Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,5,Mod(42,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.42");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.b (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: | \(4.44490841261\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 142x^{10} + 7173x^{8} + 157368x^{6} + 1510016x^{4} + 5098688x^{2} + 90352 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.5 | ||
Root | \(-2.75662i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.5.b.b.42.8 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.75662i | − | 0.689155i | −0.938758 | − | 0.344577i | \(-0.888022\pi\) | ||
0.938758 | − | 0.344577i | \(-0.111978\pi\) | |||||||
\(3\) | − | 12.3317i | − | 1.37018i | −0.728457 | − | 0.685092i | \(-0.759762\pi\) | ||
0.728457 | − | 0.685092i | \(-0.240238\pi\) | |||||||
\(4\) | 8.40105 | 0.525066 | ||||||||
\(5\) | − | 21.9831i | − | 0.879322i | −0.898164 | − | 0.439661i | \(-0.855099\pi\) | ||
0.898164 | − | 0.439661i | \(-0.144901\pi\) | |||||||
\(6\) | −33.9937 | −0.944268 | ||||||||
\(7\) | 63.3272i | 1.29239i | 0.763172 | + | 0.646196i | \(0.223641\pi\) | ||||
−0.763172 | + | 0.646196i | \(0.776359\pi\) | |||||||
\(8\) | − | 67.2644i | − | 1.05101i | ||||||
\(9\) | −71.0696 | −0.877403 | ||||||||
\(10\) | −60.5989 | −0.605989 | ||||||||
\(11\) | −1.17035 | −0.00967234 | −0.00483617 | − | 0.999988i | \(-0.501539\pi\) | ||||
−0.00483617 | + | 0.999988i | \(0.501539\pi\) | |||||||
\(12\) | − | 103.599i | − | 0.719437i | ||||||
\(13\) | −173.901 | −1.02900 | −0.514501 | − | 0.857490i | \(-0.672023\pi\) | ||||
−0.514501 | + | 0.857490i | \(0.672023\pi\) | |||||||
\(14\) | 174.569 | 0.890657 | ||||||||
\(15\) | −271.087 | −1.20483 | ||||||||
\(16\) | −51.0054 | −0.199240 | ||||||||
\(17\) | 469.315 | 1.62393 | 0.811963 | − | 0.583709i | \(-0.198399\pi\) | ||||
0.811963 | + | 0.583709i | \(0.198399\pi\) | |||||||
\(18\) | 195.912i | 0.604666i | ||||||||
\(19\) | 27.8220i | 0.0770692i | 0.999257 | + | 0.0385346i | \(0.0122690\pi\) | ||||
−0.999257 | + | 0.0385346i | \(0.987731\pi\) | |||||||
\(20\) | − | 184.681i | − | 0.461702i | ||||||
\(21\) | 780.929 | 1.77081 | ||||||||
\(22\) | 3.22622i | 0.00666574i | ||||||||
\(23\) | 79.3541 | 0.150008 | 0.0750039 | − | 0.997183i | \(-0.476103\pi\) | ||||
0.0750039 | + | 0.997183i | \(0.476103\pi\) | |||||||
\(24\) | −829.481 | −1.44007 | ||||||||
\(25\) | 141.745 | 0.226792 | ||||||||
\(26\) | 479.379i | 0.709141i | ||||||||
\(27\) | − | 122.458i | − | 0.167980i | ||||||
\(28\) | 532.015i | 0.678590i | ||||||||
\(29\) | 696.895i | 0.828650i | 0.910129 | + | 0.414325i | \(0.135982\pi\) | ||||
−0.910129 | + | 0.414325i | \(0.864018\pi\) | |||||||
\(30\) | 747.285i | 0.830316i | ||||||||
\(31\) | 1190.63 | 1.23895 | 0.619477 | − | 0.785015i | \(-0.287345\pi\) | ||||
0.619477 | + | 0.785015i | \(0.287345\pi\) | |||||||
\(32\) | − | 935.628i | − | 0.913699i | ||||||
\(33\) | 14.4324i | 0.0132529i | ||||||||
\(34\) | − | 1293.72i | − | 1.11914i | ||||||
\(35\) | 1392.12 | 1.13643 | ||||||||
\(36\) | −597.060 | −0.460694 | ||||||||
\(37\) | − | 1535.36i | − | 1.12152i | −0.827980 | − | 0.560758i | \(-0.810510\pi\) | ||
0.827980 | − | 0.560758i | \(-0.189490\pi\) | |||||||
\(38\) | 76.6946 | 0.0531126 | ||||||||
\(39\) | 2144.49i | 1.40992i | ||||||||
\(40\) | −1478.68 | −0.924173 | ||||||||
\(41\) | −2455.37 | −1.46066 | −0.730329 | − | 0.683095i | \(-0.760633\pi\) | ||||
−0.730329 | + | 0.683095i | \(0.760633\pi\) | |||||||
\(42\) | − | 2152.72i | − | 1.22036i | ||||||
\(43\) | −1435.68 | + | 1165.17i | −0.776463 | + | 0.630163i | ||||
\(44\) | −9.83220 | −0.00507861 | ||||||||
\(45\) | 1562.33i | 0.771520i | ||||||||
\(46\) | − | 218.749i | − | 0.103379i | ||||||
\(47\) | 1694.64 | 0.767154 | 0.383577 | − | 0.923509i | \(-0.374692\pi\) | ||||
0.383577 | + | 0.923509i | \(0.374692\pi\) | |||||||
\(48\) | 628.981i | 0.272995i | ||||||||
\(49\) | −1609.33 | −0.670275 | ||||||||
\(50\) | − | 390.737i | − | 0.156295i | ||||||
\(51\) | − | 5787.42i | − | 2.22508i | ||||||
\(52\) | −1460.95 | −0.540294 | ||||||||
\(53\) | −1990.15 | −0.708489 | −0.354245 | − | 0.935153i | \(-0.615262\pi\) | ||||
−0.354245 | + | 0.935153i | \(0.615262\pi\) | |||||||
\(54\) | −337.569 | −0.115764 | ||||||||
\(55\) | 25.7279i | 0.00850510i | ||||||||
\(56\) | 4259.66 | 1.35831 | ||||||||
\(57\) | 343.091 | 0.105599 | ||||||||
\(58\) | 1921.07 | 0.571068 | ||||||||
\(59\) | 3563.55 | 1.02371 | 0.511857 | − | 0.859071i | \(-0.328958\pi\) | ||||
0.511857 | + | 0.859071i | \(0.328958\pi\) | |||||||
\(60\) | −2277.42 | −0.632617 | ||||||||
\(61\) | 5447.36i | 1.46395i | 0.681331 | + | 0.731975i | \(0.261401\pi\) | ||||
−0.681331 | + | 0.731975i | \(0.738599\pi\) | |||||||
\(62\) | − | 3282.13i | − | 0.853831i | ||||||
\(63\) | − | 4500.64i | − | 1.13395i | ||||||
\(64\) | −3395.26 | −0.828920 | ||||||||
\(65\) | 3822.88i | 0.904824i | ||||||||
\(66\) | 39.7846 | 0.00913328 | ||||||||
\(67\) | 4930.23 | 1.09829 | 0.549145 | − | 0.835727i | \(-0.314953\pi\) | ||||
0.549145 | + | 0.835727i | \(0.314953\pi\) | |||||||
\(68\) | 3942.74 | 0.852668 | ||||||||
\(69\) | − | 978.567i | − | 0.205538i | ||||||
\(70\) | − | 3837.56i | − | 0.783175i | ||||||
\(71\) | 9660.68i | 1.91642i | 0.286065 | + | 0.958210i | \(0.407653\pi\) | ||||
−0.286065 | + | 0.958210i | \(0.592347\pi\) | |||||||
\(72\) | 4780.46i | 0.922156i | ||||||||
\(73\) | 5609.18i | 1.05258i | 0.850306 | + | 0.526288i | \(0.176417\pi\) | ||||
−0.850306 | + | 0.526288i | \(0.823583\pi\) | |||||||
\(74\) | −4232.39 | −0.772898 | ||||||||
\(75\) | − | 1747.95i | − | 0.310747i | ||||||
\(76\) | 233.734i | 0.0404664i | ||||||||
\(77\) | − | 74.1151i | − | 0.0125004i | ||||||
\(78\) | 5911.54 | 0.971654 | ||||||||
\(79\) | −11423.8 | −1.83044 | −0.915218 | − | 0.402959i | \(-0.867982\pi\) | ||||
−0.915218 | + | 0.402959i | \(0.867982\pi\) | |||||||
\(80\) | 1121.26i | 0.175196i | ||||||||
\(81\) | −7266.75 | −1.10757 | ||||||||
\(82\) | 6768.51i | 1.00662i | ||||||||
\(83\) | 5524.25 | 0.801894 | 0.400947 | − | 0.916101i | \(-0.368681\pi\) | ||||
0.400947 | + | 0.916101i | \(0.368681\pi\) | |||||||
\(84\) | 6560.62 | 0.929793 | ||||||||
\(85\) | − | 10317.0i | − | 1.42795i | ||||||
\(86\) | 3211.94 | + | 3957.62i | 0.434280 | + | 0.535103i | ||||
\(87\) | 8593.86 | 1.13540 | ||||||||
\(88\) | 78.7231i | 0.0101657i | ||||||||
\(89\) | 2559.89i | 0.323177i | 0.986858 | + | 0.161589i | \(0.0516618\pi\) | ||||
−0.986858 | + | 0.161589i | \(0.948338\pi\) | |||||||
\(90\) | 4306.74 | 0.531697 | ||||||||
\(91\) | − | 11012.7i | − | 1.32987i | ||||||
\(92\) | 666.658 | 0.0787640 | ||||||||
\(93\) | − | 14682.5i | − | 1.69759i | ||||||
\(94\) | − | 4671.49i | − | 0.528688i | ||||||
\(95\) | 611.612 | 0.0677686 | ||||||||
\(96\) | −11537.8 | −1.25194 | ||||||||
\(97\) | 3659.79 | 0.388967 | 0.194484 | − | 0.980906i | \(-0.437697\pi\) | ||||
0.194484 | + | 0.980906i | \(0.437697\pi\) | |||||||
\(98\) | 4436.31i | 0.461923i | ||||||||
\(99\) | 83.1766 | 0.00848654 | ||||||||
\(100\) | 1190.81 | 0.119081 | ||||||||
\(101\) | −10505.1 | −1.02981 | −0.514907 | − | 0.857246i | \(-0.672173\pi\) | ||||
−0.514907 | + | 0.857246i | \(0.672173\pi\) | |||||||
\(102\) | −15953.7 | −1.53342 | ||||||||
\(103\) | 2014.90 | 0.189924 | 0.0949619 | − | 0.995481i | \(-0.469727\pi\) | ||||
0.0949619 | + | 0.995481i | \(0.469727\pi\) | |||||||
\(104\) | 11697.4i | 1.08149i | ||||||||
\(105\) | − | 17167.2i | − | 1.55712i | ||||||
\(106\) | 5486.08i | 0.488259i | ||||||||
\(107\) | 8728.48 | 0.762379 | 0.381190 | − | 0.924497i | \(-0.375514\pi\) | ||||
0.381190 | + | 0.924497i | \(0.375514\pi\) | |||||||
\(108\) | − | 1028.77i | − | 0.0882007i | ||||||
\(109\) | −9286.44 | −0.781621 | −0.390811 | − | 0.920471i | \(-0.627805\pi\) | ||||
−0.390811 | + | 0.920471i | \(0.627805\pi\) | |||||||
\(110\) | 70.9221 | 0.00586133 | ||||||||
\(111\) | −18933.5 | −1.53668 | ||||||||
\(112\) | − | 3230.03i | − | 0.257496i | ||||||
\(113\) | − | 16690.4i | − | 1.30711i | −0.756881 | − | 0.653553i | \(-0.773278\pi\) | ||
0.756881 | − | 0.653553i | \(-0.226722\pi\) | |||||||
\(114\) | − | 945.771i | − | 0.0727740i | ||||||
\(115\) | − | 1744.45i | − | 0.131905i | ||||||
\(116\) | 5854.65i | 0.435096i | ||||||||
\(117\) | 12359.1 | 0.902849 | ||||||||
\(118\) | − | 9823.34i | − | 0.705497i | ||||||
\(119\) | 29720.4i | 2.09875i | ||||||||
\(120\) | 18234.5i | 1.26629i | ||||||||
\(121\) | −14639.6 | −0.999906 | ||||||||
\(122\) | 15016.3 | 1.00889 | ||||||||
\(123\) | 30278.7i | 2.00137i | ||||||||
\(124\) | 10002.6 | 0.650532 | ||||||||
\(125\) | − | 16855.4i | − | 1.07875i | ||||||
\(126\) | −12406.5 | −0.781466 | ||||||||
\(127\) | −17016.4 | −1.05502 | −0.527510 | − | 0.849549i | \(-0.676874\pi\) | ||||
−0.527510 | + | 0.849549i | \(0.676874\pi\) | |||||||
\(128\) | − | 5610.62i | − | 0.342445i | ||||||
\(129\) | 14368.5 | + | 17704.3i | 0.863440 | + | 1.06390i | ||||
\(130\) | 10538.2 | 0.623564 | ||||||||
\(131\) | − | 13378.5i | − | 0.779590i | −0.920902 | − | 0.389795i | \(-0.872546\pi\) | ||
0.920902 | − | 0.389795i | \(-0.127454\pi\) | |||||||
\(132\) | 121.247i | 0.00695863i | ||||||||
\(133\) | −1761.89 | −0.0996035 | ||||||||
\(134\) | − | 13590.8i | − | 0.756892i | ||||||
\(135\) | −2691.99 | −0.147709 | ||||||||
\(136\) | − | 31568.2i | − | 1.70676i | ||||||
\(137\) | 9129.47i | 0.486412i | 0.969975 | + | 0.243206i | \(0.0781991\pi\) | ||||
−0.969975 | + | 0.243206i | \(0.921801\pi\) | |||||||
\(138\) | −2697.54 | −0.141648 | ||||||||
\(139\) | 28220.0 | 1.46059 | 0.730293 | − | 0.683134i | \(-0.239384\pi\) | ||||
0.730293 | + | 0.683134i | \(0.239384\pi\) | |||||||
\(140\) | 11695.3 | 0.596700 | ||||||||
\(141\) | − | 20897.8i | − | 1.05114i | ||||||
\(142\) | 26630.8 | 1.32071 | ||||||||
\(143\) | 203.526 | 0.00995285 | ||||||||
\(144\) | 3624.94 | 0.174814 | ||||||||
\(145\) | 15319.9 | 0.728651 | ||||||||
\(146\) | 15462.4 | 0.725388 | ||||||||
\(147\) | 19845.7i | 0.918400i | ||||||||
\(148\) | − | 12898.6i | − | 0.588870i | ||||||
\(149\) | 11221.8i | 0.505464i | 0.967536 | + | 0.252732i | \(0.0813291\pi\) | ||||
−0.967536 | + | 0.252732i | \(0.918671\pi\) | |||||||
\(150\) | −4818.44 | −0.214153 | ||||||||
\(151\) | 37652.1i | 1.65133i | 0.564158 | + | 0.825667i | \(0.309201\pi\) | ||||
−0.564158 | + | 0.825667i | \(0.690799\pi\) | |||||||
\(152\) | 1871.43 | 0.0810002 | ||||||||
\(153\) | −33354.0 | −1.42484 | ||||||||
\(154\) | −204.307 | −0.00861474 | ||||||||
\(155\) | − | 26173.8i | − | 1.08944i | ||||||
\(156\) | 18016.0i | 0.740301i | ||||||||
\(157\) | − | 9904.16i | − | 0.401808i | −0.979611 | − | 0.200904i | \(-0.935612\pi\) | ||
0.979611 | − | 0.200904i | \(-0.0643879\pi\) | |||||||
\(158\) | 31490.9i | 1.26145i | ||||||||
\(159\) | 24541.8i | 0.970761i | ||||||||
\(160\) | −20568.0 | −0.803436 | ||||||||
\(161\) | 5025.27i | 0.193869i | ||||||||
\(162\) | 20031.6i | 0.763285i | ||||||||
\(163\) | 20673.8i | 0.778117i | 0.921213 | + | 0.389059i | \(0.127200\pi\) | ||||
−0.921213 | + | 0.389059i | \(0.872800\pi\) | |||||||
\(164\) | −20627.7 | −0.766942 | ||||||||
\(165\) | 317.268 | 0.0116536 | ||||||||
\(166\) | − | 15228.2i | − | 0.552629i | ||||||
\(167\) | −313.151 | −0.0112285 | −0.00561424 | − | 0.999984i | \(-0.501787\pi\) | ||||
−0.00561424 | + | 0.999984i | \(0.501787\pi\) | |||||||
\(168\) | − | 52528.7i | − | 1.86114i | ||||||
\(169\) | 1680.65 | 0.0588441 | ||||||||
\(170\) | −28439.9 | −0.984081 | ||||||||
\(171\) | − | 1977.30i | − | 0.0676207i | ||||||
\(172\) | −12061.2 | + | 9788.67i | −0.407694 | + | 0.330877i | ||||
\(173\) | −5952.11 | −0.198874 | −0.0994372 | − | 0.995044i | \(-0.531704\pi\) | ||||
−0.0994372 | + | 0.995044i | \(0.531704\pi\) | |||||||
\(174\) | − | 23690.0i | − | 0.782468i | ||||||
\(175\) | 8976.32i | 0.293104i | ||||||||
\(176\) | 59.6944 | 0.00192712 | ||||||||
\(177\) | − | 43944.4i | − | 1.40268i | ||||||
\(178\) | 7056.63 | 0.222719 | ||||||||
\(179\) | − | 39430.1i | − | 1.23062i | −0.788287 | − | 0.615308i | \(-0.789032\pi\) | ||
0.788287 | − | 0.615308i | \(-0.210968\pi\) | |||||||
\(180\) | 13125.2i | 0.405099i | ||||||||
\(181\) | 29726.1 | 0.907361 | 0.453681 | − | 0.891164i | \(-0.350111\pi\) | ||||
0.453681 | + | 0.891164i | \(0.350111\pi\) | |||||||
\(182\) | −30357.7 | −0.916488 | ||||||||
\(183\) | 67174.9 | 2.00588 | ||||||||
\(184\) | − | 5337.71i | − | 0.157659i | ||||||
\(185\) | −33751.8 | −0.986174 | ||||||||
\(186\) | −40474.0 | −1.16991 | ||||||||
\(187\) | −549.264 | −0.0157072 | ||||||||
\(188\) | 14236.8 | 0.402806 | ||||||||
\(189\) | 7754.90 | 0.217096 | ||||||||
\(190\) | − | 1685.98i | − | 0.0467031i | ||||||
\(191\) | − | 35347.9i | − | 0.968940i | −0.874808 | − | 0.484470i | \(-0.839012\pi\) | ||
0.874808 | − | 0.484470i | \(-0.160988\pi\) | |||||||
\(192\) | 41869.1i | 1.13577i | ||||||||
\(193\) | −74147.3 | −1.99058 | −0.995292 | − | 0.0969181i | \(-0.969102\pi\) | ||||
−0.995292 | + | 0.0969181i | \(0.969102\pi\) | |||||||
\(194\) | − | 10088.6i | − | 0.268058i | ||||||
\(195\) | 47142.4 | 1.23978 | ||||||||
\(196\) | −13520.1 | −0.351938 | ||||||||
\(197\) | 33924.2 | 0.874133 | 0.437066 | − | 0.899429i | \(-0.356017\pi\) | ||||
0.437066 | + | 0.899429i | \(0.356017\pi\) | |||||||
\(198\) | − | 229.286i | − | 0.00584854i | ||||||
\(199\) | 20327.0i | 0.513296i | 0.966505 | + | 0.256648i | \(0.0826182\pi\) | ||||
−0.966505 | + | 0.256648i | \(0.917382\pi\) | |||||||
\(200\) | − | 9534.40i | − | 0.238360i | ||||||
\(201\) | − | 60797.9i | − | 1.50486i | ||||||
\(202\) | 28958.6i | 0.709701i | ||||||||
\(203\) | −44132.4 | −1.07094 | ||||||||
\(204\) | − | 48620.5i | − | 1.16831i | ||||||
\(205\) | 53976.5i | 1.28439i | ||||||||
\(206\) | − | 5554.31i | − | 0.130887i | ||||||
\(207\) | −5639.67 | −0.131617 | ||||||||
\(208\) | 8869.91 | 0.205018 | ||||||||
\(209\) | − | 32.5615i | − | 0.000745439i | ||||||
\(210\) | −47323.4 | −1.07309 | ||||||||
\(211\) | 6957.00i | 0.156263i | 0.996943 | + | 0.0781316i | \(0.0248954\pi\) | ||||
−0.996943 | + | 0.0781316i | \(0.975105\pi\) | |||||||
\(212\) | −16719.3 | −0.372004 | ||||||||
\(213\) | 119132. | 2.62585 | ||||||||
\(214\) | − | 24061.1i | − | 0.525397i | ||||||
\(215\) | 25614.1 | + | 31560.6i | 0.554117 | + | 0.682761i | ||||
\(216\) | −8237.04 | −0.176548 | ||||||||
\(217\) | 75399.5i | 1.60121i | ||||||||
\(218\) | 25599.2i | 0.538658i | ||||||||
\(219\) | 69170.4 | 1.44222 | ||||||||
\(220\) | 216.142i | 0.00446574i | ||||||||
\(221\) | −81614.4 | −1.67102 | ||||||||
\(222\) | 52192.3i | 1.05901i | ||||||||
\(223\) | 2228.35i | 0.0448099i | 0.999749 | + | 0.0224050i | \(0.00713232\pi\) | ||||
−0.999749 | + | 0.0224050i | \(0.992868\pi\) | |||||||
\(224\) | 59250.7 | 1.18086 | ||||||||
\(225\) | −10073.8 | −0.198988 | ||||||||
\(226\) | −46009.1 | −0.900798 | ||||||||
\(227\) | − | 61573.4i | − | 1.19493i | −0.801896 | − | 0.597464i | \(-0.796175\pi\) | ||
0.801896 | − | 0.597464i | \(-0.203825\pi\) | |||||||
\(228\) | 2882.32 | 0.0554464 | ||||||||
\(229\) | −40330.0 | −0.769054 | −0.384527 | − | 0.923114i | \(-0.625635\pi\) | ||||
−0.384527 | + | 0.923114i | \(0.625635\pi\) | |||||||
\(230\) | −4808.77 | −0.0909031 | ||||||||
\(231\) | −913.962 | −0.0171279 | ||||||||
\(232\) | 46876.2 | 0.870917 | ||||||||
\(233\) | − | 74382.7i | − | 1.37013i | −0.728484 | − | 0.685063i | \(-0.759775\pi\) | ||
0.728484 | − | 0.685063i | \(-0.240225\pi\) | |||||||
\(234\) | − | 34069.3i | − | 0.622203i | ||||||
\(235\) | − | 37253.4i | − | 0.674576i | ||||||
\(236\) | 29937.5 | 0.537517 | ||||||||
\(237\) | 140874.i | 2.50803i | ||||||||
\(238\) | 81927.7 | 1.44636 | ||||||||
\(239\) | 11874.5 | 0.207883 | 0.103942 | − | 0.994583i | \(-0.466854\pi\) | ||||
0.103942 | + | 0.994583i | \(0.466854\pi\) | |||||||
\(240\) | 13826.9 | 0.240051 | ||||||||
\(241\) | − | 23536.3i | − | 0.405233i | −0.979258 | − | 0.202616i | \(-0.935056\pi\) | ||
0.979258 | − | 0.202616i | \(-0.0649444\pi\) | |||||||
\(242\) | 40355.9i | 0.689090i | ||||||||
\(243\) | 79691.9i | 1.34959i | ||||||||
\(244\) | 45763.6i | 0.768670i | ||||||||
\(245\) | 35378.0i | 0.589388i | ||||||||
\(246\) | 83466.9 | 1.37925 | ||||||||
\(247\) | − | 4838.28i | − | 0.0793043i | ||||||
\(248\) | − | 80087.3i | − | 1.30215i | ||||||
\(249\) | − | 68123.1i | − | 1.09874i | ||||||
\(250\) | −46463.9 | −0.743423 | ||||||||
\(251\) | −54757.4 | −0.869151 | −0.434575 | − | 0.900635i | \(-0.643102\pi\) | ||||
−0.434575 | + | 0.900635i | \(0.643102\pi\) | |||||||
\(252\) | − | 37810.1i | − | 0.595397i | ||||||
\(253\) | −92.8723 | −0.00145093 | ||||||||
\(254\) | 46907.8i | 0.727072i | ||||||||
\(255\) | −127225. | −1.95656 | ||||||||
\(256\) | −69790.4 | −1.06492 | ||||||||
\(257\) | 57759.9i | 0.874501i | 0.899340 | + | 0.437250i | \(0.144048\pi\) | ||||
−0.899340 | + | 0.437250i | \(0.855952\pi\) | |||||||
\(258\) | 48804.0 | − | 39608.5i | 0.733189 | − | 0.595043i | ||||
\(259\) | 97229.7 | 1.44944 | ||||||||
\(260\) | 32116.2i | 0.475092i | ||||||||
\(261\) | − | 49528.1i | − | 0.727060i | ||||||
\(262\) | −36879.5 | −0.537258 | ||||||||
\(263\) | − | 7567.24i | − | 0.109402i | −0.998503 | − | 0.0547011i | \(-0.982579\pi\) | ||
0.998503 | − | 0.0547011i | \(-0.0174206\pi\) | |||||||
\(264\) | 970.786 | 0.0139289 | ||||||||
\(265\) | 43749.5i | 0.622991i | ||||||||
\(266\) | 4856.85i | 0.0686422i | ||||||||
\(267\) | 31567.6 | 0.442812 | ||||||||
\(268\) | 41419.1 | 0.576675 | ||||||||
\(269\) | −39923.2 | −0.551723 | −0.275861 | − | 0.961197i | \(-0.588963\pi\) | ||||
−0.275861 | + | 0.961197i | \(0.588963\pi\) | |||||||
\(270\) | 7420.80i | 0.101794i | ||||||||
\(271\) | 119787. | 1.63107 | 0.815533 | − | 0.578710i | \(-0.196444\pi\) | ||||
0.815533 | + | 0.578710i | \(0.196444\pi\) | |||||||
\(272\) | −23937.6 | −0.323551 | ||||||||
\(273\) | −135804. | −1.82217 | ||||||||
\(274\) | 25166.5 | 0.335213 | ||||||||
\(275\) | −165.892 | −0.00219361 | ||||||||
\(276\) | − | 8221.00i | − | 0.107921i | ||||||
\(277\) | − | 37526.7i | − | 0.489081i | −0.969639 | − | 0.244540i | \(-0.921363\pi\) | ||
0.969639 | − | 0.244540i | \(-0.0786371\pi\) | |||||||
\(278\) | − | 77791.7i | − | 1.00657i | ||||||
\(279\) | −84618.0 | −1.08706 | ||||||||
\(280\) | − | 93640.4i | − | 1.19439i | ||||||
\(281\) | −29935.1 | −0.379113 | −0.189556 | − | 0.981870i | \(-0.560705\pi\) | ||||
−0.189556 | + | 0.981870i | \(0.560705\pi\) | |||||||
\(282\) | −57607.1 | −0.724399 | ||||||||
\(283\) | −54918.3 | −0.685716 | −0.342858 | − | 0.939387i | \(-0.611395\pi\) | ||||
−0.342858 | + | 0.939387i | \(0.611395\pi\) | |||||||
\(284\) | 81159.9i | 1.00625i | ||||||||
\(285\) | − | 7542.19i | − | 0.0928555i | ||||||
\(286\) | − | 561.043i | − | 0.00685905i | ||||||
\(287\) | − | 155491.i | − | 1.88774i | ||||||
\(288\) | 66494.7i | 0.801682i | ||||||||
\(289\) | 136735. | 1.63713 | ||||||||
\(290\) | − | 42231.1i | − | 0.502153i | ||||||
\(291\) | − | 45131.3i | − | 0.532956i | ||||||
\(292\) | 47123.0i | 0.552672i | ||||||||
\(293\) | −155740. | −1.81412 | −0.907060 | − | 0.421002i | \(-0.861678\pi\) | ||||
−0.907060 | + | 0.421002i | \(0.861678\pi\) | |||||||
\(294\) | 54707.0 | 0.632919 | ||||||||
\(295\) | − | 78337.6i | − | 0.900174i | ||||||
\(296\) | −103275. | −1.17872 | ||||||||
\(297\) | 143.319i | 0.00162476i | ||||||||
\(298\) | 30934.2 | 0.348343 | ||||||||
\(299\) | −13799.8 | −0.154358 | ||||||||
\(300\) | − | 14684.6i | − | 0.163163i | ||||||
\(301\) | −73787.1 | − | 90917.5i | −0.814418 | − | 1.00349i | ||||
\(302\) | 103792. | 1.13802 | ||||||||
\(303\) | 129546.i | 1.41103i | ||||||||
\(304\) | − | 1419.07i | − | 0.0153553i | ||||||
\(305\) | 119750. | 1.28728 | ||||||||
\(306\) | 91944.3i | 0.981933i | ||||||||
\(307\) | 70887.6 | 0.752131 | 0.376065 | − | 0.926593i | \(-0.377277\pi\) | ||||
0.376065 | + | 0.926593i | \(0.377277\pi\) | |||||||
\(308\) | − | 622.645i | − | 0.00656356i | ||||||
\(309\) | − | 24847.1i | − | 0.260230i | ||||||
\(310\) | −72151.2 | −0.750793 | ||||||||
\(311\) | −27909.5 | −0.288557 | −0.144278 | − | 0.989537i | \(-0.546086\pi\) | ||||
−0.144278 | + | 0.989537i | \(0.546086\pi\) | |||||||
\(312\) | 144248. | 1.48184 | ||||||||
\(313\) | 50613.7i | 0.516630i | 0.966061 | + | 0.258315i | \(0.0831672\pi\) | ||||
−0.966061 | + | 0.258315i | \(0.916833\pi\) | |||||||
\(314\) | −27302.0 | −0.276908 | ||||||||
\(315\) | −98937.8 | −0.997106 | ||||||||
\(316\) | −95971.5 | −0.961099 | ||||||||
\(317\) | 111161. | 1.10620 | 0.553099 | − | 0.833116i | \(-0.313445\pi\) | ||||
0.553099 | + | 0.833116i | \(0.313445\pi\) | |||||||
\(318\) | 67652.4 | 0.669004 | ||||||||
\(319\) | − | 815.613i | − | 0.00801498i | ||||||
\(320\) | 74638.1i | 0.728888i | ||||||||
\(321\) | − | 107637.i | − | 1.04460i | ||||||
\(322\) | 13852.8 | 0.133606 | ||||||||
\(323\) | 13057.3i | 0.125155i | ||||||||
\(324\) | −61048.3 | −0.581546 | ||||||||
\(325\) | −24649.7 | −0.233369 | ||||||||
\(326\) | 56989.8 | 0.536243 | ||||||||
\(327\) | 114517.i | 1.07096i | ||||||||
\(328\) | 165159.i | 1.53516i | ||||||||
\(329\) | 107317.i | 0.991463i | ||||||||
\(330\) | − | 874.587i | − | 0.00803110i | ||||||
\(331\) | − | 199722.i | − | 1.82293i | −0.411376 | − | 0.911466i | \(-0.634952\pi\) | ||
0.411376 | − | 0.911466i | \(-0.365048\pi\) | |||||||
\(332\) | 46409.5 | 0.421047 | ||||||||
\(333\) | 109117.i | 0.984021i | ||||||||
\(334\) | 863.238i | 0.00773816i | ||||||||
\(335\) | − | 108381.i | − | 0.965752i | ||||||
\(336\) | −39831.6 | −0.352817 | ||||||||
\(337\) | −19032.7 | −0.167588 | −0.0837938 | − | 0.996483i | \(-0.526704\pi\) | ||||
−0.0837938 | + | 0.996483i | \(0.526704\pi\) | |||||||
\(338\) | − | 4632.90i | − | 0.0405527i | ||||||
\(339\) | −205821. | −1.79097 | ||||||||
\(340\) | − | 86673.4i | − | 0.749770i | ||||||
\(341\) | −1393.46 | −0.0119836 | ||||||||
\(342\) | −5450.66 | −0.0466011 | ||||||||
\(343\) | 50134.2i | 0.426134i | ||||||||
\(344\) | 78374.6 | + | 96570.1i | 0.662306 | + | 0.816067i | ||||
\(345\) | −21511.9 | −0.180734 | ||||||||
\(346\) | 16407.7i | 0.137055i | ||||||||
\(347\) | − | 13299.5i | − | 0.110453i | −0.998474 | − | 0.0552263i | \(-0.982412\pi\) | ||
0.998474 | − | 0.0552263i | \(-0.0175880\pi\) | |||||||
\(348\) | 72197.5 | 0.596161 | ||||||||
\(349\) | 207713.i | 1.70535i | 0.522442 | + | 0.852675i | \(0.325021\pi\) | ||||
−0.522442 | + | 0.852675i | \(0.674979\pi\) | |||||||
\(350\) | 24744.3 | 0.201994 | ||||||||
\(351\) | 21295.5i | 0.172852i | ||||||||
\(352\) | 1095.01i | 0.00883760i | ||||||||
\(353\) | 69576.5 | 0.558358 | 0.279179 | − | 0.960239i | \(-0.409938\pi\) | ||||
0.279179 | + | 0.960239i | \(0.409938\pi\) | |||||||
\(354\) | −121138. | −0.966660 | ||||||||
\(355\) | 212371. | 1.68515 | ||||||||
\(356\) | 21505.7i | 0.169689i | ||||||||
\(357\) | 366501. | 2.87567 | ||||||||
\(358\) | −108694. | −0.848084 | ||||||||
\(359\) | −165095. | −1.28099 | −0.640495 | − | 0.767963i | \(-0.721271\pi\) | ||||
−0.640495 | + | 0.767963i | \(0.721271\pi\) | |||||||
\(360\) | 105089. | 0.810872 | ||||||||
\(361\) | 129547. | 0.994060 | ||||||||
\(362\) | − | 81943.4i | − | 0.625312i | ||||||
\(363\) | 180531.i | 1.37006i | ||||||||
\(364\) | − | 92518.1i | − | 0.698271i | ||||||
\(365\) | 123307. | 0.925554 | ||||||||
\(366\) | − | 185176.i | − | 1.38236i | ||||||
\(367\) | −58660.7 | −0.435527 | −0.217764 | − | 0.976002i | \(-0.569876\pi\) | ||||
−0.217764 | + | 0.976002i | \(0.569876\pi\) | |||||||
\(368\) | −4047.49 | −0.0298876 | ||||||||
\(369\) | 174502. | 1.28159 | ||||||||
\(370\) | 93040.8i | 0.679626i | ||||||||
\(371\) | − | 126030.i | − | 0.915645i | ||||||
\(372\) | − | 123348.i | − | 0.891349i | ||||||
\(373\) | − | 179031.i | − | 1.28680i | −0.765530 | − | 0.643401i | \(-0.777523\pi\) | ||
0.765530 | − | 0.643401i | \(-0.222477\pi\) | |||||||
\(374\) | 1514.11i | 0.0108247i | ||||||||
\(375\) | −207855. | −1.47808 | ||||||||
\(376\) | − | 113989.i | − | 0.806284i | ||||||
\(377\) | − | 121191.i | − | 0.852682i | ||||||
\(378\) | − | 21377.3i | − | 0.149613i | ||||||
\(379\) | −47513.9 | −0.330783 | −0.165391 | − | 0.986228i | \(-0.552889\pi\) | ||||
−0.165391 | + | 0.986228i | \(0.552889\pi\) | |||||||
\(380\) | 5138.19 | 0.0355830 | ||||||||
\(381\) | 209840.i | 1.44557i | ||||||||
\(382\) | −97440.7 | −0.667749 | ||||||||
\(383\) | 59722.7i | 0.407138i | 0.979061 | + | 0.203569i | \(0.0652541\pi\) | ||||
−0.979061 | + | 0.203569i | \(0.934746\pi\) | |||||||
\(384\) | −69188.2 | −0.469212 | ||||||||
\(385\) | −1629.28 | −0.0109919 | ||||||||
\(386\) | 204396.i | 1.37182i | ||||||||
\(387\) | 102033. | − | 82808.4i | 0.681271 | − | 0.552907i | ||||
\(388\) | 30746.1 | 0.204233 | ||||||||
\(389\) | − | 254851.i | − | 1.68417i | −0.539343 | − | 0.842086i | \(-0.681327\pi\) | ||
0.539343 | − | 0.842086i | \(-0.318673\pi\) | |||||||
\(390\) | − | 129954.i | − | 0.854397i | ||||||
\(391\) | 37242.0 | 0.243601 | ||||||||
\(392\) | 108251.i | 0.704463i | ||||||||
\(393\) | −164980. | −1.06818 | ||||||||
\(394\) | − | 93516.1i | − | 0.602413i | ||||||
\(395\) | 251129.i | 1.60954i | ||||||||
\(396\) | 698.771 | 0.00445599 | ||||||||
\(397\) | −79062.9 | −0.501639 | −0.250820 | − | 0.968034i | \(-0.580700\pi\) | ||||
−0.250820 | + | 0.968034i | \(0.580700\pi\) | |||||||
\(398\) | 56033.9 | 0.353741 | ||||||||
\(399\) | 21727.0i | 0.136475i | ||||||||
\(400\) | −7229.77 | −0.0451861 | ||||||||
\(401\) | −196389. | −1.22132 | −0.610658 | − | 0.791894i | \(-0.709095\pi\) | ||||
−0.610658 | + | 0.791894i | \(0.709095\pi\) | |||||||
\(402\) | −167597. | −1.03708 | ||||||||
\(403\) | −207053. | −1.27489 | ||||||||
\(404\) | −88254.1 | −0.540720 | ||||||||
\(405\) | 159745.i | 0.973908i | ||||||||
\(406\) | 121656.i | 0.738043i | ||||||||
\(407\) | 1796.91i | 0.0108477i | ||||||||
\(408\) | −389288. | −2.33857 | ||||||||
\(409\) | − | 115044.i | − | 0.687729i | −0.939019 | − | 0.343864i | \(-0.888264\pi\) | ||
0.939019 | − | 0.343864i | \(-0.111736\pi\) | |||||||
\(410\) | 148793. | 0.885143 | ||||||||
\(411\) | 112581. | 0.666474 | ||||||||
\(412\) | 16927.3 | 0.0997225 | ||||||||
\(413\) | 225669.i | 1.32304i | ||||||||
\(414\) | 15546.4i | 0.0907047i | ||||||||
\(415\) | − | 121440.i | − | 0.705123i | ||||||
\(416\) | 162707.i | 0.940198i | ||||||||
\(417\) | − | 347999.i | − | 2.00127i | ||||||
\(418\) | −89.7597 | −0.000513723 | ||||||||
\(419\) | 281568.i | 1.60382i | 0.597446 | + | 0.801909i | \(0.296182\pi\) | ||||
−0.597446 | + | 0.801909i | \(0.703818\pi\) | |||||||
\(420\) | − | 144223.i | − | 0.817588i | ||||||
\(421\) | 182603.i | 1.03025i | 0.857115 | + | 0.515125i | \(0.172255\pi\) | ||||
−0.857115 | + | 0.515125i | \(0.827745\pi\) | |||||||
\(422\) | 19177.8 | 0.107690 | ||||||||
\(423\) | −120438. | −0.673103 | ||||||||
\(424\) | 133866.i | 0.744627i | ||||||||
\(425\) | 66523.0 | 0.368294 | ||||||||
\(426\) | − | 328402.i | − | 1.80962i | ||||||
\(427\) | −344966. | −1.89200 | ||||||||
\(428\) | 73328.4 | 0.400299 | ||||||||
\(429\) | − | 2509.81i | − | 0.0136372i | ||||||
\(430\) | 87000.6 | − | 70608.2i | 0.470528 | − | 0.381872i | ||||
\(431\) | 295412. | 1.59028 | 0.795139 | − | 0.606427i | \(-0.207398\pi\) | ||||
0.795139 | + | 0.606427i | \(0.207398\pi\) | |||||||
\(432\) | 6246.01i | 0.0334684i | ||||||||
\(433\) | − | 315628.i | − | 1.68345i | −0.539908 | − | 0.841724i | \(-0.681541\pi\) | ||
0.539908 | − | 0.841724i | \(-0.318459\pi\) | |||||||
\(434\) | 207848. | 1.10348 | ||||||||
\(435\) | − | 188919.i | − | 0.998385i | ||||||
\(436\) | −78015.9 | −0.410403 | ||||||||
\(437\) | 2207.79i | 0.0115610i | ||||||||
\(438\) | − | 190677.i | − | 0.993915i | ||||||
\(439\) | 289252. | 1.50088 | 0.750442 | − | 0.660937i | \(-0.229841\pi\) | ||||
0.750442 | + | 0.660937i | \(0.229841\pi\) | |||||||
\(440\) | 1730.57 | 0.00893892 | ||||||||
\(441\) | 114375. | 0.588101 | ||||||||
\(442\) | 224980.i | 1.15159i | ||||||||
\(443\) | −13612.9 | −0.0693655 | −0.0346827 | − | 0.999398i | \(-0.511042\pi\) | ||||
−0.0346827 | + | 0.999398i | \(0.511042\pi\) | |||||||
\(444\) | −159061. | −0.806859 | ||||||||
\(445\) | 56274.1 | 0.284177 | ||||||||
\(446\) | 6142.72 | 0.0308810 | ||||||||
\(447\) | 138383. | 0.692578 | ||||||||
\(448\) | − | 215012.i | − | 1.07129i | ||||||
\(449\) | 164810.i | 0.817506i | 0.912645 | + | 0.408753i | \(0.134036\pi\) | ||||
−0.912645 | + | 0.408753i | \(0.865964\pi\) | |||||||
\(450\) | 27769.6i | 0.137134i | ||||||||
\(451\) | 2873.65 | 0.0141280 | ||||||||
\(452\) | − | 140217.i | − | 0.686316i | ||||||
\(453\) | 464312. | 2.26263 | ||||||||
\(454\) | −169734. | −0.823490 | ||||||||
\(455\) | −242092. | −1.16939 | ||||||||
\(456\) | − | 23077.8i | − | 0.110985i | ||||||
\(457\) | 157048.i | 0.751971i | 0.926626 | + | 0.375985i | \(0.122696\pi\) | ||||
−0.926626 | + | 0.375985i | \(0.877304\pi\) | |||||||
\(458\) | 111174.i | 0.529997i | ||||||||
\(459\) | − | 57471.2i | − | 0.272788i | ||||||
\(460\) | − | 14655.2i | − | 0.0692589i | ||||||
\(461\) | 332439. | 1.56426 | 0.782131 | − | 0.623114i | \(-0.214133\pi\) | ||||
0.782131 | + | 0.623114i | \(0.214133\pi\) | |||||||
\(462\) | 2519.44i | 0.0118038i | ||||||||
\(463\) | 197697.i | 0.922226i | 0.887341 | + | 0.461113i | \(0.152550\pi\) | ||||
−0.887341 | + | 0.461113i | \(0.847450\pi\) | |||||||
\(464\) | − | 35545.4i | − | 0.165100i | ||||||
\(465\) | −322766. | −1.49273 | ||||||||
\(466\) | −205045. | −0.944228 | ||||||||
\(467\) | − | 121639.i | − | 0.557749i | −0.960328 | − | 0.278874i | \(-0.910039\pi\) | ||
0.960328 | − | 0.278874i | \(-0.0899613\pi\) | |||||||
\(468\) | 103829. | 0.474055 | ||||||||
\(469\) | 312217.i | 1.41942i | ||||||||
\(470\) | −102694. | −0.464887 | ||||||||
\(471\) | −122135. | −0.550550 | ||||||||
\(472\) | − | 239700.i | − | 1.07593i | ||||||
\(473\) | 1680.25 | − | 1363.66i | 0.00751021 | − | 0.00609515i | ||||
\(474\) | 388335. | 1.72842 | ||||||||
\(475\) | 3943.63i | 0.0174787i | ||||||||
\(476\) | 249682.i | 1.10198i | ||||||||
\(477\) | 141439. | 0.621631 | ||||||||
\(478\) | − | 32733.5i | − | 0.143264i | ||||||
\(479\) | −141700. | −0.617586 | −0.308793 | − | 0.951129i | \(-0.599925\pi\) | ||||
−0.308793 | + | 0.951129i | \(0.599925\pi\) | |||||||
\(480\) | 253637.i | 1.10085i | ||||||||
\(481\) | 267000.i | 1.15404i | ||||||||
\(482\) | −64880.6 | −0.279268 | ||||||||
\(483\) | 61969.9 | 0.265636 | ||||||||
\(484\) | −122988. | −0.525017 | ||||||||
\(485\) | − | 80453.4i | − | 0.342027i | ||||||
\(486\) | 219680. | 0.930076 | ||||||||
\(487\) | 194637. | 0.820668 | 0.410334 | − | 0.911935i | \(-0.365412\pi\) | ||||
0.410334 | + | 0.911935i | \(0.365412\pi\) | |||||||
\(488\) | 366413. | 1.53862 | ||||||||
\(489\) | 254942. | 1.06616 | ||||||||
\(490\) | 97523.6 | 0.406179 | ||||||||
\(491\) | − | 143694.i | − | 0.596040i | −0.954560 | − | 0.298020i | \(-0.903674\pi\) | ||
0.954560 | − | 0.298020i | \(-0.0963263\pi\) | |||||||
\(492\) | 254373.i | 1.05085i | ||||||||
\(493\) | 327063.i | 1.34567i | ||||||||
\(494\) | −13337.3 | −0.0546529 | ||||||||
\(495\) | − | 1828.48i | − | 0.00746240i | ||||||
\(496\) | −60728.9 | −0.246849 | ||||||||
\(497\) | −611783. | −2.47676 | ||||||||
\(498\) | −187789. | −0.757203 | ||||||||
\(499\) | − | 328853.i | − | 1.32069i | −0.750962 | − | 0.660345i | \(-0.770410\pi\) | ||
0.750962 | − | 0.660345i | \(-0.229590\pi\) | |||||||
\(500\) | − | 141603.i | − | 0.566413i | ||||||
\(501\) | 3861.67i | 0.0153851i | ||||||||
\(502\) | 150945.i | 0.598979i | ||||||||
\(503\) | − | 278129.i | − | 1.09929i | −0.835399 | − | 0.549643i | \(-0.814764\pi\) | ||
0.835399 | − | 0.549643i | \(-0.185236\pi\) | |||||||
\(504\) | −302733. | −1.19179 | ||||||||
\(505\) | 230935.i | 0.905538i | ||||||||
\(506\) | 256.014i | 0.000999912i | ||||||||
\(507\) | − | 20725.2i | − | 0.0806273i | ||||||
\(508\) | −142956. | −0.553955 | ||||||||
\(509\) | 53485.5 | 0.206443 | 0.103222 | − | 0.994658i | \(-0.467085\pi\) | ||||
0.103222 | + | 0.994658i | \(0.467085\pi\) | |||||||
\(510\) | 350712.i | 1.34837i | ||||||||
\(511\) | −355213. | −1.36034 | ||||||||
\(512\) | 102616.i | 0.391448i | ||||||||
\(513\) | 3407.01 | 0.0129461 | ||||||||
\(514\) | 159222. | 0.602666 | ||||||||
\(515\) | − | 44293.7i | − | 0.167004i | ||||||
\(516\) | 120711. | + | 148735.i | 0.453363 | + | 0.558616i | ||||
\(517\) | −1983.33 | −0.00742017 | ||||||||
\(518\) | − | 268025.i | − | 0.998886i | ||||||
\(519\) | 73399.4i | 0.272494i | ||||||||
\(520\) | 257144. | 0.950976 | ||||||||
\(521\) | 43791.8i | 0.161331i | 0.996741 | + | 0.0806655i | \(0.0257045\pi\) | ||||
−0.996741 | + | 0.0806655i | \(0.974295\pi\) | |||||||
\(522\) | −136530. | −0.501057 | ||||||||
\(523\) | − | 104920.i | − | 0.383578i | −0.981436 | − | 0.191789i | \(-0.938571\pi\) | ||
0.981436 | − | 0.191789i | \(-0.0614290\pi\) | |||||||
\(524\) | − | 112394.i | − | 0.409336i | ||||||
\(525\) | 110693. | 0.401607 | ||||||||
\(526\) | −20860.0 | −0.0753950 | ||||||||
\(527\) | 558782. | 2.01197 | ||||||||
\(528\) | − | 736.130i | − | 0.00264050i | ||||||
\(529\) | −273544. | −0.977498 | ||||||||
\(530\) | 120601. | 0.429337 | ||||||||
\(531\) | −253260. | −0.898209 | ||||||||
\(532\) | −14801.7 | −0.0522984 | ||||||||
\(533\) | 426991. | 1.50302 | ||||||||
\(534\) | − | 87019.9i | − | 0.305166i | ||||||
\(535\) | − | 191879.i | − | 0.670377i | ||||||
\(536\) | − | 331629.i | − | 1.15431i | ||||||
\(537\) | −486239. | −1.68617 | ||||||||
\(538\) | 110053.i | 0.380222i | ||||||||
\(539\) | 1883.48 | 0.00648312 | ||||||||
\(540\) | −22615.6 | −0.0775569 | ||||||||
\(541\) | −60893.0 | −0.208052 | −0.104026 | − | 0.994575i | \(-0.533173\pi\) | ||||
−0.104026 | + | 0.994575i | \(0.533173\pi\) | |||||||
\(542\) | − | 330208.i | − | 1.12406i | ||||||
\(543\) | − | 366571.i | − | 1.24325i | ||||||
\(544\) | − | 439104.i | − | 1.48378i | ||||||
\(545\) | 204144.i | 0.687297i | ||||||||
\(546\) | 374361.i | 1.25576i | ||||||||
\(547\) | 77111.4 | 0.257717 | 0.128859 | − | 0.991663i | \(-0.458869\pi\) | ||||
0.128859 | + | 0.991663i | \(0.458869\pi\) | |||||||
\(548\) | 76697.1i | 0.255398i | ||||||||
\(549\) | − | 387142.i | − | 1.28447i | ||||||
\(550\) | 457.300i | 0.00151174i | ||||||||
\(551\) | −19389.0 | −0.0638634 | ||||||||
\(552\) | −65822.7 | −0.216022 | ||||||||
\(553\) | − | 723434.i | − | 2.36564i | ||||||
\(554\) | −103447. | −0.337052 | ||||||||
\(555\) | 416215.i | 1.35124i | ||||||||
\(556\) | 237078. | 0.766904 | ||||||||
\(557\) | −496754. | −1.60115 | −0.800573 | − | 0.599235i | \(-0.795471\pi\) | ||||
−0.800573 | + | 0.599235i | \(0.795471\pi\) | |||||||
\(558\) | 233260.i | 0.749154i | ||||||||
\(559\) | 249666. | − | 202625.i | 0.798981 | − | 0.648439i | ||||
\(560\) | −71006.0 | −0.226422 | ||||||||
\(561\) | 6773.33i | 0.0215217i | ||||||||
\(562\) | 82519.7i | 0.261267i | ||||||||
\(563\) | −510115. | −1.60935 | −0.804676 | − | 0.593714i | \(-0.797661\pi\) | ||||
−0.804676 | + | 0.593714i | \(0.797661\pi\) | |||||||
\(564\) | − | 175563.i | − | 0.551919i | ||||||
\(565\) | −366907. | −1.14937 | ||||||||
\(566\) | 151389.i | 0.472564i | ||||||||
\(567\) | − | 460182.i | − | 1.43141i | ||||||
\(568\) | 649820. | 2.01417 | ||||||||
\(569\) | −18540.2 | −0.0572650 | −0.0286325 | − | 0.999590i | \(-0.509115\pi\) | ||||
−0.0286325 | + | 0.999590i | \(0.509115\pi\) | |||||||
\(570\) | −20790.9 | −0.0639918 | ||||||||
\(571\) | 145098.i | 0.445029i | 0.974929 | + | 0.222515i | \(0.0714266\pi\) | ||||
−0.974929 | + | 0.222515i | \(0.928573\pi\) | |||||||
\(572\) | 1709.83 | 0.00522590 | ||||||||
\(573\) | −435898. | −1.32763 | ||||||||
\(574\) | −428631. | −1.30095 | ||||||||
\(575\) | 11248.1 | 0.0340206 | ||||||||
\(576\) | 241300. | 0.727297 | ||||||||
\(577\) | 492406.i | 1.47901i | 0.673150 | + | 0.739506i | \(0.264941\pi\) | ||||
−0.673150 | + | 0.739506i | \(0.735059\pi\) | |||||||
\(578\) | − | 376927.i | − | 1.12824i | ||||||
\(579\) | 914359.i | 2.72747i | ||||||||
\(580\) | 128703. | 0.382590 | ||||||||
\(581\) | 349835.i | 1.03636i | ||||||||
\(582\) | −124410. | −0.367289 | ||||||||
\(583\) | 2329.17 | 0.00685275 | ||||||||
\(584\) | 377298. | 1.10626 | ||||||||
\(585\) | − | 271691.i | − | 0.793895i | ||||||
\(586\) | 429317.i | 1.25021i | ||||||||
\(587\) | 113204.i | 0.328539i | 0.986416 | + | 0.164269i | \(0.0525266\pi\) | ||||
−0.986416 | + | 0.164269i | \(0.947473\pi\) | |||||||
\(588\) | 166725.i | 0.482220i | ||||||||
\(589\) | 33125.8i | 0.0954852i | ||||||||
\(590\) | −215947. | −0.620359 | ||||||||
\(591\) | − | 418342.i | − | 1.19772i | ||||||
\(592\) | 78311.5i | 0.223451i | ||||||||
\(593\) | − | 378754.i | − | 1.07708i | −0.842600 | − | 0.538540i | \(-0.818976\pi\) | ||
0.842600 | − | 0.538540i | \(-0.181024\pi\) | |||||||
\(594\) | 395.075 | 0.00111971 | ||||||||
\(595\) | 653344. | 1.84548 | ||||||||
\(596\) | 94275.0i | 0.265402i | ||||||||
\(597\) | 250666. | 0.703310 | ||||||||
\(598\) | 38040.7i | 0.106377i | ||||||||
\(599\) | −70600.5 | −0.196768 | −0.0983840 | − | 0.995149i | \(-0.531367\pi\) | ||||
−0.0983840 | + | 0.995149i | \(0.531367\pi\) | |||||||
\(600\) | −117575. | −0.326597 | ||||||||
\(601\) | − | 576111.i | − | 1.59499i | −0.603327 | − | 0.797494i | \(-0.706159\pi\) | ||
0.603327 | − | 0.797494i | \(-0.293841\pi\) | |||||||
\(602\) | −250625. | + | 203403.i | −0.691562 | + | 0.561260i | ||||
\(603\) | −350390. | −0.963644 | ||||||||
\(604\) | 316317.i | 0.867059i | ||||||||
\(605\) | 321824.i | 0.879240i | ||||||||
\(606\) | 357108. | 0.972420 | ||||||||
\(607\) | − | 179183.i | − | 0.486317i | −0.969987 | − | 0.243159i | \(-0.921816\pi\) | ||
0.969987 | − | 0.243159i | \(-0.0781835\pi\) | |||||||
\(608\) | 26031.0 | 0.0704180 | ||||||||
\(609\) | 544225.i | 1.46738i | ||||||||
\(610\) | − | 330104.i | − | 0.887138i | ||||||
\(611\) | −294701. | −0.789403 | ||||||||
\(612\) | −280209. | −0.748133 | ||||||||
\(613\) | 527970. | 1.40504 | 0.702519 | − | 0.711665i | \(-0.252059\pi\) | ||||
0.702519 | + | 0.711665i | \(0.252059\pi\) | |||||||
\(614\) | − | 195410.i | − | 0.518334i | ||||||
\(615\) | 665619. | 1.75985 | ||||||||
\(616\) | −4985.31 | −0.0131380 | ||||||||
\(617\) | 21720.1 | 0.0570547 | 0.0285274 | − | 0.999593i | \(-0.490918\pi\) | ||||
0.0285274 | + | 0.999593i | \(0.490918\pi\) | |||||||
\(618\) | −68493.9 | −0.179339 | ||||||||
\(619\) | −64840.3 | −0.169225 | −0.0846124 | − | 0.996414i | \(-0.526965\pi\) | ||||
−0.0846124 | + | 0.996414i | \(0.526965\pi\) | |||||||
\(620\) | − | 219887.i | − | 0.572028i | ||||||
\(621\) | − | 9717.52i | − | 0.0251984i | ||||||
\(622\) | 76935.9i | 0.198860i | ||||||||
\(623\) | −162110. | −0.417671 | ||||||||
\(624\) | − | 109381.i | − | 0.280913i | ||||||
\(625\) | −281943. | −0.721773 | ||||||||
\(626\) | 139523. | 0.356038 | ||||||||
\(627\) | −401.537 | −0.00102139 | ||||||||
\(628\) | − | 83205.4i | − | 0.210976i | ||||||
\(629\) | − | 720564.i | − | 1.82126i | ||||||
\(630\) | 272734.i | 0.687160i | ||||||||
\(631\) | 639737.i | 1.60673i | 0.595488 | + | 0.803364i | \(0.296959\pi\) | ||||
−0.595488 | + | 0.803364i | \(0.703041\pi\) | |||||||
\(632\) | 768412.i | 1.92380i | ||||||||
\(633\) | 85791.3 | 0.214109 | ||||||||
\(634\) | − | 306428.i | − | 0.762341i | ||||||
\(635\) | 374073.i | 0.927702i | ||||||||
\(636\) | 206177.i | 0.509713i | ||||||||
\(637\) | 279865. | 0.689714 | ||||||||
\(638\) | −2248.33 | −0.00552356 | ||||||||
\(639\) | − | 686581.i | − | 1.68147i | ||||||
\(640\) | −123339. | −0.301120 | ||||||||
\(641\) | 92614.4i | 0.225404i | 0.993629 | + | 0.112702i | \(0.0359506\pi\) | ||||
−0.993629 | + | 0.112702i | \(0.964049\pi\) | |||||||
\(642\) | −296713. | −0.719891 | ||||||||
\(643\) | 517514. | 1.25170 | 0.625850 | − | 0.779943i | \(-0.284752\pi\) | ||||
0.625850 | + | 0.779943i | \(0.284752\pi\) | |||||||
\(644\) | 42217.6i | 0.101794i | ||||||||
\(645\) | 389195. | − | 315864.i | 0.935508 | − | 0.759242i | ||||
\(646\) | 35993.9 | 0.0862509 | ||||||||
\(647\) | − | 320760.i | − | 0.766253i | −0.923696 | − | 0.383126i | \(-0.874847\pi\) | ||
0.923696 | − | 0.383126i | \(-0.125153\pi\) | |||||||
\(648\) | 488793.i | 1.16406i | ||||||||
\(649\) | −4170.61 | −0.00990170 | ||||||||
\(650\) | 67949.7i | 0.160828i | ||||||||
\(651\) | 929801. | 2.19396 | ||||||||
\(652\) | 173682.i | 0.408563i | ||||||||
\(653\) | 271078.i | 0.635724i | 0.948137 | + | 0.317862i | \(0.102965\pi\) | ||||
−0.948137 | + | 0.317862i | \(0.897035\pi\) | |||||||
\(654\) | 315680. | 0.738060 | ||||||||
\(655\) | −294101. | −0.685511 | ||||||||
\(656\) | 125237. | 0.291022 | ||||||||
\(657\) | − | 398642.i | − | 0.923534i | ||||||
\(658\) | 295832. | 0.683271 | ||||||||
\(659\) | −297067. | −0.684044 | −0.342022 | − | 0.939692i | \(-0.611112\pi\) | ||||
−0.342022 | + | 0.939692i | \(0.611112\pi\) | |||||||
\(660\) | 2665.38 | 0.00611888 | ||||||||
\(661\) | 91628.4 | 0.209714 | 0.104857 | − | 0.994487i | \(-0.466562\pi\) | ||||
0.104857 | + | 0.994487i | \(0.466562\pi\) | |||||||
\(662\) | −550558. | −1.25628 | ||||||||
\(663\) | 1.00644e6i | 2.28961i | ||||||||
\(664\) | − | 371585.i | − | 0.842796i | ||||||
\(665\) | 38731.7i | 0.0875836i | ||||||||
\(666\) | 300794. | 0.678143 | ||||||||
\(667\) | 55301.5i | 0.124304i | ||||||||
\(668\) | −2630.80 | −0.00589569 | ||||||||
\(669\) | 27479.3 | 0.0613978 | ||||||||
\(670\) | −298766. | −0.665552 | ||||||||
\(671\) | − | 6375.33i | − | 0.0141598i | ||||||
\(672\) | − | 730659.i | − | 1.61799i | ||||||
\(673\) | − | 601565.i | − | 1.32817i | −0.747658 | − | 0.664084i | \(-0.768822\pi\) | ||
0.747658 | − | 0.664084i | \(-0.231178\pi\) | |||||||
\(674\) | 52466.0i | 0.115494i | ||||||||
\(675\) | − | 17357.8i | − | 0.0380966i | ||||||
\(676\) | 14119.2 | 0.0308970 | ||||||||
\(677\) | 211198.i | 0.460800i | 0.973096 | + | 0.230400i | \(0.0740034\pi\) | ||||
−0.973096 | + | 0.230400i | \(0.925997\pi\) | |||||||
\(678\) | 567369.i | 1.23426i | ||||||||
\(679\) | 231764.i | 0.502698i | ||||||||
\(680\) | −693965. | −1.50079 | ||||||||
\(681\) | −759302. | −1.63727 | ||||||||
\(682\) | 3841.25i | 0.00825854i | ||||||||
\(683\) | −260659. | −0.558768 | −0.279384 | − | 0.960179i | \(-0.590130\pi\) | ||||
−0.279384 | + | 0.960179i | \(0.590130\pi\) | |||||||
\(684\) | − | 16611.4i | − | 0.0355053i | ||||||
\(685\) | 200694. | 0.427713 | ||||||||
\(686\) | 138201. | 0.293672 | ||||||||
\(687\) | 497335.i | 1.05375i | ||||||||
\(688\) | 73227.5 | − | 59430.1i | 0.154702 | − | 0.125554i | ||||
\(689\) | 346089. | 0.729037 | ||||||||
\(690\) | 59300.1i | 0.124554i | ||||||||
\(691\) | 670752.i | 1.40477i | 0.711797 | + | 0.702386i | \(0.247882\pi\) | ||||
−0.711797 | + | 0.702386i | \(0.752118\pi\) | |||||||
\(692\) | −50004.0 | −0.104422 | ||||||||
\(693\) | 5267.34i | 0.0109679i | ||||||||
\(694\) | −36661.6 | −0.0761190 | ||||||||
\(695\) | − | 620361.i | − | 1.28433i | ||||||
\(696\) | − | 578061.i | − | 1.19332i | ||||||
\(697\) | −1.15234e6 | −2.37200 | ||||||||
\(698\) | 572586. | 1.17525 | ||||||||
\(699\) | −917262. | −1.87732 | ||||||||
\(700\) | 75410.5i | 0.153899i | ||||||||
\(701\) | 104357. | 0.212366 | 0.106183 | − | 0.994347i | \(-0.466137\pi\) | ||||
0.106183 | + | 0.994347i | \(0.466137\pi\) | |||||||
\(702\) | 58703.7 | 0.119122 | ||||||||
\(703\) | 42716.6 | 0.0864343 | ||||||||
\(704\) | 3973.65 | 0.00801759 | ||||||||
\(705\) | −459396. | −0.924293 | ||||||||
\(706\) | − | 191796.i | − | 0.384795i | ||||||
\(707\) | − | 665260.i | − | 1.33092i | ||||||
\(708\) | − | 369179.i | − | 0.736497i | ||||||
\(709\) | 135186. | 0.268930 | 0.134465 | − | 0.990918i | \(-0.457068\pi\) | ||||
0.134465 | + | 0.990918i | \(0.457068\pi\) | |||||||
\(710\) | − | 585426.i | − | 1.16133i | ||||||
\(711\) | 811882. | 1.60603 | ||||||||
\(712\) | 172189. | 0.339661 | ||||||||
\(713\) | 94481.8 | 0.185853 | ||||||||
\(714\) | − | 1.01030e6i | − | 1.98178i | ||||||
\(715\) | − | 4474.12i | − | 0.00875176i | ||||||
\(716\) | − | 331255.i | − | 0.646154i | ||||||
\(717\) | − | 146432.i | − | 0.284838i | ||||||
\(718\) | 455105.i | 0.882800i | ||||||||
\(719\) | 99461.8 | 0.192397 | 0.0961985 | − | 0.995362i | \(-0.469332\pi\) | ||||
0.0961985 | + | 0.995362i | \(0.469332\pi\) | |||||||
\(720\) | − | 79687.3i | − | 0.153718i | ||||||
\(721\) | 127598.i | 0.245456i | ||||||||
\(722\) | − | 357112.i | − | 0.685061i | ||||||
\(723\) | −290242. | −0.555243 | ||||||||
\(724\) | 249730. | 0.476424 | ||||||||
\(725\) | 98781.4i | 0.187931i | ||||||||
\(726\) | 497655. | 0.944180 | ||||||||
\(727\) | 440731.i | 0.833882i | 0.908933 | + | 0.416941i | \(0.136898\pi\) | ||||
−0.908933 | + | 0.416941i | \(0.863102\pi\) | |||||||
\(728\) | −740761. | −1.39770 | ||||||||
\(729\) | 394127. | 0.741619 | ||||||||
\(730\) | − | 339910.i | − | 0.637850i | ||||||
\(731\) | −673785. | + | 546832.i | −1.26092 | + | 1.02334i | ||||
\(732\) | 564340. | 1.05322 | ||||||||
\(733\) | − | 353122.i | − | 0.657229i | −0.944464 | − | 0.328615i | \(-0.893418\pi\) | ||
0.944464 | − | 0.328615i | \(-0.106582\pi\) | |||||||
\(734\) | 161705.i | 0.300146i | ||||||||
\(735\) | 436269. | 0.807569 | ||||||||
\(736\) | − | 74245.9i | − | 0.137062i | ||||||
\(737\) | −5770.11 | −0.0106230 | ||||||||
\(738\) | − | 481036.i | − | 0.883211i | ||||||
\(739\) | 511160.i | 0.935983i | 0.883733 | + | 0.467992i | \(0.155022\pi\) | ||||
−0.883733 | + | 0.467992i | \(0.844978\pi\) | |||||||
\(740\) | −283551. | −0.517806 | ||||||||
\(741\) | −59663.9 | −0.108661 | ||||||||
\(742\) | −347418. | −0.631021 | ||||||||
\(743\) | − | 162933.i | − | 0.295141i | −0.989052 | − | 0.147571i | \(-0.952855\pi\) | ||
0.989052 | − | 0.147571i | \(-0.0471454\pi\) | |||||||
\(744\) | −987609. | −1.78418 | ||||||||
\(745\) | 246690. | 0.444466 | ||||||||
\(746\) | −493521. | −0.886805 | ||||||||
\(747\) | −392606. | −0.703584 | ||||||||
\(748\) | −4614.39 | −0.00824729 | ||||||||
\(749\) | 552750.i | 0.985292i | ||||||||
\(750\) | 572977.i | 1.01863i | ||||||||
\(751\) | 476066.i | 0.844087i | 0.906576 | + | 0.422044i | \(0.138687\pi\) | ||||
−0.906576 | + | 0.422044i | \(0.861313\pi\) | |||||||
\(752\) | −86436.0 | −0.152848 | ||||||||
\(753\) | 675249.i | 1.19090i | ||||||||
\(754\) | −334077. | −0.587630 | ||||||||
\(755\) | 827708. | 1.45205 | ||||||||
\(756\) | 65149.3 | 0.113990 | ||||||||
\(757\) | 513071.i | 0.895335i | 0.894200 | + | 0.447667i | \(0.147745\pi\) | ||||
−0.894200 | + | 0.447667i | \(0.852255\pi\) | |||||||
\(758\) | 130978.i | 0.227960i | ||||||||
\(759\) | 1145.27i | 0.00198803i | ||||||||
\(760\) | − | 41139.7i | − | 0.0712253i | ||||||
\(761\) | 132174.i | 0.228233i | 0.993467 | + | 0.114116i | \(0.0364036\pi\) | ||||
−0.993467 | + | 0.114116i | \(0.963596\pi\) | |||||||
\(762\) | 578450. | 0.996222 | ||||||||
\(763\) | − | 588084.i | − | 1.01016i | ||||||
\(764\) | − | 296960.i | − | 0.508757i | ||||||
\(765\) | 733223.i | 1.25289i | ||||||||
\(766\) | 164633. | 0.280581 | ||||||||
\(767\) | −619705. | −1.05340 | ||||||||
\(768\) | 860631.i | 1.45913i | ||||||||
\(769\) | −549403. | −0.929048 | −0.464524 | − | 0.885561i | \(-0.653775\pi\) | ||||
−0.464524 | + | 0.885561i | \(0.653775\pi\) | |||||||
\(770\) | 4491.30i | 0.00757513i | ||||||||
\(771\) | 712275. | 1.19823 | ||||||||
\(772\) | −622915. | −1.04519 | ||||||||
\(773\) | − | 357526.i | − | 0.598340i | −0.954200 | − | 0.299170i | \(-0.903290\pi\) | ||
0.954200 | − | 0.299170i | \(-0.0967098\pi\) | |||||||
\(774\) | −228271. | − | 281267.i | −0.381039 | − | 0.469501i | ||||
\(775\) | 168767. | 0.280985 | ||||||||
\(776\) | − | 246174.i | − | 0.408807i | ||||||
\(777\) | − | 1.19900e6i | − | 1.98599i | ||||||
\(778\) | −702526. | −1.16066 | ||||||||
\(779\) | − | 68313.2i | − | 0.112572i | ||||||
\(780\) | 396046. | 0.650964 | ||||||||
\(781\) | − | 11306.4i | − | 0.0185363i | ||||||
\(782\) | − | 102662.i | − | 0.167879i | ||||||
\(783\) | 85340.1 | 0.139197 | ||||||||
\(784\) | 82084.6 | 0.133546 | ||||||||
\(785\) | −217724. | −0.353319 | ||||||||
\(786\) | 454786.i | 0.736142i | ||||||||
\(787\) | 11905.5 | 0.0192221 | 0.00961103 | − | 0.999954i | \(-0.496941\pi\) | ||||
0.00961103 | + | 0.999954i | \(0.496941\pi\) | |||||||
\(788\) | 284999. | 0.458977 | ||||||||
\(789\) | −93316.5 | −0.149901 | ||||||||
\(790\) | 692267. | 1.10922 | ||||||||
\(791\) | 1.05696e6 | 1.68929 | ||||||||
\(792\) | − | 5594.82i | − | 0.00891940i | ||||||
\(793\) | − | 947303.i | − | 1.50641i | ||||||
\(794\) | 217946.i | 0.345707i | ||||||||
\(795\) | 539504. | 0.853611 | ||||||||
\(796\) | 170769.i | 0.269514i | ||||||||
\(797\) | −54534.3 | −0.0858526 | −0.0429263 | − | 0.999078i | \(-0.513668\pi\) | ||||
−0.0429263 | + | 0.999078i | \(0.513668\pi\) | |||||||
\(798\) | 59893.0 | 0.0940525 | ||||||||
\(799\) | 795321. | 1.24580 | ||||||||
\(800\) | − | 132621.i | − | 0.207220i | ||||||
\(801\) | − | 181930.i | − | 0.283557i | ||||||
\(802\) | 541370.i | 0.841676i | ||||||||
\(803\) | − | 6564.72i | − | 0.0101809i | ||||||
\(804\) | − | 510766.i | − | 0.790151i | ||||||
\(805\) | 110471. | 0.170473 | ||||||||
\(806\) | 570766.i | 0.878593i | ||||||||
\(807\) | 492319.i | 0.755962i | ||||||||
\(808\) | 706621.i | 1.08234i | ||||||||
\(809\) | 1.14580e6 | 1.75070 | 0.875350 | − | 0.483489i | \(-0.160631\pi\) | ||||
0.875350 | + | 0.483489i | \(0.160631\pi\) | |||||||
\(810\) | 440357. | 0.671174 | ||||||||
\(811\) | 56880.8i | 0.0864816i | 0.999065 | + | 0.0432408i | \(0.0137683\pi\) | ||||
−0.999065 | + | 0.0432408i | \(0.986232\pi\) | |||||||
\(812\) | −370758. | −0.562314 | ||||||||
\(813\) | − | 1.47717e6i | − | 2.23486i | ||||||
\(814\) | 4953.39 | 0.00747573 | ||||||||
\(815\) | 454473. | 0.684216 | ||||||||
\(816\) | 295190.i | 0.443324i | ||||||||
\(817\) | −32417.4 | − | 39943.4i | −0.0485662 | − | 0.0598413i | ||||
\(818\) | −317132. | −0.473952 | ||||||||
\(819\) | 782667.i | 1.16683i | ||||||||
\(820\) | 453459.i | 0.674389i | ||||||||
\(821\) | 200304. | 0.297169 | 0.148584 | − | 0.988900i | \(-0.452528\pi\) | ||||
0.148584 | + | 0.988900i | \(0.452528\pi\) | |||||||
\(822\) | − | 310344.i | − | 0.459303i | ||||||
\(823\) | −1.07152e6 | −1.58198 | −0.790989 | − | 0.611830i | \(-0.790434\pi\) | ||||
−0.790989 | + | 0.611830i | \(0.790434\pi\) | |||||||
\(824\) | − | 135531.i | − | 0.199611i | ||||||
\(825\) | 2045.72i | 0.00300565i | ||||||||
\(826\) | 622084. | 0.911778 | ||||||||
\(827\) | 767100. | 1.12161 | 0.560803 | − | 0.827949i | \(-0.310492\pi\) | ||||
0.560803 | + | 0.827949i | \(0.310492\pi\) | |||||||
\(828\) | −47379.2 | −0.0691077 | ||||||||
\(829\) | 358430.i | 0.521549i | 0.965400 | + | 0.260774i | \(0.0839778\pi\) | ||||
−0.965400 | + | 0.260774i | \(0.916022\pi\) | |||||||
\(830\) | −334763. | −0.485939 | ||||||||
\(831\) | −462766. | −0.670130 | ||||||||
\(832\) | 590439. | 0.852960 | ||||||||
\(833\) | −755282. | −1.08848 | ||||||||
\(834\) | −959300. | −1.37918 | ||||||||
\(835\) | 6884.02i | 0.00987345i | ||||||||
\(836\) | − | 273.551i | − | 0.000391405i | ||||||
\(837\) | − | 145802.i | − | 0.208120i | ||||||
\(838\) | 776176. | 1.10528 | ||||||||
\(839\) | − | 93647.6i | − | 0.133037i | −0.997785 | − | 0.0665185i | \(-0.978811\pi\) | ||
0.997785 | − | 0.0665185i | \(-0.0211891\pi\) | |||||||
\(840\) | −1.15474e6 | −1.63654 | ||||||||
\(841\) | 221619. | 0.313339 | ||||||||
\(842\) | 503366. | 0.710002 | ||||||||
\(843\) | 369150.i | 0.519454i | ||||||||
\(844\) | 58446.1i | 0.0820485i | ||||||||
\(845\) | − | 36945.8i | − | 0.0517430i | ||||||
\(846\) | 332001.i | 0.463872i | ||||||||
\(847\) | − | 927086.i | − | 1.29227i | ||||||
\(848\) | 101508. | 0.141159 | ||||||||
\(849\) | 677233.i | 0.939556i | ||||||||
\(850\) | − | 183379.i | − | 0.253811i | ||||||
\(851\) | − | 121837.i | − | 0.168236i | ||||||
\(852\) | 1.00084e6 | 1.37874 | ||||||||
\(853\) | 368391. | 0.506304 | 0.253152 | − | 0.967427i | \(-0.418533\pi\) | ||||
0.253152 | + | 0.967427i | \(0.418533\pi\) | |||||||
\(854\) | 950939.i | 1.30388i | ||||||||
\(855\) | −43467.1 | −0.0594604 | ||||||||
\(856\) | − | 587116.i | − | 0.801266i | ||||||
\(857\) | 851457. | 1.15931 | 0.579657 | − | 0.814860i | \(-0.303186\pi\) | ||||
0.579657 | + | 0.814860i | \(0.303186\pi\) | |||||||
\(858\) | −6918.59 | −0.00939816 | ||||||||
\(859\) | − | 236916.i | − | 0.321076i | −0.987030 | − | 0.160538i | \(-0.948677\pi\) | ||
0.987030 | − | 0.160538i | \(-0.0513229\pi\) | |||||||
\(860\) | 215185. | + | 265142.i | 0.290948 | + | 0.358494i | ||||
\(861\) | −1.91747e6 | −2.58655 | ||||||||
\(862\) | − | 814337.i | − | 1.09595i | ||||||
\(863\) | 22247.8i | 0.0298721i | 0.999888 | + | 0.0149361i | \(0.00475447\pi\) | ||||
−0.999888 | + | 0.0149361i | \(0.995246\pi\) | |||||||
\(864\) | −114575. | −0.153483 | ||||||||
\(865\) | 130846.i | 0.174875i | ||||||||
\(866\) | −870066. | −1.16016 | ||||||||
\(867\) | − | 1.68617e6i | − | 2.24317i | ||||||
\(868\) | 633435.i | 0.840742i | ||||||||
\(869\) | 13369.8 | 0.0177046 | ||||||||
\(870\) | −520779. | −0.688042 | ||||||||
\(871\) | −857373. | −1.13014 | ||||||||
\(872\) | 624647.i | 0.821489i | ||||||||
\(873\) | −260100. | −0.341281 | ||||||||
\(874\) | 6086.03 | 0.00796730 | ||||||||
\(875\) | 1.06740e6 | 1.39416 | ||||||||
\(876\) | 581105. | 0.757262 | ||||||||
\(877\) | 2045.84 | 0.00265995 | 0.00132998 | − | 0.999999i | \(-0.499577\pi\) | ||||
0.00132998 | + | 0.999999i | \(0.499577\pi\) | |||||||
\(878\) | − | 797357.i | − | 1.03434i | ||||||
\(879\) | 1.92054e6i | 2.48568i | ||||||||
\(880\) | − | 1312.26i | − | 0.00169456i | ||||||
\(881\) | −196655. | −0.253369 | −0.126684 | − | 0.991943i | \(-0.540434\pi\) | ||||
−0.126684 | + | 0.991943i | \(0.540434\pi\) | |||||||
\(882\) | − | 315287.i | − | 0.405293i | ||||||
\(883\) | 59837.7 | 0.0767456 | 0.0383728 | − | 0.999263i | \(-0.487783\pi\) | ||||
0.0383728 | + | 0.999263i | \(0.487783\pi\) | |||||||
\(884\) | −685647. | −0.877397 | ||||||||
\(885\) | −966033. | −1.23340 | ||||||||
\(886\) | 37525.6i | 0.0478035i | ||||||||
\(887\) | 577234.i | 0.733676i | 0.930285 | + | 0.366838i | \(0.119560\pi\) | ||||
−0.930285 | + | 0.366838i | \(0.880440\pi\) | |||||||
\(888\) | 1.27355e6i | 1.61506i | ||||||||
\(889\) | − | 1.07760e6i | − | 1.36350i | ||||||
\(890\) | − | 155126.i | − | 0.195842i | ||||||
\(891\) | 8504.66 | 0.0107128 | ||||||||
\(892\) | 18720.5i | 0.0235282i | ||||||||
\(893\) | 47148.3i | 0.0591239i | ||||||||
\(894\) | − | 381470.i | − | 0.477294i | ||||||
\(895\) | −866795. | −1.08211 | ||||||||
\(896\) | 355305. | 0.442573 | ||||||||
\(897\) | 170174.i | 0.211499i | ||||||||
\(898\) | 454318. | 0.563388 | ||||||||
\(899\) | 829747.i | 1.02666i | ||||||||
\(900\) | −84630.3 | −0.104482 | ||||||||
\(901\) | −934005. | −1.15053 | ||||||||
\(902\) | − | 7921.55i | − | 0.00973637i | ||||||
\(903\) | −1.12116e6 | + | 909916.i | −1.37497 | + | 1.11590i | ||||
\(904\) | −1.12267e6 | −1.37378 | ||||||||
\(905\) | − | 653470.i | − | 0.797863i | ||||||
\(906\) | − | 1.27993e6i | − | 1.55930i | ||||||
\(907\) | −543357. | −0.660496 | −0.330248 | − | 0.943894i | \(-0.607132\pi\) | ||||
−0.330248 | + | 0.943894i | \(0.607132\pi\) | |||||||
\(908\) | − | 517282.i | − | 0.627416i | ||||||
\(909\) | 746596. | 0.903561 | ||||||||
\(910\) | 667356.i | 0.805888i | ||||||||
\(911\) | 119998.i | 0.144590i | 0.997383 | + | 0.0722948i | \(0.0230322\pi\) | ||||
−0.997383 | + | 0.0722948i | \(0.976968\pi\) | |||||||
\(912\) | −17499.5 | −0.0210395 | ||||||||
\(913\) | −6465.32 | −0.00775619 | ||||||||
\(914\) | 432922. | 0.518224 | ||||||||
\(915\) | − | 1.47671e6i | − | 1.76382i | ||||||
\(916\) | −338814. | −0.403804 | ||||||||
\(917\) | 847225. | 1.00753 | ||||||||
\(918\) | −158426. | −0.187993 | ||||||||
\(919\) | 198081. | 0.234537 | 0.117268 | − | 0.993100i | \(-0.462586\pi\) | ||||
0.117268 | + | 0.993100i | \(0.462586\pi\) | |||||||
\(920\) | −117339. | −0.138633 | ||||||||
\(921\) | − | 874161.i | − | 1.03056i | ||||||
\(922\) | − | 916406.i | − | 1.07802i | ||||||
\(923\) | − | 1.68000e6i | − | 1.97200i | ||||||
\(924\) | −7678.24 | −0.00899328 | ||||||||
\(925\) | − | 217629.i | − | 0.254351i | ||||||
\(926\) | 544974. | 0.635556 | ||||||||
\(927\) | −143198. | −0.166640 | ||||||||
\(928\) | 652034. | 0.757137 | ||||||||
\(929\) | 1.28224e6i | 1.48573i | 0.669443 | + | 0.742864i | \(0.266533\pi\) | ||||
−0.669443 | + | 0.742864i | \(0.733467\pi\) | |||||||
\(930\) | 889743.i | 1.02872i | ||||||||
\(931\) | − | 44774.7i | − | 0.0516575i | ||||||
\(932\) | − | 624893.i | − | 0.719406i | ||||||
\(933\) | 344170.i | 0.395376i | ||||||||
\(934\) | −335312. | −0.384375 | ||||||||
\(935\) | 12074.5i | 0.0138117i | ||||||||
\(936\) | − | 831328.i | − | 0.948900i | ||||||
\(937\) | − | 1.00382e6i | − | 1.14334i | −0.820483 | − | 0.571671i | \(-0.806295\pi\) | ||
0.820483 | − | 0.571671i | \(-0.193705\pi\) | |||||||
\(938\) | 860664. | 0.978201 | ||||||||
\(939\) | 624151. | 0.707878 | ||||||||
\(940\) | − | 312968.i | − | 0.354197i | ||||||
\(941\) | 893241. | 1.00876 | 0.504382 | − | 0.863481i | \(-0.331720\pi\) | ||||
0.504382 | + | 0.863481i | \(0.331720\pi\) | |||||||
\(942\) | 336679.i | 0.379414i | ||||||||
\(943\) | −194844. | −0.219110 | ||||||||
\(944\) | −181760. | −0.203965 | ||||||||
\(945\) | − | 170476.i | − | 0.190898i | ||||||
\(946\) | −3759.10 | − | 4631.81i | −0.00420050 | − | 0.00517569i | ||||
\(947\) | −66944.6 | −0.0746475 | −0.0373238 | − | 0.999303i | \(-0.511883\pi\) | ||||
−0.0373238 | + | 0.999303i | \(0.511883\pi\) | |||||||
\(948\) | 1.18349e6i | 1.31688i | ||||||||
\(949\) | − | 975443.i | − | 1.08310i | ||||||
\(950\) | 10871.1 | 0.0120455 | ||||||||
\(951\) | − | 1.37079e6i | − | 1.51569i | ||||||
\(952\) | 1.99912e6 | 2.20580 | ||||||||
\(953\) | 863195.i | 0.950436i | 0.879868 | + | 0.475218i | \(0.157631\pi\) | ||||
−0.879868 | + | 0.475218i | \(0.842369\pi\) | |||||||
\(954\) | − | 389893.i | − | 0.428400i | ||||||
\(955\) | −777055. | −0.852011 | ||||||||
\(956\) | 99758.3 | 0.109152 | ||||||||
\(957\) | −10057.9 | −0.0109820 | ||||||||
\(958\) | 390612.i | 0.425612i | ||||||||
\(959\) | −578143. | −0.628635 | ||||||||
\(960\) | 920411. | 0.998710 | ||||||||
\(961\) | 494090. | 0.535007 | ||||||||
\(962\) | 736018. | 0.795313 | ||||||||
\(963\) | −620330. | −0.668914 | ||||||||
\(964\) | − | 197730.i | − | 0.212774i | ||||||
\(965\) | 1.62998e6i | 1.75037i | ||||||||
\(966\) | − | 170827.i | − | 0.183064i | ||||||
\(967\) | −1.55611e6 | −1.66413 | −0.832065 | − | 0.554677i | \(-0.812842\pi\) | ||||
−0.832065 | + | 0.554677i | \(0.812842\pi\) | |||||||
\(968\) | 984726.i | 1.05091i | ||||||||
\(969\) | 161018. | 0.171485 | ||||||||
\(970\) | −221779. | −0.235710 | ||||||||
\(971\) | −734703. | −0.779243 | −0.389622 | − | 0.920975i | \(-0.627394\pi\) | ||||
−0.389622 | + | 0.920975i | \(0.627394\pi\) | |||||||
\(972\) | 669496.i | 0.708623i | ||||||||
\(973\) | 1.78709e6i | 1.88765i | ||||||||
\(974\) | − | 536540.i | − | 0.565567i | ||||||
\(975\) | 303971.i | 0.319759i | ||||||||
\(976\) | − | 277845.i | − | 0.291677i | ||||||
\(977\) | −857114. | −0.897944 | −0.448972 | − | 0.893546i | \(-0.648210\pi\) | ||||
−0.448972 | + | 0.893546i | \(0.648210\pi\) | |||||||
\(978\) | − | 702778.i | − | 0.734752i | ||||||
\(979\) | − | 2995.97i | − | 0.00312588i | ||||||
\(980\) | 297212.i | 0.309467i | ||||||||
\(981\) | 659984. | 0.685797 | ||||||||
\(982\) | −396109. | −0.410764 | ||||||||
\(983\) | 116039.i | 0.120087i | 0.998196 | + | 0.0600437i | \(0.0191240\pi\) | ||||
−0.998196 | + | 0.0600437i | \(0.980876\pi\) | |||||||
\(984\) | 2.03668e6 | 2.10345 | ||||||||
\(985\) | − | 745758.i | − | 0.768645i | ||||||
\(986\) | 901588. | 0.927372 | ||||||||
\(987\) | 1.32340e6 | 1.35849 | ||||||||
\(988\) | − | 40646.6i | − | 0.0416400i | ||||||
\(989\) | −113927. | + | 92461.2i | −0.116475 | + | 0.0945294i | ||||
\(990\) | −5040.41 | −0.00514275 | ||||||||
\(991\) | 1.12664e6i | 1.14720i | 0.819136 | + | 0.573600i | \(0.194454\pi\) | ||||
−0.819136 | + | 0.573600i | \(0.805546\pi\) | |||||||
\(992\) | − | 1.11399e6i | − | 1.13203i | ||||||
\(993\) | −2.46290e6 | −2.49775 | ||||||||
\(994\) | 1.68645e6i | 1.70687i | ||||||||
\(995\) | 446851. | 0.451353 | ||||||||
\(996\) | − | 572306.i | − | 0.576912i | ||||||
\(997\) | 1.20881e6i | 1.21610i | 0.793900 | + | 0.608048i | \(0.208047\pi\) | ||||
−0.793900 | + | 0.608048i | \(0.791953\pi\) | |||||||
\(998\) | −906523. | −0.910160 | ||||||||
\(999\) | −188016. | −0.188393 |
(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 | 43.5.b.b.42.5 | ✓ | 12 | |
3.2 | odd | 2 | 387.5.b.c.343.8 | 12 | |||
4.3 | odd | 2 | 688.5.b.d.257.10 | 12 | |||
43.42 | odd | 2 | inner | 43.5.b.b.42.8 | yes | 12 | |
129.128 | even | 2 | 387.5.b.c.343.5 | 12 | |||
172.171 | even | 2 | 688.5.b.d.257.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.5.b.b.42.5 | ✓ | 12 | 1.1 | even | 1 | trivial | |
43.5.b.b.42.8 | yes | 12 | 43.42 | odd | 2 | inner | |
387.5.b.c.343.5 | 12 | 129.128 | even | 2 | |||
387.5.b.c.343.8 | 12 | 3.2 | odd | 2 | |||
688.5.b.d.257.3 | 12 | 172.171 | even | 2 | |||
688.5.b.d.257.10 | 12 | 4.3 | odd | 2 |