Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,5,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(18.2964834658\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.2 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.5.c.a.58.39 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 7.77798i | − | 1.94450i | −0.233953 | − | 0.972248i | \(-0.575166\pi\) | ||
0.233953 | − | 0.972248i | \(-0.424834\pi\) | |||||||
\(3\) | −5.19615 | −0.577350 | ||||||||
\(4\) | −44.4970 | −2.78106 | ||||||||
\(5\) | 28.5836 | 1.14334 | 0.571672 | − | 0.820482i | \(-0.306295\pi\) | ||||
0.571672 | + | 0.820482i | \(0.306295\pi\) | |||||||
\(6\) | 40.4156i | 1.12266i | ||||||||
\(7\) | 72.7001 | 1.48368 | 0.741838 | − | 0.670579i | \(-0.233954\pi\) | ||||
0.741838 | + | 0.670579i | \(0.233954\pi\) | |||||||
\(8\) | 221.650i | 3.46327i | ||||||||
\(9\) | 27.0000 | 0.333333 | ||||||||
\(10\) | − | 222.323i | − | 2.22323i | ||||||
\(11\) | − | 9.33885i | − | 0.0771806i | −0.999255 | − | 0.0385903i | \(-0.987713\pi\) | ||
0.999255 | − | 0.0385903i | \(-0.0122867\pi\) | |||||||
\(12\) | 231.213 | 1.60565 | ||||||||
\(13\) | − | 106.784i | − | 0.631858i | −0.948783 | − | 0.315929i | \(-0.897684\pi\) | ||
0.948783 | − | 0.315929i | \(-0.102316\pi\) | |||||||
\(14\) | − | 565.461i | − | 2.88500i | ||||||
\(15\) | −148.525 | −0.660110 | ||||||||
\(16\) | 1012.03 | 3.95326 | ||||||||
\(17\) | 337.515 | 1.16787 | 0.583936 | − | 0.811800i | \(-0.301512\pi\) | ||||
0.583936 | + | 0.811800i | \(0.301512\pi\) | |||||||
\(18\) | − | 210.006i | − | 0.648165i | ||||||
\(19\) | 546.806 | 1.51470 | 0.757349 | − | 0.653010i | \(-0.226494\pi\) | ||||
0.757349 | + | 0.653010i | \(0.226494\pi\) | |||||||
\(20\) | −1271.89 | −3.17972 | ||||||||
\(21\) | −377.761 | −0.856601 | ||||||||
\(22\) | −72.6374 | −0.150077 | ||||||||
\(23\) | 39.3036i | 0.0742979i | 0.999310 | + | 0.0371490i | \(0.0118276\pi\) | ||||
−0.999310 | + | 0.0371490i | \(0.988172\pi\) | |||||||
\(24\) | − | 1151.72i | − | 1.99952i | ||||||
\(25\) | 192.023 | 0.307237 | ||||||||
\(26\) | −830.565 | −1.22865 | ||||||||
\(27\) | −140.296 | −0.192450 | ||||||||
\(28\) | −3234.94 | −4.12620 | ||||||||
\(29\) | −444.446 | −0.528473 | −0.264236 | − | 0.964458i | \(-0.585120\pi\) | ||||
−0.264236 | + | 0.964458i | \(0.585120\pi\) | |||||||
\(30\) | 1155.22i | 1.28358i | ||||||||
\(31\) | 1230.69i | 1.28063i | 0.768110 | + | 0.640317i | \(0.221197\pi\) | ||||
−0.768110 | + | 0.640317i | \(0.778803\pi\) | |||||||
\(32\) | − | 4325.19i | − | 4.22382i | ||||||
\(33\) | 48.5261i | 0.0445602i | ||||||||
\(34\) | − | 2625.19i | − | 2.27092i | ||||||
\(35\) | 2078.03 | 1.69635 | ||||||||
\(36\) | −1201.42 | −0.927022 | ||||||||
\(37\) | 1943.27i | 1.41948i | 0.704464 | + | 0.709740i | \(0.251188\pi\) | ||||
−0.704464 | + | 0.709740i | \(0.748812\pi\) | |||||||
\(38\) | − | 4253.05i | − | 2.94532i | ||||||
\(39\) | 554.866i | 0.364804i | ||||||||
\(40\) | 6335.54i | 3.95971i | ||||||||
\(41\) | −835.576 | −0.497071 | −0.248535 | − | 0.968623i | \(-0.579949\pi\) | ||||
−0.248535 | + | 0.968623i | \(0.579949\pi\) | |||||||
\(42\) | 2938.22i | 1.66566i | ||||||||
\(43\) | − | 2242.91i | − | 1.21304i | −0.795069 | − | 0.606519i | \(-0.792565\pi\) | ||
0.795069 | − | 0.606519i | \(-0.207435\pi\) | |||||||
\(44\) | 415.551i | 0.214644i | ||||||||
\(45\) | 771.758 | 0.381115 | ||||||||
\(46\) | 305.703 | 0.144472 | ||||||||
\(47\) | − | 3914.09i | − | 1.77188i | −0.463797 | − | 0.885942i | \(-0.653513\pi\) | ||
0.463797 | − | 0.885942i | \(-0.346487\pi\) | |||||||
\(48\) | −5258.68 | −2.28241 | ||||||||
\(49\) | 2884.31 | 1.20130 | ||||||||
\(50\) | − | 1493.55i | − | 0.597421i | ||||||
\(51\) | −1753.78 | −0.674271 | ||||||||
\(52\) | 4751.57i | 1.75724i | ||||||||
\(53\) | 3820.28 | 1.36001 | 0.680006 | − | 0.733206i | \(-0.261977\pi\) | ||||
0.680006 | + | 0.733206i | \(0.261977\pi\) | |||||||
\(54\) | 1091.22i | 0.374218i | ||||||||
\(55\) | − | 266.938i | − | 0.0882440i | ||||||
\(56\) | 16113.9i | 5.13838i | ||||||||
\(57\) | −2841.29 | −0.874511 | ||||||||
\(58\) | 3456.89i | 1.02761i | ||||||||
\(59\) | −3000.50 | + | 1764.76i | −0.861964 | + | 0.506970i | ||||
\(60\) | 6608.91 | 1.83581 | ||||||||
\(61\) | − | 2344.07i | − | 0.629958i | −0.949099 | − | 0.314979i | \(-0.898003\pi\) | ||
0.949099 | − | 0.314979i | \(-0.101997\pi\) | |||||||
\(62\) | 9572.29 | 2.49019 | ||||||||
\(63\) | 1962.90 | 0.494559 | ||||||||
\(64\) | −17448.7 | −4.25994 | ||||||||
\(65\) | − | 3052.27i | − | 0.722432i | ||||||
\(66\) | 377.435 | 0.0866472 | ||||||||
\(67\) | − | 3650.67i | − | 0.813249i | −0.913595 | − | 0.406624i | \(-0.866706\pi\) | ||
0.913595 | − | 0.406624i | \(-0.133294\pi\) | |||||||
\(68\) | −15018.4 | −3.24793 | ||||||||
\(69\) | − | 204.228i | − | 0.0428959i | ||||||
\(70\) | − | 16162.9i | − | 3.29855i | ||||||
\(71\) | −2630.49 | −0.521819 | −0.260909 | − | 0.965363i | \(-0.584022\pi\) | ||||
−0.260909 | + | 0.965363i | \(0.584022\pi\) | |||||||
\(72\) | 5984.54i | 1.15442i | ||||||||
\(73\) | − | 8924.21i | − | 1.67465i | −0.546705 | − | 0.837325i | \(-0.684118\pi\) | ||
0.546705 | − | 0.837325i | \(-0.315882\pi\) | |||||||
\(74\) | 15114.7 | 2.76017 | ||||||||
\(75\) | −997.781 | −0.177383 | ||||||||
\(76\) | −24331.3 | −4.21247 | ||||||||
\(77\) | − | 678.935i | − | 0.114511i | ||||||
\(78\) | 4315.74 | 0.709359 | ||||||||
\(79\) | 1497.53 | 0.239951 | 0.119976 | − | 0.992777i | \(-0.461718\pi\) | ||||
0.119976 | + | 0.992777i | \(0.461718\pi\) | |||||||
\(80\) | 28927.6 | 4.51993 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | 6499.09i | 0.966552i | ||||||||
\(83\) | − | 3985.30i | − | 0.578503i | −0.957253 | − | 0.289251i | \(-0.906594\pi\) | ||
0.957253 | − | 0.289251i | \(-0.0934063\pi\) | |||||||
\(84\) | 16809.2 | 2.38226 | ||||||||
\(85\) | 9647.40 | 1.33528 | ||||||||
\(86\) | −17445.3 | −2.35875 | ||||||||
\(87\) | 2309.41 | 0.305114 | ||||||||
\(88\) | 2069.95 | 0.267297 | ||||||||
\(89\) | − | 2531.49i | − | 0.319593i | −0.987150 | − | 0.159796i | \(-0.948916\pi\) | ||
0.987150 | − | 0.159796i | \(-0.0510838\pi\) | |||||||
\(90\) | − | 6002.72i | − | 0.741076i | ||||||
\(91\) | − | 7763.21i | − | 0.937473i | ||||||
\(92\) | − | 1748.89i | − | 0.206627i | ||||||
\(93\) | − | 6394.85i | − | 0.739375i | ||||||
\(94\) | −30443.7 | −3.44542 | ||||||||
\(95\) | 15629.7 | 1.73182 | ||||||||
\(96\) | 22474.3i | 2.43862i | ||||||||
\(97\) | 9210.22i | 0.978874i | 0.872039 | + | 0.489437i | \(0.162798\pi\) | ||||
−0.872039 | + | 0.489437i | \(0.837202\pi\) | |||||||
\(98\) | − | 22434.1i | − | 2.33591i | ||||||
\(99\) | − | 252.149i | − | 0.0257269i | ||||||
\(100\) | −8544.45 | −0.854445 | ||||||||
\(101\) | 13290.3i | 1.30284i | 0.758717 | + | 0.651420i | \(0.225826\pi\) | ||||
−0.758717 | + | 0.651420i | \(0.774174\pi\) | |||||||
\(102\) | 13640.9i | 1.31112i | ||||||||
\(103\) | 14436.1i | 1.36074i | 0.732867 | + | 0.680372i | \(0.238182\pi\) | ||||
−0.732867 | + | 0.680372i | \(0.761818\pi\) | |||||||
\(104\) | 23668.6 | 2.18830 | ||||||||
\(105\) | −10797.8 | −0.979390 | ||||||||
\(106\) | − | 29714.0i | − | 2.64454i | ||||||
\(107\) | −986.412 | −0.0861570 | −0.0430785 | − | 0.999072i | \(-0.513717\pi\) | ||||
−0.0430785 | + | 0.999072i | \(0.513717\pi\) | |||||||
\(108\) | 6242.76 | 0.535216 | ||||||||
\(109\) | 14934.0i | 1.25697i | 0.777824 | + | 0.628483i | \(0.216324\pi\) | ||||
−0.777824 | + | 0.628483i | \(0.783676\pi\) | |||||||
\(110\) | −2076.24 | −0.171590 | ||||||||
\(111\) | − | 10097.5i | − | 0.819537i | ||||||
\(112\) | 73575.0 | 5.86535 | ||||||||
\(113\) | − | 19908.8i | − | 1.55915i | −0.626308 | − | 0.779576i | \(-0.715435\pi\) | ||
0.626308 | − | 0.779576i | \(-0.284565\pi\) | |||||||
\(114\) | 22099.5i | 1.70048i | ||||||||
\(115\) | 1123.44i | 0.0849481i | ||||||||
\(116\) | 19776.5 | 1.46972 | ||||||||
\(117\) | − | 2883.17i | − | 0.210619i | ||||||
\(118\) | 13726.3 | + | 23337.8i | 0.985802 | + | 1.67608i | ||||
\(119\) | 24537.4 | 1.73274 | ||||||||
\(120\) | − | 32920.5i | − | 2.28614i | ||||||
\(121\) | 14553.8 | 0.994043 | ||||||||
\(122\) | −18232.2 | −1.22495 | ||||||||
\(123\) | 4341.78 | 0.286984 | ||||||||
\(124\) | − | 54762.1i | − | 3.56153i | ||||||
\(125\) | −12376.0 | −0.792067 | ||||||||
\(126\) | − | 15267.4i | − | 0.961668i | ||||||
\(127\) | −15531.0 | −0.962922 | −0.481461 | − | 0.876468i | \(-0.659894\pi\) | ||||
−0.481461 | + | 0.876468i | \(0.659894\pi\) | |||||||
\(128\) | 66512.8i | 4.05962i | ||||||||
\(129\) | 11654.5i | 0.700348i | ||||||||
\(130\) | −23740.5 | −1.40477 | ||||||||
\(131\) | − | 1246.21i | − | 0.0726188i | −0.999341 | − | 0.0363094i | \(-0.988440\pi\) | ||
0.999341 | − | 0.0363094i | \(-0.0115602\pi\) | |||||||
\(132\) | − | 2159.27i | − | 0.123925i | ||||||
\(133\) | 39752.9 | 2.24732 | ||||||||
\(134\) | −28394.9 | −1.58136 | ||||||||
\(135\) | −4010.17 | −0.220037 | ||||||||
\(136\) | 74810.0i | 4.04466i | ||||||||
\(137\) | 16792.4 | 0.894689 | 0.447344 | − | 0.894362i | \(-0.352370\pi\) | ||||
0.447344 | + | 0.894362i | \(0.352370\pi\) | |||||||
\(138\) | −1588.48 | −0.0834110 | ||||||||
\(139\) | −35922.2 | −1.85923 | −0.929616 | − | 0.368530i | \(-0.879861\pi\) | ||||
−0.929616 | + | 0.368530i | \(0.879861\pi\) | |||||||
\(140\) | −92466.3 | −4.71767 | ||||||||
\(141\) | 20338.2i | 1.02300i | ||||||||
\(142\) | 20459.9i | 1.01467i | ||||||||
\(143\) | −997.240 | −0.0487672 | ||||||||
\(144\) | 27324.9 | 1.31775 | ||||||||
\(145\) | −12703.9 | −0.604227 | ||||||||
\(146\) | −69412.4 | −3.25635 | ||||||||
\(147\) | −14987.3 | −0.693568 | ||||||||
\(148\) | − | 86469.7i | − | 3.94767i | ||||||
\(149\) | − | 25955.6i | − | 1.16912i | −0.811351 | − | 0.584559i | \(-0.801268\pi\) | ||
0.811351 | − | 0.584559i | \(-0.198732\pi\) | |||||||
\(150\) | 7760.72i | 0.344921i | ||||||||
\(151\) | 18565.1i | 0.814222i | 0.913379 | + | 0.407111i | \(0.133464\pi\) | ||||
−0.913379 | + | 0.407111i | \(0.866536\pi\) | |||||||
\(152\) | 121199.i | 5.24581i | ||||||||
\(153\) | 9112.91 | 0.389291 | ||||||||
\(154\) | −5280.75 | −0.222666 | ||||||||
\(155\) | 35177.6i | 1.46421i | ||||||||
\(156\) | − | 24689.9i | − | 1.01454i | ||||||
\(157\) | 46527.1i | 1.88759i | 0.330537 | + | 0.943793i | \(0.392770\pi\) | ||||
−0.330537 | + | 0.943793i | \(0.607230\pi\) | |||||||
\(158\) | − | 11647.8i | − | 0.466584i | ||||||
\(159\) | −19850.7 | −0.785204 | ||||||||
\(160\) | − | 123630.i | − | 4.82928i | ||||||
\(161\) | 2857.38i | 0.110234i | ||||||||
\(162\) | − | 5670.15i | − | 0.216055i | ||||||
\(163\) | −437.670 | −0.0164730 | −0.00823648 | − | 0.999966i | \(-0.502622\pi\) | ||||
−0.00823648 | + | 0.999966i | \(0.502622\pi\) | |||||||
\(164\) | 37180.6 | 1.38239 | ||||||||
\(165\) | 1387.05i | 0.0509477i | ||||||||
\(166\) | −30997.6 | −1.12490 | ||||||||
\(167\) | 49721.0 | 1.78282 | 0.891408 | − | 0.453201i | \(-0.149718\pi\) | ||||
0.891408 | + | 0.453201i | \(0.149718\pi\) | |||||||
\(168\) | − | 83730.5i | − | 2.96664i | ||||||
\(169\) | 17158.2 | 0.600755 | ||||||||
\(170\) | − | 75037.3i | − | 2.59645i | ||||||
\(171\) | 14763.8 | 0.504899 | ||||||||
\(172\) | 99802.8i | 3.37354i | ||||||||
\(173\) | − | 30766.7i | − | 1.02799i | −0.857793 | − | 0.513995i | \(-0.828165\pi\) | ||
0.857793 | − | 0.513995i | \(-0.171835\pi\) | |||||||
\(174\) | − | 17962.5i | − | 0.593293i | ||||||
\(175\) | 13960.1 | 0.455840 | ||||||||
\(176\) | − | 9451.23i | − | 0.305115i | ||||||
\(177\) | 15591.0 | − | 9169.98i | 0.497655 | − | 0.292699i | ||||
\(178\) | −19689.9 | −0.621447 | ||||||||
\(179\) | − | 20767.6i | − | 0.648156i | −0.946030 | − | 0.324078i | \(-0.894946\pi\) | ||
0.946030 | − | 0.324078i | \(-0.105054\pi\) | |||||||
\(180\) | −34340.9 | −1.05991 | ||||||||
\(181\) | 27789.6 | 0.848252 | 0.424126 | − | 0.905603i | \(-0.360581\pi\) | ||||
0.424126 | + | 0.905603i | \(0.360581\pi\) | |||||||
\(182\) | −60382.2 | −1.82291 | ||||||||
\(183\) | 12180.2i | 0.363706i | ||||||||
\(184\) | −8711.63 | −0.257314 | ||||||||
\(185\) | 55545.6i | 1.62295i | ||||||||
\(186\) | −49739.1 | −1.43771 | ||||||||
\(187\) | − | 3152.00i | − | 0.0901370i | ||||||
\(188\) | 174165.i | 4.92772i | ||||||||
\(189\) | −10199.5 | −0.285534 | ||||||||
\(190\) | − | 121568.i | − | 3.36752i | ||||||
\(191\) | − | 22222.5i | − | 0.609153i | −0.952488 | − | 0.304576i | \(-0.901485\pi\) | ||
0.952488 | − | 0.304576i | \(-0.0985149\pi\) | |||||||
\(192\) | 90666.2 | 2.45948 | ||||||||
\(193\) | 22533.4 | 0.604941 | 0.302470 | − | 0.953159i | \(-0.402189\pi\) | ||||
0.302470 | + | 0.953159i | \(0.402189\pi\) | |||||||
\(194\) | 71637.0 | 1.90342 | ||||||||
\(195\) | 15860.1i | 0.417096i | ||||||||
\(196\) | −128343. | −3.34088 | ||||||||
\(197\) | 11138.9 | 0.287018 | 0.143509 | − | 0.989649i | \(-0.454161\pi\) | ||||
0.143509 | + | 0.989649i | \(0.454161\pi\) | |||||||
\(198\) | −1961.21 | −0.0500258 | ||||||||
\(199\) | −27923.7 | −0.705126 | −0.352563 | − | 0.935788i | \(-0.614690\pi\) | ||||
−0.352563 | + | 0.935788i | \(0.614690\pi\) | |||||||
\(200\) | 42561.8i | 1.06404i | ||||||||
\(201\) | 18969.5i | 0.469529i | ||||||||
\(202\) | 103372. | 2.53337 | ||||||||
\(203\) | −32311.3 | −0.784083 | ||||||||
\(204\) | 78038.0 | 1.87519 | ||||||||
\(205\) | −23883.8 | −0.568323 | ||||||||
\(206\) | 112284. | 2.64596 | ||||||||
\(207\) | 1061.20i | 0.0247660i | ||||||||
\(208\) | − | 108069.i | − | 2.49790i | ||||||
\(209\) | − | 5106.54i | − | 0.116905i | ||||||
\(210\) | 83984.9i | 1.90442i | ||||||||
\(211\) | 4163.53i | 0.0935182i | 0.998906 | + | 0.0467591i | \(0.0148893\pi\) | ||||
−0.998906 | + | 0.0467591i | \(0.985111\pi\) | |||||||
\(212\) | −169991. | −3.78228 | ||||||||
\(213\) | 13668.4 | 0.301272 | ||||||||
\(214\) | 7672.29i | 0.167532i | ||||||||
\(215\) | − | 64110.4i | − | 1.38692i | ||||||
\(216\) | − | 31096.6i | − | 0.666507i | ||||||
\(217\) | 89471.3i | 1.90005i | ||||||||
\(218\) | 116156. | 2.44416 | ||||||||
\(219\) | 46371.6i | 0.966860i | ||||||||
\(220\) | 11878.0i | 0.245412i | ||||||||
\(221\) | − | 36041.2i | − | 0.737930i | ||||||
\(222\) | −78538.3 | −1.59359 | ||||||||
\(223\) | −77429.7 | −1.55703 | −0.778517 | − | 0.627624i | \(-0.784028\pi\) | ||||
−0.778517 | + | 0.627624i | \(0.784028\pi\) | |||||||
\(224\) | − | 314442.i | − | 6.26678i | ||||||
\(225\) | 5184.62 | 0.102412 | ||||||||
\(226\) | −154850. | −3.03176 | ||||||||
\(227\) | − | 6994.10i | − | 0.135731i | −0.997694 | − | 0.0678656i | \(-0.978381\pi\) | ||
0.997694 | − | 0.0678656i | \(-0.0216189\pi\) | |||||||
\(228\) | 126429. | 2.43207 | ||||||||
\(229\) | 51473.3i | 0.981547i | 0.871287 | + | 0.490773i | \(0.163286\pi\) | ||||
−0.871287 | + | 0.490773i | \(0.836714\pi\) | |||||||
\(230\) | 8738.09 | 0.165181 | ||||||||
\(231\) | 3527.85i | 0.0661129i | ||||||||
\(232\) | − | 98511.2i | − | 1.83025i | ||||||
\(233\) | 79635.1i | 1.46687i | 0.679758 | + | 0.733437i | \(0.262085\pi\) | ||||
−0.679758 | + | 0.733437i | \(0.737915\pi\) | |||||||
\(234\) | −22425.2 | −0.409549 | ||||||||
\(235\) | − | 111879.i | − | 2.02587i | ||||||
\(236\) | 133513. | − | 78526.7i | 2.39718 | − | 1.40992i | ||||
\(237\) | −7781.42 | −0.138536 | ||||||||
\(238\) | − | 190851.i | − | 3.36931i | ||||||
\(239\) | −27642.4 | −0.483927 | −0.241964 | − | 0.970285i | \(-0.577792\pi\) | ||||
−0.241964 | + | 0.970285i | \(0.577792\pi\) | |||||||
\(240\) | −150312. | −2.60959 | ||||||||
\(241\) | 11767.3 | 0.202602 | 0.101301 | − | 0.994856i | \(-0.467700\pi\) | ||||
0.101301 | + | 0.994856i | \(0.467700\pi\) | |||||||
\(242\) | − | 113199.i | − | 1.93291i | ||||||
\(243\) | −3788.00 | −0.0641500 | ||||||||
\(244\) | 104304.i | 1.75195i | ||||||||
\(245\) | 82444.0 | 1.37349 | ||||||||
\(246\) | − | 33770.3i | − | 0.558039i | ||||||
\(247\) | − | 58390.2i | − | 0.957075i | ||||||
\(248\) | −272782. | −4.43519 | ||||||||
\(249\) | 20708.2i | 0.333999i | ||||||||
\(250\) | 96260.7i | 1.54017i | ||||||||
\(251\) | −98763.5 | −1.56765 | −0.783825 | − | 0.620982i | \(-0.786734\pi\) | ||||
−0.783825 | + | 0.620982i | \(0.786734\pi\) | |||||||
\(252\) | −87343.4 | −1.37540 | ||||||||
\(253\) | 367.050 | 0.00573436 | ||||||||
\(254\) | 120800.i | 1.87240i | ||||||||
\(255\) | −50129.4 | −0.770924 | ||||||||
\(256\) | 238156. | 3.63398 | ||||||||
\(257\) | 36087.2 | 0.546370 | 0.273185 | − | 0.961961i | \(-0.411923\pi\) | ||||
0.273185 | + | 0.961961i | \(0.411923\pi\) | |||||||
\(258\) | 90648.5 | 1.36182 | ||||||||
\(259\) | 141276.i | 2.10605i | ||||||||
\(260\) | 135817.i | 2.00913i | ||||||||
\(261\) | −12000.0 | −0.176158 | ||||||||
\(262\) | −9693.01 | −0.141207 | ||||||||
\(263\) | −16587.3 | −0.239808 | −0.119904 | − | 0.992786i | \(-0.538259\pi\) | ||||
−0.119904 | + | 0.992786i | \(0.538259\pi\) | |||||||
\(264\) | −10755.8 | −0.154324 | ||||||||
\(265\) | 109197. | 1.55496 | ||||||||
\(266\) | − | 309197.i | − | 4.36991i | ||||||
\(267\) | 13154.0i | 0.184517i | ||||||||
\(268\) | 162444.i | 2.26170i | ||||||||
\(269\) | 47175.2i | 0.651943i | 0.945380 | + | 0.325971i | \(0.105691\pi\) | ||||
−0.945380 | + | 0.325971i | \(0.894309\pi\) | |||||||
\(270\) | 31191.0i | 0.427861i | ||||||||
\(271\) | 37006.4 | 0.503893 | 0.251946 | − | 0.967741i | \(-0.418929\pi\) | ||||
0.251946 | + | 0.967741i | \(0.418929\pi\) | |||||||
\(272\) | 341577. | 4.61690 | ||||||||
\(273\) | 40338.8i | 0.541250i | ||||||||
\(274\) | − | 130611.i | − | 1.73972i | ||||||
\(275\) | − | 1793.27i | − | 0.0237127i | ||||||
\(276\) | 9087.52i | 0.119296i | ||||||||
\(277\) | −37499.2 | −0.488722 | −0.244361 | − | 0.969684i | \(-0.578578\pi\) | ||||
−0.244361 | + | 0.969684i | \(0.578578\pi\) | |||||||
\(278\) | 279402.i | 3.61527i | ||||||||
\(279\) | 33228.6i | 0.426878i | ||||||||
\(280\) | 460595.i | 5.87494i | ||||||||
\(281\) | −8246.03 | −0.104432 | −0.0522158 | − | 0.998636i | \(-0.516628\pi\) | ||||
−0.0522158 | + | 0.998636i | \(0.516628\pi\) | |||||||
\(282\) | 158190. | 1.98921 | ||||||||
\(283\) | − | 3380.85i | − | 0.0422137i | −0.999777 | − | 0.0211069i | \(-0.993281\pi\) | ||
0.999777 | − | 0.0211069i | \(-0.00671902\pi\) | |||||||
\(284\) | 117049. | 1.45121 | ||||||||
\(285\) | −81214.3 | −0.999868 | ||||||||
\(286\) | 7756.52i | 0.0948276i | ||||||||
\(287\) | −60746.5 | −0.737492 | ||||||||
\(288\) | − | 116780.i | − | 1.40794i | ||||||
\(289\) | 30395.4 | 0.363925 | ||||||||
\(290\) | 98810.4i | 1.17492i | ||||||||
\(291\) | − | 47857.7i | − | 0.565153i | ||||||
\(292\) | 397101.i | 4.65731i | ||||||||
\(293\) | −146875. | −1.71085 | −0.855427 | − | 0.517923i | \(-0.826705\pi\) | ||||
−0.855427 | + | 0.517923i | \(0.826705\pi\) | |||||||
\(294\) | 116571.i | 1.34864i | ||||||||
\(295\) | −85765.0 | + | 50443.3i | −0.985521 | + | 0.579642i | ||||
\(296\) | −430724. | −4.91605 | ||||||||
\(297\) | 1310.20i | 0.0148534i | ||||||||
\(298\) | −201882. | −2.27334 | ||||||||
\(299\) | 4197.00 | 0.0469458 | ||||||||
\(300\) | 44398.3 | 0.493314 | ||||||||
\(301\) | − | 163060.i | − | 1.79976i | ||||||
\(302\) | 144399. | 1.58325 | ||||||||
\(303\) | − | 69058.3i | − | 0.752195i | ||||||
\(304\) | 553386. | 5.98799 | ||||||||
\(305\) | − | 67002.1i | − | 0.720259i | ||||||
\(306\) | − | 70880.0i | − | 0.756974i | ||||||
\(307\) | 92101.3 | 0.977213 | 0.488606 | − | 0.872504i | \(-0.337505\pi\) | ||||
0.488606 | + | 0.872504i | \(0.337505\pi\) | |||||||
\(308\) | 30210.6i | 0.318462i | ||||||||
\(309\) | − | 75012.4i | − | 0.785626i | ||||||
\(310\) | 273611. | 2.84714 | ||||||||
\(311\) | −32978.0 | −0.340960 | −0.170480 | − | 0.985361i | \(-0.554532\pi\) | ||||
−0.170480 | + | 0.985361i | \(0.554532\pi\) | |||||||
\(312\) | −122986. | −1.26341 | ||||||||
\(313\) | 40714.0i | 0.415581i | 0.978173 | + | 0.207790i | \(0.0666272\pi\) | ||||
−0.978173 | + | 0.207790i | \(0.933373\pi\) | |||||||
\(314\) | 361887. | 3.67040 | ||||||||
\(315\) | 56106.9 | 0.565451 | ||||||||
\(316\) | −66635.9 | −0.667320 | ||||||||
\(317\) | 5097.47 | 0.0507266 | 0.0253633 | − | 0.999678i | \(-0.491926\pi\) | ||||
0.0253633 | + | 0.999678i | \(0.491926\pi\) | |||||||
\(318\) | 154399.i | 1.52683i | ||||||||
\(319\) | 4150.61i | 0.0407878i | ||||||||
\(320\) | −498748. | −4.87058 | ||||||||
\(321\) | 5125.54 | 0.0497428 | ||||||||
\(322\) | 22224.6 | 0.214350 | ||||||||
\(323\) | 184555. | 1.76897 | ||||||||
\(324\) | −32438.3 | −0.309007 | ||||||||
\(325\) | − | 20505.0i | − | 0.194130i | ||||||
\(326\) | 3404.19i | 0.0320316i | ||||||||
\(327\) | − | 77599.4i | − | 0.725709i | ||||||
\(328\) | − | 185205.i | − | 1.72149i | ||||||
\(329\) | − | 284555.i | − | 2.62890i | ||||||
\(330\) | 10788.5 | 0.0990676 | ||||||||
\(331\) | −18523.1 | −0.169067 | −0.0845334 | − | 0.996421i | \(-0.526940\pi\) | ||||
−0.0845334 | + | 0.996421i | \(0.526940\pi\) | |||||||
\(332\) | 177334.i | 1.60885i | ||||||||
\(333\) | 52468.2i | 0.473160i | ||||||||
\(334\) | − | 386729.i | − | 3.46668i | ||||||
\(335\) | − | 104349.i | − | 0.929823i | ||||||
\(336\) | −382307. | −3.38636 | ||||||||
\(337\) | 137124.i | 1.20741i | 0.797209 | + | 0.603704i | \(0.206309\pi\) | ||||
−0.797209 | + | 0.603704i | \(0.793691\pi\) | |||||||
\(338\) | − | 133456.i | − | 1.16817i | ||||||
\(339\) | 103449.i | 0.900176i | ||||||||
\(340\) | −429281. | −3.71350 | ||||||||
\(341\) | 11493.2 | 0.0988401 | ||||||||
\(342\) | − | 114832.i | − | 0.981775i | ||||||
\(343\) | 35136.7 | 0.298657 | ||||||||
\(344\) | 497140. | 4.20108 | ||||||||
\(345\) | − | 5837.56i | − | 0.0490448i | ||||||
\(346\) | −239303. | −1.99892 | ||||||||
\(347\) | − | 92388.3i | − | 0.767287i | −0.923481 | − | 0.383643i | \(-0.874669\pi\) | ||
0.923481 | − | 0.383643i | \(-0.125331\pi\) | |||||||
\(348\) | −102762. | −0.848542 | ||||||||
\(349\) | 192179.i | 1.57781i | 0.614513 | + | 0.788907i | \(0.289352\pi\) | ||||
−0.614513 | + | 0.788907i | \(0.710648\pi\) | |||||||
\(350\) | − | 108581.i | − | 0.886379i | ||||||
\(351\) | 14981.4i | 0.121601i | ||||||||
\(352\) | −40392.3 | −0.325997 | ||||||||
\(353\) | − | 133742.i | − | 1.07329i | −0.843808 | − | 0.536645i | \(-0.819692\pi\) | ||
0.843808 | − | 0.536645i | \(-0.180308\pi\) | |||||||
\(354\) | −71323.9 | − | 121267.i | −0.569153 | − | 0.967688i | ||||
\(355\) | −75188.9 | −0.596619 | ||||||||
\(356\) | 112644.i | 0.888808i | ||||||||
\(357\) | −127500. | −1.00040 | ||||||||
\(358\) | −161530. | −1.26034 | ||||||||
\(359\) | −63441.2 | −0.492246 | −0.246123 | − | 0.969239i | \(-0.579157\pi\) | ||||
−0.246123 | + | 0.969239i | \(0.579157\pi\) | |||||||
\(360\) | 171060.i | 1.31990i | ||||||||
\(361\) | 168676. | 1.29431 | ||||||||
\(362\) | − | 216147.i | − | 1.64942i | ||||||
\(363\) | −75623.7 | −0.573911 | ||||||||
\(364\) | 345440.i | 2.60717i | ||||||||
\(365\) | − | 255086.i | − | 1.91470i | ||||||
\(366\) | 94737.1 | 0.707225 | ||||||||
\(367\) | 62757.7i | 0.465946i | 0.972483 | + | 0.232973i | \(0.0748453\pi\) | ||||
−0.972483 | + | 0.232973i | \(0.925155\pi\) | |||||||
\(368\) | 39776.6i | 0.293719i | ||||||||
\(369\) | −22560.5 | −0.165690 | ||||||||
\(370\) | 432033. | 3.15583 | ||||||||
\(371\) | 277735. | 2.01782 | ||||||||
\(372\) | 284552.i | 2.05625i | ||||||||
\(373\) | −102419. | −0.736148 | −0.368074 | − | 0.929797i | \(-0.619983\pi\) | ||||
−0.368074 | + | 0.929797i | \(0.619983\pi\) | |||||||
\(374\) | −24516.2 | −0.175271 | ||||||||
\(375\) | 64307.8 | 0.457300 | ||||||||
\(376\) | 867556. | 6.13652 | ||||||||
\(377\) | 47459.7i | 0.333920i | ||||||||
\(378\) | 79331.9i | 0.555219i | ||||||||
\(379\) | −115222. | −0.802151 | −0.401076 | − | 0.916045i | \(-0.631364\pi\) | ||||
−0.401076 | + | 0.916045i | \(0.631364\pi\) | |||||||
\(380\) | −695475. | −4.81631 | ||||||||
\(381\) | 80701.3 | 0.555943 | ||||||||
\(382\) | −172846. | −1.18450 | ||||||||
\(383\) | 68700.2 | 0.468339 | 0.234170 | − | 0.972196i | \(-0.424763\pi\) | ||||
0.234170 | + | 0.972196i | \(0.424763\pi\) | |||||||
\(384\) | − | 345611.i | − | 2.34382i | ||||||
\(385\) | − | 19406.4i | − | 0.130925i | ||||||
\(386\) | − | 175265.i | − | 1.17631i | ||||||
\(387\) | − | 60558.5i | − | 0.404346i | ||||||
\(388\) | − | 409828.i | − | 2.72231i | ||||||
\(389\) | 1971.29 | 0.0130272 | 0.00651360 | − | 0.999979i | \(-0.497927\pi\) | ||||
0.00651360 | + | 0.999979i | \(0.497927\pi\) | |||||||
\(390\) | 123359. | 0.811042 | ||||||||
\(391\) | 13265.6i | 0.0867705i | ||||||||
\(392\) | 639306.i | 4.16041i | ||||||||
\(393\) | 6475.50i | 0.0419265i | ||||||||
\(394\) | − | 86638.0i | − | 0.558105i | ||||||
\(395\) | 42805.0 | 0.274347 | ||||||||
\(396\) | 11219.9i | 0.0715480i | ||||||||
\(397\) | − | 42440.9i | − | 0.269280i | −0.990895 | − | 0.134640i | \(-0.957012\pi\) | ||
0.990895 | − | 0.134640i | \(-0.0429877\pi\) | |||||||
\(398\) | 217190.i | 1.37111i | ||||||||
\(399\) | −206562. | −1.29749 | ||||||||
\(400\) | 194334. | 1.21459 | ||||||||
\(401\) | 103710.i | 0.644959i | 0.946576 | + | 0.322480i | \(0.104516\pi\) | ||||
−0.946576 | + | 0.322480i | \(0.895484\pi\) | |||||||
\(402\) | 147544. | 0.912998 | ||||||||
\(403\) | 131418. | 0.809180 | ||||||||
\(404\) | − | 591378.i | − | 3.62328i | ||||||
\(405\) | 20837.5 | 0.127038 | ||||||||
\(406\) | 251316.i | 1.52465i | ||||||||
\(407\) | 18147.9 | 0.109556 | ||||||||
\(408\) | − | 388724.i | − | 2.33519i | ||||||
\(409\) | − | 29250.4i | − | 0.174858i | −0.996171 | − | 0.0874289i | \(-0.972135\pi\) | ||
0.996171 | − | 0.0874289i | \(-0.0278651\pi\) | |||||||
\(410\) | 185768.i | 1.10510i | ||||||||
\(411\) | −87255.9 | −0.516549 | ||||||||
\(412\) | − | 642365.i | − | 3.78432i | ||||||
\(413\) | −218136. | + | 128299.i | −1.27887 | + | 0.752180i | ||||
\(414\) | 8253.98 | 0.0481573 | ||||||||
\(415\) | − | 113914.i | − | 0.661428i | ||||||
\(416\) | −461861. | −2.66885 | ||||||||
\(417\) | 186657. | 1.07343 | ||||||||
\(418\) | −39718.6 | −0.227322 | ||||||||
\(419\) | − | 54737.0i | − | 0.311784i | −0.987774 | − | 0.155892i | \(-0.950175\pi\) | ||
0.987774 | − | 0.155892i | \(-0.0498251\pi\) | |||||||
\(420\) | 480469. | 2.72375 | ||||||||
\(421\) | − | 135111.i | − | 0.762303i | −0.924513 | − | 0.381151i | \(-0.875528\pi\) | ||
0.924513 | − | 0.381151i | \(-0.124472\pi\) | |||||||
\(422\) | 32383.8 | 0.181846 | ||||||||
\(423\) | − | 105680.i | − | 0.590628i | ||||||
\(424\) | 846762.i | 4.71010i | ||||||||
\(425\) | 64810.6 | 0.358813 | ||||||||
\(426\) | − | 106313.i | − | 0.585823i | ||||||
\(427\) | − | 170414.i | − | 0.934653i | ||||||
\(428\) | 43892.4 | 0.239608 | ||||||||
\(429\) | 5181.81 | 0.0281557 | ||||||||
\(430\) | −498650. | −2.69686 | ||||||||
\(431\) | 332324.i | 1.78899i | 0.447081 | + | 0.894493i | \(0.352463\pi\) | ||||
−0.447081 | + | 0.894493i | \(0.647537\pi\) | |||||||
\(432\) | −141984. | −0.760805 | ||||||||
\(433\) | 245001. | 1.30675 | 0.653375 | − | 0.757035i | \(-0.273353\pi\) | ||||
0.653375 | + | 0.757035i | \(0.273353\pi\) | |||||||
\(434\) | 695907. | 3.69463 | ||||||||
\(435\) | 66011.2 | 0.348850 | ||||||||
\(436\) | − | 664519.i | − | 3.49570i | ||||||
\(437\) | 21491.5i | 0.112539i | ||||||||
\(438\) | 360677. | 1.88005 | ||||||||
\(439\) | −181499. | −0.941771 | −0.470885 | − | 0.882194i | \(-0.656066\pi\) | ||||
−0.470885 | + | 0.882194i | \(0.656066\pi\) | |||||||
\(440\) | 59166.7 | 0.305613 | ||||||||
\(441\) | 77876.4 | 0.400432 | ||||||||
\(442\) | −280328. | −1.43490 | ||||||||
\(443\) | − | 57457.9i | − | 0.292781i | −0.989227 | − | 0.146390i | \(-0.953234\pi\) | ||
0.989227 | − | 0.146390i | \(-0.0467655\pi\) | |||||||
\(444\) | 449310.i | 2.27919i | ||||||||
\(445\) | − | 72359.3i | − | 0.365405i | ||||||
\(446\) | 602247.i | 3.02765i | ||||||||
\(447\) | 134869.i | 0.674990i | ||||||||
\(448\) | −1.26852e6 | −6.32038 | ||||||||
\(449\) | 26596.2 | 0.131925 | 0.0659624 | − | 0.997822i | \(-0.478988\pi\) | ||||
0.0659624 | + | 0.997822i | \(0.478988\pi\) | |||||||
\(450\) | − | 40325.9i | − | 0.199140i | ||||||
\(451\) | 7803.31i | 0.0383642i | ||||||||
\(452\) | 885883.i | 4.33610i | ||||||||
\(453\) | − | 96466.9i | − | 0.470091i | ||||||
\(454\) | −54400.0 | −0.263929 | ||||||||
\(455\) | − | 221901.i | − | 1.07185i | ||||||
\(456\) | − | 629770.i | − | 3.02867i | ||||||
\(457\) | 300518.i | 1.43892i | 0.694532 | + | 0.719462i | \(0.255612\pi\) | ||||
−0.694532 | + | 0.719462i | \(0.744388\pi\) | |||||||
\(458\) | 400358. | 1.90861 | ||||||||
\(459\) | −47352.0 | −0.224757 | ||||||||
\(460\) | − | 49989.7i | − | 0.236246i | ||||||
\(461\) | −140059. | −0.659038 | −0.329519 | − | 0.944149i | \(-0.606887\pi\) | ||||
−0.329519 | + | 0.944149i | \(0.606887\pi\) | |||||||
\(462\) | 27439.6 | 0.128556 | ||||||||
\(463\) | − | 127338.i | − | 0.594014i | −0.954875 | − | 0.297007i | \(-0.904012\pi\) | ||
0.954875 | − | 0.297007i | \(-0.0959885\pi\) | |||||||
\(464\) | −449794. | −2.08919 | ||||||||
\(465\) | − | 182788.i | − | 0.845360i | ||||||
\(466\) | 619400. | 2.85233 | ||||||||
\(467\) | 27447.8i | 0.125856i | 0.998018 | + | 0.0629280i | \(0.0200439\pi\) | ||||
−0.998018 | + | 0.0629280i | \(0.979956\pi\) | |||||||
\(468\) | 128292.i | 0.585746i | ||||||||
\(469\) | − | 265404.i | − | 1.20660i | ||||||
\(470\) | −870192. | −3.93930 | ||||||||
\(471\) | − | 241762.i | − | 1.08980i | ||||||
\(472\) | −391159. | − | 665058.i | −1.75578 | − | 2.98522i | ||||
\(473\) | −20946.2 | −0.0936230 | ||||||||
\(474\) | 60523.7i | 0.269382i | ||||||||
\(475\) | 104999. | 0.465371 | ||||||||
\(476\) | −1.09184e6 | −4.81887 | ||||||||
\(477\) | 103147. | 0.453338 | ||||||||
\(478\) | 215002.i | 0.940995i | ||||||||
\(479\) | −403672. | −1.75937 | −0.879687 | − | 0.475554i | \(-0.842248\pi\) | ||||
−0.879687 | + | 0.475554i | \(0.842248\pi\) | |||||||
\(480\) | 642398.i | 2.78819i | ||||||||
\(481\) | 207510. | 0.896910 | ||||||||
\(482\) | − | 91526.0i | − | 0.393959i | ||||||
\(483\) | − | 14847.4i | − | 0.0636437i | ||||||
\(484\) | −647600. | −2.76450 | ||||||||
\(485\) | 263261.i | 1.11919i | ||||||||
\(486\) | 29463.0i | 0.124739i | ||||||||
\(487\) | 160164. | 0.675316 | 0.337658 | − | 0.941269i | \(-0.390365\pi\) | ||||
0.337658 | + | 0.941269i | \(0.390365\pi\) | |||||||
\(488\) | 519563. | 2.18172 | ||||||||
\(489\) | 2274.20 | 0.00951067 | ||||||||
\(490\) | − | 641248.i | − | 2.67075i | ||||||
\(491\) | −27802.8 | −0.115326 | −0.0576628 | − | 0.998336i | \(-0.518365\pi\) | ||||
−0.0576628 | + | 0.998336i | \(0.518365\pi\) | |||||||
\(492\) | −193196. | −0.798121 | ||||||||
\(493\) | −150007. | −0.617189 | ||||||||
\(494\) | −454158. | −1.86103 | ||||||||
\(495\) | − | 7207.33i | − | 0.0294147i | ||||||
\(496\) | 1.24550e6i | 5.06268i | ||||||||
\(497\) | −191237. | −0.774210 | ||||||||
\(498\) | 161068. | 0.649459 | ||||||||
\(499\) | 136913. | 0.549848 | 0.274924 | − | 0.961466i | \(-0.411347\pi\) | ||||
0.274924 | + | 0.961466i | \(0.411347\pi\) | |||||||
\(500\) | 550697. | 2.20279 | ||||||||
\(501\) | −258358. | −1.02931 | ||||||||
\(502\) | 768181.i | 3.04829i | ||||||||
\(503\) | − | 45212.1i | − | 0.178698i | −0.996000 | − | 0.0893489i | \(-0.971521\pi\) | ||
0.996000 | − | 0.0893489i | \(-0.0284786\pi\) | |||||||
\(504\) | 435077.i | 1.71279i | ||||||||
\(505\) | 379884.i | 1.48960i | ||||||||
\(506\) | − | 2854.91i | − | 0.0111504i | ||||||
\(507\) | −89156.5 | −0.346846 | ||||||||
\(508\) | 691082. | 2.67795 | ||||||||
\(509\) | − | 420229.i | − | 1.62200i | −0.585048 | − | 0.810999i | \(-0.698924\pi\) | ||
0.585048 | − | 0.810999i | \(-0.301076\pi\) | |||||||
\(510\) | 389905.i | 1.49906i | ||||||||
\(511\) | − | 648791.i | − | 2.48464i | ||||||
\(512\) | − | 788170.i | − | 3.00663i | ||||||
\(513\) | −76714.8 | −0.291504 | ||||||||
\(514\) | − | 280686.i | − | 1.06241i | ||||||
\(515\) | 412637.i | 1.55580i | ||||||||
\(516\) | − | 518590.i | − | 1.94771i | ||||||
\(517\) | −36553.1 | −0.136755 | ||||||||
\(518\) | 1.09884e6 | 4.09520 | ||||||||
\(519\) | 159869.i | 0.593510i | ||||||||
\(520\) | 676535. | 2.50198 | ||||||||
\(521\) | 176873. | 0.651608 | 0.325804 | − | 0.945437i | \(-0.394365\pi\) | ||||
0.325804 | + | 0.945437i | \(0.394365\pi\) | |||||||
\(522\) | 93336.1i | 0.342538i | ||||||||
\(523\) | −361972. | −1.32334 | −0.661670 | − | 0.749795i | \(-0.730152\pi\) | ||||
−0.661670 | + | 0.749795i | \(0.730152\pi\) | |||||||
\(524\) | 55452.7i | 0.201958i | ||||||||
\(525\) | −72538.8 | −0.263179 | ||||||||
\(526\) | 129015.i | 0.466305i | ||||||||
\(527\) | 415376.i | 1.49562i | ||||||||
\(528\) | 49110.0i | 0.176158i | ||||||||
\(529\) | 278296. | 0.994480 | ||||||||
\(530\) | − | 849335.i | − | 3.02362i | ||||||
\(531\) | −81013.4 | + | 47648.6i | −0.287321 | + | 0.168990i | ||||
\(532\) | −1.76889e6 | −6.24995 | ||||||||
\(533\) | 89226.1i | 0.314078i | ||||||||
\(534\) | 102312. | 0.358793 | ||||||||
\(535\) | −28195.2 | −0.0985071 | ||||||||
\(536\) | 809170. | 2.81650 | ||||||||
\(537\) | 107912.i | 0.374213i | ||||||||
\(538\) | 366928. | 1.26770 | ||||||||
\(539\) | − | 26936.1i | − | 0.0927166i | ||||||
\(540\) | 178441. | 0.611937 | ||||||||
\(541\) | 276519.i | 0.944779i | 0.881390 | + | 0.472390i | \(0.156608\pi\) | ||||
−0.881390 | + | 0.472390i | \(0.843392\pi\) | |||||||
\(542\) | − | 287835.i | − | 0.979818i | ||||||
\(543\) | −144399. | −0.489738 | ||||||||
\(544\) | − | 1.45982e6i | − | 4.93288i | ||||||
\(545\) | 426868.i | 1.43714i | ||||||||
\(546\) | 313755. | 1.05246 | ||||||||
\(547\) | −424332. | −1.41818 | −0.709090 | − | 0.705118i | \(-0.750894\pi\) | ||||
−0.709090 | + | 0.705118i | \(0.750894\pi\) | |||||||
\(548\) | −747213. | −2.48819 | ||||||||
\(549\) | − | 63290.0i | − | 0.209986i | ||||||
\(550\) | −13948.1 | −0.0461093 | ||||||||
\(551\) | −243026. | −0.800477 | ||||||||
\(552\) | 45266.9 | 0.148560 | ||||||||
\(553\) | 108871. | 0.356010 | ||||||||
\(554\) | 291668.i | 0.950318i | ||||||||
\(555\) | − | 288624.i | − | 0.937013i | ||||||
\(556\) | 1.59843e6 | 5.17064 | ||||||||
\(557\) | −408914. | −1.31802 | −0.659010 | − | 0.752134i | \(-0.729024\pi\) | ||||
−0.659010 | + | 0.752134i | \(0.729024\pi\) | |||||||
\(558\) | 258452. | 0.830063 | ||||||||
\(559\) | −239507. | −0.766468 | ||||||||
\(560\) | 2.10304e6 | 6.70612 | ||||||||
\(561\) | 16378.3i | 0.0520406i | ||||||||
\(562\) | 64137.5i | 0.203067i | ||||||||
\(563\) | 165648.i | 0.522600i | 0.965258 | + | 0.261300i | \(0.0841512\pi\) | ||||
−0.965258 | + | 0.261300i | \(0.915849\pi\) | |||||||
\(564\) | − | 904990.i | − | 2.84502i | ||||||
\(565\) | − | 569065.i | − | 1.78265i | ||||||
\(566\) | −26296.2 | −0.0820844 | ||||||||
\(567\) | 52998.4 | 0.164853 | ||||||||
\(568\) | − | 583047.i | − | 1.80720i | ||||||
\(569\) | 413247.i | 1.27639i | 0.769873 | + | 0.638197i | \(0.220320\pi\) | ||||
−0.769873 | + | 0.638197i | \(0.779680\pi\) | |||||||
\(570\) | 631683.i | 1.94424i | ||||||||
\(571\) | 531700.i | 1.63078i | 0.578914 | + | 0.815388i | \(0.303477\pi\) | ||||
−0.578914 | + | 0.815388i | \(0.696523\pi\) | |||||||
\(572\) | 44374.2 | 0.135625 | ||||||||
\(573\) | 115472.i | 0.351695i | ||||||||
\(574\) | 472485.i | 1.43405i | ||||||||
\(575\) | 7547.20i | 0.0228271i | ||||||||
\(576\) | −471116. | −1.41998 | ||||||||
\(577\) | −94373.0 | −0.283463 | −0.141731 | − | 0.989905i | \(-0.545267\pi\) | ||||
−0.141731 | + | 0.989905i | \(0.545267\pi\) | |||||||
\(578\) | − | 236415.i | − | 0.707651i | ||||||
\(579\) | −117087. | −0.349263 | ||||||||
\(580\) | 565284. | 1.68039 | ||||||||
\(581\) | − | 289732.i | − | 0.858310i | ||||||
\(582\) | −372237. | −1.09894 | ||||||||
\(583\) | − | 35677.0i | − | 0.104967i | ||||||
\(584\) | 1.97805e6 | 5.79977 | ||||||||
\(585\) | − | 82411.4i | − | 0.240811i | ||||||
\(586\) | 1.14239e6i | 3.32675i | ||||||||
\(587\) | 16716.5i | 0.0485142i | 0.999706 | + | 0.0242571i | \(0.00772203\pi\) | ||||
−0.999706 | + | 0.0242571i | \(0.992278\pi\) | |||||||
\(588\) | 666891. | 1.92886 | ||||||||
\(589\) | 672949.i | 1.93978i | ||||||||
\(590\) | 392347. | + | 667079.i | 1.12711 | + | 1.91634i | ||||
\(591\) | −57879.3 | −0.165710 | ||||||||
\(592\) | 1.96665e6i | 5.61157i | ||||||||
\(593\) | −406858. | −1.15700 | −0.578500 | − | 0.815683i | \(-0.696362\pi\) | ||||
−0.578500 | + | 0.815683i | \(0.696362\pi\) | |||||||
\(594\) | 10190.7 | 0.0288824 | ||||||||
\(595\) | 701367. | 1.98112 | ||||||||
\(596\) | 1.15495e6i | 3.25139i | ||||||||
\(597\) | 145096. | 0.407105 | ||||||||
\(598\) | − | 32644.2i | − | 0.0912858i | ||||||
\(599\) | −216469. | −0.603313 | −0.301656 | − | 0.953417i | \(-0.597540\pi\) | ||||
−0.301656 | + | 0.953417i | \(0.597540\pi\) | |||||||
\(600\) | − | 221158.i | − | 0.614327i | ||||||
\(601\) | − | 114850.i | − | 0.317966i | −0.987281 | − | 0.158983i | \(-0.949179\pi\) | ||
0.987281 | − | 0.158983i | \(-0.0508214\pi\) | |||||||
\(602\) | −1.26828e6 | −3.49962 | ||||||||
\(603\) | − | 98568.2i | − | 0.271083i | ||||||
\(604\) | − | 826091.i | − | 2.26440i | ||||||
\(605\) | 416000. | 1.13653 | ||||||||
\(606\) | −537134. | −1.46264 | ||||||||
\(607\) | 460090. | 1.24872 | 0.624360 | − | 0.781136i | \(-0.285360\pi\) | ||||
0.624360 | + | 0.781136i | \(0.285360\pi\) | |||||||
\(608\) | − | 2.36504e6i | − | 6.39781i | ||||||
\(609\) | 167894. | 0.452690 | ||||||||
\(610\) | −521141. | −1.40054 | ||||||||
\(611\) | −417962. | −1.11958 | ||||||||
\(612\) | −405497. | −1.08264 | ||||||||
\(613\) | − | 54204.8i | − | 0.144250i | −0.997396 | − | 0.0721252i | \(-0.977022\pi\) | ||
0.997396 | − | 0.0721252i | \(-0.0229781\pi\) | |||||||
\(614\) | − | 716363.i | − | 1.90019i | ||||||
\(615\) | 124104. | 0.328121 | ||||||||
\(616\) | 150486. | 0.396583 | ||||||||
\(617\) | −446671. | −1.17332 | −0.586662 | − | 0.809832i | \(-0.699558\pi\) | ||||
−0.586662 | + | 0.809832i | \(0.699558\pi\) | |||||||
\(618\) | −583445. | −1.52765 | ||||||||
\(619\) | 608019. | 1.58685 | 0.793425 | − | 0.608668i | \(-0.208296\pi\) | ||||
0.793425 | + | 0.608668i | \(0.208296\pi\) | |||||||
\(620\) | − | 1.56530e6i | − | 4.07205i | ||||||
\(621\) | − | 5514.14i | − | 0.0142986i | ||||||
\(622\) | 256503.i | 0.662996i | ||||||||
\(623\) | − | 184040.i | − | 0.474172i | ||||||
\(624\) | 561543.i | 1.44216i | ||||||||
\(625\) | −473767. | −1.21284 | ||||||||
\(626\) | 316673. | 0.808095 | ||||||||
\(627\) | 26534.4i | 0.0674953i | ||||||||
\(628\) | − | 2.07032e6i | − | 5.24950i | ||||||
\(629\) | 655882.i | 1.65777i | ||||||||
\(630\) | − | 436398.i | − | 1.09952i | ||||||
\(631\) | −89180.6 | −0.223981 | −0.111991 | − | 0.993709i | \(-0.535723\pi\) | ||||
−0.111991 | + | 0.993709i | \(0.535723\pi\) | |||||||
\(632\) | 331928.i | 0.831016i | ||||||||
\(633\) | − | 21634.3i | − | 0.0539928i | ||||||
\(634\) | − | 39648.0i | − | 0.0986377i | ||||||
\(635\) | −443931. | −1.10095 | ||||||||
\(636\) | 883299. | 2.18370 | ||||||||
\(637\) | − | 307998.i | − | 0.759048i | ||||||
\(638\) | 32283.4 | 0.0793118 | ||||||||
\(639\) | −71023.2 | −0.173940 | ||||||||
\(640\) | 1.90118e6i | 4.64155i | ||||||||
\(641\) | 496660. | 1.20877 | 0.604384 | − | 0.796693i | \(-0.293419\pi\) | ||||
0.604384 | + | 0.796693i | \(0.293419\pi\) | |||||||
\(642\) | − | 39866.4i | − | 0.0967246i | ||||||
\(643\) | −477619. | −1.15521 | −0.577603 | − | 0.816318i | \(-0.696012\pi\) | ||||
−0.577603 | + | 0.816318i | \(0.696012\pi\) | |||||||
\(644\) | − | 127145.i | − | 0.306568i | ||||||
\(645\) | 333128.i | 0.800739i | ||||||||
\(646\) | − | 1.43547e6i | − | 3.43976i | ||||||
\(647\) | 255266. | 0.609796 | 0.304898 | − | 0.952385i | \(-0.401378\pi\) | ||||
0.304898 | + | 0.952385i | \(0.401378\pi\) | |||||||
\(648\) | 161582.i | 0.384808i | ||||||||
\(649\) | 16480.9 | + | 28021.2i | 0.0391282 | + | 0.0665268i | ||||
\(650\) | −159487. | −0.377485 | ||||||||
\(651\) | − | 464907.i | − | 1.09699i | ||||||
\(652\) | 19475.0 | 0.0458124 | ||||||||
\(653\) | 12720.0 | 0.0298305 | 0.0149152 | − | 0.999889i | \(-0.495252\pi\) | ||||
0.0149152 | + | 0.999889i | \(0.495252\pi\) | |||||||
\(654\) | −603567. | −1.41114 | ||||||||
\(655\) | − | 35621.2i | − | 0.0830283i | ||||||
\(656\) | −845631. | −1.96505 | ||||||||
\(657\) | − | 240954.i | − | 0.558217i | ||||||
\(658\) | −2.21326e6 | −5.11189 | ||||||||
\(659\) | − | 732103.i | − | 1.68578i | −0.538084 | − | 0.842891i | \(-0.680852\pi\) | ||
0.538084 | − | 0.842891i | \(-0.319148\pi\) | |||||||
\(660\) | − | 61719.6i | − | 0.141689i | ||||||
\(661\) | 601813. | 1.37740 | 0.688698 | − | 0.725049i | \(-0.258183\pi\) | ||||
0.688698 | + | 0.725049i | \(0.258183\pi\) | |||||||
\(662\) | 144073.i | 0.328750i | ||||||||
\(663\) | 187276.i | 0.426044i | ||||||||
\(664\) | 883341. | 2.00351 | ||||||||
\(665\) | 1.13628e6 | 2.56946 | ||||||||
\(666\) | 408097. | 0.920058 | ||||||||
\(667\) | − | 17468.3i | − | 0.0392644i | ||||||
\(668\) | −2.21244e6 | −4.95813 | ||||||||
\(669\) | 402337. | 0.898954 | ||||||||
\(670\) | −811628. | −1.80804 | ||||||||
\(671\) | −21890.9 | −0.0486205 | ||||||||
\(672\) | 1.63389e6i | 3.61813i | ||||||||
\(673\) | 177803.i | 0.392563i | 0.980548 | + | 0.196282i | \(0.0628867\pi\) | ||||
−0.980548 | + | 0.196282i | \(0.937113\pi\) | |||||||
\(674\) | 1.06655e6 | 2.34780 | ||||||||
\(675\) | −26940.1 | −0.0591277 | ||||||||
\(676\) | −763488. | −1.67074 | ||||||||
\(677\) | 238228. | 0.519774 | 0.259887 | − | 0.965639i | \(-0.416315\pi\) | ||||
0.259887 | + | 0.965639i | \(0.416315\pi\) | |||||||
\(678\) | 804626. | 1.75039 | ||||||||
\(679\) | 669585.i | 1.45233i | ||||||||
\(680\) | 2.13834e6i | 4.62444i | ||||||||
\(681\) | 36342.4i | 0.0783645i | ||||||||
\(682\) | − | 89394.1i | − | 0.192194i | ||||||
\(683\) | − | 660787.i | − | 1.41651i | −0.705956 | − | 0.708256i | \(-0.749482\pi\) | ||
0.705956 | − | 0.708256i | \(-0.250518\pi\) | |||||||
\(684\) | −656944. | −1.40416 | ||||||||
\(685\) | 479988. | 1.02294 | ||||||||
\(686\) | − | 273293.i | − | 0.580737i | ||||||
\(687\) | − | 267463.i | − | 0.566696i | ||||||
\(688\) | − | 2.26990e6i | − | 4.79545i | ||||||
\(689\) | − | 407945.i | − | 0.859335i | ||||||
\(690\) | −45404.5 | −0.0953675 | ||||||||
\(691\) | − | 252072.i | − | 0.527919i | −0.964534 | − | 0.263960i | \(-0.914971\pi\) | ||
0.964534 | − | 0.263960i | \(-0.0850286\pi\) | |||||||
\(692\) | 1.36903e6i | 2.85891i | ||||||||
\(693\) | − | 18331.3i | − | 0.0381703i | ||||||
\(694\) | −718594. | −1.49199 | ||||||||
\(695\) | −1.02679e6 | −2.12574 | ||||||||
\(696\) | 511879.i | 1.05669i | ||||||||
\(697\) | −282019. | −0.580515 | ||||||||
\(698\) | 1.49477e6 | 3.06805 | ||||||||
\(699\) | − | 413796.i | − | 0.846900i | ||||||
\(700\) | −621183. | −1.26772 | ||||||||
\(701\) | 601181.i | 1.22340i | 0.791089 | + | 0.611701i | \(0.209514\pi\) | ||||
−0.791089 | + | 0.611701i | \(0.790486\pi\) | |||||||
\(702\) | 116525. | 0.236453 | ||||||||
\(703\) | 1.06259e6i | 2.15008i | ||||||||
\(704\) | 162951.i | 0.328785i | ||||||||
\(705\) | 581340.i | 1.16964i | ||||||||
\(706\) | −1.04024e6 | −2.08701 | ||||||||
\(707\) | 966205.i | 1.93299i | ||||||||
\(708\) | −693755. | + | 408037.i | −1.38401 | + | 0.814016i | ||||
\(709\) | 769466. | 1.53072 | 0.765362 | − | 0.643600i | \(-0.222560\pi\) | ||||
0.765362 | + | 0.643600i | \(0.222560\pi\) | |||||||
\(710\) | 584818.i | 1.16012i | ||||||||
\(711\) | 40433.4 | 0.0799837 | ||||||||
\(712\) | 561105. | 1.10684 | ||||||||
\(713\) | −48370.6 | −0.0951485 | ||||||||
\(714\) | 991693.i | 1.94527i | ||||||||
\(715\) | −28504.7 | −0.0557577 | ||||||||
\(716\) | 924096.i | 1.80256i | ||||||||
\(717\) | 143634. | 0.279396 | ||||||||
\(718\) | 493444.i | 0.957171i | ||||||||
\(719\) | − | 412760.i | − | 0.798435i | −0.916856 | − | 0.399218i | \(-0.869282\pi\) | ||
0.916856 | − | 0.399218i | \(-0.130718\pi\) | |||||||
\(720\) | 781045. | 1.50664 | ||||||||
\(721\) | 1.04951e6i | 2.01890i | ||||||||
\(722\) | − | 1.31196e6i | − | 2.51678i | ||||||
\(723\) | −61144.8 | −0.116972 | ||||||||
\(724\) | −1.23655e6 | −2.35904 | ||||||||
\(725\) | −85343.8 | −0.162366 | ||||||||
\(726\) | 588200.i | 1.11597i | ||||||||
\(727\) | −352870. | −0.667645 | −0.333822 | − | 0.942636i | \(-0.608339\pi\) | ||||
−0.333822 | + | 0.942636i | \(0.608339\pi\) | |||||||
\(728\) | 1.72071e6 | 3.24673 | ||||||||
\(729\) | 19683.0 | 0.0370370 | ||||||||
\(730\) | −1.98406e6 | −3.72313 | ||||||||
\(731\) | − | 757015.i | − | 1.41667i | ||||||
\(732\) | − | 541981.i | − | 1.01149i | ||||||
\(733\) | 566886. | 1.05509 | 0.527543 | − | 0.849528i | \(-0.323113\pi\) | ||||
0.527543 | + | 0.849528i | \(0.323113\pi\) | |||||||
\(734\) | 488129. | 0.906029 | ||||||||
\(735\) | −428392. | −0.792987 | ||||||||
\(736\) | 169996. | 0.313821 | ||||||||
\(737\) | −34093.1 | −0.0627670 | ||||||||
\(738\) | 175476.i | 0.322184i | ||||||||
\(739\) | 110960.i | 0.203179i | 0.994826 | + | 0.101589i | \(0.0323928\pi\) | ||||
−0.994826 | + | 0.101589i | \(0.967607\pi\) | |||||||
\(740\) | − | 2.47162e6i | − | 4.51354i | ||||||
\(741\) | 303404.i | 0.552567i | ||||||||
\(742\) | − | 2.16022e6i | − | 3.92364i | ||||||
\(743\) | −565178. | −1.02378 | −0.511891 | − | 0.859050i | \(-0.671055\pi\) | ||||
−0.511891 | + | 0.859050i | \(0.671055\pi\) | |||||||
\(744\) | 1.41742e6 | 2.56066 | ||||||||
\(745\) | − | 741904.i | − | 1.33670i | ||||||
\(746\) | 796617.i | 1.43144i | ||||||||
\(747\) | − | 107603.i | − | 0.192834i | ||||||
\(748\) | 140255.i | 0.250677i | ||||||||
\(749\) | −71712.3 | −0.127829 | ||||||||
\(750\) | − | 500185.i | − | 0.889218i | ||||||
\(751\) | 217676.i | 0.385950i | 0.981204 | + | 0.192975i | \(0.0618136\pi\) | ||||
−0.981204 | + | 0.192975i | \(0.938186\pi\) | |||||||
\(752\) | − | 3.96119e6i | − | 7.00471i | ||||||
\(753\) | 513190. | 0.905083 | ||||||||
\(754\) | 369141. | 0.649306 | ||||||||
\(755\) | 530657.i | 0.930936i | ||||||||
\(756\) | 453850. | 0.794088 | ||||||||
\(757\) | 169980. | 0.296623 | 0.148312 | − | 0.988941i | \(-0.452616\pi\) | ||||
0.148312 | + | 0.988941i | \(0.452616\pi\) | |||||||
\(758\) | 896194.i | 1.55978i | ||||||||
\(759\) | −1907.25 | −0.00331073 | ||||||||
\(760\) | 3.46431e6i | 5.99777i | ||||||||
\(761\) | 880285. | 1.52004 | 0.760019 | − | 0.649901i | \(-0.225190\pi\) | ||||
0.760019 | + | 0.649901i | \(0.225190\pi\) | |||||||
\(762\) | − | 627693.i | − | 1.08103i | ||||||
\(763\) | 1.08570e6i | 1.86493i | ||||||||
\(764\) | 988836.i | 1.69409i | ||||||||
\(765\) | 260480. | 0.445093 | ||||||||
\(766\) | − | 534349.i | − | 0.910684i | ||||||
\(767\) | 188449. | + | 320405.i | 0.320333 | + | 0.544639i | ||||
\(768\) | −1.23750e6 | −2.09808 | ||||||||
\(769\) | − | 619749.i | − | 1.04801i | −0.851717 | − | 0.524003i | \(-0.824438\pi\) | ||
0.851717 | − | 0.524003i | \(-0.175562\pi\) | |||||||
\(770\) | −150943. | −0.254584 | ||||||||
\(771\) | −187515. | −0.315447 | ||||||||
\(772\) | −1.00267e6 | −1.68238 | ||||||||
\(773\) | 1.11076e6i | 1.85892i | 0.368917 | + | 0.929462i | \(0.379729\pi\) | ||||
−0.368917 | + | 0.929462i | \(0.620271\pi\) | |||||||
\(774\) | −471023. | −0.786250 | ||||||||
\(775\) | 236321.i | 0.393458i | ||||||||
\(776\) | −2.04144e6 | −3.39011 | ||||||||
\(777\) | − | 734091.i | − | 1.21593i | ||||||
\(778\) | − | 15332.7i | − | 0.0253313i | ||||||
\(779\) | −456898. | −0.752912 | ||||||||
\(780\) | − | 705727.i | − | 1.15997i | ||||||
\(781\) | 24565.7i | 0.0402743i | ||||||||
\(782\) | 103179. | 0.168725 | ||||||||
\(783\) | 62354.0 | 0.101705 | ||||||||
\(784\) | 2.91902e6 | 4.74903 | ||||||||
\(785\) | 1.32991e6i | 2.15816i | ||||||||
\(786\) | 50366.4 | 0.0815259 | ||||||||
\(787\) | 243033. | 0.392389 | 0.196194 | − | 0.980565i | \(-0.437142\pi\) | ||||
0.196194 | + | 0.980565i | \(0.437142\pi\) | |||||||
\(788\) | −495647. | −0.798216 | ||||||||
\(789\) | 86190.0 | 0.138453 | ||||||||
\(790\) | − | 332936.i | − | 0.533466i | ||||||
\(791\) | − | 1.44737e6i | − | 2.31328i | ||||||
\(792\) | 55888.7 | 0.0890991 | ||||||||
\(793\) | −250310. | −0.398044 | ||||||||
\(794\) | −330105. | −0.523613 | ||||||||
\(795\) | −567406. | −0.897758 | ||||||||
\(796\) | 1.24252e6 | 1.96100 | ||||||||
\(797\) | 419997.i | 0.661195i | 0.943772 | + | 0.330597i | \(0.107250\pi\) | ||||
−0.943772 | + | 0.330597i | \(0.892750\pi\) | |||||||
\(798\) | 1.60664e6i | 2.52297i | ||||||||
\(799\) | − | 1.32106e6i | − | 2.06933i | ||||||
\(800\) | − | 830536.i | − | 1.29771i | ||||||
\(801\) | − | 68350.4i | − | 0.106531i | ||||||
\(802\) | 806655. | 1.25412 | ||||||||
\(803\) | −83341.8 | −0.129250 | ||||||||
\(804\) | − | 844085.i | − | 1.30579i | ||||||
\(805\) | 81674.2i | 0.126036i | ||||||||
\(806\) | − | 1.02217e6i | − | 1.57345i | ||||||
\(807\) | − | 245130.i | − | 0.376399i | ||||||
\(808\) | −2.94578e6 | −4.51209 | ||||||||
\(809\) | − | 573138.i | − | 0.875713i | −0.899045 | − | 0.437857i | \(-0.855738\pi\) | ||
0.899045 | − | 0.437857i | \(-0.144262\pi\) | |||||||
\(810\) | − | 162073.i | − | 0.247025i | ||||||
\(811\) | − | 133816.i | − | 0.203454i | −0.994812 | − | 0.101727i | \(-0.967563\pi\) | ||
0.994812 | − | 0.101727i | \(-0.0324368\pi\) | |||||||
\(812\) | 1.43776e6 | 2.18058 | ||||||||
\(813\) | −192291. | −0.290923 | ||||||||
\(814\) | − | 141154.i | − | 0.213032i | ||||||
\(815\) | −12510.2 | −0.0188343 | ||||||||
\(816\) | −1.77488e6 | −2.66557 | ||||||||
\(817\) | − | 1.22644e6i | − | 1.83739i | ||||||
\(818\) | −227509. | −0.340010 | ||||||||
\(819\) | − | 209607.i | − | 0.312491i | ||||||
\(820\) | 1.06276e6 | 1.58054 | ||||||||
\(821\) | 197462.i | 0.292952i | 0.989214 | + | 0.146476i | \(0.0467931\pi\) | ||||
−0.989214 | + | 0.146476i | \(0.953207\pi\) | |||||||
\(822\) | 678675.i | 1.00443i | ||||||||
\(823\) | − | 562096.i | − | 0.829871i | −0.909851 | − | 0.414936i | \(-0.863804\pi\) | ||
0.909851 | − | 0.414936i | \(-0.136196\pi\) | |||||||
\(824\) | −3.19976e6 | −4.71263 | ||||||||
\(825\) | 9318.12i | 0.0136905i | ||||||||
\(826\) | 997904. | + | 1.69666e6i | 1.46261 | + | 2.48677i | ||||
\(827\) | −567007. | −0.829043 | −0.414522 | − | 0.910039i | \(-0.636051\pi\) | ||||
−0.414522 | + | 0.910039i | \(0.636051\pi\) | |||||||
\(828\) | − | 47220.1i | − | 0.0688758i | ||||||
\(829\) | −430710. | −0.626723 | −0.313362 | − | 0.949634i | \(-0.601455\pi\) | ||||
−0.313362 | + | 0.949634i | \(0.601455\pi\) | |||||||
\(830\) | −886024. | −1.28614 | ||||||||
\(831\) | 194851. | 0.282164 | ||||||||
\(832\) | 1.86325e6i | 2.69168i | ||||||||
\(833\) | 973498. | 1.40296 | ||||||||
\(834\) | − | 1.45182e6i | − | 2.08728i | ||||||
\(835\) | 1.42120e6 | 2.03837 | ||||||||
\(836\) | 227226.i | 0.325121i | ||||||||
\(837\) | − | 172661.i | − | 0.246458i | ||||||
\(838\) | −425744. | −0.606262 | ||||||||
\(839\) | 53824.6i | 0.0764640i | 0.999269 | + | 0.0382320i | \(0.0121726\pi\) | ||||
−0.999269 | + | 0.0382320i | \(0.987827\pi\) | |||||||
\(840\) | − | 2.39332e6i | − | 3.39190i | ||||||
\(841\) | −509749. | −0.720716 | ||||||||
\(842\) | −1.05089e6 | −1.48229 | ||||||||
\(843\) | 42847.6 | 0.0602936 | ||||||||
\(844\) | − | 185265.i | − | 0.260080i | ||||||
\(845\) | 490442. | 0.686870 | ||||||||
\(846\) | −821981. | −1.14847 | ||||||||
\(847\) | 1.05806e6 | 1.47484 | ||||||||
\(848\) | 3.86625e6 | 5.37648 | ||||||||
\(849\) | 17567.4i | 0.0243721i | ||||||||
\(850\) | − | 504096.i | − | 0.697711i | ||||||
\(851\) | −76377.4 | −0.105464 | ||||||||
\(852\) | −608204. | −0.837858 | ||||||||
\(853\) | −418548. | −0.575237 | −0.287619 | − | 0.957745i | \(-0.592864\pi\) | ||||
−0.287619 | + | 0.957745i | \(0.592864\pi\) | |||||||
\(854\) | −1.32548e6 | −1.81743 | ||||||||
\(855\) | 422002. | 0.577274 | ||||||||
\(856\) | − | 218638.i | − | 0.298385i | ||||||
\(857\) | 1.10791e6i | 1.50849i | 0.656596 | + | 0.754243i | \(0.271996\pi\) | ||||
−0.656596 | + | 0.754243i | \(0.728004\pi\) | |||||||
\(858\) | − | 40304.0i | − | 0.0547487i | ||||||
\(859\) | − | 226154.i | − | 0.306491i | −0.988188 | − | 0.153245i | \(-0.951028\pi\) | ||
0.988188 | − | 0.153245i | \(-0.0489725\pi\) | |||||||
\(860\) | 2.85272e6i | 3.85712i | ||||||||
\(861\) | 315648. | 0.425791 | ||||||||
\(862\) | 2.58481e6 | 3.47868 | ||||||||
\(863\) | 539905.i | 0.724929i | 0.931998 | + | 0.362464i | \(0.118065\pi\) | ||||
−0.931998 | + | 0.362464i | \(0.881935\pi\) | |||||||
\(864\) | 606807.i | 0.812874i | ||||||||
\(865\) | − | 879424.i | − | 1.17535i | ||||||
\(866\) | − | 1.90561e6i | − | 2.54097i | ||||||
\(867\) | −157939. | −0.210112 | ||||||||
\(868\) | − | 3.98121e6i | − | 5.28416i | ||||||
\(869\) | − | 13985.2i | − | 0.0185196i | ||||||
\(870\) | − | 513434.i | − | 0.678338i | ||||||
\(871\) | −389834. | −0.513858 | ||||||||
\(872\) | −3.31011e6 | −4.35321 | ||||||||
\(873\) | 248676.i | 0.326291i | ||||||||
\(874\) | 167160. | 0.218832 | ||||||||
\(875\) | −899740. | −1.17517 | ||||||||
\(876\) | − | 2.06340e6i | − | 2.68890i | ||||||
\(877\) | −288067. | −0.374537 | −0.187269 | − | 0.982309i | \(-0.559963\pi\) | ||||
−0.187269 | + | 0.982309i | \(0.559963\pi\) | |||||||
\(878\) | 1.41170e6i | 1.83127i | ||||||||
\(879\) | 763186. | 0.987762 | ||||||||
\(880\) | − | 270150.i | − | 0.348851i | ||||||
\(881\) | 80450.5i | 0.103652i | 0.998656 | + | 0.0518259i | \(0.0165041\pi\) | ||||
−0.998656 | + | 0.0518259i | \(0.983496\pi\) | |||||||
\(882\) | − | 605721.i | − | 0.778638i | ||||||
\(883\) | 210993. | 0.270611 | 0.135306 | − | 0.990804i | \(-0.456798\pi\) | ||||
0.135306 | + | 0.990804i | \(0.456798\pi\) | |||||||
\(884\) | 1.60373e6i | 2.05223i | ||||||||
\(885\) | 445648. | − | 262111.i | 0.568991 | − | 0.334656i | ||||
\(886\) | −446907. | −0.569311 | ||||||||
\(887\) | − | 428946.i | − | 0.545199i | −0.962128 | − | 0.272600i | \(-0.912117\pi\) | ||
0.962128 | − | 0.272600i | \(-0.0878834\pi\) | |||||||
\(888\) | 2.23811e6 | 2.83828 | ||||||||
\(889\) | −1.12910e6 | −1.42866 | ||||||||
\(890\) | −562809. | −0.710528 | ||||||||
\(891\) | − | 6808.02i | − | 0.00857562i | ||||||
\(892\) | 3.44539e6 | 4.33021 | ||||||||
\(893\) | − | 2.14025e6i | − | 2.68387i | ||||||
\(894\) | 1.04901e6 | 1.31252 | ||||||||
\(895\) | − | 593612.i | − | 0.741066i | ||||||
\(896\) | 4.83549e6i | 6.02316i | ||||||||
\(897\) | −21808.2 | −0.0271041 | ||||||||
\(898\) | − | 206865.i | − | 0.256527i | ||||||
\(899\) | − | 546975.i | − | 0.676781i | ||||||
\(900\) | −230700. | −0.284815 | ||||||||
\(901\) | 1.28940e6 | 1.58832 | ||||||||
\(902\) | 60694.0 | 0.0745990 | ||||||||
\(903\) | 847283.i | 1.03909i | ||||||||
\(904\) | 4.41278e6 | 5.39977 | ||||||||
\(905\) | 794327. | 0.969844 | ||||||||
\(906\) | −750318. | −0.914090 | ||||||||
\(907\) | 1.21610e6 | 1.47827 | 0.739134 | − | 0.673558i | \(-0.235235\pi\) | ||||
0.739134 | + | 0.673558i | \(0.235235\pi\) | |||||||
\(908\) | 311217.i | 0.377477i | ||||||||
\(909\) | 358837.i | 0.434280i | ||||||||
\(910\) | −1.72594e6 | −2.08422 | ||||||||
\(911\) | 789820. | 0.951681 | 0.475841 | − | 0.879532i | \(-0.342144\pi\) | ||||
0.475841 | + | 0.879532i | \(0.342144\pi\) | |||||||
\(912\) | −2.87548e6 | −3.45717 | ||||||||
\(913\) | −37218.1 | −0.0446491 | ||||||||
\(914\) | 2.33742e6 | 2.79798 | ||||||||
\(915\) | 348153.i | 0.415842i | ||||||||
\(916\) | − | 2.29041e6i | − | 2.72975i | ||||||
\(917\) | − | 90599.7i | − | 0.107743i | ||||||
\(918\) | 368303.i | 0.437039i | ||||||||
\(919\) | − | 1.09607e6i | − | 1.29780i | −0.760872 | − | 0.648902i | \(-0.775228\pi\) | ||
0.760872 | − | 0.648902i | \(-0.224772\pi\) | |||||||
\(920\) | −249010. | −0.294199 | ||||||||
\(921\) | −478573. | −0.564194 | ||||||||
\(922\) | 1.08938e6i | 1.28150i | ||||||||
\(923\) | 280894.i | 0.329716i | ||||||||
\(924\) | − | 156979.i | − | 0.183864i | ||||||
\(925\) | 373152.i | 0.436116i | ||||||||
\(926\) | −990435. | −1.15506 | ||||||||
\(927\) | 389776.i | 0.453581i | ||||||||
\(928\) | 1.92231e6i | 2.23217i | ||||||||
\(929\) | 346274.i | 0.401225i | 0.979671 | + | 0.200612i | \(0.0642932\pi\) | ||||
−0.979671 | + | 0.200612i | \(0.935707\pi\) | |||||||
\(930\) | −1.42172e6 | −1.64380 | ||||||||
\(931\) | 1.57716e6 | 1.81960 | ||||||||
\(932\) | − | 3.54353e6i | − | 4.07947i | ||||||
\(933\) | 171359. | 0.196854 | ||||||||
\(934\) | 213489. | 0.244727 | ||||||||
\(935\) | − | 90095.6i | − | 0.103058i | ||||||
\(936\) | 639053. | 0.729433 | ||||||||
\(937\) | 1.06972e6i | 1.21840i | 0.793017 | + | 0.609200i | \(0.208509\pi\) | ||||
−0.793017 | + | 0.609200i | \(0.791491\pi\) | |||||||
\(938\) | −2.06431e6 | −2.34622 | ||||||||
\(939\) | − | 211556.i | − | 0.239936i | ||||||
\(940\) | 4.97828e6i | 5.63408i | ||||||||
\(941\) | − | 1.10921e6i | − | 1.25267i | −0.779555 | − | 0.626333i | \(-0.784555\pi\) | ||
0.779555 | − | 0.626333i | \(-0.215445\pi\) | |||||||
\(942\) | −1.88042e6 | −2.11911 | ||||||||
\(943\) | − | 32841.1i | − | 0.0369313i | ||||||
\(944\) | −3.03660e6 | + | 1.78600e6i | −3.40756 | + | 2.00418i | ||||
\(945\) | −291540. | −0.326463 | ||||||||
\(946\) | 162919.i | 0.182050i | ||||||||
\(947\) | −502348. | −0.560151 | −0.280075 | − | 0.959978i | \(-0.590359\pi\) | ||||
−0.280075 | + | 0.959978i | \(0.590359\pi\) | |||||||
\(948\) | 346250. | 0.385277 | ||||||||
\(949\) | −952963. | −1.05814 | ||||||||
\(950\) | − | 816683.i | − | 0.904912i | ||||||
\(951\) | −26487.2 | −0.0292870 | ||||||||
\(952\) | 5.43870e6i | 6.00097i | ||||||||
\(953\) | 498865. | 0.549284 | 0.274642 | − | 0.961547i | \(-0.411441\pi\) | ||||
0.274642 | + | 0.961547i | \(0.411441\pi\) | |||||||
\(954\) | − | 802279.i | − | 0.881513i | ||||||
\(955\) | − | 635200.i | − | 0.696472i | ||||||
\(956\) | 1.23001e6 | 1.34583 | ||||||||
\(957\) | − | 21567.2i | − | 0.0235489i | ||||||
\(958\) | 3.13976e6i | 3.42109i | ||||||||
\(959\) | 1.22081e6 | 1.32743 | ||||||||
\(960\) | 2.59157e6 | 2.81203 | ||||||||
\(961\) | −591077. | −0.640026 | ||||||||
\(962\) | − | 1.61401e6i | − | 1.74404i | ||||||
\(963\) | −26633.1 | −0.0287190 | ||||||||
\(964\) | −523611. | −0.563449 | ||||||||
\(965\) | 644087. | 0.691656 | ||||||||
\(966\) | −115483. | −0.123755 | ||||||||
\(967\) | 790210.i | 0.845064i | 0.906348 | + | 0.422532i | \(0.138859\pi\) | ||||
−0.906348 | + | 0.422532i | \(0.861141\pi\) | |||||||
\(968\) | 3.22584e6i | 3.44264i | ||||||||
\(969\) | −958977. | −1.02132 | ||||||||
\(970\) | 2.04764e6 | 2.17626 | ||||||||
\(971\) | 546860. | 0.580013 | 0.290006 | − | 0.957025i | \(-0.406343\pi\) | ||||
0.290006 | + | 0.957025i | \(0.406343\pi\) | |||||||
\(972\) | 168555. | 0.178405 | ||||||||
\(973\) | −2.61155e6 | −2.75850 | ||||||||
\(974\) | − | 1.24575e6i | − | 1.31315i | ||||||
\(975\) | 106547.i | 0.112081i | ||||||||
\(976\) | − | 2.37228e6i | − | 2.49038i | ||||||
\(977\) | − | 710431.i | − | 0.744274i | −0.928178 | − | 0.372137i | \(-0.878625\pi\) | ||
0.928178 | − | 0.372137i | \(-0.121375\pi\) | |||||||
\(978\) | − | 17688.7i | − | 0.0184935i | ||||||
\(979\) | −23641.2 | −0.0246664 | ||||||||
\(980\) | −3.66851e6 | −3.81978 | ||||||||
\(981\) | 403218.i | 0.418988i | ||||||||
\(982\) | 216250.i | 0.224250i | ||||||||
\(983\) | 1.52173e6i | 1.57482i | 0.616429 | + | 0.787410i | \(0.288579\pi\) | ||||
−0.616429 | + | 0.787410i | \(0.711421\pi\) | |||||||
\(984\) | 962353.i | 0.993903i | ||||||||
\(985\) | 318389. | 0.328160 | ||||||||
\(986\) | 1.16675e6i | 1.20012i | ||||||||
\(987\) | 1.47859e6i | 1.51780i | ||||||||
\(988\) | 2.59819e6i | 2.66169i | ||||||||
\(989\) | 88154.4 | 0.0901263 | ||||||||
\(990\) | −56058.5 | −0.0571967 | ||||||||
\(991\) | 845241.i | 0.860664i | 0.902671 | + | 0.430332i | \(0.141603\pi\) | ||||
−0.902671 | + | 0.430332i | \(0.858397\pi\) | |||||||
\(992\) | 5.32297e6 | 5.40917 | ||||||||
\(993\) | 96249.0 | 0.0976108 | ||||||||
\(994\) | 1.48744e6i | 1.50545i | ||||||||
\(995\) | −798160. | −0.806202 | ||||||||
\(996\) | − | 921456.i | − | 0.928872i | ||||||
\(997\) | −168798. | −0.169816 | −0.0849079 | − | 0.996389i | \(-0.527060\pi\) | ||||
−0.0849079 | + | 0.996389i | \(0.527060\pi\) | |||||||
\(998\) | − | 1.06491e6i | − | 1.06918i | ||||||
\(999\) | − | 272633.i | − | 0.273179i |
(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 | 177.5.c.a.58.2 | ✓ | 40 | |
3.2 | odd | 2 | 531.5.c.d.235.39 | 40 | |||
59.58 | odd | 2 | inner | 177.5.c.a.58.39 | yes | 40 | |
177.176 | even | 2 | 531.5.c.d.235.2 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.c.a.58.2 | ✓ | 40 | 1.1 | even | 1 | trivial | |
177.5.c.a.58.39 | yes | 40 | 59.58 | odd | 2 | inner | |
531.5.c.d.235.2 | 40 | 177.176 | even | 2 | |||
531.5.c.d.235.39 | 40 | 3.2 | odd | 2 |