Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,4,Mod(61,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 8]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.61");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.m (of order \(5\), degree \(4\), 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: | \(17.7005730017\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 61.1 | ||
Character | \(\chi\) | \(=\) | 300.61 |
Dual form | 300.4.m.a.241.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.927051 | − | 2.85317i | 0.178411 | − | 0.549093i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −10.7679 | − | 3.00887i | −0.963106 | − | 0.269121i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −17.8479 | −0.963698 | −0.481849 | − | 0.876254i | \(-0.660035\pi\) | ||||
−0.481849 | + | 0.876254i | \(0.660035\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −7.28115 | − | 5.29007i | −0.269672 | − | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 33.6508 | − | 24.4487i | 0.922372 | − | 0.670143i | −0.0217410 | − | 0.999764i | \(-0.506921\pi\) |
0.944113 | + | 0.329621i | \(0.106921\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −9.86695 | − | 7.16876i | −0.210508 | − | 0.152943i | 0.477536 | − | 0.878612i | \(-0.341530\pi\) |
−0.688043 | + | 0.725670i | \(0.741530\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −18.5672 | + | 27.9331i | −0.319601 | + | 0.480821i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 36.4109 | + | 112.061i | 0.519467 | + | 1.59876i | 0.775004 | + | 0.631956i | \(0.217748\pi\) |
−0.255537 | + | 0.966799i | \(0.582252\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.03136 | + | 12.4072i | 0.0486766 | + | 0.149811i | 0.972440 | − | 0.233151i | \(-0.0749038\pi\) |
−0.923764 | + | 0.382963i | \(0.874904\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −16.5460 | + | 50.9232i | −0.171934 | + | 0.529160i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −151.224 | + | 109.871i | −1.37097 | + | 0.996072i | −0.373315 | + | 0.927705i | \(0.621779\pi\) |
−0.997660 | + | 0.0683668i | \(0.978221\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 106.893 | + | 64.7981i | 0.855148 | + | 0.518384i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −21.8435 | + | 15.8702i | −0.155695 | + | 0.113119i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −13.3131 | + | 40.9734i | −0.0852474 | + | 0.262364i | −0.984590 | − | 0.174881i | \(-0.944046\pi\) |
0.899342 | + | 0.437245i | \(0.144046\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 40.4857 | + | 124.602i | 0.234563 | + | 0.721910i | 0.997179 | + | 0.0750591i | \(0.0239146\pi\) |
−0.762616 | + | 0.646851i | \(0.776085\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −38.5604 | − | 118.677i | −0.203409 | − | 0.626029i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 192.184 | + | 53.7021i | 0.928144 | + | 0.259352i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 318.449 | + | 231.367i | 1.41494 | + | 1.02801i | 0.992581 | + | 0.121584i | \(0.0387975\pi\) |
0.422358 | + | 0.906429i | \(0.361202\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −29.6008 | + | 21.5063i | −0.121537 | + | 0.0883015i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −360.662 | − | 262.037i | −1.37380 | − | 0.998128i | −0.997429 | − | 0.0716603i | \(-0.977170\pi\) |
−0.376376 | − | 0.926467i | \(-0.622830\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 180.383 | 0.639723 | 0.319861 | − | 0.947464i | \(-0.396364\pi\) | ||||
0.319861 | + | 0.947464i | \(0.396364\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 62.4853 | + | 78.8707i | 0.206995 | + | 0.261274i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 34.7074 | − | 106.818i | 0.107715 | − | 0.331512i | −0.882643 | − | 0.470044i | \(-0.844238\pi\) |
0.990358 | + | 0.138531i | \(0.0442382\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −24.4510 | −0.0712856 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 353.485 | 0.970544 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −194.546 | + | 598.752i | −0.504207 | + | 1.55179i | 0.297892 | + | 0.954599i | \(0.403716\pi\) |
−0.802100 | + | 0.597190i | \(0.796284\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −435.910 | + | 162.010i | −1.06869 | + | 0.397189i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 39.1372 | 0.0909448 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −85.2783 | − | 61.9583i | −0.188174 | − | 0.136717i | 0.489710 | − | 0.871886i | \(-0.337103\pi\) |
−0.677884 | + | 0.735169i | \(0.737103\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −153.314 | + | 111.389i | −0.321801 | + | 0.233802i | −0.736943 | − | 0.675954i | \(-0.763732\pi\) |
0.415143 | + | 0.909756i | \(0.363732\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 129.954 | + | 94.4168i | 0.259883 | + | 0.188816i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 84.6761 | + | 106.880i | 0.161581 | + | 0.203952i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 109.821 | + | 337.993i | 0.200250 | + | 0.616305i | 0.999875 | + | 0.0158060i | \(0.00503143\pi\) |
−0.799625 | + | 0.600499i | \(0.794969\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 173.287 | + | 533.324i | 0.302339 | + | 0.930503i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −31.3661 | + | 96.5350i | −0.0524292 | + | 0.161361i | −0.973843 | − | 0.227223i | \(-0.927035\pi\) |
0.921414 | + | 0.388583i | \(0.127035\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 561.527 | − | 407.973i | 0.900298 | − | 0.654105i | −0.0382444 | − | 0.999268i | \(-0.512177\pi\) |
0.938543 | + | 0.345163i | \(0.112177\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 283.976 | − | 244.914i | 0.437209 | − | 0.377070i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −600.597 | + | 436.360i | −0.888889 | + | 0.645815i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −121.320 | + | 373.384i | −0.172779 | + | 0.531759i | −0.999525 | − | 0.0308162i | \(-0.990189\pi\) |
0.826746 | + | 0.562575i | \(0.190189\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 25.0304 | + | 77.0356i | 0.0343352 | + | 0.105673i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −380.474 | − | 1170.98i | −0.503162 | − | 1.54857i | −0.803838 | − | 0.594848i | \(-0.797212\pi\) |
0.300676 | − | 0.953726i | \(-0.402788\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −54.8902 | − | 1316.21i | −0.0700433 | − | 1.67957i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 104.562 | + | 75.9688i | 0.128853 | + | 0.0936174i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −816.875 | + | 593.494i | −0.972905 | + | 0.706857i | −0.956112 | − | 0.293002i | \(-0.905346\pi\) |
−0.0167932 | + | 0.999859i | \(0.505346\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 176.105 | + | 127.948i | 0.202866 | + | 0.147391i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 393.044 | 0.438244 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.07735 | − | 145.729i | −0.00656340 | − | 0.157384i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −328.606 | + | 1011.34i | −0.343967 | + | 1.05862i | 0.618167 | + | 0.786047i | \(0.287876\pi\) |
−0.962134 | + | 0.272576i | \(0.912124\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −374.352 | −0.380038 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 242.161 | 0.238573 | 0.119287 | − | 0.992860i | \(-0.461939\pi\) | ||||
0.119287 | + | 0.992860i | \(0.461939\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −496.703 | + | 1528.69i | −0.475161 | + | 1.46240i | 0.370580 | + | 0.928801i | \(0.379159\pi\) |
−0.845741 | + | 0.533594i | \(0.820841\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 331.385 | − | 498.549i | 0.307999 | − | 0.463366i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 964.672 | 0.871574 | 0.435787 | − | 0.900050i | \(-0.356470\pi\) | ||||
0.435787 | + | 0.900050i | \(0.356470\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1617.38 | − | 1175.09i | −1.42125 | − | 1.03260i | −0.991563 | − | 0.129623i | \(-0.958623\pi\) |
−0.429688 | − | 0.902977i | \(-0.641377\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 955.348 | − | 694.101i | 0.816916 | − | 0.593524i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −728.564 | − | 529.333i | −0.606527 | − | 0.440668i | 0.241663 | − | 0.970360i | \(-0.422307\pi\) |
−0.848190 | + | 0.529693i | \(0.822307\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1958.95 | − | 728.060i | 1.58846 | − | 0.590365i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 33.9195 | + | 104.394i | 0.0268023 | + | 0.0824888i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −649.860 | − | 2000.06i | −0.500610 | − | 1.54072i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 123.334 | − | 379.582i | 0.0926625 | − | 0.285186i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1081.99 | + | 786.110i | −0.793166 | + | 0.576269i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −956.045 | − | 1019.36i | −0.684090 | − | 0.729398i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 924.753 | − | 671.872i | 0.646130 | − | 0.469441i | −0.215820 | − | 0.976433i | \(-0.569243\pi\) |
0.861951 | + | 0.506992i | \(0.169243\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 167.224 | − | 514.662i | 0.114134 | − | 0.351267i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 91.8522 | + | 282.692i | 0.0612608 | + | 0.188541i | 0.977003 | − | 0.213224i | \(-0.0683966\pi\) |
−0.915742 | + | 0.401766i | \(0.868397\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −71.9514 | − | 221.444i | −0.0469096 | − | 0.144373i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 282.959 | − | 105.164i | 0.180394 | − | 0.0670450i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1236.69 | − | 898.511i | −0.771226 | − | 0.560329i | 0.131107 | − | 0.991368i | \(-0.458147\pi\) |
−0.902333 | + | 0.431040i | \(0.858147\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1882.70 | − | 1367.86i | 1.14884 | − | 0.834681i | 0.160513 | − | 0.987034i | \(-0.448685\pi\) |
0.988326 | + | 0.152353i | \(0.0486851\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −272.596 | − | 198.052i | −0.162813 | − | 0.118291i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −507.298 | −0.296660 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 266.637 | − | 401.138i | 0.152710 | − | 0.229743i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −22.6673 | + | 69.7627i | −0.0127181 | + | 0.0391424i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3307.05 | −1.81828 | −0.909142 | − | 0.416486i | \(-0.863262\pi\) | ||||
−0.909142 | + | 0.416486i | \(0.863262\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1947.87 | 1.04977 | 0.524885 | − | 0.851173i | \(-0.324108\pi\) | ||||
0.524885 | + | 0.851173i | \(0.324108\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 327.698 | − | 1008.55i | 0.173156 | − | 0.532919i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −61.0331 | − | 1463.52i | −0.0316277 | − | 0.758402i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 948.343 | 0.482077 | 0.241038 | − | 0.970516i | \(-0.422512\pi\) | ||||
0.241038 | + | 0.970516i | \(0.422512\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1527.99 | + | 1110.15i | 0.762120 | + | 0.553713i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2699.04 | − | 1960.97i | 1.32121 | − | 0.959912i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 872.549 | + | 633.944i | 0.419284 | + | 0.304628i | 0.777350 | − | 0.629069i | \(-0.216564\pi\) |
−0.358065 | + | 0.933696i | \(0.616564\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 58.1306 | + | 1393.92i | 0.0274270 | + | 0.657674i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 483.632 | + | 1488.47i | 0.224099 | + | 0.689706i | 0.998382 | + | 0.0568662i | \(0.0181109\pi\) |
−0.774283 | + | 0.632840i | \(0.781889\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −632.945 | − | 1948.00i | −0.288095 | − | 0.886665i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 36.2822 | − | 111.665i | 0.0162255 | − | 0.0499371i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3269.90 | + | 2375.72i | −1.43703 | + | 1.04406i | −0.448373 | + | 0.893846i | \(0.647996\pi\) |
−0.988653 | + | 0.150214i | \(0.952004\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1907.83 | − | 1156.51i | −0.824104 | − | 0.499566i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −255.835 | + | 185.875i | −0.108643 | + | 0.0789334i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −624.016 | + | 1920.52i | −0.260565 | + | 0.801936i | 0.732117 | + | 0.681179i | \(0.238532\pi\) |
−0.992682 | + | 0.120758i | \(0.961468\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −330.129 | − | 1016.03i | −0.135571 | − | 0.417244i | 0.860108 | − | 0.510113i | \(-0.170396\pi\) |
−0.995678 | + | 0.0928686i | \(0.970396\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 175.682 | + | 540.694i | 0.0709661 | + | 0.218411i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2732.86 | − | 3449.50i | −1.08608 | − | 1.37088i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3965.01 | + | 2880.75i | 1.55054 | + | 1.12653i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 389.861 | − | 283.250i | 0.150043 | − | 0.109013i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 80.9997 | + | 58.8497i | 0.0306855 | + | 0.0222943i | 0.603022 | − | 0.797724i | \(-0.293963\pi\) |
−0.572337 | + | 0.820019i | \(0.693963\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2144.93 | −0.799976 | −0.399988 | − | 0.916520i | \(-0.630986\pi\) | ||||
−0.399988 | + | 0.916520i | \(0.630986\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 383.447 | − | 142.511i | 0.140816 | − | 0.0523357i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −415.322 | + | 1278.23i | −0.150206 | + | 0.462285i | −0.997644 | − | 0.0686091i | \(-0.978144\pi\) |
0.847438 | + | 0.530894i | \(0.178144\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −462.968 | −0.164919 | −0.0824595 | − | 0.996594i | \(-0.526278\pi\) | ||||
−0.0824595 | + | 0.996594i | \(0.526278\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1066.16 | 0.374135 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 237.611 | − | 731.291i | 0.0821527 | − | 0.252840i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3095.13 | + | 3906.76i | 1.05450 | + | 1.33102i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1682.31 | 0.564873 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 439.000 | + | 318.952i | 0.145293 | + | 0.105562i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1479.82 | + | 1075.15i | −0.482820 | + | 0.350789i | −0.802416 | − | 0.596765i | \(-0.796453\pi\) |
0.319597 | + | 0.947554i | \(0.396453\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 246.353 | + | 178.986i | 0.0792480 | + | 0.0575770i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1942.33 | − | 542.747i | −0.616121 | − | 0.172163i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −722.587 | − | 2223.89i | −0.226048 | − | 0.695704i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −643.453 | − | 1980.34i | −0.198541 | − | 0.611047i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 444.075 | − | 1366.72i | 0.135166 | − | 0.415999i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3906.20 | + | 2838.02i | −1.17300 | + | 0.852233i | −0.991365 | − | 0.131133i | \(-0.958139\pi\) |
−0.181634 | + | 0.983366i | \(0.558139\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −435.522 | − | 1037.28i | −0.129043 | − | 0.307342i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4464.64 | + | 3243.75i | −1.30541 | + | 0.948438i | −0.999993 | − | 0.00378020i | \(-0.998797\pi\) |
−0.305420 | + | 0.952218i | \(0.598797\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 135.094 | − | 415.778i | 0.0389838 | − | 0.119980i | −0.929671 | − | 0.368392i | \(-0.879909\pi\) |
0.968655 | + | 0.248412i | \(0.0799086\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 688.223 | + | 2118.13i | 0.196025 | + | 0.603303i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1155.52 | + | 3556.33i | 0.324896 | + | 0.999926i | 0.971488 | + | 0.237090i | \(0.0761936\pi\) |
−0.646592 | + | 0.762836i | \(0.723806\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −695.127 | + | 1045.78i | −0.192958 | + | 0.290293i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 952.858 | + | 692.292i | 0.261159 | + | 0.189743i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2833.90 | − | 2058.95i | 0.766986 | − | 0.557248i | −0.134059 | − | 0.990973i | \(-0.542801\pi\) |
0.901045 | + | 0.433726i | \(0.142801\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4492.47 | + | 3263.97i | 1.20077 | + | 0.872410i | 0.994360 | − | 0.106055i | \(-0.0338220\pi\) |
0.206410 | + | 0.978466i | \(0.433822\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 263.284 | + | 73.5696i | 0.0686556 | + | 0.0191845i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 49.1673 | − | 151.321i | 0.0126657 | − | 0.0389812i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3693.72 | −0.940081 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3738.96 | 0.940242 | 0.470121 | − | 0.882602i | \(-0.344210\pi\) | ||||
0.470121 | + | 0.882602i | \(0.344210\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2402.61 | + | 7394.48i | −0.597039 | + | 1.83750i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3806.27 | − | 1063.59i | −0.934737 | − | 0.261194i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −339.325 | −0.0823600 | −0.0411800 | − | 0.999152i | \(-0.513112\pi\) | ||||
−0.0411800 | + | 0.999152i | \(0.513112\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5683.67 | − | 4129.42i | −1.36357 | − | 0.990695i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 313.686 | − | 227.907i | 0.0743935 | − | 0.0540500i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1512.18 | + | 1098.66i | 0.354544 | + | 0.257591i | 0.750773 | − | 0.660560i | \(-0.229681\pi\) |
−0.396229 | + | 0.918152i | \(0.629681\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3896.41 | − | 5861.91i | 0.903224 | − | 1.35885i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 936.055 | + | 2880.88i | 0.214553 | + | 0.660326i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −298.297 | − | 918.065i | −0.0676115 | − | 0.208087i | 0.911543 | − | 0.411206i | \(-0.134892\pi\) |
−0.979154 | + | 0.203119i | \(0.934892\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1980.08 | − | 6094.05i | 0.443841 | − | 1.36600i | −0.439908 | − | 0.898043i | \(-0.644989\pi\) |
0.883749 | − | 0.467961i | \(-0.155011\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 528.314 | − | 383.843i | 0.117125 | − | 0.0850960i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5181.28 | − | 432.904i | 1.13616 | − | 0.0949275i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −71.9960 | + | 52.3082i | −0.0156167 | + | 0.0113462i | −0.595566 | − | 0.803306i | \(-0.703072\pi\) |
0.579950 | + | 0.814652i | \(0.303072\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 364.372 | − | 1121.42i | 0.0781876 | − | 0.240637i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2525.11 | + | 7771.48i | 0.536069 | + | 1.64985i | 0.741329 | + | 0.671142i | \(0.234196\pi\) |
−0.205260 | + | 0.978707i | \(0.565804\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2282.50 | + | 7024.82i | 0.479437 | + | 1.47556i | 0.839879 | + | 0.542774i | \(0.182626\pi\) |
−0.360442 | + | 0.932782i | \(0.617374\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −421.424 | − | 117.759i | −0.0875895 | − | 0.0244752i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6437.08 | + | 4676.81i | 1.32393 | + | 0.961894i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7257.27 | + | 5272.71i | −1.47716 | + | 1.07322i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2580.90 | + | 1875.13i | 0.519915 | + | 0.377740i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −451.780 | −0.0900794 | −0.0450397 | − | 0.998985i | \(-0.514341\pi\) | ||||
−0.0450397 | + | 0.998985i | \(0.514341\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 731.840 | + | 923.749i | 0.144439 | + | 0.182314i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −347.043 | + | 1068.09i | −0.0678030 | + | 0.208676i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2279.76 | 0.440943 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3219.46 | −0.616500 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 224.495 | − | 690.925i | 0.0425641 | − | 0.130999i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1986.02 | − | 738.121i | 0.372849 | − | 0.138573i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 622.914 | 0.115803 | 0.0579016 | − | 0.998322i | \(-0.481559\pi\) | ||||
0.0579016 | + | 0.998322i | \(0.481559\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3901.15 | + | 2834.35i | 0.718217 | + | 0.521815i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −554.429 | + | 402.816i | −0.101089 | + | 0.0734457i | −0.637182 | − | 0.770714i | \(-0.719900\pi\) |
0.536092 | + | 0.844159i | \(0.319900\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8162.49 | − | 5930.40i | −1.47403 | − | 1.07095i | −0.979421 | − | 0.201830i | \(-0.935311\pi\) |
−0.494609 | − | 0.869115i | \(-0.664689\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1115.23 | − | 1407.68i | −0.199480 | − | 0.251790i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 586.284 | + | 1804.40i | 0.103877 | + | 0.319701i | 0.989465 | − | 0.144771i | \(-0.0462444\pi\) |
−0.885588 | + | 0.464471i | \(0.846244\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 553.752 | + | 1704.27i | 0.0971918 | + | 0.299126i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 894.300 | − | 2752.37i | 0.155498 | − | 0.478575i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1243.59 | + | 903.517i | −0.214226 | + | 0.155644i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −590.191 | − | 1405.65i | −0.100732 | − | 0.239912i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4852.13 | + | 3525.28i | −0.820560 | + | 0.596172i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −619.456 | + | 1906.49i | −0.103805 | + | 0.319478i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3181.22 | + | 9790.79i | 0.528265 | + | 1.62583i | 0.757768 | + | 0.652524i | \(0.226290\pi\) |
−0.229504 | + | 0.973308i | \(0.573710\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1094.73 | − | 3369.24i | −0.180153 | − | 0.554454i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −165.557 | − | 3969.90i | −0.0270010 | − | 0.647459i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 817.018 | + | 593.598i | 0.132065 | + | 0.0959506i | 0.651856 | − | 0.758342i | \(-0.273990\pi\) |
−0.519792 | + | 0.854293i | \(0.673990\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2185.69 | + | 1588.00i | −0.350178 | + | 0.254420i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4408.74 | + | 3203.14i | 0.700137 | + | 0.508680i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6558.24 | 1.03240 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −261.235 | − | 6264.16i | −0.0407664 | − | 0.977539i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −64.3581 | + | 198.074i | −0.00995655 | + | 0.0306431i | −0.955911 | − | 0.293655i | \(-0.905128\pi\) |
0.945955 | + | 0.324298i | \(0.105128\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1067.46 | −0.163725 | −0.0818624 | − | 0.996644i | \(-0.526087\pi\) | ||||
−0.0818624 | + | 0.996644i | \(0.526087\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 329.298 | 0.0500758 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1333.79 | − | 4104.98i | 0.201106 | − | 0.618941i | −0.798745 | − | 0.601670i | \(-0.794502\pi\) |
0.999851 | − | 0.0172709i | \(-0.00549779\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 628.207 | − | 945.099i | 0.0939205 | − | 0.141298i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6308.97 | −0.935311 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4899.88 | − | 3559.97i | −0.720350 | − | 0.523365i | 0.166146 | − | 0.986101i | \(-0.446868\pi\) |
−0.886496 | + | 0.462736i | \(0.846868\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5411.36 | − | 3931.58i | 0.788943 | − | 0.573201i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −968.676 | − | 703.785i | −0.140061 | − | 0.101761i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7273.98 | + | 2703.44i | −1.04312 | + | 0.387683i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2254.77 | − | 6939.48i | −0.320704 | − | 0.987024i | −0.973343 | − | 0.229355i | \(-0.926338\pi\) |
0.652639 | − | 0.757669i | \(-0.273662\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1239.85 | + | 3815.86i | 0.174916 | + | 0.538335i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3472.25 | − | 10686.5i | 0.485903 | − | 1.49546i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2908.38 | + | 2113.06i | −0.403727 | + | 0.293325i | −0.771057 | − | 0.636766i | \(-0.780272\pi\) |
0.367330 | + | 0.930091i | \(0.380272\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3794.72 | + | 1782.76i | −0.522556 | + | 0.245496i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 425.088 | − | 308.844i | 0.0580720 | − | 0.0421917i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3122.89 | − | 9611.25i | 0.423250 | − | 1.30263i | −0.481409 | − | 0.876496i | \(-0.659875\pi\) |
0.904660 | − | 0.426135i | \(-0.140125\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1059.67 | − | 3261.34i | −0.142490 | − | 0.438539i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1828.18 | − | 5626.56i | −0.243905 | − | 0.750662i | −0.995815 | − | 0.0913961i | \(-0.970867\pi\) |
0.751910 | − | 0.659266i | \(-0.229133\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7780.09 | − | 2891.54i | 1.02990 | − | 0.382770i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1313.39 | − | 954.236i | −0.172516 | − | 0.125340i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4528.90 | + | 3290.44i | −0.590294 | + | 0.428874i | −0.842421 | − | 0.538820i | \(-0.818870\pi\) |
0.252126 | + | 0.967694i | \(0.418870\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17818.5 | − | 12945.9i | −2.30465 | − | 1.67443i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 891.720 | 0.114456 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2429.82 | − | 3655.51i | 0.309512 | − | 0.465642i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1149.34 | − | 3537.29i | 0.145298 | − | 0.447183i | −0.851751 | − | 0.523947i | \(-0.824459\pi\) |
0.997049 | + | 0.0767645i | \(0.0244590\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −698.519 | −0.0876433 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3376.07 | −0.420431 | −0.210216 | − | 0.977655i | \(-0.567417\pi\) | ||||
−0.210216 | + | 0.977655i | \(0.567417\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 493.773 | − | 1519.68i | 0.0610337 | − | 0.187842i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −37.7338 | − | 904.821i | −0.00462965 | − | 0.111015i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16372.7 | 1.99402 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2593.28 | − | 1884.13i | −0.313519 | − | 0.227785i | 0.419886 | − | 0.907577i | \(-0.362070\pi\) |
−0.733405 | + | 0.679792i | \(0.762070\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3710.08 | + | 2695.53i | −0.445268 | + | 0.323506i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1522.04 | + | 1105.83i | 0.181343 | + | 0.131754i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 573.573 | + | 13753.7i | 0.0678448 | + | 1.62685i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2157.38 | − | 6639.75i | −0.253351 | − | 0.779736i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −948.726 | − | 2919.88i | −0.110616 | − | 0.340442i | 0.880391 | − | 0.474248i | \(-0.157280\pi\) |
−0.991008 | + | 0.133806i | \(0.957280\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1381.37 | + | 4251.41i | −0.159914 | + | 0.492164i | −0.998626 | − | 0.0524116i | \(-0.983309\pi\) |
0.838712 | + | 0.544576i | \(0.183309\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −817.787 | + | 594.157i | −0.0940003 | + | 0.0682952i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3369.26 | + | 14338.0i | −0.384549 | + | 1.63646i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2736.34 | − | 1988.07i | 0.310119 | − | 0.225314i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −470.291 | + | 1447.41i | −0.0529274 | + | 0.162894i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1133.94 | − | 3489.90i | −0.126728 | − | 0.390030i | 0.867484 | − | 0.497466i | \(-0.165736\pi\) |
−0.994212 | + | 0.107436i | \(0.965736\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4041.88 | + | 12439.6i | 0.448592 | + | 1.38062i | 0.878496 | + | 0.477750i | \(0.158547\pi\) |
−0.429904 | + | 0.902875i | \(0.641453\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −897.330 | − | 1132.64i | −0.0989050 | − | 0.124841i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1972.83 | − | 1433.35i | −0.215957 | − | 0.156902i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2360.27 | − | 1714.84i | 0.256605 | − | 0.186434i | −0.452044 | − | 0.891996i | \(-0.649305\pi\) |
0.708649 | + | 0.705561i | \(0.249305\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 178.031 | + | 129.347i | 0.0192238 | + | 0.0139669i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3937.86 | 0.422332 | 0.211166 | − | 0.977450i | \(-0.432274\pi\) | ||||
0.211166 | + | 0.977450i | \(0.432274\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10581.7 | − | 3932.79i | 1.12724 | − | 0.418949i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3065.81 | + | 9435.58i | −0.324402 | + | 0.998407i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17103.5 | 1.79770 | 0.898848 | − | 0.438260i | \(-0.144405\pi\) | ||||
0.898848 | + | 0.438260i | \(0.144405\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18543.0 | −1.93605 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1805.77 | − | 5557.60i | 0.187291 | − | 0.576422i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1511.29 | − | 1907.60i | −0.155715 | − | 0.196548i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6842.22 | 0.700362 | 0.350181 | − | 0.936682i | \(-0.386120\pi\) | ||||
0.350181 | + | 0.936682i | \(0.386120\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2573.77 | − | 1869.96i | −0.261729 | − | 0.190157i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6184.42 | − | 4493.24i | 0.624809 | − | 0.453950i | −0.229789 | − | 0.973240i | \(-0.573804\pi\) |
0.854598 | + | 0.519290i | \(0.173804\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11520.6 | − | 8370.17i | −1.15638 | − | 0.840162i | −0.167067 | − | 0.985946i | \(-0.553430\pi\) |
−0.989316 | + | 0.145784i | \(0.953430\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4232.24 | − | 1182.62i | −0.422076 | − | 0.117941i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1735.26 | + | 5340.59i | 0.171945 | + | 0.529193i | 0.999481 | − | 0.0322203i | \(-0.0102578\pi\) |
−0.827536 | + | 0.561413i | \(0.810258\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1960.07 | − | 6032.48i | −0.192980 | − | 0.593932i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 879.163 | − | 2705.78i | 0.0860078 | − | 0.264705i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6070.02 | − | 4410.12i | 0.590063 | − | 0.428706i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −373.039 | + | 1587.48i | −0.0360341 | + | 0.153344i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4583.96 | − | 3330.44i | 0.440010 | − | 0.319686i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1641.63 | + | 5052.41i | −0.156593 | + | 0.481943i | −0.998319 | − | 0.0579619i | \(-0.981540\pi\) |
0.841726 | + | 0.539905i | \(0.181540\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1483.51 | − | 4565.77i | −0.140628 | − | 0.432809i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3092.83 | − | 9518.74i | −0.291363 | − | 0.896724i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6581.38 | − | 9901.28i | 0.616175 | − | 0.926998i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 647.849 | + | 470.690i | 0.0602810 | + | 0.0437967i | 0.617518 | − | 0.786557i | \(-0.288138\pi\) |
−0.557237 | + | 0.830354i | \(0.688138\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2617.65 | − | 1901.83i | 0.242074 | − | 0.175877i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3979.58 | + | 2891.34i | 0.365776 | + | 0.265752i | 0.755457 | − | 0.655198i | \(-0.227415\pi\) |
−0.389681 | + | 0.920950i | \(0.627415\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5076.27 | −0.463740 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4030.97 | + | 1126.37i | 0.366017 | + | 0.102276i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 559.821 | − | 1722.95i | 0.0505260 | − | 0.155503i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13306.5 | −1.19375 | −0.596875 | − | 0.802334i | \(-0.703591\pi\) | ||||
−0.596875 | + | 0.802334i | \(0.703591\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4695.20 | 0.418694 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4829.02 | − | 14862.2i | 0.428062 | − | 1.31744i | −0.471969 | − | 0.881615i | \(-0.656456\pi\) |
0.900031 | − | 0.435826i | \(-0.143544\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2607.55 | − | 728.629i | −0.229771 | − | 0.0642050i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6144.76 | −0.538261 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12310.3 | + | 8943.93i | 1.07199 | + | 0.778847i | 0.976269 | − | 0.216562i | \(-0.0694842\pi\) |
0.0957215 | + | 0.995408i | \(0.469484\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10022.1 | + | 7281.48i | −0.867616 | + | 0.630360i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −284.964 | − | 207.039i | −0.0245253 | − | 0.0178187i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9948.06 | − | 14966.2i | 0.851192 | − | 1.28057i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1443.64 | − | 4443.08i | −0.122807 | − | 0.377962i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3746.97 | + | 11532.0i | 0.316905 | + | 0.975333i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1552.47 | − | 4778.02i | 0.130547 | − | 0.401783i | −0.864324 | − | 0.502936i | \(-0.832253\pi\) |
0.994871 | + | 0.101153i | \(0.0322531\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5448.42 | − | 3958.51i | 0.455531 | − | 0.330963i | −0.336245 | − | 0.941775i | \(-0.609157\pi\) |
0.791776 | + | 0.610812i | \(0.209157\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5068.38 | + | 4371.21i | −0.421338 | + | 0.363382i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12489.0 | + | 9073.76i | −1.03231 | + | 0.750018i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7037.35 | − | 21658.7i | 0.578397 | − | 1.78012i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 293.161 | + | 902.256i | 0.0239587 | + | 0.0737374i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1680.16 | + | 5171.00i | 0.136540 | + | 0.420227i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10387.5 | − | 2902.57i | −0.839418 | − | 0.234559i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4901.08 | + | 3560.85i | 0.393850 | + | 0.286149i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −822.794 | + | 597.795i | −0.0657519 | + | 0.0477715i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4991.42 | − | 3626.48i | −0.396669 | − | 0.288197i | 0.371514 | − | 0.928427i | \(-0.378839\pi\) |
−0.768183 | + | 0.640231i | \(0.778839\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3204.96 | −0.253293 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13880.0 | + | 17519.7i | 1.09092 | + | 1.37699i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 262.911 | − | 809.158i | 0.0205508 | − | 0.0632488i | −0.940255 | − | 0.340471i | \(-0.889414\pi\) |
0.960806 | + | 0.277222i | \(0.0894136\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1705.56 | 0.132589 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −562.036 | −0.0434547 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2165.31 | − | 6664.13i | 0.166507 | − | 0.512455i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −12375.5 | + | 4599.47i | −0.946506 | + | 0.351777i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22738.9 | −1.72976 | −0.864882 | − | 0.501975i | \(-0.832607\pi\) | ||||
−0.864882 | + | 0.501975i | \(0.832607\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1779.82 | − | 1293.12i | −0.134666 | − | 0.0978409i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11895.0 | − | 8642.25i | 0.895203 | − | 0.650403i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1053.67 | − | 765.535i | −0.0788754 | − | 0.0573063i | 0.547649 | − | 0.836708i | \(-0.315523\pi\) |
−0.626524 | + | 0.779402i | \(0.715523\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6252.38 | + | 7891.93i | 0.465557 | + | 0.587639i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −446.741 | − | 1374.93i | −0.0330888 | − | 0.101837i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5638.24 | + | 17352.7i | 0.415408 | + | 1.27850i | 0.911885 | + | 0.410445i | \(0.134627\pi\) |
−0.496477 | + | 0.868050i | \(0.665373\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6852.65 | + | 21090.3i | −0.502232 | + | 1.54571i | 0.303143 | + | 0.952945i | \(0.401964\pi\) |
−0.805375 | + | 0.592766i | \(0.798036\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 242.999 | − | 176.549i | 0.0177163 | − | 0.0128716i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −23284.3 | + | 1945.44i | −1.68873 | + | 0.141096i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10327.0 | − | 7502.99i | 0.745092 | − | 0.541341i | −0.149210 | − | 0.988806i | \(-0.547673\pi\) |
0.894302 | + | 0.447465i | \(0.147673\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1988.46 | + | 6119.84i | −0.142725 | + | 0.439261i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6790.68 | + | 20899.6i | 0.484897 | + | 1.49236i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8092.08 | + | 24904.9i | 0.574854 | + | 1.76922i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −51.1344 | − | 1226.16i | −0.00361393 | − | 0.0866586i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20463.9 | − | 14867.9i | −1.43890 | − | 1.04543i | −0.988270 | − | 0.152717i | \(-0.951198\pi\) |
−0.450634 | − | 0.892709i | \(-0.648802\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1382.76 | + | 1004.63i | −0.0967326 | + | 0.0702804i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3261.98 | + | 2369.97i | 0.227039 | + | 0.164954i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6370.90 | −0.441183 | −0.220591 | − | 0.975366i | \(-0.570799\pi\) | ||||
−0.220591 | + | 0.975366i | \(0.570799\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 979.677 | + | 23491.7i | 0.0675006 | + | 1.61860i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −429.195 | + | 1320.92i | −0.0294234 | + | 0.0905559i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22943.4 | 1.56501 | 0.782507 | − | 0.622642i | \(-0.213941\pi\) | ||||
0.782507 | + | 0.622642i | \(0.213941\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17845.5 | −1.21121 | −0.605603 | − | 0.795767i | \(-0.707068\pi\) | ||||
−0.605603 | + | 0.795767i | \(0.707068\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 988.386 | − | 3041.94i | 0.0667499 | − | 0.205435i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2470.15 | + | 3716.19i | −0.165993 | + | 0.249727i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15935.9 | 1.06560 | 0.532798 | − | 0.846243i | \(-0.321141\pi\) | ||||
0.532798 | + | 0.846243i | \(0.321141\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1866.22 | − | 1355.89i | −0.124176 | − | 0.0902189i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1108.21 | + | 805.163i | −0.0733771 | + | 0.0533116i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22328.9 | + | 16222.9i | 1.47122 | + | 1.06890i | 0.980258 | + | 0.197720i | \(0.0633538\pi\) |
0.490960 | + | 0.871182i | \(0.336646\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 14016.0 | − | 5209.16i | 0.918990 | − | 0.341551i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5461.72 | − | 16809.5i | −0.356371 | − | 1.09680i | −0.955211 | − | 0.295927i | \(-0.904371\pi\) |
0.598840 | − | 0.800869i | \(-0.295629\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 392.316 | + | 1207.42i | 0.0254741 | + | 0.0784013i | 0.962985 | − | 0.269554i | \(-0.0868762\pi\) |
−0.937511 | + | 0.347955i | \(0.886876\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1559.59 | − | 4799.92i | 0.100780 | − | 0.310168i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14579.5 | − | 10592.7i | 0.937587 | − | 0.681197i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7227.42 | + | 13853.0i | 0.462555 | + | 0.886591i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1317.00 | − | 956.855i | 0.0838849 | − | 0.0609460i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14332.2 | + | 44110.1i | −0.908528 | + | 2.79616i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8404.62 | + | 25866.8i | 0.530242 | + | 1.63192i | 0.753711 | + | 0.657206i | \(0.228262\pi\) |
−0.223468 | + | 0.974711i | \(0.571738\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1695.72 | + | 5218.90i | 0.106475 | + | 0.327697i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11979.2 | + | 4452.17i | −0.748629 | + | 0.278235i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 241.256 | + | 175.283i | 0.0150062 | + | 0.0109026i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 739.058 | − | 536.957i | 0.0457538 | − | 0.0332421i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21841.7 | − | 15868.9i | −1.34586 | − | 0.977823i | −0.999207 | − | 0.0398293i | \(-0.987319\pi\) |
−0.346652 | − | 0.937994i | \(-0.612681\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12216.8 | 0.749275 | 0.374637 | − | 0.927171i | \(-0.377767\pi\) | ||||
0.374637 | + | 0.927171i | \(0.377767\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3349.19 | + | 5038.65i | −0.204456 | + | 0.307592i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1903.36 | − | 5857.93i | 0.115655 | − | 0.355949i | −0.876428 | − | 0.481532i | \(-0.840080\pi\) |
0.992083 | + | 0.125584i | \(0.0400804\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4384.48 | −0.265187 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7015.02 | −0.422335 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6155.05 | − | 18943.3i | 0.368860 | − | 1.13524i | −0.578668 | − | 0.815563i | \(-0.696427\pi\) |
0.947528 | − | 0.319672i | \(-0.103573\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −138.469 | − | 3320.36i | −0.00826021 | − | 0.198072i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6246.77 | −0.370943 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4382.17 | + | 3183.83i | 0.259037 | + | 0.188201i | 0.709722 | − | 0.704482i | \(-0.248820\pi\) |
−0.450686 | + | 0.892683i | \(0.648820\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14170.3 | + | 10295.3i | −0.833830 | + | 0.605813i | −0.920640 | − | 0.390412i | \(-0.872333\pi\) |
0.0868103 | + | 0.996225i | \(0.472333\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3487.81 | − | 2534.04i | −0.204307 | − | 0.148438i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 108.468 | + | 2600.97i | 0.00632514 | + | 0.151671i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2488.52 | − | 7658.89i | −0.144462 | − | 0.444608i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4476.11 | + | 13776.0i | 0.258679 | + | 0.796133i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2435.81 | + | 7496.66i | −0.140139 | + | 0.431305i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8199.83 | + | 5957.52i | −0.469659 | + | 0.341227i | −0.797308 | − | 0.603572i | \(-0.793743\pi\) |
0.327650 | + | 0.944799i | \(0.393743\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3363.28 | + | 281.007i | −0.191782 | + | 0.0160237i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13791.8 | + | 10020.4i | −0.782959 | + | 0.568853i | −0.905866 | − | 0.423565i | \(-0.860778\pi\) |
0.122907 | + | 0.992418i | \(0.460778\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5864.93 | − | 18050.4i | 0.331481 | − | 1.02019i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5116.02 | + | 15745.5i | 0.287880 | + | 0.886004i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3758.08 | + | 11566.2i | 0.210540 | + | 0.647976i | 0.999440 | + | 0.0334546i | \(0.0106509\pi\) |
−0.788900 | + | 0.614522i | \(0.789349\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10613.1 | + | 13396.1i | 0.591977 | + | 0.747209i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1061.05 | − | 770.895i | −0.0589249 | − | 0.0428115i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6211.88 | − | 4513.20i | 0.343474 | − | 0.249549i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21187.2 | − | 15393.4i | −1.16643 | − | 0.847458i | −0.175849 | − | 0.984417i | \(-0.556267\pi\) |
−0.990577 | + | 0.136959i | \(0.956267\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6681.41 | 0.366242 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −24388.4 | + | 9064.15i | −1.33108 | + | 0.494709i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16232.1 | − | 49957.3i | 0.882116 | − | 2.71487i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11218.0 | 0.607017 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4648.66 | −0.250467 | −0.125234 | − | 0.992127i | \(-0.539968\pi\) | ||||
−0.125234 | + | 0.992127i | \(0.539968\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1586.84 | + | 4883.80i | −0.0851336 | + | 0.262014i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2339.36 | + | 2952.80i | 0.124972 | + | 0.157743i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4322.07 | −0.229912 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29078.7 | + | 21126.9i | 1.54030 | + | 1.11910i | 0.950145 | + | 0.311808i | \(0.100935\pi\) |
0.590158 | + | 0.807288i | \(0.299065\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2858.57 | − | 2076.88i | 0.150780 | − | 0.109548i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19812.6 | − | 14394.7i | −1.04065 | − | 0.756080i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5462.51 | + | 1526.39i | 0.285715 | + | 0.0798374i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3247.36 | − | 9994.34i | −0.169142 | − | 0.520565i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7738.74 | − | 23817.4i | −0.401399 | − | 1.23538i | −0.923865 | − | 0.382720i | \(-0.874988\pi\) |
0.522465 | − | 0.852661i | \(-0.325012\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8865.12 | − | 27284.0i | 0.457912 | − | 1.40931i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13477.4 | − | 9791.92i | 0.693265 | − | 0.503686i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4078.08 | + | 3517.13i | −0.208905 | + | 0.180169i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2409.43 | + | 1750.55i | −0.122917 | + | 0.0893046i | −0.647545 | − | 0.762027i | \(-0.724204\pi\) |
0.524628 | + | 0.851331i | \(0.324204\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 225.273 | − | 693.320i | 0.0114451 | − | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6567.89 | + | 20213.9i | 0.332315 | + | 1.02276i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7178.34 | − | 22092.7i | −0.361716 | − | 1.11325i | −0.952012 | − | 0.306061i | \(-0.900989\pi\) |
0.590296 | − | 0.807187i | \(-0.299011\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 453.985 | − | 682.992i | 0.0227830 | − | 0.0342756i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11959.1 | + | 8688.77i | 0.597717 | + | 0.434267i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20298.9 | − | 14748.0i | 1.01043 | − | 0.734119i | 0.0461291 | − | 0.998935i | \(-0.485311\pi\) |
0.964299 | + | 0.264817i | \(0.0853114\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −386.165 | − | 280.565i | −0.0191446 | − | 0.0139093i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21482.7 | 1.06073 | 0.530367 | − | 0.847768i | \(-0.322054\pi\) | ||||
0.530367 | + | 0.847768i | \(0.322054\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 35609.9 | + | 9950.48i | 1.75120 | + | 0.489339i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3424.27 | + | 10538.8i | −0.167721 | + | 0.516191i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17217.4 | −0.839934 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24836.3 | −1.20678 | −0.603389 | − | 0.797447i | \(-0.706183\pi\) | ||||
−0.603389 | + | 0.797447i | \(0.706183\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3466.20 | − | 10667.9i | 0.167750 | − | 0.516280i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −20974.4 | − | 5860.88i | −1.01104 | − | 0.282516i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13579.1 | −0.651969 | −0.325985 | − | 0.945375i | \(-0.605696\pi\) | ||||
−0.325985 | + | 0.945375i | \(0.605696\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 18870.4 | + | 13710.1i | 0.902438 | + | 0.655660i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23520.2 | − | 17088.4i | 1.12038 | − | 0.814001i | 0.136110 | − | 0.990694i | \(-0.456540\pi\) |
0.984266 | + | 0.176693i | \(0.0565401\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28866.8 | + | 20973.0i | 1.36966 | + | 0.995115i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6563.20 | + | 9873.94i | −0.310187 | + | 0.466657i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 397.272 | + | 1222.68i | 0.0187023 | + | 0.0575598i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 412.241 | + | 1268.75i | 0.0193313 | + | 0.0594957i | 0.960257 | − | 0.279118i | \(-0.0900421\pi\) |
−0.940926 | + | 0.338614i | \(0.890042\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −314.572 | + | 968.152i | −0.0146939 | + | 0.0452233i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21454.6 | + | 15587.7i | −0.998277 | + | 0.725291i | −0.961718 | − | 0.274041i | \(-0.911640\pi\) |
−0.0365590 | + | 0.999331i | \(0.511640\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3746.32 | + | 15942.6i | −0.173641 | + | 0.738934i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −17051.0 | + | 12388.3i | −0.787260 | + | 0.571978i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1797.19 | − | 5531.18i | 0.0826586 | − | 0.254397i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1304.66 | + | 4015.34i | 0.0597754 | + | 0.183970i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −359.453 | − | 1106.28i | −0.0164059 | − | 0.0504921i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10211.6 | − | 2853.44i | −0.464291 | − | 0.129737i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18118.7 | − | 13164.0i | −0.820662 | − | 0.596246i | 0.0962401 | − | 0.995358i | \(-0.469318\pi\) |
−0.916902 | + | 0.399112i | \(0.869318\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4536.55 | − | 3295.99i | 0.204696 | − | 0.148720i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13003.4 | + | 9447.50i | 0.584509 | + | 0.424671i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2311.26 | 0.103500 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13112.8 | − | 16551.4i | −0.584987 | − | 0.738387i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1777.37 | − | 5470.18i | 0.0789933 | − | 0.243116i | −0.903759 | − | 0.428041i | \(-0.859204\pi\) |
0.982753 | + | 0.184924i | \(0.0592040\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13233.9 | 0.585961 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9087.41 | 0.400859 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8921.40 | − | 27457.3i | 0.392067 | − | 1.20666i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −34963.2 | + | 12994.4i | −1.53079 | + | 0.568933i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2895.93 | −0.126322 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15685.1 | − | 11395.9i | −0.681655 | − | 0.495251i | 0.192251 | − | 0.981346i | \(-0.438421\pi\) |
−0.873906 | + | 0.486094i | \(0.838421\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10271.5 | − | 7462.65i | 0.444734 | − | 0.323118i | −0.342779 | − | 0.939416i | \(-0.611368\pi\) |
0.787513 | + | 0.616298i | \(0.211368\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15551.7 | − | 11299.0i | −0.670876 | − | 0.487420i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7488.03 | − | 9451.60i | −0.321834 | − | 0.406227i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 727.186 | + | 2238.05i | 0.0311396 | + | 0.0958377i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −605.394 | − | 1863.21i | −0.0258293 | − | 0.0794944i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2046.46 | − | 6298.34i | 0.0869937 | − | 0.267739i | −0.898091 | − | 0.439810i | \(-0.855046\pi\) |
0.985085 | + | 0.172071i | \(0.0550458\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35068.1 | + | 25478.4i | −1.48529 | + | 1.07913i | −0.509489 | + | 0.860477i | \(0.670166\pi\) |
−0.975803 | + | 0.218651i | \(0.929834\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3568.16 | − | 15184.4i | 0.150579 | − | 0.640791i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23468.4 | − | 17050.8i | 0.986793 | − | 0.716947i | 0.0275762 | − | 0.999620i | \(-0.491221\pi\) |
0.959216 | + | 0.282673i | \(0.0912211\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −937.054 | + | 2883.96i | −0.0392584 | + | 0.120825i | −0.968765 | − | 0.247980i | \(-0.920233\pi\) |
0.929507 | + | 0.368805i | \(0.120233\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 82.5001 | + | 253.909i | 0.00344392 | + | 0.0105993i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −890.282 | − | 2740.01i | −0.0370305 | − | 0.113968i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −729.085 | − | 17482.8i | −0.0302168 | − | 0.724570i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2861.81 | − | 2079.23i | −0.118182 | − | 0.0858645i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 34179.2 | − | 24832.7i | 1.40643 | − | 1.02183i | 0.412606 | − | 0.910910i | \(-0.364619\pi\) |
0.993829 | − | 0.110925i | \(-0.0353812\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18229.5 | + | 13244.5i | 0.747449 | + | 0.543053i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24514.3 | 1.00156 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 954.178 | + | 22880.3i | 0.0388458 | + | 0.931485i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2201.25 | + | 6774.77i | −0.0892987 | + | 0.274833i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22159.0 | 0.895754 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −73577.7 | −2.96382 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3891.06 | + | 11975.5i | −0.156187 | + | 0.480694i | −0.998279 | − | 0.0586395i | \(-0.981324\pi\) |
0.842092 | + | 0.539333i | \(0.181324\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −726.667 | + | 1093.23i | −0.0290661 | + | 0.0437281i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10465.5 | −0.417146 | −0.208573 | − | 0.978007i | \(-0.566882\pi\) | ||||
−0.208573 | + | 0.978007i | \(0.566882\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26753.8 | − | 19437.8i | −1.06266 | − | 0.772069i | −0.0880833 | − | 0.996113i | \(-0.528074\pi\) |
−0.974579 | + | 0.224044i | \(0.928074\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 19311.2 | − | 14030.4i | 0.764373 | − | 0.555350i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27516.9 | − | 19992.2i | −1.08538 | − | 0.788577i | −0.106770 | − | 0.994284i | \(-0.534051\pi\) |
−0.978614 | + | 0.205706i | \(0.934051\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 42358.0 | − | 15742.7i | 1.66499 | − | 0.618808i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8316.09 | + | 25594.3i | 0.325755 | + | 1.00257i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5046.26 | + | 15530.8i | 0.196988 | + | 0.606266i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1339.40 | − | 4122.24i | 0.0521053 | − | 0.160364i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7742.70 | − | 5625.40i | 0.300173 | − | 0.218088i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 17063.4 | + | 18193.6i | 0.659256 | + | 0.702919i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32744.6 | − | 23790.3i | 1.26078 | − | 0.916012i | 0.261987 | − | 0.965071i | \(-0.415622\pi\) |
0.998796 | + | 0.0490593i | \(0.0156223\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −418.823 | + | 1289.00i | −0.0160712 | + | 0.0494619i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9724.64 | − | 29929.4i | −0.371886 | − | 1.14455i | −0.945556 | − | 0.325461i | \(-0.894481\pi\) |
0.573670 | − | 0.819087i | \(-0.305519\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5452.62 | − | 16781.4i | −0.207809 | − | 0.639570i | −0.999586 | − | 0.0287605i | \(-0.990844\pi\) |
0.791777 | − | 0.610810i | \(-0.209156\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3314.07 | − | 1231.70i | 0.125877 | − | 0.0467833i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19087.1 | − | 13867.6i | −0.722529 | − | 0.524948i | 0.164663 | − | 0.986350i | \(-0.447347\pi\) |
−0.887191 | + | 0.461402i | \(0.847347\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16504.9 | + | 11991.5i | −0.622675 | + | 0.452400i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2725.71 | + | 1980.35i | 0.102486 | + | 0.0744603i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1465.24 | 0.0549075 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12497.9 | − | 18802.3i | 0.466770 | − | 0.702227i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2113.45 | − | 6504.54i | 0.0786690 | − | 0.242118i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5644.37 | −0.209399 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −74180.5 | −2.74285 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2984.60 | + | 9185.66i | −0.109990 | + | 0.338515i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 497.677 | + | 11933.8i | 0.0182799 | + | 0.438336i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33213.9 | 1.21593 | 0.607966 | − | 0.793963i | \(-0.291986\pi\) | ||||
0.607966 | + | 0.793963i | \(0.291986\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1763.21 | − | 1281.05i | −0.0643366 | − | 0.0467432i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13321.6 | + | 9678.70i | −0.484483 | + | 0.351997i | −0.803059 | − | 0.595900i | \(-0.796795\pi\) |
0.318576 | + | 0.947897i | \(0.396795\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −41432.2 | − | 30102.3i | −1.50187 | − | 1.09117i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −264.845 | − | 6350.72i | −0.00956884 | − | 0.229452i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1639.37 | − | 5045.47i | −0.0590369 | − | 0.181697i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12005.6 | − | 36949.3i | −0.430932 | − | 1.32627i | −0.897198 | − | 0.441628i | \(-0.854401\pi\) |
0.466266 | − | 0.884645i | \(-0.345599\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 577.473 | − | 1777.28i | 0.0206606 | − | 0.0635867i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1001.52 | − | 727.650i | 0.0357157 | − | 0.0259490i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19048.0 | + | 45366.5i | 0.677076 | + | 1.61259i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11703.5 | − | 8503.06i | 0.414663 | − | 0.301270i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10093.7 | − | 31065.3i | 0.356474 | − | 1.09711i | −0.598676 | − | 0.800991i | \(-0.704306\pi\) |
0.955150 | − | 0.296123i | \(-0.0956937\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −98.5705 | − | 303.369i | −0.00346994 | − | 0.0106794i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 635.319 | + | 1955.31i | 0.0222930 | + | 0.0686109i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −34026.9 | − | 42949.7i | −1.19016 | − | 1.50225i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13700.2 | − | 9953.76i | −0.477658 | − | 0.347039i | 0.322760 | − | 0.946481i | \(-0.395389\pi\) |
−0.800418 | + | 0.599442i | \(0.795389\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24487.5 | + | 17791.2i | −0.851032 | + | 0.618311i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8939.88 | − | 6495.20i | −0.309704 | − | 0.225013i | 0.422065 | − | 0.906565i | \(-0.361305\pi\) |
−0.731770 | + | 0.681552i | \(0.761305\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 83331.0 | 2.87766 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5050.23 | + | 1876.96i | −0.173845 | + | 0.0646112i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10750.0 | + | 33085.0i | −0.368878 | + | 1.13529i | 0.578639 | + | 0.815584i | \(0.303584\pi\) |
−0.947517 | + | 0.319706i | \(0.896416\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8465.22 | −0.289560 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5691.77 | 0.194078 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 94.7665 | − | 291.661i | 0.00322118 | − | 0.00991378i | −0.949433 | − | 0.313970i | \(-0.898341\pi\) |
0.952654 | + | 0.304056i | \(0.0983410\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −695.122 | − | 877.403i | −0.0235535 | − | 0.0297299i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5375.94 | 0.181588 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22072.5 | + | 16036.6i | 0.743229 | + | 0.539988i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10214.8 | − | 7421.49i | 0.342882 | − | 0.249118i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7023.93 | − | 5103.18i | −0.235039 | − | 0.170766i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 23096.3 | + | 6453.80i | 0.770462 | + | 0.215290i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9517.31 | − | 29291.3i | −0.316500 | − | 0.974088i | −0.975132 | − | 0.221623i | \(-0.928865\pi\) |
0.658632 | − | 0.752465i | \(-0.271135\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1425.02 | + | 4385.77i | 0.0472428 | + | 0.145398i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9174.90 | − | 28237.4i | 0.303230 | − | 0.933247i | −0.677102 | − | 0.735890i | \(-0.736764\pi\) |
0.980332 | − | 0.197357i | \(-0.0632358\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −33602.3 | + | 24413.5i | −1.10713 | + | 0.804380i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4557.70 | + | 380.803i | −0.149706 | + | 0.0125081i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11685.1 | + | 8489.69i | −0.382639 | + | 0.278003i | −0.762432 | − | 0.647068i | \(-0.775995\pi\) |
0.379794 | + | 0.925071i | \(0.375995\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12978.3 | + | 39943.1i | −0.423686 | + | 1.30397i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5560.04 | + | 17112.0i | 0.180957 | + | 0.556927i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 483.034 | + | 1486.63i | 0.0156728 | + | 0.0482360i | 0.958587 | − | 0.284800i | \(-0.0919271\pi\) |
−0.942914 | + | 0.333036i | \(0.891927\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8318.16 | − | 12514.2i | 0.269075 | − | 0.404806i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4865.27 | + | 3534.82i | 0.156903 | + | 0.113997i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −27278.2 | + | 19818.8i | −0.877044 | + | 0.637210i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37144.7 | + | 26987.2i | 1.19066 | + | 0.865063i | 0.993334 | − | 0.115275i | \(-0.0367750\pi\) |
0.197324 | + | 0.980338i | \(0.436775\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 30883.9 | 0.986981 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4985.17 | + | 1393.01i | 0.158835 | + | 0.0443832i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1872.45 | − | 5762.82i | 0.0594796 | − | 0.183059i | −0.916902 | − | 0.399112i | \(-0.869318\pi\) |
0.976382 | + | 0.216053i | \(0.0693183\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10627.9 | −0.336588 |
(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 | 300.4.m.a.61.1 | ✓ | 32 | |
25.16 | even | 5 | inner | 300.4.m.a.241.1 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.4.m.a.61.1 | ✓ | 32 | 1.1 | even | 1 | trivial | |
300.4.m.a.241.1 | yes | 32 | 25.16 | even | 5 | inner |