Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(239,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 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("546.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.p (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: | \(4.35983195036\) |
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: | \( x^{20} - 4 x^{19} + 8 x^{18} - 20 x^{17} + 56 x^{16} - 140 x^{15} + 288 x^{14} - 532 x^{13} + \cdots + 59049 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 281.9 | ||
Root | \(-1.25702 + 1.19160i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.281 |
Dual form | 546.2.p.c.239.9 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 0.0462556 | − | 1.73143i | 0.0267057 | − | 0.999643i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 1.43062 | − | 1.43062i | 0.639795 | − | 0.639795i | −0.310710 | − | 0.950505i | \(-0.600567\pi\) |
0.950505 | + | 0.310710i | \(0.100567\pi\) | |||||||
\(6\) | −1.19160 | − | 1.25702i | −0.486469 | − | 0.513175i | ||||
\(7\) | −0.707107 | + | 0.707107i | −0.267261 | + | 0.267261i | ||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | −2.99572 | − | 0.160177i | −0.998574 | − | 0.0533923i | ||||
\(10\) | − | 2.02321i | − | 0.639795i | ||||||
\(11\) | −3.59738 | − | 3.59738i | −1.08465 | − | 1.08465i | −0.996069 | − | 0.0885807i | \(-0.971767\pi\) |
−0.0885807 | − | 0.996069i | \(-0.528233\pi\) | |||||||
\(12\) | −1.73143 | − | 0.0462556i | −0.499822 | − | 0.0133528i | ||||
\(13\) | 2.66989 | + | 2.42316i | 0.740494 | + | 0.672063i | ||||
\(14\) | 1.00000i | 0.267261i | ||||||||
\(15\) | −2.41086 | − | 2.54321i | −0.622480 | − | 0.656653i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 4.10312 | 0.995153 | 0.497577 | − | 0.867420i | \(-0.334223\pi\) | ||||
0.497577 | + | 0.867420i | \(0.334223\pi\) | |||||||
\(18\) | −2.23156 | + | 2.00503i | −0.525983 | + | 0.472591i | ||||
\(19\) | −4.90374 | − | 4.90374i | −1.12499 | − | 1.12499i | −0.990979 | − | 0.134015i | \(-0.957213\pi\) |
−0.134015 | − | 0.990979i | \(-0.542787\pi\) | |||||||
\(20\) | −1.43062 | − | 1.43062i | −0.319897 | − | 0.319897i | ||||
\(21\) | 1.19160 | + | 1.25702i | 0.260029 | + | 0.274303i | ||||
\(22\) | −5.08746 | −1.08465 | ||||||||
\(23\) | 4.97697 | 1.03777 | 0.518885 | − | 0.854844i | \(-0.326347\pi\) | ||||
0.518885 | + | 0.854844i | \(0.326347\pi\) | |||||||
\(24\) | −1.25702 | + | 1.19160i | −0.256587 | + | 0.243234i | ||||
\(25\) | 0.906626i | 0.181325i | ||||||||
\(26\) | 3.60133 | − | 0.174466i | 0.706278 | − | 0.0342156i | ||||
\(27\) | −0.415904 | + | 5.17948i | −0.0800408 | + | 0.996792i | ||||
\(28\) | 0.707107 | + | 0.707107i | 0.133631 | + | 0.133631i | ||||
\(29\) | 2.59352i | 0.481605i | 0.970574 | + | 0.240803i | \(0.0774107\pi\) | ||||
−0.970574 | + | 0.240803i | \(0.922589\pi\) | |||||||
\(30\) | −3.50305 | − | 0.0935847i | −0.639567 | − | 0.0170862i | ||||
\(31\) | −1.00229 | − | 1.00229i | −0.180017 | − | 0.180017i | 0.611346 | − | 0.791363i | \(-0.290628\pi\) |
−0.791363 | + | 0.611346i | \(0.790628\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | −6.39501 | + | 6.06222i | −1.11323 | + | 1.05530i | ||||
\(34\) | 2.90134 | − | 2.90134i | 0.497577 | − | 0.497577i | ||||
\(35\) | 2.02321i | 0.341985i | ||||||||
\(36\) | −0.160177 | + | 2.99572i | −0.0266961 | + | 0.499287i | ||||
\(37\) | 8.01932 | − | 8.01932i | 1.31837 | − | 1.31837i | 0.403301 | − | 0.915067i | \(-0.367863\pi\) |
0.915067 | − | 0.403301i | \(-0.132137\pi\) | |||||||
\(38\) | −6.93493 | −1.12499 | ||||||||
\(39\) | 4.31903 | − | 4.51065i | 0.691599 | − | 0.722282i | ||||
\(40\) | −2.02321 | −0.319897 | ||||||||
\(41\) | −0.185417 | + | 0.185417i | −0.0289573 | + | 0.0289573i | −0.721437 | − | 0.692480i | \(-0.756518\pi\) |
0.692480 | + | 0.721437i | \(0.256518\pi\) | |||||||
\(42\) | 1.73143 | + | 0.0462556i | 0.267166 | + | 0.00713739i | ||||
\(43\) | 8.21380i | 1.25259i | 0.779585 | + | 0.626297i | \(0.215430\pi\) | ||||
−0.779585 | + | 0.626297i | \(0.784570\pi\) | |||||||
\(44\) | −3.59738 | + | 3.59738i | −0.542325 | + | 0.542325i | ||||
\(45\) | −4.51491 | + | 4.05660i | −0.673042 | + | 0.604722i | ||||
\(46\) | 3.51925 | − | 3.51925i | 0.518885 | − | 0.518885i | ||||
\(47\) | 2.56188 | + | 2.56188i | 0.373689 | + | 0.373689i | 0.868819 | − | 0.495130i | \(-0.164880\pi\) |
−0.495130 | + | 0.868819i | \(0.664880\pi\) | |||||||
\(48\) | −0.0462556 | + | 1.73143i | −0.00667642 | + | 0.249911i | ||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0.641081 | + | 0.641081i | 0.0906626 | + | 0.0906626i | ||||
\(51\) | 0.189792 | − | 7.10428i | 0.0265762 | − | 0.994798i | ||||
\(52\) | 2.42316 | − | 2.66989i | 0.336031 | − | 0.370247i | ||||
\(53\) | − | 7.36477i | − | 1.01163i | −0.862642 | − | 0.505814i | \(-0.831192\pi\) | ||
0.862642 | − | 0.505814i | \(-0.168808\pi\) | |||||||
\(54\) | 3.36836 | + | 3.95653i | 0.458375 | + | 0.538416i | ||||
\(55\) | −10.2930 | −1.38791 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −8.71732 | + | 8.26367i | −1.15464 | + | 1.09455i | ||||
\(58\) | 1.83390 | + | 1.83390i | 0.240803 | + | 0.240803i | ||||
\(59\) | −1.33972 | − | 1.33972i | −0.174417 | − | 0.174417i | 0.614500 | − | 0.788917i | \(-0.289358\pi\) |
−0.788917 | + | 0.614500i | \(0.789358\pi\) | |||||||
\(60\) | −2.54321 | + | 2.41086i | −0.328326 | + | 0.311240i | ||||
\(61\) | −10.1389 | −1.29815 | −0.649075 | − | 0.760725i | \(-0.724844\pi\) | ||||
−0.649075 | + | 0.760725i | \(0.724844\pi\) | |||||||
\(62\) | −1.41746 | −0.180017 | ||||||||
\(63\) | 2.23156 | − | 2.00503i | 0.281150 | − | 0.252610i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 7.28624 | − | 0.352981i | 0.903747 | − | 0.0437820i | ||||
\(66\) | −0.235323 | + | 8.80859i | −0.0289663 | + | 1.08426i | ||||
\(67\) | 3.13832 | + | 3.13832i | 0.383407 | + | 0.383407i | 0.872328 | − | 0.488921i | \(-0.162609\pi\) |
−0.488921 | + | 0.872328i | \(0.662609\pi\) | |||||||
\(68\) | − | 4.10312i | − | 0.497577i | ||||||
\(69\) | 0.230213 | − | 8.61729i | 0.0277143 | − | 1.03740i | ||||
\(70\) | 1.43062 | + | 1.43062i | 0.170992 | + | 0.170992i | ||||
\(71\) | 9.44085 | − | 9.44085i | 1.12042 | − | 1.12042i | 0.128745 | − | 0.991678i | \(-0.458905\pi\) |
0.991678 | − | 0.128745i | \(-0.0410947\pi\) | |||||||
\(72\) | 2.00503 | + | 2.23156i | 0.236295 | + | 0.262991i | ||||
\(73\) | −0.868139 | + | 0.868139i | −0.101608 | + | 0.101608i | −0.756083 | − | 0.654475i | \(-0.772890\pi\) |
0.654475 | + | 0.756083i | \(0.272890\pi\) | |||||||
\(74\) | − | 11.3410i | − | 1.31837i | ||||||
\(75\) | 1.56976 | + | 0.0419365i | 0.181261 | + | 0.00484241i | ||||
\(76\) | −4.90374 | + | 4.90374i | −0.562497 | + | 0.562497i | ||||
\(77\) | 5.08746 | 0.579770 | ||||||||
\(78\) | −0.135495 | − | 6.24353i | −0.0153418 | − | 0.706940i | ||||
\(79\) | 12.6610 | 1.42448 | 0.712239 | − | 0.701937i | \(-0.247681\pi\) | ||||
0.712239 | + | 0.701937i | \(0.247681\pi\) | |||||||
\(80\) | −1.43062 | + | 1.43062i | −0.159949 | + | 0.159949i | ||||
\(81\) | 8.94869 | + | 0.959690i | 0.994299 | + | 0.106632i | ||||
\(82\) | 0.262219i | 0.0289573i | ||||||||
\(83\) | −0.232559 | + | 0.232559i | −0.0255266 | + | 0.0255266i | −0.719755 | − | 0.694228i | \(-0.755746\pi\) |
0.694228 | + | 0.719755i | \(0.255746\pi\) | |||||||
\(84\) | 1.25702 | − | 1.19160i | 0.137152 | − | 0.130014i | ||||
\(85\) | 5.87003 | − | 5.87003i | 0.636694 | − | 0.636694i | ||||
\(86\) | 5.80804 | + | 5.80804i | 0.626297 | + | 0.626297i | ||||
\(87\) | 4.49051 | + | 0.119965i | 0.481434 | + | 0.0128616i | ||||
\(88\) | 5.08746i | 0.542325i | ||||||||
\(89\) | 3.93141 | + | 3.93141i | 0.416728 | + | 0.416728i | 0.884074 | − | 0.467346i | \(-0.154790\pi\) |
−0.467346 | + | 0.884074i | \(0.654790\pi\) | |||||||
\(90\) | −0.324071 | + | 6.06097i | −0.0341601 | + | 0.638882i | ||||
\(91\) | −3.60133 | + | 0.174466i | −0.377522 | + | 0.0182890i | ||||
\(92\) | − | 4.97697i | − | 0.518885i | ||||||
\(93\) | −1.78176 | + | 1.68904i | −0.184760 | + | 0.175145i | ||||
\(94\) | 3.62305 | 0.373689 | ||||||||
\(95\) | −14.0308 | −1.43953 | ||||||||
\(96\) | 1.19160 | + | 1.25702i | 0.121617 | + | 0.128294i | ||||
\(97\) | 7.65788 | + | 7.65788i | 0.777540 | + | 0.777540i | 0.979412 | − | 0.201872i | \(-0.0647025\pi\) |
−0.201872 | + | 0.979412i | \(0.564702\pi\) | |||||||
\(98\) | −0.707107 | − | 0.707107i | −0.0714286 | − | 0.0714286i | ||||
\(99\) | 10.2005 | + | 11.3530i | 1.02519 | + | 1.14101i | ||||
\(100\) | 0.906626 | 0.0906626 | ||||||||
\(101\) | 3.05876 | 0.304358 | 0.152179 | − | 0.988353i | \(-0.451371\pi\) | ||||
0.152179 | + | 0.988353i | \(0.451371\pi\) | |||||||
\(102\) | −4.88928 | − | 5.15769i | −0.484111 | − | 0.510687i | ||||
\(103\) | 8.89812i | 0.876758i | 0.898790 | + | 0.438379i | \(0.144447\pi\) | ||||
−0.898790 | + | 0.438379i | \(0.855553\pi\) | |||||||
\(104\) | −0.174466 | − | 3.60133i | −0.0171078 | − | 0.353139i | ||||
\(105\) | 3.50305 | + | 0.0935847i | 0.341863 | + | 0.00913293i | ||||
\(106\) | −5.20768 | − | 5.20768i | −0.505814 | − | 0.505814i | ||||
\(107\) | − | 16.1853i | − | 1.56469i | −0.622844 | − | 0.782346i | \(-0.714023\pi\) | ||
0.622844 | − | 0.782346i | \(-0.285977\pi\) | |||||||
\(108\) | 5.17948 | + | 0.415904i | 0.498396 | + | 0.0400204i | ||||
\(109\) | 1.55437 | + | 1.55437i | 0.148882 | + | 0.148882i | 0.777618 | − | 0.628736i | \(-0.216428\pi\) |
−0.628736 | + | 0.777618i | \(0.716428\pi\) | |||||||
\(110\) | −7.27824 | + | 7.27824i | −0.693953 | + | 0.693953i | ||||
\(111\) | −13.5140 | − | 14.2559i | −1.28269 | − | 1.35311i | ||||
\(112\) | 0.707107 | − | 0.707107i | 0.0668153 | − | 0.0668153i | ||||
\(113\) | − | 1.67224i | − | 0.157311i | −0.996902 | − | 0.0786557i | \(-0.974937\pi\) | ||
0.996902 | − | 0.0786557i | \(-0.0250628\pi\) | |||||||
\(114\) | −0.320779 | + | 12.0074i | −0.0300437 | + | 1.12459i | ||||
\(115\) | 7.12018 | − | 7.12018i | 0.663960 | − | 0.663960i | ||||
\(116\) | 2.59352 | 0.240803 | ||||||||
\(117\) | −7.61011 | − | 7.68676i | −0.703555 | − | 0.710641i | ||||
\(118\) | −1.89465 | −0.174417 | ||||||||
\(119\) | −2.90134 | + | 2.90134i | −0.265966 | + | 0.265966i | ||||
\(120\) | −0.0935847 | + | 3.50305i | −0.00854308 | + | 0.319783i | ||||
\(121\) | 14.8822i | 1.35293i | ||||||||
\(122\) | −7.16926 | + | 7.16926i | −0.649075 | + | 0.649075i | ||||
\(123\) | 0.312461 | + | 0.329614i | 0.0281736 | + | 0.0297203i | ||||
\(124\) | −1.00229 | + | 1.00229i | −0.0900085 | + | 0.0900085i | ||||
\(125\) | 8.45017 | + | 8.45017i | 0.755806 | + | 0.755806i | ||||
\(126\) | 0.160177 | − | 2.99572i | 0.0142697 | − | 0.266880i | ||||
\(127\) | 19.5094i | 1.73118i | 0.500754 | + | 0.865590i | \(0.333056\pi\) | ||||
−0.500754 | + | 0.865590i | \(0.666944\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 14.2216 | + | 0.379934i | 1.25215 | + | 0.0334513i | ||||
\(130\) | 4.90255 | − | 5.40174i | 0.429982 | − | 0.473764i | ||||
\(131\) | − | 12.4313i | − | 1.08613i | −0.839691 | − | 0.543064i | \(-0.817264\pi\) | ||
0.839691 | − | 0.543064i | \(-0.182736\pi\) | |||||||
\(132\) | 6.06222 | + | 6.39501i | 0.527648 | + | 0.556615i | ||||
\(133\) | 6.93493 | 0.601335 | ||||||||
\(134\) | 4.43825 | 0.383407 | ||||||||
\(135\) | 6.81489 | + | 8.00490i | 0.586532 | + | 0.688952i | ||||
\(136\) | −2.90134 | − | 2.90134i | −0.248788 | − | 0.248788i | ||||
\(137\) | 9.19378 | + | 9.19378i | 0.785477 | + | 0.785477i | 0.980749 | − | 0.195272i | \(-0.0625589\pi\) |
−0.195272 | + | 0.980749i | \(0.562559\pi\) | |||||||
\(138\) | −5.93056 | − | 6.25613i | −0.504843 | − | 0.532557i | ||||
\(139\) | −19.0489 | −1.61570 | −0.807852 | − | 0.589385i | \(-0.799370\pi\) | ||||
−0.807852 | + | 0.589385i | \(0.799370\pi\) | |||||||
\(140\) | 2.02321 | 0.170992 | ||||||||
\(141\) | 4.55423 | − | 4.31722i | 0.383535 | − | 0.363576i | ||||
\(142\) | − | 13.3514i | − | 1.12042i | ||||||
\(143\) | −0.887589 | − | 18.3216i | −0.0742239 | − | 1.53213i | ||||
\(144\) | 2.99572 | + | 0.160177i | 0.249643 | + | 0.0133481i | ||||
\(145\) | 3.71036 | + | 3.71036i | 0.308129 | + | 0.308129i | ||||
\(146\) | 1.22773i | 0.101608i | ||||||||
\(147\) | −1.73143 | − | 0.0462556i | −0.142806 | − | 0.00381510i | ||||
\(148\) | −8.01932 | − | 8.01932i | −0.659184 | − | 0.659184i | ||||
\(149\) | −4.55291 | + | 4.55291i | −0.372989 | + | 0.372989i | −0.868565 | − | 0.495576i | \(-0.834957\pi\) |
0.495576 | + | 0.868565i | \(0.334957\pi\) | |||||||
\(150\) | 1.13964 | − | 1.08034i | 0.0930515 | − | 0.0882091i | ||||
\(151\) | 12.4782 | − | 12.4782i | 1.01546 | − | 1.01546i | 0.0155842 | − | 0.999879i | \(-0.495039\pi\) |
0.999879 | − | 0.0155842i | \(-0.00496082\pi\) | |||||||
\(152\) | 6.93493i | 0.562497i | ||||||||
\(153\) | −12.2918 | − | 0.657225i | −0.993734 | − | 0.0531335i | ||||
\(154\) | 3.59738 | − | 3.59738i | 0.289885 | − | 0.289885i | ||||
\(155\) | −2.86781 | −0.230348 | ||||||||
\(156\) | −4.51065 | − | 4.31903i | −0.361141 | − | 0.345799i | ||||
\(157\) | 13.8447 | 1.10493 | 0.552466 | − | 0.833536i | \(-0.313687\pi\) | ||||
0.552466 | + | 0.833536i | \(0.313687\pi\) | |||||||
\(158\) | 8.95271 | − | 8.95271i | 0.712239 | − | 0.712239i | ||||
\(159\) | −12.7516 | − | 0.340662i | −1.01127 | − | 0.0270162i | ||||
\(160\) | 2.02321i | 0.159949i | ||||||||
\(161\) | −3.51925 | + | 3.51925i | −0.277356 | + | 0.277356i | ||||
\(162\) | 7.00628 | − | 5.64907i | 0.550465 | − | 0.443833i | ||||
\(163\) | −2.76536 | + | 2.76536i | −0.216600 | + | 0.216600i | −0.807064 | − | 0.590464i | \(-0.798945\pi\) |
0.590464 | + | 0.807064i | \(0.298945\pi\) | |||||||
\(164\) | 0.185417 | + | 0.185417i | 0.0144786 | + | 0.0144786i | ||||
\(165\) | −0.476108 | + | 17.8216i | −0.0370650 | + | 1.38741i | ||||
\(166\) | 0.328888i | 0.0255266i | ||||||||
\(167\) | −13.6345 | − | 13.6345i | −1.05507 | − | 1.05507i | −0.998392 | − | 0.0566794i | \(-0.981949\pi\) |
−0.0566794 | − | 0.998392i | \(-0.518051\pi\) | |||||||
\(168\) | 0.0462556 | − | 1.73143i | 0.00356870 | − | 0.133583i | ||||
\(169\) | 1.25662 | + | 12.9391i | 0.0966630 | + | 0.995317i | ||||
\(170\) | − | 8.30147i | − | 0.636694i | ||||||
\(171\) | 13.9048 | + | 15.4757i | 1.06332 | + | 1.18346i | ||||
\(172\) | 8.21380 | 0.626297 | ||||||||
\(173\) | −21.9642 | −1.66991 | −0.834955 | − | 0.550318i | \(-0.814506\pi\) | ||||
−0.834955 | + | 0.550318i | \(0.814506\pi\) | |||||||
\(174\) | 3.26010 | − | 3.09044i | 0.247148 | − | 0.234286i | ||||
\(175\) | −0.641081 | − | 0.641081i | −0.0484612 | − | 0.0484612i | ||||
\(176\) | 3.59738 | + | 3.59738i | 0.271162 | + | 0.271162i | ||||
\(177\) | −2.38161 | + | 2.25767i | −0.179012 | + | 0.169697i | ||||
\(178\) | 5.55985 | 0.416728 | ||||||||
\(179\) | −8.56403 | −0.640105 | −0.320053 | − | 0.947400i | \(-0.603701\pi\) | ||||
−0.320053 | + | 0.947400i | \(0.603701\pi\) | |||||||
\(180\) | 4.05660 | + | 4.51491i | 0.302361 | + | 0.336521i | ||||
\(181\) | − | 0.973124i | − | 0.0723318i | −0.999346 | − | 0.0361659i | \(-0.988486\pi\) | ||
0.999346 | − | 0.0361659i | \(-0.0115145\pi\) | |||||||
\(182\) | −2.42316 | + | 2.66989i | −0.179616 | + | 0.197905i | ||||
\(183\) | −0.468979 | + | 17.5548i | −0.0346679 | + | 1.29769i | ||||
\(184\) | −3.51925 | − | 3.51925i | −0.259442 | − | 0.259442i | ||||
\(185\) | − | 22.9453i | − | 1.68697i | ||||||
\(186\) | −0.0655652 | + | 2.45423i | −0.00480747 | + | 0.179953i | ||||
\(187\) | −14.7605 | − | 14.7605i | −1.07939 | − | 1.07939i | ||||
\(188\) | 2.56188 | − | 2.56188i | 0.186844 | − | 0.186844i | ||||
\(189\) | −3.36836 | − | 3.95653i | −0.245012 | − | 0.287796i | ||||
\(190\) | −9.92128 | + | 9.92128i | −0.719765 | + | 0.719765i | ||||
\(191\) | 12.7937i | 0.925721i | 0.886431 | + | 0.462860i | \(0.153177\pi\) | ||||
−0.886431 | + | 0.462860i | \(0.846823\pi\) | |||||||
\(192\) | 1.73143 | + | 0.0462556i | 0.124955 | + | 0.00333821i | ||||
\(193\) | 8.73551 | − | 8.73551i | 0.628796 | − | 0.628796i | −0.318969 | − | 0.947765i | \(-0.603337\pi\) |
0.947765 | + | 0.318969i | \(0.103337\pi\) | |||||||
\(194\) | 10.8299 | 0.777540 | ||||||||
\(195\) | −0.274134 | − | 12.6320i | −0.0196312 | − | 0.904593i | ||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | −6.29467 | + | 6.29467i | −0.448477 | + | 0.448477i | −0.894848 | − | 0.446371i | \(-0.852716\pi\) |
0.446371 | + | 0.894848i | \(0.352716\pi\) | |||||||
\(198\) | 15.2406 | + | 0.814893i | 1.08310 | + | 0.0579119i | ||||
\(199\) | 12.0446i | 0.853823i | 0.904294 | + | 0.426911i | \(0.140398\pi\) | ||||
−0.904294 | + | 0.426911i | \(0.859602\pi\) | |||||||
\(200\) | 0.641081 | − | 0.641081i | 0.0453313 | − | 0.0453313i | ||||
\(201\) | 5.57895 | − | 5.28862i | 0.393509 | − | 0.373031i | ||||
\(202\) | 2.16287 | − | 2.16287i | 0.152179 | − | 0.152179i | ||||
\(203\) | −1.83390 | − | 1.83390i | −0.128714 | − | 0.128714i | ||||
\(204\) | −7.10428 | − | 0.189792i | −0.497399 | − | 0.0132881i | ||||
\(205\) | 0.530525i | 0.0370534i | ||||||||
\(206\) | 6.29192 | + | 6.29192i | 0.438379 | + | 0.438379i | ||||
\(207\) | −14.9096 | − | 0.797195i | −1.03629 | − | 0.0554089i | ||||
\(208\) | −2.66989 | − | 2.42316i | −0.185124 | − | 0.168016i | ||||
\(209\) | 35.2812i | 2.44045i | ||||||||
\(210\) | 2.54321 | − | 2.41086i | 0.175498 | − | 0.166365i | ||||
\(211\) | −23.3032 | −1.60426 | −0.802129 | − | 0.597151i | \(-0.796299\pi\) | ||||
−0.802129 | + | 0.597151i | \(0.796299\pi\) | |||||||
\(212\) | −7.36477 | −0.505814 | ||||||||
\(213\) | −15.9095 | − | 16.7829i | −1.09010 | − | 1.14994i | ||||
\(214\) | −11.4447 | − | 11.4447i | −0.782346 | − | 0.782346i | ||||
\(215\) | 11.7509 | + | 11.7509i | 0.801403 | + | 0.801403i | ||||
\(216\) | 3.95653 | − | 3.36836i | 0.269208 | − | 0.229188i | ||||
\(217\) | 1.41746 | 0.0962231 | ||||||||
\(218\) | 2.19822 | 0.148882 | ||||||||
\(219\) | 1.46297 | + | 1.54328i | 0.0988582 | + | 0.104285i | ||||
\(220\) | 10.2930i | 0.693953i | ||||||||
\(221\) | 10.9549 | + | 9.94251i | 0.736905 | + | 0.668805i | ||||
\(222\) | −19.6362 | − | 0.524586i | −1.31790 | − | 0.0352079i | ||||
\(223\) | 11.2055 | + | 11.2055i | 0.750374 | + | 0.750374i | 0.974549 | − | 0.224175i | \(-0.0719686\pi\) |
−0.224175 | + | 0.974549i | \(0.571969\pi\) | |||||||
\(224\) | − | 1.00000i | − | 0.0668153i | ||||||
\(225\) | 0.145221 | − | 2.71600i | 0.00968137 | − | 0.181067i | ||||
\(226\) | −1.18245 | − | 1.18245i | −0.0786557 | − | 0.0786557i | ||||
\(227\) | 2.20653 | − | 2.20653i | 0.146452 | − | 0.146452i | −0.630079 | − | 0.776531i | \(-0.716977\pi\) |
0.776531 | + | 0.630079i | \(0.216977\pi\) | |||||||
\(228\) | 8.26367 | + | 8.71732i | 0.547275 | + | 0.577318i | ||||
\(229\) | −17.4293 | + | 17.4293i | −1.15176 | + | 1.15176i | −0.165559 | + | 0.986200i | \(0.552943\pi\) |
−0.986200 | + | 0.165559i | \(0.947057\pi\) | |||||||
\(230\) | − | 10.0694i | − | 0.663960i | ||||||
\(231\) | 0.235323 | − | 8.80859i | 0.0154831 | − | 0.579563i | ||||
\(232\) | 1.83390 | − | 1.83390i | 0.120401 | − | 0.120401i | ||||
\(233\) | 7.03391 | 0.460806 | 0.230403 | − | 0.973095i | \(-0.425995\pi\) | ||||
0.230403 | + | 0.973095i | \(0.425995\pi\) | |||||||
\(234\) | −10.8165 | − | 0.0541977i | −0.707098 | − | 0.00354301i | ||||
\(235\) | 7.33018 | 0.478168 | ||||||||
\(236\) | −1.33972 | + | 1.33972i | −0.0872084 | + | 0.0872084i | ||||
\(237\) | 0.585644 | − | 21.9217i | 0.0380417 | − | 1.42397i | ||||
\(238\) | 4.10312i | 0.265966i | ||||||||
\(239\) | 2.66524 | − | 2.66524i | 0.172400 | − | 0.172400i | −0.615633 | − | 0.788033i | \(-0.711100\pi\) |
0.788033 | + | 0.615633i | \(0.211100\pi\) | |||||||
\(240\) | 2.41086 | + | 2.54321i | 0.155620 | + | 0.164163i | ||||
\(241\) | −1.43539 | + | 1.43539i | −0.0924614 | + | 0.0924614i | −0.751825 | − | 0.659363i | \(-0.770826\pi\) |
0.659363 | + | 0.751825i | \(0.270826\pi\) | |||||||
\(242\) | 10.5233 | + | 10.5233i | 0.676465 | + | 0.676465i | ||||
\(243\) | 2.07557 | − | 15.4497i | 0.133148 | − | 0.991096i | ||||
\(244\) | 10.1389i | 0.649075i | ||||||||
\(245\) | −1.43062 | − | 1.43062i | −0.0913993 | − | 0.0913993i | ||||
\(246\) | 0.454015 | + | 0.0121291i | 0.0289470 | + | 0.000773324i | ||||
\(247\) | −1.20991 | − | 24.9750i | −0.0769847 | − | 1.58912i | ||||
\(248\) | 1.41746i | 0.0900085i | ||||||||
\(249\) | 0.391903 | + | 0.413417i | 0.0248358 | + | 0.0261992i | ||||
\(250\) | 11.9503 | 0.755806 | ||||||||
\(251\) | 9.15010 | 0.577549 | 0.288775 | − | 0.957397i | \(-0.406752\pi\) | ||||
0.288775 | + | 0.957397i | \(0.406752\pi\) | |||||||
\(252\) | −2.00503 | − | 2.23156i | −0.126305 | − | 0.140575i | ||||
\(253\) | −17.9040 | − | 17.9040i | −1.12562 | − | 1.12562i | ||||
\(254\) | 13.7952 | + | 13.7952i | 0.865590 | + | 0.865590i | ||||
\(255\) | −9.89204 | − | 10.4351i | −0.619463 | − | 0.653470i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.54392 | −0.221064 | −0.110532 | − | 0.993873i | \(-0.535255\pi\) | ||||
−0.110532 | + | 0.993873i | \(0.535255\pi\) | |||||||
\(258\) | 10.3249 | − | 9.78757i | 0.642799 | − | 0.609348i | ||||
\(259\) | 11.3410i | 0.704698i | ||||||||
\(260\) | −0.352981 | − | 7.28624i | −0.0218910 | − | 0.451873i | ||||
\(261\) | 0.415423 | − | 7.76947i | 0.0257140 | − | 0.480918i | ||||
\(262\) | −8.79026 | − | 8.79026i | −0.543064 | − | 0.543064i | ||||
\(263\) | 27.6411i | 1.70442i | 0.523199 | + | 0.852211i | \(0.324739\pi\) | ||||
−0.523199 | + | 0.852211i | \(0.675261\pi\) | |||||||
\(264\) | 8.80859 | + | 0.235323i | 0.542131 | + | 0.0144831i | ||||
\(265\) | −10.5362 | − | 10.5362i | −0.647235 | − | 0.647235i | ||||
\(266\) | 4.90374 | − | 4.90374i | 0.300667 | − | 0.300667i | ||||
\(267\) | 6.98882 | − | 6.62512i | 0.427709 | − | 0.405451i | ||||
\(268\) | 3.13832 | − | 3.13832i | 0.191703 | − | 0.191703i | ||||
\(269\) | 20.0051i | 1.21973i | 0.792504 | + | 0.609867i | \(0.208777\pi\) | ||||
−0.792504 | + | 0.609867i | \(0.791223\pi\) | |||||||
\(270\) | 10.4792 | + | 0.841461i | 0.637742 | + | 0.0512097i | ||||
\(271\) | −5.17783 | + | 5.17783i | −0.314531 | + | 0.314531i | −0.846662 | − | 0.532131i | \(-0.821391\pi\) |
0.532131 | + | 0.846662i | \(0.321391\pi\) | |||||||
\(272\) | −4.10312 | −0.248788 | ||||||||
\(273\) | 0.135495 | + | 6.24353i | 0.00820052 | + | 0.377876i | ||||
\(274\) | 13.0020 | 0.785477 | ||||||||
\(275\) | 3.26148 | − | 3.26148i | 0.196674 | − | 0.196674i | ||||
\(276\) | −8.61729 | − | 0.230213i | −0.518700 | − | 0.0138572i | ||||
\(277\) | − | 11.9350i | − | 0.717107i | −0.933509 | − | 0.358554i | \(-0.883270\pi\) | ||
0.933509 | − | 0.358554i | \(-0.116730\pi\) | |||||||
\(278\) | −13.4696 | + | 13.4696i | −0.807852 | + | 0.807852i | ||||
\(279\) | 2.84204 | + | 3.16313i | 0.170149 | + | 0.189372i | ||||
\(280\) | 1.43062 | − | 1.43062i | 0.0854962 | − | 0.0854962i | ||||
\(281\) | −19.4431 | − | 19.4431i | −1.15988 | − | 1.15988i | −0.984502 | − | 0.175374i | \(-0.943887\pi\) |
−0.175374 | − | 0.984502i | \(-0.556113\pi\) | |||||||
\(282\) | 0.167586 | − | 6.27306i | 0.00997961 | − | 0.373555i | ||||
\(283\) | 10.9224i | 0.649272i | 0.945839 | + | 0.324636i | \(0.105242\pi\) | ||||
−0.945839 | + | 0.324636i | \(0.894758\pi\) | |||||||
\(284\) | −9.44085 | − | 9.44085i | −0.560211 | − | 0.560211i | ||||
\(285\) | −0.649003 | + | 24.2934i | −0.0384436 | + | 1.43902i | ||||
\(286\) | −13.5830 | − | 12.3277i | −0.803177 | − | 0.728953i | ||||
\(287\) | − | 0.262219i | − | 0.0154783i | ||||||
\(288\) | 2.23156 | − | 2.00503i | 0.131496 | − | 0.118148i | ||||
\(289\) | −0.164395 | −0.00967032 | ||||||||
\(290\) | 5.24724 | 0.308129 | ||||||||
\(291\) | 13.6133 | − | 12.9049i | 0.798027 | − | 0.756498i | ||||
\(292\) | 0.868139 | + | 0.868139i | 0.0508040 | + | 0.0508040i | ||||
\(293\) | −1.81919 | − | 1.81919i | −0.106278 | − | 0.106278i | 0.651968 | − | 0.758246i | \(-0.273944\pi\) |
−0.758246 | + | 0.651968i | \(0.773944\pi\) | |||||||
\(294\) | −1.25702 | + | 1.19160i | −0.0733106 | + | 0.0694955i | ||||
\(295\) | −3.83327 | −0.223182 | ||||||||
\(296\) | −11.3410 | −0.659184 | ||||||||
\(297\) | 20.1287 | − | 17.1364i | 1.16799 | − | 0.994353i | ||||
\(298\) | 6.43879i | 0.372989i | ||||||||
\(299\) | 13.2880 | + | 12.0600i | 0.768462 | + | 0.697447i | ||||
\(300\) | 0.0419365 | − | 1.56976i | 0.00242121 | − | 0.0906303i | ||||
\(301\) | −5.80804 | − | 5.80804i | −0.334770 | − | 0.334770i | ||||
\(302\) | − | 17.6469i | − | 1.01546i | ||||||
\(303\) | 0.141485 | − | 5.29604i | 0.00812809 | − | 0.304250i | ||||
\(304\) | 4.90374 | + | 4.90374i | 0.281249 | + | 0.281249i | ||||
\(305\) | −14.5049 | + | 14.5049i | −0.830549 | + | 0.830549i | ||||
\(306\) | −9.15635 | + | 8.22689i | −0.523434 | + | 0.470300i | ||||
\(307\) | −9.17766 | + | 9.17766i | −0.523797 | + | 0.523797i | −0.918716 | − | 0.394919i | \(-0.870773\pi\) |
0.394919 | + | 0.918716i | \(0.370773\pi\) | |||||||
\(308\) | − | 5.08746i | − | 0.289885i | ||||||
\(309\) | 15.4065 | + | 0.411588i | 0.876445 | + | 0.0234144i | ||||
\(310\) | −2.02785 | + | 2.02785i | −0.115174 | + | 0.115174i | ||||
\(311\) | −2.34596 | −0.133027 | −0.0665135 | − | 0.997786i | \(-0.521188\pi\) | ||||
−0.0665135 | + | 0.997786i | \(0.521188\pi\) | |||||||
\(312\) | −6.24353 | + | 0.135495i | −0.353470 | + | 0.00767089i | ||||
\(313\) | −13.3871 | −0.756683 | −0.378341 | − | 0.925666i | \(-0.623505\pi\) | ||||
−0.378341 | + | 0.925666i | \(0.623505\pi\) | |||||||
\(314\) | 9.78972 | − | 9.78972i | 0.552466 | − | 0.552466i | ||||
\(315\) | 0.324071 | − | 6.06097i | 0.0182593 | − | 0.341497i | ||||
\(316\) | − | 12.6610i | − | 0.712239i | ||||||
\(317\) | −12.9987 | + | 12.9987i | −0.730081 | + | 0.730081i | −0.970636 | − | 0.240555i | \(-0.922671\pi\) |
0.240555 | + | 0.970636i | \(0.422671\pi\) | |||||||
\(318\) | −9.25763 | + | 8.77586i | −0.519142 | + | 0.492126i | ||||
\(319\) | 9.32988 | − | 9.32988i | 0.522373 | − | 0.522373i | ||||
\(320\) | 1.43062 | + | 1.43062i | 0.0799743 | + | 0.0799743i | ||||
\(321\) | −28.0238 | − | 0.748661i | −1.56413 | − | 0.0417862i | ||||
\(322\) | 4.97697i | 0.277356i | ||||||||
\(323\) | −20.1206 | − | 20.1206i | −1.11954 | − | 1.11954i | ||||
\(324\) | 0.959690 | − | 8.94869i | 0.0533161 | − | 0.497149i | ||||
\(325\) | −2.19690 | + | 2.42059i | −0.121862 | + | 0.134270i | ||||
\(326\) | 3.91081i | 0.216600i | ||||||||
\(327\) | 2.76319 | − | 2.61939i | 0.152805 | − | 0.144853i | ||||
\(328\) | 0.262219 | 0.0144786 | ||||||||
\(329\) | −3.62305 | −0.199745 | ||||||||
\(330\) | 12.2651 | + | 12.9384i | 0.675173 | + | 0.712238i | ||||
\(331\) | 0.549427 | + | 0.549427i | 0.0301992 | + | 0.0301992i | 0.722045 | − | 0.691846i | \(-0.243202\pi\) |
−0.691846 | + | 0.722045i | \(0.743202\pi\) | |||||||
\(332\) | 0.232559 | + | 0.232559i | 0.0127633 | + | 0.0127633i | ||||
\(333\) | −25.3082 | + | 22.7391i | −1.38688 | + | 1.24610i | ||||
\(334\) | −19.2821 | −1.05507 | ||||||||
\(335\) | 8.97951 | 0.490603 | ||||||||
\(336\) | −1.19160 | − | 1.25702i | −0.0650071 | − | 0.0685758i | ||||
\(337\) | − | 20.1204i | − | 1.09603i | −0.836470 | − | 0.548013i | \(-0.815384\pi\) | ||
0.836470 | − | 0.548013i | \(-0.184616\pi\) | |||||||
\(338\) | 10.0379 | + | 8.26078i | 0.545990 | + | 0.449327i | ||||
\(339\) | −2.89538 | − | 0.0773505i | −0.157255 | − | 0.00420110i | ||||
\(340\) | −5.87003 | − | 5.87003i | −0.318347 | − | 0.318347i | ||||
\(341\) | 7.21124i | 0.390511i | ||||||||
\(342\) | 20.7751 | + | 1.11082i | 1.12339 | + | 0.0600660i | ||||
\(343\) | 0.707107 | + | 0.707107i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | 5.80804 | − | 5.80804i | 0.313148 | − | 0.313148i | ||||
\(345\) | −11.9988 | − | 12.6575i | −0.645991 | − | 0.681454i | ||||
\(346\) | −15.5311 | + | 15.5311i | −0.834955 | + | 0.834955i | ||||
\(347\) | − | 16.4340i | − | 0.882225i | −0.897452 | − | 0.441113i | \(-0.854584\pi\) | ||
0.897452 | − | 0.441113i | \(-0.145416\pi\) | |||||||
\(348\) | 0.119965 | − | 4.49051i | 0.00643080 | − | 0.240717i | ||||
\(349\) | 9.67441 | − | 9.67441i | 0.517859 | − | 0.517859i | −0.399064 | − | 0.916923i | \(-0.630665\pi\) |
0.916923 | + | 0.399064i | \(0.130665\pi\) | |||||||
\(350\) | −0.906626 | −0.0484612 | ||||||||
\(351\) | −13.6611 | + | 12.8208i | −0.729176 | + | 0.684326i | ||||
\(352\) | 5.08746 | 0.271162 | ||||||||
\(353\) | −2.54751 | + | 2.54751i | −0.135590 | + | 0.135590i | −0.771645 | − | 0.636054i | \(-0.780566\pi\) |
0.636054 | + | 0.771645i | \(0.280566\pi\) | |||||||
\(354\) | −0.0876382 | + | 3.28046i | −0.00465792 | + | 0.174354i | ||||
\(355\) | − | 27.0126i | − | 1.43368i | ||||||
\(356\) | 3.93141 | − | 3.93141i | 0.208364 | − | 0.208364i | ||||
\(357\) | 4.88928 | + | 5.15769i | 0.258768 | + | 0.272974i | ||||
\(358\) | −6.05568 | + | 6.05568i | −0.320053 | + | 0.320053i | ||||
\(359\) | −21.4323 | − | 21.4323i | −1.13115 | − | 1.13115i | −0.989986 | − | 0.141166i | \(-0.954915\pi\) |
−0.141166 | − | 0.989986i | \(-0.545085\pi\) | |||||||
\(360\) | 6.06097 | + | 0.324071i | 0.319441 | + | 0.0170801i | ||||
\(361\) | 29.0933i | 1.53122i | ||||||||
\(362\) | −0.688103 | − | 0.688103i | −0.0361659 | − | 0.0361659i | ||||
\(363\) | 25.7676 | + | 0.688386i | 1.35245 | + | 0.0361309i | ||||
\(364\) | 0.174466 | + | 3.60133i | 0.00914451 | + | 0.188761i | ||||
\(365\) | 2.48396i | 0.130017i | ||||||||
\(366\) | 12.0815 | + | 12.7447i | 0.631509 | + | 0.666177i | ||||
\(367\) | −12.2166 | −0.637703 | −0.318852 | − | 0.947805i | \(-0.603297\pi\) | ||||
−0.318852 | + | 0.947805i | \(0.603297\pi\) | |||||||
\(368\) | −4.97697 | −0.259442 | ||||||||
\(369\) | 0.585157 | − | 0.525758i | 0.0304621 | − | 0.0273699i | ||||
\(370\) | −16.2248 | − | 16.2248i | −0.843485 | − | 0.843485i | ||||
\(371\) | 5.20768 | + | 5.20768i | 0.270369 | + | 0.270369i | ||||
\(372\) | 1.68904 | + | 1.78176i | 0.0875727 | + | 0.0923801i | ||||
\(373\) | 5.78239 | 0.299401 | 0.149700 | − | 0.988731i | \(-0.452169\pi\) | ||||
0.149700 | + | 0.988731i | \(0.452169\pi\) | |||||||
\(374\) | −20.8745 | −1.07939 | ||||||||
\(375\) | 15.0218 | − | 14.2400i | 0.775720 | − | 0.735352i | ||||
\(376\) | − | 3.62305i | − | 0.186844i | ||||||
\(377\) | −6.28452 | + | 6.92442i | −0.323669 | + | 0.356626i | ||||
\(378\) | −5.17948 | − | 0.415904i | −0.266404 | − | 0.0213918i | ||||
\(379\) | 18.4746 | + | 18.4746i | 0.948977 | + | 0.948977i | 0.998760 | − | 0.0497833i | \(-0.0158531\pi\) |
−0.0497833 | + | 0.998760i | \(0.515853\pi\) | |||||||
\(380\) | 14.0308i | 0.719765i | ||||||||
\(381\) | 33.7792 | + | 0.902419i | 1.73056 | + | 0.0462323i | ||||
\(382\) | 9.04652 | + | 9.04652i | 0.462860 | + | 0.462860i | ||||
\(383\) | −22.5886 | + | 22.5886i | −1.15422 | + | 1.15422i | −0.168528 | + | 0.985697i | \(0.553901\pi\) |
−0.985697 | + | 0.168528i | \(0.946099\pi\) | |||||||
\(384\) | 1.25702 | − | 1.19160i | 0.0641468 | − | 0.0608086i | ||||
\(385\) | 7.27824 | − | 7.27824i | 0.370934 | − | 0.370934i | ||||
\(386\) | − | 12.3539i | − | 0.628796i | ||||||
\(387\) | 1.31566 | − | 24.6063i | 0.0668788 | − | 1.25081i | ||||
\(388\) | 7.65788 | − | 7.65788i | 0.388770 | − | 0.388770i | ||||
\(389\) | 5.36671 | 0.272103 | 0.136051 | − | 0.990702i | \(-0.456559\pi\) | ||||
0.136051 | + | 0.990702i | \(0.456559\pi\) | |||||||
\(390\) | −9.12599 | − | 8.73830i | −0.462112 | − | 0.442481i | ||||
\(391\) | 20.4211 | 1.03274 | ||||||||
\(392\) | −0.707107 | + | 0.707107i | −0.0357143 | + | 0.0357143i | ||||
\(393\) | −21.5240 | − | 0.575017i | −1.08574 | − | 0.0290058i | ||||
\(394\) | 8.90201i | 0.448477i | ||||||||
\(395\) | 18.1132 | − | 18.1132i | 0.911374 | − | 0.911374i | ||||
\(396\) | 11.3530 | − | 10.2005i | 0.570507 | − | 0.512595i | ||||
\(397\) | 14.5043 | − | 14.5043i | 0.727949 | − | 0.727949i | −0.242262 | − | 0.970211i | \(-0.577889\pi\) |
0.970211 | + | 0.242262i | \(0.0778893\pi\) | |||||||
\(398\) | 8.51685 | + | 8.51685i | 0.426911 | + | 0.426911i | ||||
\(399\) | 0.320779 | − | 12.0074i | 0.0160590 | − | 0.601120i | ||||
\(400\) | − | 0.906626i | − | 0.0453313i | ||||||
\(401\) | 24.1397 | + | 24.1397i | 1.20548 | + | 1.20548i | 0.972476 | + | 0.233004i | \(0.0748554\pi\) |
0.233004 | + | 0.972476i | \(0.425145\pi\) | |||||||
\(402\) | 0.205294 | − | 7.68454i | 0.0102391 | − | 0.383270i | ||||
\(403\) | −0.247298 | − | 5.10472i | −0.0123188 | − | 0.254284i | ||||
\(404\) | − | 3.05876i | − | 0.152179i | ||||||
\(405\) | 14.1752 | − | 11.4293i | 0.704370 | − | 0.567924i | ||||
\(406\) | −2.59352 | −0.128714 | ||||||||
\(407\) | −57.6970 | −2.85994 | ||||||||
\(408\) | −5.15769 | + | 4.88928i | −0.255344 | + | 0.242055i | ||||
\(409\) | −11.7934 | − | 11.7934i | −0.583147 | − | 0.583147i | 0.352620 | − | 0.935767i | \(-0.385291\pi\) |
−0.935767 | + | 0.352620i | \(0.885291\pi\) | |||||||
\(410\) | 0.375138 | + | 0.375138i | 0.0185267 | + | 0.0185267i | ||||
\(411\) | 16.3437 | − | 15.4931i | 0.806174 | − | 0.764220i | ||||
\(412\) | 8.89812 | 0.438379 | ||||||||
\(413\) | 1.89465 | 0.0932297 | ||||||||
\(414\) | −11.1064 | + | 9.97898i | −0.545849 | + | 0.490440i | ||||
\(415\) | 0.665409i | 0.0326636i | ||||||||
\(416\) | −3.60133 | + | 0.174466i | −0.176570 | + | 0.00855391i | ||||
\(417\) | −0.881117 | + | 32.9818i | −0.0431485 | + | 1.61513i | ||||
\(418\) | 24.9476 | + | 24.9476i | 1.22022 | + | 1.22022i | ||||
\(419\) | 37.7287i | 1.84317i | 0.388177 | + | 0.921585i | \(0.373105\pi\) | ||||
−0.388177 | + | 0.921585i | \(0.626895\pi\) | |||||||
\(420\) | 0.0935847 | − | 3.50305i | 0.00456647 | − | 0.170931i | ||||
\(421\) | −2.50345 | − | 2.50345i | −0.122011 | − | 0.122011i | 0.643465 | − | 0.765476i | \(-0.277496\pi\) |
−0.765476 | + | 0.643465i | \(0.777496\pi\) | |||||||
\(422\) | −16.4778 | + | 16.4778i | −0.802129 | + | 0.802129i | ||||
\(423\) | −7.26432 | − | 8.08503i | −0.353204 | − | 0.393108i | ||||
\(424\) | −5.20768 | + | 5.20768i | −0.252907 | + | 0.252907i | ||||
\(425\) | 3.72000i | 0.180446i | ||||||||
\(426\) | −23.1170 | − | 0.617576i | −1.12002 | − | 0.0299216i | ||||
\(427\) | 7.16926 | − | 7.16926i | 0.346945 | − | 0.346945i | ||||
\(428\) | −16.1853 | −0.782346 | ||||||||
\(429\) | −31.7637 | + | 0.689325i | −1.53357 | + | 0.0332809i | ||||
\(430\) | 16.6182 | 0.801403 | ||||||||
\(431\) | −3.13738 | + | 3.13738i | −0.151122 | + | 0.151122i | −0.778619 | − | 0.627497i | \(-0.784080\pi\) |
0.627497 | + | 0.778619i | \(0.284080\pi\) | |||||||
\(432\) | 0.415904 | − | 5.17948i | 0.0200102 | − | 0.249198i | ||||
\(433\) | 32.9365i | 1.58283i | 0.611280 | + | 0.791415i | \(0.290655\pi\) | ||||
−0.611280 | + | 0.791415i | \(0.709345\pi\) | |||||||
\(434\) | 1.00229 | − | 1.00229i | 0.0481116 | − | 0.0481116i | ||||
\(435\) | 6.59586 | − | 6.25261i | 0.316247 | − | 0.299790i | ||||
\(436\) | 1.55437 | − | 1.55437i | 0.0744410 | − | 0.0744410i | ||||
\(437\) | −24.4057 | − | 24.4057i | −1.16749 | − | 1.16749i | ||||
\(438\) | 2.12574 | + | 0.0567895i | 0.101572 | + | 0.00271351i | ||||
\(439\) | 15.3322i | 0.731768i | 0.930660 | + | 0.365884i | \(0.119233\pi\) | ||||
−0.930660 | + | 0.365884i | \(0.880767\pi\) | |||||||
\(440\) | 7.27824 | + | 7.27824i | 0.346977 | + | 0.346977i | ||||
\(441\) | −0.160177 | + | 2.99572i | −0.00762747 | + | 0.142653i | ||||
\(442\) | 14.7767 | − | 0.715856i | 0.702855 | − | 0.0340498i | ||||
\(443\) | − | 26.4837i | − | 1.25828i | −0.777292 | − | 0.629140i | \(-0.783407\pi\) | ||
0.777292 | − | 0.629140i | \(-0.216593\pi\) | |||||||
\(444\) | −14.2559 | + | 13.5140i | −0.676553 | + | 0.641345i | ||||
\(445\) | 11.2487 | 0.533241 | ||||||||
\(446\) | 15.8469 | 0.750374 | ||||||||
\(447\) | 7.67247 | + | 8.09366i | 0.362895 | + | 0.382817i | ||||
\(448\) | −0.707107 | − | 0.707107i | −0.0334077 | − | 0.0334077i | ||||
\(449\) | 3.73104 | + | 3.73104i | 0.176079 | + | 0.176079i | 0.789644 | − | 0.613565i | \(-0.210265\pi\) |
−0.613565 | + | 0.789644i | \(0.710265\pi\) | |||||||
\(450\) | −1.81781 | − | 2.02319i | −0.0856926 | − | 0.0953740i | ||||
\(451\) | 1.33403 | 0.0628170 | ||||||||
\(452\) | −1.67224 | −0.0786557 | ||||||||
\(453\) | −21.0280 | − | 22.1824i | −0.987982 | − | 1.04222i | ||||
\(454\) | − | 3.12050i | − | 0.146452i | ||||||
\(455\) | −4.90255 | + | 5.40174i | −0.229835 | + | 0.253238i | ||||
\(456\) | 12.0074 | + | 0.320779i | 0.562296 | + | 0.0150219i | ||||
\(457\) | 21.6075 | + | 21.6075i | 1.01075 | + | 1.01075i | 0.999942 | + | 0.0108124i | \(0.00344174\pi\) |
0.0108124 | + | 0.999942i | \(0.496558\pi\) | |||||||
\(458\) | 24.6487i | 1.15176i | ||||||||
\(459\) | −1.70651 | + | 21.2520i | −0.0796529 | + | 0.991960i | ||||
\(460\) | −7.12018 | − | 7.12018i | −0.331980 | − | 0.331980i | ||||
\(461\) | −7.48400 | + | 7.48400i | −0.348565 | + | 0.348565i | −0.859575 | − | 0.511010i | \(-0.829271\pi\) |
0.511010 | + | 0.859575i | \(0.329271\pi\) | |||||||
\(462\) | −6.06222 | − | 6.39501i | −0.282040 | − | 0.297523i | ||||
\(463\) | −0.469041 | + | 0.469041i | −0.0217982 | + | 0.0217982i | −0.717922 | − | 0.696124i | \(-0.754907\pi\) |
0.696124 | + | 0.717922i | \(0.254907\pi\) | |||||||
\(464\) | − | 2.59352i | − | 0.120401i | ||||||
\(465\) | −0.132652 | + | 4.96542i | −0.00615159 | + | 0.230266i | ||||
\(466\) | 4.97372 | − | 4.97372i | 0.230403 | − | 0.230403i | ||||
\(467\) | 32.9039 | 1.52261 | 0.761306 | − | 0.648393i | \(-0.224559\pi\) | ||||
0.761306 | + | 0.648393i | \(0.224559\pi\) | |||||||
\(468\) | −7.68676 | + | 7.61011i | −0.355320 | + | 0.351777i | ||||
\(469\) | −4.43825 | −0.204940 | ||||||||
\(470\) | 5.18322 | − | 5.18322i | 0.239084 | − | 0.239084i | ||||
\(471\) | 0.640397 | − | 23.9713i | 0.0295079 | − | 1.10454i | ||||
\(472\) | 1.89465i | 0.0872084i | ||||||||
\(473\) | 29.5481 | − | 29.5481i | 1.35862 | − | 1.35862i | ||||
\(474\) | −15.0869 | − | 15.9151i | −0.692964 | − | 0.731006i | ||||
\(475\) | 4.44586 | − | 4.44586i | 0.203990 | − | 0.203990i | ||||
\(476\) | 2.90134 | + | 2.90134i | 0.132983 | + | 0.132983i | ||||
\(477\) | −1.17967 | + | 22.0628i | −0.0540132 | + | 1.01019i | ||||
\(478\) | − | 3.76921i | − | 0.172400i | ||||||
\(479\) | −8.56901 | − | 8.56901i | −0.391528 | − | 0.391528i | 0.483704 | − | 0.875232i | \(-0.339291\pi\) |
−0.875232 | + | 0.483704i | \(0.839291\pi\) | |||||||
\(480\) | 3.50305 | + | 0.0935847i | 0.159892 | + | 0.00427154i | ||||
\(481\) | 40.8428 | − | 1.97863i | 1.86227 | − | 0.0902176i | ||||
\(482\) | 2.02994i | 0.0924614i | ||||||||
\(483\) | 5.93056 | + | 6.25613i | 0.269850 | + | 0.284664i | ||||
\(484\) | 14.8822 | 0.676465 | ||||||||
\(485\) | 21.9111 | 0.994932 | ||||||||
\(486\) | −9.45691 | − | 12.3922i | −0.428974 | − | 0.562122i | ||||
\(487\) | −25.4916 | − | 25.4916i | −1.15513 | − | 1.15513i | −0.985509 | − | 0.169624i | \(-0.945745\pi\) |
−0.169624 | − | 0.985509i | \(-0.554255\pi\) | |||||||
\(488\) | 7.16926 | + | 7.16926i | 0.324537 | + | 0.324537i | ||||
\(489\) | 4.66012 | + | 4.91595i | 0.210738 | + | 0.222307i | ||||
\(490\) | −2.02321 | −0.0913993 | ||||||||
\(491\) | 42.6747 | 1.92588 | 0.962941 | − | 0.269712i | \(-0.0869287\pi\) | ||||
0.962941 | + | 0.269712i | \(0.0869287\pi\) | |||||||
\(492\) | 0.329614 | − | 0.312461i | 0.0148601 | − | 0.0140868i | ||||
\(493\) | 10.6415i | 0.479271i | ||||||||
\(494\) | −18.5155 | − | 16.8044i | −0.833052 | − | 0.756067i | ||||
\(495\) | 30.8349 | + | 1.64870i | 1.38593 | + | 0.0741035i | ||||
\(496\) | 1.00229 | + | 1.00229i | 0.0450042 | + | 0.0450042i | ||||
\(497\) | 13.3514i | 0.598891i | ||||||||
\(498\) | 0.569447 | + | 0.0152129i | 0.0255175 | + | 0.000681706i | ||||
\(499\) | 21.6317 | + | 21.6317i | 0.968368 | + | 0.968368i | 0.999515 | − | 0.0311468i | \(-0.00991594\pi\) |
−0.0311468 | + | 0.999515i | \(0.509916\pi\) | |||||||
\(500\) | 8.45017 | − | 8.45017i | 0.377903 | − | 0.377903i | ||||
\(501\) | −24.2380 | + | 22.9766i | −1.08287 | + | 1.02652i | ||||
\(502\) | 6.47010 | − | 6.47010i | 0.288775 | − | 0.288775i | ||||
\(503\) | 9.32655i | 0.415850i | 0.978145 | + | 0.207925i | \(0.0666710\pi\) | ||||
−0.978145 | + | 0.207925i | \(0.933329\pi\) | |||||||
\(504\) | −2.99572 | − | 0.160177i | −0.133440 | − | 0.00713485i | ||||
\(505\) | 4.37594 | − | 4.37594i | 0.194727 | − | 0.194727i | ||||
\(506\) | −25.3201 | −1.12562 | ||||||||
\(507\) | 22.4614 | − | 1.57725i | 0.997544 | − | 0.0700479i | ||||
\(508\) | 19.5094 | 0.865590 | ||||||||
\(509\) | 1.25938 | − | 1.25938i | 0.0558209 | − | 0.0558209i | −0.678645 | − | 0.734466i | \(-0.737433\pi\) |
0.734466 | + | 0.678645i | \(0.237433\pi\) | |||||||
\(510\) | −14.3734 | − | 0.383989i | −0.636467 | − | 0.0170033i | ||||
\(511\) | − | 1.22773i | − | 0.0543117i | ||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 27.4383 | − | 23.3593i | 1.21143 | − | 1.03134i | ||||
\(514\) | −2.50593 | + | 2.50593i | −0.110532 | + | 0.110532i | ||||
\(515\) | 12.7299 | + | 12.7299i | 0.560945 | + | 0.560945i | ||||
\(516\) | 0.379934 | − | 14.2216i | 0.0167257 | − | 0.626073i | ||||
\(517\) | − | 18.4321i | − | 0.810643i | ||||||
\(518\) | 8.01932 | + | 8.01932i | 0.352349 | + | 0.352349i | ||||
\(519\) | −1.01597 | + | 38.0296i | −0.0445961 | + | 1.66931i | ||||
\(520\) | −5.40174 | − | 4.90255i | −0.236882 | − | 0.214991i | ||||
\(521\) | − | 38.5430i | − | 1.68860i | −0.535872 | − | 0.844299i | \(-0.680017\pi\) | ||
0.535872 | − | 0.844299i | \(-0.319983\pi\) | |||||||
\(522\) | −5.20010 | − | 5.78760i | −0.227602 | − | 0.253316i | ||||
\(523\) | 7.07627 | 0.309424 | 0.154712 | − | 0.987960i | \(-0.450555\pi\) | ||||
0.154712 | + | 0.987960i | \(0.450555\pi\) | |||||||
\(524\) | −12.4313 | −0.543064 | ||||||||
\(525\) | −1.13964 | + | 1.08034i | −0.0497381 | + | 0.0471497i | ||||
\(526\) | 19.5452 | + | 19.5452i | 0.852211 | + | 0.852211i | ||||
\(527\) | −4.11253 | − | 4.11253i | −0.179144 | − | 0.179144i | ||||
\(528\) | 6.39501 | − | 6.06222i | 0.278307 | − | 0.263824i | ||||
\(529\) | 1.77022 | 0.0769662 | ||||||||
\(530\) | −14.9005 | −0.647235 | ||||||||
\(531\) | 3.79884 | + | 4.22802i | 0.164855 | + | 0.183480i | ||||
\(532\) | − | 6.93493i | − | 0.300667i | ||||||
\(533\) | −0.944338 | + | 0.0457484i | −0.0409038 | + | 0.00198158i | ||||
\(534\) | 0.257174 | − | 9.62650i | 0.0111290 | − | 0.416580i | ||||
\(535\) | −23.1551 | − | 23.1551i | −1.00108 | − | 1.00108i | ||||
\(536\) | − | 4.43825i | − | 0.191703i | ||||||
\(537\) | −0.396134 | + | 14.8280i | −0.0170944 | + | 0.639877i | ||||
\(538\) | 14.1458 | + | 14.1458i | 0.609867 | + | 0.609867i | ||||
\(539\) | −3.59738 | + | 3.59738i | −0.154950 | + | 0.154950i | ||||
\(540\) | 8.00490 | − | 6.81489i | 0.344476 | − | 0.293266i | ||||
\(541\) | 6.35434 | − | 6.35434i | 0.273194 | − | 0.273194i | −0.557190 | − | 0.830385i | \(-0.688121\pi\) |
0.830385 | + | 0.557190i | \(0.188121\pi\) | |||||||
\(542\) | 7.32256i | 0.314531i | ||||||||
\(543\) | −1.68490 | − | 0.0450124i | −0.0723060 | − | 0.00193167i | ||||
\(544\) | −2.90134 | + | 2.90134i | −0.124394 | + | 0.124394i | ||||
\(545\) | 4.44745 | 0.190508 | ||||||||
\(546\) | 4.51065 | + | 4.31903i | 0.193038 | + | 0.184837i | ||||
\(547\) | 10.2100 | 0.436548 | 0.218274 | − | 0.975888i | \(-0.429957\pi\) | ||||
0.218274 | + | 0.975888i | \(0.429957\pi\) | |||||||
\(548\) | 9.19378 | − | 9.19378i | 0.392739 | − | 0.392739i | ||||
\(549\) | 30.3732 | + | 1.62401i | 1.29630 | + | 0.0693112i | ||||
\(550\) | − | 4.61242i | − | 0.196674i | ||||||
\(551\) | 12.7180 | − | 12.7180i | 0.541803 | − | 0.541803i | ||||
\(552\) | −6.25613 | + | 5.93056i | −0.266279 | + | 0.252421i | ||||
\(553\) | −8.95271 | + | 8.95271i | −0.380708 | + | 0.380708i | ||||
\(554\) | −8.43935 | − | 8.43935i | −0.358554 | − | 0.358554i | ||||
\(555\) | −39.7282 | − | 1.06135i | −1.68637 | − | 0.0450517i | ||||
\(556\) | 19.0489i | 0.807852i | ||||||||
\(557\) | 1.56817 | + | 1.56817i | 0.0664457 | + | 0.0664457i | 0.739549 | − | 0.673103i | \(-0.235039\pi\) |
−0.673103 | + | 0.739549i | \(0.735039\pi\) | |||||||
\(558\) | 4.24630 | + | 0.227044i | 0.179760 | + | 0.00961152i | ||||
\(559\) | −19.9033 | + | 21.9299i | −0.841821 | + | 0.927538i | ||||
\(560\) | − | 2.02321i | − | 0.0854962i | ||||||
\(561\) | −26.2395 | + | 24.8740i | −1.10783 | + | 1.05018i | ||||
\(562\) | −27.4966 | −1.15988 | ||||||||
\(563\) | 20.2496 | 0.853418 | 0.426709 | − | 0.904389i | \(-0.359673\pi\) | ||||
0.426709 | + | 0.904389i | \(0.359673\pi\) | |||||||
\(564\) | −4.31722 | − | 4.55423i | −0.181788 | − | 0.191767i | ||||
\(565\) | −2.39235 | − | 2.39235i | −0.100647 | − | 0.100647i | ||||
\(566\) | 7.72333 | + | 7.72333i | 0.324636 | + | 0.324636i | ||||
\(567\) | −7.00628 | + | 5.64907i | −0.294236 | + | 0.237239i | ||||
\(568\) | −13.3514 | −0.560211 | ||||||||
\(569\) | −16.8511 | −0.706437 | −0.353218 | − | 0.935541i | \(-0.614913\pi\) | ||||
−0.353218 | + | 0.935541i | \(0.614913\pi\) | |||||||
\(570\) | 16.7191 | + | 17.6370i | 0.700287 | + | 0.738731i | ||||
\(571\) | − | 8.55891i | − | 0.358179i | −0.983833 | − | 0.179090i | \(-0.942685\pi\) | ||
0.983833 | − | 0.179090i | \(-0.0573152\pi\) | |||||||
\(572\) | −18.3216 | + | 0.887589i | −0.766065 | + | 0.0371120i | ||||
\(573\) | 22.1515 | + | 0.591781i | 0.925391 | + | 0.0247220i | ||||
\(574\) | −0.185417 | − | 0.185417i | −0.00773916 | − | 0.00773916i | ||||
\(575\) | 4.51225i | 0.188174i | ||||||||
\(576\) | 0.160177 | − | 2.99572i | 0.00667404 | − | 0.124822i | ||||
\(577\) | −11.4457 | − | 11.4457i | −0.476492 | − | 0.476492i | 0.427516 | − | 0.904008i | \(-0.359389\pi\) |
−0.904008 | + | 0.427516i | \(0.859389\pi\) | |||||||
\(578\) | −0.116245 | + | 0.116245i | −0.00483516 | + | 0.00483516i | ||||
\(579\) | −14.7209 | − | 15.5290i | −0.611779 | − | 0.645364i | ||||
\(580\) | 3.71036 | − | 3.71036i | 0.154064 | − | 0.154064i | ||||
\(581\) | − | 0.328888i | − | 0.0136446i | ||||||
\(582\) | 0.500942 | − | 18.7512i | 0.0207647 | − | 0.777263i | ||||
\(583\) | −26.4938 | + | 26.4938i | −1.09726 | + | 1.09726i | ||||
\(584\) | 1.22773 | 0.0508040 | ||||||||
\(585\) | −21.8841 | − | 0.109653i | −0.904795 | − | 0.00453360i | ||||
\(586\) | −2.57273 | −0.106278 | ||||||||
\(587\) | −19.6840 | + | 19.6840i | −0.812445 | + | 0.812445i | −0.985000 | − | 0.172555i | \(-0.944798\pi\) |
0.172555 | + | 0.985000i | \(0.444798\pi\) | |||||||
\(588\) | −0.0462556 | + | 1.73143i | −0.00190755 | + | 0.0714031i | ||||
\(589\) | 9.82995i | 0.405036i | ||||||||
\(590\) | −2.71053 | + | 2.71053i | −0.111591 | + | 0.111591i | ||||
\(591\) | 10.6076 | + | 11.1900i | 0.436340 | + | 0.460294i | ||||
\(592\) | −8.01932 | + | 8.01932i | −0.329592 | + | 0.329592i | ||||
\(593\) | −18.7038 | − | 18.7038i | −0.768073 | − | 0.768073i | 0.209694 | − | 0.977767i | \(-0.432753\pi\) |
−0.977767 | + | 0.209694i | \(0.932753\pi\) | |||||||
\(594\) | 2.11590 | − | 26.3504i | 0.0868163 | − | 1.08117i | ||||
\(595\) | 8.30147i | 0.340327i | ||||||||
\(596\) | 4.55291 | + | 4.55291i | 0.186495 | + | 0.186495i | ||||
\(597\) | 20.8545 | + | 0.557132i | 0.853518 | + | 0.0228019i | ||||
\(598\) | 17.9237 | − | 0.868312i | 0.732955 | − | 0.0355079i | ||||
\(599\) | − | 6.41962i | − | 0.262299i | −0.991363 | − | 0.131149i | \(-0.958133\pi\) | ||
0.991363 | − | 0.131149i | \(-0.0418667\pi\) | |||||||
\(600\) | −1.08034 | − | 1.13964i | −0.0441045 | − | 0.0465257i | ||||
\(601\) | 35.9129 | 1.46492 | 0.732459 | − | 0.680812i | \(-0.238373\pi\) | ||||
0.732459 | + | 0.680812i | \(0.238373\pi\) | |||||||
\(602\) | −8.21380 | −0.334770 | ||||||||
\(603\) | −8.89884 | − | 9.90421i | −0.362389 | − | 0.403331i | ||||
\(604\) | −12.4782 | − | 12.4782i | −0.507731 | − | 0.507731i | ||||
\(605\) | 21.2909 | + | 21.2909i | 0.865597 | + | 0.865597i | ||||
\(606\) | −3.64482 | − | 3.84491i | −0.148061 | − | 0.156189i | ||||
\(607\) | −3.97978 | −0.161534 | −0.0807672 | − | 0.996733i | \(-0.525737\pi\) | ||||
−0.0807672 | + | 0.996733i | \(0.525737\pi\) | |||||||
\(608\) | 6.93493 | 0.281249 | ||||||||
\(609\) | −3.26010 | + | 3.09044i | −0.132106 | + | 0.125231i | ||||
\(610\) | 20.5130i | 0.830549i | ||||||||
\(611\) | 0.632099 | + | 13.0478i | 0.0255720 | + | 0.527857i | ||||
\(612\) | −0.657225 | + | 12.2918i | −0.0265668 | + | 0.496867i | ||||
\(613\) | −10.2278 | − | 10.2278i | −0.413096 | − | 0.413096i | 0.469720 | − | 0.882816i | \(-0.344355\pi\) |
−0.882816 | + | 0.469720i | \(0.844355\pi\) | |||||||
\(614\) | 12.9792i | 0.523797i | ||||||||
\(615\) | 0.918568 | + | 0.0245397i | 0.0370402 | + | 0.000989537i | ||||
\(616\) | −3.59738 | − | 3.59738i | −0.144942 | − | 0.144942i | ||||
\(617\) | 28.6473 | − | 28.6473i | 1.15330 | − | 1.15330i | 0.167410 | − | 0.985887i | \(-0.446460\pi\) |
0.985887 | − | 0.167410i | \(-0.0535403\pi\) | |||||||
\(618\) | 11.1851 | − | 10.6030i | 0.449930 | − | 0.426515i | ||||
\(619\) | −7.15856 | + | 7.15856i | −0.287727 | + | 0.287727i | −0.836181 | − | 0.548454i | \(-0.815217\pi\) |
0.548454 | + | 0.836181i | \(0.315217\pi\) | |||||||
\(620\) | 2.86781i | 0.115174i | ||||||||
\(621\) | −2.06994 | + | 25.7781i | −0.0830640 | + | 1.03444i | ||||
\(622\) | −1.65884 | + | 1.65884i | −0.0665135 | + | 0.0665135i | ||||
\(623\) | −5.55985 | −0.222751 | ||||||||
\(624\) | −4.31903 | + | 4.51065i | −0.172900 | + | 0.180571i | ||||
\(625\) | 19.6449 | 0.785796 | ||||||||
\(626\) | −9.46610 | + | 9.46610i | −0.378341 | + | 0.378341i | ||||
\(627\) | 61.0870 | + | 1.63195i | 2.43958 | + | 0.0651738i | ||||
\(628\) | − | 13.8447i | − | 0.552466i | ||||||
\(629\) | 32.9043 | − | 32.9043i | 1.31198 | − | 1.31198i | ||||
\(630\) | −4.05660 | − | 4.51491i | −0.161619 | − | 0.179878i | ||||
\(631\) | 30.9238 | − | 30.9238i | 1.23106 | − | 1.23106i | 0.267498 | − | 0.963558i | \(-0.413803\pi\) |
0.963558 | − | 0.267498i | \(-0.0861970\pi\) | |||||||
\(632\) | −8.95271 | − | 8.95271i | −0.356120 | − | 0.356120i | ||||
\(633\) | −1.07790 | + | 40.3479i | −0.0428428 | + | 1.60369i | ||||
\(634\) | 18.3830i | 0.730081i | ||||||||
\(635\) | 27.9106 | + | 27.9106i | 1.10760 | + | 1.10760i | ||||
\(636\) | −0.340662 | + | 12.7516i | −0.0135081 | + | 0.505634i | ||||
\(637\) | 2.42316 | − | 2.66989i | 0.0960090 | − | 0.105785i | ||||
\(638\) | − | 13.1944i | − | 0.522373i | ||||||
\(639\) | −29.7943 | + | 26.7699i | −1.17865 | + | 1.05900i | ||||
\(640\) | 2.02321 | 0.0799743 | ||||||||
\(641\) | −19.3831 | −0.765585 | −0.382792 | − | 0.923834i | \(-0.625038\pi\) | ||||
−0.382792 | + | 0.923834i | \(0.625038\pi\) | |||||||
\(642\) | −20.3452 | + | 19.2864i | −0.802960 | + | 0.761174i | ||||
\(643\) | 14.9960 | + | 14.9960i | 0.591384 | + | 0.591384i | 0.938005 | − | 0.346621i | \(-0.112671\pi\) |
−0.346621 | + | 0.938005i | \(0.612671\pi\) | |||||||
\(644\) | 3.51925 | + | 3.51925i | 0.138678 | + | 0.138678i | ||||
\(645\) | 20.8894 | − | 19.8023i | 0.822519 | − | 0.779715i | ||||
\(646\) | −28.4549 | −1.11954 | ||||||||
\(647\) | 17.5674 | 0.690648 | 0.345324 | − | 0.938484i | \(-0.387769\pi\) | ||||
0.345324 | + | 0.938484i | \(0.387769\pi\) | |||||||
\(648\) | −5.64907 | − | 7.00628i | −0.221917 | − | 0.275233i | ||||
\(649\) | 9.63895i | 0.378362i | ||||||||
\(650\) | 0.158176 | + | 3.26506i | 0.00620416 | + | 0.128066i | ||||
\(651\) | 0.0655652 | − | 2.45423i | 0.00256970 | − | 0.0961888i | ||||
\(652\) | 2.76536 | + | 2.76536i | 0.108300 | + | 0.108300i | ||||
\(653\) | 13.2124i | 0.517040i | 0.966006 | + | 0.258520i | \(0.0832347\pi\) | ||||
−0.966006 | + | 0.258520i | \(0.916765\pi\) | |||||||
\(654\) | 0.101680 | − | 3.80606i | 0.00397599 | − | 0.148829i | ||||
\(655\) | −17.7845 | − | 17.7845i | −0.694899 | − | 0.694899i | ||||
\(656\) | 0.185417 | − | 0.185417i | 0.00723932 | − | 0.00723932i | ||||
\(657\) | 2.73976 | − | 2.46165i | 0.106888 | − | 0.0960380i | ||||
\(658\) | −2.56188 | + | 2.56188i | −0.0998725 | + | 0.0998725i | ||||
\(659\) | 25.7020i | 1.00121i | 0.865677 | + | 0.500603i | \(0.166888\pi\) | ||||
−0.865677 | + | 0.500603i | \(0.833112\pi\) | |||||||
\(660\) | 17.8216 | + | 0.476108i | 0.693706 | + | 0.0185325i | ||||
\(661\) | 24.0774 | − | 24.0774i | 0.936502 | − | 0.936502i | −0.0615994 | − | 0.998101i | \(-0.519620\pi\) |
0.998101 | + | 0.0615994i | \(0.0196201\pi\) | |||||||
\(662\) | 0.777007 | 0.0301992 | ||||||||
\(663\) | 17.7215 | − | 18.5077i | 0.688246 | − | 0.718781i | ||||
\(664\) | 0.328888 | 0.0127633 | ||||||||
\(665\) | 9.92128 | − | 9.92128i | 0.384731 | − | 0.384731i | ||||
\(666\) | −1.81657 | + | 33.9746i | −0.0703907 | + | 1.31649i | ||||
\(667\) | 12.9079i | 0.499795i | ||||||||
\(668\) | −13.6345 | + | 13.6345i | −0.527536 | + | 0.527536i | ||||
\(669\) | 19.9199 | − | 18.8832i | 0.770146 | − | 0.730068i | ||||
\(670\) | 6.34947 | − | 6.34947i | 0.245302 | − | 0.245302i | ||||
\(671\) | 36.4733 | + | 36.4733i | 1.40804 | + | 1.40804i | ||||
\(672\) | −1.73143 | − | 0.0462556i | −0.0667915 | − | 0.00178435i | ||||
\(673\) | 18.7017i | 0.720898i | 0.932779 | + | 0.360449i | \(0.117377\pi\) | ||||
−0.932779 | + | 0.360449i | \(0.882623\pi\) | |||||||
\(674\) | −14.2273 | − | 14.2273i | −0.548013 | − | 0.548013i | ||||
\(675\) | −4.69585 | − | 0.377070i | −0.180743 | − | 0.0145134i | ||||
\(676\) | 12.9391 | − | 1.25662i | 0.497659 | − | 0.0483315i | ||||
\(677\) | − | 23.9791i | − | 0.921593i | −0.887506 | − | 0.460797i | \(-0.847564\pi\) | ||
0.887506 | − | 0.460797i | \(-0.152436\pi\) | |||||||
\(678\) | −2.10203 | + | 1.99264i | −0.0807282 | + | 0.0765271i | ||||
\(679\) | −10.8299 | −0.415613 | ||||||||
\(680\) | −8.30147 | −0.318347 | ||||||||
\(681\) | −3.71839 | − | 3.92252i | −0.142489 | − | 0.150311i | ||||
\(682\) | 5.09912 | + | 5.09912i | 0.195255 | + | 0.195255i | ||||
\(683\) | −23.6663 | − | 23.6663i | −0.905564 | − | 0.905564i | 0.0903464 | − | 0.995910i | \(-0.471203\pi\) |
−0.995910 | + | 0.0903464i | \(0.971203\pi\) | |||||||
\(684\) | 15.4757 | − | 13.9048i | 0.591728 | − | 0.531662i | ||||
\(685\) | 26.3057 | 1.00509 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 29.3714 | + | 30.9838i | 1.12059 | + | 1.18211i | ||||
\(688\) | − | 8.21380i | − | 0.313148i | ||||||
\(689\) | 17.8460 | − | 19.6631i | 0.679878 | − | 0.749105i | ||||
\(690\) | −17.4346 | − | 0.465768i | −0.663723 | − | 0.0177315i | ||||
\(691\) | 3.19271 | + | 3.19271i | 0.121456 | + | 0.121456i | 0.765222 | − | 0.643766i | \(-0.222629\pi\) |
−0.643766 | + | 0.765222i | \(0.722629\pi\) | |||||||
\(692\) | 21.9642i | 0.834955i | ||||||||
\(693\) | −15.2406 | − | 0.814893i | −0.578943 | − | 0.0309552i | ||||
\(694\) | −11.6206 | − | 11.6206i | −0.441113 | − | 0.441113i | ||||
\(695\) | −27.2518 | + | 27.2518i | −1.03372 | + | 1.03372i | ||||
\(696\) | −3.09044 | − | 3.26010i | −0.117143 | − | 0.123574i | ||||
\(697\) | −0.760789 | + | 0.760789i | −0.0288169 | + | 0.0288169i | ||||
\(698\) | − | 13.6817i | − | 0.517859i | ||||||
\(699\) | 0.325357 | − | 12.1787i | 0.0123061 | − | 0.460642i | ||||
\(700\) | −0.641081 | + | 0.641081i | −0.0242306 | + | 0.0242306i | ||||
\(701\) | −24.7374 | −0.934318 | −0.467159 | − | 0.884173i | \(-0.654722\pi\) | ||||
−0.467159 | + | 0.884173i | \(0.654722\pi\) | |||||||
\(702\) | −0.594164 | + | 18.7256i | −0.0224253 | + | 0.706751i | ||||
\(703\) | −78.6493 | −2.96631 | ||||||||
\(704\) | 3.59738 | − | 3.59738i | 0.135581 | − | 0.135581i | ||||
\(705\) | 0.339062 | − | 12.6917i | 0.0127698 | − | 0.477998i | ||||
\(706\) | 3.60273i | 0.135590i | ||||||||
\(707\) | −2.16287 | + | 2.16287i | −0.0813431 | + | 0.0813431i | ||||
\(708\) | 2.25767 | + | 2.38161i | 0.0848483 | + | 0.0895062i | ||||
\(709\) | 12.7061 | − | 12.7061i | 0.477187 | − | 0.477187i | −0.427044 | − | 0.904231i | \(-0.640445\pi\) |
0.904231 | + | 0.427044i | \(0.140445\pi\) | |||||||
\(710\) | −19.1008 | − | 19.1008i | −0.716840 | − | 0.716840i | ||||
\(711\) | −37.9289 | − | 2.02801i | −1.42245 | − | 0.0760562i | ||||
\(712\) | − | 5.55985i | − | 0.208364i | ||||||
\(713\) | −4.98838 | − | 4.98838i | −0.186816 | − | 0.186816i | ||||
\(714\) | 7.10428 | + | 0.189792i | 0.265871 | + | 0.00710280i | ||||
\(715\) | −27.4811 | − | 24.9415i | −1.02774 | − | 0.932760i | ||||
\(716\) | 8.56403i | 0.320053i | ||||||||
\(717\) | −4.49140 | − | 4.73796i | −0.167734 | − | 0.176942i | ||||
\(718\) | −30.3098 | −1.13115 | ||||||||
\(719\) | 19.2223 | 0.716870 | 0.358435 | − | 0.933555i | \(-0.383310\pi\) | ||||
0.358435 | + | 0.933555i | \(0.383310\pi\) | |||||||
\(720\) | 4.51491 | − | 4.05660i | 0.168261 | − | 0.151181i | ||||
\(721\) | −6.29192 | − | 6.29192i | −0.234323 | − | 0.234323i | ||||
\(722\) | 20.5720 | + | 20.5720i | 0.765612 | + | 0.765612i | ||||
\(723\) | 2.41888 | + | 2.55167i | 0.0899592 | + | 0.0948977i | ||||
\(724\) | −0.973124 | −0.0361659 | ||||||||
\(725\) | −2.35136 | −0.0873272 | ||||||||
\(726\) | 18.7072 | − | 17.7337i | 0.694289 | − | 0.658158i | ||||
\(727\) | − | 49.4631i | − | 1.83448i | −0.398330 | − | 0.917242i | \(-0.630410\pi\) | ||
0.398330 | − | 0.917242i | \(-0.369590\pi\) | |||||||
\(728\) | 2.66989 | + | 2.42316i | 0.0989527 | + | 0.0898082i | ||||
\(729\) | −26.6540 | − | 4.30834i | −0.987187 | − | 0.159568i | ||||
\(730\) | 1.75643 | + | 1.75643i | 0.0650083 | + | 0.0650083i | ||||
\(731\) | 33.7022i | 1.24652i | ||||||||
\(732\) | 17.5548 | + | 0.468979i | 0.648843 | + | 0.0173340i | ||||
\(733\) | −7.14061 | − | 7.14061i | −0.263744 | − | 0.263744i | 0.562829 | − | 0.826573i | \(-0.309713\pi\) |
−0.826573 | + | 0.562829i | \(0.809713\pi\) | |||||||
\(734\) | −8.63847 | + | 8.63847i | −0.318852 | + | 0.318852i | ||||
\(735\) | −2.54321 | + | 2.41086i | −0.0938075 | + | 0.0889258i | ||||
\(736\) | −3.51925 | + | 3.51925i | −0.129721 | + | 0.129721i | ||||
\(737\) | − | 22.5794i | − | 0.831724i | ||||||
\(738\) | 0.0420015 | − | 0.785536i | 0.00154610 | − | 0.0289160i | ||||
\(739\) | −23.2049 | + | 23.2049i | −0.853607 | + | 0.853607i | −0.990575 | − | 0.136968i | \(-0.956264\pi\) |
0.136968 | + | 0.990575i | \(0.456264\pi\) | |||||||
\(740\) | −22.9453 | −0.843485 | ||||||||
\(741\) | −43.2984 | + | 0.939648i | −1.59061 | + | 0.0345188i | ||||
\(742\) | 7.36477 | 0.270369 | ||||||||
\(743\) | 15.5087 | − | 15.5087i | 0.568959 | − | 0.568959i | −0.362878 | − | 0.931837i | \(-0.618206\pi\) |
0.931837 | + | 0.362878i | \(0.118206\pi\) | |||||||
\(744\) | 2.45423 | + | 0.0655652i | 0.0899764 | + | 0.00240374i | ||||
\(745\) | 13.0270i | 0.477273i | ||||||||
\(746\) | 4.08877 | − | 4.08877i | 0.149700 | − | 0.149700i | ||||
\(747\) | 0.733932 | − | 0.659431i | 0.0268532 | − | 0.0241273i | ||||
\(748\) | −14.7605 | + | 14.7605i | −0.539696 | + | 0.539696i | ||||
\(749\) | 11.4447 | + | 11.4447i | 0.418182 | + | 0.418182i | ||||
\(750\) | 0.552770 | − | 20.6912i | 0.0201843 | − | 0.755536i | ||||
\(751\) | 15.4920i | 0.565311i | 0.959221 | + | 0.282656i | \(0.0912154\pi\) | ||||
−0.959221 | + | 0.282656i | \(0.908785\pi\) | |||||||
\(752\) | −2.56188 | − | 2.56188i | −0.0934222 | − | 0.0934222i | ||||
\(753\) | 0.423243 | − | 15.8428i | 0.0154238 | − | 0.577343i | ||||
\(754\) | 0.452482 | + | 9.34013i | 0.0164784 | + | 0.340147i | ||||
\(755\) | − | 35.7033i | − | 1.29938i | ||||||
\(756\) | −3.95653 | + | 3.36836i | −0.143898 | + | 0.122506i | ||||
\(757\) | 3.34900 | 0.121721 | 0.0608607 | − | 0.998146i | \(-0.480615\pi\) | ||||
0.0608607 | + | 0.998146i | \(0.480615\pi\) | |||||||
\(758\) | 26.1270 | 0.948977 | ||||||||
\(759\) | −31.8278 | + | 30.1715i | −1.15528 | + | 1.09515i | ||||
\(760\) | 9.92128 | + | 9.92128i | 0.359883 | + | 0.359883i | ||||
\(761\) | −34.2779 | − | 34.2779i | −1.24257 | − | 1.24257i | −0.958930 | − | 0.283642i | \(-0.908457\pi\) |
−0.283642 | − | 0.958930i | \(-0.591543\pi\) | |||||||
\(762\) | 24.5236 | − | 23.2474i | 0.888397 | − | 0.842165i | ||||
\(763\) | −2.19822 | −0.0795807 | ||||||||
\(764\) | 12.7937 | 0.462860 | ||||||||
\(765\) | −18.5252 | + | 16.6447i | −0.669780 | + | 0.601791i | ||||
\(766\) | 31.9451i | 1.15422i | ||||||||
\(767\) | −0.330552 | − | 6.82326i | −0.0119356 | − | 0.246374i | ||||
\(768\) | 0.0462556 | − | 1.73143i | 0.00166910 | − | 0.0624777i | ||||
\(769\) | −26.5941 | − | 26.5941i | −0.959007 | − | 0.959007i | 0.0401857 | − | 0.999192i | \(-0.487205\pi\) |
−0.999192 | + | 0.0401857i | \(0.987205\pi\) | |||||||
\(770\) | − | 10.2930i | − | 0.370934i | ||||||
\(771\) | −0.163926 | + | 6.13606i | −0.00590365 | + | 0.220985i | ||||
\(772\) | −8.73551 | − | 8.73551i | −0.314398 | − | 0.314398i | ||||
\(773\) | −33.0906 | + | 33.0906i | −1.19018 | + | 1.19018i | −0.213170 | + | 0.977015i | \(0.568379\pi\) |
−0.977015 | + | 0.213170i | \(0.931621\pi\) | |||||||
\(774\) | −16.4689 | − | 18.3296i | −0.591964 | − | 0.658843i | ||||
\(775\) | 0.908704 | − | 0.908704i | 0.0326416 | − | 0.0326416i | ||||
\(776\) | − | 10.8299i | − | 0.388770i | ||||||
\(777\) | 19.6362 | + | 0.524586i | 0.704446 | + | 0.0188194i | ||||
\(778\) | 3.79484 | − | 3.79484i | 0.136051 | − | 0.136051i | ||||
\(779\) | 1.81847 | 0.0651536 | ||||||||
\(780\) | −12.6320 | + | 0.274134i | −0.452297 | + | 0.00981559i | ||||
\(781\) | −67.9245 | −2.43053 | ||||||||
\(782\) | 14.4399 | − | 14.4399i | 0.516370 | − | 0.516370i | ||||
\(783\) | −13.4331 | − | 1.07866i | −0.480060 | − | 0.0385481i | ||||
\(784\) | 1.00000i | 0.0357143i | ||||||||
\(785\) | 19.8066 | − | 19.8066i | 0.706929 | − | 0.706929i | ||||
\(786\) | −15.6263 | + | 14.8131i | −0.557373 | + | 0.528367i | ||||
\(787\) | −6.98321 | + | 6.98321i | −0.248925 | + | 0.248925i | −0.820529 | − | 0.571605i | \(-0.806321\pi\) |
0.571605 | + | 0.820529i | \(0.306321\pi\) | |||||||
\(788\) | 6.29467 | + | 6.29467i | 0.224238 | + | 0.224238i | ||||
\(789\) | 47.8587 | + | 1.27855i | 1.70381 | + | 0.0455177i | ||||
\(790\) | − | 25.6159i | − | 0.911374i | ||||||
\(791\) | 1.18245 | + | 1.18245i | 0.0420432 | + | 0.0420432i | ||||
\(792\) | 0.814893 | − | 15.2406i | 0.0289560 | − | 0.541551i | ||||
\(793\) | −27.0697 | − | 24.5681i | −0.961272 | − | 0.872438i | ||||
\(794\) | − | 20.5121i | − | 0.727949i | ||||||
\(795\) | −18.7301 | + | 17.7554i | −0.664289 | + | 0.629719i | ||||
\(796\) | 12.0446 | 0.426911 | ||||||||
\(797\) | −41.4764 | −1.46917 | −0.734585 | − | 0.678516i | \(-0.762623\pi\) | ||||
−0.734585 | + | 0.678516i | \(0.762623\pi\) | |||||||
\(798\) | −8.26367 | − | 8.71732i | −0.292531 | − | 0.308590i | ||||
\(799\) | 10.5117 | + | 10.5117i | 0.371877 | + | 0.371877i | ||||
\(800\) | −0.641081 | − | 0.641081i | −0.0226657 | − | 0.0226657i | ||||
\(801\) | −11.1477 | − | 12.4071i | −0.393884 | − | 0.438384i | ||||
\(802\) | 34.1387 | 1.20548 | ||||||||
\(803\) | 6.24604 | 0.220418 | ||||||||
\(804\) | −5.28862 | − | 5.57895i | −0.186515 | − | 0.196755i | ||||
\(805\) | 10.0694i | 0.354901i | ||||||||
\(806\) | −3.78445 | − | 3.43472i | −0.133302 | − | 0.120983i | ||||
\(807\) | 34.6375 | + | 0.925348i | 1.21930 | + | 0.0325738i | ||||
\(808\) | −2.16287 | − | 2.16287i | −0.0760895 | − | 0.0760895i | ||||
\(809\) | − | 15.0063i | − | 0.527595i | −0.964578 | − | 0.263797i | \(-0.915025\pi\) | ||
0.964578 | − | 0.263797i | \(-0.0849751\pi\) | |||||||
\(810\) | 1.94165 | − | 18.1051i | 0.0682228 | − | 0.636147i | ||||
\(811\) | −2.46485 | − | 2.46485i | −0.0865525 | − | 0.0865525i | 0.662505 | − | 0.749057i | \(-0.269493\pi\) |
−0.749057 | + | 0.662505i | \(0.769493\pi\) | |||||||
\(812\) | −1.83390 | + | 1.83390i | −0.0643572 | + | 0.0643572i | ||||
\(813\) | 8.72556 | + | 9.20457i | 0.306019 | + | 0.322818i | ||||
\(814\) | −40.7980 | + | 40.7980i | −1.42997 | + | 1.42997i | ||||
\(815\) | 7.91238i | 0.277159i | ||||||||
\(816\) | −0.189792 | + | 7.10428i | −0.00664406 | + | 0.248700i | ||||
\(817\) | 40.2783 | − | 40.2783i | 1.40916 | − | 1.40916i | ||||
\(818\) | −16.6784 | −0.583147 | ||||||||
\(819\) | 10.8165 | + | 0.0541977i | 0.377960 | + | 0.00189382i | ||||
\(820\) | 0.530525 | 0.0185267 | ||||||||
\(821\) | 13.9453 | − | 13.9453i | 0.486694 | − | 0.486694i | −0.420567 | − | 0.907261i | \(-0.638169\pi\) |
0.907261 | + | 0.420567i | \(0.138169\pi\) | |||||||
\(822\) | 0.601413 | − | 22.5120i | 0.0209767 | − | 0.785197i | ||||
\(823\) | 3.91631i | 0.136514i | 0.997668 | + | 0.0682570i | \(0.0217438\pi\) | ||||
−0.997668 | + | 0.0682570i | \(0.978256\pi\) | |||||||
\(824\) | 6.29192 | − | 6.29192i | 0.219189 | − | 0.219189i | ||||
\(825\) | −5.49616 | − | 5.79789i | −0.191352 | − | 0.201857i | ||||
\(826\) | 1.33972 | − | 1.33972i | 0.0466148 | − | 0.0466148i | ||||
\(827\) | 8.29105 | + | 8.29105i | 0.288308 | + | 0.288308i | 0.836411 | − | 0.548103i | \(-0.184650\pi\) |
−0.548103 | + | 0.836411i | \(0.684650\pi\) | |||||||
\(828\) | −0.797195 | + | 14.9096i | −0.0277045 | + | 0.518145i | ||||
\(829\) | − | 21.6511i | − | 0.751975i | −0.926625 | − | 0.375988i | \(-0.877304\pi\) | ||
0.926625 | − | 0.375988i | \(-0.122696\pi\) | |||||||
\(830\) | 0.470515 | + | 0.470515i | 0.0163318 | + | 0.0163318i | ||||
\(831\) | −20.6647 | − | 0.552062i | −0.716851 | − | 0.0191508i | ||||
\(832\) | −2.42316 | + | 2.66989i | −0.0840079 | + | 0.0925618i | ||||
\(833\) | − | 4.10312i | − | 0.142165i | ||||||
\(834\) | 22.6986 | + | 23.9447i | 0.785990 | + | 0.829138i | ||||
\(835\) | −39.0118 | −1.35006 | ||||||||
\(836\) | 35.2812 | 1.22022 | ||||||||
\(837\) | 5.60821 | − | 4.77450i | 0.193848 | − | 0.165031i | ||||
\(838\) | 26.6783 | + | 26.6783i | 0.921585 | + | 0.921585i | ||||
\(839\) | −27.5249 | − | 27.5249i | −0.950266 | − | 0.950266i | 0.0485547 | − | 0.998821i | \(-0.484538\pi\) |
−0.998821 | + | 0.0485547i | \(0.984538\pi\) | |||||||
\(840\) | −2.41086 | − | 2.54321i | −0.0831825 | − | 0.0877489i | ||||
\(841\) | 22.2736 | 0.768056 | ||||||||
\(842\) | −3.54041 | −0.122011 | ||||||||
\(843\) | −34.5637 | + | 32.7650i | −1.19044 | + | 1.12849i | ||||
\(844\) | 23.3032i | 0.802129i | ||||||||
\(845\) | 20.3088 | + | 16.7133i | 0.698643 | + | 0.574954i | ||||
\(846\) | −10.8536 | − | 0.580328i | −0.373156 | − | 0.0199521i | ||||
\(847\) | −10.5233 | − | 10.5233i | −0.361586 | − | 0.361586i | ||||
\(848\) | 7.36477i | 0.252907i | ||||||||
\(849\) | 18.9115 | + | 0.505224i | 0.649040 | + | 0.0173392i | ||||
\(850\) | 2.63044 | + | 2.63044i | 0.0902232 | + | 0.0902232i | ||||
\(851\) | 39.9119 | − | 39.9119i | 1.36816 | − | 1.36816i | ||||
\(852\) | −16.7829 | + | 15.9095i | −0.574972 | + | 0.545051i | ||||
\(853\) | −14.9776 | + | 14.9776i | −0.512822 | + | 0.512822i | −0.915390 | − | 0.402568i | \(-0.868118\pi\) |
0.402568 | + | 0.915390i | \(0.368118\pi\) | |||||||
\(854\) | − | 10.1389i | − | 0.346945i | ||||||
\(855\) | 42.0324 | + | 2.24741i | 1.43748 | + | 0.0768599i | ||||
\(856\) | −11.4447 | + | 11.4447i | −0.391173 | + | 0.391173i | ||||
\(857\) | −4.13872 | −0.141376 | −0.0706880 | − | 0.997498i | \(-0.522519\pi\) | ||||
−0.0706880 | + | 0.997498i | \(0.522519\pi\) | |||||||
\(858\) | −21.9729 | + | 22.9477i | −0.750142 | + | 0.783423i | ||||
\(859\) | 3.48885 | 0.119038 | 0.0595191 | − | 0.998227i | \(-0.481043\pi\) | ||||
0.0595191 | + | 0.998227i | \(0.481043\pi\) | |||||||
\(860\) | 11.7509 | − | 11.7509i | 0.400701 | − | 0.400701i | ||||
\(861\) | −0.454015 | − | 0.0121291i | −0.0154728 | − | 0.000413359i | ||||
\(862\) | 4.43693i | 0.151122i | ||||||||
\(863\) | 13.8885 | − | 13.8885i | 0.472770 | − | 0.472770i | −0.430040 | − | 0.902810i | \(-0.641500\pi\) |
0.902810 | + | 0.430040i | \(0.141500\pi\) | |||||||
\(864\) | −3.36836 | − | 3.95653i | −0.114594 | − | 0.134604i | ||||
\(865\) | −31.4226 | + | 31.4226i | −1.06840 | + | 1.06840i | ||||
\(866\) | 23.2897 | + | 23.2897i | 0.791415 | + | 0.791415i | ||||
\(867\) | −0.00760420 | + | 0.284640i | −0.000258252 | + | 0.00966687i | ||||
\(868\) | − | 1.41746i | − | 0.0481116i | ||||||
\(869\) | −45.5465 | − | 45.5465i | −1.54506 | − | 1.54506i | ||||
\(870\) | 0.242714 | − | 9.08525i | 0.00822878 | − | 0.308019i | ||||
\(871\) | 0.774325 | + | 15.9836i | 0.0262370 | + | 0.541584i | ||||
\(872\) | − | 2.19822i | − | 0.0744410i | ||||||
\(873\) | −21.7143 | − | 24.1675i | −0.734916 | − | 0.817946i | ||||
\(874\) | −34.5149 | −1.16749 | ||||||||
\(875\) | −11.9503 | −0.403995 | ||||||||
\(876\) | 1.54328 | − | 1.46297i | 0.0521426 | − | 0.0494291i | ||||
\(877\) | −18.9431 | − | 18.9431i | −0.639663 | − | 0.639663i | 0.310809 | − | 0.950472i | \(-0.399400\pi\) |
−0.950472 | + | 0.310809i | \(0.899400\pi\) | |||||||
\(878\) | 10.8415 | + | 10.8415i | 0.365884 | + | 0.365884i | ||||
\(879\) | −3.23396 | + | 3.06566i | −0.109079 | + | 0.103402i | ||||
\(880\) | 10.2930 | 0.346977 | ||||||||
\(881\) | −23.3396 | −0.786333 | −0.393166 | − | 0.919467i | \(-0.628620\pi\) | ||||
−0.393166 | + | 0.919467i | \(0.628620\pi\) | |||||||
\(882\) | 2.00503 | + | 2.23156i | 0.0675130 | + | 0.0751404i | ||||
\(883\) | − | 48.4835i | − | 1.63160i | −0.578334 | − | 0.815800i | \(-0.696297\pi\) | ||
0.578334 | − | 0.815800i | \(-0.303703\pi\) | |||||||
\(884\) | 9.94251 | − | 10.9549i | 0.334403 | − | 0.368452i | ||||
\(885\) | −0.177310 | + | 6.63706i | −0.00596022 | + | 0.223102i | ||||
\(886\) | −18.7268 | − | 18.7268i | −0.629140 | − | 0.629140i | ||||
\(887\) | − | 20.5435i | − | 0.689782i | −0.938643 | − | 0.344891i | \(-0.887916\pi\) | ||
0.938643 | − | 0.344891i | \(-0.112084\pi\) | |||||||
\(888\) | −0.524586 | + | 19.6362i | −0.0176040 | + | 0.658949i | ||||
\(889\) | −13.7952 | − | 13.7952i | −0.462677 | − | 0.462677i | ||||
\(890\) | 7.95406 | − | 7.95406i | 0.266621 | − | 0.266621i | ||||
\(891\) | −28.7394 | − | 35.6442i | −0.962807 | − | 1.19412i | ||||
\(892\) | 11.2055 | − | 11.2055i | 0.375187 | − | 0.375187i | ||||
\(893\) | − | 25.1256i | − | 0.840795i | ||||||
\(894\) | 11.1483 | + | 0.297830i | 0.372856 | + | 0.00996093i | ||||
\(895\) | −12.2519 | + | 12.2519i | −0.409536 | + | 0.409536i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 21.4957 | − | 22.4494i | 0.717720 | − | 0.749563i | ||||
\(898\) | 5.27649 | 0.176079 | ||||||||
\(899\) | 2.59947 | − | 2.59947i | 0.0866971 | − | 0.0866971i | ||||
\(900\) | −2.71600 | − | 0.145221i | −0.0905333 | − | 0.00484069i | ||||
\(901\) | − | 30.2185i | − | 1.00673i | ||||||
\(902\) | 0.943302 | − | 0.943302i | 0.0314085 | − | 0.0314085i | ||||
\(903\) | −10.3249 | + | 9.78757i | −0.343590 | + | 0.325710i | ||||
\(904\) | −1.18245 | + | 1.18245i | −0.0393278 | + | 0.0393278i | ||||
\(905\) | −1.39218 | − | 1.39218i | −0.0462775 | − | 0.0462775i | ||||
\(906\) | −30.5544 | − | 0.816266i | −1.01510 | − | 0.0271186i | ||||
\(907\) | − | 20.3036i | − | 0.674169i | −0.941474 | − | 0.337085i | \(-0.890559\pi\) | ||
0.941474 | − | 0.337085i | \(-0.109441\pi\) | |||||||
\(908\) | −2.20653 | − | 2.20653i | −0.0732261 | − | 0.0732261i | ||||
\(909\) | −9.16320 | − | 0.489943i | −0.303924 | − | 0.0162504i | ||||
\(910\) | 0.352981 | + | 7.28624i | 0.0117012 | + | 0.241536i | ||||
\(911\) | 4.80500i | 0.159197i | 0.996827 | + | 0.0795984i | \(0.0253638\pi\) | ||||
−0.996827 | + | 0.0795984i | \(0.974636\pi\) | |||||||
\(912\) | 8.71732 | − | 8.26367i | 0.288659 | − | 0.273637i | ||||
\(913\) | 1.67320 | 0.0553749 | ||||||||
\(914\) | 30.5575 | 1.01075 | ||||||||
\(915\) | 24.4434 | + | 25.7852i | 0.808072 | + | 0.852433i | ||||
\(916\) | 17.4293 | + | 17.4293i | 0.575879 | + | 0.575879i | ||||
\(917\) | 8.79026 | + | 8.79026i | 0.290280 | + | 0.290280i | ||||
\(918\) | 13.8208 | + | 16.2341i | 0.456154 | + | 0.535807i | ||||
\(919\) | 8.07961 | 0.266522 | 0.133261 | − | 0.991081i | \(-0.457455\pi\) | ||||
0.133261 | + | 0.991081i | \(0.457455\pi\) | |||||||
\(920\) | −10.0694 | −0.331980 | ||||||||
\(921\) | 15.4660 | + | 16.3150i | 0.509622 | + | 0.537598i | ||||
\(922\) | 10.5840i | 0.348565i | ||||||||
\(923\) | 48.0827 | − | 2.32936i | 1.58266 | − | 0.0766719i | ||||
\(924\) | −8.80859 | − | 0.235323i | −0.289781 | − | 0.00774157i | ||||
\(925\) | 7.27053 | + | 7.27053i | 0.239053 | + | 0.239053i | ||||
\(926\) | 0.663324i | 0.0217982i | ||||||||
\(927\) | 1.42527 | − | 26.6563i | 0.0468121 | − | 0.875507i | ||||
\(928\) | −1.83390 | − | 1.83390i | −0.0602007 | − | 0.0602007i | ||||
\(929\) | −15.7251 | + | 15.7251i | −0.515924 | + | 0.515924i | −0.916335 | − | 0.400412i | \(-0.868867\pi\) |
0.400412 | + | 0.916335i | \(0.368867\pi\) | |||||||
\(930\) | 3.41728 | + | 3.60488i | 0.112057 | + | 0.118209i | ||||
\(931\) | −4.90374 | + | 4.90374i | −0.160713 | + | 0.160713i | ||||
\(932\) | − | 7.03391i | − | 0.230403i | ||||||
\(933\) | −0.108514 | + | 4.06187i | −0.00355257 | + | 0.132980i | ||||
\(934\) | 23.2666 | − | 23.2666i | 0.761306 | − | 0.761306i | ||||
\(935\) | −42.2334 | −1.38118 | ||||||||
\(936\) | −0.0541977 | + | 10.8165i | −0.00177151 | + | 0.353549i | ||||
\(937\) | 22.7249 | 0.742389 | 0.371195 | − | 0.928555i | \(-0.378948\pi\) | ||||
0.371195 | + | 0.928555i | \(0.378948\pi\) | |||||||
\(938\) | −3.13832 | + | 3.13832i | −0.102470 | + | 0.102470i | ||||
\(939\) | −0.619227 | + | 23.1788i | −0.0202077 | + | 0.756413i | ||||
\(940\) | − | 7.33018i | − | 0.239084i | ||||||
\(941\) | 26.5724 | − | 26.5724i | 0.866234 | − | 0.866234i | −0.125819 | − | 0.992053i | \(-0.540156\pi\) |
0.992053 | + | 0.125819i | \(0.0401559\pi\) | |||||||
\(942\) | −16.4974 | − | 17.4031i | −0.537515 | − | 0.567023i | ||||
\(943\) | −0.922815 | + | 0.922815i | −0.0300510 | + | 0.0300510i | ||||
\(944\) | 1.33972 | + | 1.33972i | 0.0436042 | + | 0.0436042i | ||||
\(945\) | −10.4792 | − | 0.841461i | −0.340887 | − | 0.0273727i | ||||
\(946\) | − | 41.7874i | − | 1.35862i | ||||||
\(947\) | 14.4108 | + | 14.4108i | 0.468288 | + | 0.468288i | 0.901360 | − | 0.433071i | \(-0.142570\pi\) |
−0.433071 | + | 0.901360i | \(0.642570\pi\) | |||||||
\(948\) | −21.9217 | − | 0.585644i | −0.711985 | − | 0.0190208i | ||||
\(949\) | −4.42147 | + | 0.214198i | −0.143527 | + | 0.00695316i | ||||
\(950\) | − | 6.28739i | − | 0.203990i | ||||||
\(951\) | 21.9051 | + | 23.1077i | 0.710323 | + | 0.749318i | ||||
\(952\) | 4.10312 | 0.132983 | ||||||||
\(953\) | 11.5458 | 0.374004 | 0.187002 | − | 0.982360i | \(-0.440123\pi\) | ||||
0.187002 | + | 0.982360i | \(0.440123\pi\) | |||||||
\(954\) | 14.7666 | + | 16.4349i | 0.478086 | + | 0.532100i | ||||
\(955\) | 18.3030 | + | 18.3030i | 0.592271 | + | 0.592271i | ||||
\(956\) | −2.66524 | − | 2.66524i | −0.0861999 | − | 0.0861999i | ||||
\(957\) | −15.7225 | − | 16.5856i | −0.508236 | − | 0.536137i | ||||
\(958\) | −12.1184 | −0.391528 | ||||||||
\(959\) | −13.0020 | −0.419855 | ||||||||
\(960\) | 2.54321 | − | 2.41086i | 0.0820816 | − | 0.0778101i | ||||
\(961\) | − | 28.9908i | − | 0.935188i | ||||||
\(962\) | 27.4811 | − | 30.2793i | 0.886026 | − | 0.976244i | ||||
\(963\) | −2.59251 | + | 48.4867i | −0.0835425 | + | 1.56246i | ||||
\(964\) | 1.43539 | + | 1.43539i | 0.0462307 | + | 0.0462307i | ||||
\(965\) | − | 24.9945i | − | 0.804601i | ||||||
\(966\) | 8.61729 | + | 0.230213i | 0.277257 | + | 0.00740697i | ||||
\(967\) | 13.0289 | + | 13.0289i | 0.418982 | + | 0.418982i | 0.884853 | − | 0.465871i | \(-0.154259\pi\) |
−0.465871 | + | 0.884853i | \(0.654259\pi\) | |||||||
\(968\) | 10.5233 | − | 10.5233i | 0.338232 | − | 0.338232i | ||||
\(969\) | −35.7682 | + | 33.9068i | −1.14904 | + | 1.08924i | ||||
\(970\) | 15.4935 | − | 15.4935i | 0.497466 | − | 0.497466i | ||||
\(971\) | 34.4228i | 1.10468i | 0.833619 | + | 0.552340i | \(0.186265\pi\) | ||||
−0.833619 | + | 0.552340i | \(0.813735\pi\) | |||||||
\(972\) | −15.4497 | − | 2.07557i | −0.495548 | − | 0.0665738i | ||||
\(973\) | 13.4696 | − | 13.4696i | 0.431815 | − | 0.431815i | ||||
\(974\) | −36.0505 | −1.15513 | ||||||||
\(975\) | 4.08947 | + | 3.91575i | 0.130968 | + | 0.125404i | ||||
\(976\) | 10.1389 | 0.324537 | ||||||||
\(977\) | −13.4816 | + | 13.4816i | −0.431314 | + | 0.431314i | −0.889075 | − | 0.457761i | \(-0.848651\pi\) |
0.457761 | + | 0.889075i | \(0.348651\pi\) | |||||||
\(978\) | 6.77130 | + | 0.180897i | 0.216522 | + | 0.00578444i | ||||
\(979\) | − | 28.2855i | − | 0.904008i | ||||||
\(980\) | −1.43062 | + | 1.43062i | −0.0456996 | + | 0.0456996i | ||||
\(981\) | −4.40749 | − | 4.90544i | −0.140720 | − | 0.156619i | ||||
\(982\) | 30.1756 | − | 30.1756i | 0.962941 | − | 0.962941i | ||||
\(983\) | −5.99104 | − | 5.99104i | −0.191085 | − | 0.191085i | 0.605080 | − | 0.796165i | \(-0.293141\pi\) |
−0.796165 | + | 0.605080i | \(0.793141\pi\) | |||||||
\(984\) | 0.0121291 | − | 0.454015i | 0.000386662 | − | 0.0144735i | ||||
\(985\) | 18.0106i | 0.573866i | ||||||||
\(986\) | 7.52471 | + | 7.52471i | 0.239635 | + | 0.239635i | ||||
\(987\) | −0.167586 | + | 6.27306i | −0.00533432 | + | 0.199674i | ||||
\(988\) | −24.9750 | + | 1.20991i | −0.794559 | + | 0.0384924i | ||||
\(989\) | 40.8798i | 1.29990i | ||||||||
\(990\) | 22.9694 | − | 20.6378i | 0.730015 | − | 0.655912i | ||||
\(991\) | −18.7348 | −0.595131 | −0.297566 | − | 0.954701i | \(-0.596175\pi\) | ||||
−0.297566 | + | 0.954701i | \(0.596175\pi\) | |||||||
\(992\) | 1.41746 | 0.0450042 | ||||||||
\(993\) | 0.976710 | − | 0.925881i | 0.0309949 | − | 0.0293820i | ||||
\(994\) | 9.44085 | + | 9.44085i | 0.299445 | + | 0.299445i | ||||
\(995\) | 17.2314 | + | 17.2314i | 0.546271 | + | 0.546271i | ||||
\(996\) | 0.413417 | − | 0.391903i | 0.0130996 | − | 0.0124179i | ||||
\(997\) | −17.7862 | −0.563294 | −0.281647 | − | 0.959518i | \(-0.590881\pi\) | ||||
−0.281647 | + | 0.959518i | \(0.590881\pi\) | |||||||
\(998\) | 30.5918 | 0.968368 | ||||||||
\(999\) | 38.2007 | + | 44.8712i | 1.20862 | + | 1.41966i |
(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 | 546.2.p.c.281.9 | yes | 20 | |
3.2 | odd | 2 | 546.2.p.d.281.4 | yes | 20 | ||
13.5 | odd | 4 | 546.2.p.d.239.4 | yes | 20 | ||
39.5 | even | 4 | inner | 546.2.p.c.239.9 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.p.c.239.9 | ✓ | 20 | 39.5 | even | 4 | inner | |
546.2.p.c.281.9 | yes | 20 | 1.1 | even | 1 | trivial | |
546.2.p.d.239.4 | yes | 20 | 13.5 | odd | 4 | ||
546.2.p.d.281.4 | yes | 20 | 3.2 | odd | 2 |