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 | 83.15 | ||
Character | \(\chi\) | \(=\) | 105.83 |
Dual form | 105.3.k.d.62.15 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(-1\) |
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 | 0.915817 | + | 0.401595i | \(0.131544\pi\) |
0.401595 | + | 0.915817i | \(0.368456\pi\) | |||||||
\(3\) | −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 | ||||
\(7\) | 2.39850 | − | 6.57626i | 0.342643 | − | 0.939466i | ||||
\(8\) | −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 | \(-0.917120\pi\) | ||
0.966294 | − | 0.257442i | \(-0.0828797\pi\) | |||||||
\(12\) | −25.1165 | − | 15.7642i | −2.09304 | − | 1.31368i | ||||
\(13\) | −1.68481 | + | 1.68481i | −0.129601 | + | 0.129601i | −0.768932 | − | 0.639331i | \(-0.779211\pi\) |
0.639331 | + | 0.768932i | \(0.279211\pi\) | |||||||
\(14\) | 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 | \(-0.948049\pi\) |
0.162486 | + | 0.986711i | \(0.448049\pi\) | |||||||
\(18\) | 11.0444 | − | 31.6650i | 0.613576 | − | 1.75917i | ||||
\(19\) | 24.0066 | 1.26351 | 0.631753 | − | 0.775170i | \(-0.282336\pi\) | ||||
0.631753 | + | 0.775170i | \(0.282336\pi\) | |||||||
\(20\) | 27.5175 | + | 41.0539i | 1.37588 | + | 2.05269i | ||||
\(21\) | 12.8849 | + | 16.5825i | 0.613568 | + | 0.789642i | ||||
\(22\) | 14.9229 | − | 14.9229i | 0.678315 | − | 0.678315i | ||||
\(23\) | −3.17641 | + | 3.17641i | −0.138105 | + | 0.138105i | −0.772780 | − | 0.634675i | \(-0.781134\pi\) |
0.634675 | + | 0.772780i | \(0.281134\pi\) | |||||||
\(24\) | −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 | ||||
\(28\) | 65.0037 | + | 23.7082i | 2.32156 | + | 0.846722i | ||||
\(29\) | −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 | ||||||||
\(35\) | −8.34576 | − | 33.9904i | −0.238450 | − | 0.971155i | ||||
\(36\) | 80.1127 | − | 38.6795i | 2.22535 | − | 1.07443i | ||||
\(37\) | −13.8075 | + | 13.8075i | −0.373177 | + | 0.373177i | −0.868633 | − | 0.495456i | \(-0.835001\pi\) |
0.495456 | + | 0.868633i | \(0.335001\pi\) | |||||||
\(38\) | 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 | \(-0.725930\pi\) | ||||
−0.651668 | + | 0.758505i | \(0.725930\pi\) | |||||||
\(42\) | −9.74236 | + | 77.6415i | −0.231961 | + | 1.84861i | ||||
\(43\) | 25.9017 | + | 25.9017i | 0.602366 | + | 0.602366i | 0.940940 | − | 0.338574i | \(-0.109945\pi\) |
−0.338574 | + | 0.940940i | \(0.609945\pi\) | |||||||
\(44\) | 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 | \(-0.614767\pi\) |
0.935702 | + | 0.352791i | \(0.114767\pi\) | |||||||
\(48\) | 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 | −0.886673 | − | 0.462397i | \(-0.846989\pi\) |
0.462397 | + | 0.886673i | \(0.346989\pi\) | |||||||
\(54\) | 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 | ||||
\(63\) | −62.6848 | + | 6.29425i | −0.994997 | + | 0.0999087i | ||||
\(64\) | − | 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 | −0.710769 | − | 0.703425i | \(-0.751653\pi\) |
0.703425 | + | 0.710769i | \(0.251653\pi\) | |||||||
\(68\) | −138.501 | − | 138.501i | −2.03678 | − | 2.03678i | ||||
\(69\) | −3.00538 | − | 13.1370i | −0.0435562 | − | 0.190391i | ||||
\(70\) | 67.5692 | − | 111.548i | 0.965274 | − | 1.59355i | ||||
\(71\) | − | 54.2705i | − | 0.764374i | −0.924085 | − | 0.382187i | \(-0.875171\pi\) | ||
0.924085 | − | 0.382187i | \(-0.124829\pi\) | |||||||
\(72\) | 186.336 | + | 64.9917i | 2.58800 | + | 0.902663i | ||||
\(73\) | 30.4748 | − | 30.4748i | 0.417464 | − | 0.417464i | −0.466865 | − | 0.884329i | \(-0.654617\pi\) |
0.884329 | + | 0.466865i | \(0.154617\pi\) | |||||||
\(74\) | −72.7609 | −0.983256 | ||||||||
\(75\) | 43.6082 | + | 61.0191i | 0.581442 | + | 0.813588i | ||||
\(76\) | 237.296i | 3.12231i | ||||||||
\(77\) | −37.2462 | − | 13.5845i | −0.483717 | − | 0.176422i | ||||
\(78\) | 14.1594 | − | 22.5597i | 0.181530 | − | 0.289226i | ||||
\(79\) | 58.3371i | 0.738444i | 0.929341 | + | 0.369222i | \(0.120376\pi\) | ||||
−0.929341 | + | 0.369222i | \(0.879624\pi\) | |||||||
\(80\) | −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 | \(-0.0924042\pi\) |
−0.286236 | + | 0.958159i | \(0.592404\pi\) | |||||||
\(84\) | −163.911 | + | 127.363i | −1.95132 | + | 1.51622i | ||||
\(85\) | −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 | \(-0.136051\pi\) |
−0.414523 | + | 0.910039i | \(0.636051\pi\) | |||||||
\(98\) | −15.6722 | − | 181.910i | −0.159920 | − | 1.85623i | ||||
\(99\) | −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 | \(-0.671062\pi\) | ||||
−0.511911 | + | 0.859039i | \(0.671062\pi\) | |||||||
\(102\) | 117.757 | − | 187.619i | 1.15448 | − | 1.83940i | ||||
\(103\) | −59.9292 | + | 59.9292i | −0.581837 | + | 0.581837i | −0.935408 | − | 0.353571i | \(-0.884967\pi\) |
0.353571 | + | 0.935408i | \(0.384967\pi\) | |||||||
\(104\) | − | 52.2456i | − | 0.502361i | ||||||
\(105\) | 99.6788 | + | 33.0022i | 0.949321 | + | 0.314307i | ||||
\(106\) | −118.497 | −1.11789 | ||||||||
\(107\) | −33.4736 | − | 33.4736i | −0.312837 | − | 0.312837i | 0.533170 | − | 0.846008i | \(-0.321000\pi\) |
−0.846008 | + | 0.533170i | \(0.821000\pi\) | |||||||
\(108\) | −29.4816 | + | 265.251i | −0.272978 | + | 2.45603i | ||||
\(109\) | − | 188.925i | − | 1.73326i | −0.498954 | − | 0.866628i | \(-0.666282\pi\) | ||
0.498954 | − | 0.866628i | \(-0.333718\pi\) | |||||||
\(110\) | 20.4361 | − | 103.523i | 0.185783 | − | 0.941121i | ||||
\(111\) | −13.0641 | − | 57.1052i | −0.117694 | − | 0.514461i | ||||
\(112\) | −101.138 | + | 277.301i | −0.903013 | + | 2.47590i | ||||
\(113\) | −112.042 | + | 112.042i | −0.991524 | + | 0.991524i | −0.999964 | − | 0.00844052i | \(-0.997313\pi\) |
0.00844052 | + | 0.999964i | \(0.497313\pi\) | |||||||
\(114\) | −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 | ||||
\(126\) | −181.748 | − | 148.579i | −1.44244 | − | 1.17920i | ||||
\(127\) | −27.2567 | + | 27.2567i | −0.214620 | + | 0.214620i | −0.806227 | − | 0.591607i | \(-0.798494\pi\) |
0.591607 | + | 0.806227i | \(0.298494\pi\) | |||||||
\(128\) | 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 | \(-0.527005\pi\) | ||||
−0.0847362 | + | 0.996403i | \(0.527005\pi\) | |||||||
\(132\) | −89.2840 | + | 142.253i | −0.676394 | + | 1.07768i | ||||
\(133\) | 57.5799 | − | 157.874i | 0.432931 | − | 1.18702i | ||||
\(134\) | −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 | 0.950819 | − | 0.309748i | \(-0.100245\pi\) |
−0.309748 | + | 0.950819i | \(0.600245\pi\) | |||||||
\(138\) | 26.6950 | − | 42.5323i | 0.193442 | − | 0.308205i | ||||
\(139\) | −55.5125 | −0.399371 | −0.199685 | − | 0.979860i | \(-0.563992\pi\) | ||||
−0.199685 | + | 0.979860i | \(0.563992\pi\) | |||||||
\(140\) | 335.982 | − | 82.4945i | 2.39987 | − | 0.589246i | ||||
\(141\) | 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 | ||||||||
\(147\) | 139.955 | − | 44.9616i | 0.952076 | − | 0.305862i | ||||
\(148\) | −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 | \(-0.0380440\pi\) |
−0.119235 | + | 0.992866i | \(0.538044\pi\) | |||||||
\(158\) | −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 | 0.793570 | − | 0.608479i | \(-0.208220\pi\) |
−0.608479 | + | 0.793570i | \(0.708220\pi\) | |||||||
\(164\) | − | 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 | \(-0.950160\pi\) |
0.155939 | + | 0.987767i | \(0.450160\pi\) | |||||||
\(168\) | −456.889 | − | 57.3299i | −2.71958 | − | 0.341250i | ||||
\(169\) | 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 | \(-0.372669\pi\) |
−0.921052 | + | 0.389440i | \(0.872669\pi\) | |||||||
\(174\) | 262.689 | − | 60.0960i | 1.50971 | − | 0.345379i | ||||
\(175\) | −129.288 | − | 117.939i | −0.738786 | − | 0.673940i | ||||
\(176\) | 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 | \(0.986413\pi\) | |||||||
\(182\) | −21.2947 | + | 58.3863i | −0.117004 | + | 0.320804i | ||||
\(183\) | 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 | ||||
\(189\) | 83.9774 | − | 169.319i | 0.444325 | − | 0.895866i | ||||
\(190\) | 438.800 | + | 86.6217i | 2.30947 | + | 0.455903i | ||||
\(191\) | − | 269.579i | − | 1.41141i | −0.708508 | − | 0.705703i | \(-0.750631\pi\) | ||
0.708508 | − | 0.705703i | \(-0.249369\pi\) | |||||||
\(192\) | 228.643 | + | 143.506i | 1.19085 | + | 0.747426i | ||||
\(193\) | −81.8078 | − | 81.8078i | −0.423875 | − | 0.423875i | 0.462661 | − | 0.886535i | \(-0.346895\pi\) |
−0.886535 | + | 0.462661i | \(0.846895\pi\) | |||||||
\(194\) | 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 | 0.935125 | − | 0.354319i | \(-0.115287\pi\) |
−0.354319 | + | 0.935125i | \(0.615287\pi\) | |||||||
\(198\) | −179.342 | − | 62.5523i | −0.905769 | − | 0.315921i | ||||
\(199\) | 88.3996 | 0.444219 | 0.222110 | − | 0.975022i | \(-0.428706\pi\) | ||||
0.222110 | + | 0.975022i | \(0.428706\pi\) | |||||||
\(200\) | 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 | ||||
\(203\) | −57.8191 | + | 158.530i | −0.284823 | + | 0.780934i | ||||
\(204\) | 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 | ||||||
\(210\) | 175.681 | + | 349.591i | 0.836576 | + | 1.66472i | ||||
\(211\) | −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 | ||||
\(217\) | −156.802 | − | 57.1888i | −0.722588 | − | 0.263543i | ||||
\(218\) | 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 | \(-0.764646\pi\) |
0.673834 | + | 0.738883i | \(0.264646\pi\) | |||||||
\(224\) | −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 | \(-0.737201\pi\) |
0.734959 | + | 0.678111i | \(0.237201\pi\) | |||||||
\(228\) | −602.963 | − | 378.444i | −2.64457 | − | 1.65984i | ||||
\(229\) | −325.906 | −1.42317 | −0.711585 | − | 0.702601i | \(-0.752022\pi\) | ||||
−0.711585 | + | 0.702601i | \(0.752022\pi\) | |||||||
\(230\) | −69.5207 | + | 46.5981i | −0.302264 | + | 0.202601i | ||||
\(231\) | 93.9187 | − | 72.9768i | 0.406574 | − | 0.315917i | ||||
\(232\) | 373.767 | − | 373.767i | 1.61106 | − | 1.61106i | ||||
\(233\) | 66.9917 | − | 66.9917i | 0.287518 | − | 0.287518i | −0.548580 | − | 0.836098i | \(-0.684831\pi\) |
0.836098 | + | 0.548580i | \(0.184831\pi\) | |||||||
\(234\) | 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 | ||||
\(238\) | −177.099 | + | 485.574i | −0.744113 | + | 2.04023i | ||||
\(239\) | −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 | ||||||||
\(245\) | −243.547 | − | 26.6421i | −0.994070 | − | 0.108743i | ||||
\(246\) | 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 | \(-0.296510\pi\) | ||||
0.596620 | + | 0.802524i | \(0.296510\pi\) | |||||||
\(252\) | −62.2161 | − | 619.614i | −0.246889 | − | 2.45879i | ||||
\(253\) | 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 | \(-0.717519\pi\) |
0.775459 | + | 0.631398i | \(0.217519\pi\) | |||||||
\(258\) | −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 | −0.470374 | − | 0.882467i | \(-0.655881\pi\) |
0.882467 | + | 0.470374i | \(0.155881\pi\) | |||||||
\(264\) | −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 | ||||
\(273\) | −49.6469 | − | 6.22964i | −0.181857 | − | 0.0228192i | ||||
\(274\) | 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 | −0.959631 | − | 0.281261i | \(-0.909247\pi\) |
0.281261 | + | 0.959631i | \(0.409247\pi\) | |||||||
\(278\) | −146.266 | − | 146.266i | −0.526136 | − | 0.526136i | ||||
\(279\) | −193.247 | + | 93.3024i | −0.692643 | + | 0.334417i | ||||
\(280\) | 656.418 | + | 397.618i | 2.34435 | + | 1.42006i | ||||
\(281\) | 284.207i | 1.01141i | 0.862705 | + | 0.505707i | \(0.168768\pi\) | ||||
−0.862705 | + | 0.505707i | \(0.831232\pi\) | |||||||
\(282\) | −230.247 | + | 366.845i | −0.816477 | + | 1.30087i | ||||
\(283\) | 67.0672 | − | 67.0672i | 0.236986 | − | 0.236986i | −0.578615 | − | 0.815601i | \(-0.696406\pi\) |
0.815601 | + | 0.578615i | \(0.196406\pi\) | |||||||
\(284\) | 536.443 | 1.88888 | ||||||||
\(285\) | 10.8021 | + | 359.937i | 0.0379022 | + | 1.26294i | ||||
\(286\) | 50.2846i | 0.175820i | ||||||||
\(287\) | −128.168 | + | 351.414i | −0.446578 | + | 1.22444i | ||||
\(288\) | −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 | \(-0.497641\pi\) |
−0.999973 | + | 0.00740994i | \(0.997641\pi\) | |||||||
\(294\) | 487.223 | + | 250.291i | 1.65722 | + | 0.851331i | ||||
\(295\) | 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 | \(-0.170290\pi\) |
−0.509826 | + | 0.860277i | \(0.670290\pi\) | |||||||
\(308\) | 134.277 | − | 368.164i | 0.435964 | − | 1.19534i | ||||
\(309\) | −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 | \(-0.168215\pi\) | ||||
0.863583 | + | 0.504206i | \(0.168215\pi\) | |||||||
\(312\) | 132.755 | + | 83.3222i | 0.425496 | + | 0.267058i | ||||
\(313\) | 346.433 | − | 346.433i | 1.10682 | − | 1.10682i | 0.113249 | − | 0.993567i | \(-0.463874\pi\) |
0.993567 | − | 0.113249i | \(-0.0361258\pi\) | |||||||
\(314\) | 722.786i | 2.30187i | ||||||||
\(315\) | −242.827 | + | 200.649i | −0.770881 | + | 0.636980i | ||||
\(316\) | −576.639 | −1.82481 | ||||||||
\(317\) | −25.3251 | − | 25.3251i | −0.0798898 | − | 0.0798898i | 0.666033 | − | 0.745923i | \(-0.267991\pi\) |
−0.745923 | + | 0.666033i | \(0.767991\pi\) | |||||||
\(318\) | 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 | ||||
\(322\) | −40.1475 | + | 110.077i | −0.124682 | + | 0.341855i | ||||
\(323\) | −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 | ||||
\(336\) | −543.319 | − | 699.233i | −1.61702 | − | 2.08105i | ||||
\(337\) | 342.565 | − | 342.565i | 1.01651 | − | 1.01651i | 0.0166527 | − | 0.999861i | \(-0.494699\pi\) |
0.999861 | − | 0.0166527i | \(-0.00530098\pi\) | |||||||
\(338\) | −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 | ||||
\(343\) | −297.387 | + | 170.909i | −0.867018 | + | 0.498277i | ||||
\(344\) | −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 | 0.707735 | − | 0.706478i | \(-0.249717\pi\) |
−0.706478 | + | 0.707735i | \(0.749717\pi\) | |||||||
\(348\) | 605.468 | + | 380.016i | 1.73985 | + | 1.09200i | ||||
\(349\) | 313.871 | 0.899344 | 0.449672 | − | 0.893194i | \(-0.351541\pi\) | ||||
0.449672 | + | 0.893194i | \(0.351541\pi\) | |||||||
\(350\) | −29.9005 | − | 651.400i | −0.0854300 | − | 1.86114i | ||||
\(351\) | −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 | \(-0.242037\pi\) |
−0.689198 | + | 0.724573i | \(0.742037\pi\) | |||||||
\(354\) | −35.6430 | − | 155.801i | −0.100686 | − | 0.440116i | ||||
\(355\) | −151.082 | − | 225.403i | −0.425584 | − | 0.634937i | ||||
\(356\) | −1081.81 | −3.03879 | ||||||||
\(357\) | −412.892 | − | 51.8092i | −1.15656 | − | 0.145124i | ||||
\(358\) | −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 | \(-0.00858191\pi\) |
−0.0269576 | + | 0.999637i | \(0.508582\pi\) | |||||||
\(368\) | 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 | 0.605029 | − | 0.796203i | \(-0.293161\pi\) |
−0.796203 | + | 0.605029i | \(0.793161\pi\) | |||||||
\(374\) | 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 | ||||
\(378\) | 667.391 | − | 224.859i | 1.76558 | − | 0.594866i | ||||
\(379\) | − | 730.407i | − | 1.92720i | −0.267356 | − | 0.963598i | \(-0.586150\pi\) | ||
0.267356 | − | 0.963598i | \(-0.413850\pi\) | |||||||
\(380\) | 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 | \(-0.449136\pi\) |
−0.987260 | + | 0.159116i | \(0.949136\pi\) | |||||||
\(384\) | 38.5613 | + | 168.558i | 0.100420 | + | 0.438952i | ||||
\(385\) | −192.513 | + | 47.2681i | −0.500033 | + | 0.122774i | ||||
\(386\) | − | 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 | ||||||
\(392\) | 1070.47 | − | 92.2245i | 2.73079 | − | 0.235267i | ||||
\(393\) | 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 | −0.992208 | − | 0.124594i | \(-0.960237\pi\) |
−0.124594 | − | 0.992208i | \(-0.539763\pi\) | |||||||
\(398\) | 232.918 | + | 232.918i | 0.585220 | + | 0.585220i | ||||
\(399\) | 309.324 | + | 398.089i | 0.775247 | + | 0.997717i | ||||
\(400\) | −400.590 | + | 975.096i | −1.00147 | + | 2.43774i | ||||
\(401\) | − | 462.240i | − | 1.15272i | −0.817197 | − | 0.576359i | \(-0.804473\pi\) | ||
0.817197 | − | 0.576359i | \(-0.195527\pi\) | |||||||
\(402\) | 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 | \(-0.576673\pi\) | ||||
−0.238553 | + | 0.971130i | \(0.576673\pi\) | |||||||
\(410\) | −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 | ||||
\(413\) | 94.0240 | + | 34.2925i | 0.227661 | + | 0.0830327i | ||||
\(414\) | 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 | \(-0.153917\pi\) | |||||||
\(420\) | −326.214 | + | 985.285i | −0.776700 | + | 2.34592i | ||||
\(421\) | 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 | ||||
\(427\) | −593.704 | − | 216.536i | −1.39041 | − | 0.507111i | ||||
\(428\) | 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 | \(0.425756\pi\) | ||||
−0.231137 | + | 0.972921i | \(0.574244\pi\) | |||||||
\(432\) | −1131.54 | − | 125.767i | −2.61931 | − | 0.291126i | ||||
\(433\) | 61.2050 | − | 61.2050i | 0.141351 | − | 0.141351i | −0.632890 | − | 0.774241i | \(-0.718132\pi\) |
0.774241 | + | 0.632890i | \(0.218132\pi\) | |||||||
\(434\) | −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 | \(-0.327804\pi\) | ||||
0.514968 | + | 0.857209i | \(0.327804\pi\) | |||||||
\(440\) | 609.194 | + | 120.258i | 1.38453 | + | 0.273315i | ||||
\(441\) | −108.957 | + | 427.328i | −0.247068 | + | 0.968998i | ||||
\(442\) | 124.402 | − | 124.402i | 0.281452 | − | 0.281452i | ||||
\(443\) | −208.241 | + | 208.241i | −0.470070 | + | 0.470070i | −0.901937 | − | 0.431867i | \(-0.857855\pi\) |
0.431867 | + | 0.901937i | \(0.357855\pi\) | |||||||
\(444\) | 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 | ||||
\(448\) | −591.748 | − | 215.823i | −1.32087 | − | 0.481747i | ||||
\(449\) | 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 | ||||||||
\(455\) | 71.3283 | + | 43.2063i | 0.156766 | + | 0.0949589i | ||||
\(456\) | −352.178 | − | 1539.43i | −0.772321 | − | 3.37594i | ||||
\(457\) | 169.531 | − | 169.531i | 0.370965 | − | 0.370965i | −0.496864 | − | 0.867829i | \(-0.665515\pi\) |
0.867829 | + | 0.496864i | \(0.165515\pi\) | |||||||
\(458\) | −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 | \(-0.241932\pi\) | ||||
0.724801 | + | 0.688958i | \(0.241932\pi\) | |||||||
\(462\) | 439.740 | + | 55.1781i | 0.951819 | + | 0.119433i | ||||
\(463\) | −254.021 | − | 254.021i | −0.548641 | − | 0.548641i | 0.377407 | − | 0.926048i | \(-0.376816\pi\) |
−0.926048 | + | 0.377407i | \(0.876816\pi\) | |||||||
\(464\) | 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 | 0.584629 | − | 0.811301i | \(-0.301240\pi\) |
0.811301 | − | 0.584629i | \(-0.198760\pi\) | |||||||
\(468\) | −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 | ||||
\(483\) | −93.6007 | − | 11.7449i | −0.193790 | − | 0.0243166i | ||||
\(484\) | 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 | −0.406258 | + | 0.913758i | \(0.633167\pi\) |
−0.913758 | + | 0.406258i | \(0.866833\pi\) | |||||||
\(488\) | 1399.78 | + | 1399.78i | 2.86840 | + | 2.86840i | ||||
\(489\) | −124.776 | + | 28.5454i | −0.255166 | + | 0.0583750i | ||||
\(490\) | −571.507 | − | 711.901i | −1.16634 | − | 1.45286i | ||||
\(491\) | − | 429.307i | − | 0.874353i | −0.899376 | − | 0.437176i | \(-0.855979\pi\) | ||
0.899376 | − | 0.437176i | \(-0.144021\pi\) | |||||||
\(492\) | 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 | ||||||||
\(497\) | −356.897 | − | 130.168i | −0.718103 | − | 0.261907i | ||||
\(498\) | −746.758 | − | 468.696i | −1.49951 | − | 0.941156i | ||||
\(499\) | − | 195.516i | − | 0.391815i | −0.980622 | − | 0.195908i | \(-0.937235\pi\) | ||
0.980622 | − | 0.195908i | \(-0.0627653\pi\) | |||||||
\(500\) | 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 | \(-0.0972640\pi\) |
−0.300831 | + | 0.953677i | \(0.597264\pi\) | |||||||
\(504\) | 874.330 | − | 1069.51i | 1.73478 | − | 2.12205i | ||||
\(505\) | −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 | ||||
\(518\) | −174.517 | + | 478.495i | −0.336905 | + | 0.923735i | ||||
\(519\) | 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 | \(-0.716783\pi\) | ||||
−0.629605 | + | 0.776915i | \(0.716783\pi\) | |||||||
\(522\) | −266.239 | + | 763.329i | −0.510037 | + | 1.46232i | ||||
\(523\) | −289.472 | + | 289.472i | −0.553483 | + | 0.553483i | −0.927444 | − | 0.373961i | \(-0.877999\pi\) |
0.373961 | + | 0.927444i | \(0.377999\pi\) | |||||||
\(524\) | − | 219.447i | − | 0.418792i | ||||||
\(525\) | 505.871 | − | 140.424i | 0.963565 | − | 0.267475i | ||||
\(526\) | 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 | ||||
\(532\) | 1560.52 | + | 569.154i | 2.93331 | + | 1.06984i | ||||
\(533\) | 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 | ||||
\(546\) | −114.397 | − | 147.225i | −0.209518 | − | 0.269643i | ||||
\(547\) | 81.9004 | − | 81.9004i | 0.149727 | − | 0.149727i | −0.628269 | − | 0.777996i | \(-0.716236\pi\) |
0.777996 | + | 0.628269i | \(0.216236\pi\) | |||||||
\(548\) | −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 | ||||
\(553\) | 383.640 | + | 139.921i | 0.693743 | + | 0.253022i | ||||
\(554\) | −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 | 0.0821026 | − | 0.996624i | \(-0.473836\pi\) |
−0.996624 | + | 0.0821026i | \(0.973836\pi\) | |||||||
\(558\) | −755.008 | − | 263.337i | −1.35306 | − | 0.471931i | ||||
\(559\) | −87.2789 | −0.156134 | ||||||||
\(560\) | 351.915 | + | 1433.27i | 0.628420 | + | 2.55942i | ||||
\(561\) | −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 | \(-0.392833\pi\) |
−0.943858 | + | 0.330351i | \(0.892833\pi\) | |||||||
\(564\) | −1120.00 | + | 256.225i | −1.98582 | + | 0.454300i | ||||
\(565\) | −153.435 | + | 777.258i | −0.271567 | + | 1.37568i | ||||
\(566\) | 353.421 | 0.624418 | ||||||||
\(567\) | 296.306 | + | 483.417i | 0.522585 | + | 0.852587i | ||||
\(568\) | 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 | \(-0.258530\pi\) |
−0.725799 | + | 0.687907i | \(0.758530\pi\) | |||||||
\(578\) | 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 | \(-0.839167\pi\) |
0.484045 | + | 0.875043i | \(0.339167\pi\) | |||||||
\(588\) | 444.428 | + | 1383.40i | 0.755830 | + | 2.35272i | ||||
\(589\) | − | 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 | \(-0.283731\pi\) |
−0.777932 | + | 0.628348i | \(0.783731\pi\) | |||||||
\(594\) | 444.962 | − | 355.945i | 0.749095 | − | 0.599233i | ||||
\(595\) | 593.207 | + | 359.328i | 0.996986 | + | 0.603913i | ||||
\(596\) | 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 | \(0.888179\pi\) | |||||||
\(602\) | 897.614 | + | 327.378i | 1.49105 | + | 0.543818i | ||||
\(603\) | 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 | \(-0.436125\pi\) |
−0.979933 | + | 0.199325i | \(0.936125\pi\) | |||||||
\(608\) | −1178.32 | − | 1178.32i | −1.93802 | − | 1.93802i | ||||
\(609\) | −310.609 | − | 399.743i | −0.510031 | − | 0.656393i | ||||
\(610\) | 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 | 0.420007 | − | 0.907521i | \(-0.362028\pi\) |
−0.907521 | + | 0.420007i | \(0.862028\pi\) | |||||||
\(614\) | 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 | 0.999698 | − | 0.0245706i | \(-0.00782185\pi\) |
−0.0245706 | + | 0.999698i | \(0.507822\pi\) | |||||||
\(618\) | 503.653 | − | 802.455i | 0.814973 | − | 1.29847i | ||||
\(619\) | 620.315 | 1.00212 | 0.501062 | − | 0.865411i | \(-0.332943\pi\) | ||||
0.501062 | + | 0.865411i | \(0.332943\pi\) | |||||||
\(620\) | 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 | ||||
\(623\) | 719.732 | + | 262.501i | 1.15527 | + | 0.421350i | ||||
\(624\) | 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 | ||||||
\(630\) | −1168.48 | − | 111.134i | −1.85473 | − | 0.176403i | ||||
\(631\) | 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 | ||||
\(637\) | 116.320 | − | 10.0214i | 0.182606 | − | 0.0157322i | ||||
\(638\) | −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 | \(-0.811493\pi\) | ||
0.829708 | − | 0.558198i | \(-0.188507\pi\) | |||||||
\(642\) | 448.213 | + | 281.317i | 0.698151 | + | 0.438188i | ||||
\(643\) | −562.981 | + | 562.981i | −0.875554 | + | 0.875554i | −0.993071 | − | 0.117517i | \(-0.962506\pi\) |
0.117517 | + | 0.993071i | \(0.462506\pi\) | |||||||
\(644\) | −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 | \(-0.729334\pi\) |
0.751494 | + | 0.659740i | \(0.229334\pi\) | |||||||
\(648\) | −202.409 | − | 1764.54i | −0.312359 | − | 2.72305i | ||||
\(649\) | 80.9771 | 0.124772 | ||||||||
\(650\) | −84.3450 | + | 205.308i | −0.129762 | + | 0.315859i | ||||
\(651\) | 395.386 | − | 307.223i | 0.607351 | − | 0.471925i | ||||
\(652\) | −298.217 | + | 298.217i | −0.457388 | + | 0.457388i | ||||
\(653\) | −242.978 | + | 242.978i | −0.372094 | + | 0.372094i | −0.868240 | − | 0.496145i | \(-0.834748\pi\) |
0.496145 | + | 0.868240i | \(0.334748\pi\) | |||||||
\(654\) | 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 | ||||
\(658\) | 346.275 | − | 949.425i | 0.526254 | − | 1.44290i | ||||
\(659\) | −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 | ||||||||
\(665\) | −200.353 | − | 815.995i | −0.301283 | − | 1.22706i | ||||
\(666\) | 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 | ||||||||
\(672\) | 181.486 | − | 1446.35i | 0.270069 | − | 2.15231i | ||||
\(673\) | 172.954 | + | 172.954i | 0.256990 | + | 0.256990i | 0.823829 | − | 0.566839i | \(-0.191834\pi\) |
−0.566839 | + | 0.823829i | \(0.691834\pi\) | |||||||
\(674\) | 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 | 0.175927 | − | 0.984403i | \(-0.443708\pi\) |
0.984403 | − | 0.175927i | \(-0.0562923\pi\) | |||||||
\(678\) | 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 | −0.974132 | − | 0.225980i | \(-0.927442\pi\) |
0.225980 | + | 0.974132i | \(0.427442\pi\) | |||||||
\(684\) | 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 | ||||
\(693\) | 35.6489 | + | 355.030i | 0.0514415 | + | 0.512308i | ||||
\(694\) | 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 | ||||
\(700\) | 1165.78 | − | 1277.96i | 1.66541 | − | 1.82565i | ||||
\(701\) | − | 582.081i | − | 0.830358i | −0.909740 | − | 0.415179i | \(-0.863719\pi\) | ||
0.909740 | − | 0.415179i | \(-0.136281\pi\) | |||||||
\(702\) | −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 | ||||||||
\(707\) | −248.019 | + | 680.025i | −0.350805 | + | 0.961845i | ||||
\(708\) | 225.388 | − | 359.103i | 0.318344 | − | 0.507208i | ||||
\(709\) | − | 710.656i | − | 1.00234i | −0.865350 | − | 0.501168i | \(-0.832904\pi\) | ||
0.865350 | − | 0.501168i | \(-0.167096\pi\) | |||||||
\(710\) | 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 | ||||
\(714\) | −951.390 | − | 1224.41i | −1.33248 | − | 1.71485i | ||||
\(715\) | 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 | \(-0.214761\pi\) |
−0.624655 | + | 0.780901i | \(0.714761\pi\) | |||||||
\(728\) | −343.580 | − | 125.311i | −0.471951 | − | 0.172130i | ||||
\(729\) | 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 | \(-0.855210\pi\) |
0.439346 | + | 0.898318i | \(0.355210\pi\) | |||||||
\(734\) | 1881.12i | 2.56284i | ||||||||
\(735\) | 456.111 | − | 576.358i | 0.620559 | − | 0.784160i | ||||
\(736\) | 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 | \(0.0630223\pi\) | ||||
−0.980464 | + | 0.196699i | \(0.936978\pi\) | |||||||
\(740\) | −946.803 | − | 186.904i | −1.27946 | − | 0.252574i | ||||
\(741\) | −38.2687 | − | 167.279i | −0.0516447 | − | 0.225747i | ||||
\(742\) | −284.214 | + | 779.265i | −0.383038 | + | 1.05022i | ||||
\(743\) | 409.064 | − | 409.064i | 0.550557 | − | 0.550557i | −0.376044 | − | 0.926602i | \(-0.622716\pi\) |
0.926602 | + | 0.376044i | \(0.122716\pi\) | |||||||
\(744\) | −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 | ||||
\(756\) | 1673.65 | + | 830.083i | 2.21382 | + | 1.09799i | ||||
\(757\) | −211.010 | + | 211.010i | −0.278745 | + | 0.278745i | −0.832608 | − | 0.553863i | \(-0.813153\pi\) |
0.553863 | + | 0.832608i | \(0.313153\pi\) | |||||||
\(758\) | 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 | \(-0.754531\pi\) | ||||
−0.717100 | + | 0.696971i | \(0.754531\pi\) | |||||||
\(762\) | 229.069 | − | 364.969i | 0.300616 | − | 0.478962i | ||||
\(763\) | −1242.42 | − | 453.136i | −1.62834 | − | 0.593888i | ||||
\(764\) | 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 | \(-0.721223\pi\) | ||||
−0.640380 | + | 0.768058i | \(0.721223\pi\) | |||||||
\(770\) | −631.780 | − | 382.694i | −0.820494 | − | 0.497005i | ||||
\(771\) | 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 | \(-0.141694\pi\) |
−0.430588 | + | 0.902549i | \(0.641694\pi\) | |||||||
\(774\) | 1106.25 | − | 534.111i | 1.42926 | − | 0.690066i | ||||
\(775\) | −551.374 | − | 226.516i | −0.711451 | − | 0.292279i | ||||
\(776\) | −1490.49 | −1.92073 | ||||||||
\(777\) | −406.873 | − | 51.0539i | −0.523646 | − | 0.0657064i | ||||
\(778\) | 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 | \(-0.112703\pi\) |
−0.346716 | + | 0.937970i | \(0.612703\pi\) | |||||||
\(788\) | −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 | \(-0.717382\pi\) |
0.775729 | + | 0.631066i | \(0.217382\pi\) | |||||||
\(798\) | −233.881 | + | 1863.91i | −0.293084 | + | 2.33573i | ||||
\(799\) | 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 | ||||
\(805\) | 134.477 | + | 81.4580i | 0.167052 | + | 0.101190i | ||||
\(806\) | 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 | \(0.811483\pi\) | |||||||
\(812\) | −1567.00 | − | 571.519i | −1.92981 | − | 0.703841i | ||||
\(813\) | 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 | ||||
\(819\) | 95.0072 | − | 116.216i | 0.116004 | − | 0.141900i | ||||
\(820\) | −1470.45 | − | 2193.79i | −1.79323 | − | 2.67535i | ||||
\(821\) | 1158.65i | 1.41126i | 0.708579 | + | 0.705632i | \(0.249337\pi\) | ||||
−0.708579 | + | 0.705632i | \(0.750663\pi\) | |||||||
\(822\) | −1176.00 | − | 738.108i | −1.43066 | − | 0.897942i | ||||
\(823\) | −517.333 | − | 517.333i | −0.628594 | − | 0.628594i | 0.319120 | − | 0.947714i | \(-0.396613\pi\) |
−0.947714 | + | 0.319120i | \(0.896613\pi\) | |||||||
\(824\) | − | 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 | −0.880732 | − | 0.473615i | \(-0.842949\pi\) |
−0.473615 | − | 0.880732i | \(-0.657051\pi\) | |||||||
\(828\) | −131.609 | + | 377.333i | −0.158948 | + | 0.455716i | ||||
\(829\) | −1030.74 | −1.24335 | −0.621675 | − | 0.783275i | \(-0.713547\pi\) | ||||
−0.621675 | + | 0.783275i | \(0.713547\pi\) | |||||||
\(830\) | 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 | ||||
\(833\) | 967.386 | − | 83.3435i | 1.16133 | − | 0.100052i | ||||
\(834\) | 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 | \(-0.186597\pi\) | |||||||
\(840\) | −2057.21 | + | 1033.81i | −2.44905 | + | 1.23073i | ||||
\(841\) | −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 | ||||
\(847\) | 213.280 | − | 584.775i | 0.251806 | − | 0.690408i | ||||
\(848\) | 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 | \(-0.591624\pi\) |
0.958858 | + | 0.283886i | \(0.0916238\pi\) | |||||||
\(854\) | −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 | \(-0.886908\pi\) |
0.347861 | + | 0.937546i | \(0.386908\pi\) | |||||||
\(858\) | −127.772 | − | 80.1948i | −0.148918 | − | 0.0934671i | ||||
\(859\) | 1105.95 | 1.28749 | 0.643743 | − | 0.765242i | \(-0.277381\pi\) | ||||
0.643743 | + | 0.765242i | \(0.277381\pi\) | |||||||
\(860\) | −350.616 | + | 1776.12i | −0.407693 | + | 2.06525i | ||||
\(861\) | −688.529 | − | 886.114i | −0.799685 | − | 1.02917i | ||||
\(862\) | −2209.72 | + | 2209.72i | −2.56348 | + | 2.56348i | ||||
\(863\) | 79.6874 | − | 79.6874i | 0.0923377 | − | 0.0923377i | −0.659429 | − | 0.751767i | \(-0.729202\pi\) |
0.751767 | + | 0.659429i | \(0.229202\pi\) | |||||||
\(864\) | −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 | ||||
\(868\) | 565.289 | − | 1549.92i | 0.651255 | − | 1.78563i | ||||
\(869\) | 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 | ||||||||
\(875\) | −865.301 | − | 129.919i | −0.988916 | − | 0.148479i | ||||
\(876\) | −1245.83 | + | 285.012i | −1.42218 | + | 0.325356i | ||||
\(877\) | −662.027 | + | 662.027i | −0.754877 | + | 0.754877i | −0.975385 | − | 0.220508i | \(-0.929229\pi\) |
0.220508 | + | 0.975385i | \(0.429229\pi\) | |||||||
\(878\) | 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 | \(-0.588006\pi\) | ||||
−0.272970 | + | 0.962023i | \(0.588006\pi\) | |||||||
\(882\) | −1413.02 | + | 838.853i | −1.60206 | + | 0.951080i | ||||
\(883\) | −80.2464 | − | 80.2464i | −0.0908793 | − | 0.0908793i | 0.660206 | − | 0.751085i | \(-0.270469\pi\) |
−0.751085 | + | 0.660206i | \(0.770469\pi\) | |||||||
\(884\) | 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 | \(-0.645339\pi\) |
0.897559 | + | 0.440894i | \(0.145339\pi\) | |||||||
\(888\) | 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 | ||||
\(903\) | −95.7726 | + | 763.257i | −0.106060 | + | 0.845246i | ||||
\(904\) | − | 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 | −0.689653 | − | 0.724140i | \(-0.742237\pi\) |
0.724140 | + | 0.689653i | \(0.242237\pi\) | |||||||
\(908\) | 127.556 | + | 127.556i | 0.140480 | + | 0.140480i | ||||
\(909\) | 404.638 | + | 838.084i | 0.445146 | + | 0.921984i | ||||
\(910\) | 74.0965 | + | 301.779i | 0.0814247 | + | 0.331625i | ||||
\(911\) | − | 1159.65i | − | 1.27294i | −0.771300 | − | 0.636472i | \(-0.780393\pi\) | ||
0.771300 | − | 0.636472i | \(-0.219607\pi\) | |||||||
\(912\) | 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 | ||||||
\(917\) | −53.2488 | + | 145.999i | −0.0580685 | + | 0.159213i | ||||
\(918\) | −1981.41 | − | 220.226i | −2.15840 | − | 0.239898i | ||||
\(919\) | − | 84.8460i | − | 0.0923243i | −0.998934 | − | 0.0461621i | \(-0.985301\pi\) | ||
0.998934 | − | 0.0461621i | \(-0.0146991\pi\) | |||||||
\(920\) | −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 | ||||
\(924\) | 721.347 | + | 928.349i | 0.780679 | + | 1.00471i | ||||
\(925\) | 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 | −0.997783 | − | 0.0665554i | \(-0.978799\pi\) |
−0.0665554 | − | 0.997783i | \(-0.521201\pi\) | |||||||
\(938\) | −6.21880 | + | 17.0508i | −0.00662985 | + | 0.0181779i | ||||
\(939\) | 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 | \(-0.708661\pi\) | ||||
−0.609578 | + | 0.792726i | \(0.708661\pi\) | |||||||
\(942\) | −1836.58 | − | 1152.71i | −1.94966 | − | 1.22369i | ||||
\(943\) | 169.737 | − | 169.737i | 0.179997 | − | 0.179997i | ||||
\(944\) | − | 602.882i | − | 0.638646i | ||||||
\(945\) | −122.577 | − | 937.016i | −0.129711 | − | 0.991552i | ||||
\(946\) | 773.060 | 0.817188 | ||||||||
\(947\) | −525.181 | − | 525.181i | −0.554573 | − | 0.554573i | 0.373184 | − | 0.927757i | \(-0.378266\pi\) |
−0.927757 | + | 0.373184i | \(0.878266\pi\) | |||||||
\(948\) | 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 | ||||
\(952\) | −2857.41 | − | 1042.16i | −3.00148 | − | 1.09470i | ||||
\(953\) | −917.929 | + | 917.929i | −0.963199 | + | 0.963199i | −0.999346 | − | 0.0361471i | \(-0.988491\pi\) |
0.0361471 | + | 0.999346i | \(0.488491\pi\) | |||||||
\(954\) | 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 | ||||
\(966\) | −215.676 | − | 277.567i | −0.223267 | − | 0.287337i | ||||
\(967\) | −801.278 | + | 801.278i | −0.828623 | + | 0.828623i | −0.987326 | − | 0.158703i | \(-0.949269\pi\) |
0.158703 | + | 0.987326i | \(0.449269\pi\) | |||||||
\(968\) | −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 | \(-0.505412\pi\) | ||||
−0.0170003 | + | 0.999855i | \(0.505412\pi\) | |||||||
\(972\) | 2265.17 | − | 799.012i | 2.33042 | − | 0.822029i | ||||
\(973\) | −133.147 | + | 365.065i | −0.136841 | + | 0.375195i | ||||
\(974\) | −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 | 0.417642 | − | 0.908612i | \(-0.362857\pi\) |
−0.908612 | + | 0.417642i | \(0.862857\pi\) | |||||||
\(978\) | −403.976 | − | 253.552i | −0.413063 | − | 0.259255i | ||||
\(979\) | 619.861 | 0.633157 | ||||||||
\(980\) | 263.347 | − | 2407.37i | 0.268721 | − | 2.45650i | ||||
\(981\) | −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 | 0.960372 | + | 0.278720i | \(0.0899103\pi\) |
0.278720 | + | 0.960372i | \(0.410090\pi\) | |||||||
\(984\) | 783.920 | + | 3426.64i | 0.796666 | + | 3.48235i | ||||
\(985\) | 793.744 | + | 156.690i | 0.805832 | + | 0.159076i | ||||
\(986\) | 1779.95 | 1.80522 | ||||||||
\(987\) | 807.313 | + | 101.301i | 0.817946 | + | 0.102635i | ||||
\(988\) | −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 | \(-0.351786\pi\) |
−0.893540 | + | 0.448983i | \(0.851786\pi\) | |||||||
\(998\) | 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.83.15 | yes | 32 | |
3.2 | odd | 2 | inner | 105.3.k.d.83.1 | yes | 32 | |
5.2 | odd | 4 | inner | 105.3.k.d.62.2 | yes | 32 | |
7.6 | odd | 2 | inner | 105.3.k.d.83.16 | yes | 32 | |
15.2 | even | 4 | inner | 105.3.k.d.62.16 | yes | 32 | |
21.20 | even | 2 | inner | 105.3.k.d.83.2 | yes | 32 | |
35.27 | even | 4 | inner | 105.3.k.d.62.1 | ✓ | 32 | |
105.62 | odd | 4 | inner | 105.3.k.d.62.15 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.k.d.62.1 | ✓ | 32 | 35.27 | even | 4 | inner | |
105.3.k.d.62.2 | yes | 32 | 5.2 | odd | 4 | inner | |
105.3.k.d.62.15 | yes | 32 | 105.62 | odd | 4 | inner | |
105.3.k.d.62.16 | yes | 32 | 15.2 | even | 4 | inner | |
105.3.k.d.83.1 | yes | 32 | 3.2 | odd | 2 | inner | |
105.3.k.d.83.2 | yes | 32 | 21.20 | even | 2 | inner | |
105.3.k.d.83.15 | yes | 32 | 1.1 | even | 1 | trivial | |
105.3.k.d.83.16 | yes | 32 | 7.6 | odd | 2 | inner |