Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(265,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.265");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.o (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.35983195036\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 265.1 | ||
Root | \(-1.65222i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.265 |
Dual form | 546.2.o.c.307.1 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −0.461191 | − | 0.461191i | −0.206251 | − | 0.206251i | 0.596421 | − | 0.802672i | \(-0.296589\pi\) |
−0.802672 | + | 0.596421i | \(0.796589\pi\) | |||||||
\(6\) | −0.707107 | − | 0.707107i | −0.288675 | − | 0.288675i | ||||
\(7\) | −0.292893 | − | 2.62949i | −0.110703 | − | 0.993854i | ||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0.652223 | 0.206251 | ||||||||
\(11\) | 1.60525 | + | 1.60525i | 0.484000 | + | 0.484000i | 0.906406 | − | 0.422407i | \(-0.138815\pi\) |
−0.422407 | + | 0.906406i | \(0.638815\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −2.51608 | − | 2.58251i | −0.697834 | − | 0.716260i | ||||
\(14\) | 2.06644 | + | 1.65222i | 0.552278 | + | 0.441575i | ||||
\(15\) | 0.461191 | − | 0.461191i | 0.119079 | − | 0.119079i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −6.40303 | −1.55296 | −0.776482 | − | 0.630140i | \(-0.782998\pi\) | ||||
−0.776482 | + | 0.630140i | \(0.782998\pi\) | |||||||
\(18\) | 0.707107 | − | 0.707107i | 0.166667 | − | 0.166667i | ||||
\(19\) | −2.52763 | − | 2.52763i | −0.579878 | − | 0.579878i | 0.354992 | − | 0.934869i | \(-0.384484\pi\) |
−0.934869 | + | 0.354992i | \(0.884484\pi\) | |||||||
\(20\) | −0.461191 | + | 0.461191i | −0.103125 | + | 0.103125i | ||||
\(21\) | 2.62949 | − | 0.292893i | 0.573802 | − | 0.0639145i | ||||
\(22\) | −2.27016 | −0.484000 | ||||||||
\(23\) | − | 8.51280i | − | 1.77504i | −0.460768 | − | 0.887521i | \(-0.652426\pi\) | ||
0.460768 | − | 0.887521i | \(-0.347574\pi\) | |||||||
\(24\) | −0.707107 | + | 0.707107i | −0.144338 | + | 0.144338i | ||||
\(25\) | − | 4.57461i | − | 0.914921i | ||||||
\(26\) | 3.60525 | + | 0.0469777i | 0.707047 | + | 0.00921308i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −2.62949 | + | 0.292893i | −0.496927 | + | 0.0553516i | ||||
\(29\) | 7.91120 | 1.46907 | 0.734537 | − | 0.678569i | \(-0.237400\pi\) | ||||
0.734537 | + | 0.678569i | \(0.237400\pi\) | |||||||
\(30\) | 0.652223i | 0.119079i | ||||||||
\(31\) | −0.922382 | − | 0.922382i | −0.165665 | − | 0.165665i | 0.619406 | − | 0.785071i | \(-0.287373\pi\) |
−0.785071 | + | 0.619406i | \(0.787373\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | −1.60525 | + | 1.60525i | −0.279437 | + | 0.279437i | ||||
\(34\) | 4.52763 | − | 4.52763i | 0.776482 | − | 0.776482i | ||||
\(35\) | −1.07762 | + | 1.34778i | −0.182151 | + | 0.227816i | ||||
\(36\) | 1.00000i | 0.166667i | ||||||||
\(37\) | −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 | ||||||||
\(39\) | 2.58251 | − | 2.51608i | 0.413533 | − | 0.402894i | ||||
\(40\) | − | 0.652223i | − | 0.103125i | ||||||
\(41\) | 3.89486 | + | 3.89486i | 0.608275 | + | 0.608275i | 0.942495 | − | 0.334220i | \(-0.108473\pi\) |
−0.334220 | + | 0.942495i | \(0.608473\pi\) | |||||||
\(42\) | −1.65222 | + | 2.06644i | −0.254944 | + | 0.318858i | ||||
\(43\) | 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 | ||||
\(45\) | 0.461191 | + | 0.461191i | 0.0687503 | + | 0.0687503i | ||||
\(46\) | 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 | \(0.296597\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | −6.82843 | + | 1.54032i | −0.975490 | + | 0.220046i | ||||
\(50\) | 3.23473 | + | 3.23473i | 0.457461 | + | 0.457461i | ||||
\(51\) | − | 6.40303i | − | 0.896604i | ||||||
\(52\) | −2.58251 | + | 2.51608i | −0.358130 | + | 0.348917i | ||||
\(53\) | 9.10072 | 1.25008 | 0.625040 | − | 0.780593i | \(-0.285083\pi\) | ||||
0.625040 | + | 0.780593i | \(0.285083\pi\) | |||||||
\(54\) | 0.707107 | + | 0.707107i | 0.0962250 | + | 0.0962250i | ||||
\(55\) | − | 1.48065i | − | 0.199651i | ||||||
\(56\) | 1.65222 | − | 2.06644i | 0.220788 | − | 0.276139i | ||||
\(57\) | 2.52763 | − | 2.52763i | 0.334792 | − | 0.334792i | ||||
\(58\) | −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 | \(0.284597\pi\) | |||||||
\(60\) | −0.461191 | − | 0.461191i | −0.0595395 | − | 0.0595395i | ||||
\(61\) | − | 14.4874i | − | 1.85492i | −0.373918 | − | 0.927462i | \(-0.621986\pi\) | ||
0.373918 | − | 0.927462i | \(-0.378014\pi\) | |||||||
\(62\) | 1.30445 | 0.165665 | ||||||||
\(63\) | 0.292893 | + | 2.62949i | 0.0369011 | + | 0.331285i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −0.0306399 | + | 2.35142i | −0.00380041 | + | 0.291658i | ||||
\(66\) | − | 2.27016i | − | 0.279437i | ||||||
\(67\) | 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 | ||||||||
\(69\) | 8.51280 | 1.02482 | ||||||||
\(70\) | −0.191032 | − | 1.71501i | −0.0228327 | − | 0.204983i | ||||
\(71\) | −8.29326 | + | 8.29326i | −0.984229 | + | 0.984229i | −0.999878 | − | 0.0156481i | \(-0.995019\pi\) |
0.0156481 | + | 0.999878i | \(0.495019\pi\) | |||||||
\(72\) | −0.707107 | − | 0.707107i | −0.0833333 | − | 0.0833333i | ||||
\(73\) | 5.89851 | − | 5.89851i | 0.690368 | − | 0.690368i | −0.271945 | − | 0.962313i | \(-0.587667\pi\) |
0.962313 | + | 0.271945i | \(0.0876667\pi\) | |||||||
\(74\) | 1.34778 | 0.156676 | ||||||||
\(75\) | 4.57461 | 0.528230 | ||||||||
\(76\) | −2.52763 | + | 2.52763i | −0.289939 | + | 0.289939i | ||||
\(77\) | 3.75081 | − | 4.69114i | 0.427444 | − | 0.534605i | ||||
\(78\) | −0.0469777 | + | 3.60525i | −0.00531917 | + | 0.408214i | ||||
\(79\) | −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 | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.50817 | −0.608275 | ||||||||
\(83\) | −9.98882 | − | 9.98882i | −1.09642 | − | 1.09642i | −0.994826 | − | 0.101589i | \(-0.967607\pi\) |
−0.101589 | − | 0.994826i | \(-0.532393\pi\) | |||||||
\(84\) | −0.292893 | − | 2.62949i | −0.0319573 | − | 0.286901i | ||||
\(85\) | 2.95302 | + | 2.95302i | 0.320300 | + | 0.320300i | ||||
\(86\) | −2.95302 | − | 2.95302i | −0.318433 | − | 0.318433i | ||||
\(87\) | 7.91120i | 0.848170i | ||||||||
\(88\) | 2.27016i | 0.242000i | ||||||||
\(89\) | −8.54709 | + | 8.54709i | −0.905989 | + | 0.905989i | −0.995946 | − | 0.0899564i | \(-0.971327\pi\) |
0.0899564 | + | 0.995946i | \(0.471327\pi\) | |||||||
\(90\) | −0.652223 | −0.0687503 | ||||||||
\(91\) | −6.05374 | + | 7.37239i | −0.634605 | + | 0.772837i | ||||
\(92\) | −8.51280 | −0.887521 | ||||||||
\(93\) | 0.922382 | − | 0.922382i | 0.0956466 | − | 0.0956466i | ||||
\(94\) | − | 2.00000i | − | 0.206284i | ||||||
\(95\) | 2.33144i | 0.239201i | ||||||||
\(96\) | 0.707107 | + | 0.707107i | 0.0721688 | + | 0.0721688i | ||||
\(97\) | −0.272296 | − | 0.272296i | −0.0276474 | − | 0.0276474i | 0.693148 | − | 0.720795i | \(-0.256223\pi\) |
−0.720795 | + | 0.693148i | \(0.756223\pi\) | |||||||
\(98\) | 3.73926 | − | 5.91760i | 0.377722 | − | 0.597768i | ||||
\(99\) | −1.60525 | − | 1.60525i | −0.161333 | − | 0.161333i | ||||
\(100\) | −4.57461 | −0.457461 | ||||||||
\(101\) | 8.03892 | 0.799902 | 0.399951 | − | 0.916536i | \(-0.369027\pi\) | ||||
0.399951 | + | 0.916536i | \(0.369027\pi\) | |||||||
\(102\) | 4.52763 | + | 4.52763i | 0.448302 | + | 0.448302i | ||||
\(103\) | 7.62934 | 0.751741 | 0.375870 | − | 0.926672i | \(-0.377344\pi\) | ||||
0.375870 | + | 0.926672i | \(0.377344\pi\) | |||||||
\(104\) | 0.0469777 | − | 3.60525i | 0.00460654 | − | 0.353523i | ||||
\(105\) | −1.34778 | − | 1.07762i | −0.131530 | − | 0.105165i | ||||
\(106\) | −6.43518 | + | 6.43518i | −0.625040 | + | 0.625040i | ||||
\(107\) | −14.3986 | −1.39197 | −0.695984 | − | 0.718058i | \(-0.745031\pi\) | ||||
−0.695984 | + | 0.718058i | \(0.745031\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −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 | ||||
\(111\) | 0.953022 | − | 0.953022i | 0.0904569 | − | 0.0904569i | ||||
\(112\) | 0.292893 | + | 2.62949i | 0.0276758 | + | 0.248463i | ||||
\(113\) | 15.0256 | 1.41349 | 0.706745 | − | 0.707469i | \(-0.250163\pi\) | ||||
0.706745 | + | 0.707469i | \(0.250163\pi\) | |||||||
\(114\) | 3.57461i | 0.334792i | ||||||||
\(115\) | −3.92603 | + | 3.92603i | −0.366104 | + | 0.366104i | ||||
\(116\) | − | 7.91120i | − | 0.734537i | ||||||
\(117\) | 2.51608 | + | 2.58251i | 0.232611 | + | 0.238753i | ||||
\(118\) | − | 1.66642i | − | 0.153407i | ||||||
\(119\) | 1.87540 | + | 16.8367i | 0.171918 | + | 1.54342i | ||||
\(120\) | 0.652223 | 0.0595395 | ||||||||
\(121\) | − | 5.84638i | − | 0.531489i | ||||||
\(122\) | 10.2442 | + | 10.2442i | 0.927462 | + | 0.927462i | ||||
\(123\) | −3.89486 | + | 3.89486i | −0.351188 | + | 0.351188i | ||||
\(124\) | −0.922382 | + | 0.922382i | −0.0828324 | + | 0.0828324i | ||||
\(125\) | −4.41572 | + | 4.41572i | −0.394954 | + | 0.394954i | ||||
\(126\) | −2.06644 | − | 1.65222i | −0.184093 | − | 0.147192i | ||||
\(127\) | − | 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 | ||||
\(129\) | −4.17620 | −0.367694 | ||||||||
\(130\) | −1.64104 | − | 1.68437i | −0.143929 | − | 0.147729i | ||||
\(131\) | − | 1.75522i | − | 0.153355i | −0.997056 | − | 0.0766773i | \(-0.975569\pi\) | ||
0.997056 | − | 0.0766773i | \(-0.0244311\pi\) | |||||||
\(132\) | 1.60525 | + | 1.60525i | 0.139719 | + | 0.139719i | ||||
\(133\) | −5.90604 | + | 7.38669i | −0.512119 | + | 0.640508i | ||||
\(134\) | 4.91583i | 0.424663i | ||||||||
\(135\) | −0.461191 | + | 0.461191i | −0.0396930 | + | 0.0396930i | ||||
\(136\) | −4.52763 | − | 4.52763i | −0.388241 | − | 0.388241i | ||||
\(137\) | −1.82994 | − | 1.82994i | −0.156342 | − | 0.156342i | 0.624602 | − | 0.780944i | \(-0.285261\pi\) |
−0.780944 | + | 0.624602i | \(0.785261\pi\) | |||||||
\(138\) | −6.01946 | + | 6.01946i | −0.512410 | + | 0.512410i | ||||
\(139\) | 13.8448i | 1.17430i | 0.809479 | + | 0.587149i | \(0.199750\pi\) | ||||
−0.809479 | + | 0.587149i | \(0.800250\pi\) | |||||||
\(140\) | 1.34778 | + | 1.07762i | 0.113908 | + | 0.0910753i | ||||
\(141\) | −1.41421 | − | 1.41421i | −0.119098 | − | 0.119098i | ||||
\(142\) | − | 11.7284i | − | 0.984229i | ||||||
\(143\) | 0.106647 | − | 8.18448i | 0.00891825 | − | 0.684421i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −3.64858 | − | 3.64858i | −0.302998 | − | 0.302998i | ||||
\(146\) | 8.34175i | 0.690368i | ||||||||
\(147\) | −1.54032 | − | 6.82843i | −0.127043 | − | 0.563199i | ||||
\(148\) | −0.953022 | + | 0.953022i | −0.0783380 | + | 0.0783380i | ||||
\(149\) | −3.12824 | + | 3.12824i | −0.256276 | + | 0.256276i | −0.823537 | − | 0.567262i | \(-0.808003\pi\) |
0.567262 | + | 0.823537i | \(0.308003\pi\) | |||||||
\(150\) | −3.23473 | + | 3.23473i | −0.264115 | + | 0.264115i | ||||
\(151\) | 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 | ||||||
\(153\) | 6.40303 | 0.517654 | ||||||||
\(154\) | 0.664914 | + | 5.96936i | 0.0535803 | + | 0.481025i | ||||
\(155\) | 0.850789i | 0.0683370i | ||||||||
\(156\) | −2.51608 | − | 2.58251i | −0.201447 | − | 0.206766i | ||||
\(157\) | 18.5294i | 1.47880i | 0.673264 | + | 0.739402i | \(0.264892\pi\) | ||||
−0.673264 | + | 0.739402i | \(0.735108\pi\) | |||||||
\(158\) | 6.49699 | − | 6.49699i | 0.516873 | − | 0.516873i | ||||
\(159\) | 9.10072i | 0.721734i | ||||||||
\(160\) | −0.652223 | −0.0515627 | ||||||||
\(161\) | −22.3843 | + | 2.49334i | −1.76413 | + | 0.196503i | ||||
\(162\) | −0.707107 | + | 0.707107i | −0.0555556 | + | 0.0555556i | ||||
\(163\) | −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 | ||||
\(165\) | 1.48065 | 0.115268 | ||||||||
\(166\) | 14.1263 | 1.09642 | ||||||||
\(167\) | −9.82552 | + | 9.82552i | −0.760322 | + | 0.760322i | −0.976380 | − | 0.216059i | \(-0.930680\pi\) |
0.216059 | + | 0.976380i | \(0.430680\pi\) | |||||||
\(168\) | 2.06644 | + | 1.65222i | 0.159429 | + | 0.127472i | ||||
\(169\) | −0.338732 | + | 12.9956i | −0.0260563 | + | 0.999660i | ||||
\(170\) | −4.17620 | −0.320300 | ||||||||
\(171\) | 2.52763 | + | 2.52763i | 0.193293 | + | 0.193293i | ||||
\(172\) | 4.17620 | 0.318433 | ||||||||
\(173\) | 10.9940 | 0.835856 | 0.417928 | − | 0.908480i | \(-0.362756\pi\) | ||||
0.417928 | + | 0.908480i | \(0.362756\pi\) | |||||||
\(174\) | −5.59406 | − | 5.59406i | −0.424085 | − | 0.424085i | ||||
\(175\) | −12.0289 | + | 1.33987i | −0.909298 | + | 0.101285i | ||||
\(176\) | −1.60525 | − | 1.60525i | −0.121000 | − | 0.121000i | ||||
\(177\) | −1.17834 | − | 1.17834i | −0.0885695 | − | 0.0885695i | ||||
\(178\) | − | 12.0874i | − | 0.905989i | ||||||
\(179\) | 2.54656i | 0.190339i | 0.995461 | + | 0.0951695i | \(0.0303393\pi\) | ||||
−0.995461 | + | 0.0951695i | \(0.969661\pi\) | |||||||
\(180\) | 0.461191 | − | 0.461191i | 0.0343752 | − | 0.0343752i | ||||
\(181\) | 13.8933 | 1.03268 | 0.516339 | − | 0.856384i | \(-0.327295\pi\) | ||||
0.516339 | + | 0.856384i | \(0.327295\pi\) | |||||||
\(182\) | −0.932425 | − | 9.49371i | −0.0691159 | − | 0.703721i | ||||
\(183\) | 14.4874 | 1.07094 | ||||||||
\(184\) | 6.01946 | − | 6.01946i | 0.443760 | − | 0.443760i | ||||
\(185\) | 0.879051i | 0.0646291i | ||||||||
\(186\) | 1.30445i | 0.0956466i | ||||||||
\(187\) | −10.2784 | − | 10.2784i | −0.751634 | − | 0.751634i | ||||
\(188\) | 1.41421 | + | 1.41421i | 0.103142 | + | 0.103142i | ||||
\(189\) | −2.62949 | + | 0.292893i | −0.191267 | + | 0.0213048i | ||||
\(190\) | −1.64858 | − | 1.64858i | −0.119600 | − | 0.119600i | ||||
\(191\) | −10.2290 | −0.740142 | −0.370071 | − | 0.929004i | \(-0.620667\pi\) | ||||
−0.370071 | + | 0.929004i | \(0.620667\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 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 | ||||||||
\(195\) | −2.35142 | − | 0.0306399i | −0.168389 | − | 0.00219417i | ||||
\(196\) | 1.54032 | + | 6.82843i | 0.110023 | + | 0.487745i | ||||
\(197\) | 8.84638 | − | 8.84638i | 0.630278 | − | 0.630278i | −0.317860 | − | 0.948138i | \(-0.602964\pi\) |
0.948138 | + | 0.317860i | \(0.102964\pi\) | |||||||
\(198\) | 2.27016 | 0.161333 | ||||||||
\(199\) | 7.40980 | 0.525267 | 0.262633 | − | 0.964896i | \(-0.415409\pi\) | ||||
0.262633 | + | 0.964896i | \(0.415409\pi\) | |||||||
\(200\) | 3.23473 | − | 3.23473i | 0.228730 | − | 0.228730i | ||||
\(201\) | 3.47602 | + | 3.47602i | 0.245179 | + | 0.245179i | ||||
\(202\) | −5.68437 | + | 5.68437i | −0.399951 | + | 0.399951i | ||||
\(203\) | −2.31714 | − | 20.8024i | −0.162631 | − | 1.46004i | ||||
\(204\) | −6.40303 | −0.448302 | ||||||||
\(205\) | − | 3.59255i | − | 0.250915i | ||||||
\(206\) | −5.39475 | + | 5.39475i | −0.375870 | + | 0.375870i | ||||
\(207\) | 8.51280i | 0.591681i | ||||||||
\(208\) | 2.51608 | + | 2.58251i | 0.174458 | + | 0.179065i | ||||
\(209\) | − | 8.11492i | − | 0.561321i | ||||||
\(210\) | 1.71501 | − | 0.191032i | 0.118347 | − | 0.0131824i | ||||
\(211\) | 14.6299 | 1.00716 | 0.503581 | − | 0.863948i | \(-0.332016\pi\) | ||||
0.503581 | + | 0.863948i | \(0.332016\pi\) | |||||||
\(212\) | − | 9.10072i | − | 0.625040i | ||||||
\(213\) | −8.29326 | − | 8.29326i | −0.568245 | − | 0.568245i | ||||
\(214\) | 10.1814 | − | 10.1814i | 0.695984 | − | 0.695984i | ||||
\(215\) | 1.92603 | − | 1.92603i | 0.131354 | − | 0.131354i | ||||
\(216\) | 0.707107 | − | 0.707107i | 0.0481125 | − | 0.0481125i | ||||
\(217\) | −2.15524 | + | 2.69555i | −0.146307 | + | 0.182986i | ||||
\(218\) | − | 15.1059i | − | 1.02310i | ||||||
\(219\) | 5.89851 | + | 5.89851i | 0.398584 | + | 0.398584i | ||||
\(220\) | −1.48065 | −0.0998254 | ||||||||
\(221\) | 16.1105 | + | 16.5359i | 1.08371 | + | 1.11233i | ||||
\(222\) | 1.34778i | 0.0904569i | ||||||||
\(223\) | 11.0574 | + | 11.0574i | 0.740458 | + | 0.740458i | 0.972666 | − | 0.232208i | \(-0.0745951\pi\) |
−0.232208 | + | 0.972666i | \(0.574595\pi\) | |||||||
\(224\) | −2.06644 | − | 1.65222i | −0.138070 | − | 0.110394i | ||||
\(225\) | 4.57461i | 0.304974i | ||||||||
\(226\) | −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 | \(0.894008\pi\) | |||||||
\(228\) | −2.52763 | − | 2.52763i | −0.167396 | − | 0.167396i | ||||
\(229\) | 15.5860 | − | 15.5860i | 1.02995 | − | 1.02995i | 0.0304148 | − | 0.999537i | \(-0.490317\pi\) |
0.999537 | − | 0.0304148i | \(-0.00968282\pi\) | |||||||
\(230\) | − | 5.55224i | − | 0.366104i | ||||||
\(231\) | 4.69114 | + | 3.75081i | 0.308654 | + | 0.246785i | ||||
\(232\) | 5.59406 | + | 5.59406i | 0.367268 | + | 0.367268i | ||||
\(233\) | 14.4240i | 0.944948i | 0.881345 | + | 0.472474i | \(0.156639\pi\) | ||||
−0.881345 | + | 0.472474i | \(0.843361\pi\) | |||||||
\(234\) | −3.60525 | − | 0.0469777i | −0.235682 | − | 0.00307103i | ||||
\(235\) | 1.30445 | 0.0850927 | ||||||||
\(236\) | 1.17834 | + | 1.17834i | 0.0767034 | + | 0.0767034i | ||||
\(237\) | − | 9.18813i | − | 0.596833i | ||||||
\(238\) | −13.2315 | − | 10.5792i | −0.857668 | − | 0.685750i | ||||
\(239\) | 3.83747 | − | 3.83747i | 0.248225 | − | 0.248225i | −0.572017 | − | 0.820242i | \(-0.693839\pi\) |
0.820242 | + | 0.572017i | \(0.193839\pi\) | |||||||
\(240\) | −0.461191 | + | 0.461191i | −0.0297698 | + | 0.0297698i | ||||
\(241\) | 14.2110 | − | 14.2110i | 0.915412 | − | 0.915412i | −0.0812794 | − | 0.996691i | \(-0.525901\pi\) |
0.996691 | + | 0.0812794i | \(0.0259006\pi\) | |||||||
\(242\) | 4.13401 | + | 4.13401i | 0.265744 | + | 0.265744i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −14.4874 | −0.927462 | ||||||||
\(245\) | 3.85959 | + | 2.43883i | 0.246580 | + | 0.155811i | ||||
\(246\) | − | 5.50817i | − | 0.351188i | ||||||
\(247\) | −0.167927 | + | 12.8873i | −0.0106849 | + | 0.820001i | ||||
\(248\) | − | 1.30445i | − | 0.0828324i | ||||||
\(249\) | 9.98882 | − | 9.98882i | 0.633016 | − | 0.633016i | ||||
\(250\) | − | 6.24478i | − | 0.394954i | ||||||
\(251\) | 5.39399 | 0.340465 | 0.170233 | − | 0.985404i | \(-0.445548\pi\) | ||||
0.170233 | + | 0.985404i | \(0.445548\pi\) | |||||||
\(252\) | 2.62949 | − | 0.292893i | 0.165642 | − | 0.0184505i | ||||
\(253\) | 13.6651 | − | 13.6651i | 0.859119 | − | 0.859119i | ||||
\(254\) | 11.1702 | + | 11.1702i | 0.700879 | + | 0.700879i | ||||
\(255\) | −2.95302 | + | 2.95302i | −0.184925 | + | 0.184925i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.38508 | −0.273534 | −0.136767 | − | 0.990603i | \(-0.543671\pi\) | ||||
−0.136767 | + | 0.990603i | \(0.543671\pi\) | |||||||
\(258\) | 2.95302 | − | 2.95302i | 0.183847 | − | 0.183847i | ||||
\(259\) | −2.22683 | + | 2.78510i | −0.138368 | + | 0.173057i | ||||
\(260\) | 2.35142 | + | 0.0306399i | 0.145829 | + | 0.00190021i | ||||
\(261\) | −7.91120 | −0.489691 | ||||||||
\(262\) | 1.24113 | + | 1.24113i | 0.0766773 | + | 0.0766773i | ||||
\(263\) | −12.4336 | −0.766687 | −0.383343 | − | 0.923606i | \(-0.625227\pi\) | ||||
−0.383343 | + | 0.923606i | \(0.625227\pi\) | |||||||
\(264\) | −2.27016 | −0.139719 | ||||||||
\(265\) | −4.19717 | − | 4.19717i | −0.257830 | − | 0.257830i | ||||
\(266\) | −1.04698 | − | 9.39939i | −0.0641943 | − | 0.576313i | ||||
\(267\) | −8.54709 | − | 8.54709i | −0.523073 | − | 0.523073i | ||||
\(268\) | −3.47602 | − | 3.47602i | −0.212332 | − | 0.212332i | ||||
\(269\) | − | 29.7839i | − | 1.81596i | −0.419016 | − | 0.907979i | \(-0.637625\pi\) | ||
0.419016 | − | 0.907979i | \(-0.362375\pi\) | |||||||
\(270\) | − | 0.652223i | − | 0.0396930i | ||||||
\(271\) | −14.7173 | + | 14.7173i | −0.894010 | + | 0.894010i | −0.994898 | − | 0.100888i | \(-0.967832\pi\) |
0.100888 | + | 0.994898i | \(0.467832\pi\) | |||||||
\(272\) | 6.40303 | 0.388241 | ||||||||
\(273\) | −7.37239 | − | 6.05374i | −0.446197 | − | 0.366389i | ||||
\(274\) | 2.58792 | 0.156342 | ||||||||
\(275\) | 7.34336 | − | 7.34336i | 0.442821 | − | 0.442821i | ||||
\(276\) | − | 8.51280i | − | 0.512410i | ||||||
\(277\) | − | 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 | ||||
\(279\) | 0.922382 | + | 0.922382i | 0.0552216 | + | 0.0552216i | ||||
\(280\) | −1.71501 | + | 0.191032i | −0.102492 | + | 0.0114163i | ||||
\(281\) | −7.70534 | − | 7.70534i | −0.459662 | − | 0.459662i | 0.438882 | − | 0.898545i | \(-0.355374\pi\) |
−0.898545 | + | 0.438882i | \(0.855374\pi\) | |||||||
\(282\) | 2.00000 | 0.119098 | ||||||||
\(283\) | 6.39133 | 0.379925 | 0.189962 | − | 0.981791i | \(-0.439163\pi\) | ||||
0.189962 | + | 0.981791i | \(0.439163\pi\) | |||||||
\(284\) | 8.29326 | + | 8.29326i | 0.492115 | + | 0.492115i | ||||
\(285\) | −2.33144 | −0.138103 | ||||||||
\(286\) | 5.71189 | + | 5.86271i | 0.337751 | + | 0.346670i | ||||
\(287\) | 9.10072 | − | 11.3823i | 0.537199 | − | 0.671875i | ||||
\(288\) | −0.707107 | + | 0.707107i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | 23.9988 | 1.41170 | ||||||||
\(290\) | 5.15987 | 0.302998 | ||||||||
\(291\) | 0.272296 | − | 0.272296i | 0.0159622 | − | 0.0159622i | ||||
\(292\) | −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 | \(0.370380\pi\) | |||||||
\(294\) | 5.91760 | + | 3.73926i | 0.345121 | + | 0.218078i | ||||
\(295\) | 1.08688 | 0.0632806 | ||||||||
\(296\) | − | 1.34778i | − | 0.0783380i | ||||||
\(297\) | 1.60525 | − | 1.60525i | 0.0931458 | − | 0.0931458i | ||||
\(298\) | − | 4.42400i | − | 0.256276i | ||||||
\(299\) | −21.9844 | + | 21.4188i | −1.27139 | + | 1.23868i | ||||
\(300\) | − | 4.57461i | − | 0.264115i | ||||||
\(301\) | 10.9813 | − | 1.22318i | 0.632951 | − | 0.0705030i | ||||
\(302\) | −16.3345 | −0.939943 | ||||||||
\(303\) | 8.03892i | 0.461824i | ||||||||
\(304\) | 2.52763 | + | 2.52763i | 0.144969 | + | 0.144969i | ||||
\(305\) | −6.68147 | + | 6.68147i | −0.382580 | + | 0.382580i | ||||
\(306\) | −4.52763 | + | 4.52763i | −0.258827 | + | 0.258827i | ||||
\(307\) | −1.27177 | + | 1.27177i | −0.0725838 | + | 0.0725838i | −0.742467 | − | 0.669883i | \(-0.766344\pi\) |
0.669883 | + | 0.742467i | \(0.266344\pi\) | |||||||
\(308\) | −4.69114 | − | 3.75081i | −0.267303 | − | 0.213722i | ||||
\(309\) | 7.62934i | 0.434018i | ||||||||
\(310\) | −0.601599 | − | 0.601599i | −0.0341685 | − | 0.0341685i | ||||
\(311\) | 1.52201 | 0.0863053 | 0.0431527 | − | 0.999068i | \(-0.486260\pi\) | ||||
0.0431527 | + | 0.999068i | \(0.486260\pi\) | |||||||
\(312\) | 3.60525 | + | 0.0469777i | 0.204107 | + | 0.00265959i | ||||
\(313\) | − | 3.48506i | − | 0.196987i | −0.995138 | − | 0.0984937i | \(-0.968598\pi\) | ||
0.995138 | − | 0.0984937i | \(-0.0314024\pi\) | |||||||
\(314\) | −13.1022 | − | 13.1022i | −0.739402 | − | 0.739402i | ||||
\(315\) | 1.07762 | − | 1.34778i | 0.0607169 | − | 0.0759386i | ||||
\(316\) | 9.18813i | 0.516873i | ||||||||
\(317\) | 3.61566 | − | 3.61566i | 0.203076 | − | 0.203076i | −0.598241 | − | 0.801316i | \(-0.704133\pi\) |
0.801316 | + | 0.598241i | \(0.204133\pi\) | |||||||
\(318\) | −6.43518 | − | 6.43518i | −0.360867 | − | 0.360867i | ||||
\(319\) | 12.6994 | + | 12.6994i | 0.711031 | + | 0.711031i | ||||
\(320\) | 0.461191 | − | 0.461191i | 0.0257814 | − | 0.0257814i | ||||
\(321\) | − | 14.3986i | − | 0.803653i | ||||||
\(322\) | 14.0650 | − | 17.5912i | 0.783814 | − | 0.980317i | ||||
\(323\) | 16.1845 | + | 16.1845i | 0.900529 | + | 0.900529i | ||||
\(324\) | − | 1.00000i | − | 0.0555556i | ||||||
\(325\) | −11.8140 | + | 11.5101i | −0.655321 | + | 0.638463i | ||||
\(326\) | 18.5307 | 1.02632 | ||||||||
\(327\) | −10.6815 | − | 10.6815i | −0.590687 | − | 0.590687i | ||||
\(328\) | 5.50817i | 0.304138i | ||||||||
\(329\) | 4.13287 | + | 3.30445i | 0.227853 | + | 0.182180i | ||||
\(330\) | −1.04698 | + | 1.04698i | −0.0576342 | + | 0.0576342i | ||||
\(331\) | 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 | ||||
\(333\) | 0.953022 | + | 0.953022i | 0.0522253 | + | 0.0522253i | ||||
\(334\) | − | 13.8954i | − | 0.760322i | ||||||
\(335\) | −3.20622 | −0.175174 | ||||||||
\(336\) | −2.62949 | + | 0.292893i | −0.143450 | + | 0.0159786i | ||||
\(337\) | − | 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 | ||||
\(339\) | 15.0256i | 0.816079i | ||||||||
\(340\) | 2.95302 | − | 2.95302i | 0.160150 | − | 0.160150i | ||||
\(341\) | − | 2.96130i | − | 0.160363i | ||||||
\(342\) | −3.57461 | −0.193293 | ||||||||
\(343\) | 6.05025 | + | 17.5041i | 0.326683 | + | 0.945134i | ||||
\(344\) | −2.95302 | + | 2.95302i | −0.159216 | + | 0.159216i | ||||
\(345\) | −3.92603 | − | 3.92603i | −0.211370 | − | 0.211370i | ||||
\(346\) | −7.77391 | + | 7.77391i | −0.417928 | + | 0.417928i | ||||
\(347\) | 0.161276 | 0.00865778 | 0.00432889 | − | 0.999991i | \(-0.498622\pi\) | ||||
0.00432889 | + | 0.999991i | \(0.498622\pi\) | |||||||
\(348\) | 7.91120 | 0.424085 | ||||||||
\(349\) | −7.17995 | + | 7.17995i | −0.384334 | + | 0.384334i | −0.872661 | − | 0.488327i | \(-0.837607\pi\) |
0.488327 | + | 0.872661i | \(0.337607\pi\) | |||||||
\(350\) | 7.55827 | − | 9.45313i | 0.404006 | − | 0.505291i | ||||
\(351\) | −2.58251 | + | 2.51608i | −0.137844 | + | 0.134298i | ||||
\(352\) | 2.27016 | 0.121000 | ||||||||
\(353\) | 9.44711 | + | 9.44711i | 0.502819 | + | 0.502819i | 0.912313 | − | 0.409494i | \(-0.134295\pi\) |
−0.409494 | + | 0.912313i | \(0.634295\pi\) | |||||||
\(354\) | 1.66642 | 0.0885695 | ||||||||
\(355\) | 7.64956 | 0.405997 | ||||||||
\(356\) | 8.54709 | + | 8.54709i | 0.452995 | + | 0.452995i | ||||
\(357\) | −16.8367 | + | 1.87540i | −0.891093 | + | 0.0992569i | ||||
\(358\) | −1.80069 | − | 1.80069i | −0.0951695 | − | 0.0951695i | ||||
\(359\) | −19.1933 | − | 19.1933i | −1.01298 | − | 1.01298i | −0.999915 | − | 0.0130682i | \(-0.995840\pi\) |
−0.0130682 | − | 0.999915i | \(-0.504160\pi\) | |||||||
\(360\) | 0.652223i | 0.0343752i | ||||||||
\(361\) | − | 6.22220i | − | 0.327484i | ||||||
\(362\) | −9.82401 | + | 9.82401i | −0.516339 | + | 0.516339i | ||||
\(363\) | 5.84638 | 0.306855 | ||||||||
\(364\) | 7.37239 | + | 6.05374i | 0.386418 | + | 0.317302i | ||||
\(365\) | −5.44068 | −0.284778 | ||||||||
\(366\) | −10.2442 | + | 10.2442i | −0.535470 | + | 0.535470i | ||||
\(367\) | − | 24.3142i | − | 1.26919i | −0.772844 | − | 0.634596i | \(-0.781166\pi\) | ||
0.772844 | − | 0.634596i | \(-0.218834\pi\) | |||||||
\(368\) | 8.51280i | 0.443760i | ||||||||
\(369\) | −3.89486 | − | 3.89486i | −0.202758 | − | 0.202758i | ||||
\(370\) | −0.621583 | − | 0.621583i | −0.0323146 | − | 0.0323146i | ||||
\(371\) | −2.66554 | − | 23.9303i | −0.138388 | − | 1.24240i | ||||
\(372\) | −0.922382 | − | 0.922382i | −0.0478233 | − | 0.0478233i | ||||
\(373\) | 9.74654 | 0.504657 | 0.252328 | − | 0.967642i | \(-0.418804\pi\) | ||||
0.252328 | + | 0.967642i | \(0.418804\pi\) | |||||||
\(374\) | 14.5359 | 0.751634 | ||||||||
\(375\) | −4.41572 | − | 4.41572i | −0.228027 | − | 0.228027i | ||||
\(376\) | −2.00000 | −0.103142 | ||||||||
\(377\) | −19.9052 | − | 20.4308i | −1.02517 | − | 1.05224i | ||||
\(378\) | 1.65222 | − | 2.06644i | 0.0849812 | − | 0.106286i | ||||
\(379\) | 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 | ||||||||
\(381\) | 15.7970 | 0.809306 | ||||||||
\(382\) | 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 | \(0.478192\pi\) | |||||||
\(384\) | 0.707107 | − | 0.707107i | 0.0360844 | − | 0.0360844i | ||||
\(385\) | −3.89335 | + | 0.433672i | −0.198424 | + | 0.0221020i | ||||
\(386\) | −17.5277 | −0.892139 | ||||||||
\(387\) | − | 4.17620i | − | 0.212288i | ||||||
\(388\) | −0.272296 | + | 0.272296i | −0.0138237 | + | 0.0138237i | ||||
\(389\) | − | 6.09321i | − | 0.308938i | −0.987998 | − | 0.154469i | \(-0.950633\pi\) | ||
0.987998 | − | 0.154469i | \(-0.0493667\pi\) | |||||||
\(390\) | 1.68437 | − | 1.64104i | 0.0852915 | − | 0.0830974i | ||||
\(391\) | 54.5077i | 2.75657i | ||||||||
\(392\) | −5.91760 | − | 3.73926i | −0.298884 | − | 0.188861i | ||||
\(393\) | 1.75522 | 0.0885393 | ||||||||
\(394\) | 12.5107i | 0.630278i | ||||||||
\(395\) | 4.23748 | + | 4.23748i | 0.213211 | + | 0.213211i | ||||
\(396\) | −1.60525 | + | 1.60525i | −0.0806666 | + | 0.0806666i | ||||
\(397\) | 26.9792 | − | 26.9792i | 1.35405 | − | 1.35405i | 0.472972 | − | 0.881077i | \(-0.343181\pi\) |
0.881077 | − | 0.472972i | \(-0.156819\pi\) | |||||||
\(398\) | −5.23952 | + | 5.23952i | −0.262633 | + | 0.262633i | ||||
\(399\) | −7.38669 | − | 5.90604i | −0.369797 | − | 0.295672i | ||||
\(400\) | 4.57461i | 0.228730i | ||||||||
\(401\) | 21.4604 | + | 21.4604i | 1.07168 | + | 1.07168i | 0.997224 | + | 0.0744583i | \(0.0237228\pi\) |
0.0744583 | + | 0.997224i | \(0.476277\pi\) | |||||||
\(402\) | −4.91583 | −0.245179 | ||||||||
\(403\) | −0.0612798 | + | 4.70285i | −0.00305256 | + | 0.234265i | ||||
\(404\) | − | 8.03892i | − | 0.399951i | ||||||
\(405\) | −0.461191 | − | 0.461191i | −0.0229168 | − | 0.0229168i | ||||
\(406\) | 16.3480 | + | 13.0711i | 0.811337 | + | 0.648706i | ||||
\(407\) | − | 3.05967i | − | 0.151662i | ||||||
\(408\) | 4.52763 | − | 4.52763i | 0.224151 | − | 0.224151i | ||||
\(409\) | −4.20898 | − | 4.20898i | −0.208121 | − | 0.208121i | 0.595348 | − | 0.803468i | \(-0.297014\pi\) |
−0.803468 | + | 0.595348i | \(0.797014\pi\) | |||||||
\(410\) | 2.54032 | + | 2.54032i | 0.125457 | + | 0.125457i | ||||
\(411\) | 1.82994 | − | 1.82994i | 0.0902642 | − | 0.0902642i | ||||
\(412\) | − | 7.62934i | − | 0.375870i | ||||||
\(413\) | 3.44356 | + | 2.75330i | 0.169447 | + | 0.135481i | ||||
\(414\) | −6.01946 | − | 6.01946i | −0.295840 | − | 0.295840i | ||||
\(415\) | 9.21351i | 0.452273i | ||||||||
\(416\) | −3.60525 | − | 0.0469777i | −0.176762 | − | 0.00230327i | ||||
\(417\) | −13.8448 | −0.677981 | ||||||||
\(418\) | 5.73812 | + | 5.73812i | 0.280661 | + | 0.280661i | ||||
\(419\) | − | 3.78685i | − | 0.185000i | −0.995713 | − | 0.0924998i | \(-0.970514\pi\) | ||
0.995713 | − | 0.0924998i | \(-0.0294858\pi\) | |||||||
\(420\) | −1.07762 | + | 1.34778i | −0.0525824 | + | 0.0657648i | ||||
\(421\) | −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 | ||||
\(423\) | 1.41421 | − | 1.41421i | 0.0687614 | − | 0.0687614i | ||||
\(424\) | 6.43518 | + | 6.43518i | 0.312520 | + | 0.312520i | ||||
\(425\) | 29.2913i | 1.42084i | ||||||||
\(426\) | 11.7284 | 0.568245 | ||||||||
\(427\) | −38.0945 | + | 4.24327i | −1.84352 | + | 0.205346i | ||||
\(428\) | 14.3986i | 0.695984i | ||||||||
\(429\) | 8.18448 | + | 0.106647i | 0.395151 | + | 0.00514895i | ||||
\(430\) | 2.72382i | 0.131354i | ||||||||
\(431\) | −17.7084 | + | 17.7084i | −0.852982 | + | 0.852982i | −0.990499 | − | 0.137518i | \(-0.956088\pi\) |
0.137518 | + | 0.990499i | \(0.456088\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | 13.2092 | 0.634796 | 0.317398 | − | 0.948292i | \(-0.397191\pi\) | ||||
0.317398 | + | 0.948292i | \(0.397191\pi\) | |||||||
\(434\) | −0.382063 | − | 3.43003i | −0.0183396 | − | 0.164647i | ||||
\(435\) | 3.64858 | − | 3.64858i | 0.174936 | − | 0.174936i | ||||
\(436\) | 10.6815 | + | 10.6815i | 0.511550 | + | 0.511550i | ||||
\(437\) | −21.5172 | + | 21.5172i | −1.02931 | + | 1.02931i | ||||
\(438\) | −8.34175 | −0.398584 | ||||||||
\(439\) | 27.2638 | 1.30123 | 0.650616 | − | 0.759407i | \(-0.274511\pi\) | ||||
0.650616 | + | 0.759407i | \(0.274511\pi\) | |||||||
\(440\) | 1.04698 | − | 1.04698i | 0.0499127 | − | 0.0499127i | ||||
\(441\) | 6.82843 | − | 1.54032i | 0.325163 | − | 0.0733485i | ||||
\(442\) | −23.0845 | − | 0.300799i | −1.09802 | − | 0.0143076i | ||||
\(443\) | 22.3627 | 1.06248 | 0.531242 | − | 0.847220i | \(-0.321725\pi\) | ||||
0.531242 | + | 0.847220i | \(0.321725\pi\) | |||||||
\(444\) | −0.953022 | − | 0.953022i | −0.0452284 | − | 0.0452284i | ||||
\(445\) | 7.88368 | 0.373722 | ||||||||
\(446\) | −15.6375 | −0.740458 | ||||||||
\(447\) | −3.12824 | − | 3.12824i | −0.147961 | − | 0.147961i | ||||
\(448\) | 2.62949 | − | 0.292893i | 0.124232 | − | 0.0138379i | ||||
\(449\) | 3.36702 | + | 3.36702i | 0.158899 | + | 0.158899i | 0.782079 | − | 0.623179i | \(-0.214159\pi\) |
−0.623179 | + | 0.782079i | \(0.714159\pi\) | |||||||
\(450\) | −3.23473 | − | 3.23473i | −0.152487 | − | 0.152487i | ||||
\(451\) | 12.5044i | 0.588810i | ||||||||
\(452\) | − | 15.0256i | − | 0.706745i | ||||||
\(453\) | −11.5502 | + | 11.5502i | −0.542676 | + | 0.542676i | ||||
\(454\) | 13.1723 | 0.618207 | ||||||||
\(455\) | 6.19202 | − | 0.608149i | 0.290286 | − | 0.0285104i | ||||
\(456\) | 3.57461 | 0.167396 | ||||||||
\(457\) | −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 | ||||||||
\(459\) | 6.40303i | 0.298868i | ||||||||
\(460\) | 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 | \(0.792447\pi\) | |||||||
\(462\) | −5.96936 | + | 0.664914i | −0.277720 | + | 0.0309346i | ||||
\(463\) | −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 | ||||||||
\(465\) | −0.850789 | −0.0394544 | ||||||||
\(466\) | −10.1993 | − | 10.1993i | −0.472474 | − | 0.472474i | ||||
\(467\) | −17.0280 | −0.787964 | −0.393982 | − | 0.919118i | \(-0.628903\pi\) | ||||
−0.393982 | + | 0.919118i | \(0.628903\pi\) | |||||||
\(468\) | 2.58251 | − | 2.51608i | 0.119377 | − | 0.116306i | ||||
\(469\) | −10.1583 | − | 8.12205i | −0.469065 | − | 0.375041i | ||||
\(470\) | −0.922382 | + | 0.922382i | −0.0425463 | + | 0.0425463i | ||||
\(471\) | −18.5294 | −0.853788 | ||||||||
\(472\) | −1.66642 | −0.0767034 | ||||||||
\(473\) | −6.70383 | + | 6.70383i | −0.308243 | + | 0.308243i | ||||
\(474\) | 6.49699 | + | 6.49699i | 0.298417 | + | 0.298417i | ||||
\(475\) | −11.5629 | + | 11.5629i | −0.530542 | + | 0.530542i | ||||
\(476\) | 16.8367 | − | 1.87540i | 0.771709 | − | 0.0859590i | ||||
\(477\) | −9.10072 | −0.416693 | ||||||||
\(478\) | 5.42701i | 0.248225i | ||||||||
\(479\) | 22.7406 | − | 22.7406i | 1.03905 | − | 1.03905i | 0.0398390 | − | 0.999206i | \(-0.487315\pi\) |
0.999206 | − | 0.0398390i | \(-0.0126845\pi\) | |||||||
\(480\) | − | 0.652223i | − | 0.0297698i | ||||||
\(481\) | −0.0633154 | + | 4.85907i | −0.00288693 | + | 0.221554i | ||||
\(482\) | 20.0974i | 0.915412i | ||||||||
\(483\) | −2.49334 | − | 22.3843i | −0.113451 | − | 1.01852i | ||||
\(484\) | −5.84638 | −0.265744 | ||||||||
\(485\) | 0.251161i | 0.0114046i | ||||||||
\(486\) | −0.707107 | − | 0.707107i | −0.0320750 | − | 0.0320750i | ||||
\(487\) | −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 | ||||
\(489\) | 13.1032 | − | 13.1032i | 0.592548 | − | 0.592548i | ||||
\(490\) | −4.45366 | + | 1.00463i | −0.201196 | + | 0.0453846i | ||||
\(491\) | − | 12.3150i | − | 0.555767i | −0.960615 | − | 0.277884i | \(-0.910367\pi\) | ||
0.960615 | − | 0.277884i | \(-0.0896329\pi\) | |||||||
\(492\) | 3.89486 | + | 3.89486i | 0.175594 | + | 0.175594i | ||||
\(493\) | −50.6557 | −2.28142 | ||||||||
\(494\) | −8.99398 | − | 9.23146i | −0.404658 | − | 0.415343i | ||||
\(495\) | 1.48065i | 0.0665503i | ||||||||
\(496\) | 0.922382 | + | 0.922382i | 0.0414162 | + | 0.0414162i | ||||
\(497\) | 24.2361 | + | 19.3780i | 1.08714 | + | 0.869222i | ||||
\(498\) | 14.1263i | 0.633016i | ||||||||
\(499\) | 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 | ||||
\(501\) | −9.82552 | − | 9.82552i | −0.438972 | − | 0.438972i | ||||
\(502\) | −3.81412 | + | 3.81412i | −0.170233 | + | 0.170233i | ||||
\(503\) | − | 32.1557i | − | 1.43375i | −0.697201 | − | 0.716875i | \(-0.745572\pi\) | ||
0.697201 | − | 0.716875i | \(-0.254428\pi\) | |||||||
\(504\) | −1.65222 | + | 2.06644i | −0.0735959 | + | 0.0920464i | ||||
\(505\) | −3.70748 | − | 3.70748i | −0.164981 | − | 0.164981i | ||||
\(506\) | 19.3254i | 0.859119i | ||||||||
\(507\) | −12.9956 | − | 0.338732i | −0.577154 | − | 0.0150436i | ||||
\(508\) | −15.7970 | −0.700879 | ||||||||
\(509\) | 25.9435 | + | 25.9435i | 1.14992 | + | 1.14992i | 0.986567 | + | 0.163357i | \(0.0522322\pi\) |
0.163357 | + | 0.986567i | \(0.447768\pi\) | |||||||
\(510\) | − | 4.17620i | − | 0.184925i | ||||||
\(511\) | −17.2377 | − | 13.7824i | −0.762551 | − | 0.609699i | ||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | −2.52763 | + | 2.52763i | −0.111597 | + | 0.111597i | ||||
\(514\) | 3.10072 | − | 3.10072i | 0.136767 | − | 0.136767i | ||||
\(515\) | −3.51858 | − | 3.51858i | −0.155047 | − | 0.155047i | ||||
\(516\) | 4.17620i | 0.183847i | ||||||||
\(517\) | −4.54032 | −0.199683 | ||||||||
\(518\) | −0.394755 | − | 3.54397i | −0.0173445 | − | 0.155713i | ||||
\(519\) | 10.9940i | 0.482582i | ||||||||
\(520\) | −1.68437 | + | 1.64104i | −0.0738646 | + | 0.0719644i | ||||
\(521\) | − | 3.85949i | − | 0.169087i | −0.996420 | − | 0.0845437i | \(-0.973057\pi\) | ||
0.996420 | − | 0.0845437i | \(-0.0269433\pi\) | |||||||
\(522\) | 5.59406 | − | 5.59406i | 0.244846 | − | 0.244846i | ||||
\(523\) | − | 36.3670i | − | 1.59022i | −0.606467 | − | 0.795109i | \(-0.707414\pi\) | ||
0.606467 | − | 0.795109i | \(-0.292586\pi\) | |||||||
\(524\) | −1.75522 | −0.0766773 | ||||||||
\(525\) | −1.33987 | − | 12.0289i | −0.0584768 | − | 0.524983i | ||||
\(526\) | 8.79186 | − | 8.79186i | 0.383343 | − | 0.383343i | ||||
\(527\) | 5.90604 | + | 5.90604i | 0.257271 | + | 0.257271i | ||||
\(528\) | 1.60525 | − | 1.60525i | 0.0698593 | − | 0.0698593i | ||||
\(529\) | −49.4678 | −2.15077 | ||||||||
\(530\) | 5.93570 | 0.257830 | ||||||||
\(531\) | 1.17834 | − | 1.17834i | 0.0511356 | − | 0.0511356i | ||||
\(532\) | 7.38669 | + | 5.90604i | 0.320254 | + | 0.256060i | ||||
\(533\) | 0.258761 | − | 19.8583i | 0.0112082 | − | 0.860158i | ||||
\(534\) | 12.0874 | 0.523073 | ||||||||
\(535\) | 6.64052 | + | 6.64052i | 0.287095 | + | 0.287095i | ||||
\(536\) | 4.91583 | 0.212332 | ||||||||
\(537\) | −2.54656 | −0.109892 | ||||||||
\(538\) | 21.0604 | + | 21.0604i | 0.907979 | + | 0.907979i | ||||
\(539\) | −13.4339 | − | 8.48871i | −0.578639 | − | 0.365635i | ||||
\(540\) | 0.461191 | + | 0.461191i | 0.0198465 | + | 0.0198465i | ||||
\(541\) | 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 | ||||||
\(543\) | 13.8933i | 0.596217i | ||||||||
\(544\) | −4.52763 | + | 4.52763i | −0.194120 | + | 0.194120i | ||||
\(545\) | 9.85240 | 0.422030 | ||||||||
\(546\) | 9.49371 | − | 0.932425i | 0.406293 | − | 0.0399041i | ||||
\(547\) | 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 | ||||
\(549\) | 14.4874i | 0.618308i | ||||||||
\(550\) | 10.3851i | 0.442821i | ||||||||
\(551\) | −19.9966 | − | 19.9966i | −0.851883 | − | 0.851883i | ||||
\(552\) | 6.01946 | + | 6.01946i | 0.256205 | + | 0.256205i | ||||
\(553\) | 2.69114 | + | 24.1601i | 0.114439 | + | 1.02739i | ||||
\(554\) | 17.0604 | + | 17.0604i | 0.724827 | + | 0.724827i | ||||
\(555\) | −0.879051 | −0.0373136 | ||||||||
\(556\) | 13.8448 | 0.587149 | ||||||||
\(557\) | −27.1310 | − | 27.1310i | −1.14958 | − | 1.14958i | −0.986636 | − | 0.162939i | \(-0.947903\pi\) |
−0.162939 | − | 0.986636i | \(-0.552097\pi\) | |||||||
\(558\) | −1.30445 | −0.0552216 | ||||||||
\(559\) | 10.7851 | − | 10.5076i | 0.456161 | − | 0.444426i | ||||
\(560\) | 1.07762 | − | 1.34778i | 0.0455377 | − | 0.0569540i | ||||
\(561\) | 10.2784 | − | 10.2784i | 0.433956 | − | 0.433956i | ||||
\(562\) | 10.8970 | 0.459662 | ||||||||
\(563\) | −2.30304 | −0.0970614 | −0.0485307 | − | 0.998822i | \(-0.515454\pi\) | ||||
−0.0485307 | + | 0.998822i | \(0.515454\pi\) | |||||||
\(564\) | −1.41421 | + | 1.41421i | −0.0595491 | + | 0.0595491i | ||||
\(565\) | −6.92968 | − | 6.92968i | −0.291534 | − | 0.291534i | ||||
\(566\) | −4.51935 | + | 4.51935i | −0.189962 | + | 0.189962i | ||||
\(567\) | −0.292893 | − | 2.62949i | −0.0123004 | − | 0.110428i | ||||
\(568\) | −11.7284 | −0.492115 | ||||||||
\(569\) | 5.19115i | 0.217624i | 0.994062 | + | 0.108812i | \(0.0347047\pi\) | ||||
−0.994062 | + | 0.108812i | \(0.965295\pi\) | |||||||
\(570\) | 1.64858 | − | 1.64858i | 0.0690513 | − | 0.0690513i | ||||
\(571\) | 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 | ||||
\(573\) | − | 10.2290i | − | 0.427321i | ||||||
\(574\) | 1.61331 | + | 14.4837i | 0.0673381 | + | 0.604537i | ||||
\(575\) | −38.9427 | −1.62402 | ||||||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | 29.5340 | + | 29.5340i | 1.22952 | + | 1.22952i | 0.964147 | + | 0.265369i | \(0.0854938\pi\) |
0.265369 | + | 0.964147i | \(0.414506\pi\) | |||||||
\(578\) | −16.9697 | + | 16.9697i | −0.705848 | + | 0.705848i | ||||
\(579\) | −12.3940 | + | 12.3940i | −0.515077 | + | 0.515077i | ||||
\(580\) | −3.64858 | + | 3.64858i | −0.151499 | + | 0.151499i | ||||
\(581\) | −23.3398 | + | 29.1911i | −0.968299 | + | 1.21105i | ||||
\(582\) | 0.385084i | 0.0159622i | ||||||||
\(583\) | 14.6089 | + | 14.6089i | 0.605038 | + | 0.605038i | ||||
\(584\) | 8.34175 | 0.345184 | ||||||||
\(585\) | 0.0306399 | − | 2.35142i | 0.00126680 | − | 0.0972194i | ||||
\(586\) | − | 12.6405i | − | 0.522175i | ||||||
\(587\) | 11.2384 | + | 11.2384i | 0.463857 | + | 0.463857i | 0.899917 | − | 0.436060i | \(-0.143627\pi\) |
−0.436060 | + | 0.899917i | \(0.643627\pi\) | |||||||
\(588\) | −6.82843 | + | 1.54032i | −0.281600 | + | 0.0635217i | ||||
\(589\) | 4.66288i | 0.192131i | ||||||||
\(590\) | −0.768540 | + | 0.768540i | −0.0316403 | + | 0.0316403i | ||||
\(591\) | 8.84638 | + | 8.84638i | 0.363891 | + | 0.363891i | ||||
\(592\) | 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 | \(0.324561\pi\) | |||||||
\(594\) | 2.27016i | 0.0931458i | ||||||||
\(595\) | 6.90002 | − | 8.62986i | 0.282873 | − | 0.353790i | ||||
\(596\) | 3.12824 | + | 3.12824i | 0.128138 | + | 0.128138i | ||||
\(597\) | 7.40980i | 0.303263i | ||||||||
\(598\) | 0.399911 | − | 30.6907i | 0.0163536 | − | 1.25504i | ||||
\(599\) | 25.0503 | 1.02353 | 0.511764 | − | 0.859126i | \(-0.328992\pi\) | ||||
0.511764 | + | 0.859126i | \(0.328992\pi\) | |||||||
\(600\) | 3.23473 | + | 3.23473i | 0.132057 | + | 0.132057i | ||||
\(601\) | − | 11.5478i | − | 0.471046i | −0.971869 | − | 0.235523i | \(-0.924320\pi\) | ||
0.971869 | − | 0.235523i | \(-0.0756803\pi\) | |||||||
\(602\) | −6.90002 | + | 8.62986i | −0.281224 | + | 0.351727i | ||||
\(603\) | −3.47602 | + | 3.47602i | −0.141554 | + | 0.141554i | ||||
\(604\) | 11.5502 | − | 11.5502i | 0.469971 | − | 0.469971i | ||||
\(605\) | −2.69630 | + | 2.69630i | −0.109620 | + | 0.109620i | ||||
\(606\) | −5.68437 | − | 5.68437i | −0.230912 | − | 0.230912i | ||||
\(607\) | − | 15.2350i | − | 0.618369i | −0.951002 | − | 0.309185i | \(-0.899944\pi\) | ||
0.951002 | − | 0.309185i | \(-0.100056\pi\) | |||||||
\(608\) | −3.57461 | −0.144969 | ||||||||
\(609\) | 20.8024 | − | 2.31714i | 0.842957 | − | 0.0938951i | ||||
\(610\) | − | 9.44903i | − | 0.382580i | ||||||
\(611\) | 7.21049 | + | 0.0939553i | 0.291705 | + | 0.00380103i | ||||
\(612\) | − | 6.40303i | − | 0.258827i | ||||||
\(613\) | 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 | ||||||
\(615\) | 3.59255 | 0.144866 | ||||||||
\(616\) | 5.96936 | − | 0.664914i | 0.240512 | − | 0.0267902i | ||||
\(617\) | 14.5420 | − | 14.5420i | 0.585441 | − | 0.585441i | −0.350952 | − | 0.936393i | \(-0.614142\pi\) |
0.936393 | + | 0.350952i | \(0.114142\pi\) | |||||||
\(618\) | −5.39475 | − | 5.39475i | −0.217009 | − | 0.217009i | ||||
\(619\) | 7.62482 | − | 7.62482i | 0.306467 | − | 0.306467i | −0.537070 | − | 0.843538i | \(-0.680469\pi\) |
0.843538 | + | 0.537070i | \(0.180469\pi\) | |||||||
\(620\) | 0.850789 | 0.0341685 | ||||||||
\(621\) | −8.51280 | −0.341607 | ||||||||
\(622\) | −1.07622 | + | 1.07622i | −0.0431527 | + | 0.0431527i | ||||
\(623\) | 24.9779 | + | 19.9711i | 1.00072 | + | 0.800125i | ||||
\(624\) | −2.58251 | + | 2.51608i | −0.103383 | + | 0.100724i | ||||
\(625\) | −18.8000 | −0.752002 | ||||||||
\(626\) | 2.46431 | + | 2.46431i | 0.0984937 | + | 0.0984937i | ||||
\(627\) | 8.11492 | 0.324079 | ||||||||
\(628\) | 18.5294 | 0.739402 | ||||||||
\(629\) | 6.10223 | + | 6.10223i | 0.243312 | + | 0.243312i | ||||
\(630\) | 0.191032 | + | 1.71501i | 0.00761088 | + | 0.0683278i | ||||
\(631\) | 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 | ||||
\(633\) | 14.6299i | 0.581485i | ||||||||
\(634\) | 5.11331i | 0.203076i | ||||||||
\(635\) | −7.28545 | + | 7.28545i | −0.289114 | + | 0.289114i | ||||
\(636\) | 9.10072 | 0.360867 | ||||||||
\(637\) | 21.1587 | + | 13.7589i | 0.838339 | + | 0.545149i | ||||
\(638\) | −17.9597 | −0.711031 | ||||||||
\(639\) | 8.29326 | − | 8.29326i | 0.328076 | − | 0.328076i | ||||
\(640\) | 0.652223i | 0.0257814i | ||||||||
\(641\) | − | 13.9110i | − | 0.549453i | −0.961522 | − | 0.274726i | \(-0.911413\pi\) | ||
0.961522 | − | 0.274726i | \(-0.0885873\pi\) | |||||||
\(642\) | 10.1814 | + | 10.1814i | 0.401826 | + | 0.401826i | ||||
\(643\) | −31.6768 | − | 31.6768i | −1.24921 | − | 1.24921i | −0.956068 | − | 0.293144i | \(-0.905298\pi\) |
−0.293144 | − | 0.956068i | \(-0.594702\pi\) | |||||||
\(644\) | 2.49334 | + | 22.3843i | 0.0982514 | + | 0.882066i | ||||
\(645\) | 1.92603 | + | 1.92603i | 0.0758373 | + | 0.0758373i | ||||
\(646\) | −22.8883 | −0.900529 | ||||||||
\(647\) | −2.61086 | −0.102644 | −0.0513218 | − | 0.998682i | \(-0.516343\pi\) | ||||
−0.0513218 | + | 0.998682i | \(0.516343\pi\) | |||||||
\(648\) | 0.707107 | + | 0.707107i | 0.0277778 | + | 0.0277778i | ||||
\(649\) | −3.78305 | −0.148498 | ||||||||
\(650\) | 0.214904 | − | 16.4926i | 0.00842924 | − | 0.646892i | ||||
\(651\) | −2.69555 | − | 2.15524i | −0.105647 | − | 0.0844703i | ||||
\(652\) | −13.1032 | + | 13.1032i | −0.513162 | + | 0.513162i | ||||
\(653\) | 2.35132 | 0.0920144 | 0.0460072 | − | 0.998941i | \(-0.485350\pi\) | ||||
0.0460072 | + | 0.998941i | \(0.485350\pi\) | |||||||
\(654\) | 15.1059 | 0.590687 | ||||||||
\(655\) | −0.809494 | + | 0.809494i | −0.0316295 | + | 0.0316295i | ||||
\(656\) | −3.89486 | − | 3.89486i | −0.152069 | − | 0.152069i | ||||
\(657\) | −5.89851 | + | 5.89851i | −0.230123 | + | 0.230123i | ||||
\(658\) | −5.25898 | + | 0.585786i | −0.205016 | + | 0.0228363i | ||||
\(659\) | 13.1002 | 0.510312 | 0.255156 | − | 0.966900i | \(-0.417873\pi\) | ||||
0.255156 | + | 0.966900i | \(0.417873\pi\) | |||||||
\(660\) | − | 1.48065i | − | 0.0576342i | ||||||
\(661\) | 12.5885 | − | 12.5885i | 0.489636 | − | 0.489636i | −0.418555 | − | 0.908191i | \(-0.637463\pi\) |
0.908191 | + | 0.418555i | \(0.137463\pi\) | |||||||
\(662\) | 6.36625i | 0.247431i | ||||||||
\(663\) | −16.5359 | + | 16.1105i | −0.642201 | + | 0.625680i | ||||
\(664\) | − | 14.1263i | − | 0.548208i | ||||||
\(665\) | 6.13049 | − | 0.682863i | 0.237730 | − | 0.0264803i | ||||
\(666\) | −1.34778 | −0.0522253 | ||||||||
\(667\) | − | 67.3465i | − | 2.60767i | ||||||
\(668\) | 9.82552 | + | 9.82552i | 0.380161 | + | 0.380161i | ||||
\(669\) | −11.0574 | + | 11.0574i | −0.427503 | + | 0.427503i | ||||
\(670\) | 2.26714 | − | 2.26714i | 0.0875872 | − | 0.0875872i | ||||
\(671\) | 23.2559 | − | 23.2559i | 0.897782 | − | 0.897782i | ||||
\(672\) | 1.65222 | − | 2.06644i | 0.0637359 | − | 0.0797145i | ||||
\(673\) | − | 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 | ||||
\(675\) | −4.57461 | −0.176077 | ||||||||
\(676\) | 12.9956 | + | 0.338732i | 0.499830 | + | 0.0130282i | ||||
\(677\) | 27.2432i | 1.04704i | 0.852013 | + | 0.523520i | \(0.175381\pi\) | ||||
−0.852013 | + | 0.523520i | \(0.824619\pi\) | |||||||
\(678\) | −10.6247 | − | 10.6247i | −0.408039 | − | 0.408039i | ||||
\(679\) | −0.636245 | + | 0.795752i | −0.0244168 | + | 0.0305381i | ||||
\(680\) | 4.17620i | 0.160150i | ||||||||
\(681\) | 9.31423 | − | 9.31423i | 0.356922 | − | 0.356922i | ||||
\(682\) | 2.09396 | + | 2.09396i | 0.0801817 | + | 0.0801817i | ||||
\(683\) | −3.89033 | − | 3.89033i | −0.148859 | − | 0.148859i | 0.628749 | − | 0.777608i | \(-0.283567\pi\) |
−0.777608 | + | 0.628749i | \(0.783567\pi\) | |||||||
\(684\) | 2.52763 | − | 2.52763i | 0.0966463 | − | 0.0966463i | ||||
\(685\) | 1.68790i | 0.0644914i | ||||||||
\(686\) | −16.6555 | − | 8.09911i | −0.635908 | − | 0.309226i | ||||
\(687\) | 15.5860 | + | 15.5860i | 0.594643 | + | 0.594643i | ||||
\(688\) | − | 4.17620i | − | 0.159216i | ||||||
\(689\) | −22.8981 | − | 23.5027i | −0.872348 | − | 0.895382i | ||||
\(690\) | 5.55224 | 0.211370 | ||||||||
\(691\) | −7.75081 | − | 7.75081i | −0.294855 | − | 0.294855i | 0.544140 | − | 0.838995i | \(-0.316856\pi\) |
−0.838995 | + | 0.544140i | \(0.816856\pi\) | |||||||
\(692\) | − | 10.9940i | − | 0.417928i | ||||||
\(693\) | −3.75081 | + | 4.69114i | −0.142481 | + | 0.178202i | ||||
\(694\) | −0.114040 | + | 0.114040i | −0.00432889 | + | 0.00432889i | ||||
\(695\) | 6.38508 | − | 6.38508i | 0.242200 | − | 0.242200i | ||||
\(696\) | −5.59406 | + | 5.59406i | −0.212042 | + | 0.212042i | ||||
\(697\) | −24.9389 | − | 24.9389i | −0.944630 | − | 0.944630i | ||||
\(698\) | − | 10.1540i | − | 0.384334i | ||||||
\(699\) | −14.4240 | −0.545566 | ||||||||
\(700\) | 1.33987 | + | 12.0289i | 0.0506424 | + | 0.454649i | ||||
\(701\) | − | 5.02289i | − | 0.189712i | −0.995491 | − | 0.0948559i | \(-0.969761\pi\) | ||
0.995491 | − | 0.0948559i | \(-0.0302390\pi\) | |||||||
\(702\) | 0.0469777 | − | 3.60525i | 0.00177306 | − | 0.136071i | ||||
\(703\) | 4.81777i | 0.181706i | ||||||||
\(704\) | −1.60525 | + | 1.60525i | −0.0605000 | + | 0.0605000i | ||||
\(705\) | 1.30445i | 0.0491283i | ||||||||
\(706\) | −13.3602 | −0.502819 | ||||||||
\(707\) | −2.35454 | − | 21.1382i | −0.0885518 | − | 0.794986i | ||||
\(708\) | −1.17834 | + | 1.17834i | −0.0442847 | + | 0.0442847i | ||||
\(709\) | 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 | ||||
\(711\) | 9.18813 | 0.344582 | ||||||||
\(712\) | −12.0874 | −0.452995 | ||||||||
\(713\) | −7.85206 | + | 7.85206i | −0.294062 | + | 0.294062i | ||||
\(714\) | 10.5792 | − | 13.2315i | 0.395918 | − | 0.495175i | ||||
\(715\) | −3.82380 | + | 3.72543i | −0.143002 | + | 0.139323i | ||||
\(716\) | 2.54656 | 0.0951695 | ||||||||
\(717\) | 3.83747 | + | 3.83747i | 0.143313 | + | 0.143313i | ||||
\(718\) | 27.1434 | 1.01298 | ||||||||
\(719\) | 23.2670 | 0.867713 | 0.433857 | − | 0.900982i | \(-0.357152\pi\) | ||||
0.433857 | + | 0.900982i | \(0.357152\pi\) | |||||||
\(720\) | −0.461191 | − | 0.461191i | −0.0171876 | − | 0.0171876i | ||||
\(721\) | −2.23458 | − | 20.0613i | −0.0832201 | − | 0.747120i | ||||
\(722\) | 4.39976 | + | 4.39976i | 0.163742 | + | 0.163742i | ||||
\(723\) | 14.2110 | + | 14.2110i | 0.528513 | + | 0.528513i | ||||
\(724\) | − | 13.8933i | − | 0.516339i | ||||||
\(725\) | − | 36.1906i | − | 1.34409i | ||||||
\(726\) | −4.13401 | + | 4.13401i | −0.153428 | + | 0.153428i | ||||
\(727\) | −29.8368 | −1.10659 | −0.553293 | − | 0.832987i | \(-0.686629\pi\) | ||||
−0.553293 | + | 0.832987i | \(0.686629\pi\) | |||||||
\(728\) | −9.49371 | + | 0.932425i | −0.351860 | + | 0.0345580i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 3.84714 | − | 3.84714i | 0.142389 | − | 0.142389i | ||||
\(731\) | − | 26.7404i | − | 0.989028i | ||||||
\(732\) | − | 14.4874i | − | 0.535470i | ||||||
\(733\) | −11.7443 | − | 11.7443i | −0.433784 | − | 0.433784i | 0.456129 | − | 0.889913i | \(-0.349235\pi\) |
−0.889913 | + | 0.456129i | \(0.849235\pi\) | |||||||
\(734\) | 17.1928 | + | 17.1928i | 0.634596 | + | 0.634596i | ||||
\(735\) | −2.43883 | + | 3.85959i | −0.0899576 | + | 0.142363i | ||||
\(736\) | −6.01946 | − | 6.01946i | −0.221880 | − | 0.221880i | ||||
\(737\) | 11.1597 | 0.411074 | ||||||||
\(738\) | 5.50817 | 0.202758 | ||||||||
\(739\) | −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 | ||||||||
\(741\) | −12.8873 | − | 0.167927i | −0.473428 | − | 0.00616894i | ||||
\(742\) | 18.8061 | + | 15.0364i | 0.690392 | + | 0.552004i | ||||
\(743\) | 8.70770 | − | 8.70770i | 0.319454 | − | 0.319454i | −0.529103 | − | 0.848558i | \(-0.677472\pi\) |
0.848558 | + | 0.529103i | \(0.177472\pi\) | |||||||
\(744\) | 1.30445 | 0.0478233 | ||||||||
\(745\) | 2.88544 | 0.105714 | ||||||||
\(746\) | −6.89184 | + | 6.89184i | −0.252328 | + | 0.252328i | ||||
\(747\) | 9.98882 | + | 9.98882i | 0.365472 | + | 0.365472i | ||||
\(748\) | −10.2784 | + | 10.2784i | −0.375817 | + | 0.375817i | ||||
\(749\) | 4.21726 | + | 37.8610i | 0.154095 | + | 1.38341i | ||||
\(750\) | 6.24478 | 0.228027 | ||||||||
\(751\) | 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 | ||||
\(753\) | 5.39399i | 0.196568i | ||||||||
\(754\) | 28.5218 | + | 0.371650i | 1.03870 | + | 0.0135347i | ||||
\(755\) | − | 10.6537i | − | 0.387728i | ||||||
\(756\) | 0.292893 | + | 2.62949i | 0.0106524 | + | 0.0956336i | ||||
\(757\) | −28.0153 | −1.01823 | −0.509117 | − | 0.860697i | \(-0.670028\pi\) | ||||
−0.509117 | + | 0.860697i | \(0.670028\pi\) | |||||||
\(758\) | 20.6159i | 0.748802i | ||||||||
\(759\) | 13.6651 | + | 13.6651i | 0.496013 | + | 0.496013i | ||||
\(760\) | −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 | \(0.0313501\pi\) | |||||||
\(762\) | −11.1702 | + | 11.1702i | −0.404653 | + | 0.404653i | ||||
\(763\) | 31.2153 | + | 24.9583i | 1.13007 | + | 0.903550i | ||||
\(764\) | 10.2290i | 0.370071i | ||||||||
\(765\) | −2.95302 | − | 2.95302i | −0.106767 | − | 0.106767i | ||||
\(766\) | −29.5065 | −1.06611 | ||||||||
\(767\) | 6.00787 | + | 0.0782847i | 0.216932 | + | 0.00282670i | ||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | 24.3745 | + | 24.3745i | 0.878968 | + | 0.878968i | 0.993428 | − | 0.114460i | \(-0.0365137\pi\) |
−0.114460 | + | 0.993428i | \(0.536514\pi\) | |||||||
\(770\) | 2.44636 | − | 3.05967i | 0.0881608 | − | 0.110263i | ||||
\(771\) | − | 4.38508i | − | 0.157925i | ||||||
\(772\) | 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 | \(0.569913\pi\) | |||||||
\(774\) | 2.95302 | + | 2.95302i | 0.106144 | + | 0.106144i | ||||
\(775\) | −4.21954 | + | 4.21954i | −0.151570 | + | 0.151570i | ||||
\(776\) | − | 0.385084i | − | 0.0138237i | ||||||
\(777\) | −2.78510 | − | 2.22683i | −0.0999148 | − | 0.0798870i | ||||
\(778\) | 4.30855 | + | 4.30855i | 0.154469 | + | 0.154469i | ||||
\(779\) | − | 19.6895i | − | 0.705451i | ||||||
\(780\) | −0.0306399 | + | 2.35142i | −0.00109708 | + | 0.0841945i | ||||
\(781\) | −26.6254 | −0.952733 | ||||||||
\(782\) | −38.5428 | − | 38.5428i | −1.37829 | − | 1.37829i | ||||
\(783\) | − | 7.91120i | − | 0.282723i | ||||||
\(784\) | 6.82843 | − | 1.54032i | 0.243872 | − | 0.0550114i | ||||
\(785\) | 8.54558 | − | 8.54558i | 0.305005 | − | 0.305005i | ||||
\(786\) | −1.24113 | + | 1.24113i | −0.0442697 | + | 0.0442697i | ||||
\(787\) | −5.03100 | + | 5.03100i | −0.179336 | + | 0.179336i | −0.791066 | − | 0.611730i | \(-0.790474\pi\) |
0.611730 | + | 0.791066i | \(0.290474\pi\) | |||||||
\(788\) | −8.84638 | − | 8.84638i | −0.315139 | − | 0.315139i | ||||
\(789\) | − | 12.4336i | − | 0.442647i | ||||||
\(790\) | −5.99271 | −0.213211 | ||||||||
\(791\) | −4.40090 | − | 39.5097i | −0.156478 | − | 1.40480i | ||||
\(792\) | − | 2.27016i | − | 0.0806666i | ||||||
\(793\) | −37.4139 | + | 36.4514i | −1.32861 | + | 1.29443i | ||||
\(794\) | 38.1544i | 1.35405i | ||||||||
\(795\) | 4.19717 | − | 4.19717i | 0.148858 | − | 0.148858i | ||||
\(796\) | − | 7.40980i | − | 0.262633i | ||||||
\(797\) | 35.6777 | 1.26377 | 0.631884 | − | 0.775063i | \(-0.282282\pi\) | ||||
0.631884 | + | 0.775063i | \(0.282282\pi\) | |||||||
\(798\) | 9.39939 | − | 1.04698i | 0.332735 | − | 0.0370626i | ||||
\(799\) | 9.05526 | − | 9.05526i | 0.320352 | − | 0.320352i | ||||
\(800\) | −3.23473 | − | 3.23473i | −0.114365 | − | 0.114365i | ||||
\(801\) | 8.54709 | − | 8.54709i | 0.301996 | − | 0.301996i | ||||
\(802\) | −30.3496 | −1.07168 | ||||||||
\(803\) | 18.9371 | 0.668276 | ||||||||
\(804\) | 3.47602 | − | 3.47602i | 0.122590 | − | 0.122590i | ||||
\(805\) | 11.4734 | + | 9.17354i | 0.404383 | + | 0.323325i | ||||
\(806\) | −3.28208 | − | 3.36875i | −0.115606 | − | 0.118659i | ||||
\(807\) | 29.7839 | 1.04844 | ||||||||
\(808\) | 5.68437 | + | 5.68437i | 0.199976 | + | 0.199976i | ||||
\(809\) | −24.7540 | −0.870306 | −0.435153 | − | 0.900357i | \(-0.643306\pi\) | ||||
−0.435153 | + | 0.900357i | \(0.643306\pi\) | |||||||
\(810\) | 0.652223 | 0.0229168 | ||||||||
\(811\) | −19.5605 | − | 19.5605i | −0.686863 | − | 0.686863i | 0.274674 | − | 0.961537i | \(-0.411430\pi\) |
−0.961537 | + | 0.274674i | \(0.911430\pi\) | |||||||
\(812\) | −20.8024 | + | 2.31714i | −0.730022 | + | 0.0813156i | ||||
\(813\) | −14.7173 | − | 14.7173i | −0.516157 | − | 0.516157i | ||||
\(814\) | 2.16351 | + | 2.16351i | 0.0758311 | + | 0.0758311i | ||||
\(815\) | 12.0862i | 0.423360i | ||||||||
\(816\) | 6.40303i | 0.224151i | ||||||||
\(817\) | 10.5559 | − | 10.5559i | 0.369304 | − | 0.369304i | ||||
\(818\) | 5.95240 | 0.208121 | ||||||||
\(819\) | 6.05374 | − | 7.37239i | 0.211535 | − | 0.257612i | ||||
\(820\) | −3.59255 | −0.125457 | ||||||||
\(821\) | 8.90959 | − | 8.90959i | 0.310947 | − | 0.310947i | −0.534329 | − | 0.845276i | \(-0.679436\pi\) |
0.845276 | + | 0.534329i | \(0.179436\pi\) | |||||||
\(822\) | 2.58792i | 0.0902642i | ||||||||
\(823\) | 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 | ||||
\(825\) | 7.34336 | + | 7.34336i | 0.255663 | + | 0.255663i | ||||
\(826\) | −4.38185 | + | 0.488084i | −0.152464 | + | 0.0169826i | ||||
\(827\) | −26.8873 | − | 26.8873i | −0.934964 | − | 0.934964i | 0.0630466 | − | 0.998011i | \(-0.479918\pi\) |
−0.998011 | + | 0.0630466i | \(0.979918\pi\) | |||||||
\(828\) | 8.51280 | 0.295840 | ||||||||
\(829\) | −31.1247 | −1.08101 | −0.540503 | − | 0.841342i | \(-0.681766\pi\) | ||||
−0.540503 | + | 0.841342i | \(0.681766\pi\) | |||||||
\(830\) | −6.51494 | − | 6.51494i | −0.226137 | − | 0.226137i | ||||
\(831\) | 24.1271 | 0.836959 | ||||||||
\(832\) | 2.58251 | − | 2.51608i | 0.0895325 | − | 0.0872292i | ||||
\(833\) | 43.7226 | − | 9.86271i | 1.51490 | − | 0.341723i | ||||
\(834\) | 9.78973 | − | 9.78973i | 0.338991 | − | 0.338991i | ||||
\(835\) | 9.06289 | 0.313634 | ||||||||
\(836\) | −8.11492 | −0.280661 | ||||||||
\(837\) | −0.922382 | + | 0.922382i | −0.0318822 | + | 0.0318822i | ||||
\(838\) | 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 | \(0.177662\pi\) | |||||||
\(840\) | −0.191032 | − | 1.71501i | −0.00659122 | − | 0.0591736i | ||||
\(841\) | 33.5871 | 1.15818 | ||||||||
\(842\) | − | 23.0136i | − | 0.793099i | ||||||
\(843\) | 7.70534 | − | 7.70534i | 0.265386 | − | 0.265386i | ||||
\(844\) | − | 14.6299i | − | 0.503581i | ||||||
\(845\) | 6.14967 | − | 5.83723i | 0.211555 | − | 0.200807i | ||||
\(846\) | 2.00000i | 0.0687614i | ||||||||
\(847\) | −15.3730 | + | 1.71236i | −0.528222 | + | 0.0588375i | ||||
\(848\) | −9.10072 | −0.312520 | ||||||||
\(849\) | 6.39133i | 0.219350i | ||||||||
\(850\) | −20.7121 | − | 20.7121i | −0.710419 | − | 0.710419i | ||||
\(851\) | −8.11289 | + | 8.11289i | −0.278106 | + | 0.278106i | ||||
\(852\) | −8.29326 | + | 8.29326i | −0.284123 | + | 0.284123i | ||||
\(853\) | −9.34638 | + | 9.34638i | −0.320014 | + | 0.320014i | −0.848772 | − | 0.528758i | \(-0.822658\pi\) |
0.528758 | + | 0.848772i | \(0.322658\pi\) | |||||||
\(854\) | 23.9364 | − | 29.9373i | 0.819088 | − | 1.02443i | ||||
\(855\) | − | 2.33144i | − | 0.0797335i | ||||||
\(856\) | −10.1814 | − | 10.1814i | −0.347992 | − | 0.347992i | ||||
\(857\) | −55.3845 | −1.89190 | −0.945949 | − | 0.324315i | \(-0.894866\pi\) | ||||
−0.945949 | + | 0.324315i | \(0.894866\pi\) | |||||||
\(858\) | −5.86271 | + | 5.71189i | −0.200150 | + | 0.195001i | ||||
\(859\) | − | 42.0994i | − | 1.43641i | −0.695830 | − | 0.718206i | \(-0.744963\pi\) | ||
0.695830 | − | 0.718206i | \(-0.255037\pi\) | |||||||
\(860\) | −1.92603 | − | 1.92603i | −0.0656770 | − | 0.0656770i | ||||
\(861\) | 11.3823 | + | 9.10072i | 0.387907 | + | 0.310152i | ||||
\(862\) | − | 25.0434i | − | 0.852982i | ||||||
\(863\) | −3.47410 | + | 3.47410i | −0.118260 | + | 0.118260i | −0.763760 | − | 0.645500i | \(-0.776649\pi\) |
0.645500 | + | 0.763760i | \(0.276649\pi\) | |||||||
\(864\) | −0.707107 | − | 0.707107i | −0.0240563 | − | 0.0240563i | ||||
\(865\) | −5.07032 | − | 5.07032i | −0.172396 | − | 0.172396i | ||||
\(866\) | −9.34034 | + | 9.34034i | −0.317398 | + | 0.317398i | ||||
\(867\) | 23.9988i | 0.815043i | ||||||||
\(868\) | 2.69555 | + | 2.15524i | 0.0914931 | + | 0.0731534i | ||||
\(869\) | −14.7492 | − | 14.7492i | −0.500332 | − | 0.500332i | ||||
\(870\) | 5.15987i | 0.174936i | ||||||||
\(871\) | −17.7228 | − | 0.230934i | −0.600514 | − | 0.00782491i | ||||
\(872\) | −15.1059 | −0.511550 | ||||||||
\(873\) | 0.272296 | + | 0.272296i | 0.00921581 | + | 0.00921581i | ||||
\(874\) | − | 30.4299i | − | 1.02931i | ||||||
\(875\) | 12.9044 | + | 10.3178i | 0.436249 | + | 0.348804i | ||||
\(876\) | 5.89851 | − | 5.89851i | 0.199292 | − | 0.199292i | ||||
\(877\) | 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 | ||||
\(879\) | −8.93819 | − | 8.93819i | −0.301478 | − | 0.301478i | ||||
\(880\) | 1.48065i | 0.0499127i | ||||||||
\(881\) | −28.2254 | −0.950939 | −0.475470 | − | 0.879732i | \(-0.657722\pi\) | ||||
−0.475470 | + | 0.879732i | \(0.657722\pi\) | |||||||
\(882\) | −3.73926 | + | 5.91760i | −0.125907 | + | 0.199256i | ||||
\(883\) | 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 | ||||
\(885\) | 1.08688i | 0.0365351i | ||||||||
\(886\) | −15.8128 | + | 15.8128i | −0.531242 | + | 0.531242i | ||||
\(887\) | 57.2398i | 1.92192i | 0.276682 | + | 0.960962i | \(0.410765\pi\) | ||||
−0.276682 | + | 0.960962i | \(0.589235\pi\) | |||||||
\(888\) | 1.34778 | 0.0452284 | ||||||||
\(889\) | −41.5381 | + | 4.62684i | −1.39314 | + | 0.155179i | ||||
\(890\) | −5.57461 | + | 5.57461i | −0.186861 | + | 0.186861i | ||||
\(891\) | 1.60525 | + | 1.60525i | 0.0537777 | + | 0.0537777i | ||||
\(892\) | 11.0574 | − | 11.0574i | 0.370229 | − | 0.370229i | ||||
\(893\) | 7.14921 | 0.239239 | ||||||||
\(894\) | 4.42400 | 0.147961 | ||||||||
\(895\) | 1.17445 | − | 1.17445i | 0.0392576 | − | 0.0392576i | ||||
\(896\) | −1.65222 | + | 2.06644i | −0.0551969 | + | 0.0690348i | ||||
\(897\) | −21.4188 | − | 21.9844i | −0.715154 | − | 0.734038i | ||||
\(898\) | −4.76168 | −0.158899 | ||||||||
\(899\) | −7.29715 | − | 7.29715i | −0.243374 | − | 0.243374i | ||||
\(900\) | 4.57461 | 0.152487 | ||||||||
\(901\) | −58.2722 | −1.94133 | ||||||||
\(902\) | −8.84196 | − | 8.84196i | −0.294405 | − | 0.294405i | ||||
\(903\) | 1.22318 | + | 10.9813i | 0.0407049 | + | 0.365434i | ||||
\(904\) | 10.6247 | + | 10.6247i | 0.353372 | + | 0.353372i | ||||
\(905\) | −6.40745 | − | 6.40745i | −0.212991 | − | 0.212991i | ||||
\(906\) | − | 16.3345i | − | 0.542676i | ||||||
\(907\) | 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 | ||||
\(909\) | −8.03892 | −0.266634 | ||||||||
\(910\) | −3.94839 | + | 4.80844i | −0.130888 | + | 0.159398i | ||||
\(911\) | 27.0639 | 0.896666 | 0.448333 | − | 0.893867i | \(-0.352018\pi\) | ||||
0.448333 | + | 0.893867i | \(0.352018\pi\) | |||||||
\(912\) | −2.52763 | + | 2.52763i | −0.0836981 | + | 0.0836981i | ||||
\(913\) | − | 32.0690i | − | 1.06133i | ||||||
\(914\) | − | 17.6819i | − | 0.584866i | ||||||
\(915\) | −6.68147 | − | 6.68147i | −0.220883 | − | 0.220883i | ||||
\(916\) | −15.5860 | − | 15.5860i | −0.514976 | − | 0.514976i | ||||
\(917\) | −4.61534 | + | 0.514093i | −0.152412 | + | 0.0169768i | ||||
\(918\) | −4.52763 | − | 4.52763i | −0.149434 | − | 0.149434i | ||||
\(919\) | 38.1464 | 1.25833 | 0.629167 | − | 0.777270i | \(-0.283396\pi\) | ||||
0.629167 | + | 0.777270i | \(0.283396\pi\) | |||||||
\(920\) | −5.55224 | −0.183052 | ||||||||
\(921\) | −1.27177 | − | 1.27177i | −0.0419063 | − | 0.0419063i | ||||
\(922\) | 5.70945 | 0.188031 | ||||||||
\(923\) | 42.2839 | + | 0.550975i | 1.39179 | + | 0.0181356i | ||||
\(924\) | 3.75081 | − | 4.69114i | 0.123393 | − | 0.154327i | ||||
\(925\) | −4.35970 | + | 4.35970i | −0.143346 | + | 0.143346i | ||||
\(926\) | 18.1373 | 0.596028 | ||||||||
\(927\) | −7.62934 | −0.250580 | ||||||||
\(928\) | 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 | \(0.667093\pi\) | |||||||
\(930\) | 0.601599 | − | 0.601599i | 0.0197272 | − | 0.0197272i | ||||
\(931\) | 21.1531 | + | 13.3664i | 0.693264 | + | 0.438065i | ||||
\(932\) | 14.4240 | 0.472474 | ||||||||
\(933\) | 1.52201i | 0.0498284i | ||||||||
\(934\) | 12.0406 | − | 12.0406i | 0.393982 | − | 0.393982i | ||||
\(935\) | 9.48065i | 0.310050i | ||||||||
\(936\) | −0.0469777 | + | 3.60525i | −0.00153551 | + | 0.117841i | ||||
\(937\) | 47.2311i | 1.54297i | 0.636245 | + | 0.771487i | \(0.280487\pi\) | ||||
−0.636245 | + | 0.771487i | \(0.719513\pi\) | |||||||
\(938\) | 12.9261 | − | 1.43981i | 0.422053 | − | 0.0470116i | ||||
\(939\) | 3.48506 | 0.113731 | ||||||||
\(940\) | − | 1.30445i | − | 0.0425463i | ||||||
\(941\) | 27.0580 | + | 27.0580i | 0.882065 | + | 0.882065i | 0.993744 | − | 0.111680i | \(-0.0356231\pi\) |
−0.111680 | + | 0.993744i | \(0.535623\pi\) | |||||||
\(942\) | 13.1022 | − | 13.1022i | 0.426894 | − | 0.426894i | ||||
\(943\) | 33.1562 | − | 33.1562i | 1.07971 | − | 1.07971i | ||||
\(944\) | 1.17834 | − | 1.17834i | 0.0383517 | − | 0.0383517i | ||||
\(945\) | 1.34778 | + | 1.07762i | 0.0438432 | + | 0.0350549i | ||||
\(946\) | − | 9.48065i | − | 0.308243i | ||||||
\(947\) | −14.2815 | − | 14.2815i | −0.464085 | − | 0.464085i | 0.435907 | − | 0.899992i | \(-0.356428\pi\) |
−0.899992 | + | 0.435907i | \(0.856428\pi\) | |||||||
\(948\) | −9.18813 | −0.298417 | ||||||||
\(949\) | −30.0741 | − | 0.391876i | −0.976245 | − | 0.0127208i | ||||
\(950\) | − | 16.3524i | − | 0.530542i | ||||||
\(951\) | 3.61566 | + | 3.61566i | 0.117246 | + | 0.117246i | ||||
\(952\) | −10.5792 | + | 13.2315i | −0.342875 | + | 0.428834i | ||||
\(953\) | 6.01656i | 0.194895i | 0.995241 | + | 0.0974477i | \(0.0310679\pi\) | ||||
−0.995241 | + | 0.0974477i | \(0.968932\pi\) | |||||||
\(954\) | 6.43518 | − | 6.43518i | 0.208347 | − | 0.208347i | ||||
\(955\) | 4.71751 | + | 4.71751i | 0.152655 | + | 0.152655i | ||||
\(956\) | −3.83747 | − | 3.83747i | −0.124113 | − | 0.124113i | ||||
\(957\) | −12.6994 | + | 12.6994i | −0.410514 | + | 0.410514i | ||||
\(958\) | 32.1601i | 1.03905i | ||||||||
\(959\) | −4.27582 | + | 5.34778i | −0.138074 | + | 0.172689i | ||||
\(960\) | 0.461191 | + | 0.461191i | 0.0148849 | + | 0.0148849i | ||||
\(961\) | − | 29.2984i | − | 0.945110i | ||||||
\(962\) | −3.39111 | − | 3.48065i | −0.109334 | − | 0.112221i | ||||
\(963\) | 14.3986 | 0.463989 | ||||||||
\(964\) | −14.2110 | − | 14.2110i | −0.457706 | − | 0.457706i | ||||
\(965\) | − | 11.4320i | − | 0.368009i | ||||||
\(966\) | 17.5912 | + | 14.0650i | 0.565986 | + | 0.452535i | ||||
\(967\) | −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 | ||||
\(969\) | −16.1845 | + | 16.1845i | −0.519920 | + | 0.519920i | ||||
\(970\) | −0.177597 | − | 0.177597i | −0.00570231 | − | 0.00570231i | ||||
\(971\) | − | 37.3180i | − | 1.19759i | −0.800902 | − | 0.598795i | \(-0.795646\pi\) | ||
0.800902 | − | 0.598795i | \(-0.204354\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 36.4047 | − | 4.05504i | 1.16708 | − | 0.129999i | ||||
\(974\) | − | 11.8899i | − | 0.380978i | ||||||
\(975\) | −11.5101 | − | 11.8140i | −0.368617 | − | 0.378350i | ||||
\(976\) | 14.4874i | 0.463731i | ||||||||
\(977\) | −4.00859 | + | 4.00859i | −0.128246 | + | 0.128246i | −0.768316 | − | 0.640070i | \(-0.778905\pi\) |
0.640070 | + | 0.768316i | \(0.278905\pi\) | |||||||
\(978\) | 18.5307i | 0.592548i | ||||||||
\(979\) | −27.4403 | −0.876997 | ||||||||
\(980\) | 2.43883 | − | 3.85959i | 0.0779055 | − | 0.123290i | ||||
\(981\) | 10.6815 | − | 10.6815i | 0.341033 | − | 0.341033i | ||||
\(982\) | 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 | \(0.100468\pi\) | |||||||
\(984\) | −5.50817 | −0.175594 | ||||||||
\(985\) | −8.15974 | −0.259991 | ||||||||
\(986\) | 35.8190 | − | 35.8190i | 1.14071 | − | 1.14071i | ||||
\(987\) | −3.30445 | + | 4.13287i | −0.105182 | + | 0.131551i | ||||
\(988\) | 12.8873 | + | 0.167927i | 0.410001 | + | 0.00534246i | ||||
\(989\) | 35.5512 | 1.13046 | ||||||||
\(990\) | −1.04698 | − | 1.04698i | −0.0332751 | − | 0.0332751i | ||||
\(991\) | −16.1309 | −0.512415 | −0.256208 | − | 0.966622i | \(-0.582473\pi\) | ||||
−0.256208 | + | 0.966622i | \(0.582473\pi\) | |||||||
\(992\) | −1.30445 | −0.0414162 | ||||||||
\(993\) | 4.50162 | + | 4.50162i | 0.142855 | + | 0.142855i | ||||
\(994\) | −30.8398 | + | 3.43518i | −0.978180 | + | 0.108957i | ||||
\(995\) | −3.41733 | − | 3.41733i | −0.108337 | − | 0.108337i | ||||
\(996\) | −9.98882 | − | 9.98882i | −0.316508 | − | 0.316508i | ||||
\(997\) | − | 32.1324i | − | 1.01764i | −0.860872 | − | 0.508821i | \(-0.830081\pi\) | ||
0.860872 | − | 0.508821i | \(-0.169919\pi\) | |||||||
\(998\) | 5.84446i | 0.185003i | ||||||||
\(999\) | −0.953022 | + | 0.953022i | −0.0301523 | + | 0.0301523i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 546.2.o.c.265.1 | yes | 8 | |
3.2 | odd | 2 | 1638.2.x.a.811.4 | 8 | |||
7.6 | odd | 2 | 546.2.o.b.265.2 | ✓ | 8 | ||
13.8 | odd | 4 | 546.2.o.b.307.2 | yes | 8 | ||
21.20 | even | 2 | 1638.2.x.c.811.3 | 8 | |||
39.8 | even | 4 | 1638.2.x.c.307.3 | 8 | |||
91.34 | even | 4 | inner | 546.2.o.c.307.1 | yes | 8 | |
273.125 | odd | 4 | 1638.2.x.a.307.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.o.b.265.2 | ✓ | 8 | 7.6 | odd | 2 | ||
546.2.o.b.307.2 | yes | 8 | 13.8 | odd | 4 | ||
546.2.o.c.265.1 | yes | 8 | 1.1 | even | 1 | trivial | |
546.2.o.c.307.1 | yes | 8 | 91.34 | even | 4 | inner | |
1638.2.x.a.307.4 | 8 | 273.125 | odd | 4 | |||
1638.2.x.a.811.4 | 8 | 3.2 | odd | 2 | |||
1638.2.x.c.307.3 | 8 | 39.8 | even | 4 | |||
1638.2.x.c.811.3 | 8 | 21.20 | even | 2 |