Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,4,Mod(17,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.g (of order \(8\), degree \(4\), not 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: | \(7.55224448073\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 49.7 | ||
Character | \(\chi\) | \(=\) | 128.49 |
Dual form | 128.4.g.a.81.7 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{8}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.65706 | − | 0.686375i | 0.318900 | − | 0.132093i | −0.217491 | − | 0.976062i | \(-0.569787\pi\) |
0.536391 | + | 0.843969i | \(0.319787\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.13953 | + | 9.99370i | −0.370251 | + | 0.893864i | 0.623457 | + | 0.781858i | \(0.285728\pi\) |
−0.993708 | + | 0.112006i | \(0.964272\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −24.2273 | − | 24.2273i | −1.30815 | − | 1.30815i | −0.922748 | − | 0.385403i | \(-0.874062\pi\) |
−0.385403 | − | 0.922748i | \(-0.625938\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −16.8172 | + | 16.8172i | −0.622858 | + | 0.622858i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.73492 | − | 1.54705i | −0.102375 | − | 0.0424049i | 0.330908 | − | 0.943663i | \(-0.392645\pi\) |
−0.433283 | + | 0.901258i | \(0.642645\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −23.2063 | − | 56.0248i | −0.495097 | − | 1.19527i | −0.952095 | − | 0.305802i | \(-0.901076\pi\) |
0.456999 | − | 0.889467i | \(-0.348924\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 19.4014i | 0.333961i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 26.9981i | 0.385177i | 0.981280 | + | 0.192589i | \(0.0616883\pi\) | ||||
−0.981280 | + | 0.192589i | \(0.938312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −22.7209 | − | 54.8531i | −0.274344 | − | 0.662324i | 0.725316 | − | 0.688416i | \(-0.241694\pi\) |
−0.999660 | + | 0.0260920i | \(0.991694\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −56.7750 | − | 23.5170i | −0.589968 | − | 0.244373i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −76.0566 | + | 76.0566i | −0.689517 | + | 0.689517i | −0.962125 | − | 0.272608i | \(-0.912114\pi\) |
0.272608 | + | 0.962125i | \(0.412114\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.64994 | + | 5.64994i | 0.0451996 | + | 0.0451996i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −34.8562 | + | 84.1503i | −0.248447 | + | 0.599805i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −108.152 | + | 44.7980i | −0.692527 | + | 0.286854i | −0.701053 | − | 0.713109i | \(-0.747286\pi\) |
0.00852531 | + | 0.999964i | \(0.497286\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −176.000 | −1.01969 | −0.509846 | − | 0.860266i | \(-0.670298\pi\) | ||||
−0.509846 | + | 0.860266i | \(0.670298\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.25082 | −0.0382487 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 342.410 | − | 141.831i | 1.65365 | − | 0.684966i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 129.191 | − | 311.894i | 0.574021 | − | 1.38581i | −0.324083 | − | 0.946029i | \(-0.605056\pi\) |
0.898105 | − | 0.439782i | \(-0.144944\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −76.9081 | − | 76.9081i | −0.315773 | − | 0.315773i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 70.4988 | − | 70.4988i | 0.268538 | − | 0.268538i | −0.559973 | − | 0.828511i | \(-0.689188\pi\) |
0.828511 | + | 0.559973i | \(0.189188\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 103.155 | + | 42.7281i | 0.365836 | + | 0.151534i | 0.558026 | − | 0.829824i | \(-0.311559\pi\) |
−0.192190 | + | 0.981358i | \(0.561559\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −98.4506 | − | 237.681i | −0.326137 | − | 0.787364i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 249.437i | 0.774131i | 0.922052 | + | 0.387066i | \(0.126511\pi\) | ||||
−0.922052 | + | 0.387066i | \(0.873489\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 830.925i | 2.42252i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 18.5308 | + | 44.7374i | 0.0508792 | + | 0.122833i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 597.516 | + | 247.499i | 1.54859 | + | 0.641446i | 0.983060 | − | 0.183282i | \(-0.0586723\pi\) |
0.565528 | + | 0.824729i | \(0.308672\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 30.9216 | − | 30.9216i | 0.0758085 | − | 0.0758085i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −75.2996 | − | 75.2996i | −0.174977 | − | 0.174977i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 75.6443 | − | 182.622i | 0.166916 | − | 0.402971i | −0.818183 | − | 0.574958i | \(-0.805019\pi\) |
0.985099 | + | 0.171986i | \(0.0550185\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −309.654 | + | 128.263i | −0.649953 | + | 0.269219i | −0.683204 | − | 0.730228i | \(-0.739414\pi\) |
0.0332511 | + | 0.999447i | \(0.489414\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 814.869 | 1.62958 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 655.959 | 1.25172 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 297.717 | − | 123.318i | 0.542864 | − | 0.224862i | −0.0943627 | − | 0.995538i | \(-0.530081\pi\) |
0.637227 | + | 0.770676i | \(0.280081\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −73.8267 | + | 178.233i | −0.128807 | + | 0.310968i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −675.279 | − | 675.279i | −1.12874 | − | 1.12874i | −0.990382 | − | 0.138363i | \(-0.955816\pi\) |
−0.138363 | − | 0.990382i | \(-0.544184\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 350.175 | − | 350.175i | 0.561437 | − | 0.561437i | −0.368279 | − | 0.929715i | \(-0.620053\pi\) |
0.929715 | + | 0.368279i | \(0.120053\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 13.2403 | + | 5.48429i | 0.0203847 | + | 0.00844362i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 53.0061 | + | 127.968i | 0.0784494 | + | 0.189393i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 564.246i | 0.803578i | 0.915732 | + | 0.401789i | \(0.131611\pi\) | ||||
−0.915732 | + | 0.401789i | \(0.868389\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 478.776i | − | 0.656758i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −105.327 | − | 254.281i | −0.139290 | − | 0.336276i | 0.838806 | − | 0.544431i | \(-0.183254\pi\) |
−0.978096 | + | 0.208155i | \(0.933254\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −269.811 | − | 111.760i | −0.344296 | − | 0.142612i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −148.465 | + | 148.465i | −0.182956 | + | 0.182956i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −448.959 | − | 448.959i | −0.534715 | − | 0.534715i | 0.387257 | − | 0.921972i | \(-0.373423\pi\) |
−0.921972 | + | 0.387257i | \(0.873423\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −795.106 | + | 1919.56i | −0.915932 | + | 2.21125i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −291.641 | + | 120.802i | −0.325180 | + | 0.134694i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 642.239 | 0.693604 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1765.41 | −1.84794 | −0.923972 | − | 0.382459i | \(-0.875077\pi\) | ||||
−0.923972 | + | 0.382459i | \(0.875077\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 88.8278 | − | 36.7937i | 0.0901770 | − | 0.0373526i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 298.207 | − | 719.936i | 0.293790 | − | 0.709271i | −0.706210 | − | 0.708003i | \(-0.749596\pi\) |
0.999999 | − | 0.00126791i | \(-0.000403589\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 228.925 | + | 228.925i | 0.218997 | + | 0.218997i | 0.808076 | − | 0.589079i | \(-0.200509\pi\) |
−0.589079 | + | 0.808076i | \(0.700509\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 470.043 | − | 470.043i | 0.436872 | − | 0.436872i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1637.14 | − | 678.126i | −1.47914 | − | 0.612681i | −0.510221 | − | 0.860044i | \(-0.670436\pi\) |
−0.968923 | + | 0.247362i | \(0.920436\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 154.640 | + | 373.333i | 0.135888 | + | 0.328063i | 0.977145 | − | 0.212572i | \(-0.0681841\pi\) |
−0.841257 | + | 0.540635i | \(0.818184\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 605.498i | − | 0.517760i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 681.111i | 0.567023i | 0.958969 | + | 0.283511i | \(0.0914993\pi\) | ||||
−0.958969 | + | 0.283511i | \(0.908501\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −445.249 | − | 1074.93i | −0.361041 | − | 0.871629i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1332.44 | + | 551.916i | 1.05286 | + | 0.436108i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 654.092 | − | 654.092i | 0.503870 | − | 0.503870i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −929.603 | − | 929.603i | −0.698424 | − | 0.698424i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 68.4318 | − | 165.209i | 0.0501649 | − | 0.121109i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1329.06 | + | 550.517i | −0.951001 | + | 0.393918i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −574.582 | −0.401464 | −0.200732 | − | 0.979646i | \(-0.564332\pi\) | ||||
−0.200732 | + | 0.979646i | \(0.564332\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 200.261 | 0.136682 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −749.541 | + | 310.470i | −0.499906 | + | 0.207068i | −0.618365 | − | 0.785891i | \(-0.712205\pi\) |
0.118459 | + | 0.992959i | \(0.462205\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −778.476 | + | 1879.41i | −0.507537 | + | 1.22530i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −696.685 | − | 696.685i | −0.444156 | − | 0.444156i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −274.564 | + | 274.564i | −0.171223 | + | 0.171223i | −0.787517 | − | 0.616293i | \(-0.788634\pi\) |
0.616293 | + | 0.787517i | \(0.288634\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 239.497 | + | 99.2027i | 0.146143 | + | 0.0605343i | 0.454556 | − | 0.890718i | \(-0.349798\pi\) |
−0.308413 | + | 0.951252i | \(0.599798\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 171.208 | + | 413.331i | 0.102257 | + | 0.246871i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 245.150i | 0.143360i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1266.28i | − | 0.725233i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 570.326 | + | 1376.89i | 0.319998 | + | 0.772543i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 176.116 | + | 72.9498i | 0.0968323 | + | 0.0401092i | 0.430574 | − | 0.902555i | \(-0.358311\pi\) |
−0.333741 | + | 0.942665i | \(0.608311\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 339.506 | − | 339.506i | 0.182971 | − | 0.182971i | −0.609678 | − | 0.792649i | \(-0.708701\pi\) |
0.792649 | + | 0.609678i | \(0.208701\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −454.032 | − | 454.032i | −0.239911 | − | 0.239911i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 728.555 | − | 1758.89i | 0.377542 | − | 0.911466i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1222.00 | − | 506.170i | 0.621188 | − | 0.257304i | −0.0498158 | − | 0.998758i | \(-0.515863\pi\) |
0.671004 | + | 0.741454i | \(0.265863\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1160.00 | 0.578576 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3685.29 | 1.80399 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1346.92 | + | 557.911i | −0.647231 | + | 0.268092i | −0.682054 | − | 0.731302i | \(-0.738913\pi\) |
0.0348231 | + | 0.999393i | \(0.488913\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 30.0150 | − | 72.4626i | 0.0141616 | − | 0.0341891i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2521.77 | + | 2521.77i | 1.16851 | + | 1.16851i | 0.982560 | + | 0.185946i | \(0.0595351\pi\) |
0.185946 | + | 0.982560i | \(0.440465\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1046.74 | + | 1046.74i | −0.476440 | + | 0.476440i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1304.57 | + | 540.372i | 0.583411 | + | 0.241657i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −541.973 | − | 1308.44i | −0.238182 | − | 0.575022i | 0.758913 | − | 0.651192i | \(-0.225731\pi\) |
−0.997095 | + | 0.0761701i | \(0.975731\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 273.766i | − | 0.118256i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 354.534i | − | 0.150556i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 54.1456 | + | 130.719i | 0.0226091 | + | 0.0545833i | 0.934781 | − | 0.355225i | \(-0.115596\pi\) |
−0.912172 | + | 0.409808i | \(0.865596\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1585.39 | − | 656.689i | −0.651055 | − | 0.269676i | 0.0326139 | − | 0.999468i | \(-0.489617\pi\) |
−0.683669 | + | 0.729792i | \(0.739617\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −425.077 | + | 425.077i | −0.171708 | + | 0.171708i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2582.18 | + | 2582.18i | 1.02619 | + | 1.02619i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 41.7676 | − | 100.836i | 0.0163334 | − | 0.0394323i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2883.21 | − | 1194.26i | 1.10964 | − | 0.459629i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2679.22 | −1.01498 | −0.507490 | − | 0.861658i | \(-0.669427\pi\) | ||||
−0.507490 | + | 0.861658i | \(0.669427\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3139.34 | −1.17085 | −0.585426 | − | 0.810726i | \(-0.699073\pi\) | ||||
−0.585426 | + | 0.810726i | \(0.699073\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1086.96 | − | 450.233i | 0.399173 | − | 0.165343i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1321.44 | − | 3190.23i | 0.477911 | − | 1.15378i | −0.482675 | − | 0.875799i | \(-0.660335\pi\) |
0.960587 | − | 0.277981i | \(-0.0896652\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 106.853 | + | 106.853i | 0.0380632 | + | 0.0380632i | 0.725882 | − | 0.687819i | \(-0.241432\pi\) |
−0.687819 | + | 0.725882i | \(0.741432\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 408.691 | − | 408.691i | 0.143417 | − | 0.143417i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3705.56 | + | 1534.89i | 1.28118 | + | 0.530682i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 412.712 | + | 996.375i | 0.140610 | + | 0.339463i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 2558.11i | − | 0.858943i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 240.022i | 0.0794387i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1037.64 | + | 2505.10i | 0.338552 | + | 0.817336i | 0.997855 | + | 0.0654593i | \(0.0208512\pi\) |
−0.659304 | + | 0.751877i | \(0.729149\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1582.47 | − | 655.480i | −0.509056 | − | 0.210858i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −854.024 | + | 854.024i | −0.270902 | + | 0.270902i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4264.00 | + | 4264.00i | 1.33391 | + | 1.33391i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 339.908 | − | 820.611i | 0.104881 | − | 0.253204i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1512.57 | − | 626.526i | 0.460390 | − | 0.190700i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3307.18 | −0.993119 | −0.496559 | − | 0.868003i | \(-0.665404\pi\) | ||||
−0.496559 | + | 0.868003i | \(0.665404\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −190.032 | −0.0563058 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5187.26 | − | 2148.63i | 1.51670 | − | 0.628237i | 0.539771 | − | 0.841812i | \(-0.318511\pi\) |
0.976927 | + | 0.213575i | \(0.0685108\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1736.52 | + | 4192.34i | −0.501103 | + | 1.20977i | 0.447780 | + | 0.894144i | \(0.352215\pi\) |
−0.948883 | + | 0.315627i | \(0.897785\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 175.668 | + | 175.668i | 0.0500351 | + | 0.0500351i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −817.096 | + | 817.096i | −0.229741 | + | 0.229741i | −0.812585 | − | 0.582843i | \(-0.801940\pi\) |
0.582843 | + | 0.812585i | \(0.301940\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2492.80 | − | 1032.55i | −0.691968 | − | 0.286623i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 387.284 | + | 934.987i | 0.106147 | + | 0.256261i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2423.25i | 0.655844i | 0.944705 | + | 0.327922i | \(0.106348\pi\) | ||||
−0.944705 | + | 0.327922i | \(0.893652\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 3879.72i | − | 1.03699i | −0.855080 | − | 0.518496i | \(-0.826492\pi\) | ||
0.855080 | − | 0.518496i | \(-0.173508\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1269.74 | − | 3065.42i | −0.335200 | − | 0.809246i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8304.01 | − | 3439.63i | −2.16540 | − | 0.896940i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2545.87 | + | 2545.87i | −0.655829 | + | 0.655829i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −349.064 | − | 349.064i | −0.0888394 | − | 0.0888394i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2070.97 | − | 4999.76i | 0.520791 | − | 1.25730i | −0.416622 | − | 0.909080i | \(-0.636786\pi\) |
0.937413 | − | 0.348220i | \(-0.113214\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 401.729 | − | 166.402i | 0.0998280 | − | 0.0413501i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −523.801 | −0.128634 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1525.85 | −0.370349 | −0.185175 | − | 0.982706i | \(-0.559285\pi\) | ||||
−0.185175 | + | 0.982706i | \(0.559285\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10686.3 | + | 4426.40i | −2.56376 | + | 1.06194i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1065.43 | − | 2572.18i | 0.252677 | − | 0.610016i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −532.444 | − | 532.444i | −0.124836 | − | 0.124836i | 0.641928 | − | 0.766765i | \(-0.278135\pi\) |
−0.766765 | + | 0.641928i | \(0.778135\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4946.87 | + | 4946.87i | −1.14673 | + | 1.14673i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1052.11 | − | 435.796i | −0.241153 | − | 0.0998888i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −930.585 | − | 2246.63i | −0.210925 | − | 0.509217i | 0.782641 | − | 0.622473i | \(-0.213872\pi\) |
−0.993566 | + | 0.113256i | \(0.963872\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 3425.60i | − | 0.767862i | −0.923362 | − | 0.383931i | \(-0.874570\pi\) | ||
0.923362 | − | 0.383931i | \(-0.125430\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3726.55i | 0.826158i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.3613 | − | 29.8428i | −0.00271060 | − | 0.00654397i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4215.07 | + | 1745.94i | 0.914293 | + | 0.378712i | 0.789698 | − | 0.613495i | \(-0.210237\pi\) |
0.124594 | + | 0.992208i | \(0.460237\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2959.81 | − | 2959.81i | 0.635123 | − | 0.635123i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2404.35 | − | 2404.35i | −0.510433 | − | 0.510433i | 0.404226 | − | 0.914659i | \(-0.367541\pi\) |
−0.914659 | + | 0.404226i | \(0.867541\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3013.10 | − | 7274.27i | 0.632899 | − | 1.52795i | −0.203063 | − | 0.979166i | \(-0.565090\pi\) |
0.835962 | − | 0.548787i | \(-0.184910\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1064.23 | − | 440.817i | 0.221191 | − | 0.0916201i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3415.99 | −0.702577 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4184.10 | 0.851638 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2925.39 | + | 1211.74i | −0.589310 | + | 0.244100i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1059.63 | + | 2558.17i | −0.211277 | + | 0.510068i | −0.993620 | − | 0.112780i | \(-0.964025\pi\) |
0.782343 | + | 0.622848i | \(0.214025\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1511.93 | + | 1511.93i | 0.298401 | + | 0.298401i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 260.370 | − | 260.370i | 0.0508694 | − | 0.0508694i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6026.05 | + | 2496.07i | 1.16554 | + | 0.482781i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1463.97 | − | 3534.35i | −0.280339 | − | 0.676799i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 1397.66i | − | 0.264994i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 3625.54i | − | 0.680648i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3277.84 | + | 7913.41i | 0.609369 | + | 1.47115i | 0.863688 | + | 0.504027i | \(0.168149\pi\) |
−0.254319 | + | 0.967120i | \(0.581851\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 536.470 | + | 222.213i | 0.0987660 | + | 0.0409102i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5107.89 | + | 5107.89i | −0.931324 | + | 0.931324i | −0.997789 | − | 0.0664648i | \(-0.978828\pi\) |
0.0664648 | + | 0.997789i | \(0.478828\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1761.64 | − | 1761.64i | −0.318128 | − | 0.318128i | 0.529920 | − | 0.848048i | \(-0.322222\pi\) |
−0.848048 | + | 0.529920i | \(0.822222\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3373.17 | + | 8143.56i | −0.603355 | + | 1.45663i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4091.81 | + | 1694.88i | −0.724981 | + | 0.300297i | −0.714488 | − | 0.699648i | \(-0.753340\pi\) |
−0.0104934 | + | 0.999945i | \(0.503340\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 473.243 | 0.0830612 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3178.28 | −0.552630 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1480.93 | − | 613.422i | 0.255112 | − | 0.105671i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 185.423 | − | 447.651i | 0.0316475 | − | 0.0764038i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 512.493 | + | 512.493i | 0.0866695 | + | 0.0866695i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6043.19 | − | 6043.19i | 1.01268 | − | 1.01268i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6396.05 | − | 2649.33i | −1.06211 | − | 0.439941i | −0.217911 | − | 0.975969i | \(-0.569924\pi\) |
−0.844200 | + | 0.536028i | \(0.819924\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3072.55 | + | 7417.78i | 0.505629 | + | 1.22070i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3485.77i | 0.568502i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 3692.32i | − | 0.596835i | −0.954435 | − | 0.298418i | \(-0.903541\pi\) | ||
0.954435 | − | 0.298418i | \(-0.0964588\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 467.498 | + | 1128.64i | 0.0748997 | + | 0.180824i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 657.344 | + | 272.281i | 0.104391 | + | 0.0432400i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11821.1 | − | 11821.1i | 1.86087 | − | 1.86087i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1475.60 | − | 1475.60i | −0.230272 | − | 0.230272i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3771.01 | + | 9104.01i | −0.583395 | + | 1.40844i | 0.306322 | + | 0.951928i | \(0.400902\pi\) |
−0.889717 | + | 0.456513i | \(0.849098\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2347.30 | − | 972.282i | 0.360023 | − | 0.149126i | −0.195338 | − | 0.980736i | \(-0.562580\pi\) |
0.555360 | + | 0.831610i | \(0.312580\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5523.39 | 0.839934 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 822.940 | 0.124081 | 0.0620406 | − | 0.998074i | \(-0.480239\pi\) | ||||
0.0620406 | + | 0.998074i | \(0.480239\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9543.87 | − | 3953.20i | 1.42686 | − | 0.591026i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 634.915 | − | 1532.82i | 0.0941268 | − | 0.227242i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3701.59 | + | 3701.59i | 0.544185 | + | 0.544185i | 0.924753 | − | 0.380568i | \(-0.124272\pi\) |
−0.380568 | + | 0.924753i | \(0.624272\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2357.42 | − | 2357.42i | 0.343698 | − | 0.343698i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2178.46 | − | 902.347i | −0.314985 | − | 0.130471i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2049.99 | + | 4949.10i | 0.293976 | + | 0.709720i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 3736.68i | − | 0.531479i | −0.964045 | − | 0.265740i | \(-0.914384\pi\) | ||
0.964045 | − | 0.265740i | \(-0.0856162\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2371.18i | 0.334522i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8479.97 | − | 20472.5i | −1.18668 | − | 2.86490i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8948.08 | + | 3706.42i | 1.24213 | + | 0.514507i | 0.904379 | − | 0.426729i | \(-0.140334\pi\) |
0.337750 | + | 0.941236i | \(0.390334\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1824.47 | + | 1824.47i | −0.251241 | + | 0.251241i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5019.60 | + | 5019.60i | 0.685736 | + | 0.685736i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −761.220 | + | 1837.75i | −0.103170 | + | 0.249073i | −0.967032 | − | 0.254654i | \(-0.918038\pi\) |
0.863863 | + | 0.503727i | \(0.168038\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −952.114 | + | 394.379i | −0.128027 | + | 0.0530305i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12159.8 | 1.62229 | 0.811143 | − | 0.584848i | \(-0.198846\pi\) | ||||
0.811143 | + | 0.584848i | \(0.198846\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1498.29 | −0.198338 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2453.33 | + | 1016.20i | −0.322248 | + | 0.133480i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2365.98 | + | 5711.99i | −0.308381 | + | 0.744497i | 0.691377 | + | 0.722494i | \(0.257004\pi\) |
−0.999758 | + | 0.0220031i | \(0.992996\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2053.39 | − | 2053.39i | −0.265586 | − | 0.265586i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1028.93 | + | 1028.93i | −0.132068 | + | 0.132068i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5638.91 | − | 2335.71i | −0.718289 | − | 0.297525i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −533.914 | − | 1288.98i | −0.0674972 | − | 0.162953i | 0.886531 | − | 0.462669i | \(-0.153108\pi\) |
−0.954028 | + | 0.299716i | \(0.903108\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3648.61i | 0.457792i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4956.51i | 0.617248i | 0.951184 | + | 0.308624i | \(0.0998685\pi\) | ||||
−0.951184 | + | 0.308624i | \(0.900131\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4084.29 | + | 9860.35i | 0.504846 | + | 1.21881i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4784.75 | + | 1981.91i | 0.587052 | + | 0.243165i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −965.032 | + | 965.032i | −0.117530 | + | 0.117530i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3226.79 | − | 3226.79i | −0.390108 | − | 0.390108i | 0.484618 | − | 0.874726i | \(-0.338959\pi\) |
−0.874726 | + | 0.484618i | \(0.838959\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −266.514 | + | 643.422i | −0.0319858 | + | 0.0772205i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6257.08 | + | 2591.77i | −0.745499 | + | 0.308796i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2977.21 | 0.352158 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 464.949 | 0.0546011 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1822.54 | − | 754.920i | 0.212498 | − | 0.0880197i | −0.273895 | − | 0.961760i | \(-0.588312\pi\) |
0.486394 | + | 0.873740i | \(0.338312\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −215.665 | + | 520.662i | −0.0249664 | + | 0.0602743i | −0.935871 | − | 0.352343i | \(-0.885385\pi\) |
0.910905 | + | 0.412617i | \(0.135385\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4194.83 | − | 4194.83i | −0.482174 | − | 0.482174i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −152.538 | + | 152.538i | −0.0174098 | + | 0.0174098i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10609.5 | + | 4394.61i | 1.20242 | + | 0.498057i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 168.264 | + | 406.226i | 0.0189368 | + | 0.0457175i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2199.14i | 0.245775i | 0.992421 | + | 0.122888i | \(0.0392155\pi\) | ||||
−0.992421 | + | 0.122888i | \(0.960785\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 273.133i | − | 0.0303139i | −0.999885 | − | 0.0151569i | \(-0.995175\pi\) | ||
0.999885 | − | 0.0151569i | \(-0.00482479\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −869.143 | − | 2098.30i | −0.0957982 | − | 0.231277i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5900.01 | + | 2443.87i | 0.645849 | + | 0.267519i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2910.64 | + | 2910.64i | −0.316440 | + | 0.316440i | −0.847398 | − | 0.530958i | \(-0.821832\pi\) |
0.530958 | + | 0.847398i | \(0.321832\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13973.8 | − | 13973.8i | −1.50889 | − | 1.50889i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1439.20 | + | 3474.54i | −0.154353 | + | 0.372642i | −0.982073 | − | 0.188499i | \(-0.939638\pi\) |
0.827720 | + | 0.561142i | \(0.189638\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6345.25 | − | 2628.29i | 0.675941 | − | 0.279984i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 341.905 | 0.0361780 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13543.2 | 1.42348 | 0.711738 | − | 0.702445i | \(-0.247908\pi\) | ||||
0.711738 | + | 0.702445i | \(0.247908\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −372.373 | + | 154.242i | −0.0388788 | + | 0.0161041i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 329.552 | − | 795.609i | 0.0341804 | − | 0.0825187i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −15892.1 | − | 15892.1i | −1.63744 | − | 1.63744i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3832.14 | − | 3832.14i | 0.392253 | − | 0.392253i | −0.483237 | − | 0.875490i | \(-0.660539\pi\) |
0.875490 | + | 0.483237i | \(0.160539\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2271.90 | − | 941.053i | −0.231031 | − | 0.0956963i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6014.95 | − | 14521.4i | −0.607688 | − | 1.46709i | −0.865508 | − | 0.500895i | \(-0.833004\pi\) |
0.257821 | − | 0.966193i | \(-0.416996\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13168.4i | 1.32178i | 0.750481 | + | 0.660892i | \(0.229822\pi\) | ||||
−0.750481 | + | 0.660892i | \(0.770178\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 3414.64i | − | 0.340537i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2737.75 | + | 6609.51i | 0.271280 | + | 0.654929i | 0.999539 | − | 0.0303741i | \(-0.00966986\pi\) |
−0.728258 | + | 0.685303i | \(0.759670\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10200.6 | − | 4225.21i | −1.00430 | − | 0.415996i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1677.50 | − | 1677.50i | 0.164109 | − | 0.164109i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −319.172 | − | 319.172i | −0.0310265 | − | 0.0310265i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 181.545 | − | 438.289i | 0.0175365 | − | 0.0423370i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14210.8 | + | 5886.29i | −1.36408 | + | 0.565021i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2141.84 | 0.204307 | 0.102153 | − | 0.994769i | \(-0.467427\pi\) | ||||
0.102153 | + | 0.994769i | \(0.467427\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20471.8 | −1.94061 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6106.74 | − | 2529.49i | 0.575292 | − | 0.238294i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7307.98 | − | 17643.0i | 0.684203 | − | 1.65181i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3210.83 | + | 3210.83i | 0.298761 | + | 0.298761i | 0.840528 | − | 0.541767i | \(-0.182245\pi\) |
−0.541767 | + | 0.840528i | \(0.682245\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1848.98 | + | 1848.98i | −0.170989 | + | 0.170989i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10597.1 | − | 4389.47i | −0.974015 | − | 0.403450i | −0.161810 | − | 0.986822i | \(-0.551733\pi\) |
−0.812205 | + | 0.583372i | \(0.801733\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1209.46 | − | 2919.90i | −0.110490 | − | 0.266746i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1040.03i | 0.0944358i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 32720.4i | 2.95314i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3963.81 | − | 9569.49i | −0.355600 | − | 0.858495i | −0.995908 | − | 0.0903763i | \(-0.971193\pi\) |
0.640307 | − | 0.768119i | \(-0.278807\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5909.60 | + | 2447.83i | 0.526989 | + | 0.218286i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13198.2 | + | 13198.2i | −1.16994 | + | 1.16994i | −0.187716 | + | 0.982223i | \(0.560108\pi\) |
−0.982223 | + | 0.187716i | \(0.939892\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5960.39 | + | 5960.39i | 0.525216 | + | 0.525216i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1016.05 | + | 2452.96i | −0.0890027 | + | 0.214871i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14481.7 | + | 5998.52i | −1.26108 | + | 0.522357i | −0.910241 | − | 0.414078i | \(-0.864104\pi\) |
−0.350840 | + | 0.936435i | \(0.614104\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16967.6 | −1.46889 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5407.87 | 0.465426 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3235.45 | + | 1340.17i | −0.276837 | + | 0.114670i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 385.893 | − | 931.628i | 0.0328270 | − | 0.0792514i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1796.16 | − | 1796.16i | −0.151913 | − | 0.151913i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1814.60 | − | 1814.60i | 0.152590 | − | 0.152590i | −0.626684 | − | 0.779274i | \(-0.715588\pi\) |
0.779274 | + | 0.626684i | \(0.215588\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4063.96 | − | 1683.35i | −0.339779 | − | 0.140741i | 0.206268 | − | 0.978496i | \(-0.433868\pi\) |
−0.546047 | + | 0.837754i | \(0.683868\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −187.906 | − | 453.645i | −0.0156207 | − | 0.0377118i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 4751.66i | − | 0.392762i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 597.782i | 0.0491314i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1799.05 | + | 4343.30i | 0.147029 | + | 0.354959i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5585.70 | − | 2313.67i | −0.453927 | − | 0.188023i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13554.0 | − | 13554.0i | 1.09531 | − | 1.09531i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 179.445 | + | 179.445i | 0.0144201 | + | 0.0144201i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1285.48 | − | 3103.44i | 0.102727 | − | 0.248004i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5389.43 | − | 2232.38i | 0.428299 | − | 0.177407i | −0.158111 | − | 0.987421i | \(-0.550541\pi\) |
0.586411 | + | 0.810014i | \(0.300541\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3077.81 | −0.243244 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4371.11 | −0.343556 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20016.3 | − | 8291.01i | 1.56460 | − | 0.648077i | 0.578716 | − | 0.815529i | \(-0.303554\pi\) |
0.985880 | + | 0.167452i | \(0.0535539\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3050.48 | − | 7364.51i | 0.237143 | − | 0.572513i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4914.61 | + | 4914.61i | 0.379981 | + | 0.379981i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13670.2 | − | 13670.2i | 1.05120 | − | 1.05120i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6051.17 | + | 2506.48i | 0.462807 | + | 0.191701i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 819.599 | + | 1978.69i | 0.0623474 | + | 0.150520i | 0.951983 | − | 0.306152i | \(-0.0990414\pi\) |
−0.889635 | + | 0.456672i | \(0.849041\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6770.79i | − | 0.512297i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 195.759i | − | 0.0147325i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4297.82 | − | 10375.9i | −0.321726 | − | 0.776715i | −0.999154 | − | 0.0411260i | \(-0.986905\pi\) |
0.677428 | − | 0.735589i | \(-0.263095\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6806.82 | − | 2819.48i | −0.506841 | − | 0.209940i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −11599.5 | + | 11599.5i | −0.859139 | + | 0.859139i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3794.16 | + | 3794.16i | 0.279542 | + | 0.279542i | 0.832926 | − | 0.553384i | \(-0.186664\pi\) |
−0.553384 | + | 0.832926i | \(0.686664\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3323.60 | − | 8023.87i | 0.243587 | − | 0.588071i | −0.754047 | − | 0.656820i | \(-0.771901\pi\) |
0.997634 | + | 0.0687495i | \(0.0219009\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4439.61 | + | 1838.95i | −0.323678 | + | 0.134072i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −859.431 | −0.0623318 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7285.88 | 0.525676 | 0.262838 | − | 0.964840i | \(-0.415342\pi\) | ||||
0.262838 | + | 0.964840i | \(0.415342\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5202.06 | + | 2154.76i | −0.373385 | + | 0.154661i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3608.76 | + | 8712.31i | −0.257688 | + | 0.622113i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1848.78 | − | 1848.78i | −0.131336 | − | 0.131336i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −11031.4 | + | 11031.4i | −0.779642 | + | 0.779642i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24501.2 | + | 10148.7i | 1.72278 | + | 0.713600i | 0.999740 | + | 0.0227951i | \(0.00725653\pi\) |
0.723042 | + | 0.690804i | \(0.242743\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3998.87 | + | 9654.12i | 0.279746 | + | 0.675367i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 6193.40i | − | 0.431070i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 9134.01i | − | 0.632528i | −0.948671 | − | 0.316264i | \(-0.897572\pi\) | ||
0.948671 | − | 0.316264i | \(-0.102428\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3829.17 | + | 9244.44i | 0.263833 | + | 0.636950i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 250.401 | + | 103.720i | 0.0171662 | + | 0.00711049i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5461.25 | + | 5461.25i | −0.372522 | + | 0.372522i | −0.868395 | − | 0.495873i | \(-0.834848\pi\) |
0.495873 | + | 0.868395i | \(0.334848\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14729.8 | + | 14729.8i | 0.999738 | + | 0.999738i | 1.00000 | 0.000262159i | \(-8.34479e-5\pi\) | |
−0.000262159 | 1.00000i | \(0.500083\pi\) | ||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2932.89 | + | 7080.62i | −0.198070 | + | 0.478184i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13138.3 | − | 5442.06i | 0.882888 | − | 0.365704i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −881.096 | −0.0589169 | −0.0294585 | − | 0.999566i | \(-0.509378\pi\) | ||||
−0.0294585 | + | 0.999566i | \(0.509378\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7193.83 | 0.478668 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13974.7 | − | 5788.51i | 0.925295 | − | 0.383270i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1693.73 | + | 4089.02i | −0.111597 | + | 0.269419i | −0.969804 | − | 0.243884i | \(-0.921578\pi\) |
0.858207 | + | 0.513303i | \(0.171578\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1367.77 | + | 1367.77i | 0.0896813 | + | 0.0896813i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21041.5 | + | 21041.5i | −1.37293 | + | 1.37293i | −0.516863 | + | 0.856068i | \(0.672900\pi\) |
−0.856068 | + | 0.516863i | \(0.827100\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6142.30 | − | 2544.22i | −0.398837 | − | 0.165204i | 0.174244 | − | 0.984703i | \(-0.444252\pi\) |
−0.573081 | + | 0.819499i | \(0.694252\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3749.14 | − | 9051.24i | −0.242267 | − | 0.584885i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21754.2i | 1.39898i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 14562.4i | − | 0.931992i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 164.745 | + | 397.730i | 0.0104933 | + | 0.0253330i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8420.55 | + | 3487.90i | 0.533783 | + | 0.221100i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12002.6 | − | 12002.6i | 0.757234 | − | 0.757234i | −0.218584 | − | 0.975818i | \(-0.570144\pi\) |
0.975818 | + | 0.218584i | \(0.0701438\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3438.87 | + | 3438.87i | 0.215929 | + | 0.215929i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2378.50 | − | 5742.20i | 0.148642 | − | 0.358854i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 46552.4 | − | 19282.6i | 2.89556 | − | 1.19938i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 22712.6 | 1.40610 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8356.78 | 0.514934 | 0.257467 | − | 0.966287i | \(-0.417112\pi\) | ||||
0.257467 | + | 0.966287i | \(0.417112\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24447.4 | + | 10126.4i | −1.49939 | + | 0.621070i | −0.973337 | − | 0.229379i | \(-0.926330\pi\) |
−0.526058 | + | 0.850449i | \(0.676330\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −828.984 | + | 2001.34i | −0.0506065 | + | 0.122175i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12516.3 | − | 12516.3i | −0.760533 | − | 0.760533i | 0.215885 | − | 0.976419i | \(-0.430736\pi\) |
−0.976419 | + | 0.215885i | \(0.930736\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −565.051 | + | 565.051i | −0.0341759 | + | 0.0341759i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9992.38 | + | 4138.98i | 0.601585 | + | 0.249185i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1943.05 | − | 4690.95i | −0.116443 | − | 0.281119i | 0.854903 | − | 0.518788i | \(-0.173617\pi\) |
−0.971346 | + | 0.237669i | \(0.923617\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 8775.89i | − | 0.523515i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11777.9i | 0.699391i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3982.05 | + | 9613.52i | 0.235385 | + | 0.568269i | 0.996795 | − | 0.0800014i | \(-0.0254925\pi\) |
−0.761410 | + | 0.648271i | \(0.775492\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2718.83 | − | 1126.18i | −0.159985 | − | 0.0662680i | 0.301254 | − | 0.953544i | \(-0.402595\pi\) |
−0.461239 | + | 0.887276i | \(0.652595\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2076.38 | − | 2076.38i | 0.121629 | − | 0.121629i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −15559.7 | − | 15559.7i | −0.907339 | − | 0.907339i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4818.48 | − | 11632.8i | 0.279719 | − | 0.675301i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5480.19 | + | 2269.97i | −0.316706 | + | 0.131184i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1354.96 | 0.0779548 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4348.42 | −0.249063 | −0.124531 | − | 0.992216i | \(-0.539743\pi\) | ||||
−0.124531 | + | 0.992216i | \(0.539743\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −672.380 | + | 278.509i | −0.0383406 | + | 0.0158812i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4462.91 | + | 10774.4i | −0.253358 | + | 0.611661i | −0.998471 | − | 0.0552774i | \(-0.982396\pi\) |
0.745113 | + | 0.666939i | \(0.232396\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 42771.2 | + | 42771.2i | 2.41739 | + | 2.41739i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7120.81 | − | 7120.81i | 0.400690 | − | 0.400690i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19860.3 | − | 8226.41i | −1.11264 | − | 0.460871i | −0.250794 | − | 0.968040i | \(-0.580692\pi\) |
−0.861846 | + | 0.507170i | \(0.830692\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1607.35 | − | 3880.48i | −0.0896548 | − | 0.216446i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8138.84i | 0.451989i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 39219.3i | − | 2.16856i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 764.618 | + | 1845.95i | 0.0420947 | + | 0.101626i | 0.943528 | − | 0.331291i | \(-0.107484\pi\) |
−0.901434 | + | 0.432917i | \(0.857484\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3043.47 | − | 1260.65i | −0.166828 | − | 0.0691024i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1982.81 | + | 1982.81i | −0.108219 | + | 0.108219i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1903.34 | + | 1903.34i | 0.103435 | + | 0.103435i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −793.139 | + | 1914.81i | −0.0429174 | + | 0.103612i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22956.1 | + | 9508.72i | −1.23686 | + | 0.512324i | −0.902732 | − | 0.430203i | \(-0.858442\pi\) |
−0.334128 | + | 0.942528i | \(0.608442\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20043.6 | −1.07533 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4839.43 | −0.258530 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −24666.9 | + | 10217.4i | −1.31215 | + | 0.543512i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6852.40 | + | 16543.2i | −0.362972 | + | 0.876292i | 0.631891 | + | 0.775058i | \(0.282279\pi\) |
−0.994863 | + | 0.101234i | \(0.967721\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9489.02 | − | 9489.02i | −0.500515 | − | 0.500515i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13385.9 | − | 13385.9i | 0.703096 | − | 0.703096i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2449.95 | − | 1014.80i | −0.128144 | − | 0.0530790i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1663.25 | + | 4015.45i | 0.0866324 | + | 0.209149i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 29422.6i | − | 1.52612i | −0.646329 | − | 0.763059i | \(-0.723697\pi\) | ||
0.646329 | − | 0.763059i | \(-0.276303\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 11092.5i | − | 0.572962i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2662.94 | − | 6428.92i | −0.136979 | − | 0.330697i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −864.158 | − | 357.946i | −0.0442676 | − | 0.0183362i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11609.7 | − | 11609.7i | 0.592267 | − | 0.592267i | −0.345976 | − | 0.938243i | \(-0.612452\pi\) |
0.938243 | + | 0.345976i | \(0.112452\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4932.69 | + | 4932.69i | 0.250607 | + | 0.250607i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1153.58 | + | 2784.99i | −0.0583675 | + | 0.140912i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11834.5 | + | 4902.00i | −0.596338 | + | 0.247011i | −0.660375 | − | 0.750936i | \(-0.729603\pi\) |
0.0640365 | + | 0.997948i | \(0.479603\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −16121.1 | −0.809028 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1302.73 | −0.0651108 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16285.3 | + | 6745.57i | −0.810640 | + | 0.335778i | −0.749209 | − | 0.662333i | \(-0.769566\pi\) |
−0.0614306 | + | 0.998111i | \(0.519566\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2471.23 | + | 5966.07i | −0.122514 | + | 0.295775i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20708.3 | + | 20708.3i | 1.02249 | + | 1.02249i | 0.999741 | + | 0.0227537i | \(0.00724334\pi\) |
0.0227537 | + | 0.999741i | \(0.492757\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1458.08 | + | 1458.08i | −0.0717044 | + | 0.0717044i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6047.57 | + | 2504.99i | 0.296210 | + | 0.122694i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23234.3 | + | 56092.7i | 1.13346 | + | 2.73642i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 26417.1i | − | 1.28359i | −0.766878 | − | 0.641793i | \(-0.778191\pi\) | ||
0.766878 | − | 0.641793i | \(-0.221809\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 9706.35i | − | 0.469746i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1987.53 | + | 4798.32i | 0.0958061 | + | 0.231296i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20911.7 | − | 8661.89i | −1.00402 | − | 0.415881i | −0.180753 | − | 0.983528i | \(-0.557854\pi\) |
−0.823272 | + | 0.567648i | \(0.807854\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 551.473 | − | 551.473i | 0.0263731 | − | 0.0263731i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8497.64 | − | 8497.64i | −0.404782 | − | 0.404782i | 0.475132 | − | 0.879914i | \(-0.342400\pi\) |
−0.879914 | + | 0.475132i | \(0.842400\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5298.35 | − | 12791.4i | 0.251393 | − | 0.606918i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6416.94 | − | 2657.98i | 0.303275 | − | 0.125620i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11986.8 | −0.564298 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31834.2 | −1.49281 | −0.746405 | − | 0.665492i | \(-0.768222\pi\) | ||||
−0.746405 | + | 0.665492i | \(0.768222\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2528.41 | + | 1047.30i | −0.118105 | + | 0.0489205i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14033.5 | − | 33879.9i | 0.652976 | − | 1.57642i | −0.155463 | − | 0.987842i | \(-0.549687\pi\) |
0.808438 | − | 0.588581i | \(-0.200313\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −994.388 | − | 994.388i | −0.0460896 | − | 0.0460896i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14669.6 | + | 14669.6i | −0.677308 | + | 0.677308i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5468.87 | − | 2265.28i | −0.251531 | − | 0.104188i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1477.42 | + | 3566.80i | 0.0676904 | + | 0.163419i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 10662.5i | − | 0.486650i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14307.6i | 0.650525i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7882.13 | + | 19029.1i | 0.357011 | + | 0.861900i | 0.995717 | + | 0.0924500i | \(0.0294698\pi\) |
−0.638706 | + | 0.769450i | \(0.720530\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1247.74 | − | 516.833i | −0.0563002 | − | 0.0233203i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16501.5 | − | 16501.5i | 0.741751 | − | 0.741751i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14371.8 | + | 14371.8i | 0.643579 | + | 0.643579i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4801.83 | + | 11592.6i | −0.214218 | + | 0.517168i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28060.5 | − | 11623.0i | 1.24712 | − | 0.516574i | 0.341186 | − | 0.939996i | \(-0.389171\pi\) |
0.905933 | + | 0.423422i | \(0.139171\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6734.35 | −0.298178 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15100.4 | 0.666102 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1849.61 | + | 766.135i | −0.0812845 | + | 0.0336692i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15255.4 | + | 36829.7i | −0.667927 | + | 1.61252i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3084.06 | − | 3084.06i | −0.134528 | − | 0.134528i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14787.2 | + | 14787.2i | −0.642633 | + | 0.642633i | −0.951202 | − | 0.308569i | \(-0.900150\pi\) |
0.308569 | + | 0.951202i | \(0.400150\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26961.4 | − | 11167.8i | −1.16738 | − | 0.483544i | −0.287053 | − | 0.957915i | \(-0.592675\pi\) |
−0.880325 | + | 0.474371i | \(0.842675\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2351.25 | − | 5676.41i | −0.101429 | − | 0.244871i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 15770.2i | − | 0.677798i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 6629.18i | − | 0.283875i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −18910.1 | − | 45652.9i | −0.806802 | − | 1.94779i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26459.7 | − | 10960.0i | −1.12479 | − | 0.465902i | −0.258782 | − | 0.965936i | \(-0.583321\pi\) |
−0.866006 | + | 0.500033i | \(0.833321\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16724.6 | + | 16724.6i | −0.708363 | + | 0.708363i | −0.966191 | − | 0.257828i | \(-0.916993\pi\) |
0.257828 | + | 0.966191i | \(0.416993\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −40.9668 | − | 40.9668i | −0.00172882 | − | 0.00172882i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3883.90 | − | 9376.57i | 0.163309 | − | 0.394263i | −0.820949 | − | 0.571002i | \(-0.806555\pi\) |
0.984258 | + | 0.176739i | \(0.0565549\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4058.22 | + | 1680.97i | −0.170021 | + | 0.0704251i | −0.466071 | − | 0.884748i | \(-0.654331\pi\) |
0.296049 | + | 0.955173i | \(0.404331\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8182.98 | 0.341594 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −22433.4 | −0.933100 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −35640.8 | + | 14762.9i | −1.47713 | + | 0.611845i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6134.68 | − | 14810.4i | 0.253340 | − | 0.611617i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −724.855 | − | 724.855i | −0.0298269 | − | 0.0298269i | 0.692036 | − | 0.721863i | \(-0.256714\pi\) |
−0.721863 | + | 0.692036i | \(0.756714\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7555.66 | + | 7555.66i | −0.309798 | + | 0.309798i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5634.44 | − | 2333.86i | −0.230202 | − | 0.0953528i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6127.80 | − | 14793.8i | −0.249471 | − | 0.602275i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 45043.5i | 1.82729i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 14122.0i | − | 0.570866i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13895.8 | + | 33547.4i | 0.559743 | + | 1.35134i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23925.7 | + | 9910.36i | 0.960376 | + | 0.397801i | 0.807121 | − | 0.590386i | \(-0.201024\pi\) |
0.153255 | + | 0.988187i | \(0.451024\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10800.6 | + | 10800.6i | −0.432016 | + | 0.432016i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25248.3 | − | 25248.3i | −1.00638 | − | 1.00638i | −0.999980 | − | 0.00639889i | \(-0.997963\pi\) |
−0.00639889 | − | 0.999980i | \(-0.502037\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13363.0 | − | 32261.1i | 0.530780 | − | 1.28142i | −0.400228 | − | 0.916416i | \(-0.631069\pi\) |
0.931008 | − | 0.365000i | \(-0.118931\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5660.49 | + | 2344.65i | −0.224052 | + | 0.0928054i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37879.2 | 1.49412 | 0.747058 | − | 0.664758i | \(-0.231466\pi\) | ||||
0.747058 | + | 0.664758i | \(0.231466\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15319.7 | 0.602178 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6933.29 | − | 2871.86i | 0.271588 | − | 0.112495i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 872.919 | − | 2107.41i | 0.0340757 | − | 0.0822659i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13817.8 | − | 13817.8i | −0.537541 | − | 0.537541i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 29689.3 | − | 29689.3i | 1.15101 | − | 1.15101i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 45537.2 | + | 18862.1i | 1.75936 | + | 0.728750i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17752.3 | − | 42857.9i | −0.683527 | − | 1.65018i | −0.757432 | − | 0.652914i | \(-0.773546\pi\) |
0.0739053 | − | 0.997265i | \(-0.476454\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4966.34i | 0.190569i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 7584.20i | − | 0.290032i | −0.989429 | − | 0.145016i | \(-0.953677\pi\) | ||
0.989429 | − | 0.145016i | \(-0.0463234\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9800.89 | + | 23661.4i | 0.373529 | + | 0.901779i | 0.993147 | + | 0.116875i | \(0.0372878\pi\) |
−0.619617 | + | 0.784904i | \(0.712712\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3543.11 | + | 1467.60i | 0.134577 | + | 0.0557435i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8905.97 | − | 8905.97i | 0.337129 | − | 0.337129i | −0.518157 | − | 0.855286i | \(-0.673382\pi\) |
0.855286 | + | 0.518157i | \(0.173382\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13920.6 | + | 13920.6i | 0.525176 | + | 0.525176i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −740.693 | + | 1788.19i | −0.0278498 | + | 0.0672353i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13682.4 | − | 5667.44i | 0.512726 | − | 0.212378i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1530.51 | −0.0571611 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11698.7 | 0.435462 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 19034.7 | − | 7884.42i | 0.706165 | − | 0.292503i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6682.03 | + | 16131.8i | −0.247071 | + | 0.596481i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4851.77 | − | 4851.77i | −0.178801 | − | 0.178801i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13125.5 | − | 13125.5i | 0.482107 | − | 0.482107i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23324.8 | + | 9661.45i | 0.853900 | + | 0.353697i | 0.766319 | − | 0.642460i | \(-0.222086\pi\) |
0.0875813 | + | 0.996157i | \(0.472086\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7092.28 | + | 17122.3i | 0.258786 | + | 0.624764i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28451.4i | 1.03473i | 0.855765 | + | 0.517364i | \(0.173087\pi\) | ||||
−0.855765 | + | 0.517364i | \(0.826913\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1112.66i | 0.0403327i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2488.48 | − | 6007.71i | −0.0899087 | − | 0.217059i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 25681.2 | + | 10637.5i | 0.924830 | + | 0.383077i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23087.8 | + | 23087.8i | −0.828721 | + | 0.828721i | −0.987340 | − | 0.158618i | \(-0.949296\pi\) |
0.158618 | + | 0.987340i | \(0.449296\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10863.1 | + | 10863.1i | 0.388656 | + | 0.388656i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −22161.7 | + | 53503.1i | −0.790316 | + | 1.90799i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2492.10 | − | 1032.26i | 0.0885835 | − | 0.0366925i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7699.74 | −0.272808 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29125.2 | 1.02860 | 0.514298 | − | 0.857612i | \(-0.328053\pi\) | ||||
0.514298 | + | 0.857612i | \(0.328053\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 45578.8 | − | 18879.3i | 1.60449 | − | 0.664603i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4958.13 | + | 11970.0i | −0.173978 | + | 0.420021i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 834.826 | + | 834.826i | 0.0291997 | + | 0.0291997i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23895.1 | + | 23895.1i | −0.833105 | + | 0.833105i | −0.987940 | − | 0.154835i | \(-0.950515\pi\) |
0.154835 | + | 0.987940i | \(0.450515\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4128.29 | − | 1709.99i | −0.143473 | − | 0.0594286i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1918.84 | + | 4632.49i | 0.0664743 | + | 0.160483i | 0.953625 | − | 0.300996i | \(-0.0973190\pi\) |
−0.887151 | + | 0.461479i | \(0.847319\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10723.8i | 0.370323i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 33757.6i | 1.16205i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14686.5 | − | 35456.3i | −0.503957 | − | 1.21666i | −0.947312 | − | 0.320313i | \(-0.896212\pi\) |
0.443355 | − | 0.896346i | \(-0.353788\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27744.8 | − | 11492.3i | −0.949034 | − | 0.393103i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5617.03 | + | 5617.03i | −0.191530 | + | 0.191530i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11229.5 | + | 11229.5i | 0.381698 | + | 0.381698i | 0.871714 | − | 0.490016i | \(-0.163009\pi\) |
−0.490016 | + | 0.871714i | \(0.663009\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11090.7 | − | 26775.3i | 0.375797 | − | 0.907254i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 784.190 | − | 324.822i | 0.0264883 | − | 0.0109718i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13303.9 | 0.447972 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1184.85 | 0.0397721 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 38936.2 | − | 16127.9i | 1.30291 | − | 0.539683i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12995.4 | − | 31373.6i | 0.433509 | − | 1.04658i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23938.4 | − | 23938.4i | −0.796076 | − | 0.796076i | 0.186398 | − | 0.982474i | \(-0.440319\pi\) |
−0.982474 | + | 0.186398i | \(0.940319\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2032.95 | − | 2032.95i | 0.0673970 | − | 0.0673970i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28947.0 | − | 11990.2i | −0.956698 | − | 0.396277i | −0.150954 | − | 0.988541i | \(-0.548234\pi\) |
−0.805744 | + | 0.592264i | \(0.798234\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3398.94 | − | 8205.77i | −0.111989 | − | 0.270365i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 869.053i | − | 0.0285456i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 60103.7i | 1.96815i | 0.177743 | + | 0.984077i | \(0.443120\pi\) | ||||
−0.177743 | + | 0.984077i | \(0.556880\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 982.262 | + | 2371.39i | 0.0320666 | + | 0.0774157i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8879.00 | − | 3677.80i | −0.288975 | − | 0.119697i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 40035.9 | − | 40035.9i | 1.29903 | − | 1.29903i | 0.369995 | − | 0.929034i | \(-0.379359\pi\) |
0.929034 | − | 0.369995i | \(-0.120641\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26412.1 | + | 26412.1i | 0.854376 | + | 0.854376i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5866.01 | − | 14161.8i | 0.189176 | − | 0.456712i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11095.4 | + | 4595.85i | −0.356736 | + | 0.147765i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15618.9 | −0.500658 | −0.250329 | − | 0.968161i | \(-0.580539\pi\) | ||||
−0.250329 | + | 0.968161i | \(0.580539\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12417.0 | −0.396821 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1510.17 | + | 625.533i | −0.0481162 | + | 0.0199304i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18691.7 | − | 45125.8i | 0.593754 | − | 1.43345i | −0.286097 | − | 0.958201i | \(-0.592358\pi\) |
0.879851 | − | 0.475249i | \(-0.157642\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 21742.9 | + | 21742.9i | 0.688602 | + | 0.688602i |
(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 | 128.4.g.a.49.7 | 44 | ||
4.3 | odd | 2 | 32.4.g.a.21.1 | ✓ | 44 | ||
8.3 | odd | 2 | 256.4.g.b.97.7 | 44 | |||
8.5 | even | 2 | 256.4.g.a.97.5 | 44 | |||
32.3 | odd | 8 | 32.4.g.a.29.1 | yes | 44 | ||
32.13 | even | 8 | 256.4.g.a.161.5 | 44 | |||
32.19 | odd | 8 | 256.4.g.b.161.7 | 44 | |||
32.29 | even | 8 | inner | 128.4.g.a.81.7 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.4.g.a.21.1 | ✓ | 44 | 4.3 | odd | 2 | ||
32.4.g.a.29.1 | yes | 44 | 32.3 | odd | 8 | ||
128.4.g.a.49.7 | 44 | 1.1 | even | 1 | trivial | ||
128.4.g.a.81.7 | 44 | 32.29 | even | 8 | inner | ||
256.4.g.a.97.5 | 44 | 8.5 | even | 2 | |||
256.4.g.a.161.5 | 44 | 32.13 | even | 8 | |||
256.4.g.b.97.7 | 44 | 8.3 | odd | 2 | |||
256.4.g.b.161.7 | 44 | 32.19 | odd | 8 |