Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,4,Mod(136,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.136");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.e (of order \(3\), degree \(2\), 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: | \(23.8957735523\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.148347072.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 29x^{4} + 223x^{2} + 243 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 136.1 | ||
Root | \(4.00586i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.136 |
Dual form | 405.4.e.s.271.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.76174 | + | 3.05142i | −0.622868 | + | 1.07884i | 0.366080 | + | 0.930583i | \(0.380700\pi\) |
−0.988949 | + | 0.148257i | \(0.952634\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.20744 | − | 3.82340i | −0.275930 | − | 0.477925i | ||||
\(5\) | 2.50000 | + | 4.33013i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −12.7162 | + | 22.0252i | −0.686612 | + | 1.18925i | 0.286315 | + | 0.958135i | \(0.407570\pi\) |
−0.972927 | + | 0.231111i | \(0.925764\pi\) | |||||||
\(8\) | −12.6321 | −0.558264 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −17.6174 | −0.557111 | ||||||||
\(11\) | −35.6781 | + | 61.7962i | −0.977940 | + | 1.69384i | −0.308071 | + | 0.951363i | \(0.599683\pi\) |
−0.669870 | + | 0.742479i | \(0.733650\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 25.6968 | + | 44.5081i | 0.548231 | + | 0.949563i | 0.998396 | + | 0.0566179i | \(0.0180317\pi\) |
−0.450165 | + | 0.892945i | \(0.648635\pi\) | |||||||
\(14\) | −44.8053 | − | 77.6051i | −0.855338 | − | 1.48149i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 39.9139 | − | 69.1330i | 0.623655 | − | 1.08020i | ||||
\(17\) | 33.3191 | 0.475357 | 0.237678 | − | 0.971344i | \(-0.423614\pi\) | ||||
0.237678 | + | 0.971344i | \(0.423614\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 113.372 | 1.36891 | 0.684455 | − | 0.729055i | \(-0.260040\pi\) | ||||
0.684455 | + | 0.729055i | \(0.260040\pi\) | |||||||
\(20\) | 11.0372 | − | 19.1170i | 0.123400 | − | 0.213735i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −125.711 | − | 217.738i | −1.21826 | − | 2.11008i | ||||
\(23\) | 40.9884 | + | 70.9939i | 0.371594 | + | 0.643620i | 0.989811 | − | 0.142388i | \(-0.0454780\pi\) |
−0.618217 | + | 0.786008i | \(0.712145\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | −181.084 | −1.36590 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 112.281 | 0.757828 | ||||||||
\(29\) | −123.414 | + | 213.759i | −0.790253 | + | 1.36876i | 0.135557 | + | 0.990770i | \(0.456718\pi\) |
−0.925810 | + | 0.377989i | \(0.876616\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −111.340 | − | 192.846i | −0.645070 | − | 1.11729i | −0.984285 | − | 0.176585i | \(-0.943495\pi\) |
0.339215 | − | 0.940709i | \(-0.389838\pi\) | |||||||
\(32\) | 90.1075 | + | 156.071i | 0.497779 | + | 0.862178i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −58.6995 | + | 101.671i | −0.296085 | + | 0.512834i | ||||
\(35\) | −127.162 | −0.614124 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 22.3910 | 0.0994880 | 0.0497440 | − | 0.998762i | \(-0.484159\pi\) | ||||
0.0497440 | + | 0.998762i | \(0.484159\pi\) | |||||||
\(38\) | −199.731 | + | 345.945i | −0.852651 | + | 1.47683i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −31.5802 | − | 54.6985i | −0.124832 | − | 0.216215i | ||||
\(41\) | −217.113 | − | 376.050i | −0.827007 | − | 1.43242i | −0.900375 | − | 0.435114i | \(-0.856708\pi\) |
0.0733680 | − | 0.997305i | \(-0.476625\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 118.425 | − | 205.118i | 0.419991 | − | 0.727446i | −0.575947 | − | 0.817487i | \(-0.695367\pi\) |
0.995938 | + | 0.0900414i | \(0.0286999\pi\) | |||||||
\(44\) | 315.029 | 1.07937 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −288.843 | −0.925817 | ||||||||
\(47\) | −53.9919 | + | 93.5166i | −0.167564 | + | 0.290230i | −0.937563 | − | 0.347816i | \(-0.886924\pi\) |
0.769999 | + | 0.638046i | \(0.220257\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −151.905 | − | 263.107i | −0.442872 | − | 0.767077i | ||||
\(50\) | −44.0435 | − | 76.2855i | −0.124574 | − | 0.215768i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 113.448 | − | 196.498i | 0.302547 | − | 0.524027i | ||||
\(53\) | 123.961 | 0.321272 | 0.160636 | − | 0.987014i | \(-0.448646\pi\) | ||||
0.160636 | + | 0.987014i | \(0.448646\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −356.781 | −0.874696 | ||||||||
\(56\) | 160.632 | − | 278.223i | 0.383311 | − | 0.663913i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −434.845 | − | 753.174i | −0.984447 | − | 1.70511i | ||||
\(59\) | 85.5454 | + | 148.169i | 0.188764 | + | 0.326949i | 0.944838 | − | 0.327537i | \(-0.106219\pi\) |
−0.756074 | + | 0.654486i | \(0.772885\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 39.7196 | − | 68.7963i | 0.0833700 | − | 0.144401i | −0.821325 | − | 0.570460i | \(-0.806765\pi\) |
0.904695 | + | 0.426059i | \(0.140098\pi\) | |||||||
\(62\) | 784.604 | 1.60717 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.63945 | 0.00710830 | ||||||||
\(65\) | −128.484 | + | 222.540i | −0.245176 | + | 0.424658i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 305.753 | + | 529.580i | 0.557517 | + | 0.965648i | 0.997703 | + | 0.0677416i | \(0.0215793\pi\) |
−0.440186 | + | 0.897907i | \(0.645087\pi\) | |||||||
\(68\) | −73.5500 | − | 127.392i | −0.131165 | − | 0.227185i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 224.027 | − | 388.026i | 0.382519 | − | 0.662542i | ||||
\(71\) | −511.102 | −0.854318 | −0.427159 | − | 0.904176i | \(-0.640486\pi\) | ||||
−0.427159 | + | 0.904176i | \(0.640486\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −410.012 | −0.657373 | −0.328686 | − | 0.944439i | \(-0.606606\pi\) | ||||
−0.328686 | + | 0.944439i | \(0.606606\pi\) | |||||||
\(74\) | −39.4471 | + | 68.3243i | −0.0619680 | + | 0.107332i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −250.262 | − | 433.466i | −0.377724 | − | 0.654236i | ||||
\(77\) | −907.381 | − | 1571.63i | −1.34293 | − | 2.32602i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 396.798 | − | 687.275i | 0.565105 | − | 0.978791i | −0.431935 | − | 0.901905i | \(-0.642169\pi\) |
0.997040 | − | 0.0768858i | \(-0.0244977\pi\) | |||||||
\(80\) | 399.139 | 0.557814 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1529.98 | 2.06047 | ||||||||
\(83\) | 135.040 | − | 233.897i | 0.178586 | − | 0.309319i | −0.762811 | − | 0.646622i | \(-0.776181\pi\) |
0.941396 | + | 0.337302i | \(0.109514\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 83.2977 | + | 144.276i | 0.106293 | + | 0.184105i | ||||
\(86\) | 417.267 | + | 722.727i | 0.523198 | + | 0.906206i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 450.688 | − | 780.614i | 0.545949 | − | 0.945611i | ||||
\(89\) | −177.400 | −0.211284 | −0.105642 | − | 0.994404i | \(-0.533690\pi\) | ||||
−0.105642 | + | 0.994404i | \(0.533690\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1307.06 | −1.50569 | ||||||||
\(92\) | 180.959 | − | 313.430i | 0.205068 | − | 0.355188i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −190.239 | − | 329.504i | −0.208741 | − | 0.361550i | ||||
\(95\) | 283.430 | + | 490.914i | 0.306097 | + | 0.530176i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 440.930 | − | 763.714i | 0.461543 | − | 0.799416i | −0.537495 | − | 0.843267i | \(-0.680629\pi\) |
0.999038 | + | 0.0438508i | \(0.0139626\pi\) | |||||||
\(98\) | 1070.47 | 1.10340 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 110.372 | 0.110372 | ||||||||
\(101\) | 513.017 | − | 888.572i | 0.505417 | − | 0.875408i | −0.494563 | − | 0.869142i | \(-0.664672\pi\) |
0.999980 | − | 0.00626636i | \(-0.00199466\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 895.139 | + | 1550.43i | 0.856317 | + | 1.48318i | 0.875418 | + | 0.483367i | \(0.160586\pi\) |
−0.0191010 | + | 0.999818i | \(0.506080\pi\) | |||||||
\(104\) | −324.603 | − | 562.229i | −0.306057 | − | 0.530107i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −218.387 | + | 378.258i | −0.200110 | + | 0.346601i | ||||
\(107\) | 2007.30 | 1.81358 | 0.906788 | − | 0.421587i | \(-0.138527\pi\) | ||||
0.906788 | + | 0.421587i | \(0.138527\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −211.654 | −0.185989 | −0.0929945 | − | 0.995667i | \(-0.529644\pi\) | ||||
−0.0929945 | + | 0.995667i | \(0.529644\pi\) | |||||||
\(110\) | 628.554 | − | 1088.69i | 0.544821 | − | 0.943657i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1015.11 | + | 1758.22i | 0.856418 | + | 1.48336i | ||||
\(113\) | 0.972457 | + | 1.68434i | 0.000809567 | + | 0.00140221i | 0.866430 | − | 0.499299i | \(-0.166409\pi\) |
−0.865620 | + | 0.500701i | \(0.833076\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −204.942 | + | 354.970i | −0.166182 | + | 0.287836i | ||||
\(116\) | 1089.71 | 0.872219 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −602.835 | −0.470300 | ||||||||
\(119\) | −423.693 | + | 733.858i | −0.326386 | + | 0.565316i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1880.35 | − | 3256.86i | −1.41273 | − | 2.44693i | ||||
\(122\) | 139.951 | + | 242.402i | 0.103857 | + | 0.179886i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −491.551 | + | 851.392i | −0.355989 | + | 0.616590i | ||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1178.02 | −0.823089 | −0.411544 | − | 0.911390i | \(-0.635011\pi\) | ||||
−0.411544 | + | 0.911390i | \(0.635011\pi\) | |||||||
\(128\) | −727.272 | + | 1259.67i | −0.502206 | + | 0.869846i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −452.709 | − | 784.116i | −0.305425 | − | 0.529012i | ||||
\(131\) | 260.609 | + | 451.388i | 0.173813 | + | 0.301053i | 0.939750 | − | 0.341863i | \(-0.111058\pi\) |
−0.765937 | + | 0.642916i | \(0.777725\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1441.66 | + | 2497.03i | −0.939910 | + | 1.62797i | ||||
\(134\) | −2154.63 | −1.38904 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −420.889 | −0.265374 | ||||||||
\(137\) | −224.766 | + | 389.306i | −0.140168 | + | 0.242778i | −0.927560 | − | 0.373675i | \(-0.878098\pi\) |
0.787392 | + | 0.616453i | \(0.211431\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1172.72 | + | 2031.22i | 0.715605 | + | 1.23946i | 0.962726 | + | 0.270480i | \(0.0871823\pi\) |
−0.247121 | + | 0.968985i | \(0.579484\pi\) | |||||||
\(140\) | 280.704 | + | 486.193i | 0.169456 | + | 0.293506i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 900.427 | − | 1559.59i | 0.532128 | − | 0.921673i | ||||
\(143\) | −3667.24 | −2.14455 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1234.14 | −0.706824 | ||||||||
\(146\) | 722.333 | − | 1251.12i | 0.409457 | − | 0.709200i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −49.4268 | − | 85.6098i | −0.0274518 | − | 0.0475478i | ||||
\(149\) | −634.691 | − | 1099.32i | −0.348966 | − | 0.604427i | 0.637100 | − | 0.770781i | \(-0.280134\pi\) |
−0.986066 | + | 0.166354i | \(0.946800\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1079.16 | + | 1869.16i | −0.581594 | + | 1.00735i | 0.413697 | + | 0.910415i | \(0.364237\pi\) |
−0.995291 | + | 0.0969350i | \(0.969096\pi\) | |||||||
\(152\) | −1432.12 | −0.764213 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6394.27 | 3.34588 | ||||||||
\(155\) | 556.698 | − | 964.228i | 0.288484 | − | 0.499669i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1171.65 | + | 2029.36i | 0.595593 | + | 1.03160i | 0.993463 | + | 0.114156i | \(0.0364164\pi\) |
−0.397869 | + | 0.917442i | \(0.630250\pi\) | |||||||
\(158\) | 1398.11 | + | 2421.60i | 0.703972 | + | 1.21932i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −450.538 | + | 780.354i | −0.222613 | + | 0.385578i | ||||
\(161\) | −2084.87 | −1.02056 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3399.94 | 1.63376 | 0.816882 | − | 0.576804i | \(-0.195700\pi\) | ||||
0.816882 | + | 0.576804i | \(0.195700\pi\) | |||||||
\(164\) | −958.528 | + | 1660.22i | −0.456393 | + | 0.790496i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 475.812 | + | 824.130i | 0.222471 | + | 0.385331i | ||||
\(167\) | −904.608 | − | 1566.83i | −0.419166 | − | 0.726017i | 0.576690 | − | 0.816963i | \(-0.304344\pi\) |
−0.995856 | + | 0.0909465i | \(0.971011\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −222.146 | + | 384.769i | −0.101113 | + | 0.175134i | ||||
\(170\) | −586.995 | −0.264826 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1045.66 | −0.463553 | ||||||||
\(173\) | −663.704 | + | 1149.57i | −0.291679 | + | 0.505203i | −0.974207 | − | 0.225657i | \(-0.927547\pi\) |
0.682528 | + | 0.730860i | \(0.260881\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −317.906 | − | 550.629i | −0.137322 | − | 0.237849i | ||||
\(176\) | 2848.10 | + | 4933.06i | 1.21980 | + | 2.11275i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 312.531 | − | 541.320i | 0.131602 | − | 0.227942i | ||||
\(179\) | 448.734 | 0.187374 | 0.0936871 | − | 0.995602i | \(-0.470135\pi\) | ||||
0.0936871 | + | 0.995602i | \(0.470135\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3450.55 | −1.41700 | −0.708502 | − | 0.705709i | \(-0.750629\pi\) | ||||
−0.708502 | + | 0.705709i | \(0.750629\pi\) | |||||||
\(182\) | 2302.70 | − | 3988.40i | 0.937845 | − | 1.62439i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −517.768 | − | 896.800i | −0.207448 | − | 0.359310i | ||||
\(185\) | 55.9775 | + | 96.9559i | 0.0222462 | + | 0.0385315i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1188.76 | + | 2058.99i | −0.464870 | + | 0.805179i | ||||
\(188\) | 476.736 | 0.184944 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1997.31 | −0.762634 | ||||||||
\(191\) | −796.047 | + | 1378.79i | −0.301570 | + | 0.522335i | −0.976492 | − | 0.215554i | \(-0.930844\pi\) |
0.674922 | + | 0.737890i | \(0.264177\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −221.650 | − | 383.908i | −0.0826668 | − | 0.143183i | 0.821728 | − | 0.569880i | \(-0.193010\pi\) |
−0.904395 | + | 0.426697i | \(0.859677\pi\) | |||||||
\(194\) | 1553.61 | + | 2690.93i | 0.574961 | + | 0.995862i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −670.644 | + | 1161.59i | −0.244404 | + | 0.423320i | ||||
\(197\) | 208.992 | 0.0755839 | 0.0377919 | − | 0.999286i | \(-0.487968\pi\) | ||||
0.0377919 | + | 0.999286i | \(0.487968\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −479.916 | −0.170957 | −0.0854783 | − | 0.996340i | \(-0.527242\pi\) | ||||
−0.0854783 | + | 0.996340i | \(0.527242\pi\) | |||||||
\(200\) | 157.901 | − | 273.492i | 0.0558264 | − | 0.0966941i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1807.60 | + | 3130.86i | 0.629617 | + | 1.09053i | ||||
\(203\) | −3138.71 | − | 5436.41i | −1.08519 | − | 1.87961i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1085.56 | − | 1880.25i | 0.369849 | − | 0.640597i | ||||
\(206\) | −6308.00 | −2.13349 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4102.63 | 1.36763 | ||||||||
\(209\) | −4044.89 | + | 7005.95i | −1.33871 | + | 2.31872i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1316.07 | + | 2279.50i | 0.429393 | + | 0.743731i | 0.996819 | − | 0.0796934i | \(-0.0253941\pi\) |
−0.567426 | + | 0.823424i | \(0.692061\pi\) | |||||||
\(212\) | −273.638 | − | 473.954i | −0.0886486 | − | 0.153544i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3536.33 | + | 6125.10i | −1.12962 | + | 1.95656i | ||||
\(215\) | 1184.25 | 0.375651 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5663.28 | 1.77165 | ||||||||
\(218\) | 372.879 | − | 645.846i | 0.115847 | − | 0.200652i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 787.573 | + | 1364.12i | 0.241355 | + | 0.418040i | ||||
\(221\) | 856.192 | + | 1482.97i | 0.260605 | + | 0.451381i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1676.61 | + | 2903.97i | −0.503471 | + | 0.872038i | 0.496521 | + | 0.868025i | \(0.334611\pi\) |
−0.999992 | + | 0.00401278i | \(0.998723\pi\) | |||||||
\(224\) | −4583.31 | −1.36712 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.85286 | −0.00201701 | ||||||||
\(227\) | 345.382 | − | 598.219i | 0.100986 | − | 0.174913i | −0.811105 | − | 0.584900i | \(-0.801134\pi\) |
0.912091 | + | 0.409988i | \(0.134467\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 334.066 | + | 578.619i | 0.0964003 | + | 0.166970i | 0.910192 | − | 0.414186i | \(-0.135934\pi\) |
−0.813792 | + | 0.581156i | \(0.802600\pi\) | |||||||
\(230\) | −722.108 | − | 1250.73i | −0.207019 | − | 0.358567i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1558.97 | − | 2700.21i | 0.441170 | − | 0.764128i | ||||
\(233\) | 940.537 | 0.264449 | 0.132225 | − | 0.991220i | \(-0.457788\pi\) | ||||
0.132225 | + | 0.991220i | \(0.457788\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −539.919 | −0.149874 | ||||||||
\(236\) | 377.673 | − | 654.149i | 0.104171 | − | 0.180430i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1492.87 | − | 2585.73i | −0.406591 | − | 0.704236i | ||||
\(239\) | 553.702 | + | 959.039i | 0.149858 | + | 0.259561i | 0.931175 | − | 0.364573i | \(-0.118785\pi\) |
−0.781317 | + | 0.624134i | \(0.785452\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −614.431 | + | 1064.23i | −0.164228 | + | 0.284451i | −0.936381 | − | 0.350985i | \(-0.885847\pi\) |
0.772153 | + | 0.635437i | \(0.219180\pi\) | |||||||
\(242\) | 13250.7 | 3.51979 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −350.715 | −0.0920172 | ||||||||
\(245\) | 759.526 | − | 1315.54i | 0.198058 | − | 0.343047i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2913.29 | + | 5045.96i | 0.750478 | + | 1.29987i | ||||
\(248\) | 1406.45 | + | 2436.04i | 0.360119 | + | 0.623745i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 220.217 | − | 381.427i | 0.0557111 | − | 0.0964944i | ||||
\(251\) | −738.480 | −0.185707 | −0.0928534 | − | 0.995680i | \(-0.529599\pi\) | ||||
−0.0928534 | + | 0.995680i | \(0.529599\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5849.54 | −1.45359 | ||||||||
\(254\) | 2075.36 | − | 3594.63i | 0.512676 | − | 0.887981i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2547.97 | − | 4413.21i | −0.622062 | − | 1.07744i | ||||
\(257\) | 3156.28 | + | 5466.84i | 0.766084 | + | 1.32690i | 0.939672 | + | 0.342078i | \(0.111131\pi\) |
−0.173588 | + | 0.984818i | \(0.555536\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −284.729 | + | 493.165i | −0.0683097 | + | 0.118316i | ||||
\(260\) | 1134.48 | 0.270606 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1836.50 | −0.433051 | ||||||||
\(263\) | 2996.81 | − | 5190.62i | 0.702628 | − | 1.21699i | −0.264913 | − | 0.964272i | \(-0.585343\pi\) |
0.967541 | − | 0.252715i | \(-0.0813234\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 309.903 | + | 536.768i | 0.0718385 | + | 0.124428i | ||||
\(266\) | −5079.66 | − | 8798.24i | −1.17088 | − | 2.02802i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1349.86 | − | 2338.03i | 0.307672 | − | 0.532903i | ||||
\(269\) | 1749.70 | 0.396584 | 0.198292 | − | 0.980143i | \(-0.436461\pi\) | ||||
0.198292 | + | 0.980143i | \(0.436461\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1931.68 | −0.432994 | −0.216497 | − | 0.976283i | \(-0.569463\pi\) | ||||
−0.216497 | + | 0.976283i | \(0.569463\pi\) | |||||||
\(272\) | 1329.90 | − | 2303.45i | 0.296459 | − | 0.513482i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −791.957 | − | 1371.71i | −0.174613 | − | 0.302438i | ||||
\(275\) | −891.952 | − | 1544.91i | −0.195588 | − | 0.338768i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1895.77 | − | 3283.58i | 0.411213 | − | 0.712242i | −0.583809 | − | 0.811891i | \(-0.698438\pi\) |
0.995023 | + | 0.0996484i | \(0.0317718\pi\) | |||||||
\(278\) | −8264.13 | −1.78291 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1606.32 | 0.342843 | ||||||||
\(281\) | 2244.68 | − | 3887.90i | 0.476536 | − | 0.825384i | −0.523103 | − | 0.852269i | \(-0.675226\pi\) |
0.999639 | + | 0.0268857i | \(0.00855902\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1566.93 | − | 2714.00i | −0.329132 | − | 0.570073i | 0.653208 | − | 0.757179i | \(-0.273423\pi\) |
−0.982340 | + | 0.187105i | \(0.940089\pi\) | |||||||
\(284\) | 1128.23 | + | 1954.15i | 0.235732 | + | 0.408300i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6460.72 | − | 11190.3i | 1.33577 | − | 2.31362i | ||||
\(287\) | 11043.4 | 2.27133 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3802.84 | −0.774036 | ||||||||
\(290\) | 2174.22 | − | 3765.87i | 0.440258 | − | 0.762550i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 905.077 | + | 1567.64i | 0.181389 | + | 0.314175i | ||||
\(293\) | 1398.75 | + | 2422.71i | 0.278894 | + | 0.483058i | 0.971110 | − | 0.238632i | \(-0.0766990\pi\) |
−0.692216 | + | 0.721690i | \(0.743366\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −427.727 | + | 740.845i | −0.0844178 | + | 0.146216i | ||||
\(296\) | −282.845 | −0.0555406 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4472.64 | 0.869439 | ||||||||
\(299\) | −2106.54 | + | 3648.63i | −0.407438 | + | 0.705704i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3011.83 | + | 5216.65i | 0.576742 | + | 0.998946i | ||||
\(302\) | −3802.39 | − | 6585.93i | −0.724513 | − | 1.25489i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4525.12 | − | 7837.73i | 0.853728 | − | 1.47870i | ||||
\(305\) | 397.196 | 0.0745684 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6839.91 | −1.27158 | −0.635789 | − | 0.771863i | \(-0.719325\pi\) | ||||
−0.635789 | + | 0.771863i | \(0.719325\pi\) | |||||||
\(308\) | −4005.98 | + | 6938.57i | −0.741111 | + | 1.28364i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1961.51 | + | 3397.44i | 0.359375 | + | 0.622456i | ||||
\(311\) | 1209.70 | + | 2095.27i | 0.220566 | + | 0.382032i | 0.954980 | − | 0.296670i | \(-0.0958762\pi\) |
−0.734414 | + | 0.678702i | \(0.762543\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1951.59 | + | 3380.25i | −0.352429 | + | 0.610425i | −0.986674 | − | 0.162707i | \(-0.947978\pi\) |
0.634245 | + | 0.773132i | \(0.281311\pi\) | |||||||
\(314\) | −8256.59 | −1.48391 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3503.64 | −0.623718 | ||||||||
\(317\) | 4947.36 | − | 8569.09i | 0.876567 | − | 1.51826i | 0.0214825 | − | 0.999769i | \(-0.493161\pi\) |
0.855084 | − | 0.518489i | \(-0.173505\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8806.32 | − | 15253.0i | −1.54564 | − | 2.67713i | ||||
\(320\) | 9.09863 | + | 15.7593i | 0.00158946 | + | 0.00275303i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3673.00 | − | 6361.81i | 0.635677 | − | 1.10102i | ||||
\(323\) | 3777.44 | 0.650720 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1284.84 | −0.219292 | ||||||||
\(326\) | −5989.80 | + | 10374.6i | −1.01762 | + | 1.76257i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2742.58 | + | 4750.29i | 0.461688 | + | 0.799668i | ||||
\(329\) | −1373.15 | − | 2378.36i | −0.230103 | − | 0.398551i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2081.52 | + | 3605.30i | −0.345651 | + | 0.598686i | −0.985472 | − | 0.169839i | \(-0.945675\pi\) |
0.639820 | + | 0.768524i | \(0.279009\pi\) | |||||||
\(332\) | −1192.38 | −0.197109 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6374.73 | 1.04434 | ||||||||
\(335\) | −1528.76 | + | 2647.90i | −0.249329 | + | 0.431851i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4852.47 | − | 8404.72i | −0.784364 | − | 1.35856i | −0.929378 | − | 0.369129i | \(-0.879656\pi\) |
0.145014 | − | 0.989430i | \(-0.453677\pi\) | |||||||
\(338\) | −782.727 | − | 1355.72i | −0.125961 | − | 0.218170i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 367.750 | − | 636.961i | 0.0586589 | − | 0.101600i | ||||
\(341\) | 15889.5 | 2.52336 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −996.691 | −0.156899 | ||||||||
\(344\) | −1495.95 | + | 2591.06i | −0.234466 | + | 0.406107i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2338.55 | − | 4050.48i | −0.363355 | − | 0.629350i | ||||
\(347\) | −2716.19 | − | 4704.58i | −0.420210 | − | 0.727825i | 0.575750 | − | 0.817626i | \(-0.304710\pi\) |
−0.995960 | + | 0.0898011i | \(0.971377\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5285.97 | + | 9155.57i | −0.810749 | + | 1.40426i | 0.101592 | + | 0.994826i | \(0.467607\pi\) |
−0.912341 | + | 0.409432i | \(0.865727\pi\) | |||||||
\(350\) | 2240.27 | 0.342135 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −12859.5 | −1.94719 | ||||||||
\(353\) | −4821.49 | + | 8351.07i | −0.726975 | + | 1.25916i | 0.231181 | + | 0.972911i | \(0.425741\pi\) |
−0.958156 | + | 0.286247i | \(0.907592\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1277.75 | − | 2213.13i | −0.191031 | − | 0.330876i | ||||
\(356\) | 391.599 | + | 678.270i | 0.0582998 | + | 0.100978i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −790.552 | + | 1369.28i | −0.116709 | + | 0.202147i | ||||
\(359\) | 3002.18 | 0.441362 | 0.220681 | − | 0.975346i | \(-0.429172\pi\) | ||||
0.220681 | + | 0.975346i | \(0.429172\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5994.17 | 0.873913 | ||||||||
\(362\) | 6078.97 | − | 10529.1i | 0.882607 | − | 1.52872i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2885.27 | + | 4997.43i | 0.415465 | + | 0.719606i | ||||
\(365\) | −1025.03 | − | 1775.40i | −0.146993 | − | 0.254599i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 574.638 | − | 995.302i | 0.0817326 | − | 0.141565i | −0.822262 | − | 0.569110i | \(-0.807288\pi\) |
0.903994 | + | 0.427545i | \(0.140621\pi\) | |||||||
\(368\) | 6544.03 | 0.926986 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −394.471 | −0.0554258 | ||||||||
\(371\) | −1576.32 | + | 2730.27i | −0.220589 | + | 0.382071i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 256.607 | + | 444.456i | 0.0356209 | + | 0.0616972i | 0.883286 | − | 0.468834i | \(-0.155326\pi\) |
−0.847665 | + | 0.530531i | \(0.821992\pi\) | |||||||
\(374\) | −4188.57 | − | 7254.81i | −0.579106 | − | 1.00304i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 682.029 | − | 1181.31i | 0.0935451 | − | 0.162025i | ||||
\(377\) | −12685.3 | −1.73296 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12560.0 | 1.70228 | 0.851138 | − | 0.524942i | \(-0.175913\pi\) | ||||
0.851138 | + | 0.524942i | \(0.175913\pi\) | |||||||
\(380\) | 1251.31 | − | 2167.33i | 0.168923 | − | 0.292583i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2804.85 | − | 4858.15i | −0.375677 | − | 0.650692i | ||||
\(383\) | −136.995 | − | 237.282i | −0.0182771 | − | 0.0316568i | 0.856742 | − | 0.515745i | \(-0.172485\pi\) |
−0.875019 | + | 0.484088i | \(0.839151\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4536.91 | − | 7858.15i | 0.600577 | − | 1.04023i | ||||
\(386\) | 1561.95 | 0.205962 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3893.31 | −0.509415 | ||||||||
\(389\) | −3423.21 | + | 5929.18i | −0.446179 | + | 0.772805i | −0.998134 | − | 0.0610691i | \(-0.980549\pi\) |
0.551954 | + | 0.833874i | \(0.313882\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1365.69 | + | 2365.45i | 0.176640 | + | 0.305949i | ||||
\(392\) | 1918.88 | + | 3323.59i | 0.247239 | + | 0.428231i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −368.188 | + | 637.721i | −0.0470788 | + | 0.0815429i | ||||
\(395\) | 3967.98 | 0.505445 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12117.5 | −1.53189 | −0.765943 | − | 0.642909i | \(-0.777727\pi\) | ||||
−0.765943 | + | 0.642909i | \(0.777727\pi\) | |||||||
\(398\) | 845.486 | − | 1464.43i | 0.106483 | − | 0.184435i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 997.848 | + | 1728.32i | 0.124731 | + | 0.216041i | ||||
\(401\) | −1508.40 | − | 2612.63i | −0.187845 | − | 0.325358i | 0.756686 | − | 0.653778i | \(-0.226817\pi\) |
−0.944532 | + | 0.328421i | \(0.893484\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5722.13 | − | 9911.02i | 0.707294 | − | 1.22507i | ||||
\(404\) | −4529.82 | −0.557839 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 22118.4 | 2.70373 | ||||||||
\(407\) | −798.868 | + | 1383.68i | −0.0972933 | + | 0.168517i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3267.56 | − | 5659.59i | −0.395038 | − | 0.684226i | 0.598068 | − | 0.801445i | \(-0.295935\pi\) |
−0.993106 | + | 0.117219i | \(0.962602\pi\) | |||||||
\(410\) | 3824.96 | + | 6625.02i | 0.460735 | + | 0.798016i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3951.93 | − | 6844.95i | 0.472568 | − | 0.818511i | ||||
\(413\) | −4351.26 | −0.518430 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1350.40 | 0.159732 | ||||||||
\(416\) | −4630.94 | + | 8021.03i | −0.545795 | + | 0.945344i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −14252.1 | − | 24685.3i | −1.66768 | − | 2.88851i | ||||
\(419\) | 3574.22 | + | 6190.74i | 0.416736 | + | 0.721807i | 0.995609 | − | 0.0936102i | \(-0.0298407\pi\) |
−0.578873 | + | 0.815418i | \(0.696507\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7400.77 | + | 12818.5i | −0.856749 | + | 1.48393i | 0.0182632 | + | 0.999833i | \(0.494186\pi\) |
−0.875013 | + | 0.484100i | \(0.839147\pi\) | |||||||
\(422\) | −9274.28 | −1.06982 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1565.89 | −0.179354 | ||||||||
\(425\) | −416.489 | + | 721.379i | −0.0475357 | + | 0.0823342i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1010.17 | + | 1749.66i | 0.114486 | + | 0.198295i | ||||
\(428\) | −4430.99 | − | 7674.70i | −0.500420 | − | 0.866754i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2086.33 | + | 3613.64i | −0.233981 | + | 0.405268i | ||||
\(431\) | −2284.19 | −0.255280 | −0.127640 | − | 0.991821i | \(-0.540740\pi\) | ||||
−0.127640 | + | 0.991821i | \(0.540740\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5529.26 | 0.613670 | 0.306835 | − | 0.951763i | \(-0.400730\pi\) | ||||
0.306835 | + | 0.951763i | \(0.400730\pi\) | |||||||
\(434\) | −9977.21 | + | 17281.0i | −1.10351 | + | 1.91133i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 467.214 | + | 809.239i | 0.0513200 | + | 0.0888888i | ||||
\(437\) | 4646.93 | + | 8048.71i | 0.508679 | + | 0.881057i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5930.81 | − | 10272.5i | 0.644788 | − | 1.11681i | −0.339562 | − | 0.940584i | \(-0.610279\pi\) |
0.984350 | − | 0.176223i | \(-0.0563878\pi\) | |||||||
\(440\) | 4506.88 | 0.488311 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6033.55 | −0.649291 | ||||||||
\(443\) | −7646.81 | + | 13244.7i | −0.820115 | + | 1.42048i | 0.0854817 | + | 0.996340i | \(0.472757\pi\) |
−0.905596 | + | 0.424141i | \(0.860576\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −443.499 | − | 768.162i | −0.0472446 | − | 0.0818301i | ||||
\(446\) | −5907.49 | − | 10232.1i | −0.627193 | − | 1.08633i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −46.2801 | + | 80.1595i | −0.00488065 | + | 0.00845353i | ||||
\(449\) | −12998.8 | −1.36626 | −0.683129 | − | 0.730297i | \(-0.739381\pi\) | ||||
−0.683129 | + | 0.730297i | \(0.739381\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30984.6 | 3.23506 | ||||||||
\(452\) | 4.29329 | − | 7.43619i | 0.000446768 | − | 0.000773825i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1216.95 | + | 2107.81i | 0.125802 | + | 0.217895i | ||||
\(455\) | −3267.66 | − | 5659.75i | −0.336682 | − | 0.583150i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7155.97 | + | 12394.5i | −0.732477 | + | 1.26869i | 0.223344 | + | 0.974740i | \(0.428303\pi\) |
−0.955821 | + | 0.293948i | \(0.905031\pi\) | |||||||
\(458\) | −2354.14 | −0.240179 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1809.59 | 0.183419 | ||||||||
\(461\) | 2145.17 | − | 3715.54i | 0.216725 | − | 0.375379i | −0.737080 | − | 0.675806i | \(-0.763796\pi\) |
0.953805 | + | 0.300427i | \(0.0971290\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7255.14 | + | 12566.3i | 0.728240 | + | 1.26135i | 0.957626 | + | 0.288013i | \(0.0929947\pi\) |
−0.229386 | + | 0.973335i | \(0.573672\pi\) | |||||||
\(464\) | 9851.85 | + | 17063.9i | 0.985691 | + | 1.70727i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1656.98 | + | 2869.97i | −0.164717 | + | 0.285298i | ||||
\(467\) | 7393.05 | 0.732569 | 0.366285 | − | 0.930503i | \(-0.380630\pi\) | ||||
0.366285 | + | 0.930503i | \(0.380630\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15552.1 | −1.53119 | ||||||||
\(470\) | 951.195 | − | 1647.52i | 0.0933518 | − | 0.161690i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1080.62 | − | 1871.68i | −0.105380 | − | 0.182524i | ||||
\(473\) | 8450.34 | + | 14636.4i | 0.821452 | + | 1.42280i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1417.15 | + | 2454.57i | −0.136891 | + | 0.237102i | ||||
\(476\) | 3741.11 | 0.360239 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3901.91 | −0.373366 | ||||||||
\(479\) | 6754.93 | − | 11699.9i | 0.644344 | − | 1.11604i | −0.340109 | − | 0.940386i | \(-0.610464\pi\) |
0.984453 | − | 0.175650i | \(-0.0562027\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 575.376 | + | 996.580i | 0.0545424 | + | 0.0944702i | ||||
\(482\) | −2164.93 | − | 3749.77i | −0.204585 | − | 0.354352i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8301.53 | + | 14378.7i | −0.779632 | + | 1.35036i | ||||
\(485\) | 4409.30 | 0.412817 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11140.0 | −1.03655 | −0.518277 | − | 0.855213i | \(-0.673427\pi\) | ||||
−0.518277 | + | 0.855213i | \(0.673427\pi\) | |||||||
\(488\) | −501.740 | + | 869.040i | −0.0465425 | + | 0.0806139i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2676.17 | + | 4635.26i | 0.246729 | + | 0.427347i | ||||
\(491\) | 1006.37 | + | 1743.09i | 0.0924988 | + | 0.160213i | 0.908562 | − | 0.417750i | \(-0.137181\pi\) |
−0.816063 | + | 0.577963i | \(0.803848\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4112.03 | + | 7122.24i | −0.375652 | + | 0.650648i | ||||
\(494\) | −20529.8 | −1.86980 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −17776.0 | −1.60920 | ||||||||
\(497\) | 6499.29 | − | 11257.1i | 0.586585 | − | 1.01600i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3676.49 | − | 6367.87i | −0.329824 | − | 0.571272i | 0.652653 | − | 0.757657i | \(-0.273656\pi\) |
−0.982477 | + | 0.186385i | \(0.940323\pi\) | |||||||
\(500\) | 275.930 | + | 477.925i | 0.0246800 | + | 0.0427469i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1301.01 | − | 2253.41i | 0.115671 | − | 0.200348i | ||||
\(503\) | −16898.3 | −1.49793 | −0.748965 | − | 0.662609i | \(-0.769449\pi\) | ||||
−0.748965 | + | 0.662609i | \(0.769449\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5130.17 | 0.452059 | ||||||||
\(506\) | 10305.4 | − | 17849.4i | 0.905394 | − | 1.56819i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2600.41 | + | 4504.04i | 0.227115 | + | 0.393375i | ||||
\(509\) | −9679.31 | − | 16765.1i | −0.842884 | − | 1.45992i | −0.887446 | − | 0.460911i | \(-0.847523\pi\) |
0.0445620 | − | 0.999007i | \(-0.485811\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5213.80 | − | 9030.57i | 0.451360 | − | 0.781779i | ||||
\(512\) | 6319.06 | 0.545440 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −22242.2 | −1.90868 | ||||||||
\(515\) | −4475.69 | + | 7752.13i | −0.382957 | + | 0.663300i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3852.65 | − | 6672.99i | −0.327736 | − | 0.567655i | ||||
\(518\) | −1003.24 | − | 1737.66i | −0.0850959 | − | 0.147390i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1623.02 | − | 2811.15i | 0.136873 | − | 0.237071i | ||||
\(521\) | 146.772 | 0.0123420 | 0.00617100 | − | 0.999981i | \(-0.498036\pi\) | ||||
0.00617100 | + | 0.999981i | \(0.498036\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2872.03 | −0.240125 | −0.120062 | − | 0.992766i | \(-0.538309\pi\) | ||||
−0.120062 | + | 0.992766i | \(0.538309\pi\) | |||||||
\(524\) | 1150.56 | − | 1992.83i | 0.0959205 | − | 0.166139i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10559.2 | + | 18289.0i | 0.875289 | + | 1.51605i | ||||
\(527\) | −3709.73 | − | 6425.44i | −0.306638 | − | 0.531113i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2723.41 | − | 4717.08i | 0.223836 | − | 0.387695i | ||||
\(530\) | −2183.87 | −0.178984 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 12729.5 | 1.03740 | ||||||||
\(533\) | 11158.2 | − | 19326.5i | 0.906781 | − | 1.57059i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5018.24 | + | 8691.84i | 0.405528 | + | 0.702395i | ||||
\(536\) | −3862.29 | − | 6689.69i | −0.311242 | − | 0.539087i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3082.51 | + | 5339.07i | −0.247020 | + | 0.427851i | ||||
\(539\) | 21678.7 | 1.73241 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3810.28 | −0.302804 | −0.151402 | − | 0.988472i | \(-0.548379\pi\) | ||||
−0.151402 | + | 0.988472i | \(0.548379\pi\) | |||||||
\(542\) | 3403.12 | − | 5894.38i | 0.269698 | − | 0.467131i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3002.30 | + | 5200.14i | 0.236622 | + | 0.409842i | ||||
\(545\) | −529.135 | − | 916.490i | −0.0415884 | − | 0.0720332i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2972.79 | + | 5149.03i | −0.232372 | + | 0.402480i | −0.958506 | − | 0.285073i | \(-0.907982\pi\) |
0.726134 | + | 0.687554i | \(0.241315\pi\) | |||||||
\(548\) | 1984.63 | 0.154707 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6285.54 | 0.487303 | ||||||||
\(551\) | −13991.6 | + | 24234.2i | −1.08178 | + | 1.87371i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10091.6 | + | 17479.1i | 0.776016 | + | 1.34410i | ||||
\(554\) | 6679.72 | + | 11569.6i | 0.512264 | + | 0.887267i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5177.44 | − | 8967.59i | 0.394914 | − | 0.684012i | ||||
\(557\) | 10872.2 | 0.827059 | 0.413530 | − | 0.910491i | \(-0.364296\pi\) | ||||
0.413530 | + | 0.910491i | \(0.364296\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12172.5 | 0.921007 | ||||||||
\(560\) | −5075.55 | + | 8791.11i | −0.383002 | + | 0.663379i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7909.08 | + | 13698.9i | 0.593638 | + | 1.02821i | ||||
\(563\) | 6787.54 | + | 11756.4i | 0.508100 | + | 0.880056i | 0.999956 | + | 0.00937903i | \(0.00298548\pi\) |
−0.491856 | + | 0.870677i | \(0.663681\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.86228 | + | 8.42172i | −0.000362049 | + | 0.000627088i | ||||
\(566\) | 11042.1 | 0.820024 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6456.27 | 0.476935 | ||||||||
\(569\) | 10321.3 | − | 17877.0i | 0.760442 | − | 1.31712i | −0.182181 | − | 0.983265i | \(-0.558316\pi\) |
0.942623 | − | 0.333859i | \(-0.108351\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1365.39 | + | 2364.92i | 0.100069 | + | 0.173325i | 0.911713 | − | 0.410828i | \(-0.134760\pi\) |
−0.811644 | + | 0.584153i | \(0.801427\pi\) | |||||||
\(572\) | 8095.23 | + | 14021.3i | 0.591745 | + | 1.02493i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −19455.6 | + | 33698.1i | −1.41474 | + | 2.45040i | ||||
\(575\) | −2049.42 | −0.148638 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21953.4 | 1.58394 | 0.791970 | − | 0.610560i | \(-0.209055\pi\) | ||||
0.791970 | + | 0.610560i | \(0.209055\pi\) | |||||||
\(578\) | 6699.61 | − | 11604.1i | 0.482123 | − | 0.835061i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2724.28 | + | 4718.60i | 0.195034 | + | 0.337809i | ||||
\(581\) | 3434.41 | + | 5948.57i | 0.245238 | + | 0.424765i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4422.70 | + | 7660.34i | −0.314185 | + | 0.544184i | ||||
\(584\) | 5179.29 | 0.366988 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9856.92 | −0.694856 | ||||||||
\(587\) | 5527.67 | − | 9574.21i | 0.388674 | − | 0.673203i | −0.603598 | − | 0.797289i | \(-0.706267\pi\) |
0.992271 | + | 0.124086i | \(0.0396000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12622.8 | − | 21863.3i | −0.883042 | − | 1.52947i | ||||
\(590\) | −1507.09 | − | 2610.35i | −0.105162 | − | 0.182147i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 893.713 | − | 1547.96i | 0.0620462 | − | 0.107467i | ||||
\(593\) | −16538.0 | −1.14525 | −0.572625 | − | 0.819817i | \(-0.694075\pi\) | ||||
−0.572625 | + | 0.819817i | \(0.694075\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4236.93 | −0.291928 | ||||||||
\(596\) | −2802.09 | + | 4853.36i | −0.192581 | + | 0.333559i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7422.33 | − | 12855.8i | −0.507561 | − | 0.879122i | ||||
\(599\) | −3201.79 | − | 5545.67i | −0.218400 | − | 0.378280i | 0.735919 | − | 0.677070i | \(-0.236750\pi\) |
−0.954319 | + | 0.298790i | \(0.903417\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7105.18 | − | 12306.5i | 0.482240 | − | 0.835264i | −0.517552 | − | 0.855652i | \(-0.673157\pi\) |
0.999792 | + | 0.0203874i | \(0.00648995\pi\) | |||||||
\(602\) | −21224.3 | −1.43694 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9528.72 | 0.641917 | ||||||||
\(605\) | 9401.75 | − | 16284.3i | 0.631794 | − | 1.09430i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4457.86 | + | 7721.24i | 0.298087 | + | 0.516302i | 0.975698 | − | 0.219118i | \(-0.0703180\pi\) |
−0.677611 | + | 0.735420i | \(0.736985\pi\) | |||||||
\(608\) | 10215.7 | + | 17694.0i | 0.681414 | + | 1.18024i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −699.755 | + | 1212.01i | −0.0464463 | + | 0.0804474i | ||||
\(611\) | −5549.66 | −0.367455 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15372.5 | −1.01287 | −0.506436 | − | 0.862277i | \(-0.669037\pi\) | ||||
−0.506436 | + | 0.862277i | \(0.669037\pi\) | |||||||
\(614\) | 12050.1 | − | 20871.4i | 0.792026 | − | 1.37183i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11462.1 | + | 19852.9i | 0.749710 | + | 1.29854i | ||||
\(617\) | 8663.73 | + | 15006.0i | 0.565298 | + | 0.979124i | 0.997022 | + | 0.0771187i | \(0.0245721\pi\) |
−0.431724 | + | 0.902006i | \(0.642095\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14393.7 | − | 24930.6i | 0.934621 | − | 1.61881i | 0.159313 | − | 0.987228i | \(-0.449072\pi\) |
0.775308 | − | 0.631583i | \(-0.217595\pi\) | |||||||
\(620\) | −4915.51 | −0.318406 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −8524.73 | −0.549535 | ||||||||
\(623\) | 2255.85 | − | 3907.25i | 0.145070 | − | 0.251269i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −6876.38 | − | 11910.2i | −0.439034 | − | 0.760429i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5172.72 | − | 8959.41i | 0.328685 | − | 0.569298i | ||||
\(629\) | 746.047 | 0.0472923 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18091.0 | 1.14135 | 0.570675 | − | 0.821176i | \(-0.306682\pi\) | ||||
0.570675 | + | 0.821176i | \(0.306682\pi\) | |||||||
\(632\) | −5012.38 | + | 8681.70i | −0.315478 | + | 0.546423i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 17431.9 | + | 30193.0i | 1.09197 | + | 1.89135i | ||||
\(635\) | −2945.05 | − | 5100.97i | −0.184048 | − | 0.318781i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7806.94 | − | 13522.0i | 0.485592 | − | 0.841070i | ||||
\(638\) | 62057.7 | 3.85092 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −7272.72 | −0.449187 | ||||||||
\(641\) | 9788.76 | − | 16954.6i | 0.603171 | − | 1.04472i | −0.389167 | − | 0.921167i | \(-0.627237\pi\) |
0.992338 | − | 0.123556i | \(-0.0394297\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14985.9 | + | 25956.3i | 0.919106 | + | 1.59194i | 0.800777 | + | 0.598963i | \(0.204420\pi\) |
0.118329 | + | 0.992974i | \(0.462246\pi\) | |||||||
\(644\) | 4602.23 | + | 7971.30i | 0.281605 | + | 0.487753i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6654.87 | + | 11526.6i | −0.405313 | + | 0.702023i | ||||
\(647\) | 3635.64 | 0.220915 | 0.110457 | − | 0.993881i | \(-0.464768\pi\) | ||||
0.110457 | + | 0.993881i | \(0.464768\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12208.4 | −0.738399 | ||||||||
\(650\) | 2263.55 | − | 3920.58i | 0.136590 | − | 0.236581i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7505.17 | − | 12999.3i | −0.450805 | − | 0.780818i | ||||
\(653\) | −9703.64 | − | 16807.2i | −0.581520 | − | 1.00722i | −0.995299 | − | 0.0968453i | \(-0.969125\pi\) |
0.413779 | − | 0.910377i | \(-0.364209\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1303.04 | + | 2256.94i | −0.0777315 | + | 0.134635i | ||||
\(656\) | −34663.3 | −2.06307 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9676.49 | 0.573296 | ||||||||
\(659\) | −2813.93 | + | 4873.87i | −0.166335 | + | 0.288101i | −0.937129 | − | 0.348984i | \(-0.886527\pi\) |
0.770793 | + | 0.637085i | \(0.219860\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8331.49 | + | 14430.6i | 0.490253 | + | 0.849144i | 0.999937 | − | 0.0112181i | \(-0.00357089\pi\) |
−0.509684 | + | 0.860362i | \(0.670238\pi\) | |||||||
\(662\) | −7334.18 | − | 12703.2i | −0.430591 | − | 0.745805i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1705.84 | + | 2954.60i | −0.0996979 | + | 0.172682i | ||||
\(665\) | −14416.6 | −0.840681 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20234.1 | −1.17461 | ||||||||
\(668\) | −3993.74 | + | 6917.36i | −0.231321 | + | 0.400660i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5386.57 | − | 9329.81i | −0.310599 | − | 0.537973i | ||||
\(671\) | 2834.24 | + | 4909.04i | 0.163062 | + | 0.282431i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6319.38 | − | 10945.5i | 0.361953 | − | 0.626921i | −0.626329 | − | 0.779559i | \(-0.715443\pi\) |
0.988282 | + | 0.152638i | \(0.0487768\pi\) | |||||||
\(674\) | 34195.1 | 1.95422 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1961.50 | 0.111601 | ||||||||
\(677\) | −12658.0 | + | 21924.3i | −0.718591 | + | 1.24464i | 0.242967 | + | 0.970035i | \(0.421879\pi\) |
−0.961558 | + | 0.274602i | \(0.911454\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11213.9 | + | 19423.1i | 0.633802 | + | 1.09778i | ||||
\(680\) | −1052.22 | − | 1822.50i | −0.0593395 | − | 0.102779i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −27993.2 | + | 48485.6i | −1.57172 | + | 2.72230i | ||||
\(683\) | −24818.4 | −1.39041 | −0.695204 | − | 0.718812i | \(-0.744686\pi\) | ||||
−0.695204 | + | 0.718812i | \(0.744686\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2247.66 | −0.125370 | ||||||||
\(686\) | 1755.91 | − | 3041.32i | 0.0977273 | − | 0.169269i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9453.60 | − | 16374.1i | −0.523859 | − | 0.907351i | ||||
\(689\) | 3185.40 | + | 5517.28i | 0.176131 | + | 0.305068i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9978.98 | + | 17284.1i | −0.549375 | + | 0.951546i | 0.448942 | + | 0.893561i | \(0.351801\pi\) |
−0.998317 | + | 0.0579852i | \(0.981532\pi\) | |||||||
\(692\) | 5860.35 | 0.321932 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19140.9 | 1.04694 | ||||||||
\(695\) | −5863.62 | + | 10156.1i | −0.320028 | + | 0.554305i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7233.99 | − | 12529.6i | −0.393124 | − | 0.680910i | ||||
\(698\) | −18625.0 | − | 32259.4i | −1.00998 | − | 1.74934i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1403.52 | + | 2430.96i | −0.0757828 | + | 0.131260i | ||||
\(701\) | 5624.21 | 0.303029 | 0.151515 | − | 0.988455i | \(-0.451585\pi\) | ||||
0.151515 | + | 0.988455i | \(0.451585\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2538.51 | 0.136190 | ||||||||
\(704\) | −129.849 | + | 224.904i | −0.00695149 | + | 0.0120403i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16988.4 | − | 29424.8i | −0.905620 | − | 1.56858i | ||||
\(707\) | 13047.3 | + | 22598.6i | 0.694051 | + | 1.20213i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3857.72 | − | 6681.76i | 0.204344 | − | 0.353933i | −0.745580 | − | 0.666416i | \(-0.767827\pi\) |
0.949923 | + | 0.312483i | \(0.101161\pi\) | |||||||
\(710\) | 9004.27 | 0.475950 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2240.92 | 0.117952 | ||||||||
\(713\) | 9127.25 | − | 15808.9i | 0.479408 | − | 0.830360i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9168.11 | − | 15879.6i | −0.479535 | − | 0.830579i | ||||
\(716\) | −990.555 | − | 1715.69i | −0.0517022 | − | 0.0895508i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5289.05 | + | 9160.91i | −0.274910 | + | 0.476159i | ||||
\(719\) | −21647.8 | −1.12285 | −0.561424 | − | 0.827528i | \(-0.689746\pi\) | ||||
−0.561424 | + | 0.827528i | \(0.689746\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −45531.2 | −2.35183 | ||||||||
\(722\) | −10560.2 | + | 18290.7i | −0.544333 | + | 0.942812i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7616.90 | + | 13192.9i | 0.390994 | + | 0.677222i | ||||
\(725\) | −3085.34 | − | 5343.97i | −0.158051 | − | 0.273752i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1535.65 | − | 2659.82i | 0.0783412 | − | 0.135691i | −0.824193 | − | 0.566309i | \(-0.808371\pi\) |
0.902534 | + | 0.430618i | \(0.141704\pi\) | |||||||
\(728\) | 16510.9 | 0.840570 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7223.33 | 0.366229 | ||||||||
\(731\) | 3945.80 | − | 6834.33i | 0.199645 | − | 0.345796i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7326.01 | − | 12689.0i | −0.369157 | − | 0.639399i | 0.620277 | − | 0.784383i | \(-0.287020\pi\) |
−0.989434 | + | 0.144984i | \(0.953687\pi\) | |||||||
\(734\) | 2024.72 | + | 3506.92i | 0.101817 | + | 0.176353i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7386.72 | + | 12794.2i | −0.369943 | + | 0.640760i | ||||
\(737\) | −43634.7 | −2.18087 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17610.9 | 0.876629 | 0.438314 | − | 0.898822i | \(-0.355576\pi\) | ||||
0.438314 | + | 0.898822i | \(0.355576\pi\) | |||||||
\(740\) | 247.134 | − | 428.049i | 0.0122768 | − | 0.0212640i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5554.13 | − | 9620.04i | −0.274796 | − | 0.475960i | ||||
\(743\) | −8394.09 | − | 14539.0i | −0.414468 | − | 0.717879i | 0.580905 | − | 0.813972i | \(-0.302699\pi\) |
−0.995372 | + | 0.0960925i | \(0.969366\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3173.46 | − | 5496.59i | 0.156062 | − | 0.270308i | ||||
\(746\) | −1808.30 | −0.0887485 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10496.5 | 0.513087 | ||||||||
\(749\) | −25525.2 | + | 44211.0i | −1.24522 | + | 2.15679i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11757.1 | − | 20363.9i | −0.571269 | − | 0.989467i | −0.996436 | − | 0.0843523i | \(-0.973118\pi\) |
0.425167 | − | 0.905115i | \(-0.360215\pi\) | |||||||
\(752\) | 4310.05 | + | 7465.23i | 0.209005 | + | 0.362007i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 22348.2 | − | 38708.2i | 1.07941 | − | 1.86959i | ||||
\(755\) | −10791.6 | −0.520193 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24817.4 | 1.19155 | 0.595775 | − | 0.803151i | \(-0.296845\pi\) | ||||
0.595775 | + | 0.803151i | \(0.296845\pi\) | |||||||
\(758\) | −22127.4 | + | 38325.8i | −1.06029 | + | 1.83648i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3580.30 | − | 6201.26i | −0.170883 | − | 0.295978i | ||||
\(761\) | 16258.9 | + | 28161.2i | 0.774485 | + | 1.34145i | 0.935084 | + | 0.354427i | \(0.115324\pi\) |
−0.160599 | + | 0.987020i | \(0.551342\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2691.44 | − | 4661.72i | 0.127702 | − | 0.221187i | ||||
\(764\) | 7028.91 | 0.332850 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 965.398 | 0.0455369 | ||||||||
\(767\) | −4396.48 | + | 7614.93i | −0.206972 | + | 0.358486i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9028.92 | − | 15638.5i | −0.423395 | − | 0.733342i | 0.572874 | − | 0.819644i | \(-0.305829\pi\) |
−0.996269 | + | 0.0863014i | \(0.972495\pi\) | |||||||
\(770\) | 15985.7 | + | 27688.0i | 0.748161 | + | 1.29585i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −978.557 | + | 1694.91i | −0.0456205 | + | 0.0790171i | ||||
\(773\) | −38147.2 | −1.77498 | −0.887491 | − | 0.460825i | \(-0.847553\pi\) | ||||
−0.887491 | + | 0.460825i | \(0.847553\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5566.98 | 0.258028 | ||||||||
\(776\) | −5569.86 | + | 9647.28i | −0.257663 | + | 0.446285i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −12061.6 | − | 20891.3i | −0.555822 | − | 0.962712i | ||||
\(779\) | −24614.5 | − | 42633.5i | −1.13210 | − | 1.96085i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18235.1 | − | 31584.1i | 0.835472 | − | 1.44708i | ||||
\(782\) | −9623.98 | −0.440093 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −24252.5 | −1.10480 | ||||||||
\(785\) | −5858.27 | + | 10146.8i | −0.266357 | + | 0.461345i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2400.88 | + | 4158.44i | 0.108745 | + | 0.188351i | 0.915262 | − | 0.402859i | \(-0.131984\pi\) |
−0.806517 | + | 0.591211i | \(0.798650\pi\) | |||||||
\(788\) | −461.337 | − | 799.059i | −0.0208559 | − | 0.0361235i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6990.55 | + | 12108.0i | −0.314826 | + | 0.545295i | ||||
\(791\) | −49.4640 | −0.00222343 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4082.66 | 0.182824 | ||||||||
\(794\) | 21347.8 | − | 36975.5i | 0.954163 | − | 1.65266i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1059.39 | + | 1834.91i | 0.0471721 | + | 0.0817044i | ||||
\(797\) | −7735.49 | − | 13398.3i | −0.343796 | − | 0.595472i | 0.641338 | − | 0.767258i | \(-0.278379\pi\) |
−0.985134 | + | 0.171786i | \(0.945046\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1798.96 | + | 3115.89i | −0.0796528 | + | 0.137963i | ||||
\(800\) | −4505.38 | −0.199111 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 10629.6 | 0.468012 | ||||||||
\(803\) | 14628.4 | − | 25337.2i | 0.642871 | − | 1.11349i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5212.18 | − | 9027.75i | −0.228205 | − | 0.395263i | ||||
\(806\) | 20161.8 | + | 34921.2i | 0.881102 | + | 1.52611i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6480.47 | + | 11224.5i | −0.282156 | + | 0.488709i | ||||
\(809\) | 17007.6 | 0.739129 | 0.369564 | − | 0.929205i | \(-0.379507\pi\) | ||||
0.369564 | + | 0.929205i | \(0.379507\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7552.52 | −0.327010 | −0.163505 | − | 0.986543i | \(-0.552280\pi\) | ||||
−0.163505 | + | 0.986543i | \(0.552280\pi\) | |||||||
\(812\) | −13857.1 | + | 24001.1i | −0.598876 | + | 1.03728i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2814.79 | − | 4875.36i | −0.121202 | − | 0.209928i | ||||
\(815\) | 8499.84 | + | 14722.2i | 0.365321 | + | 0.632754i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13426.0 | − | 23254.6i | 0.574930 | − | 0.995807i | ||||
\(818\) | 23026.4 | 0.984227 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9585.28 | −0.408210 | ||||||||
\(821\) | 1872.60 | − | 3243.44i | 0.0796031 | − | 0.137877i | −0.823476 | − | 0.567352i | \(-0.807968\pi\) |
0.903079 | + | 0.429475i | \(0.141301\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15010.5 | + | 25999.0i | 0.635764 | + | 1.10118i | 0.986353 | + | 0.164646i | \(0.0526481\pi\) |
−0.350589 | + | 0.936529i | \(0.614019\pi\) | |||||||
\(824\) | −11307.5 | − | 19585.1i | −0.478051 | − | 0.828008i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7665.79 | − | 13277.5i | 0.322914 | − | 0.559303i | ||||
\(827\) | 7918.68 | 0.332962 | 0.166481 | − | 0.986045i | \(-0.446760\pi\) | ||||
0.166481 | + | 0.986045i | \(0.446760\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6976.17 | −0.292271 | −0.146135 | − | 0.989265i | \(-0.546683\pi\) | ||||
−0.146135 | + | 0.989265i | \(0.546683\pi\) | |||||||
\(830\) | −2379.06 | + | 4120.65i | −0.0994920 | + | 0.172325i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 93.5221 | + | 161.985i | 0.00389699 | + | 0.00674978i | ||||
\(833\) | −5061.34 | − | 8766.50i | −0.210522 | − | 0.364635i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4523.04 | − | 7834.14i | 0.187457 | − | 0.324684i | ||||
\(836\) | 35715.4 | 1.47756 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −25187.4 | −1.03829 | ||||||||
\(839\) | 4328.96 | − | 7497.97i | 0.178131 | − | 0.308532i | −0.763109 | − | 0.646270i | \(-0.776328\pi\) |
0.941240 | + | 0.337737i | \(0.109661\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18267.3 | − | 31640.0i | −0.748999 | − | 1.29731i | ||||
\(842\) | −26076.4 | − | 45165.7i | −1.06728 | − | 1.84859i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5810.30 | − | 10063.7i | 0.236965 | − | 0.410436i | ||||
\(845\) | −2221.46 | −0.0904386 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 95643.8 | 3.88000 | ||||||||
\(848\) | 4947.79 | − | 8569.82i | 0.200363 | − | 0.347039i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1467.49 | − | 2541.76i | −0.0592169 | − | 0.102567i | ||||
\(851\) | 917.770 | + | 1589.62i | 0.0369692 | + | 0.0640325i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9492.39 | + | 16441.3i | −0.381024 | + | 0.659952i | −0.991209 | − | 0.132306i | \(-0.957762\pi\) |
0.610185 | + | 0.792259i | \(0.291095\pi\) | |||||||
\(854\) | −7118.60 | −0.285238 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −25356.3 | −1.01245 | ||||||||
\(857\) | −18217.2 | + | 31553.1i | −0.726124 | + | 1.25768i | 0.232386 | + | 0.972624i | \(0.425347\pi\) |
−0.958510 | + | 0.285059i | \(0.907987\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8742.51 | + | 15142.5i | 0.347253 | + | 0.601461i | 0.985761 | − | 0.168155i | \(-0.0537810\pi\) |
−0.638507 | + | 0.769616i | \(0.720448\pi\) | |||||||
\(860\) | −2614.16 | − | 4527.86i | −0.103654 | − | 0.179533i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4024.14 | − | 6970.02i | 0.159006 | − | 0.275406i | ||||
\(863\) | 10423.6 | 0.411152 | 0.205576 | − | 0.978641i | \(-0.434093\pi\) | ||||
0.205576 | + | 0.978641i | \(0.434093\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6637.04 | −0.260886 | ||||||||
\(866\) | −9741.11 | + | 16872.1i | −0.382236 | + | 0.662052i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −12501.4 | − | 21653.0i | −0.488852 | − | 0.846717i | ||||
\(869\) | 28314.0 | + | 49041.3i | 1.10528 | + | 1.91440i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15713.7 | + | 27217.0i | −0.611296 | + | 1.05880i | ||||
\(872\) | 2673.63 | 0.103831 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −32746.7 | −1.26736 | ||||||||
\(875\) | 1589.53 | − | 2753.15i | 0.0614124 | − | 0.106369i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3936.62 | − | 6818.42i | −0.151574 | − | 0.262533i | 0.780232 | − | 0.625490i | \(-0.215101\pi\) |
−0.931806 | + | 0.362956i | \(0.881767\pi\) | |||||||
\(878\) | 20897.1 | + | 36194.8i | 0.803237 | + | 1.39125i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −14240.5 | + | 24665.3i | −0.545509 | + | 0.944849i | ||||
\(881\) | 35135.0 | 1.34362 | 0.671809 | − | 0.740725i | \(-0.265518\pi\) | ||||
0.671809 | + | 0.740725i | \(0.265518\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33069.4 | 1.26033 | 0.630167 | − | 0.776460i | \(-0.282987\pi\) | ||||
0.630167 | + | 0.776460i | \(0.282987\pi\) | |||||||
\(884\) | 3779.99 | − | 6547.13i | 0.143818 | − | 0.249100i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −26943.3 | − | 46667.2i | −1.02165 | − | 1.76954i | ||||
\(887\) | −25739.6 | − | 44582.2i | −0.974351 | − | 1.68763i | −0.682059 | − | 0.731297i | \(-0.738915\pi\) |
−0.292293 | − | 0.956329i | \(-0.594418\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14980.0 | − | 25946.1i | 0.565143 | − | 0.978856i | ||||
\(890\) | 3125.31 | 0.117709 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 14804.1 | 0.555692 | ||||||||
\(893\) | −6121.15 | + | 10602.2i | −0.229380 | + | 0.397298i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1121.84 | + | 1943.08i | 0.0418981 | + | 0.0725697i | ||||
\(896\) | −18496.3 | − | 32036.6i | −0.689641 | − | 1.19449i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 22900.4 | − | 39664.7i | 0.850999 | − | 1.47397i | ||||
\(899\) | 54963.3 | 2.03907 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4130.28 | 0.152719 | ||||||||
\(902\) | −54586.8 | + | 94547.2i | −2.01501 | + | 3.49011i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.2841 | − | 21.2768i | −0.000451952 | − | 0.000782804i | ||||
\(905\) | −8626.39 | − | 14941.3i | −0.316852 | − | 0.548803i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5404.90 | − | 9361.55i | 0.197868 | − | 0.342718i | −0.749969 | − | 0.661473i | \(-0.769931\pi\) |
0.947837 | + | 0.318755i | \(0.103265\pi\) | |||||||
\(908\) | −3049.64 | −0.111460 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 23027.0 | 0.838834 | ||||||||
\(911\) | 15769.9 | − | 27314.2i | 0.573523 | − | 0.993371i | −0.422677 | − | 0.906280i | \(-0.638910\pi\) |
0.996200 | − | 0.0870907i | \(-0.0277570\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9635.96 | + | 16690.0i | 0.349292 | + | 0.604992i | ||||
\(914\) | −25213.9 | − | 43671.7i | −0.912474 | − | 1.58045i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1474.86 | − | 2554.53i | 0.0531996 | − | 0.0921443i | ||||
\(917\) | −13255.9 | −0.477368 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3592.53 | 0.128952 | 0.0644759 | − | 0.997919i | \(-0.479462\pi\) | ||||
0.0644759 | + | 0.997919i | \(0.479462\pi\) | |||||||
\(920\) | 2588.84 | − | 4484.00i | 0.0927734 | − | 0.160688i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7558.45 | + | 13091.6i | 0.269983 | + | 0.467624i | ||||
\(923\) | −13133.7 | − | 22748.1i | −0.468363 | − | 0.811229i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −279.887 | + | 484.779i | −0.00994880 | + | 0.0172318i | ||||
\(926\) | −51126.7 | −1.81439 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −44482.0 | −1.57348 | ||||||||
\(929\) | 15807.4 | − | 27379.1i | 0.558259 | − | 0.966933i | −0.439383 | − | 0.898300i | \(-0.644803\pi\) |
0.997642 | − | 0.0686331i | \(-0.0218638\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17221.8 | − | 29829.0i | −0.606252 | − | 1.05006i | ||||
\(932\) | −2076.18 | − | 3596.05i | −0.0729695 | − | 0.126387i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −13024.6 | + | 22559.3i | −0.456294 | + | 0.790325i | ||||
\(935\) | −11887.6 | −0.415793 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20891.5 | −0.728382 | −0.364191 | − | 0.931324i | \(-0.618654\pi\) | ||||
−0.364191 | + | 0.931324i | \(0.618654\pi\) | |||||||
\(938\) | 27398.7 | − | 47456.0i | 0.953732 | − | 1.65191i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1191.84 | + | 2064.33i | 0.0413548 | + | 0.0716286i | ||||
\(941\) | 18884.6 | + | 32709.1i | 0.654219 | + | 1.13314i | 0.982089 | + | 0.188417i | \(0.0603358\pi\) |
−0.327870 | + | 0.944723i | \(0.606331\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17798.2 | − | 30827.4i | 0.614622 | − | 1.06456i | ||||
\(944\) | 13657.8 | 0.470894 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −59549.1 | −2.04663 | ||||||||
\(947\) | −5215.42 | + | 9033.37i | −0.178963 | + | 0.309974i | −0.941526 | − | 0.336941i | \(-0.890608\pi\) |
0.762562 | + | 0.646915i | \(0.223941\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10536.0 | − | 18248.8i | −0.360392 | − | 0.624217i | ||||
\(950\) | −4993.29 | − | 8648.63i | −0.170530 | − | 0.295367i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5352.12 | − | 9270.15i | 0.182209 | − | 0.315596i | ||||
\(953\) | 33865.3 | 1.15111 | 0.575553 | − | 0.817764i | \(-0.304787\pi\) | ||||
0.575553 | + | 0.817764i | \(0.304787\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7960.47 | −0.269733 | ||||||||
\(956\) | 2444.53 | − | 4234.05i | 0.0827005 | − | 0.143242i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 23800.8 | + | 41224.2i | 0.802683 | + | 1.39029i | ||||
\(959\) | −5716.35 | − | 9901.01i | −0.192482 | − | 0.333389i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9897.47 | + | 17142.9i | −0.332230 | + | 0.575440i | ||||
\(962\) | −4054.65 | −0.135891 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5425.28 | 0.181262 | ||||||||
\(965\) | 1108.25 | − | 1919.54i | 0.0369697 | − | 0.0640334i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23290.9 | + | 40341.0i | 0.774544 | + | 1.34155i | 0.935050 | + | 0.354515i | \(0.115354\pi\) |
−0.160506 | + | 0.987035i | \(0.551313\pi\) | |||||||
\(968\) | 23752.7 | + | 41140.9i | 0.788678 | + | 1.36603i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7768.04 | + | 13454.6i | −0.257131 | + | 0.445363i | ||||
\(971\) | −13829.5 | −0.457065 | −0.228532 | − | 0.973536i | \(-0.573393\pi\) | ||||
−0.228532 | + | 0.973536i | \(0.573393\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −59650.5 | −1.96537 | ||||||||
\(974\) | 19625.8 | − | 33992.9i | 0.645637 | − | 1.11828i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3170.73 | − | 5491.86i | −0.103988 | − | 0.180113i | ||||
\(977\) | 7971.80 | + | 13807.6i | 0.261045 | + | 0.452142i | 0.966520 | − | 0.256592i | \(-0.0825997\pi\) |
−0.705475 | + | 0.708735i | \(0.749266\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6329.27 | − | 10962.6i | 0.206624 | − | 0.357882i | ||||
\(980\) | −6706.44 | −0.218601 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7091.85 | −0.230458 | ||||||||
\(983\) | −14555.8 | + | 25211.4i | −0.472286 | + | 0.818024i | −0.999497 | − | 0.0317108i | \(-0.989904\pi\) |
0.527211 | + | 0.849734i | \(0.323238\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 522.479 | + | 904.960i | 0.0169011 | + | 0.0292735i | ||||
\(986\) | −14488.6 | − | 25095.1i | −0.467964 | − | 0.810537i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 12861.8 | − | 22277.3i | 0.414159 | − | 0.717345i | ||||
\(989\) | 19416.1 | 0.624265 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8745.85 | 0.280344 | 0.140172 | − | 0.990127i | \(-0.455234\pi\) | ||||
0.140172 | + | 0.990127i | \(0.455234\pi\) | |||||||
\(992\) | 20065.1 | − | 34753.7i | 0.642204 | − | 1.11233i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 22900.1 | + | 39664.1i | 0.730731 | + | 1.26566i | ||||
\(995\) | −1199.79 | − | 2078.10i | −0.0382270 | − | 0.0662112i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22513.4 | + | 38994.4i | −0.715153 | + | 1.23868i | 0.247747 | + | 0.968825i | \(0.420310\pi\) |
−0.962900 | + | 0.269857i | \(0.913024\pi\) | |||||||
\(998\) | 25908.0 | 0.821748 | ||||||||
\(999\) | 0 | 0 |
(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 | 405.4.e.s.136.1 | 6 | ||
3.2 | odd | 2 | 405.4.e.u.136.3 | 6 | |||
9.2 | odd | 6 | 405.4.a.g.1.1 | ✓ | 3 | ||
9.4 | even | 3 | inner | 405.4.e.s.271.1 | 6 | ||
9.5 | odd | 6 | 405.4.e.u.271.3 | 6 | |||
9.7 | even | 3 | 405.4.a.i.1.3 | yes | 3 | ||
45.29 | odd | 6 | 2025.4.a.r.1.3 | 3 | |||
45.34 | even | 6 | 2025.4.a.p.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
405.4.a.g.1.1 | ✓ | 3 | 9.2 | odd | 6 | ||
405.4.a.i.1.3 | yes | 3 | 9.7 | even | 3 | ||
405.4.e.s.136.1 | 6 | 1.1 | even | 1 | trivial | ||
405.4.e.s.271.1 | 6 | 9.4 | even | 3 | inner | ||
405.4.e.u.136.3 | 6 | 3.2 | odd | 2 | |||
405.4.e.u.271.3 | 6 | 9.5 | odd | 6 | |||
2025.4.a.p.1.1 | 3 | 45.34 | even | 6 | |||
2025.4.a.r.1.3 | 3 | 45.29 | odd | 6 |