Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(529,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.ba (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 619.6 | ||
Character | \(\chi\) | \(=\) | 1110.619 |
Dual form | 1110.2.ba.a.529.6 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −2.21345 | + | 0.317246i | −0.989884 | + | 0.141877i | ||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | −1.17143 | + | 0.676327i | −0.442760 | + | 0.255628i | −0.704768 | − | 0.709438i | \(-0.748949\pi\) |
0.262008 | + | 0.965066i | \(0.415615\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0.831981 | − | 2.07553i | 0.263096 | − | 0.656339i | ||||
\(11\) | 3.00191 | 0.905109 | 0.452555 | − | 0.891737i | \(-0.350513\pi\) | ||||
0.452555 | + | 0.891737i | \(0.350513\pi\) | |||||||
\(12\) | 0.866025 | + | 0.500000i | 0.250000 | + | 0.144338i | ||||
\(13\) | −1.12218 | − | 1.94367i | −0.311237 | − | 0.539078i | 0.667394 | − | 0.744705i | \(-0.267410\pi\) |
−0.978630 | + | 0.205627i | \(0.934077\pi\) | |||||||
\(14\) | − | 1.35265i | − | 0.361512i | ||||||
\(15\) | 1.75828 | − | 1.38147i | 0.453986 | − | 0.356693i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.19396 | − | 2.06800i | 0.289578 | − | 0.501564i | −0.684131 | − | 0.729359i | \(-0.739818\pi\) |
0.973709 | + | 0.227795i | \(0.0731517\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | 4.57549 | − | 2.64166i | 1.04969 | − | 0.606038i | 0.127127 | − | 0.991886i | \(-0.459424\pi\) |
0.922562 | + | 0.385848i | \(0.126091\pi\) | |||||||
\(20\) | 1.38147 | + | 1.75828i | 0.308905 | + | 0.393163i | ||||
\(21\) | 0.676327 | − | 1.17143i | 0.147587 | − | 0.255628i | ||||
\(22\) | −1.50095 | + | 2.59973i | −0.320004 | + | 0.554264i | ||||
\(23\) | −6.77962 | −1.41365 | −0.706824 | − | 0.707390i | \(-0.749873\pi\) | ||||
−0.706824 | + | 0.707390i | \(0.749873\pi\) | |||||||
\(24\) | −0.866025 | + | 0.500000i | −0.176777 | + | 0.102062i | ||||
\(25\) | 4.79871 | − | 1.40441i | 0.959742 | − | 0.280883i | ||||
\(26\) | 2.24436 | 0.440155 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 1.17143 | + | 0.676327i | 0.221380 | + | 0.127814i | ||||
\(29\) | 4.07927i | 0.757502i | 0.925499 | + | 0.378751i | \(0.123646\pi\) | ||||
−0.925499 | + | 0.378751i | \(0.876354\pi\) | |||||||
\(30\) | 0.317246 | + | 2.21345i | 0.0579209 | + | 0.404119i | ||||
\(31\) | − | 4.41998i | − | 0.793851i | −0.917851 | − | 0.396926i | \(-0.870077\pi\) | ||
0.917851 | − | 0.396926i | \(-0.129923\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −2.59973 | + | 1.50095i | −0.452555 | + | 0.261283i | ||||
\(34\) | 1.19396 | + | 2.06800i | 0.204763 | + | 0.354659i | ||||
\(35\) | 2.37834 | − | 1.86865i | 0.402014 | − | 0.315859i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 3.29819 | + | 5.11096i | 0.542220 | + | 0.840237i | ||||
\(38\) | 5.28332i | 0.857068i | ||||||||
\(39\) | 1.94367 | + | 1.12218i | 0.311237 | + | 0.179693i | ||||
\(40\) | −2.21345 | + | 0.317246i | −0.349977 | + | 0.0501610i | ||||
\(41\) | 2.30168 | + | 3.98662i | 0.359462 | + | 0.622606i | 0.987871 | − | 0.155277i | \(-0.0496271\pi\) |
−0.628409 | + | 0.777883i | \(0.716294\pi\) | |||||||
\(42\) | 0.676327 | + | 1.17143i | 0.104360 | + | 0.180756i | ||||
\(43\) | −3.19094 | −0.486614 | −0.243307 | − | 0.969949i | \(-0.578232\pi\) | ||||
−0.243307 | + | 0.969949i | \(0.578232\pi\) | |||||||
\(44\) | −1.50095 | − | 2.59973i | −0.226277 | − | 0.391924i | ||||
\(45\) | −0.831981 | + | 2.07553i | −0.124024 | + | 0.309401i | ||||
\(46\) | 3.38981 | − | 5.87132i | 0.499800 | − | 0.865679i | ||||
\(47\) | 12.9161i | 1.88401i | 0.335600 | + | 0.942005i | \(0.391061\pi\) | ||||
−0.335600 | + | 0.942005i | \(0.608939\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | −2.58516 | + | 4.47763i | −0.369309 | + | 0.639662i | ||||
\(50\) | −1.18310 | + | 4.85801i | −0.167315 | + | 0.687027i | ||||
\(51\) | 2.38792i | 0.334376i | ||||||||
\(52\) | −1.12218 | + | 1.94367i | −0.155618 | + | 0.269539i | ||||
\(53\) | 5.39612 | + | 3.11545i | 0.741213 | + | 0.427940i | 0.822510 | − | 0.568750i | \(-0.192573\pi\) |
−0.0812969 | + | 0.996690i | \(0.525906\pi\) | |||||||
\(54\) | −0.866025 | − | 0.500000i | −0.117851 | − | 0.0680414i | ||||
\(55\) | −6.64457 | + | 0.952343i | −0.895954 | + | 0.128414i | ||||
\(56\) | −1.17143 | + | 0.676327i | −0.156539 | + | 0.0903780i | ||||
\(57\) | −2.64166 | + | 4.57549i | −0.349896 | + | 0.606038i | ||||
\(58\) | −3.53275 | − | 2.03964i | −0.463873 | − | 0.267817i | ||||
\(59\) | 4.19055 | + | 2.41941i | 0.545563 | + | 0.314981i | 0.747330 | − | 0.664453i | \(-0.231335\pi\) |
−0.201768 | + | 0.979433i | \(0.564669\pi\) | |||||||
\(60\) | −2.07553 | − | 0.831981i | −0.267949 | − | 0.107408i | ||||
\(61\) | 9.20129 | − | 5.31237i | 1.17810 | − | 0.680179i | 0.222529 | − | 0.974926i | \(-0.428569\pi\) |
0.955575 | + | 0.294747i | \(0.0952355\pi\) | |||||||
\(62\) | 3.82781 | + | 2.20999i | 0.486132 | + | 0.280669i | ||||
\(63\) | 1.35265i | 0.170418i | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.10051 | + | 3.94621i | 0.384571 | + | 0.489467i | ||||
\(66\) | − | 3.00191i | − | 0.369509i | ||||||
\(67\) | −3.05897 | + | 1.76610i | −0.373712 | + | 0.215763i | −0.675079 | − | 0.737745i | \(-0.735891\pi\) |
0.301367 | + | 0.953508i | \(0.402557\pi\) | |||||||
\(68\) | −2.38792 | −0.289578 | ||||||||
\(69\) | 5.87132 | − | 3.38981i | 0.706824 | − | 0.408085i | ||||
\(70\) | 0.429124 | + | 2.99403i | 0.0512901 | + | 0.357855i | ||||
\(71\) | 6.08437 | + | 10.5384i | 0.722082 | + | 1.25068i | 0.960164 | + | 0.279438i | \(0.0901481\pi\) |
−0.238081 | + | 0.971245i | \(0.576519\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | − | 7.06413i | − | 0.826794i | −0.910551 | − | 0.413397i | \(-0.864342\pi\) | ||
0.910551 | − | 0.413397i | \(-0.135658\pi\) | |||||||
\(74\) | −6.07532 | + | 0.300839i | −0.706241 | + | 0.0349718i | ||||
\(75\) | −3.45360 | + | 3.61561i | −0.398787 | + | 0.417495i | ||||
\(76\) | −4.57549 | − | 2.64166i | −0.524845 | − | 0.303019i | ||||
\(77\) | −3.51653 | + | 2.03027i | −0.400746 | + | 0.231371i | ||||
\(78\) | −1.94367 | + | 1.12218i | −0.220078 | + | 0.127062i | ||||
\(79\) | 0.509669 | − | 0.294257i | 0.0573422 | − | 0.0331066i | −0.471055 | − | 0.882104i | \(-0.656127\pi\) |
0.528397 | + | 0.848997i | \(0.322793\pi\) | |||||||
\(80\) | 0.831981 | − | 2.07553i | 0.0930184 | − | 0.232051i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −4.60335 | −0.508355 | ||||||||
\(83\) | 3.56360 | + | 2.05745i | 0.391156 | + | 0.225834i | 0.682661 | − | 0.730735i | \(-0.260823\pi\) |
−0.291505 | + | 0.956569i | \(0.594156\pi\) | |||||||
\(84\) | −1.35265 | −0.147587 | ||||||||
\(85\) | −1.98671 | + | 4.95619i | −0.215489 | + | 0.537575i | ||||
\(86\) | 1.59547 | − | 2.76343i | 0.172044 | − | 0.297989i | ||||
\(87\) | −2.03964 | − | 3.53275i | −0.218672 | − | 0.378751i | ||||
\(88\) | 3.00191 | 0.320004 | ||||||||
\(89\) | 14.4684 | + | 8.35333i | 1.53365 | + | 0.885451i | 0.999189 | + | 0.0402561i | \(0.0128174\pi\) |
0.534457 | + | 0.845195i | \(0.320516\pi\) | |||||||
\(90\) | −1.38147 | − | 1.75828i | −0.145619 | − | 0.185339i | ||||
\(91\) | 2.62912 | + | 1.51792i | 0.275606 | + | 0.159121i | ||||
\(92\) | 3.38981 | + | 5.87132i | 0.353412 | + | 0.612127i | ||||
\(93\) | 2.20999 | + | 3.82781i | 0.229165 | + | 0.396926i | ||||
\(94\) | −11.1857 | − | 6.45806i | −1.15372 | − | 0.666098i | ||||
\(95\) | −9.28956 | + | 7.29873i | −0.953088 | + | 0.748834i | ||||
\(96\) | 0.866025 | + | 0.500000i | 0.0883883 | + | 0.0510310i | ||||
\(97\) | 9.59790 | 0.974519 | 0.487260 | − | 0.873257i | \(-0.337997\pi\) | ||||
0.487260 | + | 0.873257i | \(0.337997\pi\) | |||||||
\(98\) | −2.58516 | − | 4.47763i | −0.261141 | − | 0.452309i | ||||
\(99\) | 1.50095 | − | 2.59973i | 0.150852 | − | 0.261283i | ||||
\(100\) | −3.61561 | − | 3.45360i | −0.361561 | − | 0.345360i | ||||
\(101\) | −16.6462 | −1.65636 | −0.828180 | − | 0.560462i | \(-0.810624\pi\) | ||||
−0.828180 | + | 0.560462i | \(0.810624\pi\) | |||||||
\(102\) | −2.06800 | − | 1.19396i | −0.204763 | − | 0.118220i | ||||
\(103\) | 6.71339 | 0.661490 | 0.330745 | − | 0.943720i | \(-0.392700\pi\) | ||||
0.330745 | + | 0.943720i | \(0.392700\pi\) | |||||||
\(104\) | −1.12218 | − | 1.94367i | −0.110039 | − | 0.190593i | ||||
\(105\) | −1.12538 | + | 2.80747i | −0.109826 | + | 0.273981i | ||||
\(106\) | −5.39612 | + | 3.11545i | −0.524117 | + | 0.302599i | ||||
\(107\) | −0.170274 | + | 0.0983076i | −0.0164610 | + | 0.00950376i | −0.508208 | − | 0.861234i | \(-0.669692\pi\) |
0.491747 | + | 0.870738i | \(0.336359\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | −11.6161 | − | 6.70656i | −1.11262 | − | 0.642372i | −0.173114 | − | 0.984902i | \(-0.555383\pi\) |
−0.939507 | + | 0.342530i | \(0.888716\pi\) | |||||||
\(110\) | 2.49753 | − | 6.23054i | 0.238130 | − | 0.594058i | ||||
\(111\) | −5.41180 | − | 2.77713i | −0.513665 | − | 0.263593i | ||||
\(112\) | − | 1.35265i | − | 0.127814i | ||||||
\(113\) | 7.24481 | − | 12.5484i | 0.681535 | − | 1.18045i | −0.292978 | − | 0.956119i | \(-0.594646\pi\) |
0.974512 | − | 0.224333i | \(-0.0720204\pi\) | |||||||
\(114\) | −2.64166 | − | 4.57549i | −0.247414 | − | 0.428534i | ||||
\(115\) | 15.0063 | − | 2.15080i | 1.39935 | − | 0.200564i | ||||
\(116\) | 3.53275 | − | 2.03964i | 0.328008 | − | 0.189375i | ||||
\(117\) | −2.24436 | −0.207491 | ||||||||
\(118\) | −4.19055 | + | 2.41941i | −0.385771 | + | 0.222725i | ||||
\(119\) | 3.23003i | 0.296096i | ||||||||
\(120\) | 1.75828 | − | 1.38147i | 0.160508 | − | 0.126110i | ||||
\(121\) | −1.98855 | −0.180777 | ||||||||
\(122\) | 10.6247i | 0.961918i | ||||||||
\(123\) | −3.98662 | − | 2.30168i | −0.359462 | − | 0.207535i | ||||
\(124\) | −3.82781 | + | 2.20999i | −0.343748 | + | 0.198463i | ||||
\(125\) | −10.1762 | + | 4.63097i | −0.910183 | + | 0.414207i | ||||
\(126\) | −1.17143 | − | 0.676327i | −0.104360 | − | 0.0602520i | ||||
\(127\) | 8.91376 | + | 5.14636i | 0.790968 | + | 0.456666i | 0.840303 | − | 0.542117i | \(-0.182377\pi\) |
−0.0493351 | + | 0.998782i | \(0.515710\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 2.76343 | − | 1.59547i | 0.243307 | − | 0.140473i | ||||
\(130\) | −4.96778 | + | 0.712014i | −0.435703 | + | 0.0624477i | ||||
\(131\) | 3.29183 | + | 1.90054i | 0.287608 | + | 0.166051i | 0.636863 | − | 0.770977i | \(-0.280232\pi\) |
−0.349255 | + | 0.937028i | \(0.613565\pi\) | |||||||
\(132\) | 2.59973 | + | 1.50095i | 0.226277 | + | 0.130641i | ||||
\(133\) | −3.57325 | + | 6.18905i | −0.309840 | + | 0.536659i | ||||
\(134\) | − | 3.53219i | − | 0.305135i | ||||||
\(135\) | −0.317246 | − | 2.21345i | −0.0273042 | − | 0.190503i | ||||
\(136\) | 1.19396 | − | 2.06800i | 0.102381 | − | 0.177330i | ||||
\(137\) | − | 10.1698i | − | 0.868862i | −0.900705 | − | 0.434431i | \(-0.856950\pi\) | ||
0.900705 | − | 0.434431i | \(-0.143050\pi\) | |||||||
\(138\) | 6.77962i | 0.577119i | ||||||||
\(139\) | 0.463646 | − | 0.803059i | 0.0393260 | − | 0.0681146i | −0.845692 | − | 0.533671i | \(-0.820812\pi\) |
0.885018 | + | 0.465556i | \(0.154146\pi\) | |||||||
\(140\) | −2.80747 | − | 1.12538i | −0.237274 | − | 0.0951122i | ||||
\(141\) | −6.45806 | − | 11.1857i | −0.543867 | − | 0.942005i | ||||
\(142\) | −12.1687 | −1.02118 | ||||||||
\(143\) | −3.36868 | − | 5.83473i | −0.281703 | − | 0.487924i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | −1.29413 | − | 9.02926i | −0.107472 | − | 0.749839i | ||||
\(146\) | 6.11771 | + | 3.53206i | 0.506306 | + | 0.292316i | ||||
\(147\) | − | 5.17033i | − | 0.426441i | ||||||
\(148\) | 2.77713 | − | 5.41180i | 0.228278 | − | 0.444847i | ||||
\(149\) | −9.05684 | −0.741965 | −0.370983 | − | 0.928640i | \(-0.620979\pi\) | ||||
−0.370983 | + | 0.928640i | \(0.620979\pi\) | |||||||
\(150\) | −1.40441 | − | 4.79871i | −0.114670 | − | 0.391813i | ||||
\(151\) | 5.73747 | + | 9.93758i | 0.466908 | + | 0.808709i | 0.999285 | − | 0.0377983i | \(-0.0120344\pi\) |
−0.532377 | + | 0.846507i | \(0.678701\pi\) | |||||||
\(152\) | 4.57549 | − | 2.64166i | 0.371121 | − | 0.214267i | ||||
\(153\) | −1.19396 | − | 2.06800i | −0.0965260 | − | 0.167188i | ||||
\(154\) | − | 4.06054i | − | 0.327208i | ||||||
\(155\) | 1.40222 | + | 9.78339i | 0.112629 | + | 0.785821i | ||||
\(156\) | − | 2.24436i | − | 0.179693i | ||||||
\(157\) | 5.04062 | + | 2.91020i | 0.402285 | + | 0.232259i | 0.687469 | − | 0.726213i | \(-0.258722\pi\) |
−0.285184 | + | 0.958473i | \(0.592055\pi\) | |||||||
\(158\) | 0.588515i | 0.0468197i | ||||||||
\(159\) | −6.23090 | −0.494142 | ||||||||
\(160\) | 1.38147 | + | 1.75828i | 0.109215 | + | 0.139004i | ||||
\(161\) | 7.94187 | − | 4.58524i | 0.625907 | − | 0.361367i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 2.20296 | − | 3.81563i | 0.172549 | − | 0.298863i | −0.766761 | − | 0.641932i | \(-0.778133\pi\) |
0.939310 | + | 0.343069i | \(0.111466\pi\) | |||||||
\(164\) | 2.30168 | − | 3.98662i | 0.179731 | − | 0.311303i | ||||
\(165\) | 5.27819 | − | 4.14704i | 0.410907 | − | 0.322846i | ||||
\(166\) | −3.56360 | + | 2.05745i | −0.276589 | + | 0.159689i | ||||
\(167\) | 10.8349 | + | 18.7666i | 0.838431 | + | 1.45221i | 0.891206 | + | 0.453599i | \(0.149860\pi\) |
−0.0527743 | + | 0.998606i | \(0.516806\pi\) | |||||||
\(168\) | 0.676327 | − | 1.17143i | 0.0521798 | − | 0.0903780i | ||||
\(169\) | 3.98142 | − | 6.89603i | 0.306263 | − | 0.530464i | ||||
\(170\) | −3.29884 | − | 4.19863i | −0.253009 | − | 0.322021i | ||||
\(171\) | − | 5.28332i | − | 0.404026i | ||||||
\(172\) | 1.59547 | + | 2.76343i | 0.121653 | + | 0.210710i | ||||
\(173\) | −14.2574 | − | 8.23149i | −1.08397 | − | 0.625829i | −0.152003 | − | 0.988380i | \(-0.548572\pi\) |
−0.931964 | + | 0.362551i | \(0.881906\pi\) | |||||||
\(174\) | 4.07927 | 0.309249 | ||||||||
\(175\) | −4.67152 | + | 4.89067i | −0.353134 | + | 0.369700i | ||||
\(176\) | −1.50095 | + | 2.59973i | −0.113139 | + | 0.195962i | ||||
\(177\) | −4.83883 | −0.363709 | ||||||||
\(178\) | −14.4684 | + | 8.35333i | −1.08445 | + | 0.626109i | ||||
\(179\) | 21.2532i | 1.58854i | 0.607566 | + | 0.794269i | \(0.292146\pi\) | ||||
−0.607566 | + | 0.794269i | \(0.707854\pi\) | |||||||
\(180\) | 2.21345 | − | 0.317246i | 0.164981 | − | 0.0236461i | ||||
\(181\) | 9.22354 | + | 15.9756i | 0.685580 | + | 1.18746i | 0.973254 | + | 0.229731i | \(0.0737847\pi\) |
−0.287674 | + | 0.957728i | \(0.592882\pi\) | |||||||
\(182\) | −2.62912 | + | 1.51792i | −0.194883 | + | 0.112516i | ||||
\(183\) | −5.31237 | + | 9.20129i | −0.392701 | + | 0.680179i | ||||
\(184\) | −6.77962 | −0.499800 | ||||||||
\(185\) | −8.92181 | − | 10.2665i | −0.655945 | − | 0.754809i | ||||
\(186\) | −4.41998 | −0.324088 | ||||||||
\(187\) | 3.58416 | − | 6.20795i | 0.262100 | − | 0.453970i | ||||
\(188\) | 11.1857 | − | 6.45806i | 0.815800 | − | 0.471002i | ||||
\(189\) | −0.676327 | − | 1.17143i | −0.0491956 | − | 0.0852092i | ||||
\(190\) | −1.67611 | − | 11.6944i | −0.121598 | − | 0.848398i | ||||
\(191\) | − | 8.76184i | − | 0.633985i | −0.948428 | − | 0.316992i | \(-0.897327\pi\) | ||
0.948428 | − | 0.316992i | \(-0.102673\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | 13.2262 | 0.952041 | 0.476020 | − | 0.879434i | \(-0.342079\pi\) | ||||
0.476020 | + | 0.879434i | \(0.342079\pi\) | |||||||
\(194\) | −4.79895 | + | 8.31202i | −0.344545 | + | 0.596769i | ||||
\(195\) | −4.65823 | − | 1.86727i | −0.333583 | − | 0.133718i | ||||
\(196\) | 5.17033 | 0.369309 | ||||||||
\(197\) | 7.32681 | + | 4.23013i | 0.522013 | + | 0.301385i | 0.737758 | − | 0.675065i | \(-0.235885\pi\) |
−0.215745 | + | 0.976450i | \(0.569218\pi\) | |||||||
\(198\) | 1.50095 | + | 2.59973i | 0.106668 | + | 0.184755i | ||||
\(199\) | − | 7.72653i | − | 0.547719i | −0.961770 | − | 0.273860i | \(-0.911700\pi\) | ||
0.961770 | − | 0.273860i | \(-0.0883004\pi\) | |||||||
\(200\) | 4.79871 | − | 1.40441i | 0.339320 | − | 0.0993071i | ||||
\(201\) | 1.76610 | − | 3.05897i | 0.124571 | − | 0.215763i | ||||
\(202\) | 8.32311 | − | 14.4160i | 0.585612 | − | 1.01431i | ||||
\(203\) | −2.75892 | − | 4.77859i | −0.193638 | − | 0.335391i | ||||
\(204\) | 2.06800 | − | 1.19396i | 0.144789 | − | 0.0835940i | ||||
\(205\) | −6.35938 | − | 8.09398i | −0.444159 | − | 0.565308i | ||||
\(206\) | −3.35670 | + | 5.81397i | −0.233872 | + | 0.405078i | ||||
\(207\) | −3.38981 | + | 5.87132i | −0.235608 | + | 0.408085i | ||||
\(208\) | 2.24436 | 0.155618 | ||||||||
\(209\) | 13.7352 | − | 7.93002i | 0.950084 | − | 0.548531i | ||||
\(210\) | −1.86865 | − | 2.37834i | −0.128949 | − | 0.164121i | ||||
\(211\) | −14.0101 | −0.964494 | −0.482247 | − | 0.876035i | \(-0.660179\pi\) | ||||
−0.482247 | + | 0.876035i | \(0.660179\pi\) | |||||||
\(212\) | − | 6.23090i | − | 0.427940i | ||||||
\(213\) | −10.5384 | − | 6.08437i | −0.722082 | − | 0.416894i | ||||
\(214\) | − | 0.196615i | − | 0.0134403i | ||||||
\(215\) | 7.06298 | − | 1.01231i | 0.481691 | − | 0.0690391i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 2.98935 | + | 5.17770i | 0.202930 | + | 0.351485i | ||||
\(218\) | 11.6161 | − | 6.70656i | 0.786742 | − | 0.454226i | ||||
\(219\) | 3.53206 | + | 6.11771i | 0.238675 | + | 0.413397i | ||||
\(220\) | 4.14704 | + | 5.27819i | 0.279593 | + | 0.355856i | ||||
\(221\) | −5.35935 | −0.360509 | ||||||||
\(222\) | 5.11096 | − | 3.29819i | 0.343025 | − | 0.221360i | ||||
\(223\) | − | 3.10337i | − | 0.207817i | −0.994587 | − | 0.103908i | \(-0.966865\pi\) | ||
0.994587 | − | 0.103908i | \(-0.0331349\pi\) | |||||||
\(224\) | 1.17143 | + | 0.676327i | 0.0782696 | + | 0.0451890i | ||||
\(225\) | 1.18310 | − | 4.85801i | 0.0788731 | − | 0.323867i | ||||
\(226\) | 7.24481 | + | 12.5484i | 0.481918 | + | 0.834706i | ||||
\(227\) | 7.97179 | + | 13.8076i | 0.529107 | + | 0.916439i | 0.999424 | + | 0.0339421i | \(0.0108062\pi\) |
−0.470317 | + | 0.882497i | \(0.655860\pi\) | |||||||
\(228\) | 5.28332 | 0.349896 | ||||||||
\(229\) | −6.73382 | − | 11.6633i | −0.444983 | − | 0.770733i | 0.553068 | − | 0.833136i | \(-0.313457\pi\) |
−0.998051 | + | 0.0624027i | \(0.980124\pi\) | |||||||
\(230\) | −5.64052 | + | 14.0713i | −0.371925 | + | 0.927832i | ||||
\(231\) | 2.03027 | − | 3.51653i | 0.133582 | − | 0.231371i | ||||
\(232\) | 4.07927i | 0.267817i | ||||||||
\(233\) | − | 27.6386i | − | 1.81067i | −0.424703 | − | 0.905333i | \(-0.639622\pi\) | ||
0.424703 | − | 0.905333i | \(-0.360378\pi\) | |||||||
\(234\) | 1.12218 | − | 1.94367i | 0.0733592 | − | 0.127062i | ||||
\(235\) | −4.09758 | − | 28.5892i | −0.267297 | − | 1.86495i | ||||
\(236\) | − | 4.83883i | − | 0.314981i | ||||||
\(237\) | −0.294257 | + | 0.509669i | −0.0191141 | + | 0.0331066i | ||||
\(238\) | −2.79729 | − | 1.61502i | −0.181321 | − | 0.104686i | ||||
\(239\) | 11.3747 | + | 6.56719i | 0.735768 | + | 0.424796i | 0.820529 | − | 0.571605i | \(-0.193679\pi\) |
−0.0847604 | + | 0.996401i | \(0.527012\pi\) | |||||||
\(240\) | 0.317246 | + | 2.21345i | 0.0204781 | + | 0.142877i | ||||
\(241\) | 24.8544 | − | 14.3497i | 1.60101 | − | 0.924346i | 0.609730 | − | 0.792610i | \(-0.291278\pi\) |
0.991285 | − | 0.131736i | \(-0.0420553\pi\) | |||||||
\(242\) | 0.994274 | − | 1.72213i | 0.0639143 | − | 0.110703i | ||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | −9.20129 | − | 5.31237i | −0.589052 | − | 0.340089i | ||||
\(245\) | 4.30162 | − | 10.7311i | 0.274820 | − | 0.685588i | ||||
\(246\) | 3.98662 | − | 2.30168i | 0.254178 | − | 0.146750i | ||||
\(247\) | −10.2690 | − | 5.92884i | −0.653404 | − | 0.377243i | ||||
\(248\) | − | 4.41998i | − | 0.280669i | ||||||
\(249\) | −4.11489 | −0.260771 | ||||||||
\(250\) | 1.07754 | − | 11.1283i | 0.0681496 | − | 0.703815i | ||||
\(251\) | 7.61640i | 0.480743i | 0.970681 | + | 0.240372i | \(0.0772693\pi\) | ||||
−0.970681 | + | 0.240372i | \(0.922731\pi\) | |||||||
\(252\) | 1.17143 | − | 0.676327i | 0.0737933 | − | 0.0426046i | ||||
\(253\) | −20.3518 | −1.27951 | ||||||||
\(254\) | −8.91376 | + | 5.14636i | −0.559299 | + | 0.322911i | ||||
\(255\) | −0.757558 | − | 5.28554i | −0.0474401 | − | 0.330993i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 5.86850 | − | 10.1645i | 0.366067 | − | 0.634046i | −0.622880 | − | 0.782317i | \(-0.714037\pi\) |
0.988947 | + | 0.148271i | \(0.0473708\pi\) | |||||||
\(258\) | 3.19094i | 0.198659i | ||||||||
\(259\) | −7.32029 | − | 3.75649i | −0.454861 | − | 0.233417i | ||||
\(260\) | 1.86727 | − | 4.65823i | 0.115803 | − | 0.288891i | ||||
\(261\) | 3.53275 | + | 2.03964i | 0.218672 | + | 0.126250i | ||||
\(262\) | −3.29183 | + | 1.90054i | −0.203370 | + | 0.117416i | ||||
\(263\) | 12.8963 | − | 7.44568i | 0.795219 | − | 0.459120i | −0.0465775 | − | 0.998915i | \(-0.514831\pi\) |
0.841797 | + | 0.539795i | \(0.181498\pi\) | |||||||
\(264\) | −2.59973 | + | 1.50095i | −0.160002 | + | 0.0923773i | ||||
\(265\) | −12.9324 | − | 5.18399i | −0.794430 | − | 0.318450i | ||||
\(266\) | −3.57325 | − | 6.18905i | −0.219090 | − | 0.379475i | ||||
\(267\) | −16.7067 | −1.02243 | ||||||||
\(268\) | 3.05897 | + | 1.76610i | 0.186856 | + | 0.107881i | ||||
\(269\) | 11.5433 | 0.703807 | 0.351904 | − | 0.936036i | \(-0.385534\pi\) | ||||
0.351904 | + | 0.936036i | \(0.385534\pi\) | |||||||
\(270\) | 2.07553 | + | 0.831981i | 0.126312 | + | 0.0506328i | ||||
\(271\) | 0.336417 | − | 0.582692i | 0.0204359 | − | 0.0353960i | −0.855627 | − | 0.517594i | \(-0.826828\pi\) |
0.876062 | + | 0.482198i | \(0.160161\pi\) | |||||||
\(272\) | 1.19396 | + | 2.06800i | 0.0723945 | + | 0.125391i | ||||
\(273\) | −3.03584 | −0.183738 | ||||||||
\(274\) | 8.80728 | + | 5.08488i | 0.532067 | + | 0.307189i | ||||
\(275\) | 14.4053 | − | 4.21592i | 0.868672 | − | 0.254230i | ||||
\(276\) | −5.87132 | − | 3.38981i | −0.353412 | − | 0.204042i | ||||
\(277\) | 14.1902 | + | 24.5782i | 0.852607 | + | 1.47676i | 0.878847 | + | 0.477103i | \(0.158313\pi\) |
−0.0262400 | + | 0.999656i | \(0.508353\pi\) | |||||||
\(278\) | 0.463646 | + | 0.803059i | 0.0278077 | + | 0.0481643i | ||||
\(279\) | −3.82781 | − | 2.20999i | −0.229165 | − | 0.132309i | ||||
\(280\) | 2.37834 | − | 1.86865i | 0.142133 | − | 0.111673i | ||||
\(281\) | −17.3856 | − | 10.0376i | −1.03714 | − | 0.598791i | −0.118115 | − | 0.993000i | \(-0.537685\pi\) |
−0.919021 | + | 0.394209i | \(0.871018\pi\) | |||||||
\(282\) | 12.9161 | 0.769144 | ||||||||
\(283\) | 4.39309 | + | 7.60906i | 0.261142 | + | 0.452312i | 0.966546 | − | 0.256494i | \(-0.0825675\pi\) |
−0.705404 | + | 0.708806i | \(0.749234\pi\) | |||||||
\(284\) | 6.08437 | − | 10.5384i | 0.361041 | − | 0.625342i | ||||
\(285\) | 4.39562 | − | 10.9657i | 0.260374 | − | 0.649550i | ||||
\(286\) | 6.73736 | 0.398389 | ||||||||
\(287\) | −5.39252 | − | 3.11337i | −0.318310 | − | 0.183777i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 5.64892 | + | 9.78421i | 0.332289 | + | 0.575542i | ||||
\(290\) | 8.46663 | + | 3.39388i | 0.497178 | + | 0.199295i | ||||
\(291\) | −8.31202 | + | 4.79895i | −0.487260 | + | 0.281319i | ||||
\(292\) | −6.11771 | + | 3.53206i | −0.358012 | + | 0.206698i | ||||
\(293\) | 18.1855 | − | 10.4994i | 1.06241 | − | 0.613380i | 0.136309 | − | 0.990666i | \(-0.456476\pi\) |
0.926097 | + | 0.377286i | \(0.123143\pi\) | |||||||
\(294\) | 4.47763 | + | 2.58516i | 0.261141 | + | 0.150770i | ||||
\(295\) | −10.0431 | − | 4.02582i | −0.584733 | − | 0.234392i | ||||
\(296\) | 3.29819 | + | 5.11096i | 0.191704 | + | 0.297069i | ||||
\(297\) | 3.00191i | 0.174188i | ||||||||
\(298\) | 4.52842 | − | 7.84345i | 0.262324 | − | 0.454359i | ||||
\(299\) | 7.60795 | + | 13.1774i | 0.439979 | + | 0.762066i | ||||
\(300\) | 4.85801 | + | 1.18310i | 0.280477 | + | 0.0683061i | ||||
\(301\) | 3.73797 | − | 2.15812i | 0.215453 | − | 0.124392i | ||||
\(302\) | −11.4749 | −0.660308 | ||||||||
\(303\) | 14.4160 | − | 8.32311i | 0.828180 | − | 0.478150i | ||||
\(304\) | 5.28332i | 0.303019i | ||||||||
\(305\) | −18.6813 | + | 14.6777i | −1.06969 | + | 0.840444i | ||||
\(306\) | 2.38792 | 0.136508 | ||||||||
\(307\) | 16.2086i | 0.925073i | 0.886600 | + | 0.462537i | \(0.153061\pi\) | ||||
−0.886600 | + | 0.462537i | \(0.846939\pi\) | |||||||
\(308\) | 3.51653 | + | 2.03027i | 0.200373 | + | 0.115685i | ||||
\(309\) | −5.81397 | + | 3.35670i | −0.330745 | + | 0.190956i | ||||
\(310\) | −9.17377 | − | 3.67734i | −0.521035 | − | 0.208859i | ||||
\(311\) | 2.58380 | + | 1.49176i | 0.146514 | + | 0.0845899i | 0.571465 | − | 0.820626i | \(-0.306375\pi\) |
−0.424951 | + | 0.905216i | \(0.639709\pi\) | |||||||
\(312\) | 1.94367 | + | 1.12218i | 0.110039 | + | 0.0635309i | ||||
\(313\) | 2.25748 | − | 3.91006i | 0.127600 | − | 0.221010i | −0.795146 | − | 0.606418i | \(-0.792606\pi\) |
0.922746 | + | 0.385408i | \(0.125939\pi\) | |||||||
\(314\) | −5.04062 | + | 2.91020i | −0.284458 | + | 0.164232i | ||||
\(315\) | −0.429124 | − | 2.99403i | −0.0241784 | − | 0.168694i | ||||
\(316\) | −0.509669 | − | 0.294257i | −0.0286711 | − | 0.0165533i | ||||
\(317\) | 5.91704 | + | 3.41620i | 0.332334 | + | 0.191873i | 0.656877 | − | 0.753998i | \(-0.271877\pi\) |
−0.324543 | + | 0.945871i | \(0.605210\pi\) | |||||||
\(318\) | 3.11545 | − | 5.39612i | 0.174706 | − | 0.302599i | ||||
\(319\) | 12.2456i | 0.685622i | ||||||||
\(320\) | −2.21345 | + | 0.317246i | −0.123736 | + | 0.0177346i | ||||
\(321\) | 0.0983076 | − | 0.170274i | 0.00548700 | − | 0.00950376i | ||||
\(322\) | 9.17048i | 0.511051i | ||||||||
\(323\) | − | 12.6162i | − | 0.701982i | ||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | −8.11474 | − | 7.75112i | −0.450125 | − | 0.429955i | ||||
\(326\) | 2.20296 | + | 3.81563i | 0.122010 | + | 0.211328i | ||||
\(327\) | 13.4131 | 0.741747 | ||||||||
\(328\) | 2.30168 | + | 3.98662i | 0.127089 | + | 0.220124i | ||||
\(329\) | −8.73552 | − | 15.1304i | −0.481605 | − | 0.834164i | ||||
\(330\) | 0.952343 | + | 6.64457i | 0.0524247 | + | 0.365772i | ||||
\(331\) | −8.89801 | − | 5.13727i | −0.489079 | − | 0.282370i | 0.235113 | − | 0.971968i | \(-0.424454\pi\) |
−0.724192 | + | 0.689598i | \(0.757787\pi\) | |||||||
\(332\) | − | 4.11489i | − | 0.225834i | ||||||
\(333\) | 6.07532 | − | 0.300839i | 0.332925 | − | 0.0164859i | ||||
\(334\) | −21.6698 | −1.18572 | ||||||||
\(335\) | 6.21058 | − | 4.87961i | 0.339320 | − | 0.266601i | ||||
\(336\) | 0.676327 | + | 1.17143i | 0.0368967 | + | 0.0639069i | ||||
\(337\) | −17.6489 | + | 10.1896i | −0.961395 | + | 0.555062i | −0.896602 | − | 0.442837i | \(-0.853972\pi\) |
−0.0647931 | + | 0.997899i | \(0.520639\pi\) | |||||||
\(338\) | 3.98142 | + | 6.89603i | 0.216561 | + | 0.375095i | ||||
\(339\) | 14.4896i | 0.786968i | ||||||||
\(340\) | 5.28554 | − | 0.757558i | 0.286649 | − | 0.0410843i | ||||
\(341\) | − | 13.2684i | − | 0.718522i | ||||||
\(342\) | 4.57549 | + | 2.64166i | 0.247414 | + | 0.142845i | ||||
\(343\) | − | 16.4622i | − | 0.888878i | ||||||
\(344\) | −3.19094 | −0.172044 | ||||||||
\(345\) | −11.9205 | + | 9.36582i | −0.641776 | + | 0.504239i | ||||
\(346\) | 14.2574 | − | 8.23149i | 0.766480 | − | 0.442528i | ||||
\(347\) | 2.73199 | 0.146661 | 0.0733304 | − | 0.997308i | \(-0.476637\pi\) | ||||
0.0733304 | + | 0.997308i | \(0.476637\pi\) | |||||||
\(348\) | −2.03964 | + | 3.53275i | −0.109336 | + | 0.189375i | ||||
\(349\) | 6.08918 | − | 10.5468i | 0.325946 | − | 0.564556i | −0.655757 | − | 0.754972i | \(-0.727650\pi\) |
0.981703 | + | 0.190416i | \(0.0609838\pi\) | |||||||
\(350\) | −1.89969 | − | 6.49099i | −0.101543 | − | 0.346958i | ||||
\(351\) | 1.94367 | − | 1.12218i | 0.103746 | − | 0.0598975i | ||||
\(352\) | −1.50095 | − | 2.59973i | −0.0800011 | − | 0.138566i | ||||
\(353\) | −12.4776 | + | 21.6118i | −0.664115 | + | 1.15028i | 0.315410 | + | 0.948956i | \(0.397858\pi\) |
−0.979525 | + | 0.201325i | \(0.935475\pi\) | |||||||
\(354\) | 2.41941 | − | 4.19055i | 0.128590 | − | 0.222725i | ||||
\(355\) | −16.8107 | − | 21.3961i | −0.892221 | − | 1.13559i | ||||
\(356\) | − | 16.7067i | − | 0.885451i | ||||||
\(357\) | −1.61502 | − | 2.79729i | −0.0854757 | − | 0.148048i | ||||
\(358\) | −18.4058 | − | 10.6266i | −0.972777 | − | 0.561633i | ||||
\(359\) | −32.9716 | −1.74018 | −0.870088 | − | 0.492897i | \(-0.835938\pi\) | ||||
−0.870088 | + | 0.492897i | \(0.835938\pi\) | |||||||
\(360\) | −0.831981 | + | 2.07553i | −0.0438493 | + | 0.109390i | ||||
\(361\) | 4.45674 | − | 7.71930i | 0.234565 | − | 0.406279i | ||||
\(362\) | −18.4471 | −0.969557 | ||||||||
\(363\) | 1.72213 | − | 0.994274i | 0.0903885 | − | 0.0521858i | ||||
\(364\) | − | 3.03584i | − | 0.159121i | ||||||
\(365\) | 2.24106 | + | 15.6361i | 0.117303 | + | 0.818430i | ||||
\(366\) | −5.31237 | − | 9.20129i | −0.277682 | − | 0.480959i | ||||
\(367\) | 25.6297 | − | 14.7973i | 1.33786 | − | 0.772413i | 0.351369 | − | 0.936237i | \(-0.385716\pi\) |
0.986490 | + | 0.163824i | \(0.0523830\pi\) | |||||||
\(368\) | 3.38981 | − | 5.87132i | 0.176706 | − | 0.306064i | ||||
\(369\) | 4.60335 | 0.239641 | ||||||||
\(370\) | 13.3520 | − | 2.59326i | 0.694136 | − | 0.134817i | ||||
\(371\) | −8.42825 | −0.437573 | ||||||||
\(372\) | 2.20999 | − | 3.82781i | 0.114583 | − | 0.198463i | ||||
\(373\) | 1.28458 | − | 0.741651i | 0.0665129 | − | 0.0384012i | −0.466375 | − | 0.884587i | \(-0.654440\pi\) |
0.532888 | + | 0.846186i | \(0.321107\pi\) | |||||||
\(374\) | 3.58416 | + | 6.20795i | 0.185333 | + | 0.321005i | ||||
\(375\) | 6.49732 | − | 9.09861i | 0.335520 | − | 0.469850i | ||||
\(376\) | 12.9161i | 0.666098i | ||||||||
\(377\) | 7.92877 | − | 4.57768i | 0.408352 | − | 0.235762i | ||||
\(378\) | 1.35265 | 0.0695730 | ||||||||
\(379\) | −6.13208 | + | 10.6211i | −0.314984 | + | 0.545568i | −0.979434 | − | 0.201764i | \(-0.935332\pi\) |
0.664450 | + | 0.747333i | \(0.268666\pi\) | |||||||
\(380\) | 10.9657 | + | 4.39562i | 0.562527 | + | 0.225491i | ||||
\(381\) | −10.2927 | −0.527312 | ||||||||
\(382\) | 7.58798 | + | 4.38092i | 0.388235 | + | 0.224147i | ||||
\(383\) | −6.12268 | − | 10.6048i | −0.312855 | − | 0.541880i | 0.666125 | − | 0.745841i | \(-0.267952\pi\) |
−0.978979 | + | 0.203961i | \(0.934619\pi\) | |||||||
\(384\) | − | 1.00000i | − | 0.0510310i | ||||||
\(385\) | 7.13957 | − | 5.60951i | 0.363866 | − | 0.285887i | ||||
\(386\) | −6.61309 | + | 11.4542i | −0.336597 | + | 0.583003i | ||||
\(387\) | −1.59547 | + | 2.76343i | −0.0811023 | + | 0.140473i | ||||
\(388\) | −4.79895 | − | 8.31202i | −0.243630 | − | 0.421979i | ||||
\(389\) | 3.72965 | − | 2.15332i | 0.189101 | − | 0.109177i | −0.402461 | − | 0.915437i | \(-0.631845\pi\) |
0.591562 | + | 0.806260i | \(0.298512\pi\) | |||||||
\(390\) | 3.94621 | − | 3.10051i | 0.199824 | − | 0.157000i | ||||
\(391\) | −8.09460 | + | 14.0203i | −0.409361 | + | 0.709035i | ||||
\(392\) | −2.58516 | + | 4.47763i | −0.130570 | + | 0.226155i | ||||
\(393\) | −3.80107 | −0.191739 | ||||||||
\(394\) | −7.32681 | + | 4.23013i | −0.369119 | + | 0.213111i | ||||
\(395\) | −1.03477 | + | 0.813014i | −0.0520651 | + | 0.0409072i | ||||
\(396\) | −3.00191 | −0.150852 | ||||||||
\(397\) | − | 3.36805i | − | 0.169038i | −0.996422 | − | 0.0845189i | \(-0.973065\pi\) | ||
0.996422 | − | 0.0845189i | \(-0.0269353\pi\) | |||||||
\(398\) | 6.69137 | + | 3.86326i | 0.335408 | + | 0.193648i | ||||
\(399\) | − | 7.14651i | − | 0.357773i | ||||||
\(400\) | −1.18310 | + | 4.85801i | −0.0591548 | + | 0.242901i | ||||
\(401\) | − | 23.8277i | − | 1.18990i | −0.803763 | − | 0.594950i | \(-0.797172\pi\) | ||
0.803763 | − | 0.594950i | \(-0.202828\pi\) | |||||||
\(402\) | 1.76610 | + | 3.05897i | 0.0880849 | + | 0.152567i | ||||
\(403\) | −8.59099 | + | 4.96001i | −0.427947 | + | 0.247076i | ||||
\(404\) | 8.32311 | + | 14.4160i | 0.414090 | + | 0.717225i | ||||
\(405\) | 1.38147 | + | 1.75828i | 0.0686457 | + | 0.0873696i | ||||
\(406\) | 5.51784 | 0.273846 | ||||||||
\(407\) | 9.90087 | + | 15.3426i | 0.490768 | + | 0.760506i | ||||
\(408\) | 2.38792i | 0.118220i | ||||||||
\(409\) | 29.8037 | + | 17.2072i | 1.47370 | + | 0.850840i | 0.999561 | − | 0.0296121i | \(-0.00942722\pi\) |
0.474136 | + | 0.880452i | \(0.342761\pi\) | |||||||
\(410\) | 10.1893 | − | 1.46039i | 0.503213 | − | 0.0721237i | ||||
\(411\) | 5.08488 | + | 8.80728i | 0.250819 | + | 0.434431i | ||||
\(412\) | −3.35670 | − | 5.81397i | −0.165373 | − | 0.286434i | ||||
\(413\) | −6.54526 | −0.322071 | ||||||||
\(414\) | −3.38981 | − | 5.87132i | −0.166600 | − | 0.288560i | ||||
\(415\) | −8.54057 | − | 3.42351i | −0.419240 | − | 0.168054i | ||||
\(416\) | −1.12218 | + | 1.94367i | −0.0550194 | + | 0.0952964i | ||||
\(417\) | 0.927293i | 0.0454097i | ||||||||
\(418\) | 15.8600i | 0.775740i | ||||||||
\(419\) | 8.20896 | − | 14.2183i | 0.401034 | − | 0.694611i | −0.592817 | − | 0.805337i | \(-0.701984\pi\) |
0.993851 | + | 0.110726i | \(0.0353176\pi\) | |||||||
\(420\) | 2.99403 | − | 0.429124i | 0.146094 | − | 0.0209391i | ||||
\(421\) | 16.8650i | 0.821952i | 0.911646 | + | 0.410976i | \(0.134812\pi\) | ||||
−0.911646 | + | 0.410976i | \(0.865188\pi\) | |||||||
\(422\) | 7.00504 | − | 12.1331i | 0.341000 | − | 0.590630i | ||||
\(423\) | 11.1857 | + | 6.45806i | 0.543867 | + | 0.314002i | ||||
\(424\) | 5.39612 | + | 3.11545i | 0.262059 | + | 0.151300i | ||||
\(425\) | 2.82514 | − | 11.6006i | 0.137039 | − | 0.562709i | ||||
\(426\) | 10.5384 | − | 6.08437i | 0.510589 | − | 0.294789i | ||||
\(427\) | −7.18579 | + | 12.4462i | −0.347745 | + | 0.602312i | ||||
\(428\) | 0.170274 | + | 0.0983076i | 0.00823049 | + | 0.00475188i | ||||
\(429\) | 5.83473 | + | 3.36868i | 0.281703 | + | 0.162641i | ||||
\(430\) | −2.65480 | + | 6.62288i | −0.128026 | + | 0.319384i | ||||
\(431\) | −20.9618 | + | 12.1023i | −1.00969 | + | 0.582946i | −0.911102 | − | 0.412182i | \(-0.864767\pi\) |
−0.0985911 | + | 0.995128i | \(0.531434\pi\) | |||||||
\(432\) | −0.866025 | − | 0.500000i | −0.0416667 | − | 0.0240563i | ||||
\(433\) | 27.2175i | 1.30799i | 0.756499 | + | 0.653995i | \(0.226908\pi\) | ||||
−0.756499 | + | 0.653995i | \(0.773092\pi\) | |||||||
\(434\) | −5.97870 | −0.286987 | ||||||||
\(435\) | 5.63538 | + | 7.17250i | 0.270196 | + | 0.343895i | ||||
\(436\) | 13.4131i | 0.642372i | ||||||||
\(437\) | −31.0201 | + | 17.9094i | −1.48389 | + | 0.856725i | ||||
\(438\) | −7.06413 | −0.337537 | ||||||||
\(439\) | −0.303940 | + | 0.175480i | −0.0145063 | + | 0.00837519i | −0.507236 | − | 0.861807i | \(-0.669333\pi\) |
0.492729 | + | 0.870183i | \(0.335999\pi\) | |||||||
\(440\) | −6.64457 | + | 0.952343i | −0.316767 | + | 0.0454012i | ||||
\(441\) | 2.58516 | + | 4.47763i | 0.123103 | + | 0.213221i | ||||
\(442\) | 2.67968 | − | 4.64134i | 0.127459 | − | 0.220766i | ||||
\(443\) | 29.6858i | 1.41042i | 0.709001 | + | 0.705208i | \(0.249146\pi\) | ||||
−0.709001 | + | 0.705208i | \(0.750854\pi\) | |||||||
\(444\) | 0.300839 | + | 6.07532i | 0.0142772 | + | 0.288322i | ||||
\(445\) | −34.6751 | − | 13.8996i | −1.64376 | − | 0.658906i | ||||
\(446\) | 2.68760 | + | 1.55168i | 0.127261 | + | 0.0734744i | ||||
\(447\) | 7.84345 | − | 4.52842i | 0.370983 | − | 0.214187i | ||||
\(448\) | −1.17143 | + | 0.676327i | −0.0553450 | + | 0.0319534i | ||||
\(449\) | 17.7164 | − | 10.2286i | 0.836090 | − | 0.482717i | −0.0198434 | − | 0.999803i | \(-0.506317\pi\) |
0.855933 | + | 0.517086i | \(0.172983\pi\) | |||||||
\(450\) | 3.61561 | + | 3.45360i | 0.170442 | + | 0.162804i | ||||
\(451\) | 6.90942 | + | 11.9675i | 0.325352 | + | 0.563526i | ||||
\(452\) | −14.4896 | −0.681535 | ||||||||
\(453\) | −9.93758 | − | 5.73747i | −0.466908 | − | 0.269570i | ||||
\(454\) | −15.9436 | −0.748270 | ||||||||
\(455\) | −6.30097 | − | 2.52576i | −0.295394 | − | 0.118410i | ||||
\(456\) | −2.64166 | + | 4.57549i | −0.123707 | + | 0.214267i | ||||
\(457\) | −16.1935 | − | 28.0480i | −0.757502 | − | 1.31203i | −0.944121 | − | 0.329599i | \(-0.893086\pi\) |
0.186619 | − | 0.982432i | \(-0.440247\pi\) | |||||||
\(458\) | 13.4676 | 0.629301 | ||||||||
\(459\) | 2.06800 | + | 1.19396i | 0.0965260 | + | 0.0557293i | ||||
\(460\) | −9.36582 | − | 11.9205i | −0.436684 | − | 0.555795i | ||||
\(461\) | −16.5318 | − | 9.54466i | −0.769964 | − | 0.444539i | 0.0628977 | − | 0.998020i | \(-0.479966\pi\) |
−0.832862 | + | 0.553481i | \(0.813299\pi\) | |||||||
\(462\) | 2.03027 | + | 3.51653i | 0.0944568 | + | 0.163604i | ||||
\(463\) | 9.39427 | + | 16.2714i | 0.436589 | + | 0.756194i | 0.997424 | − | 0.0717334i | \(-0.0228531\pi\) |
−0.560835 | + | 0.827928i | \(0.689520\pi\) | |||||||
\(464\) | −3.53275 | − | 2.03964i | −0.164004 | − | 0.0946877i | ||||
\(465\) | −6.10605 | − | 7.77155i | −0.283161 | − | 0.360397i | ||||
\(466\) | 23.9357 | + | 13.8193i | 1.10880 | + | 0.640167i | ||||
\(467\) | −2.97790 | −0.137801 | −0.0689004 | − | 0.997624i | \(-0.521949\pi\) | ||||
−0.0689004 | + | 0.997624i | \(0.521949\pi\) | |||||||
\(468\) | 1.12218 | + | 1.94367i | 0.0518728 | + | 0.0898463i | ||||
\(469\) | 2.38892 | − | 4.13773i | 0.110310 | − | 0.191062i | ||||
\(470\) | 26.8077 | + | 10.7460i | 1.23655 | + | 0.495675i | ||||
\(471\) | −5.82040 | −0.268190 | ||||||||
\(472\) | 4.19055 | + | 2.41941i | 0.192886 | + | 0.111363i | ||||
\(473\) | −9.57891 | −0.440439 | ||||||||
\(474\) | −0.294257 | − | 0.509669i | −0.0135157 | − | 0.0234099i | ||||
\(475\) | 18.2465 | − | 19.1024i | 0.837205 | − | 0.876480i | ||||
\(476\) | 2.79729 | − | 1.61502i | 0.128214 | − | 0.0740241i | ||||
\(477\) | 5.39612 | − | 3.11545i | 0.247071 | − | 0.142647i | ||||
\(478\) | −11.3747 | + | 6.56719i | −0.520267 | + | 0.300376i | ||||
\(479\) | 28.9748 | + | 16.7286i | 1.32389 | + | 0.764350i | 0.984347 | − | 0.176239i | \(-0.0563932\pi\) |
0.339546 | + | 0.940589i | \(0.389727\pi\) | |||||||
\(480\) | −2.07553 | − | 0.831981i | −0.0947344 | − | 0.0379746i | ||||
\(481\) | 6.23287 | − | 12.1460i | 0.284194 | − | 0.553811i | ||||
\(482\) | 28.6994i | 1.30722i | ||||||||
\(483\) | −4.58524 | + | 7.94187i | −0.208636 | + | 0.361367i | ||||
\(484\) | 0.994274 | + | 1.72213i | 0.0451943 | + | 0.0782788i | ||||
\(485\) | −21.2445 | + | 3.04489i | −0.964661 | + | 0.138261i | ||||
\(486\) | −0.866025 | + | 0.500000i | −0.0392837 | + | 0.0226805i | ||||
\(487\) | −3.98263 | −0.180470 | −0.0902350 | − | 0.995920i | \(-0.528762\pi\) | ||||
−0.0902350 | + | 0.995920i | \(0.528762\pi\) | |||||||
\(488\) | 9.20129 | − | 5.31237i | 0.416523 | − | 0.240479i | ||||
\(489\) | 4.40591i | 0.199242i | ||||||||
\(490\) | 7.14264 | + | 9.09088i | 0.322671 | + | 0.410684i | ||||
\(491\) | −39.2680 | −1.77214 | −0.886070 | − | 0.463551i | \(-0.846575\pi\) | ||||
−0.886070 | + | 0.463551i | \(0.846575\pi\) | |||||||
\(492\) | 4.60335i | 0.207535i | ||||||||
\(493\) | 8.43593 | + | 4.87049i | 0.379935 | + | 0.219356i | ||||
\(494\) | 10.2690 | − | 5.92884i | 0.462026 | − | 0.266751i | ||||
\(495\) | −2.49753 | + | 6.23054i | −0.112256 | + | 0.280042i | ||||
\(496\) | 3.82781 | + | 2.20999i | 0.171874 | + | 0.0992314i | ||||
\(497\) | −14.2549 | − | 8.23005i | −0.639418 | − | 0.369168i | ||||
\(498\) | 2.05745 | − | 3.56360i | 0.0921964 | − | 0.159689i | ||||
\(499\) | −11.2105 | + | 6.47239i | −0.501851 | + | 0.289744i | −0.729478 | − | 0.684005i | \(-0.760237\pi\) |
0.227627 | + | 0.973749i | \(0.426903\pi\) | |||||||
\(500\) | 9.09861 | + | 6.49732i | 0.406902 | + | 0.290569i | ||||
\(501\) | −18.7666 | − | 10.8349i | −0.838431 | − | 0.484069i | ||||
\(502\) | −6.59600 | − | 3.80820i | −0.294394 | − | 0.169968i | ||||
\(503\) | −3.46336 | + | 5.99871i | −0.154424 | + | 0.267469i | −0.932849 | − | 0.360268i | \(-0.882685\pi\) |
0.778425 | + | 0.627737i | \(0.216019\pi\) | |||||||
\(504\) | 1.35265i | 0.0602520i | ||||||||
\(505\) | 36.8455 | − | 5.28094i | 1.63961 | − | 0.234999i | ||||
\(506\) | 10.1759 | − | 17.6252i | 0.452374 | − | 0.783534i | ||||
\(507\) | 7.96285i | 0.353643i | ||||||||
\(508\) | − | 10.2927i | − | 0.456666i | ||||||
\(509\) | −11.5336 | + | 19.9767i | −0.511216 | + | 0.885452i | 0.488700 | + | 0.872452i | \(0.337471\pi\) |
−0.999916 | + | 0.0129996i | \(0.995862\pi\) | |||||||
\(510\) | 4.95619 | + | 1.98671i | 0.219464 | + | 0.0879728i | ||||
\(511\) | 4.77766 | + | 8.27515i | 0.211351 | + | 0.366071i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 2.64166 | + | 4.57549i | 0.116632 | + | 0.202013i | ||||
\(514\) | 5.86850 | + | 10.1645i | 0.258848 | + | 0.448338i | ||||
\(515\) | −14.8598 | + | 2.12980i | −0.654799 | + | 0.0938500i | ||||
\(516\) | −2.76343 | − | 1.59547i | −0.121653 | − | 0.0702366i | ||||
\(517\) | 38.7730i | 1.70523i | ||||||||
\(518\) | 6.91336 | − | 4.46131i | 0.303756 | − | 0.196019i | ||||
\(519\) | 16.4630 | 0.722645 | ||||||||
\(520\) | 3.10051 | + | 3.94621i | 0.135966 | + | 0.173053i | ||||
\(521\) | −14.6787 | − | 25.4242i | −0.643084 | − | 1.11385i | −0.984741 | − | 0.174029i | \(-0.944321\pi\) |
0.341657 | − | 0.939825i | \(-0.389012\pi\) | |||||||
\(522\) | −3.53275 | + | 2.03964i | −0.154624 | + | 0.0892724i | ||||
\(523\) | 3.65507 | + | 6.33077i | 0.159825 | + | 0.276825i | 0.934806 | − | 0.355160i | \(-0.115574\pi\) |
−0.774980 | + | 0.631985i | \(0.782240\pi\) | |||||||
\(524\) | − | 3.80107i | − | 0.166051i | ||||||
\(525\) | 1.60032 | − | 6.57121i | 0.0698437 | − | 0.286791i | ||||
\(526\) | 14.8914i | 0.649294i | ||||||||
\(527\) | −9.14051 | − | 5.27728i | −0.398167 | − | 0.229882i | ||||
\(528\) | − | 3.00191i | − | 0.130641i | ||||||
\(529\) | 22.9632 | 0.998400 | ||||||||
\(530\) | 10.9557 | − | 8.60778i | 0.475884 | − | 0.373898i | ||||
\(531\) | 4.19055 | − | 2.41941i | 0.181854 | − | 0.104994i | ||||
\(532\) | 7.14651 | 0.309840 | ||||||||
\(533\) | 5.16579 | − | 8.94741i | 0.223755 | − | 0.387555i | ||||
\(534\) | 8.35333 | − | 14.4684i | 0.361484 | − | 0.626109i | ||||
\(535\) | 0.345705 | − | 0.271618i | 0.0149461 | − | 0.0117430i | ||||
\(536\) | −3.05897 | + | 1.76610i | −0.132127 | + | 0.0762837i | ||||
\(537\) | −10.6266 | − | 18.4058i | −0.458571 | − | 0.794269i | ||||
\(538\) | −5.77165 | + | 9.99679i | −0.248833 | + | 0.430992i | ||||
\(539\) | −7.76042 | + | 13.4414i | −0.334265 | + | 0.578964i | ||||
\(540\) | −1.75828 | + | 1.38147i | −0.0756643 | + | 0.0594489i | ||||
\(541\) | − | 20.4675i | − | 0.879965i | −0.898006 | − | 0.439982i | \(-0.854985\pi\) | ||
0.898006 | − | 0.439982i | \(-0.145015\pi\) | |||||||
\(542\) | 0.336417 | + | 0.582692i | 0.0144504 | + | 0.0250288i | ||||
\(543\) | −15.9756 | − | 9.22354i | −0.685580 | − | 0.395820i | ||||
\(544\) | −2.38792 | −0.102381 | ||||||||
\(545\) | 27.8393 | + | 11.1595i | 1.19250 | + | 0.478019i | ||||
\(546\) | 1.51792 | − | 2.62912i | 0.0649610 | − | 0.112516i | ||||
\(547\) | −11.7724 | −0.503352 | −0.251676 | − | 0.967812i | \(-0.580982\pi\) | ||||
−0.251676 | + | 0.967812i | \(0.580982\pi\) | |||||||
\(548\) | −8.80728 | + | 5.08488i | −0.376228 | + | 0.217215i | ||||
\(549\) | − | 10.6247i | − | 0.453452i | ||||||
\(550\) | −3.55155 | + | 14.5833i | −0.151438 | + | 0.621834i | ||||
\(551\) | 10.7760 | + | 18.6647i | 0.459075 | + | 0.795141i | ||||
\(552\) | 5.87132 | − | 3.38981i | 0.249900 | − | 0.144280i | ||||
\(553\) | −0.398029 | + | 0.689406i | −0.0169259 | + | 0.0293165i | ||||
\(554\) | −28.3804 | −1.20577 | ||||||||
\(555\) | 12.8598 | + | 4.43015i | 0.545867 | + | 0.188050i | ||||
\(556\) | −0.927293 | −0.0393260 | ||||||||
\(557\) | 2.72821 | − | 4.72539i | 0.115598 | − | 0.200221i | −0.802421 | − | 0.596759i | \(-0.796455\pi\) |
0.918019 | + | 0.396537i | \(0.129788\pi\) | |||||||
\(558\) | 3.82781 | − | 2.20999i | 0.162044 | − | 0.0935562i | ||||
\(559\) | 3.58081 | + | 6.20214i | 0.151452 | + | 0.262323i | ||||
\(560\) | 0.429124 | + | 2.99403i | 0.0181338 | + | 0.126521i | ||||
\(561\) | 7.16832i | 0.302647i | ||||||||
\(562\) | 17.3856 | − | 10.0376i | 0.733366 | − | 0.423409i | ||||
\(563\) | −14.7884 | −0.623255 | −0.311627 | − | 0.950204i | \(-0.600874\pi\) | ||||
−0.311627 | + | 0.950204i | \(0.600874\pi\) | |||||||
\(564\) | −6.45806 | + | 11.1857i | −0.271933 | + | 0.471002i | ||||
\(565\) | −12.0551 | + | 30.0736i | −0.507162 | + | 1.26521i | ||||
\(566\) | −8.78618 | −0.369311 | ||||||||
\(567\) | 1.17143 | + | 0.676327i | 0.0491956 | + | 0.0284031i | ||||
\(568\) | 6.08437 | + | 10.5384i | 0.255295 | + | 0.442183i | ||||
\(569\) | 7.17981i | 0.300993i | 0.988611 | + | 0.150497i | \(0.0480873\pi\) | ||||
−0.988611 | + | 0.150497i | \(0.951913\pi\) | |||||||
\(570\) | 7.29873 | + | 9.28956i | 0.305710 | + | 0.389097i | ||||
\(571\) | −7.05703 | + | 12.2231i | −0.295328 | + | 0.511523i | −0.975061 | − | 0.221937i | \(-0.928762\pi\) |
0.679733 | + | 0.733459i | \(0.262096\pi\) | |||||||
\(572\) | −3.36868 | + | 5.83473i | −0.140852 | + | 0.243962i | ||||
\(573\) | 4.38092 | + | 7.58798i | 0.183016 | + | 0.316992i | ||||
\(574\) | 5.39252 | − | 3.11337i | 0.225079 | − | 0.129950i | ||||
\(575\) | −32.5334 | + | 9.52139i | −1.35674 | + | 0.397070i | ||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | −6.70480 | + | 11.6130i | −0.279124 | + | 0.483458i | −0.971167 | − | 0.238399i | \(-0.923378\pi\) |
0.692043 | + | 0.721856i | \(0.256711\pi\) | |||||||
\(578\) | −11.2978 | −0.469928 | ||||||||
\(579\) | −11.4542 | + | 6.61309i | −0.476020 | + | 0.274830i | ||||
\(580\) | −7.17250 | + | 5.63538i | −0.297822 | + | 0.233996i | ||||
\(581\) | −5.56603 | −0.230918 | ||||||||
\(582\) | − | 9.59790i | − | 0.397846i | ||||||
\(583\) | 16.1986 | + | 9.35229i | 0.670879 | + | 0.387332i | ||||
\(584\) | − | 7.06413i | − | 0.292316i | ||||||
\(585\) | 4.96778 | − | 0.712014i | 0.205392 | − | 0.0294381i | ||||
\(586\) | 20.9988i | 0.867451i | ||||||||
\(587\) | 11.2829 | + | 19.5426i | 0.465697 | + | 0.806611i | 0.999233 | − | 0.0391668i | \(-0.0124704\pi\) |
−0.533536 | + | 0.845777i | \(0.679137\pi\) | |||||||
\(588\) | −4.47763 | + | 2.58516i | −0.184655 | + | 0.106610i | ||||
\(589\) | −11.6761 | − | 20.2236i | −0.481104 | − | 0.833297i | ||||
\(590\) | 8.50801 | − | 6.68468i | 0.350269 | − | 0.275204i | ||||
\(591\) | −8.46027 | −0.348009 | ||||||||
\(592\) | −6.07532 | + | 0.300839i | −0.249694 | + | 0.0123644i | ||||
\(593\) | 1.74844i | 0.0717997i | 0.999355 | + | 0.0358998i | \(0.0114297\pi\) | ||||
−0.999355 | + | 0.0358998i | \(0.988570\pi\) | |||||||
\(594\) | −2.59973 | − | 1.50095i | −0.106668 | − | 0.0615849i | ||||
\(595\) | −1.02471 | − | 7.14951i | −0.0420092 | − | 0.293101i | ||||
\(596\) | 4.52842 | + | 7.84345i | 0.185491 | + | 0.321280i | ||||
\(597\) | 3.86326 | + | 6.69137i | 0.158113 | + | 0.273860i | ||||
\(598\) | −15.2159 | −0.622224 | ||||||||
\(599\) | −14.3049 | − | 24.7768i | −0.584481 | − | 1.01235i | −0.994940 | − | 0.100472i | \(-0.967965\pi\) |
0.410459 | − | 0.911879i | \(-0.365369\pi\) | |||||||
\(600\) | −3.45360 | + | 3.61561i | −0.140993 | + | 0.147607i | ||||
\(601\) | −6.17497 | + | 10.6954i | −0.251882 | + | 0.436273i | −0.964044 | − | 0.265743i | \(-0.914383\pi\) |
0.712162 | + | 0.702015i | \(0.247716\pi\) | |||||||
\(602\) | 4.31624i | 0.175917i | ||||||||
\(603\) | 3.53219i | 0.143842i | ||||||||
\(604\) | 5.73747 | − | 9.93758i | 0.233454 | − | 0.404355i | ||||
\(605\) | 4.40155 | − | 0.630858i | 0.178948 | − | 0.0256480i | ||||
\(606\) | 16.6462i | 0.676206i | ||||||||
\(607\) | −18.1702 | + | 31.4717i | −0.737505 | + | 1.27740i | 0.216111 | + | 0.976369i | \(0.430663\pi\) |
−0.953616 | + | 0.301027i | \(0.902671\pi\) | |||||||
\(608\) | −4.57549 | − | 2.64166i | −0.185561 | − | 0.107133i | ||||
\(609\) | 4.77859 | + | 2.75892i | 0.193638 | + | 0.111797i | ||||
\(610\) | −3.37065 | − | 23.5173i | −0.136474 | − | 0.952187i | ||||
\(611\) | 25.1047 | − | 14.4942i | 1.01563 | − | 0.586373i | ||||
\(612\) | −1.19396 | + | 2.06800i | −0.0482630 | + | 0.0835940i | ||||
\(613\) | 0.816507 | + | 0.471410i | 0.0329784 | + | 0.0190401i | 0.516399 | − | 0.856348i | \(-0.327272\pi\) |
−0.483420 | + | 0.875388i | \(0.660606\pi\) | |||||||
\(614\) | −14.0371 | − | 8.10430i | −0.566489 | − | 0.327063i | ||||
\(615\) | 9.55438 | + | 3.82990i | 0.385270 | + | 0.154437i | ||||
\(616\) | −3.51653 | + | 2.03027i | −0.141685 | + | 0.0818020i | ||||
\(617\) | 8.06384 | + | 4.65566i | 0.324638 | + | 0.187430i | 0.653458 | − | 0.756963i | \(-0.273318\pi\) |
−0.328820 | + | 0.944393i | \(0.606651\pi\) | |||||||
\(618\) | − | 6.71339i | − | 0.270052i | ||||||
\(619\) | −0.187571 | −0.00753912 | −0.00376956 | − | 0.999993i | \(-0.501200\pi\) | ||||
−0.00376956 | + | 0.999993i | \(0.501200\pi\) | |||||||
\(620\) | 7.77155 | − | 6.10605i | 0.312113 | − | 0.245225i | ||||
\(621\) | − | 6.77962i | − | 0.272057i | ||||||
\(622\) | −2.58380 | + | 1.49176i | −0.103601 | + | 0.0598141i | ||||
\(623\) | −22.5983 | −0.905383 | ||||||||
\(624\) | −1.94367 | + | 1.12218i | −0.0778092 | + | 0.0449232i | ||||
\(625\) | 21.0552 | − | 13.4788i | 0.842210 | − | 0.539150i | ||||
\(626\) | 2.25748 | + | 3.91006i | 0.0902269 | + | 0.156278i | ||||
\(627\) | −7.93002 | + | 13.7352i | −0.316695 | + | 0.548531i | ||||
\(628\) | − | 5.82040i | − | 0.232259i | ||||||
\(629\) | 14.5074 | − | 0.718380i | 0.578447 | − | 0.0286437i | ||||
\(630\) | 2.80747 | + | 1.12538i | 0.111852 | + | 0.0448363i | ||||
\(631\) | 24.8688 | + | 14.3580i | 0.990013 | + | 0.571584i | 0.905278 | − | 0.424820i | \(-0.139662\pi\) |
0.0847345 | + | 0.996404i | \(0.472996\pi\) | |||||||
\(632\) | 0.509669 | − | 0.294257i | 0.0202735 | − | 0.0117049i | ||||
\(633\) | 12.1331 | − | 7.00504i | 0.482247 | − | 0.278425i | ||||
\(634\) | −5.91704 | + | 3.41620i | −0.234995 | + | 0.135675i | ||||
\(635\) | −21.3628 | − | 8.56335i | −0.847757 | − | 0.339826i | ||||
\(636\) | 3.11545 | + | 5.39612i | 0.123536 | + | 0.213970i | ||||
\(637\) | 11.6041 | 0.459770 | ||||||||
\(638\) | −10.6050 | − | 6.12280i | −0.419856 | − | 0.242404i | ||||
\(639\) | 12.1687 | 0.481388 | ||||||||
\(640\) | 0.831981 | − | 2.07553i | 0.0328870 | − | 0.0820424i | ||||
\(641\) | 4.13811 | − | 7.16743i | 0.163446 | − | 0.283096i | −0.772657 | − | 0.634824i | \(-0.781072\pi\) |
0.936102 | + | 0.351728i | \(0.114406\pi\) | |||||||
\(642\) | 0.0983076 | + | 0.170274i | 0.00387989 | + | 0.00672017i | ||||
\(643\) | 14.4839 | 0.571189 | 0.285595 | − | 0.958351i | \(-0.407809\pi\) | ||||
0.285595 | + | 0.958351i | \(0.407809\pi\) | |||||||
\(644\) | −7.94187 | − | 4.58524i | −0.312953 | − | 0.180684i | ||||
\(645\) | −5.61057 | + | 4.40818i | −0.220916 | + | 0.173572i | ||||
\(646\) | 10.9259 | + | 6.30808i | 0.429874 | + | 0.248188i | ||||
\(647\) | 17.3434 | + | 30.0396i | 0.681839 | + | 1.18098i | 0.974419 | + | 0.224738i | \(0.0721527\pi\) |
−0.292581 | + | 0.956241i | \(0.594514\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | 12.5796 | + | 7.26286i | 0.493794 | + | 0.285092i | ||||
\(650\) | 10.7700 | − | 3.15201i | 0.422435 | − | 0.123632i | ||||
\(651\) | −5.17770 | − | 2.98935i | −0.202930 | − | 0.117162i | ||||
\(652\) | −4.40591 | −0.172549 | ||||||||
\(653\) | −11.4681 | − | 19.8634i | −0.448783 | − | 0.777315i | 0.549524 | − | 0.835478i | \(-0.314809\pi\) |
−0.998307 | + | 0.0581630i | \(0.981476\pi\) | |||||||
\(654\) | −6.70656 | + | 11.6161i | −0.262247 | + | 0.454226i | ||||
\(655\) | −7.88922 | − | 3.16242i | −0.308257 | − | 0.123566i | ||||
\(656\) | −4.60335 | −0.179731 | ||||||||
\(657\) | −6.11771 | − | 3.53206i | −0.238675 | − | 0.137799i | ||||
\(658\) | 17.4710 | 0.681092 | ||||||||
\(659\) | −19.8771 | − | 34.4282i | −0.774303 | − | 1.34113i | −0.935186 | − | 0.354158i | \(-0.884767\pi\) |
0.160883 | − | 0.986974i | \(-0.448566\pi\) | |||||||
\(660\) | −6.23054 | − | 2.49753i | −0.242523 | − | 0.0972163i | ||||
\(661\) | −24.3780 | + | 14.0746i | −0.948194 | + | 0.547440i | −0.892519 | − | 0.451009i | \(-0.851064\pi\) |
−0.0556746 | + | 0.998449i | \(0.517731\pi\) | |||||||
\(662\) | 8.89801 | − | 5.13727i | 0.345831 | − | 0.199666i | ||||
\(663\) | 4.64134 | − | 2.67968i | 0.180255 | − | 0.104070i | ||||
\(664\) | 3.56360 | + | 2.05745i | 0.138295 | + | 0.0798444i | ||||
\(665\) | 5.94576 | − | 14.8328i | 0.230567 | − | 0.575190i | ||||
\(666\) | −2.77713 | + | 5.41180i | −0.107611 | + | 0.209703i | ||||
\(667\) | − | 27.6559i | − | 1.07084i | ||||||
\(668\) | 10.8349 | − | 18.7666i | 0.419216 | − | 0.726103i | ||||
\(669\) | 1.55168 | + | 2.68760i | 0.0599916 | + | 0.103908i | ||||
\(670\) | 1.12057 | + | 7.81833i | 0.0432915 | + | 0.302048i | ||||
\(671\) | 27.6214 | − | 15.9472i | 1.06631 | − | 0.615636i | ||||
\(672\) | −1.35265 | −0.0521798 | ||||||||
\(673\) | −10.4568 | + | 6.03721i | −0.403078 | + | 0.232717i | −0.687811 | − | 0.725890i | \(-0.741428\pi\) |
0.284733 | + | 0.958607i | \(0.408095\pi\) | |||||||
\(674\) | − | 20.3792i | − | 0.784976i | ||||||
\(675\) | 1.40441 | + | 4.79871i | 0.0540559 | + | 0.184702i | ||||
\(676\) | −7.96285 | −0.306263 | ||||||||
\(677\) | − | 32.2867i | − | 1.24088i | −0.784254 | − | 0.620440i | \(-0.786954\pi\) | ||
0.784254 | − | 0.620440i | \(-0.213046\pi\) | |||||||
\(678\) | −12.5484 | − | 7.24481i | −0.481918 | − | 0.278235i | ||||
\(679\) | −11.2433 | + | 6.49132i | −0.431478 | + | 0.249114i | ||||
\(680\) | −1.98671 | + | 4.95619i | −0.0761867 | + | 0.190061i | ||||
\(681\) | −13.8076 | − | 7.97179i | −0.529107 | − | 0.305480i | ||||
\(682\) | 11.4907 | + | 6.63418i | 0.440003 | + | 0.254036i | ||||
\(683\) | 12.6798 | − | 21.9620i | 0.485178 | − | 0.840353i | −0.514677 | − | 0.857384i | \(-0.672088\pi\) |
0.999855 | + | 0.0170311i | \(0.00542143\pi\) | |||||||
\(684\) | −4.57549 | + | 2.64166i | −0.174948 | + | 0.101006i | ||||
\(685\) | 3.22632 | + | 22.5103i | 0.123271 | + | 0.860073i | ||||
\(686\) | 14.2567 | + | 8.23112i | 0.544324 | + | 0.314266i | ||||
\(687\) | 11.6633 | + | 6.73382i | 0.444983 | + | 0.256911i | ||||
\(688\) | 1.59547 | − | 2.76343i | 0.0608267 | − | 0.105355i | ||||
\(689\) | − | 13.9844i | − | 0.532762i | ||||||
\(690\) | −2.15080 | − | 15.0063i | −0.0818797 | − | 0.571281i | ||||
\(691\) | −17.4719 | + | 30.2623i | −0.664664 | + | 1.15123i | 0.314712 | + | 0.949187i | \(0.398092\pi\) |
−0.979376 | + | 0.202045i | \(0.935241\pi\) | |||||||
\(692\) | 16.4630i | 0.625829i | ||||||||
\(693\) | 4.06054i | 0.154247i | ||||||||
\(694\) | −1.36599 | + | 2.36597i | −0.0518524 | + | 0.0898110i | ||||
\(695\) | −0.771490 | + | 1.92462i | −0.0292643 | + | 0.0730050i | ||||
\(696\) | −2.03964 | − | 3.53275i | −0.0773122 | − | 0.133909i | ||||
\(697\) | 10.9924 | 0.416369 | ||||||||
\(698\) | 6.08918 | + | 10.5468i | 0.230479 | + | 0.399201i | ||||
\(699\) | 13.8193 | + | 23.9357i | 0.522694 | + | 0.905333i | ||||
\(700\) | 6.57121 | + | 1.60032i | 0.248368 | + | 0.0604864i | ||||
\(701\) | −18.2155 | − | 10.5167i | −0.687990 | − | 0.397211i | 0.114868 | − | 0.993381i | \(-0.463355\pi\) |
−0.802859 | + | 0.596169i | \(0.796689\pi\) | |||||||
\(702\) | 2.24436i | 0.0847079i | ||||||||
\(703\) | 28.5923 | + | 14.6724i | 1.07838 | + | 0.553382i | ||||
\(704\) | 3.00191 | 0.113139 | ||||||||
\(705\) | 17.8432 | + | 22.7101i | 0.672013 | + | 0.855314i | ||||
\(706\) | −12.4776 | − | 21.6118i | −0.469600 | − | 0.813371i | ||||
\(707\) | 19.4999 | − | 11.2583i | 0.733370 | − | 0.423411i | ||||
\(708\) | 2.41941 | + | 4.19055i | 0.0909271 | + | 0.157490i | ||||
\(709\) | − | 40.1656i | − | 1.50845i | −0.656615 | − | 0.754226i | \(-0.728012\pi\) | ||
0.656615 | − | 0.754226i | \(-0.271988\pi\) | |||||||
\(710\) | 26.9349 | − | 3.86048i | 1.01085 | − | 0.144881i | ||||
\(711\) | − | 0.588515i | − | 0.0220710i | ||||||
\(712\) | 14.4684 | + | 8.35333i | 0.542226 | + | 0.313054i | ||||
\(713\) | 29.9657i | 1.12223i | ||||||||
\(714\) | 3.23003 | 0.120881 | ||||||||
\(715\) | 9.30745 | + | 11.8462i | 0.348079 | + | 0.443022i | ||||
\(716\) | 18.4058 | − | 10.6266i | 0.687857 | − | 0.397134i | ||||
\(717\) | −13.1344 | −0.490512 | ||||||||
\(718\) | 16.4858 | − | 28.5543i | 0.615245 | − | 1.06564i | ||||
\(719\) | 26.0199 | − | 45.0677i | 0.970377 | − | 1.68074i | 0.275962 | − | 0.961169i | \(-0.411004\pi\) |
0.694416 | − | 0.719574i | \(-0.255663\pi\) | |||||||
\(720\) | −1.38147 | − | 1.75828i | −0.0514842 | − | 0.0655272i | ||||
\(721\) | −7.86429 | + | 4.54045i | −0.292881 | + | 0.169095i | ||||
\(722\) | 4.45674 | + | 7.71930i | 0.165863 | + | 0.287283i | ||||
\(723\) | −14.3497 | + | 24.8544i | −0.533671 | + | 0.924346i | ||||
\(724\) | 9.22354 | − | 15.9756i | 0.342790 | − | 0.593730i | ||||
\(725\) | 5.72899 | + | 19.5752i | 0.212769 | + | 0.727006i | ||||
\(726\) | 1.98855i | 0.0738019i | ||||||||
\(727\) | −11.3516 | − | 19.6615i | −0.421008 | − | 0.729206i | 0.575031 | − | 0.818132i | \(-0.304990\pi\) |
−0.996038 | + | 0.0889253i | \(0.971657\pi\) | |||||||
\(728\) | 2.62912 | + | 1.51792i | 0.0974415 | + | 0.0562579i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −14.6618 | − | 5.87722i | −0.542657 | − | 0.217526i | ||||
\(731\) | −3.80986 | + | 6.59887i | −0.140913 | + | 0.244068i | ||||
\(732\) | 10.6247 | 0.392701 | ||||||||
\(733\) | −26.1668 | + | 15.1074i | −0.966494 | + | 0.558005i | −0.898166 | − | 0.439657i | \(-0.855100\pi\) |
−0.0683283 | + | 0.997663i | \(0.521767\pi\) | |||||||
\(734\) | 29.5946i | 1.09236i | ||||||||
\(735\) | 1.64026 | + | 11.4443i | 0.0605021 | + | 0.422128i | ||||
\(736\) | 3.38981 | + | 5.87132i | 0.124950 | + | 0.216420i | ||||
\(737\) | −9.18274 | + | 5.30166i | −0.338251 | + | 0.195289i | ||||
\(738\) | −2.30168 | + | 3.98662i | −0.0847259 | + | 0.146750i | ||||
\(739\) | −20.1078 | −0.739676 | −0.369838 | − | 0.929096i | \(-0.620587\pi\) | ||||
−0.369838 | + | 0.929096i | \(0.620587\pi\) | |||||||
\(740\) | −4.43015 | + | 12.8598i | −0.162856 | + | 0.472735i | ||||
\(741\) | 11.8577 | 0.435602 | ||||||||
\(742\) | 4.21412 | − | 7.29908i | 0.154705 | − | 0.267958i | ||||
\(743\) | −8.93959 | + | 5.16128i | −0.327962 | + | 0.189349i | −0.654936 | − | 0.755684i | \(-0.727304\pi\) |
0.326974 | + | 0.945033i | \(0.393971\pi\) | |||||||
\(744\) | 2.20999 | + | 3.82781i | 0.0810221 | + | 0.140334i | ||||
\(745\) | 20.0468 | − | 2.87324i | 0.734460 | − | 0.105268i | ||||
\(746\) | 1.48330i | 0.0543075i | ||||||||
\(747\) | 3.56360 | − | 2.05745i | 0.130385 | − | 0.0752780i | ||||
\(748\) | −7.16832 | −0.262100 | ||||||||
\(749\) | 0.132976 | − | 0.230322i | 0.00485884 | − | 0.00841577i | ||||
\(750\) | 4.63097 | + | 10.1762i | 0.169099 | + | 0.371581i | ||||
\(751\) | 15.2700 | 0.557208 | 0.278604 | − | 0.960406i | \(-0.410128\pi\) | ||||
0.278604 | + | 0.960406i | \(0.410128\pi\) | |||||||
\(752\) | −11.1857 | − | 6.45806i | −0.407900 | − | 0.235501i | ||||
\(753\) | −3.80820 | − | 6.59600i | −0.138779 | − | 0.240372i | ||||
\(754\) | 9.15535i | 0.333418i | ||||||||
\(755\) | −15.8522 | − | 20.1761i | −0.576922 | − | 0.734285i | ||||
\(756\) | −0.676327 | + | 1.17143i | −0.0245978 | + | 0.0426046i | ||||
\(757\) | 2.93517 | − | 5.08386i | 0.106680 | − | 0.184776i | −0.807743 | − | 0.589535i | \(-0.799311\pi\) |
0.914424 | + | 0.404759i | \(0.132644\pi\) | |||||||
\(758\) | −6.13208 | − | 10.6211i | −0.222727 | − | 0.385775i | ||||
\(759\) | 17.6252 | − | 10.1759i | 0.639753 | − | 0.369362i | ||||
\(760\) | −9.28956 | + | 7.29873i | −0.336968 | + | 0.264753i | ||||
\(761\) | −13.7631 | + | 23.8384i | −0.498911 | + | 0.864140i | −0.999999 | − | 0.00125666i | \(-0.999600\pi\) |
0.501088 | + | 0.865396i | \(0.332933\pi\) | |||||||
\(762\) | 5.14636 | − | 8.91376i | 0.186433 | − | 0.322911i | ||||
\(763\) | 18.1433 | 0.656832 | ||||||||
\(764\) | −7.58798 | + | 4.38092i | −0.274523 | + | 0.158496i | ||||
\(765\) | 3.29884 | + | 4.19863i | 0.119270 | + | 0.151802i | ||||
\(766\) | 12.2454 | 0.442443 | ||||||||
\(767\) | − | 10.8601i | − | 0.392134i | ||||||
\(768\) | 0.866025 | + | 0.500000i | 0.0312500 | + | 0.0180422i | ||||
\(769\) | − | 27.2786i | − | 0.983692i | −0.870682 | − | 0.491846i | \(-0.836322\pi\) | ||
0.870682 | − | 0.491846i | \(-0.163678\pi\) | |||||||
\(770\) | 1.28819 | + | 8.98780i | 0.0464232 | + | 0.323898i | ||||
\(771\) | 11.7370i | 0.422698i | ||||||||
\(772\) | −6.61309 | − | 11.4542i | −0.238010 | − | 0.412246i | ||||
\(773\) | −34.4624 | + | 19.8969i | −1.23953 | + | 0.715642i | −0.968998 | − | 0.247070i | \(-0.920532\pi\) |
−0.270530 | + | 0.962711i | \(0.587199\pi\) | |||||||
\(774\) | −1.59547 | − | 2.76343i | −0.0573480 | − | 0.0993296i | ||||
\(775\) | −6.20748 | − | 21.2102i | −0.222979 | − | 0.761892i | ||||
\(776\) | 9.59790 | 0.344545 | ||||||||
\(777\) | 8.21780 | − | 0.406931i | 0.294812 | − | 0.0145986i | ||||
\(778\) | 4.30663i | 0.154400i | ||||||||
\(779\) | 21.0626 | + | 12.1605i | 0.754646 | + | 0.435695i | ||||
\(780\) | 0.712014 | + | 4.96778i | 0.0254942 | + | 0.177875i | ||||
\(781\) | 18.2647 | + | 31.6354i | 0.653563 | + | 1.13201i | ||||
\(782\) | −8.09460 | − | 14.0203i | −0.289462 | − | 0.501363i | ||||
\(783\) | −4.07927 | −0.145781 | ||||||||
\(784\) | −2.58516 | − | 4.47763i | −0.0923273 | − | 0.159916i | ||||
\(785\) | −12.0804 | − | 4.84247i | −0.431168 | − | 0.172835i | ||||
\(786\) | 1.90054 | − | 3.29183i | 0.0677899 | − | 0.117416i | ||||
\(787\) | − | 15.7678i | − | 0.562061i | −0.959699 | − | 0.281031i | \(-0.909324\pi\) | ||
0.959699 | − | 0.281031i | \(-0.0906763\pi\) | |||||||
\(788\) | − | 8.46027i | − | 0.301385i | ||||||
\(789\) | −7.44568 | + | 12.8963i | −0.265073 | + | 0.459120i | ||||
\(790\) | −0.186704 | − | 1.30265i | −0.00664263 | − | 0.0463461i | ||||
\(791\) | 19.5994i | 0.696876i | ||||||||
\(792\) | 1.50095 | − | 2.59973i | 0.0533341 | − | 0.0923773i | ||||
\(793\) | −20.6510 | − | 11.9229i | −0.733338 | − | 0.423393i | ||||
\(794\) | 2.91682 | + | 1.68403i | 0.103514 | + | 0.0597639i | ||||
\(795\) | 13.7918 | − | 1.97673i | 0.489144 | − | 0.0701072i | ||||
\(796\) | −6.69137 | + | 3.86326i | −0.237169 | + | 0.136930i | ||||
\(797\) | −7.06082 | + | 12.2297i | −0.250107 | + | 0.433198i | −0.963555 | − | 0.267510i | \(-0.913799\pi\) |
0.713448 | + | 0.700708i | \(0.247132\pi\) | |||||||
\(798\) | 6.18905 | + | 3.57325i | 0.219090 | + | 0.126492i | ||||
\(799\) | 26.7105 | + | 15.4213i | 0.944951 | + | 0.545568i | ||||
\(800\) | −3.61561 | − | 3.45360i | −0.127831 | − | 0.122103i | ||||
\(801\) | 14.4684 | − | 8.35333i | 0.511216 | − | 0.295150i | ||||
\(802\) | 20.6354 | + | 11.9139i | 0.728661 | + | 0.420693i | ||||
\(803\) | − | 21.2059i | − | 0.748339i | ||||||
\(804\) | −3.53219 | −0.124571 | ||||||||
\(805\) | −16.1243 | + | 12.6687i | −0.568306 | + | 0.446513i | ||||
\(806\) | − | 9.92002i | − | 0.349418i | ||||||
\(807\) | −9.99679 | + | 5.77165i | −0.351904 | + | 0.203172i | ||||
\(808\) | −16.6462 | −0.585612 | ||||||||
\(809\) | −24.2202 | + | 13.9835i | −0.851537 | + | 0.491635i | −0.861169 | − | 0.508319i | \(-0.830267\pi\) |
0.00963235 | + | 0.999954i | \(0.496934\pi\) | |||||||
\(810\) | −2.21345 | + | 0.317246i | −0.0777727 | + | 0.0111469i | ||||
\(811\) | 24.4604 | + | 42.3666i | 0.858919 | + | 1.48769i | 0.872961 | + | 0.487791i | \(0.162197\pi\) |
−0.0140411 | + | 0.999901i | \(0.504470\pi\) | |||||||
\(812\) | −2.75892 | + | 4.77859i | −0.0968192 | + | 0.167696i | ||||
\(813\) | 0.672835i | 0.0235973i | ||||||||
\(814\) | −18.2375 | + | 0.903091i | −0.639226 | + | 0.0316533i | ||||
\(815\) | −3.66564 | + | 9.14458i | −0.128402 | + | 0.320321i | ||||
\(816\) | −2.06800 | − | 1.19396i | −0.0723945 | − | 0.0417970i | ||||
\(817\) | −14.6001 | + | 8.42938i | −0.510793 | + | 0.294907i | ||||
\(818\) | −29.8037 | + | 17.2072i | −1.04206 | + | 0.601634i | ||||
\(819\) | 2.62912 | − | 1.51792i | 0.0918688 | − | 0.0530405i | ||||
\(820\) | −3.82990 | + | 9.55438i | −0.133746 | + | 0.333653i | ||||
\(821\) | −7.27927 | − | 12.6081i | −0.254048 | − | 0.440025i | 0.710588 | − | 0.703608i | \(-0.248429\pi\) |
−0.964637 | + | 0.263583i | \(0.915096\pi\) | |||||||
\(822\) | −10.1698 | −0.354711 | ||||||||
\(823\) | 13.1840 | + | 7.61181i | 0.459567 | + | 0.265331i | 0.711862 | − | 0.702319i | \(-0.247852\pi\) |
−0.252295 | + | 0.967650i | \(0.581185\pi\) | |||||||
\(824\) | 6.71339 | 0.233872 | ||||||||
\(825\) | −10.3674 | + | 10.8537i | −0.360946 | + | 0.377879i | ||||
\(826\) | 3.27263 | − | 5.66836i | 0.113869 | − | 0.197228i | ||||
\(827\) | −6.92772 | − | 11.9992i | −0.240900 | − | 0.417252i | 0.720071 | − | 0.693901i | \(-0.244109\pi\) |
−0.960971 | + | 0.276649i | \(0.910776\pi\) | |||||||
\(828\) | 6.77962 | 0.235608 | ||||||||
\(829\) | 18.9388 | + | 10.9343i | 0.657770 | + | 0.379764i | 0.791427 | − | 0.611264i | \(-0.209339\pi\) |
−0.133657 | + | 0.991028i | \(0.542672\pi\) | |||||||
\(830\) | 7.23513 | − | 5.68459i | 0.251135 | − | 0.197315i | ||||
\(831\) | −24.5782 | − | 14.1902i | −0.852607 | − | 0.492253i | ||||
\(832\) | −1.12218 | − | 1.94367i | −0.0389046 | − | 0.0673847i | ||||
\(833\) | 6.17317 | + | 10.6922i | 0.213888 | + | 0.370464i | ||||
\(834\) | −0.803059 | − | 0.463646i | −0.0278077 | − | 0.0160548i | ||||
\(835\) | −29.9362 | − | 38.1017i | −1.03598 | − | 1.31856i | ||||
\(836\) | −13.7352 | − | 7.93002i | −0.475042 | − | 0.274266i | ||||
\(837\) | 4.41998 | 0.152777 | ||||||||
\(838\) | 8.20896 | + | 14.2183i | 0.283574 | + | 0.491164i | ||||
\(839\) | 14.0966 | − | 24.4161i | 0.486669 | − | 0.842936i | −0.513213 | − | 0.858261i | \(-0.671545\pi\) |
0.999883 | + | 0.0153252i | \(0.00487836\pi\) | |||||||
\(840\) | −1.12538 | + | 2.80747i | −0.0388294 | + | 0.0968669i | ||||
\(841\) | 12.3595 | 0.426191 | ||||||||
\(842\) | −14.6055 | − | 8.43252i | −0.503340 | − | 0.290604i | ||||
\(843\) | 20.0751 | 0.691424 | ||||||||
\(844\) | 7.00504 | + | 12.1331i | 0.241124 | + | 0.417638i | ||||
\(845\) | −6.62494 | + | 16.5271i | −0.227905 | + | 0.568549i | ||||
\(846\) | −11.1857 | + | 6.45806i | −0.384572 | + | 0.222033i | ||||
\(847\) | 2.32945 | − | 1.34491i | 0.0800408 | − | 0.0462116i | ||||
\(848\) | −5.39612 | + | 3.11545i | −0.185303 | + | 0.106985i | ||||
\(849\) | −7.60906 | − | 4.39309i | −0.261142 | − | 0.150771i | ||||
\(850\) | 8.63380 | + | 8.24692i | 0.296137 | + | 0.282867i | ||||
\(851\) | −22.3605 | − | 34.6504i | −0.766508 | − | 1.18780i | ||||
\(852\) | 12.1687i | 0.416894i | ||||||||
\(853\) | 12.4816 | − | 21.6188i | 0.427362 | − | 0.740213i | −0.569275 | − | 0.822147i | \(-0.692776\pi\) |
0.996638 | + | 0.0819335i | \(0.0261095\pi\) | |||||||
\(854\) | −7.18579 | − | 12.4462i | −0.245893 | − | 0.425899i | ||||
\(855\) | 1.67611 | + | 11.6944i | 0.0573218 | + | 0.399939i | ||||
\(856\) | −0.170274 | + | 0.0983076i | −0.00581984 | + | 0.00336009i | ||||
\(857\) | 25.5581 | 0.873047 | 0.436524 | − | 0.899693i | \(-0.356210\pi\) | ||||
0.436524 | + | 0.899693i | \(0.356210\pi\) | |||||||
\(858\) | −5.83473 | + | 3.36868i | −0.199194 | + | 0.115005i | ||||
\(859\) | − | 26.1665i | − | 0.892789i | −0.894836 | − | 0.446395i | \(-0.852708\pi\) | ||
0.894836 | − | 0.446395i | \(-0.147292\pi\) | |||||||
\(860\) | −4.40818 | − | 5.61057i | −0.150318 | − | 0.191319i | ||||
\(861\) | 6.22675 | 0.212207 | ||||||||
\(862\) | − | 24.2046i | − | 0.824411i | ||||||
\(863\) | −21.4938 | − | 12.4095i | −0.731658 | − | 0.422423i | 0.0873702 | − | 0.996176i | \(-0.472154\pi\) |
−0.819029 | + | 0.573753i | \(0.805487\pi\) | |||||||
\(864\) | 0.866025 | − | 0.500000i | 0.0294628 | − | 0.0170103i | ||||
\(865\) | 34.1693 | + | 13.6969i | 1.16179 | + | 0.465708i | ||||
\(866\) | −23.5710 | − | 13.6087i | −0.800977 | − | 0.462444i | ||||
\(867\) | −9.78421 | − | 5.64892i | −0.332289 | − | 0.191847i | ||||
\(868\) | 2.98935 | − | 5.17770i | 0.101465 | − | 0.175743i | ||||
\(869\) | 1.52998 | − | 0.883334i | 0.0519010 | − | 0.0299651i | ||||
\(870\) | −9.02926 | + | 1.29413i | −0.306120 | + | 0.0438752i | ||||
\(871\) | 6.86543 | + | 3.96376i | 0.232626 | + | 0.134307i | ||||
\(872\) | −11.6161 | − | 6.70656i | −0.393371 | − | 0.227113i | ||||
\(873\) | 4.79895 | − | 8.31202i | 0.162420 | − | 0.281319i | ||||
\(874\) | − | 35.8189i | − | 1.21159i | ||||||
\(875\) | 8.78863 | − | 12.3073i | 0.297110 | − | 0.416062i | ||||
\(876\) | 3.53206 | − | 6.11771i | 0.119337 | − | 0.206698i | ||||
\(877\) | − | 18.9348i | − | 0.639384i | −0.947522 | − | 0.319692i | \(-0.896421\pi\) | ||
0.947522 | − | 0.319692i | \(-0.103579\pi\) | |||||||
\(878\) | − | 0.350960i | − | 0.0118443i | ||||||
\(879\) | −10.4994 | + | 18.1855i | −0.354135 | + | 0.613380i | ||||
\(880\) | 2.49753 | − | 6.23054i | 0.0841918 | − | 0.210031i | ||||
\(881\) | 0.835883 | + | 1.44779i | 0.0281616 | + | 0.0487773i | 0.879763 | − | 0.475413i | \(-0.157701\pi\) |
−0.851601 | + | 0.524190i | \(0.824368\pi\) | |||||||
\(882\) | −5.17033 | −0.174094 | ||||||||
\(883\) | −19.4113 | − | 33.6214i | −0.653242 | − | 1.13145i | −0.982331 | − | 0.187150i | \(-0.940075\pi\) |
0.329089 | − | 0.944299i | \(-0.393258\pi\) | |||||||
\(884\) | 2.67968 | + | 4.64134i | 0.0901273 | + | 0.156105i | ||||
\(885\) | 10.7105 | − | 1.53510i | 0.360029 | − | 0.0516017i | ||||
\(886\) | −25.7087 | − | 14.8429i | −0.863700 | − | 0.498657i | ||||
\(887\) | − | 54.2705i | − | 1.82222i | −0.412159 | − | 0.911112i | \(-0.635225\pi\) | ||
0.412159 | − | 0.911112i | \(-0.364775\pi\) | |||||||
\(888\) | −5.41180 | − | 2.77713i | −0.181608 | − | 0.0931942i | ||||
\(889\) | −13.9225 | −0.466945 | ||||||||
\(890\) | 29.3750 | − | 23.0797i | 0.984652 | − | 0.773634i | ||||
\(891\) | −1.50095 | − | 2.59973i | −0.0502839 | − | 0.0870942i | ||||
\(892\) | −2.68760 | + | 1.55168i | −0.0899874 | + | 0.0519542i | ||||
\(893\) | 34.1200 | + | 59.0976i | 1.14178 | + | 1.97762i | ||||
\(894\) | 9.05684i | 0.302906i | ||||||||
\(895\) | −6.74248 | − | 47.0428i | −0.225376 | − | 1.57247i | ||||
\(896\) | − | 1.35265i | − | 0.0451890i | ||||||
\(897\) | −13.1774 | − | 7.60795i | −0.439979 | − | 0.254022i | ||||
\(898\) | 20.4572i | 0.682664i | ||||||||
\(899\) | 18.0303 | 0.601343 | ||||||||
\(900\) | −4.79871 | + | 1.40441i | −0.159957 | + | 0.0468138i | ||||
\(901\) | 12.8855 | − | 7.43945i | 0.429278 | − | 0.247844i | ||||
\(902\) | −13.8188 | −0.460117 | ||||||||
\(903\) | −2.15812 | + | 3.73797i | −0.0718177 | + | 0.124392i | ||||
\(904\) | 7.24481 | − | 12.5484i | 0.240959 | − | 0.417353i | ||||
\(905\) | −25.4840 | − | 32.4351i | −0.847118 | − | 1.07818i | ||||
\(906\) | 9.93758 | − | 5.73747i | 0.330154 | − | 0.190615i | ||||
\(907\) | −7.93667 | − | 13.7467i | −0.263533 | − | 0.456452i | 0.703645 | − | 0.710551i | \(-0.251554\pi\) |
−0.967178 | + | 0.254099i | \(0.918221\pi\) | |||||||
\(908\) | 7.97179 | − | 13.8076i | 0.264553 | − | 0.458220i | ||||
\(909\) | −8.32311 | + | 14.4160i | −0.276060 | + | 0.478150i | ||||
\(910\) | 5.33786 | − | 4.19392i | 0.176948 | − | 0.139027i | ||||
\(911\) | 54.2419i | 1.79712i | 0.438855 | + | 0.898558i | \(0.355384\pi\) | ||||
−0.438855 | + | 0.898558i | \(0.644616\pi\) | |||||||
\(912\) | −2.64166 | − | 4.57549i | −0.0874741 | − | 0.151510i | ||||
\(913\) | 10.6976 | + | 6.17626i | 0.354039 | + | 0.204405i | ||||
\(914\) | 32.3871 | 1.07127 | ||||||||
\(915\) | 8.83958 | − | 22.0519i | 0.292227 | − | 0.729013i | ||||
\(916\) | −6.73382 | + | 11.6633i | −0.222492 | + | 0.385367i | ||||
\(917\) | −5.14154 | −0.169788 | ||||||||
\(918\) | −2.06800 | + | 1.19396i | −0.0682542 | + | 0.0394066i | ||||
\(919\) | 11.6006i | 0.382667i | 0.981525 | + | 0.191333i | \(0.0612812\pi\) | ||||
−0.981525 | + | 0.191333i | \(0.938719\pi\) | |||||||
\(920\) | 15.0063 | − | 2.15080i | 0.494744 | − | 0.0709099i | ||||
\(921\) | −8.10430 | − | 14.0371i | −0.267046 | − | 0.462537i | ||||
\(922\) | 16.5318 | − | 9.54466i | 0.544447 | − | 0.314337i | ||||
\(923\) | 13.6555 | − | 23.6521i | 0.449477 | − | 0.778517i | ||||
\(924\) | −4.06054 | −0.133582 | ||||||||
\(925\) | 23.0050 | + | 19.8940i | 0.756399 | + | 0.654110i | ||||
\(926\) | −18.7885 | −0.617430 | ||||||||
\(927\) | 3.35670 | − | 5.81397i | 0.110248 | − | 0.190956i | ||||
\(928\) | 3.53275 | − | 2.03964i | 0.115968 | − | 0.0669543i | ||||
\(929\) | 22.6937 | + | 39.3066i | 0.744555 | + | 1.28961i | 0.950402 | + | 0.311023i | \(0.100672\pi\) |
−0.205847 | + | 0.978584i | \(0.565995\pi\) | |||||||
\(930\) | 9.78339 | − | 1.40222i | 0.320810 | − | 0.0459806i | ||||
\(931\) | 27.3165i | 0.895262i | ||||||||
\(932\) | −23.9357 | + | 13.8193i | −0.784041 | + | 0.452666i | ||||
\(933\) | −2.98352 | −0.0976760 | ||||||||
\(934\) | 1.48895 | − | 2.57894i | 0.0487200 | − | 0.0843854i | ||||
\(935\) | −5.96391 | + | 14.8780i | −0.195041 | + | 0.486564i | ||||
\(936\) | −2.24436 | −0.0733592 | ||||||||
\(937\) | −3.30744 | − | 1.90955i | −0.108049 | − | 0.0623823i | 0.445002 | − | 0.895530i | \(-0.353203\pi\) |
−0.553051 | + | 0.833148i | \(0.686536\pi\) | |||||||
\(938\) | 2.38892 | + | 4.13773i | 0.0780009 | + | 0.135102i | ||||
\(939\) | 4.51495i | 0.147340i | ||||||||
\(940\) | −22.7101 | + | 17.8432i | −0.740723 | + | 0.581981i | ||||
\(941\) | 13.6763 | − | 23.6880i | 0.445833 | − | 0.772206i | −0.552277 | − | 0.833661i | \(-0.686241\pi\) |
0.998110 | + | 0.0614552i | \(0.0195741\pi\) | |||||||
\(942\) | 2.91020 | − | 5.04062i | 0.0948195 | − | 0.164232i | ||||
\(943\) | −15.6045 | − | 27.0278i | −0.508152 | − | 0.880145i | ||||
\(944\) | −4.19055 | + | 2.41941i | −0.136391 | + | 0.0787452i | ||||
\(945\) | 1.86865 | + | 2.37834i | 0.0607871 | + | 0.0773676i | ||||
\(946\) | 4.78945 | − | 8.29558i | 0.155719 | − | 0.269712i | ||||
\(947\) | −17.8892 | + | 30.9851i | −0.581322 | + | 1.00688i | 0.414001 | + | 0.910277i | \(0.364131\pi\) |
−0.995323 | + | 0.0966032i | \(0.969202\pi\) | |||||||
\(948\) | 0.588515 | 0.0191141 | ||||||||
\(949\) | −13.7304 | + | 7.92722i | −0.445706 | + | 0.257328i | ||||
\(950\) | 7.41997 | + | 25.3531i | 0.240736 | + | 0.822564i | ||||
\(951\) | −6.83240 | −0.221556 | ||||||||
\(952\) | 3.23003i | 0.104686i | ||||||||
\(953\) | −2.51306 | − | 1.45091i | −0.0814059 | − | 0.0469997i | 0.458744 | − | 0.888568i | \(-0.348299\pi\) |
−0.540150 | + | 0.841568i | \(0.681633\pi\) | |||||||
\(954\) | 6.23090i | 0.201733i | ||||||||
\(955\) | 2.77966 | + | 19.3939i | 0.0899476 | + | 0.627572i | ||||
\(956\) | − | 13.1344i | − | 0.424796i | ||||||
\(957\) | −6.12280 | − | 10.6050i | −0.197922 | − | 0.342811i | ||||
\(958\) | −28.9748 | + | 16.7286i | −0.936134 | + | 0.540477i | ||||
\(959\) | 6.87809 | + | 11.9132i | 0.222105 | + | 0.384697i | ||||
\(960\) | 1.75828 | − | 1.38147i | 0.0567482 | − | 0.0445867i | ||||
\(961\) | 11.4638 | 0.369801 | ||||||||
\(962\) | 7.40233 | + | 11.4708i | 0.238661 | + | 0.369835i | ||||
\(963\) | 0.196615i | 0.00633584i | ||||||||
\(964\) | −24.8544 | − | 14.3497i | −0.800507 | − | 0.462173i | ||||
\(965\) | −29.2755 | + | 4.19595i | −0.942410 | + | 0.135072i | ||||
\(966\) | −4.58524 | − | 7.94187i | −0.147528 | − | 0.255525i | ||||
\(967\) | −26.9414 | − | 46.6639i | −0.866377 | − | 1.50061i | −0.865673 | − | 0.500610i | \(-0.833109\pi\) |
−0.000703986 | − | 1.00000i | \(-0.500224\pi\) | |||||||
\(968\) | −1.98855 | −0.0639143 | ||||||||
\(969\) | 6.30808 | + | 10.9259i | 0.202645 | + | 0.350991i | ||||
\(970\) | 7.98527 | − | 19.9207i | 0.256392 | − | 0.639615i | ||||
\(971\) | −12.2032 | + | 21.1365i | −0.391618 | + | 0.678302i | −0.992663 | − | 0.120913i | \(-0.961418\pi\) |
0.601045 | + | 0.799215i | \(0.294751\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | 1.25431i | 0.0402112i | ||||||||
\(974\) | 1.99131 | − | 3.44906i | 0.0638058 | − | 0.110515i | ||||
\(975\) | 10.9031 | + | 2.65529i | 0.349180 | + | 0.0850375i | ||||
\(976\) | 10.6247i | 0.340089i | ||||||||
\(977\) | 20.8789 | − | 36.1634i | 0.667976 | − | 1.15697i | −0.310493 | − | 0.950576i | \(-0.600494\pi\) |
0.978469 | − | 0.206393i | \(-0.0661725\pi\) | |||||||
\(978\) | −3.81563 | − | 2.20296i | −0.122010 | − | 0.0704427i | ||||
\(979\) | 43.4328 | + | 25.0759i | 1.38812 | + | 0.801430i | ||||
\(980\) | −11.4443 | + | 1.64026i | −0.365573 | + | 0.0523963i | ||||
\(981\) | −11.6161 | + | 6.70656i | −0.370874 | + | 0.214124i | ||||
\(982\) | 19.6340 | − | 34.0071i | 0.626546 | − | 1.08521i | ||||
\(983\) | −0.756705 | − | 0.436884i | −0.0241352 | − | 0.0139344i | 0.487884 | − | 0.872909i | \(-0.337769\pi\) |
−0.512019 | + | 0.858974i | \(0.671102\pi\) | |||||||
\(984\) | −3.98662 | − | 2.30168i | −0.127089 | − | 0.0733748i | ||||
\(985\) | −17.5595 | − | 7.03879i | −0.559492 | − | 0.224274i | ||||
\(986\) | −8.43593 | + | 4.87049i | −0.268655 | + | 0.155108i | ||||
\(987\) | 15.1304 | + | 8.73552i | 0.481605 | + | 0.278055i | ||||
\(988\) | 11.8577i | 0.377243i | ||||||||
\(989\) | 21.6333 | 0.687900 | ||||||||
\(990\) | −4.14704 | − | 5.27819i | −0.131802 | − | 0.167752i | ||||
\(991\) | 23.5804i | 0.749055i | 0.927216 | + | 0.374527i | \(0.122195\pi\) | ||||
−0.927216 | + | 0.374527i | \(0.877805\pi\) | |||||||
\(992\) | −3.82781 | + | 2.20999i | −0.121533 | + | 0.0701672i | ||||
\(993\) | 10.2745 | 0.326053 | ||||||||
\(994\) | 14.2549 | − | 8.23005i | 0.452137 | − | 0.261041i | ||||
\(995\) | 2.45121 | + | 17.1023i | 0.0777085 | + | 0.542179i | ||||
\(996\) | 2.05745 | + | 3.56360i | 0.0651927 | + | 0.112917i | ||||
\(997\) | 30.1315 | − | 52.1894i | 0.954276 | − | 1.65285i | 0.218258 | − | 0.975891i | \(-0.429963\pi\) |
0.736017 | − | 0.676963i | \(-0.236704\pi\) | |||||||
\(998\) | − | 12.9448i | − | 0.409760i | ||||||
\(999\) | −5.11096 | + | 3.29819i | −0.161704 | + | 0.104350i |
(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 | 1110.2.ba.a.619.6 | yes | 36 | |
5.4 | even | 2 | 1110.2.ba.b.619.13 | yes | 36 | ||
37.11 | even | 6 | 1110.2.ba.b.529.13 | yes | 36 | ||
185.159 | even | 6 | inner | 1110.2.ba.a.529.6 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.ba.a.529.6 | ✓ | 36 | 185.159 | even | 6 | inner | |
1110.2.ba.a.619.6 | yes | 36 | 1.1 | even | 1 | trivial | |
1110.2.ba.b.529.13 | yes | 36 | 37.11 | even | 6 | ||
1110.2.ba.b.619.13 | yes | 36 | 5.4 | even | 2 |