Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(81,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.g (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.13140625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 55) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 511.2 | ||
Root | \(-0.227943 + 0.701538i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.511 |
Dual form | 605.2.g.e.251.2 |
$q$-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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.227943 | + | 0.701538i | 0.161180 | + | 0.496062i | 0.998735 | − | 0.0502922i | \(-0.0160153\pi\) |
−0.837554 | + | 0.546354i | \(0.816015\pi\) | |||||||
\(3\) | 2.27460 | + | 1.65259i | 1.31324 | + | 0.954126i | 0.999990 | + | 0.00445538i | \(0.00141820\pi\) |
0.313251 | + | 0.949670i | \(0.398582\pi\) | |||||||
\(4\) | 1.17784 | − | 0.855749i | 0.588919 | − | 0.427874i | ||||
\(5\) | −0.309017 | + | 0.951057i | −0.138197 | + | 0.425325i | ||||
\(6\) | −0.640877 | + | 1.97242i | −0.261637 | + | 0.805235i | ||||
\(7\) | 0.834404 | − | 0.606230i | 0.315375 | − | 0.229133i | −0.418824 | − | 0.908067i | \(-0.637558\pi\) |
0.734199 | + | 0.678934i | \(0.237558\pi\) | |||||||
\(8\) | 2.06235 | + | 1.49838i | 0.729150 | + | 0.529758i | ||||
\(9\) | 1.51569 | + | 4.66481i | 0.505230 | + | 1.55494i | ||||
\(10\) | −0.737640 | −0.233262 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 4.09331 | 1.18164 | ||||||||
\(13\) | −1.06580 | − | 3.28018i | −0.295599 | − | 0.909759i | −0.983020 | − | 0.183500i | \(-0.941257\pi\) |
0.687421 | − | 0.726259i | \(-0.258743\pi\) | |||||||
\(14\) | 0.615490 | + | 0.447180i | 0.164497 | + | 0.119514i | ||||
\(15\) | −2.27460 | + | 1.65259i | −0.587299 | + | 0.426698i | ||||
\(16\) | 0.318714 | − | 0.980901i | 0.0796785 | − | 0.245225i | ||||
\(17\) | −0.741089 | + | 2.28084i | −0.179741 | + | 0.553185i | −0.999818 | − | 0.0190677i | \(-0.993930\pi\) |
0.820078 | + | 0.572252i | \(0.193930\pi\) | |||||||
\(18\) | −2.92705 | + | 2.12663i | −0.689913 | + | 0.501251i | ||||
\(19\) | −6.20420 | − | 4.50761i | −1.42334 | − | 1.03412i | −0.991209 | − | 0.132306i | \(-0.957762\pi\) |
−0.432131 | − | 0.901811i | \(-0.642238\pi\) | |||||||
\(20\) | 0.449894 | + | 1.38463i | 0.100599 | + | 0.309613i | ||||
\(21\) | 2.89979 | 0.632786 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.45589 | 0.512088 | 0.256044 | − | 0.966665i | \(-0.417581\pi\) | ||||
0.256044 | + | 0.966665i | \(0.417581\pi\) | |||||||
\(24\) | 2.21480 | + | 6.81645i | 0.452094 | + | 1.39140i | ||||
\(25\) | −0.809017 | − | 0.587785i | −0.161803 | − | 0.117557i | ||||
\(26\) | 2.05823 | − | 1.49539i | 0.403652 | − | 0.293271i | ||||
\(27\) | −1.65499 | + | 5.09355i | −0.318504 | + | 0.980254i | ||||
\(28\) | 0.464011 | − | 1.42808i | 0.0876899 | − | 0.269882i | ||||
\(29\) | −4.81714 | + | 3.49986i | −0.894521 | + | 0.649907i | −0.937053 | − | 0.349188i | \(-0.886458\pi\) |
0.0425320 | + | 0.999095i | \(0.486458\pi\) | |||||||
\(30\) | −1.67784 | − | 1.21902i | −0.306330 | − | 0.222562i | ||||
\(31\) | −1.13972 | − | 3.50769i | −0.204699 | − | 0.629999i | −0.999726 | − | 0.0234246i | \(-0.992543\pi\) |
0.795026 | − | 0.606575i | \(-0.207457\pi\) | |||||||
\(32\) | 5.85919 | 1.03577 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.76902 | −0.303384 | ||||||||
\(35\) | 0.318714 | + | 0.980901i | 0.0538725 | + | 0.165802i | ||||
\(36\) | 5.77714 | + | 4.19734i | 0.962857 | + | 0.699557i | ||||
\(37\) | −4.82059 | + | 3.50236i | −0.792500 | + | 0.575785i | −0.908704 | − | 0.417440i | \(-0.862927\pi\) |
0.116204 | + | 0.993225i | \(0.462927\pi\) | |||||||
\(38\) | 1.74805 | − | 5.37996i | 0.283572 | − | 0.872744i | ||||
\(39\) | 2.99655 | − | 9.22244i | 0.479832 | − | 1.47677i | ||||
\(40\) | −2.06235 | + | 1.49838i | −0.326086 | + | 0.236915i | ||||
\(41\) | 3.18450 | + | 2.31367i | 0.497335 | + | 0.361335i | 0.807998 | − | 0.589185i | \(-0.200551\pi\) |
−0.310663 | + | 0.950520i | \(0.600551\pi\) | |||||||
\(42\) | 0.660987 | + | 2.03431i | 0.101993 | + | 0.313901i | ||||
\(43\) | 7.64941 | 1.16652 | 0.583262 | − | 0.812284i | \(-0.301776\pi\) | ||||
0.583262 | + | 0.812284i | \(0.301776\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.90488 | −0.731176 | ||||||||
\(46\) | 0.559803 | + | 1.72290i | 0.0825385 | + | 0.254027i | ||||
\(47\) | −4.72704 | − | 3.43439i | −0.689509 | − | 0.500958i | 0.186989 | − | 0.982362i | \(-0.440127\pi\) |
−0.876499 | + | 0.481404i | \(0.840127\pi\) | |||||||
\(48\) | 2.34598 | − | 1.70445i | 0.338613 | − | 0.246017i | ||||
\(49\) | −1.83440 | + | 5.64571i | −0.262058 | + | 0.806531i | ||||
\(50\) | 0.227943 | − | 0.701538i | 0.0322361 | − | 0.0992124i | ||||
\(51\) | −5.45498 | + | 3.96328i | −0.763850 | + | 0.554970i | ||||
\(52\) | −4.06235 | − | 2.95147i | −0.563346 | − | 0.409295i | ||||
\(53\) | −3.66124 | − | 11.2681i | −0.502910 | − | 1.54780i | −0.804256 | − | 0.594284i | \(-0.797436\pi\) |
0.301345 | − | 0.953515i | \(-0.402564\pi\) | |||||||
\(54\) | −3.95056 | −0.537603 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.62920 | 0.351341 | ||||||||
\(57\) | −6.66281 | − | 20.5060i | −0.882511 | − | 2.71609i | ||||
\(58\) | −3.55332 | − | 2.58164i | −0.466573 | − | 0.338985i | ||||
\(59\) | −2.38361 | + | 1.73179i | −0.310319 | + | 0.225460i | −0.732033 | − | 0.681269i | \(-0.761428\pi\) |
0.421714 | + | 0.906729i | \(0.361428\pi\) | |||||||
\(60\) | −1.26490 | + | 3.89297i | −0.163298 | + | 0.502581i | ||||
\(61\) | −0.766476 | + | 2.35897i | −0.0981372 | + | 0.302035i | −0.988059 | − | 0.154079i | \(-0.950759\pi\) |
0.889921 | + | 0.456114i | \(0.150759\pi\) | |||||||
\(62\) | 2.20098 | − | 1.59911i | 0.279525 | − | 0.203087i | ||||
\(63\) | 4.09265 | + | 2.97348i | 0.515625 | + | 0.374624i | ||||
\(64\) | 0.698136 | + | 2.14864i | 0.0872670 | + | 0.268580i | ||||
\(65\) | 3.44899 | 0.427794 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.14702 | −0.750978 | −0.375489 | − | 0.926827i | \(-0.622525\pi\) | ||||
−0.375489 | + | 0.926827i | \(0.622525\pi\) | |||||||
\(68\) | 1.07894 | + | 3.32064i | 0.130841 | + | 0.402687i | ||||
\(69\) | 5.58616 | + | 4.05858i | 0.672495 | + | 0.488596i | ||||
\(70\) | −0.615490 | + | 0.447180i | −0.0735651 | + | 0.0534482i | ||||
\(71\) | 0.625187 | − | 1.92413i | 0.0741960 | − | 0.228352i | −0.907080 | − | 0.420958i | \(-0.861694\pi\) |
0.981276 | + | 0.192606i | \(0.0616940\pi\) | |||||||
\(72\) | −3.86380 | + | 11.8916i | −0.455353 | + | 1.40143i | ||||
\(73\) | −0.668140 | + | 0.485432i | −0.0781999 | + | 0.0568156i | −0.626198 | − | 0.779664i | \(-0.715390\pi\) |
0.547998 | + | 0.836479i | \(0.315390\pi\) | |||||||
\(74\) | −3.55586 | − | 2.58348i | −0.413361 | − | 0.300324i | ||||
\(75\) | −0.868820 | − | 2.67395i | −0.100323 | − | 0.308762i | ||||
\(76\) | −11.1649 | −1.28070 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 7.15293 | 0.809910 | ||||||||
\(79\) | 3.73236 | + | 11.4870i | 0.419924 | + | 1.29239i | 0.907772 | + | 0.419464i | \(0.137782\pi\) |
−0.487848 | + | 0.872928i | \(0.662218\pi\) | |||||||
\(80\) | 0.834404 | + | 0.606230i | 0.0932892 | + | 0.0677786i | ||||
\(81\) | −0.277637 | + | 0.201715i | −0.0308486 | + | 0.0224128i | ||||
\(82\) | −0.897243 | + | 2.76143i | −0.0990840 | + | 0.304949i | ||||
\(83\) | −0.497523 | + | 1.53122i | −0.0546102 | + | 0.168073i | −0.974642 | − | 0.223772i | \(-0.928163\pi\) |
0.920031 | + | 0.391845i | \(0.128163\pi\) | |||||||
\(84\) | 3.41548 | − | 2.48149i | 0.372659 | − | 0.270753i | ||||
\(85\) | −1.94020 | − | 1.40964i | −0.210444 | − | 0.152896i | ||||
\(86\) | 1.74363 | + | 5.36635i | 0.188021 | + | 0.578669i | ||||
\(87\) | −16.7409 | −1.79481 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.16116 | 0.865081 | 0.432541 | − | 0.901614i | \(-0.357617\pi\) | ||||
0.432541 | + | 0.901614i | \(0.357617\pi\) | |||||||
\(90\) | −1.11803 | − | 3.44095i | −0.117851 | − | 0.362708i | ||||
\(91\) | −2.87785 | − | 2.09088i | −0.301681 | − | 0.219184i | ||||
\(92\) | 2.89263 | − | 2.10162i | 0.301578 | − | 0.219109i | ||||
\(93\) | 3.20438 | − | 9.86208i | 0.332279 | − | 1.02265i | ||||
\(94\) | 1.33186 | − | 4.09904i | 0.137371 | − | 0.422784i | ||||
\(95\) | 6.20420 | − | 4.50761i | 0.636537 | − | 0.462471i | ||||
\(96\) | 13.3273 | + | 9.68286i | 1.36021 | + | 0.988253i | ||||
\(97\) | 0.754861 | + | 2.32322i | 0.0766445 | + | 0.235888i | 0.982037 | − | 0.188688i | \(-0.0604234\pi\) |
−0.905393 | + | 0.424575i | \(0.860423\pi\) | |||||||
\(98\) | −4.37882 | −0.442328 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.45589 | −0.145589 | ||||||||
\(101\) | 2.32496 | + | 7.15550i | 0.231342 | + | 0.711999i | 0.997586 | + | 0.0694479i | \(0.0221238\pi\) |
−0.766243 | + | 0.642551i | \(0.777876\pi\) | |||||||
\(102\) | −4.02381 | − | 2.92347i | −0.398417 | − | 0.289467i | ||||
\(103\) | 7.67135 | − | 5.57356i | 0.755881 | − | 0.549180i | −0.141763 | − | 0.989901i | \(-0.545277\pi\) |
0.897644 | + | 0.440721i | \(0.145277\pi\) | |||||||
\(104\) | 2.71693 | − | 8.36185i | 0.266417 | − | 0.819947i | ||||
\(105\) | −0.896084 | + | 2.75786i | −0.0874488 | + | 0.269140i | ||||
\(106\) | 7.07047 | − | 5.13700i | 0.686745 | − | 0.498949i | ||||
\(107\) | −3.75932 | − | 2.73131i | −0.363427 | − | 0.264046i | 0.391053 | − | 0.920368i | \(-0.372111\pi\) |
−0.754480 | + | 0.656323i | \(0.772111\pi\) | |||||||
\(108\) | 2.40948 | + | 7.41563i | 0.231853 | + | 0.713569i | ||||
\(109\) | 5.32826 | 0.510355 | 0.255178 | − | 0.966894i | \(-0.417866\pi\) | ||||
0.255178 | + | 0.966894i | \(0.417866\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −16.7529 | −1.59012 | ||||||||
\(112\) | −0.328715 | − | 1.01168i | −0.0310607 | − | 0.0955949i | ||||
\(113\) | −0.246670 | − | 0.179216i | −0.0232047 | − | 0.0168592i | 0.576122 | − | 0.817363i | \(-0.304565\pi\) |
−0.599327 | + | 0.800504i | \(0.704565\pi\) | |||||||
\(114\) | 12.8670 | − | 9.34843i | 1.20511 | − | 0.875561i | ||||
\(115\) | −0.758911 | + | 2.33569i | −0.0707688 | + | 0.217804i | ||||
\(116\) | −2.67881 | + | 8.24453i | −0.248721 | + | 0.765485i | ||||
\(117\) | 13.6860 | − | 9.94348i | 1.26527 | − | 0.919275i | ||||
\(118\) | −1.75824 | − | 1.27744i | −0.161859 | − | 0.117598i | ||||
\(119\) | 0.764345 | + | 2.35241i | 0.0700673 | + | 0.215645i | ||||
\(120\) | −7.16724 | −0.654276 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.82962 | −0.165646 | ||||||||
\(123\) | 3.41990 | + | 10.5254i | 0.308362 | + | 0.949040i | ||||
\(124\) | −4.34410 | − | 3.15617i | −0.390112 | − | 0.283433i | ||||
\(125\) | 0.809017 | − | 0.587785i | 0.0723607 | − | 0.0525731i | ||||
\(126\) | −1.15312 | + | 3.54893i | −0.102728 | + | 0.316164i | ||||
\(127\) | 3.68038 | − | 11.3270i | 0.326581 | − | 1.00511i | −0.644141 | − | 0.764907i | \(-0.722785\pi\) |
0.970722 | − | 0.240206i | \(-0.0772150\pi\) | |||||||
\(128\) | 8.13215 | − | 5.90835i | 0.718787 | − | 0.522230i | ||||
\(129\) | 17.3994 | + | 12.6414i | 1.53193 | + | 1.11301i | ||||
\(130\) | 0.786174 | + | 2.41960i | 0.0689520 | + | 0.212213i | ||||
\(131\) | 11.1875 | 0.977452 | 0.488726 | − | 0.872437i | \(-0.337462\pi\) | ||||
0.488726 | + | 0.872437i | \(0.337462\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.90945 | −0.685837 | ||||||||
\(134\) | −1.40117 | − | 4.31236i | −0.121043 | − | 0.372531i | ||||
\(135\) | −4.33283 | − | 3.14799i | −0.372911 | − | 0.270936i | ||||
\(136\) | −4.94595 | + | 3.59344i | −0.424112 | + | 0.308135i | ||||
\(137\) | −1.32298 | + | 4.07170i | −0.113030 | + | 0.347869i | −0.991531 | − | 0.129871i | \(-0.958544\pi\) |
0.878501 | + | 0.477740i | \(0.158544\pi\) | |||||||
\(138\) | −1.57392 | + | 4.84403i | −0.133981 | + | 0.412351i | ||||
\(139\) | −4.81624 | + | 3.49920i | −0.408508 | + | 0.296798i | −0.772997 | − | 0.634409i | \(-0.781243\pi\) |
0.364490 | + | 0.931207i | \(0.381243\pi\) | |||||||
\(140\) | 1.21480 | + | 0.882602i | 0.102669 | + | 0.0745935i | ||||
\(141\) | −5.07646 | − | 15.6238i | −0.427515 | − | 1.31576i | ||||
\(142\) | 1.49235 | 0.125236 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 5.05879 | 0.421566 | ||||||||
\(145\) | −1.83998 | − | 5.66289i | −0.152802 | − | 0.470277i | ||||
\(146\) | −0.492847 | − | 0.358074i | −0.0407883 | − | 0.0296345i | ||||
\(147\) | −13.5026 | + | 9.81022i | −1.11368 | + | 0.809133i | ||||
\(148\) | −2.68073 | + | 8.25043i | −0.220354 | + | 0.678181i | ||||
\(149\) | 1.16946 | − | 3.59922i | 0.0958057 | − | 0.294860i | −0.891657 | − | 0.452711i | \(-0.850457\pi\) |
0.987463 | + | 0.157852i | \(0.0504568\pi\) | |||||||
\(150\) | 1.67784 | − | 1.21902i | 0.136995 | − | 0.0995326i | ||||
\(151\) | −19.7049 | − | 14.3165i | −1.60356 | − | 1.16506i | −0.880214 | − | 0.474576i | \(-0.842601\pi\) |
−0.723350 | − | 0.690481i | \(-0.757399\pi\) | |||||||
\(152\) | −6.04108 | − | 18.5925i | −0.489996 | − | 1.50805i | ||||
\(153\) | −11.7629 | −0.950978 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.68820 | 0.296243 | ||||||||
\(156\) | −4.36264 | − | 13.4268i | −0.349291 | − | 1.07501i | ||||
\(157\) | −5.85089 | − | 4.25092i | −0.466952 | − | 0.339260i | 0.329300 | − | 0.944225i | \(-0.393187\pi\) |
−0.796252 | + | 0.604965i | \(0.793187\pi\) | |||||||
\(158\) | −7.20782 | + | 5.23679i | −0.573423 | + | 0.416616i | ||||
\(159\) | 10.2938 | − | 31.6811i | 0.816352 | − | 2.51247i | ||||
\(160\) | −1.81059 | + | 5.57242i | −0.143140 | + | 0.440539i | ||||
\(161\) | 2.04920 | − | 1.48883i | 0.161500 | − | 0.117336i | ||||
\(162\) | −0.204796 | − | 0.148793i | −0.0160903 | − | 0.0116903i | ||||
\(163\) | 5.77527 | + | 17.7744i | 0.452354 | + | 1.39220i | 0.874214 | + | 0.485541i | \(0.161377\pi\) |
−0.421860 | + | 0.906661i | \(0.638623\pi\) | |||||||
\(164\) | 5.73074 | 0.447496 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.18761 | −0.0921767 | ||||||||
\(167\) | −2.42680 | − | 7.46891i | −0.187791 | − | 0.577962i | 0.812194 | − | 0.583387i | \(-0.198273\pi\) |
−0.999985 | + | 0.00542559i | \(0.998273\pi\) | |||||||
\(168\) | 5.98037 | + | 4.34499i | 0.461395 | + | 0.335223i | ||||
\(169\) | 0.893540 | − | 0.649194i | 0.0687338 | − | 0.0499380i | ||||
\(170\) | 0.546657 | − | 1.68244i | 0.0419267 | − | 0.129037i | ||||
\(171\) | 11.6235 | − | 35.7736i | 0.888874 | − | 2.73567i | ||||
\(172\) | 9.00976 | − | 6.54598i | 0.686988 | − | 0.499126i | ||||
\(173\) | 9.06478 | + | 6.58595i | 0.689183 | + | 0.500721i | 0.876391 | − | 0.481600i | \(-0.159944\pi\) |
−0.187209 | + | 0.982320i | \(0.559944\pi\) | |||||||
\(174\) | −3.81598 | − | 11.7444i | −0.289289 | − | 0.890339i | ||||
\(175\) | −1.03138 | −0.0779650 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.28370 | −0.622641 | ||||||||
\(178\) | 1.86028 | + | 5.72536i | 0.139434 | + | 0.429134i | ||||
\(179\) | −1.18491 | − | 0.860888i | −0.0885643 | − | 0.0643458i | 0.542622 | − | 0.839977i | \(-0.317432\pi\) |
−0.631186 | + | 0.775631i | \(0.717432\pi\) | |||||||
\(180\) | −5.77714 | + | 4.19734i | −0.430603 | + | 0.312851i | ||||
\(181\) | 2.87046 | − | 8.83437i | 0.213360 | − | 0.656653i | −0.785906 | − | 0.618345i | \(-0.787803\pi\) |
0.999266 | − | 0.0383078i | \(-0.0121967\pi\) | |||||||
\(182\) | 0.810844 | − | 2.49552i | 0.0601038 | − | 0.184980i | ||||
\(183\) | −5.64185 | + | 4.09904i | −0.417057 | + | 0.303010i | ||||
\(184\) | 5.06489 | + | 3.67986i | 0.373389 | + | 0.271283i | ||||
\(185\) | −1.84130 | − | 5.66694i | −0.135375 | − | 0.416642i | ||||
\(186\) | 7.64904 | 0.560855 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −8.50666 | −0.620412 | ||||||||
\(189\) | 1.70693 | + | 5.25338i | 0.124161 | + | 0.382127i | ||||
\(190\) | 4.57646 | + | 3.32500i | 0.332012 | + | 0.241221i | ||||
\(191\) | 3.61870 | − | 2.62914i | 0.261840 | − | 0.190238i | −0.449118 | − | 0.893473i | \(-0.648262\pi\) |
0.710958 | + | 0.703235i | \(0.248262\pi\) | |||||||
\(192\) | −1.96285 | + | 6.04104i | −0.141657 | + | 0.435974i | ||||
\(193\) | 7.00418 | − | 21.5567i | 0.504172 | − | 1.55168i | −0.297986 | − | 0.954570i | \(-0.596315\pi\) |
0.802158 | − | 0.597112i | \(-0.203685\pi\) | |||||||
\(194\) | −1.45776 | + | 1.05913i | −0.104661 | + | 0.0760409i | ||||
\(195\) | 7.84507 | + | 5.69978i | 0.561797 | + | 0.408170i | ||||
\(196\) | 2.67068 | + | 8.21952i | 0.190763 | + | 0.587109i | ||||
\(197\) | 11.2080 | 0.798535 | 0.399267 | − | 0.916835i | \(-0.369265\pi\) | ||||
0.399267 | + | 0.916835i | \(0.369265\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.81979 | −0.554330 | −0.277165 | − | 0.960822i | \(-0.589395\pi\) | ||||
−0.277165 | + | 0.960822i | \(0.589395\pi\) | |||||||
\(200\) | −0.787747 | − | 2.42443i | −0.0557021 | − | 0.171433i | ||||
\(201\) | −13.9820 | − | 10.1585i | −0.986215 | − | 0.716527i | ||||
\(202\) | −4.48989 | + | 3.26210i | −0.315908 | + | 0.229520i | ||||
\(203\) | −1.89772 | + | 5.84059i | −0.133194 | + | 0.409929i | ||||
\(204\) | −3.03351 | + | 9.33619i | −0.212388 | + | 0.653664i | ||||
\(205\) | −3.18450 | + | 2.31367i | −0.222415 | + | 0.161594i | ||||
\(206\) | 5.65870 | + | 4.11128i | 0.394260 | + | 0.286447i | ||||
\(207\) | 3.72236 | + | 11.4563i | 0.258722 | + | 0.796265i | ||||
\(208\) | −3.55722 | −0.246649 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −2.13900 | −0.147605 | ||||||||
\(211\) | 7.03539 | + | 21.6527i | 0.484336 | + | 1.49063i | 0.832940 | + | 0.553363i | \(0.186656\pi\) |
−0.348604 | + | 0.937270i | \(0.613344\pi\) | |||||||
\(212\) | −13.9550 | − | 10.1389i | −0.958437 | − | 0.696345i | ||||
\(213\) | 4.60185 | − | 3.34344i | 0.315314 | − | 0.229089i | ||||
\(214\) | 1.05920 | − | 3.25989i | 0.0724056 | − | 0.222842i | ||||
\(215\) | −2.36380 | + | 7.27502i | −0.161210 | + | 0.496153i | ||||
\(216\) | −11.0453 | + | 8.02485i | −0.751535 | + | 0.546022i | ||||
\(217\) | −3.07745 | − | 2.23590i | −0.208911 | − | 0.151783i | ||||
\(218\) | 1.21454 | + | 3.73798i | 0.0822592 | + | 0.253168i | ||||
\(219\) | −2.32197 | −0.156905 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.27142 | 0.556396 | ||||||||
\(222\) | −3.81871 | − | 11.7528i | −0.256295 | − | 0.788796i | ||||
\(223\) | 12.9788 | + | 9.42965i | 0.869124 | + | 0.631456i | 0.930352 | − | 0.366668i | \(-0.119501\pi\) |
−0.0612274 | + | 0.998124i | \(0.519501\pi\) | |||||||
\(224\) | 4.88893 | − | 3.55202i | 0.326655 | − | 0.237329i | ||||
\(225\) | 1.51569 | − | 4.66481i | 0.101046 | − | 0.310988i | ||||
\(226\) | 0.0695001 | − | 0.213899i | 0.00462308 | − | 0.0142284i | ||||
\(227\) | −19.5428 | + | 14.1987i | −1.29710 | + | 0.942398i | −0.999923 | − | 0.0124240i | \(-0.996045\pi\) |
−0.297177 | + | 0.954822i | \(0.596045\pi\) | |||||||
\(228\) | −25.3957 | − | 18.4511i | −1.68187 | − | 1.22195i | ||||
\(229\) | −4.63967 | − | 14.2794i | −0.306598 | − | 0.943611i | −0.979076 | − | 0.203494i | \(-0.934770\pi\) |
0.672478 | − | 0.740117i | \(-0.265230\pi\) | |||||||
\(230\) | −1.81156 | −0.119451 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −15.1787 | −0.996534 | ||||||||
\(233\) | −3.53081 | − | 10.8667i | −0.231311 | − | 0.711902i | −0.997589 | − | 0.0693934i | \(-0.977894\pi\) |
0.766278 | − | 0.642509i | \(-0.222106\pi\) | |||||||
\(234\) | 10.0954 | + | 7.33471i | 0.659955 | + | 0.479485i | ||||
\(235\) | 4.72704 | − | 3.43439i | 0.308358 | − | 0.224035i | ||||
\(236\) | −1.32552 | + | 4.07953i | −0.0862841 | + | 0.265555i | ||||
\(237\) | −10.4938 | + | 32.2965i | −0.681644 | + | 2.09788i | ||||
\(238\) | −1.47608 | + | 1.07243i | −0.0956799 | + | 0.0695155i | ||||
\(239\) | 22.1725 | + | 16.1093i | 1.43422 | + | 1.04202i | 0.989211 | + | 0.146495i | \(0.0467993\pi\) |
0.445008 | + | 0.895526i | \(0.353201\pi\) | |||||||
\(240\) | 0.896084 | + | 2.75786i | 0.0578419 | + | 0.178019i | ||||
\(241\) | −10.9387 | −0.704624 | −0.352312 | − | 0.935883i | \(-0.614604\pi\) | ||||
−0.352312 | + | 0.935883i | \(0.614604\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.1022 | 0.968804 | ||||||||
\(244\) | 1.11590 | + | 3.43439i | 0.0714383 | + | 0.219865i | ||||
\(245\) | −4.80253 | − | 3.48924i | −0.306822 | − | 0.222920i | ||||
\(246\) | −6.60440 | + | 4.79837i | −0.421081 | + | 0.305933i | ||||
\(247\) | −8.17339 | + | 25.1551i | −0.520060 | + | 1.60058i | ||||
\(248\) | 2.90537 | − | 8.94180i | 0.184491 | − | 0.567805i | ||||
\(249\) | −3.66215 | + | 2.66071i | −0.232079 | + | 0.168615i | ||||
\(250\) | 0.596764 | + | 0.433574i | 0.0377426 | + | 0.0274216i | ||||
\(251\) | 5.32471 | + | 16.3878i | 0.336093 | + | 1.03439i | 0.966181 | + | 0.257863i | \(0.0830184\pi\) |
−0.630089 | + | 0.776523i | \(0.716982\pi\) | |||||||
\(252\) | 7.36503 | 0.463953 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 8.78527 | 0.551237 | ||||||||
\(255\) | −2.08362 | − | 6.41272i | −0.130481 | − | 0.401580i | ||||
\(256\) | 9.65409 | + | 7.01411i | 0.603381 | + | 0.438382i | ||||
\(257\) | −14.9631 | + | 10.8713i | −0.933373 | + | 0.678135i | −0.946816 | − | 0.321774i | \(-0.895721\pi\) |
0.0134434 | + | 0.999910i | \(0.495721\pi\) | |||||||
\(258\) | −4.90233 | + | 15.0878i | −0.305206 | + | 0.939327i | ||||
\(259\) | −1.89908 | + | 5.84477i | −0.118003 | + | 0.363176i | ||||
\(260\) | 4.06235 | − | 2.95147i | 0.251936 | − | 0.183042i | ||||
\(261\) | −23.6275 | − | 17.1664i | −1.46250 | − | 1.06257i | ||||
\(262\) | 2.55011 | + | 7.84842i | 0.157546 | + | 0.484877i | ||||
\(263\) | −3.69135 | −0.227618 | −0.113809 | − | 0.993503i | \(-0.536305\pi\) | ||||
−0.113809 | + | 0.993503i | \(0.536305\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.8480 | 0.727819 | ||||||||
\(266\) | −1.80291 | − | 5.54878i | −0.110543 | − | 0.340217i | ||||
\(267\) | 18.5634 | + | 13.4871i | 1.13606 | + | 0.825396i | ||||
\(268\) | −7.24018 | + | 5.26030i | −0.442265 | + | 0.321324i | ||||
\(269\) | −3.07320 | + | 9.45835i | −0.187377 | + | 0.576686i | −0.999981 | − | 0.00612956i | \(-0.998049\pi\) |
0.812605 | + | 0.582815i | \(0.198049\pi\) | |||||||
\(270\) | 1.22079 | − | 3.75721i | 0.0742949 | − | 0.228656i | ||||
\(271\) | 1.01423 | − | 0.736878i | 0.0616098 | − | 0.0447622i | −0.556554 | − | 0.830811i | \(-0.687877\pi\) |
0.618164 | + | 0.786049i | \(0.287877\pi\) | |||||||
\(272\) | 2.00108 | + | 1.45387i | 0.121333 | + | 0.0881538i | ||||
\(273\) | −3.09058 | − | 9.51183i | −0.187051 | − | 0.575682i | ||||
\(274\) | −3.15802 | −0.190783 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 10.0527 | 0.605102 | ||||||||
\(277\) | 2.50097 | + | 7.69720i | 0.150269 | + | 0.462480i | 0.997651 | − | 0.0685038i | \(-0.0218225\pi\) |
−0.847382 | + | 0.530984i | \(0.821823\pi\) | |||||||
\(278\) | −3.55265 | − | 2.58115i | −0.213074 | − | 0.154807i | ||||
\(279\) | 14.6353 | − | 10.6331i | 0.876190 | − | 0.636589i | ||||
\(280\) | −0.812466 | + | 2.50051i | −0.0485541 | + | 0.149434i | ||||
\(281\) | −7.83984 | + | 24.1285i | −0.467686 | + | 1.43939i | 0.387888 | + | 0.921707i | \(0.373205\pi\) |
−0.855573 | + | 0.517681i | \(0.826795\pi\) | |||||||
\(282\) | 9.80350 | − | 7.12266i | 0.583790 | − | 0.424148i | ||||
\(283\) | −16.5383 | − | 12.0157i | −0.983097 | − | 0.714262i | −0.0246985 | − | 0.999695i | \(-0.507863\pi\) |
−0.958399 | + | 0.285433i | \(0.907863\pi\) | |||||||
\(284\) | −0.910201 | − | 2.80131i | −0.0540105 | − | 0.166227i | ||||
\(285\) | 21.5613 | 1.27718 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.05977 | 0.239641 | ||||||||
\(288\) | 8.88072 | + | 27.3320i | 0.523301 | + | 1.61056i | ||||
\(289\) | 9.10028 | + | 6.61174i | 0.535311 | + | 0.388926i | ||||
\(290\) | 3.55332 | − | 2.58164i | 0.208658 | − | 0.151599i | ||||
\(291\) | −2.12234 | + | 6.53189i | −0.124414 | + | 0.382906i | ||||
\(292\) | −0.371552 | + | 1.14352i | −0.0217435 | + | 0.0669195i | ||||
\(293\) | 2.06224 | − | 1.49830i | 0.120477 | − | 0.0875319i | −0.525915 | − | 0.850537i | \(-0.676277\pi\) |
0.646392 | + | 0.763005i | \(0.276277\pi\) | |||||||
\(294\) | −9.96007 | − | 7.23641i | −0.580883 | − | 0.422036i | ||||
\(295\) | −0.910456 | − | 2.80210i | −0.0530088 | − | 0.163144i | ||||
\(296\) | −15.1896 | −0.882878 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.79156 | 0.161711 | ||||||||
\(299\) | −2.61747 | − | 8.05576i | −0.151372 | − | 0.465877i | ||||
\(300\) | −3.31156 | − | 2.40599i | −0.191193 | − | 0.138910i | ||||
\(301\) | 6.38270 | − | 4.63730i | 0.367893 | − | 0.267290i | ||||
\(302\) | 5.55193 | − | 17.0871i | 0.319478 | − | 0.983252i | ||||
\(303\) | −6.53677 | + | 20.1181i | −0.375528 | + | 1.15576i | ||||
\(304\) | −6.39888 | + | 4.64906i | −0.367001 | + | 0.266642i | ||||
\(305\) | −2.00666 | − | 1.45792i | −0.114901 | − | 0.0834805i | ||||
\(306\) | −2.68129 | − | 8.25215i | −0.153279 | − | 0.471744i | ||||
\(307\) | −8.99273 | −0.513242 | −0.256621 | − | 0.966512i | \(-0.582609\pi\) | ||||
−0.256621 | + | 0.966512i | \(0.582609\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 26.6601 | 1.51664 | ||||||||
\(310\) | 0.840701 | + | 2.58741i | 0.0477486 | + | 0.146955i | ||||
\(311\) | 16.2800 | + | 11.8281i | 0.923154 | + | 0.670710i | 0.944307 | − | 0.329066i | \(-0.106734\pi\) |
−0.0211533 | + | 0.999776i | \(0.506734\pi\) | |||||||
\(312\) | 19.9987 | − | 14.5299i | 1.13220 | − | 0.822593i | ||||
\(313\) | 2.19551 | − | 6.75709i | 0.124098 | − | 0.381933i | −0.869638 | − | 0.493690i | \(-0.835648\pi\) |
0.993736 | + | 0.111757i | \(0.0356477\pi\) | |||||||
\(314\) | 1.64851 | − | 5.07359i | 0.0930307 | − | 0.286319i | ||||
\(315\) | −4.09265 | + | 2.97348i | −0.230595 | + | 0.167537i | ||||
\(316\) | 14.2261 | + | 10.3359i | 0.800283 | + | 0.581439i | ||||
\(317\) | 0.708647 | + | 2.18099i | 0.0398016 | + | 0.122497i | 0.968983 | − | 0.247127i | \(-0.0794865\pi\) |
−0.929181 | + | 0.369624i | \(0.879487\pi\) | |||||||
\(318\) | 24.5719 | 1.37792 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −2.25922 | −0.126294 | ||||||||
\(321\) | −4.03722 | − | 12.4253i | −0.225335 | − | 0.693511i | ||||
\(322\) | 1.51157 | + | 1.09822i | 0.0842367 | + | 0.0612015i | ||||
\(323\) | 14.8790 | − | 10.8102i | 0.827890 | − | 0.601497i | ||||
\(324\) | −0.154394 | + | 0.475175i | −0.00857743 | + | 0.0263986i | ||||
\(325\) | −1.06580 | + | 3.28018i | −0.0591197 | + | 0.181952i | ||||
\(326\) | −11.1530 | + | 8.10314i | −0.617708 | + | 0.448791i | ||||
\(327\) | 12.1197 | + | 8.80546i | 0.670219 | + | 0.486943i | ||||
\(328\) | 3.10077 | + | 9.54319i | 0.171211 | + | 0.526935i | ||||
\(329\) | −6.02629 | −0.332240 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.3951 | 0.846192 | 0.423096 | − | 0.906085i | \(-0.360943\pi\) | ||||
0.423096 | + | 0.906085i | \(0.360943\pi\) | |||||||
\(332\) | 0.724337 | + | 2.22928i | 0.0397532 | + | 0.122348i | ||||
\(333\) | −23.6444 | − | 17.1787i | −1.29570 | − | 0.941385i | ||||
\(334\) | 4.68655 | − | 3.40498i | 0.256437 | − | 0.186312i | ||||
\(335\) | 1.89953 | − | 5.84616i | 0.103783 | − | 0.319410i | ||||
\(336\) | 0.924203 | − | 2.84440i | 0.0504194 | − | 0.155175i | ||||
\(337\) | −15.7733 | + | 11.4600i | −0.859225 | + | 0.624263i | −0.927674 | − | 0.373391i | \(-0.878195\pi\) |
0.0684492 | + | 0.997655i | \(0.478195\pi\) | |||||||
\(338\) | 0.659111 | + | 0.478872i | 0.0358509 | + | 0.0260472i | ||||
\(339\) | −0.264904 | − | 0.815290i | −0.0143876 | − | 0.0442805i | ||||
\(340\) | −3.49153 | −0.189355 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 27.7460 | 1.50033 | ||||||||
\(343\) | 4.12296 | + | 12.6892i | 0.222619 | + | 0.685151i | ||||
\(344\) | 15.7757 | + | 11.4618i | 0.850571 | + | 0.617976i | ||||
\(345\) | −5.58616 | + | 4.05858i | −0.300749 | + | 0.218507i | ||||
\(346\) | −2.55403 | + | 7.86051i | −0.137306 | + | 0.422584i | ||||
\(347\) | 0.670272 | − | 2.06288i | 0.0359821 | − | 0.110741i | −0.931452 | − | 0.363864i | \(-0.881457\pi\) |
0.967434 | + | 0.253122i | \(0.0814574\pi\) | |||||||
\(348\) | −19.7181 | + | 14.3260i | −1.05700 | + | 0.767955i | ||||
\(349\) | −20.2675 | − | 14.7252i | −1.08490 | − | 0.788222i | −0.106365 | − | 0.994327i | \(-0.533921\pi\) |
−0.978530 | + | 0.206105i | \(0.933921\pi\) | |||||||
\(350\) | −0.235096 | − | 0.723552i | −0.0125664 | − | 0.0386755i | ||||
\(351\) | 18.4717 | 0.985944 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.2532 | −1.23764 | −0.618821 | − | 0.785532i | \(-0.712389\pi\) | ||||
−0.618821 | + | 0.785532i | \(0.712389\pi\) | |||||||
\(354\) | −1.88821 | − | 5.81133i | −0.100357 | − | 0.308868i | ||||
\(355\) | 1.63676 | + | 1.18918i | 0.0868702 | + | 0.0631149i | ||||
\(356\) | 9.61252 | − | 6.98390i | 0.509463 | − | 0.370146i | ||||
\(357\) | −2.14900 | + | 6.61395i | −0.113737 | + | 0.350047i | ||||
\(358\) | 0.333853 | − | 1.02749i | 0.0176447 | − | 0.0543047i | ||||
\(359\) | 8.18917 | − | 5.94978i | 0.432208 | − | 0.314018i | −0.350323 | − | 0.936629i | \(-0.613928\pi\) |
0.782531 | + | 0.622611i | \(0.213928\pi\) | |||||||
\(360\) | −10.1156 | − | 7.34938i | −0.533137 | − | 0.387346i | ||||
\(361\) | 12.3022 | + | 37.8621i | 0.647482 | + | 1.99274i | ||||
\(362\) | 6.85194 | 0.360130 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.17891 | −0.271448 | ||||||||
\(365\) | −0.255207 | − | 0.785446i | −0.0133581 | − | 0.0411121i | ||||
\(366\) | −4.16165 | − | 3.02362i | −0.217533 | − | 0.158047i | ||||
\(367\) | −3.00084 | + | 2.18024i | −0.156643 | + | 0.113808i | −0.663346 | − | 0.748313i | \(-0.730864\pi\) |
0.506703 | + | 0.862121i | \(0.330864\pi\) | |||||||
\(368\) | 0.782725 | − | 2.40898i | 0.0408024 | − | 0.125577i | ||||
\(369\) | −5.96614 | + | 18.3619i | −0.310585 | + | 0.955882i | ||||
\(370\) | 3.55586 | − | 2.58348i | 0.184860 | − | 0.134309i | ||||
\(371\) | −9.88604 | − | 7.18263i | −0.513258 | − | 0.372904i | ||||
\(372\) | −4.66522 | − | 14.3581i | −0.241880 | − | 0.744431i | ||||
\(373\) | 9.34017 | 0.483616 | 0.241808 | − | 0.970324i | \(-0.422260\pi\) | ||||
0.241808 | + | 0.970324i | \(0.422260\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.81156 | 0.145188 | ||||||||
\(376\) | −4.60276 | − | 14.1658i | −0.237369 | − | 0.730547i | ||||
\(377\) | 16.6143 | + | 12.0710i | 0.855678 | + | 0.621687i | ||||
\(378\) | −3.29636 | + | 2.39495i | −0.169547 | + | 0.123183i | ||||
\(379\) | −3.03198 | + | 9.33148i | −0.155742 | + | 0.479326i | −0.998235 | − | 0.0593816i | \(-0.981087\pi\) |
0.842493 | + | 0.538707i | \(0.181087\pi\) | |||||||
\(380\) | 3.45015 | − | 10.6185i | 0.176989 | − | 0.544716i | ||||
\(381\) | 27.0904 | − | 19.6823i | 1.38788 | − | 1.00836i | ||||
\(382\) | 2.66930 | + | 1.93936i | 0.136573 | + | 0.0992263i | ||||
\(383\) | −5.57677 | − | 17.1635i | −0.284960 | − | 0.877015i | −0.986411 | − | 0.164298i | \(-0.947464\pi\) |
0.701451 | − | 0.712718i | \(-0.252536\pi\) | |||||||
\(384\) | 28.2615 | 1.44221 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 16.7194 | 0.850993 | ||||||||
\(387\) | 11.5941 | + | 35.6831i | 0.589363 | + | 1.81387i | ||||
\(388\) | 2.87720 | + | 2.09041i | 0.146068 | + | 0.106124i | ||||
\(389\) | −25.2345 | + | 18.3339i | −1.27944 | + | 0.929567i | −0.999536 | − | 0.0304614i | \(-0.990302\pi\) |
−0.279903 | + | 0.960028i | \(0.590302\pi\) | |||||||
\(390\) | −2.21038 | + | 6.80284i | −0.111927 | + | 0.344475i | ||||
\(391\) | −1.82003 | + | 5.60148i | −0.0920429 | + | 0.283279i | ||||
\(392\) | −12.2426 | + | 8.89478i | −0.618346 | + | 0.449254i | ||||
\(393\) | 25.4470 | + | 18.4883i | 1.28363 | + | 0.932612i | ||||
\(394\) | 2.55478 | + | 7.86281i | 0.128708 | + | 0.396123i | ||||
\(395\) | −12.0782 | −0.607719 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.6212 | −0.533062 | −0.266531 | − | 0.963826i | \(-0.585877\pi\) | ||||
−0.266531 | + | 0.963826i | \(0.585877\pi\) | |||||||
\(398\) | −1.78247 | − | 5.48588i | −0.0893472 | − | 0.274982i | ||||
\(399\) | −17.9908 | − | 13.0711i | −0.900669 | − | 0.654374i | ||||
\(400\) | −0.834404 | + | 0.606230i | −0.0417202 | + | 0.0303115i | ||||
\(401\) | −8.51895 | + | 26.2186i | −0.425416 | + | 1.30930i | 0.477179 | + | 0.878806i | \(0.341659\pi\) |
−0.902595 | + | 0.430490i | \(0.858341\pi\) | |||||||
\(402\) | 3.93948 | − | 12.1245i | 0.196483 | − | 0.604714i | ||||
\(403\) | −10.2912 | + | 7.47696i | −0.512639 | + | 0.372454i | ||||
\(404\) | 8.86173 | + | 6.43843i | 0.440888 | + | 0.320324i | ||||
\(405\) | −0.106048 | − | 0.326382i | −0.00526956 | − | 0.0162181i | ||||
\(406\) | −4.52997 | −0.224818 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −17.1886 | −0.850961 | ||||||||
\(409\) | −4.44001 | − | 13.6649i | −0.219544 | − | 0.675688i | −0.998800 | − | 0.0489814i | \(-0.984402\pi\) |
0.779255 | − | 0.626707i | \(-0.215598\pi\) | |||||||
\(410\) | −2.34901 | − | 1.70666i | −0.116010 | − | 0.0842859i | ||||
\(411\) | −9.73812 | + | 7.07516i | −0.480346 | + | 0.348992i | ||||
\(412\) | 4.26603 | − | 13.1295i | 0.210172 | − | 0.646844i | ||||
\(413\) | −0.939026 | + | 2.89003i | −0.0462065 | + | 0.142209i | ||||
\(414\) | −7.18851 | + | 5.22276i | −0.353296 | + | 0.256684i | ||||
\(415\) | −1.30253 | − | 0.946345i | −0.0639388 | − | 0.0464542i | ||||
\(416\) | −6.24470 | − | 19.2192i | −0.306172 | − | 0.942300i | ||||
\(417\) | −16.7378 | −0.819652 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −31.4707 | −1.53744 | −0.768722 | − | 0.639584i | \(-0.779107\pi\) | ||||
−0.768722 | + | 0.639584i | \(0.779107\pi\) | |||||||
\(420\) | 1.30460 | + | 4.01513i | 0.0636578 | + | 0.195919i | ||||
\(421\) | −21.4965 | − | 15.6181i | −1.04768 | − | 0.761182i | −0.0759078 | − | 0.997115i | \(-0.524185\pi\) |
−0.971769 | + | 0.235933i | \(0.924185\pi\) | |||||||
\(422\) | −13.5865 | + | 9.87118i | −0.661381 | + | 0.480521i | ||||
\(423\) | 8.85609 | − | 27.2562i | 0.430598 | − | 1.32524i | ||||
\(424\) | 9.33324 | − | 28.7248i | 0.453262 | − | 1.39500i | ||||
\(425\) | 1.94020 | − | 1.40964i | 0.0941134 | − | 0.0683774i | ||||
\(426\) | 3.39451 | + | 2.46626i | 0.164465 | + | 0.119491i | ||||
\(427\) | 0.790528 | + | 2.43300i | 0.0382563 | + | 0.117741i | ||||
\(428\) | −6.76518 | −0.327008 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.64252 | −0.272106 | ||||||||
\(431\) | 1.19549 | + | 3.67935i | 0.0575849 | + | 0.177228i | 0.975712 | − | 0.219059i | \(-0.0702986\pi\) |
−0.918127 | + | 0.396287i | \(0.870299\pi\) | |||||||
\(432\) | 4.46880 | + | 3.24677i | 0.215005 | + | 0.156210i | ||||
\(433\) | −32.4730 | + | 23.5930i | −1.56055 | + | 1.13381i | −0.624995 | + | 0.780629i | \(0.714899\pi\) |
−0.935556 | + | 0.353178i | \(0.885101\pi\) | |||||||
\(434\) | 0.867082 | − | 2.66860i | 0.0416213 | − | 0.128097i | ||||
\(435\) | 5.17323 | − | 15.9216i | 0.248037 | − | 0.763380i | ||||
\(436\) | 6.27583 | − | 4.55966i | 0.300558 | − | 0.218368i | ||||
\(437\) | −15.2368 | − | 11.0702i | −0.728875 | − | 0.529559i | ||||
\(438\) | −0.529279 | − | 1.62895i | −0.0252899 | − | 0.0778344i | ||||
\(439\) | −1.02336 | −0.0488425 | −0.0244212 | − | 0.999702i | \(-0.507774\pi\) | ||||
−0.0244212 | + | 0.999702i | \(0.507774\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −29.1166 | −1.38650 | ||||||||
\(442\) | 1.88541 | + | 5.80271i | 0.0896800 | + | 0.276007i | ||||
\(443\) | 13.0032 | + | 9.44738i | 0.617801 | + | 0.448858i | 0.852153 | − | 0.523293i | \(-0.175297\pi\) |
−0.234352 | + | 0.972152i | \(0.575297\pi\) | |||||||
\(444\) | −19.7322 | + | 14.3363i | −0.936448 | + | 0.680370i | ||||
\(445\) | −2.52194 | + | 7.76173i | −0.119551 | + | 0.367941i | ||||
\(446\) | −3.65682 | + | 11.2545i | −0.173156 | + | 0.532918i | ||||
\(447\) | 8.60810 | − | 6.25415i | 0.407149 | − | 0.295811i | ||||
\(448\) | 1.88510 | + | 1.36960i | 0.0890625 | + | 0.0647077i | ||||
\(449\) | 11.0758 | + | 34.0879i | 0.522700 | + | 1.60871i | 0.768820 | + | 0.639466i | \(0.220844\pi\) |
−0.246120 | + | 0.969239i | \(0.579156\pi\) | |||||||
\(450\) | 3.61803 | 0.170556 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.443901 | −0.0208793 | ||||||||
\(453\) | −21.1615 | − | 65.1285i | −0.994256 | − | 3.06000i | ||||
\(454\) | −14.4155 | − | 10.4735i | −0.676555 | − | 0.491546i | ||||
\(455\) | 2.87785 | − | 2.09088i | 0.134916 | − | 0.0980220i | ||||
\(456\) | 16.9849 | − | 52.2740i | 0.795389 | − | 2.44795i | ||||
\(457\) | 7.77254 | − | 23.9214i | 0.363584 | − | 1.11900i | −0.587279 | − | 0.809384i | \(-0.699801\pi\) |
0.950863 | − | 0.309612i | \(-0.100199\pi\) | |||||||
\(458\) | 8.95997 | − | 6.50980i | 0.418672 | − | 0.304183i | ||||
\(459\) | −10.3911 | − | 7.54955i | −0.485013 | − | 0.352383i | ||||
\(460\) | 1.10489 | + | 3.40050i | 0.0515157 | + | 0.158549i | ||||
\(461\) | −6.65631 | −0.310015 | −0.155008 | − | 0.987913i | \(-0.549540\pi\) | ||||
−0.155008 | + | 0.987913i | \(0.549540\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.7730 | 1.80194 | 0.900968 | − | 0.433886i | \(-0.142858\pi\) | ||||
0.900968 | + | 0.433886i | \(0.142858\pi\) | |||||||
\(464\) | 1.89772 | + | 5.84059i | 0.0880996 | + | 0.271143i | ||||
\(465\) | 8.38919 | + | 6.09510i | 0.389039 | + | 0.282654i | ||||
\(466\) | 6.81858 | − | 4.95399i | 0.315865 | − | 0.229489i | ||||
\(467\) | 6.96815 | − | 21.4458i | 0.322448 | − | 0.992392i | −0.650132 | − | 0.759821i | \(-0.725286\pi\) |
0.972580 | − | 0.232571i | \(-0.0747136\pi\) | |||||||
\(468\) | 7.61079 | − | 23.4236i | 0.351809 | − | 1.08276i | ||||
\(469\) | −5.12909 | + | 3.72651i | −0.236840 | + | 0.172074i | ||||
\(470\) | 3.48685 | + | 2.53335i | 0.160837 | + | 0.116855i | ||||
\(471\) | −6.28339 | − | 19.3383i | −0.289523 | − | 0.891062i | ||||
\(472\) | −7.51071 | −0.345708 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −25.0492 | −1.15055 | ||||||||
\(475\) | 2.36979 | + | 7.29347i | 0.108734 | + | 0.334647i | ||||
\(476\) | 2.91335 | + | 2.11667i | 0.133533 | + | 0.0970174i | ||||
\(477\) | 47.0145 | − | 34.1580i | 2.15265 | − | 1.56399i | ||||
\(478\) | −6.24718 | + | 19.2268i | −0.285739 | + | 0.879415i | ||||
\(479\) | 0.504274 | − | 1.55200i | 0.0230409 | − | 0.0709125i | −0.938875 | − | 0.344258i | \(-0.888130\pi\) |
0.961916 | + | 0.273346i | \(0.0881304\pi\) | |||||||
\(480\) | −13.3273 | + | 9.68286i | −0.608306 | + | 0.441960i | ||||
\(481\) | 16.6262 | + | 12.0796i | 0.758088 | + | 0.550783i | ||||
\(482\) | −2.49341 | − | 7.67392i | −0.113572 | − | 0.349537i | ||||
\(483\) | 7.12155 | 0.324042 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.44278 | −0.110921 | ||||||||
\(486\) | 3.44244 | + | 10.5947i | 0.156152 | + | 0.480587i | ||||
\(487\) | −0.849710 | − | 0.617350i | −0.0385040 | − | 0.0279748i | 0.568367 | − | 0.822775i | \(-0.307575\pi\) |
−0.606871 | + | 0.794800i | \(0.707575\pi\) | |||||||
\(488\) | −5.11538 | + | 3.71654i | −0.231562 | + | 0.168240i | ||||
\(489\) | −16.2375 | + | 49.9739i | −0.734286 | + | 2.25990i | ||||
\(490\) | 1.35313 | − | 4.16451i | 0.0611282 | − | 0.188133i | ||||
\(491\) | −11.2567 | + | 8.17850i | −0.508009 | + | 0.369090i | −0.812068 | − | 0.583563i | \(-0.801658\pi\) |
0.304058 | + | 0.952653i | \(0.401658\pi\) | |||||||
\(492\) | 13.0352 | + | 9.47059i | 0.587670 | + | 0.426967i | ||||
\(493\) | −4.41268 | − | 13.5808i | −0.198737 | − | 0.611650i | ||||
\(494\) | −19.5103 | −0.877811 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.80394 | −0.170802 | ||||||||
\(497\) | −0.644805 | − | 1.98451i | −0.0289235 | − | 0.0890173i | ||||
\(498\) | −2.70135 | − | 1.96264i | −0.121050 | − | 0.0879482i | ||||
\(499\) | −14.0504 | + | 10.2082i | −0.628984 | + | 0.456983i | −0.856048 | − | 0.516896i | \(-0.827087\pi\) |
0.227064 | + | 0.973880i | \(0.427087\pi\) | |||||||
\(500\) | 0.449894 | − | 1.38463i | 0.0201199 | − | 0.0619226i | ||||
\(501\) | 6.82309 | − | 20.9993i | 0.304833 | − | 0.938179i | ||||
\(502\) | −10.2829 | + | 7.47096i | −0.458948 | + | 0.333445i | ||||
\(503\) | 29.0062 | + | 21.0742i | 1.29332 | + | 0.939653i | 0.999867 | − | 0.0163204i | \(-0.00519519\pi\) |
0.293454 | + | 0.955973i | \(0.405195\pi\) | |||||||
\(504\) | 3.98504 | + | 12.2647i | 0.177508 | + | 0.546313i | ||||
\(505\) | −7.52373 | −0.334802 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.10530 | 0.137911 | ||||||||
\(508\) | −5.35822 | − | 16.4909i | −0.237732 | − | 0.731665i | ||||
\(509\) | −1.73031 | − | 1.25715i | −0.0766947 | − | 0.0557220i | 0.548777 | − | 0.835969i | \(-0.315094\pi\) |
−0.625472 | + | 0.780247i | \(0.715094\pi\) | |||||||
\(510\) | 4.02381 | − | 2.92347i | 0.178178 | − | 0.129454i | ||||
\(511\) | −0.263215 | + | 0.810093i | −0.0116440 | + | 0.0358364i | ||||
\(512\) | 3.49234 | − | 10.7483i | 0.154341 | − | 0.475013i | ||||
\(513\) | 33.2277 | − | 24.1413i | 1.46704 | − | 1.06586i | ||||
\(514\) | −11.0374 | − | 8.01913i | −0.486838 | − | 0.353709i | ||||
\(515\) | 2.93020 | + | 9.01821i | 0.129120 | + | 0.397390i | ||||
\(516\) | 31.3115 | 1.37841 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −4.53321 | −0.199178 | ||||||||
\(519\) | 9.73486 | + | 29.9608i | 0.427313 | + | 1.31513i | ||||
\(520\) | 7.11301 | + | 5.16791i | 0.311926 | + | 0.226628i | ||||
\(521\) | 10.3030 | − | 7.48558i | 0.451383 | − | 0.327949i | −0.338758 | − | 0.940873i | \(-0.610007\pi\) |
0.790142 | + | 0.612924i | \(0.210007\pi\) | |||||||
\(522\) | 6.65713 | − | 20.4885i | 0.291374 | − | 0.896758i | ||||
\(523\) | −7.38821 | + | 22.7386i | −0.323064 | + | 0.994289i | 0.649243 | + | 0.760581i | \(0.275086\pi\) |
−0.972307 | + | 0.233708i | \(0.924914\pi\) | |||||||
\(524\) | 13.1770 | − | 9.57365i | 0.575640 | − | 0.418227i | ||||
\(525\) | −2.34598 | − | 1.70445i | −0.102387 | − | 0.0743884i | ||||
\(526\) | −0.841418 | − | 2.58962i | −0.0366876 | − | 0.112913i | ||||
\(527\) | 8.84510 | 0.385299 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.9686 | −0.737766 | ||||||||
\(530\) | 2.70068 | + | 8.31184i | 0.117310 | + | 0.361043i | ||||
\(531\) | −11.6913 | − | 8.49422i | −0.507359 | − | 0.368618i | ||||
\(532\) | −9.31605 | + | 6.76851i | −0.403902 | + | 0.293452i | ||||
\(533\) | 4.19525 | − | 12.9116i | 0.181716 | − | 0.559265i | ||||
\(534\) | −5.23030 | + | 16.0972i | −0.226337 | + | 0.696594i | ||||
\(535\) | 3.75932 | − | 2.73131i | 0.162530 | − | 0.118085i | ||||
\(536\) | −12.6773 | − | 9.21058i | −0.547575 | − | 0.397837i | ||||
\(537\) | −1.27250 | − | 3.91635i | −0.0549124 | − | 0.169003i | ||||
\(538\) | −7.33590 | −0.316273 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −7.79726 | −0.335540 | ||||||||
\(541\) | −0.407657 | − | 1.25464i | −0.0175265 | − | 0.0539412i | 0.941911 | − | 0.335863i | \(-0.109028\pi\) |
−0.959437 | + | 0.281922i | \(0.909028\pi\) | |||||||
\(542\) | 0.748134 | + | 0.543551i | 0.0321351 | + | 0.0233475i | ||||
\(543\) | 21.1288 | − | 15.3509i | 0.906722 | − | 0.658772i | ||||
\(544\) | −4.34218 | + | 13.3639i | −0.186170 | + | 0.572971i | ||||
\(545\) | −1.64652 | + | 5.06748i | −0.0705293 | + | 0.217067i | ||||
\(546\) | 5.96843 | − | 4.33632i | 0.255425 | − | 0.185577i | ||||
\(547\) | 7.54108 | + | 5.47891i | 0.322433 | + | 0.234261i | 0.737213 | − | 0.675660i | \(-0.236141\pi\) |
−0.414780 | + | 0.909922i | \(0.636141\pi\) | |||||||
\(548\) | 1.92610 | + | 5.92794i | 0.0822791 | + | 0.253229i | ||||
\(549\) | −12.1659 | −0.519228 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 45.6625 | 1.94529 | ||||||||
\(552\) | 5.43929 | + | 16.7404i | 0.231512 | + | 0.712520i | ||||
\(553\) | 10.0781 | + | 7.32216i | 0.428564 | + | 0.311370i | ||||
\(554\) | −4.82980 | + | 3.50905i | −0.205198 | + | 0.149085i | ||||
\(555\) | 5.17693 | − | 15.9330i | 0.219749 | − | 0.676316i | ||||
\(556\) | −2.67831 | + | 8.24298i | −0.113585 | + | 0.349580i | ||||
\(557\) | 31.8083 | − | 23.1101i | 1.34776 | − | 0.979205i | 0.348640 | − | 0.937257i | \(-0.386644\pi\) |
0.999120 | − | 0.0419481i | \(-0.0133564\pi\) | |||||||
\(558\) | 10.7956 | + | 7.84343i | 0.457012 | + | 0.332039i | ||||
\(559\) | −8.15272 | − | 25.0915i | −0.344823 | − | 1.06126i | ||||
\(560\) | 1.06374 | 0.0449514 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −18.7141 | −0.789407 | ||||||||
\(563\) | −6.17446 | − | 19.0030i | −0.260222 | − | 0.800882i | −0.992756 | − | 0.120151i | \(-0.961662\pi\) |
0.732533 | − | 0.680731i | \(-0.238338\pi\) | |||||||
\(564\) | −19.3493 | − | 14.0581i | −0.814751 | − | 0.591951i | ||||
\(565\) | 0.246670 | − | 0.179216i | 0.0103775 | − | 0.00753968i | ||||
\(566\) | 4.65971 | − | 14.3411i | 0.195862 | − | 0.602802i | ||||
\(567\) | −0.109376 | + | 0.336624i | −0.00459335 | + | 0.0141369i | ||||
\(568\) | 4.17243 | − | 3.03145i | 0.175071 | − | 0.127197i | ||||
\(569\) | −27.9635 | − | 20.3166i | −1.17229 | − | 0.851718i | −0.181008 | − | 0.983482i | \(-0.557936\pi\) |
−0.991281 | + | 0.131764i | \(0.957936\pi\) | |||||||
\(570\) | 4.91476 | + | 15.1261i | 0.205857 | + | 0.633562i | ||||
\(571\) | −3.15090 | −0.131861 | −0.0659306 | − | 0.997824i | \(-0.521002\pi\) | ||||
−0.0659306 | + | 0.997824i | \(0.521002\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.5760 | 0.525370 | ||||||||
\(574\) | 0.925399 | + | 2.84808i | 0.0386254 | + | 0.118877i | ||||
\(575\) | −1.98685 | − | 1.44353i | −0.0828575 | − | 0.0601995i | ||||
\(576\) | −8.96485 | + | 6.51335i | −0.373536 | + | 0.271389i | ||||
\(577\) | 8.44314 | − | 25.9853i | 0.351493 | − | 1.08178i | −0.606523 | − | 0.795066i | \(-0.707436\pi\) |
0.958015 | − | 0.286717i | \(-0.0925639\pi\) | |||||||
\(578\) | −2.56404 | + | 7.89129i | −0.106650 | + | 0.328234i | ||||
\(579\) | 51.5561 | − | 37.4577i | 2.14260 | − | 1.55669i | ||||
\(580\) | −7.01321 | − | 5.09540i | −0.291208 | − | 0.211575i | ||||
\(581\) | 0.513135 | + | 1.57927i | 0.0212884 | + | 0.0655190i | ||||
\(582\) | −5.06614 | −0.209998 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −2.10530 | −0.0871180 | ||||||||
\(585\) | 5.22760 | + | 16.0889i | 0.216135 | + | 0.665194i | ||||
\(586\) | 1.52119 | + | 1.10521i | 0.0628398 | + | 0.0456558i | ||||
\(587\) | 37.3506 | − | 27.1368i | 1.54162 | − | 1.12005i | 0.592316 | − | 0.805706i | \(-0.298214\pi\) |
0.949307 | − | 0.314349i | \(-0.101786\pi\) | |||||||
\(588\) | −7.50879 | + | 23.1097i | −0.309657 | + | 0.953027i | ||||
\(589\) | −8.74027 | + | 26.8998i | −0.360137 | + | 1.10839i | ||||
\(590\) | 1.75824 | − | 1.27744i | 0.0723857 | − | 0.0525913i | ||||
\(591\) | 25.4936 | + | 18.5222i | 1.04867 | + | 0.761902i | ||||
\(592\) | 1.89908 | + | 5.84477i | 0.0780518 | + | 0.240219i | ||||
\(593\) | −39.4265 | −1.61905 | −0.809525 | − | 0.587085i | \(-0.800275\pi\) | ||||
−0.809525 | + | 0.587085i | \(0.800275\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.47347 | −0.101402 | ||||||||
\(596\) | −1.70260 | − | 5.24006i | −0.0697411 | − | 0.214641i | ||||
\(597\) | −17.7869 | − | 12.9229i | −0.727970 | − | 0.528901i | ||||
\(598\) | 5.05478 | − | 3.67251i | 0.206705 | − | 0.150180i | ||||
\(599\) | 0.324081 | − | 0.997418i | 0.0132416 | − | 0.0407534i | −0.944217 | − | 0.329323i | \(-0.893180\pi\) |
0.957459 | + | 0.288569i | \(0.0931796\pi\) | |||||||
\(600\) | 2.21480 | − | 6.81645i | 0.0904187 | − | 0.278280i | ||||
\(601\) | 22.0455 | − | 16.0170i | 0.899256 | − | 0.653348i | −0.0390187 | − | 0.999238i | \(-0.512423\pi\) |
0.938275 | + | 0.345891i | \(0.112423\pi\) | |||||||
\(602\) | 4.70814 | + | 3.42066i | 0.191889 | + | 0.139416i | ||||
\(603\) | −9.31697 | − | 28.6747i | −0.379416 | − | 1.16772i | ||||
\(604\) | −35.4605 | −1.44287 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −15.6036 | −0.633854 | ||||||||
\(607\) | −6.77418 | − | 20.8488i | −0.274955 | − | 0.846225i | −0.989231 | − | 0.146361i | \(-0.953244\pi\) |
0.714276 | − | 0.699864i | \(-0.246756\pi\) | |||||||
\(608\) | −36.3516 | − | 26.4110i | −1.47425 | − | 1.07111i | ||||
\(609\) | −13.9687 | + | 10.1488i | −0.566040 | + | 0.411252i | ||||
\(610\) | 0.565384 | − | 1.74007i | 0.0228917 | − | 0.0704535i | ||||
\(611\) | −6.22738 | + | 19.1659i | −0.251933 | + | 0.775370i | ||||
\(612\) | −13.8548 | + | 10.0661i | −0.560049 | + | 0.406899i | ||||
\(613\) | 8.56915 | + | 6.22586i | 0.346105 | + | 0.251460i | 0.747233 | − | 0.664562i | \(-0.231382\pi\) |
−0.401128 | + | 0.916022i | \(0.631382\pi\) | |||||||
\(614\) | −2.04983 | − | 6.30874i | −0.0827245 | − | 0.254600i | ||||
\(615\) | −11.0670 | −0.446265 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.60402 | 0.185351 | 0.0926755 | − | 0.995696i | \(-0.470458\pi\) | ||||
0.0926755 | + | 0.995696i | \(0.470458\pi\) | |||||||
\(618\) | 6.07699 | + | 18.7031i | 0.244453 | + | 0.752348i | ||||
\(619\) | −29.9366 | − | 21.7502i | −1.20326 | − | 0.874216i | −0.208654 | − | 0.977989i | \(-0.566908\pi\) |
−0.994601 | + | 0.103773i | \(0.966908\pi\) | |||||||
\(620\) | 4.34410 | − | 3.15617i | 0.174463 | − | 0.126755i | ||||
\(621\) | −4.06448 | + | 12.5092i | −0.163102 | + | 0.501976i | ||||
\(622\) | −4.58695 | + | 14.1172i | −0.183920 | + | 0.566047i | ||||
\(623\) | 6.80971 | − | 4.94754i | 0.272825 | − | 0.198219i | ||||
\(624\) | −8.09125 | − | 5.87864i | −0.323909 | − | 0.235334i | ||||
\(625\) | 0.309017 | + | 0.951057i | 0.0123607 | + | 0.0380423i | ||||
\(626\) | 5.24081 | 0.209465 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.5291 | −0.420157 | ||||||||
\(629\) | −4.41584 | − | 13.5906i | −0.176071 | − | 0.541891i | ||||
\(630\) | −3.01890 | − | 2.19336i | −0.120276 | − | 0.0873856i | ||||
\(631\) | 20.0965 | − | 14.6009i | 0.800028 | − | 0.581254i | −0.110895 | − | 0.993832i | \(-0.535372\pi\) |
0.910922 | + | 0.412578i | \(0.135372\pi\) | |||||||
\(632\) | −9.51455 | + | 29.2828i | −0.378468 | + | 1.16481i | ||||
\(633\) | −19.7804 | + | 60.8779i | −0.786201 | + | 2.41968i | ||||
\(634\) | −1.36852 | + | 0.994285i | −0.0543507 | + | 0.0394881i | ||||
\(635\) | 9.63536 | + | 7.00050i | 0.382368 | + | 0.277806i | ||||
\(636\) | −14.9866 | − | 46.1241i | −0.594258 | − | 1.82894i | ||||
\(637\) | 20.4741 | 0.811213 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.92328 | 0.392559 | ||||||||
\(640\) | 3.10621 | + | 9.55992i | 0.122784 | + | 0.377889i | ||||
\(641\) | 35.9440 | + | 26.1149i | 1.41970 | + | 1.03147i | 0.991820 | + | 0.127641i | \(0.0407405\pi\) |
0.427883 | + | 0.903834i | \(0.359260\pi\) | |||||||
\(642\) | 7.79654 | − | 5.66452i | 0.307705 | − | 0.223561i | ||||
\(643\) | 7.99148 | − | 24.5952i | 0.315153 | − | 0.969942i | −0.660538 | − | 0.750793i | \(-0.729672\pi\) |
0.975691 | − | 0.219149i | \(-0.0703282\pi\) | |||||||
\(644\) | 1.13956 | − | 3.50720i | 0.0449049 | − | 0.138203i | ||||
\(645\) | −17.3994 | + | 12.6414i | −0.685099 | + | 0.497754i | ||||
\(646\) | 10.9753 | + | 7.97406i | 0.431819 | + | 0.313735i | ||||
\(647\) | 6.02166 | + | 18.5328i | 0.236736 | + | 0.728598i | 0.996886 | + | 0.0788509i | \(0.0251251\pi\) |
−0.760151 | + | 0.649747i | \(0.774875\pi\) | |||||||
\(648\) | −0.874831 | −0.0343666 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −2.54411 | −0.0997883 | ||||||||
\(651\) | −3.30494 | − | 10.1716i | −0.129531 | − | 0.398654i | ||||
\(652\) | 22.0128 | + | 15.9932i | 0.862087 | + | 0.626343i | ||||
\(653\) | 13.5347 | − | 9.83353i | 0.529653 | − | 0.384816i | −0.290575 | − | 0.956852i | \(-0.593847\pi\) |
0.820228 | + | 0.572037i | \(0.193847\pi\) | |||||||
\(654\) | −3.41476 | + | 10.5096i | −0.133528 | + | 0.410956i | ||||
\(655\) | −3.45711 | + | 10.6399i | −0.135081 | + | 0.415735i | ||||
\(656\) | 3.28443 | − | 2.38628i | 0.128235 | − | 0.0931684i | ||||
\(657\) | −3.27714 | − | 2.38099i | −0.127854 | − | 0.0928911i | ||||
\(658\) | −1.37365 | − | 4.22767i | −0.0535506 | − | 0.164812i | ||||
\(659\) | 1.66127 | 0.0647137 | 0.0323569 | − | 0.999476i | \(-0.489699\pi\) | ||||
0.0323569 | + | 0.999476i | \(0.489699\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −44.0130 | −1.71191 | −0.855953 | − | 0.517053i | \(-0.827029\pi\) | ||||
−0.855953 | + | 0.517053i | \(0.827029\pi\) | |||||||
\(662\) | 3.50921 | + | 10.8002i | 0.136389 | + | 0.419763i | ||||
\(663\) | 18.8142 | + | 13.6693i | 0.730682 | + | 0.530871i | ||||
\(664\) | −3.32042 | + | 2.41242i | −0.128857 | + | 0.0936202i | ||||
\(665\) | 2.44416 | − | 7.52234i | 0.0947803 | − | 0.291704i | ||||
\(666\) | 6.66189 | − | 20.5032i | 0.258143 | − | 0.794483i | ||||
\(667\) | −11.8304 | + | 8.59526i | −0.458073 | + | 0.332810i | ||||
\(668\) | −9.24988 | − | 6.72043i | −0.357889 | − | 0.260021i | ||||
\(669\) | 13.9382 | + | 42.8974i | 0.538882 | + | 1.65851i | ||||
\(670\) | 4.53429 | 0.175175 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 16.9904 | 0.655419 | ||||||||
\(673\) | 11.9265 | + | 36.7059i | 0.459732 | + | 1.41491i | 0.865489 | + | 0.500928i | \(0.167008\pi\) |
−0.405757 | + | 0.913981i | \(0.632992\pi\) | |||||||
\(674\) | −11.6350 | − | 8.45332i | −0.448163 | − | 0.325610i | ||||
\(675\) | 4.33283 | − | 3.14799i | 0.166771 | − | 0.121166i | ||||
\(676\) | 0.496897 | − | 1.52929i | 0.0191114 | − | 0.0588189i | ||||
\(677\) | 11.9277 | − | 36.7097i | 0.458419 | − | 1.41087i | −0.408656 | − | 0.912689i | \(-0.634002\pi\) |
0.867074 | − | 0.498179i | \(-0.165998\pi\) | |||||||
\(678\) | 0.511574 | − | 0.371680i | 0.0196469 | − | 0.0142743i | ||||
\(679\) | 2.03827 | + | 1.48089i | 0.0782215 | + | 0.0568313i | ||||
\(680\) | −1.88919 | − | 5.81432i | −0.0724470 | − | 0.222969i | ||||
\(681\) | −67.9167 | −2.60257 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.748158 | −0.0286275 | −0.0143137 | − | 0.999898i | \(-0.504556\pi\) | ||||
−0.0143137 | + | 0.999898i | \(0.504556\pi\) | |||||||
\(684\) | −16.9226 | − | 52.0823i | −0.647050 | − | 1.99141i | ||||
\(685\) | −3.46360 | − | 2.51645i | −0.132337 | − | 0.0961487i | ||||
\(686\) | −7.96213 | + | 5.78483i | −0.303996 | + | 0.220866i | ||||
\(687\) | 13.0447 | − | 40.1475i | 0.497687 | − | 1.53172i | ||||
\(688\) | 2.43797 | − | 7.50331i | 0.0929469 | − | 0.286061i | ||||
\(689\) | −33.0594 | + | 24.0191i | −1.25946 | + | 0.915055i | ||||
\(690\) | −4.12058 | − | 2.99378i | −0.156868 | − | 0.113971i | ||||
\(691\) | 1.61364 | + | 4.96627i | 0.0613857 | + | 0.188926i | 0.977047 | − | 0.213026i | \(-0.0683319\pi\) |
−0.915661 | + | 0.401952i | \(0.868332\pi\) | |||||||
\(692\) | 16.3128 | 0.620118 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.59998 | 0.0607342 | ||||||||
\(695\) | −1.83964 | − | 5.66183i | −0.0697815 | − | 0.214765i | ||||
\(696\) | −34.5256 | − | 25.0843i | −1.30869 | − | 0.950818i | ||||
\(697\) | −7.63711 | + | 5.54869i | −0.289276 | + | 0.210171i | ||||
\(698\) | 5.71044 | − | 17.5749i | 0.216143 | − | 0.665221i | ||||
\(699\) | 9.92709 | − | 30.5524i | 0.375477 | − | 1.15560i | ||||
\(700\) | −1.21480 | + | 0.882602i | −0.0459150 | + | 0.0333592i | ||||
\(701\) | −11.4540 | − | 8.32185i | −0.432613 | − | 0.314312i | 0.350080 | − | 0.936720i | \(-0.386155\pi\) |
−0.782693 | + | 0.622408i | \(0.786155\pi\) | |||||||
\(702\) | 4.21049 | + | 12.9586i | 0.158915 | + | 0.489090i | ||||
\(703\) | 45.6952 | 1.72343 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.4278 | 0.618706 | ||||||||
\(706\) | −5.30041 | − | 16.3130i | −0.199483 | − | 0.613947i | ||||
\(707\) | 6.27783 | + | 4.56111i | 0.236102 | + | 0.171538i | ||||
\(708\) | −9.75685 | + | 7.08876i | −0.366685 | + | 0.266412i | ||||
\(709\) | −5.31953 | + | 16.3718i | −0.199779 | + | 0.614857i | 0.800108 | + | 0.599855i | \(0.204775\pi\) |
−0.999887 | + | 0.0150013i | \(0.995225\pi\) | |||||||
\(710\) | −0.461163 | + | 1.41931i | −0.0173071 | + | 0.0532659i | ||||
\(711\) | −47.9278 | + | 34.8216i | −1.79743 | + | 1.30591i | ||||
\(712\) | 16.8312 | + | 12.2285i | 0.630774 | + | 0.458284i | ||||
\(713\) | −2.79902 | − | 8.61448i | −0.104824 | − | 0.322615i | ||||
\(714\) | −5.12978 | −0.191977 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.13233 | −0.0796891 | ||||||||
\(717\) | 23.8115 | + | 73.2843i | 0.889257 | + | 2.73685i | ||||
\(718\) | 6.04066 | + | 4.38880i | 0.225436 | + | 0.163789i | ||||
\(719\) | 21.4842 | − | 15.6092i | 0.801226 | − | 0.582125i | −0.110048 | − | 0.993926i | \(-0.535100\pi\) |
0.911273 | + | 0.411802i | \(0.135100\pi\) | |||||||
\(720\) | −1.56325 | + | 4.81120i | −0.0582590 | + | 0.179303i | ||||
\(721\) | 3.02214 | − | 9.30121i | 0.112551 | − | 0.346395i | ||||
\(722\) | −23.7575 | + | 17.2608i | −0.884163 | + | 0.642382i | ||||
\(723\) | −24.8812 | − | 18.0772i | −0.925342 | − | 0.672300i | ||||
\(724\) | −4.17906 | − | 12.8618i | −0.155314 | − | 0.478006i | ||||
\(725\) | 5.95431 | 0.221138 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 44.1917 | 1.63898 | 0.819490 | − | 0.573094i | \(-0.194257\pi\) | ||||
0.819490 | + | 0.573094i | \(0.194257\pi\) | |||||||
\(728\) | −2.80219 | − | 8.62424i | −0.103856 | − | 0.319636i | ||||
\(729\) | 35.1843 | + | 25.5629i | 1.30312 | + | 0.946773i | ||||
\(730\) | 0.492847 | − | 0.358074i | 0.0182411 | − | 0.0132529i | ||||
\(731\) | −5.66890 | + | 17.4471i | −0.209672 | + | 0.645303i | ||||
\(732\) | −3.13743 | + | 9.65601i | −0.115963 | + | 0.356896i | ||||
\(733\) | 20.1934 | − | 14.6714i | 0.745861 | − | 0.541900i | −0.148680 | − | 0.988885i | \(-0.547502\pi\) |
0.894541 | + | 0.446986i | \(0.147502\pi\) | |||||||
\(734\) | −2.21354 | − | 1.60823i | −0.0817033 | − | 0.0593610i | ||||
\(735\) | −5.15754 | − | 15.8733i | −0.190239 | − | 0.585494i | ||||
\(736\) | 14.3895 | 0.530404 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −14.2415 | −0.524237 | ||||||||
\(739\) | −6.56174 | − | 20.1950i | −0.241377 | − | 0.742883i | −0.996211 | − | 0.0869672i | \(-0.972282\pi\) |
0.754834 | − | 0.655916i | \(-0.227718\pi\) | |||||||
\(740\) | −7.01823 | − | 5.09905i | −0.257995 | − | 0.187445i | ||||
\(741\) | −60.1624 | + | 43.7105i | −2.21012 | + | 1.60575i | ||||
\(742\) | 2.78543 | − | 8.57266i | 0.102256 | − | 0.314712i | ||||
\(743\) | 9.47222 | − | 29.1525i | 0.347502 | − | 1.06950i | −0.612729 | − | 0.790293i | \(-0.709928\pi\) |
0.960231 | − | 0.279208i | \(-0.0900718\pi\) | |||||||
\(744\) | 21.3857 | − | 15.5376i | 0.784039 | − | 0.569637i | ||||
\(745\) | 3.06168 | + | 2.22444i | 0.112171 | + | 0.0814972i | ||||
\(746\) | 2.12903 | + | 6.55248i | 0.0779493 | + | 0.239903i | ||||
\(747\) | −7.89694 | −0.288934 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.79259 | −0.175118 | ||||||||
\(750\) | 0.640877 | + | 1.97242i | 0.0234015 | + | 0.0720224i | ||||
\(751\) | 24.5191 | + | 17.8142i | 0.894716 | + | 0.650049i | 0.937103 | − | 0.349052i | \(-0.113496\pi\) |
−0.0423872 | + | 0.999101i | \(0.513496\pi\) | |||||||
\(752\) | −4.87537 | + | 3.54217i | −0.177787 | + | 0.129169i | ||||
\(753\) | −14.9707 | + | 46.0752i | −0.545564 | + | 1.67907i | ||||
\(754\) | −4.68113 | + | 14.4070i | −0.170477 | + | 0.524673i | ||||
\(755\) | 19.7049 | − | 14.3165i | 0.717136 | − | 0.521030i | ||||
\(756\) | 6.50606 | + | 4.72693i | 0.236623 | + | 0.171917i | ||||
\(757\) | −10.7752 | − | 33.1627i | −0.391632 | − | 1.20532i | −0.931553 | − | 0.363605i | \(-0.881546\pi\) |
0.539921 | − | 0.841716i | \(-0.318454\pi\) | |||||||
\(758\) | −7.23750 | −0.262878 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 19.5493 | 0.709129 | ||||||||
\(761\) | 0.831169 | + | 2.55807i | 0.0301298 | + | 0.0927301i | 0.964991 | − | 0.262285i | \(-0.0844759\pi\) |
−0.934861 | + | 0.355015i | \(0.884476\pi\) | |||||||
\(762\) | 19.9830 | + | 14.5185i | 0.723907 | + | 0.525949i | ||||
\(763\) | 4.44592 | − | 3.23015i | 0.160953 | − | 0.116939i | ||||
\(764\) | 2.01236 | − | 6.19340i | 0.0728045 | − | 0.224069i | ||||
\(765\) | 3.63495 | − | 11.1872i | 0.131422 | − | 0.404475i | ||||
\(766\) | 10.7697 | − | 7.82463i | 0.389124 | − | 0.282715i | ||||
\(767\) | 8.22103 | + | 5.97293i | 0.296844 | + | 0.215670i | ||||
\(768\) | 10.3677 | + | 31.9086i | 0.374113 | + | 1.15140i | ||||
\(769\) | 32.5735 | 1.17463 | 0.587315 | − | 0.809359i | \(-0.300185\pi\) | ||||
0.587315 | + | 0.809359i | \(0.300185\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −52.0010 | −1.87277 | ||||||||
\(772\) | −10.1973 | − | 31.3841i | −0.367009 | − | 1.12954i | ||||
\(773\) | −33.7067 | − | 24.4893i | −1.21234 | − | 0.880820i | −0.216903 | − | 0.976193i | \(-0.569595\pi\) |
−0.995442 | + | 0.0953734i | \(0.969595\pi\) | |||||||
\(774\) | −22.3902 | + | 16.2675i | −0.804800 | + | 0.584721i | ||||
\(775\) | −1.13972 | + | 3.50769i | −0.0409398 | + | 0.126000i | ||||
\(776\) | −1.92429 | + | 5.92237i | −0.0690781 | + | 0.212601i | ||||
\(777\) | −13.9787 | + | 10.1561i | −0.501483 | + | 0.364348i | ||||
\(778\) | −18.6140 | − | 13.5238i | −0.667343 | − | 0.484853i | ||||
\(779\) | −9.32811 | − | 28.7090i | −0.334214 | − | 1.02861i | ||||
\(780\) | 14.1178 | 0.505498 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −4.34451 | −0.155359 | ||||||||
\(783\) | −9.85436 | − | 30.3286i | −0.352166 | − | 1.08386i | ||||
\(784\) | 4.95323 | + | 3.59874i | 0.176901 | + | 0.128526i | ||||
\(785\) | 5.85089 | − | 4.25092i | 0.208827 | − | 0.151722i | ||||
\(786\) | −7.16978 | + | 22.0663i | −0.255738 | + | 0.787079i | ||||
\(787\) | 11.1001 | − | 34.1627i | 0.395677 | − | 1.21777i | −0.532757 | − | 0.846268i | \(-0.678844\pi\) |
0.928433 | − | 0.371499i | \(-0.121156\pi\) | |||||||
\(788\) | 13.2012 | − | 9.59120i | 0.470272 | − | 0.341672i | ||||
\(789\) | −8.39634 | − | 6.10030i | −0.298918 | − | 0.217176i | ||||
\(790\) | −2.75314 | − | 8.47330i | −0.0979524 | − | 0.301466i | ||||
\(791\) | −0.314468 | −0.0111812 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.55476 | 0.303789 | ||||||||
\(794\) | −2.42103 | − | 7.45116i | −0.0859190 | − | 0.264432i | ||||
\(795\) | 26.9495 | + | 19.5800i | 0.955802 | + | 0.694430i | ||||
\(796\) | −9.21044 | + | 6.69178i | −0.326456 | + | 0.237184i | ||||
\(797\) | −9.80193 | + | 30.1672i | −0.347202 | + | 1.06858i | 0.613192 | + | 0.789934i | \(0.289885\pi\) |
−0.960394 | + | 0.278645i | \(0.910115\pi\) | |||||||
\(798\) | 5.06899 | − | 15.6007i | 0.179440 | − | 0.552260i | ||||
\(799\) | 11.3365 | − | 8.23642i | 0.401055 | − | 0.291383i | ||||
\(800\) | −4.74018 | − | 3.44395i | −0.167591 | − | 0.121762i | ||||
\(801\) | 12.3698 | + | 38.0703i | 0.437065 | + | 1.34515i | ||||
\(802\) | −20.3352 | −0.718061 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −25.1617 | −0.887384 | ||||||||
\(805\) | 0.782725 | + | 2.40898i | 0.0275874 | + | 0.0849054i | ||||
\(806\) | −7.59117 | − | 5.51531i | −0.267388 | − | 0.194268i | ||||
\(807\) | −22.6211 | + | 16.4352i | −0.796301 | + | 0.578547i | ||||
\(808\) | −5.92680 | + | 18.2408i | −0.208504 | + | 0.641709i | ||||
\(809\) | 2.63150 | − | 8.09893i | 0.0925187 | − | 0.284743i | −0.894080 | − | 0.447906i | \(-0.852170\pi\) |
0.986599 | + | 0.163163i | \(0.0521697\pi\) | |||||||
\(810\) | 0.204796 | − | 0.148793i | 0.00719581 | − | 0.00522806i | ||||
\(811\) | 7.30566 | + | 5.30788i | 0.256537 | + | 0.186385i | 0.708619 | − | 0.705592i | \(-0.249319\pi\) |
−0.452082 | + | 0.891976i | \(0.649319\pi\) | |||||||
\(812\) | 2.76287 | + | 8.50324i | 0.0969577 | + | 0.298405i | ||||
\(813\) | 3.52472 | 0.123617 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.6892 | −0.654653 | ||||||||
\(816\) | 2.14900 | + | 6.61395i | 0.0752301 | + | 0.231534i | ||||
\(817\) | −47.4585 | − | 34.4806i | −1.66036 | − | 1.20632i | ||||
\(818\) | 8.57440 | − | 6.22967i | 0.299797 | − | 0.217815i | ||||
\(819\) | 5.39164 | − | 16.5938i | 0.188399 | − | 0.579833i | ||||
\(820\) | −1.77090 | + | 5.45026i | −0.0618424 | + | 0.190331i | ||||
\(821\) | −43.9479 | + | 31.9300i | −1.53379 | + | 1.11436i | −0.579707 | + | 0.814825i | \(0.696833\pi\) |
−0.954084 | + | 0.299539i | \(0.903167\pi\) | |||||||
\(822\) | −7.18323 | − | 5.21892i | −0.250544 | − | 0.182031i | ||||
\(823\) | 5.51887 | + | 16.9853i | 0.192376 | + | 0.592072i | 0.999997 | + | 0.00237039i | \(0.000754519\pi\) |
−0.807621 | + | 0.589701i | \(0.799245\pi\) | |||||||
\(824\) | 24.1723 | 0.842083 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.24151 | −0.0779920 | ||||||||
\(827\) | 16.0533 | + | 49.4068i | 0.558226 | + | 1.71804i | 0.687267 | + | 0.726404i | \(0.258810\pi\) |
−0.129041 | + | 0.991639i | \(0.541190\pi\) | |||||||
\(828\) | 14.1880 | + | 10.3082i | 0.493068 | + | 0.358235i | ||||
\(829\) | 15.9749 | − | 11.6064i | 0.554830 | − | 0.403107i | −0.274733 | − | 0.961520i | \(-0.588590\pi\) |
0.829563 | + | 0.558413i | \(0.188590\pi\) | |||||||
\(830\) | 0.366993 | − | 1.12949i | 0.0127385 | − | 0.0392051i | ||||
\(831\) | −7.03163 | + | 21.6411i | −0.243925 | + | 0.750723i | ||||
\(832\) | 6.30387 | − | 4.58003i | 0.218547 | − | 0.158784i | ||||
\(833\) | −11.5175 | − | 8.36796i | −0.399058 | − | 0.289933i | ||||
\(834\) | −3.81526 | − | 11.7422i | −0.132112 | − | 0.406598i | ||||
\(835\) | 7.85328 | 0.271774 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 19.7528 | 0.682757 | ||||||||
\(838\) | −7.17353 | − | 22.0779i | −0.247806 | − | 0.762667i | ||||
\(839\) | 3.33032 | + | 2.41962i | 0.114975 | + | 0.0835344i | 0.643787 | − | 0.765205i | \(-0.277362\pi\) |
−0.528812 | + | 0.848739i | \(0.677362\pi\) | |||||||
\(840\) | −5.98037 | + | 4.34499i | −0.206342 | + | 0.149916i | ||||
\(841\) | 1.99435 | − | 6.13799i | 0.0687708 | − | 0.211655i | ||||
\(842\) | 6.05673 | − | 18.6407i | 0.208729 | − | 0.642400i | ||||
\(843\) | −57.7072 | + | 41.9267i | −1.98754 | + | 1.44403i | ||||
\(844\) | 26.8158 | + | 19.4828i | 0.923038 | + | 0.670627i | ||||
\(845\) | 0.341302 | + | 1.05042i | 0.0117411 | + | 0.0361355i | ||||
\(846\) | 21.1400 | 0.726807 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −12.2198 | −0.419630 | ||||||||
\(849\) | −17.7608 | − | 54.6620i | −0.609548 | − | 1.87600i | ||||
\(850\) | 1.43117 | + | 1.03980i | 0.0490886 | + | 0.0356650i | ||||
\(851\) | −11.8388 | + | 8.60141i | −0.405830 | + | 0.294853i | ||||
\(852\) | 2.55909 | − | 7.87606i | 0.0876729 | − | 0.269829i | ||||
\(853\) | −1.70047 | + | 5.23352i | −0.0582231 | + | 0.179192i | −0.975938 | − | 0.218046i | \(-0.930032\pi\) |
0.917715 | + | 0.397239i | \(0.130032\pi\) | |||||||
\(854\) | −1.52664 | + | 1.10917i | −0.0522406 | + | 0.0379550i | ||||
\(855\) | 30.4308 | + | 22.1093i | 1.04071 | + | 0.756121i | ||||
\(856\) | −3.66048 | − | 11.2658i | −0.125113 | − | 0.385058i | ||||
\(857\) | 26.9281 | 0.919847 | 0.459924 | − | 0.887959i | \(-0.347877\pi\) | ||||
0.459924 | + | 0.887959i | \(0.347877\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.1519 | 0.653456 | 0.326728 | − | 0.945118i | \(-0.394054\pi\) | ||||
0.326728 | + | 0.945118i | \(0.394054\pi\) | |||||||
\(860\) | 3.44142 | + | 10.5916i | 0.117352 | + | 0.361171i | ||||
\(861\) | 9.23437 | + | 6.70916i | 0.314706 | + | 0.228648i | ||||
\(862\) | −2.30870 | + | 1.67737i | −0.0786346 | + | 0.0571314i | ||||
\(863\) | 1.53319 | − | 4.71867i | 0.0521904 | − | 0.160625i | −0.921564 | − | 0.388226i | \(-0.873088\pi\) |
0.973755 | + | 0.227600i | \(0.0730880\pi\) | |||||||
\(864\) | −9.69693 | + | 29.8441i | −0.329896 | + | 1.01532i | ||||
\(865\) | −9.06478 | + | 6.58595i | −0.308212 | + | 0.223929i | ||||
\(866\) | −23.9534 | − | 17.4031i | −0.813969 | − | 0.591383i | ||||
\(867\) | 9.77298 | + | 30.0781i | 0.331908 | + | 1.02151i | ||||
\(868\) | −5.53810 | −0.187975 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 12.3488 | 0.418663 | ||||||||
\(871\) | 6.55147 | + | 20.1633i | 0.221988 | + | 0.683209i | ||||
\(872\) | 10.9887 | + | 7.98378i | 0.372125 | + | 0.270365i | ||||
\(873\) | −9.69327 | + | 7.04257i | −0.328068 | + | 0.238355i | ||||
\(874\) | 4.29302 | − | 13.2126i | 0.145214 | − | 0.446922i | ||||
\(875\) | 0.318714 | − | 0.980901i | 0.0107745 | − | 0.0331605i | ||||
\(876\) | −2.73491 | + | 1.98703i | −0.0924040 | + | 0.0671354i | ||||
\(877\) | −22.0096 | − | 15.9909i | −0.743211 | − | 0.539974i | 0.150504 | − | 0.988609i | \(-0.451910\pi\) |
−0.893715 | + | 0.448635i | \(0.851910\pi\) | |||||||
\(878\) | −0.233269 | − | 0.717928i | −0.00787245 | − | 0.0242289i | ||||
\(879\) | 7.16686 | 0.241732 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.3570 | 0.348935 | 0.174467 | − | 0.984663i | \(-0.444180\pi\) | ||||
0.174467 | + | 0.984663i | \(0.444180\pi\) | |||||||
\(882\) | −6.63694 | − | 20.4264i | −0.223477 | − | 0.687792i | ||||
\(883\) | −5.98260 | − | 4.34661i | −0.201330 | − | 0.146275i | 0.482552 | − | 0.875867i | \(-0.339710\pi\) |
−0.683882 | + | 0.729592i | \(0.739710\pi\) | |||||||
\(884\) | 9.74238 | − | 7.07826i | 0.327672 | − | 0.238067i | ||||
\(885\) | 2.55980 | − | 7.87826i | 0.0860468 | − | 0.264825i | ||||
\(886\) | −3.66370 | + | 11.2757i | −0.123084 | + | 0.378815i | ||||
\(887\) | −14.6101 | + | 10.6148i | −0.490558 | + | 0.356411i | −0.805399 | − | 0.592733i | \(-0.798049\pi\) |
0.314841 | + | 0.949144i | \(0.398049\pi\) | |||||||
\(888\) | −34.5503 | − | 25.1023i | −1.15943 | − | 0.842377i | ||||
\(889\) | −3.79587 | − | 11.6825i | −0.127309 | − | 0.391818i | ||||
\(890\) | −6.02000 | −0.201791 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 23.3563 | 0.782027 | ||||||||
\(893\) | 13.8466 | + | 42.6153i | 0.463357 | + | 1.42607i | ||||
\(894\) | 6.34968 | + | 4.61331i | 0.212365 | + | 0.154292i | ||||
\(895\) | 1.18491 | − | 0.860888i | 0.0396072 | − | 0.0287763i | ||||
\(896\) | 3.20368 | − | 9.85991i | 0.107027 | − | 0.329396i | ||||
\(897\) | 7.35919 | − | 22.6493i | 0.245716 | − | 0.756237i | ||||
\(898\) | −21.3893 | + | 15.5402i | −0.713769 | + | 0.518583i | ||||
\(899\) | 17.7666 | + | 12.9082i | 0.592549 | + | 0.430512i | ||||
\(900\) | −2.20667 | − | 6.79144i | −0.0735558 | − | 0.226381i | ||||
\(901\) | 28.4141 | 0.946612 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 22.1817 | 0.738160 | ||||||||
\(904\) | −0.240184 | − | 0.739212i | −0.00798841 | − | 0.0245858i | ||||
\(905\) | 7.51496 | + | 5.45994i | 0.249806 | + | 0.181494i | ||||
\(906\) | 40.8665 | − | 29.6912i | 1.35770 | − | 0.986425i | ||||
\(907\) | 8.12624 | − | 25.0100i | 0.269827 | − | 0.830443i | −0.720715 | − | 0.693232i | \(-0.756186\pi\) |
0.990542 | − | 0.137211i | \(-0.0438138\pi\) | |||||||
\(908\) | −10.8677 | + | 33.4474i | −0.360658 | + | 1.10999i | ||||
\(909\) | −29.8551 | + | 21.6910i | −0.990233 | + | 0.719446i | ||||
\(910\) | 2.12282 | + | 1.54232i | 0.0703707 | + | 0.0511273i | ||||
\(911\) | 8.85298 | + | 27.2467i | 0.293312 | + | 0.902723i | 0.983783 | + | 0.179362i | \(0.0574035\pi\) |
−0.690471 | + | 0.723360i | \(0.742597\pi\) | |||||||
\(912\) | −22.2379 | −0.736371 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 18.5535 | 0.613694 | ||||||||
\(915\) | −2.15499 | − | 6.63239i | −0.0712419 | − | 0.219260i | ||||
\(916\) | −17.6844 | − | 12.8485i | −0.584308 | − | 0.424525i | ||||
\(917\) | 9.33485 | − | 6.78217i | 0.308264 | − | 0.223967i | ||||
\(918\) | 2.92772 | − | 9.01059i | 0.0966291 | − | 0.297394i | ||||
\(919\) | −12.0074 | + | 36.9550i | −0.396088 | + | 1.21903i | 0.532023 | + | 0.846730i | \(0.321432\pi\) |
−0.928111 | + | 0.372303i | \(0.878568\pi\) | |||||||
\(920\) | −5.06489 | + | 3.67986i | −0.166985 | + | 0.121321i | ||||
\(921\) | −20.4549 | − | 14.8613i | −0.674011 | − | 0.489697i | ||||
\(922\) | −1.51726 | − | 4.66965i | −0.0499684 | − | 0.153787i | ||||
\(923\) | −6.97781 | −0.229677 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.95858 | 0.195917 | ||||||||
\(926\) | 8.83806 | + | 27.2007i | 0.290437 | + | 0.893872i | ||||
\(927\) | 37.6270 | + | 27.3376i | 1.23583 | + | 0.897886i | ||||
\(928\) | −28.2245 | + | 20.5063i | −0.926516 | + | 0.673153i | ||||
\(929\) | 2.29331 | − | 7.05810i | 0.0752412 | − | 0.231569i | −0.906362 | − | 0.422503i | \(-0.861152\pi\) |
0.981603 | + | 0.190934i | \(0.0611517\pi\) | |||||||
\(930\) | −2.36368 | + | 7.27467i | −0.0775082 | + | 0.238546i | ||||
\(931\) | 36.8297 | − | 26.7583i | 1.20704 | − | 0.876969i | ||||
\(932\) | −13.4579 | − | 9.77773i | −0.440828 | − | 0.320280i | ||||
\(933\) | 17.4834 | + | 53.8084i | 0.572382 | + | 1.76161i | ||||
\(934\) | 16.6334 | 0.544260 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 43.1245 | 1.40957 | ||||||||
\(937\) | 4.61547 | + | 14.2049i | 0.150781 | + | 0.464055i | 0.997709 | − | 0.0676518i | \(-0.0215507\pi\) |
−0.846928 | + | 0.531707i | \(0.821551\pi\) | |||||||
\(938\) | −3.78343 | − | 2.74882i | −0.123533 | − | 0.0897522i | ||||
\(939\) | 16.1606 | − | 11.7414i | 0.527383 | − | 0.383166i | ||||
\(940\) | 2.62870 | − | 8.09031i | 0.0857388 | − | 0.263877i | ||||
\(941\) | 16.1742 | − | 49.7791i | 0.527265 | − | 1.62275i | −0.232529 | − | 0.972589i | \(-0.574700\pi\) |
0.759794 | − | 0.650164i | \(-0.225300\pi\) | |||||||
\(942\) | 12.1343 | − | 8.81607i | 0.395356 | − | 0.287243i | ||||
\(943\) | 7.82077 | + | 5.68212i | 0.254679 | + | 0.185035i | ||||
\(944\) | 0.939026 | + | 2.89003i | 0.0305627 | + | 0.0940623i | ||||
\(945\) | −5.52373 | −0.179687 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.69553 | −0.120088 | −0.0600442 | − | 0.998196i | \(-0.519124\pi\) | ||||
−0.0600442 | + | 0.998196i | \(0.519124\pi\) | |||||||
\(948\) | 15.2777 | + | 47.0201i | 0.496198 | + | 1.52714i | ||||
\(949\) | 2.30441 | + | 1.67425i | 0.0748043 | + | 0.0543485i | ||||
\(950\) | −4.57646 | + | 3.32500i | −0.148480 | + | 0.107877i | ||||
\(951\) | −1.99240 | + | 6.13199i | −0.0646081 | + | 0.198843i | ||||
\(952\) | −1.94847 | + | 5.99677i | −0.0631502 | + | 0.194356i | ||||
\(953\) | 34.9112 | − | 25.3645i | 1.13088 | − | 0.821635i | 0.145061 | − | 0.989423i | \(-0.453662\pi\) |
0.985823 | + | 0.167787i | \(0.0536622\pi\) | |||||||
\(954\) | 34.6798 | + | 25.1963i | 1.12280 | + | 0.815762i | ||||
\(955\) | 1.38222 | + | 4.25404i | 0.0447276 | + | 0.137657i | ||||
\(956\) | 39.9011 | 1.29049 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.20373 | 0.0388907 | ||||||||
\(959\) | 1.36449 | + | 4.19947i | 0.0440617 | + | 0.135608i | ||||
\(960\) | −5.13881 | − | 3.73357i | −0.165854 | − | 0.120500i | ||||
\(961\) | 14.0746 | − | 10.2258i | 0.454020 | − | 0.329865i | ||||
\(962\) | −4.68448 | + | 14.4173i | −0.151034 | + | 0.464834i | ||||
\(963\) | 7.04308 | − | 21.6764i | 0.226960 | − | 0.698511i | ||||
\(964\) | −12.8840 | + | 9.36079i | −0.414966 | + | 0.301491i | ||||
\(965\) | 18.3372 | + | 13.3227i | 0.590295 | + | 0.428874i | ||||
\(966\) | 1.62331 | + | 4.99604i | 0.0522291 | + | 0.160745i | ||||
\(967\) | 29.2144 | 0.939471 | 0.469736 | − | 0.882807i | \(-0.344349\pi\) | ||||
0.469736 | + | 0.882807i | \(0.344349\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 51.7087 | 1.66112 | ||||||||
\(970\) | −0.556816 | − | 1.71370i | −0.0178783 | − | 0.0550237i | ||||
\(971\) | 21.3618 | + | 15.5203i | 0.685533 | + | 0.498069i | 0.875189 | − | 0.483782i | \(-0.160737\pi\) |
−0.189656 | + | 0.981851i | \(0.560737\pi\) | |||||||
\(972\) | 17.7879 | − | 12.9237i | 0.570547 | − | 0.414526i | ||||
\(973\) | −1.89737 | + | 5.83949i | −0.0608268 | + | 0.187206i | ||||
\(974\) | 0.239409 | − | 0.736824i | 0.00767115 | − | 0.0236094i | ||||
\(975\) | −7.84507 | + | 5.69978i | −0.251243 | + | 0.182539i | ||||
\(976\) | 2.06963 | + | 1.50367i | 0.0662472 | + | 0.0481314i | ||||
\(977\) | −4.89588 | − | 15.0680i | −0.156633 | − | 0.482067i | 0.841690 | − | 0.539961i | \(-0.181561\pi\) |
−0.998323 | + | 0.0578948i | \(0.981561\pi\) | |||||||
\(978\) | −38.7598 | −1.23940 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −8.64252 | −0.276075 | ||||||||
\(981\) | 8.07600 | + | 24.8554i | 0.257847 | + | 0.793571i | ||||
\(982\) | −8.30342 | − | 6.03279i | −0.264973 | − | 0.192514i | ||||
\(983\) | −28.3997 | + | 20.6336i | −0.905809 | + | 0.658109i | −0.939951 | − | 0.341308i | \(-0.889130\pi\) |
0.0341426 | + | 0.999417i | \(0.489130\pi\) | |||||||
\(984\) | −8.71801 | + | 26.8313i | −0.277920 | + | 0.855350i | ||||
\(985\) | −3.46345 | + | 10.6594i | −0.110355 | + | 0.339637i | ||||
\(986\) | 8.52162 | − | 6.19132i | 0.271384 | − | 0.197172i | ||||
\(987\) | −13.7074 | − | 9.95901i | −0.436312 | − | 0.316999i | ||||
\(988\) | 11.8995 | + | 36.6230i | 0.378574 | + | 1.16513i | ||||
\(989\) | 18.7861 | 0.597363 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.9700 | 0.602600 | 0.301300 | − | 0.953529i | \(-0.402579\pi\) | ||||
0.301300 | + | 0.953529i | \(0.402579\pi\) | |||||||
\(992\) | −6.67782 | − | 20.5522i | −0.212021 | − | 0.652533i | ||||
\(993\) | 35.0177 | + | 25.4419i | 1.11125 | + | 0.807373i | ||||
\(994\) | 1.24523 | − | 0.904710i | 0.0394962 | − | 0.0286957i | ||||
\(995\) | 2.41645 | − | 7.43707i | 0.0766066 | − | 0.235771i | ||||
\(996\) | −2.03652 | + | 6.26776i | −0.0645295 | + | 0.198601i | ||||
\(997\) | 24.3795 | − | 17.7127i | 0.772106 | − | 0.560968i | −0.130494 | − | 0.991449i | \(-0.541656\pi\) |
0.902599 | + | 0.430481i | \(0.141656\pi\) | |||||||
\(998\) | −10.3642 | − | 7.53000i | −0.328072 | − | 0.238358i | ||||
\(999\) | −9.86141 | − | 30.3503i | −0.312001 | − | 0.960241i |
(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 | 605.2.g.e.511.2 | 8 | ||
11.2 | odd | 10 | 605.2.g.m.251.1 | 8 | |||
11.3 | even | 5 | 605.2.a.k.1.3 | 4 | |||
11.4 | even | 5 | 605.2.g.k.366.1 | 8 | |||
11.5 | even | 5 | 605.2.g.k.81.1 | 8 | |||
11.6 | odd | 10 | 55.2.g.b.26.2 | ✓ | 8 | ||
11.7 | odd | 10 | 55.2.g.b.36.2 | yes | 8 | ||
11.8 | odd | 10 | 605.2.a.j.1.2 | 4 | |||
11.9 | even | 5 | inner | 605.2.g.e.251.2 | 8 | ||
11.10 | odd | 2 | 605.2.g.m.511.1 | 8 | |||
33.8 | even | 10 | 5445.2.a.bp.1.3 | 4 | |||
33.14 | odd | 10 | 5445.2.a.bi.1.2 | 4 | |||
33.17 | even | 10 | 495.2.n.e.136.1 | 8 | |||
33.29 | even | 10 | 495.2.n.e.91.1 | 8 | |||
44.3 | odd | 10 | 9680.2.a.cm.1.4 | 4 | |||
44.7 | even | 10 | 880.2.bo.h.641.2 | 8 | |||
44.19 | even | 10 | 9680.2.a.cn.1.4 | 4 | |||
44.39 | even | 10 | 880.2.bo.h.81.2 | 8 | |||
55.7 | even | 20 | 275.2.z.a.124.3 | 16 | |||
55.14 | even | 10 | 3025.2.a.w.1.2 | 4 | |||
55.17 | even | 20 | 275.2.z.a.224.2 | 16 | |||
55.18 | even | 20 | 275.2.z.a.124.2 | 16 | |||
55.19 | odd | 10 | 3025.2.a.bd.1.3 | 4 | |||
55.28 | even | 20 | 275.2.z.a.224.3 | 16 | |||
55.29 | odd | 10 | 275.2.h.a.201.1 | 8 | |||
55.39 | odd | 10 | 275.2.h.a.26.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.2.g.b.26.2 | ✓ | 8 | 11.6 | odd | 10 | ||
55.2.g.b.36.2 | yes | 8 | 11.7 | odd | 10 | ||
275.2.h.a.26.1 | 8 | 55.39 | odd | 10 | |||
275.2.h.a.201.1 | 8 | 55.29 | odd | 10 | |||
275.2.z.a.124.2 | 16 | 55.18 | even | 20 | |||
275.2.z.a.124.3 | 16 | 55.7 | even | 20 | |||
275.2.z.a.224.2 | 16 | 55.17 | even | 20 | |||
275.2.z.a.224.3 | 16 | 55.28 | even | 20 | |||
495.2.n.e.91.1 | 8 | 33.29 | even | 10 | |||
495.2.n.e.136.1 | 8 | 33.17 | even | 10 | |||
605.2.a.j.1.2 | 4 | 11.8 | odd | 10 | |||
605.2.a.k.1.3 | 4 | 11.3 | even | 5 | |||
605.2.g.e.251.2 | 8 | 11.9 | even | 5 | inner | ||
605.2.g.e.511.2 | 8 | 1.1 | even | 1 | trivial | ||
605.2.g.k.81.1 | 8 | 11.5 | even | 5 | |||
605.2.g.k.366.1 | 8 | 11.4 | even | 5 | |||
605.2.g.m.251.1 | 8 | 11.2 | odd | 10 | |||
605.2.g.m.511.1 | 8 | 11.10 | odd | 2 | |||
880.2.bo.h.81.2 | 8 | 44.39 | even | 10 | |||
880.2.bo.h.641.2 | 8 | 44.7 | even | 10 | |||
3025.2.a.w.1.2 | 4 | 55.14 | even | 10 | |||
3025.2.a.bd.1.3 | 4 | 55.19 | odd | 10 | |||
5445.2.a.bi.1.2 | 4 | 33.14 | odd | 10 | |||
5445.2.a.bp.1.3 | 4 | 33.8 | even | 10 | |||
9680.2.a.cm.1.4 | 4 | 44.3 | odd | 10 | |||
9680.2.a.cn.1.4 | 4 | 44.19 | even | 10 |