Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,3,Mod(13,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.13");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.j (of order \(18\), degree \(6\), 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: | \(2.07085000914\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{18})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 93 x^{16} + 3429 x^{14} + 64261 x^{12} + 647217 x^{10} + 3386277 x^{8} + 8232133 x^{6} + 8319228 x^{4} + 2467872 x^{2} + 69312 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 13.1 | ||
Root | \(3.09175i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.13 |
Dual form | 76.3.j.a.41.1 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{5}{18}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.617749 | + | 1.69725i | −0.205916 | + | 0.565751i | −0.999063 | − | 0.0432802i | \(-0.986219\pi\) |
0.793147 | + | 0.609031i | \(0.208441\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.757040 | + | 4.29338i | 0.151408 | + | 0.858677i | 0.961997 | + | 0.273061i | \(0.0880361\pi\) |
−0.810589 | + | 0.585616i | \(0.800853\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.41011 | + | 4.17443i | −0.344301 | + | 0.596347i | −0.985227 | − | 0.171256i | \(-0.945218\pi\) |
0.640925 | + | 0.767603i | \(0.278551\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.39535 | + | 3.68814i | 0.488372 | + | 0.409793i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.0945208 | + | 0.163715i | 0.00859280 | + | 0.0148832i | 0.870290 | − | 0.492540i | \(-0.163931\pi\) |
−0.861697 | + | 0.507423i | \(0.830598\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.39295 | + | 3.82710i | 0.107150 | + | 0.294393i | 0.981667 | − | 0.190602i | \(-0.0610439\pi\) |
−0.874517 | + | 0.484994i | \(0.838822\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.75461 | − | 1.36735i | −0.516974 | − | 0.0911565i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 13.1145 | − | 11.0044i | 0.771443 | − | 0.647317i | −0.169635 | − | 0.985507i | \(-0.554259\pi\) |
0.941078 | + | 0.338190i | \(0.109814\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.88753 | − | 16.7932i | −0.467765 | − | 0.883853i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.59622 | − | 6.66931i | −0.266487 | − | 0.317586i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.45173 | − | 13.9044i | 0.106597 | − | 0.604541i | −0.883974 | − | 0.467537i | \(-0.845142\pi\) |
0.990571 | − | 0.137004i | \(-0.0437473\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.63227 | − | 2.04998i | 0.225291 | − | 0.0819992i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −23.0527 | + | 13.3095i | −0.853803 | + | 0.492943i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 18.3700 | − | 21.8925i | 0.633447 | − | 0.754913i | −0.349873 | − | 0.936797i | \(-0.613775\pi\) |
0.983320 | + | 0.181884i | \(0.0582196\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.92457 | − | 3.42055i | −0.191115 | − | 0.110340i | 0.401389 | − | 0.915908i | \(-0.368527\pi\) |
−0.592505 | + | 0.805567i | \(0.701861\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.336255 | + | 0.0592909i | −0.0101896 | + | 0.00179669i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −19.7470 | − | 7.18732i | −0.564200 | − | 0.205352i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 31.9736i | 0.864152i | 0.901837 | + | 0.432076i | \(0.142219\pi\) | ||||
−0.901837 | + | 0.432076i | \(0.857781\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.35605 | −0.188617 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 19.4006 | − | 53.3028i | 0.473186 | − | 1.30007i | −0.441993 | − | 0.897019i | \(-0.645728\pi\) |
0.915178 | − | 0.403049i | \(-0.132050\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.16167 | + | 40.6158i | 0.166550 | + | 0.944554i | 0.947451 | + | 0.319899i | \(0.103649\pi\) |
−0.780901 | + | 0.624655i | \(0.785240\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −12.5071 | + | 21.6630i | −0.277936 | + | 0.481400i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 44.9103 | + | 37.6842i | 0.955538 | + | 0.801791i | 0.980221 | − | 0.197904i | \(-0.0634134\pi\) |
−0.0246837 | + | 0.999695i | \(0.507858\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.8827 | + | 22.3136i | 0.262913 | + | 0.455379i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.5757 | + | 29.0566i | 0.207367 | + | 0.569737i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.32437 | − | 0.938830i | −0.100460 | − | 0.0177138i | 0.123192 | − | 0.992383i | \(-0.460687\pi\) |
−0.223652 | + | 0.974669i | \(0.571798\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.631335 | + | 0.529753i | −0.0114788 | + | 0.00963187i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 33.9926 | − | 4.71039i | 0.596361 | − | 0.0826385i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −36.3323 | − | 43.2991i | −0.615801 | − | 0.733883i | 0.364541 | − | 0.931187i | \(-0.381226\pi\) |
−0.980342 | + | 0.197304i | \(0.936781\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15.7238 | + | 89.1742i | −0.257767 | + | 1.46187i | 0.531100 | + | 0.847309i | \(0.321779\pi\) |
−0.788868 | + | 0.614563i | \(0.789332\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −25.9892 | + | 9.45928i | −0.412526 | + | 0.150147i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −15.3767 | + | 8.87775i | −0.236565 | + | 0.136581i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.04936 | − | 6.01760i | 0.0753637 | − | 0.0898149i | −0.727045 | − | 0.686590i | \(-0.759107\pi\) |
0.802409 | + | 0.596775i | \(0.203551\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 22.0848 | + | 12.7506i | 0.320069 | + | 0.184792i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 23.9368 | − | 4.22071i | 0.337138 | − | 0.0594466i | −0.00251622 | − | 0.999997i | \(-0.500801\pi\) |
0.339655 | + | 0.940550i | \(0.389690\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −111.851 | − | 40.7104i | −1.53220 | − | 0.557677i | −0.568044 | − | 0.822998i | \(-0.692300\pi\) |
−0.964160 | + | 0.265322i | \(0.914522\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.8258i | 0.144343i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.911222 | −0.0118340 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 47.8267 | − | 131.403i | 0.605401 | − | 1.66333i | −0.134745 | − | 0.990880i | \(-0.543022\pi\) |
0.740146 | − | 0.672446i | \(-0.234756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.618357 | + | 3.50688i | 0.00763404 | + | 0.0432948i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 52.0220 | − | 90.1047i | 0.626770 | − | 1.08560i | −0.361425 | − | 0.932401i | \(-0.617710\pi\) |
0.988196 | − | 0.153197i | \(-0.0489570\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 57.1743 | + | 47.9749i | 0.672639 | + | 0.564411i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 25.8090 | + | 44.7025i | 0.296655 | + | 0.513822i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −52.7400 | − | 144.902i | −0.592584 | − | 1.62811i | −0.765692 | − | 0.643208i | \(-0.777603\pi\) |
0.173108 | − | 0.984903i | \(-0.444619\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −19.3332 | − | 3.40896i | −0.212452 | − | 0.0374611i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.46544 | − | 7.94245i | 0.101779 | − | 0.0854027i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 65.3715 | − | 50.8707i | 0.688121 | − | 0.535481i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −52.4375 | − | 62.4925i | −0.540592 | − | 0.644253i | 0.424728 | − | 0.905321i | \(-0.360370\pi\) |
−0.965320 | + | 0.261068i | \(0.915925\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.188351 | + | 1.06819i | −0.00190253 | + | 0.0107898i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −110.337 | + | 40.1595i | −1.09245 | + | 0.397619i | −0.824528 | − | 0.565822i | \(-0.808559\pi\) |
−0.267922 | + | 0.963441i | \(0.586337\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −134.487 | + | 77.6462i | −1.30570 | + | 0.753846i | −0.981376 | − | 0.192099i | \(-0.938470\pi\) |
−0.324325 | + | 0.945946i | \(0.605137\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 24.3974 | − | 29.0756i | 0.232356 | − | 0.276911i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 138.583 | + | 80.0108i | 1.29517 | + | 0.747765i | 0.979565 | − | 0.201127i | \(-0.0644604\pi\) |
0.315601 | + | 0.948892i | \(0.397794\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −105.342 | + | 18.5747i | −0.966443 | + | 0.170410i | −0.634528 | − | 0.772900i | \(-0.718806\pi\) |
−0.331914 | + | 0.943310i | \(0.607695\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −54.2673 | − | 19.7517i | −0.488894 | − | 0.177943i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 54.9633i | − | 0.486401i | −0.969976 | − | 0.243201i | \(-0.921803\pi\) | ||
0.969976 | − | 0.243201i | \(-0.0781973\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 61.5531 | 0.535245 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.99237 | + | 21.9589i | −0.0683109 | + | 0.187683i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.3297 | + | 81.2675i | 0.120417 | + | 0.682920i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 60.4821 | − | 104.758i | 0.499852 | − | 0.865770i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 78.4835 | + | 65.8555i | 0.638077 | + | 0.535410i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 67.5604 | + | 117.018i | 0.540483 | + | 0.936145i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 57.6206 | + | 158.311i | 0.453705 | + | 1.24655i | 0.930098 | + | 0.367312i | \(0.119722\pi\) |
−0.476392 | + | 0.879233i | \(0.658056\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −73.3594 | − | 12.9352i | −0.568677 | − | 0.100273i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 26.6313 | − | 22.3463i | 0.203292 | − | 0.170582i | −0.535458 | − | 0.844562i | \(-0.679861\pi\) |
0.738750 | + | 0.673980i | \(0.235416\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 91.5220 | + | 3.37306i | 0.688135 | + | 0.0253613i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −74.5945 | − | 88.8982i | −0.552552 | − | 0.658505i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −28.3002 | + | 160.498i | −0.206571 | + | 1.17152i | 0.688378 | + | 0.725352i | \(0.258323\pi\) |
−0.894949 | + | 0.446169i | \(0.852788\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 24.9206 | − | 9.07036i | 0.179285 | − | 0.0652544i | −0.250818 | − | 0.968034i | \(-0.580700\pi\) |
0.430103 | + | 0.902780i | \(0.358477\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −91.7028 | + | 52.9447i | −0.650375 | + | 0.375494i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.494891 | + | 0.589788i | −0.00346077 | + | 0.00412439i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 107.900 | + | 62.2959i | 0.744135 | + | 0.429627i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −45.8301 | + | 8.08107i | −0.311769 | + | 0.0549733i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −147.677 | − | 53.7500i | −0.991121 | − | 0.360739i | −0.204967 | − | 0.978769i | \(-0.565709\pi\) |
−0.786154 | + | 0.618030i | \(0.787931\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 26.7672i | − | 0.177267i | −0.996064 | − | 0.0886333i | \(-0.971750\pi\) | ||
0.996064 | − | 0.0886333i | \(-0.0282499\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 98.2287 | 0.642017 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.2006 | − | 28.0260i | 0.0658104 | − | 0.180813i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 35.9951 | + | 204.138i | 0.229268 | + | 1.30024i | 0.854355 | + | 0.519689i | \(0.173952\pi\) |
−0.625087 | + | 0.780555i | \(0.714937\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.88255 | − | 8.45683i | 0.0307079 | − | 0.0531876i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 52.1342 | + | 43.7458i | 0.323815 | + | 0.271713i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −78.8734 | − | 136.613i | −0.483886 | − | 0.838115i | 0.515943 | − | 0.856623i | \(-0.327442\pi\) |
−0.999829 | + | 0.0185078i | \(0.994108\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.509117 | − | 1.39879i | −0.00308556 | − | 0.00847750i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.7322 | + | 2.06870i | 0.0702526 | + | 0.0123874i | 0.208664 | − | 0.977987i | \(-0.433088\pi\) |
−0.138411 | + | 0.990375i | \(0.544200\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 116.755 | − | 97.9692i | 0.690859 | − | 0.579699i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 22.8718 | − | 106.590i | 0.133753 | − | 0.623336i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −86.5340 | − | 103.127i | −0.500197 | − | 0.596111i | 0.455584 | − | 0.890193i | \(-0.349431\pi\) |
−0.955780 | + | 0.294082i | \(0.904986\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.01689 | + | 28.4522i | −0.0286680 | + | 0.162584i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 95.9337 | − | 34.9170i | 0.541998 | − | 0.197271i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −278.151 | + | 160.591i | −1.55392 | + | 0.897154i | −0.556099 | + | 0.831116i | \(0.687702\pi\) |
−0.997817 | + | 0.0660376i | \(0.978964\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 47.0632 | − | 56.0877i | 0.260017 | − | 0.309877i | −0.620203 | − | 0.784441i | \(-0.712950\pi\) |
0.880221 | + | 0.474564i | \(0.157394\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −141.638 | − | 81.7745i | −0.773976 | − | 0.446855i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −137.275 | + | 24.2053i | −0.742027 | + | 0.130839i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.04118 | + | 1.10690i | 0.0162630 | + | 0.00591924i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 128.309i | − | 0.678884i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 133.689 | 0.699940 | 0.349970 | − | 0.936761i | \(-0.386192\pi\) | ||||
0.349970 | + | 0.936761i | \(0.386192\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 73.5478 | − | 202.071i | 0.381077 | − | 1.04700i | −0.589827 | − | 0.807529i | \(-0.700804\pi\) |
0.970904 | − | 0.239470i | \(-0.0769736\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.56882 | − | 31.5824i | −0.0285581 | − | 0.161961i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 62.1141 | − | 107.585i | 0.315300 | − | 0.546115i | −0.664201 | − | 0.747554i | \(-0.731228\pi\) |
0.979501 | + | 0.201438i | \(0.0645616\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −212.314 | − | 178.153i | −1.06691 | − | 0.895240i | −0.0721368 | − | 0.997395i | \(-0.522982\pi\) |
−0.994769 | + | 0.102155i | \(0.967426\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.09414 | + | 12.2874i | 0.0352942 | + | 0.0611314i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 47.1150 | + | 129.447i | 0.232094 | + | 0.637672i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 243.536 | + | 42.9420i | 1.18798 | + | 0.209473i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 62.0577 | − | 52.0726i | 0.299795 | − | 0.251558i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.90924 | − | 3.04233i | 0.00913512 | − | 0.0145566i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −160.725 | − | 191.544i | −0.761729 | − | 0.907793i | 0.236227 | − | 0.971698i | \(-0.424089\pi\) |
−0.997956 | + | 0.0639050i | \(0.979645\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.62335 | + | 43.2342i | −0.0357904 | + | 0.202977i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −168.958 | + | 61.4956i | −0.785850 | + | 0.286026i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 28.5577 | − | 16.4878i | 0.131602 | − | 0.0759807i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 138.192 | − | 164.690i | 0.631012 | − | 0.752010i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 60.3829 | + | 34.8621i | 0.273226 | + | 0.157747i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 109.691 | − | 19.3415i | 0.491887 | − | 0.0867330i | 0.0777978 | − | 0.996969i | \(-0.475211\pi\) |
0.414090 | + | 0.910236i | \(0.364100\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 32.3164 | + | 11.7622i | 0.143629 | + | 0.0522765i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 345.131i | 1.52040i | 0.649689 | + | 0.760200i | \(0.274899\pi\) | ||||
−0.649689 | + | 0.760200i | \(0.725101\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −138.138 | −0.603225 | −0.301612 | − | 0.953431i | \(-0.597525\pi\) | ||||
−0.301612 | + | 0.953431i | \(0.597525\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.562906 | − | 1.54657i | 0.00243682 | − | 0.00669512i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.3333 | − | 92.6309i | −0.0701002 | − | 0.397558i | −0.999588 | − | 0.0287048i | \(-0.990862\pi\) |
0.929488 | − | 0.368853i | \(-0.120249\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −127.794 | + | 221.345i | −0.543804 | + | 0.941896i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 193.479 | + | 162.348i | 0.816366 | + | 0.685012i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 106.213 | + | 183.966i | 0.444404 | + | 0.769731i | 0.998011 | − | 0.0630478i | \(-0.0200821\pi\) |
−0.553606 | + | 0.832779i | \(0.686749\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.3102 | + | 28.3272i | 0.0427811 | + | 0.117540i | 0.959244 | − | 0.282581i | \(-0.0911904\pi\) |
−0.916462 | + | 0.400121i | \(0.868968\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −242.265 | − | 42.7178i | −0.996975 | − | 0.175794i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −86.0480 | + | 72.2028i | −0.351216 | + | 0.294705i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 51.8894 | − | 57.4057i | 0.210079 | − | 0.232412i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 120.794 | + | 143.956i | 0.485116 | + | 0.578138i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.289957 | − | 1.64443i | 0.00115521 | − | 0.00655150i | −0.984225 | − | 0.176923i | \(-0.943386\pi\) |
0.985380 | + | 0.170371i | \(0.0544968\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.50810 | − | 0.912874i | 0.00991344 | − | 0.00360820i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −116.745 | + | 67.4027i | −0.457823 | + | 0.264324i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −231.634 | + | 276.051i | −0.901299 | + | 1.07413i | 0.0955985 | + | 0.995420i | \(0.469523\pi\) |
−0.996898 | + | 0.0787067i | \(0.974921\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −133.472 | − | 77.0599i | −0.515335 | − | 0.297529i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 161.485 | − | 28.4742i | 0.618716 | − | 0.109096i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 126.255 | + | 45.9530i | 0.480056 | + | 0.174726i | 0.570702 | − | 0.821157i | \(-0.306671\pi\) |
−0.0906463 | + | 0.995883i | \(0.528893\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 23.5703i | − | 0.0889445i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 278.515 | 1.04313 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.1149 | + | 49.7703i | −0.0673417 | + | 0.185020i | −0.968799 | − | 0.247849i | \(-0.920276\pi\) |
0.901457 | + | 0.432869i | \(0.142499\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.0084 | + | 141.830i | 0.0922819 | + | 0.523357i | 0.995546 | + | 0.0942727i | \(0.0300525\pi\) |
−0.903264 | + | 0.429084i | \(0.858836\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 17.7289 | − | 30.7073i | 0.0649410 | − | 0.112481i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.867979 | + | 0.728321i | 0.00315629 | + | 0.00264844i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −36.9790 | − | 64.0496i | −0.133498 | − | 0.231226i | 0.791524 | − | 0.611137i | \(-0.209288\pi\) |
−0.925023 | + | 0.379912i | \(0.875954\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −13.4251 | − | 36.8852i | −0.0481187 | − | 0.132205i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −62.2447 | − | 10.9754i | −0.221511 | − | 0.0390584i | 0.0617909 | − | 0.998089i | \(-0.480319\pi\) |
−0.283302 | + | 0.959031i | \(0.591430\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −74.5778 | + | 62.5782i | −0.263526 | + | 0.221125i | −0.764971 | − | 0.644065i | \(-0.777247\pi\) |
0.501445 | + | 0.865190i | \(0.332802\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 45.9572 | + | 142.377i | 0.161253 | + | 0.499569i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 175.751 | + | 209.452i | 0.612373 | + | 0.729798i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.709798 | − | 4.02546i | 0.00245605 | − | 0.0139289i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 138.459 | − | 50.3949i | 0.475803 | − | 0.173178i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 337.975 | − | 195.130i | 1.15350 | − | 0.665972i | 0.203761 | − | 0.979021i | \(-0.434684\pi\) |
0.949737 | + | 0.313048i | \(0.101350\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 158.395 | − | 188.767i | 0.536931 | − | 0.639890i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.35791 | − | 2.51604i | −0.0146731 | − | 0.00847153i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 56.6289 | − | 9.98520i | 0.189394 | − | 0.0333953i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −186.808 | − | 67.9927i | −0.620626 | − | 0.225889i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 212.079i | − | 0.699930i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −394.763 | −1.29430 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.9626 | + | 46.6044i | −0.0552528 | + | 0.151806i | −0.964248 | − | 0.265000i | \(-0.914628\pi\) |
0.908996 | + | 0.416805i | \(0.136850\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −48.7058 | − | 276.224i | −0.157624 | − | 0.893930i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −106.770 | + | 184.932i | −0.343313 | + | 0.594636i | −0.985046 | − | 0.172292i | \(-0.944883\pi\) |
0.641732 | + | 0.766929i | \(0.278216\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 148.248 | + | 124.395i | 0.473635 | + | 0.397427i | 0.848118 | − | 0.529807i | \(-0.177736\pi\) |
−0.374484 | + | 0.927234i | \(0.622180\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −60.2871 | − | 104.420i | −0.191388 | − | 0.331493i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −204.114 | − | 560.798i | −0.643892 | − | 1.76908i | −0.639140 | − | 0.769090i | \(-0.720710\pi\) |
−0.00475166 | − | 0.999989i | \(-0.501513\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.32047 | + | 0.938142i | 0.0166786 | + | 0.00294088i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −221.408 | + | 185.783i | −0.689744 | + | 0.578764i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −301.355 | − | 122.433i | −0.932987 | − | 0.379050i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.6910 | + | 18.6998i | 0.0482799 | + | 0.0575378i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 33.5492 | − | 190.267i | 0.102597 | − | 0.581856i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −265.549 | + | 96.6518i | −0.807139 | + | 0.293775i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 479.438 | − | 276.804i | 1.44845 | − | 0.836265i | 0.450065 | − | 0.892996i | \(-0.351401\pi\) |
0.998390 | + | 0.0567306i | \(0.0180676\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −117.923 | + | 140.535i | −0.354123 | + | 0.422028i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 29.6584 | + | 17.1233i | 0.0885326 | + | 0.0511143i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 60.2142 | − | 10.6174i | 0.178677 | − | 0.0315056i | −0.0835936 | − | 0.996500i | \(-0.526640\pi\) |
0.262271 | + | 0.964994i | \(0.415529\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 93.2866 | + | 33.9535i | 0.275182 | + | 0.100158i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 1.29325i | − | 0.00379253i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −360.386 | −1.05069 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −38.0244 | + | 104.471i | −0.110216 | + | 0.302815i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −34.8091 | − | 197.412i | −0.100315 | − | 0.568912i | −0.992989 | − | 0.118209i | \(-0.962285\pi\) |
0.892674 | − | 0.450703i | \(-0.148826\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 127.380 | − | 220.629i | 0.364986 | − | 0.632173i | −0.623788 | − | 0.781593i | \(-0.714407\pi\) |
0.988774 | + | 0.149420i | \(0.0477406\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −83.0480 | − | 69.6856i | −0.236604 | − | 0.198534i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 48.6888 | + | 84.3315i | 0.137929 | + | 0.238899i | 0.926712 | − | 0.375771i | \(-0.122622\pi\) |
−0.788784 | + | 0.614671i | \(0.789289\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 36.2422 | + | 99.5747i | 0.102091 | + | 0.280492i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −146.784 | − | 25.8819i | −0.411158 | − | 0.0724983i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 435.611 | − | 365.521i | 1.21340 | − | 1.01817i | 0.214259 | − | 0.976777i | \(-0.431266\pi\) |
0.999143 | − | 0.0413888i | \(-0.0131782\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −203.023 | + | 298.500i | −0.562392 | + | 0.826871i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 140.438 | + | 167.368i | 0.386882 | + | 0.461068i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 90.1098 | − | 511.038i | 0.246876 | − | 1.40010i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 403.610 | − | 146.902i | 1.09975 | − | 0.400278i | 0.272529 | − | 0.962148i | \(-0.412140\pi\) |
0.827226 | + | 0.561870i | \(0.189918\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 281.860 | − | 162.732i | 0.763849 | − | 0.441009i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.7514 | − | 19.9635i | 0.0451520 | − | 0.0538101i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 168.596 | + | 97.3387i | 0.451999 | + | 0.260962i | 0.708674 | − | 0.705536i | \(-0.249294\pi\) |
−0.256675 | + | 0.966498i | \(0.582627\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −240.344 | + | 42.3792i | −0.640919 | + | 0.113011i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 109.373 | + | 39.8086i | 0.290115 | + | 0.105593i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 296.888i | 0.783345i | 0.920105 | + | 0.391672i | \(0.128103\pi\) | ||||
−0.920105 | + | 0.391672i | \(0.871897\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −304.289 | −0.798659 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −86.3957 | + | 237.370i | −0.225576 | + | 0.619766i | −0.999915 | − | 0.0130049i | \(-0.995860\pi\) |
0.774339 | + | 0.632771i | \(0.218083\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.689831 | − | 3.91222i | −0.00179177 | − | 0.0101616i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −118.319 | + | 204.934i | −0.305733 | + | 0.529545i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −218.384 | − | 183.246i | −0.561398 | − | 0.471069i | 0.317381 | − | 0.948298i | \(-0.397197\pi\) |
−0.878779 | + | 0.477229i | \(0.841641\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −120.857 | − | 209.330i | −0.309096 | − | 0.535371i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.4758 | + | 59.0044i | 0.0546459 | + | 0.150138i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 600.369 | + | 105.861i | 1.51992 | + | 0.268003i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −515.532 | + | 432.583i | −1.29857 | + | 1.08963i | −0.308178 | + | 0.951329i | \(0.599719\pi\) |
−0.990390 | + | 0.138300i | \(0.955836\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −62.2626 | + | 153.252i | −0.156047 | + | 0.384091i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 349.553 | + | 416.581i | 0.871703 | + | 1.03886i | 0.998896 | + | 0.0469775i | \(0.0149589\pi\) |
−0.127193 | + | 0.991878i | \(0.540597\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.83817 | − | 27.4386i | 0.0120054 | − | 0.0680859i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −14.5883 | + | 5.30969i | −0.0360204 | + | 0.0131103i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.23455 | + | 3.02217i | −0.0128613 | + | 0.00742548i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −388.659 | + | 463.185i | −0.950266 | + | 1.13248i | 0.0408077 | + | 0.999167i | \(0.487007\pi\) |
−0.991074 | + | 0.133316i | \(0.957438\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −254.924 | − | 147.180i | −0.620253 | − | 0.358103i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 268.314 | − | 47.3110i | 0.649670 | − | 0.114554i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 426.237 | + | 155.137i | 1.02708 | + | 0.373825i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 47.8997i | 0.114867i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 66.8368 | 0.159515 | 0.0797575 | − | 0.996814i | \(-0.474585\pi\) | ||||
0.0797575 | + | 0.996814i | \(0.474585\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −70.5506 | + | 193.836i | −0.167579 | + | 0.460419i | −0.994847 | − | 0.101389i | \(-0.967671\pi\) |
0.827268 | + | 0.561807i | \(0.189894\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 58.4119 | + | 331.271i | 0.138090 | + | 0.783145i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 51.3058 | − | 88.8643i | 0.120720 | − | 0.209092i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −334.355 | − | 280.558i | −0.783034 | − | 0.657043i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.695300 | − | 1.20429i | −0.00162075 | − | 0.00280721i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 89.0241 | + | 244.592i | 0.206552 | + | 0.567498i | 0.999105 | − | 0.0423058i | \(-0.0134704\pi\) |
−0.792552 | + | 0.609804i | \(0.791248\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −207.053 | − | 36.5090i | −0.478182 | − | 0.0843164i | −0.0706382 | − | 0.997502i | \(-0.522504\pi\) |
−0.407544 | + | 0.913186i | \(0.633615\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −172.387 | + | 144.650i | −0.396291 | + | 0.332528i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −255.290 | + | 82.4038i | −0.584187 | + | 0.188567i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 312.137 | + | 371.990i | 0.711018 | + | 0.847359i | 0.993725 | − | 0.111848i | \(-0.0356768\pi\) |
−0.282707 | + | 0.959206i | \(0.591232\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −25.6713 | + | 145.589i | −0.0582116 | + | 0.330135i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 381.133 | − | 138.721i | 0.860346 | − | 0.313140i | 0.126095 | − | 0.992018i | \(-0.459756\pi\) |
0.734251 | + | 0.678878i | \(0.237533\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 582.193 | − | 336.129i | 1.30830 | − | 0.755347i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 182.455 | − | 217.441i | 0.408176 | − | 0.486445i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.43341 | + | 4.86903i | 0.0187826 | + | 0.0108442i | 0.509362 | − | 0.860552i | \(-0.329881\pi\) |
−0.490579 | + | 0.871397i | \(0.663215\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.5602 | − | 1.86205i | 0.0234151 | − | 0.00412872i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 45.4308 | + | 16.5354i | 0.100289 | + | 0.0365021i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 85.5854i | − | 0.188100i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 233.468 | 0.510871 | 0.255435 | − | 0.966826i | \(-0.417781\pi\) | ||||
0.255435 | + | 0.966826i | \(0.417781\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −155.862 | + | 428.228i | −0.339569 | + | 0.932959i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −121.198 | − | 687.346i | −0.262902 | − | 1.49099i | −0.774944 | − | 0.632030i | \(-0.782222\pi\) |
0.512043 | − | 0.858960i | \(-0.328889\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −380.012 | + | 658.199i | −0.820759 | + | 1.42160i | 0.0843581 | + | 0.996436i | \(0.473116\pi\) |
−0.905117 | + | 0.425162i | \(0.860217\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 41.2657 | + | 34.6260i | 0.0887434 | + | 0.0744646i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −197.668 | − | 342.370i | −0.423271 | − | 0.733127i | 0.572986 | − | 0.819565i | \(-0.305785\pi\) |
−0.996257 | + | 0.0864380i | \(0.972452\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.9505 | + | 35.5813i | 0.0276131 | + | 0.0758663i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −368.710 | − | 65.0135i | −0.782824 | − | 0.138033i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.97249 | + | 5.01151i | −0.0126268 | + | 0.0105952i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −84.4828 | − | 76.3647i | −0.177858 | − | 0.160768i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −19.9399 | − | 23.7635i | −0.0418028 | − | 0.0498186i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 69.4029 | − | 393.603i | 0.144891 | − | 0.821719i | −0.822563 | − | 0.568674i | \(-0.807457\pi\) |
0.967454 | − | 0.253045i | \(-0.0814322\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −122.366 | + | 44.5377i | −0.254400 | + | 0.0925940i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −106.453 | + | 61.4609i | −0.220400 | + | 0.127248i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 228.607 | − | 272.443i | 0.471355 | − | 0.561739i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −833.507 | − | 481.226i | −1.71151 | − | 0.988143i | −0.932525 | − | 0.361105i | \(-0.882400\pi\) |
−0.778989 | − | 0.627038i | \(-0.784267\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 280.590 | − | 49.4756i | 0.573804 | − | 0.101177i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 881.263 | + | 320.754i | 1.79483 | + | 0.653266i | 0.998850 | + | 0.0479482i | \(0.0152682\pi\) |
0.795984 | + | 0.605318i | \(0.206954\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 489.260i | − | 0.992414i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.72874 | −0.00955301 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −40.0713 | + | 110.095i | −0.0806264 | + | 0.221519i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −53.2720 | − | 302.121i | −0.106758 | − | 0.605452i | −0.990504 | − | 0.137486i | \(-0.956098\pi\) |
0.883746 | − | 0.467966i | \(-0.155013\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.7587 | + | 18.6345i | −0.0214744 | + | 0.0371947i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −705.700 | − | 592.153i | −1.40298 | − | 1.17724i | −0.959757 | − | 0.280832i | \(-0.909390\pi\) |
−0.443226 | − | 0.896410i | \(-0.646166\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −255.950 | − | 443.318i | −0.506832 | − | 0.877858i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 94.1530 | + | 258.683i | 0.185706 | + | 0.510223i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 751.063 | + | 132.433i | 1.47557 | + | 0.260182i | 0.852805 | − | 0.522229i | \(-0.174900\pi\) |
0.622762 | + | 0.782412i | \(0.286011\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 439.516 | − | 368.797i | 0.860109 | − | 0.721717i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 428.390 | + | 268.840i | 0.835069 | + | 0.524055i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −435.177 | − | 518.624i | −0.845004 | − | 1.00704i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.92451 | + | 10.9144i | −0.00372245 | + | 0.0211111i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 228.489 | − | 83.1633i | 0.440249 | − | 0.160237i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.4959 | + | 21.6483i | −0.0719691 | + | 0.0415514i | −0.535553 | − | 0.844502i | \(-0.679897\pi\) |
0.463584 | + | 0.886053i | \(0.346563\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −511.250 | + | 609.284i | −0.977533 | + | 1.16498i | 0.00875793 | + | 0.999962i | \(0.497212\pi\) |
−0.986291 | + | 0.165017i | \(0.947232\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −45.1914 | − | 26.0913i | −0.0860788 | − | 0.0496976i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −115.339 | + | 20.3374i | −0.218860 | + | 0.0385909i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 309.775 | + | 112.749i | 0.585586 | + | 0.213136i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 324.313i | − | 0.610759i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 231.019 | 0.433432 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −238.605 | + | 655.561i | −0.445990 | + | 1.22535i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −100.735 | − | 571.297i | −0.187589 | − | 1.06387i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.43537 | + | 4.21819i | −0.00451832 | + | 0.00782596i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −407.967 | − | 342.325i | −0.754097 | − | 0.632763i | 0.182486 | − | 0.983209i | \(-0.441586\pi\) |
−0.936583 | + | 0.350446i | \(0.886030\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 66.1217 | + | 114.526i | 0.121771 | + | 0.210914i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −159.496 | − | 438.213i | −0.292654 | − | 0.804061i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.49765 | + | 1.14571i | 0.0118787 | + | 0.00209454i | 0.179584 | − | 0.983743i | \(-0.442525\pi\) |
−0.167706 | + | 0.985837i | \(0.553636\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −397.998 | + | 333.960i | −0.724952 | + | 0.608307i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −530.909 | − | 113.921i | −0.963536 | − | 0.206752i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 433.264 | + | 516.344i | 0.783480 | + | 0.933715i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 43.7190 | − | 247.943i | 0.0787731 | − | 0.446744i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −158.030 | + | 57.5181i | −0.283716 | + | 0.103264i | −0.479958 | − | 0.877291i | \(-0.659348\pi\) |
0.196242 | + | 0.980555i | \(0.437126\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −145.465 | + | 83.9844i | −0.260224 | + | 0.150240i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.75737 | + | 4.47786i | −0.00669763 | + | 0.00798192i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −692.075 | − | 399.570i | −1.22926 | − | 0.709715i | −0.262387 | − | 0.964963i | \(-0.584510\pi\) |
−0.966876 | + | 0.255248i | \(0.917843\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 235.979 | − | 41.6094i | 0.417661 | − | 0.0736450i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −16.1295 | − | 5.87067i | −0.0284471 | − | 0.0103539i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 799.192i | 1.40456i | 0.711903 | + | 0.702278i | \(0.247834\pi\) | ||||
−0.711903 | + | 0.702278i | \(0.752166\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 761.851 | 1.33424 | 0.667120 | − | 0.744950i | \(-0.267527\pi\) | ||||
0.667120 | + | 0.744950i | \(0.267527\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −82.5860 | + | 226.903i | −0.144129 | + | 0.395991i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.6950 | − | 83.3396i | −0.0255565 | − | 0.144938i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 88.2589 | − | 152.869i | 0.152962 | − | 0.264937i | −0.779353 | − | 0.626585i | \(-0.784452\pi\) |
0.932315 | + | 0.361647i | \(0.117786\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 297.531 | + | 249.658i | 0.513871 | + | 0.431189i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 250.757 | + | 434.324i | 0.431596 | + | 0.747546i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.349563 | − | 0.960417i | −0.000599594 | − | 0.00164737i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −100.328 | − | 17.6906i | −0.171502 | − | 0.0302404i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 260.508 | − | 218.592i | 0.443796 | − | 0.372389i | −0.393332 | − | 0.919397i | \(-0.628678\pi\) |
0.837128 | + | 0.547007i | \(0.184233\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.78722 | + | 129.893i | −0.00812771 | + | 0.220531i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 144.227 | + | 171.884i | 0.244040 | + | 0.290835i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.4003 | − | 166.737i | 0.0495789 | − | 0.281176i | −0.949932 | − | 0.312458i | \(-0.898848\pi\) |
0.999511 | + | 0.0312817i | \(0.00995889\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −338.064 | + | 123.045i | −0.568176 | + | 0.206799i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 433.527 | − | 250.297i | 0.726176 | − | 0.419258i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.9949 | + | 33.3630i | −0.0467361 | + | 0.0556979i | −0.788906 | − | 0.614514i | \(-0.789352\pi\) |
0.742170 | + | 0.670212i | \(0.233797\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 829.079 | + | 478.669i | 1.37950 | + | 0.796454i | 0.992099 | − | 0.125458i | \(-0.0400400\pi\) |
0.387400 | + | 0.921912i | \(0.373373\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 44.3875 | − | 7.82671i | 0.0736110 | − | 0.0129796i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 495.554 | + | 180.367i | 0.819098 | + | 0.298127i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 383.700i | − | 0.632124i | −0.948738 | − | 0.316062i | \(-0.897639\pi\) | ||
0.948738 | − | 0.316062i | \(-0.102361\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −248.810 | −0.408555 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −81.6635 | + | 224.369i | −0.133655 | + | 0.367215i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 92.6661 | + | 525.535i | 0.151168 | + | 0.857317i | 0.962206 | + | 0.272323i | \(0.0877920\pi\) |
−0.811038 | + | 0.584994i | \(0.801097\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −223.328 | + | 386.815i | −0.363135 | + | 0.628967i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −522.562 | − | 438.481i | −0.846940 | − | 0.710667i | 0.112174 | − | 0.993689i | \(-0.464219\pi\) |
−0.959113 | + | 0.283022i | \(0.908663\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −90.2029 | − | 156.236i | −0.145724 | − | 0.252401i | 0.783919 | − | 0.620863i | \(-0.213218\pi\) |
−0.929643 | + | 0.368462i | \(0.879884\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 128.542 | + | 353.166i | 0.206992 | + | 0.568705i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 731.992 | + | 129.070i | 1.17495 | + | 0.207175i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −336.471 | + | 282.333i | −0.538353 | + | 0.451732i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.98416 | + | 5.11985i | 0.00635433 | + | 0.00816564i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 351.850 | + | 419.319i | 0.559380 | + | 0.666644i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −104.292 | + | 591.469i | −0.165280 | + | 0.937351i | 0.783495 | + | 0.621399i | \(0.213435\pi\) |
−0.948775 | + | 0.315953i | \(0.897676\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 424.386 | − | 154.464i | 0.670437 | − | 0.244019i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −636.070 | + | 367.235i | −1.00169 | + | 0.578323i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −67.4513 | + | 80.3854i | −0.105889 | + | 0.126194i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 120.777 | + | 69.7308i | 0.189010 | + | 0.109125i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −762.921 | + | 134.524i | −1.19020 | + | 0.209865i | −0.733460 | − | 0.679733i | \(-0.762096\pi\) |
−0.456744 | + | 0.889598i | \(0.650985\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 101.877 | + | 37.0801i | 0.158440 | + | 0.0576674i | 0.420023 | − | 0.907514i | \(-0.362022\pi\) |
−0.261583 | + | 0.965181i | \(0.584244\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 324.753i | − | 0.503492i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −230.970 | −0.356986 | −0.178493 | − | 0.983941i | \(-0.557122\pi\) | ||||
−0.178493 | + | 0.983941i | \(0.557122\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.65455 | − | 10.0408i | 0.00563105 | − | 0.0154712i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.3425 | + | 58.6550i | 0.0158870 | + | 0.0900998i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 341.320 | − | 591.183i | 0.522695 | − | 0.905334i | −0.476956 | − | 0.878927i | \(-0.658260\pi\) |
0.999651 | − | 0.0264072i | \(-0.00840665\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 116.102 | + | 97.4213i | 0.177255 | + | 0.148735i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −341.478 | − | 591.458i | −0.519754 | − | 0.900240i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 212.474 | + | 583.768i | 0.322419 | + | 0.885839i | 0.989970 | + | 0.141275i | \(0.0451203\pi\) |
−0.667551 | + | 0.744564i | \(0.732657\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1006.10 | − | 177.403i | −1.52209 | − | 0.268386i | −0.650838 | − | 0.759217i | \(-0.725582\pi\) |
−0.871255 | + | 0.490831i | \(0.836693\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −96.4712 | + | 80.9489i | −0.145507 | + | 0.122095i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 54.8039 | + | 395.493i | 0.0824120 | + | 0.594726i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −259.364 | − | 309.098i | −0.388852 | − | 0.463416i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −34.9341 | + | 198.121i | −0.0522184 | + | 0.296145i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.0854 | + | 5.85459i | −0.0239722 | + | 0.00872518i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 753.056 | − | 434.777i | 1.11895 | − | 0.646028i | 0.177820 | − | 0.984063i | \(-0.443095\pi\) |
0.941134 | + | 0.338035i | \(0.109762\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −102.555 | + | 122.220i | −0.151933 | + | 0.181067i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 523.041 | + | 301.978i | 0.772587 | + | 0.446053i | 0.833797 | − | 0.552072i | \(-0.186163\pi\) |
−0.0612099 | + | 0.998125i | \(0.519496\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 387.251 | − | 68.2828i | 0.570325 | − | 0.100564i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −585.774 | − | 213.204i | −0.860167 | − | 0.313075i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 192.200i | 0.281406i | 0.990052 | + | 0.140703i | \(0.0449363\pi\) | ||||
−0.990052 | + | 0.140703i | \(0.955064\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −710.506 | −1.03724 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 85.3349 | − | 234.456i | 0.124214 | − | 0.341275i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.82359 | − | 21.6847i | −0.00554948 | − | 0.0314727i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 119.347 | − | 206.715i | 0.172716 | − | 0.299154i | −0.766652 | − | 0.642063i | \(-0.778079\pi\) |
0.939369 | + | 0.342909i | \(0.111412\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.00514 | − | 3.36071i | −0.00577942 | − | 0.00484951i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 57.8084 | + | 100.127i | 0.0831776 | + | 0.144068i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −332.135 | − | 912.533i | −0.476520 | − | 1.30923i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 167.308 | + | 29.5009i | 0.239353 | + | 0.0422044i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.1679 | − | 11.0492i | 0.0187845 | − | 0.0157621i | −0.633347 | − | 0.773868i | \(-0.718319\pi\) |
0.652132 | + | 0.758106i | \(0.273875\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 536.939 | − | 284.167i | 0.763783 | − | 0.404220i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −296.734 | − | 353.634i | −0.420900 | − | 0.501609i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 98.2820 | − | 557.385i | 0.139013 | − | 0.788380i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 89.6670 | − | 32.6361i | 0.126470 | − | 0.0460312i | −0.278010 | − | 0.960578i | \(-0.589675\pi\) |
0.404480 | + | 0.914547i | \(0.367453\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 694.847 | − | 401.170i | 0.977281 | − | 0.564233i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −62.0863 | + | 73.9916i | −0.0870776 | + | 0.103775i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.90684 | − | 1.67826i | −0.00406551 | − | 0.00234722i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −377.849 | + | 66.6249i | −0.526986 | + | 0.0929218i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −458.305 | − | 166.809i | −0.637420 | − | 0.232002i | 0.00303783 | − | 0.999995i | \(-0.499033\pi\) |
−0.640458 | + | 0.767994i | \(0.721255\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 748.543i | − | 1.03820i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −54.4475 | −0.0753077 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 58.5856 | − | 160.962i | 0.0808077 | − | 0.222017i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.77453 | − | 10.0639i | −0.00244090 | − | 0.0138430i | 0.983563 | − | 0.180565i | \(-0.0577927\pi\) |
−0.986004 | + | 0.166722i | \(0.946682\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 206.137 | − | 357.041i | 0.282767 | − | 0.489768i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 540.875 | + | 453.848i | 0.739910 | + | 0.620859i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 251.354 | + | 435.357i | 0.342911 | + | 0.593939i | 0.984972 | − | 0.172714i | \(-0.0552538\pi\) |
−0.642061 | + | 0.766653i | \(0.721920\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −69.3903 | − | 190.648i | −0.0944086 | − | 0.259385i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.46244 | + | 0.257868i | 0.00198431 | + | 0.000349888i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −172.968 | + | 145.138i | −0.234057 | + | 0.196397i | −0.752271 | − | 0.658854i | \(-0.771042\pi\) |
0.518214 | + | 0.855251i | \(0.326597\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 65.3772 | + | 123.532i | 0.0882283 | + | 0.166709i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.9359 | + | 27.3339i | 0.0308693 | + | 0.0367886i | 0.781258 | − | 0.624208i | \(-0.214578\pi\) |
−0.750389 | + | 0.660997i | \(0.770134\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 118.972 | − | 674.725i | 0.159694 | − | 0.905671i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 560.973 | − | 204.178i | 0.750968 | − | 0.273330i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −667.999 | + | 385.670i | −0.891855 | + | 0.514913i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 662.322 | − | 789.325i | 0.881920 | − | 1.05103i | −0.116406 | − | 0.993202i | \(-0.537137\pi\) |
0.998326 | − | 0.0578298i | \(-0.0184181\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.61189 | + | 1.50797i | 0.00346864 | + | 0.00200262i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 114.922 | − | 20.2639i | 0.152215 | − | 0.0268396i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1300.99 | − | 473.521i | −1.71861 | − | 0.625524i | −0.720894 | − | 0.693045i | \(-0.756269\pi\) |
−0.997718 | + | 0.0675215i | \(0.978491\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.82081i | 0.00635152i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −723.684 | −0.950965 | −0.475483 | − | 0.879725i | \(-0.657727\pi\) | ||||
−0.475483 | + | 0.879725i | \(0.657727\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 176.348 | − | 484.511i | 0.231124 | − | 0.635008i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 74.3630 | + | 421.733i | 0.0972065 | + | 0.551286i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 115.101 | − | 199.361i | 0.150067 | − | 0.259923i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 726.061 | + | 609.238i | 0.944163 | + | 0.792247i | 0.978305 | − | 0.207170i | \(-0.0664254\pi\) |
−0.0341420 | + | 0.999417i | \(0.510870\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −325.436 | − | 563.671i | −0.422095 | − | 0.731091i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −190.354 | − | 522.993i | −0.246253 | − | 0.676575i | −0.999816 | − | 0.0191990i | \(-0.993888\pi\) |
0.753562 | − | 0.657376i | \(-0.228334\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −40.3809 | − | 7.12024i | −0.0521044 | − | 0.00918740i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 213.242 | − | 178.931i | 0.274443 | − | 0.230285i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1067.55 | + | 147.932i | −1.37041 | + | 0.189899i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.95352 | + | 3.51987i | 0.00378172 | + | 0.00450687i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −132.100 | + | 749.175i | −0.168710 | + | 0.956801i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −849.194 | + | 309.082i | −1.08178 | + | 0.393734i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −296.622 | + | 171.255i | −0.376902 | + | 0.217604i | −0.676469 | − | 0.736471i | \(-0.736491\pi\) |
0.299568 | + | 0.954075i | \(0.403158\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −155.987 | + | 185.899i | −0.197703 | + | 0.235613i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 229.441 | + | 132.468i | 0.290064 | + | 0.167469i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −363.182 | + | 64.0387i | −0.457984 | + | 0.0807550i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 40.0047 | + | 14.5605i | 0.0503204 | + | 0.0183151i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1411.17i | 1.77060i | 0.465019 | + | 0.885301i | \(0.346048\pi\) | ||||
−0.465019 | + | 0.885301i | \(0.653952\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1003.67 | 1.25616 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 302.607 | − | 831.407i | 0.377787 | − | 1.03796i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.90734 | − | 22.1596i | −0.00486593 | − | 0.0275960i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −148.350 | + | 256.949i | −0.184285 | + | 0.319192i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −73.2823 | − | 61.4911i | −0.0908083 | − | 0.0761972i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 703.686 | + | 1218.82i | 0.869822 | + | 1.50658i | 0.862178 | + | 0.506605i | \(0.169100\pi\) |
0.00764386 | + | 0.999971i | \(0.497567\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 172.417 | + | 473.711i | 0.212598 | + | 0.584108i | 0.999454 | − | 0.0330281i | \(-0.0105151\pi\) |
−0.786857 | + | 0.617136i | \(0.788293\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −256.170 | − | 45.1696i | −0.315092 | − | 0.0555592i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 526.821 | − | 442.055i | 0.646406 | − | 0.542399i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 618.420 | − | 481.242i | 0.756941 | − | 0.589035i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −72.4033 | − | 86.2869i | −0.0884045 | − | 0.105356i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −210.354 | + | 1192.98i | −0.256216 | + | 1.45308i | 0.536714 | + | 0.843764i | \(0.319665\pi\) |
−0.792931 | + | 0.609312i | \(0.791446\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −385.490 | + | 140.307i | −0.468396 | + | 0.170482i | −0.565426 | − | 0.824799i | \(-0.691288\pi\) |
0.0970294 | + | 0.995282i | \(0.469066\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.77234 | + | 1.02326i | −0.00214829 | + | 0.00124031i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −283.443 | + | 337.795i | −0.342737 | + | 0.408458i | −0.909687 | − | 0.415294i | \(-0.863679\pi\) |
0.566950 | + | 0.823752i | \(0.308123\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 134.275 | + | 77.5237i | 0.161972 | + | 0.0935147i | 0.578795 | − | 0.815473i | \(-0.303523\pi\) |
−0.416823 | + | 0.908988i | \(0.636856\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 131.552 | − | 23.1962i | 0.158306 | − | 0.0279136i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 414.499 | + | 150.865i | 0.497597 | + | 0.181111i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 51.9369i | 0.0621999i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 182.103 | 0.217566 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 250.499 | − | 688.241i | 0.298569 | − | 0.820311i | −0.696171 | − | 0.717876i | \(-0.745115\pi\) |
0.994740 | − | 0.102435i | \(-0.0326633\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.21334 | + | 23.8950i | 0.00500991 | + | 0.0284126i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 57.0796 | − | 98.8648i | 0.0677101 | − | 0.117277i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 509.007 | + | 427.108i | 0.602376 | + | 0.505453i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 291.537 | + | 504.957i | 0.344200 | + | 0.596171i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −60.1406 | − | 165.235i | −0.0708370 | − | 0.194623i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 444.575 | + | 78.3906i | 0.522415 | + | 0.0921158i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −226.059 | + | 189.686i | −0.265016 | + | 0.222375i | −0.765606 | − | 0.643309i | \(-0.777561\pi\) |
0.500590 | + | 0.865685i | \(0.333116\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 474.949 | + | 17.5043i | 0.555496 | + | 0.0204729i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.3399 | + | 29.0071i | 0.0284013 | + | 0.0338473i | 0.780058 | − | 0.625707i | \(-0.215189\pi\) |
−0.751657 | + | 0.659554i | \(0.770745\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.0571 | − | 164.791i | 0.0338266 | − | 0.191840i | −0.963212 | − | 0.268743i | \(-0.913392\pi\) |
0.997039 | + | 0.0769024i | \(0.0245030\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −464.063 | + | 168.905i | −0.538981 | + | 0.196173i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1171.31 | + | 676.254i | −1.35725 | + | 0.783608i | −0.989252 | − | 0.146219i | \(-0.953290\pi\) |
−0.367997 | + | 0.929827i | \(0.619956\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 377.255 | − | 449.595i | 0.436133 | − | 0.519763i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.39375 | + | 3.69143i | 0.00737456 | + | 0.00425771i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26.0332 | − | 4.59035i | 0.0299576 | − | 0.00528234i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.0635 | + | 10.9422i | 0.0345161 | + | 0.0125628i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 468.073i | − | 0.536166i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −651.312 | −0.744356 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −171.809 | + | 472.041i | −0.195905 | + | 0.538245i | −0.998283 | − | 0.0585713i | \(-0.981346\pi\) |
0.802378 | + | 0.596816i | \(0.203568\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 122.401 | + | 694.170i | 0.139250 | + | 0.789727i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −170.295 | + | 294.960i | −0.193297 | + | 0.334801i | −0.946341 | − | 0.323170i | \(-0.895252\pi\) |
0.753044 | + | 0.657971i | \(0.228585\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1203.63 | + | 1009.96i | 1.36311 | + | 1.14379i | 0.975008 | + | 0.222169i | \(0.0713137\pi\) |
0.388102 | + | 0.921616i | \(0.373131\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 222.538 | + | 385.447i | 0.251455 | + | 0.435533i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.4753 | − | 72.7402i | −0.0298481 | − | 0.0820070i | 0.923874 | − | 0.382698i | \(-0.125005\pi\) |
−0.953722 | + | 0.300691i | \(0.902783\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −799.731 | − | 141.014i | −0.899585 | − | 0.158621i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.515680 | + | 0.432707i | −0.000578766 | + | 0.000485642i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 233.697 | − | 1089.11i | 0.261699 | − | 1.21960i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −900.048 | − | 1072.64i | −1.00564 | − | 1.19848i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18.0350 | + | 102.282i | −0.0201059 | + | 0.114027i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −183.719 | + | 66.8681i | −0.204359 | + | 0.0743805i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −80.1578 | + | 46.2792i | −0.0889654 | + | 0.0513642i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 230.801 | − | 275.058i | 0.255594 | − | 0.304605i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 276.435 | + | 159.600i | 0.305453 | + | 0.176353i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1554.83 | − | 274.159i | 1.71426 | − | 0.302270i | 0.771620 | − | 0.636083i | \(-0.219447\pi\) |
0.942639 | + | 0.333813i | \(0.108335\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −633.085 | − | 230.424i | −0.696464 | − | 0.253492i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1736.18i | 1.90580i | 0.303290 | + | 0.952898i | \(0.401915\pi\) | ||||
−0.303290 | + | 0.952898i | \(0.598085\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.6686 | 0.0215428 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 243.864 | − | 670.012i | 0.266518 | − | 0.732253i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 29.0988 | + | 165.028i | 0.0317326 | + | 0.179965i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −621.707 | + | 1076.83i | −0.676503 | + | 1.17174i | 0.299524 | + | 0.954089i | \(0.403172\pi\) |
−0.976027 | + | 0.217649i | \(0.930161\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −68.6207 | − | 57.5796i | −0.0745067 | − | 0.0625186i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 49.4959 | + | 85.7295i | 0.0536251 | + | 0.0928814i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 65.5453 | + | 180.084i | 0.0708597 | + | 0.194686i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −877.488 | − | 154.725i | −0.946589 | − | 0.166909i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 437.894 | − | 367.436i | 0.471360 | − | 0.395518i | −0.375930 | − | 0.926648i | \(-0.622677\pi\) |
0.847291 | + | 0.531130i | \(0.178232\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 260.221 | − | 414.655i | 0.279507 | − | 0.445387i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −247.919 | − | 295.458i | −0.265722 | − | 0.316675i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.45005 | + | 13.8949i | −0.00262037 | + | 0.0148609i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 76.0200 | − | 27.6690i | 0.0811313 | − | 0.0295294i | −0.301136 | − | 0.953581i | \(-0.597366\pi\) |
0.382267 | + | 0.924052i | \(0.375143\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −302.709 | + | 174.769i | −0.322374 | + | 0.186122i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 617.870 | − | 736.349i | 0.656610 | − | 0.782518i | −0.330285 | − | 0.943881i | \(-0.607145\pi\) |
0.986895 | + | 0.161364i | \(0.0515892\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −693.580 | − | 400.438i | −0.735503 | − | 0.424643i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 550.880 | − | 97.1351i | 0.582942 | − | 0.102788i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1623.43 | − | 590.881i | −1.71429 | − | 0.623951i | −0.716970 | − | 0.697104i | \(-0.754472\pi\) |
−0.997321 | + | 0.0731531i | \(0.976694\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 484.773i | − | 0.510825i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1077.91 | 1.13345 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 520.185 | − | 1429.20i | 0.545840 | − | 1.49968i | −0.293437 | − | 0.955978i | \(-0.594799\pi\) |
0.839277 | − | 0.543704i | \(-0.182979\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 101.208 | + | 573.976i | 0.105976 | + | 0.601022i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.87898 | + | 8.45063i | −0.00509820 | + | 0.00883034i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −601.783 | − | 504.956i | −0.627511 | − | 0.526544i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −457.100 | − | 791.720i | −0.475650 | − | 0.823850i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 314.029 | + | 862.788i | 0.326095 | + | 0.895938i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 923.247 | + | 162.793i | 0.956732 | + | 0.168698i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 347.163 | − | 291.304i | 0.359010 | − | 0.301245i | −0.445386 | − | 0.895339i | \(-0.646934\pi\) |
0.804396 | + | 0.594093i | \(0.202489\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 393.961 | − | 435.842i | 0.406565 | − | 0.449786i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −566.677 | − | 675.340i | −0.583602 | − | 0.695510i | 0.390761 | − | 0.920492i | \(-0.372212\pi\) |
−0.974363 | + | 0.224983i | \(0.927767\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.1978 | + | 125.890i | −0.0228138 | + | 0.129383i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −41.4313 | + | 15.0798i | −0.0424937 | + | 0.0154664i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1269.34 | + | 732.855i | −1.29922 | + | 0.750108i | −0.980270 | − | 0.197662i | \(-0.936665\pi\) |
−0.318954 | + | 0.947770i | \(0.603332\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.7376 | − | 22.3305i | 0.0191395 | − | 0.0228095i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −531.522 | − | 306.874i | −0.541817 | − | 0.312818i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1852.95 | + | 326.724i | −1.88499 | + | 0.332375i | −0.992849 | − | 0.119380i | \(-0.961909\pi\) |
−0.892142 | + | 0.451754i | \(0.850798\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 508.925 | + | 185.234i | 0.516675 | + | 0.188054i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 510.410i | − | 0.517132i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 582.299 | 0.588775 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 179.003 | − | 491.807i | 0.180629 | − | 0.496274i | −0.816024 | − | 0.578017i | \(-0.803827\pi\) |
0.996653 | + | 0.0817435i | \(0.0260488\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 173.633 | + | 984.723i | 0.174857 | + | 0.991664i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 604.148 | − | 1046.42i | 0.607184 | − | 1.05167i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 512.180 | + | 429.770i | 0.513721 | + | 0.431063i | 0.862436 | − | 0.506165i | \(-0.168937\pi\) |
−0.348715 | + | 0.937229i | \(0.613382\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −425.552 | − | 737.077i | −0.425978 | − | 0.737815i |
(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 | 76.3.j.a.13.1 | ✓ | 18 | |
4.3 | odd | 2 | 304.3.z.b.241.3 | 18 | |||
19.3 | odd | 18 | inner | 76.3.j.a.41.1 | yes | 18 | |
19.4 | even | 9 | 1444.3.c.c.721.8 | 18 | |||
19.15 | odd | 18 | 1444.3.c.c.721.11 | 18 | |||
76.3 | even | 18 | 304.3.z.b.193.3 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.3.j.a.13.1 | ✓ | 18 | 1.1 | even | 1 | trivial | |
76.3.j.a.41.1 | yes | 18 | 19.3 | odd | 18 | inner | |
304.3.z.b.193.3 | 18 | 76.3 | even | 18 | |||
304.3.z.b.241.3 | 18 | 4.3 | odd | 2 | |||
1444.3.c.c.721.8 | 18 | 19.4 | even | 9 | |||
1444.3.c.c.721.11 | 18 | 19.15 | odd | 18 |