Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [115,2,Mod(22,115)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(115, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("115.22");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 115 = 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 115.e (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: | \(0.918279623245\) |
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: | \( x^{20} - 6 x^{18} + 3 x^{16} + 80 x^{14} - 600 x^{12} + 3500 x^{10} - 15000 x^{8} + 50000 x^{6} + \cdots + 9765625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 68.5 | ||
Root | \(-2.11159 + 0.735651i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 115.68 |
Dual form | 115.2.e.a.22.5 |
$q$-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 \(\left(\mathbb{Z}/115\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.459187 | + | 0.459187i | −0.324695 | + | 0.324695i | −0.850565 | − | 0.525870i | \(-0.823740\pi\) |
0.525870 | + | 0.850565i | \(0.323740\pi\) | |||||||
\(3\) | −1.79404 | − | 1.79404i | −1.03579 | − | 1.03579i | −0.999335 | − | 0.0364530i | \(-0.988394\pi\) |
−0.0364530 | − | 0.999335i | \(-0.511606\pi\) | |||||||
\(4\) | 1.57829i | 0.789147i | ||||||||
\(5\) | −0.735651 | + | 2.11159i | −0.328993 | + | 0.944332i | ||||
\(6\) | 1.64760 | 0.672630 | ||||||||
\(7\) | 2.52854 | + | 2.52854i | 0.955698 | + | 0.955698i | 0.999059 | − | 0.0433619i | \(-0.0138069\pi\) |
−0.0433619 | + | 0.999059i | \(0.513807\pi\) | |||||||
\(8\) | −1.64311 | − | 1.64311i | −0.580926 | − | 0.580926i | ||||
\(9\) | 3.43715i | 1.14572i | ||||||||
\(10\) | −0.631815 | − | 1.30742i | −0.199797 | − | 0.413442i | ||||
\(11\) | 4.72931i | 1.42594i | 0.701194 | + | 0.712970i | \(0.252651\pi\) | ||||
−0.701194 | + | 0.712970i | \(0.747349\pi\) | |||||||
\(12\) | 2.83152 | − | 2.83152i | 0.817389 | − | 0.817389i | ||||
\(13\) | 0.0648135 | + | 0.0648135i | 0.0179760 | + | 0.0179760i | 0.716038 | − | 0.698062i | \(-0.245954\pi\) |
−0.698062 | + | 0.716038i | \(0.745954\pi\) | |||||||
\(14\) | −2.32215 | −0.620619 | ||||||||
\(15\) | 5.10806 | − | 2.46849i | 1.31890 | − | 0.637361i | ||||
\(16\) | −1.64760 | −0.411900 | ||||||||
\(17\) | −4.37241 | − | 4.37241i | −1.06047 | − | 1.06047i | −0.998050 | − | 0.0624149i | \(-0.980120\pi\) |
−0.0624149 | − | 0.998050i | \(-0.519880\pi\) | |||||||
\(18\) | −1.57829 | − | 1.57829i | −0.372007 | − | 0.372007i | ||||
\(19\) | 1.60835 | 0.368980 | 0.184490 | − | 0.982834i | \(-0.440937\pi\) | ||||
0.184490 | + | 0.982834i | \(0.440937\pi\) | |||||||
\(20\) | −3.33271 | − | 1.16107i | −0.745217 | − | 0.259624i | ||||
\(21\) | − | 9.07259i | − | 1.97980i | ||||||
\(22\) | −2.17164 | − | 2.17164i | −0.462995 | − | 0.462995i | ||||
\(23\) | 3.72923 | + | 3.01543i | 0.777598 | + | 0.628761i | ||||
\(24\) | 5.89559i | 1.20343i | ||||||||
\(25\) | −3.91764 | − | 3.10679i | −0.783527 | − | 0.621357i | ||||
\(26\) | −0.0595231 | −0.0116734 | ||||||||
\(27\) | 0.784256 | − | 0.784256i | 0.150930 | − | 0.150930i | ||||
\(28\) | −3.99078 | + | 3.99078i | −0.754186 | + | 0.754186i | ||||
\(29\) | − | 3.20459i | − | 0.595077i | −0.954710 | − | 0.297539i | \(-0.903834\pi\) | ||
0.954710 | − | 0.297539i | \(-0.0961657\pi\) | |||||||
\(30\) | −1.21206 | + | 3.47906i | −0.221290 | + | 0.635186i | ||||
\(31\) | 7.58141 | 1.36166 | 0.680831 | − | 0.732441i | \(-0.261619\pi\) | ||||
0.680831 | + | 0.732441i | \(0.261619\pi\) | |||||||
\(32\) | 4.04277 | − | 4.04277i | 0.714668 | − | 0.714668i | ||||
\(33\) | 8.48456 | − | 8.48456i | 1.47697 | − | 1.47697i | ||||
\(34\) | 4.01551 | 0.688654 | ||||||||
\(35\) | −7.19936 | + | 3.47912i | −1.21691 | + | 0.588078i | ||||
\(36\) | −5.42483 | −0.904138 | ||||||||
\(37\) | 4.93570 | + | 4.93570i | 0.811424 | + | 0.811424i | 0.984847 | − | 0.173423i | \(-0.0554828\pi\) |
−0.173423 | + | 0.984847i | \(0.555483\pi\) | |||||||
\(38\) | −0.738533 | + | 0.738533i | −0.119806 | + | 0.119806i | ||||
\(39\) | − | 0.232556i | − | 0.0372387i | ||||||
\(40\) | 4.67832 | − | 2.26082i | 0.739708 | − | 0.357467i | ||||
\(41\) | 2.15659 | 0.336802 | 0.168401 | − | 0.985719i | \(-0.446140\pi\) | ||||
0.168401 | + | 0.985719i | \(0.446140\pi\) | |||||||
\(42\) | 4.16602 | + | 4.16602i | 0.642830 | + | 0.642830i | ||||
\(43\) | 0.563291 | − | 0.563291i | 0.0859011 | − | 0.0859011i | −0.662851 | − | 0.748752i | \(-0.730654\pi\) |
0.748752 | + | 0.662851i | \(0.230654\pi\) | |||||||
\(44\) | −7.46424 | −1.12528 | ||||||||
\(45\) | −7.25785 | − | 2.52854i | −1.08194 | − | 0.376932i | ||||
\(46\) | −3.09706 | + | 0.327767i | −0.456637 | + | 0.0483266i | ||||
\(47\) | 2.59257 | − | 2.59257i | 0.378165 | − | 0.378165i | −0.492275 | − | 0.870440i | \(-0.663835\pi\) |
0.870440 | + | 0.492275i | \(0.163835\pi\) | |||||||
\(48\) | 2.95586 | + | 2.95586i | 0.426641 | + | 0.426641i | ||||
\(49\) | 5.78701i | 0.826716i | ||||||||
\(50\) | 3.22553 | − | 0.372332i | 0.456158 | − | 0.0526557i | ||||
\(51\) | 15.6885i | 2.19684i | ||||||||
\(52\) | −0.102295 | + | 0.102295i | −0.0141857 | + | 0.0141857i | ||||
\(53\) | −6.28379 | + | 6.28379i | −0.863145 | + | 0.863145i | −0.991702 | − | 0.128557i | \(-0.958965\pi\) |
0.128557 | + | 0.991702i | \(0.458965\pi\) | |||||||
\(54\) | 0.720241i | 0.0980123i | ||||||||
\(55\) | −9.98637 | − | 3.47912i | −1.34656 | − | 0.469124i | ||||
\(56\) | − | 8.30932i | − | 1.11038i | ||||||
\(57\) | −2.88544 | − | 2.88544i | −0.382185 | − | 0.382185i | ||||
\(58\) | 1.47151 | + | 1.47151i | 0.193218 | + | 0.193218i | ||||
\(59\) | − | 5.31810i | − | 0.692358i | −0.938169 | − | 0.346179i | \(-0.887479\pi\) | ||
0.938169 | − | 0.346179i | \(-0.112521\pi\) | |||||||
\(60\) | 3.89600 | + | 8.06202i | 0.502972 | + | 1.04080i | ||||
\(61\) | − | 5.90216i | − | 0.755694i | −0.925868 | − | 0.377847i | \(-0.876665\pi\) | ||
0.925868 | − | 0.377847i | \(-0.123335\pi\) | |||||||
\(62\) | −3.48129 | + | 3.48129i | −0.442124 | + | 0.442124i | ||||
\(63\) | −8.69095 | + | 8.69095i | −1.09496 | + | 1.09496i | ||||
\(64\) | 0.417581i | 0.0521976i | ||||||||
\(65\) | −0.184540 | + | 0.0891796i | −0.0228893 | + | 0.0110614i | ||||
\(66\) | 7.79201i | 0.959130i | ||||||||
\(67\) | −0.206392 | − | 0.206392i | −0.0252149 | − | 0.0252149i | 0.694387 | − | 0.719602i | \(-0.255676\pi\) |
−0.719602 | + | 0.694387i | \(0.755676\pi\) | |||||||
\(68\) | 6.90095 | − | 6.90095i | 0.836863 | − | 0.836863i | ||||
\(69\) | −1.28058 | − | 12.1002i | −0.154164 | − | 1.45669i | ||||
\(70\) | 1.70829 | − | 4.90342i | 0.204179 | − | 0.586071i | ||||
\(71\) | 3.84194 | 0.455954 | 0.227977 | − | 0.973667i | \(-0.426789\pi\) | ||||
0.227977 | + | 0.973667i | \(0.426789\pi\) | |||||||
\(72\) | 5.64760 | − | 5.64760i | 0.665576 | − | 0.665576i | ||||
\(73\) | 2.10156 | + | 2.10156i | 0.245969 | + | 0.245969i | 0.819314 | − | 0.573345i | \(-0.194355\pi\) |
−0.573345 | + | 0.819314i | \(0.694355\pi\) | |||||||
\(74\) | −4.53282 | −0.526930 | ||||||||
\(75\) | 1.45470 | + | 12.6021i | 0.167974 | + | 1.45516i | ||||
\(76\) | 2.53845i | 0.291180i | ||||||||
\(77\) | −11.9582 | + | 11.9582i | −1.36277 | + | 1.36277i | ||||
\(78\) | 0.106787 | + | 0.106787i | 0.0120912 | + | 0.0120912i | ||||
\(79\) | 9.58990 | 1.07895 | 0.539474 | − | 0.842002i | \(-0.318623\pi\) | ||||
0.539474 | + | 0.842002i | \(0.318623\pi\) | |||||||
\(80\) | 1.21206 | − | 3.47906i | 0.135512 | − | 0.388970i | ||||
\(81\) | 7.49747 | 0.833052 | ||||||||
\(82\) | −0.990278 | + | 0.990278i | −0.109358 | + | 0.109358i | ||||
\(83\) | −4.70018 | + | 4.70018i | −0.515911 | + | 0.515911i | −0.916332 | − | 0.400420i | \(-0.868864\pi\) |
0.400420 | + | 0.916332i | \(0.368864\pi\) | |||||||
\(84\) | 14.3192 | 1.56235 | ||||||||
\(85\) | 12.4493 | − | 6.01618i | 1.35032 | − | 0.652546i | ||||
\(86\) | 0.517313i | 0.0557833i | ||||||||
\(87\) | −5.74916 | + | 5.74916i | −0.616374 | + | 0.616374i | ||||
\(88\) | 7.77076 | − | 7.77076i | 0.828366 | − | 0.828366i | ||||
\(89\) | 8.50580 | 0.901613 | 0.450807 | − | 0.892622i | \(-0.351136\pi\) | ||||
0.450807 | + | 0.892622i | \(0.351136\pi\) | |||||||
\(90\) | 4.49378 | − | 2.17164i | 0.473686 | − | 0.228911i | ||||
\(91\) | 0.327767i | 0.0343593i | ||||||||
\(92\) | −4.75924 | + | 5.88582i | −0.496185 | + | 0.613639i | ||||
\(93\) | −13.6013 | − | 13.6013i | −1.41039 | − | 1.41039i | ||||
\(94\) | 2.38095i | 0.245576i | ||||||||
\(95\) | −1.18318 | + | 3.39617i | −0.121392 | + | 0.348440i | ||||
\(96\) | −14.5058 | −1.48049 | ||||||||
\(97\) | −2.58241 | − | 2.58241i | −0.262204 | − | 0.262204i | 0.563745 | − | 0.825949i | \(-0.309360\pi\) |
−0.825949 | + | 0.563745i | \(0.809360\pi\) | |||||||
\(98\) | −2.65732 | − | 2.65732i | −0.268430 | − | 0.268430i | ||||
\(99\) | −16.2553 | −1.63372 | ||||||||
\(100\) | 4.90342 | − | 6.18318i | 0.490342 | − | 0.618318i | ||||
\(101\) | 7.53167 | 0.749429 | 0.374715 | − | 0.927140i | \(-0.377741\pi\) | ||||
0.374715 | + | 0.927140i | \(0.377741\pi\) | |||||||
\(102\) | −7.20398 | − | 7.20398i | −0.713300 | − | 0.713300i | ||||
\(103\) | 5.92689 | − | 5.92689i | 0.583994 | − | 0.583994i | −0.352004 | − | 0.935998i | \(-0.614500\pi\) |
0.935998 | + | 0.352004i | \(0.114500\pi\) | |||||||
\(104\) | − | 0.212991i | − | 0.0208855i | ||||||
\(105\) | 19.1576 | + | 6.67425i | 1.86959 | + | 0.651340i | ||||
\(106\) | − | 5.77087i | − | 0.560517i | ||||||
\(107\) | −2.50380 | − | 2.50380i | −0.242052 | − | 0.242052i | 0.575647 | − | 0.817699i | \(-0.304750\pi\) |
−0.817699 | + | 0.575647i | \(0.804750\pi\) | |||||||
\(108\) | 1.23779 | + | 1.23779i | 0.119106 | + | 0.119106i | ||||
\(109\) | −18.9903 | −1.81894 | −0.909468 | − | 0.415773i | \(-0.863511\pi\) | ||||
−0.909468 | + | 0.415773i | \(0.863511\pi\) | |||||||
\(110\) | 6.18318 | − | 2.98805i | 0.589543 | − | 0.284899i | ||||
\(111\) | − | 17.7097i | − | 1.68093i | ||||||
\(112\) | −4.16602 | − | 4.16602i | −0.393652 | − | 0.393652i | ||||
\(113\) | −0.920190 | + | 0.920190i | −0.0865642 | + | 0.0865642i | −0.749063 | − | 0.662499i | \(-0.769496\pi\) |
0.662499 | + | 0.749063i | \(0.269496\pi\) | |||||||
\(114\) | 2.64991 | 0.248187 | ||||||||
\(115\) | −9.11077 | + | 5.65631i | −0.849584 | + | 0.527453i | ||||
\(116\) | 5.05778 | 0.469603 | ||||||||
\(117\) | −0.222774 | + | 0.222774i | −0.0205954 | + | 0.0205954i | ||||
\(118\) | 2.44200 | + | 2.44200i | 0.224805 | + | 0.224805i | ||||
\(119\) | − | 22.1116i | − | 2.02697i | ||||||
\(120\) | −12.4491 | − | 4.33710i | −1.13644 | − | 0.395921i | ||||
\(121\) | −11.3664 | −1.03331 | ||||||||
\(122\) | 2.71020 | + | 2.71020i | 0.245370 | + | 0.245370i | ||||
\(123\) | −3.86900 | − | 3.86900i | −0.348856 | − | 0.348856i | ||||
\(124\) | 11.9657i | 1.07455i | ||||||||
\(125\) | 9.44228 | − | 5.98694i | 0.844543 | − | 0.535488i | ||||
\(126\) | − | 7.98155i | − | 0.711053i | ||||||
\(127\) | −1.98007 | + | 1.98007i | −0.175703 | + | 0.175703i | −0.789480 | − | 0.613777i | \(-0.789649\pi\) |
0.613777 | + | 0.789480i | \(0.289649\pi\) | |||||||
\(128\) | 7.89380 | + | 7.89380i | 0.697720 | + | 0.697720i | ||||
\(129\) | −2.02113 | −0.177951 | ||||||||
\(130\) | 0.0437882 | − | 0.125689i | 0.00384048 | − | 0.0110236i | ||||
\(131\) | −7.58866 | −0.663024 | −0.331512 | − | 0.943451i | \(-0.607559\pi\) | ||||
−0.331512 | + | 0.943451i | \(0.607559\pi\) | |||||||
\(132\) | 13.3911 | + | 13.3911i | 1.16555 | + | 1.16555i | ||||
\(133\) | 4.06677 | + | 4.06677i | 0.352634 | + | 0.352634i | ||||
\(134\) | 0.189546 | 0.0163742 | ||||||||
\(135\) | 1.07909 | + | 2.23297i | 0.0928732 | + | 0.192183i | ||||
\(136\) | 14.3687i | 1.23210i | ||||||||
\(137\) | 10.6809 | + | 10.6809i | 0.912534 | + | 0.912534i | 0.996471 | − | 0.0839372i | \(-0.0267495\pi\) |
−0.0839372 | + | 0.996471i | \(0.526750\pi\) | |||||||
\(138\) | 6.14428 | + | 4.96823i | 0.523036 | + | 0.422923i | ||||
\(139\) | 15.5905i | 1.32237i | 0.750223 | + | 0.661185i | \(0.229946\pi\) | ||||
−0.750223 | + | 0.661185i | \(0.770054\pi\) | |||||||
\(140\) | −5.49107 | − | 11.3627i | −0.464080 | − | 0.960324i | ||||
\(141\) | −9.30233 | −0.783398 | ||||||||
\(142\) | −1.76417 | + | 1.76417i | −0.148046 | + | 0.148046i | ||||
\(143\) | −0.306523 | + | 0.306523i | −0.0256328 | + | 0.0256328i | ||||
\(144\) | − | 5.66304i | − | 0.471920i | ||||||
\(145\) | 6.76678 | + | 2.35746i | 0.561951 | + | 0.195776i | ||||
\(146\) | −1.93002 | −0.159729 | ||||||||
\(147\) | 10.3821 | − | 10.3821i | 0.856302 | − | 0.856302i | ||||
\(148\) | −7.78999 | + | 7.78999i | −0.640333 | + | 0.640333i | ||||
\(149\) | 8.93810 | 0.732238 | 0.366119 | − | 0.930568i | \(-0.380686\pi\) | ||||
0.366119 | + | 0.930568i | \(0.380686\pi\) | |||||||
\(150\) | −6.45470 | − | 5.11874i | −0.527024 | − | 0.417943i | ||||
\(151\) | −15.9033 | −1.29419 | −0.647097 | − | 0.762408i | \(-0.724017\pi\) | ||||
−0.647097 | + | 0.762408i | \(0.724017\pi\) | |||||||
\(152\) | −2.64269 | − | 2.64269i | −0.214350 | − | 0.214350i | ||||
\(153\) | 15.0286 | − | 15.0286i | 1.21499 | − | 1.21499i | ||||
\(154\) | − | 10.9821i | − | 0.884966i | ||||||
\(155\) | −5.57727 | + | 16.0088i | −0.447977 | + | 1.28586i | ||||
\(156\) | 0.367042 | 0.0293868 | ||||||||
\(157\) | −13.8985 | − | 13.8985i | −1.10922 | − | 1.10922i | −0.993253 | − | 0.115971i | \(-0.963002\pi\) |
−0.115971 | − | 0.993253i | \(-0.536998\pi\) | |||||||
\(158\) | −4.40356 | + | 4.40356i | −0.350329 | + | 0.350329i | ||||
\(159\) | 22.5467 | 1.78807 | ||||||||
\(160\) | 5.56261 | + | 11.5107i | 0.439763 | + | 0.910005i | ||||
\(161\) | 1.80487 | + | 17.0541i | 0.142243 | + | 1.34405i | ||||
\(162\) | −3.44274 | + | 3.44274i | −0.270487 | + | 0.270487i | ||||
\(163\) | 8.90642 | + | 8.90642i | 0.697605 | + | 0.697605i | 0.963893 | − | 0.266289i | \(-0.0857974\pi\) |
−0.266289 | + | 0.963893i | \(0.585797\pi\) | |||||||
\(164\) | 3.40373i | 0.265787i | ||||||||
\(165\) | 11.6743 | + | 24.1576i | 0.908839 | + | 1.88067i | ||||
\(166\) | − | 4.31652i | − | 0.335027i | ||||||
\(167\) | 10.5555 | − | 10.5555i | 0.816810 | − | 0.816810i | −0.168834 | − | 0.985644i | \(-0.554000\pi\) |
0.985644 | + | 0.168834i | \(0.0540003\pi\) | |||||||
\(168\) | −14.9072 | + | 14.9072i | −1.15012 | + | 1.15012i | ||||
\(169\) | − | 12.9916i | − | 0.999354i | ||||||
\(170\) | −2.95401 | + | 8.47912i | −0.226562 | + | 0.650319i | ||||
\(171\) | 5.52812i | 0.422746i | ||||||||
\(172\) | 0.889039 | + | 0.889039i | 0.0677886 | + | 0.0677886i | ||||
\(173\) | 4.14681 | + | 4.14681i | 0.315276 | + | 0.315276i | 0.846949 | − | 0.531674i | \(-0.178437\pi\) |
−0.531674 | + | 0.846949i | \(0.678437\pi\) | |||||||
\(174\) | − | 5.27988i | − | 0.400267i | ||||||
\(175\) | −2.05026 | − | 17.7615i | −0.154985 | − | 1.34264i | ||||
\(176\) | − | 7.79201i | − | 0.587345i | ||||||
\(177\) | −9.54087 | + | 9.54087i | −0.717136 | + | 0.717136i | ||||
\(178\) | −3.90576 | + | 3.90576i | −0.292749 | + | 0.292749i | ||||
\(179\) | − | 3.95924i | − | 0.295928i | −0.988993 | − | 0.147964i | \(-0.952728\pi\) | ||
0.988993 | − | 0.147964i | \(-0.0472719\pi\) | |||||||
\(180\) | 3.99078 | − | 11.4550i | 0.297455 | − | 0.853806i | ||||
\(181\) | 11.1132i | 0.826040i | 0.910722 | + | 0.413020i | \(0.135526\pi\) | ||||
−0.910722 | + | 0.413020i | \(0.864474\pi\) | |||||||
\(182\) | −0.150506 | − | 0.150506i | −0.0111563 | − | 0.0111563i | ||||
\(183\) | −10.5887 | + | 10.5887i | −0.782739 | + | 0.782739i | ||||
\(184\) | −1.17285 | − | 11.0822i | −0.0864634 | − | 0.816991i | ||||
\(185\) | −14.0531 | + | 6.79123i | −1.03321 | + | 0.499301i | ||||
\(186\) | 12.4911 | 0.915894 | ||||||||
\(187\) | 20.6785 | − | 20.6785i | 1.51216 | − | 1.51216i | ||||
\(188\) | 4.09183 | + | 4.09183i | 0.298428 | + | 0.298428i | ||||
\(189\) | 3.96604 | 0.288487 | ||||||||
\(190\) | −1.01618 | − | 2.10278i | −0.0737213 | − | 0.152552i | ||||
\(191\) | − | 5.38111i | − | 0.389363i | −0.980866 | − | 0.194682i | \(-0.937633\pi\) | ||
0.980866 | − | 0.194682i | \(-0.0623674\pi\) | |||||||
\(192\) | 0.749156 | − | 0.749156i | 0.0540657 | − | 0.0540657i | ||||
\(193\) | −13.7523 | − | 13.7523i | −0.989910 | − | 0.989910i | 0.0100391 | − | 0.999950i | \(-0.496804\pi\) |
−0.999950 | + | 0.0100391i | \(0.996804\pi\) | |||||||
\(194\) | 2.37162 | 0.170272 | ||||||||
\(195\) | 0.491063 | + | 0.171080i | 0.0351658 | + | 0.0122513i | ||||
\(196\) | −9.13360 | −0.652400 | ||||||||
\(197\) | −4.77126 | + | 4.77126i | −0.339938 | + | 0.339938i | −0.856344 | − | 0.516406i | \(-0.827270\pi\) |
0.516406 | + | 0.856344i | \(0.327270\pi\) | |||||||
\(198\) | 7.46424 | − | 7.46424i | 0.530460 | − | 0.530460i | ||||
\(199\) | −23.5388 | −1.66862 | −0.834311 | − | 0.551294i | \(-0.814134\pi\) | ||||
−0.834311 | + | 0.551294i | \(0.814134\pi\) | |||||||
\(200\) | 1.33231 | + | 11.5419i | 0.0942088 | + | 0.816134i | ||||
\(201\) | 0.740552i | 0.0522345i | ||||||||
\(202\) | −3.45845 | + | 3.45845i | −0.243336 | + | 0.243336i | ||||
\(203\) | 8.10293 | − | 8.10293i | 0.568714 | − | 0.568714i | ||||
\(204\) | −24.7611 | −1.73363 | ||||||||
\(205\) | −1.58649 | + | 4.55383i | −0.110806 | + | 0.318053i | ||||
\(206\) | 5.44311i | 0.379239i | ||||||||
\(207\) | −10.3645 | + | 12.8179i | −0.720381 | + | 0.890906i | ||||
\(208\) | −0.106787 | − | 0.106787i | −0.00740433 | − | 0.00740433i | ||||
\(209\) | 7.60637i | 0.526144i | ||||||||
\(210\) | −11.8617 | + | 5.73219i | −0.818532 | + | 0.395559i | ||||
\(211\) | −4.83469 | −0.332834 | −0.166417 | − | 0.986055i | \(-0.553220\pi\) | ||||
−0.166417 | + | 0.986055i | \(0.553220\pi\) | |||||||
\(212\) | −9.91767 | − | 9.91767i | −0.681148 | − | 0.681148i | ||||
\(213\) | −6.89258 | − | 6.89258i | −0.472272 | − | 0.472272i | ||||
\(214\) | 2.29943 | 0.157186 | ||||||||
\(215\) | 0.775056 | + | 1.60383i | 0.0528584 | + | 0.109380i | ||||
\(216\) | −2.57723 | −0.175358 | ||||||||
\(217\) | 19.1699 | + | 19.1699i | 1.30134 | + | 1.30134i | ||||
\(218\) | 8.72009 | − | 8.72009i | 0.590599 | − | 0.590599i | ||||
\(219\) | − | 7.54055i | − | 0.509543i | ||||||
\(220\) | 5.49107 | − | 15.7614i | 0.370208 | − | 1.06263i | ||||
\(221\) | − | 0.566783i | − | 0.0381259i | ||||||
\(222\) | 8.13206 | + | 8.13206i | 0.545788 | + | 0.545788i | ||||
\(223\) | 13.4411 | + | 13.4411i | 0.900080 | + | 0.900080i | 0.995443 | − | 0.0953624i | \(-0.0304010\pi\) |
−0.0953624 | + | 0.995443i | \(0.530401\pi\) | |||||||
\(224\) | 20.4446 | 1.36601 | ||||||||
\(225\) | 10.6785 | − | 13.4655i | 0.711899 | − | 0.897699i | ||||
\(226\) | − | 0.845080i | − | 0.0562139i | ||||||
\(227\) | 8.15679 | + | 8.15679i | 0.541385 | + | 0.541385i | 0.923935 | − | 0.382550i | \(-0.124954\pi\) |
−0.382550 | + | 0.923935i | \(0.624954\pi\) | |||||||
\(228\) | 4.55407 | − | 4.55407i | 0.301600 | − | 0.301600i | ||||
\(229\) | 1.36560 | 0.0902413 | 0.0451206 | − | 0.998982i | \(-0.485633\pi\) | ||||
0.0451206 | + | 0.998982i | \(0.485633\pi\) | |||||||
\(230\) | 1.58625 | − | 6.78086i | 0.104594 | − | 0.447116i | ||||
\(231\) | 42.9071 | 2.82308 | ||||||||
\(232\) | −5.26549 | + | 5.26549i | −0.345696 | + | 0.345696i | ||||
\(233\) | −1.62307 | − | 1.62307i | −0.106331 | − | 0.106331i | 0.651940 | − | 0.758271i | \(-0.273955\pi\) |
−0.758271 | + | 0.651940i | \(0.773955\pi\) | |||||||
\(234\) | − | 0.204590i | − | 0.0133744i | ||||||
\(235\) | 3.56722 | + | 7.38167i | 0.232700 | + | 0.481527i | ||||
\(236\) | 8.39352 | 0.546372 | ||||||||
\(237\) | −17.2046 | − | 17.2046i | −1.11756 | − | 1.11756i | ||||
\(238\) | 10.1534 | + | 10.1534i | 0.658145 | + | 0.658145i | ||||
\(239\) | 26.9697i | 1.74452i | 0.489040 | + | 0.872261i | \(0.337347\pi\) | ||||
−0.489040 | + | 0.872261i | \(0.662653\pi\) | |||||||
\(240\) | −8.41604 | + | 4.06708i | −0.543253 | + | 0.262529i | ||||
\(241\) | − | 25.9104i | − | 1.66904i | −0.550980 | − | 0.834519i | \(-0.685746\pi\) | ||
0.550980 | − | 0.834519i | \(-0.314254\pi\) | |||||||
\(242\) | 5.21929 | − | 5.21929i | 0.335509 | − | 0.335509i | ||||
\(243\) | −15.8035 | − | 15.8035i | −1.01380 | − | 1.01380i | ||||
\(244\) | 9.31534 | 0.596353 | ||||||||
\(245\) | −12.2198 | − | 4.25722i | −0.780694 | − | 0.271984i | ||||
\(246\) | 3.55319 | 0.226543 | ||||||||
\(247\) | 0.104243 | + | 0.104243i | 0.00663280 | + | 0.00663280i | ||||
\(248\) | −12.4571 | − | 12.4571i | −0.791025 | − | 0.791025i | ||||
\(249\) | 16.8646 | 1.06875 | ||||||||
\(250\) | −1.58665 | + | 7.08490i | −0.100348 | + | 0.448088i | ||||
\(251\) | − | 3.73401i | − | 0.235688i | −0.993032 | − | 0.117844i | \(-0.962402\pi\) | ||
0.993032 | − | 0.117844i | \(-0.0375984\pi\) | |||||||
\(252\) | −13.7169 | − | 13.7169i | −0.864082 | − | 0.864082i | ||||
\(253\) | −14.2609 | + | 17.6367i | −0.896576 | + | 1.10881i | ||||
\(254\) | − | 1.81845i | − | 0.114099i | ||||||
\(255\) | −33.1278 | − | 11.5413i | −2.07454 | − | 0.722743i | ||||
\(256\) | −8.08462 | −0.505289 | ||||||||
\(257\) | −1.27851 | + | 1.27851i | −0.0797511 | + | 0.0797511i | −0.745857 | − | 0.666106i | \(-0.767960\pi\) |
0.666106 | + | 0.745857i | \(0.267960\pi\) | |||||||
\(258\) | 0.928079 | − | 0.928079i | 0.0577796 | − | 0.0577796i | ||||
\(259\) | 24.9602i | 1.55095i | ||||||||
\(260\) | −0.140752 | − | 0.291258i | −0.00872904 | − | 0.0180631i | ||||
\(261\) | 11.0146 | 0.681789 | ||||||||
\(262\) | 3.48462 | − | 3.48462i | 0.215280 | − | 0.215280i | ||||
\(263\) | 7.28258 | − | 7.28258i | 0.449063 | − | 0.449063i | −0.445980 | − | 0.895043i | \(-0.647145\pi\) |
0.895043 | + | 0.445980i | \(0.147145\pi\) | |||||||
\(264\) | −27.8821 | −1.71602 | ||||||||
\(265\) | −8.64612 | − | 17.8915i | −0.531127 | − | 1.09906i | ||||
\(266\) | −3.73482 | −0.228996 | ||||||||
\(267\) | −15.2597 | − | 15.2597i | −0.933881 | − | 0.933881i | ||||
\(268\) | 0.325748 | − | 0.325748i | 0.0198982 | − | 0.0198982i | ||||
\(269\) | − | 19.1149i | − | 1.16546i | −0.812666 | − | 0.582729i | \(-0.801985\pi\) | ||
0.812666 | − | 0.582729i | \(-0.198015\pi\) | |||||||
\(270\) | −1.52085 | − | 0.529845i | −0.0925562 | − | 0.0322454i | ||||
\(271\) | −21.9588 | −1.33390 | −0.666952 | − | 0.745101i | \(-0.732401\pi\) | ||||
−0.666952 | + | 0.745101i | \(0.732401\pi\) | |||||||
\(272\) | 7.20398 | + | 7.20398i | 0.436805 | + | 0.436805i | ||||
\(273\) | 0.588026 | − | 0.588026i | 0.0355890 | − | 0.0355890i | ||||
\(274\) | −9.80910 | −0.592589 | ||||||||
\(275\) | 14.6930 | − | 18.5277i | 0.886018 | − | 1.11726i | ||||
\(276\) | 19.0976 | − | 2.02113i | 1.14954 | − | 0.121658i | ||||
\(277\) | 6.88936 | − | 6.88936i | 0.413942 | − | 0.413942i | −0.469167 | − | 0.883109i | \(-0.655446\pi\) |
0.883109 | + | 0.469167i | \(0.155446\pi\) | |||||||
\(278\) | −7.15897 | − | 7.15897i | −0.429366 | − | 0.429366i | ||||
\(279\) | 26.0584i | 1.56008i | ||||||||
\(280\) | 17.5459 | + | 6.11276i | 1.04857 | + | 0.365307i | ||||
\(281\) | − | 10.1497i | − | 0.605480i | −0.953073 | − | 0.302740i | \(-0.902099\pi\) | ||
0.953073 | − | 0.302740i | \(-0.0979014\pi\) | |||||||
\(282\) | 4.27151 | − | 4.27151i | 0.254365 | − | 0.254365i | ||||
\(283\) | 20.4965 | − | 20.4965i | 1.21839 | − | 1.21839i | 0.250191 | − | 0.968196i | \(-0.419507\pi\) |
0.968196 | − | 0.250191i | \(-0.0804935\pi\) | |||||||
\(284\) | 6.06370i | 0.359815i | ||||||||
\(285\) | 8.21554 | − | 3.97019i | 0.486646 | − | 0.235174i | ||||
\(286\) | − | 0.281503i | − | 0.0166456i | ||||||
\(287\) | 5.45301 | + | 5.45301i | 0.321881 | + | 0.321881i | ||||
\(288\) | 13.8956 | + | 13.8956i | 0.818806 | + | 0.818806i | ||||
\(289\) | 21.2359i | 1.24917i | ||||||||
\(290\) | −4.18974 | + | 2.02471i | −0.246030 | + | 0.118895i | ||||
\(291\) | 9.26587i | 0.543175i | ||||||||
\(292\) | −3.31687 | + | 3.31687i | −0.194105 | + | 0.194105i | ||||
\(293\) | 6.66982 | − | 6.66982i | 0.389655 | − | 0.389655i | −0.484909 | − | 0.874564i | \(-0.661147\pi\) |
0.874564 | + | 0.484909i | \(0.161147\pi\) | |||||||
\(294\) | 9.53467i | 0.556073i | ||||||||
\(295\) | 11.2297 | + | 3.91226i | 0.653816 | + | 0.227781i | ||||
\(296\) | − | 16.2198i | − | 0.942755i | ||||||
\(297\) | 3.70899 | + | 3.70899i | 0.215217 | + | 0.215217i | ||||
\(298\) | −4.10426 | + | 4.10426i | −0.237754 | + | 0.237754i | ||||
\(299\) | 0.0462638 | + | 0.437146i | 0.00267550 | + | 0.0252808i | ||||
\(300\) | −19.8898 | + | 2.29594i | −1.14834 | + | 0.132556i | ||||
\(301\) | 2.84861 | 0.164191 | ||||||||
\(302\) | 7.30260 | − | 7.30260i | 0.420217 | − | 0.420217i | ||||
\(303\) | −13.5121 | − | 13.5121i | −0.776250 | − | 0.776250i | ||||
\(304\) | −2.64991 | −0.151983 | ||||||||
\(305\) | 12.4629 | + | 4.34192i | 0.713626 | + | 0.248618i | ||||
\(306\) | 13.8019i | 0.789002i | ||||||||
\(307\) | −2.18915 | + | 2.18915i | −0.124941 | + | 0.124941i | −0.766813 | − | 0.641871i | \(-0.778158\pi\) |
0.641871 | + | 0.766813i | \(0.278158\pi\) | |||||||
\(308\) | −18.8736 | − | 18.8736i | −1.07542 | − | 1.07542i | ||||
\(309\) | −21.2661 | −1.20979 | ||||||||
\(310\) | −4.79005 | − | 9.91207i | −0.272056 | − | 0.562968i | ||||
\(311\) | 32.7348 | 1.85622 | 0.928110 | − | 0.372307i | \(-0.121433\pi\) | ||||
0.928110 | + | 0.372307i | \(0.121433\pi\) | |||||||
\(312\) | −0.382114 | + | 0.382114i | −0.0216330 | + | 0.0216330i | ||||
\(313\) | −12.1979 | + | 12.1979i | −0.689469 | + | 0.689469i | −0.962114 | − | 0.272646i | \(-0.912101\pi\) |
0.272646 | + | 0.962114i | \(0.412101\pi\) | |||||||
\(314\) | 12.7641 | 0.720318 | ||||||||
\(315\) | −11.9582 | − | 24.7452i | −0.673770 | − | 1.39424i | ||||
\(316\) | 15.1357i | 0.851449i | ||||||||
\(317\) | 0.370368 | − | 0.370368i | 0.0208020 | − | 0.0208020i | −0.696629 | − | 0.717431i | \(-0.745318\pi\) |
0.717431 | + | 0.696629i | \(0.245318\pi\) | |||||||
\(318\) | −10.3532 | + | 10.3532i | −0.580577 | + | 0.580577i | ||||
\(319\) | 15.1555 | 0.848545 | ||||||||
\(320\) | −0.881760 | − | 0.307194i | −0.0492919 | − | 0.0171726i | ||||
\(321\) | 8.98384i | 0.501429i | ||||||||
\(322\) | −8.65982 | − | 7.00227i | −0.482593 | − | 0.390221i | ||||
\(323\) | −7.03236 | − | 7.03236i | −0.391291 | − | 0.391291i | ||||
\(324\) | 11.8332i | 0.657400i | ||||||||
\(325\) | −0.0525540 | − | 0.455278i | −0.00291517 | − | 0.0252543i | ||||
\(326\) | −8.17943 | −0.453017 | ||||||||
\(327\) | 34.0692 | + | 34.0692i | 1.88403 | + | 1.88403i | ||||
\(328\) | −3.54351 | − | 3.54351i | −0.195657 | − | 0.195657i | ||||
\(329\) | 13.1108 | 0.722823 | ||||||||
\(330\) | −16.4535 | − | 5.73219i | −0.905737 | − | 0.315547i | ||||
\(331\) | 14.6888 | 0.807372 | 0.403686 | − | 0.914898i | \(-0.367729\pi\) | ||||
0.403686 | + | 0.914898i | \(0.367729\pi\) | |||||||
\(332\) | −7.41826 | − | 7.41826i | −0.407130 | − | 0.407130i | ||||
\(333\) | −16.9647 | + | 16.9647i | −0.929661 | + | 0.929661i | ||||
\(334\) | 9.69392i | 0.530428i | ||||||||
\(335\) | 0.587649 | − | 0.283984i | 0.0321067 | − | 0.0155157i | ||||
\(336\) | 14.9480i | 0.815480i | ||||||||
\(337\) | −9.43939 | − | 9.43939i | −0.514197 | − | 0.514197i | 0.401613 | − | 0.915809i | \(-0.368450\pi\) |
−0.915809 | + | 0.401613i | \(0.868450\pi\) | |||||||
\(338\) | 5.96558 | + | 5.96558i | 0.324485 | + | 0.324485i | ||||
\(339\) | 3.30171 | 0.179324 | ||||||||
\(340\) | 9.49530 | + | 19.6487i | 0.514955 | + | 1.06560i | ||||
\(341\) | 35.8548i | 1.94165i | ||||||||
\(342\) | −2.53845 | − | 2.53845i | −0.137263 | − | 0.137263i | ||||
\(343\) | 3.06709 | − | 3.06709i | 0.165608 | − | 0.165608i | ||||
\(344\) | −1.85110 | −0.0998044 | ||||||||
\(345\) | 26.4927 | + | 6.19744i | 1.42632 | + | 0.333659i | ||||
\(346\) | −3.80832 | −0.204737 | ||||||||
\(347\) | 18.6129 | − | 18.6129i | 0.999191 | − | 0.999191i | −0.000808207 | − | 1.00000i | \(-0.500257\pi\) |
1.00000 | 0.000808207i | \(0.000257260\pi\) | ||||||||
\(348\) | −9.07386 | − | 9.07386i | −0.486410 | − | 0.486410i | ||||
\(349\) | − | 12.3226i | − | 0.659614i | −0.944048 | − | 0.329807i | \(-0.893016\pi\) | ||
0.944048 | − | 0.329807i | \(-0.106984\pi\) | |||||||
\(350\) | 9.09732 | + | 7.21441i | 0.486272 | + | 0.385626i | ||||
\(351\) | 0.101661 | 0.00542625 | ||||||||
\(352\) | 19.1195 | + | 19.1195i | 1.01907 | + | 1.01907i | ||||
\(353\) | 10.6464 | + | 10.6464i | 0.566653 | + | 0.566653i | 0.931189 | − | 0.364536i | \(-0.118772\pi\) |
−0.364536 | + | 0.931189i | \(0.618772\pi\) | |||||||
\(354\) | − | 8.76210i | − | 0.465700i | ||||||
\(355\) | −2.82632 | + | 8.11260i | −0.150006 | + | 0.430572i | ||||
\(356\) | 13.4247i | 0.711506i | ||||||||
\(357\) | −39.6691 | + | 39.6691i | −2.09951 | + | 2.09951i | ||||
\(358\) | 1.81803 | + | 1.81803i | 0.0960861 | + | 0.0960861i | ||||
\(359\) | −16.0163 | −0.845308 | −0.422654 | − | 0.906291i | \(-0.638902\pi\) | ||||
−0.422654 | + | 0.906291i | \(0.638902\pi\) | |||||||
\(360\) | 7.77076 | + | 16.0801i | 0.409555 | + | 0.847495i | ||||
\(361\) | −16.4132 | −0.863854 | ||||||||
\(362\) | −5.10305 | − | 5.10305i | −0.268211 | − | 0.268211i | ||||
\(363\) | 20.3917 | + | 20.3917i | 1.07029 | + | 1.07029i | ||||
\(364\) | −0.517313 | −0.0271145 | ||||||||
\(365\) | −5.98364 | + | 2.89162i | −0.313198 | + | 0.151354i | ||||
\(366\) | − | 9.72439i | − | 0.508302i | ||||||
\(367\) | −14.0118 | − | 14.0118i | −0.731409 | − | 0.731409i | 0.239490 | − | 0.970899i | \(-0.423020\pi\) |
−0.970899 | + | 0.239490i | \(0.923020\pi\) | |||||||
\(368\) | −6.14428 | − | 4.96823i | −0.320293 | − | 0.258987i | ||||
\(369\) | 7.41251i | 0.385880i | ||||||||
\(370\) | 3.33457 | − | 9.57147i | 0.173356 | − | 0.497597i | ||||
\(371\) | −31.7776 | −1.64981 | ||||||||
\(372\) | 21.4669 | − | 21.4669i | 1.11301 | − | 1.11301i | ||||
\(373\) | 7.09974 | − | 7.09974i | 0.367610 | − | 0.367610i | −0.498995 | − | 0.866605i | \(-0.666297\pi\) |
0.866605 | + | 0.498995i | \(0.166297\pi\) | |||||||
\(374\) | 18.9906i | 0.981980i | ||||||||
\(375\) | −27.6806 | − | 6.19901i | −1.42942 | − | 0.320115i | ||||
\(376\) | −8.51974 | −0.439372 | ||||||||
\(377\) | 0.207701 | − | 0.207701i | 0.0106971 | − | 0.0106971i | ||||
\(378\) | −1.82116 | + | 1.82116i | −0.0936702 | + | 0.0936702i | ||||
\(379\) | 22.2457 | 1.14269 | 0.571343 | − | 0.820712i | \(-0.306423\pi\) | ||||
0.571343 | + | 0.820712i | \(0.306423\pi\) | |||||||
\(380\) | −5.36016 | − | 1.86741i | −0.274970 | − | 0.0957960i | ||||
\(381\) | 7.10464 | 0.363982 | ||||||||
\(382\) | 2.47094 | + | 2.47094i | 0.126424 | + | 0.126424i | ||||
\(383\) | −24.7690 | + | 24.7690i | −1.26564 | + | 1.26564i | −0.317319 | + | 0.948319i | \(0.602782\pi\) |
−0.948319 | + | 0.317319i | \(0.897218\pi\) | |||||||
\(384\) | − | 28.3235i | − | 1.44538i | ||||||
\(385\) | −16.4538 | − | 34.0480i | −0.838565 | − | 1.73525i | ||||
\(386\) | 12.6297 | 0.642837 | ||||||||
\(387\) | 1.93611 | + | 1.93611i | 0.0984182 | + | 0.0984182i | ||||
\(388\) | 4.07579 | − | 4.07579i | 0.206917 | − | 0.206917i | ||||
\(389\) | −19.8848 | −1.00820 | −0.504100 | − | 0.863645i | \(-0.668176\pi\) | ||||
−0.504100 | + | 0.863645i | \(0.668176\pi\) | |||||||
\(390\) | −0.304048 | + | 0.146932i | −0.0153961 | + | 0.00744020i | ||||
\(391\) | −3.12102 | − | 29.4904i | −0.157837 | − | 1.49140i | ||||
\(392\) | 9.50868 | − | 9.50868i | 0.480261 | − | 0.480261i | ||||
\(393\) | 13.6143 | + | 13.6143i | 0.686753 | + | 0.686753i | ||||
\(394\) | − | 4.38180i | − | 0.220752i | ||||||
\(395\) | −7.05481 | + | 20.2499i | −0.354966 | + | 1.01889i | ||||
\(396\) | − | 25.6557i | − | 1.28925i | ||||||
\(397\) | 12.1483 | − | 12.1483i | 0.609706 | − | 0.609706i | −0.333163 | − | 0.942869i | \(-0.608116\pi\) |
0.942869 | + | 0.333163i | \(0.108116\pi\) | |||||||
\(398\) | 10.8087 | − | 10.8087i | 0.541792 | − | 0.541792i | ||||
\(399\) | − | 14.5919i | − | 0.730507i | ||||||
\(400\) | 6.45470 | + | 5.11874i | 0.322735 | + | 0.255937i | ||||
\(401\) | − | 6.80871i | − | 0.340011i | −0.985443 | − | 0.170005i | \(-0.945622\pi\) | ||
0.985443 | − | 0.170005i | \(-0.0543785\pi\) | |||||||
\(402\) | −0.340052 | − | 0.340052i | −0.0169603 | − | 0.0169603i | ||||
\(403\) | 0.491378 | + | 0.491378i | 0.0244773 | + | 0.0244773i | ||||
\(404\) | 11.8872i | 0.591410i | ||||||||
\(405\) | −5.51552 | + | 15.8316i | −0.274068 | + | 0.786678i | ||||
\(406\) | 7.44152i | 0.369317i | ||||||||
\(407\) | −23.3425 | + | 23.3425i | −1.15704 | + | 1.15704i | ||||
\(408\) | 25.7780 | − | 25.7780i | 1.27620 | − | 1.27620i | ||||
\(409\) | − | 15.9374i | − | 0.788054i | −0.919099 | − | 0.394027i | \(-0.871082\pi\) | ||
0.919099 | − | 0.394027i | \(-0.128918\pi\) | |||||||
\(410\) | −1.36256 | − | 2.81956i | −0.0672922 | − | 0.139248i | ||||
\(411\) | − | 38.3240i | − | 1.89038i | ||||||
\(412\) | 9.35438 | + | 9.35438i | 0.460857 | + | 0.460857i | ||||
\(413\) | 13.4470 | − | 13.4470i | 0.661684 | − | 0.661684i | ||||
\(414\) | −1.12658 | − | 10.6451i | −0.0553685 | − | 0.523176i | ||||
\(415\) | −6.46717 | − | 13.3825i | −0.317461 | − | 0.656923i | ||||
\(416\) | 0.524053 | 0.0256938 | ||||||||
\(417\) | 27.9700 | − | 27.9700i | 1.36970 | − | 1.36970i | ||||
\(418\) | −3.49275 | − | 3.49275i | −0.170836 | − | 0.170836i | ||||
\(419\) | −13.2084 | −0.645271 | −0.322635 | − | 0.946523i | \(-0.604569\pi\) | ||||
−0.322635 | + | 0.946523i | \(0.604569\pi\) | |||||||
\(420\) | −10.5339 | + | 30.2363i | −0.514003 | + | 1.47538i | ||||
\(421\) | 19.7655i | 0.963313i | 0.876360 | + | 0.481656i | \(0.159965\pi\) | ||||
−0.876360 | + | 0.481656i | \(0.840035\pi\) | |||||||
\(422\) | 2.22003 | − | 2.22003i | 0.108069 | − | 0.108069i | ||||
\(423\) | 8.91103 | + | 8.91103i | 0.433269 | + | 0.433269i | ||||
\(424\) | 20.6499 | 1.00285 | ||||||||
\(425\) | 3.54537 | + | 30.7137i | 0.171976 | + | 1.48983i | ||||
\(426\) | 6.32997 | 0.306688 | ||||||||
\(427\) | 14.9238 | − | 14.9238i | 0.722214 | − | 0.722214i | ||||
\(428\) | 3.95174 | − | 3.95174i | 0.191014 | − | 0.191014i | ||||
\(429\) | 1.09983 | 0.0531002 | ||||||||
\(430\) | −1.09235 | − | 0.380561i | −0.0526779 | − | 0.0183523i | ||||
\(431\) | − | 14.1759i | − | 0.682830i | −0.939913 | − | 0.341415i | \(-0.889094\pi\) | ||
0.939913 | − | 0.341415i | \(-0.110906\pi\) | |||||||
\(432\) | −1.29214 | + | 1.29214i | −0.0621681 | + | 0.0621681i | ||||
\(433\) | −13.7696 | + | 13.7696i | −0.661723 | + | 0.661723i | −0.955786 | − | 0.294063i | \(-0.904992\pi\) |
0.294063 | + | 0.955786i | \(0.404992\pi\) | |||||||
\(434\) | −17.6051 | −0.845074 | ||||||||
\(435\) | −7.91050 | − | 16.3692i | −0.379279 | − | 0.784845i | ||||
\(436\) | − | 29.9722i | − | 1.43541i | ||||||
\(437\) | 5.99790 | + | 4.84986i | 0.286918 | + | 0.232000i | ||||
\(438\) | 3.46252 | + | 3.46252i | 0.165446 | + | 0.165446i | ||||
\(439\) | − | 2.77558i | − | 0.132471i | −0.997804 | − | 0.0662357i | \(-0.978901\pi\) | ||
0.997804 | − | 0.0662357i | \(-0.0210989\pi\) | |||||||
\(440\) | 10.6921 | + | 22.1252i | 0.509726 | + | 1.05478i | ||||
\(441\) | −19.8908 | −0.947181 | ||||||||
\(442\) | 0.260259 | + | 0.260259i | 0.0123793 | + | 0.0123793i | ||||
\(443\) | −21.1388 | − | 21.1388i | −1.00433 | − | 1.00433i | −0.999991 | − | 0.00434272i | \(-0.998618\pi\) |
−0.00434272 | − | 0.999991i | \(-0.501382\pi\) | |||||||
\(444\) | 27.9511 | 1.32650 | ||||||||
\(445\) | −6.25730 | + | 17.9608i | −0.296624 | + | 0.851423i | ||||
\(446\) | −12.3439 | −0.584502 | ||||||||
\(447\) | −16.0353 | − | 16.0353i | −0.758443 | − | 0.758443i | ||||
\(448\) | −1.05587 | + | 1.05587i | −0.0498851 | + | 0.0498851i | ||||
\(449\) | − | 26.8682i | − | 1.26799i | −0.773337 | − | 0.633995i | \(-0.781414\pi\) | ||
0.773337 | − | 0.633995i | \(-0.218586\pi\) | |||||||
\(450\) | 1.27976 | + | 11.0866i | 0.0603284 | + | 0.522628i | ||||
\(451\) | 10.1992i | 0.480260i | ||||||||
\(452\) | −1.45233 | − | 1.45233i | −0.0683119 | − | 0.0683119i | ||||
\(453\) | 28.5311 | + | 28.5311i | 1.34051 | + | 1.34051i | ||||
\(454\) | −7.49099 | −0.351570 | ||||||||
\(455\) | −0.692110 | − | 0.241122i | −0.0324466 | − | 0.0113040i | ||||
\(456\) | 9.48217i | 0.444043i | ||||||||
\(457\) | 1.71050 | + | 1.71050i | 0.0800137 | + | 0.0800137i | 0.745981 | − | 0.665967i | \(-0.231981\pi\) |
−0.665967 | + | 0.745981i | \(0.731981\pi\) | |||||||
\(458\) | −0.627066 | + | 0.627066i | −0.0293009 | + | 0.0293009i | ||||
\(459\) | −6.85818 | −0.320112 | ||||||||
\(460\) | −8.92731 | − | 14.3795i | −0.416238 | − | 0.670447i | ||||
\(461\) | −13.0297 | −0.606852 | −0.303426 | − | 0.952855i | \(-0.598131\pi\) | ||||
−0.303426 | + | 0.952855i | \(0.598131\pi\) | |||||||
\(462\) | −19.7024 | + | 19.7024i | −0.916638 | + | 0.916638i | ||||
\(463\) | 4.19572 | + | 4.19572i | 0.194992 | + | 0.194992i | 0.797849 | − | 0.602857i | \(-0.205971\pi\) |
−0.602857 | + | 0.797849i | \(0.705971\pi\) | |||||||
\(464\) | 5.27988i | 0.245112i | ||||||||
\(465\) | 38.7263 | − | 18.7146i | 1.79589 | − | 0.867871i | ||||
\(466\) | 1.49059 | 0.0690502 | ||||||||
\(467\) | −9.47777 | − | 9.47777i | −0.438579 | − | 0.438579i | 0.452955 | − | 0.891534i | \(-0.350370\pi\) |
−0.891534 | + | 0.452955i | \(0.850370\pi\) | |||||||
\(468\) | −0.351602 | − | 0.351602i | −0.0162528 | − | 0.0162528i | ||||
\(469\) | − | 1.04374i | − | 0.0481955i | ||||||
\(470\) | −5.02759 | − | 1.75155i | −0.231906 | − | 0.0807928i | ||||
\(471\) | 49.8690i | 2.29784i | ||||||||
\(472\) | −8.73821 | + | 8.73821i | −0.402209 | + | 0.402209i | ||||
\(473\) | 2.66398 | + | 2.66398i | 0.122490 | + | 0.122490i | ||||
\(474\) | 15.8003 | 0.725732 | ||||||||
\(475\) | −6.30092 | − | 4.99679i | −0.289106 | − | 0.229269i | ||||
\(476\) | 34.8986 | 1.59958 | ||||||||
\(477\) | −21.5983 | − | 21.5983i | −0.988918 | − | 0.988918i | ||||
\(478\) | −12.3841 | − | 12.3841i | −0.566437 | − | 0.566437i | ||||
\(479\) | −28.8261 | −1.31710 | −0.658549 | − | 0.752538i | \(-0.728830\pi\) | ||||
−0.658549 | + | 0.752538i | \(0.728830\pi\) | |||||||
\(480\) | 10.6712 | − | 30.6303i | 0.487070 | − | 1.39807i | ||||
\(481\) | 0.639801i | 0.0291724i | ||||||||
\(482\) | 11.8977 | + | 11.8977i | 0.541927 | + | 0.541927i | ||||
\(483\) | 27.3578 | − | 33.8338i | 1.24482 | − | 1.53949i | ||||
\(484\) | − | 17.9395i | − | 0.815430i | ||||||
\(485\) | 7.35273 | − | 3.55324i | 0.333870 | − | 0.161344i | ||||
\(486\) | 14.5135 | 0.658348 | ||||||||
\(487\) | 2.01855 | − | 2.01855i | 0.0914693 | − | 0.0914693i | −0.659892 | − | 0.751361i | \(-0.729398\pi\) |
0.751361 | + | 0.659892i | \(0.229398\pi\) | |||||||
\(488\) | −9.69788 | + | 9.69788i | −0.439002 | + | 0.439002i | ||||
\(489\) | − | 31.9569i | − | 1.44514i | ||||||
\(490\) | 7.56604 | − | 3.65632i | 0.341799 | − | 0.165176i | ||||
\(491\) | 6.85643 | 0.309427 | 0.154713 | − | 0.987959i | \(-0.450555\pi\) | ||||
0.154713 | + | 0.987959i | \(0.450555\pi\) | |||||||
\(492\) | 6.10642 | − | 6.10642i | 0.275299 | − | 0.275299i | ||||
\(493\) | −14.0118 | + | 14.0118i | −0.631059 | + | 0.631059i | ||||
\(494\) | −0.0957339 | −0.00430727 | ||||||||
\(495\) | 11.9582 | − | 34.3246i | 0.537483 | − | 1.54278i | ||||
\(496\) | −12.4911 | −0.560868 | ||||||||
\(497\) | 9.71448 | + | 9.71448i | 0.435754 | + | 0.435754i | ||||
\(498\) | −7.74401 | + | 7.74401i | −0.347017 | + | 0.347017i | ||||
\(499\) | 27.6178i | 1.23634i | 0.786043 | + | 0.618171i | \(0.212126\pi\) | ||||
−0.786043 | + | 0.618171i | \(0.787874\pi\) | |||||||
\(500\) | 9.44915 | + | 14.9027i | 0.422579 | + | 0.666468i | ||||
\(501\) | −37.8740 | −1.69209 | ||||||||
\(502\) | 1.71461 | + | 1.71461i | 0.0765268 | + | 0.0765268i | ||||
\(503\) | −12.7717 | + | 12.7717i | −0.569461 | + | 0.569461i | −0.931977 | − | 0.362517i | \(-0.881918\pi\) |
0.362517 | + | 0.931977i | \(0.381918\pi\) | |||||||
\(504\) | 28.5603 | 1.27218 | ||||||||
\(505\) | −5.54068 | + | 15.9038i | −0.246557 | + | 0.707711i | ||||
\(506\) | −1.55011 | − | 14.6470i | −0.0689109 | − | 0.651137i | ||||
\(507\) | −23.3074 | + | 23.3074i | −1.03512 | + | 1.03512i | ||||
\(508\) | −3.12513 | − | 3.12513i | −0.138655 | − | 0.138655i | ||||
\(509\) | 12.2985i | 0.545123i | 0.962138 | + | 0.272561i | \(0.0878708\pi\) | ||||
−0.962138 | + | 0.272561i | \(0.912129\pi\) | |||||||
\(510\) | 20.5115 | − | 9.91225i | 0.908263 | − | 0.438922i | ||||
\(511\) | 10.6277i | 0.470143i | ||||||||
\(512\) | −12.0752 | + | 12.0752i | −0.533655 | + | 0.533655i | ||||
\(513\) | 1.26136 | − | 1.26136i | 0.0556902 | − | 0.0556902i | ||||
\(514\) | − | 1.17415i | − | 0.0517895i | ||||||
\(515\) | 8.15505 | + | 16.8753i | 0.359354 | + | 0.743614i | ||||
\(516\) | − | 3.18994i | − | 0.140429i | ||||||
\(517\) | 12.2611 | + | 12.2611i | 0.539241 | + | 0.539241i | ||||
\(518\) | −11.4614 | − | 11.4614i | −0.503586 | − | 0.503586i | ||||
\(519\) | − | 14.8791i | − | 0.653118i | ||||||
\(520\) | 0.449750 | + | 0.156687i | 0.0197229 | + | 0.00687118i | ||||
\(521\) | − | 6.95572i | − | 0.304736i | −0.988324 | − | 0.152368i | \(-0.951310\pi\) | ||
0.988324 | − | 0.152368i | \(-0.0486898\pi\) | |||||||
\(522\) | −5.05778 | + | 5.05778i | −0.221373 | + | 0.221373i | ||||
\(523\) | 9.61813 | − | 9.61813i | 0.420571 | − | 0.420571i | −0.464829 | − | 0.885400i | \(-0.653884\pi\) |
0.885400 | + | 0.464829i | \(0.153884\pi\) | |||||||
\(524\) | − | 11.9771i | − | 0.523223i | ||||||
\(525\) | −28.1866 | + | 35.5431i | −1.23016 | + | 1.55123i | ||||
\(526\) | 6.68814i | 0.291617i | ||||||||
\(527\) | −33.1490 | − | 33.1490i | −1.44400 | − | 1.44400i | ||||
\(528\) | −13.9792 | + | 13.9792i | −0.608365 | + | 0.608365i | ||||
\(529\) | 4.81433 | + | 22.4905i | 0.209319 | + | 0.977848i | ||||
\(530\) | 12.1857 | + | 4.24535i | 0.529314 | + | 0.184406i | ||||
\(531\) | 18.2791 | 0.793245 | ||||||||
\(532\) | −6.41856 | + | 6.41856i | −0.278280 | + | 0.278280i | ||||
\(533\) | 0.139776 | + | 0.139776i | 0.00605437 | + | 0.00605437i | ||||
\(534\) | 14.0142 | 0.606452 | ||||||||
\(535\) | 7.12893 | − | 3.44508i | 0.308211 | − | 0.148944i | ||||
\(536\) | 0.678250i | 0.0292959i | ||||||||
\(537\) | −7.10303 | + | 7.10303i | −0.306519 | + | 0.306519i | ||||
\(538\) | 8.77734 | + | 8.77734i | 0.378418 | + | 0.378418i | ||||
\(539\) | −27.3686 | −1.17885 | ||||||||
\(540\) | −3.52428 | + | 1.70312i | −0.151661 | + | 0.0732906i | ||||
\(541\) | 32.2358 | 1.38593 | 0.692964 | − | 0.720973i | \(-0.256305\pi\) | ||||
0.692964 | + | 0.720973i | \(0.256305\pi\) | |||||||
\(542\) | 10.0832 | − | 10.0832i | 0.433111 | − | 0.433111i | ||||
\(543\) | 19.9376 | − | 19.9376i | 0.855602 | − | 0.855602i | ||||
\(544\) | −35.3533 | −1.51576 | ||||||||
\(545\) | 13.9702 | − | 40.0997i | 0.598417 | − | 1.71768i | ||||
\(546\) | 0.540029i | 0.0231111i | ||||||||
\(547\) | 19.1302 | − | 19.1302i | 0.817947 | − | 0.817947i | −0.167864 | − | 0.985810i | \(-0.553687\pi\) |
0.985810 | + | 0.167864i | \(0.0536868\pi\) | |||||||
\(548\) | −16.8577 | + | 16.8577i | −0.720123 | + | 0.720123i | ||||
\(549\) | 20.2866 | 0.865810 | ||||||||
\(550\) | 1.76087 | + | 15.2545i | 0.0750839 | + | 0.650455i | ||||
\(551\) | − | 5.15409i | − | 0.219572i | ||||||
\(552\) | −17.7778 | + | 21.9860i | −0.756672 | + | 0.935788i | ||||
\(553\) | 24.2484 | + | 24.2484i | 1.03115 | + | 1.03115i | ||||
\(554\) | 6.32702i | 0.268809i | ||||||||
\(555\) | 37.3956 | + | 13.0281i | 1.58735 | + | 0.553013i | ||||
\(556\) | −24.6064 | −1.04354 | ||||||||
\(557\) | −16.8655 | − | 16.8655i | −0.714614 | − | 0.714614i | 0.252883 | − | 0.967497i | \(-0.418621\pi\) |
−0.967497 | + | 0.252883i | \(0.918621\pi\) | |||||||
\(558\) | −11.9657 | − | 11.9657i | −0.506548 | − | 0.506548i | ||||
\(559\) | 0.0730178 | 0.00308832 | ||||||||
\(560\) | 11.8617 | − | 5.73219i | 0.501247 | − | 0.242229i | ||||
\(561\) | −74.1960 | −3.13256 | ||||||||
\(562\) | 4.66061 | + | 4.66061i | 0.196596 | + | 0.196596i | ||||
\(563\) | −16.8690 | + | 16.8690i | −0.710943 | + | 0.710943i | −0.966733 | − | 0.255789i | \(-0.917665\pi\) |
0.255789 | + | 0.966733i | \(0.417665\pi\) | |||||||
\(564\) | − | 14.6818i | − | 0.618216i | ||||||
\(565\) | −1.26613 | − | 2.62000i | −0.0532664 | − | 0.110224i | ||||
\(566\) | 18.8234i | 0.791208i | ||||||||
\(567\) | 18.9576 | + | 18.9576i | 0.796146 | + | 0.796146i | ||||
\(568\) | −6.31271 | − | 6.31271i | −0.264876 | − | 0.264876i | ||||
\(569\) | 39.9056 | 1.67293 | 0.836465 | − | 0.548020i | \(-0.184618\pi\) | ||||
0.836465 | + | 0.548020i | \(0.184618\pi\) | |||||||
\(570\) | −1.94941 | + | 5.59553i | −0.0816518 | + | 0.234371i | ||||
\(571\) | − | 26.3727i | − | 1.10366i | −0.833956 | − | 0.551831i | \(-0.813929\pi\) | ||
0.833956 | − | 0.551831i | \(-0.186071\pi\) | |||||||
\(572\) | −0.483784 | − | 0.483784i | −0.0202280 | − | 0.0202280i | ||||
\(573\) | −9.65392 | + | 9.65392i | −0.403298 | + | 0.403298i | ||||
\(574\) | −5.00791 | −0.209026 | ||||||||
\(575\) | −5.24146 | − | 23.3993i | −0.218584 | − | 0.975818i | ||||
\(576\) | −1.43529 | −0.0598036 | ||||||||
\(577\) | −24.6951 | + | 24.6951i | −1.02807 | + | 1.02807i | −0.0284752 | + | 0.999594i | \(0.509065\pi\) |
−0.999594 | + | 0.0284752i | \(0.990935\pi\) | |||||||
\(578\) | −9.75128 | − | 9.75128i | −0.405600 | − | 0.405600i | ||||
\(579\) | 49.3442i | 2.05068i | ||||||||
\(580\) | −3.72076 | + | 10.6800i | −0.154496 | + | 0.443462i | ||||
\(581\) | −23.7692 | −0.986111 | ||||||||
\(582\) | −4.25477 | − | 4.25477i | −0.176366 | − | 0.176366i | ||||
\(583\) | −29.7180 | − | 29.7180i | −1.23079 | − | 1.23079i | ||||
\(584\) | − | 6.90617i | − | 0.285779i | ||||||
\(585\) | −0.306523 | − | 0.634290i | −0.0126732 | − | 0.0262247i | ||||
\(586\) | 6.12539i | 0.253038i | ||||||||
\(587\) | −28.0118 | + | 28.0118i | −1.15617 | + | 1.15617i | −0.170878 | + | 0.985292i | \(0.554660\pi\) |
−0.985292 | + | 0.170878i | \(0.945340\pi\) | |||||||
\(588\) | 16.3860 | + | 16.3860i | 0.675748 | + | 0.675748i | ||||
\(589\) | 12.1935 | 0.502426 | ||||||||
\(590\) | −6.95298 | + | 3.36005i | −0.286250 | + | 0.138331i | ||||
\(591\) | 17.1196 | 0.704208 | ||||||||
\(592\) | −8.13206 | − | 8.13206i | −0.334226 | − | 0.334226i | ||||
\(593\) | 10.9159 | + | 10.9159i | 0.448262 | + | 0.448262i | 0.894776 | − | 0.446514i | \(-0.147335\pi\) |
−0.446514 | + | 0.894776i | \(0.647335\pi\) | |||||||
\(594\) | −3.40624 | −0.139760 | ||||||||
\(595\) | 46.6907 | + | 16.2664i | 1.91413 | + | 0.666858i | ||||
\(596\) | 14.1069i | 0.577843i | ||||||||
\(597\) | 42.2295 | + | 42.2295i | 1.72834 | + | 1.72834i | ||||
\(598\) | −0.221975 | − | 0.179488i | −0.00907725 | − | 0.00733981i | ||||
\(599\) | − | 10.4715i | − | 0.427853i | −0.976850 | − | 0.213926i | \(-0.931375\pi\) | ||
0.976850 | − | 0.213926i | \(-0.0686253\pi\) | |||||||
\(600\) | 18.3164 | − | 23.0968i | 0.747762 | − | 0.942923i | ||||
\(601\) | −21.7432 | −0.886923 | −0.443462 | − | 0.896293i | \(-0.646250\pi\) | ||||
−0.443462 | + | 0.896293i | \(0.646250\pi\) | |||||||
\(602\) | −1.30804 | + | 1.30804i | −0.0533119 | + | 0.0533119i | ||||
\(603\) | 0.709401 | − | 0.709401i | 0.0288890 | − | 0.0288890i | ||||
\(604\) | − | 25.1001i | − | 1.02131i | ||||||
\(605\) | 8.36167 | − | 24.0011i | 0.339950 | − | 0.975784i | ||||
\(606\) | 12.4092 | 0.504088 | ||||||||
\(607\) | 19.4351 | − | 19.4351i | 0.788846 | − | 0.788846i | −0.192459 | − | 0.981305i | \(-0.561646\pi\) |
0.981305 | + | 0.192459i | \(0.0616464\pi\) | |||||||
\(608\) | 6.50218 | − | 6.50218i | 0.263698 | − | 0.263698i | ||||
\(609\) | −29.0739 | −1.17813 | ||||||||
\(610\) | −7.71658 | + | 3.72907i | −0.312435 | + | 0.150986i | ||||
\(611\) | 0.336067 | 0.0135958 | ||||||||
\(612\) | 23.7196 | + | 23.7196i | 0.958806 | + | 0.958806i | ||||
\(613\) | 8.06455 | − | 8.06455i | 0.325724 | − | 0.325724i | −0.525234 | − | 0.850958i | \(-0.676022\pi\) |
0.850958 | + | 0.525234i | \(0.176022\pi\) | |||||||
\(614\) | − | 2.01046i | − | 0.0811356i | ||||||
\(615\) | 11.0160 | − | 5.32352i | 0.444207 | − | 0.214665i | ||||
\(616\) | 39.2973 | 1.58333 | ||||||||
\(617\) | 25.7148 | + | 25.7148i | 1.03524 | + | 1.03524i | 0.999356 | + | 0.0358848i | \(0.0114249\pi\) |
0.0358848 | + | 0.999356i | \(0.488575\pi\) | |||||||
\(618\) | 9.76514 | − | 9.76514i | 0.392812 | − | 0.392812i | ||||
\(619\) | −9.68692 | −0.389350 | −0.194675 | − | 0.980868i | \(-0.562365\pi\) | ||||
−0.194675 | + | 0.980868i | \(0.562365\pi\) | |||||||
\(620\) | −25.2667 | − | 8.80257i | −1.01473 | − | 0.353520i | ||||
\(621\) | 5.28954 | − | 0.559800i | 0.212262 | − | 0.0224640i | ||||
\(622\) | −15.0314 | + | 15.0314i | −0.602704 | + | 0.602704i | ||||
\(623\) | 21.5072 | + | 21.5072i | 0.861670 | + | 0.861670i | ||||
\(624\) | 0.383159i | 0.0153386i | ||||||||
\(625\) | 5.69575 | + | 24.3425i | 0.227830 | + | 0.973701i | ||||
\(626\) | − | 11.2023i | − | 0.447733i | ||||||
\(627\) | 13.6461 | − | 13.6461i | 0.544974 | − | 0.544974i | ||||
\(628\) | 21.9360 | − | 21.9360i | 0.875341 | − | 0.875341i | ||||
\(629\) | − | 43.1618i | − | 1.72097i | ||||||
\(630\) | 16.8538 | + | 5.87163i | 0.671471 | + | 0.233931i | ||||
\(631\) | 47.1576i | 1.87732i | 0.344850 | + | 0.938658i | \(0.387930\pi\) | ||||
−0.344850 | + | 0.938658i | \(0.612070\pi\) | |||||||
\(632\) | −15.7572 | − | 15.7572i | −0.626789 | − | 0.626789i | ||||
\(633\) | 8.67362 | + | 8.67362i | 0.344745 | + | 0.344745i | ||||
\(634\) | 0.340137i | 0.0135086i | ||||||||
\(635\) | −2.72446 | − | 5.63773i | −0.108117 | − | 0.223727i | ||||
\(636\) | 35.5853i | 1.41105i | ||||||||
\(637\) | −0.375077 | + | 0.375077i | −0.0148611 | + | 0.0148611i | ||||
\(638\) | −6.95921 | + | 6.95921i | −0.275518 | + | 0.275518i | ||||
\(639\) | 13.2053i | 0.522393i | ||||||||
\(640\) | −22.4755 | + | 10.8614i | −0.888424 | + | 0.429334i | ||||
\(641\) | 21.0501i | 0.831431i | 0.909495 | + | 0.415715i | \(0.136469\pi\) | ||||
−0.909495 | + | 0.415715i | \(0.863531\pi\) | |||||||
\(642\) | −4.12526 | − | 4.12526i | −0.162811 | − | 0.162811i | ||||
\(643\) | 10.9648 | − | 10.9648i | 0.432410 | − | 0.432410i | −0.457037 | − | 0.889447i | \(-0.651089\pi\) |
0.889447 | + | 0.457037i | \(0.151089\pi\) | |||||||
\(644\) | −26.9164 | + | 2.84861i | −1.06066 | + | 0.112251i | ||||
\(645\) | 1.48685 | − | 4.26781i | 0.0585446 | − | 0.168045i | ||||
\(646\) | 6.45834 | 0.254100 | ||||||||
\(647\) | −4.51232 | + | 4.51232i | −0.177398 | + | 0.177398i | −0.790220 | − | 0.612823i | \(-0.790034\pi\) |
0.612823 | + | 0.790220i | \(0.290034\pi\) | |||||||
\(648\) | −12.3191 | − | 12.3191i | −0.483942 | − | 0.483942i | ||||
\(649\) | 25.1509 | 0.987261 | ||||||||
\(650\) | 0.233190 | + | 0.184926i | 0.00914646 | + | 0.00725338i | ||||
\(651\) | − | 68.7830i | − | 2.69582i | ||||||
\(652\) | −14.0570 | + | 14.0570i | −0.550513 | + | 0.550513i | ||||
\(653\) | 4.43758 | + | 4.43758i | 0.173656 | + | 0.173656i | 0.788584 | − | 0.614928i | \(-0.210815\pi\) |
−0.614928 | + | 0.788584i | \(0.710815\pi\) | |||||||
\(654\) | −31.2883 | −1.22347 | ||||||||
\(655\) | 5.58260 | − | 16.0241i | 0.218130 | − | 0.626115i | ||||
\(656\) | −3.55319 | −0.138729 | ||||||||
\(657\) | −7.22336 | + | 7.22336i | −0.281810 | + | 0.281810i | ||||
\(658\) | −6.02032 | + | 6.02032i | −0.234697 | + | 0.234697i | ||||
\(659\) | 38.7983 | 1.51137 | 0.755683 | − | 0.654938i | \(-0.227305\pi\) | ||||
0.755683 | + | 0.654938i | \(0.227305\pi\) | |||||||
\(660\) | −38.1278 | + | 18.4254i | −1.48412 | + | 0.717208i | ||||
\(661\) | − | 29.4127i | − | 1.14402i | −0.820246 | − | 0.572011i | \(-0.806164\pi\) | ||
0.820246 | − | 0.572011i | \(-0.193836\pi\) | |||||||
\(662\) | −6.74493 | + | 6.74493i | −0.262149 | + | 0.262149i | ||||
\(663\) | −1.01683 | + | 1.01683i | −0.0394904 | + | 0.0394904i | ||||
\(664\) | 15.4458 | 0.599413 | ||||||||
\(665\) | −11.5791 | + | 5.59563i | −0.449017 | + | 0.216989i | ||||
\(666\) | − | 15.5800i | − | 0.603712i | ||||||
\(667\) | 9.66323 | − | 11.9507i | 0.374162 | − | 0.462731i | ||||
\(668\) | 16.6597 | + | 16.6597i | 0.644583 | + | 0.644583i | ||||
\(669\) | − | 48.2276i | − | 1.86459i | ||||||
\(670\) | −0.139439 | + | 0.400243i | −0.00538701 | + | 0.0154627i | ||||
\(671\) | 27.9131 | 1.07757 | ||||||||
\(672\) | −36.6784 | − | 36.6784i | −1.41490 | − | 1.41490i | ||||
\(673\) | 20.9657 | + | 20.9657i | 0.808169 | + | 0.808169i | 0.984357 | − | 0.176188i | \(-0.0563766\pi\) |
−0.176188 | + | 0.984357i | \(0.556377\pi\) | |||||||
\(674\) | 8.66890 | 0.333914 | ||||||||
\(675\) | −5.50894 | + | 0.635914i | −0.212039 | + | 0.0244763i | ||||
\(676\) | 20.5046 | 0.788637 | ||||||||
\(677\) | −12.8997 | − | 12.8997i | −0.495777 | − | 0.495777i | 0.414343 | − | 0.910121i | \(-0.364011\pi\) |
−0.910121 | + | 0.414343i | \(0.864011\pi\) | |||||||
\(678\) | −1.51611 | + | 1.51611i | −0.0582257 | + | 0.0582257i | ||||
\(679\) | − | 13.0594i | − | 0.501174i | ||||||
\(680\) | −30.3408 | − | 10.5703i | −1.16352 | − | 0.405354i | ||||
\(681\) | − | 29.2672i | − | 1.12152i | ||||||
\(682\) | −16.4641 | − | 16.4641i | −0.630443 | − | 0.630443i | ||||
\(683\) | −22.6437 | − | 22.6437i | −0.866437 | − | 0.866437i | 0.125639 | − | 0.992076i | \(-0.459902\pi\) |
−0.992076 | + | 0.125639i | \(0.959902\pi\) | |||||||
\(684\) | −8.72501 | −0.333609 | ||||||||
\(685\) | −30.4112 | + | 14.6963i | −1.16195 | + | 0.561518i | ||||
\(686\) | 2.81674i | 0.107544i | ||||||||
\(687\) | −2.44994 | − | 2.44994i | −0.0934709 | − | 0.0934709i | ||||
\(688\) | −0.928079 | + | 0.928079i | −0.0353827 | + | 0.0353827i | ||||
\(689\) | −0.814549 | −0.0310319 | ||||||||
\(690\) | −15.0109 | + | 9.31933i | −0.571455 | + | 0.354781i | ||||
\(691\) | −21.9932 | −0.836659 | −0.418330 | − | 0.908295i | \(-0.637384\pi\) | ||||
−0.418330 | + | 0.908295i | \(0.637384\pi\) | |||||||
\(692\) | −6.54488 | + | 6.54488i | −0.248799 | + | 0.248799i | ||||
\(693\) | −41.1022 | − | 41.1022i | −1.56134 | − | 1.56134i | ||||
\(694\) | 17.0936i | 0.648864i | ||||||||
\(695\) | −32.9208 | − | 11.4692i | −1.24876 | − | 0.435051i | ||||
\(696\) | 18.8930 | 0.716136 | ||||||||
\(697\) | −9.42949 | − | 9.42949i | −0.357167 | − | 0.357167i | ||||
\(698\) | 5.65838 | + | 5.65838i | 0.214173 | + | 0.214173i | ||||
\(699\) | 5.82371i | 0.220273i | ||||||||
\(700\) | 28.0329 | − | 3.23592i | 1.05954 | − | 0.122306i | ||||
\(701\) | − | 31.3567i | − | 1.18433i | −0.805818 | − | 0.592164i | \(-0.798274\pi\) | ||
0.805818 | − | 0.592164i | \(-0.201726\pi\) | |||||||
\(702\) | −0.0466813 | + | 0.0466813i | −0.00176187 | + | 0.00176187i | ||||
\(703\) | 7.93832 | + | 7.93832i | 0.299400 | + | 0.299400i | ||||
\(704\) | −1.97487 | −0.0744307 | ||||||||
\(705\) | 6.84327 | − | 19.6427i | 0.257732 | − | 0.739788i | ||||
\(706\) | −9.77742 | −0.367978 | ||||||||
\(707\) | 19.0441 | + | 19.0441i | 0.716228 | + | 0.716228i | ||||
\(708\) | −15.0583 | − | 15.0583i | −0.565926 | − | 0.565926i | ||||
\(709\) | −34.3936 | −1.29168 | −0.645839 | − | 0.763474i | \(-0.723492\pi\) | ||||
−0.645839 | + | 0.763474i | \(0.723492\pi\) | |||||||
\(710\) | −2.42739 | − | 5.02301i | −0.0910984 | − | 0.188510i | ||||
\(711\) | 32.9619i | 1.23617i | ||||||||
\(712\) | −13.9760 | − | 13.9760i | −0.523771 | − | 0.523771i | ||||
\(713\) | 28.2728 | + | 22.8612i | 1.05883 | + | 0.856160i | ||||
\(714\) | − | 36.4311i | − | 1.36340i | ||||||
\(715\) | −0.421758 | − | 0.872746i | −0.0157728 | − | 0.0326388i | ||||
\(716\) | 6.24885 | 0.233530 | ||||||||
\(717\) | 48.3846 | − | 48.3846i | 1.80696 | − | 1.80696i | ||||
\(718\) | 7.35449 | − | 7.35449i | 0.274467 | − | 0.274467i | ||||
\(719\) | 38.4456i | 1.43378i | 0.697186 | + | 0.716890i | \(0.254435\pi\) | ||||
−0.697186 | + | 0.716890i | \(0.745565\pi\) | |||||||
\(720\) | 11.9580 | + | 4.16602i | 0.445649 | + | 0.155258i | ||||
\(721\) | 29.9727 | 1.11624 | ||||||||
\(722\) | 7.53674 | − | 7.53674i | 0.280489 | − | 0.280489i | ||||
\(723\) | −46.4843 | + | 46.4843i | −1.72877 | + | 1.72877i | ||||
\(724\) | −17.5399 | −0.651867 | ||||||||
\(725\) | −9.95598 | + | 12.5544i | −0.369756 | + | 0.466259i | ||||
\(726\) | −18.7272 | −0.695032 | ||||||||
\(727\) | −10.5986 | − | 10.5986i | −0.393080 | − | 0.393080i | 0.482704 | − | 0.875784i | \(-0.339655\pi\) |
−0.875784 | + | 0.482704i | \(0.839655\pi\) | |||||||
\(728\) | 0.538556 | − | 0.538556i | 0.0199602 | − | 0.0199602i | ||||
\(729\) | 34.2118i | 1.26710i | ||||||||
\(730\) | 1.41982 | − | 4.07541i | 0.0525498 | − | 0.150838i | ||||
\(731\) | −4.92588 | −0.182190 | ||||||||
\(732\) | −16.7121 | − | 16.7121i | −0.617696 | − | 0.617696i | ||||
\(733\) | 10.2320 | − | 10.2320i | 0.377929 | − | 0.377929i | −0.492426 | − | 0.870355i | \(-0.663890\pi\) |
0.870355 | + | 0.492426i | \(0.163890\pi\) | |||||||
\(734\) | 12.8681 | 0.474969 | ||||||||
\(735\) | 14.2852 | + | 29.5604i | 0.526917 | + | 1.09035i | ||||
\(736\) | 27.2671 | − | 2.88572i | 1.00508 | − | 0.106369i | ||||
\(737\) | 0.976094 | − | 0.976094i | 0.0359549 | − | 0.0359549i | ||||
\(738\) | −3.40373 | − | 3.40373i | −0.125293 | − | 0.125293i | ||||
\(739\) | 4.63797i | 0.170610i | 0.996355 | + | 0.0853052i | \(0.0271865\pi\) | ||||
−0.996355 | + | 0.0853052i | \(0.972813\pi\) | |||||||
\(740\) | −10.7186 | − | 22.1800i | −0.394022 | − | 0.815352i | ||||
\(741\) | − | 0.374031i | − | 0.0137404i | ||||||
\(742\) | 14.5919 | − | 14.5919i | 0.535685 | − | 0.535685i | ||||
\(743\) | 1.49859 | − | 1.49859i | 0.0549781 | − | 0.0549781i | −0.679083 | − | 0.734061i | \(-0.737622\pi\) |
0.734061 | + | 0.679083i | \(0.237622\pi\) | |||||||
\(744\) | 44.6969i | 1.63867i | ||||||||
\(745\) | −6.57532 | + | 18.8736i | −0.240901 | + | 0.691476i | ||||
\(746\) | 6.52022i | 0.238722i | ||||||||
\(747\) | −16.1552 | − | 16.1552i | −0.591088 | − | 0.591088i | ||||
\(748\) | 32.6367 | + | 32.6367i | 1.19332 | + | 1.19332i | ||||
\(749\) | − | 12.6619i | − | 0.462657i | ||||||
\(750\) | 15.5571 | − | 9.86408i | 0.568065 | − | 0.360185i | ||||
\(751\) | 34.7333i | 1.26744i | 0.773564 | + | 0.633718i | \(0.218472\pi\) | ||||
−0.773564 | + | 0.633718i | \(0.781528\pi\) | |||||||
\(752\) | −4.27151 | + | 4.27151i | −0.155766 | + | 0.155766i | ||||
\(753\) | −6.69895 | + | 6.69895i | −0.244123 | + | 0.244123i | ||||
\(754\) | 0.190747i | 0.00694660i | ||||||||
\(755\) | 11.6993 | − | 33.5813i | 0.425780 | − | 1.22215i | ||||
\(756\) | 6.25958i | 0.227659i | ||||||||
\(757\) | 26.5759 | + | 26.5759i | 0.965916 | + | 0.965916i | 0.999438 | − | 0.0335216i | \(-0.0106723\pi\) |
−0.0335216 | + | 0.999438i | \(0.510672\pi\) | |||||||
\(758\) | −10.2149 | + | 10.2149i | −0.371024 | + | 0.371024i | ||||
\(759\) | 57.2255 | − | 6.05626i | 2.07715 | − | 0.219828i | ||||
\(760\) | 7.52437 | − | 3.63618i | 0.272938 | − | 0.131898i | ||||
\(761\) | −44.0823 | −1.59798 | −0.798991 | − | 0.601343i | \(-0.794632\pi\) | ||||
−0.798991 | + | 0.601343i | \(0.794632\pi\) | |||||||
\(762\) | −3.26236 | + | 3.26236i | −0.118183 | + | 0.118183i | ||||
\(763\) | −48.0176 | − | 48.0176i | −1.73835 | − | 1.73835i | ||||
\(764\) | 8.49297 | 0.307265 | ||||||||
\(765\) | 20.6785 | + | 42.7901i | 0.747632 | + | 1.54708i | ||||
\(766\) | − | 22.7472i | − | 0.821891i | ||||||
\(767\) | 0.344685 | − | 0.344685i | 0.0124458 | − | 0.0124458i | ||||
\(768\) | 14.5041 | + | 14.5041i | 0.523373 | + | 0.523373i | ||||
\(769\) | 35.5733 | 1.28281 | 0.641404 | − | 0.767203i | \(-0.278352\pi\) | ||||
0.641404 | + | 0.767203i | \(0.278352\pi\) | |||||||
\(770\) | 23.1898 | + | 8.07902i | 0.835702 | + | 0.291148i | ||||
\(771\) | 4.58738 | 0.165211 | ||||||||
\(772\) | 21.7051 | − | 21.7051i | 0.781185 | − | 0.781185i | ||||
\(773\) | 33.7415 | − | 33.7415i | 1.21360 | − | 1.21360i | 0.243761 | − | 0.969835i | \(-0.421619\pi\) |
0.969835 | − | 0.243761i | \(-0.0783813\pi\) | |||||||
\(774\) | −1.77808 | −0.0639117 | ||||||||
\(775\) | −29.7012 | − | 23.5538i | −1.06690 | − | 0.846079i | ||||
\(776\) | 8.48634i | 0.304642i | ||||||||
\(777\) | 44.7796 | − | 44.7796i | 1.60646 | − | 1.60646i | ||||
\(778\) | 9.13085 | − | 9.13085i | 0.327357 | − | 0.327357i | ||||
\(779\) | 3.46854 | 0.124273 | ||||||||
\(780\) | −0.270014 | + | 0.775042i | −0.00966806 | + | 0.0277510i | ||||
\(781\) | 18.1697i | 0.650163i | ||||||||
\(782\) | 14.9748 | + | 12.1085i | 0.535497 | + | 0.432999i | ||||
\(783\) | −2.51322 | − | 2.51322i | −0.0898151 | − | 0.0898151i | ||||
\(784\) | − | 9.53467i | − | 0.340524i | ||||||
\(785\) | 39.5725 | − | 19.1236i | 1.41240 | − | 0.682549i | ||||
\(786\) | −12.5031 | −0.445970 | ||||||||
\(787\) | 19.2374 | + | 19.2374i | 0.685739 | + | 0.685739i | 0.961287 | − | 0.275548i | \(-0.0888593\pi\) |
−0.275548 | + | 0.961287i | \(0.588859\pi\) | |||||||
\(788\) | −7.53045 | − | 7.53045i | −0.268261 | − | 0.268261i | ||||
\(789\) | −26.1305 | −0.930269 | ||||||||
\(790\) | −6.05904 | − | 12.5380i | −0.215571 | − | 0.446082i | ||||
\(791\) | −4.65347 | −0.165458 | ||||||||
\(792\) | 26.7092 | + | 26.7092i | 0.949072 | + | 0.949072i | ||||
\(793\) | 0.382540 | − | 0.382540i | 0.0135844 | − | 0.0135844i | ||||
\(794\) | 11.1567i | 0.395936i | ||||||||
\(795\) | −16.5865 | + | 47.6095i | −0.588263 | + | 1.68853i | ||||
\(796\) | − | 37.1512i | − | 1.31679i | ||||||
\(797\) | −9.21870 | − | 9.21870i | −0.326543 | − | 0.326543i | 0.524727 | − | 0.851270i | \(-0.324167\pi\) |
−0.851270 | + | 0.524727i | \(0.824167\pi\) | |||||||
\(798\) | 6.70040 | + | 6.70040i | 0.237192 | + | 0.237192i | ||||
\(799\) | −22.6715 | −0.802062 | ||||||||
\(800\) | −28.3981 | + | 3.27808i | −1.00403 | + | 0.115898i | ||||
\(801\) | 29.2357i | 1.03299i | ||||||||
\(802\) | 3.12647 | + | 3.12647i | 0.110400 | + | 0.110400i | ||||
\(803\) | −9.93891 | + | 9.93891i | −0.350737 | + | 0.350737i | ||||
\(804\) | −1.16881 | −0.0412207 | ||||||||
\(805\) | −37.3391 | − | 8.73475i | −1.31603 | − | 0.307859i | ||||
\(806\) | −0.451269 | −0.0158953 | ||||||||
\(807\) | −34.2929 | + | 34.2929i | −1.20717 | + | 1.20717i | ||||
\(808\) | −12.3753 | − | 12.3753i | −0.435363 | − | 0.435363i | ||||
\(809\) | 26.2047i | 0.921310i | 0.887579 | + | 0.460655i | \(0.152385\pi\) | ||||
−0.887579 | + | 0.460655i | \(0.847615\pi\) | |||||||
\(810\) | −4.73701 | − | 9.80232i | −0.166442 | − | 0.344418i | ||||
\(811\) | −25.3145 | −0.888914 | −0.444457 | − | 0.895800i | \(-0.646603\pi\) | ||||
−0.444457 | + | 0.895800i | \(0.646603\pi\) | |||||||
\(812\) | 12.7888 | + | 12.7888i | 0.448799 | + | 0.448799i | ||||
\(813\) | 39.3950 | + | 39.3950i | 1.38164 | + | 1.38164i | ||||
\(814\) | − | 21.4371i | − | 0.751371i | ||||||
\(815\) | −25.3587 | + | 12.2547i | −0.888278 | + | 0.429264i | ||||
\(816\) | − | 25.8484i | − | 0.904876i | ||||||
\(817\) | 0.905968 | − | 0.905968i | 0.0316958 | − | 0.0316958i | ||||
\(818\) | 7.31826 | + | 7.31826i | 0.255877 | + | 0.255877i | ||||
\(819\) | −1.12658 | −0.0393660 | ||||||||
\(820\) | −7.18729 | − | 2.50396i | −0.250991 | − | 0.0874419i | ||||
\(821\) | 44.5923 | 1.55628 | 0.778141 | − | 0.628089i | \(-0.216163\pi\) | ||||
0.778141 | + | 0.628089i | \(0.216163\pi\) | |||||||
\(822\) | 17.5979 | + | 17.5979i | 0.613797 | + | 0.613797i | ||||
\(823\) | 17.7237 | + | 17.7237i | 0.617810 | + | 0.617810i | 0.944969 | − | 0.327159i | \(-0.106091\pi\) |
−0.327159 | + | 0.944969i | \(0.606091\pi\) | |||||||
\(824\) | −19.4770 | −0.678515 | ||||||||
\(825\) | −59.5991 | + | 6.87970i | −2.07498 | + | 0.239521i | ||||
\(826\) | 12.3494i | 0.429691i | ||||||||
\(827\) | −0.817135 | − | 0.817135i | −0.0284146 | − | 0.0284146i | 0.692757 | − | 0.721171i | \(-0.256396\pi\) |
−0.721171 | + | 0.692757i | \(0.756396\pi\) | |||||||
\(828\) | −20.2304 | − | 16.3582i | −0.703056 | − | 0.568487i | ||||
\(829\) | − | 22.9852i | − | 0.798308i | −0.916884 | − | 0.399154i | \(-0.869304\pi\) | ||
0.916884 | − | 0.399154i | \(-0.130696\pi\) | |||||||
\(830\) | 9.11474 | + | 3.17545i | 0.316377 | + | 0.110222i | ||||
\(831\) | −24.7196 | −0.857512 | ||||||||
\(832\) | −0.0270649 | + | 0.0270649i | −0.000938306 | + | 0.000938306i | ||||
\(833\) | 25.3032 | − | 25.3032i | 0.876703 | − | 0.876703i | ||||
\(834\) | 25.6869i | 0.889466i | ||||||||
\(835\) | 14.5238 | + | 30.0541i | 0.502616 | + | 1.04007i | ||||
\(836\) | −12.0051 | −0.415205 | ||||||||
\(837\) | 5.94577 | − | 5.94577i | 0.205516 | − | 0.205516i | ||||
\(838\) | 6.06511 | − | 6.06511i | 0.209516 | − | 0.209516i | ||||
\(839\) | 34.9215 | 1.20563 | 0.602813 | − | 0.797883i | \(-0.294047\pi\) | ||||
0.602813 | + | 0.797883i | \(0.294047\pi\) | |||||||
\(840\) | −20.5115 | − | 42.4445i | −0.707713 | − | 1.46447i | ||||
\(841\) | 18.7306 | 0.645883 | ||||||||
\(842\) | −9.07608 | − | 9.07608i | −0.312782 | − | 0.312782i | ||||
\(843\) | −18.2089 | + | 18.2089i | −0.627149 | + | 0.627149i | ||||
\(844\) | − | 7.63056i | − | 0.262655i | ||||||
\(845\) | 27.4329 | + | 9.55728i | 0.943722 | + | 0.328780i | ||||
\(846\) | −8.18367 | −0.281360 | ||||||||
\(847\) | −28.7403 | − | 28.7403i | −0.987528 | − | 0.987528i | ||||
\(848\) | 10.3532 | − | 10.3532i | 0.355529 | − | 0.355529i | ||||
\(849\) | −73.5428 | −2.52398 | ||||||||
\(850\) | −15.7313 | − | 12.4753i | −0.539580 | − | 0.427901i | ||||
\(851\) | 3.52309 | + | 33.2896i | 0.120770 | + | 1.14115i | ||||
\(852\) | 10.8785 | − | 10.8785i | 0.372692 | − | 0.372692i | ||||
\(853\) | −12.9244 | − | 12.9244i | −0.442523 | − | 0.442523i | 0.450336 | − | 0.892859i | \(-0.351304\pi\) |
−0.892859 | + | 0.450336i | \(0.851304\pi\) | |||||||
\(854\) | 13.7057i | 0.468998i | ||||||||
\(855\) | −11.6731 | − | 4.06677i | −0.399213 | − | 0.139081i | ||||
\(856\) | 8.22803i | 0.281228i | ||||||||
\(857\) | 0.653568 | − | 0.653568i | 0.0223254 | − | 0.0223254i | −0.695856 | − | 0.718181i | \(-0.744975\pi\) |
0.718181 | + | 0.695856i | \(0.244975\pi\) | |||||||
\(858\) | −0.505028 | + | 0.505028i | −0.0172414 | + | 0.0172414i | ||||
\(859\) | 35.1106i | 1.19796i | 0.800765 | + | 0.598979i | \(0.204427\pi\) | ||||
−0.800765 | + | 0.598979i | \(0.795573\pi\) | |||||||
\(860\) | −2.53131 | + | 1.22327i | −0.0863170 | + | 0.0417130i | ||||
\(861\) | − | 19.5658i | − | 0.666802i | ||||||
\(862\) | 6.50941 | + | 6.50941i | 0.221711 | + | 0.221711i | ||||
\(863\) | −11.1928 | − | 11.1928i | −0.381006 | − | 0.381006i | 0.490459 | − | 0.871464i | \(-0.336829\pi\) |
−0.871464 | + | 0.490459i | \(0.836829\pi\) | |||||||
\(864\) | − | 6.34113i | − | 0.215730i | ||||||
\(865\) | −11.8070 | + | 5.70576i | −0.401449 | + | 0.194002i | ||||
\(866\) | − | 12.6456i | − | 0.429715i | ||||||
\(867\) | 38.0981 | − | 38.0981i | 1.29388 | − | 1.29388i | ||||
\(868\) | −30.2557 | + | 30.2557i | −1.02695 | + | 1.02695i | ||||
\(869\) | 45.3536i | 1.53852i | ||||||||
\(870\) | 11.1489 | + | 3.88415i | 0.377985 | + | 0.131685i | ||||
\(871\) | − | 0.0267541i | − | 0.000906527i | ||||||
\(872\) | 31.2030 | + | 31.2030i | 1.05667 | + | 1.05667i | ||||
\(873\) | 8.87610 | − | 8.87610i | 0.300411 | − | 0.300411i | ||||
\(874\) | −4.98116 | + | 0.527163i | −0.168490 | + | 0.0178316i | ||||
\(875\) | 39.0134 | + | 8.73695i | 1.31889 | + | 0.295363i | ||||
\(876\) | 11.9012 | 0.402104 | ||||||||
\(877\) | −27.9872 | + | 27.9872i | −0.945060 | + | 0.945060i | −0.998567 | − | 0.0535078i | \(-0.982960\pi\) |
0.0535078 | + | 0.998567i | \(0.482960\pi\) | |||||||
\(878\) | 1.27451 | + | 1.27451i | 0.0430127 | + | 0.0430127i | ||||
\(879\) | −23.9318 | −0.807200 | ||||||||
\(880\) | 16.4535 | + | 5.73219i | 0.554649 | + | 0.193232i | ||||
\(881\) | − | 7.23594i | − | 0.243785i | −0.992543 | − | 0.121893i | \(-0.961104\pi\) | ||
0.992543 | − | 0.121893i | \(-0.0388963\pi\) | |||||||
\(882\) | 9.13360 | − | 9.13360i | 0.307544 | − | 0.307544i | ||||
\(883\) | −22.2102 | − | 22.2102i | −0.747431 | − | 0.747431i | 0.226565 | − | 0.973996i | \(-0.427250\pi\) |
−0.973996 | + | 0.226565i | \(0.927250\pi\) | |||||||
\(884\) | 0.894550 | 0.0300870 | ||||||||
\(885\) | −13.1277 | − | 27.1652i | −0.441282 | − | 0.913147i | ||||
\(886\) | 19.4133 | 0.652203 | ||||||||
\(887\) | 11.9959 | − | 11.9959i | 0.402782 | − | 0.402782i | −0.476430 | − | 0.879212i | \(-0.658069\pi\) |
0.879212 | + | 0.476430i | \(0.158069\pi\) | |||||||
\(888\) | −29.0989 | + | 29.0989i | −0.976495 | + | 0.976495i | ||||
\(889\) | −10.0134 | −0.335837 | ||||||||
\(890\) | −5.37409 | − | 11.1206i | −0.180140 | − | 0.372765i | ||||
\(891\) | 35.4578i | 1.18788i | ||||||||
\(892\) | −21.2139 | + | 21.2139i | −0.710296 | + | 0.710296i | ||||
\(893\) | 4.16975 | − | 4.16975i | 0.139535 | − | 0.139535i | ||||
\(894\) | 14.7264 | 0.492525 | ||||||||
\(895\) | 8.36030 | + | 2.91262i | 0.279454 | + | 0.0973581i | ||||
\(896\) | 39.9195i | 1.33362i | ||||||||
\(897\) | 0.701257 | − | 0.867255i | 0.0234143 | − | 0.0289568i | ||||
\(898\) | 12.3375 | + | 12.3375i | 0.411709 | + | 0.411709i | ||||
\(899\) | − | 24.2953i | − | 0.810294i | ||||||
\(900\) | 21.2525 | + | 16.8538i | 0.708417 | + | 0.561793i | ||||
\(901\) | 54.9506 | 1.83067 | ||||||||
\(902\) | −4.68333 | − | 4.68333i | −0.155938 | − | 0.155938i | ||||
\(903\) | −5.11051 | − | 5.11051i | −0.170067 | − | 0.170067i | ||||
\(904\) | 3.02394 | 0.100575 | ||||||||
\(905\) | −23.4666 | − | 8.17545i | −0.780056 | − | 0.271761i | ||||
\(906\) | −26.2023 | −0.870513 | ||||||||
\(907\) | 39.2532 | + | 39.2532i | 1.30338 | + | 1.30338i | 0.926098 | + | 0.377283i | \(0.123142\pi\) |
0.377283 | + | 0.926098i | \(0.376858\pi\) | |||||||
\(908\) | −12.8738 | + | 12.8738i | −0.427233 | + | 0.427233i | ||||
\(909\) | 25.8875i | 0.858633i | ||||||||
\(910\) | 0.428528 | − | 0.207088i | 0.0142056 | − | 0.00686490i | ||||
\(911\) | − | 34.8753i | − | 1.15547i | −0.816225 | − | 0.577735i | \(-0.803937\pi\) | ||
0.816225 | − | 0.577735i | \(-0.196063\pi\) | |||||||
\(912\) | 4.75404 | + | 4.75404i | 0.157422 | + | 0.157422i | ||||
\(913\) | −22.2286 | − | 22.2286i | −0.735659 | − | 0.735659i | ||||
\(914\) | −1.57088 | −0.0519600 | ||||||||
\(915\) | −14.5694 | − | 30.1486i | −0.481650 | − | 0.996681i | ||||
\(916\) | 2.15532i | 0.0712136i | ||||||||
\(917\) | −19.1882 | − | 19.1882i | −0.633651 | − | 0.633651i | ||||
\(918\) | 3.14919 | − | 3.14919i | 0.103939 | − | 0.103939i | ||||
\(919\) | −2.37539 | −0.0783569 | −0.0391785 | − | 0.999232i | \(-0.512474\pi\) | ||||
−0.0391785 | + | 0.999232i | \(0.512474\pi\) | |||||||
\(920\) | 24.2639 | + | 5.67606i | 0.799957 | + | 0.187134i | ||||
\(921\) | 7.85484 | 0.258826 | ||||||||
\(922\) | 5.98306 | − | 5.98306i | 0.197042 | − | 0.197042i | ||||
\(923\) | 0.249009 | + | 0.249009i | 0.00819625 | + | 0.00819625i | ||||
\(924\) | 67.7200i | 2.22782i | ||||||||
\(925\) | −4.00211 | − | 34.6705i | −0.131589 | − | 1.13996i | ||||
\(926\) | −3.85324 | −0.126625 | ||||||||
\(927\) | 20.3716 | + | 20.3716i | 0.669091 | + | 0.669091i | ||||
\(928\) | −12.9554 | − | 12.9554i | −0.425283 | − | 0.425283i | ||||
\(929\) | − | 54.1771i | − | 1.77749i | −0.458398 | − | 0.888747i | \(-0.651577\pi\) | ||
0.458398 | − | 0.888747i | \(-0.348423\pi\) | |||||||
\(930\) | −9.18911 | + | 26.3762i | −0.301323 | + | 0.864909i | ||||
\(931\) | 9.30752i | 0.305042i | ||||||||
\(932\) | 2.56168 | − | 2.56168i | 0.0839108 | − | 0.0839108i | ||||
\(933\) | −58.7275 | − | 58.7275i | −1.92265 | − | 1.92265i | ||||
\(934\) | 8.70414 | 0.284808 | ||||||||
\(935\) | 28.4524 | + | 58.8766i | 0.930492 | + | 1.92547i | ||||
\(936\) | 0.732082 | 0.0239288 | ||||||||
\(937\) | −19.6245 | − | 19.6245i | −0.641106 | − | 0.641106i | 0.309721 | − | 0.950827i | \(-0.399764\pi\) |
−0.950827 | + | 0.309721i | \(0.899764\pi\) | |||||||
\(938\) | 0.479273 | + | 0.479273i | 0.0156488 | + | 0.0156488i | ||||
\(939\) | 43.7672 | 1.42829 | ||||||||
\(940\) | −11.6504 | + | 5.63012i | −0.379996 | + | 0.183634i | ||||
\(941\) | − | 25.0801i | − | 0.817588i | −0.912627 | − | 0.408794i | \(-0.865949\pi\) | ||
0.912627 | − | 0.408794i | \(-0.134051\pi\) | |||||||
\(942\) | −22.8992 | − | 22.8992i | −0.746097 | − | 0.746097i | ||||
\(943\) | 8.04241 | + | 6.50305i | 0.261897 | + | 0.211768i | ||||
\(944\) | 8.76210i | 0.285182i | ||||||||
\(945\) | −2.91762 | + | 8.37466i | −0.0949102 | + | 0.272428i | ||||
\(946\) | −2.44653 | −0.0795436 | ||||||||
\(947\) | 21.4551 | − | 21.4551i | 0.697196 | − | 0.697196i | −0.266609 | − | 0.963805i | \(-0.585903\pi\) |
0.963805 | + | 0.266609i | \(0.0859031\pi\) | |||||||
\(948\) | 27.1540 | − | 27.1540i | 0.881921 | − | 0.881921i | ||||
\(949\) | 0.272419i | 0.00884308i | ||||||||
\(950\) | 5.18777 | − | 0.598839i | 0.168313 | − | 0.0194289i | ||||
\(951\) | −1.32891 | −0.0430929 | ||||||||
\(952\) | −36.3318 | + | 36.3318i | −1.17752 | + | 1.17752i | ||||
\(953\) | 14.9127 | − | 14.9127i | 0.483071 | − | 0.483071i | −0.423040 | − | 0.906111i | \(-0.639037\pi\) |
0.906111 | + | 0.423040i | \(0.139037\pi\) | |||||||
\(954\) | 19.8353 | 0.642193 | ||||||||
\(955\) | 11.3627 | + | 3.95862i | 0.367688 | + | 0.128098i | ||||
\(956\) | −42.5661 | −1.37668 | ||||||||
\(957\) | −27.1895 | − | 27.1895i | −0.878913 | − | 0.878913i | ||||
\(958\) | 13.2366 | − | 13.2366i | 0.427655 | − | 0.427655i | ||||
\(959\) | 54.0143i | 1.74421i | ||||||||
\(960\) | 1.03079 | + | 2.13303i | 0.0332687 | + | 0.0688432i | ||||
\(961\) | 26.4778 | 0.854124 | ||||||||
\(962\) | −0.293788 | − | 0.293788i | −0.00947212 | − | 0.00947212i | ||||
\(963\) | 8.60594 | − | 8.60594i | 0.277322 | − | 0.277322i | ||||
\(964\) | 40.8943 | 1.31712 | ||||||||
\(965\) | 39.1561 | − | 18.9223i | 1.26048 | − | 0.609131i | ||||
\(966\) | 2.97369 | + | 28.0984i | 0.0956771 | + | 0.904051i | ||||
\(967\) | −21.5085 | + | 21.5085i | −0.691668 | + | 0.691668i | −0.962599 | − | 0.270931i | \(-0.912668\pi\) |
0.270931 | + | 0.962599i | \(0.412668\pi\) | |||||||
\(968\) | 18.6762 | + | 18.6762i | 0.600274 | + | 0.600274i | ||||
\(969\) | 25.2326i | 0.810589i | ||||||||
\(970\) | −1.74468 | + | 5.00788i | −0.0560183 | + | 0.160793i | ||||
\(971\) | − | 1.70133i | − | 0.0545982i | −0.999627 | − | 0.0272991i | \(-0.991309\pi\) | ||
0.999627 | − | 0.0272991i | \(-0.00869065\pi\) | |||||||
\(972\) | 24.9426 | − | 24.9426i | 0.800034 | − | 0.800034i | ||||
\(973\) | −39.4212 | + | 39.4212i | −1.26379 | + | 1.26379i | ||||
\(974\) | 1.85379i | 0.0593991i | ||||||||
\(975\) | −0.722502 | + | 0.911070i | −0.0231386 | + | 0.0291776i | ||||
\(976\) | 9.72439i | 0.311270i | ||||||||
\(977\) | 8.21439 | + | 8.21439i | 0.262802 | + | 0.262802i | 0.826191 | − | 0.563390i | \(-0.190503\pi\) |
−0.563390 | + | 0.826191i | \(0.690503\pi\) | |||||||
\(978\) | 14.6742 | + | 14.6742i | 0.469230 | + | 0.469230i | ||||
\(979\) | 40.2266i | 1.28565i | ||||||||
\(980\) | 6.71914 | − | 19.2864i | 0.214635 | − | 0.616082i | ||||
\(981\) | − | 65.2723i | − | 2.08398i | ||||||
\(982\) | −3.14839 | + | 3.14839i | −0.100469 | + | 0.100469i | ||||
\(983\) | −8.13489 | + | 8.13489i | −0.259463 | + | 0.259463i | −0.824835 | − | 0.565373i | \(-0.808732\pi\) |
0.565373 | + | 0.824835i | \(0.308732\pi\) | |||||||
\(984\) | 12.7144i | 0.405319i | ||||||||
\(985\) | −6.56497 | − | 13.5849i | −0.209177 | − | 0.432852i | ||||
\(986\) | − | 12.8681i | − | 0.409803i | ||||||
\(987\) | −23.5213 | − | 23.5213i | −0.748691 | − | 0.748691i | ||||
\(988\) | −0.164526 | + | 0.164526i | −0.00523426 | + | 0.00523426i | ||||
\(989\) | 3.79921 | − | 0.402076i | 0.120808 | − | 0.0127853i | ||||
\(990\) | 10.2704 | + | 21.2525i | 0.326413 | + | 0.675449i | ||||
\(991\) | 39.2907 | 1.24811 | 0.624055 | − | 0.781380i | \(-0.285484\pi\) | ||||
0.624055 | + | 0.781380i | \(0.285484\pi\) | |||||||
\(992\) | 30.6499 | − | 30.6499i | 0.973136 | − | 0.973136i | ||||
\(993\) | −26.3523 | − | 26.3523i | −0.836266 | − | 0.836266i | ||||
\(994\) | −8.92153 | −0.282974 | ||||||||
\(995\) | 17.3163 | − | 49.7044i | 0.548965 | − | 1.57573i | ||||
\(996\) | 26.6173i | 0.843401i | ||||||||
\(997\) | −7.56550 | + | 7.56550i | −0.239602 | + | 0.239602i | −0.816685 | − | 0.577083i | \(-0.804191\pi\) |
0.577083 | + | 0.816685i | \(0.304191\pi\) | |||||||
\(998\) | −12.6817 | − | 12.6817i | −0.401434 | − | 0.401434i | ||||
\(999\) | 7.74170 | 0.244937 |
(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 | 115.2.e.a.68.5 | yes | 20 | |
5.2 | odd | 4 | inner | 115.2.e.a.22.6 | yes | 20 | |
5.3 | odd | 4 | 575.2.e.d.482.6 | 20 | |||
5.4 | even | 2 | 575.2.e.d.68.5 | 20 | |||
23.22 | odd | 2 | inner | 115.2.e.a.68.6 | yes | 20 | |
115.22 | even | 4 | inner | 115.2.e.a.22.5 | ✓ | 20 | |
115.68 | even | 4 | 575.2.e.d.482.5 | 20 | |||
115.114 | odd | 2 | 575.2.e.d.68.6 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.2.e.a.22.5 | ✓ | 20 | 115.22 | even | 4 | inner | |
115.2.e.a.22.6 | yes | 20 | 5.2 | odd | 4 | inner | |
115.2.e.a.68.5 | yes | 20 | 1.1 | even | 1 | trivial | |
115.2.e.a.68.6 | yes | 20 | 23.22 | odd | 2 | inner | |
575.2.e.d.68.5 | 20 | 5.4 | even | 2 | |||
575.2.e.d.68.6 | 20 | 115.114 | odd | 2 | |||
575.2.e.d.482.5 | 20 | 115.68 | even | 4 | |||
575.2.e.d.482.6 | 20 | 5.3 | odd | 4 |