Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(439,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.439");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.o (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: | \(6.14848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 439.15 | ||
Character | \(\chi\) | \(=\) | 770.439 |
Dual form | 770.2.o.a.549.15 |
$q$-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 \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0.533793 | + | 0.924557i | 0.308186 | + | 0.533793i | 0.977966 | − | 0.208766i | \(-0.0669448\pi\) |
−0.669780 | + | 0.742560i | \(0.733612\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.13643 | + | 1.92576i | 0.508225 | + | 0.861224i | ||||
\(6\) | −1.06759 | −0.435840 | ||||||||
\(7\) | 1.22107 | + | 2.34712i | 0.461520 | + | 0.887130i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.930129 | − | 1.61103i | 0.310043 | − | 0.537010i | ||||
\(10\) | −2.23597 | + | 0.0212957i | −0.707075 | + | 0.00673428i | ||||
\(11\) | −2.75206 | + | 1.85099i | −0.829777 | + | 0.558095i | ||||
\(12\) | 0.533793 | − | 0.924557i | 0.154093 | − | 0.266897i | ||||
\(13\) | 1.72838i | 0.479365i | 0.970851 | + | 0.239683i | \(0.0770434\pi\) | ||||
−0.970851 | + | 0.239683i | \(0.922957\pi\) | |||||||
\(14\) | −2.64320 | − | 0.116087i | −0.706426 | − | 0.0310255i | ||||
\(15\) | −1.17386 | + | 2.07865i | −0.303088 | + | 0.536704i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.33846 | + | 0.772761i | −0.324625 | + | 0.187422i | −0.653452 | − | 0.756968i | \(-0.726680\pi\) |
0.328827 | + | 0.944390i | \(0.393347\pi\) | |||||||
\(18\) | 0.930129 | + | 1.61103i | 0.219234 | + | 0.379724i | ||||
\(19\) | 0.241835 | − | 0.418871i | 0.0554809 | − | 0.0960957i | −0.836951 | − | 0.547278i | \(-0.815664\pi\) |
0.892432 | + | 0.451182i | \(0.148997\pi\) | |||||||
\(20\) | 1.09954 | − | 1.94705i | 0.245865 | − | 0.435374i | ||||
\(21\) | −1.51825 | + | 2.38183i | −0.331310 | + | 0.519757i | ||||
\(22\) | −0.226978 | − | 3.30885i | −0.0483918 | − | 0.705449i | ||||
\(23\) | 3.47535 | + | 2.00649i | 0.724660 | + | 0.418383i | 0.816466 | − | 0.577394i | \(-0.195930\pi\) |
−0.0918052 | + | 0.995777i | \(0.529264\pi\) | |||||||
\(24\) | 0.533793 | + | 0.924557i | 0.108960 | + | 0.188724i | ||||
\(25\) | −2.41707 | + | 4.37696i | −0.483414 | + | 0.875392i | ||||
\(26\) | −1.49682 | − | 0.864188i | −0.293550 | − | 0.169481i | ||||
\(27\) | 5.18875 | 0.998575 | ||||||||
\(28\) | 1.42214 | − | 2.23104i | 0.268758 | − | 0.421627i | ||||
\(29\) | − | 1.63137i | − | 0.302938i | −0.988462 | − | 0.151469i | \(-0.951600\pi\) | ||
0.988462 | − | 0.151469i | \(-0.0484004\pi\) | |||||||
\(30\) | −1.21323 | − | 2.05591i | −0.221505 | − | 0.375356i | ||||
\(31\) | 4.21221 | − | 2.43192i | 0.756535 | − | 0.436786i | −0.0715154 | − | 0.997439i | \(-0.522783\pi\) |
0.828050 | + | 0.560654i | \(0.189450\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −3.18038 | − | 1.55639i | −0.553633 | − | 0.270932i | ||||
\(34\) | − | 1.54552i | − | 0.265055i | ||||||
\(35\) | −3.13234 | + | 5.01881i | −0.529462 | + | 0.848334i | ||||
\(36\) | −1.86026 | −0.310043 | ||||||||
\(37\) | −1.81722 | − | 1.04917i | −0.298749 | − | 0.172483i | 0.343132 | − | 0.939287i | \(-0.388512\pi\) |
−0.641881 | + | 0.766804i | \(0.721846\pi\) | |||||||
\(38\) | 0.241835 | + | 0.418871i | 0.0392309 | + | 0.0679499i | ||||
\(39\) | −1.59798 | + | 0.922596i | −0.255882 | + | 0.147734i | ||||
\(40\) | 1.13643 | + | 1.92576i | 0.179685 | + | 0.304489i | ||||
\(41\) | −8.37376 | −1.30776 | −0.653881 | − | 0.756597i | \(-0.726860\pi\) | ||||
−0.653881 | + | 0.756597i | \(0.726860\pi\) | |||||||
\(42\) | −1.30360 | − | 2.50576i | −0.201149 | − | 0.386647i | ||||
\(43\) | 1.61281 | 0.245951 | 0.122975 | − | 0.992410i | \(-0.460756\pi\) | ||||
0.122975 | + | 0.992410i | \(0.460756\pi\) | |||||||
\(44\) | 2.97904 | + | 1.45786i | 0.449107 | + | 0.219780i | ||||
\(45\) | 4.15948 | − | 0.0396155i | 0.620058 | − | 0.00590552i | ||||
\(46\) | −3.47535 | + | 2.00649i | −0.512412 | + | 0.295841i | ||||
\(47\) | 1.81833 | − | 3.14943i | 0.265230 | − | 0.459392i | −0.702394 | − | 0.711789i | \(-0.747885\pi\) |
0.967624 | + | 0.252397i | \(0.0812187\pi\) | |||||||
\(48\) | −1.06759 | −0.154093 | ||||||||
\(49\) | −4.01799 | + | 5.73200i | −0.573998 | + | 0.818856i | ||||
\(50\) | −2.58202 | − | 4.28173i | −0.365153 | − | 0.605527i | ||||
\(51\) | −1.42892 | − | 0.824989i | −0.200089 | − | 0.115522i | ||||
\(52\) | 1.49682 | − | 0.864188i | 0.207571 | − | 0.119841i | ||||
\(53\) | −9.24141 | + | 5.33553i | −1.26941 | + | 0.732892i | −0.974875 | − | 0.222751i | \(-0.928496\pi\) |
−0.294530 | + | 0.955642i | \(0.595163\pi\) | |||||||
\(54\) | −2.59437 | + | 4.49359i | −0.353050 | + | 0.611500i | ||||
\(55\) | −6.69207 | − | 3.19628i | −0.902359 | − | 0.430986i | ||||
\(56\) | 1.22107 | + | 2.34712i | 0.163172 | + | 0.313648i | ||||
\(57\) | 0.516361 | 0.0683936 | ||||||||
\(58\) | 1.41281 | + | 0.815686i | 0.185511 | + | 0.107105i | ||||
\(59\) | 3.56527 | − | 2.05841i | 0.464158 | − | 0.267982i | −0.249633 | − | 0.968341i | \(-0.580310\pi\) |
0.713791 | + | 0.700359i | \(0.246977\pi\) | |||||||
\(60\) | 2.38709 | − | 0.0227350i | 0.308172 | − | 0.00293507i | ||||
\(61\) | 0.573483 | − | 0.993302i | 0.0734270 | − | 0.127179i | −0.826974 | − | 0.562240i | \(-0.809940\pi\) |
0.900401 | + | 0.435061i | \(0.143273\pi\) | |||||||
\(62\) | 4.86384i | 0.617708i | ||||||||
\(63\) | 4.91704 | + | 0.215952i | 0.619489 | + | 0.0272073i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.32843 | + | 1.96417i | −0.412841 | + | 0.243626i | ||||
\(66\) | 2.93806 | − | 1.97610i | 0.361650 | − | 0.243241i | ||||
\(67\) | −4.81081 | + | 2.77752i | −0.587735 | + | 0.339329i | −0.764201 | − | 0.644978i | \(-0.776867\pi\) |
0.176467 | + | 0.984307i | \(0.443533\pi\) | |||||||
\(68\) | 1.33846 | + | 0.772761i | 0.162312 | + | 0.0937110i | ||||
\(69\) | 4.28421i | 0.515758i | ||||||||
\(70\) | −2.78025 | − | 5.22209i | −0.332303 | − | 0.624159i | ||||
\(71\) | −6.87538 | −0.815957 | −0.407979 | − | 0.912991i | \(-0.633766\pi\) | ||||
−0.407979 | + | 0.912991i | \(0.633766\pi\) | |||||||
\(72\) | 0.930129 | − | 1.61103i | 0.109617 | − | 0.189862i | ||||
\(73\) | 6.69748 | − | 3.86679i | 0.783881 | − | 0.452574i | −0.0539227 | − | 0.998545i | \(-0.517172\pi\) |
0.837804 | + | 0.545971i | \(0.183839\pi\) | |||||||
\(74\) | 1.81722 | − | 1.04917i | 0.211248 | − | 0.121964i | ||||
\(75\) | −5.33697 | + | 0.101669i | −0.616260 | + | 0.0117398i | ||||
\(76\) | −0.483671 | −0.0554809 | ||||||||
\(77\) | −7.70496 | − | 4.19924i | −0.878062 | − | 0.478547i | ||||
\(78\) | − | 1.84519i | − | 0.208927i | ||||||
\(79\) | 8.64592 | + | 4.99172i | 0.972741 | + | 0.561613i | 0.900071 | − | 0.435743i | \(-0.143515\pi\) |
0.0726705 | + | 0.997356i | \(0.476848\pi\) | |||||||
\(80\) | −2.23597 | + | 0.0212957i | −0.249989 | + | 0.00238093i | ||||
\(81\) | −0.0206686 | − | 0.0357991i | −0.00229651 | − | 0.00397767i | ||||
\(82\) | 4.18688 | − | 7.25189i | 0.462364 | − | 0.800837i | ||||
\(83\) | 3.34082i | 0.366703i | 0.983047 | + | 0.183351i | \(0.0586946\pi\) | ||||
−0.983047 | + | 0.183351i | \(0.941305\pi\) | |||||||
\(84\) | 2.82185 | + | 0.123933i | 0.307889 | + | 0.0135222i | ||||
\(85\) | −3.00921 | − | 1.69936i | −0.326395 | − | 0.184322i | ||||
\(86\) | −0.806403 | + | 1.39673i | −0.0869566 | + | 0.150613i | ||||
\(87\) | 1.50830 | − | 0.870816i | 0.161706 | − | 0.0933613i | ||||
\(88\) | −2.75206 | + | 1.85099i | −0.293370 | + | 0.197317i | ||||
\(89\) | 6.49734 | + | 3.75124i | 0.688716 | + | 0.397631i | 0.803131 | − | 0.595802i | \(-0.203166\pi\) |
−0.114415 | + | 0.993433i | \(0.536499\pi\) | |||||||
\(90\) | −2.04543 | + | 3.62202i | −0.215607 | + | 0.381794i | ||||
\(91\) | −4.05672 | + | 2.11046i | −0.425259 | + | 0.221237i | ||||
\(92\) | − | 4.01299i | − | 0.418383i | ||||||
\(93\) | 4.49690 | + | 2.59629i | 0.466307 | + | 0.269222i | ||||
\(94\) | 1.81833 | + | 3.14943i | 0.187546 | + | 0.324839i | ||||
\(95\) | 1.08147 | − | 0.0103001i | 0.110957 | − | 0.00105677i | ||||
\(96\) | 0.533793 | − | 0.924557i | 0.0544801 | − | 0.0943622i | ||||
\(97\) | −6.99351 | −0.710084 | −0.355042 | − | 0.934850i | \(-0.615533\pi\) | ||||
−0.355042 | + | 0.934850i | \(0.615533\pi\) | |||||||
\(98\) | −2.95506 | − | 6.34568i | −0.298506 | − | 0.641010i | ||||
\(99\) | 0.422237 | + | 6.15531i | 0.0424364 | + | 0.618632i | ||||
\(100\) | 4.99909 | − | 0.0952328i | 0.499909 | − | 0.00952328i | ||||
\(101\) | −1.06527 | − | 1.84510i | −0.105998 | − | 0.183594i | 0.808148 | − | 0.588980i | \(-0.200470\pi\) |
−0.914146 | + | 0.405386i | \(0.867137\pi\) | |||||||
\(102\) | 1.42892 | − | 0.824989i | 0.141484 | − | 0.0816861i | ||||
\(103\) | 7.74347 | − | 13.4121i | 0.762987 | − | 1.32153i | −0.178318 | − | 0.983973i | \(-0.557066\pi\) |
0.941305 | − | 0.337559i | \(-0.109601\pi\) | |||||||
\(104\) | 1.72838i | 0.169481i | ||||||||
\(105\) | −6.31220 | − | 0.217016i | −0.616008 | − | 0.0211786i | ||||
\(106\) | − | 10.6711i | − | 1.03647i | ||||||
\(107\) | 0.324320 | − | 0.561739i | 0.0313532 | − | 0.0543054i | −0.849923 | − | 0.526907i | \(-0.823352\pi\) |
0.881276 | + | 0.472602i | \(0.156685\pi\) | |||||||
\(108\) | −2.59437 | − | 4.49359i | −0.249644 | − | 0.432396i | ||||
\(109\) | 17.4081 | − | 10.0506i | 1.66739 | − | 0.962669i | 0.698354 | − | 0.715753i | \(-0.253916\pi\) |
0.969037 | − | 0.246916i | \(-0.0794171\pi\) | |||||||
\(110\) | 6.11409 | − | 4.19737i | 0.582956 | − | 0.400203i | ||||
\(111\) | − | 2.24017i | − | 0.212627i | ||||||
\(112\) | −2.64320 | − | 0.116087i | −0.249759 | − | 0.0109692i | ||||
\(113\) | 2.42255i | 0.227895i | 0.993487 | + | 0.113947i | \(0.0363495\pi\) | ||||
−0.993487 | + | 0.113947i | \(0.963651\pi\) | |||||||
\(114\) | −0.258180 | + | 0.447182i | −0.0241808 | + | 0.0418824i | ||||
\(115\) | 0.0854592 | + | 8.97290i | 0.00796912 | + | 0.836728i | ||||
\(116\) | −1.41281 | + | 0.815686i | −0.131176 | + | 0.0757346i | ||||
\(117\) | 2.78447 | + | 1.60761i | 0.257424 | + | 0.148624i | ||||
\(118\) | 4.11682i | 0.378984i | ||||||||
\(119\) | −3.44812 | − | 2.19794i | −0.316088 | − | 0.201485i | ||||
\(120\) | −1.17386 | + | 2.07865i | −0.107158 | + | 0.189754i | ||||
\(121\) | 4.14765 | − | 10.1881i | 0.377059 | − | 0.926189i | ||||
\(122\) | 0.573483 | + | 0.993302i | 0.0519207 | + | 0.0899293i | ||||
\(123\) | −4.46986 | − | 7.74202i | −0.403034 | − | 0.698075i | ||||
\(124\) | −4.21221 | − | 2.43192i | −0.378267 | − | 0.218393i | ||||
\(125\) | −11.1758 | + | 0.319396i | −0.999592 | + | 0.0285677i | ||||
\(126\) | −2.64554 | + | 4.15031i | −0.235683 | + | 0.369739i | ||||
\(127\) | −16.9566 | −1.50465 | −0.752326 | − | 0.658791i | \(-0.771068\pi\) | ||||
−0.752326 | + | 0.658791i | \(0.771068\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0.860905 | + | 1.49113i | 0.0757984 | + | 0.131287i | ||||
\(130\) | −0.0368069 | − | 3.86459i | −0.00322818 | − | 0.338947i | ||||
\(131\) | 3.04800 | − | 5.27929i | 0.266305 | − | 0.461254i | −0.701600 | − | 0.712571i | \(-0.747531\pi\) |
0.967905 | + | 0.251318i | \(0.0808638\pi\) | |||||||
\(132\) | 0.242318 | + | 3.53248i | 0.0210911 | + | 0.307463i | ||||
\(133\) | 1.27844 | + | 0.0561478i | 0.110855 | + | 0.00486863i | ||||
\(134\) | − | 5.55505i | − | 0.479883i | ||||||
\(135\) | 5.89663 | + | 9.99226i | 0.507501 | + | 0.859997i | ||||
\(136\) | −1.33846 | + | 0.772761i | −0.114772 | + | 0.0662637i | ||||
\(137\) | −8.99694 | + | 5.19438i | −0.768660 | + | 0.443786i | −0.832396 | − | 0.554181i | \(-0.813032\pi\) |
0.0637363 | + | 0.997967i | \(0.479698\pi\) | |||||||
\(138\) | −3.71024 | − | 2.14211i | −0.315836 | − | 0.182348i | ||||
\(139\) | 14.0908 | 1.19517 | 0.597584 | − | 0.801807i | \(-0.296128\pi\) | ||||
0.597584 | + | 0.801807i | \(0.296128\pi\) | |||||||
\(140\) | 5.91259 | + | 0.203278i | 0.499705 | + | 0.0171801i | ||||
\(141\) | 3.88244 | 0.326961 | ||||||||
\(142\) | 3.43769 | − | 5.95425i | 0.288484 | − | 0.499670i | ||||
\(143\) | −3.19921 | − | 4.75659i | −0.267532 | − | 0.397766i | ||||
\(144\) | 0.930129 | + | 1.61103i | 0.0775108 | + | 0.134253i | ||||
\(145\) | 3.14163 | − | 1.85393i | 0.260898 | − | 0.153961i | ||||
\(146\) | 7.73359i | 0.640036i | ||||||||
\(147\) | −7.44433 | − | 0.655159i | −0.613998 | − | 0.0540366i | ||||
\(148\) | 2.09835i | 0.172483i | ||||||||
\(149\) | 18.2929 | + | 10.5614i | 1.49861 | + | 0.865223i | 0.999999 | − | 0.00160170i | \(-0.000509838\pi\) |
0.498612 | + | 0.866825i | \(0.333843\pi\) | |||||||
\(150\) | 2.58043 | − | 4.67278i | 0.210692 | − | 0.381531i | ||||
\(151\) | 14.7836 | − | 8.53532i | 1.20307 | − | 0.694595i | 0.241836 | − | 0.970317i | \(-0.422250\pi\) |
0.961237 | + | 0.275723i | \(0.0889171\pi\) | |||||||
\(152\) | 0.241835 | − | 0.418871i | 0.0196154 | − | 0.0339750i | ||||
\(153\) | 2.87507i | 0.232436i | ||||||||
\(154\) | 7.48913 | − | 4.57307i | 0.603491 | − | 0.368509i | ||||
\(155\) | 9.47015 | + | 5.34799i | 0.760660 | + | 0.429561i | ||||
\(156\) | 1.59798 | + | 0.922596i | 0.127941 | + | 0.0738668i | ||||
\(157\) | 5.57078 | + | 9.64888i | 0.444597 | + | 0.770064i | 0.998024 | − | 0.0628331i | \(-0.0200136\pi\) |
−0.553427 | + | 0.832898i | \(0.686680\pi\) | |||||||
\(158\) | −8.64592 | + | 4.99172i | −0.687832 | + | 0.397120i | ||||
\(159\) | −9.86601 | − | 5.69614i | −0.782425 | − | 0.451733i | ||||
\(160\) | 1.09954 | − | 1.94705i | 0.0869263 | − | 0.153928i | ||||
\(161\) | −0.465855 | + | 10.6071i | −0.0367145 | + | 0.835960i | ||||
\(162\) | 0.0413372 | 0.00324776 | ||||||||
\(163\) | 16.7221 | + | 9.65452i | 1.30978 | + | 0.756200i | 0.982059 | − | 0.188575i | \(-0.0603870\pi\) |
0.327718 | + | 0.944776i | \(0.393720\pi\) | |||||||
\(164\) | 4.18688 | + | 7.25189i | 0.326940 | + | 0.566278i | ||||
\(165\) | −0.617043 | − | 7.89335i | −0.0480367 | − | 0.614497i | ||||
\(166\) | −2.89323 | − | 1.67041i | −0.224559 | − | 0.129649i | ||||
\(167\) | − | 17.1797i | − | 1.32940i | −0.747108 | − | 0.664702i | \(-0.768558\pi\) | ||
0.747108 | − | 0.664702i | \(-0.231442\pi\) | |||||||
\(168\) | −1.51825 | + | 2.38183i | −0.117136 | + | 0.183762i | ||||
\(169\) | 10.0127 | 0.770209 | ||||||||
\(170\) | 2.97630 | − | 1.75637i | 0.228272 | − | 0.134708i | ||||
\(171\) | −0.449877 | − | 0.779209i | −0.0344029 | − | 0.0595876i | ||||
\(172\) | −0.806403 | − | 1.39673i | −0.0614876 | − | 0.106500i | ||||
\(173\) | −0.606406 | − | 0.350108i | −0.0461042 | − | 0.0266182i | 0.476771 | − | 0.879028i | \(-0.341807\pi\) |
−0.522875 | + | 0.852409i | \(0.675141\pi\) | |||||||
\(174\) | 1.74163i | 0.132033i | ||||||||
\(175\) | −13.2247 | − | 0.328609i | −0.999691 | − | 0.0248405i | ||||
\(176\) | −0.226978 | − | 3.30885i | −0.0171091 | − | 0.249414i | ||||
\(177\) | 3.80623 | + | 2.19753i | 0.286094 | + | 0.165176i | ||||
\(178\) | −6.49734 | + | 3.75124i | −0.486996 | + | 0.281167i | ||||
\(179\) | 6.63861 | + | 11.4984i | 0.496193 | + | 0.859431i | 0.999990 | − | 0.00439038i | \(-0.00139751\pi\) |
−0.503797 | + | 0.863822i | \(0.668064\pi\) | |||||||
\(180\) | −2.11405 | − | 3.58240i | −0.157572 | − | 0.267017i | ||||
\(181\) | 10.9605i | 0.814687i | 0.913275 | + | 0.407344i | \(0.133545\pi\) | ||||
−0.913275 | + | 0.407344i | \(0.866455\pi\) | |||||||
\(182\) | 0.200642 | − | 4.56845i | 0.0148726 | − | 0.338636i | ||||
\(183\) | 1.22449 | 0.0905166 | ||||||||
\(184\) | 3.47535 | + | 2.00649i | 0.256206 | + | 0.147921i | ||||
\(185\) | −0.0446857 | − | 4.69183i | −0.00328536 | − | 0.344951i | ||||
\(186\) | −4.49690 | + | 2.59629i | −0.329729 | + | 0.190369i | ||||
\(187\) | 2.25315 | − | 4.60417i | 0.164767 | − | 0.336690i | ||||
\(188\) | −3.63665 | −0.265230 | ||||||||
\(189\) | 6.33581 | + | 12.1786i | 0.460862 | + | 0.885866i | ||||
\(190\) | −0.531816 | + | 0.941732i | −0.0385820 | + | 0.0683204i | ||||
\(191\) | 7.21273 | − | 12.4928i | 0.521894 | − | 0.903948i | −0.477781 | − | 0.878479i | \(-0.658559\pi\) |
0.999676 | − | 0.0254689i | \(-0.00810786\pi\) | |||||||
\(192\) | 0.533793 | + | 0.924557i | 0.0385232 | + | 0.0667242i | ||||
\(193\) | −3.60370 | − | 6.24180i | −0.259400 | − | 0.449294i | 0.706681 | − | 0.707532i | \(-0.250192\pi\) |
−0.966081 | + | 0.258238i | \(0.916858\pi\) | |||||||
\(194\) | 3.49676 | − | 6.05656i | 0.251053 | − | 0.434836i | ||||
\(195\) | −3.59268 | − | 2.02886i | −0.257277 | − | 0.145290i | ||||
\(196\) | 6.97305 | + | 0.613682i | 0.498075 | + | 0.0438344i | ||||
\(197\) | 15.3130 | 1.09101 | 0.545504 | − | 0.838108i | \(-0.316338\pi\) | ||||
0.545504 | + | 0.838108i | \(0.316338\pi\) | |||||||
\(198\) | −5.54178 | − | 2.71199i | −0.393837 | − | 0.192733i | ||||
\(199\) | 14.6472 | − | 8.45658i | 1.03831 | − | 0.599471i | 0.118959 | − | 0.992899i | \(-0.462044\pi\) |
0.919355 | + | 0.393428i | \(0.128711\pi\) | |||||||
\(200\) | −2.41707 | + | 4.37696i | −0.170913 | + | 0.309498i | ||||
\(201\) | −5.13596 | − | 2.96525i | −0.362263 | − | 0.209153i | ||||
\(202\) | 2.13053 | 0.149904 | ||||||||
\(203\) | 3.82904 | − | 1.99202i | 0.268746 | − | 0.139812i | ||||
\(204\) | 1.64998i | 0.115522i | ||||||||
\(205\) | −9.51616 | − | 16.1258i | −0.664637 | − | 1.12628i | ||||
\(206\) | 7.74347 | + | 13.4121i | 0.539513 | + | 0.934464i | ||||
\(207\) | 6.46505 | − | 3.73260i | 0.449352 | − | 0.259433i | ||||
\(208\) | −1.49682 | − | 0.864188i | −0.103786 | − | 0.0599207i | ||||
\(209\) | 0.109783 | + | 1.60039i | 0.00759382 | + | 0.110702i | ||||
\(210\) | 3.34404 | − | 5.35802i | 0.230761 | − | 0.369738i | ||||
\(211\) | − | 6.95564i | − | 0.478846i | −0.970915 | − | 0.239423i | \(-0.923042\pi\) | ||
0.970915 | − | 0.239423i | \(-0.0769583\pi\) | |||||||
\(212\) | 9.24141 | + | 5.33553i | 0.634703 | + | 0.366446i | ||||
\(213\) | −3.67003 | − | 6.35668i | −0.251466 | − | 0.435553i | ||||
\(214\) | 0.324320 | + | 0.561739i | 0.0221701 | + | 0.0383997i | ||||
\(215\) | 1.83283 | + | 3.10587i | 0.124998 | + | 0.211819i | ||||
\(216\) | 5.18875 | 0.353050 | ||||||||
\(217\) | 10.8514 | + | 6.91704i | 0.736642 | + | 0.469559i | ||||
\(218\) | 20.1011i | 1.36142i | ||||||||
\(219\) | 7.15015 | + | 4.12814i | 0.483162 | + | 0.278954i | ||||
\(220\) | 0.577979 | + | 7.39364i | 0.0389673 | + | 0.498479i | ||||
\(221\) | −1.33562 | − | 2.31337i | −0.0898437 | − | 0.155614i | ||||
\(222\) | 1.94004 | + | 1.12008i | 0.130207 | + | 0.0751751i | ||||
\(223\) | 12.4881 | 0.836264 | 0.418132 | − | 0.908386i | \(-0.362685\pi\) | ||||
0.418132 | + | 0.908386i | \(0.362685\pi\) | |||||||
\(224\) | 1.42214 | − | 2.23104i | 0.0950204 | − | 0.149067i | ||||
\(225\) | 4.80323 | + | 7.96512i | 0.320215 | + | 0.531008i | ||||
\(226\) | −2.09799 | − | 1.21128i | −0.139556 | − | 0.0805729i | ||||
\(227\) | −0.827974 | + | 0.478031i | −0.0549546 | + | 0.0317280i | −0.527226 | − | 0.849725i | \(-0.676768\pi\) |
0.472271 | + | 0.881453i | \(0.343434\pi\) | |||||||
\(228\) | −0.258180 | − | 0.447182i | −0.0170984 | − | 0.0296153i | ||||
\(229\) | −19.5904 | − | 11.3105i | −1.29457 | − | 0.747421i | −0.315110 | − | 0.949055i | \(-0.602041\pi\) |
−0.979461 | + | 0.201634i | \(0.935375\pi\) | |||||||
\(230\) | −7.81349 | − | 4.41244i | −0.515206 | − | 0.290948i | ||||
\(231\) | −0.230422 | − | 9.36520i | −0.0151607 | − | 0.616185i | ||||
\(232\) | − | 1.63137i | − | 0.107105i | ||||||
\(233\) | 2.76095 | − | 4.78210i | 0.180876 | − | 0.313286i | −0.761303 | − | 0.648396i | \(-0.775440\pi\) |
0.942179 | + | 0.335110i | \(0.108773\pi\) | |||||||
\(234\) | −2.78447 | + | 1.60761i | −0.182026 | + | 0.105093i | ||||
\(235\) | 8.13143 | − | 0.0774449i | 0.530436 | − | 0.00505195i | ||||
\(236\) | −3.56527 | − | 2.05841i | −0.232079 | − | 0.133991i | ||||
\(237\) | 10.6582i | 0.692324i | ||||||||
\(238\) | 3.62753 | − | 1.88719i | 0.235138 | − | 0.122328i | ||||
\(239\) | 3.36046i | 0.217370i | 0.994076 | + | 0.108685i | \(0.0346640\pi\) | ||||
−0.994076 | + | 0.108685i | \(0.965336\pi\) | |||||||
\(240\) | −1.21323 | − | 2.05591i | −0.0783139 | − | 0.132709i | ||||
\(241\) | −5.95532 | − | 10.3149i | −0.383616 | − | 0.664442i | 0.607960 | − | 0.793968i | \(-0.291988\pi\) |
−0.991576 | + | 0.129525i | \(0.958655\pi\) | |||||||
\(242\) | 6.74931 | + | 8.68601i | 0.433862 | + | 0.558358i | ||||
\(243\) | 7.80519 | − | 13.5190i | 0.500703 | − | 0.867243i | ||||
\(244\) | −1.14697 | −0.0734270 | ||||||||
\(245\) | −15.6046 | − | 1.22368i | −0.996939 | − | 0.0781779i | ||||
\(246\) | 8.93972 | 0.569976 | ||||||||
\(247\) | 0.723967 | + | 0.417983i | 0.0460649 | + | 0.0265956i | ||||
\(248\) | 4.21221 | − | 2.43192i | 0.267475 | − | 0.154427i | ||||
\(249\) | −3.08878 | + | 1.78331i | −0.195743 | + | 0.113013i | ||||
\(250\) | 5.31128 | − | 9.83820i | 0.335915 | − | 0.622223i | ||||
\(251\) | 20.9460i | 1.32210i | 0.750343 | + | 0.661049i | \(0.229888\pi\) | ||||
−0.750343 | + | 0.661049i | \(0.770112\pi\) | |||||||
\(252\) | −2.27150 | − | 4.36626i | −0.143091 | − | 0.275048i | ||||
\(253\) | −13.2784 | + | 0.910859i | −0.834804 | + | 0.0572652i | ||||
\(254\) | 8.47828 | − | 14.6848i | 0.531975 | − | 0.921408i | ||||
\(255\) | −0.0351374 | − | 3.68930i | −0.00220039 | − | 0.231033i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 5.95152 | − | 10.3083i | 0.371245 | − | 0.643016i | −0.618512 | − | 0.785775i | \(-0.712264\pi\) |
0.989757 | + | 0.142759i | \(0.0455975\pi\) | |||||||
\(258\) | −1.72181 | −0.107195 | ||||||||
\(259\) | 0.243591 | − | 5.54636i | 0.0151360 | − | 0.344634i | ||||
\(260\) | 3.36524 | + | 1.90042i | 0.208703 | + | 0.117859i | ||||
\(261\) | −2.62819 | − | 1.51739i | −0.162681 | − | 0.0939239i | ||||
\(262\) | 3.04800 | + | 5.27929i | 0.188306 | + | 0.326156i | ||||
\(263\) | 12.0330 | + | 20.8417i | 0.741984 | + | 1.28515i | 0.951591 | + | 0.307368i | \(0.0994484\pi\) |
−0.209606 | + | 0.977786i | \(0.567218\pi\) | |||||||
\(264\) | −3.18038 | − | 1.55639i | −0.195739 | − | 0.0957890i | ||||
\(265\) | −20.7771 | − | 11.7333i | −1.27633 | − | 0.720769i | ||||
\(266\) | −0.687846 | + | 1.07909i | −0.0421745 | + | 0.0661631i | ||||
\(267\) | 8.00955i | 0.490176i | ||||||||
\(268\) | 4.81081 | + | 2.77752i | 0.293867 | + | 0.169664i | ||||
\(269\) | −25.6188 | + | 14.7910i | −1.56200 | + | 0.901823i | −0.564950 | + | 0.825125i | \(0.691104\pi\) |
−0.997054 | + | 0.0766981i | \(0.975562\pi\) | |||||||
\(270\) | −11.6019 | + | 0.110498i | −0.706067 | + | 0.00672469i | ||||
\(271\) | 7.35747 | − | 12.7435i | 0.446934 | − | 0.774113i | −0.551250 | − | 0.834340i | \(-0.685849\pi\) |
0.998185 | + | 0.0602268i | \(0.0191824\pi\) | |||||||
\(272\) | − | 1.54552i | − | 0.0937110i | ||||||
\(273\) | −4.11669 | − | 2.62411i | −0.249154 | − | 0.158819i | ||||
\(274\) | − | 10.3888i | − | 0.627608i | ||||||
\(275\) | −1.44979 | − | 16.5196i | −0.0874259 | − | 0.996171i | ||||
\(276\) | 3.71024 | − | 2.14211i | 0.223330 | − | 0.128940i | ||||
\(277\) | −16.4309 | − | 28.4591i | −0.987235 | − | 1.70994i | −0.631549 | − | 0.775336i | \(-0.717581\pi\) |
−0.355686 | − | 0.934606i | \(-0.615753\pi\) | |||||||
\(278\) | −7.04541 | + | 12.2030i | −0.422555 | + | 0.731887i | ||||
\(279\) | − | 9.04800i | − | 0.541689i | ||||||
\(280\) | −3.13234 | + | 5.01881i | −0.187193 | + | 0.299931i | ||||
\(281\) | 13.7160i | 0.818227i | 0.912484 | + | 0.409113i | \(0.134162\pi\) | ||||
−0.912484 | + | 0.409113i | \(0.865838\pi\) | |||||||
\(282\) | −1.94122 | + | 3.36229i | −0.115598 | + | 0.200222i | ||||
\(283\) | −11.1527 | + | 6.43900i | −0.662958 | + | 0.382759i | −0.793403 | − | 0.608697i | \(-0.791693\pi\) |
0.130445 | + | 0.991455i | \(0.458359\pi\) | |||||||
\(284\) | 3.43769 | + | 5.95425i | 0.203989 | + | 0.353320i | ||||
\(285\) | 0.586806 | + | 0.994385i | 0.0347594 | + | 0.0589023i | ||||
\(286\) | 5.71894 | − | 0.392303i | 0.338168 | − | 0.0231974i | ||||
\(287\) | −10.2249 | − | 19.6543i | −0.603558 | − | 1.16015i | ||||
\(288\) | −1.86026 | −0.109617 | ||||||||
\(289\) | −7.30568 | + | 12.6538i | −0.429746 | + | 0.744342i | ||||
\(290\) | 0.0347412 | + | 3.64770i | 0.00204007 | + | 0.214200i | ||||
\(291\) | −3.73309 | − | 6.46591i | −0.218838 | − | 0.379038i | ||||
\(292\) | −6.69748 | − | 3.86679i | −0.391941 | − | 0.226287i | ||||
\(293\) | 2.61732i | 0.152905i | 0.997073 | + | 0.0764527i | \(0.0243594\pi\) | ||||
−0.997073 | + | 0.0764527i | \(0.975641\pi\) | |||||||
\(294\) | 4.28955 | − | 6.11940i | 0.250172 | − | 0.356891i | ||||
\(295\) | 8.01566 | + | 4.52661i | 0.466690 | + | 0.263549i | ||||
\(296\) | −1.81722 | − | 1.04917i | −0.105624 | − | 0.0609820i | ||||
\(297\) | −14.2797 | + | 9.60434i | −0.828594 | + | 0.557300i | ||||
\(298\) | −18.2929 | + | 10.5614i | −1.05968 | + | 0.611805i | ||||
\(299\) | −3.46798 | + | 6.00671i | −0.200558 | + | 0.347377i | ||||
\(300\) | 2.75653 | + | 4.57111i | 0.159148 | + | 0.263913i | ||||
\(301\) | 1.96934 | + | 3.78546i | 0.113511 | + | 0.218190i | ||||
\(302\) | 17.0706i | 0.982305i | ||||||||
\(303\) | 1.13726 | − | 1.96980i | 0.0653342 | − | 0.113162i | ||||
\(304\) | 0.241835 | + | 0.418871i | 0.0138702 | + | 0.0240239i | ||||
\(305\) | 2.56458 | − | 0.0244254i | 0.146847 | − | 0.00139860i | ||||
\(306\) | −2.48988 | − | 1.43754i | −0.142337 | − | 0.0821784i | ||||
\(307\) | − | 11.4180i | − | 0.651658i | −0.945429 | − | 0.325829i | \(-0.894357\pi\) | ||
0.945429 | − | 0.325829i | \(-0.105643\pi\) | |||||||
\(308\) | 0.215835 | + | 8.77231i | 0.0122983 | + | 0.499849i | ||||
\(309\) | 16.5336 | 0.940566 | ||||||||
\(310\) | −9.36657 | + | 5.52739i | −0.531985 | + | 0.313935i | ||||
\(311\) | −23.5119 | + | 13.5746i | −1.33324 | + | 0.769744i | −0.985794 | − | 0.167957i | \(-0.946283\pi\) |
−0.347442 | + | 0.937702i | \(0.612950\pi\) | |||||||
\(312\) | −1.59798 | + | 0.922596i | −0.0904680 | + | 0.0522317i | ||||
\(313\) | 14.2815 | − | 24.7363i | 0.807239 | − | 1.39818i | −0.107530 | − | 0.994202i | \(-0.534294\pi\) |
0.914769 | − | 0.403978i | \(-0.132373\pi\) | |||||||
\(314\) | −11.1416 | −0.628755 | ||||||||
\(315\) | 5.17198 | + | 9.71444i | 0.291408 | + | 0.547346i | ||||
\(316\) | − | 9.98344i | − | 0.561613i | ||||||
\(317\) | 11.7827 | + | 6.80274i | 0.661782 | + | 0.382080i | 0.792956 | − | 0.609279i | \(-0.208541\pi\) |
−0.131174 | + | 0.991359i | \(0.541875\pi\) | |||||||
\(318\) | 9.86601 | − | 5.69614i | 0.553258 | − | 0.319424i | ||||
\(319\) | 3.01966 | + | 4.48963i | 0.169068 | + | 0.251371i | ||||
\(320\) | 1.13643 | + | 1.92576i | 0.0635281 | + | 0.107653i | ||||
\(321\) | 0.692480 | 0.0386505 | ||||||||
\(322\) | −8.95313 | − | 5.70701i | −0.498938 | − | 0.318039i | ||||
\(323\) | 0.747524i | 0.0415933i | ||||||||
\(324\) | −0.0206686 | + | 0.0357991i | −0.00114826 | + | 0.00198884i | ||||
\(325\) | −7.56503 | − | 4.17761i | −0.419632 | − | 0.231732i | ||||
\(326\) | −16.7221 | + | 9.65452i | −0.926152 | + | 0.534714i | ||||
\(327\) | 18.5846 | + | 10.7298i | 1.02773 | + | 0.593361i | ||||
\(328\) | −8.37376 | −0.462364 | ||||||||
\(329\) | 9.61241 | + | 0.422167i | 0.529949 | + | 0.0232748i | ||||
\(330\) | 7.14437 | + | 3.41230i | 0.393284 | + | 0.187841i | ||||
\(331\) | 9.39302 | − | 16.2692i | 0.516287 | − | 0.894235i | −0.483534 | − | 0.875325i | \(-0.660647\pi\) |
0.999821 | − | 0.0189097i | \(-0.00601951\pi\) | |||||||
\(332\) | 2.89323 | − | 1.67041i | 0.158787 | − | 0.0916757i | ||||
\(333\) | −3.38050 | + | 1.95173i | −0.185250 | + | 0.106954i | ||||
\(334\) | 14.8781 | + | 8.58985i | 0.814091 | + | 0.470016i | ||||
\(335\) | −10.8160 | − | 6.10800i | −0.590940 | − | 0.333716i | ||||
\(336\) | −1.30360 | − | 2.50576i | −0.0711170 | − | 0.136700i | ||||
\(337\) | 1.86493 | 0.101589 | 0.0507946 | − | 0.998709i | \(-0.483825\pi\) | ||||
0.0507946 | + | 0.998709i | \(0.483825\pi\) | |||||||
\(338\) | −5.00636 | + | 8.67126i | −0.272310 | + | 0.471655i | ||||
\(339\) | −2.23979 | + | 1.29314i | −0.121649 | + | 0.0702339i | ||||
\(340\) | 0.0329129 | + | 3.45574i | 0.00178495 | + | 0.187414i | ||||
\(341\) | −7.09078 | + | 14.4896i | −0.383987 | + | 0.784653i | ||||
\(342\) | 0.899753 | 0.0486531 | ||||||||
\(343\) | −18.3599 | − | 2.43157i | −0.991344 | − | 0.131292i | ||||
\(344\) | 1.61281 | 0.0869566 | ||||||||
\(345\) | −8.25035 | + | 4.86869i | −0.444184 | + | 0.262121i | ||||
\(346\) | 0.606406 | − | 0.350108i | 0.0326006 | − | 0.0188219i | ||||
\(347\) | 5.05922 | + | 8.76283i | 0.271593 | + | 0.470414i | 0.969270 | − | 0.245999i | \(-0.0791161\pi\) |
−0.697677 | + | 0.716413i | \(0.745783\pi\) | |||||||
\(348\) | −1.50830 | − | 0.870816i | −0.0808532 | − | 0.0466806i | ||||
\(349\) | −4.65704 | −0.249286 | −0.124643 | − | 0.992202i | \(-0.539778\pi\) | ||||
−0.124643 | + | 0.992202i | \(0.539778\pi\) | |||||||
\(350\) | 6.89692 | − | 11.2886i | 0.368656 | − | 0.603401i | ||||
\(351\) | 8.96811i | 0.478682i | ||||||||
\(352\) | 2.97904 | + | 1.45786i | 0.158783 | + | 0.0777040i | ||||
\(353\) | −15.9692 | − | 27.6595i | −0.849957 | − | 1.47217i | −0.881245 | − | 0.472659i | \(-0.843294\pi\) |
0.0312881 | − | 0.999510i | \(-0.490039\pi\) | |||||||
\(354\) | −3.80623 | + | 2.19753i | −0.202299 | + | 0.116797i | ||||
\(355\) | −7.81336 | − | 13.2403i | −0.414690 | − | 0.702722i | ||||
\(356\) | − | 7.50248i | − | 0.397631i | ||||||
\(357\) | 0.191541 | − | 4.36123i | 0.0101374 | − | 0.230821i | ||||
\(358\) | −13.2772 | −0.701723 | ||||||||
\(359\) | 15.3645 | + | 8.87070i | 0.810908 | + | 0.468178i | 0.847271 | − | 0.531161i | \(-0.178244\pi\) |
−0.0363633 | + | 0.999339i | \(0.511577\pi\) | |||||||
\(360\) | 4.15948 | − | 0.0396155i | 0.219224 | − | 0.00208792i | ||||
\(361\) | 9.38303 | + | 16.2519i | 0.493844 | + | 0.855362i | ||||
\(362\) | −9.49207 | − | 5.48025i | −0.498892 | − | 0.288035i | ||||
\(363\) | 11.6335 | − | 1.60359i | 0.610598 | − | 0.0841667i | ||||
\(364\) | 3.85607 | + | 2.45799i | 0.202113 | + | 0.128833i | ||||
\(365\) | 15.0577 | + | 8.50340i | 0.788156 | + | 0.445088i | ||||
\(366\) | −0.612243 | + | 1.06044i | −0.0320025 | + | 0.0554299i | ||||
\(367\) | 4.51064 | + | 7.81267i | 0.235454 | + | 0.407818i | 0.959404 | − | 0.282034i | \(-0.0910091\pi\) |
−0.723951 | + | 0.689852i | \(0.757676\pi\) | |||||||
\(368\) | −3.47535 | + | 2.00649i | −0.181165 | + | 0.104596i | ||||
\(369\) | −7.78868 | + | 13.4904i | −0.405463 | + | 0.702282i | ||||
\(370\) | 4.08559 | + | 2.30722i | 0.212400 | + | 0.119947i | ||||
\(371\) | −23.8075 | − | 15.1757i | −1.23603 | − | 0.787883i | ||||
\(372\) | − | 5.19257i | − | 0.269222i | ||||||
\(373\) | −11.6611 | + | 20.1977i | −0.603791 | + | 1.04580i | 0.388451 | + | 0.921470i | \(0.373010\pi\) |
−0.992241 | + | 0.124327i | \(0.960323\pi\) | |||||||
\(374\) | 2.86075 | + | 4.25337i | 0.147926 | + | 0.219936i | ||||
\(375\) | −6.26086 | − | 10.1622i | −0.323309 | − | 0.524771i | ||||
\(376\) | 1.81833 | − | 3.14943i | 0.0937730 | − | 0.162420i | ||||
\(377\) | 2.81963 | 0.145218 | ||||||||
\(378\) | −13.7149 | − | 0.602345i | −0.705419 | − | 0.0309813i | ||||
\(379\) | −9.54007 | −0.490040 | −0.245020 | − | 0.969518i | \(-0.578795\pi\) | ||||
−0.245020 | + | 0.969518i | \(0.578795\pi\) | |||||||
\(380\) | −0.549656 | − | 0.931432i | −0.0281968 | − | 0.0477815i | ||||
\(381\) | −9.05130 | − | 15.6773i | −0.463712 | − | 0.803173i | ||||
\(382\) | 7.21273 | + | 12.4928i | 0.369035 | + | 0.639188i | ||||
\(383\) | 10.7286 | − | 18.5824i | 0.548204 | − | 0.949517i | −0.450194 | − | 0.892931i | \(-0.648645\pi\) |
0.998398 | − | 0.0565859i | \(-0.0180215\pi\) | |||||||
\(384\) | −1.06759 | −0.0544801 | ||||||||
\(385\) | −0.669411 | − | 19.6100i | −0.0341163 | − | 0.999418i | ||||
\(386\) | 7.20741 | 0.366847 | ||||||||
\(387\) | 1.50012 | − | 2.59828i | 0.0762553 | − | 0.132078i | ||||
\(388\) | 3.49676 | + | 6.05656i | 0.177521 | + | 0.307475i | ||||
\(389\) | 1.52868 | + | 2.64775i | 0.0775072 | + | 0.134246i | 0.902174 | − | 0.431373i | \(-0.141971\pi\) |
−0.824667 | + | 0.565619i | \(0.808637\pi\) | |||||||
\(390\) | 3.55339 | − | 2.09692i | 0.179933 | − | 0.106182i | ||||
\(391\) | −6.20216 | −0.313657 | ||||||||
\(392\) | −4.01799 | + | 5.73200i | −0.202939 | + | 0.289509i | ||||
\(393\) | 6.50801 | 0.328286 | ||||||||
\(394\) | −7.65651 | + | 13.2615i | −0.385729 | + | 0.668103i | ||||
\(395\) | 0.212604 | + | 22.3226i | 0.0106973 | + | 1.12317i | ||||
\(396\) | 5.11954 | − | 3.44333i | 0.257267 | − | 0.173034i | ||||
\(397\) | −8.08582 | + | 14.0051i | −0.405816 | + | 0.702893i | −0.994416 | − | 0.105531i | \(-0.966346\pi\) |
0.588600 | + | 0.808424i | \(0.299679\pi\) | |||||||
\(398\) | 16.9132i | 0.847780i | ||||||||
\(399\) | 0.630511 | + | 1.21196i | 0.0315650 | + | 0.0606740i | ||||
\(400\) | −2.58202 | − | 4.28173i | −0.129101 | − | 0.214086i | ||||
\(401\) | 5.34633 | − | 9.26012i | 0.266983 | − | 0.462428i | −0.701098 | − | 0.713065i | \(-0.747307\pi\) |
0.968081 | + | 0.250636i | \(0.0806399\pi\) | |||||||
\(402\) | 5.13596 | − | 2.96525i | 0.256158 | − | 0.147893i | ||||
\(403\) | 4.20327 | + | 7.28028i | 0.209380 | + | 0.362657i | ||||
\(404\) | −1.06527 | + | 1.84510i | −0.0529990 | + | 0.0917970i | ||||
\(405\) | 0.0454519 | − | 0.0804856i | 0.00225852 | − | 0.00399936i | ||||
\(406\) | −0.189381 | + | 4.31205i | −0.00939882 | + | 0.214003i | ||||
\(407\) | 6.94311 | − | 0.476278i | 0.344157 | − | 0.0236082i | ||||
\(408\) | −1.42892 | − | 0.824989i | −0.0707422 | − | 0.0408431i | ||||
\(409\) | −15.5654 | − | 26.9600i | −0.769659 | − | 1.33309i | −0.937748 | − | 0.347316i | \(-0.887093\pi\) |
0.168089 | − | 0.985772i | \(-0.446240\pi\) | |||||||
\(410\) | 18.7235 | − | 0.178325i | 0.924685 | − | 0.00880684i | ||||
\(411\) | −9.60501 | − | 5.54545i | −0.473780 | − | 0.273537i | ||||
\(412\) | −15.4869 | −0.762987 | ||||||||
\(413\) | 9.18478 | + | 5.85467i | 0.451953 | + | 0.288090i | ||||
\(414\) | 7.46519i | 0.366894i | ||||||||
\(415\) | −6.43360 | + | 3.79659i | −0.315813 | + | 0.186367i | ||||
\(416\) | 1.49682 | − | 0.864188i | 0.0733875 | − | 0.0423703i | ||||
\(417\) | 7.52158 | + | 13.0278i | 0.368334 | + | 0.637972i | ||||
\(418\) | −1.44087 | − | 0.705123i | −0.0704754 | − | 0.0344887i | ||||
\(419\) | − | 31.1314i | − | 1.52087i | −0.649414 | − | 0.760435i | \(-0.724986\pi\) | ||
0.649414 | − | 0.760435i | \(-0.275014\pi\) | |||||||
\(420\) | 2.96816 | + | 5.57503i | 0.144831 | + | 0.272034i | ||||
\(421\) | −40.0971 | −1.95421 | −0.977107 | − | 0.212748i | \(-0.931759\pi\) | ||||
−0.977107 | + | 0.212748i | \(0.931759\pi\) | |||||||
\(422\) | 6.02376 | + | 3.47782i | 0.293232 | + | 0.169298i | ||||
\(423\) | −3.38256 | − | 5.85876i | −0.164466 | − | 0.284863i | ||||
\(424\) | −9.24141 | + | 5.33553i | −0.448803 | + | 0.259116i | ||||
\(425\) | −0.147184 | − | 7.72621i | −0.00713949 | − | 0.374776i | ||||
\(426\) | 7.34006 | 0.355627 | ||||||||
\(427\) | 3.03166 | + | 0.133148i | 0.146713 | + | 0.00644347i | ||||
\(428\) | −0.648640 | −0.0313532 | ||||||||
\(429\) | 2.69002 | − | 5.49689i | 0.129876 | − | 0.265393i | ||||
\(430\) | −3.60618 | + | 0.0343458i | −0.173905 | + | 0.00165630i | ||||
\(431\) | −19.9486 | + | 11.5173i | −0.960889 | + | 0.554769i | −0.896446 | − | 0.443152i | \(-0.853860\pi\) |
−0.0644422 | + | 0.997921i | \(0.520527\pi\) | |||||||
\(432\) | −2.59437 | + | 4.49359i | −0.124822 | + | 0.216198i | ||||
\(433\) | −1.89828 | −0.0912254 | −0.0456127 | − | 0.998959i | \(-0.514524\pi\) | ||||
−0.0456127 | + | 0.998959i | \(0.514524\pi\) | |||||||
\(434\) | −11.4160 | + | 5.93908i | −0.547987 | + | 0.285085i | ||||
\(435\) | 3.39105 | + | 1.91500i | 0.162588 | + | 0.0918170i | ||||
\(436\) | −17.4081 | − | 10.0506i | −0.833695 | − | 0.481334i | ||||
\(437\) | 1.68093 | − | 0.970483i | 0.0804096 | − | 0.0464245i | ||||
\(438\) | −7.15015 | + | 4.12814i | −0.341647 | + | 0.197250i | ||||
\(439\) | −14.2518 | + | 24.6849i | −0.680203 | + | 1.17815i | 0.294716 | + | 0.955585i | \(0.404775\pi\) |
−0.974919 | + | 0.222561i | \(0.928558\pi\) | |||||||
\(440\) | −6.69207 | − | 3.19628i | −0.319032 | − | 0.152377i | ||||
\(441\) | 5.49717 | + | 11.8046i | 0.261770 | + | 0.562124i | ||||
\(442\) | 2.67124 | 0.127058 | ||||||||
\(443\) | 15.9939 | + | 9.23408i | 0.759893 | + | 0.438724i | 0.829257 | − | 0.558867i | \(-0.188764\pi\) |
−0.0693646 | + | 0.997591i | \(0.522097\pi\) | |||||||
\(444\) | −1.94004 | + | 1.12008i | −0.0920703 | + | 0.0531568i | ||||
\(445\) | 0.159770 | + | 16.7753i | 0.00757384 | + | 0.795225i | ||||
\(446\) | −6.24404 | + | 10.8150i | −0.295664 | + | 0.512105i | ||||
\(447\) | 22.5504i | 1.06660i | ||||||||
\(448\) | 1.22107 | + | 2.34712i | 0.0576900 | + | 0.110891i | ||||
\(449\) | −13.9134 | −0.656615 | −0.328308 | − | 0.944571i | \(-0.606478\pi\) | ||||
−0.328308 | + | 0.944571i | \(0.606478\pi\) | |||||||
\(450\) | −9.29961 | + | 0.177158i | −0.438388 | + | 0.00835129i | ||||
\(451\) | 23.0451 | − | 15.4998i | 1.08515 | − | 0.729856i | ||||
\(452\) | 2.09799 | − | 1.21128i | 0.0986812 | − | 0.0569736i | ||||
\(453\) | 15.7828 | + | 9.11219i | 0.741540 | + | 0.428128i | ||||
\(454\) | − | 0.956062i | − | 0.0448702i | ||||||
\(455\) | −8.67440 | − | 5.41386i | −0.406662 | − | 0.253806i | ||||
\(456\) | 0.516361 | 0.0241808 | ||||||||
\(457\) | −6.86004 | + | 11.8819i | −0.320899 | + | 0.555814i | −0.980674 | − | 0.195650i | \(-0.937318\pi\) |
0.659775 | + | 0.751464i | \(0.270652\pi\) | |||||||
\(458\) | 19.5904 | − | 11.3105i | 0.915400 | − | 0.528506i | ||||
\(459\) | −6.94494 | + | 4.00966i | −0.324162 | + | 0.187155i | ||||
\(460\) | 7.72803 | − | 4.56046i | 0.360321 | − | 0.212633i | ||||
\(461\) | −18.8586 | −0.878334 | −0.439167 | − | 0.898406i | \(-0.644726\pi\) | ||||
−0.439167 | + | 0.898406i | \(0.644726\pi\) | |||||||
\(462\) | 8.22571 | + | 4.48305i | 0.382695 | + | 0.208570i | ||||
\(463\) | − | 28.2350i | − | 1.31219i | −0.754677 | − | 0.656096i | \(-0.772207\pi\) | ||
0.754677 | − | 0.656096i | \(-0.227793\pi\) | |||||||
\(464\) | 1.41281 | + | 0.815686i | 0.0655881 | + | 0.0378673i | ||||
\(465\) | 0.110579 | + | 11.6104i | 0.00512799 | + | 0.538420i | ||||
\(466\) | 2.76095 | + | 4.78210i | 0.127898 | + | 0.221527i | ||||
\(467\) | −14.2257 | + | 24.6396i | −0.658287 | + | 1.14019i | 0.322772 | + | 0.946477i | \(0.395385\pi\) |
−0.981059 | + | 0.193710i | \(0.937948\pi\) | |||||||
\(468\) | − | 3.21523i | − | 0.148624i | ||||||
\(469\) | −12.3935 | − | 7.90004i | −0.572280 | − | 0.364790i | ||||
\(470\) | −3.99865 | + | 7.08075i | −0.184444 | + | 0.326611i | ||||
\(471\) | −5.94730 | + | 10.3010i | −0.274037 | + | 0.474646i | ||||
\(472\) | 3.56527 | − | 2.05841i | 0.164105 | − | 0.0947459i | ||||
\(473\) | −4.43853 | + | 2.98529i | −0.204084 | + | 0.137264i | ||||
\(474\) | −9.23026 | − | 5.32910i | −0.423960 | − | 0.244773i | ||||
\(475\) | 1.24885 | + | 2.07095i | 0.0573011 | + | 0.0950215i | ||||
\(476\) | −0.179415 | + | 4.08513i | −0.00822346 | + | 0.187242i | ||||
\(477\) | 19.8509i | 0.908912i | ||||||||
\(478\) | −2.91024 | − | 1.68023i | −0.133111 | − | 0.0768518i | ||||
\(479\) | −17.7278 | − | 30.7054i | −0.810002 | − | 1.40296i | −0.912862 | − | 0.408269i | \(-0.866133\pi\) |
0.102860 | − | 0.994696i | \(-0.467201\pi\) | |||||||
\(480\) | 2.38709 | − | 0.0227350i | 0.108955 | − | 0.00103770i | ||||
\(481\) | 1.81337 | − | 3.14084i | 0.0826824 | − | 0.143210i | ||||
\(482\) | 11.9106 | 0.542515 | ||||||||
\(483\) | −10.0556 | + | 5.23131i | −0.457545 | + | 0.238033i | ||||
\(484\) | −10.8970 | + | 1.50207i | −0.495316 | + | 0.0682759i | ||||
\(485\) | −7.94761 | − | 13.4678i | −0.360882 | − | 0.611541i | ||||
\(486\) | 7.80519 | + | 13.5190i | 0.354050 | + | 0.613233i | ||||
\(487\) | −9.99224 | + | 5.76902i | −0.452792 | + | 0.261419i | −0.709009 | − | 0.705200i | \(-0.750857\pi\) |
0.256217 | + | 0.966619i | \(0.417524\pi\) | |||||||
\(488\) | 0.573483 | − | 0.993302i | 0.0259604 | − | 0.0449647i | ||||
\(489\) | 20.6141i | 0.932200i | ||||||||
\(490\) | 8.86202 | − | 12.9021i | 0.400345 | − | 0.582858i | ||||
\(491\) | 42.4086i | 1.91387i | 0.290299 | + | 0.956936i | \(0.406245\pi\) | ||||
−0.290299 | + | 0.956936i | \(0.593755\pi\) | |||||||
\(492\) | −4.46986 | + | 7.74202i | −0.201517 | + | 0.349037i | ||||
\(493\) | 1.26066 | + | 2.18353i | 0.0567773 | + | 0.0983412i | ||||
\(494\) | −0.723967 | + | 0.417983i | −0.0325728 | + | 0.0188059i | ||||
\(495\) | −11.3738 | + | 7.80818i | −0.511214 | + | 0.350952i | ||||
\(496\) | 4.86384i | 0.218393i | ||||||||
\(497\) | −8.39530 | − | 16.1374i | −0.376581 | − | 0.723860i | ||||
\(498\) | − | 3.56661i | − | 0.159824i | ||||||
\(499\) | 15.5619 | − | 26.9540i | 0.696648 | − | 1.20663i | −0.272975 | − | 0.962021i | \(-0.588007\pi\) |
0.969622 | − | 0.244608i | \(-0.0786592\pi\) | |||||||
\(500\) | 5.86449 | + | 9.51881i | 0.262268 | + | 0.425694i | ||||
\(501\) | 15.8836 | − | 9.17041i | 0.709628 | − | 0.409704i | ||||
\(502\) | −18.1397 | − | 10.4730i | −0.809616 | − | 0.467432i | ||||
\(503\) | − | 35.6351i | − | 1.58889i | −0.607335 | − | 0.794446i | \(-0.707761\pi\) | ||
0.607335 | − | 0.794446i | \(-0.292239\pi\) | |||||||
\(504\) | 4.91704 | + | 0.215952i | 0.219022 | + | 0.00961925i | ||||
\(505\) | 2.34261 | − | 4.14826i | 0.104245 | − | 0.184595i | ||||
\(506\) | 5.85036 | − | 11.9548i | 0.260080 | − | 0.531457i | ||||
\(507\) | 5.34472 | + | 9.25733i | 0.237367 | + | 0.411132i | ||||
\(508\) | 8.47828 | + | 14.6848i | 0.376163 | + | 0.651534i | ||||
\(509\) | 7.10122 | + | 4.09989i | 0.314756 | + | 0.181725i | 0.649053 | − | 0.760743i | \(-0.275165\pi\) |
−0.334297 | + | 0.942468i | \(0.608499\pi\) | |||||||
\(510\) | 3.21259 | + | 1.81422i | 0.142256 | + | 0.0803350i | ||||
\(511\) | 17.2539 | + | 10.9982i | 0.763269 | + | 0.486532i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.25482 | − | 2.17342i | 0.0554018 | − | 0.0959587i | ||||
\(514\) | 5.95152 | + | 10.3083i | 0.262510 | + | 0.454681i | ||||
\(515\) | 34.6283 | − | 0.329805i | 1.52590 | − | 0.0145329i | ||||
\(516\) | 0.860905 | − | 1.49113i | 0.0378992 | − | 0.0656434i | ||||
\(517\) | 0.825439 | + | 12.0331i | 0.0363028 | + | 0.529217i | ||||
\(518\) | 4.68149 | + | 2.98413i | 0.205693 | + | 0.131115i | ||||
\(519\) | − | 0.747542i | − | 0.0328135i | ||||||
\(520\) | −3.32843 | + | 1.96417i | −0.145961 | + | 0.0861346i | ||||
\(521\) | 9.95005 | − | 5.74466i | 0.435919 | − | 0.251678i | −0.265946 | − | 0.963988i | \(-0.585684\pi\) |
0.701865 | + | 0.712310i | \(0.252351\pi\) | |||||||
\(522\) | 2.62819 | − | 1.51739i | 0.115033 | − | 0.0664143i | ||||
\(523\) | 18.0993 | + | 10.4496i | 0.791426 | + | 0.456930i | 0.840464 | − | 0.541867i | \(-0.182282\pi\) |
−0.0490385 | + | 0.998797i | \(0.515616\pi\) | |||||||
\(524\) | −6.09600 | −0.266305 | ||||||||
\(525\) | −6.75543 | − | 12.4024i | −0.294831 | − | 0.541284i | ||||
\(526\) | −24.0659 | −1.04932 | ||||||||
\(527\) | −3.75858 | + | 6.51006i | −0.163727 | + | 0.283583i | ||||
\(528\) | 2.93806 | − | 1.97610i | 0.127863 | − | 0.0859985i | ||||
\(529\) | −3.44797 | − | 5.97205i | −0.149912 | − | 0.259655i | ||||
\(530\) | 20.5499 | − | 12.1269i | 0.892629 | − | 0.526758i | ||||
\(531\) | − | 7.65834i | − | 0.332344i | ||||||
\(532\) | −0.590595 | − | 1.13524i | −0.0256055 | − | 0.0492187i | ||||
\(533\) | − | 14.4730i | − | 0.626896i | ||||||
\(534\) | −6.93647 | − | 4.00477i | −0.300170 | − | 0.173304i | ||||
\(535\) | 1.45034 | − | 0.0138132i | 0.0627036 | − | 0.000597198i | ||||
\(536\) | −4.81081 | + | 2.77752i | −0.207796 | + | 0.119971i | ||||
\(537\) | −7.08729 | + | 12.2755i | −0.305839 | + | 0.529729i | ||||
\(538\) | − | 29.5820i | − | 1.27537i | ||||||
\(539\) | 0.447855 | − | 23.2121i | 0.0192905 | − | 0.999814i | ||||
\(540\) | 5.70524 | − | 10.1028i | 0.245514 | − | 0.434754i | ||||
\(541\) | 3.66159 | + | 2.11402i | 0.157424 | + | 0.0908887i | 0.576642 | − | 0.816997i | \(-0.304363\pi\) |
−0.419219 | + | 0.907885i | \(0.637696\pi\) | |||||||
\(542\) | 7.35747 | + | 12.7435i | 0.316030 | + | 0.547381i | ||||
\(543\) | −10.1336 | + | 5.85064i | −0.434875 | + | 0.251075i | ||||
\(544\) | 1.33846 | + | 0.772761i | 0.0573860 | + | 0.0331318i | ||||
\(545\) | 39.1379 | + | 22.1020i | 1.67648 | + | 0.946745i | ||||
\(546\) | 4.33090 | − | 2.25310i | 0.185345 | − | 0.0964240i | ||||
\(547\) | 2.46701 | 0.105482 | 0.0527409 | − | 0.998608i | \(-0.483204\pi\) | ||||
0.0527409 | + | 0.998608i | \(0.483204\pi\) | |||||||
\(548\) | 8.99694 | + | 5.19438i | 0.384330 | + | 0.221893i | ||||
\(549\) | −1.06683 | − | 1.84780i | −0.0455311 | − | 0.0788621i | ||||
\(550\) | 15.0313 | + | 7.00426i | 0.640937 | + | 0.298662i | ||||
\(551\) | −0.683335 | − | 0.394524i | −0.0291111 | − | 0.0168073i | ||||
\(552\) | 4.28421i | 0.182348i | ||||||||
\(553\) | −1.15895 | + | 26.3883i | −0.0492834 | + | 1.12214i | ||||
\(554\) | 32.8617 | 1.39616 | ||||||||
\(555\) | 4.31402 | − | 2.54578i | 0.183120 | − | 0.108063i | ||||
\(556\) | −7.04541 | − | 12.2030i | −0.298792 | − | 0.517523i | ||||
\(557\) | −19.2421 | − | 33.3282i | −0.815313 | − | 1.41216i | −0.909103 | − | 0.416571i | \(-0.863232\pi\) |
0.0937905 | − | 0.995592i | \(-0.470102\pi\) | |||||||
\(558\) | 7.83580 | + | 4.52400i | 0.331716 | + | 0.191516i | ||||
\(559\) | 2.78754i | 0.117900i | ||||||||
\(560\) | −2.78025 | − | 5.22209i | −0.117487 | − | 0.220674i | ||||
\(561\) | 5.45953 | − | 0.374508i | 0.230502 | − | 0.0158118i | ||||
\(562\) | −11.8784 | − | 6.85799i | −0.501060 | − | 0.289287i | ||||
\(563\) | −4.29877 | + | 2.48190i | −0.181171 | + | 0.104599i | −0.587843 | − | 0.808975i | \(-0.700023\pi\) |
0.406671 | + | 0.913574i | \(0.366689\pi\) | |||||||
\(564\) | −1.94122 | − | 3.36229i | −0.0817401 | − | 0.141578i | ||||
\(565\) | −4.66524 | + | 2.75305i | −0.196268 | + | 0.115822i | ||||
\(566\) | − | 12.8780i | − | 0.541303i | ||||||
\(567\) | 0.0587871 | − | 0.0922248i | 0.00246883 | − | 0.00387308i | ||||
\(568\) | −6.87538 | −0.288484 | ||||||||
\(569\) | −11.2085 | − | 6.47120i | −0.469883 | − | 0.271287i | 0.246308 | − | 0.969192i | \(-0.420783\pi\) |
−0.716191 | + | 0.697905i | \(0.754116\pi\) | |||||||
\(570\) | −1.15457 | + | 0.0109962i | −0.0483594 | + | 0.000460582i | ||||
\(571\) | 23.1404 | − | 13.3601i | 0.968396 | − | 0.559104i | 0.0696493 | − | 0.997572i | \(-0.477812\pi\) |
0.898747 | + | 0.438468i | \(0.144479\pi\) | |||||||
\(572\) | −2.51972 | + | 5.14890i | −0.105355 | + | 0.215286i | ||||
\(573\) | 15.4004 | 0.643362 | ||||||||
\(574\) | 22.1336 | + | 0.972084i | 0.923837 | + | 0.0405740i | ||||
\(575\) | −17.1825 | + | 10.3616i | −0.716560 | + | 0.432109i | ||||
\(576\) | 0.930129 | − | 1.61103i | 0.0387554 | − | 0.0671263i | ||||
\(577\) | 20.1579 | + | 34.9145i | 0.839183 | + | 1.45351i | 0.890578 | + | 0.454830i | \(0.150300\pi\) |
−0.0513953 | + | 0.998678i | \(0.516367\pi\) | |||||||
\(578\) | −7.30568 | − | 12.6538i | −0.303876 | − | 0.526329i | ||||
\(579\) | 3.84727 | − | 6.66366i | 0.159887 | − | 0.276932i | ||||
\(580\) | −3.17637 | − | 1.79376i | −0.131891 | − | 0.0744819i | ||||
\(581\) | −7.84132 | + | 4.07937i | −0.325313 | + | 0.169241i | ||||
\(582\) | 7.46618 | 0.309483 | ||||||||
\(583\) | 15.5569 | − | 31.7895i | 0.644300 | − | 1.31659i | ||||
\(584\) | 6.69748 | − | 3.86679i | 0.277144 | − | 0.160009i | ||||
\(585\) | 0.0684704 | + | 7.18914i | 0.00283090 | + | 0.297234i | ||||
\(586\) | −2.26667 | − | 1.30866i | −0.0936351 | − | 0.0540603i | ||||
\(587\) | −16.9602 | −0.700021 | −0.350011 | − | 0.936746i | \(-0.613822\pi\) | ||||
−0.350011 | + | 0.936746i | \(0.613822\pi\) | |||||||
\(588\) | 3.15478 | + | 6.77456i | 0.130101 | + | 0.279378i | ||||
\(589\) | − | 2.35250i | − | 0.0969330i | ||||||
\(590\) | −7.92799 | + | 4.67846i | −0.326390 | + | 0.192609i | ||||
\(591\) | 8.17399 | + | 14.1578i | 0.336233 | + | 0.582372i | ||||
\(592\) | 1.81722 | − | 1.04917i | 0.0746874 | − | 0.0431208i | ||||
\(593\) | −15.0377 | − | 8.68202i | −0.617524 | − | 0.356528i | 0.158380 | − | 0.987378i | \(-0.449373\pi\) |
−0.775905 | + | 0.630850i | \(0.782706\pi\) | |||||||
\(594\) | −1.17773 | − | 17.1688i | −0.0483229 | − | 0.704444i | ||||
\(595\) | 0.314170 | − | 9.13803i | 0.0128797 | − | 0.374623i | ||||
\(596\) | − | 21.1228i | − | 0.865223i | ||||||
\(597\) | 15.6372 | + | 9.02813i | 0.639987 | + | 0.369497i | ||||
\(598\) | −3.46798 | − | 6.00671i | −0.141816 | − | 0.245633i | ||||
\(599\) | −14.1370 | − | 24.4860i | −0.577621 | − | 1.00047i | −0.995751 | − | 0.0920820i | \(-0.970648\pi\) |
0.418130 | − | 0.908387i | \(-0.362686\pi\) | |||||||
\(600\) | −5.33697 | + | 0.101669i | −0.217881 | + | 0.00415063i | ||||
\(601\) | 33.5631 | 1.36907 | 0.684534 | − | 0.728981i | \(-0.260006\pi\) | ||||
0.684534 | + | 0.728981i | \(0.260006\pi\) | |||||||
\(602\) | −4.26297 | − | 0.187225i | −0.173746 | − | 0.00763074i | ||||
\(603\) | 10.3338i | 0.420826i | ||||||||
\(604\) | −14.7836 | − | 8.53532i | −0.601536 | − | 0.347297i | ||||
\(605\) | 24.3333 | − | 3.59064i | 0.989288 | − | 0.145980i | ||||
\(606\) | 1.13726 | + | 1.96980i | 0.0461982 | + | 0.0800177i | ||||
\(607\) | −16.6958 | − | 9.63932i | −0.677661 | − | 0.391248i | 0.121312 | − | 0.992614i | \(-0.461290\pi\) |
−0.798973 | + | 0.601367i | \(0.794623\pi\) | |||||||
\(608\) | −0.483671 | −0.0196154 | ||||||||
\(609\) | 3.88565 | + | 2.47684i | 0.157454 | + | 0.100367i | ||||
\(610\) | −1.26114 | + | 2.23320i | −0.0510619 | + | 0.0904197i | ||||
\(611\) | 5.44341 | + | 3.14275i | 0.220217 | + | 0.127142i | ||||
\(612\) | 2.48988 | − | 1.43754i | 0.100648 | − | 0.0581089i | ||||
\(613\) | −17.0669 | − | 29.5607i | −0.689325 | − | 1.19395i | −0.972057 | − | 0.234746i | \(-0.924574\pi\) |
0.282732 | − | 0.959199i | \(-0.408759\pi\) | |||||||
\(614\) | 9.88826 | + | 5.70899i | 0.399058 | + | 0.230396i | ||||
\(615\) | 9.82958 | − | 17.4061i | 0.396367 | − | 0.701881i | ||||
\(616\) | −7.70496 | − | 4.19924i | −0.310442 | − | 0.169192i | ||||
\(617\) | − | 12.7295i | − | 0.512469i | −0.966615 | − | 0.256235i | \(-0.917518\pi\) | ||
0.966615 | − | 0.256235i | \(-0.0824820\pi\) | |||||||
\(618\) | −8.26682 | + | 14.3186i | −0.332540 | + | 0.575977i | ||||
\(619\) | 15.7044 | − | 9.06692i | 0.631212 | − | 0.364430i | −0.150009 | − | 0.988685i | \(-0.547930\pi\) |
0.781221 | + | 0.624254i | \(0.214597\pi\) | |||||||
\(620\) | −0.103579 | − | 10.8754i | −0.00415982 | − | 0.436766i | ||||
\(621\) | 18.0327 | + | 10.4112i | 0.723628 | + | 0.417787i | ||||
\(622\) | − | 27.1492i | − | 1.08858i | ||||||
\(623\) | −0.870939 | + | 19.8306i | −0.0348934 | + | 0.794495i | ||||
\(624\) | − | 1.84519i | − | 0.0738668i | ||||||
\(625\) | −13.3155 | − | 21.1588i | −0.532621 | − | 0.846354i | ||||
\(626\) | 14.2815 | + | 24.7363i | 0.570804 | + | 0.988662i | ||||
\(627\) | −1.42105 | + | 0.955780i | −0.0567515 | + | 0.0381702i | ||||
\(628\) | 5.57078 | − | 9.64888i | 0.222298 | − | 0.385032i | ||||
\(629\) | 3.24304 | 0.129309 | ||||||||
\(630\) | −10.9989 | − | 0.378149i | −0.438208 | − | 0.0150658i | ||||
\(631\) | −9.75642 | −0.388397 | −0.194198 | − | 0.980962i | \(-0.562211\pi\) | ||||
−0.194198 | + | 0.980962i | \(0.562211\pi\) | |||||||
\(632\) | 8.64592 | + | 4.99172i | 0.343916 | + | 0.198560i | ||||
\(633\) | 6.43089 | − | 3.71288i | 0.255605 | − | 0.147574i | ||||
\(634\) | −11.7827 | + | 6.80274i | −0.467950 | + | 0.270171i | ||||
\(635\) | −19.2699 | − | 32.6542i | −0.764702 | − | 1.29584i | ||||
\(636\) | 11.3923i | 0.451733i | ||||||||
\(637\) | −9.90705 | − | 6.94460i | −0.392531 | − | 0.275155i | ||||
\(638\) | −5.39797 | + | 0.370285i | −0.213708 | + | 0.0146597i | ||||
\(639\) | −6.39499 | + | 11.0764i | −0.252982 | + | 0.438177i | ||||
\(640\) | −2.23597 | + | 0.0212957i | −0.0883843 | + | 0.000841785i | ||||
\(641\) | 5.88659 | + | 10.1959i | 0.232506 | + | 0.402713i | 0.958545 | − | 0.284941i | \(-0.0919740\pi\) |
−0.726039 | + | 0.687654i | \(0.758641\pi\) | |||||||
\(642\) | −0.346240 | + | 0.599705i | −0.0136650 | + | 0.0236685i | ||||
\(643\) | 44.3171 | 1.74769 | 0.873847 | − | 0.486200i | \(-0.161618\pi\) | ||||
0.873847 | + | 0.486200i | \(0.161618\pi\) | |||||||
\(644\) | 9.41898 | − | 4.90013i | 0.371160 | − | 0.193092i | ||||
\(645\) | −1.89320 | + | 3.35245i | −0.0745447 | + | 0.132003i | ||||
\(646\) | −0.647375 | − | 0.373762i | −0.0254706 | − | 0.0147055i | ||||
\(647\) | −13.5518 | − | 23.4725i | −0.532778 | − | 0.922799i | −0.999267 | − | 0.0382719i | \(-0.987815\pi\) |
0.466489 | − | 0.884527i | \(-0.345519\pi\) | |||||||
\(648\) | −0.0206686 | − | 0.0357991i | −0.000811939 | − | 0.00140632i | ||||
\(649\) | −6.00173 | + | 12.2641i | −0.235588 | + | 0.481410i | ||||
\(650\) | 7.40043 | − | 4.46270i | 0.290269 | − | 0.175042i | ||||
\(651\) | −0.602789 | + | 13.7250i | −0.0236252 | + | 0.537926i | ||||
\(652\) | − | 19.3090i | − | 0.756200i | ||||||
\(653\) | −1.27592 | − | 0.736655i | −0.0499308 | − | 0.0288275i | 0.474827 | − | 0.880079i | \(-0.342511\pi\) |
−0.524758 | + | 0.851252i | \(0.675844\pi\) | |||||||
\(654\) | −18.5846 | + | 10.7298i | −0.726716 | + | 0.419570i | ||||
\(655\) | 13.6305 | − | 0.129818i | 0.532586 | − | 0.00507242i | ||||
\(656\) | 4.18688 | − | 7.25189i | 0.163470 | − | 0.283139i | ||||
\(657\) | − | 14.3865i | − | 0.561270i | ||||||
\(658\) | −5.17181 | + | 8.11351i | −0.201618 | + | 0.316297i | ||||
\(659\) | − | 22.0024i | − | 0.857092i | −0.903520 | − | 0.428546i | \(-0.859026\pi\) | ||
0.903520 | − | 0.428546i | \(-0.140974\pi\) | |||||||
\(660\) | −6.52732 | + | 4.48105i | −0.254076 | + | 0.174425i | ||||
\(661\) | −8.51176 | + | 4.91427i | −0.331069 | + | 0.191143i | −0.656316 | − | 0.754486i | \(-0.727886\pi\) |
0.325247 | + | 0.945629i | \(0.394553\pi\) | |||||||
\(662\) | 9.39302 | + | 16.2692i | 0.365070 | + | 0.632320i | ||||
\(663\) | 1.42589 | − | 2.46972i | 0.0553771 | − | 0.0959159i | ||||
\(664\) | 3.34082i | 0.129649i | ||||||||
\(665\) | 1.34473 | + | 2.52577i | 0.0521462 | + | 0.0979453i | ||||
\(666\) | − | 3.90347i | − | 0.151256i | ||||||
\(667\) | 3.27334 | − | 5.66959i | 0.126744 | − | 0.219527i | ||||
\(668\) | −14.8781 | + | 8.58985i | −0.575649 | + | 0.332351i | ||||
\(669\) | 6.66606 | + | 11.5460i | 0.257725 | + | 0.446392i | ||||
\(670\) | 10.6977 | − | 6.31290i | 0.413287 | − | 0.243889i | ||||
\(671\) | 0.260336 | + | 3.79514i | 0.0100502 | + | 0.146510i | ||||
\(672\) | 2.82185 | + | 0.123933i | 0.108855 | + | 0.00478081i | ||||
\(673\) | 38.5769 | 1.48703 | 0.743515 | − | 0.668719i | \(-0.233157\pi\) | ||||
0.743515 | + | 0.668719i | \(0.233157\pi\) | |||||||
\(674\) | −0.932466 | + | 1.61508i | −0.0359172 | + | 0.0622105i | ||||
\(675\) | −12.5416 | + | 22.7109i | −0.482726 | + | 0.874144i | ||||
\(676\) | −5.00636 | − | 8.67126i | −0.192552 | − | 0.333510i | ||||
\(677\) | 28.3508 | + | 16.3683i | 1.08961 | + | 0.629086i | 0.933472 | − | 0.358649i | \(-0.116763\pi\) |
0.156137 | + | 0.987735i | \(0.450096\pi\) | |||||||
\(678\) | − | 2.58628i | − | 0.0993257i | ||||||
\(679\) | −8.53955 | − | 16.4147i | −0.327718 | − | 0.629937i | ||||
\(680\) | −3.00921 | − | 1.69936i | −0.115398 | − | 0.0651676i | ||||
\(681\) | −0.883934 | − | 0.510339i | −0.0338724 | − | 0.0195563i | ||||
\(682\) | −9.00293 | − | 13.3856i | −0.344740 | − | 0.512560i | ||||
\(683\) | −10.5298 | + | 6.07940i | −0.402913 | + | 0.232622i | −0.687740 | − | 0.725957i | \(-0.741397\pi\) |
0.284827 | + | 0.958579i | \(0.408064\pi\) | |||||||
\(684\) | −0.449877 | + | 0.779209i | −0.0172015 | + | 0.0297938i | ||||
\(685\) | −20.2275 | − | 11.4229i | −0.772852 | − | 0.436445i | ||||
\(686\) | 11.2858 | − | 14.6844i | 0.430893 | − | 0.560653i | ||||
\(687\) | − | 24.1499i | − | 0.921378i | ||||||
\(688\) | −0.806403 | + | 1.39673i | −0.0307438 | + | 0.0532499i | ||||
\(689\) | −9.22181 | − | 15.9726i | −0.351323 | − | 0.608509i | ||||
\(690\) | −0.0912352 | − | 9.57935i | −0.00347326 | − | 0.364680i | ||||
\(691\) | −16.7472 | − | 9.66903i | −0.637095 | − | 0.367827i | 0.146399 | − | 0.989226i | \(-0.453232\pi\) |
−0.783495 | + | 0.621398i | \(0.786565\pi\) | |||||||
\(692\) | 0.700217i | 0.0266182i | ||||||||
\(693\) | −13.9317 | + | 8.50710i | −0.529222 | + | 0.323158i | ||||
\(694\) | −10.1184 | −0.384091 | ||||||||
\(695\) | 16.0132 | + | 27.1355i | 0.607414 | + | 1.02931i | ||||
\(696\) | 1.50830 | − | 0.870816i | 0.0571719 | − | 0.0330082i | ||||
\(697\) | 11.2080 | − | 6.47092i | 0.424532 | − | 0.245103i | ||||
\(698\) | 2.32852 | − | 4.03312i | 0.0881358 | − | 0.152656i | ||||
\(699\) | 5.89510 | 0.222973 | ||||||||
\(700\) | 6.32775 | + | 11.6172i | 0.239167 | + | 0.439089i | ||||
\(701\) | 42.5093i | 1.60556i | 0.596279 | + | 0.802778i | \(0.296645\pi\) | ||||
−0.596279 | + | 0.802778i | \(0.703355\pi\) | |||||||
\(702\) | −7.76661 | − | 4.48406i | −0.293132 | − | 0.169240i | ||||
\(703\) | −0.878938 | + | 0.507455i | −0.0331498 | + | 0.0191390i | ||||
\(704\) | −2.75206 | + | 1.85099i | −0.103722 | + | 0.0697619i | ||||
\(705\) | 4.41211 | + | 7.47664i | 0.166170 | + | 0.281586i | ||||
\(706\) | 31.9385 | 1.20202 | ||||||||
\(707\) | 3.02991 | − | 4.75330i | 0.113951 | − | 0.178766i | ||||
\(708\) | − | 4.39506i | − | 0.165176i | ||||||
\(709\) | −16.0460 | + | 27.7925i | −0.602620 | + | 1.04377i | 0.389803 | + | 0.920898i | \(0.372543\pi\) |
−0.992423 | + | 0.122870i | \(0.960790\pi\) | |||||||
\(710\) | 15.3731 | − | 0.146416i | 0.576943 | − | 0.00549489i | ||||
\(711\) | 16.0836 | − | 9.28589i | 0.603184 | − | 0.348248i | ||||
\(712\) | 6.49734 | + | 3.75124i | 0.243498 | + | 0.140584i | ||||
\(713\) | 19.5185 | 0.730974 | ||||||||
\(714\) | 3.68116 | + | 2.34649i | 0.137764 | + | 0.0878153i | ||||
\(715\) | 5.52437 | − | 11.5664i | 0.206600 | − | 0.432560i | ||||
\(716\) | 6.63861 | − | 11.4984i | 0.248096 | − | 0.429716i | ||||
\(717\) | −3.10693 | + | 1.79379i | −0.116031 | + | 0.0669903i | ||||
\(718\) | −15.3645 | + | 8.87070i | −0.573398 | + | 0.331052i | ||||
\(719\) | 32.9162 | + | 19.0042i | 1.22757 | + | 0.708736i | 0.966520 | − | 0.256591i | \(-0.0825993\pi\) |
0.261046 | + | 0.965326i | \(0.415933\pi\) | |||||||
\(720\) | −2.04543 | + | 3.62202i | −0.0762287 | + | 0.134985i | ||||
\(721\) | 40.9351 | + | 1.79783i | 1.52450 | + | 0.0669547i | ||||
\(722\) | −18.7661 | −0.698401 | ||||||||
\(723\) | 6.35782 | − | 11.0121i | 0.236450 | − | 0.409543i | ||||
\(724\) | 9.49207 | − | 5.48025i | 0.352770 | − | 0.203672i | ||||
\(725\) | 7.14045 | + | 3.94315i | 0.265190 | + | 0.146445i | ||||
\(726\) | −4.42798 | + | 10.8767i | −0.164338 | + | 0.403671i | ||||
\(727\) | −34.4594 | −1.27803 | −0.639013 | − | 0.769196i | \(-0.720657\pi\) | ||||
−0.639013 | + | 0.769196i | \(0.720657\pi\) | |||||||
\(728\) | −4.05672 | + | 2.11046i | −0.150352 | + | 0.0782190i | ||||
\(729\) | 16.5414 | 0.612645 | ||||||||
\(730\) | −14.8930 | + | 8.78865i | −0.551215 | + | 0.325283i | ||||
\(731\) | −2.15868 | + | 1.24631i | −0.0798416 | + | 0.0460966i | ||||
\(732\) | −0.612243 | − | 1.06044i | −0.0226292 | − | 0.0391948i | ||||
\(733\) | 2.49290 | + | 1.43927i | 0.0920772 | + | 0.0531608i | 0.545332 | − | 0.838220i | \(-0.316404\pi\) |
−0.453254 | + | 0.891381i | \(0.649737\pi\) | |||||||
\(734\) | −9.02129 | −0.332982 | ||||||||
\(735\) | −7.19826 | − | 15.0805i | −0.265512 | − | 0.556253i | ||||
\(736\) | − | 4.01299i | − | 0.147921i | ||||||
\(737\) | 8.09846 | − | 16.5487i | 0.298311 | − | 0.609579i | ||||
\(738\) | −7.78868 | − | 13.4904i | −0.286705 | − | 0.496588i | ||||
\(739\) | −15.8781 | + | 9.16725i | −0.584087 | + | 0.337223i | −0.762756 | − | 0.646687i | \(-0.776154\pi\) |
0.178669 | + | 0.983909i | \(0.442821\pi\) | |||||||
\(740\) | −4.04090 | + | 2.38462i | −0.148547 | + | 0.0876602i | ||||
\(741\) | 0.892466i | 0.0327856i | ||||||||
\(742\) | 25.0463 | − | 13.0301i | 0.919479 | − | 0.478350i | ||||
\(743\) | 11.1230 | 0.408063 | 0.204032 | − | 0.978964i | \(-0.434595\pi\) | ||||
0.204032 | + | 0.978964i | \(0.434595\pi\) | |||||||
\(744\) | 4.49690 | + | 2.59629i | 0.164864 | + | 0.0951844i | ||||
\(745\) | 0.449824 | + | 47.2299i | 0.0164803 | + | 1.73037i | ||||
\(746\) | −11.6611 | − | 20.1977i | −0.426945 | − | 0.739490i | ||||
\(747\) | 5.38216 | + | 3.10739i | 0.196923 | + | 0.113694i | ||||
\(748\) | −5.11390 | + | 0.350799i | −0.186983 | + | 0.0128265i | ||||
\(749\) | 1.71449 | + | 0.0752986i | 0.0626460 | + | 0.00275135i | ||||
\(750\) | 11.9311 | − | 0.340983i | 0.435663 | − | 0.0124510i | ||||
\(751\) | −21.0857 | + | 36.5215i | −0.769429 | + | 1.33269i | 0.168444 | + | 0.985711i | \(0.446126\pi\) |
−0.937873 | + | 0.346979i | \(0.887208\pi\) | |||||||
\(752\) | 1.81833 | + | 3.14943i | 0.0663075 | + | 0.114848i | ||||
\(753\) | −19.3657 | + | 11.1808i | −0.705727 | + | 0.407452i | ||||
\(754\) | −1.40981 | + | 2.44187i | −0.0513424 | + | 0.0889276i | ||||
\(755\) | 33.2374 | + | 18.7699i | 1.20963 | + | 0.683105i | ||||
\(756\) | 7.37910 | − | 11.5763i | 0.268375 | − | 0.421026i | ||||
\(757\) | 1.63573i | 0.0594518i | 0.999558 | + | 0.0297259i | \(0.00946343\pi\) | ||||
−0.999558 | + | 0.0297259i | \(0.990537\pi\) | |||||||
\(758\) | 4.77003 | − | 8.26194i | 0.173255 | − | 0.300087i | ||||
\(759\) | −7.93005 | − | 11.7904i | −0.287842 | − | 0.427964i | ||||
\(760\) | 1.08147 | − | 0.0103001i | 0.0392291 | − | 0.000373624i | ||||
\(761\) | 3.43564 | − | 5.95071i | 0.124542 | − | 0.215713i | −0.797012 | − | 0.603964i | \(-0.793587\pi\) |
0.921554 | + | 0.388251i | \(0.126921\pi\) | |||||||
\(762\) | 18.1026 | 0.655788 | ||||||||
\(763\) | 44.8463 | + | 28.5865i | 1.62355 | + | 1.03490i | ||||
\(764\) | −14.4255 | −0.521894 | ||||||||
\(765\) | −5.53668 | + | 3.26730i | −0.200179 | + | 0.118130i | ||||
\(766\) | 10.7286 | + | 18.5824i | 0.387639 | + | 0.671410i | ||||
\(767\) | 3.55771 | + | 6.16213i | 0.128461 | + | 0.222502i | ||||
\(768\) | 0.533793 | − | 0.924557i | 0.0192616 | − | 0.0333621i | ||||
\(769\) | −13.3033 | −0.479731 | −0.239865 | − | 0.970806i | \(-0.577103\pi\) | ||||
−0.239865 | + | 0.970806i | \(0.577103\pi\) | |||||||
\(770\) | 17.3175 | + | 9.22527i | 0.624078 | + | 0.332456i | ||||
\(771\) | 12.7075 | 0.457650 | ||||||||
\(772\) | −3.60370 | + | 6.24180i | −0.129700 | + | 0.224647i | ||||
\(773\) | −20.3690 | − | 35.2802i | −0.732624 | − | 1.26894i | −0.955758 | − | 0.294154i | \(-0.904962\pi\) |
0.223135 | − | 0.974788i | \(-0.428371\pi\) | |||||||
\(774\) | 1.50012 | + | 2.59828i | 0.0539206 | + | 0.0933932i | ||||
\(775\) | 0.463197 | + | 24.3148i | 0.0166385 | + | 0.873413i | ||||
\(776\) | −6.99351 | −0.251053 | ||||||||
\(777\) | 5.25795 | − | 2.73540i | 0.188628 | − | 0.0981318i | ||||
\(778\) | −3.05736 | −0.109612 | ||||||||
\(779\) | −2.02507 | + | 3.50753i | −0.0725558 | + | 0.125670i | ||||
\(780\) | 0.0392946 | + | 4.12579i | 0.00140697 | + | 0.147727i | ||||
\(781\) | 18.9214 | − | 12.7263i | 0.677062 | − | 0.455382i | ||||
\(782\) | 3.10108 | − | 5.37123i | 0.110894 | − | 0.192075i | ||||
\(783\) | − | 8.46478i | − | 0.302507i | ||||||
\(784\) | −2.95506 | − | 6.34568i | −0.105538 | − | 0.226631i | ||||
\(785\) | −12.2506 | + | 21.6932i | −0.437243 | + | 0.774264i | ||||
\(786\) | −3.25400 | + | 5.63610i | −0.116066 | + | 0.201033i | ||||
\(787\) | −19.6167 | + | 11.3257i | −0.699261 | + | 0.403718i | −0.807072 | − | 0.590453i | \(-0.798949\pi\) |
0.107811 | + | 0.994171i | \(0.465616\pi\) | |||||||
\(788\) | −7.65651 | − | 13.2615i | −0.272752 | − | 0.472420i | ||||
\(789\) | −12.8462 | + | 22.2503i | −0.457338 | + | 0.792132i | ||||
\(790\) | −19.4383 | − | 10.9772i | −0.691583 | − | 0.390551i | ||||
\(791\) | −5.68603 | + | 2.95810i | −0.202172 | + | 0.105178i | ||||
\(792\) | 0.422237 | + | 6.15531i | 0.0150035 | + | 0.218720i | ||||
\(793\) | 1.71680 | + | 0.991195i | 0.0609654 | + | 0.0351984i | ||||
\(794\) | −8.08582 | − | 14.0051i | −0.286955 | − | 0.497021i | ||||
\(795\) | −0.242606 | − | 25.4728i | −0.00860436 | − | 0.903426i | ||||
\(796\) | −14.6472 | − | 8.45658i | −0.519157 | − | 0.299735i | ||||
\(797\) | 16.3552 | 0.579332 | 0.289666 | − | 0.957128i | \(-0.406456\pi\) | ||||
0.289666 | + | 0.957128i | \(0.406456\pi\) | |||||||
\(798\) | −1.36485 | − | 0.0599427i | −0.0483150 | − | 0.00212195i | ||||
\(799\) | 5.62053i | 0.198840i | ||||||||
\(800\) | 4.99909 | − | 0.0952328i | 0.176745 | − | 0.00336699i | ||||
\(801\) | 12.0867 | − | 6.97828i | 0.427064 | − | 0.246565i | ||||
\(802\) | 5.34633 | + | 9.26012i | 0.188786 | + | 0.326986i | ||||
\(803\) | −11.2745 | + | 23.0386i | −0.397867 | + | 0.813016i | ||||
\(804\) | 5.93050i | 0.209153i | ||||||||
\(805\) | −20.9562 | + | 11.1571i | −0.738608 | + | 0.393236i | ||||
\(806\) | −8.40655 | −0.296108 | ||||||||
\(807\) | −27.3503 | − | 15.7907i | −0.962775 | − | 0.555858i | ||||
\(808\) | −1.06527 | − | 1.84510i | −0.0374760 | − | 0.0649103i | ||||
\(809\) | −3.23348 | + | 1.86685i | −0.113683 | + | 0.0656351i | −0.555763 | − | 0.831340i | \(-0.687574\pi\) |
0.442080 | + | 0.896976i | \(0.354241\pi\) | |||||||
\(810\) | 0.0469767 | + | 0.0796053i | 0.00165059 | + | 0.00279705i | ||||
\(811\) | 4.20210 | 0.147556 | 0.0737779 | − | 0.997275i | \(-0.476494\pi\) | ||||
0.0737779 | + | 0.997275i | \(0.476494\pi\) | |||||||
\(812\) | −3.63965 | − | 2.32003i | −0.127727 | − | 0.0814172i | ||||
\(813\) | 15.7095 | 0.550955 | ||||||||
\(814\) | −3.05909 | + | 6.25105i | −0.107221 | + | 0.219099i | ||||
\(815\) | 0.411199 | + | 43.1744i | 0.0144037 | + | 1.51233i | ||||
\(816\) | 1.42892 | − | 0.824989i | 0.0500223 | − | 0.0288804i | ||||
\(817\) | 0.390034 | − | 0.675558i | 0.0136455 | − | 0.0236348i | ||||
\(818\) | 31.1308 | 1.08846 | ||||||||
\(819\) | −0.373246 | + | 8.49850i | −0.0130423 | + | 0.296962i | ||||
\(820\) | −9.20729 | + | 16.3041i | −0.321533 | + | 0.569366i | ||||
\(821\) | −24.6150 | − | 14.2115i | −0.859070 | − | 0.495985i | 0.00463049 | − | 0.999989i | \(-0.498526\pi\) |
−0.863701 | + | 0.504005i | \(0.831859\pi\) | |||||||
\(822\) | 9.60501 | − | 5.54545i | 0.335013 | − | 0.193420i | ||||
\(823\) | −34.4463 | + | 19.8876i | −1.20072 | + | 0.693237i | −0.960716 | − | 0.277534i | \(-0.910483\pi\) |
−0.240006 | + | 0.970771i | \(0.577150\pi\) | |||||||
\(824\) | 7.74347 | − | 13.4121i | 0.269756 | − | 0.467232i | ||||
\(825\) | 14.4995 | − | 10.1585i | 0.504806 | − | 0.353673i | ||||
\(826\) | −9.66268 | + | 5.02691i | −0.336208 | + | 0.174909i | ||||
\(827\) | −6.76897 | −0.235380 | −0.117690 | − | 0.993050i | \(-0.537549\pi\) | ||||
−0.117690 | + | 0.993050i | \(0.537549\pi\) | |||||||
\(828\) | −6.46505 | − | 3.73260i | −0.224676 | − | 0.129717i | ||||
\(829\) | 37.3030 | − | 21.5369i | 1.29559 | − | 0.748008i | 0.315949 | − | 0.948776i | \(-0.397677\pi\) |
0.979639 | + | 0.200768i | \(0.0643437\pi\) | |||||||
\(830\) | −0.0711450 | − | 7.46996i | −0.00246948 | − | 0.259286i | ||||
\(831\) | 17.5414 | − | 30.3826i | 0.608504 | − | 1.05396i | ||||
\(832\) | 1.72838i | 0.0599207i | ||||||||
\(833\) | 0.948459 | − | 10.7770i | 0.0328622 | − | 0.373401i | ||||
\(834\) | −15.0432 | −0.520902 | ||||||||
\(835\) | 33.0839 | − | 19.5235i | 1.14492 | − | 0.675637i | ||||
\(836\) | 1.33109 | − | 0.895272i | 0.0460367 | − | 0.0309636i | ||||
\(837\) | 21.8561 | − | 12.6186i | 0.755457 | − | 0.436163i | ||||
\(838\) | 26.9606 | + | 15.5657i | 0.931339 | + | 0.537709i | ||||
\(839\) | 12.9299i | 0.446389i | 0.974774 | + | 0.223194i | \(0.0716485\pi\) | ||||
−0.974774 | + | 0.223194i | \(0.928352\pi\) | |||||||
\(840\) | −6.31220 | − | 0.217016i | −0.217792 | − | 0.00748778i | ||||
\(841\) | 26.3386 | 0.908228 | ||||||||
\(842\) | 20.0486 | − | 34.7251i | 0.690919 | − | 1.19671i | ||||
\(843\) | −12.6812 | + | 7.32150i | −0.436764 | + | 0.252166i | ||||
\(844\) | −6.02376 | + | 3.47782i | −0.207346 | + | 0.119712i | ||||
\(845\) | 11.3787 | + | 19.2820i | 0.391439 | + | 0.663322i | ||||
\(846\) | 6.76511 | 0.232589 | ||||||||
\(847\) | 28.9773 | − | 2.70528i | 0.995670 | − | 0.0929546i | ||||
\(848\) | − | 10.6711i | − | 0.366446i | ||||||
\(849\) | −11.9064 | − | 6.87419i | −0.408628 | − | 0.235922i | ||||
\(850\) | 6.76468 | + | 3.73564i | 0.232027 | + | 0.128131i | ||||
\(851\) | −4.21032 | − | 7.29249i | −0.144328 | − | 0.249983i | ||||
\(852\) | −3.67003 | + | 6.35668i | −0.125733 | + | 0.217776i | ||||
\(853\) | 23.3324i | 0.798888i | 0.916758 | + | 0.399444i | \(0.130797\pi\) | ||||
−0.916758 | + | 0.399444i | \(0.869203\pi\) | |||||||
\(854\) | −1.63114 | + | 2.55893i | −0.0558165 | + | 0.0875646i | ||||
\(855\) | 0.989315 | − | 1.75187i | 0.0338339 | − | 0.0599125i | ||||
\(856\) | 0.324320 | − | 0.561739i | 0.0110850 | − | 0.0191998i | ||||
\(857\) | −31.2079 | + | 18.0179i | −1.06604 | + | 0.615478i | −0.927097 | − | 0.374822i | \(-0.877704\pi\) |
−0.138943 | + | 0.990300i | \(0.544371\pi\) | |||||||
\(858\) | 3.41544 | + | 5.07808i | 0.116601 | + | 0.173363i | ||||
\(859\) | 21.6813 | + | 12.5177i | 0.739758 | + | 0.427099i | 0.821981 | − | 0.569514i | \(-0.192869\pi\) |
−0.0822233 | + | 0.996614i | \(0.526202\pi\) | |||||||
\(860\) | 1.77335 | − | 3.14022i | 0.0604706 | − | 0.107080i | ||||
\(861\) | 12.7135 | − | 19.9448i | 0.433275 | − | 0.679719i | ||||
\(862\) | − | 23.0346i | − | 0.784562i | ||||||
\(863\) | −7.88996 | − | 4.55527i | −0.268577 | − | 0.155063i | 0.359664 | − | 0.933082i | \(-0.382891\pi\) |
−0.628241 | + | 0.778019i | \(0.716225\pi\) | |||||||
\(864\) | −2.59437 | − | 4.49359i | −0.0882624 | − | 0.152875i | ||||
\(865\) | −0.0149116 | − | 1.56566i | −0.000507009 | − | 0.0532341i | ||||
\(866\) | 0.949139 | − | 1.64396i | 0.0322531 | − | 0.0558639i | ||||
\(867\) | −15.5989 | −0.529766 | ||||||||
\(868\) | 0.564628 | − | 12.8561i | 0.0191647 | − | 0.436365i | ||||
\(869\) | −33.0337 | + | 2.26602i | −1.12059 | + | 0.0768694i | ||||
\(870\) | −3.35396 | + | 1.97924i | −0.113710 | + | 0.0671024i | ||||
\(871\) | −4.80061 | − | 8.31490i | −0.162662 | − | 0.281740i | ||||
\(872\) | 17.4081 | − | 10.0506i | 0.589512 | − | 0.340355i | ||||
\(873\) | −6.50487 | + | 11.2668i | −0.220157 | + | 0.381322i | ||||
\(874\) | 1.94097i | 0.0656541i | ||||||||
\(875\) | −14.3960 | − | 25.8409i | −0.486675 | − | 0.873583i | ||||
\(876\) | − | 8.25628i | − | 0.278954i | ||||||
\(877\) | −24.2128 | + | 41.9378i | −0.817609 | + | 1.41614i | 0.0898309 | + | 0.995957i | \(0.471367\pi\) |
−0.907440 | + | 0.420183i | \(0.861966\pi\) | |||||||
\(878\) | −14.2518 | − | 24.6849i | −0.480976 | − | 0.833075i | ||||
\(879\) | −2.41986 | + | 1.39711i | −0.0816199 | + | 0.0471233i | ||||
\(880\) | 6.11409 | − | 4.19737i | 0.206106 | − | 0.141493i | ||||
\(881\) | 24.1928i | 0.815077i | 0.913188 | + | 0.407538i | \(0.133613\pi\) | ||||
−0.913188 | + | 0.407538i | \(0.866387\pi\) | |||||||
\(882\) | −12.9717 | − | 1.14161i | −0.436779 | − | 0.0384399i | ||||
\(883\) | 18.5791i | 0.625236i | 0.949879 | + | 0.312618i | \(0.101206\pi\) | ||||
−0.949879 | + | 0.312618i | \(0.898794\pi\) | |||||||
\(884\) | −1.33562 | + | 2.31337i | −0.0449218 | + | 0.0778069i | ||||
\(885\) | 0.0935957 | + | 9.82721i | 0.00314619 | + | 0.330338i | ||||
\(886\) | −15.9939 | + | 9.23408i | −0.537325 | + | 0.310225i | ||||
\(887\) | −39.3570 | − | 22.7228i | −1.32148 | − | 0.762956i | −0.337514 | − | 0.941320i | \(-0.609586\pi\) |
−0.983965 | + | 0.178364i | \(0.942919\pi\) | |||||||
\(888\) | − | 2.24017i | − | 0.0751751i | ||||||
\(889\) | −20.7051 | − | 39.7992i | −0.694427 | − | 1.33482i | ||||
\(890\) | −14.6077 | − | 8.24928i | −0.489652 | − | 0.276517i | ||||
\(891\) | 0.123145 | + | 0.0602637i | 0.00412551 | + | 0.00201891i | ||||
\(892\) | −6.24404 | − | 10.8150i | −0.209066 | − | 0.362113i | ||||
\(893\) | −0.879472 | − | 1.52329i | −0.0294304 | − | 0.0509749i | ||||
\(894\) | −19.5292 | − | 11.2752i | −0.653155 | − | 0.377099i | ||||
\(895\) | −14.5988 | + | 25.8514i | −0.487986 | + | 0.864118i | ||||
\(896\) | −2.64320 | − | 0.116087i | −0.0883032 | − | 0.00387819i | ||||
\(897\) | −7.40473 | −0.247237 | ||||||||
\(898\) | 6.95671 | − | 12.0494i | 0.232149 | − | 0.402093i | ||||
\(899\) | −3.96737 | − | 6.87168i | −0.132319 | − | 0.229183i | ||||
\(900\) | 4.49638 | − | 8.14227i | 0.149879 | − | 0.271409i | ||||
\(901\) | 8.24618 | − | 14.2828i | 0.274720 | − | 0.475829i | ||||
\(902\) | 1.90066 | + | 27.7075i | 0.0632850 | + | 0.922559i | ||||
\(903\) | −2.44865 | + | 3.84142i | −0.0814859 | + | 0.127835i | ||||
\(904\) | 2.42255i | 0.0805729i | ||||||||
\(905\) | −21.1072 | + | 12.4558i | −0.701628 | + | 0.414044i | ||||
\(906\) | −15.7828 | + | 9.11219i | −0.524348 | + | 0.302732i | ||||
\(907\) | 1.43738 | − | 0.829870i | 0.0477273 | − | 0.0275554i | −0.475946 | − | 0.879474i | \(-0.657894\pi\) |
0.523674 | + | 0.851919i | \(0.324561\pi\) | |||||||
\(908\) | 0.827974 | + | 0.478031i | 0.0274773 | + | 0.0158640i | ||||
\(909\) | −3.96334 | −0.131456 | ||||||||
\(910\) | 9.02574 | − | 4.80532i | 0.299200 | − | 0.159295i | ||||
\(911\) | 2.36767 | 0.0784443 | 0.0392221 | − | 0.999231i | \(-0.487512\pi\) | ||||
0.0392221 | + | 0.999231i | \(0.487512\pi\) | |||||||
\(912\) | −0.258180 | + | 0.447182i | −0.00854921 | + | 0.0148077i | ||||
\(913\) | −6.18383 | − | 9.19413i | −0.204655 | − | 0.304281i | ||||
\(914\) | −6.86004 | − | 11.8819i | −0.226910 | − | 0.393020i | ||||
\(915\) | 1.39154 | + | 2.35806i | 0.0460028 | + | 0.0779551i | ||||
\(916\) | 22.6211i | 0.747421i | ||||||||
\(917\) | 16.1130 | + | 0.707665i | 0.532097 | + | 0.0233692i | ||||
\(918\) | − | 8.01932i | − | 0.264677i | ||||||
\(919\) | 19.9149 | + | 11.4979i | 0.656933 | + | 0.379281i | 0.791107 | − | 0.611677i | \(-0.209505\pi\) |
−0.134174 | + | 0.990958i | \(0.542838\pi\) | |||||||
\(920\) | 0.0854592 | + | 8.97290i | 0.00281751 | + | 0.295828i | ||||
\(921\) | 10.5566 | − | 6.09484i | 0.347851 | − | 0.200832i | ||||
\(922\) | 9.42931 | − | 16.3320i | 0.310538 | − | 0.537867i | ||||
\(923\) | − | 11.8832i | − | 0.391142i | ||||||
\(924\) | −7.99529 | + | 4.88215i | −0.263026 | + | 0.160611i | ||||
\(925\) | 8.98455 | − | 5.41798i | 0.295410 | − | 0.178142i | ||||
\(926\) | 24.4522 | + | 14.1175i | 0.803550 | + | 0.463930i | ||||
\(927\) | −14.4049 | − | 24.9499i | −0.473117 | − | 0.819463i | ||||
\(928\) | −1.41281 | + | 0.815686i | −0.0463778 | + | 0.0267762i | ||||
\(929\) | −38.7731 | − | 22.3856i | −1.27210 | − | 0.734449i | −0.296720 | − | 0.954965i | \(-0.595893\pi\) |
−0.975383 | + | 0.220516i | \(0.929226\pi\) | |||||||
\(930\) | −10.1102 | − | 5.70944i | −0.331527 | − | 0.187220i | ||||
\(931\) | 1.42928 | + | 3.06922i | 0.0468426 | + | 0.100590i | ||||
\(932\) | −5.52190 | −0.180876 | ||||||||
\(933\) | −25.1010 | − | 14.4920i | −0.821769 | − | 0.474448i | ||||
\(934\) | −14.2257 | − | 24.6396i | −0.465479 | − | 0.806234i | ||||
\(935\) | 11.4270 | − | 0.893279i | 0.373704 | − | 0.0292133i | ||||
\(936\) | 2.78447 | + | 1.60761i | 0.0910132 | + | 0.0525465i | ||||
\(937\) | − | 49.6646i | − | 1.62247i | −0.584718 | − | 0.811236i | \(-0.698795\pi\) | ||
0.584718 | − | 0.811236i | \(-0.301205\pi\) | |||||||
\(938\) | 13.0384 | − | 6.78309i | 0.425719 | − | 0.221476i | ||||
\(939\) | 30.4935 | 0.995119 | ||||||||
\(940\) | −4.13279 | − | 7.00330i | −0.134797 | − | 0.228423i | ||||
\(941\) | −3.48321 | − | 6.03310i | −0.113549 | − | 0.196673i | 0.803650 | − | 0.595103i | \(-0.202889\pi\) |
−0.917199 | + | 0.398429i | \(0.869555\pi\) | |||||||
\(942\) | −5.94730 | − | 10.3010i | −0.193773 | − | 0.335625i | ||||
\(943\) | −29.1017 | − | 16.8019i | −0.947683 | − | 0.547145i | ||||
\(944\) | 4.11682i | 0.133991i | ||||||||
\(945\) | −16.2529 | + | 26.0413i | −0.528707 | + | 0.847125i | ||||
\(946\) | −0.366071 | − | 5.33653i | −0.0119020 | − | 0.173506i | ||||
\(947\) | −19.0548 | − | 11.0013i | −0.619198 | − | 0.357494i | 0.157359 | − | 0.987542i | \(-0.449702\pi\) |
−0.776557 | + | 0.630047i | \(0.783036\pi\) | |||||||
\(948\) | 9.23026 | − | 5.32910i | 0.299785 | − | 0.173081i | ||||
\(949\) | 6.68328 | + | 11.5758i | 0.216948 | + | 0.375766i | ||||
\(950\) | −2.41792 | + | 0.0460613i | −0.0784476 | + | 0.00149443i | ||||
\(951\) | 14.5250i | 0.471006i | ||||||||
\(952\) | −3.44812 | − | 2.19794i | −0.111754 | − | 0.0712357i | ||||
\(953\) | −36.6699 | −1.18785 | −0.593927 | − | 0.804519i | \(-0.702423\pi\) | ||||
−0.593927 | + | 0.804519i | \(0.702423\pi\) | |||||||
\(954\) | −17.1914 | − | 9.92547i | −0.556593 | − | 0.321349i | ||||
\(955\) | 32.2548 | − | 0.307200i | 1.04374 | − | 0.00994075i | ||||
\(956\) | 2.91024 | − | 1.68023i | 0.0941239 | − | 0.0543424i | ||||
\(957\) | −2.53905 | + | 5.18839i | −0.0820758 | + | 0.167717i | ||||
\(958\) | 35.4555 | 1.14552 | ||||||||
\(959\) | −23.1777 | − | 14.7742i | −0.748448 | − | 0.477085i | ||||
\(960\) | −1.17386 | + | 2.07865i | −0.0378860 | + | 0.0670880i | ||||
\(961\) | −3.67153 | + | 6.35929i | −0.118437 | + | 0.205138i | ||||
\(962\) | 1.81337 | + | 3.14084i | 0.0584653 | + | 0.101265i | ||||
\(963\) | −0.603319 | − | 1.04498i | −0.0194417 | − | 0.0336740i | ||||
\(964\) | −5.95532 | + | 10.3149i | −0.191808 | + | 0.332221i | ||||
\(965\) | 7.92484 | − | 14.0332i | 0.255110 | − | 0.451744i | ||||
\(966\) | 0.497341 | − | 11.3240i | 0.0160017 | − | 0.364345i | ||||
\(967\) | 58.1623 | 1.87037 | 0.935186 | − | 0.354157i | \(-0.115232\pi\) | ||||
0.935186 | + | 0.354157i | \(0.115232\pi\) | |||||||
\(968\) | 4.14765 | − | 10.1881i | 0.133311 | − | 0.327457i | ||||
\(969\) | −0.691129 | + | 0.399023i | −0.0222023 | + | 0.0128185i | ||||
\(970\) | 15.6373 | − | 0.148932i | 0.502082 | − | 0.00478190i | ||||
\(971\) | 37.6008 | + | 21.7088i | 1.20667 | + | 0.696669i | 0.962029 | − | 0.272946i | \(-0.0879979\pi\) |
0.244637 | + | 0.969615i | \(0.421331\pi\) | |||||||
\(972\) | −15.6104 | −0.500703 | ||||||||
\(973\) | 17.2058 | + | 33.0729i | 0.551594 | + | 1.06027i | ||||
\(974\) | − | 11.5380i | − | 0.369703i | ||||||
\(975\) | −0.175723 | − | 9.22429i | −0.00562763 | − | 0.295414i | ||||
\(976\) | 0.573483 | + | 0.993302i | 0.0183567 | + | 0.0317948i | ||||
\(977\) | 44.2882 | − | 25.5698i | 1.41690 | − | 0.818050i | 0.420878 | − | 0.907117i | \(-0.361722\pi\) |
0.996026 | + | 0.0890675i | \(0.0283887\pi\) | |||||||
\(978\) | −17.8523 | − | 10.3070i | −0.570854 | − | 0.329583i | ||||
\(979\) | −24.8246 | + | 1.70290i | −0.793397 | + | 0.0544248i | ||||
\(980\) | 6.74255 | + | 14.1258i | 0.215383 | + | 0.451232i | ||||
\(981\) | − | 37.3933i | − | 1.19387i | ||||||
\(982\) | −36.7269 | − | 21.2043i | −1.17200 | − | 0.676656i | ||||
\(983\) | −22.8638 | − | 39.6013i | −0.729243 | − | 1.26309i | −0.957203 | − | 0.289416i | \(-0.906539\pi\) |
0.227960 | − | 0.973670i | \(-0.426794\pi\) | |||||||
\(984\) | −4.46986 | − | 7.74202i | −0.142494 | − | 0.246807i | ||||
\(985\) | 17.4021 | + | 29.4891i | 0.554477 | + | 0.939602i | ||||
\(986\) | −2.52132 | −0.0802953 | ||||||||
\(987\) | 4.74072 | + | 9.11257i | 0.150899 | + | 0.290056i | ||||
\(988\) | − | 0.835966i | − | 0.0265956i | ||||||
\(989\) | 5.60506 | + | 3.23608i | 0.178231 | + | 0.102901i | ||||
\(990\) | −1.07519 | − | 13.7541i | −0.0341718 | − | 0.437134i | ||||
\(991\) | −2.30721 | − | 3.99621i | −0.0732910 | − | 0.126944i | 0.827051 | − | 0.562127i | \(-0.190017\pi\) |
−0.900342 | + | 0.435183i | \(0.856684\pi\) | |||||||
\(992\) | −4.21221 | − | 2.43192i | −0.133738 | − | 0.0772135i | ||||
\(993\) | 20.0557 | 0.636449 | ||||||||
\(994\) | 18.1730 | + | 0.798141i | 0.576413 | + | 0.0253155i | ||||
\(995\) | 32.9308 | + | 18.5967i | 1.04398 | + | 0.589555i | ||||
\(996\) | 3.08878 | + | 1.78331i | 0.0978717 | + | 0.0565063i | ||||
\(997\) | 45.4090 | − | 26.2169i | 1.43812 | − | 0.830298i | 0.440400 | − | 0.897802i | \(-0.354837\pi\) |
0.997719 | + | 0.0675035i | \(0.0215034\pi\) | |||||||
\(998\) | 15.5619 | + | 26.9540i | 0.492604 | + | 0.853216i | ||||
\(999\) | −9.42911 | − | 5.44390i | −0.298324 | − | 0.172237i |
(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 | 770.2.o.a.439.15 | yes | 48 | |
5.4 | even | 2 | 770.2.o.b.439.10 | yes | 48 | ||
7.3 | odd | 6 | inner | 770.2.o.a.549.10 | yes | 48 | |
11.10 | odd | 2 | 770.2.o.b.439.15 | yes | 48 | ||
35.24 | odd | 6 | 770.2.o.b.549.15 | yes | 48 | ||
55.54 | odd | 2 | inner | 770.2.o.a.439.10 | ✓ | 48 | |
77.10 | even | 6 | 770.2.o.b.549.10 | yes | 48 | ||
385.164 | even | 6 | inner | 770.2.o.a.549.15 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.o.a.439.10 | ✓ | 48 | 55.54 | odd | 2 | inner | |
770.2.o.a.439.15 | yes | 48 | 1.1 | even | 1 | trivial | |
770.2.o.a.549.10 | yes | 48 | 7.3 | odd | 6 | inner | |
770.2.o.a.549.15 | yes | 48 | 385.164 | even | 6 | inner | |
770.2.o.b.439.10 | yes | 48 | 5.4 | even | 2 | ||
770.2.o.b.439.15 | yes | 48 | 11.10 | odd | 2 | ||
770.2.o.b.549.10 | yes | 48 | 77.10 | even | 6 | ||
770.2.o.b.549.15 | yes | 48 | 35.24 | odd | 6 |