Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [240,2,Mod(61,240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(240, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("240.61");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 240 = 2^{4} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 240.s (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.91640964851\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{18} - 4 x^{17} + 7 x^{16} + 16 x^{15} + 6 x^{14} - 36 x^{13} - 42 x^{12} + 40 x^{11} + 136 x^{10} + 80 x^{9} - 168 x^{8} - 288 x^{7} + 96 x^{6} + 512 x^{5} + 448 x^{4} + \cdots + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 61.2 | ||
Root | \(-1.13207 + 0.847599i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 240.61 |
Dual form | 240.2.s.c.181.2 |
$q$-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 \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(161\) | \(181\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.13207 | + | 0.847599i | −0.800492 | + | 0.599343i | ||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | 0.563151 | − | 1.91908i | 0.281575 | − | 0.959539i | ||||
\(5\) | 0.707107 | − | 0.707107i | 0.316228 | − | 0.316228i | ||||
\(6\) | −1.39984 | − | 0.201149i | −0.571480 | − | 0.0821187i | ||||
\(7\) | − | 4.27253i | − | 1.61487i | −0.589959 | − | 0.807433i | \(-0.700856\pi\) | ||
0.589959 | − | 0.807433i | \(-0.299144\pi\) | |||||||
\(8\) | 0.989085 | + | 2.64985i | 0.349695 | + | 0.936864i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | −0.201149 | + | 1.39984i | −0.0636089 | + | 0.442667i | ||||
\(11\) | 2.94281 | − | 2.94281i | 0.887291 | − | 0.887291i | −0.106971 | − | 0.994262i | \(-0.534115\pi\) |
0.994262 | + | 0.106971i | \(0.0341151\pi\) | |||||||
\(12\) | 1.75520 | − | 0.958786i | 0.506683 | − | 0.276778i | ||||
\(13\) | −4.05962 | − | 4.05962i | −1.12594 | − | 1.12594i | −0.990831 | − | 0.135106i | \(-0.956863\pi\) |
−0.135106 | − | 0.990831i | \(-0.543137\pi\) | |||||||
\(14\) | 3.62140 | + | 4.83679i | 0.967859 | + | 1.29269i | ||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −3.36572 | − | 2.16146i | −0.841431 | − | 0.540365i | ||||
\(17\) | 0.160060 | 0.0388202 | 0.0194101 | − | 0.999812i | \(-0.493821\pi\) | ||||
0.0194101 | + | 0.999812i | \(0.493821\pi\) | |||||||
\(18\) | −0.847599 | − | 1.13207i | −0.199781 | − | 0.266831i | ||||
\(19\) | 4.32576 | + | 4.32576i | 0.992396 | + | 0.992396i | 0.999971 | − | 0.00757497i | \(-0.00241121\pi\) |
−0.00757497 | + | 0.999971i | \(0.502411\pi\) | |||||||
\(20\) | −0.958786 | − | 1.75520i | −0.214391 | − | 0.392475i | ||||
\(21\) | 3.02114 | − | 3.02114i | 0.659266 | − | 0.659266i | ||||
\(22\) | −0.837134 | + | 5.82579i | −0.178478 | + | 1.24206i | ||||
\(23\) | 8.40564i | 1.75270i | 0.481677 | + | 0.876349i | \(0.340028\pi\) | ||||
−0.481677 | + | 0.876349i | \(0.659972\pi\) | |||||||
\(24\) | −1.17434 | + | 2.57312i | −0.239711 | + | 0.525235i | ||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | 8.03670 | + | 1.15483i | 1.57613 | + | 0.226481i | ||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | −8.19933 | − | 2.40608i | −1.54953 | − | 0.454706i | ||||
\(29\) | −1.78072 | − | 1.78072i | −0.330671 | − | 0.330671i | 0.522171 | − | 0.852841i | \(-0.325122\pi\) |
−0.852841 | + | 0.522171i | \(0.825122\pi\) | |||||||
\(30\) | −1.13207 | + | 0.847599i | −0.206686 | + | 0.154750i | ||||
\(31\) | 7.17282 | 1.28828 | 0.644138 | − | 0.764909i | \(-0.277216\pi\) | ||||
0.644138 | + | 0.764909i | \(0.277216\pi\) | |||||||
\(32\) | 5.64228 | − | 0.405867i | 0.997423 | − | 0.0717479i | ||||
\(33\) | 4.16177 | 0.724470 | ||||||||
\(34\) | −0.181198 | + | 0.135667i | −0.0310752 | + | 0.0232666i | ||||
\(35\) | −3.02114 | − | 3.02114i | −0.510666 | − | 0.510666i | ||||
\(36\) | 1.91908 | + | 0.563151i | 0.319846 | + | 0.0938584i | ||||
\(37\) | −0.669226 | + | 0.669226i | −0.110020 | + | 0.110020i | −0.759974 | − | 0.649954i | \(-0.774788\pi\) |
0.649954 | + | 0.759974i | \(0.274788\pi\) | |||||||
\(38\) | −8.56355 | − | 1.23054i | −1.38919 | − | 0.199619i | ||||
\(39\) | − | 5.74117i | − | 0.919324i | ||||||
\(40\) | 2.57312 | + | 1.17434i | 0.406845 | + | 0.185679i | ||||
\(41\) | 3.96632i | 0.619435i | 0.950829 | + | 0.309717i | \(0.100234\pi\) | ||||
−0.950829 | + | 0.309717i | \(0.899766\pi\) | |||||||
\(42\) | −0.859415 | + | 5.98084i | −0.132611 | + | 0.922864i | ||||
\(43\) | −0.255733 | + | 0.255733i | −0.0389989 | + | 0.0389989i | −0.726337 | − | 0.687338i | \(-0.758779\pi\) |
0.687338 | + | 0.726337i | \(0.258779\pi\) | |||||||
\(44\) | −3.99024 | − | 7.30473i | −0.601551 | − | 1.10123i | ||||
\(45\) | 0.707107 | + | 0.707107i | 0.105409 | + | 0.105409i | ||||
\(46\) | −7.12462 | − | 9.51575i | −1.05047 | − | 1.40302i | ||||
\(47\) | 0.0752658 | 0.0109787 | 0.00548933 | − | 0.999985i | \(-0.498253\pi\) | ||||
0.00548933 | + | 0.999985i | \(0.498253\pi\) | |||||||
\(48\) | −0.851542 | − | 3.90831i | −0.122910 | − | 0.564116i | ||||
\(49\) | −11.2545 | −1.60779 | ||||||||
\(50\) | 0.847599 | + | 1.13207i | 0.119869 | + | 0.160098i | ||||
\(51\) | 0.113179 | + | 0.113179i | 0.0158483 | + | 0.0158483i | ||||
\(52\) | −10.0769 | + | 5.50456i | −1.39742 | + | 0.763345i | ||||
\(53\) | −2.88214 | + | 2.88214i | −0.395892 | + | 0.395892i | −0.876781 | − | 0.480889i | \(-0.840314\pi\) |
0.480889 | + | 0.876781i | \(0.340314\pi\) | |||||||
\(54\) | 0.201149 | − | 1.39984i | 0.0273729 | − | 0.190493i | ||||
\(55\) | − | 4.16177i | − | 0.561172i | ||||||
\(56\) | 11.3216 | − | 4.22590i | 1.51291 | − | 0.564710i | ||||
\(57\) | 6.11754i | 0.810288i | ||||||||
\(58\) | 3.52522 | + | 0.506556i | 0.462884 | + | 0.0665140i | ||||
\(59\) | −5.63594 | + | 5.63594i | −0.733737 | + | 0.733737i | −0.971358 | − | 0.237621i | \(-0.923632\pi\) |
0.237621 | + | 0.971358i | \(0.423632\pi\) | |||||||
\(60\) | 0.563151 | − | 1.91908i | 0.0727024 | − | 0.247752i | ||||
\(61\) | −4.48857 | − | 4.48857i | −0.574703 | − | 0.574703i | 0.358736 | − | 0.933439i | \(-0.383208\pi\) |
−0.933439 | + | 0.358736i | \(0.883208\pi\) | |||||||
\(62\) | −8.12011 | + | 6.07968i | −1.03126 | + | 0.772120i | ||||
\(63\) | 4.27253 | 0.538289 | ||||||||
\(64\) | −6.04342 | + | 5.24186i | −0.755428 | + | 0.655232i | ||||
\(65\) | −5.74117 | −0.712105 | ||||||||
\(66\) | −4.71140 | + | 3.52751i | −0.579933 | + | 0.434206i | ||||
\(67\) | −0.131176 | − | 0.131176i | −0.0160257 | − | 0.0160257i | 0.699049 | − | 0.715074i | \(-0.253607\pi\) |
−0.715074 | + | 0.699049i | \(0.753607\pi\) | |||||||
\(68\) | 0.0901377 | − | 0.307167i | 0.0109308 | − | 0.0372495i | ||||
\(69\) | −5.94369 | + | 5.94369i | −0.715536 | + | 0.715536i | ||||
\(70\) | 5.98084 | + | 0.859415i | 0.714848 | + | 0.102720i | ||||
\(71\) | − | 12.1137i | − | 1.43764i | −0.695199 | − | 0.718818i | \(-0.744684\pi\) | ||
0.695199 | − | 0.718818i | \(-0.255316\pi\) | |||||||
\(72\) | −2.64985 | + | 0.989085i | −0.312288 | + | 0.116565i | ||||
\(73\) | − | 0.382876i | − | 0.0448123i | −0.999749 | − | 0.0224061i | \(-0.992867\pi\) | ||
0.999749 | − | 0.0224061i | \(-0.00713269\pi\) | |||||||
\(74\) | 0.190373 | − | 1.32484i | 0.0221304 | − | 0.154010i | ||||
\(75\) | 0.707107 | − | 0.707107i | 0.0816497 | − | 0.0816497i | ||||
\(76\) | 10.7375 | − | 5.86541i | 1.23168 | − | 0.672809i | ||||
\(77\) | −12.5733 | − | 12.5733i | −1.43286 | − | 1.43286i | ||||
\(78\) | 4.86622 | + | 6.49939i | 0.550990 | + | 0.735911i | ||||
\(79\) | 15.3239 | 1.72408 | 0.862039 | − | 0.506841i | \(-0.169187\pi\) | ||||
0.862039 | + | 0.506841i | \(0.169187\pi\) | |||||||
\(80\) | −3.90831 | + | 0.851542i | −0.436962 | + | 0.0952053i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −3.36185 | − | 4.49014i | −0.371254 | − | 0.495853i | ||||
\(83\) | −5.54562 | − | 5.54562i | −0.608710 | − | 0.608710i | 0.333899 | − | 0.942609i | \(-0.391636\pi\) |
−0.942609 | + | 0.333899i | \(0.891636\pi\) | |||||||
\(84\) | −4.09644 | − | 7.49916i | −0.446959 | − | 0.818225i | ||||
\(85\) | 0.113179 | − | 0.113179i | 0.0122760 | − | 0.0122760i | ||||
\(86\) | 0.0727477 | − | 0.506266i | 0.00784459 | − | 0.0545921i | ||||
\(87\) | − | 2.51831i | − | 0.269991i | ||||||
\(88\) | 10.7087 | + | 4.88732i | 1.14155 | + | 0.520990i | ||||
\(89\) | 13.8991i | 1.47330i | 0.676275 | + | 0.736649i | \(0.263593\pi\) | ||||
−0.676275 | + | 0.736649i | \(0.736407\pi\) | |||||||
\(90\) | −1.39984 | − | 0.201149i | −0.147556 | − | 0.0212030i | ||||
\(91\) | −17.3449 | + | 17.3449i | −1.81824 | + | 1.81824i | ||||
\(92\) | 16.1311 | + | 4.73364i | 1.68178 | + | 0.493516i | ||||
\(93\) | 5.07195 | + | 5.07195i | 0.525937 | + | 0.525937i | ||||
\(94\) | −0.0852060 | + | 0.0637953i | −0.00878832 | + | 0.00657998i | ||||
\(95\) | 6.11754 | 0.627647 | ||||||||
\(96\) | 4.27668 | + | 3.70270i | 0.436487 | + | 0.377905i | ||||
\(97\) | 10.8999 | 1.10672 | 0.553358 | − | 0.832944i | \(-0.313346\pi\) | ||||
0.553358 | + | 0.832944i | \(0.313346\pi\) | |||||||
\(98\) | 12.7409 | − | 9.53935i | 1.28703 | − | 0.963620i | ||||
\(99\) | 2.94281 | + | 2.94281i | 0.295764 | + | 0.295764i | ||||
\(100\) | −1.91908 | − | 0.563151i | −0.191908 | − | 0.0563151i | ||||
\(101\) | −2.98972 | + | 2.98972i | −0.297489 | + | 0.297489i | −0.840029 | − | 0.542541i | \(-0.817462\pi\) |
0.542541 | + | 0.840029i | \(0.317462\pi\) | |||||||
\(102\) | −0.224057 | − | 0.0321958i | −0.0221850 | − | 0.00318786i | ||||
\(103\) | 16.8190i | 1.65723i | 0.559820 | + | 0.828615i | \(0.310870\pi\) | ||||
−0.559820 | + | 0.828615i | \(0.689130\pi\) | |||||||
\(104\) | 6.74208 | − | 14.7727i | 0.661116 | − | 1.44858i | ||||
\(105\) | − | 4.27253i | − | 0.416957i | ||||||
\(106\) | 0.819874 | − | 5.70567i | 0.0796332 | − | 0.554184i | ||||
\(107\) | 1.64447 | − | 1.64447i | 0.158977 | − | 0.158977i | −0.623136 | − | 0.782113i | \(-0.714142\pi\) |
0.782113 | + | 0.623136i | \(0.214142\pi\) | |||||||
\(108\) | 0.958786 | + | 1.75520i | 0.0922592 | + | 0.168894i | ||||
\(109\) | 4.67023 | + | 4.67023i | 0.447327 | + | 0.447327i | 0.894465 | − | 0.447138i | \(-0.147557\pi\) |
−0.447138 | + | 0.894465i | \(0.647557\pi\) | |||||||
\(110\) | 3.52751 | + | 4.71140i | 0.336335 | + | 0.449214i | ||||
\(111\) | −0.946429 | −0.0898311 | ||||||||
\(112\) | −9.23491 | + | 14.3802i | −0.872617 | + | 1.35880i | ||||
\(113\) | 5.00533 | 0.470862 | 0.235431 | − | 0.971891i | \(-0.424350\pi\) | ||||
0.235431 | + | 0.971891i | \(0.424350\pi\) | |||||||
\(114\) | −5.18522 | − | 6.92547i | −0.485641 | − | 0.648629i | ||||
\(115\) | 5.94369 | + | 5.94369i | 0.554252 | + | 0.554252i | ||||
\(116\) | −4.42014 | + | 2.41452i | −0.410400 | + | 0.224183i | ||||
\(117\) | 4.05962 | − | 4.05962i | 0.375312 | − | 0.375312i | ||||
\(118\) | 1.60324 | − | 11.1573i | 0.147590 | − | 1.02711i | ||||
\(119\) | − | 0.683861i | − | 0.0626894i | ||||||
\(120\) | 0.989085 | + | 2.64985i | 0.0902907 | + | 0.241897i | ||||
\(121\) | − | 6.32029i | − | 0.574572i | ||||||
\(122\) | 8.88588 | + | 1.27685i | 0.804489 | + | 0.115601i | ||||
\(123\) | −2.80461 | + | 2.80461i | −0.252883 | + | 0.252883i | ||||
\(124\) | 4.03938 | − | 13.7652i | 0.362747 | − | 1.23615i | ||||
\(125\) | −0.707107 | − | 0.707107i | −0.0632456 | − | 0.0632456i | ||||
\(126\) | −4.83679 | + | 3.62140i | −0.430896 | + | 0.322620i | ||||
\(127\) | 1.96679 | 0.174525 | 0.0872623 | − | 0.996185i | \(-0.472188\pi\) | ||||
0.0872623 | + | 0.996185i | \(0.472188\pi\) | |||||||
\(128\) | 2.39856 | − | 11.0565i | 0.212005 | − | 0.977269i | ||||
\(129\) | −0.361661 | −0.0318425 | ||||||||
\(130\) | 6.49939 | − | 4.86622i | 0.570035 | − | 0.426795i | ||||
\(131\) | −0.852904 | − | 0.852904i | −0.0745186 | − | 0.0745186i | 0.668865 | − | 0.743384i | \(-0.266780\pi\) |
−0.743384 | + | 0.668865i | \(0.766780\pi\) | |||||||
\(132\) | 2.34370 | − | 7.98675i | 0.203993 | − | 0.695158i | ||||
\(133\) | 18.4819 | − | 18.4819i | 1.60259 | − | 1.60259i | ||||
\(134\) | 0.259686 | + | 0.0373154i | 0.0224334 | + | 0.00322356i | ||||
\(135\) | 1.00000i | 0.0860663i | ||||||||
\(136\) | 0.158313 | + | 0.424134i | 0.0135752 | + | 0.0363692i | ||||
\(137\) | 4.12023i | 0.352015i | 0.984389 | + | 0.176007i | \(0.0563183\pi\) | ||||
−0.984389 | + | 0.176007i | \(0.943682\pi\) | |||||||
\(138\) | 1.69079 | − | 11.7665i | 0.143929 | − | 1.00163i | ||||
\(139\) | 5.73895 | − | 5.73895i | 0.486771 | − | 0.486771i | −0.420514 | − | 0.907286i | \(-0.638150\pi\) |
0.907286 | + | 0.420514i | \(0.138150\pi\) | |||||||
\(140\) | −7.49916 | + | 4.09644i | −0.633794 | + | 0.346213i | ||||
\(141\) | 0.0532210 | + | 0.0532210i | 0.00448202 | + | 0.00448202i | ||||
\(142\) | 10.2676 | + | 13.7136i | 0.861637 | + | 1.15082i | ||||
\(143\) | −23.8934 | −1.99807 | ||||||||
\(144\) | 2.16146 | − | 3.36572i | 0.180122 | − | 0.280477i | ||||
\(145\) | −2.51831 | −0.209134 | ||||||||
\(146\) | 0.324525 | + | 0.433441i | 0.0268579 | + | 0.0358719i | ||||
\(147\) | −7.95817 | − | 7.95817i | −0.656379 | − | 0.656379i | ||||
\(148\) | 0.907422 | + | 1.66117i | 0.0745897 | + | 0.136548i | ||||
\(149\) | −9.96311 | + | 9.96311i | −0.816210 | + | 0.816210i | −0.985557 | − | 0.169346i | \(-0.945834\pi\) |
0.169346 | + | 0.985557i | \(0.445834\pi\) | |||||||
\(150\) | −0.201149 | + | 1.39984i | −0.0164237 | + | 0.114296i | ||||
\(151\) | 4.01882i | 0.327047i | 0.986539 | + | 0.163524i | \(0.0522860\pi\) | ||||
−0.986539 | + | 0.163524i | \(0.947714\pi\) | |||||||
\(152\) | −7.18407 | + | 15.7411i | −0.582705 | + | 1.27678i | ||||
\(153\) | 0.160060i | 0.0129401i | ||||||||
\(154\) | 24.8909 | + | 3.57669i | 2.00576 | + | 0.288218i | ||||
\(155\) | 5.07195 | − | 5.07195i | 0.407389 | − | 0.407389i | ||||
\(156\) | −11.0178 | − | 3.23315i | −0.882127 | − | 0.258859i | ||||
\(157\) | −9.14459 | − | 9.14459i | −0.729818 | − | 0.729818i | 0.240766 | − | 0.970583i | \(-0.422601\pi\) |
−0.970583 | + | 0.240766i | \(0.922601\pi\) | |||||||
\(158\) | −17.3477 | + | 12.9886i | −1.38011 | + | 1.03332i | ||||
\(159\) | −4.07596 | −0.323244 | ||||||||
\(160\) | 3.70270 | − | 4.27668i | 0.292724 | − | 0.338101i | ||||
\(161\) | 35.9134 | 2.83037 | ||||||||
\(162\) | 1.13207 | − | 0.847599i | 0.0889436 | − | 0.0665937i | ||||
\(163\) | −0.346095 | − | 0.346095i | −0.0271082 | − | 0.0271082i | 0.693423 | − | 0.720531i | \(-0.256102\pi\) |
−0.720531 | + | 0.693423i | \(0.756102\pi\) | |||||||
\(164\) | 7.61168 | + | 2.23363i | 0.594372 | + | 0.174418i | ||||
\(165\) | 2.94281 | − | 2.94281i | 0.229098 | − | 0.229098i | ||||
\(166\) | 10.9785 | + | 1.57755i | 0.852094 | + | 0.122441i | ||||
\(167\) | 10.9882i | 0.850296i | 0.905124 | + | 0.425148i | \(0.139778\pi\) | ||||
−0.905124 | + | 0.425148i | \(0.860222\pi\) | |||||||
\(168\) | 10.9937 | + | 5.01740i | 0.848185 | + | 0.387101i | ||||
\(169\) | 19.9611i | 1.53547i | ||||||||
\(170\) | −0.0321958 | + | 0.224057i | −0.00246931 | + | 0.0171844i | ||||
\(171\) | −4.32576 | + | 4.32576i | −0.330799 | + | 0.330799i | ||||
\(172\) | 0.346755 | + | 0.634788i | 0.0264398 | + | 0.0484021i | ||||
\(173\) | 2.70605 | + | 2.70605i | 0.205737 | + | 0.205737i | 0.802453 | − | 0.596716i | \(-0.203528\pi\) |
−0.596716 | + | 0.802453i | \(0.703528\pi\) | |||||||
\(174\) | 2.13452 | + | 2.85090i | 0.161818 | + | 0.216126i | ||||
\(175\) | −4.27253 | −0.322973 | ||||||||
\(176\) | −16.2655 | + | 3.54392i | −1.22606 | + | 0.267133i | ||||
\(177\) | −7.97042 | −0.599093 | ||||||||
\(178\) | −11.7808 | − | 15.7347i | −0.883012 | − | 1.17936i | ||||
\(179\) | −10.4088 | − | 10.4088i | −0.777990 | − | 0.777990i | 0.201499 | − | 0.979489i | \(-0.435419\pi\) |
−0.979489 | + | 0.201499i | \(0.935419\pi\) | |||||||
\(180\) | 1.75520 | − | 0.958786i | 0.130825 | − | 0.0714637i | ||||
\(181\) | −15.4792 | + | 15.4792i | −1.15056 | + | 1.15056i | −0.164119 | + | 0.986441i | \(0.552478\pi\) |
−0.986441 | + | 0.164119i | \(0.947522\pi\) | |||||||
\(182\) | 4.93405 | − | 34.3371i | 0.365736 | − | 2.54523i | ||||
\(183\) | − | 6.34780i | − | 0.469243i | ||||||
\(184\) | −22.2737 | + | 8.31390i | −1.64204 | + | 0.612909i | ||||
\(185\) | 0.946429i | 0.0695828i | ||||||||
\(186\) | −10.0408 | − | 1.44280i | −0.736225 | − | 0.105792i | ||||
\(187\) | 0.471026 | − | 0.471026i | 0.0344448 | − | 0.0344448i | ||||
\(188\) | 0.0423860 | − | 0.144441i | 0.00309132 | − | 0.0105344i | ||||
\(189\) | 3.02114 | + | 3.02114i | 0.219755 | + | 0.219755i | ||||
\(190\) | −6.92547 | + | 5.18522i | −0.502426 | + | 0.376176i | ||||
\(191\) | 4.75146 | 0.343803 | 0.171902 | − | 0.985114i | \(-0.445009\pi\) | ||||
0.171902 | + | 0.985114i | \(0.445009\pi\) | |||||||
\(192\) | −7.97990 | − | 0.566790i | −0.575899 | − | 0.0409046i | ||||
\(193\) | −11.7915 | −0.848772 | −0.424386 | − | 0.905481i | \(-0.639510\pi\) | ||||
−0.424386 | + | 0.905481i | \(0.639510\pi\) | |||||||
\(194\) | −12.3394 | + | 9.23873i | −0.885917 | + | 0.663302i | ||||
\(195\) | −4.05962 | − | 4.05962i | −0.290716 | − | 0.290716i | ||||
\(196\) | −6.33801 | + | 21.5984i | −0.452715 | + | 1.54274i | ||||
\(197\) | 4.56244 | − | 4.56244i | 0.325060 | − | 0.325060i | −0.525644 | − | 0.850705i | \(-0.676176\pi\) |
0.850705 | + | 0.525644i | \(0.176176\pi\) | |||||||
\(198\) | −5.82579 | − | 0.837134i | −0.414021 | − | 0.0594926i | ||||
\(199\) | − | 3.60262i | − | 0.255383i | −0.991814 | − | 0.127691i | \(-0.959243\pi\) | ||
0.991814 | − | 0.127691i | \(-0.0407567\pi\) | |||||||
\(200\) | 2.64985 | − | 0.989085i | 0.187373 | − | 0.0699389i | ||||
\(201\) | − | 0.185511i | − | 0.0130850i | ||||||
\(202\) | 0.850479 | − | 5.91865i | 0.0598395 | − | 0.416435i | ||||
\(203\) | −7.60817 | + | 7.60817i | −0.533989 | + | 0.533989i | ||||
\(204\) | 0.280937 | − | 0.153463i | 0.0196695 | − | 0.0107446i | ||||
\(205\) | 2.80461 | + | 2.80461i | 0.195883 | + | 0.195883i | ||||
\(206\) | −14.2558 | − | 19.0403i | −0.993249 | − | 1.32660i | ||||
\(207\) | −8.40564 | −0.584233 | ||||||||
\(208\) | 4.88885 | + | 22.4383i | 0.338981 | + | 1.55582i | ||||
\(209\) | 25.4598 | 1.76109 | ||||||||
\(210\) | 3.62140 | + | 4.83679i | 0.249900 | + | 0.333771i | ||||
\(211\) | −0.975389 | − | 0.975389i | −0.0671486 | − | 0.0671486i | 0.672735 | − | 0.739884i | \(-0.265119\pi\) |
−0.739884 | + | 0.672735i | \(0.765119\pi\) | |||||||
\(212\) | 3.90797 | + | 7.15412i | 0.268400 | + | 0.491347i | ||||
\(213\) | 8.56570 | − | 8.56570i | 0.586912 | − | 0.586912i | ||||
\(214\) | −0.467799 | + | 3.25551i | −0.0319781 | + | 0.222542i | ||||
\(215\) | 0.361661i | 0.0246651i | ||||||||
\(216\) | −2.57312 | − | 1.17434i | −0.175078 | − | 0.0799036i | ||||
\(217\) | − | 30.6461i | − | 2.08039i | ||||||
\(218\) | −9.24550 | − | 1.32853i | −0.626184 | − | 0.0899793i | ||||
\(219\) | 0.270734 | − | 0.270734i | 0.0182945 | − | 0.0182945i | ||||
\(220\) | −7.98675 | − | 2.34370i | −0.538467 | − | 0.158012i | ||||
\(221\) | −0.649782 | − | 0.649782i | −0.0437091 | − | 0.0437091i | ||||
\(222\) | 1.07142 | − | 0.802193i | 0.0719091 | − | 0.0538396i | ||||
\(223\) | 4.66343 | 0.312286 | 0.156143 | − | 0.987734i | \(-0.450094\pi\) | ||||
0.156143 | + | 0.987734i | \(0.450094\pi\) | |||||||
\(224\) | −1.73408 | − | 24.1068i | −0.115863 | − | 1.61070i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −5.66637 | + | 4.24251i | −0.376921 | + | 0.282208i | ||||
\(227\) | −1.61701 | − | 1.61701i | −0.107325 | − | 0.107325i | 0.651405 | − | 0.758730i | \(-0.274180\pi\) |
−0.758730 | + | 0.651405i | \(0.774180\pi\) | |||||||
\(228\) | 11.7400 | + | 3.44510i | 0.777503 | + | 0.228157i | ||||
\(229\) | 9.14882 | − | 9.14882i | 0.604571 | − | 0.604571i | −0.336951 | − | 0.941522i | \(-0.609396\pi\) |
0.941522 | + | 0.336951i | \(0.109396\pi\) | |||||||
\(230\) | −11.7665 | − | 1.69079i | −0.775861 | − | 0.111487i | ||||
\(231\) | − | 17.7813i | − | 1.16992i | ||||||
\(232\) | 2.95735 | − | 6.47991i | 0.194160 | − | 0.425427i | ||||
\(233\) | − | 10.3002i | − | 0.674789i | −0.941363 | − | 0.337394i | \(-0.890454\pi\) | ||
0.941363 | − | 0.337394i | \(-0.109546\pi\) | |||||||
\(234\) | −1.15483 | + | 8.03670i | −0.0754937 | + | 0.525376i | ||||
\(235\) | 0.0532210 | − | 0.0532210i | 0.00347175 | − | 0.00347175i | ||||
\(236\) | 7.64192 | + | 13.9897i | 0.497447 | + | 0.910651i | ||||
\(237\) | 10.8357 | + | 10.8357i | 0.703852 | + | 0.703852i | ||||
\(238\) | 0.579640 | + | 0.774176i | 0.0375725 | + | 0.0501824i | ||||
\(239\) | 3.73825 | 0.241807 | 0.120904 | − | 0.992664i | \(-0.461421\pi\) | ||||
0.120904 | + | 0.992664i | \(0.461421\pi\) | |||||||
\(240\) | −3.36572 | − | 2.16146i | −0.217256 | − | 0.139522i | ||||
\(241\) | −9.34283 | −0.601824 | −0.300912 | − | 0.953652i | \(-0.597291\pi\) | ||||
−0.300912 | + | 0.953652i | \(0.597291\pi\) | |||||||
\(242\) | 5.35707 | + | 7.15499i | 0.344366 | + | 0.459940i | ||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | −11.1417 | + | 6.08618i | −0.713272 | + | 0.389628i | ||||
\(245\) | −7.95817 | + | 7.95817i | −0.508429 | + | 0.508429i | ||||
\(246\) | 0.797821 | − | 5.55219i | 0.0508672 | − | 0.353995i | ||||
\(247\) | − | 35.1219i | − | 2.23475i | ||||||
\(248\) | 7.09453 | + | 19.0069i | 0.450503 | + | 1.20694i | ||||
\(249\) | − | 7.84269i | − | 0.497010i | ||||||
\(250\) | 1.39984 | + | 0.201149i | 0.0885334 | + | 0.0127218i | ||||
\(251\) | −9.31174 | + | 9.31174i | −0.587752 | + | 0.587752i | −0.937022 | − | 0.349270i | \(-0.886429\pi\) |
0.349270 | + | 0.937022i | \(0.386429\pi\) | |||||||
\(252\) | 2.40608 | − | 8.19933i | 0.151569 | − | 0.516509i | ||||
\(253\) | 24.7362 | + | 24.7362i | 1.55515 | + | 1.55515i | ||||
\(254\) | −2.22654 | + | 1.66705i | −0.139706 | + | 0.104600i | ||||
\(255\) | 0.160060 | 0.0100233 | ||||||||
\(256\) | 6.65618 | + | 14.5498i | 0.416011 | + | 0.909359i | ||||
\(257\) | 8.68522 | 0.541769 | 0.270885 | − | 0.962612i | \(-0.412684\pi\) | ||||
0.270885 | + | 0.962612i | \(0.412684\pi\) | |||||||
\(258\) | 0.409424 | − | 0.306544i | 0.0254897 | − | 0.0190846i | ||||
\(259\) | 2.85929 | + | 2.85929i | 0.177668 | + | 0.177668i | ||||
\(260\) | −3.23315 | + | 11.0178i | −0.200511 | + | 0.683293i | ||||
\(261\) | 1.78072 | − | 1.78072i | 0.110224 | − | 0.110224i | ||||
\(262\) | 1.68847 | + | 0.242624i | 0.104314 | + | 0.0149893i | ||||
\(263\) | 5.18971i | 0.320011i | 0.987116 | + | 0.160006i | \(0.0511513\pi\) | ||||
−0.987116 | + | 0.160006i | \(0.948849\pi\) | |||||||
\(264\) | 4.11634 | + | 11.0281i | 0.253343 | + | 0.678730i | ||||
\(265\) | 4.07596i | 0.250384i | ||||||||
\(266\) | −5.25751 | + | 36.5881i | −0.322359 | + | 2.24336i | ||||
\(267\) | −9.82813 | + | 9.82813i | −0.601472 | + | 0.601472i | ||||
\(268\) | −0.325610 | + | 0.177866i | −0.0198898 | + | 0.0108649i | ||||
\(269\) | −7.99426 | − | 7.99426i | −0.487418 | − | 0.487418i | 0.420072 | − | 0.907491i | \(-0.362005\pi\) |
−0.907491 | + | 0.420072i | \(0.862005\pi\) | |||||||
\(270\) | −0.847599 | − | 1.13207i | −0.0515833 | − | 0.0688954i | ||||
\(271\) | −18.8342 | −1.14410 | −0.572048 | − | 0.820220i | \(-0.693851\pi\) | ||||
−0.572048 | + | 0.820220i | \(0.693851\pi\) | |||||||
\(272\) | −0.538717 | − | 0.345963i | −0.0326645 | − | 0.0209771i | ||||
\(273\) | −24.5294 | −1.48458 | ||||||||
\(274\) | −3.49230 | − | 4.66437i | −0.210978 | − | 0.281785i | ||||
\(275\) | −2.94281 | − | 2.94281i | −0.177458 | − | 0.177458i | ||||
\(276\) | 8.05921 | + | 14.7536i | 0.485107 | + | 0.888062i | ||||
\(277\) | 3.71919 | − | 3.71919i | 0.223465 | − | 0.223465i | −0.586491 | − | 0.809956i | \(-0.699491\pi\) |
0.809956 | + | 0.586491i | \(0.199491\pi\) | |||||||
\(278\) | −1.63254 | + | 11.3612i | −0.0979135 | + | 0.681400i | ||||
\(279\) | 7.17282i | 0.429425i | ||||||||
\(280\) | 5.01740 | − | 10.9937i | 0.299847 | − | 0.657001i | ||||
\(281\) | − | 11.0223i | − | 0.657538i | −0.944410 | − | 0.328769i | \(-0.893366\pi\) | ||
0.944410 | − | 0.328769i | \(-0.106634\pi\) | |||||||
\(282\) | −0.105360 | − | 0.0151396i | −0.00627408 | − | 0.000901552i | ||||
\(283\) | 10.5210 | − | 10.5210i | 0.625411 | − | 0.625411i | −0.321499 | − | 0.946910i | \(-0.604187\pi\) |
0.946910 | + | 0.321499i | \(0.104187\pi\) | |||||||
\(284\) | −23.2472 | − | 6.82186i | −1.37947 | − | 0.404803i | ||||
\(285\) | 4.32576 | + | 4.32576i | 0.256236 | + | 0.256236i | ||||
\(286\) | 27.0490 | − | 20.2521i | 1.59944 | − | 1.19753i | ||||
\(287\) | 16.9462 | 1.00030 | ||||||||
\(288\) | 0.405867 | + | 5.64228i | 0.0239160 | + | 0.332474i | ||||
\(289\) | −16.9744 | −0.998493 | ||||||||
\(290\) | 2.85090 | − | 2.13452i | 0.167410 | − | 0.125343i | ||||
\(291\) | 7.70738 | + | 7.70738i | 0.451815 | + | 0.451815i | ||||
\(292\) | −0.734769 | − | 0.215617i | −0.0429991 | − | 0.0126180i | ||||
\(293\) | 15.5643 | − | 15.5643i | 0.909274 | − | 0.909274i | −0.0869399 | − | 0.996214i | \(-0.527709\pi\) |
0.996214 | + | 0.0869399i | \(0.0277088\pi\) | |||||||
\(294\) | 15.7545 | + | 2.26384i | 0.918822 | + | 0.132030i | ||||
\(295\) | 7.97042i | 0.464056i | ||||||||
\(296\) | −2.43527 | − | 1.11143i | −0.141547 | − | 0.0646004i | ||||
\(297\) | 4.16177i | 0.241490i | ||||||||
\(298\) | 2.83418 | − | 19.7236i | 0.164180 | − | 1.14256i | ||||
\(299\) | 34.1237 | − | 34.1237i | 1.97343 | − | 1.97343i | ||||
\(300\) | −0.958786 | − | 1.75520i | −0.0553555 | − | 0.101337i | ||||
\(301\) | 1.09263 | + | 1.09263i | 0.0629780 | + | 0.0629780i | ||||
\(302\) | −3.40635 | − | 4.54958i | −0.196014 | − | 0.261799i | ||||
\(303\) | −4.22811 | −0.242898 | ||||||||
\(304\) | −5.20935 | − | 23.9092i | −0.298776 | − | 1.37129i | ||||
\(305\) | −6.34780 | −0.363474 | ||||||||
\(306\) | −0.135667 | − | 0.181198i | −0.00775554 | − | 0.0103584i | ||||
\(307\) | 19.6795 | + | 19.6795i | 1.12317 | + | 1.12317i | 0.991262 | + | 0.131908i | \(0.0421104\pi\) |
0.131908 | + | 0.991262i | \(0.457890\pi\) | |||||||
\(308\) | −31.2097 | + | 17.0484i | −1.77834 | + | 0.971425i | ||||
\(309\) | −11.8929 | + | 11.8929i | −0.676561 | + | 0.676561i | ||||
\(310\) | −1.44280 | + | 10.0408i | −0.0819458 | + | 0.570277i | ||||
\(311\) | 11.8922i | 0.674344i | 0.941443 | + | 0.337172i | \(0.109470\pi\) | ||||
−0.941443 | + | 0.337172i | \(0.890530\pi\) | |||||||
\(312\) | 15.2133 | − | 5.67851i | 0.861281 | − | 0.321482i | ||||
\(313\) | − | 9.61193i | − | 0.543298i | −0.962396 | − | 0.271649i | \(-0.912431\pi\) | ||
0.962396 | − | 0.271649i | \(-0.0875690\pi\) | |||||||
\(314\) | 18.1032 | + | 2.60134i | 1.02162 | + | 0.146802i | ||||
\(315\) | 3.02114 | − | 3.02114i | 0.170222 | − | 0.170222i | ||||
\(316\) | 8.62969 | − | 29.4079i | 0.485458 | − | 1.65432i | ||||
\(317\) | 8.10049 | + | 8.10049i | 0.454969 | + | 0.454969i | 0.897000 | − | 0.442031i | \(-0.145742\pi\) |
−0.442031 | + | 0.897000i | \(0.645742\pi\) | |||||||
\(318\) | 4.61426 | − | 3.45478i | 0.258755 | − | 0.193734i | ||||
\(319\) | −10.4806 | −0.586802 | ||||||||
\(320\) | −0.566790 | + | 7.97990i | −0.0316845 | + | 0.446090i | ||||
\(321\) | 2.32563 | 0.129804 | ||||||||
\(322\) | −40.6564 | + | 30.4402i | −2.26569 | + | 1.69636i | ||||
\(323\) | 0.692379 | + | 0.692379i | 0.0385250 | + | 0.0385250i | ||||
\(324\) | −0.563151 | + | 1.91908i | −0.0312861 | + | 0.106615i | ||||
\(325\) | −4.05962 | + | 4.05962i | −0.225187 | + | 0.225187i | ||||
\(326\) | 0.685152 | + | 0.0984526i | 0.0379470 | + | 0.00545279i | ||||
\(327\) | 6.60470i | 0.365241i | ||||||||
\(328\) | −10.5102 | + | 3.92303i | −0.580326 | + | 0.216613i | ||||
\(329\) | − | 0.321576i | − | 0.0177291i | ||||||
\(330\) | −0.837134 | + | 5.82579i | −0.0460827 | + | 0.320699i | ||||
\(331\) | −13.3267 | + | 13.3267i | −0.732501 | + | 0.732501i | −0.971115 | − | 0.238613i | \(-0.923307\pi\) |
0.238613 | + | 0.971115i | \(0.423307\pi\) | |||||||
\(332\) | −13.7655 | + | 7.51945i | −0.755479 | + | 0.412684i | ||||
\(333\) | −0.669226 | − | 0.669226i | −0.0366734 | − | 0.0366734i | ||||
\(334\) | −9.31363 | − | 12.4394i | −0.509619 | − | 0.680655i | ||||
\(335\) | −0.185511 | −0.0101356 | ||||||||
\(336\) | −16.6984 | + | 3.63824i | −0.910971 | + | 0.198482i | ||||
\(337\) | 32.6763 | 1.77999 | 0.889996 | − | 0.455967i | \(-0.150707\pi\) | ||||
0.889996 | + | 0.455967i | \(0.150707\pi\) | |||||||
\(338\) | −16.9190 | − | 22.5973i | −0.920273 | − | 1.22913i | ||||
\(339\) | 3.53930 | + | 3.53930i | 0.192229 | + | 0.192229i | ||||
\(340\) | −0.153463 | − | 0.280937i | −0.00832270 | − | 0.0152359i | ||||
\(341\) | 21.1083 | − | 21.1083i | 1.14308 | − | 1.14308i | ||||
\(342\) | 1.23054 | − | 8.56355i | 0.0665398 | − | 0.463064i | ||||
\(343\) | 18.1777i | 0.981504i | ||||||||
\(344\) | −0.930596 | − | 0.424712i | −0.0501744 | − | 0.0228990i | ||||
\(345\) | 8.40564i | 0.452545i | ||||||||
\(346\) | −5.35708 | − | 0.769784i | −0.287998 | − | 0.0413838i | ||||
\(347\) | 22.4898 | − | 22.4898i | 1.20732 | − | 1.20732i | 0.235423 | − | 0.971893i | \(-0.424352\pi\) |
0.971893 | − | 0.235423i | \(-0.0756477\pi\) | |||||||
\(348\) | −4.83284 | − | 1.41819i | −0.259067 | − | 0.0760229i | ||||
\(349\) | −22.6617 | − | 22.6617i | −1.21305 | − | 1.21305i | −0.970018 | − | 0.243032i | \(-0.921858\pi\) |
−0.243032 | − | 0.970018i | \(-0.578142\pi\) | |||||||
\(350\) | 4.83679 | − | 3.62140i | 0.258538 | − | 0.193572i | ||||
\(351\) | 5.74117 | 0.306441 | ||||||||
\(352\) | 15.4098 | − | 17.7985i | 0.821343 | − | 0.948666i | ||||
\(353\) | −10.6347 | −0.566026 | −0.283013 | − | 0.959116i | \(-0.591334\pi\) | ||||
−0.283013 | + | 0.959116i | \(0.591334\pi\) | |||||||
\(354\) | 9.02305 | − | 6.75572i | 0.479570 | − | 0.359063i | ||||
\(355\) | −8.56570 | − | 8.56570i | −0.454620 | − | 0.454620i | ||||
\(356\) | 26.6734 | + | 7.82727i | 1.41369 | + | 0.414845i | ||||
\(357\) | 0.483562 | − | 0.483562i | 0.0255928 | − | 0.0255928i | ||||
\(358\) | 20.6059 | + | 2.96096i | 1.08906 | + | 0.156492i | ||||
\(359\) | 17.0191i | 0.898235i | 0.893473 | + | 0.449118i | \(0.148262\pi\) | ||||
−0.893473 | + | 0.449118i | \(0.851738\pi\) | |||||||
\(360\) | −1.17434 | + | 2.57312i | −0.0618931 | + | 0.135615i | ||||
\(361\) | 18.4243i | 0.969701i | ||||||||
\(362\) | 4.40333 | − | 30.6436i | 0.231434 | − | 1.61059i | ||||
\(363\) | 4.46912 | − | 4.46912i | 0.234568 | − | 0.234568i | ||||
\(364\) | 23.5184 | + | 43.0540i | 1.23270 | + | 2.25664i | ||||
\(365\) | −0.270734 | − | 0.270734i | −0.0141709 | − | 0.0141709i | ||||
\(366\) | 5.38039 | + | 7.18613i | 0.281238 | + | 0.375625i | ||||
\(367\) | −25.7040 | −1.34174 | −0.670868 | − | 0.741577i | \(-0.734078\pi\) | ||||
−0.670868 | + | 0.741577i | \(0.734078\pi\) | |||||||
\(368\) | 18.1685 | − | 28.2911i | 0.947097 | − | 1.47477i | ||||
\(369\) | −3.96632 | −0.206478 | ||||||||
\(370\) | −0.802193 | − | 1.07142i | −0.0417040 | − | 0.0557005i | ||||
\(371\) | 12.3140 | + | 12.3140i | 0.639313 | + | 0.639313i | ||||
\(372\) | 12.5897 | − | 6.87720i | 0.652747 | − | 0.356566i | ||||
\(373\) | −14.7290 | + | 14.7290i | −0.762641 | + | 0.762641i | −0.976799 | − | 0.214158i | \(-0.931299\pi\) |
0.214158 | + | 0.976799i | \(0.431299\pi\) | |||||||
\(374\) | −0.133991 | + | 0.932474i | −0.00692853 | + | 0.0482171i | ||||
\(375\) | − | 1.00000i | − | 0.0516398i | ||||||
\(376\) | 0.0744443 | + | 0.199443i | 0.00383917 | + | 0.0102855i | ||||
\(377\) | 14.4581i | 0.744628i | ||||||||
\(378\) | −5.98084 | − | 0.859415i | −0.307621 | − | 0.0442036i | ||||
\(379\) | 10.0142 | − | 10.0142i | 0.514395 | − | 0.514395i | −0.401475 | − | 0.915870i | \(-0.631502\pi\) |
0.915870 | + | 0.401475i | \(0.131502\pi\) | |||||||
\(380\) | 3.44510 | − | 11.7400i | 0.176730 | − | 0.602251i | ||||
\(381\) | 1.39073 | + | 1.39073i | 0.0712494 | + | 0.0712494i | ||||
\(382\) | −5.37897 | + | 4.02733i | −0.275212 | + | 0.206056i | ||||
\(383\) | −28.1834 | −1.44010 | −0.720052 | − | 0.693920i | \(-0.755882\pi\) | ||||
−0.720052 | + | 0.693920i | \(0.755882\pi\) | |||||||
\(384\) | 9.51419 | − | 6.12211i | 0.485519 | − | 0.312418i | ||||
\(385\) | −17.7813 | −0.906218 | ||||||||
\(386\) | 13.3488 | − | 9.99448i | 0.679435 | − | 0.508706i | ||||
\(387\) | −0.255733 | − | 0.255733i | −0.0129996 | − | 0.0129996i | ||||
\(388\) | 6.13828 | − | 20.9177i | 0.311624 | − | 1.06194i | ||||
\(389\) | −11.1551 | + | 11.1551i | −0.565586 | + | 0.565586i | −0.930889 | − | 0.365303i | \(-0.880965\pi\) |
0.365303 | + | 0.930889i | \(0.380965\pi\) | |||||||
\(390\) | 8.03670 | + | 1.15483i | 0.406954 | + | 0.0584771i | ||||
\(391\) | 1.34540i | 0.0680400i | ||||||||
\(392\) | −11.1317 | − | 29.8229i | −0.562236 | − | 1.50628i | ||||
\(393\) | − | 1.20619i | − | 0.0608442i | ||||||
\(394\) | −1.29787 | + | 9.03211i | −0.0653855 | + | 0.455031i | ||||
\(395\) | 10.8357 | − | 10.8357i | 0.545202 | − | 0.545202i | ||||
\(396\) | 7.30473 | − | 3.99024i | 0.367077 | − | 0.200517i | ||||
\(397\) | 2.98216 | + | 2.98216i | 0.149670 | + | 0.149670i | 0.777971 | − | 0.628300i | \(-0.216249\pi\) |
−0.628300 | + | 0.777971i | \(0.716249\pi\) | |||||||
\(398\) | 3.05358 | + | 4.07841i | 0.153062 | + | 0.204432i | ||||
\(399\) | 26.1374 | 1.30851 | ||||||||
\(400\) | −2.16146 | + | 3.36572i | −0.108073 | + | 0.168286i | ||||
\(401\) | −15.9896 | −0.798485 | −0.399242 | − | 0.916845i | \(-0.630727\pi\) | ||||
−0.399242 | + | 0.916845i | \(0.630727\pi\) | |||||||
\(402\) | 0.157239 | + | 0.210011i | 0.00784239 | + | 0.0104744i | ||||
\(403\) | −29.1189 | − | 29.1189i | −1.45052 | − | 1.45052i | ||||
\(404\) | 4.05385 | + | 7.42118i | 0.201687 | + | 0.369217i | ||||
\(405\) | −0.707107 | + | 0.707107i | −0.0351364 | + | 0.0351364i | ||||
\(406\) | 2.16428 | − | 15.0616i | 0.107411 | − | 0.747496i | ||||
\(407\) | 3.93881i | 0.195240i | ||||||||
\(408\) | −0.187964 | + | 0.411852i | −0.00930562 | + | 0.0203897i | ||||
\(409\) | − | 27.5110i | − | 1.36033i | −0.733059 | − | 0.680165i | \(-0.761908\pi\) | ||
0.733059 | − | 0.680165i | \(-0.238092\pi\) | |||||||
\(410\) | −5.55219 | − | 0.797821i | −0.274203 | − | 0.0394015i | ||||
\(411\) | −2.91344 | + | 2.91344i | −0.143709 | + | 0.143709i | ||||
\(412\) | 32.2770 | + | 9.47165i | 1.59018 | + | 0.466635i | ||||
\(413\) | 24.0797 | + | 24.0797i | 1.18489 | + | 1.18489i | ||||
\(414\) | 9.51575 | − | 7.12462i | 0.467674 | − | 0.350156i | ||||
\(415\) | −7.84269 | −0.384982 | ||||||||
\(416\) | −24.5532 | − | 21.2578i | −1.20382 | − | 1.04225i | ||||
\(417\) | 8.11610 | 0.397447 | ||||||||
\(418\) | −28.8222 | + | 21.5797i | −1.40974 | + | 1.05550i | ||||
\(419\) | 1.95916 | + | 1.95916i | 0.0957114 | + | 0.0957114i | 0.753341 | − | 0.657630i | \(-0.228441\pi\) |
−0.657630 | + | 0.753341i | \(0.728441\pi\) | |||||||
\(420\) | −8.19933 | − | 2.40608i | −0.400086 | − | 0.117405i | ||||
\(421\) | 6.23743 | − | 6.23743i | 0.303994 | − | 0.303994i | −0.538580 | − | 0.842574i | \(-0.681039\pi\) |
0.842574 | + | 0.538580i | \(0.181039\pi\) | |||||||
\(422\) | 1.93095 | + | 0.277467i | 0.0939970 | + | 0.0135069i | ||||
\(423\) | 0.0752658i | 0.00365955i | ||||||||
\(424\) | −10.4879 | − | 4.78655i | −0.509338 | − | 0.232456i | ||||
\(425\) | − | 0.160060i | − | 0.00776404i | ||||||
\(426\) | −2.43666 | + | 16.9572i | −0.118057 | + | 0.821581i | ||||
\(427\) | −19.1776 | + | 19.1776i | −0.928068 | + | 0.928068i | ||||
\(428\) | −2.22978 | − | 4.08196i | −0.107781 | − | 0.197309i | ||||
\(429\) | −16.8952 | − | 16.8952i | −0.815708 | − | 0.815708i | ||||
\(430\) | −0.306544 | − | 0.409424i | −0.0147828 | − | 0.0197442i | ||||
\(431\) | 5.88180 | 0.283317 | 0.141658 | − | 0.989916i | \(-0.454757\pi\) | ||||
0.141658 | + | 0.989916i | \(0.454757\pi\) | |||||||
\(432\) | 3.90831 | − | 0.851542i | 0.188039 | − | 0.0409698i | ||||
\(433\) | −6.37830 | −0.306522 | −0.153261 | − | 0.988186i | \(-0.548977\pi\) | ||||
−0.153261 | + | 0.988186i | \(0.548977\pi\) | |||||||
\(434\) | 25.9756 | + | 34.6934i | 1.24687 | + | 1.66534i | ||||
\(435\) | −1.78072 | − | 1.78072i | −0.0853788 | − | 0.0853788i | ||||
\(436\) | 11.5926 | − | 6.33250i | 0.555184 | − | 0.303272i | ||||
\(437\) | −36.3608 | + | 36.3608i | −1.73937 | + | 1.73937i | ||||
\(438\) | −0.0770151 | + | 0.535963i | −0.00367992 | + | 0.0256093i | ||||
\(439\) | − | 37.2899i | − | 1.77975i | −0.456206 | − | 0.889874i | \(-0.650792\pi\) | ||
0.456206 | − | 0.889874i | \(-0.349208\pi\) | |||||||
\(440\) | 11.0281 | − | 4.11634i | 0.525742 | − | 0.196239i | ||||
\(441\) | − | 11.2545i | − | 0.535931i | ||||||
\(442\) | 1.28635 | + | 0.184842i | 0.0611855 | + | 0.00879203i | ||||
\(443\) | 28.4238 | − | 28.4238i | 1.35046 | − | 1.35046i | 0.465308 | − | 0.885149i | \(-0.345944\pi\) |
0.885149 | − | 0.465308i | \(-0.154056\pi\) | |||||||
\(444\) | −0.532982 | + | 1.81627i | −0.0252942 | + | 0.0861964i | ||||
\(445\) | 9.82813 | + | 9.82813i | 0.465898 | + | 0.465898i | ||||
\(446\) | −5.27931 | + | 3.95272i | −0.249983 | + | 0.187167i | ||||
\(447\) | −14.0900 | −0.666433 | ||||||||
\(448\) | 22.3960 | + | 25.8207i | 1.05811 | + | 1.21991i | ||||
\(449\) | 11.9658 | 0.564701 | 0.282350 | − | 0.959311i | \(-0.408886\pi\) | ||||
0.282350 | + | 0.959311i | \(0.408886\pi\) | |||||||
\(450\) | −1.13207 | + | 0.847599i | −0.0533661 | + | 0.0399562i | ||||
\(451\) | 11.6721 | + | 11.6721i | 0.549619 | + | 0.549619i | ||||
\(452\) | 2.81875 | − | 9.60562i | 0.132583 | − | 0.451810i | ||||
\(453\) | −2.84174 | + | 2.84174i | −0.133516 | + | 0.133516i | ||||
\(454\) | 3.20114 | + | 0.459986i | 0.150237 | + | 0.0215882i | ||||
\(455\) | 24.5294i | 1.14995i | ||||||||
\(456\) | −16.2106 | + | 6.05077i | −0.759130 | + | 0.283353i | ||||
\(457\) | 33.0504i | 1.54603i | 0.634385 | + | 0.773017i | \(0.281253\pi\) | ||||
−0.634385 | + | 0.773017i | \(0.718747\pi\) | |||||||
\(458\) | −2.60254 | + | 18.1116i | −0.121609 | + | 0.846300i | ||||
\(459\) | −0.113179 | + | 0.113179i | −0.00528276 | + | 0.00528276i | ||||
\(460\) | 14.7536 | − | 8.05921i | 0.687890 | − | 0.375763i | ||||
\(461\) | −20.7242 | − | 20.7242i | −0.965221 | − | 0.965221i | 0.0341939 | − | 0.999415i | \(-0.489114\pi\) |
−0.999415 | + | 0.0341939i | \(0.989114\pi\) | |||||||
\(462\) | 15.0714 | + | 20.1296i | 0.701185 | + | 0.936514i | ||||
\(463\) | 14.2359 | 0.661599 | 0.330800 | − | 0.943701i | \(-0.392682\pi\) | ||||
0.330800 | + | 0.943701i | \(0.392682\pi\) | |||||||
\(464\) | 2.14445 | + | 9.84234i | 0.0995536 | + | 0.456919i | ||||
\(465\) | 7.17282 | 0.332632 | ||||||||
\(466\) | 8.73045 | + | 11.6605i | 0.404430 | + | 0.540163i | ||||
\(467\) | 18.7991 | + | 18.7991i | 0.869918 | + | 0.869918i | 0.992463 | − | 0.122545i | \(-0.0391056\pi\) |
−0.122545 | + | 0.992463i | \(0.539106\pi\) | |||||||
\(468\) | −5.50456 | − | 10.0769i | −0.254448 | − | 0.465806i | ||||
\(469\) | −0.560456 | + | 0.560456i | −0.0258794 | + | 0.0258794i | ||||
\(470\) | −0.0151396 | + | 0.105360i | −0.000698339 | + | 0.00485988i | ||||
\(471\) | − | 12.9324i | − | 0.595894i | ||||||
\(472\) | −20.5088 | − | 9.35997i | −0.943995 | − | 0.430828i | ||||
\(473\) | 1.50515i | 0.0692068i | ||||||||
\(474\) | −21.4510 | − | 3.08239i | −0.985277 | − | 0.141579i | ||||
\(475\) | 4.32576 | − | 4.32576i | 0.198479 | − | 0.198479i | ||||
\(476\) | −1.31238 | − | 0.385117i | −0.0601529 | − | 0.0176518i | ||||
\(477\) | −2.88214 | − | 2.88214i | −0.131964 | − | 0.131964i | ||||
\(478\) | −4.23195 | + | 3.16854i | −0.193565 | + | 0.144926i | ||||
\(479\) | −26.7178 | −1.22077 | −0.610384 | − | 0.792106i | \(-0.708985\pi\) | ||||
−0.610384 | + | 0.792106i | \(0.708985\pi\) | |||||||
\(480\) | 5.64228 | − | 0.405867i | 0.257533 | − | 0.0185252i | ||||
\(481\) | 5.43361 | 0.247751 | ||||||||
\(482\) | 10.5767 | − | 7.91897i | 0.481756 | − | 0.360699i | ||||
\(483\) | 25.3946 | + | 25.3946i | 1.15549 | + | 1.15549i | ||||
\(484\) | −12.1291 | − | 3.55928i | −0.551324 | − | 0.161785i | ||||
\(485\) | 7.70738 | − | 7.70738i | 0.349974 | − | 0.349974i | ||||
\(486\) | 1.39984 | + | 0.201149i | 0.0634978 | + | 0.00912430i | ||||
\(487\) | 27.0801i | 1.22712i | 0.789650 | + | 0.613558i | \(0.210262\pi\) | ||||
−0.789650 | + | 0.613558i | \(0.789738\pi\) | |||||||
\(488\) | 7.45447 | − | 16.3336i | 0.337448 | − | 0.739389i | ||||
\(489\) | − | 0.489452i | − | 0.0221338i | ||||||
\(490\) | 2.26384 | − | 15.7545i | 0.102270 | − | 0.711717i | ||||
\(491\) | 1.51536 | − | 1.51536i | 0.0683872 | − | 0.0683872i | −0.672086 | − | 0.740473i | \(-0.734601\pi\) |
0.740473 | + | 0.672086i | \(0.234601\pi\) | |||||||
\(492\) | 3.80285 | + | 6.96169i | 0.171446 | + | 0.313857i | ||||
\(493\) | −0.285021 | − | 0.285021i | −0.0128367 | − | 0.0128367i | ||||
\(494\) | 29.7693 | + | 39.7603i | 1.33938 | + | 1.78890i | ||||
\(495\) | 4.16177 | 0.187057 | ||||||||
\(496\) | −24.1417 | − | 15.5038i | −1.08400 | − | 0.696139i | ||||
\(497\) | −51.7563 | −2.32159 | ||||||||
\(498\) | 6.64746 | + | 8.87844i | 0.297880 | + | 0.397853i | ||||
\(499\) | 7.31012 | + | 7.31012i | 0.327246 | + | 0.327246i | 0.851538 | − | 0.524292i | \(-0.175670\pi\) |
−0.524292 | + | 0.851538i | \(0.675670\pi\) | |||||||
\(500\) | −1.75520 | + | 0.958786i | −0.0784950 | + | 0.0428782i | ||||
\(501\) | −7.76986 | + | 7.76986i | −0.347132 | + | 0.347132i | ||||
\(502\) | 2.64889 | − | 18.4341i | 0.118226 | − | 0.822756i | ||||
\(503\) | 37.4924i | 1.67170i | 0.548954 | + | 0.835852i | \(0.315026\pi\) | ||||
−0.548954 | + | 0.835852i | \(0.684974\pi\) | |||||||
\(504\) | 4.22590 | + | 11.3216i | 0.188237 | + | 0.504303i | ||||
\(505\) | 4.22811i | 0.188148i | ||||||||
\(506\) | −48.9695 | − | 7.03665i | −2.17696 | − | 0.312817i | ||||
\(507\) | −14.1146 | + | 14.1146i | −0.626852 | + | 0.626852i | ||||
\(508\) | 1.10760 | − | 3.77443i | 0.0491418 | − | 0.167463i | ||||
\(509\) | 27.7592 | + | 27.7592i | 1.23040 | + | 1.23040i | 0.963809 | + | 0.266595i | \(0.0858987\pi\) |
0.266595 | + | 0.963809i | \(0.414101\pi\) | |||||||
\(510\) | −0.181198 | + | 0.135667i | −0.00802359 | + | 0.00600741i | ||||
\(511\) | −1.63585 | −0.0723658 | ||||||||
\(512\) | −19.8676 | − | 10.8295i | −0.878032 | − | 0.478602i | ||||
\(513\) | −6.11754 | −0.270096 | ||||||||
\(514\) | −9.83225 | + | 7.36159i | −0.433682 | + | 0.324706i | ||||
\(515\) | 11.8929 | + | 11.8929i | 0.524062 | + | 0.524062i | ||||
\(516\) | −0.203670 | + | 0.694056i | −0.00896605 | + | 0.0305541i | ||||
\(517\) | 0.221493 | − | 0.221493i | 0.00974126 | − | 0.00974126i | ||||
\(518\) | −5.66044 | − | 0.813376i | −0.248706 | − | 0.0357377i | ||||
\(519\) | 3.82694i | 0.167984i | ||||||||
\(520\) | −5.67851 | − | 15.2133i | −0.249019 | − | 0.667145i | ||||
\(521\) | − | 10.0782i | − | 0.441533i | −0.975327 | − | 0.220767i | \(-0.929144\pi\) | ||
0.975327 | − | 0.220767i | \(-0.0708559\pi\) | |||||||
\(522\) | −0.506556 | + | 3.52522i | −0.0221713 | + | 0.154295i | ||||
\(523\) | 8.16934 | − | 8.16934i | 0.357220 | − | 0.357220i | −0.505567 | − | 0.862787i | \(-0.668717\pi\) |
0.862787 | + | 0.505567i | \(0.168717\pi\) | |||||||
\(524\) | −2.11710 | + | 1.15648i | −0.0924861 | + | 0.0505209i | ||||
\(525\) | −3.02114 | − | 3.02114i | −0.131853 | − | 0.131853i | ||||
\(526\) | −4.39880 | − | 5.87510i | −0.191797 | − | 0.256167i | ||||
\(527\) | 1.14808 | 0.0500111 | ||||||||
\(528\) | −14.0073 | − | 8.99549i | −0.609592 | − | 0.391478i | ||||
\(529\) | −47.6548 | −2.07195 | ||||||||
\(530\) | −3.45478 | − | 4.61426i | −0.150066 | − | 0.200430i | ||||
\(531\) | −5.63594 | − | 5.63594i | −0.244579 | − | 0.244579i | ||||
\(532\) | −25.0602 | − | 45.8764i | −1.08650 | − | 1.98899i | ||||
\(533\) | 16.1018 | − | 16.1018i | 0.697445 | − | 0.697445i | ||||
\(534\) | 2.79578 | − | 19.4564i | 0.120985 | − | 0.841961i | ||||
\(535\) | − | 2.32563i | − | 0.100546i | ||||||
\(536\) | 0.217853 | − | 0.477343i | 0.00940983 | − | 0.0206181i | ||||
\(537\) | − | 14.7203i | − | 0.635226i | ||||||
\(538\) | 15.8260 | + | 2.27411i | 0.682306 | + | 0.0980437i | ||||
\(539\) | −33.1200 | + | 33.1200i | −1.42658 | + | 1.42658i | ||||
\(540\) | 1.91908 | + | 0.563151i | 0.0825840 | + | 0.0242341i | ||||
\(541\) | 1.98301 | + | 1.98301i | 0.0852564 | + | 0.0852564i | 0.748449 | − | 0.663192i | \(-0.230799\pi\) |
−0.663192 | + | 0.748449i | \(0.730799\pi\) | |||||||
\(542\) | 21.3216 | − | 15.9639i | 0.915840 | − | 0.685707i | ||||
\(543\) | −21.8909 | −0.939428 | ||||||||
\(544\) | 0.903101 | − | 0.0649630i | 0.0387201 | − | 0.00278526i | ||||
\(545\) | 6.60470 | 0.282914 | ||||||||
\(546\) | 27.7689 | − | 20.7911i | 1.18840 | − | 0.889776i | ||||
\(547\) | −14.5464 | − | 14.5464i | −0.621959 | − | 0.621959i | 0.324073 | − | 0.946032i | \(-0.394948\pi\) |
−0.946032 | + | 0.324073i | \(0.894948\pi\) | |||||||
\(548\) | 7.90704 | + | 2.32031i | 0.337772 | + | 0.0991187i | ||||
\(549\) | 4.48857 | − | 4.48857i | 0.191568 | − | 0.191568i | ||||
\(550\) | 5.82579 | + | 0.837134i | 0.248412 | + | 0.0356955i | ||||
\(551\) | − | 15.4059i | − | 0.656313i | ||||||
\(552\) | −21.6287 | − | 9.87107i | −0.920579 | − | 0.420141i | ||||
\(553\) | − | 65.4721i | − | 2.78416i | ||||||
\(554\) | −1.05799 | + | 7.36276i | −0.0449496 | + | 0.312814i | ||||
\(555\) | −0.669226 | + | 0.669226i | −0.0284071 | + | 0.0284071i | ||||
\(556\) | −7.78160 | − | 14.2454i | −0.330013 | − | 0.604139i | ||||
\(557\) | −25.6935 | − | 25.6935i | −1.08867 | − | 1.08867i | −0.995666 | − | 0.0930007i | \(-0.970354\pi\) |
−0.0930007 | − | 0.995666i | \(-0.529646\pi\) | |||||||
\(558\) | −6.07968 | − | 8.12011i | −0.257373 | − | 0.343752i | ||||
\(559\) | 2.07636 | 0.0878206 | ||||||||
\(560\) | 3.63824 | + | 16.6984i | 0.153744 | + | 0.705635i | ||||
\(561\) | 0.666131 | 0.0281241 | ||||||||
\(562\) | 9.34253 | + | 12.4780i | 0.394091 | + | 0.526354i | ||||
\(563\) | −15.8673 | − | 15.8673i | −0.668729 | − | 0.668729i | 0.288693 | − | 0.957422i | \(-0.406779\pi\) |
−0.957422 | + | 0.288693i | \(0.906779\pi\) | |||||||
\(564\) | 0.132107 | − | 0.0721638i | 0.00556269 | − | 0.00303864i | ||||
\(565\) | 3.53930 | − | 3.53930i | 0.148900 | − | 0.148900i | ||||
\(566\) | −2.99289 | + | 20.8281i | −0.125801 | + | 0.875472i | ||||
\(567\) | 4.27253i | 0.179430i | ||||||||
\(568\) | 32.0996 | − | 11.9815i | 1.34687 | − | 0.502733i | ||||
\(569\) | − | 45.0379i | − | 1.88809i | −0.329819 | − | 0.944044i | \(-0.606988\pi\) | ||
0.329819 | − | 0.944044i | \(-0.393012\pi\) | |||||||
\(570\) | −8.56355 | − | 1.23054i | −0.358688 | − | 0.0515415i | ||||
\(571\) | 23.0995 | − | 23.0995i | 0.966684 | − | 0.966684i | −0.0327783 | − | 0.999463i | \(-0.510436\pi\) |
0.999463 | + | 0.0327783i | \(0.0104355\pi\) | |||||||
\(572\) | −13.4556 | + | 45.8533i | −0.562607 | + | 1.91722i | ||||
\(573\) | 3.35979 | + | 3.35979i | 0.140357 | + | 0.140357i | ||||
\(574\) | −19.1843 | + | 14.3636i | −0.800736 | + | 0.599526i | ||||
\(575\) | 8.40564 | 0.350540 | ||||||||
\(576\) | −5.24186 | − | 6.04342i | −0.218411 | − | 0.251809i | ||||
\(577\) | −10.3572 | −0.431178 | −0.215589 | − | 0.976484i | \(-0.569167\pi\) | ||||
−0.215589 | + | 0.976484i | \(0.569167\pi\) | |||||||
\(578\) | 19.2161 | − | 14.3875i | 0.799286 | − | 0.598440i | ||||
\(579\) | −8.33786 | − | 8.33786i | −0.346510 | − | 0.346510i | ||||
\(580\) | −1.41819 | + | 4.83284i | −0.0588871 | + | 0.200673i | ||||
\(581\) | −23.6938 | + | 23.6938i | −0.982986 | + | 0.982986i | ||||
\(582\) | −15.2580 | − | 2.19250i | −0.632466 | − | 0.0908820i | ||||
\(583\) | 16.9632i | 0.702543i | ||||||||
\(584\) | 1.01456 | − | 0.378697i | 0.0419830 | − | 0.0156706i | ||||
\(585\) | − | 5.74117i | − | 0.237368i | ||||||
\(586\) | −4.42753 | + | 30.8120i | −0.182899 | + | 1.27283i | ||||
\(587\) | −23.6336 | + | 23.6336i | −0.975462 | + | 0.975462i | −0.999706 | − | 0.0242436i | \(-0.992282\pi\) |
0.0242436 | + | 0.999706i | \(0.492282\pi\) | |||||||
\(588\) | −19.7540 | + | 10.7907i | −0.814641 | + | 0.445001i | ||||
\(589\) | 31.0279 | + | 31.0279i | 1.27848 | + | 1.27848i | ||||
\(590\) | −6.75572 | − | 9.02305i | −0.278129 | − | 0.371473i | ||||
\(591\) | 6.45226 | 0.265411 | ||||||||
\(592\) | 3.69894 | − | 0.805924i | 0.152025 | − | 0.0331233i | ||||
\(593\) | −30.5649 | −1.25515 | −0.627575 | − | 0.778556i | \(-0.715952\pi\) | ||||
−0.627575 | + | 0.778556i | \(0.715952\pi\) | |||||||
\(594\) | −3.52751 | − | 4.71140i | −0.144735 | − | 0.193311i | ||||
\(595\) | −0.483562 | − | 0.483562i | −0.0198241 | − | 0.0198241i | ||||
\(596\) | 13.5093 | + | 24.7307i | 0.553361 | + | 1.01301i | ||||
\(597\) | 2.54744 | − | 2.54744i | 0.104260 | − | 0.104260i | ||||
\(598\) | −9.70710 | + | 67.5536i | −0.396953 | + | 2.76247i | ||||
\(599\) | − | 10.2816i | − | 0.420096i | −0.977691 | − | 0.210048i | \(-0.932638\pi\) | ||
0.977691 | − | 0.210048i | \(-0.0673620\pi\) | |||||||
\(600\) | 2.57312 | + | 1.17434i | 0.105047 | + | 0.0479422i | ||||
\(601\) | 22.9223i | 0.935021i | 0.883987 | + | 0.467511i | \(0.154849\pi\) | ||||
−0.883987 | + | 0.467511i | \(0.845151\pi\) | |||||||
\(602\) | −2.16304 | − | 0.310817i | −0.0881589 | − | 0.0126680i | ||||
\(603\) | 0.131176 | − | 0.131176i | 0.00534192 | − | 0.00534192i | ||||
\(604\) | 7.71244 | + | 2.26320i | 0.313815 | + | 0.0920884i | ||||
\(605\) | −4.46912 | − | 4.46912i | −0.181696 | − | 0.181696i | ||||
\(606\) | 4.78650 | − | 3.58374i | 0.194438 | − | 0.145580i | ||||
\(607\) | 39.7832 | 1.61475 | 0.807374 | − | 0.590040i | \(-0.200888\pi\) | ||||
0.807374 | + | 0.590040i | \(0.200888\pi\) | |||||||
\(608\) | 26.1628 | + | 22.6514i | 1.06104 | + | 0.918636i | ||||
\(609\) | −10.7596 | −0.436000 | ||||||||
\(610\) | 7.18613 | − | 5.38039i | 0.290958 | − | 0.217846i | ||||
\(611\) | −0.305551 | − | 0.305551i | −0.0123613 | − | 0.0123613i | ||||
\(612\) | 0.307167 | + | 0.0901377i | 0.0124165 | + | 0.00364360i | ||||
\(613\) | −26.9534 | + | 26.9534i | −1.08864 | + | 1.08864i | −0.0929665 | + | 0.995669i | \(0.529635\pi\) |
−0.995669 | + | 0.0929665i | \(0.970365\pi\) | |||||||
\(614\) | −38.9589 | − | 5.59819i | −1.57225 | − | 0.225924i | ||||
\(615\) | 3.96632i | 0.159937i | ||||||||
\(616\) | 20.8812 | − | 45.7533i | 0.841330 | − | 1.84345i | ||||
\(617\) | − | 12.2306i | − | 0.492385i | −0.969221 | − | 0.246193i | \(-0.920820\pi\) | ||
0.969221 | − | 0.246193i | \(-0.0791795\pi\) | |||||||
\(618\) | 3.38313 | − | 23.5439i | 0.136089 | − | 0.947074i | ||||
\(619\) | −4.13984 | + | 4.13984i | −0.166394 | + | 0.166394i | −0.785392 | − | 0.618998i | \(-0.787539\pi\) |
0.618998 | + | 0.785392i | \(0.287539\pi\) | |||||||
\(620\) | −6.87720 | − | 12.5897i | −0.276195 | − | 0.505616i | ||||
\(621\) | −5.94369 | − | 5.94369i | −0.238512 | − | 0.238512i | ||||
\(622\) | −10.0798 | − | 13.4628i | −0.404164 | − | 0.539807i | ||||
\(623\) | 59.3843 | 2.37918 | ||||||||
\(624\) | −12.4093 | + | 19.3232i | −0.496770 | + | 0.773547i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 8.14706 | + | 10.8813i | 0.325622 | + | 0.434906i | ||||
\(627\) | 18.0028 | + | 18.0028i | 0.718962 | + | 0.718962i | ||||
\(628\) | −22.6990 | + | 12.3994i | −0.905787 | + | 0.494790i | ||||
\(629\) | −0.107116 | + | 0.107116i | −0.00427100 | + | 0.00427100i | ||||
\(630\) | −0.859415 | + | 5.98084i | −0.0342399 | + | 0.238283i | ||||
\(631\) | − | 25.3923i | − | 1.01085i | −0.862870 | − | 0.505426i | \(-0.831336\pi\) | ||
0.862870 | − | 0.505426i | \(-0.168664\pi\) | |||||||
\(632\) | 15.1567 | + | 40.6062i | 0.602901 | + | 1.61523i | ||||
\(633\) | − | 1.37941i | − | 0.0548266i | ||||||
\(634\) | −16.0363 | − | 2.30433i | −0.636881 | − | 0.0915164i | ||||
\(635\) | 1.39073 | − | 1.39073i | 0.0551895 | − | 0.0551895i | ||||
\(636\) | −2.29538 | + | 7.82208i | −0.0910176 | + | 0.310166i | ||||
\(637\) | 45.6892 | + | 45.6892i | 1.81027 | + | 1.81027i | ||||
\(638\) | 11.8648 | − | 8.88337i | 0.469731 | − | 0.351696i | ||||
\(639\) | 12.1137 | 0.479212 | ||||||||
\(640\) | −6.12211 | − | 9.51419i | −0.241998 | − | 0.376081i | ||||
\(641\) | 42.0683 | 1.66160 | 0.830799 | − | 0.556572i | \(-0.187884\pi\) | ||||
0.830799 | + | 0.556572i | \(0.187884\pi\) | |||||||
\(642\) | −2.63277 | + | 1.97121i | −0.103907 | + | 0.0777973i | ||||
\(643\) | −8.73724 | − | 8.73724i | −0.344563 | − | 0.344563i | 0.513517 | − | 0.858080i | \(-0.328343\pi\) |
−0.858080 | + | 0.513517i | \(0.828343\pi\) | |||||||
\(644\) | 20.2247 | − | 68.9206i | 0.796963 | − | 2.71585i | ||||
\(645\) | −0.255733 | + | 0.255733i | −0.0100695 | + | 0.0100695i | ||||
\(646\) | −1.37068 | − | 0.196959i | −0.0539287 | − | 0.00774926i | ||||
\(647\) | − | 4.04843i | − | 0.159160i | −0.996828 | − | 0.0795802i | \(-0.974642\pi\) | ||
0.996828 | − | 0.0795802i | \(-0.0253580\pi\) | |||||||
\(648\) | −0.989085 | − | 2.64985i | −0.0388549 | − | 0.104096i | ||||
\(649\) | 33.1710i | 1.30208i | ||||||||
\(650\) | 1.15483 | − | 8.03670i | 0.0452962 | − | 0.315225i | ||||
\(651\) | 21.6701 | − | 21.6701i | 0.849317 | − | 0.849317i | ||||
\(652\) | −0.859086 | + | 0.469279i | −0.0336444 | + | 0.0183784i | ||||
\(653\) | −12.8095 | − | 12.8095i | −0.501275 | − | 0.501275i | 0.410559 | − | 0.911834i | \(-0.365334\pi\) |
−0.911834 | + | 0.410559i | \(0.865334\pi\) | |||||||
\(654\) | −5.59814 | − | 7.47697i | −0.218905 | − | 0.292373i | ||||
\(655\) | −1.20619 | −0.0471297 | ||||||||
\(656\) | 8.57304 | − | 13.3495i | 0.334721 | − | 0.521212i | ||||
\(657\) | 0.382876 | 0.0149374 | ||||||||
\(658\) | 0.272568 | + | 0.364045i | 0.0106258 | + | 0.0141920i | ||||
\(659\) | −29.8196 | − | 29.8196i | −1.16161 | − | 1.16161i | −0.984124 | − | 0.177481i | \(-0.943205\pi\) |
−0.177481 | − | 0.984124i | \(-0.556795\pi\) | |||||||
\(660\) | −3.99024 | − | 7.30473i | −0.155320 | − | 0.284336i | ||||
\(661\) | −30.2458 | + | 30.2458i | −1.17642 | + | 1.17642i | −0.195775 | + | 0.980649i | \(0.562722\pi\) |
−0.980649 | + | 0.195775i | \(0.937278\pi\) | |||||||
\(662\) | 3.79101 | − | 26.3824i | 0.147342 | − | 1.02538i | ||||
\(663\) | − | 0.918931i | − | 0.0356883i | ||||||
\(664\) | 9.20997 | − | 20.1801i | 0.357416 | − | 0.783141i | ||||
\(665\) | − | 26.1374i | − | 1.01357i | ||||||
\(666\) | 1.32484 | + | 0.190373i | 0.0513367 | + | 0.00737681i | ||||
\(667\) | 14.9681 | − | 14.9681i | 0.579566 | − | 0.579566i | ||||
\(668\) | 21.0873 | + | 6.18804i | 0.815892 | + | 0.239422i | ||||
\(669\) | 3.29754 | + | 3.29754i | 0.127490 | + | 0.127490i | ||||
\(670\) | 0.210011 | − | 0.157239i | 0.00811345 | − | 0.00607469i | ||||
\(671\) | −26.4181 | −1.01986 | ||||||||
\(672\) | 15.8199 | − | 18.2723i | 0.610266 | − | 0.704868i | ||||
\(673\) | 38.3587 | 1.47862 | 0.739309 | − | 0.673366i | \(-0.235152\pi\) | ||||
0.739309 | + | 0.673366i | \(0.235152\pi\) | |||||||
\(674\) | −36.9918 | + | 27.6964i | −1.42487 | + | 1.06683i | ||||
\(675\) | 0.707107 | + | 0.707107i | 0.0272166 | + | 0.0272166i | ||||
\(676\) | 38.3069 | + | 11.2411i | 1.47334 | + | 0.432350i | ||||
\(677\) | −19.3263 | + | 19.3263i | −0.742772 | + | 0.742772i | −0.973111 | − | 0.230339i | \(-0.926017\pi\) |
0.230339 | + | 0.973111i | \(0.426017\pi\) | |||||||
\(678\) | −7.00664 | − | 1.00682i | −0.269088 | − | 0.0386665i | ||||
\(679\) | − | 46.5701i | − | 1.78720i | ||||||
\(680\) | 0.411852 | + | 0.187964i | 0.0157938 | + | 0.00720810i | ||||
\(681\) | − | 2.28680i | − | 0.0876302i | ||||||
\(682\) | −6.00461 | + | 41.7873i | −0.229929 | + | 1.60012i | ||||
\(683\) | 21.3741 | − | 21.3741i | 0.817856 | − | 0.817856i | −0.167941 | − | 0.985797i | \(-0.553712\pi\) |
0.985797 | + | 0.167941i | \(0.0537119\pi\) | |||||||
\(684\) | 5.86541 | + | 10.7375i | 0.224270 | + | 0.410559i | ||||
\(685\) | 2.91344 | + | 2.91344i | 0.111317 | + | 0.111317i | ||||
\(686\) | −15.4074 | − | 20.5784i | −0.588258 | − | 0.785686i | ||||
\(687\) | 12.9384 | 0.493630 | ||||||||
\(688\) | 1.41348 | − | 0.307970i | 0.0538885 | − | 0.0117412i | ||||
\(689\) | 23.4008 | 0.891499 | ||||||||
\(690\) | −7.12462 | − | 9.51575i | −0.271230 | − | 0.362258i | ||||
\(691\) | 3.96331 | + | 3.96331i | 0.150771 | + | 0.150771i | 0.778462 | − | 0.627691i | \(-0.216000\pi\) |
−0.627691 | + | 0.778462i | \(0.716000\pi\) | |||||||
\(692\) | 6.71704 | − | 3.66921i | 0.255344 | − | 0.139482i | ||||
\(693\) | 12.5733 | − | 12.5733i | 0.477619 | − | 0.477619i | ||||
\(694\) | −6.39762 | + | 44.5223i | −0.242850 | + | 1.69004i | ||||
\(695\) | − | 8.11610i | − | 0.307861i | ||||||
\(696\) | 6.67315 | − | 2.49083i | 0.252945 | − | 0.0944145i | ||||
\(697\) | 0.634848i | 0.0240466i | ||||||||
\(698\) | 44.8625 | + | 6.44650i | 1.69807 | + | 0.244004i | ||||
\(699\) | 7.28334 | − | 7.28334i | 0.275481 | − | 0.275481i | ||||
\(700\) | −2.40608 | + | 8.19933i | −0.0909413 | + | 0.309905i | ||||
\(701\) | −27.4177 | − | 27.4177i | −1.03555 | − | 1.03555i | −0.999344 | − | 0.0362086i | \(-0.988472\pi\) |
−0.0362086 | − | 0.999344i | \(-0.511528\pi\) | |||||||
\(702\) | −6.49939 | + | 4.86622i | −0.245304 | + | 0.183663i | ||||
\(703\) | −5.78982 | −0.218367 | ||||||||
\(704\) | −2.35885 | + | 33.2105i | −0.0889024 | + | 1.25167i | ||||
\(705\) | 0.0752658 | 0.00283468 | ||||||||
\(706\) | 12.0391 | − | 9.01393i | 0.453099 | − | 0.339244i | ||||
\(707\) | 12.7737 | + | 12.7737i | 0.480404 | + | 0.480404i | ||||
\(708\) | −4.48855 | + | 15.2959i | −0.168690 | + | 0.574854i | ||||
\(709\) | 36.8453 | − | 36.8453i | 1.38376 | − | 1.38376i | 0.545915 | − | 0.837840i | \(-0.316182\pi\) |
0.837840 | − | 0.545915i | \(-0.183818\pi\) | |||||||
\(710\) | 16.9572 | + | 2.43666i | 0.636394 | + | 0.0914464i | ||||
\(711\) | 15.3239i | 0.574693i | ||||||||
\(712\) | −36.8305 | + | 13.7474i | −1.38028 | + | 0.515204i | ||||
\(713\) | 60.2922i | 2.25796i | ||||||||
\(714\) | −0.137558 | + | 0.957292i | −0.00514797 | + | 0.0358258i | ||||
\(715\) | −16.8952 | + | 16.8952i | −0.631845 | + | 0.631845i | ||||
\(716\) | −25.8370 | + | 14.1136i | −0.965575 | + | 0.527449i | ||||
\(717\) | 2.64334 | + | 2.64334i | 0.0987175 | + | 0.0987175i | ||||
\(718\) | −14.4254 | − | 19.2668i | −0.538351 | − | 0.719030i | ||||
\(719\) | −26.8739 | −1.00223 | −0.501114 | − | 0.865382i | \(-0.667076\pi\) | ||||
−0.501114 | + | 0.865382i | \(0.667076\pi\) | |||||||
\(720\) | −0.851542 | − | 3.90831i | −0.0317351 | − | 0.145654i | ||||
\(721\) | 71.8599 | 2.67620 | ||||||||
\(722\) | −15.6164 | − | 20.8576i | −0.581184 | − | 0.776238i | ||||
\(723\) | −6.60638 | − | 6.60638i | −0.245694 | − | 0.245694i | ||||
\(724\) | 20.9887 | + | 38.4229i | 0.780038 | + | 1.42798i | ||||
\(725\) | −1.78072 | + | 1.78072i | −0.0661341 | + | 0.0661341i | ||||
\(726\) | −1.27132 | + | 8.84737i | −0.0471831 | + | 0.328357i | ||||
\(727\) | 9.81023i | 0.363841i | 0.983313 | + | 0.181921i | \(0.0582314\pi\) | ||||
−0.983313 | + | 0.181921i | \(0.941769\pi\) | |||||||
\(728\) | −63.1169 | − | 28.8058i | −2.33927 | − | 1.06761i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0.535963 | + | 0.0770151i | 0.0198369 | + | 0.00285046i | ||||
\(731\) | −0.0409325 | + | 0.0409325i | −0.00151394 | + | 0.00151394i | ||||
\(732\) | −12.1819 | − | 3.57477i | −0.450257 | − | 0.132127i | ||||
\(733\) | −1.66941 | − | 1.66941i | −0.0616610 | − | 0.0616610i | 0.675604 | − | 0.737265i | \(-0.263883\pi\) |
−0.737265 | + | 0.675604i | \(0.763883\pi\) | |||||||
\(734\) | 29.0986 | − | 21.7867i | 1.07405 | − | 0.804160i | ||||
\(735\) | −11.2545 | −0.415130 | ||||||||
\(736\) | 3.41157 | + | 47.4270i | 0.125752 | + | 1.74818i | ||||
\(737\) | −0.772055 | −0.0284390 | ||||||||
\(738\) | 4.49014 | − | 3.36185i | 0.165284 | − | 0.123751i | ||||
\(739\) | 36.2208 | + | 36.2208i | 1.33240 | + | 1.33240i | 0.903214 | + | 0.429191i | \(0.141201\pi\) |
0.429191 | + | 0.903214i | \(0.358799\pi\) | |||||||
\(740\) | 1.81627 | + | 0.532982i | 0.0667675 | + | 0.0195928i | ||||
\(741\) | 24.8349 | − | 24.8349i | 0.912334 | − | 0.912334i | ||||
\(742\) | −24.3777 | − | 3.50294i | −0.894932 | − | 0.128597i | ||||
\(743\) | − | 32.7601i | − | 1.20185i | −0.799305 | − | 0.600926i | \(-0.794799\pi\) | ||
0.799305 | − | 0.600926i | \(-0.205201\pi\) | |||||||
\(744\) | −8.42332 | + | 18.4565i | −0.308814 | + | 0.676648i | ||||
\(745\) | 14.0900i | 0.516217i | ||||||||
\(746\) | 4.18993 | − | 29.1586i | 0.153404 | − | 1.06757i | ||||
\(747\) | 5.54562 | − | 5.54562i | 0.202903 | − | 0.202903i | ||||
\(748\) | −0.638677 | − | 1.16919i | −0.0233523 | − | 0.0427500i | ||||
\(749\) | −7.02606 | − | 7.02606i | −0.256727 | − | 0.256727i | ||||
\(750\) | 0.847599 | + | 1.13207i | 0.0309500 | + | 0.0413372i | ||||
\(751\) | 8.98910 | 0.328017 | 0.164008 | − | 0.986459i | \(-0.447558\pi\) | ||||
0.164008 | + | 0.986459i | \(0.447558\pi\) | |||||||
\(752\) | −0.253324 | − | 0.162684i | −0.00923777 | − | 0.00593248i | ||||
\(753\) | −13.1688 | −0.479897 | ||||||||
\(754\) | −12.2547 | − | 16.3675i | −0.446288 | − | 0.596069i | ||||
\(755\) | 2.84174 | + | 2.84174i | 0.103421 | + | 0.103421i | ||||
\(756\) | 7.49916 | − | 4.09644i | 0.272742 | − | 0.148986i | ||||
\(757\) | 27.4805 | − | 27.4805i | 0.998796 | − | 0.998796i | −0.00120342 | − | 0.999999i | \(-0.500383\pi\) |
0.999999 | + | 0.00120342i | \(0.000383062\pi\) | |||||||
\(758\) | −2.84871 | + | 19.8248i | −0.103470 | + | 0.720068i | ||||
\(759\) | 34.9823i | 1.26978i | ||||||||
\(760\) | 6.05077 | + | 16.2106i | 0.219485 | + | 0.588019i | ||||
\(761\) | 1.80961i | 0.0655984i | 0.999462 | + | 0.0327992i | \(0.0104422\pi\) | ||||
−0.999462 | + | 0.0327992i | \(0.989558\pi\) | |||||||
\(762\) | −2.75319 | − | 0.395618i | −0.0997374 | − | 0.0143317i | ||||
\(763\) | 19.9537 | − | 19.9537i | 0.722373 | − | 0.722373i | ||||
\(764\) | 2.67579 | − | 9.11842i | 0.0968065 | − | 0.329893i | ||||
\(765\) | 0.113179 | + | 0.113179i | 0.00409201 | + | 0.00409201i | ||||
\(766\) | 31.9055 | − | 23.8882i | 1.15279 | − | 0.863117i | ||||
\(767\) | 45.7596 | 1.65228 | ||||||||
\(768\) | −5.58160 | + | 14.9949i | −0.201409 | + | 0.541080i | ||||
\(769\) | 41.3952 | 1.49275 | 0.746374 | − | 0.665527i | \(-0.231793\pi\) | ||||
0.746374 | + | 0.665527i | \(0.231793\pi\) | |||||||
\(770\) | 20.1296 | − | 15.0714i | 0.725421 | − | 0.543136i | ||||
\(771\) | 6.14138 | + | 6.14138i | 0.221176 | + | 0.221176i | ||||
\(772\) | −6.64040 | + | 22.6288i | −0.238993 | + | 0.814430i | ||||
\(773\) | 20.2439 | − | 20.2439i | 0.728122 | − | 0.728122i | −0.242123 | − | 0.970246i | \(-0.577844\pi\) |
0.970246 | + | 0.242123i | \(0.0778438\pi\) | |||||||
\(774\) | 0.506266 | + | 0.0727477i | 0.0181974 | + | 0.00261486i | ||||
\(775\) | − | 7.17282i | − | 0.257655i | ||||||
\(776\) | 10.7809 | + | 28.8831i | 0.387012 | + | 1.03684i | ||||
\(777\) | 4.04365i | 0.145065i | ||||||||
\(778\) | 3.17326 | − | 22.0834i | 0.113767 | − | 0.791727i | ||||
\(779\) | −17.1573 | + | 17.1573i | −0.614725 | + | 0.614725i | ||||
\(780\) | −10.0769 | + | 5.50456i | −0.360811 | + | 0.197095i | ||||
\(781\) | −35.6484 | − | 35.6484i | −1.27560 | − | 1.27560i | ||||
\(782\) | −1.14036 | − | 1.52309i | −0.0407793 | − | 0.0544655i | ||||
\(783\) | 2.51831 | 0.0899971 | ||||||||
\(784\) | 37.8797 | + | 24.3263i | 1.35285 | + | 0.868795i | ||||
\(785\) | −12.9324 | −0.461577 | ||||||||
\(786\) | 1.02236 | + | 1.36549i | 0.0364665 | + | 0.0487053i | ||||
\(787\) | −36.5446 | − | 36.5446i | −1.30267 | − | 1.30267i | −0.926583 | − | 0.376091i | \(-0.877268\pi\) |
−0.376091 | − | 0.926583i | \(-0.622732\pi\) | |||||||
\(788\) | −6.18634 | − | 11.3250i | −0.220379 | − | 0.403437i | ||||
\(789\) | −3.66968 | + | 3.66968i | −0.130644 | + | 0.130644i | ||||
\(790\) | −3.08239 | + | 21.4510i | −0.109667 | + | 0.763193i | ||||
\(791\) | − | 21.3854i | − | 0.760379i | ||||||
\(792\) | −4.88732 | + | 10.7087i | −0.173663 | + | 0.380517i | ||||
\(793\) | 36.4438i | 1.29416i | ||||||||
\(794\) | −5.90368 | − | 0.848328i | −0.209514 | − | 0.0301060i | ||||
\(795\) | −2.88214 | + | 2.88214i | −0.102219 | + | 0.102219i | ||||
\(796\) | −6.91371 | − | 2.02882i | −0.245050 | − | 0.0719095i | ||||
\(797\) | −12.7215 | − | 12.7215i | −0.450619 | − | 0.450619i | 0.444941 | − | 0.895560i | \(-0.353225\pi\) |
−0.895560 | + | 0.444941i | \(0.853225\pi\) | |||||||
\(798\) | −29.5893 | + | 22.1541i | −1.04745 | + | 0.784245i | ||||
\(799\) | 0.0120470 | 0.000426193 | ||||||||
\(800\) | −0.405867 | − | 5.64228i | −0.0143496 | − | 0.199485i | ||||
\(801\) | −13.8991 | −0.491100 | ||||||||
\(802\) | 18.1013 | − | 13.5528i | 0.639181 | − | 0.478566i | ||||
\(803\) | −1.12673 | − | 1.12673i | −0.0397615 | − | 0.0397615i | ||||
\(804\) | −0.356011 | − | 0.104471i | −0.0125555 | − | 0.00368440i | ||||
\(805\) | 25.3946 | − | 25.3946i | 0.895042 | − | 0.895042i | ||||
\(806\) | 57.6458 | + | 8.28339i | 2.03049 | + | 0.291770i | ||||
\(807\) | − | 11.3056i | − | 0.397975i | ||||||
\(808\) | −10.8794 | − | 4.96523i | −0.382736 | − | 0.174676i | ||||
\(809\) | 5.24547i | 0.184421i | 0.995740 | + | 0.0922105i | \(0.0293933\pi\) | ||||
−0.995740 | + | 0.0922105i | \(0.970607\pi\) | |||||||
\(810\) | 0.201149 | − | 1.39984i | 0.00706765 | − | 0.0491852i | ||||
\(811\) | −2.66407 | + | 2.66407i | −0.0935481 | + | 0.0935481i | −0.752332 | − | 0.658784i | \(-0.771071\pi\) |
0.658784 | + | 0.752332i | \(0.271071\pi\) | |||||||
\(812\) | 10.3161 | + | 18.8852i | 0.362025 | + | 0.662741i | ||||
\(813\) | −13.3178 | − | 13.3178i | −0.467075 | − | 0.467075i | ||||
\(814\) | −3.33854 | − | 4.45900i | −0.117016 | − | 0.156288i | ||||
\(815\) | −0.489452 | −0.0171447 | ||||||||
\(816\) | −0.136298 | − | 0.625563i | −0.00477137 | − | 0.0218991i | ||||
\(817\) | −2.21248 | −0.0774047 | ||||||||
\(818\) | 23.3183 | + | 31.1443i | 0.815305 | + | 1.08893i | ||||
\(819\) | −17.3449 | − | 17.3449i | −0.606079 | − | 0.606079i | ||||
\(820\) | 6.96169 | − | 3.80285i | 0.243113 | − | 0.132801i | ||||
\(821\) | 1.11276 | − | 1.11276i | 0.0388357 | − | 0.0388357i | −0.687422 | − | 0.726258i | \(-0.741258\pi\) |
0.726258 | + | 0.687422i | \(0.241258\pi\) | |||||||
\(822\) | 0.828779 | − | 5.76764i | 0.0289070 | − | 0.201170i | ||||
\(823\) | 11.7558i | 0.409781i | 0.978785 | + | 0.204891i | \(0.0656838\pi\) | ||||
−0.978785 | + | 0.204891i | \(0.934316\pi\) | |||||||
\(824\) | −44.5679 | + | 16.6355i | −1.55260 | + | 0.579524i | ||||
\(825\) | − | 4.16177i | − | 0.144894i | ||||||
\(826\) | −47.6698 | − | 6.84990i | −1.65865 | − | 0.238339i | ||||
\(827\) | −30.1964 | + | 30.1964i | −1.05003 | + | 1.05003i | −0.0513511 | + | 0.998681i | \(0.516353\pi\) |
−0.998681 | + | 0.0513511i | \(0.983647\pi\) | |||||||
\(828\) | −4.73364 | + | 16.1311i | −0.164505 | + | 0.560594i | ||||
\(829\) | 0.0724462 | + | 0.0724462i | 0.00251616 | + | 0.00251616i | 0.708364 | − | 0.705848i | \(-0.249434\pi\) |
−0.705848 | + | 0.708364i | \(0.749434\pi\) | |||||||
\(830\) | 8.87844 | − | 6.64746i | 0.308175 | − | 0.230737i | ||||
\(831\) | 5.25973 | 0.182458 | ||||||||
\(832\) | 45.8140 | + | 3.25404i | 1.58831 | + | 0.112814i | ||||
\(833\) | −1.80140 | −0.0624148 | ||||||||
\(834\) | −9.18797 | + | 6.87920i | −0.318153 | + | 0.238207i | ||||
\(835\) | 7.76986 | + | 7.76986i | 0.268887 | + | 0.268887i | ||||
\(836\) | 14.3377 | − | 48.8593i | 0.495879 | − | 1.68983i | ||||
\(837\) | −5.07195 | + | 5.07195i | −0.175312 | + | 0.175312i | ||||
\(838\) | −3.87849 | − | 0.557318i | −0.133980 | − | 0.0192522i | ||||
\(839\) | − | 7.91971i | − | 0.273419i | −0.990611 | − | 0.136709i | \(-0.956347\pi\) | ||
0.990611 | − | 0.136709i | \(-0.0436527\pi\) | |||||||
\(840\) | 11.3216 | − | 4.22590i | 0.390632 | − | 0.145807i | ||||
\(841\) | − | 22.6581i | − | 0.781314i | ||||||
\(842\) | −1.77435 | + | 12.3480i | −0.0611480 | + | 0.425541i | ||||
\(843\) | 7.79397 | − | 7.79397i | 0.268439 | − | 0.268439i | ||||
\(844\) | −2.42114 | + | 1.32256i | −0.0833391 | + | 0.0455243i | ||||
\(845\) | 14.1146 | + | 14.1146i | 0.485558 | + | 0.485558i | ||||
\(846\) | −0.0637953 | − | 0.0852060i | −0.00219333 | − | 0.00292944i | ||||
\(847\) | −27.0037 | −0.927857 | ||||||||
\(848\) | 15.9301 | − | 3.47085i | 0.547042 | − | 0.119189i | ||||
\(849\) | 14.8790 | 0.510646 | ||||||||
\(850\) | 0.135667 | + | 0.181198i | 0.00465332 | + | 0.00621505i | ||||
\(851\) | −5.62528 | − | 5.62528i | −0.192832 | − | 0.192832i | ||||
\(852\) | −11.6145 | − | 21.2620i | −0.397905 | − | 0.728425i | ||||
\(853\) | −14.1305 | + | 14.1305i | −0.483817 | + | 0.483817i | −0.906348 | − | 0.422531i | \(-0.861142\pi\) |
0.422531 | + | 0.906348i | \(0.361142\pi\) | |||||||
\(854\) | 5.45540 | − | 37.9652i | 0.186680 | − | 1.29914i | ||||
\(855\) | 6.11754i | 0.209216i | ||||||||
\(856\) | 5.98413 | + | 2.73108i | 0.204533 | + | 0.0933465i | ||||
\(857\) | 4.80762i | 0.164225i | 0.996623 | + | 0.0821126i | \(0.0261667\pi\) | ||||
−0.996623 | + | 0.0821126i | \(0.973833\pi\) | |||||||
\(858\) | 33.4469 | + | 4.80613i | 1.14186 | + | 0.164079i | ||||
\(859\) | −34.8123 | + | 34.8123i | −1.18778 | + | 1.18778i | −0.210101 | + | 0.977680i | \(0.567379\pi\) |
−0.977680 | + | 0.210101i | \(0.932621\pi\) | |||||||
\(860\) | 0.694056 | + | 0.203670i | 0.0236671 | + | 0.00694508i | ||||
\(861\) | 11.9828 | + | 11.9828i | 0.408373 | + | 0.408373i | ||||
\(862\) | −6.65859 | + | 4.98541i | −0.226793 | + | 0.169804i | ||||
\(863\) | −51.5605 | −1.75514 | −0.877570 | − | 0.479449i | \(-0.840837\pi\) | ||||
−0.877570 | + | 0.479449i | \(0.840837\pi\) | |||||||
\(864\) | −3.70270 | + | 4.27668i | −0.125968 | + | 0.145496i | ||||
\(865\) | 3.82694 | 0.130120 | ||||||||
\(866\) | 7.22066 | − | 5.40624i | 0.245368 | − | 0.183712i | ||||
\(867\) | −12.0027 | − | 12.0027i | −0.407633 | − | 0.407633i | ||||
\(868\) | −58.8123 | − | 17.2584i | −1.99622 | − | 0.585788i | ||||
\(869\) | 45.0955 | − | 45.0955i | 1.52976 | − | 1.52976i | ||||
\(870\) | 3.52522 | + | 0.506556i | 0.119516 | + | 0.0171738i | ||||
\(871\) | 1.06505i | 0.0360880i | ||||||||
\(872\) | −7.75616 | + | 16.9947i | −0.262657 | + | 0.575512i | ||||
\(873\) | 10.8999i | 0.368905i | ||||||||
\(874\) | 10.3435 | − | 71.9822i | 0.349872 | − | 2.43483i | ||||
\(875\) | −3.02114 | + | 3.02114i | −0.102133 | + | 0.102133i | ||||
\(876\) | −0.367096 | − | 0.672024i | −0.0124030 | − | 0.0227056i | ||||
\(877\) | −12.4082 | − | 12.4082i | −0.418994 | − | 0.418994i | 0.465863 | − | 0.884857i | \(-0.345744\pi\) |
−0.884857 | + | 0.465863i | \(0.845744\pi\) | |||||||
\(878\) | 31.6069 | + | 42.2146i | 1.06668 | + | 1.42467i | ||||
\(879\) | 22.0112 | 0.742419 | ||||||||
\(880\) | −8.99549 | + | 14.0073i | −0.303238 | + | 0.472188i | ||||
\(881\) | −45.7147 | −1.54017 | −0.770084 | − | 0.637942i | \(-0.779786\pi\) | ||||
−0.770084 | + | 0.637942i | \(0.779786\pi\) | |||||||
\(882\) | 9.53935 | + | 12.7409i | 0.321207 | + | 0.429009i | ||||
\(883\) | −8.68322 | − | 8.68322i | −0.292213 | − | 0.292213i | 0.545741 | − | 0.837954i | \(-0.316248\pi\) |
−0.837954 | + | 0.545741i | \(0.816248\pi\) | |||||||
\(884\) | −1.61291 | + | 0.881058i | −0.0542480 | + | 0.0296332i | ||||
\(885\) | −5.63594 | + | 5.63594i | −0.189450 | + | 0.189450i | ||||
\(886\) | −8.08565 | + | 56.2697i | −0.271643 | + | 1.89042i | ||||
\(887\) | − | 5.87579i | − | 0.197290i | −0.995123 | − | 0.0986449i | \(-0.968549\pi\) | ||
0.995123 | − | 0.0986449i | \(-0.0314508\pi\) | |||||||
\(888\) | −0.936099 | − | 2.50790i | −0.0314134 | − | 0.0841595i | ||||
\(889\) | − | 8.40319i | − | 0.281834i | ||||||
\(890\) | −19.4564 | − | 2.79578i | −0.652180 | − | 0.0937148i | ||||
\(891\) | −2.94281 | + | 2.94281i | −0.0985879 | + | 0.0985879i | ||||
\(892\) | 2.62621 | − | 8.94948i | 0.0879321 | − | 0.299651i | ||||
\(893\) | 0.325582 | + | 0.325582i | 0.0108952 | + | 0.0108952i | ||||
\(894\) | 15.9508 | − | 11.9427i | 0.533474 | − | 0.399422i | ||||
\(895\) | −14.7203 | −0.492044 | ||||||||
\(896\) | −47.2394 | − | 10.2479i | −1.57816 | − | 0.342359i | ||||
\(897\) | 48.2583 | 1.61130 | ||||||||
\(898\) | −13.5461 | + | 10.1422i | −0.452039 | + | 0.338450i | ||||
\(899\) | −12.7727 | − | 12.7727i | −0.425995 | − | 0.425995i | ||||
\(900\) | 0.563151 | − | 1.91908i | 0.0187717 | − | 0.0639693i | ||||
\(901\) | −0.461314 | + | 0.461314i | −0.0153686 | + | 0.0153686i | ||||
\(902\) | −23.1069 | − | 3.32034i | −0.769377 | − | 0.110555i | ||||
\(903\) | 1.54521i | 0.0514213i | ||||||||
\(904\) | 4.95070 | + | 13.2634i | 0.164658 | + | 0.441133i | ||||
\(905\) | 21.8909i | 0.727678i | ||||||||
\(906\) | 0.808382 | − | 5.62569i | 0.0268567 | − | 0.186901i | ||||
\(907\) | 0.656960 | − | 0.656960i | 0.0218140 | − | 0.0218140i | −0.696116 | − | 0.717930i | \(-0.745090\pi\) |
0.717930 | + | 0.696116i | \(0.245090\pi\) | |||||||
\(908\) | −4.01379 | + | 2.19255i | −0.133202 | + | 0.0727622i | ||||
\(909\) | −2.98972 | − | 2.98972i | −0.0991629 | − | 0.0991629i | ||||
\(910\) | −20.7911 | − | 27.7689i | −0.689217 | − | 0.920530i | ||||
\(911\) | −3.71828 | −0.123192 | −0.0615960 | − | 0.998101i | \(-0.519619\pi\) | ||||
−0.0615960 | + | 0.998101i | \(0.519619\pi\) | |||||||
\(912\) | 13.2228 | − | 20.5900i | 0.437851 | − | 0.681801i | ||||
\(913\) | −32.6394 | −1.08021 | ||||||||
\(914\) | −28.0135 | − | 37.4153i | −0.926605 | − | 1.23759i | ||||
\(915\) | −4.48857 | − | 4.48857i | −0.148388 | − | 0.148388i | ||||
\(916\) | −12.4051 | − | 22.7095i | −0.409877 | − | 0.750341i | ||||
\(917\) | −3.64406 | + | 3.64406i | −0.120338 | + | 0.120338i | ||||
\(918\) | 0.0321958 | − | 0.224057i | 0.00106262 | − | 0.00739499i | ||||
\(919\) | 33.0548i | 1.09038i | 0.838313 | + | 0.545189i | \(0.183542\pi\) | ||||
−0.838313 | + | 0.545189i | \(0.816458\pi\) | |||||||
\(920\) | −9.87107 | + | 21.6287i | −0.325440 | + | 0.713077i | ||||
\(921\) | 27.8311i | 0.917064i | ||||||||
\(922\) | 41.0270 | + | 5.89535i | 1.35115 | + | 0.194153i | ||||
\(923\) | −49.1772 | + | 49.1772i | −1.61869 | + | 1.61869i | ||||
\(924\) | −34.1237 | − | 10.0135i | −1.12259 | − | 0.329421i | ||||
\(925\) | 0.669226 | + | 0.669226i | 0.0220040 | + | 0.0220040i | ||||
\(926\) | −16.1160 | + | 12.0664i | −0.529605 | + | 0.396525i | ||||
\(927\) | −16.8190 | −0.552410 | ||||||||
\(928\) | −10.7700 | − | 9.32455i | −0.353543 | − | 0.306093i | ||||
\(929\) | −17.6732 | −0.579839 | −0.289919 | − | 0.957051i | \(-0.593629\pi\) | ||||
−0.289919 | + | 0.957051i | \(0.593629\pi\) | |||||||
\(930\) | −8.12011 | + | 6.07968i | −0.266269 | + | 0.199360i | ||||
\(931\) | −48.6844 | − | 48.6844i | −1.59557 | − | 1.59557i | ||||
\(932\) | −19.7669 | − | 5.80057i | −0.647486 | − | 0.190004i | ||||
\(933\) | −8.40905 | + | 8.40905i | −0.275300 | + | 0.275300i | ||||
\(934\) | −37.2159 | − | 5.34773i | −1.21774 | − | 0.174983i | ||||
\(935\) | − | 0.666131i | − | 0.0217848i | ||||||
\(936\) | 14.7727 | + | 6.74208i | 0.482861 | + | 0.220372i | ||||
\(937\) | 25.9902i | 0.849061i | 0.905414 | + | 0.424531i | \(0.139561\pi\) | ||||
−0.905414 | + | 0.424531i | \(0.860439\pi\) | |||||||
\(938\) | 0.159431 | − | 1.10952i | 0.00520562 | − | 0.0362270i | ||||
\(939\) | 6.79666 | − | 6.79666i | 0.221801 | − | 0.221801i | ||||
\(940\) | −0.0721638 | − | 0.132107i | −0.00235372 | − | 0.00430884i | ||||
\(941\) | 29.0860 | + | 29.0860i | 0.948176 | + | 0.948176i | 0.998722 | − | 0.0505455i | \(-0.0160960\pi\) |
−0.0505455 | + | 0.998722i | \(0.516096\pi\) | |||||||
\(942\) | 10.9615 | + | 14.6403i | 0.357145 | + | 0.477008i | ||||
\(943\) | −33.3395 | −1.08568 | ||||||||
\(944\) | 31.1509 | − | 6.78715i | 1.01387 | − | 0.220903i | ||||
\(945\) | 4.27253 | 0.138986 | ||||||||
\(946\) | −1.27576 | − | 1.70393i | −0.0414786 | − | 0.0553995i | ||||
\(947\) | 30.8896 | + | 30.8896i | 1.00378 | + | 1.00378i | 0.999993 | + | 0.00378509i | \(0.00120483\pi\) |
0.00378509 | + | 0.999993i | \(0.498795\pi\) | |||||||
\(948\) | 26.8966 | − | 14.6924i | 0.873561 | − | 0.477186i | ||||
\(949\) | −1.55433 | + | 1.55433i | −0.0504558 | + | 0.0504558i | ||||
\(950\) | −1.23054 | + | 8.56355i | −0.0399239 | + | 0.277838i | ||||
\(951\) | 11.4558i | 0.371480i | ||||||||
\(952\) | 1.81213 | − | 0.676397i | 0.0587314 | − | 0.0219221i | ||||
\(953\) | − | 51.5794i | − | 1.67082i | −0.549626 | − | 0.835411i | \(-0.685230\pi\) | ||
0.549626 | − | 0.835411i | \(-0.314770\pi\) | |||||||
\(954\) | 5.70567 | + | 0.819874i | 0.184728 | + | 0.0265444i | ||||
\(955\) | 3.35979 | − | 3.35979i | 0.108720 | − | 0.108720i | ||||
\(956\) | 2.10520 | − | 7.17400i | 0.0680870 | − | 0.232024i | ||||
\(957\) | −7.41092 | − | 7.41092i | −0.239561 | − | 0.239561i | ||||
\(958\) | 30.2463 | − | 22.6460i | 0.977215 | − | 0.731659i | ||||
\(959\) | 17.6038 | 0.568457 | ||||||||
\(960\) | −6.04342 | + | 5.24186i | −0.195051 | + | 0.169180i | ||||
\(961\) | 20.4493 | 0.659656 | ||||||||
\(962\) | −6.15121 | + | 4.60553i | −0.198323 | + | 0.148488i | ||||
\(963\) | 1.64447 | + | 1.64447i | 0.0529924 | + | 0.0529924i | ||||
\(964\) | −5.26142 | + | 17.9296i | −0.169459 | + | 0.577474i | ||||
\(965\) | −8.33786 | + | 8.33786i | −0.268405 | + | 0.268405i | ||||
\(966\) | −50.2728 | − | 7.22394i | −1.61750 | − | 0.232426i | ||||
\(967\) | − | 5.55245i | − | 0.178555i | −0.996007 | − | 0.0892774i | \(-0.971544\pi\) | ||
0.996007 | − | 0.0892774i | \(-0.0284558\pi\) | |||||||
\(968\) | 16.7478 | − | 6.25131i | 0.538296 | − | 0.200925i | ||||
\(969\) | 0.979172i | 0.0314555i | ||||||||
\(970\) | −2.19250 | + | 15.2580i | −0.0703969 | + | 0.489906i | ||||
\(971\) | −30.5095 | + | 30.5095i | −0.979098 | + | 0.979098i | −0.999786 | − | 0.0206884i | \(-0.993414\pi\) |
0.0206884 | + | 0.999786i | \(0.493414\pi\) | |||||||
\(972\) | −1.75520 | + | 0.958786i | −0.0562981 | + | 0.0307531i | ||||
\(973\) | −24.5199 | − | 24.5199i | −0.786071 | − | 0.786071i | ||||
\(974\) | −22.9531 | − | 30.6564i | −0.735463 | − | 0.982296i | ||||
\(975\) | −5.74117 | −0.183865 | ||||||||
\(976\) | 5.40542 | + | 24.8092i | 0.173023 | + | 0.794122i | ||||
\(977\) | 31.8649 | 1.01945 | 0.509723 | − | 0.860338i | \(-0.329748\pi\) | ||||
0.509723 | + | 0.860338i | \(0.329748\pi\) | |||||||
\(978\) | 0.414859 | + | 0.554092i | 0.0132657 | + | 0.0177179i | ||||
\(979\) | 40.9024 | + | 40.9024i | 1.30725 | + | 1.30725i | ||||
\(980\) | 10.7907 | + | 19.7540i | 0.344696 | + | 0.631018i | ||||
\(981\) | −4.67023 | + | 4.67023i | −0.149109 | + | 0.149109i | ||||
\(982\) | −0.431070 | + | 2.99990i | −0.0137560 | + | 0.0957308i | ||||
\(983\) | − | 24.2289i | − | 0.772782i | −0.922335 | − | 0.386391i | \(-0.873721\pi\) | ||
0.922335 | − | 0.386391i | \(-0.126279\pi\) | |||||||
\(984\) | −10.2058 | − | 4.65780i | −0.325349 | − | 0.148485i | ||||
\(985\) | − | 6.45226i | − | 0.205586i | ||||||
\(986\) | 0.564246 | + | 0.0810791i | 0.0179693 | + | 0.00258209i | ||||
\(987\) | 0.227388 | − | 0.227388i | 0.00723786 | − | 0.00723786i | ||||
\(988\) | −67.4016 | − | 19.7789i | −2.14433 | − | 0.629251i | ||||
\(989\) | −2.14960 | − | 2.14960i | −0.0683533 | − | 0.0683533i | ||||
\(990\) | −4.71140 | + | 3.52751i | −0.149738 | + | 0.112112i | ||||
\(991\) | 38.9268 | 1.23655 | 0.618276 | − | 0.785961i | \(-0.287832\pi\) | ||||
0.618276 | + | 0.785961i | \(0.287832\pi\) | |||||||
\(992\) | 40.4710 | − | 2.91121i | 1.28496 | − | 0.0924311i | ||||
\(993\) | −18.8468 | −0.598085 | ||||||||
\(994\) | 58.5916 | − | 43.8686i | 1.85841 | − | 1.39143i | ||||
\(995\) | −2.54744 | − | 2.54744i | −0.0807592 | − | 0.0807592i | ||||
\(996\) | −15.0507 | − | 4.41661i | −0.476901 | − | 0.139946i | ||||
\(997\) | −8.00046 | + | 8.00046i | −0.253377 | + | 0.253377i | −0.822354 | − | 0.568977i | \(-0.807340\pi\) |
0.568977 | + | 0.822354i | \(0.307340\pi\) | |||||||
\(998\) | −14.4716 | − | 2.07949i | −0.458090 | − | 0.0658251i | ||||
\(999\) | − | 0.946429i | − | 0.0299437i |
(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 | 240.2.s.c.61.2 | ✓ | 20 | |
3.2 | odd | 2 | 720.2.t.d.541.9 | 20 | |||
4.3 | odd | 2 | 960.2.s.c.721.5 | 20 | |||
8.3 | odd | 2 | 1920.2.s.f.1441.10 | 20 | |||
8.5 | even | 2 | 1920.2.s.e.1441.1 | 20 | |||
12.11 | even | 2 | 2880.2.t.d.721.5 | 20 | |||
16.3 | odd | 4 | 1920.2.s.f.481.6 | 20 | |||
16.5 | even | 4 | inner | 240.2.s.c.181.2 | yes | 20 | |
16.11 | odd | 4 | 960.2.s.c.241.1 | 20 | |||
16.13 | even | 4 | 1920.2.s.e.481.5 | 20 | |||
48.5 | odd | 4 | 720.2.t.d.181.9 | 20 | |||
48.11 | even | 4 | 2880.2.t.d.2161.1 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
240.2.s.c.61.2 | ✓ | 20 | 1.1 | even | 1 | trivial | |
240.2.s.c.181.2 | yes | 20 | 16.5 | even | 4 | inner | |
720.2.t.d.181.9 | 20 | 48.5 | odd | 4 | |||
720.2.t.d.541.9 | 20 | 3.2 | odd | 2 | |||
960.2.s.c.241.1 | 20 | 16.11 | odd | 4 | |||
960.2.s.c.721.5 | 20 | 4.3 | odd | 2 | |||
1920.2.s.e.481.5 | 20 | 16.13 | even | 4 | |||
1920.2.s.e.1441.1 | 20 | 8.5 | even | 2 | |||
1920.2.s.f.481.6 | 20 | 16.3 | odd | 4 | |||
1920.2.s.f.1441.10 | 20 | 8.3 | odd | 2 | |||
2880.2.t.d.721.5 | 20 | 12.11 | even | 2 | |||
2880.2.t.d.2161.1 | 20 | 48.11 | even | 4 |