Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,4,Mod(599,1150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1150.599");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.b (of order \(2\), degree \(1\), not 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: | \(67.8521965066\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 136x^{6} + 5308x^{4} + 58833x^{2} + 116964 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 599.2 | ||
Root | \(-1.58997i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1150.599 |
Dual form | 1150.4.b.n.599.7 |
$q$-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 \(\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(277\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.00000i | − 0.707107i | ||||||||
\(3\) | − 0.589969i | − 0.113540i | −0.998387 | − | 0.0567698i | \(-0.981920\pi\) | ||||
0.998387 | − | 0.0567698i | \(-0.0180801\pi\) | |||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.17994 | −0.0802847 | ||||||||
\(7\) | − 18.5077i | − 0.999324i | −0.866220 | − | 0.499662i | \(-0.833458\pi\) | ||||
0.866220 | − | 0.499662i | \(-0.166542\pi\) | |||||||
\(8\) | 8.00000i | 0.353553i | ||||||||
\(9\) | 26.6519 | 0.987109 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 47.9296 | 1.31376 | 0.656878 | − | 0.753997i | \(-0.271877\pi\) | ||||
0.656878 | + | 0.753997i | \(0.271877\pi\) | |||||||
\(12\) | 2.35988i | 0.0567698i | ||||||||
\(13\) | − 42.3717i | − 0.903984i | −0.892022 | − | 0.451992i | \(-0.850714\pi\) | ||||
0.892022 | − | 0.451992i | \(-0.149286\pi\) | |||||||
\(14\) | −37.0155 | −0.706629 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 1.70534i | 0.0243298i | 0.999926 | + | 0.0121649i | \(0.00387230\pi\) | ||||
−0.999926 | + | 0.0121649i | \(0.996128\pi\) | |||||||
\(18\) | − 53.3039i | − 0.697991i | ||||||||
\(19\) | −21.4208 | −0.258645 | −0.129323 | − | 0.991603i | \(-0.541280\pi\) | ||||
−0.129323 | + | 0.991603i | \(0.541280\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −10.9190 | −0.113463 | ||||||||
\(22\) | − 95.8592i | − 0.928966i | ||||||||
\(23\) | 23.0000i | 0.208514i | ||||||||
\(24\) | 4.71976 | 0.0401423 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −84.7434 | −0.639213 | ||||||||
\(27\) | − 31.6530i | − 0.225616i | ||||||||
\(28\) | 74.0310i | 0.499662i | ||||||||
\(29\) | −57.6332 | −0.369042 | −0.184521 | − | 0.982829i | \(-0.559073\pi\) | ||||
−0.184521 | + | 0.982829i | \(0.559073\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 295.699 | 1.71320 | 0.856599 | − | 0.515983i | \(-0.172573\pi\) | ||||
0.856599 | + | 0.515983i | \(0.172573\pi\) | |||||||
\(32\) | − 32.0000i | − 0.176777i | ||||||||
\(33\) | − 28.2770i | − 0.149163i | ||||||||
\(34\) | 3.41069 | 0.0172038 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −106.608 | −0.493554 | ||||||||
\(37\) | − 7.85184i | − 0.0348874i | −0.999848 | − | 0.0174437i | \(-0.994447\pi\) | ||||
0.999848 | − | 0.0174437i | \(-0.00555279\pi\) | |||||||
\(38\) | 42.8416i | 0.182890i | ||||||||
\(39\) | −24.9980 | −0.102638 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 465.929 | 1.77478 | 0.887390 | − | 0.461020i | \(-0.152516\pi\) | ||||
0.887390 | + | 0.461020i | \(0.152516\pi\) | |||||||
\(42\) | 21.8380i | 0.0802304i | ||||||||
\(43\) | − 182.374i | − 0.646784i | −0.946265 | − | 0.323392i | \(-0.895177\pi\) | ||||
0.946265 | − | 0.323392i | \(-0.104823\pi\) | |||||||
\(44\) | −191.718 | −0.656878 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 46.0000 | 0.147442 | ||||||||
\(47\) | 449.193i | 1.39408i | 0.717035 | + | 0.697038i | \(0.245499\pi\) | ||||
−0.717035 | + | 0.697038i | \(0.754501\pi\) | |||||||
\(48\) | − 9.43951i | − 0.0283849i | ||||||||
\(49\) | 0.463605 | 0.00135162 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.00610 | 0.00276240 | ||||||||
\(52\) | 169.487i | 0.451992i | ||||||||
\(53\) | 368.316i | 0.954567i | 0.878749 | + | 0.477283i | \(0.158379\pi\) | ||||
−0.878749 | + | 0.477283i | \(0.841621\pi\) | |||||||
\(54\) | −63.3060 | −0.159534 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 148.062 | 0.353314 | ||||||||
\(57\) | 12.6376i | 0.0293665i | ||||||||
\(58\) | 115.266i | 0.260952i | ||||||||
\(59\) | 377.032 | 0.831955 | 0.415977 | − | 0.909375i | \(-0.363440\pi\) | ||||
0.415977 | + | 0.909375i | \(0.363440\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 849.042 | 1.78211 | 0.891055 | − | 0.453896i | \(-0.149966\pi\) | ||||
0.891055 | + | 0.453896i | \(0.149966\pi\) | |||||||
\(62\) | − 591.398i | − 1.21141i | ||||||||
\(63\) | − 493.267i | − 0.986441i | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −56.5540 | −0.105474 | ||||||||
\(67\) | 92.3424i | 0.168379i | 0.996450 | + | 0.0841897i | \(0.0268302\pi\) | ||||
−0.996450 | + | 0.0841897i | \(0.973170\pi\) | |||||||
\(68\) | − 6.82138i | − 0.0121649i | ||||||||
\(69\) | 13.5693 | 0.0236747 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −626.854 | −1.04780 | −0.523901 | − | 0.851779i | \(-0.675524\pi\) | ||||
−0.523901 | + | 0.851779i | \(0.675524\pi\) | |||||||
\(72\) | 213.215i | 0.348996i | ||||||||
\(73\) | − 439.227i | − 0.704214i | −0.935960 | − | 0.352107i | \(-0.885465\pi\) | ||||
0.935960 | − | 0.352107i | \(-0.114535\pi\) | |||||||
\(74\) | −15.7037 | −0.0246691 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 85.6831 | 0.129323 | ||||||||
\(77\) | − 887.068i | − 1.31287i | ||||||||
\(78\) | 49.9960i | 0.0725761i | ||||||||
\(79\) | −641.707 | −0.913894 | −0.456947 | − | 0.889494i | \(-0.651057\pi\) | ||||
−0.456947 | + | 0.889494i | \(0.651057\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 700.928 | 0.961492 | ||||||||
\(82\) | − 931.859i | − 1.25496i | ||||||||
\(83\) | 609.932i | 0.806611i | 0.915065 | + | 0.403306i | \(0.132139\pi\) | ||||
−0.915065 | + | 0.403306i | \(0.867861\pi\) | |||||||
\(84\) | 43.6760 | 0.0567315 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −364.747 | −0.457346 | ||||||||
\(87\) | 34.0018i | 0.0419009i | ||||||||
\(88\) | 383.437i | 0.464483i | ||||||||
\(89\) | −1122.87 | −1.33735 | −0.668673 | − | 0.743557i | \(-0.733137\pi\) | ||||
−0.668673 | + | 0.743557i | \(0.733137\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −784.204 | −0.903373 | ||||||||
\(92\) | − 92.0000i | − 0.104257i | ||||||||
\(93\) | − 174.453i | − 0.194516i | ||||||||
\(94\) | 898.386 | 0.985760 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −18.8790 | −0.0200712 | ||||||||
\(97\) | − 1428.80i | − 1.49559i | −0.663930 | − | 0.747795i | \(-0.731113\pi\) | ||||
0.663930 | − | 0.747795i | \(-0.268887\pi\) | |||||||
\(98\) | − 0.927209i | 0 0.000955737i | ||||||||
\(99\) | 1277.42 | 1.29682 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1512.15 | −1.48975 | −0.744875 | − | 0.667204i | \(-0.767491\pi\) | ||||
−0.744875 | + | 0.667204i | \(0.767491\pi\) | |||||||
\(102\) | − 2.01220i | − 0.00195331i | ||||||||
\(103\) | − 957.279i | − 0.915762i | −0.889013 | − | 0.457881i | \(-0.848609\pi\) | ||||
0.889013 | − | 0.457881i | \(-0.151391\pi\) | |||||||
\(104\) | 338.974 | 0.319607 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 736.631 | 0.674981 | ||||||||
\(107\) | − 1742.16i | − 1.57403i | −0.616936 | − | 0.787013i | \(-0.711626\pi\) | ||||
0.616936 | − | 0.787013i | \(-0.288374\pi\) | |||||||
\(108\) | 126.612i | 0.112808i | ||||||||
\(109\) | −1166.77 | −1.02529 | −0.512644 | − | 0.858601i | \(-0.671334\pi\) | ||||
−0.512644 | + | 0.858601i | \(0.671334\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.63234 | −0.00396111 | ||||||||
\(112\) | − 296.124i | − 0.249831i | ||||||||
\(113\) | 393.287i | 0.327410i | 0.986509 | + | 0.163705i | \(0.0523445\pi\) | ||||
−0.986509 | + | 0.163705i | \(0.947655\pi\) | |||||||
\(114\) | 25.2752 | 0.0207653 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 230.533 | 0.184521 | ||||||||
\(117\) | − 1129.29i | − 0.892331i | ||||||||
\(118\) | − 754.063i | − 0.588281i | ||||||||
\(119\) | 31.5621 | 0.0243134 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 966.245 | 0.725954 | ||||||||
\(122\) | − 1698.08i | − 1.26014i | ||||||||
\(123\) | − 274.884i | − 0.201508i | ||||||||
\(124\) | −1182.80 | −0.856599 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −986.534 | −0.697519 | ||||||||
\(127\) | − 1067.87i | − 0.746127i | −0.927806 | − | 0.373063i | \(-0.878307\pi\) | ||||
0.927806 | − | 0.373063i | \(-0.121693\pi\) | |||||||
\(128\) | 128.000i | 0.0883883i | ||||||||
\(129\) | −107.595 | −0.0734357 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −175.497 | −0.117047 | −0.0585237 | − | 0.998286i | \(-0.518639\pi\) | ||||
−0.0585237 | + | 0.998286i | \(0.518639\pi\) | |||||||
\(132\) | 113.108i | 0.0745817i | ||||||||
\(133\) | 396.450i | 0.258471i | ||||||||
\(134\) | 184.685 | 0.119062 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −13.6428 | −0.00860189 | ||||||||
\(137\) | 475.898i | 0.296779i | 0.988929 | + | 0.148389i | \(0.0474089\pi\) | ||||
−0.988929 | + | 0.148389i | \(0.952591\pi\) | |||||||
\(138\) | − 27.1386i | − 0.0167405i | ||||||||
\(139\) | −153.167 | −0.0934638 | −0.0467319 | − | 0.998907i | \(-0.514881\pi\) | ||||
−0.0467319 | + | 0.998907i | \(0.514881\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 265.010 | 0.158283 | ||||||||
\(142\) | 1253.71i | 0.740907i | ||||||||
\(143\) | − 2030.86i | − 1.18761i | ||||||||
\(144\) | 426.431 | 0.246777 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −878.454 | −0.497954 | ||||||||
\(147\) | − 0.273513i | 0 0.000153462i | ||||||||
\(148\) | 31.4074i | 0.0174437i | ||||||||
\(149\) | −506.906 | −0.278707 | −0.139353 | − | 0.990243i | \(-0.544502\pi\) | ||||
−0.139353 | + | 0.990243i | \(0.544502\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2437.84 | 1.31383 | 0.656916 | − | 0.753964i | \(-0.271861\pi\) | ||||
0.656916 | + | 0.753964i | \(0.271861\pi\) | |||||||
\(152\) | − 171.366i | − 0.0914450i | ||||||||
\(153\) | 45.4507i | 0.0240162i | ||||||||
\(154\) | −1774.14 | −0.928338 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 99.9920 | 0.0513190 | ||||||||
\(157\) | 255.966i | 0.130117i | 0.997881 | + | 0.0650584i | \(0.0207234\pi\) | ||||
−0.997881 | + | 0.0650584i | \(0.979277\pi\) | |||||||
\(158\) | 1283.41i | 0.646221i | ||||||||
\(159\) | 217.295 | 0.108381 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 425.678 | 0.208373 | ||||||||
\(162\) | − 1401.86i | − 0.679878i | ||||||||
\(163\) | − 321.632i | − 0.154553i | −0.997010 | − | 0.0772767i | \(-0.975378\pi\) | ||||
0.997010 | − | 0.0772767i | \(-0.0246225\pi\) | |||||||
\(164\) | −1863.72 | −0.887390 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1219.86 | 0.570360 | ||||||||
\(167\) | − 2926.22i | − 1.35591i | −0.735102 | − | 0.677957i | \(-0.762866\pi\) | ||||
0.735102 | − | 0.677957i | \(-0.237134\pi\) | |||||||
\(168\) | − 87.3520i | − 0.0401152i | ||||||||
\(169\) | 401.640 | 0.182813 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −570.905 | −0.255311 | ||||||||
\(172\) | 729.495i | 0.323392i | ||||||||
\(173\) | − 1811.84i | − 0.796254i | −0.917330 | − | 0.398127i | \(-0.869660\pi\) | ||||
0.917330 | − | 0.398127i | \(-0.130340\pi\) | |||||||
\(174\) | 68.0037 | 0.0296284 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 766.873 | 0.328439 | ||||||||
\(177\) | − 222.437i | − 0.0944599i | ||||||||
\(178\) | 2245.74i | 0.945646i | ||||||||
\(179\) | −912.664 | −0.381093 | −0.190547 | − | 0.981678i | \(-0.561026\pi\) | ||||
−0.190547 | + | 0.981678i | \(0.561026\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3670.55 | 1.50735 | 0.753673 | − | 0.657249i | \(-0.228280\pi\) | ||||
0.753673 | + | 0.657249i | \(0.228280\pi\) | |||||||
\(182\) | 1568.41i | 0.638781i | ||||||||
\(183\) | − 500.909i | − 0.202340i | ||||||||
\(184\) | −184.000 | −0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −348.907 | −0.137544 | ||||||||
\(187\) | 81.7364i | 0.0319634i | ||||||||
\(188\) | − 1796.77i | − 0.697038i | ||||||||
\(189\) | −585.826 | −0.225463 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1840.96 | −0.697419 | −0.348710 | − | 0.937231i | \(-0.613380\pi\) | ||||
−0.348710 | + | 0.937231i | \(0.613380\pi\) | |||||||
\(192\) | 37.7580i | 0.0141925i | ||||||||
\(193\) | 611.817i | 0.228184i | 0.993470 | + | 0.114092i | \(0.0363959\pi\) | ||||
−0.993470 | + | 0.114092i | \(0.963604\pi\) | |||||||
\(194\) | −2857.59 | −1.05754 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.85442 | −0.000675808 0 | ||||||||
\(197\) | 2830.26i | 1.02359i | 0.859107 | + | 0.511796i | \(0.171020\pi\) | ||||
−0.859107 | + | 0.511796i | \(0.828980\pi\) | |||||||
\(198\) | − 2554.83i | − 0.916990i | ||||||||
\(199\) | 1162.74 | 0.414195 | 0.207097 | − | 0.978320i | \(-0.433598\pi\) | ||||
0.207097 | + | 0.978320i | \(0.433598\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 54.4792 | 0.0191177 | ||||||||
\(202\) | 3024.31i | 1.05341i | ||||||||
\(203\) | 1066.66i | 0.368792i | ||||||||
\(204\) | −4.02440 | −0.00138120 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1914.56 | −0.647542 | ||||||||
\(207\) | 612.995i | 0.205826i | ||||||||
\(208\) | − 677.947i | − 0.225996i | ||||||||
\(209\) | −1026.69 | −0.339797 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1399.58 | 0.456641 | 0.228320 | − | 0.973586i | \(-0.426677\pi\) | ||||
0.228320 | + | 0.973586i | \(0.426677\pi\) | |||||||
\(212\) | − 1473.26i | − 0.477283i | ||||||||
\(213\) | 369.825i | 0.118967i | ||||||||
\(214\) | −3484.32 | −1.11300 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 253.224 | 0.0797672 | ||||||||
\(217\) | − 5472.72i | − 1.71204i | ||||||||
\(218\) | 2333.54i | 0.724988i | ||||||||
\(219\) | −259.130 | −0.0799562 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 72.2583 | 0.0219938 | ||||||||
\(222\) | 9.26469i | 0.00280092i | ||||||||
\(223\) | − 4257.98i | − 1.27863i | −0.768943 | − | 0.639317i | \(-0.779217\pi\) | ||||
0.768943 | − | 0.639317i | \(-0.220783\pi\) | |||||||
\(224\) | −592.248 | −0.176657 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 786.574 | 0.231514 | ||||||||
\(227\) | − 4025.03i | − 1.17688i | −0.808542 | − | 0.588438i | \(-0.799743\pi\) | ||||
0.808542 | − | 0.588438i | \(-0.200257\pi\) | |||||||
\(228\) | − 50.5504i | − 0.0146833i | ||||||||
\(229\) | −3623.04 | −1.04549 | −0.522745 | − | 0.852489i | \(-0.675092\pi\) | ||||
−0.522745 | + | 0.852489i | \(0.675092\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −523.343 | −0.149063 | ||||||||
\(232\) | − 461.066i | − 0.130476i | ||||||||
\(233\) | − 6502.81i | − 1.82838i | −0.405282 | − | 0.914192i | \(-0.632827\pi\) | ||||
0.405282 | − | 0.914192i | \(-0.367173\pi\) | |||||||
\(234\) | −2258.58 | −0.630973 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1508.13 | −0.415977 | ||||||||
\(237\) | 378.587i | 0.103763i | ||||||||
\(238\) | − 63.1241i | − 0.0171921i | ||||||||
\(239\) | 2690.07 | 0.728059 | 0.364030 | − | 0.931387i | \(-0.381401\pi\) | ||||
0.364030 | + | 0.931387i | \(0.381401\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −44.6958 | −0.0119465 | −0.00597326 | − | 0.999982i | \(-0.501901\pi\) | ||||
−0.00597326 | + | 0.999982i | \(0.501901\pi\) | |||||||
\(242\) | − 1932.49i | − 0.513327i | ||||||||
\(243\) | − 1268.16i | − 0.334783i | ||||||||
\(244\) | −3396.17 | −0.891055 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −549.768 | −0.142488 | ||||||||
\(247\) | 907.635i | 0.233811i | ||||||||
\(248\) | 2365.59i | 0.605707i | ||||||||
\(249\) | 359.841 | 0.0915824 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6801.41 | −1.71036 | −0.855181 | − | 0.518329i | \(-0.826554\pi\) | ||||
−0.855181 | + | 0.518329i | \(0.826554\pi\) | |||||||
\(252\) | 1973.07i | 0.493221i | ||||||||
\(253\) | 1102.38i | 0.273937i | ||||||||
\(254\) | −2135.74 | −0.527591 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 5576.00i | 1.35339i | 0.736263 | + | 0.676695i | \(0.236589\pi\) | ||||
−0.736263 | + | 0.676695i | \(0.763411\pi\) | |||||||
\(258\) | 215.190i | 0.0519269i | ||||||||
\(259\) | −145.320 | −0.0348638 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1536.04 | −0.364285 | ||||||||
\(262\) | 350.993i | 0.0827651i | ||||||||
\(263\) | 5669.58i | 1.32928i | 0.747163 | + | 0.664641i | \(0.231415\pi\) | ||||
−0.747163 | + | 0.664641i | \(0.768585\pi\) | |||||||
\(264\) | 226.216 | 0.0527372 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 792.900 | 0.182766 | ||||||||
\(267\) | 662.458i | 0.151842i | ||||||||
\(268\) | − 369.370i | − 0.0841897i | ||||||||
\(269\) | −6040.21 | −1.36906 | −0.684532 | − | 0.728983i | \(-0.739994\pi\) | ||||
−0.684532 | + | 0.728983i | \(0.739994\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6899.26 | −1.54650 | −0.773248 | − | 0.634104i | \(-0.781369\pi\) | ||||
−0.773248 | + | 0.634104i | \(0.781369\pi\) | |||||||
\(272\) | 27.2855i | 0.00608245i | ||||||||
\(273\) | 462.657i | 0.102569i | ||||||||
\(274\) | 951.795 | 0.209854 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −54.2772 | −0.0118373 | ||||||||
\(277\) | 5617.68i | 1.21853i | 0.792965 | + | 0.609267i | \(0.208536\pi\) | ||||
−0.792965 | + | 0.609267i | \(0.791464\pi\) | |||||||
\(278\) | 306.334i | 0.0660889i | ||||||||
\(279\) | 7880.96 | 1.69111 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3069.89 | 0.651723 | 0.325861 | − | 0.945418i | \(-0.394346\pi\) | ||||
0.325861 | + | 0.945418i | \(0.394346\pi\) | |||||||
\(282\) | − 530.020i | − 0.111923i | ||||||||
\(283\) | − 1404.86i | − 0.295089i | −0.989055 | − | 0.147544i | \(-0.952863\pi\) | ||||
0.989055 | − | 0.147544i | \(-0.0471369\pi\) | |||||||
\(284\) | 2507.42 | 0.523901 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4061.72 | −0.839770 | ||||||||
\(287\) | − 8623.30i | − 1.77358i | ||||||||
\(288\) | − 852.862i | − 0.174498i | ||||||||
\(289\) | 4910.09 | 0.999408 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −842.946 | −0.169809 | ||||||||
\(292\) | 1756.91i | 0.352107i | ||||||||
\(293\) | 2407.05i | 0.479936i | 0.970781 | + | 0.239968i | \(0.0771369\pi\) | ||||
−0.970781 | + | 0.239968i | \(0.922863\pi\) | |||||||
\(294\) | −0.547025 | −0.000108514 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 62.8147 | 0.0123346 | ||||||||
\(297\) | − 1517.12i | − 0.296404i | ||||||||
\(298\) | 1013.81i | 0.197076i | ||||||||
\(299\) | 974.549 | 0.188494 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3375.33 | −0.646347 | ||||||||
\(302\) | − 4875.68i | − 0.929020i | ||||||||
\(303\) | 892.124i | 0.169146i | ||||||||
\(304\) | −342.732 | −0.0646614 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 90.9015 | 0.0169820 | ||||||||
\(307\) | − 459.743i | − 0.0854689i | −0.999086 | − | 0.0427344i | \(-0.986393\pi\) | ||||
0.999086 | − | 0.0427344i | \(-0.0136069\pi\) | |||||||
\(308\) | 3548.27i | 0.656434i | ||||||||
\(309\) | −564.765 | −0.103975 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4119.48 | 0.751107 | 0.375553 | − | 0.926801i | \(-0.377453\pi\) | ||||
0.375553 | + | 0.926801i | \(0.377453\pi\) | |||||||
\(312\) | − 199.984i | − 0.0362880i | ||||||||
\(313\) | − 1684.15i | − 0.304133i | −0.988370 | − | 0.152066i | \(-0.951407\pi\) | ||||
0.988370 | − | 0.152066i | \(-0.0485927\pi\) | |||||||
\(314\) | 511.933 | 0.0920065 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2566.83 | 0.456947 | ||||||||
\(317\) | 8686.47i | 1.53906i | 0.638613 | + | 0.769528i | \(0.279508\pi\) | ||||
−0.638613 | + | 0.769528i | \(0.720492\pi\) | |||||||
\(318\) | − 434.590i | − 0.0766371i | ||||||||
\(319\) | −2762.34 | −0.484831 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1027.82 | −0.178714 | ||||||||
\(322\) | − 851.356i | − 0.147342i | ||||||||
\(323\) | − 36.5298i | − 0.00629279i | ||||||||
\(324\) | −2803.71 | −0.480746 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −643.265 | −0.109286 | ||||||||
\(327\) | 688.360i | 0.116411i | ||||||||
\(328\) | 3727.44i | 0.627479i | ||||||||
\(329\) | 8313.55 | 1.39313 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4307.91 | 0.715359 | 0.357680 | − | 0.933844i | \(-0.383568\pi\) | ||||
0.357680 | + | 0.933844i | \(0.383568\pi\) | |||||||
\(332\) | − 2439.73i | − 0.403306i | ||||||||
\(333\) | − 209.267i | − 0.0344377i | ||||||||
\(334\) | −5852.44 | −0.958776 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −174.704 | −0.0283657 | ||||||||
\(337\) | − 290.156i | − 0.0469015i | −0.999725 | − | 0.0234507i | \(-0.992535\pi\) | ||||
0.999725 | − | 0.0234507i | \(-0.00746529\pi\) | |||||||
\(338\) | − 803.280i | − 0.129268i | ||||||||
\(339\) | 232.027 | 0.0371740 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14172.7 | 2.25072 | ||||||||
\(342\) | 1141.81i | 0.180532i | ||||||||
\(343\) | − 6356.73i | − 1.00067i | ||||||||
\(344\) | 1458.99 | 0.228673 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3623.69 | −0.563037 | ||||||||
\(347\) | 1042.94i | 0.161349i | 0.996741 | + | 0.0806743i | \(0.0257074\pi\) | ||||
−0.996741 | + | 0.0806743i | \(0.974293\pi\) | |||||||
\(348\) | − 136.007i | − 0.0209505i | ||||||||
\(349\) | 1819.56 | 0.279080 | 0.139540 | − | 0.990216i | \(-0.455438\pi\) | ||||
0.139540 | + | 0.990216i | \(0.455438\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1341.19 | −0.203953 | ||||||||
\(352\) | − 1533.75i | − 0.232241i | ||||||||
\(353\) | 4514.29i | 0.680656i | 0.940307 | + | 0.340328i | \(0.110538\pi\) | ||||
−0.940307 | + | 0.340328i | \(0.889462\pi\) | |||||||
\(354\) | −444.874 | −0.0667932 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4491.47 | 0.668673 | ||||||||
\(357\) | − 18.6207i | − 0.00276053i | ||||||||
\(358\) | 1825.33i | 0.269474i | ||||||||
\(359\) | −11527.9 | −1.69476 | −0.847379 | − | 0.530988i | \(-0.821821\pi\) | ||||
−0.847379 | + | 0.530988i | \(0.821821\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6400.15 | −0.933103 | ||||||||
\(362\) | − 7341.10i | − 1.06585i | ||||||||
\(363\) | − 570.055i | − 0.0824246i | ||||||||
\(364\) | 3136.82 | 0.451686 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1001.82 | −0.143076 | ||||||||
\(367\) | 6894.09i | 0.980568i | 0.871563 | + | 0.490284i | \(0.163107\pi\) | ||||
−0.871563 | + | 0.490284i | \(0.836893\pi\) | |||||||
\(368\) | 368.000i | 0.0521286i | ||||||||
\(369\) | 12417.9 | 1.75190 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6816.69 | 0.953922 | ||||||||
\(372\) | 697.814i | 0.0972580i | ||||||||
\(373\) | − 7733.25i | − 1.07349i | −0.843744 | − | 0.536746i | \(-0.819653\pi\) | ||||
0.843744 | − | 0.536746i | \(-0.180347\pi\) | |||||||
\(374\) | 163.473 | 0.0226016 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3593.54 | −0.492880 | ||||||||
\(377\) | 2442.02i | 0.333608i | ||||||||
\(378\) | 1171.65i | 0.159427i | ||||||||
\(379\) | 9495.72 | 1.28697 | 0.643486 | − | 0.765458i | \(-0.277488\pi\) | ||||
0.643486 | + | 0.765458i | \(0.277488\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −630.011 | −0.0847150 | ||||||||
\(382\) | 3681.92i | 0.493150i | ||||||||
\(383\) | 12877.0i | 1.71797i | 0.511998 | + | 0.858987i | \(0.328906\pi\) | ||||
−0.511998 | + | 0.858987i | \(0.671094\pi\) | |||||||
\(384\) | 75.5161 | 0.0100356 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1223.63 | 0.161351 | ||||||||
\(387\) | − 4860.61i | − 0.638447i | ||||||||
\(388\) | 5715.18i | 0.747795i | ||||||||
\(389\) | 8200.40 | 1.06884 | 0.534418 | − | 0.845221i | \(-0.320531\pi\) | ||||
0.534418 | + | 0.845221i | \(0.320531\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −39.2229 | −0.00507312 | ||||||||
\(392\) | 3.70884i | 0 0.000477869i | ||||||||
\(393\) | 103.538i | 0.0132895i | ||||||||
\(394\) | 5660.52 | 0.723789 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5109.66 | −0.648410 | ||||||||
\(397\) | 7842.68i | 0.991468i | 0.868475 | + | 0.495734i | \(0.165101\pi\) | ||||
−0.868475 | + | 0.495734i | \(0.834899\pi\) | |||||||
\(398\) | − 2325.49i | − 0.292880i | ||||||||
\(399\) | 233.893 | 0.0293467 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14534.2 | −1.80999 | −0.904993 | − | 0.425427i | \(-0.860124\pi\) | ||||
−0.904993 | + | 0.425427i | \(0.860124\pi\) | |||||||
\(402\) | − 108.958i | − 0.0135183i | ||||||||
\(403\) | − 12529.3i | − 1.54870i | ||||||||
\(404\) | 6048.61 | 0.744875 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2133.32 | 0.260776 | ||||||||
\(407\) | − 376.335i | − 0.0458335i | ||||||||
\(408\) | 8.04881i | 0 0.000976655i | ||||||||
\(409\) | −13388.0 | −1.61857 | −0.809283 | − | 0.587419i | \(-0.800144\pi\) | ||||
−0.809283 | + | 0.587419i | \(0.800144\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 280.765 | 0.0336962 | ||||||||
\(412\) | 3829.12i | 0.457881i | ||||||||
\(413\) | − 6978.00i | − 0.831393i | ||||||||
\(414\) | 1225.99 | 0.145541 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1355.89 | −0.159803 | ||||||||
\(417\) | 90.3640i | 0.0106119i | ||||||||
\(418\) | 2053.38i | 0.240273i | ||||||||
\(419\) | 3103.10 | 0.361805 | 0.180903 | − | 0.983501i | \(-0.442098\pi\) | ||||
0.180903 | + | 0.983501i | \(0.442098\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6075.82 | −0.703367 | −0.351684 | − | 0.936119i | \(-0.614391\pi\) | ||||
−0.351684 | + | 0.936119i | \(0.614391\pi\) | |||||||
\(422\) | − 2799.16i | − 0.322894i | ||||||||
\(423\) | 11971.9i | 1.37610i | ||||||||
\(424\) | −2946.53 | −0.337490 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 739.649 | 0.0841224 | ||||||||
\(427\) | − 15713.8i | − 1.78090i | ||||||||
\(428\) | 6968.63i | 0.787013i | ||||||||
\(429\) | −1198.14 | −0.134841 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14120.3 | 1.57808 | 0.789040 | − | 0.614341i | \(-0.210578\pi\) | ||||
0.789040 | + | 0.614341i | \(0.210578\pi\) | |||||||
\(432\) | − 506.448i | − 0.0564039i | ||||||||
\(433\) | − 8555.96i | − 0.949592i | −0.880096 | − | 0.474796i | \(-0.842522\pi\) | ||||
0.880096 | − | 0.474796i | \(-0.157478\pi\) | |||||||
\(434\) | −10945.4 | −1.21060 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4667.09 | 0.512644 | ||||||||
\(437\) | − 492.678i | − 0.0539313i | ||||||||
\(438\) | 518.261i | 0.0565376i | ||||||||
\(439\) | 10894.1 | 1.18439 | 0.592194 | − | 0.805796i | \(-0.298262\pi\) | ||||
0.592194 | + | 0.805796i | \(0.298262\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.3560 | 0.00133419 | ||||||||
\(442\) | − 144.517i | − 0.0155519i | ||||||||
\(443\) | − 16120.5i | − 1.72891i | −0.502708 | − | 0.864456i | \(-0.667663\pi\) | ||||
0.502708 | − | 0.864456i | \(-0.332337\pi\) | |||||||
\(444\) | 18.5294 | 0.00198055 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8515.96 | −0.904130 | ||||||||
\(447\) | 299.059i | 0.0316443i | ||||||||
\(448\) | 1184.50i | 0.124915i | ||||||||
\(449\) | −4811.29 | −0.505699 | −0.252849 | − | 0.967506i | \(-0.581368\pi\) | ||||
−0.252849 | + | 0.967506i | \(0.581368\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22331.8 | 2.33163 | ||||||||
\(452\) | − 1573.15i | − 0.163705i | ||||||||
\(453\) | − 1438.25i | − 0.149172i | ||||||||
\(454\) | −8050.06 | −0.832177 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −101.101 | −0.0103826 | ||||||||
\(457\) | − 226.329i | − 0.0231667i | −0.999933 | − | 0.0115834i | \(-0.996313\pi\) | ||||
0.999933 | − | 0.0115834i | \(-0.00368718\pi\) | |||||||
\(458\) | 7246.08i | 0.739273i | ||||||||
\(459\) | 53.9793 | 0.00548919 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4349.17 | −0.439395 | −0.219697 | − | 0.975568i | \(-0.570507\pi\) | ||||
−0.219697 | + | 0.975568i | \(0.570507\pi\) | |||||||
\(462\) | 1046.69i | 0.105403i | ||||||||
\(463\) | 989.313i | 0.0993030i | 0.998767 | + | 0.0496515i | \(0.0158111\pi\) | ||||
−0.998767 | + | 0.0496515i | \(0.984189\pi\) | |||||||
\(464\) | −922.131 | −0.0922605 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13005.6 | −1.29286 | ||||||||
\(467\) | 8512.91i | 0.843535i | 0.906704 | + | 0.421767i | \(0.138590\pi\) | ||||
−0.906704 | + | 0.421767i | \(0.861410\pi\) | |||||||
\(468\) | 4517.15i | 0.446165i | ||||||||
\(469\) | 1709.05 | 0.168266 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 151.012 | 0.0147734 | ||||||||
\(472\) | 3016.25i | 0.294140i | ||||||||
\(473\) | − 8741.10i | − 0.849717i | ||||||||
\(474\) | 757.175 | 0.0733717 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −126.248 | −0.0121567 | ||||||||
\(477\) | 9816.33i | 0.942261i | ||||||||
\(478\) | − 5380.14i | − 0.514816i | ||||||||
\(479\) | 12058.6 | 1.15025 | 0.575125 | − | 0.818065i | \(-0.304953\pi\) | ||||
0.575125 | + | 0.818065i | \(0.304953\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −332.696 | −0.0315377 | ||||||||
\(482\) | 89.3916i | 0.00844746i | ||||||||
\(483\) | − 251.137i | − 0.0236587i | ||||||||
\(484\) | −3864.98 | −0.362977 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2536.31 | −0.236727 | ||||||||
\(487\) | 11605.3i | 1.07985i | 0.841714 | + | 0.539924i | \(0.181547\pi\) | ||||
−0.841714 | + | 0.539924i | \(0.818453\pi\) | |||||||
\(488\) | 6792.34i | 0.630071i | ||||||||
\(489\) | −189.753 | −0.0175479 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4651.88 | −0.427569 | −0.213785 | − | 0.976881i | \(-0.568579\pi\) | ||||
−0.213785 | + | 0.976881i | \(0.568579\pi\) | |||||||
\(492\) | 1099.54i | 0.100754i | ||||||||
\(493\) | − 98.2845i | − 0.00897872i | ||||||||
\(494\) | 1815.27 | 0.165330 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4731.19 | 0.428300 | ||||||||
\(497\) | 11601.6i | 1.04709i | ||||||||
\(498\) | − 719.682i | − 0.0647585i | ||||||||
\(499\) | 7953.03 | 0.713480 | 0.356740 | − | 0.934204i | \(-0.383888\pi\) | ||||
0.356740 | + | 0.934204i | \(0.383888\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1726.38 | −0.153950 | ||||||||
\(502\) | 13602.8i | 1.20941i | ||||||||
\(503\) | 11805.6i | 1.04649i | 0.852182 | + | 0.523245i | \(0.175279\pi\) | ||||
−0.852182 | + | 0.523245i | \(0.824721\pi\) | |||||||
\(504\) | 3946.14 | 0.348760 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2204.76 | 0.193703 | ||||||||
\(507\) | − 236.955i | − 0.0207565i | ||||||||
\(508\) | 4271.48i | 0.373063i | ||||||||
\(509\) | 2732.89 | 0.237983 | 0.118991 | − | 0.992895i | \(-0.462034\pi\) | ||||
0.118991 | + | 0.992895i | \(0.462034\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8129.09 | −0.703738 | ||||||||
\(512\) | − 512.000i | − 0.0441942i | ||||||||
\(513\) | 678.032i | 0.0583545i | ||||||||
\(514\) | 11152.0 | 0.956992 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 430.380 | 0.0367178 | ||||||||
\(517\) | 21529.6i | 1.83147i | ||||||||
\(518\) | 290.640i | 0.0246525i | ||||||||
\(519\) | −1068.93 | −0.0904065 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14710.9 | 1.23704 | 0.618518 | − | 0.785771i | \(-0.287733\pi\) | ||||
0.618518 | + | 0.785771i | \(0.287733\pi\) | |||||||
\(522\) | 3072.07i | 0.257588i | ||||||||
\(523\) | 7034.35i | 0.588127i | 0.955786 | + | 0.294064i | \(0.0950078\pi\) | ||||
−0.955786 | + | 0.294064i | \(0.904992\pi\) | |||||||
\(524\) | 701.987 | 0.0585237 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11339.2 | 0.939944 | ||||||||
\(527\) | 504.269i | 0.0416818i | ||||||||
\(528\) | − 452.432i | − 0.0372908i | ||||||||
\(529\) | −529.000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10048.6 | 0.821230 | ||||||||
\(532\) | − 1585.80i | − 0.129235i | ||||||||
\(533\) | − 19742.2i | − 1.60437i | ||||||||
\(534\) | 1324.92 | 0.107368 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −738.739 | −0.0595311 | ||||||||
\(537\) | 538.444i | 0.0432692i | ||||||||
\(538\) | 12080.4i | 0.968075i | ||||||||
\(539\) | 22.2204 | 0.00177569 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1552.90 | 0.123409 | 0.0617045 | − | 0.998094i | \(-0.480346\pi\) | ||||
0.0617045 | + | 0.998094i | \(0.480346\pi\) | |||||||
\(542\) | 13798.5i | 1.09354i | ||||||||
\(543\) | − 2165.51i | − 0.171144i | ||||||||
\(544\) | 54.5710 | 0.00430094 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 925.313 | 0.0725270 | ||||||||
\(547\) | 174.657i | 0.0136523i | 0.999977 | + | 0.00682614i | \(0.00217284\pi\) | ||||
−0.999977 | + | 0.00682614i | \(0.997827\pi\) | |||||||
\(548\) | − 1903.59i | − 0.148389i | ||||||||
\(549\) | 22628.6 | 1.75914 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1234.55 | 0.0954510 | ||||||||
\(552\) | 108.554i | 0.00837026i | ||||||||
\(553\) | 11876.5i | 0.913276i | ||||||||
\(554\) | 11235.4 | 0.861633 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 612.669 | 0.0467319 | ||||||||
\(557\) | − 1990.63i | − 0.151429i | −0.997130 | − | 0.0757143i | \(-0.975876\pi\) | ||||
0.997130 | − | 0.0757143i | \(-0.0241237\pi\) | |||||||
\(558\) | − 15761.9i | − 1.19580i | ||||||||
\(559\) | −7727.48 | −0.584683 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 48.2220 | 0.00362912 | ||||||||
\(562\) | − 6139.78i | − 0.460838i | ||||||||
\(563\) | − 208.006i | − 0.0155709i | −0.999970 | − | 0.00778543i | \(-0.997522\pi\) | ||||
0.999970 | − | 0.00778543i | \(-0.00247820\pi\) | |||||||
\(564\) | −1060.04 | −0.0791414 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2809.71 | −0.208659 | ||||||||
\(567\) | − 12972.6i | − 0.960842i | ||||||||
\(568\) | − 5014.83i | − 0.370454i | ||||||||
\(569\) | 3003.05 | 0.221256 | 0.110628 | − | 0.993862i | \(-0.464714\pi\) | ||||
0.110628 | + | 0.993862i | \(0.464714\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10796.1 | −0.791249 | −0.395624 | − | 0.918412i | \(-0.629472\pi\) | ||||
−0.395624 | + | 0.918412i | \(0.629472\pi\) | |||||||
\(572\) | 8123.43i | 0.593807i | ||||||||
\(573\) | 1086.11i | 0.0791847i | ||||||||
\(574\) | −17246.6 | −1.25411 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1705.72 | −0.123389 | ||||||||
\(577\) | − 26011.3i | − 1.87671i | −0.345667 | − | 0.938357i | \(-0.612347\pi\) | ||||
0.345667 | − | 0.938357i | \(-0.387653\pi\) | |||||||
\(578\) | − 9820.18i | − 0.706688i | ||||||||
\(579\) | 360.953 | 0.0259079 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11288.5 | 0.806066 | ||||||||
\(582\) | 1685.89i | 0.120073i | ||||||||
\(583\) | 17653.2i | 1.25407i | ||||||||
\(584\) | 3513.81 | 0.248977 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4814.09 | 0.339366 | ||||||||
\(587\) | − 2774.97i | − 0.195120i | −0.995230 | − | 0.0975598i | \(-0.968896\pi\) | ||||
0.995230 | − | 0.0975598i | \(-0.0311037\pi\) | |||||||
\(588\) | 1.09405i | 0 7.67311e-5i | ||||||||
\(589\) | −6334.11 | −0.443111 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1669.77 | 0.116218 | ||||||||
\(592\) | − 125.629i | − 0.00872185i | ||||||||
\(593\) | 2384.07i | 0.165096i | 0.996587 | + | 0.0825481i | \(0.0263058\pi\) | ||||
−0.996587 | + | 0.0825481i | \(0.973694\pi\) | |||||||
\(594\) | −3034.23 | −0.209589 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2027.62 | 0.139353 | ||||||||
\(597\) | − 685.984i | − 0.0470276i | ||||||||
\(598\) | − 1949.10i | − 0.133285i | ||||||||
\(599\) | 1090.87 | 0.0744102 | 0.0372051 | − | 0.999308i | \(-0.488155\pi\) | ||||
0.0372051 | + | 0.999308i | \(0.488155\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5192.37 | −0.352414 | −0.176207 | − | 0.984353i | \(-0.556383\pi\) | ||||
−0.176207 | + | 0.984353i | \(0.556383\pi\) | |||||||
\(602\) | 6750.65i | 0.457036i | ||||||||
\(603\) | 2461.10i | 0.166209i | ||||||||
\(604\) | −9751.36 | −0.656916 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1784.25 | 0.119604 | ||||||||
\(607\) | 1205.44i | 0.0806054i | 0.999188 | + | 0.0403027i | \(0.0128322\pi\) | ||||
−0.999188 | + | 0.0403027i | \(0.987168\pi\) | |||||||
\(608\) | 685.465i | 0.0457225i | ||||||||
\(609\) | 629.297 | 0.0418726 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19033.1 | 1.26022 | ||||||||
\(612\) | − 181.803i | − 0.0120081i | ||||||||
\(613\) | 14243.2i | 0.938466i | 0.883075 | + | 0.469233i | \(0.155469\pi\) | ||||
−0.883075 | + | 0.469233i | \(0.844531\pi\) | |||||||
\(614\) | −919.487 | −0.0604356 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7096.55 | 0.464169 | ||||||||
\(617\) | − 422.492i | − 0.0275671i | −0.999905 | − | 0.0137835i | \(-0.995612\pi\) | ||||
0.999905 | − | 0.0137835i | \(-0.00438757\pi\) | |||||||
\(618\) | 1129.53i | 0.0735217i | ||||||||
\(619\) | 8826.35 | 0.573119 | 0.286560 | − | 0.958062i | \(-0.407488\pi\) | ||||
0.286560 | + | 0.958062i | \(0.407488\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 728.019 | 0.0470441 | ||||||||
\(622\) | − 8238.96i | − 0.531113i | ||||||||
\(623\) | 20781.7i | 1.33644i | ||||||||
\(624\) | −399.968 | −0.0256595 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3368.29 | −0.215054 | ||||||||
\(627\) | 605.715i | 0.0385804i | ||||||||
\(628\) | − 1023.87i | − 0.0650584i | ||||||||
\(629\) | 13.3901 | 0.000848804 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19684.1 | −1.24186 | −0.620929 | − | 0.783867i | \(-0.713244\pi\) | ||||
−0.620929 | + | 0.783867i | \(0.713244\pi\) | |||||||
\(632\) | − 5133.65i | − 0.323110i | ||||||||
\(633\) | − 825.710i | − 0.0518468i | ||||||||
\(634\) | 17372.9 | 1.08828 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −869.180 | −0.0541906 | ||||||||
\(637\) | − 19.6437i | − 0.00122184i | ||||||||
\(638\) | 5524.67i | 0.342827i | ||||||||
\(639\) | −16706.9 | −1.03429 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15113.1 | 0.931253 | 0.465626 | − | 0.884981i | \(-0.345829\pi\) | ||||
0.465626 | + | 0.884981i | \(0.345829\pi\) | |||||||
\(642\) | 2055.64i | 0.126370i | ||||||||
\(643\) | 16917.8i | 1.03760i | 0.854897 | + | 0.518798i | \(0.173620\pi\) | ||||
−0.854897 | + | 0.518798i | \(0.826380\pi\) | |||||||
\(644\) | −1702.71 | −0.104187 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −73.0596 | −0.00444968 | ||||||||
\(647\) | 19564.5i | 1.18881i | 0.804166 | + | 0.594405i | \(0.202612\pi\) | ||||
−0.804166 | + | 0.594405i | \(0.797388\pi\) | |||||||
\(648\) | 5607.42i | 0.339939i | ||||||||
\(649\) | 18071.0 | 1.09299 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3228.74 | −0.194384 | ||||||||
\(652\) | 1286.53i | 0.0772767i | ||||||||
\(653\) | 22735.0i | 1.36247i | 0.732067 | + | 0.681233i | \(0.238556\pi\) | ||||
−0.732067 | + | 0.681233i | \(0.761444\pi\) | |||||||
\(654\) | 1376.72 | 0.0823149 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7454.87 | 0.443695 | ||||||||
\(657\) | − 11706.2i | − 0.695136i | ||||||||
\(658\) | − 16627.1i | − 0.985094i | ||||||||
\(659\) | 30730.7 | 1.81654 | 0.908269 | − | 0.418388i | \(-0.137405\pi\) | ||||
0.908269 | + | 0.418388i | \(0.137405\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29204.3 | −1.71848 | −0.859240 | − | 0.511573i | \(-0.829063\pi\) | ||||
−0.859240 | + | 0.511573i | \(0.829063\pi\) | |||||||
\(662\) | − 8615.81i | − 0.505835i | ||||||||
\(663\) | − 42.6302i | − 0.00249716i | ||||||||
\(664\) | −4879.45 | −0.285180 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −418.533 | −0.0243511 | ||||||||
\(667\) | − 1325.56i | − 0.0769506i | ||||||||
\(668\) | 11704.9i | 0.677957i | ||||||||
\(669\) | −2512.08 | −0.145176 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 40694.2 | 2.34126 | ||||||||
\(672\) | 349.408i | 0.0200576i | ||||||||
\(673\) | 17530.1i | 1.00406i | 0.864849 | + | 0.502032i | \(0.167414\pi\) | ||||
−0.864849 | + | 0.502032i | \(0.832586\pi\) | |||||||
\(674\) | −580.312 | −0.0331644 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1606.56 | −0.0914064 | ||||||||
\(677\) | − 20553.4i | − 1.16681i | −0.812180 | − | 0.583407i | \(-0.801719\pi\) | ||||
0.812180 | − | 0.583407i | \(-0.198281\pi\) | |||||||
\(678\) | − 464.055i | − 0.0262860i | ||||||||
\(679\) | −26443.8 | −1.49458 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2374.65 | −0.133622 | ||||||||
\(682\) | − 28345.5i | − 1.59150i | ||||||||
\(683\) | − 13174.8i | − 0.738098i | −0.929410 | − | 0.369049i | \(-0.879684\pi\) | ||||
0.929410 | − | 0.369049i | \(-0.120316\pi\) | |||||||
\(684\) | 2283.62 | 0.127656 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −12713.5 | −0.707584 | ||||||||
\(687\) | 2137.48i | 0.118705i | ||||||||
\(688\) | − 2917.98i | − 0.161696i | ||||||||
\(689\) | 15606.2 | 0.862913 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14800.8 | −0.814831 | −0.407415 | − | 0.913243i | \(-0.633570\pi\) | ||||
−0.407415 | + | 0.913243i | \(0.633570\pi\) | |||||||
\(692\) | 7247.38i | 0.398127i | ||||||||
\(693\) | − 23642.1i | − 1.29594i | ||||||||
\(694\) | 2085.88 | 0.114091 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −272.015 | −0.0148142 | ||||||||
\(697\) | 794.570i | 0.0431800i | ||||||||
\(698\) | − 3639.13i | − 0.197339i | ||||||||
\(699\) | −3836.46 | −0.207594 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12311.5 | −0.663336 | −0.331668 | − | 0.943396i | \(-0.607611\pi\) | ||||
−0.331668 | + | 0.943396i | \(0.607611\pi\) | |||||||
\(702\) | 2682.38i | 0.144217i | ||||||||
\(703\) | 168.192i | 0.00902347i | ||||||||
\(704\) | −3067.49 | −0.164219 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9028.59 | 0.481297 | ||||||||
\(707\) | 27986.5i | 1.48874i | ||||||||
\(708\) | 889.749i | 0.0472299i | ||||||||
\(709\) | −3893.89 | −0.206260 | −0.103130 | − | 0.994668i | \(-0.532886\pi\) | ||||
−0.103130 | + | 0.994668i | \(0.532886\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −17102.7 | −0.902113 | ||||||||
\(712\) | − 8982.94i | − 0.472823i | ||||||||
\(713\) | 6801.08i | 0.357227i | ||||||||
\(714\) | −37.2413 | −0.00195199 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3650.65 | 0.190547 | ||||||||
\(717\) | − 1587.06i | − 0.0826636i | ||||||||
\(718\) | 23055.8i | 1.19838i | ||||||||
\(719\) | 19942.5 | 1.03440 | 0.517198 | − | 0.855866i | \(-0.326975\pi\) | ||||
0.517198 | + | 0.855866i | \(0.326975\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17717.1 | −0.915143 | ||||||||
\(722\) | 12800.3i | 0.659803i | ||||||||
\(723\) | 26.3692i | 0.00135640i | ||||||||
\(724\) | −14682.2 | −0.753673 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1140.11 | −0.0582830 | ||||||||
\(727\) | 36167.0i | 1.84506i | 0.385926 | + | 0.922530i | \(0.373882\pi\) | ||||
−0.385926 | + | 0.922530i | \(0.626118\pi\) | |||||||
\(728\) | − 6273.63i | − 0.319391i | ||||||||
\(729\) | 18176.9 | 0.923481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 311.010 | 0.0157361 | ||||||||
\(732\) | 2003.64i | 0.101170i | ||||||||
\(733\) | 11669.5i | 0.588025i | 0.955802 | + | 0.294013i | \(0.0949908\pi\) | ||||
−0.955802 | + | 0.294013i | \(0.905009\pi\) | |||||||
\(734\) | 13788.2 | 0.693366 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 736.000 | 0.0368605 | ||||||||
\(737\) | 4425.93i | 0.221209i | ||||||||
\(738\) | − 24835.8i | − 1.23878i | ||||||||
\(739\) | −75.0536 | −0.00373598 | −0.00186799 | − | 0.999998i | \(-0.500595\pi\) | ||||
−0.00186799 | + | 0.999998i | \(0.500595\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 535.477 | 0.0265469 | ||||||||
\(742\) | − 13633.4i | − 0.674524i | ||||||||
\(743\) | − 28279.8i | − 1.39635i | −0.715929 | − | 0.698173i | \(-0.753997\pi\) | ||||
0.715929 | − | 0.698173i | \(-0.246003\pi\) | |||||||
\(744\) | 1395.63 | 0.0687718 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −15466.5 | −0.759074 | ||||||||
\(747\) | 16255.9i | 0.796213i | ||||||||
\(748\) | − 326.946i | − 0.0159817i | ||||||||
\(749\) | −32243.4 | −1.57296 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17268.1 | −0.839044 | −0.419522 | − | 0.907745i | \(-0.637802\pi\) | ||||
−0.419522 | + | 0.907745i | \(0.637802\pi\) | |||||||
\(752\) | 7187.09i | 0.348519i | ||||||||
\(753\) | 4012.62i | 0.194194i | ||||||||
\(754\) | 4884.03 | 0.235897 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2343.30 | 0.112732 | ||||||||
\(757\) | − 12525.8i | − 0.601400i | −0.953719 | − | 0.300700i | \(-0.902780\pi\) | ||||
0.953719 | − | 0.300700i | \(-0.0972202\pi\) | |||||||
\(758\) | − 18991.4i | − 0.910026i | ||||||||
\(759\) | 650.371 | 0.0311027 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18670.1 | −0.889343 | −0.444672 | − | 0.895694i | \(-0.646680\pi\) | ||||
−0.444672 | + | 0.895694i | \(0.646680\pi\) | |||||||
\(762\) | 1260.02i | 0.0599026i | ||||||||
\(763\) | 21594.3i | 1.02460i | ||||||||
\(764\) | 7363.83 | 0.348710 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 25754.0 | 1.21479 | ||||||||
\(767\) | − 15975.5i | − 0.752074i | ||||||||
\(768\) | − 151.032i | − 0.00709623i | ||||||||
\(769\) | 32969.6 | 1.54605 | 0.773027 | − | 0.634373i | \(-0.218742\pi\) | ||||
0.773027 | + | 0.634373i | \(0.218742\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3289.67 | 0.153664 | ||||||||
\(772\) | − 2447.27i | − 0.114092i | ||||||||
\(773\) | 23251.3i | 1.08188i | 0.841062 | + | 0.540938i | \(0.181931\pi\) | ||||
−0.841062 | + | 0.540938i | \(0.818069\pi\) | |||||||
\(774\) | −9721.23 | −0.451450 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11430.4 | 0.528771 | ||||||||
\(777\) | 85.7342i | 0.00395843i | ||||||||
\(778\) | − 16400.8i | − 0.755781i | ||||||||
\(779\) | −9980.57 | −0.459039 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30044.8 | −1.37655 | ||||||||
\(782\) | 78.4458i | 0.00358723i | ||||||||
\(783\) | 1824.26i | 0.0832617i | ||||||||
\(784\) | 7.41767 | 0.000337904 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 207.075 | 0.00939712 | ||||||||
\(787\) | − 29782.8i | − 1.34897i | −0.738288 | − | 0.674486i | \(-0.764365\pi\) | ||||
0.738288 | − | 0.674486i | \(-0.235635\pi\) | |||||||
\(788\) | − 11321.0i | − 0.511796i | ||||||||
\(789\) | 3344.88 | 0.150926 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7278.86 | 0.327189 | ||||||||
\(792\) | 10219.3i | 0.458495i | ||||||||
\(793\) | − 35975.3i | − 1.61100i | ||||||||
\(794\) | 15685.4 | 0.701073 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4650.98 | −0.207097 | ||||||||
\(797\) | 35307.2i | 1.56919i | 0.620008 | + | 0.784596i | \(0.287129\pi\) | ||||
−0.620008 | + | 0.784596i | \(0.712871\pi\) | |||||||
\(798\) | − 467.787i | − 0.0207512i | ||||||||
\(799\) | −766.029 | −0.0339176 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −29926.6 | −1.32011 | ||||||||
\(802\) | 29068.4i | 1.27985i | ||||||||
\(803\) | − 21052.0i | − 0.925165i | ||||||||
\(804\) | −217.917 | −0.00955887 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −25058.5 | −1.09510 | ||||||||
\(807\) | 3563.54i | 0.155443i | ||||||||
\(808\) | − 12097.2i | − 0.526706i | ||||||||
\(809\) | −7752.46 | −0.336912 | −0.168456 | − | 0.985709i | \(-0.553878\pi\) | ||||
−0.168456 | + | 0.985709i | \(0.553878\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23471.6 | 1.01627 | 0.508137 | − | 0.861276i | \(-0.330334\pi\) | ||||
0.508137 | + | 0.861276i | \(0.330334\pi\) | |||||||
\(812\) | − 4266.64i | − 0.184396i | ||||||||
\(813\) | 4070.35i | 0.175589i | ||||||||
\(814\) | −752.671 | −0.0324092 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 16.0976 | 0.000690600 0 | ||||||||
\(817\) | 3906.59i | 0.167288i | ||||||||
\(818\) | 26776.0i | 1.14450i | ||||||||
\(819\) | −20900.6 | −0.891727 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2467.55 | 0.104894 | 0.0524470 | − | 0.998624i | \(-0.483298\pi\) | ||||
0.0524470 | + | 0.998624i | \(0.483298\pi\) | |||||||
\(822\) | − 561.530i | − 0.0238268i | ||||||||
\(823\) | − 21984.5i | − 0.931144i | −0.885010 | − | 0.465572i | \(-0.845849\pi\) | ||||
0.885010 | − | 0.465572i | \(-0.154151\pi\) | |||||||
\(824\) | 7658.23 | 0.323771 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13956.0 | −0.587883 | ||||||||
\(827\) | − 587.293i | − 0.0246943i | −0.999924 | − | 0.0123472i | \(-0.996070\pi\) | ||||
0.999924 | − | 0.0123472i | \(-0.00393032\pi\) | |||||||
\(828\) | − 2451.98i | − 0.102913i | ||||||||
\(829\) | −41822.8 | −1.75219 | −0.876096 | − | 0.482137i | \(-0.839861\pi\) | ||||
−0.876096 | + | 0.482137i | \(0.839861\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3314.26 | 0.138352 | ||||||||
\(832\) | 2711.79i | 0.112998i | ||||||||
\(833\) | 0.790605i | 0 3.28846e-5i | ||||||||
\(834\) | 180.728 | 0.00750371 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4106.76 | 0.169898 | ||||||||
\(837\) | − 9359.77i | − 0.386524i | ||||||||
\(838\) | − 6206.20i | − 0.255835i | ||||||||
\(839\) | 10126.5 | 0.416693 | 0.208346 | − | 0.978055i | \(-0.433192\pi\) | ||||
0.208346 | + | 0.978055i | \(0.433192\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21067.4 | −0.863808 | ||||||||
\(842\) | 12151.6i | 0.497356i | ||||||||
\(843\) | − 1811.14i | − 0.0739964i | ||||||||
\(844\) | −5598.33 | −0.228320 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 23943.7 | 0.973052 | ||||||||
\(847\) | − 17883.0i | − 0.725463i | ||||||||
\(848\) | 5893.05i | 0.238642i | ||||||||
\(849\) | −828.822 | −0.0335043 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 180.592 | 0.00727453 | ||||||||
\(852\) | − 1479.30i | − 0.0594835i | ||||||||
\(853\) | − 11584.4i | − 0.464995i | −0.972597 | − | 0.232498i | \(-0.925310\pi\) | ||||
0.972597 | − | 0.232498i | \(-0.0746898\pi\) | |||||||
\(854\) | −31427.7 | −1.25929 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13937.3 | 0.556502 | ||||||||
\(857\) | − 9221.47i | − 0.367561i | −0.982967 | − | 0.183780i | \(-0.941166\pi\) | ||||
0.982967 | − | 0.183780i | \(-0.0588335\pi\) | |||||||
\(858\) | 2396.29i | 0.0953472i | ||||||||
\(859\) | −34654.2 | −1.37647 | −0.688235 | − | 0.725488i | \(-0.741614\pi\) | ||||
−0.688235 | + | 0.725488i | \(0.741614\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5087.48 | −0.201372 | ||||||||
\(862\) | − 28240.7i | − 1.11587i | ||||||||
\(863\) | − 42887.7i | − 1.69167i | −0.533441 | − | 0.845837i | \(-0.679101\pi\) | ||||
0.533441 | − | 0.845837i | \(-0.320899\pi\) | |||||||
\(864\) | −1012.90 | −0.0398836 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −17111.9 | −0.671463 | ||||||||
\(867\) | − 2896.80i | − 0.113472i | ||||||||
\(868\) | 21890.9i | 0.856020i | ||||||||
\(869\) | −30756.7 | −1.20063 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3912.70 | 0.152212 | ||||||||
\(872\) | − 9334.17i | − 0.362494i | ||||||||
\(873\) | − 38080.2i | − 1.47631i | ||||||||
\(874\) | −985.356 | −0.0381352 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1036.52 | 0.0399781 | ||||||||
\(877\) | 45935.5i | 1.76868i | 0.466846 | + | 0.884339i | \(0.345390\pi\) | ||||
−0.466846 | + | 0.884339i | \(0.654610\pi\) | |||||||
\(878\) | − 21788.2i | − 0.837488i | ||||||||
\(879\) | 1420.08 | 0.0544917 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −71.9309 | −0.00275075 | −0.00137538 | − | 0.999999i | \(-0.500438\pi\) | ||||
−0.00137538 | + | 0.999999i | \(0.500438\pi\) | |||||||
\(882\) | − 24.7119i | 0 0.000943417i | ||||||||
\(883\) | − 20003.8i | − 0.762379i | −0.924497 | − | 0.381189i | \(-0.875515\pi\) | ||||
0.924497 | − | 0.381189i | \(-0.124485\pi\) | |||||||
\(884\) | −289.033 | −0.0109969 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −32241.0 | −1.22253 | ||||||||
\(887\) | 26357.3i | 0.997737i | 0.866678 | + | 0.498869i | \(0.166251\pi\) | ||||
−0.866678 | + | 0.498869i | \(0.833749\pi\) | |||||||
\(888\) | − 37.0588i | − 0.00140046i | ||||||||
\(889\) | −19763.9 | −0.745623 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 33595.2 | 1.26317 | ||||||||
\(892\) | 17031.9i | 0.639317i | ||||||||
\(893\) | − 9622.06i | − 0.360571i | ||||||||
\(894\) | 598.118 | 0.0223759 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2368.99 | 0.0883286 | ||||||||
\(897\) | − 574.954i | − 0.0214015i | ||||||||
\(898\) | 9622.57i | 0.357583i | ||||||||
\(899\) | −17042.1 | −0.632242 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −628.105 | −0.0232244 | ||||||||
\(902\) | − 44663.6i | − 1.64871i | ||||||||
\(903\) | 1991.34i | 0.0733860i | ||||||||
\(904\) | −3146.30 | −0.115757 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2876.50 | −0.105481 | ||||||||
\(907\) | − 39300.4i | − 1.43875i | −0.694620 | − | 0.719377i | \(-0.744428\pi\) | ||||
0.694620 | − | 0.719377i | \(-0.255572\pi\) | |||||||
\(908\) | 16100.1i | 0.588438i | ||||||||
\(909\) | −40301.8 | −1.47055 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31099.2 | 1.13103 | 0.565513 | − | 0.824740i | \(-0.308678\pi\) | ||||
0.565513 | + | 0.824740i | \(0.308678\pi\) | |||||||
\(912\) | 202.202i | 0.00734163i | ||||||||
\(913\) | 29233.8i | 1.05969i | ||||||||
\(914\) | −452.657 | −0.0163814 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14492.2 | 0.522745 | ||||||||
\(917\) | 3248.05i | 0.116968i | ||||||||
\(918\) | − 107.959i | − 0.00388144i | ||||||||
\(919\) | −18935.8 | −0.679690 | −0.339845 | − | 0.940481i | \(-0.610375\pi\) | ||||
−0.339845 | + | 0.940481i | \(0.610375\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −271.235 | −0.00970411 | ||||||||
\(922\) | 8698.33i | 0.310699i | ||||||||
\(923\) | 26560.9i | 0.947195i | ||||||||
\(924\) | 2093.37 | 0.0745313 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1978.63 | 0.0702178 | ||||||||
\(927\) | − 25513.3i | − 0.903957i | ||||||||
\(928\) | 1844.26i | 0.0652380i | ||||||||
\(929\) | −40156.1 | −1.41817 | −0.709085 | − | 0.705123i | \(-0.750892\pi\) | ||||
−0.709085 | + | 0.705123i | \(0.750892\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.93077 | −0.000349590 0 | ||||||||
\(932\) | 26011.2i | 0.914192i | ||||||||
\(933\) | − 2430.37i | − 0.0852804i | ||||||||
\(934\) | 17025.8 | 0.596469 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9034.30 | 0.315486 | ||||||||
\(937\) | 126.898i | 0.00442432i | 0.999998 | + | 0.00221216i | \(0.000704153\pi\) | ||||
−0.999998 | + | 0.00221216i | \(0.999296\pi\) | |||||||
\(938\) | − 3418.10i | − 0.118982i | ||||||||
\(939\) | −993.594 | −0.0345311 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19266.6 | −0.667452 | −0.333726 | − | 0.942670i | \(-0.608306\pi\) | ||||
−0.333726 | + | 0.942670i | \(0.608306\pi\) | |||||||
\(942\) | − 302.025i | − 0.0104464i | ||||||||
\(943\) | 10716.4i | 0.370067i | ||||||||
\(944\) | 6032.51 | 0.207989 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17482.2 | −0.600840 | ||||||||
\(947\) | − 54560.4i | − 1.87220i | −0.351732 | − | 0.936101i | \(-0.614407\pi\) | ||||
0.351732 | − | 0.936101i | \(-0.385593\pi\) | |||||||
\(948\) | − 1514.35i | − 0.0518816i | ||||||||
\(949\) | −18610.8 | −0.636598 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5124.75 | 0.174744 | ||||||||
\(952\) | 252.497i | 0.00859607i | ||||||||
\(953\) | 44976.2i | 1.52877i | 0.644758 | + | 0.764387i | \(0.276958\pi\) | ||||
−0.644758 | + | 0.764387i | \(0.723042\pi\) | |||||||
\(954\) | 19632.7 | 0.666279 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −10760.3 | −0.364030 | ||||||||
\(957\) | 1629.69i | 0.0550476i | ||||||||
\(958\) | − 24117.1i | − 0.813350i | ||||||||
\(959\) | 8807.79 | 0.296578 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 57647.0 | 1.93505 | ||||||||
\(962\) | 665.391i | 0.0223005i | ||||||||
\(963\) | − 46431.9i | − 1.55374i | ||||||||
\(964\) | 178.783 | 0.00597326 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −502.274 | −0.0167292 | ||||||||
\(967\) | − 39431.7i | − 1.31131i | −0.755059 | − | 0.655656i | \(-0.772392\pi\) | ||||
0.755059 | − | 0.655656i | \(-0.227608\pi\) | |||||||
\(968\) | 7729.96i | 0.256664i | ||||||||
\(969\) | −21.5515 | −0.000714482 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20249.9 | 0.669258 | 0.334629 | − | 0.942350i | \(-0.391389\pi\) | ||||
0.334629 | + | 0.942350i | \(0.391389\pi\) | |||||||
\(972\) | 5072.63i | 0.167392i | ||||||||
\(973\) | 2834.78i | 0.0934006i | ||||||||
\(974\) | 23210.6 | 0.763567 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13584.7 | 0.445527 | ||||||||
\(977\) | − 9673.55i | − 0.316770i | −0.987377 | − | 0.158385i | \(-0.949371\pi\) | ||||
0.987377 | − | 0.158385i | \(-0.0506287\pi\) | |||||||
\(978\) | 379.507i | 0.0124083i | ||||||||
\(979\) | −53818.6 | −1.75695 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −31096.7 | −1.01207 | ||||||||
\(982\) | 9303.77i | 0.302337i | ||||||||
\(983\) | 17264.3i | 0.560168i | 0.959975 | + | 0.280084i | \(0.0903623\pi\) | ||||
−0.959975 | + | 0.280084i | \(0.909638\pi\) | |||||||
\(984\) | 2199.07 | 0.0712438 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −196.569 | −0.00634891 | ||||||||
\(987\) | − 4904.74i | − 0.158176i | ||||||||
\(988\) | − 3630.54i | − 0.116906i | ||||||||
\(989\) | 4194.60 | 0.134864 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23892.9 | 0.765876 | 0.382938 | − | 0.923774i | \(-0.374912\pi\) | ||||
0.382938 | + | 0.923774i | \(0.374912\pi\) | |||||||
\(992\) | − 9462.37i | − 0.302854i | ||||||||
\(993\) | − 2541.53i | − 0.0812217i | ||||||||
\(994\) | 23203.3 | 0.740406 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1439.36 | −0.0457912 | ||||||||
\(997\) | − 35830.2i | − 1.13817i | −0.822280 | − | 0.569083i | \(-0.807298\pi\) | ||||
0.822280 | − | 0.569083i | \(-0.192702\pi\) | |||||||
\(998\) | − 15906.1i | − 0.504507i | ||||||||
\(999\) | −248.534 | −0.00787115 |
(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 | 1150.4.b.n.599.2 | 8 | ||
5.2 | odd | 4 | 1150.4.a.p.1.2 | 4 | |||
5.3 | odd | 4 | 230.4.a.h.1.3 | ✓ | 4 | ||
5.4 | even | 2 | inner | 1150.4.b.n.599.7 | 8 | ||
15.8 | even | 4 | 2070.4.a.bj.1.2 | 4 | |||
20.3 | even | 4 | 1840.4.a.m.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.4.a.h.1.3 | ✓ | 4 | 5.3 | odd | 4 | ||
1150.4.a.p.1.2 | 4 | 5.2 | odd | 4 | |||
1150.4.b.n.599.2 | 8 | 1.1 | even | 1 | trivial | ||
1150.4.b.n.599.7 | 8 | 5.4 | even | 2 | inner | ||
1840.4.a.m.1.2 | 4 | 20.3 | even | 4 | |||
2070.4.a.bj.1.2 | 4 | 15.8 | even | 4 |