Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,3,Mod(62,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.62");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.k (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: | \(2.86104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 62.16 | ||
Character | \(\chi\) | \(=\) | 105.62 |
Dual form | 105.3.k.d.83.16 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.63482 | − | 2.63482i | 1.31741 | − | 1.31741i | 0.401595 | − | 0.915817i | \(-0.368456\pi\) |
0.915817 | − | 0.401595i | \(-0.131544\pi\) | |||||||
\(3\) | 1.59482 | + | 2.54097i | 0.531606 | + | 0.846991i | ||||
\(4\) | − | 9.88460i | − | 2.47115i | ||||||
\(5\) | −4.15332 | − | 2.78387i | −0.830663 | − | 0.556775i | ||||
\(6\) | 10.8971 | + | 2.49295i | 1.81618 | + | 0.415492i | ||||
\(7\) | 6.57626 | + | 2.39850i | 0.939466 | + | 0.342643i | ||||
\(8\) | −15.5049 | − | 15.5049i | −1.93811 | − | 1.93811i | ||||
\(9\) | −3.91310 | + | 8.10479i | −0.434789 | + | 0.900532i | ||||
\(10\) | −18.2783 | + | 3.60824i | −1.82783 | + | 0.360824i | ||||
\(11\) | 5.66373i | 0.514885i | 0.966294 | + | 0.257442i | \(0.0828797\pi\) | ||||
−0.966294 | + | 0.257442i | \(0.917120\pi\) | |||||||
\(12\) | 25.1165 | − | 15.7642i | 2.09304 | − | 1.31368i | ||||
\(13\) | 1.68481 | + | 1.68481i | 0.129601 | + | 0.129601i | 0.768932 | − | 0.639331i | \(-0.220789\pi\) |
−0.639331 | + | 0.768932i | \(0.720789\pi\) | |||||||
\(14\) | 23.6469 | − | 11.0077i | 1.68907 | − | 0.786262i | ||||
\(15\) | 0.449964 | − | 14.9932i | 0.0299976 | − | 0.999550i | ||||
\(16\) | −42.1670 | −2.63544 | ||||||||
\(17\) | 14.0118 | + | 14.0118i | 0.824224 | + | 0.824224i | 0.986711 | − | 0.162486i | \(-0.0519514\pi\) |
−0.162486 | + | 0.986711i | \(0.551951\pi\) | |||||||
\(18\) | 11.0444 | + | 31.6650i | 0.613576 | + | 1.75917i | ||||
\(19\) | −24.0066 | −1.26351 | −0.631753 | − | 0.775170i | \(-0.717664\pi\) | ||||
−0.631753 | + | 0.775170i | \(0.717664\pi\) | |||||||
\(20\) | −27.5175 | + | 41.0539i | −1.37588 | + | 2.05269i | ||||
\(21\) | 4.39342 | + | 20.5353i | 0.209211 | + | 0.977871i | ||||
\(22\) | 14.9229 | + | 14.9229i | 0.678315 | + | 0.678315i | ||||
\(23\) | −3.17641 | − | 3.17641i | −0.138105 | − | 0.138105i | 0.634675 | − | 0.772780i | \(-0.281134\pi\) |
−0.772780 | + | 0.634675i | \(0.781134\pi\) | |||||||
\(24\) | 14.6700 | − | 64.1251i | 0.611252 | − | 2.67188i | ||||
\(25\) | 9.50008 | + | 23.1246i | 0.380003 | + | 0.924985i | ||||
\(26\) | 8.87835 | 0.341475 | ||||||||
\(27\) | −26.8348 | + | 2.98258i | −0.993880 | + | 0.110466i | ||||
\(28\) | 23.7082 | − | 65.0037i | 0.846722 | − | 2.32156i | ||||
\(29\) | −24.1064 | −0.831254 | −0.415627 | − | 0.909535i | \(-0.636438\pi\) | ||||
−0.415627 | + | 0.909535i | \(0.636438\pi\) | |||||||
\(30\) | −38.3190 | − | 40.6902i | −1.27730 | − | 1.35634i | ||||
\(31\) | − | 23.8436i | − | 0.769148i | −0.923094 | − | 0.384574i | \(-0.874348\pi\) | ||
0.923094 | − | 0.384574i | \(-0.125652\pi\) | |||||||
\(32\) | −49.0830 | + | 49.0830i | −1.53384 | + | 1.53384i | ||||
\(33\) | −14.3914 | + | 9.03263i | −0.436103 | + | 0.273716i | ||||
\(34\) | 73.8374 | 2.17169 | ||||||||
\(35\) | −20.6362 | − | 28.2692i | −0.589605 | − | 0.807692i | ||||
\(36\) | 80.1127 | + | 38.6795i | 2.22535 | + | 1.07443i | ||||
\(37\) | −13.8075 | − | 13.8075i | −0.373177 | − | 0.373177i | 0.495456 | − | 0.868633i | \(-0.335001\pi\) |
−0.868633 | + | 0.495456i | \(0.835001\pi\) | |||||||
\(38\) | −63.2532 | + | 63.2532i | −1.66456 | + | 1.66456i | ||||
\(39\) | −1.59409 | + | 6.96802i | −0.0408741 | + | 0.178667i | ||||
\(40\) | 21.2331 | + | 107.560i | 0.530827 | + | 2.68901i | ||||
\(41\) | 53.4368 | 1.30334 | 0.651668 | − | 0.758505i | \(-0.274070\pi\) | ||||
0.651668 | + | 0.758505i | \(0.274070\pi\) | |||||||
\(42\) | 65.6828 | + | 42.5310i | 1.56388 | + | 1.01264i | ||||
\(43\) | 25.9017 | − | 25.9017i | 0.602366 | − | 0.602366i | −0.338574 | − | 0.940940i | \(-0.609945\pi\) |
0.940940 | + | 0.338574i | \(0.109945\pi\) | |||||||
\(44\) | 55.9837 | 1.27236 | ||||||||
\(45\) | 38.8151 | − | 22.7682i | 0.862557 | − | 0.505959i | ||||
\(46\) | −16.7386 | −0.363882 | ||||||||
\(47\) | −27.3968 | − | 27.3968i | −0.582911 | − | 0.582911i | 0.352791 | − | 0.935702i | \(-0.385233\pi\) |
−0.935702 | + | 0.352791i | \(0.885233\pi\) | |||||||
\(48\) | −67.2487 | − | 107.145i | −1.40102 | − | 2.23219i | ||||
\(49\) | 37.4944 | + | 31.5463i | 0.765192 | + | 0.643802i | ||||
\(50\) | 85.9604 | + | 35.8983i | 1.71921 | + | 0.717966i | ||||
\(51\) | −13.2573 | + | 57.9500i | −0.259948 | + | 1.13627i | ||||
\(52\) | 16.6537 | − | 16.6537i | 0.320263 | − | 0.320263i | ||||
\(53\) | −22.4866 | − | 22.4866i | −0.424276 | − | 0.424276i | 0.462397 | − | 0.886673i | \(-0.346989\pi\) |
−0.886673 | + | 0.462397i | \(0.846989\pi\) | |||||||
\(54\) | −62.8463 | + | 78.5635i | −1.16382 | + | 1.45488i | ||||
\(55\) | 15.7671 | − | 23.5233i | 0.286675 | − | 0.427696i | ||||
\(56\) | −64.7758 | − | 139.153i | −1.15671 | − | 2.48487i | ||||
\(57\) | −38.2862 | − | 61.0002i | −0.671688 | − | 1.07018i | ||||
\(58\) | −63.5160 | + | 63.5160i | −1.09510 | + | 1.09510i | ||||
\(59\) | 14.2975i | 0.242330i | 0.992632 | + | 0.121165i | \(0.0386631\pi\) | ||||
−0.992632 | + | 0.121165i | \(0.961337\pi\) | |||||||
\(60\) | −148.202 | − | 4.44772i | −2.47004 | − | 0.0741286i | ||||
\(61\) | − | 90.2799i | − | 1.48000i | −0.672608 | − | 0.739999i | \(-0.734826\pi\) | ||
0.672608 | − | 0.739999i | \(-0.265174\pi\) | |||||||
\(62\) | −62.8237 | − | 62.8237i | −1.01329 | − | 1.01329i | ||||
\(63\) | −45.1729 | + | 43.9136i | −0.717030 | + | 0.697042i | ||||
\(64\) | 89.9824i | 1.40598i | ||||||||
\(65\) | −2.30725 | − | 11.6878i | −0.0354961 | − | 0.179813i | ||||
\(66\) | −14.1194 | + | 61.7182i | −0.213931 | + | 0.935124i | ||||
\(67\) | −0.492023 | − | 0.492023i | −0.00734362 | − | 0.00734362i | 0.703425 | − | 0.710769i | \(-0.251653\pi\) |
−0.710769 | + | 0.703425i | \(0.751653\pi\) | |||||||
\(68\) | 138.501 | − | 138.501i | 2.03678 | − | 2.03678i | ||||
\(69\) | 3.00538 | − | 13.1370i | 0.0435562 | − | 0.190391i | ||||
\(70\) | −128.857 | − | 20.1117i | −1.84082 | − | 0.287310i | ||||
\(71\) | 54.2705i | 0.764374i | 0.924085 | + | 0.382187i | \(0.124829\pi\) | ||||
−0.924085 | + | 0.382187i | \(0.875171\pi\) | |||||||
\(72\) | 186.336 | − | 64.9917i | 2.58800 | − | 0.902663i | ||||
\(73\) | −30.4748 | − | 30.4748i | −0.417464 | − | 0.417464i | 0.466865 | − | 0.884329i | \(-0.345383\pi\) |
−0.884329 | + | 0.466865i | \(0.845383\pi\) | |||||||
\(74\) | −72.7609 | −0.983256 | ||||||||
\(75\) | −43.6082 | + | 61.0191i | −0.581442 | + | 0.813588i | ||||
\(76\) | 237.296i | 3.12231i | ||||||||
\(77\) | −13.5845 | + | 37.2462i | −0.176422 | + | 0.483717i | ||||
\(78\) | 14.1594 | + | 22.5597i | 0.181530 | + | 0.289226i | ||||
\(79\) | − | 58.3371i | − | 0.738444i | −0.929341 | − | 0.369222i | \(-0.879624\pi\) | ||
0.929341 | − | 0.369222i | \(-0.120376\pi\) | |||||||
\(80\) | 175.133 | + | 117.388i | 2.18916 | + | 1.46735i | ||||
\(81\) | −50.3753 | − | 63.4298i | −0.621917 | − | 0.783083i | ||||
\(82\) | 140.796 | − | 140.796i | 1.71703 | − | 1.71703i | ||||
\(83\) | −55.7696 | + | 55.7696i | −0.671923 | + | 0.671923i | −0.958159 | − | 0.286236i | \(-0.907596\pi\) |
0.286236 | + | 0.958159i | \(0.407596\pi\) | |||||||
\(84\) | 202.983 | − | 43.4272i | 2.41647 | − | 0.516991i | ||||
\(85\) | −19.1884 | − | 97.2026i | −0.225746 | − | 1.14356i | ||||
\(86\) | − | 136.493i | − | 1.58713i | ||||||
\(87\) | −38.4453 | − | 61.2536i | −0.441900 | − | 0.704065i | ||||
\(88\) | 87.8156 | − | 87.8156i | 0.997905 | − | 0.997905i | ||||
\(89\) | 109.444i | 1.22971i | 0.788641 | + | 0.614854i | \(0.210785\pi\) | ||||
−0.788641 | + | 0.614854i | \(0.789215\pi\) | |||||||
\(90\) | 42.2808 | − | 162.261i | 0.469786 | − | 1.80290i | ||||
\(91\) | 7.03872 | + | 15.1207i | 0.0773486 | + | 0.166162i | ||||
\(92\) | −31.3976 | + | 31.3976i | −0.341278 | + | 0.341278i | ||||
\(93\) | 60.5860 | − | 38.0262i | 0.651462 | − | 0.408884i | ||||
\(94\) | −144.372 | −1.53587 | ||||||||
\(95\) | 99.7071 | + | 66.8314i | 1.04955 | + | 0.703489i | ||||
\(96\) | −202.997 | − | 46.4402i | −2.11456 | − | 0.483752i | ||||
\(97\) | −48.0651 | + | 48.0651i | −0.495516 | + | 0.495516i | −0.910039 | − | 0.414523i | \(-0.863949\pi\) |
0.414523 | + | 0.910039i | \(0.363949\pi\) | |||||||
\(98\) | 181.910 | − | 15.6722i | 1.85623 | − | 0.159920i | ||||
\(99\) | −45.9034 | − | 22.1628i | −0.463670 | − | 0.223866i | ||||
\(100\) | 228.578 | − | 93.9046i | 2.28578 | − | 0.939046i | ||||
\(101\) | 103.406 | 1.02382 | 0.511911 | − | 0.859039i | \(-0.328938\pi\) | ||||
0.511911 | + | 0.859039i | \(0.328938\pi\) | |||||||
\(102\) | 117.757 | + | 187.619i | 1.15448 | + | 1.83940i | ||||
\(103\) | 59.9292 | + | 59.9292i | 0.581837 | + | 0.581837i | 0.935408 | − | 0.353571i | \(-0.115033\pi\) |
−0.353571 | + | 0.935408i | \(0.615033\pi\) | |||||||
\(104\) | − | 52.2456i | − | 0.502361i | ||||||
\(105\) | 38.9204 | − | 97.5203i | 0.370670 | − | 0.928765i | ||||
\(106\) | −118.497 | −1.11789 | ||||||||
\(107\) | −33.4736 | + | 33.4736i | −0.312837 | + | 0.312837i | −0.846008 | − | 0.533170i | \(-0.821000\pi\) |
0.533170 | + | 0.846008i | \(0.321000\pi\) | |||||||
\(108\) | 29.4816 | + | 265.251i | 0.272978 | + | 2.45603i | ||||
\(109\) | 188.925i | 1.73326i | 0.498954 | + | 0.866628i | \(0.333718\pi\) | ||||
−0.498954 | + | 0.866628i | \(0.666282\pi\) | |||||||
\(110\) | −20.4361 | − | 103.523i | −0.185783 | − | 0.941121i | ||||
\(111\) | 13.0641 | − | 57.1052i | 0.117694 | − | 0.514461i | ||||
\(112\) | −277.301 | − | 101.138i | −2.47590 | − | 0.903013i | ||||
\(113\) | −112.042 | − | 112.042i | −0.991524 | − | 0.991524i | 0.00844052 | − | 0.999964i | \(-0.497313\pi\) |
−0.999964 | + | 0.00844052i | \(0.997313\pi\) | |||||||
\(114\) | −261.602 | − | 59.8474i | −2.29476 | − | 0.524977i | ||||
\(115\) | 4.34991 | + | 22.0354i | 0.0378253 | + | 0.191612i | ||||
\(116\) | 238.282i | 2.05415i | ||||||||
\(117\) | −20.2478 | + | 7.06219i | −0.173058 | + | 0.0603606i | ||||
\(118\) | 37.6714 | + | 37.6714i | 0.319249 | + | 0.319249i | ||||
\(119\) | 58.5380 | + | 125.753i | 0.491916 | + | 1.05675i | ||||
\(120\) | −239.446 | + | 225.492i | −1.99538 | + | 1.87910i | ||||
\(121\) | 88.9221 | 0.734894 | ||||||||
\(122\) | −237.872 | − | 237.872i | −1.94977 | − | 1.94977i | ||||
\(123\) | 85.2220 | + | 135.781i | 0.692862 | + | 1.10391i | ||||
\(124\) | −235.684 | −1.90068 | ||||||||
\(125\) | 24.9192 | − | 122.491i | 0.199354 | − | 0.979928i | ||||
\(126\) | −3.31798 | + | 234.727i | −0.0263332 | + | 1.86292i | ||||
\(127\) | −27.2567 | − | 27.2567i | −0.214620 | − | 0.214620i | 0.591607 | − | 0.806227i | \(-0.298494\pi\) |
−0.806227 | + | 0.591607i | \(0.798494\pi\) | |||||||
\(128\) | 40.7558 | + | 40.7558i | 0.318405 | + | 0.318405i | ||||
\(129\) | 107.124 | + | 24.5071i | 0.830420 | + | 0.189977i | ||||
\(130\) | −36.8746 | − | 24.7162i | −0.283651 | − | 0.190125i | ||||
\(131\) | 22.2009 | 0.169472 | 0.0847362 | − | 0.996403i | \(-0.472995\pi\) | ||||
0.0847362 | + | 0.996403i | \(0.472995\pi\) | |||||||
\(132\) | 89.2840 | + | 142.253i | 0.676394 | + | 1.07768i | ||||
\(133\) | −157.874 | − | 57.5799i | −1.18702 | − | 0.432931i | ||||
\(134\) | −2.59279 | −0.0193492 | ||||||||
\(135\) | 119.756 | + | 62.3170i | 0.887084 | + | 0.461607i | ||||
\(136\) | − | 434.504i | − | 3.19488i | ||||||
\(137\) | 87.8267 | − | 87.8267i | 0.641071 | − | 0.641071i | −0.309748 | − | 0.950819i | \(-0.600245\pi\) |
0.950819 | + | 0.309748i | \(0.100245\pi\) | |||||||
\(138\) | −26.6950 | − | 42.5323i | −0.193442 | − | 0.308205i | ||||
\(139\) | 55.5125 | 0.399371 | 0.199685 | − | 0.979860i | \(-0.436008\pi\) | ||||
0.199685 | + | 0.979860i | \(0.436008\pi\) | |||||||
\(140\) | −279.430 | + | 203.980i | −1.99593 | + | 1.45700i | ||||
\(141\) | 25.9216 | − | 113.308i | 0.183841 | − | 0.803600i | ||||
\(142\) | 142.993 | + | 142.993i | 1.00700 | + | 1.00700i | ||||
\(143\) | −9.54230 | + | 9.54230i | −0.0667294 | + | 0.0667294i | ||||
\(144\) | 165.004 | − | 341.755i | 1.14586 | − | 2.37330i | ||||
\(145\) | 100.121 | + | 67.1091i | 0.690492 | + | 0.462821i | ||||
\(146\) | −160.592 | −1.09994 | ||||||||
\(147\) | −20.3616 | + | 145.583i | −0.138514 | + | 0.990360i | ||||
\(148\) | −136.482 | + | 136.482i | −0.922177 | + | 0.922177i | ||||
\(149\) | 267.880 | 1.79785 | 0.898925 | − | 0.438103i | \(-0.144349\pi\) | ||||
0.898925 | + | 0.438103i | \(0.144349\pi\) | |||||||
\(150\) | 45.8747 | + | 275.674i | 0.305831 | + | 1.83783i | ||||
\(151\) | 149.076 | 0.987261 | 0.493631 | − | 0.869672i | \(-0.335670\pi\) | ||||
0.493631 | + | 0.869672i | \(0.335670\pi\) | |||||||
\(152\) | 372.220 | + | 372.220i | 2.44882 | + | 2.44882i | ||||
\(153\) | −168.392 | + | 58.7331i | −1.10060 | + | 0.383877i | ||||
\(154\) | 62.3445 | + | 133.930i | 0.404834 | + | 0.869674i | ||||
\(155\) | −66.3776 | + | 99.0300i | −0.428242 | + | 0.638903i | ||||
\(156\) | 68.8761 | + | 15.7569i | 0.441513 | + | 0.101006i | ||||
\(157\) | −137.160 | + | 137.160i | −0.873632 | + | 0.873632i | −0.992866 | − | 0.119235i | \(-0.961956\pi\) |
0.119235 | + | 0.992866i | \(0.461956\pi\) | |||||||
\(158\) | −153.708 | − | 153.708i | −0.972835 | − | 0.972835i | ||||
\(159\) | 21.2758 | − | 93.0000i | 0.133810 | − | 0.584906i | ||||
\(160\) | 340.498 | − | 67.2164i | 2.12811 | − | 0.420102i | ||||
\(161\) | −13.2703 | − | 28.5075i | −0.0824242 | − | 0.177066i | ||||
\(162\) | −299.856 | − | 34.3963i | −1.85096 | − | 0.212323i | ||||
\(163\) | 30.1699 | − | 30.1699i | 0.185091 | − | 0.185091i | −0.608479 | − | 0.793570i | \(-0.708220\pi\) |
0.793570 | + | 0.608479i | \(0.208220\pi\) | |||||||
\(164\) | − | 528.201i | − | 3.22074i | ||||||
\(165\) | 84.9177 | + | 2.54848i | 0.514653 | + | 0.0154453i | ||||
\(166\) | 293.886i | 1.77040i | ||||||||
\(167\) | 138.915 | + | 138.915i | 0.831827 | + | 0.831827i | 0.987767 | − | 0.155939i | \(-0.0498404\pi\) |
−0.155939 | + | 0.987767i | \(0.549840\pi\) | |||||||
\(168\) | 250.278 | − | 386.517i | 1.48975 | − | 2.30070i | ||||
\(169\) | − | 163.323i | − | 0.966407i | ||||||
\(170\) | −306.670 | − | 205.554i | −1.80394 | − | 1.20914i | ||||
\(171\) | 93.9404 | − | 194.569i | 0.549359 | − | 1.13783i | ||||
\(172\) | −256.028 | − | 256.028i | −1.48854 | − | 1.48854i | ||||
\(173\) | 91.9689 | − | 91.9689i | 0.531612 | − | 0.531612i | −0.389440 | − | 0.921052i | \(-0.627331\pi\) |
0.921052 | + | 0.389440i | \(0.127331\pi\) | |||||||
\(174\) | −262.689 | − | 60.0960i | −1.50971 | − | 0.345379i | ||||
\(175\) | 7.01062 | + | 174.860i | 0.0400607 | + | 0.999197i | ||||
\(176\) | − | 238.823i | − | 1.35695i | ||||||
\(177\) | −36.3295 | + | 22.8019i | −0.205252 | + | 0.128824i | ||||
\(178\) | 288.366 | + | 288.366i | 1.62003 | + | 1.62003i | ||||
\(179\) | −138.994 | −0.776504 | −0.388252 | − | 0.921553i | \(-0.626921\pi\) | ||||
−0.388252 | + | 0.921553i | \(0.626921\pi\) | |||||||
\(180\) | −225.054 | − | 383.672i | −1.25030 | − | 2.13151i | ||||
\(181\) | 15.4468i | 0.0853414i | 0.999089 | + | 0.0426707i | \(0.0135866\pi\) | ||||
−0.999089 | + | 0.0426707i | \(0.986413\pi\) | |||||||
\(182\) | 58.3863 | + | 21.2947i | 0.320804 | + | 0.117004i | ||||
\(183\) | 229.399 | − | 143.980i | 1.25355 | − | 0.786777i | ||||
\(184\) | 98.5000i | 0.535326i | ||||||||
\(185\) | 18.9086 | + | 95.7856i | 0.102209 | + | 0.517760i | ||||
\(186\) | 59.4410 | − | 259.826i | 0.319575 | − | 1.39691i | ||||
\(187\) | −79.3591 | + | 79.3591i | −0.424380 | + | 0.424380i | ||||
\(188\) | −270.807 | + | 270.807i | −1.44046 | + | 1.44046i | ||||
\(189\) | −183.626 | − | 44.7489i | −0.971567 | − | 0.236767i | ||||
\(190\) | 438.800 | − | 86.6217i | 2.30947 | − | 0.455903i | ||||
\(191\) | 269.579i | 1.41141i | 0.708508 | + | 0.705703i | \(0.249369\pi\) | ||||
−0.708508 | + | 0.705703i | \(0.750631\pi\) | |||||||
\(192\) | −228.643 | + | 143.506i | −1.19085 | + | 0.747426i | ||||
\(193\) | −81.8078 | + | 81.8078i | −0.423875 | + | 0.423875i | −0.886535 | − | 0.462661i | \(-0.846895\pi\) |
0.462661 | + | 0.886535i | \(0.346895\pi\) | |||||||
\(194\) | 253.286i | 1.30560i | ||||||||
\(195\) | 26.0188 | − | 24.5026i | 0.133430 | − | 0.125655i | ||||
\(196\) | 311.823 | − | 370.617i | 1.59093 | − | 1.89090i | ||||
\(197\) | 114.419 | − | 114.419i | 0.580805 | − | 0.580805i | −0.354319 | − | 0.935125i | \(-0.615287\pi\) |
0.935125 | + | 0.354319i | \(0.115287\pi\) | |||||||
\(198\) | −179.342 | + | 62.5523i | −0.905769 | + | 0.315921i | ||||
\(199\) | −88.3996 | −0.444219 | −0.222110 | − | 0.975022i | \(-0.571294\pi\) | ||||
−0.222110 | + | 0.975022i | \(0.571294\pi\) | |||||||
\(200\) | 211.247 | − | 505.843i | 1.05624 | − | 2.52922i | ||||
\(201\) | 0.465530 | − | 2.03490i | 0.00231607 | − | 0.0101239i | ||||
\(202\) | 272.457 | − | 272.457i | 1.34880 | − | 1.34880i | ||||
\(203\) | −158.530 | − | 57.8191i | −0.780934 | − | 0.284823i | ||||
\(204\) | 572.813 | + | 131.044i | 2.80790 | + | 0.642371i | ||||
\(205\) | −221.940 | − | 148.761i | −1.08263 | − | 0.725665i | ||||
\(206\) | 315.806 | 1.53304 | ||||||||
\(207\) | 38.1738 | − | 13.3145i | 0.184414 | − | 0.0643214i | ||||
\(208\) | −71.0433 | − | 71.0433i | −0.341554 | − | 0.341554i | ||||
\(209\) | − | 135.967i | − | 0.650560i | ||||||
\(210\) | −154.400 | − | 359.497i | −0.735240 | − | 1.71189i | ||||
\(211\) | −167.468 | −0.793685 | −0.396842 | − | 0.917887i | \(-0.629894\pi\) | ||||
−0.396842 | + | 0.917887i | \(0.629894\pi\) | |||||||
\(212\) | −222.271 | + | 222.271i | −1.04845 | + | 1.04845i | ||||
\(213\) | −137.900 | + | 86.5517i | −0.647418 | + | 0.406346i | ||||
\(214\) | 176.394i | 0.824272i | ||||||||
\(215\) | −179.685 | + | 35.4709i | −0.835745 | + | 0.164981i | ||||
\(216\) | 462.315 | + | 369.826i | 2.14035 | + | 1.71216i | ||||
\(217\) | 57.1888 | − | 156.802i | 0.263543 | − | 0.722588i | ||||
\(218\) | 497.784 | + | 497.784i | 2.28341 | + | 2.28341i | ||||
\(219\) | 28.8339 | − | 126.038i | 0.131662 | − | 0.575514i | ||||
\(220\) | −232.518 | − | 155.852i | −1.05690 | − | 0.708417i | ||||
\(221\) | 47.2144i | 0.213640i | ||||||||
\(222\) | −116.041 | − | 184.884i | −0.522705 | − | 0.832809i | ||||
\(223\) | 14.5058 | + | 14.5058i | 0.0650483 | + | 0.0650483i | 0.738883 | − | 0.673834i | \(-0.235354\pi\) |
−0.673834 | + | 0.738883i | \(0.735354\pi\) | |||||||
\(224\) | −440.508 | + | 205.057i | −1.96656 | + | 0.915434i | ||||
\(225\) | −224.595 | − | 13.4929i | −0.998200 | − | 0.0599682i | ||||
\(226\) | −590.423 | −2.61249 | ||||||||
\(227\) | −12.9045 | − | 12.9045i | −0.0568479 | − | 0.0568479i | 0.678111 | − | 0.734959i | \(-0.262799\pi\) |
−0.734959 | + | 0.678111i | \(0.762799\pi\) | |||||||
\(228\) | −602.963 | + | 378.444i | −2.64457 | + | 1.65984i | ||||
\(229\) | 325.906 | 1.42317 | 0.711585 | − | 0.702601i | \(-0.247978\pi\) | ||||
0.711585 | + | 0.702601i | \(0.247978\pi\) | |||||||
\(230\) | 69.5207 | + | 46.5981i | 0.302264 | + | 0.202601i | ||||
\(231\) | −116.306 | + | 24.8832i | −0.503491 | + | 0.107719i | ||||
\(232\) | 373.767 | + | 373.767i | 1.61106 | + | 1.61106i | ||||
\(233\) | 66.9917 | + | 66.9917i | 0.287518 | + | 0.287518i | 0.836098 | − | 0.548580i | \(-0.184831\pi\) |
−0.548580 | + | 0.836098i | \(0.684831\pi\) | |||||||
\(234\) | −34.7419 | + | 71.9571i | −0.148470 | + | 0.307509i | ||||
\(235\) | 37.5184 | + | 190.057i | 0.159653 | + | 0.808753i | ||||
\(236\) | 141.325 | 0.598835 | ||||||||
\(237\) | 148.233 | − | 93.0371i | 0.625456 | − | 0.392562i | ||||
\(238\) | 485.574 | + | 177.099i | 2.04023 | + | 0.744113i | ||||
\(239\) | −175.883 | −0.735912 | −0.367956 | − | 0.929843i | \(-0.619942\pi\) | ||||
−0.367956 | + | 0.929843i | \(0.619942\pi\) | |||||||
\(240\) | −18.9736 | + | 632.220i | −0.0790568 | + | 2.63425i | ||||
\(241\) | 407.167i | 1.68949i | 0.535170 | + | 0.844745i | \(0.320248\pi\) | ||||
−0.535170 | + | 0.844745i | \(0.679752\pi\) | |||||||
\(242\) | 234.294 | − | 234.294i | 0.968158 | − | 0.968158i | ||||
\(243\) | 80.8340 | − | 229.161i | 0.332650 | − | 0.943050i | ||||
\(244\) | −892.381 | −3.65730 | ||||||||
\(245\) | −67.9052 | − | 235.402i | −0.277164 | − | 0.960823i | ||||
\(246\) | 582.305 | + | 133.215i | 2.36709 | + | 0.541526i | ||||
\(247\) | −40.4465 | − | 40.4465i | −0.163751 | − | 0.163751i | ||||
\(248\) | −369.693 | + | 369.693i | −1.49070 | + | 1.49070i | ||||
\(249\) | −230.652 | − | 52.7667i | −0.926312 | − | 0.211914i | ||||
\(250\) | −257.084 | − | 388.400i | −1.02834 | − | 1.55360i | ||||
\(251\) | −299.503 | −1.19324 | −0.596620 | − | 0.802524i | \(-0.703490\pi\) | ||||
−0.596620 | + | 0.802524i | \(0.703490\pi\) | |||||||
\(252\) | 434.069 | + | 446.516i | 1.72250 | + | 1.77189i | ||||
\(253\) | 17.9904 | − | 17.9904i | 0.0711081 | − | 0.0711081i | ||||
\(254\) | −143.634 | −0.565486 | ||||||||
\(255\) | 216.387 | − | 203.778i | 0.848578 | − | 0.799129i | ||||
\(256\) | −145.161 | −0.567035 | ||||||||
\(257\) | −37.0235 | − | 37.0235i | −0.144060 | − | 0.144060i | 0.631398 | − | 0.775459i | \(-0.282481\pi\) |
−0.775459 | + | 0.631398i | \(0.782481\pi\) | |||||||
\(258\) | 346.825 | − | 217.682i | 1.34428 | − | 0.843728i | ||||
\(259\) | −57.6846 | − | 123.919i | −0.222721 | − | 0.478453i | ||||
\(260\) | −115.530 | + | 22.8062i | −0.444345 | + | 0.0877163i | ||||
\(261\) | 94.3307 | − | 195.377i | 0.361420 | − | 0.748571i | ||||
\(262\) | 58.4954 | − | 58.4954i | 0.223265 | − | 0.223265i | ||||
\(263\) | 108.381 | + | 108.381i | 0.412093 | + | 0.412093i | 0.882467 | − | 0.470374i | \(-0.155881\pi\) |
−0.470374 | + | 0.882467i | \(0.655881\pi\) | |||||||
\(264\) | 363.187 | + | 83.0872i | 1.37571 | + | 0.314724i | ||||
\(265\) | 30.7941 | + | 155.994i | 0.116204 | + | 0.588657i | ||||
\(266\) | −567.683 | + | 264.257i | −2.13415 | + | 0.993447i | ||||
\(267\) | −278.094 | + | 174.543i | −1.04155 | + | 0.653720i | ||||
\(268\) | −4.86345 | + | 4.86345i | −0.0181472 | + | 0.0181472i | ||||
\(269\) | − | 98.6945i | − | 0.366894i | −0.983030 | − | 0.183447i | \(-0.941274\pi\) | ||
0.983030 | − | 0.183447i | \(-0.0587256\pi\) | |||||||
\(270\) | 479.731 | − | 151.343i | 1.77678 | − | 0.560529i | ||||
\(271\) | − | 218.741i | − | 0.807162i | −0.914944 | − | 0.403581i | \(-0.867765\pi\) | ||
0.914944 | − | 0.403581i | \(-0.132235\pi\) | |||||||
\(272\) | −590.836 | − | 590.836i | −2.17219 | − | 2.17219i | ||||
\(273\) | −27.1959 | + | 42.0001i | −0.0996188 | + | 0.153846i | ||||
\(274\) | − | 462.816i | − | 1.68911i | ||||||
\(275\) | −130.972 | + | 53.8059i | −0.476261 | + | 0.195658i | ||||
\(276\) | −129.854 | − | 29.7070i | −0.470485 | − | 0.107634i | ||||
\(277\) | −187.908 | − | 187.908i | −0.678370 | − | 0.678370i | 0.281261 | − | 0.959631i | \(-0.409247\pi\) |
−0.959631 | + | 0.281261i | \(0.909247\pi\) | |||||||
\(278\) | 146.266 | − | 146.266i | 0.526136 | − | 0.526136i | ||||
\(279\) | 193.247 | + | 93.3024i | 0.692643 | + | 0.334417i | ||||
\(280\) | −118.350 | + | 758.273i | −0.422677 | + | 2.70812i | ||||
\(281\) | − | 284.207i | − | 1.01141i | −0.862705 | − | 0.505707i | \(-0.831232\pi\) | ||
0.862705 | − | 0.505707i | \(-0.168768\pi\) | |||||||
\(282\) | −230.247 | − | 366.845i | −0.816477 | − | 1.30087i | ||||
\(283\) | −67.0672 | − | 67.0672i | −0.236986 | − | 0.236986i | 0.578615 | − | 0.815601i | \(-0.303594\pi\) |
−0.815601 | + | 0.578615i | \(0.803594\pi\) | |||||||
\(284\) | 536.443 | 1.88888 | ||||||||
\(285\) | −10.8021 | + | 359.937i | −0.0379022 | + | 1.26294i | ||||
\(286\) | 50.2846i | 0.175820i | ||||||||
\(287\) | 351.414 | + | 128.168i | 1.22444 | + | 0.446578i | ||||
\(288\) | −205.741 | − | 589.875i | −0.714378 | − | 2.04818i | ||||
\(289\) | 103.662i | 0.358692i | ||||||||
\(290\) | 440.623 | − | 86.9816i | 1.51939 | − | 0.299936i | ||||
\(291\) | −198.787 | − | 45.4770i | −0.683118 | − | 0.156278i | ||||
\(292\) | −301.232 | + | 301.232i | −1.03162 | + | 1.03162i | ||||
\(293\) | 290.821 | − | 290.821i | 0.992563 | − | 0.992563i | −0.00740994 | − | 0.999973i | \(-0.502359\pi\) |
0.999973 | + | 0.00740994i | \(0.00235868\pi\) | |||||||
\(294\) | 329.936 | + | 437.235i | 1.12223 | + | 1.48719i | ||||
\(295\) | 39.8024 | − | 59.3820i | 0.134923 | − | 0.201295i | ||||
\(296\) | 428.169i | 1.44652i | ||||||||
\(297\) | −16.8925 | − | 151.985i | −0.0568773 | − | 0.511734i | ||||
\(298\) | 705.816 | − | 705.816i | 2.36851 | − | 2.36851i | ||||
\(299\) | − | 10.7033i | − | 0.0357970i | ||||||
\(300\) | 603.149 | + | 431.050i | 2.01050 | + | 1.43683i | ||||
\(301\) | 232.462 | − | 108.211i | 0.772298 | − | 0.359506i | ||||
\(302\) | 392.790 | − | 392.790i | 1.30063 | − | 1.30063i | ||||
\(303\) | 164.914 | + | 262.752i | 0.544270 | + | 0.867168i | ||||
\(304\) | 1012.29 | 3.32989 | ||||||||
\(305\) | −251.328 | + | 374.961i | −0.824026 | + | 1.22938i | ||||
\(306\) | −288.933 | + | 598.436i | −0.944226 | + | 1.95567i | ||||
\(307\) | −107.588 | + | 107.588i | −0.350451 | + | 0.350451i | −0.860277 | − | 0.509826i | \(-0.829710\pi\) |
0.509826 | + | 0.860277i | \(0.329710\pi\) | |||||||
\(308\) | 368.164 | + | 134.277i | 1.19534 | + | 0.435964i | ||||
\(309\) | −56.7023 | + | 247.855i | −0.183503 | + | 0.802119i | ||||
\(310\) | 86.0334 | + | 435.820i | 0.277527 | + | 1.40587i | ||||
\(311\) | −537.149 | −1.72717 | −0.863583 | − | 0.504206i | \(-0.831785\pi\) | ||||
−0.863583 | + | 0.504206i | \(0.831785\pi\) | |||||||
\(312\) | 132.755 | − | 83.3222i | 0.425496 | − | 0.267058i | ||||
\(313\) | −346.433 | − | 346.433i | −1.10682 | − | 1.10682i | −0.993567 | − | 0.113249i | \(-0.963874\pi\) |
−0.113249 | − | 0.993567i | \(-0.536126\pi\) | |||||||
\(314\) | 722.786i | 2.30187i | ||||||||
\(315\) | 309.868 | − | 56.6315i | 0.983706 | − | 0.179783i | ||||
\(316\) | −576.639 | −1.82481 | ||||||||
\(317\) | −25.3251 | + | 25.3251i | −0.0798898 | + | 0.0798898i | −0.745923 | − | 0.666033i | \(-0.767991\pi\) |
0.666033 | + | 0.745923i | \(0.267991\pi\) | |||||||
\(318\) | −188.981 | − | 301.097i | −0.594279 | − | 0.946846i | ||||
\(319\) | − | 136.532i | − | 0.428000i | ||||||
\(320\) | 250.500 | − | 373.726i | 0.782812 | − | 1.16789i | ||||
\(321\) | −138.440 | − | 31.6712i | −0.431277 | − | 0.0986642i | ||||
\(322\) | −110.077 | − | 40.1475i | −0.341855 | − | 0.124682i | ||||
\(323\) | −336.376 | − | 336.376i | −1.04141 | − | 1.04141i | ||||
\(324\) | −626.978 | + | 497.939i | −1.93512 | + | 1.53685i | ||||
\(325\) | −22.9547 | + | 54.9664i | −0.0706300 | + | 0.169127i | ||||
\(326\) | − | 158.985i | − | 0.487683i | ||||||
\(327\) | −480.054 | + | 301.301i | −1.46805 | + | 0.921410i | ||||
\(328\) | −828.532 | − | 828.532i | −2.52601 | − | 2.52601i | ||||
\(329\) | −114.457 | − | 245.880i | −0.347895 | − | 0.747355i | ||||
\(330\) | 230.458 | − | 217.029i | 0.698358 | − | 0.657662i | ||||
\(331\) | 162.753 | 0.491702 | 0.245851 | − | 0.969308i | \(-0.420933\pi\) | ||||
0.245851 | + | 0.969308i | \(0.420933\pi\) | |||||||
\(332\) | 551.261 | + | 551.261i | 1.66042 | + | 1.66042i | ||||
\(333\) | 165.938 | − | 57.8769i | 0.498311 | − | 0.173805i | ||||
\(334\) | 732.034 | 2.19172 | ||||||||
\(335\) | 0.673796 | + | 3.41325i | 0.00201133 | + | 0.0101888i | ||||
\(336\) | −185.257 | − | 865.911i | −0.551361 | − | 2.57712i | ||||
\(337\) | 342.565 | + | 342.565i | 1.01651 | + | 1.01651i | 0.999861 | + | 0.0166527i | \(0.00530098\pi\) |
0.0166527 | + | 0.999861i | \(0.494699\pi\) | |||||||
\(338\) | −430.327 | − | 430.327i | −1.27316 | − | 1.27316i | ||||
\(339\) | 106.009 | − | 463.383i | 0.312712 | − | 1.36691i | ||||
\(340\) | −960.810 | + | 189.669i | −2.82591 | + | 0.557851i | ||||
\(341\) | 135.044 | 0.396023 | ||||||||
\(342\) | −265.138 | − | 760.171i | −0.775257 | − | 2.22272i | ||||
\(343\) | 170.909 | + | 297.387i | 0.498277 | + | 0.867018i | ||||
\(344\) | −803.208 | −2.33491 | ||||||||
\(345\) | −49.0540 | + | 46.1955i | −0.142186 | + | 0.133900i | ||||
\(346\) | − | 484.644i | − | 1.40070i | ||||||
\(347\) | 0.436435 | − | 0.436435i | 0.00125774 | − | 0.00125774i | −0.706478 | − | 0.707735i | \(-0.749717\pi\) |
0.707735 | + | 0.706478i | \(0.249717\pi\) | |||||||
\(348\) | −605.468 | + | 380.016i | −1.73985 | + | 1.09200i | ||||
\(349\) | −313.871 | −0.899344 | −0.449672 | − | 0.893194i | \(-0.648459\pi\) | ||||
−0.449672 | + | 0.893194i | \(0.648459\pi\) | |||||||
\(350\) | 479.196 | + | 442.252i | 1.36913 | + | 1.26358i | ||||
\(351\) | −50.2365 | − | 40.1863i | −0.143124 | − | 0.114491i | ||||
\(352\) | −277.993 | − | 277.993i | −0.789753 | − | 0.789753i | ||||
\(353\) | −12.4873 | + | 12.4873i | −0.0353746 | + | 0.0353746i | −0.724573 | − | 0.689198i | \(-0.757963\pi\) |
0.689198 | + | 0.724573i | \(0.257963\pi\) | |||||||
\(354\) | −35.6430 | + | 155.801i | −0.100686 | + | 0.440116i | ||||
\(355\) | 151.082 | − | 225.403i | 0.425584 | − | 0.634937i | ||||
\(356\) | 1081.81 | 3.03879 | ||||||||
\(357\) | −226.177 | + | 349.296i | −0.633548 | + | 0.978421i | ||||
\(358\) | −366.225 | + | 366.225i | −1.02298 | + | 1.02298i | ||||
\(359\) | 491.177 | 1.36818 | 0.684091 | − | 0.729397i | \(-0.260199\pi\) | ||||
0.684091 | + | 0.729397i | \(0.260199\pi\) | |||||||
\(360\) | −954.842 | − | 248.806i | −2.65234 | − | 0.691127i | ||||
\(361\) | 215.318 | 0.596448 | ||||||||
\(362\) | 40.6996 | + | 40.6996i | 0.112430 | + | 0.112430i | ||||
\(363\) | 141.815 | + | 225.949i | 0.390674 | + | 0.622449i | ||||
\(364\) | 149.463 | − | 69.5750i | 0.410612 | − | 0.191140i | ||||
\(365\) | 41.7335 | + | 211.410i | 0.114338 | + | 0.579205i | ||||
\(366\) | 225.064 | − | 983.789i | 0.614928 | − | 2.68795i | ||||
\(367\) | −356.973 | + | 356.973i | −0.972679 | + | 0.972679i | −0.999637 | − | 0.0269576i | \(-0.991418\pi\) |
0.0269576 | + | 0.999637i | \(0.491418\pi\) | |||||||
\(368\) | 133.940 | + | 133.940i | 0.363967 | + | 0.363967i | ||||
\(369\) | −209.104 | + | 433.094i | −0.566676 | + | 1.17370i | ||||
\(370\) | 302.199 | + | 202.557i | 0.816755 | + | 0.547452i | ||||
\(371\) | −93.9437 | − | 201.812i | −0.253218 | − | 0.543968i | ||||
\(372\) | −375.874 | − | 598.868i | −1.01041 | − | 1.60986i | ||||
\(373\) | −71.3079 | + | 71.3079i | −0.191174 | + | 0.191174i | −0.796203 | − | 0.605029i | \(-0.793161\pi\) |
0.605029 | + | 0.796203i | \(0.293161\pi\) | |||||||
\(374\) | 418.195i | 1.11817i | ||||||||
\(375\) | 350.988 | − | 132.032i | 0.935968 | − | 0.352085i | ||||
\(376\) | 849.570i | 2.25949i | ||||||||
\(377\) | −40.6146 | − | 40.6146i | −0.107731 | − | 0.107731i | ||||
\(378\) | −601.728 | + | 365.917i | −1.59187 | + | 0.968034i | ||||
\(379\) | 730.407i | 1.92720i | 0.267356 | + | 0.963598i | \(0.413850\pi\) | ||||
−0.267356 | + | 0.963598i | \(0.586150\pi\) | |||||||
\(380\) | 660.602 | − | 985.565i | 1.73843 | − | 2.59359i | ||||
\(381\) | 25.7891 | − | 112.728i | 0.0676880 | − | 0.295875i | ||||
\(382\) | 710.292 | + | 710.292i | 1.85940 | + | 1.85940i | ||||
\(383\) | 317.179 | − | 317.179i | 0.828144 | − | 0.828144i | −0.159116 | − | 0.987260i | \(-0.550864\pi\) |
0.987260 | + | 0.159116i | \(0.0508644\pi\) | |||||||
\(384\) | −38.5613 | + | 168.558i | −0.100420 | + | 0.438952i | ||||
\(385\) | 160.109 | − | 116.878i | 0.415868 | − | 0.303579i | ||||
\(386\) | 431.099i | 1.11684i | ||||||||
\(387\) | 108.572 | + | 311.284i | 0.280548 | + | 0.804352i | ||||
\(388\) | 475.104 | + | 475.104i | 1.22450 | + | 1.22450i | ||||
\(389\) | 319.504 | 0.821347 | 0.410674 | − | 0.911782i | \(-0.365294\pi\) | ||||
0.410674 | + | 0.911782i | \(0.365294\pi\) | |||||||
\(390\) | 3.99494 | − | 133.115i | 0.0102434 | − | 0.341321i | ||||
\(391\) | − | 89.0146i | − | 0.227659i | ||||||
\(392\) | −92.2245 | − | 1070.47i | −0.235267 | − | 2.73079i | ||||
\(393\) | 35.4064 | + | 56.4119i | 0.0900926 | + | 0.143542i | ||||
\(394\) | − | 602.946i | − | 1.53032i | ||||||
\(395\) | −162.403 | + | 242.292i | −0.411147 | + | 0.613398i | ||||
\(396\) | −219.070 | + | 453.737i | −0.553207 | + | 1.14580i | ||||
\(397\) | 443.370 | − | 443.370i | 1.11680 | − | 1.11680i | 0.124594 | − | 0.992208i | \(-0.460237\pi\) |
0.992208 | − | 0.124594i | \(-0.0397628\pi\) | |||||||
\(398\) | −232.918 | + | 232.918i | −0.585220 | + | 0.585220i | ||||
\(399\) | −105.471 | − | 492.983i | −0.264339 | − | 1.23555i | ||||
\(400\) | −400.590 | − | 975.096i | −1.00147 | − | 2.43774i | ||||
\(401\) | 462.240i | 1.15272i | 0.817197 | + | 0.576359i | \(0.195527\pi\) | ||||
−0.817197 | + | 0.576359i | \(0.804473\pi\) | |||||||
\(402\) | −4.13503 | − | 6.58820i | −0.0102861 | − | 0.0163886i | ||||
\(403\) | 40.1719 | − | 40.1719i | 0.0996821 | − | 0.0996821i | ||||
\(404\) | − | 1022.13i | − | 2.53002i | ||||||
\(405\) | 32.6439 | + | 403.682i | 0.0806023 | + | 0.996746i | ||||
\(406\) | −570.041 | + | 265.355i | −1.40404 | + | 0.653583i | ||||
\(407\) | 78.2022 | − | 78.2022i | 0.192143 | − | 0.192143i | ||||
\(408\) | 1104.06 | − | 692.955i | 2.70604 | − | 1.69842i | ||||
\(409\) | 195.136 | 0.477106 | 0.238553 | − | 0.971130i | \(-0.423327\pi\) | ||||
0.238553 | + | 0.971130i | \(0.423327\pi\) | |||||||
\(410\) | −976.732 | + | 192.813i | −2.38227 | + | 0.470275i | ||||
\(411\) | 363.233 | + | 83.0977i | 0.883779 | + | 0.202184i | ||||
\(412\) | 592.376 | − | 592.376i | 1.43781 | − | 1.43781i | ||||
\(413\) | −34.2925 | + | 94.0240i | −0.0830327 | + | 0.227661i | ||||
\(414\) | 65.4998 | − | 135.663i | 0.158212 | − | 0.327688i | ||||
\(415\) | 386.884 | − | 76.3733i | 0.932252 | − | 0.184032i | ||||
\(416\) | −165.391 | −0.397574 | ||||||||
\(417\) | 88.5324 | + | 141.056i | 0.212308 | + | 0.338264i | ||||
\(418\) | −358.249 | − | 358.249i | −0.857056 | − | 0.857056i | ||||
\(419\) | − | 389.604i | − | 0.929843i | −0.885352 | − | 0.464922i | \(-0.846083\pi\) | ||
0.885352 | − | 0.464922i | \(-0.153917\pi\) | |||||||
\(420\) | −963.949 | − | 384.713i | −2.29512 | − | 0.915982i | ||||
\(421\) | 22.7752 | 0.0540978 | 0.0270489 | − | 0.999634i | \(-0.491389\pi\) | ||||
0.0270489 | + | 0.999634i | \(0.491389\pi\) | |||||||
\(422\) | −441.248 | + | 441.248i | −1.04561 | + | 1.04561i | ||||
\(423\) | 329.252 | − | 114.839i | 0.778373 | − | 0.271487i | ||||
\(424\) | 697.306i | 1.64459i | ||||||||
\(425\) | −190.905 | + | 457.131i | −0.449187 | + | 1.07560i | ||||
\(426\) | −135.294 | + | 591.391i | −0.317591 | + | 1.38824i | ||||
\(427\) | 216.536 | − | 593.704i | 0.507111 | − | 1.39041i | ||||
\(428\) | 330.873 | + | 330.873i | 0.773068 | + | 0.773068i | ||||
\(429\) | −39.4650 | − | 9.02850i | −0.0919930 | − | 0.0210454i | ||||
\(430\) | −379.980 | + | 566.899i | −0.883673 | + | 1.31837i | ||||
\(431\) | − | 838.658i | − | 1.94584i | −0.231137 | − | 0.972921i | \(-0.574244\pi\) | ||
0.231137 | − | 0.972921i | \(-0.425756\pi\) | |||||||
\(432\) | 1131.54 | − | 125.767i | 2.61931 | − | 0.291126i | ||||
\(433\) | −61.2050 | − | 61.2050i | −0.141351 | − | 0.141351i | 0.632890 | − | 0.774241i | \(-0.281868\pi\) |
−0.774241 | + | 0.632890i | \(0.781868\pi\) | |||||||
\(434\) | −262.462 | − | 563.828i | −0.604752 | − | 1.29914i | ||||
\(435\) | −10.8470 | + | 361.433i | −0.0249356 | + | 0.830880i | ||||
\(436\) | 1867.45 | 4.28314 | ||||||||
\(437\) | 76.2549 | + | 76.2549i | 0.174496 | + | 0.174496i | ||||
\(438\) | −256.115 | − | 408.060i | −0.584737 | − | 0.931643i | ||||
\(439\) | −452.142 | −1.02994 | −0.514968 | − | 0.857209i | \(-0.672196\pi\) | ||||
−0.514968 | + | 0.857209i | \(0.672196\pi\) | |||||||
\(440\) | −609.194 | + | 120.258i | −1.38453 | + | 0.273315i | ||||
\(441\) | −402.396 | + | 180.440i | −0.912462 | + | 0.409162i | ||||
\(442\) | 124.402 | + | 124.402i | 0.281452 | + | 0.281452i | ||||
\(443\) | −208.241 | − | 208.241i | −0.470070 | − | 0.470070i | 0.431867 | − | 0.901937i | \(-0.357855\pi\) |
−0.901937 | + | 0.431867i | \(0.857855\pi\) | |||||||
\(444\) | −564.462 | − | 129.133i | −1.27131 | − | 0.290841i | ||||
\(445\) | 304.678 | − | 454.555i | 0.684670 | − | 1.02147i | ||||
\(446\) | 76.4403 | 0.171391 | ||||||||
\(447\) | 427.220 | + | 680.675i | 0.955749 | + | 1.52276i | ||||
\(448\) | −215.823 | + | 591.748i | −0.481747 | + | 1.32087i | ||||
\(449\) | 547.513 | 1.21941 | 0.609703 | − | 0.792630i | \(-0.291289\pi\) | ||||
0.609703 | + | 0.792630i | \(0.291289\pi\) | |||||||
\(450\) | −627.320 | + | 556.217i | −1.39404 | + | 1.23604i | ||||
\(451\) | 302.651i | 0.671067i | ||||||||
\(452\) | −1107.49 | + | 1107.49i | −2.45021 | + | 2.45021i | ||||
\(453\) | 237.750 | + | 378.799i | 0.524834 | + | 0.836202i | ||||
\(454\) | −68.0021 | −0.149784 | ||||||||
\(455\) | 12.8602 | − | 82.3962i | 0.0282642 | − | 0.181090i | ||||
\(456\) | −352.178 | + | 1539.43i | −0.772321 | + | 3.37594i | ||||
\(457\) | 169.531 | + | 169.531i | 0.370965 | + | 0.370965i | 0.867829 | − | 0.496864i | \(-0.165515\pi\) |
−0.496864 | + | 0.867829i | \(0.665515\pi\) | |||||||
\(458\) | 858.704 | − | 858.704i | 1.87490 | − | 1.87490i | ||||
\(459\) | −417.795 | − | 334.212i | −0.910229 | − | 0.728131i | ||||
\(460\) | 217.811 | − | 42.9972i | 0.473502 | − | 0.0934722i | ||||
\(461\) | −668.267 | −1.44960 | −0.724801 | − | 0.688958i | \(-0.758068\pi\) | ||||
−0.724801 | + | 0.688958i | \(0.758068\pi\) | |||||||
\(462\) | −240.884 | + | 372.010i | −0.521394 | + | 0.805216i | ||||
\(463\) | −254.021 | + | 254.021i | −0.548641 | + | 0.548641i | −0.926048 | − | 0.377407i | \(-0.876816\pi\) |
0.377407 | + | 0.926048i | \(0.376816\pi\) | |||||||
\(464\) | 1016.49 | 2.19072 | ||||||||
\(465\) | −357.493 | − | 10.7288i | −0.768802 | − | 0.0230726i | ||||
\(466\) | 353.023 | 0.757560 | ||||||||
\(467\) | −651.899 | − | 651.899i | −1.39593 | − | 1.39593i | −0.811301 | − | 0.584629i | \(-0.801240\pi\) |
−0.584629 | − | 0.811301i | \(-0.698760\pi\) | |||||||
\(468\) | 69.8069 | + | 200.142i | 0.149160 | + | 0.427654i | ||||
\(469\) | −2.05555 | − | 4.41578i | −0.00438284 | − | 0.00941532i | ||||
\(470\) | 599.621 | + | 401.912i | 1.27579 | + | 0.855133i | ||||
\(471\) | −567.266 | − | 129.775i | −1.20439 | − | 0.275530i | ||||
\(472\) | 221.681 | − | 221.681i | 0.469663 | − | 0.469663i | ||||
\(473\) | 146.700 | + | 146.700i | 0.310149 | + | 0.310149i | ||||
\(474\) | 145.432 | − | 635.704i | 0.306818 | − | 1.34115i | ||||
\(475\) | −228.065 | − | 555.144i | −0.480137 | − | 1.16872i | ||||
\(476\) | 1243.02 | − | 578.625i | 2.61138 | − | 1.21560i | ||||
\(477\) | 270.242 | − | 94.2569i | 0.566545 | − | 0.197604i | ||||
\(478\) | −463.421 | + | 463.421i | −0.969500 | + | 0.969500i | ||||
\(479\) | 686.172i | 1.43251i | 0.697839 | + | 0.716254i | \(0.254145\pi\) | ||||
−0.697839 | + | 0.716254i | \(0.745855\pi\) | |||||||
\(480\) | 713.829 | + | 758.000i | 1.48714 | + | 1.57917i | ||||
\(481\) | − | 46.5261i | − | 0.0967279i | ||||||
\(482\) | 1072.81 | + | 1072.81i | 2.22575 | + | 2.22575i | ||||
\(483\) | 51.2732 | − | 79.1839i | 0.106156 | − | 0.163942i | ||||
\(484\) | − | 878.960i | − | 1.81603i | ||||||
\(485\) | 333.437 | − | 65.8224i | 0.687498 | − | 0.135716i | ||||
\(486\) | −390.816 | − | 816.783i | −0.804149 | − | 1.68062i | ||||
\(487\) | −642.848 | − | 642.848i | −1.32002 | − | 1.32002i | −0.913758 | − | 0.406258i | \(-0.866833\pi\) |
−0.406258 | − | 0.913758i | \(-0.633167\pi\) | |||||||
\(488\) | −1399.78 | + | 1399.78i | −2.86840 | + | 2.86840i | ||||
\(489\) | 124.776 | + | 28.5454i | 0.255166 | + | 0.0583750i | ||||
\(490\) | −799.160 | − | 441.324i | −1.63094 | − | 0.900661i | ||||
\(491\) | 429.307i | 0.874353i | 0.899376 | + | 0.437176i | \(0.144021\pi\) | ||||
−0.899376 | + | 0.437176i | \(0.855979\pi\) | |||||||
\(492\) | 1342.15 | − | 842.385i | 2.72794 | − | 1.71217i | ||||
\(493\) | −337.774 | − | 337.774i | −0.685140 | − | 0.685140i | ||||
\(494\) | −213.139 | −0.431456 | ||||||||
\(495\) | 128.953 | + | 219.838i | 0.260511 | + | 0.444117i | ||||
\(496\) | 1005.41i | 2.02704i | ||||||||
\(497\) | −130.168 | + | 356.897i | −0.261907 | + | 0.718103i | ||||
\(498\) | −746.758 | + | 468.696i | −1.49951 | + | 0.941156i | ||||
\(499\) | 195.516i | 0.391815i | 0.980622 | + | 0.195908i | \(0.0627653\pi\) | ||||
−0.980622 | + | 0.195908i | \(0.937235\pi\) | |||||||
\(500\) | −1210.77 | − | 246.316i | −2.42155 | − | 0.492633i | ||||
\(501\) | −131.435 | + | 574.525i | −0.262346 | + | 1.14676i | ||||
\(502\) | −789.138 | + | 789.138i | −1.57199 | + | 1.57199i | ||||
\(503\) | −328.382 | + | 328.382i | −0.652846 | + | 0.652846i | −0.953677 | − | 0.300831i | \(-0.902736\pi\) |
0.300831 | + | 0.953677i | \(0.402736\pi\) | |||||||
\(504\) | 1381.28 | + | 19.5250i | 2.74063 | + | 0.0387401i | ||||
\(505\) | −429.478 | − | 287.869i | −0.850451 | − | 0.570038i | ||||
\(506\) | − | 94.8029i | − | 0.187357i | ||||||
\(507\) | 414.999 | − | 260.470i | 0.818539 | − | 0.513748i | ||||
\(508\) | −269.422 | + | 269.422i | −0.530359 | + | 0.530359i | ||||
\(509\) | 16.1598i | 0.0317481i | 0.999874 | + | 0.0158740i | \(0.00505308\pi\) | ||||
−0.999874 | + | 0.0158740i | \(0.994947\pi\) | |||||||
\(510\) | 33.2242 | − | 1107.06i | 0.0651454 | − | 2.17071i | ||||
\(511\) | −127.317 | − | 273.504i | −0.249152 | − | 0.535234i | ||||
\(512\) | −545.497 | + | 545.497i | −1.06542 | + | 1.06542i | ||||
\(513\) | 644.212 | − | 71.6017i | 1.25577 | − | 0.139574i | ||||
\(514\) | −195.101 | −0.379574 | ||||||||
\(515\) | −82.0696 | − | 415.740i | −0.159358 | − | 0.807263i | ||||
\(516\) | 242.243 | − | 1058.88i | 0.469462 | − | 2.05209i | ||||
\(517\) | 155.168 | − | 155.168i | 0.300132 | − | 0.300132i | ||||
\(518\) | −478.495 | − | 174.517i | −0.923735 | − | 0.336905i | ||||
\(519\) | 380.364 | + | 87.0168i | 0.732879 | + | 0.167662i | ||||
\(520\) | −145.445 | + | 216.992i | −0.279702 | + | 0.417293i | ||||
\(521\) | 656.049 | 1.25921 | 0.629605 | − | 0.776915i | \(-0.283217\pi\) | ||||
0.629605 | + | 0.776915i | \(0.283217\pi\) | |||||||
\(522\) | −266.239 | − | 763.329i | −0.510037 | − | 1.46232i | ||||
\(523\) | 289.472 | + | 289.472i | 0.553483 | + | 0.553483i | 0.927444 | − | 0.373961i | \(-0.122001\pi\) |
−0.373961 | + | 0.927444i | \(0.622001\pi\) | |||||||
\(524\) | − | 219.447i | − | 0.418792i | ||||||
\(525\) | −433.133 | + | 296.683i | −0.825015 | + | 0.565111i | ||||
\(526\) | 571.127 | 1.08579 | ||||||||
\(527\) | 334.092 | − | 334.092i | 0.633951 | − | 0.633951i | ||||
\(528\) | 606.842 | − | 380.879i | 1.14932 | − | 0.721361i | ||||
\(529\) | − | 508.821i | − | 0.961854i | ||||||
\(530\) | 492.154 | + | 329.880i | 0.928592 | + | 0.622415i | ||||
\(531\) | −115.878 | − | 55.9475i | −0.218226 | − | 0.105363i | ||||
\(532\) | −569.154 | + | 1560.52i | −1.06984 | + | 2.93331i | ||||
\(533\) | 90.0307 | + | 90.0307i | 0.168913 | + | 0.168913i | ||||
\(534\) | −272.839 | + | 1192.62i | −0.510934 | + | 2.23337i | ||||
\(535\) | 232.213 | − | 45.8402i | 0.434042 | − | 0.0856825i | ||||
\(536\) | 15.2575i | 0.0284655i | ||||||||
\(537\) | −221.671 | − | 353.181i | −0.412794 | − | 0.657692i | ||||
\(538\) | −260.043 | − | 260.043i | −0.483351 | − | 0.483351i | ||||
\(539\) | −178.670 | + | 212.358i | −0.331484 | + | 0.393986i | ||||
\(540\) | 615.979 | − | 1183.74i | 1.14070 | − | 2.19212i | ||||
\(541\) | −210.543 | −0.389174 | −0.194587 | − | 0.980885i | \(-0.562337\pi\) | ||||
−0.194587 | + | 0.980885i | \(0.562337\pi\) | |||||||
\(542\) | −576.344 | − | 576.344i | −1.06336 | − | 1.06336i | ||||
\(543\) | −39.2499 | + | 24.6349i | −0.0722835 | + | 0.0453680i | ||||
\(544\) | −1375.48 | −2.52846 | ||||||||
\(545\) | 525.944 | − | 784.665i | 0.965034 | − | 1.43975i | ||||
\(546\) | 39.0063 | + | 182.319i | 0.0714401 | + | 0.333918i | ||||
\(547\) | 81.9004 | + | 81.9004i | 0.149727 | + | 0.149727i | 0.777996 | − | 0.628269i | \(-0.216236\pi\) |
−0.628269 | + | 0.777996i | \(0.716236\pi\) | |||||||
\(548\) | −868.132 | − | 868.132i | −1.58418 | − | 1.58418i | ||||
\(549\) | 731.700 | + | 353.275i | 1.33279 | + | 0.643487i | ||||
\(550\) | −203.318 | + | 486.857i | −0.369670 | + | 0.885194i | ||||
\(551\) | 578.712 | 1.05029 | ||||||||
\(552\) | −250.286 | + | 157.090i | −0.453416 | + | 0.284583i | ||||
\(553\) | 139.921 | − | 383.640i | 0.253022 | − | 0.693743i | ||||
\(554\) | −990.211 | −1.78739 | ||||||||
\(555\) | −213.233 | + | 200.807i | −0.384203 | + | 0.361815i | ||||
\(556\) | − | 548.719i | − | 0.986905i | ||||||
\(557\) | −509.388 | + | 509.388i | −0.914521 | + | 0.914521i | −0.996624 | − | 0.0821026i | \(-0.973836\pi\) |
0.0821026 | + | 0.996624i | \(0.473836\pi\) | |||||||
\(558\) | 755.008 | − | 263.337i | 1.35306 | − | 0.471931i | ||||
\(559\) | 87.2789 | 0.156134 | ||||||||
\(560\) | 870.165 | + | 1192.03i | 1.55387 | + | 2.12862i | ||||
\(561\) | −328.213 | − | 75.0861i | −0.585050 | − | 0.133843i | ||||
\(562\) | −748.837 | − | 748.837i | −1.33245 | − | 1.33245i | ||||
\(563\) | 345.404 | − | 345.404i | 0.613507 | − | 0.613507i | −0.330351 | − | 0.943858i | \(-0.607167\pi\) |
0.943858 | + | 0.330351i | \(0.107167\pi\) | |||||||
\(564\) | −1120.00 | − | 256.225i | −1.98582 | − | 0.454300i | ||||
\(565\) | 153.435 | + | 777.258i | 0.271567 | + | 1.37568i | ||||
\(566\) | −353.421 | −0.624418 | ||||||||
\(567\) | −179.145 | − | 537.956i | −0.315952 | − | 0.948775i | ||||
\(568\) | 841.459 | − | 841.459i | 1.48144 | − | 1.48144i | ||||
\(569\) | −304.242 | −0.534696 | −0.267348 | − | 0.963600i | \(-0.586147\pi\) | ||||
−0.267348 | + | 0.963600i | \(0.586147\pi\) | |||||||
\(570\) | 919.910 | + | 976.833i | 1.61388 | + | 1.71374i | ||||
\(571\) | 10.6264 | 0.0186101 | 0.00930507 | − | 0.999957i | \(-0.497038\pi\) | ||||
0.00930507 | + | 0.999957i | \(0.497038\pi\) | |||||||
\(572\) | 94.3219 | + | 94.3219i | 0.164898 | + | 0.164898i | ||||
\(573\) | −684.992 | + | 429.929i | −1.19545 | + | 0.750313i | ||||
\(574\) | 1263.61 | − | 588.214i | 2.20142 | − | 1.02476i | ||||
\(575\) | 43.2772 | − | 103.630i | 0.0752647 | − | 0.180225i | ||||
\(576\) | −729.289 | − | 352.110i | −1.26613 | − | 0.611303i | ||||
\(577\) | 21.8636 | − | 21.8636i | 0.0378918 | − | 0.0378918i | −0.687907 | − | 0.725799i | \(-0.741470\pi\) |
0.725799 | + | 0.687907i | \(0.241470\pi\) | |||||||
\(578\) | 273.131 | + | 273.131i | 0.472545 | + | 0.472545i | ||||
\(579\) | −338.340 | − | 77.4029i | −0.584353 | − | 0.133684i | ||||
\(580\) | 663.347 | − | 989.660i | 1.14370 | − | 1.70631i | ||||
\(581\) | −500.519 | + | 232.992i | −0.861478 | + | 0.401019i | ||||
\(582\) | −643.594 | + | 403.946i | −1.10583 | + | 0.694065i | ||||
\(583\) | 127.358 | − | 127.358i | 0.218453 | − | 0.218453i | ||||
\(584\) | 945.019i | 1.61818i | ||||||||
\(585\) | 103.756 | + | 27.0359i | 0.177361 | + | 0.0462153i | ||||
\(586\) | − | 1532.52i | − | 2.61523i | ||||||
\(587\) | 229.516 | + | 229.516i | 0.390999 | + | 0.390999i | 0.875043 | − | 0.484045i | \(-0.160833\pi\) |
−0.484045 | + | 0.875043i | \(0.660833\pi\) | |||||||
\(588\) | 1439.03 | + | 201.266i | 2.44733 | + | 0.342289i | ||||
\(589\) | 572.404i | 0.971823i | ||||||||
\(590\) | −51.5888 | − | 261.334i | −0.0874386 | − | 0.442938i | ||||
\(591\) | 473.212 | + | 108.258i | 0.800697 | + | 0.183177i | ||||
\(592\) | 582.223 | + | 582.223i | 0.983484 | + | 0.983484i | ||||
\(593\) | 88.7036 | − | 88.7036i | 0.149584 | − | 0.149584i | −0.628348 | − | 0.777932i | \(-0.716269\pi\) |
0.777932 | + | 0.628348i | \(0.216269\pi\) | |||||||
\(594\) | −444.962 | − | 355.945i | −0.749095 | − | 0.599233i | ||||
\(595\) | 106.953 | − | 685.253i | 0.179753 | − | 1.15169i | ||||
\(596\) | − | 2647.88i | − | 4.44276i | ||||||
\(597\) | −140.981 | − | 224.621i | −0.236150 | − | 0.376250i | ||||
\(598\) | −28.2013 | − | 28.2013i | −0.0471594 | − | 0.0471594i | ||||
\(599\) | 861.037 | 1.43746 | 0.718728 | − | 0.695291i | \(-0.244724\pi\) | ||||
0.718728 | + | 0.695291i | \(0.244724\pi\) | |||||||
\(600\) | 1622.24 | − | 269.954i | 2.70373 | − | 0.449924i | ||||
\(601\) | 413.625i | 0.688227i | 0.938928 | + | 0.344114i | \(0.111821\pi\) | ||||
−0.938928 | + | 0.344114i | \(0.888179\pi\) | |||||||
\(602\) | 327.378 | − | 897.614i | 0.543818 | − | 1.49105i | ||||
\(603\) | 5.91307 | − | 2.06240i | 0.00980609 | − | 0.00342024i | ||||
\(604\) | − | 1473.56i | − | 2.43967i | ||||||
\(605\) | −369.322 | − | 247.548i | −0.610449 | − | 0.409170i | ||||
\(606\) | 1126.82 | + | 257.786i | 1.85945 | + | 0.425390i | ||||
\(607\) | 473.829 | − | 473.829i | 0.780608 | − | 0.780608i | −0.199325 | − | 0.979933i | \(-0.563875\pi\) |
0.979933 | + | 0.199325i | \(0.0638749\pi\) | |||||||
\(608\) | 1178.32 | − | 1178.32i | 1.93802 | − | 1.93802i | ||||
\(609\) | −105.909 | − | 495.031i | −0.173907 | − | 0.812859i | ||||
\(610\) | 325.752 | + | 1650.16i | 0.534019 | + | 2.70518i | ||||
\(611\) | − | 92.3167i | − | 0.151091i | ||||||
\(612\) | 580.554 | + | 1664.49i | 0.948618 | + | 2.71976i | ||||
\(613\) | −298.846 | + | 298.846i | −0.487514 | + | 0.487514i | −0.907521 | − | 0.420007i | \(-0.862028\pi\) |
0.420007 | + | 0.907521i | \(0.362028\pi\) | |||||||
\(614\) | 566.954i | 0.923377i | ||||||||
\(615\) | 24.0446 | − | 801.191i | 0.0390970 | − | 1.30275i | ||||
\(616\) | 788.124 | − | 366.873i | 1.27942 | − | 0.595572i | ||||
\(617\) | 601.654 | − | 601.654i | 0.975128 | − | 0.975128i | −0.0245706 | − | 0.999698i | \(-0.507822\pi\) |
0.999698 | + | 0.0245706i | \(0.00782185\pi\) | |||||||
\(618\) | 503.653 | + | 802.455i | 0.814973 | + | 1.29847i | ||||
\(619\) | −620.315 | −1.00212 | −0.501062 | − | 0.865411i | \(-0.667057\pi\) | ||||
−0.501062 | + | 0.865411i | \(0.667057\pi\) | |||||||
\(620\) | 978.872 | + | 656.116i | 1.57883 | + | 1.05825i | ||||
\(621\) | 94.7122 | + | 75.7644i | 0.152516 | + | 0.122004i | ||||
\(622\) | −1415.29 | + | 1415.29i | −2.27539 | + | 2.27539i | ||||
\(623\) | −262.501 | + | 719.732i | −0.421350 | + | 1.15527i | ||||
\(624\) | 67.2180 | − | 293.820i | 0.107721 | − | 0.470866i | ||||
\(625\) | −444.497 | + | 439.372i | −0.711195 | + | 0.702995i | ||||
\(626\) | −1825.58 | −2.91627 | ||||||||
\(627\) | 345.489 | − | 216.843i | 0.551019 | − | 0.345842i | ||||
\(628\) | 1355.77 | + | 1355.77i | 2.15888 | + | 2.15888i | ||||
\(629\) | − | 386.938i | − | 0.615163i | ||||||
\(630\) | 667.232 | − | 965.661i | 1.05910 | − | 1.53279i | ||||
\(631\) | 407.417 | 0.645669 | 0.322835 | − | 0.946455i | \(-0.395364\pi\) | ||||
0.322835 | + | 0.946455i | \(0.395364\pi\) | |||||||
\(632\) | −904.511 | + | 904.511i | −1.43119 | + | 1.43119i | ||||
\(633\) | −267.080 | − | 425.531i | −0.421928 | − | 0.672244i | ||||
\(634\) | 133.454i | 0.210496i | ||||||||
\(635\) | 37.3265 | + | 189.085i | 0.0587820 | + | 0.297772i | ||||
\(636\) | −919.268 | − | 210.303i | −1.44539 | − | 0.330665i | ||||
\(637\) | 10.0214 | + | 116.320i | 0.0157322 | + | 0.182606i | ||||
\(638\) | −359.738 | − | 359.738i | −0.563852 | − | 0.563852i | ||||
\(639\) | −439.851 | − | 212.366i | −0.688343 | − | 0.332341i | ||||
\(640\) | −55.8127 | − | 282.731i | −0.0872074 | − | 0.441767i | ||||
\(641\) | 715.610i | 1.11640i | 0.829708 | + | 0.558198i | \(0.188507\pi\) | ||||
−0.829708 | + | 0.558198i | \(0.811493\pi\) | |||||||
\(642\) | −448.213 | + | 281.317i | −0.698151 | + | 0.438188i | ||||
\(643\) | 562.981 | + | 562.981i | 0.875554 | + | 0.875554i | 0.993071 | − | 0.117517i | \(-0.0374936\pi\) |
−0.117517 | + | 0.993071i | \(0.537494\pi\) | |||||||
\(644\) | −281.786 | + | 131.172i | −0.437556 | + | 0.203683i | ||||
\(645\) | −376.696 | − | 400.006i | −0.584025 | − | 0.620164i | ||||
\(646\) | −1772.59 | −2.74394 | ||||||||
\(647\) | −59.3647 | − | 59.3647i | −0.0917537 | − | 0.0917537i | 0.659740 | − | 0.751494i | \(-0.270666\pi\) |
−0.751494 | + | 0.659740i | \(0.770666\pi\) | |||||||
\(648\) | −202.409 | + | 1764.54i | −0.312359 | + | 2.72305i | ||||
\(649\) | −80.9771 | −0.124772 | ||||||||
\(650\) | 84.3450 | + | 205.308i | 0.129762 | + | 0.315859i | ||||
\(651\) | 489.635 | − | 104.755i | 0.752127 | − | 0.160914i | ||||
\(652\) | −298.217 | − | 298.217i | −0.457388 | − | 0.457388i | ||||
\(653\) | −242.978 | − | 242.978i | −0.372094 | − | 0.372094i | 0.496145 | − | 0.868240i | \(-0.334748\pi\) |
−0.868240 | + | 0.496145i | \(0.834748\pi\) | |||||||
\(654\) | −470.981 | + | 2058.73i | −0.720155 | + | 3.14791i | ||||
\(655\) | −92.2073 | − | 61.8045i | −0.140774 | − | 0.0943579i | ||||
\(656\) | −2253.27 | −3.43486 | ||||||||
\(657\) | 366.243 | − | 127.741i | 0.557448 | − | 0.194431i | ||||
\(658\) | −949.425 | − | 346.275i | −1.44290 | − | 0.526254i | ||||
\(659\) | −1201.84 | −1.82373 | −0.911866 | − | 0.410489i | \(-0.865358\pi\) | ||||
−0.911866 | + | 0.410489i | \(0.865358\pi\) | |||||||
\(660\) | 25.1907 | − | 839.378i | 0.0381677 | − | 1.27179i | ||||
\(661\) | 618.277i | 0.935366i | 0.883896 | + | 0.467683i | \(0.154911\pi\) | ||||
−0.883896 | + | 0.467683i | \(0.845089\pi\) | |||||||
\(662\) | 428.827 | − | 428.827i | 0.647775 | − | 0.647775i | ||||
\(663\) | −119.971 | + | 75.2985i | −0.180951 | + | 0.113572i | ||||
\(664\) | 1729.40 | 2.60453 | ||||||||
\(665\) | 495.405 | + | 678.648i | 0.744969 | + | 1.02052i | ||||
\(666\) | 284.721 | − | 589.712i | 0.427509 | − | 0.885454i | ||||
\(667\) | 76.5718 | + | 76.5718i | 0.114800 | + | 0.114800i | ||||
\(668\) | 1373.12 | − | 1373.12i | 2.05557 | − | 2.05557i | ||||
\(669\) | −13.7247 | + | 59.9929i | −0.0205153 | + | 0.0896754i | ||||
\(670\) | 10.7687 | + | 7.21799i | 0.0160726 | + | 0.0107731i | ||||
\(671\) | 511.321 | 0.762029 | ||||||||
\(672\) | −1223.58 | − | 792.292i | −1.82080 | − | 1.17901i | ||||
\(673\) | 172.954 | − | 172.954i | 0.256990 | − | 0.256990i | −0.566839 | − | 0.823829i | \(-0.691834\pi\) |
0.823829 | + | 0.566839i | \(0.191834\pi\) | |||||||
\(674\) | 1805.20 | 2.67834 | ||||||||
\(675\) | −323.904 | − | 592.209i | −0.479857 | − | 0.877347i | ||||
\(676\) | −1614.38 | −2.38814 | ||||||||
\(677\) | −785.544 | − | 785.544i | −1.16033 | − | 1.16033i | −0.984403 | − | 0.175927i | \(-0.943708\pi\) |
−0.175927 | − | 0.984403i | \(-0.556292\pi\) | |||||||
\(678\) | −941.618 | − | 1500.25i | −1.38882 | − | 2.21276i | ||||
\(679\) | −431.373 | + | 200.804i | −0.635306 | + | 0.295736i | ||||
\(680\) | −1209.60 | + | 1804.63i | −1.77883 | + | 2.65387i | ||||
\(681\) | 12.2096 | − | 53.3702i | 0.0179290 | − | 0.0783704i | ||||
\(682\) | 355.816 | − | 355.816i | 0.521725 | − | 0.521725i | ||||
\(683\) | −510.988 | − | 510.988i | −0.748152 | − | 0.748152i | 0.225980 | − | 0.974132i | \(-0.427442\pi\) |
−0.974132 | + | 0.225980i | \(0.927442\pi\) | |||||||
\(684\) | −1923.23 | − | 928.563i | −2.81175 | − | 1.35755i | ||||
\(685\) | −609.271 | + | 120.274i | −0.889446 | + | 0.175582i | ||||
\(686\) | 1233.88 | + | 333.247i | 1.79866 | + | 0.485783i | ||||
\(687\) | 519.761 | + | 828.118i | 0.756566 | + | 1.20541i | ||||
\(688\) | −1092.20 | + | 1092.20i | −1.58750 | + | 1.58750i | ||||
\(689\) | − | 75.7713i | − | 0.109973i | ||||||
\(690\) | −7.53176 | + | 250.966i | −0.0109156 | + | 0.363719i | ||||
\(691\) | − | 93.1153i | − | 0.134754i | −0.997728 | − | 0.0673772i | \(-0.978537\pi\) | ||
0.997728 | − | 0.0673772i | \(-0.0214631\pi\) | |||||||
\(692\) | −909.076 | − | 909.076i | −1.31369 | − | 1.31369i | ||||
\(693\) | −248.715 | − | 255.847i | −0.358896 | − | 0.369188i | ||||
\(694\) | − | 2.29986i | − | 0.00331392i | ||||||
\(695\) | −230.561 | − | 154.540i | −0.331743 | − | 0.222360i | ||||
\(696\) | −353.641 | + | 1545.82i | −0.508105 | + | 2.22101i | ||||
\(697\) | 748.746 | + | 748.746i | 1.07424 | + | 1.07424i | ||||
\(698\) | −826.995 | + | 826.995i | −1.18481 | + | 1.18481i | ||||
\(699\) | −63.3846 | + | 277.064i | −0.0906789 | + | 0.396372i | ||||
\(700\) | 1728.42 | − | 69.2972i | 2.46917 | − | 0.0989960i | ||||
\(701\) | 582.081i | 0.830358i | 0.909740 | + | 0.415179i | \(0.136281\pi\) | ||||
−0.909740 | + | 0.415179i | \(0.863719\pi\) | |||||||
\(702\) | −238.248 | + | 26.4804i | −0.339385 | + | 0.0377214i | ||||
\(703\) | 331.472 | + | 331.472i | 0.471511 | + | 0.471511i | ||||
\(704\) | −509.636 | −0.723915 | ||||||||
\(705\) | −423.095 | + | 398.440i | −0.600134 | + | 0.565163i | ||||
\(706\) | 65.8034i | 0.0932060i | ||||||||
\(707\) | 680.025 | + | 248.019i | 0.961845 | + | 0.350805i | ||||
\(708\) | 225.388 | + | 359.103i | 0.318344 | + | 0.507208i | ||||
\(709\) | 710.656i | 1.00234i | 0.865350 | + | 0.501168i | \(0.167096\pi\) | ||||
−0.865350 | + | 0.501168i | \(0.832904\pi\) | |||||||
\(710\) | −195.821 | − | 991.972i | −0.275804 | − | 1.39714i | ||||
\(711\) | 472.810 | + | 228.279i | 0.664993 | + | 0.321067i | ||||
\(712\) | 1696.92 | − | 1696.92i | 2.38331 | − | 2.38331i | ||||
\(713\) | −75.7371 | + | 75.7371i | −0.106223 | + | 0.106223i | ||||
\(714\) | 324.399 | + | 1516.27i | 0.454340 | + | 2.12363i | ||||
\(715\) | 66.1968 | − | 13.0676i | 0.0925829 | − | 0.0182764i | ||||
\(716\) | 1373.90i | 1.91886i | ||||||||
\(717\) | −280.502 | − | 446.914i | −0.391216 | − | 0.623311i | ||||
\(718\) | 1294.17 | − | 1294.17i | 1.80246 | − | 1.80246i | ||||
\(719\) | 1307.80i | 1.81892i | 0.415790 | + | 0.909461i | \(0.363505\pi\) | ||||
−0.415790 | + | 0.909461i | \(0.636495\pi\) | |||||||
\(720\) | −1636.72 | + | 960.066i | −2.27322 | + | 1.33342i | ||||
\(721\) | 250.370 | + | 537.850i | 0.347254 | + | 0.745978i | ||||
\(722\) | 567.324 | − | 567.324i | 0.785768 | − | 0.785768i | ||||
\(723\) | −1034.60 | + | 649.358i | −1.43098 | + | 0.898143i | ||||
\(724\) | 152.685 | 0.210892 | ||||||||
\(725\) | −229.012 | − | 557.451i | −0.315879 | − | 0.768897i | ||||
\(726\) | 968.993 | + | 221.679i | 1.33470 | + | 0.305343i | ||||
\(727\) | −113.590 | + | 113.590i | −0.156245 | + | 0.156245i | −0.780901 | − | 0.624655i | \(-0.785239\pi\) |
0.624655 | + | 0.780901i | \(0.285239\pi\) | |||||||
\(728\) | 125.311 | − | 343.580i | 0.172130 | − | 0.471951i | ||||
\(729\) | 711.208 | − | 160.074i | 0.975595 | − | 0.219580i | ||||
\(730\) | 666.988 | + | 447.067i | 0.913683 | + | 0.612421i | ||||
\(731\) | 725.860 | 0.992969 | ||||||||
\(732\) | −1423.19 | − | 2267.52i | −1.94424 | − | 3.09770i | ||||
\(733\) | 336.426 | + | 336.426i | 0.458971 | + | 0.458971i | 0.898318 | − | 0.439346i | \(-0.144790\pi\) |
−0.439346 | + | 0.898318i | \(0.644790\pi\) | |||||||
\(734\) | 1881.12i | 2.56284i | ||||||||
\(735\) | 489.853 | − | 547.968i | 0.666467 | − | 0.745535i | ||||
\(736\) | 311.816 | 0.423663 | ||||||||
\(737\) | 2.78668 | − | 2.78668i | 0.00378112 | − | 0.00378112i | ||||
\(738\) | 590.175 | + | 1692.08i | 0.799695 | + | 2.29279i | ||||
\(739\) | − | 290.721i | − | 0.393398i | −0.980464 | − | 0.196699i | \(-0.936978\pi\) | ||
0.980464 | − | 0.196699i | \(-0.0630223\pi\) | |||||||
\(740\) | 946.803 | − | 186.904i | 1.27946 | − | 0.252574i | ||||
\(741\) | 38.2687 | − | 167.279i | 0.0516447 | − | 0.225747i | ||||
\(742\) | −779.265 | − | 284.214i | −1.05022 | − | 0.383038i | ||||
\(743\) | 409.064 | + | 409.064i | 0.550557 | + | 0.550557i | 0.926602 | − | 0.376044i | \(-0.122716\pi\) |
−0.376044 | + | 0.926602i | \(0.622716\pi\) | |||||||
\(744\) | −1528.97 | − | 349.787i | −2.05507 | − | 0.470143i | ||||
\(745\) | −1112.59 | − | 745.743i | −1.49341 | − | 1.00100i | ||||
\(746\) | 375.768i | 0.503710i | ||||||||
\(747\) | −233.769 | − | 670.233i | −0.312943 | − | 0.897233i | ||||
\(748\) | 784.434 | + | 784.434i | 1.04871 | + | 1.04871i | ||||
\(749\) | −300.417 | + | 139.845i | −0.401091 | + | 0.186709i | ||||
\(750\) | 576.911 | − | 1272.67i | 0.769215 | − | 1.69690i | ||||
\(751\) | 220.161 | 0.293157 | 0.146579 | − | 0.989199i | \(-0.453174\pi\) | ||||
0.146579 | + | 0.989199i | \(0.453174\pi\) | |||||||
\(752\) | 1155.24 | + | 1155.24i | 1.53622 | + | 1.53622i | ||||
\(753\) | −477.653 | − | 761.029i | −0.634334 | − | 1.01066i | ||||
\(754\) | −214.025 | −0.283852 | ||||||||
\(755\) | −619.162 | − | 415.010i | −0.820082 | − | 0.549682i | ||||
\(756\) | −442.325 | + | 1815.07i | −0.585086 | + | 2.40089i | ||||
\(757\) | −211.010 | − | 211.010i | −0.278745 | − | 0.278745i | 0.553863 | − | 0.832608i | \(-0.313153\pi\) |
−0.832608 | + | 0.553863i | \(0.813153\pi\) | |||||||
\(758\) | 1924.50 | + | 1924.50i | 2.53891 | + | 2.53891i | ||||
\(759\) | 74.4044 | + | 17.0217i | 0.0980295 | + | 0.0224264i | ||||
\(760\) | −509.734 | − | 2582.16i | −0.670703 | − | 3.39758i | ||||
\(761\) | 1091.43 | 1.43420 | 0.717100 | − | 0.696971i | \(-0.245469\pi\) | ||||
0.717100 | + | 0.696971i | \(0.245469\pi\) | |||||||
\(762\) | −229.069 | − | 364.969i | −0.300616 | − | 0.478962i | ||||
\(763\) | −453.136 | + | 1242.42i | −0.593888 | + | 1.62834i | ||||
\(764\) | 2664.68 | 3.48780 | ||||||||
\(765\) | 862.893 | + | 224.846i | 1.12796 | + | 0.293917i | ||||
\(766\) | − | 1671.42i | − | 2.18201i | ||||||
\(767\) | −24.0885 | + | 24.0885i | −0.0314061 | + | 0.0314061i | ||||
\(768\) | −231.505 | − | 368.850i | −0.301439 | − | 0.480274i | ||||
\(769\) | 984.905 | 1.28076 | 0.640380 | − | 0.768058i | \(-0.278777\pi\) | ||||
0.640380 | + | 0.768058i | \(0.278777\pi\) | |||||||
\(770\) | 113.907 | − | 729.812i | 0.147932 | − | 0.947808i | ||||
\(771\) | 35.0300 | − | 153.122i | 0.0454345 | − | 0.198601i | ||||
\(772\) | 808.638 | + | 808.638i | 1.04746 | + | 1.04746i | ||||
\(773\) | −364.826 | + | 364.826i | −0.471961 | + | 0.471961i | −0.902549 | − | 0.430588i | \(-0.858306\pi\) |
0.430588 | + | 0.902549i | \(0.358306\pi\) | |||||||
\(774\) | 1106.25 | + | 534.111i | 1.42926 | + | 0.690066i | ||||
\(775\) | 551.374 | − | 226.516i | 0.711451 | − | 0.292279i | ||||
\(776\) | 1490.49 | 1.92073 | ||||||||
\(777\) | 222.879 | − | 344.204i | 0.286846 | − | 0.442991i | ||||
\(778\) | 841.837 | − | 841.837i | 1.08205 | − | 1.08205i | ||||
\(779\) | −1282.84 | −1.64677 | ||||||||
\(780\) | −242.199 | − | 257.186i | −0.310511 | − | 0.329726i | ||||
\(781\) | −307.374 | −0.393564 | ||||||||
\(782\) | −234.538 | − | 234.538i | −0.299921 | − | 0.299921i | ||||
\(783\) | 646.888 | − | 71.8992i | 0.826166 | − | 0.0918253i | ||||
\(784\) | −1581.03 | − | 1330.21i | −2.01662 | − | 1.69670i | ||||
\(785\) | 951.506 | − | 187.833i | 1.21211 | − | 0.239278i | ||||
\(786\) | 241.925 | + | 55.3457i | 0.307793 | + | 0.0704144i | ||||
\(787\) | −465.317 | + | 465.317i | −0.591254 | + | 0.591254i | −0.937970 | − | 0.346716i | \(-0.887297\pi\) |
0.346716 | + | 0.937970i | \(0.387297\pi\) | |||||||
\(788\) | −1130.98 | − | 1130.98i | −1.43526 | − | 1.43526i | ||||
\(789\) | −102.545 | + | 448.239i | −0.129968 | + | 0.568111i | ||||
\(790\) | 210.494 | + | 1066.30i | 0.266448 | + | 1.34975i | ||||
\(791\) | −468.086 | − | 1005.55i | −0.591764 | − | 1.27124i | ||||
\(792\) | 368.096 | + | 1055.36i | 0.464767 | + | 1.33252i | ||||
\(793\) | 152.104 | − | 152.104i | 0.191809 | − | 0.191809i | ||||
\(794\) | − | 2336.41i | − | 2.94258i | ||||||
\(795\) | −347.266 | + | 327.029i | −0.436812 | + | 0.411358i | ||||
\(796\) | 873.795i | 1.09773i | ||||||||
\(797\) | −115.297 | − | 115.297i | −0.144664 | − | 0.144664i | 0.631066 | − | 0.775729i | \(-0.282618\pi\) |
−0.775729 | + | 0.631066i | \(0.782618\pi\) | |||||||
\(798\) | −1576.82 | − | 1021.02i | −1.97597 | − | 1.27948i | ||||
\(799\) | − | 767.758i | − | 0.960899i | ||||||
\(800\) | −1601.32 | − | 668.734i | −2.00165 | − | 0.835917i | ||||
\(801\) | −887.020 | − | 428.265i | −1.10739 | − | 0.534663i | ||||
\(802\) | 1217.92 | + | 1217.92i | 1.51861 | + | 1.51861i | ||||
\(803\) | 172.601 | − | 172.601i | 0.214946 | − | 0.214946i | ||||
\(804\) | −20.1142 | − | 4.60158i | −0.0250177 | − | 0.00572335i | ||||
\(805\) | −24.2457 | + | 155.344i | −0.0301189 | + | 0.192974i | ||||
\(806\) | − | 211.692i | − | 0.262645i | ||||||
\(807\) | 250.780 | − | 157.400i | 0.310756 | − | 0.195043i | ||||
\(808\) | −1603.30 | − | 1603.30i | −1.98428 | − | 1.98428i | ||||
\(809\) | −1312.90 | −1.62286 | −0.811432 | − | 0.584447i | \(-0.801311\pi\) | ||||
−0.811432 | + | 0.584447i | \(0.801311\pi\) | |||||||
\(810\) | 1149.64 | + | 977.621i | 1.41931 | + | 1.20694i | ||||
\(811\) | 905.438i | 1.11645i | 0.829691 | + | 0.558223i | \(0.188517\pi\) | ||||
−0.829691 | + | 0.558223i | \(0.811483\pi\) | |||||||
\(812\) | −571.519 | + | 1567.00i | −0.703841 | + | 1.92981i | ||||
\(813\) | 555.815 | − | 348.852i | 0.683659 | − | 0.429092i | ||||
\(814\) | − | 412.098i | − | 0.506263i | ||||||
\(815\) | −209.294 | + | 41.3159i | −0.256803 | + | 0.0506943i | ||||
\(816\) | 559.023 | − | 2443.58i | 0.685077 | − | 2.99458i | ||||
\(817\) | −621.813 | + | 621.813i | −0.761093 | + | 0.761093i | ||||
\(818\) | 514.150 | − | 514.150i | 0.628545 | − | 0.628545i | ||||
\(819\) | −150.094 | − | 2.12164i | −0.183265 | − | 0.00259053i | ||||
\(820\) | −1470.45 | + | 2193.79i | −1.79323 | + | 2.67535i | ||||
\(821\) | − | 1158.65i | − | 1.41126i | −0.708579 | − | 0.705632i | \(-0.750663\pi\) | ||
0.708579 | − | 0.705632i | \(-0.249337\pi\) | |||||||
\(822\) | 1176.00 | − | 738.108i | 1.43066 | − | 0.897942i | ||||
\(823\) | −517.333 | + | 517.333i | −0.628594 | + | 0.628594i | −0.947714 | − | 0.319120i | \(-0.896613\pi\) |
0.319120 | + | 0.947714i | \(0.396613\pi\) | |||||||
\(824\) | − | 1858.39i | − | 2.25533i | ||||||
\(825\) | −345.596 | − | 246.985i | −0.418904 | − | 0.299376i | ||||
\(826\) | 157.382 | + | 338.092i | 0.190535 | + | 0.409312i | ||||
\(827\) | −1120.04 | + | 1120.04i | −1.35435 | + | 1.35435i | −0.473615 | + | 0.880732i | \(0.657051\pi\) |
−0.880732 | + | 0.473615i | \(0.842949\pi\) | |||||||
\(828\) | −131.609 | − | 377.333i | −0.158948 | − | 0.455716i | ||||
\(829\) | 1030.74 | 1.24335 | 0.621675 | − | 0.783275i | \(-0.286453\pi\) | ||||
0.621675 | + | 0.783275i | \(0.286453\pi\) | |||||||
\(830\) | 818.143 | − | 1220.60i | 0.985714 | − | 1.47061i | ||||
\(831\) | 177.791 | − | 777.150i | 0.213948 | − | 0.935199i | ||||
\(832\) | −151.603 | + | 151.603i | −0.182215 | + | 0.182215i | ||||
\(833\) | 83.3435 | + | 967.386i | 0.100052 | + | 1.16133i | ||||
\(834\) | 604.925 | + | 138.390i | 0.725330 | + | 0.165935i | ||||
\(835\) | −190.236 | − | 963.681i | −0.227828 | − | 1.15411i | ||||
\(836\) | −1343.98 | −1.60763 | ||||||||
\(837\) | 71.1155 | + | 639.837i | 0.0849647 | + | 0.764441i | ||||
\(838\) | −1026.54 | − | 1026.54i | −1.22499 | − | 1.22499i | ||||
\(839\) | − | 928.283i | − | 1.10642i | −0.833043 | − | 0.553208i | \(-0.813403\pi\) | ||
0.833043 | − | 0.553208i | \(-0.186597\pi\) | |||||||
\(840\) | −2115.50 | + | 908.586i | −2.51845 | + | 1.08165i | ||||
\(841\) | −259.883 | −0.309017 | ||||||||
\(842\) | 60.0086 | − | 60.0086i | 0.0712692 | − | 0.0712692i | ||||
\(843\) | 722.164 | − | 453.260i | 0.856659 | − | 0.537674i | ||||
\(844\) | 1655.35i | 1.96132i | ||||||||
\(845\) | −454.670 | + | 678.332i | −0.538071 | + | 0.802759i | ||||
\(846\) | 564.941 | − | 1170.10i | 0.667779 | − | 1.38310i | ||||
\(847\) | 584.775 | + | 213.280i | 0.690408 | + | 0.251806i | ||||
\(848\) | 948.193 | + | 948.193i | 1.11815 | + | 1.11815i | ||||
\(849\) | 63.4560 | − | 277.376i | 0.0747420 | − | 0.326709i | ||||
\(850\) | 701.461 | + | 1707.46i | 0.825248 | + | 2.00878i | ||||
\(851\) | 87.7169i | 0.103075i | ||||||||
\(852\) | 855.529 | + | 1363.09i | 1.00414 | + | 1.59987i | ||||
\(853\) | −575.751 | − | 575.751i | −0.674972 | − | 0.674972i | 0.283886 | − | 0.958858i | \(-0.408376\pi\) |
−0.958858 | + | 0.283886i | \(0.908376\pi\) | |||||||
\(854\) | −993.772 | − | 2134.84i | −1.16367 | − | 2.49982i | ||||
\(855\) | −931.819 | + | 546.587i | −1.08985 | + | 0.639283i | ||||
\(856\) | 1038.01 | 1.21263 | ||||||||
\(857\) | 505.361 | + | 505.361i | 0.589686 | + | 0.589686i | 0.937546 | − | 0.347861i | \(-0.113092\pi\) |
−0.347861 | + | 0.937546i | \(0.613092\pi\) | |||||||
\(858\) | −127.772 | + | 80.1948i | −0.148918 | + | 0.0934671i | ||||
\(859\) | −1105.95 | −1.28749 | −0.643743 | − | 0.765242i | \(-0.722619\pi\) | ||||
−0.643743 | + | 0.765242i | \(0.722619\pi\) | |||||||
\(860\) | 350.616 | + | 1776.12i | 0.407693 | + | 2.06525i | ||||
\(861\) | 234.770 | + | 1097.34i | 0.272672 | + | 1.27449i | ||||
\(862\) | −2209.72 | − | 2209.72i | −2.56348 | − | 2.56348i | ||||
\(863\) | 79.6874 | + | 79.6874i | 0.0923377 | + | 0.0923377i | 0.751767 | − | 0.659429i | \(-0.229202\pi\) |
−0.659429 | + | 0.751767i | \(0.729202\pi\) | |||||||
\(864\) | 1170.74 | − | 1463.53i | 1.35502 | − | 1.69390i | ||||
\(865\) | −638.006 | + | 125.946i | −0.737579 | + | 0.145602i | ||||
\(866\) | −322.529 | −0.372435 | ||||||||
\(867\) | −263.402 | + | 165.322i | −0.303809 | + | 0.190683i | ||||
\(868\) | −1549.92 | − | 565.289i | −1.78563 | − | 0.651255i | ||||
\(869\) | 330.405 | 0.380213 | ||||||||
\(870\) | 923.732 | + | 980.892i | 1.06176 | + | 1.12746i | ||||
\(871\) | − | 1.65793i | − | 0.00190348i | ||||||
\(872\) | 2929.26 | − | 2929.26i | 3.35925 | − | 3.35925i | ||||
\(873\) | −201.474 | − | 577.641i | −0.230783 | − | 0.661674i | ||||
\(874\) | 401.837 | 0.459768 | ||||||||
\(875\) | 457.670 | − | 745.764i | 0.523051 | − | 0.852301i | ||||
\(876\) | −1245.83 | − | 285.012i | −1.42218 | − | 0.325356i | ||||
\(877\) | −662.027 | − | 662.027i | −0.754877 | − | 0.754877i | 0.220508 | − | 0.975385i | \(-0.429229\pi\) |
−0.975385 | + | 0.220508i | \(0.929229\pi\) | |||||||
\(878\) | −1191.32 | + | 1191.32i | −1.35685 | + | 1.35685i | ||||
\(879\) | 1202.78 | + | 275.162i | 1.36834 | + | 0.313039i | ||||
\(880\) | −664.852 | + | 991.906i | −0.755514 | + | 1.12717i | ||||
\(881\) | 480.973 | 0.545940 | 0.272970 | − | 0.962023i | \(-0.411994\pi\) | ||||
0.272970 | + | 0.962023i | \(0.411994\pi\) | |||||||
\(882\) | −584.814 | + | 1535.67i | −0.663054 | + | 1.74112i | ||||
\(883\) | −80.2464 | + | 80.2464i | −0.0908793 | + | 0.0908793i | −0.751085 | − | 0.660206i | \(-0.770469\pi\) |
0.660206 | + | 0.751085i | \(0.270469\pi\) | |||||||
\(884\) | 466.696 | 0.527937 | ||||||||
\(885\) | 214.366 | + | 6.43336i | 0.242221 | + | 0.00726933i | ||||
\(886\) | −1097.36 | −1.23855 | ||||||||
\(887\) | −405.061 | − | 405.061i | −0.456665 | − | 0.456665i | 0.440894 | − | 0.897559i | \(-0.354661\pi\) |
−0.897559 | + | 0.440894i | \(0.854661\pi\) | |||||||
\(888\) | −1087.97 | + | 682.853i | −1.22519 | + | 0.768978i | ||||
\(889\) | −113.872 | − | 244.623i | −0.128090 | − | 0.275166i | ||||
\(890\) | −394.900 | − | 2000.45i | −0.443708 | − | 2.24769i | ||||
\(891\) | 359.249 | − | 285.312i | 0.403198 | − | 0.320215i | ||||
\(892\) | 143.384 | − | 143.384i | 0.160744 | − | 0.160744i | ||||
\(893\) | 657.705 | + | 657.705i | 0.736511 | + | 0.736511i | ||||
\(894\) | 2919.11 | + | 667.811i | 3.26522 | + | 0.746993i | ||||
\(895\) | 577.287 | + | 386.942i | 0.645013 | + | 0.432338i | ||||
\(896\) | 170.268 | + | 365.773i | 0.190031 | + | 0.408229i | ||||
\(897\) | 27.1968 | − | 17.0698i | 0.0303197 | − | 0.0190299i | ||||
\(898\) | 1442.60 | − | 1442.60i | 1.60646 | − | 1.60646i | ||||
\(899\) | 574.782i | 0.639357i | ||||||||
\(900\) | −133.372 | + | 2220.03i | −0.148191 | + | 2.46670i | ||||
\(901\) | − | 630.157i | − | 0.699397i | ||||||
\(902\) | 797.433 | + | 797.433i | 0.884073 | + | 0.884073i | ||||
\(903\) | 645.697 | + | 418.102i | 0.715057 | + | 0.463015i | ||||
\(904\) | 3474.41i | 3.84337i | ||||||||
\(905\) | 43.0019 | − | 64.1554i | 0.0475160 | − | 0.0708900i | ||||
\(906\) | 1624.50 | + | 371.641i | 1.79305 | + | 0.410199i | ||||
\(907\) | 31.2791 | + | 31.2791i | 0.0344863 | + | 0.0344863i | 0.724140 | − | 0.689653i | \(-0.242237\pi\) |
−0.689653 | + | 0.724140i | \(0.742237\pi\) | |||||||
\(908\) | −127.556 | + | 127.556i | −0.140480 | + | 0.140480i | ||||
\(909\) | −404.638 | + | 838.084i | −0.445146 | + | 0.921984i | ||||
\(910\) | −183.215 | − | 250.984i | −0.201335 | − | 0.275806i | ||||
\(911\) | 1159.65i | 1.27294i | 0.771300 | + | 0.636472i | \(0.219607\pi\) | ||||
−0.771300 | + | 0.636472i | \(0.780393\pi\) | |||||||
\(912\) | 1614.41 | + | 2572.20i | 1.77019 | + | 2.82039i | ||||
\(913\) | −315.864 | − | 315.864i | −0.345963 | − | 0.345963i | ||||
\(914\) | 893.369 | 0.977428 | ||||||||
\(915\) | −1353.59 | − | 40.6227i | −1.47933 | − | 0.0443964i | ||||
\(916\) | − | 3221.45i | − | 3.51687i | ||||||
\(917\) | 145.999 | + | 53.2488i | 0.159213 | + | 0.0580685i | ||||
\(918\) | −1981.41 | + | 220.226i | −2.15840 | + | 0.239898i | ||||
\(919\) | 84.8460i | 0.0923243i | 0.998934 | + | 0.0461621i | \(0.0146991\pi\) | ||||
−0.998934 | + | 0.0461621i | \(0.985301\pi\) | |||||||
\(920\) | 274.212 | − | 409.102i | 0.298056 | − | 0.444676i | ||||
\(921\) | −444.964 | − | 101.795i | −0.483131 | − | 0.110527i | ||||
\(922\) | −1760.77 | + | 1760.77i | −1.90972 | + | 1.90972i | ||||
\(923\) | −91.4354 | + | 91.4354i | −0.0990633 | + | 0.0990633i | ||||
\(924\) | 245.960 | + | 1149.64i | 0.266191 | + | 1.24420i | ||||
\(925\) | 188.121 | − | 450.467i | 0.203375 | − | 0.486992i | ||||
\(926\) | 1338.60i | 1.44557i | ||||||||
\(927\) | −720.223 | + | 251.204i | −0.776939 | + | 0.270987i | ||||
\(928\) | 1183.21 | − | 1183.21i | 1.27501 | − | 1.27501i | ||||
\(929\) | − | 721.580i | − | 0.776727i | −0.921506 | − | 0.388364i | \(-0.873040\pi\) | ||
0.921506 | − | 0.388364i | \(-0.126960\pi\) | |||||||
\(930\) | −970.200 | + | 913.663i | −1.04323 | + | 0.982433i | ||||
\(931\) | −900.114 | − | 757.320i | −0.966825 | − | 0.813448i | ||||
\(932\) | 662.187 | − | 662.187i | 0.710501 | − | 0.710501i | ||||
\(933\) | −856.655 | − | 1364.88i | −0.918173 | − | 1.46290i | ||||
\(934\) | −3435.28 | −3.67803 | ||||||||
\(935\) | 550.530 | − | 108.678i | 0.588802 | − | 0.116233i | ||||
\(936\) | 423.439 | + | 204.442i | 0.452392 | + | 0.218421i | ||||
\(937\) | 997.285 | − | 997.285i | 1.06434 | − | 1.06434i | 0.0665554 | − | 0.997783i | \(-0.478799\pi\) |
0.997783 | − | 0.0665554i | \(-0.0212009\pi\) | |||||||
\(938\) | −17.0508 | − | 6.21880i | −0.0181779 | − | 0.00662985i | ||||
\(939\) | 327.780 | − | 1432.78i | 0.349073 | − | 1.52585i | ||||
\(940\) | 1878.64 | − | 370.854i | 1.99855 | − | 0.394526i | ||||
\(941\) | 1147.23 | 1.21916 | 0.609578 | − | 0.792726i | \(-0.291339\pi\) | ||||
0.609578 | + | 0.792726i | \(0.291339\pi\) | |||||||
\(942\) | −1836.58 | + | 1152.71i | −1.94966 | + | 1.22369i | ||||
\(943\) | −169.737 | − | 169.737i | −0.179997 | − | 0.179997i | ||||
\(944\) | − | 602.882i | − | 0.638646i | ||||||
\(945\) | 638.082 | + | 697.048i | 0.675219 | + | 0.737617i | ||||
\(946\) | 773.060 | 0.817188 | ||||||||
\(947\) | −525.181 | + | 525.181i | −0.554573 | + | 0.554573i | −0.927757 | − | 0.373184i | \(-0.878266\pi\) |
0.373184 | + | 0.927757i | \(0.378266\pi\) | |||||||
\(948\) | −919.635 | − | 1465.22i | −0.970079 | − | 1.54560i | ||||
\(949\) | − | 102.689i | − | 0.108207i | ||||||
\(950\) | −2063.62 | − | 861.796i | −2.17223 | − | 0.907154i | ||||
\(951\) | −104.739 | − | 23.9614i | −0.110136 | − | 0.0251960i | ||||
\(952\) | 1042.16 | − | 2857.41i | 1.09470 | − | 3.00148i | ||||
\(953\) | −917.929 | − | 917.929i | −0.963199 | − | 0.963199i | 0.0361471 | − | 0.999346i | \(-0.488491\pi\) |
−0.999346 | + | 0.0361471i | \(0.988491\pi\) | |||||||
\(954\) | 463.689 | − | 960.390i | 0.486048 | − | 1.00670i | ||||
\(955\) | 750.473 | − | 1119.65i | 0.785835 | − | 1.17240i | ||||
\(956\) | 1738.53i | 1.81855i | ||||||||
\(957\) | 346.924 | − | 217.744i | 0.362512 | − | 0.227527i | ||||
\(958\) | 1807.94 | + | 1807.94i | 1.88720 | + | 1.88720i | ||||
\(959\) | 788.224 | − | 366.919i | 0.821923 | − | 0.382606i | ||||
\(960\) | 1349.13 | + | 40.4889i | 1.40534 | + | 0.0421759i | ||||
\(961\) | 392.483 | 0.408411 | ||||||||
\(962\) | −122.588 | − | 122.588i | −0.127431 | − | 0.127431i | ||||
\(963\) | −140.311 | − | 402.282i | −0.145702 | − | 0.417738i | ||||
\(964\) | 4024.68 | 4.17498 | ||||||||
\(965\) | 567.517 | − | 112.031i | 0.588100 | − | 0.116094i | ||||
\(966\) | −73.5397 | − | 343.732i | −0.0761280 | − | 0.355830i | ||||
\(967\) | −801.278 | − | 801.278i | −0.828623 | − | 0.828623i | 0.158703 | − | 0.987326i | \(-0.449269\pi\) |
−0.987326 | + | 0.158703i | \(0.949269\pi\) | |||||||
\(968\) | −1378.73 | − | 1378.73i | −1.42431 | − | 1.42431i | ||||
\(969\) | 318.264 | − | 1391.18i | 0.328446 | − | 1.43569i | ||||
\(970\) | 705.117 | − | 1051.98i | 0.726925 | − | 1.08451i | ||||
\(971\) | 33.0145 | 0.0340005 | 0.0170003 | − | 0.999855i | \(-0.494588\pi\) | ||||
0.0170003 | + | 0.999855i | \(0.494588\pi\) | |||||||
\(972\) | −2265.17 | − | 799.012i | −2.33042 | − | 0.822029i | ||||
\(973\) | 365.065 | + | 133.147i | 0.375195 | + | 0.136841i | ||||
\(974\) | −3387.58 | −3.47801 | ||||||||
\(975\) | −176.277 | + | 29.3340i | −0.180797 | + | 0.0300862i | ||||
\(976\) | 3806.83i | 3.90044i | ||||||||
\(977\) | −479.678 | + | 479.678i | −0.490970 | + | 0.490970i | −0.908612 | − | 0.417642i | \(-0.862857\pi\) |
0.417642 | + | 0.908612i | \(0.362857\pi\) | |||||||
\(978\) | 403.976 | − | 253.552i | 0.413063 | − | 0.259255i | ||||
\(979\) | −619.861 | −0.633157 | ||||||||
\(980\) | −2326.85 | + | 671.216i | −2.37434 | + | 0.684914i | ||||
\(981\) | −1531.20 | − | 739.283i | −1.56085 | − | 0.753601i | ||||
\(982\) | 1131.15 | + | 1131.15i | 1.15188 | + | 1.15188i | ||||
\(983\) | −1218.03 | + | 1218.03i | −1.23909 | + | 1.23909i | −0.278720 | + | 0.960372i | \(0.589910\pi\) |
−0.960372 | + | 0.278720i | \(0.910090\pi\) | |||||||
\(984\) | 783.920 | − | 3426.64i | 0.796666 | − | 3.48235i | ||||
\(985\) | −793.744 | + | 156.690i | −0.805832 | + | 0.159076i | ||||
\(986\) | −1779.95 | −1.80522 | ||||||||
\(987\) | 442.236 | − | 682.967i | 0.448060 | − | 0.691963i | ||||
\(988\) | −399.798 | + | 399.798i | −0.404654 | + | 0.404654i | ||||
\(989\) | −164.549 | −0.166379 | ||||||||
\(990\) | 919.003 | + | 239.467i | 0.928286 | + | 0.241886i | ||||
\(991\) | 1368.76 | 1.38119 | 0.690593 | − | 0.723243i | \(-0.257349\pi\) | ||||
0.690593 | + | 0.723243i | \(0.257349\pi\) | |||||||
\(992\) | 1170.32 | + | 1170.32i | 1.17975 | + | 1.17975i | ||||
\(993\) | 259.562 | + | 413.552i | 0.261392 | + | 0.416468i | ||||
\(994\) | 597.392 | + | 1283.33i | 0.600998 | + | 1.29108i | ||||
\(995\) | 367.152 | + | 246.093i | 0.368997 | + | 0.247330i | ||||
\(996\) | −521.578 | + | 2279.90i | −0.523673 | + | 2.28906i | ||||
\(997\) | 443.224 | − | 443.224i | 0.444557 | − | 0.444557i | −0.448983 | − | 0.893540i | \(-0.648214\pi\) |
0.893540 | + | 0.448983i | \(0.148214\pi\) | |||||||
\(998\) | 515.150 | + | 515.150i | 0.516182 | + | 0.516182i | ||||
\(999\) | 411.704 | + | 329.340i | 0.412116 | + | 0.329670i |
(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 | 105.3.k.d.62.16 | yes | 32 | |
3.2 | odd | 2 | inner | 105.3.k.d.62.2 | yes | 32 | |
5.3 | odd | 4 | inner | 105.3.k.d.83.1 | yes | 32 | |
7.6 | odd | 2 | inner | 105.3.k.d.62.15 | yes | 32 | |
15.8 | even | 4 | inner | 105.3.k.d.83.15 | yes | 32 | |
21.20 | even | 2 | inner | 105.3.k.d.62.1 | ✓ | 32 | |
35.13 | even | 4 | inner | 105.3.k.d.83.2 | yes | 32 | |
105.83 | odd | 4 | inner | 105.3.k.d.83.16 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.k.d.62.1 | ✓ | 32 | 21.20 | even | 2 | inner | |
105.3.k.d.62.2 | yes | 32 | 3.2 | odd | 2 | inner | |
105.3.k.d.62.15 | yes | 32 | 7.6 | odd | 2 | inner | |
105.3.k.d.62.16 | yes | 32 | 1.1 | even | 1 | trivial | |
105.3.k.d.83.1 | yes | 32 | 5.3 | odd | 4 | inner | |
105.3.k.d.83.2 | yes | 32 | 35.13 | even | 4 | inner | |
105.3.k.d.83.15 | yes | 32 | 15.8 | even | 4 | inner | |
105.3.k.d.83.16 | yes | 32 | 105.83 | odd | 4 | inner |