Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,2,Mod(81,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.ba (of order \(12\), degree \(4\), 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: | \(3.57729801055\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 81.11 | ||
Character | \(\chi\) | \(=\) | 448.81 |
Dual form | 448.2.ba.c.177.11 |
$q$-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 \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | 2.46036 | − | 0.659252i | 1.42049 | − | 0.380619i | 0.534833 | − | 0.844958i | \(-0.320374\pi\) |
0.885658 | + | 0.464338i | \(0.153708\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.87532 | + | 0.502490i | 0.838668 | + | 0.224720i | 0.652491 | − | 0.757796i | \(-0.273724\pi\) |
0.186176 | + | 0.982516i | \(0.440391\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.364450 | − | 2.62053i | −0.137749 | − | 0.990467i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.02070 | − | 1.74400i | 1.00690 | − | 0.581333i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.37168 | + | 5.11917i | 0.413576 | + | 1.54349i | 0.787670 | + | 0.616097i | \(0.211287\pi\) |
−0.374094 | + | 0.927391i | \(0.622046\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.61173 | − | 3.61173i | −1.00171 | − | 1.00171i | −0.999999 | − | 0.00171617i | \(-0.999454\pi\) |
−0.00171617 | − | 0.999999i | \(-0.500546\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.94523 | 1.27685 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.294815 | + | 0.510634i | −0.0715031 | + | 0.123847i | −0.899560 | − | 0.436797i | \(-0.856113\pi\) |
0.828057 | + | 0.560644i | \(0.189446\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.137946 | − | 0.514822i | 0.0316470 | − | 0.118108i | −0.948295 | − | 0.317389i | \(-0.897194\pi\) |
0.979942 | + | 0.199281i | \(0.0638606\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.62427 | − | 6.20719i | −0.572663 | − | 1.35452i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.378033 | + | 0.218258i | −0.0788254 | + | 0.0455098i | −0.538895 | − | 0.842373i | \(-0.681158\pi\) |
0.460069 | + | 0.887883i | \(0.347825\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.06581 | − | 0.615344i | −0.213161 | − | 0.123069i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.878939 | − | 0.878939i | 0.169152 | − | 0.169152i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.68976 | + | 2.68976i | 0.499476 | + | 0.499476i | 0.911275 | − | 0.411799i | \(-0.135099\pi\) |
−0.411799 | + | 0.911275i | \(0.635099\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.94118 | + | 6.82633i | −0.707857 | + | 1.22605i | 0.257793 | + | 0.966200i | \(0.417005\pi\) |
−0.965650 | + | 0.259845i | \(0.916329\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.74965 | + | 11.6907i | 1.17496 | + | 2.03510i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.633329 | − | 5.09746i | 0.107052 | − | 0.861628i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.90863 | − | 0.779365i | −0.478176 | − | 0.128127i | 0.0116774 | − | 0.999932i | \(-0.496283\pi\) |
−0.489853 | + | 0.871805i | \(0.662950\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −11.2672 | − | 6.50513i | −1.80420 | − | 1.04165i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.95135i | 0.460923i | 0.973081 | + | 0.230461i | \(0.0740235\pi\) | ||||
−0.973081 | + | 0.230461i | \(0.925976\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.67329 | − | 7.67329i | 1.17017 | − | 1.17017i | 0.187996 | − | 0.982170i | \(-0.439801\pi\) |
0.982170 | − | 0.187996i | \(-0.0601993\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.54110 | − | 1.75268i | 0.975090 | − | 0.261275i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.01771 | − | 3.49478i | −0.294314 | − | 0.509766i | 0.680511 | − | 0.732738i | \(-0.261758\pi\) |
−0.974825 | + | 0.222971i | \(0.928424\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.73435 | + | 1.91011i | −0.962050 | + | 0.272872i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.388715 | + | 1.45070i | −0.0544310 | + | 0.203139i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.244374 | + | 0.912017i | 0.0335674 | + | 0.125275i | 0.980676 | − | 0.195637i | \(-0.0626773\pi\) |
−0.947109 | + | 0.320912i | \(0.896011\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.2893i | 1.38741i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.35759i | − | 0.179817i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.00753382 | − | 0.0281166i | −0.000980820 | − | 0.00366047i | 0.965434 | − | 0.260649i | \(-0.0839365\pi\) |
−0.966415 | + | 0.256988i | \(0.917270\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.529990 | − | 1.97795i | 0.0678583 | − | 0.253251i | −0.923661 | − | 0.383211i | \(-0.874818\pi\) |
0.991519 | + | 0.129960i | \(0.0414850\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.67110 | − | 7.28022i | −0.714491 | − | 0.917222i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.95829 | − | 8.58801i | −0.615000 | − | 1.06521i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.24795 | − | 1.67413i | 0.763309 | − | 0.204528i | 0.143895 | − | 0.989593i | \(-0.454037\pi\) |
0.619414 | + | 0.785065i | \(0.287370\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.786212 | + | 0.786212i | −0.0946488 | + | 0.0946488i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.05630i | 0.244037i | 0.992528 | + | 0.122019i | \(0.0389368\pi\) | ||||
−0.992528 | + | 0.122019i | \(0.961063\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.85664 | + | 3.95868i | 0.802509 | + | 0.463329i | 0.844348 | − | 0.535796i | \(-0.179988\pi\) |
−0.0418389 | + | 0.999124i | \(0.513322\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.02794 | − | 0.811334i | −0.349636 | − | 0.0936847i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.9150 | − | 5.46021i | 1.47180 | − | 0.622248i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.53028 | + | 11.3108i | 0.734714 | + | 1.27256i | 0.954849 | + | 0.297092i | \(0.0960169\pi\) |
−0.220135 | + | 0.975469i | \(0.570650\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.64893 | + | 6.32013i | −0.405437 | + | 0.702237i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.1551 | − | 10.1551i | −1.11467 | − | 1.11467i | −0.992510 | − | 0.122161i | \(-0.961018\pi\) |
−0.122161 | − | 0.992510i | \(-0.538982\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.809460 | + | 0.809460i | −0.0877983 | + | 0.0877983i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.39101 | + | 4.84455i | 0.899611 | + | 0.519391i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.35262 | + | 1.93564i | −0.355377 | + | 0.205177i | −0.667051 | − | 0.745012i | \(-0.732444\pi\) |
0.311674 | + | 0.950189i | \(0.399110\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.14836 | + | 10.7810i | −0.854180 | + | 1.13015i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.19647 | + | 19.3935i | −0.538849 | + | 2.01101i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.517385 | − | 0.896137i | 0.0530826 | − | 0.0919418i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.0556 | −1.22406 | −0.612029 | − | 0.790836i | \(-0.709646\pi\) | ||||
−0.612029 | + | 0.790836i | \(0.709646\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.0712 | + | 13.0712i | 1.31371 | + | 1.31371i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.694969 | − | 2.59366i | −0.0691520 | − | 0.258079i | 0.922692 | − | 0.385539i | \(-0.125984\pi\) |
−0.991844 | + | 0.127460i | \(0.959318\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.0773103 | + | 0.0446351i | −0.00761761 | + | 0.00439803i | −0.503804 | − | 0.863818i | \(-0.668067\pi\) |
0.496186 | + | 0.868216i | \(0.334733\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.80229 | − | 12.9591i | −0.175886 | − | 1.26468i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.0802 | − | 3.77279i | −1.36119 | − | 0.364729i | −0.496935 | − | 0.867788i | \(-0.665541\pi\) |
−0.864252 | + | 0.503059i | \(0.832208\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.68404 | + | 1.79098i | −0.640215 | + | 0.171545i | −0.564301 | − | 0.825569i | \(-0.690854\pi\) |
−0.0759141 | + | 0.997114i | \(0.524187\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.67008 | −0.728012 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.51142 | 0.706615 | 0.353307 | − | 0.935507i | \(-0.385057\pi\) | ||||
0.353307 | + | 0.935507i | \(0.385057\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.818604 | + | 0.219344i | −0.0763353 | + | 0.0204540i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −17.2088 | − | 4.61109i | −1.59095 | − | 0.426295i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.44558 | + | 0.586470i | 0.132516 | + | 0.0537616i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14.7981 | + | 8.54370i | −1.34528 | + | 0.776700i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.94568 | + | 7.26138i | 0.175436 | + | 0.654737i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.55366 | − | 8.55366i | −0.765063 | − | 0.765063i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.25202 | −0.377306 | −0.188653 | − | 0.982044i | \(-0.560412\pi\) | ||||
−0.188653 | + | 0.982044i | \(0.560412\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13.8204 | − | 23.9377i | 1.21682 | − | 2.10760i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.31046 | + | 4.89071i | −0.114496 | + | 0.427304i | −0.999249 | − | 0.0387565i | \(-0.987660\pi\) |
0.884753 | + | 0.466060i | \(0.154327\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.39938 | − | 0.173865i | −0.121342 | − | 0.0150760i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.08995 | − | 1.20663i | 0.179874 | − | 0.103850i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.241507 | + | 0.139434i | 0.0206333 | + | 0.0119127i | 0.510281 | − | 0.860008i | \(-0.329541\pi\) |
−0.489648 | + | 0.871920i | \(0.662875\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.1095 | − | 12.1095i | 1.02712 | − | 1.02712i | 0.0274943 | − | 0.999622i | \(-0.491247\pi\) |
0.999622 | − | 0.0274943i | \(-0.00875280\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.26825 | − | 7.26825i | −0.612097 | − | 0.612097i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.5349 | − | 23.4432i | 1.13185 | − | 1.96042i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.69258 | + | 6.39573i | 0.306652 | + | 0.531136i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −15.3097 | + | 9.13919i | −1.26272 | + | 0.753788i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 21.1901 | + | 5.67786i | 1.73596 | + | 0.465149i | 0.981542 | − | 0.191247i | \(-0.0612532\pi\) |
0.754417 | + | 0.656396i | \(0.227920\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.08773 | − | 4.66946i | −0.658170 | − | 0.379995i | 0.133409 | − | 0.991061i | \(-0.457408\pi\) |
−0.791580 | + | 0.611066i | \(0.790741\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.05663i | 0.166269i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.8211 | + | 10.8211i | −0.869174 | + | 0.869174i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.2775 | + | 3.02179i | −0.900040 | + | 0.241165i | −0.679034 | − | 0.734107i | \(-0.737601\pi\) |
−0.221007 | + | 0.975272i | \(0.570934\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.20250 | + | 2.08279i | 0.0953643 | + | 0.165176i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.709725 | + | 0.911103i | 0.0559341 | + | 0.0718050i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.82793 | + | 14.2860i | −0.299826 | + | 1.11897i | 0.637482 | + | 0.770466i | \(0.279976\pi\) |
−0.937308 | + | 0.348502i | \(0.886690\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.78326 | + | 25.3155i | 0.528076 | + | 1.97081i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.426814i | 0.0330279i | 0.999864 | + | 0.0165139i | \(0.00525679\pi\) | ||||
−0.999864 | + | 0.0165139i | \(0.994743\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0892i | 1.00686i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.481156 | − | 1.79570i | −0.0367949 | − | 0.137320i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.08986 | − | 4.06740i | 0.0828603 | − | 0.309239i | −0.912040 | − | 0.410101i | \(-0.865493\pi\) |
0.994900 | + | 0.100862i | \(0.0321601\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.22409 | + | 3.01724i | −0.0925327 | + | 0.228082i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.0370719 | − | 0.0642104i | −0.00278649 | − | 0.00482635i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.5720 | − | 3.63660i | 1.01442 | − | 0.271812i | 0.286943 | − | 0.957948i | \(-0.407361\pi\) |
0.727474 | + | 0.686135i | \(0.240694\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0681 | − | 10.0681i | 0.748356 | − | 0.748356i | −0.225814 | − | 0.974170i | \(-0.572504\pi\) |
0.974170 | + | 0.225814i | \(0.0725042\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 5.21587i | − | 0.385568i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.06298 | − | 2.92311i | −0.372238 | − | 0.214911i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.01842 | − | 0.808782i | −0.220728 | − | 0.0591440i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.62362 | − | 1.98296i | −0.190840 | − | 0.144239i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.82250 | + | 8.35282i | 0.348944 | + | 0.604389i | 0.986062 | − | 0.166377i | \(-0.0532070\pi\) |
−0.637118 | + | 0.770766i | \(0.719874\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.77970 | − | 16.9389i | 0.703959 | − | 1.21929i | −0.263108 | − | 0.964767i | \(-0.584747\pi\) |
0.967066 | − | 0.254525i | \(-0.0819193\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −17.8609 | − | 17.8609i | −1.27904 | − | 1.27904i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.33252 | + | 8.33252i | −0.593668 | + | 0.593668i | −0.938620 | − | 0.344953i | \(-0.887895\pi\) |
0.344953 | + | 0.938620i | \(0.387895\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.34374 | + | 1.35316i | 0.166144 | + | 0.0959230i | 0.580766 | − | 0.814070i | \(-0.302753\pi\) |
−0.414623 | + | 0.909993i | \(0.636086\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.2686 | − | 8.23795i | 1.00643 | − | 0.581060i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.06831 | − | 8.02888i | 0.425912 | − | 0.563517i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.48302 | + | 5.53471i | −0.103579 | + | 0.386561i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.761282 | + | 1.31858i | −0.0529128 | + | 0.0916476i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.82468 | 0.195387 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.9853 | − | 11.9853i | −0.825100 | − | 0.825100i | 0.161734 | − | 0.986834i | \(-0.448291\pi\) |
−0.986834 | + | 0.161734i | \(0.948291\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.35562 | + | 5.05923i | 0.0928854 | + | 0.346653i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 18.2456 | − | 10.5341i | 1.24434 | − | 0.718420i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.3250 | + | 7.84013i | 1.31186 | + | 0.532223i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 19.4796 | + | 5.21954i | 1.31631 | + | 0.352704i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.90907 | − | 0.779483i | 0.195685 | − | 0.0524337i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.50874 | −0.167998 | −0.0839988 | − | 0.996466i | \(-0.526769\pi\) | ||||
−0.0839988 | + | 0.996466i | \(0.526769\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.29264 | −0.286176 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.3064 | − | 4.90519i | 1.21504 | − | 0.325569i | 0.406303 | − | 0.913739i | \(-0.366818\pi\) |
0.808738 | + | 0.588170i | \(0.200151\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.1003 | + | 6.72559i | 1.65867 | + | 0.444440i | 0.962022 | − | 0.272972i | \(-0.0880066\pi\) |
0.696650 | + | 0.717412i | \(0.254673\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 28.1760 | − | 21.9483i | 1.85385 | − | 1.44410i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.2405 | − | 7.06704i | 0.801900 | − | 0.462977i | −0.0422348 | − | 0.999108i | \(-0.513448\pi\) |
0.844135 | + | 0.536130i | \(0.180114\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.02776 | − | 7.56771i | −0.132277 | − | 0.493663i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 23.5235 | + | 23.5235i | 1.52802 | + | 1.52802i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.15987 | 0.139710 | 0.0698550 | − | 0.997557i | \(-0.477746\pi\) | ||||
0.0698550 | + | 0.997557i | \(0.477746\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.85611 | − | 8.41103i | 0.312809 | − | 0.541802i | −0.666160 | − | 0.745809i | \(-0.732063\pi\) |
0.978969 | + | 0.204007i | \(0.0653966\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.77627 | + | 21.5573i | −0.370548 | + | 1.38290i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.5889 | + | 0.198113i | −0.868160 | + | 0.0126570i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.35762 | + | 1.36117i | −0.150012 | + | 0.0866094i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −31.6801 | − | 18.2905i | −2.00765 | − | 1.15912i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.1748 | − | 10.1748i | 0.642228 | − | 0.642228i | −0.308875 | − | 0.951103i | \(-0.599952\pi\) |
0.951103 | + | 0.308875i | \(0.0999525\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.63584 | − | 1.63584i | −0.102844 | − | 0.102844i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.45793 | + | 2.52520i | −0.0912990 | + | 0.158134i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.2555 | − | 22.9591i | −0.826853 | − | 1.43215i | −0.900495 | − | 0.434867i | \(-0.856795\pi\) |
0.0736418 | − | 0.997285i | \(-0.476538\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.982297 | + | 7.90619i | −0.0610370 | + | 0.491267i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.8159 | + | 3.43401i | 0.793283 | + | 0.212560i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.9812 | + | 10.3814i | 1.10877 | + | 0.640146i | 0.938509 | − | 0.345254i | \(-0.112207\pi\) |
0.170256 | + | 0.985400i | \(0.445540\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.83312i | 0.112607i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.97259 | + | 6.97259i | −0.426716 | + | 0.426716i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.1792 | − | 6.47880i | 1.47423 | − | 0.395019i | 0.569852 | − | 0.821747i | \(-0.307000\pi\) |
0.904380 | + | 0.426728i | \(0.140334\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.82072 | − | 4.88563i | −0.171347 | − | 0.296781i | 0.767544 | − | 0.640996i | \(-0.221478\pi\) |
−0.938891 | + | 0.344215i | \(0.888145\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −12.9405 | + | 31.8969i | −0.783198 | + | 1.93049i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.68811 | − | 6.30010i | 0.101797 | − | 0.379910i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.95063 | − | 18.4760i | −0.297455 | − | 1.11012i | −0.939248 | − | 0.343239i | \(-0.888476\pi\) |
0.641793 | − | 0.766878i | \(-0.278191\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 27.4937i | 1.64600i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 20.6400i | − | 1.23128i | −0.788029 | − | 0.615639i | \(-0.788898\pi\) | ||
0.788029 | − | 0.615639i | \(-0.211102\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.14544 | − | 22.9351i | −0.365309 | − | 1.36335i | −0.867002 | − | 0.498305i | \(-0.833956\pi\) |
0.501693 | − | 0.865046i | \(-0.332711\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.682175 | − | 2.54591i | 0.0404085 | − | 0.150807i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.73409 | − | 1.07562i | 0.456529 | − | 0.0634918i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.32617 | + | 14.4213i | 0.489775 | + | 0.848315i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −29.6611 | + | 7.94766i | −1.73876 | + | 0.465900i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.5268 | − | 20.5268i | 1.19919 | − | 1.19919i | 0.224778 | − | 0.974410i | \(-0.427834\pi\) |
0.974410 | − | 0.224778i | \(-0.0721656\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 0.0565132i | − | 0.00329033i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.70506 | + | 3.29382i | 0.331041 | + | 0.191127i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.15364 | + | 0.577067i | 0.124548 | + | 0.0333726i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.9046 | − | 17.3116i | −1.32020 | − | 0.997822i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.41975 | − | 5.92318i | −0.196460 | − | 0.340278i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.98780 | − | 3.44297i | 0.113821 | − | 0.197144i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.03127 | + | 6.03127i | 0.344223 | + | 0.344223i | 0.857952 | − | 0.513730i | \(-0.171737\pi\) |
−0.513730 | + | 0.857952i | \(0.671737\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.160786 | + | 0.160786i | −0.00914677 | + | 0.00914677i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.8721 | − | 8.00907i | −0.786616 | − | 0.454153i | 0.0521541 | − | 0.998639i | \(-0.483391\pi\) |
−0.838770 | + | 0.544486i | \(0.816725\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.3757 | + | 8.87715i | −0.869085 | + | 0.501766i | −0.867044 | − | 0.498232i | \(-0.833983\pi\) |
−0.00204070 | + | 0.999998i | \(0.500650\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.97687 | − | 16.5024i | −0.393102 | − | 0.929805i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.02311 | + | 15.0144i | −0.225960 | + | 0.843295i | 0.756057 | + | 0.654505i | \(0.227123\pi\) |
−0.982018 | + | 0.188790i | \(0.939544\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.0799 | + | 17.4588i | −0.564364 | + | 0.977506i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −37.1297 | −2.07238 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.222217 | + | 0.222217i | 0.0123645 | + | 0.0123645i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.62695 | + | 6.07187i | 0.0902471 | + | 0.336807i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.2645 | + | 8.81294i | −0.844126 | + | 0.487356i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.42282 | + | 6.56115i | −0.464365 | + | 0.361728i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.6818 | + | 3.93399i | 0.806987 | + | 0.216232i | 0.638649 | − | 0.769498i | \(-0.279493\pi\) |
0.168338 | + | 0.985729i | \(0.446160\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10.1453 | + | 2.71842i | −0.555959 | + | 0.148969i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.5581 | 0.686124 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.9202 | 1.03065 | 0.515325 | − | 0.856995i | \(-0.327671\pi\) | ||||
0.515325 | + | 0.856995i | \(0.327671\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.4808 | − | 4.95192i | 1.00374 | − | 0.268951i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −40.3512 | − | 10.8121i | −2.18514 | − | 0.585506i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.45983 | + | 16.9514i | 0.402793 | + | 0.915291i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.86946 | + | 1.07933i | −0.100648 | + | 0.0581094i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.58787 | + | 5.92600i | 0.0852412 | + | 0.318125i | 0.995360 | − | 0.0962234i | \(-0.0306763\pi\) |
−0.910119 | + | 0.414348i | \(0.864010\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.94202 | − | 2.94202i | −0.157483 | − | 0.157483i | 0.623968 | − | 0.781450i | \(-0.285520\pi\) |
−0.781450 | + | 0.623968i | \(0.785520\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.34899 | −0.338884 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.0287 | + | 22.5663i | −0.693446 | + | 1.20108i | 0.277256 | + | 0.960796i | \(0.410575\pi\) |
−0.970702 | + | 0.240288i | \(0.922758\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.03327 | + | 3.85621i | −0.0548402 | + | 0.204666i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.94328 | + | 0.489929i | 0.208700 | + | 0.0259298i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.7055 | + | 14.8411i | −1.35668 | + | 0.783282i | −0.989175 | − | 0.146739i | \(-0.953122\pi\) |
−0.367508 | + | 0.930020i | \(0.619789\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.2085 | + | 9.35796i | 0.853077 | + | 0.492524i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −30.7763 | + | 30.7763i | −1.61534 | + | 1.61534i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.8692 | + | 10.8692i | 0.568919 | + | 0.568919i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.21998 | + | 3.84511i | −0.115882 | + | 0.200713i | −0.918132 | − | 0.396275i | \(-0.870303\pi\) |
0.802250 | + | 0.596988i | \(0.203636\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.14714 | + | 8.91512i | 0.267950 | + | 0.464102i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.30090 | − | 0.972775i | 0.119457 | − | 0.0505039i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.6779 | − | 4.73679i | −0.915328 | − | 0.245261i | −0.229741 | − | 0.973252i | \(-0.573788\pi\) |
−0.685587 | + | 0.727990i | \(0.740455\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −26.6841 | − | 15.4061i | −1.37796 | − | 0.795567i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 19.4294i | − | 1.00066i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.71717 | + | 1.71717i | −0.0882050 | + | 0.0882050i | −0.749833 | − | 0.661628i | \(-0.769866\pi\) |
0.661628 | + | 0.749833i | \(0.269866\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.4615 | + | 2.80315i | −0.535960 | + | 0.143610i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.88728 | − | 10.1971i | −0.300826 | − | 0.521046i | 0.675497 | − | 0.737363i | \(-0.263929\pi\) |
−0.976323 | + | 0.216316i | \(0.930596\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 26.9635 | − | 3.74995i | 1.37419 | − | 0.191115i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.79646 | − | 36.5609i | 0.497982 | − | 1.85849i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.04561 | + | 15.0984i | 0.205120 | + | 0.765520i | 0.989413 | + | 0.145128i | \(0.0463595\pi\) |
−0.784292 | + | 0.620391i | \(0.786974\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 0.257382i | − | 0.0130164i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.8969i | 0.650560i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.56280 | + | 24.4927i | 0.330210 | + | 1.23236i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.836855 | + | 3.12318i | −0.0420005 | + | 0.156748i | −0.983741 | − | 0.179592i | \(-0.942522\pi\) |
0.941741 | + | 0.336340i | \(0.109189\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.55760 | + | 0.494774i | −0.178103 | + | 0.0247697i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.37385 | − | 4.11163i | −0.118544 | − | 0.205325i | 0.800647 | − | 0.599137i | \(-0.204489\pi\) |
−0.919191 | + | 0.393812i | \(0.871156\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 38.8894 | − | 10.4204i | 1.93722 | − | 0.519076i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10.0187 | + | 10.0187i | −0.497834 | + | 0.497834i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 15.9588i | − | 0.791048i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.68361 | − | 1.54938i | −0.132696 | − | 0.0766121i | 0.432182 | − | 0.901786i | \(-0.357744\pi\) |
−0.564879 | + | 0.825174i | \(0.691077\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.686118 | + | 0.183845i | 0.0338437 | + | 0.00906839i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.0709347 | + | 0.0299897i | −0.00349047 | + | 0.00147570i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.9413 | − | 24.1470i | −0.684349 | − | 1.18533i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 21.8106 | − | 37.7770i | 1.06807 | − | 1.84995i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.62329 | − | 2.62329i | −0.128156 | − | 0.128156i | 0.640119 | − | 0.768276i | \(-0.278885\pi\) |
−0.768276 | + | 0.640119i | \(0.778885\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.44059 | + | 3.44059i | −0.167684 | + | 0.167684i | −0.785961 | − | 0.618276i | \(-0.787831\pi\) |
0.618276 | + | 0.785961i | \(0.287831\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.1898 | − | 7.03778i | −0.592688 | − | 0.342189i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.628432 | − | 0.362825i | 0.0304834 | − | 0.0175996i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.37643 | − | 0.667990i | −0.260184 | − | 0.0323263i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 17.8459 | − | 66.6018i | 0.861608 | − | 3.21556i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.3945 | + | 19.7358i | −0.548853 | + | 0.950642i | 0.449500 | + | 0.893280i | \(0.351602\pi\) |
−0.998353 | + | 0.0573616i | \(0.981731\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.6448 | −0.799899 | −0.399950 | − | 0.916537i | \(-0.630972\pi\) | ||||
−0.399950 | + | 0.916537i | \(0.630972\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.3015 | + | 13.3015i | 0.637757 | + | 0.637757i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.0602155 | + | 0.224727i | 0.00288050 | + | 0.0107502i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.7406 | − | 15.4387i | 1.27626 | − | 0.736847i | 0.300099 | − | 0.953908i | \(-0.402980\pi\) |
0.976158 | + | 0.217061i | \(0.0696469\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.0112 | + | 17.5146i | −0.810057 | + | 0.834026i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.7414 | + | 3.68200i | 0.652874 | + | 0.174937i | 0.570028 | − | 0.821625i | \(-0.306932\pi\) |
0.0828461 | + | 0.996562i | \(0.473599\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.25987 | + | 1.94528i | −0.344151 | + | 0.0922149i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 55.8784 | 2.64296 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.7633 | 0.696725 | 0.348363 | − | 0.937360i | \(-0.386738\pi\) | ||||
0.348363 | + | 0.937360i | \(0.386738\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.1084 | + | 4.04830i | −0.711429 | + | 0.190627i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −22.9771 | − | 6.15670i | −1.07956 | − | 0.289267i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −20.6981 | + | 16.1232i | −0.970341 | + | 0.755869i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.80328 | + | 1.04112i | −0.0843539 | + | 0.0487017i | −0.541584 | − | 0.840647i | \(-0.682175\pi\) |
0.457230 | + | 0.889349i | \(0.348842\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.189692 | + | 0.707941i | 0.00885407 | + | 0.0330439i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.5211 | + | 10.5211i | 0.490015 | + | 0.490015i | 0.908311 | − | 0.418296i | \(-0.137372\pi\) |
−0.418296 | + | 0.908311i | \(0.637372\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.5483 | −1.23380 | −0.616902 | − | 0.787040i | \(-0.711613\pi\) | ||||
−0.616902 | + | 0.787040i | \(0.711613\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −19.4901 | + | 33.7578i | −0.903830 | + | 1.56548i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.50402 | + | 9.34512i | −0.115872 | + | 0.432440i | −0.999351 | − | 0.0360311i | \(-0.988528\pi\) |
0.883479 | + | 0.468472i | \(0.155195\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.66419 | − | 15.7628i | −0.307724 | − | 0.727859i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −25.7546 | + | 14.8694i | −1.18671 | + | 0.685146i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 49.8062 | + | 28.7556i | 2.29009 | + | 1.32218i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.463816 | + | 0.463816i | −0.0212813 | + | 0.0212813i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.32874 | + | 2.32874i | 0.106626 | + | 0.106626i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.94642 | + | 3.37130i | −0.0889342 | + | 0.154039i | −0.907061 | − | 0.420999i | \(-0.861679\pi\) |
0.818127 | + | 0.575038i | \(0.195013\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.69033 | + | 13.3200i | 0.350649 | + | 0.607342i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.34683 | + | 1.77376i | 0.106784 | + | 0.0807087i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −22.6080 | − | 6.05780i | −1.02658 | − | 0.275070i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.49944 | + | 1.44305i | 0.113260 | + | 0.0653909i | 0.555560 | − | 0.831476i | \(-0.312504\pi\) |
−0.442300 | + | 0.896867i | \(0.645837\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 37.6724i | 1.70360i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.1200 | + | 10.1200i | −0.456710 | + | 0.456710i | −0.897574 | − | 0.440864i | \(-0.854672\pi\) |
0.440864 | + | 0.897574i | \(0.354672\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.16647 | + | 0.580503i | −0.0975727 | + | 0.0261445i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 17.9446 | + | 31.0809i | 0.806549 | + | 1.39698i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.38858 | − | 0.749418i | 0.241711 | − | 0.0336160i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.96424 | − | 18.5268i | 0.222230 | − | 0.829373i | −0.761265 | − | 0.648440i | \(-0.775422\pi\) |
0.983495 | − | 0.180933i | \(-0.0579117\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.281378 | + | 1.05012i | 0.0125710 | + | 0.0469158i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 25.3179i | − | 1.12887i | −0.825477 | − | 0.564436i | \(-0.809094\pi\) | ||
0.825477 | − | 0.564436i | \(-0.190906\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 5.21315i | − | 0.231982i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.62911 | + | 32.2043i | 0.383232 | + | 1.43024i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.572369 | + | 2.13611i | −0.0253698 | + | 0.0946814i | −0.977450 | − | 0.211167i | \(-0.932274\pi\) |
0.952080 | + | 0.305849i | \(0.0989402\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.87494 | − | 19.4108i | 0.348367 | − | 0.858682i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.331251 | − | 0.573743i | −0.0146251 | − | 0.0253314i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.167410 | + | 0.0448574i | −0.00737697 | + | 0.00197665i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.1227 | − | 15.1227i | 0.665097 | − | 0.665097i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 10.7258i | − | 0.470809i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.90915 | − | 5.14370i | −0.390317 | − | 0.225349i | 0.291981 | − | 0.956424i | \(-0.405686\pi\) |
−0.682297 | + | 0.731075i | \(0.739019\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.30777 | + | 1.69016i | 0.275819 | + | 0.0739056i | 0.394077 | − | 0.919077i | \(-0.371064\pi\) |
−0.118258 | + | 0.992983i | \(0.537731\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.02259 | + | 8.23049i | −0.0446295 | + | 0.359208i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.32384 | − | 4.02501i | −0.101228 | − | 0.175332i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.4047 | + | 19.7536i | −0.495858 | + | 0.858851i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.0717927 | − | 0.0717927i | −0.00311554 | − | 0.00311554i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.6595 | − | 10.6595i | 0.461713 | − | 0.461713i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.5091 | − | 14.1503i | −1.05962 | − | 0.611773i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 30.9946 | − | 17.8947i | 1.33751 | − | 0.772214i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −19.0155 | − | 31.8542i | −0.819056 | − | 1.37206i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.75097 | + | 6.53469i | −0.0752799 | + | 0.280948i | −0.993297 | − | 0.115593i | \(-0.963123\pi\) |
0.918017 | + | 0.396542i | \(0.129790\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 18.1338 | − | 31.4086i | 0.778195 | − | 1.34787i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.4346 | −0.575477 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.78581 | + | 1.78581i | 0.0763555 | + | 0.0763555i | 0.744253 | − | 0.667898i | \(-0.232806\pi\) |
−0.667898 | + | 0.744253i | \(0.732806\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.84860 | − | 6.89909i | −0.0788965 | − | 0.294446i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.75579 | − | 1.01370i | 0.0747991 | − | 0.0431853i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 27.2603 | − | 21.2350i | 1.15922 | − | 0.903004i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −14.3838 | − | 3.85414i | −0.610560 | − | 0.163599i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.36982 | − | 0.902940i | 0.142784 | − | 0.0382588i | −0.186719 | − | 0.982413i | \(-0.559785\pi\) |
0.329503 | + | 0.944155i | \(0.393119\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −55.4278 | −2.34435 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.95959 | −0.336054 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −38.4688 | + | 10.3077i | −1.62127 | + | 0.434417i | −0.951373 | − | 0.308041i | \(-0.900327\pi\) |
−0.669893 | + | 0.742458i | \(0.733660\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.0863 | + | 3.77441i | 0.592615 | + | 0.158791i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 17.8920 | + | 7.25876i | 0.751391 | + | 0.304839i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −39.1325 | + | 22.5931i | −1.64052 | + | 0.947153i | −0.659868 | + | 0.751381i | \(0.729388\pi\) |
−0.980649 | + | 0.195772i | \(0.937279\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.44226 | − | 24.0429i | −0.269600 | − | 1.00616i | −0.959374 | − | 0.282137i | \(-0.908957\pi\) |
0.689774 | − | 0.724025i | \(-0.257710\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.3717 | + | 17.3717i | 0.725714 | + | 0.725714i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.537214 | 0.0224034 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.46579 | + | 9.46703i | −0.227544 | + | 0.394118i | −0.957080 | − | 0.289825i | \(-0.906403\pi\) |
0.729536 | + | 0.683943i | \(0.239736\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.8946 | − | 48.1232i | 0.535881 | − | 1.99993i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.9108 | + | 30.3129i | −0.950500 | + | 1.25759i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.33357 | + | 2.50199i | −0.179478 | + | 0.103622i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −29.9550 | − | 17.2945i | −1.23848 | − | 0.715040i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.44744 | − | 7.44744i | 0.307389 | − | 0.307389i | −0.536507 | − | 0.843896i | \(-0.680256\pi\) |
0.843896 | + | 0.536507i | \(0.180256\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.97067 | + | 2.97067i | 0.122404 | + | 0.122404i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.0078 | + | 25.9943i | −0.617338 | + | 1.06926i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.6447 | + | 21.9013i | 0.519256 | + | 0.899377i | 0.999750 | + | 0.0223792i | \(0.00712412\pi\) |
−0.480494 | + | 0.876998i | \(0.659543\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.41622 | + | 1.82621i | 0.0990555 | + | 0.0748672i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.65853 | + | 1.78415i | 0.272516 | + | 0.0730203i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.4613 | − | 8.92656i | −0.631730 | − | 0.364729i | 0.149692 | − | 0.988733i | \(-0.452172\pi\) |
−0.781422 | + | 0.624003i | \(0.785505\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 15.3921i | − | 0.627855i | −0.949447 | − | 0.313928i | \(-0.898355\pi\) | ||
0.949447 | − | 0.313928i | \(-0.101645\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.9535 | − | 15.9535i | 0.649676 | − | 0.649676i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −32.0443 | + | 8.58625i | −1.30279 | + | 0.349081i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.1434 | + | 26.2292i | 0.614652 | + | 1.06461i | 0.990445 | + | 0.137905i | \(0.0440370\pi\) |
−0.375793 | + | 0.926704i | \(0.622630\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.63719 | − | 23.7545i | 0.390519 | − | 0.962581i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.33478 | + | 19.9097i | −0.215822 | + | 0.805459i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.95872 | + | 14.7741i | 0.159891 | + | 0.596722i | 0.998637 | + | 0.0521982i | \(0.0166228\pi\) |
−0.838746 | + | 0.544523i | \(0.816711\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 14.5951i | 0.588531i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 39.3266i | − | 1.58323i | −0.611020 | − | 0.791615i | \(-0.709241\pi\) | ||
0.611020 | − | 0.791615i | \(-0.290759\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.39109 | + | 5.19162i | 0.0559127 | + | 0.208669i | 0.988231 | − | 0.152970i | \(-0.0488839\pi\) |
−0.932318 | + | 0.361639i | \(0.882217\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.140433 | + | 0.524103i | −0.00563538 | + | 0.0210315i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.29426 | + | 8.08020i | 0.252174 | + | 0.323726i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.66598 | − | 15.0099i | −0.346639 | − | 0.600397i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.94973 | − | 1.86217i | 0.277545 | − | 0.0743681i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.25548 | − | 1.25548i | 0.0500592 | − | 0.0500592i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.48252i | 0.297875i | 0.988847 | + | 0.148937i | \(0.0475853\pi\) | ||||
−0.988847 | + | 0.148937i | \(0.952415\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −37.3894 | − | 21.5868i | −1.48610 | − | 0.857998i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.97389 | − | 2.13660i | −0.316434 | − | 0.0847883i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 31.2215 | + | 17.4239i | 1.23704 | + | 0.690360i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.58618 | + | 6.21144i | 0.141867 | + | 0.245721i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.73385 | + | 8.19927i | −0.186976 | + | 0.323852i | −0.944241 | − | 0.329256i | \(-0.893202\pi\) |
0.757265 | + | 0.653108i | \(0.226535\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.6140 | + | 20.6140i | 0.812939 | + | 0.812939i | 0.985073 | − | 0.172135i | \(-0.0550665\pi\) |
−0.172135 | + | 0.985073i | \(0.555066\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 37.9462 | − | 37.9462i | 1.49413 | − | 1.49413i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.2216 | + | 17.4485i | 1.18813 | + | 0.685970i | 0.957882 | − | 0.287161i | \(-0.0927115\pi\) |
0.230252 | + | 0.973131i | \(0.426045\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.133600 | − | 0.0771338i | 0.00524425 | − | 0.00302777i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 52.7151 | + | 6.54954i | 2.06607 | + | 0.256697i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.3267 | − | 38.5399i | 0.404117 | − | 1.50818i | −0.401562 | − | 0.915832i | \(-0.631533\pi\) |
0.805679 | − | 0.592353i | \(-0.201801\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.91507 | + | 8.51315i | −0.192048 | + | 0.332636i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 27.6157 | 1.07739 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.66795 | + | 6.66795i | 0.259746 | + | 0.259746i | 0.824951 | − | 0.565205i | \(-0.191203\pi\) |
−0.565205 | + | 0.824951i | \(0.691203\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.649564 | + | 2.42421i | 0.0252651 | + | 0.0942907i | 0.977407 | − | 0.211365i | \(-0.0677909\pi\) |
−0.952142 | + | 0.305656i | \(0.901124\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.64349 | − | 3.83562i | 0.258012 | − | 0.148963i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.53692 | − | 1.02923i | −0.0983774 | − | 0.0399117i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.60388 | − | 0.429758i | −0.0621024 | − | 0.0166403i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.17241 | + | 1.65389i | −0.238639 | + | 0.0639432i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.8524 | 0.418954 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.8448 | −1.42026 | −0.710131 | − | 0.704070i | \(-0.751364\pi\) | ||||
−0.710131 | + | 0.704070i | \(0.751364\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.47763 | + | 0.395930i | −0.0568740 | + | 0.0152393i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.8935 | + | 4.52660i | 0.649270 | + | 0.173971i | 0.568399 | − | 0.822753i | \(-0.307563\pi\) |
0.0808713 | + | 0.996725i | \(0.474230\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.39366 | + | 31.5920i | 0.168613 | + | 1.21239i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 41.8067 | − | 24.1371i | 1.60204 | − | 0.924936i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.60472 | + | 32.1132i | 0.329250 | + | 1.22878i | 0.909970 | + | 0.414675i | \(0.136105\pi\) |
−0.580719 | + | 0.814104i | \(0.697229\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.382838 | + | 0.382838i | 0.0146275 | + | 0.0146275i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 66.1896 | 2.52529 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.41135 | − | 4.17658i | 0.0918650 | − | 0.159115i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.84416 | + | 14.3466i | −0.146239 | + | 0.545771i | 0.853458 | + | 0.521161i | \(0.174501\pi\) |
−0.999697 | + | 0.0246098i | \(0.992166\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 29.4898 | − | 39.0174i | 1.12022 | − | 1.48215i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 28.7941 | − | 16.6243i | 1.09222 | − | 0.630595i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.50706 | − | 0.870101i | −0.0570839 | − | 0.0329574i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25.4571 | − | 25.4571i | 0.962874 | − | 0.962874i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.3787 | − | 21.3787i | −0.807464 | − | 0.807464i | 0.176785 | − | 0.984249i | \(-0.443430\pi\) |
−0.984249 | + | 0.176785i | \(0.943430\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.802467 | + | 1.38991i | −0.0302656 | + | 0.0524216i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.97805 | − | 17.2825i | −0.375795 | − | 0.650897i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.54348 | + | 2.76645i | −0.246093 | + | 0.104043i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.3395 | − | 3.57430i | −0.500974 | − | 0.134236i | −0.000522056 | − | 1.00000i | \(-0.500166\pi\) |
−0.500452 | + | 0.865764i | \(0.666833\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 39.4520 | + | 22.7776i | 1.47956 | + | 0.854227i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 3.44077i | − | 0.128858i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 37.1623 | − | 37.1623i | 1.38979 | − | 1.38979i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.31405 | − | 1.42390i | 0.198457 | − | 0.0531764i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.1881 | − | 38.4309i | −0.827477 | − | 1.43323i | −0.900011 | − | 0.435866i | \(-0.856442\pi\) |
0.0725344 | − | 0.997366i | \(-0.476891\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.145143 | + | 0.186327i | 0.00540542 | + | 0.00693917i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.40280 | − | 23.8956i | 0.238123 | − | 0.888686i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.21164 | − | 4.52189i | −0.0449991 | − | 0.167939i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.44539i | 0.0536067i | 0.999641 | + | 0.0268033i | \(0.00853279\pi\) | ||||
−0.999641 | + | 0.0268033i | \(0.991467\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 34.9533i | 1.29457i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.65605 | + | 6.18045i | 0.0612511 | + | 0.228592i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.5622 | − | 39.4186i | 0.390123 | − | 1.45596i | −0.439807 | − | 0.898093i | \(-0.644953\pi\) |
0.829930 | − | 0.557868i | \(-0.188380\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −33.3029 | + | 9.44591i | −1.22840 | + | 0.348418i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.1404 | + | 29.6880i | 0.631373 | + | 1.09357i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.9326 | − | 2.92937i | 0.402161 | − | 0.107759i | −0.0520685 | − | 0.998644i | \(-0.516581\pi\) |
0.454229 | + | 0.890885i | \(0.349915\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.90325 | + | 4.90325i | −0.180125 | + | 0.180125i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.66874i | 0.354712i | 0.984147 | + | 0.177356i | \(0.0567544\pi\) | ||||
−0.984147 | + | 0.177356i | \(0.943246\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 36.8851 | + | 21.2956i | 1.35136 | + | 0.780210i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −48.3861 | − | 12.9650i | −1.77036 | − | 0.474365i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.75515 | + | 38.2727i | −0.173749 | + | 1.39845i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.8756 | − | 44.8178i | −0.944213 | − | 1.63542i | −0.757319 | − | 0.653045i | \(-0.773491\pi\) |
−0.186893 | − | 0.982380i | \(-0.559842\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18.3259 | − | 31.7415i | 0.667834 | − | 1.15672i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.8207 | − | 12.8207i | −0.466594 | − | 0.466594i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.2783 | + | 28.2783i | −1.02779 | + | 1.02779i | −0.0281911 | + | 0.999603i | \(0.508975\pi\) |
−0.999603 | + | 0.0281911i | \(0.991025\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.10318 | − | 2.94632i | −0.185234 | − | 0.106945i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.94191 | + | 2.85321i | −0.179144 | + | 0.103429i | −0.586891 | − | 0.809666i | \(-0.699648\pi\) |
0.407746 | + | 0.913095i | \(0.366315\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.12933 | + | 16.8630i | 0.258099 | + | 0.610482i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.03343 | + | 3.85683i | −0.0373639 | + | 0.139444i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.0743395 | + | 0.128760i | −0.00268425 | + | 0.00464925i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.6503 | 1.42983 | 0.714914 | − | 0.699212i | \(-0.246466\pi\) | ||||
0.714914 | + | 0.699212i | \(0.246466\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −47.7491 | − | 47.7491i | −1.71964 | − | 1.71964i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.74604 | + | 21.4445i | 0.206671 | + | 0.771305i | 0.988934 | + | 0.148357i | \(0.0473985\pi\) |
−0.782263 | + | 0.622948i | \(0.785935\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.40108 | − | 4.85037i | 0.301776 | − | 0.174230i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.79536 | + | 20.0997i | 0.100283 | + | 0.721072i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.51942 | + | 0.407126i | 0.0544387 | + | 0.0145868i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.5265 | + | 2.82057i | −0.376669 | + | 0.100928i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.72827 | 0.168975 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22.6673 | −0.809029 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.8470 | + | 5.05004i | −0.671823 | + | 0.180014i | −0.578576 | − | 0.815629i | \(-0.696391\pi\) |
−0.0932471 | + | 0.995643i | \(0.529725\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 51.0841 | + | 13.6880i | 1.81864 | + | 0.487304i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.73754 | − | 19.6839i | −0.0973357 | − | 0.699879i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.05801 | + | 5.22965i | −0.321659 | + | 0.185710i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.20849 | + | 4.51013i | 0.0428606 | + | 0.159958i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.54421 | − | 2.54421i | −0.0901206 | − | 0.0901206i | 0.660609 | − | 0.750730i | \(-0.270298\pi\) |
−0.750730 | + | 0.660609i | \(0.770298\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.37941 | 0.0841774 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.75150 | + | 11.6939i | −0.238553 | + | 0.413185i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.8601 | + | 40.5303i | −0.383244 | + | 1.43028i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.873139 | + | 2.06524i | 0.0307741 | + | 0.0727900i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 55.2185 | − | 31.8804i | 1.94378 | − | 1.12224i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.3519 | − | 11.1728i | −0.680378 | − | 0.392816i | 0.119620 | − | 0.992820i | \(-0.461832\pi\) |
−0.799997 | + | 0.600004i | \(0.795166\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.7484 | + | 31.7484i | −1.11484 | + | 1.11484i | −0.122349 | + | 0.992487i | \(0.539043\pi\) |
−0.992487 | + | 0.122349i | \(0.960957\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.1609 | − | 10.1609i | −0.356357 | − | 0.356357i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.3572 | + | 24.8673i | −0.502909 | + | 0.871065i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.89188 | − | 5.00888i | −0.101174 | − | 0.175238i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.81173 | + | 46.7767i | −0.203078 | + | 1.63451i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 46.9829 | + | 12.5890i | 1.63972 | + | 0.439361i | 0.956708 | − | 0.291050i | \(-0.0940047\pi\) |
0.683008 | + | 0.730411i | \(0.260671\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.7248 | + | 9.65608i | 0.582991 | + | 0.336590i | 0.762321 | − | 0.647199i | \(-0.224060\pi\) |
−0.179330 | + | 0.983789i | \(0.557393\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 16.6134i | − | 0.578405i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.4794 | + | 14.4794i | −0.503498 | + | 0.503498i | −0.912523 | − | 0.409025i | \(-0.865869\pi\) |
0.409025 | + | 0.912523i | \(0.365869\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.38085 | + | 0.369998i | −0.0479589 | + | 0.0128505i | −0.282719 | − | 0.959203i | \(-0.591236\pi\) |
0.234760 | + | 0.972053i | \(0.424570\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24.3607 | − | 42.1940i | −0.845064 | − | 1.46369i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.01002 | − | 4.00192i | 0.0349952 | − | 0.138658i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.214470 | + | 0.800412i | −0.00742203 | + | 0.0276994i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.53587 | + | 9.46399i | 0.0876524 | + | 0.327123i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 41.9512i | − | 1.44832i | −0.689634 | − | 0.724158i | \(-0.742228\pi\) | ||
0.689634 | − | 0.724158i | \(-0.257772\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 14.5304i | − | 0.501048i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.6069 | − | 50.7818i | −0.468648 | − | 1.74902i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.57721 | + | 24.5465i | −0.226263 | + | 0.844425i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.7822 | + | 35.6652i | 0.954608 | + | 1.22547i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −30.2400 | − | 52.3773i | −1.03784 | − | 1.79758i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.26966 | − | 0.340204i | 0.0435234 | − | 0.0116621i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.5722 | + | 34.5722i | −1.18373 | + | 1.18373i | −0.204960 | + | 0.978770i | \(0.565706\pi\) |
−0.978770 | + | 0.204960i | \(0.934294\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 3.60928i | − | 0.123435i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.21992 | − | 4.16842i | −0.246628 | − | 0.142391i | 0.371591 | − | 0.928396i | \(-0.378812\pi\) |
−0.618219 | + | 0.786006i | \(0.712146\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.6163 | − | 3.38053i | −0.430463 | − | 0.115342i | 0.0370807 | − | 0.999312i | \(-0.488194\pi\) |
−0.467543 | + | 0.883970i | \(0.654861\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.3196 | − | 7.74513i | 0.624329 | − | 0.263953i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.7192 | + | 42.8148i | 0.841450 | + | 1.45743i | 0.888669 | + | 0.458549i | \(0.151631\pi\) |
−0.0472194 | + | 0.998885i | \(0.515036\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.08766 | − | 7.08003i | 0.138985 | − | 0.240728i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 29.9927 | + | 29.9927i | 1.01861 | + | 1.01861i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −48.9443 | + | 48.9443i | −1.66032 | + | 1.66032i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28.6125 | − | 16.5194i | −0.969497 | − | 0.559739i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −36.4162 | + | 21.0249i | −1.23250 | + | 0.711585i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −19.2977 | + | 25.5325i | −0.652383 | + | 0.863156i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.9238 | + | 51.9644i | −0.470174 | + | 1.75471i | 0.168966 | + | 0.985622i | \(0.445957\pi\) |
−0.639140 | + | 0.769091i | \(0.720709\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 36.9710 | − | 64.0357i | 1.24700 | − | 2.15987i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.2319 | 0.883776 | 0.441888 | − | 0.897070i | \(-0.354309\pi\) | ||||
0.441888 | + | 0.897070i | \(0.354309\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.8278 | + | 12.8278i | 0.431688 | + | 0.431688i | 0.889202 | − | 0.457514i | \(-0.151260\pi\) |
−0.457514 | + | 0.889202i | \(0.651260\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.0372565 | − | 0.139043i | −0.00125236 | − | 0.00467388i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −46.3646 | + | 26.7686i | −1.55677 | + | 0.898801i | −0.559207 | + | 0.829028i | \(0.688894\pi\) |
−0.997563 | + | 0.0697733i | \(0.977772\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.54965 | + | 11.1425i | 0.0519736 | + | 0.373709i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −37.3590 | − | 10.0103i | −1.25157 | − | 0.335358i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.07752 | + | 0.556671i | −0.0695217 | + | 0.0186283i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27.2791 | 0.911841 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.67918 | 0.189622 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −28.9620 | + | 7.76035i | −0.965937 | + | 0.258822i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.537752 | − | 0.144090i | −0.0179151 | − | 0.00480034i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −67.7664 | − | 27.4928i | −2.25512 | − | 0.914903i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 23.9400 | − | 13.8218i | 0.795793 | − | 0.459451i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.73321 | − | 36.3248i | −0.323186 | − | 1.20615i | −0.916123 | − | 0.400897i | \(-0.868698\pi\) |
0.592937 | − | 0.805249i | \(-0.297968\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.62263 | − | 6.62263i | −0.219659 | − | 0.219659i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.6202 | −0.616914 | −0.308457 | − | 0.951238i | \(-0.599813\pi\) | ||||
−0.308457 | + | 0.951238i | \(0.599813\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 38.0563 | − | 65.9155i | 1.25948 | − | 2.18148i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.62092 | − | 9.78142i | 0.0866450 | − | 0.323364i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.2939 | + | 1.65168i | 0.439002 | + | 0.0545434i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.5605 | − | 8.98389i | 0.513295 | − | 0.296351i | −0.220892 | − | 0.975298i | \(-0.570897\pi\) |
0.734187 | + | 0.678947i | \(0.237563\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.8152 | + | 10.8630i | 0.619983 | + | 0.357947i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.42679 | − | 7.42679i | 0.244456 | − | 0.244456i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.62046 | + | 2.62046i | 0.0861602 | + | 0.0861602i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.155687 | + | 0.269658i | −0.00511344 | + | 0.00885674i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.1258 | − | 22.7345i | −0.430642 | − | 0.745894i | 0.566286 | − | 0.824209i | \(-0.308380\pi\) |
−0.996929 | + | 0.0783141i | \(0.975046\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.0543870 | + | 3.73048i | 0.00178246 | + | 0.122262i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −39.4104 | − | 10.5600i | −1.29024 | − | 0.345719i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.25408 | − | 3.03345i | −0.171827 | − | 0.0992043i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.7798i | 1.56090i | 0.625219 | + | 0.780449i | \(0.285010\pi\) | ||||
−0.625219 | + | 0.780449i | \(0.714990\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −31.9775 | + | 31.9775i | −1.04355 | + | 1.04355i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −41.8248 | + | 11.2069i | −1.36345 | + | 0.365335i | −0.865082 | − | 0.501630i | \(-0.832734\pi\) |
−0.498368 | + | 0.866966i | \(0.666067\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.644154 | − | 1.11571i | −0.0209765 | − | 0.0363324i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.92370 | − | 5.03701i | −0.127638 | − | 0.163854i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.82935 | + | 18.0234i | −0.156933 | + | 0.585681i | 0.841999 | + | 0.539478i | \(0.181379\pi\) |
−0.998932 | + | 0.0462023i | \(0.985288\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.4666 | − | 39.0620i | −0.339762 | − | 1.26801i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 39.5932i | 1.28390i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.1972i | 1.07536i | 0.843148 | + | 0.537681i | \(0.180700\pi\) | ||||
−0.843148 | + | 0.537681i | \(0.819300\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.84652 | + | 18.0875i | 0.156830 | + | 0.585296i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −13.2903 | + | 49.6002i | −0.429615 | + | 1.60335i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.277374 | − | 0.683694i | 0.00895688 | − | 0.0220776i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.5659 | − | 26.9609i | −0.502124 | − | 0.869705i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −49.1118 | + | 13.1595i | −1.58261 | + | 0.424058i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26.8517 | − | 26.8517i | 0.864387 | − | 0.864387i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 13.2736i | − | 0.426850i | −0.976959 | − | 0.213425i | \(-0.931538\pi\) | ||
0.976959 | − | 0.213425i | \(-0.0684619\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.693232 | + | 0.400238i | 0.0222698 | + | 0.0128575i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.1279 | + | 11.0202i | 1.31986 | + | 0.353655i | 0.848925 | − | 0.528514i | \(-0.177250\pi\) |
0.470934 | + | 0.882169i | \(0.343917\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −36.1467 | − | 27.3200i | −1.15881 | − | 0.875840i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.00579 | + | 13.8664i | 0.256390 | + | 0.444081i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24.4001 | + | 42.2622i | −0.780628 | + | 1.35209i | 0.150949 | + | 0.988542i | \(0.451767\pi\) |
−0.931577 | + | 0.363545i | \(0.881566\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.5076 | − | 14.5076i | −0.463664 | − | 0.463664i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.0670 | + | 17.0670i | −0.544907 | + | 0.544907i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 45.9141 | + | 26.5085i | 1.46443 | + | 0.845491i | 0.999212 | − | 0.0397033i | \(-0.0126413\pi\) |
0.465222 | + | 0.885194i | \(0.345975\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.8131 | + | 11.4391i | −0.631299 | + | 0.364481i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.3977 | + | 21.6956i | −0.521946 | + | 0.690578i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.22601 | + | 4.57551i | −0.0389847 | + | 0.145493i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.92839 | + | 12.0003i | −0.220088 | + | 0.381203i | −0.954834 | − | 0.297139i | \(-0.903968\pi\) |
0.734747 | + | 0.678341i | \(0.237301\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 38.7162 | 1.22862 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.71531 | + | 3.71531i | 0.117783 | + | 0.117783i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.93196 | − | 25.8704i | −0.219537 | − | 0.819325i | −0.984520 | − | 0.175273i | \(-0.943919\pi\) |
0.764982 | − | 0.644051i | \(-0.222748\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.24152 | + | 1.87149i | −0.102557 | + | 0.0592114i |
(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 | 448.2.ba.c.81.11 | 48 | ||
4.3 | odd | 2 | 112.2.w.c.109.11 | yes | 48 | ||
7.2 | even | 3 | inner | 448.2.ba.c.401.2 | 48 | ||
8.3 | odd | 2 | 896.2.ba.f.417.11 | 48 | |||
8.5 | even | 2 | 896.2.ba.e.417.2 | 48 | |||
16.3 | odd | 4 | 896.2.ba.f.865.2 | 48 | |||
16.5 | even | 4 | inner | 448.2.ba.c.305.2 | 48 | ||
16.11 | odd | 4 | 112.2.w.c.53.6 | yes | 48 | ||
16.13 | even | 4 | 896.2.ba.e.865.11 | 48 | |||
28.3 | even | 6 | 784.2.m.k.589.3 | 24 | |||
28.11 | odd | 6 | 784.2.m.j.589.3 | 24 | |||
28.19 | even | 6 | 784.2.x.o.765.6 | 48 | |||
28.23 | odd | 6 | 112.2.w.c.93.6 | yes | 48 | ||
28.27 | even | 2 | 784.2.x.o.557.11 | 48 | |||
56.37 | even | 6 | 896.2.ba.e.289.11 | 48 | |||
56.51 | odd | 6 | 896.2.ba.f.289.2 | 48 | |||
112.11 | odd | 12 | 784.2.m.j.197.3 | 24 | |||
112.27 | even | 4 | 784.2.x.o.165.6 | 48 | |||
112.37 | even | 12 | inner | 448.2.ba.c.177.11 | 48 | ||
112.51 | odd | 12 | 896.2.ba.f.737.11 | 48 | |||
112.59 | even | 12 | 784.2.m.k.197.3 | 24 | |||
112.75 | even | 12 | 784.2.x.o.373.11 | 48 | |||
112.93 | even | 12 | 896.2.ba.e.737.2 | 48 | |||
112.107 | odd | 12 | 112.2.w.c.37.11 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.w.c.37.11 | ✓ | 48 | 112.107 | odd | 12 | ||
112.2.w.c.53.6 | yes | 48 | 16.11 | odd | 4 | ||
112.2.w.c.93.6 | yes | 48 | 28.23 | odd | 6 | ||
112.2.w.c.109.11 | yes | 48 | 4.3 | odd | 2 | ||
448.2.ba.c.81.11 | 48 | 1.1 | even | 1 | trivial | ||
448.2.ba.c.177.11 | 48 | 112.37 | even | 12 | inner | ||
448.2.ba.c.305.2 | 48 | 16.5 | even | 4 | inner | ||
448.2.ba.c.401.2 | 48 | 7.2 | even | 3 | inner | ||
784.2.m.j.197.3 | 24 | 112.11 | odd | 12 | |||
784.2.m.j.589.3 | 24 | 28.11 | odd | 6 | |||
784.2.m.k.197.3 | 24 | 112.59 | even | 12 | |||
784.2.m.k.589.3 | 24 | 28.3 | even | 6 | |||
784.2.x.o.165.6 | 48 | 112.27 | even | 4 | |||
784.2.x.o.373.11 | 48 | 112.75 | even | 12 | |||
784.2.x.o.557.11 | 48 | 28.27 | even | 2 | |||
784.2.x.o.765.6 | 48 | 28.19 | even | 6 | |||
896.2.ba.e.289.11 | 48 | 56.37 | even | 6 | |||
896.2.ba.e.417.2 | 48 | 8.5 | even | 2 | |||
896.2.ba.e.737.2 | 48 | 112.93 | even | 12 | |||
896.2.ba.e.865.11 | 48 | 16.13 | even | 4 | |||
896.2.ba.f.289.2 | 48 | 56.51 | odd | 6 | |||
896.2.ba.f.417.11 | 48 | 8.3 | odd | 2 | |||
896.2.ba.f.737.11 | 48 | 112.51 | odd | 12 | |||
896.2.ba.f.865.2 | 48 | 16.3 | odd | 4 |