Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,4,Mod(337,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.337");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.b (of order \(2\), degree \(1\), 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: | \(29.9139683729\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 17x^{2} + 289 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.1 | ||
Root | \(3.57071 - 2.06155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.337 |
Dual form | 507.4.b.e.337.4 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 4.12311i | − 1.45774i | −0.684653 | − | 0.728869i | \(-0.740046\pi\) | ||||
0.684653 | − | 0.728869i | \(-0.259954\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | −9.00000 | −1.12500 | ||||||||
\(5\) | 3.05006i | 0.272806i | 0.990653 | + | 0.136403i | \(0.0435541\pi\) | ||||
−0.990653 | + | 0.136403i | \(0.956446\pi\) | |||||||
\(6\) | 12.3693i | 0.841625i | ||||||||
\(7\) | − 6.68324i | − 0.360861i | −0.983588 | − | 0.180431i | \(-0.942251\pi\) | ||||
0.983588 | − | 0.180431i | \(-0.0577491\pi\) | |||||||
\(8\) | 4.12311i | 0.182217i | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 12.5757 | 0.397679 | ||||||||
\(11\) | 32.2500i | 0.883975i | 0.897021 | + | 0.441988i | \(0.145727\pi\) | ||||
−0.897021 | + | 0.441988i | \(0.854273\pi\) | |||||||
\(12\) | 27.0000 | 0.649519 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −27.5557 | −0.526041 | ||||||||
\(15\) | − 9.15018i | − 0.157504i | ||||||||
\(16\) | −55.0000 | −0.859375 | ||||||||
\(17\) | 28.8586 | 0.411720 | 0.205860 | − | 0.978582i | \(-0.434001\pi\) | ||||
0.205860 | + | 0.978582i | \(0.434001\pi\) | |||||||
\(18\) | − 37.1080i | − 0.485913i | ||||||||
\(19\) | 101.194i | 1.22187i | 0.791682 | + | 0.610933i | \(0.209206\pi\) | ||||
−0.791682 | + | 0.610933i | \(0.790794\pi\) | |||||||
\(20\) | − 27.4505i | − 0.306906i | ||||||||
\(21\) | 20.0497i | 0.208343i | ||||||||
\(22\) | 132.970 | 1.28860 | ||||||||
\(23\) | 118.990 | 1.07874 | 0.539372 | − | 0.842067i | \(-0.318662\pi\) | ||||
0.539372 | + | 0.842067i | \(0.318662\pi\) | |||||||
\(24\) | − 12.3693i | − 0.105203i | ||||||||
\(25\) | 115.697 | 0.925577 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 60.1492i | 0.405969i | ||||||||
\(29\) | 160.111 | 1.02524 | 0.512620 | − | 0.858616i | \(-0.328675\pi\) | ||||
0.512620 | + | 0.858616i | \(0.328675\pi\) | |||||||
\(30\) | −37.7271 | −0.229600 | ||||||||
\(31\) | 38.0705i | 0.220570i | 0.993900 | + | 0.110285i | \(0.0351763\pi\) | ||||
−0.993900 | + | 0.110285i | \(0.964824\pi\) | |||||||
\(32\) | 259.756i | 1.43496i | ||||||||
\(33\) | − 96.7499i | − 0.510363i | ||||||||
\(34\) | − 118.987i | − 0.600179i | ||||||||
\(35\) | 20.3843 | 0.0984449 | ||||||||
\(36\) | −81.0000 | −0.375000 | ||||||||
\(37\) | − 327.568i | − 1.45545i | −0.685866 | − | 0.727727i | \(-0.740577\pi\) | ||||
0.685866 | − | 0.727727i | \(-0.259423\pi\) | |||||||
\(38\) | 417.233 | 1.78116 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −12.5757 | −0.0497099 | ||||||||
\(41\) | − 56.0846i | − 0.213633i | −0.994279 | − | 0.106816i | \(-0.965934\pi\) | ||||
0.994279 | − | 0.106816i | \(-0.0340657\pi\) | |||||||
\(42\) | 82.6671 | 0.303710 | ||||||||
\(43\) | −127.879 | −0.453519 | −0.226759 | − | 0.973951i | \(-0.572813\pi\) | ||||
−0.226759 | + | 0.973951i | \(0.572813\pi\) | |||||||
\(44\) | − 290.250i | − 0.994472i | ||||||||
\(45\) | 27.4505i | 0.0909352i | ||||||||
\(46\) | − 490.608i | − 1.57253i | ||||||||
\(47\) | − 517.983i | − 1.60757i | −0.594923 | − | 0.803783i | \(-0.702817\pi\) | ||||
0.594923 | − | 0.803783i | \(-0.297183\pi\) | |||||||
\(48\) | 165.000 | 0.496160 | ||||||||
\(49\) | 298.334 | 0.869779 | ||||||||
\(50\) | − 477.032i | − 1.34925i | ||||||||
\(51\) | −86.5757 | −0.237706 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −695.546 | −1.80265 | −0.901326 | − | 0.433141i | \(-0.857405\pi\) | ||||
−0.901326 | + | 0.433141i | \(0.857405\pi\) | |||||||
\(54\) | 111.324i | 0.280542i | ||||||||
\(55\) | −98.3643 | −0.241153 | ||||||||
\(56\) | 27.5557 | 0.0657551 | ||||||||
\(57\) | − 303.581i | − 0.705445i | ||||||||
\(58\) | − 660.156i | − 1.49453i | ||||||||
\(59\) | 656.523i | 1.44868i | 0.689444 | + | 0.724339i | \(0.257855\pi\) | ||||
−0.689444 | + | 0.724339i | \(0.742145\pi\) | |||||||
\(60\) | 82.3516i | 0.177192i | ||||||||
\(61\) | 701.304 | 1.47201 | 0.736007 | − | 0.676974i | \(-0.236709\pi\) | ||||
0.736007 | + | 0.676974i | \(0.236709\pi\) | |||||||
\(62\) | 156.969 | 0.321533 | ||||||||
\(63\) | − 60.1492i | − 0.120287i | ||||||||
\(64\) | 631.000 | 1.23242 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −398.910 | −0.743976 | ||||||||
\(67\) | 57.1750i | 0.104254i | 0.998640 | + | 0.0521271i | \(0.0166001\pi\) | ||||
−0.998640 | + | 0.0521271i | \(0.983400\pi\) | |||||||
\(68\) | −259.727 | −0.463184 | ||||||||
\(69\) | −356.970 | −0.622814 | ||||||||
\(70\) | − 84.0465i | − 0.143507i | ||||||||
\(71\) | − 309.226i | − 0.516879i | −0.966027 | − | 0.258440i | \(-0.916792\pi\) | ||||
0.966027 | − | 0.258440i | \(-0.0832083\pi\) | |||||||
\(72\) | 37.1080i | 0.0607391i | ||||||||
\(73\) | − 389.711i | − 0.624826i | −0.949946 | − | 0.312413i | \(-0.898863\pi\) | ||||
0.949946 | − | 0.312413i | \(-0.101137\pi\) | |||||||
\(74\) | −1350.60 | −2.12167 | ||||||||
\(75\) | −347.091 | −0.534382 | ||||||||
\(76\) | − 910.744i | − 1.37460i | ||||||||
\(77\) | 215.534 | 0.318992 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 901.820 | 1.28434 | 0.642169 | − | 0.766563i | \(-0.278035\pi\) | ||||
0.642169 | + | 0.766563i | \(0.278035\pi\) | |||||||
\(80\) | − 167.753i | − 0.234442i | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −231.243 | −0.311421 | ||||||||
\(83\) | − 687.095i | − 0.908657i | −0.890834 | − | 0.454328i | \(-0.849879\pi\) | ||||
0.890834 | − | 0.454328i | \(-0.150121\pi\) | |||||||
\(84\) | − 180.448i | − 0.234386i | ||||||||
\(85\) | 88.0203i | 0.112319i | ||||||||
\(86\) | 527.257i | 0.661111i | ||||||||
\(87\) | −480.334 | −0.591922 | ||||||||
\(88\) | −132.970 | −0.161076 | ||||||||
\(89\) | 1070.54i | 1.27502i | 0.770442 | + | 0.637510i | \(0.220036\pi\) | ||||
−0.770442 | + | 0.637510i | \(0.779964\pi\) | |||||||
\(90\) | 113.181 | 0.132560 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1070.91 | −1.21359 | ||||||||
\(93\) | − 114.211i | − 0.127346i | ||||||||
\(94\) | −2135.70 | −2.34341 | ||||||||
\(95\) | −308.647 | −0.333332 | ||||||||
\(96\) | − 779.267i | − 0.828475i | ||||||||
\(97\) | − 1754.48i | − 1.83650i | −0.395998 | − | 0.918251i | \(-0.629601\pi\) | ||||
0.395998 | − | 0.918251i | \(-0.370399\pi\) | |||||||
\(98\) | − 1230.06i | − 1.26791i | ||||||||
\(99\) | 290.250i | 0.294658i | ||||||||
\(100\) | −1041.27 | −1.04127 | ||||||||
\(101\) | 640.840 | 0.631346 | 0.315673 | − | 0.948868i | \(-0.397770\pi\) | ||||
0.315673 | + | 0.948868i | \(0.397770\pi\) | |||||||
\(102\) | 356.961i | 0.346514i | ||||||||
\(103\) | 693.153 | 0.663091 | 0.331546 | − | 0.943439i | \(-0.392430\pi\) | ||||
0.331546 | + | 0.943439i | \(0.392430\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −61.1528 | −0.0568372 | ||||||||
\(106\) | 2867.81i | 2.62779i | ||||||||
\(107\) | −405.676 | −0.366525 | −0.183262 | − | 0.983064i | \(-0.558666\pi\) | ||||
−0.183262 | + | 0.983064i | \(0.558666\pi\) | |||||||
\(108\) | 243.000 | 0.216506 | ||||||||
\(109\) | 479.516i | 0.421370i | 0.977554 | + | 0.210685i | \(0.0675694\pi\) | ||||
−0.977554 | + | 0.210685i | \(0.932431\pi\) | |||||||
\(110\) | 405.566i | 0.351538i | ||||||||
\(111\) | 982.704i | 0.840307i | ||||||||
\(112\) | 367.578i | 0.310115i | ||||||||
\(113\) | −1547.20 | −1.28804 | −0.644021 | − | 0.765008i | \(-0.722735\pi\) | ||||
−0.644021 | + | 0.765008i | \(0.722735\pi\) | |||||||
\(114\) | −1251.70 | −1.02835 | ||||||||
\(115\) | 362.926i | 0.294288i | ||||||||
\(116\) | −1441.00 | −1.15339 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2706.91 | 2.11179 | ||||||||
\(119\) | − 192.869i | − 0.148574i | ||||||||
\(120\) | 37.7271 | 0.0287000 | ||||||||
\(121\) | 290.940 | 0.218588 | ||||||||
\(122\) | − 2891.55i | − 2.14581i | ||||||||
\(123\) | 168.254i | 0.123341i | ||||||||
\(124\) | − 342.634i | − 0.248141i | ||||||||
\(125\) | 734.140i | 0.525308i | ||||||||
\(126\) | −248.001 | −0.175347 | ||||||||
\(127\) | 2495.15 | 1.74338 | 0.871690 | − | 0.490059i | \(-0.163025\pi\) | ||||
0.871690 | + | 0.490059i | \(0.163025\pi\) | |||||||
\(128\) | − 523.634i | − 0.361587i | ||||||||
\(129\) | 383.636 | 0.261839 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 43.7571 | 0.0291838 | 0.0145919 | − | 0.999894i | \(-0.495355\pi\) | ||||
0.0145919 | + | 0.999894i | \(0.495355\pi\) | |||||||
\(132\) | 870.749i | 0.574159i | ||||||||
\(133\) | 676.303 | 0.440924 | ||||||||
\(134\) | 235.739 | 0.151975 | ||||||||
\(135\) | − 82.3516i | − 0.0525015i | ||||||||
\(136\) | 118.987i | 0.0750224i | ||||||||
\(137\) | − 206.194i | − 0.128586i | −0.997931 | − | 0.0642932i | \(-0.979521\pi\) | ||||
0.997931 | − | 0.0642932i | \(-0.0204793\pi\) | |||||||
\(138\) | 1471.83i | 0.907899i | ||||||||
\(139\) | −100.000 | −0.0610208 | −0.0305104 | − | 0.999534i | \(-0.509713\pi\) | ||||
−0.0305104 | + | 0.999534i | \(0.509713\pi\) | |||||||
\(140\) | −183.459 | −0.110751 | ||||||||
\(141\) | 1553.95i | 0.928128i | ||||||||
\(142\) | −1274.97 | −0.753474 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −495.000 | −0.286458 | ||||||||
\(145\) | 488.349i | 0.279691i | ||||||||
\(146\) | −1606.82 | −0.910832 | ||||||||
\(147\) | −895.003 | −0.502167 | ||||||||
\(148\) | 2948.11i | 1.63739i | ||||||||
\(149\) | − 380.451i | − 0.209179i | −0.994515 | − | 0.104590i | \(-0.966647\pi\) | ||||
0.994515 | − | 0.104590i | \(-0.0333529\pi\) | |||||||
\(150\) | 1431.09i | 0.778989i | ||||||||
\(151\) | − 1517.45i | − 0.817805i | −0.912578 | − | 0.408902i | \(-0.865912\pi\) | ||||
0.912578 | − | 0.408902i | \(-0.134088\pi\) | |||||||
\(152\) | −417.233 | −0.222645 | ||||||||
\(153\) | 259.727 | 0.137240 | ||||||||
\(154\) | − 888.671i | − 0.465007i | ||||||||
\(155\) | −116.117 | −0.0601726 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1450.16 | 0.737166 | 0.368583 | − | 0.929595i | \(-0.379843\pi\) | ||||
0.368583 | + | 0.929595i | \(0.379843\pi\) | |||||||
\(158\) | − 3718.30i | − 1.87223i | ||||||||
\(159\) | 2086.64 | 1.04076 | ||||||||
\(160\) | −792.270 | −0.391465 | ||||||||
\(161\) | − 795.239i | − 0.389277i | ||||||||
\(162\) | − 333.972i | − 0.161971i | ||||||||
\(163\) | 2342.36i | 1.12557i | 0.826603 | + | 0.562785i | \(0.190270\pi\) | ||||
−0.826603 | + | 0.562785i | \(0.809730\pi\) | |||||||
\(164\) | 504.762i | 0.240337i | ||||||||
\(165\) | 295.093 | 0.139230 | ||||||||
\(166\) | −2832.97 | −1.32458 | ||||||||
\(167\) | − 40.0731i | − 0.0185686i | −0.999957 | − | 0.00928428i | \(-0.997045\pi\) | ||||
0.999957 | − | 0.00928428i | \(-0.00295532\pi\) | |||||||
\(168\) | −82.6671 | −0.0379637 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 362.917 | 0.163732 | ||||||||
\(171\) | 910.744i | 0.407289i | ||||||||
\(172\) | 1150.91 | 0.510208 | ||||||||
\(173\) | −1909.54 | −0.839189 | −0.419594 | − | 0.907712i | \(-0.637828\pi\) | ||||
−0.419594 | + | 0.907712i | \(0.637828\pi\) | |||||||
\(174\) | 1980.47i | 0.862868i | ||||||||
\(175\) | − 773.232i | − 0.334005i | ||||||||
\(176\) | − 1773.75i | − 0.759666i | ||||||||
\(177\) | − 1969.57i | − 0.836395i | ||||||||
\(178\) | 4413.94 | 1.85864 | ||||||||
\(179\) | 509.959 | 0.212939 | 0.106470 | − | 0.994316i | \(-0.466045\pi\) | ||||
0.106470 | + | 0.994316i | \(0.466045\pi\) | |||||||
\(180\) | − 247.055i | − 0.102302i | ||||||||
\(181\) | 2136.88 | 0.877531 | 0.438766 | − | 0.898602i | \(-0.355416\pi\) | ||||
0.438766 | + | 0.898602i | \(0.355416\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2103.91 | −0.849867 | ||||||||
\(184\) | 490.608i | 0.196566i | ||||||||
\(185\) | 999.101 | 0.397056 | ||||||||
\(186\) | −470.906 | −0.185637 | ||||||||
\(187\) | 930.688i | 0.363950i | ||||||||
\(188\) | 4661.85i | 1.80851i | ||||||||
\(189\) | 180.448i | 0.0694478i | ||||||||
\(190\) | 1272.58i | 0.485911i | ||||||||
\(191\) | 4057.74 | 1.53721 | 0.768607 | − | 0.639721i | \(-0.220950\pi\) | ||||
0.768607 | + | 0.639721i | \(0.220950\pi\) | |||||||
\(192\) | −1893.00 | −0.711539 | ||||||||
\(193\) | 873.394i | 0.325742i | 0.986647 | + | 0.162871i | \(0.0520755\pi\) | ||||
−0.986647 | + | 0.162871i | \(0.947925\pi\) | |||||||
\(194\) | −7233.92 | −2.67714 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2685.01 | −0.978502 | ||||||||
\(197\) | − 4147.25i | − 1.49989i | −0.661498 | − | 0.749947i | \(-0.730079\pi\) | ||||
0.661498 | − | 0.749947i | \(-0.269921\pi\) | |||||||
\(198\) | 1196.73 | 0.429535 | ||||||||
\(199\) | 2404.06 | 0.856379 | 0.428189 | − | 0.903689i | \(-0.359152\pi\) | ||||
0.428189 | + | 0.903689i | \(0.359152\pi\) | |||||||
\(200\) | 477.032i | 0.168656i | ||||||||
\(201\) | − 171.525i | − 0.0601912i | ||||||||
\(202\) | − 2642.25i | − 0.920337i | ||||||||
\(203\) | − 1070.06i | − 0.369969i | ||||||||
\(204\) | 779.181 | 0.267420 | ||||||||
\(205\) | 171.061 | 0.0582802 | ||||||||
\(206\) | − 2857.94i | − 0.966613i | ||||||||
\(207\) | 1070.91 | 0.359582 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3263.50 | −1.08010 | ||||||||
\(210\) | 252.140i | 0.0828538i | ||||||||
\(211\) | 3868.85 | 1.26229 | 0.631144 | − | 0.775665i | \(-0.282586\pi\) | ||||
0.631144 | + | 0.775665i | \(0.282586\pi\) | |||||||
\(212\) | 6259.91 | 2.02798 | ||||||||
\(213\) | 927.679i | 0.298420i | ||||||||
\(214\) | 1672.64i | 0.534297i | ||||||||
\(215\) | − 390.037i | − 0.123722i | ||||||||
\(216\) | − 111.324i | − 0.0350677i | ||||||||
\(217\) | 254.434 | 0.0795950 | ||||||||
\(218\) | 1977.09 | 0.614246 | ||||||||
\(219\) | 1169.13i | 0.360743i | ||||||||
\(220\) | 885.279 | 0.271298 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 4051.79 | 1.22495 | ||||||||
\(223\) | − 2813.55i | − 0.844885i | −0.906390 | − | 0.422443i | \(-0.861173\pi\) | ||||
0.906390 | − | 0.422443i | \(-0.138827\pi\) | |||||||
\(224\) | 1736.01 | 0.517822 | ||||||||
\(225\) | 1041.27 | 0.308526 | ||||||||
\(226\) | 6379.29i | 1.87763i | ||||||||
\(227\) | 4518.37i | 1.32112i | 0.750772 | + | 0.660561i | \(0.229682\pi\) | ||||
−0.750772 | + | 0.660561i | \(0.770318\pi\) | |||||||
\(228\) | 2732.23i | 0.793625i | ||||||||
\(229\) | − 1305.27i | − 0.376658i | −0.982106 | − | 0.188329i | \(-0.939693\pi\) | ||||
0.982106 | − | 0.188329i | \(-0.0603070\pi\) | |||||||
\(230\) | 1496.38 | 0.428994 | ||||||||
\(231\) | −646.603 | −0.184170 | ||||||||
\(232\) | 660.156i | 0.186816i | ||||||||
\(233\) | 3360.55 | 0.944879 | 0.472440 | − | 0.881363i | \(-0.343373\pi\) | ||||
0.472440 | + | 0.881363i | \(0.343373\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1579.88 | 0.438553 | ||||||||
\(236\) | − 5908.71i | − 1.62976i | ||||||||
\(237\) | −2705.46 | −0.741513 | ||||||||
\(238\) | −795.219 | −0.216581 | ||||||||
\(239\) | 4737.17i | 1.28210i | 0.767499 | + | 0.641050i | \(0.221501\pi\) | ||||
−0.767499 | + | 0.641050i | \(0.778499\pi\) | |||||||
\(240\) | 503.260i | 0.135355i | ||||||||
\(241\) | 4785.28i | 1.27903i | 0.768778 | + | 0.639516i | \(0.220865\pi\) | ||||
−0.768778 | + | 0.639516i | \(0.779135\pi\) | |||||||
\(242\) | − 1199.58i | − 0.318643i | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −6311.74 | −1.65601 | ||||||||
\(245\) | 909.937i | 0.237281i | ||||||||
\(246\) | 693.729 | 0.179799 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −156.969 | −0.0401916 | ||||||||
\(249\) | 2061.29i | 0.524613i | ||||||||
\(250\) | 3026.94 | 0.765762 | ||||||||
\(251\) | 3273.86 | 0.823284 | 0.411642 | − | 0.911346i | \(-0.364955\pi\) | ||||
0.411642 | + | 0.911346i | \(0.364955\pi\) | |||||||
\(252\) | 541.343i | 0.135323i | ||||||||
\(253\) | 3837.42i | 0.953584i | ||||||||
\(254\) | − 10287.8i | − 2.54139i | ||||||||
\(255\) | − 264.061i | − 0.0648476i | ||||||||
\(256\) | 2889.00 | 0.705322 | ||||||||
\(257\) | 6545.81 | 1.58878 | 0.794390 | − | 0.607408i | \(-0.207791\pi\) | ||||
0.794390 | + | 0.607408i | \(0.207791\pi\) | |||||||
\(258\) | − 1581.77i | − 0.381693i | ||||||||
\(259\) | −2189.22 | −0.525217 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1441.00 | 0.341746 | ||||||||
\(262\) | − 180.415i | − 0.0425424i | ||||||||
\(263\) | 88.2014 | 0.0206796 | 0.0103398 | − | 0.999947i | \(-0.496709\pi\) | ||||
0.0103398 | + | 0.999947i | \(0.496709\pi\) | |||||||
\(264\) | 398.910 | 0.0929970 | ||||||||
\(265\) | − 2121.46i | − 0.491773i | ||||||||
\(266\) | − 2788.47i | − 0.642752i | ||||||||
\(267\) | − 3211.61i | − 0.736133i | ||||||||
\(268\) | − 514.575i | − 0.117286i | ||||||||
\(269\) | −4527.60 | −1.02622 | −0.513109 | − | 0.858324i | \(-0.671506\pi\) | ||||
−0.513109 | + | 0.858324i | \(0.671506\pi\) | |||||||
\(270\) | −339.544 | −0.0765334 | ||||||||
\(271\) | 8321.82i | 1.86537i | 0.360695 | + | 0.932684i | \(0.382540\pi\) | ||||
−0.360695 | + | 0.932684i | \(0.617460\pi\) | |||||||
\(272\) | −1587.22 | −0.353821 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −850.160 | −0.187445 | ||||||||
\(275\) | 3731.23i | 0.818187i | ||||||||
\(276\) | 3212.73 | 0.700665 | ||||||||
\(277\) | 2881.31 | 0.624986 | 0.312493 | − | 0.949920i | \(-0.398836\pi\) | ||||
0.312493 | + | 0.949920i | \(0.398836\pi\) | |||||||
\(278\) | 412.311i | 0.0889523i | ||||||||
\(279\) | 342.634i | 0.0735232i | ||||||||
\(280\) | 84.0465i | 0.0179384i | ||||||||
\(281\) | − 2817.99i | − 0.598247i | −0.954214 | − | 0.299123i | \(-0.903306\pi\) | ||||
0.954214 | − | 0.299123i | \(-0.0966942\pi\) | |||||||
\(282\) | 6407.10 | 1.35297 | ||||||||
\(283\) | −264.601 | −0.0555792 | −0.0277896 | − | 0.999614i | \(-0.508847\pi\) | ||||
−0.0277896 | + | 0.999614i | \(0.508847\pi\) | |||||||
\(284\) | 2783.04i | 0.581489i | ||||||||
\(285\) | 925.941 | 0.192449 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −374.827 | −0.0770918 | ||||||||
\(288\) | 2337.80i | 0.478320i | ||||||||
\(289\) | −4080.18 | −0.830487 | ||||||||
\(290\) | 2013.52 | 0.407716 | ||||||||
\(291\) | 5263.45i | 1.06031i | ||||||||
\(292\) | 3507.40i | 0.702929i | ||||||||
\(293\) | 4292.52i | 0.855877i | 0.903808 | + | 0.427938i | \(0.140760\pi\) | ||||
−0.903808 | + | 0.427938i | \(0.859240\pi\) | |||||||
\(294\) | 3690.19i | 0.732028i | ||||||||
\(295\) | −2002.43 | −0.395208 | ||||||||
\(296\) | 1350.60 | 0.265209 | ||||||||
\(297\) | − 870.749i | − 0.170121i | ||||||||
\(298\) | −1568.64 | −0.304929 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 3123.82 | 0.601180 | ||||||||
\(301\) | 854.643i | 0.163657i | ||||||||
\(302\) | −6256.62 | −1.19214 | ||||||||
\(303\) | −1922.52 | −0.364508 | ||||||||
\(304\) | − 5565.66i | − 1.05004i | ||||||||
\(305\) | 2139.02i | 0.401573i | ||||||||
\(306\) | − 1070.88i | − 0.200060i | ||||||||
\(307\) | 7026.26i | 1.30622i | 0.757263 | + | 0.653110i | \(0.226536\pi\) | ||||
−0.757263 | + | 0.653110i | \(0.773464\pi\) | |||||||
\(308\) | −1939.81 | −0.358866 | ||||||||
\(309\) | −2079.46 | −0.382836 | ||||||||
\(310\) | 478.763i | 0.0877159i | ||||||||
\(311\) | 1133.21 | 0.206618 | 0.103309 | − | 0.994649i | \(-0.467057\pi\) | ||||
0.103309 | + | 0.994649i | \(0.467057\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5285.95 | −0.954566 | −0.477283 | − | 0.878750i | \(-0.658378\pi\) | ||||
−0.477283 | + | 0.878750i | \(0.658378\pi\) | |||||||
\(314\) | − 5979.15i | − 1.07459i | ||||||||
\(315\) | 183.459 | 0.0328150 | ||||||||
\(316\) | −8116.38 | −1.44488 | ||||||||
\(317\) | 4782.16i | 0.847296i | 0.905827 | + | 0.423648i | \(0.139251\pi\) | ||||
−0.905827 | + | 0.423648i | \(0.860749\pi\) | |||||||
\(318\) | − 8603.43i | − 1.51716i | ||||||||
\(319\) | 5163.59i | 0.906286i | ||||||||
\(320\) | 1924.59i | 0.336212i | ||||||||
\(321\) | 1217.03 | 0.211613 | ||||||||
\(322\) | −3278.85 | −0.567464 | ||||||||
\(323\) | 2920.31i | 0.503066i | ||||||||
\(324\) | −729.000 | −0.125000 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9657.80 | 1.64079 | ||||||||
\(327\) | − 1438.55i | − 0.243278i | ||||||||
\(328\) | 231.243 | 0.0389276 | ||||||||
\(329\) | −3461.81 | −0.580108 | ||||||||
\(330\) | − 1216.70i | − 0.202961i | ||||||||
\(331\) | − 8669.98i | − 1.43971i | −0.694122 | − | 0.719857i | \(-0.744207\pi\) | ||||
0.694122 | − | 0.719857i | \(-0.255793\pi\) | |||||||
\(332\) | 6183.86i | 1.02224i | ||||||||
\(333\) | − 2948.11i | − 0.485152i | ||||||||
\(334\) | −165.226 | −0.0270681 | ||||||||
\(335\) | −174.387 | −0.0284412 | ||||||||
\(336\) | − 1102.73i | − 0.179045i | ||||||||
\(337\) | −8526.59 | −1.37826 | −0.689129 | − | 0.724639i | \(-0.742007\pi\) | ||||
−0.689129 | + | 0.724639i | \(0.742007\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4641.61 | 0.743651 | ||||||||
\(340\) | − 792.183i | − 0.126359i | ||||||||
\(341\) | −1227.77 | −0.194978 | ||||||||
\(342\) | 3755.10 | 0.593720 | ||||||||
\(343\) | − 4286.19i | − 0.674731i | ||||||||
\(344\) | − 527.257i | − 0.0826389i | ||||||||
\(345\) | − 1088.78i | − 0.169907i | ||||||||
\(346\) | 7873.23i | 1.22332i | ||||||||
\(347\) | −12581.5 | −1.94643 | −0.973213 | − | 0.229907i | \(-0.926158\pi\) | ||||
−0.973213 | + | 0.229907i | \(0.926158\pi\) | |||||||
\(348\) | 4323.01 | 0.665913 | ||||||||
\(349\) | − 8961.18i | − 1.37444i | −0.726447 | − | 0.687222i | \(-0.758830\pi\) | ||||
0.726447 | − | 0.687222i | \(-0.241170\pi\) | |||||||
\(350\) | −3188.12 | −0.486892 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −8377.11 | −1.26847 | ||||||||
\(353\) | 5357.99i | 0.807868i | 0.914788 | + | 0.403934i | \(0.132357\pi\) | ||||
−0.914788 | + | 0.403934i | \(0.867643\pi\) | |||||||
\(354\) | −8120.74 | −1.21924 | ||||||||
\(355\) | 943.159 | 0.141007 | ||||||||
\(356\) | − 9634.84i | − 1.43440i | ||||||||
\(357\) | 578.606i | 0.0857790i | ||||||||
\(358\) | − 2102.61i | − 0.310409i | ||||||||
\(359\) | − 2705.40i | − 0.397731i | −0.980027 | − | 0.198866i | \(-0.936274\pi\) | ||||
0.980027 | − | 0.198866i | \(-0.0637257\pi\) | |||||||
\(360\) | −113.181 | −0.0165700 | ||||||||
\(361\) | −3381.19 | −0.492957 | ||||||||
\(362\) | − 8810.59i | − 1.27921i | ||||||||
\(363\) | −872.820 | −0.126202 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1188.64 | 0.170456 | ||||||||
\(366\) | 8674.65i | 1.23888i | ||||||||
\(367\) | 10473.8 | 1.48972 | 0.744858 | − | 0.667223i | \(-0.232517\pi\) | ||||
0.744858 | + | 0.667223i | \(0.232517\pi\) | |||||||
\(368\) | −6544.45 | −0.927046 | ||||||||
\(369\) | − 504.762i | − 0.0712110i | ||||||||
\(370\) | − 4119.40i | − 0.578804i | ||||||||
\(371\) | 4648.50i | 0.650507i | ||||||||
\(372\) | 1027.90i | 0.143264i | ||||||||
\(373\) | −12763.0 | −1.77170 | −0.885850 | − | 0.463973i | \(-0.846424\pi\) | ||||
−0.885850 | + | 0.463973i | \(0.846424\pi\) | |||||||
\(374\) | 3837.32 | 0.530544 | ||||||||
\(375\) | − 2202.42i | − 0.303287i | ||||||||
\(376\) | 2135.70 | 0.292926 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 744.004 | 0.101237 | ||||||||
\(379\) | 2318.02i | 0.314166i | 0.987585 | + | 0.157083i | \(0.0502090\pi\) | ||||
−0.987585 | + | 0.157083i | \(0.949791\pi\) | |||||||
\(380\) | 2777.82 | 0.374998 | ||||||||
\(381\) | −7485.46 | −1.00654 | ||||||||
\(382\) | − 16730.5i | − 2.24086i | ||||||||
\(383\) | − 1983.34i | − 0.264606i | −0.991209 | − | 0.132303i | \(-0.957763\pi\) | ||||
0.991209 | − | 0.132303i | \(-0.0422372\pi\) | |||||||
\(384\) | 1570.90i | 0.208763i | ||||||||
\(385\) | 657.392i | 0.0870229i | ||||||||
\(386\) | 3601.10 | 0.474847 | ||||||||
\(387\) | −1150.91 | −0.151173 | ||||||||
\(388\) | 15790.3i | 2.06607i | ||||||||
\(389\) | 3244.51 | 0.422887 | 0.211444 | − | 0.977390i | \(-0.432184\pi\) | ||||
0.211444 | + | 0.977390i | \(0.432184\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3433.88 | 0.444140 | ||||||||
\(392\) | 1230.06i | 0.158489i | ||||||||
\(393\) | −131.271 | −0.0168493 | ||||||||
\(394\) | −17099.5 | −2.18645 | ||||||||
\(395\) | 2750.60i | 0.350374i | ||||||||
\(396\) | − 2612.25i | − 0.331491i | ||||||||
\(397\) | 3759.72i | 0.475302i | 0.971351 | + | 0.237651i | \(0.0763775\pi\) | ||||
−0.971351 | + | 0.237651i | \(0.923622\pi\) | |||||||
\(398\) | − 9912.20i | − 1.24838i | ||||||||
\(399\) | −2028.91 | −0.254568 | ||||||||
\(400\) | −6363.34 | −0.795418 | ||||||||
\(401\) | − 1997.55i | − 0.248760i | −0.992235 | − | 0.124380i | \(-0.960306\pi\) | ||||
0.992235 | − | 0.124380i | \(-0.0396941\pi\) | |||||||
\(402\) | −707.216 | −0.0877431 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −5767.56 | −0.710264 | ||||||||
\(405\) | 247.055i | 0.0303117i | ||||||||
\(406\) | −4411.98 | −0.539318 | ||||||||
\(407\) | 10564.1 | 1.28659 | ||||||||
\(408\) | − 356.961i | − 0.0433142i | ||||||||
\(409\) | 5195.23i | 0.628087i | 0.949409 | + | 0.314044i | \(0.101684\pi\) | ||||
−0.949409 | + | 0.314044i | \(0.898316\pi\) | |||||||
\(410\) | − 705.304i | − 0.0849573i | ||||||||
\(411\) | 618.582i | 0.0742394i | ||||||||
\(412\) | −6238.38 | −0.745977 | ||||||||
\(413\) | 4387.70 | 0.522772 | ||||||||
\(414\) | − 4415.48i | − 0.524176i | ||||||||
\(415\) | 2095.68 | 0.247887 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 300.000 | 0.0352304 | ||||||||
\(418\) | 13455.7i | 1.57450i | ||||||||
\(419\) | −6822.11 | −0.795422 | −0.397711 | − | 0.917511i | \(-0.630195\pi\) | ||||
−0.397711 | + | 0.917511i | \(0.630195\pi\) | |||||||
\(420\) | 550.376 | 0.0639419 | ||||||||
\(421\) | − 7537.70i | − 0.872601i | −0.899801 | − | 0.436300i | \(-0.856288\pi\) | ||||
0.899801 | − | 0.436300i | \(-0.143712\pi\) | |||||||
\(422\) | − 15951.7i | − 1.84009i | ||||||||
\(423\) | − 4661.85i | − 0.535855i | ||||||||
\(424\) | − 2867.81i | − 0.328474i | ||||||||
\(425\) | 3338.85 | 0.381078 | ||||||||
\(426\) | 3824.92 | 0.435019 | ||||||||
\(427\) | − 4686.99i | − 0.531192i | ||||||||
\(428\) | 3651.08 | 0.412340 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1608.16 | −0.180355 | ||||||||
\(431\) | 13404.2i | 1.49805i | 0.662544 | + | 0.749023i | \(0.269477\pi\) | ||||
−0.662544 | + | 0.749023i | \(0.730523\pi\) | |||||||
\(432\) | 1485.00 | 0.165387 | ||||||||
\(433\) | 17715.9 | 1.96622 | 0.983110 | − | 0.183014i | \(-0.0585852\pi\) | ||||
0.983110 | + | 0.183014i | \(0.0585852\pi\) | |||||||
\(434\) | − 1049.06i | − 0.116029i | ||||||||
\(435\) | − 1465.05i | − 0.161480i | ||||||||
\(436\) | − 4315.64i | − 0.474041i | ||||||||
\(437\) | 12041.1i | 1.31808i | ||||||||
\(438\) | 4820.46 | 0.525869 | ||||||||
\(439\) | −7163.47 | −0.778801 | −0.389401 | − | 0.921068i | \(-0.627318\pi\) | ||||
−0.389401 | + | 0.921068i | \(0.627318\pi\) | |||||||
\(440\) | − 405.566i | − 0.0439423i | ||||||||
\(441\) | 2685.01 | 0.289926 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10169.2 | −1.09064 | −0.545321 | − | 0.838227i | \(-0.683592\pi\) | ||||
−0.545321 | + | 0.838227i | \(0.683592\pi\) | |||||||
\(444\) | − 8844.33i | − 0.945346i | ||||||||
\(445\) | −3265.20 | −0.347833 | ||||||||
\(446\) | −11600.6 | −1.23162 | ||||||||
\(447\) | 1141.35i | 0.120770i | ||||||||
\(448\) | − 4217.13i | − 0.444733i | ||||||||
\(449\) | − 17142.5i | − 1.80179i | −0.434037 | − | 0.900895i | \(-0.642911\pi\) | ||||
0.434037 | − | 0.900895i | \(-0.357089\pi\) | |||||||
\(450\) | − 4293.28i | − 0.449750i | ||||||||
\(451\) | 1808.73 | 0.188846 | ||||||||
\(452\) | 13924.8 | 1.44905 | ||||||||
\(453\) | 4552.36i | 0.472160i | ||||||||
\(454\) | 18629.7 | 1.92585 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1251.70 | 0.128544 | ||||||||
\(457\) | − 14091.1i | − 1.44235i | −0.692750 | − | 0.721177i | \(-0.743601\pi\) | ||||
0.692750 | − | 0.721177i | \(-0.256399\pi\) | |||||||
\(458\) | −5381.76 | −0.549068 | ||||||||
\(459\) | −779.181 | −0.0792355 | ||||||||
\(460\) | − 3266.34i | − 0.331074i | ||||||||
\(461\) | 2922.22i | 0.295231i | 0.989045 | + | 0.147616i | \(0.0471598\pi\) | ||||
−0.989045 | + | 0.147616i | \(0.952840\pi\) | |||||||
\(462\) | 2666.01i | 0.268472i | ||||||||
\(463\) | − 2072.61i | − 0.208040i | −0.994575 | − | 0.104020i | \(-0.966829\pi\) | ||||
0.994575 | − | 0.104020i | \(-0.0331706\pi\) | |||||||
\(464\) | −8806.13 | −0.881065 | ||||||||
\(465\) | 348.352 | 0.0347407 | ||||||||
\(466\) | − 13855.9i | − 1.37739i | ||||||||
\(467\) | 2664.19 | 0.263992 | 0.131996 | − | 0.991250i | \(-0.457861\pi\) | ||||
0.131996 | + | 0.991250i | \(0.457861\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 382.114 | 0.0376213 | ||||||||
\(470\) | − 6514.01i | − 0.639295i | ||||||||
\(471\) | −4350.47 | −0.425603 | ||||||||
\(472\) | −2706.91 | −0.263974 | ||||||||
\(473\) | − 4124.08i | − 0.400899i | ||||||||
\(474\) | 11154.9i | 1.08093i | ||||||||
\(475\) | 11707.8i | 1.13093i | ||||||||
\(476\) | 1735.82i | 0.167145i | ||||||||
\(477\) | −6259.91 | −0.600884 | ||||||||
\(478\) | 19531.8 | 1.86897 | ||||||||
\(479\) | − 5220.70i | − 0.497995i | −0.968504 | − | 0.248998i | \(-0.919899\pi\) | ||||
0.968504 | − | 0.248998i | \(-0.0801011\pi\) | |||||||
\(480\) | 2376.81 | 0.226013 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 19730.2 | 1.86449 | ||||||||
\(483\) | 2385.72i | 0.224749i | ||||||||
\(484\) | −2618.46 | −0.245911 | ||||||||
\(485\) | 5351.28 | 0.501008 | ||||||||
\(486\) | 1001.91i | 0.0935139i | ||||||||
\(487\) | 12224.6i | 1.13747i | 0.822520 | + | 0.568737i | \(0.192568\pi\) | ||||
−0.822520 | + | 0.568737i | \(0.807432\pi\) | |||||||
\(488\) | 2891.55i | 0.268226i | ||||||||
\(489\) | − 7027.08i | − 0.649848i | ||||||||
\(490\) | 3751.77 | 0.345893 | ||||||||
\(491\) | −19653.2 | −1.80639 | −0.903195 | − | 0.429231i | \(-0.858784\pi\) | ||||
−0.903195 | + | 0.429231i | \(0.858784\pi\) | |||||||
\(492\) | − 1514.29i | − 0.138759i | ||||||||
\(493\) | 4620.59 | 0.422111 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −885.279 | −0.0803845 | ||||||||
\(496\) | − 2093.88i | − 0.189552i | ||||||||
\(497\) | −2066.63 | −0.186522 | ||||||||
\(498\) | 8498.90 | 0.764749 | ||||||||
\(499\) | 11713.6i | 1.05084i | 0.850842 | + | 0.525422i | \(0.176093\pi\) | ||||
−0.850842 | + | 0.525422i | \(0.823907\pi\) | |||||||
\(500\) | − 6607.26i | − 0.590972i | ||||||||
\(501\) | 120.219i | 0.0107206i | ||||||||
\(502\) | − 13498.5i | − 1.20013i | ||||||||
\(503\) | 13003.3 | 1.15266 | 0.576332 | − | 0.817216i | \(-0.304483\pi\) | ||||
0.576332 | + | 0.817216i | \(0.304483\pi\) | |||||||
\(504\) | 248.001 | 0.0219184 | ||||||||
\(505\) | 1954.60i | 0.172235i | ||||||||
\(506\) | 15822.1 | 1.39008 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −22456.4 | −1.96130 | ||||||||
\(509\) | 5328.93i | 0.464049i | 0.972710 | + | 0.232024i | \(0.0745349\pi\) | ||||
−0.972710 | + | 0.232024i | \(0.925465\pi\) | |||||||
\(510\) | −1088.75 | −0.0945308 | ||||||||
\(511\) | −2604.54 | −0.225475 | ||||||||
\(512\) | − 16100.7i | − 1.38976i | ||||||||
\(513\) | − 2732.23i | − 0.235148i | ||||||||
\(514\) | − 26989.1i | − 2.31603i | ||||||||
\(515\) | 2114.16i | 0.180895i | ||||||||
\(516\) | −3452.72 | −0.294569 | ||||||||
\(517\) | 16704.9 | 1.42105 | ||||||||
\(518\) | 9026.37i | 0.765629i | ||||||||
\(519\) | 5728.62 | 0.484506 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11700.3 | −0.983876 | −0.491938 | − | 0.870630i | \(-0.663711\pi\) | ||||
−0.491938 | + | 0.870630i | \(0.663711\pi\) | |||||||
\(522\) | − 5941.41i | − 0.498177i | ||||||||
\(523\) | −4535.04 | −0.379165 | −0.189583 | − | 0.981865i | \(-0.560714\pi\) | ||||
−0.189583 | + | 0.981865i | \(0.560714\pi\) | |||||||
\(524\) | −393.814 | −0.0328318 | ||||||||
\(525\) | 2319.70i | 0.192838i | ||||||||
\(526\) | − 363.664i | − 0.0301454i | ||||||||
\(527\) | 1098.66i | 0.0908128i | ||||||||
\(528\) | 5321.24i | 0.438594i | ||||||||
\(529\) | 1991.62 | 0.163690 | ||||||||
\(530\) | −8746.98 | −0.716877 | ||||||||
\(531\) | 5908.71i | 0.482893i | ||||||||
\(532\) | −6086.73 | −0.496040 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −13241.8 | −1.07309 | ||||||||
\(535\) | − 1237.33i | − 0.0999900i | ||||||||
\(536\) | −235.739 | −0.0189969 | ||||||||
\(537\) | −1529.88 | −0.122940 | ||||||||
\(538\) | 18667.8i | 1.49596i | ||||||||
\(539\) | 9621.27i | 0.768863i | ||||||||
\(540\) | 741.164i | 0.0590641i | ||||||||
\(541\) | − 5184.89i | − 0.412044i | −0.978547 | − | 0.206022i | \(-0.933948\pi\) | ||||
0.978547 | − | 0.206022i | \(-0.0660519\pi\) | |||||||
\(542\) | 34311.7 | 2.71922 | ||||||||
\(543\) | −6410.64 | −0.506643 | ||||||||
\(544\) | 7496.18i | 0.590801i | ||||||||
\(545\) | −1462.55 | −0.114952 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5609.12 | 0.438443 | 0.219222 | − | 0.975675i | \(-0.429648\pi\) | ||||
0.219222 | + | 0.975675i | \(0.429648\pi\) | |||||||
\(548\) | 1855.75i | 0.144660i | ||||||||
\(549\) | 6311.74 | 0.490671 | ||||||||
\(550\) | 15384.2 | 1.19270 | ||||||||
\(551\) | 16202.3i | 1.25271i | ||||||||
\(552\) | − 1471.83i | − 0.113487i | ||||||||
\(553\) | − 6027.08i | − 0.463468i | ||||||||
\(554\) | − 11879.9i | − 0.911066i | ||||||||
\(555\) | −2997.30 | −0.229241 | ||||||||
\(556\) | 900.000 | 0.0686484 | ||||||||
\(557\) | − 20150.5i | − 1.53286i | −0.642326 | − | 0.766432i | \(-0.722030\pi\) | ||||
0.642326 | − | 0.766432i | \(-0.277970\pi\) | |||||||
\(558\) | 1412.72 | 0.107178 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1121.14 | −0.0846011 | ||||||||
\(561\) | − 2792.06i | − 0.210127i | ||||||||
\(562\) | −11618.9 | −0.872087 | ||||||||
\(563\) | −16292.2 | −1.21960 | −0.609800 | − | 0.792556i | \(-0.708750\pi\) | ||||
−0.609800 | + | 0.792556i | \(0.708750\pi\) | |||||||
\(564\) | − 13985.5i | − 1.04414i | ||||||||
\(565\) | − 4719.06i | − 0.351385i | ||||||||
\(566\) | 1090.98i | 0.0810200i | ||||||||
\(567\) | − 541.343i | − 0.0400957i | ||||||||
\(568\) | 1274.97 | 0.0941843 | ||||||||
\(569\) | −10460.5 | −0.770700 | −0.385350 | − | 0.922770i | \(-0.625919\pi\) | ||||
−0.385350 | + | 0.922770i | \(0.625919\pi\) | |||||||
\(570\) | − 3817.75i | − 0.280541i | ||||||||
\(571\) | −2225.96 | −0.163141 | −0.0815705 | − | 0.996668i | \(-0.525994\pi\) | ||||
−0.0815705 | + | 0.996668i | \(0.525994\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12173.2 | −0.887511 | ||||||||
\(574\) | 1545.45i | 0.112380i | ||||||||
\(575\) | 13766.8 | 0.998461 | ||||||||
\(576\) | 5679.00 | 0.410807 | ||||||||
\(577\) | − 4686.23i | − 0.338112i | −0.985606 | − | 0.169056i | \(-0.945928\pi\) | ||||
0.985606 | − | 0.169056i | \(-0.0540718\pi\) | |||||||
\(578\) | 16823.0i | 1.21063i | ||||||||
\(579\) | − 2620.18i | − 0.188067i | ||||||||
\(580\) | − 4395.14i | − 0.314652i | ||||||||
\(581\) | −4592.03 | −0.327899 | ||||||||
\(582\) | 21701.8 | 1.54565 | ||||||||
\(583\) | − 22431.3i | − 1.59350i | ||||||||
\(584\) | 1606.82 | 0.113854 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17698.5 | 1.24764 | ||||||||
\(587\) | − 12090.6i | − 0.850138i | −0.905161 | − | 0.425069i | \(-0.860250\pi\) | ||||
0.905161 | − | 0.425069i | \(-0.139750\pi\) | |||||||
\(588\) | 8055.03 | 0.564938 | ||||||||
\(589\) | −3852.50 | −0.269507 | ||||||||
\(590\) | 8256.25i | 0.576109i | ||||||||
\(591\) | 12441.7i | 0.865964i | ||||||||
\(592\) | 18016.2i | 1.25078i | ||||||||
\(593\) | 6135.97i | 0.424914i | 0.977170 | + | 0.212457i | \(0.0681466\pi\) | ||||
−0.977170 | + | 0.212457i | \(0.931853\pi\) | |||||||
\(594\) | −3590.19 | −0.247992 | ||||||||
\(595\) | 588.261 | 0.0405317 | ||||||||
\(596\) | 3424.06i | 0.235327i | ||||||||
\(597\) | −7212.18 | −0.494431 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6198.80 | −0.422831 | −0.211416 | − | 0.977396i | \(-0.567807\pi\) | ||||
−0.211416 | + | 0.977396i | \(0.567807\pi\) | |||||||
\(600\) | − 1431.09i | − 0.0973737i | ||||||||
\(601\) | 18345.4 | 1.24513 | 0.622565 | − | 0.782568i | \(-0.286091\pi\) | ||||
0.622565 | + | 0.782568i | \(0.286091\pi\) | |||||||
\(602\) | 3523.79 | 0.238569 | ||||||||
\(603\) | 514.575i | 0.0347514i | ||||||||
\(604\) | 13657.1i | 0.920030i | ||||||||
\(605\) | 887.384i | 0.0596319i | ||||||||
\(606\) | 7926.75i | 0.531357i | ||||||||
\(607\) | 10388.1 | 0.694631 | 0.347315 | − | 0.937748i | \(-0.387093\pi\) | ||||
0.347315 | + | 0.937748i | \(0.387093\pi\) | |||||||
\(608\) | −26285.7 | −1.75333 | ||||||||
\(609\) | 3210.19i | 0.213602i | ||||||||
\(610\) | 8819.40 | 0.585389 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2337.54 | −0.154395 | ||||||||
\(613\) | 804.480i | 0.0530060i | 0.999649 | + | 0.0265030i | \(0.00843715\pi\) | ||||
−0.999649 | + | 0.0265030i | \(0.991563\pi\) | |||||||
\(614\) | 28970.0 | 1.90413 | ||||||||
\(615\) | −513.184 | −0.0336481 | ||||||||
\(616\) | 888.671i | 0.0581259i | ||||||||
\(617\) | − 15218.3i | − 0.992973i | −0.868044 | − | 0.496486i | \(-0.834623\pi\) | ||||
0.868044 | − | 0.496486i | \(-0.165377\pi\) | |||||||
\(618\) | 8573.83i | 0.558074i | ||||||||
\(619\) | − 11462.5i | − 0.744291i | −0.928174 | − | 0.372145i | \(-0.878622\pi\) | ||||
0.928174 | − | 0.372145i | \(-0.121378\pi\) | |||||||
\(620\) | 1045.05 | 0.0676942 | ||||||||
\(621\) | −3212.73 | −0.207605 | ||||||||
\(622\) | − 4672.33i | − 0.301195i | ||||||||
\(623\) | 7154.66 | 0.460105 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12223.0 | 0.782270 | ||||||||
\(626\) | 21794.5i | 1.39151i | ||||||||
\(627\) | 9790.49 | 0.623596 | ||||||||
\(628\) | −13051.4 | −0.829311 | ||||||||
\(629\) | − 9453.14i | − 0.599239i | ||||||||
\(630\) | − 756.419i | − 0.0478356i | ||||||||
\(631\) | − 4468.68i | − 0.281926i | −0.990015 | − | 0.140963i | \(-0.954980\pi\) | ||||
0.990015 | − | 0.140963i | \(-0.0450199\pi\) | |||||||
\(632\) | 3718.30i | 0.234028i | ||||||||
\(633\) | −11606.6 | −0.728783 | ||||||||
\(634\) | 19717.3 | 1.23514 | ||||||||
\(635\) | 7610.37i | 0.475603i | ||||||||
\(636\) | −18779.7 | −1.17086 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 21290.0 | 1.32113 | ||||||||
\(639\) | − 2783.04i | − 0.172293i | ||||||||
\(640\) | 1597.12 | 0.0986430 | ||||||||
\(641\) | −6142.36 | −0.378484 | −0.189242 | − | 0.981930i | \(-0.560603\pi\) | ||||
−0.189242 | + | 0.981930i | \(0.560603\pi\) | |||||||
\(642\) | − 5017.93i | − 0.308477i | ||||||||
\(643\) | − 20738.2i | − 1.27190i | −0.771729 | − | 0.635951i | \(-0.780608\pi\) | ||||
0.771729 | − | 0.635951i | \(-0.219392\pi\) | |||||||
\(644\) | 7157.15i | 0.437937i | ||||||||
\(645\) | 1170.11i | 0.0714312i | ||||||||
\(646\) | 12040.7 | 0.733339 | ||||||||
\(647\) | −852.757 | −0.0518166 | −0.0259083 | − | 0.999664i | \(-0.508248\pi\) | ||||
−0.0259083 | + | 0.999664i | \(0.508248\pi\) | |||||||
\(648\) | 333.972i | 0.0202464i | ||||||||
\(649\) | −21172.8 | −1.28060 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −763.303 | −0.0459542 | ||||||||
\(652\) | − 21081.3i | − 1.26627i | ||||||||
\(653\) | −7345.75 | −0.440217 | −0.220108 | − | 0.975475i | \(-0.570641\pi\) | ||||
−0.220108 | + | 0.975475i | \(0.570641\pi\) | |||||||
\(654\) | −5931.28 | −0.354635 | ||||||||
\(655\) | 133.462i | 0.00796151i | ||||||||
\(656\) | 3084.65i | 0.183591i | ||||||||
\(657\) | − 3507.40i | − 0.208275i | ||||||||
\(658\) | 14273.4i | 0.845645i | ||||||||
\(659\) | 12540.7 | 0.741297 | 0.370648 | − | 0.928773i | \(-0.379136\pi\) | ||||
0.370648 | + | 0.928773i | \(0.379136\pi\) | |||||||
\(660\) | −2655.84 | −0.156634 | ||||||||
\(661\) | − 2242.95i | − 0.131983i | −0.997820 | − | 0.0659915i | \(-0.978979\pi\) | ||||
0.997820 | − | 0.0659915i | \(-0.0210210\pi\) | |||||||
\(662\) | −35747.3 | −2.09873 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2832.97 | 0.165573 | ||||||||
\(665\) | 2062.76i | 0.120287i | ||||||||
\(666\) | −12155.4 | −0.707224 | ||||||||
\(667\) | 19051.7 | 1.10597 | ||||||||
\(668\) | 360.658i | 0.0208896i | ||||||||
\(669\) | 8440.66i | 0.487795i | ||||||||
\(670\) | 719.016i | 0.0414597i | ||||||||
\(671\) | 22617.0i | 1.30122i | ||||||||
\(672\) | −5208.03 | −0.298964 | ||||||||
\(673\) | 4776.46 | 0.273579 | 0.136790 | − | 0.990600i | \(-0.456322\pi\) | ||||
0.136790 | + | 0.990600i | \(0.456322\pi\) | |||||||
\(674\) | 35156.0i | 2.00914i | ||||||||
\(675\) | −3123.82 | −0.178127 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7933.57 | −0.450387 | −0.225193 | − | 0.974314i | \(-0.572301\pi\) | ||||
−0.225193 | + | 0.974314i | \(0.572301\pi\) | |||||||
\(678\) | − 19137.9i | − 1.08405i | ||||||||
\(679\) | −11725.6 | −0.662723 | ||||||||
\(680\) | −362.917 | −0.0204665 | ||||||||
\(681\) | − 13555.1i | − 0.762750i | ||||||||
\(682\) | 5062.23i | 0.284227i | ||||||||
\(683\) | 23573.8i | 1.32068i | 0.750967 | + | 0.660340i | \(0.229588\pi\) | ||||
−0.750967 | + | 0.660340i | \(0.770412\pi\) | |||||||
\(684\) | − 8196.70i | − 0.458200i | ||||||||
\(685\) | 628.904 | 0.0350791 | ||||||||
\(686\) | −17672.4 | −0.983581 | ||||||||
\(687\) | 3915.81i | 0.217463i | ||||||||
\(688\) | 7033.32 | 0.389743 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −4489.15 | −0.247680 | ||||||||
\(691\) | 12543.8i | 0.690575i | 0.938497 | + | 0.345288i | \(0.112219\pi\) | ||||
−0.938497 | + | 0.345288i | \(0.887781\pi\) | |||||||
\(692\) | 17185.9 | 0.944087 | ||||||||
\(693\) | 1939.81 | 0.106331 | ||||||||
\(694\) | 51874.8i | 2.83738i | ||||||||
\(695\) | − 305.006i | − 0.0166468i | ||||||||
\(696\) | − 1980.47i | − 0.107858i | ||||||||
\(697\) | − 1618.52i | − 0.0879568i | ||||||||
\(698\) | −36947.9 | −2.00358 | ||||||||
\(699\) | −10081.6 | −0.545526 | ||||||||
\(700\) | 6959.09i | 0.375755i | ||||||||
\(701\) | 581.786 | 0.0313463 | 0.0156731 | − | 0.999877i | \(-0.495011\pi\) | ||||
0.0156731 | + | 0.999877i | \(0.495011\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 33147.9 | 1.77837 | ||||||||
\(704\) | 20349.7i | 1.08943i | ||||||||
\(705\) | −4739.64 | −0.253199 | ||||||||
\(706\) | 22091.6 | 1.17766 | ||||||||
\(707\) | − 4282.89i | − 0.227828i | ||||||||
\(708\) | 17726.1i | 0.940944i | ||||||||
\(709\) | − 20742.0i | − 1.09871i | −0.835590 | − | 0.549353i | \(-0.814874\pi\) | ||||
0.835590 | − | 0.549353i | \(-0.185126\pi\) | |||||||
\(710\) | − 3888.74i | − 0.205552i | ||||||||
\(711\) | 8116.38 | 0.428113 | ||||||||
\(712\) | −4413.94 | −0.232331 | ||||||||
\(713\) | 4530.01i | 0.237938i | ||||||||
\(714\) | 2385.66 | 0.125043 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4589.63 | −0.239556 | ||||||||
\(717\) | − 14211.5i | − 0.740221i | ||||||||
\(718\) | −11154.6 | −0.579788 | ||||||||
\(719\) | −25350.2 | −1.31489 | −0.657443 | − | 0.753504i | \(-0.728362\pi\) | ||||
−0.657443 | + | 0.753504i | \(0.728362\pi\) | |||||||
\(720\) | − 1509.78i | − 0.0781474i | ||||||||
\(721\) | − 4632.51i | − 0.239284i | ||||||||
\(722\) | 13941.0i | 0.718602i | ||||||||
\(723\) | − 14355.8i | − 0.738449i | ||||||||
\(724\) | −19231.9 | −0.987223 | ||||||||
\(725\) | 18524.4 | 0.948938 | ||||||||
\(726\) | 3598.73i | 0.183969i | ||||||||
\(727\) | −33428.2 | −1.70534 | −0.852672 | − | 0.522447i | \(-0.825019\pi\) | ||||
−0.852672 | + | 0.522447i | \(0.825019\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | − 4900.90i | − 0.248480i | ||||||||
\(731\) | −3690.39 | −0.186722 | ||||||||
\(732\) | 18935.2 | 0.956101 | ||||||||
\(733\) | 3842.67i | 0.193632i | 0.995302 | + | 0.0968160i | \(0.0308658\pi\) | ||||
−0.995302 | + | 0.0968160i | \(0.969134\pi\) | |||||||
\(734\) | − 43184.4i | − 2.17162i | ||||||||
\(735\) | − 2729.81i | − 0.136994i | ||||||||
\(736\) | 30908.3i | 1.54796i | ||||||||
\(737\) | −1843.89 | −0.0921582 | ||||||||
\(738\) | −2081.19 | −0.103807 | ||||||||
\(739\) | 29029.6i | 1.44502i | 0.691359 | + | 0.722511i | \(0.257012\pi\) | ||||
−0.691359 | + | 0.722511i | \(0.742988\pi\) | |||||||
\(740\) | −8991.91 | −0.446688 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 19166.3 | 0.948269 | ||||||||
\(743\) | 34996.7i | 1.72800i | 0.503492 | + | 0.864000i | \(0.332048\pi\) | ||||
−0.503492 | + | 0.864000i | \(0.667952\pi\) | |||||||
\(744\) | 470.906 | 0.0232046 | ||||||||
\(745\) | 1160.40 | 0.0570653 | ||||||||
\(746\) | 52623.2i | 2.58267i | ||||||||
\(747\) | − 6183.86i | − 0.302886i | ||||||||
\(748\) | − 8376.19i | − 0.409444i | ||||||||
\(749\) | 2711.23i | 0.132265i | ||||||||
\(750\) | −9080.82 | −0.442113 | ||||||||
\(751\) | −10454.1 | −0.507957 | −0.253979 | − | 0.967210i | \(-0.581739\pi\) | ||||
−0.253979 | + | 0.967210i | \(0.581739\pi\) | |||||||
\(752\) | 28489.1i | 1.38150i | ||||||||
\(753\) | −9821.58 | −0.475323 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4628.32 | 0.223102 | ||||||||
\(756\) | − 1624.03i | − 0.0781287i | ||||||||
\(757\) | −28130.4 | −1.35062 | −0.675308 | − | 0.737536i | \(-0.735989\pi\) | ||||
−0.675308 | + | 0.737536i | \(0.735989\pi\) | |||||||
\(758\) | 9557.45 | 0.457971 | ||||||||
\(759\) | − 11512.3i | − 0.550552i | ||||||||
\(760\) | − 1272.58i | − 0.0607388i | ||||||||
\(761\) | 21087.0i | 1.00447i | 0.864731 | + | 0.502236i | \(0.167489\pi\) | ||||
−0.864731 | + | 0.502236i | \(0.832511\pi\) | |||||||
\(762\) | 30863.4i | 1.46727i | ||||||||
\(763\) | 3204.72 | 0.152056 | ||||||||
\(764\) | −36519.7 | −1.72937 | ||||||||
\(765\) | 792.183i | 0.0374398i | ||||||||
\(766\) | −8177.54 | −0.385727 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −8667.00 | −0.407218 | ||||||||
\(769\) | − 19527.9i | − 0.915728i | −0.889022 | − | 0.457864i | \(-0.848615\pi\) | ||||
0.889022 | − | 0.457864i | \(-0.151385\pi\) | |||||||
\(770\) | 2710.50 | 0.126857 | ||||||||
\(771\) | −19637.4 | −0.917283 | ||||||||
\(772\) | − 7860.55i | − 0.366460i | ||||||||
\(773\) | 29352.0i | 1.36574i | 0.730540 | + | 0.682870i | \(0.239269\pi\) | ||||
−0.730540 | + | 0.682870i | \(0.760731\pi\) | |||||||
\(774\) | 4745.31i | 0.220370i | ||||||||
\(775\) | 4404.64i | 0.204154i | ||||||||
\(776\) | 7233.92 | 0.334643 | ||||||||
\(777\) | 6567.65 | 0.303234 | ||||||||
\(778\) | − 13377.5i | − 0.616459i | ||||||||
\(779\) | 5675.42 | 0.261031 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9972.54 | 0.456908 | ||||||||
\(782\) | − 14158.3i | − 0.647440i | ||||||||
\(783\) | −4323.01 | −0.197307 | ||||||||
\(784\) | −16408.4 | −0.747467 | ||||||||
\(785\) | 4423.06i | 0.201103i | ||||||||
\(786\) | 541.246i | 0.0245618i | ||||||||
\(787\) | 4463.12i | 0.202151i | 0.994879 | + | 0.101076i | \(0.0322284\pi\) | ||||
−0.994879 | + | 0.101076i | \(0.967772\pi\) | |||||||
\(788\) | 37325.2i | 1.68738i | ||||||||
\(789\) | −264.604 | −0.0119394 | ||||||||
\(790\) | 11341.0 | 0.510754 | ||||||||
\(791\) | 10340.3i | 0.464804i | ||||||||
\(792\) | −1196.73 | −0.0536919 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 15501.7 | 0.692866 | ||||||||
\(795\) | 6364.37i | 0.283926i | ||||||||
\(796\) | −21636.6 | −0.963426 | ||||||||
\(797\) | 34785.5 | 1.54600 | 0.773002 | − | 0.634404i | \(-0.218754\pi\) | ||||
0.773002 | + | 0.634404i | \(0.218754\pi\) | |||||||
\(798\) | 8365.40i | 0.371093i | ||||||||
\(799\) | − 14948.2i | − 0.661866i | ||||||||
\(800\) | 30053.0i | 1.32817i | ||||||||
\(801\) | 9634.84i | 0.425007i | ||||||||
\(802\) | −8236.09 | −0.362627 | ||||||||
\(803\) | 12568.2 | 0.552330 | ||||||||
\(804\) | 1543.72i | 0.0677152i | ||||||||
\(805\) | 2425.53 | 0.106197 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13582.8 | 0.592487 | ||||||||
\(808\) | 2642.25i | 0.115042i | ||||||||
\(809\) | −10620.0 | −0.461530 | −0.230765 | − | 0.973010i | \(-0.574123\pi\) | ||||
−0.230765 | + | 0.973010i | \(0.574123\pi\) | |||||||
\(810\) | 1018.63 | 0.0441866 | ||||||||
\(811\) | − 5497.87i | − 0.238047i | −0.992891 | − | 0.119024i | \(-0.962024\pi\) | ||||
0.992891 | − | 0.119024i | \(-0.0379764\pi\) | |||||||
\(812\) | 9630.57i | 0.416215i | ||||||||
\(813\) | − 24965.5i | − 1.07697i | ||||||||
\(814\) | − 43556.7i | − 1.87551i | ||||||||
\(815\) | −7144.34 | −0.307062 | ||||||||
\(816\) | 4761.66 | 0.204279 | ||||||||
\(817\) | − 12940.5i | − 0.554139i | ||||||||
\(818\) | 21420.5 | 0.915587 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1539.55 | −0.0655653 | ||||||||
\(821\) | − 21305.3i | − 0.905678i | −0.891592 | − | 0.452839i | \(-0.850411\pi\) | ||||
0.891592 | − | 0.452839i | \(-0.149589\pi\) | |||||||
\(822\) | 2550.48 | 0.108222 | ||||||||
\(823\) | −17342.6 | −0.734537 | −0.367268 | − | 0.930115i | \(-0.619707\pi\) | ||||
−0.367268 | + | 0.930115i | \(0.619707\pi\) | |||||||
\(824\) | 2857.94i | 0.120827i | ||||||||
\(825\) | − 11193.7i | − 0.472381i | ||||||||
\(826\) | − 18091.0i | − 0.762064i | ||||||||
\(827\) | 5129.96i | 0.215703i | 0.994167 | + | 0.107851i | \(0.0343971\pi\) | ||||
−0.994167 | + | 0.107851i | \(0.965603\pi\) | |||||||
\(828\) | −9638.19 | −0.404529 | ||||||||
\(829\) | 8471.81 | 0.354931 | 0.177466 | − | 0.984127i | \(-0.443210\pi\) | ||||
0.177466 | + | 0.984127i | \(0.443210\pi\) | |||||||
\(830\) | − 8640.72i | − 0.361354i | ||||||||
\(831\) | −8643.93 | −0.360836 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8609.50 | 0.358105 | ||||||||
\(834\) | − 1236.93i | − 0.0513566i | ||||||||
\(835\) | 122.225 | 0.00506561 | ||||||||
\(836\) | 29371.5 | 1.21511 | ||||||||
\(837\) | − 1027.90i | − 0.0424486i | ||||||||
\(838\) | 28128.3i | 1.15952i | ||||||||
\(839\) | − 19155.0i | − 0.788207i | −0.919066 | − | 0.394103i | \(-0.871055\pi\) | ||||
0.919066 | − | 0.394103i | \(-0.128945\pi\) | |||||||
\(840\) | − 252.140i | − 0.0103567i | ||||||||
\(841\) | 1246.67 | 0.0511160 | ||||||||
\(842\) | −31078.7 | −1.27202 | ||||||||
\(843\) | 8453.98i | 0.345398i | ||||||||
\(844\) | −34819.7 | −1.42007 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −19221.3 | −0.781136 | ||||||||
\(847\) | − 1944.42i | − 0.0788797i | ||||||||
\(848\) | 38255.0 | 1.54915 | ||||||||
\(849\) | 793.804 | 0.0320887 | ||||||||
\(850\) | − 13766.4i | − 0.555512i | ||||||||
\(851\) | − 38977.3i | − 1.57006i | ||||||||
\(852\) | − 8349.11i | − 0.335723i | ||||||||
\(853\) | − 18075.1i | − 0.725532i | −0.931880 | − | 0.362766i | \(-0.881832\pi\) | ||||
0.931880 | − | 0.362766i | \(-0.118168\pi\) | |||||||
\(854\) | −19324.9 | −0.774339 | ||||||||
\(855\) | −2777.82 | −0.111111 | ||||||||
\(856\) | − 1672.64i | − 0.0667871i | ||||||||
\(857\) | 21054.6 | 0.839219 | 0.419609 | − | 0.907705i | \(-0.362167\pi\) | ||||
0.419609 | + | 0.907705i | \(0.362167\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 920.322 | 0.0365553 | 0.0182776 | − | 0.999833i | \(-0.494182\pi\) | ||||
0.0182776 | + | 0.999833i | \(0.494182\pi\) | |||||||
\(860\) | 3510.33i | 0.139188i | ||||||||
\(861\) | 1124.48 | 0.0445090 | ||||||||
\(862\) | 55267.0 | 2.18376 | ||||||||
\(863\) | 19427.5i | 0.766304i | 0.923685 | + | 0.383152i | \(0.125161\pi\) | ||||
−0.923685 | + | 0.383152i | \(0.874839\pi\) | |||||||
\(864\) | − 7013.40i | − 0.276158i | ||||||||
\(865\) | − 5824.21i | − 0.228935i | ||||||||
\(866\) | − 73044.7i | − 2.86623i | ||||||||
\(867\) | 12240.5 | 0.479482 | ||||||||
\(868\) | −2289.91 | −0.0895444 | ||||||||
\(869\) | 29083.7i | 1.13532i | ||||||||
\(870\) | −6040.55 | −0.235395 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −1977.09 | −0.0767808 | ||||||||
\(873\) | − 15790.3i | − 0.612168i | ||||||||
\(874\) | 49646.5 | 1.92142 | ||||||||
\(875\) | 4906.44 | 0.189563 | ||||||||
\(876\) | − 10522.2i | − 0.405836i | ||||||||
\(877\) | − 14872.2i | − 0.572632i | −0.958135 | − | 0.286316i | \(-0.907569\pi\) | ||||
0.958135 | − | 0.286316i | \(-0.0924306\pi\) | |||||||
\(878\) | 29535.7i | 1.13529i | ||||||||
\(879\) | − 12877.6i | − 0.494141i | ||||||||
\(880\) | 5410.04 | 0.207241 | ||||||||
\(881\) | 12940.6 | 0.494870 | 0.247435 | − | 0.968905i | \(-0.420412\pi\) | ||||
0.247435 | + | 0.968905i | \(0.420412\pi\) | |||||||
\(882\) | − 11070.6i | − 0.422637i | ||||||||
\(883\) | 25585.5 | 0.975108 | 0.487554 | − | 0.873093i | \(-0.337889\pi\) | ||||
0.487554 | + | 0.873093i | \(0.337889\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6007.30 | 0.228173 | ||||||||
\(886\) | 41928.8i | 1.58987i | ||||||||
\(887\) | 3716.46 | 0.140684 | 0.0703418 | − | 0.997523i | \(-0.477591\pi\) | ||||
0.0703418 | + | 0.997523i | \(0.477591\pi\) | |||||||
\(888\) | −4051.79 | −0.153118 | ||||||||
\(889\) | − 16675.7i | − 0.629118i | ||||||||
\(890\) | 13462.8i | 0.507049i | ||||||||
\(891\) | 2612.25i | 0.0982195i | ||||||||
\(892\) | 25322.0i | 0.950496i | ||||||||
\(893\) | 52416.7 | 1.96423 | ||||||||
\(894\) | 4705.92 | 0.176051 | ||||||||
\(895\) | 1555.40i | 0.0580910i | ||||||||
\(896\) | −3499.58 | −0.130483 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −70680.3 | −2.62654 | ||||||||
\(899\) | 6095.52i | 0.226137i | ||||||||
\(900\) | −9371.47 | −0.347091 | ||||||||
\(901\) | −20072.5 | −0.742187 | ||||||||
\(902\) | − 7457.57i | − 0.275288i | ||||||||
\(903\) | − 2563.93i | − 0.0944876i | ||||||||
\(904\) | − 6379.29i | − 0.234703i | ||||||||
\(905\) | 6517.61i | 0.239395i | ||||||||
\(906\) | 18769.8 | 0.688285 | ||||||||
\(907\) | 12960.4 | 0.474469 | 0.237235 | − | 0.971452i | \(-0.423759\pi\) | ||||
0.237235 | + | 0.971452i | \(0.423759\pi\) | |||||||
\(908\) | − 40665.3i | − 1.48626i | ||||||||
\(909\) | 5767.56 | 0.210449 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36607.1 | −1.33134 | −0.665668 | − | 0.746248i | \(-0.731853\pi\) | ||||
−0.665668 | + | 0.746248i | \(0.731853\pi\) | |||||||
\(912\) | 16697.0i | 0.606242i | ||||||||
\(913\) | 22158.8 | 0.803230 | ||||||||
\(914\) | −58099.3 | −2.10258 | ||||||||
\(915\) | − 6417.06i | − 0.231849i | ||||||||
\(916\) | 11747.4i | 0.423740i | ||||||||
\(917\) | − 292.440i | − 0.0105313i | ||||||||
\(918\) | 3212.65i | 0.115505i | ||||||||
\(919\) | 20356.3 | 0.730676 | 0.365338 | − | 0.930875i | \(-0.380953\pi\) | ||||
0.365338 | + | 0.930875i | \(0.380953\pi\) | |||||||
\(920\) | −1496.38 | −0.0536243 | ||||||||
\(921\) | − 21078.8i | − 0.754147i | ||||||||
\(922\) | 12048.6 | 0.430370 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 5819.43 | 0.207192 | ||||||||
\(925\) | − 37898.7i | − 1.34714i | ||||||||
\(926\) | −8545.61 | −0.303268 | ||||||||
\(927\) | 6238.38 | 0.221030 | ||||||||
\(928\) | 41589.8i | 1.47118i | ||||||||
\(929\) | 45069.7i | 1.59170i | 0.605495 | + | 0.795849i | \(0.292975\pi\) | ||||
−0.605495 | + | 0.795849i | \(0.707025\pi\) | |||||||
\(930\) | − 1436.29i | − 0.0506428i | ||||||||
\(931\) | 30189.6i | 1.06275i | ||||||||
\(932\) | −30244.9 | −1.06299 | ||||||||
\(933\) | −3399.62 | −0.119291 | ||||||||
\(934\) | − 10984.7i | − 0.384831i | ||||||||
\(935\) | −2838.65 | −0.0992876 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6771.10 | −0.236075 | −0.118037 | − | 0.993009i | \(-0.537660\pi\) | ||||
−0.118037 | + | 0.993009i | \(0.537660\pi\) | |||||||
\(938\) | − 1575.50i | − 0.0548420i | ||||||||
\(939\) | 15857.8 | 0.551119 | ||||||||
\(940\) | −14218.9 | −0.493372 | ||||||||
\(941\) | − 36690.7i | − 1.27108i | −0.772070 | − | 0.635538i | \(-0.780778\pi\) | ||||
0.772070 | − | 0.635538i | \(-0.219222\pi\) | |||||||
\(942\) | 17937.4i | 0.620417i | ||||||||
\(943\) | − 6673.51i | − 0.230455i | ||||||||
\(944\) | − 36108.8i | − 1.24496i | ||||||||
\(945\) | −550.376 | −0.0189457 | ||||||||
\(946\) | −17004.0 | −0.584406 | ||||||||
\(947\) | − 50861.2i | − 1.74527i | −0.488375 | − | 0.872634i | \(-0.662410\pi\) | ||||
0.488375 | − | 0.872634i | \(-0.337590\pi\) | |||||||
\(948\) | 24349.1 | 0.834202 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 48272.6 | 1.64860 | ||||||||
\(951\) | − 14346.5i | − 0.489187i | ||||||||
\(952\) | 795.219 | 0.0270727 | ||||||||
\(953\) | −11855.6 | −0.402980 | −0.201490 | − | 0.979491i | \(-0.564578\pi\) | ||||
−0.201490 | + | 0.979491i | \(0.564578\pi\) | |||||||
\(954\) | 25810.3i | 0.875931i | ||||||||
\(955\) | 12376.4i | 0.419361i | ||||||||
\(956\) | − 42634.5i | − 1.44236i | ||||||||
\(957\) | − 15490.8i | − 0.523245i | ||||||||
\(958\) | −21525.5 | −0.725947 | ||||||||
\(959\) | −1378.04 | −0.0464019 | ||||||||
\(960\) | − 5773.76i | − 0.194112i | ||||||||
\(961\) | 28341.6 | 0.951349 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3651.08 | −0.122175 | ||||||||
\(964\) | − 43067.5i | − 1.43891i | ||||||||
\(965\) | −2663.90 | −0.0888643 | ||||||||
\(966\) | 9836.56 | 0.327625 | ||||||||
\(967\) | − 40661.7i | − 1.35221i | −0.736803 | − | 0.676107i | \(-0.763666\pi\) | ||||
0.736803 | − | 0.676107i | \(-0.236334\pi\) | |||||||
\(968\) | 1199.58i | 0.0398304i | ||||||||
\(969\) | − 8760.93i | − 0.290445i | ||||||||
\(970\) | − 22063.9i | − 0.730339i | ||||||||
\(971\) | 57318.3 | 1.89437 | 0.947184 | − | 0.320690i | \(-0.103915\pi\) | ||||
0.947184 | + | 0.320690i | \(0.103915\pi\) | |||||||
\(972\) | 2187.00 | 0.0721688 | ||||||||
\(973\) | 668.324i | 0.0220200i | ||||||||
\(974\) | 50403.3 | 1.65814 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −38571.7 | −1.26501 | ||||||||
\(977\) | 3026.73i | 0.0991134i | 0.998771 | + | 0.0495567i | \(0.0157808\pi\) | ||||
−0.998771 | + | 0.0495567i | \(0.984219\pi\) | |||||||
\(978\) | −28973.4 | −0.947308 | ||||||||
\(979\) | −34524.8 | −1.12709 | ||||||||
\(980\) | − 8189.43i | − 0.266941i | ||||||||
\(981\) | 4315.64i | 0.140457i | ||||||||
\(982\) | 81032.3i | 2.63324i | ||||||||
\(983\) | 33942.5i | 1.10132i | 0.834730 | + | 0.550659i | \(0.185624\pi\) | ||||
−0.834730 | + | 0.550659i | \(0.814376\pi\) | |||||||
\(984\) | −693.729 | −0.0224749 | ||||||||
\(985\) | 12649.3 | 0.409179 | ||||||||
\(986\) | − 19051.2i | − 0.615327i | ||||||||
\(987\) | 10385.4 | 0.334925 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15216.3 | −0.489231 | ||||||||
\(990\) | 3650.10i | 0.117179i | ||||||||
\(991\) | 21637.5 | 0.693580 | 0.346790 | − | 0.937943i | \(-0.387272\pi\) | ||||
0.346790 | + | 0.937943i | \(0.387272\pi\) | |||||||
\(992\) | −9889.02 | −0.316509 | ||||||||
\(993\) | 26009.9i | 0.831219i | ||||||||
\(994\) | 8520.95i | 0.271900i | ||||||||
\(995\) | 7332.53i | 0.233625i | ||||||||
\(996\) | − 18551.6i | − 0.590190i | ||||||||
\(997\) | 19624.6 | 0.623388 | 0.311694 | − | 0.950182i | \(-0.399104\pi\) | ||||
0.311694 | + | 0.950182i | \(0.399104\pi\) | |||||||
\(998\) | 48296.3 | 1.53186 | ||||||||
\(999\) | 8844.33i | 0.280102i |
(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 | 507.4.b.e.337.1 | 4 | ||
13.3 | even | 3 | 39.4.j.b.4.2 | ✓ | 4 | ||
13.4 | even | 6 | 39.4.j.b.10.2 | yes | 4 | ||
13.5 | odd | 4 | 507.4.a.k.1.1 | 4 | |||
13.8 | odd | 4 | 507.4.a.k.1.4 | 4 | |||
13.12 | even | 2 | inner | 507.4.b.e.337.4 | 4 | ||
39.5 | even | 4 | 1521.4.a.z.1.4 | 4 | |||
39.8 | even | 4 | 1521.4.a.z.1.1 | 4 | |||
39.17 | odd | 6 | 117.4.q.d.10.1 | 4 | |||
39.29 | odd | 6 | 117.4.q.d.82.1 | 4 | |||
52.3 | odd | 6 | 624.4.bv.c.433.2 | 4 | |||
52.43 | odd | 6 | 624.4.bv.c.49.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.j.b.4.2 | ✓ | 4 | 13.3 | even | 3 | ||
39.4.j.b.10.2 | yes | 4 | 13.4 | even | 6 | ||
117.4.q.d.10.1 | 4 | 39.17 | odd | 6 | |||
117.4.q.d.82.1 | 4 | 39.29 | odd | 6 | |||
507.4.a.k.1.1 | 4 | 13.5 | odd | 4 | |||
507.4.a.k.1.4 | 4 | 13.8 | odd | 4 | |||
507.4.b.e.337.1 | 4 | 1.1 | even | 1 | trivial | ||
507.4.b.e.337.4 | 4 | 13.12 | even | 2 | inner | ||
624.4.bv.c.49.1 | 4 | 52.43 | odd | 6 | |||
624.4.bv.c.433.2 | 4 | 52.3 | odd | 6 | |||
1521.4.a.z.1.1 | 4 | 39.8 | even | 4 | |||
1521.4.a.z.1.4 | 4 | 39.5 | even | 4 |