Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,5,Mod(119,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.119");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(18.2964834658\) |
Analytic rank: | \(0\) |
Dimension: | \(78\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 119.16 | ||
Character | \(\chi\) | \(=\) | 177.119 |
Dual form | 177.5.b.a.119.63 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 5.41049i | − | 1.35262i | −0.736617 | − | 0.676311i | \(-0.763578\pi\) | ||
0.736617 | − | 0.676311i | \(-0.236422\pi\) | |||||||
\(3\) | 7.81854 | − | 4.45762i | 0.868727 | − | 0.495291i | ||||
\(4\) | −13.2734 | −0.829584 | ||||||||
\(5\) | 41.9044i | 1.67617i | 0.545536 | + | 0.838087i | \(0.316326\pi\) | ||||
−0.545536 | + | 0.838087i | \(0.683674\pi\) | |||||||
\(6\) | −24.1179 | − | 42.3021i | −0.669942 | − | 1.17506i | ||||
\(7\) | −64.0047 | −1.30622 | −0.653110 | − | 0.757263i | \(-0.726536\pi\) | ||||
−0.653110 | + | 0.757263i | \(0.726536\pi\) | |||||||
\(8\) | − | 14.7525i | − | 0.230508i | ||||||
\(9\) | 41.2592 | − | 69.7042i | 0.509373 | − | 0.860546i | ||||
\(10\) | 226.723 | 2.26723 | ||||||||
\(11\) | − | 161.993i | − | 1.33878i | −0.742911 | − | 0.669391i | \(-0.766555\pi\) | ||
0.742911 | − | 0.669391i | \(-0.233445\pi\) | |||||||
\(12\) | −103.778 | + | 59.1676i | −0.720682 | + | 0.410886i | ||||
\(13\) | −266.705 | −1.57813 | −0.789067 | − | 0.614308i | \(-0.789435\pi\) | ||||
−0.789067 | + | 0.614308i | \(0.789435\pi\) | |||||||
\(14\) | 346.297i | 1.76682i | ||||||||
\(15\) | 186.794 | + | 327.631i | 0.830195 | + | 1.45614i | ||||
\(16\) | −292.192 | −1.14137 | ||||||||
\(17\) | 98.3026i | 0.340147i | 0.985431 | + | 0.170074i | \(0.0544006\pi\) | ||||
−0.985431 | + | 0.170074i | \(0.945599\pi\) | |||||||
\(18\) | −377.134 | − | 223.232i | −1.16399 | − | 0.688988i | ||||
\(19\) | −447.364 | −1.23924 | −0.619618 | − | 0.784904i | \(-0.712712\pi\) | ||||
−0.619618 | + | 0.784904i | \(0.712712\pi\) | |||||||
\(20\) | − | 556.211i | − | 1.39053i | ||||||
\(21\) | −500.424 | + | 285.309i | −1.13475 | + | 0.646959i | ||||
\(22\) | −876.458 | −1.81086 | ||||||||
\(23\) | 28.8687i | 0.0545722i | 0.999628 | + | 0.0272861i | \(0.00868651\pi\) | ||||
−0.999628 | + | 0.0272861i | \(0.991313\pi\) | |||||||
\(24\) | −65.7610 | − | 115.343i | −0.114168 | − | 0.200248i | ||||
\(25\) | −1130.98 | −1.80956 | ||||||||
\(26\) | 1443.00i | 2.13462i | ||||||||
\(27\) | 11.8714 | − | 728.903i | 0.0162846 | − | 0.999867i | ||||
\(28\) | 849.558 | 1.08362 | ||||||||
\(29\) | 337.070i | 0.400797i | 0.979715 | + | 0.200398i | \(0.0642236\pi\) | ||||
−0.979715 | + | 0.200398i | \(0.935776\pi\) | |||||||
\(30\) | 1772.64 | − | 1010.65i | 1.96960 | − | 1.12294i | ||||
\(31\) | 1735.49 | 1.80592 | 0.902958 | − | 0.429728i | \(-0.141390\pi\) | ||||
0.902958 | + | 0.429728i | \(0.141390\pi\) | |||||||
\(32\) | 1344.86i | 1.31334i | ||||||||
\(33\) | −722.102 | − | 1266.55i | −0.663087 | − | 1.16304i | ||||
\(34\) | 531.865 | 0.460090 | ||||||||
\(35\) | − | 2682.08i | − | 2.18945i | ||||||
\(36\) | −547.648 | + | 925.209i | −0.422568 | + | 0.713896i | ||||
\(37\) | −328.761 | −0.240146 | −0.120073 | − | 0.992765i | \(-0.538313\pi\) | ||||
−0.120073 | + | 0.992765i | \(0.538313\pi\) | |||||||
\(38\) | 2420.46i | 1.67622i | ||||||||
\(39\) | −2085.24 | + | 1188.87i | −1.37097 | + | 0.781636i | ||||
\(40\) | 618.194 | 0.386371 | ||||||||
\(41\) | − | 606.752i | − | 0.360947i | −0.983580 | − | 0.180473i | \(-0.942237\pi\) | ||
0.983580 | − | 0.180473i | \(-0.0577630\pi\) | |||||||
\(42\) | 1543.66 | + | 2707.54i | 0.875091 | + | 1.53488i | ||||
\(43\) | −2506.79 | −1.35575 | −0.677876 | − | 0.735176i | \(-0.737099\pi\) | ||||
−0.677876 | + | 0.735176i | \(0.737099\pi\) | |||||||
\(44\) | 2150.18i | 1.11063i | ||||||||
\(45\) | 2920.91 | + | 1728.94i | 1.44243 | + | 0.853798i | ||||
\(46\) | 156.194 | 0.0738155 | ||||||||
\(47\) | − | 2517.63i | − | 1.13971i | −0.821744 | − | 0.569857i | \(-0.806999\pi\) | ||
0.821744 | − | 0.569857i | \(-0.193001\pi\) | |||||||
\(48\) | −2284.51 | + | 1302.48i | −0.991542 | + | 0.565313i | ||||
\(49\) | 1695.61 | 0.706209 | ||||||||
\(50\) | 6119.13i | 2.44765i | ||||||||
\(51\) | 438.196 | + | 768.583i | 0.168472 | + | 0.295495i | ||||
\(52\) | 3540.06 | 1.30919 | ||||||||
\(53\) | − | 1760.77i | − | 0.626832i | −0.949616 | − | 0.313416i | \(-0.898527\pi\) | ||
0.949616 | − | 0.313416i | \(-0.101473\pi\) | |||||||
\(54\) | −3943.72 | − | 64.2303i | −1.35244 | − | 0.0220269i | ||||
\(55\) | 6788.20 | 2.24403 | ||||||||
\(56\) | 944.229i | 0.301094i | ||||||||
\(57\) | −3497.73 | + | 1994.18i | −1.07656 | + | 0.613783i | ||||
\(58\) | 1823.71 | 0.542126 | ||||||||
\(59\) | − | 453.188i | − | 0.130189i | ||||||
\(60\) | −2479.38 | − | 4348.76i | −0.688717 | − | 1.20799i | ||||
\(61\) | 1300.26 | 0.349437 | 0.174719 | − | 0.984618i | \(-0.444098\pi\) | ||||
0.174719 | + | 0.984618i | \(0.444098\pi\) | |||||||
\(62\) | − | 9389.82i | − | 2.44272i | ||||||
\(63\) | −2640.78 | + | 4461.40i | −0.665352 | + | 1.12406i | ||||
\(64\) | 2601.27 | 0.635077 | ||||||||
\(65\) | − | 11176.1i | − | 2.64523i | ||||||
\(66\) | −6852.63 | + | 3906.92i | −1.57315 | + | 0.896906i | ||||
\(67\) | 5806.28 | 1.29345 | 0.646723 | − | 0.762725i | \(-0.276139\pi\) | ||||
0.646723 | + | 0.762725i | \(0.276139\pi\) | |||||||
\(68\) | − | 1304.80i | − | 0.282181i | ||||||
\(69\) | 128.686 | + | 225.711i | 0.0270291 | + | 0.0474083i | ||||
\(70\) | −14511.3 | −2.96150 | ||||||||
\(71\) | 7039.96i | 1.39654i | 0.715834 | + | 0.698270i | \(0.246047\pi\) | ||||
−0.715834 | + | 0.698270i | \(0.753953\pi\) | |||||||
\(72\) | −1028.31 | − | 608.676i | −0.198362 | − | 0.117414i | ||||
\(73\) | 3733.10 | 0.700526 | 0.350263 | − | 0.936651i | \(-0.386092\pi\) | ||||
0.350263 | + | 0.936651i | \(0.386092\pi\) | |||||||
\(74\) | 1778.75i | 0.324827i | ||||||||
\(75\) | −8842.58 | + | 5041.47i | −1.57201 | + | 0.896261i | ||||
\(76\) | 5938.02 | 1.02805 | ||||||||
\(77\) | 10368.3i | 1.74874i | ||||||||
\(78\) | 6432.36 | + | 11282.2i | 1.05726 | + | 1.85440i | ||||
\(79\) | −4184.54 | −0.670493 | −0.335246 | − | 0.942131i | \(-0.608820\pi\) | ||||
−0.335246 | + | 0.942131i | \(0.608820\pi\) | |||||||
\(80\) | − | 12244.1i | − | 1.91314i | ||||||
\(81\) | −3156.36 | − | 5751.88i | −0.481079 | − | 0.876677i | ||||
\(82\) | −3282.82 | −0.488225 | ||||||||
\(83\) | 6012.45i | 0.872762i | 0.899762 | + | 0.436381i | \(0.143740\pi\) | ||||
−0.899762 | + | 0.436381i | \(0.856260\pi\) | |||||||
\(84\) | 6642.30 | − | 3787.01i | 0.941369 | − | 0.536707i | ||||
\(85\) | −4119.31 | −0.570146 | ||||||||
\(86\) | 13562.9i | 1.83382i | ||||||||
\(87\) | 1502.53 | + | 2635.40i | 0.198511 | + | 0.348183i | ||||
\(88\) | −2389.79 | −0.308599 | ||||||||
\(89\) | − | 13337.9i | − | 1.68387i | −0.539579 | − | 0.841935i | \(-0.681416\pi\) | ||
0.539579 | − | 0.841935i | \(-0.318584\pi\) | |||||||
\(90\) | 9354.41 | − | 15803.6i | 1.15486 | − | 1.95106i | ||||
\(91\) | 17070.4 | 2.06139 | ||||||||
\(92\) | − | 383.184i | − | 0.0452722i | ||||||
\(93\) | 13569.0 | − | 7736.14i | 1.56885 | − | 0.894455i | ||||
\(94\) | −13621.6 | −1.54160 | ||||||||
\(95\) | − | 18746.5i | − | 2.07717i | ||||||
\(96\) | 5994.88 | + | 10514.8i | 0.650486 | + | 1.14093i | ||||
\(97\) | −7745.75 | −0.823228 | −0.411614 | − | 0.911358i | \(-0.635035\pi\) | ||||
−0.411614 | + | 0.911358i | \(0.635035\pi\) | |||||||
\(98\) | − | 9174.06i | − | 0.955233i | ||||||
\(99\) | −11291.6 | − | 6683.68i | −1.15208 | − | 0.681939i | ||||
\(100\) | 15011.8 | 1.50118 | ||||||||
\(101\) | 1454.56i | 0.142590i | 0.997455 | + | 0.0712951i | \(0.0227132\pi\) | ||||
−0.997455 | + | 0.0712951i | \(0.977287\pi\) | |||||||
\(102\) | 4158.41 | − | 2370.85i | 0.399693 | − | 0.227879i | ||||
\(103\) | 11377.7 | 1.07245 | 0.536227 | − | 0.844074i | \(-0.319849\pi\) | ||||
0.536227 | + | 0.844074i | \(0.319849\pi\) | |||||||
\(104\) | 3934.56i | 0.363772i | ||||||||
\(105\) | −11955.7 | − | 20969.9i | −1.08442 | − | 1.90204i | ||||
\(106\) | −9526.63 | −0.847867 | ||||||||
\(107\) | − | 6247.21i | − | 0.545656i | −0.962063 | − | 0.272828i | \(-0.912041\pi\) | ||
0.962063 | − | 0.272828i | \(-0.0879590\pi\) | |||||||
\(108\) | −157.574 | + | 9674.99i | −0.0135094 | + | 0.829474i | ||||
\(109\) | −8355.95 | −0.703304 | −0.351652 | − | 0.936131i | \(-0.614380\pi\) | ||||
−0.351652 | + | 0.936131i | \(0.614380\pi\) | |||||||
\(110\) | − | 36727.4i | − | 3.03533i | ||||||
\(111\) | −2570.43 | + | 1465.49i | −0.208622 | + | 0.118943i | ||||
\(112\) | 18701.7 | 1.49088 | ||||||||
\(113\) | 2933.39i | 0.229727i | 0.993381 | + | 0.114864i | \(0.0366431\pi\) | ||||
−0.993381 | + | 0.114864i | \(0.963357\pi\) | |||||||
\(114\) | 10789.5 | + | 18924.4i | 0.830215 | + | 1.45617i | ||||
\(115\) | −1209.72 | −0.0914725 | ||||||||
\(116\) | − | 4474.05i | − | 0.332495i | ||||||
\(117\) | −11004.0 | + | 18590.4i | −0.803858 | + | 1.35806i | ||||
\(118\) | −2451.96 | −0.176096 | ||||||||
\(119\) | − | 6291.83i | − | 0.444307i | ||||||
\(120\) | 4833.37 | − | 2755.68i | 0.335651 | − | 0.191366i | ||||
\(121\) | −11600.6 | −0.792336 | ||||||||
\(122\) | − | 7035.02i | − | 0.472656i | ||||||
\(123\) | −2704.67 | − | 4743.91i | −0.178774 | − | 0.313564i | ||||
\(124\) | −23035.7 | −1.49816 | ||||||||
\(125\) | − | 21202.6i | − | 1.35697i | ||||||
\(126\) | 24138.3 | + | 14287.9i | 1.52043 | + | 0.899970i | ||||
\(127\) | 17272.2 | 1.07088 | 0.535438 | − | 0.844575i | \(-0.320147\pi\) | ||||
0.535438 | + | 0.844575i | \(0.320147\pi\) | |||||||
\(128\) | 7443.60i | 0.454321i | ||||||||
\(129\) | −19599.4 | + | 11174.3i | −1.17778 | + | 0.671493i | ||||
\(130\) | −60468.0 | −3.57799 | ||||||||
\(131\) | − | 8931.88i | − | 0.520476i | −0.965545 | − | 0.260238i | \(-0.916199\pi\) | ||
0.965545 | − | 0.260238i | \(-0.0838009\pi\) | |||||||
\(132\) | 9584.71 | + | 16811.3i | 0.550087 | + | 0.964836i | ||||
\(133\) | 28633.4 | 1.61871 | ||||||||
\(134\) | − | 31414.8i | − | 1.74954i | ||||||
\(135\) | 30544.2 | + | 497.466i | 1.67595 | + | 0.0272958i | ||||
\(136\) | 1450.21 | 0.0784066 | ||||||||
\(137\) | − | 27846.5i | − | 1.48364i | −0.670597 | − | 0.741822i | \(-0.733962\pi\) | ||
0.670597 | − | 0.741822i | \(-0.266038\pi\) | |||||||
\(138\) | 1221.21 | − | 696.252i | 0.0641255 | − | 0.0365602i | ||||
\(139\) | −14087.1 | −0.729111 | −0.364555 | − | 0.931182i | \(-0.618779\pi\) | ||||
−0.364555 | + | 0.931182i | \(0.618779\pi\) | |||||||
\(140\) | 35600.2i | 1.81634i | ||||||||
\(141\) | −11222.6 | − | 19684.2i | −0.564491 | − | 0.990100i | ||||
\(142\) | 38089.6 | 1.88899 | ||||||||
\(143\) | 43204.2i | 2.11278i | ||||||||
\(144\) | −12055.6 | + | 20367.0i | −0.581385 | + | 0.982205i | ||||
\(145\) | −14124.7 | −0.671805 | ||||||||
\(146\) | − | 20197.9i | − | 0.947546i | ||||||
\(147\) | 13257.2 | − | 7558.38i | 0.613503 | − | 0.349779i | ||||
\(148\) | 4363.75 | 0.199222 | ||||||||
\(149\) | 21635.1i | 0.974512i | 0.873259 | + | 0.487256i | \(0.162002\pi\) | ||||
−0.873259 | + | 0.487256i | \(0.837998\pi\) | |||||||
\(150\) | 27276.8 | + | 47842.7i | 1.21230 | + | 2.12634i | ||||
\(151\) | −10716.1 | −0.469985 | −0.234992 | − | 0.971997i | \(-0.575507\pi\) | ||||
−0.234992 | + | 0.971997i | \(0.575507\pi\) | |||||||
\(152\) | 6599.73i | 0.285653i | ||||||||
\(153\) | 6852.10 | + | 4055.88i | 0.292712 | + | 0.173262i | ||||
\(154\) | 56097.5 | 2.36539 | ||||||||
\(155\) | 72724.5i | 3.02703i | ||||||||
\(156\) | 27678.1 | − | 15780.3i | 1.13733 | − | 0.648433i | ||||
\(157\) | −43733.5 | −1.77425 | −0.887125 | − | 0.461529i | \(-0.847301\pi\) | ||||
−0.887125 | + | 0.461529i | \(0.847301\pi\) | |||||||
\(158\) | 22640.4i | 0.906923i | ||||||||
\(159\) | −7848.86 | − | 13766.7i | −0.310465 | − | 0.544546i | ||||
\(160\) | −56355.5 | −2.20139 | ||||||||
\(161\) | − | 1847.73i | − | 0.0712833i | ||||||
\(162\) | −31120.5 | + | 17077.4i | −1.18581 | + | 0.650718i | ||||
\(163\) | −29538.5 | −1.11176 | −0.555882 | − | 0.831261i | \(-0.687619\pi\) | ||||
−0.555882 | + | 0.831261i | \(0.687619\pi\) | |||||||
\(164\) | 8053.63i | 0.299436i | ||||||||
\(165\) | 53073.8 | − | 30259.2i | 1.94945 | − | 1.11145i | ||||
\(166\) | 32530.3 | 1.18052 | ||||||||
\(167\) | − | 24433.8i | − | 0.876108i | −0.898949 | − | 0.438054i | \(-0.855668\pi\) | ||
0.898949 | − | 0.438054i | \(-0.144332\pi\) | |||||||
\(168\) | 4209.02 | + | 7382.50i | 0.149129 | + | 0.261568i | ||||
\(169\) | 42570.3 | 1.49051 | ||||||||
\(170\) | 22287.4i | 0.771192i | ||||||||
\(171\) | −18457.9 | + | 31183.2i | −0.631232 | + | 1.06642i | ||||
\(172\) | 33273.5 | 1.12471 | ||||||||
\(173\) | − | 18199.7i | − | 0.608097i | −0.952656 | − | 0.304049i | \(-0.901661\pi\) | ||
0.952656 | − | 0.304049i | \(-0.0983386\pi\) | |||||||
\(174\) | 14258.8 | − | 8129.42i | 0.470959 | − | 0.268510i | ||||
\(175\) | 72387.8 | 2.36368 | ||||||||
\(176\) | 47332.9i | 1.52805i | ||||||||
\(177\) | −2020.14 | − | 3543.27i | −0.0644815 | − | 0.113099i | ||||
\(178\) | −72164.7 | −2.27764 | ||||||||
\(179\) | 36106.0i | 1.12687i | 0.826161 | + | 0.563435i | \(0.190520\pi\) | ||||
−0.826161 | + | 0.563435i | \(0.809480\pi\) | |||||||
\(180\) | −38770.3 | − | 22948.8i | −1.19661 | − | 0.708297i | ||||
\(181\) | 4609.61 | 0.140704 | 0.0703521 | − | 0.997522i | \(-0.477588\pi\) | ||||
0.0703521 | + | 0.997522i | \(0.477588\pi\) | |||||||
\(182\) | − | 92358.9i | − | 2.78828i | ||||||
\(183\) | 10166.1 | − | 5796.05i | 0.303566 | − | 0.173073i | ||||
\(184\) | 425.885 | 0.0125793 | ||||||||
\(185\) | − | 13776.5i | − | 0.402527i | ||||||
\(186\) | −41856.3 | − | 73414.7i | −1.20986 | − | 2.12206i | ||||
\(187\) | 15924.3 | 0.455383 | ||||||||
\(188\) | 33417.4i | 0.945489i | ||||||||
\(189\) | −759.829 | + | 46653.3i | −0.0212712 | + | 1.30605i | ||||
\(190\) | −101428. | −2.80963 | ||||||||
\(191\) | − | 71978.1i | − | 1.97303i | −0.163671 | − | 0.986515i | \(-0.552334\pi\) | ||
0.163671 | − | 0.986515i | \(-0.447666\pi\) | |||||||
\(192\) | 20338.2 | − | 11595.5i | 0.551708 | − | 0.314548i | ||||
\(193\) | −65292.5 | −1.75287 | −0.876433 | − | 0.481523i | \(-0.840084\pi\) | ||||
−0.876433 | + | 0.481523i | \(0.840084\pi\) | |||||||
\(194\) | 41908.3i | 1.11352i | ||||||||
\(195\) | −49818.8 | − | 87380.7i | −1.31016 | − | 2.29798i | ||||
\(196\) | −22506.4 | −0.585860 | ||||||||
\(197\) | 20345.6i | 0.524249i | 0.965034 | + | 0.262124i | \(0.0844231\pi\) | ||||
−0.965034 | + | 0.262124i | \(0.915577\pi\) | |||||||
\(198\) | −36162.0 | + | 61092.9i | −0.922405 | + | 1.55833i | ||||
\(199\) | 40599.6 | 1.02522 | 0.512608 | − | 0.858623i | \(-0.328679\pi\) | ||||
0.512608 | + | 0.858623i | \(0.328679\pi\) | |||||||
\(200\) | 16684.7i | 0.417118i | ||||||||
\(201\) | 45396.6 | − | 25882.2i | 1.12365 | − | 0.640633i | ||||
\(202\) | 7869.89 | 0.192871 | ||||||||
\(203\) | − | 21574.1i | − | 0.523528i | ||||||
\(204\) | −5816.33 | − | 10201.7i | −0.139762 | − | 0.245138i | ||||
\(205\) | 25425.6 | 0.605010 | ||||||||
\(206\) | − | 61558.6i | − | 1.45062i | ||||||
\(207\) | 2012.27 | + | 1191.10i | 0.0469619 | + | 0.0277976i | ||||
\(208\) | 77928.9 | 1.80124 | ||||||||
\(209\) | 72469.6i | 1.65906i | ||||||||
\(210\) | −113458. | + | 64686.1i | −2.57273 | + | 1.46681i | ||||
\(211\) | 75004.1 | 1.68469 | 0.842345 | − | 0.538939i | \(-0.181175\pi\) | ||||
0.842345 | + | 0.538939i | \(0.181175\pi\) | |||||||
\(212\) | 23371.3i | 0.520010i | ||||||||
\(213\) | 31381.5 | + | 55042.2i | 0.691695 | + | 1.21321i | ||||
\(214\) | −33800.5 | −0.738066 | ||||||||
\(215\) | − | 105045.i | − | 2.27248i | ||||||
\(216\) | −10753.1 | − | 175.133i | −0.230477 | − | 0.00375372i | ||||
\(217\) | −111079. | −2.35892 | ||||||||
\(218\) | 45209.7i | 0.951304i | ||||||||
\(219\) | 29187.4 | − | 16640.8i | 0.608566 | − | 0.346965i | ||||
\(220\) | −90102.1 | −1.86161 | ||||||||
\(221\) | − | 26217.7i | − | 0.536798i | ||||||
\(222\) | 7929.02 | + | 13907.3i | 0.160884 | + | 0.282186i | ||||
\(223\) | −38212.6 | −0.768418 | −0.384209 | − | 0.923246i | \(-0.625526\pi\) | ||||
−0.384209 | + | 0.923246i | \(0.625526\pi\) | |||||||
\(224\) | − | 86077.4i | − | 1.71551i | ||||||
\(225\) | −46663.2 | + | 78833.8i | −0.921741 | + | 1.55721i | ||||
\(226\) | 15871.1 | 0.310734 | ||||||||
\(227\) | 57636.8i | 1.11853i | 0.828989 | + | 0.559265i | \(0.188917\pi\) | ||||
−0.828989 | + | 0.559265i | \(0.811083\pi\) | |||||||
\(228\) | 46426.6 | − | 26469.4i | 0.893095 | − | 0.509185i | ||||
\(229\) | 18933.1 | 0.361036 | 0.180518 | − | 0.983572i | \(-0.442223\pi\) | ||||
0.180518 | + | 0.983572i | \(0.442223\pi\) | |||||||
\(230\) | 6545.20i | 0.123728i | ||||||||
\(231\) | 46217.9 | + | 81064.9i | 0.866137 | + | 1.51918i | ||||
\(232\) | 4972.62 | 0.0923867 | ||||||||
\(233\) | − | 12366.1i | − | 0.227783i | −0.993493 | − | 0.113891i | \(-0.963668\pi\) | ||
0.993493 | − | 0.113891i | \(-0.0363316\pi\) | |||||||
\(234\) | 100583. | + | 59537.0i | 1.83694 | + | 1.08732i | ||||
\(235\) | 105500. | 1.91036 | ||||||||
\(236\) | 6015.32i | 0.108003i | ||||||||
\(237\) | −32717.0 | + | 18653.1i | −0.582475 | + | 0.332089i | ||||
\(238\) | −34041.9 | −0.600979 | ||||||||
\(239\) | − | 11878.9i | − | 0.207960i | −0.994579 | − | 0.103980i | \(-0.966842\pi\) | ||
0.994579 | − | 0.103980i | \(-0.0331578\pi\) | |||||||
\(240\) | −54579.6 | − | 95731.1i | −0.947563 | − | 1.66200i | ||||
\(241\) | −45059.9 | −0.775811 | −0.387905 | − | 0.921699i | \(-0.626801\pi\) | ||||
−0.387905 | + | 0.921699i | \(0.626801\pi\) | |||||||
\(242\) | 62764.8i | 1.07173i | ||||||||
\(243\) | −50317.8 | − | 30901.4i | −0.852137 | − | 0.523319i | ||||
\(244\) | −17258.8 | −0.289888 | ||||||||
\(245\) | 71053.4i | 1.18373i | ||||||||
\(246\) | −25666.9 | + | 14633.6i | −0.424134 | + | 0.241813i | ||||
\(247\) | 119314. | 1.95568 | ||||||||
\(248\) | − | 25602.7i | − | 0.416278i | ||||||
\(249\) | 26801.3 | + | 47008.6i | 0.432271 | + | 0.758191i | ||||
\(250\) | −114716. | −1.83546 | ||||||||
\(251\) | − | 10604.9i | − | 0.168329i | −0.996452 | − | 0.0841646i | \(-0.973178\pi\) | ||
0.996452 | − | 0.0841646i | \(-0.0268221\pi\) | |||||||
\(252\) | 35052.1 | − | 59217.8i | 0.551966 | − | 0.932504i | ||||
\(253\) | 4676.51 | 0.0730602 | ||||||||
\(254\) | − | 93450.7i | − | 1.44849i | ||||||
\(255\) | −32207.0 | + | 18362.3i | −0.495301 | + | 0.282389i | ||||
\(256\) | 81893.8 | 1.24960 | ||||||||
\(257\) | − | 11638.4i | − | 0.176209i | −0.996111 | − | 0.0881046i | \(-0.971919\pi\) | ||
0.996111 | − | 0.0881046i | \(-0.0280810\pi\) | |||||||
\(258\) | 60458.4 | + | 106042.i | 0.908275 | + | 1.59309i | ||||
\(259\) | 21042.2 | 0.313684 | ||||||||
\(260\) | 148344.i | 2.19444i | ||||||||
\(261\) | 23495.2 | + | 13907.2i | 0.344904 | + | 0.204155i | ||||
\(262\) | −48325.8 | −0.704006 | ||||||||
\(263\) | − | 3594.97i | − | 0.0519737i | −0.999662 | − | 0.0259869i | \(-0.991727\pi\) | ||
0.999662 | − | 0.0259869i | \(-0.00827280\pi\) | |||||||
\(264\) | −18684.7 | + | 10652.8i | −0.268089 | + | 0.152847i | ||||
\(265\) | 73784.0 | 1.05068 | ||||||||
\(266\) | − | 154921.i | − | 2.18951i | ||||||
\(267\) | −59455.5 | − | 104283.i | −0.834007 | − | 1.46282i | ||||
\(268\) | −77068.8 | −1.07302 | ||||||||
\(269\) | − | 32803.0i | − | 0.453325i | −0.973973 | − | 0.226662i | \(-0.927219\pi\) | ||
0.973973 | − | 0.226662i | \(-0.0727814\pi\) | |||||||
\(270\) | 2691.53 | − | 165259.i | 0.0369209 | − | 2.26693i | ||||
\(271\) | 28994.4 | 0.394798 | 0.197399 | − | 0.980323i | \(-0.436751\pi\) | ||||
0.197399 | + | 0.980323i | \(0.436751\pi\) | |||||||
\(272\) | − | 28723.2i | − | 0.388235i | ||||||
\(273\) | 133465. | − | 76093.2i | 1.79078 | − | 1.02099i | ||||
\(274\) | −150663. | −2.00681 | ||||||||
\(275\) | 183210.i | 2.42261i | ||||||||
\(276\) | −1708.09 | − | 2995.94i | −0.0224230 | − | 0.0393292i | ||||
\(277\) | −88957.8 | −1.15938 | −0.579688 | − | 0.814838i | \(-0.696826\pi\) | ||||
−0.579688 | + | 0.814838i | \(0.696826\pi\) | |||||||
\(278\) | 76218.3i | 0.986211i | ||||||||
\(279\) | 71604.7 | − | 120971.i | 0.919885 | − | 1.55407i | ||||
\(280\) | −39567.3 | −0.504685 | ||||||||
\(281\) | 62305.2i | 0.789063i | 0.918882 | + | 0.394532i | \(0.129093\pi\) | ||||
−0.918882 | + | 0.394532i | \(0.870907\pi\) | |||||||
\(282\) | −106501. | + | 60719.9i | −1.33923 | + | 0.763542i | ||||
\(283\) | −102769. | −1.28318 | −0.641592 | − | 0.767046i | \(-0.721726\pi\) | ||||
−0.641592 | + | 0.767046i | \(0.721726\pi\) | |||||||
\(284\) | − | 93443.9i | − | 1.15855i | ||||||
\(285\) | −83564.8 | − | 146570.i | −1.02881 | − | 1.80450i | ||||
\(286\) | 233755. | 2.85779 | ||||||||
\(287\) | 38835.0i | 0.471476i | ||||||||
\(288\) | 93742.4 | + | 55487.8i | 1.13019 | + | 0.668979i | ||||
\(289\) | 73857.6 | 0.884300 | ||||||||
\(290\) | 76421.5i | 0.908698i | ||||||||
\(291\) | −60560.5 | + | 34527.6i | −0.715160 | + | 0.407738i | ||||
\(292\) | −49550.8 | −0.581145 | ||||||||
\(293\) | − | 124891.i | − | 1.45478i | −0.686225 | − | 0.727389i | \(-0.740733\pi\) | ||
0.686225 | − | 0.727389i | \(-0.259267\pi\) | |||||||
\(294\) | −40894.5 | − | 71727.8i | −0.473119 | − | 0.829837i | ||||
\(295\) | 18990.5 | 0.218219 | ||||||||
\(296\) | 4850.04i | 0.0553556i | ||||||||
\(297\) | −118077. | − | 1923.09i | −1.33860 | − | 0.0218015i | ||||
\(298\) | 117057. | 1.31815 | ||||||||
\(299\) | − | 7699.41i | − | 0.0861222i | ||||||
\(300\) | 117371. | − | 66917.1i | 1.30412 | − | 0.743524i | ||||
\(301\) | 160446. | 1.77091 | ||||||||
\(302\) | 57979.4i | 0.635712i | ||||||||
\(303\) | 6483.89 | + | 11372.6i | 0.0706237 | + | 0.123872i | ||||
\(304\) | 130716. | 1.41443 | ||||||||
\(305\) | 54486.4i | 0.585718i | ||||||||
\(306\) | 21944.3 | − | 37073.2i | 0.234358 | − | 0.395929i | ||||
\(307\) | 82222.6 | 0.872398 | 0.436199 | − | 0.899850i | \(-0.356324\pi\) | ||||
0.436199 | + | 0.899850i | \(0.356324\pi\) | |||||||
\(308\) | − | 137622.i | − | 1.45073i | ||||||
\(309\) | 88956.7 | − | 50717.3i | 0.931669 | − | 0.531177i | ||||
\(310\) | 393475. | 4.09443 | ||||||||
\(311\) | − | 153255.i | − | 1.58450i | −0.610195 | − | 0.792251i | \(-0.708909\pi\) | ||
0.610195 | − | 0.792251i | \(-0.291091\pi\) | |||||||
\(312\) | 17538.8 | + | 30762.5i | 0.180173 | + | 0.316018i | ||||
\(313\) | −146232. | −1.49263 | −0.746316 | − | 0.665591i | \(-0.768179\pi\) | ||||
−0.746316 | + | 0.665591i | \(0.768179\pi\) | |||||||
\(314\) | 236619.i | 2.39989i | ||||||||
\(315\) | −186952. | − | 110660.i | −1.88412 | − | 1.11525i | ||||
\(316\) | 55542.9 | 0.556230 | ||||||||
\(317\) | 47521.9i | 0.472907i | 0.971643 | + | 0.236453i | \(0.0759851\pi\) | ||||
−0.971643 | + | 0.236453i | \(0.924015\pi\) | |||||||
\(318\) | −74484.4 | + | 42466.1i | −0.736565 | + | 0.419941i | ||||
\(319\) | 54602.8 | 0.536579 | ||||||||
\(320\) | 109005.i | 1.06450i | ||||||||
\(321\) | −27847.7 | − | 48844.1i | −0.270259 | − | 0.474026i | ||||
\(322\) | −9997.13 | −0.0964193 | ||||||||
\(323\) | − | 43977.0i | − | 0.421522i | ||||||
\(324\) | 41895.5 | + | 76346.7i | 0.399096 | + | 0.727278i | ||||
\(325\) | 301636. | 2.85573 | ||||||||
\(326\) | 159817.i | 1.50380i | ||||||||
\(327\) | −65331.3 | + | 37247.7i | −0.610979 | + | 0.348340i | ||||
\(328\) | −8951.10 | −0.0832010 | ||||||||
\(329\) | 161140.i | 1.48872i | ||||||||
\(330\) | −163717. | − | 287155.i | −1.50337 | − | 2.63687i | ||||
\(331\) | 23464.2 | 0.214165 | 0.107083 | − | 0.994250i | \(-0.465849\pi\) | ||||
0.107083 | + | 0.994250i | \(0.465849\pi\) | |||||||
\(332\) | − | 79805.4i | − | 0.724029i | ||||||
\(333\) | −13564.4 | + | 22916.0i | −0.122324 | + | 0.206657i | ||||
\(334\) | −132199. | −1.18504 | ||||||||
\(335\) | 243308.i | 2.16804i | ||||||||
\(336\) | 146220. | − | 83365.0i | 1.29517 | − | 0.738423i | ||||
\(337\) | −98655.4 | −0.868682 | −0.434341 | − | 0.900748i | \(-0.643019\pi\) | ||||
−0.434341 | + | 0.900748i | \(0.643019\pi\) | |||||||
\(338\) | − | 230326.i | − | 2.01609i | ||||||
\(339\) | 13075.9 | + | 22934.8i | 0.113782 | + | 0.199570i | ||||
\(340\) | 54677.0 | 0.472985 | ||||||||
\(341\) | − | 281136.i | − | 2.41773i | ||||||
\(342\) | 168716. | + | 99866.0i | 1.44246 | + | 0.853819i | ||||
\(343\) | 45148.4 | 0.383755 | ||||||||
\(344\) | 36981.3i | 0.312511i | ||||||||
\(345\) | −9458.28 | + | 5392.50i | −0.0794646 | + | 0.0453056i | ||||
\(346\) | −98469.5 | −0.822525 | ||||||||
\(347\) | − | 166071.i | − | 1.37923i | −0.724178 | − | 0.689614i | \(-0.757780\pi\) | ||
0.724178 | − | 0.689614i | \(-0.242220\pi\) | |||||||
\(348\) | −19943.6 | − | 34980.5i | −0.164682 | − | 0.288847i | ||||
\(349\) | −4808.67 | −0.0394797 | −0.0197399 | − | 0.999805i | \(-0.506284\pi\) | ||||
−0.0197399 | + | 0.999805i | \(0.506284\pi\) | |||||||
\(350\) | − | 391653.i | − | 3.19717i | ||||||
\(351\) | −3166.17 | + | 194402.i | −0.0256992 | + | 1.57792i | ||||
\(352\) | 217857. | 1.75827 | ||||||||
\(353\) | 75307.1i | 0.604347i | 0.953253 | + | 0.302174i | \(0.0977122\pi\) | ||||
−0.953253 | + | 0.302174i | \(0.902288\pi\) | |||||||
\(354\) | −19170.8 | + | 10929.9i | −0.152980 | + | 0.0872190i | ||||
\(355\) | −295005. | −2.34085 | ||||||||
\(356\) | 177039.i | 1.39691i | ||||||||
\(357\) | −28046.6 | − | 49192.9i | −0.220061 | − | 0.385981i | ||||
\(358\) | 195351. | 1.52423 | ||||||||
\(359\) | 198922.i | 1.54346i | 0.635953 | + | 0.771728i | \(0.280607\pi\) | ||||
−0.635953 | + | 0.771728i | \(0.719393\pi\) | |||||||
\(360\) | 25506.2 | − | 43090.7i | 0.196807 | − | 0.332490i | ||||
\(361\) | 69813.4 | 0.535704 | ||||||||
\(362\) | − | 24940.2i | − | 0.190319i | ||||||
\(363\) | −90699.7 | + | 51711.1i | −0.688323 | + | 0.392437i | ||||
\(364\) | −226581. | −1.71010 | ||||||||
\(365\) | 156433.i | 1.17420i | ||||||||
\(366\) | −31359.5 | − | 55003.6i | −0.234103 | − | 0.410609i | ||||
\(367\) | −152393. | −1.13144 | −0.565722 | − | 0.824596i | \(-0.691402\pi\) | ||||
−0.565722 | + | 0.824596i | \(0.691402\pi\) | |||||||
\(368\) | − | 8435.19i | − | 0.0622873i | ||||||
\(369\) | −42293.2 | − | 25034.1i | −0.310611 | − | 0.183857i | ||||
\(370\) | −74537.6 | −0.544467 | ||||||||
\(371\) | 112698.i | 0.818780i | ||||||||
\(372\) | −180106. | + | 102685.i | −1.30149 | + | 0.742026i | ||||
\(373\) | −116970. | −0.840733 | −0.420366 | − | 0.907354i | \(-0.638098\pi\) | ||||
−0.420366 | + | 0.907354i | \(0.638098\pi\) | |||||||
\(374\) | − | 86158.1i | − | 0.615961i | ||||||
\(375\) | −94513.3 | − | 165773.i | −0.672094 | − | 1.17883i | ||||
\(376\) | −37141.3 | −0.262713 | ||||||||
\(377\) | − | 89898.1i | − | 0.632510i | ||||||
\(378\) | 252417. | + | 4111.04i | 1.76659 | + | 0.0287719i | ||||
\(379\) | −185149. | −1.28897 | −0.644487 | − | 0.764616i | \(-0.722929\pi\) | ||||
−0.644487 | + | 0.764616i | \(0.722929\pi\) | |||||||
\(380\) | 248829.i | 1.72319i | ||||||||
\(381\) | 135043. | − | 76992.8i | 0.930298 | − | 0.530396i | ||||
\(382\) | −389436. | −2.66876 | ||||||||
\(383\) | 219154.i | 1.49401i | 0.664821 | + | 0.747003i | \(0.268508\pi\) | ||||
−0.664821 | + | 0.747003i | \(0.731492\pi\) | |||||||
\(384\) | 33180.7 | + | 58198.1i | 0.225021 | + | 0.394681i | ||||
\(385\) | −434477. | −2.93120 | ||||||||
\(386\) | 353264.i | 2.37096i | ||||||||
\(387\) | −103428. | + | 174734.i | −0.690583 | + | 1.16669i | ||||
\(388\) | 102812. | 0.682937 | ||||||||
\(389\) | − | 177651.i | − | 1.17400i | −0.809586 | − | 0.587002i | \(-0.800308\pi\) | ||
0.809586 | − | 0.587002i | \(-0.199692\pi\) | |||||||
\(390\) | −472772. | + | 269544.i | −3.10830 | + | 1.77215i | ||||
\(391\) | −2837.87 | −0.0185626 | ||||||||
\(392\) | − | 25014.4i | − | 0.162787i | ||||||
\(393\) | −39815.0 | − | 69834.3i | −0.257787 | − | 0.452151i | ||||
\(394\) | 110079. | 0.709110 | ||||||||
\(395\) | − | 175351.i | − | 1.12386i | ||||||
\(396\) | 149877. | + | 88714.8i | 0.955750 | + | 0.565726i | ||||
\(397\) | 202948. | 1.28767 | 0.643834 | − | 0.765165i | \(-0.277343\pi\) | ||||
0.643834 | + | 0.765165i | \(0.277343\pi\) | |||||||
\(398\) | − | 219663.i | − | 1.38673i | ||||||
\(399\) | 223872. | − | 127637.i | 1.40622 | − | 0.801735i | ||||
\(400\) | 330462. | 2.06539 | ||||||||
\(401\) | − | 71075.9i | − | 0.442012i | −0.975272 | − | 0.221006i | \(-0.929066\pi\) | ||
0.975272 | − | 0.221006i | \(-0.0709340\pi\) | |||||||
\(402\) | −140035. | − | 245618.i | −0.866534 | − | 1.51987i | ||||
\(403\) | −462862. | −2.84998 | ||||||||
\(404\) | − | 19306.9i | − | 0.118291i | ||||||
\(405\) | 241029. | − | 132265.i | 1.46946 | − | 0.806372i | ||||
\(406\) | −116726. | −0.708136 | ||||||||
\(407\) | 53256.8i | 0.321504i | ||||||||
\(408\) | 11338.5 | − | 6464.48i | 0.0681139 | − | 0.0388341i | ||||
\(409\) | 237140. | 1.41762 | 0.708808 | − | 0.705402i | \(-0.249233\pi\) | ||||
0.708808 | + | 0.705402i | \(0.249233\pi\) | |||||||
\(410\) | − | 137565.i | − | 0.818350i | ||||||
\(411\) | −124129. | − | 217719.i | −0.734836 | − | 1.28888i | ||||
\(412\) | −151020. | −0.889690 | ||||||||
\(413\) | 29006.2i | 0.170055i | ||||||||
\(414\) | 6444.42 | − | 10887.4i | 0.0375996 | − | 0.0635216i | ||||
\(415\) | −251948. | −1.46290 | ||||||||
\(416\) | − | 358680.i | − | 2.07262i | ||||||
\(417\) | −110141. | + | 62795.2i | −0.633398 | + | 0.361122i | ||||
\(418\) | 392096. | 2.24409 | ||||||||
\(419\) | 148867.i | 0.847950i | 0.905674 | + | 0.423975i | \(0.139366\pi\) | ||||
−0.905674 | + | 0.423975i | \(0.860634\pi\) | |||||||
\(420\) | 158692. | + | 278341.i | 0.899615 | + | 1.57790i | ||||
\(421\) | −205091. | −1.15713 | −0.578565 | − | 0.815636i | \(-0.696387\pi\) | ||||
−0.578565 | + | 0.815636i | \(0.696387\pi\) | |||||||
\(422\) | − | 405808.i | − | 2.27875i | ||||||
\(423\) | −175489. | − | 103875.i | −0.980776 | − | 0.580539i | ||||
\(424\) | −25975.8 | −0.144490 | ||||||||
\(425\) | − | 111178.i | − | 0.615518i | ||||||
\(426\) | 297805. | − | 169789.i | 1.64102 | − | 0.935601i | ||||
\(427\) | −83222.6 | −0.456442 | ||||||||
\(428\) | 82921.5i | 0.452668i | ||||||||
\(429\) | 192588. | + | 337793.i | 1.04644 | + | 1.83542i | ||||
\(430\) | −568346. | −3.07380 | ||||||||
\(431\) | 209347.i | 1.12697i | 0.826126 | + | 0.563485i | \(0.190540\pi\) | ||||
−0.826126 | + | 0.563485i | \(0.809460\pi\) | |||||||
\(432\) | −3468.74 | + | 212980.i | −0.0185868 | + | 1.14122i | ||||
\(433\) | 207554. | 1.10702 | 0.553511 | − | 0.832842i | \(-0.313288\pi\) | ||||
0.553511 | + | 0.832842i | \(0.313288\pi\) | |||||||
\(434\) | 600993.i | 3.19073i | ||||||||
\(435\) | −110435. | + | 62962.6i | −0.583615 | + | 0.332739i | ||||
\(436\) | 110911. | 0.583450 | ||||||||
\(437\) | − | 12914.8i | − | 0.0676278i | ||||||
\(438\) | −90034.6 | − | 157918.i | −0.469312 | − | 0.823159i | ||||
\(439\) | 87515.8 | 0.454106 | 0.227053 | − | 0.973882i | \(-0.427091\pi\) | ||||
0.227053 | + | 0.973882i | \(0.427091\pi\) | |||||||
\(440\) | − | 100143.i | − | 0.517266i | ||||||
\(441\) | 69959.4 | − | 118191.i | 0.359724 | − | 0.607725i | ||||
\(442\) | −141851. | −0.726084 | ||||||||
\(443\) | 262305.i | 1.33659i | 0.743896 | + | 0.668296i | \(0.232976\pi\) | ||||
−0.743896 | + | 0.668296i | \(0.767024\pi\) | |||||||
\(444\) | 34118.2 | − | 19452.0i | 0.173069 | − | 0.0986729i | ||||
\(445\) | 558918. | 2.82246 | ||||||||
\(446\) | 206749.i | 1.03938i | ||||||||
\(447\) | 96441.3 | + | 169155.i | 0.482668 | + | 0.846585i | ||||
\(448\) | −166494. | −0.829549 | ||||||||
\(449\) | 171982.i | 0.853080i | 0.904469 | + | 0.426540i | \(0.140268\pi\) | ||||
−0.904469 | + | 0.426540i | \(0.859732\pi\) | |||||||
\(450\) | 426529. | + | 252470.i | 2.10632 | + | 1.24677i | ||||
\(451\) | −98289.3 | −0.483229 | ||||||||
\(452\) | − | 38935.9i | − | 0.190578i | ||||||
\(453\) | −83784.5 | + | 47768.4i | −0.408288 | + | 0.232779i | ||||
\(454\) | 311843. | 1.51295 | ||||||||
\(455\) | 715323.i | 3.45525i | ||||||||
\(456\) | 29419.1 | + | 51600.3i | 0.141482 | + | 0.248155i | ||||
\(457\) | 3157.29 | 0.0151176 | 0.00755879 | − | 0.999971i | \(-0.497594\pi\) | ||||
0.00755879 | + | 0.999971i | \(0.497594\pi\) | |||||||
\(458\) | − | 102437.i | − | 0.488345i | ||||||
\(459\) | 71653.1 | + | 1166.99i | 0.340102 | + | 0.00553915i | ||||
\(460\) | 16057.1 | 0.0758842 | ||||||||
\(461\) | − | 272235.i | − | 1.28098i | −0.767966 | − | 0.640490i | \(-0.778731\pi\) | ||
0.767966 | − | 0.640490i | \(-0.221269\pi\) | |||||||
\(462\) | 438601. | − | 250062.i | 2.05487 | − | 1.17156i | ||||
\(463\) | 249599. | 1.16434 | 0.582171 | − | 0.813066i | \(-0.302203\pi\) | ||||
0.582171 | + | 0.813066i | \(0.302203\pi\) | |||||||
\(464\) | − | 98489.1i | − | 0.457459i | ||||||
\(465\) | 324178. | + | 568599.i | 1.49926 | + | 2.62966i | ||||
\(466\) | −66906.6 | −0.308104 | ||||||||
\(467\) | − | 159468.i | − | 0.731207i | −0.930771 | − | 0.365604i | \(-0.880863\pi\) | ||
0.930771 | − | 0.365604i | \(-0.119137\pi\) | |||||||
\(468\) | 146060. | − | 246757.i | 0.666868 | − | 1.12662i | ||||
\(469\) | −371629. | −1.68952 | ||||||||
\(470\) | − | 570804.i | − | 2.58399i | ||||||
\(471\) | −341932. | + | 194947.i | −1.54134 | + | 0.878771i | ||||
\(472\) | −6685.65 | −0.0300095 | ||||||||
\(473\) | 406081.i | 1.81506i | ||||||||
\(474\) | 100922. | + | 177015.i | 0.449191 | + | 0.787868i | ||||
\(475\) | 505958. | 2.24247 | ||||||||
\(476\) | 83513.7i | 0.368590i | ||||||||
\(477\) | −122733. | − | 72648.0i | −0.539418 | − | 0.319291i | ||||
\(478\) | −64270.5 | −0.281291 | ||||||||
\(479\) | 285627.i | 1.24488i | 0.782666 | + | 0.622441i | \(0.213859\pi\) | ||||
−0.782666 | + | 0.622441i | \(0.786141\pi\) | |||||||
\(480\) | −440618. | + | 251212.i | −1.91240 | + | 1.09033i | ||||
\(481\) | 87681.9 | 0.378983 | ||||||||
\(482\) | 243796.i | 1.04938i | ||||||||
\(483\) | −8236.50 | − | 14446.6i | −0.0353060 | − | 0.0619257i | ||||
\(484\) | 153979. | 0.657309 | ||||||||
\(485\) | − | 324581.i | − | 1.37987i | ||||||
\(486\) | −167192. | + | 272244.i | −0.707852 | + | 1.15262i | ||||
\(487\) | −325973. | −1.37443 | −0.687216 | − | 0.726453i | \(-0.741167\pi\) | ||||
−0.687216 | + | 0.726453i | \(0.741167\pi\) | |||||||
\(488\) | − | 19182.0i | − | 0.0805480i | ||||||
\(489\) | −230948. | + | 131671.i | −0.965820 | + | 0.550648i | ||||
\(490\) | 384433. | 1.60114 | ||||||||
\(491\) | − | 278762.i | − | 1.15630i | −0.815931 | − | 0.578149i | \(-0.803775\pi\) | ||
0.815931 | − | 0.578149i | \(-0.196225\pi\) | |||||||
\(492\) | 35900.1 | + | 62967.6i | 0.148308 | + | 0.260128i | ||||
\(493\) | −33134.8 | −0.136330 | ||||||||
\(494\) | − | 645547.i | − | 2.64529i | ||||||
\(495\) | 280075. | − | 473166.i | 1.14305 | − | 1.93109i | ||||
\(496\) | −507095. | −2.06123 | ||||||||
\(497\) | − | 450591.i | − | 1.82419i | ||||||
\(498\) | 254339. | − | 145008.i | 1.02555 | − | 0.584699i | ||||
\(499\) | −204145. | −0.819857 | −0.409928 | − | 0.912118i | \(-0.634446\pi\) | ||||
−0.409928 | + | 0.912118i | \(0.634446\pi\) | |||||||
\(500\) | 281430.i | 1.12572i | ||||||||
\(501\) | −108917. | − | 191037.i | −0.433929 | − | 0.761099i | ||||
\(502\) | −57377.7 | −0.227686 | ||||||||
\(503\) | − | 27595.1i | − | 0.109068i | −0.998512 | − | 0.0545339i | \(-0.982633\pi\) | ||
0.998512 | − | 0.0545339i | \(-0.0173673\pi\) | |||||||
\(504\) | 65816.8 | + | 38958.1i | 0.259105 | + | 0.153369i | ||||
\(505\) | −60952.5 | −0.239006 | ||||||||
\(506\) | − | 25302.2i | − | 0.0988228i | ||||||
\(507\) | 332838. | − | 189762.i | 1.29484 | − | 0.738234i | ||||
\(508\) | −229259. | −0.888382 | ||||||||
\(509\) | 84040.5i | 0.324379i | 0.986760 | + | 0.162190i | \(0.0518556\pi\) | ||||
−0.986760 | + | 0.162190i | \(0.948144\pi\) | |||||||
\(510\) | 99349.1 | + | 174255.i | 0.381965 | + | 0.669955i | ||||
\(511\) | −238936. | −0.915041 | ||||||||
\(512\) | − | 323988.i | − | 1.23592i | ||||||
\(513\) | −5310.86 | + | 326085.i | −0.0201804 | + | 1.23907i | ||||
\(514\) | −62969.6 | −0.238344 | ||||||||
\(515\) | 476773.i | 1.79762i | ||||||||
\(516\) | 260150. | − | 148321.i | 0.977067 | − | 0.557060i | ||||
\(517\) | −407837. | −1.52583 | ||||||||
\(518\) | − | 113849.i | − | 0.424296i | ||||||
\(519\) | −81127.6 | − | 142295.i | −0.301185 | − | 0.528270i | ||||
\(520\) | −164875. | −0.609745 | ||||||||
\(521\) | − | 107436.i | − | 0.395800i | −0.980222 | − | 0.197900i | \(-0.936588\pi\) | ||
0.980222 | − | 0.197900i | \(-0.0634121\pi\) | |||||||
\(522\) | 75244.9 | − | 127120.i | 0.276144 | − | 0.466524i | ||||
\(523\) | −102442. | −0.374521 | −0.187261 | − | 0.982310i | \(-0.559961\pi\) | ||||
−0.187261 | + | 0.982310i | \(0.559961\pi\) | |||||||
\(524\) | 118556.i | 0.431778i | ||||||||
\(525\) | 565967. | − | 322678.i | 2.05340 | − | 1.17071i | ||||
\(526\) | −19450.5 | −0.0703007 | ||||||||
\(527\) | 170603.i | 0.614278i | ||||||||
\(528\) | 210992. | + | 370074.i | 0.756830 | + | 1.32746i | ||||
\(529\) | 279008. | 0.997022 | ||||||||
\(530\) | − | 399207.i | − | 1.42117i | ||||||
\(531\) | −31589.1 | − | 18698.2i | −0.112034 | − | 0.0663147i | ||||
\(532\) | −380061. | −1.34286 | ||||||||
\(533\) | 161823.i | 0.569622i | ||||||||
\(534\) | −564223. | + | 321683.i | −1.97865 | + | 1.12810i | ||||
\(535\) | 261786. | 0.914615 | ||||||||
\(536\) | − | 85657.1i | − | 0.298149i | ||||||
\(537\) | 160947. | + | 282296.i | 0.558129 | + | 0.978942i | ||||
\(538\) | −177480. | −0.613177 | ||||||||
\(539\) | − | 274676.i | − | 0.945460i | ||||||
\(540\) | −405424. | − | 6603.04i | −1.39034 | − | 0.0226442i | ||||
\(541\) | −40329.8 | −0.137794 | −0.0688972 | − | 0.997624i | \(-0.521948\pi\) | ||||
−0.0688972 | + | 0.997624i | \(0.521948\pi\) | |||||||
\(542\) | − | 156874.i | − | 0.534012i | ||||||
\(543\) | 36040.4 | − | 20547.9i | 0.122233 | − | 0.0696896i | ||||
\(544\) | −132203. | −0.446729 | ||||||||
\(545\) | − | 350151.i | − | 1.17886i | ||||||
\(546\) | −411701. | − | 722112.i | −1.38101 | − | 2.42225i | ||||
\(547\) | 123440. | 0.412556 | 0.206278 | − | 0.978493i | \(-0.433865\pi\) | ||||
0.206278 | + | 0.978493i | \(0.433865\pi\) | |||||||
\(548\) | 369616.i | 1.23081i | ||||||||
\(549\) | 53647.5 | − | 90633.4i | 0.177994 | − | 0.300707i | ||||
\(550\) | 991253. | 3.27687 | ||||||||
\(551\) | − | 150793.i | − | 0.496681i | ||||||
\(552\) | 3329.80 | − | 1898.44i | 0.0109280 | − | 0.00623042i | ||||
\(553\) | 267831. | 0.875810 | ||||||||
\(554\) | 481305.i | 1.56820i | ||||||||
\(555\) | −61410.5 | − | 107712.i | −0.199368 | − | 0.349686i | ||||
\(556\) | 186984. | 0.604859 | ||||||||
\(557\) | 309624.i | 0.997987i | 0.866606 | + | 0.498993i | \(0.166297\pi\) | ||||
−0.866606 | + | 0.498993i | \(0.833703\pi\) | |||||||
\(558\) | −654510. | − | 387416.i | −2.10207 | − | 1.24426i | ||||
\(559\) | 668571. | 2.13956 | ||||||||
\(560\) | 783681.i | 2.49898i | ||||||||
\(561\) | 124505. | − | 70984.5i | 0.395603 | − | 0.225547i | ||||
\(562\) | 337102. | 1.06730 | ||||||||
\(563\) | − | 501724.i | − | 1.58288i | −0.611247 | − | 0.791440i | \(-0.709332\pi\) | ||
0.611247 | − | 0.791440i | \(-0.290668\pi\) | |||||||
\(564\) | 148962. | + | 261275.i | 0.468293 | + | 0.821372i | ||||
\(565\) | −122922. | −0.385063 | ||||||||
\(566\) | 556030.i | 1.73566i | ||||||||
\(567\) | 202022. | + | 368148.i | 0.628395 | + | 1.14513i | ||||
\(568\) | 103857. | 0.321913 | ||||||||
\(569\) | − | 187984.i | − | 0.580627i | −0.956932 | − | 0.290313i | \(-0.906240\pi\) | ||
0.956932 | − | 0.290313i | \(-0.0937595\pi\) | |||||||
\(570\) | −793016. | + | 452126.i | −2.44080 | + | 1.39159i | ||||
\(571\) | 404837. | 1.24167 | 0.620837 | − | 0.783939i | \(-0.286793\pi\) | ||||
0.620837 | + | 0.783939i | \(0.286793\pi\) | |||||||
\(572\) | − | 573464.i | − | 1.75273i | ||||||
\(573\) | −320851. | − | 562764.i | −0.977225 | − | 1.71402i | ||||
\(574\) | 210116. | 0.637728 | ||||||||
\(575\) | − | 32649.8i | − | 0.0987518i | ||||||
\(576\) | 107326. | − | 181320.i | 0.323491 | − | 0.546513i | ||||
\(577\) | 285933. | 0.858841 | 0.429421 | − | 0.903105i | \(-0.358718\pi\) | ||||
0.429421 | + | 0.903105i | \(0.358718\pi\) | |||||||
\(578\) | − | 399605.i | − | 1.19612i | ||||||
\(579\) | −510492. | + | 291050.i | −1.52276 | + | 0.868180i | ||||
\(580\) | 187482. | 0.557319 | ||||||||
\(581\) | − | 384826.i | − | 1.14002i | ||||||
\(582\) | 186811. | + | 327661.i | 0.551515 | + | 0.967341i | ||||
\(583\) | −285232. | −0.839191 | ||||||||
\(584\) | − | 55072.6i | − | 0.161477i | ||||||
\(585\) | −779020. | − | 461116.i | −2.27634 | − | 1.34741i | ||||
\(586\) | −675722. | −1.96776 | ||||||||
\(587\) | − | 186645.i | − | 0.541676i | −0.962625 | − | 0.270838i | \(-0.912699\pi\) | ||
0.962625 | − | 0.270838i | \(-0.0873008\pi\) | |||||||
\(588\) | −175967. | + | 100325.i | −0.508952 | + | 0.290172i | ||||
\(589\) | −776394. | −2.23796 | ||||||||
\(590\) | − | 102748.i | − | 0.295168i | ||||||
\(591\) | 90692.9 | + | 159073.i | 0.259656 | + | 0.455429i | ||||
\(592\) | 96061.1 | 0.274097 | ||||||||
\(593\) | 160449.i | 0.456276i | 0.973629 | + | 0.228138i | \(0.0732637\pi\) | ||||
−0.973629 | + | 0.228138i | \(0.926736\pi\) | |||||||
\(594\) | −10404.8 | + | 638853.i | −0.0294891 | + | 1.81062i | ||||
\(595\) | 263655. | 0.744736 | ||||||||
\(596\) | − | 287171.i | − | 0.808440i | ||||||
\(597\) | 317429. | − | 180978.i | 0.890632 | − | 0.507781i | ||||
\(598\) | −41657.6 | −0.116491 | ||||||||
\(599\) | 258334.i | 0.719993i | 0.932954 | + | 0.359996i | \(0.117222\pi\) | ||||
−0.932954 | + | 0.359996i | \(0.882778\pi\) | |||||||
\(600\) | 74374.2 | + | 130450.i | 0.206595 | + | 0.362361i | ||||
\(601\) | 173281. | 0.479734 | 0.239867 | − | 0.970806i | \(-0.422896\pi\) | ||||
0.239867 | + | 0.970806i | \(0.422896\pi\) | |||||||
\(602\) | − | 868092.i | − | 2.39537i | ||||||
\(603\) | 239562. | − | 404722.i | 0.658846 | − | 1.11307i | ||||
\(604\) | 142239. | 0.389892 | ||||||||
\(605\) | − | 486115.i | − | 1.32809i | ||||||
\(606\) | 61531.1 | − | 35081.0i | 0.167552 | − | 0.0955271i | ||||
\(607\) | −592777. | −1.60884 | −0.804422 | − | 0.594058i | \(-0.797525\pi\) | ||||
−0.804422 | + | 0.594058i | \(0.797525\pi\) | |||||||
\(608\) | − | 601642.i | − | 1.62754i | ||||||
\(609\) | −96169.1 | − | 168678.i | −0.259299 | − | 0.454803i | ||||
\(610\) | 294798. | 0.792255 | ||||||||
\(611\) | 671463.i | 1.79862i | ||||||||
\(612\) | −90950.4 | − | 53835.2i | −0.242830 | − | 0.143735i | ||||
\(613\) | 144770. | 0.385264 | 0.192632 | − | 0.981271i | \(-0.438298\pi\) | ||||
0.192632 | + | 0.981271i | \(0.438298\pi\) | |||||||
\(614\) | − | 444864.i | − | 1.18002i | ||||||
\(615\) | 198791. | − | 113338.i | 0.525589 | − | 0.299656i | ||||
\(616\) | 152958. | 0.403098 | ||||||||
\(617\) | − | 57533.0i | − | 0.151129i | −0.997141 | − | 0.0755643i | \(-0.975924\pi\) | ||
0.997141 | − | 0.0755643i | \(-0.0240758\pi\) | |||||||
\(618\) | −274405. | − | 481299.i | −0.718481 | − | 1.26020i | ||||
\(619\) | 349680. | 0.912618 | 0.456309 | − | 0.889821i | \(-0.349171\pi\) | ||||
0.456309 | + | 0.889821i | \(0.349171\pi\) | |||||||
\(620\) | − | 965297.i | − | 2.51118i | ||||||
\(621\) | 21042.5 | + | 342.713i | 0.0545650 | + | 0.000888685i | ||||
\(622\) | −829182. | −2.14323 | ||||||||
\(623\) | 853691.i | 2.19950i | ||||||||
\(624\) | 609290. | − | 347378.i | 1.56479 | − | 0.892139i | ||||
\(625\) | 181622. | 0.464952 | ||||||||
\(626\) | 791185.i | 2.01897i | ||||||||
\(627\) | 323042. | + | 566607.i | 0.821721 | + | 1.44127i | ||||
\(628\) | 580490. | 1.47189 | ||||||||
\(629\) | − | 32318.0i | − | 0.0816852i | ||||||
\(630\) | −598726. | + | 1.01150e6i | −1.50851 | + | 2.54851i | ||||
\(631\) | 152337. | 0.382601 | 0.191300 | − | 0.981532i | \(-0.438730\pi\) | ||||
0.191300 | + | 0.981532i | \(0.438730\pi\) | |||||||
\(632\) | 61732.5i | 0.154554i | ||||||||
\(633\) | 586422. | − | 334340.i | 1.46354 | − | 0.834412i | ||||
\(634\) | 257117. | 0.639664 | ||||||||
\(635\) | 723779.i | 1.79497i | ||||||||
\(636\) | 104181. | + | 182730.i | 0.257557 | + | 0.451747i | ||||
\(637\) | −452226. | −1.11449 | ||||||||
\(638\) | − | 295428.i | − | 0.725788i | ||||||
\(639\) | 490715. | + | 290463.i | 1.20179 | + | 0.711360i | ||||
\(640\) | −311919. | −0.761521 | ||||||||
\(641\) | − | 367955.i | − | 0.895526i | −0.894152 | − | 0.447763i | \(-0.852221\pi\) | ||
0.894152 | − | 0.447763i | \(-0.147779\pi\) | |||||||
\(642\) | −264270. | + | 150670.i | −0.641178 | + | 0.365558i | ||||
\(643\) | −369504. | −0.893711 | −0.446856 | − | 0.894606i | \(-0.647456\pi\) | ||||
−0.446856 | + | 0.894606i | \(0.647456\pi\) | |||||||
\(644\) | 24525.6i | 0.0591355i | ||||||||
\(645\) | −468252. | − | 821301.i | −1.12554 | − | 1.97416i | ||||
\(646\) | −237937. | −0.570160 | ||||||||
\(647\) | − | 358923.i | − | 0.857419i | −0.903442 | − | 0.428709i | \(-0.858968\pi\) | ||
0.903442 | − | 0.428709i | \(-0.141032\pi\) | |||||||
\(648\) | −84854.5 | + | 46564.2i | −0.202081 | + | 0.110892i | ||||
\(649\) | −73413.0 | −0.174294 | ||||||||
\(650\) | − | 1.63200e6i | − | 3.86272i | ||||||
\(651\) | −868479. | + | 495150.i | −2.04926 | + | 1.16835i | ||||
\(652\) | 392075. | 0.922303 | ||||||||
\(653\) | − | 415428.i | − | 0.974247i | −0.873333 | − | 0.487123i | \(-0.838046\pi\) | ||
0.873333 | − | 0.487123i | \(-0.161954\pi\) | |||||||
\(654\) | 201528. | + | 353474.i | 0.471173 | + | 0.826423i | ||||
\(655\) | 374285. | 0.872408 | ||||||||
\(656\) | 177288.i | 0.411976i | ||||||||
\(657\) | 154025. | − | 260213.i | 0.356829 | − | 0.602835i | ||||
\(658\) | 871846. | 2.01367 | ||||||||
\(659\) | − | 689382.i | − | 1.58741i | −0.608303 | − | 0.793705i | \(-0.708149\pi\) | ||
0.608303 | − | 0.793705i | \(-0.291851\pi\) | |||||||
\(660\) | −704467. | + | 401641.i | −1.61723 | + | 0.922042i | ||||
\(661\) | 213731. | 0.489175 | 0.244587 | − | 0.969627i | \(-0.421347\pi\) | ||||
0.244587 | + | 0.969627i | \(0.421347\pi\) | |||||||
\(662\) | − | 126953.i | − | 0.289685i | ||||||
\(663\) | −116869. | − | 204984.i | −0.265871 | − | 0.466331i | ||||
\(664\) | 88698.7 | 0.201178 | ||||||||
\(665\) | 1.19987e6i | 2.71325i | ||||||||
\(666\) | 123987. | + | 73389.9i | 0.279529 | + | 0.165458i | ||||
\(667\) | −9730.77 | −0.0218723 | ||||||||
\(668\) | 324318.i | 0.726806i | ||||||||
\(669\) | −298767. | + | 170338.i | −0.667545 | + | 0.380591i | ||||
\(670\) | 1.31642e6 | 2.93254 | ||||||||
\(671\) | − | 210632.i | − | 0.467820i | ||||||
\(672\) | −383701. | − | 673000.i | −0.849677 | − | 1.49031i | ||||
\(673\) | −807880. | −1.78368 | −0.891840 | − | 0.452352i | \(-0.850585\pi\) | ||||
−0.891840 | + | 0.452352i | \(0.850585\pi\) | |||||||
\(674\) | 533773.i | 1.17500i | ||||||||
\(675\) | −13426.3 | + | 824372.i | −0.0294679 | + | 1.80932i | ||||
\(676\) | −565051. | −1.23650 | ||||||||
\(677\) | 189407.i | 0.413256i | 0.978420 | + | 0.206628i | \(0.0662490\pi\) | ||||
−0.978420 | + | 0.206628i | \(0.933751\pi\) | |||||||
\(678\) | 124089. | − | 70747.2i | 0.269943 | − | 0.153904i | ||||
\(679\) | 495765. | 1.07532 | ||||||||
\(680\) | 60770.0i | 0.131423i | ||||||||
\(681\) | 256923. | + | 450636.i | 0.553999 | + | 0.971698i | ||||
\(682\) | −1.52108e6 | −3.27027 | ||||||||
\(683\) | 547508.i | 1.17368i | 0.809704 | + | 0.586839i | \(0.199628\pi\) | ||||
−0.809704 | + | 0.586839i | \(0.800372\pi\) | |||||||
\(684\) | 244998. | − | 413905.i | 0.523661 | − | 0.884685i | ||||
\(685\) | 1.16689e6 | 2.48685 | ||||||||
\(686\) | − | 244275.i | − | 0.519076i | ||||||
\(687\) | 148029. | − | 84396.5i | 0.313641 | − | 0.178818i | ||||
\(688\) | 732462. | 1.54742 | ||||||||
\(689\) | 469606.i | 0.989225i | ||||||||
\(690\) | 29176.0 | + | 51173.9i | 0.0612813 | + | 0.107486i | ||||
\(691\) | 442497. | 0.926733 | 0.463366 | − | 0.886167i | \(-0.346641\pi\) | ||||
0.463366 | + | 0.886167i | \(0.346641\pi\) | |||||||
\(692\) | 241572.i | 0.504468i | ||||||||
\(693\) | 722714. | + | 427787.i | 1.50487 | + | 0.890761i | ||||
\(694\) | −898527. | −1.86557 | ||||||||
\(695\) | − | 590313.i | − | 1.22212i | ||||||
\(696\) | 38878.6 | − | 22166.1i | 0.0802588 | − | 0.0457583i | ||||
\(697\) | 59645.3 | 0.122775 | ||||||||
\(698\) | 26017.2i | 0.0534011i | ||||||||
\(699\) | −55123.4 | − | 96684.9i | −0.112819 | − | 0.197881i | ||||
\(700\) | −960829. | −1.96088 | ||||||||
\(701\) | 468708.i | 0.953820i | 0.878952 | + | 0.476910i | \(0.158243\pi\) | ||||
−0.878952 | + | 0.476910i | \(0.841757\pi\) | |||||||
\(702\) | 1.05181e6 | + | 17130.5i | 2.13433 | + | 0.0347613i | ||||
\(703\) | 147076. | 0.297598 | ||||||||
\(704\) | − | 421387.i | − | 0.850229i | ||||||
\(705\) | 824853. | − | 470278.i | 1.65958 | − | 0.946185i | ||||
\(706\) | 407448. | 0.817453 | ||||||||
\(707\) | − | 93098.9i | − | 0.186254i | ||||||
\(708\) | 26814.0 | + | 47031.0i | 0.0534928 | + | 0.0938248i | ||||
\(709\) | 532060. | 1.05844 | 0.529222 | − | 0.848483i | \(-0.322484\pi\) | ||||
0.529222 | + | 0.848483i | \(0.322484\pi\) | |||||||
\(710\) | 1.59612e6i | 3.16628i | ||||||||
\(711\) | −172651. | + | 291680.i | −0.341531 | + | 0.576990i | ||||
\(712\) | −196768. | −0.388145 | ||||||||
\(713\) | 50101.2i | 0.0985529i | ||||||||
\(714\) | −266158. | + | 151746.i | −0.522087 | + | 0.297660i | ||||
\(715\) | −1.81044e6 | −3.54138 | ||||||||
\(716\) | − | 479248.i | − | 0.934834i | ||||||
\(717\) | −52951.6 | − | 92875.5i | −0.103001 | − | 0.180660i | ||||
\(718\) | 1.07627e6 | 2.08771 | ||||||||
\(719\) | 408677.i | 0.790537i | 0.918566 | + | 0.395268i | \(0.129348\pi\) | ||||
−0.918566 | + | 0.395268i | \(0.870652\pi\) | |||||||
\(720\) | −853466. | − | 505182.i | −1.64635 | − | 0.974502i | ||||
\(721\) | −728224. | −1.40086 | ||||||||
\(722\) | − | 377725.i | − | 0.724604i | ||||||
\(723\) | −352302. | + | 200860.i | −0.673968 | + | 0.384252i | ||||
\(724\) | −61184.9 | −0.116726 | ||||||||
\(725\) | − | 381218.i | − | 0.725266i | ||||||
\(726\) | 279782. | + | 490729.i | 0.530819 | + | 0.931041i | ||||
\(727\) | −235444. | −0.445471 | −0.222735 | − | 0.974879i | \(-0.571499\pi\) | ||||
−0.222735 | + | 0.974879i | \(0.571499\pi\) | |||||||
\(728\) | − | 251830.i | − | 0.475166i | ||||||
\(729\) | −531159. | − | 17306.3i | −0.999470 | − | 0.0325648i | ||||
\(730\) | 846380. | 1.58825 | ||||||||
\(731\) | − | 246423.i | − | 0.461155i | ||||||
\(732\) | −134938. | + | 76933.0i | −0.251833 | + | 0.143579i | ||||
\(733\) | 342720. | 0.637869 | 0.318934 | − | 0.947777i | \(-0.396675\pi\) | ||||
0.318934 | + | 0.947777i | \(0.396675\pi\) | |||||||
\(734\) | 824520.i | 1.53041i | ||||||||
\(735\) | 316729. | + | 555534.i | 0.586291 | + | 1.02834i | ||||
\(736\) | −38824.3 | −0.0716718 | ||||||||
\(737\) | − | 940574.i | − | 1.73164i | ||||||
\(738\) | −135447. | + | 228827.i | −0.248688 | + | 0.420140i | ||||
\(739\) | 234714. | 0.429784 | 0.214892 | − | 0.976638i | \(-0.431060\pi\) | ||||
0.214892 | + | 0.976638i | \(0.431060\pi\) | |||||||
\(740\) | 182860.i | 0.333931i | ||||||||
\(741\) | 932861. | − | 531857.i | 1.69895 | − | 0.968631i | ||||
\(742\) | 609750. | 1.10750 | ||||||||
\(743\) | 367771.i | 0.666193i | 0.942893 | + | 0.333096i | \(0.108093\pi\) | ||||
−0.942893 | + | 0.333096i | \(0.891907\pi\) | |||||||
\(744\) | −114127. | − | 200176.i | −0.206179 | − | 0.361632i | ||||
\(745\) | −906607. | −1.63345 | ||||||||
\(746\) | 632866.i | 1.13719i | ||||||||
\(747\) | 419094. | + | 248069.i | 0.751052 | + | 0.444561i | ||||
\(748\) | −211369. | −0.377779 | ||||||||
\(749\) | 399851.i | 0.712746i | ||||||||
\(750\) | −896915. | + | 511363.i | −1.59452 | + | 0.909089i | ||||
\(751\) | 769434. | 1.36424 | 0.682122 | − | 0.731239i | \(-0.261057\pi\) | ||||
0.682122 | + | 0.731239i | \(0.261057\pi\) | |||||||
\(752\) | 735630.i | 1.30084i | ||||||||
\(753\) | −47272.7 | − | 82914.9i | −0.0833720 | − | 0.146232i | ||||
\(754\) | −486392. | −0.855547 | ||||||||
\(755\) | − | 449052.i | − | 0.787777i | ||||||
\(756\) | 10085.5 | − | 619245.i | 0.0176463 | − | 1.08348i | ||||
\(757\) | −311650. | −0.543845 | −0.271923 | − | 0.962319i | \(-0.587659\pi\) | ||||
−0.271923 | + | 0.962319i | \(0.587659\pi\) | |||||||
\(758\) | 1.00175e6i | 1.74349i | ||||||||
\(759\) | 36563.5 | − | 20846.1i | 0.0634694 | − | 0.0361861i | ||||
\(760\) | −276558. | −0.478805 | ||||||||
\(761\) | − | 825994.i | − | 1.42629i | −0.701017 | − | 0.713144i | \(-0.747270\pi\) | ||
0.701017 | − | 0.713144i | \(-0.252730\pi\) | |||||||
\(762\) | −416568. | − | 730648.i | −0.717424 | − | 1.25834i | ||||
\(763\) | 534821. | 0.918669 | ||||||||
\(764\) | 955391.i | 1.63679i | ||||||||
\(765\) | −169959. | + | 287133.i | −0.290417 | + | 0.490637i | ||||
\(766\) | 1.18573e6 | 2.02082 | ||||||||
\(767\) | 120867.i | 0.205455i | ||||||||
\(768\) | 640290. | − | 365052.i | 1.08556 | − | 0.618917i | ||||
\(769\) | −441175. | −0.746033 | −0.373016 | − | 0.927825i | \(-0.621676\pi\) | ||||
−0.373016 | + | 0.927825i | \(0.621676\pi\) | |||||||
\(770\) | 2.35073e6i | 3.96480i | ||||||||
\(771\) | −51879.8 | − | 90995.6i | −0.0872749 | − | 0.153078i | ||||
\(772\) | 866651. | 1.45415 | ||||||||
\(773\) | 550891.i | 0.921949i | 0.887413 | + | 0.460975i | \(0.152500\pi\) | ||||
−0.887413 | + | 0.460975i | \(0.847500\pi\) | |||||||
\(774\) | 945393. | + | 559595.i | 1.57809 | + | 0.934097i | ||||
\(775\) | −1.96279e6 | −3.26792 | ||||||||
\(776\) | 114269.i | 0.189760i | ||||||||
\(777\) | 164520. | − | 93798.4i | 0.272506 | − | 0.155365i | ||||
\(778\) | −961180. | −1.58798 | ||||||||
\(779\) | 271439.i | 0.447298i | ||||||||
\(780\) | 661262. | + | 1.15983e6i | 1.08689 | + | 1.90637i | ||||
\(781\) | 1.14042e6 | 1.86966 | ||||||||
\(782\) | 15354.2i | 0.0251081i | ||||||||
\(783\) | 245691. | + | 4001.51i | 0.400743 | + | 0.00652680i | ||||
\(784\) | −495443. | −0.806049 | ||||||||
\(785\) | − | 1.83262e6i | − | 2.97395i | ||||||
\(786\) | −377837. | + | 215418.i | −0.611589 | + | 0.348688i | ||||
\(787\) | −1.11051e6 | −1.79297 | −0.896484 | − | 0.443076i | \(-0.853887\pi\) | ||||
−0.896484 | + | 0.443076i | \(0.853887\pi\) | |||||||
\(788\) | − | 270054.i | − | 0.434909i | ||||||
\(789\) | −16025.0 | − | 28107.4i | −0.0257421 | − | 0.0451509i | ||||
\(790\) | −948732. | −1.52016 | ||||||||
\(791\) | − | 187751.i | − | 0.300075i | ||||||
\(792\) | −98600.9 | + | 166579.i | −0.157192 | + | 0.265564i | ||||
\(793\) | −346784. | −0.551459 | ||||||||
\(794\) | − | 1.09805e6i | − | 1.74173i | ||||||
\(795\) | 576884. | − | 328901.i | 0.912754 | − | 0.520393i | ||||
\(796\) | −538892. | −0.850503 | ||||||||
\(797\) | − | 349352.i | − | 0.549980i | −0.961447 | − | 0.274990i | \(-0.911325\pi\) | ||
0.961447 | − | 0.274990i | \(-0.0886745\pi\) | |||||||
\(798\) | −690578. | − | 1.21125e6i | −1.08444 | − | 1.90208i | ||||
\(799\) | 247489. | 0.387671 | ||||||||
\(800\) | − | 1.52100e6i | − | 2.37657i | ||||||
\(801\) | −929711. | − | 550312.i | −1.44905 | − | 0.857718i | ||||
\(802\) | −384555. | −0.597875 | ||||||||
\(803\) | − | 604735.i | − | 0.937851i | ||||||
\(804\) | −602566. | + | 343544.i | −0.932164 | + | 0.531459i | ||||
\(805\) | 77428.1 | 0.119483 | ||||||||
\(806\) | 2.50431e6i | 3.85494i | ||||||||
\(807\) | −146224. | − | 256472.i | −0.224528 | − | 0.393815i | ||||
\(808\) | 21458.4 | 0.0328681 | ||||||||
\(809\) | 396648.i | 0.606049i | 0.952983 | + | 0.303024i | \(0.0979964\pi\) | ||||
−0.952983 | + | 0.303024i | \(0.902004\pi\) | |||||||
\(810\) | −715619. | − | 1.30408e6i | −1.09072 | − | 1.98763i | ||||
\(811\) | −907516. | −1.37979 | −0.689894 | − | 0.723910i | \(-0.742343\pi\) | ||||
−0.689894 | + | 0.723910i | \(0.742343\pi\) | |||||||
\(812\) | 286360.i | 0.434311i | ||||||||
\(813\) | 226694. | − | 129246.i | 0.342972 | − | 0.195540i | ||||
\(814\) | 288145. | 0.434873 | ||||||||
\(815\) | − | 1.23779e6i | − | 1.86351i | ||||||
\(816\) | −128037. | − | 224574.i | −0.192290 | − | 0.337270i | ||||
\(817\) | 1.12145e6 | 1.68010 | ||||||||
\(818\) | − | 1.28304e6i | − | 1.91750i | ||||||
\(819\) | 704309. | − | 1.18988e6i | 1.05001 | − | 1.77392i | ||||
\(820\) | −337482. | −0.501907 | ||||||||
\(821\) | 640918.i | 0.950859i | 0.879754 | + | 0.475429i | \(0.157707\pi\) | ||||
−0.879754 | + | 0.475429i | \(0.842293\pi\) | |||||||
\(822\) | −1.17797e6 | + | 671599.i | −1.74337 | + | 0.993955i | ||||
\(823\) | −154146. | −0.227579 | −0.113789 | − | 0.993505i | \(-0.536299\pi\) | ||||
−0.113789 | + | 0.993505i | \(0.536299\pi\) | |||||||
\(824\) | − | 167849.i | − | 0.247209i | ||||||
\(825\) | 816680. | + | 1.43243e6i | 1.19990 | + | 2.10458i | ||||
\(826\) | 156937. | 0.230020 | ||||||||
\(827\) | − | 250368.i | − | 0.366073i | −0.983106 | − | 0.183036i | \(-0.941407\pi\) | ||
0.983106 | − | 0.183036i | \(-0.0585926\pi\) | |||||||
\(828\) | −26709.6 | − | 15809.9i | −0.0389589 | − | 0.0230604i | ||||
\(829\) | −262281. | −0.381644 | −0.190822 | − | 0.981625i | \(-0.561115\pi\) | ||||
−0.190822 | + | 0.981625i | \(0.561115\pi\) | |||||||
\(830\) | 1.36316e6i | 1.97875i | ||||||||
\(831\) | −695520. | + | 396540.i | −1.00718 | + | 0.574229i | ||||
\(832\) | −693772. | −1.00224 | ||||||||
\(833\) | 166683.i | 0.240215i | ||||||||
\(834\) | 339753. | + | 595916.i | 0.488462 | + | 0.856748i | ||||
\(835\) | 1.02388e6 | 1.46851 | ||||||||
\(836\) | − | 961915.i | − | 1.37633i | ||||||
\(837\) | 20602.7 | − | 1.26500e6i | 0.0294086 | − | 1.80568i | ||||
\(838\) | 805442. | 1.14695 | ||||||||
\(839\) | − | 1.23368e6i | − | 1.75258i | −0.481781 | − | 0.876291i | \(-0.660010\pi\) | ||
0.481781 | − | 0.876291i | \(-0.339990\pi\) | |||||||
\(840\) | −309359. | + | 176376.i | −0.438434 | + | 0.249966i | ||||
\(841\) | 593665. | 0.839362 | ||||||||
\(842\) | 1.10964e6i | 1.56516i | ||||||||
\(843\) | 277733. | + | 487136.i | 0.390816 | + | 0.685481i | ||||
\(844\) | −995555. | −1.39759 | ||||||||
\(845\) | 1.78388e6i | 2.49835i | ||||||||
\(846\) | −562016. | + | 949482.i | −0.785250 | + | 1.32662i | ||||
\(847\) | 742493. | 1.03496 | ||||||||
\(848\) | 514483.i | 0.715450i | ||||||||
\(849\) | −803503. | + | 458105.i | −1.11474 | + | 0.635550i | ||||
\(850\) | −601526. | −0.832562 | ||||||||
\(851\) | − | 9490.89i | − | 0.0131053i | ||||||
\(852\) | −416538. | − | 730595.i | −0.573819 | − | 1.00646i | ||||
\(853\) | −499522. | −0.686526 | −0.343263 | − | 0.939239i | \(-0.611532\pi\) | ||||
−0.343263 | + | 0.939239i | \(0.611532\pi\) | |||||||
\(854\) | 450274.i | 0.617393i | ||||||||
\(855\) | −1.30671e6 | − | 773465.i | −1.78750 | − | 1.05806i | ||||
\(856\) | −92162.0 | −0.125778 | ||||||||
\(857\) | − | 1.05701e6i | − | 1.43919i | −0.694394 | − | 0.719595i | \(-0.744328\pi\) | ||
0.694394 | − | 0.719595i | \(-0.255672\pi\) | |||||||
\(858\) | 1.82763e6 | − | 1.04199e6i | 2.48264 | − | 1.41544i | ||||
\(859\) | −540656. | −0.732715 | −0.366357 | − | 0.930474i | \(-0.619395\pi\) | ||||
−0.366357 | + | 0.930474i | \(0.619395\pi\) | |||||||
\(860\) | 1.39430e6i | 1.88521i | ||||||||
\(861\) | 173112. | + | 303633.i | 0.233518 | + | 0.409584i | ||||
\(862\) | 1.13267e6 | 1.52436 | ||||||||
\(863\) | − | 529074.i | − | 0.710386i | −0.934793 | − | 0.355193i | \(-0.884415\pi\) | ||
0.934793 | − | 0.355193i | \(-0.115585\pi\) | |||||||
\(864\) | 980272. | + | 15965.4i | 1.31317 | + | 0.0213872i | ||||
\(865\) | 762649. | 1.01928 | ||||||||
\(866\) | − | 1.12297e6i | − | 1.49738i | ||||||
\(867\) | 577459. | − | 329229.i | 0.768215 | − | 0.437986i | ||||
\(868\) | 1.47440e6 | 1.95693 | ||||||||
\(869\) | 677865.i | 0.897643i | ||||||||
\(870\) | 340658. | + | 597505.i | 0.450070 | + | 0.789410i | ||||
\(871\) | −1.54856e6 | −2.04123 | ||||||||
\(872\) | 123271.i | 0.162117i | ||||||||
\(873\) | −319583. | + | 539911.i | −0.419330 | + | 0.708425i | ||||
\(874\) | −69875.4 | −0.0914748 | ||||||||
\(875\) | 1.35707e6i | 1.77250i | ||||||||
\(876\) | −387415. | + | 220879.i | −0.504857 | + | 0.287836i | ||||
\(877\) | 111.187 | 0.000144562 | 7.22809e−5 | − | 1.00000i | \(-0.499977\pi\) | ||||
7.22809e−5 | 1.00000i | \(0.499977\pi\) | ||||||||
\(878\) | − | 473503.i | − | 0.614234i | ||||||
\(879\) | −556718. | − | 976468.i | −0.720539 | − | 1.26381i | ||||
\(880\) | −1.98345e6 | −2.56128 | ||||||||
\(881\) | 681518.i | 0.878062i | 0.898472 | + | 0.439031i | \(0.144678\pi\) | ||||
−0.898472 | + | 0.439031i | \(0.855322\pi\) | |||||||
\(882\) | −639471. | − | 378514.i | −0.822022 | − | 0.486570i | ||||
\(883\) | 28080.8 | 0.0360153 | 0.0180077 | − | 0.999838i | \(-0.494268\pi\) | ||||
0.0180077 | + | 0.999838i | \(0.494268\pi\) | |||||||
\(884\) | 347997.i | 0.445319i | ||||||||
\(885\) | 148478. | − | 84652.7i | 0.189573 | − | 0.108082i | ||||
\(886\) | 1.41920e6 | 1.80790 | ||||||||
\(887\) | − | 690151.i | − | 0.877197i | −0.898683 | − | 0.438598i | \(-0.855475\pi\) | ||
0.898683 | − | 0.438598i | \(-0.144525\pi\) | |||||||
\(888\) | 21619.6 | + | 37920.2i | 0.0274172 | + | 0.0480889i | ||||
\(889\) | −1.10550e6 | −1.39880 | ||||||||
\(890\) | − | 3.02402e6i | − | 3.81772i | ||||||
\(891\) | −931762. | + | 511307.i | −1.17368 | + | 0.644060i | ||||
\(892\) | 507210. | 0.637467 | ||||||||
\(893\) | 1.12630e6i | 1.41237i | ||||||||
\(894\) | 915212. | − | 521794.i | 1.14511 | − | 0.652866i | ||||
\(895\) | −1.51300e6 | −1.88883 | ||||||||
\(896\) | − | 476426.i | − | 0.593443i | ||||||
\(897\) | −34321.1 | − | 60198.2i | −0.0426556 | − | 0.0748167i | ||||
\(898\) | 930505. | 1.15389 | ||||||||
\(899\) | 584980.i | 0.723805i | ||||||||
\(900\) | 619376. | − | 1.04639e6i | 0.764662 | − | 1.29184i | ||||
\(901\) | 173088. | 0.213215 | ||||||||
\(902\) | 531793.i | 0.653626i | ||||||||
\(903\) | 1.25446e6 | − | 715209.i | 1.53844 | − | 0.877117i | ||||
\(904\) | 43274.8 | 0.0529539 | ||||||||
\(905\) | 193163.i | 0.235845i | ||||||||
\(906\) | 258450. | + | 453315.i | 0.314863 | + | 0.552260i | ||||
\(907\) | −1.17298e6 | −1.42586 | −0.712930 | − | 0.701236i | \(-0.752632\pi\) | ||||
−0.712930 | + | 0.701236i | \(0.752632\pi\) | |||||||
\(908\) | − | 765033.i | − | 0.927916i | ||||||
\(909\) | 101389. | + | 60014.1i | 0.122705 | + | 0.0726315i | ||||
\(910\) | 3.87024e6 | 4.67364 | ||||||||
\(911\) | 1.38486e6i | 1.66866i | 0.551262 | + | 0.834332i | \(0.314146\pi\) | ||||
−0.551262 | + | 0.834332i | \(0.685854\pi\) | |||||||
\(912\) | 1.02201e6 | − | 582683.i | 1.22875 | − | 0.700556i | ||||
\(913\) | 973973. | 1.16844 | ||||||||
\(914\) | − | 17082.5i | − | 0.0204484i | ||||||
\(915\) | 242880. | + | 426004.i | 0.290101 | + | 0.508829i | ||||
\(916\) | −251305. | −0.299510 | ||||||||
\(917\) | 571683.i | 0.679855i | ||||||||
\(918\) | 6314.00 | − | 387678.i | 0.00749237 | − | 0.460029i | ||||
\(919\) | −927791. | −1.09855 | −0.549274 | − | 0.835642i | \(-0.685096\pi\) | ||||
−0.549274 | + | 0.835642i | \(0.685096\pi\) | |||||||
\(920\) | 17846.4i | 0.0210851i | ||||||||
\(921\) | 642861. | − | 366518.i | 0.757876 | − | 0.432091i | ||||
\(922\) | −1.47292e6 | −1.73268 | ||||||||
\(923\) | − | 1.87759e6i | − | 2.20393i | ||||||
\(924\) | −613467. | − | 1.07600e6i | −0.718534 | − | 1.26029i | ||||
\(925\) | 371820. | 0.434560 | ||||||||
\(926\) | − | 1.35045e6i | − | 1.57491i | ||||||
\(927\) | 469433. | − | 793071.i | 0.546278 | − | 0.922895i | ||||
\(928\) | −453312. | −0.526382 | ||||||||
\(929\) | − | 743660.i | − | 0.861674i | −0.902430 | − | 0.430837i | \(-0.858218\pi\) | ||
0.902430 | − | 0.430837i | \(-0.141782\pi\) | |||||||
\(930\) | 3.07640e6 | − | 1.75396e6i | 3.55694 | − | 2.02794i | ||||
\(931\) | −758554. | −0.875159 | ||||||||
\(932\) | 164140.i | 0.188965i | ||||||||
\(933\) | −683151. | − | 1.19823e6i | −0.784790 | − | 1.37650i | ||||
\(934\) | −862801. | −0.989046 | ||||||||
\(935\) | 667297.i | 0.763301i | ||||||||
\(936\) | 274255. | + | 162337.i | 0.313042 | + | 0.185295i | ||||
\(937\) | 477019. | 0.543321 | 0.271661 | − | 0.962393i | \(-0.412427\pi\) | ||||
0.271661 | + | 0.962393i | \(0.412427\pi\) | |||||||
\(938\) | 2.01070e6i | 2.28529i | ||||||||
\(939\) | −1.14332e6 | + | 651846.i | −1.29669 | + | 0.739288i | ||||
\(940\) | −1.40033e6 | −1.58480 | ||||||||
\(941\) | 40142.2i | 0.0453338i | 0.999743 | + | 0.0226669i | \(0.00721572\pi\) | ||||
−0.999743 | + | 0.0226669i | \(0.992784\pi\) | |||||||
\(942\) | 1.05476e6 | + | 1.85002e6i | 1.18864 | + | 2.08485i | ||||
\(943\) | 17516.1 | 0.0196977 | ||||||||
\(944\) | 132418.i | 0.148594i | ||||||||
\(945\) | −1.95498e6 | − | 31840.2i | −2.18916 | − | 0.0356543i | ||||
\(946\) | 2.19709e6 | 2.45508 | ||||||||
\(947\) | 576964.i | 0.643352i | 0.946850 | + | 0.321676i | \(0.104246\pi\) | ||||
−0.946850 | + | 0.321676i | \(0.895754\pi\) | |||||||
\(948\) | 434265. | − | 247589.i | 0.483212 | − | 0.275496i | ||||
\(949\) | −995635. | −1.10552 | ||||||||
\(950\) | − | 2.73748e6i | − | 3.03322i | ||||||
\(951\) | 211835. | + | 371552.i | 0.234227 | + | 0.410827i | ||||
\(952\) | −92820.2 | −0.102416 | ||||||||
\(953\) | − | 1.03182e6i | − | 1.13610i | −0.822994 | − | 0.568050i | \(-0.807698\pi\) | ||
0.822994 | − | 0.568050i | \(-0.192302\pi\) | |||||||
\(954\) | −393061. | + | 664046.i | −0.431880 | + | 0.729628i | ||||
\(955\) | 3.01620e6 | 3.30714 | ||||||||
\(956\) | 157673.i | 0.172520i | ||||||||
\(957\) | 426914. | − | 243399.i | 0.466141 | − | 0.265763i | ||||
\(958\) | 1.54538e6 | 1.68385 | ||||||||
\(959\) | 1.78231e6i | 1.93796i | ||||||||
\(960\) | 485902. | + | 852258.i | 0.527238 | + | 0.924759i | ||||
\(961\) | 2.08839e6 | 2.26134 | ||||||||
\(962\) | − | 474402.i | − | 0.512621i | ||||||
\(963\) | −435457. | − | 257755.i | −0.469562 | − | 0.277942i | ||||
\(964\) | 598095. | 0.643600 | ||||||||
\(965\) | − | 2.73604e6i | − | 2.93811i | ||||||
\(966\) | −78163.0 | + | 44563.5i | −0.0837620 | + | 0.0477556i | ||||
\(967\) | 1.33664e6 | 1.42942 | 0.714710 | − | 0.699421i | \(-0.246559\pi\) | ||||
0.714710 | + | 0.699421i | \(0.246559\pi\) | |||||||
\(968\) | 171138.i | 0.182639i | ||||||||
\(969\) | −196033. | − | 343836.i | −0.208776 | − | 0.366188i | ||||
\(970\) | −1.75614e6 | −1.86645 | ||||||||
\(971\) | − | 520992.i | − | 0.552576i | −0.961075 | − | 0.276288i | \(-0.910896\pi\) | ||
0.961075 | − | 0.276288i | \(-0.0891044\pi\) | |||||||
\(972\) | 667886. | + | 410166.i | 0.706920 | + | 0.434137i | ||||
\(973\) | 901644. | 0.952379 | ||||||||
\(974\) | 1.76367e6i | 1.85909i | ||||||||
\(975\) | 2.35836e6 | − | 1.34458e6i | 2.48085 | − | 1.41442i | ||||
\(976\) | −379924. | −0.398839 | ||||||||
\(977\) | 231741.i | 0.242781i | 0.992605 | + | 0.121390i | \(0.0387353\pi\) | ||||
−0.992605 | + | 0.121390i | \(0.961265\pi\) | |||||||
\(978\) | 712406. | + | 1.24954e6i | 0.744818 | + | 1.30639i | ||||
\(979\) | −2.16065e6 | −2.25433 | ||||||||
\(980\) | − | 943117.i | − | 0.982004i | ||||||
\(981\) | −344760. | + | 582445.i | −0.358244 | + | 0.605225i | ||||
\(982\) | −1.50824e6 | −1.56403 | ||||||||
\(983\) | − | 184930.i | − | 0.191382i | −0.995411 | − | 0.0956909i | \(-0.969494\pi\) | ||
0.995411 | − | 0.0956909i | \(-0.0305060\pi\) | |||||||
\(984\) | −69984.6 | + | 39900.6i | −0.0722790 | + | 0.0412088i | ||||
\(985\) | −852569. | −0.878733 | ||||||||
\(986\) | 179276.i | 0.184403i | ||||||||
\(987\) | 718302. | + | 1.25988e6i | 0.737349 | + | 1.29329i | ||||
\(988\) | −1.58370e6 | −1.62240 | ||||||||
\(989\) | − | 72367.6i | − | 0.0739864i | ||||||
\(990\) | −2.56006e6 | − | 1.51534e6i | −2.61204 | − | 1.54611i | ||||
\(991\) | 52997.5 | 0.0539645 | 0.0269822 | − | 0.999636i | \(-0.491410\pi\) | ||||
0.0269822 | + | 0.999636i | \(0.491410\pi\) | |||||||
\(992\) | 2.33398e6i | 2.37178i | ||||||||
\(993\) | 183456. | − | 104594.i | 0.186051 | − | 0.106074i | ||||
\(994\) | −2.43792e6 | −2.46744 | ||||||||
\(995\) | 1.70130e6i | 1.71844i | ||||||||
\(996\) | −355743. | − | 623962.i | −0.358606 | − | 0.628984i | ||||
\(997\) | 1.13206e6 | 1.13888 | 0.569441 | − | 0.822032i | \(-0.307160\pi\) | ||||
0.569441 | + | 0.822032i | \(0.307160\pi\) | |||||||
\(998\) | 1.10452e6i | 1.10896i | ||||||||
\(999\) | −3902.86 | + | 239635.i | −0.00391068 | + | 0.240115i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.5.b.a.119.16 | ✓ | 78 | |
3.2 | odd | 2 | inner | 177.5.b.a.119.63 | yes | 78 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.b.a.119.16 | ✓ | 78 | 1.1 | even | 1 | trivial | |
177.5.b.a.119.63 | yes | 78 | 3.2 | odd | 2 | inner |