Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,5,Mod(91,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, 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("230.91");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(23.7750915093\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.3 | ||
Character | \(\chi\) | \(=\) | 230.91 |
Dual form | 230.5.d.a.91.14 |
$q$-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 \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.82843 | −0.707107 | ||||||||
\(3\) | 7.33271 | 0.814745 | 0.407373 | − | 0.913262i | \(-0.366445\pi\) | ||||
0.407373 | + | 0.913262i | \(0.366445\pi\) | |||||||
\(4\) | 8.00000 | 0.500000 | ||||||||
\(5\) | 11.1803i | 0.447214i | ||||||||
\(6\) | −20.7400 | −0.576112 | ||||||||
\(7\) | − | 75.6542i | − | 1.54396i | −0.635645 | − | 0.771982i | \(-0.719266\pi\) | ||
0.635645 | − | 0.771982i | \(-0.280734\pi\) | |||||||
\(8\) | −22.6274 | −0.353553 | ||||||||
\(9\) | −27.2314 | −0.336190 | ||||||||
\(10\) | − | 31.6228i | − | 0.316228i | ||||||
\(11\) | 34.1889i | 0.282553i | 0.989970 | + | 0.141276i | \(0.0451206\pi\) | ||||
−0.989970 | + | 0.141276i | \(0.954879\pi\) | |||||||
\(12\) | 58.6617 | 0.407373 | ||||||||
\(13\) | −197.432 | −1.16824 | −0.584119 | − | 0.811668i | \(-0.698560\pi\) | ||||
−0.584119 | + | 0.811668i | \(0.698560\pi\) | |||||||
\(14\) | 213.982i | 1.09175i | ||||||||
\(15\) | 81.9822i | 0.364365i | ||||||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | 398.477i | 1.37881i | 0.724375 | + | 0.689406i | \(0.242128\pi\) | ||||
−0.724375 | + | 0.689406i | \(0.757872\pi\) | |||||||
\(18\) | 77.0220 | 0.237722 | ||||||||
\(19\) | 103.242i | 0.285989i | 0.989723 | + | 0.142994i | \(0.0456731\pi\) | ||||
−0.989723 | + | 0.142994i | \(0.954327\pi\) | |||||||
\(20\) | 89.4427i | 0.223607i | ||||||||
\(21\) | − | 554.750i | − | 1.25794i | ||||||
\(22\) | − | 96.7007i | − | 0.199795i | ||||||
\(23\) | −296.326 | + | 438.214i | −0.560163 | + | 0.828383i | ||||
\(24\) | −165.920 | −0.288056 | ||||||||
\(25\) | −125.000 | −0.200000 | ||||||||
\(26\) | 558.423 | 0.826069 | ||||||||
\(27\) | −793.629 | −1.08865 | ||||||||
\(28\) | − | 605.234i | − | 0.771982i | ||||||
\(29\) | 467.608 | 0.556015 | 0.278007 | − | 0.960579i | \(-0.410326\pi\) | ||||
0.278007 | + | 0.960579i | \(0.410326\pi\) | |||||||
\(30\) | − | 231.881i | − | 0.257645i | ||||||
\(31\) | −705.269 | −0.733891 | −0.366945 | − | 0.930242i | \(-0.619596\pi\) | ||||
−0.366945 | + | 0.930242i | \(0.619596\pi\) | |||||||
\(32\) | −181.019 | −0.176777 | ||||||||
\(33\) | 250.697i | 0.230209i | ||||||||
\(34\) | − | 1127.06i | − | 0.974967i | ||||||
\(35\) | 845.840 | 0.690481 | ||||||||
\(36\) | −217.851 | −0.168095 | ||||||||
\(37\) | 1178.93i | 0.861158i | 0.902553 | + | 0.430579i | \(0.141691\pi\) | ||||
−0.902553 | + | 0.430579i | \(0.858309\pi\) | |||||||
\(38\) | − | 292.012i | − | 0.202225i | ||||||
\(39\) | −1447.71 | −0.951816 | ||||||||
\(40\) | − | 252.982i | − | 0.158114i | ||||||
\(41\) | 2869.05 | 1.70675 | 0.853376 | − | 0.521296i | \(-0.174551\pi\) | ||||
0.853376 | + | 0.521296i | \(0.174551\pi\) | |||||||
\(42\) | 1569.07i | 0.889496i | ||||||||
\(43\) | − | 1322.67i | − | 0.715344i | −0.933847 | − | 0.357672i | \(-0.883571\pi\) | ||
0.933847 | − | 0.357672i | \(-0.116429\pi\) | |||||||
\(44\) | 273.511i | 0.141276i | ||||||||
\(45\) | − | 304.456i | − | 0.150349i | ||||||
\(46\) | 838.137 | − | 1239.46i | 0.396095 | − | 0.585755i | ||||
\(47\) | −2467.58 | −1.11706 | −0.558529 | − | 0.829485i | \(-0.688634\pi\) | ||||
−0.558529 | + | 0.829485i | \(0.688634\pi\) | |||||||
\(48\) | 469.293 | 0.203686 | ||||||||
\(49\) | −3322.56 | −1.38382 | ||||||||
\(50\) | 353.553 | 0.141421 | ||||||||
\(51\) | 2921.91i | 1.12338i | ||||||||
\(52\) | −1579.46 | −0.584119 | ||||||||
\(53\) | 3210.85i | 1.14306i | 0.820582 | + | 0.571528i | \(0.193649\pi\) | ||||
−0.820582 | + | 0.571528i | \(0.806351\pi\) | |||||||
\(54\) | 2244.72 | 0.769795 | ||||||||
\(55\) | −382.243 | −0.126361 | ||||||||
\(56\) | 1711.86i | 0.545873i | ||||||||
\(57\) | 757.043i | 0.233008i | ||||||||
\(58\) | −1322.60 | −0.393162 | ||||||||
\(59\) | −6472.33 | −1.85933 | −0.929665 | − | 0.368406i | \(-0.879904\pi\) | ||||
−0.929665 | + | 0.368406i | \(0.879904\pi\) | |||||||
\(60\) | 655.857i | 0.182183i | ||||||||
\(61\) | 6608.69i | 1.77605i | 0.459794 | + | 0.888026i | \(0.347923\pi\) | ||||
−0.459794 | + | 0.888026i | \(0.652077\pi\) | |||||||
\(62\) | 1994.80 | 0.518939 | ||||||||
\(63\) | 2060.17i | 0.519065i | ||||||||
\(64\) | 512.000 | 0.125000 | ||||||||
\(65\) | − | 2207.36i | − | 0.522452i | ||||||
\(66\) | − | 709.078i | − | 0.162782i | ||||||
\(67\) | − | 5225.76i | − | 1.16413i | −0.813144 | − | 0.582063i | \(-0.802246\pi\) | ||
0.813144 | − | 0.582063i | \(-0.197754\pi\) | |||||||
\(68\) | 3187.81i | 0.689406i | ||||||||
\(69\) | −2172.87 | + | 3213.30i | −0.456390 | + | 0.674921i | ||||
\(70\) | −2392.40 | −0.488244 | ||||||||
\(71\) | −5696.69 | −1.13007 | −0.565035 | − | 0.825067i | \(-0.691138\pi\) | ||||
−0.565035 | + | 0.825067i | \(0.691138\pi\) | |||||||
\(72\) | 616.176 | 0.118861 | ||||||||
\(73\) | −7364.21 | −1.38191 | −0.690956 | − | 0.722897i | \(-0.742810\pi\) | ||||
−0.690956 | + | 0.722897i | \(0.742810\pi\) | |||||||
\(74\) | − | 3334.51i | − | 0.608931i | ||||||
\(75\) | −916.589 | −0.162949 | ||||||||
\(76\) | 825.936i | 0.142994i | ||||||||
\(77\) | 2586.53 | 0.436251 | ||||||||
\(78\) | 4094.75 | 0.673036 | ||||||||
\(79\) | − | 1905.16i | − | 0.305265i | −0.988283 | − | 0.152633i | \(-0.951225\pi\) | ||
0.988283 | − | 0.152633i | \(-0.0487752\pi\) | |||||||
\(80\) | 715.542i | 0.111803i | ||||||||
\(81\) | −3613.71 | −0.550786 | ||||||||
\(82\) | −8114.90 | −1.20686 | ||||||||
\(83\) | − | 2724.40i | − | 0.395470i | −0.980255 | − | 0.197735i | \(-0.936641\pi\) | ||
0.980255 | − | 0.197735i | \(-0.0633586\pi\) | |||||||
\(84\) | − | 4438.00i | − | 0.628968i | ||||||
\(85\) | −4455.11 | −0.616624 | ||||||||
\(86\) | 3741.08i | 0.505825i | ||||||||
\(87\) | 3428.84 | 0.453010 | ||||||||
\(88\) | − | 773.606i | − | 0.0998975i | ||||||
\(89\) | − | 4252.33i | − | 0.536843i | −0.963302 | − | 0.268421i | \(-0.913498\pi\) | ||
0.963302 | − | 0.268421i | \(-0.0865020\pi\) | |||||||
\(90\) | 861.132i | 0.106313i | ||||||||
\(91\) | 14936.6i | 1.80372i | ||||||||
\(92\) | −2370.61 | + | 3505.71i | −0.280081 | + | 0.414191i | ||||
\(93\) | −5171.53 | −0.597934 | ||||||||
\(94\) | 6979.37 | 0.789879 | ||||||||
\(95\) | −1154.28 | −0.127898 | ||||||||
\(96\) | −1327.36 | −0.144028 | ||||||||
\(97\) | − | 5482.74i | − | 0.582712i | −0.956615 | − | 0.291356i | \(-0.905894\pi\) | ||
0.956615 | − | 0.291356i | \(-0.0941064\pi\) | |||||||
\(98\) | 9397.61 | 0.978510 | ||||||||
\(99\) | − | 931.010i | − | 0.0949914i | ||||||
\(100\) | −1000.00 | −0.100000 | ||||||||
\(101\) | 19839.0 | 1.94481 | 0.972406 | − | 0.233296i | \(-0.0749510\pi\) | ||||
0.972406 | + | 0.233296i | \(0.0749510\pi\) | |||||||
\(102\) | − | 8264.42i | − | 0.794350i | ||||||
\(103\) | − | 297.020i | − | 0.0279970i | −0.999902 | − | 0.0139985i | \(-0.995544\pi\) | ||
0.999902 | − | 0.0139985i | \(-0.00445601\pi\) | |||||||
\(104\) | 4467.38 | 0.413034 | ||||||||
\(105\) | 6202.30 | 0.562567 | ||||||||
\(106\) | − | 9081.64i | − | 0.808263i | ||||||
\(107\) | − | 12365.7i | − | 1.08007i | −0.841643 | − | 0.540035i | \(-0.818411\pi\) | ||
0.841643 | − | 0.540035i | \(-0.181589\pi\) | |||||||
\(108\) | −6349.03 | −0.544327 | ||||||||
\(109\) | 12718.6i | 1.07050i | 0.844694 | + | 0.535250i | \(0.179783\pi\) | ||||
−0.844694 | + | 0.535250i | \(0.820217\pi\) | |||||||
\(110\) | 1081.15 | 0.0893510 | ||||||||
\(111\) | 8644.72i | 0.701625i | ||||||||
\(112\) | − | 4841.87i | − | 0.385991i | ||||||
\(113\) | 11813.4i | 0.925165i | 0.886576 | + | 0.462583i | \(0.153077\pi\) | ||||
−0.886576 | + | 0.462583i | \(0.846923\pi\) | |||||||
\(114\) | − | 2141.24i | − | 0.164762i | ||||||
\(115\) | −4899.39 | − | 3313.03i | −0.370464 | − | 0.250512i | ||||
\(116\) | 3740.87 | 0.278007 | ||||||||
\(117\) | 5376.35 | 0.392750 | ||||||||
\(118\) | 18306.5 | 1.31474 | ||||||||
\(119\) | 30146.4 | 2.12884 | ||||||||
\(120\) | − | 1855.04i | − | 0.128823i | ||||||
\(121\) | 13472.1 | 0.920164 | ||||||||
\(122\) | − | 18692.2i | − | 1.25586i | ||||||
\(123\) | 21037.9 | 1.39057 | ||||||||
\(124\) | −5642.15 | −0.366945 | ||||||||
\(125\) | − | 1397.54i | − | 0.0894427i | ||||||
\(126\) | − | 5827.04i | − | 0.367034i | ||||||
\(127\) | −12443.5 | −0.771501 | −0.385750 | − | 0.922603i | \(-0.626057\pi\) | ||||
−0.385750 | + | 0.922603i | \(0.626057\pi\) | |||||||
\(128\) | −1448.15 | −0.0883883 | ||||||||
\(129\) | − | 9698.77i | − | 0.582824i | ||||||
\(130\) | 6243.35i | 0.369429i | ||||||||
\(131\) | −14644.4 | −0.853352 | −0.426676 | − | 0.904405i | \(-0.640316\pi\) | ||||
−0.426676 | + | 0.904405i | \(0.640316\pi\) | |||||||
\(132\) | 2005.58i | 0.115104i | ||||||||
\(133\) | 7810.69 | 0.441556 | ||||||||
\(134\) | 14780.7i | 0.823161i | ||||||||
\(135\) | − | 8873.04i | − | 0.486861i | ||||||
\(136\) | − | 9016.50i | − | 0.487484i | ||||||
\(137\) | − | 24294.3i | − | 1.29438i | −0.762327 | − | 0.647192i | \(-0.775943\pi\) | ||
0.762327 | − | 0.647192i | \(-0.224057\pi\) | |||||||
\(138\) | 6145.81 | − | 9088.58i | 0.322717 | − | 0.477241i | ||||
\(139\) | −22683.1 | −1.17402 | −0.587008 | − | 0.809581i | \(-0.699694\pi\) | ||||
−0.587008 | + | 0.809581i | \(0.699694\pi\) | |||||||
\(140\) | 6766.72 | 0.345241 | ||||||||
\(141\) | −18094.0 | −0.910117 | ||||||||
\(142\) | 16112.7 | 0.799081 | ||||||||
\(143\) | − | 6749.98i | − | 0.330089i | ||||||
\(144\) | −1742.81 | −0.0840475 | ||||||||
\(145\) | 5228.02i | 0.248657i | ||||||||
\(146\) | 20829.1 | 0.977159 | ||||||||
\(147\) | −24363.3 | −1.12746 | ||||||||
\(148\) | 9431.40i | 0.430579i | ||||||||
\(149\) | − | 39128.9i | − | 1.76248i | −0.472666 | − | 0.881241i | \(-0.656708\pi\) | ||
0.472666 | − | 0.881241i | \(-0.343292\pi\) | |||||||
\(150\) | 2592.50 | 0.115222 | ||||||||
\(151\) | 21428.3 | 0.939798 | 0.469899 | − | 0.882720i | \(-0.344290\pi\) | ||||
0.469899 | + | 0.882720i | \(0.344290\pi\) | |||||||
\(152\) | − | 2336.10i | − | 0.101112i | ||||||
\(153\) | − | 10851.1i | − | 0.463543i | ||||||
\(154\) | −7315.82 | −0.308476 | ||||||||
\(155\) | − | 7885.15i | − | 0.328206i | ||||||
\(156\) | −11581.7 | −0.475908 | ||||||||
\(157\) | − | 11663.7i | − | 0.473193i | −0.971608 | − | 0.236596i | \(-0.923968\pi\) | ||
0.971608 | − | 0.236596i | \(-0.0760319\pi\) | |||||||
\(158\) | 5388.61i | 0.215855i | ||||||||
\(159\) | 23544.2i | 0.931300i | ||||||||
\(160\) | − | 2023.86i | − | 0.0790569i | ||||||
\(161\) | 33152.8 | + | 22418.3i | 1.27899 | + | 0.864871i | ||||
\(162\) | 10221.1 | 0.389465 | ||||||||
\(163\) | 32325.1 | 1.21665 | 0.608323 | − | 0.793690i | \(-0.291843\pi\) | ||||
0.608323 | + | 0.793690i | \(0.291843\pi\) | |||||||
\(164\) | 22952.4 | 0.853376 | ||||||||
\(165\) | −2802.88 | −0.102952 | ||||||||
\(166\) | 7705.76i | 0.279640i | ||||||||
\(167\) | −17057.6 | −0.611625 | −0.305812 | − | 0.952092i | \(-0.598928\pi\) | ||||
−0.305812 | + | 0.952092i | \(0.598928\pi\) | |||||||
\(168\) | 12552.6i | 0.444748i | ||||||||
\(169\) | 10418.5 | 0.364780 | ||||||||
\(170\) | 12600.9 | 0.436019 | ||||||||
\(171\) | − | 2811.42i | − | 0.0961465i | ||||||
\(172\) | − | 10581.4i | − | 0.357672i | ||||||
\(173\) | −44731.0 | −1.49457 | −0.747286 | − | 0.664503i | \(-0.768643\pi\) | ||||
−0.747286 | + | 0.664503i | \(0.768643\pi\) | |||||||
\(174\) | −9698.21 | −0.320327 | ||||||||
\(175\) | 9456.77i | 0.308793i | ||||||||
\(176\) | 2188.09i | 0.0706382i | ||||||||
\(177\) | −47459.7 | −1.51488 | ||||||||
\(178\) | 12027.4i | 0.379605i | ||||||||
\(179\) | 42228.4 | 1.31795 | 0.658975 | − | 0.752165i | \(-0.270990\pi\) | ||||
0.658975 | + | 0.752165i | \(0.270990\pi\) | |||||||
\(180\) | − | 2435.65i | − | 0.0751743i | ||||||
\(181\) | − | 30696.0i | − | 0.936966i | −0.883472 | − | 0.468483i | \(-0.844801\pi\) | ||
0.883472 | − | 0.468483i | \(-0.155199\pi\) | |||||||
\(182\) | − | 42247.0i | − | 1.27542i | ||||||
\(183\) | 48459.6i | 1.44703i | ||||||||
\(184\) | 6705.09 | − | 9915.66i | 0.198047 | − | 0.292877i | ||||
\(185\) | −13180.8 | −0.385122 | ||||||||
\(186\) | 14627.3 | 0.422803 | ||||||||
\(187\) | −13623.5 | −0.389587 | ||||||||
\(188\) | −19740.6 | −0.558529 | ||||||||
\(189\) | 60041.4i | 1.68084i | ||||||||
\(190\) | 3264.80 | 0.0904376 | ||||||||
\(191\) | 49203.2i | 1.34874i | 0.738395 | + | 0.674368i | \(0.235584\pi\) | ||||
−0.738395 | + | 0.674368i | \(0.764416\pi\) | |||||||
\(192\) | 3754.35 | 0.101843 | ||||||||
\(193\) | 7645.71 | 0.205260 | 0.102630 | − | 0.994720i | \(-0.467274\pi\) | ||||
0.102630 | + | 0.994720i | \(0.467274\pi\) | |||||||
\(194\) | 15507.5i | 0.412040i | ||||||||
\(195\) | − | 16185.9i | − | 0.425665i | ||||||
\(196\) | −26580.5 | −0.691911 | ||||||||
\(197\) | −24674.2 | −0.635785 | −0.317892 | − | 0.948127i | \(-0.602975\pi\) | ||||
−0.317892 | + | 0.948127i | \(0.602975\pi\) | |||||||
\(198\) | 2633.29i | 0.0671690i | ||||||||
\(199\) | 50289.1i | 1.26989i | 0.772556 | + | 0.634947i | \(0.218978\pi\) | ||||
−0.772556 | + | 0.634947i | \(0.781022\pi\) | |||||||
\(200\) | 2828.43 | 0.0707107 | ||||||||
\(201\) | − | 38319.0i | − | 0.948466i | ||||||
\(202\) | −56113.2 | −1.37519 | ||||||||
\(203\) | − | 35376.5i | − | 0.858466i | ||||||
\(204\) | 23375.3i | 0.561690i | ||||||||
\(205\) | 32077.0i | 0.763283i | ||||||||
\(206\) | 840.101i | 0.0197969i | ||||||||
\(207\) | 8069.37 | − | 11933.2i | 0.188321 | − | 0.278494i | ||||
\(208\) | −12635.7 | −0.292059 | ||||||||
\(209\) | −3529.73 | −0.0808069 | ||||||||
\(210\) | −17542.7 | −0.397795 | ||||||||
\(211\) | −2814.71 | −0.0632220 | −0.0316110 | − | 0.999500i | \(-0.510064\pi\) | ||||
−0.0316110 | + | 0.999500i | \(0.510064\pi\) | |||||||
\(212\) | 25686.8i | 0.571528i | ||||||||
\(213\) | −41772.1 | −0.920720 | ||||||||
\(214\) | 34975.5i | 0.763725i | ||||||||
\(215\) | 14787.9 | 0.319912 | ||||||||
\(216\) | 17957.8 | 0.384898 | ||||||||
\(217\) | 53356.6i | 1.13310i | ||||||||
\(218\) | − | 35973.7i | − | 0.756958i | ||||||
\(219\) | −53999.6 | −1.12591 | ||||||||
\(220\) | −3057.95 | −0.0631807 | ||||||||
\(221\) | − | 78672.1i | − | 1.61078i | ||||||
\(222\) | − | 24451.0i | − | 0.496124i | ||||||
\(223\) | 9911.25 | 0.199305 | 0.0996527 | − | 0.995022i | \(-0.468227\pi\) | ||||
0.0996527 | + | 0.995022i | \(0.468227\pi\) | |||||||
\(224\) | 13694.9i | 0.272937i | ||||||||
\(225\) | 3403.92 | 0.0672380 | ||||||||
\(226\) | − | 33413.4i | − | 0.654191i | ||||||
\(227\) | − | 38706.5i | − | 0.751160i | −0.926790 | − | 0.375580i | \(-0.877444\pi\) | ||
0.926790 | − | 0.375580i | \(-0.122556\pi\) | |||||||
\(228\) | 6056.35i | 0.116504i | ||||||||
\(229\) | 22140.6i | 0.422200i | 0.977464 | + | 0.211100i | \(0.0677046\pi\) | ||||
−0.977464 | + | 0.211100i | \(0.932295\pi\) | |||||||
\(230\) | 13857.6 | + | 9370.65i | 0.261958 | + | 0.177139i | ||||
\(231\) | 18966.3 | 0.355433 | ||||||||
\(232\) | −10580.8 | −0.196581 | ||||||||
\(233\) | 23880.5 | 0.439878 | 0.219939 | − | 0.975514i | \(-0.429414\pi\) | ||||
0.219939 | + | 0.975514i | \(0.429414\pi\) | |||||||
\(234\) | −15206.6 | −0.277716 | ||||||||
\(235\) | − | 27588.4i | − | 0.499563i | ||||||
\(236\) | −51778.6 | −0.929665 | ||||||||
\(237\) | − | 13970.0i | − | 0.248714i | ||||||
\(238\) | −85267.0 | −1.50531 | ||||||||
\(239\) | 8996.17 | 0.157493 | 0.0787466 | − | 0.996895i | \(-0.474908\pi\) | ||||
0.0787466 | + | 0.996895i | \(0.474908\pi\) | |||||||
\(240\) | 5246.86i | 0.0910913i | ||||||||
\(241\) | 88691.7i | 1.52703i | 0.645788 | + | 0.763517i | \(0.276529\pi\) | ||||
−0.645788 | + | 0.763517i | \(0.723471\pi\) | |||||||
\(242\) | −38104.9 | −0.650654 | ||||||||
\(243\) | 37785.7 | 0.639904 | ||||||||
\(244\) | 52869.5i | 0.888026i | ||||||||
\(245\) | − | 37147.3i | − | 0.618864i | ||||||
\(246\) | −59504.2 | −0.983280 | ||||||||
\(247\) | − | 20383.3i | − | 0.334103i | ||||||
\(248\) | 15958.4 | 0.259470 | ||||||||
\(249\) | − | 19977.2i | − | 0.322208i | ||||||
\(250\) | 3952.85i | 0.0632456i | ||||||||
\(251\) | 19277.9i | 0.305994i | 0.988227 | + | 0.152997i | \(0.0488925\pi\) | ||||
−0.988227 | + | 0.152997i | \(0.951108\pi\) | |||||||
\(252\) | 16481.3i | 0.259532i | ||||||||
\(253\) | −14982.1 | − | 10131.1i | −0.234062 | − | 0.158276i | ||||
\(254\) | 35195.6 | 0.545533 | ||||||||
\(255\) | −32668.0 | −0.502391 | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | 76277.1 | 1.15486 | 0.577428 | − | 0.816442i | \(-0.304056\pi\) | ||||
0.577428 | + | 0.816442i | \(0.304056\pi\) | |||||||
\(258\) | 27432.3i | 0.412118i | ||||||||
\(259\) | 89190.7 | 1.32960 | ||||||||
\(260\) | − | 17658.9i | − | 0.261226i | ||||||
\(261\) | −12733.6 | −0.186927 | ||||||||
\(262\) | 41420.5 | 0.603411 | ||||||||
\(263\) | 10783.2i | 0.155897i | 0.996957 | + | 0.0779484i | \(0.0248369\pi\) | ||||
−0.996957 | + | 0.0779484i | \(0.975163\pi\) | |||||||
\(264\) | − | 5672.63i | − | 0.0813910i | ||||||
\(265\) | −35898.3 | −0.511190 | ||||||||
\(266\) | −22092.0 | −0.312227 | ||||||||
\(267\) | − | 31181.1i | − | 0.437390i | ||||||
\(268\) | − | 41806.1i | − | 0.582063i | ||||||
\(269\) | 138116. | 1.90871 | 0.954353 | − | 0.298681i | \(-0.0965465\pi\) | ||||
0.954353 | + | 0.298681i | \(0.0965465\pi\) | |||||||
\(270\) | 25096.8i | 0.344263i | ||||||||
\(271\) | −13630.5 | −0.185598 | −0.0927991 | − | 0.995685i | \(-0.529581\pi\) | ||||
−0.0927991 | + | 0.995685i | \(0.529581\pi\) | |||||||
\(272\) | 25502.5i | 0.344703i | ||||||||
\(273\) | 109526.i | 1.46957i | ||||||||
\(274\) | 68714.6i | 0.915268i | ||||||||
\(275\) | − | 4273.61i | − | 0.0565105i | ||||||
\(276\) | −17383.0 | + | 25706.4i | −0.228195 | + | 0.337460i | ||||
\(277\) | −83154.6 | −1.08374 | −0.541872 | − | 0.840461i | \(-0.682284\pi\) | ||||
−0.541872 | + | 0.840461i | \(0.682284\pi\) | |||||||
\(278\) | 64157.6 | 0.830154 | ||||||||
\(279\) | 19205.5 | 0.246727 | ||||||||
\(280\) | −19139.2 | −0.244122 | ||||||||
\(281\) | 149656.i | 1.89531i | 0.319292 | + | 0.947656i | \(0.396555\pi\) | ||||
−0.319292 | + | 0.947656i | \(0.603445\pi\) | |||||||
\(282\) | 51177.7 | 0.643550 | ||||||||
\(283\) | − | 110094.i | − | 1.37465i | −0.726351 | − | 0.687324i | \(-0.758785\pi\) | ||
0.726351 | − | 0.687324i | \(-0.241215\pi\) | |||||||
\(284\) | −45573.5 | −0.565035 | ||||||||
\(285\) | −8464.00 | −0.104204 | ||||||||
\(286\) | 19091.8i | 0.233408i | ||||||||
\(287\) | − | 217056.i | − | 2.63516i | ||||||
\(288\) | 4929.41 | 0.0594305 | ||||||||
\(289\) | −75262.7 | −0.901123 | ||||||||
\(290\) | − | 14787.1i | − | 0.175827i | ||||||
\(291\) | − | 40203.3i | − | 0.474762i | ||||||
\(292\) | −58913.7 | −0.690956 | ||||||||
\(293\) | 49371.6i | 0.575098i | 0.957766 | + | 0.287549i | \(0.0928404\pi\) | ||||
−0.957766 | + | 0.287549i | \(0.907160\pi\) | |||||||
\(294\) | 68909.9 | 0.797237 | ||||||||
\(295\) | − | 72362.8i | − | 0.831518i | ||||||
\(296\) | − | 26676.0i | − | 0.304465i | ||||||
\(297\) | − | 27133.3i | − | 0.307602i | ||||||
\(298\) | 110673.i | 1.24626i | ||||||||
\(299\) | 58504.3 | − | 86517.6i | 0.654403 | − | 0.967748i | ||||
\(300\) | −7332.71 | −0.0814745 | ||||||||
\(301\) | −100066. | −1.10447 | ||||||||
\(302\) | −60608.5 | −0.664538 | ||||||||
\(303\) | 145474. | 1.58453 | ||||||||
\(304\) | 6607.48i | 0.0714972i | ||||||||
\(305\) | −73887.4 | −0.794274 | ||||||||
\(306\) | 30691.5i | 0.327774i | ||||||||
\(307\) | −23380.8 | −0.248075 | −0.124038 | − | 0.992278i | \(-0.539584\pi\) | ||||
−0.124038 | + | 0.992278i | \(0.539584\pi\) | |||||||
\(308\) | 20692.3 | 0.218125 | ||||||||
\(309\) | − | 2177.96i | − | 0.0228105i | ||||||
\(310\) | 22302.6i | 0.232077i | ||||||||
\(311\) | 26518.6 | 0.274176 | 0.137088 | − | 0.990559i | \(-0.456226\pi\) | ||||
0.137088 | + | 0.990559i | \(0.456226\pi\) | |||||||
\(312\) | 32758.0 | 0.336518 | ||||||||
\(313\) | − | 12279.8i | − | 0.125343i | −0.998034 | − | 0.0626716i | \(-0.980038\pi\) | ||
0.998034 | − | 0.0626716i | \(-0.0199621\pi\) | |||||||
\(314\) | 32990.0i | 0.334598i | ||||||||
\(315\) | −23033.4 | −0.232133 | ||||||||
\(316\) | − | 15241.3i | − | 0.152633i | ||||||
\(317\) | 87667.0 | 0.872404 | 0.436202 | − | 0.899849i | \(-0.356323\pi\) | ||||
0.436202 | + | 0.899849i | \(0.356323\pi\) | |||||||
\(318\) | − | 66593.0i | − | 0.658529i | ||||||
\(319\) | 15987.0i | 0.157103i | ||||||||
\(320\) | 5724.33i | 0.0559017i | ||||||||
\(321\) | − | 90674.2i | − | 0.879982i | ||||||
\(322\) | −93770.2 | − | 63408.6i | −0.904384 | − | 0.611556i | ||||
\(323\) | −41139.5 | −0.394325 | ||||||||
\(324\) | −28909.7 | −0.275393 | ||||||||
\(325\) | 24679.0 | 0.233648 | ||||||||
\(326\) | −91429.1 | −0.860298 | ||||||||
\(327\) | 93261.9i | 0.872185i | ||||||||
\(328\) | −64919.2 | −0.603428 | ||||||||
\(329\) | 186683.i | 1.72470i | ||||||||
\(330\) | 7927.74 | 0.0727983 | ||||||||
\(331\) | −91366.6 | −0.833933 | −0.416967 | − | 0.908922i | \(-0.636907\pi\) | ||||
−0.416967 | + | 0.908922i | \(0.636907\pi\) | |||||||
\(332\) | − | 21795.2i | − | 0.197735i | ||||||
\(333\) | − | 32103.8i | − | 0.289513i | ||||||
\(334\) | 48246.2 | 0.432484 | ||||||||
\(335\) | 58425.8 | 0.520613 | ||||||||
\(336\) | − | 35504.0i | − | 0.314484i | ||||||
\(337\) | − | 29057.7i | − | 0.255859i | −0.991783 | − | 0.127930i | \(-0.959167\pi\) | ||
0.991783 | − | 0.127930i | \(-0.0408332\pi\) | |||||||
\(338\) | −29467.9 | −0.257938 | ||||||||
\(339\) | 86624.5i | 0.753774i | ||||||||
\(340\) | −35640.8 | −0.308312 | ||||||||
\(341\) | − | 24112.4i | − | 0.207363i | ||||||
\(342\) | 7951.90i | 0.0679859i | ||||||||
\(343\) | 69719.7i | 0.592608i | ||||||||
\(344\) | 29928.6i | 0.252912i | ||||||||
\(345\) | −35925.8 | − | 24293.5i | −0.301834 | − | 0.204104i | ||||
\(346\) | 126518. | 1.05682 | ||||||||
\(347\) | −45410.6 | −0.377136 | −0.188568 | − | 0.982060i | \(-0.560385\pi\) | ||||
−0.188568 | + | 0.982060i | \(0.560385\pi\) | |||||||
\(348\) | 27430.7 | 0.226505 | ||||||||
\(349\) | −118826. | −0.975573 | −0.487787 | − | 0.872963i | \(-0.662196\pi\) | ||||
−0.487787 | + | 0.872963i | \(0.662196\pi\) | |||||||
\(350\) | − | 26747.8i | − | 0.218349i | ||||||
\(351\) | 156688. | 1.27181 | ||||||||
\(352\) | − | 6188.85i | − | 0.0499487i | ||||||
\(353\) | −20670.1 | −0.165880 | −0.0829398 | − | 0.996555i | \(-0.526431\pi\) | ||||
−0.0829398 | + | 0.996555i | \(0.526431\pi\) | |||||||
\(354\) | 134236. | 1.07118 | ||||||||
\(355\) | − | 63690.9i | − | 0.505383i | ||||||
\(356\) | − | 34018.7i | − | 0.268421i | ||||||
\(357\) | 221055. | 1.73446 | ||||||||
\(358\) | −119440. | −0.931932 | ||||||||
\(359\) | 77971.9i | 0.604991i | 0.953151 | + | 0.302496i | \(0.0978198\pi\) | ||||
−0.953151 | + | 0.302496i | \(0.902180\pi\) | |||||||
\(360\) | 6889.05i | 0.0531563i | ||||||||
\(361\) | 119662. | 0.918210 | ||||||||
\(362\) | 86821.3i | 0.662535i | ||||||||
\(363\) | 98787.1 | 0.749699 | ||||||||
\(364\) | 119493.i | 0.901858i | ||||||||
\(365\) | − | 82334.3i | − | 0.618010i | ||||||
\(366\) | − | 137064.i | − | 1.02320i | ||||||
\(367\) | 45694.0i | 0.339255i | 0.985508 | + | 0.169628i | \(0.0542565\pi\) | ||||
−0.985508 | + | 0.169628i | \(0.945743\pi\) | |||||||
\(368\) | −18964.9 | + | 28045.7i | −0.140041 | + | 0.207096i | ||||
\(369\) | −78128.2 | −0.573793 | ||||||||
\(370\) | 37280.9 | 0.272322 | ||||||||
\(371\) | 242914. | 1.76484 | ||||||||
\(372\) | −41372.3 | −0.298967 | ||||||||
\(373\) | 152588.i | 1.09674i | 0.836236 | + | 0.548370i | \(0.184751\pi\) | ||||
−0.836236 | + | 0.548370i | \(0.815249\pi\) | |||||||
\(374\) | 38533.0 | 0.275480 | ||||||||
\(375\) | − | 10247.8i | − | 0.0728730i | ||||||
\(376\) | 55834.9 | 0.394939 | ||||||||
\(377\) | −92320.9 | −0.649557 | ||||||||
\(378\) | − | 169823.i | − | 1.18854i | ||||||
\(379\) | − | 145616.i | − | 1.01375i | −0.862020 | − | 0.506874i | \(-0.830801\pi\) | ||
0.862020 | − | 0.506874i | \(-0.169199\pi\) | |||||||
\(380\) | −9234.24 | −0.0639490 | ||||||||
\(381\) | −91244.8 | −0.628577 | ||||||||
\(382\) | − | 139168.i | − | 0.953700i | ||||||
\(383\) | 115611.i | 0.788134i | 0.919082 | + | 0.394067i | \(0.128932\pi\) | ||||
−0.919082 | + | 0.394067i | \(0.871068\pi\) | |||||||
\(384\) | −10618.9 | −0.0720140 | ||||||||
\(385\) | 28918.3i | 0.195097i | ||||||||
\(386\) | −21625.3 | −0.145140 | ||||||||
\(387\) | 36018.2i | 0.240492i | ||||||||
\(388\) | − | 43861.9i | − | 0.291356i | ||||||
\(389\) | − | 131120.i | − | 0.866506i | −0.901272 | − | 0.433253i | \(-0.857366\pi\) | ||
0.901272 | − | 0.433253i | \(-0.142634\pi\) | |||||||
\(390\) | 45780.7i | 0.300991i | ||||||||
\(391\) | −174618. | − | 118079.i | −1.14218 | − | 0.772359i | ||||
\(392\) | 75180.9 | 0.489255 | ||||||||
\(393\) | −107383. | −0.695265 | ||||||||
\(394\) | 69789.1 | 0.449568 | ||||||||
\(395\) | 21300.4 | 0.136519 | ||||||||
\(396\) | − | 7448.08i | − | 0.0474957i | ||||||
\(397\) | −233526. | −1.48168 | −0.740838 | − | 0.671684i | \(-0.765571\pi\) | ||||
−0.740838 | + | 0.671684i | \(0.765571\pi\) | |||||||
\(398\) | − | 142239.i | − | 0.897951i | ||||||
\(399\) | 57273.5 | 0.359756 | ||||||||
\(400\) | −8000.00 | −0.0500000 | ||||||||
\(401\) | − | 139878.i | − | 0.869885i | −0.900458 | − | 0.434942i | \(-0.856769\pi\) | ||
0.900458 | − | 0.434942i | \(-0.143231\pi\) | |||||||
\(402\) | 108382.i | 0.670667i | ||||||||
\(403\) | 139243. | 0.857359 | ||||||||
\(404\) | 158712. | 0.972406 | ||||||||
\(405\) | − | 40402.5i | − | 0.246319i | ||||||
\(406\) | 100060.i | 0.607027i | ||||||||
\(407\) | −40306.1 | −0.243323 | ||||||||
\(408\) | − | 66115.4i | − | 0.397175i | ||||||
\(409\) | −161738. | −0.966863 | −0.483431 | − | 0.875382i | \(-0.660610\pi\) | ||||
−0.483431 | + | 0.875382i | \(0.660610\pi\) | |||||||
\(410\) | − | 90727.3i | − | 0.539722i | ||||||
\(411\) | − | 178143.i | − | 1.05459i | ||||||
\(412\) | − | 2376.16i | − | 0.0139985i | ||||||
\(413\) | 489659.i | 2.87074i | ||||||||
\(414\) | −22823.6 | + | 33752.1i | −0.133163 | + | 0.196925i | ||||
\(415\) | 30459.7 | 0.176860 | ||||||||
\(416\) | 35739.0 | 0.206517 | ||||||||
\(417\) | −166329. | −0.956524 | ||||||||
\(418\) | 9983.57 | 0.0571391 | ||||||||
\(419\) | − | 74698.9i | − | 0.425487i | −0.977108 | − | 0.212744i | \(-0.931760\pi\) | ||
0.977108 | − | 0.212744i | \(-0.0682399\pi\) | |||||||
\(420\) | 49618.4 | 0.281283 | ||||||||
\(421\) | 256989.i | 1.44994i | 0.688781 | + | 0.724970i | \(0.258146\pi\) | ||||
−0.688781 | + | 0.724970i | \(0.741854\pi\) | |||||||
\(422\) | 7961.19 | 0.0447047 | ||||||||
\(423\) | 67195.6 | 0.375543 | ||||||||
\(424\) | − | 72653.1i | − | 0.404131i | ||||||
\(425\) | − | 49809.6i | − | 0.275762i | ||||||
\(426\) | 118149. | 0.651047 | ||||||||
\(427\) | 499975. | 2.74216 | ||||||||
\(428\) | − | 98925.8i | − | 0.540035i | ||||||
\(429\) | − | 49495.7i | − | 0.268938i | ||||||
\(430\) | −41826.6 | −0.226212 | ||||||||
\(431\) | − | 82265.7i | − | 0.442858i | −0.975177 | − | 0.221429i | \(-0.928928\pi\) | ||
0.975177 | − | 0.221429i | \(-0.0710720\pi\) | |||||||
\(432\) | −50792.3 | −0.272164 | ||||||||
\(433\) | − | 204218.i | − | 1.08923i | −0.838687 | − | 0.544614i | \(-0.816676\pi\) | ||
0.838687 | − | 0.544614i | \(-0.183324\pi\) | |||||||
\(434\) | − | 150915.i | − | 0.801223i | ||||||
\(435\) | 38335.5i | 0.202592i | ||||||||
\(436\) | 101749.i | 0.535250i | ||||||||
\(437\) | −45242.1 | − | 30593.3i | −0.236908 | − | 0.160200i | ||||
\(438\) | 152734. | 0.796136 | ||||||||
\(439\) | −120041. | −0.622875 | −0.311437 | − | 0.950267i | \(-0.600810\pi\) | ||||
−0.311437 | + | 0.950267i | \(0.600810\pi\) | |||||||
\(440\) | 8649.18 | 0.0446755 | ||||||||
\(441\) | 90477.8 | 0.465227 | ||||||||
\(442\) | 222518.i | 1.13899i | ||||||||
\(443\) | 210137. | 1.07077 | 0.535383 | − | 0.844610i | \(-0.320167\pi\) | ||||
0.535383 | + | 0.844610i | \(0.320167\pi\) | |||||||
\(444\) | 69157.7i | 0.350812i | ||||||||
\(445\) | 47542.5 | 0.240083 | ||||||||
\(446\) | −28033.3 | −0.140930 | ||||||||
\(447\) | − | 286921.i | − | 1.43597i | ||||||
\(448\) | − | 38734.9i | − | 0.192995i | ||||||
\(449\) | 110489. | 0.548059 | 0.274029 | − | 0.961721i | \(-0.411643\pi\) | ||||
0.274029 | + | 0.961721i | \(0.411643\pi\) | |||||||
\(450\) | −9627.75 | −0.0475444 | ||||||||
\(451\) | 98089.6i | 0.482247i | ||||||||
\(452\) | 94507.5i | 0.462583i | ||||||||
\(453\) | 157128. | 0.765696 | ||||||||
\(454\) | 109479.i | 0.531150i | ||||||||
\(455\) | −166996. | −0.806646 | ||||||||
\(456\) | − | 17129.9i | − | 0.0823808i | ||||||
\(457\) | 137632.i | 0.659000i | 0.944156 | + | 0.329500i | \(0.106880\pi\) | ||||
−0.944156 | + | 0.329500i | \(0.893120\pi\) | |||||||
\(458\) | − | 62623.1i | − | 0.298541i | ||||||
\(459\) | − | 316243.i | − | 1.50105i | ||||||
\(460\) | −39195.1 | − | 26504.2i | −0.185232 | − | 0.125256i | ||||
\(461\) | −97031.1 | −0.456572 | −0.228286 | − | 0.973594i | \(-0.573312\pi\) | ||||
−0.228286 | + | 0.973594i | \(0.573312\pi\) | |||||||
\(462\) | −53644.8 | −0.251329 | ||||||||
\(463\) | −21338.9 | −0.0995427 | −0.0497713 | − | 0.998761i | \(-0.515849\pi\) | ||||
−0.0497713 | + | 0.998761i | \(0.515849\pi\) | |||||||
\(464\) | 29926.9 | 0.139004 | ||||||||
\(465\) | − | 57819.5i | − | 0.267404i | ||||||
\(466\) | −67544.4 | −0.311041 | ||||||||
\(467\) | 236374.i | 1.08384i | 0.840430 | + | 0.541920i | \(0.182302\pi\) | ||||
−0.840430 | + | 0.541920i | \(0.817698\pi\) | |||||||
\(468\) | 43010.8 | 0.196375 | ||||||||
\(469\) | −395351. | −1.79737 | ||||||||
\(470\) | 78031.7i | 0.353244i | ||||||||
\(471\) | − | 85526.7i | − | 0.385532i | ||||||
\(472\) | 146452. | 0.657372 | ||||||||
\(473\) | 45220.7 | 0.202122 | ||||||||
\(474\) | 39513.1i | 0.175867i | ||||||||
\(475\) | − | 12905.2i | − | 0.0571978i | ||||||
\(476\) | 241171. | 1.06442 | ||||||||
\(477\) | − | 87435.8i | − | 0.384284i | ||||||
\(478\) | −25445.0 | −0.111365 | ||||||||
\(479\) | − | 323857.i | − | 1.41150i | −0.708459 | − | 0.705752i | \(-0.750609\pi\) | ||
0.708459 | − | 0.705752i | \(-0.249391\pi\) | |||||||
\(480\) | − | 14840.4i | − | 0.0644113i | ||||||
\(481\) | − | 232758.i | − | 1.00604i | ||||||
\(482\) | − | 250858.i | − | 1.07978i | ||||||
\(483\) | 243100. | + | 164387.i | 1.04205 | + | 0.704650i | ||||
\(484\) | 107777. | 0.460082 | ||||||||
\(485\) | 61298.9 | 0.260597 | ||||||||
\(486\) | −106874. | −0.452480 | ||||||||
\(487\) | −62892.8 | −0.265181 | −0.132591 | − | 0.991171i | \(-0.542330\pi\) | ||||
−0.132591 | + | 0.991171i | \(0.542330\pi\) | |||||||
\(488\) | − | 149538.i | − | 0.627929i | ||||||
\(489\) | 237030. | 0.991256 | ||||||||
\(490\) | 105068.i | 0.437603i | ||||||||
\(491\) | −289126. | −1.19929 | −0.599644 | − | 0.800267i | \(-0.704691\pi\) | ||||
−0.599644 | + | 0.800267i | \(0.704691\pi\) | |||||||
\(492\) | 168303. | 0.695284 | ||||||||
\(493\) | 186331.i | 0.766640i | ||||||||
\(494\) | 57652.6i | 0.236246i | ||||||||
\(495\) | 10409.0 | 0.0424814 | ||||||||
\(496\) | −45137.2 | −0.183473 | ||||||||
\(497\) | 430978.i | 1.74479i | ||||||||
\(498\) | 56504.1i | 0.227835i | ||||||||
\(499\) | 65916.0 | 0.264722 | 0.132361 | − | 0.991202i | \(-0.457744\pi\) | ||||
0.132361 | + | 0.991202i | \(0.457744\pi\) | |||||||
\(500\) | − | 11180.3i | − | 0.0447214i | ||||||
\(501\) | −125078. | −0.498318 | ||||||||
\(502\) | − | 54526.2i | − | 0.216370i | ||||||
\(503\) | 361875.i | 1.43028i | 0.698979 | + | 0.715142i | \(0.253638\pi\) | ||||
−0.698979 | + | 0.715142i | \(0.746362\pi\) | |||||||
\(504\) | − | 46616.3i | − | 0.183517i | ||||||
\(505\) | 221807.i | 0.869746i | ||||||||
\(506\) | 42375.7 | + | 28655.0i | 0.165507 | + | 0.111918i | ||||
\(507\) | 76395.6 | 0.297203 | ||||||||
\(508\) | −99548.3 | −0.385750 | ||||||||
\(509\) | −254033. | −0.980518 | −0.490259 | − | 0.871577i | \(-0.663098\pi\) | ||||
−0.490259 | + | 0.871577i | \(0.663098\pi\) | |||||||
\(510\) | 92399.0 | 0.355244 | ||||||||
\(511\) | 557133.i | 2.13362i | ||||||||
\(512\) | −11585.2 | −0.0441942 | ||||||||
\(513\) | − | 81935.8i | − | 0.311343i | ||||||
\(514\) | −215744. | −0.816606 | ||||||||
\(515\) | 3320.79 | 0.0125207 | ||||||||
\(516\) | − | 77590.1i | − | 0.291412i | ||||||
\(517\) | − | 84363.8i | − | 0.315627i | ||||||
\(518\) | −252269. | −0.940167 | ||||||||
\(519\) | −328000. | −1.21770 | ||||||||
\(520\) | 49946.8i | 0.184715i | ||||||||
\(521\) | 101656.i | 0.374503i | 0.982312 | + | 0.187252i | \(0.0599580\pi\) | ||||
−0.982312 | + | 0.187252i | \(0.940042\pi\) | |||||||
\(522\) | 36016.1 | 0.132177 | ||||||||
\(523\) | 236479.i | 0.864547i | 0.901742 | + | 0.432274i | \(0.142289\pi\) | ||||
−0.901742 | + | 0.432274i | \(0.857711\pi\) | |||||||
\(524\) | −117155. | −0.426676 | ||||||||
\(525\) | 69343.8i | 0.251587i | ||||||||
\(526\) | − | 30499.6i | − | 0.110236i | ||||||
\(527\) | − | 281033.i | − | 1.01190i | ||||||
\(528\) | 16044.6i | 0.0575521i | ||||||||
\(529\) | −104223. | − | 259709.i | −0.372435 | − | 0.928058i | ||||
\(530\) | 101536. | 0.361466 | ||||||||
\(531\) | 176250. | 0.625088 | ||||||||
\(532\) | 62485.5 | 0.220778 | ||||||||
\(533\) | −566443. | −1.99389 | ||||||||
\(534\) | 88193.5i | 0.309282i | ||||||||
\(535\) | 138253. | 0.483022 | ||||||||
\(536\) | 118245.i | 0.411580i | ||||||||
\(537\) | 309649. | 1.07379 | ||||||||
\(538\) | −390651. | −1.34966 | ||||||||
\(539\) | − | 113595.i | − | 0.391003i | ||||||
\(540\) | − | 70984.4i | − | 0.243431i | ||||||
\(541\) | −9888.56 | −0.0337861 | −0.0168931 | − | 0.999857i | \(-0.505377\pi\) | ||||
−0.0168931 | + | 0.999857i | \(0.505377\pi\) | |||||||
\(542\) | 38552.9 | 0.131238 | ||||||||
\(543\) | − | 225084.i | − | 0.763389i | ||||||
\(544\) | − | 72132.0i | − | 0.243742i | ||||||
\(545\) | −142198. | −0.478742 | ||||||||
\(546\) | − | 309785.i | − | 1.03914i | ||||||
\(547\) | −507649. | −1.69664 | −0.848319 | − | 0.529486i | \(-0.822385\pi\) | ||||
−0.848319 | + | 0.529486i | \(0.822385\pi\) | |||||||
\(548\) | − | 194354.i | − | 0.647192i | ||||||
\(549\) | − | 179964.i | − | 0.597090i | ||||||
\(550\) | 12087.6i | 0.0399590i | ||||||||
\(551\) | 48276.8i | 0.159014i | ||||||||
\(552\) | 49166.5 | − | 72708.6i | 0.161358 | − | 0.238621i | ||||
\(553\) | −144133. | −0.471319 | ||||||||
\(554\) | 235197. | 0.766323 | ||||||||
\(555\) | −96650.9 | −0.313776 | ||||||||
\(556\) | −181465. | −0.587008 | ||||||||
\(557\) | 218863.i | 0.705444i | 0.935728 | + | 0.352722i | \(0.114744\pi\) | ||||
−0.935728 | + | 0.352722i | \(0.885256\pi\) | |||||||
\(558\) | −54321.2 | −0.174462 | ||||||||
\(559\) | 261138.i | 0.835692i | ||||||||
\(560\) | 54133.7 | 0.172620 | ||||||||
\(561\) | −99896.9 | −0.317414 | ||||||||
\(562\) | − | 423290.i | − | 1.34019i | ||||||
\(563\) | − | 559390.i | − | 1.76481i | −0.470492 | − | 0.882404i | \(-0.655923\pi\) | ||
0.470492 | − | 0.882404i | \(-0.344077\pi\) | |||||||
\(564\) | −144752. | −0.455059 | ||||||||
\(565\) | −132078. | −0.413747 | ||||||||
\(566\) | 311394.i | 0.972023i | ||||||||
\(567\) | 273392.i | 0.850394i | ||||||||
\(568\) | 128901. | 0.399540 | ||||||||
\(569\) | − | 25361.1i | − | 0.0783327i | −0.999233 | − | 0.0391663i | \(-0.987530\pi\) | ||
0.999233 | − | 0.0391663i | \(-0.0124702\pi\) | |||||||
\(570\) | 23939.8 | 0.0736836 | ||||||||
\(571\) | 527124.i | 1.61674i | 0.588675 | + | 0.808370i | \(0.299650\pi\) | ||||
−0.588675 | + | 0.808370i | \(0.700350\pi\) | |||||||
\(572\) | − | 53999.9i | − | 0.165044i | ||||||
\(573\) | 360793.i | 1.09888i | ||||||||
\(574\) | 613926.i | 1.86334i | ||||||||
\(575\) | 37040.8 | − | 54776.8i | 0.112033 | − | 0.165677i | ||||
\(576\) | −13942.5 | −0.0420237 | ||||||||
\(577\) | −283742. | −0.852261 | −0.426130 | − | 0.904662i | \(-0.640124\pi\) | ||||
−0.426130 | + | 0.904662i | \(0.640124\pi\) | |||||||
\(578\) | 212875. | 0.637190 | ||||||||
\(579\) | 56063.8 | 0.167234 | ||||||||
\(580\) | 41824.2i | 0.124329i | ||||||||
\(581\) | −206112. | −0.610592 | ||||||||
\(582\) | 113712.i | 0.335707i | ||||||||
\(583\) | −109775. | −0.322974 | ||||||||
\(584\) | 166633. | 0.488580 | ||||||||
\(585\) | 60109.4i | 0.175643i | ||||||||
\(586\) | − | 139644.i | − | 0.406656i | ||||||
\(587\) | −181654. | −0.527193 | −0.263596 | − | 0.964633i | \(-0.584909\pi\) | ||||
−0.263596 | + | 0.964633i | \(0.584909\pi\) | |||||||
\(588\) | −194907. | −0.563731 | ||||||||
\(589\) | − | 72813.4i | − | 0.209885i | ||||||
\(590\) | 204673.i | 0.587972i | ||||||||
\(591\) | −180929. | −0.518003 | ||||||||
\(592\) | 75451.2i | 0.215290i | ||||||||
\(593\) | 431300. | 1.22651 | 0.613253 | − | 0.789886i | \(-0.289860\pi\) | ||||
0.613253 | + | 0.789886i | \(0.289860\pi\) | |||||||
\(594\) | 76744.5i | 0.217508i | ||||||||
\(595\) | 337047.i | 0.952044i | ||||||||
\(596\) | − | 313031.i | − | 0.881241i | ||||||
\(597\) | 368755.i | 1.03464i | ||||||||
\(598\) | −165475. | + | 244709.i | −0.462733 | + | 0.684301i | ||||
\(599\) | 139346. | 0.388365 | 0.194182 | − | 0.980965i | \(-0.437795\pi\) | ||||
0.194182 | + | 0.980965i | \(0.437795\pi\) | |||||||
\(600\) | 20740.0 | 0.0576112 | ||||||||
\(601\) | −142142. | −0.393526 | −0.196763 | − | 0.980451i | \(-0.563043\pi\) | ||||
−0.196763 | + | 0.980451i | \(0.563043\pi\) | |||||||
\(602\) | 283028. | 0.780975 | ||||||||
\(603\) | 142305.i | 0.391367i | ||||||||
\(604\) | 171427. | 0.469899 | ||||||||
\(605\) | 150623.i | 0.411510i | ||||||||
\(606\) | −411462. | −1.12043 | ||||||||
\(607\) | −68766.9 | −0.186639 | −0.0933195 | − | 0.995636i | \(-0.529748\pi\) | ||||
−0.0933195 | + | 0.995636i | \(0.529748\pi\) | |||||||
\(608\) | − | 18688.8i | − | 0.0505561i | ||||||
\(609\) | − | 259406.i | − | 0.699431i | ||||||
\(610\) | 208985. | 0.561637 | ||||||||
\(611\) | 487180. | 1.30499 | ||||||||
\(612\) | − | 86808.6i | − | 0.231771i | ||||||
\(613\) | − | 319435.i | − | 0.850083i | −0.905174 | − | 0.425042i | \(-0.860259\pi\) | ||
0.905174 | − | 0.425042i | \(-0.139741\pi\) | |||||||
\(614\) | 66131.0 | 0.175416 | ||||||||
\(615\) | 235211.i | 0.621881i | ||||||||
\(616\) | −58526.5 | −0.154238 | ||||||||
\(617\) | − | 31986.3i | − | 0.0840221i | −0.999117 | − | 0.0420111i | \(-0.986624\pi\) | ||
0.999117 | − | 0.0420111i | \(-0.0133765\pi\) | |||||||
\(618\) | 6160.21i | 0.0161294i | ||||||||
\(619\) | 178467.i | 0.465776i | 0.972504 | + | 0.232888i | \(0.0748175\pi\) | ||||
−0.972504 | + | 0.232888i | \(0.925182\pi\) | |||||||
\(620\) | − | 63081.2i | − | 0.164103i | ||||||
\(621\) | 235173. | − | 347780.i | 0.609824 | − | 0.901822i | ||||
\(622\) | −75006.0 | −0.193872 | ||||||||
\(623\) | −321707. | −0.828866 | ||||||||
\(624\) | −92653.6 | −0.237954 | ||||||||
\(625\) | 15625.0 | 0.0400000 | ||||||||
\(626\) | 34732.4i | 0.0886311i | ||||||||
\(627\) | −25882.5 | −0.0658371 | ||||||||
\(628\) | − | 93309.8i | − | 0.236596i | ||||||
\(629\) | −469774. | −1.18738 | ||||||||
\(630\) | 65148.2 | 0.164143 | ||||||||
\(631\) | − | 531111.i | − | 1.33391i | −0.745097 | − | 0.666956i | \(-0.767597\pi\) | ||
0.745097 | − | 0.666956i | \(-0.232403\pi\) | |||||||
\(632\) | 43108.9i | 0.107928i | ||||||||
\(633\) | −20639.4 | −0.0515098 | ||||||||
\(634\) | −247960. | −0.616882 | ||||||||
\(635\) | − | 139123.i | − | 0.345026i | ||||||
\(636\) | 188354.i | 0.465650i | ||||||||
\(637\) | 655980. | 1.61663 | ||||||||
\(638\) | − | 45218.1i | − | 0.111089i | ||||||
\(639\) | 155129. | 0.379918 | ||||||||
\(640\) | − | 16190.9i | − | 0.0395285i | ||||||
\(641\) | 763524.i | 1.85826i | 0.369754 | + | 0.929130i | \(0.379442\pi\) | ||||
−0.369754 | + | 0.929130i | \(0.620558\pi\) | |||||||
\(642\) | 256465.i | 0.622241i | ||||||||
\(643\) | − | 591043.i | − | 1.42954i | −0.699358 | − | 0.714771i | \(-0.746531\pi\) | ||
0.699358 | − | 0.714771i | \(-0.253469\pi\) | |||||||
\(644\) | 265222. | + | 179347.i | 0.639496 | + | 0.432435i | ||||
\(645\) | 108436. | 0.260647 | ||||||||
\(646\) | 116360. | 0.278830 | ||||||||
\(647\) | −305043. | −0.728707 | −0.364354 | − | 0.931261i | \(-0.618710\pi\) | ||||
−0.364354 | + | 0.931261i | \(0.618710\pi\) | |||||||
\(648\) | 81768.9 | 0.194732 | ||||||||
\(649\) | − | 221282.i | − | 0.525359i | ||||||
\(650\) | −69802.8 | −0.165214 | ||||||||
\(651\) | 391248.i | 0.923188i | ||||||||
\(652\) | 258600. | 0.608323 | ||||||||
\(653\) | 211550. | 0.496119 | 0.248060 | − | 0.968745i | \(-0.420207\pi\) | ||||
0.248060 | + | 0.968745i | \(0.420207\pi\) | |||||||
\(654\) | − | 263784.i | − | 0.616728i | ||||||
\(655\) | − | 163729.i | − | 0.381631i | ||||||
\(656\) | 183619. | 0.426688 | ||||||||
\(657\) | 200538. | 0.464585 | ||||||||
\(658\) | − | 528018.i | − | 1.21954i | ||||||
\(659\) | 235761.i | 0.542876i | 0.962456 | + | 0.271438i | \(0.0874991\pi\) | ||||
−0.962456 | + | 0.271438i | \(0.912501\pi\) | |||||||
\(660\) | −22423.0 | −0.0514762 | ||||||||
\(661\) | − | 158962.i | − | 0.363824i | −0.983315 | − | 0.181912i | \(-0.941771\pi\) | ||
0.983315 | − | 0.181912i | \(-0.0582285\pi\) | |||||||
\(662\) | 258424. | 0.589680 | ||||||||
\(663\) | − | 576880.i | − | 1.31238i | ||||||
\(664\) | 61646.0i | 0.139820i | ||||||||
\(665\) | 87326.1i | 0.197470i | ||||||||
\(666\) | 90803.2i | 0.204716i | ||||||||
\(667\) | −138565. | + | 204913.i | −0.311459 | + | 0.460593i | ||||
\(668\) | −136461. | −0.305812 | ||||||||
\(669\) | 72676.3 | 0.162383 | ||||||||
\(670\) | −165253. | −0.368129 | ||||||||
\(671\) | −225944. | −0.501828 | ||||||||
\(672\) | 100421.i | 0.222374i | ||||||||
\(673\) | 47211.8 | 0.104237 | 0.0521183 | − | 0.998641i | \(-0.483403\pi\) | ||||
0.0521183 | + | 0.998641i | \(0.483403\pi\) | |||||||
\(674\) | 82187.5i | 0.180920i | ||||||||
\(675\) | 99203.7 | 0.217731 | ||||||||
\(676\) | 83347.8 | 0.182390 | ||||||||
\(677\) | − | 10943.8i | − | 0.0238776i | −0.999929 | − | 0.0119388i | \(-0.996200\pi\) | ||
0.999929 | − | 0.0119388i | \(-0.00380032\pi\) | |||||||
\(678\) | − | 245011.i | − | 0.532999i | ||||||
\(679\) | −414792. | −0.899686 | ||||||||
\(680\) | 100808. | 0.218009 | ||||||||
\(681\) | − | 283823.i | − | 0.612004i | ||||||
\(682\) | 68200.0i | 0.146628i | ||||||||
\(683\) | −878085. | −1.88233 | −0.941164 | − | 0.337951i | \(-0.890266\pi\) | ||||
−0.941164 | + | 0.337951i | \(0.890266\pi\) | |||||||
\(684\) | − | 22491.4i | − | 0.0480733i | ||||||
\(685\) | 271618. | 0.578866 | ||||||||
\(686\) | − | 197197.i | − | 0.419037i | ||||||
\(687\) | 162351.i | 0.343986i | ||||||||
\(688\) | − | 84651.0i | − | 0.178836i | ||||||
\(689\) | − | 633924.i | − | 1.33536i | ||||||
\(690\) | 101613. | + | 68712.3i | 0.213429 | + | 0.144323i | ||||
\(691\) | 620279. | 1.29907 | 0.649533 | − | 0.760334i | \(-0.274965\pi\) | ||||
0.649533 | + | 0.760334i | \(0.274965\pi\) | |||||||
\(692\) | −357848. | −0.747286 | ||||||||
\(693\) | −70434.8 | −0.146663 | ||||||||
\(694\) | 128440. | 0.266675 | ||||||||
\(695\) | − | 253605.i | − | 0.525036i | ||||||
\(696\) | −77585.7 | −0.160163 | ||||||||
\(697\) | 1.14325e6i | 2.35329i | ||||||||
\(698\) | 336090. | 0.689835 | ||||||||
\(699\) | 175109. | 0.358389 | ||||||||
\(700\) | 75654.2i | 0.154396i | ||||||||
\(701\) | 646194.i | 1.31500i | 0.753453 | + | 0.657501i | \(0.228387\pi\) | ||||
−0.753453 | + | 0.657501i | \(0.771613\pi\) | |||||||
\(702\) | −443180. | −0.899304 | ||||||||
\(703\) | −121715. | −0.246282 | ||||||||
\(704\) | 17504.7i | 0.0353191i | ||||||||
\(705\) | − | 202298.i | − | 0.407017i | ||||||
\(706\) | 58463.8 | 0.117295 | ||||||||
\(707\) | − | 1.50091e6i | − | 3.00272i | ||||||
\(708\) | −379678. | −0.757440 | ||||||||
\(709\) | − | 250757.i | − | 0.498839i | −0.968396 | − | 0.249419i | \(-0.919760\pi\) | ||
0.968396 | − | 0.249419i | \(-0.0802398\pi\) | |||||||
\(710\) | 180145.i | 0.357360i | ||||||||
\(711\) | 51880.2i | 0.102627i | ||||||||
\(712\) | 96219.3i | 0.189803i | ||||||||
\(713\) | 208990. | − | 309059.i | 0.411098 | − | 0.607942i | ||||
\(714\) | −625238. | −1.22645 | ||||||||
\(715\) | 75467.1 | 0.147620 | ||||||||
\(716\) | 337828. | 0.658975 | ||||||||
\(717\) | 65966.3 | 0.128317 | ||||||||
\(718\) | − | 220538.i | − | 0.427794i | ||||||
\(719\) | −723829. | −1.40016 | −0.700081 | − | 0.714064i | \(-0.746853\pi\) | ||||
−0.700081 | + | 0.714064i | \(0.746853\pi\) | |||||||
\(720\) | − | 19485.2i | − | 0.0375872i | ||||||
\(721\) | −22470.8 | −0.0432264 | ||||||||
\(722\) | −338456. | −0.649273 | ||||||||
\(723\) | 650350.i | 1.24414i | ||||||||
\(724\) | − | 245568.i | − | 0.468483i | ||||||
\(725\) | −58451.0 | −0.111203 | ||||||||
\(726\) | −279412. | −0.530118 | ||||||||
\(727\) | 148801.i | 0.281537i | 0.990043 | + | 0.140769i | \(0.0449573\pi\) | ||||
−0.990043 | + | 0.140769i | \(0.955043\pi\) | |||||||
\(728\) | − | 337976.i | − | 0.637710i | ||||||
\(729\) | 569782. | 1.07215 | ||||||||
\(730\) | 232877.i | 0.436999i | ||||||||
\(731\) | 527054. | 0.986326 | ||||||||
\(732\) | 387677.i | 0.723515i | ||||||||
\(733\) | 265248.i | 0.493679i | 0.969056 | + | 0.246840i | \(0.0793921\pi\) | ||||
−0.969056 | + | 0.246840i | \(0.920608\pi\) | |||||||
\(734\) | − | 129242.i | − | 0.239890i | ||||||
\(735\) | − | 272390.i | − | 0.504217i | ||||||
\(736\) | 53640.8 | − | 79325.3i | 0.0990237 | − | 0.146439i | ||||
\(737\) | 178663. | 0.328927 | ||||||||
\(738\) | 220980. | 0.405733 | ||||||||
\(739\) | 465115. | 0.851669 | 0.425835 | − | 0.904801i | \(-0.359981\pi\) | ||||
0.425835 | + | 0.904801i | \(0.359981\pi\) | |||||||
\(740\) | −105446. | −0.192561 | ||||||||
\(741\) | − | 149465.i | − | 0.272209i | ||||||
\(742\) | −687064. | −1.24793 | ||||||||
\(743\) | 1.04306e6i | 1.88943i | 0.327892 | + | 0.944715i | \(0.393662\pi\) | ||||
−0.327892 | + | 0.944715i | \(0.606338\pi\) | |||||||
\(744\) | 117018. | 0.211402 | ||||||||
\(745\) | 437474. | 0.788206 | ||||||||
\(746\) | − | 431585.i | − | 0.775512i | ||||||
\(747\) | 74189.1i | 0.132953i | ||||||||
\(748\) | −108988. | −0.194794 | ||||||||
\(749\) | −935519. | −1.66759 | ||||||||
\(750\) | 28985.1i | 0.0515290i | ||||||||
\(751\) | − | 828260.i | − | 1.46854i | −0.678856 | − | 0.734272i | \(-0.737524\pi\) | ||
0.678856 | − | 0.734272i | \(-0.262476\pi\) | |||||||
\(752\) | −157925. | −0.279264 | ||||||||
\(753\) | 141359.i | 0.249307i | ||||||||
\(754\) | 261123. | 0.459306 | ||||||||
\(755\) | 239576.i | 0.420291i | ||||||||
\(756\) | 480331.i | 0.840421i | ||||||||
\(757\) | 55911.9i | 0.0975692i | 0.998809 | + | 0.0487846i | \(0.0155348\pi\) | ||||
−0.998809 | + | 0.0487846i | \(0.984465\pi\) | |||||||
\(758\) | 411864.i | 0.716828i | ||||||||
\(759\) | −109859. | − | 74288.1i | −0.190701 | − | 0.128954i | ||||
\(760\) | 26118.4 | 0.0452188 | ||||||||
\(761\) | 1.14940e6 | 1.98472 | 0.992362 | − | 0.123357i | \(-0.0393660\pi\) | ||||
0.992362 | + | 0.123357i | \(0.0393660\pi\) | |||||||
\(762\) | 258079. | 0.444471 | ||||||||
\(763\) | 962216. | 1.65281 | ||||||||
\(764\) | 393626.i | 0.674368i | ||||||||
\(765\) | 121319. | 0.207303 | ||||||||
\(766\) | − | 326996.i | − | 0.557295i | ||||||
\(767\) | 1.27785e6 | 2.17214 | ||||||||
\(768\) | 30034.8 | 0.0509216 | ||||||||
\(769\) | − | 709531.i | − | 1.19983i | −0.800065 | − | 0.599914i | \(-0.795202\pi\) | ||
0.800065 | − | 0.599914i | \(-0.204798\pi\) | |||||||
\(770\) | − | 81793.3i | − | 0.137955i | ||||||
\(771\) | 559318. | 0.940913 | ||||||||
\(772\) | 61165.7 | 0.102630 | ||||||||
\(773\) | − | 1.08765e6i | − | 1.82025i | −0.414337 | − | 0.910124i | \(-0.635986\pi\) | ||
0.414337 | − | 0.910124i | \(-0.364014\pi\) | |||||||
\(774\) | − | 101875.i | − | 0.170053i | ||||||
\(775\) | 88158.6 | 0.146778 | ||||||||
\(776\) | 124060.i | 0.206020i | ||||||||
\(777\) | 654009. | 1.08328 | ||||||||
\(778\) | 370865.i | 0.612712i | ||||||||
\(779\) | 296206.i | 0.488112i | ||||||||
\(780\) | − | 129487.i | − | 0.212833i | ||||||
\(781\) | − | 194763.i | − | 0.319305i | ||||||
\(782\) | 493895. | + | 333978.i | 0.807646 | + | 0.546140i | ||||
\(783\) | −371108. | −0.605308 | ||||||||
\(784\) | −212644. | −0.345956 | ||||||||
\(785\) | 130404. | 0.211618 | ||||||||
\(786\) | 303725. | 0.491626 | ||||||||
\(787\) | − | 5203.80i | − | 0.00840178i | −0.999991 | − | 0.00420089i | \(-0.998663\pi\) | ||
0.999991 | − | 0.00420089i | \(-0.00133719\pi\) | |||||||
\(788\) | −197393. | −0.317892 | ||||||||
\(789\) | 79070.2i | 0.127016i | ||||||||
\(790\) | −60246.5 | −0.0965334 | ||||||||
\(791\) | 893736. | 1.42842 | ||||||||
\(792\) | 21066.4i | 0.0335845i | ||||||||
\(793\) | − | 1.30477e6i | − | 2.07485i | ||||||
\(794\) | 660510. | 1.04770 | ||||||||
\(795\) | −263232. | −0.416490 | ||||||||
\(796\) | 402313.i | 0.634947i | ||||||||
\(797\) | 884029.i | 1.39171i | 0.718181 | + | 0.695857i | \(0.244975\pi\) | ||||
−0.718181 | + | 0.695857i | \(0.755025\pi\) | |||||||
\(798\) | −161994. | −0.254386 | ||||||||
\(799\) | − | 983273.i | − | 1.54021i | ||||||
\(800\) | 22627.4 | 0.0353553 | ||||||||
\(801\) | 115797.i | 0.180481i | ||||||||
\(802\) | 395636.i | 0.615101i | ||||||||
\(803\) | − | 251774.i | − | 0.390463i | ||||||
\(804\) | − | 306552.i | − | 0.474233i | ||||||
\(805\) | −250644. | + | 370659.i | −0.386782 | + | 0.571983i | ||||
\(806\) | −393838. | −0.606244 | ||||||||
\(807\) | 1.01276e6 | 1.55511 | ||||||||
\(808\) | −448906. | −0.687595 | ||||||||
\(809\) | −57648.7 | −0.0880831 | −0.0440415 | − | 0.999030i | \(-0.514023\pi\) | ||||
−0.0440415 | + | 0.999030i | \(0.514023\pi\) | |||||||
\(810\) | 114276.i | 0.174174i | ||||||||
\(811\) | −114560. | −0.174177 | −0.0870885 | − | 0.996201i | \(-0.527756\pi\) | ||||
−0.0870885 | + | 0.996201i | \(0.527756\pi\) | |||||||
\(812\) | − | 283012.i | − | 0.429233i | ||||||
\(813\) | −99948.6 | −0.151215 | ||||||||
\(814\) | 114003. | 0.172055 | ||||||||
\(815\) | 361405.i | 0.544100i | ||||||||
\(816\) | 187002.i | 0.280845i | ||||||||
\(817\) | 136555. | 0.204580 | ||||||||
\(818\) | 457463. | 0.683675 | ||||||||
\(819\) | − | 406744.i | − | 0.606391i | ||||||
\(820\) | 256616.i | 0.381641i | ||||||||
\(821\) | −1.04781e6 | −1.55452 | −0.777260 | − | 0.629180i | \(-0.783391\pi\) | ||||
−0.777260 | + | 0.629180i | \(0.783391\pi\) | |||||||
\(822\) | 503864.i | 0.745710i | ||||||||
\(823\) | −335862. | −0.495862 | −0.247931 | − | 0.968778i | \(-0.579751\pi\) | ||||
−0.247931 | + | 0.968778i | \(0.579751\pi\) | |||||||
\(824\) | 6720.81i | 0.00989844i | ||||||||
\(825\) | − | 31337.1i | − | 0.0460417i | ||||||
\(826\) | − | 1.38496e6i | − | 2.02992i | ||||||
\(827\) | 528594.i | 0.772878i | 0.922315 | + | 0.386439i | \(0.126295\pi\) | ||||
−0.922315 | + | 0.386439i | \(0.873705\pi\) | |||||||
\(828\) | 64555.0 | − | 95465.5i | 0.0941605 | − | 0.139247i | ||||
\(829\) | 120599. | 0.175483 | 0.0877413 | − | 0.996143i | \(-0.472035\pi\) | ||||
0.0877413 | + | 0.996143i | \(0.472035\pi\) | |||||||
\(830\) | −86153.0 | −0.125059 | ||||||||
\(831\) | −609748. | −0.882976 | ||||||||
\(832\) | −101085. | −0.146030 | ||||||||
\(833\) | − | 1.32396e6i | − | 1.90803i | ||||||
\(834\) | 470449. | 0.676364 | ||||||||
\(835\) | − | 190710.i | − | 0.273527i | ||||||
\(836\) | −28237.8 | −0.0404034 | ||||||||
\(837\) | 559722. | 0.798954 | ||||||||
\(838\) | 211280.i | 0.300865i | ||||||||
\(839\) | − | 372806.i | − | 0.529613i | −0.964302 | − | 0.264806i | \(-0.914692\pi\) | ||
0.964302 | − | 0.264806i | \(-0.0853080\pi\) | |||||||
\(840\) | −140342. | −0.198897 | ||||||||
\(841\) | −488623. | −0.690848 | ||||||||
\(842\) | − | 726874.i | − | 1.02526i | ||||||
\(843\) | 1.09738e6i | 1.54420i | ||||||||
\(844\) | −22517.7 | −0.0316110 | ||||||||
\(845\) | 116482.i | 0.163134i | ||||||||
\(846\) | −190058. | −0.265549 | ||||||||
\(847\) | − | 1.01922e6i | − | 1.42070i | ||||||
\(848\) | 205494.i | 0.285764i | ||||||||
\(849\) | − | 807289.i | − | 1.11999i | ||||||
\(850\) | 140883.i | 0.194993i | ||||||||
\(851\) | −516622. | − | 349346.i | −0.713368 | − | 0.482389i | ||||
\(852\) | −334177. | −0.460360 | ||||||||
\(853\) | 1.43436e6 | 1.97133 | 0.985664 | − | 0.168720i | \(-0.0539635\pi\) | ||||
0.985664 | + | 0.168720i | \(0.0539635\pi\) | |||||||
\(854\) | −1.41414e6 | −1.93900 | ||||||||
\(855\) | 31432.6 | 0.0429980 | ||||||||
\(856\) | 279804.i | 0.381862i | ||||||||
\(857\) | −20657.6 | −0.0281267 | −0.0140633 | − | 0.999901i | \(-0.504477\pi\) | ||||
−0.0140633 | + | 0.999901i | \(0.504477\pi\) | |||||||
\(858\) | 139995.i | 0.190168i | ||||||||
\(859\) | 975464. | 1.32198 | 0.660990 | − | 0.750395i | \(-0.270136\pi\) | ||||
0.660990 | + | 0.750395i | \(0.270136\pi\) | |||||||
\(860\) | 118303. | 0.159956 | ||||||||
\(861\) | − | 1.59161e6i | − | 2.14699i | ||||||
\(862\) | 232682.i | 0.313148i | ||||||||
\(863\) | 433391. | 0.581913 | 0.290956 | − | 0.956736i | \(-0.406027\pi\) | ||||
0.290956 | + | 0.956736i | \(0.406027\pi\) | |||||||
\(864\) | 143662. | 0.192449 | ||||||||
\(865\) | − | 500108.i | − | 0.668393i | ||||||
\(866\) | 577616.i | 0.770200i | ||||||||
\(867\) | −551879. | −0.734186 | ||||||||
\(868\) | 426853.i | 0.566550i | ||||||||
\(869\) | 65135.3 | 0.0862536 | ||||||||
\(870\) | − | 108429.i | − | 0.143254i | ||||||
\(871\) | 1.03173e6i | 1.35998i | ||||||||
\(872\) | − | 287789.i | − | 0.378479i | ||||||
\(873\) | 149302.i | 0.195902i | ||||||||
\(874\) | 127964. | + | 86530.9i | 0.167519 | + | 0.113279i | ||||
\(875\) | −105730. | −0.138096 | ||||||||
\(876\) | −431997. | −0.562953 | ||||||||
\(877\) | 1.24995e6 | 1.62516 | 0.812578 | − | 0.582853i | \(-0.198063\pi\) | ||||
0.812578 | + | 0.582853i | \(0.198063\pi\) | |||||||
\(878\) | 339527. | 0.440439 | ||||||||
\(879\) | 362027.i | 0.468558i | ||||||||
\(880\) | −24463.6 | −0.0315904 | ||||||||
\(881\) | 471278.i | 0.607191i | 0.952801 | + | 0.303595i | \(0.0981871\pi\) | ||||
−0.952801 | + | 0.303595i | \(0.901813\pi\) | |||||||
\(882\) | −255910. | −0.328965 | ||||||||
\(883\) | −686292. | −0.880213 | −0.440106 | − | 0.897946i | \(-0.645059\pi\) | ||||
−0.440106 | + | 0.897946i | \(0.645059\pi\) | |||||||
\(884\) | − | 629377.i | − | 0.805390i | ||||||
\(885\) | − | 530615.i | − | 0.677475i | ||||||
\(886\) | −594356. | −0.757145 | ||||||||
\(887\) | −51577.0 | −0.0655554 | −0.0327777 | − | 0.999463i | \(-0.510435\pi\) | ||||
−0.0327777 | + | 0.999463i | \(0.510435\pi\) | |||||||
\(888\) | − | 195608.i | − | 0.248062i | ||||||
\(889\) | 941406.i | 1.19117i | ||||||||
\(890\) | −134471. | −0.169765 | ||||||||
\(891\) | − | 123549.i | − | 0.155626i | ||||||
\(892\) | 79290.0 | 0.0996527 | ||||||||
\(893\) | − | 254758.i | − | 0.319466i | ||||||
\(894\) | 811534.i | 1.01539i | ||||||||
\(895\) | 472128.i | 0.589405i | ||||||||
\(896\) | 109559.i | 0.136468i | ||||||||
\(897\) | 428995. | − | 634409.i | 0.533172 | − | 0.788468i | ||||
\(898\) | −312511. | −0.387536 | ||||||||
\(899\) | −329790. | −0.408054 | ||||||||
\(900\) | 27231.4 | 0.0336190 | ||||||||
\(901\) | −1.27945e6 | −1.57606 | ||||||||
\(902\) | − | 277439.i | − | 0.341000i | ||||||
\(903\) | −733752. | −0.899858 | ||||||||
\(904\) | − | 267308.i | − | 0.327095i | ||||||
\(905\) | 343191. | 0.419024 | ||||||||
\(906\) | −444424. | −0.541429 | ||||||||
\(907\) | − | 601451.i | − | 0.731115i | −0.930789 | − | 0.365558i | \(-0.880878\pi\) | ||
0.930789 | − | 0.365558i | \(-0.119122\pi\) | |||||||
\(908\) | − | 309652.i | − | 0.375580i | ||||||
\(909\) | −540244. | −0.653826 | ||||||||
\(910\) | 472336. | 0.570385 | ||||||||
\(911\) | 1.65516e6i | 1.99436i | 0.0750576 | + | 0.997179i | \(0.476086\pi\) | ||||
−0.0750576 | + | 0.997179i | \(0.523914\pi\) | |||||||
\(912\) | 48450.8i | 0.0582520i | ||||||||
\(913\) | 93144.0 | 0.111741 | ||||||||
\(914\) | − | 389281.i | − | 0.465983i | ||||||
\(915\) | −541795. | −0.647131 | ||||||||
\(916\) | 177125.i | 0.211100i | ||||||||
\(917\) | 1.10791e6i | 1.31754i | ||||||||
\(918\) | 894470.i | 1.06140i | ||||||||
\(919\) | 1.22836e6i | 1.45444i | 0.686404 | + | 0.727220i | \(0.259188\pi\) | ||||
−0.686404 | + | 0.727220i | \(0.740812\pi\) | |||||||
\(920\) | 110860. | + | 74965.2i | 0.130979 | + | 0.0885695i | ||||
\(921\) | −171445. | −0.202118 | ||||||||
\(922\) | 274445. | 0.322845 | ||||||||
\(923\) | 1.12471e6 | 1.32019 | ||||||||
\(924\) | 151730. | 0.177717 | ||||||||
\(925\) | − | 147366.i | − | 0.172232i | ||||||
\(926\) | 60355.4 | 0.0703873 | ||||||||
\(927\) | 8088.28i | 0.00941232i | ||||||||
\(928\) | −84646.2 | −0.0982904 | ||||||||
\(929\) | −1.14384e6 | −1.32536 | −0.662678 | − | 0.748904i | \(-0.730580\pi\) | ||||
−0.662678 | + | 0.748904i | \(0.730580\pi\) | |||||||
\(930\) | 163538.i | 0.189083i | ||||||||
\(931\) | − | 343027.i | − | 0.395758i | ||||||
\(932\) | 191044. | 0.219939 | ||||||||
\(933\) | 194453. | 0.223384 | ||||||||
\(934\) | − | 668566.i | − | 0.766391i | ||||||
\(935\) | − | 152315.i | − | 0.174229i | ||||||
\(936\) | −121653. | −0.138858 | ||||||||
\(937\) | 932474.i | 1.06208i | 0.847347 | + | 0.531040i | \(0.178199\pi\) | ||||
−0.847347 | + | 0.531040i | \(0.821801\pi\) | |||||||
\(938\) | 1.11822e6 | 1.27093 | ||||||||
\(939\) | − | 90043.9i | − | 0.102123i | ||||||
\(940\) | − | 220707.i | − | 0.249782i | ||||||
\(941\) | 669645.i | 0.756249i | 0.925755 | + | 0.378125i | \(0.123431\pi\) | ||||
−0.925755 | + | 0.378125i | \(0.876569\pi\) | |||||||
\(942\) | 241906.i | 0.272612i | ||||||||
\(943\) | −850175. | + | 1.25726e6i | −0.956059 | + | 1.41384i | ||||
\(944\) | −414229. | −0.464832 | ||||||||
\(945\) | −671283. | −0.751696 | ||||||||
\(946\) | −127903. | −0.142922 | ||||||||
\(947\) | −1.17286e6 | −1.30781 | −0.653905 | − | 0.756577i | \(-0.726870\pi\) | ||||
−0.653905 | + | 0.756577i | \(0.726870\pi\) | |||||||
\(948\) | − | 111760.i | − | 0.124357i | ||||||
\(949\) | 1.45393e6 | 1.61440 | ||||||||
\(950\) | 36501.5i | 0.0404449i | ||||||||
\(951\) | 642836. | 0.710787 | ||||||||
\(952\) | −682136. | −0.752657 | ||||||||
\(953\) | 259053.i | 0.285235i | 0.989778 | + | 0.142618i | \(0.0455519\pi\) | ||||
−0.989778 | + | 0.142618i | \(0.954448\pi\) | |||||||
\(954\) | 247306.i | 0.271730i | ||||||||
\(955\) | −550109. | −0.603173 | ||||||||
\(956\) | 71969.4 | 0.0787466 | ||||||||
\(957\) | 117228.i | 0.127999i | ||||||||
\(958\) | 916006.i | 0.998085i | ||||||||
\(959\) | −1.83797e6 | −1.99848 | ||||||||
\(960\) | 41974.9i | 0.0455457i | ||||||||
\(961\) | −426117. | −0.461404 | ||||||||
\(962\) | 658339.i | 0.711376i | ||||||||
\(963\) | 336736.i | 0.363109i | ||||||||
\(964\) | 709533.i | 0.763517i | ||||||||
\(965\) | 85481.7i | 0.0917948i | ||||||||
\(966\) | −687589. | − | 464957.i | −0.736843 | − | 0.498262i | ||||
\(967\) | −1.16404e6 | −1.24485 | −0.622423 | − | 0.782681i | \(-0.713852\pi\) | ||||
−0.622423 | + | 0.782681i | \(0.713852\pi\) | |||||||
\(968\) | −304839. | −0.325327 | ||||||||
\(969\) | −301664. | −0.321274 | ||||||||
\(970\) | −173379. | −0.184270 | ||||||||
\(971\) | − | 835673.i | − | 0.886335i | −0.896439 | − | 0.443167i | \(-0.853855\pi\) | ||
0.896439 | − | 0.443167i | \(-0.146145\pi\) | |||||||
\(972\) | 302285. | 0.319952 | ||||||||
\(973\) | 1.71608e6i | 1.81264i | ||||||||
\(974\) | 177888. | 0.187511 | ||||||||
\(975\) | 180964. | 0.190363 | ||||||||
\(976\) | 422956.i | 0.444013i | ||||||||
\(977\) | 486657.i | 0.509840i | 0.966962 | + | 0.254920i | \(0.0820492\pi\) | ||||
−0.966962 | + | 0.254920i | \(0.917951\pi\) | |||||||
\(978\) | −670423. | −0.700924 | ||||||||
\(979\) | 145382. | 0.151686 | ||||||||
\(980\) | − | 297179.i | − | 0.309432i | ||||||
\(981\) | − | 346345.i | − | 0.359891i | ||||||
\(982\) | 817770. | 0.848025 | ||||||||
\(983\) | 1.61922e6i | 1.67571i | 0.545893 | + | 0.837855i | \(0.316191\pi\) | ||||
−0.545893 | + | 0.837855i | \(0.683809\pi\) | |||||||
\(984\) | −476034. | −0.491640 | ||||||||
\(985\) | − | 275866.i | − | 0.284332i | ||||||
\(986\) | − | 527024.i | − | 0.542096i | ||||||
\(987\) | 1.36889e6i | 1.40519i | ||||||||
\(988\) | − | 163066.i | − | 0.167051i | ||||||
\(989\) | 579614. | + | 391942.i | 0.592579 | + | 0.400709i | ||||
\(990\) | −29441.1 | −0.0300389 | ||||||||
\(991\) | −263930. | −0.268745 | −0.134373 | − | 0.990931i | \(-0.542902\pi\) | ||||
−0.134373 | + | 0.990931i | \(0.542902\pi\) | |||||||
\(992\) | 127667. | 0.129735 | ||||||||
\(993\) | −669964. | −0.679443 | ||||||||
\(994\) | − | 1.21899e6i | − | 1.23375i | ||||||
\(995\) | −562249. | −0.567914 | ||||||||
\(996\) | − | 159818.i | − | 0.161104i | ||||||
\(997\) | −848999. | −0.854116 | −0.427058 | − | 0.904224i | \(-0.640450\pi\) | ||||
−0.427058 | + | 0.904224i | \(0.640450\pi\) | |||||||
\(998\) | −186439. | −0.187187 | ||||||||
\(999\) | − | 935630.i | − | 0.937504i |
(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 | 230.5.d.a.91.3 | ✓ | 32 | |
23.22 | odd | 2 | inner | 230.5.d.a.91.14 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.5.d.a.91.3 | ✓ | 32 | 1.1 | even | 1 | trivial | |
230.5.d.a.91.14 | yes | 32 | 23.22 | odd | 2 | inner |