Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [64,4,Mod(17,64)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(64, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("64.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 64 = 2^{6} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 64.e (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.77612224037\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - x^{8} + 6x^{7} + 14x^{6} - 80x^{5} + 56x^{4} + 96x^{3} - 64x^{2} - 512x + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{20} \) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(0.932438 + 1.76934i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 64.49 |
Dual form | 64.4.e.a.17.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/64\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(63\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.98356 | + | 1.98356i | −0.381737 | + | 0.381737i | −0.871728 | − | 0.489991i | \(-0.837000\pi\) |
0.489991 | + | 0.871728i | \(0.337000\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.596848 | − | 0.596848i | −0.0533837 | − | 0.0533837i | 0.679911 | − | 0.733295i | \(-0.262018\pi\) |
−0.733295 | + | 0.679911i | \(0.762018\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 29.0828i | 1.57033i | 0.619289 | + | 0.785163i | \(0.287421\pi\) | ||||
−0.619289 | + | 0.785163i | \(0.712579\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 19.1310i | 0.708554i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −12.1291 | − | 12.1291i | −0.332461 | − | 0.332461i | 0.521059 | − | 0.853520i | \(-0.325537\pi\) |
−0.853520 | + | 0.521059i | \(0.825537\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −48.5658 | + | 48.5658i | −1.03613 | + | 1.03613i | −0.0368113 | + | 0.999322i | \(0.511720\pi\) |
−0.999322 | + | 0.0368113i | \(0.988280\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.36777 | 0.0407570 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 86.7193 | 1.23721 | 0.618604 | − | 0.785703i | \(-0.287699\pi\) | ||||
0.618604 | + | 0.785703i | \(0.287699\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 54.8442 | − | 54.8442i | 0.662217 | − | 0.662217i | −0.293685 | − | 0.955902i | \(-0.594882\pi\) |
0.955902 | + | 0.293685i | \(0.0948817\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −57.6876 | − | 57.6876i | −0.599451 | − | 0.599451i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 70.2145i | 0.636554i | 0.947998 | + | 0.318277i | \(0.103104\pi\) | ||||
−0.947998 | + | 0.318277i | \(0.896896\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 124.288i | − | 0.994300i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −91.5036 | − | 91.5036i | −0.652218 | − | 0.652218i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 63.4021 | − | 63.4021i | 0.405982 | − | 0.405982i | −0.474353 | − | 0.880335i | \(-0.657318\pi\) |
0.880335 | + | 0.474353i | \(0.157318\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.86868 | 0.0513826 | 0.0256913 | − | 0.999670i | \(-0.491821\pi\) | ||||
0.0256913 | + | 0.999670i | \(0.491821\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 48.1178 | 0.253825 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 17.3580 | − | 17.3580i | 0.0838298 | − | 0.0838298i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −21.7145 | − | 21.7145i | −0.0964820 | − | 0.0964820i | 0.657218 | − | 0.753700i | \(-0.271733\pi\) |
−0.753700 | + | 0.657218i | \(0.771733\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 192.667i | − | 0.791060i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 153.274i | 0.583840i | 0.956443 | + | 0.291920i | \(0.0942941\pi\) | ||||
−0.956443 | + | 0.291920i | \(0.905706\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 120.951 | + | 120.951i | 0.428949 | + | 0.428949i | 0.888270 | − | 0.459322i | \(-0.151907\pi\) |
−0.459322 | + | 0.888270i | \(0.651907\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 11.4183 | − | 11.4183i | 0.0378253 | − | 0.0378253i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 99.9792 | 0.310286 | 0.155143 | − | 0.987892i | \(-0.450416\pi\) | ||||
0.155143 | + | 0.987892i | \(0.450416\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −502.812 | −1.46592 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −172.013 | + | 172.013i | −0.472287 | + | 0.472287i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 389.132 | + | 389.132i | 1.00852 | + | 1.00852i | 0.999963 | + | 0.00855213i | \(0.00272226\pi\) |
0.00855213 | + | 0.999963i | \(0.497278\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.4785i | 0.0354960i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 217.574i | 0.505585i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 324.819 | + | 324.819i | 0.716744 | + | 0.716744i | 0.967937 | − | 0.251193i | \(-0.0808229\pi\) |
−0.251193 | + | 0.967937i | \(0.580823\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.339194 | + | 0.339194i | −0.000711957 | + | 0.000711957i | −0.707463 | − | 0.706751i | \(-0.750160\pi\) |
0.706751 | + | 0.707463i | \(0.250160\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −556.383 | −1.11266 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 57.9728 | 0.110625 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −565.288 | + | 565.288i | −1.03076 | + | 1.03076i | −0.0312478 | + | 0.999512i | \(0.509948\pi\) |
−0.999512 | + | 0.0312478i | \(0.990052\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −139.275 | − | 139.275i | −0.242996 | − | 0.242996i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 419.500i | − | 0.701205i | −0.936524 | − | 0.350602i | \(-0.885977\pi\) | ||
0.936524 | − | 0.350602i | \(-0.114023\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 374.833i | − | 0.600971i | −0.953786 | − | 0.300485i | \(-0.902851\pi\) | ||
0.953786 | − | 0.300485i | \(-0.0971487\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 246.532 | + | 246.532i | 0.379561 | + | 0.379561i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 352.750 | − | 352.750i | 0.522072 | − | 0.522072i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 705.750 | 1.00510 | 0.502551 | − | 0.864547i | \(-0.332395\pi\) | ||||
0.502551 | + | 0.864547i | \(0.332395\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −153.530 | −0.210604 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 947.092 | − | 947.092i | 1.25249 | − | 1.25249i | 0.297893 | − | 0.954599i | \(-0.403716\pi\) |
0.954599 | − | 0.297893i | \(-0.0962839\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −51.7582 | − | 51.7582i | −0.0660467 | − | 0.0660467i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 251.524i | 0.309956i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.72918i | 0.00563249i | 0.999996 | + | 0.00281625i | \(0.000896440\pi\) | ||||
−0.999996 | + | 0.00281625i | \(0.999104\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1412.43 | − | 1412.43i | −1.62707 | − | 1.62707i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −17.5916 | + | 17.5916i | −0.0196146 | + | 0.0196146i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −65.4673 | −0.0707032 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 379.542 | 0.397285 | 0.198643 | − | 0.980072i | \(-0.436347\pi\) | ||||
0.198643 | + | 0.980072i | \(0.436347\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 232.042 | − | 232.042i | 0.235567 | − | 0.235567i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −391.005 | − | 391.005i | −0.385212 | − | 0.385212i | 0.487764 | − | 0.872976i | \(-0.337813\pi\) |
−0.872976 | + | 0.487764i | \(0.837813\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 307.935i | − | 0.294580i | −0.989093 | − | 0.147290i | \(-0.952945\pi\) | ||
0.989093 | − | 0.147290i | \(-0.0470551\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 68.8615i | 0.0640018i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 601.607 | + | 601.607i | 0.543548 | + | 0.543548i | 0.924567 | − | 0.381019i | \(-0.124427\pi\) |
−0.381019 | + | 0.924567i | \(0.624427\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −948.890 | + | 948.890i | −0.833827 | + | 0.833827i | −0.988038 | − | 0.154211i | \(-0.950717\pi\) |
0.154211 | + | 0.988038i | \(0.450717\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 86.1439 | 0.0736614 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1824.02 | 1.51849 | 0.759244 | − | 0.650807i | \(-0.225569\pi\) | ||||
0.759244 | + | 0.650807i | \(0.225569\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 41.9074 | − | 41.9074i | 0.0339816 | − | 0.0339816i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −929.111 | − | 929.111i | −0.734157 | − | 0.734157i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2522.04i | 1.94282i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 1036.77i | − | 0.778939i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −304.029 | − | 304.029i | −0.222873 | − | 0.222873i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −148.787 | + | 148.787i | −0.106463 | + | 0.106463i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −988.748 | −0.690844 | −0.345422 | − | 0.938447i | \(-0.612264\pi\) | ||||
−0.345422 | + | 0.938447i | \(0.612264\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −479.826 | −0.327491 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −793.572 | + | 793.572i | −0.529273 | + | 0.529273i | −0.920356 | − | 0.391083i | \(-0.872101\pi\) |
0.391083 | + | 0.920356i | \(0.372101\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1595.03 | + | 1595.03i | 1.03990 | + | 1.03990i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 109.227i | 0.0696356i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1595.30i | 0.994856i | 0.867505 | + | 0.497428i | \(0.165722\pi\) | ||||
−0.867505 | + | 0.497428i | \(0.834278\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 277.696 | + | 277.696i | 0.169452 | + | 0.169452i | 0.786738 | − | 0.617286i | \(-0.211768\pi\) |
−0.617286 | + | 0.786738i | \(0.711768\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −198.315 | + | 198.315i | −0.118448 | + | 0.118448i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1178.12 | 0.688948 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −75.6828 | −0.0433456 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 997.359 | − | 997.359i | 0.559597 | − | 0.559597i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −593.272 | − | 593.272i | −0.326193 | − | 0.326193i | 0.524944 | − | 0.851137i | \(-0.324086\pi\) |
−0.851137 | + | 0.524944i | \(0.824086\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 160.655i | − | 0.0865821i | −0.999063 | − | 0.0432911i | \(-0.986216\pi\) | ||
0.999063 | − | 0.0432911i | \(-0.0137843\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1659.02i | 0.876629i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.29325 | − | 5.29325i | −0.00274299 | − | 0.00274299i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −705.762 | + | 705.762i | −0.358764 | + | 0.358764i | −0.863357 | − | 0.504593i | \(-0.831642\pi\) |
0.504593 | + | 0.863357i | \(0.331642\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1543.73 | −0.769975 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2042.04 | −0.999598 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1872.64 | + | 1872.64i | −0.899855 | + | 0.899855i | −0.995423 | − | 0.0955676i | \(-0.969533\pi\) |
0.0955676 | + | 0.995423i | \(0.469533\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −28.7190 | − | 28.7190i | −0.0135501 | − | 0.0135501i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 3852.19i | − | 1.78498i | −0.451066 | − | 0.892490i | \(-0.648956\pi\) | ||
0.451066 | − | 0.892490i | \(-0.351044\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 2520.28i | − | 1.14715i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1049.22 | + | 1049.22i | 0.469217 | + | 0.469217i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2625.61 | − | 2625.61i | 1.15388 | − | 1.15388i | 0.168112 | − | 0.985768i | \(-0.446233\pi\) |
0.985768 | − | 0.168112i | \(-0.0537671\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3614.64 | 1.56138 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1288.60 | −0.547215 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1236.73 | − | 1236.73i | 0.516413 | − | 0.516413i | −0.400071 | − | 0.916484i | \(-0.631015\pi\) |
0.916484 | + | 0.400071i | \(0.131015\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1574.90 | + | 1574.90i | 0.646748 | + | 0.646748i | 0.952206 | − | 0.305458i | \(-0.0988094\pi\) |
−0.305458 | + | 0.952206i | \(0.598809\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 1.34563i | − | 0.000543560i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 25.9204i | 0.0103011i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1051.83 | − | 1051.83i | −0.411323 | − | 0.411323i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2661.19 | − | 2661.19i | 1.02419 | − | 1.02419i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3585.92 | −1.35847 | −0.679236 | − | 0.733920i | \(-0.737689\pi\) | ||||
−0.679236 | + | 0.733920i | \(0.737689\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 523.601 | 0.195283 | 0.0976415 | − | 0.995222i | \(-0.468870\pi\) | ||||
0.0976415 | + | 0.995222i | \(0.468870\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −114.993 | + | 114.993i | −0.0422297 | + | 0.0422297i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1125.64 | − | 1125.64i | −0.407098 | − | 0.407098i | 0.473627 | − | 0.880725i | \(-0.342944\pi\) |
−0.880725 | + | 0.473627i | \(0.842944\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 2312.48i | − | 0.823757i | −0.911239 | − | 0.411878i | \(-0.864873\pi\) | ||
0.911239 | − | 0.411878i | \(-0.135127\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 2242.57i | − | 0.786957i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1843.91 | + | 1843.91i | 0.637524 | + | 0.637524i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 91.4815 | − | 91.4815i | 0.0311675 | − | 0.0311675i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1343.27 | −0.451033 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1330.43 | −0.440323 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1418.59 | + | 1418.59i | −0.462842 | + | 0.462842i | −0.899586 | − | 0.436744i | \(-0.856132\pi\) |
0.436744 | + | 0.899586i | \(0.356132\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 832.105 | + | 832.105i | 0.267675 | + | 0.267675i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 144.378i | − | 0.0457977i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 257.926i | 0.0806875i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 743.504 | + | 743.504i | 0.229413 | + | 0.229413i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4211.60 | + | 4211.60i | −1.28191 | + | 1.28191i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4315.08 | 1.29578 | 0.647890 | − | 0.761734i | \(-0.275651\pi\) | ||||
0.647890 | + | 0.761734i | \(0.275651\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2377.74 | 0.704516 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −701.203 | + | 701.203i | −0.205024 | + | 0.205024i | −0.802149 | − | 0.597124i | \(-0.796310\pi\) |
0.597124 | + | 0.802149i | \(0.296310\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −663.351 | − | 663.351i | −0.191421 | − | 0.191421i | 0.604889 | − | 0.796310i | \(-0.293218\pi\) |
−0.796310 | + | 0.604889i | \(0.793218\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1399.40i | 0.398588i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3490.15i | 0.981318i | 0.871352 | + | 0.490659i | \(0.163244\pi\) | ||||
−0.871352 | + | 0.490659i | \(0.836756\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −59.6724 | − | 59.6724i | −0.0165642 | − | 0.0165642i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1399.90 | + | 1399.90i | −0.383684 | + | 0.383684i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2950.43 | −0.798525 | −0.399263 | − | 0.916837i | \(-0.630734\pi\) | ||||
−0.399263 | + | 0.916837i | \(0.630734\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1128.96 | −0.301755 | −0.150877 | − | 0.988552i | \(-0.548210\pi\) | ||||
−0.150877 | + | 0.988552i | \(0.548210\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2775.13 | − | 2775.13i | 0.732613 | − | 0.732613i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 300.102 | + | 300.102i | 0.0782565 | + | 0.0782565i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5327.11i | 1.37229i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3757.23i | 0.956244i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4621.86 | − | 4621.86i | −1.16227 | − | 1.16227i | −0.983978 | − | 0.178291i | \(-0.942943\pi\) |
−0.178291 | − | 0.983978i | \(-0.557057\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 851.642 | − | 851.642i | 0.211630 | − | 0.211630i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 205.331 | 0.0504249 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 610.977 | 0.148295 | 0.0741473 | − | 0.997247i | \(-0.476377\pi\) | ||||
0.0741473 | + | 0.997247i | \(0.476377\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 631.518 | − | 631.518i | 0.151508 | − | 0.151508i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1212.94 | + | 1212.94i | 0.287660 | + | 0.287660i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4973.57i | 1.16610i | 0.812438 | + | 0.583048i | \(0.198140\pi\) | ||||
−0.812438 | + | 0.583048i | \(0.801860\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 464.505i | − | 0.107677i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.38061 | − | 9.38061i | −0.00215013 | − | 0.00215013i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −938.415 | + | 938.415i | −0.212700 | + | 0.212700i | −0.805413 | − | 0.592714i | \(-0.798057\pi\) |
0.592714 | + | 0.805413i | \(0.298057\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4010.64 | 0.898999 | 0.449500 | − | 0.893280i | \(-0.351602\pi\) | ||||
0.449500 | + | 0.893280i | \(0.351602\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5603.29 | 1.24222 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1507.50 | + | 1507.50i | −0.330566 | + | 0.330566i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3534.99 | − | 3534.99i | −0.766776 | − | 0.766776i | 0.210762 | − | 0.977538i | \(-0.432406\pi\) |
−0.977538 | + | 0.210762i | \(0.932406\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 169.666i | 0.0364074i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 7468.35i | − | 1.58550i | −0.609550 | − | 0.792748i | \(-0.708650\pi\) | ||
0.609550 | − | 0.792748i | \(-0.291350\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2249.22 | + | 2249.22i | 0.472447 | + | 0.472447i | 0.902705 | − | 0.430259i | \(-0.141578\pi\) |
−0.430259 | + | 0.902705i | \(0.641578\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 129.858 | − | 129.858i | 0.0269900 | − | 0.0269900i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4457.66 | −0.916819 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2607.24 | 0.530682 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −752.845 | + | 752.845i | −0.151658 | + | 0.151658i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3952.79 | − | 3952.79i | −0.788139 | − | 0.788139i | 0.193050 | − | 0.981189i | \(-0.438162\pi\) |
−0.981189 | + | 0.193050i | \(0.938162\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 387.736i | − | 0.0765249i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2219.72i | 0.433674i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3410.03 | − | 3410.03i | −0.659555 | − | 0.659555i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3517.59 | + | 3517.59i | −0.673589 | + | 0.673589i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1551.16 | 0.294099 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.404895 | 7.60138e−5 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3855.24 | − | 3855.24i | 0.716711 | − | 0.716711i | −0.251219 | − | 0.967930i | \(-0.580832\pi\) |
0.967930 | + | 0.251219i | \(0.0808316\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 610.809 | + | 610.809i | 0.112452 | + | 0.112452i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 5194.39i | − | 0.947096i | −0.880768 | − | 0.473548i | \(-0.842973\pi\) | ||
0.880768 | − | 0.473548i | \(-0.157027\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 4710.01i | − | 0.850561i | −0.905062 | − | 0.425281i | \(-0.860175\pi\) | ||
0.905062 | − | 0.425281i | \(-0.139825\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 332.076 | + | 332.076i | 0.0593980 | + | 0.0593980i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5680.21 | − | 5680.21i | 1.00641 | − | 1.00641i | 0.00643263 | − | 0.999979i | \(-0.497952\pi\) |
0.999979 | − | 0.00643263i | \(-0.00204758\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1538.03 | −0.269946 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2386.65 | −0.414984 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4756.05 | − | 4756.05i | 0.819300 | − | 0.819300i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6036.13 | + | 6036.13i | 1.03023 | + | 1.03023i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 3764.36i | − | 0.636605i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2907.68i | 0.487251i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1815.80 | − | 1815.80i | −0.301526 | − | 0.301526i | 0.540084 | − | 0.841611i | \(-0.318392\pi\) |
−0.841611 | + | 0.540084i | \(0.818392\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 415.418 | − | 415.418i | 0.0683627 | − | 0.0683627i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 674.782 | 0.110052 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2683.29 | −0.433733 | −0.216867 | − | 0.976201i | \(-0.569584\pi\) | ||||
−0.216867 | + | 0.976201i | \(0.569584\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3618.05 | + | 3618.05i | −0.579662 | + | 0.579662i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −107.569 | − | 107.569i | −0.0170827 | − | 0.0170827i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 4647.79i | − | 0.731653i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 166.252i | 0.0259440i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5291.81 | + | 5291.81i | 0.818671 | + | 0.818671i | 0.985916 | − | 0.167244i | \(-0.0534868\pi\) |
−0.167244 | + | 0.985916i | \(0.553487\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 73.7084 | − | 73.7084i | 0.0113052 | − | 0.0113052i | −0.701432 | − | 0.712737i | \(-0.747455\pi\) |
0.712737 | + | 0.701432i | \(0.247455\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8887.90 | 1.35157 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5067.25 | −0.764030 | −0.382015 | − | 0.924156i | \(-0.624770\pi\) | ||||
−0.382015 | + | 0.924156i | \(0.624770\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −250.378 | + | 250.378i | −0.0374329 | + | 0.0374329i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5002.63 | − | 5002.63i | −0.741645 | − | 0.741645i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 970.230i | 0.142637i | 0.997454 | + | 0.0713186i | \(0.0227207\pi\) | ||||
−0.997454 | + | 0.0713186i | \(0.977279\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 843.224i | 0.122937i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2056.49 | + | 2056.49i | 0.297350 | + | 0.297350i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −223.718 | + | 223.718i | −0.0320821 | + | 0.0320821i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13451.4 | −1.91323 | −0.956617 | − | 0.291347i | \(-0.905896\pi\) | ||||
−0.956617 | + | 0.291347i | \(0.905896\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2932.29 | −0.413682 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11317.1 | + | 11317.1i | −1.58370 | + | 1.58370i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5898.22 | + | 5898.22i | 0.818762 | + | 0.818762i | 0.985929 | − | 0.167167i | \(-0.0534619\pi\) |
−0.167167 | + | 0.985929i | \(0.553462\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 590.255i | − | 0.0812817i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6158.35i | 0.841302i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4446.72 | + | 4446.72i | 0.602673 | + | 0.602673i | 0.941021 | − | 0.338348i | \(-0.109868\pi\) |
−0.338348 | + | 0.941021i | \(0.609868\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1961.24 | − | 1961.24i | 0.263721 | − | 0.263721i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6417.68 | 0.856209 | 0.428105 | − | 0.903729i | \(-0.359181\pi\) | ||||
0.428105 | + | 0.903729i | \(0.359181\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −421.076 | −0.0557403 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2313.90 | + | 2313.90i | −0.303933 | + | 0.303933i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6555.61 | + | 6555.61i | 0.854455 | + | 0.854455i | 0.990678 | − | 0.136223i | \(-0.0434965\pi\) |
−0.136223 | + | 0.990678i | \(0.543497\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6088.96i | 0.787549i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 3148.20i | − | 0.404086i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −421.226 | − | 421.226i | −0.0536561 | − | 0.0536561i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8902.51 | − | 8902.51i | 1.12545 | − | 1.12545i | 0.134543 | − | 0.990908i | \(-0.457043\pi\) |
0.990908 | − | 0.134543i | \(-0.0429566\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6327.66 | −0.793933 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6425.77 | −0.800218 | −0.400109 | − | 0.916468i | \(-0.631028\pi\) | ||||
−0.400109 | + | 0.916468i | \(0.631028\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −430.715 | + | 430.715i | −0.0532393 | + | 0.0532393i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 91.6341 | + | 91.6341i | 0.0112428 | + | 0.0112428i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 526.755i | 0.0641530i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12796.0i | 1.54699i | 0.633801 | + | 0.773496i | \(0.281494\pi\) | ||||
−0.633801 | + | 0.773496i | \(0.718506\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3164.37 | − | 3164.37i | −0.379773 | − | 0.379773i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9446.67 | + | 9446.67i | −1.12552 | + | 1.12552i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1130.54 | −0.133725 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1101.65 | −0.129372 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6545.21 | − | 6545.21i | 0.763137 | − | 0.763137i | −0.213751 | − | 0.976888i | \(-0.568568\pi\) |
0.976888 | + | 0.213751i | \(0.0685681\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6390.00 | − | 6390.00i | −0.739738 | − | 0.739738i | 0.232789 | − | 0.972527i | \(-0.425215\pi\) |
−0.972527 | + | 0.232789i | \(0.925215\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1912.70i | 0.219855i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 10778.1i | − | 1.23016i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.86474 | − | 9.86474i | −0.00111801 | − | 0.00111801i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2336.88 | + | 2336.88i | −0.262997 | + | 0.262997i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10639.3 | 1.18904 | 0.594519 | − | 0.804081i | \(-0.297342\pi\) | ||||
0.594519 | + | 0.804081i | \(0.297342\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3806.14 | 0.422428 | 0.211214 | − | 0.977440i | \(-0.432258\pi\) | ||||
0.211214 | + | 0.977440i | \(0.432258\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 150.121 | − | 150.121i | 0.0165466 | − | 0.0165466i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3850.86 | + | 3850.86i | 0.421537 | + | 0.421537i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 14102.8i | − | 1.53323i | −0.642106 | − | 0.766616i | \(-0.721939\pi\) | ||
0.642106 | − | 0.766616i | \(-0.278061\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 9619.28i | − | 1.03869i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7662.45 | + | 7662.45i | 0.821792 | + | 0.821792i | 0.986365 | − | 0.164573i | \(-0.0526246\pi\) |
−0.164573 | + | 0.986365i | \(0.552625\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.82260 | − | 2.82260i | 0.000300683 | − | 0.000300683i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2353.58 | 0.249040 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13679.4 | 1.43779 | 0.718897 | − | 0.695117i | \(-0.244647\pi\) | ||||
0.718897 | + | 0.695117i | \(0.244647\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1859.09 | − | 1859.09i | 0.194104 | − | 0.194104i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 318.669 | + | 318.669i | 0.0330516 | + | 0.0330516i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1686.01i | 0.173718i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7913.48i | 0.810016i | 0.914313 | + | 0.405008i | \(0.132731\pi\) | ||||
−0.914313 | + | 0.405008i | \(0.867269\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7935.13 | − | 7935.13i | −0.806929 | − | 0.806929i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −580.215 | + | 580.215i | −0.0586189 | + | 0.0586189i | −0.735809 | − | 0.677190i | \(-0.763198\pi\) |
0.677190 | + | 0.735809i | \(0.263198\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14236.5 | −1.42899 | −0.714497 | − | 0.699638i | \(-0.753344\pi\) | ||||
−0.714497 | + | 0.699638i | \(0.753344\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 20.9990 | 0.00209420 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8344.57 | − | 8344.57i | 0.826853 | − | 0.826853i | −0.160227 | − | 0.987080i | \(-0.551223\pi\) |
0.987080 | + | 0.160227i | \(0.0512225\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16440.2 | − | 16440.2i | −1.61863 | − | 1.61863i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 2799.85i | − | 0.273907i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 2934.05i | − | 0.285217i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6816.45 | − | 6816.45i | −0.658443 | − | 0.658443i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7444.46 | + | 7444.46i | −0.714588 | + | 0.714588i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5563.77 | 0.530720 | 0.265360 | − | 0.964149i | \(-0.414509\pi\) | ||||
0.265360 | + | 0.964149i | \(0.414509\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2109.16 | 0.199936 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4050.51 | − | 4050.51i | 0.381583 | − | 0.381583i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −226.529 | − | 226.529i | −0.0212085 | − | 0.0212085i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18150.5i | 1.68886i | 0.535662 | + | 0.844432i | \(0.320062\pi\) | ||||
−0.535662 | + | 0.844432i | \(0.679938\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 7428.99i | − | 0.687015i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11593.0 | − | 11593.0i | −1.06555 | − | 1.06555i | −0.997695 | − | 0.0678570i | \(-0.978384\pi\) |
−0.0678570 | − | 0.997695i | \(-0.521616\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5498.18 | − | 5498.18i | 0.502284 | − | 0.502284i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −276.988 | −0.0251509 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12200.3 | 1.10112 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3109.58 | + | 3109.58i | −0.278966 | + | 0.278966i | −0.832696 | − | 0.553730i | \(-0.813204\pi\) |
0.553730 | + | 0.832696i | \(0.313204\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7641.07 | + | 7641.07i | 0.681393 | + | 0.681393i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6221.21i | 0.551471i | 0.961233 | + | 0.275736i | \(0.0889215\pi\) | ||||
−0.961233 | + | 0.275736i | \(0.911079\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 466.740i | 0.0411281i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4999.13 | + | 4999.13i | 0.437907 | + | 0.437907i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13800.4 | − | 13800.4i | 1.20176 | − | 1.20176i | 0.228124 | − | 0.973632i | \(-0.426741\pi\) |
0.973632 | − | 0.228124i | \(-0.0732591\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10901.2 | 0.943720 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10036.9 | −0.863820 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −183.791 | + | 183.791i | −0.0157258 | + | 0.0157258i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1212.66 | − | 1212.66i | −0.103158 | − | 0.103158i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10416.1i | 0.880957i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 6874.63i | − | 0.578086i | −0.957316 | − | 0.289043i | \(-0.906663\pi\) | ||
0.957316 | − | 0.289043i | \(-0.0933371\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2306.52 | − | 2306.52i | −0.192843 | − | 0.192843i | 0.604080 | − | 0.796924i | \(-0.293541\pi\) |
−0.796924 | + | 0.604080i | \(0.793541\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7169.85 | + | 7169.85i | −0.596034 | + | 0.596034i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 769.086 | 0.0635710 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7236.92 | 0.594799 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6214.11 | + | 6214.11i | −0.507852 | + | 0.507852i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7443.90 | − | 7443.90i | −0.604936 | − | 0.604936i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 718.136i | − | 0.0580332i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4906.28i | 0.394267i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6098.68 | + | 6098.68i | 0.487363 | + | 0.487363i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13240.0 | + | 13240.0i | −1.05218 | + | 1.05218i | −0.0536210 | + | 0.998561i | \(0.517076\pi\) |
−0.998561 | + | 0.0536210i | \(0.982924\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6247.82 | −0.493775 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1132.69 | 0.0890256 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13271.3 | − | 13271.3i | 1.03737 | − | 1.03737i | 0.0380940 | − | 0.999274i | \(-0.487871\pi\) |
0.999274 | − | 0.0380940i | \(-0.0121286\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.48912 | − | 6.48912i | −0.000504460 | − | 0.000504460i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 6954.47i | − | 0.537696i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20525.2i | 1.57834i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −51.4148 | − | 51.4148i | −0.00393232 | − | 0.00393232i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8500.61 | + | 8500.61i | −0.646647 | + | 0.646647i | −0.952181 | − | 0.305534i | \(-0.901165\pi\) |
0.305534 | + | 0.952181i | \(0.401165\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11748.1 | −0.888896 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4172.74 | 0.314034 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17327.2 | + | 17327.2i | −1.29708 | + | 1.29708i | −0.366763 | + | 0.930314i | \(0.619534\pi\) |
−0.930314 | + | 0.366763i | \(0.880466\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1088.66 | − | 1088.66i | −0.0810625 | − | 0.0810625i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 4465.09i | − | 0.330716i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8998.54i | 0.662985i | 0.943458 | + | 0.331492i | \(0.107552\pi\) | ||||
−0.943458 | + | 0.331492i | \(0.892448\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9849.25 | + | 9849.25i | 0.721853 | + | 0.721853i | 0.968983 | − | 0.247129i | \(-0.0794872\pi\) |
−0.247129 | + | 0.968983i | \(0.579487\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7112.89 | − | 7112.89i | 0.518578 | − | 0.518578i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8726.79 | 0.632926 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20584.4 | −1.48516 | −0.742580 | − | 0.669757i | \(-0.766398\pi\) | ||||
−0.742580 | + | 0.669757i | \(0.766398\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1038.59 | + | 1038.59i | −0.0745467 | + | 0.0745467i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 27544.1 | + | 27544.1i | 1.96682 | + | 1.96682i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 9439.66i | − | 0.670585i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1109.08i | 0.0783840i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2586.77 | + | 2586.77i | 0.181887 | + | 0.181887i | 0.792177 | − | 0.610291i | \(-0.208947\pi\) |
−0.610291 | + | 0.792177i | \(0.708947\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 486.396 | − | 486.396i | 0.0340265 | − | 0.0340265i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4465.54 | 0.310809 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6035.89 | −0.417984 | −0.208992 | − | 0.977917i | \(-0.567018\pi\) | ||||
−0.208992 | + | 0.977917i | \(0.567018\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1505.28 | − | 1505.28i | 0.103715 | − | 0.103715i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4586.95 | + | 4586.95i | 0.314458 | + | 0.314458i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5427.20i | 0.370199i | 0.982720 | + | 0.185100i | \(0.0592608\pi\) | ||||
−0.982720 | + | 0.185100i | \(0.940739\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 17725.7i | − | 1.20307i | −0.798847 | − | 0.601535i | \(-0.794556\pi\) | ||
0.798847 | − | 0.601535i | \(-0.205444\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10814.5 | − | 10814.5i | −0.730349 | − | 0.730349i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −618.793 | + | 618.793i | −0.0415827 | + | 0.0415827i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13487.6 | −0.901884 | −0.450942 | − | 0.892553i | \(-0.648912\pi\) | ||||
−0.450942 | + | 0.892553i | \(0.648912\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7315.03 | −0.486732 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4855.57 | + | 4855.57i | −0.321498 | + | 0.321498i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16850.4 | − | 16850.4i | −1.11025 | − | 1.11025i | −0.993117 | − | 0.117129i | \(-0.962631\pi\) |
−0.117129 | − | 0.993117i | \(-0.537369\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 362.918i | 0.0237956i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 535.243i | 0.0349239i | 0.999848 | + | 0.0174620i | \(0.00555860\pi\) | ||||
−0.999848 | + | 0.0174620i | \(0.994441\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19691.0 | + | 19691.0i | 1.27859 | + | 1.27859i | 0.941458 | + | 0.337130i | \(0.109456\pi\) |
0.337130 | + | 0.941458i | \(0.390544\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6424.88 | − | 6424.88i | 0.415172 | − | 0.415172i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −137.538 | −0.00884485 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15358.3 | −0.982934 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2638.98 | − | 2638.98i | 0.168087 | − | 0.168087i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1883.06 | − | 1883.06i | −0.119368 | − | 0.119368i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 11880.2i | − | 0.749511i | −0.927124 | − | 0.374755i | \(-0.877727\pi\) | ||
0.927124 | − | 0.374755i | \(-0.122273\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 5627.72i | − | 0.353368i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 590.132 | + | 590.132i | 0.0368798 | + | 0.0368798i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24419.5 | − | 24419.5i | 1.51889 | − | 1.51889i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8025.45 | 0.496842 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18341.0 | 1.13015 | 0.565074 | − | 0.825040i | \(-0.308848\pi\) | ||||
0.565074 | + | 0.825040i | \(0.308848\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7026.21 | + | 7026.21i | −0.430928 | + | 0.430928i | −0.888944 | − | 0.458016i | \(-0.848560\pi\) |
0.458016 | + | 0.888944i | \(0.348560\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 286.383 | + | 286.383i | 0.0174827 | + | 0.0174827i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 21429.7i | − | 1.30215i | −0.759015 | − | 0.651073i | \(-0.774319\pi\) | ||
0.759015 | − | 0.651073i | \(-0.225681\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 7879.56i | − | 0.476579i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −511.613 | − | 511.613i | −0.0308014 | − | 0.0308014i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8681.22 | − | 8681.22i | 0.520248 | − | 0.520248i | −0.397398 | − | 0.917646i | \(-0.630087\pi\) |
0.917646 | + | 0.397398i | \(0.130087\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 947.284 | 0.0565091 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7170.92 | 0.425821 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4151.60 | − | 4151.60i | 0.245407 | − | 0.245407i | −0.573675 | − | 0.819083i | \(-0.694483\pi\) |
0.819083 | + | 0.573675i | \(0.194483\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12239.0 | + | 12239.0i | 0.720182 | + | 0.720182i | 0.968642 | − | 0.248460i | \(-0.0799244\pi\) |
−0.248460 | + | 0.968642i | \(0.579924\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 16707.9i | − | 0.978706i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 1903.98i | − | 0.111027i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4451.75 | + | 4451.75i | 0.258429 | + | 0.258429i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8559.23 | + | 8559.23i | −0.494647 | + | 0.494647i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.22827 | 0.000473396 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6528.62 | 0.373937 | 0.186969 | − | 0.982366i | \(-0.440134\pi\) | ||||
0.186969 | + | 0.982366i | \(0.440134\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −11372.8 | + | 11372.8i | −0.648500 | + | 0.648500i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14220.6 | − | 14220.6i | −0.807299 | − | 0.807299i | 0.176925 | − | 0.984224i | \(-0.443385\pi\) |
−0.984224 | + | 0.176925i | \(0.943385\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11038.2i | 0.623867i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 2781.76i | − | 0.156530i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21419.5 | − | 21419.5i | −1.19999 | − | 1.19999i | −0.974167 | − | 0.225827i | \(-0.927492\pi\) |
−0.225827 | − | 0.974167i | \(-0.572508\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 952.149 | − | 952.149i | 0.0531091 | − | 0.0531091i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2631.60 | 0.146145 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −37797.0 | −2.08991 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16537.1 | − | 16537.1i | 0.910423 | − | 0.910423i | −0.0858818 | − | 0.996305i | \(-0.527371\pi\) |
0.996305 | + | 0.0858818i | \(0.0273708\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6748.45 | + | 6748.45i | 0.369917 | + | 0.369917i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 331.484i | − | 0.0180920i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13291.8i | 0.722331i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6922.92 | − | 6922.92i | −0.374605 | − | 0.374605i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3026.52 | + | 3026.52i | −0.163067 | + | 0.163067i | −0.783924 | − | 0.620857i | \(-0.786785\pi\) |
0.620857 | + | 0.783924i | \(0.286785\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2381.82 | −0.127784 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 236.728 | 0.0126464 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11371.5 | − | 11371.5i | 0.604908 | − | 0.604908i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3981.14 | + | 3981.14i | 0.210881 | + | 0.210881i | 0.804642 | − | 0.593761i | \(-0.202357\pi\) |
−0.593761 | + | 0.804642i | \(0.702357\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13501.7i | 0.712170i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 622.710i | 0.0327078i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −703.160 | − | 703.160i | −0.0367786 | − | 0.0367786i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5852.36 | − | 5852.36i | 0.304826 | − | 0.304826i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5682.25 | 0.294732 | 0.147366 | − | 0.989082i | \(-0.452921\pi\) | ||||
0.147366 | + | 0.989082i | \(0.452921\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8955.64 | 0.462587 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2239.37 | − | 2239.37i | 0.115191 | − | 0.115191i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7880.09 | − | 7880.09i | −0.403668 | − | 0.403668i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18883.0i | 0.963317i | 0.876359 | + | 0.481658i | \(0.159965\pi\) | ||||
−0.876359 | + | 0.481658i | \(0.840035\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6863.99i | 0.348727i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10488.8 | + | 10488.8i | 0.530698 | + | 0.530698i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24962.5 | + | 24962.5i | −1.25786 | + | 1.25786i | −0.305748 | + | 0.952113i | \(0.598906\pi\) |
−0.952113 | + | 0.305748i | \(0.901094\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1190.54 | −0.0597467 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13712.9 | 0.685375 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6202.38 | + | 6202.38i | −0.308739 | + | 0.308739i | −0.844420 | − | 0.535681i | \(-0.820055\pi\) |
0.535681 | + | 0.844420i | \(0.320055\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10566.6 | − | 10566.6i | −0.523854 | − | 0.523854i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 30.9140i | − | 0.00152641i | −1.00000 | 0.000763205i | \(-0.999757\pi\) | |||
1.00000 | 0.000763205i | \(-0.000242936\pi\) | ||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 708.187i | 0.0348268i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 18118.8 | + | 18118.8i | 0.887459 | + | 0.887459i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17496.5 | + | 17496.5i | −0.853547 | + | 0.853547i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16318.5 | 0.792905 | 0.396453 | − | 0.918055i | \(-0.370241\pi\) | ||||
0.396453 | + | 0.918055i | \(0.370241\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18335.5 | 0.887361 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −95.8865 | + | 95.8865i | −0.00462208 | + | 0.00462208i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9854.59 | + | 9854.59i | 0.473146 | + | 0.473146i | 0.902931 | − | 0.429786i | \(-0.141411\pi\) |
−0.429786 | + | 0.902931i | \(0.641411\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3378.57i | 0.161573i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 3823.42i | − | 0.182127i | −0.995845 | − | 0.0910637i | \(-0.970973\pi\) | ||
0.995845 | − | 0.0910637i | \(-0.0290267\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −27596.4 | − | 27596.4i | −1.30938 | − | 1.30938i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 990.185 | − | 990.185i | 0.0467977 | − | 0.0467977i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −31550.2 | −1.48528 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31689.1 | 1.48601 | 0.743003 | − | 0.669288i | \(-0.233401\pi\) | ||||
0.743003 | + | 0.669288i | \(0.233401\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1211.91 | + | 1211.91i | −0.0566094 | + | 0.0566094i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1305.84 | − | 1305.84i | −0.0607604 | − | 0.0607604i | 0.676074 | − | 0.736834i | \(-0.263680\pi\) |
−0.736834 | + | 0.676074i | \(0.763680\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1102.27i | − | 0.0510898i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2505.31i | 0.115672i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8406.21 | + | 8406.21i | 0.386629 | + | 0.386629i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5088.18 | + | 5088.18i | −0.233123 | + | 0.233123i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −11603.0 | −0.529577 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 842.465 | 0.0383043 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14399.5 | + | 14399.5i | −0.652209 | + | 0.652209i | −0.953524 | − | 0.301316i | \(-0.902574\pi\) |
0.301316 | + | 0.953524i | \(0.402574\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9865.37 | − | 9865.37i | −0.445141 | − | 0.445141i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 53047.6i | 2.38452i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 32.9465i | − | 0.00147537i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 921.374 | + | 921.374i | 0.0411041 | + | 0.0411041i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5572.19 | + | 5572.19i | −0.247650 | + | 0.247650i | −0.820006 | − | 0.572356i | \(-0.806030\pi\) |
0.572356 | + | 0.820006i | \(0.306030\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8670.13 | 0.383889 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −90.4737 | −0.00399093 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4546.40 | + | 4546.40i | −0.199800 | + | 0.199800i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1218.79 | + | 1218.79i | 0.0533622 | + | 0.0533622i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 3722.81i | − | 0.162390i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 5081.28i | − | 0.220826i | −0.993886 | − | 0.110413i | \(-0.964783\pi\) | ||
0.993886 | − | 0.110413i | \(-0.0352174\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4493.19 | − | 4493.19i | −0.194546 | − | 0.194546i | 0.603111 | − | 0.797657i | \(-0.293928\pi\) |
−0.797657 | + | 0.603111i | \(0.793928\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7955.35 | + | 7955.35i | −0.343181 | + | 0.343181i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2235.36 | 0.0960752 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13266.9 | 0.568114 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 27021.2 | − | 27021.2i | 1.15287 | − | 1.15287i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2115.54 | + | 2115.54i | 0.0899304 | + | 0.0899304i | 0.750641 | − | 0.660710i | \(-0.229745\pi\) |
−0.660710 | + | 0.750641i | \(0.729745\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24432.6i | 1.03483i | 0.855734 | + | 0.517416i | \(0.173106\pi\) | ||||
−0.855734 | + | 0.517416i | \(0.826894\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 5980.44i | − | 0.252378i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21051.4 | − | 21051.4i | −0.885162 | − | 0.885162i | 0.108892 | − | 0.994054i | \(-0.465270\pi\) |
−0.994054 | + | 0.108892i | \(0.965270\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25442.0 | − | 25442.0i | 1.06591 | − | 1.06591i | 0.0682392 | − | 0.997669i | \(-0.478262\pi\) |
0.997669 | − | 0.0682392i | \(-0.0217381\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14023.7 | 0.585413 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −43603.5 | −1.81365 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2299.17 | + | 2299.17i | −0.0952889 | + | 0.0952889i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −811.516 | − | 811.516i | −0.0335127 | − | 0.0335127i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 18757.2i | − | 0.771837i | −0.922533 | − | 0.385919i | \(-0.873885\pi\) | ||
0.922533 | − | 0.385919i | \(-0.126115\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16349.4i | 0.670358i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14813.9 | + | 14813.9i | 0.605242 | + | 0.605242i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1504.22 | + | 1504.22i | −0.0612389 | + | 0.0612389i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30152.2 | 1.22319 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8922.94 | −0.360700 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1524.67 | − | 1524.67i | 0.0614160 | − | 0.0614160i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6100.17 | − | 6100.17i | −0.244860 | − | 0.244860i | 0.573997 | − | 0.818857i | \(-0.305392\pi\) |
−0.818857 | + | 0.573997i | \(0.805392\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 1252.45i | − | 0.0500971i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 2079.04i | − | 0.0828687i | −0.999141 | − | 0.0414344i | \(-0.986807\pi\) | ||
0.999141 | − | 0.0414344i | \(-0.0131927\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8301.95 | − | 8301.95i | −0.329754 | − | 0.329754i | 0.522739 | − | 0.852493i | \(-0.324910\pi\) |
−0.852493 | + | 0.522739i | \(0.824910\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8842.03 | − | 8842.03i | 0.349983 | − | 0.349983i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −43830.8 | −1.72887 | −0.864436 | − | 0.502743i | \(-0.832324\pi\) | ||||
−0.864436 | + | 0.502743i | \(0.832324\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3134.18 | −0.123197 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5171.62 | + | 5171.62i | −0.202581 | + | 0.202581i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8560.14 | − | 8560.14i | −0.334158 | − | 0.334158i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 54907.3i | − | 2.13601i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7261.01i | 0.281498i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4327.14 | − | 4327.14i | −0.167182 | − | 0.167182i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2565.89 | + | 2565.89i | −0.0987958 | + | 0.0987958i | −0.754777 | − | 0.655981i | \(-0.772255\pi\) |
0.655981 | + | 0.754777i | \(0.272255\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15681.2 | 0.601723 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26429.8 | 1.01072 | 0.505360 | − | 0.862909i | \(-0.331360\pi\) | ||||
0.505360 | + | 0.862909i | \(0.331360\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20708.4 | − | 20708.4i | 0.789232 | − | 0.789232i | −0.192136 | − | 0.981368i | \(-0.561542\pi\) |
0.981368 | + | 0.192136i | \(0.0615415\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 769.097 | + | 769.097i | 0.0292123 | + | 0.0292123i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 22350.0i | − | 0.846042i | −0.906120 | − | 0.423021i | \(-0.860970\pi\) | ||
0.906120 | − | 0.423021i | \(-0.139030\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 28755.6i | − | 1.08485i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1862.19 | + | 1862.19i | 0.0700175 | + | 0.0700175i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5483.28 | − | 5483.28i | 0.205477 | − | 0.205477i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1476.28 | −0.0551360 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13528.0 | 0.503553 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 562.292 | − | 562.292i | 0.0208604 | − | 0.0208604i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33745.2 | + | 33745.2i | 1.24774 | + | 1.24774i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 13954.7i | − | 0.514267i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1879.95i | − | 0.0690516i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4086.93 | + | 4086.93i | 0.149619 | + | 0.149619i | 0.777948 | − | 0.628329i | \(-0.216261\pi\) |
−0.628329 | + | 0.777948i | \(0.716261\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7480.29 | − | 7480.29i | 0.272944 | − | 0.272944i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20024.6 | 0.728259 | 0.364130 | − | 0.931348i | \(-0.381367\pi\) | ||||
0.364130 | + | 0.931348i | \(0.381367\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22974.8 | −0.832810 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.803134 | + | 0.803134i | −2.90173e−5 | + | 2.90173e-5i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −23079.3 | − | 23079.3i | −0.831131 | − | 0.831131i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 26977.7i | − | 0.968349i | −0.874971 | − | 0.484175i | \(-0.839120\pi\) | ||
0.874971 | − | 0.484175i | \(-0.160880\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15294.2i | 0.547189i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 20373.4 | + | 20373.4i | 0.726542 | + | 0.726542i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2698.84 | + | 2698.84i | −0.0959321 | + | 0.0959321i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5891.10 | 0.208726 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −34371.4 | −1.21387 | −0.606937 | − | 0.794750i | \(-0.707602\pi\) | ||||
−0.606937 | + | 0.794750i | \(0.707602\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27576.3 | + | 27576.3i | −0.970760 | + | 0.970760i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10303.4 | + | 10303.4i | 0.361541 | + | 0.361541i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1255.57i | 0.0439159i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 32901.8i | − | 1.14712i | −0.819163 | − | 0.573561i | \(-0.805561\pi\) | ||
0.819163 | − | 0.573561i | \(-0.194439\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9342.60 | + | 9342.60i | 0.324690 | + | 0.324690i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33381.6 | − | 33381.6i | 1.15644 | − | 1.15644i | 0.171204 | − | 0.985236i | \(-0.445234\pi\) |
0.985236 | − | 0.171204i | \(-0.0547656\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10762.1 | −0.371646 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3176.65 | −0.109351 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13611.9 | + | 13611.9i | −0.467084 | + | 0.467084i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18204.1 | + | 18204.1i | 0.622686 | + | 0.622686i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22534.1i | 0.768369i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 4572.49i | − | 0.155422i | −0.996976 | − | 0.0777112i | \(-0.975239\pi\) | ||
0.996976 | − | 0.0777112i | \(-0.0247612\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2140.25 | + | 2140.25i | 0.0725202 | + | 0.0725202i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3050.77 | − | 3050.77i | 0.103048 | − | 0.103048i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −46395.7 | −1.56225 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29712.3 | −0.997360 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11509.3 | + | 11509.3i | −0.385133 | + | 0.385133i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −312.510 | − | 312.510i | −0.0104249 | − | 0.0104249i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33060.9i | 1.09945i | 0.835346 | + | 0.549725i | \(0.185268\pi\) | ||||
−0.835346 | + | 0.549725i | \(0.814732\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18867.9i | 0.625514i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15553.4 | + | 15553.4i | 0.514041 | + | 0.514041i | 0.915762 | − | 0.401721i | \(-0.131588\pi\) |
−0.401721 | + | 0.915762i | \(0.631588\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8076.18 | + | 8076.18i | −0.266095 | + | 0.266095i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −23946.1 | −0.786551 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1241.54 | 0.0406555 | 0.0203277 | − | 0.999793i | \(-0.493529\pi\) | ||||
0.0203277 | + | 0.999793i | \(0.493529\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 57.3608 | − | 57.3608i | 0.00187258 | − | 0.00187258i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18153.2 | − | 18153.2i | −0.590812 | − | 0.590812i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 10797.7i | − | 0.350349i | −0.984537 | − | 0.175175i | \(-0.943951\pi\) | ||
0.984537 | − | 0.175175i | \(-0.0560490\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1343.67i | 0.0434648i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5767.56 | − | 5767.56i | −0.186001 | − | 0.186001i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8492.49 | + | 8492.49i | −0.273049 | + | 0.273049i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10204.8 | 0.327112 | 0.163556 | − | 0.986534i | \(-0.447704\pi\) | ||||
0.163556 | + | 0.986534i | \(0.447704\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7203.49 | 0.230207 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1380.20 | + | 1380.20i | −0.0439752 | + | 0.0439752i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15046.7 | + | 15046.7i | 0.477967 | + | 0.477967i | 0.904481 | − | 0.426514i | \(-0.140259\pi\) |
−0.426514 | + | 0.904481i | \(0.640259\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3973.90i | 0.125855i |
(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 | 64.4.e.a.49.2 | 10 | ||
3.2 | odd | 2 | 576.4.k.a.433.3 | 10 | |||
4.3 | odd | 2 | 16.4.e.a.5.4 | ✓ | 10 | ||
8.3 | odd | 2 | 128.4.e.b.97.2 | 10 | |||
8.5 | even | 2 | 128.4.e.a.97.4 | 10 | |||
12.11 | even | 2 | 144.4.k.a.37.2 | 10 | |||
16.3 | odd | 4 | 16.4.e.a.13.4 | yes | 10 | ||
16.5 | even | 4 | 128.4.e.a.33.4 | 10 | |||
16.11 | odd | 4 | 128.4.e.b.33.2 | 10 | |||
16.13 | even | 4 | inner | 64.4.e.a.17.2 | 10 | ||
32.3 | odd | 8 | 1024.4.a.n.1.7 | 10 | |||
32.5 | even | 8 | 1024.4.b.k.513.4 | 10 | |||
32.11 | odd | 8 | 1024.4.b.j.513.4 | 10 | |||
32.13 | even | 8 | 1024.4.a.m.1.7 | 10 | |||
32.19 | odd | 8 | 1024.4.a.n.1.4 | 10 | |||
32.21 | even | 8 | 1024.4.b.k.513.7 | 10 | |||
32.27 | odd | 8 | 1024.4.b.j.513.7 | 10 | |||
32.29 | even | 8 | 1024.4.a.m.1.4 | 10 | |||
48.29 | odd | 4 | 576.4.k.a.145.3 | 10 | |||
48.35 | even | 4 | 144.4.k.a.109.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.4.e.a.5.4 | ✓ | 10 | 4.3 | odd | 2 | ||
16.4.e.a.13.4 | yes | 10 | 16.3 | odd | 4 | ||
64.4.e.a.17.2 | 10 | 16.13 | even | 4 | inner | ||
64.4.e.a.49.2 | 10 | 1.1 | even | 1 | trivial | ||
128.4.e.a.33.4 | 10 | 16.5 | even | 4 | |||
128.4.e.a.97.4 | 10 | 8.5 | even | 2 | |||
128.4.e.b.33.2 | 10 | 16.11 | odd | 4 | |||
128.4.e.b.97.2 | 10 | 8.3 | odd | 2 | |||
144.4.k.a.37.2 | 10 | 12.11 | even | 2 | |||
144.4.k.a.109.2 | 10 | 48.35 | even | 4 | |||
576.4.k.a.145.3 | 10 | 48.29 | odd | 4 | |||
576.4.k.a.433.3 | 10 | 3.2 | odd | 2 | |||
1024.4.a.m.1.4 | 10 | 32.29 | even | 8 | |||
1024.4.a.m.1.7 | 10 | 32.13 | even | 8 | |||
1024.4.a.n.1.4 | 10 | 32.19 | odd | 8 | |||
1024.4.a.n.1.7 | 10 | 32.3 | odd | 8 | |||
1024.4.b.j.513.4 | 10 | 32.11 | odd | 8 | |||
1024.4.b.j.513.7 | 10 | 32.27 | odd | 8 | |||
1024.4.b.k.513.4 | 10 | 32.5 | even | 8 | |||
1024.4.b.k.513.7 | 10 | 32.21 | even | 8 |