Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,5,Mod(11,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("15.11");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.c (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: | \(1.55054944626\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 73x^{4} + 1096x^{2} + 180 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 11.5 | ||
Root | \(4.56632i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 15.11 |
Dual form | 15.5.c.a.11.2 |
$q$-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 \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(11\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.56632i | 1.14158i | 0.821096 | + | 0.570790i | \(0.193363\pi\) | ||||
−0.821096 | + | 0.570790i | \(0.806637\pi\) | |||||||
\(3\) | −7.98405 | + | 4.15391i | −0.887116 | + | 0.461546i | ||||
\(4\) | −4.85128 | −0.303205 | ||||||||
\(5\) | 11.1803i | 0.447214i | ||||||||
\(6\) | −18.9681 | − | 36.4577i | −0.526892 | − | 1.01271i | ||||
\(7\) | 61.6068 | 1.25728 | 0.628641 | − | 0.777695i | \(-0.283611\pi\) | ||||
0.628641 | + | 0.777695i | \(0.283611\pi\) | |||||||
\(8\) | 50.9086i | 0.795447i | ||||||||
\(9\) | 46.4900 | − | 66.3301i | 0.573951 | − | 0.818890i | ||||
\(10\) | −51.0530 | −0.510530 | ||||||||
\(11\) | − | 108.827i | − | 0.899393i | −0.893181 | − | 0.449696i | \(-0.851532\pi\) | ||
0.893181 | − | 0.449696i | \(-0.148468\pi\) | |||||||
\(12\) | 38.7328 | − | 20.1518i | 0.268978 | − | 0.139943i | ||||
\(13\) | −63.7026 | −0.376938 | −0.188469 | − | 0.982079i | \(-0.560353\pi\) | ||||
−0.188469 | + | 0.982079i | \(0.560353\pi\) | |||||||
\(14\) | 281.317i | 1.43529i | ||||||||
\(15\) | −46.4422 | − | 89.2644i | −0.206410 | − | 0.396730i | ||||
\(16\) | −310.086 | −1.21127 | ||||||||
\(17\) | 175.143i | 0.606033i | 0.952985 | + | 0.303016i | \(0.0979937\pi\) | ||||
−0.952985 | + | 0.303016i | \(0.902006\pi\) | |||||||
\(18\) | 302.884 | + | 212.288i | 0.934828 | + | 0.655211i | ||||
\(19\) | 301.723 | 0.835798 | 0.417899 | − | 0.908493i | \(-0.362767\pi\) | ||||
0.417899 | + | 0.908493i | \(0.362767\pi\) | |||||||
\(20\) | − | 54.2389i | − | 0.135597i | ||||||
\(21\) | −491.872 | + | 255.909i | −1.11536 | + | 0.580293i | ||||
\(22\) | 496.937 | 1.02673 | ||||||||
\(23\) | − | 1039.90i | − | 1.96578i | −0.184203 | − | 0.982888i | \(-0.558970\pi\) | ||
0.184203 | − | 0.982888i | \(-0.441030\pi\) | |||||||
\(24\) | −211.470 | − | 406.457i | −0.367136 | − | 0.705654i | ||||
\(25\) | −125.000 | −0.200000 | ||||||||
\(26\) | − | 290.886i | − | 0.430305i | ||||||
\(27\) | −95.6491 | + | 722.698i | −0.131206 | + | 0.991355i | ||||
\(28\) | −298.872 | −0.381214 | ||||||||
\(29\) | 179.873i | 0.213880i | 0.994265 | + | 0.106940i | \(0.0341053\pi\) | ||||
−0.994265 | + | 0.106940i | \(0.965895\pi\) | |||||||
\(30\) | 407.610 | − | 212.070i | 0.452900 | − | 0.235633i | ||||
\(31\) | 1068.94 | 1.11232 | 0.556159 | − | 0.831076i | \(-0.312275\pi\) | ||||
0.556159 | + | 0.831076i | \(0.312275\pi\) | |||||||
\(32\) | − | 601.411i | − | 0.587316i | ||||||
\(33\) | 452.056 | + | 868.876i | 0.415111 | + | 0.797866i | ||||
\(34\) | −799.761 | −0.691835 | ||||||||
\(35\) | 688.785i | 0.562274i | ||||||||
\(36\) | −225.536 | + | 321.785i | −0.174025 | + | 0.248291i | ||||
\(37\) | −1061.29 | −0.775229 | −0.387615 | − | 0.921822i | \(-0.626701\pi\) | ||||
−0.387615 | + | 0.921822i | \(0.626701\pi\) | |||||||
\(38\) | 1377.76i | 0.954130i | ||||||||
\(39\) | 508.604 | − | 264.615i | 0.334388 | − | 0.173974i | ||||
\(40\) | −569.176 | −0.355735 | ||||||||
\(41\) | 173.768i | 0.103372i | 0.998663 | + | 0.0516860i | \(0.0164595\pi\) | ||||
−0.998663 | + | 0.0516860i | \(0.983541\pi\) | |||||||
\(42\) | −1168.56 | − | 2246.04i | −0.662451 | − | 1.27327i | ||||
\(43\) | −3032.96 | −1.64032 | −0.820162 | − | 0.572132i | \(-0.806117\pi\) | ||||
−0.820162 | + | 0.572132i | \(0.806117\pi\) | |||||||
\(44\) | 527.948i | 0.272700i | ||||||||
\(45\) | 741.593 | + | 519.774i | 0.366219 | + | 0.256679i | ||||
\(46\) | 4748.50 | 2.24409 | ||||||||
\(47\) | − | 935.703i | − | 0.423587i | −0.977314 | − | 0.211793i | \(-0.932070\pi\) | ||
0.977314 | − | 0.211793i | \(-0.0679304\pi\) | |||||||
\(48\) | 2475.74 | − | 1288.07i | 1.07454 | − | 0.559057i | ||||
\(49\) | 1394.40 | 0.580759 | ||||||||
\(50\) | − | 570.790i | − | 0.228316i | ||||||
\(51\) | −727.531 | − | 1398.35i | −0.279712 | − | 0.537622i | ||||
\(52\) | 309.039 | 0.114289 | ||||||||
\(53\) | 423.304i | 0.150696i | 0.997157 | + | 0.0753478i | \(0.0240067\pi\) | ||||
−0.997157 | + | 0.0753478i | \(0.975993\pi\) | |||||||
\(54\) | −3300.07 | − | 436.765i | −1.13171 | − | 0.149782i | ||||
\(55\) | 1216.72 | 0.402221 | ||||||||
\(56\) | 3136.32i | 1.00010i | ||||||||
\(57\) | −2408.97 | + | 1253.33i | −0.741450 | + | 0.385759i | ||||
\(58\) | −821.359 | −0.244161 | ||||||||
\(59\) | − | 3188.72i | − | 0.916034i | −0.888943 | − | 0.458017i | \(-0.848560\pi\) | ||
0.888943 | − | 0.458017i | \(-0.151440\pi\) | |||||||
\(60\) | 225.304 | + | 433.046i | 0.0625844 | + | 0.120291i | ||||
\(61\) | −2301.35 | −0.618475 | −0.309238 | − | 0.950985i | \(-0.600074\pi\) | ||||
−0.309238 | + | 0.950985i | \(0.600074\pi\) | |||||||
\(62\) | 4881.11i | 1.26980i | ||||||||
\(63\) | 2864.10 | − | 4086.39i | 0.721618 | − | 1.02958i | ||||
\(64\) | −2215.13 | −0.540804 | ||||||||
\(65\) | − | 712.216i | − | 0.168572i | ||||||
\(66\) | −3967.57 | + | 2064.23i | −0.910828 | + | 0.473883i | ||||
\(67\) | 4219.06 | 0.939867 | 0.469933 | − | 0.882702i | \(-0.344278\pi\) | ||||
0.469933 | + | 0.882702i | \(0.344278\pi\) | |||||||
\(68\) | − | 849.669i | − | 0.183752i | ||||||
\(69\) | 4319.64 | + | 8302.58i | 0.907296 | + | 1.74387i | ||||
\(70\) | −3145.21 | −0.641880 | ||||||||
\(71\) | 475.261i | 0.0942791i | 0.998888 | + | 0.0471396i | \(0.0150106\pi\) | ||||
−0.998888 | + | 0.0471396i | \(0.984989\pi\) | |||||||
\(72\) | 3376.77 | + | 2366.74i | 0.651384 | + | 0.456548i | ||||
\(73\) | −2148.47 | −0.403166 | −0.201583 | − | 0.979471i | \(-0.564609\pi\) | ||||
−0.201583 | + | 0.979471i | \(0.564609\pi\) | |||||||
\(74\) | − | 4846.18i | − | 0.884986i | ||||||
\(75\) | 998.006 | − | 519.239i | 0.177423 | − | 0.0923092i | ||||
\(76\) | −1463.74 | −0.253418 | ||||||||
\(77\) | − | 6704.46i | − | 1.13079i | ||||||
\(78\) | 1208.32 | + | 2322.45i | 0.198606 | + | 0.381731i | ||||
\(79\) | 3106.20 | 0.497709 | 0.248855 | − | 0.968541i | \(-0.419946\pi\) | ||||
0.248855 | + | 0.968541i | \(0.419946\pi\) | |||||||
\(80\) | − | 3466.86i | − | 0.541697i | ||||||
\(81\) | −2238.36 | − | 6167.37i | −0.341161 | − | 0.940005i | ||||
\(82\) | −793.482 | −0.118007 | ||||||||
\(83\) | 3769.87i | 0.547231i | 0.961839 | + | 0.273615i | \(0.0882195\pi\) | ||||
−0.961839 | + | 0.273615i | \(0.911780\pi\) | |||||||
\(84\) | 2386.21 | − | 1241.49i | 0.338181 | − | 0.175948i | ||||
\(85\) | −1958.16 | −0.271026 | ||||||||
\(86\) | − | 13849.5i | − | 1.87256i | ||||||
\(87\) | −747.178 | − | 1436.12i | −0.0987156 | − | 0.189737i | ||||
\(88\) | 5540.21 | 0.715420 | ||||||||
\(89\) | 8260.68i | 1.04288i | 0.853287 | + | 0.521442i | \(0.174606\pi\) | ||||
−0.853287 | + | 0.521442i | \(0.825394\pi\) | |||||||
\(90\) | −2373.46 | + | 3386.35i | −0.293019 | + | 0.418068i | ||||
\(91\) | −3924.51 | −0.473918 | ||||||||
\(92\) | 5044.82i | 0.596033i | ||||||||
\(93\) | −8534.44 | + | 4440.27i | −0.986755 | + | 0.513385i | ||||
\(94\) | 4272.72 | 0.483558 | ||||||||
\(95\) | 3373.37i | 0.373780i | ||||||||
\(96\) | 2498.21 | + | 4801.70i | 0.271073 | + | 0.521018i | ||||
\(97\) | 9310.26 | 0.989505 | 0.494753 | − | 0.869034i | \(-0.335259\pi\) | ||||
0.494753 | + | 0.869034i | \(0.335259\pi\) | |||||||
\(98\) | 6367.29i | 0.662983i | ||||||||
\(99\) | −7218.47 | − | 5059.35i | −0.736504 | − | 0.516207i | ||||
\(100\) | 606.409 | 0.0606409 | ||||||||
\(101\) | 10239.8i | 1.00380i | 0.864925 | + | 0.501902i | \(0.167366\pi\) | ||||
−0.864925 | + | 0.501902i | \(0.832634\pi\) | |||||||
\(102\) | 6385.33 | − | 3322.14i | 0.613738 | − | 0.319314i | ||||
\(103\) | −5400.15 | −0.509016 | −0.254508 | − | 0.967071i | \(-0.581913\pi\) | ||||
−0.254508 | + | 0.967071i | \(0.581913\pi\) | |||||||
\(104\) | − | 3243.01i | − | 0.299835i | ||||||
\(105\) | −2861.15 | − | 5499.29i | −0.259515 | − | 0.498802i | ||||
\(106\) | −1932.94 | −0.172031 | ||||||||
\(107\) | 6786.14i | 0.592728i | 0.955075 | + | 0.296364i | \(0.0957741\pi\) | ||||
−0.955075 | + | 0.296364i | \(0.904226\pi\) | |||||||
\(108\) | 464.020 | − | 3506.01i | 0.0397823 | − | 0.300584i | ||||
\(109\) | −4600.12 | −0.387183 | −0.193591 | − | 0.981082i | \(-0.562014\pi\) | ||||
−0.193591 | + | 0.981082i | \(0.562014\pi\) | |||||||
\(110\) | 5555.92i | 0.459167i | ||||||||
\(111\) | 8473.38 | − | 4408.50i | 0.687719 | − | 0.357804i | ||||
\(112\) | −19103.4 | −1.52291 | ||||||||
\(113\) | − | 14751.6i | − | 1.15526i | −0.816298 | − | 0.577632i | \(-0.803977\pi\) | ||
0.816298 | − | 0.577632i | \(-0.196023\pi\) | |||||||
\(114\) | −5723.11 | − | 11000.1i | −0.440375 | − | 0.846425i | ||||
\(115\) | 11626.4 | 0.879122 | ||||||||
\(116\) | − | 872.615i | − | 0.0648495i | ||||||
\(117\) | −2961.53 | + | 4225.39i | −0.216344 | + | 0.308671i | ||||
\(118\) | 14560.7 | 1.04573 | ||||||||
\(119\) | 10790.0i | 0.761954i | ||||||||
\(120\) | 4544.33 | − | 2364.31i | 0.315578 | − | 0.164188i | ||||
\(121\) | 2797.78 | 0.191092 | ||||||||
\(122\) | − | 10508.7i | − | 0.706039i | ||||||
\(123\) | −721.818 | − | 1387.37i | −0.0477109 | − | 0.0917030i | ||||
\(124\) | −5185.71 | −0.337260 | ||||||||
\(125\) | − | 1397.54i | − | 0.0894427i | ||||||
\(126\) | 18659.7 | + | 13078.4i | 1.17534 | + | 0.823785i | ||||
\(127\) | −15454.5 | −0.958178 | −0.479089 | − | 0.877766i | \(-0.659033\pi\) | ||||
−0.479089 | + | 0.877766i | \(0.659033\pi\) | |||||||
\(128\) | − | 19737.6i | − | 1.20469i | ||||||
\(129\) | 24215.3 | − | 12598.6i | 1.45516 | − | 0.757084i | ||||
\(130\) | 3252.21 | 0.192438 | ||||||||
\(131\) | 21843.0i | 1.27283i | 0.771347 | + | 0.636415i | \(0.219583\pi\) | ||||
−0.771347 | + | 0.636415i | \(0.780417\pi\) | |||||||
\(132\) | −2193.05 | − | 4215.16i | −0.125864 | − | 0.241917i | ||||
\(133\) | 18588.2 | 1.05083 | ||||||||
\(134\) | 19265.6i | 1.07293i | ||||||||
\(135\) | −8080.01 | − | 1069.39i | −0.443347 | − | 0.0586771i | ||||
\(136\) | −8916.32 | −0.482067 | ||||||||
\(137\) | − | 18924.3i | − | 1.00827i | −0.863624 | − | 0.504137i | \(-0.831811\pi\) | ||
0.863624 | − | 0.504137i | \(-0.168189\pi\) | |||||||
\(138\) | −37912.2 | + | 19724.8i | −1.99077 | + | 1.03575i | ||||
\(139\) | −21796.9 | −1.12815 | −0.564073 | − | 0.825725i | \(-0.690766\pi\) | ||||
−0.564073 | + | 0.825725i | \(0.690766\pi\) | |||||||
\(140\) | − | 3341.49i | − | 0.170484i | ||||||
\(141\) | 3886.83 | + | 7470.70i | 0.195505 | + | 0.375771i | ||||
\(142\) | −2170.19 | −0.107627 | ||||||||
\(143\) | 6932.53i | 0.339016i | ||||||||
\(144\) | −14415.9 | + | 20568.0i | −0.695210 | + | 0.991898i | ||||
\(145\) | −2011.04 | −0.0956502 | ||||||||
\(146\) | − | 9810.60i | − | 0.460246i | ||||||
\(147\) | −11133.0 | + | 5792.22i | −0.515201 | + | 0.268047i | ||||
\(148\) | 5148.60 | 0.235053 | ||||||||
\(149\) | − | 31031.9i | − | 1.39777i | −0.715235 | − | 0.698884i | \(-0.753680\pi\) | ||
0.715235 | − | 0.698884i | \(-0.246320\pi\) | |||||||
\(150\) | 2371.01 | + | 4557.21i | 0.105378 | + | 0.202543i | ||||
\(151\) | 13097.0 | 0.574405 | 0.287203 | − | 0.957870i | \(-0.407275\pi\) | ||||
0.287203 | + | 0.957870i | \(0.407275\pi\) | |||||||
\(152\) | 15360.3i | 0.664834i | ||||||||
\(153\) | 11617.3 | + | 8142.42i | 0.496274 | + | 0.347833i | ||||
\(154\) | 30614.7 | 1.29089 | ||||||||
\(155\) | 11951.1i | 0.497443i | ||||||||
\(156\) | −2467.38 | + | 1283.72i | −0.101388 | + | 0.0527498i | ||||
\(157\) | 12609.6 | 0.511567 | 0.255784 | − | 0.966734i | \(-0.417667\pi\) | ||||
0.255784 | + | 0.966734i | \(0.417667\pi\) | |||||||
\(158\) | 14183.9i | 0.568175i | ||||||||
\(159\) | −1758.37 | − | 3379.68i | −0.0695529 | − | 0.133685i | ||||
\(160\) | 6723.98 | 0.262656 | ||||||||
\(161\) | − | 64064.7i | − | 2.47154i | ||||||
\(162\) | 28162.2 | − | 10221.1i | 1.07309 | − | 0.389462i | ||||
\(163\) | 1570.77 | 0.0591206 | 0.0295603 | − | 0.999563i | \(-0.490589\pi\) | ||||
0.0295603 | + | 0.999563i | \(0.490589\pi\) | |||||||
\(164\) | − | 842.998i | − | 0.0313429i | ||||||
\(165\) | −9714.33 | + | 5054.14i | −0.356817 | + | 0.185643i | ||||
\(166\) | −17214.4 | −0.624707 | ||||||||
\(167\) | 9867.19i | 0.353802i | 0.984229 | + | 0.176901i | \(0.0566073\pi\) | ||||
−0.984229 | + | 0.176901i | \(0.943393\pi\) | |||||||
\(168\) | −13028.0 | − | 25040.5i | −0.461593 | − | 0.887207i | ||||
\(169\) | −24503.0 | −0.857918 | ||||||||
\(170\) | − | 8941.60i | − | 0.309398i | ||||||
\(171\) | 14027.1 | − | 20013.3i | 0.479707 | − | 0.684427i | ||||
\(172\) | 14713.7 | 0.497354 | ||||||||
\(173\) | 21586.3i | 0.721250i | 0.932711 | + | 0.360625i | \(0.117437\pi\) | ||||
−0.932711 | + | 0.360625i | \(0.882563\pi\) | |||||||
\(174\) | 6557.77 | − | 3411.85i | 0.216600 | − | 0.112692i | ||||
\(175\) | −7700.85 | −0.251456 | ||||||||
\(176\) | 33745.5i | 1.08941i | ||||||||
\(177\) | 13245.6 | + | 25458.9i | 0.422792 | + | 0.812629i | ||||
\(178\) | −37720.9 | −1.19054 | ||||||||
\(179\) | − | 22176.0i | − | 0.692114i | −0.938213 | − | 0.346057i | \(-0.887520\pi\) | ||
0.938213 | − | 0.346057i | \(-0.112480\pi\) | |||||||
\(180\) | −3597.67 | − | 2521.57i | −0.111039 | − | 0.0778262i | ||||
\(181\) | −57041.1 | −1.74113 | −0.870565 | − | 0.492054i | \(-0.836246\pi\) | ||||
−0.870565 | + | 0.492054i | \(0.836246\pi\) | |||||||
\(182\) | − | 17920.6i | − | 0.541015i | ||||||
\(183\) | 18374.1 | − | 9559.59i | 0.548660 | − | 0.285455i | ||||
\(184\) | 52939.7 | 1.56367 | ||||||||
\(185\) | − | 11865.6i | − | 0.346693i | ||||||
\(186\) | −20275.7 | − | 38971.0i | −0.586070 | − | 1.12646i | ||||
\(187\) | 19060.3 | 0.545062 | ||||||||
\(188\) | 4539.35i | 0.128434i | ||||||||
\(189\) | −5892.64 | + | 44523.1i | −0.164963 | + | 1.24641i | ||||
\(190\) | −15403.9 | −0.426700 | ||||||||
\(191\) | 64290.5i | 1.76230i | 0.472835 | + | 0.881151i | \(0.343231\pi\) | ||||
−0.472835 | + | 0.881151i | \(0.656769\pi\) | |||||||
\(192\) | 17685.7 | − | 9201.46i | 0.479756 | − | 0.249606i | ||||
\(193\) | 36452.6 | 0.978621 | 0.489310 | − | 0.872110i | \(-0.337249\pi\) | ||||
0.489310 | + | 0.872110i | \(0.337249\pi\) | |||||||
\(194\) | 42513.6i | 1.12960i | ||||||||
\(195\) | 2958.48 | + | 5686.37i | 0.0778037 | + | 0.149543i | ||||
\(196\) | −6764.63 | −0.176089 | ||||||||
\(197\) | 63474.0i | 1.63555i | 0.575540 | + | 0.817774i | \(0.304792\pi\) | ||||
−0.575540 | + | 0.817774i | \(0.695208\pi\) | |||||||
\(198\) | 23102.6 | − | 32961.9i | 0.589292 | − | 0.840778i | ||||
\(199\) | −9634.07 | −0.243279 | −0.121639 | − | 0.992574i | \(-0.538815\pi\) | ||||
−0.121639 | + | 0.992574i | \(0.538815\pi\) | |||||||
\(200\) | − | 6363.58i | − | 0.159089i | ||||||
\(201\) | −33685.2 | + | 17525.6i | −0.833771 | + | 0.433792i | ||||
\(202\) | −46758.2 | −1.14592 | ||||||||
\(203\) | 11081.4i | 0.268908i | ||||||||
\(204\) | 3529.45 | + | 6783.80i | 0.0848100 | + | 0.163009i | ||||
\(205\) | −1942.79 | −0.0462294 | ||||||||
\(206\) | − | 24658.8i | − | 0.581082i | ||||||
\(207\) | −68976.4 | − | 48344.8i | −1.60975 | − | 1.12826i | ||||
\(208\) | 19753.2 | 0.456575 | ||||||||
\(209\) | − | 32835.5i | − | 0.751711i | ||||||
\(210\) | 25111.5 | − | 13064.9i | 0.569423 | − | 0.296257i | ||||
\(211\) | 64309.8 | 1.44448 | 0.722241 | − | 0.691641i | \(-0.243112\pi\) | ||||
0.722241 | + | 0.691641i | \(0.243112\pi\) | |||||||
\(212\) | − | 2053.56i | − | 0.0456916i | ||||||
\(213\) | −1974.19 | − | 3794.51i | −0.0435141 | − | 0.0836365i | ||||
\(214\) | −30987.7 | −0.676646 | ||||||||
\(215\) | − | 33909.5i | − | 0.733575i | ||||||
\(216\) | −36791.6 | − | 4869.37i | −0.788571 | − | 0.104367i | ||||
\(217\) | 65853.8 | 1.39850 | ||||||||
\(218\) | − | 21005.6i | − | 0.442000i | ||||||
\(219\) | 17153.5 | − | 8924.56i | 0.357655 | − | 0.186079i | ||||
\(220\) | −5902.63 | −0.121955 | ||||||||
\(221\) | − | 11157.1i | − | 0.228437i | ||||||
\(222\) | 20130.6 | + | 38692.2i | 0.408462 | + | 0.785086i | ||||
\(223\) | −51769.1 | −1.04102 | −0.520512 | − | 0.853854i | \(-0.674259\pi\) | ||||
−0.520512 | + | 0.853854i | \(0.674259\pi\) | |||||||
\(224\) | − | 37051.1i | − | 0.738422i | ||||||
\(225\) | −5811.25 | + | 8291.26i | −0.114790 | + | 0.163778i | ||||
\(226\) | 67360.3 | 1.31883 | ||||||||
\(227\) | − | 69770.7i | − | 1.35401i | −0.735979 | − | 0.677004i | \(-0.763278\pi\) | ||
0.735979 | − | 0.677004i | \(-0.236722\pi\) | |||||||
\(228\) | 11686.6 | − | 6080.26i | 0.224811 | − | 0.116964i | ||||
\(229\) | −2284.08 | −0.0435553 | −0.0217777 | − | 0.999763i | \(-0.506933\pi\) | ||||
−0.0217777 | + | 0.999763i | \(0.506933\pi\) | |||||||
\(230\) | 53089.8i | 1.00359i | ||||||||
\(231\) | 27849.7 | + | 53528.7i | 0.521912 | + | 1.00314i | ||||
\(232\) | −9157.11 | −0.170131 | ||||||||
\(233\) | − | 22464.3i | − | 0.413791i | −0.978363 | − | 0.206895i | \(-0.933664\pi\) | ||
0.978363 | − | 0.206895i | \(-0.0663360\pi\) | |||||||
\(234\) | −19294.5 | − | 13523.3i | −0.352372 | − | 0.246974i | ||||
\(235\) | 10461.5 | 0.189434 | ||||||||
\(236\) | 15469.3i | 0.277746i | ||||||||
\(237\) | −24800.1 | + | 12902.9i | −0.441526 | + | 0.229716i | ||||
\(238\) | −49270.7 | −0.869832 | ||||||||
\(239\) | 42116.1i | 0.737314i | 0.929565 | + | 0.368657i | \(0.120182\pi\) | ||||
−0.929565 | + | 0.368657i | \(0.879818\pi\) | |||||||
\(240\) | 14401.0 | + | 27679.6i | 0.250018 | + | 0.480548i | ||||
\(241\) | −975.921 | −0.0168028 | −0.00840138 | − | 0.999965i | \(-0.502674\pi\) | ||||
−0.00840138 | + | 0.999965i | \(0.502674\pi\) | |||||||
\(242\) | 12775.6i | 0.218147i | ||||||||
\(243\) | 43489.9 | + | 39942.7i | 0.736505 | + | 0.676432i | ||||
\(244\) | 11164.5 | 0.187525 | ||||||||
\(245\) | 15589.9i | 0.259723i | ||||||||
\(246\) | 6335.19 | − | 3296.05i | 0.104686 | − | 0.0544658i | ||||
\(247\) | −19220.5 | −0.315044 | ||||||||
\(248\) | 54418.1i | 0.884790i | ||||||||
\(249\) | −15659.7 | − | 30098.8i | −0.252572 | − | 0.485457i | ||||
\(250\) | 6381.63 | 0.102106 | ||||||||
\(251\) | − | 95434.5i | − | 1.51481i | −0.652945 | − | 0.757405i | \(-0.726467\pi\) | ||
0.652945 | − | 0.757405i | \(-0.273533\pi\) | |||||||
\(252\) | −13894.6 | + | 19824.2i | −0.218798 | + | 0.312172i | ||||
\(253\) | −113168. | −1.76801 | ||||||||
\(254\) | − | 70570.0i | − | 1.09384i | ||||||
\(255\) | 15634.1 | − | 8134.04i | 0.240432 | − | 0.125091i | ||||
\(256\) | 54686.0 | 0.834442 | ||||||||
\(257\) | − | 23114.1i | − | 0.349953i | −0.984573 | − | 0.174977i | \(-0.944015\pi\) | ||
0.984573 | − | 0.174977i | \(-0.0559850\pi\) | |||||||
\(258\) | 57529.4 | + | 110575.i | 0.864272 | + | 1.66118i | ||||
\(259\) | −65382.6 | −0.974682 | ||||||||
\(260\) | 3455.16i | 0.0511118i | ||||||||
\(261\) | 11931.0 | + | 8362.31i | 0.175144 | + | 0.122757i | ||||
\(262\) | −99742.2 | −1.45304 | ||||||||
\(263\) | − | 37165.6i | − | 0.537316i | −0.963236 | − | 0.268658i | \(-0.913420\pi\) | ||
0.963236 | − | 0.268658i | \(-0.0865801\pi\) | |||||||
\(264\) | −44233.3 | + | 23013.6i | −0.634661 | + | 0.330199i | ||||
\(265\) | −4732.68 | −0.0673931 | ||||||||
\(266\) | 84879.7i | 1.19961i | ||||||||
\(267\) | −34314.1 | − | 65953.7i | −0.481339 | − | 0.925159i | ||||
\(268\) | −20467.8 | −0.284972 | ||||||||
\(269\) | 134496.i | 1.85869i | 0.369216 | + | 0.929344i | \(0.379626\pi\) | ||||
−0.369216 | + | 0.929344i | \(0.620374\pi\) | |||||||
\(270\) | 4883.18 | − | 36895.9i | 0.0669846 | − | 0.506117i | ||||
\(271\) | 111796. | 1.52226 | 0.761128 | − | 0.648602i | \(-0.224646\pi\) | ||||
0.761128 | + | 0.648602i | \(0.224646\pi\) | |||||||
\(272\) | − | 54309.5i | − | 0.734070i | ||||||
\(273\) | 31333.5 | − | 16302.1i | 0.420420 | − | 0.218735i | ||||
\(274\) | 86414.3 | 1.15102 | ||||||||
\(275\) | 13603.3i | 0.179879i | ||||||||
\(276\) | −20955.7 | − | 40278.1i | −0.275096 | − | 0.528750i | ||||
\(277\) | 128402. | 1.67345 | 0.836725 | − | 0.547624i | \(-0.184467\pi\) | ||||
0.836725 | + | 0.547624i | \(0.184467\pi\) | |||||||
\(278\) | − | 99531.6i | − | 1.28787i | ||||||
\(279\) | 49694.9 | − | 70902.7i | 0.638415 | − | 0.910865i | ||||
\(280\) | −35065.1 | −0.447259 | ||||||||
\(281\) | 29381.6i | 0.372102i | 0.982540 | + | 0.186051i | \(0.0595690\pi\) | ||||
−0.982540 | + | 0.186051i | \(0.940431\pi\) | |||||||
\(282\) | −34113.6 | + | 17748.5i | −0.428972 | + | 0.223184i | ||||
\(283\) | 60115.2 | 0.750605 | 0.375303 | − | 0.926902i | \(-0.377539\pi\) | ||||
0.375303 | + | 0.926902i | \(0.377539\pi\) | |||||||
\(284\) | − | 2305.62i | − | 0.0285859i | ||||||
\(285\) | −14012.7 | − | 26933.1i | −0.172517 | − | 0.331587i | ||||
\(286\) | −31656.1 | −0.387013 | ||||||||
\(287\) | 10705.3i | 0.129968i | ||||||||
\(288\) | −39891.7 | − | 27959.6i | −0.480947 | − | 0.337090i | ||||
\(289\) | 52845.8 | 0.632724 | ||||||||
\(290\) | − | 9183.07i | − | 0.109192i | ||||||
\(291\) | −74333.5 | + | 38674.0i | −0.877806 | + | 0.456702i | ||||
\(292\) | 10422.8 | 0.122242 | ||||||||
\(293\) | 3769.43i | 0.0439076i | 0.999759 | + | 0.0219538i | \(0.00698868\pi\) | ||||
−0.999759 | + | 0.0219538i | \(0.993011\pi\) | |||||||
\(294\) | −26449.1 | − | 50836.7i | −0.305997 | − | 0.588143i | ||||
\(295\) | 35650.9 | 0.409663 | ||||||||
\(296\) | − | 54028.8i | − | 0.616654i | ||||||
\(297\) | 78648.7 | + | 10409.2i | 0.891618 | + | 0.118006i | ||||
\(298\) | 141701. | 1.59566 | ||||||||
\(299\) | 66244.0i | 0.740976i | ||||||||
\(300\) | −4841.60 | + | 2518.97i | −0.0537956 | + | 0.0279886i | ||||
\(301\) | −186851. | −2.06235 | ||||||||
\(302\) | 59805.2i | 0.655730i | ||||||||
\(303\) | −42535.2 | − | 81755.1i | −0.463302 | − | 0.890491i | ||||
\(304\) | −93560.0 | −1.01238 | ||||||||
\(305\) | − | 25729.8i | − | 0.276591i | ||||||
\(306\) | −37180.9 | + | 53048.2i | −0.397079 | + | 0.566536i | ||||
\(307\) | −140911. | −1.49509 | −0.747546 | − | 0.664210i | \(-0.768768\pi\) | ||||
−0.747546 | + | 0.664210i | \(0.768768\pi\) | |||||||
\(308\) | 32525.2i | 0.342861i | ||||||||
\(309\) | 43115.0 | − | 22431.7i | 0.451556 | − | 0.234934i | ||||
\(310\) | −54572.4 | −0.567871 | ||||||||
\(311\) | 18018.5i | 0.186294i | 0.995652 | + | 0.0931468i | \(0.0296926\pi\) | ||||
−0.995652 | + | 0.0931468i | \(0.970307\pi\) | |||||||
\(312\) | 13471.2 | + | 25892.3i | 0.138387 | + | 0.265988i | ||||
\(313\) | −44156.6 | −0.450720 | −0.225360 | − | 0.974276i | \(-0.572356\pi\) | ||||
−0.225360 | + | 0.974276i | \(0.572356\pi\) | |||||||
\(314\) | 57579.6i | 0.583995i | ||||||||
\(315\) | 45687.2 | + | 32021.6i | 0.460440 | + | 0.322717i | ||||
\(316\) | −15069.0 | −0.150908 | ||||||||
\(317\) | 193874.i | 1.92931i | 0.263525 | + | 0.964653i | \(0.415115\pi\) | ||||
−0.263525 | + | 0.964653i | \(0.584885\pi\) | |||||||
\(318\) | 15432.7 | − | 8029.27i | 0.152612 | − | 0.0794002i | ||||
\(319\) | 19575.0 | 0.192362 | ||||||||
\(320\) | − | 24765.9i | − | 0.241855i | ||||||
\(321\) | −28189.0 | − | 54180.8i | −0.273571 | − | 0.525818i | ||||
\(322\) | 292540. | 2.82146 | ||||||||
\(323\) | 52844.8i | 0.506521i | ||||||||
\(324\) | 10858.9 | + | 29919.6i | 0.103442 | + | 0.285014i | ||||
\(325\) | 7962.82 | 0.0753876 | ||||||||
\(326\) | 7172.66i | 0.0674909i | ||||||||
\(327\) | 36727.5 | − | 19108.5i | 0.343476 | − | 0.178703i | ||||
\(328\) | −8846.31 | −0.0822270 | ||||||||
\(329\) | − | 57645.7i | − | 0.532568i | ||||||
\(330\) | −23078.8 | − | 44358.7i | −0.211927 | − | 0.407335i | ||||
\(331\) | −37018.2 | −0.337878 | −0.168939 | − | 0.985627i | \(-0.554034\pi\) | ||||
−0.168939 | + | 0.985627i | \(0.554034\pi\) | |||||||
\(332\) | − | 18288.7i | − | 0.165923i | ||||||
\(333\) | −49339.3 | + | 70395.4i | −0.444943 | + | 0.634827i | ||||
\(334\) | −45056.7 | −0.403893 | ||||||||
\(335\) | 47170.6i | 0.420321i | ||||||||
\(336\) | 152522. | − | 79353.8i | 1.35100 | − | 0.702893i | ||||
\(337\) | −106760. | −0.940041 | −0.470021 | − | 0.882655i | \(-0.655754\pi\) | ||||
−0.470021 | + | 0.882655i | \(0.655754\pi\) | |||||||
\(338\) | − | 111888.i | − | 0.979382i | ||||||
\(339\) | 61276.7 | + | 117777.i | 0.533207 | + | 1.02485i | ||||
\(340\) | 9499.59 | 0.0821764 | ||||||||
\(341\) | − | 116329.i | − | 1.00041i | ||||||
\(342\) | 91387.2 | + | 64052.3i | 0.781328 | + | 0.547624i | ||||
\(343\) | −62013.3 | −0.527104 | ||||||||
\(344\) | − | 154404.i | − | 1.30479i | ||||||
\(345\) | −92825.6 | + | 48295.0i | −0.779883 | + | 0.405755i | ||||
\(346\) | −98570.0 | −0.823365 | ||||||||
\(347\) | − | 63787.6i | − | 0.529758i | −0.964282 | − | 0.264879i | \(-0.914668\pi\) | ||
0.964282 | − | 0.264879i | \(-0.0853320\pi\) | |||||||
\(348\) | 3624.77 | + | 6967.00i | 0.0299310 | + | 0.0575291i | ||||
\(349\) | 127165. | 1.04404 | 0.522021 | − | 0.852932i | \(-0.325178\pi\) | ||||
0.522021 | + | 0.852932i | \(0.325178\pi\) | |||||||
\(350\) | − | 35164.6i | − | 0.287058i | ||||||
\(351\) | 6093.09 | − | 46037.7i | 0.0494565 | − | 0.373680i | ||||
\(352\) | −65449.5 | −0.528228 | ||||||||
\(353\) | 67251.4i | 0.539699i | 0.962902 | + | 0.269850i | \(0.0869740\pi\) | ||||
−0.962902 | + | 0.269850i | \(0.913026\pi\) | |||||||
\(354\) | −116253. | + | 60483.9i | −0.927681 | + | 0.482651i | ||||
\(355\) | −5313.58 | −0.0421629 | ||||||||
\(356\) | − | 40074.8i | − | 0.316207i | ||||||
\(357\) | −44820.9 | − | 86148.1i | −0.351677 | − | 0.675942i | ||||
\(358\) | 101263. | 0.790104 | ||||||||
\(359\) | − | 143827.i | − | 1.11597i | −0.829851 | − | 0.557984i | \(-0.811575\pi\) | ||
0.829851 | − | 0.557984i | \(-0.188425\pi\) | |||||||
\(360\) | −26461.0 | + | 37753.5i | −0.204174 | + | 0.291308i | ||||
\(361\) | −39284.1 | −0.301441 | ||||||||
\(362\) | − | 260468.i | − | 1.98764i | ||||||
\(363\) | −22337.6 | + | 11621.7i | −0.169521 | + | 0.0881979i | ||||
\(364\) | 19038.9 | 0.143694 | ||||||||
\(365\) | − | 24020.6i | − | 0.180301i | ||||||
\(366\) | 43652.2 | + | 83901.8i | 0.325869 | + | 0.626339i | ||||
\(367\) | 122411. | 0.908838 | 0.454419 | − | 0.890788i | \(-0.349847\pi\) | ||||
0.454419 | + | 0.890788i | \(0.349847\pi\) | |||||||
\(368\) | 322457.i | 2.38109i | ||||||||
\(369\) | 11526.1 | + | 8078.49i | 0.0846502 | + | 0.0593304i | ||||
\(370\) | 54182.0 | 0.395778 | ||||||||
\(371\) | 26078.4i | 0.189467i | ||||||||
\(372\) | 41402.9 | − | 21541.0i | 0.299189 | − | 0.155661i | ||||
\(373\) | 193520. | 1.39094 | 0.695471 | − | 0.718554i | \(-0.255196\pi\) | ||||
0.695471 | + | 0.718554i | \(0.255196\pi\) | |||||||
\(374\) | 87035.2i | 0.622231i | ||||||||
\(375\) | 5805.27 | + | 11158.0i | 0.0412819 | + | 0.0793461i | ||||
\(376\) | 47635.4 | 0.336941 | ||||||||
\(377\) | − | 11458.4i | − | 0.0806196i | ||||||
\(378\) | −203307. | − | 26907.7i | −1.42288 | − | 0.188318i | ||||
\(379\) | 50009.6 | 0.348157 | 0.174079 | − | 0.984732i | \(-0.444305\pi\) | ||||
0.174079 | + | 0.984732i | \(0.444305\pi\) | |||||||
\(380\) | − | 16365.1i | − | 0.113332i | ||||||
\(381\) | 123389. | − | 64196.5i | 0.850016 | − | 0.442243i | ||||
\(382\) | −293571. | −2.01181 | ||||||||
\(383\) | − | 72111.0i | − | 0.491591i | −0.969322 | − | 0.245796i | \(-0.920951\pi\) | ||
0.969322 | − | 0.245796i | \(-0.0790492\pi\) | |||||||
\(384\) | 81988.2 | + | 157586.i | 0.556018 | + | 1.06870i | ||||
\(385\) | 74958.1 | 0.505705 | ||||||||
\(386\) | 166454.i | 1.11717i | ||||||||
\(387\) | −141002. | + | 201176.i | −0.941465 | + | 1.34324i | ||||
\(388\) | −45166.6 | −0.300023 | ||||||||
\(389\) | 25283.5i | 0.167085i | 0.996504 | + | 0.0835426i | \(0.0266235\pi\) | ||||
−0.996504 | + | 0.0835426i | \(0.973377\pi\) | |||||||
\(390\) | −25965.8 | + | 13509.4i | −0.170715 | + | 0.0888191i | ||||
\(391\) | 182131. | 1.19132 | ||||||||
\(392\) | 70987.1i | 0.461963i | ||||||||
\(393\) | −90734.0 | − | 174396.i | −0.587469 | − | 1.12915i | ||||
\(394\) | −289842. | −1.86711 | ||||||||
\(395\) | 34728.4i | 0.222582i | ||||||||
\(396\) | 35018.8 | + | 24544.3i | 0.223311 | + | 0.156517i | ||||
\(397\) | −28110.1 | −0.178353 | −0.0891766 | − | 0.996016i | \(-0.528424\pi\) | ||||
−0.0891766 | + | 0.996016i | \(0.528424\pi\) | |||||||
\(398\) | − | 43992.3i | − | 0.277722i | ||||||
\(399\) | −148409. | + | 77213.8i | −0.932212 | + | 0.485008i | ||||
\(400\) | 38760.7 | 0.242254 | ||||||||
\(401\) | 58113.8i | 0.361402i | 0.983538 | + | 0.180701i | \(0.0578366\pi\) | ||||
−0.983538 | + | 0.180701i | \(0.942163\pi\) | |||||||
\(402\) | −80027.6 | − | 153817.i | −0.495208 | − | 0.951817i | ||||
\(403\) | −68094.0 | −0.419275 | ||||||||
\(404\) | − | 49676.1i | − | 0.304358i | ||||||
\(405\) | 68953.3 | − | 25025.6i | 0.420383 | − | 0.152572i | ||||
\(406\) | −50601.3 | −0.306980 | ||||||||
\(407\) | 115496.i | 0.697236i | ||||||||
\(408\) | 71188.3 | − | 37037.6i | 0.427650 | − | 0.222496i | ||||
\(409\) | −8511.55 | −0.0508818 | −0.0254409 | − | 0.999676i | \(-0.508099\pi\) | ||||
−0.0254409 | + | 0.999676i | \(0.508099\pi\) | |||||||
\(410\) | − | 8871.39i | − | 0.0527745i | ||||||
\(411\) | 78609.8 | + | 151092.i | 0.465364 | + | 0.894456i | ||||
\(412\) | 26197.6 | 0.154336 | ||||||||
\(413\) | − | 196447.i | − | 1.15171i | ||||||
\(414\) | 220758. | − | 314968.i | 1.28800 | − | 1.83766i | ||||
\(415\) | −42148.4 | −0.244729 | ||||||||
\(416\) | 38311.4i | 0.221382i | ||||||||
\(417\) | 174028. | − | 90542.4i | 1.00080 | − | 0.520691i | ||||
\(418\) | 149937. | 0.858138 | ||||||||
\(419\) | − | 292724.i | − | 1.66736i | −0.552244 | − | 0.833682i | \(-0.686228\pi\) | ||
0.552244 | − | 0.833682i | \(-0.313772\pi\) | |||||||
\(420\) | 13880.2 | + | 26678.6i | 0.0786862 | + | 0.151239i | ||||
\(421\) | −152199. | −0.858713 | −0.429357 | − | 0.903135i | \(-0.641260\pi\) | ||||
−0.429357 | + | 0.903135i | \(0.641260\pi\) | |||||||
\(422\) | 293659.i | 1.64899i | ||||||||
\(423\) | −62065.3 | − | 43500.9i | −0.346871 | − | 0.243118i | ||||
\(424\) | −21549.8 | −0.119870 | ||||||||
\(425\) | − | 21892.9i | − | 0.121207i | ||||||
\(426\) | 17326.9 | − | 9014.80i | 0.0954778 | − | 0.0496749i | ||||
\(427\) | −141779. | −0.777598 | ||||||||
\(428\) | − | 32921.4i | − | 0.179718i | ||||||
\(429\) | −28797.1 | − | 55349.6i | −0.156471 | − | 0.300746i | ||||
\(430\) | 154842. | 0.837434 | ||||||||
\(431\) | 252810.i | 1.36094i | 0.732775 | + | 0.680471i | \(0.238225\pi\) | ||||
−0.732775 | + | 0.680471i | \(0.761775\pi\) | |||||||
\(432\) | 29659.4 | − | 224098.i | 0.158926 | − | 1.20080i | ||||
\(433\) | 330313. | 1.76178 | 0.880888 | − | 0.473326i | \(-0.156947\pi\) | ||||
0.880888 | + | 0.473326i | \(0.156947\pi\) | |||||||
\(434\) | 300710.i | 1.59650i | ||||||||
\(435\) | 16056.3 | − | 8353.71i | 0.0848528 | − | 0.0441469i | ||||
\(436\) | 22316.4 | 0.117396 | ||||||||
\(437\) | − | 313761.i | − | 1.64299i | ||||||
\(438\) | 40752.4 | + | 78328.3i | 0.212425 | + | 0.408292i | ||||
\(439\) | −229425. | −1.19045 | −0.595227 | − | 0.803558i | \(-0.702938\pi\) | ||||
−0.595227 | + | 0.803558i | \(0.702938\pi\) | |||||||
\(440\) | 61941.4i | 0.319945i | ||||||||
\(441\) | 64825.8 | − | 92490.8i | 0.333327 | − | 0.475578i | ||||
\(442\) | 50946.8 | 0.260779 | ||||||||
\(443\) | − | 6149.63i | − | 0.0313358i | −0.999877 | − | 0.0156679i | \(-0.995013\pi\) | ||
0.999877 | − | 0.0156679i | \(-0.00498746\pi\) | |||||||
\(444\) | −41106.7 | + | 21386.9i | −0.208520 | + | 0.108488i | ||||
\(445\) | −92357.2 | −0.466392 | ||||||||
\(446\) | − | 236394.i | − | 1.18841i | ||||||
\(447\) | 128904. | + | 247760.i | 0.645134 | + | 1.23998i | ||||
\(448\) | −136467. | −0.679943 | ||||||||
\(449\) | 219554.i | 1.08905i | 0.838744 | + | 0.544526i | \(0.183290\pi\) | ||||
−0.838744 | + | 0.544526i | \(0.816710\pi\) | |||||||
\(450\) | −37860.5 | − | 26536.0i | −0.186966 | − | 0.131042i | ||||
\(451\) | 18910.6 | 0.0929720 | ||||||||
\(452\) | 71563.9i | 0.350281i | ||||||||
\(453\) | −104567. | + | 54403.9i | −0.509564 | + | 0.265114i | ||||
\(454\) | 318595. | 1.54571 | ||||||||
\(455\) | − | 43877.4i | − | 0.211942i | ||||||
\(456\) | −63805.4 | − | 122637.i | −0.306851 | − | 0.589785i | ||||
\(457\) | −138678. | −0.664010 | −0.332005 | − | 0.943278i | \(-0.607725\pi\) | ||||
−0.332005 | + | 0.943278i | \(0.607725\pi\) | |||||||
\(458\) | − | 10429.9i | − | 0.0497219i | ||||||
\(459\) | −126576. | − | 16752.3i | −0.600794 | − | 0.0795151i | ||||
\(460\) | −56402.8 | −0.266554 | ||||||||
\(461\) | − | 3892.31i | − | 0.0183149i | −0.999958 | − | 0.00915746i | \(-0.997085\pi\) | ||
0.999958 | − | 0.00915746i | \(-0.00291495\pi\) | |||||||
\(462\) | −244429. | + | 127171.i | −1.14517 | + | 0.595804i | ||||
\(463\) | −279654. | −1.30455 | −0.652273 | − | 0.757984i | \(-0.726184\pi\) | ||||
−0.652273 | + | 0.757984i | \(0.726184\pi\) | |||||||
\(464\) | − | 55776.1i | − | 0.259067i | ||||||
\(465\) | −49643.7 | − | 95418.0i | −0.229593 | − | 0.441290i | ||||
\(466\) | 102579. | 0.472375 | ||||||||
\(467\) | − | 202921.i | − | 0.930452i | −0.885192 | − | 0.465226i | \(-0.845973\pi\) | ||
0.885192 | − | 0.465226i | \(-0.154027\pi\) | |||||||
\(468\) | 14367.2 | − | 20498.6i | 0.0655965 | − | 0.0935905i | ||||
\(469\) | 259923. | 1.18168 | ||||||||
\(470\) | 47770.5i | 0.216254i | ||||||||
\(471\) | −100676. | + | 52379.3i | −0.453820 | + | 0.236112i | ||||
\(472\) | 162333. | 0.728657 | ||||||||
\(473\) | 330066.i | 1.47530i | ||||||||
\(474\) | −58918.7 | − | 113245.i | −0.262239 | − | 0.504037i | ||||
\(475\) | −37715.4 | −0.167160 | ||||||||
\(476\) | − | 52345.4i | − | 0.231028i | ||||||
\(477\) | 28077.8 | + | 19679.4i | 0.123403 | + | 0.0864918i | ||||
\(478\) | −192316. | −0.841703 | ||||||||
\(479\) | 308474.i | 1.34446i | 0.740343 | + | 0.672230i | \(0.234663\pi\) | ||||
−0.740343 | + | 0.672230i | \(0.765337\pi\) | |||||||
\(480\) | −53684.6 | + | 27930.8i | −0.233006 | + | 0.121228i | ||||
\(481\) | 67606.8 | 0.292213 | ||||||||
\(482\) | − | 4456.37i | − | 0.0191817i | ||||||
\(483\) | 266119. | + | 511495.i | 1.14073 | + | 2.19254i | ||||
\(484\) | −13572.8 | −0.0579401 | ||||||||
\(485\) | 104092.i | 0.442520i | ||||||||
\(486\) | −182391. | + | 198589.i | −0.772202 | + | 0.840779i | ||||
\(487\) | 210519. | 0.887633 | 0.443816 | − | 0.896118i | \(-0.353624\pi\) | ||||
0.443816 | + | 0.896118i | \(0.353624\pi\) | |||||||
\(488\) | − | 117158.i | − | 0.491965i | ||||||
\(489\) | −12541.1 | + | 6524.86i | −0.0524468 | + | 0.0272869i | ||||
\(490\) | −71188.4 | −0.296495 | ||||||||
\(491\) | − | 442555.i | − | 1.83571i | −0.396913 | − | 0.917856i | \(-0.629918\pi\) | ||
0.396913 | − | 0.917856i | \(-0.370082\pi\) | |||||||
\(492\) | 3501.74 | + | 6730.53i | 0.0144662 | + | 0.0278048i | ||||
\(493\) | −31503.6 | −0.129618 | ||||||||
\(494\) | − | 87767.1i | − | 0.359648i | ||||||
\(495\) | 56565.2 | − | 80705.0i | 0.230855 | − | 0.329374i | ||||
\(496\) | −331462. | −1.34732 | ||||||||
\(497\) | 29279.3i | 0.118535i | ||||||||
\(498\) | 137441. | − | 71507.3i | 0.554188 | − | 0.288331i | ||||
\(499\) | 170123. | 0.683224 | 0.341612 | − | 0.939841i | \(-0.389027\pi\) | ||||
0.341612 | + | 0.939841i | \(0.389027\pi\) | |||||||
\(500\) | 6779.86i | 0.0271195i | ||||||||
\(501\) | −40987.4 | − | 78780.1i | −0.163296 | − | 0.313864i | ||||
\(502\) | 435785. | 1.72928 | ||||||||
\(503\) | − | 232933.i | − | 0.920653i | −0.887750 | − | 0.460327i | \(-0.847732\pi\) | ||
0.887750 | − | 0.460327i | \(-0.152268\pi\) | |||||||
\(504\) | 208032. | + | 145808.i | 0.818973 | + | 0.574009i | ||||
\(505\) | −114484. | −0.448915 | ||||||||
\(506\) | − | 516762.i | − | 2.01832i | ||||||
\(507\) | 195633. | − | 101783.i | 0.761073 | − | 0.395968i | ||||
\(508\) | 74973.8 | 0.290524 | ||||||||
\(509\) | − | 97567.9i | − | 0.376592i | −0.982112 | − | 0.188296i | \(-0.939704\pi\) | ||
0.982112 | − | 0.188296i | \(-0.0602965\pi\) | |||||||
\(510\) | 37142.6 | + | 71390.2i | 0.142801 | + | 0.274472i | ||||
\(511\) | −132360. | −0.506893 | ||||||||
\(512\) | − | 66087.5i | − | 0.252104i | ||||||
\(513\) | −28859.6 | + | 218055.i | −0.109662 | + | 0.828573i | ||||
\(514\) | 105546. | 0.399500 | ||||||||
\(515\) | − | 60375.5i | − | 0.227639i | ||||||
\(516\) | −117475. | + | 61119.5i | −0.441211 | + | 0.229552i | ||||
\(517\) | −101829. | −0.380971 | ||||||||
\(518\) | − | 298558.i | − | 1.11268i | ||||||
\(519\) | −89667.6 | − | 172346.i | −0.332890 | − | 0.639833i | ||||
\(520\) | 36258.0 | 0.134090 | ||||||||
\(521\) | 436403.i | 1.60773i | 0.594815 | + | 0.803863i | \(0.297225\pi\) | ||||
−0.594815 | + | 0.803863i | \(0.702775\pi\) | |||||||
\(522\) | −38185.0 | + | 54480.8i | −0.140137 | + | 0.199941i | ||||
\(523\) | 143160. | 0.523381 | 0.261691 | − | 0.965152i | \(-0.415720\pi\) | ||||
0.261691 | + | 0.965152i | \(0.415720\pi\) | |||||||
\(524\) | − | 105967.i | − | 0.385928i | ||||||
\(525\) | 61484.0 | − | 31988.7i | 0.223071 | − | 0.116059i | ||||
\(526\) | 169710. | 0.613389 | ||||||||
\(527\) | 187217.i | 0.674101i | ||||||||
\(528\) | −140176. | − | 269426.i | −0.502812 | − | 0.966433i | ||||
\(529\) | −801542. | −2.86428 | ||||||||
\(530\) | − | 21610.9i | − | 0.0769346i | ||||||
\(531\) | −211508. | − | 148243.i | −0.750131 | − | 0.525759i | ||||
\(532\) | −90176.5 | −0.318618 | ||||||||
\(533\) | − | 11069.5i | − | 0.0389648i | ||||||
\(534\) | 301166. | − | 156689.i | 1.05614 | − | 0.549487i | ||||
\(535\) | −75871.3 | −0.265076 | ||||||||
\(536\) | 214787.i | 0.747615i | ||||||||
\(537\) | 92117.3 | + | 177054.i | 0.319442 | + | 0.613986i | ||||
\(538\) | −614154. | −2.12184 | ||||||||
\(539\) | − | 151748.i | − | 0.522330i | ||||||
\(540\) | 39198.3 | + | 5187.91i | 0.134425 | + | 0.0177912i | ||||
\(541\) | 264951. | 0.905254 | 0.452627 | − | 0.891700i | \(-0.350487\pi\) | ||||
0.452627 | + | 0.891700i | \(0.350487\pi\) | |||||||
\(542\) | 510496.i | 1.73778i | ||||||||
\(543\) | 455419. | − | 236944.i | 1.54458 | − | 0.803611i | ||||
\(544\) | 105333. | 0.355933 | ||||||||
\(545\) | − | 51430.9i | − | 0.173153i | ||||||
\(546\) | 74440.5 | + | 143079.i | 0.249703 | + | 0.479943i | ||||
\(547\) | 241732. | 0.807903 | 0.403952 | − | 0.914780i | \(-0.367636\pi\) | ||||
0.403952 | + | 0.914780i | \(0.367636\pi\) | |||||||
\(548\) | 91806.9i | 0.305713i | ||||||||
\(549\) | −106990. | + | 152649.i | −0.354974 | + | 0.506463i | ||||
\(550\) | −62117.1 | −0.205346 | ||||||||
\(551\) | 54271.9i | 0.178761i | ||||||||
\(552\) | −422673. | + | 219907.i | −1.38716 | + | 0.721706i | ||||
\(553\) | 191363. | 0.625761 | ||||||||
\(554\) | 586325.i | 1.91038i | ||||||||
\(555\) | 49288.5 | + | 94735.3i | 0.160015 | + | 0.307557i | ||||
\(556\) | 105743. | 0.342059 | ||||||||
\(557\) | − | 246479.i | − | 0.794455i | −0.917720 | − | 0.397228i | \(-0.869972\pi\) | ||
0.917720 | − | 0.397228i | \(-0.130028\pi\) | |||||||
\(558\) | 323764. | + | 226923.i | 1.03983 | + | 0.728802i | ||||
\(559\) | 193207. | 0.618300 | ||||||||
\(560\) | − | 213582.i | − | 0.681066i | ||||||
\(561\) | −152178. | + | 79174.7i | −0.483533 | + | 0.251571i | ||||
\(562\) | −134166. | −0.424784 | ||||||||
\(563\) | 44133.4i | 0.139236i | 0.997574 | + | 0.0696179i | \(0.0221780\pi\) | ||||
−0.997574 | + | 0.0696179i | \(0.977822\pi\) | |||||||
\(564\) | −18856.1 | − | 36242.4i | −0.0592780 | − | 0.113935i | ||||
\(565\) | 164927. | 0.516649 | ||||||||
\(566\) | 274505.i | 0.856876i | ||||||||
\(567\) | −137898. | − | 379952.i | −0.428936 | − | 1.18185i | ||||
\(568\) | −24194.9 | −0.0749941 | ||||||||
\(569\) | − | 196815.i | − | 0.607901i | −0.952688 | − | 0.303951i | \(-0.901694\pi\) | ||
0.952688 | − | 0.303951i | \(-0.0983058\pi\) | |||||||
\(570\) | 122985. | − | 63986.3i | 0.378533 | − | 0.196942i | ||||
\(571\) | 200156. | 0.613897 | 0.306949 | − | 0.951726i | \(-0.400692\pi\) | ||||
0.306949 | + | 0.951726i | \(0.400692\pi\) | |||||||
\(572\) | − | 33631.6i | − | 0.102791i | ||||||
\(573\) | −267057. | − | 513299.i | −0.813383 | − | 1.56337i | ||||
\(574\) | −48883.9 | −0.148369 | ||||||||
\(575\) | 129987.i | 0.393155i | ||||||||
\(576\) | −102981. | + | 146930.i | −0.310395 | + | 0.442859i | ||||
\(577\) | −426161. | −1.28004 | −0.640018 | − | 0.768360i | \(-0.721073\pi\) | ||||
−0.640018 | + | 0.768360i | \(0.721073\pi\) | |||||||
\(578\) | 241311.i | 0.722305i | ||||||||
\(579\) | −291040. | + | 151421.i | −0.868150 | + | 0.451678i | ||||
\(580\) | 9756.13 | 0.0290016 | ||||||||
\(581\) | 232250.i | 0.688023i | ||||||||
\(582\) | −176598. | − | 339431.i | −0.521362 | − | 1.00209i | ||||
\(583\) | 46066.7 | 0.135535 | ||||||||
\(584\) | − | 109376.i | − | 0.320697i | ||||||
\(585\) | −47241.4 | − | 33110.9i | −0.138042 | − | 0.0967520i | ||||
\(586\) | −17212.4 | −0.0501241 | ||||||||
\(587\) | − | 175893.i | − | 0.510472i | −0.966879 | − | 0.255236i | \(-0.917847\pi\) | ||
0.966879 | − | 0.255236i | \(-0.0821532\pi\) | |||||||
\(588\) | 54009.1 | − | 28099.7i | 0.156211 | − | 0.0812731i | ||||
\(589\) | 322523. | 0.929673 | ||||||||
\(590\) | 162793.i | 0.467663i | ||||||||
\(591\) | −263665. | − | 506779.i | −0.754880 | − | 1.45092i | ||||
\(592\) | 329090. | 0.939013 | ||||||||
\(593\) | 338113.i | 0.961506i | 0.876856 | + | 0.480753i | \(0.159637\pi\) | ||||
−0.876856 | + | 0.480753i | \(0.840363\pi\) | |||||||
\(594\) | −47531.6 | + | 359135.i | −0.134713 | + | 1.01785i | ||||
\(595\) | −120636. | −0.340756 | ||||||||
\(596\) | 150544.i | 0.423810i | ||||||||
\(597\) | 76918.9 | − | 40019.1i | 0.215816 | − | 0.112284i | ||||
\(598\) | −302491. | −0.845883 | ||||||||
\(599\) | − | 184189.i | − | 0.513345i | −0.966498 | − | 0.256673i | \(-0.917374\pi\) | ||
0.966498 | − | 0.256673i | \(-0.0826262\pi\) | |||||||
\(600\) | 26433.8 | + | 50807.1i | 0.0734271 | + | 0.141131i | ||||
\(601\) | 459733. | 1.27279 | 0.636394 | − | 0.771364i | \(-0.280425\pi\) | ||||
0.636394 | + | 0.771364i | \(0.280425\pi\) | |||||||
\(602\) | − | 853221.i | − | 2.35434i | ||||||
\(603\) | 196144. | − | 279851.i | 0.539437 | − | 0.769647i | ||||
\(604\) | −63537.2 | −0.174162 | ||||||||
\(605\) | 31280.2i | 0.0854591i | ||||||||
\(606\) | 373320. | − | 194230.i | 1.01657 | − | 0.528896i | ||||
\(607\) | −396870. | −1.07714 | −0.538568 | − | 0.842582i | \(-0.681035\pi\) | ||||
−0.538568 | + | 0.842582i | \(0.681035\pi\) | |||||||
\(608\) | − | 181460.i | − | 0.490878i | ||||||
\(609\) | −46031.3 | − | 88474.6i | −0.124113 | − | 0.238553i | ||||
\(610\) | 117491. | 0.315750 | ||||||||
\(611\) | 59606.7i | 0.159666i | ||||||||
\(612\) | −56358.6 | − | 39501.1i | −0.150473 | − | 0.105465i | ||||
\(613\) | −112592. | −0.299631 | −0.149815 | − | 0.988714i | \(-0.547868\pi\) | ||||
−0.149815 | + | 0.988714i | \(0.547868\pi\) | |||||||
\(614\) | − | 643445.i | − | 1.70677i | ||||||
\(615\) | 15511.3 | − | 8070.17i | 0.0410108 | − | 0.0213370i | ||||
\(616\) | 341315. | 0.899485 | ||||||||
\(617\) | 705193.i | 1.85241i | 0.377019 | + | 0.926206i | \(0.376949\pi\) | ||||
−0.377019 | + | 0.926206i | \(0.623051\pi\) | |||||||
\(618\) | 102431. | + | 196877.i | 0.268196 | + | 0.515487i | ||||
\(619\) | 600978. | 1.56847 | 0.784237 | − | 0.620461i | \(-0.213055\pi\) | ||||
0.784237 | + | 0.620461i | \(0.213055\pi\) | |||||||
\(620\) | − | 57978.0i | − | 0.150827i | ||||||
\(621\) | 751530. | + | 99465.1i | 1.94878 | + | 0.257922i | ||||
\(622\) | −82278.2 | −0.212669 | ||||||||
\(623\) | 508914.i | 1.31120i | ||||||||
\(624\) | −157711. | + | 82053.2i | −0.405035 | + | 0.210730i | ||||
\(625\) | 15625.0 | 0.0400000 | ||||||||
\(626\) | − | 201633.i | − | 0.514533i | ||||||
\(627\) | 136396. | + | 262160.i | 0.346949 | + | 0.666855i | ||||
\(628\) | −61172.8 | −0.155110 | ||||||||
\(629\) | − | 185878.i | − | 0.469814i | ||||||
\(630\) | −146221. | + | 208622.i | −0.368408 | + | 0.525629i | ||||
\(631\) | 173024. | 0.434558 | 0.217279 | − | 0.976110i | \(-0.430282\pi\) | ||||
0.217279 | + | 0.976110i | \(0.430282\pi\) | |||||||
\(632\) | 158133.i | 0.395901i | ||||||||
\(633\) | −513453. | + | 267137.i | −1.28142 | + | 0.666695i | ||||
\(634\) | −885290. | −2.20246 | ||||||||
\(635\) | − | 172786.i | − | 0.428510i | ||||||
\(636\) | 8530.32 | + | 16395.7i | 0.0210888 | + | 0.0405338i | ||||
\(637\) | −88827.0 | −0.218910 | ||||||||
\(638\) | 89385.7i | 0.219597i | ||||||||
\(639\) | 31524.1 | + | 22094.9i | 0.0772042 | + | 0.0541116i | ||||
\(640\) | 220673. | 0.538752 | ||||||||
\(641\) | − | 398714.i | − | 0.970388i | −0.874407 | − | 0.485194i | \(-0.838749\pi\) | ||
0.874407 | − | 0.485194i | \(-0.161251\pi\) | |||||||
\(642\) | 247407. | − | 128720.i | 0.600264 | − | 0.312303i | ||||
\(643\) | −476538. | −1.15259 | −0.576296 | − | 0.817241i | \(-0.695502\pi\) | ||||
−0.576296 | + | 0.817241i | \(0.695502\pi\) | |||||||
\(644\) | 310795.i | 0.749381i | ||||||||
\(645\) | 140857. | + | 270735.i | 0.338578 | + | 0.650766i | ||||
\(646\) | −241306. | −0.578234 | ||||||||
\(647\) | − | 115282.i | − | 0.275392i | −0.990475 | − | 0.137696i | \(-0.956030\pi\) | ||
0.990475 | − | 0.137696i | \(-0.0439697\pi\) | |||||||
\(648\) | 313973. | − | 113952.i | 0.747725 | − | 0.271376i | ||||
\(649\) | −347017. | −0.823875 | ||||||||
\(650\) | 36360.8i | 0.0860610i | ||||||||
\(651\) | −525780. | + | 273551.i | −1.24063 | + | 0.645470i | ||||
\(652\) | −7620.26 | −0.0179256 | ||||||||
\(653\) | − | 128829.i | − | 0.302124i | −0.988524 | − | 0.151062i | \(-0.951731\pi\) | ||
0.988524 | − | 0.151062i | \(-0.0482694\pi\) | |||||||
\(654\) | 87255.4 | + | 167710.i | 0.204003 | + | 0.392105i | ||||
\(655\) | −244212. | −0.569227 | ||||||||
\(656\) | − | 53883.0i | − | 0.125212i | ||||||
\(657\) | −99882.4 | + | 142508.i | −0.231397 | + | 0.330148i | ||||
\(658\) | 263229. | 0.607969 | ||||||||
\(659\) | 273000.i | 0.628626i | 0.949319 | + | 0.314313i | \(0.101774\pi\) | ||||
−0.949319 | + | 0.314313i | \(0.898226\pi\) | |||||||
\(660\) | 47126.9 | − | 24519.0i | 0.108188 | − | 0.0562879i | ||||
\(661\) | −727370. | −1.66476 | −0.832382 | − | 0.554202i | \(-0.813023\pi\) | ||||
−0.832382 | + | 0.554202i | \(0.813023\pi\) | |||||||
\(662\) | − | 169037.i | − | 0.385714i | ||||||
\(663\) | 46345.6 | + | 89078.7i | 0.105434 | + | 0.202650i | ||||
\(664\) | −191919. | −0.435293 | ||||||||
\(665\) | 207822.i | 0.469947i | ||||||||
\(666\) | −321448. | − | 225299.i | −0.724706 | − | 0.507939i | ||||
\(667\) | 187049. | 0.420441 | ||||||||
\(668\) | − | 47868.5i | − | 0.107274i | ||||||
\(669\) | 413327. | − | 215044.i | 0.923509 | − | 0.480480i | ||||
\(670\) | −215396. | −0.479830 | ||||||||
\(671\) | 250448.i | 0.556252i | ||||||||
\(672\) | 153907. | + | 295817.i | 0.340816 | + | 0.655066i | ||||
\(673\) | 589602. | 1.30175 | 0.650877 | − | 0.759183i | \(-0.274401\pi\) | ||||
0.650877 | + | 0.759183i | \(0.274401\pi\) | |||||||
\(674\) | − | 487498.i | − | 1.07313i | ||||||
\(675\) | 11956.1 | − | 90337.2i | 0.0262412 | − | 0.198271i | ||||
\(676\) | 118871. | 0.260125 | ||||||||
\(677\) | 132672.i | 0.289470i | 0.989470 | + | 0.144735i | \(0.0462329\pi\) | ||||
−0.989470 | + | 0.144735i | \(0.953767\pi\) | |||||||
\(678\) | −537808. | + | 279809.i | −1.16995 | + | 0.608698i | ||||
\(679\) | 573575. | 1.24409 | ||||||||
\(680\) | − | 99687.4i | − | 0.215587i | ||||||
\(681\) | 289822. | + | 557053.i | 0.624937 | + | 1.20116i | ||||
\(682\) | 531194. | 1.14205 | ||||||||
\(683\) | − | 804075.i | − | 1.72367i | −0.507185 | − | 0.861837i | \(-0.669314\pi\) | ||
0.507185 | − | 0.861837i | \(-0.330686\pi\) | |||||||
\(684\) | −68049.4 | + | 97090.1i | −0.145449 | + | 0.207521i | ||||
\(685\) | 211580. | 0.450914 | ||||||||
\(686\) | − | 283173.i | − | 0.601732i | ||||||
\(687\) | 18236.2 | − | 9487.88i | 0.0386386 | − | 0.0201028i | ||||
\(688\) | 940476. | 1.98688 | ||||||||
\(689\) | − | 26965.5i | − | 0.0568029i | ||||||
\(690\) | −220530. | − | 423871.i | −0.463202 | − | 0.890299i | ||||
\(691\) | −489997. | −1.02621 | −0.513106 | − | 0.858325i | \(-0.671505\pi\) | ||||
−0.513106 | + | 0.858325i | \(0.671505\pi\) | |||||||
\(692\) | − | 104721.i | − | 0.218687i | ||||||
\(693\) | −444707. | − | 311690.i | −0.925993 | − | 0.649018i | ||||
\(694\) | 291275. | 0.604761 | ||||||||
\(695\) | − | 243697.i | − | 0.504522i | ||||||
\(696\) | 73110.8 | − | 38037.8i | 0.150926 | − | 0.0785230i | ||||
\(697\) | −30434.4 | −0.0626468 | ||||||||
\(698\) | 580678.i | 1.19186i | ||||||||
\(699\) | 93314.7 | + | 179356.i | 0.190983 | + | 0.367081i | ||||
\(700\) | 37359.0 | 0.0762428 | ||||||||
\(701\) | − | 68039.2i | − | 0.138460i | −0.997601 | − | 0.0692298i | \(-0.977946\pi\) | ||
0.997601 | − | 0.0692298i | \(-0.0220542\pi\) | |||||||
\(702\) | 210223. | + | 27823.0i | 0.426585 | + | 0.0564586i | ||||
\(703\) | −320215. | −0.647935 | ||||||||
\(704\) | 241065.i | 0.486395i | ||||||||
\(705\) | −83524.9 | + | 43456.1i | −0.168050 | + | 0.0874324i | ||||
\(706\) | −307091. | −0.616110 | ||||||||
\(707\) | 630842.i | 1.26206i | ||||||||
\(708\) | −64258.3 | − | 123508.i | −0.128192 | − | 0.246393i | ||||
\(709\) | 49483.1 | 0.0984384 | 0.0492192 | − | 0.998788i | \(-0.484327\pi\) | ||||
0.0492192 | + | 0.998788i | \(0.484327\pi\) | |||||||
\(710\) | − | 24263.5i | − | 0.0481323i | ||||||
\(711\) | 144407. | − | 206035.i | 0.285661 | − | 0.407569i | ||||
\(712\) | −420540. | −0.829559 | ||||||||
\(713\) | − | 1.11158e6i | − | 2.18657i | ||||||
\(714\) | 393380. | − | 204666.i | 0.771642 | − | 0.401467i | ||||
\(715\) | −77508.0 | −0.151612 | ||||||||
\(716\) | 107582.i | 0.209852i | ||||||||
\(717\) | −174947. | − | 336257.i | −0.340304 | − | 0.654084i | ||||
\(718\) | 656761. | 1.27397 | ||||||||
\(719\) | 772948.i | 1.49518i | 0.664163 | + | 0.747588i | \(0.268788\pi\) | ||||
−0.664163 | + | 0.747588i | \(0.731212\pi\) | |||||||
\(720\) | −229957. | − | 161174.i | −0.443590 | − | 0.310908i | ||||
\(721\) | −332686. | −0.639976 | ||||||||
\(722\) | − | 179384.i | − | 0.344119i | ||||||
\(723\) | 7791.80 | − | 4053.89i | 0.0149060 | − | 0.00775525i | ||||
\(724\) | 276722. | 0.527919 | ||||||||
\(725\) | − | 22484.2i | − | 0.0427761i | ||||||
\(726\) | −53068.6 | − | 102001.i | −0.100685 | − | 0.193522i | ||||
\(727\) | 475534. | 0.899730 | 0.449865 | − | 0.893096i | \(-0.351472\pi\) | ||||
0.449865 | + | 0.893096i | \(0.351472\pi\) | |||||||
\(728\) | − | 199792.i | − | 0.376977i | ||||||
\(729\) | −513143. | − | 138251.i | −0.965570 | − | 0.260143i | ||||
\(730\) | 109686. | 0.205828 | ||||||||
\(731\) | − | 531203.i | − | 0.994090i | ||||||
\(732\) | −89137.6 | + | 46376.2i | −0.166356 | + | 0.0865512i | ||||
\(733\) | 78220.7 | 0.145584 | 0.0727920 | − | 0.997347i | \(-0.476809\pi\) | ||||
0.0727920 | + | 0.997347i | \(0.476809\pi\) | |||||||
\(734\) | 558966.i | 1.03751i | ||||||||
\(735\) | −64759.0 | − | 124470.i | −0.119874 | − | 0.230405i | ||||
\(736\) | −625405. | −1.15453 | ||||||||
\(737\) | − | 459146.i | − | 0.845310i | ||||||
\(738\) | −36889.0 | + | 52631.7i | −0.0677304 | + | 0.0966350i | ||||
\(739\) | −493941. | −0.904454 | −0.452227 | − | 0.891903i | \(-0.649370\pi\) | ||||
−0.452227 | + | 0.891903i | \(0.649370\pi\) | |||||||
\(740\) | 57563.2i | 0.105119i | ||||||||
\(741\) | 153458. | − | 79840.4i | 0.279481 | − | 0.145407i | ||||
\(742\) | −119082. | −0.216292 | ||||||||
\(743\) | 881286.i | 1.59639i | 0.602398 | + | 0.798196i | \(0.294212\pi\) | ||||
−0.602398 | + | 0.798196i | \(0.705788\pi\) | |||||||
\(744\) | −226048. | − | 434477.i | −0.408371 | − | 0.784912i | ||||
\(745\) | 346947. | 0.625101 | ||||||||
\(746\) | 883676.i | 1.58787i | ||||||||
\(747\) | 250056. | + | 175261.i | 0.448122 | + | 0.314083i | ||||
\(748\) | −92466.6 | −0.165265 | ||||||||
\(749\) | 418072.i | 0.745226i | ||||||||
\(750\) | −50951.2 | + | 26508.7i | −0.0905799 | + | 0.0471266i | ||||
\(751\) | −455517. | −0.807653 | −0.403827 | − | 0.914836i | \(-0.632320\pi\) | ||||
−0.403827 | + | 0.914836i | \(0.632320\pi\) | |||||||
\(752\) | 290148.i | 0.513079i | ||||||||
\(753\) | 396427. | + | 761954.i | 0.699154 | + | 1.34381i | ||||
\(754\) | 52322.7 | 0.0920338 | ||||||||
\(755\) | 146429.i | 0.256882i | ||||||||
\(756\) | 28586.8 | − | 215994.i | 0.0500175 | − | 0.377918i | ||||
\(757\) | −210339. | −0.367053 | −0.183526 | − | 0.983015i | \(-0.558751\pi\) | ||||
−0.183526 | + | 0.983015i | \(0.558751\pi\) | |||||||
\(758\) | 228360.i | 0.397449i | ||||||||
\(759\) | 903541. | − | 470091.i | 1.56843 | − | 0.816016i | ||||
\(760\) | −171734. | −0.297323 | ||||||||
\(761\) | − | 299076.i | − | 0.516431i | −0.966087 | − | 0.258216i | \(-0.916866\pi\) | ||
0.966087 | − | 0.258216i | \(-0.0831345\pi\) | |||||||
\(762\) | 293142. | + | 563434.i | 0.504856 | + | 0.970361i | ||||
\(763\) | −283399. | −0.486798 | ||||||||
\(764\) | − | 311891.i | − | 0.534338i | ||||||
\(765\) | −91035.0 | + | 129885.i | −0.155556 | + | 0.221940i | ||||
\(766\) | 329282. | 0.561191 | ||||||||
\(767\) | 203129.i | 0.345288i | ||||||||
\(768\) | −436616. | + | 227161.i | −0.740247 | + | 0.385133i | ||||
\(769\) | 215663. | 0.364689 | 0.182345 | − | 0.983235i | \(-0.441631\pi\) | ||||
0.182345 | + | 0.983235i | \(0.441631\pi\) | |||||||
\(770\) | 342283.i | 0.577303i | ||||||||
\(771\) | 96013.8 | + | 184544.i | 0.161519 | + | 0.310449i | ||||
\(772\) | −176842. | −0.296722 | ||||||||
\(773\) | − | 233916.i | − | 0.391473i | −0.980657 | − | 0.195736i | \(-0.937290\pi\) | ||
0.980657 | − | 0.195736i | \(-0.0627097\pi\) | |||||||
\(774\) | −918635. | − | 643861.i | −1.53342 | − | 1.07476i | ||||
\(775\) | −133617. | −0.222463 | ||||||||
\(776\) | 473972.i | 0.787100i | ||||||||
\(777\) | 522018. | − | 271594.i | 0.864656 | − | 0.449860i | ||||
\(778\) | −115453. | −0.190741 | ||||||||
\(779\) | 52429.9i | 0.0863981i | ||||||||
\(780\) | −14352.4 | − | 27586.1i | −0.0235904 | − | 0.0453421i | ||||
\(781\) | 51721.0 | 0.0847940 | ||||||||
\(782\) | 831668.i | 1.35999i | ||||||||
\(783\) | −129994. | − | 17204.7i | −0.212031 | − | 0.0280624i | ||||
\(784\) | −432384. | −0.703457 | ||||||||
\(785\) | 140980.i | 0.228780i | ||||||||
\(786\) | 796347. | − | 414320.i | 1.28901 | − | 0.670643i | ||||
\(787\) | 381652. | 0.616194 | 0.308097 | − | 0.951355i | \(-0.400308\pi\) | ||||
0.308097 | + | 0.951355i | \(0.400308\pi\) | |||||||
\(788\) | − | 307930.i | − | 0.495906i | ||||||
\(789\) | 154383. | + | 296732.i | 0.247996 | + | 0.476662i | ||||
\(790\) | −158581. | −0.254095 | ||||||||
\(791\) | − | 908797.i | − | 1.45249i | ||||||
\(792\) | 257565. | − | 367483.i | 0.410616 | − | 0.585850i | ||||
\(793\) | 146602. | 0.233127 | ||||||||
\(794\) | − | 128360.i | − | 0.203604i | ||||||
\(795\) | 37785.9 | − | 19659.1i | 0.0597855 | − | 0.0311050i | ||||
\(796\) | 46737.5 | 0.0737632 | ||||||||
\(797\) | − | 1.02716e6i | − | 1.61705i | −0.588464 | − | 0.808523i | \(-0.700267\pi\) | ||
0.588464 | − | 0.808523i | \(-0.299733\pi\) | |||||||
\(798\) | −352583. | − | 677684.i | −0.553676 | − | 1.06419i | ||||
\(799\) | 163882. | 0.256707 | ||||||||
\(800\) | 75176.4i | 0.117463i | ||||||||
\(801\) | 547932. | + | 384039.i | 0.854007 | + | 0.598564i | ||||
\(802\) | −265366. | −0.412569 | ||||||||
\(803\) | 233811.i | 0.362604i | ||||||||
\(804\) | 163416. | − | 85021.6i | 0.252803 | − | 0.131528i | ||||
\(805\) | 716265. | 1.10530 | ||||||||
\(806\) | − | 310939.i | − | 0.478636i | ||||||
\(807\) | −558687. | − | 1.07383e6i | −0.857869 | − | 1.64887i | ||||
\(808\) | −521294. | −0.798473 | ||||||||
\(809\) | − | 674223.i | − | 1.03016i | −0.857141 | − | 0.515082i | \(-0.827761\pi\) | ||
0.857141 | − | 0.515082i | \(-0.172239\pi\) | |||||||
\(810\) | 114275. | + | 314863.i | 0.174173 | + | 0.479901i | ||||
\(811\) | 591215. | 0.898884 | 0.449442 | − | 0.893310i | \(-0.351623\pi\) | ||||
0.449442 | + | 0.893310i | \(0.351623\pi\) | |||||||
\(812\) | − | 53759.1i | − | 0.0815342i | ||||||
\(813\) | −892584. | + | 464391.i | −1.35042 | + | 0.702591i | ||||
\(814\) | −527393. | −0.795950 | ||||||||
\(815\) | 17561.8i | 0.0264395i | ||||||||
\(816\) | 225597. | + | 433609.i | 0.338807 | + | 0.651206i | ||||
\(817\) | −915114. | −1.37098 | ||||||||
\(818\) | − | 38866.5i | − | 0.0580856i | ||||||
\(819\) | −182451. | + | 260313.i | −0.272005 | + | 0.388086i | ||||
\(820\) | 9425.00 | 0.0140170 | ||||||||
\(821\) | − | 731133.i | − | 1.08470i | −0.840152 | − | 0.542351i | \(-0.817534\pi\) | ||
0.840152 | − | 0.542351i | \(-0.182466\pi\) | |||||||
\(822\) | −689936. | + | 358958.i | −1.02109 | + | 0.531251i | ||||
\(823\) | 490743. | 0.724527 | 0.362264 | − | 0.932076i | \(-0.382004\pi\) | ||||
0.362264 | + | 0.932076i | \(0.382004\pi\) | |||||||
\(824\) | − | 274914.i | − | 0.404895i | ||||||
\(825\) | −56507.0 | − | 108610.i | −0.0830222 | − | 0.159573i | ||||
\(826\) | 897038. | 1.31477 | ||||||||
\(827\) | − | 48569.2i | − | 0.0710150i | −0.999369 | − | 0.0355075i | \(-0.988695\pi\) | ||
0.999369 | − | 0.0355075i | \(-0.0113048\pi\) | |||||||
\(828\) | 334623. | + | 234534.i | 0.488085 | + | 0.342093i | ||||
\(829\) | 481266. | 0.700287 | 0.350144 | − | 0.936696i | \(-0.386133\pi\) | ||||
0.350144 | + | 0.936696i | \(0.386133\pi\) | |||||||
\(830\) | − | 192463.i | − | 0.279378i | ||||||
\(831\) | −1.02517e6 | + | 533371.i | −1.48454 | + | 0.772374i | ||||
\(832\) | 141110. | 0.203850 | ||||||||
\(833\) | 244220.i | 0.351959i | ||||||||
\(834\) | 413446. | + | 794665.i | 0.594410 | + | 1.14249i | ||||
\(835\) | −110319. | −0.158225 | ||||||||
\(836\) | 159294.i | 0.227922i | ||||||||
\(837\) | −102243. | + | 772518.i | −0.145943 | + | 1.10270i | ||||
\(838\) | 1.33667e6 | 1.90343 | ||||||||
\(839\) | 654006.i | 0.929091i | 0.885549 | + | 0.464545i | \(0.153782\pi\) | ||||
−0.885549 | + | 0.464545i | \(0.846218\pi\) | |||||||
\(840\) | 279962. | − | 145657.i | 0.396771 | − | 0.206431i | ||||
\(841\) | 674927. | 0.954255 | ||||||||
\(842\) | − | 694990.i | − | 0.980290i | ||||||
\(843\) | −122048. | − | 234584.i | −0.171742 | − | 0.330098i | ||||
\(844\) | −311985. | −0.437974 | ||||||||
\(845\) | − | 273952.i | − | 0.383672i | ||||||
\(846\) | 198639. | − | 283410.i | 0.277539 | − | 0.395981i | ||||
\(847\) | 172363. | 0.240257 | ||||||||
\(848\) | − | 131260.i | − | 0.182533i | ||||||
\(849\) | −479963. | + | 249713.i | −0.665874 | + | 0.346439i | ||||
\(850\) | 99970.1 | 0.138367 | ||||||||
\(851\) | 1.10363e6i | 1.52393i | ||||||||
\(852\) | 9577.35 | + | 18408.2i | 0.0131937 | + | 0.0253590i | ||||
\(853\) | 39930.2 | 0.0548786 | 0.0274393 | − | 0.999623i | \(-0.491265\pi\) | ||||
0.0274393 | + | 0.999623i | \(0.491265\pi\) | |||||||
\(854\) | − | 647407.i | − | 0.887690i | ||||||
\(855\) | 223756. | + | 156828.i | 0.306085 | + | 0.214532i | ||||
\(856\) | −345473. | −0.471484 | ||||||||
\(857\) | − | 558770.i | − | 0.760801i | −0.924822 | − | 0.380401i | \(-0.875786\pi\) | ||
0.924822 | − | 0.380401i | \(-0.124214\pi\) | |||||||
\(858\) | 252744. | − | 131497.i | 0.343326 | − | 0.178624i | ||||
\(859\) | −816282. | −1.10625 | −0.553126 | − | 0.833098i | \(-0.686565\pi\) | ||||
−0.553126 | + | 0.833098i | \(0.686565\pi\) | |||||||
\(860\) | 164504.i | 0.222423i | ||||||||
\(861\) | −44468.9 | − | 85471.7i | −0.0599861 | − | 0.115297i | ||||
\(862\) | −1.15441e6 | −1.55362 | ||||||||
\(863\) | 525248.i | 0.705250i | 0.935765 | + | 0.352625i | \(0.114711\pi\) | ||||
−0.935765 | + | 0.352625i | \(0.885289\pi\) | |||||||
\(864\) | 434639. | + | 57524.5i | 0.582239 | + | 0.0770593i | ||||
\(865\) | −241342. | −0.322553 | ||||||||
\(866\) | 1.50832e6i | 2.01121i | ||||||||
\(867\) | −421923. | + | 219517.i | −0.561300 | + | 0.292031i | ||||
\(868\) | −319475. | −0.424031 | ||||||||
\(869\) | − | 338037.i | − | 0.447636i | ||||||
\(870\) | 38145.7 | + | 73318.1i | 0.0503973 | + | 0.0968663i | ||||
\(871\) | −268765. | −0.354272 | ||||||||
\(872\) | − | 234186.i | − | 0.307983i | ||||||
\(873\) | 432834. | − | 617550.i | 0.567927 | − | 0.810296i | ||||
\(874\) | 1.43273e6 | 1.87561 | ||||||||
\(875\) | − | 86098.2i | − | 0.112455i | ||||||
\(876\) | −83216.3 | + | 43295.5i | −0.108443 | + | 0.0564202i | ||||
\(877\) | −53533.8 | −0.0696031 | −0.0348015 | − | 0.999394i | \(-0.511080\pi\) | ||||
−0.0348015 | + | 0.999394i | \(0.511080\pi\) | |||||||
\(878\) | − | 1.04763e6i | − | 1.35900i | ||||||
\(879\) | −15657.9 | − | 30095.3i | −0.0202654 | − | 0.0389512i | ||||
\(880\) | −377287. | −0.487199 | ||||||||
\(881\) | 1.15608e6i | 1.48949i | 0.667349 | + | 0.744746i | \(0.267429\pi\) | ||||
−0.667349 | + | 0.744746i | \(0.732571\pi\) | |||||||
\(882\) | 422343. | + | 296015.i | 0.542910 | + | 0.380519i | ||||
\(883\) | −1.24115e6 | −1.59186 | −0.795929 | − | 0.605390i | \(-0.793017\pi\) | ||||
−0.795929 | + | 0.605390i | \(0.793017\pi\) | |||||||
\(884\) | 54126.1i | 0.0692631i | ||||||||
\(885\) | −284639. | + | 148091.i | −0.363419 | + | 0.189078i | ||||
\(886\) | 28081.2 | 0.0357724 | ||||||||
\(887\) | 747316.i | 0.949855i | 0.880025 | + | 0.474927i | \(0.157526\pi\) | ||||
−0.880025 | + | 0.474927i | \(0.842474\pi\) | |||||||
\(888\) | 224431. | + | 431368.i | 0.284614 | + | 0.547044i | ||||
\(889\) | −952100. | −1.20470 | ||||||||
\(890\) | − | 421733.i | − | 0.532423i | ||||||
\(891\) | −671174. | + | 243593.i | −0.845434 | + | 0.306838i | ||||
\(892\) | 251146. | 0.315643 | ||||||||
\(893\) | − | 282323.i | − | 0.354033i | ||||||
\(894\) | −1.13135e6 | + | 588615.i | −1.41554 | + | 0.736472i | ||||
\(895\) | 247936. | 0.309523 | ||||||||
\(896\) | − | 1.21597e6i | − | 1.51463i | ||||||
\(897\) | −275172. | − | 528895.i | −0.341994 | − | 0.657332i | ||||
\(898\) | −1.00255e6 | −1.24324 | ||||||||
\(899\) | 192273.i | 0.237903i | ||||||||
\(900\) | 28192.0 | − | 40223.2i | 0.0348049 | − | 0.0496583i | ||||
\(901\) | −74138.9 | −0.0913264 | ||||||||
\(902\) | 86351.9i | 0.106135i | ||||||||
\(903\) | 1.49183e6 | − | 776162.i | 1.82954 | − | 0.951869i | ||||
\(904\) | 750982. | 0.918951 | ||||||||
\(905\) | − | 637739.i | − | 0.778657i | ||||||
\(906\) | −248425. | − | 477487.i | −0.302649 | − | 0.581708i | ||||
\(907\) | 952017. | 1.15726 | 0.578629 | − | 0.815591i | \(-0.303588\pi\) | ||||
0.578629 | + | 0.815591i | \(0.303588\pi\) | |||||||
\(908\) | 338477.i | 0.410542i | ||||||||
\(909\) | 679207. | + | 476049.i | 0.822005 | + | 0.576134i | ||||
\(910\) | 200358. | 0.241949 | ||||||||
\(911\) | − | 1824.09i | − | 0.00219790i | −0.999999 | − | 0.00109895i | \(-0.999650\pi\) | ||
0.999999 | − | 0.00109895i | \(-0.000349808\pi\) | |||||||
\(912\) | 746987. | − | 388640.i | 0.898098 | − | 0.467259i | ||||
\(913\) | 410262. | 0.492175 | ||||||||
\(914\) | − | 633248.i | − | 0.758021i | ||||||
\(915\) | 106880. | + | 205428.i | 0.127659 | + | 0.245368i | ||||
\(916\) | 11080.7 | 0.0132062 | ||||||||
\(917\) | 1.34568e6i | 1.60031i | ||||||||
\(918\) | 76496.5 | − | 577986.i | 0.0907728 | − | 0.685854i | ||||
\(919\) | −852396. | −1.00928 | −0.504638 | − | 0.863331i | \(-0.668374\pi\) | ||||
−0.504638 | + | 0.863331i | \(0.668374\pi\) | |||||||
\(920\) | 591884.i | 0.699295i | ||||||||
\(921\) | 1.12504e6 | − | 585332.i | 1.32632 | − | 0.690054i | ||||
\(922\) | 17773.5 | 0.0209079 | ||||||||
\(923\) | − | 30275.3i | − | 0.0355374i | ||||||
\(924\) | −135107. | − | 259683.i | −0.158246 | − | 0.304158i | ||||
\(925\) | 132661. | 0.155046 | ||||||||
\(926\) | − | 1.27699e6i | − | 1.48924i | ||||||
\(927\) | −251053. | + | 358192.i | −0.292150 | + | 0.416828i | ||||
\(928\) | 108178. | 0.125615 | ||||||||
\(929\) | − | 1.31428e6i | − | 1.52284i | −0.648258 | − | 0.761421i | \(-0.724502\pi\) | ||
0.648258 | − | 0.761421i | \(-0.275498\pi\) | |||||||
\(930\) | 435709. | − | 226689.i | 0.503768 | − | 0.262099i | ||||
\(931\) | 420723. | 0.485397 | ||||||||
\(932\) | 108980.i | 0.125463i | ||||||||
\(933\) | −74847.3 | − | 143861.i | −0.0859830 | − | 0.165264i | ||||
\(934\) | 926604. | 1.06219 | ||||||||
\(935\) | 213100.i | 0.243759i | ||||||||
\(936\) | −215109. | − | 150768.i | −0.245531 | − | 0.172090i | ||||
\(937\) | 1.57670e6 | 1.79585 | 0.897926 | − | 0.440146i | \(-0.145073\pi\) | ||||
0.897926 | + | 0.440146i | \(0.145073\pi\) | |||||||
\(938\) | 1.18689e6i | 1.34898i | ||||||||
\(939\) | 352548. | − | 183423.i | 0.399841 | − | 0.208028i | ||||
\(940\) | −50751.5 | −0.0574372 | ||||||||
\(941\) | 603453.i | 0.681498i | 0.940154 | + | 0.340749i | \(0.110681\pi\) | ||||
−0.940154 | + | 0.340749i | \(0.889319\pi\) | |||||||
\(942\) | −239181. | − | 459718.i | −0.269540 | − | 0.518072i | ||||
\(943\) | 180701. | 0.203206 | ||||||||
\(944\) | 988774.i | 1.10957i | ||||||||
\(945\) | −497784. | − | 65881.7i | −0.557413 | − | 0.0737737i | ||||
\(946\) | −1.50719e6 | −1.68417 | ||||||||
\(947\) | 267321.i | 0.298080i | 0.988831 | + | 0.149040i | \(0.0476183\pi\) | ||||
−0.988831 | + | 0.149040i | \(0.952382\pi\) | |||||||
\(948\) | 120312. | − | 62595.5i | 0.133873 | − | 0.0696509i | ||||
\(949\) | 136863. | 0.151969 | ||||||||
\(950\) | − | 172221.i | − | 0.190826i | ||||||
\(951\) | −805335. | − | 1.54790e6i | −0.890463 | − | 1.71152i | ||||
\(952\) | −549306. | −0.606095 | ||||||||
\(953\) | 1.44335e6i | 1.58923i | 0.607117 | + | 0.794613i | \(0.292326\pi\) | ||||
−0.607117 | + | 0.794613i | \(0.707674\pi\) | |||||||
\(954\) | −89862.4 | + | 128212.i | −0.0987374 | + | 0.140874i | ||||
\(955\) | −718790. | −0.788125 | ||||||||
\(956\) | − | 204317.i | − | 0.223557i | ||||||
\(957\) | −156288. | + | 81312.8i | −0.170648 | + | 0.0887841i | ||||
\(958\) | −1.40859e6 | −1.53481 | ||||||||
\(959\) | − | 1.16587e6i | − | 1.26768i | ||||||
\(960\) | 102875. | + | 197732.i | 0.111627 | + | 0.214553i | ||||
\(961\) | 219105. | 0.237250 | ||||||||
\(962\) | 308714.i | 0.333585i | ||||||||
\(963\) | 450125. | + | 315488.i | 0.485379 | + | 0.340196i | ||||
\(964\) | 4734.46 | 0.00509468 | ||||||||
\(965\) | 407553.i | 0.437652i | ||||||||
\(966\) | −2.33565e6 | + | 1.21518e6i | −2.50296 | + | 1.30223i | ||||
\(967\) | 890704. | 0.952534 | 0.476267 | − | 0.879301i | \(-0.341990\pi\) | ||||
0.476267 | + | 0.879301i | \(0.341990\pi\) | |||||||
\(968\) | 142431.i | 0.152004i | ||||||||
\(969\) | −219513. | − | 421916.i | −0.233783 | − | 0.449343i | ||||
\(970\) | −475317. | −0.505172 | ||||||||
\(971\) | − | 1.14658e6i | − | 1.21609i | −0.793904 | − | 0.608044i | \(-0.791955\pi\) | ||
0.793904 | − | 0.608044i | \(-0.208045\pi\) | |||||||
\(972\) | −210981. | − | 193773.i | −0.223312 | − | 0.205097i | ||||
\(973\) | −1.34284e6 | −1.41840 | ||||||||
\(974\) | 961297.i | 1.01330i | ||||||||
\(975\) | −63575.5 | + | 33076.9i | −0.0668776 | + | 0.0347949i | ||||
\(976\) | 713614. | 0.749142 | ||||||||
\(977\) | − | 352274.i | − | 0.369055i | −0.982827 | − | 0.184527i | \(-0.940925\pi\) | ||
0.982827 | − | 0.184527i | \(-0.0590755\pi\) | |||||||
\(978\) | −29794.6 | − | 57266.8i | −0.0311501 | − | 0.0598722i | ||||
\(979\) | 898981. | 0.937962 | ||||||||
\(980\) | − | 75630.9i | − | 0.0787493i | ||||||
\(981\) | −213860. | + | 305126.i | −0.222224 | + | 0.317060i | ||||
\(982\) | 2.02085e6 | 2.09561 | ||||||||
\(983\) | − | 794769.i | − | 0.822496i | −0.911524 | − | 0.411248i | \(-0.865093\pi\) | ||
0.911524 | − | 0.411248i | \(-0.134907\pi\) | |||||||
\(984\) | 70629.3 | − | 36746.8i | 0.0729449 | − | 0.0379515i | ||||
\(985\) | −709660. | −0.731439 | ||||||||
\(986\) | − | 143856.i | − | 0.147970i | ||||||
\(987\) | 239455. | + | 460246.i | 0.245805 | + | 0.472450i | ||||
\(988\) | 93244.1 | 0.0955229 | ||||||||
\(989\) | 3.15396e6i | 3.22451i | ||||||||
\(990\) | 368525. | + | 258295.i | 0.376007 | + | 0.263539i | ||||
\(991\) | 903807. | 0.920298 | 0.460149 | − | 0.887842i | \(-0.347796\pi\) | ||||
0.460149 | + | 0.887842i | \(0.347796\pi\) | |||||||
\(992\) | − | 642871.i | − | 0.653282i | ||||||
\(993\) | 295555. | − | 153770.i | 0.299737 | − | 0.155946i | ||||
\(994\) | −133699. | −0.135318 | ||||||||
\(995\) | − | 107712.i | − | 0.108797i | ||||||
\(996\) | 75969.6 | + | 146018.i | 0.0765810 | + | 0.147193i | ||||
\(997\) | −1.64889e6 | −1.65883 | −0.829413 | − | 0.558636i | \(-0.811325\pi\) | ||||
−0.829413 | + | 0.558636i | \(0.811325\pi\) | |||||||
\(998\) | 776838.i | 0.779955i | ||||||||
\(999\) | 101511. | − | 766991.i | 0.101715 | − | 0.768527i |
(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 | 15.5.c.a.11.5 | yes | 6 | |
3.2 | odd | 2 | inner | 15.5.c.a.11.2 | ✓ | 6 | |
4.3 | odd | 2 | 240.5.l.d.161.5 | 6 | |||
5.2 | odd | 4 | 75.5.d.d.74.4 | 12 | |||
5.3 | odd | 4 | 75.5.d.d.74.9 | 12 | |||
5.4 | even | 2 | 75.5.c.i.26.2 | 6 | |||
12.11 | even | 2 | 240.5.l.d.161.6 | 6 | |||
15.2 | even | 4 | 75.5.d.d.74.10 | 12 | |||
15.8 | even | 4 | 75.5.d.d.74.3 | 12 | |||
15.14 | odd | 2 | 75.5.c.i.26.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.5.c.a.11.2 | ✓ | 6 | 3.2 | odd | 2 | inner | |
15.5.c.a.11.5 | yes | 6 | 1.1 | even | 1 | trivial | |
75.5.c.i.26.2 | 6 | 5.4 | even | 2 | |||
75.5.c.i.26.5 | 6 | 15.14 | odd | 2 | |||
75.5.d.d.74.3 | 12 | 15.8 | even | 4 | |||
75.5.d.d.74.4 | 12 | 5.2 | odd | 4 | |||
75.5.d.d.74.9 | 12 | 5.3 | odd | 4 | |||
75.5.d.d.74.10 | 12 | 15.2 | even | 4 | |||
240.5.l.d.161.5 | 6 | 4.3 | odd | 2 | |||
240.5.l.d.161.6 | 6 | 12.11 | even | 2 |