Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [35,5,Mod(8,35)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(35, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("35.8");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 35 = 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 35.g (of order \(4\), degree \(2\), 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: | \(3.61794870793\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 8.1 | ||
Character | \(\chi\) | \(=\) | 35.8 |
Dual form | 35.5.g.a.22.1 |
$q$-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 \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.44757 | + | 5.44757i | −1.36189 | + | 1.36189i | −0.490387 | + | 0.871505i | \(0.663145\pi\) |
−0.871505 | + | 0.490387i | \(0.836855\pi\) | |||||||
\(3\) | 1.36639 | + | 1.36639i | 0.151821 | + | 0.151821i | 0.778931 | − | 0.627110i | \(-0.215762\pi\) |
−0.627110 | + | 0.778931i | \(0.715762\pi\) | |||||||
\(4\) | − | 43.3520i | − | 2.70950i | ||||||
\(5\) | 7.20796 | − | 23.9384i | 0.288318 | − | 0.957535i | ||||
\(6\) | −14.8870 | −0.413528 | ||||||||
\(7\) | −13.0958 | + | 13.0958i | −0.267261 | + | 0.267261i | ||||
\(8\) | 149.002 | + | 149.002i | 2.32815 | + | 2.32815i | ||||
\(9\) | − | 77.2660i | − | 0.953901i | ||||||
\(10\) | 91.1401 | + | 169.672i | 0.911401 | + | 1.69672i | ||||
\(11\) | 81.6042 | 0.674415 | 0.337207 | − | 0.941430i | \(-0.390518\pi\) | ||||
0.337207 | + | 0.941430i | \(0.390518\pi\) | |||||||
\(12\) | 59.2358 | − | 59.2358i | 0.411359 | − | 0.411359i | ||||
\(13\) | −66.7280 | − | 66.7280i | −0.394840 | − | 0.394840i | 0.481568 | − | 0.876408i | \(-0.340067\pi\) |
−0.876408 | + | 0.481568i | \(0.840067\pi\) | |||||||
\(14\) | − | 142.681i | − | 0.727962i | ||||||
\(15\) | 42.5580 | − | 22.8603i | 0.189147 | − | 0.101601i | ||||
\(16\) | −929.763 | −3.63189 | ||||||||
\(17\) | 347.598 | − | 347.598i | 1.20276 | − | 1.20276i | 0.229438 | − | 0.973323i | \(-0.426311\pi\) |
0.973323 | − | 0.229438i | \(-0.0736889\pi\) | |||||||
\(18\) | 420.912 | + | 420.912i | 1.29911 | + | 1.29911i | ||||
\(19\) | − | 69.2205i | − | 0.191746i | −0.995394 | − | 0.0958732i | \(-0.969436\pi\) | ||
0.995394 | − | 0.0958732i | \(-0.0305643\pi\) | |||||||
\(20\) | −1037.78 | − | 312.479i | −2.59444 | − | 0.781198i | ||||
\(21\) | −35.7880 | −0.0811518 | ||||||||
\(22\) | −444.544 | + | 444.544i | −0.918480 | + | 0.918480i | ||||
\(23\) | 40.2630 | + | 40.2630i | 0.0761115 | + | 0.0761115i | 0.744138 | − | 0.668026i | \(-0.232861\pi\) |
−0.668026 | + | 0.744138i | \(0.732861\pi\) | |||||||
\(24\) | 407.189i | 0.706926i | ||||||||
\(25\) | −521.091 | − | 345.093i | −0.833745 | − | 0.552149i | ||||
\(26\) | 727.010 | 1.07546 | ||||||||
\(27\) | 216.253 | − | 216.253i | 0.296644 | − | 0.296644i | ||||
\(28\) | 567.729 | + | 567.729i | 0.724144 | + | 0.724144i | ||||
\(29\) | − | 586.403i | − | 0.697268i | −0.937259 | − | 0.348634i | \(-0.886646\pi\) | ||
0.937259 | − | 0.348634i | \(-0.113354\pi\) | |||||||
\(30\) | −107.305 | + | 356.371i | −0.119228 | + | 0.395967i | ||||
\(31\) | 538.834 | 0.560701 | 0.280351 | − | 0.959898i | \(-0.409549\pi\) | ||||
0.280351 | + | 0.959898i | \(0.409549\pi\) | |||||||
\(32\) | 2680.92 | − | 2680.92i | 2.61809 | − | 2.61809i | ||||
\(33\) | 111.503 | + | 111.503i | 0.102390 | + | 0.102390i | ||||
\(34\) | 3787.13i | 3.27606i | ||||||||
\(35\) | 219.098 | + | 407.886i | 0.178856 | + | 0.332968i | ||||
\(36\) | −3349.63 | −2.58459 | ||||||||
\(37\) | −1084.74 | + | 1084.74i | −0.792356 | + | 0.792356i | −0.981877 | − | 0.189521i | \(-0.939307\pi\) |
0.189521 | + | 0.981877i | \(0.439307\pi\) | |||||||
\(38\) | 377.083 | + | 377.083i | 0.261138 | + | 0.261138i | ||||
\(39\) | − | 182.353i | − | 0.119890i | ||||||
\(40\) | 4640.86 | − | 2492.86i | 2.90054 | − | 1.55804i | ||||
\(41\) | 80.0417 | 0.0476155 | 0.0238078 | − | 0.999717i | \(-0.492421\pi\) | ||||
0.0238078 | + | 0.999717i | \(0.492421\pi\) | |||||||
\(42\) | 194.957 | − | 194.957i | 0.110520 | − | 0.110520i | ||||
\(43\) | −1323.31 | − | 1323.31i | −0.715689 | − | 0.715689i | 0.252030 | − | 0.967719i | \(-0.418902\pi\) |
−0.967719 | + | 0.252030i | \(0.918902\pi\) | |||||||
\(44\) | − | 3537.70i | − | 1.82733i | ||||||
\(45\) | −1849.62 | − | 556.930i | −0.913393 | − | 0.275027i | ||||
\(46\) | −438.671 | −0.207311 | ||||||||
\(47\) | −2670.09 | + | 2670.09i | −1.20873 | + | 1.20873i | −0.237294 | + | 0.971438i | \(0.576260\pi\) |
−0.971438 | + | 0.237294i | \(0.923740\pi\) | |||||||
\(48\) | −1270.42 | − | 1270.42i | −0.551398 | − | 0.551398i | ||||
\(49\) | − | 343.000i | − | 0.142857i | ||||||
\(50\) | 4718.60 | − | 958.758i | 1.88744 | − | 0.383503i | ||||
\(51\) | 949.909 | 0.365209 | ||||||||
\(52\) | −2892.79 | + | 2892.79i | −1.06982 | + | 1.06982i | ||||
\(53\) | 1863.94 | + | 1863.94i | 0.663560 | + | 0.663560i | 0.956217 | − | 0.292658i | \(-0.0945396\pi\) |
−0.292658 | + | 0.956217i | \(0.594540\pi\) | |||||||
\(54\) | 2356.11i | 0.807993i | ||||||||
\(55\) | 588.199 | − | 1953.47i | 0.194446 | − | 0.645776i | ||||
\(56\) | −3902.60 | −1.24445 | ||||||||
\(57\) | 94.5822 | − | 94.5822i | 0.0291112 | − | 0.0291112i | ||||
\(58\) | 3194.47 | + | 3194.47i | 0.949604 | + | 0.949604i | ||||
\(59\) | − | 1139.50i | − | 0.327350i | −0.986514 | − | 0.163675i | \(-0.947665\pi\) | ||
0.986514 | − | 0.163675i | \(-0.0523348\pi\) | |||||||
\(60\) | −991.039 | − | 1844.98i | −0.275288 | − | 0.512493i | ||||
\(61\) | 3393.50 | 0.911985 | 0.455993 | − | 0.889984i | \(-0.349284\pi\) | ||||
0.455993 | + | 0.889984i | \(0.349284\pi\) | |||||||
\(62\) | −2935.33 | + | 2935.33i | −0.763615 | + | 0.763615i | ||||
\(63\) | 1011.86 | + | 1011.86i | 0.254941 | + | 0.254941i | ||||
\(64\) | 14332.8i | 3.49921i | ||||||||
\(65\) | −2078.33 | + | 1116.39i | −0.491912 | + | 0.264233i | ||||
\(66\) | −1214.84 | −0.278889 | ||||||||
\(67\) | 1840.20 | − | 1840.20i | 0.409935 | − | 0.409935i | −0.471781 | − | 0.881716i | \(-0.656389\pi\) |
0.881716 | + | 0.471781i | \(0.156389\pi\) | |||||||
\(68\) | −15069.1 | − | 15069.1i | −3.25888 | − | 3.25888i | ||||
\(69\) | 110.030i | 0.0231107i | ||||||||
\(70\) | −3415.54 | − | 1028.43i | −0.697049 | − | 0.209885i | ||||
\(71\) | 6930.24 | 1.37477 | 0.687387 | − | 0.726291i | \(-0.258757\pi\) | ||||
0.687387 | + | 0.726291i | \(0.258757\pi\) | |||||||
\(72\) | 11512.8 | − | 11512.8i | 2.22083 | − | 2.22083i | ||||
\(73\) | −823.082 | − | 823.082i | −0.154453 | − | 0.154453i | 0.625650 | − | 0.780104i | \(-0.284834\pi\) |
−0.780104 | + | 0.625650i | \(0.784834\pi\) | |||||||
\(74\) | − | 11818.3i | − | 2.15821i | ||||||
\(75\) | −240.481 | − | 1183.55i | −0.0427522 | − | 0.210408i | ||||
\(76\) | −3000.85 | −0.519537 | ||||||||
\(77\) | −1068.67 | + | 1068.67i | −0.180245 | + | 0.180245i | ||||
\(78\) | 993.380 | + | 993.380i | 0.163277 | + | 0.163277i | ||||
\(79\) | − | 86.0479i | − | 0.0137875i | −0.999976 | − | 0.00689376i | \(-0.997806\pi\) | ||
0.999976 | − | 0.00689376i | \(-0.00219437\pi\) | |||||||
\(80\) | −6701.69 | + | 22257.0i | −1.04714 | + | 3.47766i | ||||
\(81\) | −5667.57 | −0.863827 | ||||||||
\(82\) | −436.033 | + | 436.033i | −0.0648472 | + | 0.0648472i | ||||
\(83\) | 7100.46 | + | 7100.46i | 1.03070 | + | 1.03070i | 0.999514 | + | 0.0311822i | \(0.00992720\pi\) |
0.0311822 | + | 0.999514i | \(0.490073\pi\) | |||||||
\(84\) | 1551.48i | 0.219881i | ||||||||
\(85\) | −5815.46 | − | 10826.4i | −0.804908 | − | 1.49846i | ||||
\(86\) | 14417.6 | 1.94938 | ||||||||
\(87\) | 801.255 | − | 801.255i | 0.105860 | − | 0.105860i | ||||
\(88\) | 12159.2 | + | 12159.2i | 1.57014 | + | 1.57014i | ||||
\(89\) | 12171.5i | 1.53662i | 0.640080 | + | 0.768309i | \(0.278901\pi\) | ||||
−0.640080 | + | 0.768309i | \(0.721099\pi\) | |||||||
\(90\) | 13109.8 | − | 7042.02i | 1.61850 | − | 0.869386i | ||||
\(91\) | 1747.71 | 0.211051 | ||||||||
\(92\) | 1745.48 | − | 1745.48i | 0.206224 | − | 0.206224i | ||||
\(93\) | 736.258 | + | 736.258i | 0.0851263 | + | 0.0851263i | ||||
\(94\) | − | 29091.0i | − | 3.29232i | ||||||
\(95\) | −1657.02 | − | 498.938i | −0.183604 | − | 0.0552840i | ||||
\(96\) | 7326.37 | 0.794962 | ||||||||
\(97\) | −7968.92 | + | 7968.92i | −0.846947 | + | 0.846947i | −0.989751 | − | 0.142804i | \(-0.954388\pi\) |
0.142804 | + | 0.989751i | \(0.454388\pi\) | |||||||
\(98\) | 1868.52 | + | 1868.52i | 0.194556 | + | 0.194556i | ||||
\(99\) | − | 6305.23i | − | 0.643325i | ||||||
\(100\) | −14960.5 | + | 22590.3i | −1.49605 | + | 2.25903i | ||||
\(101\) | 7550.77 | 0.740199 | 0.370100 | − | 0.928992i | \(-0.379324\pi\) | ||||
0.370100 | + | 0.928992i | \(0.379324\pi\) | |||||||
\(102\) | −5174.70 | + | 5174.70i | −0.497376 | + | 0.497376i | ||||
\(103\) | 6641.76 | + | 6641.76i | 0.626049 | + | 0.626049i | 0.947072 | − | 0.321022i | \(-0.104026\pi\) |
−0.321022 | + | 0.947072i | \(0.604026\pi\) | |||||||
\(104\) | − | 19885.2i | − | 1.83850i | ||||||
\(105\) | −257.958 | + | 856.705i | −0.0233976 | + | 0.0777057i | ||||
\(106\) | −20307.9 | −1.80739 | ||||||||
\(107\) | −863.078 | + | 863.078i | −0.0753845 | + | 0.0753845i | −0.743794 | − | 0.668409i | \(-0.766976\pi\) |
0.668409 | + | 0.743794i | \(0.266976\pi\) | |||||||
\(108\) | −9375.00 | − | 9375.00i | −0.803755 | − | 0.803755i | ||||
\(109\) | 930.380i | 0.0783083i | 0.999233 | + | 0.0391541i | \(0.0124663\pi\) | ||||
−0.999233 | + | 0.0391541i | \(0.987534\pi\) | |||||||
\(110\) | 7437.41 | + | 13845.9i | 0.614662 | + | 1.14429i | ||||
\(111\) | −2964.34 | −0.240593 | ||||||||
\(112\) | 12176.0 | − | 12176.0i | 0.970663 | − | 0.970663i | ||||
\(113\) | −10907.2 | − | 10907.2i | −0.854196 | − | 0.854196i | 0.136451 | − | 0.990647i | \(-0.456430\pi\) |
−0.990647 | + | 0.136451i | \(0.956430\pi\) | |||||||
\(114\) | 1030.49i | 0.0792925i | ||||||||
\(115\) | 1254.04 | − | 673.616i | 0.0948237 | − | 0.0509351i | ||||
\(116\) | −25421.7 | −1.88925 | ||||||||
\(117\) | −5155.80 | + | 5155.80i | −0.376638 | + | 0.376638i | ||||
\(118\) | 6207.53 | + | 6207.53i | 0.445815 | + | 0.445815i | ||||
\(119\) | 9104.15i | 0.642903i | ||||||||
\(120\) | 9747.45 | + | 2935.00i | 0.676906 | + | 0.203820i | ||||
\(121\) | −7981.76 | −0.545165 | ||||||||
\(122\) | −18486.3 | + | 18486.3i | −1.24203 | + | 1.24203i | ||||
\(123\) | 109.368 | + | 109.368i | 0.00722905 | + | 0.00722905i | ||||
\(124\) | − | 23359.5i | − | 1.51922i | ||||||
\(125\) | −12017.0 | + | 9986.64i | −0.769086 | + | 0.639145i | ||||
\(126\) | −11024.3 | −0.694403 | ||||||||
\(127\) | 9555.32 | − | 9555.32i | 0.592431 | − | 0.592431i | −0.345856 | − | 0.938287i | \(-0.612412\pi\) |
0.938287 | + | 0.345856i | \(0.112412\pi\) | |||||||
\(128\) | −35184.0 | − | 35184.0i | −2.14746 | − | 2.14746i | ||||
\(129\) | − | 3616.31i | − | 0.217314i | ||||||
\(130\) | 5240.26 | − | 17403.4i | 0.310074 | − | 1.02979i | ||||
\(131\) | 17236.3 | 1.00439 | 0.502194 | − | 0.864755i | \(-0.332526\pi\) | ||||
0.502194 | + | 0.864755i | \(0.332526\pi\) | |||||||
\(132\) | 4833.89 | − | 4833.89i | 0.277427 | − | 0.277427i | ||||
\(133\) | 906.497 | + | 906.497i | 0.0512464 | + | 0.0512464i | ||||
\(134\) | 20049.2i | 1.11657i | ||||||||
\(135\) | −3618.00 | − | 6735.49i | −0.198519 | − | 0.369574i | ||||
\(136\) | 103585. | 5.60043 | ||||||||
\(137\) | 9441.41 | − | 9441.41i | 0.503032 | − | 0.503032i | −0.409347 | − | 0.912379i | \(-0.634243\pi\) |
0.912379 | + | 0.409347i | \(0.134243\pi\) | |||||||
\(138\) | −599.396 | − | 599.396i | −0.0314742 | − | 0.0314742i | ||||
\(139\) | 26127.4i | 1.35228i | 0.736772 | + | 0.676141i | \(0.236349\pi\) | ||||
−0.736772 | + | 0.676141i | \(0.763651\pi\) | |||||||
\(140\) | 17682.7 | − | 9498.34i | 0.902177 | − | 0.484609i | ||||
\(141\) | −7296.77 | −0.367022 | ||||||||
\(142\) | −37753.0 | + | 37753.0i | −1.87229 | + | 1.87229i | ||||
\(143\) | −5445.28 | − | 5445.28i | −0.266286 | − | 0.266286i | ||||
\(144\) | 71839.0i | 3.46446i | ||||||||
\(145\) | −14037.5 | − | 4226.76i | −0.667658 | − | 0.201035i | ||||
\(146\) | 8967.59 | 0.420697 | ||||||||
\(147\) | 468.672 | − | 468.672i | 0.0216887 | − | 0.0216887i | ||||
\(148\) | 47025.4 | + | 47025.4i | 2.14689 | + | 2.14689i | ||||
\(149\) | − | 3703.79i | − | 0.166830i | −0.996515 | − | 0.0834149i | \(-0.973417\pi\) | ||
0.996515 | − | 0.0834149i | \(-0.0265827\pi\) | |||||||
\(150\) | 7757.48 | + | 5137.41i | 0.344777 | + | 0.228329i | ||||
\(151\) | 22789.3 | 0.999488 | 0.499744 | − | 0.866173i | \(-0.333427\pi\) | ||||
0.499744 | + | 0.866173i | \(0.333427\pi\) | |||||||
\(152\) | 10314.0 | − | 10314.0i | 0.446415 | − | 0.446415i | ||||
\(153\) | −26857.5 | − | 26857.5i | −1.14731 | − | 1.14731i | ||||
\(154\) | − | 11643.3i | − | 0.490948i | ||||||
\(155\) | 3883.89 | − | 12898.8i | 0.161660 | − | 0.536891i | ||||
\(156\) | −7905.36 | −0.324842 | ||||||||
\(157\) | 5151.18 | − | 5151.18i | 0.208981 | − | 0.208981i | −0.594853 | − | 0.803834i | \(-0.702790\pi\) |
0.803834 | + | 0.594853i | \(0.202790\pi\) | |||||||
\(158\) | 468.752 | + | 468.752i | 0.0187771 | + | 0.0187771i | ||||
\(159\) | 5093.74i | 0.201485i | ||||||||
\(160\) | −44852.9 | − | 83500.8i | −1.75207 | − | 3.26175i | ||||
\(161\) | −1054.55 | −0.0406833 | ||||||||
\(162\) | 30874.5 | − | 30874.5i | 1.17644 | − | 1.17644i | ||||
\(163\) | −20400.5 | − | 20400.5i | −0.767831 | − | 0.767831i | 0.209893 | − | 0.977724i | \(-0.432688\pi\) |
−0.977724 | + | 0.209893i | \(0.932688\pi\) | |||||||
\(164\) | − | 3469.97i | − | 0.129014i | ||||||
\(165\) | 3472.91 | − | 1865.49i | 0.127563 | − | 0.0685214i | ||||
\(166\) | −77360.5 | −2.80739 | ||||||||
\(167\) | 31137.0 | − | 31137.0i | 1.11646 | − | 1.11646i | 0.124204 | − | 0.992257i | \(-0.460362\pi\) |
0.992257 | − | 0.124204i | \(-0.0396376\pi\) | |||||||
\(168\) | −5332.47 | − | 5332.47i | −0.188934 | − | 0.188934i | ||||
\(169\) | − | 19655.8i | − | 0.688203i | ||||||
\(170\) | 90657.7 | + | 27297.4i | 3.13694 | + | 0.944548i | ||||
\(171\) | −5348.39 | −0.182907 | ||||||||
\(172\) | −57368.1 | + | 57368.1i | −1.93916 | + | 1.93916i | ||||
\(173\) | 17298.0 | + | 17298.0i | 0.577969 | + | 0.577969i | 0.934343 | − | 0.356374i | \(-0.115987\pi\) |
−0.356374 | + | 0.934343i | \(0.615987\pi\) | |||||||
\(174\) | 8729.78i | 0.288340i | ||||||||
\(175\) | 11343.4 | − | 2304.83i | 0.370396 | − | 0.0752597i | ||||
\(176\) | −75872.6 | −2.44940 | ||||||||
\(177\) | 1557.01 | − | 1557.01i | 0.0496986 | − | 0.0496986i | ||||
\(178\) | −66305.3 | − | 66305.3i | −2.09271 | − | 2.09271i | ||||
\(179\) | 1332.58i | 0.0415897i | 0.999784 | + | 0.0207949i | \(0.00661969\pi\) | ||||
−0.999784 | + | 0.0207949i | \(0.993380\pi\) | |||||||
\(180\) | −24144.0 | + | 80184.7i | −0.745185 | + | 2.47484i | ||||
\(181\) | 12567.7 | 0.383618 | 0.191809 | − | 0.981432i | \(-0.438565\pi\) | ||||
0.191809 | + | 0.981432i | \(0.438565\pi\) | |||||||
\(182\) | −9520.78 | + | 9520.78i | −0.287428 | + | 0.287428i | ||||
\(183\) | 4636.84 | + | 4636.84i | 0.138459 | + | 0.138459i | ||||
\(184\) | 11998.5i | 0.354399i | ||||||||
\(185\) | 18148.1 | + | 33785.5i | 0.530258 | + | 0.987159i | ||||
\(186\) | −8021.63 | −0.231866 | ||||||||
\(187\) | 28365.5 | − | 28365.5i | 0.811160 | − | 0.811160i | ||||
\(188\) | 115754. | + | 115754.i | 3.27506 | + | 3.27506i | ||||
\(189\) | 5664.02i | 0.158563i | ||||||||
\(190\) | 11744.8 | − | 6308.76i | 0.325339 | − | 0.174758i | ||||
\(191\) | −12088.8 | −0.331373 | −0.165686 | − | 0.986179i | \(-0.552984\pi\) | ||||
−0.165686 | + | 0.986179i | \(0.552984\pi\) | |||||||
\(192\) | −19584.2 | + | 19584.2i | −0.531254 | + | 0.531254i | ||||
\(193\) | −10539.9 | − | 10539.9i | −0.282957 | − | 0.282957i | 0.551330 | − | 0.834287i | \(-0.314121\pi\) |
−0.834287 | + | 0.551330i | \(0.814121\pi\) | |||||||
\(194\) | − | 86822.5i | − | 2.30690i | ||||||
\(195\) | −4365.23 | − | 1314.39i | −0.114799 | − | 0.0345665i | ||||
\(196\) | −14869.7 | −0.387071 | ||||||||
\(197\) | −6811.78 | + | 6811.78i | −0.175521 | + | 0.175521i | −0.789400 | − | 0.613879i | \(-0.789608\pi\) |
0.613879 | + | 0.789400i | \(0.289608\pi\) | |||||||
\(198\) | 34348.1 | + | 34348.1i | 0.876139 | + | 0.876139i | ||||
\(199\) | 18221.4i | 0.460125i | 0.973176 | + | 0.230063i | \(0.0738931\pi\) | ||||
−0.973176 | + | 0.230063i | \(0.926107\pi\) | |||||||
\(200\) | −26223.9 | − | 129063.i | −0.655598 | − | 3.22658i | ||||
\(201\) | 5028.86 | 0.124474 | ||||||||
\(202\) | −41133.3 | + | 41133.3i | −1.00807 | + | 1.00807i | ||||
\(203\) | 7679.41 | + | 7679.41i | 0.186353 | + | 0.186353i | ||||
\(204\) | − | 41180.5i | − | 0.989535i | ||||||
\(205\) | 576.937 | − | 1916.07i | 0.0137284 | − | 0.0455935i | ||||
\(206\) | −72362.9 | −1.70522 | ||||||||
\(207\) | 3110.96 | − | 3110.96i | 0.0726028 | − | 0.0726028i | ||||
\(208\) | 62041.2 | + | 62041.2i | 1.43401 | + | 1.43401i | ||||
\(209\) | − | 5648.68i | − | 0.129317i | ||||||
\(210\) | −3261.72 | − | 6072.20i | −0.0739618 | − | 0.137692i | ||||
\(211\) | −31576.9 | −0.709259 | −0.354630 | − | 0.935007i | \(-0.615393\pi\) | ||||
−0.354630 | + | 0.935007i | \(0.615393\pi\) | |||||||
\(212\) | 80805.5 | − | 80805.5i | 1.79791 | − | 1.79791i | ||||
\(213\) | 9469.41 | + | 9469.41i | 0.208720 | + | 0.208720i | ||||
\(214\) | − | 9403.35i | − | 0.205331i | ||||||
\(215\) | −41216.2 | + | 22139.5i | −0.891643 | + | 0.478951i | ||||
\(216\) | 64444.2 | 1.38126 | ||||||||
\(217\) | −7056.46 | + | 7056.46i | −0.149854 | + | 0.149854i | ||||
\(218\) | −5068.31 | − | 5068.31i | −0.106647 | − | 0.106647i | ||||
\(219\) | − | 2249.30i | − | 0.0468986i | ||||||
\(220\) | −84686.9 | − | 25499.6i | −1.74973 | − | 0.526852i | ||||
\(221\) | −46389.0 | −0.949797 | ||||||||
\(222\) | 16148.5 | − | 16148.5i | 0.327661 | − | 0.327661i | ||||
\(223\) | −21493.1 | − | 21493.1i | −0.432204 | − | 0.432204i | 0.457174 | − | 0.889378i | \(-0.348862\pi\) |
−0.889378 | + | 0.457174i | \(0.848862\pi\) | |||||||
\(224\) | 70217.6i | 1.39943i | ||||||||
\(225\) | −26664.0 | + | 40262.6i | −0.526696 | + | 0.795310i | ||||
\(226\) | 118836. | 2.32665 | ||||||||
\(227\) | −1.06812 | + | 1.06812i | −2.07285e−5 | + | 2.07285e-5i | −0.707117 | − | 0.707096i | \(-0.750005\pi\) |
0.707096 | + | 0.707117i | \(0.250005\pi\) | |||||||
\(228\) | −4100.33 | − | 4100.33i | −0.0788767 | − | 0.0788767i | ||||
\(229\) | 61585.7i | 1.17438i | 0.809449 | + | 0.587191i | \(0.199766\pi\) | ||||
−0.809449 | + | 0.587191i | \(0.800234\pi\) | |||||||
\(230\) | −3161.92 | + | 10501.1i | −0.0597716 | + | 0.198508i | ||||
\(231\) | −2920.45 | −0.0547300 | ||||||||
\(232\) | 87375.1 | − | 87375.1i | 1.62335 | − | 1.62335i | ||||
\(233\) | −18979.4 | − | 18979.4i | −0.349599 | − | 0.349599i | 0.510361 | − | 0.859960i | \(-0.329512\pi\) |
−0.859960 | + | 0.510361i | \(0.829512\pi\) | |||||||
\(234\) | − | 56173.1i | − | 1.02588i | ||||||
\(235\) | 44671.7 | + | 83163.4i | 0.808903 | + | 1.50590i | ||||
\(236\) | −49399.8 | −0.886954 | ||||||||
\(237\) | 117.575 | − | 117.575i | 0.00209324 | − | 0.00209324i | ||||
\(238\) | −49595.5 | − | 49595.5i | −0.875565 | − | 0.875565i | ||||
\(239\) | 105134.i | 1.84055i | 0.391269 | + | 0.920276i | \(0.372036\pi\) | ||||
−0.391269 | + | 0.920276i | \(0.627964\pi\) | |||||||
\(240\) | −39568.9 | + | 21254.6i | −0.686960 | + | 0.369004i | ||||
\(241\) | 63055.2 | 1.08564 | 0.542821 | − | 0.839848i | \(-0.317356\pi\) | ||||
0.542821 | + | 0.839848i | \(0.317356\pi\) | |||||||
\(242\) | 43481.2 | − | 43481.2i | 0.742455 | − | 0.742455i | ||||
\(243\) | −25260.6 | − | 25260.6i | −0.427791 | − | 0.427791i | ||||
\(244\) | − | 147115.i | − | 2.47102i | ||||||
\(245\) | −8210.86 | − | 2472.33i | −0.136791 | − | 0.0411883i | ||||
\(246\) | −1191.58 | −0.0196904 | ||||||||
\(247\) | −4618.94 | + | 4618.94i | −0.0757092 | + | 0.0757092i | ||||
\(248\) | 80287.2 | + | 80287.2i | 1.30540 | + | 1.30540i | ||||
\(249\) | 19404.0i | 0.312963i | ||||||||
\(250\) | 11060.3 | − | 119866.i | 0.176965 | − | 1.91786i | ||||
\(251\) | −82573.8 | −1.31067 | −0.655337 | − | 0.755337i | \(-0.727473\pi\) | ||||
−0.655337 | + | 0.755337i | \(0.727473\pi\) | |||||||
\(252\) | 43866.1 | − | 43866.1i | 0.690762 | − | 0.690762i | ||||
\(253\) | 3285.63 | + | 3285.63i | 0.0513307 | + | 0.0513307i | ||||
\(254\) | 104107.i | 1.61365i | ||||||||
\(255\) | 6846.90 | − | 22739.3i | 0.105297 | − | 0.349701i | ||||
\(256\) | 154010. | 2.35001 | ||||||||
\(257\) | 52953.5 | − | 52953.5i | 0.801730 | − | 0.801730i | −0.181636 | − | 0.983366i | \(-0.558139\pi\) |
0.983366 | + | 0.181636i | \(0.0581391\pi\) | |||||||
\(258\) | 19700.1 | + | 19700.1i | 0.295958 | + | 0.295958i | ||||
\(259\) | − | 28411.0i | − | 0.423532i | ||||||
\(260\) | 48397.6 | + | 90099.8i | 0.715940 | + | 1.33284i | ||||
\(261\) | −45309.0 | −0.665125 | ||||||||
\(262\) | −93895.9 | + | 93895.9i | −1.36787 | + | 1.36787i | ||||
\(263\) | 24595.0 | + | 24595.0i | 0.355578 | + | 0.355578i | 0.862180 | − | 0.506602i | \(-0.169099\pi\) |
−0.506602 | + | 0.862180i | \(0.669099\pi\) | |||||||
\(264\) | 33228.4i | 0.476761i | ||||||||
\(265\) | 58054.9 | − | 31184.5i | 0.826698 | − | 0.444065i | ||||
\(266\) | −9876.41 | −0.139584 | ||||||||
\(267\) | −16631.1 | + | 16631.1i | −0.233291 | + | 0.233291i | ||||
\(268\) | −79776.2 | − | 79776.2i | −1.11072 | − | 1.11072i | ||||
\(269\) | 49771.6i | 0.687823i | 0.939002 | + | 0.343912i | \(0.111752\pi\) | ||||
−0.939002 | + | 0.343912i | \(0.888248\pi\) | |||||||
\(270\) | 56401.4 | + | 16982.7i | 0.773681 | + | 0.232959i | ||||
\(271\) | 39084.7 | 0.532192 | 0.266096 | − | 0.963947i | \(-0.414266\pi\) | ||||
0.266096 | + | 0.963947i | \(0.414266\pi\) | |||||||
\(272\) | −323184. | + | 323184.i | −4.36829 | + | 4.36829i | ||||
\(273\) | 2388.06 | + | 2388.06i | 0.0320420 | + | 0.0320420i | ||||
\(274\) | 102865.i | 1.37015i | ||||||||
\(275\) | −42523.2 | − | 28161.1i | −0.562290 | − | 0.372378i | ||||
\(276\) | 4770.02 | 0.0626184 | ||||||||
\(277\) | −29445.9 | + | 29445.9i | −0.383765 | + | 0.383765i | −0.872456 | − | 0.488692i | \(-0.837474\pi\) |
0.488692 | + | 0.872456i | \(0.337474\pi\) | |||||||
\(278\) | −142331. | − | 142331.i | −1.84166 | − | 1.84166i | ||||
\(279\) | − | 41633.5i | − | 0.534853i | ||||||
\(280\) | −28129.7 | + | 93421.8i | −0.358798 | + | 1.19160i | ||||
\(281\) | 151923. | 1.92402 | 0.962010 | − | 0.273013i | \(-0.0880203\pi\) | ||||
0.962010 | + | 0.273013i | \(0.0880203\pi\) | |||||||
\(282\) | 39749.6 | − | 39749.6i | 0.499844 | − | 0.499844i | ||||
\(283\) | 76183.3 | + | 76183.3i | 0.951234 | + | 0.951234i | 0.998865 | − | 0.0476314i | \(-0.0151673\pi\) |
−0.0476314 | + | 0.998865i | \(0.515167\pi\) | |||||||
\(284\) | − | 300440.i | − | 3.72495i | ||||||
\(285\) | −1582.40 | − | 2945.89i | −0.0194817 | − | 0.0362682i | ||||
\(286\) | 59327.1 | 0.725305 | ||||||||
\(287\) | −1048.21 | + | 1048.21i | −0.0127258 | + | 0.0127258i | ||||
\(288\) | −207144. | − | 207144.i | −2.49739 | − | 2.49739i | ||||
\(289\) | − | 158128.i | − | 1.89327i | ||||||
\(290\) | 99495.9 | − | 53444.8i | 1.18307 | − | 0.635491i | ||||
\(291\) | −21777.3 | −0.257169 | ||||||||
\(292\) | −35682.2 | + | 35682.2i | −0.418491 | + | 0.418491i | ||||
\(293\) | −35656.3 | − | 35656.3i | −0.415337 | − | 0.415337i | 0.468256 | − | 0.883593i | \(-0.344883\pi\) |
−0.883593 | + | 0.468256i | \(0.844883\pi\) | |||||||
\(294\) | 5106.24i | 0.0590754i | ||||||||
\(295\) | −27277.9 | − | 8213.50i | −0.313449 | − | 0.0943809i | ||||
\(296\) | −323255. | −3.68945 | ||||||||
\(297\) | 17647.2 | − | 17647.2i | 0.200061 | − | 0.200061i | ||||
\(298\) | 20176.6 | + | 20176.6i | 0.227204 | + | 0.227204i | ||||
\(299\) | − | 5373.33i | − | 0.0601037i | ||||||
\(300\) | −51309.1 | + | 10425.3i | −0.570101 | + | 0.115837i | ||||
\(301\) | 34659.6 | 0.382552 | ||||||||
\(302\) | −124146. | + | 124146.i | −1.36120 | + | 1.36120i | ||||
\(303\) | 10317.3 | + | 10317.3i | 0.112378 | + | 0.112378i | ||||
\(304\) | 64358.6i | 0.696402i | ||||||||
\(305\) | 24460.2 | − | 81234.8i | 0.262942 | − | 0.873258i | ||||
\(306\) | 292616. | 3.12504 | ||||||||
\(307\) | 61183.2 | − | 61183.2i | 0.649165 | − | 0.649165i | −0.303626 | − | 0.952791i | \(-0.598197\pi\) |
0.952791 | + | 0.303626i | \(0.0981974\pi\) | |||||||
\(308\) | 46329.1 | + | 46329.1i | 0.488374 | + | 0.488374i | ||||
\(309\) | 18150.5i | 0.190095i | ||||||||
\(310\) | 49109.4 | + | 91424.9i | 0.511023 | + | 0.951351i | ||||
\(311\) | −143150. | −1.48003 | −0.740015 | − | 0.672591i | \(-0.765181\pi\) | ||||
−0.740015 | + | 0.672591i | \(0.765181\pi\) | |||||||
\(312\) | 27170.9 | − | 27170.9i | 0.279123 | − | 0.279123i | ||||
\(313\) | −34807.0 | − | 34807.0i | −0.355285 | − | 0.355285i | 0.506786 | − | 0.862072i | \(-0.330833\pi\) |
−0.862072 | + | 0.506786i | \(0.830833\pi\) | |||||||
\(314\) | 56122.8i | 0.569220i | ||||||||
\(315\) | 31515.7 | − | 16928.8i | 0.317619 | − | 0.170610i | ||||
\(316\) | −3730.35 | −0.0373573 | ||||||||
\(317\) | −19515.0 | + | 19515.0i | −0.194200 | + | 0.194200i | −0.797508 | − | 0.603308i | \(-0.793849\pi\) |
0.603308 | + | 0.797508i | \(0.293849\pi\) | |||||||
\(318\) | −27748.5 | − | 27748.5i | −0.274401 | − | 0.274401i | ||||
\(319\) | − | 47852.9i | − | 0.470248i | ||||||
\(320\) | 343103. | + | 103310.i | 3.35062 | + | 1.00889i | ||||
\(321\) | −2358.60 | −0.0228899 | ||||||||
\(322\) | 5744.74 | − | 5744.74i | 0.0554063 | − | 0.0554063i | ||||
\(323\) | −24060.9 | − | 24060.9i | −0.230625 | − | 0.230625i | ||||
\(324\) | 245700.i | 2.34054i | ||||||||
\(325\) | 11743.9 | + | 57798.7i | 0.111185 | + | 0.547207i | ||||
\(326\) | 222266. | 2.09141 | ||||||||
\(327\) | −1271.26 | + | 1271.26i | −0.0118889 | + | 0.0118889i | ||||
\(328\) | 11926.4 | + | 11926.4i | 0.110856 | + | 0.110856i | ||||
\(329\) | − | 69933.9i | − | 0.646094i | ||||||
\(330\) | −8756.53 | + | 29081.3i | −0.0804089 | + | 0.267046i | ||||
\(331\) | −42277.0 | −0.385876 | −0.192938 | − | 0.981211i | \(-0.561802\pi\) | ||||
−0.192938 | + | 0.981211i | \(0.561802\pi\) | |||||||
\(332\) | 307819. | − | 307819.i | 2.79267 | − | 2.79267i | ||||
\(333\) | 83813.1 | + | 83813.1i | 0.755829 | + | 0.755829i | ||||
\(334\) | 339241.i | 3.04100i | ||||||||
\(335\) | −30787.3 | − | 57315.4i | −0.274335 | − | 0.510718i | ||||
\(336\) | 33274.3 | 0.294734 | ||||||||
\(337\) | −7458.03 | + | 7458.03i | −0.0656696 | + | 0.0656696i | −0.739179 | − | 0.673509i | \(-0.764786\pi\) |
0.673509 | + | 0.739179i | \(0.264786\pi\) | |||||||
\(338\) | 107076. | + | 107076.i | 0.937258 | + | 0.937258i | ||||
\(339\) | − | 29807.1i | − | 0.259370i | ||||||
\(340\) | −469346. | + | 252112.i | −4.06009 | + | 2.18090i | ||||
\(341\) | 43971.1 | 0.378145 | ||||||||
\(342\) | 29135.7 | − | 29135.7i | 0.249100 | − | 0.249100i | ||||
\(343\) | 4491.86 | + | 4491.86i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | − | 394351.i | − | 3.33247i | ||||||
\(345\) | 2633.94 | + | 793.091i | 0.0221293 | + | 0.00666323i | ||||
\(346\) | −188464. | −1.57426 | ||||||||
\(347\) | −97115.7 | + | 97115.7i | −0.806548 | + | 0.806548i | −0.984110 | − | 0.177561i | \(-0.943179\pi\) |
0.177561 | + | 0.984110i | \(0.443179\pi\) | |||||||
\(348\) | −34736.0 | − | 34736.0i | −0.286828 | − | 0.286828i | ||||
\(349\) | 92436.0i | 0.758910i | 0.925210 | + | 0.379455i | \(0.123889\pi\) | ||||
−0.925210 | + | 0.379455i | \(0.876111\pi\) | |||||||
\(350\) | −49238.1 | + | 74349.5i | −0.401944 | + | 0.606935i | ||||
\(351\) | −28860.3 | −0.234253 | ||||||||
\(352\) | 218774. | − | 218774.i | 1.76568 | − | 1.76568i | ||||
\(353\) | −7000.38 | − | 7000.38i | −0.0561787 | − | 0.0561787i | 0.678459 | − | 0.734638i | \(-0.262648\pi\) |
−0.734638 | + | 0.678459i | \(0.762648\pi\) | |||||||
\(354\) | 16963.8i | 0.135368i | ||||||||
\(355\) | 49952.9 | − | 165899.i | 0.396373 | − | 1.31639i | ||||
\(356\) | 527661. | 4.16346 | ||||||||
\(357\) | −12439.8 | + | 12439.8i | −0.0976063 | + | 0.0976063i | ||||
\(358\) | −7259.30 | − | 7259.30i | −0.0566407 | − | 0.0566407i | ||||
\(359\) | − | 202042.i | − | 1.56766i | −0.620973 | − | 0.783832i | \(-0.713262\pi\) | ||
0.620973 | − | 0.783832i | \(-0.286738\pi\) | |||||||
\(360\) | −192613. | − | 358580.i | −1.48621 | − | 2.76682i | ||||
\(361\) | 125530. | 0.963233 | ||||||||
\(362\) | −68463.5 | + | 68463.5i | −0.522446 | + | 0.522446i | ||||
\(363\) | −10906.2 | − | 10906.2i | −0.0827675 | − | 0.0827675i | ||||
\(364\) | − | 75766.8i | − | 0.571842i | ||||||
\(365\) | −25636.0 | + | 13770.5i | −0.192426 | + | 0.103363i | ||||
\(366\) | −50519.0 | −0.377132 | ||||||||
\(367\) | −126698. | + | 126698.i | −0.940671 | + | 0.940671i | −0.998336 | − | 0.0576654i | \(-0.981634\pi\) |
0.0576654 | + | 0.998336i | \(0.481634\pi\) | |||||||
\(368\) | −37435.0 | − | 37435.0i | −0.276428 | − | 0.276428i | ||||
\(369\) | − | 6184.50i | − | 0.0454205i | ||||||
\(370\) | −282912. | − | 85186.1i | −2.06656 | − | 0.622250i | ||||
\(371\) | −48819.6 | −0.354688 | ||||||||
\(372\) | 31918.2 | − | 31918.2i | 0.230650 | − | 0.230650i | ||||
\(373\) | 110870. | + | 110870.i | 0.796889 | + | 0.796889i | 0.982604 | − | 0.185714i | \(-0.0594599\pi\) |
−0.185714 | + | 0.982604i | \(0.559460\pi\) | |||||||
\(374\) | 309046.i | 2.20943i | ||||||||
\(375\) | −30065.5 | − | 2774.22i | −0.213799 | − | 0.0197278i | ||||
\(376\) | −795696. | −5.62823 | ||||||||
\(377\) | −39129.4 | + | 39129.4i | −0.275309 | + | 0.275309i | ||||
\(378\) | −30855.1 | − | 30855.1i | −0.215945 | − | 0.215945i | ||||
\(379\) | 143098.i | 0.996219i | 0.867114 | + | 0.498110i | \(0.165972\pi\) | ||||
−0.867114 | + | 0.498110i | \(0.834028\pi\) | |||||||
\(380\) | −21630.0 | + | 71835.3i | −0.149792 | + | 0.497475i | ||||
\(381\) | 26112.6 | 0.179887 | ||||||||
\(382\) | 65854.6 | − | 65854.6i | 0.451294 | − | 0.451294i | ||||
\(383\) | −48897.7 | − | 48897.7i | −0.333343 | − | 0.333343i | 0.520512 | − | 0.853854i | \(-0.325741\pi\) |
−0.853854 | + | 0.520512i | \(0.825741\pi\) | |||||||
\(384\) | − | 96150.2i | − | 0.652060i | ||||||
\(385\) | 17879.3 | + | 33285.2i | 0.120623 | + | 0.224559i | ||||
\(386\) | 114833. | 0.770715 | ||||||||
\(387\) | −102247. | + | 102247.i | −0.682696 | + | 0.682696i | ||||
\(388\) | 345469. | + | 345469.i | 2.29480 | + | 2.29480i | ||||
\(389\) | − | 116811.i | − | 0.771943i | −0.922511 | − | 0.385971i | \(-0.873866\pi\) | ||
0.922511 | − | 0.385971i | \(-0.126134\pi\) | |||||||
\(390\) | 30940.1 | − | 16619.7i | 0.203420 | − | 0.109268i | ||||
\(391\) | 27990.7 | 0.183088 | ||||||||
\(392\) | 51107.6 | − | 51107.6i | 0.332593 | − | 0.332593i | ||||
\(393\) | 23551.5 | + | 23551.5i | 0.152487 | + | 0.152487i | ||||
\(394\) | − | 74215.3i | − | 0.478080i | ||||||
\(395\) | −2059.85 | − | 620.229i | −0.0132020 | − | 0.00397519i | ||||
\(396\) | −273344. | −1.74309 | ||||||||
\(397\) | −3607.04 | + | 3607.04i | −0.0228860 | + | 0.0228860i | −0.718457 | − | 0.695571i | \(-0.755151\pi\) |
0.695571 | + | 0.718457i | \(0.255151\pi\) | |||||||
\(398\) | −99262.4 | − | 99262.4i | −0.626641 | − | 0.626641i | ||||
\(399\) | 2477.26i | 0.0155606i | ||||||||
\(400\) | 484491. | + | 320855.i | 3.02807 | + | 2.00534i | ||||
\(401\) | −19377.6 | −0.120506 | −0.0602532 | − | 0.998183i | \(-0.519191\pi\) | ||||
−0.0602532 | + | 0.998183i | \(0.519191\pi\) | |||||||
\(402\) | −27395.0 | + | 27395.0i | −0.169520 | + | 0.169520i | ||||
\(403\) | −35955.3 | − | 35955.3i | −0.221387 | − | 0.221387i | ||||
\(404\) | − | 327341.i | − | 2.00557i | ||||||
\(405\) | −40851.6 | + | 135672.i | −0.249057 | + | 0.827144i | ||||
\(406\) | −83668.2 | −0.507585 | ||||||||
\(407\) | −88519.0 | + | 88519.0i | −0.534377 | + | 0.534377i | ||||
\(408\) | 141538. | + | 141538.i | 0.850263 | + | 0.850263i | ||||
\(409\) | − | 287642.i | − | 1.71952i | −0.510701 | − | 0.859758i | \(-0.670614\pi\) | ||
0.510701 | − | 0.859758i | \(-0.329386\pi\) | |||||||
\(410\) | 7295.01 | + | 13580.8i | 0.0433968 | + | 0.0807901i | ||||
\(411\) | 25801.3 | 0.152742 | ||||||||
\(412\) | 287933. | − | 287933.i | 1.69628 | − | 1.69628i | ||||
\(413\) | 14922.7 | + | 14922.7i | 0.0874879 | + | 0.0874879i | ||||
\(414\) | 33894.3i | 0.197754i | ||||||||
\(415\) | 221153. | − | 118794.i | 1.28410 | − | 0.689759i | ||||
\(416\) | −357785. | −2.06745 | ||||||||
\(417\) | −35700.3 | + | 35700.3i | −0.205305 | + | 0.205305i | ||||
\(418\) | 30771.6 | + | 30771.6i | 0.176115 | + | 0.176115i | ||||
\(419\) | − | 10754.6i | − | 0.0612585i | −0.999531 | − | 0.0306293i | \(-0.990249\pi\) | ||
0.999531 | − | 0.0306293i | \(-0.00975113\pi\) | |||||||
\(420\) | 37139.9 | + | 11183.0i | 0.210544 | + | 0.0633957i | ||||
\(421\) | 131257. | 0.740556 | 0.370278 | − | 0.928921i | \(-0.379262\pi\) | ||||
0.370278 | + | 0.928921i | \(0.379262\pi\) | |||||||
\(422\) | 172017. | − | 172017.i | 0.965934 | − | 0.965934i | ||||
\(423\) | 206307. | + | 206307.i | 1.15301 | + | 1.15301i | ||||
\(424\) | 555461.i | 3.08974i | ||||||||
\(425\) | −301084. | + | 61176.4i | −1.66690 | + | 0.338693i | ||||
\(426\) | −103171. | −0.568508 | ||||||||
\(427\) | −44440.6 | + | 44440.6i | −0.243738 | + | 0.243738i | ||||
\(428\) | 37416.1 | + | 37416.1i | 0.204254 | + | 0.204254i | ||||
\(429\) | − | 14880.8i | − | 0.0808557i | ||||||
\(430\) | 103922. | − | 345135.i | 0.562042 | − | 1.86660i | ||||
\(431\) | −233112. | −1.25490 | −0.627452 | − | 0.778655i | \(-0.715902\pi\) | ||||
−0.627452 | + | 0.778655i | \(0.715902\pi\) | |||||||
\(432\) | −201064. | + | 201064.i | −1.07738 | + | 1.07738i | ||||
\(433\) | −71663.4 | − | 71663.4i | −0.382227 | − | 0.382227i | 0.489677 | − | 0.871904i | \(-0.337115\pi\) |
−0.871904 | + | 0.489677i | \(0.837115\pi\) | |||||||
\(434\) | − | 76881.1i | − | 0.408169i | ||||||
\(435\) | −13405.3 | − | 24956.1i | −0.0708433 | − | 0.131886i | ||||
\(436\) | 40333.8 | 0.212176 | ||||||||
\(437\) | 2787.02 | − | 2787.02i | 0.0145941 | − | 0.0145941i | ||||
\(438\) | 12253.2 | + | 12253.2i | 0.0638708 | + | 0.0638708i | ||||
\(439\) | 299601.i | 1.55459i | 0.629139 | + | 0.777293i | \(0.283408\pi\) | ||||
−0.629139 | + | 0.777293i | \(0.716592\pi\) | |||||||
\(440\) | 378714. | − | 203428.i | 1.95616 | − | 1.05076i | ||||
\(441\) | −26502.2 | −0.136272 | ||||||||
\(442\) | 252707. | − | 252707.i | 1.29352 | − | 1.29352i | ||||
\(443\) | 129039. | + | 129039.i | 0.657528 | + | 0.657528i | 0.954795 | − | 0.297267i | \(-0.0960750\pi\) |
−0.297267 | + | 0.954795i | \(0.596075\pi\) | |||||||
\(444\) | 128510.i | 0.651886i | ||||||||
\(445\) | 291367. | + | 87732.0i | 1.47136 | + | 0.443035i | ||||
\(446\) | 234170. | 1.17723 | ||||||||
\(447\) | 5060.82 | − | 5060.82i | 0.0253283 | − | 0.0253283i | ||||
\(448\) | −187699. | − | 187699.i | −0.935203 | − | 0.935203i | ||||
\(449\) | − | 241835.i | − | 1.19957i | −0.800161 | − | 0.599786i | \(-0.795252\pi\) | ||
0.800161 | − | 0.599786i | \(-0.204748\pi\) | |||||||
\(450\) | −74079.3 | − | 364587.i | −0.365824 | − | 1.80043i | ||||
\(451\) | 6531.74 | 0.0321126 | ||||||||
\(452\) | −472850. | + | 472850.i | −2.31444 | + | 2.31444i | ||||
\(453\) | 31139.1 | + | 31139.1i | 0.151744 | + | 0.151744i | ||||
\(454\) | − | 11.6373i | − | 5.64600e-5i | ||||||
\(455\) | 12597.4 | − | 41837.4i | 0.0608498 | − | 0.202088i | ||||
\(456\) | 28185.8 | 0.135551 | ||||||||
\(457\) | −146983. | + | 146983.i | −0.703778 | + | 0.703778i | −0.965219 | − | 0.261441i | \(-0.915802\pi\) |
0.261441 | + | 0.965219i | \(0.415802\pi\) | |||||||
\(458\) | −335492. | − | 335492.i | −1.59938 | − | 1.59938i | ||||
\(459\) | − | 150338.i | − | 0.713583i | ||||||
\(460\) | −29202.6 | − | 54365.3i | −0.138009 | − | 0.256925i | ||||
\(461\) | 248662. | 1.17006 | 0.585030 | − | 0.811012i | \(-0.301083\pi\) | ||||
0.585030 | + | 0.811012i | \(0.301083\pi\) | |||||||
\(462\) | 15909.3 | − | 15909.3i | 0.0745363 | − | 0.0745363i | ||||
\(463\) | −155970. | − | 155970.i | −0.727575 | − | 0.727575i | 0.242561 | − | 0.970136i | \(-0.422013\pi\) |
−0.970136 | + | 0.242561i | \(0.922013\pi\) | |||||||
\(464\) | 545216.i | 2.53240i | ||||||||
\(465\) | 22931.7 | − | 12317.9i | 0.106055 | − | 0.0569679i | ||||
\(466\) | 206783. | 0.952233 | ||||||||
\(467\) | 210168. | − | 210168.i | 0.963678 | − | 0.963678i | −0.0356846 | − | 0.999363i | \(-0.511361\pi\) |
0.999363 | + | 0.0356846i | \(0.0113612\pi\) | |||||||
\(468\) | 223514. | + | 223514.i | 1.02050 | + | 1.02050i | ||||
\(469\) | 48197.7i | 0.219119i | ||||||||
\(470\) | −696390. | − | 209686.i | −3.15251 | − | 0.949237i | ||||
\(471\) | 14077.0 | 0.0634555 | ||||||||
\(472\) | 169788. | − | 169788.i | 0.762120 | − | 0.762120i | ||||
\(473\) | −107988. | − | 107988.i | −0.482671 | − | 0.482671i | ||||
\(474\) | 1281.00i | 0.00570153i | ||||||||
\(475\) | −23887.5 | + | 36070.1i | −0.105873 | + | 0.159868i | ||||
\(476\) | 394683. | 1.74195 | ||||||||
\(477\) | 144019. | − | 144019.i | 0.632970 | − | 0.632970i | ||||
\(478\) | −572726. | − | 572726.i | −2.50663 | − | 2.50663i | ||||
\(479\) | − | 208148.i | − | 0.907196i | −0.891206 | − | 0.453598i | \(-0.850140\pi\) | ||
0.891206 | − | 0.453598i | \(-0.149860\pi\) | |||||||
\(480\) | 52808.1 | − | 175381.i | 0.229202 | − | 0.761203i | ||||
\(481\) | 144764. | 0.625708 | ||||||||
\(482\) | −343497. | + | 343497.i | −1.47853 | + | 1.47853i | ||||
\(483\) | −1440.93 | − | 1440.93i | −0.00617659 | − | 0.00617659i | ||||
\(484\) | 346025.i | 1.47712i | ||||||||
\(485\) | 133323. | + | 248203.i | 0.566791 | + | 1.05517i | ||||
\(486\) | 275218. | 1.16521 | ||||||||
\(487\) | 39534.4 | − | 39534.4i | 0.166693 | − | 0.166693i | −0.618831 | − | 0.785524i | \(-0.712393\pi\) |
0.785524 | + | 0.618831i | \(0.212393\pi\) | |||||||
\(488\) | 505637. | + | 505637.i | 2.12324 | + | 2.12324i | ||||
\(489\) | − | 55750.1i | − | 0.233146i | ||||||
\(490\) | 58197.4 | − | 31261.0i | 0.242388 | − | 0.130200i | ||||
\(491\) | −46929.8 | −0.194664 | −0.0973319 | − | 0.995252i | \(-0.531031\pi\) | ||||
−0.0973319 | + | 0.995252i | \(0.531031\pi\) | |||||||
\(492\) | 4741.33 | − | 4741.33i | 0.0195871 | − | 0.0195871i | ||||
\(493\) | −203832. | − | 203832.i | −0.838647 | − | 0.838647i | ||||
\(494\) | − | 50324.0i | − | 0.206215i | ||||||
\(495\) | −150937. | − | 45447.8i | −0.616006 | − | 0.185482i | ||||
\(496\) | −500988. | −2.03640 | ||||||||
\(497\) | −90757.0 | + | 90757.0i | −0.367424 | + | 0.367424i | ||||
\(498\) | −105705. | − | 105705.i | −0.426222 | − | 0.426222i | ||||
\(499\) | 474425.i | 1.90532i | 0.304045 | + | 0.952658i | \(0.401663\pi\) | ||||
−0.304045 | + | 0.952658i | \(0.598337\pi\) | |||||||
\(500\) | 432941. | + | 520960.i | 1.73176 | + | 2.08384i | ||||
\(501\) | 85090.5 | 0.339005 | ||||||||
\(502\) | 449826. | − | 449826.i | 1.78500 | − | 1.78500i | ||||
\(503\) | 309798. | + | 309798.i | 1.22445 | + | 1.22445i | 0.966032 | + | 0.258422i | \(0.0832024\pi\) |
0.258422 | + | 0.966032i | \(0.416798\pi\) | |||||||
\(504\) | 301538.i | 1.18708i | ||||||||
\(505\) | 54425.6 | − | 180753.i | 0.213413 | − | 0.708766i | ||||
\(506\) | −35797.4 | −0.139814 | ||||||||
\(507\) | 26857.4 | − | 26857.4i | 0.104484 | − | 0.104484i | ||||
\(508\) | −414242. | − | 414242.i | −1.60519 | − | 1.60519i | ||||
\(509\) | 436300.i | 1.68403i | 0.539455 | + | 0.842015i | \(0.318630\pi\) | ||||
−0.539455 | + | 0.842015i | \(0.681370\pi\) | |||||||
\(510\) | 86574.8 | + | 161173.i | 0.332852 | + | 0.619657i | ||||
\(511\) | 21557.8 | 0.0825588 | ||||||||
\(512\) | −276038. | + | 276038.i | −1.05300 | + | 1.05300i | ||||
\(513\) | −14969.1 | − | 14969.1i | −0.0568803 | − | 0.0568803i | ||||
\(514\) | 576935.i | 2.18374i | ||||||||
\(515\) | 206866. | − | 111119.i | 0.779965 | − | 0.418963i | ||||
\(516\) | −156774. | −0.588811 | ||||||||
\(517\) | −217890. | + | 217890.i | −0.815186 | + | 0.815186i | ||||
\(518\) | 154771. | + | 154771.i | 0.576805 | + | 0.576805i | ||||
\(519\) | 47271.7i | 0.175496i | ||||||||
\(520\) | −476019. | − | 143331.i | −1.76042 | − | 0.530072i | ||||
\(521\) | −468198. | −1.72486 | −0.862431 | − | 0.506174i | \(-0.831059\pi\) | ||||
−0.862431 | + | 0.506174i | \(0.831059\pi\) | |||||||
\(522\) | 246824. | − | 246824.i | 0.905828 | − | 0.905828i | ||||
\(523\) | 55782.4 | + | 55782.4i | 0.203936 | + | 0.203936i | 0.801684 | − | 0.597748i | \(-0.203938\pi\) |
−0.597748 | + | 0.801684i | \(0.703938\pi\) | |||||||
\(524\) | − | 747228.i | − | 2.72139i | ||||||
\(525\) | 18648.8 | + | 12350.2i | 0.0676600 | + | 0.0448079i | ||||
\(526\) | −267966. | −0.968518 | ||||||||
\(527\) | 187298. | − | 187298.i | 0.674390 | − | 0.674390i | ||||
\(528\) | −103672. | − | 103672.i | −0.371871 | − | 0.371871i | ||||
\(529\) | − | 276599.i | − | 0.988414i | ||||||
\(530\) | −146378. | + | 486137.i | −0.521104 | + | 1.73064i | ||||
\(531\) | −88044.9 | −0.312259 | ||||||||
\(532\) | 39298.5 | − | 39298.5i | 0.138852 | − | 0.138852i | ||||
\(533\) | −5341.02 | − | 5341.02i | −0.0188005 | − | 0.0188005i | ||||
\(534\) | − | 181198.i | − | 0.635434i | ||||||
\(535\) | 14439.6 | + | 26881.7i | 0.0504486 | + | 0.0939180i | ||||
\(536\) | 548385. | 1.90878 | ||||||||
\(537\) | −1820.82 | + | 1820.82i | −0.00631420 | + | 0.00631420i | ||||
\(538\) | −271134. | − | 271134.i | −0.936741 | − | 0.936741i | ||||
\(539\) | − | 27990.2i | − | 0.0963450i | ||||||
\(540\) | −291997. | + | 156848.i | −1.00136 | + | 0.537886i | ||||
\(541\) | −272065. | −0.929561 | −0.464780 | − | 0.885426i | \(-0.653867\pi\) | ||||
−0.464780 | + | 0.885426i | \(0.653867\pi\) | |||||||
\(542\) | −212917. | + | 212917.i | −0.724788 | + | 0.724788i | ||||
\(543\) | 17172.4 | + | 17172.4i | 0.0582413 | + | 0.0582413i | ||||
\(544\) | − | 1.86376e6i | − | 6.29786i | ||||||
\(545\) | 22271.8 | + | 6706.14i | 0.0749829 | + | 0.0225777i | ||||
\(546\) | −26018.2 | −0.0872755 | ||||||||
\(547\) | 6581.91 | − | 6581.91i | 0.0219977 | − | 0.0219977i | −0.696022 | − | 0.718020i | \(-0.745049\pi\) |
0.718020 | + | 0.696022i | \(0.245049\pi\) | |||||||
\(548\) | −409304. | − | 409304.i | −1.36297 | − | 1.36297i | ||||
\(549\) | − | 262202.i | − | 0.869943i | ||||||
\(550\) | 385057. | − | 78238.7i | 1.27292 | − | 0.258640i | ||||
\(551\) | −40591.1 | −0.133699 | ||||||||
\(552\) | −16394.7 | + | 16394.7i | −0.0538052 | + | 0.0538052i | ||||
\(553\) | 1126.87 | + | 1126.87i | 0.00368487 | + | 0.00368487i | ||||
\(554\) | − | 320817.i | − | 1.04529i | ||||||
\(555\) | −21366.9 | + | 70961.6i | −0.0693673 | + | 0.230376i | ||||
\(556\) | 1.13268e6 | 3.66401 | ||||||||
\(557\) | −313808. | + | 313808.i | −1.01147 | + | 1.01147i | −0.0115379 | + | 0.999933i | \(0.503673\pi\) |
−0.999933 | + | 0.0115379i | \(0.996327\pi\) | |||||||
\(558\) | 226801. | + | 226801.i | 0.728412 | + | 0.728412i | ||||
\(559\) | 176603.i | 0.565165i | ||||||||
\(560\) | −203709. | − | 379237.i | −0.649584 | − | 1.20930i | ||||
\(561\) | 77516.6 | 0.246303 | ||||||||
\(562\) | −827609. | + | 827609.i | −2.62031 | + | 2.62031i | ||||
\(563\) | 15752.0 | + | 15752.0i | 0.0496957 | + | 0.0496957i | 0.731518 | − | 0.681822i | \(-0.238812\pi\) |
−0.681822 | + | 0.731518i | \(0.738812\pi\) | |||||||
\(564\) | 316329.i | 0.994446i | ||||||||
\(565\) | −339720. | + | 182482.i | −1.06420 | + | 0.571642i | ||||
\(566\) | −830028. | −2.59095 | ||||||||
\(567\) | 74221.4 | − | 74221.4i | 0.230868 | − | 0.230868i | ||||
\(568\) | 1.03262e6 | + | 1.03262e6i | 3.20069 | + | 3.20069i | ||||
\(569\) | − | 91745.8i | − | 0.283375i | −0.989911 | − | 0.141688i | \(-0.954747\pi\) | ||
0.989911 | − | 0.141688i | \(-0.0452528\pi\) | |||||||
\(570\) | 24668.1 | + | 7427.70i | 0.0759254 | + | 0.0228615i | ||||
\(571\) | −441760. | −1.35492 | −0.677461 | − | 0.735558i | \(-0.736920\pi\) | ||||
−0.677461 | + | 0.735558i | \(0.736920\pi\) | |||||||
\(572\) | −236064. | + | 236064.i | −0.721502 | + | 0.721502i | ||||
\(573\) | −16518.0 | − | 16518.0i | −0.0503094 | − | 0.0503094i | ||||
\(574\) | − | 11420.4i | − | 0.0346623i | ||||||
\(575\) | −7086.18 | − | 34875.2i | −0.0214327 | − | 0.105483i | ||||
\(576\) | 1.10743e6 | 3.33790 | ||||||||
\(577\) | 215875. | − | 215875.i | 0.648412 | − | 0.648412i | −0.304197 | − | 0.952609i | \(-0.598388\pi\) |
0.952609 | + | 0.304197i | \(0.0983883\pi\) | |||||||
\(578\) | 861412. | + | 861412.i | 2.57843 | + | 2.57843i | ||||
\(579\) | − | 28803.2i | − | 0.0859178i | ||||||
\(580\) | −183239. | + | 608554.i | −0.544705 | + | 1.80902i | ||||
\(581\) | −185973. | −0.550930 | ||||||||
\(582\) | 118633. | − | 118633.i | 0.350236 | − | 0.350236i | ||||
\(583\) | 152105. | + | 152105.i | 0.447515 | + | 0.447515i | ||||
\(584\) | − | 245281.i | − | 0.719182i | ||||||
\(585\) | 86258.6 | + | 160584.i | 0.252052 | + | 0.469236i | ||||
\(586\) | 388480. | 1.13129 | ||||||||
\(587\) | 415527. | − | 415527.i | 1.20593 | − | 1.20593i | 0.233601 | − | 0.972333i | \(-0.424949\pi\) |
0.972333 | − | 0.233601i | \(-0.0750509\pi\) | |||||||
\(588\) | −20317.9 | − | 20317.9i | −0.0587656 | − | 0.0587656i | ||||
\(589\) | − | 37298.3i | − | 0.107512i | ||||||
\(590\) | 193342. | − | 103854.i | 0.555420 | − | 0.298347i | ||||
\(591\) | −18615.1 | −0.0532955 | ||||||||
\(592\) | 1.00855e6 | − | 1.00855e6i | 2.87775 | − | 2.87775i | ||||
\(593\) | −186492. | − | 186492.i | −0.530337 | − | 0.530337i | 0.390336 | − | 0.920673i | \(-0.372359\pi\) |
−0.920673 | + | 0.390336i | \(0.872359\pi\) | |||||||
\(594\) | 192268.i | 0.544922i | ||||||||
\(595\) | 217938. | + | 65622.3i | 0.615602 | + | 0.185361i | ||||
\(596\) | −160567. | −0.452025 | ||||||||
\(597\) | −24897.6 | + | 24897.6i | −0.0698568 | + | 0.0698568i | ||||
\(598\) | 29271.6 | + | 29271.6i | 0.0818548 | + | 0.0818548i | ||||
\(599\) | 135461.i | 0.377538i | 0.982022 | + | 0.188769i | \(0.0604498\pi\) | ||||
−0.982022 | + | 0.188769i | \(0.939550\pi\) | |||||||
\(600\) | 140518. | − | 212183.i | 0.390329 | − | 0.589396i | ||||
\(601\) | −68623.2 | −0.189986 | −0.0949931 | − | 0.995478i | \(-0.530283\pi\) | ||||
−0.0949931 | + | 0.995478i | \(0.530283\pi\) | |||||||
\(602\) | −188810. | + | 188810.i | −0.520994 | + | 0.520994i | ||||
\(603\) | −142185. | − | 142185.i | −0.391037 | − | 0.391037i | ||||
\(604\) | − | 987963.i | − | 2.70811i | ||||||
\(605\) | −57532.1 | + | 191070.i | −0.157181 | + | 0.522014i | ||||
\(606\) | −112408. | −0.306093 | ||||||||
\(607\) | 166899. | − | 166899.i | 0.452978 | − | 0.452978i | −0.443364 | − | 0.896342i | \(-0.646215\pi\) |
0.896342 | + | 0.443364i | \(0.146215\pi\) | |||||||
\(608\) | −185574. | − | 185574.i | −0.502009 | − | 0.502009i | ||||
\(609\) | 20986.2i | 0.0565846i | ||||||||
\(610\) | 309284. | + | 575780.i | 0.831184 | + | 1.54738i | ||||
\(611\) | 356339. | 0.954511 | ||||||||
\(612\) | −1.16433e6 | + | 1.16433e6i | −3.10865 | + | 3.10865i | ||||
\(613\) | −415920. | − | 415920.i | −1.10685 | − | 1.10685i | −0.993562 | − | 0.113290i | \(-0.963861\pi\) |
−0.113290 | − | 0.993562i | \(-0.536139\pi\) | |||||||
\(614\) | 666599.i | 1.76819i | ||||||||
\(615\) | 3406.42 | − | 1829.78i | 0.00900633 | − | 0.00483780i | ||||
\(616\) | −318468. | −0.839276 | ||||||||
\(617\) | 477043. | − | 477043.i | 1.25310 | − | 1.25310i | 0.298783 | − | 0.954321i | \(-0.403419\pi\) |
0.954321 | − | 0.298783i | \(-0.0965808\pi\) | |||||||
\(618\) | −98875.9 | − | 98875.9i | −0.258889 | − | 0.258889i | ||||
\(619\) | − | 96183.1i | − | 0.251025i | −0.992092 | − | 0.125513i | \(-0.959942\pi\) | ||
0.992092 | − | 0.125513i | \(-0.0400575\pi\) | |||||||
\(620\) | −559189. | − | 168374.i | −1.45471 | − | 0.438019i | ||||
\(621\) | 17414.0 | 0.0451560 | ||||||||
\(622\) | 779819. | − | 779819.i | 2.01564 | − | 2.01564i | ||||
\(623\) | −159396. | − | 159396.i | −0.410678 | − | 0.410678i | ||||
\(624\) | 169545.i | 0.435428i | ||||||||
\(625\) | 152446. | + | 359650.i | 0.390262 | + | 0.920704i | ||||
\(626\) | 379226. | 0.967721 | ||||||||
\(627\) | 7718.30 | − | 7718.30i | 0.0196330 | − | 0.0196330i | ||||
\(628\) | −223314. | − | 223314.i | −0.566234 | − | 0.566234i | ||||
\(629\) | 754104.i | 1.90603i | ||||||||
\(630\) | −79463.0 | + | 263905.i | −0.200209 | + | 0.664915i | ||||
\(631\) | −204909. | −0.514637 | −0.257319 | − | 0.966327i | \(-0.582839\pi\) | ||||
−0.257319 | + | 0.966327i | \(0.582839\pi\) | |||||||
\(632\) | 12821.3 | − | 12821.3i | 0.0320995 | − | 0.0320995i | ||||
\(633\) | −43146.4 | − | 43146.4i | −0.107681 | − | 0.107681i | ||||
\(634\) | − | 212618.i | − | 0.528959i | ||||||
\(635\) | −159864. | − | 297613.i | −0.396465 | − | 0.738082i | ||||
\(636\) | 220824. | 0.545923 | ||||||||
\(637\) | −22887.7 | + | 22887.7i | −0.0564057 | + | 0.0564057i | ||||
\(638\) | 260682. | + | 260682.i | 0.640427 | + | 0.640427i | ||||
\(639\) | − | 535472.i | − | 1.31140i | ||||||
\(640\) | −1.09585e6 | + | 588643.i | −2.67542 | + | 1.43712i | ||||
\(641\) | −32846.1 | −0.0799408 | −0.0399704 | − | 0.999201i | \(-0.512726\pi\) | ||||
−0.0399704 | + | 0.999201i | \(0.512726\pi\) | |||||||
\(642\) | 12848.6 | − | 12848.6i | 0.0311736 | − | 0.0311736i | ||||
\(643\) | −78540.8 | − | 78540.8i | −0.189965 | − | 0.189965i | 0.605716 | − | 0.795681i | \(-0.292887\pi\) |
−0.795681 | + | 0.605716i | \(0.792887\pi\) | |||||||
\(644\) | 45716.9i | 0.110231i | ||||||||
\(645\) | −86568.7 | − | 26066.2i | −0.208085 | − | 0.0626554i | ||||
\(646\) | 262147. | 0.628173 | ||||||||
\(647\) | 303680. | − | 303680.i | 0.725449 | − | 0.725449i | −0.244260 | − | 0.969710i | \(-0.578545\pi\) |
0.969710 | + | 0.244260i | \(0.0785452\pi\) | |||||||
\(648\) | −844478. | − | 844478.i | −2.01112 | − | 2.01112i | ||||
\(649\) | − | 92988.3i | − | 0.220769i | ||||||
\(650\) | −378838. | − | 250886.i | −0.896659 | − | 0.593814i | ||||
\(651\) | −19283.8 | −0.0455019 | ||||||||
\(652\) | −884402. | + | 884402.i | −2.08044 | + | 2.08044i | ||||
\(653\) | 290141. | + | 290141.i | 0.680429 | + | 0.680429i | 0.960097 | − | 0.279668i | \(-0.0902245\pi\) |
−0.279668 | + | 0.960097i | \(0.590224\pi\) | |||||||
\(654\) | − | 13850.6i | − | 0.0323827i | ||||||
\(655\) | 124238. | − | 412609.i | 0.289583 | − | 0.961736i | ||||
\(656\) | −74419.9 | −0.172934 | ||||||||
\(657\) | −63596.2 | + | 63596.2i | −0.147333 | + | 0.147333i | ||||
\(658\) | 380970. | + | 380970.i | 0.879910 | + | 0.879910i | ||||
\(659\) | 495743.i | 1.14153i | 0.821115 | + | 0.570763i | \(0.193353\pi\) | ||||
−0.821115 | + | 0.570763i | \(0.806647\pi\) | |||||||
\(660\) | −80872.9 | − | 150558.i | −0.185659 | − | 0.345633i | ||||
\(661\) | 182581. | 0.417882 | 0.208941 | − | 0.977928i | \(-0.432998\pi\) | ||||
0.208941 | + | 0.977928i | \(0.432998\pi\) | |||||||
\(662\) | 230307. | − | 230307.i | 0.525522 | − | 0.525522i | ||||
\(663\) | −63385.5 | − | 63385.5i | −0.144199 | − | 0.144199i | ||||
\(664\) | 2.11596e6i | 4.79924i | ||||||||
\(665\) | 28234.1 | − | 15166.1i | 0.0638455 | − | 0.0342949i | ||||
\(666\) | −913155. | −2.05871 | ||||||||
\(667\) | 23610.3 | − | 23610.3i | 0.0530701 | − | 0.0530701i | ||||
\(668\) | −1.34985e6 | − | 1.34985e6i | −3.02505 | − | 3.02505i | ||||
\(669\) | − | 58735.9i | − | 0.131235i | ||||||
\(670\) | 479945. | + | 144514.i | 1.06916 | + | 0.321928i | ||||
\(671\) | 276924. | 0.615056 | ||||||||
\(672\) | −95944.6 | + | 95944.6i | −0.212462 | + | 0.212462i | ||||
\(673\) | −551601. | − | 551601.i | −1.21785 | − | 1.21785i | −0.968382 | − | 0.249470i | \(-0.919743\pi\) |
−0.249470 | − | 0.968382i | \(-0.580257\pi\) | |||||||
\(674\) | − | 81256.2i | − | 0.178870i | ||||||
\(675\) | −187315. | + | 38060.0i | −0.411117 | + | 0.0835336i | ||||
\(676\) | −852116. | −1.86469 | ||||||||
\(677\) | −112272. | + | 112272.i | −0.244959 | + | 0.244959i | −0.818898 | − | 0.573939i | \(-0.805415\pi\) |
0.573939 | + | 0.818898i | \(0.305415\pi\) | |||||||
\(678\) | 162376. | + | 162376.i | 0.353234 | + | 0.353234i | ||||
\(679\) | − | 208719.i | − | 0.452712i | ||||||
\(680\) | 746640. | − | 2.47967e6i | 1.61471 | − | 5.36260i | ||||
\(681\) | −2.91894 | −6.29406e−6 | ||||||||
\(682\) | −239536. | + | 239536.i | −0.514993 | + | 0.514993i | ||||
\(683\) | 434268. | + | 434268.i | 0.930928 | + | 0.930928i | 0.997764 | − | 0.0668362i | \(-0.0212905\pi\) |
−0.0668362 | + | 0.997764i | \(0.521291\pi\) | |||||||
\(684\) | 231863.i | 0.495587i | ||||||||
\(685\) | −157959. | − | 294065.i | −0.336637 | − | 0.626704i | ||||
\(686\) | −48939.4 | −0.103995 | ||||||||
\(687\) | −84150.1 | + | 84150.1i | −0.178296 | + | 0.178296i | ||||
\(688\) | 1.23036e6 | + | 1.23036e6i | 2.59930 | + | 2.59930i | ||||
\(689\) | − | 248754.i | − | 0.524000i | ||||||
\(690\) | −18669.0 | + | 10028.1i | −0.0392123 | + | 0.0210631i | ||||
\(691\) | 684956. | 1.43452 | 0.717260 | − | 0.696806i | \(-0.245396\pi\) | ||||
0.717260 | + | 0.696806i | \(0.245396\pi\) | |||||||
\(692\) | 749904. | − | 749904.i | 1.56601 | − | 1.56601i | ||||
\(693\) | 82572.0 | + | 82572.0i | 0.171936 | + | 0.171936i | ||||
\(694\) | − | 1.05809e6i | − | 2.19686i | ||||||
\(695\) | 625448. | + | 188325.i | 1.29486 | + | 0.389887i | ||||
\(696\) | 238777. | 0.492917 | ||||||||
\(697\) | 27822.3 | − | 27822.3i | 0.0572701 | − | 0.0572701i | ||||
\(698\) | −503552. | − | 503552.i | −1.03355 | − | 1.03355i | ||||
\(699\) | − | 51866.6i | − | 0.106153i | ||||||
\(700\) | −99918.9 | − | 491758.i | −0.203916 | − | 1.00359i | ||||
\(701\) | 809809. | 1.64796 | 0.823980 | − | 0.566619i | \(-0.191749\pi\) | ||||
0.823980 | + | 0.566619i | \(0.191749\pi\) | |||||||
\(702\) | 157218. | − | 157218.i | 0.319028 | − | 0.319028i | ||||
\(703\) | 75085.9 | + | 75085.9i | 0.151931 | + | 0.151931i | ||||
\(704\) | 1.16961e6i | 2.35992i | ||||||||
\(705\) | −52594.8 | + | 174673.i | −0.105819 | + | 0.351436i | ||||
\(706\) | 76270.0 | 0.153019 | ||||||||
\(707\) | −98883.4 | + | 98883.4i | −0.197827 | + | 0.197827i | ||||
\(708\) | −67499.4 | − | 67499.4i | −0.134658 | − | 0.134658i | ||||
\(709\) | − | 204474.i | − | 0.406768i | −0.979099 | − | 0.203384i | \(-0.934806\pi\) | ||
0.979099 | − | 0.203384i | \(-0.0651939\pi\) | |||||||
\(710\) | 631622. | + | 1.17587e6i | 1.25297 | + | 2.33260i | ||||
\(711\) | −6648.57 | −0.0131519 | ||||||||
\(712\) | −1.81358e6 | + | 1.81358e6i | −3.57748 | + | 3.57748i | ||||
\(713\) | 21695.1 | + | 21695.1i | 0.0426758 | + | 0.0426758i | ||||
\(714\) | − | 135534.i | − | 0.265858i | ||||||
\(715\) | −169600. | + | 91101.8i | −0.331753 | + | 0.178203i | ||||
\(716\) | 57769.9 | 0.112687 | ||||||||
\(717\) | −143654. | + | 143654.i | −0.279435 | + | 0.279435i | ||||
\(718\) | 1.10064e6 | + | 1.10064e6i | 2.13499 | + | 2.13499i | ||||
\(719\) | 603232.i | 1.16688i | 0.812156 | + | 0.583441i | \(0.198294\pi\) | ||||
−0.812156 | + | 0.583441i | \(0.801706\pi\) | |||||||
\(720\) | 1.71971e6 | + | 517813.i | 3.31734 | + | 0.998867i | ||||
\(721\) | −173958. | −0.334637 | ||||||||
\(722\) | −683831. | + | 683831.i | −1.31182 | + | 1.31182i | ||||
\(723\) | 86158.0 | + | 86158.0i | 0.164823 | + | 0.164823i | ||||
\(724\) | − | 544835.i | − | 1.03941i | ||||||
\(725\) | −202364. | + | 305569.i | −0.384996 | + | 0.581344i | ||||
\(726\) | 118824. | 0.225441 | ||||||||
\(727\) | −277495. | + | 277495.i | −0.525033 | + | 0.525033i | −0.919087 | − | 0.394054i | \(-0.871072\pi\) |
0.394054 | + | 0.919087i | \(0.371072\pi\) | |||||||
\(728\) | 260412. | + | 260412.i | 0.491359 | + | 0.491359i | ||||
\(729\) | 390041.i | 0.733932i | ||||||||
\(730\) | 64638.0 | − | 214669.i | 0.121295 | − | 0.402832i | ||||
\(731\) | −919959. | −1.72161 | ||||||||
\(732\) | 201016. | − | 201016.i | 0.375154 | − | 0.375154i | ||||
\(733\) | −602150. | − | 602150.i | −1.12072 | − | 1.12072i | −0.991634 | − | 0.129085i | \(-0.958796\pi\) |
−0.129085 | − | 0.991634i | \(-0.541204\pi\) | |||||||
\(734\) | − | 1.38039e6i | − | 2.56218i | ||||||
\(735\) | −7841.08 | − | 14597.4i | −0.0145145 | − | 0.0270210i | ||||
\(736\) | 215884. | 0.398533 | ||||||||
\(737\) | 150168. | − | 150168.i | 0.276466 | − | 0.276466i | ||||
\(738\) | 33690.5 | + | 33690.5i | 0.0618578 | + | 0.0618578i | ||||
\(739\) | 510748.i | 0.935228i | 0.883933 | + | 0.467614i | \(0.154886\pi\) | ||||
−0.883933 | + | 0.467614i | \(0.845114\pi\) | |||||||
\(740\) | 1.46467e6 | − | 786755.i | 2.67471 | − | 1.43673i | ||||
\(741\) | −12622.6 | −0.0229885 | ||||||||
\(742\) | 265948. | − | 265948.i | 0.483046 | − | 0.483046i | ||||
\(743\) | 483448. | + | 483448.i | 0.875735 | + | 0.875735i | 0.993090 | − | 0.117355i | \(-0.0374416\pi\) |
−0.117355 | + | 0.993090i | \(0.537442\pi\) | |||||||
\(744\) | 219407.i | 0.396374i | ||||||||
\(745\) | −88662.6 | − | 26696.7i | −0.159745 | − | 0.0481000i | ||||
\(746\) | −1.20795e6 | −2.17055 | ||||||||
\(747\) | 548624. | − | 548624.i | 0.983181 | − | 0.983181i | ||||
\(748\) | −1.22970e6 | − | 1.22970e6i | −2.19784 | − | 2.19784i | ||||
\(749\) | − | 22605.4i | − | 0.0402947i | ||||||
\(750\) | 178897. | − | 148671.i | 0.318039 | − | 0.264305i | ||||
\(751\) | −803929. | −1.42540 | −0.712702 | − | 0.701467i | \(-0.752529\pi\) | ||||
−0.712702 | + | 0.701467i | \(0.752529\pi\) | |||||||
\(752\) | 2.48255e6 | − | 2.48255e6i | 4.38998 | − | 4.38998i | ||||
\(753\) | −112828. | − | 112828.i | −0.198988 | − | 0.198988i | ||||
\(754\) | − | 426321.i | − | 0.749883i | ||||||
\(755\) | 164265. | − | 545539.i | 0.288171 | − | 0.957045i | ||||
\(756\) | 245546. | 0.429625 | ||||||||
\(757\) | −137325. | + | 137325.i | −0.239640 | + | 0.239640i | −0.816701 | − | 0.577061i | \(-0.804199\pi\) |
0.577061 | + | 0.816701i | \(0.304199\pi\) | |||||||
\(758\) | −779536. | − | 779536.i | −1.35674 | − | 1.35674i | ||||
\(759\) | 8978.90i | 0.0155862i | ||||||||
\(760\) | −172557. | − | 321242.i | −0.298748 | − | 0.556168i | ||||
\(761\) | −410285. | −0.708462 | −0.354231 | − | 0.935158i | \(-0.615257\pi\) | ||||
−0.354231 | + | 0.935158i | \(0.615257\pi\) | |||||||
\(762\) | −142250. | + | 142250.i | −0.244987 | + | 0.244987i | ||||
\(763\) | −12184.1 | − | 12184.1i | −0.0209288 | − | 0.0209288i | ||||
\(764\) | 524074.i | 0.897854i | ||||||||
\(765\) | −836512. | + | 449337.i | −1.42939 | + | 0.767802i | ||||
\(766\) | 532747. | 0.907954 | ||||||||
\(767\) | −76036.8 | + | 76036.8i | −0.129251 | + | 0.129251i | ||||
\(768\) | 210438. | + | 210438.i | 0.356781 | + | 0.356781i | ||||
\(769\) | 306046.i | 0.517529i | 0.965941 | + | 0.258764i | \(0.0833153\pi\) | ||||
−0.965941 | + | 0.258764i | \(0.916685\pi\) | |||||||
\(770\) | −278722. | − | 83924.6i | −0.470100 | − | 0.141549i | ||||
\(771\) | 144710. | 0.243439 | ||||||||
\(772\) | −456925. | + | 456925.i | −0.766673 | + | 0.766673i | ||||
\(773\) | 746945. | + | 746945.i | 1.25006 | + | 1.25006i | 0.955694 | + | 0.294363i | \(0.0951074\pi\) |
0.294363 | + | 0.955694i | \(0.404893\pi\) | |||||||
\(774\) | − | 1.11399e6i | − | 1.85952i | ||||||
\(775\) | −280781. | − | 185948.i | −0.467482 | − | 0.309591i | ||||
\(776\) | −2.37477e6 | −3.94364 | ||||||||
\(777\) | 38820.5 | − | 38820.5i | 0.0643011 | − | 0.0643011i | ||||
\(778\) | 636336. | + | 636336.i | 1.05130 | + | 1.05130i | ||||
\(779\) | − | 5540.53i | − | 0.00913011i | ||||||
\(780\) | −56981.5 | + | 189241.i | −0.0936579 | + | 0.311048i | ||||
\(781\) | 565537. | 0.927168 | ||||||||
\(782\) | −152481. | + | 152481.i | −0.249346 | + | 0.249346i | ||||
\(783\) | −126811. | − | 126811.i | −0.206840 | − | 0.206840i | ||||
\(784\) | 318909.i | 0.518841i | ||||||||
\(785\) | −86181.3 | − | 160440.i | −0.139854 | − | 0.260360i | ||||
\(786\) | −256597. | −0.415343 | ||||||||
\(787\) | −834040. | + | 834040.i | −1.34660 | + | 1.34660i | −0.457265 | + | 0.889330i | \(0.651171\pi\) |
−0.889330 | + | 0.457265i | \(0.848829\pi\) | |||||||
\(788\) | 295304. | + | 295304.i | 0.475573 | + | 0.475573i | ||||
\(789\) | 67212.7i | 0.107969i | ||||||||
\(790\) | 14599.9 | − | 7842.41i | 0.0233935 | − | 0.0125660i | ||||
\(791\) | 285678. | 0.456587 | ||||||||
\(792\) | 939490. | − | 939490.i | 1.49776 | − | 1.49776i | ||||
\(793\) | −226441. | − | 226441.i | −0.360088 | − | 0.360088i | ||||
\(794\) | − | 39299.2i | − | 0.0623365i | ||||||
\(795\) | 121936. | + | 36715.4i | 0.192929 | + | 0.0580917i | ||||
\(796\) | 789935. | 1.24671 | ||||||||
\(797\) | −346993. | + | 346993.i | −0.546267 | + | 0.546267i | −0.925359 | − | 0.379092i | \(-0.876236\pi\) |
0.379092 | + | 0.925359i | \(0.376236\pi\) | |||||||
\(798\) | −13495.0 | − | 13495.0i | −0.0211918 | − | 0.0211918i | ||||
\(799\) | 1.85623e6i | 2.90763i | ||||||||
\(800\) | −2.32217e6 | + | 471835.i | −3.62839 | + | 0.737242i | ||||
\(801\) | 940446. | 1.46578 | ||||||||
\(802\) | 105561. | − | 105561.i | 0.164117 | − | 0.164117i | ||||
\(803\) | −67166.9 | − | 67166.9i | −0.104166 | − | 0.104166i | ||||
\(804\) | − | 218011.i | − | 0.337261i | ||||||
\(805\) | −7601.16 | + | 25244.3i | −0.0117297 | + | 0.0389557i | ||||
\(806\) | 391738. | 0.603011 | ||||||||
\(807\) | −68007.4 | + | 68007.4i | −0.104426 | + | 0.104426i | ||||
\(808\) | 1.12508e6 | + | 1.12508e6i | 1.72330 | + | 1.72330i | ||||
\(809\) | − | 633306.i | − | 0.967646i | −0.875166 | − | 0.483823i | \(-0.839248\pi\) | ||
0.875166 | − | 0.483823i | \(-0.160752\pi\) | |||||||
\(810\) | −516543. | − | 961626.i | −0.787292 | − | 1.46567i | ||||
\(811\) | 730234. | 1.11025 | 0.555124 | − | 0.831767i | \(-0.312671\pi\) | ||||
0.555124 | + | 0.831767i | \(0.312671\pi\) | |||||||
\(812\) | 332918. | − | 332918.i | 0.504923 | − | 0.504923i | ||||
\(813\) | 53405.0 | + | 53405.0i | 0.0807980 | + | 0.0807980i | ||||
\(814\) | − | 964426.i | − | 1.45553i | ||||||
\(815\) | −635401. | + | 341309.i | −0.956604 | + | 0.513845i | ||||
\(816\) | −883191. | −1.32640 | ||||||||
\(817\) | −91600.1 | + | 91600.1i | −0.137231 | + | 0.137231i | ||||
\(818\) | 1.56695e6 | + | 1.56695e6i | 2.34180 | + | 2.34180i | ||||
\(819\) | − | 135039.i | − | 0.201322i | ||||||
\(820\) | −83065.4 | − | 25011.4i | −0.123536 | − | 0.0371972i | ||||
\(821\) | 804907. | 1.19415 | 0.597075 | − | 0.802185i | \(-0.296329\pi\) | ||||
0.597075 | + | 0.802185i | \(0.296329\pi\) | |||||||
\(822\) | −140554. | + | 140554.i | −0.208018 | + | 0.208018i | ||||
\(823\) | 12469.2 | + | 12469.2i | 0.0184094 | + | 0.0184094i | 0.716252 | − | 0.697842i | \(-0.245856\pi\) |
−0.697842 | + | 0.716252i | \(0.745856\pi\) | |||||||
\(824\) | 1.97927e6i | 2.91508i | ||||||||
\(825\) | −19624.3 | − | 96582.3i | −0.0288327 | − | 0.141902i | ||||
\(826\) | −162585. | −0.238298 | ||||||||
\(827\) | −447005. | + | 447005.i | −0.653585 | + | 0.653585i | −0.953854 | − | 0.300270i | \(-0.902923\pi\) |
0.300270 | + | 0.953854i | \(0.402923\pi\) | |||||||
\(828\) | −134866. | − | 134866.i | −0.196717 | − | 0.196717i | ||||
\(829\) | − | 93265.9i | − | 0.135711i | −0.997695 | − | 0.0678553i | \(-0.978384\pi\) | ||
0.997695 | − | 0.0678553i | \(-0.0216156\pi\) | |||||||
\(830\) | −557611. | + | 1.85188e6i | −0.809422 | + | 2.68818i | ||||
\(831\) | −80469.1 | −0.116527 | ||||||||
\(832\) | 956396. | − | 956396.i | 1.38163 | − | 1.38163i | ||||
\(833\) | −119226. | − | 119226.i | −0.171823 | − | 0.171823i | ||||
\(834\) | − | 388959.i | − | 0.559207i | ||||||
\(835\) | −520934. | − | 969802.i | −0.747154 | − | 1.39095i | ||||
\(836\) | −244882. | −0.350383 | ||||||||
\(837\) | 116525. | − | 116525.i | 0.166328 | − | 0.166328i | ||||
\(838\) | 58586.5 | + | 58586.5i | 0.0834275 | + | 0.0834275i | ||||
\(839\) | − | 1.14987e6i | − | 1.63353i | −0.576972 | − | 0.816764i | \(-0.695766\pi\) | ||
0.576972 | − | 0.816764i | \(-0.304234\pi\) | |||||||
\(840\) | −166087. | + | 89214.4i | −0.235384 | + | 0.126438i | ||||
\(841\) | 363413. | 0.513817 | ||||||||
\(842\) | −715031. | + | 715031.i | −1.00856 | + | 1.00856i | ||||
\(843\) | 207586. | + | 207586.i | 0.292107 | + | 0.292107i | ||||
\(844\) | 1.36892e6i | 1.92174i | ||||||||
\(845\) | −470527. | − | 141678.i | −0.658978 | − | 0.198421i | ||||
\(846\) | −2.24774e6 | −3.14055 | ||||||||
\(847\) | 104527. | − | 104527.i | 0.145701 | − | 0.145701i | ||||
\(848\) | −1.73302e6 | − | 1.73302e6i | −2.40997 | − | 2.40997i | ||||
\(849\) | 208192.i | 0.288835i | ||||||||
\(850\) | 1.30691e6 | − | 1.97344e6i | 1.80888 | − | 2.73140i | ||||
\(851\) | −87349.4 | −0.120615 | ||||||||
\(852\) | 410518. | − | 410518.i | 0.565527 | − | 0.565527i | ||||
\(853\) | −623474. | − | 623474.i | −0.856881 | − | 0.856881i | 0.134088 | − | 0.990969i | \(-0.457189\pi\) |
−0.990969 | + | 0.134088i | \(0.957189\pi\) | |||||||
\(854\) | − | 484186.i | − | 0.663891i | ||||||
\(855\) | −38550.9 | + | 128032.i | −0.0527354 | + | 0.175140i | ||||
\(856\) | −257200. | −0.351014 | ||||||||
\(857\) | 226049. | − | 226049.i | 0.307780 | − | 0.307780i | −0.536268 | − | 0.844048i | \(-0.680166\pi\) |
0.844048 | + | 0.536268i | \(0.180166\pi\) | |||||||
\(858\) | 81064.0 | + | 81064.0i | 0.110117 | + | 0.110117i | ||||
\(859\) | − | 557243.i | − | 0.755193i | −0.925970 | − | 0.377597i | \(-0.876751\pi\) | ||
0.925970 | − | 0.377597i | \(-0.123249\pi\) | |||||||
\(860\) | 959792. | + | 1.78680e6i | 1.29772 | + | 2.41591i | ||||
\(861\) | −2864.53 | −0.00386409 | ||||||||
\(862\) | 1.26989e6 | − | 1.26989e6i | 1.70904 | − | 1.70904i | ||||
\(863\) | 287700. | + | 287700.i | 0.386295 | + | 0.386295i | 0.873364 | − | 0.487069i | \(-0.161934\pi\) |
−0.487069 | + | 0.873364i | \(0.661934\pi\) | |||||||
\(864\) | − | 1.15951e6i | − | 1.55328i | ||||||
\(865\) | 538770. | − | 289403.i | 0.720064 | − | 0.386786i | ||||
\(866\) | 780782. | 1.04110 | ||||||||
\(867\) | 216064. | − | 216064.i | 0.287439 | − | 0.287439i | ||||
\(868\) | 305912. | + | 305912.i | 0.406029 | + | 0.406029i | ||||
\(869\) | − | 7021.87i | − | 0.00929851i | ||||||
\(870\) | 208977. | + | 62923.9i | 0.276096 | + | 0.0831337i | ||||
\(871\) | −245585. | −0.323717 | ||||||||
\(872\) | −138628. | + | 138628.i | −0.182314 | + | 0.182314i | ||||
\(873\) | 615726. | + | 615726.i | 0.807903 | + | 0.807903i | ||||
\(874\) | 30365.0i | 0.0397512i | ||||||||
\(875\) | 26588.7 | − | 288155.i | 0.0347281 | − | 0.376366i | ||||
\(876\) | −97511.7 | −0.127072 | ||||||||
\(877\) | −34920.8 | + | 34920.8i | −0.0454031 | + | 0.0454031i | −0.729444 | − | 0.684041i | \(-0.760221\pi\) |
0.684041 | + | 0.729444i | \(0.260221\pi\) | |||||||
\(878\) | −1.63210e6 | − | 1.63210e6i | −2.11718 | − | 2.11718i | ||||
\(879\) | − | 97440.8i | − | 0.126114i | ||||||
\(880\) | −546886. | + | 1.81627e6i | −0.706206 | + | 2.34538i | ||||
\(881\) | 575336. | 0.741258 | 0.370629 | − | 0.928781i | \(-0.379142\pi\) | ||||
0.370629 | + | 0.928781i | \(0.379142\pi\) | |||||||
\(882\) | 144373. | − | 144373.i | 0.185587 | − | 0.185587i | ||||
\(883\) | −313204. | − | 313204.i | −0.401704 | − | 0.401704i | 0.477129 | − | 0.878833i | \(-0.341677\pi\) |
−0.878833 | + | 0.477129i | \(0.841677\pi\) | |||||||
\(884\) | 2.01106e6i | 2.57347i | ||||||||
\(885\) | −26049.4 | − | 48495.1i | −0.0332591 | − | 0.0619172i | ||||
\(886\) | −1.40590e6 | −1.79096 | ||||||||
\(887\) | 740797. | − | 740797.i | 0.941569 | − | 0.941569i | −0.0568158 | − | 0.998385i | \(-0.518095\pi\) |
0.998385 | + | 0.0568158i | \(0.0180948\pi\) | |||||||
\(888\) | −441693. | − | 441693.i | −0.560137 | − | 0.560137i | ||||
\(889\) | 250269.i | 0.316668i | ||||||||
\(890\) | −2.06517e6 | + | 1.10932e6i | −2.60720 | + | 1.40047i | ||||
\(891\) | −462497. | −0.582578 | ||||||||
\(892\) | −931768. | + | 931768.i | −1.17106 | + | 1.17106i | ||||
\(893\) | 184825. | + | 184825.i | 0.231770 | + | 0.231770i | ||||
\(894\) | 55138.3i | 0.0689888i | ||||||||
\(895\) | 31899.7 | + | 9605.16i | 0.0398236 | + | 0.0119911i | ||||
\(896\) | 921526. | 1.14787 | ||||||||
\(897\) | 7342.07 | − | 7342.07i | 0.00912502 | − | 0.00912502i | ||||
\(898\) | 1.31741e6 | + | 1.31741e6i | 1.63369 | + | 1.63369i | ||||
\(899\) | − | 315974.i | − | 0.390959i | ||||||
\(900\) | 1.74546e6 | + | 1.15594e6i | 2.15489 | + | 1.42708i | ||||
\(901\) | 1.29580e6 | 1.59621 | ||||||||
\(902\) | −35582.1 | + | 35582.1i | −0.0437339 | + | 0.0437339i | ||||
\(903\) | 47358.5 | + | 47358.5i | 0.0580795 | + | 0.0580795i | ||||
\(904\) | − | 3.25039e6i | − | 3.97740i | ||||||
\(905\) | 90587.5 | − | 300850.i | 0.110604 | − | 0.367328i | ||||
\(906\) | −339265. | −0.413317 | ||||||||
\(907\) | −663473. | + | 663473.i | −0.806508 | + | 0.806508i | −0.984104 | − | 0.177596i | \(-0.943168\pi\) |
0.177596 | + | 0.984104i | \(0.443168\pi\) | |||||||
\(908\) | 46.3051 | + | 46.3051i | 5.61639e−5 | + | 5.61639e-5i | ||||
\(909\) | − | 583418.i | − | 0.706076i | ||||||
\(910\) | 159287. | + | 296537.i | 0.192352 | + | 0.358094i | ||||
\(911\) | −1.32279e6 | −1.59388 | −0.796938 | − | 0.604061i | \(-0.793548\pi\) | ||||
−0.796938 | + | 0.604061i | \(0.793548\pi\) | |||||||
\(912\) | −87939.1 | + | 87939.1i | −0.105729 | + | 0.105729i | ||||
\(913\) | 579428. | + | 579428.i | 0.695117 | + | 0.695117i | ||||
\(914\) | − | 1.60140e6i | − | 1.91694i | ||||||
\(915\) | 144421. | − | 77576.3i | 0.172499 | − | 0.0926588i | ||||
\(916\) | 2.66986e6 | 3.18198 | ||||||||
\(917\) | −225723. | + | 225723.i | −0.268434 | + | 0.268434i | ||||
\(918\) | 818978. | + | 818978.i | 0.971823 | + | 0.971823i | ||||
\(919\) | − | 1.11696e6i | − | 1.32253i | −0.750153 | − | 0.661265i | \(-0.770020\pi\) | ||
0.750153 | − | 0.661265i | \(-0.229980\pi\) | |||||||
\(920\) | 287225. | + | 86484.8i | 0.339349 | + | 0.102180i | ||||
\(921\) | 167200. | 0.197114 | ||||||||
\(922\) | −1.35460e6 | + | 1.35460e6i | −1.59349 | + | 1.59349i | ||||
\(923\) | −462441. | − | 462441.i | −0.542816 | − | 0.542816i | ||||
\(924\) | 126607.i | 0.148291i | ||||||||
\(925\) | 939581. | − | 190911.i | 1.09812 | − | 0.223124i | ||||
\(926\) | 1.69931e6 | 1.98176 | ||||||||
\(927\) | 513182. | − | 513182.i | 0.597189 | − | 0.597189i | ||||
\(928\) | −1.57210e6 | − | 1.57210e6i | −1.82551 | − | 1.82551i | ||||
\(929\) | − | 262969.i | − | 0.304701i | −0.988327 | − | 0.152350i | \(-0.951316\pi\) | ||
0.988327 | − | 0.152350i | \(-0.0486842\pi\) | |||||||
\(930\) | −57819.5 | + | 192025.i | −0.0668511 | + | 0.222019i | ||||
\(931\) | −23742.6 | −0.0273923 | ||||||||
\(932\) | −822795. | + | 822795.i | −0.947240 | + | 0.947240i | ||||
\(933\) | −195599. | − | 195599.i | −0.224700 | − | 0.224700i | ||||
\(934\) | 2.28981e6i | 2.62485i | ||||||||
\(935\) | −474566. | − | 883480.i | −0.542842 | − | 1.01059i | ||||
\(936\) | −1.53645e6 | −1.75374 | ||||||||
\(937\) | −89677.3 | + | 89677.3i | −0.102142 | + | 0.102142i | −0.756331 | − | 0.654189i | \(-0.773010\pi\) |
0.654189 | + | 0.756331i | \(0.273010\pi\) | |||||||
\(938\) | −262560. | − | 262560.i | −0.298417 | − | 0.298417i | ||||
\(939\) | − | 95119.8i | − | 0.107880i | ||||||
\(940\) | 3.60530e6 | − | 1.93661e6i | 4.08024 | − | 2.19172i | ||||
\(941\) | −13096.5 | −0.0147902 | −0.00739512 | − | 0.999973i | \(-0.502354\pi\) | ||||
−0.00739512 | + | 0.999973i | \(0.502354\pi\) | |||||||
\(942\) | −76685.6 | + | 76685.6i | −0.0864196 | + | 0.0864196i | ||||
\(943\) | 3222.72 | + | 3222.72i | 0.00362409 | + | 0.00362409i | ||||
\(944\) | 1.05947e6i | 1.18890i | ||||||||
\(945\) | 135587. | + | 40826.0i | 0.151829 | + | 0.0457165i | ||||
\(946\) | 1.17654e6 | 1.31469 | ||||||||
\(947\) | 974672. | − | 974672.i | 1.08682 | − | 1.08682i | 0.0909682 | − | 0.995854i | \(-0.471004\pi\) |
0.995854 | − | 0.0909682i | \(-0.0289962\pi\) | |||||||
\(948\) | −5097.11 | − | 5097.11i | −0.00567163 | − | 0.00567163i | ||||
\(949\) | 109845.i | 0.121969i | ||||||||
\(950\) | −66365.7 | − | 326623.i | −0.0735354 | − | 0.361910i | ||||
\(951\) | −53330.1 | −0.0589673 | ||||||||
\(952\) | −1.35654e6 | + | 1.35654e6i | −1.49678 | + | 1.49678i | ||||
\(953\) | 292946. | + | 292946.i | 0.322553 | + | 0.322553i | 0.849746 | − | 0.527193i | \(-0.176755\pi\) |
−0.527193 | + | 0.849746i | \(0.676755\pi\) | |||||||
\(954\) | 1.56911e6i | 1.72407i | ||||||||
\(955\) | −87135.6 | + | 289386.i | −0.0955407 | + | 0.317301i | ||||
\(956\) | 4.55778e6 | 4.98698 | ||||||||
\(957\) | 65385.8 | − | 65385.8i | 0.0713936 | − | 0.0713936i | ||||
\(958\) | 1.13390e6 | + | 1.13390e6i | 1.23550 | + | 1.23550i | ||||
\(959\) | 247286.i | 0.268882i | ||||||||
\(960\) | 327651. | + | 609975.i | 0.355524 | + | 0.661865i | ||||
\(961\) | −633179. | −0.685614 | ||||||||
\(962\) | −788614. | + | 788614.i | −0.852146 | + | 0.852146i | ||||
\(963\) | 66686.5 | + | 66686.5i | 0.0719094 | + | 0.0719094i | ||||
\(964\) | − | 2.73357e6i | − | 2.94155i | ||||||
\(965\) | −328278. | + | 176337.i | −0.352523 | + | 0.189360i | ||||
\(966\) | 15699.1 | 0.0168237 | ||||||||
\(967\) | −1.07763e6 | + | 1.07763e6i | −1.15244 | + | 1.15244i | −0.166378 | + | 0.986062i | \(0.553207\pi\) |
−0.986062 | + | 0.166378i | \(0.946793\pi\) | |||||||
\(968\) | −1.18930e6 | − | 1.18930e6i | −1.26923 | − | 1.26923i | ||||
\(969\) | − | 65753.2i | − | 0.0700276i | ||||||
\(970\) | −2.07839e6 | − | 625812.i | −2.20894 | − | 0.665121i | ||||
\(971\) | −1.61563e6 | −1.71357 | −0.856787 | − | 0.515670i | \(-0.827543\pi\) | ||||
−0.856787 | + | 0.515670i | \(0.827543\pi\) | |||||||
\(972\) | −1.09510e6 | + | 1.09510e6i | −1.15910 | + | 1.15910i | ||||
\(973\) | −342160. | − | 342160.i | −0.361413 | − | 0.361413i | ||||
\(974\) | 430733.i | 0.454036i | ||||||||
\(975\) | −62928.8 | + | 95022.4i | −0.0661973 | + | 0.0999578i | ||||
\(976\) | −3.15515e6 | −3.31223 | ||||||||
\(977\) | −824838. | + | 824838.i | −0.864131 | + | 0.864131i | −0.991815 | − | 0.127684i | \(-0.959246\pi\) |
0.127684 | + | 0.991815i | \(0.459246\pi\) | |||||||
\(978\) | 303702. | + | 303702.i | 0.317520 | + | 0.317520i | ||||
\(979\) | 993249.i | 1.03632i | ||||||||
\(980\) | −107180. | + | 355957.i | −0.111600 | + | 0.370634i | ||||
\(981\) | 71886.7 | 0.0746983 | ||||||||
\(982\) | 255653. | − | 255653.i | 0.265111 | − | 0.265111i | ||||
\(983\) | −203625. | − | 203625.i | −0.210729 | − | 0.210729i | 0.593848 | − | 0.804577i | \(-0.297608\pi\) |
−0.804577 | + | 0.593848i | \(0.797608\pi\) | |||||||
\(984\) | 32592.1i | 0.0336607i | ||||||||
\(985\) | 113964. | + | 212162.i | 0.117461 | + | 0.218673i | ||||
\(986\) | 2.22078e6 | 2.28429 | ||||||||
\(987\) | 95557.0 | − | 95557.0i | 0.0980908 | − | 0.0980908i | ||||
\(988\) | 200240. | + | 200240.i | 0.205134 | + | 0.205134i | ||||
\(989\) | − | 106561.i | − | 0.108944i | ||||||
\(990\) | 1.06982e6 | − | 574659.i | 1.09154 | − | 0.586326i | ||||
\(991\) | 1.10847e6 | 1.12870 | 0.564348 | − | 0.825537i | \(-0.309128\pi\) | ||||
0.564348 | + | 0.825537i | \(0.309128\pi\) | |||||||
\(992\) | 1.44457e6 | − | 1.44457e6i | 1.46796 | − | 1.46796i | ||||
\(993\) | −57766.9 | − | 57766.9i | −0.0585842 | − | 0.0585842i | ||||
\(994\) | − | 988810.i | − | 1.00078i | ||||||
\(995\) | 436191. | + | 131339.i | 0.440586 | + | 0.132662i | ||||
\(996\) | 841203. | 0.847973 | ||||||||
\(997\) | 994907. | − | 994907.i | 1.00090 | − | 1.00090i | 0.000903760 | − | 1.00000i | \(-0.499712\pi\) |
1.00000 | 0.000903760i | \(-0.000287676\pi\) | ||||||||
\(998\) | −2.58446e6 | − | 2.58446e6i | −2.59483 | − | 2.59483i | ||||
\(999\) | 469155.i | 0.470095i |
(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 | 35.5.g.a.8.1 | ✓ | 24 | |
5.2 | odd | 4 | inner | 35.5.g.a.22.1 | yes | 24 | |
5.3 | odd | 4 | 175.5.g.c.57.12 | 24 | |||
5.4 | even | 2 | 175.5.g.c.43.12 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.5.g.a.8.1 | ✓ | 24 | 1.1 | even | 1 | trivial | |
35.5.g.a.22.1 | yes | 24 | 5.2 | odd | 4 | inner | |
175.5.g.c.43.12 | 24 | 5.4 | even | 2 | |||
175.5.g.c.57.12 | 24 | 5.3 | odd | 4 |