Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [119,2,Mod(64,119)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(119, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("119.64");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 119 = 7 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 119.g (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.950219784053\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 32 x^{18} + 432 x^{16} + 3200 x^{14} + 14160 x^{12} + 38162 x^{10} + 61088 x^{8} + 53872 x^{6} + \cdots + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 64.8 | ||
Root | \(1.57229i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 119.64 |
Dual form | 119.2.g.a.106.3 |
$q$-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 \(\left(\mathbb{Z}/119\mathbb{Z}\right)^\times\).
\(n\) | \(52\) | \(71\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.57229i | 1.11178i | 0.831257 | + | 0.555889i | \(0.187622\pi\) | ||||
−0.831257 | + | 0.555889i | \(0.812378\pi\) | |||||||
\(3\) | −1.43847 | − | 1.43847i | −0.830503 | − | 0.830503i | 0.157082 | − | 0.987586i | \(-0.449791\pi\) |
−0.987586 | + | 0.157082i | \(0.949791\pi\) | |||||||
\(4\) | −0.472100 | −0.236050 | ||||||||
\(5\) | 2.40051 | + | 2.40051i | 1.07354 | + | 1.07354i | 0.997072 | + | 0.0764665i | \(0.0243638\pi\) |
0.0764665 | + | 0.997072i | \(0.475636\pi\) | |||||||
\(6\) | 2.26170 | − | 2.26170i | 0.923335 | − | 0.923335i | ||||
\(7\) | 0.707107 | − | 0.707107i | 0.267261 | − | 0.267261i | ||||
\(8\) | 2.40230i | 0.849343i | ||||||||
\(9\) | 1.13841i | 0.379471i | ||||||||
\(10\) | −3.77429 | + | 3.77429i | −1.19354 | + | 1.19354i | ||||
\(11\) | −3.30263 | + | 3.30263i | −0.995781 | + | 0.995781i | −0.999991 | − | 0.00421022i | \(-0.998660\pi\) |
0.00421022 | + | 0.999991i | \(0.498660\pi\) | |||||||
\(12\) | 0.679103 | + | 0.679103i | 0.196040 | + | 0.196040i | ||||
\(13\) | 3.63777 | 1.00894 | 0.504468 | − | 0.863430i | \(-0.331689\pi\) | ||||
0.504468 | + | 0.863430i | \(0.331689\pi\) | |||||||
\(14\) | 1.11178 | + | 1.11178i | 0.297135 | + | 0.297135i | ||||
\(15\) | − | 6.90613i | − | 1.78315i | ||||||
\(16\) | −4.72132 | −1.18033 | ||||||||
\(17\) | 1.70860 | − | 3.75243i | 0.414395 | − | 0.910097i | ||||
\(18\) | −1.78992 | −0.421888 | ||||||||
\(19\) | − | 6.19754i | − | 1.42181i | −0.703287 | − | 0.710906i | \(-0.748285\pi\) | ||
0.703287 | − | 0.710906i | \(-0.251715\pi\) | |||||||
\(20\) | −1.13328 | − | 1.13328i | −0.253409 | − | 0.253409i | ||||
\(21\) | −2.03431 | −0.443923 | ||||||||
\(22\) | −5.19270 | − | 5.19270i | −1.10709 | − | 1.10709i | ||||
\(23\) | 0.475240 | − | 0.475240i | 0.0990945 | − | 0.0990945i | −0.655822 | − | 0.754916i | \(-0.727678\pi\) |
0.754916 | + | 0.655822i | \(0.227678\pi\) | |||||||
\(24\) | 3.45565 | − | 3.45565i | 0.705382 | − | 0.705382i | ||||
\(25\) | 6.52485i | 1.30497i | ||||||||
\(26\) | 5.71963i | 1.12171i | ||||||||
\(27\) | −2.67784 | + | 2.67784i | −0.515351 | + | 0.515351i | ||||
\(28\) | −0.333825 | + | 0.333825i | −0.0630870 | + | 0.0630870i | ||||
\(29\) | −3.95461 | − | 3.95461i | −0.734353 | − | 0.734353i | 0.237126 | − | 0.971479i | \(-0.423795\pi\) |
−0.971479 | + | 0.237126i | \(0.923795\pi\) | |||||||
\(30\) | 10.8584 | 1.98247 | ||||||||
\(31\) | −5.41543 | − | 5.41543i | −0.972640 | − | 0.972640i | 0.0269959 | − | 0.999636i | \(-0.491406\pi\) |
−0.999636 | + | 0.0269959i | \(0.991406\pi\) | |||||||
\(32\) | − | 2.61868i | − | 0.462922i | ||||||
\(33\) | 9.50150 | 1.65400 | ||||||||
\(34\) | 5.89991 | + | 2.68641i | 1.01183 | + | 0.460715i | ||||
\(35\) | 3.39483 | 0.573831 | ||||||||
\(36\) | − | 0.537445i | − | 0.0895742i | ||||||
\(37\) | −0.967703 | − | 0.967703i | −0.159089 | − | 0.159089i | 0.623074 | − | 0.782163i | \(-0.285884\pi\) |
−0.782163 | + | 0.623074i | \(0.785884\pi\) | |||||||
\(38\) | 9.74433 | 1.58074 | ||||||||
\(39\) | −5.23284 | − | 5.23284i | −0.837924 | − | 0.837924i | ||||
\(40\) | −5.76674 | + | 5.76674i | −0.911802 | + | 0.911802i | ||||
\(41\) | 0.492170 | − | 0.492170i | 0.0768640 | − | 0.0768640i | −0.667630 | − | 0.744494i | \(-0.732691\pi\) |
0.744494 | + | 0.667630i | \(0.232691\pi\) | |||||||
\(42\) | − | 3.19853i | − | 0.493543i | ||||||
\(43\) | 6.64216i | 1.01292i | 0.862264 | + | 0.506460i | \(0.169046\pi\) | ||||
−0.862264 | + | 0.506460i | \(0.830954\pi\) | |||||||
\(44\) | 1.55917 | − | 1.55917i | 0.235054 | − | 0.235054i | ||||
\(45\) | −2.73277 | + | 2.73277i | −0.407377 | + | 0.407377i | ||||
\(46\) | 0.747216 | + | 0.747216i | 0.110171 | + | 0.110171i | ||||
\(47\) | 4.32592 | 0.631000 | 0.315500 | − | 0.948926i | \(-0.397828\pi\) | ||||
0.315500 | + | 0.948926i | \(0.397828\pi\) | |||||||
\(48\) | 6.79150 | + | 6.79150i | 0.980268 | + | 0.980268i | ||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | −10.2590 | −1.45084 | ||||||||
\(51\) | −7.85554 | + | 2.94000i | −1.10000 | + | 0.411682i | ||||
\(52\) | −1.71739 | −0.238159 | ||||||||
\(53\) | − | 4.07940i | − | 0.560349i | −0.959949 | − | 0.280175i | \(-0.909608\pi\) | ||
0.959949 | − | 0.280175i | \(-0.0903924\pi\) | |||||||
\(54\) | −4.21035 | − | 4.21035i | −0.572956 | − | 0.572956i | ||||
\(55\) | −15.8560 | −2.13802 | ||||||||
\(56\) | 1.69869 | + | 1.69869i | 0.226996 | + | 0.226996i | ||||
\(57\) | −8.91500 | + | 8.91500i | −1.18082 | + | 1.18082i | ||||
\(58\) | 6.21780 | − | 6.21780i | 0.816437 | − | 0.816437i | ||||
\(59\) | − | 2.73239i | − | 0.355727i | −0.984055 | − | 0.177864i | \(-0.943081\pi\) | ||
0.984055 | − | 0.177864i | \(-0.0569186\pi\) | |||||||
\(60\) | 3.26038i | 0.420914i | ||||||||
\(61\) | −8.55455 | + | 8.55455i | −1.09530 | + | 1.09530i | −0.100345 | + | 0.994953i | \(0.531995\pi\) |
−0.994953 | + | 0.100345i | \(0.968005\pi\) | |||||||
\(62\) | 8.51463 | − | 8.51463i | 1.08136 | − | 1.08136i | ||||
\(63\) | 0.804980 | + | 0.804980i | 0.101418 | + | 0.101418i | ||||
\(64\) | −5.32531 | −0.665664 | ||||||||
\(65\) | 8.73248 | + | 8.73248i | 1.08313 | + | 1.08313i | ||||
\(66\) | 14.9391i | 1.83888i | ||||||||
\(67\) | 12.5590 | 1.53433 | 0.767165 | − | 0.641450i | \(-0.221667\pi\) | ||||
0.767165 | + | 0.641450i | \(0.221667\pi\) | |||||||
\(68\) | −0.806627 | + | 1.77152i | −0.0978179 | + | 0.214828i | ||||
\(69\) | −1.36724 | −0.164597 | ||||||||
\(70\) | 5.33766i | 0.637972i | ||||||||
\(71\) | 3.04461 | + | 3.04461i | 0.361328 | + | 0.361328i | 0.864302 | − | 0.502973i | \(-0.167761\pi\) |
−0.502973 | + | 0.864302i | \(0.667761\pi\) | |||||||
\(72\) | −2.73482 | −0.322301 | ||||||||
\(73\) | −1.16753 | − | 1.16753i | −0.136649 | − | 0.136649i | 0.635474 | − | 0.772123i | \(-0.280805\pi\) |
−0.772123 | + | 0.635474i | \(0.780805\pi\) | |||||||
\(74\) | 1.52151 | − | 1.52151i | 0.176872 | − | 0.176872i | ||||
\(75\) | 9.38583 | − | 9.38583i | 1.08378 | − | 1.08378i | ||||
\(76\) | 2.92586i | 0.335619i | ||||||||
\(77\) | 4.67063i | 0.532267i | ||||||||
\(78\) | 8.22754 | − | 8.22754i | 0.931586 | − | 0.931586i | ||||
\(79\) | 7.07442 | − | 7.07442i | 0.795935 | − | 0.795935i | −0.186517 | − | 0.982452i | \(-0.559720\pi\) |
0.982452 | + | 0.186517i | \(0.0597199\pi\) | |||||||
\(80\) | −11.3336 | − | 11.3336i | −1.26713 | − | 1.26713i | ||||
\(81\) | 11.1193 | 1.23547 | ||||||||
\(82\) | 0.773834 | + | 0.773834i | 0.0854557 | + | 0.0854557i | ||||
\(83\) | 4.69160i | 0.514970i | 0.966282 | + | 0.257485i | \(0.0828938\pi\) | ||||
−0.966282 | + | 0.257485i | \(0.917106\pi\) | |||||||
\(84\) | 0.960397 | 0.104788 | ||||||||
\(85\) | 13.1092 | − | 4.90623i | 1.42189 | − | 0.532155i | ||||
\(86\) | −10.4434 | −1.12614 | ||||||||
\(87\) | 11.3772i | 1.21977i | ||||||||
\(88\) | −7.93393 | − | 7.93393i | −0.845759 | − | 0.845759i | ||||
\(89\) | −2.04706 | −0.216988 | −0.108494 | − | 0.994097i | \(-0.534603\pi\) | ||||
−0.108494 | + | 0.994097i | \(0.534603\pi\) | |||||||
\(90\) | −4.29671 | − | 4.29671i | −0.452913 | − | 0.452913i | ||||
\(91\) | 2.57229 | − | 2.57229i | 0.269649 | − | 0.269649i | ||||
\(92\) | −0.224361 | + | 0.224361i | −0.0233912 | + | 0.0233912i | ||||
\(93\) | 15.5799i | 1.61556i | ||||||||
\(94\) | 6.80161i | 0.701532i | ||||||||
\(95\) | 14.8772 | − | 14.8772i | 1.52637 | − | 1.52637i | ||||
\(96\) | −3.76691 | + | 3.76691i | −0.384459 | + | 0.384459i | ||||
\(97\) | −2.99116 | − | 2.99116i | −0.303706 | − | 0.303706i | 0.538756 | − | 0.842462i | \(-0.318895\pi\) |
−0.842462 | + | 0.538756i | \(0.818895\pi\) | |||||||
\(98\) | 1.57229 | 0.158825 | ||||||||
\(99\) | −3.75976 | − | 3.75976i | −0.377870 | − | 0.377870i | ||||
\(100\) | − | 3.08038i | − | 0.308038i | ||||||
\(101\) | −5.38529 | −0.535856 | −0.267928 | − | 0.963439i | \(-0.586339\pi\) | ||||
−0.267928 | + | 0.963439i | \(0.586339\pi\) | |||||||
\(102\) | −4.62253 | − | 12.3512i | −0.457699 | − | 1.22295i | ||||
\(103\) | −3.96255 | −0.390442 | −0.195221 | − | 0.980759i | \(-0.562542\pi\) | ||||
−0.195221 | + | 0.980759i | \(0.562542\pi\) | |||||||
\(104\) | 8.73903i | 0.856932i | ||||||||
\(105\) | −4.88337 | − | 4.88337i | −0.476568 | − | 0.476568i | ||||
\(106\) | 6.41401 | 0.622984 | ||||||||
\(107\) | 8.04673 | + | 8.04673i | 0.777907 | + | 0.777907i | 0.979475 | − | 0.201568i | \(-0.0646035\pi\) |
−0.201568 | + | 0.979475i | \(0.564604\pi\) | |||||||
\(108\) | 1.26421 | − | 1.26421i | 0.121649 | − | 0.121649i | ||||
\(109\) | −3.11536 | + | 3.11536i | −0.298398 | + | 0.298398i | −0.840386 | − | 0.541988i | \(-0.817672\pi\) |
0.541988 | + | 0.840386i | \(0.317672\pi\) | |||||||
\(110\) | − | 24.9302i | − | 2.37700i | ||||||
\(111\) | 2.78403i | 0.264248i | ||||||||
\(112\) | −3.33848 | + | 3.33848i | −0.315457 | + | 0.315457i | ||||
\(113\) | −8.20042 | + | 8.20042i | −0.771430 | + | 0.771430i | −0.978357 | − | 0.206926i | \(-0.933654\pi\) |
0.206926 | + | 0.978357i | \(0.433654\pi\) | |||||||
\(114\) | −14.0170 | − | 14.0170i | −1.31281 | − | 1.31281i | ||||
\(115\) | 2.28163 | 0.212764 | ||||||||
\(116\) | 1.86697 | + | 1.86697i | 0.173344 | + | 0.173344i | ||||
\(117\) | 4.14129i | 0.382862i | ||||||||
\(118\) | 4.29612 | 0.395490 | ||||||||
\(119\) | −1.44521 | − | 3.86153i | −0.132482 | − | 0.353985i | ||||
\(120\) | 16.5906 | 1.51451 | ||||||||
\(121\) | − | 10.8148i | − | 0.983159i | ||||||
\(122\) | −13.4502 | − | 13.4502i | −1.21773 | − | 1.21773i | ||||
\(123\) | −1.41595 | −0.127672 | ||||||||
\(124\) | 2.55662 | + | 2.55662i | 0.229591 | + | 0.229591i | ||||
\(125\) | −3.66041 | + | 3.66041i | −0.327397 | + | 0.327397i | ||||
\(126\) | −1.26566 | + | 1.26566i | −0.112754 | + | 0.112754i | ||||
\(127\) | 5.12889i | 0.455115i | 0.973765 | + | 0.227558i | \(0.0730740\pi\) | ||||
−0.973765 | + | 0.227558i | \(0.926926\pi\) | |||||||
\(128\) | − | 13.6103i | − | 1.20299i | ||||||
\(129\) | 9.55457 | − | 9.55457i | 0.841233 | − | 0.841233i | ||||
\(130\) | −13.7300 | + | 13.7300i | −1.20420 | + | 1.20420i | ||||
\(131\) | 5.90678 | + | 5.90678i | 0.516078 | + | 0.516078i | 0.916382 | − | 0.400304i | \(-0.131096\pi\) |
−0.400304 | + | 0.916382i | \(0.631096\pi\) | |||||||
\(132\) | −4.48566 | −0.390426 | ||||||||
\(133\) | −4.38232 | − | 4.38232i | −0.379995 | − | 0.379995i | ||||
\(134\) | 19.7465i | 1.70583i | ||||||||
\(135\) | −12.8564 | −1.10650 | ||||||||
\(136\) | 9.01447 | + | 4.10456i | 0.772984 | + | 0.351964i | ||||
\(137\) | −20.1939 | −1.72528 | −0.862639 | − | 0.505821i | \(-0.831190\pi\) | ||||
−0.862639 | + | 0.505821i | \(0.831190\pi\) | |||||||
\(138\) | − | 2.14970i | − | 0.182995i | ||||||
\(139\) | 5.51905 | + | 5.51905i | 0.468120 | + | 0.468120i | 0.901305 | − | 0.433185i | \(-0.142610\pi\) |
−0.433185 | + | 0.901305i | \(0.642610\pi\) | |||||||
\(140\) | −1.60270 | −0.135453 | ||||||||
\(141\) | −6.22272 | − | 6.22272i | −0.524048 | − | 0.524048i | ||||
\(142\) | −4.78701 | + | 4.78701i | −0.401717 | + | 0.401717i | ||||
\(143\) | −12.0142 | + | 12.0142i | −1.00468 | + | 1.00468i | ||||
\(144\) | − | 5.37482i | − | 0.447902i | ||||||
\(145\) | − | 18.9861i | − | 1.57671i | ||||||
\(146\) | 1.83570 | − | 1.83570i | 0.151923 | − | 0.151923i | ||||
\(147\) | −1.43847 | + | 1.43847i | −0.118643 | + | 0.118643i | ||||
\(148\) | 0.456852 | + | 0.456852i | 0.0375530 | + | 0.0375530i | ||||
\(149\) | 0.670580 | 0.0549361 | 0.0274680 | − | 0.999623i | \(-0.491256\pi\) | ||||
0.0274680 | + | 0.999623i | \(0.491256\pi\) | |||||||
\(150\) | 14.7573 | + | 14.7573i | 1.20492 | + | 1.20492i | ||||
\(151\) | 11.4237i | 0.929644i | 0.885404 | + | 0.464822i | \(0.153882\pi\) | ||||
−0.885404 | + | 0.464822i | \(0.846118\pi\) | |||||||
\(152\) | 14.8884 | 1.20761 | ||||||||
\(153\) | 4.27182 | + | 1.94509i | 0.345356 | + | 0.157251i | ||||
\(154\) | −7.34359 | −0.591763 | ||||||||
\(155\) | − | 25.9995i | − | 2.08833i | ||||||
\(156\) | 2.47042 | + | 2.47042i | 0.197792 | + | 0.197792i | ||||
\(157\) | 23.3832 | 1.86618 | 0.933090 | − | 0.359642i | \(-0.117101\pi\) | ||||
0.933090 | + | 0.359642i | \(0.117101\pi\) | |||||||
\(158\) | 11.1231 | + | 11.1231i | 0.884903 | + | 0.884903i | ||||
\(159\) | −5.86812 | + | 5.86812i | −0.465372 | + | 0.465372i | ||||
\(160\) | 6.28617 | − | 6.28617i | 0.496965 | − | 0.496965i | ||||
\(161\) | − | 0.672091i | − | 0.0529682i | ||||||
\(162\) | 17.4827i | 1.37357i | ||||||||
\(163\) | 8.53975 | − | 8.53975i | 0.668885 | − | 0.668885i | −0.288573 | − | 0.957458i | \(-0.593181\pi\) |
0.957458 | + | 0.288573i | \(0.0931808\pi\) | |||||||
\(164\) | −0.232353 | + | 0.232353i | −0.0181437 | + | 0.0181437i | ||||
\(165\) | 22.8084 | + | 22.8084i | 1.77563 | + | 1.77563i | ||||
\(166\) | −7.37656 | −0.572532 | ||||||||
\(167\) | −17.3482 | − | 17.3482i | −1.34244 | − | 1.34244i | −0.893620 | − | 0.448823i | \(-0.851843\pi\) |
−0.448823 | − | 0.893620i | \(-0.648157\pi\) | |||||||
\(168\) | − | 4.88703i | − | 0.377043i | ||||||
\(169\) | 0.233365 | 0.0179511 | ||||||||
\(170\) | 7.71402 | + | 20.6115i | 0.591638 | + | 1.58083i | ||||
\(171\) | 7.05537 | 0.539537 | ||||||||
\(172\) | − | 3.13576i | − | 0.239100i | ||||||
\(173\) | 2.52101 | + | 2.52101i | 0.191669 | + | 0.191669i | 0.796417 | − | 0.604748i | \(-0.206726\pi\) |
−0.604748 | + | 0.796417i | \(0.706726\pi\) | |||||||
\(174\) | −17.8883 | −1.35611 | ||||||||
\(175\) | 4.61377 | + | 4.61377i | 0.348768 | + | 0.348768i | ||||
\(176\) | 15.5928 | − | 15.5928i | 1.17535 | − | 1.17535i | ||||
\(177\) | −3.93047 | + | 3.93047i | −0.295433 | + | 0.295433i | ||||
\(178\) | − | 3.21857i | − | 0.241242i | ||||||
\(179\) | 3.96115i | 0.296071i | 0.988982 | + | 0.148035i | \(0.0472949\pi\) | ||||
−0.988982 | + | 0.148035i | \(0.952705\pi\) | |||||||
\(180\) | 1.29014 | − | 1.29014i | 0.0961614 | − | 0.0961614i | ||||
\(181\) | −1.36267 | + | 1.36267i | −0.101287 | + | 0.101287i | −0.755934 | − | 0.654648i | \(-0.772817\pi\) |
0.654648 | + | 0.755934i | \(0.272817\pi\) | |||||||
\(182\) | 4.04439 | + | 4.04439i | 0.299790 | + | 0.299790i | ||||
\(183\) | 24.6110 | 1.81930 | ||||||||
\(184\) | 1.14167 | + | 1.14167i | 0.0841652 | + | 0.0841652i | ||||
\(185\) | − | 4.64595i | − | 0.341577i | ||||||
\(186\) | −24.4961 | −1.79614 | ||||||||
\(187\) | 6.75002 | + | 18.0357i | 0.493610 | + | 1.31890i | ||||
\(188\) | −2.04227 | −0.148948 | ||||||||
\(189\) | 3.78704i | 0.275467i | ||||||||
\(190\) | 23.3913 | + | 23.3913i | 1.69699 | + | 1.69699i | ||||
\(191\) | −25.1726 | −1.82143 | −0.910714 | − | 0.413038i | \(-0.864468\pi\) | ||||
−0.910714 | + | 0.413038i | \(0.864468\pi\) | |||||||
\(192\) | 7.66032 | + | 7.66032i | 0.552836 | + | 0.552836i | ||||
\(193\) | 7.95263 | − | 7.95263i | 0.572443 | − | 0.572443i | −0.360367 | − | 0.932810i | \(-0.617349\pi\) |
0.932810 | + | 0.360367i | \(0.117349\pi\) | |||||||
\(194\) | 4.70297 | − | 4.70297i | 0.337654 | − | 0.337654i | ||||
\(195\) | − | 25.1229i | − | 1.79909i | ||||||
\(196\) | 0.472100i | 0.0337214i | ||||||||
\(197\) | −16.0035 | + | 16.0035i | −1.14020 | + | 1.14020i | −0.151789 | + | 0.988413i | \(0.548503\pi\) |
−0.988413 | + | 0.151789i | \(0.951497\pi\) | |||||||
\(198\) | 5.91144 | − | 5.91144i | 0.420108 | − | 0.420108i | ||||
\(199\) | −3.71192 | − | 3.71192i | −0.263131 | − | 0.263131i | 0.563194 | − | 0.826325i | \(-0.309572\pi\) |
−0.826325 | + | 0.563194i | \(0.809572\pi\) | |||||||
\(200\) | −15.6747 | −1.10837 | ||||||||
\(201\) | −18.0658 | − | 18.0658i | −1.27427 | − | 1.27427i | ||||
\(202\) | − | 8.46724i | − | 0.595753i | ||||||
\(203\) | −5.59267 | −0.392528 | ||||||||
\(204\) | 3.70860 | − | 1.38797i | 0.259654 | − | 0.0971775i | ||||
\(205\) | 2.36291 | 0.165033 | ||||||||
\(206\) | − | 6.23029i | − | 0.434085i | ||||||
\(207\) | 0.541021 | + | 0.541021i | 0.0376035 | + | 0.0376035i | ||||
\(208\) | −17.1751 | −1.19088 | ||||||||
\(209\) | 20.4682 | + | 20.4682i | 1.41581 | + | 1.41581i | ||||
\(210\) | 7.67808 | − | 7.67808i | 0.529838 | − | 0.529838i | ||||
\(211\) | −6.87817 | + | 6.87817i | −0.473513 | + | 0.473513i | −0.903050 | − | 0.429536i | \(-0.858677\pi\) |
0.429536 | + | 0.903050i | \(0.358677\pi\) | |||||||
\(212\) | 1.92589i | 0.132270i | ||||||||
\(213\) | − | 8.75918i | − | 0.600169i | ||||||
\(214\) | −12.6518 | + | 12.6518i | −0.864860 | + | 0.864860i | ||||
\(215\) | −15.9445 | + | 15.9445i | −1.08741 | + | 1.08741i | ||||
\(216\) | −6.43299 | − | 6.43299i | −0.437710 | − | 0.437710i | ||||
\(217\) | −7.65857 | −0.519898 | ||||||||
\(218\) | −4.89826 | − | 4.89826i | −0.331752 | − | 0.331752i | ||||
\(219\) | 3.35892i | 0.226975i | ||||||||
\(220\) | 7.48560 | 0.504679 | ||||||||
\(221\) | 6.21547 | − | 13.6505i | 0.418098 | − | 0.918229i | ||||
\(222\) | −4.37731 | −0.293786 | ||||||||
\(223\) | − | 17.5438i | − | 1.17482i | −0.809289 | − | 0.587411i | \(-0.800147\pi\) | ||
0.809289 | − | 0.587411i | \(-0.199853\pi\) | |||||||
\(224\) | −1.85169 | − | 1.85169i | −0.123721 | − | 0.123721i | ||||
\(225\) | −7.42798 | −0.495199 | ||||||||
\(226\) | −12.8934 | − | 12.8934i | −0.857659 | − | 0.857659i | ||||
\(227\) | −5.89982 | + | 5.89982i | −0.391585 | + | 0.391585i | −0.875252 | − | 0.483667i | \(-0.839305\pi\) |
0.483667 | + | 0.875252i | \(0.339305\pi\) | |||||||
\(228\) | 4.20877 | − | 4.20877i | 0.278732 | − | 0.278732i | ||||
\(229\) | 15.3443i | 1.01398i | 0.861952 | + | 0.506990i | \(0.169242\pi\) | ||||
−0.861952 | + | 0.506990i | \(0.830758\pi\) | |||||||
\(230\) | 3.58739i | 0.236546i | ||||||||
\(231\) | 6.71857 | − | 6.71857i | 0.442050 | − | 0.442050i | ||||
\(232\) | 9.50018 | − | 9.50018i | 0.623717 | − | 0.623717i | ||||
\(233\) | 17.3081 | + | 17.3081i | 1.13389 | + | 1.13389i | 0.989524 | + | 0.144371i | \(0.0461158\pi\) |
0.144371 | + | 0.989524i | \(0.453884\pi\) | |||||||
\(234\) | −6.51131 | −0.425658 | ||||||||
\(235\) | 10.3844 | + | 10.3844i | 0.677403 | + | 0.677403i | ||||
\(236\) | 1.28996i | 0.0839694i | ||||||||
\(237\) | −20.3527 | −1.32205 | ||||||||
\(238\) | 6.07144 | − | 2.27229i | 0.393553 | − | 0.147290i | ||||
\(239\) | 14.5771 | 0.942916 | 0.471458 | − | 0.881889i | \(-0.343728\pi\) | ||||
0.471458 | + | 0.881889i | \(0.343728\pi\) | |||||||
\(240\) | 32.6061i | 2.10471i | ||||||||
\(241\) | −10.7589 | − | 10.7589i | −0.693041 | − | 0.693041i | 0.269859 | − | 0.962900i | \(-0.413023\pi\) |
−0.962900 | + | 0.269859i | \(0.913023\pi\) | |||||||
\(242\) | 17.0039 | 1.09305 | ||||||||
\(243\) | −7.96123 | − | 7.96123i | −0.510713 | − | 0.510713i | ||||
\(244\) | 4.03860 | − | 4.03860i | 0.258545 | − | 0.258545i | ||||
\(245\) | 2.40051 | − | 2.40051i | 0.153363 | − | 0.153363i | ||||
\(246\) | − | 2.22628i | − | 0.141942i | ||||||
\(247\) | − | 22.5452i | − | 1.43452i | ||||||
\(248\) | 13.0095 | − | 13.0095i | 0.826104 | − | 0.826104i | ||||
\(249\) | 6.74874 | − | 6.74874i | 0.427684 | − | 0.427684i | ||||
\(250\) | −5.75524 | − | 5.75524i | −0.363993 | − | 0.363993i | ||||
\(251\) | 1.54033 | 0.0972246 | 0.0486123 | − | 0.998818i | \(-0.484520\pi\) | ||||
0.0486123 | + | 0.998818i | \(0.484520\pi\) | |||||||
\(252\) | −0.380031 | − | 0.380031i | −0.0239397 | − | 0.0239397i | ||||
\(253\) | 3.13909i | 0.197353i | ||||||||
\(254\) | −8.06411 | −0.505987 | ||||||||
\(255\) | −25.9147 | − | 11.7998i | −1.62284 | − | 0.738931i | ||||
\(256\) | 10.7487 | 0.671797 | ||||||||
\(257\) | − | 4.02923i | − | 0.251337i | −0.992072 | − | 0.125668i | \(-0.959893\pi\) | ||
0.992072 | − | 0.125668i | \(-0.0401075\pi\) | |||||||
\(258\) | 15.0226 | + | 15.0226i | 0.935264 | + | 0.935264i | ||||
\(259\) | −1.36854 | −0.0850368 | ||||||||
\(260\) | −4.12260 | − | 4.12260i | −0.255673 | − | 0.255673i | ||||
\(261\) | 4.50199 | − | 4.50199i | 0.278666 | − | 0.278666i | ||||
\(262\) | −9.28718 | + | 9.28718i | −0.573764 | + | 0.573764i | ||||
\(263\) | 17.9741i | 1.10833i | 0.832407 | + | 0.554164i | \(0.186962\pi\) | ||||
−0.832407 | + | 0.554164i | \(0.813038\pi\) | |||||||
\(264\) | 22.8255i | 1.40481i | ||||||||
\(265\) | 9.79263 | − | 9.79263i | 0.601557 | − | 0.601557i | ||||
\(266\) | 6.89028 | − | 6.89028i | 0.422470 | − | 0.422470i | ||||
\(267\) | 2.94464 | + | 2.94464i | 0.180209 | + | 0.180209i | ||||
\(268\) | −5.92912 | −0.362178 | ||||||||
\(269\) | 12.7503 | + | 12.7503i | 0.777400 | + | 0.777400i | 0.979388 | − | 0.201988i | \(-0.0647403\pi\) |
−0.201988 | + | 0.979388i | \(0.564740\pi\) | |||||||
\(270\) | − | 20.2139i | − | 1.23018i | ||||||
\(271\) | 16.7080 | 1.01494 | 0.507469 | − | 0.861670i | \(-0.330581\pi\) | ||||
0.507469 | + | 0.861670i | \(0.330581\pi\) | |||||||
\(272\) | −8.06683 | + | 17.7164i | −0.489123 | + | 1.07422i | ||||
\(273\) | −7.40035 | −0.447889 | ||||||||
\(274\) | − | 31.7506i | − | 1.91812i | ||||||
\(275\) | −21.5492 | − | 21.5492i | −1.29946 | − | 1.29946i | ||||
\(276\) | 0.645475 | 0.0388530 | ||||||||
\(277\) | −0.737934 | − | 0.737934i | −0.0443381 | − | 0.0443381i | 0.684590 | − | 0.728928i | \(-0.259981\pi\) |
−0.728928 | + | 0.684590i | \(0.759981\pi\) | |||||||
\(278\) | −8.67755 | + | 8.67755i | −0.520445 | + | 0.520445i | ||||
\(279\) | 6.16500 | − | 6.16500i | 0.369089 | − | 0.369089i | ||||
\(280\) | 8.15541i | 0.487379i | ||||||||
\(281\) | − | 3.53036i | − | 0.210604i | −0.994440 | − | 0.105302i | \(-0.966419\pi\) | ||
0.994440 | − | 0.105302i | \(-0.0335809\pi\) | |||||||
\(282\) | 9.78393 | − | 9.78393i | 0.582625 | − | 0.582625i | ||||
\(283\) | −1.28939 | + | 1.28939i | −0.0766462 | + | 0.0766462i | −0.744391 | − | 0.667744i | \(-0.767260\pi\) |
0.667744 | + | 0.744391i | \(0.267260\pi\) | |||||||
\(284\) | −1.43736 | − | 1.43736i | −0.0852915 | − | 0.0852915i | ||||
\(285\) | −42.8010 | −2.53531 | ||||||||
\(286\) | −18.8898 | − | 18.8898i | −1.11698 | − | 1.11698i | ||||
\(287\) | − | 0.696033i | − | 0.0410855i | ||||||
\(288\) | 2.98115 | 0.175666 | ||||||||
\(289\) | −11.1614 | − | 12.8228i | −0.656553 | − | 0.754280i | ||||
\(290\) | 29.8517 | 1.75295 | ||||||||
\(291\) | 8.60540i | 0.504458i | ||||||||
\(292\) | 0.551191 | + | 0.551191i | 0.0322560 | + | 0.0322560i | ||||
\(293\) | 14.9585 | 0.873883 | 0.436942 | − | 0.899490i | \(-0.356062\pi\) | ||||
0.436942 | + | 0.899490i | \(0.356062\pi\) | |||||||
\(294\) | −2.26170 | − | 2.26170i | −0.131905 | − | 0.131905i | ||||
\(295\) | 6.55912 | − | 6.55912i | 0.381887 | − | 0.381887i | ||||
\(296\) | 2.32472 | − | 2.32472i | 0.135121 | − | 0.135121i | ||||
\(297\) | − | 17.6879i | − | 1.02635i | ||||||
\(298\) | 1.05435i | 0.0610767i | ||||||||
\(299\) | 1.72882 | − | 1.72882i | 0.0999800 | − | 0.0999800i | ||||
\(300\) | −4.43105 | + | 4.43105i | −0.255827 | + | 0.255827i | ||||
\(301\) | 4.69671 | + | 4.69671i | 0.270714 | + | 0.270714i | ||||
\(302\) | −17.9613 | −1.03356 | ||||||||
\(303\) | 7.74659 | + | 7.74659i | 0.445030 | + | 0.445030i | ||||
\(304\) | 29.2606i | 1.67821i | ||||||||
\(305\) | −41.0705 | −2.35169 | ||||||||
\(306\) | −3.05825 | + | 6.71654i | −0.174828 | + | 0.383959i | ||||
\(307\) | −7.16409 | −0.408876 | −0.204438 | − | 0.978879i | \(-0.565537\pi\) | ||||
−0.204438 | + | 0.978879i | \(0.565537\pi\) | |||||||
\(308\) | − | 2.20500i | − | 0.125642i | ||||||
\(309\) | 5.70003 | + | 5.70003i | 0.324263 | + | 0.324263i | ||||
\(310\) | 40.8788 | 2.32176 | ||||||||
\(311\) | −4.45087 | − | 4.45087i | −0.252386 | − | 0.252386i | 0.569562 | − | 0.821948i | \(-0.307113\pi\) |
−0.821948 | + | 0.569562i | \(0.807113\pi\) | |||||||
\(312\) | 12.5709 | − | 12.5709i | 0.711685 | − | 0.711685i | ||||
\(313\) | 22.1833 | − | 22.1833i | 1.25387 | − | 1.25387i | 0.299905 | − | 0.953969i | \(-0.403045\pi\) |
0.953969 | − | 0.299905i | \(-0.0969550\pi\) | |||||||
\(314\) | 36.7652i | 2.07478i | ||||||||
\(315\) | 3.86472i | 0.217752i | ||||||||
\(316\) | −3.33983 | + | 3.33983i | −0.187880 | + | 0.187880i | ||||
\(317\) | 11.7136 | − | 11.7136i | 0.657900 | − | 0.657900i | −0.296983 | − | 0.954883i | \(-0.595980\pi\) |
0.954883 | + | 0.296983i | \(0.0959805\pi\) | |||||||
\(318\) | −9.22639 | − | 9.22639i | −0.517390 | − | 0.517390i | ||||
\(319\) | 26.1213 | 1.46251 | ||||||||
\(320\) | −12.7834 | − | 12.7834i | −0.714616 | − | 0.714616i | ||||
\(321\) | − | 23.1500i | − | 1.29211i | ||||||
\(322\) | 1.05672 | 0.0588889 | ||||||||
\(323\) | −23.2558 | − | 10.5891i | −1.29399 | − | 0.589192i | ||||
\(324\) | −5.24940 | −0.291633 | ||||||||
\(325\) | 23.7359i | 1.31663i | ||||||||
\(326\) | 13.4270 | + | 13.4270i | 0.743651 | + | 0.743651i | ||||
\(327\) | 8.96274 | 0.495640 | ||||||||
\(328\) | 1.18234 | + | 1.18234i | 0.0652839 | + | 0.0652839i | ||||
\(329\) | 3.05889 | − | 3.05889i | 0.168642 | − | 0.168642i | ||||
\(330\) | −35.8614 | + | 35.8614i | −1.97411 | + | 1.97411i | ||||
\(331\) | 4.73294i | 0.260146i | 0.991504 | + | 0.130073i | \(0.0415212\pi\) | ||||
−0.991504 | + | 0.130073i | \(0.958479\pi\) | |||||||
\(332\) | − | 2.21490i | − | 0.121559i | ||||||
\(333\) | 1.10165 | − | 1.10165i | 0.0603698 | − | 0.0603698i | ||||
\(334\) | 27.2764 | − | 27.2764i | 1.49250 | − | 1.49250i | ||||
\(335\) | 30.1480 | + | 30.1480i | 1.64716 | + | 1.64716i | ||||
\(336\) | 9.60463 | 0.523975 | ||||||||
\(337\) | 17.0523 | + | 17.0523i | 0.928898 | + | 0.928898i | 0.997635 | − | 0.0687369i | \(-0.0218969\pi\) |
−0.0687369 | + | 0.997635i | \(0.521897\pi\) | |||||||
\(338\) | 0.366917i | 0.0199577i | ||||||||
\(339\) | 23.5922 | 1.28135 | ||||||||
\(340\) | −6.18886 | + | 2.31623i | −0.335638 | + | 0.125615i | ||||
\(341\) | 35.7703 | 1.93707 | ||||||||
\(342\) | 11.0931i | 0.599846i | ||||||||
\(343\) | −0.707107 | − | 0.707107i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | −15.9565 | −0.860316 | ||||||||
\(345\) | −3.28207 | − | 3.28207i | −0.176701 | − | 0.176701i | ||||
\(346\) | −3.96376 | + | 3.96376i | −0.213093 | + | 0.213093i | ||||
\(347\) | −16.1971 | + | 16.1971i | −0.869505 | + | 0.869505i | −0.992418 | − | 0.122912i | \(-0.960777\pi\) |
0.122912 | + | 0.992418i | \(0.460777\pi\) | |||||||
\(348\) | − | 5.37118i | − | 0.287925i | ||||||
\(349\) | − | 10.1897i | − | 0.545442i | −0.962093 | − | 0.272721i | \(-0.912076\pi\) | ||
0.962093 | − | 0.272721i | \(-0.0879235\pi\) | |||||||
\(350\) | −7.25419 | + | 7.25419i | −0.387753 | + | 0.387753i | ||||
\(351\) | −9.74137 | + | 9.74137i | −0.519956 | + | 0.519956i | ||||
\(352\) | 8.64855 | + | 8.64855i | 0.460969 | + | 0.460969i | ||||
\(353\) | −16.7999 | −0.894167 | −0.447084 | − | 0.894492i | \(-0.647537\pi\) | ||||
−0.447084 | + | 0.894492i | \(0.647537\pi\) | |||||||
\(354\) | −6.17985 | − | 6.17985i | −0.328455 | − | 0.328455i | ||||
\(355\) | 14.6172i | 0.775800i | ||||||||
\(356\) | 0.966416 | 0.0512199 | ||||||||
\(357\) | −3.47581 | + | 7.63360i | −0.183959 | + | 0.404013i | ||||
\(358\) | −6.22809 | −0.329165 | ||||||||
\(359\) | 28.2418i | 1.49055i | 0.666759 | + | 0.745273i | \(0.267681\pi\) | ||||
−0.666759 | + | 0.745273i | \(0.732319\pi\) | |||||||
\(360\) | −6.56494 | − | 6.56494i | −0.346003 | − | 0.346003i | ||||
\(361\) | −19.4095 | −1.02155 | ||||||||
\(362\) | −2.14252 | − | 2.14252i | −0.112608 | − | 0.112608i | ||||
\(363\) | −15.5567 | + | 15.5567i | −0.816517 | + | 0.816517i | ||||
\(364\) | −1.21438 | + | 1.21438i | −0.0636507 | + | 0.0636507i | ||||
\(365\) | − | 5.60532i | − | 0.293396i | ||||||
\(366\) | 38.6956i | 2.02265i | ||||||||
\(367\) | −13.3024 | + | 13.3024i | −0.694382 | + | 0.694382i | −0.963193 | − | 0.268811i | \(-0.913369\pi\) |
0.268811 | + | 0.963193i | \(0.413369\pi\) | |||||||
\(368\) | −2.24376 | + | 2.24376i | −0.116964 | + | 0.116964i | ||||
\(369\) | 0.560293 | + | 0.560293i | 0.0291677 | + | 0.0291677i | ||||
\(370\) | 7.30479 | 0.379758 | ||||||||
\(371\) | −2.88457 | − | 2.88457i | −0.149760 | − | 0.149760i | ||||
\(372\) | − | 7.35527i | − | 0.381353i | ||||||
\(373\) | 30.9655 | 1.60333 | 0.801666 | − | 0.597772i | \(-0.203947\pi\) | ||||
0.801666 | + | 0.597772i | \(0.203947\pi\) | |||||||
\(374\) | −28.3574 | + | 10.6130i | −1.46633 | + | 0.548785i | ||||
\(375\) | 10.5308 | 0.543809 | ||||||||
\(376\) | 10.3922i | 0.535936i | ||||||||
\(377\) | −14.3860 | − | 14.3860i | −0.740915 | − | 0.740915i | ||||
\(378\) | −5.95433 | −0.306258 | ||||||||
\(379\) | −8.80375 | − | 8.80375i | −0.452218 | − | 0.452218i | 0.443872 | − | 0.896090i | \(-0.353604\pi\) |
−0.896090 | + | 0.443872i | \(0.853604\pi\) | |||||||
\(380\) | −7.02353 | + | 7.02353i | −0.360300 | + | 0.360300i | ||||
\(381\) | 7.37778 | − | 7.37778i | 0.377975 | − | 0.377975i | ||||
\(382\) | − | 39.5787i | − | 2.02502i | ||||||
\(383\) | − | 29.8457i | − | 1.52505i | −0.646961 | − | 0.762523i | \(-0.723960\pi\) | ||
0.646961 | − | 0.762523i | \(-0.276040\pi\) | |||||||
\(384\) | −19.5781 | + | 19.5781i | −0.999089 | + | 0.999089i | ||||
\(385\) | −11.2119 | + | 11.2119i | −0.571409 | + | 0.571409i | ||||
\(386\) | 12.5039 | + | 12.5039i | 0.636429 | + | 0.636429i | ||||
\(387\) | −7.56153 | −0.384374 | ||||||||
\(388\) | 1.41212 | + | 1.41212i | 0.0716898 | + | 0.0716898i | ||||
\(389\) | − | 20.9404i | − | 1.06172i | −0.847459 | − | 0.530861i | \(-0.821869\pi\) | ||
0.847459 | − | 0.530861i | \(-0.178131\pi\) | |||||||
\(390\) | 39.5005 | 2.00019 | ||||||||
\(391\) | −0.971311 | − | 2.59530i | −0.0491213 | − | 0.131250i | ||||
\(392\) | 2.40230 | 0.121335 | ||||||||
\(393\) | − | 16.9935i | − | 0.857208i | ||||||
\(394\) | −25.1622 | − | 25.1622i | −1.26765 | − | 1.26765i | ||||
\(395\) | 33.9644 | 1.70893 | ||||||||
\(396\) | 1.77498 | + | 1.77498i | 0.0891963 | + | 0.0891963i | ||||
\(397\) | −20.0540 | + | 20.0540i | −1.00648 | + | 1.00648i | −0.00650493 | + | 0.999979i | \(0.502071\pi\) |
−0.999979 | + | 0.00650493i | \(0.997929\pi\) | |||||||
\(398\) | 5.83622 | − | 5.83622i | 0.292543 | − | 0.292543i | ||||
\(399\) | 12.6077i | 0.631175i | ||||||||
\(400\) | − | 30.8059i | − | 1.54030i | ||||||
\(401\) | 2.31141 | − | 2.31141i | 0.115426 | − | 0.115426i | −0.647034 | − | 0.762461i | \(-0.723991\pi\) |
0.762461 | + | 0.647034i | \(0.223991\pi\) | |||||||
\(402\) | 28.4048 | − | 28.4048i | 1.41670 | − | 1.41670i | ||||
\(403\) | −19.7001 | − | 19.7001i | −0.981331 | − | 0.981331i | ||||
\(404\) | 2.54239 | 0.126489 | ||||||||
\(405\) | 26.6918 | + | 26.6918i | 1.32633 | + | 1.32633i | ||||
\(406\) | − | 8.79330i | − | 0.436404i | ||||||
\(407\) | 6.39193 | 0.316836 | ||||||||
\(408\) | −7.06277 | − | 18.8714i | −0.349659 | − | 0.934273i | ||||
\(409\) | −34.3864 | −1.70030 | −0.850149 | − | 0.526542i | \(-0.823488\pi\) | ||||
−0.850149 | + | 0.526542i | \(0.823488\pi\) | |||||||
\(410\) | 3.71518i | 0.183480i | ||||||||
\(411\) | 29.0483 | + | 29.0483i | 1.43285 | + | 1.43285i | ||||
\(412\) | 1.87072 | 0.0921638 | ||||||||
\(413\) | −1.93209 | − | 1.93209i | −0.0950721 | − | 0.0950721i | ||||
\(414\) | −0.850642 | + | 0.850642i | −0.0418068 | + | 0.0418068i | ||||
\(415\) | −11.2622 | + | 11.2622i | −0.552840 | + | 0.552840i | ||||
\(416\) | − | 9.52617i | − | 0.467059i | ||||||
\(417\) | − | 15.8780i | − | 0.777550i | ||||||
\(418\) | −32.1819 | + | 32.1819i | −1.57407 | + | 1.57407i | ||||
\(419\) | −12.3869 | + | 12.3869i | −0.605140 | + | 0.605140i | −0.941672 | − | 0.336532i | \(-0.890746\pi\) |
0.336532 | + | 0.941672i | \(0.390746\pi\) | |||||||
\(420\) | 2.30544 | + | 2.30544i | 0.112494 | + | 0.112494i | ||||
\(421\) | −13.1028 | −0.638593 | −0.319296 | − | 0.947655i | \(-0.603447\pi\) | ||||
−0.319296 | + | 0.947655i | \(0.603447\pi\) | |||||||
\(422\) | −10.8145 | − | 10.8145i | −0.526441 | − | 0.526441i | ||||
\(423\) | 4.92469i | 0.239447i | ||||||||
\(424\) | 9.79997 | 0.475929 | ||||||||
\(425\) | 24.4840 | + | 11.1483i | 1.18765 | + | 0.540773i | ||||
\(426\) | 13.7720 | 0.667254 | ||||||||
\(427\) | 12.0980i | 0.585461i | ||||||||
\(428\) | −3.79886 | − | 3.79886i | −0.183625 | − | 0.183625i | ||||
\(429\) | 34.5643 | 1.66878 | ||||||||
\(430\) | −25.0695 | − | 25.0695i | −1.20896 | − | 1.20896i | ||||
\(431\) | 18.5848 | − | 18.5848i | 0.895197 | − | 0.895197i | −0.0998095 | − | 0.995007i | \(-0.531823\pi\) |
0.995007 | + | 0.0998095i | \(0.0318233\pi\) | |||||||
\(432\) | 12.6430 | − | 12.6430i | 0.608284 | − | 0.608284i | ||||
\(433\) | 0.783681i | 0.0376613i | 0.999823 | + | 0.0188307i | \(0.00599434\pi\) | ||||
−0.999823 | + | 0.0188307i | \(0.994006\pi\) | |||||||
\(434\) | − | 12.0415i | − | 0.578011i | ||||||
\(435\) | −27.3111 | + | 27.3111i | −1.30947 | + | 1.30947i | ||||
\(436\) | 1.47076 | − | 1.47076i | 0.0704367 | − | 0.0704367i | ||||
\(437\) | −2.94532 | − | 2.94532i | −0.140894 | − | 0.140894i | ||||
\(438\) | −5.28120 | −0.252346 | ||||||||
\(439\) | 17.7866 | + | 17.7866i | 0.848908 | + | 0.848908i | 0.989997 | − | 0.141089i | \(-0.0450604\pi\) |
−0.141089 | + | 0.989997i | \(0.545060\pi\) | |||||||
\(440\) | − | 38.0909i | − | 1.81591i | ||||||
\(441\) | 1.13841 | 0.0542102 | ||||||||
\(442\) | 21.4625 | + | 9.77254i | 1.02087 | + | 0.464832i | ||||
\(443\) | −12.1317 | −0.576395 | −0.288197 | − | 0.957571i | \(-0.593056\pi\) | ||||
−0.288197 | + | 0.957571i | \(0.593056\pi\) | |||||||
\(444\) | − | 1.31434i | − | 0.0623758i | ||||||
\(445\) | −4.91397 | − | 4.91397i | −0.232945 | − | 0.232945i | ||||
\(446\) | 27.5840 | 1.30614 | ||||||||
\(447\) | −0.964612 | − | 0.964612i | −0.0456246 | − | 0.0456246i | ||||
\(448\) | −3.76556 | + | 3.76556i | −0.177906 | + | 0.177906i | ||||
\(449\) | 26.1661 | − | 26.1661i | 1.23485 | − | 1.23485i | 0.272777 | − | 0.962077i | \(-0.412058\pi\) |
0.962077 | − | 0.272777i | \(-0.0879421\pi\) | |||||||
\(450\) | − | 11.6790i | − | 0.550551i | ||||||
\(451\) | 3.25091i | 0.153079i | ||||||||
\(452\) | 3.87142 | − | 3.87142i | 0.182096 | − | 0.182096i | ||||
\(453\) | 16.4326 | − | 16.4326i | 0.772073 | − | 0.772073i | ||||
\(454\) | −9.27624 | − | 9.27624i | −0.435355 | − | 0.435355i | ||||
\(455\) | 12.3496 | 0.578958 | ||||||||
\(456\) | −21.4165 | − | 21.4165i | −1.00292 | − | 1.00292i | ||||
\(457\) | 12.7879i | 0.598192i | 0.954223 | + | 0.299096i | \(0.0966851\pi\) | ||||
−0.954223 | + | 0.299096i | \(0.903315\pi\) | |||||||
\(458\) | −24.1257 | −1.12732 | ||||||||
\(459\) | 5.47306 | + | 14.6238i | 0.255460 | + | 0.682578i | ||||
\(460\) | −1.07716 | −0.0502228 | ||||||||
\(461\) | − | 4.58089i | − | 0.213353i | −0.994294 | − | 0.106677i | \(-0.965979\pi\) | ||
0.994294 | − | 0.106677i | \(-0.0340210\pi\) | |||||||
\(462\) | 10.5636 | + | 10.5636i | 0.491461 | + | 0.491461i | ||||
\(463\) | −1.53844 | −0.0714973 | −0.0357486 | − | 0.999361i | \(-0.511382\pi\) | ||||
−0.0357486 | + | 0.999361i | \(0.511382\pi\) | |||||||
\(464\) | 18.6710 | + | 18.6710i | 0.866779 | + | 0.866779i | ||||
\(465\) | −37.3996 | + | 37.3996i | −1.73437 | + | 1.73437i | ||||
\(466\) | −27.2134 | + | 27.2134i | −1.26064 | + | 1.26064i | ||||
\(467\) | − | 11.0027i | − | 0.509143i | −0.967054 | − | 0.254572i | \(-0.918066\pi\) | ||
0.967054 | − | 0.254572i | \(-0.0819345\pi\) | |||||||
\(468\) | − | 1.95510i | − | 0.0903746i | ||||||
\(469\) | 8.88058 | − | 8.88058i | 0.410067 | − | 0.410067i | ||||
\(470\) | −16.3273 | + | 16.3273i | −0.753122 | + | 0.753122i | ||||
\(471\) | −33.6361 | − | 33.6361i | −1.54987 | − | 1.54987i | ||||
\(472\) | 6.56404 | 0.302134 | ||||||||
\(473\) | −21.9366 | − | 21.9366i | −1.00865 | − | 1.00865i | ||||
\(474\) | − | 32.0004i | − | 1.46983i | ||||||
\(475\) | 40.4380 | 1.85542 | ||||||||
\(476\) | 0.682282 | + | 1.82303i | 0.0312723 | + | 0.0835582i | ||||
\(477\) | 4.64405 | 0.212637 | ||||||||
\(478\) | 22.9195i | 1.04831i | ||||||||
\(479\) | 16.4487 | + | 16.4487i | 0.751558 | + | 0.751558i | 0.974770 | − | 0.223212i | \(-0.0716542\pi\) |
−0.223212 | + | 0.974770i | \(0.571654\pi\) | |||||||
\(480\) | −18.0850 | −0.825462 | ||||||||
\(481\) | −3.52028 | − | 3.52028i | −0.160511 | − | 0.160511i | ||||
\(482\) | 16.9161 | − | 16.9161i | 0.770508 | − | 0.770508i | ||||
\(483\) | −0.966786 | + | 0.966786i | −0.0439903 | + | 0.0439903i | ||||
\(484\) | 5.10564i | 0.232075i | ||||||||
\(485\) | − | 14.3606i | − | 0.652080i | ||||||
\(486\) | 12.5174 | − | 12.5174i | 0.567800 | − | 0.567800i | ||||
\(487\) | 15.5818 | − | 15.5818i | 0.706079 | − | 0.706079i | −0.259629 | − | 0.965708i | \(-0.583600\pi\) |
0.965708 | + | 0.259629i | \(0.0836003\pi\) | |||||||
\(488\) | −20.5506 | − | 20.5506i | −0.930283 | − | 0.930283i | ||||
\(489\) | −24.5684 | −1.11102 | ||||||||
\(490\) | 3.77429 | + | 3.77429i | 0.170505 | + | 0.170505i | ||||
\(491\) | − | 19.2671i | − | 0.869512i | −0.900548 | − | 0.434756i | \(-0.856835\pi\) | ||
0.900548 | − | 0.434756i | \(-0.143165\pi\) | |||||||
\(492\) | 0.668468 | 0.0301369 | ||||||||
\(493\) | −21.5962 | + | 8.08256i | −0.972645 | + | 0.364020i | ||||
\(494\) | 35.4476 | 1.59486 | ||||||||
\(495\) | − | 18.0507i | − | 0.811317i | ||||||
\(496\) | 25.5680 | + | 25.5680i | 1.14804 | + | 1.14804i | ||||
\(497\) | 4.30572 | 0.193138 | ||||||||
\(498\) | 10.6110 | + | 10.6110i | 0.475490 | + | 0.475490i | ||||
\(499\) | 29.9541 | − | 29.9541i | 1.34093 | − | 1.34093i | 0.445793 | − | 0.895136i | \(-0.352922\pi\) |
0.895136 | − | 0.445793i | \(-0.147078\pi\) | |||||||
\(500\) | 1.72808 | − | 1.72808i | 0.0772821 | − | 0.0772821i | ||||
\(501\) | 49.9099i | 2.22981i | ||||||||
\(502\) | 2.42184i | 0.108092i | ||||||||
\(503\) | −7.89613 | + | 7.89613i | −0.352071 | + | 0.352071i | −0.860880 | − | 0.508809i | \(-0.830086\pi\) |
0.508809 | + | 0.860880i | \(0.330086\pi\) | |||||||
\(504\) | −1.93381 | + | 1.93381i | −0.0861386 | + | 0.0861386i | ||||
\(505\) | −12.9274 | − | 12.9274i | −0.575262 | − | 0.575262i | ||||
\(506\) | −4.93556 | −0.219412 | ||||||||
\(507\) | −0.335689 | − | 0.335689i | −0.0149085 | − | 0.0149085i | ||||
\(508\) | − | 2.42135i | − | 0.107430i | ||||||
\(509\) | −33.7960 | −1.49798 | −0.748991 | − | 0.662580i | \(-0.769462\pi\) | ||||
−0.748991 | + | 0.662580i | \(0.769462\pi\) | |||||||
\(510\) | 18.5527 | − | 40.7455i | 0.821527 | − | 1.80424i | ||||
\(511\) | −1.65114 | −0.0730420 | ||||||||
\(512\) | − | 10.3205i | − | 0.456104i | ||||||
\(513\) | 16.5960 | + | 16.5960i | 0.732733 | + | 0.732733i | ||||
\(514\) | 6.33513 | 0.279430 | ||||||||
\(515\) | −9.51213 | − | 9.51213i | −0.419154 | − | 0.419154i | ||||
\(516\) | −4.51071 | + | 4.51071i | −0.198573 | + | 0.198573i | ||||
\(517\) | −14.2869 | + | 14.2869i | −0.628338 | + | 0.628338i | ||||
\(518\) | − | 2.15174i | − | 0.0945420i | ||||||
\(519\) | − | 7.25281i | − | 0.318363i | ||||||
\(520\) | −20.9781 | + | 20.9781i | −0.919950 | + | 0.919950i | ||||
\(521\) | 10.4802 | − | 10.4802i | 0.459145 | − | 0.459145i | −0.439230 | − | 0.898375i | \(-0.644749\pi\) |
0.898375 | + | 0.439230i | \(0.144749\pi\) | |||||||
\(522\) | 7.07843 | + | 7.07843i | 0.309815 | + | 0.309815i | ||||
\(523\) | −2.75940 | −0.120660 | −0.0603300 | − | 0.998178i | \(-0.519215\pi\) | ||||
−0.0603300 | + | 0.998178i | \(0.519215\pi\) | |||||||
\(524\) | −2.78859 | − | 2.78859i | −0.121820 | − | 0.121820i | ||||
\(525\) | − | 13.2736i | − | 0.579306i | ||||||
\(526\) | −28.2605 | −1.23221 | ||||||||
\(527\) | −29.5738 | + | 11.0682i | −1.28825 | + | 0.482139i | ||||
\(528\) | −44.8596 | −1.95226 | ||||||||
\(529\) | 22.5483i | 0.980361i | ||||||||
\(530\) | 15.3969 | + | 15.3969i | 0.668797 | + | 0.668797i | ||||
\(531\) | 3.11059 | 0.134988 | ||||||||
\(532\) | 2.06889 | + | 2.06889i | 0.0896979 | + | 0.0896979i | ||||
\(533\) | 1.79040 | − | 1.79040i | 0.0775508 | − | 0.0775508i | ||||
\(534\) | −4.62983 | + | 4.62983i | −0.200352 | + | 0.200352i | ||||
\(535\) | 38.6325i | 1.67023i | ||||||||
\(536\) | 30.1706i | 1.30317i | ||||||||
\(537\) | 5.69802 | − | 5.69802i | 0.245888 | − | 0.245888i | ||||
\(538\) | −20.0472 | + | 20.0472i | −0.864296 | + | 0.864296i | ||||
\(539\) | 3.30263 | + | 3.30263i | 0.142254 | + | 0.142254i | ||||
\(540\) | 6.06948 | 0.261189 | ||||||||
\(541\) | 7.88750 | + | 7.88750i | 0.339110 | + | 0.339110i | 0.856032 | − | 0.516922i | \(-0.172922\pi\) |
−0.516922 | + | 0.856032i | \(0.672922\pi\) | |||||||
\(542\) | 26.2698i | 1.12839i | ||||||||
\(543\) | 3.92034 | 0.168238 | ||||||||
\(544\) | −9.82642 | − | 4.47427i | −0.421304 | − | 0.191833i | ||||
\(545\) | −14.9569 | −0.640683 | ||||||||
\(546\) | − | 11.6355i | − | 0.497954i | ||||||
\(547\) | 5.17129 | + | 5.17129i | 0.221108 | + | 0.221108i | 0.808965 | − | 0.587857i | \(-0.200028\pi\) |
−0.587857 | + | 0.808965i | \(0.700028\pi\) | |||||||
\(548\) | 9.53351 | 0.407252 | ||||||||
\(549\) | −9.73862 | − | 9.73862i | −0.415634 | − | 0.415634i | ||||
\(550\) | 33.8816 | − | 33.8816i | 1.44472 | − | 1.44472i | ||||
\(551\) | −24.5089 | + | 24.5089i | −1.04411 | + | 1.04411i | ||||
\(552\) | − | 3.28453i | − | 0.139799i | ||||||
\(553\) | − | 10.0047i | − | 0.425445i | ||||||
\(554\) | 1.16025 | − | 1.16025i | 0.0492942 | − | 0.0492942i | ||||
\(555\) | −6.68308 | + | 6.68308i | −0.283681 | + | 0.283681i | ||||
\(556\) | −2.60554 | − | 2.60554i | −0.110500 | − | 0.110500i | ||||
\(557\) | 15.3543 | 0.650583 | 0.325291 | − | 0.945614i | \(-0.394538\pi\) | ||||
0.325291 | + | 0.945614i | \(0.394538\pi\) | |||||||
\(558\) | 9.69318 | + | 9.69318i | 0.410345 | + | 0.410345i | ||||
\(559\) | 24.1626i | 1.02197i | ||||||||
\(560\) | −16.0281 | −0.677310 | ||||||||
\(561\) | 16.2342 | − | 35.6537i | 0.685409 | − | 1.50530i | ||||
\(562\) | 5.55076 | 0.234145 | ||||||||
\(563\) | − | 6.62599i | − | 0.279252i | −0.990204 | − | 0.139626i | \(-0.955410\pi\) | ||
0.990204 | − | 0.139626i | \(-0.0445901\pi\) | |||||||
\(564\) | 2.93775 | + | 2.93775i | 0.123701 | + | 0.123701i | ||||
\(565\) | −39.3703 | −1.65632 | ||||||||
\(566\) | −2.02730 | − | 2.02730i | −0.0852136 | − | 0.0852136i | ||||
\(567\) | 7.86250 | − | 7.86250i | 0.330194 | − | 0.330194i | ||||
\(568\) | −7.31407 | + | 7.31407i | −0.306892 | + | 0.306892i | ||||
\(569\) | − | 36.9677i | − | 1.54977i | −0.632105 | − | 0.774883i | \(-0.717809\pi\) | ||
0.632105 | − | 0.774883i | \(-0.282191\pi\) | |||||||
\(570\) | − | 67.2956i | − | 2.81870i | ||||||
\(571\) | −25.8702 | + | 25.8702i | −1.08264 | + | 1.08264i | −0.0863725 | + | 0.996263i | \(0.527528\pi\) |
−0.996263 | + | 0.0863725i | \(0.972472\pi\) | |||||||
\(572\) | 5.67191 | − | 5.67191i | 0.237154 | − | 0.237154i | ||||
\(573\) | 36.2102 | + | 36.2102i | 1.51270 | + | 1.51270i | ||||
\(574\) | 1.09437 | 0.0456780 | ||||||||
\(575\) | 3.10087 | + | 3.10087i | 0.129315 | + | 0.129315i | ||||
\(576\) | − | 6.06241i | − | 0.252600i | ||||||
\(577\) | 6.70916 | 0.279306 | 0.139653 | − | 0.990200i | \(-0.455401\pi\) | ||||
0.139653 | + | 0.990200i | \(0.455401\pi\) | |||||||
\(578\) | 20.1611 | − | 17.5490i | 0.838591 | − | 0.729941i | ||||
\(579\) | −22.8793 | −0.950832 | ||||||||
\(580\) | 8.96335i | 0.372183i | ||||||||
\(581\) | 3.31746 | + | 3.31746i | 0.137632 | + | 0.137632i | ||||
\(582\) | −13.5302 | −0.560845 | ||||||||
\(583\) | 13.4728 | + | 13.4728i | 0.557985 | + | 0.557985i | ||||
\(584\) | 2.80476 | − | 2.80476i | 0.116062 | − | 0.116062i | ||||
\(585\) | −9.94118 | + | 9.94118i | −0.411017 | + | 0.411017i | ||||
\(586\) | 23.5191i | 0.971564i | ||||||||
\(587\) | − | 0.653601i | − | 0.0269770i | −0.999909 | − | 0.0134885i | \(-0.995706\pi\) | ||
0.999909 | − | 0.0134885i | \(-0.00429365\pi\) | |||||||
\(588\) | 0.679103 | − | 0.679103i | 0.0280057 | − | 0.0280057i | ||||
\(589\) | −33.5623 | + | 33.5623i | −1.38291 | + | 1.38291i | ||||
\(590\) | 10.3129 | + | 10.3129i | 0.424573 | + | 0.424573i | ||||
\(591\) | 46.0412 | 1.89388 | ||||||||
\(592\) | 4.56883 | + | 4.56883i | 0.187778 | + | 0.187778i | ||||
\(593\) | 27.7090i | 1.13787i | 0.822381 | + | 0.568937i | \(0.192645\pi\) | ||||
−0.822381 | + | 0.568937i | \(0.807355\pi\) | |||||||
\(594\) | 27.8105 | 1.14108 | ||||||||
\(595\) | 5.80039 | − | 12.7388i | 0.237793 | − | 0.522241i | ||||
\(596\) | −0.316581 | −0.0129677 | ||||||||
\(597\) | 10.6790i | 0.437063i | ||||||||
\(598\) | 2.71820 | + | 2.71820i | 0.111155 | + | 0.111155i | ||||
\(599\) | −7.54536 | −0.308295 | −0.154148 | − | 0.988048i | \(-0.549263\pi\) | ||||
−0.154148 | + | 0.988048i | \(0.549263\pi\) | |||||||
\(600\) | 22.5476 | + | 22.5476i | 0.920503 | + | 0.920503i | ||||
\(601\) | 12.8735 | − | 12.8735i | 0.525119 | − | 0.525119i | −0.393994 | − | 0.919113i | \(-0.628907\pi\) |
0.919113 | + | 0.393994i | \(0.128907\pi\) | |||||||
\(602\) | −7.38460 | + | 7.38460i | −0.300974 | + | 0.300974i | ||||
\(603\) | 14.2974i | 0.582234i | ||||||||
\(604\) | − | 5.39311i | − | 0.219442i | ||||||
\(605\) | 25.9609 | − | 25.9609i | 1.05546 | − | 1.05546i | ||||
\(606\) | −12.1799 | + | 12.1799i | −0.494775 | + | 0.494775i | ||||
\(607\) | −8.64742 | − | 8.64742i | −0.350988 | − | 0.350988i | 0.509489 | − | 0.860477i | \(-0.329834\pi\) |
−0.860477 | + | 0.509489i | \(0.829834\pi\) | |||||||
\(608\) | −16.2294 | −0.658189 | ||||||||
\(609\) | 8.04490 | + | 8.04490i | 0.325996 | + | 0.325996i | ||||
\(610\) | − | 64.5748i | − | 2.61456i | ||||||
\(611\) | 15.7367 | 0.636639 | ||||||||
\(612\) | −2.01672 | − | 0.918276i | −0.0815212 | − | 0.0371191i | ||||
\(613\) | −39.4099 | −1.59175 | −0.795876 | − | 0.605460i | \(-0.792989\pi\) | ||||
−0.795876 | + | 0.605460i | \(0.792989\pi\) | |||||||
\(614\) | − | 11.2640i | − | 0.454580i | ||||||
\(615\) | −3.39899 | − | 3.39899i | −0.137060 | − | 0.137060i | ||||
\(616\) | −11.2203 | −0.452077 | ||||||||
\(617\) | 10.4142 | + | 10.4142i | 0.419260 | + | 0.419260i | 0.884948 | − | 0.465689i | \(-0.154193\pi\) |
−0.465689 | + | 0.884948i | \(0.654193\pi\) | |||||||
\(618\) | −8.96211 | + | 8.96211i | −0.360509 | + | 0.360509i | ||||
\(619\) | 26.1584 | − | 26.1584i | 1.05140 | − | 1.05140i | 0.0527903 | − | 0.998606i | \(-0.483188\pi\) |
0.998606 | − | 0.0527903i | \(-0.0168115\pi\) | |||||||
\(620\) | 12.2744i | 0.492951i | ||||||||
\(621\) | 2.54524i | 0.102137i | ||||||||
\(622\) | 6.99806 | − | 6.99806i | 0.280597 | − | 0.280597i | ||||
\(623\) | −1.44749 | + | 1.44749i | −0.0579924 | + | 0.0579924i | ||||
\(624\) | 24.7059 | + | 24.7059i | 0.989028 | + | 0.989028i | ||||
\(625\) | 15.0506 | 0.602023 | ||||||||
\(626\) | 34.8786 | + | 34.8786i | 1.39403 | + | 1.39403i | ||||
\(627\) | − | 58.8859i | − | 2.35168i | ||||||
\(628\) | −11.0392 | −0.440512 | ||||||||
\(629\) | −5.28464 | + | 1.97782i | −0.210713 | + | 0.0788609i | ||||
\(630\) | −6.07647 | −0.242092 | ||||||||
\(631\) | 31.7794i | 1.26512i | 0.774512 | + | 0.632559i | \(0.217996\pi\) | ||||
−0.774512 | + | 0.632559i | \(0.782004\pi\) | |||||||
\(632\) | 16.9949 | + | 16.9949i | 0.676021 | + | 0.676021i | ||||
\(633\) | 19.7881 | 0.786508 | ||||||||
\(634\) | 18.4171 | + | 18.4171i | 0.731438 | + | 0.731438i | ||||
\(635\) | −12.3119 | + | 12.3119i | −0.488584 | + | 0.488584i | ||||
\(636\) | 2.77034 | − | 2.77034i | 0.109851 | − | 0.109851i | ||||
\(637\) | − | 3.63777i | − | 0.144134i | ||||||
\(638\) | 41.0702i | 1.62599i | ||||||||
\(639\) | −3.46602 | + | 3.46602i | −0.137114 | + | 0.137114i | ||||
\(640\) | 32.6716 | − | 32.6716i | 1.29146 | − | 1.29146i | ||||
\(641\) | −13.4016 | − | 13.4016i | −0.529331 | − | 0.529331i | 0.391042 | − | 0.920373i | \(-0.372115\pi\) |
−0.920373 | + | 0.391042i | \(0.872115\pi\) | |||||||
\(642\) | 36.3986 | 1.43654 | ||||||||
\(643\) | −19.0600 | − | 19.0600i | −0.751652 | − | 0.751652i | 0.223135 | − | 0.974787i | \(-0.428371\pi\) |
−0.974787 | + | 0.223135i | \(0.928371\pi\) | |||||||
\(644\) | 0.317294i | 0.0125031i | ||||||||
\(645\) | 45.8716 | 1.80619 | ||||||||
\(646\) | 16.6491 | − | 36.5649i | 0.655051 | − | 1.43863i | ||||
\(647\) | 0.816139 | 0.0320858 | 0.0160429 | − | 0.999871i | \(-0.494893\pi\) | ||||
0.0160429 | + | 0.999871i | \(0.494893\pi\) | |||||||
\(648\) | 26.7118i | 1.04934i | ||||||||
\(649\) | 9.02408 | + | 9.02408i | 0.354226 | + | 0.354226i | ||||
\(650\) | −37.3198 | −1.46380 | ||||||||
\(651\) | 11.0167 | + | 11.0167i | 0.431777 | + | 0.431777i | ||||
\(652\) | −4.03161 | + | 4.03161i | −0.157890 | + | 0.157890i | ||||
\(653\) | 18.7492 | − | 18.7492i | 0.733712 | − | 0.733712i | −0.237641 | − | 0.971353i | \(-0.576374\pi\) |
0.971353 | + | 0.237641i | \(0.0763743\pi\) | |||||||
\(654\) | 14.0920i | 0.551042i | ||||||||
\(655\) | 28.3585i | 1.10806i | ||||||||
\(656\) | −2.32369 | + | 2.32369i | −0.0907249 | + | 0.0907249i | ||||
\(657\) | 1.32913 | − | 1.32913i | 0.0518544 | − | 0.0518544i | ||||
\(658\) | 4.80946 | + | 4.80946i | 0.187492 | + | 0.187492i | ||||
\(659\) | −15.6995 | −0.611566 | −0.305783 | − | 0.952101i | \(-0.598918\pi\) | ||||
−0.305783 | + | 0.952101i | \(0.598918\pi\) | |||||||
\(660\) | −10.7678 | − | 10.7678i | −0.419138 | − | 0.419138i | ||||
\(661\) | − | 15.5120i | − | 0.603348i | −0.953411 | − | 0.301674i | \(-0.902455\pi\) | ||
0.953411 | − | 0.301674i | \(-0.0975454\pi\) | |||||||
\(662\) | −7.44156 | −0.289224 | ||||||||
\(663\) | −28.5766 | + | 10.6950i | −1.10982 | + | 0.415361i | ||||
\(664\) | −11.2707 | −0.437386 | ||||||||
\(665\) | − | 21.0396i | − | 0.815880i | ||||||
\(666\) | 1.73211 | + | 1.73211i | 0.0671179 | + | 0.0671179i | ||||
\(667\) | −3.75878 | −0.145541 | ||||||||
\(668\) | 8.19008 | + | 8.19008i | 0.316884 | + | 0.316884i | ||||
\(669\) | −25.2364 | + | 25.2364i | −0.975694 | + | 0.975694i | ||||
\(670\) | −47.4015 | + | 47.4015i | −1.83128 | + | 1.83128i | ||||
\(671\) | − | 56.5050i | − | 2.18135i | ||||||
\(672\) | 5.32721i | 0.205502i | ||||||||
\(673\) | 25.7151 | − | 25.7151i | 0.991243 | − | 0.991243i | −0.00871919 | − | 0.999962i | \(-0.502775\pi\) |
0.999962 | + | 0.00871919i | \(0.00277544\pi\) | |||||||
\(674\) | −26.8112 | + | 26.8112i | −1.03273 | + | 1.03273i | ||||
\(675\) | −17.4725 | − | 17.4725i | −0.672518 | − | 0.672518i | ||||
\(676\) | −0.110171 | −0.00423736 | ||||||||
\(677\) | −20.2679 | − | 20.2679i | −0.778959 | − | 0.778959i | 0.200695 | − | 0.979654i | \(-0.435680\pi\) |
−0.979654 | + | 0.200695i | \(0.935680\pi\) | |||||||
\(678\) | 37.0938i | 1.42458i | ||||||||
\(679\) | −4.23013 | −0.162338 | ||||||||
\(680\) | 11.7863 | + | 31.4923i | 0.451982 | + | 1.20768i | ||||
\(681\) | 16.9735 | 0.650425 | ||||||||
\(682\) | 56.2414i | 2.15359i | ||||||||
\(683\) | 13.9866 | + | 13.9866i | 0.535181 | + | 0.535181i | 0.922110 | − | 0.386929i | \(-0.126464\pi\) |
−0.386929 | + | 0.922110i | \(0.626464\pi\) | |||||||
\(684\) | −3.33084 | −0.127358 | ||||||||
\(685\) | −48.4754 | − | 48.4754i | −1.85215 | − | 1.85215i | ||||
\(686\) | 1.11178 | − | 1.11178i | 0.0424479 | − | 0.0424479i | ||||
\(687\) | 22.0724 | − | 22.0724i | 0.842114 | − | 0.842114i | ||||
\(688\) | − | 31.3598i | − | 1.19558i | ||||||
\(689\) | − | 14.8399i | − | 0.565356i | ||||||
\(690\) | 5.16037 | − | 5.16037i | 0.196452 | − | 0.196452i | ||||
\(691\) | 26.6547 | − | 26.6547i | 1.01399 | − | 1.01399i | 0.0140930 | − | 0.999901i | \(-0.495514\pi\) |
0.999901 | − | 0.0140930i | \(-0.00448608\pi\) | |||||||
\(692\) | −1.19017 | − | 1.19017i | −0.0452434 | − | 0.0452434i | ||||
\(693\) | −5.31711 | −0.201980 | ||||||||
\(694\) | −25.4665 | − | 25.4665i | −0.966697 | − | 0.966697i | ||||
\(695\) | 26.4970i | 1.00509i | ||||||||
\(696\) | −27.3315 | −1.03600 | ||||||||
\(697\) | −1.00591 | − | 2.68775i | −0.0381016 | − | 0.101806i | ||||
\(698\) | 16.0212 | 0.606410 | ||||||||
\(699\) | − | 49.7946i | − | 1.88341i | ||||||
\(700\) | −2.17816 | − | 2.17816i | −0.0823267 | − | 0.0823267i | ||||
\(701\) | 12.4612 | 0.470652 | 0.235326 | − | 0.971916i | \(-0.424384\pi\) | ||||
0.235326 | + | 0.971916i | \(0.424384\pi\) | |||||||
\(702\) | −15.3163 | − | 15.3163i | −0.578076 | − | 0.578076i | ||||
\(703\) | −5.99737 | + | 5.99737i | −0.226195 | + | 0.226195i | ||||
\(704\) | 17.5875 | − | 17.5875i | 0.662855 | − | 0.662855i | ||||
\(705\) | − | 29.8754i | − | 1.12517i | ||||||
\(706\) | − | 26.4143i | − | 0.994116i | ||||||
\(707\) | −3.80797 | + | 3.80797i | −0.143214 | + | 0.143214i | ||||
\(708\) | 1.85558 | − | 1.85558i | 0.0697368 | − | 0.0697368i | ||||
\(709\) | −10.2099 | − | 10.2099i | −0.383439 | − | 0.383439i | 0.488900 | − | 0.872340i | \(-0.337398\pi\) |
−0.872340 | + | 0.488900i | \(0.837398\pi\) | |||||||
\(710\) | −22.9825 | −0.862517 | ||||||||
\(711\) | 8.05362 | + | 8.05362i | 0.302034 | + | 0.302034i | ||||
\(712\) | − | 4.91766i | − | 0.184297i | ||||||
\(713\) | −5.14726 | −0.192766 | ||||||||
\(714\) | −12.0022 | − | 5.46499i | −0.449172 | − | 0.204522i | ||||
\(715\) | −57.6804 | −2.15712 | ||||||||
\(716\) | − | 1.87006i | − | 0.0698874i | ||||||
\(717\) | −20.9688 | − | 20.9688i | −0.783095 | − | 0.783095i | ||||
\(718\) | −44.4044 | −1.65716 | ||||||||
\(719\) | −6.54115 | − | 6.54115i | −0.243944 | − | 0.243944i | 0.574536 | − | 0.818479i | \(-0.305183\pi\) |
−0.818479 | + | 0.574536i | \(0.805183\pi\) | |||||||
\(720\) | 12.9023 | − | 12.9023i | 0.480840 | − | 0.480840i | ||||
\(721\) | −2.80195 | + | 2.80195i | −0.104350 | + | 0.104350i | ||||
\(722\) | − | 30.5173i | − | 1.13574i | ||||||
\(723\) | 30.9528i | 1.15115i | ||||||||
\(724\) | 0.643317 | − | 0.643317i | 0.0239087 | − | 0.0239087i | ||||
\(725\) | 25.8033 | − | 25.8033i | 0.958309 | − | 0.958309i | ||||
\(726\) | −24.4597 | − | 24.4597i | −0.907785 | − | 0.907785i | ||||
\(727\) | 33.0618 | 1.22619 | 0.613096 | − | 0.790008i | \(-0.289924\pi\) | ||||
0.613096 | + | 0.790008i | \(0.289924\pi\) | |||||||
\(728\) | 6.17943 | + | 6.17943i | 0.229025 | + | 0.229025i | ||||
\(729\) | − | 10.4537i | − | 0.387175i | ||||||
\(730\) | 8.81320 | 0.326191 | ||||||||
\(731\) | 24.9242 | + | 11.3488i | 0.921855 | + | 0.419749i | ||||
\(732\) | −11.6188 | −0.429445 | ||||||||
\(733\) | 1.81758i | 0.0671338i | 0.999436 | + | 0.0335669i | \(0.0106867\pi\) | ||||
−0.999436 | + | 0.0335669i | \(0.989313\pi\) | |||||||
\(734\) | −20.9153 | − | 20.9153i | −0.771998 | − | 0.771998i | ||||
\(735\) | −6.90613 | −0.254736 | ||||||||
\(736\) | −1.24450 | − | 1.24450i | −0.0458730 | − | 0.0458730i | ||||
\(737\) | −41.4779 | + | 41.4779i | −1.52786 | + | 1.52786i | ||||
\(738\) | −0.880943 | + | 0.880943i | −0.0324280 | + | 0.0324280i | ||||
\(739\) | − | 30.1602i | − | 1.10946i | −0.832031 | − | 0.554730i | \(-0.812822\pi\) | ||
0.832031 | − | 0.554730i | \(-0.187178\pi\) | |||||||
\(740\) | 2.19335i | 0.0806292i | ||||||||
\(741\) | −32.4307 | + | 32.4307i | −1.19137 | + | 1.19137i | ||||
\(742\) | 4.53539 | − | 4.53539i | 0.166499 | − | 0.166499i | ||||
\(743\) | 28.0426 | + | 28.0426i | 1.02878 | + | 1.02878i | 0.999573 | + | 0.0292082i | \(0.00929860\pi\) |
0.0292082 | + | 0.999573i | \(0.490701\pi\) | |||||||
\(744\) | −37.4277 | −1.37216 | ||||||||
\(745\) | 1.60973 | + | 1.60973i | 0.0589760 | + | 0.0589760i | ||||
\(746\) | 48.6867i | 1.78255i | ||||||||
\(747\) | −5.34098 | −0.195416 | ||||||||
\(748\) | −3.18668 | − | 8.51467i | −0.116517 | − | 0.311327i | ||||
\(749\) | 11.3798 | 0.415809 | ||||||||
\(750\) | 16.5575i | 0.604595i | ||||||||
\(751\) | −29.5789 | − | 29.5789i | −1.07935 | − | 1.07935i | −0.996568 | − | 0.0827803i | \(-0.973620\pi\) |
−0.0827803 | − | 0.996568i | \(-0.526380\pi\) | |||||||
\(752\) | −20.4241 | −0.744789 | ||||||||
\(753\) | −2.21572 | − | 2.21572i | −0.0807454 | − | 0.0807454i | ||||
\(754\) | 22.6189 | − | 22.6189i | 0.823733 | − | 0.823733i | ||||
\(755\) | −27.4226 | + | 27.4226i | −0.998009 | + | 0.998009i | ||||
\(756\) | − | 1.78786i | − | 0.0650239i | ||||||
\(757\) | 29.9024i | 1.08682i | 0.839467 | + | 0.543411i | \(0.182867\pi\) | ||||
−0.839467 | + | 0.543411i | \(0.817133\pi\) | |||||||
\(758\) | 13.8421 | − | 13.8421i | 0.502766 | − | 0.502766i | ||||
\(759\) | 4.51550 | − | 4.51550i | 0.163902 | − | 0.163902i | ||||
\(760\) | 35.7396 | + | 35.7396i | 1.29641 | + | 1.29641i | ||||
\(761\) | −29.8807 | −1.08318 | −0.541588 | − | 0.840644i | \(-0.682177\pi\) | ||||
−0.541588 | + | 0.840644i | \(0.682177\pi\) | |||||||
\(762\) | 11.6000 | + | 11.6000i | 0.420224 | + | 0.420224i | ||||
\(763\) | 4.40579i | 0.159500i | ||||||||
\(764\) | 11.8840 | 0.429948 | ||||||||
\(765\) | 5.58532 | + | 14.9237i | 0.201938 | + | 0.539568i | ||||
\(766\) | 46.9262 | 1.69551 | ||||||||
\(767\) | − | 9.93981i | − | 0.358906i | ||||||
\(768\) | −15.4618 | − | 15.4618i | −0.557929 | − | 0.557929i | ||||
\(769\) | 35.8821 | 1.29394 | 0.646971 | − | 0.762514i | \(-0.276035\pi\) | ||||
0.646971 | + | 0.762514i | \(0.276035\pi\) | |||||||
\(770\) | −17.6283 | − | 17.6283i | −0.635280 | − | 0.635280i | ||||
\(771\) | −5.79594 | + | 5.79594i | −0.208736 | + | 0.208736i | ||||
\(772\) | −3.75444 | + | 3.75444i | −0.135125 | + | 0.135125i | ||||
\(773\) | 13.1964i | 0.474642i | 0.971431 | + | 0.237321i | \(0.0762692\pi\) | ||||
−0.971431 | + | 0.237321i | \(0.923731\pi\) | |||||||
\(774\) | − | 11.8889i | − | 0.427338i | ||||||
\(775\) | 35.3349 | − | 35.3349i | 1.26927 | − | 1.26927i | ||||
\(776\) | 7.18567 | − | 7.18567i | 0.257950 | − | 0.257950i | ||||
\(777\) | 1.96861 | + | 1.96861i | 0.0706234 | + | 0.0706234i | ||||
\(778\) | 32.9245 | 1.18040 | ||||||||
\(779\) | −3.05024 | − | 3.05024i | −0.109286 | − | 0.109286i | ||||
\(780\) | 11.8605i | 0.424675i | ||||||||
\(781\) | −20.1104 | −0.719608 | ||||||||
\(782\) | 4.08056 | − | 1.52718i | 0.145921 | − | 0.0546120i | ||||
\(783\) | 21.1797 | 0.756899 | ||||||||
\(784\) | 4.72132i | 0.168619i | ||||||||
\(785\) | 56.1314 | + | 56.1314i | 2.00342 | + | 2.00342i | ||||
\(786\) | 26.7187 | 0.953025 | ||||||||
\(787\) | 20.2916 | + | 20.2916i | 0.723318 | + | 0.723318i | 0.969280 | − | 0.245962i | \(-0.0791038\pi\) |
−0.245962 | + | 0.969280i | \(0.579104\pi\) | |||||||
\(788\) | 7.55525 | − | 7.55525i | 0.269144 | − | 0.269144i | ||||
\(789\) | 25.8552 | − | 25.8552i | 0.920470 | − | 0.920470i | ||||
\(790\) | 53.4019i | 1.89995i | ||||||||
\(791\) | 11.5971i | 0.412347i | ||||||||
\(792\) | 9.03209 | − | 9.03209i | 0.320941 | − | 0.320941i | ||||
\(793\) | −31.1195 | + | 31.1195i | −1.10508 | + | 1.10508i | ||||
\(794\) | −31.5308 | − | 31.5308i | −1.11899 | − | 1.11899i | ||||
\(795\) | −28.1729 | −0.999189 | ||||||||
\(796\) | 1.75240 | + | 1.75240i | 0.0621121 | + | 0.0621121i | ||||
\(797\) | 10.8120i | 0.382980i | 0.981495 | + | 0.191490i | \(0.0613320\pi\) | ||||
−0.981495 | + | 0.191490i | \(0.938668\pi\) | |||||||
\(798\) | −19.8230 | −0.701726 | ||||||||
\(799\) | 7.39125 | − | 16.2327i | 0.261484 | − | 0.574272i | ||||
\(800\) | 17.0865 | 0.604100 | ||||||||
\(801\) | − | 2.33040i | − | 0.0823406i | ||||||
\(802\) | 3.63421 | + | 3.63421i | 0.128328 | + | 0.128328i | ||||
\(803\) | 7.71184 | 0.272145 | ||||||||
\(804\) | 8.52888 | + | 8.52888i | 0.300790 | + | 0.300790i | ||||
\(805\) | 1.61336 | − | 1.61336i | 0.0568634 | − | 0.0568634i | ||||
\(806\) | 30.9743 | − | 30.9743i | 1.09102 | − | 1.09102i | ||||
\(807\) | − | 36.6820i | − | 1.29127i | ||||||
\(808\) | − | 12.9371i | − | 0.455125i | ||||||
\(809\) | 36.0543 | − | 36.0543i | 1.26760 | − | 1.26760i | 0.320276 | − | 0.947324i | \(-0.396224\pi\) |
0.947324 | − | 0.320276i | \(-0.103776\pi\) | |||||||
\(810\) | −41.9673 | + | 41.9673i | −1.47458 | + | 1.47458i | ||||
\(811\) | 10.8591 | + | 10.8591i | 0.381315 | + | 0.381315i | 0.871576 | − | 0.490261i | \(-0.163098\pi\) |
−0.490261 | + | 0.871576i | \(0.663098\pi\) | |||||||
\(812\) | 2.64030 | 0.0926562 | ||||||||
\(813\) | −24.0340 | − | 24.0340i | −0.842910 | − | 0.842910i | ||||
\(814\) | 10.0500i | 0.352251i | ||||||||
\(815\) | 40.9994 | 1.43615 | ||||||||
\(816\) | 37.0885 | − | 13.8807i | 1.29836 | − | 0.485921i | ||||
\(817\) | 41.1650 | 1.44018 | ||||||||
\(818\) | − | 54.0654i | − | 1.89035i | ||||||
\(819\) | 2.92833 | + | 2.92833i | 0.102324 | + | 0.102324i | ||||
\(820\) | −1.11553 | −0.0389560 | ||||||||
\(821\) | 9.85365 | + | 9.85365i | 0.343895 | + | 0.343895i | 0.857829 | − | 0.513935i | \(-0.171813\pi\) |
−0.513935 | + | 0.857829i | \(0.671813\pi\) | |||||||
\(822\) | −45.6724 | + | 45.6724i | −1.59301 | + | 1.59301i | ||||
\(823\) | 8.67935 | − | 8.67935i | 0.302543 | − | 0.302543i | −0.539465 | − | 0.842008i | \(-0.681373\pi\) |
0.842008 | + | 0.539465i | \(0.181373\pi\) | |||||||
\(824\) | − | 9.51926i | − | 0.331619i | ||||||
\(825\) | 61.9959i | 2.15842i | ||||||||
\(826\) | 3.03781 | − | 3.03781i | 0.105699 | − | 0.105699i | ||||
\(827\) | 11.8528 | − | 11.8528i | 0.412162 | − | 0.412162i | −0.470329 | − | 0.882491i | \(-0.655865\pi\) |
0.882491 | + | 0.470329i | \(0.155865\pi\) | |||||||
\(828\) | −0.255416 | − | 0.255416i | −0.00887631 | − | 0.00887631i | ||||
\(829\) | −43.4266 | −1.50827 | −0.754134 | − | 0.656721i | \(-0.771943\pi\) | ||||
−0.754134 | + | 0.656721i | \(0.771943\pi\) | |||||||
\(830\) | −17.7075 | − | 17.7075i | −0.614635 | − | 0.614635i | ||||
\(831\) | 2.12300i | 0.0736459i | ||||||||
\(832\) | −19.3722 | −0.671612 | ||||||||
\(833\) | −3.75243 | − | 1.70860i | −0.130014 | − | 0.0591993i | ||||
\(834\) | 24.9649 | 0.864463 | ||||||||
\(835\) | − | 83.2889i | − | 2.88233i | ||||||
\(836\) | −9.66303 | − | 9.66303i | −0.334203 | − | 0.334203i | ||||
\(837\) | 29.0033 | 1.00250 | ||||||||
\(838\) | −19.4758 | − | 19.4758i | −0.672781 | − | 0.672781i | ||||
\(839\) | 4.20215 | − | 4.20215i | 0.145074 | − | 0.145074i | −0.630839 | − | 0.775914i | \(-0.717289\pi\) |
0.775914 | + | 0.630839i | \(0.217289\pi\) | |||||||
\(840\) | 11.7313 | − | 11.7313i | 0.404770 | − | 0.404770i | ||||
\(841\) | 2.27792i | 0.0785488i | ||||||||
\(842\) | − | 20.6015i | − | 0.709973i | ||||||
\(843\) | −5.07834 | + | 5.07834i | −0.174907 | + | 0.174907i | ||||
\(844\) | 3.24718 | − | 3.24718i | 0.111773 | − | 0.111773i | ||||
\(845\) | 0.560193 | + | 0.560193i | 0.0192712 | + | 0.0192712i | ||||
\(846\) | −7.74305 | −0.266211 | ||||||||
\(847\) | −7.64718 | − | 7.64718i | −0.262760 | − | 0.262760i | ||||
\(848\) | 19.2602i | 0.661397i | ||||||||
\(849\) | 3.70950 | 0.127310 | ||||||||
\(850\) | −17.5284 | + | 38.4960i | −0.601220 | + | 1.32040i | ||||
\(851\) | −0.919783 | −0.0315297 | ||||||||
\(852\) | 4.13521i | 0.141670i | ||||||||
\(853\) | −9.18348 | − | 9.18348i | −0.314436 | − | 0.314436i | 0.532189 | − | 0.846625i | \(-0.321370\pi\) |
−0.846625 | + | 0.532189i | \(0.821370\pi\) | |||||||
\(854\) | −19.0215 | −0.650903 | ||||||||
\(855\) | 16.9364 | + | 16.9364i | 0.579214 | + | 0.579214i | ||||
\(856\) | −19.3307 | + | 19.3307i | −0.660710 | + | 0.660710i | ||||
\(857\) | −20.3600 | + | 20.3600i | −0.695483 | + | 0.695483i | −0.963433 | − | 0.267950i | \(-0.913654\pi\) |
0.267950 | + | 0.963433i | \(0.413654\pi\) | |||||||
\(858\) | 54.3451i | 1.85531i | ||||||||
\(859\) | 8.24733i | 0.281395i | 0.990053 | + | 0.140698i | \(0.0449345\pi\) | ||||
−0.990053 | + | 0.140698i | \(0.955065\pi\) | |||||||
\(860\) | 7.52741 | − | 7.52741i | 0.256683 | − | 0.256683i | ||||
\(861\) | −1.00123 | + | 1.00123i | −0.0341217 | + | 0.0341217i | ||||
\(862\) | 29.2207 | + | 29.2207i | 0.995260 | + | 0.995260i | ||||
\(863\) | −35.6828 | −1.21466 | −0.607329 | − | 0.794450i | \(-0.707759\pi\) | ||||
−0.607329 | + | 0.794450i | \(0.707759\pi\) | |||||||
\(864\) | 7.01242 | + | 7.01242i | 0.238567 | + | 0.238567i | ||||
\(865\) | 12.1034i | 0.411527i | ||||||||
\(866\) | −1.23218 | −0.0418710 | ||||||||
\(867\) | −2.38981 | + | 34.5006i | −0.0811621 | + | 1.17170i | ||||
\(868\) | 3.61561 | 0.122722 | ||||||||
\(869\) | 46.7284i | 1.58515i | ||||||||
\(870\) | −42.9409 | − | 42.9409i | −1.45583 | − | 1.45583i | ||||
\(871\) | 45.6869 | 1.54804 | ||||||||
\(872\) | −7.48405 | − | 7.48405i | −0.253442 | − | 0.253442i | ||||
\(873\) | 3.40518 | − | 3.40518i | 0.115248 | − | 0.115248i | ||||
\(874\) | 4.63090 | − | 4.63090i | 0.156643 | − | 0.156643i | ||||
\(875\) | 5.17661i | 0.175001i | ||||||||
\(876\) | − | 1.58575i | − | 0.0535774i | ||||||
\(877\) | −9.95149 | + | 9.95149i | −0.336038 | + | 0.336038i | −0.854874 | − | 0.518836i | \(-0.826366\pi\) |
0.518836 | + | 0.854874i | \(0.326366\pi\) | |||||||
\(878\) | −27.9657 | + | 27.9657i | −0.943797 | + | 0.943797i | ||||
\(879\) | −21.5174 | − | 21.5174i | −0.725763 | − | 0.725763i | ||||
\(880\) | 74.8611 | 2.52357 | ||||||||
\(881\) | 10.4454 | + | 10.4454i | 0.351914 | + | 0.351914i | 0.860821 | − | 0.508907i | \(-0.169950\pi\) |
−0.508907 | + | 0.860821i | \(0.669950\pi\) | |||||||
\(882\) | 1.78992i | 0.0602697i | ||||||||
\(883\) | 4.72305 | 0.158943 | 0.0794717 | − | 0.996837i | \(-0.474677\pi\) | ||||
0.0794717 | + | 0.996837i | \(0.474677\pi\) | |||||||
\(884\) | −2.93432 | + | 6.44438i | −0.0986920 | + | 0.216748i | ||||
\(885\) | −18.8703 | −0.634317 | ||||||||
\(886\) | − | 19.0746i | − | 0.640823i | ||||||
\(887\) | −31.9047 | − | 31.9047i | −1.07126 | − | 1.07126i | −0.997258 | − | 0.0739977i | \(-0.976424\pi\) |
−0.0739977 | − | 0.997258i | \(-0.523576\pi\) | |||||||
\(888\) | −6.68809 | −0.224437 | ||||||||
\(889\) | 3.62667 | + | 3.62667i | 0.121635 | + | 0.121635i | ||||
\(890\) | 7.72620 | − | 7.72620i | 0.258983 | − | 0.258983i | ||||
\(891\) | −36.7228 | + | 36.7228i | −1.23026 | + | 1.23026i | ||||
\(892\) | 8.28245i | 0.277317i | ||||||||
\(893\) | − | 26.8101i | − | 0.897164i | ||||||
\(894\) | 1.51665 | − | 1.51665i | 0.0507244 | − | 0.0507244i | ||||
\(895\) | −9.50877 | + | 9.50877i | −0.317843 | + | 0.317843i | ||||
\(896\) | −9.62394 | − | 9.62394i | −0.321513 | − | 0.321513i | ||||
\(897\) | −4.97371 | −0.166067 | ||||||||
\(898\) | 41.1407 | + | 41.1407i | 1.37288 | + | 1.37288i | ||||
\(899\) | 42.8318i | 1.42852i | ||||||||
\(900\) | 3.50675 | 0.116892 | ||||||||
\(901\) | −15.3077 | − | 6.97005i | −0.509972 | − | 0.232206i | ||||
\(902\) | −5.11138 | −0.170190 | ||||||||
\(903\) | − | 13.5122i | − | 0.449658i | ||||||
\(904\) | −19.6999 | − | 19.6999i | −0.655209 | − | 0.655209i | ||||
\(905\) | −6.54220 | −0.217470 | ||||||||
\(906\) | 25.8369 | + | 25.8369i | 0.858373 | + | 0.858373i | ||||
\(907\) | 23.9495 | − | 23.9495i | 0.795231 | − | 0.795231i | −0.187108 | − | 0.982339i | \(-0.559911\pi\) |
0.982339 | + | 0.187108i | \(0.0599114\pi\) | |||||||
\(908\) | 2.78530 | − | 2.78530i | 0.0924336 | − | 0.0924336i | ||||
\(909\) | − | 6.13069i | − | 0.203342i | ||||||
\(910\) | 19.4172i | 0.643673i | ||||||||
\(911\) | 7.16704 | − | 7.16704i | 0.237455 | − | 0.237455i | −0.578341 | − | 0.815795i | \(-0.696300\pi\) |
0.815795 | + | 0.578341i | \(0.196300\pi\) | |||||||
\(912\) | 42.0906 | − | 42.0906i | 1.39376 | − | 1.39376i | ||||
\(913\) | −15.4946 | − | 15.4946i | −0.512797 | − | 0.512797i | ||||
\(914\) | −20.1063 | −0.665057 | ||||||||
\(915\) | 59.0788 | + | 59.0788i | 1.95309 | + | 1.95309i | ||||
\(916\) | − | 7.24404i | − | 0.239350i | ||||||
\(917\) | 8.35345 | 0.275855 | ||||||||
\(918\) | −22.9928 | + | 8.60524i | −0.758876 | + | 0.284015i | ||||
\(919\) | −7.90071 | −0.260620 | −0.130310 | − | 0.991473i | \(-0.541597\pi\) | ||||
−0.130310 | + | 0.991473i | \(0.541597\pi\) | |||||||
\(920\) | 5.48118i | 0.180709i | ||||||||
\(921\) | 10.3054 | + | 10.3054i | 0.339573 | + | 0.339573i | ||||
\(922\) | 7.20249 | 0.237201 | ||||||||
\(923\) | 11.0756 | + | 11.0756i | 0.364557 | + | 0.364557i | ||||
\(924\) | −3.17184 | + | 3.17184i | −0.104346 | + | 0.104346i | ||||
\(925\) | 6.31412 | − | 6.31412i | 0.207607 | − | 0.207607i | ||||
\(926\) | − | 2.41887i | − | 0.0794891i | ||||||
\(927\) | − | 4.51103i | − | 0.148162i | ||||||
\(928\) | −10.3559 | + | 10.3559i | −0.339948 | + | 0.339948i | ||||
\(929\) | −6.47675 | + | 6.47675i | −0.212495 | + | 0.212495i | −0.805327 | − | 0.592831i | \(-0.798010\pi\) |
0.592831 | + | 0.805327i | \(0.298010\pi\) | |||||||
\(930\) | −58.8031 | − | 58.8031i | −1.92823 | − | 1.92823i | ||||
\(931\) | −6.19754 | −0.203116 | ||||||||
\(932\) | −8.17117 | − | 8.17117i | −0.267656 | − | 0.267656i | ||||
\(933\) | 12.8049i | 0.419214i | ||||||||
\(934\) | 17.2994 | 0.566054 | ||||||||
\(935\) | −27.0914 | + | 59.4984i | −0.885985 | + | 1.94580i | ||||
\(936\) | −9.94863 | −0.325181 | ||||||||
\(937\) | 53.4400i | 1.74581i | 0.487891 | + | 0.872905i | \(0.337766\pi\) | ||||
−0.487891 | + | 0.872905i | \(0.662234\pi\) | |||||||
\(938\) | 13.9629 | + | 13.9629i | 0.455903 | + | 0.455903i | ||||
\(939\) | −63.8202 | −2.08269 | ||||||||
\(940\) | −4.90247 | − | 4.90247i | −0.159901 | − | 0.159901i | ||||
\(941\) | 35.4583 | − | 35.4583i | 1.15591 | − | 1.15591i | 0.170562 | − | 0.985347i | \(-0.445442\pi\) |
0.985347 | − | 0.170562i | \(-0.0545582\pi\) | |||||||
\(942\) | 52.8857 | − | 52.8857i | 1.72311 | − | 1.72311i | ||||
\(943\) | − | 0.467798i | − | 0.0152336i | ||||||
\(944\) | 12.9005i | 0.419876i | ||||||||
\(945\) | −9.09081 | + | 9.09081i | −0.295724 | + | 0.295724i | ||||
\(946\) | 34.4907 | − | 34.4907i | 1.12139 | − | 1.12139i | ||||
\(947\) | −10.3757 | − | 10.3757i | −0.337165 | − | 0.337165i | 0.518135 | − | 0.855299i | \(-0.326627\pi\) |
−0.855299 | + | 0.518135i | \(0.826627\pi\) | |||||||
\(948\) | 9.60853 | 0.312070 | ||||||||
\(949\) | −4.24720 | − | 4.24720i | −0.137870 | − | 0.137870i | ||||
\(950\) | 63.5803i | 2.06282i | ||||||||
\(951\) | −33.6993 | −1.09278 | ||||||||
\(952\) | 9.27656 | − | 3.47183i | 0.300655 | − | 0.112523i | ||||
\(953\) | −4.66197 | −0.151016 | −0.0755080 | − | 0.997145i | \(-0.524058\pi\) | ||||
−0.0755080 | + | 0.997145i | \(0.524058\pi\) | |||||||
\(954\) | 7.30180i | 0.236405i | ||||||||
\(955\) | −60.4270 | − | 60.4270i | −1.95537 | − | 1.95537i | ||||
\(956\) | −6.88186 | −0.222575 | ||||||||
\(957\) | −37.5747 | − | 37.5747i | −1.21462 | − | 1.21462i | ||||
\(958\) | −25.8621 | + | 25.8621i | −0.835566 | + | 0.835566i | ||||
\(959\) | −14.2792 | + | 14.2792i | −0.461100 | + | 0.461100i | ||||
\(960\) | 36.7773i | 1.18698i | ||||||||
\(961\) | 27.6537i | 0.892056i | ||||||||
\(962\) | 5.53490 | − | 5.53490i | 0.178452 | − | 0.178452i | ||||
\(963\) | −9.16052 | + | 9.16052i | −0.295194 | + | 0.295194i | ||||
\(964\) | 5.07927 | + | 5.07927i | 0.163592 | + | 0.163592i | ||||
\(965\) | 38.1807 | 1.22908 | ||||||||
\(966\) | −1.52007 | − | 1.52007i | −0.0489074 | − | 0.0489074i | ||||
\(967\) | 15.2606i | 0.490748i | 0.969428 | + | 0.245374i | \(0.0789108\pi\) | ||||
−0.969428 | + | 0.245374i | \(0.921089\pi\) | |||||||
\(968\) | 25.9803 | 0.835039 | ||||||||
\(969\) | 18.2207 | + | 48.6850i | 0.585335 | + | 1.56399i | ||||
\(970\) | 22.5790 | 0.724968 | ||||||||
\(971\) | − | 18.5971i | − | 0.596810i | −0.954439 | − | 0.298405i | \(-0.903545\pi\) | ||
0.954439 | − | 0.298405i | \(-0.0964546\pi\) | |||||||
\(972\) | 3.75850 | + | 3.75850i | 0.120554 | + | 0.120554i | ||||
\(973\) | 7.80511 | 0.250220 | ||||||||
\(974\) | 24.4991 | + | 24.4991i | 0.785003 | + | 0.785003i | ||||
\(975\) | 34.1435 | − | 34.1435i | 1.09347 | − | 1.09347i | ||||
\(976\) | 40.3888 | − | 40.3888i | 1.29281 | − | 1.29281i | ||||
\(977\) | 21.7450i | 0.695683i | 0.937553 | + | 0.347842i | \(0.113085\pi\) | ||||
−0.937553 | + | 0.347842i | \(0.886915\pi\) | |||||||
\(978\) | − | 38.6287i | − | 1.23521i | ||||||
\(979\) | 6.76068 | − | 6.76068i | 0.216072 | − | 0.216072i | ||||
\(980\) | −1.13328 | + | 1.13328i | −0.0362012 | + | 0.0362012i | ||||
\(981\) | −3.54657 | − | 3.54657i | −0.113233 | − | 0.113233i | ||||
\(982\) | 30.2935 | 0.966704 | ||||||||
\(983\) | −2.52556 | − | 2.52556i | −0.0805529 | − | 0.0805529i | 0.665682 | − | 0.746235i | \(-0.268141\pi\) |
−0.746235 | + | 0.665682i | \(0.768141\pi\) | |||||||
\(984\) | − | 3.40153i | − | 0.108437i | ||||||
\(985\) | −76.8329 | −2.44810 | ||||||||
\(986\) | −12.7081 | − | 33.9556i | −0.404710 | − | 1.08137i | ||||
\(987\) | −8.80026 | −0.280115 | ||||||||
\(988\) | 10.6436i | 0.338618i | ||||||||
\(989\) | 3.15662 | + | 3.15662i | 0.100375 | + | 0.100375i | ||||
\(990\) | 28.3809 | 0.902004 | ||||||||
\(991\) | −0.300053 | − | 0.300053i | −0.00953151 | − | 0.00953151i | 0.702325 | − | 0.711856i | \(-0.252145\pi\) |
−0.711856 | + | 0.702325i | \(0.752145\pi\) | |||||||
\(992\) | −14.1813 | + | 14.1813i | −0.450257 | + | 0.450257i | ||||
\(993\) | 6.80821 | − | 6.80821i | 0.216052 | − | 0.216052i | ||||
\(994\) | 6.76985i | 0.214727i | ||||||||
\(995\) | − | 17.8210i | − | 0.564963i | ||||||
\(996\) | −3.18608 | + | 3.18608i | −0.100955 | + | 0.100955i | ||||
\(997\) | −26.4732 | + | 26.4732i | −0.838416 | + | 0.838416i | −0.988650 | − | 0.150234i | \(-0.951997\pi\) |
0.150234 | + | 0.988650i | \(0.451997\pi\) | |||||||
\(998\) | 47.0966 | + | 47.0966i | 1.49082 | + | 1.49082i | ||||
\(999\) | 5.18271 | 0.163974 |
(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 | 119.2.g.a.64.8 | ✓ | 20 | |
3.2 | odd | 2 | 1071.2.n.c.64.3 | 20 | |||
7.2 | even | 3 | 833.2.o.g.557.8 | 40 | |||
7.3 | odd | 6 | 833.2.o.f.30.3 | 40 | |||
7.4 | even | 3 | 833.2.o.g.30.3 | 40 | |||
7.5 | odd | 6 | 833.2.o.f.557.8 | 40 | |||
7.6 | odd | 2 | 833.2.g.h.540.8 | 20 | |||
17.2 | even | 8 | 2023.2.a.m.1.3 | 10 | |||
17.4 | even | 4 | inner | 119.2.g.a.106.3 | yes | 20 | |
17.15 | even | 8 | 2023.2.a.n.1.3 | 10 | |||
51.38 | odd | 4 | 1071.2.n.c.820.8 | 20 | |||
119.4 | even | 12 | 833.2.o.g.667.8 | 40 | |||
119.38 | odd | 12 | 833.2.o.f.667.8 | 40 | |||
119.55 | odd | 4 | 833.2.g.h.344.3 | 20 | |||
119.72 | even | 12 | 833.2.o.g.361.3 | 40 | |||
119.89 | odd | 12 | 833.2.o.f.361.3 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
119.2.g.a.64.8 | ✓ | 20 | 1.1 | even | 1 | trivial | |
119.2.g.a.106.3 | yes | 20 | 17.4 | even | 4 | inner | |
833.2.g.h.344.3 | 20 | 119.55 | odd | 4 | |||
833.2.g.h.540.8 | 20 | 7.6 | odd | 2 | |||
833.2.o.f.30.3 | 40 | 7.3 | odd | 6 | |||
833.2.o.f.361.3 | 40 | 119.89 | odd | 12 | |||
833.2.o.f.557.8 | 40 | 7.5 | odd | 6 | |||
833.2.o.f.667.8 | 40 | 119.38 | odd | 12 | |||
833.2.o.g.30.3 | 40 | 7.4 | even | 3 | |||
833.2.o.g.361.3 | 40 | 119.72 | even | 12 | |||
833.2.o.g.557.8 | 40 | 7.2 | even | 3 | |||
833.2.o.g.667.8 | 40 | 119.4 | even | 12 | |||
1071.2.n.c.64.3 | 20 | 3.2 | odd | 2 | |||
1071.2.n.c.820.8 | 20 | 51.38 | odd | 4 | |||
2023.2.a.m.1.3 | 10 | 17.2 | even | 8 | |||
2023.2.a.n.1.3 | 10 | 17.15 | even | 8 |