Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [18,4,Mod(7,18)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(18, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("18.7");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 18 = 2 \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 18.c (of order \(3\), 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: | \(1.06203438010\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 13.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 18.13 |
Dual form | 18.4.c.a.7.1 |
$q$-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 \(\left(\mathbb{Z}/18\mathbb{Z}\right)^\times\).
\(n\) | \(11\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.73205i | −0.353553 | − | 0.612372i | ||||
\(3\) | − | 5.19615i | − | 1.00000i | ||||||
\(4\) | −2.00000 | + | 3.46410i | −0.250000 | + | 0.433013i | ||||
\(5\) | 4.50000 | − | 7.79423i | 0.402492 | − | 0.697137i | −0.591534 | − | 0.806280i | \(-0.701477\pi\) |
0.994026 | + | 0.109143i | \(0.0348107\pi\) | |||||||
\(6\) | −9.00000 | + | 5.19615i | −0.612372 | + | 0.353553i | ||||
\(7\) | 15.5000 | + | 26.8468i | 0.836921 | + | 1.44959i | 0.892456 | + | 0.451134i | \(0.148980\pi\) |
−0.0555351 | + | 0.998457i | \(0.517686\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | −27.0000 | −1.00000 | ||||||||
\(10\) | −18.0000 | −0.569210 | ||||||||
\(11\) | 7.50000 | + | 12.9904i | 0.205576 | + | 0.356068i | 0.950316 | − | 0.311287i | \(-0.100760\pi\) |
−0.744740 | + | 0.667355i | \(0.767427\pi\) | |||||||
\(12\) | 18.0000 | + | 10.3923i | 0.433013 | + | 0.250000i | ||||
\(13\) | 18.5000 | − | 32.0429i | 0.394691 | − | 0.683624i | −0.598371 | − | 0.801219i | \(-0.704185\pi\) |
0.993062 | + | 0.117595i | \(0.0375185\pi\) | |||||||
\(14\) | 31.0000 | − | 53.6936i | 0.591793 | − | 1.02502i | ||||
\(15\) | −40.5000 | − | 23.3827i | −0.697137 | − | 0.402492i | ||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | −42.0000 | −0.599206 | −0.299603 | − | 0.954064i | \(-0.596854\pi\) | ||||
−0.299603 | + | 0.954064i | \(0.596854\pi\) | |||||||
\(18\) | 27.0000 | + | 46.7654i | 0.353553 | + | 0.612372i | ||||
\(19\) | −28.0000 | −0.338086 | −0.169043 | − | 0.985609i | \(-0.554068\pi\) | ||||
−0.169043 | + | 0.985609i | \(0.554068\pi\) | |||||||
\(20\) | 18.0000 | + | 31.1769i | 0.201246 | + | 0.348569i | ||||
\(21\) | 139.500 | − | 80.5404i | 1.44959 | − | 0.836921i | ||||
\(22\) | 15.0000 | − | 25.9808i | 0.145364 | − | 0.251778i | ||||
\(23\) | −97.5000 | + | 168.875i | −0.883920 | + | 1.53099i | −0.0369731 | + | 0.999316i | \(0.511772\pi\) |
−0.846947 | + | 0.531678i | \(0.821562\pi\) | |||||||
\(24\) | − | 41.5692i | − | 0.353553i | ||||||
\(25\) | 22.0000 | + | 38.1051i | 0.176000 | + | 0.304841i | ||||
\(26\) | −74.0000 | −0.558177 | ||||||||
\(27\) | 140.296i | 1.00000i | ||||||||
\(28\) | −124.000 | −0.836921 | ||||||||
\(29\) | −55.5000 | − | 96.1288i | −0.355382 | − | 0.615540i | 0.631801 | − | 0.775131i | \(-0.282316\pi\) |
−0.987183 | + | 0.159590i | \(0.948983\pi\) | |||||||
\(30\) | 93.5307i | 0.569210i | ||||||||
\(31\) | 102.500 | − | 177.535i | 0.593856 | − | 1.02859i | −0.399851 | − | 0.916580i | \(-0.630938\pi\) |
0.993707 | − | 0.112009i | \(-0.0357285\pi\) | |||||||
\(32\) | −16.0000 | + | 27.7128i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 67.5000 | − | 38.9711i | 0.356068 | − | 0.205576i | ||||
\(34\) | 42.0000 | + | 72.7461i | 0.211851 | + | 0.366937i | ||||
\(35\) | 279.000 | 1.34742 | ||||||||
\(36\) | 54.0000 | − | 93.5307i | 0.250000 | − | 0.433013i | ||||
\(37\) | −166.000 | −0.737574 | −0.368787 | − | 0.929514i | \(-0.620227\pi\) | ||||
−0.368787 | + | 0.929514i | \(0.620227\pi\) | |||||||
\(38\) | 28.0000 | + | 48.4974i | 0.119532 | + | 0.207035i | ||||
\(39\) | −166.500 | − | 96.1288i | −0.683624 | − | 0.394691i | ||||
\(40\) | 36.0000 | − | 62.3538i | 0.142302 | − | 0.246475i | ||||
\(41\) | 130.500 | − | 226.033i | 0.497090 | − | 0.860985i | −0.502905 | − | 0.864342i | \(-0.667735\pi\) |
0.999994 | + | 0.00335732i | \(0.00106867\pi\) | |||||||
\(42\) | −279.000 | − | 161.081i | −1.02502 | − | 0.591793i | ||||
\(43\) | 21.5000 | + | 37.2391i | 0.0762493 | + | 0.132068i | 0.901629 | − | 0.432511i | \(-0.142372\pi\) |
−0.825380 | + | 0.564578i | \(0.809039\pi\) | |||||||
\(44\) | −60.0000 | −0.205576 | ||||||||
\(45\) | −121.500 | + | 210.444i | −0.402492 | + | 0.697137i | ||||
\(46\) | 390.000 | 1.25005 | ||||||||
\(47\) | −88.5000 | − | 153.286i | −0.274661 | − | 0.475726i | 0.695389 | − | 0.718634i | \(-0.255232\pi\) |
−0.970049 | + | 0.242907i | \(0.921899\pi\) | |||||||
\(48\) | −72.0000 | + | 41.5692i | −0.216506 | + | 0.125000i | ||||
\(49\) | −309.000 | + | 535.204i | −0.900875 | + | 1.56036i | ||||
\(50\) | 44.0000 | − | 76.2102i | 0.124451 | − | 0.215555i | ||||
\(51\) | 218.238i | 0.599206i | ||||||||
\(52\) | 74.0000 | + | 128.172i | 0.197345 | + | 0.341812i | ||||
\(53\) | 114.000 | 0.295455 | 0.147727 | − | 0.989028i | \(-0.452804\pi\) | ||||
0.147727 | + | 0.989028i | \(0.452804\pi\) | |||||||
\(54\) | 243.000 | − | 140.296i | 0.612372 | − | 0.353553i | ||||
\(55\) | 135.000 | 0.330971 | ||||||||
\(56\) | 124.000 | + | 214.774i | 0.295896 | + | 0.512508i | ||||
\(57\) | 145.492i | 0.338086i | ||||||||
\(58\) | −111.000 | + | 192.258i | −0.251293 | + | 0.435253i | ||||
\(59\) | −79.5000 | + | 137.698i | −0.175424 | + | 0.303843i | −0.940308 | − | 0.340325i | \(-0.889463\pi\) |
0.764884 | + | 0.644168i | \(0.222796\pi\) | |||||||
\(60\) | 162.000 | − | 93.5307i | 0.348569 | − | 0.201246i | ||||
\(61\) | −95.5000 | − | 165.411i | −0.200451 | − | 0.347192i | 0.748223 | − | 0.663448i | \(-0.230907\pi\) |
−0.948674 | + | 0.316256i | \(0.897574\pi\) | |||||||
\(62\) | −410.000 | −0.839840 | ||||||||
\(63\) | −418.500 | − | 724.863i | −0.836921 | − | 1.44959i | ||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −166.500 | − | 288.386i | −0.317720 | − | 0.550307i | ||||
\(66\) | −135.000 | − | 77.9423i | −0.251778 | − | 0.145364i | ||||
\(67\) | 210.500 | − | 364.597i | 0.383831 | − | 0.664815i | −0.607775 | − | 0.794109i | \(-0.707938\pi\) |
0.991606 | + | 0.129294i | \(0.0412712\pi\) | |||||||
\(68\) | 84.0000 | − | 145.492i | 0.149801 | − | 0.259464i | ||||
\(69\) | 877.500 | + | 506.625i | 1.53099 | + | 0.883920i | ||||
\(70\) | −279.000 | − | 483.242i | −0.476384 | − | 0.825121i | ||||
\(71\) | 156.000 | 0.260758 | 0.130379 | − | 0.991464i | \(-0.458381\pi\) | ||||
0.130379 | + | 0.991464i | \(0.458381\pi\) | |||||||
\(72\) | −216.000 | −0.353553 | ||||||||
\(73\) | 182.000 | 0.291801 | 0.145901 | − | 0.989299i | \(-0.453392\pi\) | ||||
0.145901 | + | 0.989299i | \(0.453392\pi\) | |||||||
\(74\) | 166.000 | + | 287.520i | 0.260772 | + | 0.451670i | ||||
\(75\) | 198.000 | − | 114.315i | 0.304841 | − | 0.176000i | ||||
\(76\) | 56.0000 | − | 96.9948i | 0.0845216 | − | 0.146396i | ||||
\(77\) | −232.500 | + | 402.702i | −0.344102 | + | 0.596002i | ||||
\(78\) | 384.515i | 0.558177i | ||||||||
\(79\) | −566.500 | − | 981.207i | −0.806788 | − | 1.39740i | −0.915078 | − | 0.403278i | \(-0.867871\pi\) |
0.108290 | − | 0.994119i | \(-0.465463\pi\) | |||||||
\(80\) | −144.000 | −0.201246 | ||||||||
\(81\) | 729.000 | 1.00000 | ||||||||
\(82\) | −522.000 | −0.702991 | ||||||||
\(83\) | 541.500 | + | 937.906i | 0.716113 | + | 1.24034i | 0.962529 | + | 0.271179i | \(0.0874136\pi\) |
−0.246416 | + | 0.969164i | \(0.579253\pi\) | |||||||
\(84\) | 644.323i | 0.836921i | ||||||||
\(85\) | −189.000 | + | 327.358i | −0.241176 | + | 0.417728i | ||||
\(86\) | 43.0000 | − | 74.4782i | 0.0539164 | − | 0.0933859i | ||||
\(87\) | −499.500 | + | 288.386i | −0.615540 | + | 0.355382i | ||||
\(88\) | 60.0000 | + | 103.923i | 0.0726821 | + | 0.125889i | ||||
\(89\) | −1050.00 | −1.25056 | −0.625280 | − | 0.780401i | \(-0.715015\pi\) | ||||
−0.625280 | + | 0.780401i | \(0.715015\pi\) | |||||||
\(90\) | 486.000 | 0.569210 | ||||||||
\(91\) | 1147.00 | 1.32130 | ||||||||
\(92\) | −390.000 | − | 675.500i | −0.441960 | − | 0.765497i | ||||
\(93\) | −922.500 | − | 532.606i | −1.02859 | − | 0.593856i | ||||
\(94\) | −177.000 | + | 306.573i | −0.194214 | + | 0.336389i | ||||
\(95\) | −126.000 | + | 218.238i | −0.136077 | + | 0.235693i | ||||
\(96\) | 144.000 | + | 83.1384i | 0.153093 | + | 0.0883883i | ||||
\(97\) | 450.500 | + | 780.289i | 0.471560 | + | 0.816766i | 0.999471 | − | 0.0325338i | \(-0.0103576\pi\) |
−0.527910 | + | 0.849300i | \(0.677024\pi\) | |||||||
\(98\) | 1236.00 | 1.27403 | ||||||||
\(99\) | −202.500 | − | 350.740i | −0.205576 | − | 0.356068i | ||||
\(100\) | −176.000 | −0.176000 | ||||||||
\(101\) | −193.500 | − | 335.152i | −0.190633 | − | 0.330187i | 0.754827 | − | 0.655924i | \(-0.227721\pi\) |
−0.945460 | + | 0.325737i | \(0.894387\pi\) | |||||||
\(102\) | 378.000 | − | 218.238i | 0.366937 | − | 0.211851i | ||||
\(103\) | −275.500 | + | 477.180i | −0.263552 | + | 0.456485i | −0.967183 | − | 0.254080i | \(-0.918227\pi\) |
0.703631 | + | 0.710565i | \(0.251561\pi\) | |||||||
\(104\) | 148.000 | − | 256.344i | 0.139544 | − | 0.241698i | ||||
\(105\) | − | 1449.73i | − | 1.34742i | ||||||
\(106\) | −114.000 | − | 197.454i | −0.104459 | − | 0.180928i | ||||
\(107\) | −12.0000 | −0.0108419 | −0.00542095 | − | 0.999985i | \(-0.501726\pi\) | ||||
−0.00542095 | + | 0.999985i | \(0.501726\pi\) | |||||||
\(108\) | −486.000 | − | 280.592i | −0.433013 | − | 0.250000i | ||||
\(109\) | −502.000 | −0.441127 | −0.220564 | − | 0.975373i | \(-0.570790\pi\) | ||||
−0.220564 | + | 0.975373i | \(0.570790\pi\) | |||||||
\(110\) | −135.000 | − | 233.827i | −0.117016 | − | 0.202677i | ||||
\(111\) | 862.561i | 0.737574i | ||||||||
\(112\) | 248.000 | − | 429.549i | 0.209230 | − | 0.362398i | ||||
\(113\) | 700.500 | − | 1213.30i | 0.583164 | − | 1.01007i | −0.411938 | − | 0.911212i | \(-0.635148\pi\) |
0.995102 | − | 0.0988572i | \(-0.0315187\pi\) | |||||||
\(114\) | 252.000 | − | 145.492i | 0.207035 | − | 0.119532i | ||||
\(115\) | 877.500 | + | 1519.87i | 0.711542 | + | 1.23243i | ||||
\(116\) | 444.000 | 0.355382 | ||||||||
\(117\) | −499.500 | + | 865.159i | −0.394691 | + | 0.683624i | ||||
\(118\) | 318.000 | 0.248087 | ||||||||
\(119\) | −651.000 | − | 1127.57i | −0.501488 | − | 0.868603i | ||||
\(120\) | −324.000 | − | 187.061i | −0.246475 | − | 0.142302i | ||||
\(121\) | 553.000 | − | 957.824i | 0.415477 | − | 0.719627i | ||||
\(122\) | −191.000 | + | 330.822i | −0.141740 | + | 0.245502i | ||||
\(123\) | −1174.50 | − | 678.098i | −0.860985 | − | 0.497090i | ||||
\(124\) | 410.000 | + | 710.141i | 0.296928 | + | 0.514295i | ||||
\(125\) | 1521.00 | 1.08834 | ||||||||
\(126\) | −837.000 | + | 1449.73i | −0.591793 | + | 1.02502i | ||||
\(127\) | −880.000 | −0.614861 | −0.307431 | − | 0.951571i | \(-0.599469\pi\) | ||||
−0.307431 | + | 0.951571i | \(0.599469\pi\) | |||||||
\(128\) | −64.0000 | − | 110.851i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 193.500 | − | 111.717i | 0.132068 | − | 0.0762493i | ||||
\(130\) | −333.000 | + | 576.773i | −0.224662 | + | 0.389126i | ||||
\(131\) | −751.500 | + | 1301.64i | −0.501213 | + | 0.868126i | 0.498786 | + | 0.866725i | \(0.333779\pi\) |
−0.999999 | + | 0.00140084i | \(0.999554\pi\) | |||||||
\(132\) | 311.769i | 0.205576i | ||||||||
\(133\) | −434.000 | − | 751.710i | −0.282952 | − | 0.490087i | ||||
\(134\) | −842.000 | −0.542819 | ||||||||
\(135\) | 1093.50 | + | 631.333i | 0.697137 | + | 0.402492i | ||||
\(136\) | −336.000 | −0.211851 | ||||||||
\(137\) | 1330.50 | + | 2304.49i | 0.829725 | + | 1.43713i | 0.898254 | + | 0.439476i | \(0.144836\pi\) |
−0.0685295 | + | 0.997649i | \(0.521831\pi\) | |||||||
\(138\) | − | 2026.50i | − | 1.25005i | ||||||
\(139\) | 60.5000 | − | 104.789i | 0.0369176 | − | 0.0639431i | −0.846976 | − | 0.531631i | \(-0.821579\pi\) |
0.883894 | + | 0.467688i | \(0.154913\pi\) | |||||||
\(140\) | −558.000 | + | 966.484i | −0.336854 | + | 0.583449i | ||||
\(141\) | −796.500 | + | 459.859i | −0.475726 | + | 0.274661i | ||||
\(142\) | −156.000 | − | 270.200i | −0.0921918 | − | 0.159681i | ||||
\(143\) | 555.000 | 0.324555 | ||||||||
\(144\) | 216.000 | + | 374.123i | 0.125000 | + | 0.216506i | ||||
\(145\) | −999.000 | −0.572155 | ||||||||
\(146\) | −182.000 | − | 315.233i | −0.103167 | − | 0.178691i | ||||
\(147\) | 2781.00 | + | 1605.61i | 1.56036 | + | 0.900875i | ||||
\(148\) | 332.000 | − | 575.041i | 0.184393 | − | 0.319379i | ||||
\(149\) | 1414.50 | − | 2449.99i | 0.777721 | − | 1.34705i | −0.155532 | − | 0.987831i | \(-0.549709\pi\) |
0.933253 | − | 0.359221i | \(-0.116957\pi\) | |||||||
\(150\) | −396.000 | − | 228.631i | −0.215555 | − | 0.124451i | ||||
\(151\) | −230.500 | − | 399.238i | −0.124224 | − | 0.215162i | 0.797205 | − | 0.603708i | \(-0.206311\pi\) |
−0.921429 | + | 0.388546i | \(0.872977\pi\) | |||||||
\(152\) | −224.000 | −0.119532 | ||||||||
\(153\) | 1134.00 | 0.599206 | ||||||||
\(154\) | 930.000 | 0.486633 | ||||||||
\(155\) | −922.500 | − | 1597.82i | −0.478045 | − | 0.827998i | ||||
\(156\) | 666.000 | − | 384.515i | 0.341812 | − | 0.197345i | ||||
\(157\) | 1488.50 | − | 2578.16i | 0.756658 | − | 1.31057i | −0.187889 | − | 0.982190i | \(-0.560164\pi\) |
0.944546 | − | 0.328379i | \(-0.106502\pi\) | |||||||
\(158\) | −1133.00 | + | 1962.41i | −0.570485 | + | 0.988109i | ||||
\(159\) | − | 592.361i | − | 0.295455i | ||||||
\(160\) | 144.000 | + | 249.415i | 0.0711512 | + | 0.123238i | ||||
\(161\) | −6045.00 | −2.95909 | ||||||||
\(162\) | −729.000 | − | 1262.67i | −0.353553 | − | 0.612372i | ||||
\(163\) | −3316.00 | −1.59343 | −0.796715 | − | 0.604355i | \(-0.793431\pi\) | ||||
−0.796715 | + | 0.604355i | \(0.793431\pi\) | |||||||
\(164\) | 522.000 | + | 904.131i | 0.248545 | + | 0.430492i | ||||
\(165\) | − | 701.481i | − | 0.330971i | ||||||
\(166\) | 1083.00 | − | 1875.81i | 0.506368 | − | 0.877055i | ||||
\(167\) | 340.500 | − | 589.763i | 0.157777 | − | 0.273277i | −0.776290 | − | 0.630376i | \(-0.782901\pi\) |
0.934067 | + | 0.357099i | \(0.116234\pi\) | |||||||
\(168\) | 1116.00 | − | 644.323i | 0.512508 | − | 0.295896i | ||||
\(169\) | 414.000 | + | 717.069i | 0.188439 | + | 0.326386i | ||||
\(170\) | 756.000 | 0.341074 | ||||||||
\(171\) | 756.000 | 0.338086 | ||||||||
\(172\) | −172.000 | −0.0762493 | ||||||||
\(173\) | 1990.50 | + | 3447.65i | 0.874768 | + | 1.51514i | 0.857009 | + | 0.515301i | \(0.172320\pi\) |
0.0177589 | + | 0.999842i | \(0.494347\pi\) | |||||||
\(174\) | 999.000 | + | 576.773i | 0.435253 | + | 0.251293i | ||||
\(175\) | −682.000 | + | 1181.26i | −0.294596 | + | 0.510256i | ||||
\(176\) | 120.000 | − | 207.846i | 0.0513940 | − | 0.0890170i | ||||
\(177\) | 715.500 | + | 413.094i | 0.303843 | + | 0.175424i | ||||
\(178\) | 1050.00 | + | 1818.65i | 0.442139 | + | 0.765808i | ||||
\(179\) | 2004.00 | 0.836793 | 0.418397 | − | 0.908264i | \(-0.362592\pi\) | ||||
0.418397 | + | 0.908264i | \(0.362592\pi\) | |||||||
\(180\) | −486.000 | − | 841.777i | −0.201246 | − | 0.348569i | ||||
\(181\) | 1274.00 | 0.523181 | 0.261590 | − | 0.965179i | \(-0.415753\pi\) | ||||
0.261590 | + | 0.965179i | \(0.415753\pi\) | |||||||
\(182\) | −1147.00 | − | 1986.66i | −0.467150 | − | 0.809128i | ||||
\(183\) | −859.500 | + | 496.233i | −0.347192 | + | 0.200451i | ||||
\(184\) | −780.000 | + | 1351.00i | −0.312513 | + | 0.541288i | ||||
\(185\) | −747.000 | + | 1293.84i | −0.296868 | + | 0.514190i | ||||
\(186\) | 2130.42i | 0.839840i | ||||||||
\(187\) | −315.000 | − | 545.596i | −0.123182 | − | 0.213358i | ||||
\(188\) | 708.000 | 0.274661 | ||||||||
\(189\) | −3766.50 | + | 2174.59i | −1.44959 | + | 0.836921i | ||||
\(190\) | 504.000 | 0.192442 | ||||||||
\(191\) | −580.500 | − | 1005.46i | −0.219914 | − | 0.380902i | 0.734868 | − | 0.678210i | \(-0.237244\pi\) |
−0.954781 | + | 0.297309i | \(0.903911\pi\) | |||||||
\(192\) | − | 332.554i | − | 0.125000i | ||||||
\(193\) | −1805.50 | + | 3127.22i | −0.673382 | + | 1.16633i | 0.303557 | + | 0.952813i | \(0.401826\pi\) |
−0.976939 | + | 0.213519i | \(0.931508\pi\) | |||||||
\(194\) | 901.000 | − | 1560.58i | 0.333443 | − | 0.577541i | ||||
\(195\) | −1498.50 | + | 865.159i | −0.550307 | + | 0.317720i | ||||
\(196\) | −1236.00 | − | 2140.81i | −0.450437 | − | 0.780180i | ||||
\(197\) | 2046.00 | 0.739957 | 0.369978 | − | 0.929040i | \(-0.379365\pi\) | ||||
0.369978 | + | 0.929040i | \(0.379365\pi\) | |||||||
\(198\) | −405.000 | + | 701.481i | −0.145364 | + | 0.251778i | ||||
\(199\) | 2996.00 | 1.06724 | 0.533620 | − | 0.845724i | \(-0.320831\pi\) | ||||
0.533620 | + | 0.845724i | \(0.320831\pi\) | |||||||
\(200\) | 176.000 | + | 304.841i | 0.0622254 | + | 0.107778i | ||||
\(201\) | −1894.50 | − | 1093.79i | −0.664815 | − | 0.383831i | ||||
\(202\) | −387.000 | + | 670.304i | −0.134798 | + | 0.233477i | ||||
\(203\) | 1720.50 | − | 2979.99i | 0.594854 | − | 1.03032i | ||||
\(204\) | −756.000 | − | 436.477i | −0.259464 | − | 0.149801i | ||||
\(205\) | −1174.50 | − | 2034.29i | −0.400149 | − | 0.693079i | ||||
\(206\) | 1102.00 | 0.372718 | ||||||||
\(207\) | 2632.50 | − | 4559.62i | 0.883920 | − | 1.53099i | ||||
\(208\) | −592.000 | −0.197345 | ||||||||
\(209\) | −210.000 | − | 363.731i | −0.0695024 | − | 0.120382i | ||||
\(210\) | −2511.00 | + | 1449.73i | −0.825121 | + | 0.476384i | ||||
\(211\) | −377.500 | + | 653.849i | −0.123167 | + | 0.213331i | −0.921015 | − | 0.389528i | \(-0.872638\pi\) |
0.797848 | + | 0.602858i | \(0.205972\pi\) | |||||||
\(212\) | −228.000 | + | 394.908i | −0.0738637 | + | 0.127936i | ||||
\(213\) | − | 810.600i | − | 0.260758i | ||||||
\(214\) | 12.0000 | + | 20.7846i | 0.00383319 | + | 0.00663928i | ||||
\(215\) | 387.000 | 0.122759 | ||||||||
\(216\) | 1122.37i | 0.353553i | ||||||||
\(217\) | 6355.00 | 1.98804 | ||||||||
\(218\) | 502.000 | + | 869.490i | 0.155962 | + | 0.270134i | ||||
\(219\) | − | 945.700i | − | 0.291801i | ||||||
\(220\) | −270.000 | + | 467.654i | −0.0827427 | + | 0.143315i | ||||
\(221\) | −777.000 | + | 1345.80i | −0.236501 | + | 0.409631i | ||||
\(222\) | 1494.00 | − | 862.561i | 0.451670 | − | 0.260772i | ||||
\(223\) | 1731.50 | + | 2999.05i | 0.519954 | + | 0.900587i | 0.999731 | + | 0.0231966i | \(0.00738438\pi\) |
−0.479777 | + | 0.877391i | \(0.659282\pi\) | |||||||
\(224\) | −992.000 | −0.295896 | ||||||||
\(225\) | −594.000 | − | 1028.84i | −0.176000 | − | 0.304841i | ||||
\(226\) | −2802.00 | −0.824718 | ||||||||
\(227\) | −3112.50 | − | 5391.01i | −0.910061 | − | 1.57627i | −0.813976 | − | 0.580899i | \(-0.802701\pi\) |
−0.0960856 | − | 0.995373i | \(-0.530632\pi\) | |||||||
\(228\) | −504.000 | − | 290.985i | −0.146396 | − | 0.0845216i | ||||
\(229\) | 732.500 | − | 1268.73i | 0.211375 | − | 0.366113i | −0.740770 | − | 0.671759i | \(-0.765539\pi\) |
0.952145 | + | 0.305646i | \(0.0988724\pi\) | |||||||
\(230\) | 1755.00 | − | 3039.75i | 0.503136 | − | 0.871457i | ||||
\(231\) | 2092.50 | + | 1208.11i | 0.596002 | + | 0.344102i | ||||
\(232\) | −444.000 | − | 769.031i | −0.125647 | − | 0.217626i | ||||
\(233\) | 2634.00 | 0.740597 | 0.370298 | − | 0.928913i | \(-0.379255\pi\) | ||||
0.370298 | + | 0.928913i | \(0.379255\pi\) | |||||||
\(234\) | 1998.00 | 0.558177 | ||||||||
\(235\) | −1593.00 | −0.442195 | ||||||||
\(236\) | −318.000 | − | 550.792i | −0.0877120 | − | 0.151922i | ||||
\(237\) | −5098.50 | + | 2943.62i | −1.39740 | + | 0.806788i | ||||
\(238\) | −1302.00 | + | 2255.13i | −0.354606 | + | 0.614195i | ||||
\(239\) | −3457.50 | + | 5988.57i | −0.935762 | + | 1.62079i | −0.162492 | + | 0.986710i | \(0.551953\pi\) |
−0.773270 | + | 0.634077i | \(0.781380\pi\) | |||||||
\(240\) | 748.246i | 0.201246i | ||||||||
\(241\) | 744.500 | + | 1289.51i | 0.198994 | + | 0.344667i | 0.948202 | − | 0.317667i | \(-0.102899\pi\) |
−0.749209 | + | 0.662334i | \(0.769566\pi\) | |||||||
\(242\) | −2212.00 | −0.587573 | ||||||||
\(243\) | − | 3788.00i | − | 1.00000i | ||||||
\(244\) | 764.000 | 0.200451 | ||||||||
\(245\) | 2781.00 | + | 4816.83i | 0.725190 | + | 1.25607i | ||||
\(246\) | 2712.39i | 0.702991i | ||||||||
\(247\) | −518.000 | + | 897.202i | −0.133439 | + | 0.231124i | ||||
\(248\) | 820.000 | − | 1420.28i | 0.209960 | − | 0.363661i | ||||
\(249\) | 4873.50 | − | 2813.72i | 1.24034 | − | 0.716113i | ||||
\(250\) | −1521.00 | − | 2634.45i | −0.384786 | − | 0.666469i | ||||
\(251\) | −4620.00 | −1.16180 | −0.580900 | − | 0.813975i | \(-0.697299\pi\) | ||||
−0.580900 | + | 0.813975i | \(0.697299\pi\) | |||||||
\(252\) | 3348.00 | 0.836921 | ||||||||
\(253\) | −2925.00 | −0.726850 | ||||||||
\(254\) | 880.000 | + | 1524.20i | 0.217386 | + | 0.376524i | ||||
\(255\) | 1701.00 | + | 982.073i | 0.417728 | + | 0.241176i | ||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −1675.50 | + | 2902.05i | −0.406672 | + | 0.704377i | −0.994515 | − | 0.104598i | \(-0.966644\pi\) |
0.587842 | + | 0.808976i | \(0.299978\pi\) | |||||||
\(258\) | −387.000 | − | 223.435i | −0.0933859 | − | 0.0539164i | ||||
\(259\) | −2573.00 | − | 4456.57i | −0.617291 | − | 1.06918i | ||||
\(260\) | 1332.00 | 0.317720 | ||||||||
\(261\) | 1498.50 | + | 2595.48i | 0.355382 | + | 0.615540i | ||||
\(262\) | 3006.00 | 0.708822 | ||||||||
\(263\) | 301.500 | + | 522.213i | 0.0706893 | + | 0.122437i | 0.899204 | − | 0.437530i | \(-0.144147\pi\) |
−0.828514 | + | 0.559968i | \(0.810813\pi\) | |||||||
\(264\) | 540.000 | − | 311.769i | 0.125889 | − | 0.0726821i | ||||
\(265\) | 513.000 | − | 888.542i | 0.118918 | − | 0.205972i | ||||
\(266\) | −868.000 | + | 1503.42i | −0.200077 | + | 0.346544i | ||||
\(267\) | 5455.96i | 1.25056i | ||||||||
\(268\) | 842.000 | + | 1458.39i | 0.191915 | + | 0.332407i | ||||
\(269\) | −1470.00 | −0.333188 | −0.166594 | − | 0.986026i | \(-0.553277\pi\) | ||||
−0.166594 | + | 0.986026i | \(0.553277\pi\) | |||||||
\(270\) | − | 2525.33i | − | 0.569210i | ||||||
\(271\) | 2072.00 | 0.464447 | 0.232223 | − | 0.972662i | \(-0.425400\pi\) | ||||
0.232223 | + | 0.972662i | \(0.425400\pi\) | |||||||
\(272\) | 336.000 | + | 581.969i | 0.0749007 | + | 0.129732i | ||||
\(273\) | − | 5959.99i | − | 1.32130i | ||||||
\(274\) | 2661.00 | − | 4608.99i | 0.586704 | − | 1.01620i | ||||
\(275\) | −330.000 | + | 571.577i | −0.0723627 | + | 0.125336i | ||||
\(276\) | −3510.00 | + | 2026.50i | −0.765497 | + | 0.441960i | ||||
\(277\) | −3569.50 | − | 6182.56i | −0.774262 | − | 1.34106i | −0.935209 | − | 0.354097i | \(-0.884788\pi\) |
0.160947 | − | 0.986963i | \(-0.448545\pi\) | |||||||
\(278\) | −242.000 | −0.0522093 | ||||||||
\(279\) | −2767.50 | + | 4793.45i | −0.593856 | + | 1.02859i | ||||
\(280\) | 2232.00 | 0.476384 | ||||||||
\(281\) | −4213.50 | − | 7298.00i | −0.894507 | − | 1.54933i | −0.834414 | − | 0.551138i | \(-0.814194\pi\) |
−0.0600924 | − | 0.998193i | \(-0.519140\pi\) | |||||||
\(282\) | 1593.00 | + | 919.719i | 0.336389 | + | 0.194214i | ||||
\(283\) | 228.500 | − | 395.774i | 0.0479962 | − | 0.0831318i | −0.841029 | − | 0.540990i | \(-0.818050\pi\) |
0.889025 | + | 0.457858i | \(0.151383\pi\) | |||||||
\(284\) | −312.000 | + | 540.400i | −0.0651894 | + | 0.112911i | ||||
\(285\) | 1134.00 | + | 654.715i | 0.235693 | + | 0.136077i | ||||
\(286\) | −555.000 | − | 961.288i | −0.114748 | − | 0.198749i | ||||
\(287\) | 8091.00 | 1.66410 | ||||||||
\(288\) | 432.000 | − | 748.246i | 0.0883883 | − | 0.153093i | ||||
\(289\) | −3149.00 | −0.640953 | ||||||||
\(290\) | 999.000 | + | 1730.32i | 0.202287 | + | 0.350372i | ||||
\(291\) | 4054.50 | − | 2340.87i | 0.816766 | − | 0.471560i | ||||
\(292\) | −364.000 | + | 630.466i | −0.0729503 | + | 0.126354i | ||||
\(293\) | 2944.50 | − | 5100.02i | 0.587097 | − | 1.01688i | −0.407513 | − | 0.913199i | \(-0.633604\pi\) |
0.994610 | − | 0.103683i | \(-0.0330628\pi\) | |||||||
\(294\) | − | 6422.44i | − | 1.27403i | ||||||
\(295\) | 715.500 | + | 1239.28i | 0.141214 | + | 0.244589i | ||||
\(296\) | −1328.00 | −0.260772 | ||||||||
\(297\) | −1822.50 | + | 1052.22i | −0.356068 | + | 0.205576i | ||||
\(298\) | −5658.00 | −1.09986 | ||||||||
\(299\) | 3607.50 | + | 6248.37i | 0.697750 | + | 1.20854i | ||||
\(300\) | 914.523i | 0.176000i | ||||||||
\(301\) | −666.500 | + | 1154.41i | −0.127629 | + | 0.221060i | ||||
\(302\) | −461.000 | + | 798.475i | −0.0878396 | + | 0.152143i | ||||
\(303\) | −1741.50 | + | 1005.46i | −0.330187 | + | 0.190633i | ||||
\(304\) | 224.000 | + | 387.979i | 0.0422608 | + | 0.0731978i | ||||
\(305\) | −1719.00 | −0.322720 | ||||||||
\(306\) | −1134.00 | − | 1964.15i | −0.211851 | − | 0.366937i | ||||
\(307\) | −1204.00 | −0.223830 | −0.111915 | − | 0.993718i | \(-0.535698\pi\) | ||||
−0.111915 | + | 0.993718i | \(0.535698\pi\) | |||||||
\(308\) | −930.000 | − | 1610.81i | −0.172051 | − | 0.298001i | ||||
\(309\) | 2479.50 | + | 1431.54i | 0.456485 | + | 0.263552i | ||||
\(310\) | −1845.00 | + | 3195.63i | −0.338029 | + | 0.585483i | ||||
\(311\) | 1642.50 | − | 2844.89i | 0.299478 | − | 0.518711i | −0.676539 | − | 0.736407i | \(-0.736521\pi\) |
0.976017 | + | 0.217696i | \(0.0698542\pi\) | |||||||
\(312\) | −1332.00 | − | 769.031i | −0.241698 | − | 0.139544i | ||||
\(313\) | 5028.50 | + | 8709.62i | 0.908075 | + | 1.57283i | 0.816735 | + | 0.577013i | \(0.195782\pi\) |
0.0913406 | + | 0.995820i | \(0.470885\pi\) | |||||||
\(314\) | −5954.00 | −1.07008 | ||||||||
\(315\) | −7533.00 | −1.34742 | ||||||||
\(316\) | 4532.00 | 0.806788 | ||||||||
\(317\) | −1147.50 | − | 1987.53i | −0.203312 | − | 0.352147i | 0.746281 | − | 0.665631i | \(-0.231837\pi\) |
−0.949594 | + | 0.313483i | \(0.898504\pi\) | |||||||
\(318\) | −1026.00 | + | 592.361i | −0.180928 | + | 0.104459i | ||||
\(319\) | 832.500 | − | 1441.93i | 0.146116 | − | 0.253081i | ||||
\(320\) | 288.000 | − | 498.831i | 0.0503115 | − | 0.0871421i | ||||
\(321\) | 62.3538i | 0.0108419i | ||||||||
\(322\) | 6045.00 | + | 10470.2i | 1.04619 | + | 1.81206i | ||||
\(323\) | 1176.00 | 0.202583 | ||||||||
\(324\) | −1458.00 | + | 2525.33i | −0.250000 | + | 0.433013i | ||||
\(325\) | 1628.00 | 0.277862 | ||||||||
\(326\) | 3316.00 | + | 5743.48i | 0.563363 | + | 0.975773i | ||||
\(327\) | 2608.47i | 0.441127i | ||||||||
\(328\) | 1044.00 | − | 1808.26i | 0.175748 | − | 0.304404i | ||||
\(329\) | 2743.50 | − | 4751.88i | 0.459739 | − | 0.796291i | ||||
\(330\) | −1215.00 | + | 701.481i | −0.202677 | + | 0.117016i | ||||
\(331\) | 3339.50 | + | 5784.18i | 0.554548 | + | 0.960506i | 0.997939 | + | 0.0641773i | \(0.0204423\pi\) |
−0.443390 | + | 0.896329i | \(0.646224\pi\) | |||||||
\(332\) | −4332.00 | −0.716113 | ||||||||
\(333\) | 4482.00 | 0.737574 | ||||||||
\(334\) | −1362.00 | −0.223130 | ||||||||
\(335\) | −1894.50 | − | 3281.37i | −0.308978 | − | 0.535165i | ||||
\(336\) | −2232.00 | − | 1288.65i | −0.362398 | − | 0.209230i | ||||
\(337\) | −1091.50 | + | 1890.53i | −0.176433 | + | 0.305590i | −0.940656 | − | 0.339361i | \(-0.889789\pi\) |
0.764224 | + | 0.644951i | \(0.223122\pi\) | |||||||
\(338\) | 828.000 | − | 1434.14i | 0.133246 | − | 0.230789i | ||||
\(339\) | −6304.50 | − | 3639.90i | −1.01007 | − | 0.583164i | ||||
\(340\) | −756.000 | − | 1309.43i | −0.120588 | − | 0.208864i | ||||
\(341\) | 3075.00 | 0.488330 | ||||||||
\(342\) | −756.000 | − | 1309.43i | −0.119532 | − | 0.207035i | ||||
\(343\) | −8525.00 | −1.34200 | ||||||||
\(344\) | 172.000 | + | 297.913i | 0.0269582 | + | 0.0466930i | ||||
\(345\) | 7897.50 | − | 4559.62i | 1.23243 | − | 0.711542i | ||||
\(346\) | 3981.00 | − | 6895.29i | 0.618555 | − | 1.07137i | ||||
\(347\) | −1945.50 | + | 3369.70i | −0.300980 | + | 0.521312i | −0.976358 | − | 0.216159i | \(-0.930647\pi\) |
0.675379 | + | 0.737471i | \(0.263980\pi\) | |||||||
\(348\) | − | 2307.09i | − | 0.355382i | ||||||
\(349\) | −1397.50 | − | 2420.54i | −0.214345 | − | 0.371257i | 0.738725 | − | 0.674007i | \(-0.235428\pi\) |
−0.953070 | + | 0.302751i | \(0.902095\pi\) | |||||||
\(350\) | 2728.00 | 0.416622 | ||||||||
\(351\) | 4495.50 | + | 2595.48i | 0.683624 | + | 0.394691i | ||||
\(352\) | −480.000 | −0.0726821 | ||||||||
\(353\) | −2377.50 | − | 4117.95i | −0.358475 | − | 0.620896i | 0.629232 | − | 0.777218i | \(-0.283370\pi\) |
−0.987706 | + | 0.156322i | \(0.950036\pi\) | |||||||
\(354\) | − | 1652.38i | − | 0.248087i | ||||||
\(355\) | 702.000 | − | 1215.90i | 0.104953 | − | 0.181784i | ||||
\(356\) | 2100.00 | − | 3637.31i | 0.312640 | − | 0.541508i | ||||
\(357\) | −5859.00 | + | 3382.70i | −0.868603 | + | 0.501488i | ||||
\(358\) | −2004.00 | − | 3471.03i | −0.295851 | − | 0.512429i | ||||
\(359\) | 4608.00 | 0.677440 | 0.338720 | − | 0.940887i | \(-0.390006\pi\) | ||||
0.338720 | + | 0.940887i | \(0.390006\pi\) | |||||||
\(360\) | −972.000 | + | 1683.55i | −0.142302 | + | 0.246475i | ||||
\(361\) | −6075.00 | −0.885698 | ||||||||
\(362\) | −1274.00 | − | 2206.63i | −0.184972 | − | 0.320381i | ||||
\(363\) | −4977.00 | − | 2873.47i | −0.719627 | − | 0.415477i | ||||
\(364\) | −2294.00 | + | 3973.32i | −0.330325 | + | 0.572140i | ||||
\(365\) | 819.000 | − | 1418.55i | 0.117448 | − | 0.203425i | ||||
\(366\) | 1719.00 | + | 992.465i | 0.245502 | + | 0.141740i | ||||
\(367\) | −1922.50 | − | 3329.87i | −0.273443 | − | 0.473618i | 0.696298 | − | 0.717753i | \(-0.254829\pi\) |
−0.969741 | + | 0.244135i | \(0.921496\pi\) | |||||||
\(368\) | 3120.00 | 0.441960 | ||||||||
\(369\) | −3523.50 | + | 6102.88i | −0.497090 | + | 0.860985i | ||||
\(370\) | 2988.00 | 0.419834 | ||||||||
\(371\) | 1767.00 | + | 3060.53i | 0.247272 | + | 0.428288i | ||||
\(372\) | 3690.00 | − | 2130.42i | 0.514295 | − | 0.296928i | ||||
\(373\) | 4158.50 | − | 7202.73i | 0.577263 | − | 0.999848i | −0.418529 | − | 0.908203i | \(-0.637454\pi\) |
0.995792 | − | 0.0916449i | \(-0.0292125\pi\) | |||||||
\(374\) | −630.000 | + | 1091.19i | −0.0871030 | + | 0.150867i | ||||
\(375\) | − | 7903.35i | − | 1.08834i | ||||||
\(376\) | −708.000 | − | 1226.29i | −0.0971072 | − | 0.168195i | ||||
\(377\) | −4107.00 | −0.561064 | ||||||||
\(378\) | 7533.00 | + | 4349.18i | 1.02502 | + | 0.591793i | ||||
\(379\) | 12560.0 | 1.70228 | 0.851140 | − | 0.524939i | \(-0.175912\pi\) | ||||
0.851140 | + | 0.524939i | \(0.175912\pi\) | |||||||
\(380\) | −504.000 | − | 872.954i | −0.0680386 | − | 0.117846i | ||||
\(381\) | 4572.61i | 0.614861i | ||||||||
\(382\) | −1161.00 | + | 2010.91i | −0.155502 | + | 0.269338i | ||||
\(383\) | −6043.50 | + | 10467.6i | −0.806288 | + | 1.39653i | 0.109130 | + | 0.994028i | \(0.465194\pi\) |
−0.915418 | + | 0.402505i | \(0.868140\pi\) | |||||||
\(384\) | −576.000 | + | 332.554i | −0.0765466 | + | 0.0441942i | ||||
\(385\) | 2092.50 | + | 3624.32i | 0.276997 | + | 0.479772i | ||||
\(386\) | 7222.00 | 0.952306 | ||||||||
\(387\) | −580.500 | − | 1005.46i | −0.0762493 | − | 0.132068i | ||||
\(388\) | −3604.00 | −0.471560 | ||||||||
\(389\) | 4270.50 | + | 7396.72i | 0.556614 | + | 0.964084i | 0.997776 | + | 0.0666565i | \(0.0212332\pi\) |
−0.441162 | + | 0.897428i | \(0.645433\pi\) | |||||||
\(390\) | 2997.00 | + | 1730.32i | 0.389126 | + | 0.224662i | ||||
\(391\) | 4095.00 | − | 7092.75i | 0.529650 | − | 0.917380i | ||||
\(392\) | −2472.00 | + | 4281.63i | −0.318507 | + | 0.551671i | ||||
\(393\) | 6763.50 | + | 3904.91i | 0.868126 | + | 0.501213i | ||||
\(394\) | −2046.00 | − | 3543.78i | −0.261614 | − | 0.453129i | ||||
\(395\) | −10197.0 | −1.29890 | ||||||||
\(396\) | 1620.00 | 0.205576 | ||||||||
\(397\) | −13174.0 | −1.66545 | −0.832726 | − | 0.553686i | \(-0.813221\pi\) | ||||
−0.832726 | + | 0.553686i | \(0.813221\pi\) | |||||||
\(398\) | −2996.00 | − | 5189.22i | −0.377326 | − | 0.653549i | ||||
\(399\) | −3906.00 | + | 2255.13i | −0.490087 | + | 0.282952i | ||||
\(400\) | 352.000 | − | 609.682i | 0.0440000 | − | 0.0762102i | ||||
\(401\) | −4801.50 | + | 8316.44i | −0.597944 | + | 1.03567i | 0.395180 | + | 0.918604i | \(0.370682\pi\) |
−0.993124 | + | 0.117066i | \(0.962651\pi\) | |||||||
\(402\) | 4375.16i | 0.542819i | ||||||||
\(403\) | −3792.50 | − | 6568.80i | −0.468779 | − | 0.811949i | ||||
\(404\) | 1548.00 | 0.190633 | ||||||||
\(405\) | 3280.50 | − | 5681.99i | 0.402492 | − | 0.697137i | ||||
\(406\) | −6882.00 | −0.841251 | ||||||||
\(407\) | −1245.00 | − | 2156.40i | −0.151627 | − | 0.262626i | ||||
\(408\) | 1745.91i | 0.211851i | ||||||||
\(409\) | −5735.50 | + | 9934.18i | −0.693404 | + | 1.20101i | 0.277312 | + | 0.960780i | \(0.410557\pi\) |
−0.970716 | + | 0.240231i | \(0.922777\pi\) | |||||||
\(410\) | −2349.00 | + | 4068.59i | −0.282948 | + | 0.490081i | ||||
\(411\) | 11974.5 | − | 6913.48i | 1.43713 | − | 0.829725i | ||||
\(412\) | −1102.00 | − | 1908.72i | −0.131776 | − | 0.228242i | ||||
\(413\) | −4929.00 | −0.587264 | ||||||||
\(414\) | −10530.0 | −1.25005 | ||||||||
\(415\) | 9747.00 | 1.15292 | ||||||||
\(416\) | 592.000 | + | 1025.37i | 0.0697721 | + | 0.120849i | ||||
\(417\) | −544.500 | − | 314.367i | −0.0639431 | − | 0.0369176i | ||||
\(418\) | −420.000 | + | 727.461i | −0.0491456 | + | 0.0851227i | ||||
\(419\) | 2986.50 | − | 5172.77i | 0.348210 | − | 0.603118i | −0.637721 | − | 0.770267i | \(-0.720123\pi\) |
0.985932 | + | 0.167149i | \(0.0534562\pi\) | |||||||
\(420\) | 5022.00 | + | 2899.45i | 0.583449 | + | 0.336854i | ||||
\(421\) | 4452.50 | + | 7711.96i | 0.515443 | + | 0.892774i | 0.999839 | + | 0.0179250i | \(0.00570601\pi\) |
−0.484396 | + | 0.874849i | \(0.660961\pi\) | |||||||
\(422\) | 1510.00 | 0.174184 | ||||||||
\(423\) | 2389.50 | + | 4138.74i | 0.274661 | + | 0.475726i | ||||
\(424\) | 912.000 | 0.104459 | ||||||||
\(425\) | −924.000 | − | 1600.41i | −0.105460 | − | 0.182662i | ||||
\(426\) | −1404.00 | + | 810.600i | −0.159681 | + | 0.0921918i | ||||
\(427\) | 2960.50 | − | 5127.74i | 0.335524 | − | 0.581144i | ||||
\(428\) | 24.0000 | − | 41.5692i | 0.00271048 | − | 0.00469468i | ||||
\(429\) | − | 2883.86i | − | 0.324555i | ||||||
\(430\) | −387.000 | − | 670.304i | −0.0434019 | − | 0.0751742i | ||||
\(431\) | 1416.00 | 0.158251 | 0.0791257 | − | 0.996865i | \(-0.474787\pi\) | ||||
0.0791257 | + | 0.996865i | \(0.474787\pi\) | |||||||
\(432\) | 1944.00 | − | 1122.37i | 0.216506 | − | 0.125000i | ||||
\(433\) | 10766.0 | 1.19488 | 0.597438 | − | 0.801915i | \(-0.296186\pi\) | ||||
0.597438 | + | 0.801915i | \(0.296186\pi\) | |||||||
\(434\) | −6355.00 | − | 11007.2i | −0.702880 | − | 1.21742i | ||||
\(435\) | 5190.96i | 0.572155i | ||||||||
\(436\) | 1004.00 | − | 1738.98i | 0.110282 | − | 0.191014i | ||||
\(437\) | 2730.00 | − | 4728.50i | 0.298841 | − | 0.517608i | ||||
\(438\) | −1638.00 | + | 945.700i | −0.178691 | + | 0.103167i | ||||
\(439\) | −2174.50 | − | 3766.34i | −0.236408 | − | 0.409471i | 0.723273 | − | 0.690562i | \(-0.242637\pi\) |
−0.959681 | + | 0.281091i | \(0.909304\pi\) | |||||||
\(440\) | 1080.00 | 0.117016 | ||||||||
\(441\) | 8343.00 | − | 14450.5i | 0.900875 | − | 1.56036i | ||||
\(442\) | 3108.00 | 0.334463 | ||||||||
\(443\) | 7273.50 | + | 12598.1i | 0.780078 | + | 1.35113i | 0.931896 | + | 0.362726i | \(0.118154\pi\) |
−0.151818 | + | 0.988408i | \(0.548513\pi\) | |||||||
\(444\) | −2988.00 | − | 1725.12i | −0.319379 | − | 0.184393i | ||||
\(445\) | −4725.00 | + | 8183.94i | −0.503340 | + | 0.871811i | ||||
\(446\) | 3463.00 | − | 5998.09i | 0.367663 | − | 0.636811i | ||||
\(447\) | −12730.5 | − | 7349.96i | −1.34705 | − | 0.777721i | ||||
\(448\) | 992.000 | + | 1718.19i | 0.104615 | + | 0.181199i | ||||
\(449\) | −3330.00 | −0.350005 | −0.175003 | − | 0.984568i | \(-0.555993\pi\) | ||||
−0.175003 | + | 0.984568i | \(0.555993\pi\) | |||||||
\(450\) | −1188.00 | + | 2057.68i | −0.124451 | + | 0.215555i | ||||
\(451\) | 3915.00 | 0.408759 | ||||||||
\(452\) | 2802.00 | + | 4853.21i | 0.291582 | + | 0.505035i | ||||
\(453\) | −2074.50 | + | 1197.71i | −0.215162 | + | 0.124224i | ||||
\(454\) | −6225.00 | + | 10782.0i | −0.643510 | + | 1.11459i | ||||
\(455\) | 5161.50 | − | 8939.98i | 0.531813 | − | 0.921127i | ||||
\(456\) | 1163.94i | 0.119532i | ||||||||
\(457\) | −4073.50 | − | 7055.51i | −0.416959 | − | 0.722194i | 0.578673 | − | 0.815560i | \(-0.303571\pi\) |
−0.995632 | + | 0.0933655i | \(0.970237\pi\) | |||||||
\(458\) | −2930.00 | −0.298930 | ||||||||
\(459\) | − | 5892.44i | − | 0.599206i | ||||||
\(460\) | −7020.00 | −0.711542 | ||||||||
\(461\) | −4015.50 | − | 6955.05i | −0.405684 | − | 0.702666i | 0.588717 | − | 0.808340i | \(-0.299633\pi\) |
−0.994401 | + | 0.105674i | \(0.966300\pi\) | |||||||
\(462\) | − | 4832.42i | − | 0.486633i | ||||||
\(463\) | −2141.50 | + | 3709.19i | −0.214955 | + | 0.372312i | −0.953259 | − | 0.302156i | \(-0.902294\pi\) |
0.738304 | + | 0.674468i | \(0.235627\pi\) | |||||||
\(464\) | −888.000 | + | 1538.06i | −0.0888456 | + | 0.153885i | ||||
\(465\) | −8302.50 | + | 4793.45i | −0.827998 | + | 0.478045i | ||||
\(466\) | −2634.00 | − | 4562.22i | −0.261841 | − | 0.453521i | ||||
\(467\) | 5460.00 | 0.541025 | 0.270512 | − | 0.962716i | \(-0.412807\pi\) | ||||
0.270512 | + | 0.962716i | \(0.412807\pi\) | |||||||
\(468\) | −1998.00 | − | 3460.64i | −0.197345 | − | 0.341812i | ||||
\(469\) | 13051.0 | 1.28494 | ||||||||
\(470\) | 1593.00 | + | 2759.16i | 0.156340 | + | 0.270788i | ||||
\(471\) | −13396.5 | − | 7734.47i | −1.31057 | − | 0.756658i | ||||
\(472\) | −636.000 | + | 1101.58i | −0.0620218 | + | 0.107425i | ||||
\(473\) | −322.500 | + | 558.586i | −0.0313500 | + | 0.0542999i | ||||
\(474\) | 10197.0 | + | 5887.24i | 0.988109 | + | 0.570485i | ||||
\(475\) | −616.000 | − | 1066.94i | −0.0595032 | − | 0.103063i | ||||
\(476\) | 5208.00 | 0.501488 | ||||||||
\(477\) | −3078.00 | −0.295455 | ||||||||
\(478\) | 13830.0 | 1.32337 | ||||||||
\(479\) | −214.500 | − | 371.525i | −0.0204609 | − | 0.0354393i | 0.855614 | − | 0.517615i | \(-0.173180\pi\) |
−0.876075 | + | 0.482176i | \(0.839847\pi\) | |||||||
\(480\) | 1296.00 | − | 748.246i | 0.123238 | − | 0.0711512i | ||||
\(481\) | −3071.00 | + | 5319.13i | −0.291113 | + | 0.504223i | ||||
\(482\) | 1489.00 | − | 2579.02i | 0.140710 | − | 0.243716i | ||||
\(483\) | 31410.7i | 2.95909i | ||||||||
\(484\) | 2212.00 | + | 3831.30i | 0.207739 | + | 0.359814i | ||||
\(485\) | 8109.00 | 0.759197 | ||||||||
\(486\) | −6561.00 | + | 3788.00i | −0.612372 | + | 0.353553i | ||||
\(487\) | −11296.0 | −1.05107 | −0.525535 | − | 0.850772i | \(-0.676135\pi\) | ||||
−0.525535 | + | 0.850772i | \(0.676135\pi\) | |||||||
\(488\) | −764.000 | − | 1323.29i | −0.0708702 | − | 0.122751i | ||||
\(489\) | 17230.4i | 1.59343i | ||||||||
\(490\) | 5562.00 | − | 9633.67i | 0.512787 | − | 0.888173i | ||||
\(491\) | 7336.50 | − | 12707.2i | 0.674321 | − | 1.16796i | −0.302346 | − | 0.953198i | \(-0.597770\pi\) |
0.976667 | − | 0.214760i | \(-0.0688969\pi\) | |||||||
\(492\) | 4698.00 | − | 2712.39i | 0.430492 | − | 0.248545i | ||||
\(493\) | 2331.00 | + | 4037.41i | 0.212947 | + | 0.368835i | ||||
\(494\) | 2072.00 | 0.188712 | ||||||||
\(495\) | −3645.00 | −0.330971 | ||||||||
\(496\) | −3280.00 | −0.296928 | ||||||||
\(497\) | 2418.00 | + | 4188.10i | 0.218234 | + | 0.377992i | ||||
\(498\) | −9747.00 | − | 5627.43i | −0.877055 | − | 0.506368i | ||||
\(499\) | −6719.50 | + | 11638.5i | −0.602818 | + | 1.04411i | 0.389574 | + | 0.920995i | \(0.372622\pi\) |
−0.992392 | + | 0.123116i | \(0.960711\pi\) | |||||||
\(500\) | −3042.00 | + | 5268.90i | −0.272085 | + | 0.471265i | ||||
\(501\) | −3064.50 | − | 1769.29i | −0.273277 | − | 0.157777i | ||||
\(502\) | 4620.00 | + | 8002.07i | 0.410758 | + | 0.711454i | ||||
\(503\) | −17388.0 | −1.54134 | −0.770669 | − | 0.637236i | \(-0.780078\pi\) | ||||
−0.770669 | + | 0.637236i | \(0.780078\pi\) | |||||||
\(504\) | −3348.00 | − | 5798.91i | −0.295896 | − | 0.512508i | ||||
\(505\) | −3483.00 | −0.306914 | ||||||||
\(506\) | 2925.00 | + | 5066.25i | 0.256980 | + | 0.445103i | ||||
\(507\) | 3726.00 | − | 2151.21i | 0.326386 | − | 0.188439i | ||||
\(508\) | 1760.00 | − | 3048.41i | 0.153715 | − | 0.266243i | ||||
\(509\) | 1894.50 | − | 3281.37i | 0.164975 | − | 0.285745i | −0.771671 | − | 0.636021i | \(-0.780579\pi\) |
0.936646 | + | 0.350276i | \(0.113912\pi\) | |||||||
\(510\) | − | 3928.29i | − | 0.341074i | ||||||
\(511\) | 2821.00 | + | 4886.12i | 0.244215 | + | 0.422992i | ||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | − | 3928.29i | − | 0.338086i | ||||||
\(514\) | 6702.00 | 0.575122 | ||||||||
\(515\) | 2479.50 | + | 4294.62i | 0.212155 | + | 0.367463i | ||||
\(516\) | 893.738i | 0.0762493i | ||||||||
\(517\) | 1327.50 | − | 2299.30i | 0.112927 | − | 0.195596i | ||||
\(518\) | −5146.00 | + | 8913.13i | −0.436491 | + | 0.756024i | ||||
\(519\) | 17914.5 | − | 10342.9i | 1.51514 | − | 0.874768i | ||||
\(520\) | −1332.00 | − | 2307.09i | −0.112331 | − | 0.194563i | ||||
\(521\) | 9786.00 | 0.822903 | 0.411451 | − | 0.911432i | \(-0.365022\pi\) | ||||
0.411451 | + | 0.911432i | \(0.365022\pi\) | |||||||
\(522\) | 2997.00 | − | 5190.96i | 0.251293 | − | 0.435253i | ||||
\(523\) | −8008.00 | −0.669532 | −0.334766 | − | 0.942301i | \(-0.608657\pi\) | ||||
−0.334766 | + | 0.942301i | \(0.608657\pi\) | |||||||
\(524\) | −3006.00 | − | 5206.54i | −0.250606 | − | 0.434063i | ||||
\(525\) | 6138.00 | + | 3543.78i | 0.510256 | + | 0.294596i | ||||
\(526\) | 603.000 | − | 1044.43i | 0.0499849 | − | 0.0865764i | ||||
\(527\) | −4305.00 | + | 7456.48i | −0.355842 | + | 0.616336i | ||||
\(528\) | −1080.00 | − | 623.538i | −0.0890170 | − | 0.0513940i | ||||
\(529\) | −12929.0 | − | 22393.7i | −1.06263 | − | 1.84053i | ||||
\(530\) | −2052.00 | −0.168176 | ||||||||
\(531\) | 2146.50 | − | 3717.85i | 0.175424 | − | 0.303843i | ||||
\(532\) | 3472.00 | 0.282952 | ||||||||
\(533\) | −4828.50 | − | 8363.21i | −0.392393 | − | 0.679645i | ||||
\(534\) | 9450.00 | − | 5455.96i | 0.765808 | − | 0.442139i | ||||
\(535\) | −54.0000 | + | 93.5307i | −0.00436378 | + | 0.00755829i | ||||
\(536\) | 1684.00 | − | 2916.77i | 0.135705 | − | 0.235047i | ||||
\(537\) | − | 10413.1i | − | 0.836793i | ||||||
\(538\) | 1470.00 | + | 2546.11i | 0.117800 | + | 0.204035i | ||||
\(539\) | −9270.00 | −0.740793 | ||||||||
\(540\) | −4374.00 | + | 2525.33i | −0.348569 | + | 0.201246i | ||||
\(541\) | −2938.00 | −0.233483 | −0.116742 | − | 0.993162i | \(-0.537245\pi\) | ||||
−0.116742 | + | 0.993162i | \(0.537245\pi\) | |||||||
\(542\) | −2072.00 | − | 3588.81i | −0.164207 | − | 0.284414i | ||||
\(543\) | − | 6619.90i | − | 0.523181i | ||||||
\(544\) | 672.000 | − | 1163.94i | 0.0529628 | − | 0.0917343i | ||||
\(545\) | −2259.00 | + | 3912.70i | −0.177550 | + | 0.307526i | ||||
\(546\) | −10323.0 | + | 5959.99i | −0.809128 | + | 0.467150i | ||||
\(547\) | 5187.50 | + | 8985.01i | 0.405487 | + | 0.702324i | 0.994378 | − | 0.105888i | \(-0.0337686\pi\) |
−0.588891 | + | 0.808213i | \(0.700435\pi\) | |||||||
\(548\) | −10644.0 | −0.829725 | ||||||||
\(549\) | 2578.50 | + | 4466.09i | 0.200451 | + | 0.347192i | ||||
\(550\) | 1320.00 | 0.102336 | ||||||||
\(551\) | 1554.00 | + | 2691.61i | 0.120150 | + | 0.208106i | ||||
\(552\) | 7020.00 | + | 4053.00i | 0.541288 | + | 0.312513i | ||||
\(553\) | 17561.5 | − | 30417.4i | 1.35044 | − | 2.33902i | ||||
\(554\) | −7139.00 | + | 12365.1i | −0.547486 | + | 0.948273i | ||||
\(555\) | 6723.00 | + | 3881.53i | 0.514190 | + | 0.296868i | ||||
\(556\) | 242.000 | + | 419.156i | 0.0184588 | + | 0.0319716i | ||||
\(557\) | 3306.00 | 0.251490 | 0.125745 | − | 0.992063i | \(-0.459868\pi\) | ||||
0.125745 | + | 0.992063i | \(0.459868\pi\) | |||||||
\(558\) | 11070.0 | 0.839840 | ||||||||
\(559\) | 1591.00 | 0.120379 | ||||||||
\(560\) | −2232.00 | − | 3865.94i | −0.168427 | − | 0.291724i | ||||
\(561\) | −2835.00 | + | 1636.79i | −0.213358 | + | 0.123182i | ||||
\(562\) | −8427.00 | + | 14596.0i | −0.632512 | + | 1.09554i | ||||
\(563\) | 10546.5 | − | 18267.1i | 0.789488 | − | 1.36743i | −0.136792 | − | 0.990600i | \(-0.543679\pi\) |
0.926281 | − | 0.376834i | \(-0.122987\pi\) | |||||||
\(564\) | − | 3678.88i | − | 0.274661i | ||||||
\(565\) | −6304.50 | − | 10919.7i | −0.469438 | − | 0.813090i | ||||
\(566\) | −914.000 | −0.0678768 | ||||||||
\(567\) | 11299.5 | + | 19571.3i | 0.836921 | + | 1.44959i | ||||
\(568\) | 1248.00 | 0.0921918 | ||||||||
\(569\) | −643.500 | − | 1114.57i | −0.0474111 | − | 0.0821185i | 0.841346 | − | 0.540497i | \(-0.181764\pi\) |
−0.888757 | + | 0.458379i | \(0.848430\pi\) | |||||||
\(570\) | − | 2618.86i | − | 0.192442i | ||||||
\(571\) | −7517.50 | + | 13020.7i | −0.550959 | + | 0.954289i | 0.447247 | + | 0.894411i | \(0.352405\pi\) |
−0.998206 | + | 0.0598783i | \(0.980929\pi\) | |||||||
\(572\) | −1110.00 | + | 1922.58i | −0.0811389 | + | 0.140537i | ||||
\(573\) | −5224.50 | + | 3016.37i | −0.380902 | + | 0.219914i | ||||
\(574\) | −8091.00 | − | 14014.0i | −0.588348 | − | 1.01905i | ||||
\(575\) | −8580.00 | −0.622280 | ||||||||
\(576\) | −1728.00 | −0.125000 | ||||||||
\(577\) | 1190.00 | 0.0858585 | 0.0429292 | − | 0.999078i | \(-0.486331\pi\) | ||||
0.0429292 | + | 0.999078i | \(0.486331\pi\) | |||||||
\(578\) | 3149.00 | + | 5454.23i | 0.226611 | + | 0.392502i | ||||
\(579\) | 16249.5 | + | 9381.65i | 1.16633 | + | 0.673382i | ||||
\(580\) | 1998.00 | − | 3460.64i | 0.143039 | − | 0.247750i | ||||
\(581\) | −16786.5 | + | 29075.1i | −1.19866 | + | 2.07614i | ||||
\(582\) | −8109.00 | − | 4681.73i | −0.577541 | − | 0.333443i | ||||
\(583\) | 855.000 | + | 1480.90i | 0.0607384 | + | 0.105202i | ||||
\(584\) | 1456.00 | 0.103167 | ||||||||
\(585\) | 4495.50 | + | 7786.43i | 0.317720 | + | 0.550307i | ||||
\(586\) | −11778.0 | −0.830281 | ||||||||
\(587\) | 8941.50 | + | 15487.1i | 0.628714 | + | 1.08896i | 0.987810 | + | 0.155664i | \(0.0497518\pi\) |
−0.359096 | + | 0.933301i | \(0.616915\pi\) | |||||||
\(588\) | −11124.0 | + | 6422.44i | −0.780180 | + | 0.450437i | ||||
\(589\) | −2870.00 | + | 4970.99i | −0.200775 | + | 0.347752i | ||||
\(590\) | 1431.00 | − | 2478.56i | 0.0998531 | − | 0.172951i | ||||
\(591\) | − | 10631.3i | − | 0.739957i | ||||||
\(592\) | 1328.00 | + | 2300.16i | 0.0921967 | + | 0.159689i | ||||
\(593\) | 20118.0 | 1.39317 | 0.696583 | − | 0.717476i | \(-0.254703\pi\) | ||||
0.696583 | + | 0.717476i | \(0.254703\pi\) | |||||||
\(594\) | 3645.00 | + | 2104.44i | 0.251778 | + | 0.145364i | ||||
\(595\) | −11718.0 | −0.807380 | ||||||||
\(596\) | 5658.00 | + | 9799.94i | 0.388860 | + | 0.673526i | ||||
\(597\) | − | 15567.7i | − | 1.06724i | ||||||
\(598\) | 7215.00 | − | 12496.7i | 0.493383 | − | 0.854565i | ||||
\(599\) | 532.500 | − | 922.317i | 0.0363228 | − | 0.0629129i | −0.847293 | − | 0.531127i | \(-0.821769\pi\) |
0.883615 | + | 0.468214i | \(0.155102\pi\) | |||||||
\(600\) | 1584.00 | − | 914.523i | 0.107778 | − | 0.0622254i | ||||
\(601\) | 10362.5 | + | 17948.4i | 0.703320 | + | 1.21819i | 0.967294 | + | 0.253656i | \(0.0816331\pi\) |
−0.263975 | + | 0.964530i | \(0.585034\pi\) | |||||||
\(602\) | 2666.00 | 0.180495 | ||||||||
\(603\) | −5683.50 | + | 9844.11i | −0.383831 | + | 0.664815i | ||||
\(604\) | 1844.00 | 0.124224 | ||||||||
\(605\) | −4977.00 | − | 8620.42i | −0.334453 | − | 0.579289i | ||||
\(606\) | 3483.00 | + | 2010.91i | 0.233477 | + | 0.134798i | ||||
\(607\) | 7872.50 | − | 13635.6i | 0.526417 | − | 0.911780i | −0.473110 | − | 0.881004i | \(-0.656869\pi\) |
0.999526 | − | 0.0307768i | \(-0.00979812\pi\) | |||||||
\(608\) | 448.000 | − | 775.959i | 0.0298829 | − | 0.0517587i | ||||
\(609\) | −15484.5 | − | 8939.98i | −1.03032 | − | 0.594854i | ||||
\(610\) | 1719.00 | + | 2977.40i | 0.114099 | + | 0.197625i | ||||
\(611\) | −6549.00 | −0.433624 | ||||||||
\(612\) | −2268.00 | + | 3928.29i | −0.149801 | + | 0.259464i | ||||
\(613\) | 5042.00 | 0.332210 | 0.166105 | − | 0.986108i | \(-0.446881\pi\) | ||||
0.166105 | + | 0.986108i | \(0.446881\pi\) | |||||||
\(614\) | 1204.00 | + | 2085.39i | 0.0791360 | + | 0.137068i | ||||
\(615\) | −10570.5 | + | 6102.88i | −0.693079 | + | 0.400149i | ||||
\(616\) | −1860.00 | + | 3221.61i | −0.121658 | + | 0.210718i | ||||
\(617\) | 5026.50 | − | 8706.15i | 0.327973 | − | 0.568066i | −0.654137 | − | 0.756376i | \(-0.726968\pi\) |
0.982110 | + | 0.188311i | \(0.0603012\pi\) | |||||||
\(618\) | − | 5726.16i | − | 0.372718i | ||||||
\(619\) | 2991.50 | + | 5181.43i | 0.194246 | + | 0.336445i | 0.946653 | − | 0.322254i | \(-0.104441\pi\) |
−0.752407 | + | 0.658699i | \(0.771107\pi\) | |||||||
\(620\) | 7380.00 | 0.478045 | ||||||||
\(621\) | −23692.5 | − | 13678.9i | −1.53099 | − | 0.883920i | ||||
\(622\) | −6570.00 | −0.423526 | ||||||||
\(623\) | −16275.0 | − | 28189.1i | −1.04662 | − | 1.81280i | ||||
\(624\) | 3076.12i | 0.197345i | ||||||||
\(625\) | 4094.50 | − | 7091.88i | 0.262048 | − | 0.453880i | ||||
\(626\) | 10057.0 | − | 17419.2i | 0.642106 | − | 1.11216i | ||||
\(627\) | −1890.00 | + | 1091.19i | −0.120382 | + | 0.0695024i | ||||
\(628\) | 5954.00 | + | 10312.6i | 0.378329 | + | 0.655285i | ||||
\(629\) | 6972.00 | 0.441958 | ||||||||
\(630\) | 7533.00 | + | 13047.5i | 0.476384 | + | 0.825121i | ||||
\(631\) | −19696.0 | −1.24261 | −0.621304 | − | 0.783570i | \(-0.713397\pi\) | ||||
−0.621304 | + | 0.783570i | \(0.713397\pi\) | |||||||
\(632\) | −4532.00 | − | 7849.65i | −0.285243 | − | 0.494055i | ||||
\(633\) | 3397.50 | + | 1961.55i | 0.213331 | + | 0.123167i | ||||
\(634\) | −2295.00 | + | 3975.06i | −0.143764 | + | 0.249006i | ||||
\(635\) | −3960.00 | + | 6858.92i | −0.247477 | + | 0.428642i | ||||
\(636\) | 2052.00 | + | 1184.72i | 0.127936 | + | 0.0738637i | ||||
\(637\) | 11433.0 | + | 19802.5i | 0.711133 | + | 1.23172i | ||||
\(638\) | −3330.00 | −0.206639 | ||||||||
\(639\) | −4212.00 | −0.260758 | ||||||||
\(640\) | −1152.00 | −0.0711512 | ||||||||
\(641\) | 5488.50 | + | 9506.36i | 0.338195 | + | 0.585770i | 0.984093 | − | 0.177653i | \(-0.0568505\pi\) |
−0.645899 | + | 0.763423i | \(0.723517\pi\) | |||||||
\(642\) | 108.000 | − | 62.3538i | 0.00663928 | − | 0.00383319i | ||||
\(643\) | 7914.50 | − | 13708.3i | 0.485408 | − | 0.840752i | −0.514451 | − | 0.857520i | \(-0.672004\pi\) |
0.999859 | + | 0.0167681i | \(0.00533770\pi\) | |||||||
\(644\) | 12090.0 | − | 20940.5i | 0.739771 | − | 1.28132i | ||||
\(645\) | − | 2010.91i | − | 0.122759i | ||||||
\(646\) | −1176.00 | − | 2036.89i | −0.0716240 | − | 0.124056i | ||||
\(647\) | 28224.0 | 1.71499 | 0.857496 | − | 0.514490i | \(-0.172019\pi\) | ||||
0.857496 | + | 0.514490i | \(0.172019\pi\) | |||||||
\(648\) | 5832.00 | 0.353553 | ||||||||
\(649\) | −2385.00 | −0.144252 | ||||||||
\(650\) | −1628.00 | − | 2819.78i | −0.0982391 | − | 0.170155i | ||||
\(651\) | − | 33021.5i | − | 1.98804i | ||||||
\(652\) | 6632.00 | − | 11487.0i | 0.398358 | − | 0.689976i | ||||
\(653\) | −14083.5 | + | 24393.3i | −0.843997 | + | 1.46185i | 0.0424927 | + | 0.999097i | \(0.486470\pi\) |
−0.886490 | + | 0.462749i | \(0.846863\pi\) | |||||||
\(654\) | 4518.00 | − | 2608.47i | 0.270134 | − | 0.155962i | ||||
\(655\) | 6763.50 | + | 11714.7i | 0.403468 | + | 0.698828i | ||||
\(656\) | −4176.00 | −0.248545 | ||||||||
\(657\) | −4914.00 | −0.291801 | ||||||||
\(658\) | −10974.0 | −0.650169 | ||||||||
\(659\) | −5368.50 | − | 9298.51i | −0.317340 | − | 0.549649i | 0.662592 | − | 0.748980i | \(-0.269456\pi\) |
−0.979932 | + | 0.199331i | \(0.936123\pi\) | |||||||
\(660\) | 2430.00 | + | 1402.96i | 0.143315 | + | 0.0827427i | ||||
\(661\) | −5063.50 | + | 8770.24i | −0.297954 | + | 0.516071i | −0.975668 | − | 0.219255i | \(-0.929637\pi\) |
0.677714 | + | 0.735326i | \(0.262971\pi\) | |||||||
\(662\) | 6679.00 | − | 11568.4i | 0.392125 | − | 0.679180i | ||||
\(663\) | 6993.00 | + | 4037.41i | 0.409631 | + | 0.236501i | ||||
\(664\) | 4332.00 | + | 7503.24i | 0.253184 | + | 0.438528i | ||||
\(665\) | −7812.00 | −0.455543 | ||||||||
\(666\) | −4482.00 | − | 7763.05i | −0.260772 | − | 0.451670i | ||||
\(667\) | 21645.0 | 1.25652 | ||||||||
\(668\) | 1362.00 | + | 2359.05i | 0.0788883 | + | 0.136638i | ||||
\(669\) | 15583.5 | − | 8997.14i | 0.900587 | − | 0.519954i | ||||
\(670\) | −3789.00 | + | 6562.74i | −0.218480 | + | 0.378419i | ||||
\(671\) | 1432.50 | − | 2481.16i | 0.0824159 | − | 0.142748i | ||||
\(672\) | 5154.58i | 0.295896i | ||||||||
\(673\) | −125.500 | − | 217.372i | −0.00718822 | − | 0.0124504i | 0.862409 | − | 0.506212i | \(-0.168955\pi\) |
−0.869597 | + | 0.493762i | \(0.835621\pi\) | |||||||
\(674\) | 4366.00 | 0.249513 | ||||||||
\(675\) | −5346.00 | + | 3086.51i | −0.304841 | + | 0.176000i | ||||
\(676\) | −3312.00 | −0.188439 | ||||||||
\(677\) | −4225.50 | − | 7318.78i | −0.239881 | − | 0.415485i | 0.720799 | − | 0.693144i | \(-0.243775\pi\) |
−0.960680 | + | 0.277659i | \(0.910442\pi\) | |||||||
\(678\) | 14559.6i | 0.824718i | ||||||||
\(679\) | −13965.5 | + | 24189.0i | −0.789318 | + | 1.36714i | ||||
\(680\) | −1512.00 | + | 2618.86i | −0.0852685 | + | 0.147689i | ||||
\(681\) | −28012.5 | + | 16173.0i | −1.57627 | + | 0.910061i | ||||
\(682\) | −3075.00 | − | 5326.06i | −0.172651 | − | 0.299040i | ||||
\(683\) | −25884.0 | −1.45011 | −0.725054 | − | 0.688692i | \(-0.758185\pi\) | ||||
−0.725054 | + | 0.688692i | \(0.758185\pi\) | |||||||
\(684\) | −1512.00 | + | 2618.86i | −0.0845216 | + | 0.146396i | ||||
\(685\) | 23949.0 | 1.33583 | ||||||||
\(686\) | 8525.00 | + | 14765.7i | 0.474469 | + | 0.821805i | ||||
\(687\) | −6592.50 | − | 3806.18i | −0.366113 | − | 0.211375i | ||||
\(688\) | 344.000 | − | 595.825i | 0.0190623 | − | 0.0330169i | ||||
\(689\) | 2109.00 | − | 3652.90i | 0.116613 | − | 0.201980i | ||||
\(690\) | −15795.0 | − | 9119.25i | −0.871457 | − | 0.503136i | ||||
\(691\) | −3182.50 | − | 5512.25i | −0.175207 | − | 0.303467i | 0.765026 | − | 0.643999i | \(-0.222726\pi\) |
−0.940233 | + | 0.340532i | \(0.889393\pi\) | |||||||
\(692\) | −15924.0 | −0.874768 | ||||||||
\(693\) | 6277.50 | − | 10872.9i | 0.344102 | − | 0.596002i | ||||
\(694\) | 7782.00 | 0.425649 | ||||||||
\(695\) | −544.500 | − | 943.102i | −0.0297181 | − | 0.0514732i | ||||
\(696\) | −3996.00 | + | 2307.09i | −0.217626 | + | 0.125647i | ||||
\(697\) | −5481.00 | + | 9493.37i | −0.297859 | + | 0.515907i | ||||
\(698\) | −2795.00 | + | 4841.08i | −0.151565 | + | 0.262518i | ||||
\(699\) | − | 13686.7i | − | 0.740597i | ||||||
\(700\) | −2728.00 | − | 4725.03i | −0.147298 | − | 0.255128i | ||||
\(701\) | 1122.00 | 0.0604527 | 0.0302264 | − | 0.999543i | \(-0.490377\pi\) | ||||
0.0302264 | + | 0.999543i | \(0.490377\pi\) | |||||||
\(702\) | − | 10381.9i | − | 0.558177i | ||||||
\(703\) | 4648.00 | 0.249364 | ||||||||
\(704\) | 480.000 | + | 831.384i | 0.0256970 | + | 0.0445085i | ||||
\(705\) | 8277.47i | 0.442195i | ||||||||
\(706\) | −4755.00 | + | 8235.90i | −0.253480 | + | 0.439040i | ||||
\(707\) | 5998.50 | − | 10389.7i | 0.319090 | − | 0.552681i | ||||
\(708\) | −2862.00 | + | 1652.38i | −0.151922 | + | 0.0877120i | ||||
\(709\) | −2141.50 | − | 3709.19i | −0.113435 | − | 0.196476i | 0.803718 | − | 0.595011i | \(-0.202852\pi\) |
−0.917153 | + | 0.398535i | \(0.869519\pi\) | |||||||
\(710\) | −2808.00 | −0.148426 | ||||||||
\(711\) | 15295.5 | + | 26492.6i | 0.806788 | + | 1.39740i | ||||
\(712\) | −8400.00 | −0.442139 | ||||||||
\(713\) | 19987.5 | + | 34619.4i | 1.04984 | + | 1.81838i | ||||
\(714\) | 11718.0 | + | 6765.39i | 0.614195 | + | 0.354606i | ||||
\(715\) | 2497.50 | − | 4325.80i | 0.130631 | − | 0.226260i | ||||
\(716\) | −4008.00 | + | 6942.06i | −0.209198 | + | 0.362342i | ||||
\(717\) | 31117.5 | + | 17965.7i | 1.62079 | + | 0.935762i | ||||
\(718\) | −4608.00 | − | 7981.29i | −0.239511 | − | 0.414846i | ||||
\(719\) | 4032.00 | 0.209135 | 0.104568 | − | 0.994518i | \(-0.466654\pi\) | ||||
0.104568 | + | 0.994518i | \(0.466654\pi\) | |||||||
\(720\) | 3888.00 | 0.201246 | ||||||||
\(721\) | −17081.0 | −0.882288 | ||||||||
\(722\) | 6075.00 | + | 10522.2i | 0.313141 | + | 0.542377i | ||||
\(723\) | 6700.50 | − | 3868.54i | 0.344667 | − | 0.198994i | ||||
\(724\) | −2548.00 | + | 4413.27i | −0.130795 | + | 0.226544i | ||||
\(725\) | 2442.00 | − | 4229.67i | 0.125095 | − | 0.216670i | ||||
\(726\) | 11493.9i | 0.587573i | ||||||||
\(727\) | −12002.5 | − | 20788.9i | −0.612308 | − | 1.06055i | −0.990850 | − | 0.134965i | \(-0.956908\pi\) |
0.378542 | − | 0.925584i | \(-0.376426\pi\) | |||||||
\(728\) | 9176.00 | 0.467150 | ||||||||
\(729\) | −19683.0 | −1.00000 | ||||||||
\(730\) | −3276.00 | −0.166096 | ||||||||
\(731\) | −903.000 | − | 1564.04i | −0.0456890 | − | 0.0791357i | ||||
\(732\) | − | 3969.86i | − | 0.200451i | ||||||
\(733\) | 18750.5 | − | 32476.8i | 0.944837 | − | 1.63651i | 0.188760 | − | 0.982023i | \(-0.439553\pi\) |
0.756077 | − | 0.654482i | \(-0.227113\pi\) | |||||||
\(734\) | −3845.00 | + | 6659.74i | −0.193354 | + | 0.334898i | ||||
\(735\) | 25029.0 | − | 14450.5i | 1.25607 | − | 0.725190i | ||||
\(736\) | −3120.00 | − | 5404.00i | −0.156256 | − | 0.270644i | ||||
\(737\) | 6315.00 | 0.315626 | ||||||||
\(738\) | 14094.0 | 0.702991 | ||||||||
\(739\) | −880.000 | −0.0438042 | −0.0219021 | − | 0.999760i | \(-0.506972\pi\) | ||||
−0.0219021 | + | 0.999760i | \(0.506972\pi\) | |||||||
\(740\) | −2988.00 | − | 5175.37i | −0.148434 | − | 0.257095i | ||||
\(741\) | 4662.00 | + | 2691.61i | 0.231124 | + | 0.133439i | ||||
\(742\) | 3534.00 | − | 6121.07i | 0.174848 | − | 0.302846i | ||||
\(743\) | −811.500 | + | 1405.56i | −0.0400687 | + | 0.0694010i | −0.885364 | − | 0.464898i | \(-0.846091\pi\) |
0.845296 | + | 0.534299i | \(0.179424\pi\) | |||||||
\(744\) | −7380.00 | − | 4260.84i | −0.363661 | − | 0.209960i | ||||
\(745\) | −12730.5 | − | 22049.9i | −0.626053 | − | 1.08436i | ||||
\(746\) | −16634.0 | −0.816373 | ||||||||
\(747\) | −14620.5 | − | 25323.4i | −0.716113 | − | 1.24034i | ||||
\(748\) | 2520.00 | 0.123182 | ||||||||
\(749\) | −186.000 | − | 322.161i | −0.00907382 | − | 0.0157163i | ||||
\(750\) | −13689.0 | + | 7903.35i | −0.666469 | + | 0.384786i | ||||
\(751\) | 3444.50 | − | 5966.05i | 0.167366 | − | 0.289886i | −0.770127 | − | 0.637890i | \(-0.779807\pi\) |
0.937493 | + | 0.348005i | \(0.113141\pi\) | |||||||
\(752\) | −1416.00 | + | 2452.58i | −0.0686652 | + | 0.118932i | ||||
\(753\) | 24006.2i | 1.16180i | ||||||||
\(754\) | 4107.00 | + | 7113.53i | 0.198366 | + | 0.343580i | ||||
\(755\) | −4149.00 | −0.199997 | ||||||||
\(756\) | − | 17396.7i | − | 0.836921i | ||||||
\(757\) | −12850.0 | −0.616963 | −0.308482 | − | 0.951230i | \(-0.599821\pi\) | ||||
−0.308482 | + | 0.951230i | \(0.599821\pi\) | |||||||
\(758\) | −12560.0 | − | 21754.6i | −0.601847 | − | 1.04243i | ||||
\(759\) | 15198.7i | 0.726850i | ||||||||
\(760\) | −1008.00 | + | 1745.91i | −0.0481105 | + | 0.0833299i | ||||
\(761\) | −2305.50 | + | 3993.24i | −0.109822 | + | 0.190217i | −0.915698 | − | 0.401867i | \(-0.868361\pi\) |
0.805876 | + | 0.592084i | \(0.201695\pi\) | |||||||
\(762\) | 7920.00 | − | 4572.61i | 0.376524 | − | 0.217386i | ||||
\(763\) | −7781.00 | − | 13477.1i | −0.369189 | − | 0.639454i | ||||
\(764\) | 4644.00 | 0.219914 | ||||||||
\(765\) | 5103.00 | − | 8838.66i | 0.241176 | − | 0.417728i | ||||
\(766\) | 24174.0 | 1.14026 | ||||||||
\(767\) | 2941.50 | + | 5094.83i | 0.138476 | + | 0.239848i | ||||
\(768\) | 1152.00 | + | 665.108i | 0.0541266 | + | 0.0312500i | ||||
\(769\) | 1152.50 | − | 1996.19i | 0.0540445 | − | 0.0936078i | −0.837737 | − | 0.546073i | \(-0.816122\pi\) |
0.891782 | + | 0.452465i | \(0.149455\pi\) | |||||||
\(770\) | 4185.00 | − | 7248.63i | 0.195866 | − | 0.339250i | ||||
\(771\) | 15079.5 | + | 8706.15i | 0.704377 | + | 0.406672i | ||||
\(772\) | −7222.00 | − | 12508.9i | −0.336691 | − | 0.583166i | ||||
\(773\) | −34902.0 | −1.62398 | −0.811991 | − | 0.583670i | \(-0.801616\pi\) | ||||
−0.811991 | + | 0.583670i | \(0.801616\pi\) | |||||||
\(774\) | −1161.00 | + | 2010.91i | −0.0539164 | + | 0.0933859i | ||||
\(775\) | 9020.00 | 0.418075 | ||||||||
\(776\) | 3604.00 | + | 6242.31i | 0.166722 | + | 0.288771i | ||||
\(777\) | −23157.0 | + | 13369.7i | −1.06918 | + | 0.617291i | ||||
\(778\) | 8541.00 | − | 14793.4i | 0.393586 | − | 0.681710i | ||||
\(779\) | −3654.00 | + | 6328.91i | −0.168059 | + | 0.291087i | ||||
\(780\) | − | 6921.28i | − | 0.317720i | ||||||
\(781\) | 1170.00 | + | 2026.50i | 0.0536055 | + | 0.0928474i | ||||
\(782\) | −16380.0 | −0.749038 | ||||||||
\(783\) | 13486.5 | − | 7786.43i | 0.615540 | − | 0.355382i | ||||
\(784\) | 9888.00 | 0.450437 | ||||||||
\(785\) | −13396.5 | − | 23203.4i | −0.609098 | − | 1.05499i | ||||
\(786\) | − | 15619.6i | − | 0.708822i | ||||||
\(787\) | −13127.5 | + | 22737.5i | −0.594593 | + | 1.02987i | 0.399011 | + | 0.916946i | \(0.369354\pi\) |
−0.993604 | + | 0.112919i | \(0.963980\pi\) | |||||||
\(788\) | −4092.00 | + | 7087.55i | −0.184989 | + | 0.320411i | ||||
\(789\) | 2713.50 | − | 1566.64i | 0.122437 | − | 0.0706893i | ||||
\(790\) | 10197.0 | + | 17661.7i | 0.459232 | + | 0.795412i | ||||
\(791\) | 43431.0 | 1.95225 | ||||||||
\(792\) | −1620.00 | − | 2805.92i | −0.0726821 | − | 0.125889i | ||||
\(793\) | −7067.00 | −0.316465 | ||||||||
\(794\) | 13174.0 | + | 22818.0i | 0.588826 | + | 1.01988i | ||||
\(795\) | −4617.00 | − | 2665.63i | −0.205972 | − | 0.118918i | ||||
\(796\) | −5992.00 | + | 10378.4i | −0.266810 | + | 0.462129i | ||||
\(797\) | 718.500 | − | 1244.48i | 0.0319330 | − | 0.0553095i | −0.849617 | − | 0.527400i | \(-0.823167\pi\) |
0.881550 | + | 0.472090i | \(0.156500\pi\) | |||||||
\(798\) | 7812.00 | + | 4510.26i | 0.346544 | + | 0.200077i | ||||
\(799\) | 3717.00 | + | 6438.03i | 0.164578 | + | 0.285058i | ||||
\(800\) | −1408.00 | −0.0622254 | ||||||||
\(801\) | 28350.0 | 1.25056 | ||||||||
\(802\) | 19206.0 | 0.845620 | ||||||||
\(803\) | 1365.00 | + | 2364.25i | 0.0599873 | + | 0.103901i | ||||
\(804\) | 7578.00 | − | 4375.16i | 0.332407 | − | 0.191915i | ||||
\(805\) | −27202.5 | + | 47116.1i | −1.19101 | + | 2.06289i | ||||
\(806\) | −7585.00 | + | 13137.6i | −0.331477 | + | 0.574135i | ||||
\(807\) | 7638.34i | 0.333188i | ||||||||
\(808\) | −1548.00 | − | 2681.21i | −0.0673991 | − | 0.116739i | ||||
\(809\) | 25734.0 | 1.11837 | 0.559184 | − | 0.829044i | \(-0.311115\pi\) | ||||
0.559184 | + | 0.829044i | \(0.311115\pi\) | |||||||
\(810\) | −13122.0 | −0.569210 | ||||||||
\(811\) | −3220.00 | −0.139420 | −0.0697099 | − | 0.997567i | \(-0.522207\pi\) | ||||
−0.0697099 | + | 0.997567i | \(0.522207\pi\) | |||||||
\(812\) | 6882.00 | + | 11920.0i | 0.297427 | + | 0.515159i | ||||
\(813\) | − | 10766.4i | − | 0.464447i | ||||||
\(814\) | −2490.00 | + | 4312.81i | −0.107217 | + | 0.185705i | ||||
\(815\) | −14922.0 | + | 25845.7i | −0.641343 | + | 1.11084i | ||||
\(816\) | 3024.00 | − | 1745.91i | 0.129732 | − | 0.0749007i | ||||
\(817\) | −602.000 | − | 1042.69i | −0.0257788 | − | 0.0446503i | ||||
\(818\) | 22942.0 | 0.980621 | ||||||||
\(819\) | −30969.0 | −1.32130 | ||||||||
\(820\) | 9396.00 | 0.400149 | ||||||||
\(821\) | −22315.5 | − | 38651.6i | −0.948619 | − | 1.64306i | −0.748337 | − | 0.663318i | \(-0.769148\pi\) |
−0.200282 | − | 0.979738i | \(-0.564186\pi\) | |||||||
\(822\) | −23949.0 | − | 13827.0i | −1.01620 | − | 0.586704i | ||||
\(823\) | −12473.5 | + | 21604.7i | −0.528310 | + | 0.915059i | 0.471146 | + | 0.882055i | \(0.343841\pi\) |
−0.999455 | + | 0.0330037i | \(0.989493\pi\) | |||||||
\(824\) | −2204.00 | + | 3817.44i | −0.0931796 | + | 0.161392i | ||||
\(825\) | 2970.00 | + | 1714.73i | 0.125336 | + | 0.0723627i | ||||
\(826\) | 4929.00 | + | 8537.28i | 0.207629 | + | 0.359625i | ||||
\(827\) | −14964.0 | −0.629201 | −0.314601 | − | 0.949224i | \(-0.601871\pi\) | ||||
−0.314601 | + | 0.949224i | \(0.601871\pi\) | |||||||
\(828\) | 10530.0 | + | 18238.5i | 0.441960 | + | 0.765497i | ||||
\(829\) | −7462.00 | −0.312625 | −0.156312 | − | 0.987708i | \(-0.549961\pi\) | ||||
−0.156312 | + | 0.987708i | \(0.549961\pi\) | |||||||
\(830\) | −9747.00 | − | 16882.3i | −0.407618 | − | 0.706016i | ||||
\(831\) | −32125.5 | + | 18547.7i | −1.34106 | + | 0.774262i | ||||
\(832\) | 1184.00 | − | 2050.75i | 0.0493363 | − | 0.0854530i | ||||
\(833\) | 12978.0 | − | 22478.6i | 0.539809 | − | 0.934977i | ||||
\(834\) | 1257.47i | 0.0522093i | ||||||||
\(835\) | −3064.50 | − | 5307.87i | −0.127008 | − | 0.219984i | ||||
\(836\) | 1680.00 | 0.0695024 | ||||||||
\(837\) | 24907.5 | + | 14380.4i | 1.02859 | + | 0.593856i | ||||
\(838\) | −11946.0 | −0.492444 | ||||||||
\(839\) | −1348.50 | − | 2335.67i | −0.0554891 | − | 0.0961100i | 0.836947 | − | 0.547285i | \(-0.184338\pi\) |
−0.892436 | + | 0.451175i | \(0.851005\pi\) | |||||||
\(840\) | − | 11597.8i | − | 0.476384i | ||||||
\(841\) | 6034.00 | − | 10451.2i | 0.247407 | − | 0.428521i | ||||
\(842\) | 8905.00 | − | 15423.9i | 0.364473 | − | 0.631286i | ||||
\(843\) | −37921.5 | + | 21894.0i | −1.54933 | + | 0.894507i | ||||
\(844\) | −1510.00 | − | 2615.40i | −0.0615833 | − | 0.106665i | ||||
\(845\) | 7452.00 | 0.303381 | ||||||||
\(846\) | 4779.00 | − | 8277.47i | 0.194214 | − | 0.336389i | ||||
\(847\) | 34286.0 | 1.39089 | ||||||||
\(848\) | −912.000 | − | 1579.63i | −0.0369318 | − | 0.0639678i | ||||
\(849\) | −2056.50 | − | 1187.32i | −0.0831318 | − | 0.0479962i | ||||
\(850\) | −1848.00 | + | 3200.83i | −0.0745716 | + | 0.129162i | ||||
\(851\) | 16185.0 | − | 28033.2i | 0.651956 | − | 1.12922i | ||||
\(852\) | 2808.00 | + | 1621.20i | 0.112911 | + | 0.0651894i | ||||
\(853\) | 19812.5 | + | 34316.3i | 0.795272 | + | 1.37745i | 0.922666 | + | 0.385599i | \(0.126005\pi\) |
−0.127394 | + | 0.991852i | \(0.540661\pi\) | |||||||
\(854\) | −11842.0 | −0.474502 | ||||||||
\(855\) | 3402.00 | − | 5892.44i | 0.136077 | − | 0.235693i | ||||
\(856\) | −96.0000 | −0.00383319 | ||||||||
\(857\) | 1486.50 | + | 2574.69i | 0.0592507 | + | 0.102625i | 0.894129 | − | 0.447809i | \(-0.147796\pi\) |
−0.834879 | + | 0.550434i | \(0.814462\pi\) | |||||||
\(858\) | −4995.00 | + | 2883.86i | −0.198749 | + | 0.114748i | ||||
\(859\) | 22614.5 | − | 39169.5i | 0.898250 | − | 1.55581i | 0.0685200 | − | 0.997650i | \(-0.478172\pi\) |
0.829730 | − | 0.558165i | \(-0.188494\pi\) | |||||||
\(860\) | −774.000 | + | 1340.61i | −0.0306897 | + | 0.0531562i | ||||
\(861\) | − | 42042.1i | − | 1.66410i | ||||||
\(862\) | −1416.00 | − | 2452.58i | −0.0559503 | − | 0.0969087i | ||||
\(863\) | 1416.00 | 0.0558531 | 0.0279265 | − | 0.999610i | \(-0.491110\pi\) | ||||
0.0279265 | + | 0.999610i | \(0.491110\pi\) | |||||||
\(864\) | −3888.00 | − | 2244.74i | −0.153093 | − | 0.0883883i | ||||
\(865\) | 35829.0 | 1.40835 | ||||||||
\(866\) | −10766.0 | − | 18647.3i | −0.422452 | − | 0.731709i | ||||
\(867\) | 16362.7i | 0.640953i | ||||||||
\(868\) | −12710.0 | + | 22014.4i | −0.497011 | + | 0.860848i | ||||
\(869\) | 8497.50 | − | 14718.1i | 0.331712 | − | 0.574542i | ||||
\(870\) | 8991.00 | − | 5190.96i | 0.350372 | − | 0.202287i | ||||
\(871\) | −7788.50 | − | 13490.1i | −0.302989 | − | 0.524792i | ||||
\(872\) | −4016.00 | −0.155962 | ||||||||
\(873\) | −12163.5 | − | 21067.8i | −0.471560 | − | 0.816766i | ||||
\(874\) | −10920.0 | −0.422625 | ||||||||
\(875\) | 23575.5 | + | 40834.0i | 0.910854 | + | 1.57765i | ||||
\(876\) | 3276.00 | + | 1891.40i | 0.126354 | + | 0.0729503i | ||||
\(877\) | −8777.50 | + | 15203.1i | −0.337965 | + | 0.585372i | −0.984050 | − | 0.177893i | \(-0.943072\pi\) |
0.646085 | + | 0.763265i | \(0.276405\pi\) | |||||||
\(878\) | −4349.00 | + | 7532.69i | −0.167166 | + | 0.289540i | ||||
\(879\) | −26500.5 | − | 15300.1i | −1.01688 | − | 0.587097i | ||||
\(880\) | −1080.00 | − | 1870.61i | −0.0413714 | − | 0.0716573i | ||||
\(881\) | 30030.0 | 1.14840 | 0.574198 | − | 0.818717i | \(-0.305314\pi\) | ||||
0.574198 | + | 0.818717i | \(0.305314\pi\) | |||||||
\(882\) | −33372.0 | −1.27403 | ||||||||
\(883\) | −35740.0 | −1.36211 | −0.681057 | − | 0.732230i | \(-0.738479\pi\) | ||||
−0.681057 | + | 0.732230i | \(0.738479\pi\) | |||||||
\(884\) | −3108.00 | − | 5383.21i | −0.118250 | − | 0.204816i | ||||
\(885\) | 6439.50 | − | 3717.85i | 0.244589 | − | 0.141214i | ||||
\(886\) | 14547.0 | − | 25196.1i | 0.551598 | − | 0.955396i | ||||
\(887\) | −373.500 | + | 646.921i | −0.0141386 | + | 0.0244887i | −0.873008 | − | 0.487706i | \(-0.837834\pi\) |
0.858870 | + | 0.512194i | \(0.171167\pi\) | |||||||
\(888\) | 6900.49i | 0.260772i | ||||||||
\(889\) | −13640.0 | − | 23625.2i | −0.514590 | − | 0.891297i | ||||
\(890\) | 18900.0 | 0.711831 | ||||||||
\(891\) | 5467.50 | + | 9469.99i | 0.205576 | + | 0.356068i | ||||
\(892\) | −13852.0 | −0.519954 | ||||||||
\(893\) | 2478.00 | + | 4292.02i | 0.0928590 | + | 0.160837i | ||||
\(894\) | 29399.8i | 1.09986i | ||||||||
\(895\) | 9018.00 | − | 15619.6i | 0.336803 | − | 0.583360i | ||||
\(896\) | 1984.00 | − | 3436.39i | 0.0739741 | − | 0.128127i | ||||
\(897\) | 32467.5 | − | 18745.1i | 1.20854 | − | 0.697750i | ||||
\(898\) | 3330.00 | + | 5767.73i | 0.123746 | + | 0.214334i | ||||
\(899\) | −22755.0 | −0.844184 | ||||||||
\(900\) | 4752.00 | 0.176000 | ||||||||
\(901\) | −4788.00 | −0.177038 | ||||||||
\(902\) | −3915.00 | − | 6780.98i | −0.144518 | − | 0.250313i | ||||
\(903\) | 5998.50 | + | 3463.24i | 0.221060 | + | 0.127629i | ||||
\(904\) | 5604.00 | − | 9706.41i | 0.206179 | − | 0.357113i | ||||
\(905\) | 5733.00 | − | 9929.85i | 0.210576 | − | 0.364728i | ||||
\(906\) | 4149.00 | + | 2395.43i | 0.152143 | + | 0.0878396i | ||||
\(907\) | 10269.5 | + | 17787.3i | 0.375957 | + | 0.651177i | 0.990470 | − | 0.137730i | \(-0.0439806\pi\) |
−0.614513 | + | 0.788907i | \(0.710647\pi\) | |||||||
\(908\) | 24900.0 | 0.910061 | ||||||||
\(909\) | 5224.50 | + | 9049.10i | 0.190633 | + | 0.330187i | ||||
\(910\) | −20646.0 | −0.752097 | ||||||||
\(911\) | 12061.5 | + | 20891.1i | 0.438656 | + | 0.759774i | 0.997586 | − | 0.0694406i | \(-0.0221214\pi\) |
−0.558930 | + | 0.829215i | \(0.688788\pi\) | |||||||
\(912\) | 2016.00 | − | 1163.94i | 0.0731978 | − | 0.0422608i | ||||
\(913\) | −8122.50 | + | 14068.6i | −0.294431 | + | 0.509969i | ||||
\(914\) | −8147.00 | + | 14111.0i | −0.294835 | + | 0.510668i | ||||
\(915\) | 8932.19i | 0.322720i | ||||||||
\(916\) | 2930.00 | + | 5074.91i | 0.105688 | + | 0.183056i | ||||
\(917\) | −46593.0 | −1.67790 | ||||||||
\(918\) | −10206.0 | + | 5892.44i | −0.366937 | + | 0.211851i | ||||
\(919\) | 23312.0 | 0.836770 | 0.418385 | − | 0.908270i | \(-0.362596\pi\) | ||||
0.418385 | + | 0.908270i | \(0.362596\pi\) | |||||||
\(920\) | 7020.00 | + | 12159.0i | 0.251568 | + | 0.435729i | ||||
\(921\) | 6256.17i | 0.223830i | ||||||||
\(922\) | −8031.00 | + | 13910.1i | −0.286862 | + | 0.496860i | ||||
\(923\) | 2886.00 | − | 4998.70i | 0.102919 | − | 0.178260i | ||||
\(924\) | −8370.00 | + | 4832.42i | −0.298001 | + | 0.172051i | ||||
\(925\) | −3652.00 | − | 6325.45i | −0.129813 | − | 0.224843i | ||||
\(926\) | 8566.00 | 0.303992 | ||||||||
\(927\) | 7438.50 | − | 12883.9i | 0.263552 | − | 0.456485i | ||||
\(928\) | 3552.00 | 0.125647 | ||||||||
\(929\) | −9349.50 | − | 16193.8i | −0.330191 | − | 0.571907i | 0.652358 | − | 0.757911i | \(-0.273780\pi\) |
−0.982549 | + | 0.186004i | \(0.940446\pi\) | |||||||
\(930\) | 16605.0 | + | 9586.90i | 0.585483 | + | 0.338029i | ||||
\(931\) | 8652.00 | − | 14985.7i | 0.304573 | − | 0.527537i | ||||
\(932\) | −5268.00 | + | 9124.44i | −0.185149 | + | 0.320688i | ||||
\(933\) | −14782.5 | − | 8534.68i | −0.518711 | − | 0.299478i | ||||
\(934\) | −5460.00 | − | 9457.00i | −0.191281 | − | 0.331309i | ||||
\(935\) | −5670.00 | −0.198320 | ||||||||
\(936\) | −3996.00 | + | 6921.28i | −0.139544 | + | 0.241698i | ||||
\(937\) | −31234.0 | −1.08898 | −0.544488 | − | 0.838769i | \(-0.683276\pi\) | ||||
−0.544488 | + | 0.838769i | \(0.683276\pi\) | |||||||
\(938\) | −13051.0 | − | 22605.0i | −0.454297 | − | 0.786865i | ||||
\(939\) | 45256.5 | − | 26128.9i | 1.57283 | − | 0.908075i | ||||
\(940\) | 3186.00 | − | 5518.31i | 0.110549 | − | 0.191476i | ||||
\(941\) | −5875.50 | + | 10176.7i | −0.203545 | + | 0.352550i | −0.949668 | − | 0.313258i | \(-0.898580\pi\) |
0.746123 | + | 0.665808i | \(0.231913\pi\) | |||||||
\(942\) | 30937.9i | 1.07008i | ||||||||
\(943\) | 25447.5 | + | 44076.4i | 0.878775 | + | 1.52208i | ||||
\(944\) | 2544.00 | 0.0877120 | ||||||||
\(945\) | 39142.6i | 1.34742i | ||||||||
\(946\) | 1290.00 | 0.0443356 | ||||||||
\(947\) | 12943.5 | + | 22418.8i | 0.444147 | + | 0.769285i | 0.997992 | − | 0.0633343i | \(-0.0201735\pi\) |
−0.553845 | + | 0.832620i | \(0.686840\pi\) | |||||||
\(948\) | − | 23549.0i | − | 0.806788i | ||||||
\(949\) | 3367.00 | − | 5831.82i | 0.115171 | − | 0.199482i | ||||
\(950\) | −1232.00 | + | 2133.89i | −0.0420751 | + | 0.0728762i | ||||
\(951\) | −10327.5 | + | 5962.58i | −0.352147 | + | 0.203312i | ||||
\(952\) | −5208.00 | − | 9020.52i | −0.177303 | − | 0.307097i | ||||
\(953\) | −41130.0 | −1.39804 | −0.699020 | − | 0.715102i | \(-0.746380\pi\) | ||||
−0.699020 | + | 0.715102i | \(0.746380\pi\) | |||||||
\(954\) | 3078.00 | + | 5331.25i | 0.104459 | + | 0.180928i | ||||
\(955\) | −10449.0 | −0.354054 | ||||||||
\(956\) | −13830.0 | − | 23954.3i | −0.467881 | − | 0.810394i | ||||
\(957\) | −7492.50 | − | 4325.80i | −0.253081 | − | 0.146116i | ||||
\(958\) | −429.000 | + | 743.050i | −0.0144680 | + | 0.0250593i | ||||
\(959\) | −41245.5 | + | 71439.3i | −1.38883 | + | 2.40552i | ||||
\(960\) | −2592.00 | − | 1496.49i | −0.0871421 | − | 0.0503115i | ||||
\(961\) | −6117.00 | − | 10595.0i | −0.205330 | − | 0.355643i | ||||
\(962\) | 12284.0 | 0.411697 | ||||||||
\(963\) | 324.000 | 0.0108419 | ||||||||
\(964\) | −5956.00 | −0.198994 | ||||||||
\(965\) | 16249.5 | + | 28145.0i | 0.542062 | + | 0.938879i | ||||
\(966\) | 54405.0 | − | 31410.7i | 1.81206 | − | 1.04619i | ||||
\(967\) | 14322.5 | − | 24807.3i | 0.476298 | − | 0.824973i | −0.523333 | − | 0.852128i | \(-0.675312\pi\) |
0.999631 | + | 0.0271553i | \(0.00864488\pi\) | |||||||
\(968\) | 4424.00 | − | 7662.59i | 0.146893 | − | 0.254427i | ||||
\(969\) | − | 6110.68i | − | 0.202583i | ||||||
\(970\) | −8109.00 | − | 14045.2i | −0.268417 | − | 0.464912i | ||||
\(971\) | −32256.0 | −1.06606 | −0.533030 | − | 0.846096i | \(-0.678947\pi\) | ||||
−0.533030 | + | 0.846096i | \(0.678947\pi\) | |||||||
\(972\) | 13122.0 | + | 7575.99i | 0.433013 | + | 0.250000i | ||||
\(973\) | 3751.00 | 0.123588 | ||||||||
\(974\) | 11296.0 | + | 19565.2i | 0.371609 | + | 0.643646i | ||||
\(975\) | − | 8459.34i | − | 0.277862i | ||||||
\(976\) | −1528.00 | + | 2646.57i | −0.0501128 | + | 0.0867979i | ||||
\(977\) | −4507.50 | + | 7807.22i | −0.147603 | + | 0.255655i | −0.930341 | − | 0.366696i | \(-0.880489\pi\) |
0.782738 | + | 0.622351i | \(0.213822\pi\) | |||||||
\(978\) | 29844.0 | − | 17230.4i | 0.975773 | − | 0.563363i | ||||
\(979\) | −7875.00 | − | 13639.9i | −0.257085 | − | 0.445284i | ||||
\(980\) | −22248.0 | −0.725190 | ||||||||
\(981\) | 13554.0 | 0.441127 | ||||||||
\(982\) | −29346.0 | −0.953634 | ||||||||
\(983\) | −7942.50 | − | 13756.8i | −0.257707 | − | 0.446362i | 0.707920 | − | 0.706293i | \(-0.249634\pi\) |
−0.965627 | + | 0.259930i | \(0.916300\pi\) | |||||||
\(984\) | −9396.00 | − | 5424.78i | −0.304404 | − | 0.175748i | ||||
\(985\) | 9207.00 | − | 15947.0i | 0.297827 | − | 0.515851i | ||||
\(986\) | 4662.00 | − | 8074.82i | 0.150576 | − | 0.260806i | ||||
\(987\) | −24691.5 | − | 14255.6i | −0.796291 | − | 0.459739i | ||||
\(988\) | −2072.00 | − | 3588.81i | −0.0667197 | − | 0.115562i | ||||
\(989\) | −8385.00 | −0.269593 | ||||||||
\(990\) | 3645.00 | + | 6313.33i | 0.117016 | + | 0.202677i | ||||
\(991\) | 34904.0 | 1.11883 | 0.559416 | − | 0.828887i | \(-0.311026\pi\) | ||||
0.559416 | + | 0.828887i | \(0.311026\pi\) | |||||||
\(992\) | 3280.00 | + | 5681.13i | 0.104980 | + | 0.181831i | ||||
\(993\) | 30055.5 | − | 17352.6i | 0.960506 | − | 0.554548i | ||||
\(994\) | 4836.00 | − | 8376.20i | 0.154314 | − | 0.267281i | ||||
\(995\) | 13482.0 | − | 23351.5i | 0.429556 | − | 0.744013i | ||||
\(996\) | 22509.7i | 0.716113i | ||||||||
\(997\) | 17670.5 | + | 30606.2i | 0.561314 | + | 0.972225i | 0.997382 | + | 0.0723111i | \(0.0230374\pi\) |
−0.436068 | + | 0.899914i | \(0.643629\pi\) | |||||||
\(998\) | 26878.0 | 0.852513 | ||||||||
\(999\) | − | 23289.2i | − | 0.737574i |
(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 | 18.4.c.a.13.1 | yes | 2 | |
3.2 | odd | 2 | 54.4.c.a.37.1 | 2 | |||
4.3 | odd | 2 | 144.4.i.a.49.1 | 2 | |||
9.2 | odd | 6 | 54.4.c.a.19.1 | 2 | |||
9.4 | even | 3 | 162.4.a.d.1.1 | 1 | |||
9.5 | odd | 6 | 162.4.a.a.1.1 | 1 | |||
9.7 | even | 3 | inner | 18.4.c.a.7.1 | ✓ | 2 | |
12.11 | even | 2 | 432.4.i.a.145.1 | 2 | |||
36.7 | odd | 6 | 144.4.i.a.97.1 | 2 | |||
36.11 | even | 6 | 432.4.i.a.289.1 | 2 | |||
36.23 | even | 6 | 1296.4.a.g.1.1 | 1 | |||
36.31 | odd | 6 | 1296.4.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
18.4.c.a.7.1 | ✓ | 2 | 9.7 | even | 3 | inner | |
18.4.c.a.13.1 | yes | 2 | 1.1 | even | 1 | trivial | |
54.4.c.a.19.1 | 2 | 9.2 | odd | 6 | |||
54.4.c.a.37.1 | 2 | 3.2 | odd | 2 | |||
144.4.i.a.49.1 | 2 | 4.3 | odd | 2 | |||
144.4.i.a.97.1 | 2 | 36.7 | odd | 6 | |||
162.4.a.a.1.1 | 1 | 9.5 | odd | 6 | |||
162.4.a.d.1.1 | 1 | 9.4 | even | 3 | |||
432.4.i.a.145.1 | 2 | 12.11 | even | 2 | |||
432.4.i.a.289.1 | 2 | 36.11 | even | 6 | |||
1296.4.a.b.1.1 | 1 | 36.31 | odd | 6 | |||
1296.4.a.g.1.1 | 1 | 36.23 | even | 6 |