Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,4,Mod(541,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("1620.541");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.i (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: | \(95.5830942093\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 306x^{10} + 30777x^{8} + 1381040x^{6} + 28918584x^{4} + 243888288x^{2} + 366645904 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{13} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1081.2 | ||
Root | \(-5.63924i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.1081 |
Dual form | 1620.4.i.x.541.2 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.50000 | − | 4.33013i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.28565 | − | 14.3512i | −0.447383 | − | 0.774890i | 0.550832 | − | 0.834616i | \(-0.314311\pi\) |
−0.998215 | + | 0.0597263i | \(0.980977\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 36.2684 | + | 62.8188i | 0.994122 | + | 1.72187i | 0.590822 | + | 0.806802i | \(0.298804\pi\) |
0.403300 | + | 0.915068i | \(0.367863\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 29.9488 | − | 51.8728i | 0.638946 | − | 1.10669i | −0.346719 | − | 0.937969i | \(-0.612704\pi\) |
0.985664 | − | 0.168717i | \(-0.0539625\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 15.8529 | 0.226170 | 0.113085 | − | 0.993585i | \(-0.463927\pi\) | ||||
0.113085 | + | 0.993585i | \(0.463927\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −136.646 | −1.64993 | −0.824966 | − | 0.565182i | \(-0.808806\pi\) | ||||
−0.824966 | + | 0.565182i | \(0.808806\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −81.5503 | + | 141.249i | −0.739322 | + | 1.28054i | 0.213479 | + | 0.976948i | \(0.431520\pi\) |
−0.952801 | + | 0.303595i | \(0.901813\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.79923 | − | 10.0446i | −0.0371342 | − | 0.0643183i | 0.846861 | − | 0.531814i | \(-0.178490\pi\) |
−0.883995 | + | 0.467496i | \(0.845156\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 20.5009 | − | 35.5086i | 0.118776 | − | 0.205727i | −0.800507 | − | 0.599324i | \(-0.795436\pi\) |
0.919283 | + | 0.393597i | \(0.128770\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −82.8565 | −0.400151 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −242.545 | −1.07768 | −0.538841 | − | 0.842408i | \(-0.681138\pi\) | ||||
−0.538841 | + | 0.842408i | \(0.681138\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −28.9332 | + | 50.1138i | −0.110210 | + | 0.190889i | −0.915855 | − | 0.401510i | \(-0.868486\pi\) |
0.805645 | + | 0.592399i | \(0.201819\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 132.252 | + | 229.067i | 0.469029 | + | 0.812383i | 0.999373 | − | 0.0354000i | \(-0.0112705\pi\) |
−0.530344 | + | 0.847783i | \(0.677937\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −299.945 | − | 519.519i | −0.930882 | − | 1.61233i | −0.781818 | − | 0.623506i | \(-0.785708\pi\) |
−0.149063 | − | 0.988828i | \(-0.547626\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 34.1961 | − | 59.2294i | 0.0996971 | − | 0.172680i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 592.285 | 1.53503 | 0.767516 | − | 0.641030i | \(-0.221493\pi\) | ||||
0.767516 | + | 0.641030i | \(0.221493\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 362.684 | 0.889170 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −144.446 | + | 250.188i | −0.318734 | + | 0.552063i | −0.980224 | − | 0.197890i | \(-0.936591\pi\) |
0.661490 | + | 0.749954i | \(0.269924\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −412.690 | − | 714.800i | −0.866222 | − | 1.50034i | −0.865829 | − | 0.500340i | \(-0.833208\pi\) |
−0.000392970 | − | 1.00000i | \(-0.500125\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −149.744 | − | 259.364i | −0.285745 | − | 0.494925i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −405.264 | + | 701.938i | −0.738968 | + | 1.27993i | 0.213992 | + | 0.976835i | \(0.431353\pi\) |
−0.952960 | + | 0.303095i | \(0.901980\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −966.126 | −1.61490 | −0.807451 | − | 0.589935i | \(-0.799153\pi\) | ||||
−0.807451 | + | 0.589935i | \(0.799153\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 802.840 | 1.28720 | 0.643598 | − | 0.765364i | \(-0.277441\pi\) | ||||
0.643598 | + | 0.765364i | \(0.277441\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 601.015 | − | 1040.99i | 0.889506 | − | 1.54067i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 581.001 | + | 1006.32i | 0.827440 | + | 1.43317i | 0.900040 | + | 0.435807i | \(0.143537\pi\) |
−0.0726002 | + | 0.997361i | \(0.523130\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −251.187 | − | 435.069i | −0.332186 | − | 0.575362i | 0.650755 | − | 0.759288i | \(-0.274453\pi\) |
−0.982940 | + | 0.183926i | \(0.941119\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 39.6322 | − | 68.6450i | 0.0505731 | − | 0.0875952i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.76580 | 0.0104401 | 0.00522007 | − | 0.999986i | \(-0.498338\pi\) | ||||
0.00522007 | + | 0.999986i | \(0.498338\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −992.580 | −1.14341 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −341.615 | + | 591.694i | −0.368936 | + | 0.639016i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −69.1820 | − | 119.827i | −0.0724161 | − | 0.125428i | 0.827544 | − | 0.561401i | \(-0.189738\pi\) |
−0.899960 | + | 0.435973i | \(0.856404\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 662.889 | + | 1148.16i | 0.653068 | + | 1.13115i | 0.982374 | + | 0.186924i | \(0.0598519\pi\) |
−0.329306 | + | 0.944223i | \(0.606815\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −166.772 | + | 288.857i | −0.159539 | + | 0.276330i | −0.934703 | − | 0.355431i | \(-0.884334\pi\) |
0.775164 | + | 0.631761i | \(0.217667\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 584.004 | 0.527643 | 0.263821 | − | 0.964572i | \(-0.415017\pi\) | ||||
0.263821 | + | 0.964572i | \(0.415017\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1915.42 | −1.68315 | −0.841577 | − | 0.540137i | \(-0.818372\pi\) | ||||
−0.841577 | + | 0.540137i | \(0.818372\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −618.658 | + | 1071.55i | −0.515030 | + | 0.892058i | 0.484818 | + | 0.874615i | \(0.338886\pi\) |
−0.999848 | + | 0.0174432i | \(0.994447\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 407.751 | + | 706.246i | 0.330635 | + | 0.572676i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −131.351 | − | 227.507i | −0.101185 | − | 0.175257i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1965.30 | + | 3403.99i | −1.47656 | + | 2.55747i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1785.42 | −1.24749 | −0.623743 | − | 0.781629i | \(-0.714389\pi\) | ||||
−0.623743 | + | 0.781629i | \(0.714389\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −360.906 | + | 625.108i | −0.240706 | + | 0.416915i | −0.960916 | − | 0.276841i | \(-0.910712\pi\) |
0.720209 | + | 0.693757i | \(0.244046\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1132.20 | + | 1961.03i | 0.738152 | + | 1.27852i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 554.493 | + | 960.411i | 0.345792 | + | 0.598930i | 0.985497 | − | 0.169691i | \(-0.0542768\pi\) |
−0.639705 | + | 0.768621i | \(0.720943\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −218.385 | + | 378.254i | −0.133260 | + | 0.230813i | −0.924932 | − | 0.380134i | \(-0.875878\pi\) |
0.791671 | + | 0.610947i | \(0.209211\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4344.78 | 2.54076 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −57.9923 | −0.0332138 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 88.5585 | − | 153.388i | 0.0486912 | − | 0.0843357i | −0.840653 | − | 0.541575i | \(-0.817828\pi\) |
0.889344 | + | 0.457239i | \(0.151162\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −414.329 | − | 717.639i | −0.223296 | − | 0.386759i | 0.732511 | − | 0.680755i | \(-0.238348\pi\) |
−0.955807 | + | 0.293996i | \(0.905015\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −102.504 | − | 177.543i | −0.0531184 | − | 0.0920038i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 433.262 | − | 750.432i | 0.220242 | − | 0.381471i | −0.734639 | − | 0.678458i | \(-0.762648\pi\) |
0.954882 | + | 0.296987i | \(0.0959818\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2702.79 | 1.32304 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2984.70 | 1.43423 | 0.717116 | − | 0.696954i | \(-0.245462\pi\) | ||||
0.717116 | + | 0.696954i | \(0.245462\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −979.720 | + | 1696.92i | −0.453970 | + | 0.786299i | −0.998628 | − | 0.0523588i | \(-0.983326\pi\) |
0.544658 | + | 0.838658i | \(0.316659\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −695.358 | − | 1204.40i | −0.316503 | − | 0.548200i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −253.472 | − | 439.027i | −0.111394 | − | 0.192940i | 0.804939 | − | 0.593358i | \(-0.202198\pi\) |
−0.916333 | + | 0.400418i | \(0.868865\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −207.141 | + | 358.779i | −0.0894766 | + | 0.154978i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3122.26 | −1.30374 | −0.651869 | − | 0.758332i | \(-0.726015\pi\) | ||||
−0.651869 | + | 0.758332i | \(0.726015\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2828.38 | −1.16150 | −0.580751 | − | 0.814082i | \(-0.697241\pi\) | ||||
−0.580751 | + | 0.814082i | \(0.697241\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −606.363 | + | 1050.25i | −0.240977 | + | 0.417384i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 574.959 | + | 995.858i | 0.224840 | + | 0.389435i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2039.32 | − | 3532.20i | −0.772565 | − | 1.33812i | −0.936153 | − | 0.351593i | \(-0.885640\pi\) |
0.163588 | − | 0.986529i | \(-0.447693\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1521.56 | + | 2635.42i | −0.567483 | + | 0.982909i | 0.429331 | + | 0.903147i | \(0.358749\pi\) |
−0.996814 | + | 0.0797619i | \(0.974584\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1338.21 | 0.483978 | 0.241989 | − | 0.970279i | \(-0.422200\pi\) | ||||
0.241989 | + | 0.970279i | \(0.422200\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 453.645 | 0.161598 | 0.0807991 | − | 0.996730i | \(-0.474253\pi\) | ||||
0.0807991 | + | 0.996730i | \(0.474253\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −96.1008 | + | 166.451i | −0.0332264 | + | 0.0575498i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 144.666 | + | 250.569i | 0.0492874 | + | 0.0853683i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4955.93 | − | 8583.92i | −1.64023 | − | 2.84097i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −952.979 | + | 1650.61i | −0.310928 | + | 0.538543i | −0.978564 | − | 0.205945i | \(-0.933973\pi\) |
0.667636 | + | 0.744488i | \(0.267306\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1322.52 | 0.419513 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −679.452 | −0.212554 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 474.774 | − | 822.333i | 0.144510 | − | 0.250299i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2227.76 | − | 3858.59i | −0.668976 | − | 1.15870i | −0.978191 | − | 0.207708i | \(-0.933400\pi\) |
0.309215 | − | 0.950992i | \(-0.399934\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −85.6173 | − | 148.294i | −0.0250336 | − | 0.0433594i | 0.853237 | − | 0.521523i | \(-0.174636\pi\) |
−0.878271 | + | 0.478164i | \(0.841303\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2214.97 | + | 3836.44i | −0.639168 | + | 1.10707i | 0.346448 | + | 0.938069i | \(0.387388\pi\) |
−0.985616 | + | 0.169002i | \(0.945946\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −762.810 | −0.214478 | −0.107239 | − | 0.994233i | \(-0.534201\pi\) | ||||
−0.107239 | + | 0.994233i | \(0.534201\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2999.45 | −0.832606 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1522.14 | + | 2636.43i | −0.411963 | + | 0.713542i | −0.995104 | − | 0.0988294i | \(-0.968490\pi\) |
0.583141 | + | 0.812371i | \(0.301824\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1009.16 | + | 1747.91i | 0.269733 | + | 0.467190i | 0.968793 | − | 0.247872i | \(-0.0797314\pi\) |
−0.699060 | + | 0.715063i | \(0.746398\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −170.981 | − | 296.147i | −0.0445859 | − | 0.0772250i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4092.38 | + | 7088.20i | −1.05422 | + | 1.82596i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3031.55 | 0.762351 | 0.381175 | − | 0.924503i | \(-0.375519\pi\) | ||||
0.381175 | + | 0.924503i | \(0.375519\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11830.8 | −2.93990 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2377.31 | + | 4117.62i | −0.577013 | + | 0.999417i | 0.418806 | + | 0.908076i | \(0.362449\pi\) |
−0.995820 | + | 0.0913409i | \(0.970885\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2009.65 | + | 3480.81i | 0.482136 | + | 0.835084i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1982.43 | + | 3433.67i | 0.464798 | + | 0.805053i | 0.999192 | − | 0.0401818i | \(-0.0127937\pi\) |
−0.534395 | + | 0.845235i | \(0.679460\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1480.71 | − | 2564.67i | 0.343243 | − | 0.594515i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3989.09 | 0.904161 | 0.452080 | − | 0.891977i | \(-0.350682\pi\) | ||||
0.452080 | + | 0.891977i | \(0.350682\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2684.00 | 0.601628 | 0.300814 | − | 0.953683i | \(-0.402742\pi\) | ||||
0.300814 | + | 0.953683i | \(0.402742\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 906.711 | − | 1570.47i | 0.198824 | − | 0.344374i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.7606 | − | 46.3507i | −0.00580465 | − | 0.0100540i | 0.863108 | − | 0.505019i | \(-0.168514\pi\) |
−0.868913 | + | 0.494965i | \(0.835181\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1819.03 | − | 3150.65i | −0.386172 | − | 0.668869i | 0.605759 | − | 0.795648i | \(-0.292870\pi\) |
−0.991931 | + | 0.126779i | \(0.959536\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3663.02 | + | 6344.53i | −0.769412 | + | 1.33266i | 0.168470 | + | 0.985707i | \(0.446117\pi\) |
−0.937882 | + | 0.346954i | \(0.887216\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 958.922 | 0.197224 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4661.69 | −0.948847 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1261.12 | + | 2184.32i | −0.251452 | + | 0.435527i | −0.963926 | − | 0.266172i | \(-0.914241\pi\) |
0.712474 | + | 0.701698i | \(0.247575\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 722.231 | + | 1250.94i | 0.142542 | + | 0.246890i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4884.66 | + | 8460.48i | 0.944773 | + | 1.63640i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2191.59 | − | 3795.94i | 0.419671 | − | 0.726892i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4126.90 | −0.774772 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 640.204 | 0.119017 | 0.0595087 | − | 0.998228i | \(-0.481047\pi\) | ||||
0.0595087 | + | 0.998228i | \(0.481047\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2437.17 | − | 4221.30i | 0.444371 | − | 0.769673i | −0.553637 | − | 0.832758i | \(-0.686761\pi\) |
0.998008 | + | 0.0630852i | \(0.0200940\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2581.99 | + | 4472.14i | 0.466270 | + | 0.807604i | 0.999258 | − | 0.0385190i | \(-0.0122640\pi\) |
−0.532987 | + | 0.846123i | \(0.678931\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3655.00 | − | 6330.64i | −0.647587 | − | 1.12165i | −0.983697 | − | 0.179831i | \(-0.942445\pi\) |
0.336110 | − | 0.941823i | \(-0.390889\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 420.658 | − | 728.601i | 0.0738318 | − | 0.127880i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2166.23 | −0.373165 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1497.44 | −0.255578 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4970.47 | + | 8609.11i | −0.832921 | + | 1.44266i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5867.79 | + | 10163.3i | 0.974390 | + | 1.68769i | 0.681934 | + | 0.731414i | \(0.261139\pi\) |
0.292456 | + | 0.956279i | \(0.405527\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2026.32 | + | 3509.69i | 0.330477 | + | 0.572402i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1125.51 | + | 1949.44i | −0.181930 | + | 0.315112i | −0.942538 | − | 0.334100i | \(-0.891568\pi\) |
0.760608 | + | 0.649212i | \(0.224901\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2974.14 | 0.472313 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6817.30 | −1.07318 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3479.50 | + | 6026.66i | −0.538297 | + | 0.932358i | 0.460699 | + | 0.887557i | \(0.347599\pi\) |
−0.998996 | + | 0.0448014i | \(0.985734\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1462.00 | + | 2532.26i | 0.224238 | + | 0.388392i | 0.956091 | − | 0.293071i | \(-0.0946772\pi\) |
−0.731852 | + | 0.681463i | \(0.761344\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3276.24 | + | 5674.61i | 0.493984 | + | 0.855606i | 0.999976 | − | 0.00693255i | \(-0.00220672\pi\) |
−0.505992 | + | 0.862538i | \(0.668873\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2415.31 | + | 4183.45i | −0.361103 | + | 0.625449i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1324.66 | −0.194743 | −0.0973717 | − | 0.995248i | \(-0.531044\pi\) | ||||
−0.0973717 | + | 0.995248i | \(0.531044\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11813.1 | 1.72228 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2007.10 | − | 3476.40i | 0.287826 | − | 0.498529i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1628.11 | + | 2819.96i | 0.231571 | + | 0.401092i | 0.958271 | − | 0.285863i | \(-0.0922802\pi\) |
−0.726700 | + | 0.686955i | \(0.758947\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4907.47 | − | 8499.98i | −0.686747 | − | 1.18948i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2272.33 | − | 3935.79i | 0.315433 | − | 0.546347i | −0.664096 | − | 0.747647i | \(-0.731183\pi\) |
0.979530 | + | 0.201301i | \(0.0645168\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −694.720 | −0.0949069 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2484.30 | −0.336701 | −0.168351 | − | 0.985727i | \(-0.553844\pi\) | ||||
−0.168351 | + | 0.985727i | \(0.553844\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1414.43 | − | 2449.87i | 0.188705 | − | 0.326847i | −0.756114 | − | 0.654440i | \(-0.772904\pi\) |
0.944819 | + | 0.327593i | \(0.106238\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3005.07 | − | 5204.94i | −0.397799 | − | 0.689009i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1295.09 | − | 2243.16i | −0.168801 | − | 0.292371i | 0.769198 | − | 0.639011i | \(-0.220656\pi\) |
−0.937998 | + | 0.346639i | \(0.887323\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1292.81 | + | 2239.21i | −0.167212 | + | 0.289620i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5810.01 | 0.740085 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12207.4 | 1.54325 | 0.771625 | − | 0.636077i | \(-0.219444\pi\) | ||||
0.771625 | + | 0.636077i | \(0.219444\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4760.20 | + | 8244.91i | −0.592801 | + | 1.02676i | 0.401052 | + | 0.916055i | \(0.368645\pi\) |
−0.993853 | + | 0.110706i | \(0.964689\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1227.95 | − | 2126.88i | −0.151783 | − | 0.262896i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8796.74 | − | 15236.4i | −1.07135 | − | 1.85563i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5623.36 | + | 9739.94i | −0.679846 | + | 1.17753i | 0.295181 | + | 0.955441i | \(0.404620\pi\) |
−0.975027 | + | 0.222087i | \(0.928713\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4787.32 | 0.570384 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2511.87 | −0.297116 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5340.99 | − | 9250.87i | 0.622731 | − | 1.07860i | −0.366244 | − | 0.930519i | \(-0.619356\pi\) |
0.988975 | − | 0.148083i | \(-0.0473104\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5411.99 | − | 9373.84i | −0.626518 | − | 1.08516i | −0.988245 | − | 0.152877i | \(-0.951146\pi\) |
0.361727 | − | 0.932284i | \(-0.382187\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −198.161 | − | 343.225i | −0.0226170 | − | 0.0391738i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6838.81 | + | 11845.2i | −0.775066 | + | 1.34245i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −235.904 | −0.0263645 | −0.0131823 | − | 0.999913i | \(-0.504196\pi\) | ||||
−0.0131823 | + | 0.999913i | \(0.504196\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11895.5 | −1.32024 | −0.660118 | − | 0.751162i | \(-0.729494\pi\) | ||||
−0.660118 | + | 0.751162i | \(0.729494\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11143.5 | − | 19301.1i | 1.21983 | − | 2.11281i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1905.52 | − | 3300.46i | −0.207166 | − | 0.358821i | 0.743655 | − | 0.668564i | \(-0.233091\pi\) |
−0.950821 | + | 0.309742i | \(0.899757\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4016.11 | + | 6956.12i | 0.430725 | + | 0.746038i | 0.996936 | − | 0.0782223i | \(-0.0249244\pi\) |
−0.566210 | + | 0.824261i | \(0.691591\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.9145 | − | 37.9570i | 0.00233449 | − | 0.00404345i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12271.3 | 1.28980 | 0.644898 | − | 0.764269i | \(-0.276900\pi\) | ||||
0.644898 | + | 0.764269i | \(0.276900\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4197.45 | −0.438249 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2481.45 | + | 4298.00i | −0.255675 | + | 0.442842i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4972.00 | − | 8611.76i | −0.508929 | − | 0.881490i | −0.999947 | − | 0.0103406i | \(-0.996708\pi\) |
0.491018 | − | 0.871149i | \(-0.336625\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3374.74 | − | 5845.22i | −0.340949 | − | 0.590540i | 0.643661 | − | 0.765311i | \(-0.277415\pi\) |
−0.984609 | + | 0.174771i | \(0.944082\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4780.08 | − | 8279.34i | 0.479804 | − | 0.831044i | −0.519928 | − | 0.854210i | \(-0.674041\pi\) |
0.999732 | + | 0.0231659i | \(0.00737460\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6517.56 | −0.645818 | −0.322909 | − | 0.946430i | \(-0.604661\pi\) | ||||
−0.322909 | + | 0.946430i | \(0.604661\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13431.5 | 1.32241 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9593.15 | + | 16615.8i | −0.932545 | + | 1.61521i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1708.07 | + | 2958.47i | 0.164993 | + | 0.285777i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2376.37 | + | 4115.99i | 0.226678 | + | 0.392619i | 0.956822 | − | 0.290676i | \(-0.0938800\pi\) |
−0.730143 | + | 0.683294i | \(0.760547\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7263.94 | + | 12581.5i | −0.688580 | + | 1.19266i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −691.820 | −0.0647710 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8412.56 | −0.782771 | −0.391386 | − | 0.920227i | \(-0.628004\pi\) | ||||
−0.391386 | + | 0.920227i | \(0.628004\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2785.22 | − | 4824.15i | 0.255999 | − | 0.443403i | −0.709167 | − | 0.705040i | \(-0.750929\pi\) |
0.965166 | + | 0.261637i | \(0.0842623\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −91.9345 | − | 159.235i | −0.00839863 | − | 0.0145469i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8004.98 | + | 13865.0i | 0.722479 | + | 1.25137i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7912.32 | − | 13704.5i | 0.709828 | − | 1.22946i | −0.255093 | − | 0.966916i | \(-0.582106\pi\) |
0.964921 | − | 0.262541i | \(-0.0845605\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15946.4 | −1.41354 | −0.706772 | − | 0.707441i | \(-0.749849\pi\) | ||||
−0.706772 | + | 0.707441i | \(0.749849\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6628.89 | 0.584122 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7319.34 | − | 12677.5i | 0.637375 | − | 1.10397i | −0.348631 | − | 0.937260i | \(-0.613353\pi\) |
0.986007 | − | 0.166707i | \(-0.0533133\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6652.05 | − | 11521.7i | −0.575869 | − | 0.997435i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 833.859 | + | 1444.29i | 0.0713480 | + | 0.123578i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21757.0 | − | 37684.3i | 1.85082 | − | 3.20571i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13001.4 | −1.09329 | −0.546644 | − | 0.837365i | \(-0.684095\pi\) | ||||
−0.546644 | + | 0.837365i | \(0.684095\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1938.88 | −0.162106 | −0.0810531 | − | 0.996710i | \(-0.525828\pi\) | ||||
−0.0810531 | + | 0.996710i | \(0.525828\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 324.998 | − | 562.913i | 0.0268636 | − | 0.0465292i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7217.39 | − | 12500.9i | −0.593194 | − | 1.02744i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1733.03 | + | 3001.69i | 0.140836 | + | 0.243936i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1460.01 | − | 2528.81i | 0.117984 | − | 0.204355i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4960.96 | 0.396444 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7574.14 | −0.601918 | −0.300959 | − | 0.953637i | \(-0.597307\pi\) | ||||
−0.300959 | + | 0.953637i | \(0.597307\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4788.55 | + | 8294.00i | −0.376365 | + | 0.651883i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1570.94 | + | 2720.94i | 0.122794 | + | 0.212686i | 0.920869 | − | 0.389873i | \(-0.127481\pi\) |
−0.798074 | + | 0.602559i | \(0.794148\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 792.442 | + | 1372.55i | 0.0612689 | + | 0.106121i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9627.94 | − | 16676.1i | 0.740365 | − | 1.28235i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12191.5 | 0.927412 | 0.463706 | − | 0.885989i | \(-0.346519\pi\) | ||||
0.463706 | + | 0.885989i | \(0.346519\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15843.2 | 1.19874 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1091.42 | − | 1890.40i | 0.0817016 | − | 0.141511i | −0.822279 | − | 0.569084i | \(-0.807298\pi\) |
0.903981 | + | 0.427573i | \(0.140631\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3093.29 | + | 5357.73i | 0.230328 | + | 0.398941i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 892.967 | + | 1546.66i | 0.0657911 | + | 0.113953i | 0.897045 | − | 0.441940i | \(-0.145710\pi\) |
−0.831254 | + | 0.555893i | \(0.812376\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1702.15 | + | 2948.21i | −0.124751 | + | 0.216075i | −0.921636 | − | 0.388057i | \(-0.873146\pi\) |
0.796885 | + | 0.604131i | \(0.206480\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4077.51 | 0.295729 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4174.78 | −0.301210 | −0.150605 | − | 0.988594i | \(-0.548122\pi\) | ||||
−0.150605 | + | 0.988594i | \(0.548122\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4162.50 | + | 7209.66i | −0.297228 | + | 0.514815i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21481.3 | + | 37206.6i | 1.52601 | + | 2.64312i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9308.47 | + | 16122.8i | 0.654518 | + | 1.13366i | 0.982014 | + | 0.188806i | \(0.0604616\pi\) |
−0.327497 | + | 0.944852i | \(0.606205\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2801.36 | + | 4852.10i | −0.195973 | + | 0.339435i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24181.4 | 1.67456 | 0.837278 | − | 0.546777i | \(-0.184145\pi\) | ||||
0.837278 | + | 0.546777i | \(0.184145\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1313.51 | −0.0905022 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2669.72 | + | 4624.08i | −0.182106 | + | 0.315417i | −0.942598 | − | 0.333931i | \(-0.891625\pi\) |
0.760491 | + | 0.649348i | \(0.224958\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4582.86 | − | 7937.75i | −0.311046 | − | 0.538748i | 0.667543 | − | 0.744571i | \(-0.267346\pi\) |
−0.978589 | + | 0.205823i | \(0.934013\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9826.49 | + | 17020.0i | 0.660336 | + | 1.14374i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5715.85 | + | 9900.15i | −0.382206 | + | 0.662001i | −0.991377 | − | 0.131038i | \(-0.958169\pi\) |
0.609171 | + | 0.793039i | \(0.291502\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −35931.9 | −2.37913 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29975.6 | 1.97505 | 0.987523 | − | 0.157477i | \(-0.0503361\pi\) | ||||
0.987523 | + | 0.157477i | \(0.0503361\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3056.36 | − | 5293.77i | 0.199424 | − | 0.345412i | −0.748918 | − | 0.662663i | \(-0.769426\pi\) |
0.948342 | + | 0.317251i | \(0.102760\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −693.987 | − | 1202.02i | −0.0450625 | − | 0.0780505i | 0.842614 | − | 0.538517i | \(-0.181015\pi\) |
−0.887677 | + | 0.460467i | \(0.847682\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −72.6303 | − | 125.799i | −0.00467074 | − | 0.00808996i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3845.04 | −0.243739 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18608.3 | 1.17399 | 0.586993 | − | 0.809592i | \(-0.300312\pi\) | ||||
0.586993 | + | 0.809592i | \(0.300312\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4463.56 | + | 7731.12i | −0.278947 | + | 0.483150i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2048.26 | − | 3547.70i | −0.127402 | − | 0.220667i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4019.77 | − | 6962.45i | −0.247693 | − | 0.429018i | 0.715192 | − | 0.698928i | \(-0.246339\pi\) |
−0.962885 | + | 0.269910i | \(0.913006\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13330.7 | − | 23089.5i | 0.817592 | − | 1.41611i | −0.0898593 | − | 0.995954i | \(-0.528642\pi\) |
0.907452 | − | 0.420157i | \(-0.138025\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6303.13 | −0.383001 | −0.191501 | − | 0.981492i | \(-0.561335\pi\) | ||||
−0.191501 | + | 0.981492i | \(0.561335\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20955.4 | −1.26744 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11299.2 | + | 19570.7i | −0.677136 | + | 1.17283i | 0.298703 | + | 0.954346i | \(0.403446\pi\) |
−0.975839 | + | 0.218489i | \(0.929887\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1804.53 | + | 3125.54i | 0.107647 | + | 0.186450i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1198.87 | + | 2076.50i | 0.0708667 | + | 0.122745i | 0.899281 | − | 0.437370i | \(-0.144090\pi\) |
−0.828415 | + | 0.560115i | \(0.810757\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2531.81 | − | 4385.23i | 0.148980 | − | 0.258042i | −0.781870 | − | 0.623441i | \(-0.785734\pi\) |
0.930851 | + | 0.365399i | \(0.119068\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11322.0 | 0.660223 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1891.72 | 0.109816 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29935.2 | − | 51849.3i | 1.72226 | − | 2.98304i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3640.66 | − | 6305.81i | −0.208525 | − | 0.361176i | 0.742725 | − | 0.669596i | \(-0.233533\pi\) |
−0.951250 | + | 0.308421i | \(0.900200\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14482.1 | − | 25083.8i | −0.822146 | − | 1.42400i | −0.904081 | − | 0.427361i | \(-0.859443\pi\) |
0.0819349 | − | 0.996638i | \(-0.473890\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1146.43 | + | 1985.68i | −0.0647955 | + | 0.112229i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9158.42 | −0.513085 | −0.256543 | − | 0.966533i | \(-0.582583\pi\) | ||||
−0.256543 | + | 0.966533i | \(0.582583\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5544.93 | 0.309286 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 17738.2 | − | 30723.5i | 0.980802 | − | 1.69880i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5014.15 | − | 8684.76i | −0.276045 | − | 0.478124i | 0.694353 | − | 0.719634i | \(-0.255691\pi\) |
−0.970398 | + | 0.241510i | \(0.922357\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1091.92 | + | 1891.27i | 0.0595958 | + | 0.103223i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −458.675 | + | 794.448i | −0.0249262 | + | 0.0431734i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27626.7 | −1.48851 | −0.744256 | − | 0.667894i | \(-0.767196\pi\) | ||||
−0.744256 | + | 0.667894i | \(0.767196\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 33142.8 | 1.77810 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10984.9 | − | 19026.4i | 0.584343 | − | 1.01211i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4851.84 | − | 8403.64i | −0.257003 | − | 0.445142i | 0.708435 | − | 0.705776i | \(-0.249402\pi\) |
−0.965438 | + | 0.260635i | \(0.916068\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3343.70 | + | 5791.47i | 0.175628 | + | 0.304197i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10861.9 | − | 18813.4i | 0.568131 | − | 0.984032i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32045.4 | −1.66216 | −0.831080 | − | 0.556153i | \(-0.812277\pi\) | ||||
−0.831080 | + | 0.556153i | \(0.812277\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5527.25 | 0.285500 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −144.981 | + | 251.114i | −0.00742683 | + | 0.0128637i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3723.63 | + | 6449.51i | 0.189961 | + | 0.329022i | 0.945237 | − | 0.326385i | \(-0.105830\pi\) |
−0.755276 | + | 0.655407i | \(0.772497\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2096.58 | + | 3631.38i | 0.106080 | + | 0.183736i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9072.37 | − | 15713.8i | 0.457156 | − | 0.791818i | −0.541653 | − | 0.840602i | \(-0.682201\pi\) |
0.998809 | + | 0.0487844i | \(0.0155347\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −58793.1 | −2.93850 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25920.2 | 1.29024 | 0.645121 | − | 0.764081i | \(-0.276807\pi\) | ||||
0.645121 | + | 0.764081i | \(0.276807\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4656.55 | + | 8065.38i | −0.229922 | + | 0.398237i | −0.957785 | − | 0.287486i | \(-0.907181\pi\) |
0.727863 | + | 0.685723i | \(0.240514\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −442.792 | − | 766.939i | −0.0217754 | − | 0.0377161i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4838.85 | − | 8381.13i | −0.236058 | − | 0.408865i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2492.14 | − | 4316.52i | 0.121091 | − | 0.209736i | −0.799107 | − | 0.601189i | \(-0.794694\pi\) |
0.920198 | + | 0.391453i | \(0.128027\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4143.29 | −0.199722 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10452.6 | −0.501857 | −0.250928 | − | 0.968006i | \(-0.580736\pi\) | ||||
−0.250928 | + | 0.968006i | \(0.580736\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4702.97 | − | 8145.78i | 0.224024 | − | 0.388022i | −0.732002 | − | 0.681303i | \(-0.761414\pi\) |
0.956026 | + | 0.293281i | \(0.0947471\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15870.5 | + | 27488.5i | 0.753014 | + | 1.30426i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8651.98 | + | 14985.7i | 0.407307 | + | 0.705477i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11784.1 | − | 20410.7i | 0.552596 | − | 0.957125i | −0.445490 | − | 0.895287i | \(-0.646970\pi\) |
0.998086 | − | 0.0618381i | \(-0.0196962\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3172.70 | 0.147625 | 0.0738125 | − | 0.997272i | \(-0.476483\pi\) | ||||
0.0738125 | + | 0.997272i | \(0.476483\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1025.04 | −0.0475106 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3953.60 | − | 6847.84i | 0.181839 | − | 0.314954i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −35039.9 | − | 60690.8i | −1.60541 | − | 2.78065i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2166.31 | − | 3752.16i | −0.0984954 | − | 0.170599i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7721.19 | + | 13373.5i | −0.349721 | + | 0.605735i | −0.986200 | − | 0.165559i | \(-0.947057\pi\) |
0.636479 | + | 0.771294i | \(0.280390\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20503.9 | 0.921663 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −49438.2 | −2.21388 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4984.27 | + | 8633.02i | −0.221521 | + | 0.383685i | −0.955270 | − | 0.295735i | \(-0.904435\pi\) |
0.733749 | + | 0.679420i | \(0.237769\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4754.99 | − | 8235.88i | −0.210537 | − | 0.364661i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 29117.7 | + | 50433.4i | 1.27963 | + | 2.21638i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6756.97 | − | 11703.4i | 0.295841 | − | 0.512411i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10439.0 | 0.453667 | 0.226833 | − | 0.973934i | \(-0.427163\pi\) | ||||
0.226833 | + | 0.973934i | \(0.427163\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17472.9 | 0.756544 | 0.378272 | − | 0.925694i | \(-0.376518\pi\) | ||||
0.378272 | + | 0.925694i | \(0.376518\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7461.75 | − | 12924.1i | 0.320704 | − | 0.555476i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18071.7 | − | 31301.1i | −0.773867 | − | 1.34038i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9750.89 | − | 16889.0i | −0.414505 | − | 0.717943i | 0.580872 | − | 0.813995i | \(-0.302712\pi\) |
−0.995376 | + | 0.0960521i | \(0.969378\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8296.21 | − | 14369.5i | 0.351383 | − | 0.608612i | −0.635109 | − | 0.772422i | \(-0.719045\pi\) |
0.986492 | + | 0.163810i | \(0.0523783\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32449.4 | 1.36442 | 0.682210 | − | 0.731156i | \(-0.261019\pi\) | ||||
0.682210 | + | 0.731156i | \(0.261019\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7197.10 | 0.301527 | 0.150763 | − | 0.988570i | \(-0.451827\pi\) | ||||
0.150763 | + | 0.988570i | \(0.451827\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 542.107 | − | 938.956i | 0.0225485 | − | 0.0390551i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4898.60 | + | 8484.62i | 0.203022 | + | 0.351644i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7715.97 | + | 13364.4i | 0.317503 | + | 0.549931i | 0.979966 | − | 0.199163i | \(-0.0638224\pi\) |
−0.662464 | + | 0.749094i | \(0.730489\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12127.2 | − | 21005.0i | 0.497242 | − | 0.861249i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6953.58 | −0.283089 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 65135.0 | 2.64235 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19779.6 | − | 34259.3i | 0.796753 | − | 1.38002i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3957.37 | − | 6854.36i | −0.158848 | − | 0.275134i | 0.775605 | − | 0.631218i | \(-0.217445\pi\) |
−0.934454 | + | 0.356085i | \(0.884111\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13406.4 | − | 23220.6i | −0.534369 | − | 0.925554i | −0.999194 | − | 0.0401510i | \(-0.987216\pi\) |
0.464825 | − | 0.885403i | \(-0.346117\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −809.265 | + | 1401.69i | −0.0321441 | + | 0.0556752i | −0.881650 | − | 0.471904i | \(-0.843567\pi\) |
0.849506 | + | 0.527579i | \(0.176900\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16678.5 | 0.657869 | 0.328935 | − | 0.944353i | \(-0.393310\pi\) | ||||
0.328935 | + | 0.944353i | \(0.393310\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2534.72 | −0.0996338 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −42144.0 | + | 72995.6i | −1.64515 | + | 2.84949i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24274.3 | + | 42044.3i | 0.944321 | + | 1.63561i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1035.71 | + | 1793.90i | 0.0400151 | + | 0.0693083i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1064.16 | − | 1843.17i | 0.0409738 | − | 0.0709686i | −0.844811 | − | 0.535064i | \(-0.820287\pi\) |
0.885785 | + | 0.464096i | \(0.153621\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2379.31 | 0.0909886 | 0.0454943 | − | 0.998965i | \(-0.485514\pi\) | ||||
0.0454943 | + | 0.998965i | \(0.485514\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36926.5 | −1.40733 | −0.703666 | − | 0.710531i | \(-0.748455\pi\) | ||||
−0.703666 | + | 0.710531i | \(0.748455\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2390.70 | − | 4140.81i | 0.0904981 | − | 0.156747i | −0.817223 | − | 0.576322i | \(-0.804487\pi\) |
0.907721 | + | 0.419575i | \(0.137821\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14793.4 | + | 25622.9i | 0.558104 | + | 0.966665i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 40986.2 | + | 70990.2i | 1.53589 | + | 2.66024i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7805.66 | + | 13519.8i | −0.291525 | + | 0.504935i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −475.558 | −0.0176426 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9389.43 | 0.347178 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7070.95 | + | 12247.2i | −0.259720 | + | 0.449847i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24032.4 | − | 41625.3i | −0.879804 | − | 1.52387i | −0.851556 | − | 0.524264i | \(-0.824340\pi\) |
−0.0282484 | − | 0.999601i | \(-0.508993\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12817.2 | − | 22200.1i | −0.466140 | − | 0.807378i | 0.533112 | − | 0.846044i | \(-0.321022\pi\) |
−0.999252 | + | 0.0386666i | \(0.987689\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18220.3 | − | 31558.6i | 0.660466 | − | 1.14396i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11961.4 | 0.430751 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9651.68 | −0.346441 | −0.173221 | − | 0.984883i | \(-0.555417\pi\) | ||||
−0.173221 | + | 0.984883i | \(0.555417\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −28934.3 | + | 50115.6i | −1.03183 | + | 1.78719i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3031.82 | + | 5251.26i | 0.107768 | + | 0.186660i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −166.997 | − | 289.248i | −0.00589775 | − | 0.0102152i | 0.863061 | − | 0.505099i | \(-0.168544\pi\) |
−0.868959 | + | 0.494884i | \(0.835211\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4672.76 | + | 8093.45i | −0.164493 | + | 0.284911i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5749.59 | 0.201103 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11567.3 | 0.403295 | 0.201648 | − | 0.979458i | \(-0.435370\pi\) | ||||
0.201648 | + | 0.979458i | \(0.435370\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10130.8 | − | 17547.1i | 0.350963 | − | 0.607886i | −0.635455 | − | 0.772138i | \(-0.719188\pi\) |
0.986418 | + | 0.164252i | \(0.0525209\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4719.02 | − | 8173.59i | −0.162961 | − | 0.282257i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13676.7 | − | 23688.8i | −0.469307 | − | 0.812863i | 0.530077 | − | 0.847949i | \(-0.322163\pi\) |
−0.999384 | + | 0.0350859i | \(0.988830\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24044.1 | − | 41645.5i | 0.822448 | − | 1.42452i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45432.0 | 1.54427 | 0.772133 | − | 0.635460i | \(-0.219190\pi\) | ||||
0.772133 | + | 0.635460i | \(0.219190\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20393.2 | −0.691003 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9188.67 | − | 15915.2i | 0.309403 | − | 0.535902i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14054.9 | + | 24343.8i | 0.471784 | + | 0.817154i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7607.79 | + | 13177.1i | 0.253786 | + | 0.439570i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3567.09 | − | 6178.39i | 0.118625 | − | 0.205464i | −0.800598 | − | 0.599202i | \(-0.795485\pi\) |
0.919223 | + | 0.393738i | \(0.128818\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31719.4 | 1.04833 | 0.524163 | − | 0.851618i | \(-0.324378\pi\) | ||||
0.524163 | + | 0.851618i | \(0.324378\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7237.84 | 0.238473 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8785.15 | − | 15216.3i | 0.287678 | − | 0.498274i | −0.685577 | − | 0.728000i | \(-0.740450\pi\) |
0.973255 | + | 0.229727i | \(0.0737832\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 317.922 | + | 550.656i | 0.0103788 | + | 0.0179766i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28993.6 | + | 50218.5i | 0.940746 | + | 1.62942i | 0.764052 | + | 0.645154i | \(0.223207\pi\) |
0.176694 | + | 0.984266i | \(0.443460\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3345.53 | − | 5794.63i | 0.108221 | − | 0.187444i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −43140.8 | −1.38705 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20741.2 | 0.664851 | 0.332425 | − | 0.943130i | \(-0.392133\pi\) | ||||
0.332425 | + | 0.943130i | \(0.392133\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1134.11 | − | 1964.34i | 0.0361344 | − | 0.0625867i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4960.70 | + | 8592.19i | 0.157580 | + | 0.272936i | 0.933995 | − | 0.357285i | \(-0.116298\pi\) |
−0.776416 | + | 0.630221i | \(0.782964\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1620.4.i.x.1081.2 | 12 | ||
3.2 | odd | 2 | 1620.4.i.w.1081.2 | 12 | |||
9.2 | odd | 6 | 1620.4.i.w.541.2 | 12 | |||
9.4 | even | 3 | 1620.4.a.i.1.5 | ✓ | 6 | ||
9.5 | odd | 6 | 1620.4.a.j.1.5 | yes | 6 | ||
9.7 | even | 3 | inner | 1620.4.i.x.541.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1620.4.a.i.1.5 | ✓ | 6 | 9.4 | even | 3 | ||
1620.4.a.j.1.5 | yes | 6 | 9.5 | odd | 6 | ||
1620.4.i.w.541.2 | 12 | 9.2 | odd | 6 | |||
1620.4.i.w.1081.2 | 12 | 3.2 | odd | 2 | |||
1620.4.i.x.541.2 | 12 | 9.7 | even | 3 | inner | ||
1620.4.i.x.1081.2 | 12 | 1.1 | even | 1 | trivial |