Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(76,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.76");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.e (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: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} + 48 x^{12} - 60 x^{11} + 1605 x^{10} - 1800 x^{9} + 23232 x^{8} - 2346 x^{7} + \cdots + 82944 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{6} \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 76.7 | ||
Root | \(-2.69252 + 4.66357i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.76 |
Dual form | 225.4.e.d.151.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.69252 | + | 4.66357i | 0.951948 | + | 1.64882i | 0.741203 | + | 0.671281i | \(0.234256\pi\) |
0.210745 | + | 0.977541i | \(0.432411\pi\) | |||||||
\(3\) | 4.09553 | + | 3.19791i | 0.788185 | + | 0.615438i | ||||
\(4\) | −10.4993 | + | 18.1853i | −1.31241 | + | 2.27316i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.88642 | + | 27.7102i | −0.264437 | + | 1.88544i | ||||
\(7\) | 6.28510 | + | 10.8861i | 0.339363 | + | 0.587795i | 0.984313 | − | 0.176430i | \(-0.0564550\pi\) |
−0.644950 | + | 0.764225i | \(0.723122\pi\) | |||||||
\(8\) | −69.9976 | −3.09349 | ||||||||
\(9\) | 6.54673 | + | 26.1943i | 0.242471 | + | 0.970159i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.41534 | − | 11.1117i | −0.175845 | − | 0.304573i | 0.764608 | − | 0.644495i | \(-0.222933\pi\) |
−0.940454 | + | 0.339922i | \(0.889599\pi\) | |||||||
\(12\) | −101.155 | + | 40.9026i | −2.43341 | + | 0.983964i | ||||
\(13\) | 29.9322 | − | 51.8442i | 0.638593 | − | 1.10608i | −0.347148 | − | 0.937810i | \(-0.612850\pi\) |
0.985742 | − | 0.168266i | \(-0.0538167\pi\) | |||||||
\(14\) | −33.8455 | + | 58.6220i | −0.646113 | + | 1.11910i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −104.475 | − | 180.957i | −1.63243 | − | 2.82745i | ||||
\(17\) | 110.011 | 1.56950 | 0.784752 | − | 0.619810i | \(-0.212790\pi\) | ||||
0.784752 | + | 0.619810i | \(0.212790\pi\) | |||||||
\(18\) | −104.532 | + | 101.060i | −1.36880 | + | 1.32333i | ||||
\(19\) | −12.0872 | −0.145947 | −0.0729733 | − | 0.997334i | \(-0.523249\pi\) | ||||
−0.0729733 | + | 0.997334i | \(0.523249\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −9.07201 | + | 64.6836i | −0.0942702 | + | 0.672148i | ||||
\(22\) | 34.5468 | − | 59.8368i | 0.334791 | − | 0.579875i | ||||
\(23\) | −33.8608 | + | 58.6485i | −0.306976 | + | 0.531699i | −0.977699 | − | 0.210009i | \(-0.932651\pi\) |
0.670723 | + | 0.741708i | \(0.265984\pi\) | |||||||
\(24\) | −286.677 | − | 223.846i | −2.43824 | − | 1.90385i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 322.372 | 2.43163 | ||||||||
\(27\) | −56.9547 | + | 128.215i | −0.405960 | + | 0.913891i | ||||
\(28\) | −263.956 | −1.78154 | ||||||||
\(29\) | −99.9790 | − | 173.169i | −0.640194 | − | 1.10885i | −0.985389 | − | 0.170318i | \(-0.945521\pi\) |
0.345195 | − | 0.938531i | \(-0.387813\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −38.3143 | + | 66.3624i | −0.221982 | + | 0.384485i | −0.955410 | − | 0.295283i | \(-0.904586\pi\) |
0.733427 | + | 0.679768i | \(0.237919\pi\) | |||||||
\(32\) | 282.613 | − | 489.500i | 1.56123 | − | 2.70413i | ||||
\(33\) | 9.26000 | − | 66.0240i | 0.0488473 | − | 0.348282i | ||||
\(34\) | 296.206 | + | 513.044i | 1.49409 | + | 2.58783i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −545.086 | − | 155.967i | −2.52355 | − | 0.722069i | ||||
\(37\) | 22.4815 | 0.0998900 | 0.0499450 | − | 0.998752i | \(-0.484095\pi\) | ||||
0.0499450 | + | 0.998752i | \(0.484095\pi\) | |||||||
\(38\) | −32.5449 | − | 56.3694i | −0.138934 | − | 0.240640i | ||||
\(39\) | 288.381 | − | 116.609i | 1.18405 | − | 0.478778i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −43.8807 | + | 76.0037i | −0.167147 | + | 0.289507i | −0.937416 | − | 0.348213i | \(-0.886789\pi\) |
0.770269 | + | 0.637719i | \(0.220122\pi\) | |||||||
\(42\) | −326.083 | + | 131.854i | −1.19799 | + | 0.484415i | ||||
\(43\) | 59.7050 | + | 103.412i | 0.211743 | + | 0.366749i | 0.952260 | − | 0.305288i | \(-0.0987528\pi\) |
−0.740517 | + | 0.672037i | \(0.765419\pi\) | |||||||
\(44\) | 269.426 | 0.923124 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −364.682 | −1.16890 | ||||||||
\(47\) | 121.578 | + | 210.579i | 0.377317 | + | 0.653533i | 0.990671 | − | 0.136276i | \(-0.0435133\pi\) |
−0.613354 | + | 0.789808i | \(0.710180\pi\) | |||||||
\(48\) | 150.801 | − | 1075.22i | 0.453465 | − | 3.23321i | ||||
\(49\) | 92.4951 | − | 160.206i | 0.269665 | − | 0.467073i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 450.553 | + | 351.805i | 1.23706 | + | 0.965932i | ||||
\(52\) | 628.534 | + | 1088.65i | 1.67619 | + | 2.90325i | ||||
\(53\) | 293.518 | 0.760712 | 0.380356 | − | 0.924840i | \(-0.375801\pi\) | ||||
0.380356 | + | 0.924840i | \(0.375801\pi\) | |||||||
\(54\) | −751.293 | + | 79.6094i | −1.89330 | + | 0.200620i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −439.942 | − | 762.002i | −1.04982 | − | 1.81834i | ||||
\(57\) | −49.5034 | − | 38.6537i | −0.115033 | − | 0.0898212i | ||||
\(58\) | 538.390 | − | 932.519i | 1.21886 | − | 2.11113i | ||||
\(59\) | 290.692 | − | 503.493i | 0.641438 | − | 1.11100i | −0.343674 | − | 0.939089i | \(-0.611672\pi\) |
0.985112 | − | 0.171914i | \(-0.0549951\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 386.847 | + | 670.038i | 0.811977 | + | 1.40639i | 0.911478 | + | 0.411349i | \(0.134942\pi\) |
−0.0995008 | + | 0.995037i | \(0.531725\pi\) | |||||||
\(62\) | −412.648 | −0.845263 | ||||||||
\(63\) | −244.007 | + | 235.902i | −0.487968 | + | 0.471760i | ||||
\(64\) | 1372.15 | 2.67998 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 332.840 | − | 134.586i | 0.620755 | − | 0.251006i | ||||
\(67\) | −115.719 | + | 200.431i | −0.211005 | + | 0.365471i | −0.952029 | − | 0.306007i | \(-0.901007\pi\) |
0.741024 | + | 0.671478i | \(0.234340\pi\) | |||||||
\(68\) | −1155.03 | + | 2000.58i | −2.05983 | + | 3.56773i | ||||
\(69\) | −326.231 | + | 131.913i | −0.569182 | + | 0.230152i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −744.342 | −1.24418 | −0.622092 | − | 0.782944i | \(-0.713717\pi\) | ||||
−0.622092 | + | 0.782944i | \(0.713717\pi\) | |||||||
\(72\) | −458.255 | − | 1833.54i | −0.750082 | − | 3.00117i | ||||
\(73\) | 264.839 | 0.424616 | 0.212308 | − | 0.977203i | \(-0.431902\pi\) | ||||
0.212308 | + | 0.977203i | \(0.431902\pi\) | |||||||
\(74\) | 60.5317 | + | 104.844i | 0.0950901 | + | 0.164701i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 126.907 | − | 219.809i | 0.191542 | − | 0.331760i | ||||
\(77\) | 80.6421 | − | 139.676i | 0.119351 | − | 0.206722i | ||||
\(78\) | 1320.28 | + | 1030.92i | 1.91657 | + | 1.49652i | ||||
\(79\) | −279.858 | − | 484.729i | −0.398564 | − | 0.690333i | 0.594985 | − | 0.803737i | \(-0.297158\pi\) |
−0.993549 | + | 0.113404i | \(0.963825\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −643.281 | + | 342.974i | −0.882415 | + | 0.470471i | ||||
\(82\) | −472.598 | −0.636460 | ||||||||
\(83\) | −610.443 | − | 1057.32i | −0.807288 | − | 1.39826i | −0.914736 | − | 0.404052i | \(-0.867601\pi\) |
0.107448 | − | 0.994211i | \(-0.465732\pi\) | |||||||
\(84\) | −1081.04 | − | 844.108i | −1.40418 | − | 1.09643i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −321.513 | + | 556.878i | −0.403136 | + | 0.698252i | ||||
\(87\) | 144.311 | − | 1028.94i | 0.177837 | − | 1.26798i | ||||
\(88\) | 449.059 | + | 777.792i | 0.543975 | + | 0.942193i | ||||
\(89\) | −255.905 | −0.304785 | −0.152392 | − | 0.988320i | \(-0.548698\pi\) | ||||
−0.152392 | + | 0.988320i | \(0.548698\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 752.509 | 0.866861 | ||||||||
\(92\) | −711.027 | − | 1231.53i | −0.805757 | − | 1.39561i | ||||
\(93\) | −369.138 | + | 149.263i | −0.411590 | + | 0.166429i | ||||
\(94\) | −654.699 | + | 1133.97i | −0.718373 | + | 1.24426i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2722.83 | − | 1100.99i | 2.89476 | − | 1.17051i | ||||
\(97\) | 524.759 | + | 908.909i | 0.549291 | + | 0.951400i | 0.998323 | + | 0.0578842i | \(0.0184354\pi\) |
−0.449032 | + | 0.893515i | \(0.648231\pi\) | |||||||
\(98\) | 996.177 | 1.02683 | ||||||||
\(99\) | 249.064 | − | 240.791i | 0.252847 | − | 0.244448i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −44.3635 | − | 76.8398i | −0.0437062 | − | 0.0757014i | 0.843345 | − | 0.537373i | \(-0.180583\pi\) |
−0.887051 | + | 0.461671i | \(0.847250\pi\) | |||||||
\(102\) | −427.548 | + | 3048.43i | −0.415035 | + | 2.95921i | ||||
\(103\) | −772.035 | + | 1337.20i | −0.738552 | + | 1.27921i | 0.214595 | + | 0.976703i | \(0.431157\pi\) |
−0.953147 | + | 0.302507i | \(0.902176\pi\) | |||||||
\(104\) | −2095.19 | + | 3628.97i | −1.97548 | + | 3.42163i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 790.301 | + | 1368.84i | 0.724158 | + | 1.25428i | ||||
\(107\) | 585.772 | 0.529240 | 0.264620 | − | 0.964353i | \(-0.414753\pi\) | ||||
0.264620 | + | 0.964353i | \(0.414753\pi\) | |||||||
\(108\) | −1733.65 | − | 2381.90i | −1.54463 | − | 2.12221i | ||||
\(109\) | 1367.04 | 1.20127 | 0.600634 | − | 0.799524i | \(-0.294915\pi\) | ||||
0.600634 | + | 0.799524i | \(0.294915\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 92.0735 | + | 71.8937i | 0.0787318 | + | 0.0614761i | ||||
\(112\) | 1313.28 | − | 2274.66i | 1.10797 | − | 1.91907i | ||||
\(113\) | 85.2146 | − | 147.596i | 0.0709408 | − | 0.122873i | −0.828373 | − | 0.560177i | \(-0.810733\pi\) |
0.899314 | + | 0.437304i | \(0.144067\pi\) | |||||||
\(114\) | 46.9758 | − | 334.938i | 0.0385937 | − | 0.275174i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4198.83 | 3.36079 | ||||||||
\(117\) | 1553.98 | + | 444.644i | 1.22791 | + | 0.351345i | ||||
\(118\) | 3130.77 | 2.44246 | ||||||||
\(119\) | 691.429 | + | 1197.59i | 0.532632 | + | 0.922546i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 583.187 | − | 1010.11i | 0.438157 | − | 0.758910i | ||||
\(122\) | −2083.18 | + | 3608.17i | −1.54592 | + | 2.67761i | ||||
\(123\) | −422.768 | + | 170.949i | −0.309916 | + | 0.125316i | ||||
\(124\) | −804.545 | − | 1393.51i | −0.582664 | − | 1.00920i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1757.14 | − | 502.775i | −1.24237 | − | 0.355482i | ||||
\(127\) | −1809.74 | −1.26447 | −0.632237 | − | 0.774775i | \(-0.717863\pi\) | ||||
−0.632237 | + | 0.774775i | \(0.717863\pi\) | |||||||
\(128\) | 1433.63 | + | 2483.13i | 0.989973 | + | 1.71468i | ||||
\(129\) | −86.1791 | + | 614.459i | −0.0588190 | + | 0.419381i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 619.147 | − | 1072.39i | 0.412940 | − | 0.715232i | −0.582270 | − | 0.812995i | \(-0.697835\pi\) |
0.995210 | + | 0.0977630i | \(0.0311687\pi\) | |||||||
\(132\) | 1103.44 | + | 861.600i | 0.727593 | + | 0.568126i | ||||
\(133\) | −75.9691 | − | 131.582i | −0.0495290 | − | 0.0857867i | ||||
\(134\) | −1246.30 | −0.803462 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7700.50 | −4.85524 | ||||||||
\(137\) | 253.091 | + | 438.367i | 0.157832 | + | 0.273374i | 0.934087 | − | 0.357046i | \(-0.116216\pi\) |
−0.776254 | + | 0.630420i | \(0.782883\pi\) | |||||||
\(138\) | −1493.57 | − | 1166.22i | −0.921311 | − | 0.719387i | ||||
\(139\) | 106.840 | − | 185.052i | 0.0651946 | − | 0.112920i | −0.831586 | − | 0.555396i | \(-0.812567\pi\) |
0.896780 | + | 0.442476i | \(0.145900\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −175.487 | + | 1251.23i | −0.104813 | + | 0.747320i | ||||
\(142\) | −2004.15 | − | 3471.29i | −1.18440 | − | 2.05144i | ||||
\(143\) | −768.103 | −0.449175 | ||||||||
\(144\) | 4056.06 | − | 3921.33i | 2.34726 | − | 2.26929i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 713.082 | + | 1235.09i | 0.404213 | + | 0.700117i | ||||
\(147\) | 891.141 | − | 360.338i | 0.500001 | − | 0.202178i | ||||
\(148\) | −236.039 | + | 408.832i | −0.131097 | + | 0.227066i | ||||
\(149\) | 452.655 | − | 784.022i | 0.248879 | − | 0.431071i | −0.714336 | − | 0.699803i | \(-0.753271\pi\) |
0.963215 | + | 0.268732i | \(0.0866046\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −679.335 | − | 1176.64i | −0.366116 | − | 0.634131i | 0.622839 | − | 0.782350i | \(-0.285979\pi\) |
−0.988955 | + | 0.148219i | \(0.952646\pi\) | |||||||
\(152\) | 846.073 | 0.451484 | ||||||||
\(153\) | 720.211 | + | 2881.66i | 0.380560 | + | 1.52267i | ||||
\(154\) | 868.521 | 0.454464 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −907.235 | + | 6468.60i | −0.465622 | + | 3.31989i | ||||
\(157\) | 950.670 | − | 1646.61i | 0.483259 | − | 0.837030i | −0.516556 | − | 0.856254i | \(-0.672786\pi\) |
0.999815 | + | 0.0192236i | \(0.00611945\pi\) | |||||||
\(158\) | 1507.05 | − | 2610.28i | 0.758824 | − | 1.31432i | ||||
\(159\) | 1202.11 | + | 938.643i | 0.599582 | + | 0.468172i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −851.273 | −0.416706 | ||||||||
\(162\) | −3331.53 | − | 2076.53i | −1.61574 | − | 1.00708i | ||||
\(163\) | 2325.15 | 1.11730 | 0.558649 | − | 0.829404i | \(-0.311320\pi\) | ||||
0.558649 | + | 0.829404i | \(0.311320\pi\) | |||||||
\(164\) | −921.432 | − | 1595.97i | −0.438730 | − | 0.759903i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3287.26 | − | 5693.69i | 1.53699 | − | 2.66215i | ||||
\(167\) | 982.901 | − | 1702.43i | 0.455444 | − | 0.788853i | −0.543269 | − | 0.839558i | \(-0.682814\pi\) |
0.998714 | + | 0.0507059i | \(0.0161471\pi\) | |||||||
\(168\) | 635.019 | − | 4527.70i | 0.291624 | − | 2.07928i | ||||
\(169\) | −693.379 | − | 1200.97i | −0.315603 | − | 0.546640i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −79.1314 | − | 316.615i | −0.0353879 | − | 0.141591i | ||||
\(172\) | −2507.44 | −1.11157 | ||||||||
\(173\) | −1148.95 | − | 1990.04i | −0.504932 | − | 0.874567i | −0.999984 | − | 0.00570381i | \(-0.998184\pi\) |
0.495052 | − | 0.868863i | \(-0.335149\pi\) | |||||||
\(174\) | 5187.10 | − | 2097.43i | 2.25996 | − | 0.913828i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1340.49 | + | 2321.80i | −0.574110 | + | 0.994387i | ||||
\(177\) | 2800.66 | − | 1132.46i | 1.18933 | − | 0.480911i | ||||
\(178\) | −689.027 | − | 1193.43i | −0.290139 | − | 0.502536i | ||||
\(179\) | −873.696 | −0.364822 | −0.182411 | − | 0.983222i | \(-0.558390\pi\) | ||||
−0.182411 | + | 0.983222i | \(0.558390\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1494.20 | 0.613609 | 0.306805 | − | 0.951772i | \(-0.400740\pi\) | ||||
0.306805 | + | 0.951772i | \(0.400740\pi\) | |||||||
\(182\) | 2026.14 | + | 3509.38i | 0.825206 | + | 1.42930i | ||||
\(183\) | −558.380 | + | 3981.26i | −0.225555 | + | 1.60821i | ||||
\(184\) | 2370.17 | − | 4105.26i | 0.949627 | − | 1.64480i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1690.01 | − | 1319.61i | −0.666224 | − | 0.520207i | ||||
\(187\) | −705.758 | − | 1222.41i | −0.275990 | − | 0.478028i | ||||
\(188\) | −5105.91 | −1.98078 | ||||||||
\(189\) | −1753.73 | + | 185.831i | −0.674948 | + | 0.0715196i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2525.13 | − | 4373.65i | −0.956607 | − | 1.65689i | −0.730648 | − | 0.682754i | \(-0.760782\pi\) |
−0.225959 | − | 0.974137i | \(-0.572551\pi\) | |||||||
\(192\) | 5619.68 | + | 4388.02i | 2.11232 | + | 1.64936i | ||||
\(193\) | 2580.80 | − | 4470.08i | 0.962539 | − | 1.66717i | 0.246452 | − | 0.969155i | \(-0.420735\pi\) |
0.716087 | − | 0.698011i | \(-0.245931\pi\) | |||||||
\(194\) | −2825.84 | + | 4894.50i | −1.04579 | + | 1.81137i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1942.26 | + | 3364.10i | 0.707822 | + | 1.22598i | ||||
\(197\) | −374.025 | −0.135270 | −0.0676350 | − | 0.997710i | \(-0.521545\pi\) | ||||
−0.0676350 | + | 0.997710i | \(0.521545\pi\) | |||||||
\(198\) | 1793.55 | + | 513.194i | 0.643748 | + | 0.184197i | ||||
\(199\) | 603.342 | 0.214924 | 0.107462 | − | 0.994209i | \(-0.465728\pi\) | ||||
0.107462 | + | 0.994209i | \(0.465728\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1114.89 | + | 450.813i | −0.391236 | + | 0.158198i | ||||
\(202\) | 238.899 | − | 413.785i | 0.0832121 | − | 0.144128i | ||||
\(203\) | 1256.76 | − | 2176.76i | 0.434517 | − | 0.752606i | ||||
\(204\) | −11128.2 | + | 4499.73i | −3.81925 | + | 1.54433i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8314.87 | −2.81225 | ||||||||
\(207\) | −1757.93 | − | 503.002i | −0.590265 | − | 0.168894i | ||||
\(208\) | −12508.7 | −4.16983 | ||||||||
\(209\) | 77.5434 | + | 134.309i | 0.0256640 | + | 0.0444514i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1205.91 | + | 2088.69i | −0.393450 | + | 0.681476i | −0.992902 | − | 0.118935i | \(-0.962052\pi\) |
0.599452 | + | 0.800411i | \(0.295385\pi\) | |||||||
\(212\) | −3081.72 | + | 5337.70i | −0.998366 | + | 1.72922i | ||||
\(213\) | −3048.47 | − | 2380.34i | −0.980648 | − | 0.765719i | ||||
\(214\) | 1577.20 | + | 2731.79i | 0.503809 | + | 0.872623i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3986.69 | − | 8974.76i | 1.25583 | − | 2.82711i | ||||
\(217\) | −963.237 | −0.301331 | ||||||||
\(218\) | 3680.76 | + | 6375.27i | 1.14354 | + | 1.98068i | ||||
\(219\) | 1084.65 | + | 846.930i | 0.334676 | + | 0.261325i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3292.87 | − | 5703.42i | 1.00227 | − | 1.73599i | ||||
\(222\) | −87.3724 | + | 622.966i | −0.0264146 | + | 0.188337i | ||||
\(223\) | 2740.64 | + | 4746.93i | 0.822990 | + | 1.42546i | 0.903446 | + | 0.428703i | \(0.141029\pi\) |
−0.0804554 | + | 0.996758i | \(0.525637\pi\) | |||||||
\(224\) | 7105.00 | 2.11930 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 917.766 | 0.270128 | ||||||||
\(227\) | −2736.24 | − | 4739.30i | −0.800046 | − | 1.38572i | −0.919585 | − | 0.392891i | \(-0.871475\pi\) |
0.119539 | − | 0.992830i | \(-0.461858\pi\) | |||||||
\(228\) | 1222.68 | − | 494.397i | 0.355148 | − | 0.143606i | ||||
\(229\) | −1637.99 | + | 2837.08i | −0.472670 | + | 0.818689i | −0.999511 | − | 0.0312750i | \(-0.990043\pi\) |
0.526840 | + | 0.849964i | \(0.323377\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 776.945 | − | 314.162i | 0.221295 | − | 0.0894820i | ||||
\(232\) | 6998.29 | + | 12121.4i | 1.98043 | + | 3.43021i | ||||
\(233\) | −3446.21 | −0.968965 | −0.484483 | − | 0.874801i | \(-0.660992\pi\) | ||||
−0.484483 | + | 0.874801i | \(0.660992\pi\) | |||||||
\(234\) | 2110.48 | + | 8444.31i | 0.589601 | + | 2.35907i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6104.11 | + | 10572.6i | 1.68366 | + | 2.91618i | ||||
\(237\) | 403.952 | − | 2880.18i | 0.110715 | − | 0.789401i | ||||
\(238\) | −3723.37 | + | 6449.06i | −1.01408 | + | 1.75643i | ||||
\(239\) | 862.406 | − | 1493.73i | 0.233408 | − | 0.404274i | −0.725401 | − | 0.688326i | \(-0.758346\pi\) |
0.958809 | + | 0.284053i | \(0.0916790\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2787.86 | + | 4828.71i | 0.745152 | + | 1.29064i | 0.950124 | + | 0.311873i | \(0.100956\pi\) |
−0.204972 | + | 0.978768i | \(0.565710\pi\) | |||||||
\(242\) | 6280.96 | 1.66841 | ||||||||
\(243\) | −3731.37 | − | 652.496i | −0.985053 | − | 0.172254i | ||||
\(244\) | −16246.4 | −4.26259 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1935.54 | − | 1511.33i | −0.501649 | − | 0.391702i | ||||
\(247\) | −361.796 | + | 626.649i | −0.0932006 | + | 0.161428i | ||||
\(248\) | 2681.91 | − | 4645.21i | 0.686700 | − | 1.18940i | ||||
\(249\) | 881.123 | − | 6282.42i | 0.224253 | − | 1.59893i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1356.38 | −0.341090 | −0.170545 | − | 0.985350i | \(-0.554553\pi\) | ||||
−0.170545 | + | 0.985350i | \(0.554553\pi\) | |||||||
\(252\) | −1728.05 | − | 6914.14i | −0.431971 | − | 1.72837i | ||||
\(253\) | 868.913 | 0.215921 | ||||||||
\(254\) | −4872.75 | − | 8439.84i | −1.20371 | − | 2.08489i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2231.56 | + | 3865.18i | −0.544815 | + | 0.943647i | ||||
\(257\) | −2043.91 | + | 3540.16i | −0.496092 | + | 0.859256i | −0.999990 | − | 0.00450688i | \(-0.998565\pi\) |
0.503898 | + | 0.863763i | \(0.331899\pi\) | |||||||
\(258\) | −3097.61 | + | 1252.54i | −0.747476 | + | 0.302246i | ||||
\(259\) | 141.298 | + | 244.736i | 0.0338990 | + | 0.0587148i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3881.49 | − | 3752.57i | 0.920530 | − | 0.889954i | ||||
\(262\) | 6668.25 | 1.57239 | ||||||||
\(263\) | −215.130 | − | 372.616i | −0.0504391 | − | 0.0873631i | 0.839704 | − | 0.543045i | \(-0.182729\pi\) |
−0.890143 | + | 0.455682i | \(0.849395\pi\) | |||||||
\(264\) | −648.178 | + | 4621.52i | −0.151108 | + | 1.07741i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 409.096 | − | 708.575i | 0.0942980 | − | 0.163329i | ||||
\(267\) | −1048.06 | − | 818.360i | −0.240227 | − | 0.187576i | ||||
\(268\) | −2429.93 | − | 4208.76i | −0.553849 | − | 0.959295i | ||||
\(269\) | 3467.85 | 0.786017 | 0.393008 | − | 0.919535i | \(-0.371434\pi\) | ||||
0.393008 | + | 0.919535i | \(0.371434\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −55.4415 | −0.0124274 | −0.00621371 | − | 0.999981i | \(-0.501978\pi\) | ||||
−0.00621371 | + | 0.999981i | \(0.501978\pi\) | |||||||
\(272\) | −11493.4 | − | 19907.2i | −2.56210 | − | 4.43769i | ||||
\(273\) | 3081.92 | + | 2406.46i | 0.683247 | + | 0.533499i | ||||
\(274\) | −1362.90 | + | 2360.62i | −0.300497 | + | 0.520475i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1026.31 | − | 7317.59i | 0.223828 | − | 1.59589i | ||||
\(277\) | −786.769 | − | 1362.72i | −0.170658 | − | 0.295589i | 0.767992 | − | 0.640460i | \(-0.221256\pi\) |
−0.938650 | + | 0.344871i | \(0.887923\pi\) | |||||||
\(278\) | 1150.67 | 0.248247 | ||||||||
\(279\) | −1989.15 | − | 569.160i | −0.426836 | − | 0.122132i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4073.23 | − | 7055.04i | −0.864727 | − | 1.49775i | −0.867318 | − | 0.497755i | \(-0.834158\pi\) |
0.00259078 | − | 0.999997i | \(-0.499175\pi\) | |||||||
\(282\) | −6307.68 | + | 2550.55i | −1.33198 | + | 0.538592i | ||||
\(283\) | 1549.15 | − | 2683.21i | 0.325398 | − | 0.563605i | −0.656195 | − | 0.754591i | \(-0.727835\pi\) |
0.981593 | + | 0.190986i | \(0.0611685\pi\) | |||||||
\(284\) | 7815.05 | − | 13536.1i | 1.63288 | − | 2.82823i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2068.13 | − | 3582.10i | −0.427591 | − | 0.740609i | ||||
\(287\) | −1103.18 | −0.226894 | ||||||||
\(288\) | 14672.3 | + | 4198.22i | 3.00199 | + | 0.858967i | ||||
\(289\) | 7189.39 | 1.46334 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −757.445 | + | 5400.60i | −0.152585 | + | 1.08793i | ||||
\(292\) | −2780.61 | + | 4816.16i | −0.557271 | + | 0.965221i | ||||
\(293\) | 61.0799 | − | 105.794i | 0.0121786 | − | 0.0210939i | −0.859872 | − | 0.510510i | \(-0.829457\pi\) |
0.872050 | + | 0.489416i | \(0.162790\pi\) | |||||||
\(294\) | 4079.87 | + | 3185.69i | 0.809330 | + | 0.631949i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1573.65 | −0.309008 | ||||||||
\(297\) | 1790.07 | − | 189.682i | 0.349733 | − | 0.0370588i | ||||
\(298\) | 4875.12 | 0.947679 | ||||||||
\(299\) | 2027.06 | + | 3510.97i | 0.392066 | + | 0.679078i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −750.504 | + | 1299.91i | −0.143715 | + | 0.248922i | ||||
\(302\) | 3658.24 | − | 6336.25i | 0.697046 | − | 1.20732i | ||||
\(303\) | 64.0349 | − | 456.570i | 0.0121410 | − | 0.0865652i | ||||
\(304\) | 1262.81 | + | 2187.25i | 0.238247 | + | 0.412657i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −11499.6 | + | 11117.7i | −2.14833 | + | 2.07697i | ||||
\(307\) | 1928.53 | 0.358525 | 0.179263 | − | 0.983801i | \(-0.442629\pi\) | ||||
0.179263 | + | 0.983801i | \(0.442629\pi\) | |||||||
\(308\) | 1693.37 | + | 2933.00i | 0.313275 | + | 0.542608i | ||||
\(309\) | −7438.15 | + | 3007.66i | −1.36939 | + | 0.553721i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3969.65 | + | 6875.63i | −0.723788 | + | 1.25364i | 0.235683 | + | 0.971830i | \(0.424267\pi\) |
−0.959471 | + | 0.281807i | \(0.909066\pi\) | |||||||
\(312\) | −20186.0 | + | 8162.33i | −3.66285 | + | 1.48109i | ||||
\(313\) | −3379.44 | − | 5853.37i | −0.610279 | − | 1.05703i | −0.991193 | − | 0.132424i | \(-0.957724\pi\) |
0.380914 | − | 0.924611i | \(-0.375609\pi\) | |||||||
\(314\) | 10238.8 | 1.84015 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11753.2 | 2.09232 | ||||||||
\(317\) | 4212.12 | + | 7295.60i | 0.746297 | + | 1.29262i | 0.949587 | + | 0.313505i | \(0.101503\pi\) |
−0.203290 | + | 0.979119i | \(0.565163\pi\) | |||||||
\(318\) | −1140.73 | + | 8133.44i | −0.201161 | + | 1.43428i | ||||
\(319\) | −1282.80 | + | 2221.87i | −0.225150 | + | 0.389972i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2399.05 | + | 1873.25i | 0.417139 | + | 0.325715i | ||||
\(322\) | −2292.06 | − | 3969.97i | −0.396683 | − | 0.687074i | ||||
\(323\) | −1329.72 | −0.229064 | ||||||||
\(324\) | 516.912 | − | 15299.2i | 0.0886337 | − | 2.62332i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6260.49 | + | 10843.5i | 1.06361 | + | 1.84222i | ||||
\(327\) | 5598.73 | + | 4371.66i | 0.946822 | + | 0.739307i | ||||
\(328\) | 3071.55 | − | 5320.08i | 0.517067 | − | 0.895586i | ||||
\(329\) | −1528.25 | + | 2647.01i | −0.256095 | + | 0.443570i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −128.837 | − | 223.153i | −0.0213944 | − | 0.0370562i | 0.855130 | − | 0.518414i | \(-0.173477\pi\) |
−0.876524 | + | 0.481357i | \(0.840144\pi\) | |||||||
\(332\) | 25636.9 | 4.23797 | ||||||||
\(333\) | 147.180 | + | 588.886i | 0.0242205 | + | 0.0969091i | ||||
\(334\) | 10585.9 | 1.73424 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 12652.7 | − | 5116.20i | 2.05435 | − | 0.830690i | ||||
\(337\) | −5549.76 | + | 9612.47i | −0.897077 | + | 1.55378i | −0.0658636 | + | 0.997829i | \(0.520980\pi\) |
−0.831213 | + | 0.555954i | \(0.812353\pi\) | |||||||
\(338\) | 3733.87 | − | 6467.25i | 0.600874 | − | 1.04075i | ||||
\(339\) | 820.997 | − | 331.975i | 0.131535 | − | 0.0531870i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 983.198 | 0.156138 | ||||||||
\(342\) | 1263.49 | − | 1221.53i | 0.199772 | − | 0.193136i | ||||
\(343\) | 6636.94 | 1.04478 | ||||||||
\(344\) | −4179.21 | − | 7238.60i | −0.655023 | − | 1.13453i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6187.14 | − | 10716.4i | 0.961337 | − | 1.66508i | ||||
\(347\) | 4943.28 | − | 8562.02i | 0.764753 | − | 1.32459i | −0.175624 | − | 0.984457i | \(-0.556194\pi\) |
0.940377 | − | 0.340134i | \(-0.110472\pi\) | |||||||
\(348\) | 17196.4 | + | 13427.5i | 2.64892 | + | 2.06836i | ||||
\(349\) | −3029.60 | − | 5247.42i | −0.464673 | − | 0.804837i | 0.534514 | − | 0.845160i | \(-0.320495\pi\) |
−0.999187 | + | 0.0403230i | \(0.987161\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4942.43 | + | 6790.54i | 0.751589 | + | 1.03263i | ||||
\(352\) | −7252.23 | −1.09814 | ||||||||
\(353\) | −4548.34 | − | 7877.96i | −0.685790 | − | 1.18782i | −0.973188 | − | 0.230012i | \(-0.926123\pi\) |
0.287398 | − | 0.957811i | \(-0.407210\pi\) | |||||||
\(354\) | 12822.2 | + | 10011.9i | 1.92511 | + | 1.50318i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2686.81 | − | 4653.70i | 0.400002 | − | 0.692824i | ||||
\(357\) | −998.020 | + | 7115.90i | −0.147957 | + | 1.05494i | ||||
\(358\) | −2352.44 | − | 4074.55i | −0.347291 | − | 0.601527i | ||||
\(359\) | −8804.63 | −1.29440 | −0.647201 | − | 0.762319i | \(-0.724061\pi\) | ||||
−0.647201 | + | 0.762319i | \(0.724061\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6712.90 | −0.978700 | ||||||||
\(362\) | 4023.17 | + | 6968.33i | 0.584124 | + | 1.01173i | ||||
\(363\) | 5618.70 | − | 2271.95i | 0.812411 | − | 0.328503i | ||||
\(364\) | −7900.80 | + | 13684.6i | −1.13768 | + | 1.97051i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −20070.3 | + | 8115.56i | −2.86638 | + | 1.15904i | ||||
\(367\) | 4326.18 | + | 7493.17i | 0.615326 | + | 1.06578i | 0.990327 | + | 0.138752i | \(0.0443091\pi\) |
−0.375001 | + | 0.927025i | \(0.622358\pi\) | |||||||
\(368\) | 14150.5 | 2.00447 | ||||||||
\(369\) | −2278.14 | − | 651.849i | −0.321396 | − | 0.0919619i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1844.79 | + | 3195.27i | 0.258158 | + | 0.447143i | ||||
\(372\) | 1161.29 | − | 8280.04i | 0.161855 | − | 1.15403i | ||||
\(373\) | −5959.31 | + | 10321.8i | −0.827243 | + | 1.43283i | 0.0729500 | + | 0.997336i | \(0.476759\pi\) |
−0.900193 | + | 0.435491i | \(0.856575\pi\) | |||||||
\(374\) | 3800.53 | − | 6582.70i | 0.525456 | − | 0.910116i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8510.14 | − | 14740.0i | −1.16723 | − | 2.02170i | ||||
\(377\) | −11970.4 | −1.63529 | ||||||||
\(378\) | −5588.59 | − | 7678.30i | −0.760439 | − | 1.04479i | ||||
\(379\) | 5052.23 | 0.684738 | 0.342369 | − | 0.939566i | \(-0.388771\pi\) | ||||
0.342369 | + | 0.939566i | \(0.388771\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7411.83 | − | 5787.38i | −0.996640 | − | 0.778206i | ||||
\(382\) | 13597.9 | − | 23552.2i | 1.82128 | − | 3.15455i | ||||
\(383\) | −2665.19 | + | 4616.24i | −0.355573 | + | 0.615871i | −0.987216 | − | 0.159388i | \(-0.949048\pi\) |
0.631642 | + | 0.775260i | \(0.282381\pi\) | |||||||
\(384\) | −2069.33 | + | 14754.4i | −0.275000 | + | 1.96076i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 27795.4 | 3.66515 | ||||||||
\(387\) | −2317.93 | + | 2240.94i | −0.304463 | + | 0.294350i | ||||
\(388\) | −22038.4 | −2.88358 | ||||||||
\(389\) | −1669.76 | − | 2892.11i | −0.217635 | − | 0.376955i | 0.736449 | − | 0.676493i | \(-0.236501\pi\) |
−0.954085 | + | 0.299537i | \(0.903168\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3725.05 | + | 6451.98i | −0.481800 | + | 0.834503i | ||||
\(392\) | −6474.43 | + | 11214.0i | −0.834205 | + | 1.44488i | ||||
\(393\) | 5965.15 | − | 2412.04i | 0.765654 | − | 0.309597i | ||||
\(394\) | −1007.07 | − | 1744.29i | −0.128770 | − | 0.223036i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1763.86 | + | 7057.42i | 0.223831 | + | 0.895577i | ||||
\(397\) | −9041.65 | −1.14304 | −0.571520 | − | 0.820588i | \(-0.693646\pi\) | ||||
−0.571520 | + | 0.820588i | \(0.693646\pi\) | |||||||
\(398\) | 1624.51 | + | 2813.73i | 0.204596 | + | 0.354371i | ||||
\(399\) | 109.655 | − | 781.842i | 0.0137584 | − | 0.0980978i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 835.978 | − | 1447.96i | 0.104107 | − | 0.180318i | −0.809266 | − | 0.587442i | \(-0.800135\pi\) |
0.913373 | + | 0.407124i | \(0.133468\pi\) | |||||||
\(402\) | −5104.26 | − | 3985.56i | −0.633277 | − | 0.494482i | ||||
\(403\) | 2293.67 | + | 3972.75i | 0.283513 | + | 0.491059i | ||||
\(404\) | 1863.14 | 0.229442 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 13535.3 | 1.65455 | ||||||||
\(407\) | −144.226 | − | 249.807i | −0.0175652 | − | 0.0304238i | ||||
\(408\) | −31537.6 | − | 24625.5i | −3.82683 | − | 2.98810i | ||||
\(409\) | −236.363 | + | 409.393i | −0.0285755 | + | 0.0494943i | −0.879960 | − | 0.475049i | \(-0.842430\pi\) |
0.851384 | + | 0.524543i | \(0.175764\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −365.316 | + | 2604.71i | −0.0438436 | + | 0.312605i | ||||
\(412\) | −16211.6 | − | 28079.4i | −1.93857 | − | 3.35770i | ||||
\(413\) | 7308.11 | 0.870722 | ||||||||
\(414\) | −2387.48 | − | 9552.59i | −0.283425 | − | 1.13402i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −16918.5 | − | 29303.7i | −1.99398 | − | 3.45368i | ||||
\(417\) | 1029.35 | − | 416.222i | 0.120881 | − | 0.0488789i | ||||
\(418\) | −417.573 | + | 723.258i | −0.0488617 | + | 0.0846309i | ||||
\(419\) | −6269.65 | + | 10859.3i | −0.731008 | + | 1.26614i | 0.225445 | + | 0.974256i | \(0.427616\pi\) |
−0.956453 | + | 0.291887i | \(0.905717\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3375.88 | + | 5847.19i | 0.390808 | + | 0.676900i | 0.992556 | − | 0.121786i | \(-0.0388623\pi\) |
−0.601748 | + | 0.798686i | \(0.705529\pi\) | |||||||
\(422\) | −12987.7 | −1.49818 | ||||||||
\(423\) | −4720.02 | + | 4563.24i | −0.542542 | + | 0.524521i | ||||
\(424\) | −20545.5 | −2.35325 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2892.82 | − | 20625.9i | 0.329009 | − | 2.34584i | ||||
\(427\) | −4862.74 | + | 8422.51i | −0.551111 | + | 0.954552i | ||||
\(428\) | −6150.18 | + | 10652.4i | −0.694580 | + | 1.20305i | ||||
\(429\) | −3145.79 | − | 2456.32i | −0.354033 | − | 0.276439i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7535.06 | 0.842114 | 0.421057 | − | 0.907034i | \(-0.361659\pi\) | ||||
0.421057 | + | 0.907034i | \(0.361659\pi\) | |||||||
\(432\) | 29151.8 | − | 3089.01i | 3.24668 | − | 0.344028i | ||||
\(433\) | 5135.13 | 0.569928 | 0.284964 | − | 0.958538i | \(-0.408018\pi\) | ||||
0.284964 | + | 0.958538i | \(0.408018\pi\) | |||||||
\(434\) | −2593.53 | − | 4492.13i | −0.286851 | − | 0.496841i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14352.9 | + | 24859.9i | −1.57656 | + | 2.73068i | ||||
\(437\) | 409.281 | − | 708.895i | 0.0448022 | − | 0.0775996i | ||||
\(438\) | −1029.27 | + | 7338.74i | −0.112284 | + | 0.800590i | ||||
\(439\) | −8486.60 | − | 14699.2i | −0.922650 | − | 1.59808i | −0.795297 | − | 0.606220i | \(-0.792685\pi\) |
−0.127353 | − | 0.991857i | \(-0.540648\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4802.02 | + | 1374.02i | 0.518521 | + | 0.148366i | ||||
\(442\) | 35464.4 | 3.81645 | ||||||||
\(443\) | 5676.15 | + | 9831.39i | 0.608763 | + | 1.05441i | 0.991445 | + | 0.130529i | \(0.0416675\pi\) |
−0.382681 | + | 0.923880i | \(0.624999\pi\) | |||||||
\(444\) | −2274.11 | + | 919.550i | −0.243073 | + | 0.0982881i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −14758.4 | + | 25562.3i | −1.56689 | + | 2.71393i | ||||
\(447\) | 4361.09 | − | 1763.43i | 0.461460 | − | 0.186594i | ||||
\(448\) | 8624.10 | + | 14937.4i | 0.909488 | + | 1.57528i | ||||
\(449\) | 11059.8 | 1.16246 | 0.581230 | − | 0.813740i | \(-0.302572\pi\) | ||||
0.581230 | + | 0.813740i | \(0.302572\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1126.04 | 0.117568 | ||||||||
\(452\) | 1789.38 | + | 3099.30i | 0.186207 | + | 0.322520i | ||||
\(453\) | 980.562 | − | 6991.42i | 0.101702 | − | 0.725134i | ||||
\(454\) | 14734.7 | − | 25521.3i | 1.52320 | − | 2.63827i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3465.12 | + | 2705.67i | 0.355853 | + | 0.277861i | ||||
\(457\) | 178.342 | + | 308.897i | 0.0182549 | + | 0.0316184i | 0.875009 | − | 0.484107i | \(-0.160856\pi\) |
−0.856754 | + | 0.515726i | \(0.827522\pi\) | |||||||
\(458\) | −17641.3 | −1.79983 | ||||||||
\(459\) | −6265.63 | + | 14105.1i | −0.637156 | + | 1.43435i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5159.88 | − | 8937.17i | −0.521300 | − | 0.902918i | −0.999693 | − | 0.0247726i | \(-0.992114\pi\) |
0.478393 | − | 0.878146i | \(-0.341219\pi\) | |||||||
\(462\) | 3557.05 | + | 2777.45i | 0.358201 | + | 0.279694i | ||||
\(463\) | −9084.27 | + | 15734.4i | −0.911839 | + | 1.57935i | −0.100376 | + | 0.994950i | \(0.532004\pi\) |
−0.811464 | + | 0.584403i | \(0.801329\pi\) | |||||||
\(464\) | −20890.7 | + | 36183.7i | −2.09014 | + | 3.62023i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9278.98 | − | 16071.7i | −0.922404 | − | 1.59765i | ||||
\(467\) | −3817.15 | −0.378237 | −0.189118 | − | 0.981954i | \(-0.560563\pi\) | ||||
−0.189118 | + | 0.981954i | \(0.560563\pi\) | |||||||
\(468\) | −24401.6 | + | 23591.1i | −2.41018 | + | 2.33013i | ||||
\(469\) | −2909.22 | −0.286429 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9159.21 | − | 3703.58i | 0.896038 | − | 0.362318i | ||||
\(472\) | −20347.7 | + | 35243.3i | −1.98428 | + | 3.43687i | ||||
\(473\) | 766.056 | − | 1326.85i | 0.0744679 | − | 0.128982i | ||||
\(474\) | 14519.6 | − | 5871.08i | 1.40698 | − | 0.568919i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −29038.0 | −2.79613 | ||||||||
\(477\) | 1921.58 | + | 7688.48i | 0.184451 | + | 0.738012i | ||||
\(478\) | 9288.17 | 0.888768 | ||||||||
\(479\) | −1453.28 | − | 2517.16i | −0.138627 | − | 0.240109i | 0.788350 | − | 0.615227i | \(-0.210936\pi\) |
−0.926977 | + | 0.375118i | \(0.877602\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 672.921 | − | 1165.53i | 0.0637891 | − | 0.110486i | ||||
\(482\) | −15012.7 | + | 26002.7i | −1.41869 | + | 2.45725i | ||||
\(483\) | −3486.41 | − | 2722.29i | −0.328442 | − | 0.256457i | ||||
\(484\) | 12246.1 | + | 21210.8i | 1.15008 | + | 1.99200i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −7003.82 | − | 19158.4i | −0.653703 | − | 1.78815i | ||||
\(487\) | −10411.1 | −0.968734 | −0.484367 | − | 0.874865i | \(-0.660950\pi\) | ||||
−0.484367 | + | 0.874865i | \(0.660950\pi\) | |||||||
\(488\) | −27078.3 | − | 46901.0i | −2.51184 | − | 4.35064i | ||||
\(489\) | 9522.70 | + | 7435.61i | 0.880637 | + | 0.687628i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7316.26 | + | 12672.1i | −0.672460 | + | 1.16474i | 0.304744 | + | 0.952434i | \(0.401429\pi\) |
−0.977204 | + | 0.212301i | \(0.931904\pi\) | |||||||
\(492\) | 1330.01 | − | 9482.99i | 0.121873 | − | 0.868956i | ||||
\(493\) | −10998.8 | − | 19050.4i | −1.00479 | − | 1.74034i | ||||
\(494\) | −3896.57 | −0.354888 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 16011.6 | 1.44948 | ||||||||
\(497\) | −4678.26 | − | 8102.99i | −0.422231 | − | 0.731325i | ||||
\(498\) | 31671.0 | − | 12806.3i | 2.84982 | − | 1.15234i | ||||
\(499\) | −4083.42 | + | 7072.69i | −0.366330 | + | 0.634503i | −0.988989 | − | 0.147991i | \(-0.952719\pi\) |
0.622658 | + | 0.782494i | \(0.286053\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9469.74 | − | 3829.14i | 0.844464 | − | 0.341464i | ||||
\(502\) | −3652.06 | − | 6325.56i | −0.324700 | − | 0.562397i | ||||
\(503\) | 8080.38 | 0.716275 | 0.358137 | − | 0.933669i | \(-0.383412\pi\) | ||||
0.358137 | + | 0.933669i | \(0.383412\pi\) | |||||||
\(504\) | 17079.9 | − | 16512.6i | 1.50952 | − | 1.45938i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2339.56 | + | 4052.24i | 0.205546 | + | 0.356016i | ||||
\(507\) | 1000.83 | − | 7135.96i | 0.0876698 | − | 0.625087i | ||||
\(508\) | 19000.9 | − | 32910.6i | 1.65951 | − | 2.87435i | ||||
\(509\) | −58.0903 | + | 100.615i | −0.00505856 | + | 0.00876169i | −0.868544 | − | 0.495613i | \(-0.834944\pi\) |
0.863485 | + | 0.504374i | \(0.168277\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1664.54 | + | 2883.06i | 0.144099 | + | 0.249587i | ||||
\(512\) | −1095.90 | −0.0945947 | ||||||||
\(513\) | 688.421 | − | 1549.76i | 0.0592486 | − | 0.133379i | ||||
\(514\) | −22013.0 | −1.88901 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −10269.3 | − | 8018.57i | −0.876124 | − | 0.684104i | ||||
\(517\) | 1559.92 | − | 2701.87i | 0.132699 | − | 0.229841i | ||||
\(518\) | −760.895 | + | 1317.91i | −0.0645402 | + | 0.111787i | ||||
\(519\) | 1658.41 | − | 11824.5i | 0.140263 | − | 1.00007i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14479.3 | −1.21756 | −0.608780 | − | 0.793339i | \(-0.708341\pi\) | ||||
−0.608780 | + | 0.793339i | \(0.708341\pi\) | |||||||
\(522\) | 27951.3 | + | 7997.79i | 2.34367 | + | 0.670601i | ||||
\(523\) | −6841.05 | −0.571966 | −0.285983 | − | 0.958235i | \(-0.592320\pi\) | ||||
−0.285983 | + | 0.958235i | \(0.592320\pi\) | |||||||
\(524\) | 13001.2 | + | 22518.7i | 1.08389 | + | 1.87736i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1158.48 | − | 2006.55i | 0.0960308 | − | 0.166330i | ||||
\(527\) | −4214.99 | + | 7300.58i | −0.348402 | + | 0.603450i | ||||
\(528\) | −12914.9 | + | 5222.22i | −1.06449 | + | 0.430432i | ||||
\(529\) | 3790.40 | + | 6565.16i | 0.311531 | + | 0.539588i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15091.7 | + | 4318.23i | 1.23338 | + | 0.352910i | ||||
\(532\) | 3190.48 | 0.260009 | ||||||||
\(533\) | 2626.90 | + | 4549.92i | 0.213478 | + | 0.369754i | ||||
\(534\) | 994.552 | − | 7091.17i | 0.0805964 | − | 0.574654i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8100.05 | − | 14029.7i | 0.652741 | − | 1.13058i | ||||
\(537\) | −3578.25 | − | 2794.00i | −0.287547 | − | 0.224525i | ||||
\(538\) | 9337.24 | + | 16172.6i | 0.748247 | + | 1.29600i | ||||
\(539\) | −2373.55 | −0.189677 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12746.0 | −1.01293 | −0.506465 | − | 0.862261i | \(-0.669048\pi\) | ||||
−0.506465 | + | 0.862261i | \(0.669048\pi\) | |||||||
\(542\) | −149.277 | − | 258.555i | −0.0118303 | − | 0.0204906i | ||||
\(543\) | 6119.56 | + | 4778.33i | 0.483638 | + | 0.377639i | ||||
\(544\) | 31090.5 | − | 53850.3i | 2.45036 | − | 4.24414i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2924.56 | + | 20852.2i | −0.229230 | + | 1.63442i | ||||
\(547\) | 2490.27 | + | 4313.28i | 0.194655 | + | 0.337152i | 0.946787 | − | 0.321860i | \(-0.104308\pi\) |
−0.752132 | + | 0.659012i | \(0.770975\pi\) | |||||||
\(548\) | −10629.1 | −0.828563 | ||||||||
\(549\) | −15018.6 | + | 14519.7i | −1.16754 | + | 1.12876i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1208.46 | + | 2093.12i | 0.0934342 | + | 0.161833i | ||||
\(552\) | 22835.4 | − | 9233.61i | 1.76076 | − | 0.711972i | ||||
\(553\) | 3517.88 | − | 6093.14i | 0.270516 | − | 0.468547i | ||||
\(554\) | 4236.77 | − | 7338.31i | 0.324916 | − | 0.562771i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2243.48 | + | 3885.83i | 0.171124 | + | 0.296395i | ||||
\(557\) | 635.610 | 0.0483513 | 0.0241756 | − | 0.999708i | \(-0.492304\pi\) | ||||
0.0241756 | + | 0.999708i | \(0.492304\pi\) | |||||||
\(558\) | −2701.49 | − | 10809.0i | −0.204952 | − | 0.820039i | ||||
\(559\) | 7148.42 | 0.540869 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1018.70 | − | 7263.36i | 0.0766660 | − | 0.546630i | ||||
\(562\) | 21934.4 | − | 37991.6i | 1.64635 | − | 2.85156i | ||||
\(563\) | −3768.84 | + | 6527.82i | −0.282127 | + | 0.488659i | −0.971908 | − | 0.235359i | \(-0.924373\pi\) |
0.689781 | + | 0.724018i | \(0.257707\pi\) | |||||||
\(564\) | −20911.4 | − | 16328.2i | −1.56122 | − | 1.21905i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 16684.5 | 1.23905 | ||||||||
\(567\) | −7776.73 | − | 4847.20i | −0.576000 | − | 0.359018i | ||||
\(568\) | 52102.2 | 3.84887 | ||||||||
\(569\) | 1129.18 | + | 1955.79i | 0.0831943 | + | 0.144097i | 0.904620 | − | 0.426218i | \(-0.140154\pi\) |
−0.821426 | + | 0.570315i | \(0.806821\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5688.66 | + | 9853.06i | −0.416923 | + | 0.722132i | −0.995628 | − | 0.0934047i | \(-0.970225\pi\) |
0.578705 | + | 0.815537i | \(0.303558\pi\) | |||||||
\(572\) | 8064.52 | − | 13968.2i | 0.589501 | − | 1.02105i | ||||
\(573\) | 3644.81 | − | 25987.5i | 0.265731 | − | 1.89467i | ||||
\(574\) | −2970.33 | − | 5144.76i | −0.215991 | − | 0.374108i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 8983.10 | + | 35942.5i | 0.649819 | + | 2.60001i | ||||
\(577\) | 25027.9 | 1.80576 | 0.902881 | − | 0.429890i | \(-0.141447\pi\) | ||||
0.902881 | + | 0.429890i | \(0.141447\pi\) | |||||||
\(578\) | 19357.5 | + | 33528.3i | 1.39302 | + | 2.41279i | ||||
\(579\) | 24864.6 | − | 10054.2i | 1.78470 | − | 0.721652i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7673.39 | − | 13290.7i | 0.547928 | − | 0.949039i | ||||
\(582\) | −27225.5 | + | 11008.8i | −1.93906 | + | 0.784071i | ||||
\(583\) | −1883.02 | − | 3261.48i | −0.133768 | − | 0.231692i | ||||
\(584\) | −18538.1 | −1.31355 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 657.835 | 0.0463736 | ||||||||
\(587\) | 74.1295 | + | 128.396i | 0.00521235 | + | 0.00902806i | 0.868620 | − | 0.495479i | \(-0.165008\pi\) |
−0.863407 | + | 0.504507i | \(0.831674\pi\) | |||||||
\(588\) | −2803.49 | + | 19988.9i | −0.196622 | + | 1.40192i | ||||
\(589\) | 463.112 | − | 802.133i | 0.0323976 | − | 0.0561143i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1531.83 | − | 1196.10i | −0.106618 | − | 0.0832503i | ||||
\(592\) | −2348.76 | − | 4068.17i | −0.163063 | − | 0.282434i | ||||
\(593\) | 27452.6 | 1.90109 | 0.950544 | − | 0.310590i | \(-0.100527\pi\) | ||||
0.950544 | + | 0.310590i | \(0.100527\pi\) | |||||||
\(594\) | 5704.40 | + | 7837.42i | 0.394031 | + | 0.541369i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9505.10 | + | 16463.3i | 0.653262 | + | 1.13148i | ||||
\(597\) | 2471.01 | + | 1929.43i | 0.169400 | + | 0.132272i | ||||
\(598\) | −10915.8 | + | 18906.7i | −0.746453 | + | 1.29289i | ||||
\(599\) | 1906.00 | − | 3301.29i | 0.130012 | − | 0.225187i | −0.793669 | − | 0.608350i | \(-0.791832\pi\) |
0.923681 | + | 0.383163i | \(0.125165\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11584.3 | − | 20064.6i | −0.786247 | − | 1.36182i | −0.928251 | − | 0.371954i | \(-0.878688\pi\) |
0.142004 | − | 0.989866i | \(-0.454646\pi\) | |||||||
\(602\) | −8082.97 | −0.547238 | ||||||||
\(603\) | −6007.73 | − | 1719.01i | −0.405728 | − | 0.116092i | ||||
\(604\) | 28530.1 | 1.92197 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2301.66 | − | 930.691i | 0.154288 | − | 0.0623873i | ||||
\(607\) | 3676.39 | − | 6367.69i | 0.245832 | − | 0.425794i | −0.716533 | − | 0.697553i | \(-0.754272\pi\) |
0.962365 | + | 0.271759i | \(0.0876055\pi\) | |||||||
\(608\) | −3415.99 | + | 5916.67i | −0.227856 | + | 0.394659i | ||||
\(609\) | 12108.2 | − | 4896.01i | 0.805662 | − | 0.325774i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14556.4 | 0.963809 | ||||||||
\(612\) | −59965.4 | − | 17158.1i | −3.96072 | − | 1.13329i | ||||
\(613\) | −19902.6 | −1.31135 | −0.655676 | − | 0.755043i | \(-0.727616\pi\) | ||||
−0.655676 | + | 0.755043i | \(0.727616\pi\) | |||||||
\(614\) | 5192.61 | + | 8993.86i | 0.341297 | + | 0.591144i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5644.76 | + | 9777.01i | −0.369211 | + | 0.639492i | ||||
\(617\) | 12542.6 | − | 21724.4i | 0.818390 | − | 1.41749i | −0.0884785 | − | 0.996078i | \(-0.528200\pi\) |
0.906868 | − | 0.421414i | \(-0.138466\pi\) | |||||||
\(618\) | −34053.8 | − | 26590.2i | −2.21658 | − | 1.73077i | ||||
\(619\) | 1565.52 | + | 2711.56i | 0.101654 | + | 0.176069i | 0.912366 | − | 0.409375i | \(-0.134253\pi\) |
−0.810712 | + | 0.585445i | \(0.800920\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5591.11 | − | 7681.78i | −0.361294 | − | 0.496391i | ||||
\(622\) | −42753.3 | −2.75603 | ||||||||
\(623\) | −1608.39 | − | 2785.81i | −0.103433 | − | 0.179151i | ||||
\(624\) | −51229.9 | − | 40001.8i | −3.28660 | − | 2.56627i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 18198.4 | − | 31520.6i | 1.16191 | − | 2.01248i | ||||
\(627\) | −111.927 | + | 798.043i | −0.00712910 | + | 0.0508306i | ||||
\(628\) | 19962.7 | + | 34576.4i | 1.26847 | + | 2.19705i | ||||
\(629\) | 2473.21 | 0.156778 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22527.2 | −1.42123 | −0.710614 | − | 0.703582i | \(-0.751583\pi\) | ||||
−0.710614 | + | 0.703582i | \(0.751583\pi\) | |||||||
\(632\) | 19589.4 | + | 33929.9i | 1.23295 | + | 2.13553i | ||||
\(633\) | −11618.3 | + | 4697.92i | −0.729518 | + | 0.294985i | ||||
\(634\) | −22682.4 | + | 39287.0i | −1.42087 | + | 2.46102i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −29690.8 | + | 12005.6i | −1.85113 | + | 0.748513i | ||||
\(637\) | −5537.17 | − | 9590.66i | −0.344412 | − | 0.596540i | ||||
\(638\) | −13815.8 | −0.857325 | ||||||||
\(639\) | −4873.00 | − | 19497.5i | −0.301679 | − | 1.20706i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3462.88 | + | 5997.88i | 0.213378 | + | 0.369582i | 0.952770 | − | 0.303694i | \(-0.0982200\pi\) |
−0.739391 | + | 0.673276i | \(0.764887\pi\) | |||||||
\(642\) | −2276.55 | + | 16231.9i | −0.139951 | + | 0.997852i | ||||
\(643\) | −7482.26 | + | 12959.7i | −0.458898 | + | 0.794835i | −0.998903 | − | 0.0468271i | \(-0.985089\pi\) |
0.540005 | + | 0.841662i | \(0.318422\pi\) | |||||||
\(644\) | 8937.75 | − | 15480.6i | 0.546889 | − | 0.947240i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3580.29 | − | 6201.25i | −0.218057 | − | 0.377685i | ||||
\(647\) | 2371.74 | 0.144115 | 0.0720577 | − | 0.997400i | \(-0.477043\pi\) | ||||
0.0720577 | + | 0.997400i | \(0.477043\pi\) | |||||||
\(648\) | 45028.1 | − | 24007.3i | 2.72974 | − | 1.45540i | ||||
\(649\) | −7459.55 | −0.451176 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3944.97 | − | 3080.35i | −0.237505 | − | 0.185451i | ||||
\(652\) | −24412.4 | + | 42283.4i | −1.46635 | + | 2.53980i | ||||
\(653\) | −7985.85 | + | 13831.9i | −0.478577 | + | 0.828919i | −0.999698 | − | 0.0245632i | \(-0.992180\pi\) |
0.521122 | + | 0.853482i | \(0.325514\pi\) | |||||||
\(654\) | −5312.87 | + | 37880.9i | −0.317660 | + | 2.26492i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 18337.8 | 1.09142 | ||||||||
\(657\) | 1733.83 | + | 6937.25i | 0.102957 | + | 0.411945i | ||||
\(658\) | −16459.4 | −0.975158 | ||||||||
\(659\) | 3421.46 | + | 5926.15i | 0.202248 | + | 0.350304i | 0.949252 | − | 0.314515i | \(-0.101842\pi\) |
−0.747005 | + | 0.664819i | \(0.768509\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6695.50 | − | 11597.0i | 0.393986 | − | 0.682404i | −0.598985 | − | 0.800760i | \(-0.704429\pi\) |
0.992971 | + | 0.118356i | \(0.0377624\pi\) | |||||||
\(662\) | 693.793 | − | 1201.68i | 0.0407327 | − | 0.0705511i | ||||
\(663\) | 31725.1 | − | 12828.2i | 1.85837 | − | 0.751443i | ||||
\(664\) | 42729.6 | + | 74009.8i | 2.49733 | + | 4.32551i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2350.03 | + | 2271.97i | −0.136729 | + | 0.132188i | ||||
\(667\) | 13541.5 | 0.786098 | ||||||||
\(668\) | 20639.5 | + | 35748.7i | 1.19546 | + | 2.07060i | ||||
\(669\) | −3955.88 | + | 28205.5i | −0.228615 | + | 1.63003i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4963.51 | − | 8597.05i | 0.285565 | − | 0.494613i | ||||
\(672\) | 29098.7 | + | 22721.2i | 1.67040 | + | 1.30430i | ||||
\(673\) | −15951.1 | − | 27628.1i | −0.913624 | − | 1.58244i | −0.808904 | − | 0.587941i | \(-0.799939\pi\) |
−0.104720 | − | 0.994502i | \(-0.533395\pi\) | |||||||
\(674\) | −59771.3 | −3.41588 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 29119.9 | 1.65680 | ||||||||
\(677\) | −5930.38 | − | 10271.7i | −0.336666 | − | 0.583123i | 0.647137 | − | 0.762373i | \(-0.275966\pi\) |
−0.983803 | + | 0.179251i | \(0.942633\pi\) | |||||||
\(678\) | 3758.74 | + | 2934.93i | 0.212911 | + | 0.166247i | ||||
\(679\) | −6596.33 | + | 11425.2i | −0.372818 | + | 0.645741i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3949.53 | − | 28160.2i | 0.222241 | − | 1.58458i | ||||
\(682\) | 2647.28 | + | 4585.22i | 0.148636 | + | 0.257444i | ||||
\(683\) | −7639.34 | −0.427981 | −0.213991 | − | 0.976836i | \(-0.568646\pi\) | ||||
−0.213991 | + | 0.976836i | \(0.568646\pi\) | |||||||
\(684\) | 6588.55 | + | 1885.20i | 0.368303 | + | 0.105384i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 17870.1 | + | 30951.9i | 0.994580 | + | 1.72266i | ||||
\(687\) | −15781.2 | + | 6381.21i | −0.876405 | + | 0.354379i | ||||
\(688\) | 12475.4 | − | 21608.0i | 0.691309 | − | 1.19738i | ||||
\(689\) | 8785.64 | − | 15217.2i | 0.485786 | − | 0.841406i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7863.00 | + | 13619.1i | 0.432883 | + | 0.749776i | 0.997120 | − | 0.0758369i | \(-0.0241628\pi\) |
−0.564237 | + | 0.825613i | \(0.690829\pi\) | |||||||
\(692\) | 48252.6 | 2.65071 | ||||||||
\(693\) | 4186.66 | + | 1197.94i | 0.229492 | + | 0.0656652i | ||||
\(694\) | 53239.5 | 2.91202 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −10101.4 | + | 72023.4i | −0.550135 | + | 3.92247i | ||||
\(697\) | −4827.36 | + | 8361.23i | −0.262338 | + | 0.454382i | ||||
\(698\) | 16314.5 | − | 28257.5i | 0.884688 | − | 1.53232i | ||||
\(699\) | −14114.1 | − | 11020.7i | −0.763724 | − | 0.596338i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6338.17 | −0.341497 | −0.170748 | − | 0.985315i | \(-0.554619\pi\) | ||||
−0.170748 | + | 0.985315i | \(0.554619\pi\) | |||||||
\(702\) | −18360.6 | + | 41333.0i | −0.987146 | + | 2.22224i | ||||
\(703\) | −271.737 | −0.0145786 | ||||||||
\(704\) | −8802.82 | − | 15246.9i | −0.471262 | − | 0.816250i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 24493.0 | − | 42423.1i | 1.30567 | − | 2.26149i | ||||
\(707\) | 557.658 | − | 965.892i | 0.0296646 | − | 0.0513806i | ||||
\(708\) | −8810.76 | + | 62820.9i | −0.467696 | + | 3.33468i | ||||
\(709\) | −17191.8 | − | 29777.1i | −0.910651 | − | 1.57729i | −0.813147 | − | 0.582059i | \(-0.802247\pi\) |
−0.0975047 | − | 0.995235i | \(-0.531086\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10865.0 | − | 10504.1i | 0.573092 | − | 0.554056i | ||||
\(712\) | 17912.7 | 0.942847 | ||||||||
\(713\) | −2594.70 | − | 4494.16i | −0.136287 | − | 0.236055i | ||||
\(714\) | −35872.7 | + | 14505.3i | −1.88025 | + | 0.760292i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9173.18 | − | 15888.4i | 0.478796 | − | 0.829299i | ||||
\(717\) | 8308.83 | − | 3359.72i | 0.432774 | − | 0.174995i | ||||
\(718\) | −23706.6 | − | 41061.0i | −1.23220 | − | 2.13424i | ||||
\(719\) | −988.886 | −0.0512924 | −0.0256462 | − | 0.999671i | \(-0.508164\pi\) | ||||
−0.0256462 | + | 0.999671i | \(0.508164\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19409.3 | −1.00255 | ||||||||
\(722\) | −18074.6 | − | 31306.1i | −0.931671 | − | 1.61370i | ||||
\(723\) | −4024.03 | + | 28691.4i | −0.206992 | + | 1.47586i | ||||
\(724\) | −15688.1 | + | 27172.5i | −0.805307 | + | 1.39483i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 25723.8 | + | 20085.9i | 1.31502 | + | 1.02680i | ||||
\(727\) | −6845.92 | − | 11857.5i | −0.349245 | − | 0.604910i | 0.636871 | − | 0.770971i | \(-0.280229\pi\) |
−0.986116 | + | 0.166061i | \(0.946895\pi\) | |||||||
\(728\) | −52673.8 | −2.68162 | ||||||||
\(729\) | −13195.3 | − | 14604.9i | −0.670392 | − | 0.742007i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6568.20 | + | 11376.5i | 0.332331 | + | 0.575614i | ||||
\(732\) | −66537.8 | − | 51954.7i | −3.35971 | − | 2.62336i | ||||
\(733\) | −1250.97 | + | 2166.74i | −0.0630363 | + | 0.109182i | −0.895821 | − | 0.444415i | \(-0.853412\pi\) |
0.832785 | + | 0.553597i | \(0.186745\pi\) | |||||||
\(734\) | −23296.6 | + | 40350.9i | −1.17152 | + | 2.02913i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 19139.0 | + | 33149.7i | 0.958521 | + | 1.66021i | ||||
\(737\) | 2969.51 | 0.148417 | ||||||||
\(738\) | −3093.97 | − | 12379.4i | −0.154323 | − | 0.617468i | ||||
\(739\) | 26453.1 | 1.31677 | 0.658384 | − | 0.752682i | \(-0.271240\pi\) | ||||
0.658384 | + | 0.752682i | \(0.271240\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3485.72 | + | 1409.47i | −0.172808 | + | 0.0698760i | ||||
\(742\) | −9934.24 | + | 17206.6i | −0.491506 | + | 0.851313i | ||||
\(743\) | −10441.4 | + | 18085.0i | −0.515555 | + | 0.892967i | 0.484282 | + | 0.874912i | \(0.339081\pi\) |
−0.999837 | + | 0.0180555i | \(0.994252\pi\) | |||||||
\(744\) | 25838.8 | − | 10448.1i | 1.27325 | − | 0.514845i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −64182.2 | −3.14997 | ||||||||
\(747\) | 23699.3 | − | 22912.1i | 1.16079 | − | 1.12224i | ||||
\(748\) | 29639.8 | 1.44885 | ||||||||
\(749\) | 3681.64 | + | 6376.78i | 0.179605 | + | 0.311085i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8847.65 | − | 15324.6i | 0.429901 | − | 0.744610i | −0.566963 | − | 0.823743i | \(-0.691882\pi\) |
0.996864 | + | 0.0791332i | \(0.0252152\pi\) | |||||||
\(752\) | 25403.7 | − | 44000.6i | 1.23189 | − | 2.13369i | ||||
\(753\) | −5555.08 | − | 4337.57i | −0.268842 | − | 0.209920i | ||||
\(754\) | −32230.4 | − | 55824.8i | −1.55672 | − | 2.69631i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 15033.5 | − | 33843.2i | 0.723233 | − | 1.62813i | ||||
\(757\) | −7755.61 | −0.372368 | −0.186184 | − | 0.982515i | \(-0.559612\pi\) | ||||
−0.186184 | + | 0.982515i | \(0.559612\pi\) | |||||||
\(758\) | 13603.2 | + | 23561.4i | 0.651835 | + | 1.12901i | ||||
\(759\) | 3558.66 | + | 2778.71i | 0.170186 | + | 0.132886i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8527.15 | + | 14769.5i | −0.406188 | + | 0.703538i | −0.994459 | − | 0.105126i | \(-0.966476\pi\) |
0.588271 | + | 0.808664i | \(0.299809\pi\) | |||||||
\(762\) | 7033.40 | − | 50148.2i | 0.334374 | − | 2.38409i | ||||
\(763\) | 8591.95 | + | 14881.7i | 0.407667 | + | 0.706099i | ||||
\(764\) | 106048. | 5.02184 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −28704.2 | −1.35395 | ||||||||
\(767\) | −17402.1 | − | 30141.3i | −0.819236 | − | 1.41896i | ||||
\(768\) | −21499.9 | + | 8693.61i | −1.01017 | + | 0.408468i | ||||
\(769\) | 5024.16 | − | 8702.11i | 0.235599 | − | 0.408070i | −0.723847 | − | 0.689960i | \(-0.757628\pi\) |
0.959447 | + | 0.281890i | \(0.0909613\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19692.0 | + | 7962.57i | −0.919831 | + | 0.371939i | ||||
\(772\) | 54193.0 | + | 93865.1i | 2.52649 | + | 4.37601i | ||||
\(773\) | −7293.24 | −0.339352 | −0.169676 | − | 0.985500i | \(-0.554272\pi\) | ||||
−0.169676 | + | 0.985500i | \(0.554272\pi\) | |||||||
\(774\) | −16691.9 | − | 4776.09i | −0.775164 | − | 0.221800i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −36731.9 | − | 63621.5i | −1.69922 | − | 2.94314i | ||||
\(777\) | −203.952 | + | 1454.18i | −0.00941665 | + | 0.0671409i | ||||
\(778\) | 8991.70 | − | 15574.1i | 0.414355 | − | 0.717684i | ||||
\(779\) | 530.394 | − | 918.670i | 0.0243945 | − | 0.0422526i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4775.21 | + | 8270.90i | 0.218784 | + | 0.378945i | ||||
\(782\) | −40119.0 | −1.83460 | ||||||||
\(783\) | 27897.1 | − | 2956.07i | 1.27326 | − | 0.134919i | ||||
\(784\) | −38653.8 | −1.76083 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 27310.0 | + | 21324.5i | 1.23933 | + | 0.967708i | ||||
\(787\) | 14228.1 | − | 24643.8i | 0.644445 | − | 1.11621i | −0.339985 | − | 0.940431i | \(-0.610422\pi\) |
0.984429 | − | 0.175780i | \(-0.0562448\pi\) | |||||||
\(788\) | 3926.99 | − | 6801.75i | 0.177530 | − | 0.307490i | ||||
\(789\) | 310.522 | − | 2214.03i | 0.0140112 | − | 0.0999004i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2142.33 | 0.0962989 | ||||||||
\(792\) | −17433.9 | + | 16854.8i | −0.782178 | + | 0.756197i | ||||
\(793\) | 46316.7 | 2.07409 | ||||||||
\(794\) | −24344.8 | − | 42166.4i | −1.08812 | − | 1.88467i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6334.66 | + | 10971.9i | −0.282068 | + | 0.488556i | ||||
\(797\) | 2040.73 | − | 3534.65i | 0.0906981 | − | 0.157094i | −0.817107 | − | 0.576486i | \(-0.804424\pi\) |
0.907805 | + | 0.419392i | \(0.137757\pi\) | |||||||
\(798\) | 3941.42 | − | 1593.74i | 0.174843 | − | 0.0706988i | ||||
\(799\) | 13374.9 | + | 23165.9i | 0.592201 | + | 1.02572i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1675.34 | − | 6703.24i | −0.0739015 | − | 0.295689i | ||||
\(802\) | 9003.54 | 0.396416 | ||||||||
\(803\) | −1699.03 | − | 2942.81i | −0.0746668 | − | 0.129327i | ||||
\(804\) | 3507.40 | − | 25007.8i | 0.153851 | − | 1.09696i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12351.5 | + | 21393.4i | −0.539779 | + | 0.934925i | ||||
\(807\) | 14202.7 | + | 11089.9i | 0.619527 | + | 0.483745i | ||||
\(808\) | 3105.34 | + | 5378.60i | 0.135205 | + | 0.234181i | ||||
\(809\) | 14209.7 | 0.617536 | 0.308768 | − | 0.951137i | \(-0.400083\pi\) | ||||
0.308768 | + | 0.951137i | \(0.400083\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4901.79 | 0.212238 | 0.106119 | − | 0.994353i | \(-0.466158\pi\) | ||||
0.106119 | + | 0.994353i | \(0.466158\pi\) | |||||||
\(812\) | 26390.0 | + | 45708.9i | 1.14053 | + | 1.97545i | ||||
\(813\) | −227.062 | − | 177.297i | −0.00979511 | − | 0.00764831i | ||||
\(814\) | 776.663 | − | 1345.22i | 0.0334423 | − | 0.0579237i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 16589.8 | − | 118286.i | 0.711714 | − | 5.07454i | ||||
\(817\) | −721.665 | − | 1249.96i | −0.0309031 | − | 0.0535258i | ||||
\(818\) | −2545.64 | −0.108810 | ||||||||
\(819\) | 4926.47 | + | 19711.4i | 0.210189 | + | 0.840992i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7259.82 | + | 12574.4i | 0.308611 | + | 0.534530i | 0.978059 | − | 0.208329i | \(-0.0668026\pi\) |
−0.669448 | + | 0.742859i | \(0.733469\pi\) | |||||||
\(822\) | −13130.9 | + | 5309.54i | −0.557167 | + | 0.225294i | ||||
\(823\) | −19203.2 | + | 33260.9i | −0.813344 | + | 1.40875i | 0.0971672 | + | 0.995268i | \(0.469022\pi\) |
−0.910511 | + | 0.413485i | \(0.864312\pi\) | |||||||
\(824\) | 54040.6 | − | 93601.1i | 2.28470 | − | 3.95722i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 19677.2 | + | 34081.9i | 0.828882 | + | 1.43567i | ||||
\(827\) | 10446.4 | 0.439248 | 0.219624 | − | 0.975585i | \(-0.429517\pi\) | ||||
0.219624 | + | 0.975585i | \(0.429517\pi\) | |||||||
\(828\) | 27604.3 | − | 26687.4i | 1.15859 | − | 1.12011i | ||||
\(829\) | −6474.00 | −0.271232 | −0.135616 | − | 0.990761i | \(-0.543301\pi\) | ||||
−0.135616 | + | 0.990761i | \(0.543301\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1135.63 | − | 8097.09i | 0.0474064 | − | 0.338008i | ||||
\(832\) | 41071.6 | − | 71138.0i | 1.71142 | − | 2.96426i | ||||
\(833\) | 10175.5 | − | 17624.4i | 0.423240 | − | 0.733073i | ||||
\(834\) | 4712.61 | + | 3679.75i | 0.195665 | + | 0.152781i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3256.60 | −0.134727 | ||||||||
\(837\) | −6326.49 | − | 8692.13i | −0.261261 | − | 0.358953i | ||||
\(838\) | −67524.5 | −2.78353 | ||||||||
\(839\) | −7919.71 | − | 13717.3i | −0.325886 | − | 0.564452i | 0.655805 | − | 0.754930i | \(-0.272329\pi\) |
−0.981691 | + | 0.190478i | \(0.938996\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7797.09 | + | 13505.0i | −0.319697 | + | 0.553731i | ||||
\(842\) | −18179.2 | + | 31487.3i | −0.744058 | + | 1.28875i | ||||
\(843\) | 5879.36 | − | 41919.9i | 0.240209 | − | 1.71269i | ||||
\(844\) | −25322.3 | − | 43859.5i | −1.03274 | − | 1.78875i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −33989.7 | − | 9725.57i | −1.38131 | − | 0.395239i | ||||
\(847\) | 14661.5 | 0.594778 | ||||||||
\(848\) | −30665.4 | − | 53114.0i | −1.24181 | − | 2.15087i | ||||
\(849\) | 14925.3 | − | 6035.12i | 0.603338 | − | 0.243963i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −761.239 | + | 1318.51i | −0.0306639 | + | 0.0531114i | ||||
\(852\) | 75293.9 | − | 30445.5i | 3.02761 | − | 1.22423i | ||||
\(853\) | −9420.17 | − | 16316.2i | −0.378125 | − | 0.654931i | 0.612665 | − | 0.790343i | \(-0.290098\pi\) |
−0.990789 | + | 0.135412i | \(0.956764\pi\) | |||||||
\(854\) | −52372.0 | −2.09852 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −41002.6 | −1.63720 | ||||||||
\(857\) | 4528.11 | + | 7842.91i | 0.180487 | + | 0.312612i | 0.942046 | − | 0.335483i | \(-0.108899\pi\) |
−0.761560 | + | 0.648095i | \(0.775566\pi\) | |||||||
\(858\) | 2985.17 | − | 21284.3i | 0.118778 | − | 0.846893i | ||||
\(859\) | −11027.7 | + | 19100.6i | −0.438022 | + | 0.758676i | −0.997537 | − | 0.0701440i | \(-0.977654\pi\) |
0.559515 | + | 0.828820i | \(0.310987\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4518.10 | − | 3527.87i | −0.178835 | − | 0.139639i | ||||
\(862\) | 20288.3 | + | 35140.3i | 0.801649 | + | 1.38850i | ||||
\(863\) | −13105.6 | −0.516941 | −0.258471 | − | 0.966019i | \(-0.583219\pi\) | ||||
−0.258471 | + | 0.966019i | \(0.583219\pi\) | |||||||
\(864\) | 46665.2 | + | 64114.6i | 1.83748 | + | 2.52456i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 13826.4 | + | 23948.1i | 0.542542 | + | 0.939710i | ||||
\(867\) | 29444.4 | + | 22991.0i | 1.15338 | + | 0.900596i | ||||
\(868\) | 10113.3 | − | 17516.7i | 0.395470 | − | 0.684973i | ||||
\(869\) | −3590.78 | + | 6219.41i | −0.140171 | + | 0.242784i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6927.46 | + | 11998.7i | 0.269492 | + | 0.466775i | ||||
\(872\) | −95689.2 | −3.71611 | ||||||||
\(873\) | −20372.8 | + | 19696.1i | −0.789821 | + | 0.763586i | ||||
\(874\) | 4407.98 | 0.170597 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −26789.7 | + | 10832.6i | −1.03327 | + | 0.417807i | ||||
\(877\) | −18361.1 | + | 31802.4i | −0.706967 | + | 1.22450i | 0.259010 | + | 0.965875i | \(0.416604\pi\) |
−0.965977 | + | 0.258628i | \(0.916730\pi\) | |||||||
\(878\) | 45700.6 | − | 79155.8i | 1.75663 | − | 3.04257i | ||||
\(879\) | 588.473 | − | 237.952i | 0.0225810 | − | 0.00913076i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36054.4 | 1.37878 | 0.689390 | − | 0.724390i | \(-0.257879\pi\) | ||||
0.689390 | + | 0.724390i | \(0.257879\pi\) | |||||||
\(882\) | 6521.70 | + | 26094.1i | 0.248976 | + | 0.996186i | ||||
\(883\) | −13524.6 | −0.515446 | −0.257723 | − | 0.966219i | \(-0.582972\pi\) | ||||
−0.257723 | + | 0.966219i | \(0.582972\pi\) | |||||||
\(884\) | 69145.6 | + | 119764.i | 2.63079 | + | 4.55666i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −30566.3 | + | 52942.3i | −1.15902 | + | 2.00749i | ||||
\(887\) | −19865.1 | + | 34407.4i | −0.751978 | + | 1.30246i | 0.194884 | + | 0.980826i | \(0.437567\pi\) |
−0.946863 | + | 0.321639i | \(0.895766\pi\) | |||||||
\(888\) | −6444.92 | − | 5032.39i | −0.243556 | − | 0.190176i | ||||
\(889\) | −11374.4 | − | 19701.0i | −0.429116 | − | 0.743251i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7937.89 | + | 4947.65i | 0.298462 | + | 0.186030i | ||||
\(892\) | −115099. | −4.32040 | ||||||||
\(893\) | −1469.53 | − | 2545.30i | −0.0550682 | − | 0.0953810i | ||||
\(894\) | 19966.2 | + | 15590.2i | 0.746946 | + | 0.583238i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −18021.1 | + | 31213.4i | −0.671921 | + | 1.16380i | ||||
\(897\) | −2925.88 | + | 20861.6i | −0.108910 | + | 0.776532i | ||||
\(898\) | 29778.7 | + | 51578.2i | 1.10660 | + | 1.91669i | ||||
\(899\) | 15322.5 | 0.568447 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32290.1 | 1.19394 | ||||||||
\(902\) | 3031.88 | + | 5251.37i | 0.111919 | + | 0.193849i | ||||
\(903\) | −7230.71 | + | 2923.78i | −0.266471 | + | 0.107749i | ||||
\(904\) | −5964.81 | + | 10331.4i | −0.219454 | + | 0.380106i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 35245.2 | − | 14251.6i | 1.29243 | − | 0.522602i | ||||
\(907\) | 11511.2 | + | 19938.0i | 0.421415 | + | 0.729912i | 0.996078 | − | 0.0884783i | \(-0.0282004\pi\) |
−0.574663 | + | 0.818390i | \(0.694867\pi\) | |||||||
\(908\) | 114914. | 4.19995 | ||||||||
\(909\) | 1722.33 | − | 1665.12i | 0.0628449 | − | 0.0607574i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15940.1 | − | 27609.1i | −0.579714 | − | 1.00409i | −0.995512 | − | 0.0946365i | \(-0.969831\pi\) |
0.415798 | − | 0.909457i | \(-0.363502\pi\) | |||||||
\(912\) | −1822.76 | + | 12996.3i | −0.0661817 | + | 0.471877i | ||||
\(913\) | −7832.41 | + | 13566.1i | −0.283916 | + | 0.491756i | ||||
\(914\) | −960.376 | + | 1663.42i | −0.0347554 | + | 0.0601981i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −34395.5 | − | 59574.7i | −1.24067 | − | 2.14891i | ||||
\(917\) | 15565.6 | 0.560547 | ||||||||
\(918\) | −82650.4 | + | 8757.89i | −2.97153 | + | 0.314873i | ||||
\(919\) | 38459.6 | 1.38049 | 0.690243 | − | 0.723578i | \(-0.257504\pi\) | ||||
0.690243 | + | 0.723578i | \(0.257504\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7898.37 | + | 6167.28i | 0.282584 | + | 0.220650i | ||||
\(922\) | 27786.1 | − | 48126.9i | 0.992501 | − | 1.71906i | ||||
\(923\) | −22279.8 | + | 38589.8i | −0.794528 | + | 1.37616i | ||||
\(924\) | −2444.23 | + | 17427.4i | −0.0870231 | + | 0.620477i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −97838.1 | −3.47209 | ||||||||
\(927\) | −40081.4 | − | 11468.6i | −1.42011 | − | 0.406341i | ||||
\(928\) | −113021. | −3.99796 | ||||||||
\(929\) | 18600.5 | + | 32217.1i | 0.656903 | + | 1.13779i | 0.981413 | + | 0.191908i | \(0.0614675\pi\) |
−0.324509 | + | 0.945882i | \(0.605199\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1118.00 | + | 1936.44i | −0.0393567 | + | 0.0681678i | ||||
\(932\) | 36182.7 | − | 62670.3i | 1.27168 | − | 2.20261i | ||||
\(933\) | −38245.5 | + | 15464.8i | −1.34201 | + | 0.542651i | ||||
\(934\) | −10277.7 | − | 17801.5i | −0.360062 | − | 0.623645i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −108775. | − | 31124.0i | −3.79852 | − | 1.08688i | ||||
\(937\) | 23593.7 | 0.822595 | 0.411298 | − | 0.911501i | \(-0.365076\pi\) | ||||
0.411298 | + | 0.911501i | \(0.365076\pi\) | |||||||
\(938\) | −7833.12 | − | 13567.4i | −0.272666 | − | 0.472271i | ||||
\(939\) | 4877.94 | − | 34779.8i | 0.169527 | − | 1.20873i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18285.8 | + | 31672.0i | −0.633477 | + | 1.09721i | 0.353359 | + | 0.935488i | \(0.385039\pi\) |
−0.986836 | + | 0.161726i | \(0.948294\pi\) | |||||||
\(942\) | 41933.2 | + | 32742.7i | 1.45038 | + | 1.13250i | ||||
\(943\) | −2971.67 | − | 5147.08i | −0.102620 | − | 0.177744i | ||||
\(944\) | −121481. | −4.18841 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8250.48 | 0.283558 | ||||||||
\(947\) | 16455.9 | + | 28502.4i | 0.564671 | + | 0.978039i | 0.997080 | + | 0.0763615i | \(0.0243303\pi\) |
−0.432409 | + | 0.901678i | \(0.642336\pi\) | |||||||
\(948\) | 48135.8 | + | 37585.8i | 1.64913 | + | 1.28769i | ||||
\(949\) | 7927.21 | − | 13730.3i | 0.271157 | − | 0.469658i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6079.83 | + | 43349.3i | −0.207310 | + | 1.47813i | ||||
\(952\) | −48398.4 | − | 83828.5i | −1.64769 | − | 2.85388i | ||||
\(953\) | 21564.5 | 0.732993 | 0.366497 | − | 0.930419i | \(-0.380557\pi\) | ||||
0.366497 | + | 0.930419i | \(0.380557\pi\) | |||||||
\(954\) | −30681.9 | + | 29662.8i | −1.04126 | + | 1.00668i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 18109.3 | + | 31366.2i | 0.612653 | + | 1.06115i | ||||
\(957\) | −12359.1 | + | 4997.47i | −0.417464 | + | 0.168804i | ||||
\(958\) | 7825.98 | − | 13555.0i | 0.263931 | − | 0.457142i | ||||
\(959\) | −3181.41 | + | 5510.36i | −0.107125 | + | 0.185546i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11959.5 | + | 20714.5i | 0.401448 | + | 0.695328i | ||||
\(962\) | 7247.40 | 0.242895 | ||||||||
\(963\) | 3834.89 | + | 15343.9i | 0.128326 | + | 0.513447i | ||||
\(964\) | −117082. | −3.91178 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3308.40 | − | 23589.0i | 0.110193 | − | 0.785675i | ||||
\(967\) | 14881.9 | − | 25776.2i | 0.494901 | − | 0.857193i | −0.505082 | − | 0.863071i | \(-0.668538\pi\) |
0.999983 | + | 0.00587841i | \(0.00187117\pi\) | |||||||
\(968\) | −40821.7 | + | 70705.2i | −1.35543 | + | 2.34768i | ||||
\(969\) | −5445.91 | − | 4252.33i | −0.180545 | − | 0.140975i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29812.3 | 0.985297 | 0.492648 | − | 0.870228i | \(-0.336029\pi\) | ||||
0.492648 | + | 0.870228i | \(0.336029\pi\) | |||||||
\(972\) | 51042.6 | − | 61005.4i | 1.68435 | − | 2.01311i | ||||
\(973\) | 2686.00 | 0.0884986 | ||||||||
\(974\) | −28032.1 | − | 48553.1i | −0.922184 | − | 1.59727i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 80831.9 | − | 140005.i | 2.65099 | − | 4.59165i | ||||
\(977\) | −2879.87 | + | 4988.07i | −0.0943041 | + | 0.163339i | −0.909318 | − | 0.416102i | \(-0.863396\pi\) |
0.815014 | + | 0.579441i | \(0.196729\pi\) | |||||||
\(978\) | −9036.49 | + | 64430.3i | −0.295455 | + | 2.10660i | ||||
\(979\) | 1641.72 | + | 2843.54i | 0.0535950 | + | 0.0928292i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8949.61 | + | 35808.5i | 0.291273 | + | 1.16542i | ||||
\(982\) | −78796.5 | −2.56059 | ||||||||
\(983\) | −8825.70 | − | 15286.6i | −0.286364 | − | 0.495998i | 0.686575 | − | 0.727059i | \(-0.259113\pi\) |
−0.972939 | + | 0.231062i | \(0.925780\pi\) | |||||||
\(984\) | 29592.7 | − | 11966.0i | 0.958722 | − | 0.387665i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 59228.7 | − | 102587.i | 1.91301 | − | 3.31343i | ||||
\(987\) | −14723.9 | + | 5953.70i | −0.474841 | + | 0.192005i | ||||
\(988\) | −7597.20 | − | 13158.7i | −0.244635 | − | 0.423720i | ||||
\(989\) | −8086.63 | −0.260000 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5186.45 | −0.166249 | −0.0831246 | − | 0.996539i | \(-0.526490\pi\) | ||||
−0.0831246 | + | 0.996539i | \(0.526490\pi\) | |||||||
\(992\) | 21656.2 | + | 37509.7i | 0.693131 | + | 1.20054i | ||||
\(993\) | 185.966 | − | 1325.94i | 0.00594305 | − | 0.0423740i | ||||
\(994\) | 25192.6 | − | 43634.8i | 0.803884 | − | 1.39237i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 104996. | + | 81984.4i | 3.34030 | + | 2.60821i | ||||
\(997\) | −8055.12 | − | 13951.9i | −0.255876 | − | 0.443190i | 0.709257 | − | 0.704950i | \(-0.249030\pi\) |
−0.965133 | + | 0.261760i | \(0.915697\pi\) | |||||||
\(998\) | −43978.6 | −1.39491 | ||||||||
\(999\) | −1280.42 | + | 2882.47i | −0.0405514 | + | 0.0912885i |
(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 | 225.4.e.d.76.7 | 14 | ||
5.2 | odd | 4 | 225.4.k.d.49.1 | 28 | |||
5.3 | odd | 4 | 225.4.k.d.49.14 | 28 | |||
5.4 | even | 2 | 45.4.e.c.31.1 | yes | 14 | ||
9.4 | even | 3 | 2025.4.a.bb.1.1 | 7 | |||
9.5 | odd | 6 | 2025.4.a.ba.1.7 | 7 | |||
9.7 | even | 3 | inner | 225.4.e.d.151.7 | 14 | ||
15.14 | odd | 2 | 135.4.e.c.91.7 | 14 | |||
45.4 | even | 6 | 405.4.a.m.1.7 | 7 | |||
45.7 | odd | 12 | 225.4.k.d.124.14 | 28 | |||
45.14 | odd | 6 | 405.4.a.n.1.1 | 7 | |||
45.29 | odd | 6 | 135.4.e.c.46.7 | 14 | |||
45.34 | even | 6 | 45.4.e.c.16.1 | ✓ | 14 | ||
45.43 | odd | 12 | 225.4.k.d.124.1 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.e.c.16.1 | ✓ | 14 | 45.34 | even | 6 | ||
45.4.e.c.31.1 | yes | 14 | 5.4 | even | 2 | ||
135.4.e.c.46.7 | 14 | 45.29 | odd | 6 | |||
135.4.e.c.91.7 | 14 | 15.14 | odd | 2 | |||
225.4.e.d.76.7 | 14 | 1.1 | even | 1 | trivial | ||
225.4.e.d.151.7 | 14 | 9.7 | even | 3 | inner | ||
225.4.k.d.49.1 | 28 | 5.2 | odd | 4 | |||
225.4.k.d.49.14 | 28 | 5.3 | odd | 4 | |||
225.4.k.d.124.1 | 28 | 45.43 | odd | 12 | |||
225.4.k.d.124.14 | 28 | 45.7 | odd | 12 | |||
405.4.a.m.1.7 | 7 | 45.4 | even | 6 | |||
405.4.a.n.1.1 | 7 | 45.14 | odd | 6 | |||
2025.4.a.ba.1.7 | 7 | 9.5 | odd | 6 | |||
2025.4.a.bb.1.1 | 7 | 9.4 | even | 3 |