Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [231,4,Mod(1,231)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(231, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("231.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 231 = 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 231.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: | \(13.6294412113\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 30x^{3} + 11x^{2} + 185x + 162 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.59998\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 231.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.59998 | 0.565678 | 0.282839 | − | 0.959167i | \(-0.408724\pi\) | ||||
0.282839 | + | 0.959167i | \(0.408724\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | −5.44007 | −0.680008 | ||||||||
\(5\) | −17.2762 | −1.54523 | −0.772616 | − | 0.634873i | \(-0.781052\pi\) | ||||
−0.772616 | + | 0.634873i | \(0.781052\pi\) | |||||||
\(6\) | −4.79994 | −0.326594 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | −21.5038 | −0.950344 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −27.6416 | −0.874104 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 16.3202 | 0.392603 | ||||||||
\(13\) | 46.1062 | 0.983658 | 0.491829 | − | 0.870692i | \(-0.336328\pi\) | ||||
0.491829 | + | 0.870692i | \(0.336328\pi\) | |||||||
\(14\) | 11.1999 | 0.213806 | ||||||||
\(15\) | 51.8287 | 0.892140 | ||||||||
\(16\) | 9.11483 | 0.142419 | ||||||||
\(17\) | 19.8752 | 0.283555 | 0.141778 | − | 0.989899i | \(-0.454718\pi\) | ||||
0.141778 | + | 0.989899i | \(0.454718\pi\) | |||||||
\(18\) | 14.3998 | 0.188559 | ||||||||
\(19\) | 76.5707 | 0.924553 | 0.462277 | − | 0.886736i | \(-0.347033\pi\) | ||||
0.462277 | + | 0.886736i | \(0.347033\pi\) | |||||||
\(20\) | 93.9838 | 1.05077 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | 17.5998 | 0.170558 | ||||||||
\(23\) | −163.205 | −1.47960 | −0.739798 | − | 0.672829i | \(-0.765079\pi\) | ||||
−0.739798 | + | 0.672829i | \(0.765079\pi\) | |||||||
\(24\) | 64.5115 | 0.548681 | ||||||||
\(25\) | 173.468 | 1.38774 | ||||||||
\(26\) | 73.7690 | 0.556434 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −38.0805 | −0.257019 | ||||||||
\(29\) | 158.858 | 1.01721 | 0.508605 | − | 0.861000i | \(-0.330161\pi\) | ||||
0.508605 | + | 0.861000i | \(0.330161\pi\) | |||||||
\(30\) | 82.9248 | 0.504664 | ||||||||
\(31\) | 170.768 | 0.989380 | 0.494690 | − | 0.869069i | \(-0.335282\pi\) | ||||
0.494690 | + | 0.869069i | \(0.335282\pi\) | |||||||
\(32\) | 186.614 | 1.03091 | ||||||||
\(33\) | −33.0000 | −0.174078 | ||||||||
\(34\) | 31.7999 | 0.160401 | ||||||||
\(35\) | −120.934 | −0.584043 | ||||||||
\(36\) | −48.9606 | −0.226669 | ||||||||
\(37\) | −245.971 | −1.09290 | −0.546452 | − | 0.837490i | \(-0.684022\pi\) | ||||
−0.546452 | + | 0.837490i | \(0.684022\pi\) | |||||||
\(38\) | 122.511 | 0.523000 | ||||||||
\(39\) | −138.319 | −0.567915 | ||||||||
\(40\) | 371.505 | 1.46850 | ||||||||
\(41\) | −3.33673 | −0.0127100 | −0.00635500 | − | 0.999980i | \(-0.502023\pi\) | ||||
−0.00635500 | + | 0.999980i | \(0.502023\pi\) | |||||||
\(42\) | −33.5996 | −0.123441 | ||||||||
\(43\) | −122.798 | −0.435502 | −0.217751 | − | 0.976004i | \(-0.569872\pi\) | ||||
−0.217751 | + | 0.976004i | \(0.569872\pi\) | |||||||
\(44\) | −59.8407 | −0.205030 | ||||||||
\(45\) | −155.486 | −0.515077 | ||||||||
\(46\) | −261.125 | −0.836975 | ||||||||
\(47\) | 390.972 | 1.21338 | 0.606692 | − | 0.794937i | \(-0.292496\pi\) | ||||
0.606692 | + | 0.794937i | \(0.292496\pi\) | |||||||
\(48\) | −27.3445 | −0.0822258 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 277.545 | 0.785016 | ||||||||
\(51\) | −59.6255 | −0.163711 | ||||||||
\(52\) | −250.821 | −0.668896 | ||||||||
\(53\) | −410.957 | −1.06508 | −0.532541 | − | 0.846404i | \(-0.678763\pi\) | ||||
−0.532541 | + | 0.846404i | \(0.678763\pi\) | |||||||
\(54\) | −43.1995 | −0.108865 | ||||||||
\(55\) | −190.038 | −0.465905 | ||||||||
\(56\) | −150.527 | −0.359196 | ||||||||
\(57\) | −229.712 | −0.533791 | ||||||||
\(58\) | 254.169 | 0.575414 | ||||||||
\(59\) | 408.774 | 0.901998 | 0.450999 | − | 0.892524i | \(-0.351068\pi\) | ||||
0.450999 | + | 0.892524i | \(0.351068\pi\) | |||||||
\(60\) | −281.951 | −0.606663 | ||||||||
\(61\) | −21.9747 | −0.0461241 | −0.0230621 | − | 0.999734i | \(-0.507342\pi\) | ||||
−0.0230621 | + | 0.999734i | \(0.507342\pi\) | |||||||
\(62\) | 273.225 | 0.559671 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 225.660 | 0.440743 | ||||||||
\(65\) | −796.541 | −1.51998 | ||||||||
\(66\) | −52.7993 | −0.0984719 | ||||||||
\(67\) | 618.424 | 1.12765 | 0.563824 | − | 0.825895i | \(-0.309329\pi\) | ||||
0.563824 | + | 0.825895i | \(0.309329\pi\) | |||||||
\(68\) | −108.122 | −0.192820 | ||||||||
\(69\) | 489.616 | 0.854245 | ||||||||
\(70\) | −193.491 | −0.330380 | ||||||||
\(71\) | 929.041 | 1.55291 | 0.776457 | − | 0.630171i | \(-0.217015\pi\) | ||||
0.776457 | + | 0.630171i | \(0.217015\pi\) | |||||||
\(72\) | −193.534 | −0.316781 | ||||||||
\(73\) | 868.090 | 1.39181 | 0.695906 | − | 0.718133i | \(-0.255003\pi\) | ||||
0.695906 | + | 0.718133i | \(0.255003\pi\) | |||||||
\(74\) | −393.549 | −0.618232 | ||||||||
\(75\) | −520.404 | −0.801214 | ||||||||
\(76\) | −416.549 | −0.628704 | ||||||||
\(77\) | 77.0000 | 0.113961 | ||||||||
\(78\) | −221.307 | −0.321257 | ||||||||
\(79\) | 152.702 | 0.217472 | 0.108736 | − | 0.994071i | \(-0.465320\pi\) | ||||
0.108736 | + | 0.994071i | \(0.465320\pi\) | |||||||
\(80\) | −157.470 | −0.220071 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −5.33871 | −0.00718977 | ||||||||
\(83\) | −100.924 | −0.133469 | −0.0667343 | − | 0.997771i | \(-0.521258\pi\) | ||||
−0.0667343 | + | 0.997771i | \(0.521258\pi\) | |||||||
\(84\) | 114.241 | 0.148390 | ||||||||
\(85\) | −343.368 | −0.438159 | ||||||||
\(86\) | −196.475 | −0.246354 | ||||||||
\(87\) | −476.573 | −0.587287 | ||||||||
\(88\) | −236.542 | −0.286540 | ||||||||
\(89\) | −1063.23 | −1.26631 | −0.633156 | − | 0.774024i | \(-0.718241\pi\) | ||||
−0.633156 | + | 0.774024i | \(0.718241\pi\) | |||||||
\(90\) | −248.774 | −0.291368 | ||||||||
\(91\) | 322.743 | 0.371788 | ||||||||
\(92\) | 887.848 | 1.00614 | ||||||||
\(93\) | −512.303 | −0.571219 | ||||||||
\(94\) | 625.547 | 0.686385 | ||||||||
\(95\) | −1322.85 | −1.42865 | ||||||||
\(96\) | −559.843 | −0.595195 | ||||||||
\(97\) | 1415.50 | 1.48167 | 0.740836 | − | 0.671686i | \(-0.234430\pi\) | ||||
0.740836 | + | 0.671686i | \(0.234430\pi\) | |||||||
\(98\) | 78.3990 | 0.0808112 | ||||||||
\(99\) | 99.0000 | 0.100504 | ||||||||
\(100\) | −943.677 | −0.943677 | ||||||||
\(101\) | −774.140 | −0.762671 | −0.381336 | − | 0.924437i | \(-0.624536\pi\) | ||||
−0.381336 | + | 0.924437i | \(0.624536\pi\) | |||||||
\(102\) | −95.3997 | −0.0926076 | ||||||||
\(103\) | 759.159 | 0.726235 | 0.363118 | − | 0.931743i | \(-0.381712\pi\) | ||||
0.363118 | + | 0.931743i | \(0.381712\pi\) | |||||||
\(104\) | −991.460 | −0.934814 | ||||||||
\(105\) | 362.801 | 0.337197 | ||||||||
\(106\) | −657.523 | −0.602493 | ||||||||
\(107\) | −1181.22 | −1.06722 | −0.533612 | − | 0.845729i | \(-0.679166\pi\) | ||||
−0.533612 | + | 0.845729i | \(0.679166\pi\) | |||||||
\(108\) | 146.882 | 0.130868 | ||||||||
\(109\) | 738.091 | 0.648590 | 0.324295 | − | 0.945956i | \(-0.394873\pi\) | ||||
0.324295 | + | 0.945956i | \(0.394873\pi\) | |||||||
\(110\) | −304.058 | −0.263552 | ||||||||
\(111\) | 737.914 | 0.630989 | ||||||||
\(112\) | 63.8038 | 0.0538294 | ||||||||
\(113\) | 620.181 | 0.516298 | 0.258149 | − | 0.966105i | \(-0.416887\pi\) | ||||
0.258149 | + | 0.966105i | \(0.416887\pi\) | |||||||
\(114\) | −367.534 | −0.301954 | ||||||||
\(115\) | 2819.57 | 2.28632 | ||||||||
\(116\) | −864.195 | −0.691711 | ||||||||
\(117\) | 414.956 | 0.327886 | ||||||||
\(118\) | 654.031 | 0.510241 | ||||||||
\(119\) | 139.126 | 0.107174 | ||||||||
\(120\) | −1114.51 | −0.847840 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −35.1591 | −0.0260914 | ||||||||
\(123\) | 10.0102 | 0.00733813 | ||||||||
\(124\) | −928.988 | −0.672787 | ||||||||
\(125\) | −837.342 | −0.599153 | ||||||||
\(126\) | 100.799 | 0.0712688 | ||||||||
\(127\) | −2291.79 | −1.60129 | −0.800645 | − | 0.599139i | \(-0.795510\pi\) | ||||
−0.800645 | + | 0.599139i | \(0.795510\pi\) | |||||||
\(128\) | −1131.86 | −0.781589 | ||||||||
\(129\) | 368.395 | 0.251437 | ||||||||
\(130\) | −1274.45 | −0.859820 | ||||||||
\(131\) | −1491.77 | −0.994938 | −0.497469 | − | 0.867482i | \(-0.665737\pi\) | ||||
−0.497469 | + | 0.867482i | \(0.665737\pi\) | |||||||
\(132\) | 179.522 | 0.118374 | ||||||||
\(133\) | 535.995 | 0.349448 | ||||||||
\(134\) | 989.465 | 0.637886 | ||||||||
\(135\) | 466.458 | 0.297380 | ||||||||
\(136\) | −427.393 | −0.269475 | ||||||||
\(137\) | 2590.79 | 1.61566 | 0.807831 | − | 0.589414i | \(-0.200641\pi\) | ||||
0.807831 | + | 0.589414i | \(0.200641\pi\) | |||||||
\(138\) | 783.376 | 0.483228 | ||||||||
\(139\) | 2674.14 | 1.63178 | 0.815890 | − | 0.578207i | \(-0.196248\pi\) | ||||
0.815890 | + | 0.578207i | \(0.196248\pi\) | |||||||
\(140\) | 657.886 | 0.397154 | ||||||||
\(141\) | −1172.92 | −0.700548 | ||||||||
\(142\) | 1486.45 | 0.878449 | ||||||||
\(143\) | 507.168 | 0.296584 | ||||||||
\(144\) | 82.0335 | 0.0474731 | ||||||||
\(145\) | −2744.46 | −1.57183 | ||||||||
\(146\) | 1388.93 | 0.787318 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | 1338.10 | 0.743184 | ||||||||
\(149\) | 822.355 | 0.452147 | 0.226074 | − | 0.974110i | \(-0.427411\pi\) | ||||
0.226074 | + | 0.974110i | \(0.427411\pi\) | |||||||
\(150\) | −832.635 | −0.453229 | ||||||||
\(151\) | −138.803 | −0.0748053 | −0.0374027 | − | 0.999300i | \(-0.511908\pi\) | ||||
−0.0374027 | + | 0.999300i | \(0.511908\pi\) | |||||||
\(152\) | −1646.56 | −0.878644 | ||||||||
\(153\) | 178.877 | 0.0945184 | ||||||||
\(154\) | 123.198 | 0.0644650 | ||||||||
\(155\) | −2950.22 | −1.52882 | ||||||||
\(156\) | 752.462 | 0.386187 | ||||||||
\(157\) | −634.746 | −0.322664 | −0.161332 | − | 0.986900i | \(-0.551579\pi\) | ||||
−0.161332 | + | 0.986900i | \(0.551579\pi\) | |||||||
\(158\) | 244.320 | 0.123019 | ||||||||
\(159\) | 1232.87 | 0.614925 | ||||||||
\(160\) | −3223.99 | −1.59299 | ||||||||
\(161\) | −1142.44 | −0.559235 | ||||||||
\(162\) | 129.598 | 0.0628531 | ||||||||
\(163\) | −608.367 | −0.292337 | −0.146169 | − | 0.989260i | \(-0.546694\pi\) | ||||
−0.146169 | + | 0.989260i | \(0.546694\pi\) | |||||||
\(164\) | 18.1520 | 0.00864291 | ||||||||
\(165\) | 570.115 | 0.268990 | ||||||||
\(166\) | −161.477 | −0.0755003 | ||||||||
\(167\) | −1545.50 | −0.716135 | −0.358067 | − | 0.933696i | \(-0.616564\pi\) | ||||
−0.358067 | + | 0.933696i | \(0.616564\pi\) | |||||||
\(168\) | 451.580 | 0.207382 | ||||||||
\(169\) | −71.2185 | −0.0324163 | ||||||||
\(170\) | −549.382 | −0.247857 | ||||||||
\(171\) | 689.136 | 0.308184 | ||||||||
\(172\) | 668.031 | 0.296145 | ||||||||
\(173\) | 126.598 | 0.0556362 | 0.0278181 | − | 0.999613i | \(-0.491144\pi\) | ||||
0.0278181 | + | 0.999613i | \(0.491144\pi\) | |||||||
\(174\) | −762.506 | −0.332215 | ||||||||
\(175\) | 1214.28 | 0.524518 | ||||||||
\(176\) | 100.263 | 0.0429410 | ||||||||
\(177\) | −1226.32 | −0.520769 | ||||||||
\(178\) | −1701.14 | −0.716325 | ||||||||
\(179\) | −144.263 | −0.0602387 | −0.0301194 | − | 0.999546i | \(-0.509589\pi\) | ||||
−0.0301194 | + | 0.999546i | \(0.509589\pi\) | |||||||
\(180\) | 845.854 | 0.350257 | ||||||||
\(181\) | 2925.01 | 1.20118 | 0.600591 | − | 0.799556i | \(-0.294932\pi\) | ||||
0.600591 | + | 0.799556i | \(0.294932\pi\) | |||||||
\(182\) | 516.383 | 0.210312 | ||||||||
\(183\) | 65.9241 | 0.0266298 | ||||||||
\(184\) | 3509.54 | 1.40612 | ||||||||
\(185\) | 4249.46 | 1.68879 | ||||||||
\(186\) | −819.675 | −0.323126 | ||||||||
\(187\) | 218.627 | 0.0854951 | ||||||||
\(188\) | −2126.91 | −0.825111 | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | −2116.54 | −0.808156 | ||||||||
\(191\) | −3771.70 | −1.42885 | −0.714426 | − | 0.699711i | \(-0.753312\pi\) | ||||
−0.714426 | + | 0.699711i | \(0.753312\pi\) | |||||||
\(192\) | −676.981 | −0.254463 | ||||||||
\(193\) | −1282.92 | −0.478480 | −0.239240 | − | 0.970960i | \(-0.576898\pi\) | ||||
−0.239240 | + | 0.970960i | \(0.576898\pi\) | |||||||
\(194\) | 2264.77 | 0.838149 | ||||||||
\(195\) | 2389.62 | 0.877561 | ||||||||
\(196\) | −266.563 | −0.0971440 | ||||||||
\(197\) | 3052.31 | 1.10390 | 0.551949 | − | 0.833878i | \(-0.313884\pi\) | ||||
0.551949 | + | 0.833878i | \(0.313884\pi\) | |||||||
\(198\) | 158.398 | 0.0568528 | ||||||||
\(199\) | 5040.28 | 1.79546 | 0.897729 | − | 0.440547i | \(-0.145216\pi\) | ||||
0.897729 | + | 0.440547i | \(0.145216\pi\) | |||||||
\(200\) | −3730.22 | −1.31883 | ||||||||
\(201\) | −1855.27 | −0.651048 | ||||||||
\(202\) | −1238.61 | −0.431426 | ||||||||
\(203\) | 1112.00 | 0.384469 | ||||||||
\(204\) | 324.367 | 0.111325 | ||||||||
\(205\) | 57.6462 | 0.0196399 | ||||||||
\(206\) | 1214.64 | 0.410815 | ||||||||
\(207\) | −1468.85 | −0.493198 | ||||||||
\(208\) | 420.250 | 0.140092 | ||||||||
\(209\) | 842.277 | 0.278763 | ||||||||
\(210\) | 580.474 | 0.190745 | ||||||||
\(211\) | 3556.28 | 1.16031 | 0.580153 | − | 0.814508i | \(-0.302993\pi\) | ||||
0.580153 | + | 0.814508i | \(0.302993\pi\) | |||||||
\(212\) | 2235.63 | 0.724264 | ||||||||
\(213\) | −2787.12 | −0.896575 | ||||||||
\(214\) | −1889.93 | −0.603706 | ||||||||
\(215\) | 2121.49 | 0.672952 | ||||||||
\(216\) | 580.603 | 0.182894 | ||||||||
\(217\) | 1195.37 | 0.373951 | ||||||||
\(218\) | 1180.93 | 0.366893 | ||||||||
\(219\) | −2604.27 | −0.803563 | ||||||||
\(220\) | 1033.82 | 0.316819 | ||||||||
\(221\) | 916.369 | 0.278922 | ||||||||
\(222\) | 1180.65 | 0.356937 | ||||||||
\(223\) | 1767.85 | 0.530870 | 0.265435 | − | 0.964129i | \(-0.414484\pi\) | ||||
0.265435 | + | 0.964129i | \(0.414484\pi\) | |||||||
\(224\) | 1306.30 | 0.389646 | ||||||||
\(225\) | 1561.21 | 0.462581 | ||||||||
\(226\) | 992.277 | 0.292059 | ||||||||
\(227\) | 4836.74 | 1.41421 | 0.707105 | − | 0.707109i | \(-0.250001\pi\) | ||||
0.707105 | + | 0.707109i | \(0.250001\pi\) | |||||||
\(228\) | 1249.65 | 0.362982 | ||||||||
\(229\) | 4941.30 | 1.42590 | 0.712949 | − | 0.701216i | \(-0.247359\pi\) | ||||
0.712949 | + | 0.701216i | \(0.247359\pi\) | |||||||
\(230\) | 4511.26 | 1.29332 | ||||||||
\(231\) | −231.000 | −0.0657952 | ||||||||
\(232\) | −3416.04 | −0.966700 | ||||||||
\(233\) | 4822.14 | 1.35583 | 0.677916 | − | 0.735140i | \(-0.262883\pi\) | ||||
0.677916 | + | 0.735140i | \(0.262883\pi\) | |||||||
\(234\) | 663.921 | 0.185478 | ||||||||
\(235\) | −6754.51 | −1.87496 | ||||||||
\(236\) | −2223.76 | −0.613366 | ||||||||
\(237\) | −458.106 | −0.125558 | ||||||||
\(238\) | 222.599 | 0.0606259 | ||||||||
\(239\) | 4821.80 | 1.30501 | 0.652503 | − | 0.757786i | \(-0.273719\pi\) | ||||
0.652503 | + | 0.757786i | \(0.273719\pi\) | |||||||
\(240\) | 472.409 | 0.127058 | ||||||||
\(241\) | 1544.41 | 0.412798 | 0.206399 | − | 0.978468i | \(-0.433825\pi\) | ||||
0.206399 | + | 0.978468i | \(0.433825\pi\) | |||||||
\(242\) | 193.598 | 0.0514253 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 119.544 | 0.0313648 | ||||||||
\(245\) | −846.535 | −0.220747 | ||||||||
\(246\) | 16.0161 | 0.00415102 | ||||||||
\(247\) | 3530.38 | 0.909445 | ||||||||
\(248\) | −3672.16 | −0.940252 | ||||||||
\(249\) | 302.773 | 0.0770581 | ||||||||
\(250\) | −1339.73 | −0.338928 | ||||||||
\(251\) | −7568.20 | −1.90319 | −0.951595 | − | 0.307354i | \(-0.900556\pi\) | ||||
−0.951595 | + | 0.307354i | \(0.900556\pi\) | |||||||
\(252\) | −342.724 | −0.0856730 | ||||||||
\(253\) | −1795.26 | −0.446115 | ||||||||
\(254\) | −3666.82 | −0.905815 | ||||||||
\(255\) | 1030.10 | 0.252971 | ||||||||
\(256\) | −3616.24 | −0.882871 | ||||||||
\(257\) | 1415.19 | 0.343490 | 0.171745 | − | 0.985141i | \(-0.445059\pi\) | ||||
0.171745 | + | 0.985141i | \(0.445059\pi\) | |||||||
\(258\) | 589.425 | 0.142233 | ||||||||
\(259\) | −1721.80 | −0.413079 | ||||||||
\(260\) | 4333.23 | 1.03360 | ||||||||
\(261\) | 1429.72 | 0.339070 | ||||||||
\(262\) | −2386.81 | −0.562815 | ||||||||
\(263\) | −7875.57 | −1.84650 | −0.923248 | − | 0.384204i | \(-0.874476\pi\) | ||||
−0.923248 | + | 0.384204i | \(0.874476\pi\) | |||||||
\(264\) | 709.626 | 0.165434 | ||||||||
\(265\) | 7099.79 | 1.64580 | ||||||||
\(266\) | 857.580 | 0.197675 | ||||||||
\(267\) | 3189.68 | 0.731105 | ||||||||
\(268\) | −3364.27 | −0.766810 | ||||||||
\(269\) | −2062.01 | −0.467371 | −0.233685 | − | 0.972312i | \(-0.575079\pi\) | ||||
−0.233685 | + | 0.972312i | \(0.575079\pi\) | |||||||
\(270\) | 746.323 | 0.168221 | ||||||||
\(271\) | −8247.07 | −1.84861 | −0.924306 | − | 0.381651i | \(-0.875355\pi\) | ||||
−0.924306 | + | 0.381651i | \(0.875355\pi\) | |||||||
\(272\) | 181.159 | 0.0403837 | ||||||||
\(273\) | −968.230 | −0.214652 | ||||||||
\(274\) | 4145.21 | 0.913945 | ||||||||
\(275\) | 1908.15 | 0.418420 | ||||||||
\(276\) | −2663.55 | −0.580893 | ||||||||
\(277\) | −6637.33 | −1.43971 | −0.719853 | − | 0.694126i | \(-0.755791\pi\) | ||||
−0.719853 | + | 0.694126i | \(0.755791\pi\) | |||||||
\(278\) | 4278.57 | 0.923062 | ||||||||
\(279\) | 1536.91 | 0.329793 | ||||||||
\(280\) | 2600.53 | 0.555042 | ||||||||
\(281\) | 5600.82 | 1.18903 | 0.594515 | − | 0.804085i | \(-0.297344\pi\) | ||||
0.594515 | + | 0.804085i | \(0.297344\pi\) | |||||||
\(282\) | −1876.64 | −0.396285 | ||||||||
\(283\) | −934.745 | −0.196342 | −0.0981711 | − | 0.995170i | \(-0.531299\pi\) | ||||
−0.0981711 | + | 0.995170i | \(0.531299\pi\) | |||||||
\(284\) | −5054.04 | −1.05599 | ||||||||
\(285\) | 3968.56 | 0.824831 | ||||||||
\(286\) | 811.459 | 0.167771 | ||||||||
\(287\) | −23.3571 | −0.00480393 | ||||||||
\(288\) | 1679.53 | 0.343636 | ||||||||
\(289\) | −4517.98 | −0.919596 | ||||||||
\(290\) | −4391.08 | −0.889148 | ||||||||
\(291\) | −4246.50 | −0.855444 | ||||||||
\(292\) | −4722.47 | −0.946444 | ||||||||
\(293\) | 9169.86 | 1.82836 | 0.914179 | − | 0.405311i | \(-0.132837\pi\) | ||||
0.914179 | + | 0.405311i | \(0.132837\pi\) | |||||||
\(294\) | −235.197 | −0.0466564 | ||||||||
\(295\) | −7062.08 | −1.39380 | ||||||||
\(296\) | 5289.33 | 1.03864 | ||||||||
\(297\) | −297.000 | −0.0580259 | ||||||||
\(298\) | 1315.75 | 0.255770 | ||||||||
\(299\) | −7524.78 | −1.45542 | ||||||||
\(300\) | 2831.03 | 0.544832 | ||||||||
\(301\) | −859.589 | −0.164604 | ||||||||
\(302\) | −222.081 | −0.0423157 | ||||||||
\(303\) | 2322.42 | 0.440328 | ||||||||
\(304\) | 697.929 | 0.131674 | ||||||||
\(305\) | 379.640 | 0.0712725 | ||||||||
\(306\) | 286.199 | 0.0534670 | ||||||||
\(307\) | −6193.71 | −1.15144 | −0.575722 | − | 0.817645i | \(-0.695279\pi\) | ||||
−0.575722 | + | 0.817645i | \(0.695279\pi\) | |||||||
\(308\) | −418.885 | −0.0774941 | ||||||||
\(309\) | −2277.48 | −0.419292 | ||||||||
\(310\) | −4720.29 | −0.864822 | ||||||||
\(311\) | −3373.58 | −0.615106 | −0.307553 | − | 0.951531i | \(-0.599510\pi\) | ||||
−0.307553 | + | 0.951531i | \(0.599510\pi\) | |||||||
\(312\) | 2974.38 | 0.539715 | ||||||||
\(313\) | 7175.09 | 1.29572 | 0.647860 | − | 0.761760i | \(-0.275664\pi\) | ||||
0.647860 | + | 0.761760i | \(0.275664\pi\) | |||||||
\(314\) | −1015.58 | −0.182524 | ||||||||
\(315\) | −1088.40 | −0.194681 | ||||||||
\(316\) | −830.709 | −0.147883 | ||||||||
\(317\) | −6302.06 | −1.11659 | −0.558295 | − | 0.829643i | \(-0.688544\pi\) | ||||
−0.558295 | + | 0.829643i | \(0.688544\pi\) | |||||||
\(318\) | 1972.57 | 0.347850 | ||||||||
\(319\) | 1747.43 | 0.306700 | ||||||||
\(320\) | −3898.56 | −0.681050 | ||||||||
\(321\) | 3543.66 | 0.616162 | ||||||||
\(322\) | −1827.88 | −0.316347 | ||||||||
\(323\) | 1521.86 | 0.262162 | ||||||||
\(324\) | −440.645 | −0.0755565 | ||||||||
\(325\) | 7997.94 | 1.36506 | ||||||||
\(326\) | −973.375 | −0.165369 | ||||||||
\(327\) | −2214.27 | −0.374463 | ||||||||
\(328\) | 71.7526 | 0.0120789 | ||||||||
\(329\) | 2736.80 | 0.458616 | ||||||||
\(330\) | 912.173 | 0.152162 | ||||||||
\(331\) | −7404.03 | −1.22949 | −0.614747 | − | 0.788725i | \(-0.710742\pi\) | ||||
−0.614747 | + | 0.788725i | \(0.710742\pi\) | |||||||
\(332\) | 549.035 | 0.0907597 | ||||||||
\(333\) | −2213.74 | −0.364301 | ||||||||
\(334\) | −2472.77 | −0.405102 | ||||||||
\(335\) | −10684.0 | −1.74248 | ||||||||
\(336\) | −191.411 | −0.0310784 | ||||||||
\(337\) | 7008.68 | 1.13290 | 0.566450 | − | 0.824096i | \(-0.308316\pi\) | ||||
0.566450 | + | 0.824096i | \(0.308316\pi\) | |||||||
\(338\) | −113.948 | −0.0183372 | ||||||||
\(339\) | −1860.54 | −0.298085 | ||||||||
\(340\) | 1867.94 | 0.297952 | ||||||||
\(341\) | 1878.45 | 0.298309 | ||||||||
\(342\) | 1102.60 | 0.174333 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 2640.64 | 0.413877 | ||||||||
\(345\) | −8458.72 | −1.32001 | ||||||||
\(346\) | 202.554 | 0.0314722 | ||||||||
\(347\) | −10025.8 | −1.55104 | −0.775521 | − | 0.631322i | \(-0.782513\pi\) | ||||
−0.775521 | + | 0.631322i | \(0.782513\pi\) | |||||||
\(348\) | 2592.59 | 0.399360 | ||||||||
\(349\) | −10746.5 | −1.64827 | −0.824136 | − | 0.566391i | \(-0.808339\pi\) | ||||
−0.824136 | + | 0.566391i | \(0.808339\pi\) | |||||||
\(350\) | 1942.82 | 0.296708 | ||||||||
\(351\) | −1244.87 | −0.189305 | ||||||||
\(352\) | 2052.76 | 0.310830 | ||||||||
\(353\) | −606.136 | −0.0913919 | −0.0456960 | − | 0.998955i | \(-0.514551\pi\) | ||||
−0.0456960 | + | 0.998955i | \(0.514551\pi\) | |||||||
\(354\) | −1962.09 | −0.294588 | ||||||||
\(355\) | −16050.3 | −2.39961 | ||||||||
\(356\) | 5784.02 | 0.861102 | ||||||||
\(357\) | −417.379 | −0.0618768 | ||||||||
\(358\) | −230.818 | −0.0340757 | ||||||||
\(359\) | 8527.32 | 1.25363 | 0.626817 | − | 0.779166i | \(-0.284357\pi\) | ||||
0.626817 | + | 0.779166i | \(0.284357\pi\) | |||||||
\(360\) | 3343.54 | 0.489501 | ||||||||
\(361\) | −995.934 | −0.145201 | ||||||||
\(362\) | 4679.95 | 0.679483 | ||||||||
\(363\) | −363.000 | −0.0524864 | ||||||||
\(364\) | −1755.75 | −0.252819 | ||||||||
\(365\) | −14997.3 | −2.15067 | ||||||||
\(366\) | 105.477 | 0.0150639 | ||||||||
\(367\) | 5504.16 | 0.782874 | 0.391437 | − | 0.920205i | \(-0.371978\pi\) | ||||
0.391437 | + | 0.920205i | \(0.371978\pi\) | |||||||
\(368\) | −1487.59 | −0.210723 | ||||||||
\(369\) | −30.0306 | −0.00423667 | ||||||||
\(370\) | 6799.05 | 0.955312 | ||||||||
\(371\) | −2876.70 | −0.402563 | ||||||||
\(372\) | 2786.96 | 0.388434 | ||||||||
\(373\) | −7091.36 | −0.984387 | −0.492194 | − | 0.870486i | \(-0.663805\pi\) | ||||
−0.492194 | + | 0.870486i | \(0.663805\pi\) | |||||||
\(374\) | 349.799 | 0.0483627 | ||||||||
\(375\) | 2512.03 | 0.345921 | ||||||||
\(376\) | −8407.39 | −1.15313 | ||||||||
\(377\) | 7324.32 | 1.00059 | ||||||||
\(378\) | −302.396 | −0.0411470 | ||||||||
\(379\) | −77.3370 | −0.0104816 | −0.00524081 | − | 0.999986i | \(-0.501668\pi\) | ||||
−0.00524081 | + | 0.999986i | \(0.501668\pi\) | |||||||
\(380\) | 7196.40 | 0.971493 | ||||||||
\(381\) | 6875.38 | 0.924505 | ||||||||
\(382\) | −6034.65 | −0.808271 | ||||||||
\(383\) | 4843.75 | 0.646224 | 0.323112 | − | 0.946361i | \(-0.395271\pi\) | ||||
0.323112 | + | 0.946361i | \(0.395271\pi\) | |||||||
\(384\) | 3395.59 | 0.451251 | ||||||||
\(385\) | −1330.27 | −0.176096 | ||||||||
\(386\) | −2052.65 | −0.270666 | ||||||||
\(387\) | −1105.19 | −0.145167 | ||||||||
\(388\) | −7700.41 | −1.00755 | ||||||||
\(389\) | 9882.00 | 1.28801 | 0.644007 | − | 0.765020i | \(-0.277271\pi\) | ||||
0.644007 | + | 0.765020i | \(0.277271\pi\) | |||||||
\(390\) | 3823.35 | 0.496417 | ||||||||
\(391\) | −3243.74 | −0.419547 | ||||||||
\(392\) | −1053.69 | −0.135763 | ||||||||
\(393\) | 4475.32 | 0.574428 | ||||||||
\(394\) | 4883.63 | 0.624451 | ||||||||
\(395\) | −2638.11 | −0.336045 | ||||||||
\(396\) | −538.566 | −0.0683434 | ||||||||
\(397\) | −10135.5 | −1.28133 | −0.640663 | − | 0.767823i | \(-0.721340\pi\) | ||||
−0.640663 | + | 0.767823i | \(0.721340\pi\) | |||||||
\(398\) | 8064.35 | 1.01565 | ||||||||
\(399\) | −1607.98 | −0.201754 | ||||||||
\(400\) | 1581.13 | 0.197641 | ||||||||
\(401\) | 9220.96 | 1.14831 | 0.574155 | − | 0.818746i | \(-0.305331\pi\) | ||||
0.574155 | + | 0.818746i | \(0.305331\pi\) | |||||||
\(402\) | −2968.40 | −0.368284 | ||||||||
\(403\) | 7873.45 | 0.973212 | ||||||||
\(404\) | 4211.37 | 0.518623 | ||||||||
\(405\) | −1399.37 | −0.171692 | ||||||||
\(406\) | 1779.18 | 0.217486 | ||||||||
\(407\) | −2705.69 | −0.329523 | ||||||||
\(408\) | 1282.18 | 0.155582 | ||||||||
\(409\) | −5710.89 | −0.690429 | −0.345214 | − | 0.938524i | \(-0.612194\pi\) | ||||
−0.345214 | + | 0.938524i | \(0.612194\pi\) | |||||||
\(410\) | 92.2327 | 0.0111099 | ||||||||
\(411\) | −7772.36 | −0.932803 | ||||||||
\(412\) | −4129.88 | −0.493846 | ||||||||
\(413\) | 2861.42 | 0.340923 | ||||||||
\(414\) | −2350.13 | −0.278992 | ||||||||
\(415\) | 1743.59 | 0.206240 | ||||||||
\(416\) | 8604.07 | 1.01406 | ||||||||
\(417\) | −8022.41 | −0.942108 | ||||||||
\(418\) | 1347.63 | 0.157690 | ||||||||
\(419\) | 4520.73 | 0.527093 | 0.263547 | − | 0.964647i | \(-0.415108\pi\) | ||||
0.263547 | + | 0.964647i | \(0.415108\pi\) | |||||||
\(420\) | −1973.66 | −0.229297 | ||||||||
\(421\) | 3798.26 | 0.439705 | 0.219853 | − | 0.975533i | \(-0.429442\pi\) | ||||
0.219853 | + | 0.975533i | \(0.429442\pi\) | |||||||
\(422\) | 5689.98 | 0.656359 | ||||||||
\(423\) | 3518.75 | 0.404462 | ||||||||
\(424\) | 8837.15 | 1.01219 | ||||||||
\(425\) | 3447.71 | 0.393502 | ||||||||
\(426\) | −4459.34 | −0.507173 | ||||||||
\(427\) | −153.823 | −0.0174333 | ||||||||
\(428\) | 6425.92 | 0.725721 | ||||||||
\(429\) | −1521.50 | −0.171233 | ||||||||
\(430\) | 3394.35 | 0.380674 | ||||||||
\(431\) | −3468.51 | −0.387638 | −0.193819 | − | 0.981037i | \(-0.562088\pi\) | ||||
−0.193819 | + | 0.981037i | \(0.562088\pi\) | |||||||
\(432\) | −246.100 | −0.0274086 | ||||||||
\(433\) | −9859.98 | −1.09432 | −0.547160 | − | 0.837028i | \(-0.684291\pi\) | ||||
−0.547160 | + | 0.837028i | \(0.684291\pi\) | |||||||
\(434\) | 1912.57 | 0.211536 | ||||||||
\(435\) | 8233.37 | 0.907494 | ||||||||
\(436\) | −4015.26 | −0.441046 | ||||||||
\(437\) | −12496.8 | −1.36796 | ||||||||
\(438\) | −4166.78 | −0.454558 | ||||||||
\(439\) | 8464.33 | 0.920228 | 0.460114 | − | 0.887860i | \(-0.347808\pi\) | ||||
0.460114 | + | 0.887860i | \(0.347808\pi\) | |||||||
\(440\) | 4086.55 | 0.442770 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 1466.17 | 0.157780 | ||||||||
\(443\) | −7825.41 | −0.839270 | −0.419635 | − | 0.907693i | \(-0.637842\pi\) | ||||
−0.419635 | + | 0.907693i | \(0.637842\pi\) | |||||||
\(444\) | −4014.30 | −0.429077 | ||||||||
\(445\) | 18368.5 | 1.95675 | ||||||||
\(446\) | 2828.52 | 0.300302 | ||||||||
\(447\) | −2467.06 | −0.261047 | ||||||||
\(448\) | 1579.62 | 0.166585 | ||||||||
\(449\) | 1050.94 | 0.110461 | 0.0552303 | − | 0.998474i | \(-0.482411\pi\) | ||||
0.0552303 | + | 0.998474i | \(0.482411\pi\) | |||||||
\(450\) | 2497.91 | 0.261672 | ||||||||
\(451\) | −36.7041 | −0.00383221 | ||||||||
\(452\) | −3373.83 | −0.351087 | ||||||||
\(453\) | 416.408 | 0.0431889 | ||||||||
\(454\) | 7738.68 | 0.799988 | ||||||||
\(455\) | −5575.79 | −0.574499 | ||||||||
\(456\) | 4939.69 | 0.507285 | ||||||||
\(457\) | 14397.2 | 1.47369 | 0.736843 | − | 0.676064i | \(-0.236316\pi\) | ||||
0.736843 | + | 0.676064i | \(0.236316\pi\) | |||||||
\(458\) | 7905.98 | 0.806599 | ||||||||
\(459\) | −536.630 | −0.0545702 | ||||||||
\(460\) | −15338.7 | −1.55472 | ||||||||
\(461\) | −5755.83 | −0.581509 | −0.290755 | − | 0.956798i | \(-0.593906\pi\) | ||||
−0.290755 | + | 0.956798i | \(0.593906\pi\) | |||||||
\(462\) | −369.595 | −0.0372189 | ||||||||
\(463\) | −10056.0 | −1.00938 | −0.504689 | − | 0.863302i | \(-0.668393\pi\) | ||||
−0.504689 | + | 0.863302i | \(0.668393\pi\) | |||||||
\(464\) | 1447.96 | 0.144870 | ||||||||
\(465\) | 8850.67 | 0.882666 | ||||||||
\(466\) | 7715.32 | 0.766964 | ||||||||
\(467\) | 2607.32 | 0.258356 | 0.129178 | − | 0.991621i | \(-0.458766\pi\) | ||||
0.129178 | + | 0.991621i | \(0.458766\pi\) | |||||||
\(468\) | −2257.39 | −0.222965 | ||||||||
\(469\) | 4328.97 | 0.426211 | ||||||||
\(470\) | −10807.1 | −1.06062 | ||||||||
\(471\) | 1904.24 | 0.186290 | ||||||||
\(472\) | −8790.21 | −0.857208 | ||||||||
\(473\) | −1350.78 | −0.131309 | ||||||||
\(474\) | −732.960 | −0.0710253 | ||||||||
\(475\) | 13282.5 | 1.28304 | ||||||||
\(476\) | −756.856 | −0.0728791 | ||||||||
\(477\) | −3698.61 | −0.355027 | ||||||||
\(478\) | 7714.79 | 0.738214 | ||||||||
\(479\) | −5944.97 | −0.567083 | −0.283541 | − | 0.958960i | \(-0.591509\pi\) | ||||
−0.283541 | + | 0.958960i | \(0.591509\pi\) | |||||||
\(480\) | 9671.96 | 0.919714 | ||||||||
\(481\) | −11340.8 | −1.07504 | ||||||||
\(482\) | 2471.03 | 0.233511 | ||||||||
\(483\) | 3427.32 | 0.322874 | ||||||||
\(484\) | −658.248 | −0.0618189 | ||||||||
\(485\) | −24454.5 | −2.28953 | ||||||||
\(486\) | −388.795 | −0.0362883 | ||||||||
\(487\) | 15895.1 | 1.47901 | 0.739504 | − | 0.673152i | \(-0.235060\pi\) | ||||
0.739504 | + | 0.673152i | \(0.235060\pi\) | |||||||
\(488\) | 472.540 | 0.0438338 | ||||||||
\(489\) | 1825.10 | 0.168781 | ||||||||
\(490\) | −1354.44 | −0.124872 | ||||||||
\(491\) | 3655.59 | 0.335997 | 0.167999 | − | 0.985787i | \(-0.446270\pi\) | ||||
0.167999 | + | 0.985787i | \(0.446270\pi\) | |||||||
\(492\) | −54.4561 | −0.00498998 | ||||||||
\(493\) | 3157.32 | 0.288435 | ||||||||
\(494\) | 5648.54 | 0.514453 | ||||||||
\(495\) | −1710.35 | −0.155302 | ||||||||
\(496\) | 1556.52 | 0.140907 | ||||||||
\(497\) | 6503.28 | 0.586946 | ||||||||
\(498\) | 484.431 | 0.0435901 | ||||||||
\(499\) | 21171.9 | 1.89937 | 0.949684 | − | 0.313208i | \(-0.101404\pi\) | ||||
0.949684 | + | 0.313208i | \(0.101404\pi\) | |||||||
\(500\) | 4555.19 | 0.407429 | ||||||||
\(501\) | 4636.50 | 0.413460 | ||||||||
\(502\) | −12109.0 | −1.07659 | ||||||||
\(503\) | −12270.3 | −1.08768 | −0.543842 | − | 0.839188i | \(-0.683031\pi\) | ||||
−0.543842 | + | 0.839188i | \(0.683031\pi\) | |||||||
\(504\) | −1354.74 | −0.119732 | ||||||||
\(505\) | 13374.2 | 1.17850 | ||||||||
\(506\) | −2872.38 | −0.252357 | ||||||||
\(507\) | 213.656 | 0.0187155 | ||||||||
\(508\) | 12467.5 | 1.08889 | ||||||||
\(509\) | −3168.41 | −0.275908 | −0.137954 | − | 0.990439i | \(-0.544053\pi\) | ||||
−0.137954 | + | 0.990439i | \(0.544053\pi\) | |||||||
\(510\) | 1648.15 | 0.143100 | ||||||||
\(511\) | 6076.63 | 0.526056 | ||||||||
\(512\) | 3268.99 | 0.282168 | ||||||||
\(513\) | −2067.41 | −0.177930 | ||||||||
\(514\) | 2264.27 | 0.194305 | ||||||||
\(515\) | −13115.4 | −1.12220 | ||||||||
\(516\) | −2004.09 | −0.170979 | ||||||||
\(517\) | 4300.69 | 0.365849 | ||||||||
\(518\) | −2754.85 | −0.233670 | ||||||||
\(519\) | −379.794 | −0.0321216 | ||||||||
\(520\) | 17128.7 | 1.44450 | ||||||||
\(521\) | −1305.16 | −0.109751 | −0.0548755 | − | 0.998493i | \(-0.517476\pi\) | ||||
−0.0548755 | + | 0.998493i | \(0.517476\pi\) | |||||||
\(522\) | 2287.52 | 0.191805 | ||||||||
\(523\) | 707.998 | 0.0591943 | 0.0295971 | − | 0.999562i | \(-0.490578\pi\) | ||||
0.0295971 | + | 0.999562i | \(0.490578\pi\) | |||||||
\(524\) | 8115.35 | 0.676566 | ||||||||
\(525\) | −3642.83 | −0.302830 | ||||||||
\(526\) | −12600.8 | −1.04452 | ||||||||
\(527\) | 3394.04 | 0.280544 | ||||||||
\(528\) | −300.789 | −0.0247920 | ||||||||
\(529\) | 14469.0 | 1.18920 | ||||||||
\(530\) | 11359.5 | 0.930992 | ||||||||
\(531\) | 3678.97 | 0.300666 | ||||||||
\(532\) | −2915.85 | −0.237628 | ||||||||
\(533\) | −153.844 | −0.0125023 | ||||||||
\(534\) | 5103.42 | 0.413570 | ||||||||
\(535\) | 20407.0 | 1.64911 | ||||||||
\(536\) | −13298.5 | −1.07165 | ||||||||
\(537\) | 432.789 | 0.0347788 | ||||||||
\(538\) | −3299.17 | −0.264382 | ||||||||
\(539\) | 539.000 | 0.0430730 | ||||||||
\(540\) | −2537.56 | −0.202221 | ||||||||
\(541\) | −5424.05 | −0.431050 | −0.215525 | − | 0.976498i | \(-0.569146\pi\) | ||||
−0.215525 | + | 0.976498i | \(0.569146\pi\) | |||||||
\(542\) | −13195.1 | −1.04572 | ||||||||
\(543\) | −8775.02 | −0.693503 | ||||||||
\(544\) | 3708.99 | 0.292319 | ||||||||
\(545\) | −12751.4 | −1.00222 | ||||||||
\(546\) | −1549.15 | −0.121424 | ||||||||
\(547\) | −15353.7 | −1.20014 | −0.600071 | − | 0.799947i | \(-0.704861\pi\) | ||||
−0.600071 | + | 0.799947i | \(0.704861\pi\) | |||||||
\(548\) | −14094.0 | −1.09866 | ||||||||
\(549\) | −197.772 | −0.0153747 | ||||||||
\(550\) | 3053.00 | 0.236691 | ||||||||
\(551\) | 12163.8 | 0.940465 | ||||||||
\(552\) | −10528.6 | −0.811826 | ||||||||
\(553\) | 1068.91 | 0.0821968 | ||||||||
\(554\) | −10619.6 | −0.814410 | ||||||||
\(555\) | −12748.4 | −0.975024 | ||||||||
\(556\) | −14547.5 | −1.10962 | ||||||||
\(557\) | 13685.2 | 1.04104 | 0.520519 | − | 0.853850i | \(-0.325738\pi\) | ||||
0.520519 | + | 0.853850i | \(0.325738\pi\) | |||||||
\(558\) | 2459.02 | 0.186557 | ||||||||
\(559\) | −5661.77 | −0.428385 | ||||||||
\(560\) | −1102.29 | −0.0831789 | ||||||||
\(561\) | −655.881 | −0.0493606 | ||||||||
\(562\) | 8961.21 | 0.672608 | ||||||||
\(563\) | −1565.67 | −0.117203 | −0.0586015 | − | 0.998281i | \(-0.518664\pi\) | ||||
−0.0586015 | + | 0.998281i | \(0.518664\pi\) | |||||||
\(564\) | 6380.73 | 0.476378 | ||||||||
\(565\) | −10714.4 | −0.797801 | ||||||||
\(566\) | −1495.57 | −0.111066 | ||||||||
\(567\) | 567.000 | 0.0419961 | ||||||||
\(568\) | −19977.9 | −1.47580 | ||||||||
\(569\) | 20508.1 | 1.51097 | 0.755487 | − | 0.655164i | \(-0.227400\pi\) | ||||
0.755487 | + | 0.655164i | \(0.227400\pi\) | |||||||
\(570\) | 6349.61 | 0.466589 | ||||||||
\(571\) | 971.535 | 0.0712040 | 0.0356020 | − | 0.999366i | \(-0.488665\pi\) | ||||
0.0356020 | + | 0.999366i | \(0.488665\pi\) | |||||||
\(572\) | −2759.03 | −0.201680 | ||||||||
\(573\) | 11315.1 | 0.824949 | ||||||||
\(574\) | −37.3709 | −0.00271748 | ||||||||
\(575\) | −28310.9 | −2.05330 | ||||||||
\(576\) | 2030.94 | 0.146914 | ||||||||
\(577\) | 13961.1 | 1.00729 | 0.503647 | − | 0.863910i | \(-0.331991\pi\) | ||||
0.503647 | + | 0.863910i | \(0.331991\pi\) | |||||||
\(578\) | −7228.67 | −0.520196 | ||||||||
\(579\) | 3848.77 | 0.276251 | ||||||||
\(580\) | 14930.0 | 1.06885 | ||||||||
\(581\) | −706.471 | −0.0504464 | ||||||||
\(582\) | −6794.31 | −0.483906 | ||||||||
\(583\) | −4520.53 | −0.321134 | ||||||||
\(584\) | −18667.3 | −1.32270 | ||||||||
\(585\) | −7168.87 | −0.506660 | ||||||||
\(586\) | 14671.6 | 1.03426 | ||||||||
\(587\) | −23834.3 | −1.67589 | −0.837946 | − | 0.545753i | \(-0.816244\pi\) | ||||
−0.837946 | + | 0.545753i | \(0.816244\pi\) | |||||||
\(588\) | 799.690 | 0.0560861 | ||||||||
\(589\) | 13075.8 | 0.914735 | ||||||||
\(590\) | −11299.2 | −0.788440 | ||||||||
\(591\) | −9156.93 | −0.637336 | ||||||||
\(592\) | −2241.99 | −0.155651 | ||||||||
\(593\) | 25102.9 | 1.73837 | 0.869184 | − | 0.494489i | \(-0.164645\pi\) | ||||
0.869184 | + | 0.494489i | \(0.164645\pi\) | |||||||
\(594\) | −475.194 | −0.0328240 | ||||||||
\(595\) | −2403.58 | −0.165608 | ||||||||
\(596\) | −4473.66 | −0.307464 | ||||||||
\(597\) | −15120.9 | −1.03661 | ||||||||
\(598\) | −12039.5 | −0.823297 | ||||||||
\(599\) | −12122.2 | −0.826875 | −0.413437 | − | 0.910533i | \(-0.635672\pi\) | ||||
−0.413437 | + | 0.910533i | \(0.635672\pi\) | |||||||
\(600\) | 11190.7 | 0.761429 | ||||||||
\(601\) | 20672.9 | 1.40310 | 0.701552 | − | 0.712619i | \(-0.252491\pi\) | ||||
0.701552 | + | 0.712619i | \(0.252491\pi\) | |||||||
\(602\) | −1375.32 | −0.0931130 | ||||||||
\(603\) | 5565.81 | 0.375883 | ||||||||
\(604\) | 755.096 | 0.0508682 | ||||||||
\(605\) | −2090.42 | −0.140476 | ||||||||
\(606\) | 3715.82 | 0.249084 | ||||||||
\(607\) | −3571.58 | −0.238824 | −0.119412 | − | 0.992845i | \(-0.538101\pi\) | ||||
−0.119412 | + | 0.992845i | \(0.538101\pi\) | |||||||
\(608\) | 14289.2 | 0.953129 | ||||||||
\(609\) | −3336.01 | −0.221973 | ||||||||
\(610\) | 607.416 | 0.0403173 | ||||||||
\(611\) | 18026.2 | 1.19356 | ||||||||
\(612\) | −973.101 | −0.0642733 | ||||||||
\(613\) | −25996.1 | −1.71284 | −0.856420 | − | 0.516280i | \(-0.827317\pi\) | ||||
−0.856420 | + | 0.516280i | \(0.827317\pi\) | |||||||
\(614\) | −9909.81 | −0.651347 | ||||||||
\(615\) | −172.938 | −0.0113391 | ||||||||
\(616\) | −1655.79 | −0.108302 | ||||||||
\(617\) | 7266.40 | 0.474123 | 0.237062 | − | 0.971495i | \(-0.423816\pi\) | ||||
0.237062 | + | 0.971495i | \(0.423816\pi\) | |||||||
\(618\) | −3643.92 | −0.237184 | ||||||||
\(619\) | 16227.6 | 1.05371 | 0.526853 | − | 0.849957i | \(-0.323372\pi\) | ||||
0.526853 | + | 0.849957i | \(0.323372\pi\) | |||||||
\(620\) | 16049.4 | 1.03961 | ||||||||
\(621\) | 4406.55 | 0.284748 | ||||||||
\(622\) | −5397.65 | −0.347952 | ||||||||
\(623\) | −7442.58 | −0.478621 | ||||||||
\(624\) | −1260.75 | −0.0808821 | ||||||||
\(625\) | −7217.38 | −0.461912 | ||||||||
\(626\) | 11480.0 | 0.732960 | ||||||||
\(627\) | −2526.83 | −0.160944 | ||||||||
\(628\) | 3453.06 | 0.219414 | ||||||||
\(629\) | −4888.73 | −0.309899 | ||||||||
\(630\) | −1741.42 | −0.110127 | ||||||||
\(631\) | −3162.02 | −0.199490 | −0.0997450 | − | 0.995013i | \(-0.531803\pi\) | ||||
−0.0997450 | + | 0.995013i | \(0.531803\pi\) | |||||||
\(632\) | −3283.68 | −0.206674 | ||||||||
\(633\) | −10668.8 | −0.669903 | ||||||||
\(634\) | −10083.2 | −0.631630 | ||||||||
\(635\) | 39593.5 | 2.47436 | ||||||||
\(636\) | −6706.90 | −0.418154 | ||||||||
\(637\) | 2259.20 | 0.140523 | ||||||||
\(638\) | 2795.86 | 0.173494 | ||||||||
\(639\) | 8361.36 | 0.517638 | ||||||||
\(640\) | 19554.3 | 1.20774 | ||||||||
\(641\) | −8679.48 | −0.534819 | −0.267409 | − | 0.963583i | \(-0.586168\pi\) | ||||
−0.267409 | + | 0.963583i | \(0.586168\pi\) | |||||||
\(642\) | 5669.79 | 0.348550 | ||||||||
\(643\) | −19226.2 | −1.17917 | −0.589586 | − | 0.807705i | \(-0.700709\pi\) | ||||
−0.589586 | + | 0.807705i | \(0.700709\pi\) | |||||||
\(644\) | 6214.94 | 0.380284 | ||||||||
\(645\) | −6364.48 | −0.388529 | ||||||||
\(646\) | 2434.94 | 0.148299 | ||||||||
\(647\) | 11211.6 | 0.681258 | 0.340629 | − | 0.940198i | \(-0.389360\pi\) | ||||
0.340629 | + | 0.940198i | \(0.389360\pi\) | |||||||
\(648\) | −1741.81 | −0.105594 | ||||||||
\(649\) | 4496.52 | 0.271963 | ||||||||
\(650\) | 12796.5 | 0.772188 | ||||||||
\(651\) | −3586.12 | −0.215901 | ||||||||
\(652\) | 3309.56 | 0.198792 | ||||||||
\(653\) | −12404.5 | −0.743378 | −0.371689 | − | 0.928357i | \(-0.621221\pi\) | ||||
−0.371689 | + | 0.928357i | \(0.621221\pi\) | |||||||
\(654\) | −3542.79 | −0.211826 | ||||||||
\(655\) | 25772.2 | 1.53741 | ||||||||
\(656\) | −30.4138 | −0.00181015 | ||||||||
\(657\) | 7812.81 | 0.463937 | ||||||||
\(658\) | 4378.83 | 0.259429 | ||||||||
\(659\) | 20954.9 | 1.23868 | 0.619339 | − | 0.785124i | \(-0.287401\pi\) | ||||
0.619339 | + | 0.785124i | \(0.287401\pi\) | |||||||
\(660\) | −3101.46 | −0.182916 | ||||||||
\(661\) | −20349.0 | −1.19741 | −0.598703 | − | 0.800971i | \(-0.704317\pi\) | ||||
−0.598703 | + | 0.800971i | \(0.704317\pi\) | |||||||
\(662\) | −11846.3 | −0.695498 | ||||||||
\(663\) | −2749.11 | −0.161035 | ||||||||
\(664\) | 2170.26 | 0.126841 | ||||||||
\(665\) | −9259.96 | −0.539979 | ||||||||
\(666\) | −3541.94 | −0.206077 | ||||||||
\(667\) | −25926.4 | −1.50506 | ||||||||
\(668\) | 8407.63 | 0.486977 | ||||||||
\(669\) | −5303.55 | −0.306498 | ||||||||
\(670\) | −17094.2 | −0.985683 | ||||||||
\(671\) | −241.722 | −0.0139070 | ||||||||
\(672\) | −3918.90 | −0.224962 | ||||||||
\(673\) | 31712.5 | 1.81639 | 0.908193 | − | 0.418553i | \(-0.137462\pi\) | ||||
0.908193 | + | 0.418553i | \(0.137462\pi\) | |||||||
\(674\) | 11213.7 | 0.640857 | ||||||||
\(675\) | −4683.63 | −0.267071 | ||||||||
\(676\) | 387.433 | 0.0220433 | ||||||||
\(677\) | 1195.61 | 0.0678744 | 0.0339372 | − | 0.999424i | \(-0.489195\pi\) | ||||
0.0339372 | + | 0.999424i | \(0.489195\pi\) | |||||||
\(678\) | −2976.83 | −0.168620 | ||||||||
\(679\) | 9908.49 | 0.560019 | ||||||||
\(680\) | 7383.73 | 0.416402 | ||||||||
\(681\) | −14510.2 | −0.816494 | ||||||||
\(682\) | 3005.47 | 0.168747 | ||||||||
\(683\) | 16709.8 | 0.936140 | 0.468070 | − | 0.883691i | \(-0.344949\pi\) | ||||
0.468070 | + | 0.883691i | \(0.344949\pi\) | |||||||
\(684\) | −3748.94 | −0.209568 | ||||||||
\(685\) | −44759.0 | −2.49657 | ||||||||
\(686\) | 548.793 | 0.0305438 | ||||||||
\(687\) | −14823.9 | −0.823242 | ||||||||
\(688\) | −1119.29 | −0.0620238 | ||||||||
\(689\) | −18947.7 | −1.04768 | ||||||||
\(690\) | −13533.8 | −0.746699 | ||||||||
\(691\) | −11154.4 | −0.614088 | −0.307044 | − | 0.951695i | \(-0.599340\pi\) | ||||
−0.307044 | + | 0.951695i | \(0.599340\pi\) | |||||||
\(692\) | −688.701 | −0.0378331 | ||||||||
\(693\) | 693.000 | 0.0379869 | ||||||||
\(694\) | −16041.0 | −0.877391 | ||||||||
\(695\) | −46199.0 | −2.52148 | ||||||||
\(696\) | 10248.1 | 0.558124 | ||||||||
\(697\) | −66.3182 | −0.00360399 | ||||||||
\(698\) | −17194.2 | −0.932392 | ||||||||
\(699\) | −14466.4 | −0.782790 | ||||||||
\(700\) | −6605.74 | −0.356676 | ||||||||
\(701\) | 10388.9 | 0.559749 | 0.279874 | − | 0.960037i | \(-0.409707\pi\) | ||||
0.279874 | + | 0.960037i | \(0.409707\pi\) | |||||||
\(702\) | −1991.76 | −0.107086 | ||||||||
\(703\) | −18834.2 | −1.01045 | ||||||||
\(704\) | 2482.26 | 0.132889 | ||||||||
\(705\) | 20263.5 | 1.08251 | ||||||||
\(706\) | −969.805 | −0.0516984 | ||||||||
\(707\) | −5418.98 | −0.288263 | ||||||||
\(708\) | 6671.28 | 0.354127 | ||||||||
\(709\) | −4288.90 | −0.227183 | −0.113592 | − | 0.993528i | \(-0.536236\pi\) | ||||
−0.113592 | + | 0.993528i | \(0.536236\pi\) | |||||||
\(710\) | −25680.2 | −1.35741 | ||||||||
\(711\) | 1374.32 | 0.0724908 | ||||||||
\(712\) | 22863.4 | 1.20343 | ||||||||
\(713\) | −27870.2 | −1.46388 | ||||||||
\(714\) | −667.798 | −0.0350024 | ||||||||
\(715\) | −8761.95 | −0.458291 | ||||||||
\(716\) | 784.800 | 0.0409628 | ||||||||
\(717\) | −14465.4 | −0.753446 | ||||||||
\(718\) | 13643.5 | 0.709153 | ||||||||
\(719\) | 31876.4 | 1.65339 | 0.826697 | − | 0.562647i | \(-0.190217\pi\) | ||||
0.826697 | + | 0.562647i | \(0.190217\pi\) | |||||||
\(720\) | −1417.23 | −0.0733569 | ||||||||
\(721\) | 5314.12 | 0.274491 | ||||||||
\(722\) | −1593.47 | −0.0821371 | ||||||||
\(723\) | −4633.24 | −0.238329 | ||||||||
\(724\) | −15912.2 | −0.816814 | ||||||||
\(725\) | 27556.7 | 1.41163 | ||||||||
\(726\) | −580.793 | −0.0296904 | ||||||||
\(727\) | 14030.2 | 0.715754 | 0.357877 | − | 0.933769i | \(-0.383501\pi\) | ||||
0.357877 | + | 0.933769i | \(0.383501\pi\) | |||||||
\(728\) | −6940.22 | −0.353326 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −23995.4 | −1.21659 | ||||||||
\(731\) | −2440.64 | −0.123489 | ||||||||
\(732\) | −358.631 | −0.0181085 | ||||||||
\(733\) | −5466.09 | −0.275436 | −0.137718 | − | 0.990471i | \(-0.543977\pi\) | ||||
−0.137718 | + | 0.990471i | \(0.543977\pi\) | |||||||
\(734\) | 8806.54 | 0.442855 | ||||||||
\(735\) | 2539.60 | 0.127449 | ||||||||
\(736\) | −30456.5 | −1.52533 | ||||||||
\(737\) | 6802.66 | 0.339999 | ||||||||
\(738\) | −48.0484 | −0.00239659 | ||||||||
\(739\) | 28957.0 | 1.44141 | 0.720704 | − | 0.693243i | \(-0.243819\pi\) | ||||
0.720704 | + | 0.693243i | \(0.243819\pi\) | |||||||
\(740\) | −23117.3 | −1.14839 | ||||||||
\(741\) | −10591.1 | −0.525068 | ||||||||
\(742\) | −4602.66 | −0.227721 | ||||||||
\(743\) | −17742.1 | −0.876037 | −0.438019 | − | 0.898966i | \(-0.644320\pi\) | ||||
−0.438019 | + | 0.898966i | \(0.644320\pi\) | |||||||
\(744\) | 11016.5 | 0.542855 | ||||||||
\(745\) | −14207.2 | −0.698672 | ||||||||
\(746\) | −11346.0 | −0.556846 | ||||||||
\(747\) | −908.320 | −0.0444895 | ||||||||
\(748\) | −1189.35 | −0.0581374 | ||||||||
\(749\) | −8268.55 | −0.403373 | ||||||||
\(750\) | 4019.19 | 0.195680 | ||||||||
\(751\) | 30053.7 | 1.46029 | 0.730143 | − | 0.683294i | \(-0.239453\pi\) | ||||
0.730143 | + | 0.683294i | \(0.239453\pi\) | |||||||
\(752\) | 3563.64 | 0.172809 | ||||||||
\(753\) | 22704.6 | 1.09881 | ||||||||
\(754\) | 11718.8 | 0.566011 | ||||||||
\(755\) | 2397.99 | 0.115592 | ||||||||
\(756\) | 1028.17 | 0.0494633 | ||||||||
\(757\) | −8581.32 | −0.412012 | −0.206006 | − | 0.978551i | \(-0.566047\pi\) | ||||
−0.206006 | + | 0.978551i | \(0.566047\pi\) | |||||||
\(758\) | −123.738 | −0.00592923 | ||||||||
\(759\) | 5385.78 | 0.257565 | ||||||||
\(760\) | 28446.4 | 1.35771 | ||||||||
\(761\) | 30413.3 | 1.44873 | 0.724363 | − | 0.689419i | \(-0.242134\pi\) | ||||
0.724363 | + | 0.689419i | \(0.242134\pi\) | |||||||
\(762\) | 11000.5 | 0.522972 | ||||||||
\(763\) | 5166.63 | 0.245144 | ||||||||
\(764\) | 20518.3 | 0.971632 | ||||||||
\(765\) | −3090.31 | −0.146053 | ||||||||
\(766\) | 7749.90 | 0.365555 | ||||||||
\(767\) | 18847.0 | 0.887258 | ||||||||
\(768\) | 10848.7 | 0.509726 | ||||||||
\(769\) | −24735.2 | −1.15992 | −0.579958 | − | 0.814646i | \(-0.696931\pi\) | ||||
−0.579958 | + | 0.814646i | \(0.696931\pi\) | |||||||
\(770\) | −2128.40 | −0.0996134 | ||||||||
\(771\) | −4245.56 | −0.198314 | ||||||||
\(772\) | 6979.18 | 0.325371 | ||||||||
\(773\) | 25108.1 | 1.16827 | 0.584137 | − | 0.811655i | \(-0.301433\pi\) | ||||
0.584137 | + | 0.811655i | \(0.301433\pi\) | |||||||
\(774\) | −1768.27 | −0.0821180 | ||||||||
\(775\) | 29622.7 | 1.37301 | ||||||||
\(776\) | −30438.7 | −1.40810 | ||||||||
\(777\) | 5165.40 | 0.238491 | ||||||||
\(778\) | 15811.0 | 0.728601 | ||||||||
\(779\) | −255.496 | −0.0117511 | ||||||||
\(780\) | −12999.7 | −0.596749 | ||||||||
\(781\) | 10219.4 | 0.468221 | ||||||||
\(782\) | −5189.92 | −0.237329 | ||||||||
\(783\) | −4289.15 | −0.195762 | ||||||||
\(784\) | 446.627 | 0.0203456 | ||||||||
\(785\) | 10966.0 | 0.498591 | ||||||||
\(786\) | 7160.42 | 0.324941 | ||||||||
\(787\) | −36364.0 | −1.64706 | −0.823531 | − | 0.567271i | \(-0.807999\pi\) | ||||
−0.823531 | + | 0.567271i | \(0.807999\pi\) | |||||||
\(788\) | −16604.8 | −0.750660 | ||||||||
\(789\) | 23626.7 | 1.06608 | ||||||||
\(790\) | −4220.93 | −0.190094 | ||||||||
\(791\) | 4341.27 | 0.195142 | ||||||||
\(792\) | −2128.88 | −0.0955132 | ||||||||
\(793\) | −1013.17 | −0.0453704 | ||||||||
\(794\) | −16216.6 | −0.724818 | ||||||||
\(795\) | −21299.4 | −0.950202 | ||||||||
\(796\) | −27419.5 | −1.22093 | ||||||||
\(797\) | −18605.4 | −0.826897 | −0.413448 | − | 0.910528i | \(-0.635676\pi\) | ||||
−0.413448 | + | 0.910528i | \(0.635676\pi\) | |||||||
\(798\) | −2572.74 | −0.114128 | ||||||||
\(799\) | 7770.63 | 0.344062 | ||||||||
\(800\) | 32371.6 | 1.43063 | ||||||||
\(801\) | −9569.04 | −0.422104 | ||||||||
\(802\) | 14753.3 | 0.649574 | ||||||||
\(803\) | 9548.99 | 0.419647 | ||||||||
\(804\) | 10092.8 | 0.442718 | ||||||||
\(805\) | 19737.0 | 0.864147 | ||||||||
\(806\) | 12597.4 | 0.550525 | ||||||||
\(807\) | 6186.02 | 0.269837 | ||||||||
\(808\) | 16647.0 | 0.724800 | ||||||||
\(809\) | 26846.8 | 1.16673 | 0.583364 | − | 0.812211i | \(-0.301736\pi\) | ||||
0.583364 | + | 0.812211i | \(0.301736\pi\) | |||||||
\(810\) | −2238.97 | −0.0971227 | ||||||||
\(811\) | −32344.3 | −1.40045 | −0.700224 | − | 0.713924i | \(-0.746916\pi\) | ||||
−0.700224 | + | 0.713924i | \(0.746916\pi\) | |||||||
\(812\) | −6049.37 | −0.261442 | ||||||||
\(813\) | 24741.2 | 1.06730 | ||||||||
\(814\) | −4329.04 | −0.186404 | ||||||||
\(815\) | 10510.3 | 0.451729 | ||||||||
\(816\) | −543.477 | −0.0233156 | ||||||||
\(817\) | −9402.76 | −0.402645 | ||||||||
\(818\) | −9137.31 | −0.390561 | ||||||||
\(819\) | 2904.69 | 0.123929 | ||||||||
\(820\) | −313.599 | −0.0133553 | ||||||||
\(821\) | 16953.3 | 0.720677 | 0.360338 | − | 0.932822i | \(-0.382661\pi\) | ||||
0.360338 | + | 0.932822i | \(0.382661\pi\) | |||||||
\(822\) | −12435.6 | −0.527667 | ||||||||
\(823\) | 37814.0 | 1.60159 | 0.800797 | − | 0.598936i | \(-0.204410\pi\) | ||||
0.800797 | + | 0.598936i | \(0.204410\pi\) | |||||||
\(824\) | −16324.8 | −0.690173 | ||||||||
\(825\) | −5724.44 | −0.241575 | ||||||||
\(826\) | 4578.21 | 0.192853 | ||||||||
\(827\) | −11894.6 | −0.500141 | −0.250071 | − | 0.968228i | \(-0.580454\pi\) | ||||
−0.250071 | + | 0.968228i | \(0.580454\pi\) | |||||||
\(828\) | 7990.64 | 0.335379 | ||||||||
\(829\) | 30744.7 | 1.28807 | 0.644033 | − | 0.764998i | \(-0.277260\pi\) | ||||
0.644033 | + | 0.764998i | \(0.277260\pi\) | |||||||
\(830\) | 2789.71 | 0.116665 | ||||||||
\(831\) | 19912.0 | 0.831215 | ||||||||
\(832\) | 10404.3 | 0.433540 | ||||||||
\(833\) | 973.884 | 0.0405079 | ||||||||
\(834\) | −12835.7 | −0.532930 | ||||||||
\(835\) | 26700.4 | 1.10659 | ||||||||
\(836\) | −4582.04 | −0.189561 | ||||||||
\(837\) | −4610.73 | −0.190406 | ||||||||
\(838\) | 7233.08 | 0.298165 | ||||||||
\(839\) | −24677.8 | −1.01546 | −0.507731 | − | 0.861516i | \(-0.669516\pi\) | ||||
−0.507731 | + | 0.861516i | \(0.669516\pi\) | |||||||
\(840\) | −7801.60 | −0.320453 | ||||||||
\(841\) | 846.708 | 0.0347168 | ||||||||
\(842\) | 6077.14 | 0.248732 | ||||||||
\(843\) | −16802.5 | −0.686486 | ||||||||
\(844\) | −19346.4 | −0.789017 | ||||||||
\(845\) | 1230.39 | 0.0500907 | ||||||||
\(846\) | 5629.92 | 0.228795 | ||||||||
\(847\) | 847.000 | 0.0343604 | ||||||||
\(848\) | −3745.80 | −0.151688 | ||||||||
\(849\) | 2804.24 | 0.113358 | ||||||||
\(850\) | 5516.26 | 0.222595 | ||||||||
\(851\) | 40143.9 | 1.61706 | ||||||||
\(852\) | 15162.1 | 0.609678 | ||||||||
\(853\) | −1855.69 | −0.0744873 | −0.0372437 | − | 0.999306i | \(-0.511858\pi\) | ||||
−0.0372437 | + | 0.999306i | \(0.511858\pi\) | |||||||
\(854\) | −246.114 | −0.00986163 | ||||||||
\(855\) | −11905.7 | −0.476217 | ||||||||
\(856\) | 25400.8 | 1.01423 | ||||||||
\(857\) | 3984.84 | 0.158832 | 0.0794162 | − | 0.996842i | \(-0.474694\pi\) | ||||
0.0794162 | + | 0.996842i | \(0.474694\pi\) | |||||||
\(858\) | −2434.38 | −0.0968627 | ||||||||
\(859\) | −12526.1 | −0.497538 | −0.248769 | − | 0.968563i | \(-0.580026\pi\) | ||||
−0.248769 | + | 0.968563i | \(0.580026\pi\) | |||||||
\(860\) | −11541.1 | −0.457613 | ||||||||
\(861\) | 70.0714 | 0.00277355 | ||||||||
\(862\) | −5549.54 | −0.219279 | ||||||||
\(863\) | −22040.9 | −0.869387 | −0.434693 | − | 0.900579i | \(-0.643143\pi\) | ||||
−0.434693 | + | 0.900579i | \(0.643143\pi\) | |||||||
\(864\) | −5038.58 | −0.198398 | ||||||||
\(865\) | −2187.14 | −0.0859709 | ||||||||
\(866\) | −15775.8 | −0.619033 | ||||||||
\(867\) | 13553.9 | 0.530929 | ||||||||
\(868\) | −6502.91 | −0.254290 | ||||||||
\(869\) | 1679.72 | 0.0655704 | ||||||||
\(870\) | 13173.2 | 0.513350 | ||||||||
\(871\) | 28513.2 | 1.10922 | ||||||||
\(872\) | −15871.8 | −0.616383 | ||||||||
\(873\) | 12739.5 | 0.493891 | ||||||||
\(874\) | −19994.5 | −0.773828 | ||||||||
\(875\) | −5861.39 | −0.226459 | ||||||||
\(876\) | 14167.4 | 0.546430 | ||||||||
\(877\) | 21039.5 | 0.810096 | 0.405048 | − | 0.914295i | \(-0.367255\pi\) | ||||
0.405048 | + | 0.914295i | \(0.367255\pi\) | |||||||
\(878\) | 13542.7 | 0.520553 | ||||||||
\(879\) | −27509.6 | −1.05560 | ||||||||
\(880\) | −1732.17 | −0.0663538 | ||||||||
\(881\) | 33610.9 | 1.28533 | 0.642667 | − | 0.766146i | \(-0.277828\pi\) | ||||
0.642667 | + | 0.766146i | \(0.277828\pi\) | |||||||
\(882\) | 705.591 | 0.0269371 | ||||||||
\(883\) | −4618.52 | −0.176020 | −0.0880099 | − | 0.996120i | \(-0.528051\pi\) | ||||
−0.0880099 | + | 0.996120i | \(0.528051\pi\) | |||||||
\(884\) | −4985.11 | −0.189669 | ||||||||
\(885\) | 21186.2 | 0.804709 | ||||||||
\(886\) | −12520.5 | −0.474757 | ||||||||
\(887\) | −40095.6 | −1.51779 | −0.758895 | − | 0.651213i | \(-0.774260\pi\) | ||||
−0.758895 | + | 0.651213i | \(0.774260\pi\) | |||||||
\(888\) | −15868.0 | −0.599656 | ||||||||
\(889\) | −16042.6 | −0.605231 | ||||||||
\(890\) | 29389.3 | 1.10689 | ||||||||
\(891\) | 891.000 | 0.0335013 | ||||||||
\(892\) | −9617.22 | −0.360996 | ||||||||
\(893\) | 29937.0 | 1.12184 | ||||||||
\(894\) | −3947.25 | −0.147669 | ||||||||
\(895\) | 2492.32 | 0.0930828 | ||||||||
\(896\) | −7923.03 | −0.295413 | ||||||||
\(897\) | 22574.4 | 0.840285 | ||||||||
\(898\) | 1681.48 | 0.0624852 | ||||||||
\(899\) | 27127.7 | 1.00641 | ||||||||
\(900\) | −8493.09 | −0.314559 | ||||||||
\(901\) | −8167.85 | −0.302009 | ||||||||
\(902\) | −58.7258 | −0.00216780 | ||||||||
\(903\) | 2578.77 | 0.0950343 | ||||||||
\(904\) | −13336.3 | −0.490661 | ||||||||
\(905\) | −50533.1 | −1.85611 | ||||||||
\(906\) | 666.244 | 0.0244310 | ||||||||
\(907\) | −52281.2 | −1.91397 | −0.956984 | − | 0.290141i | \(-0.906298\pi\) | ||||
−0.956984 | + | 0.290141i | \(0.906298\pi\) | |||||||
\(908\) | −26312.2 | −0.961674 | ||||||||
\(909\) | −6967.26 | −0.254224 | ||||||||
\(910\) | −8921.15 | −0.324981 | ||||||||
\(911\) | 30635.6 | 1.11416 | 0.557081 | − | 0.830458i | \(-0.311921\pi\) | ||||
0.557081 | + | 0.830458i | \(0.311921\pi\) | |||||||
\(912\) | −2093.79 | −0.0760221 | ||||||||
\(913\) | −1110.17 | −0.0402423 | ||||||||
\(914\) | 23035.3 | 0.833632 | ||||||||
\(915\) | −1138.92 | −0.0411492 | ||||||||
\(916\) | −26881.0 | −0.969622 | ||||||||
\(917\) | −10442.4 | −0.376051 | ||||||||
\(918\) | −858.597 | −0.0308692 | ||||||||
\(919\) | −14574.9 | −0.523159 | −0.261579 | − | 0.965182i | \(-0.584243\pi\) | ||||
−0.261579 | + | 0.965182i | \(0.584243\pi\) | |||||||
\(920\) | −60631.6 | −2.17279 | ||||||||
\(921\) | 18581.1 | 0.664787 | ||||||||
\(922\) | −9209.21 | −0.328947 | ||||||||
\(923\) | 42834.5 | 1.52754 | ||||||||
\(924\) | 1256.66 | 0.0447413 | ||||||||
\(925\) | −42668.1 | −1.51667 | ||||||||
\(926\) | −16089.4 | −0.570983 | ||||||||
\(927\) | 6832.44 | 0.242078 | ||||||||
\(928\) | 29645.1 | 1.04865 | ||||||||
\(929\) | −18955.8 | −0.669451 | −0.334726 | − | 0.942316i | \(-0.608644\pi\) | ||||
−0.334726 | + | 0.942316i | \(0.608644\pi\) | |||||||
\(930\) | 14160.9 | 0.499305 | ||||||||
\(931\) | 3751.96 | 0.132079 | ||||||||
\(932\) | −26232.7 | −0.921976 | ||||||||
\(933\) | 10120.7 | 0.355132 | ||||||||
\(934\) | 4171.66 | 0.146147 | ||||||||
\(935\) | −3777.05 | −0.132110 | ||||||||
\(936\) | −8923.14 | −0.311605 | ||||||||
\(937\) | 6520.68 | 0.227344 | 0.113672 | − | 0.993518i | \(-0.463739\pi\) | ||||
0.113672 | + | 0.993518i | \(0.463739\pi\) | |||||||
\(938\) | 6926.26 | 0.241098 | ||||||||
\(939\) | −21525.3 | −0.748084 | ||||||||
\(940\) | 36745.0 | 1.27499 | ||||||||
\(941\) | 12631.4 | 0.437589 | 0.218795 | − | 0.975771i | \(-0.429788\pi\) | ||||
0.218795 | + | 0.975771i | \(0.429788\pi\) | |||||||
\(942\) | 3046.74 | 0.105380 | ||||||||
\(943\) | 544.573 | 0.0188057 | ||||||||
\(944\) | 3725.91 | 0.128462 | ||||||||
\(945\) | 3265.21 | 0.112399 | ||||||||
\(946\) | −2161.22 | −0.0742785 | ||||||||
\(947\) | −35170.9 | −1.20686 | −0.603432 | − | 0.797415i | \(-0.706200\pi\) | ||||
−0.603432 | + | 0.797415i | \(0.706200\pi\) | |||||||
\(948\) | 2492.13 | 0.0853803 | ||||||||
\(949\) | 40024.3 | 1.36907 | ||||||||
\(950\) | 21251.8 | 0.725789 | ||||||||
\(951\) | 18906.2 | 0.644663 | ||||||||
\(952\) | −2991.75 | −0.101852 | ||||||||
\(953\) | 39539.0 | 1.34396 | 0.671980 | − | 0.740570i | \(-0.265444\pi\) | ||||
0.671980 | + | 0.740570i | \(0.265444\pi\) | |||||||
\(954\) | −5917.71 | −0.200831 | ||||||||
\(955\) | 65160.8 | 2.20791 | ||||||||
\(956\) | −26230.9 | −0.887415 | ||||||||
\(957\) | −5242.30 | −0.177074 | ||||||||
\(958\) | −9511.83 | −0.320786 | ||||||||
\(959\) | 18135.5 | 0.610663 | ||||||||
\(960\) | 11695.7 | 0.393204 | ||||||||
\(961\) | −629.373 | −0.0211263 | ||||||||
\(962\) | −18145.1 | −0.608129 | ||||||||
\(963\) | −10631.0 | −0.355741 | ||||||||
\(964\) | −8401.70 | −0.280706 | ||||||||
\(965\) | 22164.0 | 0.739363 | ||||||||
\(966\) | 5483.63 | 0.182643 | ||||||||
\(967\) | −29986.0 | −0.997194 | −0.498597 | − | 0.866834i | \(-0.666151\pi\) | ||||
−0.498597 | + | 0.866834i | \(0.666151\pi\) | |||||||
\(968\) | −2601.96 | −0.0863949 | ||||||||
\(969\) | −4565.57 | −0.151359 | ||||||||
\(970\) | −39126.7 | −1.29514 | ||||||||
\(971\) | −14879.8 | −0.491777 | −0.245889 | − | 0.969298i | \(-0.579080\pi\) | ||||
−0.245889 | + | 0.969298i | \(0.579080\pi\) | |||||||
\(972\) | 1321.94 | 0.0436225 | ||||||||
\(973\) | 18719.0 | 0.616755 | ||||||||
\(974\) | 25431.9 | 0.836643 | ||||||||
\(975\) | −23993.8 | −0.788121 | ||||||||
\(976\) | −200.296 | −0.00656896 | ||||||||
\(977\) | 40864.1 | 1.33813 | 0.669067 | − | 0.743202i | \(-0.266694\pi\) | ||||
0.669067 | + | 0.743202i | \(0.266694\pi\) | |||||||
\(978\) | 2920.13 | 0.0954758 | ||||||||
\(979\) | −11695.5 | −0.381807 | ||||||||
\(980\) | 4605.21 | 0.150110 | ||||||||
\(981\) | 6642.82 | 0.216197 | ||||||||
\(982\) | 5848.88 | 0.190066 | ||||||||
\(983\) | 48180.6 | 1.56330 | 0.781650 | − | 0.623718i | \(-0.214379\pi\) | ||||
0.781650 | + | 0.623718i | \(0.214379\pi\) | |||||||
\(984\) | −215.258 | −0.00697374 | ||||||||
\(985\) | −52732.4 | −1.70578 | ||||||||
\(986\) | 5051.65 | 0.163162 | ||||||||
\(987\) | −8210.41 | −0.264782 | ||||||||
\(988\) | −19205.5 | −0.618430 | ||||||||
\(989\) | 20041.4 | 0.644367 | ||||||||
\(990\) | −2736.52 | −0.0878508 | ||||||||
\(991\) | −22380.4 | −0.717392 | −0.358696 | − | 0.933454i | \(-0.616779\pi\) | ||||
−0.358696 | + | 0.933454i | \(0.616779\pi\) | |||||||
\(992\) | 31867.7 | 1.01996 | ||||||||
\(993\) | 22212.1 | 0.709848 | ||||||||
\(994\) | 10405.1 | 0.332023 | ||||||||
\(995\) | −87077.1 | −2.77440 | ||||||||
\(996\) | −1647.11 | −0.0524002 | ||||||||
\(997\) | −12425.1 | −0.394691 | −0.197346 | − | 0.980334i | \(-0.563232\pi\) | ||||
−0.197346 | + | 0.980334i | \(0.563232\pi\) | |||||||
\(998\) | 33874.6 | 1.07443 | ||||||||
\(999\) | 6641.23 | 0.210330 |
(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 | 231.4.a.k.1.4 | ✓ | 5 | |
3.2 | odd | 2 | 693.4.a.p.1.2 | 5 | |||
7.6 | odd | 2 | 1617.4.a.n.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.4.a.k.1.4 | ✓ | 5 | 1.1 | even | 1 | trivial | |
693.4.a.p.1.2 | 5 | 3.2 | odd | 2 | |||
1617.4.a.n.1.4 | 5 | 7.6 | odd | 2 |