Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,2,Mod(113,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 0, 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("360.113");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.bs (of order \(12\), 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: | \(2.87461447277\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 113.9 | ||
Character | \(\chi\) | \(=\) | 360.113 |
Dual form | 360.2.bs.a.137.9 |
$q$-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 \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(217\) | \(271\) | \(281\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.254049 | − | 1.71332i | 0.146675 | − | 0.989185i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.831407 | − | 2.07576i | −0.371817 | − | 0.928306i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.77070 | − | 0.474457i | −0.669260 | − | 0.179328i | −0.0918386 | − | 0.995774i | \(-0.529274\pi\) |
−0.577422 | + | 0.816446i | \(0.695941\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.87092 | − | 0.870532i | −0.956973 | − | 0.290177i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.26602 | − | 0.730936i | 0.381719 | − | 0.220386i | −0.296847 | − | 0.954925i | \(-0.595935\pi\) |
0.678566 | + | 0.734539i | \(0.262602\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.80362 | + | 1.55507i | −1.60963 | + | 0.431300i | −0.947934 | − | 0.318468i | \(-0.896832\pi\) |
−0.661700 | + | 0.749768i | \(0.730165\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.76765 | + | 0.897122i | −0.972803 | + | 0.231636i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.23679 | + | 5.23679i | 1.27011 | + | 1.27011i | 0.946030 | + | 0.324078i | \(0.105054\pi\) |
0.324078 | + | 0.946030i | \(0.394946\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 7.79507i | − | 1.78831i | −0.447757 | − | 0.894155i | \(-0.647777\pi\) | ||
0.447757 | − | 0.894155i | \(-0.352223\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.26274 | + | 2.91323i | −0.275552 | + | 0.635719i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.159588 | − | 0.595592i | −0.0332765 | − | 0.124190i | 0.947290 | − | 0.320378i | \(-0.103810\pi\) |
−0.980566 | + | 0.196189i | \(0.937143\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.61752 | + | 3.45160i | −0.723505 | + | 0.690319i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.22085 | + | 4.69764i | −0.427403 | + | 0.904061i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.16701 | − | 3.75337i | −0.402404 | − | 0.696983i | 0.591612 | − | 0.806223i | \(-0.298492\pi\) |
−0.994015 | + | 0.109240i | \(0.965158\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.30635 | − | 7.45881i | 0.773443 | − | 1.33964i | −0.162223 | − | 0.986754i | \(-0.551866\pi\) |
0.935666 | − | 0.352888i | \(-0.114800\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.930696 | − | 2.35479i | −0.162013 | − | 0.409916i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.487314 | + | 4.07000i | 0.0823710 | + | 0.687955i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.01827 | − | 2.01827i | 0.331802 | − | 0.331802i | −0.521469 | − | 0.853271i | \(-0.674616\pi\) |
0.853271 | + | 0.521469i | \(0.174616\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.18994 | + | 10.3385i | 0.190542 | + | 1.65549i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.08175 | + | 0.624550i | 0.168941 | + | 0.0975383i | 0.582087 | − | 0.813127i | \(-0.302236\pi\) |
−0.413145 | + | 0.910665i | \(0.635570\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00528 | − | 3.75176i | 0.153304 | − | 0.572137i | −0.845941 | − | 0.533277i | \(-0.820960\pi\) |
0.999245 | − | 0.0388607i | \(-0.0123729\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.579890 | + | 6.68309i | 0.0864449 | + | 0.996257i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.559597 | − | 2.08844i | 0.0816256 | − | 0.304631i | −0.913028 | − | 0.407896i | \(-0.866262\pi\) |
0.994654 | + | 0.103265i | \(0.0329291\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.15192 | − | 1.81976i | −0.450275 | − | 0.259966i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.3027 | − | 7.64189i | 1.44266 | − | 1.07008i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.07847 | − | 4.07847i | 0.560221 | − | 0.560221i | −0.369149 | − | 0.929370i | \(-0.620351\pi\) |
0.929370 | + | 0.369149i | \(0.120351\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.56982 | − | 2.02024i | −0.346515 | − | 0.272409i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −13.3554 | − | 1.98033i | −1.76897 | − | 0.262301i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.12738 | − | 8.88087i | 0.667527 | − | 1.15619i | −0.311066 | − | 0.950388i | \(-0.600686\pi\) |
0.978593 | − | 0.205803i | \(-0.0659806\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.400201 | + | 0.693169i | 0.0512405 | + | 0.0887512i | 0.890508 | − | 0.454968i | \(-0.150349\pi\) |
−0.839267 | + | 0.543719i | \(0.817016\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.67049 | + | 2.90357i | 0.588427 | + | 0.365816i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.05313 | + | 10.7540i | 0.998867 | + | 1.33387i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.72680 | + | 6.44449i | 0.210962 | + | 0.787319i | 0.987549 | + | 0.157310i | \(0.0502822\pi\) |
−0.776588 | + | 0.630009i | \(0.783051\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.06098 | + | 0.122116i | −0.127727 | + | 0.0147011i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.50776i | 0.891008i | 0.895280 | + | 0.445504i | \(0.146975\pi\) | ||||
−0.895280 | + | 0.445504i | \(0.853025\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.173786 | + | 0.173786i | 0.0203401 | + | 0.0203401i | 0.717204 | − | 0.696864i | \(-0.245422\pi\) |
−0.696864 | + | 0.717204i | \(0.745422\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.99466 | + | 7.07484i | 0.576733 | + | 0.816933i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.58853 | + | 0.693595i | −0.294991 | + | 0.0790425i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.61017 | − | 1.50698i | 0.293667 | − | 0.169549i | −0.345927 | − | 0.938261i | \(-0.612436\pi\) |
0.639594 | + | 0.768713i | \(0.279102\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.48435 | + | 4.99846i | 0.831594 | + | 0.555384i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.38340 | + | 1.97838i | 0.810433 | + | 0.217155i | 0.640160 | − | 0.768242i | \(-0.278868\pi\) |
0.170273 | + | 0.985397i | \(0.445535\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.51639 | − | 15.2242i | 0.706802 | − | 1.65130i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.98124 | + | 2.75924i | −0.748468 | + | 0.295821i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.3650 | 1.31069 | 0.655343 | − | 0.755332i | \(-0.272524\pi\) | ||||
0.655343 | + | 0.755332i | \(0.272524\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.0143 | 1.15461 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −11.6853 | − | 9.27304i | −1.21171 | − | 0.961570i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −16.1807 | + | 6.48088i | −1.66010 | + | 0.664924i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.515150 | + | 0.138034i | 0.0523055 | + | 0.0140152i | 0.284877 | − | 0.958564i | \(-0.408047\pi\) |
−0.232571 | + | 0.972579i | \(0.574714\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.27094 | + | 0.996348i | −0.429246 | + | 0.100137i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.43379 | − | 2.55985i | 0.441179 | − | 0.254715i | −0.262919 | − | 0.964818i | \(-0.584685\pi\) |
0.704098 | + | 0.710103i | \(0.251352\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.8189 | + | 3.70276i | −1.36161 | + | 0.364843i | −0.864409 | − | 0.502789i | \(-0.832307\pi\) |
−0.497205 | + | 0.867633i | \(0.665640\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.09700 | + | 0.199055i | 0.692597 | + | 0.0194257i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.72473 | + | 2.72473i | 0.263409 | + | 0.263409i | 0.826438 | − | 0.563028i | \(-0.190364\pi\) |
−0.563028 | + | 0.826438i | \(0.690364\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.1331i | 1.44949i | 0.689017 | + | 0.724745i | \(0.258042\pi\) | ||||
−0.689017 | + | 0.724745i | \(0.741958\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.94520 | − | 3.97068i | −0.279546 | − | 0.376881i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.175699 | − | 0.655717i | −0.0165284 | − | 0.0616847i | 0.957169 | − | 0.289529i | \(-0.0934988\pi\) |
−0.973697 | + | 0.227845i | \(0.926832\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.10362 | + | 0.826446i | −0.102913 | + | 0.0770665i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 18.0155 | + | 0.587745i | 1.66553 | + | 0.0543370i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.78813 | − | 11.7574i | −0.622267 | − | 1.07780i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.43146 | + | 7.67552i | −0.402860 | + | 0.697775i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.34487 | − | 1.69472i | 0.121263 | − | 0.152808i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.1723 | + | 4.63941i | 0.909839 | + | 0.414962i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.70790 | + | 2.70790i | −0.240287 | + | 0.240287i | −0.816969 | − | 0.576682i | \(-0.804347\pi\) |
0.576682 | + | 0.816969i | \(0.304347\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.17256 | − | 2.67549i | −0.543464 | − | 0.235564i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.28977 | + | 0.744648i | 0.112688 | + | 0.0650602i | 0.555284 | − | 0.831661i | \(-0.312609\pi\) |
−0.442597 | + | 0.896721i | \(0.645943\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.69842 | + | 13.8027i | −0.320694 | + | 1.19685i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.5976 | + | 0.704295i | 0.998161 | + | 0.0606161i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.14839 | − | 19.2141i | 0.439857 | − | 1.64157i | −0.289312 | − | 0.957235i | \(-0.593427\pi\) |
0.729169 | − | 0.684334i | \(-0.239907\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.84605 | + | 4.52992i | 0.665493 | + | 0.384223i | 0.794367 | − | 0.607438i | \(-0.207803\pi\) |
−0.128874 | + | 0.991661i | \(0.541136\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.43601 | − | 1.48933i | −0.289364 | − | 0.125425i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.21083 | + | 6.21083i | −0.519376 | + | 0.519376i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.98941 | + | 7.61876i | −0.497394 | + | 0.632704i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.91858 | + | 4.93794i | −0.323199 | + | 0.407274i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.39200 | + | 7.60718i | −0.359807 | + | 0.623204i | −0.987928 | − | 0.154911i | \(-0.950491\pi\) |
0.628121 | + | 0.778115i | \(0.283824\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.02080 | − | 10.4283i | −0.489966 | − | 0.848645i | 0.509968 | − | 0.860194i | \(-0.329657\pi\) |
−0.999933 | + | 0.0115482i | \(0.996324\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.4756 | − | 19.5932i | −0.846902 | − | 1.58402i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.0630 | − | 2.73761i | −1.53118 | − | 0.219890i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.14188 | − | 7.99361i | −0.170941 | − | 0.637959i | −0.997208 | − | 0.0746804i | \(-0.976206\pi\) |
0.826267 | − | 0.563279i | \(-0.190460\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.95159 | − | 8.02385i | −0.471992 | − | 0.636332i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.13033i | 0.0890825i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.1653 | − | 15.1653i | −1.18784 | − | 1.18784i | −0.977663 | − | 0.210178i | \(-0.932596\pi\) |
−0.210178 | − | 0.977663i | \(-0.567404\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.11417 | + | 3.88968i | −0.320288 | + | 0.302812i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.34829 | + | 2.23692i | −0.646010 | + | 0.173098i | −0.566924 | − | 0.823770i | \(-0.691867\pi\) |
−0.0790857 | + | 0.996868i | \(0.525200\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 20.0054 | − | 11.5501i | 1.53888 | − | 0.888471i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.78586 | + | 22.3790i | −0.518928 | + | 1.71137i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.52603 | + | 2.55249i | 0.724250 | + | 0.194062i | 0.602067 | − | 0.798445i | \(-0.294344\pi\) |
0.122183 | + | 0.992508i | \(0.461011\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.04317 | − | 4.39537i | 0.608006 | − | 0.332259i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −13.9132 | − | 11.0410i | −1.04578 | − | 0.829892i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.0695 | −1.12635 | −0.563175 | − | 0.826338i | \(-0.690420\pi\) | ||||
−0.563175 | + | 0.826338i | \(0.690420\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.20300 | 0.386736 | 0.193368 | − | 0.981126i | \(-0.438059\pi\) | ||||
0.193368 | + | 0.981126i | \(0.438059\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.28929 | − | 0.509573i | 0.0953070 | − | 0.0376687i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.86745 | − | 2.51143i | −0.431383 | − | 0.184644i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.4576 | + | 2.80211i | 0.764738 | + | 0.204911i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.16128 | − | 7.26439i | 0.448167 | − | 0.528407i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.00774 | − | 3.46857i | 0.434705 | − | 0.250977i | −0.266644 | − | 0.963795i | \(-0.585915\pi\) |
0.701349 | + | 0.712818i | \(0.252582\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.43559 | + | 0.920564i | −0.247299 | + | 0.0662636i | −0.380339 | − | 0.924847i | \(-0.624193\pi\) |
0.133040 | + | 0.991111i | \(0.457526\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 20.4709 | − | 11.0655i | 1.46595 | − | 0.792419i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.5113 | − | 13.5113i | −0.962643 | − | 0.962643i | 0.0366836 | − | 0.999327i | \(-0.488321\pi\) |
−0.999327 | + | 0.0366836i | \(0.988321\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 3.62623i | − | 0.257057i | −0.991706 | − | 0.128528i | \(-0.958975\pi\) | ||
0.991706 | − | 0.128528i | \(-0.0410253\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.4801 | − | 1.32134i | 0.809747 | − | 0.0931999i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.05630 | + | 7.67423i | 0.144324 | + | 0.538625i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.397036 | − | 2.76471i | 0.0277302 | − | 0.193096i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.0603169 | + | 1.84882i | −0.00419231 | + | 0.128502i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.69770 | − | 9.86870i | −0.394118 | − | 0.682632i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.18158 | + | 2.04656i | −0.0813433 | + | 0.140891i | −0.903827 | − | 0.427898i | \(-0.859254\pi\) |
0.822484 | + | 0.568788i | \(0.192588\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.8632 | + | 1.90734i | 0.881371 | + | 0.130689i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.62353 | + | 1.03252i | −0.588120 | + | 0.0704174i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.1641 | + | 11.1641i | −0.757869 | + | 0.757869i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.341901 | − | 0.253601i | 0.0231035 | − | 0.0171367i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −38.5359 | − | 22.2487i | −2.59221 | − | 1.49661i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.96195 | + | 14.7862i | −0.265312 | + | 0.990157i | 0.696747 | + | 0.717317i | \(0.254630\pi\) |
−0.962059 | + | 0.272841i | \(0.912037\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.3903 | − | 6.76008i | 0.892690 | − | 0.450672i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.56474 | − | 9.57172i | 0.170227 | − | 0.635297i | −0.827088 | − | 0.562072i | \(-0.810004\pi\) |
0.997315 | − | 0.0732250i | \(-0.0233291\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.54945 | + | 4.35868i | 0.498882 | + | 0.288030i | 0.728252 | − | 0.685310i | \(-0.240333\pi\) |
−0.229370 | + | 0.973339i | \(0.573667\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.530736 | + | 4.61119i | 0.0349199 | + | 0.303394i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.0201 | + | 20.0201i | −1.31156 | + | 1.31156i | −0.391295 | + | 0.920265i | \(0.627973\pi\) |
−0.920265 | + | 0.391295i | \(0.872027\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.80035 | + | 0.574761i | −0.313141 | + | 0.0374933i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.91883 | − | 4.85490i | −0.124641 | − | 0.315359i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.254031 | + | 0.439994i | −0.0164319 | + | 0.0284608i | −0.874124 | − | 0.485702i | \(-0.838564\pi\) |
0.857693 | + | 0.514163i | \(0.171897\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.88251 | − | 6.72471i | −0.250095 | − | 0.433177i | 0.713457 | − | 0.700699i | \(-0.247128\pi\) |
−0.963552 | + | 0.267522i | \(0.913795\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.4653 | − | 11.5532i | 0.671351 | − | 0.741139i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.15685 | + | 8.05559i | −0.0739086 | + | 0.514653i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.1219 | + | 45.2396i | 0.771299 | + | 2.87853i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.26533 | − | 12.1475i | 0.333677 | − | 0.769817i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.5557i | 0.918750i | 0.888242 | + | 0.459375i | \(0.151927\pi\) | ||||
−0.888242 | + | 0.459375i | \(0.848073\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.637382 | − | 0.637382i | −0.0400718 | − | 0.0400718i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −24.4284 | − | 15.0323i | −1.52977 | − | 0.941362i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.7382 | − | 5.28884i | 1.23124 | − | 0.329909i | 0.416176 | − | 0.909284i | \(-0.363370\pi\) |
0.815061 | + | 0.579375i | \(0.196703\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.53133 | + | 2.61616i | −0.281563 | + | 0.162561i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.95388 | + | 12.6621i | 0.182840 | + | 0.783763i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.1042 | + | 4.31511i | 0.993028 | + | 0.266081i | 0.718522 | − | 0.695504i | \(-0.244819\pi\) |
0.274506 | + | 0.961585i | \(0.411486\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.8568 | − | 5.07504i | −0.728356 | − | 0.311757i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.14131 | − | 21.1851i | 0.192245 | − | 1.29651i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.1547 | −0.924001 | −0.462001 | − | 0.886880i | \(-0.652868\pi\) | ||||
−0.462001 | + | 0.886880i | \(0.652868\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.8037 | 1.14225 | 0.571123 | − | 0.820864i | \(-0.306508\pi\) | ||||
0.571123 | + | 0.820864i | \(0.306508\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.79816 | − | 18.8709i | 0.169352 | − | 1.14212i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.05696 | + | 7.01397i | −0.124039 | + | 0.422958i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.2663 | + | 5.16238i | 1.15760 | + | 0.310177i | 0.786006 | − | 0.618219i | \(-0.212145\pi\) |
0.371592 | + | 0.928396i | \(0.378812\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −18.8563 | + | 17.6648i | −1.12890 | + | 1.05757i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.01544 | + | 2.31831i | −0.239541 | + | 0.138299i | −0.614966 | − | 0.788554i | \(-0.710830\pi\) |
0.375425 | + | 0.926853i | \(0.377497\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.4603 | − | 5.75027i | 1.27568 | − | 0.341818i | 0.443478 | − | 0.896285i | \(-0.353745\pi\) |
0.832206 | + | 0.554467i | \(0.187078\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.99313 | + | 29.3691i | 0.414237 | + | 1.73967i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.61913 | − | 1.61913i | −0.0955743 | − | 0.0955743i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 37.8479i | 2.22635i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.367369 | − | 0.847548i | 0.0215356 | − | 0.0496841i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.41478 | + | 20.2082i | 0.316335 | + | 1.18058i | 0.922741 | + | 0.385422i | \(0.125944\pi\) |
−0.606406 | + | 0.795155i | \(0.707389\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −22.6975 | − | 3.25955i | −1.32150 | − | 0.189779i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.622035 | + | 7.57060i | 0.0360941 | + | 0.439291i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.85238 | + | 3.20842i | 0.107126 | + | 0.185547i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.56009 | + | 6.16626i | −0.205200 | + | 0.355417i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.25944 | − | 8.24683i | −0.187250 | − | 0.473768i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.10612 | − | 1.40703i | 0.0633362 | − | 0.0805660i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.56011 | − | 2.56011i | 0.146113 | − | 0.146113i | −0.630266 | − | 0.776379i | \(-0.717054\pi\) |
0.776379 | + | 0.630266i | \(0.217054\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.83333 | + | 24.6168i | 0.161183 | + | 1.40040i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.91524 | − | 5.14722i | −0.505537 | − | 0.291872i | 0.225460 | − | 0.974252i | \(-0.427611\pi\) |
−0.730997 | + | 0.682381i | \(0.760945\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.629684 | + | 2.35001i | −0.0355918 | + | 0.132830i | −0.981436 | − | 0.191791i | \(-0.938570\pi\) |
0.945844 | + | 0.324622i | \(0.105237\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.14403 | − | 12.1089i | 0.120802 | − | 0.682257i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.26665 | + | 4.72720i | −0.0711422 | + | 0.265506i | −0.992331 | − | 0.123610i | \(-0.960553\pi\) |
0.921189 | + | 0.389116i | \(0.127220\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.48695 | − | 3.16789i | −0.307210 | − | 0.177368i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.36054 | − | 3.97611i | 0.299196 | − | 0.221925i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 40.8211 | − | 40.8211i | 2.27135 | − | 2.27135i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.6272 | − | 25.6573i | 0.866843 | − | 1.42321i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 25.9278 | + | 3.84455i | 1.43381 | + | 0.212604i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.98175 | + | 3.43250i | −0.109258 | + | 0.189240i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.76782 | − | 16.9184i | −0.536888 | − | 0.929918i | −0.999069 | − | 0.0431321i | \(-0.986266\pi\) |
0.462181 | − | 0.886786i | \(-0.347067\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.55127 | + | 4.03732i | −0.413807 | + | 0.221244i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.9415 | − | 8.94240i | 0.652434 | − | 0.488575i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.15676 | + | 4.31709i | 0.0630127 | + | 0.235167i | 0.990249 | − | 0.139311i | \(-0.0444887\pi\) |
−0.927236 | + | 0.374478i | \(0.877822\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.16809 | + | 0.134444i | −0.0634418 | + | 0.00730200i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 12.5907i | − | 0.681822i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.7914 | + | 13.7914i | 0.744664 | + | 0.744664i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.13559 | + | 2.10081i | 0.0611382 | + | 0.113104i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.4554 | + | 3.87331i | −0.776006 | + | 0.207930i | −0.625023 | − | 0.780606i | \(-0.714911\pi\) |
−0.150983 | + | 0.988536i | \(0.548244\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.3093 | − | 8.26145i | 0.765957 | − | 0.442225i | −0.0654736 | − | 0.997854i | \(-0.520856\pi\) |
0.831430 | + | 0.555629i | \(0.187522\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.58380 | − | 30.7169i | 0.298041 | − | 1.63955i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.2963 | + | 7.04608i | 1.39961 | + | 0.375025i | 0.878206 | − | 0.478283i | \(-0.158741\pi\) |
0.521407 | + | 0.853308i | \(0.325407\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.5843 | − | 6.24201i | 0.827128 | − | 0.331291i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −21.8687 | + | 8.64328i | −1.15741 | + | 0.457451i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.0540 | 1.26952 | 0.634760 | − | 0.772709i | \(-0.281099\pi\) | ||||
0.634760 | + | 0.772709i | \(0.281099\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −41.7631 | −2.19806 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.0248 | + | 9.54246i | 0.631138 | + | 0.500849i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.216250 | − | 0.505224i | 0.0113191 | − | 0.0264446i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.9352 | − | 6.68136i | −1.30161 | − | 0.348764i | −0.459549 | − | 0.888152i | \(-0.651989\pi\) |
−0.842057 | + | 0.539388i | \(0.818656\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.56193 | − | 2.73473i | −0.133369 | − | 0.142364i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.15679 | + | 5.28667i | −0.475397 | + | 0.274470i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.2848 | − | 3.55965i | 0.687861 | − | 0.184312i | 0.102074 | − | 0.994777i | \(-0.467452\pi\) |
0.585787 | + | 0.810465i | \(0.300785\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.5331 | − | 16.2498i | 0.543924 | − | 0.839134i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.4133 | + | 18.4133i | 0.948331 | + | 0.948331i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.7180i | 1.06421i | 0.846677 | + | 0.532107i | \(0.178599\pi\) | ||||
−0.846677 | + | 0.532107i | \(0.821401\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.95155 | + | 5.32743i | 0.202444 | + | 0.272932i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.40046 | + | 12.6907i | 0.173755 | + | 0.648464i | 0.996760 | + | 0.0804295i | \(0.0256292\pi\) |
−0.823005 | + | 0.568034i | \(0.807704\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.59186 | + | 4.79650i | 0.183058 | + | 0.244452i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.15210 | + | 9.89586i | −0.312729 | + | 0.503035i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.34592 | − | 12.7235i | −0.372453 | − | 0.645108i | 0.617489 | − | 0.786579i | \(-0.288150\pi\) |
−0.989942 | + | 0.141472i | \(0.954817\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.28326 | − | 3.95472i | 0.115469 | − | 0.199999i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.60348 | − | 2.02061i | 0.0808850 | − | 0.101926i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.29824 | − | 4.16516i | −0.266583 | − | 0.209572i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.3106 | − | 21.3106i | 1.06955 | − | 1.06955i | 0.0721575 | − | 0.997393i | \(-0.477012\pi\) |
0.997393 | − | 0.0721575i | \(-0.0229884\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 22.7088 | + | 9.84313i | 1.13686 | + | 0.492773i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.3918 | + | 18.1240i | 1.56763 | + | 0.905071i | 0.996445 | + | 0.0842496i | \(0.0268493\pi\) |
0.571185 | + | 0.820822i | \(0.306484\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.3934 | + | 49.9848i | −0.667172 | + | 2.48992i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.15303 | − | 19.6914i | 0.206366 | − | 0.978475i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.07994 | − | 4.03040i | 0.0535308 | − | 0.199780i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.1733 | + | 9.33767i | 0.799719 | + | 0.461718i | 0.843373 | − | 0.537329i | \(-0.180567\pi\) |
−0.0436539 | + | 0.999047i | \(0.513900\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −31.6119 | − | 13.7021i | −1.55930 | − | 0.675877i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.2926 | + | 13.2926i | −0.654087 | + | 0.654087i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.03199 | − | 16.9710i | −0.0997463 | − | 0.833072i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.75447 | − | 12.2920i | 0.477679 | − | 0.601940i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.61327 | − | 13.1866i | 0.371933 | − | 0.644206i | −0.617930 | − | 0.786233i | \(-0.712029\pi\) |
0.989863 | + | 0.142027i | \(0.0453619\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.527028 | − | 0.912840i | −0.0256858 | − | 0.0444891i | 0.852897 | − | 0.522080i | \(-0.174844\pi\) |
−0.878583 | + | 0.477590i | \(0.841510\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.42462 | + | 5.50861i | −0.166511 | + | 0.267838i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −37.0195 | − | 0.868924i | −1.79571 | − | 0.0421490i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.379756 | − | 1.41727i | −0.0183777 | − | 0.0685865i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.06327 | + | 12.2190i | 0.437579 | + | 0.589938i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.98631i | 0.432855i | 0.976299 | + | 0.216428i | \(0.0694406\pi\) | ||||
−0.976299 | + | 0.216428i | \(0.930559\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.68320 | − | 6.68320i | −0.321174 | − | 0.321174i | 0.528043 | − | 0.849217i | \(-0.322926\pi\) |
−0.849217 | + | 0.528043i | \(0.822926\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.5318 | + | 12.1973i | 0.552906 | + | 0.584816i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.64268 | + | 1.24400i | −0.222089 | + | 0.0595087i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.4340 | − | 17.5711i | 1.45253 | − | 0.838620i | 0.453909 | − | 0.891048i | \(-0.350029\pi\) |
0.998625 | + | 0.0524278i | \(0.0166959\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.46475 | + | 7.96824i | 0.355464 | + | 0.379440i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.6926 | − | 3.13303i | −0.555533 | − | 0.148855i | −0.0298795 | − | 0.999554i | \(-0.509512\pi\) |
−0.525653 | + | 0.850699i | \(0.676179\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.2803 | − | 25.6667i | −0.487335 | − | 1.21672i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.9177 | + | 9.45749i | 0.563689 | + | 0.447324i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.8523 | −1.12566 | −0.562830 | − | 0.826573i | \(-0.690287\pi\) | ||||
−0.562830 | + | 0.826573i | \(0.690287\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.82602 | 0.0859841 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −19.3966 | + | 7.66624i | −0.911333 | + | 0.360191i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.15733 | − | 22.8629i | −0.429302 | − | 1.07183i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.1504 | − | 7.54288i | −1.31682 | − | 0.352841i | −0.469035 | − | 0.883180i | \(-0.655398\pi\) |
−0.847786 | + | 0.530339i | \(0.822065\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −36.2307 | + | 12.9704i | −1.69110 | + | 0.605407i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.5491 | + | 17.6375i | −1.42281 | + | 0.821462i | −0.996539 | − | 0.0831308i | \(-0.973508\pi\) |
−0.426276 | + | 0.904593i | \(0.640175\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.7523 | + | 9.84776i | −1.70803 | + | 0.457664i | −0.974939 | − | 0.222471i | \(-0.928588\pi\) |
−0.733086 | + | 0.680135i | \(0.761921\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.53333 | + | 31.9655i | −0.442098 | + | 1.48236i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.21539 | − | 8.21539i | −0.380163 | − | 0.380163i | 0.490998 | − | 0.871161i | \(-0.336632\pi\) |
−0.871161 | + | 0.490998i | \(0.836632\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 12.2305i | − | 0.564753i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.2397 | + | 1.63896i | −0.656132 | + | 0.0755192i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.46959 | − | 5.48459i | −0.0675719 | − | 0.252182i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 26.9054 | + | 28.1988i | 1.23451 | + | 1.29385i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −15.2594 | + | 8.15852i | −0.698680 | + | 0.373553i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.9516 | + | 29.3611i | 0.774540 | + | 1.34154i | 0.935053 | + | 0.354508i | \(0.115352\pi\) |
−0.160513 | + | 0.987034i | \(0.551315\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.57472 | + | 14.8518i | −0.390974 | + | 0.677186i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.93661 | + | 0.287159i | 0.0881190 | + | 0.0130662i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.141774 | − | 1.18409i | −0.00643765 | − | 0.0537666i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.1199 | − | 25.1199i | 1.13829 | − | 1.13829i | 0.149532 | − | 0.988757i | \(-0.452223\pi\) |
0.988757 | − | 0.149532i | \(-0.0477768\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −29.8358 | + | 22.1303i | −1.34922 | + | 1.00077i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.6088 | + | 7.27970i | 0.569027 | + | 0.328528i | 0.756761 | − | 0.653692i | \(-0.226781\pi\) |
−0.187733 | + | 0.982220i | \(0.560114\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.30744 | − | 31.0038i | 0.374148 | − | 1.39634i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.61907 | + | 8.03706i | 0.252558 | + | 0.361239i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.56211 | − | 13.2940i | 0.159782 | − | 0.596316i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −34.7190 | − | 20.0450i | −1.55424 | − | 0.897339i | −0.997789 | − | 0.0664573i | \(-0.978830\pi\) |
−0.556448 | − | 0.830882i | \(-0.687836\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.71168 | + | 14.8716i | 0.0764722 | + | 0.664412i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.0724 | − | 14.0724i | 0.627459 | − | 0.627459i | −0.319969 | − | 0.947428i | \(-0.603672\pi\) |
0.947428 | + | 0.319969i | \(0.103672\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.99992 | − | 7.07519i | −0.400491 | − | 0.314842i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.7067 | − | 37.2099i | −0.653147 | − | 1.65255i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.24682 | − | 9.08776i | 0.232561 | − | 0.402808i | −0.726000 | − | 0.687695i | \(-0.758623\pi\) |
0.958561 | + | 0.284887i | \(0.0919560\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.225268 | − | 0.390176i | −0.00996528 | − | 0.0172604i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 36.6184 | + | 17.3117i | 1.61674 | + | 0.764330i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 19.1751 | + | 25.6061i | 0.844957 | + | 1.12834i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.818060 | − | 3.05304i | −0.0359782 | − | 0.134273i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.79330 | − | 15.6727i | 0.298193 | − | 0.687953i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 20.4281i | − | 0.894970i | −0.894291 | − | 0.447485i | \(-0.852320\pi\) | ||
0.894291 | − | 0.447485i | \(-0.147680\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.6965 | − | 24.6965i | −1.07990 | − | 1.07990i | −0.996517 | − | 0.0833870i | \(-0.973426\pi\) |
−0.0833870 | − | 0.996517i | \(-0.526574\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.48731 | − | 14.8971i | −0.239486 | − | 0.650165i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 61.6116 | − | 16.5088i | 2.68385 | − | 0.719134i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.5893 | − | 11.3099i | 0.851710 | − | 0.491735i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −22.4514 | + | 21.0327i | −0.974306 | + | 0.912742i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.24930 | − | 1.94244i | −0.314002 | − | 0.0841366i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.39051 | − | 7.92123i | 0.146585 | − | 0.342465i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.82839 | + | 25.8189i | −0.165207 | + | 1.11417i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.32052 | −0.229171 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.43317 | 0.0616167 | 0.0308083 | − | 0.999525i | \(-0.490192\pi\) | ||||
0.0308083 | + | 0.999525i | \(0.490192\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.32182 | − | 8.91440i | 0.0567246 | − | 0.382554i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 31.4127 | − | 12.5818i | 1.34557 | − | 0.538944i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.2567 | − | 8.64315i | −1.37920 | − | 0.369554i | −0.508366 | − | 0.861141i | \(-0.669750\pi\) |
−0.870829 | + | 0.491587i | \(0.836417\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.545519 | − | 2.33842i | −0.0232822 | − | 0.0998013i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −29.2578 | + | 16.8920i | −1.24642 | + | 0.719623i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.33681 | + | 1.42999i | −0.226944 | + | 0.0608096i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.79350 | + | 9.41478i | −0.245921 | + | 0.399635i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.50833 | + | 7.50833i | 0.318138 | + | 0.318138i | 0.848052 | − | 0.529913i | \(-0.177776\pi\) |
−0.529913 | + | 0.848052i | \(0.677776\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.3370i | 0.987052i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.45766 | − | 17.2054i | 0.314863 | − | 0.726412i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.30163 | + | 8.58979i | 0.0970020 | + | 0.362017i | 0.997315 | − | 0.0732258i | \(-0.0233294\pi\) |
−0.900313 | + | 0.435242i | \(0.856663\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.21503 | + | 0.909876i | −0.0511167 | + | 0.0382788i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −10.8810 | − | 12.4017i | −0.456957 | − | 0.520824i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.40287 | − | 2.42983i | −0.0588112 | − | 0.101864i | 0.835121 | − | 0.550067i | \(-0.185398\pi\) |
−0.893932 | + | 0.448203i | \(0.852064\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.8577 | − | 22.2702i | 0.538078 | − | 0.931978i | −0.460930 | − | 0.887437i | \(-0.652484\pi\) |
0.999008 | − | 0.0445413i | \(-0.0141826\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.41651 | − | 11.1744i | −0.184502 | − | 0.466815i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.63306 | + | 1.60373i | 0.109806 | + | 0.0668803i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.0019 | − | 13.0019i | 0.541278 | − | 0.541278i | −0.382625 | − | 0.923904i | \(-0.624980\pi\) |
0.923904 | + | 0.382625i | \(0.124980\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.704411 | + | 6.12013i | 0.0292743 | + | 0.254344i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.1351 | − | 7.00620i | −0.503449 | − | 0.290666i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.18232 | − | 8.14452i | 0.0903824 | − | 0.337312i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −13.7582 | − | 37.8843i | −0.568830 | − | 1.56632i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.405924 | + | 1.51493i | −0.0167543 | + | 0.0625278i | −0.973797 | − | 0.227420i | \(-0.926971\pi\) |
0.957043 | + | 0.289947i | \(0.0936378\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −58.1419 | − | 33.5683i | −2.39570 | − | 1.38316i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −26.5818 | + | 19.7167i | −1.09343 | + | 0.811036i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.47807 | + | 3.47807i | −0.142827 | + | 0.142827i | −0.774905 | − | 0.632078i | \(-0.782202\pi\) |
0.632078 | + | 0.774905i | \(0.282202\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.7618 | + | 23.8657i | −0.769158 | + | 0.978398i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.21289 | − | 0.921239i | −0.254277 | − | 0.0377038i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.1505 | − | 26.2415i | 0.619033 | − | 1.07220i | −0.370629 | − | 0.928781i | \(-0.620858\pi\) |
0.989662 | − | 0.143416i | \(-0.0458088\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.302116 | + | 0.523281i | 0.0123236 | + | 0.0213451i | 0.872121 | − | 0.489290i | \(-0.162744\pi\) |
−0.859798 | + | 0.510635i | \(0.829411\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.652647 | − | 20.0048i | 0.0265778 | − | 0.814660i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 19.6169 | + | 2.81715i | 0.797539 | + | 0.114534i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.07322 | − | 4.00531i | −0.0435606 | − | 0.162570i | 0.940719 | − | 0.339186i | \(-0.110152\pi\) |
−0.984280 | + | 0.176616i | \(0.943485\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 13.6708 | − | 1.57347i | 0.553969 | − | 0.0637604i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.9908i | 0.525550i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.1010 | + | 25.1010i | 1.01382 | + | 1.01382i | 0.999903 | + | 0.0139172i | \(0.00443013\pi\) |
0.0139172 | + | 0.999903i | \(0.495570\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.63596 | − | 1.38262i | −0.186940 | − | 0.0557526i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.88928 | + | 0.506231i | −0.0760595 | + | 0.0203801i | −0.296648 | − | 0.954987i | \(-0.595869\pi\) |
0.220589 | + | 0.975367i | \(0.429202\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.7306 | + | 18.8970i | −1.31555 | + | 0.759535i | −0.983010 | − | 0.183553i | \(-0.941240\pi\) |
−0.332543 | + | 0.943088i | \(0.607907\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.15230 | + | 0.573033i | 0.126497 | + | 0.0229950i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −21.8946 | − | 5.86664i | −0.877189 | − | 0.235042i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.17296 | − | 24.9725i | 0.0469183 | − | 0.998899i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −18.3557 | + | 7.25484i | −0.733057 | + | 0.289730i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.1385 | 0.842849 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.9460 | 0.913467 | 0.456734 | − | 0.889604i | \(-0.349019\pi\) | ||||
0.456734 | + | 0.889604i | \(0.349019\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.20622 | + | 2.54435i | 0.127436 | + | 0.101129i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.87230 | + | 3.36957i | 0.312403 | + | 0.133717i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.1224 | + | 5.65974i | 0.836901 | + | 0.224247i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.53575 | − | 21.5542i | 0.258550 | − | 0.852670i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.807840 | − | 0.466407i | 0.0319078 | − | 0.0184220i | −0.483961 | − | 0.875089i | \(-0.660802\pi\) |
0.515869 | + | 0.856667i | \(0.327469\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.64822 | + | 2.58523i | −0.380489 | + | 0.101952i | −0.443994 | − | 0.896030i | \(-0.646439\pi\) |
0.0635050 | + | 0.997982i | \(0.479772\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.421757 | + | 15.0372i | −0.0166067 | + | 0.592087i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.9808 | − | 14.9808i | −0.588955 | − | 0.588955i | 0.348393 | − | 0.937348i | \(-0.386727\pi\) |
−0.937348 | + | 0.348393i | \(0.886727\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 14.9911i | − | 0.588454i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.2914 | + | 21.9639i | 0.638512 | + | 0.860833i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.93068 | − | 10.9375i | −0.114687 | − | 0.428016i | 0.884577 | − | 0.466395i | \(-0.154447\pi\) |
−0.999263 | + | 0.0383787i | \(0.987781\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.473385 | − | 3.29635i | 0.0184967 | − | 0.128799i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.347639 | − | 0.650212i | −0.0135627 | − | 0.0253672i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.3472 | + | 28.3142i | 0.636796 | + | 1.10296i | 0.986132 | + | 0.165965i | \(0.0530739\pi\) |
−0.349336 | + | 0.936998i | \(0.613593\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.0453877 | − | 0.0786137i | 0.00176538 | − | 0.00305772i | −0.865141 | − | 0.501528i | \(-0.832771\pi\) |
0.866907 | + | 0.498470i | \(0.166105\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −47.9092 | + | 60.3720i | −1.86064 | + | 2.34466i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 31.7259 | − | 3.79864i | 1.23028 | − | 0.147305i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.88965 | + | 1.88965i | −0.0731674 | + | 0.0731674i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.3269 | + | 10.5445i | 0.940534 | + | 0.407674i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.01332 | + | 0.585043i | 0.0391190 | + | 0.0225853i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.20385 | + | 11.9569i | −0.123499 | + | 0.460906i | −0.999782 | − | 0.0208918i | \(-0.993349\pi\) |
0.876282 | + | 0.481798i | \(0.160016\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.18037 | − | 24.6593i | −0.314863 | − | 0.949137i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.19243 | + | 19.3784i | −0.199561 | + | 0.744773i | 0.791477 | + | 0.611198i | \(0.209312\pi\) |
−0.991039 | + | 0.133575i | \(0.957354\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.846682 | − | 0.488832i | −0.0324927 | − | 0.0187597i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.7478 | − | 6.82589i | −0.603458 | − | 0.261569i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.05629 | + | 3.05629i | −0.116946 | + | 0.116946i | −0.763158 | − | 0.646212i | \(-0.776352\pi\) |
0.646212 | + | 0.763158i | \(0.276352\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −44.1641 | + | 5.28791i | −1.68742 | + | 0.202041i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.38573 | − | 11.8273i | 0.358088 | − | 0.451240i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −17.3276 | + | 30.0122i | −0.660127 | + | 1.14337i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.3415 | + | 17.9120i | 0.393410 | + | 0.681406i | 0.992897 | − | 0.118978i | \(-0.0379619\pi\) |
−0.599487 | + | 0.800385i | \(0.704629\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.03526 | + | 0.262146i | 0.305234 | + | 0.00995811i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.87974 | − | 20.0527i | 0.109235 | − | 0.760642i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.39427 | + | 8.93554i | 0.0906895 | + | 0.338458i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 29.2147 | + | 39.3869i | 1.10500 | + | 1.48975i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 46.6921i | − | 1.76354i | −0.471682 | − | 0.881769i | \(-0.656353\pi\) | ||
0.471682 | − | 0.881769i | \(-0.343647\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.7326 | − | 15.7326i | −0.593365 | − | 0.593365i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.234775 | + | 8.37055i | −0.00884212 | + | 0.315253i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.06544 | + | 2.42908i | −0.340941 | + | 0.0913548i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.1385 | + | 8.16289i | −0.530984 | + | 0.306564i | −0.741417 | − | 0.671045i | \(-0.765846\pi\) |
0.210433 | + | 0.977608i | \(0.432513\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.80546 | + | 2.05419i | −0.330231 | + | 0.0770380i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.12965 | − | 1.37449i | −0.192107 | − | 0.0514749i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.0559 | + | 7.72844i | 0.675252 | + | 0.289027i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.689313 | + | 0.547015i | 0.0257429 | + | 0.0204287i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 44.7865 | 1.67026 | 0.835128 | − | 0.550056i | \(-0.185394\pi\) | ||||
0.835128 | + | 0.550056i | \(0.185394\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26.2258 | 0.976701 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.5079 | + | 4.94358i | −0.465175 | + | 0.183854i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 20.7943 | + | 6.09826i | 0.772282 | + | 0.226484i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.9830 | + | 4.55058i | 0.629865 | + | 0.168772i | 0.559608 | − | 0.828757i | \(-0.310952\pi\) |
0.0702565 | + | 0.997529i | \(0.477618\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −17.1356 | − | 20.8655i | −0.634653 | − | 0.772797i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.9116 | − | 14.3827i | 0.921389 | − | 0.531964i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 44.6819 | − | 11.9725i | 1.65036 | − | 0.442214i | 0.690650 | − | 0.723190i | \(-0.257325\pi\) |
0.959715 | + | 0.280976i | \(0.0906581\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 13.5079 | + | 4.02857i | 0.498246 | + | 0.148596i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.89666 | + | 6.89666i | 0.254042 | + | 0.254042i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 26.3743i | − | 0.970194i | −0.874460 | − | 0.485097i | \(-0.838784\pi\) | ||
0.874460 | − | 0.485097i | \(-0.161216\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 80.5894 | − | 9.27563i | 2.96052 | − | 0.340749i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.327054 | + | 1.22058i | 0.0119985 | + | 0.0447789i | 0.971666 | − | 0.236360i | \(-0.0759545\pi\) |
−0.959667 | + | 0.281139i | \(0.909288\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.4422 | + | 2.79207i | 0.712306 | + | 0.102293i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −19.4749 | − | 12.1072i | −0.712549 | − | 0.442981i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.53190 | − | 6.11743i | −0.129053 | − | 0.223526i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.9258 | + | 29.3164i | −0.617633 | + | 1.06977i | 0.372284 | + | 0.928119i | \(0.378575\pi\) |
−0.989916 | + | 0.141652i | \(0.954759\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.9386 | + | 3.69787i | 0.908813 | + | 0.134758i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.6409 | + | 21.1679i | −0.605625 | + | 0.770379i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.27687 | + | 7.27687i | −0.264482 | + | 0.264482i | −0.826872 | − | 0.562390i | \(-0.809882\pi\) |
0.562390 | + | 0.826872i | \(0.309882\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.25396 | + | 0.930112i | −0.0455160 | + | 0.0337609i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.3111 | + | 22.1189i | 1.38878 | + | 0.801810i | 0.993177 | − | 0.116614i | \(-0.0372040\pi\) |
0.395598 | + | 0.918424i | \(0.370537\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.18001 | − | 26.7962i | 0.259934 | − | 0.970086i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −31.9612 | + | 38.0347i | −1.15556 | + | 1.37515i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.9469 | + | 59.5147i | −0.575809 | + | 2.14895i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.7495 | + | 15.4438i | 0.964611 | + | 0.556918i | 0.897589 | − | 0.440833i | \(-0.145317\pi\) |
0.0670216 | + | 0.997752i | \(0.478650\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.04700 | − | 35.1615i | −0.145749 | − | 1.26631i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.78933 | + | 3.78933i | −0.136293 | + | 0.136293i | −0.771962 | − | 0.635669i | \(-0.780724\pi\) |
0.635669 | + | 0.771962i | \(0.280724\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.1665 | + | 41.8462i | 0.365191 | + | 1.50316i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.33114 | + | 8.42824i | 0.119504 | + | 0.302362i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.86841 | − | 8.43233i | 0.174429 | − | 0.302120i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.48770 | + | 9.50497i | 0.196365 | + | 0.340115i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 22.4446 | − | 1.84415i | 0.802104 | − | 0.0659045i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.8120 | + | 11.0920i | −0.528663 | + | 0.395889i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.36210 | − | 8.81547i | −0.0841997 | − | 0.314238i | 0.910962 | − | 0.412491i | \(-0.135341\pi\) |
−0.995161 | + | 0.0982533i | \(0.968674\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.4844 | − | 26.4954i | 0.408856 | − | 0.943261i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.24444i | 0.0442471i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.40054 | − | 3.40054i | −0.120757 | − | 0.120757i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11.7074 | + | 19.0251i | −0.415217 | + | 0.674752i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.0705 | + | 4.84198i | −0.640090 | + | 0.171512i | −0.564244 | − | 0.825608i | \(-0.690832\pi\) |
−0.0758457 | + | 0.997120i | \(0.524166\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.8672 | − | 8.00625i | 0.490588 | − | 0.283241i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −35.4988 | − | 10.7641i | −1.25429 | − | 0.380331i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.347043 | + | 0.0929899i | 0.0122469 | + | 0.00328154i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.34629 | − | 0.939765i | 0.0826958 | − | 0.0331223i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.85004 | + | 25.9649i | −0.135528 | + | 0.914008i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17.3943 | −0.611551 | −0.305776 | − | 0.952104i | \(-0.598916\pi\) | ||||
−0.305776 | + | 0.952104i | \(0.598916\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.0872 | −0.424441 | −0.212220 | − | 0.977222i | \(-0.568069\pi\) | ||||
−0.212220 | + | 0.977222i | \(0.568069\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.77707 | − | 32.2168i | 0.167539 | − | 1.12989i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.8710 | + | 44.0881i | −0.661021 | + | 1.54434i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −29.2452 | − | 7.83622i | −1.02316 | − | 0.274155i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −31.6210 | − | 9.58827i | −1.10493 | − | 0.335041i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.7757 | − | 15.4590i | 0.934480 | − | 0.539522i | 0.0462541 | − | 0.998930i | \(-0.485272\pi\) |
0.888226 | + | 0.459408i | \(0.151938\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.7879 | − | 4.49831i | 0.585190 | − | 0.156801i | 0.0459362 | − | 0.998944i | \(-0.485373\pi\) |
0.539254 | + | 0.842143i | \(0.318706\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11.4946 | + | 5.30611i | 0.400190 | + | 0.184735i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.3405 | − | 31.3405i | −1.08982 | − | 1.08982i | −0.995547 | − | 0.0942693i | \(-0.969949\pi\) |
−0.0942693 | − | 0.995547i | \(-0.530051\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.7122i | 1.41399i | 0.707216 | + | 0.706997i | \(0.249951\pi\) | ||||
−0.707216 | + | 0.706997i | \(0.750049\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.7394 | − | 31.6978i | 0.476614 | − | 1.09958i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.97624 | − | 26.0357i | −0.241712 | − | 0.902083i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.5841 | + | 15.4692i | 0.400885 | + | 0.535334i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 25.4750 | + | 36.7946i | 0.880546 | + | 1.27181i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.5669 | − | 26.9626i | −0.537427 | − | 0.930851i | −0.999042 | − | 0.0437707i | \(-0.986063\pi\) |
0.461614 | − | 0.887081i | \(-0.347270\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.10814 | − | 8.84756i | 0.176143 | − | 0.305088i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.95189 | + | 7.46869i | 0.101669 | + | 0.257235i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −40.6079 | − | 31.9235i | −1.39695 | − | 1.09820i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.4885 | − | 11.4885i | 0.394749 | − | 0.394749i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.40008 | − | 38.2292i | −0.151010 | − | 1.31202i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.52416 | − | 0.879974i | −0.0522475 | − | 0.0301651i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.58215 | − | 5.90466i | 0.0541718 | − | 0.202172i | −0.933536 | − | 0.358484i | \(-0.883294\pi\) |
0.987708 | + | 0.156312i | \(0.0499605\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 52.0952 | − | 4.52028i | 1.78162 | − | 0.154590i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.19733 | + | 34.3249i | −0.314175 | + | 1.17252i | 0.610581 | + | 0.791954i | \(0.290936\pi\) |
−0.924755 | + | 0.380562i | \(0.875731\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.0418217 | − | 0.0241458i | −0.00142694 | − | 0.000823843i | 0.499286 | − | 0.866437i | \(-0.333596\pi\) |
−0.500713 | + | 0.865613i | \(0.666929\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.18543 | + | 2.36275i | −0.108559 | + | 0.0805223i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.6902 | + | 17.6902i | −0.602182 | + | 0.602182i | −0.940891 | − | 0.338709i | \(-0.890010\pi\) |
0.338709 | + | 0.940891i | \(0.390010\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.62166 | − | 21.8959i | −0.0891391 | − | 0.744482i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 64.8456 | + | 9.61522i | 2.20227 | + | 0.326550i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.20302 | − | 3.81573i | 0.0747322 | − | 0.129440i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.0433 | − | 34.7160i | −0.679142 | − | 1.17631i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.35879 | − | 0.844739i | −0.0459881 | − | 0.0285901i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15.8109 | − | 13.0413i | −0.534505 | − | 0.440877i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.46068 | + | 35.3077i | 0.319464 | + | 1.19226i | 0.919761 | + | 0.392480i | \(0.128383\pi\) |
−0.600296 | + | 0.799778i | \(0.704951\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 35.9987 | − | 4.14336i | 1.21421 | − | 0.139752i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 11.1310i | − | 0.375012i | −0.982264 | − | 0.187506i | \(-0.939960\pi\) | ||
0.982264 | − | 0.187506i | \(-0.0600403\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.73609 | + | 8.73609i | 0.293993 | + | 0.293993i | 0.838655 | − | 0.544662i | \(-0.183342\pi\) |
−0.544662 | + | 0.838655i | \(0.683342\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −11.3509 | + | 38.0599i | −0.381557 | + | 1.27937i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.73775 | − | 1.80538i | 0.226232 | − | 0.0606186i | −0.143922 | − | 0.989589i | \(-0.545972\pi\) |
0.370154 | + | 0.928970i | \(0.379305\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.07964 | − | 3.51008i | 0.203905 | − | 0.117724i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.1289 | + | 0.857558i | 0.439834 | + | 0.0287293i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16.2796 | − | 4.36210i | −0.544775 | − | 0.145972i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.5289 | + | 31.2807i | 0.418795 | + | 1.04560i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.96763 | − | 2.35862i | 0.199253 | − | 0.0787521i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −37.3276 | −1.24494 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 42.7162 | 1.42308 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.66032 | + | 7.66610i | 0.321475 | + | 0.255112i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.32581 | − | 10.8002i | −0.143795 | − | 0.359010i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.02482 | − | 2.41819i | −0.299664 | − | 0.0802948i | 0.105854 | − | 0.994382i | \(-0.466242\pi\) |
−0.405518 | + | 0.914087i | \(0.632909\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14.9575 | + | 3.48937i | −0.496109 | + | 0.115735i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.7455 | − | 18.9056i | 1.08491 | − | 0.626372i | 0.152692 | − | 0.988274i | \(-0.451206\pi\) |
0.932216 | + | 0.361902i | \(0.117872\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.7936 | − | 2.89213i | 0.357216 | − | 0.0957156i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.12967 | − | 2.25259i | −0.0704049 | − | 0.0744682i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.93048 | − | 1.93048i | −0.0637502 | − | 0.0637502i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 4.94192i | − | 0.163019i | −0.996673 | − | 0.0815094i | \(-0.974026\pi\) | ||
0.996673 | − | 0.0815094i | \(-0.0259741\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.73590 | − | 5.03668i | −0.123102 | − | 0.165964i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.6751 | − | 43.5722i | −0.384292 | − | 1.43420i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.334886 | + | 14.2674i | −0.0110110 | + | 0.469110i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 42.8962 | + | 1.39947i | 1.40890 | + | 0.0459645i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.1464 | + | 34.8946i | 0.660983 | + | 1.14486i | 0.980358 | + | 0.197227i | \(0.0631937\pi\) |
−0.319375 | + | 0.947628i | \(0.603473\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.1852 | + | 24.5694i | −0.464900 | + | 0.805231i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −11.0837 | + | 13.9670i | −0.362865 | + | 0.457259i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.87805 | − | 24.0372i | −0.0941222 | − | 0.786100i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.5389 | + | 13.5389i | −0.442297 | + | 0.442297i | −0.892783 | − | 0.450486i | \(-0.851251\pi\) |
0.450486 | + | 0.892783i | \(0.351251\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.86635 | + | 1.67587i | 0.126173 | + | 0.0546898i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34.6711 | + | 20.0174i | 1.13025 | + | 0.652547i | 0.943997 | − | 0.329955i | \(-0.107034\pi\) |
0.186248 | + | 0.982503i | \(0.440367\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.199342 | − | 0.743954i | 0.00649146 | − | 0.0242265i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −20.2016 | − | 6.74964i | −0.657159 | − | 0.219566i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.97013 | + | 7.35262i | −0.0640206 | + | 0.238928i | −0.990520 | − | 0.137368i | \(-0.956136\pi\) |
0.926500 | + | 0.376296i | \(0.122802\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.27884 | − | 0.738337i | −0.0415128 | − | 0.0239674i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.77741 | + | 3.37111i | 0.252200 | + | 0.109316i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.0032 | − | 11.0032i | 0.356429 | − | 0.356429i | −0.506066 | − | 0.862495i | \(-0.668901\pi\) |
0.862495 | + | 0.506066i | \(0.168901\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.1948 | − | 9.58681i | −0.394614 | − | 0.310222i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.82156 | + | 8.59609i | −0.220510 | + | 0.277872i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.2325 | + | 31.5796i | −0.588757 | + | 1.01976i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.5892 | − | 37.3936i | −0.696427 | − | 1.20625i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.45051 | − | 10.1944i | −0.175640 | − | 0.328511i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.76724 | + | 6.36608i | 0.153463 | + | 0.204931i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.648313 | − | 2.41954i | −0.0208483 | − | 0.0778070i | 0.954718 | − | 0.297513i | \(-0.0961570\pi\) |
−0.975566 | + | 0.219706i | \(0.929490\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −59.5690 | − | 80.3101i | −1.91363 | − | 2.57993i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.0074i | 0.513701i | 0.966451 | + | 0.256850i | \(0.0826848\pi\) | ||||
−0.966451 | + | 0.256850i | \(0.917315\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.7437 | − | 11.7437i | −0.376486 | − | 0.376486i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −39.9890 | − | 33.2926i | −1.28067 | − | 1.06622i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.1641 | − | 3.25935i | 0.389163 | − | 0.104276i | −0.0589319 | − | 0.998262i | \(-0.518769\pi\) |
0.448094 | + | 0.893986i | \(0.352103\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.6543 | − | 9.03801i | 0.500313 | − | 0.288856i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.1739 | − | 43.4460i | 0.420609 | − | 1.38712i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −51.1769 | − | 13.7128i | −1.63229 | − | 0.437371i | −0.677712 | − | 0.735328i | \(-0.737028\pi\) |
−0.954579 | + | 0.297957i | \(0.903695\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.8128 | + | 39.2797i | −0.535701 | + | 1.25155i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.37750 | + | 4.26739i | 0.171168 | + | 0.135833i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.39495 | −0.0761549 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.4832 | 0.460073 | 0.230036 | − | 0.973182i | \(-0.426115\pi\) | ||||
0.230036 | + | 0.973182i | \(0.426115\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −31.4680 | + | 12.4373i | −0.998608 | + | 0.394686i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.52717 | + | 3.01488i | −0.238627 | + | 0.0955780i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −55.8004 | − | 14.9517i | −1.76722 | − | 0.473524i | −0.779058 | − | 0.626952i | \(-0.784302\pi\) |
−0.988160 | + | 0.153428i | \(0.950969\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.99883 | + | 13.9634i | 0.158156 | + | 0.441782i |
(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 | 360.2.bs.a.113.9 | ✓ | 72 | |
3.2 | odd | 2 | 1080.2.bt.a.233.12 | 72 | |||
4.3 | odd | 2 | 720.2.cu.e.113.10 | 72 | |||
5.2 | odd | 4 | inner | 360.2.bs.a.257.1 | yes | 72 | |
9.2 | odd | 6 | inner | 360.2.bs.a.353.1 | yes | 72 | |
9.7 | even | 3 | 1080.2.bt.a.953.18 | 72 | |||
15.2 | even | 4 | 1080.2.bt.a.17.18 | 72 | |||
20.7 | even | 4 | 720.2.cu.e.257.18 | 72 | |||
36.11 | even | 6 | 720.2.cu.e.353.18 | 72 | |||
45.2 | even | 12 | inner | 360.2.bs.a.137.9 | yes | 72 | |
45.7 | odd | 12 | 1080.2.bt.a.737.12 | 72 | |||
180.47 | odd | 12 | 720.2.cu.e.497.10 | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.bs.a.113.9 | ✓ | 72 | 1.1 | even | 1 | trivial | |
360.2.bs.a.137.9 | yes | 72 | 45.2 | even | 12 | inner | |
360.2.bs.a.257.1 | yes | 72 | 5.2 | odd | 4 | inner | |
360.2.bs.a.353.1 | yes | 72 | 9.2 | odd | 6 | inner | |
720.2.cu.e.113.10 | 72 | 4.3 | odd | 2 | |||
720.2.cu.e.257.18 | 72 | 20.7 | even | 4 | |||
720.2.cu.e.353.18 | 72 | 36.11 | even | 6 | |||
720.2.cu.e.497.10 | 72 | 180.47 | odd | 12 | |||
1080.2.bt.a.17.18 | 72 | 15.2 | even | 4 | |||
1080.2.bt.a.233.12 | 72 | 3.2 | odd | 2 | |||
1080.2.bt.a.737.12 | 72 | 45.7 | odd | 12 | |||
1080.2.bt.a.953.18 | 72 | 9.7 | even | 3 |