Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,2,Mod(32,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(36))
chi = DirichletCharacter(H, H._module([10, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.32");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.ba (of order \(36\), degree \(12\), 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: | \(5.38990213644\) |
Analytic rank: | \(0\) |
Dimension: | \(192\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{36})\) |
Twist minimal: | no (minimal twist has level 135) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{36}]$ |
Embedding invariants
Embedding label | 68.16 | ||
Character | \(\chi\) | \(=\) | 675.68 |
Dual form | 675.2.ba.b.407.16 |
$q$-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 \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.52658 | − | 2.18018i | 1.07945 | − | 1.54162i | 0.262484 | − | 0.964936i | \(-0.415458\pi\) |
0.816969 | − | 0.576682i | \(-0.195653\pi\) | |||||||
\(3\) | −1.25829 | + | 1.19025i | −0.726474 | + | 0.687193i | ||||
\(4\) | −1.73870 | − | 4.77703i | −0.869348 | − | 2.38851i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.674088 | + | 4.56031i | 0.275195 | + | 1.86174i | ||||
\(7\) | −2.78918 | + | 1.30062i | −1.05421 | + | 0.491587i | −0.870896 | − | 0.491468i | \(-0.836461\pi\) |
−0.183315 | + | 0.983054i | \(0.558683\pi\) | |||||||
\(8\) | −7.92739 | − | 2.12414i | −2.80276 | − | 0.750996i | ||||
\(9\) | 0.166591 | − | 2.99537i | 0.0555302 | − | 0.998457i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.426793 | − | 0.508631i | −0.128683 | − | 0.153358i | 0.697856 | − | 0.716238i | \(-0.254138\pi\) |
−0.826538 | + | 0.562880i | \(0.809693\pi\) | |||||||
\(12\) | 7.87366 | + | 3.94140i | 2.27293 | + | 1.13778i | ||||
\(13\) | −0.384347 | + | 0.269123i | −0.106599 | + | 0.0746412i | −0.625660 | − | 0.780096i | \(-0.715170\pi\) |
0.519062 | + | 0.854737i | \(0.326282\pi\) | |||||||
\(14\) | −1.42232 | + | 8.06640i | −0.380132 | + | 2.15584i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.94423 | + | 7.50510i | −2.23606 | + | 1.87627i | ||||
\(17\) | −4.50051 | + | 1.20591i | −1.09153 | + | 0.292476i | −0.759313 | − | 0.650726i | \(-0.774465\pi\) |
−0.332221 | + | 0.943201i | \(0.607798\pi\) | |||||||
\(18\) | −6.27613 | − | 4.93586i | −1.47930 | − | 1.16339i | ||||
\(19\) | −4.80938 | + | 2.77670i | −1.10335 | + | 0.637018i | −0.937098 | − | 0.349066i | \(-0.886499\pi\) |
−0.166249 | + | 0.986084i | \(0.553166\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.96154 | − | 4.95639i | 0.428042 | − | 1.08157i | ||||
\(22\) | −1.76044 | + | 0.154018i | −0.375327 | + | 0.0328368i | ||||
\(23\) | −0.0280775 | + | 0.0602123i | −0.00585456 | + | 0.0125551i | −0.909213 | − | 0.416331i | \(-0.863316\pi\) |
0.903359 | + | 0.428886i | \(0.141094\pi\) | |||||||
\(24\) | 12.5032 | − | 6.76283i | 2.55221 | − | 1.38046i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.24878i | 0.244906i | ||||||||
\(27\) | 3.35563 | + | 3.96733i | 0.645792 | + | 0.763513i | ||||
\(28\) | 11.0626 | + | 11.0626i | 2.09064 | + | 2.09064i | ||||
\(29\) | −0.434735 | − | 2.46551i | −0.0807283 | − | 0.457833i | −0.998197 | − | 0.0600247i | \(-0.980882\pi\) |
0.917469 | − | 0.397808i | \(-0.130229\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.76652 | − | 0.642961i | 0.317276 | − | 0.115479i | −0.178473 | − | 0.983945i | \(-0.557116\pi\) |
0.495749 | + | 0.868466i | \(0.334893\pi\) | |||||||
\(32\) | 1.27781 | + | 14.6055i | 0.225888 | + | 2.58191i | ||||
\(33\) | 1.14243 | + | 0.132015i | 0.198871 | + | 0.0229808i | ||||
\(34\) | −4.24128 | + | 11.6528i | −0.727373 | + | 1.99844i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −14.5986 | + | 4.41223i | −2.43310 | + | 0.735372i | ||||
\(37\) | −0.656295 | − | 2.44933i | −0.107894 | − | 0.402667i | 0.890763 | − | 0.454468i | \(-0.150170\pi\) |
−0.998657 | + | 0.0518010i | \(0.983504\pi\) | |||||||
\(38\) | −1.28820 | + | 14.7241i | −0.208973 | + | 2.38857i | ||||
\(39\) | 0.163296 | − | 0.796105i | 0.0261483 | − | 0.127479i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.62695 | + | 0.286875i | 0.254087 | + | 0.0448023i | 0.299241 | − | 0.954178i | \(-0.403267\pi\) |
−0.0451539 | + | 0.998980i | \(0.514378\pi\) | |||||||
\(42\) | −7.81137 | − | 11.8428i | −1.20532 | − | 1.82738i | ||||
\(43\) | −8.36925 | − | 0.732214i | −1.27630 | − | 0.111662i | −0.571224 | − | 0.820794i | \(-0.693531\pi\) |
−0.705075 | + | 0.709133i | \(0.749087\pi\) | |||||||
\(44\) | −1.68769 | + | 2.92316i | −0.254428 | + | 0.440682i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.0884111 | + | 0.153133i | 0.0130355 | + | 0.0225782i | ||||
\(47\) | −1.73166 | − | 3.71355i | −0.252588 | − | 0.541677i | 0.738599 | − | 0.674145i | \(-0.235488\pi\) |
−0.991187 | + | 0.132468i | \(0.957710\pi\) | |||||||
\(48\) | 2.32146 | − | 20.0895i | 0.335075 | − | 2.89967i | ||||
\(49\) | 1.58841 | − | 1.89299i | 0.226916 | − | 0.270428i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.22761 | − | 6.87413i | 0.591984 | − | 0.962571i | ||||
\(52\) | 1.95387 | + | 1.36812i | 0.270953 | + | 0.189723i | ||||
\(53\) | 7.52870 | − | 7.52870i | 1.03415 | − | 1.03415i | 0.0347509 | − | 0.999396i | \(-0.488936\pi\) |
0.999396 | − | 0.0347509i | \(-0.0110638\pi\) | |||||||
\(54\) | 13.7721 | − | 1.25944i | 1.87415 | − | 0.171388i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 24.8736 | − | 4.38589i | 3.32388 | − | 0.586089i | ||||
\(57\) | 2.74662 | − | 9.21828i | 0.363799 | − | 1.22099i | ||||
\(58\) | −6.03890 | − | 2.81598i | −0.792946 | − | 0.369757i | ||||
\(59\) | 3.49452 | + | 2.93225i | 0.454948 | + | 0.381747i | 0.841268 | − | 0.540618i | \(-0.181810\pi\) |
−0.386320 | + | 0.922365i | \(0.626254\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.84534 | − | 2.12753i | −0.748419 | − | 0.272402i | −0.0604785 | − | 0.998169i | \(-0.519263\pi\) |
−0.687940 | + | 0.725767i | \(0.741485\pi\) | |||||||
\(62\) | 1.29496 | − | 4.83286i | 0.164460 | − | 0.613773i | ||||
\(63\) | 3.43118 | + | 8.57130i | 0.432288 | + | 1.07988i | ||||
\(64\) | 13.5701 | + | 7.83468i | 1.69626 | + | 0.979335i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.03182 | − | 2.28917i | 0.250100 | − | 0.281777i | ||||
\(67\) | −3.13881 | − | 4.48268i | −0.383466 | − | 0.547646i | 0.580297 | − | 0.814405i | \(-0.302936\pi\) |
−0.963763 | + | 0.266758i | \(0.914047\pi\) | |||||||
\(68\) | 13.5857 | + | 19.4024i | 1.64751 | + | 2.35288i | ||||
\(69\) | −0.0363384 | − | 0.109184i | −0.00437462 | − | 0.0131442i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.33043 | − | 3.07752i | −0.632605 | − | 0.365235i | 0.149155 | − | 0.988814i | \(-0.452345\pi\) |
−0.781760 | + | 0.623579i | \(0.785678\pi\) | |||||||
\(72\) | −7.68321 | + | 23.3916i | −0.905475 | + | 2.75673i | ||||
\(73\) | 3.64803 | − | 13.6146i | 0.426970 | − | 1.59347i | −0.332613 | − | 0.943063i | \(-0.607930\pi\) |
0.759583 | − | 0.650410i | \(-0.225403\pi\) | |||||||
\(74\) | −6.34185 | − | 2.30824i | −0.737225 | − | 0.268328i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 21.6264 | + | 18.1467i | 2.48072 | + | 2.08157i | ||||
\(77\) | 1.85194 | + | 0.863572i | 0.211048 | + | 0.0984131i | ||||
\(78\) | −1.48637 | − | 1.57133i | −0.168298 | − | 0.177918i | ||||
\(79\) | 5.34198 | − | 0.941936i | 0.601020 | − | 0.105976i | 0.135144 | − | 0.990826i | \(-0.456850\pi\) |
0.465876 | + | 0.884850i | \(0.345739\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.94450 | − | 0.998001i | −0.993833 | − | 0.110889i | ||||
\(82\) | 3.10910 | − | 3.10910i | 0.343343 | − | 0.343343i | ||||
\(83\) | −4.64599 | − | 3.25316i | −0.509964 | − | 0.357081i | 0.290099 | − | 0.956997i | \(-0.406312\pi\) |
−0.800063 | + | 0.599916i | \(0.795201\pi\) | |||||||
\(84\) | −27.0873 | − | 0.752663i | −2.95547 | − | 0.0821222i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −14.3727 | + | 17.1287i | −1.54984 | + | 1.84703i | ||||
\(87\) | 3.48160 | + | 2.58488i | 0.373267 | + | 0.277128i | ||||
\(88\) | 2.30295 | + | 4.93869i | 0.245495 | + | 0.526466i | ||||
\(89\) | 3.08131 | + | 5.33699i | 0.326619 | + | 0.565720i | 0.981839 | − | 0.189718i | \(-0.0607574\pi\) |
−0.655220 | + | 0.755438i | \(0.727424\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.721988 | − | 1.25052i | 0.0756849 | − | 0.131090i | ||||
\(92\) | 0.336454 | + | 0.0294359i | 0.0350778 | + | 0.00306891i | ||||
\(93\) | −1.45751 | + | 2.91164i | −0.151137 | + | 0.301923i | ||||
\(94\) | −10.7397 | − | 1.89370i | −1.10772 | − | 0.195320i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −18.9921 | − | 16.8570i | −1.93837 | − | 1.72046i | ||||
\(97\) | 1.18828 | − | 13.5821i | 0.120652 | − | 1.37906i | −0.658669 | − | 0.752433i | \(-0.728880\pi\) |
0.779321 | − | 0.626625i | \(-0.215564\pi\) | |||||||
\(98\) | −1.70223 | − | 6.35281i | −0.171951 | − | 0.641731i | ||||
\(99\) | −1.59464 | + | 1.19367i | −0.160267 | + | 0.119968i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.629841 | + | 1.73048i | −0.0626716 | + | 0.172189i | −0.967076 | − | 0.254487i | \(-0.918093\pi\) |
0.904405 | + | 0.426676i | \(0.140316\pi\) | |||||||
\(102\) | −8.53305 | − | 19.7108i | −0.844898 | − | 1.95166i | ||||
\(103\) | 1.42347 | + | 16.2704i | 0.140259 | + | 1.60317i | 0.661627 | + | 0.749833i | \(0.269866\pi\) |
−0.521368 | + | 0.853332i | \(0.674578\pi\) | |||||||
\(104\) | 3.61852 | − | 1.31704i | 0.354826 | − | 0.129146i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.92077 | − | 27.9071i | −0.477947 | − | 2.71057i | ||||
\(107\) | 10.4880 | + | 10.4880i | 1.01391 | + | 1.01391i | 0.999902 | + | 0.0140087i | \(0.00445924\pi\) |
0.0140087 | + | 0.999902i | \(0.495541\pi\) | |||||||
\(108\) | 13.1176 | − | 22.9279i | 1.26225 | − | 2.20624i | ||||
\(109\) | − | 9.34913i | − | 0.895484i | −0.894163 | − | 0.447742i | \(-0.852228\pi\) | ||
0.894163 | − | 0.447742i | \(-0.147772\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.74113 | + | 2.30081i | 0.355092 | + | 0.218383i | ||||
\(112\) | 15.1858 | − | 32.5661i | 1.43492 | − | 3.07721i | ||||
\(113\) | −20.6993 | + | 1.81095i | −1.94722 | + | 0.170360i | −0.992064 | − | 0.125734i | \(-0.959871\pi\) |
−0.955159 | + | 0.296094i | \(0.904316\pi\) | |||||||
\(114\) | −15.9045 | − | 20.0605i | −1.48960 | − | 1.87884i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −11.0219 | + | 6.36351i | −1.02336 | + | 0.590837i | ||||
\(117\) | 0.742094 | + | 1.19610i | 0.0686066 | + | 0.110579i | ||||
\(118\) | 11.7275 | − | 3.14237i | 1.07960 | − | 0.289278i | ||||
\(119\) | 10.9843 | − | 9.21693i | 1.00693 | − | 0.844915i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.83358 | − | 10.3987i | 0.166689 | − | 0.945339i | ||||
\(122\) | −13.5617 | + | 9.49604i | −1.22782 | + | 0.859731i | ||||
\(123\) | −2.38863 | + | 1.57551i | −0.215375 | + | 0.142059i | ||||
\(124\) | −6.14289 | − | 7.32081i | −0.551648 | − | 0.657428i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 23.9249 | + | 5.60417i | 2.13140 | + | 0.499259i | ||||
\(127\) | −7.35416 | − | 1.97054i | −0.652576 | − | 0.174857i | −0.0826829 | − | 0.996576i | \(-0.526349\pi\) |
−0.569893 | + | 0.821719i | \(0.693016\pi\) | |||||||
\(128\) | 11.2214 | − | 5.23265i | 0.991845 | − | 0.462505i | ||||
\(129\) | 11.4025 | − | 9.04019i | 1.00393 | − | 0.795945i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.01388 | + | 11.0280i | 0.350694 | + | 0.963524i | 0.982148 | + | 0.188111i | \(0.0602363\pi\) |
−0.631454 | + | 0.775414i | \(0.717541\pi\) | |||||||
\(132\) | −1.35570 | − | 5.68695i | −0.117999 | − | 0.494986i | ||||
\(133\) | 9.80281 | − | 13.9999i | 0.850012 | − | 1.21394i | ||||
\(134\) | −14.5647 | −1.25820 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 38.2388 | 3.27895 | ||||||||
\(137\) | −3.85643 | + | 5.50755i | −0.329477 | + | 0.470542i | −0.949377 | − | 0.314139i | \(-0.898284\pi\) |
0.619900 | + | 0.784681i | \(0.287173\pi\) | |||||||
\(138\) | −0.293514 | − | 0.0874536i | −0.0249855 | − | 0.00744454i | ||||
\(139\) | 0.519349 | + | 1.42690i | 0.0440506 | + | 0.121028i | 0.959767 | − | 0.280796i | \(-0.0905985\pi\) |
−0.915717 | + | 0.401824i | \(0.868376\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.59899 | + | 2.61161i | 0.555735 | + | 0.219937i | ||||
\(142\) | −14.8468 | + | 6.92320i | −1.24592 | + | 0.580982i | ||||
\(143\) | 0.300921 | + | 0.0806315i | 0.0251643 | + | 0.00674274i | ||||
\(144\) | 20.9905 | + | 28.0416i | 1.74921 | + | 2.33680i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −24.1133 | − | 28.7372i | −1.99563 | − | 2.37830i | ||||
\(147\) | 0.254462 | + | 4.27255i | 0.0209876 | + | 0.352394i | ||||
\(148\) | −10.5594 | + | 7.39377i | −0.867978 | + | 0.607764i | ||||
\(149\) | −3.69731 | + | 20.9685i | −0.302895 | + | 1.71780i | 0.330355 | + | 0.943857i | \(0.392832\pi\) |
−0.633250 | + | 0.773947i | \(0.718280\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.08208 | − | 5.10347i | 0.494952 | − | 0.415314i | −0.360845 | − | 0.932626i | \(-0.617512\pi\) |
0.855797 | + | 0.517312i | \(0.173067\pi\) | |||||||
\(152\) | 44.0239 | − | 11.7962i | 3.57081 | − | 0.956797i | ||||
\(153\) | 2.86240 | + | 13.6816i | 0.231411 | + | 1.10609i | ||||
\(154\) | 4.70986 | − | 2.71924i | 0.379531 | − | 0.219123i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.08694 | + | 0.604116i | −0.327217 | + | 0.0483680i | ||||
\(157\) | 13.6200 | − | 1.19160i | 1.08699 | − | 0.0950997i | 0.470455 | − | 0.882424i | \(-0.344090\pi\) |
0.616539 | + | 0.787324i | \(0.288534\pi\) | |||||||
\(158\) | 6.10136 | − | 13.0844i | 0.485398 | − | 1.04094i | ||||
\(159\) | −0.512227 | + | 18.4344i | −0.0406223 | + | 1.46194i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 0.204461i | − | 0.0161138i | ||||||
\(162\) | −15.8303 | + | 17.9771i | −1.24374 | + | 1.41241i | ||||
\(163\) | −13.8462 | − | 13.8462i | −1.08452 | − | 1.08452i | −0.996082 | − | 0.0884330i | \(-0.971814\pi\) |
−0.0884330 | − | 0.996082i | \(-0.528186\pi\) | |||||||
\(164\) | −1.45836 | − | 8.27077i | −0.113879 | − | 0.645839i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.1849 | + | 5.16289i | −1.10096 | + | 0.400718i | ||||
\(167\) | 1.91506 | + | 21.8892i | 0.148192 | + | 1.69384i | 0.598627 | + | 0.801028i | \(0.295713\pi\) |
−0.450435 | + | 0.892809i | \(0.648731\pi\) | |||||||
\(168\) | −26.0779 | + | 35.1246i | −2.01195 | + | 2.70992i | ||||
\(169\) | −4.37097 | + | 12.0091i | −0.336228 | + | 0.923779i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.51604 | + | 14.8685i | 0.574766 | + | 1.13702i | ||||
\(172\) | 11.0538 | + | 41.2533i | 0.842842 | + | 3.14553i | ||||
\(173\) | 0.327061 | − | 3.73833i | 0.0248660 | − | 0.284220i | −0.973573 | − | 0.228374i | \(-0.926659\pi\) |
0.998439 | − | 0.0558456i | \(-0.0177854\pi\) | |||||||
\(174\) | 10.9504 | − | 3.64450i | 0.830149 | − | 0.276288i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.63466 | + | 1.34620i | 0.575484 | + | 0.101473i | ||||
\(177\) | −7.88725 | + | 0.469743i | −0.592842 | + | 0.0353081i | ||||
\(178\) | 16.3394 | + | 1.42952i | 1.22469 | + | 0.107147i | ||||
\(179\) | 7.21345 | − | 12.4941i | 0.539158 | − | 0.933850i | −0.459791 | − | 0.888027i | \(-0.652076\pi\) |
0.998950 | − | 0.0458226i | \(-0.0145909\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.06370 | − | 12.2347i | −0.525041 | − | 0.909397i | −0.999575 | − | 0.0291599i | \(-0.990717\pi\) |
0.474534 | − | 0.880237i | \(-0.342617\pi\) | |||||||
\(182\) | −1.62419 | − | 3.48308i | −0.120393 | − | 0.258183i | ||||
\(183\) | 9.88743 | − | 4.28039i | 0.730900 | − | 0.316415i | ||||
\(184\) | 0.350480 | − | 0.417686i | 0.0258378 | − | 0.0307922i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.12289 | + | 7.62247i | 0.302305 | + | 0.558907i | ||||
\(187\) | 2.53415 | + | 1.77443i | 0.185315 | + | 0.129759i | ||||
\(188\) | −14.7289 | + | 14.7289i | −1.07422 | + | 1.07422i | ||||
\(189\) | −14.5194 | − | 6.70121i | −1.05613 | − | 0.487442i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.54718 | + | 0.449136i | −0.184307 | + | 0.0324983i | −0.265040 | − | 0.964237i | \(-0.585385\pi\) |
0.0807326 | + | 0.996736i | \(0.474274\pi\) | |||||||
\(192\) | −26.4003 | + | 6.29352i | −1.90528 | + | 0.454195i | ||||
\(193\) | 12.9195 | + | 6.02445i | 0.929963 | + | 0.433649i | 0.827740 | − | 0.561112i | \(-0.189626\pi\) |
0.102224 | + | 0.994761i | \(0.467404\pi\) | |||||||
\(194\) | −27.7975 | − | 23.3248i | −1.99574 | − | 1.67463i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −11.8046 | − | 4.29654i | −0.843189 | − | 0.306896i | ||||
\(197\) | 2.16013 | − | 8.06170i | 0.153903 | − | 0.574372i | −0.845294 | − | 0.534301i | \(-0.820575\pi\) |
0.999197 | − | 0.0400711i | \(-0.0127585\pi\) | |||||||
\(198\) | 0.168070 | + | 5.29882i | 0.0119442 | + | 0.376571i | ||||
\(199\) | −3.27312 | − | 1.88973i | −0.232025 | − | 0.133960i | 0.379481 | − | 0.925200i | \(-0.376103\pi\) |
−0.611506 | + | 0.791240i | \(0.709436\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.28506 | + | 1.90454i | 0.654917 | + | 0.134336i | ||||
\(202\) | 2.81124 | + | 4.01487i | 0.197798 | + | 0.282485i | ||||
\(203\) | 4.41923 | + | 6.31132i | 0.310169 | + | 0.442968i | ||||
\(204\) | −40.1885 | − | 8.24340i | −2.81376 | − | 0.577153i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 37.6453 | + | 21.7345i | 2.62287 | + | 1.51432i | ||||
\(207\) | 0.175681 | + | 0.0941332i | 0.0122107 | + | 0.00654271i | ||||
\(208\) | 1.41790 | − | 5.29166i | 0.0983134 | − | 0.366911i | ||||
\(209\) | 3.46492 | + | 1.26113i | 0.239674 | + | 0.0872341i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.6392 | − | 11.4447i | −0.938964 | − | 0.787885i | 0.0384403 | − | 0.999261i | \(-0.487761\pi\) |
−0.977405 | + | 0.211376i | \(0.932205\pi\) | |||||||
\(212\) | −49.0550 | − | 22.8747i | −3.36911 | − | 1.57104i | ||||
\(213\) | 10.3703 | − | 2.47214i | 0.710558 | − | 0.169388i | ||||
\(214\) | 38.8763 | − | 6.85495i | 2.65753 | − | 0.468594i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −18.1743 | − | 38.5784i | −1.23660 | − | 2.62493i | ||||
\(217\) | −4.09090 | + | 4.09090i | −0.277708 | + | 0.277708i | ||||
\(218\) | −20.3828 | − | 14.2722i | −1.38049 | − | 0.966633i | ||||
\(219\) | 11.6146 | + | 21.4733i | 0.784842 | + | 1.45103i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.40522 | − | 1.67468i | 0.0945254 | − | 0.112651i | ||||
\(222\) | 10.7273 | − | 4.64397i | 0.719968 | − | 0.311683i | ||||
\(223\) | 8.09113 | + | 17.3515i | 0.541822 | + | 1.16194i | 0.966516 | + | 0.256605i | \(0.0826039\pi\) |
−0.424694 | + | 0.905337i | \(0.639618\pi\) | |||||||
\(224\) | −22.5602 | − | 39.0754i | −1.50737 | − | 2.61083i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −27.6508 | + | 47.8926i | −1.83930 | + | 3.18577i | ||||
\(227\) | −0.480953 | − | 0.0420779i | −0.0319220 | − | 0.00279281i | 0.0711836 | − | 0.997463i | \(-0.477322\pi\) |
−0.103106 | + | 0.994670i | \(0.532878\pi\) | |||||||
\(228\) | −48.8115 | + | 2.90709i | −3.23262 | + | 0.192526i | ||||
\(229\) | −14.7979 | − | 2.60927i | −0.977875 | − | 0.172426i | −0.338203 | − | 0.941073i | \(-0.609819\pi\) |
−0.639672 | + | 0.768648i | \(0.720930\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.35814 | + | 1.11765i | −0.220950 | + | 0.0735359i | ||||
\(232\) | −1.79076 | + | 20.4685i | −0.117569 | + | 1.34382i | ||||
\(233\) | 0.143242 | + | 0.534587i | 0.00938411 | + | 0.0350220i | 0.970459 | − | 0.241266i | \(-0.0775625\pi\) |
−0.961075 | + | 0.276287i | \(0.910896\pi\) | |||||||
\(234\) | 3.74056 | + | 0.208035i | 0.244528 | + | 0.0135997i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.93154 | − | 21.7917i | 0.516299 | − | 1.41852i | ||||
\(237\) | −5.60062 | + | 7.54355i | −0.363800 | + | 0.490006i | ||||
\(238\) | −3.32615 | − | 38.0181i | −0.215602 | − | 2.46435i | ||||
\(239\) | 5.32354 | − | 1.93761i | 0.344351 | − | 0.125334i | −0.164054 | − | 0.986451i | \(-0.552457\pi\) |
0.508406 | + | 0.861118i | \(0.330235\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.317967 | + | 1.80328i | 0.0204821 | + | 0.116160i | 0.993335 | − | 0.115266i | \(-0.0367721\pi\) |
−0.972853 | + | 0.231426i | \(0.925661\pi\) | |||||||
\(242\) | −19.8720 | − | 19.8720i | −1.27742 | − | 1.27742i | ||||
\(243\) | 12.4426 | − | 9.39045i | 0.798196 | − | 0.602397i | ||||
\(244\) | 31.6225i | 2.02442i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.211532 | + | 7.61277i | −0.0134868 | + | 0.485372i | ||||
\(247\) | 1.10120 | − | 2.36153i | 0.0700677 | − | 0.150261i | ||||
\(248\) | −15.3696 | + | 1.34467i | −0.975973 | + | 0.0853866i | ||||
\(249\) | 9.71810 | − | 1.43649i | 0.615859 | − | 0.0910340i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.8470 | + | 9.72663i | −1.06337 | + | 0.613939i | −0.926364 | − | 0.376630i | \(-0.877083\pi\) |
−0.137011 | + | 0.990570i | \(0.543749\pi\) | |||||||
\(252\) | 34.9796 | − | 31.2937i | 2.20351 | − | 1.97132i | ||||
\(253\) | 0.0426091 | − | 0.0114171i | 0.00267881 | − | 0.000717786i | ||||
\(254\) | −15.5228 | + | 13.0252i | −0.973988 | + | 0.817273i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.280392 | − | 1.59018i | 0.0175245 | − | 0.0993864i | ||||
\(257\) | 24.5109 | − | 17.1627i | 1.52895 | − | 1.07058i | 0.558428 | − | 0.829553i | \(-0.311405\pi\) |
0.970518 | − | 0.241027i | \(-0.0774842\pi\) | |||||||
\(258\) | −2.30248 | − | 38.6600i | −0.143346 | − | 2.40686i | ||||
\(259\) | 5.01616 | + | 5.97802i | 0.311689 | + | 0.371456i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.45753 | + | 0.891463i | −0.461609 | + | 0.0551802i | ||||
\(262\) | 30.1706 | + | 8.08418i | 1.86394 | + | 0.499442i | ||||
\(263\) | −7.60797 | + | 3.54766i | −0.469128 | + | 0.218758i | −0.642782 | − | 0.766049i | \(-0.722220\pi\) |
0.173655 | + | 0.984807i | \(0.444442\pi\) | |||||||
\(264\) | −8.77607 | − | 3.47321i | −0.540130 | − | 0.213761i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −15.5574 | − | 42.7437i | −0.953888 | − | 2.62079i | ||||
\(267\) | −10.2296 | − | 3.04794i | −0.626039 | − | 0.186531i | ||||
\(268\) | −15.9565 | + | 22.7882i | −0.974696 | + | 1.39201i | ||||
\(269\) | 2.21545 | 0.135079 | 0.0675393 | − | 0.997717i | \(-0.478485\pi\) | ||||
0.0675393 | + | 0.997717i | \(0.478485\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.87725 | −0.357017 | −0.178509 | − | 0.983938i | \(-0.557127\pi\) | ||||
−0.178509 | + | 0.983938i | \(0.557127\pi\) | |||||||
\(272\) | 31.2031 | − | 44.5627i | 1.89197 | − | 2.70201i | ||||
\(273\) | 0.579966 | + | 2.43287i | 0.0351011 | + | 0.147244i | ||||
\(274\) | 6.12031 | + | 16.8154i | 0.369741 | + | 1.01586i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.458394 | + | 0.363427i | −0.0275920 | + | 0.0218757i | ||||
\(277\) | −10.2541 | + | 4.78156i | −0.616108 | + | 0.287296i | −0.705510 | − | 0.708700i | \(-0.749282\pi\) |
0.0894020 | + | 0.995996i | \(0.471504\pi\) | |||||||
\(278\) | 3.90372 | + | 1.04600i | 0.234130 | + | 0.0627348i | ||||
\(279\) | −1.63162 | − | 5.39850i | −0.0976826 | − | 0.323199i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.9719 | + | 16.6511i | 0.833496 | + | 0.993322i | 0.999974 | + | 0.00727642i | \(0.00231618\pi\) |
−0.166478 | + | 0.986045i | \(0.553239\pi\) | |||||||
\(282\) | 15.7676 | − | 10.4001i | 0.938950 | − | 0.619320i | ||||
\(283\) | −10.7514 | + | 7.52820i | −0.639103 | + | 0.447505i | −0.847685 | − | 0.530500i | \(-0.822004\pi\) |
0.208582 | + | 0.978005i | \(0.433115\pi\) | |||||||
\(284\) | −5.43342 | + | 30.8145i | −0.322414 | + | 1.82850i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.635170 | − | 0.532971i | 0.0375584 | − | 0.0315152i | ||||
\(287\) | −4.91097 | + | 1.31589i | −0.289885 | + | 0.0776745i | ||||
\(288\) | 43.9617 | − | 1.39439i | 2.59047 | − | 0.0821654i | ||||
\(289\) | 4.07794 | − | 2.35440i | 0.239879 | − | 0.138494i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.6710 | + | 18.5046i | 0.860029 | + | 1.08476i | ||||
\(292\) | −71.3804 | + | 6.24497i | −4.17722 | + | 0.365460i | ||||
\(293\) | −1.80181 | + | 3.86399i | −0.105263 | + | 0.225736i | −0.951884 | − | 0.306460i | \(-0.900855\pi\) |
0.846621 | + | 0.532196i | \(0.178633\pi\) | |||||||
\(294\) | 9.70336 | + | 5.96760i | 0.565912 | + | 0.348037i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 20.8108i | 1.20960i | ||||||||
\(297\) | 0.585751 | − | 3.40001i | 0.0339887 | − | 0.197288i | ||||
\(298\) | 40.0708 | + | 40.0708i | 2.32124 | + | 2.32124i | ||||
\(299\) | −0.00541301 | − | 0.0306987i | −0.000313043 | − | 0.00177535i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.2957 | − | 8.84290i | 1.40038 | − | 0.509696i | ||||
\(302\) | −1.84171 | − | 21.0508i | −0.105978 | − | 1.21134i | ||||
\(303\) | −1.26718 | − | 2.92711i | −0.0727977 | − | 0.168158i | ||||
\(304\) | 22.1768 | − | 60.9303i | 1.27193 | − | 3.49459i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 34.1980 | + | 14.6455i | 1.95497 | + | 0.837225i | ||||
\(307\) | 4.82189 | + | 17.9955i | 0.275200 | + | 1.02706i | 0.955707 | + | 0.294318i | \(0.0950926\pi\) |
−0.680508 | + | 0.732741i | \(0.738241\pi\) | |||||||
\(308\) | 0.905354 | − | 10.3482i | 0.0515873 | − | 0.589646i | ||||
\(309\) | −21.1570 | − | 18.7785i | −1.20358 | − | 1.06827i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.07539 | − | 1.42391i | −0.457913 | − | 0.0807425i | −0.0600667 | − | 0.998194i | \(-0.519131\pi\) |
−0.397847 | + | 0.917452i | \(0.630242\pi\) | |||||||
\(312\) | −2.98555 | + | 5.96418i | −0.169023 | + | 0.337655i | ||||
\(313\) | 18.9940 | + | 1.66176i | 1.07360 | + | 0.0939283i | 0.610222 | − | 0.792230i | \(-0.291080\pi\) |
0.463382 | + | 0.886158i | \(0.346636\pi\) | |||||||
\(314\) | 18.1941 | − | 31.5131i | 1.02675 | − | 1.77839i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.7877 | − | 23.8811i | −0.775621 | − | 1.34342i | ||||
\(317\) | 7.17642 | + | 15.3899i | 0.403068 | + | 0.864382i | 0.998155 | + | 0.0607206i | \(0.0193399\pi\) |
−0.595087 | + | 0.803661i | \(0.702882\pi\) | |||||||
\(318\) | 39.4082 | + | 29.2582i | 2.20990 | + | 1.64072i | ||||
\(319\) | −1.06849 | + | 1.27338i | −0.0598241 | + | 0.0712956i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −25.6803 | − | 0.713566i | −1.43333 | − | 0.0398274i | ||||
\(322\) | −0.445761 | − | 0.312125i | −0.0248413 | − | 0.0173941i | ||||
\(323\) | 18.2962 | − | 18.2962i | 1.01803 | − | 1.01803i | ||||
\(324\) | 10.7843 | + | 44.4633i | 0.599127 | + | 2.47019i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −51.3243 | + | 9.04986i | −2.84259 | + | 0.501225i | ||||
\(327\) | 11.1278 | + | 11.7639i | 0.615371 | + | 0.650546i | ||||
\(328\) | −12.2881 | − | 5.73003i | −0.678497 | − | 0.316388i | ||||
\(329\) | 9.65980 | + | 8.10554i | 0.532562 | + | 0.446873i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.3657 | + | 4.86470i | 0.734643 | + | 0.267388i | 0.682129 | − | 0.731232i | \(-0.261054\pi\) |
0.0525142 | + | 0.998620i | \(0.483277\pi\) | |||||||
\(332\) | −7.46247 | + | 27.8503i | −0.409556 | + | 1.52848i | ||||
\(333\) | −7.44597 | + | 1.55781i | −0.408037 | + | 0.0853676i | ||||
\(334\) | 50.6458 | + | 29.2404i | 2.77122 | + | 1.59996i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 19.6537 | + | 59.0526i | 1.07220 | + | 3.22158i | ||||
\(337\) | 3.90887 | + | 5.58245i | 0.212930 | + | 0.304095i | 0.911382 | − | 0.411561i | \(-0.135016\pi\) |
−0.698452 | + | 0.715657i | \(0.746128\pi\) | |||||||
\(338\) | 19.5094 | + | 27.8623i | 1.06117 | + | 1.51551i | ||||
\(339\) | 23.8902 | − | 26.9161i | 1.29754 | − | 1.46188i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.08097 | − | 0.624097i | −0.0585377 | − | 0.0337968i | ||||
\(342\) | 43.8897 | + | 6.31153i | 2.37328 | + | 0.341288i | ||||
\(343\) | 3.60734 | − | 13.4628i | 0.194778 | − | 0.726922i | ||||
\(344\) | 64.7910 | + | 23.5820i | 3.49330 | + | 1.27146i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.65094 | − | 6.41990i | −0.411317 | − | 0.345136i | ||||
\(347\) | 12.4642 | + | 5.81216i | 0.669114 | + | 0.312013i | 0.727327 | − | 0.686291i | \(-0.240762\pi\) |
−0.0582130 | + | 0.998304i | \(0.518540\pi\) | |||||||
\(348\) | 6.29459 | − | 21.1260i | 0.337425 | − | 1.13247i | ||||
\(349\) | −26.3484 | + | 4.64594i | −1.41040 | + | 0.248691i | −0.826409 | − | 0.563070i | \(-0.809620\pi\) |
−0.583990 | + | 0.811761i | \(0.698509\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.35743 | − | 0.621756i | −0.125830 | − | 0.0331869i | ||||
\(352\) | 6.88345 | − | 6.88345i | 0.366889 | − | 0.366889i | ||||
\(353\) | 0.0387563 | + | 0.0271374i | 0.00206279 | + | 0.00144438i | 0.574607 | − | 0.818429i | \(-0.305155\pi\) |
−0.572545 | + | 0.819874i | \(0.694044\pi\) | |||||||
\(354\) | −11.0164 | + | 17.9127i | −0.585513 | + | 0.952049i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 20.1375 | − | 23.9989i | 1.06729 | − | 1.27194i | ||||
\(357\) | −2.85097 | + | 24.6717i | −0.150889 | + | 1.30576i | ||||
\(358\) | −16.2274 | − | 34.7997i | −0.857644 | − | 1.83922i | ||||
\(359\) | 9.42597 | + | 16.3263i | 0.497484 | + | 0.861667i | 0.999996 | − | 0.00290290i | \(-0.000924023\pi\) |
−0.502512 | + | 0.864570i | \(0.667591\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.92010 | − | 10.2539i | 0.311584 | − | 0.539680i | ||||
\(362\) | −37.4571 | − | 3.27707i | −1.96870 | − | 0.172239i | ||||
\(363\) | 10.0700 | + | 15.2670i | 0.528535 | + | 0.801312i | ||||
\(364\) | −7.22909 | − | 1.27468i | −0.378907 | − | 0.0668116i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5.76192 | − | 28.0907i | 0.301180 | − | 1.46832i | ||||
\(367\) | 1.72794 | − | 19.7504i | 0.0901977 | − | 1.03096i | −0.807357 | − | 0.590063i | \(-0.799103\pi\) |
0.897555 | − | 0.440902i | \(-0.145341\pi\) | |||||||
\(368\) | −0.200768 | − | 0.749277i | −0.0104658 | − | 0.0390588i | ||||
\(369\) | 1.13033 | − | 4.82552i | 0.0588427 | − | 0.251207i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.2070 | + | 30.7909i | −0.581836 | + | 1.59858i | ||||
\(372\) | 16.4432 | + | 1.90011i | 0.852538 | + | 0.0985160i | ||||
\(373\) | −1.84840 | − | 21.1273i | −0.0957063 | − | 1.09393i | −0.880460 | − | 0.474120i | \(-0.842766\pi\) |
0.784754 | − | 0.619808i | \(-0.212789\pi\) | |||||||
\(374\) | 7.73714 | − | 2.81609i | 0.400078 | − | 0.145616i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.83943 | + | 33.1170i | 0.301145 | + | 1.70788i | ||||
\(377\) | 0.830613 | + | 0.830613i | 0.0427788 | + | 0.0427788i | ||||
\(378\) | −36.7749 | + | 21.4250i | −1.89150 | + | 1.10199i | ||||
\(379\) | − | 4.95221i | − | 0.254378i | −0.991878 | − | 0.127189i | \(-0.959405\pi\) | ||
0.991878 | − | 0.127189i | \(-0.0405955\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.5991 | − | 6.27381i | 0.594241 | − | 0.321417i | ||||
\(382\) | −2.90926 | + | 6.23894i | −0.148851 | + | 0.319212i | ||||
\(383\) | 28.1753 | − | 2.46502i | 1.43969 | − | 0.125957i | 0.659596 | − | 0.751620i | \(-0.270727\pi\) |
0.780093 | + | 0.625663i | \(0.215172\pi\) | |||||||
\(384\) | −7.89166 | + | 19.9406i | −0.402720 | + | 1.01759i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 32.8569 | − | 18.9699i | 1.67237 | − | 0.965545i | ||||
\(387\) | −3.58749 | + | 24.9470i | −0.182362 | + | 1.26813i | ||||
\(388\) | −66.9484 | + | 17.9388i | −3.39879 | + | 0.910703i | ||||
\(389\) | −22.5434 | + | 18.9162i | −1.14300 | + | 0.959088i | −0.999533 | − | 0.0305681i | \(-0.990268\pi\) |
−0.143463 | + | 0.989656i | \(0.545824\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.0537524 | − | 0.304845i | 0.00271838 | − | 0.0154167i | ||||
\(392\) | −16.6129 | + | 11.6325i | −0.839080 | + | 0.587530i | ||||
\(393\) | −18.1768 | − | 9.09894i | −0.916898 | − | 0.458981i | ||||
\(394\) | −14.2783 | − | 17.0163i | −0.719332 | − | 0.857267i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 8.47479 | + | 5.54221i | 0.425874 | + | 0.278507i | ||||
\(397\) | −18.9334 | − | 5.07320i | −0.950242 | − | 0.254616i | −0.249777 | − | 0.968303i | \(-0.580357\pi\) |
−0.700465 | + | 0.713687i | \(0.747024\pi\) | |||||||
\(398\) | −9.11662 | + | 4.25115i | −0.456975 | + | 0.213091i | ||||
\(399\) | 4.32861 | + | 29.2837i | 0.216702 | + | 1.46602i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.0115561 | − | 0.0317502i | −0.000577086 | − | 0.00158553i | 0.939404 | − | 0.342813i | \(-0.111380\pi\) |
−0.939981 | + | 0.341227i | \(0.889157\pi\) | |||||||
\(402\) | 18.3266 | − | 17.3356i | 0.914047 | − | 0.864624i | ||||
\(403\) | −0.505922 | + | 0.722531i | −0.0252018 | + | 0.0359918i | ||||
\(404\) | 9.36163 | 0.465759 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 20.5061 | 1.01770 | ||||||||
\(407\) | −0.965702 | + | 1.37917i | −0.0478681 | + | 0.0683627i | ||||
\(408\) | −48.1156 | + | 45.5139i | −2.38207 | + | 2.25327i | ||||
\(409\) | −3.01485 | − | 8.28322i | −0.149075 | − | 0.409579i | 0.842569 | − | 0.538589i | \(-0.181042\pi\) |
−0.991643 | + | 0.129010i | \(0.958820\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.70288 | − | 11.5202i | −0.0839967 | − | 0.568251i | ||||
\(412\) | 75.2490 | − | 35.0892i | 3.70725 | − | 1.72872i | ||||
\(413\) | −13.5606 | − | 3.63355i | −0.667272 | − | 0.178795i | ||||
\(414\) | 0.473417 | − | 0.239314i | 0.0232672 | − | 0.0117616i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.42180 | − | 5.26969i | −0.216796 | − | 0.258368i | ||||
\(417\) | −2.35187 | − | 1.17730i | −0.115171 | − | 0.0576525i | ||||
\(418\) | 8.03896 | − | 5.62894i | 0.393198 | − | 0.275320i | ||||
\(419\) | 5.75122 | − | 32.6168i | 0.280966 | − | 1.59344i | −0.438384 | − | 0.898788i | \(-0.644449\pi\) |
0.719350 | − | 0.694648i | \(-0.244440\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.7180 | − | 10.6716i | 0.619835 | − | 0.520104i | −0.277916 | − | 0.960605i | \(-0.589644\pi\) |
0.897752 | + | 0.440502i | \(0.145199\pi\) | |||||||
\(422\) | −45.7728 | + | 12.2648i | −2.22819 | + | 0.597040i | ||||
\(423\) | −11.4119 | + | 4.56831i | −0.554867 | + | 0.222119i | ||||
\(424\) | −75.6750 | + | 43.6910i | −3.67510 | + | 2.12182i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10.4413 | − | 26.3829i | 0.505882 | − | 1.27826i | ||||
\(427\) | 19.0708 | − | 1.66848i | 0.922901 | − | 0.0807433i | ||||
\(428\) | 31.8660 | − | 68.3368i | 1.54030 | − | 3.30318i | ||||
\(429\) | −0.474618 | + | 0.256714i | −0.0229148 | + | 0.0123943i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 14.4385i | − | 0.695480i | −0.937591 | − | 0.347740i | \(-0.886949\pi\) | ||
0.937591 | − | 0.347740i | \(-0.113051\pi\) | |||||||
\(432\) | −59.7888 | − | 10.3004i | −2.87659 | − | 0.495577i | ||||
\(433\) | −16.4822 | − | 16.4822i | −0.792085 | − | 0.792085i | 0.189748 | − | 0.981833i | \(-0.439233\pi\) |
−0.981833 | + | 0.189748i | \(0.939233\pi\) | |||||||
\(434\) | 2.67381 | + | 15.1640i | 0.128347 | + | 0.727893i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −44.6611 | + | 16.2553i | −2.13888 | + | 0.778488i | ||||
\(437\) | −0.0321562 | − | 0.367547i | −0.00153824 | − | 0.0175821i | ||||
\(438\) | 64.5461 | + | 7.45870i | 3.08413 | + | 0.356390i | ||||
\(439\) | 10.9388 | − | 30.0541i | 0.522080 | − | 1.43440i | −0.346121 | − | 0.938190i | \(-0.612501\pi\) |
0.868201 | − | 0.496213i | \(-0.165277\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.40560 | − | 5.07323i | −0.257410 | − | 0.241582i | ||||
\(442\) | −1.50592 | − | 5.62015i | −0.0716291 | − | 0.267323i | ||||
\(443\) | 1.56526 | − | 17.8910i | 0.0743677 | − | 0.850027i | −0.863798 | − | 0.503839i | \(-0.831920\pi\) |
0.938165 | − | 0.346188i | \(-0.112524\pi\) | |||||||
\(444\) | 4.48633 | − | 21.8719i | 0.212912 | − | 1.03799i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 50.1811 | + | 8.84827i | 2.37614 | + | 0.418978i | ||||
\(447\) | −20.3055 | − | 30.7852i | −0.960418 | − | 1.45609i | ||||
\(448\) | −48.0392 | − | 4.20289i | −2.26964 | − | 0.198568i | ||||
\(449\) | 6.63475 | − | 11.4917i | 0.313113 | − | 0.542328i | −0.665921 | − | 0.746022i | \(-0.731961\pi\) |
0.979035 | + | 0.203694i | \(0.0652947\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.548456 | − | 0.949953i | −0.0258258 | − | 0.0447316i | ||||
\(452\) | 44.6407 | + | 95.7323i | 2.09972 | + | 4.50287i | ||||
\(453\) | −1.57860 | + | 13.6609i | −0.0741689 | + | 0.641843i | ||||
\(454\) | −0.825948 | + | 0.984327i | −0.0387637 | + | 0.0461968i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −41.3545 | + | 67.2427i | −1.93660 | + | 3.14893i | ||||
\(457\) | −6.59496 | − | 4.61784i | −0.308499 | − | 0.216013i | 0.409066 | − | 0.912505i | \(-0.365855\pi\) |
−0.717565 | + | 0.696491i | \(0.754743\pi\) | |||||||
\(458\) | −28.2789 | + | 28.2789i | −1.32138 | + | 1.32138i | ||||
\(459\) | −19.8863 | − | 13.8084i | −0.928213 | − | 0.644522i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.1578 | + | 2.49640i | −0.659393 | + | 0.116269i | −0.493324 | − | 0.869846i | \(-0.664218\pi\) |
−0.166068 | + | 0.986114i | \(0.553107\pi\) | |||||||
\(462\) | −2.68979 | + | 9.02752i | −0.125140 | + | 0.419998i | ||||
\(463\) | −18.8558 | − | 8.79261i | −0.876304 | − | 0.408627i | −0.0682032 | − | 0.997671i | \(-0.521727\pi\) |
−0.808101 | + | 0.589044i | \(0.799504\pi\) | |||||||
\(464\) | 22.3922 | + | 18.7893i | 1.03953 | + | 0.872272i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.38417 | + | 0.503795i | 0.0641202 | + | 0.0233378i | ||||
\(467\) | 6.38314 | − | 23.8222i | 0.295376 | − | 1.10236i | −0.645542 | − | 0.763725i | \(-0.723368\pi\) |
0.940918 | − | 0.338635i | \(-0.109965\pi\) | |||||||
\(468\) | 4.42351 | − | 5.62465i | 0.204477 | − | 0.260000i | ||||
\(469\) | 14.5849 | + | 8.42062i | 0.673470 | + | 0.388828i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.7196 | + | 17.7106i | −0.724322 | + | 0.816063i | ||||
\(472\) | −21.4739 | − | 30.6679i | −0.988418 | − | 1.41161i | ||||
\(473\) | 3.19951 | + | 4.56937i | 0.147113 | + | 0.210100i | ||||
\(474\) | 7.89648 | + | 23.7262i | 0.362698 | + | 1.08978i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −63.1279 | − | 36.4469i | −2.89346 | − | 1.67054i | ||||
\(477\) | −21.2970 | − | 23.8055i | −0.975125 | − | 1.08998i | ||||
\(478\) | 3.90246 | − | 14.5642i | 0.178494 | − | 0.666150i | ||||
\(479\) | −25.2593 | − | 9.19362i | −1.15412 | − | 0.420067i | −0.307130 | − | 0.951668i | \(-0.599368\pi\) |
−0.846995 | + | 0.531601i | \(0.821591\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.911414 | + | 0.764768i | 0.0415569 | + | 0.0348704i | ||||
\(482\) | 4.41687 | + | 2.05962i | 0.201183 | + | 0.0938132i | ||||
\(483\) | 0.243361 | + | 0.257271i | 0.0110733 | + | 0.0117063i | ||||
\(484\) | −52.8631 | + | 9.32118i | −2.40287 | + | 0.423690i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.47818 | − | 41.4624i | −0.0670516 | − | 1.88077i | ||||
\(487\) | −1.39406 | + | 1.39406i | −0.0631711 | + | 0.0631711i | −0.737987 | − | 0.674815i | \(-0.764223\pi\) |
0.674815 | + | 0.737987i | \(0.264223\pi\) | |||||||
\(488\) | 41.8191 | + | 29.2821i | 1.89306 | + | 1.32554i | ||||
\(489\) | 33.9029 | + | 0.942045i | 1.53314 | + | 0.0426008i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.2423 | + | 18.1651i | −0.687875 | + | 0.819777i | −0.991097 | − | 0.133143i | \(-0.957493\pi\) |
0.303222 | + | 0.952920i | \(0.401938\pi\) | |||||||
\(492\) | 11.6794 | + | 8.67121i | 0.526546 | + | 0.390928i | ||||
\(493\) | 4.92970 | + | 10.5718i | 0.222023 | + | 0.476129i | ||||
\(494\) | −3.46749 | − | 6.00587i | −0.156010 | − | 0.270217i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.9747 | + | 19.0087i | −0.492778 | + | 0.853516i | ||||
\(497\) | 18.8702 | + | 1.65093i | 0.846444 | + | 0.0740542i | ||||
\(498\) | 11.7036 | − | 23.3801i | 0.524451 | − | 1.04769i | ||||
\(499\) | −30.8900 | − | 5.44673i | −1.38282 | − | 0.243829i | −0.567758 | − | 0.823196i | \(-0.692189\pi\) |
−0.815067 | + | 0.579366i | \(0.803300\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −28.4634 | − | 25.2636i | −1.27165 | − | 1.12869i | ||||
\(502\) | −4.51248 | + | 51.5779i | −0.201402 | + | 2.30204i | ||||
\(503\) | 1.59547 | + | 5.95437i | 0.0711385 | + | 0.265492i | 0.992330 | − | 0.123617i | \(-0.0394495\pi\) |
−0.921192 | + | 0.389109i | \(0.872783\pi\) | |||||||
\(504\) | −8.99365 | − | 75.2363i | −0.400609 | − | 3.35129i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.0401548 | − | 0.110325i | 0.00178510 | − | 0.00490452i | ||||
\(507\) | −8.79397 | − | 20.3135i | −0.390554 | − | 0.902156i | ||||
\(508\) | 3.37332 | + | 38.5572i | 0.149667 | + | 1.71070i | ||||
\(509\) | −18.3832 | + | 6.69092i | −0.814819 | + | 0.296570i | −0.715613 | − | 0.698497i | \(-0.753853\pi\) |
−0.0992061 | + | 0.995067i | \(0.531630\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.53240 | + | 42.7184i | 0.333214 | + | 1.88975i | ||||
\(512\) | 14.4712 | + | 14.4712i | 0.639545 | + | 0.639545i | ||||
\(513\) | −27.1546 | − | 9.76284i | −1.19890 | − | 0.431040i | ||||
\(514\) | − | 79.6382i | − | 3.51269i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −63.0107 | − | 38.7518i | −2.77389 | − | 1.70595i | ||||
\(517\) | −1.14977 | + | 2.46569i | −0.0505668 | + | 0.108441i | ||||
\(518\) | 20.6907 | − | 1.81020i | 0.909097 | − | 0.0795357i | ||||
\(519\) | 4.03802 | + | 5.09319i | 0.177250 | + | 0.223566i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.02507 | − | 0.591824i | 0.0449091 | − | 0.0259283i | −0.477377 | − | 0.878698i | \(-0.658413\pi\) |
0.522286 | + | 0.852770i | \(0.325079\pi\) | |||||||
\(522\) | −9.44094 | + | 17.6196i | −0.413219 | + | 0.771190i | ||||
\(523\) | −43.1925 | + | 11.5734i | −1.88868 | + | 0.506069i | −0.889926 | + | 0.456106i | \(0.849244\pi\) |
−0.998751 | + | 0.0499636i | \(0.984089\pi\) | |||||||
\(524\) | 45.7023 | − | 38.3488i | 1.99652 | − | 1.67528i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.87963 | + | 22.0025i | −0.169160 | + | 0.959354i | ||||
\(527\) | −7.17489 | + | 5.02391i | −0.312543 | + | 0.218845i | ||||
\(528\) | −11.2089 | + | 7.39328i | −0.487806 | + | 0.321751i | ||||
\(529\) | 14.7813 | + | 17.6156i | 0.642664 | + | 0.765897i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.36533 | − | 9.97890i | 0.406421 | − | 0.433047i | ||||
\(532\) | −83.9219 | − | 22.4868i | −3.63848 | − | 0.974927i | ||||
\(533\) | −0.702518 | + | 0.327589i | −0.0304294 | + | 0.0141895i | ||||
\(534\) | −22.2613 | + | 17.6493i | −0.963339 | + | 0.763762i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 15.3607 | + | 42.2032i | 0.663482 | + | 1.82290i | ||||
\(537\) | 5.79449 | + | 24.3070i | 0.250051 | + | 1.04892i | ||||
\(538\) | 3.38206 | − | 4.83008i | 0.145811 | − | 0.208240i | ||||
\(539\) | −1.64076 | −0.0706724 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.781277 | −0.0335897 | −0.0167949 | − | 0.999859i | \(-0.505346\pi\) | ||||
−0.0167949 | + | 0.999859i | \(0.505346\pi\) | |||||||
\(542\) | −8.97207 | + | 12.8134i | −0.385383 | + | 0.550384i | ||||
\(543\) | 23.4506 | + | 6.98719i | 1.00636 | + | 0.299849i | ||||
\(544\) | −23.3637 | − | 64.1912i | −1.00171 | − | 2.75218i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 6.18944 | + | 2.44953i | 0.264884 | + | 0.104830i | ||||
\(547\) | 10.0522 | − | 4.68743i | 0.429802 | − | 0.200420i | −0.195665 | − | 0.980671i | \(-0.562686\pi\) |
0.625467 | + | 0.780251i | \(0.284909\pi\) | |||||||
\(548\) | 33.0149 | + | 8.84632i | 1.41033 | + | 0.377896i | ||||
\(549\) | −7.34652 | + | 17.1545i | −0.313542 | + | 0.732137i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.93677 | + | 10.6504i | 0.380719 | + | 0.453724i | ||||
\(552\) | 0.0561466 | + | 0.942732i | 0.00238976 | + | 0.0401253i | ||||
\(553\) | −13.6747 | + | 9.57510i | −0.581505 | + | 0.407175i | ||||
\(554\) | −5.22900 | + | 29.6551i | −0.222159 | + | 1.25993i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.91335 | − | 4.96189i | 0.250782 | − | 0.210431i | ||||
\(557\) | −13.0192 | + | 3.48849i | −0.551642 | + | 0.147812i | −0.523864 | − | 0.851802i | \(-0.675510\pi\) |
−0.0277782 | + | 0.999614i | \(0.508843\pi\) | |||||||
\(558\) | −14.2605 | − | 4.68399i | −0.603694 | − | 0.198289i | ||||
\(559\) | 3.41375 | − | 1.97093i | 0.144386 | − | 0.0833615i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.30071 | + | 0.783531i | −0.223796 | + | 0.0330807i | ||||
\(562\) | 57.6316 | − | 5.04211i | 2.43104 | − | 0.212689i | ||||
\(563\) | −15.8881 | + | 34.0720i | −0.669601 | + | 1.43596i | 0.218277 | + | 0.975887i | \(0.429956\pi\) |
−0.887878 | + | 0.460078i | \(0.847821\pi\) | |||||||
\(564\) | 1.00210 | − | 36.0644i | 0.0421962 | − | 1.51858i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 34.9323i | 1.46831i | ||||||||
\(567\) | 26.2458 | − | 8.84975i | 1.10222 | − | 0.371654i | ||||
\(568\) | 35.7193 | + | 35.7193i | 1.49875 | + | 1.49875i | ||||
\(569\) | −2.09817 | − | 11.8993i | −0.0879598 | − | 0.498845i | −0.996679 | − | 0.0814360i | \(-0.974049\pi\) |
0.908719 | − | 0.417409i | \(-0.137062\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.672547 | − | 0.244787i | 0.0281452 | − | 0.0102440i | −0.327909 | − | 0.944709i | \(-0.606344\pi\) |
0.356054 | + | 0.934465i | \(0.384122\pi\) | |||||||
\(572\) | −0.138031 | − | 1.57770i | −0.00577137 | − | 0.0659670i | ||||
\(573\) | 2.67050 | − | 3.59693i | 0.111562 | − | 0.150264i | ||||
\(574\) | −4.62809 | + | 12.7156i | −0.193173 | + | 0.530738i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 25.7284 | − | 39.3422i | 1.07202 | − | 1.63926i | ||||
\(577\) | −9.67417 | − | 36.1045i | −0.402741 | − | 1.50305i | −0.808184 | − | 0.588930i | \(-0.799549\pi\) |
0.405443 | − | 0.914120i | \(-0.367117\pi\) | |||||||
\(578\) | 1.09228 | − | 12.4848i | 0.0454328 | − | 0.519300i | ||||
\(579\) | −23.4271 | + | 7.79694i | −0.973596 | + | 0.324030i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.1896 | + | 3.03100i | 0.713146 | + | 0.125747i | ||||
\(582\) | 62.7398 | − | 3.73662i | 2.60065 | − | 0.154888i | ||||
\(583\) | −7.04253 | − | 0.616142i | −0.291672 | − | 0.0255180i | ||||
\(584\) | −57.8388 | + | 100.180i | −2.39339 | + | 4.14547i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.67358 | + | 9.82693i | 0.234373 | + | 0.405947i | ||||
\(587\) | −3.89170 | − | 8.34577i | −0.160628 | − | 0.344467i | 0.809478 | − | 0.587150i | \(-0.199750\pi\) |
−0.970106 | + | 0.242683i | \(0.921972\pi\) | |||||||
\(588\) | 19.9677 | − | 8.64423i | 0.823452 | − | 0.356482i | ||||
\(589\) | −6.71056 | + | 7.99734i | −0.276504 | + | 0.329525i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.87740 | + | 12.7151i | 0.282899 | + | 0.523028i | ||||
\(592\) | 24.2525 | + | 16.9818i | 0.996771 | + | 0.697946i | ||||
\(593\) | 9.96484 | − | 9.96484i | 0.409207 | − | 0.409207i | −0.472255 | − | 0.881462i | \(-0.656560\pi\) |
0.881462 | + | 0.472255i | \(0.156560\pi\) | |||||||
\(594\) | −6.51843 | − | 6.46741i | −0.267454 | − | 0.265361i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 106.595 | − | 18.7957i | 4.36632 | − | 0.769900i | ||||
\(597\) | 6.36780 | − | 1.51800i | 0.260617 | − | 0.0621278i | ||||
\(598\) | −0.0751920 | − | 0.0350626i | −0.00307483 | − | 0.00143382i | ||||
\(599\) | 5.73610 | + | 4.81316i | 0.234371 | + | 0.196660i | 0.752407 | − | 0.658698i | \(-0.228893\pi\) |
−0.518037 | + | 0.855358i | \(0.673337\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.4882 | − | 7.45708i | −0.835730 | − | 0.304181i | −0.111522 | − | 0.993762i | \(-0.535572\pi\) |
−0.724208 | + | 0.689581i | \(0.757795\pi\) | |||||||
\(602\) | 17.8101 | − | 66.4682i | 0.725886 | − | 2.70904i | ||||
\(603\) | −13.9502 | + | 8.65512i | −0.568095 | + | 0.352464i | ||||
\(604\) | −34.9543 | − | 20.1809i | −1.42227 | − | 0.821148i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −8.31607 | − | 1.70578i | −0.337817 | − | 0.0692926i | ||||
\(607\) | −13.1267 | − | 18.7469i | −0.532796 | − | 0.760912i | 0.459042 | − | 0.888415i | \(-0.348193\pi\) |
−0.991838 | + | 0.127503i | \(0.959304\pi\) | |||||||
\(608\) | −46.7005 | − | 66.6953i | −1.89396 | − | 2.70485i | ||||
\(609\) | −13.0727 | − | 2.68146i | −0.529734 | − | 0.108658i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.66496 | + | 0.961264i | 0.0673570 | + | 0.0388886i | ||||
\(612\) | 60.3805 | − | 37.4619i | 2.44074 | − | 1.51431i | ||||
\(613\) | −3.87633 | + | 14.4667i | −0.156564 | + | 0.584303i | 0.842403 | + | 0.538848i | \(0.181140\pi\) |
−0.998966 | + | 0.0454549i | \(0.985526\pi\) | |||||||
\(614\) | 46.5944 | + | 16.9590i | 1.88040 | + | 0.684409i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.8467 | − | 10.7796i | −0.517607 | − | 0.434324i | ||||
\(617\) | 0.430054 | + | 0.200538i | 0.0173133 | + | 0.00807334i | 0.431256 | − | 0.902230i | \(-0.358071\pi\) |
−0.413942 | + | 0.910303i | \(0.635848\pi\) | |||||||
\(618\) | −73.2383 | + | 17.4591i | −2.94608 | + | 0.702309i | ||||
\(619\) | 10.1152 | − | 1.78359i | 0.406565 | − | 0.0716885i | 0.0333743 | − | 0.999443i | \(-0.489375\pi\) |
0.373191 | + | 0.927754i | \(0.378264\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.333100 | + | 0.0906578i | −0.0133668 | + | 0.00363797i | ||||
\(622\) | −15.4321 | + | 15.4321i | −0.618770 | + | 0.618770i | ||||
\(623\) | −15.5357 | − | 10.8782i | −0.622425 | − | 0.435827i | ||||
\(624\) | 4.51429 | + | 8.34610i | 0.180716 | + | 0.334111i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 32.6187 | − | 38.8735i | 1.30371 | − | 1.55370i | ||||
\(627\) | −5.86095 | + | 2.53727i | −0.234064 | + | 0.101329i | ||||
\(628\) | −29.3733 | − | 62.9913i | −1.17212 | − | 2.51363i | ||||
\(629\) | 5.90732 | + | 10.2318i | 0.235540 | + | 0.407968i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.48152 | + | 11.2263i | −0.258025 | + | 0.446913i | −0.965713 | − | 0.259613i | \(-0.916405\pi\) |
0.707688 | + | 0.706526i | \(0.249738\pi\) | |||||||
\(632\) | −44.3488 | − | 3.88002i | −1.76410 | − | 0.154339i | ||||
\(633\) | 30.7842 | − | 1.83343i | 1.22356 | − | 0.0728722i | ||||
\(634\) | 44.5080 | + | 7.84797i | 1.76764 | + | 0.311683i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 88.9521 | − | 29.6048i | 3.52718 | − | 1.17391i | ||||
\(637\) | −0.101053 | + | 1.15504i | −0.00400388 | + | 0.0457645i | ||||
\(638\) | 1.14506 | + | 4.27341i | 0.0453333 | + | 0.169186i | ||||
\(639\) | −10.1063 | + | 15.4539i | −0.399800 | + | 0.611347i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.0051 | − | 43.9737i | 0.632164 | − | 1.73686i | −0.0428806 | − | 0.999080i | \(-0.513653\pi\) |
0.675045 | − | 0.737777i | \(-0.264124\pi\) | |||||||
\(642\) | −40.7586 | + | 54.8982i | −1.60861 | + | 2.16666i | ||||
\(643\) | 1.93250 | + | 22.0886i | 0.0762103 | + | 0.871088i | 0.934043 | + | 0.357160i | \(0.116255\pi\) |
−0.857833 | + | 0.513928i | \(0.828190\pi\) | |||||||
\(644\) | −0.976716 | + | 0.355496i | −0.0384880 | + | 0.0140085i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11.9584 | − | 67.8196i | −0.470498 | − | 2.66833i | ||||
\(647\) | −23.9696 | − | 23.9696i | −0.942341 | − | 0.942341i | 0.0560849 | − | 0.998426i | \(-0.482138\pi\) |
−0.998426 | + | 0.0560849i | \(0.982138\pi\) | |||||||
\(648\) | 68.7866 | + | 26.9109i | 2.70219 | + | 1.05716i | ||||
\(649\) | − | 3.02889i | − | 0.118894i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.278331 | − | 10.0167i | 0.0109086 | − | 0.392587i | ||||
\(652\) | −42.0693 | + | 90.2178i | −1.64756 | + | 3.53320i | ||||
\(653\) | −9.67068 | + | 0.846075i | −0.378443 | + | 0.0331095i | −0.274791 | − | 0.961504i | \(-0.588609\pi\) |
−0.103652 | + | 0.994614i | \(0.533053\pi\) | |||||||
\(654\) | 42.6349 | − | 6.30213i | 1.66716 | − | 0.246433i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −16.7048 | + | 9.64453i | −0.652214 | + | 0.376556i | ||||
\(657\) | −40.1732 | − | 13.1953i | −1.56731 | − | 0.514797i | ||||
\(658\) | 32.4179 | − | 8.68636i | 1.26378 | − | 0.338629i | ||||
\(659\) | 15.9731 | − | 13.4030i | 0.622224 | − | 0.522108i | −0.276278 | − | 0.961078i | \(-0.589101\pi\) |
0.898502 | + | 0.438970i | \(0.144657\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.68365 | + | 37.9049i | −0.259964 | + | 1.47433i | 0.523038 | + | 0.852310i | \(0.324799\pi\) |
−0.783002 | + | 0.622020i | \(0.786312\pi\) | |||||||
\(662\) | 31.0096 | − | 21.7132i | 1.20522 | − | 0.843906i | ||||
\(663\) | 0.225115 | + | 3.77980i | 0.00874274 | + | 0.146795i | ||||
\(664\) | 29.9205 | + | 35.6578i | 1.16114 | + | 1.38379i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.97054 | + | 18.6117i | −0.308852 | + | 0.721187i | ||||
\(667\) | 0.160660 | + | 0.0430488i | 0.00622079 | + | 0.00166685i | ||||
\(668\) | 101.236 | − | 47.2070i | 3.91693 | − | 1.82649i | ||||
\(669\) | −30.8337 | − | 12.2027i | −1.19210 | − | 0.471784i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.41262 | + | 3.88114i | 0.0545335 | + | 0.149830i | ||||
\(672\) | 74.8969 | + | 22.3158i | 2.88921 | + | 0.860853i | ||||
\(673\) | 11.8077 | − | 16.8631i | 0.455153 | − | 0.650026i | −0.524339 | − | 0.851510i | \(-0.675687\pi\) |
0.979492 | + | 0.201484i | \(0.0645763\pi\) | |||||||
\(674\) | 18.1379 | 0.698646 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 64.9678 | 2.49876 | ||||||||
\(677\) | −13.0007 | + | 18.5670i | −0.499659 | + | 0.713588i | −0.987195 | − | 0.159515i | \(-0.949007\pi\) |
0.487536 | + | 0.873103i | \(0.337896\pi\) | |||||||
\(678\) | −22.2116 | − | 93.1743i | −0.853032 | − | 3.57834i | ||||
\(679\) | 14.3508 | + | 39.4285i | 0.550734 | + | 1.51313i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.655262 | − | 0.519510i | 0.0251097 | − | 0.0199077i | ||||
\(682\) | −3.01082 | + | 1.40397i | −0.115290 | + | 0.0537608i | ||||
\(683\) | −7.91835 | − | 2.12172i | −0.302987 | − | 0.0811852i | 0.104122 | − | 0.994564i | \(-0.466797\pi\) |
−0.407110 | + | 0.913379i | \(0.633463\pi\) | |||||||
\(684\) | 57.9589 | − | 61.7561i | 2.21611 | − | 2.36130i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −23.8444 | − | 28.4166i | −0.910382 | − | 1.08495i | ||||
\(687\) | 21.7258 | − | 14.3301i | 0.828891 | − | 0.546726i | ||||
\(688\) | 80.3518 | − | 56.2630i | 3.06338 | − | 2.14500i | ||||
\(689\) | −0.867490 | + | 4.91978i | −0.0330487 | + | 0.187429i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.09562 | − | 1.75844i | 0.0797212 | − | 0.0668941i | −0.602056 | − | 0.798454i | \(-0.705652\pi\) |
0.681777 | + | 0.731560i | \(0.261207\pi\) | |||||||
\(692\) | −18.4268 | + | 4.93744i | −0.700481 | + | 0.187693i | ||||
\(693\) | 2.89523 | − | 5.40337i | 0.109981 | − | 0.205257i | ||||
\(694\) | 31.6991 | − | 18.3015i | 1.20328 | − | 0.694715i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −22.1094 | − | 27.8867i | −0.838054 | − | 1.05704i | ||||
\(697\) | −7.66804 | + | 0.670867i | −0.290448 | + | 0.0254109i | ||||
\(698\) | −30.0939 | + | 64.5366i | −1.13907 | + | 2.44275i | ||||
\(699\) | −0.816535 | − | 0.502171i | −0.0308842 | − | 0.0189939i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 45.2015i | − | 1.70724i | −0.520899 | − | 0.853618i | \(-0.674403\pi\) | ||
0.520899 | − | 0.853618i | \(-0.325597\pi\) | |||||||
\(702\) | −4.95433 | + | 4.19045i | −0.186989 | + | 0.158158i | ||||
\(703\) | 9.95741 | + | 9.95741i | 0.375551 | + | 0.375551i | ||||
\(704\) | −1.80664 | − | 10.2459i | −0.0680901 | − | 0.386158i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.118329 | − | 0.0430682i | 0.00445337 | − | 0.00162089i | ||||
\(707\) | −0.493942 | − | 5.64579i | −0.0185766 | − | 0.212332i | ||||
\(708\) | 15.9575 | + | 36.8609i | 0.599720 | + | 1.38532i | ||||
\(709\) | 6.90171 | − | 18.9623i | 0.259199 | − | 0.712144i | −0.740018 | − | 0.672587i | \(-0.765183\pi\) |
0.999217 | − | 0.0395569i | \(-0.0125946\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.93152 | − | 16.1581i | −0.0724378 | − | 0.605978i | ||||
\(712\) | −13.0903 | − | 48.8536i | −0.490579 | − | 1.83086i | ||||
\(713\) | −0.0108853 | + | 0.124419i | −0.000407656 | + | 0.00465953i | ||||
\(714\) | 49.4365 | + | 43.8788i | 1.85011 | + | 1.64212i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −72.2265 | − | 12.7355i | −2.69923 | − | 0.475947i | ||||
\(717\) | −4.39231 | + | 8.77444i | −0.164034 | + | 0.327688i | ||||
\(718\) | 49.9836 | + | 4.37300i | 1.86537 | + | 0.163199i | ||||
\(719\) | −18.2157 | + | 31.5505i | −0.679331 | + | 1.17664i | 0.295852 | + | 0.955234i | \(0.404396\pi\) |
−0.975183 | + | 0.221402i | \(0.928937\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −25.1318 | − | 43.5295i | −0.935957 | − | 1.62113i | ||||
\(722\) | −13.3179 | − | 28.5603i | −0.495640 | − | 1.06290i | ||||
\(723\) | −2.54646 | − | 1.89059i | −0.0947037 | − | 0.0703118i | ||||
\(724\) | −46.1638 | + | 55.0159i | −1.71566 | + | 2.04465i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 48.6574 | + | 1.35202i | 1.80585 | + | 0.0501782i | ||||
\(727\) | −10.9561 | − | 7.67153i | −0.406338 | − | 0.284521i | 0.352485 | − | 0.935817i | \(-0.385337\pi\) |
−0.758824 | + | 0.651296i | \(0.774226\pi\) | |||||||
\(728\) | −8.37976 | + | 8.37976i | −0.310575 | + | 0.310575i | ||||
\(729\) | −4.47945 | + | 26.6258i | −0.165906 | + | 0.986142i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 38.5489 | − | 6.79721i | 1.42578 | − | 0.251404i | ||||
\(732\) | −37.6388 | − | 39.7903i | −1.39117 | − | 1.47069i | ||||
\(733\) | 38.0568 | + | 17.7462i | 1.40566 | + | 0.655470i | 0.969656 | − | 0.244474i | \(-0.0786152\pi\) |
0.436005 | + | 0.899944i | \(0.356393\pi\) | |||||||
\(734\) | −40.4216 | − | 33.9178i | −1.49199 | − | 1.25193i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.915308 | − | 0.333145i | −0.0337387 | − | 0.0122799i | ||||
\(737\) | −0.940413 | + | 3.50967i | −0.0346406 | + | 0.129280i | ||||
\(738\) | −8.79496 | − | 9.83085i | −0.323747 | − | 0.361879i | ||||
\(739\) | −34.0711 | − | 19.6709i | −1.25332 | − | 0.723607i | −0.281556 | − | 0.959545i | \(-0.590850\pi\) |
−0.971768 | + | 0.235938i | \(0.924184\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.42519 | + | 4.28220i | 0.0523557 | + | 0.157310i | ||||
\(742\) | 50.0213 | + | 71.4378i | 1.83634 | + | 2.62256i | ||||
\(743\) | −7.43173 | − | 10.6136i | −0.272644 | − | 0.389376i | 0.659358 | − | 0.751829i | \(-0.270828\pi\) |
−0.932002 | + | 0.362453i | \(0.881939\pi\) | |||||||
\(744\) | 17.7390 | − | 19.9858i | 0.650342 | − | 0.732714i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −48.8829 | − | 28.2225i | −1.78973 | − | 1.03330i | ||||
\(747\) | −10.5184 | + | 13.3745i | −0.384848 | + | 0.489349i | ||||
\(748\) | 4.07039 | − | 15.1909i | 0.148828 | − | 0.555434i | ||||
\(749\) | −42.8937 | − | 15.6120i | −1.56730 | − | 0.570451i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.6700 | + | 25.7352i | 1.11916 | + | 0.939089i | 0.998562 | − | 0.0536119i | \(-0.0170734\pi\) |
0.120601 | + | 0.992701i | \(0.461518\pi\) | |||||||
\(752\) | 43.3589 | + | 20.2186i | 1.58114 | + | 0.737296i | ||||
\(753\) | 9.62128 | − | 32.2912i | 0.350619 | − | 1.17676i | ||||
\(754\) | 3.07888 | − | 0.542889i | 0.112126 | − | 0.0197709i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −6.76700 | + | 81.0112i | −0.246113 | + | 2.94635i | ||||
\(757\) | −0.846964 | + | 0.846964i | −0.0307834 | + | 0.0307834i | −0.722331 | − | 0.691548i | \(-0.756929\pi\) |
0.691548 | + | 0.722331i | \(0.256929\pi\) | |||||||
\(758\) | −10.7967 | − | 7.55993i | −0.392154 | − | 0.274589i | ||||
\(759\) | −0.0400255 | + | 0.0650817i | −0.00145283 | + | 0.00236232i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.25980 | + | 3.88488i | −0.118168 | + | 0.140827i | −0.821885 | − | 0.569653i | \(-0.807078\pi\) |
0.703718 | + | 0.710480i | \(0.251522\pi\) | |||||||
\(762\) | 4.02893 | − | 34.8656i | 0.145953 | − | 1.26305i | ||||
\(763\) | 12.1596 | + | 26.0764i | 0.440208 | + | 0.944029i | ||||
\(764\) | 6.57430 | + | 11.3870i | 0.237850 | + | 0.411968i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 37.6375 | − | 65.1901i | 1.35990 | − | 2.35542i | ||||
\(767\) | −2.13224 | − | 0.186547i | −0.0769909 | − | 0.00673583i | ||||
\(768\) | 1.53991 | + | 2.33465i | 0.0555666 | + | 0.0842444i | ||||
\(769\) | −26.0795 | − | 4.59852i | −0.940451 | − | 0.165827i | −0.317651 | − | 0.948208i | \(-0.602894\pi\) |
−0.622800 | + | 0.782381i | \(0.714005\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.4138 | + | 50.7698i | −0.375045 | + | 1.82843i | ||||
\(772\) | 6.31593 | − | 72.1914i | 0.227315 | − | 2.59822i | ||||
\(773\) | 2.81189 | + | 10.4941i | 0.101137 | + | 0.377447i | 0.997878 | − | 0.0651074i | \(-0.0207390\pi\) |
−0.896742 | + | 0.442555i | \(0.854072\pi\) | |||||||
\(774\) | 48.9124 | + | 45.9049i | 1.75812 | + | 1.65002i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −38.2703 | + | 105.147i | −1.37383 | + | 3.77455i | ||||
\(777\) | −13.4271 | − | 1.55159i | −0.481696 | − | 0.0556629i | ||||
\(778\) | 6.82635 | + | 78.0256i | 0.244737 | + | 2.79735i | ||||
\(779\) | −8.62118 | + | 3.13785i | −0.308886 | + | 0.112425i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.709661 | + | 4.02469i | 0.0253937 | + | 0.144015i | ||||
\(782\) | −0.582559 | − | 0.582559i | −0.0208323 | − | 0.0208323i | ||||
\(783\) | 8.32267 | − | 9.99807i | 0.297428 | − | 0.357302i | ||||
\(784\) | 28.8525i | 1.03045i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −47.5856 | + | 25.7384i | −1.69732 | + | 0.918058i | ||||
\(787\) | −3.36829 | + | 7.22332i | −0.120067 | + | 0.257484i | −0.957151 | − | 0.289591i | \(-0.906481\pi\) |
0.837084 | + | 0.547074i | \(0.184259\pi\) | |||||||
\(788\) | −42.2668 | + | 3.69786i | −1.50569 | + | 0.131731i | ||||
\(789\) | 5.35043 | − | 13.5194i | 0.190480 | − | 0.481303i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 55.3786 | − | 31.9729i | 1.96904 | − | 1.13682i | ||||
\(792\) | 15.1769 | − | 6.07544i | 0.539286 | − | 0.215882i | ||||
\(793\) | 2.81921 | − | 0.755404i | 0.100113 | − | 0.0268252i | ||||
\(794\) | −39.9638 | + | 33.5336i | −1.41826 | + | 1.19006i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.33636 | + | 18.9215i | −0.118254 | + | 0.670653i | ||||
\(797\) | 0.621792 | − | 0.435383i | 0.0220250 | − | 0.0154221i | −0.562512 | − | 0.826789i | \(-0.690165\pi\) |
0.584537 | + | 0.811367i | \(0.301276\pi\) | |||||||
\(798\) | 70.4517 | + | 35.2667i | 2.49396 | + | 1.24843i | ||||
\(799\) | 12.2715 | + | 14.6246i | 0.434136 | + | 0.517383i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.4996 | − | 8.34059i | 0.582984 | − | 0.294700i | ||||
\(802\) | −0.0868625 | − | 0.0232747i | −0.00306722 | − | 0.000821859i | ||||
\(803\) | −8.48179 | + | 3.95512i | −0.299316 | + | 0.139573i | ||||
\(804\) | −7.04587 | − | 47.6664i | −0.248489 | − | 1.68106i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.802918 | + | 2.20600i | 0.0282816 | + | 0.0777030i | ||||
\(807\) | −2.78768 | + | 2.63695i | −0.0981311 | + | 0.0928251i | ||||
\(808\) | 8.66877 | − | 12.3803i | 0.304966 | − | 0.435537i | ||||
\(809\) | 3.88327 | 0.136528 | 0.0682642 | − | 0.997667i | \(-0.478254\pi\) | ||||
0.0682642 | + | 0.997667i | \(0.478254\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.9810 | −0.806974 | −0.403487 | − | 0.914985i | \(-0.632202\pi\) | ||||
−0.403487 | + | 0.914985i | \(0.632202\pi\) | |||||||
\(812\) | 22.4656 | − | 32.0843i | 0.788390 | − | 1.12594i | ||||
\(813\) | 7.39528 | − | 6.99542i | 0.259364 | − | 0.245340i | ||||
\(814\) | 1.53261 | + | 4.21081i | 0.0537179 | + | 0.147589i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 13.7783 | + | 93.2125i | 0.482337 | + | 3.26309i | ||||
\(817\) | 42.2840 | − | 19.7174i | 1.47933 | − | 0.689824i | ||||
\(818\) | −22.6613 | − | 6.07207i | −0.792333 | − | 0.212305i | ||||
\(819\) | −3.62550 | − | 2.37095i | −0.126685 | − | 0.0828476i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.59034 | − | 1.89529i | −0.0555031 | − | 0.0661461i | 0.737579 | − | 0.675261i | \(-0.235969\pi\) |
−0.793082 | + | 0.609115i | \(0.791525\pi\) | |||||||
\(822\) | −27.7157 | − | 13.8739i | −0.966697 | − | 0.483909i | ||||
\(823\) | −26.9245 | + | 18.8527i | −0.938528 | + | 0.657164i | −0.939396 | − | 0.342835i | \(-0.888613\pi\) |
0.000867529 | 1.00000i | \(0.499724\pi\) | ||||||||
\(824\) | 23.2761 | − | 132.005i | 0.810860 | − | 4.59862i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −28.6230 | + | 24.0176i | −0.995923 | + | 0.835678i | ||||
\(827\) | −8.32126 | + | 2.22968i | −0.289359 | + | 0.0775334i | −0.400579 | − | 0.916262i | \(-0.631191\pi\) |
0.111220 | + | 0.993796i | \(0.464524\pi\) | |||||||
\(828\) | 0.144222 | − | 1.00290i | 0.00501205 | − | 0.0348532i | ||||
\(829\) | 7.38409 | − | 4.26321i | 0.256460 | − | 0.148067i | −0.366259 | − | 0.930513i | \(-0.619361\pi\) |
0.622719 | + | 0.782446i | \(0.286028\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.21135 | − | 18.2216i | 0.250159 | − | 0.632099i | ||||
\(832\) | −7.32410 | + | 0.640776i | −0.253918 | + | 0.0222149i | ||||
\(833\) | −4.86588 | + | 10.4349i | −0.168593 | + | 0.361548i | ||||
\(834\) | −6.15702 | + | 3.33025i | −0.213200 | + | 0.115317i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 18.7448i | − | 0.648301i | ||||||
\(837\) | 8.47863 | + | 4.85083i | 0.293064 | + | 0.167669i | ||||
\(838\) | −62.3307 | − | 62.3307i | −2.15318 | − | 2.15318i | ||||
\(839\) | −8.06541 | − | 45.7412i | −0.278449 | − | 1.57916i | −0.727789 | − | 0.685802i | \(-0.759452\pi\) |
0.449340 | − | 0.893361i | \(-0.351659\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.3614 | − | 7.77490i | 0.736599 | − | 0.268100i | ||||
\(842\) | −3.85112 | − | 44.0185i | −0.132718 | − | 1.51698i | ||||
\(843\) | −37.3998 | − | 4.32178i | −1.28812 | − | 0.148850i | ||||
\(844\) | −30.9571 | + | 85.0539i | −1.06559 | + | 2.92768i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.46146 | + | 31.8539i | −0.256530 | + | 1.09516i | ||||
\(847\) | 8.41058 | + | 31.3887i | 0.288991 | + | 1.07853i | ||||
\(848\) | −10.8348 | + | 123.842i | −0.372068 | + | 4.25276i | ||||
\(849\) | 4.56789 | − | 22.2695i | 0.156770 | − | 0.764288i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.165907 | + | 0.0292538i | 0.00568721 | + | 0.00100281i | ||||
\(852\) | −29.8402 | − | 45.2407i | −1.02231 | − | 1.54992i | ||||
\(853\) | −20.6498 | − | 1.80662i | −0.707035 | − | 0.0618575i | −0.272034 | − | 0.962288i | \(-0.587696\pi\) |
−0.435001 | + | 0.900430i | \(0.643252\pi\) | |||||||
\(854\) | 25.4755 | − | 44.1248i | 0.871752 | − | 1.50992i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −60.8644 | − | 105.420i | −2.08030 | − | 3.60319i | ||||
\(857\) | 1.85929 | + | 3.98725i | 0.0635120 | + | 0.136202i | 0.935502 | − | 0.353322i | \(-0.114948\pi\) |
−0.871990 | + | 0.489524i | \(0.837170\pi\) | |||||||
\(858\) | −0.164858 | + | 1.42665i | −0.00562814 | + | 0.0487049i | ||||
\(859\) | 27.5782 | − | 32.8664i | 0.940956 | − | 1.12139i | −0.0514862 | − | 0.998674i | \(-0.516396\pi\) |
0.992442 | − | 0.122714i | \(-0.0391598\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.61318 | − | 7.50107i | 0.157217 | − | 0.255636i | ||||
\(862\) | −31.4786 | − | 22.0415i | −1.07217 | − | 0.750738i | ||||
\(863\) | 29.7115 | − | 29.7115i | 1.01139 | − | 1.01139i | 0.0114553 | − | 0.999934i | \(-0.496354\pi\) |
0.999934 | − | 0.0114553i | \(-0.00364642\pi\) | |||||||
\(864\) | −53.6570 | + | 54.0802i | −1.82545 | + | 1.83985i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −61.0955 | + | 10.7728i | −2.07611 | + | 0.366074i | ||||
\(867\) | −2.32890 | + | 7.81631i | −0.0790936 | + | 0.265456i | ||||
\(868\) | 26.6552 | + | 12.4295i | 0.904736 | + | 0.421885i | ||||
\(869\) | −2.75902 | − | 2.31509i | −0.0935932 | − | 0.0785340i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.41278 | + | 0.878181i | 0.0817540 | + | 0.0297560i | ||||
\(872\) | −19.8588 | + | 74.1142i | −0.672505 | + | 2.50982i | ||||
\(873\) | −40.4856 | − | 5.82201i | −1.37023 | − | 0.197045i | ||||
\(874\) | −0.850406 | − | 0.490982i | −0.0287654 | − | 0.0166077i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 82.3842 | − | 92.8188i | 2.78350 | − | 3.13606i | ||||
\(877\) | −6.63310 | − | 9.47306i | −0.223984 | − | 0.319882i | 0.691394 | − | 0.722478i | \(-0.256997\pi\) |
−0.915378 | + | 0.402596i | \(0.868108\pi\) | |||||||
\(878\) | −48.8243 | − | 69.7284i | −1.64774 | − | 2.35322i | ||||
\(879\) | −2.33193 | − | 7.00662i | −0.0786540 | − | 0.236328i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.7653 | + | 7.37007i | 0.430075 | + | 0.248304i | 0.699379 | − | 0.714751i | \(-0.253460\pi\) |
−0.269304 | + | 0.963055i | \(0.586794\pi\) | |||||||
\(882\) | −19.3126 | + | 4.04050i | −0.650289 | + | 0.136051i | ||||
\(883\) | −4.11349 | + | 15.3517i | −0.138430 | + | 0.516627i | 0.861530 | + | 0.507706i | \(0.169506\pi\) |
−0.999960 | + | 0.00892106i | \(0.997160\pi\) | |||||||
\(884\) | −10.4432 | − | 3.80103i | −0.351244 | − | 0.127842i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −36.6160 | − | 30.7245i | −1.23014 | − | 1.03221i | ||||
\(887\) | 6.76369 | + | 3.15396i | 0.227102 | + | 0.105900i | 0.532839 | − | 0.846216i | \(-0.321125\pi\) |
−0.305737 | + | 0.952116i | \(0.598903\pi\) | |||||||
\(888\) | −24.7702 | − | 26.1861i | −0.831232 | − | 0.878747i | ||||
\(889\) | 23.0750 | − | 4.06875i | 0.773911 | − | 0.136461i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.30983 | + | 4.97539i | 0.110883 | + | 0.166682i | ||||
\(892\) | 68.8206 | − | 68.8206i | 2.30428 | − | 2.30428i | ||||
\(893\) | 18.6396 | + | 13.0516i | 0.623750 | + | 0.436755i | ||||
\(894\) | −98.1150 | − | 2.72628i | −3.28146 | − | 0.0911803i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −24.4930 | + | 29.1896i | −0.818253 | + | 0.975156i | ||||
\(897\) | 0.0433504 | + | 0.0321851i | 0.00144743 | + | 0.00107463i | ||||
\(898\) | −14.9255 | − | 32.0079i | −0.498072 | − | 1.06812i | ||||
\(899\) | −2.35319 | − | 4.07585i | −0.0784834 | − | 0.135937i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.8041 | + | 42.9619i | −0.826344 | + | 1.43127i | ||||
\(902\) | −2.90833 | − | 0.254446i | −0.0968367 | − | 0.00847211i | ||||
\(903\) | −20.0457 | + | 40.0450i | −0.667080 | + | 1.33261i | ||||
\(904\) | 167.938 | + | 29.6120i | 5.58553 | + | 0.984880i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 27.3733 | + | 24.2960i | 0.909415 | + | 0.807180i | ||||
\(907\) | −1.42792 | + | 16.3212i | −0.0474134 | + | 0.541937i | 0.934928 | + | 0.354838i | \(0.115464\pi\) |
−0.982341 | + | 0.187099i | \(0.940092\pi\) | |||||||
\(908\) | 0.635223 | + | 2.37069i | 0.0210806 | + | 0.0786740i | ||||
\(909\) | 5.07849 | + | 2.17489i | 0.168443 | + | 0.0721365i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.825532 | + | 2.26813i | −0.0273511 | + | 0.0751465i | −0.952617 | − | 0.304173i | \(-0.901620\pi\) |
0.925266 | + | 0.379320i | \(0.123842\pi\) | |||||||
\(912\) | 44.6177 | + | 103.064i | 1.47744 | + | 3.41279i | ||||
\(913\) | 0.328216 | + | 3.75152i | 0.0108624 | + | 0.124157i | ||||
\(914\) | −20.1354 | + | 7.32869i | −0.666020 | + | 0.242412i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.2645 | + | 75.2269i | 0.438273 | + | 2.48557i | ||||
\(917\) | −25.5387 | − | 25.5387i | −0.843361 | − | 0.843361i | ||||
\(918\) | −60.4628 | + | 22.2760i | −1.99557 | + | 0.735218i | ||||
\(919\) | 5.68243i | 0.187446i | 0.995598 | + | 0.0937230i | \(0.0298768\pi\) | ||||
−0.995598 | + | 0.0937230i | \(0.970123\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −27.4866 | − | 16.9043i | −0.905714 | − | 0.557017i | ||||
\(922\) | −16.1703 | + | 34.6774i | −0.532541 | + | 1.14204i | ||||
\(923\) | 2.87697 | − | 0.251702i | 0.0946965 | − | 0.00828487i | ||||
\(924\) | 11.1778 | + | 14.0987i | 0.367724 | + | 0.463813i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −47.9543 | + | 27.6864i | −1.57588 | + | 0.909832i | ||||
\(927\) | 48.9729 | − | 1.55334i | 1.60848 | − | 0.0510183i | ||||
\(928\) | 35.4544 | − | 9.49998i | 1.16385 | − | 0.311852i | ||||
\(929\) | 31.5686 | − | 26.4892i | 1.03573 | − | 0.869082i | 0.0442093 | − | 0.999022i | \(-0.485923\pi\) |
0.991522 | + | 0.129941i | \(0.0414787\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.38300 | + | 13.5147i | −0.0780996 | + | 0.442925i | ||||
\(932\) | 2.30468 | − | 1.61376i | 0.0754924 | − | 0.0528604i | ||||
\(933\) | 11.8560 | − | 7.82008i | 0.388148 | − | 0.256018i | ||||
\(934\) | −42.1923 | − | 50.2828i | −1.38057 | − | 1.64530i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.34220 | − | 11.0582i | −0.109243 | − | 0.361450i | ||||
\(937\) | −7.80116 | − | 2.09031i | −0.254853 | − | 0.0682876i | 0.129131 | − | 0.991628i | \(-0.458781\pi\) |
−0.383983 | + | 0.923340i | \(0.625448\pi\) | |||||||
\(938\) | 40.6235 | − | 18.9430i | 1.32640 | − | 0.618512i | ||||
\(939\) | −25.8779 | + | 20.5167i | −0.844493 | + | 0.669538i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.0461 | + | 46.8337i | 0.555686 | + | 1.52673i | 0.825833 | + | 0.563915i | \(0.190706\pi\) |
−0.270147 | + | 0.962819i | \(0.587072\pi\) | |||||||
\(942\) | 14.6151 | + | 61.3082i | 0.476186 | + | 1.99753i | ||||
\(943\) | −0.0629540 | + | 0.0899076i | −0.00205006 | + | 0.00292780i | ||||
\(944\) | −53.2626 | −1.73355 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14.8463 | 0.482696 | ||||||||
\(947\) | 27.9030 | − | 39.8496i | 0.906726 | − | 1.29494i | −0.0484276 | − | 0.998827i | \(-0.515421\pi\) |
0.955153 | − | 0.296112i | \(-0.0956901\pi\) | |||||||
\(948\) | 45.7735 | + | 13.6384i | 1.48666 | + | 0.442955i | ||||
\(949\) | 2.26190 | + | 6.21452i | 0.0734244 | + | 0.201732i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −27.3479 | − | 10.8232i | −0.886816 | − | 0.350966i | ||||
\(952\) | −106.655 | + | 49.7340i | −3.45671 | + | 1.61189i | ||||
\(953\) | 48.5541 | + | 13.0100i | 1.57282 | + | 0.421436i | 0.936694 | − | 0.350148i | \(-0.113869\pi\) |
0.636127 | + | 0.771584i | \(0.280535\pi\) | |||||||
\(954\) | −84.4117 | + | 10.0905i | −2.73293 | + | 0.326691i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −18.5120 | − | 22.0618i | −0.598722 | − | 0.713529i | ||||
\(957\) | −0.171171 | − | 2.87406i | −0.00553318 | − | 0.0929051i | ||||
\(958\) | −58.6039 | + | 41.0349i | −1.89341 | + | 1.32578i | ||||
\(959\) | 3.59307 | − | 20.3773i | 0.116026 | − | 0.658017i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.0402 | + | 17.6548i | −0.678716 | + | 0.569510i | ||||
\(962\) | 3.05867 | − | 0.819569i | 0.0986156 | − | 0.0264240i | ||||
\(963\) | 33.1626 | − | 29.6682i | 1.06865 | − | 0.956043i | ||||
\(964\) | 8.06148 | − | 4.65430i | 0.259643 | − | 0.149905i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.932406 | − | 0.137825i | 0.0299997 | − | 0.00443444i | ||||
\(967\) | 49.5607 | − | 4.33600i | 1.59377 | − | 0.139436i | 0.744581 | − | 0.667533i | \(-0.232650\pi\) |
0.849185 | + | 0.528096i | \(0.177094\pi\) | |||||||
\(968\) | −36.6238 | + | 78.5400i | −1.17713 | + | 2.52437i | ||||
\(969\) | −1.24481 | + | 44.7991i | −0.0399891 | + | 1.43916i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 40.2818i | − | 1.29270i | −0.763039 | − | 0.646352i | \(-0.776294\pi\) | ||
0.763039 | − | 0.646352i | \(-0.223706\pi\) | |||||||
\(972\) | −66.4924 | − | 43.1118i | −2.13275 | − | 1.38281i | ||||
\(973\) | −3.30441 | − | 3.30441i | −0.105934 | − | 0.105934i | ||||
\(974\) | 0.911162 | + | 5.16745i | 0.0291955 | + | 0.165576i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 68.2493 | − | 24.8407i | 2.18461 | − | 0.795132i | ||||
\(977\) | −3.30670 | − | 37.7958i | −0.105791 | − | 1.20919i | −0.844644 | − | 0.535328i | \(-0.820188\pi\) |
0.738854 | − | 0.673866i | \(-0.235367\pi\) | |||||||
\(978\) | 53.8093 | − | 72.4763i | 1.72063 | − | 2.31754i | ||||
\(979\) | 1.39948 | − | 3.84504i | 0.0447276 | − | 0.122888i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −28.0041 | − | 1.55748i | −0.894102 | − | 0.0497264i | ||||
\(982\) | 16.3345 | + | 60.9612i | 0.521255 | + | 1.94535i | ||||
\(983\) | −3.12235 | + | 35.6886i | −0.0995874 | + | 1.13829i | 0.767811 | + | 0.640676i | \(0.221346\pi\) |
−0.867399 | + | 0.497614i | \(0.834210\pi\) | |||||||
\(984\) | 22.2822 | − | 7.41591i | 0.710330 | − | 0.236411i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 30.5739 | + | 5.39101i | 0.973672 | + | 0.171685i | ||||
\(987\) | −21.8025 | + | 1.29850i | −0.693981 | + | 0.0413316i | ||||
\(988\) | −13.1958 | − | 1.15448i | −0.419813 | − | 0.0367289i | ||||
\(989\) | 0.279076 | − | 0.483373i | 0.00887409 | − | 0.0153704i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.8850 | + | 37.9060i | 0.695201 | + | 1.20412i | 0.970113 | + | 0.242654i | \(0.0780179\pi\) |
−0.274912 | + | 0.961469i | \(0.588649\pi\) | |||||||
\(992\) | 11.6480 | + | 24.9793i | 0.369826 | + | 0.793094i | ||||
\(993\) | −22.6081 | + | 9.78732i | −0.717447 | + | 0.310591i | ||||
\(994\) | 32.4061 | − | 38.6201i | 1.02786 | − | 1.22495i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −23.7590 | − | 43.9260i | −0.752833 | − | 1.39185i | ||||
\(997\) | 19.9603 | + | 13.9764i | 0.632150 | + | 0.442636i | 0.845233 | − | 0.534398i | \(-0.179462\pi\) |
−0.213083 | + | 0.977034i | \(0.568351\pi\) | |||||||
\(998\) | −59.0307 | + | 59.0307i | −1.86859 | + | 1.86859i | ||||
\(999\) | 7.51500 | − | 10.8228i | 0.237764 | − | 0.342418i |
(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 | 675.2.ba.b.68.16 | 192 | ||
5.2 | odd | 4 | inner | 675.2.ba.b.257.16 | 192 | ||
5.3 | odd | 4 | 135.2.q.a.122.1 | yes | 192 | ||
5.4 | even | 2 | 135.2.q.a.68.1 | yes | 192 | ||
15.8 | even | 4 | 405.2.r.a.152.16 | 192 | |||
15.14 | odd | 2 | 405.2.r.a.233.16 | 192 | |||
27.2 | odd | 18 | inner | 675.2.ba.b.218.16 | 192 | ||
135.2 | even | 36 | inner | 675.2.ba.b.407.16 | 192 | ||
135.29 | odd | 18 | 135.2.q.a.83.1 | yes | 192 | ||
135.79 | even | 18 | 405.2.r.a.8.16 | 192 | |||
135.83 | even | 36 | 135.2.q.a.2.1 | ✓ | 192 | ||
135.133 | odd | 36 | 405.2.r.a.332.16 | 192 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.2.q.a.2.1 | ✓ | 192 | 135.83 | even | 36 | ||
135.2.q.a.68.1 | yes | 192 | 5.4 | even | 2 | ||
135.2.q.a.83.1 | yes | 192 | 135.29 | odd | 18 | ||
135.2.q.a.122.1 | yes | 192 | 5.3 | odd | 4 | ||
405.2.r.a.8.16 | 192 | 135.79 | even | 18 | |||
405.2.r.a.152.16 | 192 | 15.8 | even | 4 | |||
405.2.r.a.233.16 | 192 | 15.14 | odd | 2 | |||
405.2.r.a.332.16 | 192 | 135.133 | odd | 36 | |||
675.2.ba.b.68.16 | 192 | 1.1 | even | 1 | trivial | ||
675.2.ba.b.218.16 | 192 | 27.2 | odd | 18 | inner | ||
675.2.ba.b.257.16 | 192 | 5.2 | odd | 4 | inner | ||
675.2.ba.b.407.16 | 192 | 135.2 | even | 36 | inner |