Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,5,Mod(23,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.23");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.g (of order \(12\), degree \(4\), 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: | \(7.64937726820\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 23.7 | ||
Character | \(\chi\) | \(=\) | 74.23 |
Dual form | 74.5.g.a.29.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{5}{12}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.732051 | + | 2.73205i | 0.183013 | + | 0.683013i | ||||
\(3\) | 13.7481 | − | 7.93744i | 1.52756 | − | 0.881938i | 0.528098 | − | 0.849183i | \(-0.322905\pi\) |
0.999463 | − | 0.0327547i | \(-0.0104280\pi\) | |||||||
\(4\) | −6.92820 | + | 4.00000i | −0.433013 | + | 0.250000i | ||||
\(5\) | 5.58720 | − | 20.8517i | 0.223488 | − | 0.834068i | −0.759517 | − | 0.650488i | \(-0.774564\pi\) |
0.983005 | − | 0.183581i | \(-0.0587688\pi\) | |||||||
\(6\) | 31.7498 | + | 31.7498i | 0.881938 | + | 0.881938i | ||||
\(7\) | 10.7825 | + | 18.6759i | 0.220051 | + | 0.381140i | 0.954823 | − | 0.297174i | \(-0.0960442\pi\) |
−0.734772 | + | 0.678314i | \(0.762711\pi\) | |||||||
\(8\) | −16.0000 | − | 16.0000i | −0.250000 | − | 0.250000i | ||||
\(9\) | 85.5060 | − | 148.101i | 1.05563 | − | 1.82840i | ||||
\(10\) | 61.0580 | 0.610580 | ||||||||
\(11\) | 84.9630i | 0.702174i | 0.936343 | + | 0.351087i | \(0.114188\pi\) | ||||
−0.936343 | + | 0.351087i | \(0.885812\pi\) | |||||||
\(12\) | −63.4995 | + | 109.984i | −0.440969 | + | 0.763781i | ||||
\(13\) | 66.1127 | − | 246.736i | 0.391200 | − | 1.45998i | −0.436958 | − | 0.899482i | \(-0.643944\pi\) |
0.828158 | − | 0.560495i | \(-0.189389\pi\) | |||||||
\(14\) | −43.1300 | + | 43.1300i | −0.220051 | + | 0.220051i | ||||
\(15\) | −88.6961 | − | 331.019i | −0.394205 | − | 1.47119i | ||||
\(16\) | 32.0000 | − | 55.4256i | 0.125000 | − | 0.216506i | ||||
\(17\) | −68.7695 | + | 18.4267i | −0.237957 | + | 0.0637603i | −0.375826 | − | 0.926690i | \(-0.622641\pi\) |
0.137870 | + | 0.990450i | \(0.455974\pi\) | |||||||
\(18\) | 467.213 | + | 125.189i | 1.44202 | + | 0.386387i | ||||
\(19\) | −122.946 | + | 458.841i | −0.340571 | + | 1.27103i | 0.557132 | + | 0.830424i | \(0.311902\pi\) |
−0.897702 | + | 0.440603i | \(0.854765\pi\) | |||||||
\(20\) | 44.6976 | + | 166.814i | 0.111744 | + | 0.417034i | ||||
\(21\) | 296.477 | + | 171.171i | 0.672283 | + | 0.388143i | ||||
\(22\) | −232.123 | + | 62.1972i | −0.479594 | + | 0.128507i | ||||
\(23\) | 340.952 | + | 340.952i | 0.644521 | + | 0.644521i | 0.951664 | − | 0.307143i | \(-0.0993728\pi\) |
−0.307143 | + | 0.951664i | \(0.599373\pi\) | |||||||
\(24\) | −346.968 | − | 92.9698i | −0.602375 | − | 0.161406i | ||||
\(25\) | 137.689 | + | 79.4947i | 0.220302 | + | 0.127191i | ||||
\(26\) | 722.494 | 1.06878 | ||||||||
\(27\) | − | 1428.93i | − | 1.96012i | ||||||
\(28\) | −149.407 | − | 86.2601i | −0.190570 | − | 0.110026i | ||||
\(29\) | 302.089 | − | 302.089i | 0.359203 | − | 0.359203i | −0.504316 | − | 0.863519i | \(-0.668255\pi\) |
0.863519 | + | 0.504316i | \(0.168255\pi\) | |||||||
\(30\) | 839.429 | − | 484.645i | 0.932699 | − | 0.538494i | ||||
\(31\) | −941.814 | + | 941.814i | −0.980036 | + | 0.980036i | −0.999805 | − | 0.0197687i | \(-0.993707\pi\) |
0.0197687 | + | 0.999805i | \(0.493707\pi\) | |||||||
\(32\) | 174.851 | + | 46.8513i | 0.170753 | + | 0.0457532i | ||||
\(33\) | 674.389 | + | 1168.08i | 0.619274 | + | 1.07261i | ||||
\(34\) | −100.686 | − | 174.392i | −0.0870982 | − | 0.150859i | ||||
\(35\) | 449.668 | − | 120.488i | 0.367076 | − | 0.0983576i | ||||
\(36\) | 1368.10i | 1.05563i | ||||||||
\(37\) | −615.430 | + | 1222.87i | −0.449547 | + | 0.893257i | ||||
\(38\) | −1343.58 | −0.930456 | ||||||||
\(39\) | −1049.53 | − | 3916.91i | −0.690028 | − | 2.57522i | ||||
\(40\) | −423.023 | + | 244.232i | −0.264389 | + | 0.152645i | ||||
\(41\) | −2613.28 | + | 1508.78i | −1.55460 | + | 0.897549i | −0.556843 | + | 0.830618i | \(0.687987\pi\) |
−0.997758 | + | 0.0669312i | \(0.978679\pi\) | |||||||
\(42\) | −250.612 | + | 935.296i | −0.142070 | + | 0.530213i | ||||
\(43\) | −1783.94 | − | 1783.94i | −0.964812 | − | 0.964812i | 0.0345899 | − | 0.999402i | \(-0.488987\pi\) |
−0.999402 | + | 0.0345899i | \(0.988987\pi\) | |||||||
\(44\) | −339.852 | − | 588.641i | −0.175543 | − | 0.304050i | ||||
\(45\) | −2610.41 | − | 2610.41i | −1.28909 | − | 1.28909i | ||||
\(46\) | −681.903 | + | 1181.09i | −0.322260 | + | 0.558172i | ||||
\(47\) | −42.3456 | −0.0191696 | −0.00958479 | − | 0.999954i | \(-0.503051\pi\) | ||||
−0.00958479 | + | 0.999954i | \(0.503051\pi\) | |||||||
\(48\) | − | 1015.99i | − | 0.440969i | ||||||
\(49\) | 967.975 | − | 1676.58i | 0.403155 | − | 0.698285i | ||||
\(50\) | −116.388 | + | 434.367i | −0.0465553 | + | 0.173747i | ||||
\(51\) | −799.186 | + | 799.186i | −0.307261 | + | 0.307261i | ||||
\(52\) | 528.902 | + | 1973.89i | 0.195600 | + | 0.729989i | ||||
\(53\) | 457.121 | − | 791.757i | 0.162734 | − | 0.281864i | −0.773114 | − | 0.634267i | \(-0.781302\pi\) |
0.935848 | + | 0.352403i | \(0.114635\pi\) | |||||||
\(54\) | 3903.91 | − | 1046.05i | 1.33879 | − | 0.358728i | ||||
\(55\) | 1771.62 | + | 474.705i | 0.585661 | + | 0.156927i | ||||
\(56\) | 126.294 | − | 471.334i | 0.0402722 | − | 0.150298i | ||||
\(57\) | 1951.75 | + | 7284.04i | 0.600724 | + | 2.24193i | ||||
\(58\) | 1046.47 | + | 604.179i | 0.311079 | + | 0.179601i | ||||
\(59\) | −3272.46 | + | 876.854i | −0.940093 | + | 0.251897i | −0.696153 | − | 0.717893i | \(-0.745107\pi\) |
−0.243940 | + | 0.969790i | \(0.578440\pi\) | |||||||
\(60\) | 1938.58 | + | 1938.58i | 0.538494 | + | 0.538494i | ||||
\(61\) | 2614.07 | + | 700.438i | 0.702518 | + | 0.188239i | 0.592358 | − | 0.805675i | \(-0.298197\pi\) |
0.110160 | + | 0.993914i | \(0.464864\pi\) | |||||||
\(62\) | −3262.54 | − | 1883.63i | −0.848736 | − | 0.490018i | ||||
\(63\) | 3687.88 | 0.929170 | ||||||||
\(64\) | 512.000i | 0.125000i | ||||||||
\(65\) | −4775.49 | − | 2757.13i | −1.13029 | − | 0.652575i | ||||
\(66\) | −2697.56 | + | 2697.56i | −0.619274 | + | 0.619274i | ||||
\(67\) | 4396.29 | − | 2538.20i | 0.979348 | − | 0.565427i | 0.0772749 | − | 0.997010i | \(-0.475378\pi\) |
0.902073 | + | 0.431583i | \(0.142045\pi\) | |||||||
\(68\) | 402.742 | − | 402.742i | 0.0870982 | − | 0.0870982i | ||||
\(69\) | 7393.71 | + | 1981.14i | 1.55297 | + | 0.416118i | ||||
\(70\) | 658.359 | + | 1140.31i | 0.134359 | + | 0.232717i | ||||
\(71\) | 3192.16 | + | 5528.98i | 0.633239 | + | 1.09680i | 0.986885 | + | 0.161423i | \(0.0516082\pi\) |
−0.353647 | + | 0.935379i | \(0.615058\pi\) | |||||||
\(72\) | −3737.71 | + | 1001.52i | −0.721008 | + | 0.193194i | ||||
\(73\) | − | 6020.79i | − | 1.12982i | −0.825154 | − | 0.564908i | \(-0.808912\pi\) | ||
0.825154 | − | 0.564908i | \(-0.191088\pi\) | |||||||
\(74\) | −3791.46 | − | 786.185i | −0.692378 | − | 0.143569i | ||||
\(75\) | 2523.94 | 0.448700 | ||||||||
\(76\) | −983.568 | − | 3670.73i | −0.170285 | − | 0.635513i | ||||
\(77\) | −1586.76 | + | 916.114i | −0.267626 | + | 0.154514i | ||||
\(78\) | 9932.88 | − | 5734.75i | 1.63262 | − | 0.942595i | ||||
\(79\) | −1307.86 | + | 4880.99i | −0.209559 | + | 0.782084i | 0.778453 | + | 0.627703i | \(0.216005\pi\) |
−0.988011 | + | 0.154381i | \(0.950662\pi\) | |||||||
\(80\) | −976.929 | − | 976.929i | −0.152645 | − | 0.152645i | ||||
\(81\) | −4416.06 | − | 7648.85i | −0.673078 | − | 1.16581i | ||||
\(82\) | −6035.12 | − | 6035.12i | −0.897549 | − | 0.897549i | ||||
\(83\) | −3998.24 | + | 6925.16i | −0.580381 | + | 1.00525i | 0.415053 | + | 0.909797i | \(0.363763\pi\) |
−0.995434 | + | 0.0954516i | \(0.969570\pi\) | |||||||
\(84\) | −2738.74 | −0.388143 | ||||||||
\(85\) | 1536.92i | 0.212722i | ||||||||
\(86\) | 3567.87 | − | 6179.74i | 0.482406 | − | 0.835551i | ||||
\(87\) | 1755.32 | − | 6550.96i | 0.231910 | − | 0.865498i | ||||
\(88\) | 1359.41 | − | 1359.41i | 0.175543 | − | 0.175543i | ||||
\(89\) | −1321.79 | − | 4932.98i | −0.166871 | − | 0.622772i | −0.997794 | − | 0.0663846i | \(-0.978854\pi\) |
0.830923 | − | 0.556388i | \(-0.187813\pi\) | |||||||
\(90\) | 5220.83 | − | 9042.74i | 0.644547 | − | 1.11639i | ||||
\(91\) | 5320.87 | − | 1425.72i | 0.642539 | − | 0.172168i | ||||
\(92\) | −3725.99 | − | 998.376i | −0.440216 | − | 0.117956i | ||||
\(93\) | −5472.52 | + | 20423.7i | −0.632734 | + | 2.36140i | ||||
\(94\) | −30.9991 | − | 115.690i | −0.00350828 | − | 0.0130931i | ||||
\(95\) | 8880.69 | + | 5127.27i | 0.984010 | + | 0.568118i | ||||
\(96\) | 2775.74 | − | 743.758i | 0.301187 | − | 0.0807029i | ||||
\(97\) | −6689.12 | − | 6689.12i | −0.710928 | − | 0.710928i | 0.255801 | − | 0.966729i | \(-0.417661\pi\) |
−0.966729 | + | 0.255801i | \(0.917661\pi\) | |||||||
\(98\) | 5289.11 | + | 1417.21i | 0.550720 | + | 0.147565i | ||||
\(99\) | 12583.1 | + | 7264.85i | 1.28386 | + | 0.741235i | ||||
\(100\) | −1271.91 | −0.127191 | ||||||||
\(101\) | 17485.0i | 1.71405i | 0.515273 | + | 0.857026i | \(0.327690\pi\) | ||||
−0.515273 | + | 0.857026i | \(0.672310\pi\) | |||||||
\(102\) | −2768.46 | − | 1598.37i | −0.266096 | − | 0.153630i | ||||
\(103\) | 7350.34 | − | 7350.34i | 0.692840 | − | 0.692840i | −0.270016 | − | 0.962856i | \(-0.587029\pi\) |
0.962856 | + | 0.270016i | \(0.0870289\pi\) | |||||||
\(104\) | −5005.58 | + | 2889.97i | −0.462794 | + | 0.267194i | ||||
\(105\) | 5225.69 | − | 5225.69i | 0.473985 | − | 0.473985i | ||||
\(106\) | 2497.76 | + | 669.271i | 0.222299 | + | 0.0595649i | ||||
\(107\) | −4548.65 | − | 7878.50i | −0.397297 | − | 0.688138i | 0.596095 | − | 0.802914i | \(-0.296718\pi\) |
−0.993391 | + | 0.114776i | \(0.963385\pi\) | |||||||
\(108\) | 5715.72 | + | 9899.92i | 0.490031 | + | 0.848758i | ||||
\(109\) | 12377.3 | − | 3316.48i | 1.04177 | − | 0.279142i | 0.302924 | − | 0.953015i | \(-0.402037\pi\) |
0.738847 | + | 0.673873i | \(0.235371\pi\) | |||||||
\(110\) | 5187.68i | 0.428734i | ||||||||
\(111\) | 1245.48 | + | 21697.0i | 0.101086 | + | 1.76098i | ||||
\(112\) | 1380.16 | 0.110026 | ||||||||
\(113\) | −4789.48 | − | 17874.6i | −0.375086 | − | 1.39984i | −0.853218 | − | 0.521554i | \(-0.825353\pi\) |
0.478132 | − | 0.878288i | \(-0.341314\pi\) | |||||||
\(114\) | −18471.6 | + | 10664.6i | −1.42133 | + | 0.820605i | ||||
\(115\) | 9014.39 | − | 5204.46i | 0.681617 | − | 0.393532i | ||||
\(116\) | −884.579 | + | 3301.29i | −0.0657386 | + | 0.245340i | ||||
\(117\) | −30888.8 | − | 30888.8i | −2.25647 | − | 2.25647i | ||||
\(118\) | −4791.22 | − | 8298.64i | −0.344098 | − | 0.595995i | ||||
\(119\) | −1085.64 | − | 1085.64i | −0.0766643 | − | 0.0766643i | ||||
\(120\) | −3877.16 | + | 6715.44i | −0.269247 | + | 0.466350i | ||||
\(121\) | 7422.29 | 0.506952 | ||||||||
\(122\) | 7654.53i | 0.514279i | ||||||||
\(123\) | −23951.7 | + | 41485.6i | −1.58317 | + | 2.74212i | ||||
\(124\) | 2757.82 | − | 10292.3i | 0.179359 | − | 0.669377i | ||||
\(125\) | 11967.2 | − | 11967.2i | 0.765902 | − | 0.765902i | ||||
\(126\) | 2699.71 | + | 10075.5i | 0.170050 | + | 0.634635i | ||||
\(127\) | −1514.51 | + | 2623.21i | −0.0939000 | + | 0.162640i | −0.909149 | − | 0.416471i | \(-0.863267\pi\) |
0.815249 | + | 0.579111i | \(0.196600\pi\) | |||||||
\(128\) | −1398.81 | + | 374.810i | −0.0853766 | + | 0.0228766i | ||||
\(129\) | −38685.6 | − | 10365.8i | −2.32471 | − | 0.622905i | ||||
\(130\) | 4036.72 | − | 15065.2i | 0.238859 | − | 0.891434i | ||||
\(131\) | 1069.14 | + | 3990.08i | 0.0623004 | + | 0.232508i | 0.990055 | − | 0.140683i | \(-0.0449300\pi\) |
−0.927754 | + | 0.373192i | \(0.878263\pi\) | |||||||
\(132\) | −9344.61 | − | 5395.11i | −0.536307 | − | 0.309637i | ||||
\(133\) | −9894.91 | + | 2651.33i | −0.559382 | + | 0.149886i | ||||
\(134\) | 10152.8 | + | 10152.8i | 0.565427 | + | 0.565427i | ||||
\(135\) | −29795.6 | − | 7983.72i | −1.63488 | − | 0.438064i | ||||
\(136\) | 1395.14 | + | 805.484i | 0.0754293 | + | 0.0435491i | ||||
\(137\) | −20039.9 | −1.06771 | −0.533856 | − | 0.845576i | \(-0.679257\pi\) | ||||
−0.533856 | + | 0.845576i | \(0.679257\pi\) | |||||||
\(138\) | 21650.3i | 1.13686i | ||||||||
\(139\) | 32083.3 | + | 18523.3i | 1.66054 | + | 0.958713i | 0.972458 | + | 0.233080i | \(0.0748803\pi\) |
0.688082 | + | 0.725633i | \(0.258453\pi\) | |||||||
\(140\) | −2633.44 | + | 2633.44i | −0.134359 | + | 0.134359i | ||||
\(141\) | −582.170 | + | 336.116i | −0.0292827 | + | 0.0169064i | ||||
\(142\) | −12768.6 | + | 12768.6i | −0.633239 | + | 0.633239i | ||||
\(143\) | 20963.4 | + | 5617.14i | 1.02516 | + | 0.274690i | ||||
\(144\) | −5472.38 | − | 9478.45i | −0.263907 | − | 0.457101i | ||||
\(145\) | −4611.25 | − | 7986.91i | −0.219322 | − | 0.379877i | ||||
\(146\) | 16449.1 | − | 4407.52i | 0.771679 | − | 0.206771i | ||||
\(147\) | − | 30733.0i | − | 1.42223i | ||||||
\(148\) | −627.647 | − | 10934.0i | −0.0286545 | − | 0.499178i | ||||
\(149\) | 2615.82 | 0.117825 | 0.0589123 | − | 0.998263i | \(-0.481237\pi\) | ||||
0.0589123 | + | 0.998263i | \(0.481237\pi\) | |||||||
\(150\) | 1847.65 | + | 6895.52i | 0.0821178 | + | 0.306468i | ||||
\(151\) | −1581.52 | + | 913.093i | −0.0693620 | + | 0.0400462i | −0.534280 | − | 0.845308i | \(-0.679417\pi\) |
0.464918 | + | 0.885354i | \(0.346084\pi\) | |||||||
\(152\) | 9308.59 | − | 5374.32i | 0.402899 | − | 0.232614i | ||||
\(153\) | −3151.19 | + | 11760.4i | −0.134615 | + | 0.502388i | ||||
\(154\) | −3664.46 | − | 3664.46i | −0.154514 | − | 0.154514i | ||||
\(155\) | 14376.3 | + | 24900.5i | 0.598391 | + | 1.03644i | ||||
\(156\) | 22939.0 | + | 22939.0i | 0.942595 | + | 0.942595i | ||||
\(157\) | 20857.0 | − | 36125.3i | 0.846158 | − | 1.46559i | −0.0384530 | − | 0.999260i | \(-0.512243\pi\) |
0.884611 | − | 0.466329i | \(-0.154424\pi\) | |||||||
\(158\) | −14292.5 | −0.572525 | ||||||||
\(159\) | − | 14513.5i | − | 0.574087i | ||||||
\(160\) | 1953.86 | − | 3384.18i | 0.0763226 | − | 0.132195i | ||||
\(161\) | −2691.25 | + | 10043.9i | −0.103825 | + | 0.387480i | ||||
\(162\) | 17664.3 | − | 17664.3i | 0.673078 | − | 0.673078i | ||||
\(163\) | −7201.89 | − | 26877.8i | −0.271064 | − | 1.01162i | −0.958433 | − | 0.285316i | \(-0.907901\pi\) |
0.687370 | − | 0.726308i | \(-0.258765\pi\) | |||||||
\(164\) | 12070.2 | − | 20906.3i | 0.448775 | − | 0.777300i | ||||
\(165\) | 28124.3 | − | 7535.89i | 1.03303 | − | 0.276800i | ||||
\(166\) | −21846.8 | − | 5853.83i | −0.792815 | − | 0.212434i | ||||
\(167\) | 7812.95 | − | 29158.3i | 0.280144 | − | 1.04551i | −0.672170 | − | 0.740396i | \(-0.734638\pi\) |
0.952315 | − | 0.305117i | \(-0.0986956\pi\) | |||||||
\(168\) | −2004.89 | − | 7482.37i | −0.0710351 | − | 0.265107i | ||||
\(169\) | −31773.3 | − | 18344.3i | −1.11247 | − | 0.642285i | ||||
\(170\) | −4198.93 | + | 1125.10i | −0.145292 | + | 0.0389308i | ||||
\(171\) | 57442.0 | + | 57442.0i | 1.96443 | + | 1.96443i | ||||
\(172\) | 19495.2 | + | 5223.73i | 0.658979 | + | 0.176573i | ||||
\(173\) | 19521.5 | + | 11270.7i | 0.652259 | + | 0.376582i | 0.789321 | − | 0.613980i | \(-0.210433\pi\) |
−0.137062 | + | 0.990562i | \(0.543766\pi\) | |||||||
\(174\) | 19182.5 | 0.633589 | ||||||||
\(175\) | 3428.61i | 0.111955i | ||||||||
\(176\) | 4709.13 | + | 2718.82i | 0.152025 | + | 0.0877717i | ||||
\(177\) | −38030.0 | + | 38030.0i | −1.21389 | + | 1.21389i | ||||
\(178\) | 12509.5 | − | 7222.38i | 0.394822 | − | 0.227951i | ||||
\(179\) | −21254.5 | + | 21254.5i | −0.663352 | + | 0.663352i | −0.956169 | − | 0.292816i | \(-0.905408\pi\) |
0.292816 | + | 0.956169i | \(0.405408\pi\) | |||||||
\(180\) | 28527.1 | + | 7643.82i | 0.880467 | + | 0.235921i | ||||
\(181\) | −1788.15 | − | 3097.17i | −0.0545817 | − | 0.0945383i | 0.837444 | − | 0.546524i | \(-0.184049\pi\) |
−0.892025 | + | 0.451985i | \(0.850716\pi\) | |||||||
\(182\) | 7790.29 | + | 13493.2i | 0.235186 | + | 0.407354i | ||||
\(183\) | 41498.1 | − | 11119.4i | 1.23916 | − | 0.332031i | ||||
\(184\) | − | 10910.5i | − | 0.322260i | ||||||
\(185\) | 22060.4 | + | 19665.2i | 0.644569 | + | 0.574585i | ||||
\(186\) | −59804.8 | −1.72866 | ||||||||
\(187\) | −1565.59 | − | 5842.86i | −0.0447708 | − | 0.167087i | ||||
\(188\) | 293.379 | − | 169.382i | 0.00830067 | − | 0.00479239i | ||||
\(189\) | 26686.5 | − | 15407.5i | 0.747081 | − | 0.431328i | ||||
\(190\) | −7506.84 | + | 28015.9i | −0.207946 | + | 0.776064i | ||||
\(191\) | −45087.3 | − | 45087.3i | −1.23591 | − | 1.23591i | −0.961657 | − | 0.274256i | \(-0.911568\pi\) |
−0.274256 | − | 0.961657i | \(-0.588432\pi\) | |||||||
\(192\) | 4063.97 | + | 7039.00i | 0.110242 | + | 0.190945i | ||||
\(193\) | −30365.9 | − | 30365.9i | −0.815213 | − | 0.815213i | 0.170197 | − | 0.985410i | \(-0.445560\pi\) |
−0.985410 | + | 0.170197i | \(0.945560\pi\) | |||||||
\(194\) | 13378.2 | − | 23171.8i | 0.355464 | − | 0.615682i | ||||
\(195\) | −87538.2 | −2.30212 | ||||||||
\(196\) | 15487.6i | 0.403155i | ||||||||
\(197\) | −27055.7 | + | 46861.9i | −0.697151 | + | 1.20750i | 0.272300 | + | 0.962212i | \(0.412216\pi\) |
−0.969450 | + | 0.245288i | \(0.921118\pi\) | |||||||
\(198\) | −10636.5 | + | 39695.9i | −0.271311 | + | 1.01255i | ||||
\(199\) | 43561.1 | − | 43561.1i | 1.10000 | − | 1.10000i | 0.105591 | − | 0.994410i | \(-0.466327\pi\) |
0.994410 | − | 0.105591i | \(-0.0336733\pi\) | |||||||
\(200\) | −931.106 | − | 3474.94i | −0.0232777 | − | 0.0868734i | ||||
\(201\) | 40293.7 | − | 69790.7i | 0.997343 | − | 1.72745i | ||||
\(202\) | −47770.0 | + | 12799.9i | −1.17072 | + | 0.313693i | ||||
\(203\) | 8899.06 | + | 2384.50i | 0.215949 | + | 0.0578635i | ||||
\(204\) | 2340.18 | − | 8733.66i | 0.0562327 | − | 0.209863i | ||||
\(205\) | 16859.7 | + | 62921.3i | 0.401183 | + | 1.49723i | ||||
\(206\) | 25462.3 | + | 14700.7i | 0.600017 | + | 0.346420i | ||||
\(207\) | 79648.6 | − | 21341.8i | 1.85882 | − | 0.498069i | ||||
\(208\) | −11559.9 | − | 11559.9i | −0.267194 | − | 0.267194i | ||||
\(209\) | −38984.5 | − | 10445.9i | −0.892482 | − | 0.239140i | ||||
\(210\) | 18102.3 | + | 10451.4i | 0.410483 | + | 0.236993i | ||||
\(211\) | 22233.1 | 0.499384 | 0.249692 | − | 0.968325i | \(-0.419671\pi\) | ||||
0.249692 | + | 0.968325i | \(0.419671\pi\) | |||||||
\(212\) | 7313.93i | 0.162734i | ||||||||
\(213\) | 87771.9 | + | 50675.1i | 1.93462 | + | 1.11695i | ||||
\(214\) | 18194.6 | − | 18194.6i | 0.397297 | − | 0.397297i | ||||
\(215\) | −47165.3 | + | 27230.9i | −1.02034 | + | 0.589095i | ||||
\(216\) | −22862.9 | + | 22862.9i | −0.490031 | + | 0.490031i | ||||
\(217\) | −27744.3 | − | 7434.07i | −0.589189 | − | 0.157873i | ||||
\(218\) | 18121.6 | + | 31387.5i | 0.381315 | + | 0.660456i | ||||
\(219\) | −47789.7 | − | 82774.1i | −0.996428 | − | 1.72586i | ||||
\(220\) | −14173.0 | + | 3797.64i | −0.292830 | + | 0.0784637i | ||||
\(221\) | 18186.2i | 0.372354i | ||||||||
\(222\) | −58365.6 | + | 19286.0i | −1.18427 | + | 0.391324i | ||||
\(223\) | −71074.0 | −1.42923 | −0.714614 | − | 0.699519i | \(-0.753397\pi\) | ||||
−0.714614 | + | 0.699519i | \(0.753397\pi\) | |||||||
\(224\) | 1010.35 | + | 3770.67i | 0.0201361 | + | 0.0751489i | ||||
\(225\) | 23546.4 | − | 13594.5i | 0.465115 | − | 0.268534i | ||||
\(226\) | 45328.1 | − | 26170.2i | 0.887464 | − | 0.512378i | ||||
\(227\) | 11464.9 | − | 42787.5i | 0.222494 | − | 0.830358i | −0.760899 | − | 0.648870i | \(-0.775242\pi\) |
0.983393 | − | 0.181488i | \(-0.0580914\pi\) | |||||||
\(228\) | −42658.3 | − | 42658.3i | −0.820605 | − | 0.820605i | ||||
\(229\) | 1278.25 | + | 2213.99i | 0.0243750 | + | 0.0422187i | 0.877956 | − | 0.478742i | \(-0.158907\pi\) |
−0.853581 | + | 0.520961i | \(0.825574\pi\) | |||||||
\(230\) | 20817.8 | + | 20817.8i | 0.393532 | + | 0.393532i | ||||
\(231\) | −14543.2 | + | 25189.6i | −0.272544 | + | 0.472060i | ||||
\(232\) | −9666.86 | −0.179601 | ||||||||
\(233\) | 61126.3i | 1.12594i | 0.826476 | + | 0.562972i | \(0.190342\pi\) | ||||
−0.826476 | + | 0.562972i | \(0.809658\pi\) | |||||||
\(234\) | 61777.5 | − | 107002.i | 1.12823 | − | 1.95416i | ||||
\(235\) | −236.593 | + | 882.978i | −0.00428417 | + | 0.0159887i | ||||
\(236\) | 19164.9 | − | 19164.9i | 0.344098 | − | 0.344098i | ||||
\(237\) | 20762.1 | + | 77485.1i | 0.369636 | + | 1.37950i | ||||
\(238\) | 2171.29 | − | 3760.78i | 0.0383321 | − | 0.0663932i | ||||
\(239\) | −46714.3 | + | 12517.1i | −0.817813 | + | 0.219132i | −0.643390 | − | 0.765538i | \(-0.722473\pi\) |
−0.174423 | + | 0.984671i | \(0.555806\pi\) | |||||||
\(240\) | −21185.2 | − | 5676.55i | −0.367798 | − | 0.0985513i | ||||
\(241\) | 2438.25 | − | 9099.69i | 0.0419802 | − | 0.156672i | −0.941754 | − | 0.336303i | \(-0.890823\pi\) |
0.983734 | + | 0.179630i | \(0.0574901\pi\) | |||||||
\(242\) | 5433.49 | + | 20278.1i | 0.0927787 | + | 0.346255i | ||||
\(243\) | −21187.9 | − | 12232.9i | −0.358819 | − | 0.207165i | ||||
\(244\) | −20912.6 | + | 5603.51i | −0.351259 | + | 0.0941196i | ||||
\(245\) | −29551.3 | − | 29551.3i | −0.492317 | − | 0.492317i | ||||
\(246\) | −130875. | − | 35067.7i | −2.16264 | − | 0.579479i | ||||
\(247\) | 105084. | + | 60670.4i | 1.72244 | + | 0.994451i | ||||
\(248\) | 30138.1 | 0.490018 | ||||||||
\(249\) | 126943.i | 2.04744i | ||||||||
\(250\) | 41455.6 | + | 23934.4i | 0.663290 | + | 0.382951i | ||||
\(251\) | −6373.78 | + | 6373.78i | −0.101169 | + | 0.101169i | −0.755880 | − | 0.654710i | \(-0.772791\pi\) |
0.654710 | + | 0.755880i | \(0.272791\pi\) | |||||||
\(252\) | −25550.4 | + | 14751.5i | −0.402342 | + | 0.232293i | ||||
\(253\) | −28968.3 | + | 28968.3i | −0.452566 | + | 0.452566i | ||||
\(254\) | −8275.45 | − | 2217.40i | −0.128270 | − | 0.0343698i | ||||
\(255\) | 12199.2 | + | 21129.6i | 0.187608 | + | 0.324946i | ||||
\(256\) | −2048.00 | − | 3547.24i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 32125.3 | − | 8607.94i | 0.486386 | − | 0.130327i | −0.00728881 | − | 0.999973i | \(-0.502320\pi\) |
0.493674 | + | 0.869647i | \(0.335653\pi\) | |||||||
\(258\) | − | 113279.i | − | 1.70181i | ||||||
\(259\) | −29474.0 | + | 1691.90i | −0.439379 | + | 0.0252218i | ||||
\(260\) | 44114.0 | 0.652575 | ||||||||
\(261\) | −18909.2 | − | 70570.1i | −0.277583 | − | 1.03595i | ||||
\(262\) | −10118.4 | + | 5841.88i | −0.147404 | + | 0.0851040i | ||||
\(263\) | 2089.26 | − | 1206.24i | 0.0302052 | − | 0.0174390i | −0.484821 | − | 0.874613i | \(-0.661115\pi\) |
0.515027 | + | 0.857174i | \(0.327782\pi\) | |||||||
\(264\) | 7898.99 | − | 29479.4i | 0.113335 | − | 0.422972i | ||||
\(265\) | −13955.5 | − | 13955.5i | −0.198725 | − | 0.198725i | ||||
\(266\) | −14487.2 | − | 25092.5i | −0.204748 | − | 0.354634i | ||||
\(267\) | −57327.3 | − | 57327.3i | −0.804153 | − | 0.804153i | ||||
\(268\) | −20305.6 | + | 35170.4i | −0.282713 | + | 0.489674i | ||||
\(269\) | −58633.5 | −0.810291 | −0.405145 | − | 0.914252i | \(-0.632779\pi\) | ||||
−0.405145 | + | 0.914252i | \(0.632779\pi\) | |||||||
\(270\) | − | 87247.7i | − | 1.19681i | ||||||
\(271\) | 41087.1 | − | 71164.9i | 0.559457 | − | 0.969008i | −0.438085 | − | 0.898934i | \(-0.644343\pi\) |
0.997542 | − | 0.0700744i | \(-0.0223237\pi\) | |||||||
\(272\) | −1179.31 | + | 4401.25i | −0.0159401 | + | 0.0594892i | ||||
\(273\) | 61835.0 | − | 61835.0i | 0.829677 | − | 0.829677i | ||||
\(274\) | −14670.2 | − | 54750.0i | −0.195405 | − | 0.729260i | ||||
\(275\) | −6754.11 | + | 11698.5i | −0.0893105 | + | 0.154690i | ||||
\(276\) | −59149.6 | + | 15849.1i | −0.776487 | + | 0.208059i | ||||
\(277\) | −41044.1 | − | 10997.7i | −0.534923 | − | 0.143332i | −0.0187621 | − | 0.999824i | \(-0.505973\pi\) |
−0.516160 | + | 0.856492i | \(0.672639\pi\) | |||||||
\(278\) | −27120.0 | + | 101213.i | −0.350913 | + | 1.30963i | ||||
\(279\) | 58952.6 | + | 220014.i | 0.757347 | + | 2.82646i | ||||
\(280\) | −9122.49 | − | 5266.87i | −0.116358 | − | 0.0671795i | ||||
\(281\) | −125058. | + | 33509.2i | −1.58379 | + | 0.424376i | −0.940098 | − | 0.340905i | \(-0.889266\pi\) |
−0.643696 | + | 0.765282i | \(0.722600\pi\) | |||||||
\(282\) | −1344.46 | − | 1344.46i | −0.0169064 | − | 0.0169064i | ||||
\(283\) | −35615.7 | − | 9543.21i | −0.444702 | − | 0.119158i | 0.0295174 | − | 0.999564i | \(-0.490603\pi\) |
−0.474219 | + | 0.880407i | \(0.657270\pi\) | |||||||
\(284\) | −44231.8 | − | 25537.3i | −0.548401 | − | 0.316619i | ||||
\(285\) | 162790. | 2.00418 | ||||||||
\(286\) | 61385.2i | 0.750467i | ||||||||
\(287\) | −56355.5 | − | 32536.9i | −0.684183 | − | 0.395013i | ||||
\(288\) | 21889.5 | − | 21889.5i | 0.263907 | − | 0.263907i | ||||
\(289\) | −67941.6 | + | 39226.1i | −0.813467 | + | 0.469656i | ||||
\(290\) | 18445.0 | − | 18445.0i | 0.219322 | − | 0.219322i | ||||
\(291\) | −145057. | − | 38867.9i | −1.71298 | − | 0.458992i | ||||
\(292\) | 24083.2 | + | 41713.2i | 0.282454 | + | 0.489225i | ||||
\(293\) | −5063.08 | − | 8769.50i | −0.0589765 | − | 0.102150i | 0.835030 | − | 0.550205i | \(-0.185450\pi\) |
−0.894006 | + | 0.448055i | \(0.852117\pi\) | |||||||
\(294\) | 83964.1 | − | 22498.1i | 0.971402 | − | 0.260286i | ||||
\(295\) | 73135.6i | 0.840398i | ||||||||
\(296\) | 29412.8 | − | 9719.01i | 0.335701 | − | 0.110927i | ||||
\(297\) | 121406. | 1.37635 | ||||||||
\(298\) | 1914.91 | + | 7146.56i | 0.0215634 | + | 0.0804757i | ||||
\(299\) | 106666. | − | 61583.8i | 1.19312 | − | 0.688849i | ||||
\(300\) | −17486.4 | + | 10095.7i | −0.194293 | + | 0.112175i | ||||
\(301\) | 14081.2 | − | 52551.9i | 0.155420 | − | 0.580036i | ||||
\(302\) | −3652.37 | − | 3652.37i | −0.0400462 | − | 0.0400462i | ||||
\(303\) | 138787. | + | 240385.i | 1.51169 | + | 2.61832i | ||||
\(304\) | 21497.3 | + | 21497.3i | 0.232614 | + | 0.232614i | ||||
\(305\) | 29210.7 | − | 50594.4i | 0.314009 | − | 0.543879i | ||||
\(306\) | −34436.9 | −0.367774 | ||||||||
\(307\) | 53438.5i | 0.566993i | 0.958973 | + | 0.283497i | \(0.0914944\pi\) | ||||
−0.958973 | + | 0.283497i | \(0.908506\pi\) | |||||||
\(308\) | 7328.92 | − | 12694.1i | 0.0772571 | − | 0.133813i | ||||
\(309\) | 42710.0 | − | 159396.i | 0.447314 | − | 1.66940i | ||||
\(310\) | −57505.4 | + | 57505.4i | −0.598391 | + | 0.598391i | ||||
\(311\) | 30150.9 | + | 112525.i | 0.311730 | + | 1.16339i | 0.926995 | + | 0.375073i | \(0.122382\pi\) |
−0.615265 | + | 0.788320i | \(0.710951\pi\) | |||||||
\(312\) | −45878.0 | + | 79463.0i | −0.471298 | + | 0.816312i | ||||
\(313\) | 185526. | − | 49711.5i | 1.89372 | − | 0.507421i | 0.895691 | − | 0.444677i | \(-0.146681\pi\) |
0.998030 | − | 0.0627444i | \(-0.0199853\pi\) | |||||||
\(314\) | 113965. | + | 30536.7i | 1.15587 | + | 0.309715i | ||||
\(315\) | 20604.9 | − | 76898.5i | 0.207658 | − | 0.774992i | ||||
\(316\) | −10462.9 | − | 39047.9i | −0.104779 | − | 0.391042i | ||||
\(317\) | 14447.4 | + | 8341.22i | 0.143771 | + | 0.0830063i | 0.570160 | − | 0.821534i | \(-0.306881\pi\) |
−0.426389 | + | 0.904540i | \(0.640215\pi\) | |||||||
\(318\) | 39651.6 | − | 10624.6i | 0.392108 | − | 0.105065i | ||||
\(319\) | 25666.4 | + | 25666.4i | 0.252223 | + | 0.252223i | ||||
\(320\) | 10676.1 | + | 2860.65i | 0.104259 | + | 0.0279360i | ||||
\(321\) | −125070. | − | 72209.3i | −1.21379 | − | 0.700782i | ||||
\(322\) | −29410.5 | −0.283655 | ||||||||
\(323\) | − | 33819.7i | − | 0.324164i | ||||||
\(324\) | 61190.8 | + | 35328.5i | 0.582903 | + | 0.336539i | ||||
\(325\) | 28717.2 | − | 28717.2i | 0.271879 | − | 0.271879i | ||||
\(326\) | 68159.5 | − | 39351.9i | 0.641344 | − | 0.370280i | ||||
\(327\) | 143839. | − | 143839.i | 1.34518 | − | 1.34518i | ||||
\(328\) | 65953.0 | + | 17672.1i | 0.613037 | + | 0.164263i | ||||
\(329\) | −456.592 | − | 790.840i | −0.00421829 | − | 0.00730629i | ||||
\(330\) | 41176.9 | + | 71320.5i | 0.378116 | + | 0.654917i | ||||
\(331\) | −187861. | + | 50337.3i | −1.71467 | + | 0.459445i | −0.976563 | − | 0.215233i | \(-0.930949\pi\) |
−0.738111 | + | 0.674679i | \(0.764282\pi\) | |||||||
\(332\) | − | 63971.9i | − | 0.580381i | ||||||
\(333\) | 128485. | + | 195708.i | 1.15868 | + | 1.76490i | ||||
\(334\) | 85381.5 | 0.765369 | ||||||||
\(335\) | −28362.9 | − | 105852.i | −0.252732 | − | 0.943210i | ||||
\(336\) | 18974.5 | − | 10954.9i | 0.168071 | − | 0.0970358i | ||||
\(337\) | 67112.4 | − | 38747.4i | 0.590939 | − | 0.341179i | −0.174529 | − | 0.984652i | \(-0.555840\pi\) |
0.765469 | + | 0.643473i | \(0.222507\pi\) | |||||||
\(338\) | 26857.9 | − | 100235.i | 0.235093 | − | 0.877378i | ||||
\(339\) | −207724. | − | 207724.i | −1.80754 | − | 1.80754i | ||||
\(340\) | −6147.66 | − | 10648.1i | −0.0531805 | − | 0.0921113i | ||||
\(341\) | −80019.4 | − | 80019.4i | −0.688155 | − | 0.688155i | ||||
\(342\) | −114884. | + | 198985.i | −0.982217 | + | 1.70125i | ||||
\(343\) | 93526.4 | 0.794961 | ||||||||
\(344\) | 57086.0i | 0.482406i | ||||||||
\(345\) | 82620.2 | − | 143102.i | 0.694142 | − | 1.20229i | ||||
\(346\) | −16501.5 | + | 61584.4i | −0.137839 | + | 0.514421i | ||||
\(347\) | −37720.2 | + | 37720.2i | −0.313267 | + | 0.313267i | −0.846174 | − | 0.532907i | \(-0.821100\pi\) |
0.532907 | + | 0.846174i | \(0.321100\pi\) | |||||||
\(348\) | 14042.6 | + | 52407.7i | 0.115955 | + | 0.432749i | ||||
\(349\) | −33282.1 | + | 57646.4i | −0.273250 | + | 0.473283i | −0.969692 | − | 0.244330i | \(-0.921432\pi\) |
0.696442 | + | 0.717613i | \(0.254765\pi\) | |||||||
\(350\) | −9367.13 | + | 2509.91i | −0.0764664 | + | 0.0204891i | ||||
\(351\) | −352569. | − | 94470.5i | −2.86174 | − | 0.766800i | ||||
\(352\) | −3980.62 | + | 14855.9i | −0.0321267 | + | 0.119898i | ||||
\(353\) | −19606.3 | − | 73171.7i | −0.157343 | − | 0.587210i | −0.998893 | − | 0.0470324i | \(-0.985024\pi\) |
0.841551 | − | 0.540178i | \(-0.181643\pi\) | |||||||
\(354\) | −131740. | − | 76060.1i | −1.05126 | − | 0.606946i | ||||
\(355\) | 133124. | − | 35670.4i | 1.05633 | − | 0.283043i | ||||
\(356\) | 28889.5 | + | 28889.5i | 0.227951 | + | 0.227951i | ||||
\(357\) | −23542.7 | − | 6308.25i | −0.184723 | − | 0.0494963i | ||||
\(358\) | −73627.7 | − | 42509.0i | −0.574480 | − | 0.331676i | ||||
\(359\) | 121559. | 0.943190 | 0.471595 | − | 0.881815i | \(-0.343678\pi\) | ||||
0.471595 | + | 0.881815i | \(0.343678\pi\) | |||||||
\(360\) | 83533.3i | 0.644547i | ||||||||
\(361\) | −82557.8 | − | 47664.8i | −0.633496 | − | 0.365749i | ||||
\(362\) | 7152.61 | − | 7152.61i | 0.0545817 | − | 0.0545817i | ||||
\(363\) | 102042. | − | 58914.0i | 0.774401 | − | 0.447100i | ||||
\(364\) | −31161.2 | + | 31161.2i | −0.235186 | + | 0.235186i | ||||
\(365\) | −125544. | − | 33639.3i | −0.942344 | − | 0.252500i | ||||
\(366\) | 60757.4 | + | 105235.i | 0.453562 | + | 0.785593i | ||||
\(367\) | 14675.0 | + | 25417.8i | 0.108955 | + | 0.188715i | 0.915347 | − | 0.402666i | \(-0.131916\pi\) |
−0.806392 | + | 0.591381i | \(0.798583\pi\) | |||||||
\(368\) | 29807.9 | − | 7987.00i | 0.220108 | − | 0.0589778i | ||||
\(369\) | 516039.i | 3.78992i | ||||||||
\(370\) | −37577.0 | + | 74665.9i | −0.274485 | + | 0.545405i | ||||
\(371\) | 19715.6 | 0.143240 | ||||||||
\(372\) | −43780.1 | − | 163390.i | −0.316367 | − | 1.18070i | ||||
\(373\) | −221805. | + | 128059.i | −1.59424 | + | 0.920436i | −0.601675 | + | 0.798741i | \(0.705500\pi\) |
−0.992568 | + | 0.121695i | \(0.961167\pi\) | |||||||
\(374\) | 14816.9 | − | 8554.55i | 0.105929 | − | 0.0611581i | ||||
\(375\) | 69536.8 | − | 259515.i | 0.494484 | − | 1.84544i | ||||
\(376\) | 677.530 | + | 677.530i | 0.00479239 | + | 0.00479239i | ||||
\(377\) | −54564.4 | − | 94508.3i | −0.383908 | − | 0.664947i | ||||
\(378\) | 61629.8 | + | 61629.8i | 0.431328 | + | 0.431328i | ||||
\(379\) | 29127.1 | − | 50449.7i | 0.202777 | − | 0.351220i | −0.746645 | − | 0.665223i | \(-0.768337\pi\) |
0.949422 | + | 0.314002i | \(0.101670\pi\) | |||||||
\(380\) | −82036.3 | −0.568118 | ||||||||
\(381\) | 48085.4i | 0.331256i | ||||||||
\(382\) | 90174.7 | − | 156187.i | 0.617957 | − | 1.07033i | ||||
\(383\) | 39260.9 | − | 146524.i | 0.267647 | − | 0.998873i | −0.692963 | − | 0.720973i | \(-0.743695\pi\) |
0.960610 | − | 0.277900i | \(-0.0896382\pi\) | |||||||
\(384\) | −16255.9 | + | 16255.9i | −0.110242 | + | 0.110242i | ||||
\(385\) | 10237.0 | + | 38205.1i | 0.0690641 | + | 0.257751i | ||||
\(386\) | 60731.8 | − | 105190.i | 0.407607 | − | 0.705995i | ||||
\(387\) | −416740. | + | 111665.i | −2.78255 | + | 0.745582i | ||||
\(388\) | 73100.1 | + | 19587.1i | 0.485573 | + | 0.130109i | ||||
\(389\) | 30291.7 | − | 113050.i | 0.200181 | − | 0.747087i | −0.790683 | − | 0.612226i | \(-0.790274\pi\) |
0.990864 | − | 0.134861i | \(-0.0430589\pi\) | |||||||
\(390\) | −64082.4 | − | 239159.i | −0.421318 | − | 1.57238i | ||||
\(391\) | −29729.7 | − | 17164.4i | −0.194463 | − | 0.112273i | ||||
\(392\) | −42312.9 | + | 11337.7i | −0.275360 | + | 0.0737825i | ||||
\(393\) | 46369.6 | + | 46369.6i | 0.300226 | + | 0.300226i | ||||
\(394\) | −147835. | − | 39612.3i | −0.952325 | − | 0.255175i | ||||
\(395\) | 94469.7 | + | 54542.1i | 0.605478 | + | 0.349573i | ||||
\(396\) | −116238. | −0.741235 | ||||||||
\(397\) | 43050.6i | 0.273148i | 0.990630 | + | 0.136574i | \(0.0436092\pi\) | ||||
−0.990630 | + | 0.136574i | \(0.956391\pi\) | |||||||
\(398\) | 150900. | + | 87122.2i | 0.952628 | + | 0.550000i | ||||
\(399\) | −114991. | + | 114991.i | −0.722300 | + | 0.722300i | ||||
\(400\) | 8812.08 | − | 5087.66i | 0.0550755 | − | 0.0317979i | ||||
\(401\) | 21173.2 | − | 21173.2i | 0.131674 | − | 0.131674i | −0.638198 | − | 0.769872i | \(-0.720320\pi\) |
0.769872 | + | 0.638198i | \(0.220320\pi\) | |||||||
\(402\) | 220169. | + | 58994.0i | 1.36240 | + | 0.365053i | ||||
\(403\) | 170114. | + | 294646.i | 1.04744 | + | 1.81422i | ||||
\(404\) | −69940.2 | − | 121140.i | −0.428513 | − | 0.742206i | ||||
\(405\) | −184165. | + | 49346.9i | −1.12279 | + | 0.300850i | ||||
\(406\) | 26058.2i | 0.158086i | ||||||||
\(407\) | −103899. | − | 52288.8i | −0.627221 | − | 0.315660i | ||||
\(408\) | 25573.9 | 0.153630 | ||||||||
\(409\) | 45786.1 | + | 170876.i | 0.273708 | + | 1.02149i | 0.956702 | + | 0.291068i | \(0.0940105\pi\) |
−0.682995 | + | 0.730423i | \(0.739323\pi\) | |||||||
\(410\) | −159562. | + | 92123.2i | −0.949209 | + | 0.548026i | ||||
\(411\) | −275509. | + | 159065.i | −1.63100 | + | 0.941655i | ||||
\(412\) | −21523.3 | + | 80326.0i | −0.126799 | + | 0.473219i | ||||
\(413\) | −51661.4 | − | 51661.4i | −0.302877 | − | 0.302877i | ||||
\(414\) | 116614. | + | 201981.i | 0.680375 | + | 1.17844i | ||||
\(415\) | 122062. | + | 122062.i | 0.708738 | + | 0.708738i | ||||
\(416\) | 23119.8 | − | 40044.7i | 0.133597 | − | 0.231397i | ||||
\(417\) | 588110. | 3.38210 | ||||||||
\(418\) | − | 114155.i | − | 0.653342i | ||||||
\(419\) | −66013.7 | + | 114339.i | −0.376015 | + | 0.651278i | −0.990478 | − | 0.137668i | \(-0.956039\pi\) |
0.614463 | + | 0.788946i | \(0.289373\pi\) | |||||||
\(420\) | −15301.9 | + | 57107.4i | −0.0867453 | + | 0.323738i | ||||
\(421\) | 186639. | − | 186639.i | 1.05302 | − | 1.05302i | 0.0545078 | − | 0.998513i | \(-0.482641\pi\) |
0.998513 | − | 0.0545078i | \(-0.0173590\pi\) | |||||||
\(422\) | 16275.7 | + | 60741.8i | 0.0913936 | + | 0.341085i | ||||
\(423\) | −3620.80 | + | 6271.41i | −0.0202360 | + | 0.0350497i | ||||
\(424\) | −19982.0 | + | 5354.17i | −0.111150 | + | 0.0297825i | ||||
\(425\) | −10933.6 | − | 2929.65i | −0.0605321 | − | 0.0162195i | ||||
\(426\) | −74193.5 | + | 276894.i | −0.408834 | + | 1.52579i | ||||
\(427\) | 15105.0 | + | 56372.5i | 0.0828445 | + | 0.309180i | ||||
\(428\) | 63028.0 | + | 36389.2i | 0.344069 | + | 0.198648i | ||||
\(429\) | 332792. | − | 89171.4i | 1.80825 | − | 0.484519i | ||||
\(430\) | −108924. | − | 108924.i | −0.589095 | − | 0.589095i | ||||
\(431\) | 111290. | + | 29820.1i | 0.599103 | + | 0.160529i | 0.545610 | − | 0.838039i | \(-0.316298\pi\) |
0.0534927 | + | 0.998568i | \(0.482965\pi\) | |||||||
\(432\) | −79199.3 | − | 45725.8i | −0.424379 | − | 0.245015i | ||||
\(433\) | −179261. | −0.956114 | −0.478057 | − | 0.878329i | \(-0.658659\pi\) | ||||
−0.478057 | + | 0.878329i | \(0.658659\pi\) | |||||||
\(434\) | − | 81241.0i | − | 0.431316i | ||||||
\(435\) | −126791. | − | 73203.0i | −0.670056 | − | 0.386857i | ||||
\(436\) | −72486.4 | + | 72486.4i | −0.381315 | + | 0.381315i | ||||
\(437\) | −198361. | + | 114524.i | −1.03871 | + | 0.599699i | ||||
\(438\) | 191159. | − | 191159.i | 0.996428 | − | 0.996428i | ||||
\(439\) | −125960. | − | 33750.9i | −0.653589 | − | 0.175129i | −0.0832378 | − | 0.996530i | \(-0.526526\pi\) |
−0.570351 | + | 0.821401i | \(0.693193\pi\) | |||||||
\(440\) | −20750.7 | − | 35941.3i | −0.107183 | − | 0.185647i | ||||
\(441\) | −165535. | − | 286716.i | −0.851165 | − | 1.47426i | ||||
\(442\) | −49685.5 | + | 13313.2i | −0.254323 | + | 0.0681456i | ||||
\(443\) | − | 181957.i | − | 0.927174i | −0.886052 | − | 0.463587i | \(-0.846562\pi\) | ||
0.886052 | − | 0.463587i | \(-0.153438\pi\) | |||||||
\(444\) | −95416.9 | − | 145339.i | −0.484016 | − | 0.737254i | ||||
\(445\) | −110246. | −0.556729 | ||||||||
\(446\) | −52029.8 | − | 194178.i | −0.261567 | − | 0.976180i | ||||
\(447\) | 35962.5 | − | 20762.9i | 0.179984 | − | 0.103914i | ||||
\(448\) | −9562.04 | + | 5520.64i | −0.0476425 | + | 0.0275064i | ||||
\(449\) | −24501.6 | + | 91441.2i | −0.121535 | + | 0.453575i | −0.999693 | − | 0.0247967i | \(-0.992106\pi\) |
0.878157 | + | 0.478372i | \(0.158773\pi\) | |||||||
\(450\) | 54378.2 | + | 54378.2i | 0.268534 | + | 0.268534i | ||||
\(451\) | −128190. | − | 222032.i | −0.630235 | − | 1.09160i | ||||
\(452\) | 104681. | + | 104681.i | 0.512378 | + | 0.512378i | ||||
\(453\) | −14495.2 | + | 25106.5i | −0.0706365 | + | 0.122346i | ||||
\(454\) | 125291. | 0.607864 | ||||||||
\(455\) | − | 118915.i | − | 0.574399i | ||||||
\(456\) | 85316.6 | − | 147773.i | 0.410302 | − | 0.710665i | ||||
\(457\) | −79075.8 | + | 295115.i | −0.378627 | + | 1.41305i | 0.469346 | + | 0.883015i | \(0.344490\pi\) |
−0.847973 | + | 0.530040i | \(0.822177\pi\) | |||||||
\(458\) | −5113.00 | + | 5113.00i | −0.0243750 | + | 0.0243750i | ||||
\(459\) | 26330.5 | + | 98266.8i | 0.124978 | + | 0.466425i | ||||
\(460\) | −41635.7 | + | 72115.1i | −0.196766 | + | 0.340809i | ||||
\(461\) | −99739.3 | + | 26725.1i | −0.469315 | + | 0.125753i | −0.485723 | − | 0.874113i | \(-0.661444\pi\) |
0.0164081 | + | 0.999865i | \(0.494777\pi\) | |||||||
\(462\) | −79465.6 | − | 21292.7i | −0.372302 | − | 0.0997580i | ||||
\(463\) | 38820.7 | − | 144881.i | 0.181093 | − | 0.675848i | −0.814340 | − | 0.580388i | \(-0.802901\pi\) |
0.995433 | − | 0.0954604i | \(-0.0304323\pi\) | |||||||
\(464\) | −7076.63 | − | 26410.3i | −0.0328693 | − | 0.122670i | ||||
\(465\) | 395293. | + | 228223.i | 1.82816 | + | 1.05549i | ||||
\(466\) | −167000. | + | 44747.6i | −0.769034 | + | 0.206062i | ||||
\(467\) | 117038. | + | 117038.i | 0.536651 | + | 0.536651i | 0.922544 | − | 0.385892i | \(-0.126106\pi\) |
−0.385892 | + | 0.922544i | \(0.626106\pi\) | |||||||
\(468\) | 337559. | + | 90448.6i | 1.54119 | + | 0.412962i | ||||
\(469\) | 94806.2 | + | 54736.4i | 0.431013 | + | 0.248846i | ||||
\(470\) | −2585.54 | −0.0117046 | ||||||||
\(471\) | − | 662204.i | − | 2.98504i | ||||||
\(472\) | 66389.1 | + | 38329.8i | 0.297998 | + | 0.172049i | ||||
\(473\) | 151569. | − | 151569.i | 0.677465 | − | 0.677465i | ||||
\(474\) | −196494. | + | 113446.i | −0.874568 | + | 0.504932i | ||||
\(475\) | −53403.7 | + | 53403.7i | −0.236692 | + | 0.236692i | ||||
\(476\) | 11864.1 | + | 3178.98i | 0.0523627 | + | 0.0140305i | ||||
\(477\) | −78173.2 | − | 135400.i | −0.343574 | − | 0.595088i | ||||
\(478\) | −68394.5 | − | 118463.i | −0.299340 | − | 0.518473i | ||||
\(479\) | −185004. | + | 49571.8i | −0.806327 | + | 0.216055i | −0.638360 | − | 0.769738i | \(-0.720387\pi\) |
−0.167967 | + | 0.985793i | \(0.553720\pi\) | |||||||
\(480\) | − | 62034.5i | − | 0.269247i | ||||||
\(481\) | 261038. | + | 232696.i | 1.12827 | + | 1.00577i | ||||
\(482\) | 26645.7 | 0.114692 | ||||||||
\(483\) | 42723.3 | + | 159445.i | 0.183134 | + | 0.683467i | ||||
\(484\) | −51423.1 | + | 29689.1i | −0.219517 | + | 0.126738i | ||||
\(485\) | −176853. | + | 102106.i | −0.751847 | + | 0.434079i | ||||
\(486\) | 17910.1 | − | 66841.6i | 0.0758275 | − | 0.282992i | ||||
\(487\) | 172222. | + | 172222.i | 0.726159 | + | 0.726159i | 0.969852 | − | 0.243694i | \(-0.0783592\pi\) |
−0.243694 | + | 0.969852i | \(0.578359\pi\) | |||||||
\(488\) | −30618.1 | − | 53032.2i | −0.128570 | − | 0.222689i | ||||
\(489\) | −312353. | − | 312353.i | −1.30626 | − | 1.30626i | ||||
\(490\) | 59102.7 | − | 102369.i | 0.246159 | − | 0.426359i | ||||
\(491\) | 396124. | 1.64312 | 0.821559 | − | 0.570124i | \(-0.193105\pi\) | ||||
0.821559 | + | 0.570124i | \(0.193105\pi\) | |||||||
\(492\) | − | 383227.i | − | 1.58317i | ||||||
\(493\) | −15208.0 | + | 26341.1i | −0.0625718 | + | 0.108378i | ||||
\(494\) | −88827.7 | + | 331509.i | −0.363994 | + | 1.35844i | ||||
\(495\) | 221789. | − | 221789.i | 0.905168 | − | 0.905168i | ||||
\(496\) | 22062.6 | + | 82338.7i | 0.0896795 | + | 0.334688i | ||||
\(497\) | −68838.9 | + | 119232.i | −0.278690 | + | 0.482705i | ||||
\(498\) | −346815. | + | 92928.9i | −1.39843 | + | 0.374707i | ||||
\(499\) | 169361. | + | 45380.1i | 0.680161 | + | 0.182249i | 0.582327 | − | 0.812954i | \(-0.302142\pi\) |
0.0978333 | + | 0.995203i | \(0.468809\pi\) | |||||||
\(500\) | −35042.4 | + | 130780.i | −0.140170 | + | 0.523121i | ||||
\(501\) | −124030. | − | 462885.i | −0.494140 | − | 1.84416i | ||||
\(502\) | −22079.4 | − | 12747.6i | −0.0876153 | − | 0.0505847i | ||||
\(503\) | 241274. | − | 64649.2i | 0.953618 | − | 0.255521i | 0.251721 | − | 0.967800i | \(-0.419003\pi\) |
0.701897 | + | 0.712279i | \(0.252337\pi\) | |||||||
\(504\) | −59006.0 | − | 59006.0i | −0.232293 | − | 0.232293i | ||||
\(505\) | 364593. | + | 97692.4i | 1.42964 | + | 0.383070i | ||||
\(506\) | −100349. | − | 57936.6i | −0.391933 | − | 0.226283i | ||||
\(507\) | −582427. | −2.26582 | ||||||||
\(508\) | − | 24232.2i | − | 0.0939000i | ||||||
\(509\) | 152742. | + | 88185.6i | 0.589553 | + | 0.340379i | 0.764921 | − | 0.644124i | \(-0.222778\pi\) |
−0.175368 | + | 0.984503i | \(0.556111\pi\) | |||||||
\(510\) | −48796.7 | + | 48796.7i | −0.187608 | + | 0.187608i | ||||
\(511\) | 112443. | − | 64919.2i | 0.430618 | − | 0.248617i | ||||
\(512\) | 8192.00 | − | 8192.00i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 655651. | + | 175681.i | 2.49137 | + | 0.667561i | ||||
\(514\) | 47034.7 | + | 81466.5i | 0.178029 | + | 0.308356i | ||||
\(515\) | −112199. | − | 194335.i | −0.423035 | − | 0.732718i | ||||
\(516\) | 309484. | − | 82926.1i | 1.16236 | − | 0.311453i | ||||
\(517\) | − | 3597.81i | − | 0.0134604i | ||||||
\(518\) | −26198.8 | − | 79285.9i | −0.0976388 | − | 0.295486i | ||||
\(519\) | 357843. | 1.32849 | ||||||||
\(520\) | 32293.7 | + | 120522.i | 0.119429 | + | 0.445717i | ||||
\(521\) | −78718.8 | + | 45448.3i | −0.290003 | + | 0.167434i | −0.637943 | − | 0.770083i | \(-0.720215\pi\) |
0.347940 | + | 0.937517i | \(0.386881\pi\) | |||||||
\(522\) | 178959. | − | 103322.i | 0.656767 | − | 0.379185i | ||||
\(523\) | −21173.3 | + | 79020.0i | −0.0774080 | + | 0.288891i | −0.993769 | − | 0.111463i | \(-0.964446\pi\) |
0.916361 | + | 0.400354i | \(0.131113\pi\) | |||||||
\(524\) | −23367.5 | − | 23367.5i | −0.0851040 | − | 0.0851040i | ||||
\(525\) | 27214.4 | + | 47136.7i | 0.0987370 | + | 0.171017i | ||||
\(526\) | 4824.95 | + | 4824.95i | 0.0174390 | + | 0.0174390i | ||||
\(527\) | 47413.5 | − | 82122.7i | 0.170719 | − | 0.295694i | ||||
\(528\) | 86321.8 | 0.309637 | ||||||||
\(529\) | − | 47345.0i | − | 0.169185i | ||||||
\(530\) | 27910.9 | − | 48343.1i | 0.0993624 | − | 0.172101i | ||||
\(531\) | −149953. | + | 559631.i | −0.531820 | + | 1.98478i | ||||
\(532\) | 57948.6 | − | 57948.6i | 0.204748 | − | 0.204748i | ||||
\(533\) | 199499. | + | 744541.i | 0.702242 | + | 2.62080i | ||||
\(534\) | 114655. | − | 198587.i | 0.402076 | − | 0.696417i | ||||
\(535\) | −189694. | + | 50828.4i | −0.662746 | + | 0.177582i | ||||
\(536\) | −110952. | − | 29729.5i | −0.386194 | − | 0.103480i | ||||
\(537\) | −123501. | + | 460914.i | −0.428276 | + | 1.59835i | ||||
\(538\) | −42922.7 | − | 160190.i | −0.148294 | − | 0.553439i | ||||
\(539\) | 142447. | + | 82242.1i | 0.490317 | + | 0.283085i | ||||
\(540\) | 238365. | − | 63869.7i | 0.817439 | − | 0.219032i | ||||
\(541\) | −133198. | − | 133198.i | −0.455098 | − | 0.455098i | 0.441945 | − | 0.897042i | \(-0.354289\pi\) |
−0.897042 | + | 0.441945i | \(0.854289\pi\) | |||||||
\(542\) | 224504. | + | 60155.7i | 0.764233 | + | 0.204776i | ||||
\(543\) | −49167.2 | − | 28386.7i | −0.166754 | − | 0.0962754i | ||||
\(544\) | −12887.7 | −0.0435491 | ||||||||
\(545\) | − | 276617.i | − | 0.931293i | ||||||
\(546\) | 214203. | + | 123670.i | 0.718521 | + | 0.414839i | ||||
\(547\) | −109219. | + | 109219.i | −0.365025 | + | 0.365025i | −0.865659 | − | 0.500634i | \(-0.833100\pi\) |
0.500634 | + | 0.865659i | \(0.333100\pi\) | |||||||
\(548\) | 138840. | − | 80159.5i | 0.462333 | − | 0.266928i | ||||
\(549\) | 327254. | − | 327254.i | 1.08578 | − | 1.08578i | ||||
\(550\) | −36905.1 | − | 9888.70i | −0.122000 | − | 0.0326899i | ||||
\(551\) | 101470. | + | 175752.i | 0.334222 | + | 0.578890i | ||||
\(552\) | −86601.1 | − | 149997.i | −0.284214 | − | 0.492273i | ||||
\(553\) | −105259. | + | 28203.9i | −0.344197 | + | 0.0922273i | ||||
\(554\) | − | 120185.i | − | 0.391590i | ||||||
\(555\) | 459378. | + | 95255.1i | 1.49137 | + | 0.309245i | ||||
\(556\) | −296373. | −0.958713 | ||||||||
\(557\) | 100899. | + | 376560.i | 0.325219 | + | 1.21373i | 0.914091 | + | 0.405508i | \(0.132905\pi\) |
−0.588872 | + | 0.808226i | \(0.700428\pi\) | |||||||
\(558\) | −557934. | + | 322123.i | −1.79190 | + | 1.03455i | ||||
\(559\) | −558103. | + | 322221.i | −1.78604 | + | 1.03117i | ||||
\(560\) | 7711.24 | − | 28778.7i | 0.0245894 | − | 0.0917689i | ||||
\(561\) | −67901.2 | − | 67901.2i | −0.215751 | − | 0.215751i | ||||
\(562\) | −183097. | − | 317134.i | −0.579709 | − | 1.00408i | ||||
\(563\) | −342627. | − | 342627.i | −1.08095 | − | 1.08095i | −0.996421 | − | 0.0845268i | \(-0.973062\pi\) |
−0.0845268 | − | 0.996421i | \(-0.526938\pi\) | |||||||
\(564\) | 2688.93 | − | 4657.36i | 0.00845319 | − | 0.0146414i | ||||
\(565\) | −399475. | −1.25139 | ||||||||
\(566\) | − | 104290.i | − | 0.325544i | ||||||
\(567\) | 95232.5 | − | 164948.i | 0.296223 | − | 0.513074i | ||||
\(568\) | 37389.1 | − | 139538.i | 0.115891 | − | 0.432510i | ||||
\(569\) | −135904. | + | 135904.i | −0.419767 | + | 0.419767i | −0.885123 | − | 0.465356i | \(-0.845926\pi\) |
0.465356 | + | 0.885123i | \(0.345926\pi\) | |||||||
\(570\) | 119170. | + | 444750.i | 0.366791 | + | 1.36888i | ||||
\(571\) | −4479.51 | + | 7758.74i | −0.0137391 | + | 0.0237968i | −0.872813 | − | 0.488054i | \(-0.837707\pi\) |
0.859074 | + | 0.511851i | \(0.171040\pi\) | |||||||
\(572\) | −167708. | + | 44937.1i | −0.512579 | + | 0.137345i | ||||
\(573\) | −977741. | − | 261985.i | −2.97793 | − | 0.797934i | ||||
\(574\) | 47637.3 | − | 177785.i | 0.144585 | − | 0.539598i | ||||
\(575\) | 19841.4 | + | 74049.0i | 0.0600117 | + | 0.223967i | ||||
\(576\) | 75827.6 | + | 43779.1i | 0.228551 | + | 0.131954i | ||||
\(577\) | −143413. | + | 38427.3i | −0.430760 | + | 0.115422i | −0.467683 | − | 0.883896i | \(-0.654911\pi\) |
0.0369227 | + | 0.999318i | \(0.488244\pi\) | |||||||
\(578\) | −156904. | − | 156904.i | −0.469656 | − | 0.469656i | ||||
\(579\) | −658499. | − | 176444.i | −1.96426 | − | 0.526321i | ||||
\(580\) | 63895.3 | + | 36890.0i | 0.189938 | + | 0.109661i | ||||
\(581\) | −172444. | −0.510854 | ||||||||
\(582\) | − | 424756.i | − | 1.25399i | ||||||
\(583\) | 67270.0 | + | 38838.4i | 0.197918 | + | 0.114268i | ||||
\(584\) | −96332.6 | + | 96332.6i | −0.282454 | + | 0.282454i | ||||
\(585\) | −816665. | + | 471502.i | −2.38634 | + | 1.37775i | ||||
\(586\) | 20252.3 | − | 20252.3i | 0.0589765 | − | 0.0589765i | ||||
\(587\) | 305670. | + | 81904.1i | 0.887109 | + | 0.237700i | 0.673472 | − | 0.739213i | \(-0.264802\pi\) |
0.213637 | + | 0.976913i | \(0.431469\pi\) | |||||||
\(588\) | 122932. | + | 212924.i | 0.355558 | + | 0.615844i | ||||
\(589\) | −316350. | − | 547935.i | −0.911880 | − | 1.57942i | ||||
\(590\) | −199810. | + | 53539.0i | −0.574003 | + | 0.153804i | ||||
\(591\) | 859013.i | 2.45937i | ||||||||
\(592\) | 48084.5 | + | 73242.4i | 0.137202 | + | 0.208987i | ||||
\(593\) | 174574. | 0.496444 | 0.248222 | − | 0.968703i | \(-0.420154\pi\) | ||||
0.248222 | + | 0.968703i | \(0.420154\pi\) | |||||||
\(594\) | 88875.5 | + | 331688.i | 0.251889 | + | 0.940063i | ||||
\(595\) | −28703.2 | + | 16571.8i | −0.0810768 | + | 0.0468097i | ||||
\(596\) | −18122.9 | + | 10463.3i | −0.0510195 | + | 0.0294561i | ||||
\(597\) | 253117. | − | 944644.i | 0.710186 | − | 2.65045i | ||||
\(598\) | 246335. | + | 246335.i | 0.688849 | + | 0.688849i | ||||
\(599\) | 192009. | + | 332569.i | 0.535141 | + | 0.926891i | 0.999157 | + | 0.0410642i | \(0.0130748\pi\) |
−0.464016 | + | 0.885827i | \(0.653592\pi\) | |||||||
\(600\) | −40383.0 | − | 40383.0i | −0.112175 | − | 0.112175i | ||||
\(601\) | 307764. | − | 533062.i | 0.852056 | − | 1.47580i | −0.0272929 | − | 0.999627i | \(-0.508689\pi\) |
0.879349 | − | 0.476177i | \(-0.157978\pi\) | |||||||
\(602\) | 153883. | 0.424616 | ||||||||
\(603\) | − | 868126.i | − | 2.38753i | ||||||
\(604\) | 7304.74 | − | 12652.2i | 0.0200231 | − | 0.0346810i | ||||
\(605\) | 41469.8 | − | 154767.i | 0.113298 | − | 0.422833i | ||||
\(606\) | −555146. | + | 555146.i | −1.51169 | + | 1.51169i | ||||
\(607\) | −90260.7 | − | 336857.i | −0.244975 | − | 0.914258i | −0.973396 | − | 0.229129i | \(-0.926412\pi\) |
0.728422 | − | 0.685129i | \(-0.240254\pi\) | |||||||
\(608\) | −42994.5 | + | 74468.7i | −0.116307 | + | 0.201450i | ||||
\(609\) | 141272. | − | 37853.6i | 0.380908 | − | 0.102064i | ||||
\(610\) | 159610. | + | 42767.4i | 0.428944 | + | 0.114935i | ||||
\(611\) | −2799.58 | + | 10448.2i | −0.00749913 | + | 0.0279871i | ||||
\(612\) | −25209.5 | − | 94083.3i | −0.0673073 | − | 0.251194i | ||||
\(613\) | 79666.5 | + | 45995.5i | 0.212009 | + | 0.122404i | 0.602245 | − | 0.798311i | \(-0.294273\pi\) |
−0.390236 | + | 0.920715i | \(0.627606\pi\) | |||||||
\(614\) | −145997. | + | 39119.7i | −0.387263 | + | 0.103767i | ||||
\(615\) | 731222. | + | 731222.i | 1.93330 | + | 1.93330i | ||||
\(616\) | 40045.9 | + | 10730.3i | 0.105535 | + | 0.0282781i | ||||
\(617\) | −526542. | − | 303999.i | −1.38313 | − | 0.798550i | −0.390601 | − | 0.920560i | \(-0.627733\pi\) |
−0.992529 | + | 0.122010i | \(0.961066\pi\) | |||||||
\(618\) | 466743. | 1.22208 | ||||||||
\(619\) | − | 268422.i | − | 0.700546i | −0.936648 | − | 0.350273i | \(-0.886089\pi\) | ||
0.936648 | − | 0.350273i | \(-0.113911\pi\) | |||||||
\(620\) | −199204. | − | 115011.i | −0.518222 | − | 0.299195i | ||||
\(621\) | 487196. | − | 487196.i | 1.26334 | − | 1.26334i | ||||
\(622\) | −285351. | + | 164747.i | −0.737562 | + | 0.425832i | ||||
\(623\) | 77875.4 | − | 77875.4i | 0.200643 | − | 0.200643i | ||||
\(624\) | −250682. | − | 67170.1i | −0.643805 | − | 0.172507i | ||||
\(625\) | −132990. | − | 230345.i | −0.340453 | − | 0.589682i | ||||
\(626\) | 271629. | + | 470475.i | 0.693150 | + | 1.20057i | ||||
\(627\) | −618874. | + | 165827.i | −1.57423 | + | 0.421813i | ||||
\(628\) | 333711.i | 0.846158i | ||||||||
\(629\) | 19789.4 | − | 95436.4i | 0.0500185 | − | 0.241220i | ||||
\(630\) | 225175. | 0.567333 | ||||||||
\(631\) | 3298.13 | + | 12308.8i | 0.00828340 | + | 0.0309141i | 0.969944 | − | 0.243329i | \(-0.0782394\pi\) |
−0.961660 | + | 0.274243i | \(0.911573\pi\) | |||||||
\(632\) | 99021.5 | − | 57170.1i | 0.247911 | − | 0.143131i | ||||
\(633\) | 305661. | − | 176474.i | 0.762839 | − | 0.440425i | ||||
\(634\) | −12212.4 | + | 45577.3i | −0.0303824 | + | 0.113389i | ||||
\(635\) | 46236.6 | + | 46236.6i | 0.114667 | + | 0.114667i | ||||
\(636\) | 58053.9 | + | 100552.i | 0.143522 | + | 0.248587i | ||||
\(637\) | −349678. | − | 349678.i | −0.861766 | − | 0.861766i | ||||
\(638\) | −51332.8 | + | 88911.1i | −0.126111 | + | 0.218431i | ||||
\(639\) | 1.09179e6 | 2.67386 | ||||||||
\(640\) | 31261.7i | 0.0763226i | ||||||||
\(641\) | 37672.0 | − | 65249.8i | 0.0916860 | − | 0.158805i | −0.816535 | − | 0.577296i | \(-0.804108\pi\) |
0.908221 | + | 0.418492i | \(0.137441\pi\) | |||||||
\(642\) | 105722. | − | 394559.i | 0.256504 | − | 0.957287i | ||||
\(643\) | 397860. | − | 397860.i | 0.962295 | − | 0.962295i | −0.0370200 | − | 0.999315i | \(-0.511787\pi\) |
0.999315 | + | 0.0370200i | \(0.0117865\pi\) | |||||||
\(644\) | −21530.0 | − | 80351.0i | −0.0519125 | − | 0.193740i | ||||
\(645\) | −432288. | + | 748744.i | −1.03909 | + | 1.79976i | ||||
\(646\) | 92397.2 | − | 24757.8i | 0.221408 | − | 0.0593262i | ||||
\(647\) | 693730. | + | 185884.i | 1.65723 | + | 0.444052i | 0.961623 | − | 0.274374i | \(-0.0884707\pi\) |
0.695603 | + | 0.718426i | \(0.255137\pi\) | |||||||
\(648\) | −51724.5 | + | 193039.i | −0.123182 | + | 0.459721i | ||||
\(649\) | −74500.2 | − | 278038.i | −0.176876 | − | 0.660109i | ||||
\(650\) | 99479.3 | + | 57434.4i | 0.235454 | + | 0.135939i | ||||
\(651\) | −440438. | + | 118015.i | −1.03926 | + | 0.278468i | ||||
\(652\) | 157408. | + | 157408.i | 0.370280 | + | 0.370280i | ||||
\(653\) | 327415. | + | 87730.6i | 0.767843 | + | 0.205743i | 0.621418 | − | 0.783479i | \(-0.286557\pi\) |
0.146425 | + | 0.989222i | \(0.453223\pi\) | |||||||
\(654\) | 498273. | + | 287678.i | 1.16496 | + | 0.672592i | ||||
\(655\) | 89173.4 | 0.207851 | ||||||||
\(656\) | 193124.i | 0.448775i | ||||||||
\(657\) | −891683. | − | 514814.i | −2.06576 | − | 1.19267i | ||||
\(658\) | 1826.37 | − | 1826.37i | 0.00421829 | − | 0.00421829i | ||||
\(659\) | −494696. | + | 285613.i | −1.13912 | + | 0.657669i | −0.946212 | − | 0.323549i | \(-0.895124\pi\) |
−0.192904 | + | 0.981218i | \(0.561791\pi\) | |||||||
\(660\) | −164708. | + | 164708.i | −0.378116 | + | 0.378116i | ||||
\(661\) | 689050. | + | 184630.i | 1.57706 | + | 0.422572i | 0.938014 | − | 0.346597i | \(-0.112663\pi\) |
0.639045 | + | 0.769169i | \(0.279330\pi\) | |||||||
\(662\) | −275048. | − | 476397.i | −0.627614 | − | 1.08706i | ||||
\(663\) | 144352. | + | 250024.i | 0.328394 | + | 0.568794i | ||||
\(664\) | 174774. | − | 46830.7i | 0.396407 | − | 0.106217i | ||||
\(665\) | 221139.i | 0.500061i | ||||||||
\(666\) | −440627. | + | 494295.i | −0.993398 | + | 1.11439i | ||||
\(667\) | 205996. | 0.463027 | ||||||||
\(668\) | 62503.6 | + | 233267.i | 0.140072 | + | 0.522757i | ||||
\(669\) | −977130. | + | 564146.i | −2.18323 | + | 1.26049i | ||||
\(670\) | 268429. | − | 154978.i | 0.597971 | − | 0.345239i | ||||
\(671\) | −59511.4 | + | 222099.i | −0.132177 | + | 0.493290i | ||||
\(672\) | 43819.8 | + | 43819.8i | 0.0970358 | + | 0.0970358i | ||||
\(673\) | 325418. | + | 563640.i | 0.718474 | + | 1.24443i | 0.961604 | + | 0.274440i | \(0.0884926\pi\) |
−0.243130 | + | 0.969994i | \(0.578174\pi\) | |||||||
\(674\) | 154989. | + | 154989.i | 0.341179 | + | 0.341179i | ||||
\(675\) | 113592. | − | 196748.i | 0.249311 | − | 0.431819i | ||||
\(676\) | 293509. | 0.642285 | ||||||||
\(677\) | − | 580336.i | − | 1.26620i | −0.774070 | − | 0.633100i | \(-0.781782\pi\) | ||
0.774070 | − | 0.633100i | \(-0.218218\pi\) | |||||||
\(678\) | 415449. | − | 719579.i | 0.903771 | − | 1.56538i | ||||
\(679\) | 52799.6 | − | 197051.i | 0.114522 | − | 0.427404i | ||||
\(680\) | 24590.7 | − | 24590.7i | 0.0531805 | − | 0.0531805i | ||||
\(681\) | −182004. | − | 679247.i | −0.392451 | − | 1.46465i | ||||
\(682\) | 160039. | − | 277195.i | 0.344078 | − | 0.595960i | ||||
\(683\) | 93149.4 | − | 24959.3i | 0.199682 | − | 0.0535046i | −0.157592 | − | 0.987504i | \(-0.550373\pi\) |
0.357274 | + | 0.934000i | \(0.383706\pi\) | |||||||
\(684\) | −627738. | − | 168202.i | −1.34173 | − | 0.359516i | ||||
\(685\) | −111967. | + | 417866.i | −0.238621 | + | 0.890544i | ||||
\(686\) | 68466.1 | + | 255519.i | 0.145488 | + | 0.542969i | ||||
\(687\) | 35146.9 | + | 20292.1i | 0.0744686 | + | 0.0429945i | ||||
\(688\) | −155962. | + | 41789.8i | −0.329489 | + | 0.0882864i | ||||
\(689\) | −165133. | − | 165133.i | −0.347854 | − | 0.347854i | ||||
\(690\) | 451445. | + | 120964.i | 0.948215 | + | 0.254073i | ||||
\(691\) | −375694. | − | 216907.i | −0.786826 | − | 0.454274i | 0.0520182 | − | 0.998646i | \(-0.483435\pi\) |
−0.838844 | + | 0.544372i | \(0.816768\pi\) | |||||||
\(692\) | −180332. | −0.376582 | ||||||||
\(693\) | 313333.i | 0.652439i | ||||||||
\(694\) | −130667. | − | 75440.3i | −0.271297 | − | 0.156634i | ||||
\(695\) | 565498. | − | 565498.i | 1.17074 | − | 1.17074i | ||||
\(696\) | −132901. | + | 76730.1i | −0.274352 | + | 0.158397i | ||||
\(697\) | 151912. | − | 151912.i | 0.312700 | − | 0.312700i | ||||
\(698\) | −181857. | − | 48728.4i | −0.373267 | − | 0.100017i | ||||
\(699\) | 485187. | + | 840368.i | 0.993012 | + | 1.71995i | ||||
\(700\) | −13714.4 | − | 23754.1i | −0.0279886 | − | 0.0484777i | ||||
\(701\) | −63539.8 | + | 17025.4i | −0.129303 | + | 0.0346467i | −0.322890 | − | 0.946436i | \(-0.604654\pi\) |
0.193587 | + | 0.981083i | \(0.437988\pi\) | |||||||
\(702\) | − | 1.03239e6i | − | 2.09494i | ||||||
\(703\) | −485437. | − | 432731.i | −0.982250 | − | 0.875604i | ||||
\(704\) | −43501.1 | −0.0877717 | ||||||||
\(705\) | 3755.89 | + | 14017.2i | 0.00755675 | + | 0.0282022i | ||||
\(706\) | 185556. | − | 107131.i | 0.372276 | − | 0.214934i | ||||
\(707\) | −326548. | + | 188533.i | −0.653294 | + | 0.377179i | ||||
\(708\) | 111360. | − | 415600.i | 0.222158 | − | 0.829104i | ||||
\(709\) | −323873. | − | 323873.i | −0.644292 | − | 0.644292i | 0.307316 | − | 0.951608i | \(-0.400569\pi\) |
−0.951608 | + | 0.307316i | \(0.900569\pi\) | |||||||
\(710\) | 194907. | + | 337589.i | 0.386643 | + | 0.669686i | ||||
\(711\) | 611048. | + | 611048.i | 1.20875 | + | 1.20875i | ||||
\(712\) | −57779.1 | + | 100076.i | −0.113975 | + | 0.197411i | ||||
\(713\) | −642226. | −1.26331 | ||||||||
\(714\) | − | 68937.8i | − | 0.135226i | ||||||
\(715\) | 234254. | − | 405740.i | 0.458221 | − | 0.793662i | ||||
\(716\) | 62237.4 | − | 232273.i | 0.121402 | − | 0.453078i | ||||
\(717\) | −542877. | + | 542877.i | −1.05600 | + | 1.05600i | ||||
\(718\) | 88987.5 | + | 332106.i | 0.172616 | + | 0.644211i | ||||
\(719\) | 58296.8 | − | 100973.i | 0.112768 | − | 0.195320i | −0.804117 | − | 0.594471i | \(-0.797362\pi\) |
0.916885 | + | 0.399150i | \(0.130695\pi\) | |||||||
\(720\) | −228217. | + | 61150.6i | −0.440234 | + | 0.117960i | ||||
\(721\) | 216529. | + | 58018.8i | 0.416529 | + | 0.111609i | ||||
\(722\) | 69786.0 | − | 260445.i | 0.133873 | − | 0.499622i | ||||
\(723\) | −38707.0 | − | 144457.i | −0.0740479 | − | 0.276351i | ||||
\(724\) | 24777.4 | + | 14305.2i | 0.0472692 | + | 0.0272909i | ||||
\(725\) | 65608.8 | − | 17579.8i | 0.124821 | − | 0.0334456i | ||||
\(726\) | 235656. | + | 235656.i | 0.447100 | + | 0.447100i | ||||
\(727\) | −268499. | − | 71944.2i | −0.508012 | − | 0.136121i | −0.00429628 | − | 0.999991i | \(-0.501368\pi\) |
−0.503716 | + | 0.863869i | \(0.668034\pi\) | |||||||
\(728\) | −107945. | − | 62322.3i | −0.203677 | − | 0.117593i | ||||
\(729\) | 327012. | 0.615331 | ||||||||
\(730\) | − | 367618.i | − | 0.689844i | ||||||
\(731\) | 155553. | + | 89808.3i | 0.291100 | + | 0.168067i | ||||
\(732\) | −243030. | + | 243030.i | −0.453562 | + | 0.453562i | ||||
\(733\) | 745442. | − | 430381.i | 1.38741 | − | 0.801023i | 0.394390 | − | 0.918943i | \(-0.370956\pi\) |
0.993023 | + | 0.117920i | \(0.0376225\pi\) | |||||||
\(734\) | −58699.9 | + | 58699.9i | −0.108955 | + | 0.108955i | ||||
\(735\) | −640835. | − | 171711.i | −1.18624 | − | 0.317851i | ||||
\(736\) | 43641.8 | + | 75589.8i | 0.0805651 | + | 0.139543i | ||||
\(737\) | 215653. | + | 373522.i | 0.397028 | + | 0.687673i | ||||
\(738\) | −1.40984e6 | + | 377767.i | −2.58856 | + | 0.693603i | ||||
\(739\) | 249552.i | 0.456953i | 0.973549 | + | 0.228477i | \(0.0733744\pi\) | ||||
−0.973549 | + | 0.228477i | \(0.926626\pi\) | |||||||
\(740\) | −231499. | − | 48002.9i | −0.422753 | − | 0.0876606i | ||||
\(741\) | 1.92627e6 | 3.50818 | ||||||||
\(742\) | 14432.9 | + | 53864.1i | 0.0262147 | + | 0.0978345i | ||||
\(743\) | 436633. | − | 252090.i | 0.790931 | − | 0.456644i | −0.0493593 | − | 0.998781i | \(-0.515718\pi\) |
0.840290 | + | 0.542137i | \(0.182385\pi\) | |||||||
\(744\) | 414340. | − | 239219.i | 0.748533 | − | 0.432165i | ||||
\(745\) | 14615.1 | − | 54544.4i | 0.0263324 | − | 0.0982737i | ||||
\(746\) | −512237. | − | 512237.i | −0.920436 | − | 0.920436i | ||||
\(747\) | 683747. | + | 1.18429e6i | 1.22533 | + | 2.12234i | ||||
\(748\) | 34218.2 | + | 34218.2i | 0.0611581 | + | 0.0611581i | ||||
\(749\) | 98091.7 | − | 169900.i | 0.174851 | − | 0.302851i | ||||
\(750\) | 759913. | 1.35096 | ||||||||
\(751\) | 125536.i | 0.222581i | 0.993788 | + | 0.111291i | \(0.0354984\pi\) | ||||
−0.993788 | + | 0.111291i | \(0.964502\pi\) | |||||||
\(752\) | −1355.06 | + | 2347.03i | −0.00239620 | + | 0.00415034i | ||||
\(753\) | −37035.5 | + | 138219.i | −0.0653174 | + | 0.243768i | ||||
\(754\) | 218258. | − | 218258.i | 0.383908 | − | 0.383908i | ||||
\(755\) | 10203.3 | + | 38079.1i | 0.0178997 | + | 0.0668025i | ||||
\(756\) | −123260. | + | 213492.i | −0.215664 | + | 0.373541i | ||||
\(757\) | −192951. | + | 51701.2i | −0.336710 | + | 0.0902212i | −0.423213 | − | 0.906030i | \(-0.639098\pi\) |
0.0865024 | + | 0.996252i | \(0.472431\pi\) | |||||||
\(758\) | 159154. | + | 42645.1i | 0.276999 | + | 0.0742216i | ||||
\(759\) | −168323. | + | 628191.i | −0.292187 | + | 1.09046i | ||||
\(760\) | −60054.7 | − | 224127.i | −0.103973 | − | 0.388032i | ||||
\(761\) | −119653. | − | 69081.7i | −0.206612 | − | 0.119287i | 0.393124 | − | 0.919485i | \(-0.371394\pi\) |
−0.599736 | + | 0.800198i | \(0.704728\pi\) | |||||||
\(762\) | −131372. | + | 35201.0i | −0.226252 | + | 0.0606240i | ||||
\(763\) | 195396. | + | 195396.i | 0.335635 | + | 0.335635i | ||||
\(764\) | 492724. | + | 132025.i | 0.844144 | + | 0.226188i | ||||
\(765\) | 227618. | + | 131416.i | 0.388942 | + | 0.224556i | ||||
\(766\) | 429051. | 0.731226 | ||||||||
\(767\) | 865406.i | 1.47106i | ||||||||
\(768\) | −56312.0 | − | 32511.8i | −0.0954726 | − | 0.0551211i | ||||
\(769\) | −334643. | + | 334643.i | −0.565886 | + | 0.565886i | −0.930973 | − | 0.365087i | \(-0.881039\pi\) |
0.365087 | + | 0.930973i | \(0.381039\pi\) | |||||||
\(770\) | −96884.3 | + | 55936.2i | −0.163407 | + | 0.0943433i | ||||
\(771\) | 373335. | − | 373335.i | 0.628044 | − | 0.628044i | ||||
\(772\) | 331844. | + | 88917.5i | 0.556801 | + | 0.149194i | ||||
\(773\) | 340586. | + | 589912.i | 0.569990 | + | 0.987252i | 0.996566 | + | 0.0828003i | \(0.0263863\pi\) |
−0.426576 | + | 0.904452i | \(0.640280\pi\) | |||||||
\(774\) | −610149. | − | 1.05681e6i | −1.01848 | − | 1.76407i | ||||
\(775\) | −204547. | + | 54808.1i | −0.340556 | + | 0.0912517i | ||||
\(776\) | 214052.i | 0.355464i | ||||||||
\(777\) | −391781. | + | 257208.i | −0.648935 | + | 0.426033i | ||||
\(778\) | 331033. | 0.546906 | ||||||||
\(779\) | −370997. | − | 1.38458e6i | −0.611358 | − | 2.28162i | ||||
\(780\) | 606482. | − | 350153.i | 0.996848 | − | 0.575530i | ||||
\(781\) | −469759. | + | 271215.i | −0.770145 | + | 0.444644i | ||||
\(782\) | 25130.5 | − | 93788.3i | 0.0410949 | − | 0.153368i | ||||
\(783\) | −431665. | − | 431665.i | −0.704081 | − | 0.704081i | ||||
\(784\) | −61950.4 | − | 107301.i | −0.100789 | − | 0.174571i | ||||
\(785\) | −636743. | − | 636743.i | −1.03330 | − | 1.03330i | ||||
\(786\) | −92739.1 | + | 160629.i | −0.150113 | + | 0.260003i | ||||
\(787\) | −401631. | −0.648452 | −0.324226 | − | 0.945980i | \(-0.605104\pi\) | ||||
−0.324226 | + | 0.945980i | \(0.605104\pi\) | |||||||
\(788\) | − | 432891.i | − | 0.697151i | ||||||
\(789\) | 19148.9 | − | 33166.8i | 0.0307602 | − | 0.0532782i | ||||
\(790\) | −79855.2 | + | 298024.i | −0.127953 | + | 0.477525i | ||||
\(791\) | 282180. | − | 282180.i | 0.450997 | − | 0.450997i | ||||
\(792\) | −85091.8 | − | 317567.i | −0.135655 | − | 0.506273i | ||||
\(793\) | 345647. | − | 598678.i | 0.549650 | − | 0.952022i | ||||
\(794\) | −117616. | + | 31515.2i | −0.186564 | + | 0.0499896i | ||||
\(795\) | −302631. | − | 81089.7i | −0.478828 | − | 0.128301i | ||||
\(796\) | −127556. | + | 476045.i | −0.201314 | + | 0.751314i | ||||
\(797\) | 230523. | + | 860324.i | 0.362909 | + | 1.35440i | 0.870233 | + | 0.492640i | \(0.163968\pi\) |
−0.507324 | + | 0.861756i | \(0.669365\pi\) | |||||||
\(798\) | −398340. | − | 229982.i | −0.625530 | − | 0.361150i | ||||
\(799\) | 2912.09 | − | 780.291i | 0.00456153 | − | 0.00122226i | ||||
\(800\) | 20350.6 | + | 20350.6i | 0.0317979 | + | 0.0317979i | ||||
\(801\) | −843599. | − | 226042.i | −1.31483 | − | 0.352309i | ||||
\(802\) | 73346.3 | + | 42346.5i | 0.114033 | + | 0.0658368i | ||||
\(803\) | 511544. | 0.793327 | ||||||||
\(804\) | 644699.i | 0.997343i | ||||||||
\(805\) | 194395. | + | 112234.i | 0.299981 | + | 0.173194i | ||||
\(806\) | −680455. | + | 680455.i | −1.04744 | + | 1.04744i | ||||
\(807\) | −806096. | + | 465400.i | −1.23777 | + | 0.714626i | ||||
\(808\) | 279761. | − | 279761.i | 0.428513 | − | 0.428513i | ||||
\(809\) | 161720. | + | 43332.6i | 0.247096 | + | 0.0662092i | 0.380241 | − | 0.924887i | \(-0.375841\pi\) |
−0.133145 | + | 0.991097i | \(0.542508\pi\) | |||||||
\(810\) | −269636. | − | 467024.i | −0.410968 | − | 0.711818i | ||||
\(811\) | −5559.95 | − | 9630.12i | −0.00845336 | − | 0.0146416i | 0.861768 | − | 0.507303i | \(-0.169357\pi\) |
−0.870221 | + | 0.492661i | \(0.836024\pi\) | |||||||
\(812\) | −71192.5 | + | 19076.0i | −0.107975 | + | 0.0289317i | ||||
\(813\) | − | 1.30451e6i | − | 1.97363i | ||||||
\(814\) | 66796.6 | − | 322134.i | 0.100811 | − | 0.486170i | ||||
\(815\) | −600687. | −0.904343 | ||||||||
\(816\) | 18721.4 | + | 69869.3i | 0.0281163 | + | 0.104932i | ||||
\(817\) | 1.03787e6 | − | 599215.i | 1.55489 | − | 0.897715i | ||||
\(818\) | −433324. | + | 250180.i | −0.647599 | + | 0.373892i | ||||
\(819\) | 243816. | − | 909932.i | 0.363491 | − | 1.35657i | ||||
\(820\) | −368493. | − | 368493.i | −0.548026 | − | 0.548026i | ||||
\(821\) | −492837. | − | 853618.i | −0.731167 | − | 1.26642i | −0.956385 | − | 0.292110i | \(-0.905643\pi\) |
0.225218 | − | 0.974308i | \(-0.427691\pi\) | |||||||
\(822\) | −636261. | − | 636261.i | −0.941655 | − | 0.941655i | ||||
\(823\) | 265830. | − | 460431.i | 0.392468 | − | 0.679775i | −0.600306 | − | 0.799770i | \(-0.704955\pi\) |
0.992774 | + | 0.119995i | \(0.0382879\pi\) | |||||||
\(824\) | −235211. | −0.346420 | ||||||||
\(825\) | 214441.i | 0.315065i | ||||||||
\(826\) | 103323. | − | 178960.i | 0.151438 | − | 0.262299i | ||||
\(827\) | −68128.9 | + | 254261.i | −0.0996140 | + | 0.371765i | −0.997679 | − | 0.0680991i | \(-0.978307\pi\) |
0.898065 | + | 0.439864i | \(0.144973\pi\) | |||||||
\(828\) | −466455. | + | 466455.i | −0.680375 | + | 0.680375i | ||||
\(829\) | 1081.36 | + | 4035.70i | 0.00157348 | + | 0.00587232i | 0.966708 | − | 0.255882i | \(-0.0823658\pi\) |
−0.965135 | + | 0.261754i | \(0.915699\pi\) | |||||||
\(830\) | −244125. | + | 422837.i | −0.354369 | + | 0.613785i | ||||
\(831\) | −651570. | + | 174588.i | −0.943537 | + | 0.252820i | ||||
\(832\) | 126329. | + | 33849.7i | 0.182497 | + | 0.0489000i | ||||
\(833\) | −35673.2 | + | 133134.i | −0.0514106 | + | 0.191867i | ||||
\(834\) | 430527. | + | 1.60675e6i | 0.618968 | + | 2.31002i | ||||
\(835\) | −564348. | − | 325827.i | −0.809421 | − | 0.467319i | ||||
\(836\) | 311876. | − | 83566.9i | 0.446241 | − | 0.119570i | ||||
\(837\) | 1.34579e6 | + | 1.34579e6i | 1.92099 | + | 1.92099i | ||||
\(838\) | −360705. | − | 96650.7i | −0.513647 | − | 0.137631i | ||||
\(839\) | −56804.5 | − | 32796.1i | −0.0806973 | − | 0.0465906i | 0.459108 | − | 0.888380i | \(-0.348169\pi\) |
−0.539806 | + | 0.841790i | \(0.681502\pi\) | |||||||
\(840\) | −167222. | −0.236993 | ||||||||
\(841\) | 524765.i | 0.741947i | ||||||||
\(842\) | 646535. | + | 373277.i | 0.911943 | + | 0.526511i | ||||
\(843\) | −1.45333e6 | + | 1.45333e6i | −2.04507 | + | 2.04507i | ||||
\(844\) | −154035. | + | 88932.2i | −0.216239 | + | 0.124846i | ||||
\(845\) | −560034. | + | 560034.i | −0.784333 | + | 0.784333i | ||||
\(846\) | −19784.4 | − | 5301.22i | −0.0276429 | − | 0.00740688i | ||||
\(847\) | 80030.9 | + | 138618.i | 0.111555 | + | 0.193220i | ||||
\(848\) | −29255.7 | − | 50672.4i | −0.0406836 | − | 0.0704661i | ||||
\(849\) | −565396. | + | 151497.i | −0.784399 | + | 0.210179i | ||||
\(850\) | − | 32015.9i | − | 0.0443126i | ||||||
\(851\) | −626771. | + | 207107.i | −0.865465 | + | 0.285980i | ||||
\(852\) | −810802. | −1.11695 | ||||||||
\(853\) | 186231. | + | 695023.i | 0.255949 | + | 0.955215i | 0.967560 | + | 0.252641i | \(0.0812992\pi\) |
−0.711611 | + | 0.702574i | \(0.752034\pi\) | |||||||
\(854\) | −142955. | + | 82535.1i | −0.196012 | + | 0.113168i | ||||
\(855\) | 1.51870e6 | − | 876824.i | 2.07750 | − | 1.19945i | ||||
\(856\) | −53277.5 | + | 198834.i | −0.0727104 | + | 0.271359i | ||||
\(857\) | 695178. | + | 695178.i | 0.946529 | + | 0.946529i | 0.998641 | − | 0.0521119i | \(-0.0165952\pi\) |
−0.0521119 | + | 0.998641i | \(0.516595\pi\) | |||||||
\(858\) | 487242. | + | 843927.i | 0.661866 | + | 1.14639i | ||||
\(859\) | −57024.4 | − | 57024.4i | −0.0772813 | − | 0.0772813i | 0.667410 | − | 0.744691i | \(-0.267403\pi\) |
−0.744691 | + | 0.667410i | \(0.767403\pi\) | |||||||
\(860\) | 217847. | − | 377323.i | 0.294548 | − | 0.510171i | ||||
\(861\) | −1.03304e6 | −1.39351 | ||||||||
\(862\) | 325880.i | 0.438574i | ||||||||
\(863\) | 334819. | − | 579923.i | 0.449561 | − | 0.778662i | −0.548797 | − | 0.835956i | \(-0.684914\pi\) |
0.998357 | + | 0.0572941i | \(0.0182473\pi\) | |||||||
\(864\) | 66947.2 | − | 249850.i | 0.0896819 | − | 0.334697i | ||||
\(865\) | 344084. | − | 344084.i | 0.459867 | − | 0.459867i | ||||
\(866\) | −131228. | − | 489750.i | −0.174981 | − | 0.653038i | ||||
\(867\) | −622710. | + | 1.07857e6i | −0.828414 | + | 1.43486i | ||||
\(868\) | 221954. | − | 59472.5i | 0.294594 | − | 0.0789363i | ||||
\(869\) | −414703. | − | 111119.i | −0.549159 | − | 0.147147i | ||||
\(870\) | 107177. | − | 399989.i | 0.141599 | − | 0.528456i | ||||
\(871\) | −335615. | − | 1.25253e6i | −0.442390 | − | 1.65102i | ||||
\(872\) | −251100. | − | 144973.i | −0.330228 | − | 0.190657i | ||||
\(873\) | −1.56262e6 | + | 418704.i | −2.05034 | + | 0.549387i | ||||
\(874\) | −458095. | − | 458095.i | −0.599699 | − | 0.599699i | ||||
\(875\) | 352535. | + | 94461.3i | 0.460453 | + | 0.123378i | ||||
\(876\) | 662193. | + | 382317.i | 0.862932 | + | 0.498214i | ||||
\(877\) | 339432. | 0.441320 | 0.220660 | − | 0.975351i | \(-0.429179\pi\) | ||||
0.220660 | + | 0.975351i | \(0.429179\pi\) | |||||||
\(878\) | − | 368837.i | − | 0.478460i | ||||||
\(879\) | −139215. | − | 80375.8i | −0.180181 | − | 0.104027i | ||||
\(880\) | 83002.8 | − | 83002.8i | 0.107183 | − | 0.107183i | ||||
\(881\) | −385361. | + | 222488.i | −0.496496 | + | 0.286652i | −0.727265 | − | 0.686357i | \(-0.759209\pi\) |
0.230770 | + | 0.973008i | \(0.425876\pi\) | |||||||
\(882\) | 662141. | − | 662141.i | 0.851165 | − | 0.851165i | ||||
\(883\) | −414151. | − | 110971.i | −0.531174 | − | 0.142328i | −0.0167437 | − | 0.999860i | \(-0.505330\pi\) |
−0.514430 | + | 0.857532i | \(0.671997\pi\) | |||||||
\(884\) | −72744.6 | − | 125997.i | −0.0930886 | − | 0.161234i | ||||
\(885\) | 580510. | + | 1.00547e6i | 0.741179 | + | 1.28376i | ||||
\(886\) | 497115. | − | 133202.i | 0.633271 | − | 0.169685i | ||||
\(887\) | 329892.i | 0.419300i | 0.977776 | + | 0.209650i | \(0.0672325\pi\) | ||||
−0.977776 | + | 0.209650i | \(0.932768\pi\) | |||||||
\(888\) | 327224. | − | 367080.i | 0.414973 | − | 0.465516i | ||||
\(889\) | −65321.0 | −0.0826512 | ||||||||
\(890\) | −80705.8 | − | 301198.i | −0.101888 | − | 0.380253i | ||||
\(891\) | 649869. | − | 375202.i | 0.818598 | − | 0.472618i | ||||
\(892\) | 492415. | − | 284296.i | 0.618873 | − | 0.357307i | ||||
\(893\) | 5206.22 | − | 19429.9i | 0.00652859 | − | 0.0243650i | ||||
\(894\) | 83051.8 | + | 83051.8i | 0.103914 | + | 0.103914i | ||||
\(895\) | 324439. | + | 561945.i | 0.405030 | + | 0.701533i | ||||
\(896\) | −22082.6 | − | 22082.6i | −0.0275064 | − | 0.0275064i | ||||
\(897\) | 977636. | − | 1.69332e6i | 1.21505 | − | 2.10452i | ||||
\(898\) | −267758. | −0.332040 | ||||||||
\(899\) | 569024.i | 0.704063i | ||||||||
\(900\) | −108756. | + | 188371.i | −0.134267 | + | 0.232557i | ||||
\(901\) | −16846.5 | + | 62872.0i | −0.0207520 | + | 0.0774475i | ||||
\(902\) | 512762. | − | 512762.i | 0.630235 | − | 0.630235i | ||||
\(903\) | −223538. | − | 834255.i | −0.274142 | − | 1.02311i | ||||
\(904\) | −209362. | + | 362625.i | −0.256189 | + | 0.443732i | ||||
\(905\) | −74572.1 | + | 19981.5i | −0.0910498 | + | 0.0243967i | ||||
\(906\) | −79203.5 | − | 21222.5i | −0.0964912 | − | 0.0258548i | ||||
\(907\) | −88886.5 | + | 331729.i | −0.108049 | + | 0.403245i | −0.998673 | − | 0.0514954i | \(-0.983601\pi\) |
0.890624 | + | 0.454740i | \(0.150268\pi\) | |||||||
\(908\) | 91719.0 | + | 342300.i | 0.111247 | + | 0.415179i | ||||
\(909\) | 2.58955e6 | + | 1.49508e6i | 3.13398 | + | 1.80940i | ||||
\(910\) | 324882. | − | 87051.8i | 0.392322 | − | 0.105122i | ||||
\(911\) | 350788. | + | 350788.i | 0.422676 | + | 0.422676i | 0.886124 | − | 0.463448i | \(-0.153388\pi\) |
−0.463448 | + | 0.886124i | \(0.653388\pi\) | |||||||
\(912\) | 466179. | + | 124912.i | 0.560484 | + | 0.150181i | ||||
\(913\) | −588382. | − | 339703.i | −0.705859 | − | 0.407528i | ||||
\(914\) | −864157. | −1.03443 | ||||||||
\(915\) | − | 927432.i | − | 1.10775i | ||||||
\(916\) | −17711.9 | − | 10226.0i | −0.0211094 | − | 0.0121875i | ||||
\(917\) | −62990.1 | + | 62990.1i | −0.0749089 | + | 0.0749089i | ||||
\(918\) | −249195. | + | 143873.i | −0.295701 | + | 0.170723i | ||||
\(919\) | −486669. | + | 486669.i | −0.576239 | + | 0.576239i | −0.933865 | − | 0.357626i | \(-0.883586\pi\) |
0.357626 | + | 0.933865i | \(0.383586\pi\) | |||||||
\(920\) | −227502. | − | 60958.9i | −0.268787 | − | 0.0720213i | ||||
\(921\) | 424165. | + | 734676.i | 0.500053 | + | 0.866117i | ||||
\(922\) | −146028. | − | 252929.i | −0.171781 | − | 0.297534i | ||||
\(923\) | 1.57524e6 | − | 422084.i | 1.84903 | − | 0.495446i | ||||
\(924\) | − | 232691.i | − | 0.272544i | ||||||
\(925\) | −181949. | + | 119452.i | −0.212651 | + | 0.139608i | ||||
\(926\) | 424241. | 0.494755 | ||||||||
\(927\) | −460093. | − | 1.71709e6i | −0.535409 | − | 1.99817i | ||||
\(928\) | 66974.0 | − | 38667.4i | 0.0777696 | − | 0.0449003i | ||||
\(929\) | 1.46827e6 | − | 847708.i | 1.70128 | − | 0.982234i | 0.756808 | − | 0.653637i | \(-0.226758\pi\) |
0.944470 | − | 0.328597i | \(-0.106576\pi\) | |||||||
\(930\) | −334141. | + | 1.24703e6i | −0.386335 | + | 1.44182i | ||||
\(931\) | 650275. | + | 650275.i | 0.750236 | + | 0.750236i | ||||
\(932\) | −244505. | − | 423496.i | −0.281486 | − | 0.487548i | ||||
\(933\) | 1.30767e6 | + | 1.30767e6i | 1.50223 | + | 1.50223i | ||||
\(934\) | −234076. | + | 405431.i | −0.268326 | + | 0.464754i | ||||
\(935\) | −130581. | −0.149368 | ||||||||
\(936\) | 988440.i | 1.12823i | ||||||||
\(937\) | −53304.5 | + | 92326.2i | −0.0607135 | + | 0.105159i | −0.894785 | − | 0.446498i | \(-0.852671\pi\) |
0.834071 | + | 0.551657i | \(0.186004\pi\) | |||||||
\(938\) | −80139.6 | + | 299085.i | −0.0910839 | + | 0.339930i | ||||
\(939\) | 2.15604e6 | − | 2.15604e6i | 2.44526 | − | 2.44526i | ||||
\(940\) | −1892.75 | − | 7063.83i | −0.00214208 | − | 0.00799437i | ||||
\(941\) | 429045. | − | 743127.i | 0.484533 | − | 0.839235i | −0.515309 | − | 0.857004i | \(-0.672323\pi\) |
0.999842 | + | 0.0177689i | \(0.00565633\pi\) | |||||||
\(942\) | 1.80917e6 | − | 484767.i | 2.03882 | − | 0.546300i | ||||
\(943\) | −1.40542e6 | − | 376582.i | −1.58046 | − | 0.423483i | ||||
\(944\) | −56118.7 | + | 209438.i | −0.0629743 | + | 0.235023i | ||||
\(945\) | −172169. | − | 642543.i | −0.192793 | − | 0.719513i | ||||
\(946\) | 525049. | + | 303137.i | 0.586702 | + | 0.338733i | ||||
\(947\) | −1.37739e6 | + | 369072.i | −1.53588 | + | 0.411539i | −0.924933 | − | 0.380130i | \(-0.875879\pi\) |
−0.610950 | + | 0.791669i | \(0.709212\pi\) | |||||||
\(948\) | −453784. | − | 453784.i | −0.504932 | − | 0.504932i | ||||
\(949\) | −1.48555e6 | − | 398051.i | −1.64951 | − | 0.441984i | ||||
\(950\) | −184996. | − | 106807.i | −0.204981 | − | 0.118346i | ||||
\(951\) | 264832. | 0.292826 | ||||||||
\(952\) | 34740.6i | 0.0383321i | ||||||||
\(953\) | 699088. | + | 403619.i | 0.769744 | + | 0.444412i | 0.832783 | − | 0.553599i | \(-0.186746\pi\) |
−0.0630396 | + | 0.998011i | \(0.520079\pi\) | |||||||
\(954\) | 312693. | − | 312693.i | 0.343574 | − | 0.343574i | ||||
\(955\) | −1.19206e6 | + | 688236.i | −1.30705 | + | 0.754624i | ||||
\(956\) | 273578. | − | 273578.i | 0.299340 | − | 0.299340i | ||||
\(957\) | 556589. | + | 149138.i | 0.607730 | + | 0.162841i | ||||
\(958\) | −270865. | − | 469153.i | −0.295136 | − | 0.511191i | ||||
\(959\) | −216080. | − | 374262.i | −0.234951 | − | 0.406947i | ||||
\(960\) | 169481. | − | 45412.4i | 0.183899 | − | 0.0492756i | ||||
\(961\) | − | 850508.i | − | 0.920941i | ||||||
\(962\) | −444644. | + | 883514.i | −0.480466 | + | 0.954692i | ||||
\(963\) | −1.55575e6 | −1.67759 | ||||||||
\(964\) | 19506.0 | + | 72797.5i | 0.0209901 | + | 0.0783362i | ||||
\(965\) | −802841. | + | 463520.i | −0.862134 | + | 0.497753i | ||||
\(966\) | −404337. | + | 233444.i | −0.433301 | + | 0.250166i | ||||
\(967\) | −332629. | + | 1.24139e6i | −0.355719 | + | 1.32756i | 0.523858 | + | 0.851806i | \(0.324492\pi\) |
−0.879577 | + | 0.475756i | \(0.842174\pi\) | |||||||
\(968\) | −118757. | − | 118757.i | −0.126738 | − | 0.126738i | ||||
\(969\) | −268442. | − | 464956.i | −0.285893 | − | 0.495181i | ||||
\(970\) | −408425. | − | 408425.i | −0.434079 | − | 0.434079i | ||||
\(971\) | 450019. | − | 779456.i | 0.477301 | − | 0.826710i | −0.522361 | − | 0.852725i | \(-0.674948\pi\) |
0.999662 | + | 0.0260152i | \(0.00828181\pi\) | |||||||
\(972\) | 195726. | 0.207165 | ||||||||
\(973\) | 798910.i | 0.843864i | ||||||||
\(974\) | −344445. | + | 596596.i | −0.363079 | + | 0.628872i | ||||
\(975\) | 166864. | − | 622746.i | 0.175531 | − | 0.655092i | ||||
\(976\) | 122473. | − | 122473.i | 0.128570 | − | 0.128570i | ||||
\(977\) | 240414. | + | 897238.i | 0.251867 | + | 0.939980i | 0.969807 | + | 0.243875i | \(0.0784186\pi\) |
−0.717940 | + | 0.696105i | \(0.754915\pi\) | |||||||
\(978\) | 624707. | − | 1.08202e6i | 0.653128 | − | 1.13125i | ||||
\(979\) | 419121. | − | 112303.i | 0.437294 | − | 0.117173i | ||||
\(980\) | 322943. | + | 86532.3i | 0.336259 | + | 0.0901003i | ||||
\(981\) | 567158. | − | 2.11666e6i | 0.589340 | − | 2.19945i | ||||
\(982\) | 289983. | + | 1.08223e6i | 0.300711 | + | 1.12227i | ||||
\(983\) | −564812. | − | 326094.i | −0.584517 | − | 0.337471i | 0.178410 | − | 0.983956i | \(-0.442905\pi\) |
−0.762926 | + | 0.646485i | \(0.776238\pi\) | |||||||
\(984\) | 1.04700e6 | − | 280542.i | 1.08132 | − | 0.289739i | ||||
\(985\) | 825985. | + | 825985.i | 0.851333 | + | 0.851333i | ||||
\(986\) | −83098.1 | − | 22266.1i | −0.0854747 | − | 0.0229029i | ||||
\(987\) | −12554.5 | − | 7248.34i | −0.0128874 | − | 0.00744054i | ||||
\(988\) | −970727. | −0.994451 | ||||||||
\(989\) | − | 1.21647e6i | − | 1.24368i | ||||||
\(990\) | 768299. | + | 443577.i | 0.783898 | + | 0.452584i | ||||
\(991\) | −93432.8 | + | 93432.8i | −0.0951376 | + | 0.0951376i | −0.753074 | − | 0.657936i | \(-0.771430\pi\) |
0.657936 | + | 0.753074i | \(0.271430\pi\) | |||||||
\(992\) | −208803. | + | 120552.i | −0.212184 | + | 0.122504i | ||||
\(993\) | −2.18318e6 | + | 2.18318e6i | −2.21407 | + | 2.21407i | ||||
\(994\) | −376143. | − | 100787.i | −0.380697 | − | 0.102008i | ||||
\(995\) | −664939. | − | 1.15171e6i | −0.671639 | − | 1.16331i | ||||
\(996\) | −507773. | − | 879489.i | −0.511860 | − | 0.886567i | ||||
\(997\) | 1.42946e6 | − | 383023.i | 1.43808 | − | 0.385331i | 0.546217 | − | 0.837644i | \(-0.316067\pi\) |
0.891860 | + | 0.452312i | \(0.149401\pi\) | |||||||
\(998\) | 495923.i | 0.497912i | ||||||||
\(999\) | 1.74739e6 | + | 879407.i | 1.75089 | + | 0.881168i |
(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 | 74.5.g.a.23.7 | ✓ | 28 | |
37.29 | odd | 12 | inner | 74.5.g.a.29.7 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.5.g.a.23.7 | ✓ | 28 | 1.1 | even | 1 | trivial | |
74.5.g.a.29.7 | yes | 28 | 37.29 | odd | 12 | inner |