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 | 619.3 | ||
Character | \(\chi\) | \(=\) | 1110.619 |
Dual form | 1110.2.ba.b.529.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 | ||||
\(5\) | −1.56260 | − | 1.59947i | −0.698814 | − | 0.715303i | ||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | −0.998396 | + | 0.576424i | −0.377358 | + | 0.217868i | −0.676668 | − | 0.736288i | \(-0.736577\pi\) |
0.299310 | + | 0.954156i | \(0.403244\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | −2.16648 | + | 0.553515i | −0.685100 | + | 0.175037i | ||||
\(11\) | 1.60140 | 0.482840 | 0.241420 | − | 0.970421i | \(-0.422387\pi\) | ||||
0.241420 | + | 0.970421i | \(0.422387\pi\) | |||||||
\(12\) | 0.866025 | + | 0.500000i | 0.250000 | + | 0.144338i | ||||
\(13\) | −1.89712 | − | 3.28591i | −0.526167 | − | 0.911349i | −0.999535 | − | 0.0304838i | \(-0.990295\pi\) |
0.473368 | − | 0.880865i | \(-0.343038\pi\) | |||||||
\(14\) | 1.15285i | 0.308112i | ||||||||
\(15\) | 2.15298 | + | 0.603880i | 0.555897 | + | 0.155921i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −3.28940 | + | 5.69741i | −0.797798 | + | 1.38183i | 0.123250 | + | 0.992376i | \(0.460668\pi\) |
−0.921048 | + | 0.389450i | \(0.872665\pi\) | |||||||
\(18\) | −0.500000 | − | 0.866025i | −0.117851 | − | 0.204124i | ||||
\(19\) | −0.174421 | + | 0.100702i | −0.0400150 | + | 0.0231027i | −0.519874 | − | 0.854243i | \(-0.674021\pi\) |
0.479859 | + | 0.877346i | \(0.340688\pi\) | |||||||
\(20\) | −0.603880 | + | 2.15298i | −0.135032 | + | 0.481421i | ||||
\(21\) | 0.576424 | − | 0.998396i | 0.125786 | − | 0.217868i | ||||
\(22\) | 0.800700 | − | 1.38685i | 0.170710 | − | 0.295678i | ||||
\(23\) | 0.633422 | 0.132078 | 0.0660388 | − | 0.997817i | \(-0.478964\pi\) | ||||
0.0660388 | + | 0.997817i | \(0.478964\pi\) | |||||||
\(24\) | 0.866025 | − | 0.500000i | 0.176777 | − | 0.102062i | ||||
\(25\) | −0.116584 | + | 4.99864i | −0.0233168 | + | 0.999728i | ||||
\(26\) | −3.79425 | −0.744113 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0.998396 | + | 0.576424i | 0.188679 | + | 0.108934i | ||||
\(29\) | − | 5.73899i | − | 1.06570i | −0.846208 | − | 0.532852i | \(-0.821120\pi\) | ||
0.846208 | − | 0.532852i | \(-0.178880\pi\) | |||||||
\(30\) | 1.59947 | − | 1.56260i | 0.292021 | − | 0.285290i | ||||
\(31\) | 8.34912i | 1.49955i | 0.661695 | + | 0.749773i | \(0.269837\pi\) | ||||
−0.661695 | + | 0.749773i | \(0.730163\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −1.38685 | + | 0.800700i | −0.241420 | + | 0.139384i | ||||
\(34\) | 3.28940 | + | 5.69741i | 0.564128 | + | 0.977098i | ||||
\(35\) | 2.48206 | + | 0.696182i | 0.419545 | + | 0.117676i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | −6.07690 | − | 0.267030i | −0.999036 | − | 0.0438995i | ||||
\(38\) | 0.201405i | 0.0326721i | ||||||||
\(39\) | 3.28591 | + | 1.89712i | 0.526167 | + | 0.303783i | ||||
\(40\) | 1.56260 | + | 1.59947i | 0.247068 | + | 0.252898i | ||||
\(41\) | 4.00330 | + | 6.93392i | 0.625211 | + | 1.08290i | 0.988500 | + | 0.151220i | \(0.0483203\pi\) |
−0.363289 | + | 0.931676i | \(0.618346\pi\) | |||||||
\(42\) | −0.576424 | − | 0.998396i | −0.0889442 | − | 0.154056i | ||||
\(43\) | −1.95146 | −0.297595 | −0.148798 | − | 0.988868i | \(-0.547540\pi\) | ||||
−0.148798 | + | 0.988868i | \(0.547540\pi\) | |||||||
\(44\) | −0.800700 | − | 1.38685i | −0.120710 | − | 0.209076i | ||||
\(45\) | −2.16648 | + | 0.553515i | −0.322959 | + | 0.0825132i | ||||
\(46\) | 0.316711 | − | 0.548560i | 0.0466965 | − | 0.0808807i | ||||
\(47\) | 4.65434i | 0.678905i | 0.940623 | + | 0.339453i | \(0.110242\pi\) | ||||
−0.940623 | + | 0.339453i | \(0.889758\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | −2.83547 | + | 4.91118i | −0.405067 | + | 0.701597i | ||||
\(50\) | 4.27066 | + | 2.60029i | 0.603962 | + | 0.367736i | ||||
\(51\) | − | 6.57881i | − | 0.921217i | ||||||
\(52\) | −1.89712 | + | 3.28591i | −0.263084 | + | 0.455674i | ||||
\(53\) | 7.47374 | + | 4.31497i | 1.02660 | + | 0.592706i | 0.916008 | − | 0.401160i | \(-0.131393\pi\) |
0.110589 | + | 0.993866i | \(0.464726\pi\) | |||||||
\(54\) | 0.866025 | + | 0.500000i | 0.117851 | + | 0.0680414i | ||||
\(55\) | −2.50234 | − | 2.56138i | −0.337416 | − | 0.345377i | ||||
\(56\) | 0.998396 | − | 0.576424i | 0.133416 | − | 0.0770279i | ||||
\(57\) | 0.100702 | − | 0.174421i | 0.0133383 | − | 0.0231027i | ||||
\(58\) | −4.97011 | − | 2.86950i | −0.652608 | − | 0.376783i | ||||
\(59\) | 10.3918 | + | 5.99970i | 1.35289 | + | 0.781094i | 0.988654 | − | 0.150211i | \(-0.0479953\pi\) |
0.364241 | + | 0.931305i | \(0.381329\pi\) | |||||||
\(60\) | −0.553515 | − | 2.16648i | −0.0714585 | − | 0.279691i | ||||
\(61\) | −11.3423 | + | 6.54846i | −1.45223 | + | 0.838445i | −0.998608 | − | 0.0527502i | \(-0.983201\pi\) |
−0.453621 | + | 0.891195i | \(0.649868\pi\) | |||||||
\(62\) | 7.23055 | + | 4.17456i | 0.918280 | + | 0.530169i | ||||
\(63\) | 1.15285i | 0.145245i | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.29127 | + | 8.16894i | −0.284197 | + | 1.01323i | ||||
\(66\) | 1.60140i | 0.197119i | ||||||||
\(67\) | −9.33087 | + | 5.38718i | −1.13995 | + | 0.658149i | −0.946417 | − | 0.322946i | \(-0.895327\pi\) |
−0.193529 | + | 0.981094i | \(0.561993\pi\) | |||||||
\(68\) | 6.57881 | 0.797798 | ||||||||
\(69\) | −0.548560 | + | 0.316711i | −0.0660388 | + | 0.0381275i | ||||
\(70\) | 1.84394 | − | 1.80144i | 0.220393 | − | 0.215313i | ||||
\(71\) | −5.52164 | − | 9.56376i | −0.655298 | − | 1.13501i | −0.981819 | − | 0.189819i | \(-0.939210\pi\) |
0.326521 | − | 0.945190i | \(-0.394124\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | − | 4.32373i | − | 0.506054i | −0.967459 | − | 0.253027i | \(-0.918574\pi\) | ||
0.967459 | − | 0.253027i | \(-0.0814262\pi\) | |||||||
\(74\) | −3.26970 | + | 5.12923i | −0.380095 | + | 0.596261i | ||||
\(75\) | −2.39836 | − | 4.38724i | −0.276938 | − | 0.506595i | ||||
\(76\) | 0.174421 | + | 0.100702i | 0.0200075 | + | 0.0115513i | ||||
\(77\) | −1.59883 | + | 0.923086i | −0.182204 | + | 0.105195i | ||||
\(78\) | 3.28591 | − | 1.89712i | 0.372057 | − | 0.214807i | ||||
\(79\) | 6.91117 | − | 3.99017i | 0.777568 | − | 0.448929i | −0.0580000 | − | 0.998317i | \(-0.518472\pi\) |
0.835568 | + | 0.549388i | \(0.185139\pi\) | |||||||
\(80\) | 2.16648 | − | 0.553515i | 0.242219 | − | 0.0618849i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 8.00660 | 0.884181 | ||||||||
\(83\) | −12.4882 | − | 7.21006i | −1.37076 | − | 0.791407i | −0.379734 | − | 0.925096i | \(-0.623984\pi\) |
−0.991023 | + | 0.133689i | \(0.957318\pi\) | |||||||
\(84\) | −1.15285 | −0.125786 | ||||||||
\(85\) | 14.2528 | − | 3.64147i | 1.54594 | − | 0.394973i | ||||
\(86\) | −0.975731 | + | 1.69002i | −0.105216 | + | 0.182239i | ||||
\(87\) | 2.86950 | + | 4.97011i | 0.307642 | + | 0.532852i | ||||
\(88\) | −1.60140 | −0.170710 | ||||||||
\(89\) | 15.6356 | + | 9.02723i | 1.65737 | + | 0.956885i | 0.973920 | + | 0.226890i | \(0.0728557\pi\) |
0.683452 | + | 0.729995i | \(0.260478\pi\) | |||||||
\(90\) | −0.603880 | + | 2.15298i | −0.0636545 | + | 0.226944i | ||||
\(91\) | 3.78816 | + | 2.18710i | 0.397107 | + | 0.229270i | ||||
\(92\) | −0.316711 | − | 0.548560i | −0.0330194 | − | 0.0571913i | ||||
\(93\) | −4.17456 | − | 7.23055i | −0.432882 | − | 0.749773i | ||||
\(94\) | 4.03078 | + | 2.32717i | 0.415743 | + | 0.240029i | ||||
\(95\) | 0.433620 | + | 0.121624i | 0.0444885 | + | 0.0124784i | ||||
\(96\) | −0.866025 | − | 0.500000i | −0.0883883 | − | 0.0510310i | ||||
\(97\) | −2.93176 | −0.297675 | −0.148838 | − | 0.988862i | \(-0.547553\pi\) | ||||
−0.148838 | + | 0.988862i | \(0.547553\pi\) | |||||||
\(98\) | 2.83547 | + | 4.91118i | 0.286426 | + | 0.496104i | ||||
\(99\) | 0.800700 | − | 1.38685i | 0.0804734 | − | 0.139384i | ||||
\(100\) | 4.38724 | − | 2.39836i | 0.438724 | − | 0.239836i | ||||
\(101\) | −14.8756 | −1.48018 | −0.740088 | − | 0.672510i | \(-0.765216\pi\) | ||||
−0.740088 | + | 0.672510i | \(0.765216\pi\) | |||||||
\(102\) | −5.69741 | − | 3.28940i | −0.564128 | − | 0.325699i | ||||
\(103\) | 2.82877 | 0.278727 | 0.139363 | − | 0.990241i | \(-0.455494\pi\) | ||||
0.139363 | + | 0.990241i | \(0.455494\pi\) | |||||||
\(104\) | 1.89712 | + | 3.28591i | 0.186028 | + | 0.322210i | ||||
\(105\) | −2.49762 | + | 0.638119i | −0.243743 | + | 0.0622741i | ||||
\(106\) | 7.47374 | − | 4.31497i | 0.725914 | − | 0.419107i | ||||
\(107\) | 8.16662 | − | 4.71500i | 0.789497 | − | 0.455816i | −0.0502882 | − | 0.998735i | \(-0.516014\pi\) |
0.839786 | + | 0.542918i | \(0.182681\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | −11.8873 | − | 6.86312i | −1.13859 | − | 0.657367i | −0.192512 | − | 0.981295i | \(-0.561663\pi\) |
−0.946082 | + | 0.323927i | \(0.894997\pi\) | |||||||
\(110\) | −3.46940 | + | 0.886399i | −0.330794 | + | 0.0845148i | ||||
\(111\) | 5.39626 | − | 2.80719i | 0.512191 | − | 0.266447i | ||||
\(112\) | − | 1.15285i | − | 0.108934i | ||||||
\(113\) | −4.45519 | + | 7.71661i | −0.419109 | + | 0.725917i | −0.995850 | − | 0.0910093i | \(-0.970991\pi\) |
0.576741 | + | 0.816927i | \(0.304324\pi\) | |||||||
\(114\) | −0.100702 | − | 0.174421i | −0.00943163 | − | 0.0163361i | ||||
\(115\) | −0.989784 | − | 1.01314i | −0.0922978 | − | 0.0944756i | ||||
\(116\) | −4.97011 | + | 2.86950i | −0.461463 | + | 0.266426i | ||||
\(117\) | −3.79425 | −0.350778 | ||||||||
\(118\) | 10.3918 | − | 5.99970i | 0.956641 | − | 0.552317i | ||||
\(119\) | − | 7.58437i | − | 0.695258i | ||||||
\(120\) | −2.15298 | − | 0.603880i | −0.196539 | − | 0.0551265i | ||||
\(121\) | −8.43552 | −0.766865 | ||||||||
\(122\) | 13.0969i | 1.18574i | ||||||||
\(123\) | −6.93392 | − | 4.00330i | −0.625211 | − | 0.360966i | ||||
\(124\) | 7.23055 | − | 4.17456i | 0.649322 | − | 0.374886i | ||||
\(125\) | 8.17733 | − | 7.62439i | 0.731403 | − | 0.681946i | ||||
\(126\) | 0.998396 | + | 0.576424i | 0.0889442 | + | 0.0513520i | ||||
\(127\) | −10.7457 | − | 6.20405i | −0.953529 | − | 0.550520i | −0.0593538 | − | 0.998237i | \(-0.518904\pi\) |
−0.894175 | + | 0.447717i | \(0.852237\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 1.69002 | − | 0.975731i | 0.148798 | − | 0.0859083i | ||||
\(130\) | 5.92888 | + | 6.06877i | 0.519997 | + | 0.532266i | ||||
\(131\) | −0.150501 | − | 0.0868917i | −0.0131493 | − | 0.00759176i | 0.493411 | − | 0.869796i | \(-0.335750\pi\) |
−0.506560 | + | 0.862205i | \(0.669083\pi\) | |||||||
\(132\) | 1.38685 | + | 0.800700i | 0.120710 | + | 0.0696920i | ||||
\(133\) | 0.116094 | − | 0.201082i | 0.0100667 | − | 0.0174360i | ||||
\(134\) | 10.7744i | 0.930763i | ||||||||
\(135\) | 1.59947 | − | 1.56260i | 0.137660 | − | 0.134487i | ||||
\(136\) | 3.28940 | − | 5.69741i | 0.282064 | − | 0.488549i | ||||
\(137\) | − | 0.163889i | − | 0.0140020i | −0.999975 | − | 0.00700100i | \(-0.997771\pi\) | ||
0.999975 | − | 0.00700100i | \(-0.00222850\pi\) | |||||||
\(138\) | 0.633422i | 0.0539205i | ||||||||
\(139\) | −0.808880 | + | 1.40102i | −0.0686083 | + | 0.118833i | −0.898289 | − | 0.439405i | \(-0.855189\pi\) |
0.829681 | + | 0.558238i | \(0.188523\pi\) | |||||||
\(140\) | −0.638119 | − | 2.49762i | −0.0539309 | − | 0.211087i | ||||
\(141\) | −2.32717 | − | 4.03078i | −0.195983 | − | 0.339453i | ||||
\(142\) | −11.0433 | −0.926731 | ||||||||
\(143\) | −3.03805 | − | 5.26206i | −0.254055 | − | 0.440036i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | −9.17932 | + | 8.96773i | −0.762301 | + | 0.744729i | ||||
\(146\) | −3.74446 | − | 2.16187i | −0.309894 | − | 0.178917i | ||||
\(147\) | − | 5.67094i | − | 0.467731i | ||||||
\(148\) | 2.80719 | + | 5.39626i | 0.230750 | + | 0.443570i | ||||
\(149\) | −16.0986 | −1.31885 | −0.659423 | − | 0.751772i | \(-0.729200\pi\) | ||||
−0.659423 | + | 0.751772i | \(0.729200\pi\) | |||||||
\(150\) | −4.99864 | − | 0.116584i | −0.408137 | − | 0.00951905i | ||||
\(151\) | 3.14518 | + | 5.44761i | 0.255951 | + | 0.443320i | 0.965153 | − | 0.261685i | \(-0.0842780\pi\) |
−0.709202 | + | 0.705005i | \(0.750945\pi\) | |||||||
\(152\) | 0.174421 | − | 0.100702i | 0.0141474 | − | 0.00816803i | ||||
\(153\) | 3.28940 | + | 5.69741i | 0.265933 | + | 0.460609i | ||||
\(154\) | 1.84617i | 0.148769i | ||||||||
\(155\) | 13.3541 | − | 13.0463i | 1.07263 | − | 1.04790i | ||||
\(156\) | − | 3.79425i | − | 0.303783i | ||||||
\(157\) | 3.38321 | + | 1.95330i | 0.270009 | + | 0.155890i | 0.628892 | − | 0.777493i | \(-0.283509\pi\) |
−0.358883 | + | 0.933383i | \(0.616842\pi\) | |||||||
\(158\) | − | 7.98033i | − | 0.634881i | ||||||
\(159\) | −8.62993 | −0.684398 | ||||||||
\(160\) | 0.603880 | − | 2.15298i | 0.0477409 | − | 0.170208i | ||||
\(161\) | −0.632406 | + | 0.365120i | −0.0498406 | + | 0.0287755i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 3.44377 | − | 5.96478i | 0.269737 | − | 0.467198i | −0.699057 | − | 0.715066i | \(-0.746397\pi\) |
0.968794 | + | 0.247868i | \(0.0797300\pi\) | |||||||
\(164\) | 4.00330 | − | 6.93392i | 0.312605 | − | 0.541448i | ||||
\(165\) | 3.44778 | + | 0.967053i | 0.268410 | + | 0.0752850i | ||||
\(166\) | −12.4882 | + | 7.21006i | −0.969272 | + | 0.559609i | ||||
\(167\) | −2.06388 | − | 3.57474i | −0.159708 | − | 0.276622i | 0.775055 | − | 0.631893i | \(-0.217722\pi\) |
−0.934763 | + | 0.355271i | \(0.884389\pi\) | |||||||
\(168\) | −0.576424 | + | 0.998396i | −0.0444721 | + | 0.0770279i | ||||
\(169\) | −0.698155 | + | 1.20924i | −0.0537042 | + | 0.0930185i | ||||
\(170\) | 3.97281 | − | 14.1640i | 0.304701 | − | 1.08633i | ||||
\(171\) | 0.201405i | 0.0154018i | ||||||||
\(172\) | 0.975731 | + | 1.69002i | 0.0743988 | + | 0.128862i | ||||
\(173\) | 20.7126 | + | 11.9584i | 1.57475 | + | 0.909181i | 0.995574 | + | 0.0939768i | \(0.0299579\pi\) |
0.579173 | + | 0.815204i | \(0.303375\pi\) | |||||||
\(174\) | 5.73899 | 0.435072 | ||||||||
\(175\) | −2.76494 | − | 5.05783i | −0.209010 | − | 0.382336i | ||||
\(176\) | −0.800700 | + | 1.38685i | −0.0603550 | + | 0.104538i | ||||
\(177\) | −11.9994 | −0.901930 | ||||||||
\(178\) | 15.6356 | − | 9.02723i | 1.17194 | − | 0.676620i | ||||
\(179\) | − | 16.2259i | − | 1.21278i | −0.795167 | − | 0.606390i | \(-0.792617\pi\) | ||
0.795167 | − | 0.606390i | \(-0.207383\pi\) | |||||||
\(180\) | 1.56260 | + | 1.59947i | 0.116469 | + | 0.119217i | ||||
\(181\) | −2.06172 | − | 3.57100i | −0.153246 | − | 0.265431i | 0.779173 | − | 0.626809i | \(-0.215639\pi\) |
−0.932419 | + | 0.361379i | \(0.882306\pi\) | |||||||
\(182\) | 3.78816 | − | 2.18710i | 0.280797 | − | 0.162118i | ||||
\(183\) | 6.54846 | − | 11.3423i | 0.484076 | − | 0.838445i | ||||
\(184\) | −0.633422 | −0.0466965 | ||||||||
\(185\) | 9.06863 | + | 10.1371i | 0.666739 | + | 0.745291i | ||||
\(186\) | −8.34912 | −0.612187 | ||||||||
\(187\) | −5.26765 | + | 9.12384i | −0.385209 | + | 0.667201i | ||||
\(188\) | 4.03078 | − | 2.32717i | 0.293975 | − | 0.169726i | ||||
\(189\) | −0.576424 | − | 0.998396i | −0.0419287 | − | 0.0726226i | ||||
\(190\) | 0.322140 | − | 0.314714i | 0.0233705 | − | 0.0228318i | ||||
\(191\) | 4.40002i | 0.318374i | 0.987248 | + | 0.159187i | \(0.0508873\pi\) | ||||
−0.987248 | + | 0.159187i | \(0.949113\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | −1.15300 | −0.0829950 | −0.0414975 | − | 0.999139i | \(-0.513213\pi\) | ||||
−0.0414975 | + | 0.999139i | \(0.513213\pi\) | |||||||
\(194\) | −1.46588 | + | 2.53898i | −0.105244 | + | 0.182288i | ||||
\(195\) | −2.10017 | − | 8.22015i | −0.150397 | − | 0.588657i | ||||
\(196\) | 5.67094 | 0.405067 | ||||||||
\(197\) | −1.50044 | − | 0.866279i | −0.106902 | − | 0.0617199i | 0.445596 | − | 0.895234i | \(-0.352992\pi\) |
−0.552498 | + | 0.833514i | \(0.686325\pi\) | |||||||
\(198\) | −0.800700 | − | 1.38685i | −0.0569033 | − | 0.0985593i | ||||
\(199\) | − | 19.8702i | − | 1.40856i | −0.709922 | − | 0.704281i | \(-0.751270\pi\) | ||
0.709922 | − | 0.704281i | \(-0.248730\pi\) | |||||||
\(200\) | 0.116584 | − | 4.99864i | 0.00824374 | − | 0.353457i | ||||
\(201\) | 5.38718 | − | 9.33087i | 0.379982 | − | 0.658149i | ||||
\(202\) | −7.43779 | + | 12.8826i | −0.523321 | + | 0.906419i | ||||
\(203\) | 3.30809 | + | 5.72979i | 0.232183 | + | 0.402152i | ||||
\(204\) | −5.69741 | + | 3.28940i | −0.398899 | + | 0.230304i | ||||
\(205\) | 4.83503 | − | 17.2381i | 0.337693 | − | 1.20396i | ||||
\(206\) | 1.41438 | − | 2.44978i | 0.0985447 | − | 0.170684i | ||||
\(207\) | 0.316711 | − | 0.548560i | 0.0220129 | − | 0.0381275i | ||||
\(208\) | 3.79425 | 0.263084 | ||||||||
\(209\) | −0.279319 | + | 0.161265i | −0.0193209 | + | 0.0111549i | ||||
\(210\) | −0.696182 | + | 2.48206i | −0.0480411 | + | 0.171279i | ||||
\(211\) | −15.6536 | −1.07764 | −0.538820 | − | 0.842421i | \(-0.681130\pi\) | ||||
−0.538820 | + | 0.842421i | \(0.681130\pi\) | |||||||
\(212\) | − | 8.62993i | − | 0.592706i | ||||||
\(213\) | 9.56376 | + | 5.52164i | 0.655298 | + | 0.378336i | ||||
\(214\) | − | 9.43000i | − | 0.644622i | ||||||
\(215\) | 3.04935 | + | 3.12130i | 0.207964 | + | 0.212871i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −4.81263 | − | 8.33573i | −0.326703 | − | 0.565866i | ||||
\(218\) | −11.8873 | + | 6.86312i | −0.805107 | + | 0.464829i | ||||
\(219\) | 2.16187 | + | 3.74446i | 0.146085 | + | 0.253027i | ||||
\(220\) | −0.967053 | + | 3.44778i | −0.0651987 | + | 0.232450i | ||||
\(221\) | 24.9616 | 1.67910 | ||||||||
\(222\) | 0.267030 | − | 6.07690i | 0.0179219 | − | 0.407855i | ||||
\(223\) | − | 16.3946i | − | 1.09786i | −0.835867 | − | 0.548932i | \(-0.815035\pi\) | ||
0.835867 | − | 0.548932i | \(-0.184965\pi\) | |||||||
\(224\) | −0.998396 | − | 0.576424i | −0.0667081 | − | 0.0385140i | ||||
\(225\) | 4.27066 | + | 2.60029i | 0.284711 | + | 0.173352i | ||||
\(226\) | 4.45519 | + | 7.71661i | 0.296355 | + | 0.513301i | ||||
\(227\) | 13.6135 | + | 23.5793i | 0.903562 | + | 1.56502i | 0.822836 | + | 0.568279i | \(0.192390\pi\) |
0.0807258 | + | 0.996736i | \(0.474276\pi\) | |||||||
\(228\) | −0.201405 | −0.0133383 | ||||||||
\(229\) | −6.12750 | − | 10.6131i | −0.404917 | − | 0.701336i | 0.589395 | − | 0.807845i | \(-0.299366\pi\) |
−0.994312 | + | 0.106509i | \(0.966033\pi\) | |||||||
\(230\) | −1.37229 | + | 0.350609i | −0.0904864 | + | 0.0231185i | ||||
\(231\) | 0.923086 | − | 1.59883i | 0.0607346 | − | 0.105195i | ||||
\(232\) | 5.73899i | 0.376783i | ||||||||
\(233\) | 12.4646i | 0.816581i | 0.912852 | + | 0.408290i | \(0.133875\pi\) | ||||
−0.912852 | + | 0.408290i | \(0.866125\pi\) | |||||||
\(234\) | −1.89712 | + | 3.28591i | −0.124019 | + | 0.214807i | ||||
\(235\) | 7.44446 | − | 7.27285i | 0.485623 | − | 0.474429i | ||||
\(236\) | − | 11.9994i | − | 0.781094i | ||||||
\(237\) | −3.99017 | + | 6.91117i | −0.259189 | + | 0.448929i | ||||
\(238\) | −6.56826 | − | 3.79218i | −0.425757 | − | 0.245811i | ||||
\(239\) | −13.9717 | − | 8.06659i | −0.903757 | − | 0.521784i | −0.0253399 | − | 0.999679i | \(-0.508067\pi\) |
−0.878417 | + | 0.477894i | \(0.841400\pi\) | |||||||
\(240\) | −1.59947 | + | 1.56260i | −0.103245 | + | 0.100865i | ||||
\(241\) | −0.462479 | + | 0.267013i | −0.0297909 | + | 0.0171998i | −0.514821 | − | 0.857297i | \(-0.672142\pi\) |
0.485031 | + | 0.874497i | \(0.338808\pi\) | |||||||
\(242\) | −4.21776 | + | 7.30537i | −0.271128 | + | 0.469607i | ||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 11.3423 | + | 6.54846i | 0.726114 | + | 0.419222i | ||||
\(245\) | 12.2860 | − | 3.13895i | 0.784921 | − | 0.200540i | ||||
\(246\) | −6.93392 | + | 4.00330i | −0.442091 | + | 0.255241i | ||||
\(247\) | 0.661798 | + | 0.382089i | 0.0421092 | + | 0.0243118i | ||||
\(248\) | − | 8.34912i | − | 0.530169i | ||||||
\(249\) | 14.4201 | 0.913838 | ||||||||
\(250\) | −2.51425 | − | 10.8940i | −0.159015 | − | 0.688995i | ||||
\(251\) | − | 17.0952i | − | 1.07904i | −0.841973 | − | 0.539520i | \(-0.818606\pi\) | ||
0.841973 | − | 0.539520i | \(-0.181394\pi\) | |||||||
\(252\) | 0.998396 | − | 0.576424i | 0.0628930 | − | 0.0363113i | ||||
\(253\) | 1.01436 | 0.0637724 | ||||||||
\(254\) | −10.7457 | + | 6.20405i | −0.674247 | + | 0.389277i | ||||
\(255\) | −10.5226 | + | 10.2800i | −0.658949 | + | 0.643760i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −2.85889 | + | 4.95174i | −0.178333 | + | 0.308881i | −0.941310 | − | 0.337544i | \(-0.890404\pi\) |
0.762977 | + | 0.646426i | \(0.223737\pi\) | |||||||
\(258\) | − | 1.95146i | − | 0.121493i | ||||||
\(259\) | 6.22107 | − | 3.23627i | 0.386559 | − | 0.201092i | ||||
\(260\) | 8.22015 | − | 2.10017i | 0.509792 | − | 0.130247i | ||||
\(261\) | −4.97011 | − | 2.86950i | −0.307642 | − | 0.177617i | ||||
\(262\) | −0.150501 | + | 0.0868917i | −0.00929797 | + | 0.00536819i | ||||
\(263\) | −26.5295 | + | 15.3168i | −1.63588 | + | 0.944474i | −0.653645 | + | 0.756802i | \(0.726761\pi\) |
−0.982232 | + | 0.187672i | \(0.939906\pi\) | |||||||
\(264\) | 1.38685 | − | 0.800700i | 0.0853549 | − | 0.0492797i | ||||
\(265\) | −4.77680 | − | 18.6965i | −0.293436 | − | 1.14852i | ||||
\(266\) | −0.116094 | − | 0.201082i | −0.00711821 | − | 0.0123291i | ||||
\(267\) | −18.0545 | −1.10492 | ||||||||
\(268\) | 9.33087 | + | 5.38718i | 0.569973 | + | 0.329074i | ||||
\(269\) | 11.7982 | 0.719351 | 0.359675 | − | 0.933077i | \(-0.382887\pi\) | ||||
0.359675 | + | 0.933077i | \(0.382887\pi\) | |||||||
\(270\) | −0.553515 | − | 2.16648i | −0.0336859 | − | 0.131848i | ||||
\(271\) | −5.06391 | + | 8.77094i | −0.307610 | + | 0.532797i | −0.977839 | − | 0.209358i | \(-0.932863\pi\) |
0.670229 | + | 0.742155i | \(0.266196\pi\) | |||||||
\(272\) | −3.28940 | − | 5.69741i | −0.199449 | − | 0.345456i | ||||
\(273\) | −4.37419 | −0.264738 | ||||||||
\(274\) | −0.141932 | − | 0.0819446i | −0.00857443 | − | 0.00495045i | ||||
\(275\) | −0.186698 | + | 8.00482i | −0.0112583 | + | 0.482709i | ||||
\(276\) | 0.548560 | + | 0.316711i | 0.0330194 | + | 0.0190638i | ||||
\(277\) | 14.9276 | + | 25.8554i | 0.896913 | + | 1.55350i | 0.831419 | + | 0.555646i | \(0.187529\pi\) |
0.0654936 | + | 0.997853i | \(0.479138\pi\) | |||||||
\(278\) | 0.808880 | + | 1.40102i | 0.0485134 | + | 0.0840277i | ||||
\(279\) | 7.23055 | + | 4.17456i | 0.432882 | + | 0.249924i | ||||
\(280\) | −2.48206 | − | 0.696182i | −0.148332 | − | 0.0416048i | ||||
\(281\) | −14.1619 | − | 8.17640i | −0.844831 | − | 0.487763i | 0.0140724 | − | 0.999901i | \(-0.495520\pi\) |
−0.858903 | + | 0.512138i | \(0.828854\pi\) | |||||||
\(282\) | −4.65434 | −0.277162 | ||||||||
\(283\) | 2.38752 | + | 4.13531i | 0.141924 | + | 0.245819i | 0.928221 | − | 0.372029i | \(-0.121338\pi\) |
−0.786297 | + | 0.617848i | \(0.788005\pi\) | |||||||
\(284\) | −5.52164 | + | 9.56376i | −0.327649 | + | 0.567505i | ||||
\(285\) | −0.436338 | + | 0.111480i | −0.0258464 | + | 0.00660353i | ||||
\(286\) | −6.07611 | −0.359288 | ||||||||
\(287\) | −7.99376 | − | 4.61520i | −0.471857 | − | 0.272427i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −13.1403 | − | 22.7598i | −0.772962 | − | 1.33881i | ||||
\(290\) | 3.17662 | + | 12.4334i | 0.186538 | + | 0.730114i | ||||
\(291\) | 2.53898 | − | 1.46588i | 0.148838 | − | 0.0859314i | ||||
\(292\) | −3.74446 | + | 2.16187i | −0.219128 | + | 0.126514i | ||||
\(293\) | 3.03946 | − | 1.75483i | 0.177567 | − | 0.102518i | −0.408582 | − | 0.912722i | \(-0.633977\pi\) |
0.586149 | + | 0.810203i | \(0.300643\pi\) | |||||||
\(294\) | −4.91118 | − | 2.83547i | −0.286426 | − | 0.165368i | ||||
\(295\) | −6.64185 | − | 25.9964i | −0.386703 | − | 1.51357i | ||||
\(296\) | 6.07690 | + | 0.267030i | 0.353213 | + | 0.0155208i | ||||
\(297\) | 1.60140i | 0.0929226i | ||||||||
\(298\) | −8.04929 | + | 13.9418i | −0.466283 | + | 0.807625i | ||||
\(299\) | −1.20168 | − | 2.08137i | −0.0694950 | − | 0.120369i | ||||
\(300\) | −2.60029 | + | 4.27066i | −0.150128 | + | 0.246567i | ||||
\(301\) | 1.94833 | − | 1.12487i | 0.112300 | − | 0.0648364i | ||||
\(302\) | 6.29036 | 0.361970 | ||||||||
\(303\) | 12.8826 | − | 7.43779i | 0.740088 | − | 0.427290i | ||||
\(304\) | − | 0.201405i | − | 0.0115513i | ||||||
\(305\) | 28.1974 | + | 7.90897i | 1.61458 | + | 0.452866i | ||||
\(306\) | 6.57881 | 0.376085 | ||||||||
\(307\) | − | 13.8678i | − | 0.791479i | −0.918363 | − | 0.395739i | \(-0.870488\pi\) | ||
0.918363 | − | 0.395739i | \(-0.129512\pi\) | |||||||
\(308\) | 1.59883 | + | 0.923086i | 0.0911019 | + | 0.0525977i | ||||
\(309\) | −2.44978 | + | 1.41438i | −0.139363 | + | 0.0804614i | ||||
\(310\) | −4.62136 | − | 18.0882i | −0.262476 | − | 1.02734i | ||||
\(311\) | −13.6673 | − | 7.89080i | −0.775000 | − | 0.447446i | 0.0596555 | − | 0.998219i | \(-0.481000\pi\) |
−0.834655 | + | 0.550773i | \(0.814333\pi\) | |||||||
\(312\) | −3.28591 | − | 1.89712i | −0.186028 | − | 0.107403i | ||||
\(313\) | −6.99253 | + | 12.1114i | −0.395241 | + | 0.684578i | −0.993132 | − | 0.117000i | \(-0.962672\pi\) |
0.597891 | + | 0.801578i | \(0.296006\pi\) | |||||||
\(314\) | 3.38321 | − | 1.95330i | 0.190925 | − | 0.110231i | ||||
\(315\) | 1.84394 | − | 1.80144i | 0.103894 | − | 0.101499i | ||||
\(316\) | −6.91117 | − | 3.99017i | −0.388784 | − | 0.224464i | ||||
\(317\) | 4.22693 | + | 2.44042i | 0.237408 | + | 0.137068i | 0.613985 | − | 0.789318i | \(-0.289566\pi\) |
−0.376577 | + | 0.926385i | \(0.622899\pi\) | |||||||
\(318\) | −4.31497 | + | 7.47374i | −0.241971 | + | 0.419107i | ||||
\(319\) | − | 9.19042i | − | 0.514565i | ||||||
\(320\) | −1.56260 | − | 1.59947i | −0.0873518 | − | 0.0894129i | ||||
\(321\) | −4.71500 | + | 8.16662i | −0.263166 | + | 0.455816i | ||||
\(322\) | 0.730240i | 0.0406947i | ||||||||
\(323\) | − | 1.32500i | − | 0.0737251i | ||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 16.6463 | − | 9.09995i | 0.923369 | − | 0.504775i | ||||
\(326\) | −3.44377 | − | 5.96478i | −0.190733 | − | 0.330359i | ||||
\(327\) | 13.7262 | 0.759063 | ||||||||
\(328\) | −4.00330 | − | 6.93392i | −0.221045 | − | 0.382862i | ||||
\(329\) | −2.68287 | − | 4.64687i | −0.147912 | − | 0.256190i | ||||
\(330\) | 2.56138 | − | 2.50234i | 0.141000 | − | 0.137749i | ||||
\(331\) | 8.03353 | + | 4.63816i | 0.441563 | + | 0.254936i | 0.704260 | − | 0.709942i | \(-0.251279\pi\) |
−0.262698 | + | 0.964878i | \(0.584612\pi\) | |||||||
\(332\) | 14.4201i | 0.791407i | ||||||||
\(333\) | −3.26970 | + | 5.12923i | −0.179179 | + | 0.281080i | ||||
\(334\) | −4.12776 | −0.225861 | ||||||||
\(335\) | 23.1970 | + | 6.50642i | 1.26739 | + | 0.355484i | ||||
\(336\) | 0.576424 | + | 0.998396i | 0.0314465 | + | 0.0544670i | ||||
\(337\) | −26.0610 | + | 15.0463i | −1.41963 | + | 0.819625i | −0.996266 | − | 0.0863330i | \(-0.972485\pi\) |
−0.423367 | + | 0.905958i | \(0.639152\pi\) | |||||||
\(338\) | 0.698155 | + | 1.20924i | 0.0379746 | + | 0.0657740i | ||||
\(339\) | − | 8.91037i | − | 0.483945i | ||||||
\(340\) | −10.2800 | − | 10.5226i | −0.557512 | − | 0.570667i | ||||
\(341\) | 13.3703i | 0.724041i | ||||||||
\(342\) | 0.174421 | + | 0.100702i | 0.00943163 | + | 0.00544536i | ||||
\(343\) | − | 14.6077i | − | 0.788740i | ||||||
\(344\) | 1.95146 | 0.105216 | ||||||||
\(345\) | 1.36375 | + | 0.382511i | 0.0734216 | + | 0.0205937i | ||||
\(346\) | 20.7126 | − | 11.9584i | 1.11351 | − | 0.642888i | ||||
\(347\) | −24.1815 | −1.29813 | −0.649066 | − | 0.760733i | \(-0.724840\pi\) | ||||
−0.649066 | + | 0.760733i | \(0.724840\pi\) | |||||||
\(348\) | 2.86950 | − | 4.97011i | 0.153821 | − | 0.266426i | ||||
\(349\) | −3.22778 | + | 5.59068i | −0.172779 | + | 0.299262i | −0.939390 | − | 0.342849i | \(-0.888608\pi\) |
0.766611 | + | 0.642111i | \(0.221941\pi\) | |||||||
\(350\) | −5.76268 | − | 0.134404i | −0.308028 | − | 0.00718419i | ||||
\(351\) | 3.28591 | − | 1.89712i | 0.175389 | − | 0.101261i | ||||
\(352\) | 0.800700 | + | 1.38685i | 0.0426774 | + | 0.0739195i | ||||
\(353\) | 5.33390 | − | 9.23859i | 0.283895 | − | 0.491721i | −0.688446 | − | 0.725288i | \(-0.741707\pi\) |
0.972341 | + | 0.233567i | \(0.0750399\pi\) | |||||||
\(354\) | −5.99970 | + | 10.3918i | −0.318880 | + | 0.552317i | ||||
\(355\) | −6.66882 | + | 23.7760i | −0.353944 | + | 1.26190i | ||||
\(356\) | − | 18.0545i | − | 0.956885i | ||||||
\(357\) | 3.79218 | + | 6.56826i | 0.200704 | + | 0.347629i | ||||
\(358\) | −14.0520 | − | 8.11294i | −0.742673 | − | 0.428782i | ||||
\(359\) | −7.32628 | −0.386666 | −0.193333 | − | 0.981133i | \(-0.561930\pi\) | ||||
−0.193333 | + | 0.981133i | \(0.561930\pi\) | |||||||
\(360\) | 2.16648 | − | 0.553515i | 0.114183 | − | 0.0291728i | ||||
\(361\) | −9.47972 | + | 16.4194i | −0.498933 | + | 0.864176i | ||||
\(362\) | −4.12344 | −0.216723 | ||||||||
\(363\) | 7.30537 | − | 4.21776i | 0.383433 | − | 0.221375i | ||||
\(364\) | − | 4.37419i | − | 0.229270i | ||||||
\(365\) | −6.91566 | + | 6.75625i | −0.361982 | + | 0.353638i | ||||
\(366\) | −6.54846 | − | 11.3423i | −0.342294 | − | 0.592870i | ||||
\(367\) | −3.73951 | + | 2.15901i | −0.195201 | + | 0.112699i | −0.594415 | − | 0.804159i | \(-0.702616\pi\) |
0.399214 | + | 0.916858i | \(0.369283\pi\) | |||||||
\(368\) | −0.316711 | + | 0.548560i | −0.0165097 | + | 0.0285957i | ||||
\(369\) | 8.00660 | 0.416807 | ||||||||
\(370\) | 13.3133 | − | 2.78514i | 0.692124 | − | 0.144793i | ||||
\(371\) | −9.94900 | −0.516527 | ||||||||
\(372\) | −4.17456 | + | 7.23055i | −0.216441 | + | 0.374886i | ||||
\(373\) | −0.164880 | + | 0.0951938i | −0.00853719 | + | 0.00492895i | −0.504263 | − | 0.863550i | \(-0.668236\pi\) |
0.495725 | + | 0.868479i | \(0.334902\pi\) | |||||||
\(374\) | 5.26765 | + | 9.12384i | 0.272384 | + | 0.471782i | ||||
\(375\) | −3.26958 | + | 10.6916i | −0.168841 | + | 0.552111i | ||||
\(376\) | − | 4.65434i | − | 0.240029i | ||||||
\(377\) | −18.8578 | + | 10.8876i | −0.971228 | + | 0.560739i | ||||
\(378\) | −1.15285 | −0.0592961 | ||||||||
\(379\) | −15.9392 | + | 27.6075i | −0.818742 | + | 1.41810i | 0.0878680 | + | 0.996132i | \(0.471995\pi\) |
−0.906610 | + | 0.421970i | \(0.861339\pi\) | |||||||
\(380\) | −0.111480 | − | 0.436338i | −0.00571883 | − | 0.0223837i | ||||
\(381\) | 12.4081 | 0.635686 | ||||||||
\(382\) | 3.81053 | + | 2.20001i | 0.194963 | + | 0.112562i | ||||
\(383\) | 11.9491 | + | 20.6964i | 0.610569 | + | 1.05754i | 0.991145 | + | 0.132787i | \(0.0423926\pi\) |
−0.380575 | + | 0.924750i | \(0.624274\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | 3.97477 | + | 1.11487i | 0.202573 | + | 0.0568188i | ||||
\(386\) | −0.576502 | + | 0.998530i | −0.0293432 | + | 0.0508238i | ||||
\(387\) | −0.975731 | + | 1.69002i | −0.0495992 | + | 0.0859083i | ||||
\(388\) | 1.46588 | + | 2.53898i | 0.0744188 | + | 0.128897i | ||||
\(389\) | 6.13244 | − | 3.54056i | 0.310927 | − | 0.179514i | −0.336414 | − | 0.941714i | \(-0.609214\pi\) |
0.647341 | + | 0.762200i | \(0.275881\pi\) | |||||||
\(390\) | −8.16894 | − | 2.29127i | −0.413651 | − | 0.116023i | ||||
\(391\) | −2.08358 | + | 3.60887i | −0.105371 | + | 0.182508i | ||||
\(392\) | 2.83547 | − | 4.91118i | 0.143213 | − | 0.248052i | ||||
\(393\) | 0.173783 | 0.00876621 | ||||||||
\(394\) | −1.50044 | + | 0.866279i | −0.0755911 | + | 0.0436425i | ||||
\(395\) | −17.1815 | − | 4.81916i | −0.864496 | − | 0.242478i | ||||
\(396\) | −1.60140 | −0.0804734 | ||||||||
\(397\) | − | 1.61077i | − | 0.0808422i | −0.999183 | − | 0.0404211i | \(-0.987130\pi\) | ||
0.999183 | − | 0.0404211i | \(-0.0128699\pi\) | |||||||
\(398\) | −17.2081 | − | 9.93510i | −0.862564 | − | 0.498002i | ||||
\(399\) | 0.232189i | 0.0116240i | ||||||||
\(400\) | −4.27066 | − | 2.60029i | −0.213533 | − | 0.130014i | ||||
\(401\) | − | 8.93803i | − | 0.446344i | −0.974779 | − | 0.223172i | \(-0.928359\pi\) | ||
0.974779 | − | 0.223172i | \(-0.0716411\pi\) | |||||||
\(402\) | −5.38718 | − | 9.33087i | −0.268688 | − | 0.465381i | ||||
\(403\) | 27.4345 | − | 15.8393i | 1.36661 | − | 0.789012i | ||||
\(404\) | 7.43779 | + | 12.8826i | 0.370044 | + | 0.640935i | ||||
\(405\) | −0.603880 | + | 2.15298i | −0.0300070 | + | 0.106983i | ||||
\(406\) | 6.61619 | 0.328356 | ||||||||
\(407\) | −9.73154 | − | 0.427622i | −0.482375 | − | 0.0211964i | ||||
\(408\) | 6.57881i | 0.325699i | ||||||||
\(409\) | −24.5929 | − | 14.1987i | −1.21604 | − | 0.702080i | −0.251971 | − | 0.967735i | \(-0.581079\pi\) |
−0.964068 | + | 0.265654i | \(0.914412\pi\) | |||||||
\(410\) | −12.5111 | − | 12.8063i | −0.617879 | − | 0.632458i | ||||
\(411\) | 0.0819446 | + | 0.141932i | 0.00404203 | + | 0.00700100i | ||||
\(412\) | −1.41438 | − | 2.44978i | −0.0696816 | − | 0.120692i | ||||
\(413\) | −13.8335 | −0.680701 | ||||||||
\(414\) | −0.316711 | − | 0.548560i | −0.0155655 | − | 0.0269602i | ||||
\(415\) | 7.98176 | + | 31.2409i | 0.391809 | + | 1.53355i | ||||
\(416\) | 1.89712 | − | 3.28591i | 0.0930141 | − | 0.161105i | ||||
\(417\) | − | 1.61776i | − | 0.0792221i | ||||||
\(418\) | 0.322529i | 0.0157754i | ||||||||
\(419\) | −17.6867 | + | 30.6343i | −0.864053 | + | 1.49658i | 0.00393056 | + | 0.999992i | \(0.498749\pi\) |
−0.867984 | + | 0.496592i | \(0.834584\pi\) | |||||||
\(420\) | 1.80144 | + | 1.84394i | 0.0879011 | + | 0.0899752i | ||||
\(421\) | 6.87298i | 0.334968i | 0.985875 | + | 0.167484i | \(0.0535643\pi\) | ||||
−0.985875 | + | 0.167484i | \(0.946436\pi\) | |||||||
\(422\) | −7.82681 | + | 13.5564i | −0.381003 | + | 0.659917i | ||||
\(423\) | 4.03078 | + | 2.32717i | 0.195983 | + | 0.113151i | ||||
\(424\) | −7.47374 | − | 4.31497i | −0.362957 | − | 0.209553i | ||||
\(425\) | −28.0958 | − | 17.1068i | −1.36285 | − | 0.829800i | ||||
\(426\) | 9.56376 | − | 5.52164i | 0.463366 | − | 0.267524i | ||||
\(427\) | 7.54938 | − | 13.0759i | 0.365340 | − | 0.632788i | ||||
\(428\) | −8.16662 | − | 4.71500i | −0.394749 | − | 0.227908i | ||||
\(429\) | 5.26206 | + | 3.03805i | 0.254055 | + | 0.146679i | ||||
\(430\) | 4.22780 | − | 1.08016i | 0.203882 | − | 0.0520901i | ||||
\(431\) | 29.8230 | − | 17.2183i | 1.43652 | − | 0.829376i | 0.438915 | − | 0.898529i | \(-0.355363\pi\) |
0.997606 | + | 0.0691529i | \(0.0220296\pi\) | |||||||
\(432\) | −0.866025 | − | 0.500000i | −0.0416667 | − | 0.0240563i | ||||
\(433\) | 17.7398i | 0.852520i | 0.904601 | + | 0.426260i | \(0.140169\pi\) | ||||
−0.904601 | + | 0.426260i | \(0.859831\pi\) | |||||||
\(434\) | −9.62527 | −0.462028 | ||||||||
\(435\) | 3.46566 | − | 12.3559i | 0.166166 | − | 0.592422i | ||||
\(436\) | 13.7262i | 0.657367i | ||||||||
\(437\) | −0.110482 | + | 0.0637871i | −0.00528509 | + | 0.00305135i | ||||
\(438\) | 4.32373 | 0.206596 | ||||||||
\(439\) | −4.36970 | + | 2.52285i | −0.208554 | + | 0.120409i | −0.600639 | − | 0.799520i | \(-0.705087\pi\) |
0.392085 | + | 0.919929i | \(0.371754\pi\) | |||||||
\(440\) | 2.50234 | + | 2.56138i | 0.119294 | + | 0.122109i | ||||
\(441\) | 2.83547 | + | 4.91118i | 0.135022 | + | 0.233866i | ||||
\(442\) | 12.4808 | − | 21.6174i | 0.593652 | − | 1.02823i | ||||
\(443\) | − | 5.67021i | − | 0.269400i | −0.990886 | − | 0.134700i | \(-0.956993\pi\) | ||
0.990886 | − | 0.134700i | \(-0.0430070\pi\) | |||||||
\(444\) | −5.12923 | − | 3.26970i | −0.243423 | − | 0.155173i | ||||
\(445\) | −9.99342 | − | 39.1146i | −0.473734 | − | 1.85421i | ||||
\(446\) | −14.1981 | − | 8.19730i | −0.672301 | − | 0.388153i | ||||
\(447\) | 13.9418 | − | 8.04929i | 0.659423 | − | 0.380718i | ||||
\(448\) | −0.998396 | + | 0.576424i | −0.0471698 | + | 0.0272335i | ||||
\(449\) | −5.83240 | + | 3.36734i | −0.275248 | + | 0.158914i | −0.631270 | − | 0.775563i | \(-0.717466\pi\) |
0.356022 | + | 0.934477i | \(0.384133\pi\) | |||||||
\(450\) | 4.38724 | − | 2.39836i | 0.206817 | − | 0.113060i | ||||
\(451\) | 6.41089 | + | 11.1040i | 0.301877 | + | 0.522866i | ||||
\(452\) | 8.91037 | 0.419109 | ||||||||
\(453\) | −5.44761 | − | 3.14518i | −0.255951 | − | 0.147773i | ||||
\(454\) | 27.2271 | 1.27783 | ||||||||
\(455\) | −2.42118 | − | 9.47659i | −0.113507 | − | 0.444269i | ||||
\(456\) | −0.100702 | + | 0.174421i | −0.00471582 | + | 0.00816803i | ||||
\(457\) | 12.5902 | + | 21.8068i | 0.588944 | + | 1.02008i | 0.994371 | + | 0.105953i | \(0.0337894\pi\) |
−0.405427 | + | 0.914127i | \(0.632877\pi\) | |||||||
\(458\) | −12.2550 | −0.572639 | ||||||||
\(459\) | −5.69741 | − | 3.28940i | −0.265933 | − | 0.153536i | ||||
\(460\) | −0.382511 | + | 1.36375i | −0.0178347 | + | 0.0635850i | ||||
\(461\) | 30.6749 | + | 17.7102i | 1.42867 | + | 0.824846i | 0.997016 | − | 0.0771914i | \(-0.0245952\pi\) |
0.431658 | + | 0.902037i | \(0.357929\pi\) | |||||||
\(462\) | −0.923086 | − | 1.59883i | −0.0429458 | − | 0.0743844i | ||||
\(463\) | 10.5328 | + | 18.2434i | 0.489502 | + | 0.847842i | 0.999927 | − | 0.0120800i | \(-0.00384527\pi\) |
−0.510425 | + | 0.859922i | \(0.670512\pi\) | |||||||
\(464\) | 4.97011 | + | 2.86950i | 0.230732 | + | 0.133213i | ||||
\(465\) | −5.04187 | + | 17.9755i | −0.233811 | + | 0.833594i | ||||
\(466\) | 10.7946 | + | 6.23228i | 0.500052 | + | 0.288705i | ||||
\(467\) | 36.8742 | 1.70634 | 0.853168 | − | 0.521636i | \(-0.174678\pi\) | ||||
0.853168 | + | 0.521636i | \(0.174678\pi\) | |||||||
\(468\) | 1.89712 | + | 3.28591i | 0.0876946 | + | 0.151891i | ||||
\(469\) | 6.21060 | − | 10.7571i | 0.286779 | − | 0.496716i | ||||
\(470\) | −2.57625 | − | 10.0835i | −0.118833 | − | 0.465118i | ||||
\(471\) | −3.90659 | −0.180006 | ||||||||
\(472\) | −10.3918 | − | 5.99970i | −0.478320 | − | 0.276158i | ||||
\(473\) | −3.12507 | −0.143691 | ||||||||
\(474\) | 3.99017 | + | 6.91117i | 0.183274 | + | 0.317441i | ||||
\(475\) | −0.483040 | − | 0.883611i | −0.0221634 | − | 0.0405428i | ||||
\(476\) | −6.56826 | + | 3.79218i | −0.301055 | + | 0.173814i | ||||
\(477\) | 7.47374 | − | 4.31497i | 0.342199 | − | 0.197569i | ||||
\(478\) | −13.9717 | + | 8.06659i | −0.639053 | + | 0.368957i | ||||
\(479\) | 3.93591 | + | 2.27240i | 0.179836 | + | 0.103829i | 0.587216 | − | 0.809430i | \(-0.300224\pi\) |
−0.407379 | + | 0.913259i | \(0.633557\pi\) | |||||||
\(480\) | 0.553515 | + | 2.16648i | 0.0252644 | + | 0.0988857i | ||||
\(481\) | 10.6512 | + | 20.4748i | 0.485652 | + | 0.933569i | ||||
\(482\) | 0.534025i | 0.0243242i | ||||||||
\(483\) | 0.365120 | − | 0.632406i | 0.0166135 | − | 0.0287755i | ||||
\(484\) | 4.21776 | + | 7.30537i | 0.191716 | + | 0.332062i | ||||
\(485\) | 4.58116 | + | 4.68925i | 0.208020 | + | 0.212928i | ||||
\(486\) | 0.866025 | − | 0.500000i | 0.0392837 | − | 0.0226805i | ||||
\(487\) | 26.0473 | 1.18032 | 0.590158 | − | 0.807288i | \(-0.299065\pi\) | ||||
0.590158 | + | 0.807288i | \(0.299065\pi\) | |||||||
\(488\) | 11.3423 | − | 6.54846i | 0.513440 | − | 0.296435i | ||||
\(489\) | 6.88754i | 0.311465i | ||||||||
\(490\) | 3.42457 | − | 12.2094i | 0.154706 | − | 0.551566i | ||||
\(491\) | 28.0039 | 1.26380 | 0.631900 | − | 0.775050i | \(-0.282276\pi\) | ||||
0.631900 | + | 0.775050i | \(0.282276\pi\) | |||||||
\(492\) | 8.00660i | 0.360966i | ||||||||
\(493\) | 32.6974 | + | 18.8779i | 1.47262 | + | 0.850216i | ||||
\(494\) | 0.661798 | − | 0.382089i | 0.0297757 | − | 0.0171910i | ||||
\(495\) | −3.46940 | + | 0.886399i | −0.155938 | + | 0.0398407i | ||||
\(496\) | −7.23055 | − | 4.17456i | −0.324661 | − | 0.187443i | ||||
\(497\) | 11.0256 | + | 6.36561i | 0.494564 | + | 0.285537i | ||||
\(498\) | 7.21006 | − | 12.4882i | 0.323091 | − | 0.559609i | ||||
\(499\) | 22.5995 | − | 13.0478i | 1.01169 | − | 0.584100i | 0.100005 | − | 0.994987i | \(-0.468114\pi\) |
0.911686 | + | 0.410887i | \(0.134781\pi\) | |||||||
\(500\) | −10.6916 | − | 3.26958i | −0.478142 | − | 0.146220i | ||||
\(501\) | 3.57474 | + | 2.06388i | 0.159708 | + | 0.0922073i | ||||
\(502\) | −14.8049 | − | 8.54760i | −0.660774 | − | 0.381498i | ||||
\(503\) | 14.5457 | − | 25.1938i | 0.648559 | − | 1.12334i | −0.334908 | − | 0.942251i | \(-0.608705\pi\) |
0.983467 | − | 0.181087i | \(-0.0579615\pi\) | |||||||
\(504\) | − | 1.15285i | − | 0.0513520i | ||||||
\(505\) | 23.2445 | + | 23.7930i | 1.03437 | + | 1.05877i | ||||
\(506\) | 0.507181 | − | 0.878464i | 0.0225470 | − | 0.0390525i | ||||
\(507\) | − | 1.39631i | − | 0.0620123i | ||||||
\(508\) | 12.4081i | 0.550520i | ||||||||
\(509\) | −5.98303 | + | 10.3629i | −0.265193 | + | 0.459328i | −0.967614 | − | 0.252434i | \(-0.918769\pi\) |
0.702421 | + | 0.711762i | \(0.252102\pi\) | |||||||
\(510\) | 3.64147 | + | 14.2528i | 0.161247 | + | 0.631126i | ||||
\(511\) | 2.49230 | + | 4.31680i | 0.110253 | + | 0.190964i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −0.100702 | − | 0.174421i | −0.00444611 | − | 0.00770090i | ||||
\(514\) | 2.85889 | + | 4.95174i | 0.126100 | + | 0.218412i | ||||
\(515\) | −4.42022 | − | 4.52451i | −0.194778 | − | 0.199374i | ||||
\(516\) | −1.69002 | − | 0.975731i | −0.0743988 | − | 0.0429542i | ||||
\(517\) | 7.45346i | 0.327803i | ||||||||
\(518\) | 0.307845 | − | 7.00574i | 0.0135259 | − | 0.307815i | ||||
\(519\) | −23.9168 | −1.04983 | ||||||||
\(520\) | 2.29127 | − | 8.16894i | 0.100479 | − | 0.358232i | ||||
\(521\) | 18.7348 | + | 32.4496i | 0.820787 | + | 1.42164i | 0.905097 | + | 0.425205i | \(0.139798\pi\) |
−0.0843099 | + | 0.996440i | \(0.526869\pi\) | |||||||
\(522\) | −4.97011 | + | 2.86950i | −0.217536 | + | 0.125594i | ||||
\(523\) | −17.4308 | − | 30.1910i | −0.762195 | − | 1.32016i | −0.941717 | − | 0.336407i | \(-0.890788\pi\) |
0.179522 | − | 0.983754i | \(-0.442545\pi\) | |||||||
\(524\) | 0.173783i | 0.00759176i | ||||||||
\(525\) | 4.92342 | + | 2.99773i | 0.214876 | + | 0.130832i | ||||
\(526\) | 30.6336i | 1.33569i | ||||||||
\(527\) | −47.5684 | − | 27.4636i | −2.07211 | − | 1.19633i | ||||
\(528\) | − | 1.60140i | − | 0.0696920i | ||||||
\(529\) | −22.5988 | −0.982555 | ||||||||
\(530\) | −18.5801 | − | 5.21144i | −0.807067 | − | 0.226371i | ||||
\(531\) | 10.3918 | − | 5.99970i | 0.450965 | − | 0.260365i | ||||
\(532\) | −0.232189 | −0.0100667 | ||||||||
\(533\) | 15.1895 | − | 26.3090i | 0.657931 | − | 1.13957i | ||||
\(534\) | −9.02723 | + | 15.6356i | −0.390647 | + | 0.676620i | ||||
\(535\) | −20.3026 | − | 5.69459i | −0.877759 | − | 0.246199i | ||||
\(536\) | 9.33087 | − | 5.38718i | 0.403032 | − | 0.232691i | ||||
\(537\) | 8.11294 | + | 14.0520i | 0.350099 | + | 0.606390i | ||||
\(538\) | 5.89911 | − | 10.2176i | 0.254329 | − | 0.440511i | ||||
\(539\) | −4.54072 | + | 7.86476i | −0.195583 | + | 0.338759i | ||||
\(540\) | −2.15298 | − | 0.603880i | −0.0926496 | − | 0.0259869i | ||||
\(541\) | 6.10400i | 0.262432i | 0.991354 | + | 0.131216i | \(0.0418881\pi\) | ||||
−0.991354 | + | 0.131216i | \(0.958112\pi\) | |||||||
\(542\) | 5.06391 | + | 8.77094i | 0.217513 | + | 0.376744i | ||||
\(543\) | 3.57100 | + | 2.06172i | 0.153246 | + | 0.0884769i | ||||
\(544\) | −6.57881 | −0.282064 | ||||||||
\(545\) | 7.59768 | + | 29.7376i | 0.325449 | + | 1.27382i | ||||
\(546\) | −2.18710 | + | 3.78816i | −0.0935991 | + | 0.162118i | ||||
\(547\) | 28.0504 | 1.19935 | 0.599675 | − | 0.800243i | \(-0.295296\pi\) | ||||
0.599675 | + | 0.800243i | \(0.295296\pi\) | |||||||
\(548\) | −0.141932 | + | 0.0819446i | −0.00606304 | + | 0.00350050i | ||||
\(549\) | 13.0969i | 0.558963i | ||||||||
\(550\) | 6.83903 | + | 4.16410i | 0.291617 | + | 0.177558i | ||||
\(551\) | 0.577930 | + | 1.00100i | 0.0246206 | + | 0.0426442i | ||||
\(552\) | 0.548560 | − | 0.316711i | 0.0233483 | − | 0.0134801i | ||||
\(553\) | −4.60006 | + | 7.96753i | −0.195614 | + | 0.338814i | ||||
\(554\) | 29.8552 | 1.26843 | ||||||||
\(555\) | −12.9222 | − | 4.24463i | −0.548517 | − | 0.180174i | ||||
\(556\) | 1.61776 | 0.0686083 | ||||||||
\(557\) | −1.04224 | + | 1.80521i | −0.0441610 | + | 0.0764890i | −0.887261 | − | 0.461268i | \(-0.847395\pi\) |
0.843100 | + | 0.537757i | \(0.180728\pi\) | |||||||
\(558\) | 7.23055 | − | 4.17456i | 0.306093 | − | 0.176723i | ||||
\(559\) | 3.70216 | + | 6.41234i | 0.156585 | + | 0.271213i | ||||
\(560\) | −1.84394 | + | 1.80144i | −0.0779208 | + | 0.0761246i | ||||
\(561\) | − | 10.5353i | − | 0.444801i | ||||||
\(562\) | −14.1619 | + | 8.17640i | −0.597386 | + | 0.344901i | ||||
\(563\) | 6.83925 | 0.288240 | 0.144120 | − | 0.989560i | \(-0.453965\pi\) | ||||
0.144120 | + | 0.989560i | \(0.453965\pi\) | |||||||
\(564\) | −2.32717 | + | 4.03078i | −0.0979915 | + | 0.169726i | ||||
\(565\) | 19.3041 | − | 4.93203i | 0.812130 | − | 0.207492i | ||||
\(566\) | 4.77505 | 0.200710 | ||||||||
\(567\) | 0.998396 | + | 0.576424i | 0.0419287 | + | 0.0242075i | ||||
\(568\) | 5.52164 | + | 9.56376i | 0.231683 | + | 0.401286i | ||||
\(569\) | − | 1.30706i | − | 0.0547947i | −0.999625 | − | 0.0273973i | \(-0.991278\pi\) | ||
0.999625 | − | 0.0273973i | \(-0.00872194\pi\) | |||||||
\(570\) | −0.121624 | + | 0.433620i | −0.00509428 | + | 0.0181624i | ||||
\(571\) | 12.5935 | − | 21.8126i | 0.527022 | − | 0.912829i | −0.472482 | − | 0.881340i | \(-0.656642\pi\) |
0.999504 | − | 0.0314890i | \(-0.0100249\pi\) | |||||||
\(572\) | −3.03805 | + | 5.26206i | −0.127027 | + | 0.220018i | ||||
\(573\) | −2.20001 | − | 3.81053i | −0.0919066 | − | 0.159187i | ||||
\(574\) | −7.99376 | + | 4.61520i | −0.333653 | + | 0.192635i | ||||
\(575\) | −0.0738470 | + | 3.16625i | −0.00307963 | + | 0.132042i | ||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 14.3582 | − | 24.8692i | 0.597741 | − | 1.03532i | −0.395413 | − | 0.918503i | \(-0.629399\pi\) |
0.993154 | − | 0.116814i | \(-0.0372681\pi\) | |||||||
\(578\) | −26.2807 | −1.09313 | ||||||||
\(579\) | 0.998530 | − | 0.576502i | 0.0414975 | − | 0.0239586i | ||||
\(580\) | 12.3559 | + | 3.46566i | 0.513053 | + | 0.143904i | ||||
\(581\) | 16.6242 | 0.689689 | ||||||||
\(582\) | − | 2.93176i | − | 0.121525i | ||||||
\(583\) | 11.9684 | + | 6.90999i | 0.495682 | + | 0.286182i | ||||
\(584\) | 4.32373i | 0.178917i | ||||||||
\(585\) | 5.92888 | + | 6.06877i | 0.245129 | + | 0.250913i | ||||
\(586\) | − | 3.50966i | − | 0.144983i | ||||||
\(587\) | −19.0536 | − | 33.0018i | −0.786427 | − | 1.36213i | −0.928143 | − | 0.372224i | \(-0.878595\pi\) |
0.141716 | − | 0.989907i | \(-0.454738\pi\) | |||||||
\(588\) | −4.91118 | + | 2.83547i | −0.202534 | + | 0.116933i | ||||
\(589\) | −0.840775 | − | 1.45627i | −0.0346435 | − | 0.0600044i | ||||
\(590\) | −25.8345 | − | 7.24620i | −1.06359 | − | 0.298321i | ||||
\(591\) | 1.73256 | 0.0712679 | ||||||||
\(592\) | 3.26970 | − | 5.12923i | 0.134384 | − | 0.210810i | ||||
\(593\) | − | 10.9777i | − | 0.450800i | −0.974266 | − | 0.225400i | \(-0.927631\pi\) | ||
0.974266 | − | 0.225400i | \(-0.0723688\pi\) | |||||||
\(594\) | 1.38685 | + | 0.800700i | 0.0569033 | + | 0.0328531i | ||||
\(595\) | −12.1309 | + | 11.8513i | −0.497320 | + | 0.485856i | ||||
\(596\) | 8.04929 | + | 13.9418i | 0.329712 | + | 0.571077i | ||||
\(597\) | 9.93510 | + | 17.2081i | 0.406617 | + | 0.704281i | ||||
\(598\) | −2.40336 | −0.0982807 | ||||||||
\(599\) | 6.68729 | + | 11.5827i | 0.273235 | + | 0.473258i | 0.969688 | − | 0.244345i | \(-0.0785729\pi\) |
−0.696453 | + | 0.717602i | \(0.745240\pi\) | |||||||
\(600\) | 2.39836 | + | 4.38724i | 0.0979125 | + | 0.179108i | ||||
\(601\) | −8.44195 | + | 14.6219i | −0.344354 | + | 0.596439i | −0.985236 | − | 0.171200i | \(-0.945235\pi\) |
0.640882 | + | 0.767639i | \(0.278569\pi\) | |||||||
\(602\) | − | 2.24974i | − | 0.0916926i | ||||||
\(603\) | 10.7744i | 0.438766i | ||||||||
\(604\) | 3.14518 | − | 5.44761i | 0.127976 | − | 0.221660i | ||||
\(605\) | 13.1813 | + | 13.4923i | 0.535897 | + | 0.548541i | ||||
\(606\) | − | 14.8756i | − | 0.604279i | ||||||
\(607\) | −12.0273 | + | 20.8319i | −0.488172 | + | 0.845539i | −0.999907 | − | 0.0136043i | \(-0.995669\pi\) |
0.511735 | + | 0.859143i | \(0.329003\pi\) | |||||||
\(608\) | −0.174421 | − | 0.100702i | −0.00707372 | − | 0.00408402i | ||||
\(609\) | −5.72979 | − | 3.30809i | −0.232183 | − | 0.134051i | ||||
\(610\) | 20.9481 | − | 20.4652i | 0.848163 | − | 0.828612i | ||||
\(611\) | 15.2938 | − | 8.82986i | 0.618719 | − | 0.357218i | ||||
\(612\) | 3.28940 | − | 5.69741i | 0.132966 | − | 0.230304i | ||||
\(613\) | −17.7700 | − | 10.2595i | −0.717724 | − | 0.414378i | 0.0961906 | − | 0.995363i | \(-0.469334\pi\) |
−0.813914 | + | 0.580985i | \(0.802668\pi\) | |||||||
\(614\) | −12.0099 | − | 6.93391i | −0.484680 | − | 0.279830i | ||||
\(615\) | 4.43178 | + | 17.3461i | 0.178706 | + | 0.699463i | ||||
\(616\) | 1.59883 | − | 0.923086i | 0.0644188 | − | 0.0371922i | ||||
\(617\) | 17.4897 | + | 10.0977i | 0.704108 | + | 0.406517i | 0.808876 | − | 0.587980i | \(-0.200076\pi\) |
−0.104767 | + | 0.994497i | \(0.533410\pi\) | |||||||
\(618\) | 2.82877i | 0.113790i | ||||||||
\(619\) | 1.21856 | 0.0489782 | 0.0244891 | − | 0.999700i | \(-0.492204\pi\) | ||||
0.0244891 | + | 0.999700i | \(0.492204\pi\) | |||||||
\(620\) | −17.9755 | − | 5.04187i | −0.721913 | − | 0.202486i | ||||
\(621\) | 0.633422i | 0.0254184i | ||||||||
\(622\) | −13.6673 | + | 7.89080i | −0.548008 | + | 0.316392i | ||||
\(623\) | −20.8141 | −0.833898 | ||||||||
\(624\) | −3.28591 | + | 1.89712i | −0.131542 | + | 0.0759457i | ||||
\(625\) | −24.9728 | − | 1.16552i | −0.998913 | − | 0.0466210i | ||||
\(626\) | 6.99253 | + | 12.1114i | 0.279478 | + | 0.484070i | ||||
\(627\) | 0.161265 | − | 0.279319i | 0.00644029 | − | 0.0111549i | ||||
\(628\) | − | 3.90659i | − | 0.155890i | ||||||
\(629\) | 21.5108 | − | 33.7442i | 0.857690 | − | 1.34547i | ||||
\(630\) | −0.638119 | − | 2.49762i | −0.0254233 | − | 0.0995075i | ||||
\(631\) | 35.4811 | + | 20.4850i | 1.41248 | + | 0.815497i | 0.995622 | − | 0.0934743i | \(-0.0297973\pi\) |
0.416860 | + | 0.908971i | \(0.363131\pi\) | |||||||
\(632\) | −6.91117 | + | 3.99017i | −0.274912 | + | 0.158720i | ||||
\(633\) | 13.5564 | − | 7.82681i | 0.538820 | − | 0.311088i | ||||
\(634\) | 4.22693 | − | 2.44042i | 0.167873 | − | 0.0969215i | ||||
\(635\) | 6.86807 | + | 26.8819i | 0.272551 | + | 1.06677i | ||||
\(636\) | 4.31497 | + | 7.47374i | 0.171100 | + | 0.296353i | ||||
\(637\) | 21.5169 | 0.852533 | ||||||||
\(638\) | −7.95914 | − | 4.59521i | −0.315105 | − | 0.181926i | ||||
\(639\) | −11.0433 | −0.436865 | ||||||||
\(640\) | −2.16648 | + | 0.553515i | −0.0856375 | + | 0.0218796i | ||||
\(641\) | −7.32583 | + | 12.6887i | −0.289353 | + | 0.501174i | −0.973655 | − | 0.228024i | \(-0.926773\pi\) |
0.684302 | + | 0.729198i | \(0.260107\pi\) | |||||||
\(642\) | 4.71500 | + | 8.16662i | 0.186086 | + | 0.322311i | ||||
\(643\) | −26.8103 | −1.05730 | −0.528648 | − | 0.848841i | \(-0.677301\pi\) | ||||
−0.528648 | + | 0.848841i | \(0.677301\pi\) | |||||||
\(644\) | 0.632406 | + | 0.365120i | 0.0249203 | + | 0.0143877i | ||||
\(645\) | −4.20146 | − | 1.17845i | −0.165432 | − | 0.0464014i | ||||
\(646\) | −1.14749 | − | 0.662501i | −0.0451472 | − | 0.0260657i | ||||
\(647\) | −10.9636 | − | 18.9895i | −0.431024 | − | 0.746555i | 0.565938 | − | 0.824448i | \(-0.308514\pi\) |
−0.996962 | + | 0.0778928i | \(0.975181\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | 16.6414 | + | 9.60791i | 0.653232 | + | 0.377144i | ||||
\(650\) | 0.442349 | − | 18.9661i | 0.0173504 | − | 0.743911i | ||||
\(651\) | 8.33573 | + | 4.81263i | 0.326703 | + | 0.188622i | ||||
\(652\) | −6.88754 | −0.269737 | ||||||||
\(653\) | −13.8367 | − | 23.9659i | −0.541473 | − | 0.937859i | −0.998820 | − | 0.0485707i | \(-0.984533\pi\) |
0.457346 | − | 0.889289i | \(-0.348800\pi\) | |||||||
\(654\) | 6.86312 | − | 11.8873i | 0.268369 | − | 0.464829i | ||||
\(655\) | 0.0961918 | + | 0.376498i | 0.00375852 | + | 0.0147110i | ||||
\(656\) | −8.00660 | −0.312605 | ||||||||
\(657\) | −3.74446 | − | 2.16187i | −0.146085 | − | 0.0843424i | ||||
\(658\) | −5.36575 | −0.209179 | ||||||||
\(659\) | −24.2847 | − | 42.0624i | −0.945998 | − | 1.63852i | −0.753740 | − | 0.657172i | \(-0.771752\pi\) |
−0.192258 | − | 0.981344i | \(-0.561581\pi\) | |||||||
\(660\) | −0.886399 | − | 3.46940i | −0.0345030 | − | 0.135046i | ||||
\(661\) | −24.9498 | + | 14.4048i | −0.970434 | + | 0.560280i | −0.899368 | − | 0.437192i | \(-0.855973\pi\) |
−0.0710652 | + | 0.997472i | \(0.522640\pi\) | |||||||
\(662\) | 8.03353 | − | 4.63816i | 0.312232 | − | 0.180267i | ||||
\(663\) | −21.6174 | + | 12.4808i | −0.839550 | + | 0.484714i | ||||
\(664\) | 12.4882 | + | 7.21006i | 0.484636 | + | 0.279805i | ||||
\(665\) | −0.503032 | + | 0.128520i | −0.0195067 | + | 0.00498380i | ||||
\(666\) | 2.80719 | + | 5.39626i | 0.108777 | + | 0.209101i | ||||
\(667\) | − | 3.63521i | − | 0.140756i | ||||||
\(668\) | −2.06388 | + | 3.57474i | −0.0798539 | + | 0.138311i | ||||
\(669\) | 8.19730 | + | 14.1981i | 0.316926 | + | 0.548932i | ||||
\(670\) | 17.2332 | − | 16.8360i | 0.665777 | − | 0.650430i | ||||
\(671\) | −18.1635 | + | 10.4867i | −0.701194 | + | 0.404835i | ||||
\(672\) | 1.15285 | 0.0444721 | ||||||||
\(673\) | 25.5316 | − | 14.7407i | 0.984171 | − | 0.568211i | 0.0806443 | − | 0.996743i | \(-0.474302\pi\) |
0.903527 | + | 0.428532i | \(0.140969\pi\) | |||||||
\(674\) | 30.0926i | 1.15913i | ||||||||
\(675\) | −4.99864 | − | 0.116584i | −0.192398 | − | 0.00448733i | ||||
\(676\) | 1.39631 | 0.0537042 | ||||||||
\(677\) | 15.7058i | 0.603625i | 0.953367 | + | 0.301812i | \(0.0975916\pi\) | ||||
−0.953367 | + | 0.301812i | \(0.902408\pi\) | |||||||
\(678\) | −7.71661 | − | 4.45519i | −0.296355 | − | 0.171100i | ||||
\(679\) | 2.92706 | − | 1.68994i | 0.112330 | − | 0.0648539i | ||||
\(680\) | −14.2528 | + | 3.64147i | −0.546571 | + | 0.139644i | ||||
\(681\) | −23.5793 | − | 13.6135i | −0.903562 | − | 0.521672i | ||||
\(682\) | 11.5790 | + | 6.68514i | 0.443383 | + | 0.255987i | ||||
\(683\) | −10.5991 | + | 18.3581i | −0.405562 | + | 0.702454i | −0.994387 | − | 0.105807i | \(-0.966257\pi\) |
0.588825 | + | 0.808261i | \(0.299591\pi\) | |||||||
\(684\) | 0.174421 | − | 0.100702i | 0.00666917 | − | 0.00385045i | ||||
\(685\) | −0.262135 | + | 0.256093i | −0.0100157 | + | 0.00978479i | ||||
\(686\) | −12.6506 | − | 7.30384i | −0.483003 | − | 0.278862i | ||||
\(687\) | 10.6131 | + | 6.12750i | 0.404917 | + | 0.233779i | ||||
\(688\) | 0.975731 | − | 1.69002i | 0.0371994 | − | 0.0644312i | ||||
\(689\) | − | 32.7441i | − | 1.24745i | ||||||
\(690\) | 1.01314 | − | 0.989784i | 0.0385695 | − | 0.0376804i | ||||
\(691\) | −24.3436 | + | 42.1643i | −0.926073 | + | 1.60401i | −0.136247 | + | 0.990675i | \(0.543504\pi\) |
−0.789826 | + | 0.613331i | \(0.789829\pi\) | |||||||
\(692\) | − | 23.9168i | − | 0.909181i | ||||||
\(693\) | 1.84617i | 0.0701303i | ||||||||
\(694\) | −12.0908 | + | 20.9418i | −0.458959 | + | 0.794940i | ||||
\(695\) | 3.50484 | − | 0.895455i | 0.132946 | − | 0.0339665i | ||||
\(696\) | −2.86950 | − | 4.97011i | −0.108768 | − | 0.188392i | ||||
\(697\) | −52.6739 | −1.99517 | ||||||||
\(698\) | 3.22778 | + | 5.59068i | 0.122173 | + | 0.211610i | ||||
\(699\) | −6.23228 | − | 10.7946i | −0.235727 | − | 0.408290i | ||||
\(700\) | −2.99773 | + | 4.92342i | −0.113304 | + | 0.186088i | ||||
\(701\) | −26.2855 | − | 15.1759i | −0.992788 | − | 0.573186i | −0.0866814 | − | 0.996236i | \(-0.527626\pi\) |
−0.906106 | + | 0.423050i | \(0.860960\pi\) | |||||||
\(702\) | − | 3.79425i | − | 0.143205i | ||||||
\(703\) | 1.08683 | − | 0.565382i | 0.0409906 | − | 0.0213238i | ||||
\(704\) | 1.60140 | 0.0603550 | ||||||||
\(705\) | −2.81066 | + | 10.0207i | −0.105856 | + | 0.377402i | ||||
\(706\) | −5.33390 | − | 9.23859i | −0.200744 | − | 0.347699i | ||||
\(707\) | 14.8517 | − | 8.57465i | 0.558557 | − | 0.322483i | ||||
\(708\) | 5.99970 | + | 10.3918i | 0.225482 | + | 0.390547i | ||||
\(709\) | 12.2106i | 0.458577i | 0.973358 | + | 0.229289i | \(0.0736400\pi\) | ||||
−0.973358 | + | 0.229289i | \(0.926360\pi\) | |||||||
\(710\) | 17.2562 | + | 17.6633i | 0.647613 | + | 0.662894i | ||||
\(711\) | − | 7.98033i | − | 0.299286i | ||||||
\(712\) | −15.6356 | − | 9.02723i | −0.585970 | − | 0.338310i | ||||
\(713\) | 5.28852i | 0.198057i | ||||||||
\(714\) | 7.58437 | 0.283838 | ||||||||
\(715\) | −3.66924 | + | 13.0817i | −0.137222 | + | 0.489230i | ||||
\(716\) | −14.0520 | + | 8.11294i | −0.525149 | + | 0.303195i | ||||
\(717\) | 16.1332 | 0.602505 | ||||||||
\(718\) | −3.66314 | + | 6.34474i | −0.136707 | + | 0.236784i | ||||
\(719\) | −6.58657 | + | 11.4083i | −0.245637 | + | 0.425457i | −0.962311 | − | 0.271953i | \(-0.912331\pi\) |
0.716673 | + | 0.697409i | \(0.245664\pi\) | |||||||
\(720\) | 0.603880 | − | 2.15298i | 0.0225053 | − | 0.0802369i | ||||
\(721\) | −2.82423 | + | 1.63057i | −0.105180 | + | 0.0607256i | ||||
\(722\) | 9.47972 | + | 16.4194i | 0.352799 | + | 0.611065i | ||||
\(723\) | 0.267013 | − | 0.462479i | 0.00993031 | − | 0.0171998i | ||||
\(724\) | −2.06172 | + | 3.57100i | −0.0766232 | + | 0.132715i | ||||
\(725\) | 28.6872 | + | 0.669075i | 1.06541 | + | 0.0248488i | ||||
\(726\) | − | 8.43552i | − | 0.313071i | ||||||
\(727\) | −4.14865 | − | 7.18568i | −0.153865 | − | 0.266502i | 0.778780 | − | 0.627297i | \(-0.215839\pi\) |
−0.932645 | + | 0.360795i | \(0.882505\pi\) | |||||||
\(728\) | −3.78816 | − | 2.18710i | −0.140399 | − | 0.0810592i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 2.39325 | + | 9.36726i | 0.0885782 | + | 0.346698i | ||||
\(731\) | 6.41915 | − | 11.1183i | 0.237421 | − | 0.411225i | ||||
\(732\) | −13.0969 | −0.484076 | ||||||||
\(733\) | −25.5218 | + | 14.7350i | −0.942669 | + | 0.544250i | −0.890796 | − | 0.454404i | \(-0.849852\pi\) |
−0.0518729 | + | 0.998654i | \(0.516519\pi\) | |||||||
\(734\) | 4.31801i | 0.159381i | ||||||||
\(735\) | −9.07048 | + | 8.86139i | −0.334570 | + | 0.326857i | ||||
\(736\) | 0.316711 | + | 0.548560i | 0.0116741 | + | 0.0202202i | ||||
\(737\) | −14.9424 | + | 8.62703i | −0.550412 | + | 0.317781i | ||||
\(738\) | 4.00330 | − | 6.93392i | 0.147364 | − | 0.255241i | ||||
\(739\) | 45.4776 | 1.67292 | 0.836461 | − | 0.548027i | \(-0.184621\pi\) | ||||
0.836461 | + | 0.548027i | \(0.184621\pi\) | |||||||
\(740\) | 4.24463 | − | 12.9222i | 0.156036 | − | 0.475029i | ||||
\(741\) | −0.764179 | −0.0280728 | ||||||||
\(742\) | −4.97450 | + | 8.61609i | −0.182620 | + | 0.316307i | ||||
\(743\) | 19.0245 | − | 10.9838i | 0.697941 | − | 0.402957i | −0.108639 | − | 0.994081i | \(-0.534649\pi\) |
0.806580 | + | 0.591125i | \(0.201316\pi\) | |||||||
\(744\) | 4.17456 | + | 7.23055i | 0.153047 | + | 0.265085i | ||||
\(745\) | 25.1556 | + | 25.7491i | 0.921629 | + | 0.943375i | ||||
\(746\) | 0.190388i | 0.00697058i | ||||||||
\(747\) | −12.4882 | + | 7.21006i | −0.456919 | + | 0.263802i | ||||
\(748\) | 10.5353 | 0.385209 | ||||||||
\(749\) | −5.43568 | + | 9.41488i | −0.198616 | + | 0.344012i | ||||
\(750\) | 7.62439 | + | 8.17733i | 0.278403 | + | 0.298594i | ||||
\(751\) | 20.1290 | 0.734517 | 0.367258 | − | 0.930119i | \(-0.380296\pi\) | ||||
0.367258 | + | 0.930119i | \(0.380296\pi\) | |||||||
\(752\) | −4.03078 | − | 2.32717i | −0.146987 | − | 0.0848631i | ||||
\(753\) | 8.54760 | + | 14.8049i | 0.311492 | + | 0.539520i | ||||
\(754\) | 21.7752i | 0.793004i | ||||||||
\(755\) | 3.79862 | − | 13.5430i | 0.138246 | − | 0.492881i | ||||
\(756\) | −0.576424 | + | 0.998396i | −0.0209643 | + | 0.0363113i | ||||
\(757\) | 9.99404 | − | 17.3102i | 0.363239 | − | 0.629149i | −0.625253 | − | 0.780422i | \(-0.715004\pi\) |
0.988492 | + | 0.151273i | \(0.0483374\pi\) | |||||||
\(758\) | 15.9392 | + | 27.6075i | 0.578938 | + | 1.00275i | ||||
\(759\) | −0.878464 | + | 0.507181i | −0.0318862 | + | 0.0184095i | ||||
\(760\) | −0.433620 | − | 0.121624i | −0.0157291 | − | 0.00441177i | ||||
\(761\) | −3.62729 | + | 6.28264i | −0.131489 | + | 0.227746i | −0.924251 | − | 0.381786i | \(-0.875309\pi\) |
0.792762 | + | 0.609532i | \(0.208642\pi\) | |||||||
\(762\) | 6.20405 | − | 10.7457i | 0.224749 | − | 0.389277i | ||||
\(763\) | 15.8243 | 0.572877 | ||||||||
\(764\) | 3.81053 | − | 2.20001i | 0.137860 | − | 0.0795935i | ||||
\(765\) | 3.97281 | − | 14.1640i | 0.143637 | − | 0.512102i | ||||
\(766\) | 23.8982 | 0.863475 | ||||||||
\(767\) | − | 45.5287i | − | 1.64394i | ||||||
\(768\) | 0.866025 | + | 0.500000i | 0.0312500 | + | 0.0180422i | ||||
\(769\) | − | 17.8233i | − | 0.642724i | −0.946956 | − | 0.321362i | \(-0.895859\pi\) | ||
0.946956 | − | 0.321362i | \(-0.104141\pi\) | |||||||
\(770\) | 2.95289 | − | 2.88482i | 0.106415 | − | 0.103962i | ||||
\(771\) | − | 5.71778i | − | 0.205921i | ||||||
\(772\) | 0.576502 | + | 0.998530i | 0.0207487 | + | 0.0359379i | ||||
\(773\) | −40.0301 | + | 23.1114i | −1.43978 | + | 0.831260i | −0.997834 | − | 0.0657804i | \(-0.979046\pi\) |
−0.441950 | + | 0.897040i | \(0.645713\pi\) | |||||||
\(774\) | 0.975731 | + | 1.69002i | 0.0350719 | + | 0.0607464i | ||||
\(775\) | −41.7342 | − | 0.973374i | −1.49914 | − | 0.0349646i | ||||
\(776\) | 2.93176 | 0.105244 | ||||||||
\(777\) | −3.76947 | + | 5.91323i | −0.135229 | + | 0.212136i | ||||
\(778\) | − | 7.08113i | − | 0.253871i | ||||||
\(779\) | −1.39652 | − | 0.806283i | −0.0500356 | − | 0.0288881i | ||||
\(780\) | −6.06877 | + | 5.92888i | −0.217297 | + | 0.212288i | ||||
\(781\) | −8.84235 | − | 15.3154i | −0.316404 | − | 0.548028i | ||||
\(782\) | 2.08358 | + | 3.60887i | 0.0745087 | + | 0.129053i | ||||
\(783\) | 5.73899 | 0.205095 | ||||||||
\(784\) | −2.83547 | − | 4.91118i | −0.101267 | − | 0.175399i | ||||
\(785\) | −2.16236 | − | 8.46354i | −0.0771778 | − | 0.302077i | ||||
\(786\) | 0.0868917 | − | 0.150501i | 0.00309932 | − | 0.00536819i | ||||
\(787\) | 37.3668i | 1.33198i | 0.745960 | + | 0.665991i | \(0.231991\pi\) | ||||
−0.745960 | + | 0.665991i | \(0.768009\pi\) | |||||||
\(788\) | 1.73256i | 0.0617199i | ||||||||
\(789\) | 15.3168 | − | 26.5295i | 0.545292 | − | 0.944474i | ||||
\(790\) | −12.7643 | + | 12.4700i | −0.454132 | + | 0.443664i | ||||
\(791\) | − | 10.2723i | − | 0.365241i | ||||||
\(792\) | −0.800700 | + | 1.38685i | −0.0284516 | + | 0.0492797i | ||||
\(793\) | 43.0354 | + | 24.8465i | 1.52823 | + | 0.882324i | ||||
\(794\) | −1.39497 | − | 0.805384i | −0.0495055 | − | 0.0285820i | ||||
\(795\) | 13.4851 | + | 13.8033i | 0.478267 | + | 0.489552i | ||||
\(796\) | −17.2081 | + | 9.93510i | −0.609925 | + | 0.352140i | ||||
\(797\) | 0.885326 | − | 1.53343i | 0.0313598 | − | 0.0543168i | −0.849920 | − | 0.526913i | \(-0.823350\pi\) |
0.881279 | + | 0.472596i | \(0.156683\pi\) | |||||||
\(798\) | 0.201082 | + | 0.116094i | 0.00711821 | + | 0.00410970i | ||||
\(799\) | −26.5177 | − | 15.3100i | −0.938129 | − | 0.541629i | ||||
\(800\) | −4.38724 | + | 2.39836i | −0.155112 | + | 0.0847947i | ||||
\(801\) | 15.6356 | − | 9.02723i | 0.552458 | − | 0.318962i | ||||
\(802\) | −7.74056 | − | 4.46901i | −0.273329 | − | 0.157806i | ||||
\(803\) | − | 6.92402i | − | 0.244343i | ||||||
\(804\) | −10.7744 | −0.379982 | ||||||||
\(805\) | 1.57219 | + | 0.440977i | 0.0554125 | + | 0.0155424i | ||||
\(806\) | − | 31.6786i | − | 1.11583i | ||||||
\(807\) | −10.2176 | + | 5.89911i | −0.359675 | + | 0.207659i | ||||
\(808\) | 14.8756 | 0.523321 | ||||||||
\(809\) | −1.26629 | + | 0.731091i | −0.0445202 | + | 0.0257038i | −0.522095 | − | 0.852887i | \(-0.674849\pi\) |
0.477575 | + | 0.878591i | \(0.341516\pi\) | |||||||
\(810\) | 1.56260 | + | 1.59947i | 0.0549040 | + | 0.0561995i | ||||
\(811\) | 13.5792 | + | 23.5198i | 0.476830 | + | 0.825893i | 0.999647 | − | 0.0265514i | \(-0.00845256\pi\) |
−0.522818 | + | 0.852444i | \(0.675119\pi\) | |||||||
\(812\) | 3.30809 | − | 5.72979i | 0.116091 | − | 0.201076i | ||||
\(813\) | − | 10.1278i | − | 0.355198i | ||||||
\(814\) | −5.23610 | + | 8.21395i | −0.183525 | + | 0.287899i | ||||
\(815\) | −14.9217 | + | 3.81236i | −0.522684 | + | 0.133541i | ||||
\(816\) | 5.69741 | + | 3.28940i | 0.199449 | + | 0.115152i | ||||
\(817\) | 0.340377 | − | 0.196517i | 0.0119083 | − | 0.00687525i | ||||
\(818\) | −24.5929 | + | 14.1987i | −0.859869 | + | 0.496446i | ||||
\(819\) | 3.78816 | − | 2.18710i | 0.132369 | − | 0.0764233i | ||||
\(820\) | −17.3461 | + | 4.43178i | −0.605753 | + | 0.154764i | ||||
\(821\) | −22.8564 | − | 39.5884i | −0.797693 | − | 1.38164i | −0.921115 | − | 0.389291i | \(-0.872720\pi\) |
0.123422 | − | 0.992354i | \(-0.460613\pi\) | |||||||
\(822\) | 0.163889 | 0.00571629 | ||||||||
\(823\) | −13.9921 | − | 8.07837i | −0.487735 | − | 0.281594i | 0.235899 | − | 0.971778i | \(-0.424196\pi\) |
−0.723634 | + | 0.690183i | \(0.757530\pi\) | |||||||
\(824\) | −2.82877 | −0.0985447 | ||||||||
\(825\) | −3.84073 | − | 7.02573i | −0.133717 | − | 0.244604i | ||||
\(826\) | −6.91674 | + | 11.9801i | −0.240664 | + | 0.416843i | ||||
\(827\) | 8.32393 | + | 14.4175i | 0.289452 | + | 0.501345i | 0.973679 | − | 0.227924i | \(-0.0731938\pi\) |
−0.684227 | + | 0.729269i | \(0.739860\pi\) | |||||||
\(828\) | −0.633422 | −0.0220129 | ||||||||
\(829\) | −21.9579 | − | 12.6774i | −0.762630 | − | 0.440305i | 0.0676091 | − | 0.997712i | \(-0.478463\pi\) |
−0.830239 | + | 0.557407i | \(0.811796\pi\) | |||||||
\(830\) | 31.0463 | + | 8.70802i | 1.07763 | + | 0.302260i | ||||
\(831\) | −25.8554 | − | 14.9276i | −0.896913 | − | 0.517833i | ||||
\(832\) | −1.89712 | − | 3.28591i | −0.0657709 | − | 0.113919i | ||||
\(833\) | −18.6540 | − | 32.3097i | −0.646323 | − | 1.11946i | ||||
\(834\) | −1.40102 | − | 0.808880i | −0.0485134 | − | 0.0280092i | ||||
\(835\) | −2.49267 | + | 8.88699i | −0.0862625 | + | 0.307547i | ||||
\(836\) | 0.279319 | + | 0.161265i | 0.00966043 | + | 0.00557745i | ||||
\(837\) | −8.34912 | −0.288588 | ||||||||
\(838\) | 17.6867 | + | 30.6343i | 0.610978 | + | 1.05825i | ||||
\(839\) | −20.0824 | + | 34.7837i | −0.693322 | + | 1.20087i | 0.277422 | + | 0.960748i | \(0.410520\pi\) |
−0.970743 | + | 0.240120i | \(0.922813\pi\) | |||||||
\(840\) | 2.49762 | − | 0.638119i | 0.0861761 | − | 0.0220172i | ||||
\(841\) | −3.93603 | −0.135725 | ||||||||
\(842\) | 5.95217 | + | 3.43649i | 0.205125 | + | 0.118429i | ||||
\(843\) | 16.3528 | 0.563221 | ||||||||
\(844\) | 7.82681 | + | 13.5564i | 0.269410 | + | 0.466632i | ||||
\(845\) | 3.02507 | − | 0.772879i | 0.104066 | − | 0.0265878i | ||||
\(846\) | 4.03078 | − | 2.32717i | 0.138581 | − | 0.0800097i | ||||
\(847\) | 8.42199 | − | 4.86244i | 0.289383 | − | 0.167075i | ||||
\(848\) | −7.47374 | + | 4.31497i | −0.256649 | + | 0.148177i | ||||
\(849\) | −4.13531 | − | 2.38752i | −0.141924 | − | 0.0819396i | ||||
\(850\) | −28.8628 | + | 15.7783i | −0.989986 | + | 0.541192i | ||||
\(851\) | −3.84924 | − | 0.169143i | −0.131950 | − | 0.00579814i | ||||
\(852\) | − | 11.0433i | − | 0.378336i | ||||||
\(853\) | 1.89354 | − | 3.27971i | 0.0648336 | − | 0.112295i | −0.831787 | − | 0.555096i | \(-0.812682\pi\) |
0.896620 | + | 0.442801i | \(0.146015\pi\) | |||||||
\(854\) | −7.54938 | − | 13.0759i | −0.258335 | − | 0.447449i | ||||
\(855\) | 0.322140 | − | 0.314714i | 0.0110169 | − | 0.0107630i | ||||
\(856\) | −8.16662 | + | 4.71500i | −0.279129 | + | 0.161155i | ||||
\(857\) | −28.2901 | −0.966370 | −0.483185 | − | 0.875518i | \(-0.660520\pi\) | ||||
−0.483185 | + | 0.875518i | \(0.660520\pi\) | |||||||
\(858\) | 5.26206 | − | 3.03805i | 0.179644 | − | 0.103717i | ||||
\(859\) | 19.6040i | 0.668881i | 0.942417 | + | 0.334441i | \(0.108547\pi\) | ||||
−0.942417 | + | 0.334441i | \(0.891453\pi\) | |||||||
\(860\) | 1.17845 | − | 4.20146i | 0.0401848 | − | 0.143269i | ||||
\(861\) | 9.23040 | 0.314571 | ||||||||
\(862\) | − | 34.4366i | − | 1.17291i | ||||||
\(863\) | 4.36914 | + | 2.52252i | 0.148727 | + | 0.0858676i | 0.572517 | − | 0.819893i | \(-0.305967\pi\) |
−0.423790 | + | 0.905761i | \(0.639300\pi\) | |||||||
\(864\) | −0.866025 | + | 0.500000i | −0.0294628 | + | 0.0170103i | ||||
\(865\) | −13.2383 | − | 51.8152i | −0.450117 | − | 1.76177i | ||||
\(866\) | 15.3631 | + | 8.86990i | 0.522060 | + | 0.301411i | ||||
\(867\) | 22.7598 | + | 13.1403i | 0.772962 | + | 0.446270i | ||||
\(868\) | −4.81263 | + | 8.33573i | −0.163351 | + | 0.282933i | ||||
\(869\) | 11.0675 | − | 6.38985i | 0.375441 | − | 0.216761i | ||||
\(870\) | −8.96773 | − | 9.17932i | −0.304034 | − | 0.311208i | ||||
\(871\) | 35.4036 | + | 20.4403i | 1.19961 | + | 0.692593i | ||||
\(872\) | 11.8873 | + | 6.86312i | 0.402554 | + | 0.232415i | ||||
\(873\) | −1.46588 | + | 2.53898i | −0.0496125 | + | 0.0859314i | ||||
\(874\) | 0.127574i | 0.00431526i | ||||||||
\(875\) | −3.76933 | + | 12.3258i | −0.127427 | + | 0.416687i | ||||
\(876\) | 2.16187 | − | 3.74446i | 0.0730427 | − | 0.126514i | ||||
\(877\) | 18.6496i | 0.629752i | 0.949133 | + | 0.314876i | \(0.101963\pi\) | ||||
−0.949133 | + | 0.314876i | \(0.898037\pi\) | |||||||
\(878\) | 5.04569i | 0.170284i | ||||||||
\(879\) | −1.75483 | + | 3.03946i | −0.0591890 | + | 0.102518i | ||||
\(880\) | 3.46940 | − | 0.886399i | 0.116953 | − | 0.0298805i | ||||
\(881\) | −4.23407 | − | 7.33362i | −0.142649 | − | 0.247076i | 0.785844 | − | 0.618425i | \(-0.212229\pi\) |
−0.928493 | + | 0.371349i | \(0.878895\pi\) | |||||||
\(882\) | 5.67094 | 0.190950 | ||||||||
\(883\) | −22.3120 | − | 38.6455i | −0.750858 | − | 1.30052i | −0.947407 | − | 0.320030i | \(-0.896307\pi\) |
0.196549 | − | 0.980494i | \(-0.437026\pi\) | |||||||
\(884\) | −12.4808 | − | 21.6174i | −0.419775 | − | 0.727072i | ||||
\(885\) | 18.7502 | + | 19.1926i | 0.630281 | + | 0.645153i | ||||
\(886\) | −4.91055 | − | 2.83510i | −0.164973 | − | 0.0952472i | ||||
\(887\) | − | 10.6967i | − | 0.359159i | −0.983743 | − | 0.179579i | \(-0.942526\pi\) | ||
0.983743 | − | 0.179579i | \(-0.0574737\pi\) | |||||||
\(888\) | −5.39626 | + | 2.80719i | −0.181087 | + | 0.0942033i | ||||
\(889\) | 14.3047 | 0.479763 | ||||||||
\(890\) | −38.8709 | − | 10.9027i | −1.30296 | − | 0.365460i | ||||
\(891\) | −0.800700 | − | 1.38685i | −0.0268245 | − | 0.0464613i | ||||
\(892\) | −14.1981 | + | 8.19730i | −0.475389 | + | 0.274466i | ||||
\(893\) | −0.468703 | − | 0.811817i | −0.0156845 | − | 0.0271664i | ||||
\(894\) | − | 16.0986i | − | 0.538417i | ||||||
\(895\) | −25.9528 | + | 25.3545i | −0.867505 | + | 0.847508i | ||||
\(896\) | 1.15285i | 0.0385140i | ||||||||
\(897\) | 2.08137 | + | 1.20168i | 0.0694950 | + | 0.0401229i | ||||
\(898\) | 6.73467i | 0.224739i | ||||||||
\(899\) | 47.9155 | 1.59807 | ||||||||
\(900\) | 0.116584 | − | 4.99864i | 0.00388614 | − | 0.166621i | ||||
\(901\) | −49.1683 | + | 28.3873i | −1.63803 | + | 0.945719i | ||||
\(902\) | 12.8218 | 0.426918 | ||||||||
\(903\) | −1.12487 | + | 1.94833i | −0.0374333 | + | 0.0648364i | ||||
\(904\) | 4.45519 | − | 7.71661i | 0.148177 | − | 0.256651i | ||||
\(905\) | −2.49006 | + | 8.87769i | −0.0827725 | + | 0.295104i | ||||
\(906\) | −5.44761 | + | 3.14518i | −0.180985 | + | 0.104492i | ||||
\(907\) | 9.54454 | + | 16.5316i | 0.316921 | + | 0.548924i | 0.979844 | − | 0.199764i | \(-0.0640175\pi\) |
−0.662923 | + | 0.748688i | \(0.730684\pi\) | |||||||
\(908\) | 13.6135 | − | 23.5793i | 0.451781 | − | 0.782508i | ||||
\(909\) | −7.43779 | + | 12.8826i | −0.246696 | + | 0.427290i | ||||
\(910\) | −9.41755 | − | 2.64149i | −0.312189 | − | 0.0875645i | ||||
\(911\) | − | 40.2529i | − | 1.33364i | −0.745219 | − | 0.666819i | \(-0.767655\pi\) | ||
0.745219 | − | 0.666819i | \(-0.232345\pi\) | |||||||
\(912\) | 0.100702 | + | 0.174421i | 0.00333459 | + | 0.00577567i | ||||
\(913\) | −19.9986 | − | 11.5462i | −0.661857 | − | 0.382123i | ||||
\(914\) | 25.1804 | 0.832892 | ||||||||
\(915\) | −28.3742 | + | 7.24935i | −0.938021 | + | 0.239656i | ||||
\(916\) | −6.12750 | + | 10.6131i | −0.202458 | + | 0.350668i | ||||
\(917\) | 0.200346 | 0.00661601 | ||||||||
\(918\) | −5.69741 | + | 3.28940i | −0.188043 | + | 0.108566i | ||||
\(919\) | − | 36.0859i | − | 1.19036i | −0.803591 | − | 0.595181i | \(-0.797080\pi\) | ||
0.803591 | − | 0.595181i | \(-0.202920\pi\) | |||||||
\(920\) | 0.989784 | + | 1.01314i | 0.0326322 | + | 0.0334022i | ||||
\(921\) | 6.93391 | + | 12.0099i | 0.228480 | + | 0.395739i | ||||
\(922\) | 30.6749 | − | 17.7102i | 1.01023 | − | 0.583254i | ||||
\(923\) | −20.9505 | + | 36.2873i | −0.689593 | + | 1.19441i | ||||
\(924\) | −1.84617 | −0.0607346 | ||||||||
\(925\) | 2.04326 | − | 30.3451i | 0.0671819 | − | 0.997741i | ||||
\(926\) | 21.0657 | 0.692260 | ||||||||
\(927\) | 1.41438 | − | 2.44978i | 0.0464544 | − | 0.0804614i | ||||
\(928\) | 4.97011 | − | 2.86950i | 0.163152 | − | 0.0941958i | ||||
\(929\) | −11.7507 | − | 20.3528i | −0.385528 | − | 0.667753i | 0.606315 | − | 0.795225i | \(-0.292647\pi\) |
−0.991842 | + | 0.127471i | \(0.959314\pi\) | |||||||
\(930\) | 13.0463 | + | 13.3541i | 0.427805 | + | 0.437899i | ||||
\(931\) | − | 1.14215i | − | 0.0374326i | ||||||
\(932\) | 10.7946 | − | 6.23228i | 0.353590 | − | 0.204145i | ||||
\(933\) | 15.7816 | 0.516666 | ||||||||
\(934\) | 18.4371 | − | 31.9340i | 0.603281 | − | 1.04491i | ||||
\(935\) | 22.8245 | − | 5.83145i | 0.746440 | − | 0.190709i | ||||
\(936\) | 3.79425 | 0.124019 | ||||||||
\(937\) | 40.1652 | + | 23.1894i | 1.31214 | + | 0.757564i | 0.982450 | − | 0.186525i | \(-0.0597226\pi\) |
0.329690 | + | 0.944089i | \(0.393056\pi\) | |||||||
\(938\) | −6.21060 | − | 10.7571i | −0.202783 | − | 0.351231i | ||||
\(939\) | − | 13.9851i | − | 0.456385i | ||||||
\(940\) | −10.0207 | − | 2.81066i | −0.326839 | − | 0.0916737i | ||||
\(941\) | −15.7891 | + | 27.3476i | −0.514711 | + | 0.891506i | 0.485143 | + | 0.874435i | \(0.338768\pi\) |
−0.999854 | + | 0.0170715i | \(0.994566\pi\) | |||||||
\(942\) | −1.95330 | + | 3.38321i | −0.0636418 | + | 0.110231i | ||||
\(943\) | 2.53578 | + | 4.39210i | 0.0825764 | + | 0.143026i | ||||
\(944\) | −10.3918 | + | 5.99970i | −0.338224 | + | 0.195274i | ||||
\(945\) | −0.696182 | + | 2.48206i | −0.0226468 | + | 0.0807415i | ||||
\(946\) | −1.56254 | + | 2.70639i | −0.0508024 | + | 0.0879924i | ||||
\(947\) | 17.5747 | − | 30.4402i | 0.571100 | − | 0.989174i | −0.425354 | − | 0.905027i | \(-0.639850\pi\) |
0.996453 | − | 0.0841466i | \(-0.0268164\pi\) | |||||||
\(948\) | 7.98033 | 0.259189 | ||||||||
\(949\) | −14.2074 | + | 8.20265i | −0.461192 | + | 0.266269i | ||||
\(950\) | −1.00675 | − | 0.0234806i | −0.0326633 | − | 0.000761810i | ||||
\(951\) | −4.88084 | −0.158272 | ||||||||
\(952\) | 7.58437i | 0.245811i | ||||||||
\(953\) | −26.4316 | − | 15.2603i | −0.856203 | − | 0.494329i | 0.00653627 | − | 0.999979i | \(-0.497919\pi\) |
−0.862739 | + | 0.505650i | \(0.831253\pi\) | |||||||
\(954\) | − | 8.62993i | − | 0.279404i | ||||||
\(955\) | 7.03768 | − | 6.87545i | 0.227734 | − | 0.222484i | ||||
\(956\) | 16.1332i | 0.521784i | ||||||||
\(957\) | 4.59521 | + | 7.95914i | 0.148542 | + | 0.257282i | ||||
\(958\) | 3.93591 | − | 2.27240i | 0.127163 | − | 0.0734179i | ||||
\(959\) | 0.0944697 | + | 0.163626i | 0.00305058 | + | 0.00528377i | ||||
\(960\) | 2.15298 | + | 0.603880i | 0.0694872 | + | 0.0194901i | ||||
\(961\) | −38.7077 | −1.24864 | ||||||||
\(962\) | 23.0573 | + | 1.01318i | 0.743396 | + | 0.0326662i | ||||
\(963\) | − | 9.43000i | − | 0.303878i | ||||||
\(964\) | 0.462479 | + | 0.267013i | 0.0148955 | + | 0.00859990i | ||||
\(965\) | 1.80168 | + | 1.84419i | 0.0579981 | + | 0.0593666i | ||||
\(966\) | −0.365120 | − | 0.632406i | −0.0117475 | − | 0.0203473i | ||||
\(967\) | 11.3064 | + | 19.5833i | 0.363590 | + | 0.629757i | 0.988549 | − | 0.150901i | \(-0.0482175\pi\) |
−0.624959 | + | 0.780658i | \(0.714884\pi\) | |||||||
\(968\) | 8.43552 | 0.271128 | ||||||||
\(969\) | 0.662501 | + | 1.14749i | 0.0212826 | + | 0.0368625i | ||||
\(970\) | 6.35159 | − | 1.62277i | 0.203937 | − | 0.0521041i | ||||
\(971\) | 16.9557 | − | 29.3682i | 0.544135 | − | 0.942470i | −0.454526 | − | 0.890734i | \(-0.650191\pi\) |
0.998661 | − | 0.0517360i | \(-0.0164754\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | − | 1.86503i | − | 0.0597902i | ||||||
\(974\) | 13.0237 | − | 22.5576i | 0.417305 | − | 0.722793i | ||||
\(975\) | −9.86612 | + | 16.2039i | −0.315969 | + | 0.518941i | ||||
\(976\) | − | 13.0969i | − | 0.419222i | ||||||
\(977\) | −9.31401 | + | 16.1323i | −0.297982 | + | 0.516119i | −0.975674 | − | 0.219226i | \(-0.929647\pi\) |
0.677693 | + | 0.735345i | \(0.262980\pi\) | |||||||
\(978\) | 5.96478 | + | 3.44377i | 0.190733 | + | 0.110120i | ||||
\(979\) | 25.0389 | + | 14.4562i | 0.800246 | + | 0.462022i | ||||
\(980\) | −8.86139 | − | 9.07048i | −0.283067 | − | 0.289746i | ||||
\(981\) | −11.8873 | + | 6.86312i | −0.379531 | + | 0.219122i | ||||
\(982\) | 14.0020 | − | 24.2521i | 0.446820 | − | 0.773916i | ||||
\(983\) | −6.82940 | − | 3.94296i | −0.217824 | − | 0.125761i | 0.387118 | − | 0.922030i | \(-0.373471\pi\) |
−0.604942 | + | 0.796269i | \(0.706804\pi\) | |||||||
\(984\) | 6.93392 | + | 4.00330i | 0.221045 | + | 0.127621i | ||||
\(985\) | 0.958998 | + | 3.75355i | 0.0305562 | + | 0.119598i | ||||
\(986\) | 32.6974 | − | 18.8779i | 1.04130 | − | 0.601193i | ||||
\(987\) | 4.64687 | + | 2.68287i | 0.147912 | + | 0.0853968i | ||||
\(988\) | − | 0.764179i | − | 0.0243118i | ||||||
\(989\) | −1.23610 | −0.0393057 | ||||||||
\(990\) | −0.967053 | + | 3.44778i | −0.0307350 | + | 0.109578i | ||||
\(991\) | 8.71571i | 0.276864i | 0.990372 | + | 0.138432i | \(0.0442062\pi\) | ||||
−0.990372 | + | 0.138432i | \(0.955794\pi\) | |||||||
\(992\) | −7.23055 | + | 4.17456i | −0.229570 | + | 0.132542i | ||||
\(993\) | −9.27632 | −0.294375 | ||||||||
\(994\) | 11.0256 | − | 6.36561i | 0.349710 | − | 0.201905i | ||||
\(995\) | −31.7817 | + | 31.0491i | −1.00755 | + | 0.984323i | ||||
\(996\) | −7.21006 | − | 12.4882i | −0.228460 | − | 0.395704i | ||||
\(997\) | 28.8512 | − | 49.9718i | 0.913728 | − | 1.58262i | 0.104975 | − | 0.994475i | \(-0.466524\pi\) |
0.808753 | − | 0.588149i | \(-0.200143\pi\) | |||||||
\(998\) | − | 26.0956i | − | 0.826042i | ||||||
\(999\) | 0.267030 | − | 6.07690i | 0.00844846 | − | 0.192265i |
(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.b.619.3 | yes | 36 | |
5.4 | even | 2 | 1110.2.ba.a.619.16 | yes | 36 | ||
37.11 | even | 6 | 1110.2.ba.a.529.16 | ✓ | 36 | ||
185.159 | even | 6 | inner | 1110.2.ba.b.529.3 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.ba.a.529.16 | ✓ | 36 | 37.11 | even | 6 | ||
1110.2.ba.a.619.16 | yes | 36 | 5.4 | even | 2 | ||
1110.2.ba.b.529.3 | yes | 36 | 185.159 | even | 6 | inner | |
1110.2.ba.b.619.3 | yes | 36 | 1.1 | even | 1 | trivial |