Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,2,Mod(19,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.o (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.69520363885\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.432972864.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + x^{6} + 4x^{5} - 6x^{4} + 8x^{3} + 4x^{2} - 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.1 | ||
Root | \(-1.41156 + 0.0865986i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.31 |
Dual form | 588.2.o.a.19.1 |
$q$-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 \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41156 | − | 0.0865986i | −0.998123 | − | 0.0612344i | ||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | 1.98500 | + | 0.244478i | 0.992501 | + | 0.122239i | ||||
\(5\) | 1.46890 | − | 0.848071i | 0.656913 | − | 0.379269i | −0.134187 | − | 0.990956i | \(-0.542842\pi\) |
0.791100 | + | 0.611687i | \(0.209509\pi\) | |||||||
\(6\) | 0.780776 | − | 1.17915i | 0.318751 | − | 0.481385i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.78078 | − | 0.516994i | −0.983153 | − | 0.182785i | ||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −2.14688 | + | 1.06990i | −0.678904 | + | 0.338331i | ||||
\(11\) | −2.61578 | − | 1.51022i | −0.788689 | − | 0.455350i | 0.0508120 | − | 0.998708i | \(-0.483819\pi\) |
−0.839501 | + | 0.543359i | \(0.817152\pi\) | |||||||
\(12\) | −1.20422 | + | 1.59682i | −0.347630 | + | 0.460963i | ||||
\(13\) | − | 6.04090i | − | 1.67544i | −0.546098 | − | 0.837722i | \(-0.683887\pi\) | ||
0.546098 | − | 0.837722i | \(-0.316113\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.69614i | 0.437942i | ||||||||
\(16\) | 3.88046 | + | 0.970579i | 0.970115 | + | 0.242645i | ||||
\(17\) | −3.76267 | − | 2.17238i | −0.912581 | − | 0.526879i | −0.0313203 | − | 0.999509i | \(-0.509971\pi\) |
−0.881261 | + | 0.472630i | \(0.843305\pi\) | |||||||
\(18\) | 0.630783 | + | 1.26575i | 0.148677 | + | 0.298339i | ||||
\(19\) | −0.561553 | − | 0.972638i | −0.128829 | − | 0.223138i | 0.794394 | − | 0.607403i | \(-0.207789\pi\) |
−0.923223 | + | 0.384264i | \(0.874455\pi\) | |||||||
\(20\) | 3.12311 | − | 1.32431i | 0.698348 | − | 0.296124i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.56155 | + | 2.35829i | 0.759326 | + | 0.502790i | ||||
\(23\) | −2.61578 | + | 1.51022i | −0.545429 | + | 0.314903i | −0.747276 | − | 0.664514i | \(-0.768639\pi\) |
0.201847 | + | 0.979417i | \(0.435305\pi\) | |||||||
\(24\) | 1.83812 | − | 2.14973i | 0.375204 | − | 0.438811i | ||||
\(25\) | −1.06155 | + | 1.83866i | −0.212311 | + | 0.367733i | ||||
\(26\) | −0.523133 | + | 8.52708i | −0.102595 | + | 1.67230i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0.146883 | − | 2.39420i | 0.0268171 | − | 0.437120i | ||||
\(31\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(32\) | −5.39345 | − | 1.70607i | −0.953436 | − | 0.301594i | ||||
\(33\) | 2.61578 | − | 1.51022i | 0.455350 | − | 0.262896i | ||||
\(34\) | 5.12311 | + | 3.39228i | 0.878605 | + | 0.581772i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.780776 | − | 1.84130i | −0.130129 | − | 0.306883i | ||||
\(37\) | 3.56155 | + | 6.16879i | 0.585516 | + | 1.01414i | 0.994811 | + | 0.101741i | \(0.0324413\pi\) |
−0.409295 | + | 0.912402i | \(0.634225\pi\) | |||||||
\(38\) | 0.708436 | + | 1.42157i | 0.114924 | + | 0.230608i | ||||
\(39\) | 5.23157 | + | 3.02045i | 0.837722 | + | 0.483659i | ||||
\(40\) | −4.52313 | + | 1.59888i | −0.715170 | + | 0.252805i | ||||
\(41\) | − | 7.73704i | − | 1.20832i | −0.796862 | − | 0.604161i | \(-0.793508\pi\) | ||
0.796862 | − | 0.604161i | \(-0.206492\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.10887i | − | 1.23659i | −0.785946 | − | 0.618296i | \(-0.787823\pi\) | ||
0.785946 | − | 0.618296i | \(-0.212177\pi\) | |||||||
\(44\) | −4.82312 | − | 3.63730i | −0.727113 | − | 0.548343i | ||||
\(45\) | −1.46890 | − | 0.848071i | −0.218971 | − | 0.126423i | ||||
\(46\) | 3.82312 | − | 1.90525i | 0.563688 | − | 0.280913i | ||||
\(47\) | −5.12311 | − | 8.87348i | −0.747282 | − | 1.29433i | −0.949121 | − | 0.314911i | \(-0.898025\pi\) |
0.201839 | − | 0.979419i | \(-0.435308\pi\) | |||||||
\(48\) | −2.78078 | + | 2.87529i | −0.401371 | + | 0.415012i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.65767 | − | 2.50345i | 0.234430 | − | 0.354042i | ||||
\(51\) | 3.76267 | − | 2.17238i | 0.526879 | − | 0.304194i | ||||
\(52\) | 1.47687 | − | 11.9912i | 0.204805 | − | 1.66288i | ||||
\(53\) | 2.12311 | − | 3.67733i | 0.291631 | − | 0.505120i | −0.682565 | − | 0.730825i | \(-0.739135\pi\) |
0.974196 | + | 0.225706i | \(0.0724687\pi\) | |||||||
\(54\) | −1.41156 | − | 0.0865986i | −0.192089 | − | 0.0117846i | ||||
\(55\) | −5.12311 | −0.690799 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.12311 | 0.148759 | ||||||||
\(58\) | 2.82312 | + | 0.173197i | 0.370694 | + | 0.0227419i | ||||
\(59\) | 2.00000 | − | 3.46410i | 0.260378 | − | 0.450988i | −0.705965 | − | 0.708247i | \(-0.749486\pi\) |
0.966342 | + | 0.257260i | \(0.0828195\pi\) | |||||||
\(60\) | −0.414669 | + | 3.36684i | −0.0535336 | + | 0.434657i | ||||
\(61\) | 8.16937 | − | 4.71659i | 1.04598 | − | 0.603897i | 0.124459 | − | 0.992225i | \(-0.460280\pi\) |
0.921521 | + | 0.388327i | \(0.126947\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.46543 | + | 2.87529i | 0.933179 | + | 0.359411i | ||||
\(65\) | −5.12311 | − | 8.87348i | −0.635443 | − | 1.10062i | ||||
\(66\) | −3.82312 | + | 1.90525i | −0.470593 | + | 0.234520i | ||||
\(67\) | −1.79092 | − | 1.03399i | −0.218796 | − | 0.126322i | 0.386597 | − | 0.922249i | \(-0.373650\pi\) |
−0.605392 | + | 0.795927i | \(0.706984\pi\) | |||||||
\(68\) | −6.93780 | − | 5.23206i | −0.841332 | − | 0.634481i | ||||
\(69\) | − | 3.02045i | − | 0.363619i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.4536i | 1.47797i | 0.673720 | + | 0.738987i | \(0.264695\pi\) | ||||
−0.673720 | + | 0.738987i | \(0.735305\pi\) | |||||||
\(72\) | 0.942658 | + | 2.66672i | 0.111093 | + | 0.314276i | ||||
\(73\) | −2.93780 | − | 1.69614i | −0.343844 | − | 0.198518i | 0.318127 | − | 0.948048i | \(-0.396946\pi\) |
−0.661970 | + | 0.749530i | \(0.730280\pi\) | |||||||
\(74\) | −4.49314 | − | 9.01604i | −0.522316 | − | 1.04809i | ||||
\(75\) | −1.06155 | − | 1.83866i | −0.122578 | − | 0.212311i | ||||
\(76\) | −0.876894 | − | 2.06798i | −0.100587 | − | 0.237213i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −7.12311 | − | 4.71659i | −0.806533 | − | 0.534049i | ||||
\(79\) | 4.08469 | − | 2.35829i | 0.459563 | − | 0.265329i | −0.252297 | − | 0.967650i | \(-0.581186\pi\) |
0.711861 | + | 0.702321i | \(0.247853\pi\) | |||||||
\(80\) | 6.52313 | − | 1.86522i | 0.729308 | − | 0.208538i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −0.670016 | + | 10.9213i | −0.0739909 | + | 1.20605i | ||||
\(83\) | −6.24621 | −0.685611 | −0.342805 | − | 0.939406i | \(-0.611377\pi\) | ||||
−0.342805 | + | 0.939406i | \(0.611377\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.36932 | −0.799315 | ||||||||
\(86\) | −0.702217 | + | 11.4462i | −0.0757220 | + | 1.23427i | ||||
\(87\) | 1.00000 | − | 1.73205i | 0.107211 | − | 0.185695i | ||||
\(88\) | 6.49314 | + | 5.55194i | 0.692171 | + | 0.591839i | ||||
\(89\) | 6.70047 | − | 3.86852i | 0.710248 | − | 0.410062i | −0.100905 | − | 0.994896i | \(-0.532174\pi\) |
0.811153 | + | 0.584834i | \(0.198840\pi\) | |||||||
\(90\) | 2.00000 | + | 1.32431i | 0.210819 | + | 0.139594i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.56155 | + | 2.35829i | −0.579832 | + | 0.245869i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.46314 | + | 12.9691i | 0.666622 | + | 1.33766i | ||||
\(95\) | −1.64973 | − | 0.952473i | −0.169259 | − | 0.0977216i | ||||
\(96\) | 4.17423 | − | 3.81783i | 0.426030 | − | 0.389656i | ||||
\(97\) | 8.68951i | 0.882286i | 0.897437 | + | 0.441143i | \(0.145427\pi\) | ||||
−0.897437 | + | 0.441143i | \(0.854573\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.02045i | 0.303566i | ||||||||
\(100\) | −2.55670 | + | 3.39022i | −0.255670 | + | 0.339022i | ||||
\(101\) | 6.05643 | + | 3.49668i | 0.602638 | + | 0.347933i | 0.770079 | − | 0.637949i | \(-0.220217\pi\) |
−0.167441 | + | 0.985882i | \(0.553550\pi\) | |||||||
\(102\) | −5.49936 | + | 2.74060i | −0.544517 | + | 0.271360i | ||||
\(103\) | −4.00000 | − | 6.92820i | −0.394132 | − | 0.682656i | 0.598858 | − | 0.800855i | \(-0.295621\pi\) |
−0.992990 | + | 0.118199i | \(0.962288\pi\) | |||||||
\(104\) | −3.12311 | + | 16.7984i | −0.306246 | + | 1.64722i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.31534 | + | 5.00691i | −0.322014 | + | 0.486314i | ||||
\(107\) | −4.90955 | + | 2.83453i | −0.474624 | + | 0.274024i | −0.718173 | − | 0.695864i | \(-0.755022\pi\) |
0.243549 | + | 0.969889i | \(0.421688\pi\) | |||||||
\(108\) | 1.98500 | + | 0.244478i | 0.191007 | + | 0.0235249i | ||||
\(109\) | −4.12311 | + | 7.14143i | −0.394922 | + | 0.684025i | −0.993091 | − | 0.117345i | \(-0.962562\pi\) |
0.598169 | + | 0.801370i | \(0.295895\pi\) | |||||||
\(110\) | 7.23157 | + | 0.443654i | 0.689503 | + | 0.0423007i | ||||
\(111\) | −7.12311 | −0.676095 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.2462 | 1.15203 | 0.576013 | − | 0.817440i | \(-0.304608\pi\) | ||||
0.576013 | + | 0.817440i | \(0.304608\pi\) | |||||||
\(114\) | −1.58533 | − | 0.0972594i | −0.148480 | − | 0.00910917i | ||||
\(115\) | −2.56155 | + | 4.43674i | −0.238866 | + | 0.413728i | ||||
\(116\) | −3.97000 | − | 0.488956i | −0.368606 | − | 0.0453985i | ||||
\(117\) | −5.23157 | + | 3.02045i | −0.483659 | + | 0.279241i | ||||
\(118\) | −3.12311 | + | 4.71659i | −0.287505 | + | 0.434197i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.876894 | − | 4.71659i | 0.0800491 | − | 0.430564i | ||||
\(121\) | −0.938447 | − | 1.62544i | −0.0853134 | − | 0.147767i | ||||
\(122\) | −11.9400 | + | 5.95029i | −1.08100 | + | 0.538714i | ||||
\(123\) | 6.70047 | + | 3.86852i | 0.604161 | + | 0.348813i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0818i | 1.08063i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 19.4470i | − | 1.72564i | −0.505510 | − | 0.862821i | \(-0.668696\pi\) | ||
0.505510 | − | 0.862821i | \(-0.331304\pi\) | |||||||
\(128\) | −10.2889 | − | 4.70514i | −0.909420 | − | 0.415879i | ||||
\(129\) | 7.02249 | + | 4.05444i | 0.618296 | + | 0.356973i | ||||
\(130\) | 6.46314 | + | 12.9691i | 0.566855 | + | 1.13747i | ||||
\(131\) | 11.1231 | + | 19.2658i | 0.971830 | + | 1.68326i | 0.690022 | + | 0.723789i | \(0.257601\pi\) |
0.281809 | + | 0.959471i | \(0.409066\pi\) | |||||||
\(132\) | 5.56155 | − | 2.35829i | 0.484071 | − | 0.205263i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.43845 | + | 1.61463i | 0.210650 | + | 0.139482i | ||||
\(135\) | 1.46890 | − | 0.848071i | 0.126423 | − | 0.0729903i | ||||
\(136\) | 9.34003 | + | 7.98617i | 0.800901 | + | 0.684809i | ||||
\(137\) | 8.12311 | − | 14.0696i | 0.694004 | − | 1.20205i | −0.276512 | − | 0.961011i | \(-0.589178\pi\) |
0.970515 | − | 0.241039i | \(-0.0774882\pi\) | |||||||
\(138\) | −0.261567 | + | 4.26354i | −0.0222660 | + | 0.362937i | ||||
\(139\) | 12.0000 | 1.01783 | 0.508913 | − | 0.860818i | \(-0.330047\pi\) | ||||
0.508913 | + | 0.860818i | \(0.330047\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.2462 | 0.862887 | ||||||||
\(142\) | 1.07847 | − | 17.5790i | 0.0905029 | − | 1.47520i | ||||
\(143\) | −9.12311 | + | 15.8017i | −0.762912 | + | 1.32140i | ||||
\(144\) | −1.09968 | − | 3.84587i | −0.0916404 | − | 0.320489i | ||||
\(145\) | −2.93780 | + | 1.69614i | −0.243971 | + | 0.140857i | ||||
\(146\) | 4.00000 | + | 2.64861i | 0.331042 | + | 0.219201i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.56155 | + | 13.1158i | 0.457157 | + | 1.07811i | ||||
\(149\) | 5.00000 | + | 8.66025i | 0.409616 | + | 0.709476i | 0.994847 | − | 0.101391i | \(-0.0323294\pi\) |
−0.585231 | + | 0.810867i | \(0.698996\pi\) | |||||||
\(150\) | 1.33922 | + | 2.68731i | 0.109347 | + | 0.219418i | ||||
\(151\) | −7.02249 | − | 4.05444i | −0.571482 | − | 0.329945i | 0.186259 | − | 0.982501i | \(-0.440364\pi\) |
−0.757741 | + | 0.652555i | \(0.773697\pi\) | |||||||
\(152\) | 1.05871 | + | 2.99501i | 0.0858723 | + | 0.242927i | ||||
\(153\) | 4.34475i | 0.351253i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 9.64624 | + | 7.27460i | 0.772317 | + | 0.582434i | ||||
\(157\) | 3.58184 | + | 2.06798i | 0.285862 | + | 0.165042i | 0.636074 | − | 0.771628i | \(-0.280557\pi\) |
−0.350212 | + | 0.936670i | \(0.613891\pi\) | |||||||
\(158\) | −5.97000 | + | 2.97515i | −0.474948 | + | 0.236690i | ||||
\(159\) | 2.12311 | + | 3.67733i | 0.168373 | + | 0.291631i | ||||
\(160\) | −9.36932 | + | 2.06798i | −0.740710 | + | 0.163488i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.780776 | − | 1.17915i | 0.0613436 | − | 0.0926426i | ||||
\(163\) | −9.96029 | + | 5.75058i | −0.780150 | + | 0.450420i | −0.836484 | − | 0.547992i | \(-0.815392\pi\) |
0.0563333 | + | 0.998412i | \(0.482059\pi\) | |||||||
\(164\) | 1.89154 | − | 15.3580i | 0.147704 | − | 1.19926i | ||||
\(165\) | 2.56155 | − | 4.43674i | 0.199417 | − | 0.345400i | ||||
\(166\) | 8.81690 | + | 0.540913i | 0.684324 | + | 0.0419830i | ||||
\(167\) | 2.24621 | 0.173817 | 0.0869085 | − | 0.996216i | \(-0.472301\pi\) | ||||
0.0869085 | + | 0.996216i | \(0.472301\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.4924 | −1.80711 | ||||||||
\(170\) | 10.4022 | + | 0.638172i | 0.797815 | + | 0.0489456i | ||||
\(171\) | −0.561553 | + | 0.972638i | −0.0429430 | + | 0.0743795i | ||||
\(172\) | 1.98244 | − | 16.0961i | 0.151160 | − | 1.22732i | ||||
\(173\) | −7.34451 | + | 4.24035i | −0.558392 | + | 0.322388i | −0.752500 | − | 0.658592i | \(-0.771152\pi\) |
0.194108 | + | 0.980980i | \(0.437819\pi\) | |||||||
\(174\) | −1.56155 | + | 2.35829i | −0.118381 | + | 0.178782i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −8.68466 | − | 8.39919i | −0.654631 | − | 0.633113i | ||||
\(177\) | 2.00000 | + | 3.46410i | 0.150329 | + | 0.260378i | ||||
\(178\) | −9.79312 | + | 4.88039i | −0.734026 | + | 0.365801i | ||||
\(179\) | 1.97175 | + | 1.13839i | 0.147375 | + | 0.0850873i | 0.571874 | − | 0.820341i | \(-0.306216\pi\) |
−0.424499 | + | 0.905428i | \(0.639550\pi\) | |||||||
\(180\) | −2.70844 | − | 2.04254i | −0.201875 | − | 0.152242i | ||||
\(181\) | 6.04090i | 0.449016i | 0.974472 | + | 0.224508i | \(0.0720775\pi\) | ||||
−0.974472 | + | 0.224508i | \(0.927922\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.43318i | 0.697321i | ||||||||
\(184\) | 8.05469 | − | 2.84725i | 0.593800 | − | 0.209902i | ||||
\(185\) | 10.4631 | + | 6.04090i | 0.769265 | + | 0.444135i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.56155 | + | 11.3649i | 0.479828 | + | 0.831087i | ||||
\(188\) | −8.00000 | − | 18.8664i | −0.583460 | − | 1.37597i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.24621 | + | 1.48734i | 0.162957 | + | 0.107903i | ||||
\(191\) | 7.84735 | − | 4.53067i | 0.567815 | − | 0.327828i | −0.188461 | − | 0.982081i | \(-0.560350\pi\) |
0.756276 | + | 0.654253i | \(0.227017\pi\) | |||||||
\(192\) | −6.22279 | + | 5.02761i | −0.449091 | + | 0.362837i | ||||
\(193\) | −4.68466 | + | 8.11407i | −0.337209 | + | 0.584063i | −0.983907 | − | 0.178683i | \(-0.942816\pi\) |
0.646698 | + | 0.762747i | \(0.276150\pi\) | |||||||
\(194\) | 0.752499 | − | 12.2658i | 0.0540263 | − | 0.880630i | ||||
\(195\) | 10.2462 | 0.733746 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.246211 | 0.0175418 | 0.00877091 | − | 0.999962i | \(-0.497208\pi\) | ||||
0.00877091 | + | 0.999962i | \(0.497208\pi\) | |||||||
\(198\) | 0.261567 | − | 4.26354i | 0.0185887 | − | 0.302997i | ||||
\(199\) | 2.56155 | − | 4.43674i | 0.181584 | − | 0.314512i | −0.760836 | − | 0.648944i | \(-0.775211\pi\) |
0.942420 | + | 0.334432i | \(0.108544\pi\) | |||||||
\(200\) | 3.90252 | − | 4.56410i | 0.275950 | − | 0.322730i | ||||
\(201\) | 1.79092 | − | 1.03399i | 0.126322 | − | 0.0729319i | ||||
\(202\) | −8.24621 | − | 5.46026i | −0.580201 | − | 0.384182i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 8.00000 | − | 3.39228i | 0.560112 | − | 0.237507i | ||||
\(205\) | −6.56155 | − | 11.3649i | −0.458279 | − | 0.793762i | ||||
\(206\) | 5.04627 | + | 10.1260i | 0.351590 | + | 0.705510i | ||||
\(207\) | 2.61578 | + | 1.51022i | 0.181810 | + | 0.104968i | ||||
\(208\) | 5.86317 | − | 23.4415i | 0.406537 | − | 1.62537i | ||||
\(209\) | 3.39228i | 0.234649i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.97292i | 0.273507i | 0.990605 | + | 0.136754i | \(0.0436668\pi\) | ||||
−0.990605 | + | 0.136754i | \(0.956333\pi\) | |||||||
\(212\) | 5.11339 | − | 6.78045i | 0.351189 | − | 0.465683i | ||||
\(213\) | −10.7852 | − | 6.22681i | −0.738987 | − | 0.426654i | ||||
\(214\) | 7.17559 | − | 3.57595i | 0.490513 | − | 0.244447i | ||||
\(215\) | −6.87689 | − | 11.9111i | −0.469000 | − | 0.812332i | ||||
\(216\) | −2.78078 | − | 0.516994i | −0.189208 | − | 0.0351770i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 6.43845 | − | 9.72350i | 0.436067 | − | 0.658558i | ||||
\(219\) | 2.93780 | − | 1.69614i | 0.198518 | − | 0.114615i | ||||
\(220\) | −10.1694 | − | 1.25249i | −0.685619 | − | 0.0844427i | ||||
\(221\) | −13.1231 | + | 22.7299i | −0.882756 | + | 1.52898i | ||||
\(222\) | 10.0547 | + | 0.616851i | 0.674827 | + | 0.0414003i | ||||
\(223\) | −18.8769 | −1.26409 | −0.632045 | − | 0.774932i | \(-0.717784\pi\) | ||||
−0.632045 | + | 0.774932i | \(0.717784\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.12311 | 0.141540 | ||||||||
\(226\) | −17.2863 | − | 1.06050i | −1.14986 | − | 0.0705437i | ||||
\(227\) | 8.24621 | − | 14.2829i | 0.547320 | − | 0.947987i | −0.451137 | − | 0.892455i | \(-0.648981\pi\) |
0.998457 | − | 0.0555316i | \(-0.0176854\pi\) | |||||||
\(228\) | 2.22937 | + | 0.274575i | 0.147643 | + | 0.0181842i | ||||
\(229\) | −15.6947 | + | 9.06134i | −1.03714 | + | 0.598790i | −0.919021 | − | 0.394209i | \(-0.871018\pi\) |
−0.118115 | + | 0.993000i | \(0.537685\pi\) | |||||||
\(230\) | 4.00000 | − | 6.04090i | 0.263752 | − | 0.398325i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.56155 | + | 1.03399i | 0.365134 | + | 0.0678846i | ||||
\(233\) | 5.24621 | + | 9.08670i | 0.343691 | + | 0.595290i | 0.985115 | − | 0.171897i | \(-0.0549895\pi\) |
−0.641424 | + | 0.767186i | \(0.721656\pi\) | |||||||
\(234\) | 7.64624 | − | 3.81050i | 0.499850 | − | 0.249100i | ||||
\(235\) | −15.0507 | − | 8.68951i | −0.981798 | − | 0.566841i | ||||
\(236\) | 4.81690 | − | 6.38729i | 0.313553 | − | 0.415777i | ||||
\(237\) | 4.71659i | 0.306375i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.27678i | 0.147273i | 0.997285 | + | 0.0736363i | \(0.0234604\pi\) | ||||
−0.997285 | + | 0.0736363i | \(0.976540\pi\) | |||||||
\(240\) | −1.64624 | + | 6.58181i | −0.106264 | + | 0.424854i | ||||
\(241\) | 1.64973 | + | 0.952473i | 0.106269 | + | 0.0613542i | 0.552192 | − | 0.833717i | \(-0.313791\pi\) |
−0.445924 | + | 0.895071i | \(0.647125\pi\) | |||||||
\(242\) | 1.18391 | + | 2.37567i | 0.0761048 | + | 0.152714i | ||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 17.3693 | − | 7.36520i | 1.11196 | − | 0.471509i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −9.12311 | − | 6.04090i | −0.581668 | − | 0.385153i | ||||
\(247\) | −5.87560 | + | 3.39228i | −0.373856 | + | 0.215846i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.12311 | − | 5.40938i | 0.197919 | − | 0.342805i | ||||
\(250\) | 1.04627 | − | 17.0542i | 0.0661717 | − | 1.07860i | ||||
\(251\) | 22.2462 | 1.40417 | 0.702084 | − | 0.712094i | \(-0.252253\pi\) | ||||
0.702084 | + | 0.712094i | \(0.252253\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.12311 | 0.573565 | ||||||||
\(254\) | −1.68408 | + | 27.4506i | −0.105669 | + | 1.72240i | ||||
\(255\) | 3.68466 | − | 6.38202i | 0.230742 | − | 0.399657i | ||||
\(256\) | 14.1160 | + | 7.53259i | 0.882247 | + | 0.470787i | ||||
\(257\) | −17.1636 | + | 9.90941i | −1.07064 | + | 0.618132i | −0.928355 | − | 0.371694i | \(-0.878777\pi\) |
−0.142281 | + | 0.989826i | \(0.545444\pi\) | |||||||
\(258\) | −9.56155 | − | 6.33122i | −0.595276 | − | 0.394164i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −8.00000 | − | 18.8664i | −0.496139 | − | 1.17004i | ||||
\(261\) | 1.00000 | + | 1.73205i | 0.0618984 | + | 0.107211i | ||||
\(262\) | −14.0325 | − | 28.1580i | −0.866933 | − | 1.73961i | ||||
\(263\) | 4.26552 | + | 2.46270i | 0.263023 | + | 0.151856i | 0.625713 | − | 0.780054i | \(-0.284808\pi\) |
−0.362690 | + | 0.931910i | \(0.618142\pi\) | |||||||
\(264\) | −8.05469 | + | 2.84725i | −0.495732 | + | 0.175236i | ||||
\(265\) | − | 7.20217i | − | 0.442426i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.73704i | 0.473499i | ||||||||
\(268\) | −3.30219 | − | 2.49031i | −0.201713 | − | 0.152120i | ||||
\(269\) | −19.4574 | − | 11.2337i | −1.18634 | − | 0.684932i | −0.228865 | − | 0.973458i | \(-0.573501\pi\) |
−0.957472 | + | 0.288526i | \(0.906835\pi\) | |||||||
\(270\) | −2.14688 | + | 1.06990i | −0.130655 | + | 0.0651119i | ||||
\(271\) | 2.24621 | + | 3.89055i | 0.136448 | + | 0.236334i | 0.926150 | − | 0.377157i | \(-0.123098\pi\) |
−0.789702 | + | 0.613491i | \(0.789765\pi\) | |||||||
\(272\) | −12.4924 | − | 12.0818i | −0.757464 | − | 0.732566i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.6847 | + | 19.1567i | −0.766308 | + | 1.15730i | ||||
\(275\) | 5.55359 | − | 3.20636i | 0.334894 | − | 0.193351i | ||||
\(276\) | 0.738433 | − | 5.99559i | 0.0444485 | − | 0.360892i | ||||
\(277\) | −1.56155 | + | 2.70469i | −0.0938246 | + | 0.162509i | −0.909117 | − | 0.416540i | \(-0.863243\pi\) |
0.815293 | + | 0.579049i | \(0.196576\pi\) | |||||||
\(278\) | −16.9387 | − | 1.03918i | −1.01592 | − | 0.0623261i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.246211 | −0.0146877 | −0.00734387 | − | 0.999973i | \(-0.502338\pi\) | ||||
−0.00734387 | + | 0.999973i | \(0.502338\pi\) | |||||||
\(282\) | −14.4631 | − | 0.887307i | −0.861267 | − | 0.0528384i | ||||
\(283\) | 8.56155 | − | 14.8290i | 0.508931 | − | 0.881495i | −0.491015 | − | 0.871151i | \(-0.663374\pi\) |
0.999946 | − | 0.0103441i | \(-0.00329268\pi\) | |||||||
\(284\) | −3.04464 | + | 24.7205i | −0.180666 | + | 1.46689i | ||||
\(285\) | 1.64973 | − | 0.952473i | 0.0977216 | − | 0.0564196i | ||||
\(286\) | 14.2462 | − | 21.5150i | 0.842396 | − | 1.27221i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.21922 | + | 5.52390i | 0.0718434 | + | 0.325499i | ||||
\(289\) | 0.938447 | + | 1.62544i | 0.0552028 | + | 0.0956140i | ||||
\(290\) | 4.29377 | − | 2.13979i | 0.252139 | − | 0.125653i | ||||
\(291\) | −7.52534 | − | 4.34475i | −0.441143 | − | 0.254694i | ||||
\(292\) | −5.41687 | − | 4.08507i | −0.316998 | − | 0.239061i | ||||
\(293\) | − | 6.99337i | − | 0.408557i | −0.978913 | − | 0.204278i | \(-0.934515\pi\) | ||
0.978913 | − | 0.204278i | \(-0.0654848\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 6.78456i | − | 0.395013i | ||||||
\(296\) | −6.71466 | − | 18.9953i | −0.390281 | − | 1.10408i | ||||
\(297\) | −2.61578 | − | 1.51022i | −0.151783 | − | 0.0876321i | ||||
\(298\) | −6.30783 | − | 12.6575i | −0.365403 | − | 0.733227i | ||||
\(299\) | 9.12311 | + | 15.8017i | 0.527603 | + | 0.913835i | ||||
\(300\) | −1.65767 | − | 3.90928i | −0.0957057 | − | 0.225702i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 9.56155 | + | 6.33122i | 0.550206 | + | 0.364320i | ||||
\(303\) | −6.05643 | + | 3.49668i | −0.347933 | + | 0.200879i | ||||
\(304\) | −1.23506 | − | 4.31932i | −0.0708357 | − | 0.247730i | ||||
\(305\) | 8.00000 | − | 13.8564i | 0.458079 | − | 0.793416i | ||||
\(306\) | 0.376250 | − | 6.13288i | 0.0215088 | − | 0.350593i | ||||
\(307\) | 21.6155 | 1.23366 | 0.616832 | − | 0.787095i | \(-0.288416\pi\) | ||||
0.616832 | + | 0.787095i | \(0.288416\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.00000 | 0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.00000 | − | 6.92820i | 0.226819 | − | 0.392862i | −0.730044 | − | 0.683400i | \(-0.760501\pi\) |
0.956864 | + | 0.290537i | \(0.0938340\pi\) | |||||||
\(312\) | −12.9863 | − | 11.1039i | −0.735203 | − | 0.628633i | ||||
\(313\) | −22.2143 | + | 12.8255i | −1.25563 | + | 0.724938i | −0.972222 | − | 0.234062i | \(-0.924798\pi\) |
−0.283407 | + | 0.959000i | \(0.591465\pi\) | |||||||
\(314\) | −4.87689 | − | 3.22925i | −0.275219 | − | 0.182237i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.68466 | − | 3.68260i | 0.488550 | − | 0.207163i | ||||
\(317\) | −9.24621 | − | 16.0149i | −0.519319 | − | 0.899487i | −0.999748 | − | 0.0224532i | \(-0.992852\pi\) |
0.480429 | − | 0.877034i | \(-0.340481\pi\) | |||||||
\(318\) | −2.67844 | − | 5.37462i | −0.150199 | − | 0.301394i | ||||
\(319\) | 5.23157 | + | 3.02045i | 0.292912 | + | 0.169113i | ||||
\(320\) | 13.4044 | − | 2.10770i | 0.749331 | − | 0.117824i | ||||
\(321\) | − | 5.66906i | − | 0.316416i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.87962i | 0.271509i | ||||||||
\(324\) | −1.20422 | + | 1.59682i | −0.0669014 | + | 0.0887124i | ||||
\(325\) | 11.1072 | + | 6.41273i | 0.616115 | + | 0.355714i | ||||
\(326\) | 14.5575 | − | 7.25473i | 0.806267 | − | 0.401803i | ||||
\(327\) | −4.12311 | − | 7.14143i | −0.228008 | − | 0.394922i | ||||
\(328\) | −4.00000 | + | 21.5150i | −0.220863 | + | 1.18797i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.00000 | + | 6.04090i | −0.220193 | + | 0.332540i | ||||
\(331\) | 4.72872 | − | 2.73013i | 0.259914 | − | 0.150061i | −0.364381 | − | 0.931250i | \(-0.618720\pi\) |
0.624295 | + | 0.781188i | \(0.285386\pi\) | |||||||
\(332\) | −12.3987 | − | 1.52706i | −0.680469 | − | 0.0838084i | ||||
\(333\) | 3.56155 | − | 6.16879i | 0.195172 | − | 0.338048i | ||||
\(334\) | −3.17066 | − | 0.194519i | −0.173491 | − | 0.0106436i | ||||
\(335\) | −3.50758 | −0.191639 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.24621 | −0.449200 | −0.224600 | − | 0.974451i | \(-0.572108\pi\) | ||||
−0.224600 | + | 0.974451i | \(0.572108\pi\) | |||||||
\(338\) | 33.1610 | + | 2.03441i | 1.80372 | + | 0.110657i | ||||
\(339\) | −6.12311 | + | 10.6055i | −0.332561 | + | 0.576013i | ||||
\(340\) | −14.6281 | − | 1.80164i | −0.793320 | − | 0.0977075i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.876894 | − | 1.32431i | 0.0474170 | − | 0.0716103i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −4.19224 | + | 22.5490i | −0.226030 | + | 1.21576i | ||||
\(345\) | −2.56155 | − | 4.43674i | −0.137909 | − | 0.238866i | ||||
\(346\) | 10.7344 | − | 5.34949i | 0.577086 | − | 0.287590i | ||||
\(347\) | 30.0617 | + | 17.3561i | 1.61380 | + | 0.931726i | 0.988479 | + | 0.151355i | \(0.0483638\pi\) |
0.625317 | + | 0.780371i | \(0.284970\pi\) | |||||||
\(348\) | 2.40845 | − | 3.19365i | 0.129106 | − | 0.171197i | ||||
\(349\) | − | 4.13595i | − | 0.221392i | −0.993854 | − | 0.110696i | \(-0.964692\pi\) | ||
0.993854 | − | 0.110696i | \(-0.0353080\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 6.04090i | − | 0.322439i | ||||||
\(352\) | 11.5316 | + | 12.6080i | 0.614634 | + | 0.672011i | ||||
\(353\) | −5.41240 | − | 3.12485i | −0.288073 | − | 0.166319i | 0.349000 | − | 0.937123i | \(-0.386521\pi\) |
−0.637072 | + | 0.770804i | \(0.719855\pi\) | |||||||
\(354\) | −2.52313 | − | 5.06298i | −0.134103 | − | 0.269095i | ||||
\(355\) | 10.5616 | + | 18.2931i | 0.560549 | + | 0.970899i | ||||
\(356\) | 14.2462 | − | 6.04090i | 0.755048 | − | 0.320167i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.68466 | − | 1.77766i | −0.141889 | − | 0.0939520i | ||||
\(359\) | −0.966053 | + | 0.557751i | −0.0509863 | + | 0.0294370i | −0.525276 | − | 0.850932i | \(-0.676038\pi\) |
0.474290 | + | 0.880369i | \(0.342705\pi\) | |||||||
\(360\) | 3.64624 | + | 3.11771i | 0.192174 | + | 0.164318i | ||||
\(361\) | 8.86932 | − | 15.3621i | 0.466806 | − | 0.808532i | ||||
\(362\) | 0.523133 | − | 8.52708i | 0.0274953 | − | 0.448174i | ||||
\(363\) | 1.87689 | 0.0985114 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.75379 | −0.301167 | ||||||||
\(366\) | 0.816900 | − | 13.3155i | 0.0427000 | − | 0.696012i | ||||
\(367\) | −4.31534 | + | 7.47439i | −0.225259 | + | 0.390160i | −0.956397 | − | 0.292069i | \(-0.905656\pi\) |
0.731138 | + | 0.682229i | \(0.238989\pi\) | |||||||
\(368\) | −11.6162 | + | 3.32154i | −0.605538 | + | 0.173147i | ||||
\(369\) | −6.70047 | + | 3.86852i | −0.348813 | + | 0.201387i | ||||
\(370\) | −14.2462 | − | 9.43318i | −0.740625 | − | 0.490408i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.00000 | + | 8.66025i | 0.258890 | + | 0.448411i | 0.965945 | − | 0.258748i | \(-0.0833099\pi\) |
−0.707055 | + | 0.707159i | \(0.749977\pi\) | |||||||
\(374\) | −8.27784 | − | 16.6105i | −0.428037 | − | 0.858909i | ||||
\(375\) | −10.4631 | − | 6.04090i | −0.540314 | − | 0.311951i | ||||
\(376\) | 9.65868 | + | 27.3238i | 0.498108 | + | 1.40912i | ||||
\(377\) | 12.0818i | 0.622244i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 18.7033i | − | 0.960725i | −0.877070 | − | 0.480363i | \(-0.840505\pi\) | ||
0.877070 | − | 0.480363i | \(-0.159495\pi\) | |||||||
\(380\) | −3.04186 | − | 2.29398i | −0.156044 | − | 0.117679i | ||||
\(381\) | 16.8416 | + | 9.72350i | 0.862821 | + | 0.498150i | ||||
\(382\) | −11.4694 | + | 5.71574i | −0.586823 | + | 0.292443i | ||||
\(383\) | −13.1231 | − | 22.7299i | −0.670559 | − | 1.16144i | −0.977746 | − | 0.209794i | \(-0.932721\pi\) |
0.307186 | − | 0.951649i | \(-0.400613\pi\) | |||||||
\(384\) | 9.21922 | − | 6.55789i | 0.470467 | − | 0.334656i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.31534 | − | 11.0478i | 0.372341 | − | 0.562318i | ||||
\(387\) | −7.02249 | + | 4.05444i | −0.356973 | + | 0.206099i | ||||
\(388\) | −2.12440 | + | 17.2487i | −0.107850 | + | 0.875669i | ||||
\(389\) | −0.123106 | + | 0.213225i | −0.00624170 | + | 0.0108109i | −0.869129 | − | 0.494585i | \(-0.835320\pi\) |
0.862888 | + | 0.505396i | \(0.168653\pi\) | |||||||
\(390\) | −14.4631 | − | 0.887307i | −0.732369 | − | 0.0449306i | ||||
\(391\) | 13.1231 | 0.663664 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −22.2462 | −1.12217 | ||||||||
\(394\) | −0.347542 | − | 0.0213215i | −0.0175089 | − | 0.00107416i | ||||
\(395\) | 4.00000 | − | 6.92820i | 0.201262 | − | 0.348596i | ||||
\(396\) | −0.738433 | + | 5.99559i | −0.0371077 | + | 0.301290i | ||||
\(397\) | 14.0450 | − | 8.10887i | 0.704897 | − | 0.406973i | −0.104272 | − | 0.994549i | \(-0.533251\pi\) |
0.809169 | + | 0.587576i | \(0.199918\pi\) | |||||||
\(398\) | −4.00000 | + | 6.04090i | −0.200502 | + | 0.302803i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.90388 | + | 6.10454i | −0.295194 | + | 0.305227i | ||||
\(401\) | 4.12311 | + | 7.14143i | 0.205898 | + | 0.356626i | 0.950418 | − | 0.310974i | \(-0.100655\pi\) |
−0.744520 | + | 0.667600i | \(0.767322\pi\) | |||||||
\(402\) | −2.61753 | + | 1.30444i | −0.130551 | + | 0.0650598i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 11.1672 | + | 8.42159i | 0.555587 | + | 0.418990i | ||||
\(405\) | 1.69614i | 0.0842819i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 21.5150i | − | 1.06646i | ||||||
\(408\) | −11.5862 | + | 4.09562i | −0.573605 | + | 0.202763i | ||||
\(409\) | −23.8641 | − | 13.7779i | −1.18000 | − | 0.681275i | −0.223988 | − | 0.974592i | \(-0.571908\pi\) |
−0.956015 | + | 0.293317i | \(0.905241\pi\) | |||||||
\(410\) | 8.27784 | + | 16.6105i | 0.408813 | + | 0.820335i | ||||
\(411\) | 8.12311 | + | 14.0696i | 0.400683 | + | 0.694004i | ||||
\(412\) | −6.24621 | − | 14.7304i | −0.307729 | − | 0.725715i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.56155 | − | 2.35829i | −0.175041 | − | 0.115904i | ||||
\(415\) | −9.17507 | + | 5.29723i | −0.450386 | + | 0.260031i | ||||
\(416\) | −10.3062 | + | 32.5813i | −0.505303 | + | 1.59743i | ||||
\(417\) | −6.00000 | + | 10.3923i | −0.293821 | + | 0.508913i | ||||
\(418\) | 0.293767 | − | 4.78841i | 0.0143686 | − | 0.234209i | ||||
\(419\) | −16.4924 | −0.805708 | −0.402854 | − | 0.915264i | \(-0.631982\pi\) | ||||
−0.402854 | + | 0.915264i | \(0.631982\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.1231 | 0.932003 | 0.466002 | − | 0.884784i | \(-0.345694\pi\) | ||||
0.466002 | + | 0.884784i | \(0.345694\pi\) | |||||||
\(422\) | 0.344049 | − | 5.60801i | 0.0167481 | − | 0.272994i | ||||
\(423\) | −5.12311 | + | 8.87348i | −0.249094 | + | 0.431443i | ||||
\(424\) | −7.80504 | + | 9.12819i | −0.379046 | + | 0.443304i | ||||
\(425\) | 7.98854 | − | 4.61219i | 0.387501 | − | 0.223724i | ||||
\(426\) | 14.6847 | + | 9.72350i | 0.711474 | + | 0.471105i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −10.4384 | + | 4.42627i | −0.504561 | + | 0.213952i | ||||
\(429\) | −9.12311 | − | 15.8017i | −0.440468 | − | 0.762912i | ||||
\(430\) | 8.67566 | + | 17.4088i | 0.418377 | + | 0.839527i | ||||
\(431\) | 13.0789 | + | 7.55112i | 0.629990 | + | 0.363725i | 0.780748 | − | 0.624846i | \(-0.214838\pi\) |
−0.150758 | + | 0.988571i | \(0.548172\pi\) | |||||||
\(432\) | 3.88046 | + | 0.970579i | 0.186699 | + | 0.0466970i | ||||
\(433\) | − | 6.78456i | − | 0.326045i | −0.986622 | − | 0.163023i | \(-0.947876\pi\) | ||
0.986622 | − | 0.163023i | \(-0.0521244\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 3.39228i | − | 0.162647i | ||||||
\(436\) | −9.93029 | + | 13.1677i | −0.475575 | + | 0.630620i | ||||
\(437\) | 2.93780 | + | 1.69614i | 0.140534 | + | 0.0811374i | ||||
\(438\) | −4.29377 | + | 2.13979i | −0.205164 | + | 0.102243i | ||||
\(439\) | −15.6847 | − | 27.1666i | −0.748588 | − | 1.29659i | −0.948500 | − | 0.316778i | \(-0.897399\pi\) |
0.199912 | − | 0.979814i | \(-0.435934\pi\) | |||||||
\(440\) | 14.2462 | + | 2.64861i | 0.679161 | + | 0.126268i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 20.4924 | − | 30.9481i | 0.974725 | − | 1.47205i | ||||
\(443\) | 31.0674 | − | 17.9368i | 1.47606 | − | 0.852202i | 0.476422 | − | 0.879217i | \(-0.341934\pi\) |
0.999635 | + | 0.0270153i | \(0.00860028\pi\) | |||||||
\(444\) | −14.1394 | − | 1.74144i | −0.671025 | − | 0.0826453i | ||||
\(445\) | 6.56155 | − | 11.3649i | 0.311047 | − | 0.538750i | ||||
\(446\) | 26.6459 | + | 1.63471i | 1.26172 | + | 0.0774059i | ||||
\(447\) | −10.0000 | −0.472984 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.2462 | 1.33302 | 0.666511 | − | 0.745496i | \(-0.267787\pi\) | ||||
0.666511 | + | 0.745496i | \(0.267787\pi\) | |||||||
\(450\) | −2.99689 | − | 0.183858i | −0.141275 | − | 0.00866715i | ||||
\(451\) | −11.6847 | + | 20.2384i | −0.550209 | + | 0.952990i | ||||
\(452\) | 24.3087 | + | 2.99393i | 1.14339 | + | 0.140823i | ||||
\(453\) | 7.02249 | − | 4.05444i | 0.329945 | − | 0.190494i | ||||
\(454\) | −12.8769 | + | 19.4470i | −0.604343 | + | 0.912693i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.12311 | − | 0.580639i | −0.146253 | − | 0.0271909i | ||||
\(457\) | 8.12311 | + | 14.0696i | 0.379983 | + | 0.658150i | 0.991059 | − | 0.133422i | \(-0.0425966\pi\) |
−0.611076 | + | 0.791572i | \(0.709263\pi\) | |||||||
\(458\) | 22.9387 | − | 11.4315i | 1.07186 | − | 0.534158i | ||||
\(459\) | −3.76267 | − | 2.17238i | −0.175626 | − | 0.101398i | ||||
\(460\) | −6.16937 | + | 8.18069i | −0.287648 | + | 0.381427i | ||||
\(461\) | − | 17.1702i | − | 0.799697i | −0.916581 | − | 0.399848i | \(-0.869063\pi\) | ||
0.916581 | − | 0.399848i | \(-0.130937\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.4746i | 1.83454i | 0.398264 | + | 0.917271i | \(0.369613\pi\) | ||||
−0.398264 | + | 0.917271i | \(0.630387\pi\) | |||||||
\(464\) | −7.76092 | − | 1.94116i | −0.360292 | − | 0.0901160i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.61844 | − | 13.2807i | −0.306594 | − | 0.615218i | ||||
\(467\) | 8.87689 | + | 15.3752i | 0.410774 | + | 0.711481i | 0.994975 | − | 0.100128i | \(-0.0319253\pi\) |
−0.584201 | + | 0.811609i | \(0.698592\pi\) | |||||||
\(468\) | −11.1231 | + | 4.71659i | −0.514166 | + | 0.218024i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 20.4924 | + | 13.5691i | 0.945245 | + | 0.625897i | ||||
\(471\) | −3.58184 | + | 2.06798i | −0.165042 | + | 0.0952873i | ||||
\(472\) | −7.35247 | + | 8.59890i | −0.338425 | + | 0.395797i | ||||
\(473\) | −12.2462 | + | 21.2111i | −0.563081 | + | 0.975286i | ||||
\(474\) | 0.408450 | − | 6.65775i | 0.0187607 | − | 0.305800i | ||||
\(475\) | 2.38447 | 0.109407 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.24621 | −0.194421 | ||||||||
\(478\) | 0.197166 | − | 3.21381i | 0.00901816 | − | 0.146996i | ||||
\(479\) | −10.2462 | + | 17.7470i | −0.468161 | + | 0.810879i | −0.999338 | − | 0.0363819i | \(-0.988417\pi\) |
0.531177 | + | 0.847261i | \(0.321750\pi\) | |||||||
\(480\) | 2.89374 | − | 9.14805i | 0.132081 | − | 0.417550i | ||||
\(481\) | 37.2650 | − | 21.5150i | 1.69914 | − | 0.980998i | ||||
\(482\) | −2.24621 | − | 1.48734i | −0.102312 | − | 0.0677463i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.46543 | − | 3.45593i | −0.0666107 | − | 0.157088i | ||||
\(485\) | 7.36932 | + | 12.7640i | 0.334623 | + | 0.579585i | ||||
\(486\) | 0.630783 | + | 1.26575i | 0.0286129 | + | 0.0574154i | ||||
\(487\) | −27.9488 | − | 16.1362i | −1.26648 | − | 0.731202i | −0.292159 | − | 0.956370i | \(-0.594374\pi\) |
−0.974320 | + | 0.225167i | \(0.927707\pi\) | |||||||
\(488\) | −25.1556 | + | 8.89226i | −1.13874 | + | 0.402534i | ||||
\(489\) | − | 11.5012i | − | 0.520100i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.7100i | 0.528463i | 0.964459 | + | 0.264231i | \(0.0851183\pi\) | ||||
−0.964459 | + | 0.264231i | \(0.914882\pi\) | |||||||
\(492\) | 12.3547 | + | 9.31713i | 0.556992 | + | 0.420049i | ||||
\(493\) | 7.52534 | + | 4.34475i | 0.338924 | + | 0.195678i | ||||
\(494\) | 8.58753 | − | 4.27959i | 0.386371 | − | 0.192548i | ||||
\(495\) | 2.56155 | + | 4.43674i | 0.115133 | + | 0.199417i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.87689 | + | 7.36520i | −0.218539 | + | 0.330043i | ||||
\(499\) | 15.1919 | − | 8.77102i | 0.680081 | − | 0.392645i | −0.119805 | − | 0.992797i | \(-0.538227\pi\) |
0.799886 | + | 0.600153i | \(0.204893\pi\) | |||||||
\(500\) | −2.95373 | + | 23.9824i | −0.132095 | + | 1.07252i | ||||
\(501\) | −1.12311 | + | 1.94528i | −0.0501767 | + | 0.0869085i | ||||
\(502\) | −31.4019 | − | 1.92649i | −1.40153 | − | 0.0859835i | ||||
\(503\) | −22.7386 | −1.01387 | −0.506933 | − | 0.861986i | \(-0.669221\pi\) | ||||
−0.506933 | + | 0.861986i | \(0.669221\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.8617 | 0.527840 | ||||||||
\(506\) | −12.8778 | − | 0.790048i | −0.572488 | − | 0.0351219i | ||||
\(507\) | 11.7462 | − | 20.3450i | 0.521668 | − | 0.903555i | ||||
\(508\) | 4.75436 | − | 38.6023i | 0.210941 | − | 1.71270i | ||||
\(509\) | −1.46890 | + | 0.848071i | −0.0651079 | + | 0.0375901i | −0.532201 | − | 0.846618i | \(-0.678635\pi\) |
0.467093 | + | 0.884208i | \(0.345301\pi\) | |||||||
\(510\) | −5.75379 | + | 8.68951i | −0.254782 | + | 0.384778i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −19.2732 | − | 11.8551i | −0.851763 | − | 0.523927i | ||||
\(513\) | −0.561553 | − | 0.972638i | −0.0247932 | − | 0.0429430i | ||||
\(514\) | 25.0856 | − | 12.5014i | 1.10648 | − | 0.551412i | ||||
\(515\) | −11.7512 | − | 6.78456i | −0.517820 | − | 0.298964i | ||||
\(516\) | 12.9484 | + | 9.76490i | 0.570023 | + | 0.429876i | ||||
\(517\) | 30.9481i | 1.36110i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 8.48071i | − | 0.372262i | ||||||
\(520\) | 9.65868 | + | 27.3238i | 0.423561 | + | 1.19823i | ||||
\(521\) | 29.2765 | + | 16.9028i | 1.28263 | + | 0.740524i | 0.977328 | − | 0.211732i | \(-0.0679105\pi\) |
0.305298 | + | 0.952257i | \(0.401244\pi\) | |||||||
\(522\) | −1.26157 | − | 2.53149i | −0.0552173 | − | 0.110800i | ||||
\(523\) | −0.246211 | − | 0.426450i | −0.0107661 | − | 0.0186474i | 0.860592 | − | 0.509295i | \(-0.170094\pi\) |
−0.871358 | + | 0.490647i | \(0.836760\pi\) | |||||||
\(524\) | 17.3693 | + | 40.9620i | 0.758782 | + | 1.78943i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.80776 | − | 3.84563i | −0.253231 | − | 0.167677i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 11.6162 | − | 3.32154i | 0.505532 | − | 0.144551i | ||||
\(529\) | −6.93845 | + | 12.0177i | −0.301672 | + | 0.522511i | ||||
\(530\) | −0.623698 | + | 10.1663i | −0.0270917 | + | 0.441596i | ||||
\(531\) | −4.00000 | −0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −46.7386 | −2.02447 | ||||||||
\(534\) | 0.670016 | − | 10.9213i | 0.0289944 | − | 0.472610i | ||||
\(535\) | −4.80776 | + | 8.32729i | −0.207858 | + | 0.360020i | ||||
\(536\) | 4.44558 | + | 3.80118i | 0.192020 | + | 0.164186i | ||||
\(537\) | −1.97175 | + | 1.13839i | −0.0850873 | + | 0.0491251i | ||||
\(538\) | 26.4924 | + | 17.5420i | 1.14217 | + | 0.756291i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.12311 | − | 1.32431i | 0.134397 | − | 0.0569891i | ||||
\(541\) | −5.56155 | − | 9.63289i | −0.239110 | − | 0.414150i | 0.721349 | − | 0.692571i | \(-0.243522\pi\) |
−0.960459 | + | 0.278421i | \(0.910189\pi\) | |||||||
\(542\) | −2.83374 | − | 5.68627i | −0.121720 | − | 0.244246i | ||||
\(543\) | −5.23157 | − | 3.02045i | −0.224508 | − | 0.129620i | ||||
\(544\) | 16.5875 | + | 18.1360i | 0.711185 | + | 0.777574i | ||||
\(545\) | 13.9867i | 0.599126i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.0161i | 1.41167i | 0.708378 | + | 0.705834i | \(0.249427\pi\) | ||||
−0.708378 | + | 0.705834i | \(0.750573\pi\) | |||||||
\(548\) | 19.5641 | − | 25.9423i | 0.835737 | − | 1.10820i | ||||
\(549\) | −8.16937 | − | 4.71659i | −0.348660 | − | 0.201299i | ||||
\(550\) | −8.11689 | + | 4.04504i | −0.346105 | + | 0.172481i | ||||
\(551\) | 1.12311 | + | 1.94528i | 0.0478459 | + | 0.0828715i | ||||
\(552\) | −1.56155 | + | 8.39919i | −0.0664641 | + | 0.357493i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2.43845 | − | 3.68260i | 0.103600 | − | 0.156459i | ||||
\(555\) | −10.4631 | + | 6.04090i | −0.444135 | + | 0.256422i | ||||
\(556\) | 23.8200 | + | 2.93374i | 1.01019 | + | 0.124418i | ||||
\(557\) | −7.00000 | + | 12.1244i | −0.296600 | + | 0.513725i | −0.975356 | − | 0.220638i | \(-0.929186\pi\) |
0.678756 | + | 0.734364i | \(0.262519\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −48.9848 | −2.07184 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.1231 | −0.554058 | ||||||||
\(562\) | 0.347542 | + | 0.0213215i | 0.0146602 | + | 0.000899395i | ||||
\(563\) | −7.12311 | + | 12.3376i | −0.300203 | + | 0.519967i | −0.976182 | − | 0.216954i | \(-0.930388\pi\) |
0.675979 | + | 0.736921i | \(0.263721\pi\) | |||||||
\(564\) | 20.3387 | + | 2.50497i | 0.856416 | + | 0.105478i | ||||
\(565\) | 17.9885 | − | 10.3857i | 0.756781 | − | 0.436928i | ||||
\(566\) | −13.3693 | + | 20.1907i | −0.561954 | + | 0.848677i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.43845 | − | 34.6307i | 0.270151 | − | 1.45307i | ||||
\(569\) | −17.4924 | − | 30.2978i | −0.733320 | − | 1.27015i | −0.955456 | − | 0.295133i | \(-0.904636\pi\) |
0.222136 | − | 0.975016i | \(-0.428697\pi\) | |||||||
\(570\) | −2.41118 | + | 1.20161i | −0.100993 | + | 0.0503298i | ||||
\(571\) | 35.4741 | + | 20.4810i | 1.48454 | + | 0.857102i | 0.999845 | − | 0.0175783i | \(-0.00559565\pi\) |
0.484699 | + | 0.874681i | \(0.338929\pi\) | |||||||
\(572\) | −21.9725 | + | 29.1360i | −0.918718 | + | 1.21824i | ||||
\(573\) | 9.06134i | 0.378543i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 6.41273i | − | 0.267429i | ||||||
\(576\) | −1.24264 | − | 7.90290i | −0.0517769 | − | 0.329288i | ||||
\(577\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(578\) | −1.18391 | − | 2.37567i | −0.0492443 | − | 0.0988149i | ||||
\(579\) | −4.68466 | − | 8.11407i | −0.194688 | − | 0.337209i | ||||
\(580\) | −6.24621 | + | 2.64861i | −0.259360 | + | 0.109978i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 10.2462 | + | 6.78456i | 0.424719 | + | 0.281229i | ||||
\(583\) | −11.1072 | + | 6.41273i | −0.460012 | + | 0.265588i | ||||
\(584\) | 7.29248 | + | 6.23541i | 0.301765 | + | 0.258023i | ||||
\(585\) | −5.12311 | + | 8.87348i | −0.211814 | + | 0.366873i | ||||
\(586\) | −0.605616 | + | 9.87156i | −0.0250178 | + | 0.407790i | ||||
\(587\) | 38.2462 | 1.57859 | 0.789295 | − | 0.614014i | \(-0.210446\pi\) | ||||
0.789295 | + | 0.614014i | \(0.210446\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −0.587534 | + | 9.57682i | −0.0241884 | + | 0.394271i | ||||
\(591\) | −0.123106 | + | 0.213225i | −0.00506389 | + | 0.00877091i | ||||
\(592\) | 7.83317 | + | 27.3945i | 0.321941 | + | 1.12591i | ||||
\(593\) | 18.8133 | − | 10.8619i | 0.772571 | − | 0.446044i | −0.0612198 | − | 0.998124i | \(-0.519499\pi\) |
0.833791 | + | 0.552080i | \(0.186166\pi\) | |||||||
\(594\) | 3.56155 | + | 2.35829i | 0.146132 | + | 0.0967620i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.80776 | + | 18.4130i | 0.319818 | + | 0.754226i | ||||
\(597\) | 2.56155 | + | 4.43674i | 0.104837 | + | 0.181584i | ||||
\(598\) | −11.5094 | − | 23.0951i | −0.470655 | − | 0.944427i | ||||
\(599\) | −16.6608 | − | 9.61909i | −0.680740 | − | 0.393026i | 0.119394 | − | 0.992847i | \(-0.461905\pi\) |
−0.800134 | + | 0.599821i | \(0.795238\pi\) | |||||||
\(600\) | 2.00136 | + | 5.66173i | 0.0817053 | + | 0.231139i | ||||
\(601\) | 5.29723i | 0.216078i | 0.994147 | + | 0.108039i | \(0.0344572\pi\) | ||||
−0.994147 | + | 0.108039i | \(0.965543\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.06798i | 0.0842145i | ||||||||
\(604\) | −12.9484 | − | 9.76490i | −0.526864 | − | 0.397328i | ||||
\(605\) | −2.75697 | − | 1.59174i | −0.112087 | − | 0.0647134i | ||||
\(606\) | 8.85183 | − | 4.41130i | 0.359581 | − | 0.179197i | ||||
\(607\) | −16.8078 | − | 29.1119i | −0.682206 | − | 1.18162i | −0.974306 | − | 0.225228i | \(-0.927687\pi\) |
0.292100 | − | 0.956388i | \(-0.405646\pi\) | |||||||
\(608\) | 1.36932 | + | 6.20393i | 0.0555331 | + | 0.251602i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.4924 | + | 18.8664i | −0.505803 | + | 0.763876i | ||||
\(611\) | −53.6038 | + | 30.9481i | −2.16858 | + | 1.25203i | ||||
\(612\) | −1.06220 | + | 8.62434i | −0.0429368 | + | 0.348618i | ||||
\(613\) | 20.3693 | − | 35.2807i | 0.822709 | − | 1.42497i | −0.0809488 | − | 0.996718i | \(-0.525795\pi\) |
0.903658 | − | 0.428255i | \(-0.140872\pi\) | |||||||
\(614\) | −30.5116 | − | 1.87187i | −1.23135 | − | 0.0755427i | ||||
\(615\) | 13.1231 | 0.529175 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.7538 | 0.634224 | 0.317112 | − | 0.948388i | \(-0.397287\pi\) | ||||
0.317112 | + | 0.948388i | \(0.397287\pi\) | |||||||
\(618\) | −11.2925 | − | 0.692789i | −0.454250 | − | 0.0278680i | ||||
\(619\) | 10.0000 | − | 17.3205i | 0.401934 | − | 0.696170i | −0.592025 | − | 0.805919i | \(-0.701671\pi\) |
0.993959 | + | 0.109749i | \(0.0350048\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.61578 | + | 1.51022i | −0.104968 | + | 0.0606032i | ||||
\(622\) | −6.24621 | + | 9.43318i | −0.250450 | + | 0.378236i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 17.3693 | + | 16.7984i | 0.695329 | + | 0.672473i | ||||
\(625\) | 4.93845 | + | 8.55364i | 0.197538 | + | 0.342146i | ||||
\(626\) | 32.4675 | − | 16.1802i | 1.29766 | − | 0.646690i | ||||
\(627\) | −2.93780 | − | 1.69614i | −0.117325 | − | 0.0677373i | ||||
\(628\) | 6.60438 | + | 4.98061i | 0.263543 | + | 0.198748i | ||||
\(629\) | − | 30.9481i | − | 1.23398i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 17.9597i | − | 0.714963i | −0.933920 | − | 0.357481i | \(-0.883636\pi\) | ||
0.933920 | − | 0.357481i | \(-0.116364\pi\) | |||||||
\(632\) | −12.5778 | + | 4.44613i | −0.500319 | + | 0.176858i | ||||
\(633\) | −3.44065 | − | 1.98646i | −0.136754 | − | 0.0789547i | ||||
\(634\) | 11.6647 | + | 23.4067i | 0.463265 | + | 0.929599i | ||||
\(635\) | −16.4924 | − | 28.5657i | −0.654482 | − | 1.13360i | ||||
\(636\) | 3.31534 | + | 7.81855i | 0.131462 | + | 0.310026i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −7.12311 | − | 4.71659i | −0.282006 | − | 0.186732i | ||||
\(639\) | 10.7852 | − | 6.22681i | 0.426654 | − | 0.246329i | ||||
\(640\) | −19.1037 | + | 1.81434i | −0.755139 | + | 0.0717181i | ||||
\(641\) | 4.75379 | − | 8.23380i | 0.187763 | − | 0.325216i | −0.756741 | − | 0.653715i | \(-0.773210\pi\) |
0.944504 | + | 0.328499i | \(0.106543\pi\) | |||||||
\(642\) | −0.490933 | + | 8.00222i | −0.0193756 | + | 0.315822i | ||||
\(643\) | −29.6155 | −1.16792 | −0.583961 | − | 0.811782i | \(-0.698498\pi\) | ||||
−0.583961 | + | 0.811782i | \(0.698498\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.7538 | 0.541555 | ||||||||
\(646\) | 0.422568 | − | 6.88787i | 0.0166257 | − | 0.271000i | ||||
\(647\) | 16.4924 | − | 28.5657i | 0.648384 | − | 1.12303i | −0.335125 | − | 0.942174i | \(-0.608778\pi\) |
0.983509 | − | 0.180860i | \(-0.0578882\pi\) | |||||||
\(648\) | 1.83812 | − | 2.14973i | 0.0722081 | − | 0.0844492i | ||||
\(649\) | −10.4631 | + | 6.04090i | −0.410714 | + | 0.237126i | ||||
\(650\) | −15.1231 | − | 10.0138i | −0.593177 | − | 0.392774i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −21.1771 | + | 8.97983i | −0.829358 | + | 0.351677i | ||||
\(653\) | 16.3693 | + | 28.3525i | 0.640581 | + | 1.10952i | 0.985303 | + | 0.170814i | \(0.0546397\pi\) |
−0.344722 | + | 0.938705i | \(0.612027\pi\) | |||||||
\(654\) | 5.20157 | + | 10.4376i | 0.203398 | + | 0.408143i | ||||
\(655\) | 32.6775 | + | 18.8664i | 1.27682 | + | 0.737170i | ||||
\(656\) | 7.50940 | − | 30.0233i | 0.293193 | − | 1.17221i | ||||
\(657\) | 3.39228i | 0.132346i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 38.1045i | − | 1.48434i | −0.670210 | − | 0.742171i | \(-0.733796\pi\) | ||
0.670210 | − | 0.742171i | \(-0.266204\pi\) | |||||||
\(660\) | 6.16937 | − | 8.18069i | 0.240142 | − | 0.318433i | ||||
\(661\) | 2.29377 | + | 1.32431i | 0.0892172 | + | 0.0515096i | 0.543945 | − | 0.839121i | \(-0.316930\pi\) |
−0.454728 | + | 0.890631i | \(0.650263\pi\) | |||||||
\(662\) | −6.91130 | + | 3.44424i | −0.268615 | + | 0.133864i | ||||
\(663\) | −13.1231 | − | 22.7299i | −0.509659 | − | 0.882756i | ||||
\(664\) | 17.3693 | + | 3.22925i | 0.674060 | + | 0.125319i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.56155 | + | 8.39919i | −0.215506 | + | 0.325462i | ||||
\(667\) | 5.23157 | − | 3.02045i | 0.202567 | − | 0.116952i | ||||
\(668\) | 4.45873 | + | 0.549150i | 0.172514 | + | 0.0212472i | ||||
\(669\) | 9.43845 | − | 16.3479i | 0.364911 | − | 0.632045i | ||||
\(670\) | 4.95115 | + | 0.303751i | 0.191280 | + | 0.0117349i | ||||
\(671\) | −28.4924 | −1.09994 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.8617 | 1.15109 | 0.575543 | − | 0.817772i | \(-0.304791\pi\) | ||||
0.575543 | + | 0.817772i | \(0.304791\pi\) | |||||||
\(674\) | 11.6400 | + | 0.714110i | 0.448357 | + | 0.0275065i | ||||
\(675\) | −1.06155 | + | 1.83866i | −0.0408592 | + | 0.0707702i | ||||
\(676\) | −46.6325 | − | 5.74338i | −1.79356 | − | 0.220899i | ||||
\(677\) | 28.2708 | − | 16.3221i | 1.08653 | − | 0.627311i | 0.153883 | − | 0.988089i | \(-0.450822\pi\) |
0.932652 | + | 0.360778i | \(0.117489\pi\) | |||||||
\(678\) | 9.56155 | − | 14.4401i | 0.367209 | − | 0.554568i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 20.4924 | + | 3.80989i | 0.785849 | + | 0.146103i | ||||
\(681\) | 8.24621 | + | 14.2829i | 0.315996 | + | 0.547320i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.1918 | − | 14.5445i | −0.963937 | − | 0.556529i | −0.0665546 | − | 0.997783i | \(-0.521201\pi\) |
−0.897383 | + | 0.441253i | \(0.854534\pi\) | |||||||
\(684\) | −1.35247 | + | 1.79340i | −0.0517131 | + | 0.0685724i | ||||
\(685\) | − | 27.5559i | − | 1.05286i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 18.1227i | − | 0.691424i | ||||||
\(688\) | 7.87030 | − | 31.4662i | 0.300052 | − | 1.19964i | ||||
\(689\) | −22.2143 | − | 12.8255i | −0.846299 | − | 0.488611i | ||||
\(690\) | 3.23157 | + | 6.48455i | 0.123024 | + | 0.246863i | ||||
\(691\) | 6.00000 | + | 10.3923i | 0.228251 | + | 0.395342i | 0.957290 | − | 0.289130i | \(-0.0933661\pi\) |
−0.729039 | + | 0.684472i | \(0.760033\pi\) | |||||||
\(692\) | −15.6155 | + | 6.62153i | −0.593613 | + | 0.251713i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −40.9309 | − | 27.1025i | −1.55371 | − | 1.02880i | ||||
\(695\) | 17.6268 | − | 10.1768i | 0.668623 | − | 0.386030i | ||||
\(696\) | −3.67624 | + | 4.29945i | −0.139347 | + | 0.162970i | ||||
\(697\) | −16.8078 | + | 29.1119i | −0.636639 | + | 1.10269i | ||||
\(698\) | −0.358167 | + | 5.83814i | −0.0135568 | + | 0.220977i | ||||
\(699\) | −10.4924 | −0.396860 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.0000 | −1.28416 | −0.642081 | − | 0.766637i | \(-0.721929\pi\) | ||||
−0.642081 | + | 0.766637i | \(0.721929\pi\) | |||||||
\(702\) | −0.523133 | + | 8.52708i | −0.0197444 | + | 0.321834i | ||||
\(703\) | 4.00000 | − | 6.92820i | 0.150863 | − | 0.261302i | ||||
\(704\) | −15.1856 | − | 18.7956i | −0.572330 | − | 0.708386i | ||||
\(705\) | 15.0507 | − | 8.68951i | 0.566841 | − | 0.327266i | ||||
\(706\) | 7.36932 | + | 4.87962i | 0.277348 | + | 0.183647i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 3.12311 | + | 7.36520i | 0.117373 | + | 0.276801i | ||||
\(709\) | −3.00000 | − | 5.19615i | −0.112667 | − | 0.195146i | 0.804178 | − | 0.594389i | \(-0.202606\pi\) |
−0.916845 | + | 0.399244i | \(0.869273\pi\) | |||||||
\(710\) | −13.3241 | − | 26.7365i | −0.500045 | − | 1.00340i | ||||
\(711\) | −4.08469 | − | 2.35829i | −0.153188 | − | 0.0884430i | ||||
\(712\) | −20.6325 | + | 7.29338i | −0.773236 | + | 0.273331i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 30.9481i | 1.15740i | ||||||||
\(716\) | 3.63561 | + | 2.74175i | 0.135869 | + | 0.102464i | ||||
\(717\) | −1.97175 | − | 1.13839i | −0.0736363 | − | 0.0425139i | ||||
\(718\) | 1.41194 | − | 0.703640i | 0.0526932 | − | 0.0262596i | ||||
\(719\) | −2.24621 | − | 3.89055i | −0.0837695 | − | 0.145093i | 0.821097 | − | 0.570789i | \(-0.193363\pi\) |
−0.904866 | + | 0.425696i | \(0.860029\pi\) | |||||||
\(720\) | −4.87689 | − | 4.71659i | −0.181751 | − | 0.175777i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −13.8499 | + | 20.9165i | −0.515440 | + | 0.778430i | ||||
\(723\) | −1.64973 | + | 0.952473i | −0.0613542 | + | 0.0354228i | ||||
\(724\) | −1.47687 | + | 11.9912i | −0.0548873 | + | 0.445649i | ||||
\(725\) | 2.12311 | − | 3.67733i | 0.0788502 | − | 0.136572i | ||||
\(726\) | −2.64935 | − | 0.162536i | −0.0983265 | − | 0.00603229i | ||||
\(727\) | 32.9848 | 1.22334 | 0.611670 | − | 0.791113i | \(-0.290498\pi\) | ||||
0.611670 | + | 0.791113i | \(0.290498\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 8.12182 | + | 0.498270i | 0.300602 | + | 0.0184418i | ||||
\(731\) | −17.6155 | + | 30.5110i | −0.651534 | + | 1.12849i | ||||
\(732\) | −2.30621 | + | 18.7249i | −0.0852398 | + | 0.692091i | ||||
\(733\) | −14.4066 | + | 8.31768i | −0.532121 | + | 0.307220i | −0.741880 | − | 0.670533i | \(-0.766066\pi\) |
0.209759 | + | 0.977753i | \(0.432732\pi\) | |||||||
\(734\) | 6.73863 | − | 10.1768i | 0.248728 | − | 0.375634i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.6847 | − | 3.68260i | 0.615005 | − | 0.135742i | ||||
\(737\) | 3.12311 | + | 5.40938i | 0.115041 | + | 0.199257i | ||||
\(738\) | 9.79312 | − | 4.88039i | 0.360490 | − | 0.179650i | ||||
\(739\) | −5.09038 | − | 2.93893i | −0.187253 | − | 0.108110i | 0.403443 | − | 0.915005i | \(-0.367813\pi\) |
−0.590696 | + | 0.806894i | \(0.701147\pi\) | |||||||
\(740\) | 19.2925 | + | 14.5492i | 0.709206 | + | 0.534839i | ||||
\(741\) | − | 6.78456i | − | 0.249237i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 13.6149i | − | 0.499482i | −0.968313 | − | 0.249741i | \(-0.919654\pi\) | ||
0.968313 | − | 0.249741i | \(-0.0803455\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.6890 | + | 8.48071i | 0.538164 | + | 0.310709i | ||||
\(746\) | −6.30783 | − | 12.6575i | −0.230946 | − | 0.463422i | ||||
\(747\) | 3.12311 | + | 5.40938i | 0.114268 | + | 0.197919i | ||||
\(748\) | 10.2462 | + | 24.1636i | 0.374639 | + | 0.883508i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 14.2462 | + | 9.43318i | 0.520198 | + | 0.344451i | ||||
\(751\) | 26.6607 | − | 15.3926i | 0.972863 | − | 0.561682i | 0.0727548 | − | 0.997350i | \(-0.476821\pi\) |
0.900108 | + | 0.435667i | \(0.143488\pi\) | |||||||
\(752\) | −11.2676 | − | 39.4056i | −0.410887 | − | 1.43697i | ||||
\(753\) | −11.1231 | + | 19.2658i | −0.405349 | + | 0.702084i | ||||
\(754\) | 1.04627 | − | 17.0542i | 0.0381028 | − | 0.621076i | ||||
\(755\) | −13.7538 | −0.500552 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.9848 | 1.12616 | 0.563082 | − | 0.826401i | \(-0.309616\pi\) | ||||
0.563082 | + | 0.826401i | \(0.309616\pi\) | |||||||
\(758\) | −1.61968 | + | 26.4009i | −0.0588295 | + | 0.958922i | ||||
\(759\) | −4.56155 | + | 7.90084i | −0.165574 | + | 0.286782i | ||||
\(760\) | 4.09511 | + | 3.50151i | 0.148545 | + | 0.127013i | ||||
\(761\) | 29.2765 | − | 16.9028i | 1.06127 | − | 0.612725i | 0.135488 | − | 0.990779i | \(-0.456740\pi\) |
0.925784 | + | 0.378054i | \(0.123407\pi\) | |||||||
\(762\) | −22.9309 | − | 15.1838i | −0.830698 | − | 0.550049i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 16.6847 | − | 7.07488i | 0.603630 | − | 0.255960i | ||||
\(765\) | 3.68466 | + | 6.38202i | 0.133219 | + | 0.230742i | ||||
\(766\) | 16.5557 | + | 33.2210i | 0.598181 | + | 1.20032i | ||||
\(767\) | −20.9263 | − | 12.0818i | −0.755604 | − | 0.436248i | ||||
\(768\) | −13.5814 | + | 8.45848i | −0.490076 | + | 0.305219i | ||||
\(769\) | − | 44.5173i | − | 1.60533i | −0.596427 | − | 0.802667i | \(-0.703414\pi\) | ||
0.596427 | − | 0.802667i | \(-0.296586\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 19.8188i | − | 0.713758i | ||||||
\(772\) | −11.2828 | + | 14.9611i | −0.406076 | + | 0.538463i | ||||
\(773\) | −1.46890 | − | 0.848071i | −0.0528327 | − | 0.0305030i | 0.473351 | − | 0.880874i | \(-0.343044\pi\) |
−0.526184 | + | 0.850371i | \(0.676378\pi\) | |||||||
\(774\) | 10.2638 | − | 5.11494i | 0.368924 | − | 0.183853i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.49242 | − | 24.1636i | 0.161269 | − | 0.867422i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.192236 | − | 0.290319i | 0.00689199 | − | 0.0104085i | ||||
\(779\) | −7.52534 | + | 4.34475i | −0.269623 | + | 0.155667i | ||||
\(780\) | 20.3387 | + | 2.50497i | 0.728244 | + | 0.0896925i | ||||
\(781\) | 18.8078 | − | 32.5760i | 0.672995 | − | 1.16566i | ||||
\(782\) | −18.5240 | − | 1.13644i | −0.662419 | − | 0.0406391i | ||||
\(783\) | −2.00000 | −0.0714742 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.01515 | 0.250382 | ||||||||
\(786\) | 31.4019 | + | 1.92649i | 1.12007 | + | 0.0687156i | ||||
\(787\) | 10.4924 | − | 18.1734i | 0.374014 | − | 0.647812i | −0.616165 | − | 0.787617i | \(-0.711314\pi\) |
0.990179 | + | 0.139805i | \(0.0446477\pi\) | |||||||
\(788\) | 0.488730 | + | 0.0601933i | 0.0174103 | + | 0.00214430i | ||||
\(789\) | −4.26552 | + | 2.46270i | −0.151856 | + | 0.0876743i | ||||
\(790\) | −6.24621 | + | 9.43318i | −0.222230 | + | 0.335617i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.56155 | − | 8.39919i | 0.0554874 | − | 0.298452i | ||||
\(793\) | −28.4924 | − | 49.3503i | −1.01180 | − | 1.75248i | ||||
\(794\) | −20.5275 | + | 10.2299i | −0.728495 | + | 0.363045i | ||||
\(795\) | 6.23726 | + | 3.60109i | 0.221213 | + | 0.127717i | ||||
\(796\) | 6.16937 | − | 8.18069i | 0.218668 | − | 0.289957i | ||||
\(797\) | 34.1316i | 1.20900i | 0.796604 | + | 0.604502i | \(0.206628\pi\) | ||||
−0.796604 | + | 0.604502i | \(0.793372\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 44.5173i | 1.57491i | ||||||||
\(800\) | 8.86233 | − | 8.10566i | 0.313331 | − | 0.286578i | ||||
\(801\) | −6.70047 | − | 3.86852i | −0.236749 | − | 0.136687i | ||||
\(802\) | −5.20157 | − | 10.4376i | −0.183674 | − | 0.368565i | ||||
\(803\) | 5.12311 | + | 8.87348i | 0.180790 | + | 0.313138i | ||||
\(804\) | 3.80776 | − | 1.61463i | 0.134289 | − | 0.0569435i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 19.4574 | − | 11.2337i | 0.684932 | − | 0.395446i | ||||
\(808\) | −15.0338 | − | 12.8546i | −0.528888 | − | 0.452225i | ||||
\(809\) | 5.24621 | − | 9.08670i | 0.184447 | − | 0.319472i | −0.758943 | − | 0.651157i | \(-0.774284\pi\) |
0.943390 | + | 0.331685i | \(0.107617\pi\) | |||||||
\(810\) | 0.146883 | − | 2.39420i | 0.00516096 | − | 0.0841238i | ||||
\(811\) | 32.4924 | 1.14096 | 0.570482 | − | 0.821310i | \(-0.306757\pi\) | ||||
0.570482 | + | 0.821310i | \(0.306757\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.49242 | −0.157556 | ||||||||
\(814\) | −1.86317 | + | 30.3697i | −0.0653039 | + | 1.06446i | ||||
\(815\) | −9.75379 | + | 16.8941i | −0.341660 | + | 0.591773i | ||||
\(816\) | 16.7093 | − | 4.77786i | 0.584944 | − | 0.167259i | ||||
\(817\) | −7.88700 | + | 4.55356i | −0.275931 | + | 0.159309i | ||||
\(818\) | 32.4924 | + | 21.5150i | 1.13607 | + | 0.752253i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.2462 | − | 24.1636i | −0.357813 | − | 0.843829i | ||||
\(821\) | −12.6155 | − | 21.8507i | −0.440285 | − | 0.762596i | 0.557425 | − | 0.830227i | \(-0.311789\pi\) |
−0.997710 | + | 0.0676311i | \(0.978456\pi\) | |||||||
\(822\) | −10.2478 | − | 20.5636i | −0.357434 | − | 0.717237i | ||||
\(823\) | 39.0559 | + | 22.5490i | 1.36140 | + | 0.786007i | 0.989811 | − | 0.142388i | \(-0.0454782\pi\) |
0.371594 | + | 0.928396i | \(0.378811\pi\) | |||||||
\(824\) | 7.54127 | + | 21.3338i | 0.262713 | + | 0.743197i | ||||
\(825\) | 6.41273i | 0.223263i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.9939i | 1.07776i | 0.842381 | + | 0.538882i | \(0.181153\pi\) | ||||
−0.842381 | + | 0.538882i | \(0.818847\pi\) | |||||||
\(828\) | 4.82312 | + | 3.63730i | 0.167615 | + | 0.126405i | ||||
\(829\) | −27.4459 | − | 15.8459i | −0.953236 | − | 0.550351i | −0.0591514 | − | 0.998249i | \(-0.518839\pi\) |
−0.894085 | + | 0.447898i | \(0.852173\pi\) | |||||||
\(830\) | 13.4099 | − | 6.68280i | 0.465464 | − | 0.231964i | ||||
\(831\) | −1.56155 | − | 2.70469i | −0.0541697 | − | 0.0938246i | ||||
\(832\) | 17.3693 | − | 45.0979i | 0.602173 | − | 1.56349i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 9.36932 | − | 14.1498i | 0.324433 | − | 0.489966i | ||||
\(835\) | 3.29946 | − | 1.90495i | 0.114183 | − | 0.0659234i | ||||
\(836\) | −0.829339 | + | 6.73368i | −0.0286833 | + | 0.232889i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 23.2800 | + | 1.42822i | 0.804196 | + | 0.0493371i | ||||
\(839\) | −6.73863 | −0.232643 | −0.116322 | − | 0.993212i | \(-0.537110\pi\) | ||||
−0.116322 | + | 0.993212i | \(0.537110\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | −26.9934 | − | 1.65603i | −0.930254 | − | 0.0570707i | ||||
\(843\) | 0.123106 | − | 0.213225i | 0.00423998 | − | 0.00734387i | ||||
\(844\) | −0.971292 | + | 7.88625i | −0.0334333 | + | 0.271456i | ||||
\(845\) | −34.5080 | + | 19.9232i | −1.18711 | + | 0.685380i | ||||
\(846\) | 8.00000 | − | 12.0818i | 0.275046 | − | 0.415381i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 11.8078 | − | 12.2091i | 0.405480 | − | 0.419262i | ||||
\(849\) | 8.56155 | + | 14.8290i | 0.293832 | + | 0.508931i | ||||
\(850\) | −11.6757 | + | 5.81858i | −0.400474 | + | 0.199576i | ||||
\(851\) | −18.6325 | − | 10.7575i | −0.638714 | − | 0.368762i | ||||
\(852\) | −19.8862 | − | 14.9970i | −0.681291 | − | 0.513788i | ||||
\(853\) | − | 37.4067i | − | 1.28078i | −0.768050 | − | 0.640390i | \(-0.778773\pi\) | ||
0.768050 | − | 0.640390i | \(-0.221227\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.90495i | 0.0651478i | ||||||||
\(856\) | 15.1178 | − | 5.34399i | 0.516716 | − | 0.182654i | ||||
\(857\) | −17.5253 | − | 10.1182i | −0.598652 | − | 0.345632i | 0.169859 | − | 0.985468i | \(-0.445669\pi\) |
−0.768511 | + | 0.639837i | \(0.779002\pi\) | |||||||
\(858\) | 11.5094 | + | 23.0951i | 0.392925 | + | 0.788453i | ||||
\(859\) | 15.9309 | + | 27.5931i | 0.543554 | + | 0.941464i | 0.998696 | + | 0.0510448i | \(0.0162551\pi\) |
−0.455142 | + | 0.890419i | \(0.650412\pi\) | |||||||
\(860\) | −10.7386 | − | 25.3249i | −0.366184 | − | 0.863571i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −17.8078 | − | 11.7915i | −0.606535 | − | 0.401619i | ||||
\(863\) | −18.9545 | + | 10.9434i | −0.645220 | + | 0.372518i | −0.786622 | − | 0.617434i | \(-0.788172\pi\) |
0.141403 | + | 0.989952i | \(0.454839\pi\) | |||||||
\(864\) | −5.39345 | − | 1.70607i | −0.183489 | − | 0.0580418i | ||||
\(865\) | −7.19224 | + | 12.4573i | −0.244543 | + | 0.423562i | ||||
\(866\) | −0.587534 | + | 9.57682i | −0.0199652 | + | 0.325433i | ||||
\(867\) | −1.87689 | −0.0637427 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.2462 | −0.483270 | ||||||||
\(870\) | −0.293767 | + | 4.78841i | −0.00995963 | + | 0.162342i | ||||
\(871\) | −6.24621 | + | 10.8188i | −0.211645 | + | 0.366580i | ||||
\(872\) | 15.1575 | − | 17.7271i | 0.513298 | − | 0.600315i | ||||
\(873\) | 7.52534 | − | 4.34475i | 0.254694 | − | 0.147048i | ||||
\(874\) | −4.00000 | − | 2.64861i | −0.135302 | − | 0.0895907i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.24621 | − | 2.64861i | 0.211040 | − | 0.0894884i | ||||
\(877\) | −9.87689 | − | 17.1073i | −0.333519 | − | 0.577672i | 0.649680 | − | 0.760208i | \(-0.274903\pi\) |
−0.983199 | + | 0.182536i | \(0.941569\pi\) | |||||||
\(878\) | 19.7872 | + | 39.7056i | 0.667787 | + | 1.34000i | ||||
\(879\) | 6.05643 | + | 3.49668i | 0.204278 | + | 0.117940i | ||||
\(880\) | −19.8800 | − | 4.97238i | −0.670155 | − | 0.167619i | ||||
\(881\) | − | 39.1028i | − | 1.31741i | −0.752403 | − | 0.658703i | \(-0.771105\pi\) | ||
0.752403 | − | 0.658703i | \(-0.228895\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 26.9752i | − | 0.907789i | −0.891056 | − | 0.453894i | \(-0.850034\pi\) | ||
0.891056 | − | 0.453894i | \(-0.149966\pi\) | |||||||
\(884\) | −31.6063 | + | 41.9105i | −1.06304 | + | 1.40960i | ||||
\(885\) | 5.87560 | + | 3.39228i | 0.197506 | + | 0.114030i | ||||
\(886\) | −45.4068 | + | 22.6284i | −1.52547 | + | 0.760217i | ||||
\(887\) | 11.3693 | + | 19.6922i | 0.381744 | + | 0.661201i | 0.991312 | − | 0.131534i | \(-0.0419902\pi\) |
−0.609567 | + | 0.792734i | \(0.708657\pi\) | |||||||
\(888\) | 19.8078 | + | 3.68260i | 0.664705 | + | 0.123580i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −10.2462 | + | 15.4741i | −0.343454 | + | 0.518692i | ||||
\(891\) | 2.61578 | − | 1.51022i | 0.0876321 | − | 0.0505944i | ||||
\(892\) | −37.4707 | − | 4.61499i | −1.25461 | − | 0.154521i | ||||
\(893\) | −5.75379 | + | 9.96585i | −0.192543 | + | 0.333495i | ||||
\(894\) | 14.1156 | + | 0.865986i | 0.472096 | + | 0.0289629i | ||||
\(895\) | 3.86174 | 0.129084 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18.2462 | −0.609223 | ||||||||
\(898\) | −39.8712 | − | 2.44608i | −1.33052 | − | 0.0816268i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 4.21437 | + | 0.519053i | 0.140479 | + | 0.0173018i | ||||
\(901\) | −15.9771 | + | 9.22437i | −0.532274 | + | 0.307308i | ||||
\(902\) | 18.2462 | − | 27.5559i | 0.607532 | − | 0.917510i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −34.0540 | − | 6.33122i | −1.13262 | − | 0.210573i | ||||
\(905\) | 5.12311 | + | 8.87348i | 0.170298 | + | 0.294964i | ||||
\(906\) | −10.2638 | + | 5.11494i | −0.340991 | + | 0.169933i | ||||
\(907\) | 10.3220 | + | 5.95938i | 0.342735 | + | 0.197878i | 0.661481 | − | 0.749962i | \(-0.269928\pi\) |
−0.318746 | + | 0.947840i | \(0.603262\pi\) | |||||||
\(908\) | 19.8606 | − | 26.3355i | 0.659097 | − | 0.873973i | ||||
\(909\) | − | 6.99337i | − | 0.231955i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 6.41273i | − | 0.212463i | −0.994341 | − | 0.106232i | \(-0.966122\pi\) | ||
0.994341 | − | 0.106232i | \(-0.0338785\pi\) | |||||||
\(912\) | 4.35817 | + | 1.09006i | 0.144313 | + | 0.0360956i | ||||
\(913\) | 16.3387 | + | 9.43318i | 0.540733 | + | 0.312193i | ||||
\(914\) | −10.2478 | − | 20.5636i | −0.338968 | − | 0.680183i | ||||
\(915\) | 8.00000 | + | 13.8564i | 0.264472 | + | 0.458079i | ||||
\(916\) | −33.3693 | + | 14.1498i | −1.10255 | + | 0.467521i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.12311 | + | 3.39228i | 0.169088 | + | 0.111962i | ||||
\(919\) | 7.02249 | − | 4.05444i | 0.231651 | − | 0.133743i | −0.379683 | − | 0.925117i | \(-0.623967\pi\) |
0.611333 | + | 0.791373i | \(0.290634\pi\) | |||||||
\(920\) | 9.41687 | − | 11.0133i | 0.310465 | − | 0.363097i | ||||
\(921\) | −10.8078 | + | 18.7196i | −0.356128 | + | 0.616832i | ||||
\(922\) | −1.48692 | + | 24.2368i | −0.0489690 | + | 0.798196i | ||||
\(923\) | 75.2311 | 2.47626 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.1231 | −0.497245 | ||||||||
\(926\) | 3.41845 | − | 55.7208i | 0.112337 | − | 1.83110i | ||||
\(927\) | −4.00000 | + | 6.92820i | −0.131377 | + | 0.227552i | ||||
\(928\) | 10.7869 | + | 3.41214i | 0.354097 | + | 0.112009i | ||||
\(929\) | −43.9655 | + | 25.3835i | −1.44246 | + | 0.832805i | −0.998014 | − | 0.0629997i | \(-0.979933\pi\) |
−0.444447 | + | 0.895805i | \(0.646600\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 8.19224 | + | 19.3197i | 0.268346 | + | 0.632838i | ||||
\(933\) | 4.00000 | + | 6.92820i | 0.130954 | + | 0.226819i | ||||
\(934\) | −11.1988 | − | 22.4718i | −0.366436 | − | 0.735299i | ||||
\(935\) | 19.2765 | + | 11.1293i | 0.630410 | + | 0.363968i | ||||
\(936\) | 16.1094 | − | 5.69450i | 0.526551 | − | 0.186131i | ||||
\(937\) | 56.5991i | 1.84901i | 0.381169 | + | 0.924505i | \(0.375522\pi\) | ||||
−0.381169 | + | 0.924505i | \(0.624478\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 25.6509i | − | 0.837086i | ||||||
\(940\) | −27.7512 | − | 20.9282i | −0.905145 | − | 0.682604i | ||||
\(941\) | 11.5704 | + | 6.68016i | 0.377184 | + | 0.217767i | 0.676592 | − | 0.736358i | \(-0.263456\pi\) |
−0.299409 | + | 0.954125i | \(0.596789\pi\) | |||||||
\(942\) | 5.23506 | − | 2.60889i | 0.170568 | − | 0.0850022i | ||||
\(943\) | 11.6847 | + | 20.2384i | 0.380505 | + | 0.659054i | ||||
\(944\) | 11.1231 | − | 11.5012i | 0.362026 | − | 0.374331i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 19.1231 | − | 28.8802i | 0.621746 | − | 0.938975i | ||||
\(947\) | 36.5813 | − | 21.1202i | 1.18873 | − | 0.686316i | 0.230715 | − | 0.973021i | \(-0.425893\pi\) |
0.958019 | + | 0.286705i | \(0.0925601\pi\) | |||||||
\(948\) | −1.15310 | + | 9.36244i | −0.0374510 | + | 0.304078i | ||||
\(949\) | −10.2462 | + | 17.7470i | −0.332606 | + | 0.576091i | ||||
\(950\) | −3.36582 | − | 0.206492i | −0.109202 | − | 0.00669948i | ||||
\(951\) | 18.4924 | 0.599658 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 61.2311 | 1.98347 | 0.991734 | − | 0.128309i | \(-0.0409549\pi\) | ||||
0.991734 | + | 0.128309i | \(0.0409549\pi\) | |||||||
\(954\) | 5.99378 | + | 0.367716i | 0.194056 | + | 0.0119052i | ||||
\(955\) | 7.68466 | − | 13.3102i | 0.248670 | − | 0.430709i | ||||
\(956\) | −0.556623 | + | 4.51941i | −0.0180025 | + | 0.146168i | ||||
\(957\) | −5.23157 | + | 3.02045i | −0.169113 | + | 0.0976372i | ||||
\(958\) | 16.0000 | − | 24.1636i | 0.516937 | − | 0.780690i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −4.87689 | + | 12.6624i | −0.157401 | + | 0.408678i | ||||
\(961\) | 15.5000 | + | 26.8468i | 0.500000 | + | 0.866025i | ||||
\(962\) | −54.4650 | + | 27.1426i | −1.75602 | + | 0.875111i | ||||
\(963\) | 4.90955 | + | 2.83453i | 0.158208 | + | 0.0913415i | ||||
\(964\) | 3.04186 | + | 2.29398i | 0.0979717 | + | 0.0738842i | ||||
\(965\) | 15.8917i | 0.511571i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.9620i | 1.31725i | 0.752472 | + | 0.658624i | \(0.228861\pi\) | ||||
−0.752472 | + | 0.658624i | \(0.771139\pi\) | |||||||
\(968\) | 1.76927 | + | 5.00515i | 0.0568665 | + | 0.160872i | ||||
\(969\) | −4.22587 | − | 2.43981i | −0.135755 | − | 0.0783780i | ||||
\(970\) | −9.29688 | − | 18.6554i | −0.298505 | − | 0.598988i | ||||
\(971\) | −6.00000 | − | 10.3923i | −0.192549 | − | 0.333505i | 0.753545 | − | 0.657396i | \(-0.228342\pi\) |
−0.946094 | + | 0.323891i | \(0.895009\pi\) | |||||||
\(972\) | −0.780776 | − | 1.84130i | −0.0250434 | − | 0.0590597i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 38.0540 | + | 25.1976i | 1.21933 | + | 0.807382i | ||||
\(975\) | −11.1072 | + | 6.41273i | −0.355714 | + | 0.205372i | ||||
\(976\) | 36.2787 | − | 10.3735i | 1.16125 | − | 0.332048i | ||||
\(977\) | 30.3693 | − | 52.6012i | 0.971601 | − | 1.68286i | 0.280875 | − | 0.959744i | \(-0.409375\pi\) |
0.690725 | − | 0.723117i | \(-0.257291\pi\) | |||||||
\(978\) | −0.995984 | + | 16.2346i | −0.0318480 | + | 0.519124i | ||||
\(979\) | −23.3693 | −0.746887 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.24621 | 0.263281 | ||||||||
\(982\) | 1.01407 | − | 16.5293i | 0.0323601 | − | 0.527471i | ||||
\(983\) | 27.3693 | − | 47.4050i | 0.872946 | − | 1.51199i | 0.0140105 | − | 0.999902i | \(-0.495540\pi\) |
0.858935 | − | 0.512084i | \(-0.171126\pi\) | |||||||
\(984\) | −16.6325 | − | 14.2216i | −0.530225 | − | 0.453368i | ||||
\(985\) | 0.361660 | − | 0.208805i | 0.0115234 | − | 0.00665306i | ||||
\(986\) | −10.2462 | − | 6.78456i | −0.326306 | − | 0.216065i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.4924 | + | 5.29723i | −0.397437 | + | 0.168527i | ||||
\(989\) | 12.2462 | + | 21.2111i | 0.389407 | + | 0.674472i | ||||
\(990\) | −3.23157 | − | 6.48455i | −0.102706 | − | 0.206093i | ||||
\(991\) | 9.31626 | + | 5.37874i | 0.295941 | + | 0.170861i | 0.640618 | − | 0.767860i | \(-0.278678\pi\) |
−0.344677 | + | 0.938721i | \(0.612012\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.46026i | 0.173276i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 8.68951i | − | 0.275476i | ||||||
\(996\) | 7.52184 | − | 9.97409i | 0.238339 | − | 0.316041i | ||||
\(997\) | −33.6832 | − | 19.4470i | −1.06676 | − | 0.615892i | −0.139463 | − | 0.990227i | \(-0.544538\pi\) |
−0.927294 | + | 0.374335i | \(0.877871\pi\) | |||||||
\(998\) | −22.2038 | + | 11.0652i | −0.702848 | + | 0.350264i | ||||
\(999\) | 3.56155 | + | 6.16879i | 0.112683 | + | 0.195172i |
(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 | 588.2.o.a.31.1 | 8 | ||
4.3 | odd | 2 | 588.2.o.c.31.3 | 8 | |||
7.2 | even | 3 | inner | 588.2.o.a.19.3 | 8 | ||
7.3 | odd | 6 | 84.2.b.a.55.3 | ✓ | 4 | ||
7.4 | even | 3 | 84.2.b.b.55.3 | yes | 4 | ||
7.5 | odd | 6 | 588.2.o.c.19.3 | 8 | |||
7.6 | odd | 2 | 588.2.o.c.31.1 | 8 | |||
21.11 | odd | 6 | 252.2.b.d.55.2 | 4 | |||
21.17 | even | 6 | 252.2.b.e.55.2 | 4 | |||
28.3 | even | 6 | 84.2.b.b.55.4 | yes | 4 | ||
28.11 | odd | 6 | 84.2.b.a.55.4 | yes | 4 | ||
28.19 | even | 6 | inner | 588.2.o.a.19.1 | 8 | ||
28.23 | odd | 6 | 588.2.o.c.19.1 | 8 | |||
28.27 | even | 2 | inner | 588.2.o.a.31.3 | 8 | ||
56.3 | even | 6 | 1344.2.b.e.895.3 | 4 | |||
56.11 | odd | 6 | 1344.2.b.f.895.2 | 4 | |||
56.45 | odd | 6 | 1344.2.b.f.895.3 | 4 | |||
56.53 | even | 6 | 1344.2.b.e.895.2 | 4 | |||
84.11 | even | 6 | 252.2.b.e.55.1 | 4 | |||
84.59 | odd | 6 | 252.2.b.d.55.1 | 4 | |||
168.11 | even | 6 | 4032.2.b.n.3583.3 | 4 | |||
168.53 | odd | 6 | 4032.2.b.j.3583.3 | 4 | |||
168.59 | odd | 6 | 4032.2.b.j.3583.2 | 4 | |||
168.101 | even | 6 | 4032.2.b.n.3583.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.2.b.a.55.3 | ✓ | 4 | 7.3 | odd | 6 | ||
84.2.b.a.55.4 | yes | 4 | 28.11 | odd | 6 | ||
84.2.b.b.55.3 | yes | 4 | 7.4 | even | 3 | ||
84.2.b.b.55.4 | yes | 4 | 28.3 | even | 6 | ||
252.2.b.d.55.1 | 4 | 84.59 | odd | 6 | |||
252.2.b.d.55.2 | 4 | 21.11 | odd | 6 | |||
252.2.b.e.55.1 | 4 | 84.11 | even | 6 | |||
252.2.b.e.55.2 | 4 | 21.17 | even | 6 | |||
588.2.o.a.19.1 | 8 | 28.19 | even | 6 | inner | ||
588.2.o.a.19.3 | 8 | 7.2 | even | 3 | inner | ||
588.2.o.a.31.1 | 8 | 1.1 | even | 1 | trivial | ||
588.2.o.a.31.3 | 8 | 28.27 | even | 2 | inner | ||
588.2.o.c.19.1 | 8 | 28.23 | odd | 6 | |||
588.2.o.c.19.3 | 8 | 7.5 | odd | 6 | |||
588.2.o.c.31.1 | 8 | 7.6 | odd | 2 | |||
588.2.o.c.31.3 | 8 | 4.3 | odd | 2 | |||
1344.2.b.e.895.2 | 4 | 56.53 | even | 6 | |||
1344.2.b.e.895.3 | 4 | 56.3 | even | 6 | |||
1344.2.b.f.895.2 | 4 | 56.11 | odd | 6 | |||
1344.2.b.f.895.3 | 4 | 56.45 | odd | 6 | |||
4032.2.b.j.3583.2 | 4 | 168.59 | odd | 6 | |||
4032.2.b.j.3583.3 | 4 | 168.53 | odd | 6 | |||
4032.2.b.n.3583.2 | 4 | 168.101 | even | 6 | |||
4032.2.b.n.3583.3 | 4 | 168.11 | even | 6 |