Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,5,Mod(7,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("15.7");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.f (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: | \(1.55054944626\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 60x^{5} + 1973x^{4} - 3300x^{3} + 1800x^{2} + 31560x + 276676 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 7.4 | ||
Root | \(3.80336 + 3.80336i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 15.7 |
Dual form | 15.5.f.a.13.4 |
$q$-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 \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(11\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.80336 | + | 3.80336i | 0.950841 | + | 0.950841i | 0.998847 | − | 0.0480062i | \(-0.0152867\pi\) |
−0.0480062 | + | 0.998847i | \(0.515287\pi\) | |||||||
\(3\) | −3.67423 | + | 3.67423i | −0.408248 | + | 0.408248i | ||||
\(4\) | 12.9311i | 0.808197i | ||||||||
\(5\) | 6.56915 | − | 24.1215i | 0.262766 | − | 0.964860i | ||||
\(6\) | −27.9489 | −0.776358 | ||||||||
\(7\) | 16.6149 | + | 16.6149i | 0.339079 | + | 0.339079i | 0.856021 | − | 0.516941i | \(-0.172929\pi\) |
−0.516941 | + | 0.856021i | \(0.672929\pi\) | |||||||
\(8\) | 11.6720 | − | 11.6720i | 0.182374 | − | 0.182374i | ||||
\(9\) | − | 27.0000i | − | 0.333333i | ||||||
\(10\) | 116.728 | − | 66.7579i | 1.16728 | − | 0.667579i | ||||
\(11\) | −215.278 | −1.77916 | −0.889580 | − | 0.456779i | \(-0.849003\pi\) | ||||
−0.889580 | + | 0.456779i | \(0.849003\pi\) | |||||||
\(12\) | −47.5121 | − | 47.5121i | −0.329945 | − | 0.329945i | ||||
\(13\) | −29.9347 | + | 29.9347i | −0.177128 | + | 0.177128i | −0.790103 | − | 0.612975i | \(-0.789973\pi\) |
0.612975 | + | 0.790103i | \(0.289973\pi\) | |||||||
\(14\) | 126.385i | 0.644821i | ||||||||
\(15\) | 64.4914 | + | 112.765i | 0.286628 | + | 0.501176i | ||||
\(16\) | 295.684 | 1.15501 | ||||||||
\(17\) | −3.97694 | − | 3.97694i | −0.0137611 | − | 0.0137611i | 0.700193 | − | 0.713954i | \(-0.253097\pi\) |
−0.713954 | + | 0.700193i | \(0.753097\pi\) | |||||||
\(18\) | 102.691 | − | 102.691i | 0.316947 | − | 0.316947i | ||||
\(19\) | 604.349i | 1.67410i | 0.547128 | + | 0.837049i | \(0.315721\pi\) | ||||
−0.547128 | + | 0.837049i | \(0.684279\pi\) | |||||||
\(20\) | 311.919 | + | 84.9467i | 0.779796 | + | 0.212367i | ||||
\(21\) | −122.094 | −0.276857 | ||||||||
\(22\) | −818.782 | − | 818.782i | −1.69170 | − | 1.69170i | ||||
\(23\) | 376.379 | − | 376.379i | 0.711491 | − | 0.711491i | −0.255356 | − | 0.966847i | \(-0.582193\pi\) |
0.966847 | + | 0.255356i | \(0.0821926\pi\) | |||||||
\(24\) | 85.7710i | 0.148908i | ||||||||
\(25\) | −538.692 | − | 316.916i | −0.861908 | − | 0.507065i | ||||
\(26\) | −227.705 | −0.336841 | ||||||||
\(27\) | 99.2043 | + | 99.2043i | 0.136083 | + | 0.136083i | ||||
\(28\) | −214.850 | + | 214.850i | −0.274043 | + | 0.274043i | ||||
\(29\) | − | 624.166i | − | 0.742171i | −0.928599 | − | 0.371086i | \(-0.878986\pi\) | ||
0.928599 | − | 0.371086i | \(-0.121014\pi\) | |||||||
\(30\) | −183.601 | + | 674.169i | −0.204001 | + | 0.749077i | ||||
\(31\) | 263.888 | 0.274597 | 0.137299 | − | 0.990530i | \(-0.456158\pi\) | ||||
0.137299 | + | 0.990530i | \(0.456158\pi\) | |||||||
\(32\) | 937.842 | + | 937.842i | 0.915861 | + | 0.915861i | ||||
\(33\) | 790.983 | − | 790.983i | 0.726339 | − | 0.726339i | ||||
\(34\) | − | 30.2515i | − | 0.0261691i | ||||||
\(35\) | 509.922 | − | 291.630i | 0.416263 | − | 0.238065i | ||||
\(36\) | 349.141 | 0.269399 | ||||||||
\(37\) | 979.613 | + | 979.613i | 0.715568 | + | 0.715568i | 0.967694 | − | 0.252126i | \(-0.0811298\pi\) |
−0.252126 | + | 0.967694i | \(0.581130\pi\) | |||||||
\(38\) | −2298.56 | + | 2298.56i | −1.59180 | + | 1.59180i | ||||
\(39\) | − | 219.974i | − | 0.144625i | ||||||
\(40\) | −204.870 | − | 358.220i | −0.128044 | − | 0.223887i | ||||
\(41\) | −1579.25 | −0.939468 | −0.469734 | − | 0.882808i | \(-0.655650\pi\) | ||||
−0.469734 | + | 0.882808i | \(0.655650\pi\) | |||||||
\(42\) | −464.368 | − | 464.368i | −0.263247 | − | 0.263247i | ||||
\(43\) | −30.8409 | + | 30.8409i | −0.0166797 | + | 0.0166797i | −0.715397 | − | 0.698718i | \(-0.753754\pi\) |
0.698718 | + | 0.715397i | \(0.253754\pi\) | |||||||
\(44\) | − | 2783.80i | − | 1.43791i | ||||||
\(45\) | −651.280 | − | 177.367i | −0.321620 | − | 0.0875887i | ||||
\(46\) | 2863.01 | 1.35303 | ||||||||
\(47\) | 1785.16 | + | 1785.16i | 0.808129 | + | 0.808129i | 0.984351 | − | 0.176221i | \(-0.0563874\pi\) |
−0.176221 | + | 0.984351i | \(0.556387\pi\) | |||||||
\(48\) | −1086.41 | + | 1086.41i | −0.471533 | + | 0.471533i | ||||
\(49\) | − | 1848.89i | − | 0.770050i | ||||||
\(50\) | −843.498 | − | 3254.19i | −0.337399 | − | 1.30168i | ||||
\(51\) | 29.2245 | 0.0112359 | ||||||||
\(52\) | −387.089 | − | 387.089i | −0.143154 | − | 0.143154i | ||||
\(53\) | 707.912 | − | 707.912i | 0.252016 | − | 0.252016i | −0.569781 | − | 0.821797i | \(-0.692972\pi\) |
0.821797 | + | 0.569781i | \(0.192972\pi\) | |||||||
\(54\) | 754.620i | 0.258786i | ||||||||
\(55\) | −1414.20 | + | 5192.84i | −0.467503 | + | 1.71664i | ||||
\(56\) | 387.857 | 0.123679 | ||||||||
\(57\) | −2220.52 | − | 2220.52i | −0.683448 | − | 0.683448i | ||||
\(58\) | 2373.93 | − | 2373.93i | 0.705687 | − | 0.705687i | ||||
\(59\) | 1366.84i | 0.392657i | 0.980538 | + | 0.196329i | \(0.0629020\pi\) | ||||
−0.980538 | + | 0.196329i | \(0.937098\pi\) | |||||||
\(60\) | −1458.18 | + | 833.948i | −0.405049 | + | 0.231652i | ||||
\(61\) | −2983.71 | −0.801856 | −0.400928 | − | 0.916110i | \(-0.631312\pi\) | ||||
−0.400928 | + | 0.916110i | \(0.631312\pi\) | |||||||
\(62\) | 1003.66 | + | 1003.66i | 0.261098 | + | 0.261098i | ||||
\(63\) | 448.602 | − | 448.602i | 0.113026 | − | 0.113026i | ||||
\(64\) | 2402.96i | 0.586661i | ||||||||
\(65\) | 525.423 | + | 918.714i | 0.124361 | + | 0.217447i | ||||
\(66\) | 6016.80 | 1.38127 | ||||||||
\(67\) | −986.003 | − | 986.003i | −0.219649 | − | 0.219649i | 0.588702 | − | 0.808350i | \(-0.299639\pi\) |
−0.808350 | + | 0.588702i | \(0.799639\pi\) | |||||||
\(68\) | 51.4265 | − | 51.4265i | 0.0111216 | − | 0.0111216i | ||||
\(69\) | 2765.81i | 0.580930i | ||||||||
\(70\) | 3048.59 | + | 830.242i | 0.622162 | + | 0.169437i | ||||
\(71\) | 68.0686 | 0.0135030 | 0.00675150 | − | 0.999977i | \(-0.497851\pi\) | ||||
0.00675150 | + | 0.999977i | \(0.497851\pi\) | |||||||
\(72\) | −315.143 | − | 315.143i | −0.0607914 | − | 0.0607914i | ||||
\(73\) | 2476.90 | − | 2476.90i | 0.464797 | − | 0.464797i | −0.435427 | − | 0.900224i | \(-0.643403\pi\) |
0.900224 | + | 0.435427i | \(0.143403\pi\) | |||||||
\(74\) | 7451.65i | 1.36078i | ||||||||
\(75\) | 3143.70 | − | 814.860i | 0.558881 | − | 0.144864i | ||||
\(76\) | −7814.93 | −1.35300 | ||||||||
\(77\) | −3576.83 | − | 3576.83i | −0.603277 | − | 0.603277i | ||||
\(78\) | 836.641 | − | 836.641i | 0.137515 | − | 0.137515i | ||||
\(79\) | − | 6047.25i | − | 0.968955i | −0.874804 | − | 0.484478i | \(-0.839010\pi\) | ||
0.874804 | − | 0.484478i | \(-0.160990\pi\) | |||||||
\(80\) | 1942.39 | − | 7132.33i | 0.303499 | − | 1.11443i | ||||
\(81\) | −729.000 | −0.111111 | ||||||||
\(82\) | −6006.45 | − | 6006.45i | −0.893285 | − | 0.893285i | ||||
\(83\) | −5158.95 | + | 5158.95i | −0.748868 | + | 0.748868i | −0.974267 | − | 0.225398i | \(-0.927632\pi\) |
0.225398 | + | 0.974267i | \(0.427632\pi\) | |||||||
\(84\) | − | 1578.82i | − | 0.223755i | ||||||
\(85\) | −122.055 | + | 69.8047i | −0.0168934 | + | 0.00966154i | ||||
\(86\) | −234.598 | −0.0317196 | ||||||||
\(87\) | 2293.33 | + | 2293.33i | 0.302990 | + | 0.302990i | ||||
\(88\) | −2512.72 | + | 2512.72i | −0.324473 | + | 0.324473i | ||||
\(89\) | − | 7028.50i | − | 0.887325i | −0.896194 | − | 0.443662i | \(-0.853679\pi\) | ||
0.896194 | − | 0.443662i | \(-0.146321\pi\) | |||||||
\(90\) | −1802.46 | − | 3151.65i | −0.222526 | − | 0.389092i | ||||
\(91\) | −994.722 | −0.120121 | ||||||||
\(92\) | 4867.01 | + | 4867.01i | 0.575025 | + | 0.575025i | ||||
\(93\) | −969.586 | + | 969.586i | −0.112104 | + | 0.112104i | ||||
\(94\) | 13579.2i | 1.53681i | ||||||||
\(95\) | 14577.8 | + | 3970.06i | 1.61527 | + | 0.439896i | ||||
\(96\) | −6891.70 | −0.747797 | ||||||||
\(97\) | 10869.3 | + | 10869.3i | 1.15520 | + | 1.15520i | 0.985495 | + | 0.169703i | \(0.0542810\pi\) |
0.169703 | + | 0.985495i | \(0.445719\pi\) | |||||||
\(98\) | 7032.00 | − | 7032.00i | 0.732195 | − | 0.732195i | ||||
\(99\) | 5812.52i | 0.593054i | ||||||||
\(100\) | 4098.08 | − | 6965.91i | 0.409808 | − | 0.696591i | ||||
\(101\) | −4043.94 | −0.396426 | −0.198213 | − | 0.980159i | \(-0.563514\pi\) | ||||
−0.198213 | + | 0.980159i | \(0.563514\pi\) | |||||||
\(102\) | 111.151 | + | 111.151i | 0.0106835 | + | 0.0106835i | ||||
\(103\) | −119.716 | + | 119.716i | −0.0112844 | + | 0.0112844i | −0.712726 | − | 0.701442i | \(-0.752540\pi\) |
0.701442 | + | 0.712726i | \(0.252540\pi\) | |||||||
\(104\) | 698.792i | 0.0646073i | ||||||||
\(105\) | −802.054 | + | 2945.09i | −0.0727487 | + | 0.267128i | ||||
\(106\) | 5384.89 | 0.479254 | ||||||||
\(107\) | −8330.41 | − | 8330.41i | −0.727610 | − | 0.727610i | 0.242533 | − | 0.970143i | \(-0.422022\pi\) |
−0.970143 | + | 0.242533i | \(0.922022\pi\) | |||||||
\(108\) | −1282.83 | + | 1282.83i | −0.109982 | + | 0.109982i | ||||
\(109\) | − | 8380.72i | − | 0.705389i | −0.935739 | − | 0.352694i | \(-0.885266\pi\) | ||
0.935739 | − | 0.352694i | \(-0.114734\pi\) | |||||||
\(110\) | −25128.9 | + | 14371.5i | −2.07677 | + | 1.18773i | ||||
\(111\) | −7198.66 | −0.584259 | ||||||||
\(112\) | 4912.75 | + | 4912.75i | 0.391642 | + | 0.391642i | ||||
\(113\) | 968.067 | − | 968.067i | 0.0758139 | − | 0.0758139i | −0.668183 | − | 0.743997i | \(-0.732928\pi\) |
0.743997 | + | 0.668183i | \(0.232928\pi\) | |||||||
\(114\) | − | 16890.9i | − | 1.29970i | ||||||
\(115\) | −6606.33 | − | 11551.3i | −0.499533 | − | 0.873445i | ||||
\(116\) | 8071.19 | 0.599821 | ||||||||
\(117\) | 808.236 | + | 808.236i | 0.0590427 | + | 0.0590427i | ||||
\(118\) | −5198.59 | + | 5198.59i | −0.373355 | + | 0.373355i | ||||
\(119\) | − | 132.153i | − | 0.00933218i | ||||||
\(120\) | 2068.92 | + | 563.443i | 0.143675 | + | 0.0391280i | ||||
\(121\) | 31703.8 | 2.16541 | ||||||||
\(122\) | −11348.1 | − | 11348.1i | −0.762437 | − | 0.762437i | ||||
\(123\) | 5802.52 | − | 5802.52i | 0.383536 | − | 0.383536i | ||||
\(124\) | 3412.37i | 0.221929i | ||||||||
\(125\) | −11183.2 | + | 10912.2i | −0.715727 | + | 0.698381i | ||||
\(126\) | 3412.39 | 0.214940 | ||||||||
\(127\) | −12023.3 | − | 12023.3i | −0.745446 | − | 0.745446i | 0.228174 | − | 0.973620i | \(-0.426724\pi\) |
−0.973620 | + | 0.228174i | \(0.926724\pi\) | |||||||
\(128\) | 5866.12 | − | 5866.12i | 0.358039 | − | 0.358039i | ||||
\(129\) | − | 226.633i | − | 0.0136190i | ||||||
\(130\) | −1495.83 | + | 5492.58i | −0.0885105 | + | 0.325005i | ||||
\(131\) | 4866.47 | 0.283577 | 0.141789 | − | 0.989897i | \(-0.454715\pi\) | ||||
0.141789 | + | 0.989897i | \(0.454715\pi\) | |||||||
\(132\) | 10228.3 | + | 10228.3i | 0.587025 | + | 0.587025i | ||||
\(133\) | −10041.2 | + | 10041.2i | −0.567652 | + | 0.567652i | ||||
\(134\) | − | 7500.26i | − | 0.417702i | ||||||
\(135\) | 3044.64 | − | 1741.27i | 0.167059 | − | 0.0955428i | ||||
\(136\) | −92.8374 | −0.00501933 | ||||||||
\(137\) | 10167.9 | + | 10167.9i | 0.541736 | + | 0.541736i | 0.924038 | − | 0.382301i | \(-0.124868\pi\) |
−0.382301 | + | 0.924038i | \(0.624868\pi\) | |||||||
\(138\) | −10519.4 | + | 10519.4i | −0.552372 | + | 0.552372i | ||||
\(139\) | − | 4195.51i | − | 0.217148i | −0.994088 | − | 0.108574i | \(-0.965372\pi\) | ||
0.994088 | − | 0.108574i | \(-0.0346284\pi\) | |||||||
\(140\) | 3771.11 | + | 6593.87i | 0.192404 | + | 0.336422i | ||||
\(141\) | −13118.2 | −0.659835 | ||||||||
\(142\) | 258.890 | + | 258.890i | 0.0128392 | + | 0.0128392i | ||||
\(143\) | 6444.29 | − | 6444.29i | 0.315139 | − | 0.315139i | ||||
\(144\) | − | 7983.46i | − | 0.385005i | ||||||
\(145\) | −15055.8 | − | 4100.24i | −0.716091 | − | 0.195018i | ||||
\(146\) | 18841.1 | 0.883895 | ||||||||
\(147\) | 6793.26 | + | 6793.26i | 0.314372 | + | 0.314372i | ||||
\(148\) | −12667.5 | + | 12667.5i | −0.578320 | + | 0.578320i | ||||
\(149\) | 24880.4i | 1.12069i | 0.828259 | + | 0.560345i | \(0.189331\pi\) | ||||
−0.828259 | + | 0.560345i | \(0.810669\pi\) | |||||||
\(150\) | 15055.9 | + | 8857.44i | 0.669149 | + | 0.393664i | ||||
\(151\) | −37791.8 | −1.65746 | −0.828732 | − | 0.559645i | \(-0.810937\pi\) | ||||
−0.828732 | + | 0.559645i | \(0.810937\pi\) | |||||||
\(152\) | 7053.94 | + | 7053.94i | 0.305312 | + | 0.305312i | ||||
\(153\) | −107.377 | + | 107.377i | −0.00458702 | + | 0.00458702i | ||||
\(154\) | − | 27208.0i | − | 1.14724i | ||||||
\(155\) | 1733.52 | − | 6365.37i | 0.0721548 | − | 0.264948i | ||||
\(156\) | 2844.52 | 0.116885 | ||||||||
\(157\) | 18627.8 | + | 18627.8i | 0.755723 | + | 0.755723i | 0.975541 | − | 0.219818i | \(-0.0705463\pi\) |
−0.219818 | + | 0.975541i | \(0.570546\pi\) | |||||||
\(158\) | 22999.9 | − | 22999.9i | 0.921322 | − | 0.921322i | ||||
\(159\) | 5202.07i | 0.205770i | ||||||||
\(160\) | 28783.0 | − | 16461.3i | 1.12433 | − | 0.643020i | ||||
\(161\) | 12507.0 | 0.482504 | ||||||||
\(162\) | −2772.65 | − | 2772.65i | −0.105649 | − | 0.105649i | ||||
\(163\) | −280.411 | + | 280.411i | −0.0105541 | + | 0.0105541i | −0.712364 | − | 0.701810i | \(-0.752376\pi\) |
0.701810 | + | 0.712364i | \(0.252376\pi\) | |||||||
\(164\) | − | 20421.5i | − | 0.759275i | ||||||
\(165\) | −13883.6 | − | 24275.8i | −0.509958 | − | 0.891673i | ||||
\(166\) | −39242.8 | −1.42411 | ||||||||
\(167\) | −25855.1 | − | 25855.1i | −0.927073 | − | 0.927073i | 0.0704428 | − | 0.997516i | \(-0.477559\pi\) |
−0.997516 | + | 0.0704428i | \(0.977559\pi\) | |||||||
\(168\) | −1425.08 | + | 1425.08i | −0.0504916 | + | 0.0504916i | ||||
\(169\) | 26768.8i | 0.937251i | ||||||||
\(170\) | −729.712 | − | 198.727i | −0.0252495 | − | 0.00687636i | ||||
\(171\) | 16317.4 | 0.558033 | ||||||||
\(172\) | −398.808 | − | 398.808i | −0.0134805 | − | 0.0134805i | ||||
\(173\) | −31991.2 | + | 31991.2i | −1.06890 | + | 1.06890i | −0.0714600 | + | 0.997443i | \(0.522766\pi\) |
−0.997443 | + | 0.0714600i | \(0.977234\pi\) | |||||||
\(174\) | 17444.8i | 0.576191i | ||||||||
\(175\) | −3684.80 | − | 14215.8i | −0.120320 | − | 0.464190i | ||||
\(176\) | −63654.3 | −2.05496 | ||||||||
\(177\) | −5022.09 | − | 5022.09i | −0.160302 | − | 0.160302i | ||||
\(178\) | 26731.9 | − | 26731.9i | 0.843705 | − | 0.843705i | ||||
\(179\) | 17987.8i | 0.561400i | 0.959796 | + | 0.280700i | \(0.0905666\pi\) | ||||
−0.959796 | + | 0.280700i | \(0.909433\pi\) | |||||||
\(180\) | 2293.56 | − | 8421.80i | 0.0707889 | − | 0.259932i | ||||
\(181\) | 23072.1 | 0.704255 | 0.352127 | − | 0.935952i | \(-0.385458\pi\) | ||||
0.352127 | + | 0.935952i | \(0.385458\pi\) | |||||||
\(182\) | −3783.29 | − | 3783.29i | −0.114216 | − | 0.114216i | ||||
\(183\) | 10962.8 | − | 10962.8i | 0.327356 | − | 0.327356i | ||||
\(184\) | − | 8786.16i | − | 0.259515i | ||||||
\(185\) | 30065.0 | − | 17194.5i | 0.878450 | − | 0.502396i | ||||
\(186\) | −7375.38 | −0.213186 | ||||||||
\(187\) | 856.150 | + | 856.150i | 0.0244831 | + | 0.0244831i | ||||
\(188\) | −23084.1 | + | 23084.1i | −0.653128 | + | 0.653128i | ||||
\(189\) | 3296.54i | 0.0922857i | ||||||||
\(190\) | 40345.1 | + | 70544.3i | 1.11759 | + | 1.95414i | ||||
\(191\) | 51892.0 | 1.42244 | 0.711220 | − | 0.702970i | \(-0.248143\pi\) | ||||
0.711220 | + | 0.702970i | \(0.248143\pi\) | |||||||
\(192\) | −8829.06 | − | 8829.06i | −0.239503 | − | 0.239503i | ||||
\(193\) | 50542.0 | − | 50542.0i | 1.35687 | − | 1.35687i | 0.479118 | − | 0.877751i | \(-0.340957\pi\) |
0.877751 | − | 0.479118i | \(-0.159043\pi\) | |||||||
\(194\) | 82679.5i | 2.19682i | ||||||||
\(195\) | −5306.10 | − | 1445.04i | −0.139542 | − | 0.0380024i | ||||
\(196\) | 23908.3 | 0.622352 | ||||||||
\(197\) | −22327.7 | − | 22327.7i | −0.575323 | − | 0.575323i | 0.358288 | − | 0.933611i | \(-0.383360\pi\) |
−0.933611 | + | 0.358288i | \(0.883360\pi\) | |||||||
\(198\) | −22107.1 | + | 22107.1i | −0.563900 | + | 0.563900i | ||||
\(199\) | 57027.8i | 1.44006i | 0.693943 | + | 0.720030i | \(0.255872\pi\) | ||||
−0.693943 | + | 0.720030i | \(0.744128\pi\) | |||||||
\(200\) | −9986.62 | + | 2588.57i | −0.249665 | + | 0.0647143i | ||||
\(201\) | 7245.61 | 0.179342 | ||||||||
\(202\) | −15380.6 | − | 15380.6i | −0.376938 | − | 0.376938i | ||||
\(203\) | 10370.5 | − | 10370.5i | 0.251655 | − | 0.251655i | ||||
\(204\) | 377.906i | 0.00908078i | ||||||||
\(205\) | −10374.3 | + | 38093.8i | −0.246860 | + | 0.906455i | ||||
\(206\) | −910.647 | −0.0214593 | ||||||||
\(207\) | −10162.2 | − | 10162.2i | −0.237164 | − | 0.237164i | ||||
\(208\) | −8851.19 | + | 8851.19i | −0.204586 | + | 0.204586i | ||||
\(209\) | − | 130103.i | − | 2.97849i | ||||||
\(210\) | −14251.7 | + | 8150.74i | −0.323169 | + | 0.184824i | ||||
\(211\) | −50695.3 | −1.13868 | −0.569341 | − | 0.822101i | \(-0.692802\pi\) | ||||
−0.569341 | + | 0.822101i | \(0.692802\pi\) | |||||||
\(212\) | 9154.12 | + | 9154.12i | 0.203678 | + | 0.203678i | ||||
\(213\) | −250.100 | + | 250.100i | −0.00551258 | + | 0.00551258i | ||||
\(214\) | − | 63367.1i | − | 1.38368i | ||||||
\(215\) | 541.329 | + | 946.526i | 0.0117107 | + | 0.0204765i | ||||
\(216\) | 2315.82 | 0.0496360 | ||||||||
\(217\) | 4384.47 | + | 4384.47i | 0.0931102 | + | 0.0931102i | ||||
\(218\) | 31874.9 | − | 31874.9i | 0.670712 | − | 0.670712i | ||||
\(219\) | 18201.4i | 0.379505i | ||||||||
\(220\) | −67149.3 | − | 18287.2i | −1.38738 | − | 0.377835i | ||||
\(221\) | 238.097 | 0.00487494 | ||||||||
\(222\) | −27379.1 | − | 27379.1i | −0.555537 | − | 0.555537i | ||||
\(223\) | −18991.4 | + | 18991.4i | −0.381898 | + | 0.381898i | −0.871786 | − | 0.489888i | \(-0.837038\pi\) |
0.489888 | + | 0.871786i | \(0.337038\pi\) | |||||||
\(224\) | 31164.3i | 0.621099i | ||||||||
\(225\) | −8556.72 | + | 14544.7i | −0.169022 | + | 0.287303i | ||||
\(226\) | 7363.82 | 0.144174 | ||||||||
\(227\) | 24016.1 | + | 24016.1i | 0.466069 | + | 0.466069i | 0.900638 | − | 0.434570i | \(-0.143100\pi\) |
−0.434570 | + | 0.900638i | \(0.643100\pi\) | |||||||
\(228\) | 28713.9 | − | 28713.9i | 0.552360 | − | 0.552360i | ||||
\(229\) | − | 4953.50i | − | 0.0944586i | −0.998884 | − | 0.0472293i | \(-0.984961\pi\) | ||
0.998884 | − | 0.0472293i | \(-0.0150391\pi\) | |||||||
\(230\) | 18807.6 | − | 69060.1i | 0.355530 | − | 1.30548i | ||||
\(231\) | 26284.2 | 0.492573 | ||||||||
\(232\) | −7285.24 | − | 7285.24i | −0.135353 | − | 0.135353i | ||||
\(233\) | −60878.5 | + | 60878.5i | −1.12138 | + | 1.12138i | −0.129844 | + | 0.991534i | \(0.541448\pi\) |
−0.991534 | + | 0.129844i | \(0.958552\pi\) | |||||||
\(234\) | 6148.03i | 0.112280i | ||||||||
\(235\) | 54787.6 | − | 31333.7i | 0.992080 | − | 0.567382i | ||||
\(236\) | −17674.8 | −0.317345 | ||||||||
\(237\) | 22219.0 | + | 22219.0i | 0.395574 | + | 0.395574i | ||||
\(238\) | 502.626 | − | 502.626i | 0.00887342 | − | 0.00887342i | ||||
\(239\) | 40609.0i | 0.710929i | 0.934690 | + | 0.355464i | \(0.115677\pi\) | ||||
−0.934690 | + | 0.355464i | \(0.884323\pi\) | |||||||
\(240\) | 19069.1 | + | 33342.7i | 0.331060 | + | 0.578866i | ||||
\(241\) | 24443.6 | 0.420854 | 0.210427 | − | 0.977610i | \(-0.432515\pi\) | ||||
0.210427 | + | 0.977610i | \(0.432515\pi\) | |||||||
\(242\) | 120581. | + | 120581.i | 2.05896 | + | 2.05896i | ||||
\(243\) | 2678.52 | − | 2678.52i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | − | 38582.7i | − | 0.648057i | ||||||
\(245\) | −44598.0 | − | 12145.6i | −0.742990 | − | 0.202343i | ||||
\(246\) | 44138.2 | 0.729364 | ||||||||
\(247\) | −18091.0 | − | 18091.0i | −0.296530 | − | 0.296530i | ||||
\(248\) | 3080.09 | − | 3080.09i | 0.0500795 | − | 0.0500795i | ||||
\(249\) | − | 37910.4i | − | 0.611448i | ||||||
\(250\) | −84036.9 | − | 1030.83i | −1.34459 | − | 0.0164932i | ||||
\(251\) | −71951.0 | −1.14206 | −0.571030 | − | 0.820929i | \(-0.693456\pi\) | ||||
−0.571030 | + | 0.820929i | \(0.693456\pi\) | |||||||
\(252\) | 5800.94 | + | 5800.94i | 0.0913476 | + | 0.0913476i | ||||
\(253\) | −81026.3 | + | 81026.3i | −1.26586 | + | 1.26586i | ||||
\(254\) | − | 91457.9i | − | 1.41760i | ||||||
\(255\) | 191.980 | − | 704.937i | 0.00295240 | − | 0.0108410i | ||||
\(256\) | 83069.4 | 1.26754 | ||||||||
\(257\) | 33507.3 | + | 33507.3i | 0.507310 | + | 0.507310i | 0.913700 | − | 0.406390i | \(-0.133213\pi\) |
−0.406390 | + | 0.913700i | \(0.633213\pi\) | |||||||
\(258\) | 861.968 | − | 861.968i | 0.0129495 | − | 0.0129495i | ||||
\(259\) | 32552.3i | 0.485269i | ||||||||
\(260\) | −11880.0 | + | 6794.32i | −0.175740 | + | 0.100508i | ||||
\(261\) | −16852.5 | −0.247390 | ||||||||
\(262\) | 18508.9 | + | 18508.9i | 0.269637 | + | 0.269637i | ||||
\(263\) | −18051.0 | + | 18051.0i | −0.260969 | + | 0.260969i | −0.825448 | − | 0.564479i | \(-0.809077\pi\) |
0.564479 | + | 0.825448i | \(0.309077\pi\) | |||||||
\(264\) | − | 18464.6i | − | 0.264931i | ||||||
\(265\) | −12425.5 | − | 21726.3i | −0.176939 | − | 0.309381i | ||||
\(266\) | −76380.6 | −1.07949 | ||||||||
\(267\) | 25824.4 | + | 25824.4i | 0.362249 | + | 0.362249i | ||||
\(268\) | 12750.2 | − | 12750.2i | 0.177519 | − | 0.177519i | ||||
\(269\) | − | 90057.7i | − | 1.24456i | −0.782794 | − | 0.622281i | \(-0.786206\pi\) | ||
0.782794 | − | 0.622281i | \(-0.213794\pi\) | |||||||
\(270\) | 18202.6 | + | 4957.22i | 0.249692 | + | 0.0680002i | ||||
\(271\) | 28019.1 | 0.381518 | 0.190759 | − | 0.981637i | \(-0.438905\pi\) | ||||
0.190759 | + | 0.981637i | \(0.438905\pi\) | |||||||
\(272\) | −1175.92 | − | 1175.92i | −0.0158942 | − | 0.0158942i | ||||
\(273\) | 3654.84 | − | 3654.84i | 0.0490392 | − | 0.0490392i | ||||
\(274\) | 77344.1i | 1.03021i | ||||||||
\(275\) | 115969. | + | 68225.1i | 1.53347 | + | 0.902150i | ||||
\(276\) | −35765.1 | −0.469506 | ||||||||
\(277\) | −77139.7 | − | 77139.7i | −1.00535 | − | 1.00535i | −0.999986 | − | 0.00536651i | \(-0.998292\pi\) |
−0.00536651 | − | 0.999986i | \(-0.501708\pi\) | |||||||
\(278\) | 15957.1 | − | 15957.1i | 0.206473 | − | 0.206473i | ||||
\(279\) | − | 7124.97i | − | 0.0915324i | ||||||
\(280\) | 2547.89 | − | 9355.68i | 0.0324986 | − | 0.119333i | ||||
\(281\) | 59704.3 | 0.756125 | 0.378062 | − | 0.925780i | \(-0.376591\pi\) | ||||
0.378062 | + | 0.925780i | \(0.376591\pi\) | |||||||
\(282\) | −49893.2 | − | 49893.2i | −0.627398 | − | 0.627398i | ||||
\(283\) | 71516.3 | − | 71516.3i | 0.892960 | − | 0.892960i | −0.101841 | − | 0.994801i | \(-0.532473\pi\) |
0.994801 | + | 0.101841i | \(0.0324733\pi\) | |||||||
\(284\) | 880.205i | 0.0109131i | ||||||||
\(285\) | −68149.2 | + | 38975.3i | −0.839018 | + | 0.479844i | ||||
\(286\) | 49019.9 | 0.599295 | ||||||||
\(287\) | −26239.0 | − | 26239.0i | −0.318554 | − | 0.318554i | ||||
\(288\) | 25321.7 | − | 25321.7i | 0.305287 | − | 0.305287i | ||||
\(289\) | − | 83489.4i | − | 0.999621i | ||||||
\(290\) | −41668.0 | − | 72857.5i | −0.495458 | − | 0.866319i | ||||
\(291\) | −79872.5 | −0.943216 | ||||||||
\(292\) | 32029.2 | + | 32029.2i | 0.375647 | + | 0.375647i | ||||
\(293\) | 2048.52 | − | 2048.52i | 0.0238619 | − | 0.0238619i | −0.695075 | − | 0.718937i | \(-0.744629\pi\) |
0.718937 | + | 0.695075i | \(0.244629\pi\) | |||||||
\(294\) | 51674.5i | 0.597835i | ||||||||
\(295\) | 32970.2 | + | 8978.99i | 0.378859 | + | 0.103177i | ||||
\(296\) | 22868.0 | 0.261003 | ||||||||
\(297\) | −21356.6 | − | 21356.6i | −0.242113 | − | 0.242113i | ||||
\(298\) | −94629.4 | + | 94629.4i | −1.06560 | + | 1.06560i | ||||
\(299\) | 22533.5i | 0.252050i | ||||||||
\(300\) | 10537.1 | + | 40651.7i | 0.117079 | + | 0.451686i | ||||
\(301\) | −1024.83 | −0.0113115 | ||||||||
\(302\) | −143736. | − | 143736.i | −1.57598 | − | 1.57598i | ||||
\(303\) | 14858.4 | − | 14858.4i | 0.161840 | − | 0.161840i | ||||
\(304\) | 178696.i | 1.93361i | ||||||||
\(305\) | −19600.4 | + | 71971.4i | −0.210701 | + | 0.773678i | ||||
\(306\) | −816.791 | −0.00872305 | ||||||||
\(307\) | −28977.5 | − | 28977.5i | −0.307457 | − | 0.307457i | 0.536465 | − | 0.843922i | \(-0.319759\pi\) |
−0.843922 | + | 0.536465i | \(0.819759\pi\) | |||||||
\(308\) | 46252.5 | − | 46252.5i | 0.487566 | − | 0.487566i | ||||
\(309\) | − | 879.729i | − | 0.00921366i | ||||||
\(310\) | 30803.0 | − | 17616.6i | 0.320531 | − | 0.183315i | ||||
\(311\) | −20134.0 | −0.208166 | −0.104083 | − | 0.994569i | \(-0.533191\pi\) | ||||
−0.104083 | + | 0.994569i | \(0.533191\pi\) | |||||||
\(312\) | −2567.53 | − | 2567.53i | −0.0263758 | − | 0.0263758i | ||||
\(313\) | 115839. | − | 115839.i | 1.18240 | − | 1.18240i | 0.203283 | − | 0.979120i | \(-0.434839\pi\) |
0.979120 | − | 0.203283i | \(-0.0651611\pi\) | |||||||
\(314\) | 141697.i | 1.43715i | ||||||||
\(315\) | −7874.01 | − | 13767.9i | −0.0793551 | − | 0.138754i | ||||
\(316\) | 78197.9 | 0.783106 | ||||||||
\(317\) | 56563.1 | + | 56563.1i | 0.562879 | + | 0.562879i | 0.930124 | − | 0.367245i | \(-0.119699\pi\) |
−0.367245 | + | 0.930124i | \(0.619699\pi\) | |||||||
\(318\) | −19785.4 | + | 19785.4i | −0.195655 | + | 0.195655i | ||||
\(319\) | 134370.i | 1.32044i | ||||||||
\(320\) | 57963.1 | + | 15785.4i | 0.566046 | + | 0.154155i | ||||
\(321\) | 61215.7 | 0.594091 | ||||||||
\(322\) | 47568.6 | + | 47568.6i | 0.458785 | + | 0.458785i | ||||
\(323\) | 2403.46 | − | 2403.46i | 0.0230373 | − | 0.0230373i | ||||
\(324\) | − | 9426.81i | − | 0.0897996i | ||||||
\(325\) | 25612.3 | − | 6638.82i | 0.242484 | − | 0.0628527i | ||||
\(326\) | −2133.01 | −0.0200705 | ||||||||
\(327\) | 30792.7 | + | 30792.7i | 0.287974 | + | 0.287974i | ||||
\(328\) | −18432.9 | + | 18432.9i | −0.171335 | + | 0.171335i | ||||
\(329\) | 59320.4i | 0.548040i | ||||||||
\(330\) | 39525.3 | − | 145134.i | 0.362950 | − | 1.33273i | ||||
\(331\) | −76249.8 | −0.695958 | −0.347979 | − | 0.937502i | \(-0.613132\pi\) | ||||
−0.347979 | + | 0.937502i | \(0.613132\pi\) | |||||||
\(332\) | −66711.2 | − | 66711.2i | −0.605233 | − | 0.605233i | ||||
\(333\) | 26449.6 | − | 26449.6i | 0.238523 | − | 0.238523i | ||||
\(334\) | − | 196673.i | − | 1.76300i | ||||||
\(335\) | −30261.1 | + | 17306.7i | −0.269646 | + | 0.154214i | ||||
\(336\) | −36101.2 | −0.319774 | ||||||||
\(337\) | 88861.9 | + | 88861.9i | 0.782448 | + | 0.782448i | 0.980243 | − | 0.197795i | \(-0.0633780\pi\) |
−0.197795 | + | 0.980243i | \(0.563378\pi\) | |||||||
\(338\) | −101812. | + | 101812.i | −0.891177 | + | 0.891177i | ||||
\(339\) | 7113.81i | 0.0619018i | ||||||||
\(340\) | −902.654 | − | 1578.31i | −0.00780843 | − | 0.0136532i | ||||
\(341\) | −56809.4 | −0.488552 | ||||||||
\(342\) | 62061.1 | + | 62061.1i | 0.530600 | + | 0.530600i | ||||
\(343\) | 70611.5 | − | 70611.5i | 0.600188 | − | 0.600188i | ||||
\(344\) | 719.946i | 0.00608392i | ||||||||
\(345\) | 66715.4 | + | 18169.0i | 0.560516 | + | 0.152649i | ||||
\(346\) | −243348. | −2.03271 | ||||||||
\(347\) | −41523.5 | − | 41523.5i | −0.344854 | − | 0.344854i | 0.513334 | − | 0.858189i | \(-0.328410\pi\) |
−0.858189 | + | 0.513334i | \(0.828410\pi\) | |||||||
\(348\) | −29655.4 | + | 29655.4i | −0.244876 | + | 0.244876i | ||||
\(349\) | − | 94995.3i | − | 0.779922i | −0.920831 | − | 0.389961i | \(-0.872489\pi\) | ||
0.920831 | − | 0.389961i | \(-0.127511\pi\) | |||||||
\(350\) | 40053.3 | − | 68082.6i | 0.326966 | − | 0.555776i | ||||
\(351\) | −5939.30 | −0.0482082 | ||||||||
\(352\) | −201897. | − | 201897.i | −1.62946 | − | 1.62946i | ||||
\(353\) | 54491.3 | − | 54491.3i | 0.437298 | − | 0.437298i | −0.453804 | − | 0.891102i | \(-0.649933\pi\) |
0.891102 | + | 0.453804i | \(0.149933\pi\) | |||||||
\(354\) | − | 38201.7i | − | 0.304843i | ||||||
\(355\) | 447.153 | − | 1641.92i | 0.00354813 | − | 0.0130285i | ||||
\(356\) | 90886.6 | 0.717133 | ||||||||
\(357\) | 485.561 | + | 485.561i | 0.00380985 | + | 0.00380985i | ||||
\(358\) | −68414.2 | + | 68414.2i | −0.533802 | + | 0.533802i | ||||
\(359\) | − | 60457.0i | − | 0.469092i | −0.972105 | − | 0.234546i | \(-0.924640\pi\) | ||
0.972105 | − | 0.234546i | \(-0.0753603\pi\) | |||||||
\(360\) | −9671.94 | + | 5531.49i | −0.0746291 | + | 0.0426813i | ||||
\(361\) | −234917. | −1.80260 | ||||||||
\(362\) | 87751.6 | + | 87751.6i | 0.669634 | + | 0.669634i | ||||
\(363\) | −116487. | + | 116487.i | −0.884026 | + | 0.884026i | ||||
\(364\) | − | 12862.9i | − | 0.0970814i | ||||||
\(365\) | −43475.4 | − | 76017.7i | −0.326331 | − | 0.570596i | ||||
\(366\) | 83391.3 | 0.622527 | ||||||||
\(367\) | 84336.6 | + | 84336.6i | 0.626158 | + | 0.626158i | 0.947099 | − | 0.320941i | \(-0.103999\pi\) |
−0.320941 | + | 0.947099i | \(0.603999\pi\) | |||||||
\(368\) | 111289. | − | 111289.i | 0.821783 | − | 0.821783i | ||||
\(369\) | 42639.7i | 0.313156i | ||||||||
\(370\) | 179745. | + | 48951.0i | 1.31296 | + | 0.357568i | ||||
\(371\) | 23523.8 | 0.170907 | ||||||||
\(372\) | −12537.9 | − | 12537.9i | −0.0906020 | − | 0.0906020i | ||||
\(373\) | −67604.9 | + | 67604.9i | −0.485915 | + | 0.485915i | −0.907015 | − | 0.421099i | \(-0.861644\pi\) |
0.421099 | + | 0.907015i | \(0.361644\pi\) | |||||||
\(374\) | 6512.50i | 0.0465591i | ||||||||
\(375\) | 995.828 | − | 81183.8i | 0.00708145 | − | 0.577307i | ||||
\(376\) | 41672.6 | 0.294764 | ||||||||
\(377\) | 18684.2 | + | 18684.2i | 0.131459 | + | 0.131459i | ||||
\(378\) | −12537.9 | + | 12537.9i | −0.0877490 | + | 0.0877490i | ||||
\(379\) | − | 128651.i | − | 0.895645i | −0.894123 | − | 0.447822i | \(-0.852200\pi\) | ||
0.894123 | − | 0.447822i | \(-0.147800\pi\) | |||||||
\(380\) | −51337.5 | + | 188508.i | −0.355523 | + | 1.30546i | ||||
\(381\) | 88352.8 | 0.608654 | ||||||||
\(382\) | 197364. | + | 197364.i | 1.35251 | + | 1.35251i | ||||
\(383\) | 147476. | − | 147476.i | 1.00536 | − | 1.00536i | 0.00537910 | − | 0.999986i | \(-0.498288\pi\) |
0.999986 | − | 0.00537910i | \(-0.00171223\pi\) | |||||||
\(384\) | 43107.0i | 0.292338i | ||||||||
\(385\) | −109775. | + | 62781.7i | −0.740598 | + | 0.423557i | ||||
\(386\) | 384459. | 2.58033 | ||||||||
\(387\) | 832.703 | + | 832.703i | 0.00555992 | + | 0.00555992i | ||||
\(388\) | −140552. | + | 140552.i | −0.933628 | + | 0.933628i | ||||
\(389\) | 175663.i | 1.16086i | 0.814309 | + | 0.580432i | \(0.197116\pi\) | ||||
−0.814309 | + | 0.580432i | \(0.802884\pi\) | |||||||
\(390\) | −14685.0 | − | 25677.0i | −0.0965483 | − | 0.168817i | ||||
\(391\) | −2993.68 | −0.0195817 | ||||||||
\(392\) | −21580.2 | − | 21580.2i | −0.140437 | − | 0.140437i | ||||
\(393\) | −17880.5 | + | 17880.5i | −0.115770 | + | 0.115770i | ||||
\(394\) | − | 169841.i | − | 1.09408i | ||||||
\(395\) | −145869. | − | 39725.3i | −0.934906 | − | 0.254609i | ||||
\(396\) | −75162.5 | −0.479304 | ||||||||
\(397\) | 59199.8 | + | 59199.8i | 0.375612 | + | 0.375612i | 0.869516 | − | 0.493904i | \(-0.164431\pi\) |
−0.493904 | + | 0.869516i | \(0.664431\pi\) | |||||||
\(398\) | −216897. | + | 216897.i | −1.36927 | + | 1.36927i | ||||
\(399\) | − | 73787.4i | − | 0.463486i | ||||||
\(400\) | −159283. | − | 93706.8i | −0.995516 | − | 0.585667i | ||||
\(401\) | 81929.2 | 0.509507 | 0.254753 | − | 0.967006i | \(-0.418006\pi\) | ||||
0.254753 | + | 0.967006i | \(0.418006\pi\) | |||||||
\(402\) | 27557.7 | + | 27557.7i | 0.170526 | + | 0.170526i | ||||
\(403\) | −7899.39 | + | 7899.39i | −0.0486389 | + | 0.0486389i | ||||
\(404\) | − | 52292.8i | − | 0.320390i | ||||||
\(405\) | −4788.91 | + | 17584.6i | −0.0291962 | + | 0.107207i | ||||
\(406\) | 78885.2 | 0.478568 | ||||||||
\(407\) | −210890. | − | 210890.i | −1.27311 | − | 1.27311i | ||||
\(408\) | 341.107 | − | 341.107i | 0.00204913 | − | 0.00204913i | ||||
\(409\) | 107251.i | 0.641145i | 0.947224 | + | 0.320573i | \(0.103875\pi\) | ||||
−0.947224 | + | 0.320573i | \(0.896125\pi\) | |||||||
\(410\) | −184342. | + | 105427.i | −1.09662 | + | 0.627170i | ||||
\(411\) | −74718.1 | −0.442326 | ||||||||
\(412\) | −1548.07 | − | 1548.07i | −0.00912000 | − | 0.00912000i | ||||
\(413\) | −22709.9 | + | 22709.9i | −0.133142 | + | 0.133142i | ||||
\(414\) | − | 77301.3i | − | 0.451010i | ||||||
\(415\) | 90551.7 | + | 158332.i | 0.525775 | + | 0.919330i | ||||
\(416\) | −56147.9 | −0.324449 | ||||||||
\(417\) | 15415.3 | + | 15415.3i | 0.0886502 | + | 0.0886502i | ||||
\(418\) | 494830. | − | 494830.i | 2.83207 | − | 2.83207i | ||||
\(419\) | − | 25226.4i | − | 0.143690i | −0.997416 | − | 0.0718451i | \(-0.977111\pi\) | ||
0.997416 | − | 0.0718451i | \(-0.0228887\pi\) | |||||||
\(420\) | −38083.4 | − | 10371.5i | −0.215892 | − | 0.0587953i | ||||
\(421\) | 165855. | 0.935762 | 0.467881 | − | 0.883792i | \(-0.345018\pi\) | ||||
0.467881 | + | 0.883792i | \(0.345018\pi\) | |||||||
\(422\) | −192813. | − | 192813.i | −1.08271 | − | 1.08271i | ||||
\(423\) | 48199.3 | − | 48199.3i | 0.269376 | − | 0.269376i | ||||
\(424\) | − | 16525.4i | − | 0.0919224i | ||||||
\(425\) | 881.994 | + | 3402.70i | 0.00488301 | + | 0.0188385i | ||||
\(426\) | −1902.44 | −0.0104832 | ||||||||
\(427\) | −49573.9 | − | 49573.9i | −0.271893 | − | 0.271893i | ||||
\(428\) | 107722. | − | 107722.i | 0.588052 | − | 0.588052i | ||||
\(429\) | 47355.6i | 0.257310i | ||||||||
\(430\) | −1541.11 | + | 5658.85i | −0.00833483 | + | 0.0306049i | ||||
\(431\) | −181899. | −0.979210 | −0.489605 | − | 0.871944i | \(-0.662859\pi\) | ||||
−0.489605 | + | 0.871944i | \(0.662859\pi\) | |||||||
\(432\) | 29333.1 | + | 29333.1i | 0.157178 | + | 0.157178i | ||||
\(433\) | −178342. | + | 178342.i | −0.951214 | + | 0.951214i | −0.998864 | − | 0.0476501i | \(-0.984827\pi\) |
0.0476501 | + | 0.998864i | \(0.484827\pi\) | |||||||
\(434\) | 33351.5i | 0.177066i | ||||||||
\(435\) | 70383.9 | − | 40253.3i | 0.371959 | − | 0.212727i | ||||
\(436\) | 108372. | 0.570093 | ||||||||
\(437\) | 227464. | + | 227464.i | 1.19111 | + | 1.19111i | ||||
\(438\) | −69226.7 | + | 69226.7i | −0.360849 | + | 0.360849i | ||||
\(439\) | 24924.4i | 0.129329i | 0.997907 | + | 0.0646645i | \(0.0205977\pi\) | ||||
−0.997907 | + | 0.0646645i | \(0.979402\pi\) | |||||||
\(440\) | 44104.1 | + | 77117.0i | 0.227811 | + | 0.398332i | ||||
\(441\) | −49920.1 | −0.256683 | ||||||||
\(442\) | 905.569 | + | 905.569i | 0.00463529 | + | 0.00463529i | ||||
\(443\) | −75101.4 | + | 75101.4i | −0.382684 | + | 0.382684i | −0.872068 | − | 0.489384i | \(-0.837222\pi\) |
0.489384 | + | 0.872068i | \(0.337222\pi\) | |||||||
\(444\) | − | 93086.9i | − | 0.472196i | ||||||
\(445\) | −169538. | − | 46171.3i | −0.856144 | − | 0.233159i | ||||
\(446\) | −144462. | −0.726248 | ||||||||
\(447\) | −91416.6 | − | 91416.6i | −0.457520 | − | 0.457520i | ||||
\(448\) | −39925.0 | + | 39925.0i | −0.198925 | + | 0.198925i | ||||
\(449\) | − | 226867.i | − | 1.12533i | −0.826687 | − | 0.562663i | \(-0.809777\pi\) | ||
0.826687 | − | 0.562663i | \(-0.190223\pi\) | |||||||
\(450\) | −87863.1 | + | 22774.5i | −0.433892 | + | 0.112466i | ||||
\(451\) | 339978. | 1.67147 | ||||||||
\(452\) | 12518.2 | + | 12518.2i | 0.0612725 | + | 0.0612725i | ||||
\(453\) | 138856. | − | 138856.i | 0.676657 | − | 0.676657i | ||||
\(454\) | 182684.i | 0.886314i | ||||||||
\(455\) | −6534.48 | + | 23994.2i | −0.0315637 | + | 0.115900i | ||||
\(456\) | −51835.7 | −0.249287 | ||||||||
\(457\) | −3272.88 | − | 3272.88i | −0.0156710 | − | 0.0156710i | 0.699228 | − | 0.714899i | \(-0.253527\pi\) |
−0.714899 | + | 0.699228i | \(0.753527\pi\) | |||||||
\(458\) | 18840.0 | − | 18840.0i | 0.0898151 | − | 0.0898151i | ||||
\(459\) | − | 789.060i | − | 0.00374528i | ||||||
\(460\) | 149372. | − | 85427.4i | 0.705915 | − | 0.403721i | ||||
\(461\) | 94982.0 | 0.446930 | 0.223465 | − | 0.974712i | \(-0.428263\pi\) | ||||
0.223465 | + | 0.974712i | \(0.428263\pi\) | |||||||
\(462\) | 99968.4 | + | 99968.4i | 0.468359 | + | 0.468359i | ||||
\(463\) | −216080. | + | 216080.i | −1.00798 | + | 1.00798i | −0.00801234 | + | 0.999968i | \(0.502550\pi\) |
−0.999968 | + | 0.00801234i | \(0.997450\pi\) | |||||||
\(464\) | − | 184556.i | − | 0.857219i | ||||||
\(465\) | 17018.5 | + | 29757.2i | 0.0787074 | + | 0.137622i | ||||
\(466\) | −463086. | −2.13250 | ||||||||
\(467\) | 7732.59 | + | 7732.59i | 0.0354561 | + | 0.0354561i | 0.724613 | − | 0.689156i | \(-0.242019\pi\) |
−0.689156 | + | 0.724613i | \(0.742019\pi\) | |||||||
\(468\) | −10451.4 | + | 10451.4i | −0.0477181 | + | 0.0477181i | ||||
\(469\) | − | 32764.7i | − | 0.148957i | ||||||
\(470\) | 327551. | + | 89203.9i | 1.48280 | + | 0.403820i | ||||
\(471\) | −136886. | −0.617045 | ||||||||
\(472\) | 15953.7 | + | 15953.7i | 0.0716106 | + | 0.0716106i | ||||
\(473\) | 6639.37 | − | 6639.37i | 0.0296759 | − | 0.0296759i | ||||
\(474\) | 169014.i | 0.752256i | ||||||||
\(475\) | 191528. | − | 325558.i | 0.848876 | − | 1.44292i | ||||
\(476\) | 1708.89 | 0.00754224 | ||||||||
\(477\) | −19113.6 | − | 19113.6i | −0.0840052 | − | 0.0840052i | ||||
\(478\) | −154451. | + | 154451.i | −0.675980 | + | 0.675980i | ||||
\(479\) | 320749.i | 1.39796i | 0.715142 | + | 0.698980i | \(0.246362\pi\) | ||||
−0.715142 | + | 0.698980i | \(0.753638\pi\) | |||||||
\(480\) | −45272.6 | + | 166238.i | −0.196496 | + | 0.721519i | ||||
\(481\) | −58648.8 | −0.253495 | ||||||||
\(482\) | 92967.9 | + | 92967.9i | 0.400165 | + | 0.400165i | ||||
\(483\) | −45953.6 | + | 45953.6i | −0.196981 | + | 0.196981i | ||||
\(484\) | 409967.i | 1.75008i | ||||||||
\(485\) | 333585. | − | 190781.i | 1.41815 | − | 0.811057i | ||||
\(486\) | 20374.7 | 0.0862620 | ||||||||
\(487\) | 5262.88 | + | 5262.88i | 0.0221904 | + | 0.0221904i | 0.718115 | − | 0.695925i | \(-0.245005\pi\) |
−0.695925 | + | 0.718115i | \(0.745005\pi\) | |||||||
\(488\) | −34825.7 | + | 34825.7i | −0.146238 | + | 0.146238i | ||||
\(489\) | − | 2060.59i | − | 0.00861737i | ||||||
\(490\) | −123428. | − | 215817.i | −0.514070 | − | 0.898862i | ||||
\(491\) | 191704. | 0.795183 | 0.397592 | − | 0.917562i | \(-0.369846\pi\) | ||||
0.397592 | + | 0.917562i | \(0.369846\pi\) | |||||||
\(492\) | 75033.3 | + | 75033.3i | 0.309973 | + | 0.309973i | ||||
\(493\) | −2482.27 | + | 2482.27i | −0.0102131 | + | 0.0102131i | ||||
\(494\) | − | 137613.i | − | 0.563905i | ||||||
\(495\) | 140207. | + | 38183.3i | 0.572213 | + | 0.155834i | ||||
\(496\) | 78027.4 | 0.317164 | ||||||||
\(497\) | 1130.95 | + | 1130.95i | 0.00457859 | + | 0.00457859i | ||||
\(498\) | 144187. | − | 144187.i | 0.581390 | − | 0.581390i | ||||
\(499\) | − | 261730.i | − | 1.05112i | −0.850756 | − | 0.525561i | \(-0.823855\pi\) | ||
0.850756 | − | 0.525561i | \(-0.176145\pi\) | |||||||
\(500\) | −141107. | − | 144612.i | −0.564429 | − | 0.578448i | ||||
\(501\) | 189996. | 0.756952 | ||||||||
\(502\) | −273656. | − | 273656.i | −1.08592 | − | 1.08592i | ||||
\(503\) | 206538. | − | 206538.i | 0.816328 | − | 0.816328i | −0.169245 | − | 0.985574i | \(-0.554133\pi\) |
0.985574 | + | 0.169245i | \(0.0541331\pi\) | |||||||
\(504\) | − | 10472.1i | − | 0.0412263i | ||||||
\(505\) | −26565.3 | + | 97545.8i | −0.104167 | + | 0.382495i | ||||
\(506\) | −616345. | −2.40726 | ||||||||
\(507\) | −98355.0 | − | 98355.0i | −0.382631 | − | 0.382631i | ||||
\(508\) | 155475. | − | 155475.i | 0.602467 | − | 0.602467i | ||||
\(509\) | 44082.3i | 0.170149i | 0.996375 | + | 0.0850743i | \(0.0271128\pi\) | ||||
−0.996375 | + | 0.0850743i | \(0.972887\pi\) | |||||||
\(510\) | 3411.30 | − | 1950.96i | 0.0131153 | − | 0.00750082i | ||||
\(511\) | 82306.9 | 0.315206 | ||||||||
\(512\) | 222085. | + | 222085.i | 0.847188 | + | 0.847188i | ||||
\(513\) | −59954.1 | + | 59954.1i | −0.227816 | + | 0.227816i | ||||
\(514\) | 254881.i | 0.964741i | ||||||||
\(515\) | 2101.30 | + | 3674.16i | 0.00792269 | + | 0.0138530i | ||||
\(516\) | 2930.63 | 0.0110068 | ||||||||
\(517\) | −384306. | − | 384306.i | −1.43779 | − | 1.43779i | ||||
\(518\) | −123808. | + | 123808.i | −0.461414 | + | 0.461414i | ||||
\(519\) | − | 235086.i | − | 0.872756i | ||||||
\(520\) | 16855.9 | + | 4590.47i | 0.0623369 | + | 0.0169766i | ||||
\(521\) | −507981. | −1.87142 | −0.935712 | − | 0.352764i | \(-0.885242\pi\) | ||||
−0.935712 | + | 0.352764i | \(0.885242\pi\) | |||||||
\(522\) | −64096.1 | − | 64096.1i | −0.235229 | − | 0.235229i | ||||
\(523\) | −119838. | + | 119838.i | −0.438119 | + | 0.438119i | −0.891378 | − | 0.453260i | \(-0.850261\pi\) |
0.453260 | + | 0.891378i | \(0.350261\pi\) | |||||||
\(524\) | 62929.0i | 0.229186i | ||||||||
\(525\) | 65771.1 | + | 38693.5i | 0.238625 | + | 0.140385i | ||||
\(526\) | −137309. | −0.496280 | ||||||||
\(527\) | −1049.47 | − | 1049.47i | −0.00377875 | − | 0.00377875i | ||||
\(528\) | 233881. | − | 233881.i | 0.838933 | − | 0.838933i | ||||
\(529\) | − | 3481.11i | − | 0.0124396i | ||||||
\(530\) | 35374.2 | − | 129892.i | 0.125932 | − | 0.462413i | ||||
\(531\) | 36904.7 | 0.130886 | ||||||||
\(532\) | −129844. | − | 129844.i | −0.458775 | − | 0.458775i | ||||
\(533\) | 47274.2 | − | 47274.2i | 0.166406 | − | 0.166406i | ||||
\(534\) | 196439.i | 0.688882i | ||||||||
\(535\) | −255666. | + | 146218.i | −0.893233 | + | 0.510850i | ||||
\(536\) | −23017.2 | −0.0801166 | ||||||||
\(537\) | −66091.5 | − | 66091.5i | −0.229191 | − | 0.229191i | ||||
\(538\) | 342522. | − | 342522.i | 1.18338 | − | 1.18338i | ||||
\(539\) | 398026.i | 1.37004i | ||||||||
\(540\) | 22516.6 | + | 39370.8i | 0.0772174 | + | 0.135016i | ||||
\(541\) | 509491. | 1.74077 | 0.870387 | − | 0.492368i | \(-0.163869\pi\) | ||||
0.870387 | + | 0.492368i | \(0.163869\pi\) | |||||||
\(542\) | 106567. | + | 106567.i | 0.362763 | + | 0.362763i | ||||
\(543\) | −84772.3 | + | 84772.3i | −0.287511 | + | 0.287511i | ||||
\(544\) | − | 7459.49i | − | 0.0252064i | ||||||
\(545\) | −202156. | − | 55054.3i | −0.680601 | − | 0.185352i | ||||
\(546\) | 27801.4 | 0.0932569 | ||||||||
\(547\) | 376658. | + | 376658.i | 1.25885 | + | 1.25885i | 0.951644 | + | 0.307204i | \(0.0993933\pi\) |
0.307204 | + | 0.951644i | \(0.400607\pi\) | |||||||
\(548\) | −131482. | + | 131482.i | −0.437830 | + | 0.437830i | ||||
\(549\) | 80560.0i | 0.267285i | ||||||||
\(550\) | 181587. | + | 700557.i | 0.600288 | + | 2.31589i | ||||
\(551\) | 377214. | 1.24247 | ||||||||
\(552\) | 32282.4 | + | 32282.4i | 0.105947 | + | 0.105947i | ||||
\(553\) | 100474. | − | 100474.i | 0.328553 | − | 0.328553i | ||||
\(554\) | − | 586780.i | − | 1.91186i | ||||||
\(555\) | −47289.1 | + | 173642.i | −0.153523 | + | 0.563728i | ||||
\(556\) | 54252.8 | 0.175498 | ||||||||
\(557\) | −76108.6 | − | 76108.6i | −0.245315 | − | 0.245315i | 0.573730 | − | 0.819045i | \(-0.305496\pi\) |
−0.819045 | + | 0.573730i | \(0.805496\pi\) | |||||||
\(558\) | 27098.9 | − | 27098.9i | 0.0870327 | − | 0.0870327i | ||||
\(559\) | − | 1846.42i | − | 0.00590891i | ||||||
\(560\) | 150776. | − | 86230.3i | 0.480789 | − | 0.274969i | ||||
\(561\) | −6291.39 | −0.0199904 | ||||||||
\(562\) | 227077. | + | 227077.i | 0.718954 | + | 0.718954i | ||||
\(563\) | −242876. | + | 242876.i | −0.766244 | + | 0.766244i | −0.977443 | − | 0.211199i | \(-0.932263\pi\) |
0.211199 | + | 0.977443i | \(0.432263\pi\) | |||||||
\(564\) | − | 169633.i | − | 0.533276i | ||||||
\(565\) | −16991.8 | − | 29710.6i | −0.0532284 | − | 0.0930711i | ||||
\(566\) | 544005. | 1.69813 | ||||||||
\(567\) | −12112.3 | − | 12112.3i | −0.0376755 | − | 0.0376755i | ||||
\(568\) | 794.494 | − | 794.494i | 0.00246260 | − | 0.00246260i | ||||
\(569\) | 285859.i | 0.882934i | 0.897278 | + | 0.441467i | \(0.145542\pi\) | ||||
−0.897278 | + | 0.441467i | \(0.854458\pi\) | |||||||
\(570\) | −407434. | − | 110959.i | −1.25403 | − | 0.341517i | ||||
\(571\) | −28753.2 | −0.0881890 | −0.0440945 | − | 0.999027i | \(-0.514040\pi\) | ||||
−0.0440945 | + | 0.999027i | \(0.514040\pi\) | |||||||
\(572\) | 83332.0 | + | 83332.0i | 0.254695 | + | 0.254695i | ||||
\(573\) | −190663. | + | 190663.i | −0.580708 | + | 0.580708i | ||||
\(574\) | − | 199593.i | − | 0.605789i | ||||||
\(575\) | −322033. | + | 83472.2i | −0.974012 | + | 0.252468i | ||||
\(576\) | 64880.0 | 0.195554 | ||||||||
\(577\) | −429650. | − | 429650.i | −1.29052 | − | 1.29052i | −0.934467 | − | 0.356048i | \(-0.884124\pi\) |
−0.356048 | − | 0.934467i | \(-0.615876\pi\) | |||||||
\(578\) | 317540. | − | 317540.i | 0.950481 | − | 0.950481i | ||||
\(579\) | 371406.i | 1.10788i | ||||||||
\(580\) | 53020.9 | − | 194689.i | 0.157613 | − | 0.578743i | ||||
\(581\) | −171431. | −0.507852 | ||||||||
\(582\) | −303784. | − | 303784.i | −0.896848 | − | 0.896848i | ||||
\(583\) | −152398. | + | 152398.i | −0.448376 | + | 0.448376i | ||||
\(584\) | − | 57820.6i | − | 0.169534i | ||||||
\(585\) | 24805.3 | − | 14186.4i | 0.0724824 | − | 0.0414535i | ||||
\(586\) | 15582.6 | 0.0453778 | ||||||||
\(587\) | −116615. | − | 116615.i | −0.338436 | − | 0.338436i | 0.517343 | − | 0.855778i | \(-0.326921\pi\) |
−0.855778 | + | 0.517343i | \(0.826921\pi\) | |||||||
\(588\) | −87844.6 | + | 87844.6i | −0.254074 | + | 0.254074i | ||||
\(589\) | 159480.i | 0.459703i | ||||||||
\(590\) | 91247.4 | + | 159548.i | 0.262130 | + | 0.458340i | ||||
\(591\) | 164074. | 0.469749 | ||||||||
\(592\) | 289656. | + | 289656.i | 0.826492 | + | 0.826492i | ||||
\(593\) | −80973.9 | + | 80973.9i | −0.230269 | + | 0.230269i | −0.812805 | − | 0.582536i | \(-0.802061\pi\) |
0.582536 | + | 0.812805i | \(0.302061\pi\) | |||||||
\(594\) | − | 162453.i | − | 0.460422i | ||||||
\(595\) | −3187.73 | − | 868.133i | −0.00900424 | − | 0.00245218i | ||||
\(596\) | −321733. | −0.905738 | ||||||||
\(597\) | −209533. | − | 209533.i | −0.587902 | − | 0.587902i | ||||
\(598\) | −85703.3 | + | 85703.3i | −0.239660 | + | 0.239660i | ||||
\(599\) | − | 683966.i | − | 1.90626i | −0.302569 | − | 0.953128i | \(-0.597844\pi\) | ||
0.302569 | − | 0.953128i | \(-0.402156\pi\) | |||||||
\(600\) | 27182.2 | − | 46204.2i | 0.0755060 | − | 0.128345i | ||||
\(601\) | −211089. | −0.584408 | −0.292204 | − | 0.956356i | \(-0.594389\pi\) | ||||
−0.292204 | + | 0.956356i | \(0.594389\pi\) | |||||||
\(602\) | −3897.82 | − | 3897.82i | −0.0107555 | − | 0.0107555i | ||||
\(603\) | −26622.1 | + | 26622.1i | −0.0732162 | + | 0.0732162i | ||||
\(604\) | − | 488692.i | − | 1.33956i | ||||||
\(605\) | 208267. | − | 764743.i | 0.568997 | − | 2.08932i | ||||
\(606\) | 113024. | 0.307768 | ||||||||
\(607\) | 502579. | + | 502579.i | 1.36404 | + | 1.36404i | 0.868699 | + | 0.495340i | \(0.164956\pi\) |
0.495340 | + | 0.868699i | \(0.335044\pi\) | |||||||
\(608\) | −566784. | + | 566784.i | −1.53324 | + | 1.53324i | ||||
\(609\) | 76207.0i | 0.205475i | ||||||||
\(610\) | −348281. | + | 199186.i | −0.935987 | + | 0.535302i | ||||
\(611\) | −106876. | −0.286285 | ||||||||
\(612\) | −1388.51 | − | 1388.51i | −0.00370721 | − | 0.00370721i | ||||
\(613\) | 402276. | − | 402276.i | 1.07054 | − | 1.07054i | 0.0732238 | − | 0.997316i | \(-0.476671\pi\) |
0.997316 | − | 0.0732238i | \(-0.0233287\pi\) | |||||||
\(614\) | − | 220424.i | − | 0.584685i | ||||||
\(615\) | −101848. | − | 178083.i | −0.269278 | − | 0.470839i | ||||
\(616\) | −83497.2 | −0.220044 | ||||||||
\(617\) | 439415. | + | 439415.i | 1.15426 | + | 1.15426i | 0.985689 | + | 0.168574i | \(0.0539163\pi\) |
0.168574 | + | 0.985689i | \(0.446084\pi\) | |||||||
\(618\) | 3345.93 | − | 3345.93i | 0.00876072 | − | 0.00876072i | ||||
\(619\) | − | 555813.i | − | 1.45060i | −0.688434 | − | 0.725299i | \(-0.741701\pi\) | ||
0.688434 | − | 0.725299i | \(-0.258299\pi\) | |||||||
\(620\) | 82311.5 | + | 22416.4i | 0.214130 | + | 0.0583153i | ||||
\(621\) | 74676.8 | 0.193643 | ||||||||
\(622\) | −76576.9 | − | 76576.9i | −0.197932 | − | 0.197932i | ||||
\(623\) | 116778. | − | 116778.i | 0.300874 | − | 0.300874i | ||||
\(624\) | − | 65042.7i | − | 0.167043i | ||||||
\(625\) | 189754. | + | 341440.i | 0.485771 | + | 0.874086i | ||||
\(626\) | 881154. | 2.24855 | ||||||||
\(627\) | 478030. | + | 478030.i | 1.21596 | + | 1.21596i | ||||
\(628\) | −240879. | + | 240879.i | −0.610773 | + | 0.610773i | ||||
\(629\) | − | 7791.73i | − | 0.0196939i | ||||||
\(630\) | 22416.5 | − | 82312.0i | 0.0564791 | − | 0.207387i | ||||
\(631\) | −448846. | −1.12730 | −0.563648 | − | 0.826015i | \(-0.690603\pi\) | ||||
−0.563648 | + | 0.826015i | \(0.690603\pi\) | |||||||
\(632\) | −70583.2 | − | 70583.2i | −0.176713 | − | 0.176713i | ||||
\(633\) | 186266. | − | 186266.i | 0.464865 | − | 0.464865i | ||||
\(634\) | 430260.i | 1.07042i | ||||||||
\(635\) | −369003. | + | 211037.i | −0.915128 | + | 0.523373i | ||||
\(636\) | −67268.7 | −0.166303 | ||||||||
\(637\) | 55345.9 | + | 55345.9i | 0.136398 | + | 0.136398i | ||||
\(638\) | −511056. | + | 511056.i | −1.25553 | + | 1.25553i | ||||
\(639\) | − | 1837.85i | − | 0.00450100i | ||||||
\(640\) | −102964. | − | 180035.i | −0.251377 | − | 0.439538i | ||||
\(641\) | −579776. | −1.41106 | −0.705528 | − | 0.708682i | \(-0.749290\pi\) | ||||
−0.705528 | + | 0.708682i | \(0.749290\pi\) | |||||||
\(642\) | 232826. | + | 232826.i | 0.564886 | + | 0.564886i | ||||
\(643\) | 485382. | − | 485382.i | 1.17398 | − | 1.17398i | 0.192731 | − | 0.981252i | \(-0.438266\pi\) |
0.981252 | − | 0.192731i | \(-0.0617344\pi\) | |||||||
\(644\) | 161730.i | 0.389958i | ||||||||
\(645\) | −5466.73 | − | 1488.79i | −0.0131404 | − | 0.00357860i | ||||
\(646\) | 18282.5 | 0.0438097 | ||||||||
\(647\) | 227180. | + | 227180.i | 0.542703 | + | 0.542703i | 0.924320 | − | 0.381618i | \(-0.124633\pi\) |
−0.381618 | + | 0.924320i | \(0.624633\pi\) | |||||||
\(648\) | −8508.86 | + | 8508.86i | −0.0202638 | + | 0.0202638i | ||||
\(649\) | − | 294251.i | − | 0.698601i | ||||||
\(650\) | 122663. | + | 72163.2i | 0.290326 | + | 0.170800i | ||||
\(651\) | −32219.1 | −0.0760242 | ||||||||
\(652\) | −3626.04 | − | 3626.04i | −0.00852977 | − | 0.00852977i | ||||
\(653\) | 51532.9 | − | 51532.9i | 0.120853 | − | 0.120853i | −0.644093 | − | 0.764947i | \(-0.722765\pi\) |
0.764947 | + | 0.644093i | \(0.222765\pi\) | |||||||
\(654\) | 234232.i | 0.547634i | ||||||||
\(655\) | 31968.6 | − | 117386.i | 0.0745145 | − | 0.273612i | ||||
\(656\) | −466958. | −1.08510 | ||||||||
\(657\) | −66876.3 | − | 66876.3i | −0.154932 | − | 0.154932i | ||||
\(658\) | −225617. | + | 225617.i | −0.521099 | + | 0.521099i | ||||
\(659\) | 447720.i | 1.03095i | 0.856906 | + | 0.515473i | \(0.172384\pi\) | ||||
−0.856906 | + | 0.515473i | \(0.827616\pi\) | |||||||
\(660\) | 313914. | − | 179531.i | 0.720647 | − | 0.412146i | ||||
\(661\) | −99640.8 | −0.228052 | −0.114026 | − | 0.993478i | \(-0.536375\pi\) | ||||
−0.114026 | + | 0.993478i | \(0.536375\pi\) | |||||||
\(662\) | −290006. | − | 290006.i | −0.661745 | − | 0.661745i | ||||
\(663\) | −874.824 | + | 874.824i | −0.00199019 | + | 0.00199019i | ||||
\(664\) | 120430.i | 0.273149i | ||||||||
\(665\) | 176246. | + | 308171.i | 0.398545 | + | 0.696864i | ||||
\(666\) | 201195. | 0.453594 | ||||||||
\(667\) | −234923. | − | 234923.i | −0.528048 | − | 0.528048i | ||||
\(668\) | 334337. | − | 334337.i | 0.749257 | − | 0.749257i | ||||
\(669\) | − | 139558.i | − | 0.311818i | ||||||
\(670\) | −180917. | − | 49270.3i | −0.403024 | − | 0.109758i | ||||
\(671\) | 642327. | 1.42663 | ||||||||
\(672\) | −114505. | − | 114505.i | −0.253563 | − | 0.253563i | ||||
\(673\) | −170652. | + | 170652.i | −0.376774 | + | 0.376774i | −0.869937 | − | 0.493163i | \(-0.835841\pi\) |
0.493163 | + | 0.869937i | \(0.335841\pi\) | |||||||
\(674\) | 675948.i | 1.48797i | ||||||||
\(675\) | −22001.2 | − | 84880.0i | −0.0482880 | − | 0.186294i | ||||
\(676\) | −346152. | −0.757483 | ||||||||
\(677\) | −178335. | − | 178335.i | −0.389099 | − | 0.389099i | 0.485267 | − | 0.874366i | \(-0.338722\pi\) |
−0.874366 | + | 0.485267i | \(0.838722\pi\) | |||||||
\(678\) | −27056.4 | + | 27056.4i | −0.0588587 | + | 0.0588587i | ||||
\(679\) | 361183.i | 0.783408i | ||||||||
\(680\) | −609.863 | + | 2239.38i | −0.00131891 | + | 0.00484294i | ||||
\(681\) | −176481. | −0.380543 | ||||||||
\(682\) | −216067. | − | 216067.i | −0.464536 | − | 0.464536i | ||||
\(683\) | 621359. | − | 621359.i | 1.33199 | − | 1.33199i | 0.428402 | − | 0.903588i | \(-0.359077\pi\) |
0.903588 | − | 0.428402i | \(-0.140923\pi\) | |||||||
\(684\) | 211003.i | 0.451000i | ||||||||
\(685\) | 312058. | − | 178470.i | 0.665049 | − | 0.380350i | ||||
\(686\) | 537122. | 1.14137 | ||||||||
\(687\) | 18200.3 | + | 18200.3i | 0.0385626 | + | 0.0385626i | ||||
\(688\) | −9119.14 | + | 9119.14i | −0.0192654 | + | 0.0192654i | ||||
\(689\) | 42382.2i | 0.0892782i | ||||||||
\(690\) | 184640. | + | 322846.i | 0.387817 | + | 0.678106i | ||||
\(691\) | −142980. | −0.299446 | −0.149723 | − | 0.988728i | \(-0.547838\pi\) | ||||
−0.149723 | + | 0.988728i | \(0.547838\pi\) | |||||||
\(692\) | −413683. | − | 413683.i | −0.863884 | − | 0.863884i | ||||
\(693\) | −96574.3 | + | 96574.3i | −0.201092 | + | 0.201092i | ||||
\(694\) | − | 315858.i | − | 0.655803i | ||||||
\(695\) | −101202. | − | 27561.0i | −0.209517 | − | 0.0570591i | ||||
\(696\) | 53535.4 | 0.110515 | ||||||||
\(697\) | 6280.57 | + | 6280.57i | 0.0129281 | + | 0.0129281i | ||||
\(698\) | 361301. | − | 361301.i | 0.741582 | − | 0.741582i | ||||
\(699\) | − | 447364.i | − | 0.915601i | ||||||
\(700\) | 183827. | − | 47648.7i | 0.375157 | − | 0.0972422i | ||||
\(701\) | 248096. | 0.504876 | 0.252438 | − | 0.967613i | \(-0.418768\pi\) | ||||
0.252438 | + | 0.967613i | \(0.418768\pi\) | |||||||
\(702\) | −22589.3 | − | 22589.3i | −0.0458383 | − | 0.0458383i | ||||
\(703\) | −592028. | + | 592028.i | −1.19793 | + | 1.19793i | ||||
\(704\) | − | 517306.i | − | 1.04376i | ||||||
\(705\) | −86175.3 | + | 316430.i | −0.173382 | + | 0.636648i | ||||
\(706\) | 414500. | 0.831602 | ||||||||
\(707\) | −67189.6 | − | 67189.6i | −0.134420 | − | 0.134420i | ||||
\(708\) | 64941.4 | − | 64941.4i | 0.129555 | − | 0.129555i | ||||
\(709\) | 669146.i | 1.33115i | 0.746329 | + | 0.665577i | \(0.231814\pi\) | ||||
−0.746329 | + | 0.665577i | \(0.768186\pi\) | |||||||
\(710\) | 7945.49 | − | 4544.12i | 0.0157617 | − | 0.00901432i | ||||
\(711\) | −163276. | −0.322985 | ||||||||
\(712\) | −82036.4 | − | 82036.4i | −0.161825 | − | 0.161825i | ||||
\(713\) | 99321.8 | − | 99321.8i | 0.195373 | − | 0.195373i | ||||
\(714\) | 3693.53i | 0.00724511i | ||||||||
\(715\) | −113112. | − | 197779.i | −0.221257 | − | 0.386873i | ||||
\(716\) | −232603. | −0.453722 | ||||||||
\(717\) | −149207. | − | 149207.i | −0.290235 | − | 0.290235i | ||||
\(718\) | 229940. | − | 229940.i | 0.446031 | − | 0.446031i | ||||
\(719\) | 244719.i | 0.473380i | 0.971585 | + | 0.236690i | \(0.0760626\pi\) | ||||
−0.971585 | + | 0.236690i | \(0.923937\pi\) | |||||||
\(720\) | −192573. | − | 52444.6i | −0.371476 | − | 0.101166i | ||||
\(721\) | −3978.14 | −0.00765260 | ||||||||
\(722\) | −893475. | − | 893475.i | −1.71399 | − | 1.71399i | ||||
\(723\) | −89811.5 | + | 89811.5i | −0.171813 | + | 0.171813i | ||||
\(724\) | 298349.i | 0.569177i | ||||||||
\(725\) | −197808. | + | 336234.i | −0.376329 | + | 0.639683i | ||||
\(726\) | −886086. | −1.68114 | ||||||||
\(727\) | −515647. | − | 515647.i | −0.975626 | − | 0.975626i | 0.0240837 | − | 0.999710i | \(-0.492333\pi\) |
−0.999710 | + | 0.0240837i | \(0.992333\pi\) | |||||||
\(728\) | −11610.4 | + | 11610.4i | −0.0219070 | + | 0.0219070i | ||||
\(729\) | 19683.0i | 0.0370370i | ||||||||
\(730\) | 123770. | − | 454476.i | 0.232258 | − | 0.852835i | ||||
\(731\) | 245.305 | 0.000459062 | ||||||||
\(732\) | 141762. | + | 141762.i | 0.264568 | + | 0.264568i | ||||
\(733\) | 98009.3 | − | 98009.3i | 0.182414 | − | 0.182414i | −0.609993 | − | 0.792407i | \(-0.708828\pi\) |
0.792407 | + | 0.609993i | \(0.208828\pi\) | |||||||
\(734\) | 641526.i | 1.19075i | ||||||||
\(735\) | 208489. | − | 119238.i | 0.385931 | − | 0.220718i | ||||
\(736\) | 705967. | 1.30325 | ||||||||
\(737\) | 212265. | + | 212265.i | 0.390790 | + | 0.390790i | ||||
\(738\) | −162174. | + | 162174.i | −0.297762 | + | 0.297762i | ||||
\(739\) | − | 31323.0i | − | 0.0573554i | −0.999589 | − | 0.0286777i | \(-0.990870\pi\) | ||
0.999589 | − | 0.0286777i | \(-0.00912965\pi\) | |||||||
\(740\) | 222345. | + | 388774.i | 0.406035 | + | 0.709961i | ||||
\(741\) | 132941. | 0.242116 | ||||||||
\(742\) | 89469.4 | + | 89469.4i | 0.162505 | + | 0.162505i | ||||
\(743\) | 46804.2 | − | 46804.2i | 0.0847828 | − | 0.0847828i | −0.663444 | − | 0.748226i | \(-0.730906\pi\) |
0.748226 | + | 0.663444i | \(0.230906\pi\) | |||||||
\(744\) | 22633.9i | 0.0408897i | ||||||||
\(745\) | 600153. | + | 163443.i | 1.08131 | + | 0.294479i | ||||
\(746\) | −514252. | −0.924056 | ||||||||
\(747\) | 139292. | + | 139292.i | 0.249623 | + | 0.249623i | ||||
\(748\) | −11071.0 | + | 11071.0i | −0.0197872 | + | 0.0197872i | ||||
\(749\) | − | 276818.i | − | 0.493435i | ||||||
\(750\) | 312559. | − | 304984.i | 0.555660 | − | 0.542194i | ||||
\(751\) | −186.753 | −0.000331121 | −0.000165561 | − | 1.00000i | \(-0.500053\pi\) | ||||
−0.000165561 | 1.00000i | \(0.500053\pi\) | ||||||||
\(752\) | 527842. | + | 527842.i | 0.933401 | + | 0.933401i | ||||
\(753\) | 264365. | − | 264365.i | 0.466244 | − | 0.466244i | ||||
\(754\) | 142126.i | 0.249994i | ||||||||
\(755\) | −248260. | + | 911596.i | −0.435525 | + | 1.59922i | ||||
\(756\) | −42628.0 | −0.0745850 | ||||||||
\(757\) | 596186. | + | 596186.i | 1.04037 | + | 1.04037i | 0.999150 | + | 0.0412248i | \(0.0131260\pi\) |
0.0412248 | + | 0.999150i | \(0.486874\pi\) | |||||||
\(758\) | 489308. | − | 489308.i | 0.851616 | − | 0.851616i | ||||
\(759\) | − | 595419.i | − | 1.03357i | ||||||
\(760\) | 216490. | − | 123813.i | 0.374809 | − | 0.214358i | ||||
\(761\) | −1.04441e6 | −1.80344 | −0.901722 | − | 0.432315i | \(-0.857697\pi\) | ||||
−0.901722 | + | 0.432315i | \(0.857697\pi\) | |||||||
\(762\) | 336038. | + | 336038.i | 0.578733 | + | 0.578733i | ||||
\(763\) | 139245. | − | 139245.i | 0.239183 | − | 0.239183i | ||||
\(764\) | 671023.i | 1.14961i | ||||||||
\(765\) | 1884.73 | + | 3295.48i | 0.00322051 | + | 0.00563114i | ||||
\(766\) | 1.12181e6 | 1.91188 | ||||||||
\(767\) | −40915.9 | − | 40915.9i | −0.0695507 | − | 0.0695507i | ||||
\(768\) | −305216. | + | 305216.i | −0.517470 | + | 0.517470i | ||||
\(769\) | 577158.i | 0.975982i | 0.872849 | + | 0.487991i | \(0.162270\pi\) | ||||
−0.872849 | + | 0.487991i | \(0.837730\pi\) | |||||||
\(770\) | −656296. | − | 178733.i | −1.10693 | − | 0.301456i | ||||
\(771\) | −246227. | −0.414217 | ||||||||
\(772\) | 653566. | + | 653566.i | 1.09662 | + | 1.09662i | ||||
\(773\) | −414104. | + | 414104.i | −0.693027 | + | 0.693027i | −0.962897 | − | 0.269870i | \(-0.913019\pi\) |
0.269870 | + | 0.962897i | \(0.413019\pi\) | |||||||
\(774\) | 6334.14i | 0.0105732i | ||||||||
\(775\) | −142154. | − | 83630.2i | −0.236677 | − | 0.139239i | ||||
\(776\) | 253731. | 0.421357 | ||||||||
\(777\) | −119605. | − | 119605.i | −0.198110 | − | 0.198110i | ||||
\(778\) | −668111. | + | 668111.i | −1.10380 | + | 1.10380i | ||||
\(779\) | − | 954417.i | − | 1.57276i | ||||||
\(780\) | 18686.1 | − | 68613.9i | 0.0307134 | − | 0.112778i | ||||
\(781\) | −14653.7 | −0.0240240 | ||||||||
\(782\) | −11386.0 | − | 11386.0i | −0.0186191 | − | 0.0186191i | ||||
\(783\) | 61920.0 | − | 61920.0i | 0.100997 | − | 0.100997i | ||||
\(784\) | − | 546687.i | − | 0.889419i | ||||||
\(785\) | 571700. | − | 326962.i | 0.927745 | − | 0.530588i | ||||
\(786\) | −136012. | −0.220157 | ||||||||
\(787\) | −337250. | − | 337250.i | −0.544505 | − | 0.544505i | 0.380341 | − | 0.924846i | \(-0.375807\pi\) |
−0.924846 | + | 0.380341i | \(0.875807\pi\) | |||||||
\(788\) | 288723. | − | 288723.i | 0.464974 | − | 0.464974i | ||||
\(789\) | − | 132647.i | − | 0.213080i | ||||||
\(790\) | −403702. | − | 705881.i | −0.646854 | − | 1.13104i | ||||
\(791\) | 32168.7 | 0.0514138 | ||||||||
\(792\) | 67843.5 | + | 67843.5i | 0.108158 | + | 0.108158i | ||||
\(793\) | 89316.2 | − | 89316.2i | 0.142031 | − | 0.142031i | ||||
\(794\) | 450317.i | 0.714294i | ||||||||
\(795\) | 125482. | + | 34173.2i | 0.198539 | + | 0.0540694i | ||||
\(796\) | −737435. | −1.16385 | ||||||||
\(797\) | −365276. | − | 365276.i | −0.575048 | − | 0.575048i | 0.358487 | − | 0.933535i | \(-0.383293\pi\) |
−0.933535 | + | 0.358487i | \(0.883293\pi\) | |||||||
\(798\) | 280640. | − | 280640.i | 0.440701 | − | 0.440701i | ||||
\(799\) | − | 14198.9i | − | 0.0222414i | ||||||
\(800\) | −207992. | − | 802425.i | −0.324987 | − | 1.25379i | ||||
\(801\) | −189770. | −0.295775 | ||||||||
\(802\) | 311606. | + | 311606.i | 0.484460 | + | 0.484460i | ||||
\(803\) | −533223. | + | 533223.i | −0.826948 | + | 0.826948i | ||||
\(804\) | 93694.1i | 0.144944i | ||||||||
\(805\) | 82160.3 | − | 301687.i | 0.126786 | − | 0.465549i | ||||
\(806\) | −60088.5 | −0.0924957 | ||||||||
\(807\) | 330893. | + | 330893.i | 0.508090 | + | 0.508090i | ||||
\(808\) | −47200.7 | + | 47200.7i | −0.0722979 | + | 0.0722979i | ||||
\(809\) | − | 1.04908e6i | − | 1.60292i | −0.598051 | − | 0.801458i | \(-0.704058\pi\) | ||
0.598051 | − | 0.801458i | \(-0.295942\pi\) | |||||||
\(810\) | −85094.5 | + | 48666.5i | −0.129697 | + | 0.0741755i | ||||
\(811\) | −882064. | −1.34109 | −0.670546 | − | 0.741868i | \(-0.733940\pi\) | ||||
−0.670546 | + | 0.741868i | \(0.733940\pi\) | |||||||
\(812\) | 134102. | + | 134102.i | 0.203387 | + | 0.203387i | ||||
\(813\) | −102949. | + | 102949.i | −0.155754 | + | 0.155754i | ||||
\(814\) | − | 1.60418e6i | − | 2.42105i | ||||||
\(815\) | 4921.87 | + | 8606.00i | 0.00740995 | + | 0.0129565i | ||||
\(816\) | 8641.20 | 0.0129776 | ||||||||
\(817\) | −18638.6 | − | 18638.6i | −0.0279235 | − | 0.0279235i | ||||
\(818\) | −407916. | + | 407916.i | −0.609627 | + | 0.609627i | ||||
\(819\) | 26857.5i | 0.0400403i | ||||||||
\(820\) | −492596. | − | 134152.i | −0.732594 | − | 0.199512i | ||||
\(821\) | 1.11452e6 | 1.65348 | 0.826742 | − | 0.562581i | \(-0.190191\pi\) | ||||
0.826742 | + | 0.562581i | \(0.190191\pi\) | |||||||
\(822\) | −284180. | − | 284180.i | −0.420582 | − | 0.420582i | ||||
\(823\) | −258025. | + | 258025.i | −0.380945 | + | 0.380945i | −0.871443 | − | 0.490497i | \(-0.836815\pi\) |
0.490497 | + | 0.871443i | \(0.336815\pi\) | |||||||
\(824\) | 2794.64i | 0.00411596i | ||||||||
\(825\) | −676772. | + | 175422.i | −0.994339 | + | 0.257736i | ||||
\(826\) | −172748. | −0.253194 | ||||||||
\(827\) | −55607.8 | − | 55607.8i | −0.0813063 | − | 0.0813063i | 0.665284 | − | 0.746590i | \(-0.268310\pi\) |
−0.746590 | + | 0.665284i | \(0.768310\pi\) | |||||||
\(828\) | 131409. | − | 131409.i | 0.191675 | − | 0.191675i | ||||
\(829\) | 1.03445e6i | 1.50522i | 0.658468 | + | 0.752609i | \(0.271205\pi\) | ||||
−0.658468 | + | 0.752609i | \(0.728795\pi\) | |||||||
\(830\) | −257792. | + | 946594.i | −0.374208 | + | 1.37407i | ||||
\(831\) | 566858. | 0.820867 | ||||||||
\(832\) | −71931.9 | − | 71931.9i | −0.103914 | − | 0.103914i | ||||
\(833\) | −7352.94 | + | 7352.94i | −0.0105967 | + | 0.0105967i | ||||
\(834\) | 117260.i | 0.168584i | ||||||||
\(835\) | −793511. | + | 453818.i | −1.13810 | + | 0.650892i | ||||
\(836\) | 1.68239e6 | 2.40720 | ||||||||
\(837\) | 26178.8 | + | 26178.8i | 0.0373679 | + | 0.0373679i | ||||
\(838\) | 95945.1 | − | 95945.1i | 0.136626 | − | 0.136626i | ||||
\(839\) | − | 426954.i | − | 0.606537i | −0.952905 | − | 0.303268i | \(-0.901922\pi\) | ||
0.952905 | − | 0.303268i | \(-0.0980778\pi\) | |||||||
\(840\) | 25013.4 | + | 43736.5i | 0.0354498 | + | 0.0619848i | ||||
\(841\) | 317698. | 0.449182 | ||||||||
\(842\) | 630808. | + | 630808.i | 0.889761 | + | 0.889761i | ||||
\(843\) | −219368. | + | 219368.i | −0.308687 | + | 0.308687i | ||||
\(844\) | − | 655548.i | − | 0.920279i | ||||||
\(845\) | 645704. | + | 175849.i | 0.904316 | + | 0.246278i | ||||
\(846\) | 366639. | 0.512268 | ||||||||
\(847\) | 526755. | + | 526755.i | 0.734247 | + | 0.734247i | ||||
\(848\) | 209318. | − | 209318.i | 0.291082 | − | 0.291082i | ||||
\(849\) | 525535.i | 0.729099i | ||||||||
\(850\) | −9587.18 | + | 16296.3i | −0.0132695 | + | 0.0225554i | ||||
\(851\) | 737411. | 1.01824 | ||||||||
\(852\) | −3234.08 | − | 3234.08i | −0.00445525 | − | 0.00445525i | ||||
\(853\) | −63890.0 | + | 63890.0i | −0.0878081 | + | 0.0878081i | −0.749647 | − | 0.661838i | \(-0.769776\pi\) |
0.661838 | + | 0.749647i | \(0.269776\pi\) | |||||||
\(854\) | − | 377095.i | − | 0.517053i | ||||||
\(855\) | 107192. | − | 393601.i | 0.146632 | − | 0.538423i | ||||
\(856\) | −194464. | −0.265395 | ||||||||
\(857\) | −104328. | − | 104328.i | −0.142049 | − | 0.142049i | 0.632506 | − | 0.774555i | \(-0.282026\pi\) |
−0.774555 | + | 0.632506i | \(0.782026\pi\) | |||||||
\(858\) | −180111. | + | 180111.i | −0.244661 | + | 0.244661i | ||||
\(859\) | − | 1.25585e6i | − | 1.70196i | −0.525196 | − | 0.850982i | \(-0.676008\pi\) | ||
0.525196 | − | 0.850982i | \(-0.323992\pi\) | |||||||
\(860\) | −12239.7 | + | 7000.01i | −0.0165490 | + | 0.00946458i | ||||
\(861\) | 192817. | 0.260099 | ||||||||
\(862\) | −691828. | − | 691828.i | −0.931073 | − | 0.931073i | ||||
\(863\) | 618705. | − | 618705.i | 0.830734 | − | 0.830734i | −0.156883 | − | 0.987617i | \(-0.550145\pi\) |
0.987617 | + | 0.156883i | \(0.0501446\pi\) | |||||||
\(864\) | 186076.i | 0.249266i | ||||||||
\(865\) | 561520. | + | 981831.i | 0.750470 | + | 1.31221i | ||||
\(866\) | −1.35660e6 | −1.80891 | ||||||||
\(867\) | 306760. | + | 306760.i | 0.408094 | + | 0.408094i | ||||
\(868\) | −56696.2 | + | 56696.2i | −0.0752514 | + | 0.0752514i | ||||
\(869\) | 1.30184e6i | 1.72393i | ||||||||
\(870\) | 420794. | + | 114597.i | 0.555943 | + | 0.151403i | ||||
\(871\) | 59031.3 | 0.0778119 | ||||||||
\(872\) | −97819.4 | − | 97819.4i | −0.128645 | − | 0.128645i | ||||
\(873\) | 293470. | − | 293470.i | 0.385066 | − | 0.385066i | ||||
\(874\) | 1.73026e6i | 2.26510i | ||||||||
\(875\) | −367113. | − | 4503.14i | −0.479495 | − | 0.00588165i | ||||
\(876\) | −235365. | −0.306715 | ||||||||
\(877\) | −446207. | − | 446207.i | −0.580146 | − | 0.580146i | 0.354797 | − | 0.934943i | \(-0.384550\pi\) |
−0.934943 | + | 0.354797i | \(0.884550\pi\) | |||||||
\(878\) | −94796.6 | + | 94796.6i | −0.122971 | + | 0.122971i | ||||
\(879\) | 15053.5i | 0.0194832i | ||||||||
\(880\) | −418155. | + | 1.53544e6i | −0.539973 | + | 1.98274i | ||||
\(881\) | −226795. | −0.292201 | −0.146101 | − | 0.989270i | \(-0.546672\pi\) | ||||
−0.146101 | + | 0.989270i | \(0.546672\pi\) | |||||||
\(882\) | −189864. | − | 189864.i | −0.244065 | − | 0.244065i | ||||
\(883\) | 235051. | − | 235051.i | 0.301467 | − | 0.301467i | −0.540121 | − | 0.841588i | \(-0.681621\pi\) |
0.841588 | + | 0.540121i | \(0.181621\pi\) | |||||||
\(884\) | 3078.87i | 0.00393991i | ||||||||
\(885\) | −154131. | + | 88149.5i | −0.196791 | + | 0.112547i | ||||
\(886\) | −571276. | −0.727744 | ||||||||
\(887\) | −789601. | − | 789601.i | −1.00360 | − | 1.00360i | −0.999993 | − | 0.00360590i | \(-0.998852\pi\) |
−0.00360590 | − | 0.999993i | \(-0.501148\pi\) | |||||||
\(888\) | −84022.4 | + | 84022.4i | −0.106554 | + | 0.106554i | ||||
\(889\) | − | 399531.i | − | 0.505531i | ||||||
\(890\) | −469208. | − | 820421.i | −0.592360 | − | 1.03575i | ||||
\(891\) | 156938. | 0.197685 | ||||||||
\(892\) | −245581. | − | 245581.i | −0.308649 | − | 0.308649i | ||||
\(893\) | −1.07886e6 | + | 1.07886e6i | −1.35289 | + | 1.35289i | ||||
\(894\) | − | 695381.i | − | 0.870057i | ||||||
\(895\) | 433893. | + | 118165.i | 0.541672 | + | 0.147517i | ||||
\(896\) | 194930. | 0.242808 | ||||||||
\(897\) | −82793.5 | − | 82793.5i | −0.102899 | − | 0.102899i | ||||
\(898\) | 862857. | − | 862857.i | 1.07001 | − | 1.07001i | ||||
\(899\) | − | 164710.i | − | 0.203798i | ||||||
\(900\) | −188080. | − | 110648.i | −0.232197 | − | 0.136603i | ||||
\(901\) | −5630.65 | −0.00693600 | ||||||||
\(902\) | 1.29306e6 | + | 1.29306e6i | 1.58930 | + | 1.58930i | ||||
\(903\) | 3765.48 | − | 3765.48i | 0.00461791 | − | 0.00461791i | ||||
\(904\) | − | 22598.5i | − | 0.0276530i | ||||||
\(905\) | 151564. | − | 556533.i | 0.185054 | − | 0.679507i | ||||
\(906\) | 1.05624e6 | 1.28679 | ||||||||
\(907\) | −36080.2 | − | 36080.2i | −0.0438585 | − | 0.0438585i | 0.684837 | − | 0.728696i | \(-0.259873\pi\) |
−0.728696 | + | 0.684837i | \(0.759873\pi\) | |||||||
\(908\) | −310555. | + | 310555.i | −0.376675 | + | 0.376675i | ||||
\(909\) | 109186.i | 0.132142i | ||||||||
\(910\) | −116112. | + | 66405.6i | −0.140214 | + | 0.0801903i | ||||
\(911\) | 216456. | 0.260815 | 0.130407 | − | 0.991460i | \(-0.458371\pi\) | ||||
0.130407 | + | 0.991460i | \(0.458371\pi\) | |||||||
\(912\) | −656572. | − | 656572.i | −0.789392 | − | 0.789392i | ||||
\(913\) | 1.11061e6 | − | 1.11061e6i | 1.33236 | − | 1.33236i | ||||
\(914\) | − | 24895.9i | − | 0.0298013i | ||||||
\(915\) | −192423. | − | 336456.i | −0.229835 | − | 0.401871i | ||||
\(916\) | 64054.5 | 0.0763411 | ||||||||
\(917\) | 80855.8 | + | 80855.8i | 0.0961552 | + | 0.0961552i | ||||
\(918\) | 3001.08 | − | 3001.08i | 0.00356117 | − | 0.00356117i | ||||
\(919\) | − | 358123.i | − | 0.424034i | −0.977266 | − | 0.212017i | \(-0.931997\pi\) | ||
0.977266 | − | 0.212017i | \(-0.0680032\pi\) | |||||||
\(920\) | −211935. | − | 57717.6i | −0.250396 | − | 0.0681919i | ||||
\(921\) | 212940. | 0.251037 | ||||||||
\(922\) | 361251. | + | 361251.i | 0.424959 | + | 0.424959i | ||||
\(923\) | −2037.61 | + | 2037.61i | −0.00239176 | + | 0.00239176i | ||||
\(924\) | 339885.i | 0.398096i | ||||||||
\(925\) | −217256. | − | 838165.i | −0.253914 | − | 0.979594i | ||||
\(926\) | −1.64366e6 | −1.91686 | ||||||||
\(927\) | 3232.33 | + | 3232.33i | 0.00376146 | + | 0.00376146i | ||||
\(928\) | 585369. | − | 585369.i | 0.679726 | − | 0.679726i | ||||
\(929\) | 12991.3i | 0.0150530i | 0.999972 | + | 0.00752649i | \(0.00239578\pi\) | ||||
−0.999972 | + | 0.00752649i | \(0.997604\pi\) | |||||||
\(930\) | −48450.0 | + | 177905.i | −0.0560180 | + | 0.205694i | ||||
\(931\) | 1.11738e6 | 1.28914 | ||||||||
\(932\) | −787229. | − | 787229.i | −0.906294 | − | 0.906294i | ||||
\(933\) | 73977.0 | − | 73977.0i | 0.0849832 | − | 0.0849832i | ||||
\(934\) | 58819.7i | 0.0674262i | ||||||||
\(935\) | 26275.8 | − | 15027.4i | 0.0300561 | − | 0.0171894i | ||||
\(936\) | 18867.4 | 0.0215358 | ||||||||
\(937\) | 253354. | + | 253354.i | 0.288568 | + | 0.288568i | 0.836514 | − | 0.547946i | \(-0.184590\pi\) |
−0.547946 | + | 0.836514i | \(0.684590\pi\) | |||||||
\(938\) | 124616. | − | 124616.i | 0.141634 | − | 0.141634i | ||||
\(939\) | 851238.i | 0.965428i | ||||||||
\(940\) | 405181. | + | 708467.i | 0.458557 | + | 0.801796i | ||||
\(941\) | −1.24657e6 | −1.40779 | −0.703893 | − | 0.710306i | \(-0.748557\pi\) | ||||
−0.703893 | + | 0.710306i | \(0.748557\pi\) | |||||||
\(942\) | −520627. | − | 520627.i | −0.586712 | − | 0.586712i | ||||
\(943\) | −594395. | + | 594395.i | −0.668424 | + | 0.668424i | ||||
\(944\) | 404153.i | 0.453525i | ||||||||
\(945\) | 79517.4 | + | 21655.5i | 0.0890428 | + | 0.0242496i | ||||
\(946\) | 50503.9 | 0.0564342 | ||||||||
\(947\) | 550159. | + | 550159.i | 0.613462 | + | 0.613462i | 0.943847 | − | 0.330384i | \(-0.107178\pi\) |
−0.330384 | + | 0.943847i | \(0.607178\pi\) | |||||||
\(948\) | −287317. | + | 287317.i | −0.319702 | + | 0.319702i | ||||
\(949\) | 148290.i | 0.164657i | ||||||||
\(950\) | 1.96667e6 | − | 509768.i | 2.17913 | − | 0.564839i | ||||
\(951\) | −415652. | −0.459589 | ||||||||
\(952\) | −1542.48 | − | 1542.48i | −0.00170195 | − | 0.00170195i | ||||
\(953\) | 457502. | − | 457502.i | 0.503741 | − | 0.503741i | −0.408858 | − | 0.912598i | \(-0.634073\pi\) |
0.912598 | + | 0.408858i | \(0.134073\pi\) | |||||||
\(954\) | − | 145392.i | − | 0.159751i | ||||||
\(955\) | 340887. | − | 1.25171e6i | 0.373769 | − | 1.37245i | ||||
\(956\) | −525121. | −0.574570 | ||||||||
\(957\) | −493705. | − | 493705.i | −0.539068 | − | 0.539068i | ||||
\(958\) | −1.21993e6 | + | 1.21993e6i | −1.32924 | + | 1.32924i | ||||
\(959\) | 337875.i | 0.367383i | ||||||||
\(960\) | −270969. | + | 154971.i | −0.294021 | + | 0.168154i | ||||
\(961\) | −853884. | −0.924596 | ||||||||
\(962\) | −223063. | − | 223063.i | −0.241033 | − | 0.241033i | ||||
\(963\) | −224921. | + | 224921.i | −0.242537 | + | 0.242537i | ||||
\(964\) | 316084.i | 0.340133i | ||||||||
\(965\) | −887130. | − | 1.55117e6i | −0.952648 | − | 1.66573i | ||||
\(966\) | −349557. | −0.374596 | ||||||||
\(967\) | 72229.7 | + | 72229.7i | 0.0772437 | + | 0.0772437i | 0.744673 | − | 0.667429i | \(-0.232605\pi\) |
−0.667429 | + | 0.744673i | \(0.732605\pi\) | |||||||
\(968\) | 370045. | − | 370045.i | 0.394916 | − | 0.394916i | ||||
\(969\) | 17661.8i | 0.0188099i | ||||||||
\(970\) | 1.99435e6 | + | 543134.i | 2.11962 | + | 0.577250i | ||||
\(971\) | 864636. | 0.917054 | 0.458527 | − | 0.888680i | \(-0.348377\pi\) | ||||
0.458527 | + | 0.888680i | \(0.348377\pi\) | |||||||
\(972\) | 34636.3 | + | 34636.3i | 0.0366606 | + | 0.0366606i | ||||
\(973\) | 69708.0 | − | 69708.0i | 0.0736303 | − | 0.0736303i | ||||
\(974\) | 40033.3i | 0.0421992i | ||||||||
\(975\) | −69713.1 | + | 118498.i | −0.0733340 | + | 0.124653i | ||||
\(976\) | −882233. | −0.926155 | ||||||||
\(977\) | 838896. | + | 838896.i | 0.878859 | + | 0.878859i | 0.993417 | − | 0.114558i | \(-0.0365451\pi\) |
−0.114558 | + | 0.993417i | \(0.536545\pi\) | |||||||
\(978\) | 7837.19 | − | 7837.19i | 0.00819374 | − | 0.00819374i | ||||
\(979\) | 1.51308e6i | 1.57869i | ||||||||
\(980\) | 157057. | − | 576703.i | 0.163533 | − | 0.600482i | ||||
\(981\) | −226280. | −0.235130 | ||||||||
\(982\) | 729119. | + | 729119.i | 0.756093 | + | 0.756093i | ||||
\(983\) | −1.04189e6 | + | 1.04189e6i | −1.07823 | + | 1.07823i | −0.0815669 | + | 0.996668i | \(0.525992\pi\) |
−0.996668 | + | 0.0815669i | \(0.974008\pi\) | |||||||
\(984\) | − | 135454.i | − | 0.139894i | ||||||
\(985\) | −685251. | + | 391903.i | −0.706281 | + | 0.403930i | ||||
\(986\) | −18882.0 | −0.0194220 | ||||||||
\(987\) | −217957. | − | 217957.i | −0.223736 | − | 0.223736i | ||||
\(988\) | 233937. | − | 233937.i | 0.239654 | − | 0.239654i | ||||
\(989\) | 23215.7i | 0.0237350i | ||||||||
\(990\) | 388032. | + | 678482.i | 0.395910 | + | 0.692258i | ||||
\(991\) | −1.02008e6 | −1.03869 | −0.519347 | − | 0.854564i | \(-0.673825\pi\) | ||||
−0.519347 | + | 0.854564i | \(0.673825\pi\) | |||||||
\(992\) | 247485. | + | 247485.i | 0.251493 | + | 0.251493i | ||||
\(993\) | 280160. | − | 280160.i | 0.284124 | − | 0.284124i | ||||
\(994\) | 8602.85i | 0.00870702i | ||||||||
\(995\) | 1.37560e6 | + | 374624.i | 1.38945 | + | 0.378399i | ||||
\(996\) | 490225. | 0.494171 | ||||||||
\(997\) | −398909. | − | 398909.i | −0.401313 | − | 0.401313i | 0.477382 | − | 0.878696i | \(-0.341586\pi\) |
−0.878696 | + | 0.477382i | \(0.841586\pi\) | |||||||
\(998\) | 995456. | − | 995456.i | 0.999450 | − | 0.999450i | ||||
\(999\) | 194364.i | 0.194753i |
(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 | 15.5.f.a.7.4 | ✓ | 8 | |
3.2 | odd | 2 | 45.5.g.e.37.1 | 8 | |||
4.3 | odd | 2 | 240.5.bg.c.97.4 | 8 | |||
5.2 | odd | 4 | 75.5.f.e.43.1 | 8 | |||
5.3 | odd | 4 | inner | 15.5.f.a.13.4 | yes | 8 | |
5.4 | even | 2 | 75.5.f.e.7.1 | 8 | |||
15.2 | even | 4 | 225.5.g.m.118.4 | 8 | |||
15.8 | even | 4 | 45.5.g.e.28.1 | 8 | |||
15.14 | odd | 2 | 225.5.g.m.82.4 | 8 | |||
20.3 | even | 4 | 240.5.bg.c.193.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.5.f.a.7.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
15.5.f.a.13.4 | yes | 8 | 5.3 | odd | 4 | inner | |
45.5.g.e.28.1 | 8 | 15.8 | even | 4 | |||
45.5.g.e.37.1 | 8 | 3.2 | odd | 2 | |||
75.5.f.e.7.1 | 8 | 5.4 | even | 2 | |||
75.5.f.e.43.1 | 8 | 5.2 | odd | 4 | |||
225.5.g.m.82.4 | 8 | 15.14 | odd | 2 | |||
225.5.g.m.118.4 | 8 | 15.2 | even | 4 | |||
240.5.bg.c.97.4 | 8 | 4.3 | odd | 2 | |||
240.5.bg.c.193.4 | 8 | 20.3 | even | 4 |