Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(41,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.41");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.bl (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: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 146.4 | ||
Character | \(\chi\) | \(=\) | 315.146 |
Dual form | 315.2.bl.i.41.4 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.13192 | − | 0.653515i | −0.800389 | − | 0.462105i | 0.0432184 | − | 0.999066i | \(-0.486239\pi\) |
−0.843607 | + | 0.536961i | \(0.819572\pi\) | |||||||
\(3\) | −0.957531 | − | 1.44331i | −0.552831 | − | 0.833293i | ||||
\(4\) | −0.145837 | − | 0.252598i | −0.0729187 | − | 0.126299i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0.140627 | + | 2.25947i | 0.0574109 | + | 0.922424i | ||||
\(7\) | 0.709992 | + | 2.54871i | 0.268352 | + | 0.963321i | ||||
\(8\) | 2.99529i | 1.05899i | ||||||||
\(9\) | −1.16627 | + | 2.76402i | −0.388756 | + | 0.921341i | ||||
\(10\) | − | 1.30703i | − | 0.413319i | ||||||
\(11\) | 4.98971 | + | 2.88081i | 1.50445 | + | 0.868596i | 0.999987 | + | 0.00516464i | \(0.00164396\pi\) |
0.504466 | + | 0.863432i | \(0.331689\pi\) | |||||||
\(12\) | −0.224932 | + | 0.452359i | −0.0649324 | + | 0.130585i | ||||
\(13\) | 3.14058 | − | 1.81321i | 0.871039 | − | 0.502895i | 0.00334565 | − | 0.999994i | \(-0.498935\pi\) |
0.867693 | + | 0.497100i | \(0.165602\pi\) | |||||||
\(14\) | 0.861964 | − | 3.34892i | 0.230369 | − | 0.895038i | ||||
\(15\) | 0.771174 | − | 1.55090i | 0.199116 | − | 0.400441i | ||||
\(16\) | 1.66579 | − | 2.88523i | 0.416447 | − | 0.721307i | ||||
\(17\) | −4.92433 | −1.19433 | −0.597163 | − | 0.802120i | \(-0.703705\pi\) | ||||
−0.597163 | + | 0.802120i | \(0.703705\pi\) | |||||||
\(18\) | 3.12645 | − | 2.36648i | 0.736912 | − | 0.557785i | ||||
\(19\) | − | 3.02122i | − | 0.693116i | −0.938029 | − | 0.346558i | \(-0.887350\pi\) | ||
0.938029 | − | 0.346558i | \(-0.112650\pi\) | |||||||
\(20\) | 0.145837 | − | 0.252598i | 0.0326103 | − | 0.0564826i | ||||
\(21\) | 2.99873 | − | 3.46520i | 0.654376 | − | 0.756169i | ||||
\(22\) | −3.76530 | − | 6.52169i | −0.802765 | − | 1.39043i | ||||
\(23\) | −5.93663 | + | 3.42751i | −1.23787 | + | 0.714686i | −0.968659 | − | 0.248394i | \(-0.920097\pi\) |
−0.269214 | + | 0.963080i | \(0.586764\pi\) | |||||||
\(24\) | 4.32312 | − | 2.86808i | 0.882452 | − | 0.585444i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | −4.73984 | −0.929560 | ||||||||
\(27\) | 5.10607 | − | 0.963357i | 0.982663 | − | 0.185398i | ||||
\(28\) | 0.540255 | − | 0.551040i | 0.102099 | − | 0.104137i | ||||
\(29\) | 7.16276 | + | 4.13542i | 1.33009 | + | 0.767929i | 0.985313 | − | 0.170755i | \(-0.0546208\pi\) |
0.344778 | + | 0.938684i | \(0.387954\pi\) | |||||||
\(30\) | −1.88644 | + | 1.25152i | −0.344416 | + | 0.228495i | ||||
\(31\) | 3.18657 | − | 1.83977i | 0.572325 | − | 0.330432i | −0.185753 | − | 0.982597i | \(-0.559472\pi\) |
0.758077 | + | 0.652165i | \(0.226139\pi\) | |||||||
\(32\) | 1.41691 | − | 0.818053i | 0.250476 | − | 0.144613i | ||||
\(33\) | −0.619911 | − | 9.96014i | −0.107913 | − | 1.73384i | ||||
\(34\) | 5.57395 | + | 3.21812i | 0.955924 | + | 0.551903i | ||||
\(35\) | −1.85225 | + | 1.88922i | −0.313087 | + | 0.319337i | ||||
\(36\) | 0.868272 | − | 0.108501i | 0.144712 | − | 0.0180836i | ||||
\(37\) | 2.80891 | 0.461782 | 0.230891 | − | 0.972980i | \(-0.425836\pi\) | ||||
0.230891 | + | 0.972980i | \(0.425836\pi\) | |||||||
\(38\) | −1.97441 | + | 3.41978i | −0.320292 | + | 0.554762i | ||||
\(39\) | −5.62422 | − | 2.79661i | −0.900596 | − | 0.447815i | ||||
\(40\) | −2.59399 | + | 1.49764i | −0.410146 | + | 0.236798i | ||||
\(41\) | 5.57799 | + | 9.66136i | 0.871136 | + | 1.50885i | 0.860823 | + | 0.508905i | \(0.169949\pi\) |
0.0103128 | + | 0.999947i | \(0.496717\pi\) | |||||||
\(42\) | −5.65888 | + | 1.96262i | −0.873184 | + | 0.302839i | ||||
\(43\) | −0.136193 | + | 0.235894i | −0.0207693 | + | 0.0359735i | −0.876223 | − | 0.481905i | \(-0.839945\pi\) |
0.855454 | + | 0.517879i | \(0.173278\pi\) | |||||||
\(44\) | − | 1.68052i | − | 0.253348i | ||||||
\(45\) | −2.97685 | + | 0.371994i | −0.443762 | + | 0.0554536i | ||||
\(46\) | 8.95972 | 1.32104 | ||||||||
\(47\) | 1.88231 | − | 3.26026i | 0.274564 | − | 0.475558i | −0.695461 | − | 0.718564i | \(-0.744800\pi\) |
0.970025 | + | 0.243005i | \(0.0781333\pi\) | |||||||
\(48\) | −5.75931 | + | 0.358455i | −0.831285 | + | 0.0517385i | ||||
\(49\) | −5.99182 | + | 3.61912i | −0.855975 | + | 0.517017i | ||||
\(50\) | 1.13192 | − | 0.653515i | 0.160078 | − | 0.0924209i | ||||
\(51\) | 4.71520 | + | 7.10732i | 0.660260 | + | 0.995223i | ||||
\(52\) | −0.916027 | − | 0.528869i | −0.127030 | − | 0.0733409i | ||||
\(53\) | 3.51435i | 0.482733i | 0.970434 | + | 0.241367i | \(0.0775957\pi\) | ||||
−0.970434 | + | 0.241367i | \(0.922404\pi\) | |||||||
\(54\) | −6.40923 | − | 2.24645i | −0.872186 | − | 0.305703i | ||||
\(55\) | 5.76162i | 0.776896i | ||||||||
\(56\) | −7.63411 | + | 2.12663i | −1.02015 | + | 0.284183i | ||||
\(57\) | −4.36055 | + | 2.89291i | −0.577569 | + | 0.383176i | ||||
\(58\) | −5.40512 | − | 9.36194i | −0.709727 | − | 1.22928i | ||||
\(59\) | −4.33885 | − | 7.51511i | −0.564870 | − | 0.978384i | −0.997062 | − | 0.0766018i | \(-0.975593\pi\) |
0.432192 | − | 0.901782i | \(-0.357740\pi\) | |||||||
\(60\) | −0.504220 | + | 0.0313822i | −0.0650946 | + | 0.00405143i | ||||
\(61\) | 7.81138 | + | 4.50990i | 1.00014 | + | 0.577434i | 0.908291 | − | 0.418339i | \(-0.137387\pi\) |
0.0918536 | + | 0.995773i | \(0.470721\pi\) | |||||||
\(62\) | −4.80926 | −0.610776 | ||||||||
\(63\) | −7.87273 | − | 1.01004i | −0.991870 | − | 0.127253i | ||||
\(64\) | −8.80159 | −1.10020 | ||||||||
\(65\) | 3.14058 | + | 1.81321i | 0.389540 | + | 0.224901i | ||||
\(66\) | −5.80741 | + | 11.6792i | −0.714842 | + | 1.43761i | ||||
\(67\) | 1.65886 | + | 2.87323i | 0.202662 | + | 0.351021i | 0.949385 | − | 0.314114i | \(-0.101707\pi\) |
−0.746723 | + | 0.665135i | \(0.768374\pi\) | |||||||
\(68\) | 0.718152 | + | 1.24388i | 0.0870887 | + | 0.150842i | ||||
\(69\) | 10.6315 | + | 5.28642i | 1.27988 | + | 0.636411i | ||||
\(70\) | 3.33124 | − | 0.927980i | 0.398159 | − | 0.110915i | ||||
\(71\) | − | 6.95342i | − | 0.825220i | −0.910908 | − | 0.412610i | \(-0.864617\pi\) | ||
0.910908 | − | 0.412610i | \(-0.135383\pi\) | |||||||
\(72\) | −8.27904 | − | 3.49330i | −0.975694 | − | 0.411690i | ||||
\(73\) | 2.88131i | 0.337232i | 0.985682 | + | 0.168616i | \(0.0539298\pi\) | ||||
−0.985682 | + | 0.168616i | \(0.946070\pi\) | |||||||
\(74\) | −3.17946 | − | 1.83566i | −0.369605 | − | 0.213392i | ||||
\(75\) | 1.72871 | − | 0.107593i | 0.199614 | − | 0.0124238i | ||||
\(76\) | −0.763154 | + | 0.440607i | −0.0875398 | + | 0.0505411i | ||||
\(77\) | −3.79969 | + | 14.7627i | −0.433015 | + | 1.68236i | ||||
\(78\) | 4.53855 | + | 6.84105i | 0.513889 | + | 0.774596i | ||||
\(79\) | 5.15417 | − | 8.92729i | 0.579889 | − | 1.00440i | −0.415602 | − | 0.909547i | \(-0.636429\pi\) |
0.995491 | − | 0.0948515i | \(-0.0302376\pi\) | |||||||
\(80\) | 3.33158 | 0.372481 | ||||||||
\(81\) | −6.27964 | − | 6.44718i | −0.697738 | − | 0.716353i | ||||
\(82\) | − | 14.5812i | − | 1.61022i | ||||||
\(83\) | 1.69417 | − | 2.93439i | 0.185959 | − | 0.322091i | −0.757940 | − | 0.652324i | \(-0.773794\pi\) |
0.943899 | + | 0.330233i | \(0.107127\pi\) | |||||||
\(84\) | −1.31263 | − | 0.252116i | −0.143220 | − | 0.0275081i | ||||
\(85\) | −2.46216 | − | 4.26459i | −0.267059 | − | 0.462560i | ||||
\(86\) | 0.308320 | − | 0.178009i | 0.0332470 | − | 0.0191952i | ||||
\(87\) | −0.889887 | − | 14.2979i | −0.0954059 | − | 1.53289i | ||||
\(88\) | −8.62884 | + | 14.9456i | −0.919838 | + | 1.59321i | ||||
\(89\) | −4.68832 | −0.496961 | −0.248481 | − | 0.968637i | \(-0.579931\pi\) | ||||
−0.248481 | + | 0.968637i | \(0.579931\pi\) | |||||||
\(90\) | 3.61266 | + | 1.52435i | 0.380808 | + | 0.160680i | ||||
\(91\) | 6.85113 | + | 6.71705i | 0.718194 | + | 0.704138i | ||||
\(92\) | 1.73157 | + | 0.999720i | 0.180528 | + | 0.104228i | ||||
\(93\) | −5.70659 | − | 2.83756i | −0.591746 | − | 0.294241i | ||||
\(94\) | −4.26126 | + | 2.46024i | −0.439515 | + | 0.253754i | ||||
\(95\) | 2.61645 | − | 1.51061i | 0.268443 | − | 0.154985i | ||||
\(96\) | −2.53744 | − | 1.26172i | −0.258976 | − | 0.128774i | ||||
\(97\) | 4.00495 | + | 2.31226i | 0.406642 | + | 0.234775i | 0.689346 | − | 0.724433i | \(-0.257898\pi\) |
−0.282704 | + | 0.959207i | \(0.591231\pi\) | |||||||
\(98\) | 9.14742 | − | 0.180814i | 0.924029 | − | 0.0182650i | ||||
\(99\) | −13.7819 | + | 10.4319i | −1.38514 | + | 1.04844i | ||||
\(100\) | 0.291675 | 0.0291675 | ||||||||
\(101\) | −4.98278 | + | 8.63043i | −0.495805 | + | 0.858760i | −0.999988 | − | 0.00483690i | \(-0.998460\pi\) |
0.504183 | + | 0.863597i | \(0.331794\pi\) | |||||||
\(102\) | −0.692496 | − | 11.1264i | −0.0685673 | − | 1.10167i | ||||
\(103\) | −8.37044 | + | 4.83267i | −0.824763 | + | 0.476177i | −0.852056 | − | 0.523450i | \(-0.824645\pi\) |
0.0272929 | + | 0.999627i | \(0.491311\pi\) | |||||||
\(104\) | 5.43109 | + | 9.40692i | 0.532562 | + | 0.922425i | ||||
\(105\) | 4.50032 | + | 0.864373i | 0.439186 | + | 0.0843541i | ||||
\(106\) | 2.29668 | − | 3.97797i | 0.223073 | − | 0.386374i | ||||
\(107\) | − | 9.46949i | − | 0.915450i | −0.889094 | − | 0.457725i | \(-0.848664\pi\) | ||
0.889094 | − | 0.457725i | \(-0.151336\pi\) | |||||||
\(108\) | −0.987998 | − | 1.14929i | −0.0950702 | − | 0.110590i | ||||
\(109\) | −8.33627 | −0.798470 | −0.399235 | − | 0.916849i | \(-0.630724\pi\) | ||||
−0.399235 | + | 0.916849i | \(0.630724\pi\) | |||||||
\(110\) | 3.76530 | − | 6.52169i | 0.359007 | − | 0.621819i | ||||
\(111\) | −2.68962 | − | 4.05412i | −0.255287 | − | 0.384800i | ||||
\(112\) | 8.53630 | + | 2.19712i | 0.806605 | + | 0.207608i | ||||
\(113\) | 4.68004 | − | 2.70202i | 0.440261 | − | 0.254185i | −0.263447 | − | 0.964674i | \(-0.584859\pi\) |
0.703708 | + | 0.710489i | \(0.251526\pi\) | |||||||
\(114\) | 6.82636 | − | 0.424867i | 0.639347 | − | 0.0397924i | ||||
\(115\) | −5.93663 | − | 3.42751i | −0.553594 | − | 0.319617i | ||||
\(116\) | − | 2.41240i | − | 0.223986i | ||||||
\(117\) | 1.34901 | + | 10.7953i | 0.124716 | + | 0.998027i | ||||
\(118\) | 11.3420i | 1.04412i | ||||||||
\(119\) | −3.49623 | − | 12.5507i | −0.320499 | − | 1.15052i | ||||
\(120\) | 4.64539 | + | 2.30989i | 0.424064 | + | 0.210863i | ||||
\(121\) | 11.0981 | + | 19.2225i | 1.00892 | + | 1.74750i | ||||
\(122\) | −5.89457 | − | 10.2097i | −0.533670 | − | 0.924343i | ||||
\(123\) | 8.60321 | − | 17.3018i | 0.775725 | − | 1.56005i | ||||
\(124\) | −0.929443 | − | 0.536614i | −0.0834664 | − | 0.0481894i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 8.25122 | + | 6.28823i | 0.735077 | + | 0.560200i | ||||
\(127\) | 9.75881 | 0.865955 | 0.432977 | − | 0.901405i | \(-0.357463\pi\) | ||||
0.432977 | + | 0.901405i | \(0.357463\pi\) | |||||||
\(128\) | 7.12888 | + | 4.11586i | 0.630110 | + | 0.363794i | ||||
\(129\) | 0.470877 | − | 0.0293070i | 0.0414584 | − | 0.00258033i | ||||
\(130\) | −2.36992 | − | 4.10482i | −0.207856 | − | 0.360017i | ||||
\(131\) | −8.91007 | − | 15.4327i | −0.778476 | − | 1.34836i | −0.932820 | − | 0.360343i | \(-0.882660\pi\) |
0.154344 | − | 0.988017i | \(-0.450674\pi\) | |||||||
\(132\) | −2.42550 | + | 1.60915i | −0.211113 | + | 0.140059i | ||||
\(133\) | 7.70021 | − | 2.14504i | 0.667693 | − | 0.185999i | ||||
\(134\) | − | 4.33636i | − | 0.374604i | ||||||
\(135\) | 3.38733 | + | 3.94031i | 0.291535 | + | 0.339128i | ||||
\(136\) | − | 14.7498i | − | 1.26478i | ||||||
\(137\) | 1.19435 | + | 0.689559i | 0.102040 | + | 0.0589130i | 0.550152 | − | 0.835065i | \(-0.314570\pi\) |
−0.448111 | + | 0.893978i | \(0.647903\pi\) | |||||||
\(138\) | −8.57921 | − | 12.9316i | −0.730311 | − | 1.10081i | ||||
\(139\) | −10.5156 | + | 6.07121i | −0.891926 | + | 0.514954i | −0.874572 | − | 0.484896i | \(-0.838858\pi\) |
−0.0173539 | + | 0.999849i | \(0.505524\pi\) | |||||||
\(140\) | 0.747342 | + | 0.192355i | 0.0631619 | + | 0.0162569i | ||||
\(141\) | −6.50793 | + | 0.405048i | −0.548067 | + | 0.0341112i | ||||
\(142\) | −4.54416 | + | 7.87072i | −0.381338 | + | 0.660496i | ||||
\(143\) | 20.8941 | 1.74725 | ||||||||
\(144\) | 6.03208 | + | 7.96922i | 0.502674 | + | 0.664102i | ||||
\(145\) | 8.27085i | 0.686856i | ||||||||
\(146\) | 1.88298 | − | 3.26142i | 0.155837 | − | 0.269917i | ||||
\(147\) | 10.9609 | + | 5.18262i | 0.904037 | + | 0.427455i | ||||
\(148\) | −0.409644 | − | 0.709525i | −0.0336726 | − | 0.0583226i | ||||
\(149\) | 5.61055 | − | 3.23925i | 0.459634 | − | 0.265370i | −0.252256 | − | 0.967661i | \(-0.581173\pi\) |
0.711891 | + | 0.702290i | \(0.247839\pi\) | |||||||
\(150\) | −2.02707 | − | 1.00795i | −0.165510 | − | 0.0822986i | ||||
\(151\) | −9.46471 | + | 16.3934i | −0.770227 | + | 1.33407i | 0.167212 | + | 0.985921i | \(0.446524\pi\) |
−0.937438 | + | 0.348151i | \(0.886810\pi\) | |||||||
\(152\) | 9.04942 | 0.734005 | ||||||||
\(153\) | 5.74309 | − | 13.6110i | 0.464301 | − | 1.10038i | ||||
\(154\) | 13.9486 | − | 14.2270i | 1.12401 | − | 1.14644i | ||||
\(155\) | 3.18657 | + | 1.83977i | 0.255951 | + | 0.147774i | ||||
\(156\) | 0.113805 | + | 1.82852i | 0.00911172 | + | 0.146399i | ||||
\(157\) | −0.754717 | + | 0.435736i | −0.0602330 | + | 0.0347755i | −0.529814 | − | 0.848114i | \(-0.677738\pi\) |
0.469581 | + | 0.882889i | \(0.344405\pi\) | |||||||
\(158\) | −11.6682 | + | 6.73665i | −0.928274 | + | 0.535939i | ||||
\(159\) | 5.07229 | − | 3.36510i | 0.402259 | − | 0.266870i | ||||
\(160\) | 1.41691 | + | 0.818053i | 0.112016 | + | 0.0646727i | ||||
\(161\) | −12.9507 | − | 12.6972i | −1.02066 | − | 1.00068i | ||||
\(162\) | 2.89473 | + | 11.4015i | 0.227431 | + | 0.895789i | ||||
\(163\) | 10.7991 | 0.845849 | 0.422924 | − | 0.906165i | \(-0.361004\pi\) | ||||
0.422924 | + | 0.906165i | \(0.361004\pi\) | |||||||
\(164\) | 1.62696 | − | 2.81798i | 0.127044 | − | 0.220047i | ||||
\(165\) | 8.31578 | − | 5.51693i | 0.647382 | − | 0.429492i | ||||
\(166\) | −3.83533 | + | 2.21433i | −0.297679 | + | 0.171865i | ||||
\(167\) | −3.22089 | − | 5.57874i | −0.249240 | − | 0.431696i | 0.714075 | − | 0.700069i | \(-0.246847\pi\) |
−0.963315 | + | 0.268373i | \(0.913514\pi\) | |||||||
\(168\) | 10.3793 | + | 8.98205i | 0.800778 | + | 0.692980i | ||||
\(169\) | 0.0754780 | − | 0.130732i | 0.00580600 | − | 0.0100563i | ||||
\(170\) | 6.43624i | 0.493637i | ||||||||
\(171\) | 8.35072 | + | 3.52355i | 0.638596 | + | 0.269453i | ||||
\(172\) | 0.0794484 | 0.00605788 | ||||||||
\(173\) | −2.37437 | + | 4.11252i | −0.180520 | + | 0.312669i | −0.942058 | − | 0.335451i | \(-0.891111\pi\) |
0.761538 | + | 0.648120i | \(0.224445\pi\) | |||||||
\(174\) | −8.33658 | + | 16.7656i | −0.631994 | + | 1.27100i | ||||
\(175\) | −2.56224 | − | 0.659483i | −0.193687 | − | 0.0498522i | ||||
\(176\) | 16.6236 | − | 9.59763i | 1.25305 | − | 0.723448i | ||||
\(177\) | −6.69202 | + | 13.4582i | −0.503003 | + | 1.01158i | ||||
\(178\) | 5.30681 | + | 3.06389i | 0.397762 | + | 0.229648i | ||||
\(179\) | 19.6922i | 1.47186i | 0.677056 | + | 0.735932i | \(0.263256\pi\) | ||||
−0.677056 | + | 0.735932i | \(0.736744\pi\) | |||||||
\(180\) | 0.528101 | + | 0.697695i | 0.0393623 | + | 0.0520031i | ||||
\(181\) | − | 26.6033i | − | 1.97741i | −0.149883 | − | 0.988704i | \(-0.547890\pi\) | ||
0.149883 | − | 0.988704i | \(-0.452110\pi\) | |||||||
\(182\) | −3.36525 | − | 12.0805i | −0.249449 | − | 0.895464i | ||||
\(183\) | −0.970470 | − | 15.5926i | −0.0717392 | − | 1.15264i | ||||
\(184\) | −10.2664 | − | 17.7819i | −0.756848 | − | 1.31090i | ||||
\(185\) | 1.40446 | + | 2.43259i | 0.103258 | + | 0.178847i | ||||
\(186\) | 4.60501 | + | 6.94123i | 0.337656 | + | 0.508956i | ||||
\(187\) | −24.5710 | − | 14.1860i | −1.79681 | − | 1.03739i | ||||
\(188\) | −1.09805 | −0.0800833 | ||||||||
\(189\) | 6.08058 | + | 12.3299i | 0.442297 | + | 0.896869i | ||||
\(190\) | −3.94882 | −0.286478 | ||||||||
\(191\) | −9.69208 | − | 5.59572i | −0.701294 | − | 0.404892i | 0.106535 | − | 0.994309i | \(-0.466024\pi\) |
−0.807829 | + | 0.589417i | \(0.799358\pi\) | |||||||
\(192\) | 8.42780 | + | 12.7034i | 0.608224 | + | 0.916788i | ||||
\(193\) | −0.463712 | − | 0.803173i | −0.0333787 | − | 0.0578137i | 0.848853 | − | 0.528628i | \(-0.177293\pi\) |
−0.882232 | + | 0.470815i | \(0.843960\pi\) | |||||||
\(194\) | −3.02219 | − | 5.23459i | −0.216981 | − | 0.375822i | ||||
\(195\) | −0.390179 | − | 6.26902i | −0.0279413 | − | 0.448934i | ||||
\(196\) | 1.78802 | + | 0.985719i | 0.127715 | + | 0.0704085i | ||||
\(197\) | 7.07291i | 0.503924i | 0.967737 | + | 0.251962i | \(0.0810758\pi\) | ||||
−0.967737 | + | 0.251962i | \(0.918924\pi\) | |||||||
\(198\) | 22.4174 | − | 2.80134i | 1.59314 | − | 0.199082i | ||||
\(199\) | 4.14124i | 0.293565i | 0.989169 | + | 0.146782i | \(0.0468917\pi\) | ||||
−0.989169 | + | 0.146782i | \(0.953108\pi\) | |||||||
\(200\) | −2.59399 | − | 1.49764i | −0.183423 | − | 0.105899i | ||||
\(201\) | 2.55854 | − | 5.14545i | 0.180466 | − | 0.362932i | ||||
\(202\) | 11.2802 | − | 6.51264i | 0.793674 | − | 0.458228i | ||||
\(203\) | −5.45448 | + | 21.1919i | −0.382830 | + | 1.48738i | ||||
\(204\) | 1.10764 | − | 2.22756i | 0.0775504 | − | 0.155961i | ||||
\(205\) | −5.57799 | + | 9.66136i | −0.389584 | + | 0.674779i | ||||
\(206\) | 12.6329 | 0.880175 | ||||||||
\(207\) | −2.55003 | − | 20.4064i | −0.177239 | − | 1.41834i | ||||
\(208\) | − | 12.0817i | − | 0.837716i | ||||||
\(209\) | 8.70356 | − | 15.0750i | 0.602038 | − | 1.04276i | ||||
\(210\) | −4.52912 | − | 3.91942i | −0.312539 | − | 0.270466i | ||||
\(211\) | −7.38983 | − | 12.7996i | −0.508737 | − | 0.881159i | −0.999949 | − | 0.0101183i | \(-0.996779\pi\) |
0.491212 | − | 0.871040i | \(-0.336554\pi\) | |||||||
\(212\) | 0.887718 | − | 0.512524i | 0.0609687 | − | 0.0352003i | ||||
\(213\) | −10.0359 | + | 6.65812i | −0.687650 | + | 0.456207i | ||||
\(214\) | −6.18845 | + | 10.7187i | −0.423034 | + | 0.732716i | ||||
\(215\) | −0.272387 | −0.0185766 | ||||||||
\(216\) | 2.88553 | + | 15.2941i | 0.196335 | + | 1.04063i | ||||
\(217\) | 6.95147 | + | 6.81542i | 0.471896 | + | 0.462661i | ||||
\(218\) | 9.43599 | + | 5.44787i | 0.639086 | + | 0.368977i | ||||
\(219\) | 4.15862 | − | 2.75895i | 0.281013 | − | 0.186432i | ||||
\(220\) | 1.45537 | − | 0.840260i | 0.0981212 | − | 0.0566503i | ||||
\(221\) | −15.4652 | + | 8.92886i | −1.04030 | + | 0.600620i | ||||
\(222\) | 0.395010 | + | 6.34664i | 0.0265113 | + | 0.425959i | ||||
\(223\) | −5.55505 | − | 3.20721i | −0.371994 | − | 0.214771i | 0.302335 | − | 0.953202i | \(-0.402234\pi\) |
−0.674329 | + | 0.738431i | \(0.735567\pi\) | |||||||
\(224\) | 3.09097 | + | 3.03048i | 0.206524 | + | 0.202482i | ||||
\(225\) | −1.81058 | − | 2.39203i | −0.120705 | − | 0.159469i | ||||
\(226\) | −7.06324 | −0.469840 | ||||||||
\(227\) | −2.28750 | + | 3.96207i | −0.151827 | + | 0.262972i | −0.931899 | − | 0.362718i | \(-0.881849\pi\) |
0.780072 | + | 0.625690i | \(0.215182\pi\) | |||||||
\(228\) | 1.36668 | + | 0.679570i | 0.0905103 | + | 0.0450056i | ||||
\(229\) | 5.09205 | − | 2.93990i | 0.336492 | − | 0.194274i | −0.322227 | − | 0.946662i | \(-0.604432\pi\) |
0.658720 | + | 0.752388i | \(0.271098\pi\) | |||||||
\(230\) | 4.47986 | + | 7.75935i | 0.295393 | + | 0.511636i | ||||
\(231\) | 24.9453 | − | 8.65159i | 1.64128 | − | 0.569233i | ||||
\(232\) | −12.3868 | + | 21.4545i | −0.813232 | + | 1.40856i | ||||
\(233\) | − | 9.82356i | − | 0.643563i | −0.946814 | − | 0.321781i | \(-0.895718\pi\) | ||
0.946814 | − | 0.321781i | \(-0.104282\pi\) | |||||||
\(234\) | 5.52792 | − | 13.1010i | 0.361372 | − | 0.856441i | ||||
\(235\) | 3.76463 | 0.245577 | ||||||||
\(236\) | −1.26553 | + | 2.19197i | −0.0823792 | + | 0.142685i | ||||
\(237\) | −17.8201 | + | 1.10911i | −1.15754 | + | 0.0720443i | ||||
\(238\) | −4.24459 | + | 16.4912i | −0.275136 | + | 1.06897i | ||||
\(239\) | 15.9544 | − | 9.21127i | 1.03200 | − | 0.595827i | 0.114445 | − | 0.993430i | \(-0.463491\pi\) |
0.917558 | + | 0.397602i | \(0.130158\pi\) | |||||||
\(240\) | −3.19009 | − | 4.80848i | −0.205919 | − | 0.310386i | ||||
\(241\) | 3.82945 | + | 2.21093i | 0.246677 | + | 0.142419i | 0.618241 | − | 0.785988i | \(-0.287845\pi\) |
−0.371565 | + | 0.928407i | \(0.621179\pi\) | |||||||
\(242\) | − | 29.0111i | − | 1.86490i | ||||||
\(243\) | −3.29230 | + | 15.2368i | −0.211201 | + | 0.977443i | ||||
\(244\) | − | 2.63085i | − | 0.168423i | ||||||
\(245\) | −6.13016 | − | 3.37951i | −0.391642 | − | 0.215909i | ||||
\(246\) | −21.0451 | + | 13.9619i | −1.34179 | + | 0.890181i | ||||
\(247\) | −5.47812 | − | 9.48838i | −0.348564 | − | 0.603731i | ||||
\(248\) | 5.51063 | + | 9.54469i | 0.349925 | + | 0.606088i | ||||
\(249\) | −5.85744 | + | 0.364562i | −0.371200 | + | 0.0231032i | ||||
\(250\) | 1.13192 | + | 0.653515i | 0.0715889 | + | 0.0413319i | ||||
\(251\) | −11.0078 | −0.694809 | −0.347405 | − | 0.937715i | \(-0.612937\pi\) | ||||
−0.347405 | + | 0.937715i | \(0.612937\pi\) | |||||||
\(252\) | 0.893004 | + | 2.13594i | 0.0562540 | + | 0.134551i | ||||
\(253\) | −39.4960 | −2.48309 | ||||||||
\(254\) | −11.0462 | − | 6.37753i | −0.693100 | − | 0.400162i | ||||
\(255\) | −3.79752 | + | 7.63714i | −0.237810 | + | 0.478256i | ||||
\(256\) | 3.42204 | + | 5.92715i | 0.213877 | + | 0.370447i | ||||
\(257\) | 2.36224 | + | 4.09152i | 0.147352 | + | 0.255222i | 0.930248 | − | 0.366931i | \(-0.119592\pi\) |
−0.782896 | + | 0.622153i | \(0.786258\pi\) | |||||||
\(258\) | −0.552147 | − | 0.274552i | −0.0343752 | − | 0.0170928i | ||||
\(259\) | 1.99430 | + | 7.15909i | 0.123920 | + | 0.444844i | ||||
\(260\) | − | 1.05774i | − | 0.0655981i | ||||||
\(261\) | −19.7841 | + | 14.9750i | −1.22461 | + | 0.926931i | ||||
\(262\) | 23.2914i | 1.43895i | ||||||||
\(263\) | 3.45803 | + | 1.99649i | 0.213231 | + | 0.123109i | 0.602812 | − | 0.797883i | \(-0.294047\pi\) |
−0.389581 | + | 0.920992i | \(0.627380\pi\) | |||||||
\(264\) | 29.8335 | − | 1.85681i | 1.83612 | − | 0.114279i | ||||
\(265\) | −3.04352 | + | 1.75718i | −0.186962 | + | 0.107942i | ||||
\(266\) | −10.1178 | − | 2.60418i | −0.620365 | − | 0.159673i | ||||
\(267\) | 4.48922 | + | 6.76669i | 0.274735 | + | 0.414114i | ||||
\(268\) | 0.483848 | − | 0.838049i | 0.0295557 | − | 0.0511920i | ||||
\(269\) | −21.2854 | −1.29779 | −0.648896 | − | 0.760877i | \(-0.724769\pi\) | ||||
−0.648896 | + | 0.760877i | \(0.724769\pi\) | |||||||
\(270\) | −1.25914 | − | 6.67378i | −0.0766285 | − | 0.406153i | ||||
\(271\) | − | 8.91274i | − | 0.541411i | −0.962662 | − | 0.270705i | \(-0.912743\pi\) | ||
0.962662 | − | 0.270705i | \(-0.0872569\pi\) | |||||||
\(272\) | −8.20289 | + | 14.2078i | −0.497373 | + | 0.861476i | ||||
\(273\) | 3.13458 | − | 16.3201i | 0.189714 | − | 0.987735i | ||||
\(274\) | −0.901273 | − | 1.56105i | −0.0544479 | − | 0.0943066i | ||||
\(275\) | −4.98971 | + | 2.88081i | −0.300891 | + | 0.173719i | ||||
\(276\) | −0.215126 | − | 3.45644i | −0.0129491 | − | 0.208053i | ||||
\(277\) | 13.7461 | − | 23.8089i | 0.825922 | − | 1.43054i | −0.0752903 | − | 0.997162i | \(-0.523988\pi\) |
0.901212 | − | 0.433378i | \(-0.142678\pi\) | |||||||
\(278\) | 15.8705 | 0.951850 | ||||||||
\(279\) | 1.36876 | + | 10.9534i | 0.0819458 | + | 0.655763i | ||||
\(280\) | −5.65877 | − | 5.54802i | −0.338176 | − | 0.331558i | ||||
\(281\) | −3.43914 | − | 1.98559i | −0.205162 | − | 0.118450i | 0.393899 | − | 0.919154i | \(-0.371126\pi\) |
−0.599061 | + | 0.800703i | \(0.704459\pi\) | |||||||
\(282\) | 7.63117 | + | 3.79455i | 0.454429 | + | 0.225962i | ||||
\(283\) | 1.02668 | − | 0.592756i | 0.0610300 | − | 0.0352357i | −0.469175 | − | 0.883105i | \(-0.655448\pi\) |
0.530205 | + | 0.847870i | \(0.322115\pi\) | |||||||
\(284\) | −1.75642 | + | 1.01407i | −0.104224 | + | 0.0601740i | ||||
\(285\) | −4.68561 | − | 2.32989i | −0.277552 | − | 0.138011i | ||||
\(286\) | −23.6504 | − | 13.6546i | −1.39848 | − | 0.807412i | ||||
\(287\) | −20.6637 | + | 21.0762i | −1.21974 | + | 1.24409i | ||||
\(288\) | 0.608621 | + | 4.87044i | 0.0358634 | + | 0.286993i | ||||
\(289\) | 7.24902 | 0.426413 | ||||||||
\(290\) | 5.40512 | − | 9.36194i | 0.317399 | − | 0.549752i | ||||
\(291\) | −0.497567 | − | 7.99444i | −0.0291679 | − | 0.468642i | ||||
\(292\) | 0.727814 | − | 0.420204i | 0.0425921 | − | 0.0245906i | ||||
\(293\) | −13.7335 | − | 23.7871i | −0.802318 | − | 1.38966i | −0.918087 | − | 0.396379i | \(-0.870267\pi\) |
0.115769 | − | 0.993276i | \(-0.463067\pi\) | |||||||
\(294\) | −9.01991 | − | 13.0294i | −0.526052 | − | 0.759890i | ||||
\(295\) | 4.33885 | − | 7.51511i | 0.252618 | − | 0.437546i | ||||
\(296\) | 8.41349i | 0.489024i | ||||||||
\(297\) | 28.2530 | + | 9.90274i | 1.63941 | + | 0.574615i | ||||
\(298\) | −8.46760 | −0.490515 | ||||||||
\(299\) | −12.4296 | + | 21.5287i | −0.718824 | + | 1.24504i | ||||
\(300\) | −0.279288 | − | 0.420976i | −0.0161247 | − | 0.0243051i | ||||
\(301\) | −0.697921 | − | 0.179634i | −0.0402275 | − | 0.0103540i | ||||
\(302\) | 21.4266 | − | 12.3706i | 1.23296 | − | 0.711851i | ||||
\(303\) | 17.2275 | − | 1.07223i | 0.989696 | − | 0.0615978i | ||||
\(304\) | −8.71692 | − | 5.03271i | −0.499949 | − | 0.288646i | ||||
\(305\) | 9.01980i | 0.516473i | ||||||||
\(306\) | −15.3957 | + | 11.6533i | −0.880112 | + | 0.666177i | ||||
\(307\) | 7.49498i | 0.427761i | 0.976860 | + | 0.213881i | \(0.0686104\pi\) | ||||
−0.976860 | + | 0.213881i | \(0.931390\pi\) | |||||||
\(308\) | 4.28315 | − | 1.19315i | 0.244055 | − | 0.0679863i | ||||
\(309\) | 14.9900 | + | 7.45367i | 0.852750 | + | 0.424024i | ||||
\(310\) | −2.40463 | − | 4.16494i | −0.136574 | − | 0.236553i | ||||
\(311\) | −9.95114 | − | 17.2359i | −0.564278 | − | 0.977357i | −0.997116 | − | 0.0758862i | \(-0.975821\pi\) |
0.432839 | − | 0.901471i | \(-0.357512\pi\) | |||||||
\(312\) | 8.37663 | − | 16.8461i | 0.474234 | − | 0.953725i | ||||
\(313\) | 28.3246 | + | 16.3532i | 1.60100 | + | 0.924339i | 0.991287 | + | 0.131718i | \(0.0420495\pi\) |
0.609715 | + | 0.792621i | \(0.291284\pi\) | |||||||
\(314\) | 1.13904 | 0.0642797 | ||||||||
\(315\) | −3.06164 | − | 7.32300i | −0.172504 | − | 0.412604i | ||||
\(316\) | −3.00669 | −0.169139 | ||||||||
\(317\) | −7.62204 | − | 4.40059i | −0.428097 | − | 0.247162i | 0.270439 | − | 0.962737i | \(-0.412831\pi\) |
−0.698535 | + | 0.715575i | \(0.746165\pi\) | |||||||
\(318\) | −7.94057 | + | 0.494214i | −0.445285 | + | 0.0277142i | ||||
\(319\) | 23.8267 | + | 41.2691i | 1.33404 | + | 2.31063i | ||||
\(320\) | −4.40079 | − | 7.62240i | −0.246012 | − | 0.426105i | ||||
\(321\) | −13.6674 | + | 9.06734i | −0.762839 | + | 0.506089i | ||||
\(322\) | 6.36133 | + | 22.8357i | 0.354503 | + | 1.27258i | ||||
\(323\) | 14.8775i | 0.827806i | ||||||||
\(324\) | −0.712737 | + | 2.52646i | −0.0395965 | + | 0.140359i | ||||
\(325\) | 3.62642i | 0.201158i | ||||||||
\(326\) | −12.2237 | − | 7.05735i | −0.677007 | − | 0.390870i | ||||
\(327\) | 7.98224 | + | 12.0318i | 0.441419 | + | 0.665360i | ||||
\(328\) | −28.9385 | + | 16.7077i | −1.59786 | + | 0.922527i | ||||
\(329\) | 9.64588 | + | 2.48271i | 0.531795 | + | 0.136876i | ||||
\(330\) | −13.0182 | + | 0.810241i | −0.716628 | + | 0.0446023i | ||||
\(331\) | 7.15743 | − | 12.3970i | 0.393408 | − | 0.681402i | −0.599489 | − | 0.800383i | \(-0.704629\pi\) |
0.992897 | + | 0.118981i | \(0.0379628\pi\) | |||||||
\(332\) | −0.988293 | −0.0542396 | ||||||||
\(333\) | −3.27594 | + | 7.76389i | −0.179520 | + | 0.425459i | ||||
\(334\) | 8.41959i | 0.460700i | ||||||||
\(335\) | −1.65886 | + | 2.87323i | −0.0906332 | + | 0.156981i | ||||
\(336\) | −5.00266 | − | 14.4243i | −0.272918 | − | 0.786911i | ||||
\(337\) | −13.5173 | − | 23.4126i | −0.736332 | − | 1.27536i | −0.954136 | − | 0.299372i | \(-0.903223\pi\) |
0.217804 | − | 0.975993i | \(-0.430111\pi\) | |||||||
\(338\) | −0.170870 | + | 0.0986520i | −0.00929412 | + | 0.00536596i | ||||
\(339\) | −8.38113 | − | 4.16746i | −0.455201 | − | 0.226345i | ||||
\(340\) | −0.718152 | + | 1.24388i | −0.0389473 | + | 0.0674586i | ||||
\(341\) | 21.2001 | 1.14805 | ||||||||
\(342\) | −7.14966 | − | 9.44570i | −0.386609 | − | 0.510765i | ||||
\(343\) | −13.4782 | − | 12.7019i | −0.727756 | − | 0.685836i | ||||
\(344\) | −0.706569 | − | 0.407938i | −0.0380957 | − | 0.0219945i | ||||
\(345\) | 0.737555 | + | 11.8503i | 0.0397086 | + | 0.638000i | ||||
\(346\) | 5.37519 | − | 3.10337i | 0.288972 | − | 0.166838i | ||||
\(347\) | 8.99376 | − | 5.19255i | 0.482811 | − | 0.278751i | −0.238776 | − | 0.971075i | \(-0.576746\pi\) |
0.721587 | + | 0.692324i | \(0.243413\pi\) | |||||||
\(348\) | −3.48183 | + | 2.30995i | −0.186646 | + | 0.123826i | ||||
\(349\) | −0.871278 | − | 0.503033i | −0.0466385 | − | 0.0269267i | 0.476499 | − | 0.879175i | \(-0.341905\pi\) |
−0.523138 | + | 0.852248i | \(0.675239\pi\) | |||||||
\(350\) | 2.46927 | + | 2.42094i | 0.131988 | + | 0.129405i | ||||
\(351\) | 14.2892 | − | 12.2839i | 0.762703 | − | 0.655665i | ||||
\(352\) | 9.42661 | 0.502440 | ||||||||
\(353\) | 3.86581 | − | 6.69578i | 0.205756 | − | 0.356381i | −0.744617 | − | 0.667492i | \(-0.767368\pi\) |
0.950373 | + | 0.311111i | \(0.100701\pi\) | |||||||
\(354\) | 16.3700 | − | 10.8603i | 0.870055 | − | 0.577220i | ||||
\(355\) | 6.02184 | − | 3.47671i | 0.319606 | − | 0.184525i | ||||
\(356\) | 0.683733 | + | 1.18426i | 0.0362378 | + | 0.0627657i | ||||
\(357\) | −14.7667 | + | 17.0638i | −0.781538 | + | 0.903112i | ||||
\(358\) | 12.8691 | − | 22.2900i | 0.680155 | − | 1.17806i | ||||
\(359\) | − | 19.0140i | − | 1.00352i | −0.865007 | − | 0.501760i | \(-0.832686\pi\) | ||
0.865007 | − | 0.501760i | \(-0.167314\pi\) | |||||||
\(360\) | −1.11423 | − | 8.91651i | −0.0587250 | − | 0.469941i | ||||
\(361\) | 9.87222 | 0.519591 | ||||||||
\(362\) | −17.3856 | + | 30.1128i | −0.913769 | + | 1.58269i | ||||
\(363\) | 17.1171 | − | 34.4241i | 0.898417 | − | 1.80680i | ||||
\(364\) | 0.697560 | − | 2.71018i | 0.0365621 | − | 0.142052i | ||||
\(365\) | −2.49529 | + | 1.44066i | −0.130610 | + | 0.0754074i | ||||
\(366\) | −9.09149 | + | 18.2838i | −0.475220 | + | 0.955709i | ||||
\(367\) | −9.92332 | − | 5.72923i | −0.517993 | − | 0.299063i | 0.218120 | − | 0.975922i | \(-0.430008\pi\) |
−0.736113 | + | 0.676859i | \(0.763341\pi\) | |||||||
\(368\) | 22.8380i | 1.19052i | ||||||||
\(369\) | −33.2097 | + | 4.14996i | −1.72883 | + | 0.216038i | ||||
\(370\) | − | 3.67133i | − | 0.190863i | ||||||
\(371\) | −8.95706 | + | 2.49516i | −0.465027 | + | 0.129542i | ||||
\(372\) | 0.115472 | + | 1.85530i | 0.00598695 | + | 0.0961926i | ||||
\(373\) | −7.14969 | − | 12.3836i | −0.370197 | − | 0.641200i | 0.619399 | − | 0.785076i | \(-0.287376\pi\) |
−0.989596 | + | 0.143877i | \(0.954043\pi\) | |||||||
\(374\) | 18.5416 | + | 32.1149i | 0.958762 | + | 1.66062i | ||||
\(375\) | 0.957531 | + | 1.44331i | 0.0494467 | + | 0.0745320i | ||||
\(376\) | 9.76542 | + | 5.63807i | 0.503613 | + | 0.290761i | ||||
\(377\) | 29.9936 | 1.54475 | ||||||||
\(378\) | 1.17504 | − | 17.9302i | 0.0604374 | − | 0.922231i | ||||
\(379\) | 6.30700 | 0.323969 | 0.161984 | − | 0.986793i | \(-0.448211\pi\) | ||||
0.161984 | + | 0.986793i | \(0.448211\pi\) | |||||||
\(380\) | −0.763154 | − | 0.440607i | −0.0391490 | − | 0.0226027i | ||||
\(381\) | −9.34437 | − | 14.0850i | −0.478727 | − | 0.721594i | ||||
\(382\) | 7.31377 | + | 12.6678i | 0.374205 | + | 0.648142i | ||||
\(383\) | −14.9406 | − | 25.8780i | −0.763432 | − | 1.32230i | −0.941072 | − | 0.338207i | \(-0.890180\pi\) |
0.177640 | − | 0.984095i | \(-0.443154\pi\) | |||||||
\(384\) | −0.885677 | − | 14.2302i | −0.0451970 | − | 0.726183i | ||||
\(385\) | −14.6847 | + | 4.09070i | −0.748400 | + | 0.208481i | ||||
\(386\) | 1.21217i | 0.0616979i | ||||||||
\(387\) | −0.493178 | − | 0.651557i | −0.0250696 | − | 0.0331205i | ||||
\(388\) | − | 1.34886i | − | 0.0684779i | ||||||
\(389\) | −6.79001 | − | 3.92022i | −0.344267 | − | 0.198763i | 0.317890 | − | 0.948128i | \(-0.397026\pi\) |
−0.662158 | + | 0.749365i | \(0.730359\pi\) | |||||||
\(390\) | −3.65525 | + | 7.35102i | −0.185091 | + | 0.372233i | ||||
\(391\) | 29.2339 | − | 16.8782i | 1.47842 | − | 0.853568i | ||||
\(392\) | −10.8403 | − | 17.9472i | −0.547518 | − | 0.906472i | ||||
\(393\) | −13.7424 | + | 27.6372i | −0.693214 | + | 1.39411i | ||||
\(394\) | 4.62225 | − | 8.00598i | 0.232866 | − | 0.403335i | ||||
\(395\) | 10.3083 | 0.518669 | ||||||||
\(396\) | 4.64499 | + | 1.95993i | 0.233420 | + | 0.0984904i | ||||
\(397\) | 0.325200i | 0.0163213i | 0.999967 | + | 0.00816066i | \(0.00259765\pi\) | ||||
−0.999967 | + | 0.00816066i | \(0.997402\pi\) | |||||||
\(398\) | 2.70636 | − | 4.68756i | 0.135658 | − | 0.234966i | ||||
\(399\) | −10.4691 | − | 9.05982i | −0.524113 | − | 0.453558i | ||||
\(400\) | 1.66579 | + | 2.88523i | 0.0832894 | + | 0.144261i | ||||
\(401\) | −0.562380 | + | 0.324690i | −0.0280839 | + | 0.0162142i | −0.513976 | − | 0.857804i | \(-0.671828\pi\) |
0.485892 | + | 0.874019i | \(0.338495\pi\) | |||||||
\(402\) | −6.25869 | + | 4.15220i | −0.312155 | + | 0.207093i | ||||
\(403\) | 6.67178 | − | 11.5559i | 0.332345 | − | 0.575638i | ||||
\(404\) | 2.90671 | 0.144614 | ||||||||
\(405\) | 2.44360 | − | 8.66192i | 0.121423 | − | 0.430414i | ||||
\(406\) | 20.0233 | − | 20.4230i | 0.993738 | − | 1.01357i | ||||
\(407\) | 14.0156 | + | 8.09193i | 0.694729 | + | 0.401102i | ||||
\(408\) | −21.2884 | + | 14.1234i | −1.05394 | + | 0.699211i | ||||
\(409\) | 18.7974 | − | 10.8527i | 0.929470 | − | 0.536630i | 0.0428259 | − | 0.999083i | \(-0.486364\pi\) |
0.886644 | + | 0.462453i | \(0.153031\pi\) | |||||||
\(410\) | 12.6277 | − | 7.29060i | 0.623637 | − | 0.360057i | ||||
\(411\) | −0.148384 | − | 2.38409i | −0.00731923 | − | 0.117598i | ||||
\(412\) | 2.44145 | + | 1.40957i | 0.120281 | + | 0.0694445i | ||||
\(413\) | 16.0733 | − | 16.3941i | 0.790914 | − | 0.806702i | ||||
\(414\) | −10.4494 | + | 24.7649i | −0.513562 | + | 1.21713i | ||||
\(415\) | 3.38834 | 0.166327 | ||||||||
\(416\) | 2.96661 | − | 5.13831i | 0.145450 | − | 0.251927i | ||||
\(417\) | 18.8317 | + | 9.36393i | 0.922192 | + | 0.458554i | ||||
\(418\) | −19.7035 | + | 11.3758i | −0.963728 | + | 0.556409i | ||||
\(419\) | −1.44983 | − | 2.51117i | −0.0708287 | − | 0.122679i | 0.828436 | − | 0.560084i | \(-0.189231\pi\) |
−0.899265 | + | 0.437405i | \(0.855898\pi\) | |||||||
\(420\) | −0.437976 | − | 1.26283i | −0.0213711 | − | 0.0616197i | ||||
\(421\) | 6.16736 | − | 10.6822i | 0.300579 | − | 0.520618i | −0.675688 | − | 0.737187i | \(-0.736153\pi\) |
0.976267 | + | 0.216569i | \(0.0694868\pi\) | |||||||
\(422\) | 19.3175i | 0.940359i | ||||||||
\(423\) | 6.81616 | + | 9.00509i | 0.331413 | + | 0.437843i | ||||
\(424\) | −10.5265 | −0.511212 | ||||||||
\(425\) | 2.46216 | − | 4.26459i | 0.119433 | − | 0.206863i | ||||
\(426\) | 15.7110 | − | 0.977842i | 0.761203 | − | 0.0473766i | ||||
\(427\) | −5.94841 | + | 23.1109i | −0.287864 | + | 1.11842i | ||||
\(428\) | −2.39197 | + | 1.38101i | −0.115620 | + | 0.0667535i | ||||
\(429\) | −20.0067 | − | 30.1565i | −0.965934 | − | 1.45597i | ||||
\(430\) | 0.308320 | + | 0.178009i | 0.0148685 | + | 0.00858434i | ||||
\(431\) | − | 25.3358i | − | 1.22038i | −0.792254 | − | 0.610192i | \(-0.791092\pi\) | ||
0.792254 | − | 0.610192i | \(-0.208908\pi\) | |||||||
\(432\) | 5.72612 | − | 16.3369i | 0.275498 | − | 0.786011i | ||||
\(433\) | 29.9796i | 1.44073i | 0.693596 | + | 0.720365i | \(0.256026\pi\) | ||||
−0.693596 | + | 0.720365i | \(0.743974\pi\) | |||||||
\(434\) | −3.41453 | − | 12.2574i | −0.163903 | − | 0.588374i | ||||
\(435\) | 11.9374 | − | 7.91959i | 0.572353 | − | 0.379715i | ||||
\(436\) | 1.21574 | + | 2.10572i | 0.0582234 | + | 0.100846i | ||||
\(437\) | 10.3553 | + | 17.9359i | 0.495360 | + | 0.857989i | ||||
\(438\) | −6.51024 | + | 0.405192i | −0.311071 | + | 0.0193608i | ||||
\(439\) | 19.3472 | + | 11.1701i | 0.923391 | + | 0.533120i | 0.884715 | − | 0.466132i | \(-0.154353\pi\) |
0.0386756 | + | 0.999252i | \(0.487686\pi\) | |||||||
\(440\) | −17.2577 | −0.822728 | ||||||||
\(441\) | −3.01527 | − | 20.7824i | −0.143584 | − | 0.989638i | ||||
\(442\) | 23.3405 | 1.11020 | ||||||||
\(443\) | 11.3552 | + | 6.55595i | 0.539504 | + | 0.311483i | 0.744878 | − | 0.667201i | \(-0.232508\pi\) |
−0.205374 | + | 0.978684i | \(0.565841\pi\) | |||||||
\(444\) | −0.631815 | + | 1.27063i | −0.0299846 | + | 0.0603017i | ||||
\(445\) | −2.34416 | − | 4.06021i | −0.111124 | − | 0.192472i | ||||
\(446\) | 4.19192 | + | 7.26062i | 0.198493 | + | 0.343800i | ||||
\(447\) | −10.0475 | − | 4.99606i | −0.475231 | − | 0.236306i | ||||
\(448\) | −6.24905 | − | 22.4327i | −0.295240 | − | 1.05984i | ||||
\(449\) | 29.0097i | 1.36905i | 0.728989 | + | 0.684526i | \(0.239991\pi\) | ||||
−0.728989 | + | 0.684526i | \(0.760009\pi\) | |||||||
\(450\) | 0.486207 | + | 3.89083i | 0.0229200 | + | 0.183415i | ||||
\(451\) | 64.2765i | 3.02666i | ||||||||
\(452\) | −1.36505 | − | 0.788112i | −0.0642066 | − | 0.0370697i | ||||
\(453\) | 32.7234 | − | 2.03668i | 1.53748 | − | 0.0956914i | ||||
\(454\) | 5.17854 | − | 2.98983i | 0.243041 | − | 0.140320i | ||||
\(455\) | −2.39157 | + | 9.29178i | −0.112118 | + | 0.435605i | ||||
\(456\) | −8.66510 | − | 13.0611i | −0.405781 | − | 0.611642i | ||||
\(457\) | 2.70505 | − | 4.68528i | 0.126537 | − | 0.219168i | −0.795796 | − | 0.605565i | \(-0.792947\pi\) |
0.922333 | + | 0.386397i | \(0.126280\pi\) | |||||||
\(458\) | −7.68507 | −0.359100 | ||||||||
\(459\) | −25.1440 | + | 4.74389i | −1.17362 | + | 0.221426i | ||||
\(460\) | 1.99944i | 0.0932244i | ||||||||
\(461\) | −6.99868 | + | 12.1221i | −0.325961 | + | 0.564581i | −0.981706 | − | 0.190401i | \(-0.939021\pi\) |
0.655745 | + | 0.754982i | \(0.272354\pi\) | |||||||
\(462\) | −33.8901 | − | 6.50924i | −1.57671 | − | 0.302837i | ||||
\(463\) | −5.11805 | − | 8.86472i | −0.237856 | − | 0.411978i | 0.722243 | − | 0.691639i | \(-0.243111\pi\) |
−0.960099 | + | 0.279661i | \(0.909778\pi\) | |||||||
\(464\) | 23.8633 | − | 13.7775i | 1.10783 | − | 0.639603i | ||||
\(465\) | −0.395893 | − | 6.36083i | −0.0183591 | − | 0.294976i | ||||
\(466\) | −6.41984 | + | 11.1195i | −0.297393 | + | 0.515100i | ||||
\(467\) | 5.78707 | 0.267794 | 0.133897 | − | 0.990995i | \(-0.457251\pi\) | ||||
0.133897 | + | 0.990995i | \(0.457251\pi\) | |||||||
\(468\) | 2.53014 | − | 1.91512i | 0.116956 | − | 0.0885264i | ||||
\(469\) | −6.14525 | + | 6.26792i | −0.283761 | + | 0.289426i | ||||
\(470\) | −4.26126 | − | 2.46024i | −0.196557 | − | 0.113482i | ||||
\(471\) | 1.35157 | + | 0.672057i | 0.0622769 | + | 0.0309668i | ||||
\(472\) | 22.5099 | − | 12.9961i | 1.03610 | − | 0.598194i | ||||
\(473\) | −1.35913 | + | 0.784694i | −0.0624928 | + | 0.0360803i | ||||
\(474\) | 20.8957 | + | 10.3903i | 0.959773 | + | 0.477241i | ||||
\(475\) | 2.61645 | + | 1.51061i | 0.120051 | + | 0.0693116i | ||||
\(476\) | −2.66039 | + | 2.71350i | −0.121939 | + | 0.124373i | ||||
\(477\) | −9.71375 | − | 4.09867i | −0.444762 | − | 0.187665i | ||||
\(478\) | −24.0788 | −1.10134 | ||||||||
\(479\) | 5.91876 | − | 10.2516i | 0.270435 | − | 0.468407i | −0.698538 | − | 0.715573i | \(-0.746166\pi\) |
0.968973 | + | 0.247165i | \(0.0794991\pi\) | |||||||
\(480\) | −0.176034 | − | 2.82834i | −0.00803481 | − | 0.129096i | ||||
\(481\) | 8.82160 | − | 5.09315i | 0.402230 | − | 0.232228i | ||||
\(482\) | −2.88975 | − | 5.00520i | −0.131625 | − | 0.227981i | ||||
\(483\) | −5.92530 | + | 30.8498i | −0.269610 | + | 1.40371i | ||||
\(484\) | 3.23704 | − | 5.60672i | 0.147138 | − | 0.254851i | ||||
\(485\) | 4.62452i | 0.209989i | ||||||||
\(486\) | 13.6841 | − | 15.0953i | 0.620724 | − | 0.684737i | ||||
\(487\) | 20.5456 | 0.931012 | 0.465506 | − | 0.885045i | \(-0.345872\pi\) | ||||
0.465506 | + | 0.885045i | \(0.345872\pi\) | |||||||
\(488\) | −13.5084 | + | 23.3973i | −0.611499 | + | 1.05915i | ||||
\(489\) | −10.3404 | − | 15.5864i | −0.467611 | − | 0.704840i | ||||
\(490\) | 4.73030 | + | 7.83149i | 0.213693 | + | 0.353791i | ||||
\(491\) | 6.02013 | − | 3.47573i | 0.271685 | − | 0.156857i | −0.357968 | − | 0.933734i | \(-0.616530\pi\) |
0.629653 | + | 0.776876i | \(0.283197\pi\) | |||||||
\(492\) | −5.62507 | + | 0.350100i | −0.253598 | + | 0.0157837i | ||||
\(493\) | −35.2718 | − | 20.3642i | −1.58856 | − | 0.917157i | ||||
\(494\) | 14.3201i | 0.644292i | ||||||||
\(495\) | −15.9252 | − | 6.71958i | −0.715786 | − | 0.302023i | ||||
\(496\) | − | 12.2586i | − | 0.550429i | ||||||
\(497\) | 17.7222 | − | 4.93687i | 0.794951 | − | 0.221449i | ||||
\(498\) | 6.86840 | + | 3.41527i | 0.307780 | + | 0.153042i | ||||
\(499\) | 13.4054 | + | 23.2188i | 0.600108 | + | 1.03942i | 0.992804 | + | 0.119750i | \(0.0382092\pi\) |
−0.392696 | + | 0.919668i | \(0.628457\pi\) | |||||||
\(500\) | 0.145837 | + | 0.252598i | 0.00652205 | + | 0.0112965i | ||||
\(501\) | −4.96774 | + | 9.99055i | −0.221942 | + | 0.446345i | ||||
\(502\) | 12.4600 | + | 7.19379i | 0.556117 | + | 0.321075i | ||||
\(503\) | −14.8532 | −0.662273 | −0.331137 | − | 0.943583i | \(-0.607432\pi\) | ||||
−0.331137 | + | 0.943583i | \(0.607432\pi\) | |||||||
\(504\) | 3.02537 | − | 23.5811i | 0.134760 | − | 1.05038i | ||||
\(505\) | −9.96556 | −0.443462 | ||||||||
\(506\) | 44.7064 | + | 25.8112i | 1.98744 | + | 1.14745i | ||||
\(507\) | −0.260959 | + | 0.0162418i | −0.0115896 | + | 0.000721326i | ||||
\(508\) | −1.42320 | − | 2.46506i | −0.0631443 | − | 0.109369i | ||||
\(509\) | 19.6497 | + | 34.0343i | 0.870958 | + | 1.50854i | 0.861007 | + | 0.508593i | \(0.169834\pi\) |
0.00995035 | + | 0.999950i | \(0.496833\pi\) | |||||||
\(510\) | 9.28947 | − | 6.16290i | 0.411345 | − | 0.272898i | ||||
\(511\) | −7.34363 | + | 2.04571i | −0.324863 | + | 0.0904968i | ||||
\(512\) | − | 25.4089i | − | 1.12292i | ||||||
\(513\) | −2.91051 | − | 15.4266i | −0.128502 | − | 0.681100i | ||||
\(514\) | − | 6.17503i | − | 0.272369i | ||||||
\(515\) | −8.37044 | − | 4.83267i | −0.368845 | − | 0.212953i | ||||
\(516\) | −0.0760743 | − | 0.114668i | −0.00334899 | − | 0.00504799i | ||||
\(517\) | 18.7844 | − | 10.8452i | 0.826136 | − | 0.476970i | ||||
\(518\) | 2.42118 | − | 9.40683i | 0.106380 | − | 0.413312i | ||||
\(519\) | 8.20916 | − | 0.510932i | 0.360342 | − | 0.0224274i | ||||
\(520\) | −5.43109 | + | 9.40692i | −0.238169 | + | 0.412521i | ||||
\(521\) | −39.4804 | −1.72967 | −0.864835 | − | 0.502056i | \(-0.832577\pi\) | ||||
−0.864835 | + | 0.502056i | \(0.832577\pi\) | |||||||
\(522\) | 32.1804 | − | 4.02134i | 1.40850 | − | 0.176009i | ||||
\(523\) | 15.0977i | 0.660177i | 0.943950 | + | 0.330089i | \(0.107079\pi\) | ||||
−0.943950 | + | 0.330089i | \(0.892921\pi\) | |||||||
\(524\) | −2.59884 | + | 4.50133i | −0.113531 | + | 0.196641i | ||||
\(525\) | 1.50159 | + | 4.32958i | 0.0655348 | + | 0.188958i | ||||
\(526\) | −2.60948 | − | 4.51974i | −0.113779 | − | 0.197070i | ||||
\(527\) | −15.6917 | + | 9.05962i | −0.683542 | + | 0.394643i | ||||
\(528\) | −29.7699 | − | 14.8029i | −1.29557 | − | 0.644213i | ||||
\(529\) | 11.9957 | − | 20.7772i | 0.521553 | − | 0.903356i | ||||
\(530\) | 4.59336 | 0.199523 | ||||||||
\(531\) | 25.8322 | − | 3.22805i | 1.12102 | − | 0.140086i | ||||
\(532\) | −1.66481 | − | 1.63223i | −0.0721788 | − | 0.0707661i | ||||
\(533\) | 35.0362 | + | 20.2282i | 1.51759 | + | 0.876179i | ||||
\(534\) | −0.659307 | − | 10.5931i | −0.0285310 | − | 0.458409i | ||||
\(535\) | 8.20082 | − | 4.73475i | 0.354552 | − | 0.204701i | ||||
\(536\) | −8.60614 | + | 4.96876i | −0.371729 | + | 0.214618i | ||||
\(537\) | 28.4219 | − | 18.8559i | 1.22649 | − | 0.813692i | ||||
\(538\) | 24.0933 | + | 13.9103i | 1.03874 | + | 0.599716i | ||||
\(539\) | −40.3234 | + | 0.797061i | −1.73685 | + | 0.0343319i | ||||
\(540\) | 0.501314 | − | 1.43028i | 0.0215731 | − | 0.0615493i | ||||
\(541\) | −36.6140 | −1.57416 | −0.787080 | − | 0.616851i | \(-0.788408\pi\) | ||||
−0.787080 | + | 0.616851i | \(0.788408\pi\) | |||||||
\(542\) | −5.82461 | + | 10.0885i | −0.250188 | + | 0.433339i | ||||
\(543\) | −38.3967 | + | 25.4735i | −1.64776 | + | 1.09317i | ||||
\(544\) | −6.97733 | + | 4.02836i | −0.299150 | + | 0.172715i | ||||
\(545\) | −4.16813 | − | 7.21942i | −0.178543 | − | 0.309246i | ||||
\(546\) | −14.2135 | + | 16.4245i | −0.608281 | + | 0.702904i | ||||
\(547\) | 13.0028 | − | 22.5215i | 0.555960 | − | 0.962951i | −0.441868 | − | 0.897080i | \(-0.645684\pi\) |
0.997828 | − | 0.0658711i | \(-0.0209826\pi\) | |||||||
\(548\) | − | 0.402254i | − | 0.0171834i | ||||||
\(549\) | −21.5756 | + | 16.3311i | −0.920825 | + | 0.696993i | ||||
\(550\) | 7.53060 | 0.321106 | ||||||||
\(551\) | 12.4940 | − | 21.6403i | 0.532264 | − | 0.921907i | ||||
\(552\) | −15.8343 | + | 31.8443i | −0.673955 | + | 1.35538i | ||||
\(553\) | 26.4125 | + | 6.79818i | 1.12317 | + | 0.289088i | ||||
\(554\) | −31.1189 | + | 17.9665i | −1.32212 | + | 0.763325i | ||||
\(555\) | 2.16616 | − | 4.35634i | 0.0919484 | − | 0.184916i | ||||
\(556\) | 3.06715 | + | 1.77082i | 0.130076 | + | 0.0750995i | ||||
\(557\) | − | 5.40214i | − | 0.228896i | −0.993429 | − | 0.114448i | \(-0.963490\pi\) | ||
0.993429 | − | 0.114448i | \(-0.0365099\pi\) | |||||||
\(558\) | 5.60888 | − | 13.2929i | 0.237443 | − | 0.562733i | ||||
\(559\) | 0.987790i | 0.0417791i | ||||||||
\(560\) | 2.36539 | + | 8.49121i | 0.0999560 | + | 0.358819i | ||||
\(561\) | 3.05264 | + | 49.0470i | 0.128883 | + | 2.07077i | ||||
\(562\) | 2.59522 | + | 4.49506i | 0.109473 | + | 0.189613i | ||||
\(563\) | 0.653430 | + | 1.13177i | 0.0275388 | + | 0.0476986i | 0.879466 | − | 0.475961i | \(-0.157900\pi\) |
−0.851928 | + | 0.523660i | \(0.824566\pi\) | |||||||
\(564\) | 1.05141 | + | 1.58482i | 0.0442726 | + | 0.0667329i | ||||
\(565\) | 4.68004 | + | 2.70202i | 0.196891 | + | 0.113675i | ||||
\(566\) | −1.54950 | −0.0651303 | ||||||||
\(567\) | 11.9735 | − | 20.5824i | 0.502839 | − | 0.864380i | ||||
\(568\) | 20.8275 | 0.873902 | ||||||||
\(569\) | 0.0109445 | + | 0.00631883i | 0.000458818 | + | 0.000264899i | 0.500229 | − | 0.865893i | \(-0.333249\pi\) |
−0.499771 | + | 0.866158i | \(0.666582\pi\) | |||||||
\(570\) | 3.78112 | + | 5.69936i | 0.158374 | + | 0.238720i | ||||
\(571\) | −1.19240 | − | 2.06530i | −0.0499004 | − | 0.0864301i | 0.839996 | − | 0.542592i | \(-0.182557\pi\) |
−0.889897 | + | 0.456162i | \(0.849224\pi\) | |||||||
\(572\) | −3.04714 | − | 5.27780i | −0.127407 | − | 0.220676i | ||||
\(573\) | 1.20412 | + | 19.3467i | 0.0503030 | + | 0.808221i | ||||
\(574\) | 37.1632 | − | 10.3525i | 1.55116 | − | 0.432106i | ||||
\(575\) | − | 6.85503i | − | 0.285874i | ||||||
\(576\) | 10.2650 | − | 24.3278i | 0.427709 | − | 1.01366i | ||||
\(577\) | − | 14.0085i | − | 0.583181i | −0.956543 | − | 0.291590i | \(-0.905816\pi\) | ||
0.956543 | − | 0.291590i | \(-0.0941844\pi\) | |||||||
\(578\) | −8.20531 | − | 4.73734i | −0.341296 | − | 0.197047i | ||||
\(579\) | −0.715206 | + | 1.43834i | −0.0297229 | + | 0.0597755i | ||||
\(580\) | 2.08920 | − | 1.20620i | 0.0867493 | − | 0.0500847i | ||||
\(581\) | 8.68174 | + | 2.23455i | 0.360179 | + | 0.0927048i | ||||
\(582\) | −4.66128 | + | 9.37424i | −0.193216 | + | 0.388575i | ||||
\(583\) | −10.1242 | + | 17.5356i | −0.419300 | + | 0.726250i | ||||
\(584\) | −8.63036 | −0.357127 | ||||||||
\(585\) | −8.67451 | + | 6.56593i | −0.358647 | + | 0.271468i | ||||
\(586\) | 35.9001i | 1.48302i | ||||||||
\(587\) | 22.1238 | − | 38.3196i | 0.913148 | − | 1.58162i | 0.103558 | − | 0.994623i | \(-0.466977\pi\) |
0.809590 | − | 0.586996i | \(-0.199689\pi\) | |||||||
\(588\) | −0.289387 | − | 3.52451i | −0.0119341 | − | 0.145348i | ||||
\(589\) | −5.55834 | − | 9.62733i | −0.229028 | − | 0.396687i | ||||
\(590\) | −9.82246 | + | 5.67100i | −0.404384 | + | 0.233471i | ||||
\(591\) | 10.2084 | − | 6.77254i | 0.419917 | − | 0.278585i | ||||
\(592\) | 4.67905 | − | 8.10435i | 0.192308 | − | 0.333087i | ||||
\(593\) | 10.0021 | 0.410736 | 0.205368 | − | 0.978685i | \(-0.434161\pi\) | ||||
0.205368 | + | 0.978685i | \(0.434161\pi\) | |||||||
\(594\) | −25.5086 | − | 29.6729i | −1.04663 | − | 1.21749i | ||||
\(595\) | 9.12109 | − | 9.30316i | 0.373928 | − | 0.381393i | ||||
\(596\) | −1.63646 | − | 0.944809i | −0.0670319 | − | 0.0387009i | ||||
\(597\) | 5.97708 | − | 3.96537i | 0.244626 | − | 0.162292i | ||||
\(598\) | 28.1387 | − | 16.2459i | 1.15068 | − | 0.664343i | ||||
\(599\) | −23.6768 | + | 13.6698i | −0.967407 | + | 0.558532i | −0.898445 | − | 0.439087i | \(-0.855302\pi\) |
−0.0689620 | + | 0.997619i | \(0.521969\pi\) | |||||||
\(600\) | 0.322272 | + | 5.17797i | 0.0131567 | + | 0.211390i | ||||
\(601\) | −34.6432 | − | 20.0013i | −1.41313 | − | 0.815869i | −0.417444 | − | 0.908703i | \(-0.637074\pi\) |
−0.995682 | + | 0.0928341i | \(0.970407\pi\) | |||||||
\(602\) | 0.672597 | + | 0.659433i | 0.0274130 | + | 0.0268765i | ||||
\(603\) | −9.87634 | + | 1.23417i | −0.402196 | + | 0.0502594i | ||||
\(604\) | 5.52124 | 0.224656 | ||||||||
\(605\) | −11.0981 | + | 19.2225i | −0.451202 | + | 0.781505i | ||||
\(606\) | −20.2009 | − | 10.0448i | −0.820606 | − | 0.408041i | ||||
\(607\) | −19.4976 | + | 11.2569i | −0.791381 | + | 0.456904i | −0.840449 | − | 0.541891i | \(-0.817708\pi\) |
0.0490673 | + | 0.998795i | \(0.484375\pi\) | |||||||
\(608\) | −2.47152 | − | 4.28080i | −0.100233 | − | 0.173609i | ||||
\(609\) | 35.8093 | − | 12.4194i | 1.45106 | − | 0.503260i | ||||
\(610\) | 5.89457 | − | 10.2097i | 0.238664 | − | 0.413379i | ||||
\(611\) | − | 13.6521i | − | 0.552306i | ||||||
\(612\) | −4.27566 | + | 0.534296i | −0.172833 | + | 0.0215977i | ||||
\(613\) | 31.9991 | 1.29243 | 0.646216 | − | 0.763154i | \(-0.276350\pi\) | ||||
0.646216 | + | 0.763154i | \(0.276350\pi\) | |||||||
\(614\) | 4.89808 | − | 8.48373i | 0.197670 | − | 0.342375i | ||||
\(615\) | 19.2854 | − | 1.20031i | 0.777663 | − | 0.0484011i | ||||
\(616\) | −44.2184 | − | 11.3812i | −1.78161 | − | 0.458560i | ||||
\(617\) | −0.991996 | + | 0.572729i | −0.0399363 | + | 0.0230572i | −0.519835 | − | 0.854267i | \(-0.674007\pi\) |
0.479899 | + | 0.877324i | \(0.340673\pi\) | |||||||
\(618\) | −12.0964 | − | 18.2331i | −0.486588 | − | 0.733444i | ||||
\(619\) | −7.02781 | − | 4.05751i | −0.282471 | − | 0.163085i | 0.352070 | − | 0.935974i | \(-0.385478\pi\) |
−0.634542 | + | 0.772889i | \(0.718811\pi\) | |||||||
\(620\) | − | 1.07323i | − | 0.0431019i | ||||||
\(621\) | −27.0109 | + | 23.2202i | −1.08391 | + | 0.931795i | ||||
\(622\) | 26.0129i | 1.04302i | ||||||||
\(623\) | −3.32867 | − | 11.9492i | −0.133360 | − | 0.478733i | ||||
\(624\) | −17.4376 | + | 11.5686i | −0.698063 | + | 0.463115i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −21.3741 | − | 37.0211i | −0.854283 | − | 1.47966i | ||||
\(627\) | −30.0918 | + | 1.87289i | −1.20175 | + | 0.0747959i | ||||
\(628\) | 0.220132 | + | 0.127093i | 0.00878423 | + | 0.00507158i | ||||
\(629\) | −13.8320 | −0.551518 | ||||||||
\(630\) | −1.32015 | + | 10.2899i | −0.0525962 | + | 0.409959i | ||||
\(631\) | −19.8404 | −0.789835 | −0.394917 | − | 0.918717i | \(-0.629227\pi\) | ||||
−0.394917 | + | 0.918717i | \(0.629227\pi\) | |||||||
\(632\) | 26.7398 | + | 15.4382i | 1.06365 | + | 0.614099i | ||||
\(633\) | −11.3977 | + | 22.9218i | −0.453018 | + | 0.911059i | ||||
\(634\) | 5.75170 | + | 9.96223i | 0.228429 | + | 0.395651i | ||||
\(635\) | 4.87941 | + | 8.45138i | 0.193633 | + | 0.335383i | ||||
\(636\) | −1.58975 | − | 0.790491i | −0.0630376 | − | 0.0313450i | ||||
\(637\) | −12.2555 | + | 22.2306i | −0.485582 | + | 0.880808i | ||||
\(638\) | − | 62.2844i | − | 2.46586i | ||||||
\(639\) | 19.2194 | + | 8.10955i | 0.760309 | + | 0.320809i | ||||
\(640\) | 8.23172i | 0.325387i | ||||||||
\(641\) | 26.4557 | + | 15.2742i | 1.04494 | + | 0.603294i | 0.921228 | − | 0.389024i | \(-0.127188\pi\) |
0.123709 | + | 0.992319i | \(0.460521\pi\) | |||||||
\(642\) | 21.3960 | − | 1.33167i | 0.844434 | − | 0.0525569i | ||||
\(643\) | 31.1031 | − | 17.9574i | 1.22658 | − | 0.708169i | 0.260271 | − | 0.965536i | \(-0.416188\pi\) |
0.966314 | + | 0.257367i | \(0.0828548\pi\) | |||||||
\(644\) | −1.31860 | + | 5.12305i | −0.0519600 | + | 0.201876i | ||||
\(645\) | 0.260819 | + | 0.393138i | 0.0102697 | + | 0.0154798i | ||||
\(646\) | 9.72266 | − | 16.8401i | 0.382533 | − | 0.662566i | ||||
\(647\) | 5.35102 | 0.210370 | 0.105185 | − | 0.994453i | \(-0.466456\pi\) | ||||
0.105185 | + | 0.994453i | \(0.466456\pi\) | |||||||
\(648\) | 19.3111 | − | 18.8093i | 0.758613 | − | 0.738900i | ||||
\(649\) | − | 49.9976i | − | 1.96258i | ||||||
\(650\) | 2.36992 | − | 4.10482i | 0.0929560 | − | 0.161004i | ||||
\(651\) | 3.18049 | − | 16.5591i | 0.124653 | − | 0.649001i | ||||
\(652\) | −1.57491 | − | 2.72782i | −0.0616782 | − | 0.106830i | ||||
\(653\) | 29.5953 | − | 17.0869i | 1.15815 | − | 0.668660i | 0.207293 | − | 0.978279i | \(-0.433535\pi\) |
0.950861 | + | 0.309619i | \(0.100201\pi\) | |||||||
\(654\) | −1.17231 | − | 18.8355i | −0.0458409 | − | 0.736528i | ||||
\(655\) | 8.91007 | − | 15.4327i | 0.348145 | − | 0.603005i | ||||
\(656\) | 37.1670 | 1.45113 | ||||||||
\(657\) | −7.96402 | − | 3.36038i | −0.310706 | − | 0.131101i | ||||
\(658\) | −9.29589 | − | 9.11395i | −0.362391 | − | 0.355299i | ||||
\(659\) | −16.6480 | − | 9.61174i | −0.648515 | − | 0.374420i | 0.139372 | − | 0.990240i | \(-0.455492\pi\) |
−0.787887 | + | 0.615820i | \(0.788825\pi\) | |||||||
\(660\) | −2.60632 | − | 1.29597i | −0.101451 | − | 0.0504457i | ||||
\(661\) | −14.1032 | + | 8.14247i | −0.548550 | + | 0.316705i | −0.748537 | − | 0.663093i | \(-0.769243\pi\) |
0.199987 | + | 0.979799i | \(0.435910\pi\) | |||||||
\(662\) | −16.2033 | + | 9.35496i | −0.629758 | + | 0.363591i | ||||
\(663\) | 27.6955 | + | 13.7714i | 1.07560 | + | 0.534837i | ||||
\(664\) | 8.78933 | + | 5.07452i | 0.341092 | + | 0.196930i | ||||
\(665\) | 5.70777 | + | 5.59606i | 0.221338 | + | 0.217006i | ||||
\(666\) | 8.78192 | − | 6.64723i | 0.340292 | − | 0.257575i | ||||
\(667\) | −56.6969 | −2.19531 | ||||||||
\(668\) | −0.939453 | + | 1.62718i | −0.0363485 | + | 0.0629575i | ||||
\(669\) | 0.690148 | + | 11.0887i | 0.0266827 | + | 0.428712i | ||||
\(670\) | 3.75539 | − | 2.16818i | 0.145084 | − | 0.0837640i | ||||
\(671\) | 25.9843 | + | 45.0062i | 1.00311 | + | 1.73744i | ||||
\(672\) | 1.41420 | − | 7.36299i | 0.0545541 | − | 0.284034i | ||||
\(673\) | −7.55471 | + | 13.0851i | −0.291213 | + | 0.504395i | −0.974097 | − | 0.226131i | \(-0.927392\pi\) |
0.682884 | + | 0.730527i | \(0.260725\pi\) | |||||||
\(674\) | 35.3349i | 1.36105i | ||||||||
\(675\) | −1.71874 | + | 4.90366i | −0.0661545 | + | 0.188742i | ||||
\(676\) | −0.0440301 | −0.00169347 | ||||||||
\(677\) | −19.8465 | + | 34.3752i | −0.762764 | + | 1.32115i | 0.178656 | + | 0.983912i | \(0.442825\pi\) |
−0.941420 | + | 0.337235i | \(0.890508\pi\) | |||||||
\(678\) | 6.76328 | + | 10.1944i | 0.259742 | + | 0.391515i | ||||
\(679\) | −3.04980 | + | 11.8491i | −0.117040 | + | 0.454729i | ||||
\(680\) | 12.7737 | − | 7.37489i | 0.489848 | − | 0.282814i | ||||
\(681\) | 7.90884 | − | 0.492240i | 0.303067 | − | 0.0188627i | ||||
\(682\) | −23.9968 | − | 13.8545i | −0.918884 | − | 0.530518i | ||||
\(683\) | − | 9.81578i | − | 0.375591i | −0.982208 | − | 0.187795i | \(-0.939866\pi\) | ||
0.982208 | − | 0.187795i | \(-0.0601342\pi\) | |||||||
\(684\) | −0.327807 | − | 2.62324i | −0.0125340 | − | 0.100302i | ||||
\(685\) | 1.37912i | 0.0526934i | ||||||||
\(686\) | 6.95543 | + | 23.1857i | 0.265560 | + | 0.885235i | ||||
\(687\) | −9.11898 | − | 4.53435i | −0.347911 | − | 0.172996i | ||||
\(688\) | 0.453739 | + | 0.785898i | 0.0172986 | + | 0.0299621i | ||||
\(689\) | 6.37227 | + | 11.0371i | 0.242764 | + | 0.420480i | ||||
\(690\) | 6.90951 | − | 13.8956i | 0.263040 | − | 0.528998i | ||||
\(691\) | 33.1911 | + | 19.1629i | 1.26265 | + | 0.728990i | 0.973586 | − | 0.228320i | \(-0.0733234\pi\) |
0.289062 | + | 0.957310i | \(0.406657\pi\) | |||||||
\(692\) | 1.38509 | 0.0526531 | ||||||||
\(693\) | −36.3728 | − | 27.7196i | −1.38169 | − | 1.05298i | ||||
\(694\) | −13.5736 | −0.515248 | ||||||||
\(695\) | −10.5156 | − | 6.07121i | −0.398881 | − | 0.230294i | ||||
\(696\) | 42.8262 | − | 2.66547i | 1.62332 | − | 0.101034i | ||||
\(697\) | −27.4679 | − | 47.5757i | −1.04042 | − | 1.80206i | ||||
\(698\) | 0.657479 | + | 1.13879i | 0.0248859 | + | 0.0431037i | ||||
\(699\) | −14.1784 | + | 9.40637i | −0.536277 | + | 0.355781i | ||||
\(700\) | 0.207087 | + | 0.743394i | 0.00782715 | + | 0.0280977i | ||||
\(701\) | 0.509304i | 0.0192362i | 0.999954 | + | 0.00961808i | \(0.00306158\pi\) | ||||
−0.999954 | + | 0.00961808i | \(0.996938\pi\) | |||||||
\(702\) | −24.2020 | + | 4.56616i | −0.913444 | + | 0.172339i | ||||
\(703\) | − | 8.48634i | − | 0.320068i | ||||||
\(704\) | −43.9173 | − | 25.3557i | −1.65520 | − | 0.955628i | ||||
\(705\) | −3.60475 | − | 5.43351i | −0.135763 | − | 0.204638i | ||||
\(706\) | −8.75158 | + | 5.05273i | −0.329370 | + | 0.190162i | ||||
\(707\) | −25.5342 | − | 6.57212i | −0.960312 | − | 0.247170i | ||||
\(708\) | 4.37547 | − | 0.272326i | 0.164440 | − | 0.0102346i | ||||
\(709\) | −8.37903 | + | 14.5129i | −0.314681 | + | 0.545044i | −0.979370 | − | 0.202077i | \(-0.935231\pi\) |
0.664688 | + | 0.747121i | \(0.268564\pi\) | |||||||
\(710\) | −9.08833 | −0.341079 | ||||||||
\(711\) | 18.6641 | + | 24.6578i | 0.699958 | + | 0.924741i | ||||
\(712\) | − | 14.0429i | − | 0.526279i | ||||||
\(713\) | −12.6117 | + | 21.8440i | −0.472310 | + | 0.818065i | ||||
\(714\) | 27.8662 | − | 9.66460i | 1.04287 | − | 0.361688i | ||||
\(715\) | 10.4470 | + | 18.0948i | 0.390697 | + | 0.676707i | ||||
\(716\) | 4.97421 | − | 2.87186i | 0.185895 | − | 0.107326i | ||||
\(717\) | −28.5715 | − | 14.2070i | −1.06702 | − | 0.530570i | ||||
\(718\) | −12.4259 | + | 21.5223i | −0.463731 | + | 0.803205i | ||||
\(719\) | −0.103522 | −0.00386073 | −0.00193037 | − | 0.999998i | \(-0.500614\pi\) | ||||
−0.00193037 | + | 0.999998i | \(0.500614\pi\) | |||||||
\(720\) | −3.88551 | + | 9.20855i | −0.144804 | + | 0.343182i | ||||
\(721\) | −18.2600 | − | 17.9026i | −0.680038 | − | 0.666729i | ||||
\(722\) | −11.1746 | − | 6.45164i | −0.415874 | − | 0.240105i | ||||
\(723\) | −0.475763 | − | 7.64411i | −0.0176938 | − | 0.284287i | ||||
\(724\) | −6.71994 | + | 3.87976i | −0.249745 | + | 0.144190i | ||||
\(725\) | −7.16276 | + | 4.13542i | −0.266018 | + | 0.153586i | ||||
\(726\) | −41.8719 | + | 27.7790i | −1.55401 | + | 1.03098i | ||||
\(727\) | −42.0055 | − | 24.2519i | −1.55790 | − | 0.899453i | −0.997458 | − | 0.0712586i | \(-0.977298\pi\) |
−0.560441 | − | 0.828195i | \(-0.689368\pi\) | |||||||
\(728\) | −20.1195 | + | 20.5211i | −0.745677 | + | 0.760562i | ||||
\(729\) | 25.1439 | − | 9.83793i | 0.931255 | − | 0.364368i | ||||
\(730\) | 3.76596 | 0.139384 | ||||||||
\(731\) | 0.670661 | − | 1.16162i | 0.0248053 | − | 0.0429640i | ||||
\(732\) | −3.79713 | + | 2.51912i | −0.140346 | + | 0.0931095i | ||||
\(733\) | −9.42982 | + | 5.44431i | −0.348298 | + | 0.201090i | −0.663936 | − | 0.747790i | \(-0.731115\pi\) |
0.315637 | + | 0.948880i | \(0.397782\pi\) | |||||||
\(734\) | 7.48827 | + | 12.9701i | 0.276397 | + | 0.478734i | ||||
\(735\) | 0.992154 | + | 12.0837i | 0.0365962 | + | 0.445714i | ||||
\(736\) | −5.60777 | + | 9.71295i | −0.206705 | + | 0.358024i | ||||
\(737\) | 19.1154i | 0.704126i | ||||||||
\(738\) | 40.3027 | + | 17.0056i | 1.48356 | + | 0.625984i | ||||
\(739\) | −44.1464 | −1.62395 | −0.811975 | − | 0.583692i | \(-0.801607\pi\) | ||||
−0.811975 | + | 0.583692i | \(0.801607\pi\) | |||||||
\(740\) | 0.409644 | − | 0.709525i | 0.0150588 | − | 0.0260827i | ||||
\(741\) | −8.44917 | + | 16.9920i | −0.310388 | + | 0.624217i | ||||
\(742\) | 11.7693 | + | 3.02924i | 0.432065 | + | 0.111207i | ||||
\(743\) | −40.8891 | + | 23.6073i | −1.50008 | + | 0.866069i | −0.500076 | + | 0.865981i | \(0.666695\pi\) |
−1.00000 | 8.81124e-5i | \(0.999972\pi\) | ||||||||
\(744\) | 8.49931 | − | 17.0929i | 0.311600 | − | 0.626655i | ||||
\(745\) | 5.61055 | + | 3.23925i | 0.205555 | + | 0.118677i | ||||
\(746\) | 18.6897i | 0.684278i | ||||||||
\(747\) | 6.13486 | + | 8.10500i | 0.224463 | + | 0.296546i | ||||
\(748\) | 8.27543i | 0.302580i | ||||||||
\(749\) | 24.1350 | − | 6.72326i | 0.881873 | − | 0.245663i | ||||
\(750\) | −0.140627 | − | 2.25947i | −0.00513499 | − | 0.0825041i | ||||
\(751\) | 13.1860 | + | 22.8389i | 0.481166 | + | 0.833403i | 0.999766 | − | 0.0216131i | \(-0.00688020\pi\) |
−0.518601 | + | 0.855017i | \(0.673547\pi\) | |||||||
\(752\) | −6.27107 | − | 10.8618i | −0.228682 | − | 0.396089i | ||||
\(753\) | 10.5404 | + | 15.8877i | 0.384112 | + | 0.578980i | ||||
\(754\) | −33.9504 | − | 19.6013i | −1.23640 | − | 0.713836i | ||||
\(755\) | −18.9294 | −0.688912 | ||||||||
\(756\) | 2.22773 | − | 3.33410i | 0.0810218 | − | 0.121260i | ||||
\(757\) | −29.2002 | −1.06130 | −0.530649 | − | 0.847592i | \(-0.678052\pi\) | ||||
−0.530649 | + | 0.847592i | \(0.678052\pi\) | |||||||
\(758\) | −7.13902 | − | 4.12172i | −0.259301 | − | 0.149708i | ||||
\(759\) | 37.8187 | + | 57.0049i | 1.37273 | + | 2.06915i | ||||
\(760\) | 4.52471 | + | 7.83703i | 0.164129 | + | 0.284279i | ||||
\(761\) | −17.7331 | − | 30.7147i | −0.642826 | − | 1.11341i | −0.984799 | − | 0.173697i | \(-0.944429\pi\) |
0.341974 | − | 0.939710i | \(-0.388905\pi\) | |||||||
\(762\) | 1.37236 | + | 22.0497i | 0.0497153 | + | 0.798778i | ||||
\(763\) | −5.91868 | − | 21.2467i | −0.214271 | − | 0.769183i | ||||
\(764\) | 3.26426i | 0.118097i | ||||||||
\(765\) | 14.6590 | − | 1.83182i | 0.529996 | − | 0.0662296i | ||||
\(766\) | 39.0557i | 1.41114i | ||||||||
\(767\) | −27.2530 | − | 15.7345i | −0.984048 | − | 0.568140i | ||||
\(768\) | 5.27798 | − | 10.6145i | 0.190453 | − | 0.383017i | ||||
\(769\) | 29.0445 | − | 16.7688i | 1.04737 | − | 0.604700i | 0.125459 | − | 0.992099i | \(-0.459960\pi\) |
0.921912 | + | 0.387399i | \(0.126626\pi\) | |||||||
\(770\) | 19.2952 | + | 4.96630i | 0.695351 | + | 0.178973i | ||||
\(771\) | 3.64340 | − | 7.32719i | 0.131214 | − | 0.263882i | ||||
\(772\) | −0.135253 | + | 0.234265i | −0.00486787 | + | 0.00843140i | ||||
\(773\) | 29.1971 | 1.05015 | 0.525073 | − | 0.851057i | \(-0.324038\pi\) | ||||
0.525073 | + | 0.851057i | \(0.324038\pi\) | |||||||
\(774\) | 0.132436 | + | 1.05981i | 0.00476033 | + | 0.0380941i | ||||
\(775\) | 3.67953i | 0.132173i | ||||||||
\(776\) | −6.92589 | + | 11.9960i | −0.248625 | + | 0.430631i | ||||
\(777\) | 8.42316 | − | 9.73344i | 0.302179 | − | 0.349185i | ||||
\(778\) | 5.12384 | + | 8.87475i | 0.183698 | + | 0.318175i | ||||
\(779\) | 29.1891 | − | 16.8523i | 1.04581 | − | 0.603798i | ||||
\(780\) | −1.52664 | + | 1.01282i | −0.0546625 | + | 0.0362647i | ||||
\(781\) | 20.0315 | − | 34.6955i | 0.716783 | − | 1.24150i | ||||
\(782\) | −44.1206 | −1.57775 | ||||||||
\(783\) | 40.5575 | + | 14.2155i | 1.44941 | + | 0.508019i | ||||
\(784\) | 0.460890 | + | 23.3165i | 0.0164604 | + | 0.832731i | ||||
\(785\) | −0.754717 | − | 0.435736i | −0.0269370 | − | 0.0155521i | ||||
\(786\) | 33.6167 | − | 22.3023i | 1.19907 | − | 0.795496i | ||||
\(787\) | 20.7541 | − | 11.9824i | 0.739803 | − | 0.427126i | −0.0821945 | − | 0.996616i | \(-0.526193\pi\) |
0.821998 | + | 0.569491i | \(0.192860\pi\) | |||||||
\(788\) | 1.78660 | − | 1.03150i | 0.0636451 | − | 0.0367455i | ||||
\(789\) | −0.429618 | − | 6.90270i | −0.0152948 | − | 0.245743i | ||||
\(790\) | −11.6682 | − | 6.73665i | −0.415137 | − | 0.239679i | ||||
\(791\) | 10.2095 | + | 10.0096i | 0.363006 | + | 0.355902i | ||||
\(792\) | −31.2464 | − | 41.2809i | −1.11029 | − | 1.46685i | ||||
\(793\) | 32.7096 | 1.16155 | ||||||||
\(794\) | 0.212523 | − | 0.368100i | 0.00754215 | − | 0.0130634i | ||||
\(795\) | 5.45041 | + | 2.71018i | 0.193306 | + | 0.0961201i | ||||
\(796\) | 1.04607 | − | 0.603948i | 0.0370769 | − | 0.0214064i | ||||
\(797\) | 16.1948 | + | 28.0502i | 0.573648 | + | 0.993588i | 0.996187 | + | 0.0872431i | \(0.0278057\pi\) |
−0.422539 | + | 0.906345i | \(0.638861\pi\) | |||||||
\(798\) | 5.92952 | + | 17.0967i | 0.209903 | + | 0.605218i | ||||
\(799\) | −9.26913 | + | 16.0546i | −0.327918 | + | 0.567971i | ||||
\(800\) | 1.63611i | 0.0578451i | ||||||||
\(801\) | 5.46784 | − | 12.9586i | 0.193197 | − | 0.457871i | ||||
\(802\) | 0.848759 | 0.0299707 | ||||||||
\(803\) | −8.30051 | + | 14.3769i | −0.292919 | + | 0.507350i | ||||
\(804\) | −1.67286 | + | 0.104117i | −0.0589973 | + | 0.00367194i | ||||
\(805\) | 4.52078 | − | 17.5642i | 0.159336 | − | 0.619058i | ||||
\(806\) | −15.1038 | + | 8.72020i | −0.532010 | + | 0.307156i | ||||
\(807\) | 20.3814 | + | 30.7213i | 0.717460 | + | 1.08144i | ||||
\(808\) | −25.8506 | − | 14.9249i | −0.909421 | − | 0.525055i | ||||
\(809\) | 4.89038i | 0.171937i | 0.996298 | + | 0.0859683i | \(0.0273984\pi\) | ||||
−0.996298 | + | 0.0859683i | \(0.972602\pi\) | |||||||
\(810\) | −8.42665 | + | 8.20767i | −0.296082 | + | 0.288388i | ||||
\(811\) | − | 8.79200i | − | 0.308729i | −0.988014 | − | 0.154364i | \(-0.950667\pi\) | ||
0.988014 | − | 0.154364i | \(-0.0493330\pi\) | |||||||
\(812\) | 6.14850 | − | 1.71278i | 0.215770 | − | 0.0601069i | ||||
\(813\) | −12.8638 | + | 8.53423i | −0.451154 | + | 0.299309i | ||||
\(814\) | −10.5764 | − | 18.3188i | −0.370702 | − | 0.642075i | ||||
\(815\) | 5.39954 | + | 9.35227i | 0.189137 | + | 0.327596i | ||||
\(816\) | 28.3608 | − | 1.76515i | 0.992825 | − | 0.0617926i | ||||
\(817\) | 0.712688 | + | 0.411470i | 0.0249338 | + | 0.0143955i | ||||
\(818\) | −28.3695 | −0.991916 | ||||||||
\(819\) | −26.5563 | + | 11.1028i | −0.927953 | + | 0.387964i | ||||
\(820\) | 3.25392 | 0.113632 | ||||||||
\(821\) | −37.8062 | − | 21.8274i | −1.31945 | − | 0.761783i | −0.335807 | − | 0.941931i | \(-0.609009\pi\) |
−0.983640 | + | 0.180148i | \(0.942342\pi\) | |||||||
\(822\) | −1.39008 | + | 2.79557i | −0.0484845 | + | 0.0975067i | ||||
\(823\) | 0.415923 | + | 0.720400i | 0.0144982 | + | 0.0251116i | 0.873183 | − | 0.487392i | \(-0.162052\pi\) |
−0.858685 | + | 0.512503i | \(0.828718\pi\) | |||||||
\(824\) | −14.4752 | − | 25.0718i | −0.504269 | − | 0.873419i | ||||
\(825\) | 8.93569 | + | 4.44321i | 0.311101 | + | 0.154693i | ||||
\(826\) | −28.9075 | + | 8.05273i | −1.00582 | + | 0.280190i | ||||
\(827\) | 31.2225i | 1.08571i | 0.839826 | + | 0.542856i | \(0.182657\pi\) | ||||
−0.839826 | + | 0.542856i | \(0.817343\pi\) | |||||||
\(828\) | −4.78272 | + | 3.62015i | −0.166211 | + | 0.125809i | ||||
\(829\) | 17.2401i | 0.598772i | 0.954132 | + | 0.299386i | \(0.0967819\pi\) | ||||
−0.954132 | + | 0.299386i | \(0.903218\pi\) | |||||||
\(830\) | −3.83533 | − | 2.21433i | −0.133126 | − | 0.0768604i | ||||
\(831\) | −47.5259 | + | 2.95797i | −1.64865 | + | 0.102611i | ||||
\(832\) | −27.6421 | + | 15.9591i | −0.958316 | + | 0.553284i | ||||
\(833\) | 29.5057 | − | 17.8218i | 1.02231 | − | 0.617487i | ||||
\(834\) | −15.1965 | − | 22.9060i | −0.526212 | − | 0.793170i | ||||
\(835\) | 3.22089 | − | 5.57874i | 0.111463 | − | 0.193060i | ||||
\(836\) | −5.07722 | −0.175599 | ||||||||
\(837\) | 14.4985 | − | 12.4638i | 0.501141 | − | 0.430811i | ||||
\(838\) | 3.78993i | 0.130921i | ||||||||
\(839\) | 23.3177 | − | 40.3874i | 0.805016 | − | 1.39433i | −0.111265 | − | 0.993791i | \(-0.535490\pi\) |
0.916280 | − | 0.400537i | \(-0.131177\pi\) | |||||||
\(840\) | −2.58904 | + | 13.4797i | −0.0893305 | + | 0.465095i | ||||
\(841\) | 19.7034 | + | 34.1274i | 0.679429 | + | 1.17681i | ||||
\(842\) | −13.9619 | + | 8.06092i | −0.481160 | + | 0.277798i | ||||
\(843\) | 0.427272 | + | 6.86500i | 0.0147160 | + | 0.236443i | ||||
\(844\) | −2.15543 | + | 3.73331i | −0.0741930 | + | 0.128506i | ||||
\(845\) | 0.150956 | 0.00519305 | ||||||||
\(846\) | −1.83039 | − | 14.6475i | −0.0629300 | − | 0.503592i | ||||
\(847\) | −41.1129 | + | 41.9336i | −1.41266 | + | 1.44086i | ||||
\(848\) | 10.1397 | + | 5.85417i | 0.348199 | + | 0.201033i | ||||
\(849\) | −1.83861 | − | 0.914236i | −0.0631009 | − | 0.0313765i | ||||
\(850\) | −5.57395 | + | 3.21812i | −0.191185 | + | 0.110381i | ||||
\(851\) | −16.6755 | + | 9.62758i | −0.571627 | + | 0.330029i | ||||
\(852\) | 3.14544 | + | 1.56405i | 0.107761 | + | 0.0535835i | ||||
\(853\) | 29.6463 | + | 17.1163i | 1.01507 | + | 0.586051i | 0.912672 | − | 0.408692i | \(-0.134015\pi\) |
0.102398 | + | 0.994743i | \(0.467348\pi\) | |||||||
\(854\) | 21.8364 | − | 22.2723i | 0.747228 | − | 0.762144i | ||||
\(855\) | 1.12388 | + | 8.99371i | 0.0384358 | + | 0.307579i | ||||
\(856\) | 28.3638 | 0.969456 | ||||||||
\(857\) | 4.58831 | − | 7.94718i | 0.156734 | − | 0.271471i | −0.776955 | − | 0.629556i | \(-0.783237\pi\) |
0.933689 | + | 0.358085i | \(0.116570\pi\) | |||||||
\(858\) | 2.93828 | + | 47.2095i | 0.100311 | + | 1.61171i | ||||
\(859\) | −14.7502 | + | 8.51605i | −0.503271 | + | 0.290564i | −0.730063 | − | 0.683379i | \(-0.760510\pi\) |
0.226792 | + | 0.973943i | \(0.427176\pi\) | |||||||
\(860\) | 0.0397242 | + | 0.0688043i | 0.00135458 | + | 0.00234621i | ||||
\(861\) | 50.2055 | + | 9.64292i | 1.71100 | + | 0.328630i | ||||
\(862\) | −16.5573 | + | 28.6781i | −0.563945 | + | 0.976781i | ||||
\(863\) | − | 48.0982i | − | 1.63728i | −0.574307 | − | 0.818640i | \(-0.694728\pi\) | ||
0.574307 | − | 0.818640i | \(-0.305272\pi\) | |||||||
\(864\) | 6.44676 | − | 5.54202i | 0.219323 | − | 0.188543i | ||||
\(865\) | −4.74873 | −0.161462 | ||||||||
\(866\) | 19.5921 | − | 33.9346i | 0.665768 | − | 1.15314i | ||||
\(867\) | −6.94116 | − | 10.4626i | −0.235734 | − | 0.355327i | ||||
\(868\) | 0.707776 | − | 2.74987i | 0.0240235 | − | 0.0933366i | ||||
\(869\) | 51.4356 | − | 29.6963i | 1.74483 | − | 1.00738i | ||||
\(870\) | −18.6877 | + | 1.16311i | −0.633573 | + | 0.0394331i | ||||
\(871\) | 10.4195 | + | 6.01573i | 0.353053 | + | 0.203835i | ||||
\(872\) | − | 24.9695i | − | 0.845574i | ||||||
\(873\) | −11.0620 | + | 8.37307i | −0.374392 | + | 0.283385i | ||||
\(874\) | − | 27.0693i | − | 0.915633i | ||||||
\(875\) | −0.709992 | − | 2.54871i | −0.0240021 | − | 0.0861621i | ||||
\(876\) | −1.30339 | − | 0.648101i | −0.0440374 | − | 0.0218973i | ||||
\(877\) | 20.2172 | + | 35.0172i | 0.682685 | + | 1.18245i | 0.974158 | + | 0.225867i | \(0.0725214\pi\) |
−0.291473 | + | 0.956579i | \(0.594145\pi\) | |||||||
\(878\) | −14.5997 | − | 25.2873i | −0.492714 | − | 0.853406i | ||||
\(879\) | −21.1818 | + | 42.5985i | −0.714444 | + | 1.43681i | ||||
\(880\) | 16.6236 | + | 9.59763i | 0.560381 | + | 0.323536i | ||||
\(881\) | 47.9451 | 1.61531 | 0.807656 | − | 0.589653i | \(-0.200736\pi\) | ||||
0.807656 | + | 0.589653i | \(0.200736\pi\) | |||||||
\(882\) | −10.1686 | + | 25.4945i | −0.342393 | + | 0.858446i | ||||
\(883\) | 22.4684 | 0.756122 | 0.378061 | − | 0.925781i | \(-0.376591\pi\) | ||||
0.378061 | + | 0.925781i | \(0.376591\pi\) | |||||||
\(884\) | 4.51082 | + | 2.60432i | 0.151715 | + | 0.0875929i | ||||
\(885\) | −15.0012 | + | 0.933661i | −0.504259 | + | 0.0313847i | ||||
\(886\) | −8.56882 | − | 14.8416i | −0.287875 | − | 0.498614i | ||||
\(887\) | 4.00551 | + | 6.93775i | 0.134492 | + | 0.232947i | 0.925403 | − | 0.378984i | \(-0.123726\pi\) |
−0.790911 | + | 0.611931i | \(0.790393\pi\) | |||||||
\(888\) | 12.1432 | − | 8.05618i | 0.407501 | − | 0.270348i | ||||
\(889\) | 6.92868 | + | 24.8724i | 0.232380 | + | 0.834192i | ||||
\(890\) | 6.12777i | 0.205403i | ||||||||
\(891\) | −12.7605 | − | 50.2600i | −0.427492 | − | 1.68377i | ||||
\(892\) | 1.87093i | 0.0626433i | ||||||||
\(893\) | −9.84997 | − | 5.68689i | −0.329617 | − | 0.190304i | ||||
\(894\) | 8.10799 | + | 12.2213i | 0.271172 | + | 0.408743i | ||||
\(895\) | −17.0539 | + | 9.84610i | −0.570050 | + | 0.329119i | ||||
\(896\) | −5.42868 | + | 21.0917i | −0.181360 | + | 0.704623i | ||||
\(897\) | 42.9743 | − | 2.67469i | 1.43487 | − | 0.0893052i | ||||
\(898\) | 18.9582 | − | 32.8366i | 0.632645 | − | 1.09577i | ||||
\(899\) | 30.4329 | 1.01499 | ||||||||
\(900\) | −0.340171 | + | 0.806196i | −0.0113390 | + | 0.0268732i | ||||
\(901\) | − | 17.3058i | − | 0.576541i | ||||||
\(902\) | 42.0056 | − | 72.7558i | 1.39863 | − | 2.42250i | ||||
\(903\) | 0.409013 | + | 1.17932i | 0.0136111 | + | 0.0392453i | ||||
\(904\) | 8.09333 | + | 14.0181i | 0.269180 | + | 0.466234i | ||||
\(905\) | 23.0391 | − | 13.3016i | 0.765847 | − | 0.442162i | ||||
\(906\) | −38.3713 | − | 19.0799i | −1.27480 | − | 0.633886i | ||||
\(907\) | 5.25834 | − | 9.10772i | 0.174600 | − | 0.302417i | −0.765423 | − | 0.643528i | \(-0.777470\pi\) |
0.940023 | + | 0.341111i | \(0.110803\pi\) | |||||||
\(908\) | 1.33442 | 0.0442841 | ||||||||
\(909\) | −18.0434 | − | 23.8379i | −0.598463 | − | 0.790654i | ||||
\(910\) | 8.77937 | − | 8.95463i | 0.291033 | − | 0.296843i | ||||
\(911\) | 25.7026 | + | 14.8394i | 0.851567 | + | 0.491652i | 0.861179 | − | 0.508302i | \(-0.169726\pi\) |
−0.00961242 | + | 0.999954i | \(0.503060\pi\) | |||||||
\(912\) | 1.08297 | + | 17.4002i | 0.0358608 | + | 0.576177i | ||||
\(913\) | 16.9068 | − | 9.76115i | 0.559534 | − | 0.323047i | ||||
\(914\) | −6.12380 | + | 3.53558i | −0.202557 | + | 0.116947i | ||||
\(915\) | 13.0183 | − | 8.63675i | 0.430373 | − | 0.285522i | ||||
\(916\) | −1.48523 | − | 0.857495i | −0.0490732 | − | 0.0283324i | ||||
\(917\) | 33.0073 | − | 33.6662i | 1.09000 | − | 1.11176i | ||||
\(918\) | 31.5612 | + | 11.0622i | 1.04167 | + | 0.365109i | ||||
\(919\) | 7.29885 | 0.240767 | 0.120383 | − | 0.992727i | \(-0.461588\pi\) | ||||
0.120383 | + | 0.992727i | \(0.461588\pi\) | |||||||
\(920\) | 10.2664 | − | 17.7819i | 0.338473 | − | 0.586252i | ||||
\(921\) | 10.8176 | − | 7.17668i | 0.356451 | − | 0.236480i | ||||
\(922\) | 15.8439 | − | 9.14747i | 0.521791 | − | 0.301256i | ||||
\(923\) | −12.6080 | − | 21.8378i | −0.414999 | − | 0.718799i | ||||
\(924\) | −5.82334 | − | 5.03942i | −0.191574 | − | 0.165785i | ||||
\(925\) | −1.40446 | + | 2.43259i | −0.0461782 | + | 0.0799830i | ||||
\(926\) | 13.3789i | 0.439657i | ||||||||
\(927\) | −3.59545 | − | 28.7723i | −0.118090 | − | 0.945005i | ||||
\(928\) | 13.5320 | 0.444209 | ||||||||
\(929\) | 12.1110 | − | 20.9768i | 0.397348 | − | 0.688227i | −0.596050 | − | 0.802948i | \(-0.703264\pi\) |
0.993398 | + | 0.114720i | \(0.0365972\pi\) | |||||||
\(930\) | −3.70878 | + | 7.45868i | −0.121616 | + | 0.244580i | ||||
\(931\) | 10.9342 | + | 18.1026i | 0.358353 | + | 0.593290i | ||||
\(932\) | −2.48141 | + | 1.43264i | −0.0812813 | + | 0.0469278i | ||||
\(933\) | −15.3481 | + | 30.8665i | −0.502475 | + | 1.01052i | ||||
\(934\) | −6.55050 | − | 3.78193i | −0.214339 | − | 0.123749i | ||||
\(935\) | − | 28.3721i | − | 0.927867i | ||||||
\(936\) | −32.3350 | + | 4.04067i | −1.05690 | + | 0.132073i | ||||
\(937\) | − | 21.2312i | − | 0.693594i | −0.937940 | − | 0.346797i | \(-0.887269\pi\) | ||
0.937940 | − | 0.346797i | \(-0.112731\pi\) | |||||||
\(938\) | 11.0521 | − | 3.07878i | 0.360864 | − | 0.100526i | ||||
\(939\) | −3.51899 | − | 56.5398i | −0.114838 | − | 1.84511i | ||||
\(940\) | −0.549024 | − | 0.950937i | −0.0179072 | − | 0.0310161i | ||||
\(941\) | 2.03848 | + | 3.53075i | 0.0664524 | + | 0.115099i | 0.897337 | − | 0.441345i | \(-0.145499\pi\) |
−0.830885 | + | 0.556444i | \(0.812165\pi\) | |||||||
\(942\) | −1.09067 | − | 1.64398i | −0.0355358 | − | 0.0535639i | ||||
\(943\) | −66.2289 | − | 38.2373i | −2.15671 | − | 1.24518i | ||||
\(944\) | −28.9104 | −0.940954 | ||||||||
\(945\) | −7.63772 | + | 11.4309i | −0.248455 | + | 0.371847i | ||||
\(946\) | 2.05124 | 0.0666914 | ||||||||
\(947\) | −18.2207 | − | 10.5197i | −0.592093 | − | 0.341845i | 0.173832 | − | 0.984775i | \(-0.444385\pi\) |
−0.765925 | + | 0.642930i | \(0.777718\pi\) | |||||||
\(948\) | 2.87900 | + | 4.33957i | 0.0935054 | + | 0.140943i | ||||
\(949\) | 5.22443 | + | 9.04899i | 0.169592 | + | 0.293743i | ||||
\(950\) | −1.97441 | − | 3.41978i | −0.0640584 | − | 0.110952i | ||||
\(951\) | 0.946947 | + | 15.2146i | 0.0307069 | + | 0.493369i | ||||
\(952\) | 37.5929 | − | 10.4722i | 1.21839 | − | 0.339406i | ||||
\(953\) | − | 45.0425i | − | 1.45907i | −0.683944 | − | 0.729535i | \(-0.739737\pi\) | ||
0.683944 | − | 0.729535i | \(-0.260263\pi\) | |||||||
\(954\) | 8.31665 | + | 10.9874i | 0.269261 | + | 0.355732i | ||||
\(955\) | − | 11.1914i | − | 0.362147i | ||||||
\(956\) | −4.65349 | − | 2.68670i | −0.150505 | − | 0.0868940i | ||||
\(957\) | 36.7491 | − | 73.9057i | 1.18793 | − | 2.38903i | ||||
\(958\) | −13.3991 | + | 7.73599i | −0.432906 | + | 0.249939i | ||||
\(959\) | −0.909505 | + | 3.53363i | −0.0293694 | + | 0.114107i | ||||
\(960\) | −6.78756 | + | 13.6504i | −0.219068 | + | 0.440564i | ||||
\(961\) | −8.73052 | + | 15.1217i | −0.281630 | + | 0.487797i | ||||
\(962\) | −13.3138 | −0.429254 | ||||||||
\(963\) | 26.1739 | + | 11.0440i | 0.843442 | + | 0.355887i | ||||
\(964\) | − | 1.28975i | − | 0.0415400i | ||||||
\(965\) | 0.463712 | − | 0.803173i | 0.0149274 | − | 0.0258551i | ||||
\(966\) | 26.8678 | − | 31.0473i | 0.864456 | − | 0.998929i | ||||
\(967\) | 17.2648 | + | 29.9034i | 0.555197 | + | 0.961630i | 0.997888 | + | 0.0649554i | \(0.0206905\pi\) |
−0.442691 | + | 0.896674i | \(0.645976\pi\) | |||||||
\(968\) | −57.5768 | + | 33.2420i | −1.85059 | + | 1.06844i | ||||
\(969\) | 21.4728 | − | 14.2457i | 0.689805 | − | 0.457637i | ||||
\(970\) | 3.02219 | − | 5.23459i | 0.0970368 | − | 0.168073i | ||||
\(971\) | 52.4564 | 1.68341 | 0.841704 | − | 0.539940i | \(-0.181553\pi\) | ||||
0.841704 | + | 0.539940i | \(0.181553\pi\) | |||||||
\(972\) | 4.32893 | − | 1.39047i | 0.138851 | − | 0.0445994i | ||||
\(973\) | −22.9398 | − | 22.4908i | −0.735415 | − | 0.721022i | ||||
\(974\) | −23.2560 | − | 13.4269i | −0.745171 | − | 0.430225i | ||||
\(975\) | 5.23404 | − | 3.47242i | 0.167624 | − | 0.111206i | ||||
\(976\) | 26.0242 | − | 15.0251i | 0.833014 | − | 0.480941i | ||||
\(977\) | 28.8591 | − | 16.6618i | 0.923286 | − | 0.533059i | 0.0386041 | − | 0.999255i | \(-0.487709\pi\) |
0.884682 | + | 0.466195i | \(0.154376\pi\) | |||||||
\(978\) | 1.51865 | + | 24.4002i | 0.0485609 | + | 0.780231i | ||||
\(979\) | −23.3933 | − | 13.5062i | −0.747654 | − | 0.431659i | ||||
\(980\) | 0.0403503 | + | 2.04133i | 0.00128894 | + | 0.0652078i | ||||
\(981\) | 9.72232 | − | 23.0416i | 0.310410 | − | 0.735663i | ||||
\(982\) | −9.08575 | −0.289938 | ||||||||
\(983\) | −10.6537 | + | 18.4527i | −0.339800 | + | 0.588550i | −0.984395 | − | 0.175974i | \(-0.943693\pi\) |
0.644595 | + | 0.764524i | \(0.277026\pi\) | |||||||
\(984\) | 51.8239 | + | 25.7691i | 1.65208 | + | 0.821488i | ||||
\(985\) | −6.12532 | + | 3.53646i | −0.195169 | + | 0.112681i | ||||
\(986\) | 26.6166 | + | 46.1013i | 0.847645 | + | 1.46816i | ||||
\(987\) | −5.65293 | − | 16.2992i | −0.179935 | − | 0.518810i | ||||
\(988\) | −1.59783 | + | 2.76752i | −0.0508337 | + | 0.0880466i | ||||
\(989\) | − | 1.86722i | − | 0.0593741i | ||||||
\(990\) | 13.6348 | + | 18.0134i | 0.433341 | + | 0.572504i | ||||
\(991\) | 6.50275 | 0.206567 | 0.103283 | − | 0.994652i | \(-0.467065\pi\) | ||||
0.103283 | + | 0.994652i | \(0.467065\pi\) | |||||||
\(992\) | 3.01005 | − | 5.21356i | 0.0955692 | − | 0.165531i | ||||
\(993\) | −24.7462 | + | 1.54018i | −0.785296 | + | 0.0488762i | ||||
\(994\) | −23.2865 | − | 5.99360i | −0.738603 | − | 0.190105i | ||||
\(995\) | −3.58642 | + | 2.07062i | −0.113697 | + | 0.0656431i | ||||
\(996\) | 0.946322 | + | 1.42641i | 0.0299854 | + | 0.0451975i | ||||
\(997\) | −18.8609 | − | 10.8893i | −0.597330 | − | 0.344869i | 0.170660 | − | 0.985330i | \(-0.445410\pi\) |
−0.767991 | + | 0.640461i | \(0.778743\pi\) | |||||||
\(998\) | − | 35.0425i | − | 1.10925i | ||||||
\(999\) | 14.3425 | − | 2.70598i | 0.453776 | − | 0.0856135i |
(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 | 315.2.bl.i.146.4 | yes | 24 | |
3.2 | odd | 2 | 945.2.bl.i.251.9 | 24 | |||
7.6 | odd | 2 | 315.2.bl.j.146.4 | yes | 24 | ||
9.4 | even | 3 | 945.2.bl.j.881.9 | 24 | |||
9.5 | odd | 6 | 315.2.bl.j.41.4 | yes | 24 | ||
21.20 | even | 2 | 945.2.bl.j.251.9 | 24 | |||
63.13 | odd | 6 | 945.2.bl.i.881.9 | 24 | |||
63.41 | even | 6 | inner | 315.2.bl.i.41.4 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.bl.i.41.4 | ✓ | 24 | 63.41 | even | 6 | inner | |
315.2.bl.i.146.4 | yes | 24 | 1.1 | even | 1 | trivial | |
315.2.bl.j.41.4 | yes | 24 | 9.5 | odd | 6 | ||
315.2.bl.j.146.4 | yes | 24 | 7.6 | odd | 2 | ||
945.2.bl.i.251.9 | 24 | 3.2 | odd | 2 | |||
945.2.bl.i.881.9 | 24 | 63.13 | odd | 6 | |||
945.2.bl.j.251.9 | 24 | 21.20 | even | 2 | |||
945.2.bl.j.881.9 | 24 | 9.4 | even | 3 |