Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [354,3,Mod(235,354)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(354, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("354.235");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 354.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.64580135835\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 300 x^{18} - 88 x^{17} + 37952 x^{16} + 27000 x^{15} - 2574056 x^{14} - 3295208 x^{13} + \cdots + 2455573689828 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 235.5 | ||
Root | \(7.71614 + 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 354.235 |
Dual form | 354.3.d.a.235.15 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/354\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 0.707107i | ||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 7.71614 | 1.54323 | 0.771614 | − | 0.636091i | \(-0.219450\pi\) | ||||
0.771614 | + | 0.636091i | \(0.219450\pi\) | |||||||
\(6\) | 2.44949i | 0.408248i | ||||||||
\(7\) | −7.56506 | −1.08072 | −0.540362 | − | 0.841433i | \(-0.681713\pi\) | ||||
−0.540362 | + | 0.841433i | \(0.681713\pi\) | |||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | − | 10.9123i | − | 1.09123i | ||||||
\(11\) | 2.42694i | 0.220631i | 0.993897 | + | 0.110316i | \(0.0351862\pi\) | ||||
−0.993897 | + | 0.110316i | \(0.964814\pi\) | |||||||
\(12\) | 3.46410 | 0.288675 | ||||||||
\(13\) | − | 20.7553i | − | 1.59656i | −0.602285 | − | 0.798281i | \(-0.705743\pi\) | ||
0.602285 | − | 0.798281i | \(-0.294257\pi\) | |||||||
\(14\) | 10.6986i | 0.764187i | ||||||||
\(15\) | −13.3647 | −0.890983 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 31.7647 | 1.86851 | 0.934255 | − | 0.356606i | \(-0.116066\pi\) | ||||
0.934255 | + | 0.356606i | \(0.116066\pi\) | |||||||
\(18\) | − | 4.24264i | − | 0.235702i | ||||||
\(19\) | −4.95867 | −0.260983 | −0.130491 | − | 0.991449i | \(-0.541655\pi\) | ||||
−0.130491 | + | 0.991449i | \(0.541655\pi\) | |||||||
\(20\) | −15.4323 | −0.771614 | ||||||||
\(21\) | 13.1031 | 0.623956 | ||||||||
\(22\) | 3.43222 | 0.156010 | ||||||||
\(23\) | − | 31.3139i | − | 1.36147i | −0.732529 | − | 0.680736i | \(-0.761660\pi\) | ||
0.732529 | − | 0.680736i | \(-0.238340\pi\) | |||||||
\(24\) | − | 4.89898i | − | 0.204124i | ||||||
\(25\) | 34.5388 | 1.38155 | ||||||||
\(26\) | −29.3524 | −1.12894 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 15.1301 | 0.540362 | ||||||||
\(29\) | −11.8424 | −0.408359 | −0.204180 | − | 0.978933i | \(-0.565453\pi\) | ||||
−0.204180 | + | 0.978933i | \(0.565453\pi\) | |||||||
\(30\) | 18.9006i | 0.630020i | ||||||||
\(31\) | − | 8.07558i | − | 0.260503i | −0.991481 | − | 0.130251i | \(-0.958422\pi\) | ||
0.991481 | − | 0.130251i | \(-0.0415784\pi\) | |||||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | − | 4.20359i | − | 0.127382i | ||||||
\(34\) | − | 44.9220i | − | 1.32124i | ||||||
\(35\) | −58.3731 | −1.66780 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | − | 41.8766i | − | 1.13180i | −0.824474 | − | 0.565900i | \(-0.808529\pi\) | ||
0.824474 | − | 0.565900i | \(-0.191471\pi\) | |||||||
\(38\) | 7.01262i | 0.184543i | ||||||||
\(39\) | 35.9493i | 0.921776i | ||||||||
\(40\) | 21.8245i | 0.545613i | ||||||||
\(41\) | −44.4010 | −1.08295 | −0.541476 | − | 0.840716i | \(-0.682134\pi\) | ||||
−0.541476 | + | 0.840716i | \(0.682134\pi\) | |||||||
\(42\) | − | 18.5305i | − | 0.441203i | ||||||
\(43\) | − | 6.57752i | − | 0.152966i | −0.997071 | − | 0.0764828i | \(-0.975631\pi\) | ||
0.997071 | − | 0.0764828i | \(-0.0243690\pi\) | |||||||
\(44\) | − | 4.85389i | − | 0.110316i | ||||||
\(45\) | 23.1484 | 0.514409 | ||||||||
\(46\) | −44.2845 | −0.962706 | ||||||||
\(47\) | − | 92.7318i | − | 1.97302i | −0.163710 | − | 0.986509i | \(-0.552346\pi\) | ||
0.163710 | − | 0.986509i | \(-0.447654\pi\) | |||||||
\(48\) | −6.92820 | −0.144338 | ||||||||
\(49\) | 8.23017 | 0.167963 | ||||||||
\(50\) | − | 48.8452i | − | 0.976905i | ||||||
\(51\) | −55.0180 | −1.07878 | ||||||||
\(52\) | 41.5106i | 0.798281i | ||||||||
\(53\) | 45.1599 | 0.852074 | 0.426037 | − | 0.904706i | \(-0.359909\pi\) | ||||
0.426037 | + | 0.904706i | \(0.359909\pi\) | |||||||
\(54\) | 7.34847i | 0.136083i | ||||||||
\(55\) | 18.7266i | 0.340484i | ||||||||
\(56\) | − | 21.3972i | − | 0.382093i | ||||||
\(57\) | 8.58867 | 0.150678 | ||||||||
\(58\) | 16.7477i | 0.288754i | ||||||||
\(59\) | 55.8007 | + | 19.1647i | 0.945774 | + | 0.324826i | ||||
\(60\) | 26.7295 | 0.445491 | ||||||||
\(61\) | − | 42.6199i | − | 0.698687i | −0.936995 | − | 0.349343i | \(-0.886405\pi\) | ||
0.936995 | − | 0.349343i | \(-0.113595\pi\) | |||||||
\(62\) | −11.4206 | −0.184203 | ||||||||
\(63\) | −22.6952 | −0.360241 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | − | 160.151i | − | 2.46386i | ||||||
\(66\) | −5.94477 | −0.0900723 | ||||||||
\(67\) | 76.9923i | 1.14914i | 0.818456 | + | 0.574570i | \(0.194831\pi\) | ||||
−0.818456 | + | 0.574570i | \(0.805169\pi\) | |||||||
\(68\) | −63.5293 | −0.934255 | ||||||||
\(69\) | 54.2372i | 0.786046i | ||||||||
\(70\) | 82.5520i | 1.17931i | ||||||||
\(71\) | −32.2995 | −0.454923 | −0.227461 | − | 0.973787i | \(-0.573043\pi\) | ||||
−0.227461 | + | 0.973787i | \(0.573043\pi\) | |||||||
\(72\) | 8.48528i | 0.117851i | ||||||||
\(73\) | 119.215i | 1.63309i | 0.577284 | + | 0.816543i | \(0.304112\pi\) | ||||
−0.577284 | + | 0.816543i | \(0.695888\pi\) | |||||||
\(74\) | −59.2224 | −0.800303 | ||||||||
\(75\) | −59.8230 | −0.797639 | ||||||||
\(76\) | 9.91734 | 0.130491 | ||||||||
\(77\) | − | 18.3600i | − | 0.238441i | ||||||
\(78\) | 50.8399 | 0.651794 | ||||||||
\(79\) | 94.3895 | 1.19480 | 0.597402 | − | 0.801942i | \(-0.296200\pi\) | ||||
0.597402 | + | 0.801942i | \(0.296200\pi\) | |||||||
\(80\) | 30.8646 | 0.385807 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 62.7925i | 0.765763i | ||||||||
\(83\) | 108.087i | 1.30225i | 0.758969 | + | 0.651127i | \(0.225704\pi\) | ||||
−0.758969 | + | 0.651127i | \(0.774296\pi\) | |||||||
\(84\) | −26.2061 | −0.311978 | ||||||||
\(85\) | 245.101 | 2.88354 | ||||||||
\(86\) | −9.30201 | −0.108163 | ||||||||
\(87\) | 20.5117 | 0.235766 | ||||||||
\(88\) | −6.86443 | −0.0780049 | ||||||||
\(89\) | 58.7505i | 0.660118i | 0.943960 | + | 0.330059i | \(0.107069\pi\) | ||||
−0.943960 | + | 0.330059i | \(0.892931\pi\) | |||||||
\(90\) | − | 32.7368i | − | 0.363742i | ||||||
\(91\) | 157.015i | 1.72544i | ||||||||
\(92\) | 62.6277i | 0.680736i | ||||||||
\(93\) | 13.9873i | 0.150401i | ||||||||
\(94\) | −131.143 | −1.39513 | ||||||||
\(95\) | −38.2618 | −0.402756 | ||||||||
\(96\) | 9.79796i | 0.102062i | ||||||||
\(97\) | 21.2762i | 0.219343i | 0.993968 | + | 0.109671i | \(0.0349798\pi\) | ||||
−0.993968 | + | 0.109671i | \(0.965020\pi\) | |||||||
\(98\) | − | 11.6392i | − | 0.118767i | ||||||
\(99\) | 7.28083i | 0.0735438i | ||||||||
\(100\) | −69.0776 | −0.690776 | ||||||||
\(101\) | − | 68.9296i | − | 0.682471i | −0.939978 | − | 0.341235i | \(-0.889155\pi\) | ||
0.939978 | − | 0.341235i | \(-0.110845\pi\) | |||||||
\(102\) | 77.8072i | 0.762816i | ||||||||
\(103\) | 91.3137i | 0.886540i | 0.896388 | + | 0.443270i | \(0.146182\pi\) | ||||
−0.896388 | + | 0.443270i | \(0.853818\pi\) | |||||||
\(104\) | 58.7049 | 0.564470 | ||||||||
\(105\) | 101.105 | 0.962906 | ||||||||
\(106\) | − | 63.8658i | − | 0.602508i | ||||||
\(107\) | 138.265 | 1.29219 | 0.646096 | − | 0.763256i | \(-0.276400\pi\) | ||||
0.646096 | + | 0.763256i | \(0.276400\pi\) | |||||||
\(108\) | 10.3923 | 0.0962250 | ||||||||
\(109\) | − | 122.018i | − | 1.11943i | −0.828685 | − | 0.559715i | \(-0.810910\pi\) | ||
0.828685 | − | 0.559715i | \(-0.189090\pi\) | |||||||
\(110\) | 26.4835 | 0.240759 | ||||||||
\(111\) | 72.5324i | 0.653445i | ||||||||
\(112\) | −30.2602 | −0.270181 | ||||||||
\(113\) | 25.8859i | 0.229079i | 0.993419 | + | 0.114539i | \(0.0365392\pi\) | ||||
−0.993419 | + | 0.114539i | \(0.963461\pi\) | |||||||
\(114\) | − | 12.1462i | − | 0.106546i | ||||||
\(115\) | − | 241.622i | − | 2.10106i | ||||||
\(116\) | 23.6848 | 0.204180 | ||||||||
\(117\) | − | 62.2659i | − | 0.532188i | ||||||
\(118\) | 27.1030 | − | 78.9140i | 0.229687 | − | 0.668763i | ||||
\(119\) | −240.302 | −2.01934 | ||||||||
\(120\) | − | 37.8012i | − | 0.315010i | ||||||
\(121\) | 115.110 | 0.951322 | ||||||||
\(122\) | −60.2736 | −0.494046 | ||||||||
\(123\) | 76.9048 | 0.625243 | ||||||||
\(124\) | 16.1512i | 0.130251i | ||||||||
\(125\) | 73.6027 | 0.588821 | ||||||||
\(126\) | 32.0958i | 0.254729i | ||||||||
\(127\) | 114.217 | 0.899348 | 0.449674 | − | 0.893193i | \(-0.351540\pi\) | ||||
0.449674 | + | 0.893193i | \(0.351540\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | 11.3926i | 0.0883147i | ||||||||
\(130\) | −226.488 | −1.74221 | ||||||||
\(131\) | − | 197.744i | − | 1.50949i | −0.656017 | − | 0.754746i | \(-0.727760\pi\) | ||
0.656017 | − | 0.754746i | \(-0.272240\pi\) | |||||||
\(132\) | 8.40718i | 0.0636908i | ||||||||
\(133\) | 37.5127 | 0.282050 | ||||||||
\(134\) | 108.884 | 0.812564 | ||||||||
\(135\) | −40.0942 | −0.296994 | ||||||||
\(136\) | 89.8440i | 0.660618i | ||||||||
\(137\) | −163.072 | −1.19031 | −0.595154 | − | 0.803612i | \(-0.702909\pi\) | ||||
−0.595154 | + | 0.803612i | \(0.702909\pi\) | |||||||
\(138\) | 76.7030 | 0.555819 | ||||||||
\(139\) | −77.3221 | −0.556274 | −0.278137 | − | 0.960541i | \(-0.589717\pi\) | ||||
−0.278137 | + | 0.960541i | \(0.589717\pi\) | |||||||
\(140\) | 116.746 | 0.833901 | ||||||||
\(141\) | 160.616i | 1.13912i | ||||||||
\(142\) | 45.6784i | 0.321679i | ||||||||
\(143\) | 50.3720 | 0.352252 | ||||||||
\(144\) | 12.0000 | 0.0833333 | ||||||||
\(145\) | −91.3777 | −0.630191 | ||||||||
\(146\) | 168.596 | 1.15477 | ||||||||
\(147\) | −14.2551 | −0.0969732 | ||||||||
\(148\) | 83.7532i | 0.565900i | ||||||||
\(149\) | 12.7571i | 0.0856183i | 0.999083 | + | 0.0428092i | \(0.0136307\pi\) | ||||
−0.999083 | + | 0.0428092i | \(0.986369\pi\) | |||||||
\(150\) | 84.6024i | 0.564016i | ||||||||
\(151\) | − | 124.275i | − | 0.823011i | −0.911407 | − | 0.411506i | \(-0.865003\pi\) | ||
0.911407 | − | 0.411506i | \(-0.134997\pi\) | |||||||
\(152\) | − | 14.0252i | − | 0.0922713i | ||||||
\(153\) | 95.2940 | 0.622836 | ||||||||
\(154\) | −25.9649 | −0.168603 | ||||||||
\(155\) | − | 62.3123i | − | 0.402015i | ||||||
\(156\) | − | 71.8985i | − | 0.460888i | ||||||
\(157\) | 273.654i | 1.74302i | 0.490381 | + | 0.871508i | \(0.336858\pi\) | ||||
−0.490381 | + | 0.871508i | \(0.663142\pi\) | |||||||
\(158\) | − | 133.487i | − | 0.844854i | ||||||
\(159\) | −78.2193 | −0.491945 | ||||||||
\(160\) | − | 43.6491i | − | 0.272807i | ||||||
\(161\) | 236.891i | 1.47137i | ||||||||
\(162\) | − | 12.7279i | − | 0.0785674i | ||||||
\(163\) | 210.141 | 1.28921 | 0.644605 | − | 0.764516i | \(-0.277022\pi\) | ||||
0.644605 | + | 0.764516i | \(0.277022\pi\) | |||||||
\(164\) | 88.8021 | 0.541476 | ||||||||
\(165\) | − | 32.4355i | − | 0.196579i | ||||||
\(166\) | 152.858 | 0.920833 | ||||||||
\(167\) | −169.518 | −1.01508 | −0.507539 | − | 0.861629i | \(-0.669445\pi\) | ||||
−0.507539 | + | 0.861629i | \(0.669445\pi\) | |||||||
\(168\) | 37.0611i | 0.220602i | ||||||||
\(169\) | −261.783 | −1.54901 | ||||||||
\(170\) | − | 346.624i | − | 2.03897i | ||||||
\(171\) | −14.8760 | −0.0869942 | ||||||||
\(172\) | 13.1550i | 0.0764828i | ||||||||
\(173\) | 317.891i | 1.83752i | 0.394814 | + | 0.918761i | \(0.370809\pi\) | ||||
−0.394814 | + | 0.918761i | \(0.629191\pi\) | |||||||
\(174\) | − | 29.0079i | − | 0.166712i | ||||||
\(175\) | −261.288 | −1.49308 | ||||||||
\(176\) | 9.70778i | 0.0551578i | ||||||||
\(177\) | −96.6496 | − | 33.1943i | −0.546043 | − | 0.187538i | ||||
\(178\) | 83.0858 | 0.466774 | ||||||||
\(179\) | 257.362i | 1.43778i | 0.695125 | + | 0.718889i | \(0.255349\pi\) | ||||
−0.695125 | + | 0.718889i | \(0.744651\pi\) | |||||||
\(180\) | −46.2968 | −0.257205 | ||||||||
\(181\) | 25.3182 | 0.139879 | 0.0699397 | − | 0.997551i | \(-0.477719\pi\) | ||||
0.0699397 | + | 0.997551i | \(0.477719\pi\) | |||||||
\(182\) | 222.053 | 1.22007 | ||||||||
\(183\) | 73.8198i | 0.403387i | ||||||||
\(184\) | 88.5690 | 0.481353 | ||||||||
\(185\) | − | 323.126i | − | 1.74662i | ||||||
\(186\) | 19.7811 | 0.106350 | ||||||||
\(187\) | 77.0910i | 0.412252i | ||||||||
\(188\) | 185.464i | 0.986509i | ||||||||
\(189\) | 39.3092 | 0.207985 | ||||||||
\(190\) | 54.1103i | 0.284791i | ||||||||
\(191\) | 221.080i | 1.15749i | 0.815510 | + | 0.578743i | \(0.196457\pi\) | ||||
−0.815510 | + | 0.578743i | \(0.803543\pi\) | |||||||
\(192\) | 13.8564 | 0.0721688 | ||||||||
\(193\) | 57.6741 | 0.298830 | 0.149415 | − | 0.988775i | \(-0.452261\pi\) | ||||
0.149415 | + | 0.988775i | \(0.452261\pi\) | |||||||
\(194\) | 30.0891 | 0.155099 | ||||||||
\(195\) | 277.389i | 1.42251i | ||||||||
\(196\) | −16.4603 | −0.0839813 | ||||||||
\(197\) | −308.022 | −1.56356 | −0.781782 | − | 0.623551i | \(-0.785689\pi\) | ||||
−0.781782 | + | 0.623551i | \(0.785689\pi\) | |||||||
\(198\) | 10.2967 | 0.0520033 | ||||||||
\(199\) | −73.8733 | −0.371223 | −0.185611 | − | 0.982623i | \(-0.559427\pi\) | ||||
−0.185611 | + | 0.982623i | \(0.559427\pi\) | |||||||
\(200\) | 97.6905i | 0.488452i | ||||||||
\(201\) | − | 133.355i | − | 0.663456i | ||||||
\(202\) | −97.4811 | −0.482580 | ||||||||
\(203\) | 89.5886 | 0.441323 | ||||||||
\(204\) | 110.036 | 0.539392 | ||||||||
\(205\) | −342.604 | −1.67124 | ||||||||
\(206\) | 129.137 | 0.626879 | ||||||||
\(207\) | − | 93.9416i | − | 0.453824i | ||||||
\(208\) | − | 83.0213i | − | 0.399141i | ||||||
\(209\) | − | 12.0344i | − | 0.0575809i | ||||||
\(210\) | − | 142.984i | − | 0.680877i | ||||||
\(211\) | 6.70616i | 0.0317828i | 0.999874 | + | 0.0158914i | \(0.00505860\pi\) | ||||
−0.999874 | + | 0.0158914i | \(0.994941\pi\) | |||||||
\(212\) | −90.3199 | −0.426037 | ||||||||
\(213\) | 55.9444 | 0.262650 | ||||||||
\(214\) | − | 195.536i | − | 0.913718i | ||||||
\(215\) | − | 50.7530i | − | 0.236061i | ||||||
\(216\) | − | 14.6969i | − | 0.0680414i | ||||||
\(217\) | 61.0923i | 0.281531i | ||||||||
\(218\) | −172.559 | −0.791557 | ||||||||
\(219\) | − | 206.487i | − | 0.942863i | ||||||
\(220\) | − | 37.4533i | − | 0.170242i | ||||||
\(221\) | − | 659.286i | − | 2.98319i | ||||||
\(222\) | 102.576 | 0.462055 | ||||||||
\(223\) | −38.3888 | −0.172147 | −0.0860735 | − | 0.996289i | \(-0.527432\pi\) | ||||
−0.0860735 | + | 0.996289i | \(0.527432\pi\) | |||||||
\(224\) | 42.7945i | 0.191047i | ||||||||
\(225\) | 103.616 | 0.460517 | ||||||||
\(226\) | 36.6082 | 0.161983 | ||||||||
\(227\) | − | 198.932i | − | 0.876354i | −0.898889 | − | 0.438177i | \(-0.855624\pi\) | ||
0.898889 | − | 0.438177i | \(-0.144376\pi\) | |||||||
\(228\) | −17.1773 | −0.0753392 | ||||||||
\(229\) | − | 176.710i | − | 0.771659i | −0.922570 | − | 0.385830i | \(-0.873915\pi\) | ||
0.922570 | − | 0.385830i | \(-0.126085\pi\) | |||||||
\(230\) | −341.705 | −1.48568 | ||||||||
\(231\) | 31.8004i | 0.137664i | ||||||||
\(232\) | − | 33.4954i | − | 0.144377i | ||||||
\(233\) | 41.0416i | 0.176144i | 0.996114 | + | 0.0880720i | \(0.0280706\pi\) | ||||
−0.996114 | + | 0.0880720i | \(0.971929\pi\) | |||||||
\(234\) | −88.0573 | −0.376313 | ||||||||
\(235\) | − | 715.531i | − | 3.04481i | ||||||
\(236\) | −111.601 | − | 38.3295i | −0.472887 | − | 0.162413i | ||||
\(237\) | −163.487 | −0.689820 | ||||||||
\(238\) | 339.838i | 1.42789i | ||||||||
\(239\) | 8.01774 | 0.0335470 | 0.0167735 | − | 0.999859i | \(-0.494661\pi\) | ||||
0.0167735 | + | 0.999859i | \(0.494661\pi\) | |||||||
\(240\) | −53.4590 | −0.222746 | ||||||||
\(241\) | −95.3184 | −0.395512 | −0.197756 | − | 0.980251i | \(-0.563365\pi\) | ||||
−0.197756 | + | 0.980251i | \(0.563365\pi\) | |||||||
\(242\) | − | 162.790i | − | 0.672686i | ||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 85.2398i | 0.349343i | ||||||||
\(245\) | 63.5051 | 0.259205 | ||||||||
\(246\) | − | 108.760i | − | 0.442113i | ||||||
\(247\) | 102.919i | 0.416675i | ||||||||
\(248\) | 22.8412 | 0.0921016 | ||||||||
\(249\) | − | 187.212i | − | 0.751857i | ||||||
\(250\) | − | 104.090i | − | 0.416360i | ||||||
\(251\) | 58.2290 | 0.231988 | 0.115994 | − | 0.993250i | \(-0.462995\pi\) | ||||
0.115994 | + | 0.993250i | \(0.462995\pi\) | |||||||
\(252\) | 45.3904 | 0.180121 | ||||||||
\(253\) | 75.9970 | 0.300383 | ||||||||
\(254\) | − | 161.527i | − | 0.635935i | ||||||
\(255\) | −424.527 | −1.66481 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 277.153 | 1.07841 | 0.539207 | − | 0.842173i | \(-0.318724\pi\) | ||||
0.539207 | + | 0.842173i | \(0.318724\pi\) | |||||||
\(258\) | 16.1116 | 0.0624479 | ||||||||
\(259\) | 316.799i | 1.22316i | ||||||||
\(260\) | 320.302i | 1.23193i | ||||||||
\(261\) | −35.5273 | −0.136120 | ||||||||
\(262\) | −279.652 | −1.06737 | ||||||||
\(263\) | −250.510 | −0.952510 | −0.476255 | − | 0.879307i | \(-0.658006\pi\) | ||||
−0.476255 | + | 0.879307i | \(0.658006\pi\) | |||||||
\(264\) | 11.8895 | 0.0450362 | ||||||||
\(265\) | 348.460 | 1.31494 | ||||||||
\(266\) | − | 53.0509i | − | 0.199439i | ||||||
\(267\) | − | 101.759i | − | 0.381119i | ||||||
\(268\) | − | 153.985i | − | 0.574570i | ||||||
\(269\) | 475.178i | 1.76646i | 0.468939 | + | 0.883231i | \(0.344637\pi\) | ||||
−0.468939 | + | 0.883231i | \(0.655363\pi\) | |||||||
\(270\) | 56.7018i | 0.210007i | ||||||||
\(271\) | −224.434 | −0.828171 | −0.414085 | − | 0.910238i | \(-0.635899\pi\) | ||||
−0.414085 | + | 0.910238i | \(0.635899\pi\) | |||||||
\(272\) | 127.059 | 0.467127 | ||||||||
\(273\) | − | 271.958i | − | 0.996185i | ||||||
\(274\) | 230.619i | 0.841675i | ||||||||
\(275\) | 83.8237i | 0.304814i | ||||||||
\(276\) | − | 108.474i | − | 0.393023i | ||||||
\(277\) | −232.425 | −0.839079 | −0.419539 | − | 0.907737i | \(-0.637808\pi\) | ||||
−0.419539 | + | 0.907737i | \(0.637808\pi\) | |||||||
\(278\) | 109.350i | 0.393345i | ||||||||
\(279\) | − | 24.2268i | − | 0.0868342i | ||||||
\(280\) | − | 165.104i | − | 0.589657i | ||||||
\(281\) | 46.3684 | 0.165012 | 0.0825060 | − | 0.996591i | \(-0.473708\pi\) | ||||
0.0825060 | + | 0.996591i | \(0.473708\pi\) | |||||||
\(282\) | 227.146 | 0.805481 | ||||||||
\(283\) | 190.008i | 0.671407i | 0.941968 | + | 0.335703i | \(0.108974\pi\) | ||||
−0.941968 | + | 0.335703i | \(0.891026\pi\) | |||||||
\(284\) | 64.5990 | 0.227461 | ||||||||
\(285\) | 66.2714 | 0.232531 | ||||||||
\(286\) | − | 71.2367i | − | 0.249080i | ||||||
\(287\) | 335.897 | 1.17037 | ||||||||
\(288\) | − | 16.9706i | − | 0.0589256i | ||||||
\(289\) | 719.994 | 2.49133 | ||||||||
\(290\) | 129.228i | 0.445613i | ||||||||
\(291\) | − | 36.8515i | − | 0.126638i | ||||||
\(292\) | − | 238.431i | − | 0.816543i | ||||||
\(293\) | 380.760 | 1.29952 | 0.649761 | − | 0.760139i | \(-0.274869\pi\) | ||||
0.649761 | + | 0.760139i | \(0.274869\pi\) | |||||||
\(294\) | 20.1597i | 0.0685704i | ||||||||
\(295\) | 430.566 | + | 147.878i | 1.45954 | + | 0.501281i | ||||
\(296\) | 118.445 | 0.400152 | ||||||||
\(297\) | − | 12.6108i | − | 0.0424605i | ||||||
\(298\) | 18.0413 | 0.0605413 | ||||||||
\(299\) | −649.929 | −2.17368 | ||||||||
\(300\) | 119.646 | 0.398820 | ||||||||
\(301\) | 49.7593i | 0.165313i | ||||||||
\(302\) | −175.751 | −0.581957 | ||||||||
\(303\) | 119.389i | 0.394025i | ||||||||
\(304\) | −19.8347 | −0.0652457 | ||||||||
\(305\) | − | 328.861i | − | 1.07823i | ||||||
\(306\) | − | 134.766i | − | 0.440412i | ||||||
\(307\) | −67.6965 | −0.220510 | −0.110255 | − | 0.993903i | \(-0.535167\pi\) | ||||
−0.110255 | + | 0.993903i | \(0.535167\pi\) | |||||||
\(308\) | 36.7200i | 0.119221i | ||||||||
\(309\) | − | 158.160i | − | 0.511844i | ||||||
\(310\) | −88.1229 | −0.284268 | ||||||||
\(311\) | 143.194 | 0.460430 | 0.230215 | − | 0.973140i | \(-0.426057\pi\) | ||||
0.230215 | + | 0.973140i | \(0.426057\pi\) | |||||||
\(312\) | −101.680 | −0.325897 | ||||||||
\(313\) | − | 233.140i | − | 0.744857i | −0.928061 | − | 0.372428i | \(-0.878525\pi\) | ||
0.928061 | − | 0.372428i | \(-0.121475\pi\) | |||||||
\(314\) | 387.005 | 1.23250 | ||||||||
\(315\) | −175.119 | −0.555934 | ||||||||
\(316\) | −188.779 | −0.597402 | ||||||||
\(317\) | 141.408 | 0.446083 | 0.223042 | − | 0.974809i | \(-0.428401\pi\) | ||||
0.223042 | + | 0.974809i | \(0.428401\pi\) | |||||||
\(318\) | 110.619i | 0.347858i | ||||||||
\(319\) | − | 28.7409i | − | 0.0900968i | ||||||
\(320\) | −61.7291 | −0.192903 | ||||||||
\(321\) | −239.481 | −0.746048 | ||||||||
\(322\) | 335.015 | 1.04042 | ||||||||
\(323\) | −157.510 | −0.487649 | ||||||||
\(324\) | −18.0000 | −0.0555556 | ||||||||
\(325\) | − | 716.864i | − | 2.20573i | ||||||
\(326\) | − | 297.185i | − | 0.911609i | ||||||
\(327\) | 211.341i | 0.646304i | ||||||||
\(328\) | − | 125.585i | − | 0.382881i | ||||||
\(329\) | 701.522i | 2.13229i | ||||||||
\(330\) | −45.8707 | −0.139002 | ||||||||
\(331\) | −239.335 | −0.723067 | −0.361533 | − | 0.932359i | \(-0.617747\pi\) | ||||
−0.361533 | + | 0.932359i | \(0.617747\pi\) | |||||||
\(332\) | − | 216.174i | − | 0.651127i | ||||||
\(333\) | − | 125.630i | − | 0.377267i | ||||||
\(334\) | 239.735i | 0.717769i | ||||||||
\(335\) | 594.084i | 1.77338i | ||||||||
\(336\) | 52.4123 | 0.155989 | ||||||||
\(337\) | 89.3149i | 0.265029i | 0.991181 | + | 0.132515i | \(0.0423052\pi\) | ||||
−0.991181 | + | 0.132515i | \(0.957695\pi\) | |||||||
\(338\) | 370.217i | 1.09532i | ||||||||
\(339\) | − | 44.8357i | − | 0.132259i | ||||||
\(340\) | −490.201 | −1.44177 | ||||||||
\(341\) | 19.5990 | 0.0574750 | ||||||||
\(342\) | 21.0379i | 0.0615142i | ||||||||
\(343\) | 308.426 | 0.899202 | ||||||||
\(344\) | 18.6040 | 0.0540815 | ||||||||
\(345\) | 418.502i | 1.21305i | ||||||||
\(346\) | 449.566 | 1.29932 | ||||||||
\(347\) | − | 243.475i | − | 0.701657i | −0.936440 | − | 0.350829i | \(-0.885900\pi\) | ||
0.936440 | − | 0.350829i | \(-0.114100\pi\) | |||||||
\(348\) | −41.0233 | −0.117883 | ||||||||
\(349\) | 179.758i | 0.515065i | 0.966270 | + | 0.257533i | \(0.0829095\pi\) | ||||
−0.966270 | + | 0.257533i | \(0.917090\pi\) | |||||||
\(350\) | 369.517i | 1.05576i | ||||||||
\(351\) | 107.848i | 0.307259i | ||||||||
\(352\) | 13.7289 | 0.0390025 | ||||||||
\(353\) | − | 562.170i | − | 1.59255i | −0.604935 | − | 0.796275i | \(-0.706801\pi\) | ||
0.604935 | − | 0.796275i | \(-0.293199\pi\) | |||||||
\(354\) | −46.9438 | + | 136.683i | −0.132610 | + | 0.386111i | ||||
\(355\) | −249.227 | −0.702049 | ||||||||
\(356\) | − | 117.501i | − | 0.330059i | ||||||
\(357\) | 416.215 | 1.16587 | ||||||||
\(358\) | 363.965 | 1.01666 | ||||||||
\(359\) | −458.013 | −1.27580 | −0.637901 | − | 0.770118i | \(-0.720197\pi\) | ||||
−0.637901 | + | 0.770118i | \(0.720197\pi\) | |||||||
\(360\) | 65.4736i | 0.181871i | ||||||||
\(361\) | −336.412 | −0.931888 | ||||||||
\(362\) | − | 35.8053i | − | 0.0989097i | ||||||
\(363\) | −199.376 | −0.549246 | ||||||||
\(364\) | − | 314.031i | − | 0.862721i | ||||||
\(365\) | 919.882i | 2.52022i | ||||||||
\(366\) | 104.397 | 0.285238 | ||||||||
\(367\) | − | 320.619i | − | 0.873622i | −0.899553 | − | 0.436811i | \(-0.856108\pi\) | ||
0.899553 | − | 0.436811i | \(-0.143892\pi\) | |||||||
\(368\) | − | 125.255i | − | 0.340368i | ||||||
\(369\) | −133.203 | −0.360984 | ||||||||
\(370\) | −456.969 | −1.23505 | ||||||||
\(371\) | −341.638 | −0.920856 | ||||||||
\(372\) | − | 27.9746i | − | 0.0752007i | ||||||
\(373\) | 517.511 | 1.38743 | 0.693714 | − | 0.720250i | \(-0.255973\pi\) | ||||
0.693714 | + | 0.720250i | \(0.255973\pi\) | |||||||
\(374\) | 109.023 | 0.291506 | ||||||||
\(375\) | −127.484 | −0.339956 | ||||||||
\(376\) | 262.285 | 0.697567 | ||||||||
\(377\) | 245.793i | 0.651971i | ||||||||
\(378\) | − | 55.5916i | − | 0.147068i | ||||||
\(379\) | −130.956 | −0.345530 | −0.172765 | − | 0.984963i | \(-0.555270\pi\) | ||||
−0.172765 | + | 0.984963i | \(0.555270\pi\) | |||||||
\(380\) | 76.5236 | 0.201378 | ||||||||
\(381\) | −197.830 | −0.519239 | ||||||||
\(382\) | 312.654 | 0.818466 | ||||||||
\(383\) | 380.323 | 0.993011 | 0.496505 | − | 0.868034i | \(-0.334616\pi\) | ||||
0.496505 | + | 0.868034i | \(0.334616\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | − | 141.668i | − | 0.367969i | ||||||
\(386\) | − | 81.5635i | − | 0.211304i | ||||||
\(387\) | − | 19.7325i | − | 0.0509885i | ||||||
\(388\) | − | 42.5525i | − | 0.109671i | ||||||
\(389\) | −432.621 | −1.11214 | −0.556068 | − | 0.831137i | \(-0.687691\pi\) | ||||
−0.556068 | + | 0.831137i | \(0.687691\pi\) | |||||||
\(390\) | 392.288 | 1.00587 | ||||||||
\(391\) | − | 994.674i | − | 2.54392i | ||||||
\(392\) | 23.2784i | 0.0593837i | ||||||||
\(393\) | 342.502i | 0.871506i | ||||||||
\(394\) | 435.609i | 1.10561i | ||||||||
\(395\) | 728.323 | 1.84385 | ||||||||
\(396\) | − | 14.5617i | − | 0.0367719i | ||||||
\(397\) | − | 438.440i | − | 1.10438i | −0.833717 | − | 0.552191i | \(-0.813792\pi\) | ||
0.833717 | − | 0.552191i | \(-0.186208\pi\) | |||||||
\(398\) | 104.473i | 0.262494i | ||||||||
\(399\) | −64.9738 | −0.162842 | ||||||||
\(400\) | 138.155 | 0.345388 | ||||||||
\(401\) | − | 177.376i | − | 0.442334i | −0.975236 | − | 0.221167i | \(-0.929013\pi\) | ||
0.975236 | − | 0.221167i | \(-0.0709867\pi\) | |||||||
\(402\) | −188.592 | −0.469134 | ||||||||
\(403\) | −167.611 | −0.415909 | ||||||||
\(404\) | 137.859i | 0.341235i | ||||||||
\(405\) | 69.4452 | 0.171470 | ||||||||
\(406\) | − | 126.697i | − | 0.312063i | ||||||
\(407\) | 101.632 | 0.249710 | ||||||||
\(408\) | − | 155.614i | − | 0.381408i | ||||||
\(409\) | 598.274i | 1.46277i | 0.681963 | + | 0.731387i | \(0.261126\pi\) | ||||
−0.681963 | + | 0.731387i | \(0.738874\pi\) | |||||||
\(410\) | 484.516i | 1.18175i | ||||||||
\(411\) | 282.449 | 0.687225 | ||||||||
\(412\) | − | 182.627i | − | 0.443270i | ||||||
\(413\) | −422.135 | − | 144.982i | −1.02212 | − | 0.351047i | ||||
\(414\) | −132.853 | −0.320902 | ||||||||
\(415\) | 834.015i | 2.00968i | ||||||||
\(416\) | −117.410 | −0.282235 | ||||||||
\(417\) | 133.926 | 0.321165 | ||||||||
\(418\) | −17.0192 | −0.0407159 | ||||||||
\(419\) | 415.349i | 0.991287i | 0.868526 | + | 0.495643i | \(0.165068\pi\) | ||||
−0.868526 | + | 0.495643i | \(0.834932\pi\) | |||||||
\(420\) | −202.210 | −0.481453 | ||||||||
\(421\) | 102.071i | 0.242448i | 0.992625 | + | 0.121224i | \(0.0386819\pi\) | ||||
−0.992625 | + | 0.121224i | \(0.961318\pi\) | |||||||
\(422\) | 9.48395 | 0.0224738 | ||||||||
\(423\) | − | 278.195i | − | 0.657672i | ||||||
\(424\) | 127.732i | 0.301254i | ||||||||
\(425\) | 1097.11 | 2.58144 | ||||||||
\(426\) | − | 79.1173i | − | 0.185721i | ||||||
\(427\) | 322.422i | 0.755087i | ||||||||
\(428\) | −276.529 | −0.646096 | ||||||||
\(429\) | −87.2468 | −0.203373 | ||||||||
\(430\) | −71.7756 | −0.166920 | ||||||||
\(431\) | − | 541.413i | − | 1.25618i | −0.778141 | − | 0.628090i | \(-0.783837\pi\) | ||
0.778141 | − | 0.628090i | \(-0.216163\pi\) | |||||||
\(432\) | −20.7846 | −0.0481125 | ||||||||
\(433\) | 569.163 | 1.31446 | 0.657232 | − | 0.753688i | \(-0.271727\pi\) | ||||
0.657232 | + | 0.753688i | \(0.271727\pi\) | |||||||
\(434\) | 86.3976 | 0.199073 | ||||||||
\(435\) | 158.271 | 0.363841 | ||||||||
\(436\) | 244.036i | 0.559715i | ||||||||
\(437\) | 155.275i | 0.355321i | ||||||||
\(438\) | −292.017 | −0.666705 | ||||||||
\(439\) | 30.3026 | 0.0690263 | 0.0345132 | − | 0.999404i | \(-0.489012\pi\) | ||||
0.0345132 | + | 0.999404i | \(0.489012\pi\) | |||||||
\(440\) | −52.9669 | −0.120379 | ||||||||
\(441\) | 24.6905 | 0.0559875 | ||||||||
\(442\) | −932.371 | −2.10944 | ||||||||
\(443\) | 765.726i | 1.72850i | 0.503061 | + | 0.864251i | \(0.332207\pi\) | ||||
−0.503061 | + | 0.864251i | \(0.667793\pi\) | |||||||
\(444\) | − | 145.065i | − | 0.326722i | ||||||
\(445\) | 453.327i | 1.01871i | ||||||||
\(446\) | 54.2899i | 0.121726i | ||||||||
\(447\) | − | 22.0960i | − | 0.0494318i | ||||||
\(448\) | 60.5205 | 0.135090 | ||||||||
\(449\) | 801.900 | 1.78597 | 0.892985 | − | 0.450087i | \(-0.148607\pi\) | ||||
0.892985 | + | 0.450087i | \(0.148607\pi\) | |||||||
\(450\) | − | 146.536i | − | 0.325635i | ||||||
\(451\) | − | 107.759i | − | 0.238933i | ||||||
\(452\) | − | 51.7718i | − | 0.114539i | ||||||
\(453\) | 215.250i | 0.475166i | ||||||||
\(454\) | −281.333 | −0.619676 | ||||||||
\(455\) | 1211.55i | 2.66275i | ||||||||
\(456\) | 24.2924i | 0.0532729i | ||||||||
\(457\) | − | 25.7788i | − | 0.0564087i | −0.999602 | − | 0.0282043i | \(-0.991021\pi\) | ||
0.999602 | − | 0.0282043i | \(-0.00897891\pi\) | |||||||
\(458\) | −249.906 | −0.545645 | ||||||||
\(459\) | −165.054 | −0.359595 | ||||||||
\(460\) | 483.244i | 1.05053i | ||||||||
\(461\) | −589.030 | −1.27772 | −0.638861 | − | 0.769322i | \(-0.720594\pi\) | ||||
−0.638861 | + | 0.769322i | \(0.720594\pi\) | |||||||
\(462\) | 44.9726 | 0.0973433 | ||||||||
\(463\) | 668.771i | 1.44443i | 0.691669 | + | 0.722215i | \(0.256876\pi\) | ||||
−0.691669 | + | 0.722215i | \(0.743124\pi\) | |||||||
\(464\) | −47.3697 | −0.102090 | ||||||||
\(465\) | 107.928i | 0.232103i | ||||||||
\(466\) | 58.0415 | 0.124553 | ||||||||
\(467\) | − | 294.089i | − | 0.629741i | −0.949135 | − | 0.314871i | \(-0.898039\pi\) | ||
0.949135 | − | 0.314871i | \(-0.101961\pi\) | |||||||
\(468\) | 124.532i | 0.266094i | ||||||||
\(469\) | − | 582.452i | − | 1.24190i | ||||||
\(470\) | −1011.91 | −2.15301 | ||||||||
\(471\) | − | 473.982i | − | 1.00633i | ||||||
\(472\) | −54.2061 | + | 157.828i | −0.114843 | + | 0.334382i | ||||
\(473\) | 15.9633 | 0.0337490 | ||||||||
\(474\) | 231.206i | 0.487777i | ||||||||
\(475\) | −171.267 | −0.360561 | ||||||||
\(476\) | 480.603 | 1.00967 | ||||||||
\(477\) | 135.480 | 0.284025 | ||||||||
\(478\) | − | 11.3388i | − | 0.0237213i | ||||||
\(479\) | −24.8902 | −0.0519629 | −0.0259814 | − | 0.999662i | \(-0.508271\pi\) | ||||
−0.0259814 | + | 0.999662i | \(0.508271\pi\) | |||||||
\(480\) | 75.6024i | 0.157505i | ||||||||
\(481\) | −869.162 | −1.80699 | ||||||||
\(482\) | 134.801i | 0.279669i | ||||||||
\(483\) | − | 410.308i | − | 0.849499i | ||||||
\(484\) | −230.220 | −0.475661 | ||||||||
\(485\) | 164.170i | 0.338496i | ||||||||
\(486\) | 22.0454i | 0.0453609i | ||||||||
\(487\) | 745.105 | 1.52999 | 0.764995 | − | 0.644037i | \(-0.222742\pi\) | ||||
0.764995 | + | 0.644037i | \(0.222742\pi\) | |||||||
\(488\) | 120.547 | 0.247023 | ||||||||
\(489\) | −363.975 | −0.744326 | ||||||||
\(490\) | − | 89.8098i | − | 0.183285i | ||||||
\(491\) | −896.795 | −1.82647 | −0.913233 | − | 0.407437i | \(-0.866423\pi\) | ||||
−0.913233 | + | 0.407437i | \(0.866423\pi\) | |||||||
\(492\) | −153.810 | −0.312621 | ||||||||
\(493\) | −376.170 | −0.763023 | ||||||||
\(494\) | 145.549 | 0.294634 | ||||||||
\(495\) | 56.1799i | 0.113495i | ||||||||
\(496\) | − | 32.3023i | − | 0.0651257i | ||||||
\(497\) | 244.348 | 0.491645 | ||||||||
\(498\) | −264.758 | −0.531643 | ||||||||
\(499\) | 844.318 | 1.69202 | 0.846010 | − | 0.533167i | \(-0.178998\pi\) | ||||
0.846010 | + | 0.533167i | \(0.178998\pi\) | |||||||
\(500\) | −147.205 | −0.294411 | ||||||||
\(501\) | 293.614 | 0.586056 | ||||||||
\(502\) | − | 82.3482i | − | 0.164040i | ||||||
\(503\) | − | 456.901i | − | 0.908352i | −0.890912 | − | 0.454176i | \(-0.849934\pi\) | ||
0.890912 | − | 0.454176i | \(-0.150066\pi\) | |||||||
\(504\) | − | 64.1917i | − | 0.127364i | ||||||
\(505\) | − | 531.870i | − | 1.05321i | ||||||
\(506\) | − | 107.476i | − | 0.212403i | ||||||
\(507\) | 453.422 | 0.894323 | ||||||||
\(508\) | −228.434 | −0.449674 | ||||||||
\(509\) | − | 369.383i | − | 0.725704i | −0.931847 | − | 0.362852i | \(-0.881803\pi\) | ||
0.931847 | − | 0.362852i | \(-0.118197\pi\) | |||||||
\(510\) | 600.371i | 1.17720i | ||||||||
\(511\) | − | 901.871i | − | 1.76491i | ||||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | 25.7660 | 0.0502261 | ||||||||
\(514\) | − | 391.953i | − | 0.762555i | ||||||
\(515\) | 704.589i | 1.36813i | ||||||||
\(516\) | − | 22.7852i | − | 0.0441573i | ||||||
\(517\) | 225.055 | 0.435309 | ||||||||
\(518\) | 448.021 | 0.864906 | ||||||||
\(519\) | − | 550.604i | − | 1.06089i | ||||||
\(520\) | 452.975 | 0.871106 | ||||||||
\(521\) | 700.980 | 1.34545 | 0.672725 | − | 0.739892i | \(-0.265124\pi\) | ||||
0.672725 | + | 0.739892i | \(0.265124\pi\) | |||||||
\(522\) | 50.2431i | 0.0962512i | ||||||||
\(523\) | 65.5084 | 0.125255 | 0.0626275 | − | 0.998037i | \(-0.480052\pi\) | ||||
0.0626275 | + | 0.998037i | \(0.480052\pi\) | |||||||
\(524\) | 395.487i | 0.754746i | ||||||||
\(525\) | 452.564 | 0.862027 | ||||||||
\(526\) | 354.275i | 0.673526i | ||||||||
\(527\) | − | 256.518i | − | 0.486752i | ||||||
\(528\) | − | 16.8144i | − | 0.0318454i | ||||||
\(529\) | −451.558 | −0.853607 | ||||||||
\(530\) | − | 492.797i | − | 0.929806i | ||||||
\(531\) | 167.402 | + | 57.4942i | 0.315258 | + | 0.108275i | ||||
\(532\) | −75.0253 | −0.141025 | ||||||||
\(533\) | 921.557i | 1.72900i | ||||||||
\(534\) | −143.909 | −0.269492 | ||||||||
\(535\) | 1066.87 | 1.99415 | ||||||||
\(536\) | −217.767 | −0.406282 | ||||||||
\(537\) | − | 445.764i | − | 0.830101i | ||||||
\(538\) | 672.003 | 1.24908 | ||||||||
\(539\) | 19.9742i | 0.0370578i | ||||||||
\(540\) | 80.1885 | 0.148497 | ||||||||
\(541\) | 664.599i | 1.22846i | 0.789126 | + | 0.614232i | \(0.210534\pi\) | ||||
−0.789126 | + | 0.614232i | \(0.789466\pi\) | |||||||
\(542\) | 317.398i | 0.585605i | ||||||||
\(543\) | −43.8524 | −0.0807594 | ||||||||
\(544\) | − | 179.688i | − | 0.330309i | ||||||
\(545\) | − | 941.507i | − | 1.72754i | ||||||
\(546\) | −384.607 | −0.704409 | ||||||||
\(547\) | −202.532 | −0.370260 | −0.185130 | − | 0.982714i | \(-0.559271\pi\) | ||||
−0.185130 | + | 0.982714i | \(0.559271\pi\) | |||||||
\(548\) | 326.144 | 0.595154 | ||||||||
\(549\) | − | 127.860i | − | 0.232896i | ||||||
\(550\) | 118.545 | 0.215536 | ||||||||
\(551\) | 58.7227 | 0.106575 | ||||||||
\(552\) | −153.406 | −0.277909 | ||||||||
\(553\) | −714.063 | −1.29125 | ||||||||
\(554\) | 328.698i | 0.593318i | ||||||||
\(555\) | 559.670i | 1.00841i | ||||||||
\(556\) | 154.644 | 0.278137 | ||||||||
\(557\) | −805.762 | −1.44661 | −0.723305 | − | 0.690529i | \(-0.757378\pi\) | ||||
−0.723305 | + | 0.690529i | \(0.757378\pi\) | |||||||
\(558\) | −34.2618 | −0.0614011 | ||||||||
\(559\) | −136.518 | −0.244219 | ||||||||
\(560\) | −233.492 | −0.416950 | ||||||||
\(561\) | − | 133.526i | − | 0.238014i | ||||||
\(562\) | − | 65.5748i | − | 0.116681i | ||||||
\(563\) | − | 36.2162i | − | 0.0643272i | −0.999483 | − | 0.0321636i | \(-0.989760\pi\) | ||
0.999483 | − | 0.0321636i | \(-0.0102398\pi\) | |||||||
\(564\) | − | 321.232i | − | 0.569561i | ||||||
\(565\) | 199.739i | 0.353521i | ||||||||
\(566\) | 268.712 | 0.474756 | ||||||||
\(567\) | −68.0856 | −0.120080 | ||||||||
\(568\) | − | 91.3568i | − | 0.160839i | ||||||
\(569\) | − | 657.898i | − | 1.15624i | −0.815953 | − | 0.578118i | \(-0.803787\pi\) | ||
0.815953 | − | 0.578118i | \(-0.196213\pi\) | |||||||
\(570\) | − | 93.7219i | − | 0.164424i | ||||||
\(571\) | 594.370i | 1.04093i | 0.853884 | + | 0.520464i | \(0.174241\pi\) | ||||
−0.853884 | + | 0.520464i | \(0.825759\pi\) | |||||||
\(572\) | −100.744 | −0.176126 | ||||||||
\(573\) | − | 382.921i | − | 0.668275i | ||||||
\(574\) | − | 475.029i | − | 0.827577i | ||||||
\(575\) | − | 1081.54i | − | 1.88094i | ||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | −842.498 | −1.46014 | −0.730068 | − | 0.683375i | \(-0.760512\pi\) | ||||
−0.730068 | + | 0.683375i | \(0.760512\pi\) | |||||||
\(578\) | − | 1018.22i | − | 1.76163i | ||||||
\(579\) | −99.8945 | −0.172529 | ||||||||
\(580\) | 182.755 | 0.315096 | ||||||||
\(581\) | − | 817.686i | − | 1.40738i | ||||||
\(582\) | −52.1159 | −0.0895462 | ||||||||
\(583\) | 109.601i | 0.187994i | ||||||||
\(584\) | −337.192 | −0.577383 | ||||||||
\(585\) | − | 480.453i | − | 0.821287i | ||||||
\(586\) | − | 538.476i | − | 0.918901i | ||||||
\(587\) | − | 917.410i | − | 1.56288i | −0.623981 | − | 0.781439i | \(-0.714486\pi\) | ||
0.623981 | − | 0.781439i | \(-0.285514\pi\) | |||||||
\(588\) | 28.5101 | 0.0484866 | ||||||||
\(589\) | 40.0442i | 0.0679867i | ||||||||
\(590\) | 209.131 | − | 608.912i | 0.354459 | − | 1.03205i | ||||
\(591\) | 533.510 | 0.902724 | ||||||||
\(592\) | − | 167.506i | − | 0.282950i | ||||||
\(593\) | 721.800 | 1.21720 | 0.608600 | − | 0.793477i | \(-0.291731\pi\) | ||||
0.608600 | + | 0.793477i | \(0.291731\pi\) | |||||||
\(594\) | −17.8343 | −0.0300241 | ||||||||
\(595\) | −1854.20 | −3.11630 | ||||||||
\(596\) | − | 25.5143i | − | 0.0428092i | ||||||
\(597\) | 127.952 | 0.214325 | ||||||||
\(598\) | 919.139i | 1.53702i | ||||||||
\(599\) | −439.404 | −0.733562 | −0.366781 | − | 0.930307i | \(-0.619540\pi\) | ||||
−0.366781 | + | 0.930307i | \(0.619540\pi\) | |||||||
\(600\) | − | 169.205i | − | 0.282008i | ||||||
\(601\) | 657.294i | 1.09367i | 0.837241 | + | 0.546834i | \(0.184167\pi\) | ||||
−0.837241 | + | 0.546834i | \(0.815833\pi\) | |||||||
\(602\) | 70.3703 | 0.116894 | ||||||||
\(603\) | 230.977i | 0.383046i | ||||||||
\(604\) | 248.549i | 0.411506i | ||||||||
\(605\) | 888.204 | 1.46811 | ||||||||
\(606\) | 168.842 | 0.278618 | ||||||||
\(607\) | 1173.83 | 1.93383 | 0.966913 | − | 0.255108i | \(-0.0821110\pi\) | ||||
0.966913 | + | 0.255108i | \(0.0821110\pi\) | |||||||
\(608\) | 28.0505i | 0.0461357i | ||||||||
\(609\) | −155.172 | −0.254798 | ||||||||
\(610\) | −465.080 | −0.762426 | ||||||||
\(611\) | −1924.68 | −3.15005 | ||||||||
\(612\) | −190.588 | −0.311418 | ||||||||
\(613\) | 872.138i | 1.42274i | 0.702819 | + | 0.711369i | \(0.251924\pi\) | ||||
−0.702819 | + | 0.711369i | \(0.748076\pi\) | |||||||
\(614\) | 95.7373i | 0.155924i | ||||||||
\(615\) | 593.408 | 0.964892 | ||||||||
\(616\) | 51.9299 | 0.0843017 | ||||||||
\(617\) | 668.521 | 1.08350 | 0.541751 | − | 0.840539i | \(-0.317762\pi\) | ||||
0.541751 | + | 0.840539i | \(0.317762\pi\) | |||||||
\(618\) | −223.672 | −0.361929 | ||||||||
\(619\) | 268.471 | 0.433717 | 0.216858 | − | 0.976203i | \(-0.430419\pi\) | ||||
0.216858 | + | 0.976203i | \(0.430419\pi\) | |||||||
\(620\) | 124.625i | 0.201008i | ||||||||
\(621\) | 162.712i | 0.262015i | ||||||||
\(622\) | − | 202.506i | − | 0.325573i | ||||||
\(623\) | − | 444.451i | − | 0.713405i | ||||||
\(624\) | 143.797i | 0.230444i | ||||||||
\(625\) | −295.541 | −0.472866 | ||||||||
\(626\) | −329.710 | −0.526693 | ||||||||
\(627\) | 20.8442i | 0.0332444i | ||||||||
\(628\) | − | 547.307i | − | 0.871508i | ||||||
\(629\) | − | 1330.20i | − | 2.11478i | ||||||
\(630\) | 247.656i | 0.393105i | ||||||||
\(631\) | 754.307 | 1.19542 | 0.597708 | − | 0.801714i | \(-0.296078\pi\) | ||||
0.597708 | + | 0.801714i | \(0.296078\pi\) | |||||||
\(632\) | 266.974i | 0.422427i | ||||||||
\(633\) | − | 11.6154i | − | 0.0183498i | ||||||
\(634\) | − | 199.982i | − | 0.315429i | ||||||
\(635\) | 881.315 | 1.38790 | ||||||||
\(636\) | 156.439 | 0.245973 | ||||||||
\(637\) | − | 170.820i | − | 0.268163i | ||||||
\(638\) | −40.6457 | −0.0637081 | ||||||||
\(639\) | −96.8985 | −0.151641 | ||||||||
\(640\) | 87.2981i | 0.136403i | ||||||||
\(641\) | 969.139 | 1.51192 | 0.755958 | − | 0.654620i | \(-0.227171\pi\) | ||||
0.755958 | + | 0.654620i | \(0.227171\pi\) | |||||||
\(642\) | 338.678i | 0.527535i | ||||||||
\(643\) | −487.180 | −0.757667 | −0.378833 | − | 0.925465i | \(-0.623675\pi\) | ||||
−0.378833 | + | 0.925465i | \(0.623675\pi\) | |||||||
\(644\) | − | 473.783i | − | 0.735687i | ||||||
\(645\) | 87.9068i | 0.136290i | ||||||||
\(646\) | 222.753i | 0.344820i | ||||||||
\(647\) | −54.3687 | −0.0840321 | −0.0420160 | − | 0.999117i | \(-0.513378\pi\) | ||||
−0.0420160 | + | 0.999117i | \(0.513378\pi\) | |||||||
\(648\) | 25.4558i | 0.0392837i | ||||||||
\(649\) | −46.5118 | + | 135.425i | −0.0716668 | + | 0.208667i | ||||
\(650\) | −1013.80 | −1.55969 | ||||||||
\(651\) | − | 105.815i | − | 0.162542i | ||||||
\(652\) | −420.282 | −0.644605 | ||||||||
\(653\) | 367.514 | 0.562809 | 0.281404 | − | 0.959589i | \(-0.409200\pi\) | ||||
0.281404 | + | 0.959589i | \(0.409200\pi\) | |||||||
\(654\) | 298.882 | 0.457006 | ||||||||
\(655\) | − | 1525.82i | − | 2.32949i | ||||||
\(656\) | −177.604 | −0.270738 | ||||||||
\(657\) | 357.646i | 0.544362i | ||||||||
\(658\) | 992.102 | 1.50775 | ||||||||
\(659\) | 581.630i | 0.882595i | 0.897361 | + | 0.441297i | \(0.145482\pi\) | ||||
−0.897361 | + | 0.441297i | \(0.854518\pi\) | |||||||
\(660\) | 64.8710i | 0.0982893i | ||||||||
\(661\) | 199.768 | 0.302222 | 0.151111 | − | 0.988517i | \(-0.451715\pi\) | ||||
0.151111 | + | 0.988517i | \(0.451715\pi\) | |||||||
\(662\) | 338.471i | 0.511285i | ||||||||
\(663\) | 1141.92i | 1.72235i | ||||||||
\(664\) | −305.717 | −0.460417 | ||||||||
\(665\) | 289.453 | 0.435267 | ||||||||
\(666\) | −177.667 | −0.266768 | ||||||||
\(667\) | 370.832i | 0.555970i | ||||||||
\(668\) | 339.036 | 0.507539 | ||||||||
\(669\) | 66.4913 | 0.0993891 | ||||||||
\(670\) | 840.161 | 1.25397 | ||||||||
\(671\) | 103.436 | 0.154152 | ||||||||
\(672\) | − | 74.1222i | − | 0.110301i | ||||||
\(673\) | − | 103.561i | − | 0.153880i | −0.997036 | − | 0.0769400i | \(-0.975485\pi\) | ||
0.997036 | − | 0.0769400i | \(-0.0245150\pi\) | |||||||
\(674\) | 126.310 | 0.187404 | ||||||||
\(675\) | −179.469 | −0.265880 | ||||||||
\(676\) | 523.566 | 0.774506 | ||||||||
\(677\) | −452.064 | −0.667746 | −0.333873 | − | 0.942618i | \(-0.608356\pi\) | ||||
−0.333873 | + | 0.942618i | \(0.608356\pi\) | |||||||
\(678\) | −63.4073 | −0.0935211 | ||||||||
\(679\) | − | 160.956i | − | 0.237049i | ||||||
\(680\) | 693.249i | 1.01948i | ||||||||
\(681\) | 344.561i | 0.505963i | ||||||||
\(682\) | − | 27.7172i | − | 0.0406410i | ||||||
\(683\) | − | 604.103i | − | 0.884485i | −0.896895 | − | 0.442243i | \(-0.854183\pi\) | ||
0.896895 | − | 0.442243i | \(-0.145817\pi\) | |||||||
\(684\) | 29.7520 | 0.0434971 | ||||||||
\(685\) | −1258.29 | −1.83692 | ||||||||
\(686\) | − | 436.181i | − | 0.635832i | ||||||
\(687\) | 306.071i | 0.445518i | ||||||||
\(688\) | − | 26.3101i | − | 0.0382414i | ||||||
\(689\) | − | 937.309i | − | 1.36039i | ||||||
\(690\) | 591.851 | 0.857755 | ||||||||
\(691\) | − | 146.347i | − | 0.211790i | −0.994377 | − | 0.105895i | \(-0.966229\pi\) | ||
0.994377 | − | 0.105895i | \(-0.0337707\pi\) | |||||||
\(692\) | − | 635.783i | − | 0.918761i | ||||||
\(693\) | − | 55.0799i | − | 0.0794804i | ||||||
\(694\) | −344.326 | −0.496147 | ||||||||
\(695\) | −596.628 | −0.858458 | ||||||||
\(696\) | 58.0158i | 0.0833560i | ||||||||
\(697\) | −1410.38 | −2.02351 | ||||||||
\(698\) | 254.216 | 0.364206 | ||||||||
\(699\) | − | 71.0861i | − | 0.101697i | ||||||
\(700\) | 522.576 | 0.746538 | ||||||||
\(701\) | 429.224i | 0.612302i | 0.951983 | + | 0.306151i | \(0.0990413\pi\) | ||||
−0.951983 | + | 0.306151i | \(0.900959\pi\) | |||||||
\(702\) | 152.520 | 0.217265 | ||||||||
\(703\) | 207.652i | 0.295380i | ||||||||
\(704\) | − | 19.4156i | − | 0.0275789i | ||||||
\(705\) | 1239.34i | 1.75792i | ||||||||
\(706\) | −795.028 | −1.12610 | ||||||||
\(707\) | 521.456i | 0.737562i | ||||||||
\(708\) | 193.299 | + | 66.3886i | 0.273021 | + | 0.0937692i | ||||
\(709\) | −948.196 | −1.33737 | −0.668686 | − | 0.743545i | \(-0.733143\pi\) | ||||
−0.668686 | + | 0.743545i | \(0.733143\pi\) | |||||||
\(710\) | 352.461i | 0.496424i | ||||||||
\(711\) | 283.169 | 0.398268 | ||||||||
\(712\) | −166.172 | −0.233387 | ||||||||
\(713\) | −252.878 | −0.354667 | ||||||||
\(714\) | − | 588.616i | − | 0.824393i | ||||||
\(715\) | 388.677 | 0.543604 | ||||||||
\(716\) | − | 514.724i | − | 0.718889i | ||||||
\(717\) | −13.8871 | −0.0193684 | ||||||||
\(718\) | 647.728i | 0.902129i | ||||||||
\(719\) | 841.219i | 1.16998i | 0.811039 | + | 0.584992i | \(0.198902\pi\) | ||||
−0.811039 | + | 0.584992i | \(0.801098\pi\) | |||||||
\(720\) | 92.5937 | 0.128602 | ||||||||
\(721\) | − | 690.794i | − | 0.958105i | ||||||
\(722\) | 475.758i | 0.658944i | ||||||||
\(723\) | 165.096 | 0.228349 | ||||||||
\(724\) | −50.6363 | −0.0699397 | ||||||||
\(725\) | −409.023 | −0.564169 | ||||||||
\(726\) | 281.961i | 0.388376i | ||||||||
\(727\) | 1330.58 | 1.83023 | 0.915116 | − | 0.403190i | \(-0.132099\pi\) | ||||
0.915116 | + | 0.403190i | \(0.132099\pi\) | |||||||
\(728\) | −444.106 | −0.610036 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 1300.91 | 1.78207 | ||||||||
\(731\) | − | 208.933i | − | 0.285817i | ||||||
\(732\) | − | 147.640i | − | 0.201693i | ||||||
\(733\) | −908.813 | −1.23985 | −0.619927 | − | 0.784660i | \(-0.712838\pi\) | ||||
−0.619927 | + | 0.784660i | \(0.712838\pi\) | |||||||
\(734\) | −453.424 | −0.617744 | ||||||||
\(735\) | −109.994 | −0.149652 | ||||||||
\(736\) | −177.138 | −0.240677 | ||||||||
\(737\) | −186.856 | −0.253536 | ||||||||
\(738\) | 188.378i | 0.255254i | ||||||||
\(739\) | 91.6635i | 0.124037i | 0.998075 | + | 0.0620186i | \(0.0197538\pi\) | ||||
−0.998075 | + | 0.0620186i | \(0.980246\pi\) | |||||||
\(740\) | 646.251i | 0.873312i | ||||||||
\(741\) | − | 178.261i | − | 0.240568i | ||||||
\(742\) | 483.149i | 0.651144i | ||||||||
\(743\) | 342.901 | 0.461509 | 0.230754 | − | 0.973012i | \(-0.425881\pi\) | ||||
0.230754 | + | 0.973012i | \(0.425881\pi\) | |||||||
\(744\) | −39.5621 | −0.0531749 | ||||||||
\(745\) | 98.4358i | 0.132129i | ||||||||
\(746\) | − | 731.871i | − | 0.981060i | ||||||
\(747\) | 324.261i | 0.434085i | ||||||||
\(748\) | − | 154.182i | − | 0.206126i | ||||||
\(749\) | −1045.98 | −1.39650 | ||||||||
\(750\) | 180.289i | 0.240385i | ||||||||
\(751\) | − | 395.722i | − | 0.526927i | −0.964669 | − | 0.263463i | \(-0.915135\pi\) | ||
0.964669 | − | 0.263463i | \(-0.0848648\pi\) | |||||||
\(752\) | − | 370.927i | − | 0.493254i | ||||||
\(753\) | −100.856 | −0.133938 | ||||||||
\(754\) | 347.604 | 0.461013 | ||||||||
\(755\) | − | 958.921i | − | 1.27009i | ||||||
\(756\) | −78.6184 | −0.103993 | ||||||||
\(757\) | 271.976 | 0.359282 | 0.179641 | − | 0.983732i | \(-0.442506\pi\) | ||||
0.179641 | + | 0.983732i | \(0.442506\pi\) | |||||||
\(758\) | 185.200i | 0.244327i | ||||||||
\(759\) | −131.631 | −0.173426 | ||||||||
\(760\) | − | 108.221i | − | 0.142396i | ||||||
\(761\) | −239.313 | −0.314472 | −0.157236 | − | 0.987561i | \(-0.550258\pi\) | ||||
−0.157236 | + | 0.987561i | \(0.550258\pi\) | |||||||
\(762\) | 279.774i | 0.367157i | ||||||||
\(763\) | 923.073i | 1.20979i | ||||||||
\(764\) | − | 442.160i | − | 0.578743i | ||||||
\(765\) | 735.302 | 0.961179 | ||||||||
\(766\) | − | 537.858i | − | 0.702165i | ||||||
\(767\) | 397.770 | − | 1158.16i | 0.518605 | − | 1.50999i | ||||
\(768\) | −27.7128 | −0.0360844 | ||||||||
\(769\) | 901.993i | 1.17294i | 0.809970 | + | 0.586472i | \(0.199483\pi\) | ||||
−0.809970 | + | 0.586472i | \(0.800517\pi\) | |||||||
\(770\) | −200.349 | −0.260194 | ||||||||
\(771\) | −480.042 | −0.622623 | ||||||||
\(772\) | −115.348 | −0.149415 | ||||||||
\(773\) | − | 267.398i | − | 0.345923i | −0.984929 | − | 0.172961i | \(-0.944666\pi\) | ||
0.984929 | − | 0.172961i | \(-0.0553336\pi\) | |||||||
\(774\) | −27.9060 | −0.0360543 | ||||||||
\(775\) | − | 278.921i | − | 0.359898i | ||||||
\(776\) | −60.1783 | −0.0775493 | ||||||||
\(777\) | − | 548.712i | − | 0.706193i | ||||||
\(778\) | 611.819i | 0.786399i | ||||||||
\(779\) | 220.170 | 0.282632 | ||||||||
\(780\) | − | 554.779i | − | 0.711255i | ||||||
\(781\) | − | 78.3891i | − | 0.100370i | ||||||
\(782\) | −1406.68 | −1.79883 | ||||||||
\(783\) | 61.5350 | 0.0785888 | ||||||||
\(784\) | 32.9207 | 0.0419906 | ||||||||
\(785\) | 2111.55i | 2.68987i | ||||||||
\(786\) | 484.371 | 0.616248 | ||||||||
\(787\) | 129.107 | 0.164050 | 0.0820249 | − | 0.996630i | \(-0.473861\pi\) | ||||
0.0820249 | + | 0.996630i | \(0.473861\pi\) | |||||||
\(788\) | 616.044 | 0.781782 | ||||||||
\(789\) | 433.896 | 0.549932 | ||||||||
\(790\) | − | 1030.00i | − | 1.30380i | ||||||
\(791\) | − | 195.829i | − | 0.247571i | ||||||
\(792\) | −20.5933 | −0.0260016 | ||||||||
\(793\) | −884.589 | −1.11550 | ||||||||
\(794\) | −620.048 | −0.780917 | ||||||||
\(795\) | −603.551 | −0.759184 | ||||||||
\(796\) | 147.747 | 0.185611 | ||||||||
\(797\) | 268.793i | 0.337256i | 0.985680 | + | 0.168628i | \(0.0539337\pi\) | ||||
−0.985680 | + | 0.168628i | \(0.946066\pi\) | |||||||
\(798\) | 91.8869i | 0.115146i | ||||||||
\(799\) | − | 2945.59i | − | 3.68660i | ||||||
\(800\) | − | 195.381i | − | 0.244226i | ||||||
\(801\) | 176.252i | 0.220039i | ||||||||
\(802\) | −250.848 | −0.312778 | ||||||||
\(803\) | −289.329 | −0.360310 | ||||||||
\(804\) | 266.709i | 0.331728i | ||||||||
\(805\) | 1827.89i | 2.27067i | ||||||||
\(806\) | 237.038i | 0.294092i | ||||||||
\(807\) | − | 823.033i | − | 1.01987i | ||||||
\(808\) | 194.962 | 0.241290 | ||||||||
\(809\) | 344.470i | 0.425797i | 0.977074 | + | 0.212899i | \(0.0682904\pi\) | ||||
−0.977074 | + | 0.212899i | \(0.931710\pi\) | |||||||
\(810\) | − | 98.2104i | − | 0.121247i | ||||||
\(811\) | 86.1187i | 0.106188i | 0.998590 | + | 0.0530942i | \(0.0169083\pi\) | ||||
−0.998590 | + | 0.0530942i | \(0.983092\pi\) | |||||||
\(812\) | −179.177 | −0.220662 | ||||||||
\(813\) | 388.732 | 0.478145 | ||||||||
\(814\) | − | 143.730i | − | 0.176572i | ||||||
\(815\) | 1621.48 | 1.98954 | ||||||||
\(816\) | −220.072 | −0.269696 | ||||||||
\(817\) | 32.6157i | 0.0399213i | ||||||||
\(818\) | 846.088 | 1.03434 | ||||||||
\(819\) | 471.046i | 0.575147i | ||||||||
\(820\) | 685.209 | 0.835621 | ||||||||
\(821\) | − | 1450.65i | − | 1.76693i | −0.468500 | − | 0.883463i | \(-0.655206\pi\) | ||
0.468500 | − | 0.883463i | \(-0.344794\pi\) | |||||||
\(822\) | − | 399.444i | − | 0.485941i | ||||||
\(823\) | 1600.34i | 1.94451i | 0.233915 | + | 0.972257i | \(0.424846\pi\) | ||||
−0.233915 | + | 0.972257i | \(0.575154\pi\) | |||||||
\(824\) | −258.274 | −0.313439 | ||||||||
\(825\) | − | 145.187i | − | 0.175984i | ||||||
\(826\) | −205.036 | + | 596.990i | −0.248228 | + | 0.722748i | ||||
\(827\) | 140.513 | 0.169907 | 0.0849535 | − | 0.996385i | \(-0.472926\pi\) | ||||
0.0849535 | + | 0.996385i | \(0.472926\pi\) | |||||||
\(828\) | 187.883i | 0.226912i | ||||||||
\(829\) | 1350.26 | 1.62878 | 0.814392 | − | 0.580315i | \(-0.197071\pi\) | ||||
0.814392 | + | 0.580315i | \(0.197071\pi\) | |||||||
\(830\) | 1179.48 | 1.42106 | ||||||||
\(831\) | 402.572 | 0.484442 | ||||||||
\(832\) | 166.043i | 0.199570i | ||||||||
\(833\) | 261.428 | 0.313840 | ||||||||
\(834\) | − | 189.400i | − | 0.227098i | ||||||
\(835\) | −1308.03 | −1.56650 | ||||||||
\(836\) | 24.0688i | 0.0287905i | ||||||||
\(837\) | 41.9620i | 0.0501338i | ||||||||
\(838\) | 587.392 | 0.700946 | ||||||||
\(839\) | 102.717i | 0.122428i | 0.998125 | + | 0.0612142i | \(0.0194973\pi\) | ||||
−0.998125 | + | 0.0612142i | \(0.980503\pi\) | |||||||
\(840\) | 285.968i | 0.340439i | ||||||||
\(841\) | −700.757 | −0.833243 | ||||||||
\(842\) | 144.350 | 0.171437 | ||||||||
\(843\) | −80.3124 | −0.0952698 | ||||||||
\(844\) | − | 13.4123i | − | 0.0158914i | ||||||
\(845\) | −2019.95 | −2.39048 | ||||||||
\(846\) | −393.428 | −0.465045 | ||||||||
\(847\) | −870.814 | −1.02812 | ||||||||
\(848\) | 180.640 | 0.213019 | ||||||||
\(849\) | − | 329.104i | − | 0.387637i | ||||||
\(850\) | − | 1551.55i | − | 1.82536i | ||||||
\(851\) | −1311.32 | −1.54091 | ||||||||
\(852\) | −111.889 | −0.131325 | ||||||||
\(853\) | −582.081 | −0.682393 | −0.341197 | − | 0.939992i | \(-0.610832\pi\) | ||||
−0.341197 | + | 0.939992i | \(0.610832\pi\) | |||||||
\(854\) | 455.974 | 0.533927 | ||||||||
\(855\) | −114.785 | −0.134252 | ||||||||
\(856\) | 391.071i | 0.456859i | ||||||||
\(857\) | − | 781.711i | − | 0.912148i | −0.889942 | − | 0.456074i | \(-0.849255\pi\) | ||
0.889942 | − | 0.456074i | \(-0.150745\pi\) | |||||||
\(858\) | 123.386i | 0.143806i | ||||||||
\(859\) | − | 1068.99i | − | 1.24446i | −0.782834 | − | 0.622231i | \(-0.786227\pi\) | ||
0.782834 | − | 0.622231i | \(-0.213773\pi\) | |||||||
\(860\) | 101.506i | 0.118030i | ||||||||
\(861\) | −581.790 | −0.675714 | ||||||||
\(862\) | −765.674 | −0.888253 | ||||||||
\(863\) | 987.568i | 1.14434i | 0.820134 | + | 0.572172i | \(0.193899\pi\) | ||||
−0.820134 | + | 0.572172i | \(0.806101\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | 2452.89i | 2.83571i | ||||||||
\(866\) | − | 804.918i | − | 0.929467i | ||||||
\(867\) | −1247.07 | −1.43837 | ||||||||
\(868\) | − | 122.185i | − | 0.140766i | ||||||
\(869\) | 229.078i | 0.263611i | ||||||||
\(870\) | − | 223.829i | − | 0.257275i | ||||||
\(871\) | 1598.00 | 1.83467 | ||||||||
\(872\) | 345.119 | 0.395779 | ||||||||
\(873\) | 63.8287i | 0.0731142i | ||||||||
\(874\) | 219.592 | 0.251250 | ||||||||
\(875\) | −556.809 | −0.636353 | ||||||||
\(876\) | 412.974i | 0.471431i | ||||||||
\(877\) | −518.873 | −0.591645 | −0.295823 | − | 0.955243i | \(-0.595594\pi\) | ||||
−0.295823 | + | 0.955243i | \(0.595594\pi\) | |||||||
\(878\) | − | 42.8543i | − | 0.0488090i | ||||||
\(879\) | −659.495 | −0.750279 | ||||||||
\(880\) | 74.9065i | 0.0851211i | ||||||||
\(881\) | − | 638.669i | − | 0.724937i | −0.931996 | − | 0.362468i | \(-0.881934\pi\) | ||
0.931996 | − | 0.362468i | \(-0.118066\pi\) | |||||||
\(882\) | − | 34.9176i | − | 0.0395892i | ||||||
\(883\) | 1237.73 | 1.40173 | 0.700866 | − | 0.713293i | \(-0.252797\pi\) | ||||
0.700866 | + | 0.713293i | \(0.252797\pi\) | |||||||
\(884\) | 1318.57i | 1.49160i | ||||||||
\(885\) | −745.761 | − | 256.132i | −0.842668 | − | 0.289415i | ||||
\(886\) | 1082.90 | 1.22224 | ||||||||
\(887\) | 756.022i | 0.852336i | 0.904644 | + | 0.426168i | \(0.140137\pi\) | ||||
−0.904644 | + | 0.426168i | \(0.859863\pi\) | |||||||
\(888\) | −205.153 | −0.231028 | ||||||||
\(889\) | −864.060 | −0.971946 | ||||||||
\(890\) | 641.101 | 0.720338 | ||||||||
\(891\) | 21.8425i | 0.0245146i | ||||||||
\(892\) | 76.7775 | 0.0860735 | ||||||||
\(893\) | 459.827i | 0.514923i | ||||||||
\(894\) | −31.2485 | −0.0349535 | ||||||||
\(895\) | 1985.84i | 2.21882i | ||||||||
\(896\) | − | 85.5889i | − | 0.0955233i | ||||||
\(897\) | 1125.71 | 1.25497 | ||||||||
\(898\) | − | 1134.06i | − | 1.26287i | ||||||
\(899\) | 95.6344i | 0.106379i | ||||||||
\(900\) | −207.233 | −0.230259 | ||||||||
\(901\) | 1434.49 | 1.59211 | ||||||||
\(902\) | −152.394 | −0.168951 | ||||||||
\(903\) | − | 86.1857i | − | 0.0954437i | ||||||
\(904\) | −73.2164 | −0.0809916 | ||||||||
\(905\) | 195.359 | 0.215866 | ||||||||
\(906\) | 304.410 | 0.335993 | ||||||||
\(907\) | −810.443 | −0.893542 | −0.446771 | − | 0.894648i | \(-0.647426\pi\) | ||||
−0.446771 | + | 0.894648i | \(0.647426\pi\) | |||||||
\(908\) | 397.865i | 0.438177i | ||||||||
\(909\) | − | 206.789i | − | 0.227490i | ||||||
\(910\) | 1713.39 | 1.88285 | ||||||||
\(911\) | 1138.70 | 1.24995 | 0.624974 | − | 0.780646i | \(-0.285110\pi\) | ||||
0.624974 | + | 0.780646i | \(0.285110\pi\) | |||||||
\(912\) | 34.3547 | 0.0376696 | ||||||||
\(913\) | −262.321 | −0.287318 | ||||||||
\(914\) | −36.4567 | −0.0398870 | ||||||||
\(915\) | 569.604i | 0.622518i | ||||||||
\(916\) | 353.420i | 0.385830i | ||||||||
\(917\) | 1495.94i | 1.63134i | ||||||||
\(918\) | 233.422i | 0.254272i | ||||||||
\(919\) | 237.117i | 0.258016i | 0.991644 | + | 0.129008i | \(0.0411793\pi\) | ||||
−0.991644 | + | 0.129008i | \(0.958821\pi\) | |||||||
\(920\) | 683.411 | 0.742838 | ||||||||
\(921\) | 117.254 | 0.127311 | ||||||||
\(922\) | 833.014i | 0.903486i | ||||||||
\(923\) | 670.386i | 0.726312i | ||||||||
\(924\) | − | 63.6008i | − | 0.0688321i | ||||||
\(925\) | − | 1446.37i | − | 1.56364i | ||||||
\(926\) | 945.785 | 1.02137 | ||||||||
\(927\) | 273.941i | 0.295513i | ||||||||
\(928\) | 66.9908i | 0.0721884i | ||||||||
\(929\) | 259.206i | 0.279016i | 0.990221 | + | 0.139508i | \(0.0445521\pi\) | ||||
−0.990221 | + | 0.139508i | \(0.955448\pi\) | |||||||
\(930\) | 152.633 | 0.164122 | ||||||||
\(931\) | −40.8107 | −0.0438353 | ||||||||
\(932\) | − | 82.0831i | − | 0.0880720i | ||||||
\(933\) | −248.019 | −0.265829 | ||||||||
\(934\) | −415.905 | −0.445294 | ||||||||
\(935\) | 594.845i | 0.636198i | ||||||||
\(936\) | 176.115 | 0.188157 | ||||||||
\(937\) | − | 324.007i | − | 0.345792i | −0.984940 | − | 0.172896i | \(-0.944688\pi\) | ||
0.984940 | − | 0.172896i | \(-0.0553124\pi\) | |||||||
\(938\) | −823.711 | −0.878157 | ||||||||
\(939\) | 403.811i | 0.430043i | ||||||||
\(940\) | 1431.06i | 1.52241i | ||||||||
\(941\) | 299.570i | 0.318353i | 0.987250 | + | 0.159176i | \(0.0508838\pi\) | ||||
−0.987250 | + | 0.159176i | \(0.949116\pi\) | |||||||
\(942\) | −670.312 | −0.711583 | ||||||||
\(943\) | 1390.37i | 1.47441i | ||||||||
\(944\) | 223.203 | + | 76.6590i | 0.236443 | + | 0.0812065i | ||||
\(945\) | 303.315 | 0.320969 | ||||||||
\(946\) | − | 22.5755i | − | 0.0238641i | ||||||
\(947\) | 1191.15 | 1.25782 | 0.628909 | − | 0.777479i | \(-0.283502\pi\) | ||||
0.628909 | + | 0.777479i | \(0.283502\pi\) | |||||||
\(948\) | 326.975 | 0.344910 | ||||||||
\(949\) | 2474.35 | 2.60732 | ||||||||
\(950\) | 242.207i | 0.254955i | ||||||||
\(951\) | −244.927 | −0.257546 | ||||||||
\(952\) | − | 679.676i | − | 0.713945i | ||||||
\(953\) | −342.984 | −0.359899 | −0.179950 | − | 0.983676i | \(-0.557593\pi\) | ||||
−0.179950 | + | 0.983676i | \(0.557593\pi\) | |||||||
\(954\) | − | 191.597i | − | 0.200836i | ||||||
\(955\) | 1705.88i | 1.78626i | ||||||||
\(956\) | −16.0355 | −0.0167735 | ||||||||
\(957\) | 49.7807i | 0.0520174i | ||||||||
\(958\) | 35.2001i | 0.0367433i | ||||||||
\(959\) | 1233.65 | 1.28639 | ||||||||
\(960\) | 106.918 | 0.111373 | ||||||||
\(961\) | 895.785 | 0.932138 | ||||||||
\(962\) | 1229.18i | 1.27773i | ||||||||
\(963\) | 414.794 | 0.430731 | ||||||||
\(964\) | 190.637 | 0.197756 | ||||||||
\(965\) | 445.022 | 0.461162 | ||||||||
\(966\) | −580.263 | −0.600686 | ||||||||
\(967\) | − | 826.131i | − | 0.854324i | −0.904175 | − | 0.427162i | \(-0.859513\pi\) | ||
0.904175 | − | 0.427162i | \(-0.140487\pi\) | |||||||
\(968\) | 325.580i | 0.336343i | ||||||||
\(969\) | 272.816 | 0.281544 | ||||||||
\(970\) | 232.172 | 0.239353 | ||||||||
\(971\) | −124.784 | −0.128511 | −0.0642555 | − | 0.997933i | \(-0.520467\pi\) | ||||
−0.0642555 | + | 0.997933i | \(0.520467\pi\) | |||||||
\(972\) | 31.1769 | 0.0320750 | ||||||||
\(973\) | 584.947 | 0.601178 | ||||||||
\(974\) | − | 1053.74i | − | 1.08187i | ||||||
\(975\) | 1241.64i | 1.27348i | ||||||||
\(976\) | − | 170.480i | − | 0.174672i | ||||||
\(977\) | − | 980.254i | − | 1.00333i | −0.865062 | − | 0.501665i | \(-0.832721\pi\) | ||
0.865062 | − | 0.501665i | \(-0.167279\pi\) | |||||||
\(978\) | 514.739i | 0.526318i | ||||||||
\(979\) | −142.584 | −0.145643 | ||||||||
\(980\) | −127.010 | −0.129602 | ||||||||
\(981\) | − | 366.054i | − | 0.373144i | ||||||
\(982\) | 1268.26i | 1.29151i | ||||||||
\(983\) | − | 1676.08i | − | 1.70507i | −0.522673 | − | 0.852533i | \(-0.675065\pi\) | ||
0.522673 | − | 0.852533i | \(-0.324935\pi\) | |||||||
\(984\) | 217.520i | 0.221057i | ||||||||
\(985\) | −2376.74 | −2.41294 | ||||||||
\(986\) | 531.985i | 0.539539i | ||||||||
\(987\) | − | 1215.07i | − | 1.23108i | ||||||
\(988\) | − | 205.838i | − | 0.208338i | ||||||
\(989\) | −205.967 | −0.208258 | ||||||||
\(990\) | 79.4504 | 0.0802529 | ||||||||
\(991\) | − | 122.726i | − | 0.123840i | −0.998081 | − | 0.0619201i | \(-0.980278\pi\) | ||
0.998081 | − | 0.0619201i | \(-0.0197224\pi\) | |||||||
\(992\) | −45.6824 | −0.0460508 | ||||||||
\(993\) | 414.540 | 0.417463 | ||||||||
\(994\) | − | 345.560i | − | 0.347646i | ||||||
\(995\) | −570.017 | −0.572881 | ||||||||
\(996\) | 374.425i | 0.375929i | ||||||||
\(997\) | 833.148 | 0.835655 | 0.417828 | − | 0.908526i | \(-0.362792\pi\) | ||||
0.417828 | + | 0.908526i | \(0.362792\pi\) | |||||||
\(998\) | − | 1194.05i | − | 1.19644i | ||||||
\(999\) | 217.597i | 0.217815i |
(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 | 354.3.d.a.235.5 | ✓ | 20 | |
3.2 | odd | 2 | 1062.3.d.f.235.12 | 20 | |||
59.58 | odd | 2 | inner | 354.3.d.a.235.15 | yes | 20 | |
177.176 | even | 2 | 1062.3.d.f.235.2 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
354.3.d.a.235.5 | ✓ | 20 | 1.1 | even | 1 | trivial | |
354.3.d.a.235.15 | yes | 20 | 59.58 | odd | 2 | inner | |
1062.3.d.f.235.2 | 20 | 177.176 | even | 2 | |||
1062.3.d.f.235.12 | 20 | 3.2 | odd | 2 |