Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(529,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.ba (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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 619.12 | ||
Character | \(\chi\) | \(=\) | 1110.619 |
Dual form | 1110.2.ba.a.529.12 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 | ||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −2.12688 | − | 0.690199i | −0.951170 | − | 0.308666i | ||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 3.89483 | − | 2.24868i | 1.47211 | − | 0.849921i | 0.472599 | − | 0.881278i | \(-0.343316\pi\) |
0.999508 | + | 0.0313565i | \(0.00998272\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 1.66117 | − | 1.49683i | 0.525308 | − | 0.473340i | ||||
\(11\) | 0.412574 | 0.124396 | 0.0621979 | − | 0.998064i | \(-0.480189\pi\) | ||||
0.0621979 | + | 0.998064i | \(0.480189\pi\) | |||||||
\(12\) | −0.866025 | − | 0.500000i | −0.250000 | − | 0.144338i | ||||
\(13\) | 1.10249 | + | 1.90957i | 0.305776 | + | 0.529620i | 0.977434 | − | 0.211242i | \(-0.0677507\pi\) |
−0.671658 | + | 0.740862i | \(0.734417\pi\) | |||||||
\(14\) | 4.49736i | 1.20197i | ||||||||
\(15\) | −2.18703 | + | 0.465711i | −0.564690 | + | 0.120246i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.63267 | + | 2.82787i | −0.395981 | + | 0.685860i | −0.993226 | − | 0.116199i | \(-0.962929\pi\) |
0.597245 | + | 0.802059i | \(0.296262\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | 2.06416 | − | 1.19174i | 0.473550 | − | 0.273404i | −0.244175 | − | 0.969731i | \(-0.578517\pi\) |
0.717725 | + | 0.696327i | \(0.245184\pi\) | |||||||
\(20\) | 0.465711 | + | 2.18703i | 0.104136 | + | 0.489035i | ||||
\(21\) | 2.24868 | − | 3.89483i | 0.490702 | − | 0.849921i | ||||
\(22\) | −0.206287 | + | 0.357299i | −0.0439805 | + | 0.0761765i | ||||
\(23\) | −1.63566 | −0.341058 | −0.170529 | − | 0.985353i | \(-0.554548\pi\) | ||||
−0.170529 | + | 0.985353i | \(0.554548\pi\) | |||||||
\(24\) | 0.866025 | − | 0.500000i | 0.176777 | − | 0.102062i | ||||
\(25\) | 4.04725 | + | 2.93594i | 0.809450 | + | 0.587189i | ||||
\(26\) | −2.20498 | −0.432433 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −3.89483 | − | 2.24868i | −0.736053 | − | 0.424961i | ||||
\(29\) | − | 9.16257i | − | 1.70145i | −0.525614 | − | 0.850723i | \(-0.676164\pi\) | ||
0.525614 | − | 0.850723i | \(-0.323836\pi\) | |||||||
\(30\) | 0.690199 | − | 2.12688i | 0.126013 | − | 0.388314i | ||||
\(31\) | − | 6.51360i | − | 1.16988i | −0.811077 | − | 0.584939i | \(-0.801118\pi\) | ||
0.811077 | − | 0.584939i | \(-0.198882\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0.357299 | − | 0.206287i | 0.0621979 | − | 0.0359099i | ||||
\(34\) | −1.63267 | − | 2.82787i | −0.280001 | − | 0.484976i | ||||
\(35\) | −9.83588 | + | 2.09447i | −1.66257 | + | 0.354030i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 5.42955 | − | 2.74226i | 0.892613 | − | 0.450825i | ||||
\(38\) | 2.38348i | 0.386652i | ||||||||
\(39\) | 1.90957 | + | 1.10249i | 0.305776 | + | 0.176540i | ||||
\(40\) | −2.12688 | − | 0.690199i | −0.336289 | − | 0.109130i | ||||
\(41\) | −1.68174 | − | 2.91286i | −0.262644 | − | 0.454913i | 0.704300 | − | 0.709903i | \(-0.251261\pi\) |
−0.966944 | + | 0.254990i | \(0.917928\pi\) | |||||||
\(42\) | 2.24868 | + | 3.89483i | 0.346979 | + | 0.600985i | ||||
\(43\) | −9.32116 | −1.42146 | −0.710732 | − | 0.703463i | \(-0.751636\pi\) | ||||
−0.710732 | + | 0.703463i | \(0.751636\pi\) | |||||||
\(44\) | −0.206287 | − | 0.357299i | −0.0310989 | − | 0.0538649i | ||||
\(45\) | −1.66117 | + | 1.49683i | −0.247633 | + | 0.223135i | ||||
\(46\) | 0.817829 | − | 1.41652i | 0.120582 | − | 0.208855i | ||||
\(47\) | − | 6.71516i | − | 0.979507i | −0.871861 | − | 0.489753i | \(-0.837087\pi\) | ||
0.871861 | − | 0.489753i | \(-0.162913\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 6.61313 | − | 11.4543i | 0.944732 | − | 1.63632i | ||||
\(50\) | −4.56623 | + | 2.03705i | −0.645762 | + | 0.288082i | ||||
\(51\) | 3.26535i | 0.457240i | ||||||||
\(52\) | 1.10249 | − | 1.90957i | 0.152888 | − | 0.264810i | ||||
\(53\) | 10.0924 | + | 5.82686i | 1.38630 | + | 0.800380i | 0.992896 | − | 0.118986i | \(-0.0379643\pi\) |
0.393403 | + | 0.919366i | \(0.371298\pi\) | |||||||
\(54\) | 0.866025 | + | 0.500000i | 0.117851 | + | 0.0680414i | ||||
\(55\) | −0.877496 | − | 0.284758i | −0.118322 | − | 0.0383968i | ||||
\(56\) | 3.89483 | − | 2.24868i | 0.520468 | − | 0.300493i | ||||
\(57\) | 1.19174 | − | 2.06416i | 0.157850 | − | 0.273404i | ||||
\(58\) | 7.93502 | + | 4.58129i | 1.04192 | + | 0.601552i | ||||
\(59\) | 4.76276 | + | 2.74978i | 0.620058 | + | 0.357991i | 0.776892 | − | 0.629634i | \(-0.216795\pi\) |
−0.156834 | + | 0.987625i | \(0.550129\pi\) | |||||||
\(60\) | 1.49683 | + | 1.66117i | 0.193240 | + | 0.214456i | ||||
\(61\) | 6.46982 | − | 3.73535i | 0.828376 | − | 0.478263i | −0.0249202 | − | 0.999689i | \(-0.507933\pi\) |
0.853296 | + | 0.521426i | \(0.174600\pi\) | |||||||
\(62\) | 5.64095 | + | 3.25680i | 0.716401 | + | 0.413614i | ||||
\(63\) | − | 4.49736i | − | 0.566614i | ||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.02688 | − | 4.82237i | −0.127369 | − | 0.598142i | ||||
\(66\) | 0.412574i | 0.0507843i | ||||||||
\(67\) | 2.71578 | − | 1.56796i | 0.331785 | − | 0.191556i | −0.324848 | − | 0.945766i | \(-0.605313\pi\) |
0.656633 | + | 0.754210i | \(0.271980\pi\) | |||||||
\(68\) | 3.26535 | 0.395981 | ||||||||
\(69\) | −1.41652 | + | 0.817829i | −0.170529 | + | 0.0984550i | ||||
\(70\) | 3.10407 | − | 9.56535i | 0.371008 | − | 1.14328i | ||||
\(71\) | −1.01489 | − | 1.75784i | −0.120445 | − | 0.208617i | 0.799498 | − | 0.600669i | \(-0.205099\pi\) |
−0.919943 | + | 0.392051i | \(0.871766\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | 6.57476i | 0.769517i | 0.923017 | + | 0.384759i | \(0.125715\pi\) | ||||
−0.923017 | + | 0.384759i | \(0.874285\pi\) | |||||||
\(74\) | −0.339909 | + | 6.07326i | −0.0395136 | + | 0.706002i | ||||
\(75\) | 4.97299 | + | 0.518977i | 0.574232 | + | 0.0599263i | ||||
\(76\) | −2.06416 | − | 1.19174i | −0.236775 | − | 0.136702i | ||||
\(77\) | 1.60690 | − | 0.927747i | 0.183124 | − | 0.105727i | ||||
\(78\) | −1.90957 | + | 1.10249i | −0.216216 | + | 0.124833i | ||||
\(79\) | −7.72926 | + | 4.46249i | −0.869610 | + | 0.502069i | −0.867219 | − | 0.497928i | \(-0.834095\pi\) |
−0.00239128 | + | 0.999997i | \(0.500761\pi\) | |||||||
\(80\) | 1.66117 | − | 1.49683i | 0.185725 | − | 0.167351i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 3.36348 | 0.371435 | ||||||||
\(83\) | 3.38588 | + | 1.95484i | 0.371649 | + | 0.214571i | 0.674178 | − | 0.738568i | \(-0.264498\pi\) |
−0.302530 | + | 0.953140i | \(0.597831\pi\) | |||||||
\(84\) | −4.49736 | −0.490702 | ||||||||
\(85\) | 5.42430 | − | 4.88768i | 0.588348 | − | 0.530143i | ||||
\(86\) | 4.66058 | − | 8.07236i | 0.502563 | − | 0.870465i | ||||
\(87\) | −4.58129 | − | 7.93502i | −0.491165 | − | 0.850723i | ||||
\(88\) | 0.412574 | 0.0439805 | ||||||||
\(89\) | −2.49674 | − | 1.44149i | −0.264654 | − | 0.152798i | 0.361802 | − | 0.932255i | \(-0.382162\pi\) |
−0.626456 | + | 0.779457i | \(0.715495\pi\) | |||||||
\(90\) | −0.465711 | − | 2.18703i | −0.0490902 | − | 0.230534i | ||||
\(91\) | 8.58804 | + | 4.95830i | 0.900271 | + | 0.519772i | ||||
\(92\) | 0.817829 | + | 1.41652i | 0.0852646 | + | 0.147683i | ||||
\(93\) | −3.25680 | − | 5.64095i | −0.337715 | − | 0.584939i | ||||
\(94\) | 5.81550 | + | 3.35758i | 0.599823 | + | 0.346308i | ||||
\(95\) | −5.21275 | + | 1.11001i | −0.534817 | + | 0.113885i | ||||
\(96\) | −0.866025 | − | 0.500000i | −0.0883883 | − | 0.0510310i | ||||
\(97\) | 10.9274 | 1.10951 | 0.554753 | − | 0.832015i | \(-0.312813\pi\) | ||||
0.554753 | + | 0.832015i | \(0.312813\pi\) | |||||||
\(98\) | 6.61313 | + | 11.4543i | 0.668027 | + | 1.15706i | ||||
\(99\) | 0.206287 | − | 0.357299i | 0.0207326 | − | 0.0359099i | ||||
\(100\) | 0.518977 | − | 4.97299i | 0.0518977 | − | 0.497299i | ||||
\(101\) | −17.2184 | −1.71329 | −0.856647 | − | 0.515903i | \(-0.827457\pi\) | ||||
−0.856647 | + | 0.515903i | \(0.827457\pi\) | |||||||
\(102\) | −2.82787 | − | 1.63267i | −0.280001 | − | 0.161659i | ||||
\(103\) | −16.9033 | −1.66554 | −0.832768 | − | 0.553622i | \(-0.813245\pi\) | ||||
−0.832768 | + | 0.553622i | \(0.813245\pi\) | |||||||
\(104\) | 1.10249 | + | 1.90957i | 0.108108 | + | 0.187249i | ||||
\(105\) | −7.47088 | + | 6.73180i | −0.729084 | + | 0.656957i | ||||
\(106\) | −10.0924 | + | 5.82686i | −0.980262 | + | 0.565954i | ||||
\(107\) | 7.58132 | − | 4.37708i | 0.732914 | − | 0.423148i | −0.0865732 | − | 0.996245i | \(-0.527592\pi\) |
0.819487 | + | 0.573097i | \(0.194258\pi\) | |||||||
\(108\) | −0.866025 | + | 0.500000i | −0.0833333 | + | 0.0481125i | ||||
\(109\) | 9.65596 | + | 5.57487i | 0.924873 | + | 0.533976i | 0.885186 | − | 0.465236i | \(-0.154031\pi\) |
0.0396866 | + | 0.999212i | \(0.487364\pi\) | |||||||
\(110\) | 0.685356 | − | 0.617555i | 0.0653461 | − | 0.0588815i | ||||
\(111\) | 3.33100 | − | 5.08964i | 0.316164 | − | 0.483087i | ||||
\(112\) | 4.49736i | 0.424961i | ||||||||
\(113\) | 0.817025 | − | 1.41513i | 0.0768593 | − | 0.133124i | −0.825034 | − | 0.565083i | \(-0.808844\pi\) |
0.901893 | + | 0.431959i | \(0.142177\pi\) | |||||||
\(114\) | 1.19174 | + | 2.06416i | 0.111617 | + | 0.193326i | ||||
\(115\) | 3.47885 | + | 1.12893i | 0.324404 | + | 0.105273i | ||||
\(116\) | −7.93502 | + | 4.58129i | −0.736748 | + | 0.425362i | ||||
\(117\) | 2.20498 | 0.203851 | ||||||||
\(118\) | −4.76276 | + | 2.74978i | −0.438447 | + | 0.253138i | ||||
\(119\) | 14.6854i | 1.34621i | ||||||||
\(120\) | −2.18703 | + | 0.465711i | −0.199648 | + | 0.0425134i | ||||
\(121\) | −10.8298 | −0.984526 | ||||||||
\(122\) | 7.47071i | 0.676366i | ||||||||
\(123\) | −2.91286 | − | 1.68174i | −0.262644 | − | 0.151638i | ||||
\(124\) | −5.64095 | + | 3.25680i | −0.506572 | + | 0.292469i | ||||
\(125\) | −6.58164 | − | 9.03781i | −0.588679 | − | 0.808367i | ||||
\(126\) | 3.89483 | + | 2.24868i | 0.346979 | + | 0.200328i | ||||
\(127\) | 7.90697 | + | 4.56509i | 0.701630 | + | 0.405086i | 0.807954 | − | 0.589245i | \(-0.200575\pi\) |
−0.106324 | + | 0.994332i | \(0.533908\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −8.07236 | + | 4.66058i | −0.710732 | + | 0.410341i | ||||
\(130\) | 4.68974 | + | 1.52188i | 0.411317 | + | 0.133478i | ||||
\(131\) | −9.85183 | − | 5.68796i | −0.860758 | − | 0.496959i | 0.00350776 | − | 0.999994i | \(-0.498883\pi\) |
−0.864266 | + | 0.503035i | \(0.832217\pi\) | |||||||
\(132\) | −0.357299 | − | 0.206287i | −0.0310989 | − | 0.0179550i | ||||
\(133\) | 5.35969 | − | 9.28325i | 0.464744 | − | 0.804960i | ||||
\(134\) | 3.13591i | 0.270902i | ||||||||
\(135\) | −0.690199 | + | 2.12688i | −0.0594029 | + | 0.183053i | ||||
\(136\) | −1.63267 | + | 2.82787i | −0.140001 | + | 0.242488i | ||||
\(137\) | − | 2.47409i | − | 0.211376i | −0.994399 | − | 0.105688i | \(-0.966296\pi\) | ||
0.994399 | − | 0.105688i | \(-0.0337044\pi\) | |||||||
\(138\) | − | 1.63566i | − | 0.139236i | ||||||
\(139\) | 9.45191 | − | 16.3712i | 0.801701 | − | 1.38859i | −0.116795 | − | 0.993156i | \(-0.537262\pi\) |
0.918496 | − | 0.395431i | \(-0.129405\pi\) | |||||||
\(140\) | 6.73180 | + | 7.47088i | 0.568941 | + | 0.631405i | ||||
\(141\) | −3.35758 | − | 5.81550i | −0.282759 | − | 0.489753i | ||||
\(142\) | 2.02978 | 0.170335 | ||||||||
\(143\) | 0.454859 | + | 0.787840i | 0.0380373 | + | 0.0658825i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | −6.32400 | + | 19.4877i | −0.525180 | + | 1.61837i | ||||
\(146\) | −5.69391 | − | 3.28738i | −0.471231 | − | 0.272065i | ||||
\(147\) | − | 13.2263i | − | 1.09088i | ||||||
\(148\) | −5.08964 | − | 3.33100i | −0.418366 | − | 0.273806i | ||||
\(149\) | 7.98719 | 0.654336 | 0.327168 | − | 0.944966i | \(-0.393906\pi\) | ||||
0.327168 | + | 0.944966i | \(0.393906\pi\) | |||||||
\(150\) | −2.93594 | + | 4.04725i | −0.239719 | + | 0.330457i | ||||
\(151\) | −2.15436 | − | 3.73146i | −0.175319 | − | 0.303662i | 0.764952 | − | 0.644087i | \(-0.222762\pi\) |
−0.940272 | + | 0.340425i | \(0.889429\pi\) | |||||||
\(152\) | 2.06416 | − | 1.19174i | 0.167425 | − | 0.0966630i | ||||
\(153\) | 1.63267 | + | 2.82787i | 0.131994 | + | 0.228620i | ||||
\(154\) | 1.85549i | 0.149520i | ||||||||
\(155\) | −4.49568 | + | 13.8537i | −0.361102 | + | 1.11275i | ||||
\(156\) | − | 2.20498i | − | 0.176540i | ||||||
\(157\) | −3.79620 | − | 2.19174i | −0.302970 | − | 0.174920i | 0.340806 | − | 0.940133i | \(-0.389300\pi\) |
−0.643776 | + | 0.765214i | \(0.722633\pi\) | |||||||
\(158\) | − | 8.92498i | − | 0.710033i | ||||||
\(159\) | 11.6537 | 0.924199 | ||||||||
\(160\) | 0.465711 | + | 2.18703i | 0.0368177 | + | 0.172900i | ||||
\(161\) | −6.37061 | + | 3.67807i | −0.502074 | + | 0.289873i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −8.00959 | + | 13.8730i | −0.627360 | + | 1.08662i | 0.360720 | + | 0.932674i | \(0.382531\pi\) |
−0.988079 | + | 0.153945i | \(0.950802\pi\) | |||||||
\(164\) | −1.68174 | + | 2.91286i | −0.131322 | + | 0.227456i | ||||
\(165\) | −0.902313 | + | 0.192140i | −0.0702450 | + | 0.0149581i | ||||
\(166\) | −3.38588 | + | 1.95484i | −0.262795 | + | 0.151725i | ||||
\(167\) | 6.66540 | + | 11.5448i | 0.515784 | + | 0.893365i | 0.999832 | + | 0.0183231i | \(0.00583275\pi\) |
−0.484048 | + | 0.875042i | \(0.660834\pi\) | |||||||
\(168\) | 2.24868 | − | 3.89483i | 0.173489 | − | 0.300493i | ||||
\(169\) | 4.06902 | − | 7.04775i | 0.313002 | − | 0.542135i | ||||
\(170\) | 1.52071 | + | 7.14142i | 0.116633 | + | 0.547722i | ||||
\(171\) | − | 2.38348i | − | 0.182269i | ||||||
\(172\) | 4.66058 | + | 8.07236i | 0.355366 | + | 0.615512i | ||||
\(173\) | 22.0473 | + | 12.7290i | 1.67622 | + | 0.967768i | 0.964033 | + | 0.265781i | \(0.0856299\pi\) |
0.712190 | + | 0.701987i | \(0.247703\pi\) | |||||||
\(174\) | 9.16257 | 0.694613 | ||||||||
\(175\) | 22.3653 | + | 2.33403i | 1.69066 | + | 0.176436i | ||||
\(176\) | −0.206287 | + | 0.357299i | −0.0155495 | + | 0.0269325i | ||||
\(177\) | 5.49956 | 0.413372 | ||||||||
\(178\) | 2.49674 | − | 1.44149i | 0.187138 | − | 0.108044i | ||||
\(179\) | 3.35687i | 0.250904i | 0.992100 | + | 0.125452i | \(0.0400382\pi\) | ||||
−0.992100 | + | 0.125452i | \(0.959962\pi\) | |||||||
\(180\) | 2.12688 | + | 0.690199i | 0.158528 | + | 0.0514444i | ||||
\(181\) | 4.85498 | + | 8.40907i | 0.360868 | + | 0.625041i | 0.988104 | − | 0.153788i | \(-0.0491472\pi\) |
−0.627236 | + | 0.778829i | \(0.715814\pi\) | |||||||
\(182\) | −8.58804 | + | 4.95830i | −0.636588 | + | 0.367534i | ||||
\(183\) | 3.73535 | − | 6.46982i | 0.276125 | − | 0.478263i | ||||
\(184\) | −1.63566 | −0.120582 | ||||||||
\(185\) | −13.4407 | + | 2.08499i | −0.988181 | + | 0.153292i | ||||
\(186\) | 6.51360 | 0.477601 | ||||||||
\(187\) | −0.673598 | + | 1.16671i | −0.0492584 | + | 0.0853180i | ||||
\(188\) | −5.81550 | + | 3.35758i | −0.424139 | + | 0.244877i | ||||
\(189\) | −2.24868 | − | 3.89483i | −0.163567 | − | 0.283307i | ||||
\(190\) | 1.64508 | − | 5.06938i | 0.119346 | − | 0.367772i | ||||
\(191\) | 18.7526i | 1.35689i | 0.734651 | + | 0.678446i | \(0.237346\pi\) | ||||
−0.734651 | + | 0.678446i | \(0.762654\pi\) | |||||||
\(192\) | 0.866025 | − | 0.500000i | 0.0625000 | − | 0.0360844i | ||||
\(193\) | −25.6781 | −1.84835 | −0.924174 | − | 0.381971i | \(-0.875245\pi\) | ||||
−0.924174 | + | 0.381971i | \(0.875245\pi\) | |||||||
\(194\) | −5.46368 | + | 9.46337i | −0.392269 | + | 0.679431i | ||||
\(195\) | −3.30049 | − | 3.66286i | −0.236353 | − | 0.262303i | ||||
\(196\) | −13.2263 | −0.944732 | ||||||||
\(197\) | 15.5562 | + | 8.98138i | 1.10833 | + | 0.639897i | 0.938397 | − | 0.345558i | \(-0.112311\pi\) |
0.169936 | + | 0.985455i | \(0.445644\pi\) | |||||||
\(198\) | 0.206287 | + | 0.357299i | 0.0146602 | + | 0.0253922i | ||||
\(199\) | − | 8.12120i | − | 0.575697i | −0.957676 | − | 0.287848i | \(-0.907060\pi\) | ||
0.957676 | − | 0.287848i | \(-0.0929399\pi\) | |||||||
\(200\) | 4.04725 | + | 2.93594i | 0.286184 | + | 0.207603i | ||||
\(201\) | 1.56796 | − | 2.71578i | 0.110595 | − | 0.191556i | ||||
\(202\) | 8.60920 | − | 14.9116i | 0.605741 | − | 1.04917i | ||||
\(203\) | −20.6037 | − | 35.6866i | −1.44610 | − | 2.50471i | ||||
\(204\) | 2.82787 | − | 1.63267i | 0.197991 | − | 0.114310i | ||||
\(205\) | 1.56641 | + | 7.35605i | 0.109403 | + | 0.513769i | ||||
\(206\) | 8.45167 | − | 14.6387i | 0.588856 | − | 1.01993i | ||||
\(207\) | −0.817829 | + | 1.41652i | −0.0568430 | + | 0.0984550i | ||||
\(208\) | −2.20498 | −0.152888 | ||||||||
\(209\) | 0.851617 | − | 0.491681i | 0.0589076 | − | 0.0340103i | ||||
\(210\) | −2.09447 | − | 9.83588i | −0.144532 | − | 0.678740i | ||||
\(211\) | −8.47435 | −0.583399 | −0.291699 | − | 0.956510i | \(-0.594221\pi\) | ||||
−0.291699 | + | 0.956510i | \(0.594221\pi\) | |||||||
\(212\) | − | 11.6537i | − | 0.800380i | ||||||
\(213\) | −1.75784 | − | 1.01489i | −0.120445 | − | 0.0695391i | ||||
\(214\) | 8.75416i | 0.598422i | ||||||||
\(215\) | 19.8250 | + | 6.43346i | 1.35205 | + | 0.438758i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −14.6470 | − | 25.3694i | −0.994304 | − | 1.72219i | ||||
\(218\) | −9.65596 | + | 5.57487i | −0.653984 | + | 0.377578i | ||||
\(219\) | 3.28738 | + | 5.69391i | 0.222140 | + | 0.384759i | ||||
\(220\) | 0.192140 | + | 0.902313i | 0.0129541 | + | 0.0608339i | ||||
\(221\) | −7.20004 | −0.484327 | ||||||||
\(222\) | 2.74226 | + | 5.42955i | 0.184048 | + | 0.364408i | ||||
\(223\) | − | 18.7191i | − | 1.25352i | −0.779212 | − | 0.626761i | \(-0.784380\pi\) | ||
0.779212 | − | 0.626761i | \(-0.215620\pi\) | |||||||
\(224\) | −3.89483 | − | 2.24868i | −0.260234 | − | 0.150246i | ||||
\(225\) | 4.56623 | − | 2.03705i | 0.304415 | − | 0.135803i | ||||
\(226\) | 0.817025 | + | 1.41513i | 0.0543477 | + | 0.0941330i | ||||
\(227\) | 2.24825 | + | 3.89408i | 0.149222 | + | 0.258459i | 0.930940 | − | 0.365172i | \(-0.118990\pi\) |
−0.781718 | + | 0.623632i | \(0.785657\pi\) | |||||||
\(228\) | −2.38348 | −0.157850 | ||||||||
\(229\) | 10.1818 | + | 17.6353i | 0.672829 | + | 1.16537i | 0.977098 | + | 0.212788i | \(0.0682545\pi\) |
−0.304269 | + | 0.952586i | \(0.598412\pi\) | |||||||
\(230\) | −2.71711 | + | 2.44831i | −0.179161 | + | 0.161437i | ||||
\(231\) | 0.927747 | − | 1.60690i | 0.0610413 | − | 0.105727i | ||||
\(232\) | − | 9.16257i | − | 0.601552i | ||||||
\(233\) | − | 2.94072i | − | 0.192653i | −0.995350 | − | 0.0963266i | \(-0.969291\pi\) | ||
0.995350 | − | 0.0963266i | \(-0.0307093\pi\) | |||||||
\(234\) | −1.10249 | + | 1.90957i | −0.0720722 | + | 0.124833i | ||||
\(235\) | −4.63480 | + | 14.2823i | −0.302341 | + | 0.931678i | ||||
\(236\) | − | 5.49956i | − | 0.357991i | ||||||
\(237\) | −4.46249 | + | 7.72926i | −0.289870 | + | 0.502069i | ||||
\(238\) | −12.7180 | − | 7.34272i | −0.824383 | − | 0.475958i | ||||
\(239\) | −8.01145 | − | 4.62541i | −0.518218 | − | 0.299193i | 0.217987 | − | 0.975952i | \(-0.430051\pi\) |
−0.736205 | + | 0.676758i | \(0.763384\pi\) | |||||||
\(240\) | 0.690199 | − | 2.12688i | 0.0445522 | − | 0.137290i | ||||
\(241\) | 0.691167 | − | 0.399045i | 0.0445220 | − | 0.0257048i | −0.477574 | − | 0.878592i | \(-0.658484\pi\) |
0.522096 | + | 0.852887i | \(0.325150\pi\) | |||||||
\(242\) | 5.41489 | − | 9.37887i | 0.348082 | − | 0.602896i | ||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | −6.46982 | − | 3.73535i | −0.414188 | − | 0.239132i | ||||
\(245\) | −21.9711 | + | 19.7975i | −1.40368 | + | 1.26482i | ||||
\(246\) | 2.91286 | − | 1.68174i | 0.185717 | − | 0.107224i | ||||
\(247\) | 4.55143 | + | 2.62777i | 0.289601 | + | 0.167201i | ||||
\(248\) | − | 6.51360i | − | 0.413614i | ||||||
\(249\) | 3.90968 | 0.247766 | ||||||||
\(250\) | 11.1178 | − | 1.18096i | 0.703151 | − | 0.0746902i | ||||
\(251\) | 13.7566i | 0.868306i | 0.900839 | + | 0.434153i | \(0.142952\pi\) | ||||
−0.900839 | + | 0.434153i | \(0.857048\pi\) | |||||||
\(252\) | −3.89483 | + | 2.24868i | −0.245351 | + | 0.141654i | ||||
\(253\) | −0.674830 | −0.0424262 | ||||||||
\(254\) | −7.90697 | + | 4.56509i | −0.496127 | + | 0.286439i | ||||
\(255\) | 2.25374 | − | 6.94500i | 0.141135 | − | 0.434913i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −9.61645 | + | 16.6562i | −0.599858 | + | 1.03898i | 0.392984 | + | 0.919545i | \(0.371443\pi\) |
−0.992842 | + | 0.119439i | \(0.961890\pi\) | |||||||
\(258\) | − | 9.32116i | − | 0.580310i | ||||||
\(259\) | 14.9807 | − | 22.8900i | 0.930856 | − | 1.42231i | ||||
\(260\) | −3.66286 | + | 3.30049i | −0.227161 | + | 0.204688i | ||||
\(261\) | −7.93502 | − | 4.58129i | −0.491165 | − | 0.283574i | ||||
\(262\) | 9.85183 | − | 5.68796i | 0.608648 | − | 0.351403i | ||||
\(263\) | 5.05664 | − | 2.91945i | 0.311806 | − | 0.180021i | −0.335929 | − | 0.941887i | \(-0.609050\pi\) |
0.647734 | + | 0.761866i | \(0.275717\pi\) | |||||||
\(264\) | 0.357299 | − | 0.206287i | 0.0219903 | − | 0.0126961i | ||||
\(265\) | −17.4437 | − | 19.3588i | −1.07156 | − | 1.18920i | ||||
\(266\) | 5.35969 | + | 9.28325i | 0.328624 | + | 0.569193i | ||||
\(267\) | −2.88298 | −0.176436 | ||||||||
\(268\) | −2.71578 | − | 1.56796i | −0.165893 | − | 0.0957782i | ||||
\(269\) | −21.9627 | −1.33909 | −0.669545 | − | 0.742771i | \(-0.733511\pi\) | ||||
−0.669545 | + | 0.742771i | \(0.733511\pi\) | |||||||
\(270\) | −1.49683 | − | 1.66117i | −0.0910944 | − | 0.101096i | ||||
\(271\) | −1.50615 | + | 2.60873i | −0.0914920 | + | 0.158469i | −0.908139 | − | 0.418668i | \(-0.862497\pi\) |
0.816647 | + | 0.577137i | \(0.195830\pi\) | |||||||
\(272\) | −1.63267 | − | 2.82787i | −0.0989953 | − | 0.171465i | ||||
\(273\) | 9.91661 | 0.600180 | ||||||||
\(274\) | 2.14262 | + | 1.23704i | 0.129441 | + | 0.0747325i | ||||
\(275\) | 1.66979 | + | 1.21129i | 0.100692 | + | 0.0730438i | ||||
\(276\) | 1.41652 | + | 0.817829i | 0.0852646 | + | 0.0492275i | ||||
\(277\) | 7.28820 | + | 12.6235i | 0.437905 | + | 0.758475i | 0.997528 | − | 0.0702733i | \(-0.0223871\pi\) |
−0.559622 | + | 0.828748i | \(0.689054\pi\) | |||||||
\(278\) | 9.45191 | + | 16.3712i | 0.566888 | + | 0.981879i | ||||
\(279\) | −5.64095 | − | 3.25680i | −0.337715 | − | 0.194980i | ||||
\(280\) | −9.83588 | + | 2.09447i | −0.587806 | + | 0.125168i | ||||
\(281\) | 12.4391 | + | 7.18169i | 0.742052 | + | 0.428424i | 0.822815 | − | 0.568310i | \(-0.192402\pi\) |
−0.0807631 | + | 0.996733i | \(0.525736\pi\) | |||||||
\(282\) | 6.71516 | 0.399882 | ||||||||
\(283\) | 13.5334 | + | 23.4405i | 0.804478 | + | 1.39340i | 0.916643 | + | 0.399706i | \(0.130888\pi\) |
−0.112166 | + | 0.993690i | \(0.535779\pi\) | |||||||
\(284\) | −1.01489 | + | 1.75784i | −0.0602227 | + | 0.104309i | ||||
\(285\) | −3.95937 | + | 3.56768i | −0.234533 | + | 0.211331i | ||||
\(286\) | −0.909719 | −0.0537928 | ||||||||
\(287\) | −13.1002 | − | 7.56340i | −0.773280 | − | 0.446453i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 3.16876 | + | 5.48845i | 0.186397 | + | 0.322850i | ||||
\(290\) | −13.7148 | − | 15.2206i | −0.805364 | − | 0.893784i | ||||
\(291\) | 9.46337 | − | 5.46368i | 0.554753 | − | 0.320287i | ||||
\(292\) | 5.69391 | − | 3.28738i | 0.333211 | − | 0.192379i | ||||
\(293\) | −15.0447 | + | 8.68606i | −0.878920 | + | 0.507445i | −0.870302 | − | 0.492518i | \(-0.836077\pi\) |
−0.00861800 | + | 0.999963i | \(0.502743\pi\) | |||||||
\(294\) | 11.4543 | + | 6.61313i | 0.668027 | + | 0.385685i | ||||
\(295\) | −8.23192 | − | 9.13570i | −0.479281 | − | 0.531901i | ||||
\(296\) | 5.42955 | − | 2.74226i | 0.315586 | − | 0.159391i | ||||
\(297\) | − | 0.412574i | − | 0.0239400i | ||||||
\(298\) | −3.99360 | + | 6.91711i | −0.231343 | + | 0.400697i | ||||
\(299\) | −1.80330 | − | 3.12341i | −0.104288 | − | 0.180631i | ||||
\(300\) | −2.03705 | − | 4.56623i | −0.117609 | − | 0.263631i | ||||
\(301\) | −36.3043 | + | 20.9603i | −2.09255 | + | 1.20813i | ||||
\(302\) | 4.30872 | 0.247939 | ||||||||
\(303\) | −14.9116 | + | 8.60920i | −0.856647 | + | 0.494585i | ||||
\(304\) | 2.38348i | 0.136702i | ||||||||
\(305\) | −16.3387 | + | 3.47919i | −0.935551 | + | 0.199218i | ||||
\(306\) | −3.26535 | −0.186667 | ||||||||
\(307\) | − | 19.0895i | − | 1.08949i | −0.838600 | − | 0.544747i | \(-0.816626\pi\) | ||
0.838600 | − | 0.544747i | \(-0.183374\pi\) | |||||||
\(308\) | −1.60690 | − | 0.927747i | −0.0915619 | − | 0.0528633i | ||||
\(309\) | −14.6387 | + | 8.45167i | −0.832768 | + | 0.480799i | ||||
\(310\) | −9.74978 | − | 10.8202i | −0.553750 | − | 0.614547i | ||||
\(311\) | 1.51782 | + | 0.876316i | 0.0860679 | + | 0.0496913i | 0.542416 | − | 0.840110i | \(-0.317510\pi\) |
−0.456348 | + | 0.889801i | \(0.650843\pi\) | |||||||
\(312\) | 1.90957 | + | 1.10249i | 0.108108 | + | 0.0624163i | ||||
\(313\) | −3.08712 | + | 5.34705i | −0.174495 | + | 0.302233i | −0.939986 | − | 0.341212i | \(-0.889162\pi\) |
0.765492 | + | 0.643446i | \(0.222496\pi\) | |||||||
\(314\) | 3.79620 | − | 2.19174i | 0.214232 | − | 0.123687i | ||||
\(315\) | −3.10407 | + | 9.56535i | −0.174895 | + | 0.538947i | ||||
\(316\) | 7.72926 | + | 4.46249i | 0.434805 | + | 0.251035i | ||||
\(317\) | 14.2460 | + | 8.22494i | 0.800136 | + | 0.461959i | 0.843519 | − | 0.537100i | \(-0.180480\pi\) |
−0.0433825 | + | 0.999059i | \(0.513813\pi\) | |||||||
\(318\) | −5.82686 | + | 10.0924i | −0.326754 | + | 0.565954i | ||||
\(319\) | − | 3.78024i | − | 0.211653i | ||||||
\(320\) | −2.12688 | − | 0.690199i | −0.118896 | − | 0.0385833i | ||||
\(321\) | 4.37708 | − | 7.58132i | 0.244305 | − | 0.423148i | ||||
\(322\) | − | 7.35614i | − | 0.409942i | ||||||
\(323\) | 7.78289i | 0.433052i | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | −1.14434 | + | 10.9654i | −0.0634764 | + | 0.608249i | ||||
\(326\) | −8.00959 | − | 13.8730i | −0.443610 | − | 0.768356i | ||||
\(327\) | 11.1497 | 0.616582 | ||||||||
\(328\) | −1.68174 | − | 2.91286i | −0.0928587 | − | 0.160836i | ||||
\(329\) | −15.1002 | − | 26.1544i | −0.832504 | − | 1.44194i | ||||
\(330\) | 0.284758 | − | 0.877496i | 0.0156754 | − | 0.0483046i | ||||
\(331\) | 9.69676 | + | 5.59843i | 0.532982 | + | 0.307717i | 0.742230 | − | 0.670145i | \(-0.233768\pi\) |
−0.209248 | + | 0.977863i | \(0.567102\pi\) | |||||||
\(332\) | − | 3.90968i | − | 0.214571i | ||||||
\(333\) | 0.339909 | − | 6.07326i | 0.0186269 | − | 0.332812i | ||||
\(334\) | −13.3308 | −0.729429 | ||||||||
\(335\) | −6.85834 | + | 1.46043i | −0.374711 | + | 0.0797917i | ||||
\(336\) | 2.24868 | + | 3.89483i | 0.122676 | + | 0.212480i | ||||
\(337\) | −26.6165 | + | 15.3670i | −1.44989 | + | 0.837095i | −0.998474 | − | 0.0552182i | \(-0.982415\pi\) |
−0.451417 | + | 0.892313i | \(0.649081\pi\) | |||||||
\(338\) | 4.06902 | + | 7.04775i | 0.221326 | + | 0.383347i | ||||
\(339\) | − | 1.63405i | − | 0.0887495i | ||||||
\(340\) | −6.94500 | − | 2.25374i | −0.376646 | − | 0.122226i | ||||
\(341\) | − | 2.68734i | − | 0.145528i | ||||||
\(342\) | 2.06416 | + | 1.19174i | 0.111617 | + | 0.0644420i | ||||
\(343\) | − | 28.0017i | − | 1.51195i | ||||||
\(344\) | −9.32116 | −0.502563 | ||||||||
\(345\) | 3.57724 | − | 0.761743i | 0.192592 | − | 0.0410109i | ||||
\(346\) | −22.0473 | + | 12.7290i | −1.18527 | + | 0.684315i | ||||
\(347\) | −6.51035 | −0.349494 | −0.174747 | − | 0.984613i | \(-0.555911\pi\) | ||||
−0.174747 | + | 0.984613i | \(0.555911\pi\) | |||||||
\(348\) | −4.58129 | + | 7.93502i | −0.245583 | + | 0.425362i | ||||
\(349\) | −5.75901 | + | 9.97489i | −0.308273 | + | 0.533944i | −0.977985 | − | 0.208677i | \(-0.933084\pi\) |
0.669712 | + | 0.742621i | \(0.266418\pi\) | |||||||
\(350\) | −13.2040 | + | 18.2019i | −0.705783 | + | 0.972935i | ||||
\(351\) | 1.90957 | − | 1.10249i | 0.101925 | − | 0.0588467i | ||||
\(352\) | −0.206287 | − | 0.357299i | −0.0109951 | − | 0.0190441i | ||||
\(353\) | −13.7639 | + | 23.8398i | −0.732580 | + | 1.26887i | 0.223197 | + | 0.974773i | \(0.428351\pi\) |
−0.955777 | + | 0.294093i | \(0.904983\pi\) | |||||||
\(354\) | −2.74978 | + | 4.76276i | −0.146149 | + | 0.253138i | ||||
\(355\) | 0.945290 | + | 4.43920i | 0.0501708 | + | 0.235608i | ||||
\(356\) | 2.88298i | 0.152798i | ||||||||
\(357\) | 7.34272 | + | 12.7180i | 0.388618 | + | 0.673106i | ||||
\(358\) | −2.90714 | − | 1.67844i | −0.153647 | − | 0.0887081i | ||||
\(359\) | −10.4314 | −0.550546 | −0.275273 | − | 0.961366i | \(-0.588768\pi\) | ||||
−0.275273 | + | 0.961366i | \(0.588768\pi\) | |||||||
\(360\) | −1.66117 | + | 1.49683i | −0.0875514 | + | 0.0788901i | ||||
\(361\) | −6.65951 | + | 11.5346i | −0.350500 | + | 0.607084i | ||||
\(362\) | −9.70996 | −0.510344 | ||||||||
\(363\) | −9.37887 | + | 5.41489i | −0.492263 | + | 0.284208i | ||||
\(364\) | − | 9.91661i | − | 0.519772i | ||||||
\(365\) | 4.53789 | − | 13.9837i | 0.237524 | − | 0.731942i | ||||
\(366\) | 3.73535 | + | 6.46982i | 0.195250 | + | 0.338183i | ||||
\(367\) | −6.94787 | + | 4.01136i | −0.362676 | + | 0.209391i | −0.670254 | − | 0.742132i | \(-0.733815\pi\) |
0.307578 | + | 0.951523i | \(0.400481\pi\) | |||||||
\(368\) | 0.817829 | − | 1.41652i | 0.0426323 | − | 0.0738413i | ||||
\(369\) | −3.36348 | −0.175096 | ||||||||
\(370\) | 4.91470 | − | 12.6825i | 0.255503 | − | 0.659332i | ||||
\(371\) | 52.4109 | 2.72104 | ||||||||
\(372\) | −3.25680 | + | 5.64095i | −0.168857 | + | 0.292469i | ||||
\(373\) | 20.3157 | − | 11.7293i | 1.05191 | − | 0.607318i | 0.128724 | − | 0.991680i | \(-0.458912\pi\) |
0.923182 | + | 0.384362i | \(0.125579\pi\) | |||||||
\(374\) | −0.673598 | − | 1.16671i | −0.0348309 | − | 0.0603290i | ||||
\(375\) | −10.2188 | − | 4.53616i | −0.527695 | − | 0.234246i | ||||
\(376\) | − | 6.71516i | − | 0.346308i | ||||||
\(377\) | 17.4966 | − | 10.1017i | 0.901120 | − | 0.520262i | ||||
\(378\) | 4.49736 | 0.231319 | ||||||||
\(379\) | −8.83500 | + | 15.3027i | −0.453823 | + | 0.786045i | −0.998620 | − | 0.0525234i | \(-0.983274\pi\) |
0.544796 | + | 0.838568i | \(0.316607\pi\) | |||||||
\(380\) | 3.56768 | + | 3.95937i | 0.183018 | + | 0.203111i | ||||
\(381\) | 9.13018 | 0.467753 | ||||||||
\(382\) | −16.2402 | − | 9.37630i | −0.830923 | − | 0.479733i | ||||
\(383\) | 11.8360 | + | 20.5006i | 0.604793 | + | 1.04753i | 0.992084 | + | 0.125575i | \(0.0400775\pi\) |
−0.387291 | + | 0.921957i | \(0.626589\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | −4.05803 | + | 0.864123i | −0.206816 | + | 0.0440398i | ||||
\(386\) | 12.8390 | − | 22.2379i | 0.653490 | − | 1.13188i | ||||
\(387\) | −4.66058 | + | 8.07236i | −0.236911 | + | 0.410341i | ||||
\(388\) | −5.46368 | − | 9.46337i | −0.277376 | − | 0.480430i | ||||
\(389\) | −12.3967 | + | 7.15722i | −0.628536 | + | 0.362886i | −0.780185 | − | 0.625549i | \(-0.784875\pi\) |
0.151649 | + | 0.988434i | \(0.451542\pi\) | |||||||
\(390\) | 4.82237 | − | 1.02688i | 0.244190 | − | 0.0519983i | ||||
\(391\) | 2.67049 | − | 4.62543i | 0.135053 | − | 0.233918i | ||||
\(392\) | 6.61313 | − | 11.4543i | 0.334013 | − | 0.578528i | ||||
\(393\) | −11.3759 | −0.573839 | ||||||||
\(394\) | −15.5562 | + | 8.98138i | −0.783710 | + | 0.452475i | ||||
\(395\) | 19.5192 | − | 4.15646i | 0.982119 | − | 0.209134i | ||||
\(396\) | −0.412574 | −0.0207326 | ||||||||
\(397\) | 30.2416i | 1.51778i | 0.651218 | + | 0.758891i | \(0.274258\pi\) | ||||
−0.651218 | + | 0.758891i | \(0.725742\pi\) | |||||||
\(398\) | 7.03317 | + | 4.06060i | 0.352541 | + | 0.203540i | ||||
\(399\) | − | 10.7194i | − | 0.536640i | ||||||
\(400\) | −4.56623 | + | 2.03705i | −0.228311 | + | 0.101852i | ||||
\(401\) | − | 3.30061i | − | 0.164824i | −0.996598 | − | 0.0824122i | \(-0.973738\pi\) | ||
0.996598 | − | 0.0824122i | \(-0.0262624\pi\) | |||||||
\(402\) | 1.56796 | + | 2.71578i | 0.0782025 | + | 0.135451i | ||||
\(403\) | 12.4382 | − | 7.18120i | 0.619591 | − | 0.357721i | ||||
\(404\) | 8.60920 | + | 14.9116i | 0.428324 | + | 0.741878i | ||||
\(405\) | 0.465711 | + | 2.18703i | 0.0231414 | + | 0.108675i | ||||
\(406\) | 41.2074 | 2.04509 | ||||||||
\(407\) | 2.24009 | − | 1.13138i | 0.111037 | − | 0.0560807i | ||||
\(408\) | 3.26535i | 0.161659i | ||||||||
\(409\) | −24.6098 | − | 14.2085i | −1.21688 | − | 0.702565i | −0.252630 | − | 0.967563i | \(-0.581295\pi\) |
−0.964249 | + | 0.264998i | \(0.914629\pi\) | |||||||
\(410\) | −7.15373 | − | 2.32147i | −0.353298 | − | 0.114649i | ||||
\(411\) | −1.23704 | − | 2.14262i | −0.0610189 | − | 0.105688i | ||||
\(412\) | 8.45167 | + | 14.6387i | 0.416384 | + | 0.721198i | ||||
\(413\) | 24.7335 | 1.21706 | ||||||||
\(414\) | −0.817829 | − | 1.41652i | −0.0401941 | − | 0.0696182i | ||||
\(415\) | −5.85214 | − | 6.49464i | −0.287270 | − | 0.318809i | ||||
\(416\) | 1.10249 | − | 1.90957i | 0.0540541 | − | 0.0936245i | ||||
\(417\) | − | 18.9038i | − | 0.925724i | ||||||
\(418\) | 0.983363i | 0.0480978i | ||||||||
\(419\) | 2.15871 | − | 3.73900i | 0.105460 | − | 0.182662i | −0.808466 | − | 0.588543i | \(-0.799702\pi\) |
0.913926 | + | 0.405881i | \(0.133035\pi\) | |||||||
\(420\) | 9.56535 | + | 3.10407i | 0.466741 | + | 0.151463i | ||||
\(421\) | 31.2190i | 1.52152i | 0.649034 | + | 0.760759i | \(0.275173\pi\) | ||||
−0.649034 | + | 0.760759i | \(0.724827\pi\) | |||||||
\(422\) | 4.23718 | − | 7.33901i | 0.206263 | − | 0.357257i | ||||
\(423\) | −5.81550 | − | 3.35758i | −0.282759 | − | 0.163251i | ||||
\(424\) | 10.0924 | + | 5.82686i | 0.490131 | + | 0.282977i | ||||
\(425\) | −14.9103 | + | 6.65167i | −0.723256 | + | 0.322653i | ||||
\(426\) | 1.75784 | − | 1.01489i | 0.0851677 | − | 0.0491716i | ||||
\(427\) | 16.7992 | − | 29.0971i | 0.812972 | − | 1.40811i | ||||
\(428\) | −7.58132 | − | 4.37708i | −0.366457 | − | 0.211574i | ||||
\(429\) | 0.787840 | + | 0.454859i | 0.0380373 | + | 0.0219608i | ||||
\(430\) | −15.4840 | + | 13.9522i | −0.746707 | + | 0.672836i | ||||
\(431\) | 19.5309 | − | 11.2762i | 0.940770 | − | 0.543154i | 0.0505684 | − | 0.998721i | \(-0.483897\pi\) |
0.890202 | + | 0.455567i | \(0.150563\pi\) | |||||||
\(432\) | 0.866025 | + | 0.500000i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | − | 3.06164i | − | 0.147133i | −0.997290 | − | 0.0735664i | \(-0.976562\pi\) | ||
0.997290 | − | 0.0735664i | \(-0.0234381\pi\) | |||||||
\(434\) | 29.2940 | 1.40616 | ||||||||
\(435\) | 4.26711 | + | 20.0388i | 0.204592 | + | 0.960789i | ||||
\(436\) | − | 11.1497i | − | 0.533976i | ||||||
\(437\) | −3.37625 | + | 1.94928i | −0.161508 | + | 0.0932467i | ||||
\(438\) | −6.57476 | −0.314154 | ||||||||
\(439\) | 3.33982 | − | 1.92824i | 0.159401 | − | 0.0920301i | −0.418178 | − | 0.908365i | \(-0.637331\pi\) |
0.577579 | + | 0.816335i | \(0.303998\pi\) | |||||||
\(440\) | −0.877496 | − | 0.284758i | −0.0418330 | − | 0.0135753i | ||||
\(441\) | −6.61313 | − | 11.4543i | −0.314911 | − | 0.545442i | ||||
\(442\) | 3.60002 | − | 6.23541i | 0.171235 | − | 0.296588i | ||||
\(443\) | − | 25.4109i | − | 1.20731i | −0.797247 | − | 0.603654i | \(-0.793711\pi\) | ||
0.797247 | − | 0.603654i | \(-0.206289\pi\) | |||||||
\(444\) | −6.07326 | − | 0.339909i | −0.288224 | − | 0.0161313i | ||||
\(445\) | 4.31535 | + | 4.78913i | 0.204567 | + | 0.227026i | ||||
\(446\) | 16.2112 | + | 9.35953i | 0.767622 | + | 0.443187i | ||||
\(447\) | 6.91711 | − | 3.99360i | 0.327168 | − | 0.188891i | ||||
\(448\) | 3.89483 | − | 2.24868i | 0.184013 | − | 0.106240i | ||||
\(449\) | 29.8241 | − | 17.2189i | 1.40749 | − | 0.812612i | 0.412340 | − | 0.911030i | \(-0.364712\pi\) |
0.995145 | + | 0.0984178i | \(0.0313782\pi\) | |||||||
\(450\) | −0.518977 | + | 4.97299i | −0.0244648 | + | 0.234429i | ||||
\(451\) | −0.693843 | − | 1.20177i | −0.0326718 | − | 0.0565892i | ||||
\(452\) | −1.63405 | −0.0768593 | ||||||||
\(453\) | −3.73146 | − | 2.15436i | −0.175319 | − | 0.101221i | ||||
\(454\) | −4.49650 | −0.211031 | ||||||||
\(455\) | −14.8435 | − | 16.4732i | −0.695875 | − | 0.772275i | ||||
\(456\) | 1.19174 | − | 2.06416i | 0.0558084 | − | 0.0966630i | ||||
\(457\) | −0.681427 | − | 1.18027i | −0.0318758 | − | 0.0552105i | 0.849647 | − | 0.527351i | \(-0.176815\pi\) |
−0.881523 | + | 0.472141i | \(0.843481\pi\) | |||||||
\(458\) | −20.3635 | −0.951524 | ||||||||
\(459\) | 2.82787 | + | 1.63267i | 0.131994 | + | 0.0762067i | ||||
\(460\) | −0.761743 | − | 3.57724i | −0.0355165 | − | 0.166790i | ||||
\(461\) | −10.7687 | − | 6.21733i | −0.501550 | − | 0.289570i | 0.227803 | − | 0.973707i | \(-0.426846\pi\) |
−0.729353 | + | 0.684137i | \(0.760179\pi\) | |||||||
\(462\) | 0.927747 | + | 1.60690i | 0.0431627 | + | 0.0747600i | ||||
\(463\) | −2.33045 | − | 4.03646i | −0.108305 | − | 0.187590i | 0.806778 | − | 0.590854i | \(-0.201209\pi\) |
−0.915084 | + | 0.403264i | \(0.867876\pi\) | |||||||
\(464\) | 7.93502 | + | 4.58129i | 0.368374 | + | 0.212681i | ||||
\(465\) | 3.03345 | + | 14.2455i | 0.140673 | + | 0.660618i | ||||
\(466\) | 2.54674 | + | 1.47036i | 0.117975 | + | 0.0681132i | ||||
\(467\) | 24.9564 | 1.15484 | 0.577422 | − | 0.816446i | \(-0.304059\pi\) | ||||
0.577422 | + | 0.816446i | \(0.304059\pi\) | |||||||
\(468\) | −1.10249 | − | 1.90957i | −0.0509627 | − | 0.0882700i | ||||
\(469\) | 7.05166 | − | 12.2138i | 0.325616 | − | 0.563983i | ||||
\(470\) | −10.0515 | − | 11.1550i | −0.463640 | − | 0.514543i | ||||
\(471\) | −4.38347 | −0.201980 | ||||||||
\(472\) | 4.76276 | + | 2.74978i | 0.219224 | + | 0.126569i | ||||
\(473\) | −3.84567 | −0.176824 | ||||||||
\(474\) | −4.46249 | − | 7.72926i | −0.204969 | − | 0.355017i | ||||
\(475\) | 11.8530 | + | 1.23697i | 0.543855 | + | 0.0567562i | ||||
\(476\) | 12.7180 | − | 7.34272i | 0.582927 | − | 0.336553i | ||||
\(477\) | 10.0924 | − | 5.82686i | 0.462100 | − | 0.266793i | ||||
\(478\) | 8.01145 | − | 4.62541i | 0.366435 | − | 0.211562i | ||||
\(479\) | −10.0078 | − | 5.77801i | −0.457268 | − | 0.264004i | 0.253627 | − | 0.967302i | \(-0.418377\pi\) |
−0.710895 | + | 0.703298i | \(0.751710\pi\) | |||||||
\(480\) | 1.49683 | + | 1.66117i | 0.0683208 | + | 0.0758217i | ||||
\(481\) | 11.2226 | + | 7.34480i | 0.511706 | + | 0.334894i | ||||
\(482\) | 0.798091i | 0.0363520i | ||||||||
\(483\) | −3.67807 | + | 6.37061i | −0.167358 | + | 0.289873i | ||||
\(484\) | 5.41489 | + | 9.37887i | 0.246131 | + | 0.426312i | ||||
\(485\) | −23.2412 | − | 7.54206i | −1.05533 | − | 0.342467i | ||||
\(486\) | 0.866025 | − | 0.500000i | 0.0392837 | − | 0.0226805i | ||||
\(487\) | 34.7877 | 1.57638 | 0.788190 | − | 0.615432i | \(-0.211019\pi\) | ||||
0.788190 | + | 0.615432i | \(0.211019\pi\) | |||||||
\(488\) | 6.46982 | − | 3.73535i | 0.292875 | − | 0.169092i | ||||
\(489\) | 16.0192i | 0.724413i | ||||||||
\(490\) | −6.15961 | − | 28.9263i | −0.278263 | − | 1.30675i | ||||
\(491\) | 4.56055 | 0.205815 | 0.102907 | − | 0.994691i | \(-0.467186\pi\) | ||||
0.102907 | + | 0.994691i | \(0.467186\pi\) | |||||||
\(492\) | 3.36348i | 0.151638i | ||||||||
\(493\) | 25.9106 | + | 14.9595i | 1.16695 | + | 0.673741i | ||||
\(494\) | −4.55143 | + | 2.62777i | −0.204779 | + | 0.118229i | ||||
\(495\) | −0.685356 | + | 0.617555i | −0.0308044 | + | 0.0277570i | ||||
\(496\) | 5.64095 | + | 3.25680i | 0.253286 | + | 0.146235i | ||||
\(497\) | −7.90565 | − | 4.56433i | −0.354617 | − | 0.204738i | ||||
\(498\) | −1.95484 | + | 3.38588i | −0.0875984 | + | 0.151725i | ||||
\(499\) | 3.45818 | − | 1.99658i | 0.154809 | − | 0.0893792i | −0.420594 | − | 0.907249i | \(-0.638178\pi\) |
0.575404 | + | 0.817870i | \(0.304845\pi\) | |||||||
\(500\) | −4.53616 | + | 10.2188i | −0.202863 | + | 0.456997i | ||||
\(501\) | 11.5448 | + | 6.66540i | 0.515784 | + | 0.297788i | ||||
\(502\) | −11.9135 | − | 6.87828i | −0.531727 | − | 0.306993i | ||||
\(503\) | 11.2212 | − | 19.4356i | 0.500327 | − | 0.866593i | −0.499672 | − | 0.866214i | \(-0.666546\pi\) |
1.00000 | 0.000378200i | \(-0.000120385\pi\) | ||||||||
\(504\) | − | 4.49736i | − | 0.200328i | ||||||
\(505\) | 36.6215 | + | 11.8841i | 1.62963 | + | 0.528836i | ||||
\(506\) | 0.337415 | − | 0.584420i | 0.0149999 | − | 0.0259806i | ||||
\(507\) | − | 8.13804i | − | 0.361423i | ||||||
\(508\) | − | 9.13018i | − | 0.405086i | ||||||
\(509\) | 16.6264 | − | 28.7978i | 0.736952 | − | 1.27644i | −0.216910 | − | 0.976192i | \(-0.569598\pi\) |
0.953862 | − | 0.300246i | \(-0.0970689\pi\) | |||||||
\(510\) | 4.88768 | + | 5.42430i | 0.216430 | + | 0.240192i | ||||
\(511\) | 14.7845 | + | 25.6076i | 0.654029 | + | 1.13281i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.19174 | − | 2.06416i | −0.0526167 | − | 0.0911347i | ||||
\(514\) | −9.61645 | − | 16.6562i | −0.424164 | − | 0.734673i | ||||
\(515\) | 35.9514 | + | 11.6667i | 1.58421 | + | 0.514095i | ||||
\(516\) | 8.07236 | + | 4.66058i | 0.355366 | + | 0.205171i | ||||
\(517\) | − | 2.77050i | − | 0.121846i | ||||||
\(518\) | 12.3329 | + | 24.4186i | 0.541878 | + | 1.07289i | ||||
\(519\) | 25.4580 | 1.11748 | ||||||||
\(520\) | −1.02688 | − | 4.82237i | −0.0450319 | − | 0.211475i | ||||
\(521\) | −7.83325 | − | 13.5676i | −0.343181 | − | 0.594407i | 0.641841 | − | 0.766838i | \(-0.278171\pi\) |
−0.985022 | + | 0.172431i | \(0.944838\pi\) | |||||||
\(522\) | 7.93502 | − | 4.58129i | 0.347306 | − | 0.200517i | ||||
\(523\) | 9.39805 | + | 16.2779i | 0.410948 | + | 0.711783i | 0.994994 | − | 0.0999381i | \(-0.0318645\pi\) |
−0.584046 | + | 0.811721i | \(0.698531\pi\) | |||||||
\(524\) | 11.3759i | 0.496959i | ||||||||
\(525\) | 20.5360 | − | 9.16135i | 0.896263 | − | 0.399834i | ||||
\(526\) | 5.83890i | 0.254588i | ||||||||
\(527\) | 18.4196 | + | 10.6346i | 0.802372 | + | 0.463250i | ||||
\(528\) | 0.412574i | 0.0179550i | ||||||||
\(529\) | −20.3246 | −0.883679 | ||||||||
\(530\) | 25.4871 | − | 5.42726i | 1.10709 | − | 0.235745i | ||||
\(531\) | 4.76276 | − | 2.74978i | 0.206686 | − | 0.119330i | ||||
\(532\) | −10.7194 | −0.464744 | ||||||||
\(533\) | 3.70821 | − | 6.42282i | 0.160621 | − | 0.278203i | ||||
\(534\) | 1.44149 | − | 2.49674i | 0.0623795 | − | 0.108044i | ||||
\(535\) | −19.1456 | + | 4.07690i | −0.827738 | + | 0.176260i | ||||
\(536\) | 2.71578 | − | 1.56796i | 0.117304 | − | 0.0677254i | ||||
\(537\) | 1.67844 | + | 2.90714i | 0.0724299 | + | 0.125452i | ||||
\(538\) | 10.9814 | − | 19.0203i | 0.473440 | − | 0.820022i | ||||
\(539\) | 2.72840 | − | 4.72573i | 0.117521 | − | 0.203552i | ||||
\(540\) | 2.18703 | − | 0.465711i | 0.0941149 | − | 0.0200410i | ||||
\(541\) | 21.1376i | 0.908776i | 0.890804 | + | 0.454388i | \(0.150142\pi\) | ||||
−0.890804 | + | 0.454388i | \(0.849858\pi\) | |||||||
\(542\) | −1.50615 | − | 2.60873i | −0.0646946 | − | 0.112054i | ||||
\(543\) | 8.40907 | + | 4.85498i | 0.360868 | + | 0.208347i | ||||
\(544\) | 3.26535 | 0.140001 | ||||||||
\(545\) | −16.6893 | − | 18.5216i | −0.714891 | − | 0.793379i | ||||
\(546\) | −4.95830 | + | 8.58804i | −0.212196 | + | 0.367534i | ||||
\(547\) | 12.0432 | 0.514932 | 0.257466 | − | 0.966287i | \(-0.417112\pi\) | ||||
0.257466 | + | 0.966287i | \(0.417112\pi\) | |||||||
\(548\) | −2.14262 | + | 1.23704i | −0.0915283 | + | 0.0528439i | ||||
\(549\) | − | 7.47071i | − | 0.318842i | ||||||
\(550\) | −1.88391 | + | 0.840433i | −0.0803300 | + | 0.0358362i | ||||
\(551\) | −10.9194 | − | 18.9130i | −0.465183 | − | 0.805720i | ||||
\(552\) | −1.41652 | + | 0.817829i | −0.0602911 | + | 0.0348091i | ||||
\(553\) | −20.0694 | + | 34.7613i | −0.853439 | + | 1.47820i | ||||
\(554\) | −14.5764 | −0.619292 | ||||||||
\(555\) | −10.5975 | + | 8.52601i | −0.449839 | + | 0.361909i | ||||
\(556\) | −18.9038 | −0.801701 | ||||||||
\(557\) | 9.83047 | − | 17.0269i | 0.416530 | − | 0.721452i | −0.579057 | − | 0.815287i | \(-0.696579\pi\) |
0.995588 | + | 0.0938350i | \(0.0299126\pi\) | |||||||
\(558\) | 5.64095 | − | 3.25680i | 0.238800 | − | 0.137871i | ||||
\(559\) | −10.2765 | − | 17.7994i | −0.434650 | − | 0.752836i | ||||
\(560\) | 3.10407 | − | 9.56535i | 0.131171 | − | 0.404210i | ||||
\(561\) | 1.34720i | 0.0568787i | ||||||||
\(562\) | −12.4391 | + | 7.18169i | −0.524710 | + | 0.302941i | ||||
\(563\) | 40.6424 | 1.71287 | 0.856436 | − | 0.516252i | \(-0.172673\pi\) | ||||
0.856436 | + | 0.516252i | \(0.172673\pi\) | |||||||
\(564\) | −3.35758 | + | 5.81550i | −0.141380 | + | 0.244877i | ||||
\(565\) | −2.71444 | + | 2.44590i | −0.114197 | + | 0.102900i | ||||
\(566\) | −27.0668 | −1.13770 | ||||||||
\(567\) | −3.89483 | − | 2.24868i | −0.163567 | − | 0.0944357i | ||||
\(568\) | −1.01489 | − | 1.75784i | −0.0425838 | − | 0.0737574i | ||||
\(569\) | − | 12.5423i | − | 0.525799i | −0.964823 | − | 0.262900i | \(-0.915321\pi\) | ||
0.964823 | − | 0.262900i | \(-0.0846788\pi\) | |||||||
\(570\) | −1.11001 | − | 5.21275i | −0.0464933 | − | 0.218338i | ||||
\(571\) | −19.7682 | + | 34.2396i | −0.827275 | + | 1.43288i | 0.0728934 | + | 0.997340i | \(0.476777\pi\) |
−0.900168 | + | 0.435542i | \(0.856557\pi\) | |||||||
\(572\) | 0.454859 | − | 0.787840i | 0.0190186 | − | 0.0329412i | ||||
\(573\) | 9.37630 | + | 16.2402i | 0.391701 | + | 0.678446i | ||||
\(574\) | 13.1002 | − | 7.56340i | 0.546791 | − | 0.315690i | ||||
\(575\) | −6.61992 | − | 4.80220i | −0.276070 | − | 0.200266i | ||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | −16.0103 | + | 27.7306i | −0.666516 | + | 1.15444i | 0.312356 | + | 0.949965i | \(0.398882\pi\) |
−0.978872 | + | 0.204474i | \(0.934452\pi\) | |||||||
\(578\) | −6.33751 | −0.263606 | ||||||||
\(579\) | −22.2379 | + | 12.8390i | −0.924174 | + | 0.533572i | ||||
\(580\) | 20.0388 | − | 4.26711i | 0.832068 | − | 0.177182i | ||||
\(581\) | 17.5832 | 0.729475 | ||||||||
\(582\) | 10.9274i | 0.452954i | ||||||||
\(583\) | 4.16386 | + | 2.40401i | 0.172450 | + | 0.0995639i | ||||
\(584\) | 6.57476i | 0.272065i | ||||||||
\(585\) | −4.68974 | − | 1.52188i | −0.193897 | − | 0.0629219i | ||||
\(586\) | − | 17.3721i | − | 0.717635i | ||||||
\(587\) | −23.6410 | − | 40.9474i | −0.975769 | − | 1.69008i | −0.677373 | − | 0.735639i | \(-0.736882\pi\) |
−0.298396 | − | 0.954442i | \(-0.596451\pi\) | |||||||
\(588\) | −11.4543 | + | 6.61313i | −0.472366 | + | 0.272721i | ||||
\(589\) | −7.76253 | − | 13.4451i | −0.319849 | − | 0.553995i | ||||
\(590\) | 12.0277 | − | 2.56120i | 0.495173 | − | 0.105443i | ||||
\(591\) | 17.9628 | 0.738889 | ||||||||
\(592\) | −0.339909 | + | 6.07326i | −0.0139702 | + | 0.249609i | ||||
\(593\) | − | 33.0223i | − | 1.35606i | −0.735033 | − | 0.678032i | \(-0.762833\pi\) | ||
0.735033 | − | 0.678032i | \(-0.237167\pi\) | |||||||
\(594\) | 0.357299 | + | 0.206287i | 0.0146602 | + | 0.00846406i | ||||
\(595\) | 10.1359 | − | 31.2342i | 0.415531 | − | 1.28048i | ||||
\(596\) | −3.99360 | − | 6.91711i | −0.163584 | − | 0.283336i | ||||
\(597\) | −4.06060 | − | 7.03317i | −0.166189 | − | 0.287848i | ||||
\(598\) | 3.60660 | 0.147485 | ||||||||
\(599\) | 7.17181 | + | 12.4219i | 0.293032 | + | 0.507547i | 0.974525 | − | 0.224278i | \(-0.0720024\pi\) |
−0.681493 | + | 0.731825i | \(0.738669\pi\) | |||||||
\(600\) | 4.97299 | + | 0.518977i | 0.203022 | + | 0.0211871i | ||||
\(601\) | 15.3756 | − | 26.6314i | 0.627185 | − | 1.08632i | −0.360929 | − | 0.932593i | \(-0.617540\pi\) |
0.988114 | − | 0.153723i | \(-0.0491263\pi\) | |||||||
\(602\) | − | 41.9206i | − | 1.70856i | ||||||
\(603\) | − | 3.13591i | − | 0.127704i | ||||||
\(604\) | −2.15436 | + | 3.73146i | −0.0876597 | + | 0.151831i | ||||
\(605\) | 23.0337 | + | 7.47471i | 0.936452 | + | 0.303890i | ||||
\(606\) | − | 17.2184i | − | 0.699449i | ||||||
\(607\) | −9.17110 | + | 15.8848i | −0.372243 | + | 0.644745i | −0.989910 | − | 0.141695i | \(-0.954745\pi\) |
0.617667 | + | 0.786440i | \(0.288078\pi\) | |||||||
\(608\) | −2.06416 | − | 1.19174i | −0.0837126 | − | 0.0483315i | ||||
\(609\) | −35.6866 | − | 20.6037i | −1.44610 | − | 0.834904i | ||||
\(610\) | 5.15628 | − | 15.8893i | 0.208772 | − | 0.643340i | ||||
\(611\) | 12.8231 | − | 7.40341i | 0.518766 | − | 0.299510i | ||||
\(612\) | 1.63267 | − | 2.82787i | 0.0659969 | − | 0.114310i | ||||
\(613\) | 16.8714 | + | 9.74069i | 0.681429 | + | 0.393423i | 0.800393 | − | 0.599476i | \(-0.204624\pi\) |
−0.118965 | + | 0.992899i | \(0.537957\pi\) | |||||||
\(614\) | 16.5320 | + | 9.54474i | 0.667176 | + | 0.385194i | ||||
\(615\) | 5.03458 | + | 5.58732i | 0.203014 | + | 0.225303i | ||||
\(616\) | 1.60690 | − | 0.927747i | 0.0647440 | − | 0.0373800i | ||||
\(617\) | 26.0408 | + | 15.0346i | 1.04836 | + | 0.605272i | 0.922190 | − | 0.386737i | \(-0.126398\pi\) |
0.126171 | + | 0.992008i | \(0.459731\pi\) | |||||||
\(618\) | − | 16.9033i | − | 0.679952i | ||||||
\(619\) | −25.2132 | −1.01340 | −0.506702 | − | 0.862121i | \(-0.669135\pi\) | ||||
−0.506702 | + | 0.862121i | \(0.669135\pi\) | |||||||
\(620\) | 14.2455 | − | 3.03345i | 0.572112 | − | 0.121826i | ||||
\(621\) | 1.63566i | 0.0656367i | ||||||||
\(622\) | −1.51782 | + | 0.876316i | −0.0608592 | + | 0.0351371i | ||||
\(623\) | −12.9658 | −0.519465 | ||||||||
\(624\) | −1.90957 | + | 1.10249i | −0.0764441 | + | 0.0441350i | ||||
\(625\) | 7.76047 | + | 23.7650i | 0.310419 | + | 0.950600i | ||||
\(626\) | −3.08712 | − | 5.34705i | −0.123386 | − | 0.213711i | ||||
\(627\) | 0.491681 | − | 0.851617i | 0.0196359 | − | 0.0340103i | ||||
\(628\) | 4.38347i | 0.174920i | ||||||||
\(629\) | −1.10992 | + | 19.8313i | −0.0442554 | + | 0.790725i | ||||
\(630\) | −6.73180 | − | 7.47088i | −0.268201 | − | 0.297647i | ||||
\(631\) | −3.21095 | − | 1.85384i | −0.127826 | − | 0.0738003i | 0.434724 | − | 0.900564i | \(-0.356846\pi\) |
−0.562549 | + | 0.826764i | \(0.690179\pi\) | |||||||
\(632\) | −7.72926 | + | 4.46249i | −0.307454 | + | 0.177508i | ||||
\(633\) | −7.33901 | + | 4.23718i | −0.291699 | + | 0.168413i | ||||
\(634\) | −14.2460 | + | 8.22494i | −0.565782 | + | 0.326654i | ||||
\(635\) | −13.6664 | − | 15.1668i | −0.542333 | − | 0.601876i | ||||
\(636\) | −5.82686 | − | 10.0924i | −0.231050 | − | 0.400190i | ||||
\(637\) | 29.1637 | 1.15551 | ||||||||
\(638\) | 3.27378 | + | 1.89012i | 0.129610 | + | 0.0748305i | ||||
\(639\) | −2.02978 | −0.0802969 | ||||||||
\(640\) | 1.66117 | − | 1.49683i | 0.0656635 | − | 0.0591676i | ||||
\(641\) | −21.6941 | + | 37.5752i | −0.856864 | + | 1.48413i | 0.0180408 | + | 0.999837i | \(0.494257\pi\) |
−0.874905 | + | 0.484295i | \(0.839076\pi\) | |||||||
\(642\) | 4.37708 | + | 7.58132i | 0.172750 | + | 0.299211i | ||||
\(643\) | −20.0324 | −0.790003 | −0.395001 | − | 0.918681i | \(-0.629256\pi\) | ||||
−0.395001 | + | 0.918681i | \(0.629256\pi\) | |||||||
\(644\) | 6.37061 | + | 3.67807i | 0.251037 | + | 0.144936i | ||||
\(645\) | 20.3857 | − | 4.34097i | 0.802686 | − | 0.170925i | ||||
\(646\) | −6.74018 | − | 3.89145i | −0.265189 | − | 0.153107i | ||||
\(647\) | −3.87468 | − | 6.71115i | −0.152329 | − | 0.263842i | 0.779754 | − | 0.626086i | \(-0.215344\pi\) |
−0.932083 | + | 0.362244i | \(0.882011\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | 1.96499 | + | 1.13449i | 0.0771326 | + | 0.0445325i | ||||
\(650\) | −8.92412 | − | 6.47371i | −0.350033 | − | 0.253920i | ||||
\(651\) | −25.3694 | − | 14.6470i | −0.994304 | − | 0.574062i | ||||
\(652\) | 16.0192 | 0.627360 | ||||||||
\(653\) | −16.5210 | − | 28.6152i | −0.646516 | − | 1.11980i | −0.983949 | − | 0.178449i | \(-0.942892\pi\) |
0.337433 | − | 0.941350i | \(-0.390441\pi\) | |||||||
\(654\) | −5.57487 | + | 9.65596i | −0.217995 | + | 0.377578i | ||||
\(655\) | 17.0279 | + | 18.8973i | 0.665333 | + | 0.738380i | ||||
\(656\) | 3.36348 | 0.131322 | ||||||||
\(657\) | 5.69391 | + | 3.28738i | 0.222140 | + | 0.128253i | ||||
\(658\) | 30.2005 | 1.17734 | ||||||||
\(659\) | 7.97035 | + | 13.8051i | 0.310481 | + | 0.537768i | 0.978467 | − | 0.206406i | \(-0.0661766\pi\) |
−0.667986 | + | 0.744174i | \(0.732843\pi\) | |||||||
\(660\) | 0.617555 | + | 0.685356i | 0.0240383 | + | 0.0266774i | ||||
\(661\) | 22.0245 | − | 12.7158i | 0.856653 | − | 0.494589i | −0.00623711 | − | 0.999981i | \(-0.501985\pi\) |
0.862890 | + | 0.505392i | \(0.168652\pi\) | |||||||
\(662\) | −9.69676 | + | 5.59843i | −0.376875 | + | 0.217589i | ||||
\(663\) | −6.23541 | + | 3.60002i | −0.242163 | + | 0.139813i | ||||
\(664\) | 3.38588 | + | 1.95484i | 0.131398 | + | 0.0758625i | ||||
\(665\) | −17.8067 | + | 16.0451i | −0.690515 | + | 0.622203i | ||||
\(666\) | 5.08964 | + | 3.33100i | 0.197220 | + | 0.129074i | ||||
\(667\) | 14.9868i | 0.580292i | ||||||||
\(668\) | 6.66540 | − | 11.5448i | 0.257892 | − | 0.446682i | ||||
\(669\) | −9.35953 | − | 16.2112i | −0.361860 | − | 0.626761i | ||||
\(670\) | 2.16440 | − | 6.66971i | 0.0836182 | − | 0.257674i | ||||
\(671\) | 2.66928 | − | 1.54111i | 0.103046 | − | 0.0594939i | ||||
\(672\) | −4.49736 | −0.173489 | ||||||||
\(673\) | −29.2455 | + | 16.8849i | −1.12733 | + | 0.650866i | −0.943263 | − | 0.332047i | \(-0.892261\pi\) |
−0.184070 | + | 0.982913i | \(0.558927\pi\) | |||||||
\(674\) | − | 30.7340i | − | 1.18383i | ||||||
\(675\) | 2.93594 | − | 4.04725i | 0.113005 | − | 0.155779i | ||||
\(676\) | −8.13804 | −0.313002 | ||||||||
\(677\) | 15.8792i | 0.610288i | 0.952306 | + | 0.305144i | \(0.0987045\pi\) | ||||
−0.952306 | + | 0.305144i | \(0.901295\pi\) | |||||||
\(678\) | 1.41513 | + | 0.817025i | 0.0543477 | + | 0.0313777i | ||||
\(679\) | 42.5602 | − | 24.5721i | 1.63331 | − | 0.942992i | ||||
\(680\) | 5.42430 | − | 4.88768i | 0.208012 | − | 0.187434i | ||||
\(681\) | 3.89408 | + | 2.24825i | 0.149222 | + | 0.0861531i | ||||
\(682\) | 2.32731 | + | 1.34367i | 0.0891172 | + | 0.0514518i | ||||
\(683\) | −16.4618 | + | 28.5127i | −0.629894 | + | 1.09101i | 0.357678 | + | 0.933845i | \(0.383569\pi\) |
−0.987572 | + | 0.157164i | \(0.949765\pi\) | |||||||
\(684\) | −2.06416 | + | 1.19174i | −0.0789250 | + | 0.0455674i | ||||
\(685\) | −1.70761 | + | 5.26209i | −0.0652445 | + | 0.201054i | ||||
\(686\) | 24.2502 | + | 14.0009i | 0.925877 | + | 0.534555i | ||||
\(687\) | 17.6353 | + | 10.1818i | 0.672829 | + | 0.388458i | ||||
\(688\) | 4.66058 | − | 8.07236i | 0.177683 | − | 0.307756i | ||||
\(689\) | 25.6962i | 0.978949i | ||||||||
\(690\) | −1.12893 | + | 3.47885i | −0.0429776 | + | 0.132438i | ||||
\(691\) | −18.6030 | + | 32.2214i | −0.707693 | + | 1.22576i | 0.258018 | + | 0.966140i | \(0.416930\pi\) |
−0.965711 | + | 0.259619i | \(0.916403\pi\) | |||||||
\(692\) | − | 25.4580i | − | 0.967768i | ||||||
\(693\) | − | 1.85549i | − | 0.0704844i | ||||||
\(694\) | 3.25518 | − | 5.63813i | 0.123565 | − | 0.214020i | ||||
\(695\) | −31.4025 | + | 28.2959i | −1.19116 | + | 1.07332i | ||||
\(696\) | −4.58129 | − | 7.93502i | −0.173653 | − | 0.300776i | ||||
\(697\) | 10.9829 | 0.416008 | ||||||||
\(698\) | −5.75901 | − | 9.97489i | −0.217982 | − | 0.377555i | ||||
\(699\) | −1.47036 | − | 2.54674i | −0.0556142 | − | 0.0963266i | ||||
\(700\) | −9.16135 | − | 20.5360i | −0.346266 | − | 0.776187i | ||||
\(701\) | 7.57252 | + | 4.37200i | 0.286010 | + | 0.165128i | 0.636141 | − | 0.771573i | \(-0.280530\pi\) |
−0.350131 | + | 0.936701i | \(0.613863\pi\) | |||||||
\(702\) | 2.20498i | 0.0832218i | ||||||||
\(703\) | 7.93938 | − | 12.1311i | 0.299439 | − | 0.457532i | ||||
\(704\) | 0.412574 | 0.0155495 | ||||||||
\(705\) | 3.12732 | + | 14.6863i | 0.117782 | + | 0.553117i | ||||
\(706\) | −13.7639 | − | 23.8398i | −0.518012 | − | 0.897224i | ||||
\(707\) | −67.0627 | + | 38.7187i | −2.52215 | + | 1.45617i | ||||
\(708\) | −2.74978 | − | 4.76276i | −0.103343 | − | 0.178995i | ||||
\(709\) | − | 8.59568i | − | 0.322817i | −0.986888 | − | 0.161409i | \(-0.948396\pi\) | ||
0.986888 | − | 0.161409i | \(-0.0516037\pi\) | |||||||
\(710\) | −4.31710 | − | 1.40095i | −0.162018 | − | 0.0525768i | ||||
\(711\) | 8.92498i | 0.334713i | ||||||||
\(712\) | −2.49674 | − | 1.44149i | −0.0935692 | − | 0.0540222i | ||||
\(713\) | 10.6540i | 0.398996i | ||||||||
\(714\) | −14.6854 | −0.549589 | ||||||||
\(715\) | −0.423666 | − | 1.98959i | −0.0158442 | − | 0.0744063i | ||||
\(716\) | 2.90714 | − | 1.67844i | 0.108645 | − | 0.0627261i | ||||
\(717\) | −9.25083 | −0.345478 | ||||||||
\(718\) | 5.21568 | − | 9.03383i | 0.194648 | − | 0.337139i | ||||
\(719\) | −18.9145 | + | 32.7608i | −0.705391 | + | 1.22177i | 0.261160 | + | 0.965296i | \(0.415895\pi\) |
−0.966550 | + | 0.256477i | \(0.917438\pi\) | |||||||
\(720\) | −0.465711 | − | 2.18703i | −0.0173560 | − | 0.0815059i | ||||
\(721\) | −65.8356 | + | 38.0102i | −2.45185 | + | 1.41557i | ||||
\(722\) | −6.65951 | − | 11.5346i | −0.247841 | − | 0.429273i | ||||
\(723\) | 0.399045 | − | 0.691167i | 0.0148407 | − | 0.0257048i | ||||
\(724\) | 4.85498 | − | 8.40907i | 0.180434 | − | 0.312521i | ||||
\(725\) | 26.9008 | − | 37.0832i | 0.999071 | − | 1.37724i | ||||
\(726\) | − | 10.8298i | − | 0.401931i | ||||||
\(727\) | 11.9500 | + | 20.6980i | 0.443200 | + | 0.767646i | 0.997925 | − | 0.0643884i | \(-0.0205096\pi\) |
−0.554724 | + | 0.832034i | \(0.687176\pi\) | |||||||
\(728\) | 8.58804 | + | 4.95830i | 0.318294 | + | 0.183767i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 9.84132 | + | 10.9218i | 0.364244 | + | 0.404234i | ||||
\(731\) | 15.2184 | − | 26.3591i | 0.562873 | − | 0.974925i | ||||
\(732\) | −7.47071 | −0.276125 | ||||||||
\(733\) | −18.4978 | + | 10.6797i | −0.683233 | + | 0.394465i | −0.801072 | − | 0.598568i | \(-0.795737\pi\) |
0.117839 | + | 0.993033i | \(0.462403\pi\) | |||||||
\(734\) | − | 8.02271i | − | 0.296124i | ||||||
\(735\) | −9.12875 | + | 28.1307i | −0.336719 | + | 1.03762i | ||||
\(736\) | 0.817829 | + | 1.41652i | 0.0301456 | + | 0.0522137i | ||||
\(737\) | 1.12046 | − | 0.646898i | 0.0412727 | − | 0.0238288i | ||||
\(738\) | 1.68174 | − | 2.91286i | 0.0619058 | − | 0.107224i | ||||
\(739\) | 40.7382 | 1.49858 | 0.749289 | − | 0.662243i | \(-0.230396\pi\) | ||||
0.749289 | + | 0.662243i | \(0.230396\pi\) | |||||||
\(740\) | 8.52601 | + | 10.5975i | 0.313422 | + | 0.389572i | ||||
\(741\) | 5.25554 | 0.193067 | ||||||||
\(742\) | −26.2055 | + | 45.3892i | −0.962033 | + | 1.66629i | ||||
\(743\) | −17.7672 | + | 10.2579i | −0.651816 | + | 0.376326i | −0.789152 | − | 0.614199i | \(-0.789479\pi\) |
0.137336 | + | 0.990525i | \(0.456146\pi\) | |||||||
\(744\) | −3.25680 | − | 5.64095i | −0.119400 | − | 0.206807i | ||||
\(745\) | −16.9878 | − | 5.51275i | −0.622385 | − | 0.201972i | ||||
\(746\) | 23.4585i | 0.858878i | ||||||||
\(747\) | 3.38588 | − | 1.95484i | 0.123883 | − | 0.0715238i | ||||
\(748\) | 1.34720 | 0.0492584 | ||||||||
\(749\) | 19.6853 | − | 34.0959i | 0.719285 | − | 1.24584i | ||||
\(750\) | 9.03781 | − | 6.58164i | 0.330014 | − | 0.240327i | ||||
\(751\) | 37.7421 | 1.37723 | 0.688614 | − | 0.725128i | \(-0.258219\pi\) | ||||
0.688614 | + | 0.725128i | \(0.258219\pi\) | |||||||
\(752\) | 5.81550 | + | 3.35758i | 0.212069 | + | 0.122438i | ||||
\(753\) | 6.87828 | + | 11.9135i | 0.250658 | + | 0.434153i | ||||
\(754\) | 20.2033i | 0.735762i | ||||||||
\(755\) | 2.00662 | + | 9.42331i | 0.0730283 | + | 0.342949i | ||||
\(756\) | −2.24868 | + | 3.89483i | −0.0817837 | + | 0.141654i | ||||
\(757\) | 16.4384 | − | 28.4721i | 0.597462 | − | 1.03484i | −0.395732 | − | 0.918366i | \(-0.629509\pi\) |
0.993194 | − | 0.116469i | \(-0.0371576\pi\) | |||||||
\(758\) | −8.83500 | − | 15.3027i | −0.320901 | − | 0.555818i | ||||
\(759\) | −0.584420 | + | 0.337415i | −0.0212131 | + | 0.0122474i | ||||
\(760\) | −5.21275 | + | 1.11001i | −0.189086 | + | 0.0402644i | ||||
\(761\) | 9.42311 | − | 16.3213i | 0.341587 | − | 0.591647i | −0.643140 | − | 0.765748i | \(-0.722369\pi\) |
0.984728 | + | 0.174102i | \(0.0557021\pi\) | |||||||
\(762\) | −4.56509 | + | 7.90697i | −0.165376 | + | 0.286439i | ||||
\(763\) | 50.1444 | 1.81535 | ||||||||
\(764\) | 16.2402 | − | 9.37630i | 0.587551 | − | 0.339223i | ||||
\(765\) | −1.52071 | − | 7.14142i | −0.0549813 | − | 0.258199i | ||||
\(766\) | −23.6721 | −0.855306 | ||||||||
\(767\) | 12.1264i | 0.437860i | ||||||||
\(768\) | −0.866025 | − | 0.500000i | −0.0312500 | − | 0.0180422i | ||||
\(769\) | − | 11.5220i | − | 0.415493i | −0.978183 | − | 0.207746i | \(-0.933387\pi\) | ||
0.978183 | − | 0.207746i | \(-0.0666129\pi\) | |||||||
\(770\) | 1.28066 | − | 3.94642i | 0.0461518 | − | 0.142219i | ||||
\(771\) | 19.2329i | 0.692656i | ||||||||
\(772\) | 12.8390 | + | 22.2379i | 0.462087 | + | 0.800358i | ||||
\(773\) | −22.3027 | + | 12.8765i | −0.802173 | + | 0.463135i | −0.844230 | − | 0.535980i | \(-0.819942\pi\) |
0.0420574 | + | 0.999115i | \(0.486609\pi\) | |||||||
\(774\) | −4.66058 | − | 8.07236i | −0.167521 | − | 0.290155i | ||||
\(775\) | 19.1236 | − | 26.3622i | 0.686939 | − | 0.946958i | ||||
\(776\) | 10.9274 | 0.392269 | ||||||||
\(777\) | 1.52869 | − | 27.3136i | 0.0548415 | − | 0.979871i | ||||
\(778\) | − | 14.3144i | − | 0.513198i | ||||||
\(779\) | −6.94276 | − | 4.00840i | −0.248750 | − | 0.143616i | ||||
\(780\) | −1.52188 | + | 4.68974i | −0.0544920 | + | 0.167920i | ||||
\(781\) | −0.418717 | − | 0.725240i | −0.0149829 | − | 0.0259511i | ||||
\(782\) | 2.67049 | + | 4.62543i | 0.0954967 | + | 0.165405i | ||||
\(783\) | −9.16257 | −0.327444 | ||||||||
\(784\) | 6.61313 | + | 11.4543i | 0.236183 | + | 0.409081i | ||||
\(785\) | 6.56133 | + | 7.28170i | 0.234184 | + | 0.259895i | ||||
\(786\) | 5.68796 | − | 9.85183i | 0.202883 | − | 0.351403i | ||||
\(787\) | − | 44.7546i | − | 1.59533i | −0.603102 | − | 0.797664i | \(-0.706069\pi\) | ||
0.603102 | − | 0.797664i | \(-0.293931\pi\) | |||||||
\(788\) | − | 17.9628i | − | 0.639897i | ||||||
\(789\) | 2.91945 | − | 5.05664i | 0.103935 | − | 0.180021i | ||||
\(790\) | −6.16002 | + | 18.9824i | −0.219164 | + | 0.675363i | ||||
\(791\) | − | 7.34892i | − | 0.261297i | ||||||
\(792\) | 0.206287 | − | 0.357299i | 0.00733009 | − | 0.0126961i | ||||
\(793\) | 14.2659 | + | 8.23640i | 0.506596 | + | 0.292483i | ||||
\(794\) | −26.1900 | − | 15.1208i | −0.929448 | − | 0.536617i | ||||
\(795\) | −24.7861 | − | 8.04338i | −0.879071 | − | 0.285269i | ||||
\(796\) | −7.03317 | + | 4.06060i | −0.249284 | + | 0.143924i | ||||
\(797\) | 25.3243 | − | 43.8629i | 0.897031 | − | 1.55370i | 0.0657607 | − | 0.997835i | \(-0.479053\pi\) |
0.831270 | − | 0.555868i | \(-0.187614\pi\) | |||||||
\(798\) | 9.28325 | + | 5.35969i | 0.328624 | + | 0.189731i | ||||
\(799\) | 18.9896 | + | 10.9637i | 0.671804 | + | 0.387866i | ||||
\(800\) | 0.518977 | − | 4.97299i | 0.0183486 | − | 0.175822i | ||||
\(801\) | −2.49674 | + | 1.44149i | −0.0882179 | + | 0.0509326i | ||||
\(802\) | 2.85841 | + | 1.65030i | 0.100934 | + | 0.0582742i | ||||
\(803\) | 2.71257i | 0.0957246i | ||||||||
\(804\) | −3.13591 | −0.110595 | ||||||||
\(805\) | 16.0881 | − | 3.42583i | 0.567032 | − | 0.120745i | ||||
\(806\) | 14.3624i | 0.505894i | ||||||||
\(807\) | −19.0203 | + | 10.9814i | −0.669545 | + | 0.386562i | ||||
\(808\) | −17.2184 | −0.605741 | ||||||||
\(809\) | 30.4793 | − | 17.5972i | 1.07160 | − | 0.618686i | 0.142979 | − | 0.989726i | \(-0.454332\pi\) |
0.928617 | + | 0.371040i | \(0.120999\pi\) | |||||||
\(810\) | −2.12688 | − | 0.690199i | −0.0747310 | − | 0.0242511i | ||||
\(811\) | −24.7519 | − | 42.8716i | −0.869158 | − | 1.50543i | −0.862858 | − | 0.505446i | \(-0.831328\pi\) |
−0.00629997 | − | 0.999980i | \(-0.502005\pi\) | |||||||
\(812\) | −20.6037 | + | 35.6866i | −0.723048 | + | 1.25236i | ||||
\(813\) | 3.01230i | 0.105646i | ||||||||
\(814\) | −0.140237 | + | 2.50567i | −0.00491532 | + | 0.0878236i | ||||
\(815\) | 26.6106 | − | 23.9781i | 0.932129 | − | 0.839915i | ||||
\(816\) | −2.82787 | − | 1.63267i | −0.0989953 | − | 0.0571550i | ||||
\(817\) | −19.2403 | + | 11.1084i | −0.673134 | + | 0.388634i | ||||
\(818\) | 24.6098 | − | 14.2085i | 0.860463 | − | 0.496789i | ||||
\(819\) | 8.58804 | − | 4.95830i | 0.300090 | − | 0.173257i | ||||
\(820\) | 5.58732 | − | 5.03458i | 0.195118 | − | 0.175815i | ||||
\(821\) | 12.3439 | + | 21.3802i | 0.430804 | + | 0.746174i | 0.996943 | − | 0.0781356i | \(-0.0248967\pi\) |
−0.566139 | + | 0.824310i | \(0.691563\pi\) | |||||||
\(822\) | 2.47409 | 0.0862937 | ||||||||
\(823\) | −19.9965 | − | 11.5450i | −0.697036 | − | 0.402434i | 0.109207 | − | 0.994019i | \(-0.465169\pi\) |
−0.806242 | + | 0.591585i | \(0.798502\pi\) | |||||||
\(824\) | −16.9033 | −0.588856 | ||||||||
\(825\) | 2.05173 | + | 0.214116i | 0.0714320 | + | 0.00745458i | ||||
\(826\) | −12.3667 | + | 21.4198i | −0.430294 | + | 0.745291i | ||||
\(827\) | −26.9683 | − | 46.7104i | −0.937779 | − | 1.62428i | −0.769603 | − | 0.638523i | \(-0.779546\pi\) |
−0.168176 | − | 0.985757i | \(-0.553788\pi\) | |||||||
\(828\) | 1.63566 | 0.0568430 | ||||||||
\(829\) | 4.52451 | + | 2.61222i | 0.157143 | + | 0.0907263i | 0.576509 | − | 0.817091i | \(-0.304414\pi\) |
−0.419367 | + | 0.907817i | \(0.637748\pi\) | |||||||
\(830\) | 8.55059 | − | 1.82078i | 0.296795 | − | 0.0632002i | ||||
\(831\) | 12.6235 | + | 7.28820i | 0.437905 | + | 0.252825i | ||||
\(832\) | 1.10249 | + | 1.90957i | 0.0382220 | + | 0.0662025i | ||||
\(833\) | 21.5941 | + | 37.4022i | 0.748193 | + | 1.29591i | ||||
\(834\) | 16.3712 | + | 9.45191i | 0.566888 | + | 0.327293i | ||||
\(835\) | −6.20830 | − | 29.1549i | −0.214847 | − | 1.00895i | ||||
\(836\) | −0.851617 | − | 0.491681i | −0.0294538 | − | 0.0170052i | ||||
\(837\) | −6.51360 | −0.225143 | ||||||||
\(838\) | 2.15871 | + | 3.73900i | 0.0745715 | + | 0.129162i | ||||
\(839\) | 9.37644 | − | 16.2405i | 0.323711 | − | 0.560684i | −0.657540 | − | 0.753420i | \(-0.728403\pi\) |
0.981251 | + | 0.192736i | \(0.0617362\pi\) | |||||||
\(840\) | −7.47088 | + | 6.73180i | −0.257770 | + | 0.232269i | ||||
\(841\) | −54.9527 | −1.89492 | ||||||||
\(842\) | −27.0364 | − | 15.6095i | −0.931736 | − | 0.537938i | ||||
\(843\) | 14.3634 | 0.494701 | ||||||||
\(844\) | 4.23718 | + | 7.33901i | 0.145850 | + | 0.252619i | ||||
\(845\) | −13.5187 | + | 12.1813i | −0.465057 | + | 0.419049i | ||||
\(846\) | 5.81550 | − | 3.35758i | 0.199941 | − | 0.115436i | ||||
\(847\) | −42.1801 | + | 24.3527i | −1.44933 | + | 0.836769i | ||||
\(848\) | −10.0924 | + | 5.82686i | −0.346575 | + | 0.200095i | ||||
\(849\) | 23.4405 | + | 13.5334i | 0.804478 | + | 0.464465i | ||||
\(850\) | 1.69464 | − | 16.2385i | 0.0581257 | − | 0.556977i | ||||
\(851\) | −8.88089 | + | 4.48540i | −0.304433 | + | 0.153757i | ||||
\(852\) | 2.02978i | 0.0695391i | ||||||||
\(853\) | −13.8286 | + | 23.9518i | −0.473482 | + | 0.820095i | −0.999539 | − | 0.0303541i | \(-0.990337\pi\) |
0.526057 | + | 0.850449i | \(0.323670\pi\) | |||||||
\(854\) | 16.7992 | + | 29.0971i | 0.574858 | + | 0.995683i | ||||
\(855\) | −1.64508 | + | 5.06938i | −0.0562605 | + | 0.173369i | ||||
\(856\) | 7.58132 | − | 4.37708i | 0.259124 | − | 0.149605i | ||||
\(857\) | 45.7437 | 1.56257 | 0.781287 | − | 0.624172i | \(-0.214563\pi\) | ||||
0.781287 | + | 0.624172i | \(0.214563\pi\) | |||||||
\(858\) | −0.787840 | + | 0.454859i | −0.0268964 | + | 0.0155286i | ||||
\(859\) | − | 38.2079i | − | 1.30364i | −0.758375 | − | 0.651819i | \(-0.774006\pi\) | ||
0.758375 | − | 0.651819i | \(-0.225994\pi\) | |||||||
\(860\) | −4.34097 | − | 20.3857i | −0.148026 | − | 0.695146i | ||||
\(861\) | −15.1268 | −0.515520 | ||||||||
\(862\) | 22.5523i | 0.768135i | ||||||||
\(863\) | 0.812686 | + | 0.469204i | 0.0276642 | + | 0.0159719i | 0.513768 | − | 0.857929i | \(-0.328249\pi\) |
−0.486104 | + | 0.873901i | \(0.661582\pi\) | |||||||
\(864\) | −0.866025 | + | 0.500000i | −0.0294628 | + | 0.0170103i | ||||
\(865\) | −38.1064 | − | 42.2901i | −1.29566 | − | 1.43791i | ||||
\(866\) | 2.65145 | + | 1.53082i | 0.0901001 | + | 0.0520193i | ||||
\(867\) | 5.48845 | + | 3.16876i | 0.186397 | + | 0.107617i | ||||
\(868\) | −14.6470 | + | 25.3694i | −0.497152 | + | 0.861093i | ||||
\(869\) | −3.18889 | + | 1.84111i | −0.108176 | + | 0.0624553i | ||||
\(870\) | −19.4877 | − | 6.32400i | −0.660695 | − | 0.214404i | ||||
\(871\) | 5.98825 | + | 3.45732i | 0.202904 | + | 0.117147i | ||||
\(872\) | 9.65596 | + | 5.57487i | 0.326992 | + | 0.188789i | ||||
\(873\) | 5.46368 | − | 9.46337i | 0.184918 | − | 0.320287i | ||||
\(874\) | − | 3.89856i | − | 0.131871i | ||||||
\(875\) | −45.9575 | − | 20.4007i | −1.55365 | − | 0.689671i | ||||
\(876\) | 3.28738 | − | 5.69391i | 0.111070 | − | 0.192379i | ||||
\(877\) | 7.26127i | 0.245196i | 0.992456 | + | 0.122598i | \(0.0391225\pi\) | ||||
−0.992456 | + | 0.122598i | \(0.960877\pi\) | |||||||
\(878\) | 3.85649i | 0.130150i | ||||||||
\(879\) | −8.68606 | + | 15.0447i | −0.292973 | + | 0.507445i | ||||
\(880\) | 0.685356 | − | 0.617555i | 0.0231033 | − | 0.0208178i | ||||
\(881\) | −20.2490 | − | 35.0723i | −0.682206 | − | 1.18161i | −0.974306 | − | 0.225227i | \(-0.927688\pi\) |
0.292101 | − | 0.956388i | \(-0.405646\pi\) | |||||||
\(882\) | 13.2263 | 0.445351 | ||||||||
\(883\) | 20.9204 | + | 36.2352i | 0.704028 | + | 1.21941i | 0.967041 | + | 0.254619i | \(0.0819502\pi\) |
−0.263014 | + | 0.964792i | \(0.584716\pi\) | |||||||
\(884\) | 3.60002 | + | 6.23541i | 0.121082 | + | 0.209720i | ||||
\(885\) | −11.6969 | − | 3.79579i | −0.393187 | − | 0.127594i | ||||
\(886\) | 22.0065 | + | 12.7054i | 0.739322 | + | 0.426848i | ||||
\(887\) | 45.9708i | 1.54355i | 0.635896 | + | 0.771775i | \(0.280631\pi\) | ||||
−0.635896 | + | 0.771775i | \(0.719369\pi\) | |||||||
\(888\) | 3.33100 | − | 5.08964i | 0.111781 | − | 0.170797i | ||||
\(889\) | 41.0617 | 1.37717 | ||||||||
\(890\) | −6.30518 | + | 1.34264i | −0.211350 | + | 0.0450053i | ||||
\(891\) | −0.206287 | − | 0.357299i | −0.00691087 | − | 0.0119700i | ||||
\(892\) | −16.2112 | + | 9.35953i | −0.542791 | + | 0.313380i | ||||
\(893\) | −8.00273 | − | 13.8611i | −0.267801 | − | 0.463845i | ||||
\(894\) | 7.98719i | 0.267132i | ||||||||
\(895\) | 2.31691 | − | 7.13967i | 0.0774458 | − | 0.238653i | ||||
\(896\) | 4.49736i | 0.150246i | ||||||||
\(897\) | −3.12341 | − | 1.80330i | −0.104288 | − | 0.0602104i | ||||
\(898\) | 34.4379i | 1.14921i | ||||||||
\(899\) | −59.6814 | −1.99048 | ||||||||
\(900\) | −4.04725 | − | 2.93594i | −0.134908 | − | 0.0978648i | ||||
\(901\) | −32.9552 | + | 19.0267i | −1.09790 | + | 0.633871i | ||||
\(902\) | 1.38769 | 0.0462049 | ||||||||
\(903\) | −20.9603 | + | 36.3043i | −0.697516 | + | 1.20813i | ||||
\(904\) | 0.817025 | − | 1.41513i | 0.0271739 | − | 0.0470665i | ||||
\(905\) | −4.52203 | − | 21.2360i | −0.150317 | − | 0.705909i | ||||
\(906\) | 3.73146 | − | 2.15436i | 0.123969 | − | 0.0715738i | ||||
\(907\) | −22.9264 | − | 39.7096i | −0.761257 | − | 1.31854i | −0.942203 | − | 0.335043i | \(-0.891249\pi\) |
0.180945 | − | 0.983493i | \(-0.442084\pi\) | |||||||
\(908\) | 2.24825 | − | 3.89408i | 0.0746108 | − | 0.129230i | ||||
\(909\) | −8.60920 | + | 14.9116i | −0.285549 | + | 0.494585i | ||||
\(910\) | 21.6880 | − | 4.61827i | 0.718949 | − | 0.153094i | ||||
\(911\) | − | 27.2436i | − | 0.902621i | −0.892367 | − | 0.451311i | \(-0.850957\pi\) | ||
0.892367 | − | 0.451311i | \(-0.149043\pi\) | |||||||
\(912\) | 1.19174 | + | 2.06416i | 0.0394625 | + | 0.0683510i | ||||
\(913\) | 1.39693 | + | 0.806515i | 0.0462315 | + | 0.0266918i | ||||
\(914\) | 1.36285 | 0.0450792 | ||||||||
\(915\) | −12.4101 | + | 11.1824i | −0.410266 | + | 0.369679i | ||||
\(916\) | 10.1818 | − | 17.6353i | 0.336415 | − | 0.582687i | ||||
\(917\) | −51.1616 | −1.68950 | ||||||||
\(918\) | −2.82787 | + | 1.63267i | −0.0933337 | + | 0.0538862i | ||||
\(919\) | 8.75052i | 0.288653i | 0.989530 | + | 0.144326i | \(0.0461015\pi\) | ||||
−0.989530 | + | 0.144326i | \(0.953898\pi\) | |||||||
\(920\) | 3.47885 | + | 1.12893i | 0.114694 | + | 0.0372197i | ||||
\(921\) | −9.54474 | − | 16.5320i | −0.314510 | − | 0.544747i | ||||
\(922\) | 10.7687 | − | 6.21733i | 0.354649 | − | 0.204757i | ||||
\(923\) | 2.23782 | − | 3.87601i | 0.0736586 | − | 0.127581i | ||||
\(924\) | −1.85549 | −0.0610413 | ||||||||
\(925\) | 30.0259 | + | 4.84224i | 0.987244 | + | 0.159212i | ||||
\(926\) | 4.66091 | 0.153167 | ||||||||
\(927\) | −8.45167 | + | 14.6387i | −0.277589 | + | 0.480799i | ||||
\(928\) | −7.93502 | + | 4.58129i | −0.260480 | + | 0.150388i | ||||
\(929\) | 9.61913 | + | 16.6608i | 0.315593 | + | 0.546624i | 0.979563 | − | 0.201135i | \(-0.0644631\pi\) |
−0.663970 | + | 0.747759i | \(0.731130\pi\) | |||||||
\(930\) | −13.8537 | − | 4.49568i | −0.454280 | − | 0.147419i | ||||
\(931\) | − | 31.5245i | − | 1.03318i | ||||||
\(932\) | −2.54674 | + | 1.47036i | −0.0834213 | + | 0.0481633i | ||||
\(933\) | 1.75263 | 0.0573786 | ||||||||
\(934\) | −12.4782 | + | 21.6129i | −0.408299 | + | 0.707194i | ||||
\(935\) | 2.23792 | − | 2.01653i | 0.0731879 | − | 0.0659476i | ||||
\(936\) | 2.20498 | 0.0720722 | ||||||||
\(937\) | −22.5574 | − | 13.0235i | −0.736917 | − | 0.425459i | 0.0840301 | − | 0.996463i | \(-0.473221\pi\) |
−0.820947 | + | 0.571004i | \(0.806554\pi\) | |||||||
\(938\) | 7.05166 | + | 12.2138i | 0.230245 | + | 0.398796i | ||||
\(939\) | 6.17425i | 0.201489i | ||||||||
\(940\) | 14.6863 | − | 3.12732i | 0.479013 | − | 0.102002i | ||||
\(941\) | −0.822234 | + | 1.42415i | −0.0268041 | + | 0.0464260i | −0.879116 | − | 0.476607i | \(-0.841866\pi\) |
0.852312 | + | 0.523033i | \(0.175200\pi\) | |||||||
\(942\) | 2.19174 | − | 3.79620i | 0.0714107 | − | 0.123687i | ||||
\(943\) | 2.75075 | + | 4.76445i | 0.0895769 | + | 0.155152i | ||||
\(944\) | −4.76276 | + | 2.74978i | −0.155015 | + | 0.0894977i | ||||
\(945\) | 2.09447 | + | 9.83588i | 0.0681331 | + | 0.319961i | ||||
\(946\) | 1.92283 | − | 3.33045i | 0.0625167 | − | 0.108282i | ||||
\(947\) | −20.1455 | + | 34.8931i | −0.654641 | + | 1.13387i | 0.327342 | + | 0.944906i | \(0.393847\pi\) |
−0.981984 | + | 0.188966i | \(0.939486\pi\) | |||||||
\(948\) | 8.92498 | 0.289870 | ||||||||
\(949\) | −12.5550 | + | 7.24862i | −0.407552 | + | 0.235300i | ||||
\(950\) | −6.99777 | + | 9.64655i | −0.227038 | + | 0.312975i | ||||
\(951\) | 16.4499 | 0.533424 | ||||||||
\(952\) | 14.6854i | 0.475958i | ||||||||
\(953\) | −17.7933 | − | 10.2730i | −0.576381 | − | 0.332774i | 0.183313 | − | 0.983055i | \(-0.441318\pi\) |
−0.759694 | + | 0.650281i | \(0.774651\pi\) | |||||||
\(954\) | 11.6537i | 0.377303i | ||||||||
\(955\) | 12.9430 | − | 39.8846i | 0.418827 | − | 1.29063i | ||||
\(956\) | 9.25083i | 0.299193i | ||||||||
\(957\) | −1.89012 | − | 3.27378i | −0.0610989 | − | 0.105826i | ||||
\(958\) | 10.0078 | − | 5.77801i | 0.323338 | − | 0.186679i | ||||
\(959\) | −5.56343 | − | 9.63615i | −0.179653 | − | 0.311167i | ||||
\(960\) | −2.18703 | + | 0.465711i | −0.0705862 | + | 0.0150307i | ||||
\(961\) | −11.4270 | −0.368614 | ||||||||
\(962\) | −11.9721 | + | 6.04664i | −0.385995 | + | 0.194951i | ||||
\(963\) | − | 8.75416i | − | 0.282099i | ||||||
\(964\) | −0.691167 | − | 0.399045i | −0.0222610 | − | 0.0128524i | ||||
\(965\) | 54.6142 | + | 17.7230i | 1.75809 | + | 0.570523i | ||||
\(966\) | −3.67807 | − | 6.37061i | −0.118340 | − | 0.204971i | ||||
\(967\) | −22.3500 | − | 38.7114i | −0.718729 | − | 1.24487i | −0.961504 | − | 0.274792i | \(-0.911391\pi\) |
0.242775 | − | 0.970083i | \(-0.421942\pi\) | |||||||
\(968\) | −10.8298 | −0.348082 | ||||||||
\(969\) | 3.89145 | + | 6.74018i | 0.125011 | + | 0.216526i | ||||
\(970\) | 18.1522 | − | 16.3564i | 0.582832 | − | 0.525174i | ||||
\(971\) | −0.443756 | + | 0.768607i | −0.0142408 | + | 0.0246658i | −0.873058 | − | 0.487616i | \(-0.837866\pi\) |
0.858817 | + | 0.512282i | \(0.171200\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | − | 85.0173i | − | 2.72553i | ||||||
\(974\) | −17.3938 | + | 30.1270i | −0.557334 | + | 0.965331i | ||||
\(975\) | 4.49166 | + | 10.0685i | 0.143848 | + | 0.322449i | ||||
\(976\) | 7.47071i | 0.239132i | ||||||||
\(977\) | −7.95604 | + | 13.7803i | −0.254536 | + | 0.440870i | −0.964769 | − | 0.263097i | \(-0.915256\pi\) |
0.710233 | + | 0.703967i | \(0.248590\pi\) | |||||||
\(978\) | −13.8730 | − | 8.00959i | −0.443610 | − | 0.256119i | ||||
\(979\) | −1.03009 | − | 0.594722i | −0.0329218 | − | 0.0190074i | ||||
\(980\) | 28.1307 | + | 9.12875i | 0.898601 | + | 0.291607i | ||||
\(981\) | 9.65596 | − | 5.57487i | 0.308291 | − | 0.177992i | ||||
\(982\) | −2.28027 | + | 3.94955i | −0.0727664 | + | 0.126035i | ||||
\(983\) | −14.3688 | − | 8.29582i | −0.458293 | − | 0.264596i | 0.253033 | − | 0.967458i | \(-0.418572\pi\) |
−0.711326 | + | 0.702862i | \(0.751905\pi\) | |||||||
\(984\) | −2.91286 | − | 1.68174i | −0.0928587 | − | 0.0536120i | ||||
\(985\) | −26.8873 | − | 29.8392i | −0.856699 | − | 0.950756i | ||||
\(986\) | −25.9106 | + | 14.9595i | −0.825161 | + | 0.476407i | ||||
\(987\) | −26.1544 | − | 15.1002i | −0.832504 | − | 0.480646i | ||||
\(988\) | − | 5.25554i | − | 0.167201i | ||||||
\(989\) | 15.2462 | 0.484802 | ||||||||
\(990\) | −0.192140 | − | 0.902313i | −0.00610661 | − | 0.0286774i | ||||
\(991\) | − | 12.0478i | − | 0.382710i | −0.981521 | − | 0.191355i | \(-0.938712\pi\) | ||
0.981521 | − | 0.191355i | \(-0.0612882\pi\) | |||||||
\(992\) | −5.64095 | + | 3.25680i | −0.179100 | + | 0.103404i | ||||
\(993\) | 11.1969 | 0.355321 | ||||||||
\(994\) | 7.90565 | − | 4.56433i | 0.250752 | − | 0.144772i | ||||
\(995\) | −5.60525 | + | 17.2728i | −0.177698 | + | 0.547586i | ||||
\(996\) | −1.95484 | − | 3.38588i | −0.0619414 | − | 0.107286i | ||||
\(997\) | −10.4395 | + | 18.0817i | −0.330621 | + | 0.572653i | −0.982634 | − | 0.185555i | \(-0.940592\pi\) |
0.652013 | + | 0.758208i | \(0.273925\pi\) | |||||||
\(998\) | 3.99316i | 0.126401i | ||||||||
\(999\) | −2.74226 | − | 5.42955i | −0.0867613 | − | 0.171783i |
(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 | 1110.2.ba.a.619.12 | yes | 36 | |
5.4 | even | 2 | 1110.2.ba.b.619.7 | yes | 36 | ||
37.11 | even | 6 | 1110.2.ba.b.529.7 | yes | 36 | ||
185.159 | even | 6 | inner | 1110.2.ba.a.529.12 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.ba.a.529.12 | ✓ | 36 | 185.159 | even | 6 | inner | |
1110.2.ba.a.619.12 | yes | 36 | 1.1 | even | 1 | trivial | |
1110.2.ba.b.529.7 | yes | 36 | 37.11 | even | 6 | ||
1110.2.ba.b.619.7 | yes | 36 | 5.4 | even | 2 |