Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,4,Mod(4,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.4");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.23904011012\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.9924270768.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 25x^{4} + 12x^{3} + 582x^{2} - 144x + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 4.3 | ||
Root | \(-2.27818 - 3.94593i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.4 |
Dual form | 21.4.e.b.16.3 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.27818 | + | 3.94593i | 0.805459 | + | 1.39510i | 0.915981 | + | 0.401223i | \(0.131415\pi\) |
−0.110521 | + | 0.993874i | \(0.535252\pi\) | |||||||
\(3\) | 1.50000 | − | 2.59808i | 0.288675 | − | 0.500000i | ||||
\(4\) | −6.38024 | + | 11.0509i | −0.797530 | + | 1.38136i | ||||
\(5\) | −8.93660 | − | 15.4786i | −0.799314 | − | 1.38445i | −0.920063 | − | 0.391769i | \(-0.871863\pi\) |
0.120749 | − | 0.992683i | \(-0.461470\pi\) | |||||||
\(6\) | 13.6691 | 0.930064 | ||||||||
\(7\) | 2.26047 | + | 18.3818i | 0.122054 | + | 0.992523i | ||||
\(8\) | −21.6905 | −0.958592 | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.166667 | − | 0.288675i | ||||
\(10\) | 40.7184 | − | 70.5264i | 1.28763 | − | 2.23024i | ||||
\(11\) | 5.69708 | − | 9.86762i | 0.156158 | − | 0.270473i | −0.777322 | − | 0.629102i | \(-0.783423\pi\) |
0.933480 | + | 0.358630i | \(0.116756\pi\) | |||||||
\(12\) | 19.1407 | + | 33.1527i | 0.460454 | + | 0.797530i | ||||
\(13\) | −13.0987 | −0.279455 | −0.139728 | − | 0.990190i | \(-0.544623\pi\) | ||||
−0.139728 | + | 0.990190i | \(0.544623\pi\) | |||||||
\(14\) | −67.3835 | + | 50.7968i | −1.28636 | + | 0.969714i | ||||
\(15\) | −53.6196 | −0.922968 | ||||||||
\(16\) | 1.62706 | + | 2.81815i | 0.0254228 | + | 0.0440336i | ||||
\(17\) | −26.6337 | + | 46.1309i | −0.379977 | + | 0.658140i | −0.991059 | − | 0.133428i | \(-0.957402\pi\) |
0.611081 | + | 0.791568i | \(0.290735\pi\) | |||||||
\(18\) | 20.5036 | − | 35.5134i | 0.268486 | − | 0.465032i | ||||
\(19\) | 21.2111 | + | 36.7388i | 0.256114 | + | 0.443603i | 0.965198 | − | 0.261522i | \(-0.0842244\pi\) |
−0.709083 | + | 0.705125i | \(0.750891\pi\) | |||||||
\(20\) | 228.071 | 2.54991 | ||||||||
\(21\) | 51.1480 | + | 21.6998i | 0.531496 | + | 0.225490i | ||||
\(22\) | 51.9159 | 0.503114 | ||||||||
\(23\) | −76.0427 | − | 131.710i | −0.689391 | − | 1.19406i | −0.972035 | − | 0.234836i | \(-0.924545\pi\) |
0.282644 | − | 0.959225i | \(-0.408789\pi\) | |||||||
\(24\) | −32.5357 | + | 56.3535i | −0.276722 | + | 0.479296i | ||||
\(25\) | −97.2257 | + | 168.400i | −0.777806 | + | 1.34720i | ||||
\(26\) | −29.8412 | − | 51.6864i | −0.225090 | − | 0.389867i | ||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −217.558 | − | 92.2999i | −1.46838 | − | 0.622966i | ||||
\(29\) | 186.493 | 1.19417 | 0.597085 | − | 0.802178i | \(-0.296325\pi\) | ||||
0.597085 | + | 0.802178i | \(0.296325\pi\) | |||||||
\(30\) | −122.155 | − | 211.579i | −0.743413 | − | 1.28763i | ||||
\(31\) | 78.9369 | − | 136.723i | 0.457338 | − | 0.792133i | −0.541481 | − | 0.840713i | \(-0.682136\pi\) |
0.998819 | + | 0.0485801i | \(0.0154696\pi\) | |||||||
\(32\) | −94.1753 | + | 163.116i | −0.520250 | + | 0.901099i | ||||
\(33\) | −17.0912 | − | 29.6029i | −0.0901576 | − | 0.156158i | ||||
\(34\) | −242.706 | −1.22423 | ||||||||
\(35\) | 264.324 | − | 199.260i | 1.27654 | − | 0.962316i | ||||
\(36\) | 114.844 | 0.531686 | ||||||||
\(37\) | −1.87294 | − | 3.24403i | −0.00832188 | − | 0.0144139i | 0.861834 | − | 0.507190i | \(-0.169316\pi\) |
−0.870156 | + | 0.492776i | \(0.835982\pi\) | |||||||
\(38\) | −96.6457 | + | 167.395i | −0.412579 | + | 0.714608i | ||||
\(39\) | −19.6480 | + | 34.0313i | −0.0806718 | + | 0.139728i | ||||
\(40\) | 193.839 | + | 335.739i | 0.766216 | + | 1.32712i | ||||
\(41\) | −39.3230 | −0.149786 | −0.0748930 | − | 0.997192i | \(-0.523862\pi\) | ||||
−0.0748930 | + | 0.997192i | \(0.523862\pi\) | |||||||
\(42\) | 30.8986 | + | 251.263i | 0.113518 | + | 0.923111i | ||||
\(43\) | 429.439 | 1.52300 | 0.761498 | − | 0.648168i | \(-0.224464\pi\) | ||||
0.761498 | + | 0.648168i | \(0.224464\pi\) | |||||||
\(44\) | 72.6974 | + | 125.916i | 0.249080 | + | 0.431420i | ||||
\(45\) | −80.4294 | + | 139.308i | −0.266438 | + | 0.461484i | ||||
\(46\) | 346.478 | − | 600.118i | 1.11055 | − | 1.92354i | ||||
\(47\) | −10.5934 | − | 18.3484i | −0.0328768 | − | 0.0569444i | 0.849119 | − | 0.528202i | \(-0.177134\pi\) |
−0.881996 | + | 0.471258i | \(0.843800\pi\) | |||||||
\(48\) | 9.76236 | 0.0293557 | ||||||||
\(49\) | −332.781 | + | 83.1031i | −0.970206 | + | 0.242283i | ||||
\(50\) | −885.992 | −2.50596 | ||||||||
\(51\) | 79.9010 | + | 138.393i | 0.219380 | + | 0.379977i | ||||
\(52\) | 83.5726 | − | 144.752i | 0.222874 | − | 0.386029i | ||||
\(53\) | −182.952 | + | 316.882i | −0.474158 | + | 0.821266i | −0.999562 | − | 0.0295866i | \(-0.990581\pi\) |
0.525404 | + | 0.850853i | \(0.323914\pi\) | |||||||
\(54\) | −61.5109 | − | 106.540i | −0.155011 | − | 0.268486i | ||||
\(55\) | −203.650 | −0.499276 | ||||||||
\(56\) | −49.0307 | − | 398.709i | −0.117000 | − | 0.951425i | ||||
\(57\) | 127.267 | 0.295735 | ||||||||
\(58\) | 424.866 | + | 735.889i | 0.961856 | + | 1.66598i | ||||
\(59\) | 113.289 | − | 196.222i | 0.249982 | − | 0.432982i | −0.713538 | − | 0.700616i | \(-0.752909\pi\) |
0.963521 | + | 0.267634i | \(0.0862419\pi\) | |||||||
\(60\) | 342.106 | − | 592.545i | 0.736095 | − | 1.27495i | ||||
\(61\) | −325.987 | − | 564.626i | −0.684235 | − | 1.18513i | −0.973677 | − | 0.227934i | \(-0.926803\pi\) |
0.289442 | − | 0.957196i | \(-0.406530\pi\) | |||||||
\(62\) | 719.331 | 1.47347 | ||||||||
\(63\) | 133.100 | − | 100.337i | 0.266174 | − | 0.200655i | ||||
\(64\) | −832.161 | −1.62532 | ||||||||
\(65\) | 117.058 | + | 202.750i | 0.223372 | + | 0.386892i | ||||
\(66\) | 77.8739 | − | 134.882i | 0.145237 | − | 0.251557i | ||||
\(67\) | −72.7166 | + | 125.949i | −0.132593 | + | 0.229658i | −0.924675 | − | 0.380756i | \(-0.875664\pi\) |
0.792082 | + | 0.610414i | \(0.208997\pi\) | |||||||
\(68\) | −339.858 | − | 588.652i | −0.606086 | − | 1.04977i | ||||
\(69\) | −456.256 | −0.796041 | ||||||||
\(70\) | 1388.44 | + | 589.055i | 2.37073 | + | 1.00579i | ||||
\(71\) | −368.962 | −0.616728 | −0.308364 | − | 0.951268i | \(-0.599782\pi\) | ||||
−0.308364 | + | 0.951268i | \(0.599782\pi\) | |||||||
\(72\) | 97.6071 | + | 169.060i | 0.159765 | + | 0.276722i | ||||
\(73\) | −304.453 | + | 527.328i | −0.488130 | + | 0.845466i | −0.999907 | − | 0.0136522i | \(-0.995654\pi\) |
0.511777 | + | 0.859119i | \(0.328988\pi\) | |||||||
\(74\) | 8.53380 | − | 14.7810i | 0.0134059 | − | 0.0232197i | ||||
\(75\) | 291.677 | + | 505.200i | 0.449066 | + | 0.777806i | ||||
\(76\) | −541.328 | −0.817034 | ||||||||
\(77\) | 194.263 | + | 82.4170i | 0.287510 | + | 0.121978i | ||||
\(78\) | −179.047 | −0.259911 | ||||||||
\(79\) | −455.119 | − | 788.289i | −0.648163 | − | 1.12265i | −0.983561 | − | 0.180574i | \(-0.942204\pi\) |
0.335399 | − | 0.942076i | \(-0.391129\pi\) | |||||||
\(80\) | 29.0808 | − | 50.3694i | 0.0406416 | − | 0.0703933i | ||||
\(81\) | −40.5000 | + | 70.1481i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −89.5850 | − | 155.166i | −0.120646 | − | 0.208966i | ||||
\(83\) | −327.929 | −0.433674 | −0.216837 | − | 0.976208i | \(-0.569574\pi\) | ||||
−0.216837 | + | 0.976208i | \(0.569574\pi\) | |||||||
\(84\) | −566.139 | + | 426.781i | −0.735367 | + | 0.554353i | ||||
\(85\) | 952.058 | 1.21489 | ||||||||
\(86\) | 978.340 | + | 1694.53i | 1.22671 | + | 2.12473i | ||||
\(87\) | 279.740 | − | 484.524i | 0.344727 | − | 0.597085i | ||||
\(88\) | −123.572 | + | 214.033i | −0.149691 | + | 0.259273i | ||||
\(89\) | 18.8059 | + | 32.5728i | 0.0223980 | + | 0.0387945i | 0.877007 | − | 0.480477i | \(-0.159537\pi\) |
−0.854609 | + | 0.519272i | \(0.826203\pi\) | |||||||
\(90\) | −732.932 | −0.858420 | ||||||||
\(91\) | −29.6092 | − | 240.777i | −0.0341086 | − | 0.277366i | ||||
\(92\) | 1940.68 | 2.19924 | ||||||||
\(93\) | −236.811 | − | 410.168i | −0.264044 | − | 0.457338i | ||||
\(94\) | 48.2676 | − | 83.6019i | 0.0529619 | − | 0.0917327i | ||||
\(95\) | 379.111 | − | 656.640i | 0.409431 | − | 0.709156i | ||||
\(96\) | 282.526 | + | 489.349i | 0.300366 | + | 0.520250i | ||||
\(97\) | 722.013 | 0.755766 | 0.377883 | − | 0.925853i | \(-0.376652\pi\) | ||||
0.377883 | + | 0.925853i | \(0.376652\pi\) | |||||||
\(98\) | −1086.05 | − | 1123.80i | −1.11947 | − | 1.15838i | ||||
\(99\) | −102.547 | −0.104105 | ||||||||
\(100\) | −1240.65 | − | 2148.86i | −1.24065 | − | 2.14886i | ||||
\(101\) | −759.336 | + | 1315.21i | −0.748087 | + | 1.29572i | 0.200652 | + | 0.979663i | \(0.435694\pi\) |
−0.948739 | + | 0.316062i | \(0.897639\pi\) | |||||||
\(102\) | −364.058 | + | 630.568i | −0.353403 | + | 0.612113i | ||||
\(103\) | 525.942 | + | 910.957i | 0.503132 | + | 0.871450i | 0.999993 | + | 0.00361990i | \(0.00115225\pi\) |
−0.496862 | + | 0.867830i | \(0.665514\pi\) | |||||||
\(104\) | 284.116 | 0.267883 | ||||||||
\(105\) | −121.206 | − | 985.625i | −0.112652 | − | 0.916068i | ||||
\(106\) | −1667.19 | −1.52766 | ||||||||
\(107\) | −383.260 | − | 663.826i | −0.346273 | − | 0.599762i | 0.639312 | − | 0.768948i | \(-0.279219\pi\) |
−0.985584 | + | 0.169186i | \(0.945886\pi\) | |||||||
\(108\) | 172.266 | − | 298.374i | 0.153485 | − | 0.265843i | ||||
\(109\) | 713.524 | − | 1235.86i | 0.627002 | − | 1.08600i | −0.361148 | − | 0.932509i | \(-0.617615\pi\) |
0.988150 | − | 0.153491i | \(-0.0490516\pi\) | |||||||
\(110\) | −463.952 | − | 803.588i | −0.402146 | − | 0.696538i | ||||
\(111\) | −11.2376 | −0.00960928 | ||||||||
\(112\) | −48.1247 | + | 36.2786i | −0.0406014 | + | 0.0306072i | ||||
\(113\) | 362.564 | 0.301833 | 0.150917 | − | 0.988546i | \(-0.451778\pi\) | ||||
0.150917 | + | 0.988546i | \(0.451778\pi\) | |||||||
\(114\) | 289.937 | + | 502.186i | 0.238203 | + | 0.412579i | ||||
\(115\) | −1359.13 | + | 2354.08i | −1.10208 | + | 1.90886i | ||||
\(116\) | −1189.87 | + | 2060.92i | −0.952386 | + | 1.64958i | ||||
\(117\) | 58.9440 | + | 102.094i | 0.0465759 | + | 0.0806718i | ||||
\(118\) | 1032.37 | 0.805402 | ||||||||
\(119\) | −908.173 | − | 385.297i | −0.699597 | − | 0.296808i | ||||
\(120\) | 1163.03 | 0.884750 | ||||||||
\(121\) | 600.587 | + | 1040.25i | 0.451230 | + | 0.781553i | ||||
\(122\) | 1485.31 | − | 2572.64i | 1.10225 | − | 1.90915i | ||||
\(123\) | −58.9845 | + | 102.164i | −0.0432395 | + | 0.0748930i | ||||
\(124\) | 1007.27 | + | 1744.65i | 0.729481 | + | 1.26350i | ||||
\(125\) | 1241.32 | 0.888216 | ||||||||
\(126\) | 699.147 | + | 296.617i | 0.494325 | + | 0.209720i | ||||
\(127\) | 974.777 | 0.681082 | 0.340541 | − | 0.940230i | \(-0.389390\pi\) | ||||
0.340541 | + | 0.940230i | \(0.389390\pi\) | |||||||
\(128\) | −1142.41 | − | 1978.72i | −0.788875 | − | 1.36637i | ||||
\(129\) | 644.158 | − | 1115.71i | 0.439651 | − | 0.761498i | ||||
\(130\) | −533.357 | + | 923.802i | −0.359835 | + | 0.623252i | ||||
\(131\) | 896.351 | + | 1552.53i | 0.597821 | + | 1.03546i | 0.993142 | + | 0.116914i | \(0.0373001\pi\) |
−0.395321 | + | 0.918543i | \(0.629367\pi\) | |||||||
\(132\) | 436.184 | 0.287613 | ||||||||
\(133\) | −627.377 | + | 472.946i | −0.409026 | + | 0.308343i | ||||
\(134\) | −662.647 | −0.427194 | ||||||||
\(135\) | 241.288 | + | 417.924i | 0.153828 | + | 0.266438i | ||||
\(136\) | 577.697 | − | 1000.60i | 0.364243 | − | 0.630888i | ||||
\(137\) | −842.208 | + | 1458.75i | −0.525217 | + | 0.909702i | 0.474352 | + | 0.880335i | \(0.342682\pi\) |
−0.999569 | + | 0.0293665i | \(0.990651\pi\) | |||||||
\(138\) | −1039.44 | − | 1800.35i | −0.641178 | − | 1.11055i | ||||
\(139\) | 315.089 | 0.192270 | 0.0961350 | − | 0.995368i | \(-0.469352\pi\) | ||||
0.0961350 | + | 0.995368i | \(0.469352\pi\) | |||||||
\(140\) | 515.547 | + | 4192.35i | 0.311226 | + | 2.53084i | ||||
\(141\) | −63.5606 | −0.0379629 | ||||||||
\(142\) | −840.563 | − | 1455.90i | −0.496750 | − | 0.860396i | ||||
\(143\) | −74.6241 | + | 129.253i | −0.0436390 | + | 0.0755850i | ||||
\(144\) | 14.6435 | − | 25.3633i | 0.00847427 | − | 0.0146779i | ||||
\(145\) | −1666.62 | − | 2886.67i | −0.954517 | − | 1.65327i | ||||
\(146\) | −2774.40 | −1.57268 | ||||||||
\(147\) | −283.263 | + | 989.244i | −0.158933 | + | 0.555044i | ||||
\(148\) | 47.7992 | 0.0265478 | ||||||||
\(149\) | −946.887 | − | 1640.06i | −0.520617 | − | 0.901736i | −0.999713 | − | 0.0239729i | \(-0.992368\pi\) |
0.479095 | − | 0.877763i | \(-0.340965\pi\) | |||||||
\(150\) | −1328.99 | + | 2301.87i | −0.723409 | + | 1.25298i | ||||
\(151\) | 1005.92 | − | 1742.31i | 0.542124 | − | 0.938986i | −0.456658 | − | 0.889642i | \(-0.650954\pi\) |
0.998782 | − | 0.0493434i | \(-0.0157129\pi\) | |||||||
\(152\) | −460.079 | − | 796.881i | −0.245509 | − | 0.425234i | ||||
\(153\) | 479.406 | 0.253318 | ||||||||
\(154\) | 117.355 | + | 954.308i | 0.0614071 | + | 0.499353i | ||||
\(155\) | −2821.71 | −1.46223 | ||||||||
\(156\) | −250.718 | − | 434.256i | −0.128676 | − | 0.222874i | ||||
\(157\) | 1914.25 | − | 3315.58i | 0.973082 | − | 1.68543i | 0.286956 | − | 0.957944i | \(-0.407357\pi\) |
0.686125 | − | 0.727483i | \(-0.259310\pi\) | |||||||
\(158\) | 2073.69 | − | 3591.73i | 1.04414 | − | 1.80850i | ||||
\(159\) | 548.856 | + | 950.647i | 0.273755 | + | 0.474158i | ||||
\(160\) | 3366.43 | 1.66337 | ||||||||
\(161\) | 2249.17 | − | 1695.53i | 1.10099 | − | 0.829977i | ||||
\(162\) | −369.066 | −0.178991 | ||||||||
\(163\) | 1754.63 | + | 3039.11i | 0.843148 | + | 1.46038i | 0.887220 | + | 0.461347i | \(0.152634\pi\) |
−0.0440718 | + | 0.999028i | \(0.514033\pi\) | |||||||
\(164\) | 250.890 | − | 434.554i | 0.119459 | − | 0.206909i | ||||
\(165\) | −305.475 | + | 529.098i | −0.144128 | + | 0.249638i | ||||
\(166\) | −747.083 | − | 1293.99i | −0.349307 | − | 0.605017i | ||||
\(167\) | −343.008 | −0.158939 | −0.0794694 | − | 0.996837i | \(-0.525323\pi\) | ||||
−0.0794694 | + | 0.996837i | \(0.525323\pi\) | |||||||
\(168\) | −1109.42 | − | 470.679i | −0.509487 | − | 0.216153i | ||||
\(169\) | −2025.42 | −0.921905 | ||||||||
\(170\) | 2168.96 | + | 3756.75i | 0.978541 | + | 1.69488i | ||||
\(171\) | 190.900 | − | 330.649i | 0.0853714 | − | 0.147868i | ||||
\(172\) | −2739.92 | + | 4745.68i | −1.21463 | + | 2.10381i | ||||
\(173\) | 2093.61 | + | 3626.23i | 0.920081 | + | 1.59363i | 0.799288 | + | 0.600949i | \(0.205210\pi\) |
0.120793 | + | 0.992678i | \(0.461456\pi\) | |||||||
\(174\) | 2549.20 | 1.11066 | ||||||||
\(175\) | −3315.27 | − | 1406.52i | −1.43206 | − | 0.607559i | ||||
\(176\) | 37.0779 | 0.0158798 | ||||||||
\(177\) | −339.866 | − | 588.666i | −0.144327 | − | 0.249982i | ||||
\(178\) | −85.6866 | + | 148.413i | −0.0360813 | + | 0.0624947i | ||||
\(179\) | 985.143 | − | 1706.32i | 0.411358 | − | 0.712493i | −0.583681 | − | 0.811983i | \(-0.698388\pi\) |
0.995039 | + | 0.0994906i | \(0.0317213\pi\) | |||||||
\(180\) | −1026.32 | − | 1777.63i | −0.424984 | − | 0.736095i | ||||
\(181\) | −3613.10 | −1.48376 | −0.741878 | − | 0.670535i | \(-0.766065\pi\) | ||||
−0.741878 | + | 0.670535i | \(0.766065\pi\) | |||||||
\(182\) | 882.634 | − | 665.370i | 0.359479 | − | 0.270992i | ||||
\(183\) | −1955.92 | −0.790086 | ||||||||
\(184\) | 1649.40 | + | 2856.85i | 0.660845 | + | 1.14462i | ||||
\(185\) | −33.4755 | + | 57.9812i | −0.0133036 | + | 0.0230425i | ||||
\(186\) | 1079.00 | − | 1868.88i | 0.425354 | − | 0.736734i | ||||
\(187\) | 303.468 | + | 525.622i | 0.118673 | + | 0.205547i | ||||
\(188\) | 270.355 | 0.104881 | ||||||||
\(189\) | −61.0328 | − | 496.308i | −0.0234893 | − | 0.191011i | ||||
\(190\) | 3454.74 | 1.31912 | ||||||||
\(191\) | −953.884 | − | 1652.18i | −0.361365 | − | 0.625902i | 0.626821 | − | 0.779163i | \(-0.284356\pi\) |
−0.988186 | + | 0.153261i | \(0.951022\pi\) | |||||||
\(192\) | −1248.24 | + | 2162.02i | −0.469188 | + | 0.812658i | ||||
\(193\) | −1199.96 | + | 2078.40i | −0.447540 | + | 0.775162i | −0.998225 | − | 0.0595509i | \(-0.981033\pi\) |
0.550685 | + | 0.834713i | \(0.314366\pi\) | |||||||
\(194\) | 1644.88 | + | 2849.01i | 0.608738 | + | 1.05437i | ||||
\(195\) | 702.346 | 0.257928 | ||||||||
\(196\) | 1204.86 | − | 4207.74i | 0.439087 | − | 1.53343i | ||||
\(197\) | 1514.32 | 0.547668 | 0.273834 | − | 0.961777i | \(-0.411708\pi\) | ||||
0.273834 | + | 0.961777i | \(0.411708\pi\) | |||||||
\(198\) | −233.622 | − | 404.645i | −0.0838524 | − | 0.145237i | ||||
\(199\) | −683.889 | + | 1184.53i | −0.243616 | + | 0.421955i | −0.961742 | − | 0.273958i | \(-0.911667\pi\) |
0.718126 | + | 0.695914i | \(0.245000\pi\) | |||||||
\(200\) | 2108.87 | − | 3652.67i | 0.745598 | − | 1.29141i | ||||
\(201\) | 218.150 | + | 377.847i | 0.0765527 | + | 0.132593i | ||||
\(202\) | −6919.63 | −2.41021 | ||||||||
\(203\) | 421.563 | + | 3428.08i | 0.145753 | + | 1.18524i | ||||
\(204\) | −2039.15 | −0.699848 | ||||||||
\(205\) | 351.414 | + | 608.667i | 0.119726 | + | 0.207371i | ||||
\(206\) | −2396.38 | + | 4150.66i | −0.810504 | + | 1.40383i | ||||
\(207\) | −684.384 | + | 1185.39i | −0.229797 | + | 0.398020i | ||||
\(208\) | −21.3123 | − | 36.9140i | −0.00710453 | − | 0.0123054i | ||||
\(209\) | 483.366 | 0.159977 | ||||||||
\(210\) | 3613.08 | − | 2723.70i | 1.18727 | − | 0.895016i | ||||
\(211\) | 4302.52 | 1.40378 | 0.701891 | − | 0.712285i | \(-0.252339\pi\) | ||||
0.701891 | + | 0.712285i | \(0.252339\pi\) | |||||||
\(212\) | −2334.55 | − | 4043.57i | −0.756311 | − | 1.30997i | ||||
\(213\) | −553.443 | + | 958.591i | −0.178034 | + | 0.308364i | ||||
\(214\) | 1746.27 | − | 3024.64i | 0.557817 | − | 0.966167i | ||||
\(215\) | −3837.72 | − | 6647.13i | −1.21735 | − | 2.10851i | ||||
\(216\) | 585.642 | 0.184481 | ||||||||
\(217\) | 2691.64 | + | 1141.94i | 0.842030 | + | 0.357236i | ||||
\(218\) | 6502.16 | 2.02010 | ||||||||
\(219\) | 913.359 | + | 1581.98i | 0.281822 | + | 0.488130i | ||||
\(220\) | 1299.34 | − | 2250.51i | 0.398187 | − | 0.689680i | ||||
\(221\) | 348.866 | − | 604.253i | 0.106187 | − | 0.183921i | ||||
\(222\) | −25.6014 | − | 44.3429i | −0.00773988 | − | 0.0134059i | ||||
\(223\) | −1497.19 | −0.449592 | −0.224796 | − | 0.974406i | \(-0.572172\pi\) | ||||
−0.224796 | + | 0.974406i | \(0.572172\pi\) | |||||||
\(224\) | −3211.25 | − | 1362.39i | −0.957861 | − | 0.406377i | ||||
\(225\) | 1750.06 | 0.518537 | ||||||||
\(226\) | 825.987 | + | 1430.65i | 0.243114 | + | 0.421086i | ||||
\(227\) | −801.662 | + | 1388.52i | −0.234397 | + | 0.405988i | −0.959097 | − | 0.283076i | \(-0.908645\pi\) |
0.724700 | + | 0.689065i | \(0.241978\pi\) | |||||||
\(228\) | −811.992 | + | 1406.41i | −0.235858 | + | 0.408517i | ||||
\(229\) | −505.261 | − | 875.137i | −0.145802 | − | 0.252536i | 0.783870 | − | 0.620925i | \(-0.213243\pi\) |
−0.929672 | + | 0.368389i | \(0.879909\pi\) | |||||||
\(230\) | −12385.4 | −3.55072 | ||||||||
\(231\) | 505.520 | − | 381.084i | 0.143986 | − | 0.108543i | ||||
\(232\) | −4045.13 | −1.14472 | ||||||||
\(233\) | −99.1084 | − | 171.661i | −0.0278661 | − | 0.0482656i | 0.851756 | − | 0.523939i | \(-0.175538\pi\) |
−0.879622 | + | 0.475673i | \(0.842205\pi\) | |||||||
\(234\) | −268.571 | + | 465.178i | −0.0750299 | + | 0.129956i | ||||
\(235\) | −189.339 | + | 327.944i | −0.0525578 | + | 0.0910329i | ||||
\(236\) | 1445.62 | + | 2503.88i | 0.398736 | + | 0.690631i | ||||
\(237\) | −2730.71 | −0.748434 | ||||||||
\(238\) | −548.629 | − | 4461.36i | −0.149422 | − | 1.21507i | ||||
\(239\) | −1201.19 | −0.325098 | −0.162549 | − | 0.986700i | \(-0.551972\pi\) | ||||
−0.162549 | + | 0.986700i | \(0.551972\pi\) | |||||||
\(240\) | −87.2423 | − | 151.108i | −0.0234644 | − | 0.0406416i | ||||
\(241\) | 1366.35 | − | 2366.58i | 0.365204 | − | 0.632551i | −0.623605 | − | 0.781739i | \(-0.714333\pi\) |
0.988809 | + | 0.149188i | \(0.0476660\pi\) | |||||||
\(242\) | −2736.49 | + | 4739.74i | −0.726894 | + | 1.25902i | ||||
\(243\) | 121.500 | + | 210.444i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 8319.49 | 2.18279 | ||||||||
\(245\) | 4260.25 | + | 4408.33i | 1.11093 | + | 1.14954i | ||||
\(246\) | −537.510 | −0.139311 | ||||||||
\(247\) | −277.838 | − | 481.229i | −0.0715724 | − | 0.123967i | ||||
\(248\) | −1712.18 | + | 2965.58i | −0.438401 | + | 0.759332i | ||||
\(249\) | −491.894 | + | 851.985i | −0.125191 | + | 0.216837i | ||||
\(250\) | 2827.95 | + | 4898.16i | 0.715422 | + | 1.23915i | ||||
\(251\) | 7565.82 | 1.90259 | 0.951295 | − | 0.308281i | \(-0.0997537\pi\) | ||||
0.951295 | + | 0.308281i | \(0.0997537\pi\) | |||||||
\(252\) | 259.602 | + | 2111.04i | 0.0648945 | + | 0.527711i | ||||
\(253\) | −1732.88 | −0.430615 | ||||||||
\(254\) | 2220.72 | + | 3846.40i | 0.548584 | + | 0.950175i | ||||
\(255\) | 1428.09 | − | 2473.52i | 0.350707 | − | 0.607443i | ||||
\(256\) | 1876.61 | − | 3250.38i | 0.458156 | − | 0.793550i | ||||
\(257\) | −2504.34 | − | 4337.64i | −0.607846 | − | 1.05282i | −0.991595 | − | 0.129382i | \(-0.958701\pi\) |
0.383749 | − | 0.923437i | \(-0.374633\pi\) | |||||||
\(258\) | 5870.04 | 1.41648 | ||||||||
\(259\) | 55.3973 | − | 41.7610i | 0.0132904 | − | 0.0100189i | ||||
\(260\) | −2987.42 | −0.712584 | ||||||||
\(261\) | −839.220 | − | 1453.57i | −0.199028 | − | 0.344727i | ||||
\(262\) | −4084.10 | + | 7073.88i | −0.963041 | + | 1.66804i | ||||
\(263\) | 3124.40 | − | 5411.63i | 0.732544 | − | 1.26880i | −0.223249 | − | 0.974761i | \(-0.571666\pi\) |
0.955793 | − | 0.294042i | \(-0.0950004\pi\) | |||||||
\(264\) | 370.716 | + | 642.100i | 0.0864243 | + | 0.149691i | ||||
\(265\) | 6539.88 | 1.51601 | ||||||||
\(266\) | −3295.49 | − | 1398.13i | −0.759622 | − | 0.322274i | ||||
\(267\) | 112.835 | 0.0258630 | ||||||||
\(268\) | −927.898 | − | 1607.17i | −0.211494 | − | 0.366318i | ||||
\(269\) | 1794.22 | − | 3107.69i | 0.406676 | − | 0.704383i | −0.587839 | − | 0.808978i | \(-0.700021\pi\) |
0.994515 | + | 0.104595i | \(0.0333546\pi\) | |||||||
\(270\) | −1099.40 | + | 1904.21i | −0.247804 | + | 0.429210i | ||||
\(271\) | 991.571 | + | 1717.45i | 0.222264 | + | 0.384973i | 0.955495 | − | 0.295007i | \(-0.0953218\pi\) |
−0.733231 | + | 0.679980i | \(0.761988\pi\) | |||||||
\(272\) | −173.338 | −0.0386404 | ||||||||
\(273\) | −669.971 | − | 284.239i | −0.148529 | − | 0.0630143i | ||||
\(274\) | −7674.81 | −1.69216 | ||||||||
\(275\) | 1107.80 | + | 1918.77i | 0.242920 | + | 0.420751i | ||||
\(276\) | 2911.02 | − | 5042.04i | 0.634866 | − | 1.09962i | ||||
\(277\) | −3681.96 | + | 6377.33i | −0.798654 | + | 1.38331i | 0.121838 | + | 0.992550i | \(0.461121\pi\) |
−0.920493 | + | 0.390760i | \(0.872212\pi\) | |||||||
\(278\) | 717.831 | + | 1243.32i | 0.154866 | + | 0.268235i | ||||
\(279\) | −1420.86 | −0.304892 | ||||||||
\(280\) | −5733.32 | + | 4322.04i | −1.22368 | + | 0.922468i | ||||
\(281\) | −5312.05 | −1.12772 | −0.563861 | − | 0.825869i | \(-0.690685\pi\) | ||||
−0.563861 | + | 0.825869i | \(0.690685\pi\) | |||||||
\(282\) | −144.803 | − | 250.806i | −0.0305776 | − | 0.0529619i | ||||
\(283\) | 545.882 | − | 945.495i | 0.114662 | − | 0.198600i | −0.802983 | − | 0.596002i | \(-0.796755\pi\) |
0.917645 | + | 0.397402i | \(0.130088\pi\) | |||||||
\(284\) | 2354.06 | − | 4077.36i | 0.491859 | − | 0.851925i | ||||
\(285\) | −1137.33 | − | 1969.92i | −0.236385 | − | 0.409431i | ||||
\(286\) | −680.030 | −0.140598 | ||||||||
\(287\) | −88.8886 | − | 722.827i | −0.0182820 | − | 0.148666i | ||||
\(288\) | 1695.16 | 0.346833 | ||||||||
\(289\) | 1037.79 | + | 1797.51i | 0.211234 | + | 0.365869i | ||||
\(290\) | 7593.72 | − | 13152.7i | 1.53765 | − | 2.66329i | ||||
\(291\) | 1083.02 | − | 1875.84i | 0.218171 | − | 0.377883i | ||||
\(292\) | −3884.96 | − | 6728.95i | −0.778597 | − | 1.34857i | ||||
\(293\) | −7191.86 | −1.43397 | −0.716985 | − | 0.697089i | \(-0.754478\pi\) | ||||
−0.716985 | + | 0.697089i | \(0.754478\pi\) | |||||||
\(294\) | −4548.81 | + | 1135.94i | −0.902354 | + | 0.225339i | ||||
\(295\) | −4049.67 | −0.799257 | ||||||||
\(296\) | 40.6249 | + | 70.3645i | 0.00797729 | + | 0.0138171i | ||||
\(297\) | −153.821 | + | 266.426i | −0.0300525 | + | 0.0520525i | ||||
\(298\) | 4314.36 | − | 7472.70i | 0.838672 | − | 1.45262i | ||||
\(299\) | 996.058 | + | 1725.22i | 0.192654 | + | 0.333687i | ||||
\(300\) | −7443.88 | −1.43257 | ||||||||
\(301\) | 970.735 | + | 7893.85i | 0.185888 | + | 1.51161i | ||||
\(302\) | 9166.69 | 1.74663 | ||||||||
\(303\) | 2278.01 | + | 3945.63i | 0.431908 | + | 0.748087i | ||||
\(304\) | −69.0236 | + | 119.552i | −0.0130223 | + | 0.0225552i | ||||
\(305\) | −5826.43 | + | 10091.7i | −1.09384 | + | 1.89458i | ||||
\(306\) | 1092.18 | + | 1891.70i | 0.204038 | + | 0.353403i | ||||
\(307\) | 541.355 | 0.100641 | 0.0503204 | − | 0.998733i | \(-0.483976\pi\) | ||||
0.0503204 | + | 0.998733i | \(0.483976\pi\) | |||||||
\(308\) | −2150.22 | + | 1620.94i | −0.397793 | + | 0.299875i | ||||
\(309\) | 3155.65 | 0.580966 | ||||||||
\(310\) | −6428.37 | − | 11134.3i | −1.17776 | − | 2.03995i | ||||
\(311\) | −27.0084 | + | 46.7799i | −0.00492446 | + | 0.00852941i | −0.868477 | − | 0.495729i | \(-0.834901\pi\) |
0.863553 | + | 0.504259i | \(0.168234\pi\) | |||||||
\(312\) | 426.174 | − | 738.155i | 0.0773313 | − | 0.133942i | ||||
\(313\) | −1886.47 | − | 3267.46i | −0.340670 | − | 0.590058i | 0.643887 | − | 0.765120i | \(-0.277321\pi\) |
−0.984557 | + | 0.175063i | \(0.943987\pi\) | |||||||
\(314\) | 17444.1 | 3.13511 | ||||||||
\(315\) | −2742.54 | − | 1163.54i | −0.490554 | − | 0.208120i | ||||
\(316\) | 11615.1 | 2.06772 | ||||||||
\(317\) | −859.618 | − | 1488.90i | −0.152306 | − | 0.263802i | 0.779769 | − | 0.626068i | \(-0.215337\pi\) |
−0.932075 | + | 0.362266i | \(0.882003\pi\) | |||||||
\(318\) | −2500.79 | + | 4331.49i | −0.440998 | + | 0.763831i | ||||
\(319\) | 1062.47 | − | 1840.25i | 0.186479 | − | 0.322991i | ||||
\(320\) | 7436.70 | + | 12880.7i | 1.29914 | + | 2.25017i | ||||
\(321\) | −2299.56 | −0.399841 | ||||||||
\(322\) | 11814.5 | + | 5012.34i | 2.04470 | + | 0.867475i | ||||
\(323\) | −2259.72 | −0.389270 | ||||||||
\(324\) | −516.799 | − | 895.122i | −0.0886144 | − | 0.153485i | ||||
\(325\) | 1273.53 | − | 2205.81i | 0.217362 | − | 0.376482i | ||||
\(326\) | −7994.73 | + | 13847.3i | −1.35824 | + | 2.35255i | ||||
\(327\) | −2140.57 | − | 3707.58i | −0.362000 | − | 0.627002i | ||||
\(328\) | 852.934 | 0.143584 | ||||||||
\(329\) | 313.330 | − | 236.202i | 0.0525059 | − | 0.0395813i | ||||
\(330\) | −2783.71 | −0.464358 | ||||||||
\(331\) | −4204.11 | − | 7281.73i | −0.698123 | − | 1.20918i | −0.969117 | − | 0.246603i | \(-0.920686\pi\) |
0.270994 | − | 0.962581i | \(-0.412648\pi\) | |||||||
\(332\) | 2092.27 | − | 3623.91i | 0.345868 | − | 0.599060i | ||||
\(333\) | −16.8565 | + | 29.1963i | −0.00277396 | + | 0.00480464i | ||||
\(334\) | −781.436 | − | 1353.49i | −0.128019 | − | 0.221735i | ||||
\(335\) | 2599.36 | 0.423935 | ||||||||
\(336\) | 22.0675 | + | 179.450i | 0.00358298 | + | 0.0291362i | ||||
\(337\) | 2789.46 | 0.450894 | 0.225447 | − | 0.974255i | \(-0.427616\pi\) | ||||
0.225447 | + | 0.974255i | \(0.427616\pi\) | |||||||
\(338\) | −4614.29 | − | 7992.18i | −0.742557 | − | 1.28615i | ||||
\(339\) | 543.846 | − | 941.969i | 0.0871317 | − | 0.150917i | ||||
\(340\) | −6074.36 | + | 10521.1i | −0.968907 | + | 1.67820i | ||||
\(341\) | −899.419 | − | 1557.84i | −0.142834 | − | 0.247395i | ||||
\(342\) | 1739.62 | 0.275053 | ||||||||
\(343\) | −2279.82 | − | 5929.25i | −0.358889 | − | 0.933380i | ||||
\(344\) | −9314.72 | −1.45993 | ||||||||
\(345\) | 4077.38 | + | 7062.23i | 0.636286 | + | 1.10208i | ||||
\(346\) | −9539.24 | + | 16522.4i | −1.48217 | + | 2.56720i | ||||
\(347\) | 1735.98 | − | 3006.81i | 0.268566 | − | 0.465170i | −0.699926 | − | 0.714216i | \(-0.746784\pi\) |
0.968492 | + | 0.249046i | \(0.0801170\pi\) | |||||||
\(348\) | 3569.61 | + | 6182.75i | 0.549860 | + | 0.952386i | ||||
\(349\) | −6626.12 | −1.01630 | −0.508149 | − | 0.861269i | \(-0.669670\pi\) | ||||
−0.508149 | + | 0.861269i | \(0.669670\pi\) | |||||||
\(350\) | −2002.76 | − | 16286.1i | −0.305863 | − | 2.48723i | ||||
\(351\) | 353.664 | 0.0537812 | ||||||||
\(352\) | 1073.05 | + | 1858.57i | 0.162482 | + | 0.281427i | ||||
\(353\) | −4734.20 | + | 8199.87i | −0.713813 | + | 1.23636i | 0.249603 | + | 0.968348i | \(0.419700\pi\) |
−0.963416 | + | 0.268012i | \(0.913633\pi\) | |||||||
\(354\) | 1548.56 | − | 2682.18i | 0.232499 | − | 0.402701i | ||||
\(355\) | 3297.27 | + | 5711.03i | 0.492960 | + | 0.853831i | ||||
\(356\) | −479.944 | −0.0714522 | ||||||||
\(357\) | −2363.29 | + | 1781.56i | −0.350360 | + | 0.264118i | ||||
\(358\) | 8977.35 | 1.32533 | ||||||||
\(359\) | 3139.78 | + | 5438.25i | 0.461591 | + | 0.799499i | 0.999040 | − | 0.0437971i | \(-0.0139455\pi\) |
−0.537450 | + | 0.843296i | \(0.680612\pi\) | |||||||
\(360\) | 1744.55 | − | 3021.65i | 0.255405 | − | 0.442375i | ||||
\(361\) | 2529.68 | − | 4381.53i | 0.368811 | − | 0.638800i | ||||
\(362\) | −8231.31 | − | 14257.0i | −1.19510 | − | 2.06998i | ||||
\(363\) | 3603.52 | 0.521035 | ||||||||
\(364\) | 2849.71 | + | 1209.01i | 0.410345 | + | 0.174091i | ||||
\(365\) | 10883.1 | 1.56068 | ||||||||
\(366\) | −4455.94 | − | 7717.92i | −0.636382 | − | 1.10225i | ||||
\(367\) | 5413.91 | − | 9377.17i | 0.770038 | − | 1.33374i | −0.167504 | − | 0.985871i | \(-0.553571\pi\) |
0.937542 | − | 0.347873i | \(-0.113096\pi\) | |||||||
\(368\) | 247.452 | − | 428.599i | 0.0350525 | − | 0.0607127i | ||||
\(369\) | 176.954 | + | 306.493i | 0.0249643 | + | 0.0432395i | ||||
\(370\) | −305.053 | −0.0428620 | ||||||||
\(371\) | −6238.42 | − | 2646.68i | −0.872999 | − | 0.370374i | ||||
\(372\) | 6043.63 | 0.842332 | ||||||||
\(373\) | −2619.61 | − | 4537.30i | −0.363642 | − | 0.629846i | 0.624915 | − | 0.780693i | \(-0.285134\pi\) |
−0.988557 | + | 0.150846i | \(0.951800\pi\) | |||||||
\(374\) | −1382.71 | + | 2394.93i | −0.191172 | + | 0.331120i | ||||
\(375\) | 1861.98 | − | 3225.04i | 0.256406 | − | 0.444108i | ||||
\(376\) | 229.777 | + | 397.985i | 0.0315155 | + | 0.0545864i | ||||
\(377\) | −2442.81 | −0.333717 | ||||||||
\(378\) | 1819.35 | − | 1371.51i | 0.247559 | − | 0.186622i | ||||
\(379\) | −11050.4 | −1.49768 | −0.748839 | − | 0.662751i | \(-0.769389\pi\) | ||||
−0.748839 | + | 0.662751i | \(0.769389\pi\) | |||||||
\(380\) | 4837.64 | + | 8379.03i | 0.653067 | + | 1.13115i | ||||
\(381\) | 1462.16 | − | 2532.54i | 0.196611 | − | 0.340541i | ||||
\(382\) | 4346.25 | − | 7527.92i | 0.582129 | − | 1.00828i | ||||
\(383\) | 5234.02 | + | 9065.59i | 0.698292 | + | 1.20948i | 0.969058 | + | 0.246832i | \(0.0793897\pi\) |
−0.270766 | + | 0.962645i | \(0.587277\pi\) | |||||||
\(384\) | −6854.48 | −0.910915 | ||||||||
\(385\) | −460.345 | − | 3743.45i | −0.0609386 | − | 0.495543i | ||||
\(386\) | −10934.9 | −1.44190 | ||||||||
\(387\) | −1932.47 | − | 3347.14i | −0.253833 | − | 0.439651i | ||||
\(388\) | −4606.61 | + | 7978.88i | −0.602745 | + | 1.04399i | ||||
\(389\) | 5807.02 | − | 10058.1i | 0.756884 | − | 1.31096i | −0.187549 | − | 0.982255i | \(-0.560054\pi\) |
0.944432 | − | 0.328705i | \(-0.106612\pi\) | |||||||
\(390\) | 1600.07 | + | 2771.41i | 0.207751 | + | 0.359835i | ||||
\(391\) | 8101.19 | 1.04781 | ||||||||
\(392\) | 7218.16 | − | 1802.54i | 0.930031 | − | 0.232251i | ||||
\(393\) | 5378.11 | 0.690304 | ||||||||
\(394\) | 3449.89 | + | 5975.38i | 0.441124 | + | 0.764049i | ||||
\(395\) | −8134.43 | + | 14089.2i | −1.03617 | + | 1.79470i | ||||
\(396\) | 654.276 | − | 1133.24i | 0.0830268 | − | 0.143807i | ||||
\(397\) | 3353.65 | + | 5808.69i | 0.423967 | + | 0.734332i | 0.996323 | − | 0.0856726i | \(-0.0273039\pi\) |
−0.572356 | + | 0.820005i | \(0.693971\pi\) | |||||||
\(398\) | −6232.10 | −0.784892 | ||||||||
\(399\) | 287.683 | + | 2339.39i | 0.0360957 | + | 0.293524i | ||||
\(400\) | −632.768 | −0.0790960 | ||||||||
\(401\) | −2763.19 | − | 4785.98i | −0.344107 | − | 0.596011i | 0.641084 | − | 0.767471i | \(-0.278485\pi\) |
−0.985191 | + | 0.171459i | \(0.945152\pi\) | |||||||
\(402\) | −993.970 | + | 1721.61i | −0.123320 | + | 0.213597i | ||||
\(403\) | −1033.97 | + | 1790.89i | −0.127805 | + | 0.221366i | ||||
\(404\) | −9689.49 | − | 16782.7i | −1.19324 | − | 2.06676i | ||||
\(405\) | 1447.73 | 0.177625 | ||||||||
\(406\) | −12566.6 | + | 9473.26i | −1.53613 | + | 1.15800i | ||||
\(407\) | −42.6811 | −0.00519810 | ||||||||
\(408\) | −1733.09 | − | 3001.80i | −0.210296 | − | 0.364243i | ||||
\(409\) | 659.453 | − | 1142.21i | 0.0797258 | − | 0.138089i | −0.823406 | − | 0.567453i | \(-0.807929\pi\) |
0.903132 | + | 0.429364i | \(0.141262\pi\) | |||||||
\(410\) | −1601.17 | + | 2773.31i | −0.192869 | + | 0.334059i | ||||
\(411\) | 2526.62 | + | 4376.24i | 0.303234 | + | 0.525217i | ||||
\(412\) | −13422.5 | −1.60505 | ||||||||
\(413\) | 3863.00 | + | 1638.90i | 0.460256 | + | 0.195266i | ||||
\(414\) | −6236.61 | −0.740369 | ||||||||
\(415\) | 2930.57 | + | 5075.90i | 0.346641 | + | 0.600401i | ||||
\(416\) | 1233.57 | − | 2136.61i | 0.145387 | − | 0.251817i | ||||
\(417\) | 472.634 | − | 818.626i | 0.0555036 | − | 0.0961350i | ||||
\(418\) | 1101.20 | + | 1907.33i | 0.128855 | + | 0.223183i | ||||
\(419\) | 3656.13 | 0.426286 | 0.213143 | − | 0.977021i | \(-0.431630\pi\) | ||||
0.213143 | + | 0.977021i | \(0.431630\pi\) | |||||||
\(420\) | 11665.4 | + | 4949.09i | 1.35526 | + | 0.574978i | ||||
\(421\) | −135.389 | −0.0156733 | −0.00783663 | − | 0.999969i | \(-0.502495\pi\) | ||||
−0.00783663 | + | 0.999969i | \(0.502495\pi\) | |||||||
\(422\) | 9801.93 | + | 16977.4i | 1.13069 | + | 1.95841i | ||||
\(423\) | −95.3409 | + | 165.135i | −0.0109589 | + | 0.0189815i | ||||
\(424\) | 3968.31 | − | 6873.32i | 0.454524 | − | 0.787259i | ||||
\(425\) | −5178.96 | − | 8970.22i | −0.591097 | − | 1.02381i | ||||
\(426\) | −5043.38 | −0.573597 | ||||||||
\(427\) | 9641.94 | − | 7268.54i | 1.09276 | − | 0.823769i | ||||
\(428\) | 9781.16 | 1.10465 | ||||||||
\(429\) | 223.872 | + | 387.758i | 0.0251950 | + | 0.0436390i | ||||
\(430\) | 17486.1 | − | 30286.8i | 1.96105 | − | 3.39665i | ||||
\(431\) | −4194.58 | + | 7265.23i | −0.468784 | + | 0.811958i | −0.999363 | − | 0.0356776i | \(-0.988641\pi\) |
0.530579 | + | 0.847635i | \(0.321974\pi\) | |||||||
\(432\) | −43.9306 | − | 76.0900i | −0.00489262 | − | 0.00847427i | ||||
\(433\) | −8243.02 | −0.914859 | −0.457430 | − | 0.889246i | \(-0.651230\pi\) | ||||
−0.457430 | + | 0.889246i | \(0.651230\pi\) | |||||||
\(434\) | 1626.03 | + | 13222.6i | 0.179843 | + | 1.46245i | ||||
\(435\) | −9999.70 | −1.10218 | ||||||||
\(436\) | 9104.91 | + | 15770.2i | 1.00011 | + | 1.73223i | ||||
\(437\) | 3225.91 | − | 5587.43i | 0.353126 | − | 0.611632i | ||||
\(438\) | −4161.60 | + | 7208.10i | −0.453993 | + | 0.786338i | ||||
\(439\) | 9141.59 | + | 15833.7i | 0.993859 | + | 1.72142i | 0.592755 | + | 0.805383i | \(0.298040\pi\) |
0.401104 | + | 0.916032i | \(0.368626\pi\) | |||||||
\(440\) | 4417.26 | 0.478602 | ||||||||
\(441\) | 2145.24 | + | 2219.80i | 0.231642 | + | 0.239694i | ||||
\(442\) | 3179.12 | 0.342116 | ||||||||
\(443\) | −605.218 | − | 1048.27i | −0.0649092 | − | 0.112426i | 0.831745 | − | 0.555159i | \(-0.187342\pi\) |
−0.896654 | + | 0.442733i | \(0.854009\pi\) | |||||||
\(444\) | 71.6988 | − | 124.186i | 0.00766368 | − | 0.0132739i | ||||
\(445\) | 336.122 | − | 582.180i | 0.0358061 | − | 0.0620179i | ||||
\(446\) | −3410.86 | − | 5907.79i | −0.362128 | − | 0.627224i | ||||
\(447\) | −5681.32 | −0.601157 | ||||||||
\(448\) | −1881.08 | − | 15296.6i | −0.198376 | − | 1.61316i | ||||
\(449\) | −8301.16 | −0.872508 | −0.436254 | − | 0.899824i | \(-0.643695\pi\) | ||||
−0.436254 | + | 0.899824i | \(0.643695\pi\) | |||||||
\(450\) | 3986.96 | + | 6905.62i | 0.417661 | + | 0.723409i | ||||
\(451\) | −224.026 | + | 388.025i | −0.0233902 | + | 0.0405130i | ||||
\(452\) | −2313.24 | + | 4006.66i | −0.240721 | + | 0.416941i | ||||
\(453\) | −3017.76 | − | 5226.92i | −0.312995 | − | 0.542124i | ||||
\(454\) | −7305.34 | −0.755190 | ||||||||
\(455\) | −3462.30 | + | 2610.04i | −0.356736 | + | 0.268924i | ||||
\(456\) | −2760.48 | −0.283489 | ||||||||
\(457\) | 6146.88 | + | 10646.7i | 0.629188 | + | 1.08979i | 0.987715 | + | 0.156266i | \(0.0499458\pi\) |
−0.358527 | + | 0.933519i | \(0.616721\pi\) | |||||||
\(458\) | 2302.15 | − | 3987.45i | 0.234875 | − | 0.406815i | ||||
\(459\) | 719.109 | − | 1245.53i | 0.0731267 | − | 0.126659i | ||||
\(460\) | −17343.1 | − | 30039.1i | −1.75788 | − | 3.04474i | ||||
\(461\) | 19434.2 | 1.96343 | 0.981717 | − | 0.190346i | \(-0.0609609\pi\) | ||||
0.981717 | + | 0.190346i | \(0.0609609\pi\) | |||||||
\(462\) | 2655.40 | + | 1126.57i | 0.267403 | + | 0.113447i | ||||
\(463\) | −12491.1 | −1.25380 | −0.626902 | − | 0.779098i | \(-0.715678\pi\) | ||||
−0.626902 | + | 0.779098i | \(0.715678\pi\) | |||||||
\(464\) | 303.436 | + | 525.566i | 0.0303592 | + | 0.0525836i | ||||
\(465\) | −4232.56 | + | 7331.02i | −0.422109 | + | 0.731113i | ||||
\(466\) | 451.574 | − | 782.150i | 0.0448901 | − | 0.0777519i | ||||
\(467\) | −1692.59 | − | 2931.65i | −0.167716 | − | 0.290493i | 0.769900 | − | 0.638164i | \(-0.220306\pi\) |
−0.937617 | + | 0.347671i | \(0.886973\pi\) | |||||||
\(468\) | −1504.31 | −0.148583 | ||||||||
\(469\) | −2479.54 | − | 1051.96i | −0.244125 | − | 0.103571i | ||||
\(470\) | −1725.39 | −0.169333 | ||||||||
\(471\) | −5742.75 | − | 9946.74i | −0.561809 | − | 0.973082i | ||||
\(472\) | −2457.29 | + | 4256.14i | −0.239631 | + | 0.415053i | ||||
\(473\) | 2446.54 | − | 4237.54i | 0.237827 | − | 0.411929i | ||||
\(474\) | −6221.06 | − | 10775.2i | −0.602833 | − | 1.04414i | ||||
\(475\) | −8249.07 | −0.796828 | ||||||||
\(476\) | 10052.2 | − | 7577.84i | 0.967948 | − | 0.729684i | ||||
\(477\) | 3293.14 | 0.316106 | ||||||||
\(478\) | −2736.53 | − | 4739.80i | −0.261853 | − | 0.453543i | ||||
\(479\) | −2989.71 | + | 5178.32i | −0.285184 | + | 0.493953i | −0.972654 | − | 0.232260i | \(-0.925388\pi\) |
0.687470 | + | 0.726213i | \(0.258721\pi\) | |||||||
\(480\) | 5049.64 | − | 8746.24i | 0.480174 | − | 0.831686i | ||||
\(481\) | 24.5330 | + | 42.4925i | 0.00232559 | + | 0.00402804i | ||||
\(482\) | 12451.1 | 1.17663 | ||||||||
\(483\) | −1031.35 | − | 8386.81i | −0.0971600 | − | 0.790089i | ||||
\(484\) | −15327.5 | −1.43948 | ||||||||
\(485\) | −6452.34 | − | 11175.8i | −0.604094 | − | 1.04632i | ||||
\(486\) | −553.598 | + | 958.861i | −0.0516702 | + | 0.0894955i | ||||
\(487\) | 557.481 | − | 965.586i | 0.0518725 | − | 0.0898457i | −0.838923 | − | 0.544250i | \(-0.816814\pi\) |
0.890796 | + | 0.454404i | \(0.150148\pi\) | |||||||
\(488\) | 7070.80 | + | 12247.0i | 0.655902 | + | 1.13606i | ||||
\(489\) | 10527.8 | 0.973583 | ||||||||
\(490\) | −7689.34 | + | 26853.6i | −0.708916 | + | 2.47576i | ||||
\(491\) | 1086.23 | 0.0998387 | 0.0499194 | − | 0.998753i | \(-0.484104\pi\) | ||||
0.0499194 | + | 0.998753i | \(0.484104\pi\) | |||||||
\(492\) | −752.670 | − | 1303.66i | −0.0689695 | − | 0.119459i | ||||
\(493\) | −4967.00 | + | 8603.10i | −0.453758 | + | 0.785932i | ||||
\(494\) | 1265.93 | − | 2192.66i | 0.115297 | − | 0.199701i | ||||
\(495\) | 916.425 | + | 1587.29i | 0.0832126 | + | 0.144128i | ||||
\(496\) | 513.740 | 0.0465073 | ||||||||
\(497\) | −834.028 | − | 6782.18i | −0.0752742 | − | 0.612117i | ||||
\(498\) | −4482.50 | −0.403344 | ||||||||
\(499\) | 1106.75 | + | 1916.95i | 0.0992884 | + | 0.171973i | 0.911390 | − | 0.411543i | \(-0.135010\pi\) |
−0.812102 | + | 0.583516i | \(0.801677\pi\) | |||||||
\(500\) | −7919.92 | + | 13717.7i | −0.708379 | + | 1.22695i | ||||
\(501\) | −514.512 | + | 891.162i | −0.0458817 | + | 0.0794694i | ||||
\(502\) | 17236.3 | + | 29854.2i | 1.53246 | + | 2.65430i | ||||
\(503\) | −2643.32 | −0.234314 | −0.117157 | − | 0.993113i | \(-0.537378\pi\) | ||||
−0.117157 | + | 0.993113i | \(0.537378\pi\) | |||||||
\(504\) | −2886.99 | + | 2176.35i | −0.255153 | + | 0.192346i | ||||
\(505\) | 27143.5 | 2.39183 | ||||||||
\(506\) | −3947.83 | − | 6837.84i | −0.346843 | − | 0.600749i | ||||
\(507\) | −3038.14 | + | 5262.21i | −0.266131 | + | 0.460952i | ||||
\(508\) | −6219.31 | + | 10772.2i | −0.543183 | + | 0.940821i | ||||
\(509\) | 332.584 | + | 576.053i | 0.0289618 | + | 0.0501633i | 0.880143 | − | 0.474709i | \(-0.157447\pi\) |
−0.851181 | + | 0.524872i | \(0.824113\pi\) | |||||||
\(510\) | 13013.8 | 1.12992 | ||||||||
\(511\) | −10381.4 | − | 4404.38i | −0.898724 | − | 0.381288i | ||||
\(512\) | −1177.58 | −0.101645 | ||||||||
\(513\) | −572.701 | − | 991.947i | −0.0492892 | − | 0.0853714i | ||||
\(514\) | 11410.7 | − | 19763.9i | 0.979190 | − | 1.69601i | ||||
\(515\) | 9400.26 | − | 16281.7i | 0.804320 | − | 1.39312i | ||||
\(516\) | 8219.76 | + | 14237.0i | 0.701269 | + | 1.21463i | ||||
\(517\) | −241.406 | −0.0205359 | ||||||||
\(518\) | 290.991 | + | 123.455i | 0.0246823 | + | 0.0104716i | ||||
\(519\) | 12561.6 | 1.06242 | ||||||||
\(520\) | −2539.03 | − | 4397.73i | −0.214123 | − | 0.370872i | ||||
\(521\) | 5880.99 | − | 10186.2i | 0.494531 | − | 0.856554i | −0.505449 | − | 0.862857i | \(-0.668673\pi\) |
0.999980 | + | 0.00630307i | \(0.00200634\pi\) | |||||||
\(522\) | 3823.79 | − | 6623.01i | 0.320619 | − | 0.555328i | ||||
\(523\) | −5061.30 | − | 8766.43i | −0.423165 | − | 0.732943i | 0.573082 | − | 0.819498i | \(-0.305748\pi\) |
−0.996247 | + | 0.0865547i | \(0.972414\pi\) | |||||||
\(524\) | −22875.7 | −1.90712 | ||||||||
\(525\) | −8627.15 | + | 6503.54i | −0.717180 | + | 0.540643i | ||||
\(526\) | 28471.9 | 2.36014 | ||||||||
\(527\) | 4204.76 | + | 7282.85i | 0.347556 | + | 0.601985i | ||||
\(528\) | 55.6169 | − | 96.3312i | 0.00458412 | − | 0.00793992i | ||||
\(529\) | −5481.49 | + | 9494.22i | −0.450521 | + | 0.780325i | ||||
\(530\) | 14899.0 | + | 25805.9i | 1.22108 | + | 2.11497i | ||||
\(531\) | −2039.20 | −0.166655 | ||||||||
\(532\) | −1223.66 | − | 9950.58i | −0.0997224 | − | 0.810926i | ||||
\(533\) | 515.079 | 0.0418585 | ||||||||
\(534\) | 257.060 | + | 445.240i | 0.0208316 | + | 0.0360813i | ||||
\(535\) | −6850.09 | + | 11864.7i | −0.553561 | + | 0.958796i | ||||
\(536\) | 1577.26 | − | 2731.89i | 0.127103 | − | 0.220148i | ||||
\(537\) | −2955.43 | − | 5118.95i | −0.237498 | − | 0.411358i | ||||
\(538\) | 16350.3 | 1.31024 | ||||||||
\(539\) | −1075.85 | + | 3757.20i | −0.0859740 | + | 0.300249i | ||||
\(540\) | −6157.90 | −0.490730 | ||||||||
\(541\) | −8058.98 | − | 13958.6i | −0.640449 | − | 1.10929i | −0.985333 | − | 0.170644i | \(-0.945415\pi\) |
0.344884 | − | 0.938645i | \(-0.387918\pi\) | |||||||
\(542\) | −4517.96 | + | 7825.34i | −0.358050 | + | 0.620161i | ||||
\(543\) | −5419.65 | + | 9387.11i | −0.428323 | + | 0.741878i | ||||
\(544\) | −5016.47 | − | 8688.78i | −0.395366 | − | 0.684795i | ||||
\(545\) | −25505.9 | −2.00469 | ||||||||
\(546\) | −404.731 | − | 3291.20i | −0.0317232 | − | 0.257968i | ||||
\(547\) | −626.100 | −0.0489399 | −0.0244699 | − | 0.999701i | \(-0.507790\pi\) | ||||
−0.0244699 | + | 0.999701i | \(0.507790\pi\) | |||||||
\(548\) | −10747.0 | − | 18614.3i | −0.837751 | − | 1.45103i | ||||
\(549\) | −2933.88 | + | 5081.63i | −0.228078 | + | 0.395043i | ||||
\(550\) | −5047.56 | + | 8742.64i | −0.391325 | + | 0.677795i | ||||
\(551\) | 3955.74 | + | 6851.54i | 0.305844 | + | 0.529737i | ||||
\(552\) | 9896.41 | 0.763078 | ||||||||
\(553\) | 13461.4 | − | 10147.8i | 1.03515 | − | 0.780341i | ||||
\(554\) | −33552.7 | −2.57313 | ||||||||
\(555\) | 100.426 | + | 173.944i | 0.00768083 | + | 0.0133036i | ||||
\(556\) | −2010.34 | + | 3482.02i | −0.153341 | + | 0.265594i | ||||
\(557\) | −10385.6 | + | 17988.4i | −0.790039 | + | 1.36839i | 0.135903 | + | 0.990722i | \(0.456606\pi\) |
−0.925942 | + | 0.377665i | \(0.876727\pi\) | |||||||
\(558\) | −3236.99 | − | 5606.63i | −0.245578 | − | 0.425354i | ||||
\(559\) | −5625.08 | −0.425609 | ||||||||
\(560\) | 991.615 | + | 420.698i | 0.0748275 | + | 0.0317460i | ||||
\(561\) | 1820.81 | 0.137031 | ||||||||
\(562\) | −12101.8 | − | 20961.0i | −0.908335 | − | 1.57328i | ||||
\(563\) | 2760.86 | − | 4781.95i | 0.206672 | − | 0.357966i | −0.743992 | − | 0.668188i | \(-0.767070\pi\) |
0.950664 | + | 0.310222i | \(0.100403\pi\) | |||||||
\(564\) | 405.532 | − | 702.402i | 0.0302765 | − | 0.0524405i | ||||
\(565\) | −3240.09 | − | 5612.00i | −0.241260 | − | 0.417874i | ||||
\(566\) | 4974.48 | 0.369422 | ||||||||
\(567\) | −1381.00 | − | 585.895i | −0.102286 | − | 0.0433955i | ||||
\(568\) | 8002.95 | 0.591191 | ||||||||
\(569\) | −3787.40 | − | 6559.97i | −0.279044 | − | 0.483319i | 0.692103 | − | 0.721799i | \(-0.256684\pi\) |
−0.971147 | + | 0.238480i | \(0.923351\pi\) | |||||||
\(570\) | 5182.11 | − | 8975.67i | 0.380797 | − | 0.659560i | ||||
\(571\) | 165.624 | − | 286.869i | 0.0121386 | − | 0.0210247i | −0.859892 | − | 0.510476i | \(-0.829469\pi\) |
0.872031 | + | 0.489451i | \(0.162803\pi\) | |||||||
\(572\) | −952.239 | − | 1649.33i | −0.0696068 | − | 0.120563i | ||||
\(573\) | −5723.31 | −0.417268 | ||||||||
\(574\) | 2649.72 | − | 1997.48i | 0.192678 | − | 0.145250i | ||||
\(575\) | 29573.2 | 2.14485 | ||||||||
\(576\) | 3744.73 | + | 6486.06i | 0.270886 | + | 0.469188i | ||||
\(577\) | −1019.06 | + | 1765.06i | −0.0735248 | + | 0.127349i | −0.900444 | − | 0.434972i | \(-0.856758\pi\) |
0.826919 | + | 0.562321i | \(0.190091\pi\) | |||||||
\(578\) | −4728.57 | + | 8190.13i | −0.340281 | + | 0.589385i | ||||
\(579\) | 3599.89 | + | 6235.19i | 0.258387 | + | 0.447540i | ||||
\(580\) | 42533.6 | 3.04502 | ||||||||
\(581\) | −741.275 | − | 6027.93i | −0.0529316 | − | 0.430431i | ||||
\(582\) | 9869.26 | 0.702911 | ||||||||
\(583\) | 2084.58 | + | 3610.60i | 0.148087 | + | 0.256494i | ||||
\(584\) | 6603.72 | − | 11438.0i | 0.467918 | − | 0.810457i | ||||
\(585\) | 1053.52 | − | 1824.75i | 0.0744575 | − | 0.128964i | ||||
\(586\) | −16384.4 | − | 28378.6i | −1.15500 | − | 2.00053i | ||||
\(587\) | 5232.90 | 0.367947 | 0.183973 | − | 0.982931i | \(-0.441104\pi\) | ||||
0.183973 | + | 0.982931i | \(0.441104\pi\) | |||||||
\(588\) | −9124.74 | − | 9441.91i | −0.639963 | − | 0.662207i | ||||
\(589\) | 6697.36 | 0.468523 | ||||||||
\(590\) | −9225.88 | − | 15979.7i | −0.643769 | − | 1.11504i | ||||
\(591\) | 2271.47 | − | 3934.31i | 0.158098 | − | 0.273834i | ||||
\(592\) | 6.09477 | − | 10.5565i | 0.000423131 | − | 0.000732884i | ||||
\(593\) | 2860.12 | + | 4953.87i | 0.198062 | + | 0.343054i | 0.947900 | − | 0.318568i | \(-0.103202\pi\) |
−0.749838 | + | 0.661622i | \(0.769868\pi\) | |||||||
\(594\) | −1401.73 | −0.0968244 | ||||||||
\(595\) | 2152.10 | + | 17500.5i | 0.148282 | + | 1.20580i | ||||
\(596\) | 24165.5 | 1.66083 | ||||||||
\(597\) | 2051.67 | + | 3553.59i | 0.140652 | + | 0.243616i | ||||
\(598\) | −4538.41 | + | 7860.75i | −0.310350 | + | 0.537542i | ||||
\(599\) | −9044.21 | + | 15665.0i | −0.616922 | + | 1.06854i | 0.373122 | + | 0.927782i | \(0.378287\pi\) |
−0.990044 | + | 0.140758i | \(0.955046\pi\) | |||||||
\(600\) | −6326.61 | − | 10958.0i | −0.430471 | − | 0.745598i | ||||
\(601\) | −1821.43 | −0.123623 | −0.0618117 | − | 0.998088i | \(-0.519688\pi\) | ||||
−0.0618117 | + | 0.998088i | \(0.519688\pi\) | |||||||
\(602\) | −28937.1 | + | 21814.1i | −1.95911 | + | 1.47687i | ||||
\(603\) | 1308.90 | 0.0883955 | ||||||||
\(604\) | 12836.0 | + | 22232.6i | 0.864719 | + | 1.49774i | ||||
\(605\) | 10734.4 | − | 18592.5i | 0.721348 | − | 1.24941i | ||||
\(606\) | −10379.4 | + | 17977.7i | −0.695769 | + | 1.20511i | ||||
\(607\) | −1186.10 | − | 2054.39i | −0.0793120 | − | 0.137372i | 0.823641 | − | 0.567111i | \(-0.191939\pi\) |
−0.902953 | + | 0.429739i | \(0.858606\pi\) | |||||||
\(608\) | −7990.26 | −0.532974 | ||||||||
\(609\) | 9538.76 | + | 4046.87i | 0.634696 | + | 0.269273i | ||||
\(610\) | −53094.7 | −3.52416 | ||||||||
\(611\) | 138.760 | + | 240.339i | 0.00918760 | + | 0.0159134i | ||||
\(612\) | −3058.72 | + | 5297.87i | −0.202029 | + | 0.349924i | ||||
\(613\) | −4862.54 | + | 8422.16i | −0.320385 | + | 0.554923i | −0.980567 | − | 0.196182i | \(-0.937146\pi\) |
0.660182 | + | 0.751105i | \(0.270479\pi\) | |||||||
\(614\) | 1233.30 | + | 2136.15i | 0.0810621 | + | 0.140404i | ||||
\(615\) | 2108.48 | 0.138248 | ||||||||
\(616\) | −4213.65 | − | 1787.66i | −0.275605 | − | 0.116927i | ||||
\(617\) | −5329.51 | −0.347744 | −0.173872 | − | 0.984768i | \(-0.555628\pi\) | ||||
−0.173872 | + | 0.984768i | \(0.555628\pi\) | |||||||
\(618\) | 7189.15 | + | 12452.0i | 0.467945 | + | 0.810504i | ||||
\(619\) | 7988.29 | − | 13836.1i | 0.518702 | − | 0.898418i | −0.481062 | − | 0.876687i | \(-0.659749\pi\) |
0.999764 | − | 0.0217314i | \(-0.00691786\pi\) | |||||||
\(620\) | 18003.2 | − | 31182.4i | 1.16617 | − | 2.01986i | ||||
\(621\) | 2053.15 | + | 3556.17i | 0.132673 | + | 0.229797i | ||||
\(622\) | −246.120 | −0.0158658 | ||||||||
\(623\) | −556.236 | + | 419.316i | −0.0357706 | + | 0.0269656i | ||||
\(624\) | −127.874 | −0.00820361 | ||||||||
\(625\) | 1060.03 | + | 1836.03i | 0.0678420 | + | 0.117506i | ||||
\(626\) | 8595.45 | − | 14887.8i | 0.548791 | − | 0.950535i | ||||
\(627\) | 725.049 | − | 1255.82i | 0.0461813 | − | 0.0799883i | ||||
\(628\) | 24426.7 | + | 42308.4i | 1.55212 | + | 2.68836i | ||||
\(629\) | 199.533 | 0.0126485 | ||||||||
\(630\) | −1656.77 | − | 13472.6i | −0.104774 | − | 0.852002i | ||||
\(631\) | −4199.98 | −0.264974 | −0.132487 | − | 0.991185i | \(-0.542296\pi\) | ||||
−0.132487 | + | 0.991185i | \(0.542296\pi\) | |||||||
\(632\) | 9871.73 | + | 17098.3i | 0.621324 | + | 1.07616i | ||||
\(633\) | 6453.78 | − | 11178.3i | 0.405237 | − | 0.701891i | ||||
\(634\) | 3916.74 | − | 6783.99i | 0.245352 | − | 0.424963i | ||||
\(635\) | −8711.19 | − | 15088.2i | −0.544399 | − | 0.942926i | ||||
\(636\) | −14007.3 | −0.873312 | ||||||||
\(637\) | 4358.98 | − | 1088.54i | 0.271129 | − | 0.0677072i | ||||
\(638\) | 9681.97 | 0.600804 | ||||||||
\(639\) | 1660.33 | + | 2875.77i | 0.102788 | + | 0.178034i | ||||
\(640\) | −20418.6 | + | 35366.0i | −1.26112 | + | 2.18432i | ||||
\(641\) | −1324.25 | + | 2293.67i | −0.0815988 | + | 0.141333i | −0.903937 | − | 0.427666i | \(-0.859336\pi\) |
0.822338 | + | 0.568999i | \(0.192669\pi\) | |||||||
\(642\) | −5238.82 | − | 9073.91i | −0.322056 | − | 0.557817i | ||||
\(643\) | 13.4305 | 0.000823715 | 0.000411857 | − | 1.00000i | \(-0.499869\pi\) | ||||
0.000411857 | 1.00000i | \(0.499869\pi\) | ||||||||
\(644\) | 4386.86 | + | 35673.2i | 0.268426 | + | 2.18280i | ||||
\(645\) | −23026.3 | −1.40568 | ||||||||
\(646\) | −5148.06 | − | 8916.70i | −0.313541 | − | 0.543070i | ||||
\(647\) | −5812.07 | + | 10066.8i | −0.353162 | + | 0.611695i | −0.986802 | − | 0.161934i | \(-0.948227\pi\) |
0.633639 | + | 0.773628i | \(0.281560\pi\) | |||||||
\(648\) | 878.463 | − | 1521.54i | 0.0532551 | − | 0.0922405i | ||||
\(649\) | −1290.83 | − | 2235.78i | −0.0780732 | − | 0.135227i | ||||
\(650\) | 11605.3 | 0.700305 | ||||||||
\(651\) | 7004.32 | − | 5280.18i | 0.421691 | − | 0.317890i | ||||
\(652\) | −44779.8 | −2.68974 | ||||||||
\(653\) | 14258.3 | + | 24696.1i | 0.854471 | + | 1.47999i | 0.877135 | + | 0.480244i | \(0.159452\pi\) |
−0.0226638 | + | 0.999743i | \(0.507215\pi\) | |||||||
\(654\) | 9753.23 | − | 16893.1i | 0.583152 | − | 1.01005i | ||||
\(655\) | 16020.7 | − | 27748.6i | 0.955694 | − | 1.65531i | ||||
\(656\) | −63.9809 | − | 110.818i | −0.00380798 | − | 0.00659561i | ||||
\(657\) | 5480.15 | 0.325420 | ||||||||
\(658\) | 1645.86 | + | 698.265i | 0.0975111 | + | 0.0413696i | ||||
\(659\) | 18048.6 | 1.06688 | 0.533440 | − | 0.845838i | \(-0.320899\pi\) | ||||
0.533440 | + | 0.845838i | \(0.320899\pi\) | |||||||
\(660\) | −3898.01 | − | 6751.54i | −0.229893 | − | 0.398187i | ||||
\(661\) | −8920.72 | + | 15451.1i | −0.524926 | + | 0.909198i | 0.474653 | + | 0.880173i | \(0.342574\pi\) |
−0.999579 | + | 0.0290250i | \(0.990760\pi\) | |||||||
\(662\) | 19155.5 | − | 33178.2i | 1.12462 | − | 1.94790i | ||||
\(663\) | −1046.60 | − | 1812.76i | −0.0613069 | − | 0.106187i | ||||
\(664\) | 7112.94 | 0.415716 | ||||||||
\(665\) | 12927.2 | + | 5484.42i | 0.753826 | + | 0.319815i | ||||
\(666\) | −153.608 | −0.00893725 | ||||||||
\(667\) | −14181.5 | − | 24563.0i | −0.823251 | − | 1.42591i | ||||
\(668\) | 2188.47 | − | 3790.55i | 0.126758 | − | 0.219552i | ||||
\(669\) | −2245.78 | + | 3889.80i | −0.129786 | + | 0.224796i | ||||
\(670\) | 5921.81 | + | 10256.9i | 0.341462 | + | 0.591430i | ||||
\(671\) | −7428.68 | −0.427394 | ||||||||
\(672\) | −8356.47 | + | 6299.49i | −0.479699 | + | 0.361619i | ||||
\(673\) | −6826.13 | −0.390978 | −0.195489 | − | 0.980706i | \(-0.562629\pi\) | ||||
−0.195489 | + | 0.980706i | \(0.562629\pi\) | |||||||
\(674\) | 6354.89 | + | 11007.0i | 0.363177 | + | 0.629041i | ||||
\(675\) | 2625.09 | − | 4546.80i | 0.149689 | − | 0.259269i | ||||
\(676\) | 12922.7 | − | 22382.8i | 0.735246 | − | 1.27348i | ||||
\(677\) | 10643.4 | + | 18435.0i | 0.604225 | + | 1.04655i | 0.992173 | + | 0.124867i | \(0.0398505\pi\) |
−0.387949 | + | 0.921681i | \(0.626816\pi\) | |||||||
\(678\) | 4955.92 | 0.280724 | ||||||||
\(679\) | 1632.09 | + | 13271.9i | 0.0922443 | + | 0.750115i | ||||
\(680\) | −20650.6 | −1.16458 | ||||||||
\(681\) | 2404.99 | + | 4165.56i | 0.135329 | + | 0.234397i | ||||
\(682\) | 4098.08 | − | 7098.08i | 0.230093 | − | 0.398533i | ||||
\(683\) | 10348.4 | − | 17924.0i | 0.579753 | − | 1.00416i | −0.415755 | − | 0.909477i | \(-0.636483\pi\) |
0.995507 | − | 0.0946842i | \(-0.0301841\pi\) | |||||||
\(684\) | 2435.98 | + | 4219.24i | 0.136172 | + | 0.235858i | ||||
\(685\) | 30105.9 | 1.67925 | ||||||||
\(686\) | 18202.5 | − | 22503.9i | 1.01308 | − | 1.25248i | ||||
\(687\) | −3031.56 | −0.168357 | ||||||||
\(688\) | 698.722 | + | 1210.22i | 0.0387188 | + | 0.0670629i | ||||
\(689\) | 2396.43 | − | 4150.74i | 0.132506 | − | 0.229507i | ||||
\(690\) | −18578.0 | + | 32178.1i | −1.02501 | + | 1.77536i | ||||
\(691\) | −15671.0 | − | 27142.9i | −0.862738 | − | 1.49431i | −0.869276 | − | 0.494327i | \(-0.835415\pi\) |
0.00653825 | − | 0.999979i | \(-0.497919\pi\) | |||||||
\(692\) | −53430.8 | −2.93517 | ||||||||
\(693\) | −231.805 | − | 1885.00i | −0.0127064 | − | 0.103327i | ||||
\(694\) | 15819.5 | 0.865276 | ||||||||
\(695\) | −2815.83 | − | 4877.16i | −0.153684 | − | 0.266189i | ||||
\(696\) | −6067.69 | + | 10509.5i | −0.330453 | + | 0.572361i | ||||
\(697\) | 1047.32 | − | 1814.01i | 0.0569153 | − | 0.0985801i | ||||
\(698\) | −15095.5 | − | 26146.2i | −0.818587 | − | 1.41783i | ||||
\(699\) | −594.651 | −0.0321770 | ||||||||
\(700\) | 36695.5 | − | 27662.7i | 1.98137 | − | 1.49365i | ||||
\(701\) | −9213.32 | −0.496408 | −0.248204 | − | 0.968708i | \(-0.579840\pi\) | ||||
−0.248204 | + | 0.968708i | \(0.579840\pi\) | |||||||
\(702\) | 805.712 | + | 1395.53i | 0.0433185 | + | 0.0750299i | ||||
\(703\) | 79.4544 | − | 137.619i | 0.00426270 | − | 0.00738322i | ||||
\(704\) | −4740.89 | + | 8211.46i | −0.253805 | + | 0.439604i | ||||
\(705\) | 568.016 | + | 983.833i | 0.0303443 | + | 0.0525578i | ||||
\(706\) | −43141.5 | −2.29979 | ||||||||
\(707\) | −25892.4 | − | 10985.0i | −1.37734 | − | 0.584345i | ||||
\(708\) | 8673.71 | 0.460421 | ||||||||
\(709\) | −7258.27 | − | 12571.7i | −0.384471 | − | 0.665923i | 0.607225 | − | 0.794530i | \(-0.292283\pi\) |
−0.991696 | + | 0.128607i | \(0.958949\pi\) | |||||||
\(710\) | −15023.5 | + | 26021.6i | −0.794118 | + | 1.37545i | ||||
\(711\) | −4096.07 | + | 7094.60i | −0.216054 | + | 0.374217i | ||||
\(712\) | −407.908 | − | 706.518i | −0.0214705 | − | 0.0371880i | ||||
\(713\) | −24010.3 | −1.26114 | ||||||||
\(714\) | −12413.9 | − | 5266.66i | −0.650671 | − | 0.276050i | ||||
\(715\) | 2667.54 | 0.139525 | ||||||||
\(716\) | 12570.9 | + | 21773.4i | 0.656140 | + | 1.13647i | ||||
\(717\) | −1801.78 | + | 3120.78i | −0.0938477 | + | 0.162549i | ||||
\(718\) | −14306.0 | + | 24778.7i | −0.743585 | + | 1.28793i | ||||
\(719\) | −12941.2 | − | 22414.8i | −0.671246 | − | 1.16263i | −0.977551 | − | 0.210698i | \(-0.932426\pi\) |
0.306306 | − | 0.951933i | \(-0.400907\pi\) | |||||||
\(720\) | −523.454 | −0.0270944 | ||||||||
\(721\) | −15556.2 | + | 11726.9i | −0.803525 | + | 0.605734i | ||||
\(722\) | 23052.3 | 1.18825 | ||||||||
\(723\) | −4099.04 | − | 7099.74i | −0.210850 | − | 0.365204i | ||||
\(724\) | 23052.4 | − | 39928.0i | 1.18334 | − | 2.04960i | ||||
\(725\) | −18132.0 | + | 31405.5i | −0.928833 | + | 1.60879i | ||||
\(726\) | 8209.48 | + | 14219.2i | 0.419673 | + | 0.726894i | ||||
\(727\) | 32181.2 | 1.64172 | 0.820862 | − | 0.571127i | \(-0.193494\pi\) | ||||
0.820862 | + | 0.571127i | \(0.193494\pi\) | |||||||
\(728\) | 642.237 | + | 5222.56i | 0.0326963 | + | 0.265881i | ||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 24793.7 | + | 42943.9i | 1.25706 | + | 2.17730i | ||||
\(731\) | −11437.5 | + | 19810.4i | −0.578704 | + | 1.00234i | ||||
\(732\) | 12479.2 | − | 21614.7i | 0.630117 | − | 1.09139i | ||||
\(733\) | −10418.1 | − | 18044.6i | −0.524966 | − | 0.909268i | −0.999577 | − | 0.0290722i | \(-0.990745\pi\) |
0.474611 | − | 0.880195i | \(-0.342589\pi\) | |||||||
\(734\) | 49335.5 | 2.48094 | ||||||||
\(735\) | 17843.6 | − | 4455.95i | 0.895469 | − | 0.223620i | ||||
\(736\) | 28645.4 | 1.43462 | ||||||||
\(737\) | 828.544 | + | 1435.08i | 0.0414109 | + | 0.0717257i | ||||
\(738\) | −806.265 | + | 1396.49i | −0.0402155 | + | 0.0696553i | ||||
\(739\) | −13217.4 | + | 22893.3i | −0.657931 | + | 1.13957i | 0.323219 | + | 0.946324i | \(0.395235\pi\) |
−0.981150 | + | 0.193246i | \(0.938098\pi\) | |||||||
\(740\) | −427.163 | − | 739.867i | −0.0212200 | − | 0.0367541i | ||||
\(741\) | −1667.03 | −0.0826447 | ||||||||
\(742\) | −3768.64 | − | 30646.0i | −0.186457 | − | 1.51624i | ||||
\(743\) | 9954.69 | 0.491524 | 0.245762 | − | 0.969330i | \(-0.420962\pi\) | ||||
0.245762 | + | 0.969330i | \(0.420962\pi\) | |||||||
\(744\) | 5136.53 | + | 8896.73i | 0.253111 | + | 0.438401i | ||||
\(745\) | −16923.9 | + | 29313.1i | −0.832274 | + | 1.44154i | ||||
\(746\) | 11935.9 | − | 20673.6i | 0.585798 | − | 1.01463i | ||||
\(747\) | 1475.68 | + | 2555.96i | 0.0722790 | + | 0.125191i | ||||
\(748\) | −7744.79 | −0.378580 | ||||||||
\(749\) | 11336.0 | − | 8545.57i | 0.553014 | − | 0.416887i | ||||
\(750\) | 16967.7 | 0.826098 | ||||||||
\(751\) | 16602.3 | + | 28756.0i | 0.806692 | + | 1.39723i | 0.915143 | + | 0.403129i | \(0.132077\pi\) |
−0.108451 | + | 0.994102i | \(0.534589\pi\) | |||||||
\(752\) | 34.4723 | − | 59.7078i | 0.00167164 | − | 0.00289537i | ||||
\(753\) | 11348.7 | − | 19656.6i | 0.549231 | − | 0.951295i | ||||
\(754\) | −5565.18 | − | 9639.17i | −0.268796 | − | 0.465568i | ||||
\(755\) | −35958.1 | −1.73331 | ||||||||
\(756\) | 5874.05 | + | 2492.10i | 0.282589 | + | 0.119890i | ||||
\(757\) | 1964.06 | 0.0942998 | 0.0471499 | − | 0.998888i | \(-0.484986\pi\) | ||||
0.0471499 | + | 0.998888i | \(0.484986\pi\) | |||||||
\(758\) | −25174.8 | − | 43604.0i | −1.20632 | − | 2.08941i | ||||
\(759\) | −2599.33 | + | 4502.17i | −0.124308 | + | 0.215307i | ||||
\(760\) | −8223.09 | + | 14242.8i | −0.392477 | + | 0.679791i | ||||
\(761\) | 19276.9 | + | 33388.6i | 0.918248 | + | 1.59045i | 0.802075 | + | 0.597224i | \(0.203730\pi\) |
0.116174 | + | 0.993229i | \(0.462937\pi\) | |||||||
\(762\) | 13324.3 | 0.633450 | ||||||||
\(763\) | 24330.2 | + | 10322.2i | 1.15441 | + | 0.489764i | ||||
\(764\) | 24344.0 | 1.15280 | ||||||||
\(765\) | −4284.26 | − | 7420.56i | −0.202481 | − | 0.350707i | ||||
\(766\) | −23848.1 | + | 41306.1i | −1.12489 | + | 1.94837i | ||||
\(767\) | −1483.93 | + | 2570.25i | −0.0698588 | + | 0.120999i | ||||
\(768\) | −5629.83 | − | 9751.15i | −0.264517 | − | 0.458156i | ||||
\(769\) | −19715.0 | −0.924501 | −0.462251 | − | 0.886749i | \(-0.652958\pi\) | ||||
−0.462251 | + | 0.886749i | \(0.652958\pi\) | |||||||
\(770\) | 13722.6 | − | 10344.8i | 0.642246 | − | 0.484155i | ||||
\(771\) | −15026.0 | −0.701880 | ||||||||
\(772\) | −15312.1 | − | 26521.3i | −0.713853 | − | 1.23643i | ||||
\(773\) | 7350.34 | − | 12731.2i | 0.342010 | − | 0.592378i | −0.642796 | − | 0.766037i | \(-0.722226\pi\) |
0.984806 | + | 0.173659i | \(0.0555591\pi\) | |||||||
\(774\) | 8805.06 | − | 15250.8i | 0.408904 | − | 0.708242i | ||||
\(775\) | 15349.4 | + | 26585.9i | 0.711440 | + | 1.23225i | ||||
\(776\) | −15660.8 | −0.724471 | ||||||||
\(777\) | −25.4024 | − | 206.568i | −0.00117285 | − | 0.00953744i | ||||
\(778\) | 52917.8 | 2.43856 | ||||||||
\(779\) | −834.086 | − | 1444.68i | −0.0383623 | − | 0.0664454i | ||||
\(780\) | −4481.13 | + | 7761.55i | −0.205705 | + | 0.356292i | ||||
\(781\) | −2102.00 | + | 3640.78i | −0.0963068 | + | 0.166808i | ||||
\(782\) | 18456.0 | + | 31966.7i | 0.843970 | + | 1.46180i | ||||
\(783\) | −5035.32 | −0.229818 | ||||||||
\(784\) | −775.650 | − | 802.612i | −0.0353339 | − | 0.0365621i | ||||
\(785\) | −68427.6 | −3.11119 | ||||||||
\(786\) | 12252.3 | + | 21221.6i | 0.556012 | + | 0.963041i | ||||
\(787\) | 11959.3 | − | 20714.1i | 0.541681 | − | 0.938218i | −0.457127 | − | 0.889401i | \(-0.651122\pi\) |
0.998808 | − | 0.0488169i | \(-0.0155451\pi\) | |||||||
\(788\) | −9661.69 | + | 16734.5i | −0.436781 | + | 0.756527i | ||||
\(789\) | −9373.21 | − | 16234.9i | −0.422934 | − | 0.732544i | ||||
\(790\) | −74126.9 | −3.33837 | ||||||||
\(791\) | 819.566 | + | 6664.58i | 0.0368400 | + | 0.299577i | ||||
\(792\) | 2224.30 | 0.0997942 | ||||||||
\(793\) | 4269.99 | + | 7395.84i | 0.191213 | + | 0.331191i | ||||
\(794\) | −15280.5 | + | 26466.5i | −0.682976 | + | 1.18295i | ||||
\(795\) | 9809.82 | − | 16991.1i | 0.437633 | − | 0.758003i | ||||
\(796\) | −8726.75 | − | 15115.2i | −0.388582 | − | 0.673044i | ||||
\(797\) | 38252.7 | 1.70010 | 0.850051 | − | 0.526700i | \(-0.176571\pi\) | ||||
0.850051 | + | 0.526700i | \(0.176571\pi\) | |||||||
\(798\) | −8575.68 | + | 6464.74i | −0.380421 | + | 0.286779i | ||||
\(799\) | 1128.57 | 0.0499698 | ||||||||
\(800\) | −18312.5 | − | 31718.2i | −0.809307 | − | 1.40176i | ||||
\(801\) | 169.253 | − | 293.155i | 0.00746600 | − | 0.0129315i | ||||
\(802\) | 12590.1 | − | 21806.7i | 0.554329 | − | 0.960126i | ||||
\(803\) | 3468.98 | + | 6008.45i | 0.152450 | + | 0.264052i | ||||
\(804\) | −5567.39 | −0.244212 | ||||||||
\(805\) | −46344.4 | − | 19661.9i | −2.02910 | − | 0.860857i | ||||
\(806\) | −9422.27 | −0.411769 | ||||||||
\(807\) | −5382.67 | − | 9323.06i | −0.234794 | − | 0.406676i | ||||
\(808\) | 16470.3 | − | 28527.5i | 0.717110 | − | 1.24207i | ||||
\(809\) | 15717.8 | − | 27224.0i | 0.683075 | − | 1.18312i | −0.290962 | − | 0.956734i | \(-0.593975\pi\) |
0.974038 | − | 0.226386i | \(-0.0726912\pi\) | |||||||
\(810\) | 3298.19 | + | 5712.64i | 0.143070 | + | 0.247804i | ||||
\(811\) | 11467.0 | 0.496501 | 0.248250 | − | 0.968696i | \(-0.420144\pi\) | ||||
0.248250 | + | 0.968696i | \(0.420144\pi\) | |||||||
\(812\) | −40573.0 | − | 17213.3i | −1.75349 | − | 0.743928i | ||||
\(813\) | 5949.43 | 0.256649 | ||||||||
\(814\) | −97.2354 | − | 168.417i | −0.00418686 | − | 0.00725185i | ||||
\(815\) | 31360.8 | − | 54318.6i | 1.34788 | − | 2.33460i | ||||
\(816\) | −260.007 | + | 450.346i | −0.0111545 | + | 0.0193202i | ||||
\(817\) | 9108.88 | + | 15777.1i | 0.390061 | + | 0.675605i | ||||
\(818\) | 6009.42 | 0.256864 | ||||||||
\(819\) | −1743.43 | + | 1314.28i | −0.0743838 | + | 0.0560740i | ||||
\(820\) | −8968.42 | −0.381940 | ||||||||
\(821\) | 2515.29 | + | 4356.60i | 0.106923 | + | 0.185197i | 0.914522 | − | 0.404535i | \(-0.132567\pi\) |
−0.807599 | + | 0.589732i | \(0.799233\pi\) | |||||||
\(822\) | −11512.2 | + | 19939.8i | −0.488485 | + | 0.846081i | ||||
\(823\) | 6992.59 | − | 12111.5i | 0.296168 | − | 0.512978i | −0.679088 | − | 0.734057i | \(-0.737625\pi\) |
0.975256 | + | 0.221079i | \(0.0709578\pi\) | |||||||
\(824\) | −11407.9 | − | 19759.1i | −0.482298 | − | 0.835364i | ||||
\(825\) | 6646.83 | 0.280500 | ||||||||
\(826\) | 2333.65 | + | 18976.8i | 0.0983025 | + | 0.799380i | ||||
\(827\) | −13939.5 | −0.586125 | −0.293063 | − | 0.956093i | \(-0.594674\pi\) | ||||
−0.293063 | + | 0.956093i | \(0.594674\pi\) | |||||||
\(828\) | −8733.07 | − | 15126.1i | −0.366540 | − | 0.634866i | ||||
\(829\) | 10052.2 | − | 17410.9i | 0.421143 | − | 0.729441i | −0.574909 | − | 0.818218i | \(-0.694962\pi\) |
0.996052 | + | 0.0887769i | \(0.0282958\pi\) | |||||||
\(830\) | −13352.8 | + | 23127.7i | −0.558411 | + | 0.967197i | ||||
\(831\) | 11045.9 | + | 19132.0i | 0.461103 | + | 0.798654i | ||||
\(832\) | 10900.2 | 0.454203 | ||||||||
\(833\) | 5029.55 | − | 17564.8i | 0.209200 | − | 0.730593i | ||||
\(834\) | 4306.99 | 0.178823 | ||||||||
\(835\) | 3065.33 | + | 5309.31i | 0.127042 | + | 0.220043i | ||||
\(836\) | −3083.99 | + | 5341.62i | −0.127586 | + | 0.220986i | ||||
\(837\) | −2131.30 | + | 3691.51i | −0.0880148 | + | 0.152446i | ||||
\(838\) | 8329.33 | + | 14426.8i | 0.343356 | + | 0.594710i | ||||
\(839\) | 15949.5 | 0.656302 | 0.328151 | − | 0.944625i | \(-0.393575\pi\) | ||||
0.328151 | + | 0.944625i | \(0.393575\pi\) | |||||||
\(840\) | 2629.01 | + | 21378.6i | 0.107987 | + | 0.878135i | ||||
\(841\) | 10390.8 | 0.426043 | ||||||||
\(842\) | −308.440 | − | 534.235i | −0.0126242 | − | 0.0218657i | ||||
\(843\) | −7968.07 | + | 13801.1i | −0.325546 | + | 0.563861i | ||||
\(844\) | −27451.1 | + | 47546.7i | −1.11956 | + | 1.93913i | ||||
\(845\) | 18100.4 | + | 31350.8i | 0.736891 | + | 1.27633i | ||||
\(846\) | −868.817 | −0.0353080 | ||||||||
\(847\) | −17764.0 | + | 13391.3i | −0.720635 | + | 0.543248i | ||||
\(848\) | −1190.70 | −0.0482177 | ||||||||
\(849\) | −1637.65 | − | 2836.49i | −0.0662001 | − | 0.114662i | ||||
\(850\) | 23597.2 | − | 40871.6i | 0.952210 | − | 1.64928i | ||||
\(851\) | −284.847 | + | 493.369i | −0.0114741 | + | 0.0198737i | ||||
\(852\) | −7062.19 | − | 12232.1i | −0.283975 | − | 0.491859i | ||||
\(853\) | 11802.0 | 0.473730 | 0.236865 | − | 0.971543i | \(-0.423880\pi\) | ||||
0.236865 | + | 0.971543i | \(0.423880\pi\) | |||||||
\(854\) | 50647.3 | + | 21487.4i | 2.02941 | + | 0.860986i | ||||
\(855\) | −6824.00 | −0.272954 | ||||||||
\(856\) | 8313.09 | + | 14398.7i | 0.331934 | + | 0.574927i | ||||
\(857\) | −4797.64 | + | 8309.76i | −0.191230 | + | 0.331220i | −0.945658 | − | 0.325162i | \(-0.894581\pi\) |
0.754428 | + | 0.656383i | \(0.227914\pi\) | |||||||
\(858\) | −1020.04 | + | 1766.77i | −0.0405871 | + | 0.0702989i | ||||
\(859\) | −10920.4 | − | 18914.7i | −0.433760 | − | 0.751295i | 0.563433 | − | 0.826162i | \(-0.309480\pi\) |
−0.997194 | + | 0.0748666i | \(0.976147\pi\) | |||||||
\(860\) | 97942.3 | 3.88350 | ||||||||
\(861\) | −2011.29 | − | 853.302i | −0.0796106 | − | 0.0337752i | ||||
\(862\) | −38224.1 | −1.51035 | ||||||||
\(863\) | 13265.8 | + | 22977.1i | 0.523260 | + | 0.906313i | 0.999634 | + | 0.0270699i | \(0.00861768\pi\) |
−0.476374 | + | 0.879243i | \(0.658049\pi\) | |||||||
\(864\) | 2542.73 | − | 4404.14i | 0.100122 | − | 0.173417i | ||||
\(865\) | 37419.5 | − | 64812.4i | 1.47087 | − | 2.54762i | ||||
\(866\) | −18779.1 | − | 32526.4i | −0.736882 | − | 1.27632i | ||||
\(867\) | 6226.77 | 0.243912 | ||||||||
\(868\) | −29792.8 | + | 22459.2i | −1.16502 | + | 0.878242i | ||||
\(869\) | −10371.4 | −0.404862 | ||||||||
\(870\) | −22781.2 | − | 39458.1i | −0.887762 | − | 1.53765i | ||||
\(871\) | 952.491 | − | 1649.76i | 0.0370539 | − | 0.0641792i | ||||
\(872\) | −15476.7 | + | 26806.4i | −0.601039 | + | 1.04103i | ||||
\(873\) | −3249.06 | − | 5627.53i | −0.125961 | − | 0.218171i | ||||
\(874\) | 29396.8 | 1.13771 | ||||||||
\(875\) | 2805.97 | + | 22817.7i | 0.108410 | + | 0.881576i | ||||
\(876\) | −23309.8 | −0.899046 | ||||||||
\(877\) | 3416.23 | + | 5917.09i | 0.131537 | + | 0.227829i | 0.924269 | − | 0.381741i | \(-0.124675\pi\) |
−0.792732 | + | 0.609570i | \(0.791342\pi\) | |||||||
\(878\) | −41652.4 | + | 72144.1i | −1.60103 | + | 2.77306i | ||||
\(879\) | −10787.8 | + | 18685.0i | −0.413951 | + | 0.716985i | ||||
\(880\) | −331.351 | − | 573.916i | −0.0126930 | − | 0.0219849i | ||||
\(881\) | −3994.77 | −0.152766 | −0.0763832 | − | 0.997079i | \(-0.524337\pi\) | ||||
−0.0763832 | + | 0.997079i | \(0.524337\pi\) | |||||||
\(882\) | −3871.95 | + | 13522.1i | −0.147818 | + | 0.516227i | ||||
\(883\) | 13727.0 | 0.523161 | 0.261580 | − | 0.965182i | \(-0.415756\pi\) | ||||
0.261580 | + | 0.965182i | \(0.415756\pi\) | |||||||
\(884\) | 4451.69 | + | 7710.56i | 0.169374 | + | 0.293364i | ||||
\(885\) | −6074.50 | + | 10521.3i | −0.230726 | + | 0.399628i | ||||
\(886\) | 2757.59 | − | 4776.29i | 0.104563 | − | 0.181109i | ||||
\(887\) | −22059.7 | − | 38208.5i | −0.835054 | − | 1.44636i | −0.893987 | − | 0.448093i | \(-0.852103\pi\) |
0.0589333 | − | 0.998262i | \(-0.481230\pi\) | |||||||
\(888\) | 243.750 | 0.00921138 | ||||||||
\(889\) | 2203.46 | + | 17918.1i | 0.0831288 | + | 0.675990i | ||||
\(890\) | 3062.99 | 0.115361 | ||||||||
\(891\) | 461.463 | + | 799.278i | 0.0173508 | + | 0.0300525i | ||||
\(892\) | 9552.40 | − | 16545.2i | 0.358563 | − | 0.621049i | ||||
\(893\) | 449.398 | − | 778.380i | 0.0168405 | − | 0.0291685i | ||||
\(894\) | −12943.1 | − | 22418.1i | −0.484208 | − | 0.838672i | ||||
\(895\) | −35215.3 | −1.31522 | ||||||||
\(896\) | 33790.0 | − | 25472.4i | 1.25987 | − | 0.949749i | ||||
\(897\) | 5976.35 | 0.222458 | ||||||||
\(898\) | −18911.6 | − | 32755.8i | −0.702769 | − | 1.21723i | ||||
\(899\) | 14721.2 | − | 25497.9i | 0.546140 | − | 0.945942i | ||||
\(900\) | −11165.8 | + | 19339.8i | −0.413549 | + | 0.716287i | ||||
\(901\) | −9745.37 | − | 16879.5i | −0.360339 | − | 0.624125i | ||||
\(902\) | −2041.49 | −0.0753594 | ||||||||
\(903\) | 21964.9 | + | 9318.74i | 0.809465 | + | 0.343420i | ||||
\(904\) | −7864.18 | −0.289335 | ||||||||
\(905\) | 32288.9 | + | 55925.9i | 1.18599 | + | 2.05419i | ||||
\(906\) | 13750.0 | − | 23815.7i | 0.504210 | − | 0.873317i | ||||
\(907\) | −18452.9 | + | 31961.4i | −0.675545 | + | 1.17008i | 0.300764 | + | 0.953698i | \(0.402758\pi\) |
−0.976309 | + | 0.216380i | \(0.930575\pi\) | |||||||
\(908\) | −10229.6 | − | 17718.2i | −0.373878 | − | 0.647575i | ||||
\(909\) | 13668.1 | 0.498725 | ||||||||
\(910\) | −18186.8 | − | 7715.83i | −0.662512 | − | 0.281074i | ||||
\(911\) | −3169.56 | −0.115271 | −0.0576356 | − | 0.998338i | \(-0.518356\pi\) | ||||
−0.0576356 | + | 0.998338i | \(0.518356\pi\) | |||||||
\(912\) | 207.071 | + | 358.657i | 0.00751842 | + | 0.0130223i | ||||
\(913\) | −1868.24 | + | 3235.88i | −0.0677214 | + | 0.117297i | ||||
\(914\) | −28007.4 | + | 48510.3i | −1.01357 | + | 1.75556i | ||||
\(915\) | 17479.3 | + | 30275.0i | 0.631527 | + | 1.09384i | ||||
\(916\) | 12894.7 | 0.465124 | ||||||||
\(917\) | −26512.0 | + | 19986.0i | −0.954749 | + | 0.719733i | ||||
\(918\) | 6553.05 | 0.235602 | ||||||||
\(919\) | −4363.50 | − | 7557.80i | −0.156625 | − | 0.271283i | 0.777024 | − | 0.629470i | \(-0.216728\pi\) |
−0.933650 | + | 0.358188i | \(0.883395\pi\) | |||||||
\(920\) | 29480.1 | − | 51061.0i | 1.05645 | − | 1.82982i | ||||
\(921\) | 812.032 | − | 1406.48i | 0.0290525 | − | 0.0503204i | ||||
\(922\) | 44274.8 | + | 76686.2i | 1.58147 | + | 2.73918i | ||||
\(923\) | 4832.91 | 0.172348 | ||||||||
\(924\) | 985.983 | + | 8017.85i | 0.0351044 | + | 0.285463i | ||||
\(925\) | 728.392 | 0.0258912 | ||||||||
\(926\) | −28457.1 | − | 49289.1i | −1.00989 | − | 1.74918i | ||||
\(927\) | 4733.47 | − | 8198.62i | 0.167711 | − | 0.290483i | ||||
\(928\) | −17563.1 | + | 30420.1i | −0.621267 | + | 1.07607i | ||||
\(929\) | −9702.54 | − | 16805.3i | −0.342659 | − | 0.593502i | 0.642267 | − | 0.766481i | \(-0.277994\pi\) |
−0.984926 | + | 0.172979i | \(0.944661\pi\) | |||||||
\(930\) | −38570.2 | −1.35997 | ||||||||
\(931\) | −10111.8 | − | 10463.2i | −0.355961 | − | 0.368334i | ||||
\(932\) | 2529.34 | 0.0888963 | ||||||||
\(933\) | 81.0252 | + | 140.340i | 0.00284314 | + | 0.00492446i | ||||
\(934\) | 7712.04 | − | 13357.6i | 0.270177 | − | 0.467961i | ||||
\(935\) | 5423.95 | − | 9394.55i | 0.189713 | − | 0.328593i | ||||
\(936\) | −1278.52 | − | 2214.47i | −0.0446472 | − | 0.0773313i | ||||
\(937\) | −615.692 | −0.0214662 | −0.0107331 | − | 0.999942i | \(-0.503417\pi\) | ||||
−0.0107331 | + | 0.999942i | \(0.503417\pi\) | |||||||
\(938\) | −1497.90 | − | 12180.6i | −0.0521407 | − | 0.424000i | ||||
\(939\) | −11318.8 | −0.393372 | ||||||||
\(940\) | −2416.05 | − | 4184.72i | −0.0838329 | − | 0.145203i | ||||
\(941\) | 14801.0 | − | 25636.1i | 0.512751 | − | 0.888111i | −0.487140 | − | 0.873324i | \(-0.661960\pi\) |
0.999891 | − | 0.0147865i | \(-0.00470687\pi\) | |||||||
\(942\) | 26166.1 | − | 45321.0i | 0.905029 | − | 1.56756i | ||||
\(943\) | 2990.23 | + | 5179.23i | 0.103261 | + | 0.178854i | ||||
\(944\) | 737.310 | 0.0254210 | ||||||||
\(945\) | −7136.76 | + | 5380.02i | −0.245671 | + | 0.185198i | ||||
\(946\) | 22294.7 | 0.766240 | ||||||||
\(947\) | −6768.71 | − | 11723.8i | −0.232264 | − | 0.402292i | 0.726210 | − | 0.687473i | \(-0.241280\pi\) |
−0.958474 | + | 0.285180i | \(0.907947\pi\) | |||||||
\(948\) | 17422.6 | − | 30176.8i | 0.596898 | − | 1.03386i | ||||
\(949\) | 3987.93 | − | 6907.29i | 0.136411 | − | 0.236270i | ||||
\(950\) | −18792.9 | − | 32550.3i | −0.641813 | − | 1.11165i | ||||
\(951\) | −5157.71 | −0.175868 | ||||||||
\(952\) | 19698.7 | + | 8357.27i | 0.670628 | + | 0.284518i | ||||
\(953\) | 33468.5 | 1.13762 | 0.568810 | − | 0.822469i | \(-0.307404\pi\) | ||||
0.568810 | + | 0.822469i | \(0.307404\pi\) | |||||||
\(954\) | 7502.37 | + | 12994.5i | 0.254610 | + | 0.440998i | ||||
\(955\) | −17049.0 | + | 29529.7i | −0.577688 | + | 1.00058i | ||||
\(956\) | 7663.86 | − | 13274.2i | 0.259275 | − | 0.449078i | ||||
\(957\) | −3187.40 | − | 5520.74i | −0.107664 | − | 0.186479i | ||||
\(958\) | −27244.4 | −0.918817 | ||||||||
\(959\) | −28718.2 | − | 12183.8i | −0.967005 | − | 0.410257i | ||||
\(960\) | 44620.2 | 1.50011 | ||||||||
\(961\) | 2433.44 | + | 4214.85i | 0.0816838 | + | 0.141480i | ||||
\(962\) | −111.781 | + | 193.611i | −0.00374634 | + | 0.00648885i | ||||
\(963\) | −3449.34 | + | 5974.44i | −0.115424 | + | 0.199921i | ||||
\(964\) | 17435.2 | + | 30198.7i | 0.582521 | + | 1.00896i | ||||
\(965\) | 42894.4 | 1.43090 | ||||||||
\(966\) | 30744.1 | − | 23176.3i | 1.02399 | − | 0.771932i | ||||
\(967\) | −55733.5 | −1.85343 | −0.926715 | − | 0.375764i | \(-0.877380\pi\) | ||||
−0.926715 | + | 0.375764i | \(0.877380\pi\) | |||||||
\(968\) | −13027.0 | − | 22563.4i | −0.432545 | − | 0.749190i | ||||
\(969\) | −3389.58 | + | 5870.93i | −0.112373 | + | 0.194635i | ||||
\(970\) | 29399.2 | − | 50920.9i | 0.973146 | − | 1.68554i | ||||
\(971\) | 9745.65 | + | 16880.0i | 0.322094 | + | 0.557882i | 0.980920 | − | 0.194413i | \(-0.0622801\pi\) |
−0.658826 | + | 0.752295i | \(0.728947\pi\) | |||||||
\(972\) | −3100.79 | −0.102323 | ||||||||
\(973\) | 712.251 | + | 5791.91i | 0.0234673 | + | 0.190832i | ||||
\(974\) | 5080.18 | 0.167125 | ||||||||
\(975\) | −3820.58 | − | 6617.44i | −0.125494 | − | 0.217362i | ||||
\(976\) | 1060.80 | − | 1837.36i | 0.0347903 | − | 0.0602586i | ||||
\(977\) | 3120.78 | − | 5405.35i | 0.102193 | − | 0.177004i | −0.810395 | − | 0.585884i | \(-0.800747\pi\) |
0.912588 | + | 0.408881i | \(0.134081\pi\) | |||||||
\(978\) | 23984.2 | + | 41541.8i | 0.784182 | + | 1.35824i | ||||
\(979\) | 428.554 | 0.0139905 | ||||||||
\(980\) | −75897.4 | + | 18953.4i | −2.47393 | + | 0.617799i | ||||
\(981\) | −12843.4 | −0.418001 | ||||||||
\(982\) | 2474.63 | + | 4286.18i | 0.0804160 | + | 0.139285i | ||||
\(983\) | −29847.3 | + | 51697.0i | −0.968444 | + | 1.67739i | −0.268382 | + | 0.963313i | \(0.586489\pi\) |
−0.700062 | + | 0.714082i | \(0.746845\pi\) | |||||||
\(984\) | 1279.40 | − | 2215.99i | 0.0414490 | − | 0.0717918i | ||||
\(985\) | −13532.8 | − | 23439.6i | −0.437758 | − | 0.758220i | ||||
\(986\) | −45263.0 | −1.46193 | ||||||||
\(987\) | −143.677 | − | 1168.36i | −0.00463353 | − | 0.0376791i | ||||
\(988\) | 7090.68 | 0.228324 | ||||||||
\(989\) | −32655.7 | − | 56561.3i | −1.04994 | − | 1.81855i | ||||
\(990\) | −4175.57 | + | 7232.30i | −0.134049 | + | 0.232179i | ||||
\(991\) | −7780.82 | + | 13476.8i | −0.249411 | + | 0.431992i | −0.963362 | − | 0.268203i | \(-0.913570\pi\) |
0.713952 | + | 0.700195i | \(0.246904\pi\) | |||||||
\(992\) | 14867.8 | + | 25751.8i | 0.475860 | + | 0.824214i | ||||
\(993\) | −25224.6 | −0.806123 | ||||||||
\(994\) | 24861.9 | − | 18742.1i | 0.793333 | − | 0.598050i | ||||
\(995\) | 24446.6 | 0.778903 | ||||||||
\(996\) | −6276.80 | − | 10871.7i | −0.199687 | − | 0.345868i | ||||
\(997\) | −9942.47 | + | 17220.9i | −0.315829 | + | 0.547031i | −0.979613 | − | 0.200892i | \(-0.935616\pi\) |
0.663785 | + | 0.747924i | \(0.268949\pi\) | |||||||
\(998\) | −5042.76 | + | 8734.31i | −0.159946 | + | 0.277034i | ||||
\(999\) | 50.5694 | + | 87.5888i | 0.00160155 | + | 0.00277396i |
(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 | 21.4.e.b.4.3 | ✓ | 6 | |
3.2 | odd | 2 | 63.4.e.c.46.1 | 6 | |||
4.3 | odd | 2 | 336.4.q.k.193.1 | 6 | |||
7.2 | even | 3 | inner | 21.4.e.b.16.3 | yes | 6 | |
7.3 | odd | 6 | 147.4.a.m.1.1 | 3 | |||
7.4 | even | 3 | 147.4.a.l.1.1 | 3 | |||
7.5 | odd | 6 | 147.4.e.n.79.3 | 6 | |||
7.6 | odd | 2 | 147.4.e.n.67.3 | 6 | |||
21.2 | odd | 6 | 63.4.e.c.37.1 | 6 | |||
21.5 | even | 6 | 441.4.e.w.226.1 | 6 | |||
21.11 | odd | 6 | 441.4.a.s.1.3 | 3 | |||
21.17 | even | 6 | 441.4.a.t.1.3 | 3 | |||
21.20 | even | 2 | 441.4.e.w.361.1 | 6 | |||
28.3 | even | 6 | 2352.4.a.cg.1.1 | 3 | |||
28.11 | odd | 6 | 2352.4.a.ci.1.3 | 3 | |||
28.23 | odd | 6 | 336.4.q.k.289.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.e.b.4.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
21.4.e.b.16.3 | yes | 6 | 7.2 | even | 3 | inner | |
63.4.e.c.37.1 | 6 | 21.2 | odd | 6 | |||
63.4.e.c.46.1 | 6 | 3.2 | odd | 2 | |||
147.4.a.l.1.1 | 3 | 7.4 | even | 3 | |||
147.4.a.m.1.1 | 3 | 7.3 | odd | 6 | |||
147.4.e.n.67.3 | 6 | 7.6 | odd | 2 | |||
147.4.e.n.79.3 | 6 | 7.5 | odd | 6 | |||
336.4.q.k.193.1 | 6 | 4.3 | odd | 2 | |||
336.4.q.k.289.1 | 6 | 28.23 | odd | 6 | |||
441.4.a.s.1.3 | 3 | 21.11 | odd | 6 | |||
441.4.a.t.1.3 | 3 | 21.17 | even | 6 | |||
441.4.e.w.226.1 | 6 | 21.5 | even | 6 | |||
441.4.e.w.361.1 | 6 | 21.20 | even | 2 | |||
2352.4.a.cg.1.1 | 3 | 28.3 | even | 6 | |||
2352.4.a.ci.1.3 | 3 | 28.11 | odd | 6 |