Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(43,1110)]
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, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.l (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 | 697.6 | ||
Character | \(\chi\) | \(=\) | 1110.697 |
Dual form | 1110.2.l.b.43.6 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −0.707107 | − | 0.707107i | −0.408248 | − | 0.408248i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 2.21384 | + | 0.314477i | 0.990061 | + | 0.140638i | ||||
\(6\) | 0.707107 | − | 0.707107i | 0.288675 | − | 0.288675i | ||||
\(7\) | −0.376687 | − | 0.376687i | −0.142374 | − | 0.142374i | 0.632327 | − | 0.774702i | \(-0.282100\pi\) |
−0.774702 | + | 0.632327i | \(0.782100\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 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 | ||||
\(13\) | − | 5.12767i | − | 1.42216i | −0.703112 | − | 0.711080i | \(-0.748207\pi\) | ||
0.703112 | − | 0.711080i | \(-0.251793\pi\) | |||||||
\(14\) | 0.376687 | − | 0.376687i | 0.100674 | − | 0.100674i | ||||
\(15\) | −1.34306 | − | 1.78779i | −0.346775 | − | 0.461606i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.31038 | −0.560349 | −0.280175 | − | 0.959949i | \(-0.590392\pi\) | ||||
−0.280175 | + | 0.959949i | \(0.590392\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 3.87466 | + | 3.87466i | 0.888908 | + | 0.888908i | 0.994418 | − | 0.105510i | \(-0.0336476\pi\) |
−0.105510 | + | 0.994418i | \(0.533648\pi\) | |||||||
\(20\) | −2.21384 | − | 0.314477i | −0.495031 | − | 0.0703192i | ||||
\(21\) | 0.532716i | 0.116248i | ||||||||
\(22\) | 1.28566 | 0.274104 | ||||||||
\(23\) | − | 6.29757i | − | 1.31313i | −0.754268 | − | 0.656567i | \(-0.772008\pi\) | ||
0.754268 | − | 0.656567i | \(-0.227992\pi\) | |||||||
\(24\) | −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 | −0.806170 | − | 0.591684i | \(-0.798463\pi\) |
0.591684 | + | 0.806170i | \(0.298463\pi\) | |||||||
\(30\) | 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 | \(-0.608744\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −0.909099 | + | 0.909099i | −0.158254 | + | 0.158254i | ||||
\(34\) | − | 2.31038i | − | 0.396227i | ||||||
\(35\) | −0.715467 | − | 0.952386i | −0.120936 | − | 0.160983i | ||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | 5.17182 | − | 3.20192i | 0.850242 | − | 0.526392i | ||||
\(38\) | −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 | \(0.946836\pi\) | |||||||
\(42\) | −0.532716 | −0.0821999 | ||||||||
\(43\) | − | 2.56124i | − | 0.390585i | −0.980745 | − | 0.195292i | \(-0.937434\pi\) | ||
0.980745 | − | 0.195292i | \(-0.0625656\pi\) | |||||||
\(44\) | 1.28566i | 0.193821i | ||||||||
\(45\) | −0.314477 | + | 2.21384i | −0.0468795 | + | 0.330020i | ||||
\(46\) | 6.29757 | 0.928526 | ||||||||
\(47\) | 2.64523 | + | 2.64523i | 0.385847 | + | 0.385847i | 0.873203 | − | 0.487356i | \(-0.162039\pi\) |
−0.487356 | + | 0.873203i | \(0.662039\pi\) | |||||||
\(48\) | −0.707107 | − | 0.707107i | −0.102062 | − | 0.102062i | ||||
\(49\) | − | 6.71621i | − | 0.959459i | ||||||
\(50\) | −1.39241 | + | 4.80221i | −0.196916 | + | 0.679135i | ||||
\(51\) | 1.63368 | + | 1.63368i | 0.228762 | + | 0.228762i | ||||
\(52\) | 5.12767i | 0.711080i | ||||||||
\(53\) | 0.572887 | − | 0.572887i | 0.0786920 | − | 0.0786920i | −0.666665 | − | 0.745357i | \(-0.732279\pi\) |
0.745357 | + | 0.666665i | \(0.232279\pi\) | |||||||
\(54\) | 0.707107 | + | 0.707107i | 0.0962250 | + | 0.0962250i | ||||
\(55\) | 0.404311 | − | 2.84625i | 0.0545172 | − | 0.383788i | ||||
\(56\) | −0.376687 | + | 0.376687i | −0.0503369 | + | 0.0503369i | ||||
\(57\) | − | 5.47960i | − | 0.725790i | ||||||
\(58\) | −1.15504 | − | 1.15504i | −0.151664 | − | 0.151664i | ||||
\(59\) | −1.04438 | − | 1.04438i | −0.135966 | − | 0.135966i | 0.635848 | − | 0.771814i | \(-0.280651\pi\) |
−0.771814 | + | 0.635848i | \(0.780651\pi\) | |||||||
\(60\) | 1.34306 | + | 1.78779i | 0.173388 | + | 0.230803i | ||||
\(61\) | 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 | \(-0.597920\pi\) |
0.953055 | + | 0.302797i | \(0.0979203\pi\) | |||||||
\(68\) | 2.31038 | 0.280175 | ||||||||
\(69\) | −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 | \(0.416198\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 9.81049 | + | 9.81049i | 1.14823 | + | 1.14823i | 0.986901 | + | 0.161330i | \(0.0515783\pi\) |
0.161330 | + | 0.986901i | \(0.448422\pi\) | |||||||
\(74\) | 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 | \(-0.888418\pi\) |
−0.343409 | − | 0.939186i | \(-0.611582\pi\) | |||||||
\(80\) | 2.21384 | + | 0.314477i | 0.247515 | + | 0.0351596i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −2.12896 | −0.235104 | ||||||||
\(83\) | 11.5202 | − | 11.5202i | 1.26450 | − | 1.26450i | 0.315617 | − | 0.948887i | \(-0.397788\pi\) |
0.948887 | − | 0.315617i | \(-0.102212\pi\) | |||||||
\(84\) | − | 0.532716i | − | 0.0581241i | ||||||
\(85\) | −5.11482 | − | 0.726561i | −0.554780 | − | 0.0788066i | ||||
\(86\) | 2.56124 | 0.276185 | ||||||||
\(87\) | 1.63348 | 0.175127 | ||||||||
\(88\) | −1.28566 | −0.137052 | ||||||||
\(89\) | 8.09354 | − | 8.09354i | 0.857914 | − | 0.857914i | −0.133179 | − | 0.991092i | \(-0.542518\pi\) |
0.991092 | + | 0.133179i | \(0.0425184\pi\) | |||||||
\(90\) | −2.21384 | − | 0.314477i | −0.233360 | − | 0.0331488i | ||||
\(91\) | −1.93153 | + | 1.93153i | −0.202479 | + | 0.202479i | ||||
\(92\) | 6.29757i | 0.656567i | ||||||||
\(93\) | 10.0569i | 1.04286i | ||||||||
\(94\) | −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 | ||||
\(97\) | 8.07546 | 0.819939 | 0.409969 | − | 0.912099i | \(-0.365539\pi\) | ||||
0.409969 | + | 0.912099i | \(0.365539\pi\) | |||||||
\(98\) | 6.71621 | 0.678440 | ||||||||
\(99\) | 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 | ||||
\(103\) | −9.00947 | −0.887729 | −0.443865 | − | 0.896094i | \(-0.646393\pi\) | ||||
−0.443865 | + | 0.896094i | \(0.646393\pi\) | |||||||
\(104\) | −5.12767 | −0.502809 | ||||||||
\(105\) | −0.167527 | + | 1.17935i | −0.0163490 | + | 0.115093i | ||||
\(106\) | 0.572887 | + | 0.572887i | 0.0556437 | + | 0.0556437i | ||||
\(107\) | 1.41163 | + | 1.41163i | 0.136468 | + | 0.136468i | 0.772041 | − | 0.635573i | \(-0.219236\pi\) |
−0.635573 | + | 0.772041i | \(0.719236\pi\) | |||||||
\(108\) | −0.707107 | + | 0.707107i | −0.0680414 | + | 0.0680414i | ||||
\(109\) | −1.15892 | − | 1.15892i | −0.111004 | − | 0.111004i | 0.649423 | − | 0.760427i | \(-0.275010\pi\) |
−0.760427 | + | 0.649423i | \(0.775010\pi\) | |||||||
\(110\) | 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 | ||||
\(113\) | 2.77598 | 0.261142 | 0.130571 | − | 0.991439i | \(-0.458319\pi\) | ||||
0.130571 | + | 0.991439i | \(0.458319\pi\) | |||||||
\(114\) | 5.47960 | 0.513211 | ||||||||
\(115\) | 1.98044 | − | 13.9418i | 0.184677 | − | 1.30008i | ||||
\(116\) | 1.15504 | − | 1.15504i | 0.107243 | − | 0.107243i | ||||
\(117\) | 5.12767 | 0.474053 | ||||||||
\(118\) | 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 | ||||
\(125\) | 10.1935 | + | 4.59275i | 0.911731 | + | 0.410788i | ||||
\(126\) | 0.376687 | + | 0.376687i | 0.0335580 | + | 0.0335580i | ||||
\(127\) | −10.6282 | − | 10.6282i | −0.943105 | − | 0.943105i | 0.0553618 | − | 0.998466i | \(-0.482369\pi\) |
−0.998466 | + | 0.0553618i | \(0.982369\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −1.81107 | + | 1.81107i | −0.159456 | + | 0.159456i | ||||
\(130\) | 11.3519 | + | 1.61253i | 0.995623 | + | 0.141429i | ||||
\(131\) | 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 | ||||
\(133\) | − | 2.91907i | − | 0.253115i | ||||||
\(134\) | 5.32260 | + | 5.32260i | 0.459802 | + | 0.459802i | ||||
\(135\) | 1.78779 | − | 1.34306i | 0.153869 | − | 0.115592i | ||||
\(136\) | 2.31038i | 0.198113i | ||||||||
\(137\) | 8.98795 | + | 8.98795i | 0.767892 | + | 0.767892i | 0.977735 | − | 0.209843i | \(-0.0672953\pi\) |
−0.209843 | + | 0.977735i | \(0.567295\pi\) | |||||||
\(138\) | −4.45305 | − | 4.45305i | −0.379069 | − | 0.379069i | ||||
\(139\) | −19.4517 | −1.64987 | −0.824937 | − | 0.565225i | \(-0.808789\pi\) | ||||
−0.824937 | + | 0.565225i | \(0.808789\pi\) | |||||||
\(140\) | 0.715467 | + | 0.952386i | 0.0604680 | + | 0.0804913i | ||||
\(141\) | − | 3.74092i | − | 0.315042i | ||||||
\(142\) | 4.38568i | 0.368038i | ||||||||
\(143\) | −6.59244 | −0.551287 | ||||||||
\(144\) | 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 | ||||
\(148\) | −5.17182 | + | 3.20192i | −0.425121 | + | 0.263196i | ||||
\(149\) | 15.6534i | 1.28238i | 0.767382 | + | 0.641190i | \(0.221559\pi\) | ||||
−0.767382 | + | 0.641190i | \(0.778441\pi\) | |||||||
\(150\) | 4.38025 | − | 2.41109i | 0.357646 | − | 0.196865i | ||||
\(151\) | 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 | ||||
\(153\) | − | 2.31038i | − | 0.186783i | ||||||
\(154\) | −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 | 0.00219308 | − | 0.999998i | \(-0.499302\pi\) |
−0.999998 | + | 0.00219308i | \(0.999302\pi\) | |||||||
\(158\) | 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 | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | −8.61293 | −0.674617 | −0.337308 | − | 0.941394i | \(-0.609517\pi\) | ||||
−0.337308 | + | 0.941394i | \(0.609517\pi\) | |||||||
\(164\) | − | 2.12896i | − | 0.166244i | ||||||
\(165\) | −2.29849 | + | 1.72671i | −0.178938 | + | 0.134424i | ||||
\(166\) | 11.5202 | + | 11.5202i | 0.894139 | + | 0.894139i | ||||
\(167\) | −21.8398 | −1.69001 | −0.845007 | − | 0.534755i | \(-0.820404\pi\) | ||||
−0.845007 | + | 0.534755i | \(0.820404\pi\) | |||||||
\(168\) | 0.532716 | 0.0410999 | ||||||||
\(169\) | −13.2930 | −1.02254 | ||||||||
\(170\) | 0.726561 | − | 5.11482i | 0.0557247 | − | 0.392289i | ||||
\(171\) | −3.87466 | + | 3.87466i | −0.296303 | + | 0.296303i | ||||
\(172\) | 2.56124i | 0.195292i | ||||||||
\(173\) | 1.32378 | + | 1.32378i | 0.100645 | + | 0.100645i | 0.755636 | − | 0.654991i | \(-0.227328\pi\) |
−0.654991 | + | 0.755636i | \(0.727328\pi\) | |||||||
\(174\) | 1.63348i | 0.123833i | ||||||||
\(175\) | −1.28443 | − | 2.33343i | −0.0970937 | − | 0.176391i | ||||
\(176\) | − | 1.28566i | − | 0.0969103i | ||||||
\(177\) | 1.47697i | 0.111016i | ||||||||
\(178\) | 8.09354 | + | 8.09354i | 0.606636 | + | 0.606636i | ||||
\(179\) | −17.8003 | + | 17.8003i | −1.33046 | + | 1.33046i | −0.425501 | + | 0.904958i | \(0.639902\pi\) |
−0.904958 | + | 0.425501i | \(0.860098\pi\) | |||||||
\(180\) | 0.314477 | − | 2.21384i | 0.0234397 | − | 0.165010i | ||||
\(181\) | −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 | ||||
\(183\) | − | 4.87737i | − | 0.360546i | ||||||
\(184\) | −6.29757 | −0.464263 | ||||||||
\(185\) | 12.4565 | − | 5.46213i | 0.915822 | − | 0.401584i | ||||
\(186\) | −10.0569 | −0.737411 | ||||||||
\(187\) | 2.97036i | 0.217214i | ||||||||
\(188\) | −2.64523 | − | 2.64523i | −0.192923 | − | 0.192923i | ||||
\(189\) | −0.532716 | −0.0387494 | ||||||||
\(190\) | −9.79638 | + | 7.35940i | −0.710704 | + | 0.533907i | ||||
\(191\) | −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 | ||||
\(193\) | 2.09366i | 0.150705i | 0.997157 | + | 0.0753524i | \(0.0240082\pi\) | ||||
−0.997157 | + | 0.0753524i | \(0.975992\pi\) | |||||||
\(194\) | 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 | 0.517327 | − | 0.855788i | \(-0.326927\pi\) |
−0.855788 | + | 0.517327i | \(0.826927\pi\) | |||||||
\(198\) | 1.28566i | 0.0913679i | ||||||||
\(199\) | 4.93690 | − | 4.93690i | 0.349968 | − | 0.349968i | −0.510130 | − | 0.860097i | \(-0.670403\pi\) |
0.860097 | + | 0.510130i | \(0.170403\pi\) | |||||||
\(200\) | 1.39241 | − | 4.80221i | 0.0984580 | − | 0.339567i | ||||
\(201\) | −7.52729 | −0.530934 | ||||||||
\(202\) | −15.8768 | −1.11709 | ||||||||
\(203\) | 0.870179 | 0.0610746 | ||||||||
\(204\) | −1.63368 | − | 1.63368i | −0.114381 | − | 0.114381i | ||||
\(205\) | −0.669508 | + | 4.71318i | −0.0467605 | + | 0.329183i | ||||
\(206\) | − | 9.00947i | − | 0.627719i | ||||||
\(207\) | 6.29757 | 0.437711 | ||||||||
\(208\) | − | 5.12767i | − | 0.355540i | ||||||
\(209\) | 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 | ||||
\(217\) | 5.35750i | 0.363690i | ||||||||
\(218\) | 1.15892 | − | 1.15892i | 0.0784919 | − | 0.0784919i | ||||
\(219\) | − | 13.8741i | − | 0.937526i | ||||||
\(220\) | −0.404311 | + | 2.84625i | −0.0272586 | + | 0.191894i | ||||
\(221\) | 11.8469i | 0.796906i | ||||||||
\(222\) | 1.39293 | − | 5.92113i | 0.0934874 | − | 0.397400i | ||||
\(223\) | −13.0670 | + | 13.0670i | −0.875031 | + | 0.875031i | −0.993015 | − | 0.117984i | \(-0.962357\pi\) |
0.117984 | + | 0.993015i | \(0.462357\pi\) | |||||||
\(224\) | 0.376687 | − | 0.376687i | 0.0251685 | − | 0.0251685i | ||||
\(225\) | −1.39241 | + | 4.80221i | −0.0928271 | + | 0.320147i | ||||
\(226\) | 2.77598i | 0.184655i | ||||||||
\(227\) | 16.0865 | 1.06770 | 0.533848 | − | 0.845580i | \(-0.320745\pi\) | ||||
0.533848 | + | 0.845580i | \(0.320745\pi\) | |||||||
\(228\) | 5.47960i | 0.362895i | ||||||||
\(229\) | 6.71533i | 0.443762i | 0.975074 | + | 0.221881i | \(0.0712196\pi\) | ||||
−0.975074 | + | 0.221881i | \(0.928780\pi\) | |||||||
\(230\) | 13.9418 | + | 1.98044i | 0.919297 | + | 0.130586i | ||||
\(231\) | 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 | \(-0.181383\pi\) |
−0.539490 | + | 0.841992i | \(0.681383\pi\) | |||||||
\(234\) | 5.12767i | 0.335206i | ||||||||
\(235\) | 5.02426 | + | 6.68799i | 0.327747 | + | 0.436277i | ||||
\(236\) | 1.04438 | + | 1.04438i | 0.0679832 | + | 0.0679832i | ||||
\(237\) | 16.1220i | 1.04723i | ||||||||
\(238\) | −0.870290 | + | 0.870290i | −0.0564125 | + | 0.0564125i | ||||
\(239\) | 13.1078 | + | 13.1078i | 0.847873 | + | 0.847873i | 0.989867 | − | 0.141995i | \(-0.0453516\pi\) |
−0.141995 | + | 0.989867i | \(0.545352\pi\) | |||||||
\(240\) | −1.34306 | − | 1.78779i | −0.0866938 | − | 0.115402i | ||||
\(241\) | −12.6538 | + | 12.6538i | −0.815103 | + | 0.815103i | −0.985394 | − | 0.170291i | \(-0.945529\pi\) |
0.170291 | + | 0.985394i | \(0.445529\pi\) | |||||||
\(242\) | 9.34708i | 0.600853i | ||||||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | −3.44882 | − | 3.44882i | −0.220788 | − | 0.220788i | ||||
\(245\) | 2.11209 | − | 14.8686i | 0.134937 | − | 0.949923i | ||||
\(246\) | 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 | ||||
\(253\) | −8.09653 | −0.509025 | ||||||||
\(254\) | 10.6282 | − | 10.6282i | 0.666876 | − | 0.666876i | ||||
\(255\) | 3.10297 | + | 4.13048i | 0.194315 | + | 0.258661i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.61238 | −0.599604 | −0.299802 | − | 0.954001i | \(-0.596921\pi\) | ||||
−0.299802 | + | 0.954001i | \(0.596921\pi\) | |||||||
\(258\) | −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 | \(-0.0867866\pi\) |
−0.269283 | + | 0.963061i | \(0.586787\pi\) | |||||||
\(264\) | 0.909099 | + | 0.909099i | 0.0559512 | + | 0.0559512i | ||||
\(265\) | 1.44844 | − | 1.08812i | 0.0889770 | − | 0.0668428i | ||||
\(266\) | 2.91907 | 0.178980 | ||||||||
\(267\) | −11.4460 | −0.700483 | ||||||||
\(268\) | −5.32260 | + | 5.32260i | −0.325129 | + | 0.325129i | ||||
\(269\) | − | 23.2912i | − | 1.42009i | −0.704158 | − | 0.710043i | \(-0.748675\pi\) | ||
0.704158 | − | 0.710043i | \(-0.251325\pi\) | |||||||
\(270\) | 1.34306 | + | 1.78779i | 0.0817357 | + | 0.108802i | ||||
\(271\) | 13.8775 | 0.842996 | 0.421498 | − | 0.906829i | \(-0.361504\pi\) | ||||
0.421498 | + | 0.906829i | \(0.361504\pi\) | |||||||
\(272\) | −2.31038 | −0.140087 | ||||||||
\(273\) | 2.73159 | 0.165323 | ||||||||
\(274\) | −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 | ||||
\(277\) | − | 6.57502i | − | 0.395055i | −0.980297 | − | 0.197527i | \(-0.936709\pi\) | ||
0.980297 | − | 0.197527i | \(-0.0632912\pi\) | |||||||
\(278\) | − | 19.4517i | − | 1.16664i | ||||||
\(279\) | 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 | \(0.444326\pi\) | |||||||
\(282\) | 3.74092 | 0.222769 | ||||||||
\(283\) | 8.54984 | 0.508235 | 0.254118 | − | 0.967173i | \(-0.418215\pi\) | ||||
0.254118 | + | 0.967173i | \(0.418215\pi\) | |||||||
\(284\) | −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 | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −11.6621 | −0.686009 | ||||||||
\(290\) | −2.19385 | − | 2.92032i | −0.128827 | − | 0.171487i | ||||
\(291\) | −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 | −0.448752 | − | 0.893656i | \(-0.648131\pi\) |
0.893656 | + | 0.448752i | \(0.148131\pi\) | |||||||
\(294\) | −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 | ||||
\(298\) | −15.6534 | −0.906779 | ||||||||
\(299\) | −32.2918 | −1.86749 | ||||||||
\(300\) | 2.41109 | + | 4.38025i | 0.139205 | + | 0.252894i | ||||
\(301\) | −0.964785 | + | 0.964785i | −0.0556093 | + | 0.0556093i | ||||
\(302\) | −3.10992 | −0.178956 | ||||||||
\(303\) | 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 | 0.131482 | − | 0.991319i | \(-0.458026\pi\) |
0.991319 | − | 0.131482i | \(-0.0419736\pi\) | |||||||
\(308\) | 0.484292 | − | 0.484292i | 0.0275951 | − | 0.0275951i | ||||
\(309\) | 6.37065 | + | 6.37065i | 0.362414 | + | 0.362414i | ||||
\(310\) | 17.9797 | − | 13.5070i | 1.02118 | − | 0.767147i | ||||
\(311\) | −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 | ||||
\(313\) | − | 18.9968i | − | 1.07376i | −0.843659 | − | 0.536880i | \(-0.819603\pi\) | ||
0.843659 | − | 0.536880i | \(-0.180397\pi\) | |||||||
\(314\) | 12.5025 | − | 12.5025i | 0.705554 | − | 0.705554i | ||||
\(315\) | 0.952386 | − | 0.715467i | 0.0536609 | − | 0.0403120i | ||||
\(316\) | 11.4000 | + | 11.4000i | 0.641297 | + | 0.641297i | ||||
\(317\) | −17.8153 | + | 17.8153i | −1.00061 | + | 1.00061i | −0.000608272 | 1.00000i | \(0.500194\pi\) | |
−1.00000 | 0.000608272i | \(0.999806\pi\) | ||||||||
\(318\) | − | 0.810184i | − | 0.0454329i | ||||||
\(319\) | 1.48499 | + | 1.48499i | 0.0831435 | + | 0.0831435i | ||||
\(320\) | −2.21384 | − | 0.314477i | −0.123758 | − | 0.0175798i | ||||
\(321\) | − | 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 | ||||||||
\(325\) | 7.13980 | − | 24.6241i | 0.396045 | − | 1.36590i | ||||
\(326\) | − | 8.61293i | − | 0.477026i | ||||||
\(327\) | 1.63896i | 0.0906347i | ||||||||
\(328\) | 2.12896 | 0.117552 | ||||||||
\(329\) | − | 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 | ||||
\(333\) | 3.20192 | + | 5.17182i | 0.175464 | + | 0.283414i | ||||
\(334\) | − | 21.8398i | − | 1.19502i | ||||||
\(335\) | 13.4572 | − | 10.1096i | 0.735247 | − | 0.552344i | ||||
\(336\) | 0.532716i | 0.0290621i | ||||||||
\(337\) | 19.6821 | − | 19.6821i | 1.07215 | − | 1.07215i | 0.0749653 | − | 0.997186i | \(-0.476115\pi\) |
0.997186 | − | 0.0749653i | \(-0.0238846\pi\) | |||||||
\(338\) | − | 13.2930i | − | 0.723042i | ||||||
\(339\) | −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 | ||||
\(347\) | − | 3.98304i | − | 0.213821i | −0.994269 | − | 0.106910i | \(-0.965904\pi\) | ||
0.994269 | − | 0.106910i | \(-0.0340958\pi\) | |||||||
\(348\) | −1.63348 | −0.0875635 | ||||||||
\(349\) | 7.69090i | 0.411684i | 0.978585 | + | 0.205842i | \(0.0659934\pi\) | ||||
−0.978585 | + | 0.205842i | \(0.934007\pi\) | |||||||
\(350\) | 2.33343 | − | 1.28443i | 0.124727 | − | 0.0686556i | ||||
\(351\) | −3.62581 | − | 3.62581i | −0.193531 | − | 0.193531i | ||||
\(352\) | 1.28566 | 0.0685259 | ||||||||
\(353\) | −21.0577 | −1.12079 | −0.560395 | − | 0.828226i | \(-0.689351\pi\) | ||||
−0.560395 | + | 0.828226i | \(0.689351\pi\) | |||||||
\(354\) | −1.47697 | −0.0785002 | ||||||||
\(355\) | 9.70920 | + | 1.37919i | 0.515311 | + | 0.0732000i | ||||
\(356\) | −8.09354 | + | 8.09354i | −0.428957 | + | 0.428957i | ||||
\(357\) | − | 1.23078i | − | 0.0651396i | ||||||
\(358\) | −17.8003 | − | 17.8003i | −0.940777 | − | 0.940777i | ||||
\(359\) | 19.0802i | 1.00701i | 0.863992 | + | 0.503506i | \(0.167957\pi\) | ||||
−0.863992 | + | 0.503506i | \(0.832043\pi\) | |||||||
\(360\) | 2.21384 | + | 0.314477i | 0.116680 | + | 0.0165744i | ||||
\(361\) | 11.0260i | 0.580315i | ||||||||
\(362\) | − | 1.98719i | − | 0.104444i | ||||||
\(363\) | −6.60938 | − | 6.60938i | −0.346903 | − | 0.346903i | ||||
\(364\) | 1.93153 | − | 1.93153i | 0.101240 | − | 0.101240i | ||||
\(365\) | 18.6337 | + | 24.8041i | 0.975333 | + | 1.29830i | ||||
\(366\) | 4.87737 | 0.254944 | ||||||||
\(367\) | 13.0910 | + | 13.0910i | 0.683346 | + | 0.683346i | 0.960753 | − | 0.277407i | \(-0.0894750\pi\) |
−0.277407 | + | 0.960753i | \(0.589475\pi\) | |||||||
\(368\) | − | 6.29757i | − | 0.328283i | ||||||
\(369\) | −2.12896 | −0.110829 | ||||||||
\(370\) | 5.46213 | + | 12.4565i | 0.283963 | + | 0.647584i | ||||
\(371\) | −0.431598 | −0.0224075 | ||||||||
\(372\) | − | 10.0569i | − | 0.521428i | ||||||
\(373\) | 17.5157 | + | 17.5157i | 0.906927 | + | 0.906927i | 0.996023 | − | 0.0890959i | \(-0.0283978\pi\) |
−0.0890959 | + | 0.996023i | \(0.528398\pi\) | |||||||
\(374\) | −2.97036 | −0.153594 | ||||||||
\(375\) | −3.96030 | − | 10.4554i | −0.204509 | − | 0.539916i | ||||
\(376\) | 2.64523 | − | 2.64523i | 0.136417 | − | 0.136417i | ||||
\(377\) | 5.92267 | + | 5.92267i | 0.305033 | + | 0.305033i | ||||
\(378\) | − | 0.532716i | − | 0.0274000i | ||||||
\(379\) | 21.8739i | 1.12358i | 0.827278 | + | 0.561792i | \(0.189888\pi\) | ||||
−0.827278 | + | 0.561792i | \(0.810112\pi\) | |||||||
\(380\) | −7.35940 | − | 9.79638i | −0.377529 | − | 0.502544i | ||||
\(381\) | 15.0306i | 0.770042i | ||||||||
\(382\) | −4.41456 | − | 4.41456i | −0.225868 | − | 0.225868i | ||||
\(383\) | 5.61751i | 0.287042i | 0.989647 | + | 0.143521i | \(0.0458424\pi\) | ||||
−0.989647 | + | 0.143521i | \(0.954158\pi\) | |||||||
\(384\) | −0.707107 | + | 0.707107i | −0.0360844 | + | 0.0360844i | ||||
\(385\) | −1.22444 | + | 0.919848i | −0.0624035 | + | 0.0468798i | ||||
\(386\) | −2.09366 | −0.106564 | ||||||||
\(387\) | 2.56124 | 0.130195 | ||||||||
\(388\) | −8.07546 | −0.409969 | ||||||||
\(389\) | −5.37334 | − | 5.37334i | −0.272439 | − | 0.272439i | 0.557642 | − | 0.830081i | \(-0.311706\pi\) |
−0.830081 | + | 0.557642i | \(0.811706\pi\) | |||||||
\(390\) | −6.88674 | − | 9.16721i | −0.348724 | − | 0.464200i | ||||
\(391\) | 14.5498i | 0.735814i | ||||||||
\(392\) | −6.71621 | −0.339220 | ||||||||
\(393\) | − | 15.0691i | − | 0.760136i | ||||||
\(394\) | 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 | \(-0.970382\pi\) |
0.0929128 | + | 0.995674i | \(0.470382\pi\) | |||||||
\(398\) | 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 | \(0.569664\pi\) | |||||||
\(402\) | − | 7.52729i | − | 0.375427i | ||||||
\(403\) | −36.4645 | + | 36.4645i | −1.81643 | + | 1.81643i | ||||
\(404\) | − | 15.8768i | − | 0.789902i | ||||||
\(405\) | −2.21384 | − | 0.314477i | −0.110007 | − | 0.0156265i | ||||
\(406\) | 0.870179i | 0.0431863i | ||||||||
\(407\) | −4.11658 | − | 6.64920i | −0.204051 | − | 0.329589i | ||||
\(408\) | 1.63368 | − | 1.63368i | 0.0808795 | − | 0.0808795i | ||||
\(409\) | 27.1312 | − | 27.1312i | 1.34155 | − | 1.34155i | 0.447033 | − | 0.894517i | \(-0.352481\pi\) |
0.894517 | − | 0.447033i | \(-0.147519\pi\) | |||||||
\(410\) | −4.71318 | − | 0.669508i | −0.232767 | − | 0.0330646i | ||||
\(411\) | − | 12.7109i | − | 0.626981i | ||||||
\(412\) | 9.00947 | 0.443865 | ||||||||
\(413\) | 0.786807i | 0.0387163i | ||||||||
\(414\) | 6.29757i | 0.309509i | ||||||||
\(415\) | 29.1267 | − | 21.8810i | 1.42977 | − | 1.07410i | ||||
\(416\) | 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 | \(0.0562716\pi\) | ||||
−0.984415 | + | 0.175863i | \(0.943728\pi\) | |||||||
\(420\) | 0.167527 | − | 1.17935i | 0.00817448 | − | 0.0575464i | ||||
\(421\) | 6.17926 | + | 6.17926i | 0.301159 | + | 0.301159i | 0.841467 | − | 0.540308i | \(-0.181692\pi\) |
−0.540308 | + | 0.841467i | \(0.681692\pi\) | |||||||
\(422\) | − | 13.1658i | − | 0.640903i | ||||||
\(423\) | −2.64523 | + | 2.64523i | −0.128616 | + | 0.128616i | ||||
\(424\) | −0.572887 | − | 0.572887i | −0.0278218 | − | 0.0278218i | ||||
\(425\) | −11.0949 | − | 3.21699i | −0.538183 | − | 0.156047i | ||||
\(426\) | 3.10114 | − | 3.10114i | 0.150251 | − | 0.150251i | ||||
\(427\) | − | 2.59825i | − | 0.125738i | ||||||
\(428\) | −1.41163 | − | 1.41163i | −0.0682340 | − | 0.0682340i | ||||
\(429\) | 4.66156 | + | 4.66156i | 0.225062 | + | 0.225062i | ||||
\(430\) | 5.67018 | + | 0.805450i | 0.273440 | + | 0.0388423i | ||||
\(431\) | 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 | −0.369061 | + | 0.929405i | \(0.620321\pi\) |
−0.929405 | + | 0.369061i | \(0.879679\pi\) | |||||||
\(434\) | −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 | ||||
\(438\) | 13.8741 | 0.662931 | ||||||||
\(439\) | 8.21948 | − | 8.21948i | 0.392294 | − | 0.392294i | −0.483210 | − | 0.875504i | \(-0.660529\pi\) |
0.875504 | + | 0.483210i | \(0.160529\pi\) | |||||||
\(440\) | −2.84625 | − | 0.404311i | −0.135690 | − | 0.0192748i | ||||
\(441\) | 6.71621 | 0.319820 | ||||||||
\(442\) | −11.8469 | −0.563497 | ||||||||
\(443\) | −7.35664 | − | 7.35664i | −0.349525 | − | 0.349525i | 0.510408 | − | 0.859932i | \(-0.329494\pi\) |
−0.859932 | + | 0.510408i | \(0.829494\pi\) | |||||||
\(444\) | 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 | 0.969206 | − | 0.246250i | \(-0.0791986\pi\) |
−0.246250 | + | 0.969206i | \(0.579199\pi\) | |||||||
\(450\) | −4.80221 | − | 1.39241i | −0.226378 | − | 0.0656387i | ||||
\(451\) | 2.73711 | 0.128886 | ||||||||
\(452\) | −2.77598 | −0.130571 | ||||||||
\(453\) | 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 | ||||||||
\(457\) | 11.9041 | 0.556852 | 0.278426 | − | 0.960458i | \(-0.410187\pi\) | ||||
0.278426 | + | 0.960458i | \(0.410187\pi\) | |||||||
\(458\) | −6.71533 | −0.313787 | ||||||||
\(459\) | −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 | \(0.997792\pi\) | |||||||
\(462\) | 0.684892i | 0.0318641i | ||||||||
\(463\) | − | 7.74140i | − | 0.359773i | −0.983687 | − | 0.179887i | \(-0.942427\pi\) | ||
0.983687 | − | 0.179887i | \(-0.0575731\pi\) | |||||||
\(464\) | −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 | ||||
\(467\) | 40.6171 | 1.87954 | 0.939768 | − | 0.341813i | \(-0.111041\pi\) | ||||
0.939768 | + | 0.341813i | \(0.111041\pi\) | |||||||
\(468\) | −5.12767 | −0.237027 | ||||||||
\(469\) | −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 | ||||
\(473\) | −3.29288 | −0.151407 | ||||||||
\(474\) | −16.1220 | −0.740506 | ||||||||
\(475\) | 13.2118 | + | 24.0020i | 0.606200 | + | 1.10129i | ||||
\(476\) | −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 | 0.807585 | − | 0.589752i | \(-0.200774\pi\) |
−0.589752 | + | 0.807585i | \(0.700774\pi\) | |||||||
\(480\) | 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 | ||||
\(483\) | 3.35482 | 0.152649 | ||||||||
\(484\) | −9.34708 | −0.424867 | ||||||||
\(485\) | 17.8778 | + | 2.53955i | 0.811789 | + | 0.115315i | ||||
\(486\) | −0.707107 | + | 0.707107i | −0.0320750 | + | 0.0320750i | ||||
\(487\) | −16.5284 | −0.748971 | −0.374486 | − | 0.927233i | \(-0.622181\pi\) | ||||
−0.374486 | + | 0.927233i | \(0.622181\pi\) | |||||||
\(488\) | 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 | ||||
\(495\) | 2.84625 | + | 0.404311i | 0.127929 | + | 0.0181724i | ||||
\(496\) | −7.11133 | − | 7.11133i | −0.319308 | − | 0.319308i | ||||
\(497\) | −1.65203 | − | 1.65203i | −0.0741036 | − | 0.0741036i | ||||
\(498\) | − | 16.2920i | − | 0.730062i | ||||||
\(499\) | 11.0278 | − | 11.0278i | 0.493674 | − | 0.493674i | −0.415788 | − | 0.909462i | \(-0.636494\pi\) |
0.909462 | + | 0.415788i | \(0.136494\pi\) | |||||||
\(500\) | −10.1935 | − | 4.59275i | −0.455865 | − | 0.205394i | ||||
\(501\) | 15.4431 | + | 15.4431i | 0.689946 | + | 0.689946i | ||||
\(502\) | 0.829972 | − | 0.829972i | 0.0370435 | − | 0.0370435i | ||||
\(503\) | − | 17.9392i | − | 0.799870i | −0.916543 | − | 0.399935i | \(-0.869033\pi\) | ||
0.916543 | − | 0.399935i | \(-0.130967\pi\) | |||||||
\(504\) | −0.376687 | − | 0.376687i | −0.0167790 | − | 0.0167790i | ||||
\(505\) | −4.99290 | + | 35.1488i | −0.222181 | + | 1.56410i | ||||
\(506\) | − | 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 | \(-0.427942\pi\) | ||||
0.224448 | + | 0.974486i | \(0.427942\pi\) | |||||||
\(510\) | −4.13048 | + | 3.10297i | −0.182901 | + | 0.137402i | ||||
\(511\) | − | 7.39097i | − | 0.326957i | ||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 5.47960 | 0.241930 | ||||||||
\(514\) | − | 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 | ||||
\(518\) | 0.742037 | − | 3.15428i | 0.0326032 | − | 0.138591i | ||||
\(519\) | − | 1.87211i | − | 0.0821764i | ||||||
\(520\) | −11.3519 | − | 1.61253i | −0.497812 | − | 0.0707143i | ||||
\(521\) | − | 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 | ||||
\(523\) | 27.3470i | 1.19580i | 0.801570 | + | 0.597901i | \(0.203998\pi\) | ||||
−0.801570 | + | 0.597901i | \(0.796002\pi\) | |||||||
\(524\) | −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 | ||||
\(532\) | 2.91907i | 0.126558i | ||||||||
\(533\) | 10.9166 | 0.472850 | ||||||||
\(534\) | − | 11.4460i | − | 0.495317i | ||||||
\(535\) | 2.68121 | + | 3.56907i | 0.115919 | + | 0.154304i | ||||
\(536\) | −5.32260 | − | 5.32260i | −0.229901 | − | 0.229901i | ||||
\(537\) | 25.1735 | 1.08632 | ||||||||
\(538\) | 23.2912 | 1.00415 | ||||||||
\(539\) | −8.63477 | −0.371926 | ||||||||
\(540\) | −1.78779 | + | 1.34306i | −0.0769344 | + | 0.0577959i | ||||
\(541\) | 24.0214 | − | 24.0214i | 1.03276 | − | 1.03276i | 0.0333158 | − | 0.999445i | \(-0.489393\pi\) |
0.999445 | − | 0.0333158i | \(-0.0106067\pi\) | |||||||
\(542\) | 13.8775i | 0.596088i | ||||||||
\(543\) | 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 | ||||||||
\(547\) | 37.8077i | 1.61654i | 0.588810 | + | 0.808271i | \(0.299596\pi\) | ||||
−0.588810 | + | 0.808271i | \(0.700404\pi\) | |||||||
\(548\) | −8.98795 | − | 8.98795i | −0.383946 | − | 0.383946i | ||||
\(549\) | −3.44882 | + | 3.44882i | −0.147192 | + | 0.147192i | ||||
\(550\) | 6.17401 | + | 1.79016i | 0.263261 | + | 0.0763327i | ||||
\(551\) | −8.95079 | −0.381316 | ||||||||
\(552\) | 4.45305 | + | 4.45305i | 0.189535 | + | 0.189535i | ||||
\(553\) | 8.58843i | 0.365217i | ||||||||
\(554\) | 6.57502 | 0.279346 | ||||||||
\(555\) | −12.6704 | − | 4.94579i | −0.537829 | − | 0.209937i | ||||
\(556\) | 19.4517 | 0.824937 | ||||||||
\(557\) | − | 18.1545i | − | 0.769231i | −0.923077 | − | 0.384615i | \(-0.874334\pi\) | ||
0.923077 | − | 0.384615i | \(-0.125666\pi\) | |||||||
\(558\) | 7.11133 | + | 7.11133i | 0.301047 | + | 0.301047i | ||||
\(559\) | −13.1332 | −0.555474 | ||||||||
\(560\) | −0.715467 | − | 0.952386i | −0.0302340 | − | 0.0402457i | ||||
\(561\) | 2.10036 | − | 2.10036i | 0.0886774 | − | 0.0886774i | ||||
\(562\) | −13.5903 | − | 13.5903i | −0.573272 | − | 0.573272i | ||||
\(563\) | − | 19.8695i | − | 0.837398i | −0.908125 | − | 0.418699i | \(-0.862486\pi\) | ||
0.908125 | − | 0.418699i | \(-0.137514\pi\) | |||||||
\(564\) | 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 | ||||
\(568\) | − | 4.38568i | − | 0.184019i | ||||||
\(569\) | −6.05236 | + | 6.05236i | −0.253728 | + | 0.253728i | −0.822497 | − | 0.568769i | \(-0.807420\pi\) |
0.568769 | + | 0.822497i | \(0.307420\pi\) | |||||||
\(570\) | 12.1310 | + | 1.72321i | 0.508111 | + | 0.0721772i | ||||
\(571\) | 12.1222 | 0.507297 | 0.253648 | − | 0.967296i | \(-0.418369\pi\) | ||||
0.253648 | + | 0.967296i | \(0.418369\pi\) | |||||||
\(572\) | 6.59244 | 0.275644 | ||||||||
\(573\) | 6.24313 | 0.260810 | ||||||||
\(574\) | 0.801951 | + | 0.801951i | 0.0334728 | + | 0.0334728i | ||||
\(575\) | 8.76877 | − | 30.2422i | 0.365683 | − | 1.26119i | ||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | 36.8080 | 1.53234 | 0.766168 | − | 0.642641i | \(-0.222161\pi\) | ||||
0.766168 | + | 0.642641i | \(0.222161\pi\) | |||||||
\(578\) | − | 11.6621i | − | 0.485081i | ||||||
\(579\) | 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 | ||||
\(587\) | − | 14.5475i | − | 0.600439i | −0.953870 | − | 0.300220i | \(-0.902940\pi\) | ||
0.953870 | − | 0.300220i | \(-0.0970600\pi\) | |||||||
\(588\) | 4.74908 | − | 4.74908i | 0.195849 | − | 0.195849i | ||||
\(589\) | − | 55.1080i | − | 2.27068i | ||||||
\(590\) | 2.64052 | − | 1.98366i | 0.108709 | − | 0.0816658i | ||||
\(591\) | 6.71825i | 0.276352i | ||||||||
\(592\) | 5.17182 | − | 3.20192i | 0.212560 | − | 0.131598i | ||||
\(593\) | −16.6115 | + | 16.6115i | −0.682153 | + | 0.682153i | −0.960485 | − | 0.278332i | \(-0.910219\pi\) |
0.278332 | + | 0.960485i | \(0.410219\pi\) | |||||||
\(594\) | 0.909099 | − | 0.909099i | 0.0373008 | − | 0.0373008i | ||||
\(595\) | 1.65300 | + | 2.20037i | 0.0677664 | + | 0.0902065i | ||||
\(596\) | − | 15.6534i | − | 0.641190i | ||||||
\(597\) | −6.98183 | −0.285747 | ||||||||
\(598\) | − | 32.2918i | − | 1.32051i | ||||||
\(599\) | 13.5361i | 0.553069i | 0.961004 | + | 0.276535i | \(0.0891861\pi\) | ||||
−0.961004 | + | 0.276535i | \(0.910814\pi\) | |||||||
\(600\) | −4.38025 | + | 2.41109i | −0.178823 | + | 0.0984325i | ||||
\(601\) | 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 | ||||||
\(605\) | 20.6930 | + | 2.93944i | 0.841289 | + | 0.119505i | ||||
\(606\) | 11.2266 | + | 11.2266i | 0.456050 | + | 0.456050i | ||||
\(607\) | − | 1.05689i | − | 0.0428979i | −0.999770 | − | 0.0214489i | \(-0.993172\pi\) | ||
0.999770 | − | 0.0214489i | \(-0.00682793\pi\) | |||||||
\(608\) | −3.87466 | + | 3.87466i | −0.157138 | + | 0.157138i | ||||
\(609\) | −0.615309 | − | 0.615309i | −0.0249336 | − | 0.0249336i | ||||
\(610\) | −8.71973 | + | 6.55058i | −0.353051 | + | 0.265225i | ||||
\(611\) | 13.5639 | − | 13.5639i | 0.548735 | − | 0.548735i | ||||
\(612\) | 2.31038i | 0.0933915i | ||||||||
\(613\) | −31.3429 | − | 31.3429i | −1.26593 | − | 1.26593i | −0.948174 | − | 0.317753i | \(-0.897072\pi\) |
−0.317753 | − | 0.948174i | \(-0.602928\pi\) | |||||||
\(614\) | 19.6731 | + | 19.6731i | 0.793940 | + | 0.793940i | ||||
\(615\) | 3.80613 | − | 2.85931i | 0.153478 | − | 0.115298i | ||||
\(616\) | 0.484292 | + | 0.484292i | 0.0195127 | + | 0.0195127i | ||||
\(617\) | 18.9748 | − | 18.9748i | 0.763896 | − | 0.763896i | −0.213128 | − | 0.977024i | \(-0.568365\pi\) |
0.977024 | + | 0.213128i | \(0.0683652\pi\) | |||||||
\(618\) | −6.37065 | + | 6.37065i | −0.256265 | + | 0.256265i | ||||
\(619\) | 14.1356 | 0.568157 | 0.284079 | − | 0.958801i | \(-0.408312\pi\) | ||||
0.284079 | + | 0.958801i | \(0.408312\pi\) | |||||||
\(620\) | 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 | ||||
\(623\) | −6.09747 | −0.244290 | ||||||||
\(624\) | −3.62581 | + | 3.62581i | −0.145149 | + | 0.145149i | ||||
\(625\) | 21.1224 | + | 13.3732i | 0.844896 | + | 0.534930i | ||||
\(626\) | 18.9968 | 0.759263 | ||||||||
\(627\) | −7.04490 | −0.281346 | ||||||||
\(628\) | 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 | ||||
\(635\) | −20.1869 | − | 26.8716i | −0.801094 | − | 1.06637i | ||||
\(636\) | 0.810184 | 0.0321259 | ||||||||
\(637\) | −34.4385 | −1.36450 | ||||||||
\(638\) | −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 | \(0.339206\pi\) | |||||||
\(642\) | 1.99635 | 0.0787898 | ||||||||
\(643\) | −1.49125 | −0.0588093 | −0.0294046 | − | 0.999568i | \(-0.509361\pi\) | ||||
−0.0294046 | + | 0.999568i | \(0.509361\pi\) | |||||||
\(644\) | 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 | ||||
\(647\) | 32.4023i | 1.27386i | 0.770920 | + | 0.636932i | \(0.219797\pi\) | ||||
−0.770920 | + | 0.636932i | \(0.780203\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | −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 | ||||
\(652\) | 8.61293 | 0.337308 | ||||||||
\(653\) | −49.0619 | −1.91994 | −0.959971 | − | 0.280099i | \(-0.909633\pi\) | ||||
−0.959971 | + | 0.280099i | \(0.909633\pi\) | |||||||
\(654\) | −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 | ||||
\(658\) | 1.99285 | 0.0776894 | ||||||||
\(659\) | 11.1464 | 0.434200 | 0.217100 | − | 0.976149i | \(-0.430340\pi\) | ||||
0.217100 | + | 0.976149i | \(0.430340\pi\) | |||||||
\(660\) | 2.29849 | − | 1.72671i | 0.0894688 | − | 0.0672122i | ||||
\(661\) | 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 | ||||
\(668\) | 21.8398 | 0.845007 | ||||||||
\(669\) | 18.4795 | 0.714460 | ||||||||
\(670\) | 10.1096 | + | 13.4572i | 0.390566 | + | 0.519898i | ||||
\(671\) | 4.43401 | − | 4.43401i | 0.171173 | − | 0.171173i | ||||
\(672\) | −0.532716 | −0.0205500 | ||||||||
\(673\) | −1.81889 | + | 1.81889i | −0.0701132 | + | 0.0701132i | −0.741294 | − | 0.671181i | \(-0.765787\pi\) |
0.671181 | + | 0.741294i | \(0.265787\pi\) | |||||||
\(674\) | 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 | \(-0.667899\pi\) |
0.864083 | + | 0.503349i | \(0.167899\pi\) | |||||||
\(678\) | 1.96291 | − | 1.96291i | 0.0753853 | − | 0.0753853i | ||||
\(679\) | −3.04192 | − | 3.04192i | −0.116738 | − | 0.116738i | ||||
\(680\) | −0.726561 | + | 5.11482i | −0.0278624 | + | 0.196144i | ||||
\(681\) | −11.3749 | − | 11.3749i | −0.435885 | − | 0.435885i | ||||
\(682\) | −9.14275 | − | 9.14275i | −0.350094 | − | 0.350094i | ||||
\(683\) | 0.539905i | 0.0206589i | 0.999947 | + | 0.0103295i | \(0.00328802\pi\) | ||||
−0.999947 | + | 0.0103295i | \(0.996712\pi\) | |||||||
\(684\) | 3.87466 | − | 3.87466i | 0.148151 | − | 0.148151i | ||||
\(685\) | 17.0714 | + | 22.7244i | 0.652265 | + | 0.868255i | ||||
\(686\) | −5.16672 | − | 5.16672i | −0.197266 | − | 0.197266i | ||||
\(687\) | 4.74846 | − | 4.74846i | 0.181165 | − | 0.181165i | ||||
\(688\) | − | 2.56124i | − | 0.0976462i | ||||||
\(689\) | −2.93757 | − | 2.93757i | −0.111913 | − | 0.111913i | ||||
\(690\) | −8.45798 | − | 11.2587i | −0.321990 | − | 0.428613i | ||||
\(691\) | − | 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 | ||||||||
\(695\) | −43.0631 | − | 6.11712i | −1.63348 | − | 0.232036i | ||||
\(696\) | − | 1.63348i | − | 0.0619167i | ||||||
\(697\) | − | 4.91870i | − | 0.186309i | ||||||
\(698\) | −7.69090 | −0.291105 | ||||||||
\(699\) | − | 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 | ||||
\(703\) | 32.4454 | + | 7.63270i | 1.22370 | + | 0.287873i | ||||
\(704\) | 1.28566i | 0.0484551i | ||||||||
\(705\) | 1.17643 | − | 8.28182i | 0.0443071 | − | 0.311911i | ||||
\(706\) | − | 21.0577i | − | 0.792518i | ||||||
\(707\) | 5.98060 | − | 5.98060i | 0.224924 | − | 0.224924i | ||||
\(708\) | − | 1.47697i | − | 0.0555080i | ||||||
\(709\) | −16.8933 | − | 16.8933i | −0.634441 | − | 0.634441i | 0.314738 | − | 0.949179i | \(-0.398083\pi\) |
−0.949179 | + | 0.314738i | \(0.898083\pi\) | |||||||
\(710\) | −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 | ||||
\(717\) | − | 18.5372i | − | 0.692285i | ||||||
\(718\) | −19.0802 | −0.712065 | ||||||||
\(719\) | − | 13.6649i | − | 0.509614i | −0.966992 | − | 0.254807i | \(-0.917988\pi\) | ||
0.966992 | − | 0.254807i | \(-0.0820120\pi\) | |||||||
\(720\) | −0.314477 | + | 2.21384i | −0.0117199 | + | 0.0825051i | ||||
\(721\) | 3.39375 | + | 3.39375i | 0.126390 | + | 0.126390i | ||||
\(722\) | −11.0260 | −0.410345 | ||||||||
\(723\) | 17.8952 | 0.665529 | ||||||||
\(724\) | 1.98719 | 0.0738533 | ||||||||
\(725\) | −7.15504 | + | 3.93846i | −0.265731 | + | 0.146271i | ||||
\(726\) | 6.60938 | − | 6.60938i | 0.245297 | − | 0.245297i | ||||
\(727\) | − | 6.24565i | − | 0.231638i | −0.993270 | − | 0.115819i | \(-0.963051\pi\) | ||
0.993270 | − | 0.115819i | \(-0.0369493\pi\) | |||||||
\(728\) | 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 | ||||||||
\(732\) | 4.87737i | 0.180273i | ||||||||
\(733\) | 11.6047 | + | 11.6047i | 0.428628 | + | 0.428628i | 0.888161 | − | 0.459533i | \(-0.151983\pi\) |
−0.459533 | + | 0.888161i | \(0.651983\pi\) | |||||||
\(734\) | −13.0910 | + | 13.0910i | −0.483198 | + | 0.483198i | ||||
\(735\) | −12.0072 | + | 9.02024i | −0.442892 | + | 0.332717i | ||||
\(736\) | 6.29757 | 0.232131 | ||||||||
\(737\) | −6.84305 | − | 6.84305i | −0.252067 | − | 0.252067i | ||||
\(738\) | − | 2.12896i | − | 0.0783680i | ||||||
\(739\) | 26.9960 | 0.993065 | 0.496533 | − | 0.868018i | \(-0.334606\pi\) | ||||
0.496533 | + | 0.868018i | \(0.334606\pi\) | |||||||
\(740\) | −12.4565 | + | 5.46213i | −0.457911 | + | 0.200792i | ||||
\(741\) | −28.0976 | −1.03219 | ||||||||
\(742\) | − | 0.431598i | − | 0.0158445i | ||||||
\(743\) | −2.59470 | − | 2.59470i | −0.0951901 | − | 0.0951901i | 0.657908 | − | 0.753098i | \(-0.271442\pi\) |
−0.753098 | + | 0.657908i | \(0.771442\pi\) | |||||||
\(744\) | 10.0569 | 0.368705 | ||||||||
\(745\) | −4.92265 | + | 34.6543i | −0.180352 | + | 1.26963i | ||||
\(746\) | −17.5157 | + | 17.5157i | −0.641294 | + | 0.641294i | ||||
\(747\) | 11.5202 | + | 11.5202i | 0.421501 | + | 0.421501i | ||||
\(748\) | − | 2.97036i | − | 0.108607i | ||||||
\(749\) | − | 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 | ||||
\(753\) | 1.17376i | 0.0427741i | ||||||||
\(754\) | −5.92267 | + | 5.92267i | −0.215691 | + | 0.215691i | ||||
\(755\) | −0.977999 | + | 6.88488i | −0.0355930 | + | 0.250566i | ||||
\(756\) | 0.532716 | 0.0193747 | ||||||||
\(757\) | −27.3872 | −0.995406 | −0.497703 | − | 0.867347i | \(-0.665823\pi\) | ||||
−0.497703 | + | 0.867347i | \(0.665823\pi\) | |||||||
\(758\) | −21.8739 | −0.794494 | ||||||||
\(759\) | 5.72511 | + | 5.72511i | 0.207808 | + | 0.207808i | ||||
\(760\) | 9.79638 | − | 7.35940i | 0.355352 | − | 0.266954i | ||||
\(761\) | 41.7778i | 1.51444i | 0.653157 | + | 0.757222i | \(0.273444\pi\) | ||||
−0.653157 | + | 0.757222i | \(0.726556\pi\) | |||||||
\(762\) | −15.0306 | −0.544502 | ||||||||
\(763\) | 0.873100i | 0.0316083i | ||||||||
\(764\) | 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 | −0.00167616 | − | 0.999999i | \(-0.500534\pi\) |
0.999999 | + | 0.00167616i | \(0.000533537\pi\) | |||||||
\(770\) | −0.919848 | − | 1.22444i | −0.0331490 | − | 0.0441259i | ||||
\(771\) | 6.79698 | + | 6.79698i | 0.244787 | + | 0.244787i | ||||
\(772\) | − | 2.09366i | − | 0.0753524i | ||||||
\(773\) | 19.1232 | − | 19.1232i | 0.687812 | − | 0.687812i | −0.273936 | − | 0.961748i | \(-0.588326\pi\) |
0.961748 | + | 0.273936i | \(0.0883256\pi\) | |||||||
\(774\) | 2.56124i | 0.0920618i | ||||||||
\(775\) | −24.2482 | − | 44.0520i | −0.871022 | − | 1.58239i | ||||
\(776\) | − | 8.07546i | − | 0.289892i | ||||||
\(777\) | 1.70571 | + | 2.75511i | 0.0611921 | + | 0.0988391i | ||||
\(778\) | 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 | ||||||
\(782\) | −14.5498 | −0.520299 | ||||||||
\(783\) | 1.63348i | 0.0583757i | ||||||||
\(784\) | − | 6.71621i | − | 0.239865i | ||||||
\(785\) | −23.7467 | − | 31.6102i | −0.847558 | − | 1.12822i | ||||
\(786\) | 15.0691 | 0.537497 | ||||||||
\(787\) | −5.34065 | − | 5.34065i | −0.190374 | − | 0.190374i | 0.605484 | − | 0.795858i | \(-0.292980\pi\) |
−0.795858 | + | 0.605484i | \(0.792980\pi\) | |||||||
\(788\) | 4.75052 | + | 4.75052i | 0.169230 | + | 0.169230i | ||||
\(789\) | − | 15.9116i | − | 0.566468i | ||||||
\(790\) | 28.8227 | − | 21.6527i | 1.02547 | − | 0.770368i | ||||
\(791\) | −1.04568 | − | 1.04568i | −0.0371800 | − | 0.0371800i | ||||
\(792\) | − | 1.28566i | − | 0.0456839i | ||||||
\(793\) | 17.6844 | − | 17.6844i | 0.627992 | − | 0.627992i | ||||
\(794\) | −17.9874 | − | 17.9874i | −0.638349 | − | 0.638349i | ||||
\(795\) | −1.79362 | − | 0.254784i | −0.0636132 | − | 0.00903627i | ||||
\(796\) | −4.93690 | + | 4.93690i | −0.174984 | + | 0.174984i | ||||
\(797\) | − | 25.8297i | − | 0.914934i | −0.889227 | − | 0.457467i | \(-0.848757\pi\) | ||
0.889227 | − | 0.457467i | \(-0.151243\pi\) | |||||||
\(798\) | −2.06409 | − | 2.06409i | −0.0730682 | − | 0.0730682i | ||||
\(799\) | −6.11149 | − | 6.11149i | −0.216209 | − | 0.216209i | ||||
\(800\) | −1.39241 | + | 4.80221i | −0.0492290 | + | 0.169784i | ||||
\(801\) | 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 | ||||
\(808\) | 15.8768 | 0.558545 | ||||||||
\(809\) | −32.2660 | + | 32.2660i | −1.13441 | + | 1.13441i | −0.144976 | + | 0.989435i | \(0.546311\pi\) |
−0.989435 | + | 0.144976i | \(0.953689\pi\) | |||||||
\(810\) | 0.314477 | − | 2.21384i | 0.0110496 | − | 0.0777865i | ||||
\(811\) | −16.4212 | −0.576628 | −0.288314 | − | 0.957536i | \(-0.593095\pi\) | ||||
−0.288314 | + | 0.957536i | \(0.593095\pi\) | |||||||
\(812\) | −0.870179 | −0.0305373 | ||||||||
\(813\) | −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 | ||||
\(820\) | 0.669508 | − | 4.71318i | 0.0233802 | − | 0.164591i | ||||
\(821\) | −31.7926 | −1.10957 | −0.554784 | − | 0.831994i | \(-0.687199\pi\) | ||||
−0.554784 | + | 0.831994i | \(0.687199\pi\) | |||||||
\(822\) | 12.7109 | 0.443343 | ||||||||
\(823\) | −25.1623 | + | 25.1623i | −0.877102 | + | 0.877102i | −0.993234 | − | 0.116132i | \(-0.962951\pi\) |
0.116132 | + | 0.993234i | \(0.462951\pi\) | |||||||
\(824\) | 9.00947i | 0.313860i | ||||||||
\(825\) | −5.63152 | + | 3.09985i | −0.196064 | + | 0.107923i | ||||
\(826\) | −0.786807 | −0.0273765 | ||||||||
\(827\) | 13.8706 | 0.482329 | 0.241165 | − | 0.970484i | \(-0.422471\pi\) | ||||
0.241165 | + | 0.970484i | \(0.422471\pi\) | |||||||
\(828\) | −6.29757 | −0.218856 | ||||||||
\(829\) | 19.5830 | − | 19.5830i | 0.680147 | − | 0.680147i | −0.279886 | − | 0.960033i | \(-0.590297\pi\) |
0.960033 | + | 0.279886i | \(0.0902967\pi\) | |||||||
\(830\) | 21.8810 | + | 29.1267i | 0.759502 | + | 1.01100i | ||||
\(831\) | −4.64924 | + | 4.64924i | −0.161280 | + | 0.161280i | ||||
\(832\) | 5.12767i | 0.177770i | ||||||||
\(833\) | 15.5170i | 0.537632i | ||||||||
\(834\) | −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 | ||||
\(837\) | −10.0569 | −0.347619 | ||||||||
\(838\) | −7.19965 | −0.248708 | ||||||||
\(839\) | 29.1983 | 1.00804 | 0.504019 | − | 0.863692i | \(-0.331854\pi\) | ||||
0.504019 | + | 0.863692i | \(0.331854\pi\) | |||||||
\(840\) | 1.17935 | + | 0.167527i | 0.0406915 | + | 0.00578023i | ||||
\(841\) | 26.3318i | 0.907992i | ||||||||
\(842\) | −6.17926 | + | 6.17926i | −0.212951 | + | 0.212951i | ||||
\(843\) | 19.2196 | 0.661957 | ||||||||
\(844\) | 13.1658 | 0.453187 | ||||||||
\(845\) | −29.4286 | − | 4.18033i | −1.01237 | − | 0.143808i | ||||
\(846\) | −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 | ||||
\(853\) | 6.30510 | 0.215883 | 0.107941 | − | 0.994157i | \(-0.465574\pi\) | ||||
0.107941 | + | 0.994157i | \(0.465574\pi\) | |||||||
\(854\) | 2.59825 | 0.0889104 | ||||||||
\(855\) | −9.79638 | + | 7.35940i | −0.335029 | + | 0.251686i | ||||
\(856\) | 1.41163 | − | 1.41163i | 0.0482487 | − | 0.0482487i | ||||
\(857\) | −5.70445 | −0.194860 | −0.0974302 | − | 0.995242i | \(-0.531062\pi\) | ||||
−0.0974302 | + | 0.995242i | \(0.531062\pi\) | |||||||
\(858\) | −4.66156 | + | 4.66156i | −0.159143 | + | 0.159143i | ||||
\(859\) | −9.67146 | − | 9.67146i | −0.329986 | − | 0.329986i | 0.522595 | − | 0.852581i | \(-0.324964\pi\) |
−0.852581 | + | 0.522595i | \(0.824964\pi\) | |||||||
\(860\) | −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 | −0.875108 | − | 0.483928i | \(-0.839210\pi\) |
0.483928 | + | 0.875108i | \(0.339210\pi\) | |||||||
\(864\) | 0.707107 | + | 0.707107i | 0.0240563 | + | 0.0240563i | ||||
\(865\) | 2.51434 | + | 3.34694i | 0.0854903 | + | 0.113799i | ||||
\(866\) | −27.0193 | − | 27.0193i | −0.918154 | − | 0.918154i | ||||
\(867\) | 8.24638 | + | 8.24638i | 0.280062 | + | 0.280062i | ||||
\(868\) | − | 5.35750i | − | 0.181845i | ||||||
\(869\) | −14.6565 | + | 14.6565i | −0.497186 | + | 0.497186i | ||||
\(870\) | −0.513691 | + | 3.61626i | −0.0174157 | + | 0.122603i | ||||
\(871\) | −27.2925 | − | 27.2925i | −0.924771 | − | 0.924771i | ||||
\(872\) | −1.15892 | + | 1.15892i | −0.0392460 | + | 0.0392460i | ||||
\(873\) | 8.07546i | 0.273313i | ||||||||
\(874\) | 24.4009 | + | 24.4009i | 0.825374 | + | 0.825374i | ||||
\(875\) | −2.10971 | − | 5.56978i | −0.0713214 | − | 0.188293i | ||||
\(876\) | 13.8741i | 0.468763i | ||||||||
\(877\) | 9.10608 | + | 9.10608i | 0.307490 | + | 0.307490i | 0.843935 | − | 0.536445i | \(-0.180233\pi\) |
−0.536445 | + | 0.843935i | \(0.680233\pi\) | |||||||
\(878\) | 8.21948 | + | 8.21948i | 0.277394 | + | 0.277394i | ||||
\(879\) | −10.7700 | −0.363263 | ||||||||
\(880\) | 0.404311 | − | 2.84625i | 0.0136293 | − | 0.0959471i | ||||
\(881\) | − | 2.47471i | − | 0.0833752i | −0.999131 | − | 0.0416876i | \(-0.986727\pi\) | ||
0.999131 | − | 0.0416876i | \(-0.0132734\pi\) | |||||||
\(882\) | 6.71621i | 0.226147i | ||||||||
\(883\) | 42.6117 | 1.43400 | 0.716999 | − | 0.697075i | \(-0.245515\pi\) | ||||
0.716999 | + | 0.697075i | \(0.245515\pi\) | |||||||
\(884\) | − | 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 | \(-0.638629\pi\) |
0.906652 | + | 0.421878i | \(0.138629\pi\) | |||||||
\(888\) | −1.39293 | + | 5.92113i | −0.0467437 | + | 0.198700i | ||||
\(889\) | 8.00705i | 0.268548i | ||||||||
\(890\) | 15.3726 | + | 20.4631i | 0.515291 | + | 0.685924i | ||||
\(891\) | 1.28566i | 0.0430712i | ||||||||
\(892\) | 13.0670 | − | 13.0670i | 0.437516 | − | 0.437516i | ||||
\(893\) | 20.4987i | 0.685964i | ||||||||
\(894\) | 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 | ||||
\(902\) | 2.73711i | 0.0911359i | ||||||||
\(903\) | 1.36441 | 0.0454048 | ||||||||
\(904\) | − | 2.77598i | − | 0.0923277i | ||||||
\(905\) | −4.39933 | − | 0.624925i | −0.146239 | − | 0.0207732i | ||||
\(906\) | 2.19905 | + | 2.19905i | 0.0730584 | + | 0.0730584i | ||||
\(907\) | −20.9996 | −0.697281 | −0.348641 | − | 0.937256i | \(-0.613357\pi\) | ||||
−0.348641 | + | 0.937256i | \(0.613357\pi\) | |||||||
\(908\) | −16.0865 | −0.533848 | ||||||||
\(909\) | −15.8768 | −0.526601 | ||||||||
\(910\) | −3.66868 | − | 4.88352i | −0.121615 | − | 0.161887i | ||||
\(911\) | 2.09529 | − | 2.09529i | 0.0694199 | − | 0.0694199i | −0.671544 | − | 0.740964i | \(-0.734369\pi\) |
0.740964 | + | 0.671544i | \(0.234369\pi\) | |||||||
\(912\) | − | 5.47960i | − | 0.181448i | ||||||
\(913\) | −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 | ||||||
\(917\) | − | 8.02756i | − | 0.265093i | ||||||
\(918\) | −1.63368 | − | 1.63368i | −0.0539196 | − | 0.0539196i | ||||
\(919\) | −26.2479 | + | 26.2479i | −0.865840 | + | 0.865840i | −0.992009 | − | 0.126169i | \(-0.959732\pi\) |
0.126169 | + | 0.992009i | \(0.459732\pi\) | |||||||
\(920\) | −13.9418 | − | 1.98044i | −0.459649 | − | 0.0652932i | ||||
\(921\) | −27.8219 | −0.916763 | ||||||||
\(922\) | −21.6193 | − | 21.6193i | −0.711994 | − | 0.711994i | ||||
\(923\) | − | 22.4883i | − | 0.740211i | ||||||
\(924\) | −0.684892 | −0.0225313 | ||||||||
\(925\) | 29.2945 | − | 8.17501i | 0.963198 | − | 0.268793i | ||||
\(926\) | 7.74140 | 0.254398 | ||||||||
\(927\) | − | 9.00947i | − | 0.295910i | ||||||
\(928\) | −1.15504 | − | 1.15504i | −0.0379161 | − | 0.0379161i | ||||
\(929\) | 36.8972 | 1.21056 | 0.605279 | − | 0.796014i | \(-0.293062\pi\) | ||||
0.605279 | + | 0.796014i | \(0.293062\pi\) | |||||||
\(930\) | −22.2645 | − | 3.16268i | −0.730082 | − | 0.103708i | ||||
\(931\) | 26.0230 | − | 26.0230i | 0.852871 | − | 0.852871i | ||||
\(932\) | −4.61749 | − | 4.61749i | −0.151251 | − | 0.151251i | ||||
\(933\) | 5.45953i | 0.178737i | ||||||||
\(934\) | 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 | 0.589420 | − | 0.807827i | \(-0.299356\pi\) |
−0.807827 | + | 0.589420i | \(0.799356\pi\) | |||||||
\(938\) | − | 4.00991i | − | 0.130928i | ||||||
\(939\) | −13.4327 | + | 13.4327i | −0.438361 | + | 0.438361i | ||||
\(940\) | −5.02426 | − | 6.68799i | −0.163873 | − | 0.218138i | ||||
\(941\) | −5.71005 | −0.186142 | −0.0930711 | − | 0.995659i | \(-0.529668\pi\) | ||||
−0.0930711 | + | 0.995659i | \(0.529668\pi\) | |||||||
\(942\) | −17.6811 | −0.576083 | ||||||||
\(943\) | 13.4073 | 0.436600 | ||||||||
\(944\) | −1.04438 | − | 1.04438i | −0.0339916 | − | 0.0339916i | ||||
\(945\) | −1.17935 | − | 0.167527i | −0.0383643 | − | 0.00544965i | ||||
\(946\) | − | 3.29288i | − | 0.107061i | ||||||
\(947\) | −31.5411 | −1.02495 | −0.512474 | − | 0.858703i | \(-0.671271\pi\) | ||||
−0.512474 | + | 0.858703i | \(0.671271\pi\) | |||||||
\(948\) | − | 16.1220i | − | 0.523617i | ||||||
\(949\) | 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 | −0.878227 | − | 0.478245i | \(-0.841273\pi\) |
−0.478245 | − | 0.878227i | \(-0.658727\pi\) | |||||||
\(954\) | −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 | ||||
\(957\) | − | 2.10009i | − | 0.0678864i | ||||||
\(958\) | −4.76750 | + | 4.76750i | −0.154031 | + | 0.154031i | ||||
\(959\) | − | 6.77129i | − | 0.218656i | ||||||
\(960\) | 1.34306 | + | 1.78779i | 0.0433469 | + | 0.0577008i | ||||
\(961\) | 70.1421i | 2.26265i | ||||||||
\(962\) | 26.5194 | − | 16.4184i | 0.855019 | − | 0.529350i | ||||
\(963\) | −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 | ||||||||
\(967\) | 20.2774 | 0.652076 | 0.326038 | − | 0.945357i | \(-0.394286\pi\) | ||||
0.326038 | + | 0.945357i | \(0.394286\pi\) | |||||||
\(968\) | − | 9.34708i | − | 0.300426i | ||||||
\(969\) | 12.6599i | 0.406696i | ||||||||
\(970\) | −2.53955 | + | 17.8778i | −0.0815399 | + | 0.574022i | ||||
\(971\) | 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 | ||||||
\(975\) | −22.4605 | + | 12.3633i | −0.719311 | + | 0.395942i | ||||
\(976\) | 3.44882 | + | 3.44882i | 0.110394 | + | 0.110394i | ||||
\(977\) | 45.6145i | 1.45934i | 0.683801 | + | 0.729669i | \(0.260326\pi\) | ||||
−0.683801 | + | 0.729669i | \(0.739674\pi\) | |||||||
\(978\) | −6.09026 | + | 6.09026i | −0.194745 | + | 0.194745i | ||||
\(979\) | −10.4055 | − | 10.4055i | −0.332563 | − | 0.332563i | ||||
\(980\) | −2.11209 | + | 14.8686i | −0.0674684 | + | 0.474962i | ||||
\(981\) | 1.15892 | − | 1.15892i | 0.0370014 | − | 0.0370014i | ||||
\(982\) | − | 11.4600i | − | 0.365705i | ||||||
\(983\) | 18.8451 | + | 18.8451i | 0.601066 | + | 0.601066i | 0.940595 | − | 0.339530i | \(-0.110268\pi\) |
−0.339530 | + | 0.940595i | \(0.610268\pi\) | |||||||
\(984\) | −1.50540 | − | 1.50540i | −0.0479904 | − | 0.0479904i | ||||
\(985\) | −9.02298 | − | 12.0108i | −0.287496 | − | 0.382697i | ||||
\(986\) | 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 | ||||
\(993\) | 1.57774 | 0.0500682 | ||||||||
\(994\) | 1.65203 | − | 1.65203i | 0.0523992 | − | 0.0523992i | ||||
\(995\) | 12.4821 | − | 9.37699i | 0.395708 | − | 0.297270i | ||||
\(996\) | 16.2920 | 0.516232 | ||||||||
\(997\) | −34.7231 | −1.09969 | −0.549846 | − | 0.835266i | \(-0.685313\pi\) | ||||
−0.549846 | + | 0.835266i | \(0.685313\pi\) | |||||||
\(998\) | 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.l.b.697.6 | yes | 40 | |
5.3 | odd | 4 | 1110.2.o.b.253.15 | yes | 40 | ||
37.6 | odd | 4 | 1110.2.o.b.487.15 | yes | 40 | ||
185.43 | even | 4 | inner | 1110.2.l.b.43.6 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.l.b.43.6 | ✓ | 40 | 185.43 | even | 4 | inner | |
1110.2.l.b.697.6 | yes | 40 | 1.1 | even | 1 | trivial | |
1110.2.o.b.253.15 | yes | 40 | 5.3 | odd | 4 | ||
1110.2.o.b.487.15 | yes | 40 | 37.6 | odd | 4 |