Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [150,3,Mod(29,150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(150, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("150.29");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 150 = 2 \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 150.i (of order \(10\), degree \(4\), 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: | \(4.08720396540\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 29.18 | ||
Character | \(\chi\) | \(=\) | 150.29 |
Dual form | 150.3.i.a.119.18 |
$q$-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 \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{10}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.437016 | − | 1.34500i | 0.218508 | − | 0.672499i | ||||
\(3\) | 1.66776 | + | 2.49371i | 0.555918 | + | 0.831237i | ||||
\(4\) | −1.61803 | − | 1.17557i | −0.404508 | − | 0.293893i | ||||
\(5\) | 1.13734 | − | 4.86893i | 0.227468 | − | 0.973786i | ||||
\(6\) | 4.08287 | − | 1.15333i | 0.680478 | − | 0.192222i | ||||
\(7\) | − | 10.7444i | − | 1.53491i | −0.641101 | − | 0.767457i | \(-0.721522\pi\) | ||
0.641101 | − | 0.767457i | \(-0.278478\pi\) | |||||||
\(8\) | −2.28825 | + | 1.66251i | −0.286031 | + | 0.207813i | ||||
\(9\) | −3.43719 | + | 8.31780i | −0.381910 | + | 0.924200i | ||||
\(10\) | −6.05166 | − | 3.65752i | −0.605166 | − | 0.365752i | ||||
\(11\) | 5.39938 | + | 1.75436i | 0.490852 | + | 0.159488i | 0.543977 | − | 0.839100i | \(-0.316918\pi\) |
−0.0531243 | + | 0.998588i | \(0.516918\pi\) | |||||||
\(12\) | 0.233048 | − | 5.99547i | 0.0194207 | − | 0.499623i | ||||
\(13\) | 17.4086 | − | 5.65639i | 1.33912 | − | 0.435107i | 0.450102 | − | 0.892977i | \(-0.351388\pi\) |
0.889019 | + | 0.457870i | \(0.151388\pi\) | |||||||
\(14\) | −14.4512 | − | 4.69547i | −1.03223 | − | 0.335391i | ||||
\(15\) | 14.0385 | − | 5.28399i | 0.935900 | − | 0.352266i | ||||
\(16\) | 1.23607 | + | 3.80423i | 0.0772542 | + | 0.237764i | ||||
\(17\) | −7.89674 | + | 5.73731i | −0.464514 | + | 0.337489i | −0.795299 | − | 0.606217i | \(-0.792686\pi\) |
0.330785 | + | 0.943706i | \(0.392686\pi\) | |||||||
\(18\) | 9.68531 | + | 8.25802i | 0.538073 | + | 0.458779i | ||||
\(19\) | 17.8734 | − | 12.9858i | 0.940706 | − | 0.683463i | −0.00788420 | − | 0.999969i | \(-0.502510\pi\) |
0.948591 | + | 0.316506i | \(0.102510\pi\) | |||||||
\(20\) | −7.56402 | + | 6.54107i | −0.378201 | + | 0.327054i | ||||
\(21\) | 26.7934 | − | 17.9190i | 1.27588 | − | 0.853286i | ||||
\(22\) | 4.71923 | − | 6.49546i | 0.214510 | − | 0.295248i | ||||
\(23\) | −8.92126 | + | 27.4568i | −0.387881 | + | 1.19377i | 0.546488 | + | 0.837467i | \(0.315964\pi\) |
−0.934369 | + | 0.356307i | \(0.884036\pi\) | |||||||
\(24\) | −7.96205 | − | 2.93357i | −0.331752 | − | 0.122232i | ||||
\(25\) | −22.4129 | − | 11.0752i | −0.896517 | − | 0.443009i | ||||
\(26\) | − | 25.8864i | − | 0.995632i | ||||||
\(27\) | −26.4746 | + | 5.30070i | −0.980539 | + | 0.196322i | ||||
\(28\) | −12.6308 | + | 17.3848i | −0.451100 | + | 0.620885i | ||||
\(29\) | −7.14969 | + | 9.84070i | −0.246541 | + | 0.339334i | −0.914296 | − | 0.405046i | \(-0.867255\pi\) |
0.667755 | + | 0.744381i | \(0.267255\pi\) | |||||||
\(30\) | −0.971900 | − | 21.1909i | −0.0323967 | − | 0.706364i | ||||
\(31\) | −45.6777 | + | 33.1868i | −1.47348 | + | 1.07054i | −0.493888 | + | 0.869526i | \(0.664425\pi\) |
−0.979588 | + | 0.201017i | \(0.935575\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | 4.62996 | + | 16.3903i | 0.140302 | + | 0.496677i | ||||
\(34\) | 4.26567 | + | 13.1284i | 0.125461 | + | 0.386129i | ||||
\(35\) | −52.3137 | − | 12.2200i | −1.49468 | − | 0.349143i | ||||
\(36\) | 15.3396 | − | 9.41782i | 0.426101 | − | 0.261606i | ||||
\(37\) | 30.5541 | − | 9.92763i | 0.825786 | − | 0.268314i | 0.134517 | − | 0.990911i | \(-0.457052\pi\) |
0.691269 | + | 0.722597i | \(0.257052\pi\) | |||||||
\(38\) | −9.65489 | − | 29.7147i | −0.254076 | − | 0.781966i | ||||
\(39\) | 43.1386 | + | 33.9785i | 1.10612 | + | 0.871243i | ||||
\(40\) | 5.49212 | + | 13.0321i | 0.137303 | + | 0.325803i | ||||
\(41\) | 15.7057 | − | 5.10308i | 0.383065 | − | 0.124465i | −0.111153 | − | 0.993803i | \(-0.535454\pi\) |
0.494218 | + | 0.869338i | \(0.335454\pi\) | |||||||
\(42\) | −12.3919 | − | 43.8679i | −0.295045 | − | 1.04447i | ||||
\(43\) | − | 4.27620i | − | 0.0994465i | −0.998763 | − | 0.0497233i | \(-0.984166\pi\) | ||
0.998763 | − | 0.0497233i | \(-0.0158339\pi\) | |||||||
\(44\) | −6.67400 | − | 9.18597i | −0.151682 | − | 0.208772i | ||||
\(45\) | 36.5895 | + | 26.1956i | 0.813100 | + | 0.582123i | ||||
\(46\) | 33.0306 | + | 23.9981i | 0.718056 | + | 0.521699i | ||||
\(47\) | 38.0423 | + | 27.6393i | 0.809410 | + | 0.588071i | 0.913659 | − | 0.406481i | \(-0.133244\pi\) |
−0.104250 | + | 0.994551i | \(0.533244\pi\) | |||||||
\(48\) | −7.42518 | + | 9.42691i | −0.154691 | + | 0.196394i | ||||
\(49\) | −66.4420 | −1.35596 | ||||||||
\(50\) | −24.6910 | + | 25.3053i | −0.493819 | + | 0.506105i | ||||
\(51\) | −27.4770 | − | 10.1237i | −0.538765 | − | 0.198505i | ||||
\(52\) | −34.8172 | − | 11.3128i | −0.669561 | − | 0.217553i | ||||
\(53\) | 46.4184 | + | 33.7249i | 0.875818 | + | 0.636319i | 0.932142 | − | 0.362093i | \(-0.117938\pi\) |
−0.0563236 | + | 0.998413i | \(0.517938\pi\) | |||||||
\(54\) | −4.44038 | + | 37.9247i | −0.0822293 | + | 0.702309i | ||||
\(55\) | 14.6828 | − | 24.2939i | 0.266960 | − | 0.441707i | ||||
\(56\) | 17.8626 | + | 24.5858i | 0.318976 | + | 0.439032i | ||||
\(57\) | 62.1913 | + | 22.9140i | 1.09108 | + | 0.402000i | ||||
\(58\) | 10.1112 | + | 13.9169i | 0.174331 | + | 0.239946i | ||||
\(59\) | −108.045 | + | 35.1060i | −1.83128 | + | 0.595018i | −0.832092 | + | 0.554638i | \(0.812857\pi\) |
−0.999184 | + | 0.0403794i | \(0.987143\pi\) | |||||||
\(60\) | −28.9265 | − | 7.95357i | −0.482108 | − | 0.132560i | ||||
\(61\) | 13.2413 | − | 40.7526i | 0.217071 | − | 0.668076i | −0.781929 | − | 0.623367i | \(-0.785764\pi\) |
0.999000 | − | 0.0447083i | \(-0.0142358\pi\) | |||||||
\(62\) | 24.6743 | + | 75.9396i | 0.397972 | + | 1.22483i | ||||
\(63\) | 89.3697 | + | 36.9305i | 1.41857 | + | 0.586198i | ||||
\(64\) | 2.47214 | − | 7.60845i | 0.0386271 | − | 0.118882i | ||||
\(65\) | −7.74113 | − | 91.1943i | −0.119094 | − | 1.40299i | ||||
\(66\) | 24.0683 | + | 0.935553i | 0.364671 | + | 0.0141750i | ||||
\(67\) | 52.4788 | + | 72.2309i | 0.783266 | + | 1.07807i | 0.994914 | + | 0.100727i | \(0.0321169\pi\) |
−0.211648 | + | 0.977346i | \(0.567883\pi\) | |||||||
\(68\) | 19.5218 | 0.287085 | ||||||||
\(69\) | −83.3478 | + | 23.5442i | −1.20794 | + | 0.341220i | ||||
\(70\) | −39.2978 | + | 65.0214i | −0.561397 | + | 0.928877i | ||||
\(71\) | −15.3975 | + | 21.1928i | −0.216866 | + | 0.298490i | −0.903565 | − | 0.428452i | \(-0.859059\pi\) |
0.686699 | + | 0.726942i | \(0.259059\pi\) | |||||||
\(72\) | −5.96328 | − | 24.7475i | −0.0828233 | − | 0.343715i | ||||
\(73\) | −30.3947 | − | 9.87585i | −0.416366 | − | 0.135286i | 0.0933396 | − | 0.995634i | \(-0.470246\pi\) |
−0.509706 | + | 0.860349i | \(0.670246\pi\) | |||||||
\(74\) | − | 45.4337i | − | 0.613969i | ||||||
\(75\) | −9.76085 | − | 74.3621i | −0.130145 | − | 0.991495i | ||||
\(76\) | −44.1855 | −0.581389 | ||||||||
\(77\) | 18.8496 | − | 58.0130i | 0.244800 | − | 0.753416i | ||||
\(78\) | 64.5532 | − | 43.1722i | 0.827606 | − | 0.553490i | ||||
\(79\) | 81.0358 | + | 58.8759i | 1.02577 | + | 0.745265i | 0.967458 | − | 0.253033i | \(-0.0814282\pi\) |
0.0583119 | + | 0.998298i | \(0.481428\pi\) | |||||||
\(80\) | 19.9283 | − | 1.69164i | 0.249104 | − | 0.0211455i | ||||
\(81\) | −57.3715 | − | 57.1796i | −0.708290 | − | 0.705921i | ||||
\(82\) | − | 23.3542i | − | 0.284807i | ||||||
\(83\) | −25.3592 | + | 18.4245i | −0.305533 | + | 0.221983i | −0.729977 | − | 0.683471i | \(-0.760469\pi\) |
0.424445 | + | 0.905454i | \(0.360469\pi\) | |||||||
\(84\) | −64.4177 | − | 2.50396i | −0.766877 | − | 0.0298091i | ||||
\(85\) | 18.9533 | + | 44.9739i | 0.222980 | + | 0.529105i | ||||
\(86\) | −5.75148 | − | 1.86877i | −0.0668776 | − | 0.0217299i | ||||
\(87\) | −36.4638 | − | 1.41737i | −0.419124 | − | 0.0162917i | ||||
\(88\) | −15.2717 | + | 4.96209i | −0.173543 | + | 0.0563874i | ||||
\(89\) | −29.3681 | − | 9.54229i | −0.329979 | − | 0.107217i | 0.139342 | − | 0.990244i | \(-0.455501\pi\) |
−0.469321 | + | 0.883028i | \(0.655501\pi\) | |||||||
\(90\) | 51.2232 | − | 37.7649i | 0.569146 | − | 0.419610i | ||||
\(91\) | −60.7745 | − | 187.045i | −0.667851 | − | 2.05544i | ||||
\(92\) | 46.7123 | − | 33.9385i | 0.507743 | − | 0.368897i | ||||
\(93\) | −158.938 | − | 58.5596i | −1.70901 | − | 0.629673i | ||||
\(94\) | 53.7999 | − | 39.0879i | 0.572339 | − | 0.415829i | ||||
\(95\) | −42.8988 | − | 101.794i | −0.451567 | − | 1.07151i | ||||
\(96\) | 9.43425 | + | 14.1066i | 0.0982734 | + | 0.146943i | ||||
\(97\) | 30.6184 | − | 42.1426i | 0.315654 | − | 0.434460i | −0.621480 | − | 0.783430i | \(-0.713468\pi\) |
0.937134 | + | 0.348970i | \(0.113468\pi\) | |||||||
\(98\) | −29.0362 | + | 89.3643i | −0.296288 | + | 0.911880i | ||||
\(99\) | −33.1511 | + | 38.8808i | −0.334860 | + | 0.392736i | ||||
\(100\) | 23.2452 | + | 44.2681i | 0.232452 | + | 0.442681i | ||||
\(101\) | − | 47.2486i | − | 0.467808i | −0.972260 | − | 0.233904i | \(-0.924850\pi\) | ||
0.972260 | − | 0.233904i | \(-0.0751501\pi\) | |||||||
\(102\) | −25.6243 | + | 32.5323i | −0.251219 | + | 0.318944i | ||||
\(103\) | 14.1633 | − | 19.4940i | 0.137507 | − | 0.189263i | −0.734710 | − | 0.678382i | \(-0.762682\pi\) |
0.872217 | + | 0.489119i | \(0.162682\pi\) | |||||||
\(104\) | −30.4313 | + | 41.8851i | −0.292609 | + | 0.402741i | ||||
\(105\) | −56.7733 | − | 150.835i | −0.540698 | − | 1.43653i | ||||
\(106\) | 65.6455 | − | 47.6942i | 0.619297 | − | 0.449946i | ||||
\(107\) | 180.539 | 1.68728 | 0.843638 | − | 0.536913i | \(-0.180409\pi\) | ||||
0.843638 | + | 0.536913i | \(0.180409\pi\) | |||||||
\(108\) | 49.0681 | + | 22.5460i | 0.454334 | + | 0.208759i | ||||
\(109\) | 9.24039 | + | 28.4390i | 0.0847742 | + | 0.260908i | 0.984454 | − | 0.175642i | \(-0.0562001\pi\) |
−0.899680 | + | 0.436550i | \(0.856200\pi\) | |||||||
\(110\) | −26.2586 | − | 30.3651i | −0.238714 | − | 0.276047i | ||||
\(111\) | 75.7134 | + | 59.6362i | 0.682102 | + | 0.537263i | ||||
\(112\) | 40.8741 | − | 13.2808i | 0.364947 | − | 0.118579i | ||||
\(113\) | −30.2461 | − | 93.0880i | −0.267665 | − | 0.823788i | −0.991067 | − | 0.133361i | \(-0.957423\pi\) |
0.723403 | − | 0.690426i | \(-0.242577\pi\) | |||||||
\(114\) | 57.9979 | − | 73.6334i | 0.508753 | − | 0.645907i | ||||
\(115\) | 123.539 | + | 74.6646i | 1.07425 | + | 0.649258i | ||||
\(116\) | 23.1369 | − | 7.51763i | 0.199456 | − | 0.0648071i | ||||
\(117\) | −12.7878 | + | 164.243i | −0.109298 | + | 1.40379i | ||||
\(118\) | 160.662i | 1.36155i | ||||||||
\(119\) | 61.6440 | + | 84.8456i | 0.518016 | + | 0.712989i | ||||
\(120\) | −23.3389 | + | 35.4302i | −0.194491 | + | 0.295251i | ||||
\(121\) | −71.8156 | − | 52.1771i | −0.593517 | − | 0.431215i | ||||
\(122\) | −49.0255 | − | 35.6191i | −0.401848 | − | 0.291960i | ||||
\(123\) | 38.9188 | + | 30.6547i | 0.316413 | + | 0.249225i | ||||
\(124\) | 112.922 | 0.910658 | ||||||||
\(125\) | −79.4156 | + | 96.5307i | −0.635325 | + | 0.772245i | ||||
\(126\) | 88.7274 | − | 104.063i | 0.704185 | − | 0.825895i | ||||
\(127\) | 42.5592 | + | 13.8283i | 0.335112 | + | 0.108885i | 0.471739 | − | 0.881738i | \(-0.343626\pi\) |
−0.136627 | + | 0.990623i | \(0.543626\pi\) | |||||||
\(128\) | −9.15298 | − | 6.65003i | −0.0715077 | − | 0.0519534i | ||||
\(129\) | 10.6636 | − | 7.13165i | 0.0826636 | − | 0.0552841i | ||||
\(130\) | −126.039 | − | 29.4416i | −0.969532 | − | 0.226474i | ||||
\(131\) | −40.6958 | − | 56.0130i | −0.310655 | − | 0.427580i | 0.624930 | − | 0.780681i | \(-0.285127\pi\) |
−0.935585 | + | 0.353100i | \(0.885127\pi\) | |||||||
\(132\) | 11.7766 | − | 31.9630i | 0.0892163 | − | 0.242144i | ||||
\(133\) | −139.525 | − | 192.039i | −1.04906 | − | 1.44390i | ||||
\(134\) | 120.084 | − | 39.0178i | 0.896152 | − | 0.291178i | ||||
\(135\) | −4.30179 | + | 134.931i | −0.0318651 | + | 0.999492i | ||||
\(136\) | 8.53134 | − | 26.2568i | 0.0627305 | − | 0.193064i | ||||
\(137\) | 22.5835 | + | 69.5049i | 0.164843 | + | 0.507335i | 0.999025 | − | 0.0441551i | \(-0.0140596\pi\) |
−0.834182 | + | 0.551490i | \(0.814060\pi\) | |||||||
\(138\) | −4.75746 | + | 122.392i | −0.0344743 | + | 0.886897i | ||||
\(139\) | 31.6022 | − | 97.2614i | 0.227354 | − | 0.699723i | −0.770691 | − | 0.637210i | \(-0.780089\pi\) |
0.998044 | − | 0.0625129i | \(-0.0199115\pi\) | |||||||
\(140\) | 70.2798 | + | 81.2708i | 0.501999 | + | 0.580506i | ||||
\(141\) | −5.47929 | + | 140.962i | −0.0388602 | + | 0.999730i | ||||
\(142\) | 21.7753 | + | 29.9711i | 0.153347 | + | 0.211064i | ||||
\(143\) | 103.919 | 0.726705 | ||||||||
\(144\) | −35.8914 | − | 2.79447i | −0.249246 | − | 0.0194060i | ||||
\(145\) | 39.7821 | + | 46.0035i | 0.274359 | + | 0.317266i | ||||
\(146\) | −26.5660 | + | 36.5649i | −0.181959 | + | 0.250445i | ||||
\(147\) | −110.809 | − | 165.687i | −0.753802 | − | 1.12712i | ||||
\(148\) | −61.1082 | − | 19.8553i | −0.412893 | − | 0.134157i | ||||
\(149\) | − | 243.028i | − | 1.63106i | −0.578712 | − | 0.815532i | \(-0.696445\pi\) | ||
0.578712 | − | 0.815532i | \(-0.303555\pi\) | |||||||
\(150\) | −104.282 | − | 19.3691i | −0.695217 | − | 0.129128i | ||||
\(151\) | −206.162 | −1.36531 | −0.682654 | − | 0.730742i | \(-0.739174\pi\) | ||||
−0.682654 | + | 0.730742i | \(0.739174\pi\) | |||||||
\(152\) | −19.3098 | + | 59.4294i | −0.127038 | + | 0.390983i | ||||
\(153\) | −20.5793 | − | 85.4037i | −0.134505 | − | 0.558194i | ||||
\(154\) | −69.7898 | − | 50.7052i | −0.453180 | − | 0.329255i | ||||
\(155\) | 109.633 | + | 260.146i | 0.707311 | + | 1.67836i | ||||
\(156\) | −29.8557 | − | 105.691i | −0.191383 | − | 0.677506i | ||||
\(157\) | 53.5181i | 0.340880i | 0.985368 | + | 0.170440i | \(0.0545189\pi\) | ||||
−0.985368 | + | 0.170440i | \(0.945481\pi\) | |||||||
\(158\) | 114.602 | − | 83.2632i | 0.725329 | − | 0.526982i | ||||
\(159\) | −6.68572 | + | 171.999i | −0.0420486 | + | 1.08175i | ||||
\(160\) | 6.43375 | − | 27.5428i | 0.0402110 | − | 0.172143i | ||||
\(161\) | 295.007 | + | 95.8535i | 1.83234 | + | 0.595363i | ||||
\(162\) | −101.979 | + | 52.1761i | −0.629498 | + | 0.322075i | ||||
\(163\) | −240.196 | + | 78.0445i | −1.47360 | + | 0.478801i | −0.932193 | − | 0.361962i | \(-0.882107\pi\) |
−0.541404 | + | 0.840762i | \(0.682107\pi\) | |||||||
\(164\) | −31.4113 | − | 10.2062i | −0.191532 | − | 0.0622327i | ||||
\(165\) | 85.0692 | − | 3.90161i | 0.515571 | − | 0.0236461i | ||||
\(166\) | 13.6986 | + | 42.1599i | 0.0825216 | + | 0.253975i | ||||
\(167\) | 98.6670 | − | 71.6858i | 0.590820 | − | 0.429256i | −0.251788 | − | 0.967782i | \(-0.581019\pi\) |
0.842609 | + | 0.538526i | \(0.181019\pi\) | |||||||
\(168\) | −31.5194 | + | 85.5474i | −0.187615 | + | 0.509210i | ||||
\(169\) | 134.340 | − | 97.6037i | 0.794911 | − | 0.577537i | ||||
\(170\) | 68.7727 | − | 5.83784i | 0.404545 | − | 0.0343402i | ||||
\(171\) | 46.5790 | + | 193.302i | 0.272392 | + | 1.13042i | ||||
\(172\) | −5.02697 | + | 6.91904i | −0.0292266 | + | 0.0402270i | ||||
\(173\) | −6.05485 | + | 18.6349i | −0.0349991 | + | 0.107716i | −0.967030 | − | 0.254663i | \(-0.918035\pi\) |
0.932031 | + | 0.362379i | \(0.118035\pi\) | |||||||
\(174\) | −17.8416 | + | 48.4243i | −0.102538 | + | 0.278300i | ||||
\(175\) | −118.997 | + | 240.813i | −0.679981 | + | 1.37608i | ||||
\(176\) | 22.7090i | 0.129028i | ||||||||
\(177\) | −267.737 | − | 210.885i | −1.51264 | − | 1.19144i | ||||
\(178\) | −25.6687 | + | 35.3299i | −0.144206 | + | 0.198483i | ||||
\(179\) | −21.4825 | + | 29.5681i | −0.120014 | + | 0.165185i | −0.864797 | − | 0.502122i | \(-0.832553\pi\) |
0.744783 | + | 0.667307i | \(0.232553\pi\) | |||||||
\(180\) | −28.4084 | − | 85.3989i | −0.157824 | − | 0.474438i | ||||
\(181\) | 257.579 | − | 187.142i | 1.42309 | − | 1.03393i | 0.431835 | − | 0.901953i | \(-0.357866\pi\) |
0.991252 | − | 0.131981i | \(-0.0421338\pi\) | |||||||
\(182\) | −278.134 | −1.52821 | ||||||||
\(183\) | 123.709 | − | 34.9453i | 0.676003 | − | 0.190958i | ||||
\(184\) | −25.2331 | − | 77.6596i | −0.137137 | − | 0.422063i | ||||
\(185\) | −13.5866 | − | 160.057i | −0.0734410 | − | 0.865172i | ||||
\(186\) | −148.221 | + | 188.179i | −0.796886 | + | 1.01172i | ||||
\(187\) | −52.7028 | + | 17.1242i | −0.281833 | + | 0.0915731i | ||||
\(188\) | −29.0617 | − | 89.4427i | −0.154583 | − | 0.475759i | ||||
\(189\) | 56.9528 | + | 284.453i | 0.301338 | + | 1.50504i | ||||
\(190\) | −155.660 | + | 13.2133i | −0.819261 | + | 0.0695438i | ||||
\(191\) | −229.392 | + | 74.5340i | −1.20101 | + | 0.390230i | −0.840131 | − | 0.542384i | \(-0.817522\pi\) |
−0.360875 | + | 0.932614i | \(0.617522\pi\) | |||||||
\(192\) | 23.0962 | − | 6.52424i | 0.120293 | − | 0.0339804i | ||||
\(193\) | 52.0777i | 0.269833i | 0.990857 | + | 0.134916i | \(0.0430765\pi\) | ||||
−0.990857 | + | 0.134916i | \(0.956923\pi\) | |||||||
\(194\) | −43.3010 | − | 59.5987i | −0.223201 | − | 0.307210i | ||||
\(195\) | 214.502 | − | 171.394i | 1.10001 | − | 0.878943i | ||||
\(196\) | 107.505 | + | 78.1072i | 0.548497 | + | 0.398506i | ||||
\(197\) | −82.7097 | − | 60.0921i | −0.419846 | − | 0.305036i | 0.357730 | − | 0.933825i | \(-0.383551\pi\) |
−0.777576 | + | 0.628789i | \(0.783551\pi\) | |||||||
\(198\) | 37.8071 | + | 61.5797i | 0.190945 | + | 0.311009i | ||||
\(199\) | −230.058 | −1.15607 | −0.578036 | − | 0.816011i | \(-0.696181\pi\) | ||||
−0.578036 | + | 0.816011i | \(0.696181\pi\) | |||||||
\(200\) | 69.6989 | − | 11.9188i | 0.348495 | − | 0.0595941i | ||||
\(201\) | −92.6011 | + | 251.330i | −0.460702 | + | 1.25040i | ||||
\(202\) | −63.5492 | − | 20.6484i | −0.314600 | − | 0.102220i | ||||
\(203\) | 105.732 | + | 76.8190i | 0.520849 | + | 0.378419i | ||||
\(204\) | 32.5576 | + | 48.6817i | 0.159596 | + | 0.238636i | ||||
\(205\) | −6.98388 | − | 82.2736i | −0.0340677 | − | 0.401335i | ||||
\(206\) | −20.0299 | − | 27.5687i | −0.0972324 | − | 0.133829i | ||||
\(207\) | −197.716 | − | 168.579i | −0.955151 | − | 0.814393i | ||||
\(208\) | 43.0364 | + | 59.2345i | 0.206906 | + | 0.284781i | ||||
\(209\) | 119.287 | − | 38.7587i | 0.570752 | − | 0.185449i | ||||
\(210\) | −227.684 | + | 10.4425i | −1.08421 | + | 0.0497261i | ||||
\(211\) | −112.652 | + | 346.708i | −0.533897 | + | 1.64317i | 0.212123 | + | 0.977243i | \(0.431962\pi\) |
−0.746020 | + | 0.665923i | \(0.768038\pi\) | |||||||
\(212\) | −35.4605 | − | 109.136i | −0.167266 | − | 0.514793i | ||||
\(213\) | −78.5279 | − | 3.05244i | −0.368676 | − | 0.0143307i | ||||
\(214\) | 78.8982 | − | 242.824i | 0.368683 | − | 1.13469i | ||||
\(215\) | −20.8205 | − | 4.86348i | −0.0968396 | − | 0.0226209i | ||||
\(216\) | 51.7678 | − | 56.1435i | 0.239666 | − | 0.259923i | ||||
\(217\) | 356.572 | + | 490.780i | 1.64319 | + | 2.26166i | ||||
\(218\) | 42.2886 | 0.193984 | ||||||||
\(219\) | −26.0635 | − | 92.2662i | −0.119011 | − | 0.421307i | ||||
\(220\) | −52.3164 | + | 22.0477i | −0.237802 | + | 0.100217i | ||||
\(221\) | −105.018 | + | 144.546i | −0.475197 | + | 0.654052i | ||||
\(222\) | 113.298 | − | 75.7723i | 0.510354 | − | 0.341317i | ||||
\(223\) | 199.645 | + | 64.8685i | 0.895268 | + | 0.290890i | 0.720283 | − | 0.693681i | \(-0.244012\pi\) |
0.174986 | + | 0.984571i | \(0.444012\pi\) | |||||||
\(224\) | − | 60.7795i | − | 0.271337i | ||||||
\(225\) | 169.159 | − | 148.359i | 0.751817 | − | 0.659371i | ||||
\(226\) | −138.421 | −0.612483 | ||||||||
\(227\) | −34.4887 | + | 106.145i | −0.151933 | + | 0.467600i | −0.997837 | − | 0.0657339i | \(-0.979061\pi\) |
0.845905 | + | 0.533334i | \(0.179061\pi\) | |||||||
\(228\) | −73.6906 | − | 110.186i | −0.323205 | − | 0.483272i | ||||
\(229\) | 11.0271 | + | 8.01164i | 0.0481532 | + | 0.0349853i | 0.611601 | − | 0.791166i | \(-0.290526\pi\) |
−0.563448 | + | 0.826151i | \(0.690526\pi\) | |||||||
\(230\) | 154.412 | − | 133.530i | 0.671357 | − | 0.580564i | ||||
\(231\) | 176.104 | − | 49.7461i | 0.762356 | − | 0.215351i | ||||
\(232\) | − | 34.4044i | − | 0.148295i | ||||||
\(233\) | −2.07945 | + | 1.51081i | −0.00892468 | + | 0.00648416i | −0.592239 | − | 0.805763i | \(-0.701756\pi\) |
0.583314 | + | 0.812247i | \(0.301756\pi\) | |||||||
\(234\) | 215.318 | + | 88.9764i | 0.920162 | + | 0.380241i | ||||
\(235\) | 177.841 | − | 153.790i | 0.756769 | − | 0.654425i | ||||
\(236\) | 216.091 | + | 70.2121i | 0.915638 | + | 0.297509i | ||||
\(237\) | −11.6717 | + | 300.270i | −0.0492478 | + | 1.26696i | ||||
\(238\) | 141.057 | − | 45.8320i | 0.592674 | − | 0.192572i | ||||
\(239\) | 147.333 | + | 47.8714i | 0.616456 | + | 0.200299i | 0.600566 | − | 0.799575i | \(-0.294942\pi\) |
0.0158898 | + | 0.999874i | \(0.494942\pi\) | |||||||
\(240\) | 37.4540 | + | 46.8743i | 0.156058 | + | 0.195309i | ||||
\(241\) | −57.8325 | − | 177.990i | −0.239969 | − | 0.738548i | −0.996423 | − | 0.0845018i | \(-0.973070\pi\) |
0.756454 | − | 0.654046i | \(-0.226930\pi\) | |||||||
\(242\) | −101.563 | + | 73.7895i | −0.419680 | + | 0.304915i | ||||
\(243\) | 46.9078 | − | 238.430i | 0.193036 | − | 0.981192i | ||||
\(244\) | −69.3325 | + | 50.3730i | −0.284150 | + | 0.206447i | ||||
\(245\) | −75.5670 | + | 323.501i | −0.308437 | + | 1.32041i | ||||
\(246\) | 58.2386 | − | 38.9491i | 0.236742 | − | 0.158330i | ||||
\(247\) | 237.698 | − | 327.163i | 0.962341 | − | 1.32455i | ||||
\(248\) | 49.3485 | − | 151.879i | 0.198986 | − | 0.612416i | ||||
\(249\) | −88.2385 | − | 32.5109i | −0.354371 | − | 0.130566i | ||||
\(250\) | 95.1276 | + | 148.999i | 0.380510 | + | 0.595997i | ||||
\(251\) | − | 125.493i | − | 0.499972i | −0.968249 | − | 0.249986i | \(-0.919574\pi\) | ||
0.968249 | − | 0.249986i | \(-0.0804260\pi\) | |||||||
\(252\) | −101.189 | − | 164.815i | −0.401543 | − | 0.654028i | ||||
\(253\) | −96.3385 | + | 132.599i | −0.380785 | + | 0.524105i | ||||
\(254\) | 37.1981 | − | 51.1988i | 0.146449 | − | 0.201570i | ||||
\(255\) | −80.5424 | + | 122.270i | −0.315853 | + | 0.479488i | ||||
\(256\) | −12.9443 | + | 9.40456i | −0.0505636 | + | 0.0367366i | ||||
\(257\) | −135.710 | −0.528053 | −0.264026 | − | 0.964515i | \(-0.585051\pi\) | ||||
−0.264026 | + | 0.964515i | \(0.585051\pi\) | |||||||
\(258\) | −4.93189 | − | 17.4592i | −0.0191158 | − | 0.0676712i | ||||
\(259\) | −106.666 | − | 328.285i | −0.411839 | − | 1.26751i | ||||
\(260\) | −94.6800 | + | 156.656i | −0.364154 | + | 0.602522i | ||||
\(261\) | −57.2781 | − | 93.2940i | −0.219456 | − | 0.357448i | ||||
\(262\) | −93.1221 | + | 30.2572i | −0.355428 | + | 0.115485i | ||||
\(263\) | −133.102 | − | 409.647i | −0.506093 | − | 1.55759i | −0.798926 | − | 0.601430i | \(-0.794598\pi\) |
0.292833 | − | 0.956164i | \(-0.405402\pi\) | |||||||
\(264\) | −37.8435 | − | 29.8078i | −0.143347 | − | 0.112908i | ||||
\(265\) | 216.998 | − | 187.651i | 0.818859 | − | 0.708117i | ||||
\(266\) | −319.266 | + | 103.736i | −1.20025 | + | 0.389985i | ||||
\(267\) | −25.1832 | − | 89.1498i | −0.0943189 | − | 0.333894i | ||||
\(268\) | − | 178.565i | − | 0.666286i | ||||||
\(269\) | 210.481 | + | 289.702i | 0.782457 | + | 1.07696i | 0.995007 | + | 0.0998098i | \(0.0318234\pi\) |
−0.212549 | + | 0.977150i | \(0.568177\pi\) | |||||||
\(270\) | 179.602 | + | 64.7531i | 0.665194 | + | 0.239826i | ||||
\(271\) | 77.1071 | + | 56.0216i | 0.284528 | + | 0.206722i | 0.720890 | − | 0.693049i | \(-0.243733\pi\) |
−0.436362 | + | 0.899771i | \(0.643733\pi\) | |||||||
\(272\) | −31.5869 | − | 22.9493i | −0.116128 | − | 0.0843723i | ||||
\(273\) | 365.078 | − | 463.499i | 1.33728 | − | 1.69780i | ||||
\(274\) | 103.353 | 0.377201 | ||||||||
\(275\) | −101.586 | − | 99.1198i | −0.369403 | − | 0.360436i | ||||
\(276\) | 162.537 | + | 59.8859i | 0.588904 | + | 0.216978i | ||||
\(277\) | −61.1400 | − | 19.8656i | −0.220722 | − | 0.0717170i | 0.196568 | − | 0.980490i | \(-0.437020\pi\) |
−0.417291 | + | 0.908773i | \(0.637020\pi\) | |||||||
\(278\) | −117.006 | − | 85.0096i | −0.420884 | − | 0.305790i | ||||
\(279\) | −119.038 | − | 494.008i | −0.426661 | − | 1.77064i | ||||
\(280\) | 140.022 | − | 59.0095i | 0.500080 | − | 0.210748i | ||||
\(281\) | −82.6559 | − | 113.766i | −0.294149 | − | 0.404861i | 0.636207 | − | 0.771518i | \(-0.280502\pi\) |
−0.930356 | + | 0.366657i | \(0.880502\pi\) | |||||||
\(282\) | 187.199 | + | 68.9723i | 0.663826 | + | 0.244583i | ||||
\(283\) | −110.380 | − | 151.924i | −0.390034 | − | 0.536835i | 0.568174 | − | 0.822908i | \(-0.307650\pi\) |
−0.958208 | + | 0.286073i | \(0.907650\pi\) | |||||||
\(284\) | 49.8272 | − | 16.1899i | 0.175448 | − | 0.0570065i | ||||
\(285\) | 182.299 | − | 276.744i | 0.639646 | − | 0.971032i | ||||
\(286\) | 45.4142 | − | 139.771i | 0.158791 | − | 0.488708i | ||||
\(287\) | −54.8295 | − | 168.748i | −0.191043 | − | 0.587971i | ||||
\(288\) | −19.4437 | + | 47.0526i | −0.0675127 | + | 0.163377i | ||||
\(289\) | −59.8642 | + | 184.243i | −0.207143 | + | 0.637520i | ||||
\(290\) | 79.2600 | − | 33.4025i | 0.273310 | − | 0.115181i | ||||
\(291\) | 156.156 | + | 6.06988i | 0.536617 | + | 0.0208587i | ||||
\(292\) | 37.5700 | + | 51.7106i | 0.128664 | + | 0.177091i | ||||
\(293\) | −498.902 | −1.70274 | −0.851368 | − | 0.524569i | \(-0.824226\pi\) | ||||
−0.851368 | + | 0.524569i | \(0.824226\pi\) | |||||||
\(294\) | −271.274 | + | 76.6298i | −0.922700 | + | 0.260646i | ||||
\(295\) | 48.0448 | + | 565.992i | 0.162864 | + | 1.91862i | ||||
\(296\) | −53.4105 | + | 73.5133i | −0.180441 | + | 0.248356i | ||||
\(297\) | −152.246 | − | 17.8255i | −0.512611 | − | 0.0600186i | ||||
\(298\) | −326.873 | − | 106.207i | −1.09689 | − | 0.356400i | ||||
\(299\) | 528.446i | 1.76738i | ||||||||
\(300\) | −71.6245 | + | 131.795i | −0.238748 | + | 0.439317i | ||||
\(301\) | −45.9452 | −0.152642 | ||||||||
\(302\) | −90.0959 | + | 277.287i | −0.298331 | + | 0.918168i | ||||
\(303\) | 117.824 | − | 78.7991i | 0.388859 | − | 0.260063i | ||||
\(304\) | 71.4937 | + | 51.9432i | 0.235177 | + | 0.170866i | ||||
\(305\) | −183.362 | − | 110.821i | −0.601186 | − | 0.363346i | ||||
\(306\) | −123.861 | − | 9.64372i | −0.404775 | − | 0.0315154i | ||||
\(307\) | 281.408i | 0.916638i | 0.888788 | + | 0.458319i | \(0.151548\pi\) | ||||
−0.888788 | + | 0.458319i | \(0.848452\pi\) | |||||||
\(308\) | −98.6977 | + | 71.7080i | −0.320447 | + | 0.232818i | ||||
\(309\) | 72.2333 | + | 2.80776i | 0.233765 | + | 0.00908661i | ||||
\(310\) | 397.807 | − | 33.7683i | 1.28325 | − | 0.108930i | ||||
\(311\) | −172.030 | − | 55.8960i | −0.553151 | − | 0.179730i | 0.0190860 | − | 0.999818i | \(-0.493924\pi\) |
−0.572237 | + | 0.820088i | \(0.693924\pi\) | |||||||
\(312\) | −155.201 | − | 6.03279i | −0.497440 | − | 0.0193359i | ||||
\(313\) | 216.891 | − | 70.4723i | 0.692943 | − | 0.225151i | 0.0586901 | − | 0.998276i | \(-0.481308\pi\) |
0.634253 | + | 0.773125i | \(0.281308\pi\) | |||||||
\(314\) | 71.9817 | + | 23.3883i | 0.229241 | + | 0.0744849i | ||||
\(315\) | 281.455 | − | 393.132i | 0.893509 | − | 1.24804i | ||||
\(316\) | −61.9058 | − | 190.527i | −0.195905 | − | 0.602932i | ||||
\(317\) | 104.200 | − | 75.7055i | 0.328706 | − | 0.238819i | −0.411176 | − | 0.911556i | \(-0.634882\pi\) |
0.739881 | + | 0.672738i | \(0.234882\pi\) | |||||||
\(318\) | 228.416 | + | 84.1585i | 0.718290 | + | 0.264649i | ||||
\(319\) | −55.8680 | + | 40.5905i | −0.175135 | + | 0.127243i | ||||
\(320\) | −34.2334 | − | 20.6900i | −0.106979 | − | 0.0646563i | ||||
\(321\) | 301.094 | + | 450.211i | 0.937988 | + | 1.40253i | ||||
\(322\) | 257.845 | − | 354.894i | 0.800762 | − | 1.10215i | ||||
\(323\) | −66.6381 | + | 205.091i | −0.206310 | + | 0.634956i | ||||
\(324\) | 25.6104 | + | 159.963i | 0.0790443 | + | 0.493712i | ||||
\(325\) | −452.823 | − | 66.0278i | −1.39330 | − | 0.203162i | ||||
\(326\) | 357.170i | 1.09561i | ||||||||
\(327\) | −55.5079 | + | 70.4721i | −0.169749 | + | 0.215511i | ||||
\(328\) | −27.4545 | + | 37.7879i | −0.0837027 | + | 0.115207i | ||||
\(329\) | 296.968 | − | 408.741i | 0.902637 | − | 1.24237i | ||||
\(330\) | 31.9289 | − | 116.123i | 0.0967544 | − | 0.351887i | ||||
\(331\) | −235.296 | + | 170.953i | −0.710864 | + | 0.516473i | −0.883452 | − | 0.468521i | \(-0.844787\pi\) |
0.172588 | + | 0.984994i | \(0.444787\pi\) | |||||||
\(332\) | 62.6914 | 0.188830 | ||||||||
\(333\) | −22.4441 | + | 288.266i | −0.0673997 | + | 0.865663i | ||||
\(334\) | −53.2981 | − | 164.035i | −0.159575 | − | 0.491122i | ||||
\(335\) | 411.373 | − | 173.365i | 1.22798 | − | 0.517506i | ||||
\(336\) | 101.286 | + | 79.7791i | 0.301448 | + | 0.237438i | ||||
\(337\) | −541.009 | + | 175.784i | −1.60537 | + | 0.521616i | −0.968427 | − | 0.249297i | \(-0.919800\pi\) |
−0.636941 | + | 0.770913i | \(0.719800\pi\) | |||||||
\(338\) | −72.5680 | − | 223.341i | −0.214698 | − | 0.660773i | ||||
\(339\) | 181.691 | − | 230.673i | 0.535963 | − | 0.680452i | ||||
\(340\) | 22.2029 | − | 95.0503i | 0.0653026 | − | 0.279560i | ||||
\(341\) | −304.853 | + | 99.0528i | −0.893998 | + | 0.290477i | ||||
\(342\) | 280.347 | + | 21.8275i | 0.819727 | + | 0.0638232i | ||||
\(343\) | 187.403i | 0.546366i | ||||||||
\(344\) | 7.10922 | + | 9.78500i | 0.0206663 | + | 0.0284448i | ||||
\(345\) | 19.8404 | + | 432.592i | 0.0575084 | + | 1.25389i | ||||
\(346\) | 22.4178 | + | 16.2875i | 0.0647914 | + | 0.0470737i | ||||
\(347\) | −531.211 | − | 385.948i | −1.53087 | − | 1.11224i | −0.955754 | − | 0.294168i | \(-0.904957\pi\) |
−0.575115 | − | 0.818073i | \(-0.695043\pi\) | |||||||
\(348\) | 57.3334 | + | 45.1591i | 0.164751 | + | 0.129768i | ||||
\(349\) | 580.681 | 1.66384 | 0.831921 | − | 0.554894i | \(-0.187241\pi\) | ||||
0.831921 | + | 0.554894i | \(0.187241\pi\) | |||||||
\(350\) | 271.890 | + | 265.289i | 0.776828 | + | 0.757970i | ||||
\(351\) | −430.902 | + | 242.028i | −1.22764 | + | 0.689539i | ||||
\(352\) | 30.5435 | + | 9.92418i | 0.0867713 | + | 0.0281937i | ||||
\(353\) | 379.891 | + | 276.007i | 1.07618 | + | 0.781889i | 0.977013 | − | 0.213182i | \(-0.0683827\pi\) |
0.0991655 | + | 0.995071i | \(0.468383\pi\) | |||||||
\(354\) | −400.646 | + | 267.946i | −1.13177 | + | 0.756909i | ||||
\(355\) | 85.6741 | + | 99.0725i | 0.241335 | + | 0.279078i | ||||
\(356\) | 36.3010 | + | 49.9641i | 0.101969 | + | 0.140348i | ||||
\(357\) | −108.773 | + | 295.224i | −0.304687 | + | 0.826958i | ||||
\(358\) | 30.3808 | + | 41.8156i | 0.0848626 | + | 0.116803i | ||||
\(359\) | −555.853 | + | 180.608i | −1.54834 | + | 0.503085i | −0.953662 | − | 0.300880i | \(-0.902720\pi\) |
−0.594676 | + | 0.803966i | \(0.702720\pi\) | |||||||
\(360\) | −127.276 | + | 0.888490i | −0.353545 | + | 0.00246803i | ||||
\(361\) | 39.2730 | − | 120.870i | 0.108790 | − | 0.334820i | ||||
\(362\) | −139.139 | − | 428.227i | −0.384363 | − | 1.18295i | ||||
\(363\) | 10.3437 | − | 266.106i | 0.0284951 | − | 0.733074i | ||||
\(364\) | −121.549 | + | 374.089i | −0.333926 | + | 1.02772i | ||||
\(365\) | −82.6539 | + | 136.758i | −0.226449 | + | 0.374678i | ||||
\(366\) | 7.06123 | − | 181.659i | 0.0192930 | − | 0.496337i | ||||
\(367\) | −80.2646 | − | 110.475i | −0.218705 | − | 0.301021i | 0.685541 | − | 0.728034i | \(-0.259566\pi\) |
−0.904245 | + | 0.427013i | \(0.859566\pi\) | |||||||
\(368\) | −115.479 | −0.313802 | ||||||||
\(369\) | −11.5369 | + | 148.177i | −0.0312653 | + | 0.401563i | ||||
\(370\) | −221.213 | − | 51.6734i | −0.597874 | − | 0.139658i | ||||
\(371\) | 362.354 | − | 498.737i | 0.976695 | − | 1.34430i | ||||
\(372\) | 188.326 | + | 281.594i | 0.506252 | + | 0.756973i | ||||
\(373\) | −66.5552 | − | 21.6251i | −0.178432 | − | 0.0579761i | 0.218438 | − | 0.975851i | \(-0.429904\pi\) |
−0.396870 | + | 0.917875i | \(0.629904\pi\) | |||||||
\(374\) | 78.3686i | 0.209542i | ||||||||
\(375\) | −373.165 | − | 37.0500i | −0.995107 | − | 0.0987999i | ||||
\(376\) | −133.001 | −0.353725 | ||||||||
\(377\) | −68.8031 | + | 211.754i | −0.182501 | + | 0.561682i | ||||
\(378\) | 407.478 | + | 47.7092i | 1.07798 | + | 0.126215i | ||||
\(379\) | 37.0251 | + | 26.9003i | 0.0976915 | + | 0.0709770i | 0.635559 | − | 0.772053i | \(-0.280770\pi\) |
−0.537867 | + | 0.843030i | \(0.680770\pi\) | |||||||
\(380\) | −50.2539 | + | 215.136i | −0.132247 | + | 0.566148i | ||||
\(381\) | 36.4945 | + | 129.193i | 0.0957861 | + | 0.339088i | ||||
\(382\) | 341.104i | 0.892943i | ||||||||
\(383\) | 243.336 | − | 176.794i | 0.635341 | − | 0.461602i | −0.222906 | − | 0.974840i | \(-0.571554\pi\) |
0.858246 | + | 0.513238i | \(0.171554\pi\) | |||||||
\(384\) | 1.31832 | − | 33.9155i | 0.00343313 | − | 0.0883216i | ||||
\(385\) | −261.023 | − | 157.758i | −0.677982 | − | 0.409760i | ||||
\(386\) | 70.0443 | + | 22.7588i | 0.181462 | + | 0.0589606i | ||||
\(387\) | 35.5686 | + | 14.6981i | 0.0919084 | + | 0.0379796i | ||||
\(388\) | −99.0833 | + | 32.1941i | −0.255369 | + | 0.0829745i | ||||
\(389\) | −543.991 | − | 176.753i | −1.39843 | − | 0.454379i | −0.489750 | − | 0.871863i | \(-0.662912\pi\) |
−0.908684 | + | 0.417484i | \(0.862912\pi\) | |||||||
\(390\) | −136.784 | − | 363.406i | −0.350727 | − | 0.931812i | ||||
\(391\) | −87.0795 | − | 268.003i | −0.222710 | − | 0.685430i | ||||
\(392\) | 152.036 | − | 110.460i | 0.387846 | − | 0.281786i | ||||
\(393\) | 71.8096 | − | 194.900i | 0.182722 | − | 0.495928i | ||||
\(394\) | −116.969 | + | 84.9831i | −0.296876 | + | 0.215693i | ||||
\(395\) | 378.828 | − | 327.596i | 0.959058 | − | 0.829356i | ||||
\(396\) | 99.3468 | − | 23.9391i | 0.250876 | − | 0.0604522i | ||||
\(397\) | 271.005 | − | 373.006i | 0.682632 | − | 0.939562i | −0.317330 | − | 0.948315i | \(-0.602786\pi\) |
0.999962 | + | 0.00875294i | \(0.00278618\pi\) | |||||||
\(398\) | −100.539 | + | 309.428i | −0.252611 | + | 0.777457i | ||||
\(399\) | 246.197 | − | 668.208i | 0.617035 | − | 1.67471i | ||||
\(400\) | 14.4288 | − | 98.9536i | 0.0360720 | − | 0.247384i | ||||
\(401\) | − | 739.000i | − | 1.84289i | −0.388505 | − | 0.921446i | \(-0.627008\pi\) | ||
0.388505 | − | 0.921446i | \(-0.372992\pi\) | |||||||
\(402\) | 297.570 | + | 234.384i | 0.740225 | + | 0.583044i | ||||
\(403\) | −607.467 | + | 836.107i | −1.50736 | + | 2.07471i | ||||
\(404\) | −55.5440 | + | 76.4498i | −0.137485 | + | 0.189232i | ||||
\(405\) | −343.654 | + | 214.305i | −0.848529 | + | 0.529149i | ||||
\(406\) | 149.528 | − | 108.639i | 0.368296 | − | 0.267583i | ||||
\(407\) | 182.390 | 0.448132 | ||||||||
\(408\) | 79.7050 | − | 22.5152i | 0.195355 | − | 0.0551842i | ||||
\(409\) | 55.0616 | + | 169.462i | 0.134625 | + | 0.414333i | 0.995531 | − | 0.0944303i | \(-0.0301029\pi\) |
−0.860907 | + | 0.508763i | \(0.830103\pi\) | |||||||
\(410\) | −113.710 | − | 26.5616i | −0.277341 | − | 0.0647844i | ||||
\(411\) | −135.661 | + | 172.234i | −0.330076 | + | 0.419060i | ||||
\(412\) | −45.8332 | + | 14.8921i | −0.111246 | + | 0.0361459i | ||||
\(413\) | 377.193 | + | 1160.88i | 0.913300 | + | 2.81085i | ||||
\(414\) | −313.144 | + | 192.256i | −0.756386 | + | 0.464386i | ||||
\(415\) | 60.8658 | + | 144.427i | 0.146665 | + | 0.348017i | ||||
\(416\) | 98.4778 | − | 31.9974i | 0.236725 | − | 0.0769168i | ||||
\(417\) | 295.247 | − | 83.4016i | 0.708025 | − | 0.200004i | ||||
\(418\) | − | 177.379i | − | 0.424352i | ||||||
\(419\) | −63.3107 | − | 87.1397i | −0.151100 | − | 0.207971i | 0.726757 | − | 0.686895i | \(-0.241027\pi\) |
−0.877856 | + | 0.478924i | \(0.841027\pi\) | |||||||
\(420\) | −85.4563 | + | 310.797i | −0.203467 | + | 0.739994i | ||||
\(421\) | 397.404 | + | 288.731i | 0.943952 | + | 0.685821i | 0.949369 | − | 0.314164i | \(-0.101724\pi\) |
−0.00541690 | + | 0.999985i | \(0.501724\pi\) | |||||||
\(422\) | 417.090 | + | 303.034i | 0.988366 | + | 0.718090i | ||||
\(423\) | −360.657 | + | 221.426i | −0.852616 | + | 0.523466i | ||||
\(424\) | −162.285 | −0.382747 | ||||||||
\(425\) | 240.531 | − | 41.1318i | 0.565955 | − | 0.0967808i | ||||
\(426\) | −38.4235 | + | 104.286i | −0.0901959 | + | 0.244802i | ||||
\(427\) | −437.862 | − | 142.270i | −1.02544 | − | 0.333185i | ||||
\(428\) | −292.117 | − | 212.236i | −0.682517 | − | 0.495878i | ||||
\(429\) | 173.311 | + | 259.144i | 0.403989 | + | 0.604064i | ||||
\(430\) | −15.6403 | + | 25.8781i | −0.0363727 | + | 0.0601816i | ||||
\(431\) | 193.058 | + | 265.722i | 0.447931 | + | 0.616525i | 0.971952 | − | 0.235181i | \(-0.0755684\pi\) |
−0.524020 | + | 0.851706i | \(0.675568\pi\) | |||||||
\(432\) | −52.8894 | − | 94.1632i | −0.122429 | − | 0.217970i | ||||
\(433\) | −145.933 | − | 200.860i | −0.337029 | − | 0.463880i | 0.606542 | − | 0.795051i | \(-0.292556\pi\) |
−0.943571 | + | 0.331171i | \(0.892556\pi\) | |||||||
\(434\) | 815.925 | − | 265.110i | 1.88001 | − | 0.610853i | ||||
\(435\) | −48.3727 | + | 175.928i | −0.111202 | + | 0.404431i | ||||
\(436\) | 18.4808 | − | 56.8780i | 0.0423871 | − | 0.130454i | ||||
\(437\) | 197.095 | + | 606.597i | 0.451019 | + | 1.38809i | ||||
\(438\) | −135.488 | − | 5.26651i | −0.309333 | − | 0.0120240i | ||||
\(439\) | 49.6041 | − | 152.666i | 0.112993 | − | 0.347758i | −0.878530 | − | 0.477687i | \(-0.841475\pi\) |
0.991523 | + | 0.129930i | \(0.0414752\pi\) | |||||||
\(440\) | 6.79093 | + | 80.0006i | 0.0154339 | + | 0.181820i | ||||
\(441\) | 228.373 | − | 552.651i | 0.517854 | − | 1.25318i | ||||
\(442\) | 148.519 | + | 204.418i | 0.336015 | + | 0.462485i | ||||
\(443\) | 54.0408 | 0.121988 | 0.0609941 | − | 0.998138i | \(-0.480573\pi\) | ||||
0.0609941 | + | 0.998138i | \(0.480573\pi\) | |||||||
\(444\) | −52.4002 | − | 185.500i | −0.118019 | − | 0.417792i | ||||
\(445\) | −79.8622 | + | 132.139i | −0.179466 | + | 0.296941i | ||||
\(446\) | 174.496 | − | 240.173i | 0.391247 | − | 0.538505i | ||||
\(447\) | 606.043 | − | 405.312i | 1.35580 | − | 0.906738i | ||||
\(448\) | −81.7482 | − | 26.5616i | −0.182474 | − | 0.0592893i | ||||
\(449\) | 327.606i | 0.729634i | 0.931079 | + | 0.364817i | \(0.118868\pi\) | ||||
−0.931079 | + | 0.364817i | \(0.881132\pi\) | |||||||
\(450\) | −125.617 | − | 292.353i | −0.279148 | − | 0.649674i | ||||
\(451\) | 93.7534 | 0.207879 | ||||||||
\(452\) | −60.4923 | + | 186.176i | −0.133832 | + | 0.411894i | ||||
\(453\) | −343.827 | − | 514.107i | −0.759000 | − | 1.13489i | ||||
\(454\) | 127.693 | + | 92.7744i | 0.281262 | + | 0.204349i | ||||
\(455\) | −979.828 | + | 83.1737i | −2.15347 | + | 0.182799i | ||||
\(456\) | −180.404 | + | 50.9607i | −0.395622 | + | 0.111756i | ||||
\(457\) | − | 461.110i | − | 1.00899i | −0.863414 | − | 0.504497i | \(-0.831678\pi\) | ||
0.863414 | − | 0.504497i | \(-0.168322\pi\) | |||||||
\(458\) | 15.5946 | − | 11.3302i | 0.0340494 | − | 0.0247384i | ||||
\(459\) | 178.651 | − | 193.751i | 0.389218 | − | 0.422116i | ||||
\(460\) | −112.116 | − | 266.038i | −0.243731 | − | 0.578344i | ||||
\(461\) | −183.777 | − | 59.7127i | −0.398648 | − | 0.129529i | 0.102830 | − | 0.994699i | \(-0.467210\pi\) |
−0.501478 | + | 0.865170i | \(0.667210\pi\) | |||||||
\(462\) | 10.0519 | − | 258.599i | 0.0217575 | − | 0.559739i | ||||
\(463\) | −57.8338 | + | 18.7914i | −0.124911 | + | 0.0405861i | −0.370806 | − | 0.928711i | \(-0.620918\pi\) |
0.245894 | + | 0.969297i | \(0.420918\pi\) | |||||||
\(464\) | −46.2737 | − | 15.0353i | −0.0997279 | − | 0.0324036i | ||||
\(465\) | −465.888 | + | 707.254i | −1.00191 | + | 1.52098i | ||||
\(466\) | 1.12328 | + | 3.45710i | 0.00241047 | + | 0.00741868i | ||||
\(467\) | 127.368 | − | 92.5379i | 0.272736 | − | 0.198154i | −0.443007 | − | 0.896518i | \(-0.646088\pi\) |
0.715743 | + | 0.698364i | \(0.246088\pi\) | |||||||
\(468\) | 213.770 | − | 250.718i | 0.456774 | − | 0.535722i | ||||
\(469\) | 776.077 | − | 563.853i | 1.65475 | − | 1.20225i | ||||
\(470\) | −129.128 | − | 306.404i | −0.274739 | − | 0.651923i | ||||
\(471\) | −133.459 | + | 89.2551i | −0.283352 | + | 0.189501i | ||||
\(472\) | 188.870 | − | 259.957i | 0.400148 | − | 0.550757i | ||||
\(473\) | 7.50201 | − | 23.0888i | 0.0158605 | − | 0.0488136i | ||||
\(474\) | 398.762 | + | 146.921i | 0.841270 | + | 0.309961i | ||||
\(475\) | −544.416 | + | 93.0975i | −1.14614 | + | 0.195995i | ||||
\(476\) | − | 209.750i | − | 0.440651i | ||||||
\(477\) | −440.066 | + | 270.180i | −0.922569 | + | 0.566415i | ||||
\(478\) | 128.774 | − | 177.242i | 0.269401 | − | 0.370799i | ||||
\(479\) | 25.8292 | − | 35.5508i | 0.0539231 | − | 0.0742188i | −0.781204 | − | 0.624276i | \(-0.785394\pi\) |
0.835127 | + | 0.550057i | \(0.185394\pi\) | |||||||
\(480\) | 79.4137 | − | 29.8908i | 0.165445 | − | 0.0622724i | ||||
\(481\) | 475.749 | − | 345.652i | 0.989083 | − | 0.718611i | ||||
\(482\) | −264.670 | −0.549108 | ||||||||
\(483\) | 252.968 | + | 895.522i | 0.523743 | + | 1.85408i | ||||
\(484\) | 54.8622 | + | 168.849i | 0.113352 | + | 0.348861i | ||||
\(485\) | −170.366 | − | 197.009i | −0.351270 | − | 0.406205i | ||||
\(486\) | −300.188 | − | 167.288i | −0.617670 | − | 0.344215i | ||||
\(487\) | 835.528 | − | 271.479i | 1.71566 | − | 0.557452i | 0.724403 | − | 0.689377i | \(-0.242116\pi\) |
0.991260 | + | 0.131925i | \(0.0421157\pi\) | |||||||
\(488\) | 37.4521 | + | 115.266i | 0.0767462 | + | 0.236200i | ||||
\(489\) | −595.209 | − | 468.821i | −1.21720 | − | 0.958734i | ||||
\(490\) | 402.084 | + | 243.013i | 0.820580 | + | 0.495944i | ||||
\(491\) | 456.837 | − | 148.435i | 0.930421 | − | 0.302312i | 0.195686 | − | 0.980667i | \(-0.437307\pi\) |
0.734735 | + | 0.678355i | \(0.237307\pi\) | |||||||
\(492\) | −26.9352 | − | 95.3521i | −0.0547463 | − | 0.193805i | ||||
\(493\) | − | 118.729i | − | 0.240830i | ||||||
\(494\) | −336.156 | − | 462.679i | −0.680478 | − | 0.936597i | ||||
\(495\) | 151.604 | + | 205.631i | 0.306271 | + | 0.415416i | ||||
\(496\) | −182.711 | − | 132.747i | −0.368369 | − | 0.267636i | ||||
\(497\) | 227.704 | + | 165.436i | 0.458156 | + | 0.332870i | ||||
\(498\) | −82.2887 | + | 104.473i | −0.165238 | + | 0.209784i | ||||
\(499\) | −234.536 | −0.470012 | −0.235006 | − | 0.971994i | \(-0.575511\pi\) | ||||
−0.235006 | + | 0.971994i | \(0.575511\pi\) | |||||||
\(500\) | 241.976 | − | 62.8313i | 0.483951 | − | 0.125663i | ||||
\(501\) | 343.316 | + | 126.493i | 0.685261 | + | 0.252480i | ||||
\(502\) | −168.788 | − | 54.8424i | −0.336230 | − | 0.109248i | ||||
\(503\) | 51.1143 | + | 37.1367i | 0.101619 | + | 0.0738304i | 0.637434 | − | 0.770505i | \(-0.279996\pi\) |
−0.535815 | + | 0.844335i | \(0.679996\pi\) | |||||||
\(504\) | −265.897 | + | 64.0718i | −0.527573 | + | 0.127127i | ||||
\(505\) | −230.050 | − | 53.7376i | −0.455544 | − | 0.106411i | ||||
\(506\) | 136.243 | + | 187.523i | 0.269255 | + | 0.370598i | ||||
\(507\) | 467.442 | + | 172.226i | 0.921976 | + | 0.339696i | ||||
\(508\) | −52.6061 | − | 72.4061i | −0.103555 | − | 0.142532i | ||||
\(509\) | −473.533 | + | 153.860i | −0.930320 | + | 0.302279i | −0.734693 | − | 0.678399i | \(-0.762674\pi\) |
−0.195626 | + | 0.980679i | \(0.562674\pi\) | |||||||
\(510\) | 129.254 | + | 161.763i | 0.253439 | + | 0.317182i | ||||
\(511\) | −106.110 | + | 326.573i | −0.207652 | + | 0.639086i | ||||
\(512\) | 6.99226 | + | 21.5200i | 0.0136568 | + | 0.0420312i | ||||
\(513\) | −404.357 | + | 438.535i | −0.788221 | + | 0.854844i | ||||
\(514\) | −59.3073 | + | 182.529i | −0.115384 | + | 0.355115i | ||||
\(515\) | −78.8067 | − | 91.1312i | −0.153023 | − | 0.176954i | ||||
\(516\) | −25.6378 | − | 0.996561i | −0.0496857 | − | 0.00193132i | ||||
\(517\) | 156.915 | + | 215.975i | 0.303511 | + | 0.417747i | ||||
\(518\) | −488.157 | −0.942389 | ||||||||
\(519\) | −56.5681 | + | 15.9794i | −0.108994 | + | 0.0307889i | ||||
\(520\) | 169.325 | + | 195.805i | 0.325625 | + | 0.376549i | ||||
\(521\) | 443.746 | − | 610.764i | 0.851720 | − | 1.17229i | −0.131761 | − | 0.991281i | \(-0.542063\pi\) |
0.983481 | − | 0.181010i | \(-0.0579367\pi\) | |||||||
\(522\) | −150.512 | + | 36.2680i | −0.288336 | + | 0.0694789i | ||||
\(523\) | 525.939 | + | 170.888i | 1.00562 | + | 0.326746i | 0.765109 | − | 0.643901i | \(-0.222685\pi\) |
0.240511 | + | 0.970646i | \(0.422685\pi\) | |||||||
\(524\) | 138.472i | 0.264259i | ||||||||
\(525\) | −798.976 | + | 104.874i | −1.52186 | + | 0.199761i | ||||
\(526\) | −609.142 | −1.15806 | ||||||||
\(527\) | 170.302 | − | 524.135i | 0.323153 | − | 0.994564i | ||||
\(528\) | −56.6296 | + | 37.8730i | −0.107253 | + | 0.0717291i | ||||
\(529\) | −246.318 | − | 178.960i | −0.465629 | − | 0.338299i | ||||
\(530\) | −157.559 | − | 373.868i | −0.297281 | − | 0.705411i | ||||
\(531\) | 79.3668 | − | 1019.36i | 0.149467 | − | 1.91971i | ||||
\(532\) | 474.747i | 0.892381i | ||||||||
\(533\) | 244.548 | − | 177.675i | 0.458815 | − | 0.333348i | ||||
\(534\) | −130.912 | − | 5.08863i | −0.245153 | − | 0.00952927i | ||||
\(535\) | 205.333 | − | 879.029i | 0.383800 | − | 1.64305i | ||||
\(536\) | −240.169 | − | 78.0356i | −0.448076 | − | 0.145589i | ||||
\(537\) | −109.562 | − | 4.25875i | −0.204026 | − | 0.00793063i | ||||
\(538\) | 481.632 | − | 156.492i | 0.895227 | − | 0.290877i | ||||
\(539\) | −358.745 | − | 116.563i | −0.665576 | − | 0.216259i | ||||
\(540\) | 165.582 | − | 213.267i | 0.306633 | − | 0.394938i | ||||
\(541\) | 155.137 | + | 477.462i | 0.286759 | + | 0.882555i | 0.985866 | + | 0.167537i | \(0.0535814\pi\) |
−0.699106 | + | 0.715018i | \(0.746419\pi\) | |||||||
\(542\) | 109.046 | − | 79.2265i | 0.201192 | − | 0.146174i | ||||
\(543\) | 896.256 | + | 330.220i | 1.65056 | + | 0.608140i | ||||
\(544\) | −44.6707 | + | 32.4552i | −0.0821152 | + | 0.0596602i | ||||
\(545\) | 148.977 | − | 12.6461i | 0.273352 | − | 0.0232038i | ||||
\(546\) | −463.859 | − | 693.585i | −0.849559 | − | 1.27030i | ||||
\(547\) | −196.590 | + | 270.583i | −0.359397 | + | 0.494667i | −0.949981 | − | 0.312309i | \(-0.898898\pi\) |
0.590584 | + | 0.806976i | \(0.298898\pi\) | |||||||
\(548\) | 45.1670 | − | 139.010i | 0.0824215 | − | 0.253667i | ||||
\(549\) | 293.459 | + | 250.213i | 0.534534 | + | 0.455761i | ||||
\(550\) | −177.710 | + | 93.3157i | −0.323110 | + | 0.169665i | ||||
\(551\) | 268.731i | 0.487716i | ||||||||
\(552\) | 151.578 | − | 192.441i | 0.274598 | − | 0.348626i | ||||
\(553\) | 632.586 | − | 870.680i | 1.14392 | − | 1.57447i | ||||
\(554\) | −53.4384 | + | 73.5516i | −0.0964591 | + | 0.132765i | ||||
\(555\) | 376.476 | − | 300.816i | 0.678335 | − | 0.542012i | ||||
\(556\) | −165.471 | + | 120.222i | −0.297610 | + | 0.216226i | ||||
\(557\) | 645.778 | 1.15939 | 0.579693 | − | 0.814835i | \(-0.303172\pi\) | ||||
0.579693 | + | 0.814835i | \(0.303172\pi\) | |||||||
\(558\) | −716.460 | − | 55.7829i | −1.28398 | − | 0.0999694i | ||||
\(559\) | −24.1879 | − | 74.4426i | −0.0432699 | − | 0.133171i | ||||
\(560\) | −18.1756 | − | 214.118i | −0.0324565 | − | 0.382353i | ||||
\(561\) | −130.598 | − | 102.867i | −0.232795 | − | 0.183363i | ||||
\(562\) | −189.137 | + | 61.4543i | −0.336543 | + | 0.109349i | ||||
\(563\) | 126.556 | + | 389.500i | 0.224789 | + | 0.691829i | 0.998313 | + | 0.0580620i | \(0.0184921\pi\) |
−0.773524 | + | 0.633767i | \(0.781508\pi\) | |||||||
\(564\) | 174.576 | − | 221.640i | 0.309533 | − | 0.392979i | ||||
\(565\) | −487.639 | + | 41.3937i | −0.863078 | + | 0.0732633i | ||||
\(566\) | −252.576 | + | 82.0668i | −0.446246 | + | 0.144994i | ||||
\(567\) | −614.360 | + | 616.422i | −1.08353 | + | 1.08716i | ||||
\(568\) | − | 74.0927i | − | 0.130445i | ||||||
\(569\) | 335.206 | + | 461.371i | 0.589114 | + | 0.810845i | 0.994657 | − | 0.103230i | \(-0.0329179\pi\) |
−0.405544 | + | 0.914076i | \(0.632918\pi\) | |||||||
\(570\) | −292.552 | − | 366.133i | −0.513250 | − | 0.642339i | ||||
\(571\) | −397.542 | − | 288.831i | −0.696221 | − | 0.505834i | 0.182479 | − | 0.983210i | \(-0.441588\pi\) |
−0.878699 | + | 0.477376i | \(0.841588\pi\) | |||||||
\(572\) | −168.144 | − | 122.164i | −0.293958 | − | 0.213573i | ||||
\(573\) | −568.436 | − | 447.733i | −0.992035 | − | 0.781384i | ||||
\(574\) | −250.927 | −0.437154 | ||||||||
\(575\) | 504.042 | − | 516.582i | 0.876595 | − | 0.898404i | ||||
\(576\) | 54.7884 | + | 46.7144i | 0.0951187 | + | 0.0811014i | ||||
\(577\) | −585.703 | − | 190.306i | −1.01508 | − | 0.329821i | −0.246207 | − | 0.969217i | \(-0.579184\pi\) |
−0.768877 | + | 0.639397i | \(0.779184\pi\) | |||||||
\(578\) | 221.645 | + | 161.034i | 0.383469 | + | 0.278606i | ||||
\(579\) | −129.867 | + | 86.8528i | −0.224295 | + | 0.150005i | ||||
\(580\) | −10.2883 | − | 121.202i | −0.0177385 | − | 0.208969i | ||||
\(581\) | 197.961 | + | 272.469i | 0.340724 | + | 0.468966i | ||||
\(582\) | 76.4064 | − | 207.376i | 0.131283 | − | 0.356316i | ||||
\(583\) | 191.464 | + | 263.528i | 0.328412 | + | 0.452021i | ||||
\(584\) | 85.9693 | − | 27.9331i | 0.147208 | − | 0.0478307i | ||||
\(585\) | 785.144 | + | 249.063i | 1.34213 | + | 0.425748i | ||||
\(586\) | −218.028 | + | 671.021i | −0.372061 | + | 1.14509i | ||||
\(587\) | 19.9835 | + | 61.5030i | 0.0340435 | + | 0.104775i | 0.966634 | − | 0.256160i | \(-0.0824575\pi\) |
−0.932591 | + | 0.360935i | \(0.882457\pi\) | |||||||
\(588\) | −15.4842 | + | 398.351i | −0.0263337 | + | 0.677468i | ||||
\(589\) | −385.460 | + | 1186.32i | −0.654431 | + | 2.01413i | ||||
\(590\) | 782.254 | + | 182.727i | 1.32585 | + | 0.309708i | ||||
\(591\) | 11.9128 | − | 306.473i | 0.0201571 | − | 0.518567i | ||||
\(592\) | 75.5339 | + | 103.963i | 0.127591 | + | 0.175614i | ||||
\(593\) | 146.438 | 0.246945 | 0.123472 | − | 0.992348i | \(-0.460597\pi\) | ||||
0.123472 | + | 0.992348i | \(0.460597\pi\) | |||||||
\(594\) | −90.5090 | + | 196.980i | −0.152372 | + | 0.331616i | ||||
\(595\) | 483.217 | − | 203.642i | 0.812130 | − | 0.342255i | ||||
\(596\) | −285.697 | + | 393.228i | −0.479357 | + | 0.659779i | ||||
\(597\) | −383.681 | − | 573.699i | −0.642682 | − | 0.960970i | ||||
\(598\) | 710.759 | + | 230.939i | 1.18856 | + | 0.386186i | ||||
\(599\) | − | 54.5992i | − | 0.0911506i | −0.998961 | − | 0.0455753i | \(-0.985488\pi\) | ||
0.998961 | − | 0.0455753i | \(-0.0145121\pi\) | |||||||
\(600\) | 145.963 | + | 153.931i | 0.243271 | + | 0.256552i | ||||
\(601\) | 800.099 | 1.33128 | 0.665640 | − | 0.746273i | \(-0.268159\pi\) | ||||
0.665640 | + | 0.746273i | \(0.268159\pi\) | |||||||
\(602\) | −20.0788 | + | 61.7961i | −0.0333534 | + | 0.102651i | ||||
\(603\) | −781.181 | + | 188.237i | −1.29549 | + | 0.312168i | ||||
\(604\) | 333.576 | + | 242.357i | 0.552279 | + | 0.401254i | ||||
\(605\) | −335.725 | + | 290.322i | −0.554917 | + | 0.479871i | ||||
\(606\) | −54.4934 | − | 192.910i | −0.0899231 | − | 0.318333i | ||||
\(607\) | − | 825.813i | − | 1.36048i | −0.732988 | − | 0.680241i | \(-0.761875\pi\) | ||
0.732988 | − | 0.680241i | \(-0.238125\pi\) | |||||||
\(608\) | 101.107 | − | 73.4588i | 0.166295 | − | 0.120820i | ||||
\(609\) | −15.2288 | + | 391.781i | −0.0250063 | + | 0.643319i | ||||
\(610\) | −229.185 | + | 198.191i | −0.375714 | + | 0.324903i | ||||
\(611\) | 818.600 | + | 265.979i | 1.33977 | + | 0.435318i | ||||
\(612\) | −67.1001 | + | 162.378i | −0.109641 | + | 0.265324i | ||||
\(613\) | 1155.81 | − | 375.544i | 1.88549 | − | 0.612633i | 0.901980 | − | 0.431778i | \(-0.142114\pi\) |
0.983510 | − | 0.180855i | \(-0.0578864\pi\) | |||||||
\(614\) | 378.493 | + | 122.980i | 0.616438 | + | 0.200293i | ||||
\(615\) | 193.519 | − | 154.628i | 0.314665 | − | 0.251428i | ||||
\(616\) | 53.3146 | + | 164.086i | 0.0865498 | + | 0.266373i | ||||
\(617\) | 569.666 | − | 413.887i | 0.923284 | − | 0.670805i | −0.0210556 | − | 0.999778i | \(-0.506703\pi\) |
0.944339 | + | 0.328974i | \(0.106703\pi\) | |||||||
\(618\) | 35.3436 | − | 95.9266i | 0.0571902 | − | 0.155221i | ||||
\(619\) | −237.496 | + | 172.551i | −0.383678 | + | 0.278758i | −0.762860 | − | 0.646564i | \(-0.776205\pi\) |
0.379182 | + | 0.925322i | \(0.376205\pi\) | |||||||
\(620\) | 128.430 | − | 549.807i | 0.207145 | − | 0.886786i | ||||
\(621\) | 90.6461 | − | 774.196i | 0.145968 | − | 1.24669i | ||||
\(622\) | −150.360 | + | 206.952i | −0.241736 | + | 0.332721i | ||||
\(623\) | −102.526 | + | 315.543i | −0.164568 | + | 0.506489i | ||||
\(624\) | −75.9395 | + | 206.109i | −0.121698 | + | 0.330303i | ||||
\(625\) | 379.679 | + | 496.457i | 0.607486 | + | 0.794331i | ||||
\(626\) | − | 322.516i | − | 0.515201i | ||||||
\(627\) | 295.595 | + | 232.828i | 0.471443 | + | 0.371336i | ||||
\(628\) | 62.9143 | − | 86.5941i | 0.100182 | − | 0.137889i | ||||
\(629\) | −184.320 | + | 253.694i | −0.293036 | + | 0.403330i | ||||
\(630\) | −405.761 | − | 550.362i | −0.644065 | − | 0.873590i | ||||
\(631\) | 4.12853 | − | 2.99955i | 0.00654284 | − | 0.00475365i | −0.584509 | − | 0.811387i | \(-0.698713\pi\) |
0.591052 | + | 0.806634i | \(0.298713\pi\) | |||||||
\(632\) | −283.312 | −0.448278 | ||||||||
\(633\) | −1052.47 | + | 297.302i | −1.66266 | + | 0.469671i | ||||
\(634\) | −56.2867 | − | 173.233i | −0.0887803 | − | 0.273238i | ||||
\(635\) | 115.733 | − | 191.490i | 0.182257 | − | 0.301560i | ||||
\(636\) | 213.015 | − | 270.440i | 0.334928 | − | 0.425221i | ||||
\(637\) | −1156.66 | + | 375.822i | −1.81579 | + | 0.589987i | ||||
\(638\) | 30.1789 | + | 92.8810i | 0.0473023 | + | 0.145582i | ||||
\(639\) | −123.353 | − | 200.917i | −0.193041 | − | 0.314423i | ||||
\(640\) | −42.7886 | + | 37.0019i | −0.0668571 | + | 0.0578154i | ||||
\(641\) | −704.333 | + | 228.852i | −1.09880 | + | 0.357023i | −0.801642 | − | 0.597804i | \(-0.796040\pi\) |
−0.297162 | + | 0.954827i | \(0.596040\pi\) | |||||||
\(642\) | 737.115 | − | 208.221i | 1.14815 | − | 0.324332i | ||||
\(643\) | 994.252i | 1.54627i | 0.634241 | + | 0.773135i | \(0.281313\pi\) | ||||
−0.634241 | + | 0.773135i | \(0.718687\pi\) | |||||||
\(644\) | −364.648 | − | 501.895i | −0.566224 | − | 0.779341i | ||||
\(645\) | −22.5954 | − | 60.0314i | −0.0350316 | − | 0.0930720i | ||||
\(646\) | 246.725 | + | 179.256i | 0.381927 | + | 0.277486i | ||||
\(647\) | 824.393 | + | 598.957i | 1.27418 | + | 0.925744i | 0.999361 | − | 0.0357523i | \(-0.0113827\pi\) |
0.274817 | + | 0.961497i | \(0.411383\pi\) | |||||||
\(648\) | 226.342 | + | 35.4605i | 0.349293 | + | 0.0547230i | ||||
\(649\) | −644.966 | −0.993784 | ||||||||
\(650\) | −286.698 | + | 580.190i | −0.441074 | + | 0.892601i | ||||
\(651\) | −629.187 | + | 1707.69i | −0.966493 | + | 2.62318i | ||||
\(652\) | 480.393 | + | 156.089i | 0.736799 | + | 0.239400i | ||||
\(653\) | −53.3390 | − | 38.7530i | −0.0816829 | − | 0.0593461i | 0.546194 | − | 0.837659i | \(-0.316076\pi\) |
−0.627877 | + | 0.778312i | \(0.716076\pi\) | |||||||
\(654\) | 70.5270 | + | 105.455i | 0.107839 | + | 0.161247i | ||||
\(655\) | −319.008 | + | 134.439i | −0.487035 | + | 0.205251i | ||||
\(656\) | 38.8265 | + | 53.4401i | 0.0591868 | + | 0.0814636i | ||||
\(657\) | 186.618 | − | 218.872i | 0.284045 | − | 0.333139i | ||||
\(658\) | −419.976 | − | 578.047i | −0.638261 | − | 0.878491i | ||||
\(659\) | −712.635 | + | 231.549i | −1.08139 | + | 0.351364i | −0.794913 | − | 0.606723i | \(-0.792484\pi\) |
−0.286475 | + | 0.958088i | \(0.592484\pi\) | |||||||
\(660\) | −142.231 | − | 93.6919i | −0.215502 | − | 0.141957i | ||||
\(661\) | −187.036 | + | 575.636i | −0.282959 | + | 0.870857i | 0.704045 | + | 0.710156i | \(0.251375\pi\) |
−0.987003 | + | 0.160701i | \(0.948625\pi\) | |||||||
\(662\) | 127.103 | + | 391.181i | 0.191998 | + | 0.590908i | ||||
\(663\) | −535.600 | − | 20.8192i | −0.807843 | − | 0.0314014i | ||||
\(664\) | 27.3972 | − | 84.3198i | 0.0412608 | − | 0.126988i | ||||
\(665\) | −1093.71 | + | 460.922i | −1.64468 | + | 0.693115i | ||||
\(666\) | 377.908 | + | 156.164i | 0.567430 | + | 0.234481i | ||||
\(667\) | −206.410 | − | 284.099i | −0.309460 | − | 0.425936i | ||||
\(668\) | −243.918 | −0.365147 | ||||||||
\(669\) | 171.195 | + | 606.041i | 0.255897 | + | 0.905891i | ||||
\(670\) | −53.3983 | − | 629.059i | −0.0796990 | − | 0.938894i | ||||
\(671\) | 142.990 | − | 196.809i | 0.213100 | − | 0.293306i | ||||
\(672\) | 151.566 | − | 101.365i | 0.225545 | − | 0.150841i | ||||
\(673\) | −460.927 | − | 149.764i | −0.684885 | − | 0.222533i | −0.0541520 | − | 0.998533i | \(-0.517246\pi\) |
−0.630733 | + | 0.776000i | \(0.717246\pi\) | |||||||
\(674\) | 804.476i | 1.19358i | ||||||||
\(675\) | 652.079 | + | 174.408i | 0.966043 | + | 0.258382i | ||||
\(676\) | −332.107 | −0.491282 | ||||||||
\(677\) | 116.715 | − | 359.212i | 0.172400 | − | 0.530594i | −0.827105 | − | 0.562048i | \(-0.810014\pi\) |
0.999505 | + | 0.0314538i | \(0.0100137\pi\) | |||||||
\(678\) | −230.853 | − | 345.182i | −0.340491 | − | 0.509118i | ||||
\(679\) | −452.797 | − | 328.976i | −0.666858 | − | 0.484501i | ||||
\(680\) | −118.139 | − | 71.4013i | −0.173734 | − | 0.105002i | ||||
\(681\) | −322.214 | + | 91.0195i | −0.473149 | + | 0.133656i | ||||
\(682\) | 453.314i | 0.664684i | ||||||||
\(683\) | −152.279 | + | 110.637i | −0.222955 | + | 0.161987i | −0.693656 | − | 0.720306i | \(-0.744001\pi\) |
0.470701 | + | 0.882293i | \(0.344001\pi\) | |||||||
\(684\) | 151.874 | − | 367.526i | 0.222038 | − | 0.537319i | ||||
\(685\) | 364.099 | − | 30.9069i | 0.531532 | − | 0.0451196i | ||||
\(686\) | 252.057 | + | 81.8983i | 0.367430 | + | 0.119385i | ||||
\(687\) | −1.58825 | + | 40.8598i | −0.00231186 | + | 0.0594757i | ||||
\(688\) | 16.2676 | − | 5.28567i | 0.0236448 | − | 0.00768267i | ||||
\(689\) | 998.839 | + | 324.542i | 1.44969 | + | 0.471034i | ||||
\(690\) | 590.506 | + | 162.364i | 0.855806 | + | 0.235311i | ||||
\(691\) | −12.9839 | − | 39.9602i | −0.0187900 | − | 0.0578296i | 0.941222 | − | 0.337789i | \(-0.109679\pi\) |
−0.960012 | + | 0.279959i | \(0.909679\pi\) | |||||||
\(692\) | 31.7036 | − | 23.0340i | 0.0458145 | − | 0.0332862i | ||||
\(693\) | 417.751 | + | 356.189i | 0.602815 | + | 0.513981i | ||||
\(694\) | −751.246 | + | 545.812i | −1.08249 | + | 0.786473i | ||||
\(695\) | −437.617 | − | 264.488i | −0.629664 | − | 0.380558i | ||||
\(696\) | 85.7945 | − | 57.3780i | 0.123268 | − | 0.0824397i | ||||
\(697\) | −94.7455 | + | 130.406i | −0.135933 | + | 0.187096i | ||||
\(698\) | 253.767 | − | 781.014i | 0.363563 | − | 1.11893i | ||||
\(699\) | −7.23554 | − | 2.66589i | −0.0103513 | − | 0.00381386i | ||||
\(700\) | 475.634 | − | 249.755i | 0.679477 | − | 0.356793i | ||||
\(701\) | − | 805.755i | − | 1.14944i | −0.818351 | − | 0.574718i | \(-0.805112\pi\) | ||
0.818351 | − | 0.574718i | \(-0.194888\pi\) | |||||||
\(702\) | 137.216 | + | 685.332i | 0.195465 | + | 0.976256i | ||||
\(703\) | 417.188 | − | 574.210i | 0.593439 | − | 0.816799i | ||||
\(704\) | 26.6960 | − | 36.7439i | 0.0379204 | − | 0.0521930i | ||||
\(705\) | 680.102 | + | 187.000i | 0.964684 | + | 0.265248i | ||||
\(706\) | 537.247 | − | 390.333i | 0.760973 | − | 0.552879i | ||||
\(707\) | −507.657 | −0.718044 | ||||||||
\(708\) | 185.298 | + | 655.964i | 0.261720 | + | 0.926503i | ||||
\(709\) | 76.7737 | + | 236.285i | 0.108284 | + | 0.333265i | 0.990487 | − | 0.137604i | \(-0.0439402\pi\) |
−0.882203 | + | 0.470870i | \(0.843940\pi\) | |||||||
\(710\) | 170.693 | − | 71.9351i | 0.240413 | − | 0.101317i | ||||
\(711\) | −768.253 | + | 471.672i | −1.08052 | + | 0.663392i | ||||
\(712\) | 83.0656 | − | 26.9897i | 0.116665 | − | 0.0379068i | ||||
\(713\) | −503.701 | − | 1550.23i | −0.706454 | − | 2.17424i | ||||
\(714\) | 349.540 | + | 275.318i | 0.489551 | + | 0.385599i | ||||
\(715\) | 118.191 | − | 505.973i | 0.165302 | − | 0.707655i | ||||
\(716\) | 69.5188 | − | 22.5880i | 0.0970932 | − | 0.0315475i | ||||
\(717\) | 126.338 | + | 447.244i | 0.176204 | + | 0.623771i | ||||
\(718\) | 826.549i | 1.15118i | ||||||||
\(719\) | −202.462 | − | 278.665i | −0.281589 | − | 0.387573i | 0.644671 | − | 0.764460i | \(-0.276994\pi\) |
−0.926259 | + | 0.376887i | \(0.876994\pi\) | |||||||
\(720\) | −54.4267 | + | 171.574i | −0.0755926 | + | 0.238298i | ||||
\(721\) | −209.452 | − | 152.176i | −0.290502 | − | 0.211062i | ||||
\(722\) | −145.407 | − | 105.644i | −0.201395 | − | 0.146322i | ||||
\(723\) | 347.405 | − | 441.061i | 0.480505 | − | 0.610043i | ||||
\(724\) | −636.770 | −0.879516 | ||||||||
\(725\) | 269.233 | − | 141.374i | 0.371356 | − | 0.194999i | ||||
\(726\) | −353.391 | − | 130.205i | −0.486765 | − | 0.179345i | ||||
\(727\) | −350.810 | − | 113.985i | −0.482545 | − | 0.156788i | 0.0576354 | − | 0.998338i | \(-0.481644\pi\) |
−0.540180 | + | 0.841549i | \(0.681644\pi\) | |||||||
\(728\) | 450.030 | + | 326.966i | 0.618173 | + | 0.449129i | ||||
\(729\) | 672.805 | − | 280.667i | 0.922915 | − | 0.385003i | ||||
\(730\) | 147.818 | + | 170.934i | 0.202490 | + | 0.234157i | ||||
\(731\) | 24.5339 | + | 33.7680i | 0.0335621 | + | 0.0461943i | ||||
\(732\) | −241.245 | − | 88.8853i | −0.329570 | − | 0.121428i | ||||
\(733\) | 52.4471 | + | 72.1873i | 0.0715513 | + | 0.0984819i | 0.843293 | − | 0.537455i | \(-0.180614\pi\) |
−0.771741 | + | 0.635936i | \(0.780614\pi\) | |||||||
\(734\) | −183.665 | + | 59.6764i | −0.250225 | + | 0.0813030i | ||||
\(735\) | −932.746 | + | 351.079i | −1.26904 | + | 0.477658i | ||||
\(736\) | −50.4663 | + | 155.319i | −0.0685683 | + | 0.211031i | ||||
\(737\) | 156.634 | + | 482.069i | 0.212529 | + | 0.654096i | ||||
\(738\) | 194.255 | + | 80.2727i | 0.263219 | + | 0.108771i | ||||
\(739\) | 98.6633 | − | 303.655i | 0.133509 | − | 0.410899i | −0.861846 | − | 0.507170i | \(-0.830692\pi\) |
0.995355 | + | 0.0962710i | \(0.0306915\pi\) | |||||||
\(740\) | −166.174 | + | 274.949i | −0.224560 | + | 0.371553i | ||||
\(741\) | 1212.27 | + | 47.1219i | 1.63600 | + | 0.0635924i | ||||
\(742\) | −512.446 | − | 705.321i | −0.690627 | − | 0.950567i | ||||
\(743\) | −271.347 | −0.365205 | −0.182603 | − | 0.983187i | \(-0.558452\pi\) | ||||
−0.182603 | + | 0.983187i | \(0.558452\pi\) | |||||||
\(744\) | 461.044 | − | 130.236i | 0.619683 | − | 0.175049i | ||||
\(745\) | −1183.29 | − | 276.405i | −1.58831 | − | 0.371014i | ||||
\(746\) | −58.1714 | + | 80.0661i | −0.0779777 | + | 0.107327i | ||||
\(747\) | −66.0873 | − | 274.261i | −0.0884703 | − | 0.367151i | ||||
\(748\) | 105.406 | + | 34.2484i | 0.140917 | + | 0.0457866i | ||||
\(749\) | − | 1939.78i | − | 2.58982i | ||||||
\(750\) | −212.911 | + | 485.715i | −0.283882 | + | 0.647620i | ||||
\(751\) | 335.603 | 0.446874 | 0.223437 | − | 0.974718i | \(-0.428272\pi\) | ||||
0.223437 | + | 0.974718i | \(0.428272\pi\) | |||||||
\(752\) | −58.1234 | + | 178.885i | −0.0772917 | + | 0.237880i | ||||
\(753\) | 312.943 | − | 209.292i | 0.415595 | − | 0.277944i | ||||
\(754\) | 254.741 | + | 185.080i | 0.337852 | + | 0.245464i | ||||
\(755\) | −234.475 | + | 1003.79i | −0.310563 | + | 1.32952i | ||||
\(756\) | 242.243 | − | 527.207i | 0.320427 | − | 0.697364i | ||||
\(757\) | − | 299.536i | − | 0.395688i | −0.980234 | − | 0.197844i | \(-0.936606\pi\) | ||
0.980234 | − | 0.197844i | \(-0.0633939\pi\) | |||||||
\(758\) | 52.3614 | − | 38.0428i | 0.0690783 | − | 0.0501883i | ||||
\(759\) | −491.331 | − | 19.0984i | −0.647340 | − | 0.0251626i | ||||
\(760\) | 267.396 | + | 161.609i | 0.351837 | + | 0.212644i | ||||
\(761\) | −928.556 | − | 301.706i | −1.22018 | − | 0.396460i | −0.373032 | − | 0.927819i | \(-0.621682\pi\) |
−0.847147 | + | 0.531359i | \(0.821682\pi\) | |||||||
\(762\) | 189.713 | + | 7.37426i | 0.248967 | + | 0.00967751i | ||||
\(763\) | 305.560 | − | 99.2824i | 0.400471 | − | 0.130121i | ||||
\(764\) | 458.784 | + | 149.068i | 0.600503 | + | 0.195115i | ||||
\(765\) | −439.230 | + | 3.06618i | −0.574157 | + | 0.00400808i | ||||
\(766\) | −131.445 | − | 404.547i | −0.171600 | − | 0.528129i | ||||
\(767\) | −1682.34 | + | 1222.29i | −2.19340 | + | 1.59360i | ||||
\(768\) | −45.0401 | − | 16.5948i | −0.0586460 | − | 0.0216078i | ||||
\(769\) | −158.573 | + | 115.210i | −0.206207 | + | 0.149818i | −0.686096 | − | 0.727511i | \(-0.740677\pi\) |
0.479889 | + | 0.877329i | \(0.340677\pi\) | |||||||
\(770\) | −326.255 | + | 282.132i | −0.423707 | + | 0.366406i | ||||
\(771\) | −226.330 | − | 338.420i | −0.293554 | − | 0.438937i | ||||
\(772\) | 61.2210 | − | 84.2635i | 0.0793018 | − | 0.109150i | ||||
\(773\) | −20.6629 | + | 63.5937i | −0.0267307 | + | 0.0822687i | −0.963532 | − | 0.267593i | \(-0.913772\pi\) |
0.936801 | + | 0.349862i | \(0.113772\pi\) | |||||||
\(774\) | 35.3129 | − | 41.4163i | 0.0456239 | − | 0.0535094i | ||||
\(775\) | 1391.32 | − | 237.922i | 1.79526 | − | 0.306997i | ||||
\(776\) | 147.336i | 0.189866i | ||||||||
\(777\) | 640.755 | − | 813.494i | 0.824652 | − | 1.04697i | ||||
\(778\) | −475.465 | + | 654.422i | −0.611138 | + | 0.841159i | ||||
\(779\) | 214.446 | − | 295.160i | 0.275284 | − | 0.378896i | ||||
\(780\) | −548.557 | + | 25.1590i | −0.703279 | + | 0.0322552i | ||||
\(781\) | −120.317 | + | 87.4151i | −0.154055 | + | 0.111927i | ||||
\(782\) | −398.519 | −0.509615 | ||||||||
\(783\) | 137.122 | − | 298.427i | 0.175124 | − | 0.381132i | ||||
\(784\) | −82.1268 | − | 252.760i | −0.104754 | − | 0.322398i | ||||
\(785\) | 260.576 | + | 60.8682i | 0.331944 | + | 0.0775391i | ||||
\(786\) | −230.757 | − | 181.758i | −0.293585 | − | 0.231244i | ||||
\(787\) | 171.036 | − | 55.5731i | 0.217327 | − | 0.0706138i | −0.198330 | − | 0.980135i | \(-0.563552\pi\) |
0.415657 | + | 0.909522i | \(0.363552\pi\) | |||||||
\(788\) | 63.1846 | + | 194.462i | 0.0801835 | + | 0.246779i | ||||
\(789\) | 799.559 | − | 1015.11i | 1.01338 | − | 1.28658i | ||||
\(790\) | −275.061 | − | 652.687i | −0.348179 | − | 0.826186i | ||||
\(791\) | −1000.17 | + | 324.976i | −1.26444 | + | 0.410842i | ||||
\(792\) | 11.2182 | − | 144.083i | 0.0141643 | − | 0.181923i | ||||
\(793\) | − | 784.343i | − | 0.989083i | ||||||
\(794\) | −383.259 | − | 527.510i | −0.482694 | − | 0.664371i | ||||
\(795\) | 829.846 | + | 228.173i | 1.04383 | + | 0.287010i | ||||
\(796\) | 372.242 | + | 270.450i | 0.467641 | + | 0.339761i | ||||
\(797\) | −933.552 | − | 678.265i | −1.17133 | − | 0.851023i | −0.180165 | − | 0.983636i | \(-0.557663\pi\) |
−0.991168 | + | 0.132614i | \(0.957663\pi\) | |||||||
\(798\) | −791.146 | − | 623.152i | −0.991411 | − | 0.780892i | ||||
\(799\) | −458.985 | −0.574449 | ||||||||
\(800\) | −126.787 | − | 62.6510i | −0.158483 | − | 0.0783137i | ||||
\(801\) | 180.315 | − | 211.480i | 0.225112 | − | 0.264019i | ||||
\(802\) | −993.953 | − | 322.955i | −1.23934 | − | 0.402687i | ||||
\(803\) | −146.787 | − | 106.647i | −0.182798 | − | 0.132811i | ||||
\(804\) | 445.288 | − | 297.802i | 0.553841 | − | 0.370400i | ||||
\(805\) | 802.226 | − | 1327.35i | 0.996554 | − | 1.64888i | ||||
\(806\) | 859.088 | + | 1182.43i | 1.06587 | + | 1.46704i | ||||
\(807\) | −371.403 | + | 1008.03i | −0.460227 | + | 1.24911i | ||||
\(808\) | 78.5511 | + | 108.116i | 0.0972167 | + | 0.133807i | ||||
\(809\) | −40.9097 | + | 13.2924i | −0.0505683 | + | 0.0164306i | −0.334192 | − | 0.942505i | \(-0.608463\pi\) |
0.283624 | + | 0.958936i | \(0.408463\pi\) | |||||||
\(810\) | 138.057 | + | 555.869i | 0.170441 | + | 0.686258i | ||||
\(811\) | 136.537 | − | 420.218i | 0.168357 | − | 0.518149i | −0.830911 | − | 0.556405i | \(-0.812180\pi\) |
0.999268 | + | 0.0382564i | \(0.0121803\pi\) | |||||||
\(812\) | −80.7723 | − | 248.592i | −0.0994733 | − | 0.306147i | ||||
\(813\) | −11.1059 | + | 285.713i | −0.0136604 | + | 0.351431i | ||||
\(814\) | 79.7072 | − | 245.314i | 0.0979204 | − | 0.301368i | ||||
\(815\) | 106.809 | + | 1258.26i | 0.131054 | + | 1.54388i | ||||
\(816\) | 4.54952 | − | 117.042i | 0.00557540 | − | 0.143434i | ||||
\(817\) | −55.5299 | − | 76.4303i | −0.0679680 | − | 0.0935500i | ||||
\(818\) | 251.989 | 0.308055 | ||||||||
\(819\) | 1764.69 | + | 137.397i | 2.15469 | + | 0.167762i | ||||
\(820\) | −85.4183 | + | 141.332i | −0.104169 | + | 0.172356i | ||||
\(821\) | −801.953 | + | 1103.79i | −0.976801 | + | 1.34445i | −0.0382655 | + | 0.999268i | \(0.512183\pi\) |
−0.938535 | + | 0.345183i | \(0.887817\pi\) | |||||||
\(822\) | 172.368 | + | 257.733i | 0.209693 | + | 0.313544i | ||||
\(823\) | −367.027 | − | 119.254i | −0.445963 | − | 0.144902i | 0.0774224 | − | 0.996998i | \(-0.475331\pi\) |
−0.523385 | + | 0.852096i | \(0.675331\pi\) | |||||||
\(824\) | 68.1537i | 0.0827108i | ||||||||
\(825\) | 77.7557 | − | 418.633i | 0.0942494 | − | 0.507434i | ||||
\(826\) | 1726.22 | 2.08986 | ||||||||
\(827\) | 313.007 | − | 963.336i | 0.378485 | − | 1.16486i | −0.562613 | − | 0.826720i | \(-0.690204\pi\) |
0.941098 | − | 0.338135i | \(-0.109796\pi\) | |||||||
\(828\) | 121.735 | + | 505.196i | 0.147022 | + | 0.610141i | ||||
\(829\) | 931.210 | + | 676.564i | 1.12329 | + | 0.816120i | 0.984705 | − | 0.174230i | \(-0.0557436\pi\) |
0.138588 | + | 0.990350i | \(0.455744\pi\) | |||||||
\(830\) | 220.853 | − | 18.7474i | 0.266088 | − | 0.0225872i | ||||
\(831\) | −52.4276 | − | 185.597i | −0.0630897 | − | 0.223341i | ||||
\(832\) | − | 146.436i | − | 0.176004i | ||||||
\(833\) | 524.675 | − | 381.199i | 0.629862 | − | 0.457621i | ||||
\(834\) | 16.8525 | − | 433.554i | 0.0202069 | − | 0.519848i | ||||
\(835\) | −236.815 | − | 561.933i | −0.283611 | − | 0.672974i | ||||
\(836\) | −238.574 | − | 77.5175i | −0.285376 | − | 0.0927243i | ||||
\(837\) | 1033.39 | − | 1120.73i | 1.23463 | − | 1.33899i | ||||
\(838\) | −144.870 | + | 47.0713i | −0.172876 | + | 0.0561710i | ||||
\(839\) | 245.827 | + | 79.8739i | 0.293000 | + | 0.0952014i | 0.451829 | − | 0.892105i | \(-0.350772\pi\) |
−0.158829 | + | 0.987306i | \(0.550772\pi\) | |||||||
\(840\) | 380.676 | + | 250.762i | 0.453185 | + | 0.298526i | ||||
\(841\) | 214.162 | + | 659.123i | 0.254652 | + | 0.783737i | ||||
\(842\) | 562.014 | − | 408.327i | 0.667475 | − | 0.484949i | ||||
\(843\) | 145.850 | − | 395.854i | 0.173013 | − | 0.469577i | ||||
\(844\) | 589.855 | − | 428.555i | 0.698880 | − | 0.507766i | ||||
\(845\) | −322.436 | − | 765.100i | −0.381581 | − | 0.905444i | ||||
\(846\) | 140.205 | + | 581.849i | 0.165727 | + | 0.687765i | ||||
\(847\) | −560.611 | + | 771.615i | −0.661878 | + | 0.910997i | ||||
\(848\) | −70.9209 | + | 218.272i | −0.0836332 | + | 0.257397i | ||||
\(849\) | 194.769 | − | 528.627i | 0.229410 | − | 0.622647i | ||||
\(850\) | 49.7937 | − | 341.489i | 0.0585809 | − | 0.401752i | ||||
\(851\) | 927.485i | 1.08988i | ||||||||
\(852\) | 123.472 | + | 97.2540i | 0.144921 | + | 0.114148i | ||||
\(853\) | −631.627 | + | 869.360i | −0.740477 | + | 1.01918i | 0.258114 | + | 0.966114i | \(0.416899\pi\) |
−0.998591 | + | 0.0530648i | \(0.983101\pi\) | |||||||
\(854\) | −382.705 | + | 526.749i | −0.448133 | + | 0.616802i | ||||
\(855\) | 994.150 | − | 6.93997i | 1.16275 | − | 0.00811693i | ||||
\(856\) | −413.116 | + | 300.147i | −0.482613 | + | 0.350639i | ||||
\(857\) | 687.853 | 0.802629 | 0.401315 | − | 0.915940i | \(-0.368553\pi\) | ||||
0.401315 | + | 0.915940i | \(0.368553\pi\) | |||||||
\(858\) | 424.287 | − | 119.853i | 0.494507 | − | 0.139689i | ||||
\(859\) | 158.818 | + | 488.791i | 0.184887 | + | 0.569023i | 0.999946 | − | 0.0103539i | \(-0.00329582\pi\) |
−0.815060 | + | 0.579377i | \(0.803296\pi\) | |||||||
\(860\) | 27.9709 | + | 32.3453i | 0.0325243 | + | 0.0376108i | ||||
\(861\) | 329.366 | − | 418.159i | 0.382539 | − | 0.485666i | ||||
\(862\) | 441.765 | − | 143.538i | 0.512488 | − | 0.166518i | ||||
\(863\) | −183.034 | − | 563.322i | −0.212091 | − | 0.652748i | −0.999347 | − | 0.0361226i | \(-0.988499\pi\) |
0.787257 | − | 0.616625i | \(-0.211501\pi\) | |||||||
\(864\) | −149.763 | + | 29.9853i | −0.173337 | + | 0.0347052i | ||||
\(865\) | 83.8457 | + | 50.6748i | 0.0969314 | + | 0.0585836i | ||||
\(866\) | −333.931 | + | 108.501i | −0.385602 | + | 0.125290i | ||||
\(867\) | −559.288 | + | 157.988i | −0.645084 | + | 0.182224i | ||||
\(868\) | − | 1213.27i | − | 1.39778i | ||||||
\(869\) | 334.253 | + | 460.060i | 0.384641 | + | 0.529413i | ||||
\(870\) | 215.482 | + | 141.944i | 0.247681 | + | 0.163154i | ||||
\(871\) | 1322.15 | + | 960.596i | 1.51797 | + | 1.10287i | ||||
\(872\) | −68.4243 | − | 49.7132i | −0.0784683 | − | 0.0570105i | ||||
\(873\) | 245.293 | + | 399.530i | 0.280977 | + | 0.457652i | ||||
\(874\) | 902.005 | 1.03204 | ||||||||
\(875\) | 1037.16 | + | 853.272i | 1.18533 | + | 0.975168i | ||||
\(876\) | −66.2938 | + | 179.929i | −0.0756779 | + | 0.205399i | ||||
\(877\) | 1160.13 | + | 376.948i | 1.32283 | + | 0.429815i | 0.883467 | − | 0.468492i | \(-0.155203\pi\) |
0.439367 | + | 0.898308i | \(0.355203\pi\) | |||||||
\(878\) | −183.657 | − | 133.435i | −0.209177 | − | 0.151976i | ||||
\(879\) | −832.046 | − | 1244.12i | −0.946582 | − | 1.41538i | ||||
\(880\) | 110.568 | + | 25.8278i | 0.125646 | + | 0.0293497i | ||||
\(881\) | 224.081 | + | 308.421i | 0.254348 | + | 0.350080i | 0.917028 | − | 0.398822i | \(-0.130581\pi\) |
−0.662680 | + | 0.748903i | \(0.730581\pi\) | |||||||
\(882\) | −643.511 | − | 548.679i | −0.729604 | − | 0.622085i | ||||
\(883\) | −260.923 | − | 359.129i | −0.295496 | − | 0.406715i | 0.635294 | − | 0.772270i | \(-0.280879\pi\) |
−0.930789 | + | 0.365556i | \(0.880879\pi\) | |||||||
\(884\) | 339.847 | − | 110.423i | 0.384442 | − | 0.124913i | ||||
\(885\) | −1331.29 | + | 1063.75i | −1.50429 | + | 1.20197i | ||||
\(886\) | 23.6167 | − | 72.6847i | 0.0266554 | − | 0.0820369i | ||||
\(887\) | −79.2617 | − | 243.943i | −0.0893593 | − | 0.275020i | 0.896383 | − | 0.443280i | \(-0.146185\pi\) |
−0.985743 | + | 0.168260i | \(0.946185\pi\) | |||||||
\(888\) | −272.396 | − | 10.5882i | −0.306753 | − | 0.0119237i | ||||
\(889\) | 148.577 | − | 457.273i | 0.167128 | − | 0.514368i | ||||
\(890\) | 142.825 | + | 165.161i | 0.160477 | + | 0.185574i | ||||
\(891\) | −209.456 | − | 409.385i | −0.235080 | − | 0.459467i | ||||
\(892\) | −246.775 | − | 339.656i | −0.276653 | − | 0.380780i | ||||
\(893\) | 1038.86 | 1.16334 | ||||||||
\(894\) | −280.293 | − | 992.253i | −0.313527 | − | 1.10990i | ||||
\(895\) | 119.532 | + | 138.226i | 0.133555 | + | 0.154442i | ||||
\(896\) | −71.4505 | + | 98.3432i | −0.0797439 | + | 0.109758i | ||||
\(897\) | −1317.79 | + | 881.319i | −1.46911 | + | 0.982518i | ||||
\(898\) | 440.628 | + | 143.169i | 0.490678 | + | 0.159431i | ||||
\(899\) | − | 686.776i | − | 0.763934i | ||||||
\(900\) | −448.111 | + | 41.1909i | −0.497901 | + | 0.0457677i | ||||
\(901\) | −560.044 | −0.621580 | ||||||||
\(902\) | 40.9717 | − | 126.098i | 0.0454232 | − | 0.139798i | ||||
\(903\) | −76.6253 | − | 114.574i | −0.0848564 | − | 0.126881i | ||||
\(904\) | 223.970 | + | 162.724i | 0.247755 | + | 0.180004i | ||||
\(905\) | −618.227 | − | 1466.98i | −0.683123 | − | 1.62097i | ||||
\(906\) | −841.731 | + | 237.773i | −0.929063 | + | 0.262443i | ||||
\(907\) | − | 1145.21i | − | 1.26263i | −0.775525 | − | 0.631317i | \(-0.782515\pi\) | ||
0.775525 | − | 0.631317i | \(-0.217485\pi\) | |||||||
\(908\) | 180.585 | − | 131.203i | 0.198882 | − | 0.144496i | ||||
\(909\) | 393.004 | + | 162.402i | 0.432348 | + | 0.178660i | ||||
\(910\) | −316.332 | + | 1354.21i | −0.347618 | + | 1.48815i | ||||
\(911\) | 619.295 | + | 201.221i | 0.679797 | + | 0.220880i | 0.628507 | − | 0.777804i | \(-0.283667\pi\) |
0.0512906 | + | 0.998684i | \(0.483667\pi\) | |||||||
\(912\) | −10.2974 | + | 264.913i | −0.0112910 | + | 0.290475i | ||||
\(913\) | −169.247 | + | 54.9918i | −0.185375 | + | 0.0602320i | ||||
\(914\) | −620.192 | − | 201.512i | −0.678547 | − | 0.220473i | ||||
\(915\) | −29.4480 | − | 642.072i | −0.0321836 | − | 0.701719i | ||||
\(916\) | −8.42394 | − | 25.9262i | −0.00919644 | − | 0.0283037i | ||||
\(917\) | −601.826 | + | 437.252i | −0.656299 | + | 0.476829i | ||||
\(918\) | −182.521 | − | 324.957i | −0.198825 | − | 0.353984i | ||||
\(919\) | −228.741 | + | 166.190i | −0.248902 | + | 0.180838i | −0.705240 | − | 0.708969i | \(-0.749161\pi\) |
0.456338 | + | 0.889806i | \(0.349161\pi\) | |||||||
\(920\) | −406.818 | + | 34.5331i | −0.442193 | + | 0.0375360i | ||||
\(921\) | −701.750 | + | 469.320i | −0.761944 | + | 0.509576i | ||||
\(922\) | −160.627 | + | 221.084i | −0.174216 | + | 0.239787i | ||||
\(923\) | −148.173 | + | 456.031i | −0.160534 | + | 0.494074i | ||||
\(924\) | −343.423 | − | 126.532i | −0.371670 | − | 0.136939i | ||||
\(925\) | −794.757 | − | 115.886i | −0.859197 | − | 0.125283i | ||||
\(926\) | 85.9985i | 0.0928709i | ||||||||
\(927\) | 113.466 | + | 184.812i | 0.122401 | + | 0.199365i | ||||
\(928\) | −40.4447 | + | 55.6674i | −0.0435827 | + | 0.0599864i | ||||
\(929\) | 57.7599 | − | 79.4996i | 0.0621742 | − | 0.0855755i | −0.776798 | − | 0.629750i | \(-0.783157\pi\) |
0.838972 | + | 0.544175i | \(0.183157\pi\) | |||||||
\(930\) | 747.654 | + | 935.700i | 0.803929 | + | 1.00613i | ||||
\(931\) | −1187.55 | + | 862.802i | −1.27556 | + | 0.926748i | ||||
\(932\) | 5.14068 | 0.00551576 | ||||||||
\(933\) | −147.516 | − | 522.214i | −0.158109 | − | 0.559715i | ||||
\(934\) | −68.8016 | − | 211.750i | −0.0736634 | − | 0.226713i | ||||
\(935\) | 23.4355 | + | 276.082i | 0.0250647 | + | 0.295275i | ||||
\(936\) | −243.794 | − | 397.088i | −0.260463 | − | 0.424240i | ||||
\(937\) | −1108.39 | + | 360.137i | −1.18291 | + | 0.384351i | −0.833447 | − | 0.552599i | \(-0.813636\pi\) |
−0.349464 | + | 0.936950i | \(0.613636\pi\) | |||||||
\(938\) | −419.222 | − | 1290.23i | −0.446932 | − | 1.37552i | ||||
\(939\) | 537.459 | + | 423.334i | 0.572374 | + | 0.450835i | ||||
\(940\) | −468.543 | + | 39.7728i | −0.498450 | + | 0.0423115i | ||||
\(941\) | −1440.19 | + | 467.945i | −1.53049 | + | 0.497285i | −0.948733 | − | 0.316080i | \(-0.897633\pi\) |
−0.581753 | + | 0.813365i | \(0.697633\pi\) | |||||||
\(942\) | 61.7243 | + | 218.507i | 0.0655247 | + | 0.231961i | ||||
\(943\) | 476.753i | 0.505571i | ||||||||
\(944\) | −267.103 | − | 367.635i | −0.282948 | − | 0.389444i | ||||
\(945\) | 1449.76 | + | 46.2201i | 1.53413 | + | 0.0489101i | ||||
\(946\) | −27.7759 | − | 20.1804i | −0.0293614 | − | 0.0213323i | ||||
\(947\) | −1088.00 | − | 790.476i | −1.14889 | − | 0.834716i | −0.160555 | − | 0.987027i | \(-0.551329\pi\) |
−0.988333 | + | 0.152311i | \(0.951329\pi\) | |||||||
\(948\) | 371.874 | − | 472.127i | 0.392273 | − | 0.498024i | ||||
\(949\) | −584.991 | −0.616429 | ||||||||
\(950\) | −112.703 | + | 772.924i | −0.118635 | + | 0.813604i | ||||
\(951\) | 362.567 | + | 133.586i | 0.381248 | + | 0.140469i | ||||
\(952\) | −282.113 | − | 91.6641i | −0.296337 | − | 0.0962858i | ||||
\(953\) | −557.578 | − | 405.104i | −0.585076 | − | 0.425083i | 0.255474 | − | 0.966816i | \(-0.417768\pi\) |
−0.840551 | + | 0.541733i | \(0.817768\pi\) | |||||||
\(954\) | 171.075 | + | 709.960i | 0.179324 | + | 0.744193i | ||||
\(955\) | 102.004 | + | 1201.66i | 0.106811 | + | 1.25829i | ||||
\(956\) | −182.114 | − | 250.658i | −0.190495 | − | 0.262194i | ||||
\(957\) | −194.395 | − | 71.6237i | −0.203130 | − | 0.0748419i | ||||
\(958\) | −36.5280 | − | 50.2764i | −0.0381294 | − | 0.0524806i | ||||
\(959\) | 746.787 | − | 242.646i | 0.778715 | − | 0.253020i | ||||
\(960\) | −5.49790 | − | 119.874i | −0.00572698 | − | 0.124869i | ||||
\(961\) | 688.126 | − | 2117.83i | 0.716052 | − | 2.20378i | ||||
\(962\) | −256.991 | − | 790.936i | −0.267142 | − | 0.822179i | ||||
\(963\) | −620.544 | + | 1501.68i | −0.644387 | + | 1.55938i | ||||
\(964\) | −115.665 | + | 355.980i | −0.119984 | + | 0.369274i | ||||
\(965\) | 253.562 | + | 59.2299i | 0.262759 | + | 0.0613781i | ||||
\(966\) | 1315.03 | + | 51.1160i | 1.36131 | + | 0.0529151i | ||||
\(967\) | 694.997 | + | 956.581i | 0.718714 | + | 0.989225i | 0.999566 | + | 0.0294738i | \(0.00938317\pi\) |
−0.280851 | + | 0.959751i | \(0.590617\pi\) | |||||||
\(968\) | 251.076 | 0.259377 | ||||||||
\(969\) | −622.573 | + | 175.865i | −0.642491 | + | 0.181492i | ||||
\(970\) | −339.429 | + | 143.046i | −0.349927 | + | 0.147470i | ||||
\(971\) | 891.361 | − | 1226.85i | 0.917983 | − | 1.26350i | −0.0463832 | − | 0.998924i | \(-0.514770\pi\) |
0.964366 | − | 0.264571i | \(-0.0852305\pi\) | |||||||
\(972\) | −356.189 | + | 330.644i | −0.366450 | + | 0.340168i | ||||
\(973\) | −1045.02 | − | 339.546i | −1.07401 | − | 0.348968i | ||||
\(974\) | − | 1242.42i | − | 1.27559i | ||||||
\(975\) | −590.544 | − | 1239.33i | −0.605686 | − | 1.27111i | ||||
\(976\) | 171.399 | 0.175614 | ||||||||
\(977\) | −397.705 | + | 1224.01i | −0.407068 | + | 1.25283i | 0.512089 | + | 0.858932i | \(0.328872\pi\) |
−0.919156 | + | 0.393893i | \(0.871128\pi\) | |||||||
\(978\) | −890.679 | + | 595.672i | −0.910715 | + | 0.609072i | ||||
\(979\) | −141.829 | − | 103.045i | −0.144871 | − | 0.105255i | ||||
\(980\) | 502.568 | − | 434.602i | 0.512825 | − | 0.443471i | ||||
\(981\) | −268.311 | − | 20.8904i | −0.273507 | − | 0.0212950i | ||||
\(982\) | − | 679.312i | − | 0.691764i | ||||||
\(983\) | 608.165 | − | 441.858i | 0.618682 | − | 0.449499i | −0.233779 | − | 0.972290i | \(-0.575109\pi\) |
0.852461 | + | 0.522791i | \(0.175109\pi\) | |||||||
\(984\) | −140.019 | − | 5.44266i | −0.142296 | − | 0.00553115i | ||||
\(985\) | −386.653 | + | 334.363i | −0.392541 | + | 0.339454i | ||||
\(986\) | −159.691 | − | 51.8867i | −0.161958 | − | 0.0526234i | ||||
\(987\) | 1514.55 | + | 58.8717i | 1.53450 | + | 0.0596471i | ||||
\(988\) | −769.207 | + | 249.931i | −0.778550 | + | 0.252966i | ||||
\(989\) | 117.411 | + | 38.1491i | 0.118717 | + | 0.0385734i | ||||
\(990\) | 342.827 | − | 114.043i | 0.346289 | − | 0.115195i | ||||
\(991\) | 282.980 | + | 870.924i | 0.285550 | + | 0.878834i | 0.986233 | + | 0.165361i | \(0.0528788\pi\) |
−0.700683 | + | 0.713473i | \(0.747121\pi\) | |||||||
\(992\) | −258.392 | + | 187.733i | −0.260476 | + | 0.189247i | ||||
\(993\) | −818.722 | − | 301.653i | −0.824494 | − | 0.303780i | ||||
\(994\) | 322.022 | − | 233.962i | 0.323965 | − | 0.235375i | ||||
\(995\) | −261.654 | + | 1120.14i | −0.262969 | + | 1.12577i | ||||
\(996\) | 104.554 | + | 156.334i | 0.104974 | + | 0.156962i | ||||
\(997\) | −765.781 | + | 1054.01i | −0.768085 | + | 1.05718i | 0.228413 | + | 0.973564i | \(0.426646\pi\) |
−0.996498 | + | 0.0836142i | \(0.973354\pi\) | |||||||
\(998\) | −102.496 | + | 315.450i | −0.102701 | + | 0.316082i | ||||
\(999\) | −756.283 | + | 424.788i | −0.757040 | + | 0.425213i |
(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 | 150.3.i.a.29.18 | yes | 80 | |
3.2 | odd | 2 | inner | 150.3.i.a.29.2 | ✓ | 80 | |
25.19 | even | 10 | inner | 150.3.i.a.119.2 | yes | 80 | |
75.44 | odd | 10 | inner | 150.3.i.a.119.18 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.3.i.a.29.2 | ✓ | 80 | 3.2 | odd | 2 | inner | |
150.3.i.a.29.18 | yes | 80 | 1.1 | even | 1 | trivial | |
150.3.i.a.119.2 | yes | 80 | 25.19 | even | 10 | inner | |
150.3.i.a.119.18 | yes | 80 | 75.44 | odd | 10 | inner |