0493733 | ||||||||
\(393\) | −15747.7 | −2.02129 | ||||||||
\(394\) | 13652.5 | 1.74569 | ||||||||
\(395\) | −10718.0 | −1.36526 | ||||||||
\(396\) | −1134.33 | −0.143945 | ||||||||
\(397\) | −14254.0 | −1.80199 | −0.900993 | − | 0.433833i | \(-0.857161\pi\) | ||||
−0.900993 | + | 0.433833i | \(0.857161\pi\) | |||||||
\(398\) | −8027.03 | −1.01095 | ||||||||
\(399\) | 3296.85 | 0.413657 | ||||||||
\(400\) | −13514.2 | −1.68928 | ||||||||
\(401\) | 9909.27 | 1.23403 | 0.617014 | − | 0.786952i | \(-0.288342\pi\) | ||||
0.617014 | + | 0.786952i | \(0.288342\pi\) | |||||||
\(402\) | 2831.64 | 0.351316 | ||||||||
\(403\) | −770.576 | −0.0952484 | ||||||||
\(404\) | 11152.1 | 1.37336 | ||||||||
\(405\) | −16140.1 | −1.98026 | ||||||||
\(406\) | 17570.1 | 2.14776 | ||||||||
\(407\) | 1200.07 | 0.146156 | ||||||||
\(408\) | −496.343 | −0.0602270 | ||||||||
\(409\) | 5805.87 | 0.701912 | 0.350956 | − | 0.936392i | \(-0.385857\pi\) | ||||
0.350956 | + | 0.936392i | \(0.385857\pi\) | |||||||
\(410\) | −22187.9 | −2.67264 | ||||||||
\(411\) | 15076.4 | 1.80941 | ||||||||
\(412\) | 6805.23 | 0.813761 | ||||||||
\(413\) | −4711.15 | −0.561309 | ||||||||
\(414\) | 3784.64 | 0.449287 | ||||||||
\(415\) | 5265.95 | 0.622881 | ||||||||
\(416\) | −1156.45 | −0.136298 | ||||||||
\(417\) | −1988.95 | −0.233571 | ||||||||
\(418\) | −612.415 | −0.0716608 | ||||||||
\(419\) | 12260.9 | 1.42955 | 0.714777 | − | 0.699353i | \(-0.246528\pi\) | ||||
0.714777 | + | 0.699353i | \(0.246528\pi\) | |||||||
\(420\) | −24235.3 | −2.81562 | ||||||||
\(421\) | 5837.85 | 0.675818 | 0.337909 | − | 0.941179i | \(-0.390280\pi\) | ||||
0.337909 | + | 0.941179i | \(0.390280\pi\) | |||||||
\(422\) | −17076.9 | −1.96988 | ||||||||
\(423\) | 2052.05 | 0.235872 | ||||||||
\(424\) | 183.507 | 0.0210186 | ||||||||
\(425\) | −12757.9 | −1.45612 | ||||||||
\(426\) | −12563.5 | −1.42888 | ||||||||
\(427\) | −10439.9 | −1.18319 | ||||||||
\(428\) | −10072.8 | −1.13759 | ||||||||
\(429\) | 249.463 | 0.0280750 | ||||||||
\(430\) | 32260.7 | 3.61802 | ||||||||
\(431\) | −2770.16 | −0.309591 | −0.154796 | − | 0.987946i | \(-0.549472\pi\) | ||||
−0.154796 | + | 0.987946i | \(0.549472\pi\) | |||||||
\(432\) | 3960.01 | 0.441033 | ||||||||
\(433\) | 5663.00 | 0.628513 | 0.314257 | − | 0.949338i | \(-0.398245\pi\) | ||||
0.314257 | + | 0.949338i | \(0.398245\pi\) | |||||||
\(434\) | 17276.2 | 1.91079 | ||||||||
\(435\) | 20901.8 | 2.30383 | ||||||||
\(436\) | 6704.65 | 0.736455 | ||||||||
\(437\) | 1002.25 | 0.109712 | ||||||||
\(438\) | −22456.6 | −2.44982 | ||||||||
\(439\) | −8399.20 | −0.913148 | −0.456574 | − | 0.889685i | \(-0.650924\pi\) | ||||
−0.456574 | + | 0.889685i | \(0.650924\pi\) | |||||||
\(440\) | −174.184 | −0.0188725 | ||||||||
\(441\) | 5875.56 | 0.634442 | ||||||||
\(442\) | −1132.46 | −0.121868 | ||||||||
\(443\) | 6154.68 | 0.660085 | 0.330043 | − | 0.943966i | \(-0.392937\pi\) | ||||
0.330043 | + | 0.943966i | \(0.392937\pi\) | |||||||
\(444\) | −7631.58 | −0.815717 | ||||||||
\(445\) | −17497.6 | −1.86397 | ||||||||
\(446\) | −3271.69 | −0.347352 | ||||||||
\(447\) | 12029.2 | 1.27284 | ||||||||
\(448\) | 12225.0 | 1.28923 | ||||||||
\(449\) | 3445.03 | 0.362095 | 0.181048 | − | 0.983474i | \(-0.442051\pi\) | ||||
0.181048 | + | 0.983474i | \(0.442051\pi\) | |||||||
\(450\) | −14625.4 | −1.53211 | ||||||||
\(451\) | −2511.63 | −0.262235 | ||||||||
\(452\) | −9099.24 | −0.946885 | ||||||||
\(453\) | −15800.6 | −1.63880 | ||||||||
\(454\) | 5948.57 | 0.614935 | ||||||||
\(455\) | 2139.44 | 0.220437 | ||||||||
\(456\) | −150.683 | −0.0154745 | ||||||||
\(457\) | −502.346 | −0.0514196 | −0.0257098 | − | 0.999669i | \(-0.508185\pi\) | ||||
−0.0257098 | + | 0.999669i | \(0.508185\pi\) | |||||||
\(458\) | 20805.1 | 2.12262 | ||||||||
\(459\) | 3738.39 | 0.380159 | ||||||||
\(460\) | −7367.60 | −0.746774 | ||||||||
\(461\) | 546.259 | 0.0551883 | 0.0275942 | − | 0.999619i | \(-0.491215\pi\) | ||||
0.0275942 | + | 0.999619i | \(0.491215\pi\) | |||||||
\(462\) | −5592.91 | −0.563216 | ||||||||
\(463\) | 18540.2 | 1.86098 | 0.930490 | − | 0.366316i | \(-0.119381\pi\) | ||||
0.930490 | + | 0.366316i | \(0.119381\pi\) | |||||||
\(464\) | −11377.6 | −1.13835 | ||||||||
\(465\) | 20552.1 | 2.04964 | ||||||||
\(466\) | −8476.18 | −0.842599 | ||||||||
\(467\) | 12475.1 | 1.23614 | 0.618070 | − | 0.786123i | \(-0.287915\pi\) | ||||
0.618070 | + | 0.786123i | \(0.287915\pi\) | |||||||
\(468\) | −636.795 | −0.0628972 | ||||||||
\(469\) | 2748.98 | 0.270653 | ||||||||
\(470\) | −8144.05 | −0.799271 | ||||||||
\(471\) | −9659.49 | −0.944981 | ||||||||
\(472\) | 215.324 | 0.0209981 | ||||||||
\(473\) | 3651.85 | 0.354994 | ||||||||
\(474\) | 15729.3 | 1.52420 | ||||||||
\(475\) | −3873.13 | −0.374130 | ||||||||
\(476\) | 12453.8 | 1.19920 | ||||||||
\(477\) | 2813.71 | 0.270086 | ||||||||
\(478\) | −14949.6 | −1.43050 | ||||||||
\(479\) | −10569.2 | −1.00818 | −0.504091 | − | 0.863651i | \(-0.668172\pi\) | ||||
−0.504091 | + | 0.863651i | \(0.668172\pi\) | |||||||
\(480\) | 30843.9 | 2.93297 | ||||||||
\(481\) | 673.701 | 0.0638631 | ||||||||
\(482\) | −25421.5 | −2.40232 | ||||||||
\(483\) | 9153.13 | 0.862282 | ||||||||
\(484\) | −9741.76 | −0.914891 | ||||||||
\(485\) | −3980.36 | −0.372657 | ||||||||
\(486\) | 17295.7 | 1.61430 | ||||||||
\(487\) | −11227.9 | −1.04473 | −0.522366 | − | 0.852721i | \(-0.674951\pi\) | ||||
−0.522366 | + | 0.852721i | \(0.674951\pi\) | |||||||
\(488\) | 477.157 | 0.0442621 | ||||||||
\(489\) | 856.256 | 0.0791846 | ||||||||
\(490\) | −23318.6 | −2.14985 | ||||||||
\(491\) | −536.840 | −0.0493427 | −0.0246713 | − | 0.999696i | \(-0.507854\pi\) | ||||
−0.0246713 | + | 0.999696i | \(0.507854\pi\) | |||||||
\(492\) | 15972.1 | 1.46357 | ||||||||
\(493\) | −10740.9 | −0.981226 | ||||||||
\(494\) | −343.799 | −0.0313123 | ||||||||
\(495\) | −2670.77 | −0.242509 | ||||||||
\(496\) | −11187.3 | −1.01275 | ||||||||
\(497\) | −12196.7 | −1.10080 | ||||||||
\(498\) | −7728.11 | −0.695391 | ||||||||
\(499\) | 1319.91 | 0.118412 | 0.0592058 | − | 0.998246i | \(-0.481143\pi\) | ||||
0.0592058 | + | 0.998246i | \(0.481143\pi\) | |||||||
\(500\) | 11012.8 | 0.985018 | ||||||||
\(501\) | 22962.7 | 2.04770 | ||||||||
\(502\) | 24874.3 | 2.21154 | ||||||||
\(503\) | 1749.27 | 0.155062 | 0.0775310 | − | 0.996990i | \(-0.475296\pi\) | ||||
0.0775310 | + | 0.996990i | \(0.475296\pi\) | |||||||
\(504\) | −552.390 | −0.0488202 | ||||||||
\(505\) | 26257.3 | 2.31373 | ||||||||
\(506\) | −1700.26 | −0.149379 | ||||||||
\(507\) | −14615.2 | −1.28025 | ||||||||
\(508\) | 6835.59 | 0.597009 | ||||||||
\(509\) | 1882.19 | 0.163903 | 0.0819516 | − | 0.996636i | \(-0.473885\pi\) | ||||
0.0819516 | + | 0.996636i | \(0.473885\pi\) | |||||||
\(510\) | 30203.9 | 2.62245 | ||||||||
\(511\) | −21801.1 | −1.88733 | ||||||||
\(512\) | −16163.2 | −1.39515 | ||||||||
\(513\) | 1134.93 | 0.0976769 | ||||||||
\(514\) | 12616.8 | 1.08269 | ||||||||
\(515\) | 16022.8 | 1.37097 | ||||||||
\(516\) | −23223.0 | −1.98127 | ||||||||
\(517\) | −921.891 | −0.0784231 | ||||||||
\(518\) | −15104.3 | −1.28116 | ||||||||
\(519\) | −2435.25 | −0.205964 | ||||||||
\(520\) | −97.7837 | −0.00824635 | ||||||||
\(521\) | −3238.50 | −0.272325 | −0.136163 | − | 0.990686i | \(-0.543477\pi\) | ||||
−0.136163 | + | 0.990686i | \(0.543477\pi\) | |||||||
\(522\) | −12313.1 | −1.03244 | ||||||||
\(523\) | 99.0144 | 0.00827839 | 0.00413919 | − | 0.999991i | \(-0.498682\pi\) | ||||
0.00413919 | + | 0.999991i | \(0.498682\pi\) | |||||||
\(524\) | −18059.4 | −1.50559 | ||||||||
\(525\) | −35371.6 | −2.94046 | ||||||||
\(526\) | 10398.5 | 0.861969 | ||||||||
\(527\) | −10561.2 | −0.872963 | ||||||||
\(528\) | 3621.71 | 0.298513 | ||||||||
\(529\) | −9384.42 | −0.771301 | ||||||||
\(530\) | −11166.9 | −0.915207 | ||||||||
\(531\) | 3301.57 | 0.269823 | ||||||||
\(532\) | 3780.82 | 0.308119 | ||||||||
\(533\) | −1409.98 | −0.114584 | ||||||||
\(534\) | 25678.8 | 2.08096 | ||||||||
\(535\) | −23716.2 | −1.91653 | ||||||||
\(536\) | −125.643 | −0.0101249 | ||||||||
\(537\) | 16238.8 | 1.30495 | ||||||||
\(538\) | −29500.4 | −2.36404 | ||||||||
\(539\) | −2639.62 | −0.210940 | ||||||||
\(540\) | −8342.88 | −0.664853 | ||||||||
\(541\) | 17183.7 | 1.36559 | 0.682794 | − | 0.730611i | \(-0.260765\pi\) | ||||
0.682794 | + | 0.730611i | \(0.260765\pi\) | |||||||
\(542\) | 15868.1 | 1.25755 | ||||||||
\(543\) | −16418.4 | −1.29757 | ||||||||
\(544\) | −15849.8 | −1.24918 | ||||||||
\(545\) | 15786.0 | 1.24073 | ||||||||
\(546\) | −3139.77 | −0.246098 | ||||||||
\(547\) | −1965.86 | −0.153664 | −0.0768319 | − | 0.997044i | \(-0.524480\pi\) | ||||
−0.0768319 | + | 0.997044i | \(0.524480\pi\) | |||||||
\(548\) | 17289.6 | 1.34777 | ||||||||
\(549\) | 7316.27 | 0.568762 | ||||||||
\(550\) | 6570.54 | 0.509398 | ||||||||
\(551\) | −3260.79 | −0.252113 | ||||||||
\(552\) | −418.346 | −0.0322572 | ||||||||
\(553\) | 15270.1 | 1.17423 | ||||||||
\(554\) | 23104.4 | 1.77186 | ||||||||
\(555\) | −17968.4 | −1.37426 | ||||||||
\(556\) | −2280.92 | −0.173979 | ||||||||
\(557\) | 6039.93 | 0.459461 | 0.229731 | − | 0.973254i | \(-0.426215\pi\) | ||||
0.229731 | + | 0.973254i | \(0.426215\pi\) | |||||||
\(558\) | −12107.1 | −0.918523 | ||||||||
\(559\) | 2050.09 | 0.155115 | ||||||||
\(560\) | 31060.5 | 2.34384 | ||||||||
\(561\) | 3419.02 | 0.257311 | ||||||||
\(562\) | 29736.6 | 2.23197 | ||||||||
\(563\) | 5260.06 | 0.393757 | 0.196878 | − | 0.980428i | \(-0.436920\pi\) | ||||
0.196878 | + | 0.980428i | \(0.436920\pi\) | |||||||
\(564\) | 5862.53 | 0.437690 | ||||||||
\(565\) | −21424.0 | −1.59524 | ||||||||
\(566\) | −23422.3 | −1.73942 | ||||||||
\(567\) | 22995.1 | 1.70318 | ||||||||
\(568\) | 557.454 | 0.0411800 | ||||||||
\(569\) | 20567.4 | 1.51534 | 0.757672 | − | 0.652635i | \(-0.226337\pi\) | ||||
0.757672 | + | 0.652635i | \(0.226337\pi\) | |||||||
\(570\) | 9169.52 | 0.673805 | ||||||||
\(571\) | 11462.4 | 0.840080 | 0.420040 | − | 0.907506i | \(-0.362016\pi\) | ||||
0.420040 | + | 0.907506i | \(0.362016\pi\) | |||||||
\(572\) | 286.083 | 0.0209121 | ||||||||
\(573\) | −9319.64 | −0.679466 | ||||||||
\(574\) | 31611.6 | 2.29868 | ||||||||
\(575\) | −10753.1 | −0.779886 | ||||||||
\(576\) | −8567.25 | −0.619737 | ||||||||
\(577\) | −27029.6 | −1.95019 | −0.975094 | − | 0.221790i | \(-0.928810\pi\) | ||||
−0.975094 | + | 0.221790i | \(0.928810\pi\) | |||||||
\(578\) | 3947.19 | 0.284051 | ||||||||
\(579\) | −21545.5 | −1.54646 | ||||||||
\(580\) | 23970.2 | 1.71605 | ||||||||
\(581\) | −7502.52 | −0.535726 | ||||||||
\(582\) | 5841.42 | 0.416039 | ||||||||
\(583\) | −1264.07 | −0.0897986 | ||||||||
\(584\) | 996.425 | 0.0706034 | ||||||||
\(585\) | −1499.32 | −0.105965 | ||||||||
\(586\) | −12860.9 | −0.906619 | ||||||||
\(587\) | 15200.4 | 1.06881 | 0.534403 | − | 0.845230i | \(-0.320536\pi\) | ||||
0.534403 | + | 0.845230i | \(0.320536\pi\) | |||||||
\(588\) | 16786.0 | 1.17729 | ||||||||
\(589\) | −3206.23 | −0.224296 | ||||||||
\(590\) | −13103.1 | −0.914316 | ||||||||
\(591\) | −23139.4 | −1.61054 | ||||||||
\(592\) | 9780.83 | 0.679036 | ||||||||
\(593\) | −19026.7 | −1.31759 | −0.658796 | − | 0.752322i | \(-0.728934\pi\) | ||||
−0.658796 | + | 0.752322i | \(0.728934\pi\) | |||||||
\(594\) | −1925.34 | −0.132992 | ||||||||
\(595\) | 29322.2 | 2.02033 | ||||||||
\(596\) | 13795.0 | 0.948096 | ||||||||
\(597\) | 13604.9 | 0.932681 | ||||||||
\(598\) | −954.499 | −0.0652715 | ||||||||
\(599\) | 3927.31 | 0.267889 | 0.133945 | − | 0.990989i | \(-0.457236\pi\) | ||||
0.133945 | + | 0.990989i | \(0.457236\pi\) | |||||||
\(600\) | 1616.67 | 0.110000 | ||||||||
\(601\) | 13718.1 | 0.931069 | 0.465534 | − | 0.885030i | \(-0.345862\pi\) | ||||
0.465534 | + | 0.885030i | \(0.345862\pi\) | |||||||
\(602\) | −45962.6 | −3.11178 | ||||||||
\(603\) | −1926.48 | −0.130104 | ||||||||
\(604\) | −18120.1 | −1.22069 | ||||||||
\(605\) | −22936.8 | −1.54134 | ||||||||
\(606\) | −38534.2 | −2.58308 | ||||||||
\(607\) | 26461.5 | 1.76942 | 0.884712 | − | 0.466138i | \(-0.154355\pi\) | ||||
0.884712 | + | 0.466138i | \(0.154355\pi\) | |||||||
\(608\) | −4811.81 | −0.320961 | ||||||||
\(609\) | −29779.3 | −1.98148 | ||||||||
\(610\) | −29036.4 | −1.92729 | ||||||||
\(611\) | −517.534 | −0.0342671 | ||||||||
\(612\) | −8727.63 | −0.576460 | ||||||||
\(613\) | −233.384 | −0.0153773 | −0.00768865 | − | 0.999970i | \(-0.502447\pi\) | ||||
−0.00768865 | + | 0.999970i | \(0.502447\pi\) | |||||||
\(614\) | −29676.3 | −1.95055 | ||||||||
\(615\) | 37605.9 | 2.46572 | ||||||||
\(616\) | 248.163 | 0.0162318 | ||||||||
\(617\) | 4202.77 | 0.274225 | 0.137113 | − | 0.990555i | \(-0.456218\pi\) | ||||
0.137113 | + | 0.990555i | \(0.456218\pi\) | |||||||
\(618\) | −23514.4 | −1.53056 | ||||||||
\(619\) | −23009.4 | −1.49407 | −0.747033 | − | 0.664787i | \(-0.768522\pi\) | ||||
−0.747033 | + | 0.664787i | \(0.768522\pi\) | |||||||
\(620\) | 23569.1 | 1.52671 | ||||||||
\(621\) | 3150.93 | 0.203611 | ||||||||
\(622\) | −8466.89 | −0.545806 | ||||||||
\(623\) | 24929.2 | 1.60316 | ||||||||
\(624\) | 2033.17 | 0.130436 | ||||||||
\(625\) | 448.344 | 0.0286940 | ||||||||
\(626\) | −8765.82 | −0.559668 | ||||||||
\(627\) | 1037.97 | 0.0661126 | ||||||||
\(628\) | −11077.5 | −0.703884 | ||||||||
\(629\) | 9233.45 | 0.585313 | ||||||||
\(630\) | 33614.5 | 2.12577 | ||||||||
\(631\) | 18819.3 | 1.18730 | 0.593650 | − | 0.804723i | \(-0.297686\pi\) | ||||
0.593650 | + | 0.804723i | \(0.297686\pi\) | |||||||
\(632\) | −697.924 | −0.0439271 | ||||||||
\(633\) | 28943.3 | 1.81737 | ||||||||
\(634\) | −1701.24 | −0.106569 | ||||||||
\(635\) | 16094.3 | 1.00580 | ||||||||
\(636\) | 8038.56 | 0.501178 | ||||||||
\(637\) | −1481.84 | −0.0921705 | ||||||||
\(638\) | 5531.74 | 0.343266 | ||||||||
\(639\) | 8547.46 | 0.529159 | ||||||||
\(640\) | −2739.06 | −0.169173 | ||||||||
\(641\) | 25253.7 | 1.55610 | 0.778052 | − | 0.628200i | \(-0.216208\pi\) | ||||
0.778052 | + | 0.628200i | \(0.216208\pi\) | |||||||
\(642\) | 34805.0 | 2.13963 | ||||||||
\(643\) | 11712.1 | 0.718324 | 0.359162 | − | 0.933275i | \(-0.383063\pi\) | ||||
0.359162 | + | 0.933275i | \(0.383063\pi\) | |||||||
\(644\) | 10496.8 | 0.642284 | ||||||||
\(645\) | −54678.1 | −3.33791 | ||||||||
\(646\) | −4711.96 | −0.286981 | ||||||||
\(647\) | −26533.3 | −1.61226 | −0.806131 | − | 0.591737i | \(-0.798442\pi\) | ||||
−0.806131 | + | 0.591737i | \(0.798442\pi\) | |||||||
\(648\) | −1051.00 | −0.0637146 | ||||||||
\(649\) | −1483.25 | −0.0897111 | ||||||||
\(650\) | 3688.59 | 0.222582 | ||||||||
\(651\) | −29281.1 | −1.76285 | ||||||||
\(652\) | 981.952 | 0.0589819 | ||||||||
\(653\) | 27898.9 | 1.67193 | 0.835964 | − | 0.548785i | \(-0.184909\pi\) | ||||
0.835964 | + | 0.548785i | \(0.184909\pi\) | |||||||
\(654\) | −23166.9 | −1.38516 | ||||||||
\(655\) | −42520.4 | −2.53650 | ||||||||
\(656\) | −20470.2 | −1.21834 | ||||||||
\(657\) | 15278.2 | 0.907245 | ||||||||
\(658\) | 11603.0 | 0.687436 | ||||||||
\(659\) | −1274.66 | −0.0753468 | −0.0376734 | − | 0.999290i | \(-0.511995\pi\) | ||||
−0.0376734 | + | 0.999290i | \(0.511995\pi\) | |||||||
\(660\) | −7630.16 | −0.450006 | ||||||||
\(661\) | −5049.52 | −0.297131 | −0.148565 | − | 0.988903i | \(-0.547466\pi\) | ||||
−0.148565 | + | 0.988903i | \(0.547466\pi\) | |||||||
\(662\) | 3033.17 | 0.178078 | ||||||||
\(663\) | 1919.38 | 0.112432 | ||||||||
\(664\) | 342.904 | 0.0200411 | ||||||||
\(665\) | 8901.86 | 0.519097 | ||||||||
\(666\) | 10585.1 | 0.615860 | ||||||||
\(667\) | −9053.01 | −0.525538 | ||||||||
\(668\) | 26333.6 | 1.52526 | ||||||||
\(669\) | 5545.14 | 0.320460 | ||||||||
\(670\) | 7645.73 | 0.440866 | ||||||||
\(671\) | −3286.86 | −0.189103 | ||||||||
\(672\) | −43944.1 | −2.52259 | ||||||||
\(673\) | 8398.64 | 0.481045 | 0.240523 | − | 0.970644i | \(-0.422681\pi\) | ||||
0.240523 | + | 0.970644i | \(0.422681\pi\) | |||||||
\(674\) | 12085.1 | 0.690653 | ||||||||
\(675\) | −12176.5 | −0.694333 | ||||||||
\(676\) | −16760.7 | −0.953612 | ||||||||
\(677\) | 9875.31 | 0.560619 | 0.280309 | − | 0.959910i | \(-0.409563\pi\) | ||||
0.280309 | + | 0.959910i | \(0.409563\pi\) | |||||||
\(678\) | 31441.0 | 1.78095 | ||||||||
\(679\) | 5670.91 | 0.320515 | ||||||||
\(680\) | −1340.18 | −0.0755787 | ||||||||
\(681\) | −10082.1 | −0.567325 | ||||||||
\(682\) | 5439.18 | 0.305392 | ||||||||
\(683\) | −8653.78 | −0.484814 | −0.242407 | − | 0.970175i | \(-0.577937\pi\) | ||||
−0.242407 | + | 0.970175i | \(0.577937\pi\) | |||||||
\(684\) | −2649.60 | −0.148114 | ||||||||
\(685\) | 40708.0 | 2.27062 | ||||||||
\(686\) | −1893.05 | −0.105360 | ||||||||
\(687\) | −35262.2 | −1.95828 | ||||||||
\(688\) | 29763.2 | 1.64929 | ||||||||
\(689\) | −709.629 | −0.0392376 | ||||||||
\(690\) | 25457.6 | 1.40457 | ||||||||
\(691\) | 2916.50 | 0.160563 | 0.0802813 | − | 0.996772i | \(-0.474418\pi\) | ||||
0.0802813 | + | 0.996772i | \(0.474418\pi\) | |||||||
\(692\) | −2792.73 | −0.153416 | ||||||||
\(693\) | 3805.10 | 0.208577 | ||||||||
\(694\) | 23406.9 | 1.28028 | ||||||||
\(695\) | −5370.37 | −0.293108 | ||||||||
\(696\) | 1361.07 | 0.0741254 | ||||||||
\(697\) | −19324.6 | −1.05017 | ||||||||
\(698\) | 47976.5 | 2.60163 | ||||||||
\(699\) | 14366.1 | 0.777363 | ||||||||
\(700\) | −40564.0 | −2.19025 | ||||||||
\(701\) | −9070.78 | −0.488729 | −0.244364 | − | 0.969683i | \(-0.578579\pi\) | ||||
−0.244364 | + | 0.969683i | \(0.578579\pi\) | |||||||
\(702\) | −1080.85 | −0.0581112 | ||||||||
\(703\) | 2803.16 | 0.150388 | ||||||||
\(704\) | 3848.88 | 0.206051 | ||||||||
\(705\) | 13803.2 | 0.737389 | ||||||||
\(706\) | 9591.00 | 0.511278 | ||||||||
\(707\) | −37409.4 | −1.98999 | ||||||||
\(708\) | 9432.34 | 0.500690 | ||||||||
\(709\) | −5957.11 | −0.315549 | −0.157774 | − | 0.987475i | \(-0.550432\pi\) | ||||
−0.157774 | + | 0.987475i | \(0.550432\pi\) | |||||||
\(710\) | −33922.7 | −1.79309 | ||||||||
\(711\) | −10701.3 | −0.564459 | ||||||||
\(712\) | −1139.40 | −0.0599729 | ||||||||
\(713\) | −8901.55 | −0.467553 | ||||||||
\(714\) | −43032.2 | −2.25552 | ||||||||
\(715\) | 673.577 | 0.0352312 | ||||||||
\(716\) | 18622.6 | 0.972010 | ||||||||
\(717\) | 25337.8 | 1.31975 | ||||||||
\(718\) | 5768.71 | 0.299842 | ||||||||
\(719\) | −31140.8 | −1.61524 | −0.807620 | − | 0.589703i | \(-0.799245\pi\) | ||||
−0.807620 | + | 0.589703i | \(0.799245\pi\) | |||||||
\(720\) | −21767.2 | −1.12669 | ||||||||
\(721\) | −22828.0 | −1.17914 | ||||||||
\(722\) | −1430.49 | −0.0737359 | ||||||||
\(723\) | 43086.4 | 2.21632 | ||||||||
\(724\) | −18828.6 | −0.966519 | ||||||||
\(725\) | 34984.7 | 1.79214 | ||||||||
\(726\) | 33661.1 | 1.72077 | ||||||||
\(727\) | 14969.7 | 0.763682 | 0.381841 | − | 0.924228i | \(-0.375290\pi\) | ||||
0.381841 | + | 0.924228i | \(0.375290\pi\) | |||||||
\(728\) | 139.315 | 0.00709251 | ||||||||
\(729\) | −5283.30 | −0.268420 | ||||||||
\(730\) | −60635.4 | −3.07427 | ||||||||
\(731\) | 28097.5 | 1.42165 | ||||||||
\(732\) | 20902.0 | 1.05541 | ||||||||
\(733\) | −12414.1 | −0.625545 | −0.312772 | − | 0.949828i | \(-0.601258\pi\) | ||||
−0.312772 | + | 0.949828i | \(0.601258\pi\) | |||||||
\(734\) | −34806.5 | −1.75031 | ||||||||
\(735\) | 39522.3 | 1.98341 | ||||||||
\(736\) | −13359.1 | −0.669055 | ||||||||
\(737\) | 865.481 | 0.0432570 | ||||||||
\(738\) | −22153.4 | −1.10498 | ||||||||
\(739\) | 1324.11 | 0.0659111 | 0.0329555 | − | 0.999457i | \(-0.489508\pi\) | ||||
0.0329555 | + | 0.999457i | \(0.489508\pi\) | |||||||
\(740\) | −20606.1 | −1.02364 | ||||||||
\(741\) | 582.700 | 0.0288880 | ||||||||
\(742\) | 15909.8 | 0.787150 | ||||||||
\(743\) | −4391.55 | −0.216838 | −0.108419 | − | 0.994105i | \(-0.534579\pi\) | ||||
−0.108419 | + | 0.994105i | \(0.534579\pi\) | |||||||
\(744\) | 1338.30 | 0.0659468 | ||||||||
\(745\) | 32480.1 | 1.59729 | ||||||||
\(746\) | 36455.0 | 1.78916 | ||||||||
\(747\) | 5257.76 | 0.257525 | ||||||||
\(748\) | 3920.92 | 0.191662 | ||||||||
\(749\) | 33789.0 | 1.64836 | ||||||||
\(750\) | −38053.1 | −1.85267 | ||||||||
\(751\) | −31947.5 | −1.55230 | −0.776152 | − | 0.630546i | \(-0.782831\pi\) | ||||
−0.776152 | + | 0.630546i | \(0.782831\pi\) | |||||||
\(752\) | −7513.58 | −0.364351 | ||||||||
\(753\) | −42159.0 | −2.04032 | ||||||||
\(754\) | 3105.42 | 0.149990 | ||||||||
\(755\) | −42663.4 | −2.05653 | ||||||||
\(756\) | 11886.3 | 0.571826 | ||||||||
\(757\) | 18569.8 | 0.891585 | 0.445793 | − | 0.895136i | \(-0.352922\pi\) | ||||
0.445793 | + | 0.895136i | \(0.352922\pi\) | |||||||
\(758\) | 24414.9 | 1.16991 | ||||||||
\(759\) | 2881.75 | 0.137814 | ||||||||
\(760\) | −406.861 | −0.0194190 | ||||||||
\(761\) | 5507.32 | 0.262339 | 0.131170 | − | 0.991360i | \(-0.458127\pi\) | ||||
0.131170 | + | 0.991360i | \(0.458127\pi\) | |||||||
\(762\) | −23619.3 | −1.12288 | ||||||||
\(763\) | −22490.6 | −1.06712 | ||||||||
\(764\) | −10687.7 | −0.506111 | ||||||||
\(765\) | −20549.0 | −0.971178 | ||||||||
\(766\) | −10424.7 | −0.491723 | ||||||||
\(767\) | −832.669 | −0.0391994 | ||||||||
\(768\) | 29442.7 | 1.38336 | ||||||||
\(769\) | −14977.9 | −0.702362 | −0.351181 | − | 0.936308i | \(-0.614220\pi\) | ||||
−0.351181 | + | 0.936308i | \(0.614220\pi\) | |||||||
\(770\) | −15101.5 | −0.706778 | ||||||||
\(771\) | −21384.0 | −0.998864 | ||||||||
\(772\) | −24708.3 | −1.15190 | ||||||||
\(773\) | 19545.6 | 0.909450 | 0.454725 | − | 0.890632i | \(-0.349738\pi\) | ||||
0.454725 | + | 0.890632i | \(0.349738\pi\) | |||||||
\(774\) | 32210.5 | 1.49585 | ||||||||
\(775\) | 34399.4 | 1.59440 | ||||||||
\(776\) | −259.190 | −0.0119902 | ||||||||
\(777\) | 25600.0 | 1.18197 | ||||||||
\(778\) | 23246.4 | 1.07124 | ||||||||
\(779\) | −5866.70 | −0.269829 | ||||||||
\(780\) | −4283.44 | −0.196631 | ||||||||
\(781\) | −3839.98 | −0.175935 | ||||||||
\(782\) | −13081.9 | −0.598221 | ||||||||
\(783\) | −10251.4 | −0.467887 | ||||||||
\(784\) | −21513.4 | −0.980020 | ||||||||
\(785\) | −26081.7 | −1.18585 | ||||||||
\(786\) | 62401.3 | 2.83178 | ||||||||
\(787\) | −4274.62 | −0.193613 | −0.0968067 | − | 0.995303i | \(-0.530863\pi\) | ||||
−0.0968067 | + | 0.995303i | \(0.530863\pi\) | |||||||
\(788\) | −26536.2 | −1.19963 | ||||||||
\(789\) | −17624.2 | −0.795233 | ||||||||
\(790\) | 42470.7 | 1.91271 | ||||||||
\(791\) | 30523.2 | 1.37204 | ||||||||
\(792\) | −173.913 | −0.00780268 | ||||||||
\(793\) | −1845.19 | −0.0826287 | ||||||||
\(794\) | 56482.6 | 2.52455 | ||||||||
\(795\) | 18926.6 | 0.844350 | ||||||||
\(796\) | 15602.0 | 0.694722 | ||||||||
\(797\) | −25450.6 | −1.13112 | −0.565562 | − | 0.824706i | \(-0.691341\pi\) | ||||
−0.565562 | + | 0.824706i | \(0.691341\pi\) | |||||||
\(798\) | −13064.0 | −0.579525 | ||||||||
\(799\) | −7093.08 | −0.314062 | ||||||||
\(800\) | 51625.4 | 2.28154 | ||||||||
\(801\) | −17470.4 | −0.770645 | ||||||||
\(802\) | −39266.2 | −1.72885 | ||||||||
\(803\) | −6863.81 | −0.301642 | ||||||||
\(804\) | −5503.81 | −0.241423 | ||||||||
\(805\) | 24714.5 | 1.08207 | ||||||||
\(806\) | 3053.46 | 0.133441 | ||||||||
\(807\) | 49999.7 | 2.18101 | ||||||||
\(808\) | 1709.80 | 0.0744439 | ||||||||
\(809\) | 4002.04 | 0.173924 | 0.0869619 | − | 0.996212i | \(-0.472284\pi\) | ||||
0.0869619 | + | 0.996212i | \(0.472284\pi\) | |||||||
\(810\) | 63956.2 | 2.77431 | ||||||||
\(811\) | −37915.1 | −1.64165 | −0.820826 | − | 0.571179i | \(-0.806486\pi\) | ||||
−0.820826 | + | 0.571179i | \(0.806486\pi\) | |||||||
\(812\) | −34150.8 | −1.47593 | ||||||||
\(813\) | −26894.5 | −1.16019 | ||||||||
\(814\) | −4755.39 | −0.204762 | ||||||||
\(815\) | 2311.99 | 0.0993685 | ||||||||
\(816\) | 27865.7 | 1.19546 | ||||||||
\(817\) | 8530.05 | 0.365274 | ||||||||
\(818\) | −23006.2 | −0.983366 | ||||||||
\(819\) | 2136.12 | 0.0911379 | ||||||||
\(820\) | 43126.3 | 1.83663 | ||||||||
\(821\) | 4739.43 | 0.201470 | 0.100735 | − | 0.994913i | \(-0.467881\pi\) | ||||
0.100735 | + | 0.994913i | \(0.467881\pi\) | |||||||
\(822\) | −59741.5 | −2.53494 | ||||||||
\(823\) | 20752.2 | 0.878952 | 0.439476 | − | 0.898254i | \(-0.355164\pi\) | ||||
0.439476 | + | 0.898254i | \(0.355164\pi\) | |||||||
\(824\) | 1043.36 | 0.0441106 | ||||||||
\(825\) | −11136.3 | −0.469959 | ||||||||
\(826\) | 18668.3 | 0.786384 | ||||||||
\(827\) | 34264.8 | 1.44075 | 0.720377 | − | 0.693583i | \(-0.243969\pi\) | ||||
0.720377 | + | 0.693583i | \(0.243969\pi\) | |||||||
\(828\) | −7356.14 | −0.308748 | ||||||||
\(829\) | −39707.5 | −1.66357 | −0.831784 | − | 0.555100i | \(-0.812680\pi\) | ||||
−0.831784 | + | 0.555100i | \(0.812680\pi\) | |||||||
\(830\) | −20866.7 | −0.872645 | ||||||||
\(831\) | −39159.3 | −1.63468 | ||||||||
\(832\) | 2160.69 | 0.0900343 | ||||||||
\(833\) | −20309.4 | −0.844753 | ||||||||
\(834\) | 7881.35 | 0.327229 | ||||||||
\(835\) | 62001.8 | 2.56965 | ||||||||
\(836\) | 1190.34 | 0.0492450 | ||||||||
\(837\) | −10079.9 | −0.416263 | ||||||||
\(838\) | −48584.6 | −2.00278 | ||||||||
\(839\) | −4524.04 | −0.186159 | −0.0930794 | − | 0.995659i | \(-0.529671\pi\) | ||||
−0.0930794 | + | 0.995659i | \(0.529671\pi\) | |||||||
\(840\) | −3715.68 | −0.152623 | ||||||||
\(841\) | 5064.59 | 0.207659 | ||||||||
\(842\) | −23132.9 | −0.946809 | ||||||||
\(843\) | −50400.1 | −2.05916 | ||||||||
\(844\) | 33192.1 | 1.35370 | ||||||||
\(845\) | −39462.7 | −1.60658 | ||||||||
\(846\) | −8131.39 | −0.330453 | ||||||||
\(847\) | 32678.5 | 1.32568 | ||||||||
\(848\) | −10302.4 | −0.417201 | ||||||||
\(849\) | 39698.0 | 1.60475 | ||||||||
\(850\) | 50554.1 | 2.03999 | ||||||||
\(851\) | 7782.47 | 0.313490 | ||||||||
\(852\) | 24419.4 | 0.981920 | ||||||||
\(853\) | −7595.54 | −0.304884 | −0.152442 | − | 0.988312i | \(-0.548714\pi\) | ||||
−0.152442 | + | 0.988312i | \(0.548714\pi\) | |||||||
\(854\) | 41368.8 | 1.65762 | ||||||||
\(855\) | −6238.42 | −0.249531 | ||||||||
\(856\) | −1544.34 | −0.0616639 | ||||||||
\(857\) | −19528.9 | −0.778405 | −0.389203 | − | 0.921152i | \(-0.627249\pi\) | ||||
−0.389203 | + | 0.921152i | \(0.627249\pi\) | |||||||
\(858\) | −988.515 | −0.0393326 | ||||||||
\(859\) | 25980.8 | 1.03196 | 0.515979 | − | 0.856601i | \(-0.327428\pi\) | ||||
0.515979 | + | 0.856601i | \(0.327428\pi\) | |||||||
\(860\) | −62704.7 | −2.48629 | ||||||||
\(861\) | −53578.0 | −2.12071 | ||||||||
\(862\) | 10977.0 | 0.433732 | ||||||||
\(863\) | −48294.6 | −1.90494 | −0.952472 | − | 0.304625i | \(-0.901469\pi\) | ||||
−0.952472 | + | 0.304625i | \(0.901469\pi\) | |||||||
\(864\) | −15127.6 | −0.595660 | ||||||||
\(865\) | −6575.43 | −0.258464 | ||||||||
\(866\) | −22440.1 | −0.880536 | ||||||||
\(867\) | −6690.03 | −0.262059 | ||||||||
\(868\) | −33579.4 | −1.31309 | ||||||||
\(869\) | 4807.61 | 0.187672 | ||||||||
\(870\) | −82825.1 | −3.22763 | ||||||||
\(871\) | 485.866 | 0.0189012 | ||||||||
\(872\) | 1027.94 | 0.0399201 | ||||||||
\(873\) | −3974.17 | −0.154072 | ||||||||
\(874\) | −3971.51 | −0.153705 | ||||||||
\(875\) | −36942.3 | −1.42729 | ||||||||
\(876\) | 43648.7 | 1.68351 | ||||||||
\(877\) | 44377.5 | 1.70869 | 0.854346 | − | 0.519705i | \(-0.173958\pi\) | ||||
0.854346 | + | 0.519705i | \(0.173958\pi\) | |||||||
\(878\) | 33282.5 | 1.27930 | ||||||||
\(879\) | 21797.7 | 0.836426 | ||||||||
\(880\) | 9779.02 | 0.374603 | ||||||||
\(881\) | −12139.4 | −0.464231 | −0.232116 | − | 0.972688i | \(-0.574565\pi\) | ||||
−0.232116 | + | 0.972688i | \(0.574565\pi\) | |||||||
\(882\) | −23282.4 | −0.888841 | ||||||||
\(883\) | 5048.07 | 0.192391 | 0.0961954 | − | 0.995362i | \(-0.469333\pi\) | ||||
0.0961954 | + | 0.995362i | \(0.469333\pi\) | |||||||
\(884\) | 2201.14 | 0.0837470 | ||||||||
\(885\) | 22208.2 | 0.843527 | ||||||||
\(886\) | −24388.4 | −0.924767 | ||||||||
\(887\) | 20373.4 | 0.771221 | 0.385610 | − | 0.922662i | \(-0.373991\pi\) | ||||
0.385610 | + | 0.922662i | \(0.373991\pi\) | |||||||
\(888\) | −1170.05 | −0.0442166 | ||||||||
\(889\) | −22929.9 | −0.865065 | ||||||||
\(890\) | 69335.6 | 2.61139 | ||||||||
\(891\) | 7239.72 | 0.272211 | ||||||||
\(892\) | 6359.14 | 0.238699 | ||||||||
\(893\) | −2153.37 | −0.0806940 | ||||||||
\(894\) | −47666.5 | −1.78323 | ||||||||
\(895\) | 43846.5 | 1.63757 | ||||||||
\(896\) | 3902.40 | 0.145502 | ||||||||
\(897\) | 1617.76 | 0.0602180 | ||||||||
\(898\) | −13651.2 | −0.507289 | ||||||||
\(899\) | 28960.8 | 1.07441 | ||||||||
\(900\) | 28427.3 | 1.05286 | ||||||||
\(901\) | −9725.85 | −0.359617 | ||||||||
\(902\) | 9952.52 | 0.367386 | ||||||||
\(903\) | 77901.2 | 2.87086 | ||||||||
\(904\) | −1395.07 | −0.0513267 | ||||||||
\(905\) | −44331.6 | −1.62832 | ||||||||
\(906\) | 62611.1 | 2.29593 | ||||||||
\(907\) | −7456.13 | −0.272962 | −0.136481 | − | 0.990643i | \(-0.543579\pi\) | ||||
−0.136481 | + | 0.990643i | \(0.543579\pi\) | |||||||
\(908\) | −11562.2 | −0.422581 | ||||||||
\(909\) | 26216.5 | 0.956596 | ||||||||
\(910\) | −8477.71 | −0.308828 | ||||||||
\(911\) | −10653.2 | −0.387440 | −0.193720 | − | 0.981057i | \(-0.562055\pi\) | ||||
−0.193720 | + | 0.981057i | \(0.562055\pi\) | |||||||
\(912\) | 8459.66 | 0.307157 | ||||||||
\(913\) | −2362.07 | −0.0856224 | ||||||||
\(914\) | 1990.59 | 0.0720380 | ||||||||
\(915\) | 49213.3 | 1.77808 | ||||||||
\(916\) | −40438.6 | −1.45866 | ||||||||
\(917\) | 60579.8 | 2.18159 | ||||||||
\(918\) | −14813.6 | −0.532596 | ||||||||
\(919\) | −12569.7 | −0.451183 | −0.225591 | − | 0.974222i | \(-0.572431\pi\) | ||||
−0.225591 | + | 0.974222i | \(0.572431\pi\) | |||||||
\(920\) | −1129.58 | −0.0404795 | ||||||||
\(921\) | 50297.8 | 1.79953 | ||||||||
\(922\) | −2164.59 | −0.0773179 | ||||||||
\(923\) | −2155.70 | −0.0768752 | ||||||||
\(924\) | 10870.9 | 0.387040 | ||||||||
\(925\) | −30074.8 | −1.06903 | ||||||||
\(926\) | −73466.8 | −2.60720 | ||||||||
\(927\) | 15997.9 | 0.566816 | ||||||||
\(928\) | 43463.4 | 1.53745 | ||||||||
\(929\) | 4920.06 | 0.173759 | 0.0868795 | − | 0.996219i | \(-0.472311\pi\) | ||||
0.0868795 | + | 0.996219i | \(0.472311\pi\) | |||||||
\(930\) | −81439.4 | −2.87151 | ||||||||
\(931\) | −6165.67 | −0.217048 | ||||||||
\(932\) | 16475.0 | 0.579031 | ||||||||
\(933\) | 14350.4 | 0.503548 | ||||||||
\(934\) | −49433.4 | −1.73181 | ||||||||
\(935\) | 9231.74 | 0.322898 | ||||||||
\(936\) | −97.6317 | −0.00340939 | ||||||||
\(937\) | 1991.87 | 0.0694465 | 0.0347233 | − | 0.999397i | \(-0.488945\pi\) | ||||
0.0347233 | + | 0.999397i | \(0.488945\pi\) | |||||||
\(938\) | −10893.0 | −0.379179 | ||||||||
\(939\) | 14857.0 | 0.516337 | ||||||||
\(940\) | 15829.5 | 0.549256 | ||||||||
\(941\) | −7640.33 | −0.264684 | −0.132342 | − | 0.991204i | \(-0.542250\pi\) | ||||
−0.132342 | + | 0.991204i | \(0.542250\pi\) | |||||||
\(942\) | 38276.5 | 1.32390 | ||||||||
\(943\) | −16287.9 | −0.562467 | ||||||||
\(944\) | −12088.7 | −0.416795 | ||||||||
\(945\) | 27986.0 | 0.963371 | ||||||||
\(946\) | −14470.7 | −0.497340 | ||||||||
\(947\) | −6521.15 | −0.223769 | −0.111884 | − | 0.993721i | \(-0.535689\pi\) | ||||
−0.111884 | + | 0.993721i | \(0.535689\pi\) | |||||||
\(948\) | −30572.8 | −1.04742 | ||||||||
\(949\) | −3853.22 | −0.131803 | ||||||||
\(950\) | 15347.6 | 0.524149 | ||||||||
\(951\) | 2883.40 | 0.0983182 | ||||||||
\(952\) | 1909.38 | 0.0650037 | ||||||||
\(953\) | −35757.9 | −1.21544 | −0.607719 | − | 0.794152i | \(-0.707915\pi\) | ||||
−0.607719 | + | 0.794152i | \(0.707915\pi\) | |||||||
\(954\) | −11149.6 | −0.378386 | ||||||||
\(955\) | −25164.1 | −0.852659 | ||||||||
\(956\) | 29057.3 | 0.983034 | ||||||||
\(957\) | −9375.64 | −0.316689 | ||||||||
\(958\) | 41881.3 | 1.41244 | ||||||||
\(959\) | −57997.6 | −1.95291 | ||||||||
\(960\) | −57628.1 | −1.93744 | ||||||||
\(961\) | −1314.75 | −0.0441323 | ||||||||
\(962\) | −2669.59 | −0.0894710 | ||||||||
\(963\) | −23679.3 | −0.792374 | ||||||||
\(964\) | 49411.4 | 1.65086 | ||||||||
\(965\) | −58175.1 | −1.94065 | ||||||||
\(966\) | −36270.0 | −1.20804 | ||||||||
\(967\) | −6342.30 | −0.210915 | −0.105457 | − | 0.994424i | \(-0.533631\pi\) | ||||
−0.105457 | + | 0.994424i | \(0.533631\pi\) | |||||||
\(968\) | −1493.58 | −0.0495924 | ||||||||
\(969\) | 7986.21 | 0.264762 | ||||||||
\(970\) | 15772.5 | 0.522086 | ||||||||
\(971\) | 30351.2 | 1.00311 | 0.501553 | − | 0.865127i | \(-0.332762\pi\) | ||||
0.501553 | + | 0.865127i | \(0.332762\pi\) | |||||||
\(972\) | −33617.5 | −1.10934 | ||||||||
\(973\) | 7651.29 | 0.252096 | ||||||||
\(974\) | 44491.4 | 1.46365 | ||||||||
\(975\) | −6251.73 | −0.205349 | ||||||||
\(976\) | −26788.5 | −0.878566 | ||||||||
\(977\) | 39843.6 | 1.30472 | 0.652359 | − | 0.757910i | \(-0.273780\pi\) | ||||
0.652359 | + | 0.757910i | \(0.273780\pi\) | |||||||
\(978\) | −3392.98 | −0.110936 | ||||||||
\(979\) | 7848.66 | 0.256225 | ||||||||
\(980\) | 45324.1 | 1.47737 | ||||||||
\(981\) | 15761.4 | 0.512969 | ||||||||
\(982\) | 2127.27 | 0.0691282 | ||||||||
\(983\) | 24068.7 | 0.780949 | 0.390475 | − | 0.920614i | \(-0.372311\pi\) | ||||
0.390475 | + | 0.920614i | \(0.372311\pi\) | |||||||
\(984\) | 2448.79 | 0.0793340 | ||||||||
\(985\) | −62478.9 | −2.02106 | ||||||||
\(986\) | 42561.5 | 1.37468 | ||||||||
\(987\) | −19665.8 | −0.634213 | ||||||||
\(988\) | 668.238 | 0.0215177 | ||||||||
\(989\) | 23682.2 | 0.761426 | ||||||||
\(990\) | 10583.1 | 0.339751 | ||||||||
\(991\) | 3235.83 | 0.103723 | 0.0518615 | − | 0.998654i | \(-0.483485\pi\) | ||||
0.0518615 | + | 0.998654i | \(0.483485\pi\) | |||||||
\(992\) | 42736.2 | 1.36782 | ||||||||
\(993\) | −5140.86 | −0.164290 | ||||||||
\(994\) | 48330.4 | 1.54220 | ||||||||
\(995\) | 36734.6 | 1.17042 | ||||||||
\(996\) | 15021.0 | 0.477871 | ||||||||
\(997\) | 19444.5 | 0.617665 | 0.308833 | − | 0.951116i | \(-0.400062\pi\) | ||||
0.308833 | + | 0.951116i | \(0.400062\pi\) | |||||||
\(998\) | −5230.25 | −0.165892 | ||||||||
\(999\) | 8812.68 | 0.279100 |
(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 | 19.4.a.b.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 171.4.a.f.1.3 | 3 | |||
4.3 | odd | 2 | 304.4.a.i.1.1 | 3 | |||
5.2 | odd | 4 | 475.4.b.f.324.2 | 6 | |||
5.3 | odd | 4 | 475.4.b.f.324.5 | 6 | |||
5.4 | even | 2 | 475.4.a.f.1.3 | 3 | |||
7.6 | odd | 2 | 931.4.a.c.1.1 | 3 | |||
8.3 | odd | 2 | 1216.4.a.u.1.3 | 3 | |||
8.5 | even | 2 | 1216.4.a.s.1.1 | 3 | |||
11.10 | odd | 2 | 2299.4.a.h.1.3 | 3 | |||
19.18 | odd | 2 | 361.4.a.i.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
19.4.a.b.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
171.4.a.f.1.3 | 3 | 3.2 | odd | 2 | |||
304.4.a.i.1.1 | 3 | 4.3 | odd | 2 | |||
361.4.a.i.1.3 | 3 | 19.18 | odd | 2 | |||
475.4.a.f.1.3 | 3 | 5.4 | even | 2 | |||
475.4.b.f.324.2 | 6 | 5.2 | odd | 4 | |||
475.4.b.f.324.5 | 6 | 5.3 | odd | 4 | |||
931.4.a.c.1.1 | 3 | 7.6 | odd | 2 | |||
1216.4.a.s.1.1 | 3 | 8.5 | even | 2 | |||
1216.4.a.u.1.3 | 3 | 8.3 | odd | 2 | |||
2299.4.a.h.1.3 | 3 | 11.10 | odd | 2 |