Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(221,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.221");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.s (of order \(6\), 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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 221.2 | ||
Character | \(\chi\) | \(=\) | 570.221 |
Dual form | 570.2.s.b.521.2 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | −1.67336 | + | 0.447064i | −0.966115 | + | 0.258113i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.866025 | − | 0.500000i | 0.387298 | − | 0.223607i | ||||
\(6\) | −1.22385 | − | 1.22564i | −0.499634 | − | 0.500366i | ||||
\(7\) | 3.20940 | 1.21304 | 0.606520 | − | 0.795068i | \(-0.292565\pi\) | ||||
0.606520 | + | 0.795068i | \(0.292565\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.60027 | − | 1.49620i | 0.866756 | − | 0.498733i | ||||
\(10\) | 0.866025 | + | 0.500000i | 0.273861 | + | 0.158114i | ||||
\(11\) | − | 2.81844i | − | 0.849791i | −0.905242 | − | 0.424896i | \(-0.860311\pi\) | ||
0.905242 | − | 0.424896i | \(-0.139689\pi\) | |||||||
\(12\) | 0.449511 | − | 1.67270i | 0.129763 | − | 0.482868i | ||||
\(13\) | −1.17608 | − | 0.679010i | −0.326186 | − | 0.188323i | 0.327961 | − | 0.944691i | \(-0.393639\pi\) |
−0.654146 | + | 0.756368i | \(0.726972\pi\) | |||||||
\(14\) | 1.60470 | + | 2.77942i | 0.428874 | + | 0.742832i | ||||
\(15\) | −1.22564 | + | 1.22385i | −0.316459 | + | 0.315996i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 2.48891 | − | 1.43697i | 0.603648 | − | 0.348516i | −0.166827 | − | 0.985986i | \(-0.553352\pi\) |
0.770475 | + | 0.637470i | \(0.220019\pi\) | |||||||
\(18\) | 2.59588 | + | 1.50380i | 0.611855 | + | 0.354449i | ||||
\(19\) | 4.04290 | + | 1.62940i | 0.927505 | + | 0.373810i | ||||
\(20\) | 1.00000i | 0.223607i | ||||||||
\(21\) | −5.37049 | + | 1.43481i | −1.17194 | + | 0.313101i | ||||
\(22\) | 2.44084 | − | 1.40922i | 0.520389 | − | 0.300447i | ||||
\(23\) | 3.23945 | + | 1.87030i | 0.675471 | + | 0.389984i | 0.798147 | − | 0.602463i | \(-0.205814\pi\) |
−0.122675 | + | 0.992447i | \(0.539147\pi\) | |||||||
\(24\) | 1.67336 | − | 0.447064i | 0.341573 | − | 0.0912566i | ||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | − | 1.35802i | − | 0.266329i | ||||||
\(27\) | −3.68229 | + | 3.66616i | −0.708656 | + | 0.705554i | ||||
\(28\) | −1.60470 | + | 2.77942i | −0.303260 | + | 0.525262i | ||||
\(29\) | 1.23451 | − | 2.13824i | 0.229243 | − | 0.397061i | −0.728341 | − | 0.685215i | \(-0.759708\pi\) |
0.957584 | + | 0.288154i | \(0.0930415\pi\) | |||||||
\(30\) | −1.67270 | − | 0.449511i | −0.305393 | − | 0.0820691i | ||||
\(31\) | 6.20471i | 1.11440i | 0.830379 | + | 0.557199i | \(0.188124\pi\) | ||||
−0.830379 | + | 0.557199i | \(0.811876\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 1.26002 | + | 4.71626i | 0.219342 | + | 0.820996i | ||||
\(34\) | 2.48891 | + | 1.43697i | 0.426844 | + | 0.246438i | ||||
\(35\) | 2.77942 | − | 1.60470i | 0.469808 | − | 0.271244i | ||||
\(36\) | −0.00438801 | + | 3.00000i | −0.000731334 | + | 0.499999i | ||||
\(37\) | 11.8172i | 1.94274i | 0.237572 | + | 0.971370i | \(0.423649\pi\) | ||||
−0.237572 | + | 0.971370i | \(0.576351\pi\) | |||||||
\(38\) | 0.610351 | + | 4.31596i | 0.0990120 | + | 0.700140i | ||||
\(39\) | 2.27156 | + | 0.610445i | 0.363741 | + | 0.0977494i | ||||
\(40\) | −0.866025 | + | 0.500000i | −0.136931 | + | 0.0790569i | ||||
\(41\) | −5.87998 | − | 10.1844i | −0.918299 | − | 1.59054i | −0.801998 | − | 0.597326i | \(-0.796230\pi\) |
−0.116301 | − | 0.993214i | \(-0.537104\pi\) | |||||||
\(42\) | −3.92782 | − | 3.93357i | −0.606076 | − | 0.606963i | ||||
\(43\) | 2.63866 | + | 4.57030i | 0.402393 | + | 0.696964i | 0.994014 | − | 0.109251i | \(-0.0348453\pi\) |
−0.591622 | + | 0.806216i | \(0.701512\pi\) | |||||||
\(44\) | 2.44084 | + | 1.40922i | 0.367970 | + | 0.212448i | ||||
\(45\) | 1.50380 | − | 2.59588i | 0.224173 | − | 0.386971i | ||||
\(46\) | 3.74059i | 0.551520i | ||||||||
\(47\) | 8.22978 | + | 4.75146i | 1.20044 | + | 0.693072i | 0.960652 | − | 0.277754i | \(-0.0895899\pi\) |
0.239784 | + | 0.970826i | \(0.422923\pi\) | |||||||
\(48\) | 1.22385 | + | 1.22564i | 0.176647 | + | 0.176906i | ||||
\(49\) | 3.30026 | 0.471466 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −3.52242 | + | 3.51727i | −0.493237 | + | 0.492516i | ||||
\(52\) | 1.17608 | − | 0.679010i | 0.163093 | − | 0.0941617i | ||||
\(53\) | 1.96402 | − | 3.40178i | 0.269779 | − | 0.467271i | −0.699026 | − | 0.715097i | \(-0.746383\pi\) |
0.968805 | + | 0.247826i | \(0.0797160\pi\) | |||||||
\(54\) | −5.01614 | − | 1.35587i | −0.682610 | − | 0.184511i | ||||
\(55\) | −1.40922 | − | 2.44084i | −0.190019 | − | 0.329123i | ||||
\(56\) | −3.20940 | −0.428874 | ||||||||
\(57\) | −7.49368 | − | 0.919133i | −0.992562 | − | 0.121742i | ||||
\(58\) | 2.46903 | 0.324199 | ||||||||
\(59\) | −1.85319 | − | 3.20982i | −0.241265 | − | 0.417883i | 0.719810 | − | 0.694171i | \(-0.244229\pi\) |
−0.961075 | + | 0.276288i | \(0.910896\pi\) | |||||||
\(60\) | −0.447064 | − | 1.67336i | −0.0577157 | − | 0.216030i | ||||
\(61\) | 0.946137 | − | 1.63876i | 0.121140 | − | 0.209821i | −0.799077 | − | 0.601228i | \(-0.794678\pi\) |
0.920218 | + | 0.391407i | \(0.128012\pi\) | |||||||
\(62\) | −5.37344 | + | 3.10235i | −0.682427 | + | 0.393999i | ||||
\(63\) | 8.34530 | − | 4.80190i | 1.05141 | − | 0.604983i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.35802 | −0.168442 | ||||||||
\(66\) | −3.45439 | + | 3.44934i | −0.425206 | + | 0.424585i | ||||
\(67\) | −9.15518 | − | 5.28574i | −1.11848 | − | 0.645756i | −0.177470 | − | 0.984126i | \(-0.556791\pi\) |
−0.941013 | + | 0.338370i | \(0.890125\pi\) | |||||||
\(68\) | 2.87394i | 0.348516i | ||||||||
\(69\) | −6.25690 | − | 1.68144i | −0.753243 | − | 0.202421i | ||||
\(70\) | 2.77942 | + | 1.60470i | 0.332205 | + | 0.191798i | ||||
\(71\) | −0.825761 | − | 1.43026i | −0.0979999 | − | 0.169741i | 0.812857 | − | 0.582464i | \(-0.197911\pi\) |
−0.910857 | + | 0.412723i | \(0.864578\pi\) | |||||||
\(72\) | −2.60027 | + | 1.49620i | −0.306444 | + | 0.176329i | ||||
\(73\) | −4.52170 | − | 7.83182i | −0.529225 | − | 0.916645i | −0.999419 | − | 0.0340817i | \(-0.989149\pi\) |
0.470194 | − | 0.882563i | \(-0.344184\pi\) | |||||||
\(74\) | −10.2340 | + | 5.90861i | −1.18968 | + | 0.686862i | ||||
\(75\) | −0.449511 | + | 1.67270i | −0.0519051 | + | 0.193147i | ||||
\(76\) | −3.43255 | + | 2.68656i | −0.393741 | + | 0.308169i | ||||
\(77\) | − | 9.04550i | − | 1.03083i | ||||||
\(78\) | 0.607122 | + | 2.27245i | 0.0687430 | + | 0.257305i | ||||
\(79\) | 7.55110 | − | 4.35963i | 0.849565 | − | 0.490497i | −0.0109389 | − | 0.999940i | \(-0.503482\pi\) |
0.860504 | + | 0.509443i | \(0.170149\pi\) | |||||||
\(80\) | −0.866025 | − | 0.500000i | −0.0968246 | − | 0.0559017i | ||||
\(81\) | 4.52278 | − | 7.78103i | 0.502531 | − | 0.864559i | ||||
\(82\) | 5.87998 | − | 10.1844i | 0.649335 | − | 1.12468i | ||||
\(83\) | 8.01355i | 0.879602i | 0.898095 | + | 0.439801i | \(0.144951\pi\) | ||||
−0.898095 | + | 0.439801i | \(0.855049\pi\) | |||||||
\(84\) | 1.44266 | − | 5.36838i | 0.157407 | − | 0.585738i | ||||
\(85\) | 1.43697 | − | 2.48891i | 0.155861 | − | 0.269960i | ||||
\(86\) | −2.63866 | + | 4.57030i | −0.284535 | + | 0.492828i | ||||
\(87\) | −1.10986 | + | 4.12995i | −0.118989 | + | 0.442777i | ||||
\(88\) | 2.81844i | 0.300447i | ||||||||
\(89\) | 1.31900 | − | 2.28458i | 0.139814 | − | 0.242165i | −0.787612 | − | 0.616171i | \(-0.788683\pi\) |
0.927426 | + | 0.374006i | \(0.122016\pi\) | |||||||
\(90\) | 3.00000 | + | 0.00438801i | 0.316227 | + | 0.000462536i | ||||
\(91\) | −3.77451 | − | 2.17921i | −0.395676 | − | 0.228444i | ||||
\(92\) | −3.23945 | + | 1.87030i | −0.337736 | + | 0.194992i | ||||
\(93\) | −2.77390 | − | 10.3827i | −0.287640 | − | 1.07664i | ||||
\(94\) | 9.50293i | 0.980152i | ||||||||
\(95\) | 4.31596 | − | 0.610351i | 0.442808 | − | 0.0626207i | ||||
\(96\) | −0.449511 | + | 1.67270i | −0.0458780 | + | 0.170720i | ||||
\(97\) | 8.27383 | − | 4.77690i | 0.840080 | − | 0.485021i | −0.0172113 | − | 0.999852i | \(-0.505479\pi\) |
0.857291 | + | 0.514831i | \(0.172145\pi\) | |||||||
\(98\) | 1.65013 | + | 2.85811i | 0.166688 | + | 0.288713i | ||||
\(99\) | −4.21694 | − | 7.32869i | −0.423819 | − | 0.736562i | ||||
\(100\) | 0.500000 | + | 0.866025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | −16.9742 | − | 9.80004i | −1.68899 | − | 0.975140i | −0.955291 | − | 0.295667i | \(-0.904458\pi\) |
−0.733701 | − | 0.679472i | \(-0.762209\pi\) | |||||||
\(102\) | −4.80725 | − | 1.29187i | −0.475989 | − | 0.127914i | ||||
\(103\) | 1.41243i | 0.139171i | 0.997576 | + | 0.0695853i | \(0.0221676\pi\) | ||||
−0.997576 | + | 0.0695853i | \(0.977832\pi\) | |||||||
\(104\) | 1.17608 | + | 0.679010i | 0.115324 | + | 0.0665824i | ||||
\(105\) | −3.93357 | + | 3.92782i | −0.383877 | + | 0.383316i | ||||
\(106\) | 3.92804 | 0.381525 | ||||||||
\(107\) | 0.133041 | 0.0128615 | 0.00643076 | − | 0.999979i | \(-0.497953\pi\) | ||||
0.00643076 | + | 0.999979i | \(0.497953\pi\) | |||||||
\(108\) | −1.33385 | − | 5.02204i | −0.128350 | − | 0.483246i | ||||
\(109\) | −9.72530 | + | 5.61490i | −0.931514 | + | 0.537810i | −0.887290 | − | 0.461211i | \(-0.847415\pi\) |
−0.0442242 | + | 0.999022i | \(0.514082\pi\) | |||||||
\(110\) | 1.40922 | − | 2.44084i | 0.134364 | − | 0.232725i | ||||
\(111\) | −5.28306 | − | 19.7745i | −0.501446 | − | 1.87691i | ||||
\(112\) | −1.60470 | − | 2.77942i | −0.151630 | − | 0.262631i | ||||
\(113\) | 11.8510 | 1.11485 | 0.557423 | − | 0.830229i | \(-0.311790\pi\) | ||||
0.557423 | + | 0.830229i | \(0.311790\pi\) | |||||||
\(114\) | −2.95085 | − | 6.94928i | −0.276372 | − | 0.650860i | ||||
\(115\) | 3.74059 | 0.348812 | ||||||||
\(116\) | 1.23451 | + | 2.13824i | 0.114622 | + | 0.198531i | ||||
\(117\) | −4.07405 | − | 0.00595899i | −0.376646 | − | 0.000550909i | ||||
\(118\) | 1.85319 | − | 3.20982i | 0.170600 | − | 0.295488i | ||||
\(119\) | 7.98790 | − | 4.61182i | 0.732249 | − | 0.422764i | ||||
\(120\) | 1.22564 | − | 1.22385i | 0.111885 | − | 0.111722i | ||||
\(121\) | 3.05640 | 0.277855 | ||||||||
\(122\) | 1.89227 | 0.171319 | ||||||||
\(123\) | 14.3924 | + | 14.4135i | 1.29772 | + | 1.29962i | ||||
\(124\) | −5.37344 | − | 3.10235i | −0.482549 | − | 0.278600i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 8.33122 | + | 4.82629i | 0.742204 | + | 0.429960i | ||||
\(127\) | −1.19910 | − | 0.692300i | −0.106403 | − | 0.0614317i | 0.445854 | − | 0.895106i | \(-0.352900\pi\) |
−0.552257 | + | 0.833674i | \(0.686233\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −6.45865 | − | 6.46811i | −0.568653 | − | 0.569485i | ||||
\(130\) | −0.679010 | − | 1.17608i | −0.0595531 | − | 0.103149i | ||||
\(131\) | −16.9209 | + | 9.76931i | −1.47839 | + | 0.853549i | −0.999701 | − | 0.0244360i | \(-0.992221\pi\) |
−0.478689 | + | 0.877985i | \(0.658888\pi\) | |||||||
\(132\) | −4.71441 | − | 1.26692i | −0.410337 | − | 0.110271i | ||||
\(133\) | 12.9753 | + | 5.22939i | 1.12510 | + | 0.453446i | ||||
\(134\) | − | 10.5715i | − | 0.913238i | ||||||
\(135\) | −1.35587 | + | 5.01614i | −0.116695 | + | 0.431720i | ||||
\(136\) | −2.48891 | + | 1.43697i | −0.213422 | + | 0.123219i | ||||
\(137\) | −4.09190 | − | 2.36246i | −0.349595 | − | 0.201839i | 0.314912 | − | 0.949121i | \(-0.398025\pi\) |
−0.664507 | + | 0.747282i | \(0.731358\pi\) | |||||||
\(138\) | −1.67228 | − | 6.25936i | −0.142354 | − | 0.532832i | ||||
\(139\) | 1.29172 | − | 2.23732i | 0.109562 | − | 0.189767i | −0.806031 | − | 0.591874i | \(-0.798388\pi\) |
0.915593 | + | 0.402106i | \(0.131722\pi\) | |||||||
\(140\) | 3.20940i | 0.271244i | ||||||||
\(141\) | −15.8956 | − | 4.27167i | −1.33865 | − | 0.359740i | ||||
\(142\) | 0.825761 | − | 1.43026i | 0.0692964 | − | 0.120025i | ||||
\(143\) | −1.91375 | + | 3.31471i | −0.160036 | + | 0.277190i | ||||
\(144\) | −2.59588 | − | 1.50380i | −0.216323 | − | 0.125317i | ||||
\(145\) | − | 2.46903i | − | 0.205042i | ||||||
\(146\) | 4.52170 | − | 7.83182i | 0.374219 | − | 0.648166i | ||||
\(147\) | −5.52253 | + | 1.47543i | −0.455490 | + | 0.121691i | ||||
\(148\) | −10.2340 | − | 5.90861i | −0.841231 | − | 0.485685i | ||||
\(149\) | −10.2414 | + | 5.91288i | −0.839009 | + | 0.484402i | −0.856927 | − | 0.515437i | \(-0.827630\pi\) |
0.0179181 | + | 0.999839i | \(0.494296\pi\) | |||||||
\(150\) | −1.67336 | + | 0.447064i | −0.136629 | + | 0.0365026i | ||||
\(151\) | 5.46814i | 0.444991i | 0.974934 | + | 0.222495i | \(0.0714202\pi\) | ||||
−0.974934 | + | 0.222495i | \(0.928580\pi\) | |||||||
\(152\) | −4.04290 | − | 1.62940i | −0.327923 | − | 0.132162i | ||||
\(153\) | 4.32183 | − | 7.46040i | 0.349399 | − | 0.603138i | ||||
\(154\) | 7.83364 | − | 4.52275i | 0.631252 | − | 0.364454i | ||||
\(155\) | 3.10235 | + | 5.37344i | 0.249187 | + | 0.431605i | ||||
\(156\) | −1.66444 | + | 1.66201i | −0.133262 | + | 0.133067i | ||||
\(157\) | 8.57463 | + | 14.8517i | 0.684330 | + | 1.18529i | 0.973647 | + | 0.228061i | \(0.0732384\pi\) |
−0.289317 | + | 0.957233i | \(0.593428\pi\) | |||||||
\(158\) | 7.55110 | + | 4.35963i | 0.600733 | + | 0.346834i | ||||
\(159\) | −1.76570 | + | 6.57045i | −0.140029 | + | 0.521071i | ||||
\(160\) | − | 1.00000i | − | 0.0790569i | ||||||
\(161\) | 10.3967 | + | 6.00253i | 0.819374 | + | 0.473066i | ||||
\(162\) | 8.99996 | + | 0.0263280i | 0.707104 | + | 0.00206852i | ||||
\(163\) | 3.07053 | 0.240502 | 0.120251 | − | 0.992744i | \(-0.461630\pi\) | ||||
0.120251 | + | 0.992744i | \(0.461630\pi\) | |||||||
\(164\) | 11.7600 | 0.918299 | ||||||||
\(165\) | 3.44934 | + | 3.45439i | 0.268531 | + | 0.268924i | ||||
\(166\) | −6.93994 | + | 4.00678i | −0.538644 | + | 0.310986i | ||||
\(167\) | −11.6737 | + | 20.2195i | −0.903339 | + | 1.56463i | −0.0802078 | + | 0.996778i | \(0.525558\pi\) |
−0.823131 | + | 0.567851i | \(0.807775\pi\) | |||||||
\(168\) | 5.37049 | − | 1.43481i | 0.414342 | − | 0.110698i | ||||
\(169\) | −5.57789 | − | 9.66119i | −0.429069 | − | 0.743169i | ||||
\(170\) | 2.87394 | 0.220421 | ||||||||
\(171\) | 12.9505 | − | 1.81211i | 0.990352 | − | 0.138576i | ||||
\(172\) | −5.27733 | −0.402393 | ||||||||
\(173\) | −4.79757 | − | 8.30963i | −0.364752 | − | 0.631769i | 0.623984 | − | 0.781437i | \(-0.285513\pi\) |
−0.988736 | + | 0.149668i | \(0.952180\pi\) | |||||||
\(174\) | −4.13157 | + | 1.10381i | −0.313214 | + | 0.0836799i | ||||
\(175\) | 1.60470 | − | 2.77942i | 0.121304 | − | 0.210105i | ||||
\(176\) | −2.44084 | + | 1.40922i | −0.183985 | + | 0.106224i | ||||
\(177\) | 4.53605 | + | 4.54269i | 0.340950 | + | 0.341449i | ||||
\(178\) | 2.63801 | 0.197727 | ||||||||
\(179\) | 18.3924 | 1.37471 | 0.687357 | − | 0.726320i | \(-0.258771\pi\) | ||||
0.687357 | + | 0.726320i | \(0.258771\pi\) | |||||||
\(180\) | 1.49620 | + | 2.60027i | 0.111520 | + | 0.193812i | ||||
\(181\) | −12.8805 | − | 7.43657i | −0.957402 | − | 0.552756i | −0.0620293 | − | 0.998074i | \(-0.519757\pi\) |
−0.895372 | + | 0.445318i | \(0.853091\pi\) | |||||||
\(182\) | − | 4.35843i | − | 0.323068i | ||||||
\(183\) | −0.850599 | + | 3.16522i | −0.0628781 | + | 0.233980i | ||||
\(184\) | −3.23945 | − | 1.87030i | −0.238815 | − | 0.137880i | ||||
\(185\) | 5.90861 | + | 10.2340i | 0.434410 | + | 0.752420i | ||||
\(186\) | 7.60474 | − | 7.59363i | 0.557607 | − | 0.556792i | ||||
\(187\) | −4.05001 | − | 7.01483i | −0.296166 | − | 0.512975i | ||||
\(188\) | −8.22978 | + | 4.75146i | −0.600218 | + | 0.346536i | ||||
\(189\) | −11.8179 | + | 11.7662i | −0.859629 | + | 0.855865i | ||||
\(190\) | 2.68656 | + | 3.43255i | 0.194903 | + | 0.249023i | ||||
\(191\) | − | 1.89205i | − | 0.136904i | −0.997654 | − | 0.0684520i | \(-0.978194\pi\) | ||
0.997654 | − | 0.0684520i | \(-0.0218060\pi\) | |||||||
\(192\) | −1.67336 | + | 0.447064i | −0.120764 | + | 0.0322641i | ||||
\(193\) | −17.5241 | + | 10.1175i | −1.26141 | + | 0.728277i | −0.973348 | − | 0.229334i | \(-0.926345\pi\) |
−0.288065 | + | 0.957611i | \(0.593012\pi\) | |||||||
\(194\) | 8.27383 | + | 4.77690i | 0.594026 | + | 0.342961i | ||||
\(195\) | 2.27245 | − | 0.607122i | 0.162734 | − | 0.0434769i | ||||
\(196\) | −1.65013 | + | 2.85811i | −0.117867 | + | 0.204151i | ||||
\(197\) | − | 8.39151i | − | 0.597871i | −0.954273 | − | 0.298935i | \(-0.903369\pi\) | ||
0.954273 | − | 0.298935i | \(-0.0966315\pi\) | |||||||
\(198\) | 4.23836 | − | 7.31633i | 0.301207 | − | 0.519949i | ||||
\(199\) | −0.537524 | + | 0.931019i | −0.0381041 | + | 0.0659982i | −0.884449 | − | 0.466638i | \(-0.845465\pi\) |
0.846344 | + | 0.532636i | \(0.178799\pi\) | |||||||
\(200\) | −0.500000 | + | 0.866025i | −0.0353553 | + | 0.0612372i | ||||
\(201\) | 17.6830 | + | 4.75200i | 1.24726 | + | 0.335180i | ||||
\(202\) | − | 19.6001i | − | 1.37906i | ||||||
\(203\) | 3.96205 | − | 6.86247i | 0.278081 | − | 0.481651i | ||||
\(204\) | −1.28484 | − | 4.80914i | −0.0899565 | − | 0.336707i | ||||
\(205\) | −10.1844 | − | 5.87998i | −0.711311 | − | 0.410676i | ||||
\(206\) | −1.22320 | + | 0.706213i | −0.0852242 | + | 0.0492042i | ||||
\(207\) | 11.2218 | + | 0.0164137i | 0.779966 | + | 0.00114083i | ||||
\(208\) | 1.35802i | 0.0941617i | ||||||||
\(209\) | 4.59236 | − | 11.3947i | 0.317660 | − | 0.788186i | ||||
\(210\) | −5.36838 | − | 1.44266i | −0.370453 | − | 0.0995531i | ||||
\(211\) | 21.4433 | − | 12.3803i | 1.47622 | − | 0.852293i | 0.476576 | − | 0.879133i | \(-0.341878\pi\) |
0.999640 | + | 0.0268399i | \(0.00854442\pi\) | |||||||
\(212\) | 1.96402 | + | 3.40178i | 0.134890 | + | 0.233636i | ||||
\(213\) | 2.02121 | + | 2.02417i | 0.138491 | + | 0.138694i | ||||
\(214\) | 0.0665203 | + | 0.115217i | 0.00454724 | + | 0.00787604i | ||||
\(215\) | 4.57030 | + | 2.63866i | 0.311692 | + | 0.179955i | ||||
\(216\) | 3.68229 | − | 3.66616i | 0.250548 | − | 0.249451i | ||||
\(217\) | 19.9134i | 1.35181i | ||||||||
\(218\) | −9.72530 | − | 5.61490i | −0.658680 | − | 0.380289i | ||||
\(219\) | 11.0678 | + | 11.0840i | 0.747890 | + | 0.748985i | ||||
\(220\) | 2.81844 | 0.190019 | ||||||||
\(221\) | −3.90287 | −0.262535 | ||||||||
\(222\) | 14.4837 | − | 14.4625i | 0.972080 | − | 0.970659i | ||||
\(223\) | 5.77968 | − | 3.33690i | 0.387036 | − | 0.223455i | −0.293839 | − | 0.955855i | \(-0.594933\pi\) |
0.680875 | + | 0.732400i | \(0.261600\pi\) | |||||||
\(224\) | 1.60470 | − | 2.77942i | 0.107219 | − | 0.185708i | ||||
\(225\) | 0.00438801 | − | 3.00000i | 0.000292534 | − | 0.200000i | ||||
\(226\) | 5.92548 | + | 10.2632i | 0.394157 | + | 0.682701i | ||||
\(227\) | −24.0873 | −1.59873 | −0.799367 | − | 0.600843i | \(-0.794832\pi\) | ||||
−0.799367 | + | 0.600843i | \(0.794832\pi\) | |||||||
\(228\) | 4.54283 | − | 6.03015i | 0.300856 | − | 0.399356i | ||||
\(229\) | −21.6662 | −1.43174 | −0.715872 | − | 0.698232i | \(-0.753970\pi\) | ||||
−0.715872 | + | 0.698232i | \(0.753970\pi\) | |||||||
\(230\) | 1.87030 | + | 3.23945i | 0.123324 | + | 0.213603i | ||||
\(231\) | 4.04392 | + | 15.1364i | 0.266070 | + | 0.995901i | ||||
\(232\) | −1.23451 | + | 2.13824i | −0.0810498 | + | 0.140382i | ||||
\(233\) | −15.3569 | + | 8.86633i | −1.00607 | + | 0.580852i | −0.910037 | − | 0.414526i | \(-0.863947\pi\) |
−0.0960285 | + | 0.995379i | \(0.530614\pi\) | |||||||
\(234\) | −2.03187 | − | 3.53121i | −0.132827 | − | 0.230843i | ||||
\(235\) | 9.50293 | 0.619903 | ||||||||
\(236\) | 3.70638 | 0.241265 | ||||||||
\(237\) | −10.6867 | + | 10.6711i | −0.694174 | + | 0.693160i | ||||
\(238\) | 7.98790 | + | 4.61182i | 0.517779 | + | 0.298940i | ||||
\(239\) | 10.0104i | 0.647519i | 0.946139 | + | 0.323759i | \(0.104947\pi\) | ||||
−0.946139 | + | 0.323759i | \(0.895053\pi\) | |||||||
\(240\) | 1.67270 | + | 0.449511i | 0.107973 | + | 0.0290158i | ||||
\(241\) | 4.57707 | + | 2.64257i | 0.294835 | + | 0.170223i | 0.640120 | − | 0.768275i | \(-0.278884\pi\) |
−0.345285 | + | 0.938498i | \(0.612218\pi\) | |||||||
\(242\) | 1.52820 | + | 2.64692i | 0.0982365 | + | 0.170151i | ||||
\(243\) | −4.08962 | + | 15.0424i | −0.262349 | + | 0.964973i | ||||
\(244\) | 0.946137 | + | 1.63876i | 0.0605702 | + | 0.104911i | ||||
\(245\) | 2.85811 | − | 1.65013i | 0.182598 | − | 0.105423i | ||||
\(246\) | −5.28624 | + | 19.6709i | −0.337038 | + | 1.25417i | ||||
\(247\) | −3.64840 | − | 4.66147i | −0.232142 | − | 0.296602i | ||||
\(248\) | − | 6.20471i | − | 0.393999i | ||||||
\(249\) | −3.58257 | − | 13.4096i | −0.227036 | − | 0.849796i | ||||
\(250\) | 0.866025 | − | 0.500000i | 0.0547723 | − | 0.0316228i | ||||
\(251\) | −20.3061 | − | 11.7237i | −1.28171 | − | 0.739996i | −0.304549 | − | 0.952497i | \(-0.598506\pi\) |
−0.977161 | + | 0.212501i | \(0.931839\pi\) | |||||||
\(252\) | −0.0140829 | + | 9.62820i | −0.000887138 | + | 0.606519i | ||||
\(253\) | 5.27131 | − | 9.13018i | 0.331405 | − | 0.574010i | ||||
\(254\) | − | 1.38460i | − | 0.0868775i | ||||||
\(255\) | −1.29187 | + | 4.80725i | −0.0808999 | + | 0.301042i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 1.54668 | − | 2.67892i | 0.0964790 | − | 0.167106i | −0.813746 | − | 0.581221i | \(-0.802575\pi\) |
0.910225 | + | 0.414114i | \(0.135909\pi\) | |||||||
\(258\) | 2.37222 | − | 8.82741i | 0.147688 | − | 0.549571i | ||||
\(259\) | 37.9262i | 2.35662i | ||||||||
\(260\) | 0.679010 | − | 1.17608i | 0.0421104 | − | 0.0729373i | ||||
\(261\) | 0.0108341 | − | 7.40707i | 0.000670614 | − | 0.458486i | ||||
\(262\) | −16.9209 | − | 9.76931i | −1.04538 | − | 0.603550i | ||||
\(263\) | −6.03680 | + | 3.48535i | −0.372245 | + | 0.214916i | −0.674439 | − | 0.738331i | \(-0.735614\pi\) |
0.302194 | + | 0.953247i | \(0.402281\pi\) | |||||||
\(264\) | −1.26002 | − | 4.71626i | −0.0775490 | − | 0.290266i | ||||
\(265\) | − | 3.92804i | − | 0.241298i | ||||||
\(266\) | 1.95886 | + | 13.8516i | 0.120106 | + | 0.849298i | ||||
\(267\) | −1.18581 | + | 4.41260i | −0.0725706 | + | 0.270047i | ||||
\(268\) | 9.15518 | − | 5.28574i | 0.559241 | − | 0.322878i | ||||
\(269\) | 5.00015 | + | 8.66052i | 0.304865 | + | 0.528041i | 0.977231 | − | 0.212177i | \(-0.0680554\pi\) |
−0.672366 | + | 0.740218i | \(0.734722\pi\) | |||||||
\(270\) | −5.02204 | + | 1.33385i | −0.305631 | + | 0.0811754i | ||||
\(271\) | −8.30819 | − | 14.3902i | −0.504687 | − | 0.874143i | −0.999985 | − | 0.00542045i | \(-0.998275\pi\) |
0.495298 | − | 0.868723i | \(-0.335059\pi\) | |||||||
\(272\) | −2.48891 | − | 1.43697i | −0.150912 | − | 0.0871291i | ||||
\(273\) | 7.29036 | + | 1.95916i | 0.441233 | + | 0.118574i | ||||
\(274\) | − | 4.72492i | − | 0.285443i | ||||||
\(275\) | −2.44084 | − | 1.40922i | −0.147188 | − | 0.0849791i | ||||
\(276\) | 4.58462 | − | 4.57792i | 0.275962 | − | 0.275558i | ||||
\(277\) | 28.0673 | 1.68640 | 0.843199 | − | 0.537601i | \(-0.180669\pi\) | ||||
0.843199 | + | 0.537601i | \(0.180669\pi\) | |||||||
\(278\) | 2.58344 | 0.154944 | ||||||||
\(279\) | 9.28347 | + | 16.1339i | 0.555787 | + | 0.965911i | ||||
\(280\) | −2.77942 | + | 1.60470i | −0.166102 | + | 0.0958992i | ||||
\(281\) | 2.46716 | − | 4.27325i | 0.147179 | − | 0.254921i | −0.783005 | − | 0.622015i | \(-0.786314\pi\) |
0.930184 | + | 0.367094i | \(0.119647\pi\) | |||||||
\(282\) | −4.24842 | − | 15.9018i | −0.252990 | − | 0.946940i | ||||
\(283\) | −4.00792 | − | 6.94192i | −0.238246 | − | 0.412654i | 0.721965 | − | 0.691929i | \(-0.243239\pi\) |
−0.960211 | + | 0.279275i | \(0.909906\pi\) | |||||||
\(284\) | 1.65152 | 0.0979999 | ||||||||
\(285\) | −6.94928 | + | 2.95085i | −0.411640 | + | 0.174793i | ||||
\(286\) | −3.82749 | −0.226324 | ||||||||
\(287\) | −18.8712 | − | 32.6859i | −1.11393 | − | 1.92939i | ||||
\(288\) | 0.00438801 | − | 3.00000i | 0.000258566 | − | 0.176777i | ||||
\(289\) | −4.37023 | + | 7.56947i | −0.257073 | + | 0.445263i | ||||
\(290\) | 2.13824 | − | 1.23451i | 0.125562 | − | 0.0724931i | ||||
\(291\) | −11.7095 | + | 11.6924i | −0.686424 | + | 0.685421i | ||||
\(292\) | 9.04340 | 0.529225 | ||||||||
\(293\) | −18.1274 | −1.05902 | −0.529508 | − | 0.848305i | \(-0.677624\pi\) | ||||
−0.529508 | + | 0.848305i | \(0.677624\pi\) | |||||||
\(294\) | −4.03902 | − | 4.04493i | −0.235561 | − | 0.235905i | ||||
\(295\) | −3.20982 | − | 1.85319i | −0.186883 | − | 0.107897i | ||||
\(296\) | − | 11.8172i | − | 0.686862i | ||||||
\(297\) | 10.3329 | + | 10.3783i | 0.599573 | + | 0.602210i | ||||
\(298\) | −10.2414 | − | 5.91288i | −0.593269 | − | 0.342524i | ||||
\(299\) | −2.53990 | − | 4.39923i | −0.146886 | − | 0.254414i | ||||
\(300\) | −1.22385 | − | 1.22564i | −0.0706589 | − | 0.0707624i | ||||
\(301\) | 8.46854 | + | 14.6679i | 0.488118 | + | 0.845446i | ||||
\(302\) | −4.73555 | + | 2.73407i | −0.272500 | + | 0.157328i | ||||
\(303\) | 32.7851 | + | 8.81045i | 1.88346 | + | 0.506147i | ||||
\(304\) | −0.610351 | − | 4.31596i | −0.0350060 | − | 0.247537i | ||||
\(305\) | − | 1.89227i | − | 0.108351i | ||||||
\(306\) | 8.62181 | + | 0.0126109i | 0.492876 | + | 0.000720915i | ||||
\(307\) | −18.4910 | + | 10.6758i | −1.05534 | + | 0.609300i | −0.924139 | − | 0.382056i | \(-0.875216\pi\) |
−0.131200 | + | 0.991356i | \(0.541883\pi\) | |||||||
\(308\) | 7.83364 | + | 4.52275i | 0.446363 | + | 0.257708i | ||||
\(309\) | −0.631445 | − | 2.36350i | −0.0359217 | − | 0.134455i | ||||
\(310\) | −3.10235 | + | 5.37344i | −0.176202 | + | 0.305191i | ||||
\(311\) | 11.1447i | 0.631960i | 0.948766 | + | 0.315980i | \(0.102333\pi\) | ||||
−0.948766 | + | 0.315980i | \(0.897667\pi\) | |||||||
\(312\) | −2.27156 | − | 0.610445i | −0.128602 | − | 0.0345596i | ||||
\(313\) | 0.759314 | − | 1.31517i | 0.0429189 | − | 0.0743378i | −0.843768 | − | 0.536708i | \(-0.819668\pi\) |
0.886687 | + | 0.462370i | \(0.153001\pi\) | |||||||
\(314\) | −8.57463 | + | 14.8517i | −0.483894 | + | 0.838129i | ||||
\(315\) | 4.82629 | − | 8.33122i | 0.271931 | − | 0.469411i | ||||
\(316\) | 8.71926i | 0.490497i | ||||||||
\(317\) | 1.84677 | − | 3.19870i | 0.103725 | − | 0.179657i | −0.809492 | − | 0.587131i | \(-0.800257\pi\) |
0.913217 | + | 0.407475i | \(0.133591\pi\) | |||||||
\(318\) | −6.57303 | + | 1.75609i | −0.368597 | + | 0.0984764i | ||||
\(319\) | −6.02650 | − | 3.47940i | −0.337419 | − | 0.194809i | ||||
\(320\) | 0.866025 | − | 0.500000i | 0.0484123 | − | 0.0279508i | ||||
\(321\) | −0.222625 | + | 0.0594777i | −0.0124257 | + | 0.00331972i | ||||
\(322\) | 12.0051i | 0.669016i | ||||||||
\(323\) | 12.4038 | − | 1.75411i | 0.690166 | − | 0.0976014i | ||||
\(324\) | 4.47718 | + | 7.80736i | 0.248732 | + | 0.433742i | ||||
\(325\) | −1.17608 | + | 0.679010i | −0.0652371 | + | 0.0376647i | ||||
\(326\) | 1.53526 | + | 2.65915i | 0.0850303 | + | 0.147277i | ||||
\(327\) | 13.7637 | − | 13.7436i | 0.761134 | − | 0.760022i | ||||
\(328\) | 5.87998 | + | 10.1844i | 0.324668 | + | 0.562341i | ||||
\(329\) | 26.4127 | + | 15.2494i | 1.45618 | + | 0.840725i | ||||
\(330\) | −1.26692 | + | 4.71441i | −0.0697416 | + | 0.259520i | ||||
\(331\) | − | 30.9937i | − | 1.70357i | −0.523892 | − | 0.851784i | \(-0.675521\pi\) | ||
0.523892 | − | 0.851784i | \(-0.324479\pi\) | |||||||
\(332\) | −6.93994 | − | 4.00678i | −0.380879 | − | 0.219900i | ||||
\(333\) | 17.6809 | + | 30.7279i | 0.968908 | + | 1.68388i | ||||
\(334\) | −23.3474 | −1.27751 | ||||||||
\(335\) | −10.5715 | −0.577582 | ||||||||
\(336\) | 3.92782 | + | 3.93357i | 0.214280 | + | 0.214594i | ||||
\(337\) | 11.8763 | − | 6.85679i | 0.646944 | − | 0.373513i | −0.140340 | − | 0.990103i | \(-0.544820\pi\) |
0.787284 | + | 0.616590i | \(0.211486\pi\) | |||||||
\(338\) | 5.57789 | − | 9.66119i | 0.303397 | − | 0.525500i | ||||
\(339\) | −19.8309 | + | 5.29814i | −1.07707 | + | 0.287756i | ||||
\(340\) | 1.43697 | + | 2.48891i | 0.0779307 | + | 0.134980i | ||||
\(341\) | 17.4876 | 0.947006 | ||||||||
\(342\) | 8.04460 | + | 10.3094i | 0.435002 | + | 0.557470i | ||||
\(343\) | −11.8739 | −0.641133 | ||||||||
\(344\) | −2.63866 | − | 4.57030i | −0.142267 | − | 0.246414i | ||||
\(345\) | −6.25936 | + | 1.67228i | −0.336992 | + | 0.0900327i | ||||
\(346\) | 4.79757 | − | 8.30963i | 0.257919 | − | 0.446728i | ||||
\(347\) | 16.3458 | − | 9.43723i | 0.877486 | − | 0.506617i | 0.00765736 | − | 0.999971i | \(-0.497563\pi\) |
0.869829 | + | 0.493354i | \(0.164229\pi\) | |||||||
\(348\) | −3.02172 | − | 3.02614i | −0.161981 | − | 0.162218i | ||||
\(349\) | −8.31293 | −0.444981 | −0.222491 | − | 0.974935i | \(-0.571419\pi\) | ||||
−0.222491 | + | 0.974935i | \(0.571419\pi\) | |||||||
\(350\) | 3.20940 | 0.171550 | ||||||||
\(351\) | 6.82002 | − | 1.81139i | 0.364026 | − | 0.0966849i | ||||
\(352\) | −2.44084 | − | 1.40922i | −0.130097 | − | 0.0751116i | ||||
\(353\) | 32.9930i | 1.75604i | 0.478623 | + | 0.878020i | \(0.341136\pi\) | ||||
−0.478623 | + | 0.878020i | \(0.658864\pi\) | |||||||
\(354\) | −1.66606 | + | 6.19968i | −0.0885500 | + | 0.329509i | ||||
\(355\) | −1.43026 | − | 0.825761i | −0.0759104 | − | 0.0438269i | ||||
\(356\) | 1.31900 | + | 2.28458i | 0.0699070 | + | 0.121083i | ||||
\(357\) | −11.3049 | + | 11.2883i | −0.598316 | + | 0.597442i | ||||
\(358\) | 9.19621 | + | 15.9283i | 0.486035 | + | 0.841837i | ||||
\(359\) | 15.5156 | − | 8.95794i | 0.818882 | − | 0.472782i | −0.0311486 | − | 0.999515i | \(-0.509917\pi\) |
0.850031 | + | 0.526733i | \(0.176583\pi\) | |||||||
\(360\) | −1.50380 | + | 2.59588i | −0.0792571 | + | 0.136815i | ||||
\(361\) | 13.6901 | + | 13.1750i | 0.720533 | + | 0.693421i | ||||
\(362\) | − | 14.8731i | − | 0.781715i | ||||||
\(363\) | −5.11446 | + | 1.36641i | −0.268440 | + | 0.0717178i | ||||
\(364\) | 3.77451 | − | 2.17921i | 0.197838 | − | 0.114222i | ||||
\(365\) | −7.83182 | − | 4.52170i | −0.409936 | − | 0.236677i | ||||
\(366\) | −3.16646 | + | 0.845968i | −0.165513 | + | 0.0442195i | ||||
\(367\) | −7.66209 | + | 13.2711i | −0.399958 | + | 0.692747i | −0.993720 | − | 0.111893i | \(-0.964308\pi\) |
0.593763 | + | 0.804640i | \(0.297642\pi\) | |||||||
\(368\) | − | 3.74059i | − | 0.194992i | ||||||
\(369\) | −30.5274 | − | 17.6846i | −1.58920 | − | 0.920624i | ||||
\(370\) | −5.90861 | + | 10.2340i | −0.307174 | + | 0.532041i | ||||
\(371\) | 6.30333 | − | 10.9177i | 0.327253 | − | 0.566818i | ||||
\(372\) | 10.3786 | + | 2.78909i | 0.538108 | + | 0.144607i | ||||
\(373\) | − | 8.21379i | − | 0.425294i | −0.977129 | − | 0.212647i | \(-0.931792\pi\) | ||
0.977129 | − | 0.212647i | \(-0.0682084\pi\) | |||||||
\(374\) | 4.05001 | − | 7.01483i | 0.209421 | − | 0.362728i | ||||
\(375\) | 0.447064 | + | 1.67336i | 0.0230863 | + | 0.0864119i | ||||
\(376\) | −8.22978 | − | 4.75146i | −0.424418 | − | 0.245038i | ||||
\(377\) | −2.90377 | + | 1.67649i | −0.149552 | + | 0.0863438i | ||||
\(378\) | −16.0988 | − | 4.35154i | −0.828033 | − | 0.223819i | ||||
\(379\) | 30.2639i | 1.55455i | 0.629161 | + | 0.777275i | \(0.283399\pi\) | ||||
−0.629161 | + | 0.777275i | \(0.716601\pi\) | |||||||
\(380\) | −1.62940 | + | 4.04290i | −0.0835864 | + | 0.207397i | ||||
\(381\) | 2.31603 | + | 0.622393i | 0.118654 | + | 0.0318862i | ||||
\(382\) | 1.63856 | − | 0.946026i | 0.0838363 | − | 0.0484029i | ||||
\(383\) | −10.9707 | − | 19.0019i | −0.560578 | − | 0.970949i | −0.997446 | − | 0.0714239i | \(-0.977246\pi\) |
0.436868 | − | 0.899526i | \(-0.356088\pi\) | |||||||
\(384\) | −1.22385 | − | 1.22564i | −0.0624543 | − | 0.0625457i | ||||
\(385\) | −4.52275 | − | 7.83364i | −0.230501 | − | 0.399239i | ||||
\(386\) | −17.5241 | − | 10.1175i | −0.891953 | − | 0.514970i | ||||
\(387\) | 13.6993 | + | 7.93604i | 0.696375 | + | 0.403412i | ||||
\(388\) | 9.55380i | 0.485021i | ||||||||
\(389\) | 20.5871 | + | 11.8860i | 1.04381 | + | 0.602643i | 0.920910 | − | 0.389776i | \(-0.127447\pi\) |
0.122899 | + | 0.992419i | \(0.460781\pi\) | |||||||
\(390\) | 1.66201 | + | 1.66444i | 0.0841592 | + | 0.0842823i | ||||
\(391\) | 10.7502 | 0.543663 | ||||||||
\(392\) | −3.30026 | −0.166688 | ||||||||
\(393\) | 23.9473 | − | 23.9123i | 1.20798 | − | 1.20622i | ||||
\(394\) | 7.26726 | − | 4.19576i | 0.366119 | − | 0.211379i | ||||
\(395\) | 4.35963 | − | 7.55110i | 0.219357 | − | 0.379937i | ||||
\(396\) | 8.45531 | + | 0.0123673i | 0.424895 | + | 0.000621481i | ||||
\(397\) | −15.7374 | − | 27.2581i | −0.789840 | − | 1.36804i | −0.926065 | − | 0.377364i | \(-0.876830\pi\) |
0.136225 | − | 0.990678i | \(-0.456503\pi\) | |||||||
\(398\) | −1.07505 | −0.0538873 | ||||||||
\(399\) | −24.0502 | − | 2.94987i | −1.20402 | − | 0.147678i | ||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 14.4572 | + | 25.0407i | 0.721960 | + | 1.25047i | 0.960213 | + | 0.279268i | \(0.0900918\pi\) |
−0.238253 | + | 0.971203i | \(0.576575\pi\) | |||||||
\(402\) | 4.72613 | + | 17.6899i | 0.235718 | + | 0.882292i | ||||
\(403\) | 4.21306 | − | 7.29723i | 0.209867 | − | 0.363501i | ||||
\(404\) | 16.9742 | − | 9.80004i | 0.844496 | − | 0.487570i | ||||
\(405\) | 0.0263280 | − | 8.99996i | 0.00130825 | − | 0.447212i | ||||
\(406\) | 7.92410 | 0.393266 | ||||||||
\(407\) | 33.3061 | 1.65092 | ||||||||
\(408\) | 3.52242 | − | 3.51727i | 0.174386 | − | 0.174131i | ||||
\(409\) | 28.2766 | + | 16.3255i | 1.39819 | + | 0.807244i | 0.994203 | − | 0.107522i | \(-0.0342916\pi\) |
0.403985 | + | 0.914766i | \(0.367625\pi\) | |||||||
\(410\) | − | 11.7600i | − | 0.580783i | ||||||
\(411\) | 7.90339 | + | 2.12390i | 0.389846 | + | 0.104764i | ||||
\(412\) | −1.22320 | − | 0.706213i | −0.0602626 | − | 0.0347926i | ||||
\(413\) | −5.94763 | − | 10.3016i | −0.292664 | − | 0.506909i | ||||
\(414\) | 5.59667 | + | 9.72654i | 0.275061 | + | 0.478033i | ||||
\(415\) | 4.00678 | + | 6.93994i | 0.196685 | + | 0.340668i | ||||
\(416\) | −1.17608 | + | 0.679010i | −0.0576620 | + | 0.0332912i | ||||
\(417\) | −1.16128 | + | 4.32133i | −0.0568684 | + | 0.211616i | ||||
\(418\) | 12.1643 | − | 1.72024i | 0.594973 | − | 0.0841395i | ||||
\(419\) | − | 6.89309i | − | 0.336750i | −0.985723 | − | 0.168375i | \(-0.946148\pi\) | ||
0.985723 | − | 0.168375i | \(-0.0538519\pi\) | |||||||
\(420\) | −1.43481 | − | 5.37049i | −0.0700115 | − | 0.262053i | ||||
\(421\) | −16.3349 | + | 9.43094i | −0.796113 | + | 0.459636i | −0.842110 | − | 0.539306i | \(-0.818687\pi\) |
0.0459975 | + | 0.998942i | \(0.485353\pi\) | |||||||
\(422\) | 21.4433 | + | 12.3803i | 1.04384 | + | 0.602662i | ||||
\(423\) | 28.5088 | + | 0.0416989i | 1.38614 | + | 0.00202747i | ||||
\(424\) | −1.96402 | + | 3.40178i | −0.0953813 | + | 0.165205i | ||||
\(425\) | − | 2.87394i | − | 0.139407i | ||||||
\(426\) | −0.742378 | + | 2.76251i | −0.0359683 | + | 0.133844i | ||||
\(427\) | 3.03654 | − | 5.25943i | 0.146948 | − | 0.254522i | ||||
\(428\) | −0.0665203 | + | 0.115217i | −0.00321538 | + | 0.00556920i | ||||
\(429\) | 1.72050 | − | 6.40227i | 0.0830666 | − | 0.309104i | ||||
\(430\) | 5.27733i | 0.254495i | ||||||||
\(431\) | −5.45320 | + | 9.44522i | −0.262671 | + | 0.454960i | −0.966951 | − | 0.254963i | \(-0.917937\pi\) |
0.704280 | + | 0.709923i | \(0.251270\pi\) | |||||||
\(432\) | 5.01614 | + | 1.35587i | 0.241339 | + | 0.0652344i | ||||
\(433\) | −16.5710 | − | 9.56729i | −0.796353 | − | 0.459774i | 0.0458415 | − | 0.998949i | \(-0.485403\pi\) |
−0.842194 | + | 0.539174i | \(0.818736\pi\) | |||||||
\(434\) | −17.2455 | + | 9.95670i | −0.827811 | + | 0.477937i | ||||
\(435\) | 1.10381 | + | 4.13157i | 0.0529238 | + | 0.198094i | ||||
\(436\) | − | 11.2298i | − | 0.537810i | ||||||
\(437\) | 10.0493 | + | 12.8398i | 0.480724 | + | 0.614210i | ||||
\(438\) | −4.06511 | + | 15.1269i | −0.194239 | + | 0.722793i | ||||
\(439\) | 16.7584 | − | 9.67549i | 0.799837 | − | 0.461786i | −0.0435774 | − | 0.999050i | \(-0.513876\pi\) |
0.843414 | + | 0.537264i | \(0.180542\pi\) | |||||||
\(440\) | 1.40922 | + | 2.44084i | 0.0671819 | + | 0.116362i | ||||
\(441\) | 8.58157 | − | 4.93785i | 0.408646 | − | 0.235136i | ||||
\(442\) | −1.95143 | − | 3.37998i | −0.0928202 | − | 0.160769i | ||||
\(443\) | −16.8746 | − | 9.74255i | −0.801736 | − | 0.462882i | 0.0423420 | − | 0.999103i | \(-0.486518\pi\) |
−0.844078 | + | 0.536221i | \(0.819851\pi\) | |||||||
\(444\) | 19.7667 | + | 5.31197i | 0.938087 | + | 0.252095i | ||||
\(445\) | − | 2.63801i | − | 0.125053i | ||||||
\(446\) | 5.77968 | + | 3.33690i | 0.273676 | + | 0.158007i | ||||
\(447\) | 14.4941 | − | 14.4729i | 0.685549 | − | 0.684547i | ||||
\(448\) | 3.20940 | 0.151630 | ||||||||
\(449\) | −10.3060 | −0.486372 | −0.243186 | − | 0.969980i | \(-0.578193\pi\) | ||||
−0.243186 | + | 0.969980i | \(0.578193\pi\) | |||||||
\(450\) | 2.60027 | − | 1.49620i | 0.122578 | − | 0.0705315i | ||||
\(451\) | −28.7042 | + | 16.5724i | −1.35163 | + | 0.780362i | ||||
\(452\) | −5.92548 | + | 10.2632i | −0.278711 | + | 0.482742i | ||||
\(453\) | −2.44461 | − | 9.15017i | −0.114858 | − | 0.429912i | ||||
\(454\) | −12.0437 | − | 20.8603i | −0.565238 | − | 0.979020i | ||||
\(455\) | −4.35843 | −0.204326 | ||||||||
\(456\) | 7.49368 | + | 0.919133i | 0.350924 | + | 0.0430424i | ||||
\(457\) | −3.18775 | −0.149117 | −0.0745583 | − | 0.997217i | \(-0.523755\pi\) | ||||
−0.0745583 | + | 0.997217i | \(0.523755\pi\) | |||||||
\(458\) | −10.8331 | − | 18.7635i | −0.506198 | − | 0.876760i | ||||
\(459\) | −3.89670 | + | 14.4161i | −0.181882 | + | 0.672885i | ||||
\(460\) | −1.87030 | + | 3.23945i | −0.0872030 | + | 0.151040i | ||||
\(461\) | 28.6530 | − | 16.5428i | 1.33450 | − | 0.770477i | 0.348518 | − | 0.937302i | \(-0.386685\pi\) |
0.985986 | + | 0.166825i | \(0.0533516\pi\) | |||||||
\(462\) | −11.0865 | + | 11.0703i | −0.515792 | + | 0.515038i | ||||
\(463\) | −5.36206 | −0.249196 | −0.124598 | − | 0.992207i | \(-0.539764\pi\) | ||||
−0.124598 | + | 0.992207i | \(0.539764\pi\) | |||||||
\(464\) | −2.46903 | −0.114622 | ||||||||
\(465\) | −7.59363 | − | 7.60474i | −0.352146 | − | 0.352661i | ||||
\(466\) | −15.3569 | − | 8.86633i | −0.711396 | − | 0.410725i | ||||
\(467\) | 41.3216i | 1.91213i | 0.293148 | + | 0.956067i | \(0.405297\pi\) | ||||
−0.293148 | + | 0.956067i | \(0.594703\pi\) | |||||||
\(468\) | 2.04219 | − | 3.52525i | 0.0944001 | − | 0.162955i | ||||
\(469\) | −29.3826 | − | 16.9641i | −1.35676 | − | 0.783328i | ||||
\(470\) | 4.75146 | + | 8.22978i | 0.219169 | + | 0.379611i | ||||
\(471\) | −20.9881 | − | 21.0188i | −0.967080 | − | 0.968496i | ||||
\(472\) | 1.85319 | + | 3.20982i | 0.0853000 | + | 0.147744i | ||||
\(473\) | 12.8811 | − | 7.43692i | 0.592274 | − | 0.341950i | ||||
\(474\) | −14.5847 | − | 3.91940i | −0.669899 | − | 0.180024i | ||||
\(475\) | 3.43255 | − | 2.68656i | 0.157496 | − | 0.123268i | ||||
\(476\) | 9.22363i | 0.422764i | ||||||||
\(477\) | 0.0172363 | − | 11.7841i | 0.000789195 | − | 0.539558i | ||||
\(478\) | −8.66926 | + | 5.00520i | −0.396523 | + | 0.228932i | ||||
\(479\) | 6.39802 | + | 3.69390i | 0.292333 | + | 0.168779i | 0.638994 | − | 0.769212i | \(-0.279351\pi\) |
−0.346660 | + | 0.937991i | \(0.612684\pi\) | |||||||
\(480\) | 0.447064 | + | 1.67336i | 0.0204056 | + | 0.0763781i | ||||
\(481\) | 8.02401 | − | 13.8980i | 0.365863 | − | 0.633694i | ||||
\(482\) | 5.28515i | 0.240732i | ||||||||
\(483\) | −20.0809 | − | 5.39641i | −0.913713 | − | 0.245545i | ||||
\(484\) | −1.52820 | + | 2.64692i | −0.0694637 | + | 0.120315i | ||||
\(485\) | 4.77690 | − | 8.27383i | 0.216908 | − | 0.375695i | ||||
\(486\) | −15.0719 | + | 3.97950i | −0.683677 | + | 0.180514i | ||||
\(487\) | − | 2.64014i | − | 0.119636i | −0.998209 | − | 0.0598180i | \(-0.980948\pi\) | ||
0.998209 | − | 0.0598180i | \(-0.0190520\pi\) | |||||||
\(488\) | −0.946137 | + | 1.63876i | −0.0428296 | + | 0.0741831i | ||||
\(489\) | −5.13809 | + | 1.37272i | −0.232353 | + | 0.0620766i | ||||
\(490\) | 2.85811 | + | 1.65013i | 0.129116 | + | 0.0745453i | ||||
\(491\) | −14.1387 | + | 8.16297i | −0.638070 | + | 0.368390i | −0.783871 | − | 0.620924i | \(-0.786757\pi\) |
0.145801 | + | 0.989314i | \(0.453424\pi\) | |||||||
\(492\) | −19.6787 | + | 5.25746i | −0.887182 | + | 0.237024i | ||||
\(493\) | − | 7.09584i | − | 0.319580i | ||||||
\(494\) | 2.21275 | − | 5.49034i | 0.0995565 | − | 0.247022i | ||||
\(495\) | −7.31633 | − | 4.23836i | −0.328844 | − | 0.190500i | ||||
\(496\) | 5.37344 | − | 3.10235i | 0.241274 | − | 0.139300i | ||||
\(497\) | −2.65020 | − | 4.59028i | −0.118878 | − | 0.205902i | ||||
\(498\) | 9.82173 | − | 9.80738i | 0.440122 | − | 0.439479i | ||||
\(499\) | −6.98906 | − | 12.1054i | −0.312873 | − | 0.541912i | 0.666110 | − | 0.745854i | \(-0.267958\pi\) |
−0.978983 | + | 0.203941i | \(0.934625\pi\) | |||||||
\(500\) | 0.866025 | + | 0.500000i | 0.0387298 | + | 0.0223607i | ||||
\(501\) | 10.4949 | − | 39.0533i | 0.468879 | − | 1.74477i | ||||
\(502\) | − | 23.4475i | − | 1.04651i | ||||||
\(503\) | −16.0900 | − | 9.28957i | −0.717418 | − | 0.414201i | 0.0963836 | − | 0.995344i | \(-0.469272\pi\) |
−0.813802 | + | 0.581143i | \(0.802606\pi\) | |||||||
\(504\) | −8.34530 | + | 4.80190i | −0.371729 | + | 0.213894i | ||||
\(505\) | −19.6001 | −0.872192 | ||||||||
\(506\) | 10.5426 | 0.468677 | ||||||||
\(507\) | 13.6530 | + | 13.6730i | 0.606351 | + | 0.607238i | ||||
\(508\) | 1.19910 | − | 0.692300i | 0.0532014 | − | 0.0307158i | ||||
\(509\) | 7.26580 | − | 12.5847i | 0.322051 | − | 0.557808i | −0.658860 | − | 0.752265i | \(-0.728961\pi\) |
0.980911 | + | 0.194457i | \(0.0622945\pi\) | |||||||
\(510\) | −4.80914 | + | 1.28484i | −0.212952 | + | 0.0568935i | ||||
\(511\) | −14.5120 | − | 25.1355i | −0.641971 | − | 1.11193i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −20.8608 | + | 8.82203i | −0.921025 | + | 0.389502i | ||||
\(514\) | 3.09335 | 0.136442 | ||||||||
\(515\) | 0.706213 | + | 1.22320i | 0.0311195 | + | 0.0539005i | ||||
\(516\) | 8.83087 | − | 2.35930i | 0.388758 | − | 0.103863i | ||||
\(517\) | 13.3917 | − | 23.1951i | 0.588967 | − | 1.02012i | ||||
\(518\) | −32.8451 | + | 18.9631i | −1.44313 | + | 0.833191i | ||||
\(519\) | 11.7430 | + | 11.7602i | 0.515460 | + | 0.516215i | ||||
\(520\) | 1.35802 | 0.0595531 | ||||||||
\(521\) | −36.4420 | −1.59655 | −0.798276 | − | 0.602291i | \(-0.794255\pi\) | ||||
−0.798276 | + | 0.602291i | \(0.794255\pi\) | |||||||
\(522\) | 6.42013 | − | 3.69415i | 0.281001 | − | 0.161689i | ||||
\(523\) | −17.8504 | − | 10.3060i | −0.780545 | − | 0.450648i | 0.0560782 | − | 0.998426i | \(-0.482140\pi\) |
−0.836624 | + | 0.547778i | \(0.815474\pi\) | |||||||
\(524\) | − | 19.5386i | − | 0.853549i | ||||||
\(525\) | −1.44266 | + | 5.36838i | −0.0629629 | + | 0.234295i | ||||
\(526\) | −6.03680 | − | 3.48535i | −0.263217 | − | 0.151968i | ||||
\(527\) | 8.91598 | + | 15.4429i | 0.388386 | + | 0.672705i | ||||
\(528\) | 3.45439 | − | 3.44934i | 0.150333 | − | 0.150113i | ||||
\(529\) | −4.50399 | − | 7.80114i | −0.195826 | − | 0.339180i | ||||
\(530\) | 3.40178 | − | 1.96402i | 0.147764 | − | 0.0853116i | ||||
\(531\) | −9.62131 | − | 5.57365i | −0.417529 | − | 0.241876i | ||||
\(532\) | −11.0164 | + | 8.62224i | −0.477623 | + | 0.373822i | ||||
\(533\) | 15.9703i | 0.691749i | ||||||||
\(534\) | −4.41433 | + | 1.17936i | −0.191027 | + | 0.0510358i | ||||
\(535\) | 0.115217 | − | 0.0665203i | 0.00498125 | − | 0.00287592i | ||||
\(536\) | 9.15518 | + | 5.28574i | 0.395443 | + | 0.228309i | ||||
\(537\) | −30.7771 | + | 8.22259i | −1.32813 | + | 0.354831i | ||||
\(538\) | −5.00015 | + | 8.66052i | −0.215572 | + | 0.373381i | ||||
\(539\) | − | 9.30159i | − | 0.400648i | ||||||
\(540\) | −3.66616 | − | 3.68229i | −0.157767 | − | 0.158460i | ||||
\(541\) | −20.9329 | + | 36.2568i | −0.899975 | + | 1.55880i | −0.0724514 | + | 0.997372i | \(0.523082\pi\) |
−0.827524 | + | 0.561431i | \(0.810251\pi\) | |||||||
\(542\) | 8.30819 | − | 14.3902i | 0.356868 | − | 0.618113i | ||||
\(543\) | 24.8784 | + | 6.68565i | 1.06763 | + | 0.286909i | ||||
\(544\) | − | 2.87394i | − | 0.123219i | ||||||
\(545\) | −5.61490 | + | 9.72530i | −0.240516 | + | 0.416586i | ||||
\(546\) | 1.94850 | + | 7.29322i | 0.0833880 | + | 0.312121i | ||||
\(547\) | −0.131381 | − | 0.0758528i | −0.00561744 | − | 0.00324323i | 0.497189 | − | 0.867642i | \(-0.334366\pi\) |
−0.502806 | + | 0.864399i | \(0.667699\pi\) | |||||||
\(548\) | 4.09190 | − | 2.36246i | 0.174797 | − | 0.100919i | ||||
\(549\) | 0.00830331 | − | 5.67682i | 0.000354377 | − | 0.242281i | ||||
\(550\) | − | 2.81844i | − | 0.120179i | ||||||
\(551\) | 8.47506 | − | 6.63318i | 0.361050 | − | 0.282583i | ||||
\(552\) | 6.25690 | + | 1.68144i | 0.266311 | + | 0.0715667i | ||||
\(553\) | 24.2345 | − | 13.9918i | 1.03056 | − | 0.594992i | ||||
\(554\) | 14.0336 | + | 24.3070i | 0.596232 | + | 1.03270i | ||||
\(555\) | −14.4625 | − | 14.4837i | −0.613899 | − | 0.614797i | ||||
\(556\) | 1.29172 | + | 2.23732i | 0.0547811 | + | 0.0948837i | ||||
\(557\) | 8.93906 | + | 5.16097i | 0.378760 | + | 0.218677i | 0.677279 | − | 0.735727i | \(-0.263159\pi\) |
−0.298518 | + | 0.954404i | \(0.596492\pi\) | |||||||
\(558\) | −9.33063 | + | 16.1067i | −0.394997 | + | 0.681850i | ||||
\(559\) | − | 7.16671i | − | 0.303120i | ||||||
\(560\) | −2.77942 | − | 1.60470i | −0.117452 | − | 0.0678110i | ||||
\(561\) | 9.91321 | + | 9.92772i | 0.418536 | + | 0.419149i | ||||
\(562\) | 4.93433 | 0.208142 | ||||||||
\(563\) | −42.9116 | −1.80851 | −0.904255 | − | 0.426994i | \(-0.859573\pi\) | ||||
−0.904255 | + | 0.426994i | \(0.859573\pi\) | |||||||
\(564\) | 11.6472 | − | 11.6301i | 0.490434 | − | 0.489718i | ||||
\(565\) | 10.2632 | − | 5.92548i | 0.431778 | − | 0.249287i | ||||
\(566\) | 4.00792 | − | 6.94192i | 0.168465 | − | 0.291790i | ||||
\(567\) | 14.5154 | − | 24.9725i | 0.609591 | − | 1.04874i | ||||
\(568\) | 0.825761 | + | 1.43026i | 0.0346482 | + | 0.0600124i | ||||
\(569\) | 14.9370 | 0.626192 | 0.313096 | − | 0.949722i | \(-0.398634\pi\) | ||||
0.313096 | + | 0.949722i | \(0.398634\pi\) | |||||||
\(570\) | −6.03015 | − | 4.54283i | −0.252575 | − | 0.190278i | ||||
\(571\) | −9.17120 | −0.383803 | −0.191901 | − | 0.981414i | \(-0.561465\pi\) | ||||
−0.191901 | + | 0.981414i | \(0.561465\pi\) | |||||||
\(572\) | −1.91375 | − | 3.31471i | −0.0800178 | − | 0.138595i | ||||
\(573\) | 0.845868 | + | 3.16608i | 0.0353366 | + | 0.132265i | ||||
\(574\) | 18.8712 | − | 32.6859i | 0.787670 | − | 1.36428i | ||||
\(575\) | 3.23945 | − | 1.87030i | 0.135094 | − | 0.0779967i | ||||
\(576\) | 2.60027 | − | 1.49620i | 0.108344 | − | 0.0623416i | ||||
\(577\) | 11.1217 | 0.463001 | 0.231500 | − | 0.972835i | \(-0.425637\pi\) | ||||
0.231500 | + | 0.972835i | \(0.425637\pi\) | |||||||
\(578\) | −8.74047 | −0.363555 | ||||||||
\(579\) | 24.8009 | − | 24.7647i | 1.03069 | − | 1.02919i | ||||
\(580\) | 2.13824 | + | 1.23451i | 0.0887856 | + | 0.0512604i | ||||
\(581\) | 25.7187i | 1.06699i | ||||||||
\(582\) | −15.9807 | − | 4.29454i | −0.662420 | − | 0.178014i | ||||
\(583\) | −9.58772 | − | 5.53547i | −0.397083 | − | 0.229256i | ||||
\(584\) | 4.52170 | + | 7.83182i | 0.187109 | + | 0.324083i | ||||
\(585\) | −3.53121 | + | 2.03187i | −0.145998 | + | 0.0840073i | ||||
\(586\) | −9.06372 | − | 15.6988i | −0.374419 | − | 0.648513i | ||||
\(587\) | 2.96690 | − | 1.71294i | 0.122457 | − | 0.0707005i | −0.437520 | − | 0.899209i | \(-0.644143\pi\) |
0.559977 | + | 0.828508i | \(0.310810\pi\) | |||||||
\(588\) | 1.48350 | − | 5.52036i | 0.0611787 | − | 0.227656i | ||||
\(589\) | −10.1099 | + | 25.0850i | −0.416573 | + | 1.03361i | ||||
\(590\) | − | 3.70638i | − | 0.152589i | ||||||
\(591\) | 3.75154 | + | 14.0420i | 0.154318 | + | 0.577612i | ||||
\(592\) | 10.2340 | − | 5.90861i | 0.420616 | − | 0.242842i | ||||
\(593\) | −37.6958 | − | 21.7637i | −1.54798 | − | 0.893727i | −0.998296 | − | 0.0583555i | \(-0.981414\pi\) |
−0.549685 | − | 0.835372i | \(-0.685252\pi\) | |||||||
\(594\) | −3.82144 | + | 14.1377i | −0.156796 | + | 0.580076i | ||||
\(595\) | 4.61182 | − | 7.98790i | 0.189066 | − | 0.327472i | ||||
\(596\) | − | 11.8258i | − | 0.484402i | ||||||
\(597\) | 0.483246 | − | 1.79824i | 0.0197780 | − | 0.0735970i | ||||
\(598\) | 2.53990 | − | 4.39923i | 0.103864 | − | 0.179898i | ||||
\(599\) | 8.31767 | − | 14.4066i | 0.339851 | − | 0.588639i | −0.644554 | − | 0.764559i | \(-0.722957\pi\) |
0.984404 | + | 0.175920i | \(0.0562901\pi\) | |||||||
\(600\) | 0.449511 | − | 1.67270i | 0.0183512 | − | 0.0682879i | ||||
\(601\) | − | 33.9509i | − | 1.38489i | −0.721472 | − | 0.692444i | \(-0.756534\pi\) | ||
0.721472 | − | 0.692444i | \(-0.243466\pi\) | |||||||
\(602\) | −8.46854 | + | 14.6679i | −0.345152 | + | 0.597820i | ||||
\(603\) | −31.7144 | − | 0.0463877i | −1.29151 | − | 0.00188906i | ||||
\(604\) | −4.73555 | − | 2.73407i | −0.192687 | − | 0.111248i | ||||
\(605\) | 2.64692 | − | 1.52820i | 0.107613 | − | 0.0621302i | ||||
\(606\) | 8.76249 | + | 32.7980i | 0.355952 | + | 1.33233i | ||||
\(607\) | 25.0735i | 1.01770i | 0.860854 | + | 0.508852i | \(0.169930\pi\) | ||||
−0.860854 | + | 0.508852i | \(0.830070\pi\) | |||||||
\(608\) | 3.43255 | − | 2.68656i | 0.139208 | − | 0.108954i | ||||
\(609\) | −3.56197 | + | 13.2547i | −0.144338 | + | 0.537107i | ||||
\(610\) | 1.63876 | − | 0.946137i | 0.0663514 | − | 0.0383080i | ||||
\(611\) | −6.45258 | − | 11.1762i | −0.261043 | − | 0.452141i | ||||
\(612\) | 4.29998 | + | 7.47301i | 0.173817 | + | 0.302079i | ||||
\(613\) | −7.45511 | − | 12.9126i | −0.301109 | − | 0.521536i | 0.675278 | − | 0.737563i | \(-0.264024\pi\) |
−0.976387 | + | 0.216027i | \(0.930690\pi\) | |||||||
\(614\) | −18.4910 | − | 10.6758i | −0.746238 | − | 0.430840i | ||||
\(615\) | 19.6709 | + | 5.28624i | 0.793209 | + | 0.213162i | ||||
\(616\) | 9.04550i | 0.364454i | ||||||||
\(617\) | −5.34291 | − | 3.08473i | −0.215097 | − | 0.124187i | 0.388581 | − | 0.921415i | \(-0.372965\pi\) |
−0.603678 | + | 0.797228i | \(0.706299\pi\) | |||||||
\(618\) | 1.73113 | − | 1.72860i | 0.0696361 | − | 0.0695343i | ||||
\(619\) | 30.6509 | 1.23196 | 0.615982 | − | 0.787760i | \(-0.288759\pi\) | ||||
0.615982 | + | 0.787760i | \(0.288759\pi\) | |||||||
\(620\) | −6.20471 | −0.249187 | ||||||||
\(621\) | −18.7854 | + | 4.98938i | −0.753832 | + | 0.200217i | ||||
\(622\) | −9.65163 | + | 5.57237i | −0.386995 | + | 0.223432i | ||||
\(623\) | 4.23321 | − | 7.33214i | 0.169600 | − | 0.293756i | ||||
\(624\) | −0.607122 | − | 2.27245i | −0.0243043 | − | 0.0909710i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 1.51863 | 0.0606965 | ||||||||
\(627\) | −2.59052 | + | 21.1205i | −0.103455 | + | 0.843470i | ||||
\(628\) | −17.1493 | −0.684330 | ||||||||
\(629\) | 16.9810 | + | 29.4120i | 0.677077 | + | 1.17273i | ||||
\(630\) | 9.62820 | + | 0.0140829i | 0.383597 | + | 0.000561075i | ||||
\(631\) | −4.52634 | + | 7.83986i | −0.180191 | + | 0.312100i | −0.941945 | − | 0.335766i | \(-0.891005\pi\) |
0.761755 | + | 0.647866i | \(0.224338\pi\) | |||||||
\(632\) | −7.55110 | + | 4.35963i | −0.300367 | + | 0.173417i | ||||
\(633\) | −30.3475 | + | 30.3032i | −1.20621 | + | 1.20444i | ||||
\(634\) | 3.69354 | 0.146689 | ||||||||
\(635\) | −1.38460 | −0.0549462 | ||||||||
\(636\) | −4.80733 | − | 4.81437i | −0.190623 | − | 0.190902i | ||||
\(637\) | −3.88137 | − | 2.24091i | −0.153785 | − | 0.0887881i | ||||
\(638\) | − | 6.95880i | − | 0.275502i | ||||||
\(639\) | −4.28715 | − | 2.48356i | −0.169597 | − | 0.0982480i | ||||
\(640\) | 0.866025 | + | 0.500000i | 0.0342327 | + | 0.0197642i | ||||
\(641\) | 7.29491 | + | 12.6352i | 0.288132 | + | 0.499059i | 0.973364 | − | 0.229266i | \(-0.0736325\pi\) |
−0.685232 | + | 0.728325i | \(0.740299\pi\) | |||||||
\(642\) | −0.162822 | − | 0.163060i | −0.00642606 | − | 0.00643546i | ||||
\(643\) | −13.5090 | − | 23.3983i | −0.532743 | − | 0.922739i | −0.999269 | − | 0.0382309i | \(-0.987828\pi\) |
0.466526 | − | 0.884508i | \(-0.345506\pi\) | |||||||
\(644\) | −10.3967 | + | 6.00253i | −0.409687 | + | 0.236533i | ||||
\(645\) | −8.82741 | − | 2.37222i | −0.347579 | − | 0.0934060i | ||||
\(646\) | 7.72101 | + | 9.86495i | 0.303779 | + | 0.388131i | ||||
\(647\) | − | 10.8293i | − | 0.425743i | −0.977080 | − | 0.212872i | \(-0.931718\pi\) | ||
0.977080 | − | 0.212872i | \(-0.0682816\pi\) | |||||||
\(648\) | −4.52278 | + | 7.78103i | −0.177672 | + | 0.305668i | ||||
\(649\) | −9.04668 | + | 5.22310i | −0.355113 | + | 0.205025i | ||||
\(650\) | −1.17608 | − | 0.679010i | −0.0461296 | − | 0.0266329i | ||||
\(651\) | −8.90257 | − | 33.3223i | −0.348919 | − | 1.30600i | ||||
\(652\) | −1.53526 | + | 2.65915i | −0.0601255 | + | 0.104140i | ||||
\(653\) | − | 39.3283i | − | 1.53904i | −0.638625 | − | 0.769518i | \(-0.720497\pi\) | ||
0.638625 | − | 0.769518i | \(-0.279503\pi\) | |||||||
\(654\) | 18.7841 | + | 5.04792i | 0.734518 | + | 0.197389i | ||||
\(655\) | −9.76931 | + | 16.9209i | −0.381719 | + | 0.661156i | ||||
\(656\) | −5.87998 | + | 10.1844i | −0.229575 | + | 0.397635i | ||||
\(657\) | −23.4756 | − | 13.5995i | −0.915870 | − | 0.530565i | ||||
\(658\) | 30.4987i | 1.18896i | ||||||||
\(659\) | −15.2330 | + | 26.3843i | −0.593392 | + | 1.02779i | 0.400379 | + | 0.916350i | \(0.368878\pi\) |
−0.993772 | + | 0.111436i | \(0.964455\pi\) | |||||||
\(660\) | −4.71626 | + | 1.26002i | −0.183580 | + | 0.0490463i | ||||
\(661\) | 30.2120 | + | 17.4429i | 1.17511 | + | 0.678450i | 0.954878 | − | 0.296998i | \(-0.0959854\pi\) |
0.220231 | + | 0.975448i | \(0.429319\pi\) | |||||||
\(662\) | 26.8413 | − | 15.4969i | 1.04322 | − | 0.602303i | ||||
\(663\) | 6.53090 | − | 1.74483i | 0.253639 | − | 0.0677636i | ||||
\(664\) | − | 8.01355i | − | 0.310986i | ||||||
\(665\) | 13.8516 | − | 1.95886i | 0.537143 | − | 0.0759614i | ||||
\(666\) | −17.7707 | + | 30.6761i | −0.688602 | + | 1.18867i | ||||
\(667\) | 7.99828 | − | 4.61781i | 0.309695 | − | 0.178802i | ||||
\(668\) | −11.6737 | − | 20.2195i | −0.451670 | − | 0.782315i | ||||
\(669\) | −8.17968 | + | 8.16772i | −0.316245 | + | 0.315782i | ||||
\(670\) | −5.28574 | − | 9.15518i | −0.204206 | − | 0.353695i | ||||
\(671\) | −4.61874 | − | 2.66663i | −0.178304 | − | 0.102944i | ||||
\(672\) | −1.44266 | + | 5.36838i | −0.0556519 | + | 0.207090i | ||||
\(673\) | 19.8592i | 0.765516i | 0.923849 | + | 0.382758i | \(0.125026\pi\) | ||||
−0.923849 | + | 0.382758i | \(0.874974\pi\) | |||||||
\(674\) | 11.8763 | + | 6.85679i | 0.457458 | + | 0.264114i | ||||
\(675\) | 1.33385 | + | 5.02204i | 0.0513398 | + | 0.193298i | ||||
\(676\) | 11.1558 | 0.429069 | ||||||||
\(677\) | 31.0348 | 1.19276 | 0.596382 | − | 0.802701i | \(-0.296605\pi\) | ||||
0.596382 | + | 0.802701i | \(0.296605\pi\) | |||||||
\(678\) | −14.5038 | − | 14.5250i | −0.557015 | − | 0.557830i | ||||
\(679\) | 26.5540 | − | 15.3310i | 1.01905 | − | 0.588349i | ||||
\(680\) | −1.43697 | + | 2.48891i | −0.0551053 | + | 0.0954452i | ||||
\(681\) | 40.3068 | − | 10.7686i | 1.54456 | − | 0.412653i | ||||
\(682\) | 8.74380 | + | 15.1447i | 0.334817 | + | 0.579920i | ||||
\(683\) | 0.186788 | 0.00714726 | 0.00357363 | − | 0.999994i | \(-0.498862\pi\) | ||||
0.00357363 | + | 0.999994i | \(0.498862\pi\) | |||||||
\(684\) | −4.90593 | + | 12.1215i | −0.187583 | + | 0.463479i | ||||
\(685\) | −4.72492 | −0.180530 | ||||||||
\(686\) | −5.93697 | − | 10.2831i | −0.226675 | − | 0.392612i | ||||
\(687\) | 36.2554 | − | 9.68618i | 1.38323 | − | 0.369551i | ||||
\(688\) | 2.63866 | − | 4.57030i | 0.100598 | − | 0.174241i | ||||
\(689\) | −4.61969 | + | 2.66718i | −0.175996 | + | 0.101611i | ||||
\(690\) | −4.57792 | − | 4.58462i | −0.174278 | − | 0.174533i | ||||
\(691\) | 45.2803 | 1.72254 | 0.861272 | − | 0.508144i | \(-0.169668\pi\) | ||||
0.861272 | + | 0.508144i | \(0.169668\pi\) | |||||||
\(692\) | 9.59513 | 0.364752 | ||||||||
\(693\) | −13.5339 | − | 23.5207i | −0.514109 | − | 0.893479i | ||||
\(694\) | 16.3458 | + | 9.43723i | 0.620476 | + | 0.358232i | ||||
\(695\) | − | 2.58344i | − | 0.0979954i | ||||||
\(696\) | 1.10986 | − | 4.12995i | 0.0420689 | − | 0.156545i | ||||
\(697\) | −29.2694 | − | 16.8987i | −1.10866 | − | 0.640085i | ||||
\(698\) | −4.15647 | − | 7.19921i | −0.157325 | − | 0.272494i | ||||
\(699\) | 21.7339 | − | 21.7021i | 0.822050 | − | 0.820848i | ||||
\(700\) | 1.60470 | + | 2.77942i | 0.0606520 | + | 0.105052i | ||||
\(701\) | 14.6766 | − | 8.47353i | 0.554327 | − | 0.320041i | −0.196539 | − | 0.980496i | \(-0.562970\pi\) |
0.750865 | + | 0.660455i | \(0.229637\pi\) | |||||||
\(702\) | 4.97872 | + | 5.00062i | 0.187910 | + | 0.188736i | ||||
\(703\) | −19.2550 | + | 47.7759i | −0.726215 | + | 1.80190i | ||||
\(704\) | − | 2.81844i | − | 0.106224i | ||||||
\(705\) | −15.9018 | + | 4.24842i | −0.598897 | + | 0.160005i | ||||
\(706\) | −28.5728 | + | 16.4965i | −1.07535 | + | 0.620854i | ||||
\(707\) | −54.4769 | − | 31.4523i | −2.04881 | − | 1.18288i | ||||
\(708\) | −6.20211 | + | 1.65699i | −0.233089 | + | 0.0622735i | ||||
\(709\) | 12.7967 | − | 22.1645i | 0.480589 | − | 0.832405i | −0.519163 | − | 0.854675i | \(-0.673756\pi\) |
0.999752 | + | 0.0222707i | \(0.00708956\pi\) | |||||||
\(710\) | − | 1.65152i | − | 0.0619806i | ||||||
\(711\) | 13.1120 | − | 22.6341i | 0.491739 | − | 0.848847i | ||||
\(712\) | −1.31900 | + | 2.28458i | −0.0494317 | + | 0.0856183i | ||||
\(713\) | −11.6046 | + | 20.0998i | −0.434597 | + | 0.752744i | ||||
\(714\) | −15.4284 | − | 4.14613i | −0.577394 | − | 0.155165i | ||||
\(715\) | 3.82749i | 0.143140i | ||||||||
\(716\) | −9.19621 | + | 15.9283i | −0.343679 | + | 0.595269i | ||||
\(717\) | −4.47529 | − | 16.7510i | −0.167133 | − | 0.625577i | ||||
\(718\) | 15.5156 | + | 8.95794i | 0.579037 | + | 0.334307i | ||||
\(719\) | −38.2562 | + | 22.0872i | −1.42671 | + | 0.823714i | −0.996860 | − | 0.0791847i | \(-0.974768\pi\) |
−0.429854 | + | 0.902898i | \(0.641435\pi\) | |||||||
\(720\) | −3.00000 | − | 0.00438801i | −0.111803 | − | 0.000163531i | ||||
\(721\) | 4.53304i | 0.168819i | ||||||||
\(722\) | −4.56482 | + | 18.4435i | −0.169885 | + | 0.686396i | ||||
\(723\) | −8.84049 | − | 2.37573i | −0.328781 | − | 0.0883544i | ||||
\(724\) | 12.8805 | − | 7.43657i | 0.478701 | − | 0.276378i | ||||
\(725\) | −1.23451 | − | 2.13824i | −0.0458487 | − | 0.0794122i | ||||
\(726\) | −3.74057 | − | 3.74605i | −0.138826 | − | 0.139029i | ||||
\(727\) | −5.60464 | − | 9.70752i | −0.207865 | − | 0.360032i | 0.743177 | − | 0.669095i | \(-0.233318\pi\) |
−0.951042 | + | 0.309063i | \(0.899985\pi\) | |||||||
\(728\) | 3.77451 | + | 2.17921i | 0.139893 | + | 0.0807671i | ||||
\(729\) | 0.118476 | − | 26.9997i | 0.00438799 | − | 0.999990i | ||||
\(730\) | − | 9.04340i | − | 0.334711i | ||||||
\(731\) | 13.1348 | + | 7.58337i | 0.485807 | + | 0.280481i | ||||
\(732\) | −2.31586 | − | 2.31925i | −0.0855966 | − | 0.0857219i | ||||
\(733\) | −4.73362 | −0.174840 | −0.0874202 | − | 0.996172i | \(-0.527862\pi\) | ||||
−0.0874202 | + | 0.996172i | \(0.527862\pi\) | |||||||
\(734\) | −15.3242 | −0.565625 | ||||||||
\(735\) | −4.04493 | + | 4.03902i | −0.149200 | + | 0.148982i | ||||
\(736\) | 3.23945 | − | 1.87030i | 0.119408 | − | 0.0689400i | ||||
\(737\) | −14.8975 | + | 25.8033i | −0.548758 | + | 0.950477i | ||||
\(738\) | 0.0516028 | − | 35.2799i | 0.00189952 | − | 1.29867i | ||||
\(739\) | 3.93967 | + | 6.82371i | 0.144923 | + | 0.251014i | 0.929344 | − | 0.369214i | \(-0.120373\pi\) |
−0.784421 | + | 0.620229i | \(0.787040\pi\) | |||||||
\(740\) | −11.8172 | −0.434410 | ||||||||
\(741\) | 8.18906 | + | 6.16925i | 0.300832 | + | 0.226633i | ||||
\(742\) | 12.6067 | 0.462805 | ||||||||
\(743\) | 6.72320 | + | 11.6449i | 0.246650 | + | 0.427211i | 0.962594 | − | 0.270947i | \(-0.0873368\pi\) |
−0.715944 | + | 0.698158i | \(0.754003\pi\) | |||||||
\(744\) | 2.77390 | + | 10.3827i | 0.101696 | + | 0.380649i | ||||
\(745\) | −5.91288 | + | 10.2414i | −0.216631 | + | 0.375216i | ||||
\(746\) | 7.11335 | − | 4.10690i | 0.260438 | − | 0.150364i | ||||
\(747\) | 11.9899 | + | 20.8374i | 0.438686 | + | 0.762400i | ||||
\(748\) | 8.10003 | 0.296166 | ||||||||
\(749\) | 0.426981 | 0.0156015 | ||||||||
\(750\) | −1.22564 | + | 1.22385i | −0.0447541 | + | 0.0446886i | ||||
\(751\) | 28.4743 | + | 16.4397i | 1.03904 | + | 0.599892i | 0.919562 | − | 0.392944i | \(-0.128543\pi\) |
0.119481 | + | 0.992836i | \(0.461877\pi\) | |||||||
\(752\) | − | 9.50293i | − | 0.346536i | ||||||
\(753\) | 39.2207 | + | 10.5399i | 1.42928 | + | 0.384095i | ||||
\(754\) | −2.90377 | − | 1.67649i | −0.105749 | − | 0.0610543i | ||||
\(755\) | 2.73407 | + | 4.73555i | 0.0995030 | + | 0.172344i | ||||
\(756\) | −4.28085 | − | 16.1177i | −0.155693 | − | 0.586196i | ||||
\(757\) | 22.4848 | + | 38.9449i | 0.817225 | + | 1.41548i | 0.907719 | + | 0.419578i | \(0.137822\pi\) |
−0.0904939 | + | 0.995897i | \(0.528845\pi\) | |||||||
\(758\) | −26.2093 | + | 15.1319i | −0.951963 | + | 0.549616i | ||||
\(759\) | −4.73903 | + | 17.6347i | −0.172016 | + | 0.640099i | ||||
\(760\) | −4.31596 | + | 0.610351i | −0.156556 | + | 0.0221398i | ||||
\(761\) | − | 9.71303i | − | 0.352097i | −0.984381 | − | 0.176049i | \(-0.943668\pi\) | ||
0.984381 | − | 0.176049i | \(-0.0563316\pi\) | |||||||
\(762\) | 0.619005 | + | 2.31693i | 0.0224242 | + | 0.0839337i | ||||
\(763\) | −31.2124 | + | 18.0205i | −1.12996 | + | 0.652385i | ||||
\(764\) | 1.63856 | + | 0.946026i | 0.0592812 | + | 0.0342260i | ||||
\(765\) | 0.0126109 | − | 8.62181i | 0.000455947 | − | 0.311722i | ||||
\(766\) | 10.9707 | − | 19.0019i | 0.396388 | − | 0.686565i | ||||
\(767\) | 5.03333i | 0.181743i | ||||||||
\(768\) | 0.449511 | − | 1.67270i | 0.0162203 | − | 0.0603585i | ||||
\(769\) | 13.8272 | − | 23.9494i | 0.498621 | − | 0.863638i | −0.501377 | − | 0.865229i | \(-0.667173\pi\) |
0.999999 | + | 0.00159104i | \(0.000506444\pi\) | |||||||
\(770\) | 4.52275 | − | 7.83364i | 0.162989 | − | 0.282305i | ||||
\(771\) | −1.39050 | + | 5.17426i | −0.0500775 | + | 0.186346i | ||||
\(772\) | − | 20.2351i | − | 0.728277i | ||||||
\(773\) | −0.918990 | + | 1.59174i | −0.0330538 | + | 0.0572508i | −0.882079 | − | 0.471101i | \(-0.843857\pi\) |
0.849025 | + | 0.528352i | \(0.177190\pi\) | |||||||
\(774\) | −0.0231570 | + | 15.8320i | −0.000832359 | + | 0.569069i | ||||
\(775\) | 5.37344 | + | 3.10235i | 0.193019 | + | 0.111440i | ||||
\(776\) | −8.27383 | + | 4.77690i | −0.297013 | + | 0.171481i | ||||
\(777\) | −16.9555 | − | 63.4642i | −0.608274 | − | 2.27677i | ||||
\(778\) | 23.7720i | 0.852267i | ||||||||
\(779\) | −7.17771 | − | 50.7555i | −0.257168 | − | 1.81850i | ||||
\(780\) | −0.610445 | + | 2.27156i | −0.0218574 | + | 0.0813351i | ||||
\(781\) | −4.03110 | + | 2.32736i | −0.144244 | + | 0.0832794i | ||||
\(782\) | 5.37512 | + | 9.30998i | 0.192214 | + | 0.332924i | ||||
\(783\) | 3.29331 | + | 12.3995i | 0.117693 | + | 0.443124i | ||||
\(784\) | −1.65013 | − | 2.85811i | −0.0589333 | − | 0.102075i | ||||
\(785\) | 14.8517 | + | 8.57463i | 0.530079 | + | 0.306042i | ||||
\(786\) | 32.6823 | + | 8.78283i | 1.16574 | + | 0.313273i | ||||
\(787\) | 52.3955i | 1.86770i | 0.357666 | + | 0.933850i | \(0.383573\pi\) | ||||
−0.357666 | + | 0.933850i | \(0.616427\pi\) | |||||||
\(788\) | 7.26726 | + | 4.19576i | 0.258886 | + | 0.149468i | ||||
\(789\) | 8.54357 | − | 8.53108i | 0.304159 | − | 0.303715i | ||||
\(790\) | 8.71926 | 0.310217 | ||||||||
\(791\) | 38.0345 | 1.35235 | ||||||||
\(792\) | 4.21694 | + | 7.32869i | 0.149843 | + | 0.260414i | ||||
\(793\) | −2.22546 | + | 1.28487i | −0.0790286 | + | 0.0456272i | ||||
\(794\) | 15.7374 | − | 27.2581i | 0.558501 | − | 0.967352i | ||||
\(795\) | 1.75609 | + | 6.57303i | 0.0622820 | + | 0.233121i | ||||
\(796\) | −0.537524 | − | 0.931019i | −0.0190520 | − | 0.0329991i | ||||
\(797\) | 48.3530 | 1.71275 | 0.856375 | − | 0.516354i | \(-0.172711\pi\) | ||||
0.856375 | + | 0.516354i | \(0.172711\pi\) | |||||||
\(798\) | −9.47045 | − | 22.3030i | −0.335250 | − | 0.789519i | ||||
\(799\) | 27.3109 | 0.966189 | ||||||||
\(800\) | −0.500000 | − | 0.866025i | −0.0176777 | − | 0.0306186i | ||||
\(801\) | 0.0115756 | − | 7.91401i | 0.000409003 | − | 0.279628i | ||||
\(802\) | −14.4572 | + | 25.0407i | −0.510503 | + | 0.884217i | ||||
\(803\) | −22.0735 | + | 12.7441i | −0.778957 | + | 0.449731i | ||||
\(804\) | −12.9568 | + | 12.9379i | −0.456953 | + | 0.456285i | ||||
\(805\) | 12.0051 | 0.423123 | ||||||||
\(806\) | 8.42611 | 0.296797 | ||||||||
\(807\) | −12.2389 | − | 12.2568i | −0.430828 | − | 0.431459i | ||||
\(808\) | 16.9742 | + | 9.80004i | 0.597149 | + | 0.344764i | ||||
\(809\) | − | 30.0431i | − | 1.05626i | −0.849164 | − | 0.528129i | \(-0.822894\pi\) | ||
0.849164 | − | 0.528129i | \(-0.177106\pi\) | |||||||
\(810\) | 7.80736 | − | 4.47718i | 0.274323 | − | 0.157312i | ||||
\(811\) | 5.51238 | + | 3.18257i | 0.193566 | + | 0.111755i | 0.593651 | − | 0.804723i | \(-0.297686\pi\) |
−0.400085 | + | 0.916478i | \(0.631019\pi\) | |||||||
\(812\) | 3.96205 | + | 6.86247i | 0.139041 | + | 0.240826i | ||||
\(813\) | 20.3359 | + | 20.3657i | 0.713213 | + | 0.714257i | ||||
\(814\) | 16.6531 | + | 28.8440i | 0.583690 | + | 1.01098i | ||||
\(815\) | 2.65915 | − | 1.53526i | 0.0931461 | − | 0.0537779i | ||||
\(816\) | 4.80725 | + | 1.29187i | 0.168288 | + | 0.0452244i | ||||
\(817\) | 3.22102 | + | 22.7767i | 0.112689 | + | 0.796857i | ||||
\(818\) | 32.6510i | 1.14162i | ||||||||
\(819\) | −13.0753 | − | 0.0191248i | −0.456887 | − | 0.000668275i | ||||
\(820\) | 10.1844 | − | 5.87998i | 0.355656 | − | 0.205338i | ||||
\(821\) | 44.8460 | + | 25.8919i | 1.56514 | + | 0.903632i | 0.996723 | + | 0.0808894i | \(0.0257761\pi\) |
0.568414 | + | 0.822743i | \(0.307557\pi\) | |||||||
\(822\) | 2.11234 | + | 7.90649i | 0.0736764 | + | 0.275771i | ||||
\(823\) | 12.4036 | − | 21.4836i | 0.432361 | − | 0.748871i | −0.564715 | − | 0.825286i | \(-0.691014\pi\) |
0.997076 | + | 0.0764150i | \(0.0243474\pi\) | |||||||
\(824\) | − | 1.41243i | − | 0.0492042i | ||||||
\(825\) | 4.71441 | + | 1.26692i | 0.164135 | + | 0.0441085i | ||||
\(826\) | 5.94763 | − | 10.3016i | 0.206945 | − | 0.358439i | ||||
\(827\) | 16.9483 | − | 29.3554i | 0.589352 | − | 1.02079i | −0.404966 | − | 0.914332i | \(-0.632717\pi\) |
0.994317 | − | 0.106455i | \(-0.0339501\pi\) | |||||||
\(828\) | −5.62510 | + | 9.71012i | −0.195486 | + | 0.337450i | ||||
\(829\) | − | 38.0529i | − | 1.32163i | −0.750548 | − | 0.660816i | \(-0.770210\pi\) | ||
0.750548 | − | 0.660816i | \(-0.229790\pi\) | |||||||
\(830\) | −4.00678 | + | 6.93994i | −0.139077 | + | 0.240889i | ||||
\(831\) | −46.9666 | + | 12.5479i | −1.62925 | + | 0.435281i | ||||
\(832\) | −1.17608 | − | 0.679010i | −0.0407732 | − | 0.0235404i | ||||
\(833\) | 8.21404 | − | 4.74238i | 0.284600 | − | 0.164314i | ||||
\(834\) | −4.32302 | + | 1.15496i | −0.149694 | + | 0.0399931i | ||||
\(835\) | 23.3474i | 0.807971i | ||||||||
\(836\) | 7.57190 | + | 9.67444i | 0.261880 | + | 0.334597i | ||||
\(837\) | −22.7475 | − | 22.8475i | −0.786268 | − | 0.789726i | ||||
\(838\) | 5.96959 | − | 3.44655i | 0.206216 | − | 0.119059i | ||||
\(839\) | 7.01424 | + | 12.1490i | 0.242158 | + | 0.419431i | 0.961329 | − | 0.275403i | \(-0.0888113\pi\) |
−0.719170 | + | 0.694834i | \(0.755478\pi\) | |||||||
\(840\) | 3.93357 | − | 3.92782i | 0.135721 | − | 0.135523i | ||||
\(841\) | 11.4520 | + | 19.8354i | 0.394895 | + | 0.683978i | ||||
\(842\) | −16.3349 | − | 9.43094i | −0.562937 | − | 0.325012i | ||||
\(843\) | −2.21804 | + | 8.25367i | −0.0763932 | + | 0.284272i | ||||
\(844\) | 24.7606i | 0.852293i | ||||||||
\(845\) | −9.66119 | − | 5.57789i | −0.332355 | − | 0.191885i | ||||
\(846\) | 14.2183 | + | 24.7102i | 0.488834 | + | 0.849553i | ||||
\(847\) | 9.80922 | 0.337049 | ||||||||
\(848\) | −3.92804 | −0.134890 | ||||||||
\(849\) | 9.81017 | + | 9.82453i | 0.336684 | + | 0.337177i | ||||
\(850\) | 2.48891 | − | 1.43697i | 0.0853688 | − | 0.0492877i | ||||
\(851\) | −22.1017 | + | 38.2813i | −0.757637 | + | 1.31227i | ||||
\(852\) | −2.76359 | + | 0.738337i | −0.0946791 | + | 0.0252950i | ||||
\(853\) | 24.0528 | + | 41.6607i | 0.823553 | + | 1.42644i | 0.903020 | + | 0.429598i | \(0.141345\pi\) |
−0.0794674 | + | 0.996837i | \(0.525322\pi\) | |||||||
\(854\) | 6.07307 | 0.207816 | ||||||||
\(855\) | 10.3094 | − | 8.04460i | 0.352575 | − | 0.275120i | ||||
\(856\) | −0.133041 | −0.00454724 | ||||||||
\(857\) | 9.49407 | + | 16.4442i | 0.324311 | + | 0.561724i | 0.981373 | − | 0.192113i | \(-0.0615341\pi\) |
−0.657061 | + | 0.753837i | \(0.728201\pi\) | |||||||
\(858\) | 6.40477 | − | 1.71113i | 0.218655 | − | 0.0584172i | ||||
\(859\) | −6.40982 | + | 11.1021i | −0.218700 | + | 0.378800i | −0.954411 | − | 0.298496i | \(-0.903515\pi\) |
0.735711 | + | 0.677296i | \(0.236848\pi\) | |||||||
\(860\) | −4.57030 | + | 2.63866i | −0.155846 | + | 0.0899777i | ||||
\(861\) | 46.1911 | + | 46.2587i | 1.57419 | + | 1.57649i | ||||
\(862\) | −10.9064 | −0.371473 | ||||||||
\(863\) | 35.5443 | 1.20994 | 0.604971 | − | 0.796247i | \(-0.293185\pi\) | ||||
0.604971 | + | 0.796247i | \(0.293185\pi\) | |||||||
\(864\) | 1.33385 | + | 5.02204i | 0.0453784 | + | 0.170853i | ||||
\(865\) | −8.30963 | − | 4.79757i | −0.282536 | − | 0.163122i | ||||
\(866\) | − | 19.1346i | − | 0.650219i | ||||||
\(867\) | 3.92894 | − | 14.6202i | 0.133434 | − | 0.496529i | ||||
\(868\) | −17.2455 | − | 9.95670i | −0.585351 | − | 0.337953i | ||||
\(869\) | −12.2874 | − | 21.2823i | −0.416820 | − | 0.721953i | ||||
\(870\) | −3.02614 | + | 3.02172i | −0.102596 | + | 0.102446i | ||||
\(871\) | 7.17814 | + | 12.4329i | 0.243222 | + | 0.421273i | ||||
\(872\) | 9.72530 | − | 5.61490i | 0.329340 | − | 0.190145i | ||||
\(873\) | 14.3670 | − | 24.8005i | 0.486249 | − | 0.839370i | ||||
\(874\) | −6.09491 | + | 15.1228i | −0.206163 | + | 0.511538i | ||||
\(875\) | − | 3.20940i | − | 0.108498i | ||||||
\(876\) | −15.1329 | + | 4.04298i | −0.511292 | + | 0.136600i | ||||
\(877\) | −13.5878 | + | 7.84493i | −0.458828 | + | 0.264904i | −0.711551 | − | 0.702634i | \(-0.752007\pi\) |
0.252723 | + | 0.967539i | \(0.418674\pi\) | |||||||
\(878\) | 16.7584 | + | 9.67549i | 0.565570 | + | 0.326532i | ||||
\(879\) | 30.3337 | − | 8.10413i | 1.02313 | − | 0.273346i | ||||
\(880\) | −1.40922 | + | 2.44084i | −0.0475048 | + | 0.0822807i | ||||
\(881\) | − | 3.34699i | − | 0.112763i | −0.998409 | − | 0.0563814i | \(-0.982044\pi\) | ||
0.998409 | − | 0.0563814i | \(-0.0179563\pi\) | |||||||
\(882\) | 8.56708 | + | 4.96293i | 0.288469 | + | 0.167111i | ||||
\(883\) | −15.8500 | + | 27.4530i | −0.533396 | + | 0.923868i | 0.465844 | + | 0.884867i | \(0.345751\pi\) |
−0.999239 | + | 0.0390012i | \(0.987582\pi\) | |||||||
\(884\) | 1.95143 | − | 3.37998i | 0.0656338 | − | 0.113681i | ||||
\(885\) | 6.19968 | + | 1.66606i | 0.208400 | + | 0.0560040i | ||||
\(886\) | − | 19.4851i | − | 0.654614i | ||||||
\(887\) | −14.2516 | + | 24.6845i | −0.478521 | + | 0.828823i | −0.999697 | − | 0.0246262i | \(-0.992160\pi\) |
0.521175 | + | 0.853450i | \(0.325494\pi\) | |||||||
\(888\) | 5.28306 | + | 19.7745i | 0.177288 | + | 0.663588i | ||||
\(889\) | −3.84839 | − | 2.22187i | −0.129071 | − | 0.0745191i | ||||
\(890\) | 2.28458 | − | 1.31900i | 0.0765793 | − | 0.0442131i | ||||
\(891\) | −21.9304 | − | 12.7472i | −0.734695 | − | 0.427047i | ||||
\(892\) | 6.67380i | 0.223455i | ||||||||
\(893\) | 25.5302 | + | 32.6193i | 0.854334 | + | 1.09156i | ||||
\(894\) | 19.7810 | + | 5.31581i | 0.661576 | + | 0.177787i | ||||
\(895\) | 15.9283 | − | 9.19621i | 0.532424 | − | 0.307395i | ||||
\(896\) | 1.60470 | + | 2.77942i | 0.0536093 | + | 0.0928540i | ||||
\(897\) | 6.21690 | + | 6.22600i | 0.207576 | + | 0.207880i | ||||
\(898\) | −5.15302 | − | 8.92529i | −0.171958 | − | 0.297841i | ||||
\(899\) | 13.2672 | + | 7.65980i | 0.442484 | + | 0.255468i | ||||
\(900\) | 2.59588 | + | 1.50380i | 0.0865293 | + | 0.0501266i | ||||
\(901\) | − | 11.2890i | − | 0.376090i | ||||||
\(902\) | −28.7042 | − | 16.5724i | −0.955745 | − | 0.551800i | ||||
\(903\) | −20.7284 | − | 20.7588i | −0.689799 | − | 0.690808i | ||||
\(904\) | −11.8510 | −0.394157 | ||||||||
\(905\) | −14.8731 | −0.494400 | ||||||||
\(906\) | 6.70197 | − | 6.69218i | 0.222658 | − | 0.222333i | ||||
\(907\) | 18.7055 | − | 10.7996i | 0.621105 | − | 0.358595i | −0.156194 | − | 0.987726i | \(-0.549923\pi\) |
0.777299 | + | 0.629131i | \(0.216589\pi\) | |||||||
\(908\) | 12.0437 | − | 20.8603i | 0.399683 | − | 0.692272i | ||||
\(909\) | −58.8001 | − | 0.0860052i | −1.95028 | − | 0.00285261i | ||||
\(910\) | −2.17921 | − | 3.77451i | −0.0722403 | − | 0.125124i | ||||
\(911\) | 26.3839 | 0.874137 | 0.437068 | − | 0.899428i | \(-0.356017\pi\) | ||||
0.437068 | + | 0.899428i | \(0.356017\pi\) | |||||||
\(912\) | 2.95085 | + | 6.94928i | 0.0977123 | + | 0.230114i | ||||
\(913\) | 22.5857 | 0.747478 | ||||||||
\(914\) | −1.59387 | − | 2.76067i | −0.0527207 | − | 0.0913149i | ||||
\(915\) | 0.845968 | + | 3.16646i | 0.0279668 | + | 0.104680i | ||||
\(916\) | 10.8331 | − | 18.7635i | 0.357936 | − | 0.619963i | ||||
\(917\) | −54.3061 | + | 31.3537i | −1.79335 | + | 1.03539i | ||||
\(918\) | −14.4330 | + | 3.83340i | −0.476361 | + | 0.126521i | ||||
\(919\) | 16.4871 | 0.543860 | 0.271930 | − | 0.962317i | \(-0.412338\pi\) | ||||
0.271930 | + | 0.962317i | \(0.412338\pi\) | |||||||
\(920\) | −3.74059 | −0.123324 | ||||||||
\(921\) | 26.1694 | − | 26.1311i | 0.862311 | − | 0.861050i | ||||
\(922\) | 28.6530 | + | 16.5428i | 0.943637 | + | 0.544809i | ||||
\(923\) | 2.24280i | 0.0738226i | ||||||||
\(924\) | −15.1305 | − | 4.06606i | −0.497755 | − | 0.133763i | ||||
\(925\) | 10.2340 | + | 5.90861i | 0.336492 | + | 0.194274i | ||||
\(926\) | −2.68103 | − | 4.64368i | −0.0881041 | − | 0.152601i | ||||
\(927\) | 2.11327 | + | 3.67269i | 0.0694089 | + | 0.120627i | ||||
\(928\) | −1.23451 | − | 2.13824i | −0.0405249 | − | 0.0701912i | ||||
\(929\) | −6.99418 | + | 4.03809i | −0.229472 | + | 0.132485i | −0.610328 | − | 0.792149i | \(-0.708962\pi\) |
0.380857 | + | 0.924634i | \(0.375629\pi\) | |||||||
\(930\) | 2.78909 | − | 10.3786i | 0.0914577 | − | 0.340329i | ||||
\(931\) | 13.3426 | + | 5.37744i | 0.437287 | + | 0.176239i | ||||
\(932\) | − | 17.7327i | − | 0.580852i | ||||||
\(933\) | −4.98241 | − | 18.6492i | −0.163117 | − | 0.610546i | ||||
\(934\) | −35.7855 | + | 20.6608i | −1.17094 | + | 0.676042i | ||||
\(935\) | −7.01483 | − | 4.05001i | −0.229409 | − | 0.132450i | ||||
\(936\) | 4.07405 | + | 0.00595899i | 0.133165 | + | 0.000194776i | ||||
\(937\) | −4.76274 | + | 8.24931i | −0.155592 | + | 0.269493i | −0.933274 | − | 0.359164i | \(-0.883062\pi\) |
0.777682 | + | 0.628657i | \(0.216395\pi\) | |||||||
\(938\) | − | 33.9282i | − | 1.10779i | ||||||
\(939\) | −0.682640 | + | 2.54021i | −0.0222771 | + | 0.0828968i | ||||
\(940\) | −4.75146 | + | 8.22978i | −0.154976 | + | 0.268426i | ||||
\(941\) | −14.0778 | + | 24.3835i | −0.458925 | + | 0.794881i | −0.998904 | − | 0.0467973i | \(-0.985099\pi\) |
0.539980 | + | 0.841678i | \(0.318432\pi\) | |||||||
\(942\) | 7.70878 | − | 28.6856i | 0.251166 | − | 0.934628i | ||||
\(943\) | − | 43.9892i | − | 1.43249i | ||||||
\(944\) | −1.85319 | + | 3.20982i | −0.0603162 | + | 0.104471i | ||||
\(945\) | −4.35154 | + | 16.0988i | −0.141556 | + | 0.523694i | ||||
\(946\) | 12.8811 | + | 7.43692i | 0.418801 | + | 0.241795i | ||||
\(947\) | 8.11070 | − | 4.68272i | 0.263562 | − | 0.152168i | −0.362396 | − | 0.932024i | \(-0.618041\pi\) |
0.625959 | + | 0.779856i | \(0.284708\pi\) | |||||||
\(948\) | −3.89807 | − | 14.5905i | −0.126603 | − | 0.473876i | ||||
\(949\) | 12.2811i | 0.398662i | ||||||||
\(950\) | 4.04290 | + | 1.62940i | 0.131169 | + | 0.0528647i | ||||
\(951\) | −1.66029 | + | 6.17820i | −0.0538385 | + | 0.200342i | ||||
\(952\) | −7.98790 | + | 4.61182i | −0.258889 | + | 0.149470i | ||||
\(953\) | −23.5528 | − | 40.7947i | −0.762951 | − | 1.32147i | −0.941323 | − | 0.337506i | \(-0.890417\pi\) |
0.178373 | − | 0.983963i | \(-0.442917\pi\) | |||||||
\(954\) | 10.2140 | − | 5.87713i | 0.330689 | − | 0.190279i | ||||
\(955\) | −0.946026 | − | 1.63856i | −0.0306127 | − | 0.0530227i | ||||
\(956\) | −8.66926 | − | 5.00520i | −0.280384 | − | 0.161880i | ||||
\(957\) | 11.6400 | + | 3.12806i | 0.376268 | + | 0.101116i | ||||
\(958\) | 7.38780i | 0.238689i | ||||||||
\(959\) | −13.1326 | − | 7.58208i | −0.424072 | − | 0.244838i | ||||
\(960\) | −1.22564 | + | 1.22385i | −0.0395574 | + | 0.0394996i | ||||
\(961\) | −7.49841 | −0.241884 | ||||||||
\(962\) | 16.0480 | 0.517409 | ||||||||
\(963\) | 0.345941 | − | 0.199055i | 0.0111478 | − | 0.00641446i | ||||
\(964\) | −4.57707 | + | 2.64257i | −0.147418 | + | 0.0851116i | ||||
\(965\) | −10.1175 | + | 17.5241i | −0.325695 | + | 0.564121i | ||||
\(966\) | −5.36703 | − | 20.0888i | −0.172681 | − | 0.646346i | ||||
\(967\) | −13.5335 | − | 23.4406i | −0.435206 | − | 0.753800i | 0.562106 | − | 0.827065i | \(-0.309991\pi\) |
−0.997312 | + | 0.0732655i | \(0.976658\pi\) | |||||||
\(968\) | −3.05640 | −0.0982365 | ||||||||
\(969\) | −19.9718 | + | 8.48055i | −0.641587 | + | 0.272435i | ||||
\(970\) | 9.55380 | 0.306754 | ||||||||
\(971\) | 0.875674 | + | 1.51671i | 0.0281017 | + | 0.0486736i | 0.879734 | − | 0.475466i | \(-0.157720\pi\) |
−0.851633 | + | 0.524139i | \(0.824387\pi\) | |||||||
\(972\) | −10.9823 | − | 11.0629i | −0.352258 | − | 0.354844i | ||||
\(973\) | 4.14565 | − | 7.18047i | 0.132903 | − | 0.230195i | ||||
\(974\) | 2.28643 | − | 1.32007i | 0.0732618 | − | 0.0422977i | ||||
\(975\) | 1.66444 | − | 1.66201i | 0.0533048 | − | 0.0532269i | ||||
\(976\) | −1.89227 | −0.0605702 | ||||||||
\(977\) | −9.85378 | −0.315250 | −0.157625 | − | 0.987499i | \(-0.550384\pi\) | ||||
−0.157625 | + | 0.987499i | \(0.550384\pi\) | |||||||
\(978\) | −3.75786 | − | 3.76336i | −0.120163 | − | 0.120339i | ||||
\(979\) | −6.43895 | − | 3.71753i | −0.205790 | − | 0.118813i | ||||
\(980\) | 3.30026i | 0.105423i | ||||||||
\(981\) | −16.8874 | + | 29.1512i | −0.539172 | + | 0.930727i | ||||
\(982\) | −14.1387 | − | 8.16297i | −0.451183 | − | 0.260491i | ||||
\(983\) | −26.3520 | − | 45.6430i | −0.840499 | − | 1.45579i | −0.889474 | − | 0.456986i | \(-0.848929\pi\) |
0.0489751 | − | 0.998800i | \(-0.484404\pi\) | |||||||
\(984\) | −14.3924 | − | 14.4135i | −0.458814 | − | 0.459485i | ||||
\(985\) | −4.19576 | − | 7.26726i | −0.133688 | − | 0.231554i | ||||
\(986\) | 6.14517 | − | 3.54792i | 0.195702 | − | 0.112989i | ||||
\(987\) | −51.0153 | − | 13.7095i | −1.62384 | − | 0.436379i | ||||
\(988\) | 5.86115 | − | 0.828868i | 0.186468 | − | 0.0263698i | ||||
\(989\) | 19.7403i | 0.627706i | ||||||||
\(990\) | 0.0123673 | − | 8.45531i | 0.000393059 | − | 0.268727i | ||||
\(991\) | −4.35746 | + | 2.51578i | −0.138419 | + | 0.0799164i | −0.567610 | − | 0.823297i | \(-0.692132\pi\) |
0.429191 | + | 0.903214i | \(0.358799\pi\) | |||||||
\(992\) | 5.37344 | + | 3.10235i | 0.170607 | + | 0.0984998i | ||||
\(993\) | 13.8562 | + | 51.8636i | 0.439713 | + | 1.64584i | ||||
\(994\) | 2.65020 | − | 4.59028i | 0.0840593 | − | 0.145595i | ||||
\(995\) | 1.07505i | 0.0340813i | ||||||||
\(996\) | 13.4043 | + | 3.60218i | 0.424732 | + | 0.114140i | ||||
\(997\) | −8.30937 | + | 14.3922i | −0.263160 | + | 0.455807i | −0.967080 | − | 0.254473i | \(-0.918098\pi\) |
0.703920 | + | 0.710280i | \(0.251431\pi\) | |||||||
\(998\) | 6.98906 | − | 12.1054i | 0.221235 | − | 0.383190i | ||||
\(999\) | −43.3239 | − | 43.5144i | −1.37071 | − | 1.37674i |
(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 | 570.2.s.b.221.2 | yes | 24 | |
3.2 | odd | 2 | 570.2.s.a.221.2 | ✓ | 24 | ||
19.8 | odd | 6 | 570.2.s.a.521.2 | yes | 24 | ||
57.8 | even | 6 | inner | 570.2.s.b.521.2 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.s.a.221.2 | ✓ | 24 | 3.2 | odd | 2 | ||
570.2.s.a.521.2 | yes | 24 | 19.8 | odd | 6 | ||
570.2.s.b.221.2 | yes | 24 | 1.1 | even | 1 | trivial | |
570.2.s.b.521.2 | yes | 24 | 57.8 | even | 6 | inner |