Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1638,2,Mod(307,1638)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1638, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1638.307");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1638.x (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: | \(13.0794958511\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.836829184.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 14x^{6} + 61x^{4} + 84x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 546) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 811.3 | ||
Root | \(-1.65222i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1638.811 |
Dual form | 1638.2.x.c.307.3 |
$q$-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 \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).
\(n\) | \(379\) | \(703\) | \(911\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −0.461191 | − | 0.461191i | −0.206251 | − | 0.206251i | 0.596421 | − | 0.802672i | \(-0.296589\pi\) |
−0.802672 | + | 0.596421i | \(0.796589\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.62949 | − | 0.292893i | −0.993854 | − | 0.110703i | ||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.652223 | −0.206251 | ||||||||
\(11\) | −1.60525 | − | 1.60525i | −0.484000 | − | 0.484000i | 0.422407 | − | 0.906406i | \(-0.361185\pi\) |
−0.906406 | + | 0.422407i | \(0.861185\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.51608 | + | 2.58251i | 0.697834 | + | 0.716260i | ||||
\(14\) | −2.06644 | + | 1.65222i | −0.552278 | + | 0.441575i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −6.40303 | −1.55296 | −0.776482 | − | 0.630140i | \(-0.782998\pi\) | ||||
−0.776482 | + | 0.630140i | \(0.782998\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.52763 | + | 2.52763i | 0.579878 | + | 0.579878i | 0.934869 | − | 0.354992i | \(-0.115516\pi\) |
−0.354992 | + | 0.934869i | \(0.615516\pi\) | |||||||
\(20\) | −0.461191 | + | 0.461191i | −0.103125 | + | 0.103125i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.27016 | −0.484000 | ||||||||
\(23\) | 8.51280i | 1.77504i | 0.460768 | + | 0.887521i | \(0.347574\pi\) | ||||
−0.460768 | + | 0.887521i | \(0.652426\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 4.57461i | − | 0.914921i | ||||||
\(26\) | 3.60525 | + | 0.0469777i | 0.707047 | + | 0.00921308i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.292893 | + | 2.62949i | −0.0553516 | + | 0.496927i | ||||
\(29\) | −7.91120 | −1.46907 | −0.734537 | − | 0.678569i | \(-0.762600\pi\) | ||||
−0.734537 | + | 0.678569i | \(0.762600\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.922382 | + | 0.922382i | 0.165665 | + | 0.165665i | 0.785071 | − | 0.619406i | \(-0.212627\pi\) |
−0.619406 | + | 0.785071i | \(0.712627\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.52763 | + | 4.52763i | −0.776482 | + | 0.776482i | ||||
\(35\) | 1.07762 | + | 1.34778i | 0.182151 | + | 0.227816i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.953022 | − | 0.953022i | −0.156676 | − | 0.156676i | 0.624416 | − | 0.781092i | \(-0.285337\pi\) |
−0.781092 | + | 0.624416i | \(0.785337\pi\) | |||||||
\(38\) | 3.57461 | 0.579878 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.652223i | 0.103125i | ||||||||
\(41\) | 3.89486 | + | 3.89486i | 0.608275 | + | 0.608275i | 0.942495 | − | 0.334220i | \(-0.108473\pi\) |
−0.334220 | + | 0.942495i | \(0.608473\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.17620i | 0.636865i | 0.947946 | + | 0.318433i | \(0.103156\pi\) | ||||
−0.947946 | + | 0.318433i | \(0.896844\pi\) | |||||||
\(44\) | −1.60525 | + | 1.60525i | −0.242000 | + | 0.242000i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.01946 | + | 6.01946i | 0.887521 | + | 0.887521i | ||||
\(47\) | −1.41421 | + | 1.41421i | −0.206284 | + | 0.206284i | −0.802686 | − | 0.596402i | \(-0.796597\pi\) |
0.596402 | + | 0.802686i | \(0.296597\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.82843 | + | 1.54032i | 0.975490 | + | 0.220046i | ||||
\(50\) | −3.23473 | − | 3.23473i | −0.457461 | − | 0.457461i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.58251 | − | 2.51608i | 0.358130 | − | 0.348917i | ||||
\(53\) | −9.10072 | −1.25008 | −0.625040 | − | 0.780593i | \(-0.714917\pi\) | ||||
−0.625040 | + | 0.780593i | \(0.714917\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.48065i | 0.199651i | ||||||||
\(56\) | 1.65222 | + | 2.06644i | 0.220788 | + | 0.276139i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.59406 | + | 5.59406i | −0.734537 | + | 0.734537i | ||||
\(59\) | −1.17834 | + | 1.17834i | −0.153407 | + | 0.153407i | −0.779638 | − | 0.626231i | \(-0.784597\pi\) |
0.626231 | + | 0.779638i | \(0.284597\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.4874i | 1.85492i | 0.373918 | + | 0.927462i | \(0.378014\pi\) | ||||
−0.373918 | + | 0.927462i | \(0.621986\pi\) | |||||||
\(62\) | 1.30445 | 0.165665 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0.0306399 | − | 2.35142i | 0.00380041 | − | 0.291658i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.47602 | − | 3.47602i | 0.424663 | − | 0.424663i | −0.462142 | − | 0.886806i | \(-0.652919\pi\) |
0.886806 | + | 0.462142i | \(0.152919\pi\) | |||||||
\(68\) | 6.40303i | 0.776482i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.71501 | + | 0.191032i | 0.204983 | + | 0.0228327i | ||||
\(71\) | 8.29326 | − | 8.29326i | 0.984229 | − | 0.984229i | −0.0156481 | − | 0.999878i | \(-0.504981\pi\) |
0.999878 | + | 0.0156481i | \(0.00498116\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.89851 | + | 5.89851i | −0.690368 | + | 0.690368i | −0.962313 | − | 0.271945i | \(-0.912333\pi\) |
0.271945 | + | 0.962313i | \(0.412333\pi\) | |||||||
\(74\) | −1.34778 | −0.156676 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.52763 | − | 2.52763i | 0.289939 | − | 0.289939i | ||||
\(77\) | 3.75081 | + | 4.69114i | 0.427444 | + | 0.534605i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.18813 | −1.03375 | −0.516873 | − | 0.856062i | \(-0.672904\pi\) | ||||
−0.516873 | + | 0.856062i | \(0.672904\pi\) | |||||||
\(80\) | 0.461191 | + | 0.461191i | 0.0515627 | + | 0.0515627i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.50817 | 0.608275 | ||||||||
\(83\) | −9.98882 | − | 9.98882i | −1.09642 | − | 1.09642i | −0.994826 | − | 0.101589i | \(-0.967607\pi\) |
−0.101589 | − | 0.994826i | \(-0.532393\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.95302 | + | 2.95302i | 0.320300 | + | 0.320300i | ||||
\(86\) | 2.95302 | + | 2.95302i | 0.318433 | + | 0.318433i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.27016i | 0.242000i | ||||||||
\(89\) | −8.54709 | + | 8.54709i | −0.905989 | + | 0.905989i | −0.995946 | − | 0.0899564i | \(-0.971327\pi\) |
0.0899564 | + | 0.995946i | \(0.471327\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.85959 | − | 7.52763i | −0.614252 | − | 0.789110i | ||||
\(92\) | 8.51280 | 0.887521 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.00000i | 0.206284i | ||||||||
\(95\) | − | 2.33144i | − | 0.239201i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.272296 | + | 0.272296i | 0.0276474 | + | 0.0276474i | 0.720795 | − | 0.693148i | \(-0.243777\pi\) |
−0.693148 | + | 0.720795i | \(0.743777\pi\) | |||||||
\(98\) | 5.91760 | − | 3.73926i | 0.597768 | − | 0.377722i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.57461 | −0.457461 | ||||||||
\(101\) | 8.03892 | 0.799902 | 0.399951 | − | 0.916536i | \(-0.369027\pi\) | ||||
0.399951 | + | 0.916536i | \(0.369027\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.62934 | −0.751741 | −0.375870 | − | 0.926672i | \(-0.622656\pi\) | ||||
−0.375870 | + | 0.926672i | \(0.622656\pi\) | |||||||
\(104\) | 0.0469777 | − | 3.60525i | 0.00460654 | − | 0.353523i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.43518 | + | 6.43518i | −0.625040 | + | 0.625040i | ||||
\(107\) | 14.3986 | 1.39197 | 0.695984 | − | 0.718058i | \(-0.254969\pi\) | ||||
0.695984 | + | 0.718058i | \(0.254969\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.6815 | + | 10.6815i | −1.02310 | + | 1.02310i | −0.0233724 | + | 0.999727i | \(0.507440\pi\) |
−0.999727 | + | 0.0233724i | \(0.992560\pi\) | |||||||
\(110\) | 1.04698 | + | 1.04698i | 0.0998254 | + | 0.0998254i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.62949 | + | 0.292893i | 0.248463 | + | 0.0276758i | ||||
\(113\) | −15.0256 | −1.41349 | −0.706745 | − | 0.707469i | \(-0.749837\pi\) | ||||
−0.706745 | + | 0.707469i | \(0.749837\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.92603 | − | 3.92603i | 0.366104 | − | 0.366104i | ||||
\(116\) | 7.91120i | 0.734537i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.66642i | 0.153407i | ||||||||
\(119\) | 16.8367 | + | 1.87540i | 1.54342 | + | 0.171918i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 5.84638i | − | 0.531489i | ||||||
\(122\) | 10.2442 | + | 10.2442i | 0.927462 | + | 0.927462i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.922382 | − | 0.922382i | 0.0828324 | − | 0.0828324i | ||||
\(125\) | −4.41572 | + | 4.41572i | −0.394954 | + | 0.394954i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 15.7970i | − | 1.40176i | −0.713280 | − | 0.700879i | \(-0.752791\pi\) | ||
0.713280 | − | 0.700879i | \(-0.247209\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.64104 | − | 1.68437i | −0.143929 | − | 0.147729i | ||||
\(131\) | − | 1.75522i | − | 0.153355i | −0.997056 | − | 0.0766773i | \(-0.975569\pi\) | ||
0.997056 | − | 0.0766773i | \(-0.0244311\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.90604 | − | 7.38669i | −0.512119 | − | 0.640508i | ||||
\(134\) | − | 4.91583i | − | 0.424663i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.52763 | + | 4.52763i | 0.388241 | + | 0.388241i | ||||
\(137\) | 1.82994 | + | 1.82994i | 0.156342 | + | 0.156342i | 0.780944 | − | 0.624602i | \(-0.214739\pi\) |
−0.624602 | + | 0.780944i | \(0.714739\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 13.8448i | − | 1.17430i | −0.809479 | − | 0.587149i | \(-0.800250\pi\) | ||
0.809479 | − | 0.587149i | \(-0.199750\pi\) | |||||||
\(140\) | 1.34778 | − | 1.07762i | 0.113908 | − | 0.0910753i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 11.7284i | − | 0.984229i | ||||||
\(143\) | 0.106647 | − | 8.18448i | 0.00891825 | − | 0.684421i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.64858 | + | 3.64858i | 0.302998 | + | 0.302998i | ||||
\(146\) | 8.34175i | 0.690368i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.953022 | + | 0.953022i | −0.0783380 | + | 0.0783380i | ||||
\(149\) | 3.12824 | − | 3.12824i | 0.256276 | − | 0.256276i | −0.567262 | − | 0.823537i | \(-0.691997\pi\) |
0.823537 | + | 0.567262i | \(0.191997\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.5502 | + | 11.5502i | 0.939943 | + | 0.939943i | 0.998296 | − | 0.0583534i | \(-0.0185850\pi\) |
−0.0583534 | + | 0.998296i | \(0.518585\pi\) | |||||||
\(152\) | − | 3.57461i | − | 0.289939i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.96936 | + | 0.664914i | 0.481025 | + | 0.0535803i | ||||
\(155\) | − | 0.850789i | − | 0.0683370i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 18.5294i | − | 1.47880i | −0.673264 | − | 0.739402i | \(-0.735108\pi\) | ||
0.673264 | − | 0.739402i | \(-0.264892\pi\) | |||||||
\(158\) | −6.49699 | + | 6.49699i | −0.516873 | + | 0.516873i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.652223 | 0.0515627 | ||||||||
\(161\) | 2.49334 | − | 22.3843i | 0.196503 | − | 1.76413i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.1032 | − | 13.1032i | −1.02632 | − | 1.02632i | −0.999644 | − | 0.0266792i | \(-0.991507\pi\) |
−0.0266792 | − | 0.999644i | \(-0.508493\pi\) | |||||||
\(164\) | 3.89486 | − | 3.89486i | 0.304138 | − | 0.304138i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.1263 | −1.09642 | ||||||||
\(167\) | −9.82552 | + | 9.82552i | −0.760322 | + | 0.760322i | −0.976380 | − | 0.216059i | \(-0.930680\pi\) |
0.216059 | + | 0.976380i | \(0.430680\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.338732 | + | 12.9956i | −0.0260563 | + | 0.999660i | ||||
\(170\) | 4.17620 | 0.320300 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.17620 | 0.318433 | ||||||||
\(173\) | 10.9940 | 0.835856 | 0.417928 | − | 0.908480i | \(-0.362756\pi\) | ||||
0.417928 | + | 0.908480i | \(0.362756\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.33987 | + | 12.0289i | −0.101285 | + | 0.909298i | ||||
\(176\) | 1.60525 | + | 1.60525i | 0.121000 | + | 0.121000i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 12.0874i | 0.905989i | ||||||||
\(179\) | − | 2.54656i | − | 0.190339i | −0.995461 | − | 0.0951695i | \(-0.969661\pi\) | ||
0.995461 | − | 0.0951695i | \(-0.0303393\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.8933 | −1.03268 | −0.516339 | − | 0.856384i | \(-0.672705\pi\) | ||||
−0.516339 | + | 0.856384i | \(0.672705\pi\) | |||||||
\(182\) | −9.46619 | − | 1.17948i | −0.701681 | − | 0.0874288i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.01946 | − | 6.01946i | 0.443760 | − | 0.443760i | ||||
\(185\) | 0.879051i | 0.0646291i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.2784 | + | 10.2784i | 0.751634 | + | 0.751634i | ||||
\(188\) | 1.41421 | + | 1.41421i | 0.103142 | + | 0.103142i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.64858 | − | 1.64858i | −0.119600 | − | 0.119600i | ||||
\(191\) | 10.2290 | 0.740142 | 0.370071 | − | 0.929004i | \(-0.379333\pi\) | ||||
0.370071 | + | 0.929004i | \(0.379333\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.3940 | + | 12.3940i | 0.892139 | + | 0.892139i | 0.994724 | − | 0.102585i | \(-0.0327115\pi\) |
−0.102585 | + | 0.994724i | \(0.532712\pi\) | |||||||
\(194\) | 0.385084 | 0.0276474 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.54032 | − | 6.82843i | 0.110023 | − | 0.487745i | ||||
\(197\) | −8.84638 | + | 8.84638i | −0.630278 | + | 0.630278i | −0.948138 | − | 0.317860i | \(-0.897036\pi\) |
0.317860 | + | 0.948138i | \(0.397036\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.40980 | −0.525267 | −0.262633 | − | 0.964896i | \(-0.584591\pi\) | ||||
−0.262633 | + | 0.964896i | \(0.584591\pi\) | |||||||
\(200\) | −3.23473 | + | 3.23473i | −0.228730 | + | 0.228730i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.68437 | − | 5.68437i | 0.399951 | − | 0.399951i | ||||
\(203\) | 20.8024 | + | 2.31714i | 1.46004 | + | 0.162631i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 3.59255i | − | 0.250915i | ||||||
\(206\) | −5.39475 | + | 5.39475i | −0.375870 | + | 0.375870i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.51608 | − | 2.58251i | −0.174458 | − | 0.179065i | ||||
\(209\) | − | 8.11492i | − | 0.561321i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.6299 | 1.00716 | 0.503581 | − | 0.863948i | \(-0.332016\pi\) | ||||
0.503581 | + | 0.863948i | \(0.332016\pi\) | |||||||
\(212\) | 9.10072i | 0.625040i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 10.1814 | − | 10.1814i | 0.695984 | − | 0.695984i | ||||
\(215\) | 1.92603 | − | 1.92603i | 0.131354 | − | 0.131354i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.15524 | − | 2.69555i | −0.146307 | − | 0.182986i | ||||
\(218\) | 15.1059i | 1.02310i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.48065 | 0.0998254 | ||||||||
\(221\) | −16.1105 | − | 16.5359i | −1.08371 | − | 1.11233i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.0574 | − | 11.0574i | −0.740458 | − | 0.740458i | 0.232208 | − | 0.972666i | \(-0.425405\pi\) |
−0.972666 | + | 0.232208i | \(0.925405\pi\) | |||||||
\(224\) | 2.06644 | − | 1.65222i | 0.138070 | − | 0.110394i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.6247 | + | 10.6247i | −0.706745 | + | 0.706745i | ||||
\(227\) | −9.31423 | − | 9.31423i | −0.618207 | − | 0.618207i | 0.326864 | − | 0.945071i | \(-0.394008\pi\) |
−0.945071 | + | 0.326864i | \(0.894008\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.5860 | + | 15.5860i | −1.02995 | + | 1.02995i | −0.0304148 | + | 0.999537i | \(0.509683\pi\) |
−0.999537 | + | 0.0304148i | \(0.990317\pi\) | |||||||
\(230\) | − | 5.55224i | − | 0.366104i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.59406 | + | 5.59406i | 0.367268 | + | 0.367268i | ||||
\(233\) | − | 14.4240i | − | 0.944948i | −0.881345 | − | 0.472474i | \(-0.843361\pi\) | ||
0.881345 | − | 0.472474i | \(-0.156639\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.30445 | 0.0850927 | ||||||||
\(236\) | 1.17834 | + | 1.17834i | 0.0767034 | + | 0.0767034i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 13.2315 | − | 10.5792i | 0.857668 | − | 0.685750i | ||||
\(239\) | −3.83747 | + | 3.83747i | −0.248225 | + | 0.248225i | −0.820242 | − | 0.572017i | \(-0.806161\pi\) |
0.572017 | + | 0.820242i | \(0.306161\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.2110 | + | 14.2110i | −0.915412 | + | 0.915412i | −0.996691 | − | 0.0812794i | \(-0.974099\pi\) |
0.0812794 | + | 0.996691i | \(0.474099\pi\) | |||||||
\(242\) | −4.13401 | − | 4.13401i | −0.265744 | − | 0.265744i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 14.4874 | 0.927462 | ||||||||
\(245\) | −2.43883 | − | 3.85959i | −0.155811 | − | 0.246580i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.167927 | + | 12.8873i | −0.0106849 | + | 0.820001i | ||||
\(248\) | − | 1.30445i | − | 0.0828324i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.24478i | 0.394954i | ||||||||
\(251\) | 5.39399 | 0.340465 | 0.170233 | − | 0.985404i | \(-0.445548\pi\) | ||||
0.170233 | + | 0.985404i | \(0.445548\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.6651 | − | 13.6651i | 0.859119 | − | 0.859119i | ||||
\(254\) | −11.1702 | − | 11.1702i | −0.700879 | − | 0.700879i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.38508 | −0.273534 | −0.136767 | − | 0.990603i | \(-0.543671\pi\) | ||||
−0.136767 | + | 0.990603i | \(0.543671\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.22683 | + | 2.78510i | 0.138368 | + | 0.173057i | ||||
\(260\) | −2.35142 | − | 0.0306399i | −0.145829 | − | 0.00190021i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.24113 | − | 1.24113i | −0.0766773 | − | 0.0766773i | ||||
\(263\) | 12.4336 | 0.766687 | 0.383343 | − | 0.923606i | \(-0.374773\pi\) | ||||
0.383343 | + | 0.923606i | \(0.374773\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.19717 | + | 4.19717i | 0.257830 | + | 0.257830i | ||||
\(266\) | −9.39939 | − | 1.04698i | −0.576313 | − | 0.0641943i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.47602 | − | 3.47602i | −0.212332 | − | 0.212332i | ||||
\(269\) | − | 29.7839i | − | 1.81596i | −0.419016 | − | 0.907979i | \(-0.637625\pi\) | ||
0.419016 | − | 0.907979i | \(-0.362375\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.7173 | − | 14.7173i | 0.894010 | − | 0.894010i | −0.100888 | − | 0.994898i | \(-0.532168\pi\) |
0.994898 | + | 0.100888i | \(0.0321682\pi\) | |||||||
\(272\) | 6.40303 | 0.388241 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.58792 | 0.156342 | ||||||||
\(275\) | −7.34336 | + | 7.34336i | −0.442821 | + | 0.442821i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 24.1271i | − | 1.44965i | −0.688930 | − | 0.724827i | \(-0.741919\pi\) | ||
0.688930 | − | 0.724827i | \(-0.258081\pi\) | |||||||
\(278\) | −9.78973 | − | 9.78973i | −0.587149 | − | 0.587149i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.191032 | − | 1.71501i | 0.0114163 | − | 0.102492i | ||||
\(281\) | 7.70534 | + | 7.70534i | 0.459662 | + | 0.459662i | 0.898545 | − | 0.438882i | \(-0.144626\pi\) |
−0.438882 | + | 0.898545i | \(0.644626\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.39133 | −0.379925 | −0.189962 | − | 0.981791i | \(-0.560837\pi\) | ||||
−0.189962 | + | 0.981791i | \(0.560837\pi\) | |||||||
\(284\) | −8.29326 | − | 8.29326i | −0.492115 | − | 0.492115i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.71189 | − | 5.86271i | −0.337751 | − | 0.346670i | ||||
\(287\) | −9.10072 | − | 11.3823i | −0.537199 | − | 0.671875i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 23.9988 | 1.41170 | ||||||||
\(290\) | 5.15987 | 0.302998 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.89851 | + | 5.89851i | 0.345184 | + | 0.345184i | ||||
\(293\) | −8.93819 | + | 8.93819i | −0.522175 | + | 0.522175i | −0.918228 | − | 0.396053i | \(-0.870380\pi\) |
0.396053 | + | 0.918228i | \(0.370380\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.08688 | 0.0632806 | ||||||||
\(296\) | 1.34778i | 0.0783380i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 4.42400i | − | 0.256276i | ||||||
\(299\) | −21.9844 | + | 21.4188i | −1.27139 | + | 1.23868i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.22318 | − | 10.9813i | 0.0705030 | − | 0.632951i | ||||
\(302\) | 16.3345 | 0.939943 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.52763 | − | 2.52763i | −0.144969 | − | 0.144969i | ||||
\(305\) | 6.68147 | − | 6.68147i | 0.382580 | − | 0.382580i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.27177 | − | 1.27177i | 0.0725838 | − | 0.0725838i | −0.669883 | − | 0.742467i | \(-0.733656\pi\) |
0.742467 | + | 0.669883i | \(0.233656\pi\) | |||||||
\(308\) | 4.69114 | − | 3.75081i | 0.267303 | − | 0.213722i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.601599 | − | 0.601599i | −0.0341685 | − | 0.0341685i | ||||
\(311\) | 1.52201 | 0.0863053 | 0.0431527 | − | 0.999068i | \(-0.486260\pi\) | ||||
0.0431527 | + | 0.999068i | \(0.486260\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.48506i | 0.196987i | 0.995138 | + | 0.0984937i | \(0.0314024\pi\) | ||||
−0.995138 | + | 0.0984937i | \(0.968598\pi\) | |||||||
\(314\) | −13.1022 | − | 13.1022i | −0.739402 | − | 0.739402i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.18813i | 0.516873i | ||||||||
\(317\) | −3.61566 | + | 3.61566i | −0.203076 | + | 0.203076i | −0.801316 | − | 0.598241i | \(-0.795867\pi\) |
0.598241 | + | 0.801316i | \(0.295867\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.6994 | + | 12.6994i | 0.711031 | + | 0.711031i | ||||
\(320\) | 0.461191 | − | 0.461191i | 0.0257814 | − | 0.0257814i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −14.0650 | − | 17.5912i | −0.783814 | − | 0.980317i | ||||
\(323\) | −16.1845 | − | 16.1845i | −0.900529 | − | 0.900529i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.8140 | − | 11.5101i | 0.655321 | − | 0.638463i | ||||
\(326\) | −18.5307 | −1.02632 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 5.50817i | − | 0.304138i | ||||||
\(329\) | 4.13287 | − | 3.30445i | 0.227853 | − | 0.182180i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.50162 | − | 4.50162i | 0.247431 | − | 0.247431i | −0.572484 | − | 0.819916i | \(-0.694020\pi\) |
0.819916 | + | 0.572484i | \(0.194020\pi\) | |||||||
\(332\) | −9.98882 | + | 9.98882i | −0.548208 | + | 0.548208i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 13.8954i | 0.760322i | ||||||||
\(335\) | −3.20622 | −0.175174 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 20.7331i | − | 1.12940i | −0.825295 | − | 0.564701i | \(-0.808991\pi\) | ||
0.825295 | − | 0.564701i | \(-0.191009\pi\) | |||||||
\(338\) | 8.94975 | + | 9.42879i | 0.486802 | + | 0.512858i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.95302 | − | 2.95302i | 0.160150 | − | 0.160150i | ||||
\(341\) | − | 2.96130i | − | 0.160363i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.5041 | − | 6.05025i | −0.945134 | − | 0.326683i | ||||
\(344\) | 2.95302 | − | 2.95302i | 0.159216 | − | 0.159216i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.77391 | − | 7.77391i | 0.417928 | − | 0.417928i | ||||
\(347\) | −0.161276 | −0.00865778 | −0.00432889 | − | 0.999991i | \(-0.501378\pi\) | ||||
−0.00432889 | + | 0.999991i | \(0.501378\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.17995 | − | 7.17995i | 0.384334 | − | 0.384334i | −0.488327 | − | 0.872661i | \(-0.662393\pi\) |
0.872661 | + | 0.488327i | \(0.162393\pi\) | |||||||
\(350\) | 7.55827 | + | 9.45313i | 0.404006 | + | 0.505291i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.27016 | 0.121000 | ||||||||
\(353\) | 9.44711 | + | 9.44711i | 0.502819 | + | 0.502819i | 0.912313 | − | 0.409494i | \(-0.134295\pi\) |
−0.409494 | + | 0.912313i | \(0.634295\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.64956 | −0.405997 | ||||||||
\(356\) | 8.54709 | + | 8.54709i | 0.452995 | + | 0.452995i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.80069 | − | 1.80069i | −0.0951695 | − | 0.0951695i | ||||
\(359\) | 19.1933 | + | 19.1933i | 1.01298 | + | 1.01298i | 0.999915 | + | 0.0130682i | \(0.00415986\pi\) |
0.0130682 | + | 0.999915i | \(0.495840\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 6.22220i | − | 0.327484i | ||||||
\(362\) | −9.82401 | + | 9.82401i | −0.516339 | + | 0.516339i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.52763 | + | 5.85959i | −0.394555 | + | 0.307126i | ||||
\(365\) | 5.44068 | 0.284778 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.3142i | 1.26919i | 0.772844 | + | 0.634596i | \(0.218834\pi\) | ||||
−0.772844 | + | 0.634596i | \(0.781166\pi\) | |||||||
\(368\) | − | 8.51280i | − | 0.443760i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.621583 | + | 0.621583i | 0.0323146 | + | 0.0323146i | ||||
\(371\) | 23.9303 | + | 2.66554i | 1.24240 | + | 0.138388i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.74654 | 0.504657 | 0.252328 | − | 0.967642i | \(-0.418804\pi\) | ||||
0.252328 | + | 0.967642i | \(0.418804\pi\) | |||||||
\(374\) | 14.5359 | 0.751634 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.00000 | 0.103142 | ||||||||
\(377\) | −19.9052 | − | 20.4308i | −1.02517 | − | 1.05224i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.5776 | − | 14.5776i | 0.748802 | − | 0.748802i | −0.225452 | − | 0.974254i | \(-0.572386\pi\) |
0.974254 | + | 0.225452i | \(0.0723859\pi\) | |||||||
\(380\) | −2.33144 | −0.119600 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7.23297 | − | 7.23297i | 0.370071 | − | 0.370071i | ||||
\(383\) | 20.8642 | + | 20.8642i | 1.06611 | + | 1.06611i | 0.997654 | + | 0.0684580i | \(0.0218079\pi\) |
0.0684580 | + | 0.997654i | \(0.478192\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.433672 | − | 3.89335i | 0.0221020 | − | 0.198424i | ||||
\(386\) | 17.5277 | 0.892139 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.272296 | − | 0.272296i | 0.0138237 | − | 0.0138237i | ||||
\(389\) | 6.09321i | 0.308938i | 0.987998 | + | 0.154469i | \(0.0493667\pi\) | ||||
−0.987998 | + | 0.154469i | \(0.950633\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 54.5077i | − | 2.75657i | ||||||
\(392\) | −3.73926 | − | 5.91760i | −0.188861 | − | 0.298884i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.5107i | 0.630278i | ||||||||
\(395\) | 4.23748 | + | 4.23748i | 0.213211 | + | 0.213211i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.9792 | + | 26.9792i | −1.35405 | + | 1.35405i | −0.472972 | + | 0.881077i | \(0.656819\pi\) |
−0.881077 | + | 0.472972i | \(0.843181\pi\) | |||||||
\(398\) | −5.23952 | + | 5.23952i | −0.262633 | + | 0.262633i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.57461i | 0.228730i | ||||||||
\(401\) | −21.4604 | − | 21.4604i | −1.07168 | − | 1.07168i | −0.997224 | − | 0.0744583i | \(-0.976277\pi\) |
−0.0744583 | − | 0.997224i | \(-0.523723\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0612798 | + | 4.70285i | −0.00305256 | + | 0.234265i | ||||
\(404\) | − | 8.03892i | − | 0.399951i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 16.3480 | − | 13.0711i | 0.811337 | − | 0.648706i | ||||
\(407\) | 3.05967i | 0.151662i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.20898 | + | 4.20898i | 0.208121 | + | 0.208121i | 0.803468 | − | 0.595348i | \(-0.202986\pi\) |
−0.595348 | + | 0.803468i | \(0.702986\pi\) | |||||||
\(410\) | −2.54032 | − | 2.54032i | −0.125457 | − | 0.125457i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.62934i | 0.375870i | ||||||||
\(413\) | 3.44356 | − | 2.75330i | 0.169447 | − | 0.135481i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.21351i | 0.452273i | ||||||||
\(416\) | −3.60525 | − | 0.0469777i | −0.176762 | − | 0.00230327i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.73812 | − | 5.73812i | −0.280661 | − | 0.280661i | ||||
\(419\) | − | 3.78685i | − | 0.185000i | −0.995713 | − | 0.0924998i | \(-0.970514\pi\) | ||
0.995713 | − | 0.0924998i | \(-0.0294858\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.2730 | + | 16.2730i | −0.793099 | + | 0.793099i | −0.981997 | − | 0.188897i | \(-0.939509\pi\) |
0.188897 | + | 0.981997i | \(0.439509\pi\) | |||||||
\(422\) | 10.3449 | − | 10.3449i | 0.503581 | − | 0.503581i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.43518 | + | 6.43518i | 0.312520 | + | 0.312520i | ||||
\(425\) | 29.2913i | 1.42084i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.24327 | − | 38.0945i | 0.205346 | − | 1.84352i | ||||
\(428\) | − | 14.3986i | − | 0.695984i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 2.72382i | − | 0.131354i | ||||||
\(431\) | 17.7084 | − | 17.7084i | 0.852982 | − | 0.852982i | −0.137518 | − | 0.990499i | \(-0.543912\pi\) |
0.990499 | + | 0.137518i | \(0.0439123\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.2092 | −0.634796 | −0.317398 | − | 0.948292i | \(-0.602809\pi\) | ||||
−0.317398 | + | 0.948292i | \(0.602809\pi\) | |||||||
\(434\) | −3.43003 | − | 0.382063i | −0.164647 | − | 0.0183396i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.6815 | + | 10.6815i | 0.511550 | + | 0.511550i | ||||
\(437\) | −21.5172 | + | 21.5172i | −1.02931 | + | 1.02931i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.2638 | −1.30123 | −0.650616 | − | 0.759407i | \(-0.725489\pi\) | ||||
−0.650616 | + | 0.759407i | \(0.725489\pi\) | |||||||
\(440\) | 1.04698 | − | 1.04698i | 0.0499127 | − | 0.0499127i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −23.0845 | − | 0.300799i | −1.09802 | − | 0.0143076i | ||||
\(443\) | −22.3627 | −1.06248 | −0.531242 | − | 0.847220i | \(-0.678275\pi\) | ||||
−0.531242 | + | 0.847220i | \(0.678275\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.88368 | 0.373722 | ||||||||
\(446\) | −15.6375 | −0.740458 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.292893 | − | 2.62949i | 0.0138379 | − | 0.124232i | ||||
\(449\) | −3.36702 | − | 3.36702i | −0.158899 | − | 0.158899i | 0.623179 | − | 0.782079i | \(-0.285841\pi\) |
−0.782079 | + | 0.623179i | \(0.785841\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 12.5044i | − | 0.588810i | ||||||
\(452\) | 15.0256i | 0.706745i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −13.1723 | −0.618207 | ||||||||
\(455\) | −0.769283 | + | 6.17407i | −0.0360646 | + | 0.289445i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.5030 | + | 12.5030i | −0.584866 | + | 0.584866i | −0.936237 | − | 0.351370i | \(-0.885716\pi\) |
0.351370 | + | 0.936237i | \(0.385716\pi\) | |||||||
\(458\) | 22.0419i | 1.02995i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.92603 | − | 3.92603i | −0.183052 | − | 0.183052i | ||||
\(461\) | −4.03719 | − | 4.03719i | −0.188031 | − | 0.188031i | 0.606814 | − | 0.794844i | \(-0.292447\pi\) |
−0.794844 | + | 0.606814i | \(0.792447\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.8250 | − | 12.8250i | −0.596028 | − | 0.596028i | 0.343225 | − | 0.939253i | \(-0.388481\pi\) |
−0.939253 | + | 0.343225i | \(0.888481\pi\) | |||||||
\(464\) | 7.91120 | 0.367268 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.1993 | − | 10.1993i | −0.472474 | − | 0.472474i | ||||
\(467\) | −17.0280 | −0.787964 | −0.393982 | − | 0.919118i | \(-0.628903\pi\) | ||||
−0.393982 | + | 0.919118i | \(0.628903\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.1583 | + | 8.12205i | −0.469065 | + | 0.375041i | ||||
\(470\) | 0.922382 | − | 0.922382i | 0.0425463 | − | 0.0425463i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.66642 | 0.0767034 | ||||||||
\(473\) | 6.70383 | − | 6.70383i | 0.308243 | − | 0.308243i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.5629 | − | 11.5629i | 0.530542 | − | 0.530542i | ||||
\(476\) | 1.87540 | − | 16.8367i | 0.0859590 | − | 0.771709i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.42701i | 0.248225i | ||||||||
\(479\) | 22.7406 | − | 22.7406i | 1.03905 | − | 1.03905i | 0.0398390 | − | 0.999206i | \(-0.487315\pi\) |
0.999206 | − | 0.0398390i | \(-0.0126845\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.0633154 | − | 4.85907i | 0.00288693 | − | 0.221554i | ||||
\(482\) | 20.0974i | 0.915412i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.84638 | −0.265744 | ||||||||
\(485\) | − | 0.251161i | − | 0.0114046i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.40745 | + | 8.40745i | −0.380978 | + | 0.380978i | −0.871454 | − | 0.490477i | \(-0.836823\pi\) |
0.490477 | + | 0.871454i | \(0.336823\pi\) | |||||||
\(488\) | 10.2442 | − | 10.2442i | 0.463731 | − | 0.463731i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.45366 | − | 1.00463i | −0.201196 | − | 0.0453846i | ||||
\(491\) | 12.3150i | 0.555767i | 0.960615 | + | 0.277884i | \(0.0896329\pi\) | ||||
−0.960615 | + | 0.277884i | \(0.910367\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 50.6557 | 2.28142 | ||||||||
\(494\) | 8.99398 | + | 9.23146i | 0.404658 | + | 0.415343i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.922382 | − | 0.922382i | −0.0414162 | − | 0.0414162i | ||||
\(497\) | −24.2361 | + | 19.3780i | −1.08714 | + | 0.869222i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.13266 | − | 4.13266i | 0.185003 | − | 0.185003i | −0.608529 | − | 0.793532i | \(-0.708240\pi\) |
0.793532 | + | 0.608529i | \(0.208240\pi\) | |||||||
\(500\) | 4.41572 | + | 4.41572i | 0.197477 | + | 0.197477i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.81412 | − | 3.81412i | 0.170233 | − | 0.170233i | ||||
\(503\) | − | 32.1557i | − | 1.43375i | −0.697201 | − | 0.716875i | \(-0.745572\pi\) | ||
0.697201 | − | 0.716875i | \(-0.254428\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.70748 | − | 3.70748i | −0.164981 | − | 0.164981i | ||||
\(506\) | − | 19.3254i | − | 0.859119i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −15.7970 | −0.700879 | ||||||||
\(509\) | 25.9435 | + | 25.9435i | 1.14992 | + | 1.14992i | 0.986567 | + | 0.163357i | \(0.0522322\pi\) |
0.163357 | + | 0.986567i | \(0.447768\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.2377 | − | 13.7824i | 0.762551 | − | 0.609699i | ||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.10072 | + | 3.10072i | −0.136767 | + | 0.136767i | ||||
\(515\) | 3.51858 | + | 3.51858i | 0.155047 | + | 0.155047i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.54032 | 0.199683 | ||||||||
\(518\) | 3.54397 | + | 0.394755i | 0.155713 | + | 0.0173445i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.68437 | + | 1.64104i | −0.0738646 | + | 0.0719644i | ||||
\(521\) | − | 3.85949i | − | 0.169087i | −0.996420 | − | 0.0845437i | \(-0.973057\pi\) | ||
0.996420 | − | 0.0845437i | \(-0.0269433\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.3670i | 1.59022i | 0.606467 | + | 0.795109i | \(0.292586\pi\) | ||||
−0.606467 | + | 0.795109i | \(0.707414\pi\) | |||||||
\(524\) | −1.75522 | −0.0766773 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.79186 | − | 8.79186i | 0.383343 | − | 0.383343i | ||||
\(527\) | −5.90604 | − | 5.90604i | −0.257271 | − | 0.257271i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −49.4678 | −2.15077 | ||||||||
\(530\) | 5.93570 | 0.257830 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.38669 | + | 5.90604i | −0.320254 | + | 0.256060i | ||||
\(533\) | −0.258761 | + | 19.8583i | −0.0112082 | + | 0.860158i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.64052 | − | 6.64052i | −0.287095 | − | 0.287095i | ||||
\(536\) | −4.91583 | −0.212332 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −21.0604 | − | 21.0604i | −0.907979 | − | 0.907979i | ||||
\(539\) | −8.48871 | − | 13.4339i | −0.365635 | − | 0.578639i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.4800 | + | 18.4800i | 0.794518 | + | 0.794518i | 0.982225 | − | 0.187707i | \(-0.0601055\pi\) |
−0.187707 | + | 0.982225i | \(0.560105\pi\) | |||||||
\(542\) | − | 20.8134i | − | 0.894010i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.52763 | − | 4.52763i | 0.194120 | − | 0.194120i | ||||
\(545\) | 9.85240 | 0.422030 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.22661 | 0.137960 | 0.0689800 | − | 0.997618i | \(-0.478026\pi\) | ||||
0.0689800 | + | 0.997618i | \(0.478026\pi\) | |||||||
\(548\) | 1.82994 | − | 1.82994i | 0.0781711 | − | 0.0781711i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 10.3851i | 0.442821i | ||||||||
\(551\) | −19.9966 | − | 19.9966i | −0.851883 | − | 0.851883i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.1601 | + | 2.69114i | 1.02739 | + | 0.114439i | ||||
\(554\) | −17.0604 | − | 17.0604i | −0.724827 | − | 0.724827i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.8448 | −0.587149 | ||||||||
\(557\) | 27.1310 | + | 27.1310i | 1.14958 | + | 1.14958i | 0.986636 | + | 0.162939i | \(0.0520975\pi\) |
0.162939 | + | 0.986636i | \(0.447903\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.7851 | + | 10.5076i | −0.456161 | + | 0.444426i | ||||
\(560\) | −1.07762 | − | 1.34778i | −0.0455377 | − | 0.0569540i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.8970 | 0.459662 | ||||||||
\(563\) | −2.30304 | −0.0970614 | −0.0485307 | − | 0.998822i | \(-0.515454\pi\) | ||||
−0.0485307 | + | 0.998822i | \(0.515454\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.92968 | + | 6.92968i | 0.291534 | + | 0.291534i | ||||
\(566\) | −4.51935 | + | 4.51935i | −0.189962 | + | 0.189962i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.7284 | −0.492115 | ||||||||
\(569\) | − | 5.19115i | − | 0.217624i | −0.994062 | − | 0.108812i | \(-0.965295\pi\) | ||
0.994062 | − | 0.108812i | \(-0.0347047\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.8508i | 0.495941i | 0.968768 | + | 0.247970i | \(0.0797636\pi\) | ||||
−0.968768 | + | 0.247970i | \(0.920236\pi\) | |||||||
\(572\) | −8.18448 | − | 0.106647i | −0.342210 | − | 0.00445913i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −14.4837 | − | 1.61331i | −0.604537 | − | 0.0673381i | ||||
\(575\) | 38.9427 | 1.62402 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.5340 | − | 29.5340i | −1.22952 | − | 1.22952i | −0.964147 | − | 0.265369i | \(-0.914506\pi\) |
−0.265369 | − | 0.964147i | \(-0.585494\pi\) | |||||||
\(578\) | 16.9697 | − | 16.9697i | 0.705848 | − | 0.705848i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.64858 | − | 3.64858i | 0.151499 | − | 0.151499i | ||||
\(581\) | 23.3398 | + | 29.1911i | 0.968299 | + | 1.21105i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.6089 | + | 14.6089i | 0.605038 | + | 0.605038i | ||||
\(584\) | 8.34175 | 0.345184 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.6405i | 0.522175i | ||||||||
\(587\) | 11.2384 | + | 11.2384i | 0.463857 | + | 0.463857i | 0.899917 | − | 0.436060i | \(-0.143627\pi\) |
−0.436060 | + | 0.899917i | \(0.643627\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.66288i | 0.192131i | ||||||||
\(590\) | 0.768540 | − | 0.768540i | 0.0316403 | − | 0.0316403i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.953022 | + | 0.953022i | 0.0391690 | + | 0.0391690i | ||||
\(593\) | −7.99323 | + | 7.99323i | −0.328243 | + | 0.328243i | −0.851918 | − | 0.523675i | \(-0.824561\pi\) |
0.523675 | + | 0.851918i | \(0.324561\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.90002 | − | 8.62986i | −0.282873 | − | 0.353790i | ||||
\(596\) | −3.12824 | − | 3.12824i | −0.128138 | − | 0.128138i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.399911 | + | 30.6907i | −0.0163536 | + | 1.25504i | ||||
\(599\) | −25.0503 | −1.02353 | −0.511764 | − | 0.859126i | \(-0.671008\pi\) | ||||
−0.511764 | + | 0.859126i | \(0.671008\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.5478i | 0.471046i | 0.971869 | + | 0.235523i | \(0.0756803\pi\) | ||||
−0.971869 | + | 0.235523i | \(0.924320\pi\) | |||||||
\(602\) | −6.90002 | − | 8.62986i | −0.281224 | − | 0.351727i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11.5502 | − | 11.5502i | 0.469971 | − | 0.469971i | ||||
\(605\) | −2.69630 | + | 2.69630i | −0.109620 | + | 0.109620i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.2350i | 0.618369i | 0.951002 | + | 0.309185i | \(0.100056\pi\) | ||||
−0.951002 | + | 0.309185i | \(0.899944\pi\) | |||||||
\(608\) | −3.57461 | −0.144969 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 9.44903i | − | 0.382580i | ||||||
\(611\) | −7.21049 | − | 0.0939553i | −0.291705 | − | 0.00380103i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.5903 | − | 11.5903i | 0.468129 | − | 0.468129i | −0.433179 | − | 0.901308i | \(-0.642608\pi\) |
0.901308 | + | 0.433179i | \(0.142608\pi\) | |||||||
\(614\) | − | 1.79855i | − | 0.0725838i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.664914 | − | 5.96936i | 0.0267902 | − | 0.240512i | ||||
\(617\) | −14.5420 | + | 14.5420i | −0.585441 | + | 0.585441i | −0.936393 | − | 0.350952i | \(-0.885858\pi\) |
0.350952 | + | 0.936393i | \(0.385858\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.62482 | + | 7.62482i | −0.306467 | + | 0.306467i | −0.843538 | − | 0.537070i | \(-0.819531\pi\) |
0.537070 | + | 0.843538i | \(0.319531\pi\) | |||||||
\(620\) | −0.850789 | −0.0341685 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.07622 | − | 1.07622i | 0.0431527 | − | 0.0431527i | ||||
\(623\) | 24.9779 | − | 19.9711i | 1.00072 | − | 0.800125i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.8000 | −0.752002 | ||||||||
\(626\) | 2.46431 | + | 2.46431i | 0.0984937 | + | 0.0984937i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −18.5294 | −0.739402 | ||||||||
\(629\) | 6.10223 | + | 6.10223i | 0.243312 | + | 0.243312i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.8742 | + | 28.8742i | 1.14946 | + | 1.14946i | 0.986658 | + | 0.162807i | \(0.0520548\pi\) |
0.162807 | + | 0.986658i | \(0.447945\pi\) | |||||||
\(632\) | 6.49699 | + | 6.49699i | 0.258436 | + | 0.258436i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.11331i | 0.203076i | ||||||||
\(635\) | −7.28545 | + | 7.28545i | −0.289114 | + | 0.289114i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.2029 | + | 21.5101i | 0.523120 | + | 0.852259i | ||||
\(638\) | 17.9597 | 0.711031 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 0.652223i | − | 0.0257814i | ||||||
\(641\) | 13.9110i | 0.549453i | 0.961522 | + | 0.274726i | \(0.0885873\pi\) | ||||
−0.961522 | + | 0.274726i | \(0.911413\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.6768 | + | 31.6768i | 1.24921 | + | 1.24921i | 0.956068 | + | 0.293144i | \(0.0947017\pi\) |
0.293144 | + | 0.956068i | \(0.405298\pi\) | |||||||
\(644\) | −22.3843 | − | 2.49334i | −0.882066 | − | 0.0982514i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −22.8883 | −0.900529 | ||||||||
\(647\) | −2.61086 | −0.102644 | −0.0513218 | − | 0.998682i | \(-0.516343\pi\) | ||||
−0.0513218 | + | 0.998682i | \(0.516343\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.78305 | 0.148498 | ||||||||
\(650\) | 0.214904 | − | 16.4926i | 0.00842924 | − | 0.646892i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13.1032 | + | 13.1032i | −0.513162 | + | 0.513162i | ||||
\(653\) | −2.35132 | −0.0920144 | −0.0460072 | − | 0.998941i | \(-0.514650\pi\) | ||||
−0.0460072 | + | 0.998941i | \(0.514650\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.809494 | + | 0.809494i | −0.0316295 | + | 0.0316295i | ||||
\(656\) | −3.89486 | − | 3.89486i | −0.152069 | − | 0.152069i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.585786 | − | 5.25898i | 0.0228363 | − | 0.205016i | ||||
\(659\) | −13.1002 | −0.510312 | −0.255156 | − | 0.966900i | \(-0.582127\pi\) | ||||
−0.255156 | + | 0.966900i | \(0.582127\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.5885 | + | 12.5885i | −0.489636 | + | 0.489636i | −0.908191 | − | 0.418555i | \(-0.862537\pi\) |
0.418555 | + | 0.908191i | \(0.362537\pi\) | |||||||
\(662\) | − | 6.36625i | − | 0.247431i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.1263i | 0.548208i | ||||||||
\(665\) | −0.682863 | + | 6.13049i | −0.0264803 | + | 0.237730i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 67.3465i | − | 2.60767i | ||||||
\(668\) | 9.82552 | + | 9.82552i | 0.380161 | + | 0.380161i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.26714 | + | 2.26714i | −0.0875872 | + | 0.0875872i | ||||
\(671\) | 23.2559 | − | 23.2559i | 0.897782 | − | 0.897782i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 7.32134i | − | 0.282217i | −0.989994 | − | 0.141109i | \(-0.954933\pi\) | ||
0.989994 | − | 0.141109i | \(-0.0450667\pi\) | |||||||
\(674\) | −14.6605 | − | 14.6605i | −0.564701 | − | 0.564701i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.9956 | + | 0.338732i | 0.499830 | + | 0.0130282i | ||||
\(677\) | 27.2432i | 1.04704i | 0.852013 | + | 0.523520i | \(0.175381\pi\) | ||||
−0.852013 | + | 0.523520i | \(0.824619\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.636245 | − | 0.795752i | −0.0244168 | − | 0.0305381i | ||||
\(680\) | − | 4.17620i | − | 0.160150i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.09396 | − | 2.09396i | −0.0801817 | − | 0.0801817i | ||||
\(683\) | 3.89033 | + | 3.89033i | 0.148859 | + | 0.148859i | 0.777608 | − | 0.628749i | \(-0.216433\pi\) |
−0.628749 | + | 0.777608i | \(0.716433\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1.68790i | − | 0.0644914i | ||||||
\(686\) | −16.6555 | + | 8.09911i | −0.635908 | + | 0.309226i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 4.17620i | − | 0.159216i | ||||||
\(689\) | −22.8981 | − | 23.5027i | −0.872348 | − | 0.895382i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.75081 | + | 7.75081i | 0.294855 | + | 0.294855i | 0.838995 | − | 0.544140i | \(-0.183144\pi\) |
−0.544140 | + | 0.838995i | \(0.683144\pi\) | |||||||
\(692\) | − | 10.9940i | − | 0.417928i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.114040 | + | 0.114040i | −0.00432889 | + | 0.00432889i | ||||
\(695\) | −6.38508 | + | 6.38508i | −0.242200 | + | 0.242200i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.9389 | − | 24.9389i | −0.944630 | − | 0.944630i | ||||
\(698\) | − | 10.1540i | − | 0.384334i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 12.0289 | + | 1.33987i | 0.454649 | + | 0.0506424i | ||||
\(701\) | 5.02289i | 0.189712i | 0.995491 | + | 0.0948559i | \(0.0302390\pi\) | ||||
−0.995491 | + | 0.0948559i | \(0.969761\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 4.81777i | − | 0.181706i | ||||||
\(704\) | 1.60525 | − | 1.60525i | 0.0605000 | − | 0.0605000i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.3602 | 0.502819 | ||||||||
\(707\) | −21.1382 | − | 2.35454i | −0.794986 | − | 0.0885518i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.80002 | + | 4.80002i | 0.180269 | + | 0.180269i | 0.791473 | − | 0.611204i | \(-0.209315\pi\) |
−0.611204 | + | 0.791473i | \(0.709315\pi\) | |||||||
\(710\) | −5.40906 | + | 5.40906i | −0.202998 | + | 0.202998i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.0874 | 0.452995 | ||||||||
\(713\) | −7.85206 | + | 7.85206i | −0.294062 | + | 0.294062i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.82380 | + | 3.72543i | −0.143002 | + | 0.139323i | ||||
\(716\) | −2.54656 | −0.0951695 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 27.1434 | 1.01298 | ||||||||
\(719\) | 23.2670 | 0.867713 | 0.433857 | − | 0.900982i | \(-0.357152\pi\) | ||||
0.433857 | + | 0.900982i | \(0.357152\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.0613 | + | 2.23458i | 0.747120 | + | 0.0832201i | ||||
\(722\) | −4.39976 | − | 4.39976i | −0.163742 | − | 0.163742i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13.8933i | 0.516339i | ||||||||
\(725\) | 36.1906i | 1.34409i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.8368 | 1.10659 | 0.553293 | − | 0.832987i | \(-0.313371\pi\) | ||||
0.553293 | + | 0.832987i | \(0.313371\pi\) | |||||||
\(728\) | −1.17948 | + | 9.46619i | −0.0437144 | + | 0.350840i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.84714 | − | 3.84714i | 0.142389 | − | 0.142389i | ||||
\(731\) | − | 26.7404i | − | 0.989028i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.7443 | + | 11.7443i | 0.433784 | + | 0.433784i | 0.889913 | − | 0.456129i | \(-0.150765\pi\) |
−0.456129 | + | 0.889913i | \(0.650765\pi\) | |||||||
\(734\) | 17.1928 | + | 17.1928i | 0.634596 | + | 0.634596i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.01946 | − | 6.01946i | −0.221880 | − | 0.221880i | ||||
\(737\) | −11.1597 | −0.411074 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.9136 | − | 21.9136i | −0.806103 | − | 0.806103i | 0.177938 | − | 0.984042i | \(-0.443057\pi\) |
−0.984042 | + | 0.177938i | \(0.943057\pi\) | |||||||
\(740\) | 0.879051 | 0.0323146 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 18.8061 | − | 15.0364i | 0.690392 | − | 0.552004i | ||||
\(743\) | −8.70770 | + | 8.70770i | −0.319454 | + | 0.319454i | −0.848558 | − | 0.529103i | \(-0.822528\pi\) |
0.529103 | + | 0.848558i | \(0.322528\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.88544 | −0.105714 | ||||||||
\(746\) | 6.89184 | − | 6.89184i | 0.252328 | − | 0.252328i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10.2784 | − | 10.2784i | 0.375817 | − | 0.375817i | ||||
\(749\) | −37.8610 | − | 4.21726i | −1.38341 | − | 0.154095i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.2765i | 1.25077i | 0.780318 | + | 0.625384i | \(0.215057\pi\) | ||||
−0.780318 | + | 0.625384i | \(0.784943\pi\) | |||||||
\(752\) | 1.41421 | − | 1.41421i | 0.0515711 | − | 0.0515711i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −28.5218 | − | 0.371650i | −1.03870 | − | 0.0135347i | ||||
\(755\) | − | 10.6537i | − | 0.387728i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.0153 | −1.01823 | −0.509117 | − | 0.860697i | \(-0.670028\pi\) | ||||
−0.509117 | + | 0.860697i | \(0.670028\pi\) | |||||||
\(758\) | − | 20.6159i | − | 0.748802i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.64858 | + | 1.64858i | −0.0598002 | + | 0.0598002i | ||||
\(761\) | 24.7400 | − | 24.7400i | 0.896824 | − | 0.896824i | −0.0983300 | − | 0.995154i | \(-0.531350\pi\) |
0.995154 | + | 0.0983300i | \(0.0313501\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 31.2153 | − | 24.9583i | 1.13007 | − | 0.903550i | ||||
\(764\) | − | 10.2290i | − | 0.370071i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 29.5065 | 1.06611 | ||||||||
\(767\) | −6.00787 | − | 0.0782847i | −0.216932 | − | 0.00282670i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.3745 | − | 24.3745i | −0.878968 | − | 0.878968i | 0.114460 | − | 0.993428i | \(-0.463486\pi\) |
−0.993428 | + | 0.114460i | \(0.963486\pi\) | |||||||
\(770\) | −2.44636 | − | 3.05967i | −0.0881608 | − | 0.110263i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 12.3940 | − | 12.3940i | 0.446069 | − | 0.446069i | ||||
\(773\) | 21.0774 | + | 21.0774i | 0.758100 | + | 0.758100i | 0.975976 | − | 0.217876i | \(-0.0699128\pi\) |
−0.217876 | + | 0.975976i | \(0.569913\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.21954 | − | 4.21954i | 0.151570 | − | 0.151570i | ||||
\(776\) | − | 0.385084i | − | 0.0138237i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.30855 | + | 4.30855i | 0.154469 | + | 0.154469i | ||||
\(779\) | 19.6895i | 0.705451i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.6254 | −0.952733 | ||||||||
\(782\) | −38.5428 | − | 38.5428i | −1.37829 | − | 1.37829i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.82843 | − | 1.54032i | −0.243872 | − | 0.0550114i | ||||
\(785\) | −8.54558 | + | 8.54558i | −0.305005 | + | 0.305005i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.03100 | − | 5.03100i | 0.179336 | − | 0.179336i | −0.611730 | − | 0.791066i | \(-0.709526\pi\) |
0.791066 | + | 0.611730i | \(0.209526\pi\) | |||||||
\(788\) | 8.84638 | + | 8.84638i | 0.315139 | + | 0.315139i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.99271 | 0.213211 | ||||||||
\(791\) | 39.5097 | + | 4.40090i | 1.40480 | + | 0.156478i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −37.4139 | + | 36.4514i | −1.32861 | + | 1.29443i | ||||
\(794\) | 38.1544i | 1.35405i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.40980i | 0.262633i | ||||||||
\(797\) | 35.6777 | 1.26377 | 0.631884 | − | 0.775063i | \(-0.282282\pi\) | ||||
0.631884 | + | 0.775063i | \(0.282282\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.05526 | − | 9.05526i | 0.320352 | − | 0.320352i | ||||
\(800\) | 3.23473 | + | 3.23473i | 0.114365 | + | 0.114365i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −30.3496 | −1.07168 | ||||||||
\(803\) | 18.9371 | 0.668276 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.4734 | + | 9.17354i | −0.404383 | + | 0.323325i | ||||
\(806\) | 3.28208 | + | 3.36875i | 0.115606 | + | 0.118659i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.68437 | − | 5.68437i | −0.199976 | − | 0.199976i | ||||
\(809\) | 24.7540 | 0.870306 | 0.435153 | − | 0.900357i | \(-0.356694\pi\) | ||||
0.435153 | + | 0.900357i | \(0.356694\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.5605 | + | 19.5605i | 0.686863 | + | 0.686863i | 0.961537 | − | 0.274674i | \(-0.0885701\pi\) |
−0.274674 | + | 0.961537i | \(0.588570\pi\) | |||||||
\(812\) | 2.31714 | − | 20.8024i | 0.0813156 | − | 0.730022i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.16351 | + | 2.16351i | 0.0758311 | + | 0.0758311i | ||||
\(815\) | 12.0862i | 0.423360i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.5559 | + | 10.5559i | −0.369304 | + | 0.369304i | ||||
\(818\) | 5.95240 | 0.208121 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.59255 | −0.125457 | ||||||||
\(821\) | −8.90959 | + | 8.90959i | −0.310947 | + | 0.310947i | −0.845276 | − | 0.534329i | \(-0.820564\pi\) |
0.534329 | + | 0.845276i | \(0.320564\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.11934i | 0.213307i | 0.994296 | + | 0.106653i | \(0.0340135\pi\) | ||||
−0.994296 | + | 0.106653i | \(0.965986\pi\) | |||||||
\(824\) | 5.39475 | + | 5.39475i | 0.187935 | + | 0.187935i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.488084 | − | 4.38185i | 0.0169826 | − | 0.152464i | ||||
\(827\) | 26.8873 | + | 26.8873i | 0.934964 | + | 0.934964i | 0.998011 | − | 0.0630466i | \(-0.0200817\pi\) |
−0.0630466 | + | 0.998011i | \(0.520082\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.1247 | 1.08101 | 0.540503 | − | 0.841342i | \(-0.318234\pi\) | ||||
0.540503 | + | 0.841342i | \(0.318234\pi\) | |||||||
\(830\) | 6.51494 | + | 6.51494i | 0.226137 | + | 0.226137i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.58251 | + | 2.51608i | −0.0895325 | + | 0.0872292i | ||||
\(833\) | −43.7226 | − | 9.86271i | −1.51490 | − | 0.341723i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.06289 | 0.313634 | ||||||||
\(836\) | −8.11492 | −0.280661 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.67771 | − | 2.67771i | −0.0924998 | − | 0.0924998i | ||||
\(839\) | 9.22932 | − | 9.22932i | 0.318632 | − | 0.318632i | −0.529610 | − | 0.848241i | \(-0.677662\pi\) |
0.848241 | + | 0.529610i | \(0.177662\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33.5871 | 1.15818 | ||||||||
\(842\) | 23.0136i | 0.793099i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 14.6299i | − | 0.503581i | ||||||
\(845\) | 6.14967 | − | 5.83723i | 0.211555 | − | 0.200807i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.71236 | + | 15.3730i | −0.0588375 | + | 0.528222i | ||||
\(848\) | 9.10072 | 0.312520 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 20.7121 | + | 20.7121i | 0.710419 | + | 0.710419i | ||||
\(851\) | 8.11289 | − | 8.11289i | 0.278106 | − | 0.278106i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.34638 | − | 9.34638i | 0.320014 | − | 0.320014i | −0.528758 | − | 0.848772i | \(-0.677342\pi\) |
0.848772 | + | 0.528758i | \(0.177342\pi\) | |||||||
\(854\) | −23.9364 | − | 29.9373i | −0.819088 | − | 1.02443i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.1814 | − | 10.1814i | −0.347992 | − | 0.347992i | ||||
\(857\) | −55.3845 | −1.89190 | −0.945949 | − | 0.324315i | \(-0.894866\pi\) | ||||
−0.945949 | + | 0.324315i | \(0.894866\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.0994i | 1.43641i | 0.695830 | + | 0.718206i | \(0.255037\pi\) | ||||
−0.695830 | + | 0.718206i | \(0.744963\pi\) | |||||||
\(860\) | −1.92603 | − | 1.92603i | −0.0656770 | − | 0.0656770i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 25.0434i | − | 0.852982i | ||||||
\(863\) | 3.47410 | − | 3.47410i | 0.118260 | − | 0.118260i | −0.645500 | − | 0.763760i | \(-0.723351\pi\) |
0.763760 | + | 0.645500i | \(0.223351\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.07032 | − | 5.07032i | −0.172396 | − | 0.172396i | ||||
\(866\) | −9.34034 | + | 9.34034i | −0.317398 | + | 0.317398i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.69555 | + | 2.15524i | −0.0914931 | + | 0.0731534i | ||||
\(869\) | 14.7492 | + | 14.7492i | 0.500332 | + | 0.500332i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.7228 | + | 0.230934i | 0.600514 | + | 0.00782491i | ||||
\(872\) | 15.1059 | 0.511550 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 30.4299i | 1.02931i | ||||||||
\(875\) | 12.9044 | − | 10.3178i | 0.436249 | − | 0.348804i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.8673 | − | 16.8673i | 0.569570 | − | 0.569570i | −0.362438 | − | 0.932008i | \(-0.618056\pi\) |
0.932008 | + | 0.362438i | \(0.118056\pi\) | |||||||
\(878\) | −19.2784 | + | 19.2784i | −0.650616 | + | 0.650616i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 1.48065i | − | 0.0499127i | ||||||
\(881\) | −28.2254 | −0.950939 | −0.475470 | − | 0.879732i | \(-0.657722\pi\) | ||||
−0.475470 | + | 0.879732i | \(0.657722\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.1795i | 1.41945i | 0.704478 | + | 0.709726i | \(0.251181\pi\) | ||||
−0.704478 | + | 0.709726i | \(0.748819\pi\) | |||||||
\(884\) | −16.5359 | + | 16.1105i | −0.556163 | + | 0.541855i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.8128 | + | 15.8128i | −0.531242 | + | 0.531242i | ||||
\(887\) | 57.2398i | 1.92192i | 0.276682 | + | 0.960962i | \(0.410765\pi\) | ||||
−0.276682 | + | 0.960962i | \(0.589235\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.62684 | + | 41.5381i | −0.155179 | + | 1.39314i | ||||
\(890\) | 5.57461 | − | 5.57461i | 0.186861 | − | 0.186861i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.0574 | + | 11.0574i | −0.370229 | + | 0.370229i | ||||
\(893\) | −7.14921 | −0.239239 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.17445 | + | 1.17445i | −0.0392576 | + | 0.0392576i | ||||
\(896\) | −1.65222 | − | 2.06644i | −0.0551969 | − | 0.0690348i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.76168 | −0.158899 | ||||||||
\(899\) | −7.29715 | − | 7.29715i | −0.243374 | − | 0.243374i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 58.2722 | 1.94133 | ||||||||
\(902\) | −8.84196 | − | 8.84196i | −0.294405 | − | 0.294405i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.6247 | + | 10.6247i | 0.353372 | + | 0.353372i | ||||
\(905\) | 6.40745 | + | 6.40745i | 0.212991 | + | 0.212991i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.7641i | 0.955097i | 0.878605 | + | 0.477549i | \(0.158475\pi\) | ||||
−0.878605 | + | 0.477549i | \(0.841525\pi\) | |||||||
\(908\) | −9.31423 | + | 9.31423i | −0.309104 | + | 0.309104i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.82176 | + | 4.90969i | 0.126690 | + | 0.162755i | ||||
\(911\) | −27.0639 | −0.896666 | −0.448333 | − | 0.893867i | \(-0.647982\pi\) | ||||
−0.448333 | + | 0.893867i | \(0.647982\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.0690i | 1.06133i | ||||||||
\(914\) | 17.6819i | 0.584866i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.5860 | + | 15.5860i | 0.514976 | + | 0.514976i | ||||
\(917\) | −0.514093 | + | 4.61534i | −0.0169768 | + | 0.152412i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.1464 | 1.25833 | 0.629167 | − | 0.777270i | \(-0.283396\pi\) | ||||
0.629167 | + | 0.777270i | \(0.283396\pi\) | |||||||
\(920\) | −5.55224 | −0.183052 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.70945 | −0.188031 | ||||||||
\(923\) | 42.2839 | + | 0.550975i | 1.39179 | + | 0.0181356i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.35970 | + | 4.35970i | −0.143346 | + | 0.143346i | ||||
\(926\) | −18.1373 | −0.596028 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.59406 | − | 5.59406i | 0.183634 | − | 0.183634i | ||||
\(929\) | 11.1005 | + | 11.1005i | 0.364196 | + | 0.364196i | 0.865355 | − | 0.501159i | \(-0.167093\pi\) |
−0.501159 | + | 0.865355i | \(0.667093\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.3664 | + | 21.1531i | 0.438065 | + | 0.693264i | ||||
\(932\) | −14.4240 | −0.472474 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −12.0406 | + | 12.0406i | −0.393982 | + | 0.393982i | ||||
\(935\) | − | 9.48065i | − | 0.310050i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 47.2311i | − | 1.54297i | −0.636245 | − | 0.771487i | \(-0.719513\pi\) | ||
0.636245 | − | 0.771487i | \(-0.280487\pi\) | |||||||
\(938\) | −1.43981 | + | 12.9261i | −0.0470116 | + | 0.422053i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | − | 1.30445i | − | 0.0425463i | ||||||
\(941\) | 27.0580 | + | 27.0580i | 0.882065 | + | 0.882065i | 0.993744 | − | 0.111680i | \(-0.0356231\pi\) |
−0.111680 | + | 0.993744i | \(0.535623\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −33.1562 | + | 33.1562i | −1.07971 | + | 1.07971i | ||||
\(944\) | 1.17834 | − | 1.17834i | 0.0383517 | − | 0.0383517i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 9.48065i | − | 0.308243i | ||||||
\(947\) | 14.2815 | + | 14.2815i | 0.464085 | + | 0.464085i | 0.899992 | − | 0.435907i | \(-0.143572\pi\) |
−0.435907 | + | 0.899992i | \(0.643572\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.0741 | − | 0.391876i | −0.976245 | − | 0.0127208i | ||||
\(950\) | − | 16.3524i | − | 0.530542i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −10.5792 | − | 13.2315i | −0.342875 | − | 0.428834i | ||||
\(953\) | − | 6.01656i | − | 0.194895i | −0.995241 | − | 0.0974477i | \(-0.968932\pi\) | ||
0.995241 | − | 0.0974477i | \(-0.0310679\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.71751 | − | 4.71751i | −0.152655 | − | 0.152655i | ||||
\(956\) | 3.83747 | + | 3.83747i | 0.124113 | + | 0.124113i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 32.1601i | − | 1.03905i | ||||||
\(959\) | −4.27582 | − | 5.34778i | −0.138074 | − | 0.172689i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 29.2984i | − | 0.945110i | ||||||
\(962\) | −3.39111 | − | 3.48065i | −0.109334 | − | 0.112221i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 14.2110 | + | 14.2110i | 0.457706 | + | 0.457706i | ||||
\(965\) | − | 11.4320i | − | 0.368009i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.0413 | + | 29.0413i | −0.933906 | + | 0.933906i | −0.997947 | − | 0.0640416i | \(-0.979601\pi\) |
0.0640416 | + | 0.997947i | \(0.479601\pi\) | |||||||
\(968\) | −4.13401 | + | 4.13401i | −0.132872 | + | 0.132872i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.177597 | − | 0.177597i | −0.00570231 | − | 0.00570231i | ||||
\(971\) | − | 37.3180i | − | 1.19759i | −0.800902 | − | 0.598795i | \(-0.795646\pi\) | ||
0.800902 | − | 0.598795i | \(-0.204354\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.05504 | + | 36.4047i | −0.129999 | + | 1.16708i | ||||
\(974\) | 11.8899i | 0.380978i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 14.4874i | − | 0.463731i | ||||||
\(977\) | 4.00859 | − | 4.00859i | 0.128246 | − | 0.128246i | −0.640070 | − | 0.768316i | \(-0.721095\pi\) |
0.768316 | + | 0.640070i | \(0.221095\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.4403 | 0.876997 | ||||||||
\(980\) | −3.85959 | + | 2.43883i | −0.123290 | + | 0.0779055i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8.70800 | + | 8.70800i | 0.277884 | + | 0.277884i | ||||
\(983\) | 20.0717 | − | 20.0717i | 0.640188 | − | 0.640188i | −0.310414 | − | 0.950601i | \(-0.600468\pi\) |
0.950601 | + | 0.310414i | \(0.100468\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.15974 | 0.259991 | ||||||||
\(986\) | 35.8190 | − | 35.8190i | 1.14071 | − | 1.14071i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 12.8873 | + | 0.167927i | 0.410001 | + | 0.00534246i | ||||
\(989\) | −35.5512 | −1.13046 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.1309 | −0.512415 | −0.256208 | − | 0.966622i | \(-0.582473\pi\) | ||||
−0.256208 | + | 0.966622i | \(0.582473\pi\) | |||||||
\(992\) | −1.30445 | −0.0414162 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.43518 | + | 30.8398i | −0.108957 | + | 0.978180i | ||||
\(995\) | 3.41733 | + | 3.41733i | 0.108337 | + | 0.108337i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.1324i | 1.01764i | 0.860872 | + | 0.508821i | \(0.169919\pi\) | ||||
−0.860872 | + | 0.508821i | \(0.830081\pi\) | |||||||
\(998\) | − | 5.84446i | − | 0.185003i | ||||||
\(999\) | 0 | 0 |
(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 | 1638.2.x.c.811.3 | 8 | ||
3.2 | odd | 2 | 546.2.o.b.265.2 | ✓ | 8 | ||
7.6 | odd | 2 | 1638.2.x.a.811.4 | 8 | |||
13.8 | odd | 4 | 1638.2.x.a.307.4 | 8 | |||
21.20 | even | 2 | 546.2.o.c.265.1 | yes | 8 | ||
39.8 | even | 4 | 546.2.o.c.307.1 | yes | 8 | ||
91.34 | even | 4 | inner | 1638.2.x.c.307.3 | 8 | ||
273.125 | odd | 4 | 546.2.o.b.307.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.o.b.265.2 | ✓ | 8 | 3.2 | odd | 2 | ||
546.2.o.b.307.2 | yes | 8 | 273.125 | odd | 4 | ||
546.2.o.c.265.1 | yes | 8 | 21.20 | even | 2 | ||
546.2.o.c.307.1 | yes | 8 | 39.8 | even | 4 | ||
1638.2.x.a.307.4 | 8 | 13.8 | odd | 4 | |||
1638.2.x.a.811.4 | 8 | 7.6 | odd | 2 | |||
1638.2.x.c.307.3 | 8 | 91.34 | even | 4 | inner | ||
1638.2.x.c.811.3 | 8 | 1.1 | even | 1 | trivial |