Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(253,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.253");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.o (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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 253.15 | ||
Character | \(\chi\) | \(=\) | 1110.253 |
Dual form | 1110.2.o.b.487.15 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0.707107 | − | 0.707107i | 0.408248 | − | 0.408248i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.314477 | − | 2.21384i | −0.140638 | − | 0.990061i | ||||
\(6\) | 0.707107 | − | 0.707107i | 0.288675 | − | 0.288675i | ||||
\(7\) | −0.376687 | + | 0.376687i | −0.142374 | + | 0.142374i | −0.774702 | − | 0.632327i | \(-0.782100\pi\) |
0.632327 | + | 0.774702i | \(0.282100\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | −0.314477 | − | 2.21384i | −0.0994464 | − | 0.700079i | ||||
\(11\) | − | 1.28566i | − | 0.387641i | −0.981037 | − | 0.193821i | \(-0.937912\pi\) | ||
0.981037 | − | 0.193821i | \(-0.0620880\pi\) | |||||||
\(12\) | 0.707107 | − | 0.707107i | 0.204124 | − | 0.204124i | ||||
\(13\) | 5.12767 | 1.42216 | 0.711080 | − | 0.703112i | \(-0.248207\pi\) | ||||
0.711080 | + | 0.703112i | \(0.248207\pi\) | |||||||
\(14\) | −0.376687 | + | 0.376687i | −0.100674 | + | 0.100674i | ||||
\(15\) | −1.78779 | − | 1.34306i | −0.461606 | − | 0.346775i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.31038i | 0.560349i | 0.959949 | + | 0.280175i | \(0.0903924\pi\) | ||||
−0.959949 | + | 0.280175i | \(0.909608\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | −3.87466 | − | 3.87466i | −0.888908 | − | 0.888908i | 0.105510 | − | 0.994418i | \(-0.466352\pi\) |
−0.994418 | + | 0.105510i | \(0.966352\pi\) | |||||||
\(20\) | −0.314477 | − | 2.21384i | −0.0703192 | − | 0.495031i | ||||
\(21\) | 0.532716i | 0.116248i | ||||||||
\(22\) | − | 1.28566i | − | 0.274104i | ||||||
\(23\) | 6.29757 | 1.31313 | 0.656567 | − | 0.754268i | \(-0.272008\pi\) | ||||
0.656567 | + | 0.754268i | \(0.272008\pi\) | |||||||
\(24\) | 0.707107 | − | 0.707107i | 0.144338 | − | 0.144338i | ||||
\(25\) | −4.80221 | + | 1.39241i | −0.960442 | + | 0.278481i | ||||
\(26\) | 5.12767 | 1.00562 | ||||||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | −0.376687 | + | 0.376687i | −0.0711872 | + | 0.0711872i | ||||
\(29\) | 1.15504 | − | 1.15504i | 0.214486 | − | 0.214486i | −0.591684 | − | 0.806170i | \(-0.701537\pi\) |
0.806170 | + | 0.591684i | \(0.201537\pi\) | |||||||
\(30\) | −1.78779 | − | 1.34306i | −0.326405 | − | 0.245207i | ||||
\(31\) | −7.11133 | − | 7.11133i | −1.27723 | − | 1.27723i | −0.942210 | − | 0.335023i | \(-0.891256\pi\) |
−0.335023 | − | 0.942210i | \(-0.608744\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.909099 | − | 0.909099i | −0.158254 | − | 0.158254i | ||||
\(34\) | 2.31038i | 0.396227i | ||||||||
\(35\) | 0.952386 | + | 0.715467i | 0.160983 | + | 0.120936i | ||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | −3.20192 | − | 5.17182i | −0.526392 | − | 0.850242i | ||||
\(38\) | −3.87466 | − | 3.87466i | −0.628553 | − | 0.628553i | ||||
\(39\) | 3.62581 | − | 3.62581i | 0.580594 | − | 0.580594i | ||||
\(40\) | −0.314477 | − | 2.21384i | −0.0497232 | − | 0.350039i | ||||
\(41\) | 2.12896i | 0.332487i | 0.986085 | + | 0.166244i | \(0.0531638\pi\) | ||||
−0.986085 | + | 0.166244i | \(0.946836\pi\) | |||||||
\(42\) | 0.532716i | 0.0821999i | ||||||||
\(43\) | 2.56124 | 0.390585 | 0.195292 | − | 0.980745i | \(-0.437434\pi\) | ||||
0.195292 | + | 0.980745i | \(0.437434\pi\) | |||||||
\(44\) | − | 1.28566i | − | 0.193821i | ||||||
\(45\) | −2.21384 | + | 0.314477i | −0.330020 | + | 0.0468795i | ||||
\(46\) | 6.29757 | 0.928526 | ||||||||
\(47\) | 2.64523 | − | 2.64523i | 0.385847 | − | 0.385847i | −0.487356 | − | 0.873203i | \(-0.662039\pi\) |
0.873203 | + | 0.487356i | \(0.162039\pi\) | |||||||
\(48\) | 0.707107 | − | 0.707107i | 0.102062 | − | 0.102062i | ||||
\(49\) | 6.71621i | 0.959459i | ||||||||
\(50\) | −4.80221 | + | 1.39241i | −0.679135 | + | 0.196916i | ||||
\(51\) | 1.63368 | + | 1.63368i | 0.228762 | + | 0.228762i | ||||
\(52\) | 5.12767 | 0.711080 | ||||||||
\(53\) | 0.572887 | + | 0.572887i | 0.0786920 | + | 0.0786920i | 0.745357 | − | 0.666665i | \(-0.232279\pi\) |
−0.666665 | + | 0.745357i | \(0.732279\pi\) | |||||||
\(54\) | −0.707107 | − | 0.707107i | −0.0962250 | − | 0.0962250i | ||||
\(55\) | −2.84625 | + | 0.404311i | −0.383788 | + | 0.0545172i | ||||
\(56\) | −0.376687 | + | 0.376687i | −0.0503369 | + | 0.0503369i | ||||
\(57\) | −5.47960 | −0.725790 | ||||||||
\(58\) | 1.15504 | − | 1.15504i | 0.151664 | − | 0.151664i | ||||
\(59\) | 1.04438 | + | 1.04438i | 0.135966 | + | 0.135966i | 0.771814 | − | 0.635848i | \(-0.219349\pi\) |
−0.635848 | + | 0.771814i | \(0.719349\pi\) | |||||||
\(60\) | −1.78779 | − | 1.34306i | −0.230803 | − | 0.173388i | ||||
\(61\) | 3.44882 | + | 3.44882i | 0.441576 | + | 0.441576i | 0.892542 | − | 0.450965i | \(-0.148920\pi\) |
−0.450965 | + | 0.892542i | \(0.648920\pi\) | |||||||
\(62\) | −7.11133 | − | 7.11133i | −0.903140 | − | 0.903140i | ||||
\(63\) | 0.376687 | + | 0.376687i | 0.0474581 | + | 0.0474581i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.61253 | − | 11.3519i | −0.200010 | − | 1.40802i | ||||
\(66\) | −0.909099 | − | 0.909099i | −0.111902 | − | 0.111902i | ||||
\(67\) | −5.32260 | − | 5.32260i | −0.650259 | − | 0.650259i | 0.302797 | − | 0.953055i | \(-0.402080\pi\) |
−0.953055 | + | 0.302797i | \(0.902080\pi\) | |||||||
\(68\) | 2.31038i | 0.280175i | ||||||||
\(69\) | 4.45305 | − | 4.45305i | 0.536085 | − | 0.536085i | ||||
\(70\) | 0.952386 | + | 0.715467i | 0.113832 | + | 0.0855147i | ||||
\(71\) | 4.38568 | 0.520484 | 0.260242 | − | 0.965543i | \(-0.416198\pi\) | ||||
0.260242 | + | 0.965543i | \(0.416198\pi\) | |||||||
\(72\) | − | 1.00000i | − | 0.117851i | ||||||
\(73\) | −9.81049 | + | 9.81049i | −1.14823 | + | 1.14823i | −0.161330 | + | 0.986901i | \(0.551578\pi\) |
−0.986901 | + | 0.161330i | \(0.948422\pi\) | |||||||
\(74\) | −3.20192 | − | 5.17182i | −0.372215 | − | 0.601212i | ||||
\(75\) | −2.41109 | + | 4.38025i | −0.278409 | + | 0.505788i | ||||
\(76\) | −3.87466 | − | 3.87466i | −0.444454 | − | 0.444454i | ||||
\(77\) | 0.484292 | + | 0.484292i | 0.0551902 | + | 0.0551902i | ||||
\(78\) | 3.62581 | − | 3.62581i | 0.410542 | − | 0.410542i | ||||
\(79\) | 11.4000 | + | 11.4000i | 1.28259 | + | 1.28259i | 0.939186 | + | 0.343409i | \(0.111582\pi\) |
0.343409 | + | 0.939186i | \(0.388418\pi\) | |||||||
\(80\) | −0.314477 | − | 2.21384i | −0.0351596 | − | 0.247515i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 2.12896i | 0.235104i | ||||||||
\(83\) | 11.5202 | + | 11.5202i | 1.26450 | + | 1.26450i | 0.948887 | + | 0.315617i | \(0.102212\pi\) |
0.315617 | + | 0.948887i | \(0.397788\pi\) | |||||||
\(84\) | 0.532716i | 0.0581241i | ||||||||
\(85\) | 5.11482 | − | 0.726561i | 0.554780 | − | 0.0788066i | ||||
\(86\) | 2.56124 | 0.276185 | ||||||||
\(87\) | − | 1.63348i | − | 0.175127i | ||||||
\(88\) | − | 1.28566i | − | 0.137052i | ||||||
\(89\) | −8.09354 | + | 8.09354i | −0.857914 | + | 0.857914i | −0.991092 | − | 0.133179i | \(-0.957482\pi\) |
0.133179 | + | 0.991092i | \(0.457482\pi\) | |||||||
\(90\) | −2.21384 | + | 0.314477i | −0.233360 | + | 0.0331488i | ||||
\(91\) | −1.93153 | + | 1.93153i | −0.202479 | + | 0.202479i | ||||
\(92\) | 6.29757 | 0.656567 | ||||||||
\(93\) | −10.0569 | −1.04286 | ||||||||
\(94\) | 2.64523 | − | 2.64523i | 0.272835 | − | 0.272835i | ||||
\(95\) | −7.35940 | + | 9.79638i | −0.755059 | + | 1.00509i | ||||
\(96\) | 0.707107 | − | 0.707107i | 0.0721688 | − | 0.0721688i | ||||
\(97\) | − | 8.07546i | − | 0.819939i | −0.912099 | − | 0.409969i | \(-0.865539\pi\) | ||
0.912099 | − | 0.409969i | \(-0.134461\pi\) | |||||||
\(98\) | 6.71621i | 0.678440i | ||||||||
\(99\) | −1.28566 | −0.129214 | ||||||||
\(100\) | −4.80221 | + | 1.39241i | −0.480221 | + | 0.139241i | ||||
\(101\) | 15.8768i | 1.57980i | 0.613233 | + | 0.789902i | \(0.289869\pi\) | ||||
−0.613233 | + | 0.789902i | \(0.710131\pi\) | |||||||
\(102\) | 1.63368 | + | 1.63368i | 0.161759 | + | 0.161759i | ||||
\(103\) | − | 9.00947i | − | 0.887729i | −0.896094 | − | 0.443865i | \(-0.853607\pi\) | ||
0.896094 | − | 0.443865i | \(-0.146393\pi\) | |||||||
\(104\) | 5.12767 | 0.502809 | ||||||||
\(105\) | 1.17935 | − | 0.167527i | 0.115093 | − | 0.0163490i | ||||
\(106\) | 0.572887 | + | 0.572887i | 0.0556437 | + | 0.0556437i | ||||
\(107\) | 1.41163 | − | 1.41163i | 0.136468 | − | 0.136468i | −0.635573 | − | 0.772041i | \(-0.719236\pi\) |
0.772041 | + | 0.635573i | \(0.219236\pi\) | |||||||
\(108\) | −0.707107 | − | 0.707107i | −0.0680414 | − | 0.0680414i | ||||
\(109\) | 1.15892 | + | 1.15892i | 0.111004 | + | 0.111004i | 0.760427 | − | 0.649423i | \(-0.224990\pi\) |
−0.649423 | + | 0.760427i | \(0.724990\pi\) | |||||||
\(110\) | −2.84625 | + | 0.404311i | −0.271379 | + | 0.0385495i | ||||
\(111\) | −5.92113 | − | 1.39293i | −0.562009 | − | 0.132211i | ||||
\(112\) | −0.376687 | + | 0.376687i | −0.0355936 | + | 0.0355936i | ||||
\(113\) | 2.77598i | 0.261142i | 0.991439 | + | 0.130571i | \(0.0416811\pi\) | ||||
−0.991439 | + | 0.130571i | \(0.958319\pi\) | |||||||
\(114\) | −5.47960 | −0.513211 | ||||||||
\(115\) | −1.98044 | − | 13.9418i | −0.184677 | − | 1.30008i | ||||
\(116\) | 1.15504 | − | 1.15504i | 0.107243 | − | 0.107243i | ||||
\(117\) | − | 5.12767i | − | 0.474053i | ||||||
\(118\) | 1.04438 | + | 1.04438i | 0.0961427 | + | 0.0961427i | ||||
\(119\) | −0.870290 | − | 0.870290i | −0.0797794 | − | 0.0797794i | ||||
\(120\) | −1.78779 | − | 1.34306i | −0.163202 | − | 0.122604i | ||||
\(121\) | 9.34708 | 0.849734 | ||||||||
\(122\) | 3.44882 | + | 3.44882i | 0.312242 | + | 0.312242i | ||||
\(123\) | 1.50540 | + | 1.50540i | 0.135737 | + | 0.135737i | ||||
\(124\) | −7.11133 | − | 7.11133i | −0.638616 | − | 0.638616i | ||||
\(125\) | 4.59275 | + | 10.1935i | 0.410788 | + | 0.911731i | ||||
\(126\) | 0.376687 | + | 0.376687i | 0.0335580 | + | 0.0335580i | ||||
\(127\) | −10.6282 | + | 10.6282i | −0.943105 | + | 0.943105i | −0.998466 | − | 0.0553618i | \(-0.982369\pi\) |
0.0553618 | + | 0.998466i | \(0.482369\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 1.81107 | − | 1.81107i | 0.159456 | − | 0.159456i | ||||
\(130\) | −1.61253 | − | 11.3519i | −0.141429 | − | 0.995623i | ||||
\(131\) | 10.6555 | + | 10.6555i | 0.930972 | + | 0.930972i | 0.997767 | − | 0.0667945i | \(-0.0212772\pi\) |
−0.0667945 | + | 0.997767i | \(0.521277\pi\) | |||||||
\(132\) | −0.909099 | − | 0.909099i | −0.0791269 | − | 0.0791269i | ||||
\(133\) | 2.91907 | 0.253115 | ||||||||
\(134\) | −5.32260 | − | 5.32260i | −0.459802 | − | 0.459802i | ||||
\(135\) | −1.34306 | + | 1.78779i | −0.115592 | + | 0.153869i | ||||
\(136\) | 2.31038i | 0.198113i | ||||||||
\(137\) | 8.98795 | − | 8.98795i | 0.767892 | − | 0.767892i | −0.209843 | − | 0.977735i | \(-0.567295\pi\) |
0.977735 | + | 0.209843i | \(0.0672953\pi\) | |||||||
\(138\) | 4.45305 | − | 4.45305i | 0.379069 | − | 0.379069i | ||||
\(139\) | 19.4517 | 1.64987 | 0.824937 | − | 0.565225i | \(-0.191211\pi\) | ||||
0.824937 | + | 0.565225i | \(0.191211\pi\) | |||||||
\(140\) | 0.952386 | + | 0.715467i | 0.0804913 | + | 0.0604680i | ||||
\(141\) | − | 3.74092i | − | 0.315042i | ||||||
\(142\) | 4.38568 | 0.368038 | ||||||||
\(143\) | − | 6.59244i | − | 0.551287i | ||||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | −2.92032 | − | 2.19385i | −0.242519 | − | 0.182189i | ||||
\(146\) | −9.81049 | + | 9.81049i | −0.811922 | + | 0.811922i | ||||
\(147\) | 4.74908 | + | 4.74908i | 0.391698 | + | 0.391698i | ||||
\(148\) | −3.20192 | − | 5.17182i | −0.263196 | − | 0.425121i | ||||
\(149\) | − | 15.6534i | − | 1.28238i | −0.767382 | − | 0.641190i | \(-0.778441\pi\) | ||
0.767382 | − | 0.641190i | \(-0.221559\pi\) | |||||||
\(150\) | −2.41109 | + | 4.38025i | −0.196865 | + | 0.357646i | ||||
\(151\) | 3.10992i | 0.253082i | 0.991961 | + | 0.126541i | \(0.0403875\pi\) | ||||
−0.991961 | + | 0.126541i | \(0.959612\pi\) | |||||||
\(152\) | −3.87466 | − | 3.87466i | −0.314276 | − | 0.314276i | ||||
\(153\) | 2.31038 | 0.186783 | ||||||||
\(154\) | 0.484292 | + | 0.484292i | 0.0390253 | + | 0.0390253i | ||||
\(155\) | −13.5070 | + | 17.9797i | −1.08491 | + | 1.44417i | ||||
\(156\) | 3.62581 | − | 3.62581i | 0.290297 | − | 0.290297i | ||||
\(157\) | −12.5025 | + | 12.5025i | −0.997805 | + | 0.997805i | −0.999998 | − | 0.00219308i | \(-0.999302\pi\) |
0.00219308 | + | 0.999998i | \(0.499302\pi\) | |||||||
\(158\) | 11.4000 | + | 11.4000i | 0.906931 | + | 0.906931i | ||||
\(159\) | 0.810184 | 0.0642518 | ||||||||
\(160\) | −0.314477 | − | 2.21384i | −0.0248616 | − | 0.175020i | ||||
\(161\) | −2.37221 | + | 2.37221i | −0.186957 | + | 0.186957i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | − | 8.61293i | − | 0.674617i | −0.941394 | − | 0.337308i | \(-0.890483\pi\) | ||
0.941394 | − | 0.337308i | \(-0.109517\pi\) | |||||||
\(164\) | 2.12896i | 0.166244i | ||||||||
\(165\) | −1.72671 | + | 2.29849i | −0.134424 | + | 0.178938i | ||||
\(166\) | 11.5202 | + | 11.5202i | 0.894139 | + | 0.894139i | ||||
\(167\) | 21.8398i | 1.69001i | 0.534755 | + | 0.845007i | \(0.320404\pi\) | ||||
−0.534755 | + | 0.845007i | \(0.679596\pi\) | |||||||
\(168\) | 0.532716i | 0.0410999i | ||||||||
\(169\) | 13.2930 | 1.02254 | ||||||||
\(170\) | 5.11482 | − | 0.726561i | 0.392289 | − | 0.0557247i | ||||
\(171\) | −3.87466 | + | 3.87466i | −0.296303 | + | 0.296303i | ||||
\(172\) | 2.56124 | 0.195292 | ||||||||
\(173\) | −1.32378 | + | 1.32378i | −0.100645 | + | 0.100645i | −0.755636 | − | 0.654991i | \(-0.772672\pi\) |
0.654991 | + | 0.755636i | \(0.272672\pi\) | |||||||
\(174\) | − | 1.63348i | − | 0.123833i | ||||||
\(175\) | 1.28443 | − | 2.33343i | 0.0970937 | − | 0.176391i | ||||
\(176\) | − | 1.28566i | − | 0.0969103i | ||||||
\(177\) | 1.47697 | 0.111016 | ||||||||
\(178\) | −8.09354 | + | 8.09354i | −0.606636 | + | 0.606636i | ||||
\(179\) | 17.8003 | − | 17.8003i | 1.33046 | − | 1.33046i | 0.425501 | − | 0.904958i | \(-0.360098\pi\) |
0.904958 | − | 0.425501i | \(-0.139902\pi\) | |||||||
\(180\) | −2.21384 | + | 0.314477i | −0.165010 | + | 0.0234397i | ||||
\(181\) | −1.98719 | −0.147707 | −0.0738533 | − | 0.997269i | \(-0.523530\pi\) | ||||
−0.0738533 | + | 0.997269i | \(0.523530\pi\) | |||||||
\(182\) | −1.93153 | + | 1.93153i | −0.143174 | + | 0.143174i | ||||
\(183\) | 4.87737 | 0.360546 | ||||||||
\(184\) | 6.29757 | 0.464263 | ||||||||
\(185\) | −10.4427 | + | 8.71497i | −0.767760 | + | 0.640737i | ||||
\(186\) | −10.0569 | −0.737411 | ||||||||
\(187\) | 2.97036 | 0.217214 | ||||||||
\(188\) | 2.64523 | − | 2.64523i | 0.192923 | − | 0.192923i | ||||
\(189\) | 0.532716 | 0.0387494 | ||||||||
\(190\) | −7.35940 | + | 9.79638i | −0.533907 | + | 0.710704i | ||||
\(191\) | −4.41456 | + | 4.41456i | −0.319426 | + | 0.319426i | −0.848547 | − | 0.529120i | \(-0.822522\pi\) |
0.529120 | + | 0.848547i | \(0.322522\pi\) | |||||||
\(192\) | 0.707107 | − | 0.707107i | 0.0510310 | − | 0.0510310i | ||||
\(193\) | −2.09366 | −0.150705 | −0.0753524 | − | 0.997157i | \(-0.524008\pi\) | ||||
−0.0753524 | + | 0.997157i | \(0.524008\pi\) | |||||||
\(194\) | − | 8.07546i | − | 0.579784i | ||||||
\(195\) | −9.16721 | − | 6.88674i | −0.656477 | − | 0.493170i | ||||
\(196\) | 6.71621i | 0.479730i | ||||||||
\(197\) | −4.75052 | + | 4.75052i | −0.338460 | + | 0.338460i | −0.855788 | − | 0.517327i | \(-0.826927\pi\) |
0.517327 | + | 0.855788i | \(0.326927\pi\) | |||||||
\(198\) | −1.28566 | −0.0913679 | ||||||||
\(199\) | −4.93690 | + | 4.93690i | −0.349968 | + | 0.349968i | −0.860097 | − | 0.510130i | \(-0.829597\pi\) |
0.510130 | + | 0.860097i | \(0.329597\pi\) | |||||||
\(200\) | −4.80221 | + | 1.39241i | −0.339567 | + | 0.0984580i | ||||
\(201\) | −7.52729 | −0.530934 | ||||||||
\(202\) | 15.8768i | 1.11709i | ||||||||
\(203\) | 0.870179i | 0.0610746i | ||||||||
\(204\) | 1.63368 | + | 1.63368i | 0.114381 | + | 0.114381i | ||||
\(205\) | 4.71318 | − | 0.669508i | 0.329183 | − | 0.0467605i | ||||
\(206\) | − | 9.00947i | − | 0.627719i | ||||||
\(207\) | − | 6.29757i | − | 0.437711i | ||||||
\(208\) | 5.12767 | 0.355540 | ||||||||
\(209\) | −4.98150 | + | 4.98150i | −0.344577 | + | 0.344577i | ||||
\(210\) | 1.17935 | − | 0.167527i | 0.0813829 | − | 0.0115605i | ||||
\(211\) | −13.1658 | −0.906374 | −0.453187 | − | 0.891416i | \(-0.649713\pi\) | ||||
−0.453187 | + | 0.891416i | \(0.649713\pi\) | |||||||
\(212\) | 0.572887 | + | 0.572887i | 0.0393460 | + | 0.0393460i | ||||
\(213\) | 3.10114 | − | 3.10114i | 0.212487 | − | 0.212487i | ||||
\(214\) | 1.41163 | − | 1.41163i | 0.0964974 | − | 0.0964974i | ||||
\(215\) | −0.805450 | − | 5.67018i | −0.0549312 | − | 0.386703i | ||||
\(216\) | −0.707107 | − | 0.707107i | −0.0481125 | − | 0.0481125i | ||||
\(217\) | 5.35750 | 0.363690 | ||||||||
\(218\) | 1.15892 | + | 1.15892i | 0.0784919 | + | 0.0784919i | ||||
\(219\) | 13.8741i | 0.937526i | ||||||||
\(220\) | −2.84625 | + | 0.404311i | −0.191894 | + | 0.0272586i | ||||
\(221\) | 11.8469i | 0.796906i | ||||||||
\(222\) | −5.92113 | − | 1.39293i | −0.397400 | − | 0.0934874i | ||||
\(223\) | −13.0670 | − | 13.0670i | −0.875031 | − | 0.875031i | 0.117984 | − | 0.993015i | \(-0.462357\pi\) |
−0.993015 | + | 0.117984i | \(0.962357\pi\) | |||||||
\(224\) | −0.376687 | + | 0.376687i | −0.0251685 | + | 0.0251685i | ||||
\(225\) | 1.39241 | + | 4.80221i | 0.0928271 | + | 0.320147i | ||||
\(226\) | 2.77598i | 0.184655i | ||||||||
\(227\) | − | 16.0865i | − | 1.06770i | −0.845580 | − | 0.533848i | \(-0.820745\pi\) | ||
0.845580 | − | 0.533848i | \(-0.179255\pi\) | |||||||
\(228\) | −5.47960 | −0.362895 | ||||||||
\(229\) | − | 6.71533i | − | 0.443762i | −0.975074 | − | 0.221881i | \(-0.928780\pi\) | ||
0.975074 | − | 0.221881i | \(-0.0712196\pi\) | |||||||
\(230\) | −1.98044 | − | 13.9418i | −0.130586 | − | 0.919297i | ||||
\(231\) | 0.684892 | 0.0450626 | ||||||||
\(232\) | 1.15504 | − | 1.15504i | 0.0758322 | − | 0.0758322i | ||||
\(233\) | −4.61749 | + | 4.61749i | −0.302502 | + | 0.302502i | −0.841992 | − | 0.539490i | \(-0.818617\pi\) |
0.539490 | + | 0.841992i | \(0.318617\pi\) | |||||||
\(234\) | − | 5.12767i | − | 0.335206i | ||||||
\(235\) | −6.68799 | − | 5.02426i | −0.436277 | − | 0.327747i | ||||
\(236\) | 1.04438 | + | 1.04438i | 0.0679832 | + | 0.0679832i | ||||
\(237\) | 16.1220 | 1.04723 | ||||||||
\(238\) | −0.870290 | − | 0.870290i | −0.0564125 | − | 0.0564125i | ||||
\(239\) | −13.1078 | − | 13.1078i | −0.847873 | − | 0.847873i | 0.141995 | − | 0.989867i | \(-0.454648\pi\) |
−0.989867 | + | 0.141995i | \(0.954648\pi\) | |||||||
\(240\) | −1.78779 | − | 1.34306i | −0.115402 | − | 0.0866938i | ||||
\(241\) | −12.6538 | + | 12.6538i | −0.815103 | + | 0.815103i | −0.985394 | − | 0.170291i | \(-0.945529\pi\) |
0.170291 | + | 0.985394i | \(0.445529\pi\) | |||||||
\(242\) | 9.34708 | 0.600853 | ||||||||
\(243\) | −0.707107 | + | 0.707107i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | 3.44882 | + | 3.44882i | 0.220788 | + | 0.220788i | ||||
\(245\) | 14.8686 | − | 2.11209i | 0.949923 | − | 0.134937i | ||||
\(246\) | 1.50540 | + | 1.50540i | 0.0959808 | + | 0.0959808i | ||||
\(247\) | −19.8680 | − | 19.8680i | −1.26417 | − | 1.26417i | ||||
\(248\) | −7.11133 | − | 7.11133i | −0.451570 | − | 0.451570i | ||||
\(249\) | 16.2920 | 1.03246 | ||||||||
\(250\) | 4.59275 | + | 10.1935i | 0.290471 | + | 0.644691i | ||||
\(251\) | −0.829972 | − | 0.829972i | −0.0523874 | − | 0.0523874i | 0.680428 | − | 0.732815i | \(-0.261794\pi\) |
−0.732815 | + | 0.680428i | \(0.761794\pi\) | |||||||
\(252\) | 0.376687 | + | 0.376687i | 0.0237291 | + | 0.0237291i | ||||
\(253\) | − | 8.09653i | − | 0.509025i | ||||||
\(254\) | −10.6282 | + | 10.6282i | −0.666876 | + | 0.666876i | ||||
\(255\) | 3.10297 | − | 4.13048i | 0.194315 | − | 0.258661i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.61238i | 0.599604i | 0.954001 | + | 0.299802i | \(0.0969206\pi\) | ||||
−0.954001 | + | 0.299802i | \(0.903079\pi\) | |||||||
\(258\) | 1.81107 | − | 1.81107i | 0.112752 | − | 0.112752i | ||||
\(259\) | 3.15428 | + | 0.742037i | 0.195997 | + | 0.0461079i | ||||
\(260\) | −1.61253 | − | 11.3519i | −0.100005 | − | 0.704012i | ||||
\(261\) | −1.15504 | − | 1.15504i | −0.0714953 | − | 0.0714953i | ||||
\(262\) | 10.6555 | + | 10.6555i | 0.658297 | + | 0.658297i | ||||
\(263\) | −11.2512 | + | 11.2512i | −0.693779 | + | 0.693779i | −0.963061 | − | 0.269283i | \(-0.913213\pi\) |
0.269283 | + | 0.963061i | \(0.413213\pi\) | |||||||
\(264\) | −0.909099 | − | 0.909099i | −0.0559512 | − | 0.0559512i | ||||
\(265\) | 1.08812 | − | 1.44844i | 0.0668428 | − | 0.0889770i | ||||
\(266\) | 2.91907 | 0.178980 | ||||||||
\(267\) | 11.4460i | 0.700483i | ||||||||
\(268\) | −5.32260 | − | 5.32260i | −0.325129 | − | 0.325129i | ||||
\(269\) | 23.2912i | 1.42009i | 0.704158 | + | 0.710043i | \(0.251325\pi\) | ||||
−0.704158 | + | 0.710043i | \(0.748675\pi\) | |||||||
\(270\) | −1.34306 | + | 1.78779i | −0.0817357 | + | 0.108802i | ||||
\(271\) | 13.8775 | 0.842996 | 0.421498 | − | 0.906829i | \(-0.361504\pi\) | ||||
0.421498 | + | 0.906829i | \(0.361504\pi\) | |||||||
\(272\) | 2.31038i | 0.140087i | ||||||||
\(273\) | 2.73159i | 0.165323i | ||||||||
\(274\) | 8.98795 | − | 8.98795i | 0.542982 | − | 0.542982i | ||||
\(275\) | 1.79016 | + | 6.17401i | 0.107951 | + | 0.372307i | ||||
\(276\) | 4.45305 | − | 4.45305i | 0.268042 | − | 0.268042i | ||||
\(277\) | −6.57502 | −0.395055 | −0.197527 | − | 0.980297i | \(-0.563291\pi\) | ||||
−0.197527 | + | 0.980297i | \(0.563291\pi\) | |||||||
\(278\) | 19.4517 | 1.16664 | ||||||||
\(279\) | −7.11133 | + | 7.11133i | −0.425744 | + | 0.425744i | ||||
\(280\) | 0.952386 | + | 0.715467i | 0.0569160 | + | 0.0427573i | ||||
\(281\) | −13.5903 | + | 13.5903i | −0.810729 | + | 0.810729i | −0.984743 | − | 0.174015i | \(-0.944326\pi\) |
0.174015 | + | 0.984743i | \(0.444326\pi\) | |||||||
\(282\) | − | 3.74092i | − | 0.222769i | ||||||
\(283\) | 8.54984i | 0.508235i | 0.967173 | + | 0.254118i | \(0.0817850\pi\) | ||||
−0.967173 | + | 0.254118i | \(0.918215\pi\) | |||||||
\(284\) | 4.38568 | 0.260242 | ||||||||
\(285\) | 1.72321 | + | 12.1310i | 0.102074 | + | 0.718577i | ||||
\(286\) | − | 6.59244i | − | 0.389819i | ||||||
\(287\) | −0.801951 | − | 0.801951i | −0.0473377 | − | 0.0473377i | ||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 11.6621 | 0.686009 | ||||||||
\(290\) | −2.92032 | − | 2.19385i | −0.171487 | − | 0.128827i | ||||
\(291\) | −5.71021 | − | 5.71021i | −0.334739 | − | 0.334739i | ||||
\(292\) | −9.81049 | + | 9.81049i | −0.574115 | + | 0.574115i | ||||
\(293\) | 7.61554 | + | 7.61554i | 0.444905 | + | 0.444905i | 0.893656 | − | 0.448752i | \(-0.148131\pi\) |
−0.448752 | + | 0.893656i | \(0.648131\pi\) | |||||||
\(294\) | 4.74908 | + | 4.74908i | 0.276972 | + | 0.276972i | ||||
\(295\) | 1.98366 | − | 2.64052i | 0.115493 | − | 0.153737i | ||||
\(296\) | −3.20192 | − | 5.17182i | −0.186108 | − | 0.300606i | ||||
\(297\) | −0.909099 | + | 0.909099i | −0.0527513 | + | 0.0527513i | ||||
\(298\) | − | 15.6534i | − | 0.906779i | ||||||
\(299\) | 32.2918 | 1.86749 | ||||||||
\(300\) | −2.41109 | + | 4.38025i | −0.139205 | + | 0.252894i | ||||
\(301\) | −0.964785 | + | 0.964785i | −0.0556093 | + | 0.0556093i | ||||
\(302\) | 3.10992i | 0.178956i | ||||||||
\(303\) | 11.2266 | + | 11.2266i | 0.644952 | + | 0.644952i | ||||
\(304\) | −3.87466 | − | 3.87466i | −0.222227 | − | 0.222227i | ||||
\(305\) | 6.55058 | − | 8.71973i | 0.375085 | − | 0.499290i | ||||
\(306\) | 2.31038 | 0.132076 | ||||||||
\(307\) | −19.6731 | − | 19.6731i | −1.12280 | − | 1.12280i | −0.991319 | − | 0.131482i | \(-0.958026\pi\) |
−0.131482 | − | 0.991319i | \(-0.541974\pi\) | |||||||
\(308\) | 0.484292 | + | 0.484292i | 0.0275951 | + | 0.0275951i | ||||
\(309\) | −6.37065 | − | 6.37065i | −0.362414 | − | 0.362414i | ||||
\(310\) | −13.5070 | + | 17.9797i | −0.767147 | + | 1.02118i | ||||
\(311\) | −3.86047 | − | 3.86047i | −0.218907 | − | 0.218907i | 0.589131 | − | 0.808038i | \(-0.299470\pi\) |
−0.808038 | + | 0.589131i | \(0.799470\pi\) | |||||||
\(312\) | 3.62581 | − | 3.62581i | 0.205271 | − | 0.205271i | ||||
\(313\) | 18.9968 | 1.07376 | 0.536880 | − | 0.843659i | \(-0.319603\pi\) | ||||
0.536880 | + | 0.843659i | \(0.319603\pi\) | |||||||
\(314\) | −12.5025 | + | 12.5025i | −0.705554 | + | 0.705554i | ||||
\(315\) | 0.715467 | − | 0.952386i | 0.0403120 | − | 0.0536609i | ||||
\(316\) | 11.4000 | + | 11.4000i | 0.641297 | + | 0.641297i | ||||
\(317\) | 17.8153 | + | 17.8153i | 1.00061 | + | 1.00061i | 1.00000 | 0.000608272i | \(0.000193619\pi\) | |
0.000608272 | 1.00000i | \(0.499806\pi\) | ||||||||
\(318\) | 0.810184 | 0.0454329 | ||||||||
\(319\) | −1.48499 | − | 1.48499i | −0.0831435 | − | 0.0831435i | ||||
\(320\) | −0.314477 | − | 2.21384i | −0.0175798 | − | 0.123758i | ||||
\(321\) | − | 1.99635i | − | 0.111426i | ||||||
\(322\) | −2.37221 | + | 2.37221i | −0.132198 | + | 0.132198i | ||||
\(323\) | 8.95194 | − | 8.95194i | 0.498099 | − | 0.498099i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −24.6241 | + | 7.13980i | −1.36590 | + | 0.396045i | ||||
\(326\) | − | 8.61293i | − | 0.477026i | ||||||
\(327\) | 1.63896 | 0.0906347 | ||||||||
\(328\) | 2.12896i | 0.117552i | ||||||||
\(329\) | 1.99285i | 0.109869i | ||||||||
\(330\) | −1.72671 | + | 2.29849i | −0.0950524 | + | 0.126528i | ||||
\(331\) | −1.11563 | + | 1.11563i | −0.0613208 | + | 0.0613208i | −0.737102 | − | 0.675781i | \(-0.763806\pi\) |
0.675781 | + | 0.737102i | \(0.263806\pi\) | |||||||
\(332\) | 11.5202 | + | 11.5202i | 0.632252 | + | 0.632252i | ||||
\(333\) | −5.17182 | + | 3.20192i | −0.283414 | + | 0.175464i | ||||
\(334\) | 21.8398i | 1.19502i | ||||||||
\(335\) | −10.1096 | + | 13.4572i | −0.552344 | + | 0.735247i | ||||
\(336\) | 0.532716i | 0.0290621i | ||||||||
\(337\) | −19.6821 | − | 19.6821i | −1.07215 | − | 1.07215i | −0.997186 | − | 0.0749653i | \(-0.976115\pi\) |
−0.0749653 | − | 0.997186i | \(-0.523885\pi\) | |||||||
\(338\) | 13.2930 | 0.723042 | ||||||||
\(339\) | 1.96291 | + | 1.96291i | 0.106611 | + | 0.106611i | ||||
\(340\) | 5.11482 | − | 0.726561i | 0.277390 | − | 0.0394033i | ||||
\(341\) | −9.14275 | + | 9.14275i | −0.495108 | + | 0.495108i | ||||
\(342\) | −3.87466 | + | 3.87466i | −0.209518 | + | 0.209518i | ||||
\(343\) | −5.16672 | − | 5.16672i | −0.278977 | − | 0.278977i | ||||
\(344\) | 2.56124 | 0.138093 | ||||||||
\(345\) | −11.2587 | − | 8.45798i | −0.606151 | − | 0.455362i | ||||
\(346\) | −1.32378 | + | 1.32378i | −0.0711669 | + | 0.0711669i | ||||
\(347\) | −3.98304 | −0.213821 | −0.106910 | − | 0.994269i | \(-0.534096\pi\) | ||||
−0.106910 | + | 0.994269i | \(0.534096\pi\) | |||||||
\(348\) | − | 1.63348i | − | 0.0875635i | ||||||
\(349\) | − | 7.69090i | − | 0.411684i | −0.978585 | − | 0.205842i | \(-0.934007\pi\) | ||
0.978585 | − | 0.205842i | \(-0.0659934\pi\) | |||||||
\(350\) | 1.28443 | − | 2.33343i | 0.0686556 | − | 0.124727i | ||||
\(351\) | −3.62581 | − | 3.62581i | −0.193531 | − | 0.193531i | ||||
\(352\) | − | 1.28566i | − | 0.0685259i | ||||||
\(353\) | − | 21.0577i | − | 1.12079i | −0.828226 | − | 0.560395i | \(-0.810649\pi\) | ||
0.828226 | − | 0.560395i | \(-0.189351\pi\) | |||||||
\(354\) | 1.47697 | 0.0785002 | ||||||||
\(355\) | −1.37919 | − | 9.70920i | −0.0732000 | − | 0.515311i | ||||
\(356\) | −8.09354 | + | 8.09354i | −0.428957 | + | 0.428957i | ||||
\(357\) | −1.23078 | −0.0651396 | ||||||||
\(358\) | 17.8003 | − | 17.8003i | 0.940777 | − | 0.940777i | ||||
\(359\) | − | 19.0802i | − | 1.00701i | −0.863992 | − | 0.503506i | \(-0.832043\pi\) | ||
0.863992 | − | 0.503506i | \(-0.167957\pi\) | |||||||
\(360\) | −2.21384 | + | 0.314477i | −0.116680 | + | 0.0165744i | ||||
\(361\) | 11.0260i | 0.580315i | ||||||||
\(362\) | −1.98719 | −0.104444 | ||||||||
\(363\) | 6.60938 | − | 6.60938i | 0.346903 | − | 0.346903i | ||||
\(364\) | −1.93153 | + | 1.93153i | −0.101240 | + | 0.101240i | ||||
\(365\) | 24.8041 | + | 18.6337i | 1.29830 | + | 0.975333i | ||||
\(366\) | 4.87737 | 0.254944 | ||||||||
\(367\) | 13.0910 | − | 13.0910i | 0.683346 | − | 0.683346i | −0.277407 | − | 0.960753i | \(-0.589475\pi\) |
0.960753 | + | 0.277407i | \(0.0894750\pi\) | |||||||
\(368\) | 6.29757 | 0.328283 | ||||||||
\(369\) | 2.12896 | 0.110829 | ||||||||
\(370\) | −10.4427 | + | 8.71497i | −0.542889 | + | 0.453070i | ||||
\(371\) | −0.431598 | −0.0224075 | ||||||||
\(372\) | −10.0569 | −0.521428 | ||||||||
\(373\) | −17.5157 | + | 17.5157i | −0.906927 | + | 0.906927i | −0.996023 | − | 0.0890959i | \(-0.971602\pi\) |
0.0890959 | + | 0.996023i | \(0.471602\pi\) | |||||||
\(374\) | 2.97036 | 0.153594 | ||||||||
\(375\) | 10.4554 | + | 3.96030i | 0.539916 | + | 0.204509i | ||||
\(376\) | 2.64523 | − | 2.64523i | 0.136417 | − | 0.136417i | ||||
\(377\) | 5.92267 | − | 5.92267i | 0.305033 | − | 0.305033i | ||||
\(378\) | 0.532716 | 0.0274000 | ||||||||
\(379\) | − | 21.8739i | − | 1.12358i | −0.827278 | − | 0.561792i | \(-0.810112\pi\) | ||
0.827278 | − | 0.561792i | \(-0.189888\pi\) | |||||||
\(380\) | −7.35940 | + | 9.79638i | −0.377529 | + | 0.502544i | ||||
\(381\) | 15.0306i | 0.770042i | ||||||||
\(382\) | −4.41456 | + | 4.41456i | −0.225868 | + | 0.225868i | ||||
\(383\) | −5.61751 | −0.287042 | −0.143521 | − | 0.989647i | \(-0.545842\pi\) | ||||
−0.143521 | + | 0.989647i | \(0.545842\pi\) | |||||||
\(384\) | 0.707107 | − | 0.707107i | 0.0360844 | − | 0.0360844i | ||||
\(385\) | 0.919848 | − | 1.22444i | 0.0468798 | − | 0.0624035i | ||||
\(386\) | −2.09366 | −0.106564 | ||||||||
\(387\) | − | 2.56124i | − | 0.130195i | ||||||
\(388\) | − | 8.07546i | − | 0.409969i | ||||||
\(389\) | 5.37334 | + | 5.37334i | 0.272439 | + | 0.272439i | 0.830081 | − | 0.557642i | \(-0.188294\pi\) |
−0.557642 | + | 0.830081i | \(0.688294\pi\) | |||||||
\(390\) | −9.16721 | − | 6.88674i | −0.464200 | − | 0.348724i | ||||
\(391\) | 14.5498i | 0.735814i | ||||||||
\(392\) | 6.71621i | 0.339220i | ||||||||
\(393\) | 15.0691 | 0.760136 | ||||||||
\(394\) | −4.75052 | + | 4.75052i | −0.239328 | + | 0.239328i | ||||
\(395\) | 21.6527 | − | 28.8227i | 1.08946 | − | 1.45023i | ||||
\(396\) | −1.28566 | −0.0646069 | ||||||||
\(397\) | 17.9874 | + | 17.9874i | 0.902761 | + | 0.902761i | 0.995674 | − | 0.0929128i | \(-0.0296178\pi\) |
−0.0929128 | + | 0.995674i | \(0.529618\pi\) | |||||||
\(398\) | −4.93690 | + | 4.93690i | −0.247465 | + | 0.247465i | ||||
\(399\) | 2.06409 | − | 2.06409i | 0.103334 | − | 0.103334i | ||||
\(400\) | −4.80221 | + | 1.39241i | −0.240110 | + | 0.0696203i | ||||
\(401\) | 15.1996 | + | 15.1996i | 0.759033 | + | 0.759033i | 0.976146 | − | 0.217113i | \(-0.0696641\pi\) |
−0.217113 | + | 0.976146i | \(0.569664\pi\) | |||||||
\(402\) | −7.52729 | −0.375427 | ||||||||
\(403\) | −36.4645 | − | 36.4645i | −1.81643 | − | 1.81643i | ||||
\(404\) | 15.8768i | 0.789902i | ||||||||
\(405\) | 0.314477 | + | 2.21384i | 0.0156265 | + | 0.110007i | ||||
\(406\) | 0.870179i | 0.0431863i | ||||||||
\(407\) | −6.64920 | + | 4.11658i | −0.329589 | + | 0.204051i | ||||
\(408\) | 1.63368 | + | 1.63368i | 0.0808795 | + | 0.0808795i | ||||
\(409\) | −27.1312 | + | 27.1312i | −1.34155 | + | 1.34155i | −0.447033 | + | 0.894517i | \(0.647519\pi\) |
−0.894517 | + | 0.447033i | \(0.852481\pi\) | |||||||
\(410\) | 4.71318 | − | 0.669508i | 0.232767 | − | 0.0330646i | ||||
\(411\) | − | 12.7109i | − | 0.626981i | ||||||
\(412\) | − | 9.00947i | − | 0.443865i | ||||||
\(413\) | −0.786807 | −0.0387163 | ||||||||
\(414\) | − | 6.29757i | − | 0.309509i | ||||||
\(415\) | 21.8810 | − | 29.1267i | 1.07410 | − | 1.42977i | ||||
\(416\) | 5.12767 | 0.251405 | ||||||||
\(417\) | 13.7544 | − | 13.7544i | 0.673558 | − | 0.673558i | ||||
\(418\) | −4.98150 | + | 4.98150i | −0.243653 | + | 0.243653i | ||||
\(419\) | − | 7.19965i | − | 0.351726i | −0.984415 | − | 0.175863i | \(-0.943728\pi\) | ||
0.984415 | − | 0.175863i | \(-0.0562716\pi\) | |||||||
\(420\) | 1.17935 | − | 0.167527i | 0.0575464 | − | 0.00817448i | ||||
\(421\) | 6.17926 | + | 6.17926i | 0.301159 | + | 0.301159i | 0.841467 | − | 0.540308i | \(-0.181692\pi\) |
−0.540308 | + | 0.841467i | \(0.681692\pi\) | |||||||
\(422\) | −13.1658 | −0.640903 | ||||||||
\(423\) | −2.64523 | − | 2.64523i | −0.128616 | − | 0.128616i | ||||
\(424\) | 0.572887 | + | 0.572887i | 0.0278218 | + | 0.0278218i | ||||
\(425\) | −3.21699 | − | 11.0949i | −0.156047 | − | 0.538183i | ||||
\(426\) | 3.10114 | − | 3.10114i | 0.150251 | − | 0.150251i | ||||
\(427\) | −2.59825 | −0.125738 | ||||||||
\(428\) | 1.41163 | − | 1.41163i | 0.0682340 | − | 0.0682340i | ||||
\(429\) | −4.66156 | − | 4.66156i | −0.225062 | − | 0.225062i | ||||
\(430\) | −0.805450 | − | 5.67018i | −0.0388423 | − | 0.273440i | ||||
\(431\) | 19.0871 | + | 19.0871i | 0.919394 | + | 0.919394i | 0.996985 | − | 0.0775910i | \(-0.0247228\pi\) |
−0.0775910 | + | 0.996985i | \(0.524723\pi\) | |||||||
\(432\) | −0.707107 | − | 0.707107i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | −27.0193 | − | 27.0193i | −1.29847 | − | 1.29847i | −0.929405 | − | 0.369061i | \(-0.879679\pi\) |
−0.369061 | − | 0.929405i | \(-0.620321\pi\) | |||||||
\(434\) | 5.35750 | 0.257168 | ||||||||
\(435\) | −3.61626 | + | 0.513691i | −0.173386 | + | 0.0246296i | ||||
\(436\) | 1.15892 | + | 1.15892i | 0.0555022 | + | 0.0555022i | ||||
\(437\) | −24.4009 | − | 24.4009i | −1.16726 | − | 1.16726i | ||||
\(438\) | 13.8741i | 0.662931i | ||||||||
\(439\) | −8.21948 | + | 8.21948i | −0.392294 | + | 0.392294i | −0.875504 | − | 0.483210i | \(-0.839471\pi\) |
0.483210 | + | 0.875504i | \(0.339471\pi\) | |||||||
\(440\) | −2.84625 | + | 0.404311i | −0.135690 | + | 0.0192748i | ||||
\(441\) | 6.71621 | 0.319820 | ||||||||
\(442\) | 11.8469i | 0.563497i | ||||||||
\(443\) | 7.35664 | − | 7.35664i | 0.349525 | − | 0.349525i | −0.510408 | − | 0.859932i | \(-0.670506\pi\) |
0.859932 | + | 0.510408i | \(0.170506\pi\) | |||||||
\(444\) | −5.92113 | − | 1.39293i | −0.281004 | − | 0.0661055i | ||||
\(445\) | 20.4631 | + | 15.3726i | 0.970042 | + | 0.728731i | ||||
\(446\) | −13.0670 | − | 13.0670i | −0.618740 | − | 0.618740i | ||||
\(447\) | −11.0687 | − | 11.0687i | −0.523529 | − | 0.523529i | ||||
\(448\) | −0.376687 | + | 0.376687i | −0.0177968 | + | 0.0177968i | ||||
\(449\) | −15.3192 | − | 15.3192i | −0.722956 | − | 0.722956i | 0.246250 | − | 0.969206i | \(-0.420801\pi\) |
−0.969206 | + | 0.246250i | \(0.920801\pi\) | |||||||
\(450\) | 1.39241 | + | 4.80221i | 0.0656387 | + | 0.226378i | ||||
\(451\) | 2.73711 | 0.128886 | ||||||||
\(452\) | 2.77598i | 0.130571i | ||||||||
\(453\) | 2.19905 | + | 2.19905i | 0.103320 | + | 0.103320i | ||||
\(454\) | − | 16.0865i | − | 0.754975i | ||||||
\(455\) | 4.88352 | + | 3.66868i | 0.228943 | + | 0.171990i | ||||
\(456\) | −5.47960 | −0.256606 | ||||||||
\(457\) | − | 11.9041i | − | 0.556852i | −0.960458 | − | 0.278426i | \(-0.910187\pi\) | ||
0.960458 | − | 0.278426i | \(-0.0898127\pi\) | |||||||
\(458\) | − | 6.71533i | − | 0.313787i | ||||||
\(459\) | 1.63368 | − | 1.63368i | 0.0762539 | − | 0.0762539i | ||||
\(460\) | −1.98044 | − | 13.9418i | −0.0923385 | − | 0.650041i | ||||
\(461\) | −21.6193 | + | 21.6193i | −1.00691 | + | 1.00691i | −0.00693591 | + | 0.999976i | \(0.502208\pi\) |
−0.999976 | + | 0.00693591i | \(0.997792\pi\) | |||||||
\(462\) | 0.684892 | 0.0318641 | ||||||||
\(463\) | 7.74140 | 0.359773 | 0.179887 | − | 0.983687i | \(-0.442427\pi\) | ||||
0.179887 | + | 0.983687i | \(0.442427\pi\) | |||||||
\(464\) | 1.15504 | − | 1.15504i | 0.0536215 | − | 0.0536215i | ||||
\(465\) | 3.16268 | + | 22.2645i | 0.146666 | + | 1.03249i | ||||
\(466\) | −4.61749 | + | 4.61749i | −0.213901 | + | 0.213901i | ||||
\(467\) | − | 40.6171i | − | 1.87954i | −0.341813 | − | 0.939768i | \(-0.611041\pi\) | ||
0.341813 | − | 0.939768i | \(-0.388959\pi\) | |||||||
\(468\) | − | 5.12767i | − | 0.237027i | ||||||
\(469\) | 4.00991 | 0.185160 | ||||||||
\(470\) | −6.68799 | − | 5.02426i | −0.308494 | − | 0.231752i | ||||
\(471\) | 17.6811i | 0.814704i | ||||||||
\(472\) | 1.04438 | + | 1.04438i | 0.0480714 | + | 0.0480714i | ||||
\(473\) | − | 3.29288i | − | 0.151407i | ||||||
\(474\) | 16.1220 | 0.740506 | ||||||||
\(475\) | 24.0020 | + | 13.2118i | 1.10129 | + | 0.606200i | ||||
\(476\) | −0.870290 | − | 0.870290i | −0.0398897 | − | 0.0398897i | ||||
\(477\) | 0.572887 | − | 0.572887i | 0.0262307 | − | 0.0262307i | ||||
\(478\) | −13.1078 | − | 13.1078i | −0.599537 | − | 0.599537i | ||||
\(479\) | −4.76750 | − | 4.76750i | −0.217833 | − | 0.217833i | 0.589752 | − | 0.807585i | \(-0.299226\pi\) |
−0.807585 | + | 0.589752i | \(0.799226\pi\) | |||||||
\(480\) | −1.78779 | − | 1.34306i | −0.0816012 | − | 0.0613018i | ||||
\(481\) | −16.4184 | − | 26.5194i | −0.748613 | − | 1.20918i | ||||
\(482\) | −12.6538 | + | 12.6538i | −0.576365 | + | 0.576365i | ||||
\(483\) | 3.35482i | 0.152649i | ||||||||
\(484\) | 9.34708 | 0.424867 | ||||||||
\(485\) | −17.8778 | + | 2.53955i | −0.811789 | + | 0.115315i | ||||
\(486\) | −0.707107 | + | 0.707107i | −0.0320750 | + | 0.0320750i | ||||
\(487\) | 16.5284i | 0.748971i | 0.927233 | + | 0.374486i | \(0.122181\pi\) | ||||
−0.927233 | + | 0.374486i | \(0.877819\pi\) | |||||||
\(488\) | 3.44882 | + | 3.44882i | 0.156121 | + | 0.156121i | ||||
\(489\) | −6.09026 | − | 6.09026i | −0.275411 | − | 0.275411i | ||||
\(490\) | 14.8686 | − | 2.11209i | 0.671697 | − | 0.0954147i | ||||
\(491\) | −11.4600 | −0.517185 | −0.258592 | − | 0.965987i | \(-0.583259\pi\) | ||||
−0.258592 | + | 0.965987i | \(0.583259\pi\) | |||||||
\(492\) | 1.50540 | + | 1.50540i | 0.0678687 | + | 0.0678687i | ||||
\(493\) | 2.66858 | + | 2.66858i | 0.120187 | + | 0.120187i | ||||
\(494\) | −19.8680 | − | 19.8680i | −0.893902 | − | 0.893902i | ||||
\(495\) | 0.404311 | + | 2.84625i | 0.0181724 | + | 0.127929i | ||||
\(496\) | −7.11133 | − | 7.11133i | −0.319308 | − | 0.319308i | ||||
\(497\) | −1.65203 | + | 1.65203i | −0.0741036 | + | 0.0741036i | ||||
\(498\) | 16.2920 | 0.730062 | ||||||||
\(499\) | −11.0278 | + | 11.0278i | −0.493674 | + | 0.493674i | −0.909462 | − | 0.415788i | \(-0.863506\pi\) |
0.415788 | + | 0.909462i | \(0.363506\pi\) | |||||||
\(500\) | 4.59275 | + | 10.1935i | 0.205394 | + | 0.455865i | ||||
\(501\) | 15.4431 | + | 15.4431i | 0.689946 | + | 0.689946i | ||||
\(502\) | −0.829972 | − | 0.829972i | −0.0370435 | − | 0.0370435i | ||||
\(503\) | 17.9392 | 0.799870 | 0.399935 | − | 0.916543i | \(-0.369033\pi\) | ||||
0.399935 | + | 0.916543i | \(0.369033\pi\) | |||||||
\(504\) | 0.376687 | + | 0.376687i | 0.0167790 | + | 0.0167790i | ||||
\(505\) | 35.1488 | − | 4.99290i | 1.56410 | − | 0.222181i | ||||
\(506\) | − | 8.09653i | − | 0.359935i | ||||||
\(507\) | 9.39955 | − | 9.39955i | 0.417449 | − | 0.417449i | ||||
\(508\) | −10.6282 | + | 10.6282i | −0.471552 | + | 0.471552i | ||||
\(509\) | −10.1276 | −0.448897 | −0.224448 | − | 0.974486i | \(-0.572058\pi\) | ||||
−0.224448 | + | 0.974486i | \(0.572058\pi\) | |||||||
\(510\) | 3.10297 | − | 4.13048i | 0.137402 | − | 0.182901i | ||||
\(511\) | − | 7.39097i | − | 0.326957i | ||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 5.47960i | 0.241930i | ||||||||
\(514\) | 9.61238i | 0.423984i | ||||||||
\(515\) | −19.9455 | + | 2.83327i | −0.878906 | + | 0.124849i | ||||
\(516\) | 1.81107 | − | 1.81107i | 0.0797278 | − | 0.0797278i | ||||
\(517\) | −3.40087 | − | 3.40087i | −0.149570 | − | 0.149570i | ||||
\(518\) | 3.15428 | + | 0.742037i | 0.138591 | + | 0.0326032i | ||||
\(519\) | 1.87211i | 0.0821764i | ||||||||
\(520\) | −1.61253 | − | 11.3519i | −0.0707143 | − | 0.497812i | ||||
\(521\) | − | 2.42962i | − | 0.106444i | −0.998583 | − | 0.0532219i | \(-0.983051\pi\) | ||
0.998583 | − | 0.0532219i | \(-0.0169491\pi\) | |||||||
\(522\) | −1.15504 | − | 1.15504i | −0.0505548 | − | 0.0505548i | ||||
\(523\) | −27.3470 | −1.19580 | −0.597901 | − | 0.801570i | \(-0.703998\pi\) | ||||
−0.597901 | + | 0.801570i | \(0.703998\pi\) | |||||||
\(524\) | 10.6555 | + | 10.6555i | 0.465486 | + | 0.465486i | ||||
\(525\) | −0.741757 | − | 2.55821i | −0.0323729 | − | 0.111650i | ||||
\(526\) | −11.2512 | + | 11.2512i | −0.490576 | + | 0.490576i | ||||
\(527\) | 16.4299 | − | 16.4299i | 0.715696 | − | 0.715696i | ||||
\(528\) | −0.909099 | − | 0.909099i | −0.0395635 | − | 0.0395635i | ||||
\(529\) | 16.6594 | 0.724321 | ||||||||
\(530\) | 1.08812 | − | 1.44844i | 0.0472650 | − | 0.0629163i | ||||
\(531\) | 1.04438 | − | 1.04438i | 0.0453221 | − | 0.0453221i | ||||
\(532\) | 2.91907 | 0.126558 | ||||||||
\(533\) | 10.9166i | 0.472850i | ||||||||
\(534\) | 11.4460i | 0.495317i | ||||||||
\(535\) | −3.56907 | − | 2.68121i | −0.154304 | − | 0.115919i | ||||
\(536\) | −5.32260 | − | 5.32260i | −0.229901 | − | 0.229901i | ||||
\(537\) | − | 25.1735i | − | 1.08632i | ||||||
\(538\) | 23.2912i | 1.00415i | ||||||||
\(539\) | 8.63477 | 0.371926 | ||||||||
\(540\) | −1.34306 | + | 1.78779i | −0.0577959 | + | 0.0769344i | ||||
\(541\) | 24.0214 | − | 24.0214i | 1.03276 | − | 1.03276i | 0.0333158 | − | 0.999445i | \(-0.489393\pi\) |
0.999445 | − | 0.0333158i | \(-0.0106067\pi\) | |||||||
\(542\) | 13.8775 | 0.596088 | ||||||||
\(543\) | −1.40516 | + | 1.40516i | −0.0603010 | + | 0.0603010i | ||||
\(544\) | 2.31038i | 0.0990567i | ||||||||
\(545\) | 2.20121 | − | 2.93012i | 0.0942896 | − | 0.125513i | ||||
\(546\) | 2.73159i | 0.116901i | ||||||||
\(547\) | 37.8077 | 1.61654 | 0.808271 | − | 0.588810i | \(-0.200404\pi\) | ||||
0.808271 | + | 0.588810i | \(0.200404\pi\) | |||||||
\(548\) | 8.98795 | − | 8.98795i | 0.383946 | − | 0.383946i | ||||
\(549\) | 3.44882 | − | 3.44882i | 0.147192 | − | 0.147192i | ||||
\(550\) | 1.79016 | + | 6.17401i | 0.0763327 | + | 0.263261i | ||||
\(551\) | −8.95079 | −0.381316 | ||||||||
\(552\) | 4.45305 | − | 4.45305i | 0.189535 | − | 0.189535i | ||||
\(553\) | −8.58843 | −0.365217 | ||||||||
\(554\) | −6.57502 | −0.279346 | ||||||||
\(555\) | −1.22167 | + | 13.5465i | −0.0518571 | + | 0.575017i | ||||
\(556\) | 19.4517 | 0.824937 | ||||||||
\(557\) | −18.1545 | −0.769231 | −0.384615 | − | 0.923077i | \(-0.625666\pi\) | ||||
−0.384615 | + | 0.923077i | \(0.625666\pi\) | |||||||
\(558\) | −7.11133 | + | 7.11133i | −0.301047 | + | 0.301047i | ||||
\(559\) | 13.1332 | 0.555474 | ||||||||
\(560\) | 0.952386 | + | 0.715467i | 0.0402457 | + | 0.0302340i | ||||
\(561\) | 2.10036 | − | 2.10036i | 0.0886774 | − | 0.0886774i | ||||
\(562\) | −13.5903 | + | 13.5903i | −0.573272 | + | 0.573272i | ||||
\(563\) | 19.8695 | 0.837398 | 0.418699 | − | 0.908125i | \(-0.362486\pi\) | ||||
0.418699 | + | 0.908125i | \(0.362486\pi\) | |||||||
\(564\) | − | 3.74092i | − | 0.157521i | ||||||
\(565\) | 6.14558 | − | 0.872982i | 0.258547 | − | 0.0367266i | ||||
\(566\) | 8.54984i | 0.359376i | ||||||||
\(567\) | 0.376687 | − | 0.376687i | 0.0158194 | − | 0.0158194i | ||||
\(568\) | 4.38568 | 0.184019 | ||||||||
\(569\) | 6.05236 | − | 6.05236i | 0.253728 | − | 0.253728i | −0.568769 | − | 0.822497i | \(-0.692580\pi\) |
0.822497 | + | 0.568769i | \(0.192580\pi\) | |||||||
\(570\) | 1.72321 | + | 12.1310i | 0.0721772 | + | 0.508111i | ||||
\(571\) | 12.1222 | 0.507297 | 0.253648 | − | 0.967296i | \(-0.418369\pi\) | ||||
0.253648 | + | 0.967296i | \(0.418369\pi\) | |||||||
\(572\) | − | 6.59244i | − | 0.275644i | ||||||
\(573\) | 6.24313i | 0.260810i | ||||||||
\(574\) | −0.801951 | − | 0.801951i | −0.0334728 | − | 0.0334728i | ||||
\(575\) | −30.2422 | + | 8.76877i | −1.26119 | + | 0.365683i | ||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | − | 36.8080i | − | 1.53234i | −0.642641 | − | 0.766168i | \(-0.722161\pi\) | ||
0.642641 | − | 0.766168i | \(-0.277839\pi\) | |||||||
\(578\) | 11.6621 | 0.485081 | ||||||||
\(579\) | −1.48044 | + | 1.48044i | −0.0615249 | + | 0.0615249i | ||||
\(580\) | −2.92032 | − | 2.19385i | −0.121260 | − | 0.0910946i | ||||
\(581\) | −8.67901 | −0.360066 | ||||||||
\(582\) | −5.71021 | − | 5.71021i | −0.236696 | − | 0.236696i | ||||
\(583\) | 0.736538 | − | 0.736538i | 0.0305043 | − | 0.0305043i | ||||
\(584\) | −9.81049 | + | 9.81049i | −0.405961 | + | 0.405961i | ||||
\(585\) | −11.3519 | + | 1.61253i | −0.469341 | + | 0.0666701i | ||||
\(586\) | 7.61554 | + | 7.61554i | 0.314595 | + | 0.314595i | ||||
\(587\) | −14.5475 | −0.600439 | −0.300220 | − | 0.953870i | \(-0.597060\pi\) | ||||
−0.300220 | + | 0.953870i | \(0.597060\pi\) | |||||||
\(588\) | 4.74908 | + | 4.74908i | 0.195849 | + | 0.195849i | ||||
\(589\) | 55.1080i | 2.27068i | ||||||||
\(590\) | 1.98366 | − | 2.64052i | 0.0816658 | − | 0.108709i | ||||
\(591\) | 6.71825i | 0.276352i | ||||||||
\(592\) | −3.20192 | − | 5.17182i | −0.131598 | − | 0.212560i | ||||
\(593\) | −16.6115 | − | 16.6115i | −0.682153 | − | 0.682153i | 0.278332 | − | 0.960485i | \(-0.410219\pi\) |
−0.960485 | + | 0.278332i | \(0.910219\pi\) | |||||||
\(594\) | −0.909099 | + | 0.909099i | −0.0373008 | + | 0.0373008i | ||||
\(595\) | −1.65300 | + | 2.20037i | −0.0677664 | + | 0.0902065i | ||||
\(596\) | − | 15.6534i | − | 0.641190i | ||||||
\(597\) | 6.98183i | 0.285747i | ||||||||
\(598\) | 32.2918 | 1.32051 | ||||||||
\(599\) | − | 13.5361i | − | 0.553069i | −0.961004 | − | 0.276535i | \(-0.910814\pi\) | ||
0.961004 | − | 0.276535i | \(-0.0891861\pi\) | |||||||
\(600\) | −2.41109 | + | 4.38025i | −0.0984325 | + | 0.178823i | ||||
\(601\) | 8.79388 | 0.358710 | 0.179355 | − | 0.983784i | \(-0.442599\pi\) | ||||
0.179355 | + | 0.983784i | \(0.442599\pi\) | |||||||
\(602\) | −0.964785 | + | 0.964785i | −0.0393217 | + | 0.0393217i | ||||
\(603\) | −5.32260 | + | 5.32260i | −0.216753 | + | 0.216753i | ||||
\(604\) | 3.10992i | 0.126541i | ||||||||
\(605\) | −2.93944 | − | 20.6930i | −0.119505 | − | 0.841289i | ||||
\(606\) | 11.2266 | + | 11.2266i | 0.456050 | + | 0.456050i | ||||
\(607\) | −1.05689 | −0.0428979 | −0.0214489 | − | 0.999770i | \(-0.506828\pi\) | ||||
−0.0214489 | + | 0.999770i | \(0.506828\pi\) | |||||||
\(608\) | −3.87466 | − | 3.87466i | −0.157138 | − | 0.157138i | ||||
\(609\) | 0.615309 | + | 0.615309i | 0.0249336 | + | 0.0249336i | ||||
\(610\) | 6.55058 | − | 8.71973i | 0.265225 | − | 0.353051i | ||||
\(611\) | 13.5639 | − | 13.5639i | 0.548735 | − | 0.548735i | ||||
\(612\) | 2.31038 | 0.0933915 | ||||||||
\(613\) | 31.3429 | − | 31.3429i | 1.26593 | − | 1.26593i | 0.317753 | − | 0.948174i | \(-0.397072\pi\) |
0.948174 | − | 0.317753i | \(-0.102928\pi\) | |||||||
\(614\) | −19.6731 | − | 19.6731i | −0.793940 | − | 0.793940i | ||||
\(615\) | 2.85931 | − | 3.80613i | 0.115298 | − | 0.153478i | ||||
\(616\) | 0.484292 | + | 0.484292i | 0.0195127 | + | 0.0195127i | ||||
\(617\) | −18.9748 | − | 18.9748i | −0.763896 | − | 0.763896i | 0.213128 | − | 0.977024i | \(-0.431635\pi\) |
−0.977024 | + | 0.213128i | \(0.931635\pi\) | |||||||
\(618\) | −6.37065 | − | 6.37065i | −0.256265 | − | 0.256265i | ||||
\(619\) | −14.1356 | −0.568157 | −0.284079 | − | 0.958801i | \(-0.591688\pi\) | ||||
−0.284079 | + | 0.958801i | \(0.591688\pi\) | |||||||
\(620\) | −13.5070 | + | 17.9797i | −0.542455 | + | 0.722083i | ||||
\(621\) | −4.45305 | − | 4.45305i | −0.178695 | − | 0.178695i | ||||
\(622\) | −3.86047 | − | 3.86047i | −0.154791 | − | 0.154791i | ||||
\(623\) | − | 6.09747i | − | 0.244290i | ||||||
\(624\) | 3.62581 | − | 3.62581i | 0.145149 | − | 0.145149i | ||||
\(625\) | 21.1224 | − | 13.3732i | 0.844896 | − | 0.534930i | ||||
\(626\) | 18.9968 | 0.759263 | ||||||||
\(627\) | 7.04490i | 0.281346i | ||||||||
\(628\) | −12.5025 | + | 12.5025i | −0.498902 | + | 0.498902i | ||||
\(629\) | 11.9489 | − | 7.39765i | 0.476432 | − | 0.294963i | ||||
\(630\) | 0.715467 | − | 0.952386i | 0.0285049 | − | 0.0379440i | ||||
\(631\) | −13.8331 | − | 13.8331i | −0.550688 | − | 0.550688i | 0.375951 | − | 0.926639i | \(-0.377316\pi\) |
−0.926639 | + | 0.375951i | \(0.877316\pi\) | |||||||
\(632\) | 11.4000 | + | 11.4000i | 0.453466 | + | 0.453466i | ||||
\(633\) | −9.30966 | + | 9.30966i | −0.370026 | + | 0.370026i | ||||
\(634\) | 17.8153 | + | 17.8153i | 0.707537 | + | 0.707537i | ||||
\(635\) | 26.8716 | + | 20.1869i | 1.06637 | + | 0.801094i | ||||
\(636\) | 0.810184 | 0.0321259 | ||||||||
\(637\) | 34.4385i | 1.36450i | ||||||||
\(638\) | −1.48499 | − | 1.48499i | −0.0587914 | − | 0.0587914i | ||||
\(639\) | − | 4.38568i | − | 0.173495i | ||||||
\(640\) | −0.314477 | − | 2.21384i | −0.0124308 | − | 0.0875099i | ||||
\(641\) | 24.5047 | 0.967877 | 0.483938 | − | 0.875102i | \(-0.339206\pi\) | ||||
0.483938 | + | 0.875102i | \(0.339206\pi\) | |||||||
\(642\) | − | 1.99635i | − | 0.0787898i | ||||||
\(643\) | − | 1.49125i | − | 0.0588093i | −0.999568 | − | 0.0294046i | \(-0.990639\pi\) | ||
0.999568 | − | 0.0294046i | \(-0.00936114\pi\) | |||||||
\(644\) | −2.37221 | + | 2.37221i | −0.0934783 | + | 0.0934783i | ||||
\(645\) | −4.57896 | − | 3.43988i | −0.180296 | − | 0.135445i | ||||
\(646\) | 8.95194 | − | 8.95194i | 0.352209 | − | 0.352209i | ||||
\(647\) | 32.4023 | 1.27386 | 0.636932 | − | 0.770920i | \(-0.280203\pi\) | ||||
0.636932 | + | 0.770920i | \(0.280203\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 1.34271 | − | 1.34271i | 0.0527062 | − | 0.0527062i | ||||
\(650\) | −24.6241 | + | 7.13980i | −0.965838 | + | 0.280046i | ||||
\(651\) | 3.78832 | − | 3.78832i | 0.148476 | − | 0.148476i | ||||
\(652\) | − | 8.61293i | − | 0.337308i | ||||||
\(653\) | − | 49.0619i | − | 1.91994i | −0.280099 | − | 0.959971i | \(-0.590367\pi\) | ||
0.280099 | − | 0.959971i | \(-0.409633\pi\) | |||||||
\(654\) | 1.63896 | 0.0640884 | ||||||||
\(655\) | 20.2386 | − | 26.9404i | 0.790789 | − | 1.05265i | ||||
\(656\) | 2.12896i | 0.0831218i | ||||||||
\(657\) | 9.81049 | + | 9.81049i | 0.382743 | + | 0.382743i | ||||
\(658\) | 1.99285i | 0.0776894i | ||||||||
\(659\) | −11.1464 | −0.434200 | −0.217100 | − | 0.976149i | \(-0.569660\pi\) | ||||
−0.217100 | + | 0.976149i | \(0.569660\pi\) | |||||||
\(660\) | −1.72671 | + | 2.29849i | −0.0672122 | + | 0.0894688i | ||||
\(661\) | 31.4369 | + | 31.4369i | 1.22275 | + | 1.22275i | 0.966649 | + | 0.256103i | \(0.0824386\pi\) |
0.256103 | + | 0.966649i | \(0.417561\pi\) | |||||||
\(662\) | −1.11563 | + | 1.11563i | −0.0433603 | + | 0.0433603i | ||||
\(663\) | 8.37699 | + | 8.37699i | 0.325335 | + | 0.325335i | ||||
\(664\) | 11.5202 | + | 11.5202i | 0.447070 | + | 0.447070i | ||||
\(665\) | −0.917981 | − | 6.46237i | −0.0355978 | − | 0.250600i | ||||
\(666\) | −5.17182 | + | 3.20192i | −0.200404 | + | 0.124072i | ||||
\(667\) | 7.27396 | − | 7.27396i | 0.281649 | − | 0.281649i | ||||
\(668\) | 21.8398i | 0.845007i | ||||||||
\(669\) | −18.4795 | −0.714460 | ||||||||
\(670\) | −10.1096 | + | 13.4572i | −0.390566 | + | 0.519898i | ||||
\(671\) | 4.43401 | − | 4.43401i | 0.171173 | − | 0.171173i | ||||
\(672\) | 0.532716i | 0.0205500i | ||||||||
\(673\) | −1.81889 | − | 1.81889i | −0.0701132 | − | 0.0701132i | 0.671181 | − | 0.741294i | \(-0.265787\pi\) |
−0.741294 | + | 0.671181i | \(0.765787\pi\) | |||||||
\(674\) | −19.6821 | − | 19.6821i | −0.758126 | − | 0.758126i | ||||
\(675\) | 4.38025 | + | 2.41109i | 0.168596 | + | 0.0928031i | ||||
\(676\) | 13.2930 | 0.511268 | ||||||||
\(677\) | −9.38604 | − | 9.38604i | −0.360735 | − | 0.360735i | 0.503349 | − | 0.864083i | \(-0.332101\pi\) |
−0.864083 | + | 0.503349i | \(0.832101\pi\) | |||||||
\(678\) | 1.96291 | + | 1.96291i | 0.0753853 | + | 0.0753853i | ||||
\(679\) | 3.04192 | + | 3.04192i | 0.116738 | + | 0.116738i | ||||
\(680\) | 5.11482 | − | 0.726561i | 0.196144 | − | 0.0278624i | ||||
\(681\) | −11.3749 | − | 11.3749i | −0.435885 | − | 0.435885i | ||||
\(682\) | −9.14275 | + | 9.14275i | −0.350094 | + | 0.350094i | ||||
\(683\) | −0.539905 | −0.0206589 | −0.0103295 | − | 0.999947i | \(-0.503288\pi\) | ||||
−0.0103295 | + | 0.999947i | \(0.503288\pi\) | |||||||
\(684\) | −3.87466 | + | 3.87466i | −0.148151 | + | 0.148151i | ||||
\(685\) | −22.7244 | − | 17.0714i | −0.868255 | − | 0.652265i | ||||
\(686\) | −5.16672 | − | 5.16672i | −0.197266 | − | 0.197266i | ||||
\(687\) | −4.74846 | − | 4.74846i | −0.181165 | − | 0.181165i | ||||
\(688\) | 2.56124 | 0.0976462 | ||||||||
\(689\) | 2.93757 | + | 2.93757i | 0.111913 | + | 0.111913i | ||||
\(690\) | −11.2587 | − | 8.45798i | −0.428613 | − | 0.321990i | ||||
\(691\) | − | 40.4342i | − | 1.53819i | −0.639135 | − | 0.769094i | \(-0.720708\pi\) | ||
0.639135 | − | 0.769094i | \(-0.279292\pi\) | |||||||
\(692\) | −1.32378 | + | 1.32378i | −0.0503226 | + | 0.0503226i | ||||
\(693\) | 0.484292 | − | 0.484292i | 0.0183967 | − | 0.0183967i | ||||
\(694\) | −3.98304 | −0.151194 | ||||||||
\(695\) | −6.11712 | − | 43.0631i | −0.232036 | − | 1.63348i | ||||
\(696\) | − | 1.63348i | − | 0.0619167i | ||||||
\(697\) | −4.91870 | −0.186309 | ||||||||
\(698\) | − | 7.69090i | − | 0.291105i | ||||||
\(699\) | 6.53012i | 0.246992i | ||||||||
\(700\) | 1.28443 | − | 2.33343i | 0.0485469 | − | 0.0881954i | ||||
\(701\) | 23.7123 | − | 23.7123i | 0.895601 | − | 0.895601i | −0.0994419 | − | 0.995043i | \(-0.531706\pi\) |
0.995043 | + | 0.0994419i | \(0.0317057\pi\) | |||||||
\(702\) | −3.62581 | − | 3.62581i | −0.136847 | − | 0.136847i | ||||
\(703\) | −7.63270 | + | 32.4454i | −0.287873 | + | 1.22370i | ||||
\(704\) | − | 1.28566i | − | 0.0484551i | ||||||
\(705\) | −8.28182 | + | 1.17643i | −0.311911 | + | 0.0443071i | ||||
\(706\) | − | 21.0577i | − | 0.792518i | ||||||
\(707\) | −5.98060 | − | 5.98060i | −0.224924 | − | 0.224924i | ||||
\(708\) | 1.47697 | 0.0555080 | ||||||||
\(709\) | 16.8933 | + | 16.8933i | 0.634441 | + | 0.634441i | 0.949179 | − | 0.314738i | \(-0.101917\pi\) |
−0.314738 | + | 0.949179i | \(0.601917\pi\) | |||||||
\(710\) | −1.37919 | − | 9.70920i | −0.0517602 | − | 0.364380i | ||||
\(711\) | 11.4000 | − | 11.4000i | 0.427532 | − | 0.427532i | ||||
\(712\) | −8.09354 | + | 8.09354i | −0.303318 | + | 0.303318i | ||||
\(713\) | −44.7841 | − | 44.7841i | −1.67718 | − | 1.67718i | ||||
\(714\) | −1.23078 | −0.0460607 | ||||||||
\(715\) | −14.5946 | + | 2.07317i | −0.545808 | + | 0.0775322i | ||||
\(716\) | 17.8003 | − | 17.8003i | 0.665230 | − | 0.665230i | ||||
\(717\) | −18.5372 | −0.692285 | ||||||||
\(718\) | − | 19.0802i | − | 0.712065i | ||||||
\(719\) | 13.6649i | 0.509614i | 0.966992 | + | 0.254807i | \(0.0820120\pi\) | ||||
−0.966992 | + | 0.254807i | \(0.917988\pi\) | |||||||
\(720\) | −2.21384 | + | 0.314477i | −0.0825051 | + | 0.0117199i | ||||
\(721\) | 3.39375 | + | 3.39375i | 0.126390 | + | 0.126390i | ||||
\(722\) | 11.0260i | 0.410345i | ||||||||
\(723\) | 17.8952i | 0.665529i | ||||||||
\(724\) | −1.98719 | −0.0738533 | ||||||||
\(725\) | −3.93846 | + | 7.15504i | −0.146271 | + | 0.265731i | ||||
\(726\) | 6.60938 | − | 6.60938i | 0.245297 | − | 0.245297i | ||||
\(727\) | −6.24565 | −0.231638 | −0.115819 | − | 0.993270i | \(-0.536949\pi\) | ||||
−0.115819 | + | 0.993270i | \(0.536949\pi\) | |||||||
\(728\) | −1.93153 | + | 1.93153i | −0.0715871 | + | 0.0715871i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 24.8041 | + | 18.6337i | 0.918039 | + | 0.689665i | ||||
\(731\) | 5.91743i | 0.218864i | ||||||||
\(732\) | 4.87737 | 0.180273 | ||||||||
\(733\) | −11.6047 | + | 11.6047i | −0.428628 | + | 0.428628i | −0.888161 | − | 0.459533i | \(-0.848017\pi\) |
0.459533 | + | 0.888161i | \(0.348017\pi\) | |||||||
\(734\) | 13.0910 | − | 13.0910i | 0.483198 | − | 0.483198i | ||||
\(735\) | 9.02024 | − | 12.0072i | 0.332717 | − | 0.442892i | ||||
\(736\) | 6.29757 | 0.232131 | ||||||||
\(737\) | −6.84305 | + | 6.84305i | −0.252067 | + | 0.252067i | ||||
\(738\) | 2.12896 | 0.0783680 | ||||||||
\(739\) | −26.9960 | −0.993065 | −0.496533 | − | 0.868018i | \(-0.665394\pi\) | ||||
−0.496533 | + | 0.868018i | \(0.665394\pi\) | |||||||
\(740\) | −10.4427 | + | 8.71497i | −0.383880 | + | 0.320369i | ||||
\(741\) | −28.0976 | −1.03219 | ||||||||
\(742\) | −0.431598 | −0.0158445 | ||||||||
\(743\) | 2.59470 | − | 2.59470i | 0.0951901 | − | 0.0951901i | −0.657908 | − | 0.753098i | \(-0.728558\pi\) |
0.753098 | + | 0.657908i | \(0.228558\pi\) | |||||||
\(744\) | −10.0569 | −0.368705 | ||||||||
\(745\) | −34.6543 | + | 4.92265i | −1.26963 | + | 0.180352i | ||||
\(746\) | −17.5157 | + | 17.5157i | −0.641294 | + | 0.641294i | ||||
\(747\) | 11.5202 | − | 11.5202i | 0.421501 | − | 0.421501i | ||||
\(748\) | 2.97036 | 0.108607 | ||||||||
\(749\) | 1.06349i | 0.0388591i | ||||||||
\(750\) | 10.4554 | + | 3.96030i | 0.381778 | + | 0.144610i | ||||
\(751\) | − | 37.6977i | − | 1.37561i | −0.725897 | − | 0.687803i | \(-0.758575\pi\) | ||
0.725897 | − | 0.687803i | \(-0.241425\pi\) | |||||||
\(752\) | 2.64523 | − | 2.64523i | 0.0964617 | − | 0.0964617i | ||||
\(753\) | −1.17376 | −0.0427741 | ||||||||
\(754\) | 5.92267 | − | 5.92267i | 0.215691 | − | 0.215691i | ||||
\(755\) | 6.88488 | − | 0.977999i | 0.250566 | − | 0.0355930i | ||||
\(756\) | 0.532716 | 0.0193747 | ||||||||
\(757\) | 27.3872i | 0.995406i | 0.867347 | + | 0.497703i | \(0.165823\pi\) | ||||
−0.867347 | + | 0.497703i | \(0.834177\pi\) | |||||||
\(758\) | − | 21.8739i | − | 0.794494i | ||||||
\(759\) | −5.72511 | − | 5.72511i | −0.207808 | − | 0.207808i | ||||
\(760\) | −7.35940 | + | 9.79638i | −0.266954 | + | 0.355352i | ||||
\(761\) | 41.7778i | 1.51444i | 0.653157 | + | 0.757222i | \(0.273444\pi\) | ||||
−0.653157 | + | 0.757222i | \(0.726556\pi\) | |||||||
\(762\) | 15.0306i | 0.544502i | ||||||||
\(763\) | −0.873100 | −0.0316083 | ||||||||
\(764\) | −4.41456 | + | 4.41456i | −0.159713 | + | 0.159713i | ||||
\(765\) | −0.726561 | − | 5.11482i | −0.0262689 | − | 0.184927i | ||||
\(766\) | −5.61751 | −0.202969 | ||||||||
\(767\) | 5.35522 | + | 5.35522i | 0.193366 | + | 0.193366i | ||||
\(768\) | 0.707107 | − | 0.707107i | 0.0255155 | − | 0.0255155i | ||||
\(769\) | −27.6843 | + | 27.6843i | −0.998322 | + | 0.998322i | −0.999999 | − | 0.00167616i | \(-0.999466\pi\) |
0.00167616 | + | 0.999999i | \(0.499466\pi\) | |||||||
\(770\) | 0.919848 | − | 1.22444i | 0.0331490 | − | 0.0441259i | ||||
\(771\) | 6.79698 | + | 6.79698i | 0.244787 | + | 0.244787i | ||||
\(772\) | −2.09366 | −0.0753524 | ||||||||
\(773\) | 19.1232 | + | 19.1232i | 0.687812 | + | 0.687812i | 0.961748 | − | 0.273936i | \(-0.0883256\pi\) |
−0.273936 | + | 0.961748i | \(0.588326\pi\) | |||||||
\(774\) | − | 2.56124i | − | 0.0920618i | ||||||
\(775\) | 44.0520 | + | 24.2482i | 1.58239 | + | 0.871022i | ||||
\(776\) | − | 8.07546i | − | 0.289892i | ||||||
\(777\) | 2.75511 | − | 1.70571i | 0.0988391 | − | 0.0611921i | ||||
\(778\) | 5.37334 | + | 5.37334i | 0.192644 | + | 0.192644i | ||||
\(779\) | 8.24898 | − | 8.24898i | 0.295551 | − | 0.295551i | ||||
\(780\) | −9.16721 | − | 6.88674i | −0.328239 | − | 0.246585i | ||||
\(781\) | − | 5.63849i | − | 0.201761i | ||||||
\(782\) | 14.5498i | 0.520299i | ||||||||
\(783\) | −1.63348 | −0.0583757 | ||||||||
\(784\) | 6.71621i | 0.239865i | ||||||||
\(785\) | 31.6102 | + | 23.7467i | 1.12822 | + | 0.847558i | ||||
\(786\) | 15.0691 | 0.537497 | ||||||||
\(787\) | −5.34065 | + | 5.34065i | −0.190374 | + | 0.190374i | −0.795858 | − | 0.605484i | \(-0.792980\pi\) |
0.605484 | + | 0.795858i | \(0.292980\pi\) | |||||||
\(788\) | −4.75052 | + | 4.75052i | −0.169230 | + | 0.169230i | ||||
\(789\) | 15.9116i | 0.566468i | ||||||||
\(790\) | 21.6527 | − | 28.8227i | 0.770368 | − | 1.02547i | ||||
\(791\) | −1.04568 | − | 1.04568i | −0.0371800 | − | 0.0371800i | ||||
\(792\) | −1.28566 | −0.0456839 | ||||||||
\(793\) | 17.6844 | + | 17.6844i | 0.627992 | + | 0.627992i | ||||
\(794\) | 17.9874 | + | 17.9874i | 0.638349 | + | 0.638349i | ||||
\(795\) | −0.254784 | − | 1.79362i | −0.00903627 | − | 0.0636132i | ||||
\(796\) | −4.93690 | + | 4.93690i | −0.174984 | + | 0.174984i | ||||
\(797\) | −25.8297 | −0.914934 | −0.457467 | − | 0.889227i | \(-0.651243\pi\) | ||||
−0.457467 | + | 0.889227i | \(0.651243\pi\) | |||||||
\(798\) | 2.06409 | − | 2.06409i | 0.0730682 | − | 0.0730682i | ||||
\(799\) | 6.11149 | + | 6.11149i | 0.216209 | + | 0.216209i | ||||
\(800\) | −4.80221 | + | 1.39241i | −0.169784 | + | 0.0492290i | ||||
\(801\) | 8.09354 | + | 8.09354i | 0.285971 | + | 0.285971i | ||||
\(802\) | 15.1996 | + | 15.1996i | 0.536718 | + | 0.536718i | ||||
\(803\) | 12.6129 | + | 12.6129i | 0.445101 | + | 0.445101i | ||||
\(804\) | −7.52729 | −0.265467 | ||||||||
\(805\) | 5.99772 | + | 4.50570i | 0.211392 | + | 0.158805i | ||||
\(806\) | −36.4645 | − | 36.4645i | −1.28441 | − | 1.28441i | ||||
\(807\) | 16.4693 | + | 16.4693i | 0.579748 | + | 0.579748i | ||||
\(808\) | 15.8768i | 0.558545i | ||||||||
\(809\) | 32.2660 | − | 32.2660i | 1.13441 | − | 1.13441i | 0.144976 | − | 0.989435i | \(-0.453689\pi\) |
0.989435 | − | 0.144976i | \(-0.0463105\pi\) | |||||||
\(810\) | 0.314477 | + | 2.21384i | 0.0110496 | + | 0.0777865i | ||||
\(811\) | −16.4212 | −0.576628 | −0.288314 | − | 0.957536i | \(-0.593095\pi\) | ||||
−0.288314 | + | 0.957536i | \(0.593095\pi\) | |||||||
\(812\) | 0.870179i | 0.0305373i | ||||||||
\(813\) | 9.81285 | − | 9.81285i | 0.344152 | − | 0.344152i | ||||
\(814\) | −6.64920 | + | 4.11658i | −0.233054 | + | 0.144286i | ||||
\(815\) | −19.0677 | + | 2.70857i | −0.667912 | + | 0.0948770i | ||||
\(816\) | 1.63368 | + | 1.63368i | 0.0571904 | + | 0.0571904i | ||||
\(817\) | −9.92392 | − | 9.92392i | −0.347194 | − | 0.347194i | ||||
\(818\) | −27.1312 | + | 27.1312i | −0.948620 | + | 0.948620i | ||||
\(819\) | 1.93153 | + | 1.93153i | 0.0674930 | + | 0.0674930i | ||||
\(820\) | 4.71318 | − | 0.669508i | 0.164591 | − | 0.0233802i | ||||
\(821\) | −31.7926 | −1.10957 | −0.554784 | − | 0.831994i | \(-0.687199\pi\) | ||||
−0.554784 | + | 0.831994i | \(0.687199\pi\) | |||||||
\(822\) | − | 12.7109i | − | 0.443343i | ||||||
\(823\) | −25.1623 | − | 25.1623i | −0.877102 | − | 0.877102i | 0.116132 | − | 0.993234i | \(-0.462951\pi\) |
−0.993234 | + | 0.116132i | \(0.962951\pi\) | |||||||
\(824\) | − | 9.00947i | − | 0.313860i | ||||||
\(825\) | 5.63152 | + | 3.09985i | 0.196064 | + | 0.107923i | ||||
\(826\) | −0.786807 | −0.0273765 | ||||||||
\(827\) | − | 13.8706i | − | 0.482329i | −0.970484 | − | 0.241165i | \(-0.922471\pi\) | ||
0.970484 | − | 0.241165i | \(-0.0775294\pi\) | |||||||
\(828\) | − | 6.29757i | − | 0.218856i | ||||||
\(829\) | −19.5830 | + | 19.5830i | −0.680147 | + | 0.680147i | −0.960033 | − | 0.279886i | \(-0.909703\pi\) |
0.279886 | + | 0.960033i | \(0.409703\pi\) | |||||||
\(830\) | 21.8810 | − | 29.1267i | 0.759502 | − | 1.01100i | ||||
\(831\) | −4.64924 | + | 4.64924i | −0.161280 | + | 0.161280i | ||||
\(832\) | 5.12767 | 0.177770 | ||||||||
\(833\) | −15.5170 | −0.537632 | ||||||||
\(834\) | 13.7544 | − | 13.7544i | 0.476277 | − | 0.476277i | ||||
\(835\) | 48.3499 | − | 6.86812i | 1.67322 | − | 0.237681i | ||||
\(836\) | −4.98150 | + | 4.98150i | −0.172289 | + | 0.172289i | ||||
\(837\) | 10.0569i | 0.347619i | ||||||||
\(838\) | − | 7.19965i | − | 0.248708i | ||||||
\(839\) | −29.1983 | −1.00804 | −0.504019 | − | 0.863692i | \(-0.668146\pi\) | ||||
−0.504019 | + | 0.863692i | \(0.668146\pi\) | |||||||
\(840\) | 1.17935 | − | 0.167527i | 0.0406915 | − | 0.00578023i | ||||
\(841\) | 26.3318i | 0.907992i | ||||||||
\(842\) | 6.17926 | + | 6.17926i | 0.212951 | + | 0.212951i | ||||
\(843\) | 19.2196i | 0.661957i | ||||||||
\(844\) | −13.1658 | −0.453187 | ||||||||
\(845\) | −4.18033 | − | 29.4286i | −0.143808 | − | 1.01237i | ||||
\(846\) | −2.64523 | − | 2.64523i | −0.0909449 | − | 0.0909449i | ||||
\(847\) | −3.52093 | + | 3.52093i | −0.120980 | + | 0.120980i | ||||
\(848\) | 0.572887 | + | 0.572887i | 0.0196730 | + | 0.0196730i | ||||
\(849\) | 6.04565 | + | 6.04565i | 0.207486 | + | 0.207486i | ||||
\(850\) | −3.21699 | − | 11.0949i | −0.110342 | − | 0.380553i | ||||
\(851\) | −20.1643 | − | 32.5699i | −0.691223 | − | 1.11648i | ||||
\(852\) | 3.10114 | − | 3.10114i | 0.106243 | − | 0.106243i | ||||
\(853\) | 6.30510i | 0.215883i | 0.994157 | + | 0.107941i | \(0.0344259\pi\) | ||||
−0.994157 | + | 0.107941i | \(0.965574\pi\) | |||||||
\(854\) | −2.59825 | −0.0889104 | ||||||||
\(855\) | 9.79638 | + | 7.35940i | 0.335029 | + | 0.251686i | ||||
\(856\) | 1.41163 | − | 1.41163i | 0.0482487 | − | 0.0482487i | ||||
\(857\) | 5.70445i | 0.194860i | 0.995242 | + | 0.0974302i | \(0.0310623\pi\) | ||||
−0.995242 | + | 0.0974302i | \(0.968938\pi\) | |||||||
\(858\) | −4.66156 | − | 4.66156i | −0.159143 | − | 0.159143i | ||||
\(859\) | 9.67146 | + | 9.67146i | 0.329986 | + | 0.329986i | 0.852581 | − | 0.522595i | \(-0.175036\pi\) |
−0.522595 | + | 0.852581i | \(0.675036\pi\) | |||||||
\(860\) | −0.805450 | − | 5.67018i | −0.0274656 | − | 0.193351i | ||||
\(861\) | −1.13413 | −0.0386510 | ||||||||
\(862\) | 19.0871 | + | 19.0871i | 0.650110 | + | 0.650110i | ||||
\(863\) | −11.4917 | − | 11.4917i | −0.391181 | − | 0.391181i | 0.483928 | − | 0.875108i | \(-0.339210\pi\) |
−0.875108 | + | 0.483928i | \(0.839210\pi\) | |||||||
\(864\) | −0.707107 | − | 0.707107i | −0.0240563 | − | 0.0240563i | ||||
\(865\) | 3.34694 | + | 2.51434i | 0.113799 | + | 0.0854903i | ||||
\(866\) | −27.0193 | − | 27.0193i | −0.918154 | − | 0.918154i | ||||
\(867\) | 8.24638 | − | 8.24638i | 0.280062 | − | 0.280062i | ||||
\(868\) | 5.35750 | 0.181845 | ||||||||
\(869\) | 14.6565 | − | 14.6565i | 0.497186 | − | 0.497186i | ||||
\(870\) | −3.61626 | + | 0.513691i | −0.122603 | + | 0.0174157i | ||||
\(871\) | −27.2925 | − | 27.2925i | −0.924771 | − | 0.924771i | ||||
\(872\) | 1.15892 | + | 1.15892i | 0.0392460 | + | 0.0392460i | ||||
\(873\) | −8.07546 | −0.273313 | ||||||||
\(874\) | −24.4009 | − | 24.4009i | −0.825374 | − | 0.825374i | ||||
\(875\) | −5.56978 | − | 2.10971i | −0.188293 | − | 0.0713214i | ||||
\(876\) | 13.8741i | 0.468763i | ||||||||
\(877\) | 9.10608 | − | 9.10608i | 0.307490 | − | 0.307490i | −0.536445 | − | 0.843935i | \(-0.680233\pi\) |
0.843935 | + | 0.536445i | \(0.180233\pi\) | |||||||
\(878\) | −8.21948 | + | 8.21948i | −0.277394 | + | 0.277394i | ||||
\(879\) | 10.7700 | 0.363263 | ||||||||
\(880\) | −2.84625 | + | 0.404311i | −0.0959471 | + | 0.0136293i | ||||
\(881\) | − | 2.47471i | − | 0.0833752i | −0.999131 | − | 0.0416876i | \(-0.986727\pi\) | ||
0.999131 | − | 0.0416876i | \(-0.0132734\pi\) | |||||||
\(882\) | 6.71621 | 0.226147 | ||||||||
\(883\) | 42.6117i | 1.43400i | 0.697075 | + | 0.716999i | \(0.254485\pi\) | ||||
−0.697075 | + | 0.716999i | \(0.745515\pi\) | |||||||
\(884\) | 11.8469i | 0.398453i | ||||||||
\(885\) | −0.464474 | − | 3.26979i | −0.0156131 | − | 0.109913i | ||||
\(886\) | 7.35664 | − | 7.35664i | 0.247151 | − | 0.247151i | ||||
\(887\) | −14.4378 | − | 14.4378i | −0.484774 | − | 0.484774i | 0.421878 | − | 0.906652i | \(-0.361371\pi\) |
−0.906652 | + | 0.421878i | \(0.861371\pi\) | |||||||
\(888\) | −5.92113 | − | 1.39293i | −0.198700 | − | 0.0467437i | ||||
\(889\) | − | 8.00705i | − | 0.268548i | ||||||
\(890\) | 20.4631 | + | 15.3726i | 0.685924 | + | 0.515291i | ||||
\(891\) | 1.28566i | 0.0430712i | ||||||||
\(892\) | −13.0670 | − | 13.0670i | −0.437516 | − | 0.437516i | ||||
\(893\) | −20.4987 | −0.685964 | ||||||||
\(894\) | −11.0687 | − | 11.0687i | −0.370191 | − | 0.370191i | ||||
\(895\) | −45.0049 | − | 33.8094i | −1.50435 | − | 1.13012i | ||||
\(896\) | −0.376687 | + | 0.376687i | −0.0125842 | + | 0.0125842i | ||||
\(897\) | 22.8338 | − | 22.8338i | 0.762398 | − | 0.762398i | ||||
\(898\) | −15.3192 | − | 15.3192i | −0.511207 | − | 0.511207i | ||||
\(899\) | −16.4278 | −0.547897 | ||||||||
\(900\) | 1.39241 | + | 4.80221i | 0.0464135 | + | 0.160074i | ||||
\(901\) | −1.32359 | + | 1.32359i | −0.0440950 | + | 0.0440950i | ||||
\(902\) | 2.73711 | 0.0911359 | ||||||||
\(903\) | 1.36441i | 0.0454048i | ||||||||
\(904\) | 2.77598i | 0.0923277i | ||||||||
\(905\) | 0.624925 | + | 4.39933i | 0.0207732 | + | 0.146239i | ||||
\(906\) | 2.19905 | + | 2.19905i | 0.0730584 | + | 0.0730584i | ||||
\(907\) | 20.9996i | 0.697281i | 0.937256 | + | 0.348641i | \(0.113357\pi\) | ||||
−0.937256 | + | 0.348641i | \(0.886643\pi\) | |||||||
\(908\) | − | 16.0865i | − | 0.533848i | ||||||
\(909\) | 15.8768 | 0.526601 | ||||||||
\(910\) | 4.88352 | + | 3.66868i | 0.161887 | + | 0.121615i | ||||
\(911\) | 2.09529 | − | 2.09529i | 0.0694199 | − | 0.0694199i | −0.671544 | − | 0.740964i | \(-0.734369\pi\) |
0.740964 | + | 0.671544i | \(0.234369\pi\) | |||||||
\(912\) | −5.47960 | −0.181448 | ||||||||
\(913\) | 14.8110 | − | 14.8110i | 0.490174 | − | 0.490174i | ||||
\(914\) | − | 11.9041i | − | 0.393754i | ||||||
\(915\) | −1.53382 | − | 10.7977i | −0.0507066 | − | 0.356962i | ||||
\(916\) | − | 6.71533i | − | 0.221881i | ||||||
\(917\) | −8.02756 | −0.265093 | ||||||||
\(918\) | 1.63368 | − | 1.63368i | 0.0539196 | − | 0.0539196i | ||||
\(919\) | 26.2479 | − | 26.2479i | 0.865840 | − | 0.865840i | −0.126169 | − | 0.992009i | \(-0.540268\pi\) |
0.992009 | + | 0.126169i | \(0.0402681\pi\) | |||||||
\(920\) | −1.98044 | − | 13.9418i | −0.0652932 | − | 0.459649i | ||||
\(921\) | −27.8219 | −0.916763 | ||||||||
\(922\) | −21.6193 | + | 21.6193i | −0.711994 | + | 0.711994i | ||||
\(923\) | 22.4883 | 0.740211 | ||||||||
\(924\) | 0.684892 | 0.0225313 | ||||||||
\(925\) | 22.5776 | + | 20.3778i | 0.742345 | + | 0.670017i | ||||
\(926\) | 7.74140 | 0.254398 | ||||||||
\(927\) | −9.00947 | −0.295910 | ||||||||
\(928\) | 1.15504 | − | 1.15504i | 0.0379161 | − | 0.0379161i | ||||
\(929\) | −36.8972 | −1.21056 | −0.605279 | − | 0.796014i | \(-0.706938\pi\) | ||||
−0.605279 | + | 0.796014i | \(0.706938\pi\) | |||||||
\(930\) | 3.16268 | + | 22.2645i | 0.103708 | + | 0.730082i | ||||
\(931\) | 26.0230 | − | 26.0230i | 0.852871 | − | 0.852871i | ||||
\(932\) | −4.61749 | + | 4.61749i | −0.151251 | + | 0.151251i | ||||
\(933\) | −5.45953 | −0.178737 | ||||||||
\(934\) | − | 40.6171i | − | 1.32903i | ||||||
\(935\) | −0.934111 | − | 6.57592i | −0.0305487 | − | 0.215056i | ||||
\(936\) | − | 5.12767i | − | 0.167603i | ||||||
\(937\) | −6.68552 | + | 6.68552i | −0.218406 | + | 0.218406i | −0.807827 | − | 0.589420i | \(-0.799356\pi\) |
0.589420 | + | 0.807827i | \(0.299356\pi\) | |||||||
\(938\) | 4.00991 | 0.130928 | ||||||||
\(939\) | 13.4327 | − | 13.4327i | 0.438361 | − | 0.438361i | ||||
\(940\) | −6.68799 | − | 5.02426i | −0.218138 | − | 0.163873i | ||||
\(941\) | −5.71005 | −0.186142 | −0.0930711 | − | 0.995659i | \(-0.529668\pi\) | ||||
−0.0930711 | + | 0.995659i | \(0.529668\pi\) | |||||||
\(942\) | 17.6811i | 0.576083i | ||||||||
\(943\) | 13.4073i | 0.436600i | ||||||||
\(944\) | 1.04438 | + | 1.04438i | 0.0339916 | + | 0.0339916i | ||||
\(945\) | −0.167527 | − | 1.17935i | −0.00544965 | − | 0.0383643i | ||||
\(946\) | − | 3.29288i | − | 0.107061i | ||||||
\(947\) | 31.5411i | 1.02495i | 0.858703 | + | 0.512474i | \(0.171271\pi\) | ||||
−0.858703 | + | 0.512474i | \(0.828729\pi\) | |||||||
\(948\) | 16.1220 | 0.523617 | ||||||||
\(949\) | −50.3049 | + | 50.3049i | −1.63297 | + | 1.63297i | ||||
\(950\) | 24.0020 | + | 13.2118i | 0.778729 | + | 0.428648i | ||||
\(951\) | 25.1947 | 0.816993 | ||||||||
\(952\) | −0.870290 | − | 0.870290i | −0.0282063 | − | 0.0282063i | ||||
\(953\) | 41.8752 | − | 41.8752i | 1.35647 | − | 1.35647i | 0.478245 | − | 0.878227i | \(-0.341273\pi\) |
0.878227 | − | 0.478245i | \(-0.158727\pi\) | |||||||
\(954\) | 0.572887 | − | 0.572887i | 0.0185479 | − | 0.0185479i | ||||
\(955\) | 11.1614 | + | 8.38487i | 0.361175 | + | 0.271328i | ||||
\(956\) | −13.1078 | − | 13.1078i | −0.423936 | − | 0.423936i | ||||
\(957\) | −2.10009 | −0.0678864 | ||||||||
\(958\) | −4.76750 | − | 4.76750i | −0.154031 | − | 0.154031i | ||||
\(959\) | 6.77129i | 0.218656i | ||||||||
\(960\) | −1.78779 | − | 1.34306i | −0.0577008 | − | 0.0433469i | ||||
\(961\) | 70.1421i | 2.26265i | ||||||||
\(962\) | −16.4184 | − | 26.5194i | −0.529350 | − | 0.855019i | ||||
\(963\) | −1.41163 | − | 1.41163i | −0.0454893 | − | 0.0454893i | ||||
\(964\) | −12.6538 | + | 12.6538i | −0.407552 | + | 0.407552i | ||||
\(965\) | 0.658407 | + | 4.63503i | 0.0211949 | + | 0.149207i | ||||
\(966\) | 3.35482i | 0.107939i | ||||||||
\(967\) | − | 20.2774i | − | 0.652076i | −0.945357 | − | 0.326038i | \(-0.894286\pi\) | ||
0.945357 | − | 0.326038i | \(-0.105714\pi\) | |||||||
\(968\) | 9.34708 | 0.300426 | ||||||||
\(969\) | − | 12.6599i | − | 0.406696i | ||||||
\(970\) | −17.8778 | + | 2.53955i | −0.574022 | + | 0.0815399i | ||||
\(971\) | 16.4316 | 0.527316 | 0.263658 | − | 0.964616i | \(-0.415071\pi\) | ||||
0.263658 | + | 0.964616i | \(0.415071\pi\) | |||||||
\(972\) | −0.707107 | + | 0.707107i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | −7.32722 | + | 7.32722i | −0.234900 | + | 0.234900i | ||||
\(974\) | 16.5284i | 0.529603i | ||||||||
\(975\) | −12.3633 | + | 22.4605i | −0.395942 | + | 0.719311i | ||||
\(976\) | 3.44882 | + | 3.44882i | 0.110394 | + | 0.110394i | ||||
\(977\) | 45.6145 | 1.45934 | 0.729669 | − | 0.683801i | \(-0.239674\pi\) | ||||
0.729669 | + | 0.683801i | \(0.239674\pi\) | |||||||
\(978\) | −6.09026 | − | 6.09026i | −0.194745 | − | 0.194745i | ||||
\(979\) | 10.4055 | + | 10.4055i | 0.332563 | + | 0.332563i | ||||
\(980\) | 14.8686 | − | 2.11209i | 0.474962 | − | 0.0674684i | ||||
\(981\) | 1.15892 | − | 1.15892i | 0.0370014 | − | 0.0370014i | ||||
\(982\) | −11.4600 | −0.365705 | ||||||||
\(983\) | −18.8451 | + | 18.8451i | −0.601066 | + | 0.601066i | −0.940595 | − | 0.339530i | \(-0.889732\pi\) |
0.339530 | + | 0.940595i | \(0.389732\pi\) | |||||||
\(984\) | 1.50540 | + | 1.50540i | 0.0479904 | + | 0.0479904i | ||||
\(985\) | 12.0108 | + | 9.02298i | 0.382697 | + | 0.287496i | ||||
\(986\) | 2.66858 | + | 2.66858i | 0.0849850 | + | 0.0849850i | ||||
\(987\) | 1.40916 | + | 1.40916i | 0.0448540 | + | 0.0448540i | ||||
\(988\) | −19.8680 | − | 19.8680i | −0.632084 | − | 0.632084i | ||||
\(989\) | 16.1296 | 0.512890 | ||||||||
\(990\) | 0.404311 | + | 2.84625i | 0.0128498 | + | 0.0904598i | ||||
\(991\) | 28.3442 | + | 28.3442i | 0.900383 | + | 0.900383i | 0.995469 | − | 0.0950859i | \(-0.0303126\pi\) |
−0.0950859 | + | 0.995469i | \(0.530313\pi\) | |||||||
\(992\) | −7.11133 | − | 7.11133i | −0.225785 | − | 0.225785i | ||||
\(993\) | 1.57774i | 0.0500682i | ||||||||
\(994\) | −1.65203 | + | 1.65203i | −0.0523992 | + | 0.0523992i | ||||
\(995\) | 12.4821 | + | 9.37699i | 0.395708 | + | 0.297270i | ||||
\(996\) | 16.2920 | 0.516232 | ||||||||
\(997\) | 34.7231i | 1.09969i | 0.835266 | + | 0.549846i | \(0.185313\pi\) | ||||
−0.835266 | + | 0.549846i | \(0.814687\pi\) | |||||||
\(998\) | −11.0278 | + | 11.0278i | −0.349080 | + | 0.349080i | ||||
\(999\) | −1.39293 | + | 5.92113i | −0.0440704 | + | 0.187336i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1110.2.o.b.253.15 | yes | 40 | |
5.2 | odd | 4 | 1110.2.l.b.697.6 | yes | 40 | ||
37.6 | odd | 4 | 1110.2.l.b.43.6 | ✓ | 40 | ||
185.117 | even | 4 | inner | 1110.2.o.b.487.15 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.l.b.43.6 | ✓ | 40 | 37.6 | odd | 4 | ||
1110.2.l.b.697.6 | yes | 40 | 5.2 | odd | 4 | ||
1110.2.o.b.253.15 | yes | 40 | 1.1 | even | 1 | trivial | |
1110.2.o.b.487.15 | yes | 40 | 185.117 | even | 4 | inner |