Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(373,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.373");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.k (of order \(3\), 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: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} + 15x^{8} + 14x^{7} + 110x^{6} + 36x^{5} + 233x^{4} + 164x^{3} + 345x^{2} + 76x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 445.5 | ||
Root | \(-1.10337 + 1.91109i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.445 |
Dual form | 546.2.k.e.373.5 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.10337 | + | 1.91109i | 0.493442 | + | 0.854666i | 0.999971 | − | 0.00755619i | \(-0.00240523\pi\) |
−0.506530 | + | 0.862223i | \(0.669072\pi\) | |||||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | 1.44928 | − | 2.21350i | 0.547778 | − | 0.836624i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.20674 | 0.697832 | ||||||||
\(11\) | −1.05547 | −0.318235 | −0.159118 | − | 0.987260i | \(-0.550865\pi\) | ||||
−0.159118 | + | 0.987260i | \(0.550865\pi\) | |||||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | 3.18376 | + | 1.69224i | 0.883015 | + | 0.469344i | ||||
\(14\) | −1.19230 | − | 2.36187i | −0.318657 | − | 0.631235i | ||||
\(15\) | −1.10337 | − | 1.91109i | −0.284889 | − | 0.493442i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0.472267 | + | 0.817990i | 0.114541 | + | 0.198392i | 0.917596 | − | 0.397513i | \(-0.130127\pi\) |
−0.803055 | + | 0.595905i | \(0.796793\pi\) | |||||||
\(18\) | 0.500000 | − | 0.866025i | 0.117851 | − | 0.204124i | ||||
\(19\) | 3.92744 | 0.901016 | 0.450508 | − | 0.892772i | \(-0.351243\pi\) | ||||
0.450508 | + | 0.892772i | \(0.351243\pi\) | |||||||
\(20\) | 1.10337 | − | 1.91109i | 0.246721 | − | 0.427333i | ||||
\(21\) | −1.44928 | + | 2.21350i | −0.316260 | + | 0.483025i | ||||
\(22\) | −0.527733 | + | 0.914061i | −0.112513 | + | 0.194879i | ||||
\(23\) | 3.11385 | − | 5.39335i | 0.649284 | − | 1.12459i | −0.334011 | − | 0.942569i | \(-0.608402\pi\) |
0.983294 | − | 0.182023i | \(-0.0582645\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0.0651512 | − | 0.112845i | 0.0130302 | − | 0.0225690i | ||||
\(26\) | 3.05741 | − | 1.91109i | 0.599606 | − | 0.374796i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.64159 | − | 0.148368i | −0.499213 | − | 0.0280389i | ||||
\(29\) | 0.888084 | + | 1.53821i | 0.164913 | + | 0.285638i | 0.936624 | − | 0.350335i | \(-0.113932\pi\) |
−0.771711 | + | 0.635973i | \(0.780599\pi\) | |||||||
\(30\) | −2.20674 | −0.402894 | ||||||||
\(31\) | 3.63304 | − | 6.29261i | 0.652513 | − | 1.13019i | −0.329997 | − | 0.943982i | \(-0.607048\pi\) |
0.982511 | − | 0.186205i | \(-0.0596188\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 1.05547 | 0.183733 | ||||||||
\(34\) | 0.944533 | 0.161986 | ||||||||
\(35\) | 5.82930 | + | 0.327409i | 0.985331 | + | 0.0553423i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | −1.13110 | + | 1.95913i | −0.185952 | + | 0.322079i | −0.943897 | − | 0.330240i | \(-0.892870\pi\) |
0.757945 | + | 0.652319i | \(0.226204\pi\) | |||||||
\(38\) | 1.96372 | − | 3.40126i | 0.318557 | − | 0.551758i | ||||
\(39\) | −3.18376 | − | 1.69224i | −0.509809 | − | 0.270976i | ||||
\(40\) | −1.10337 | − | 1.91109i | −0.174458 | − | 0.302170i | ||||
\(41\) | −1.63110 | − | 2.82515i | −0.254735 | − | 0.441215i | 0.710088 | − | 0.704113i | \(-0.248655\pi\) |
−0.964824 | + | 0.262898i | \(0.915322\pi\) | |||||||
\(42\) | 1.19230 | + | 2.36187i | 0.183976 | + | 0.364444i | ||||
\(43\) | 0.537418 | − | 0.930835i | 0.0819554 | − | 0.141951i | −0.822134 | − | 0.569293i | \(-0.807217\pi\) |
0.904090 | + | 0.427343i | \(0.140550\pi\) | |||||||
\(44\) | 0.527733 | + | 0.914061i | 0.0795588 | + | 0.137800i | ||||
\(45\) | 1.10337 | + | 1.91109i | 0.164481 | + | 0.284889i | ||||
\(46\) | −3.11385 | − | 5.39335i | −0.459113 | − | 0.795207i | ||||
\(47\) | 2.42678 | + | 4.20330i | 0.353982 | + | 0.613114i | 0.986943 | − | 0.161069i | \(-0.0514942\pi\) |
−0.632961 | + | 0.774183i | \(0.718161\pi\) | |||||||
\(48\) | 0.500000 | − | 0.866025i | 0.0721688 | − | 0.125000i | ||||
\(49\) | −2.79915 | − | 6.41598i | −0.399879 | − | 0.916568i | ||||
\(50\) | −0.0651512 | − | 0.112845i | −0.00921377 | − | 0.0159587i | ||||
\(51\) | −0.472267 | − | 0.817990i | −0.0661305 | − | 0.114541i | ||||
\(52\) | −0.126352 | − | 3.60334i | −0.0175218 | − | 0.499693i | ||||
\(53\) | −4.94074 | + | 8.55761i | −0.678663 | + | 1.17548i | 0.296721 | + | 0.954964i | \(0.404107\pi\) |
−0.975384 | + | 0.220514i | \(0.929227\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | −1.16457 | − | 2.01709i | −0.157031 | − | 0.271985i | ||||
\(56\) | −1.44928 | + | 2.21350i | −0.193669 | + | 0.295791i | ||||
\(57\) | −3.92744 | −0.520202 | ||||||||
\(58\) | 1.77617 | 0.233222 | ||||||||
\(59\) | 0.509684 | + | 0.882799i | 0.0663552 | + | 0.114931i | 0.897294 | − | 0.441433i | \(-0.145530\pi\) |
−0.830939 | + | 0.556363i | \(0.812196\pi\) | |||||||
\(60\) | −1.10337 | + | 1.91109i | −0.142444 | + | 0.246721i | ||||
\(61\) | 0.0764368 | 0.00978673 | 0.00489336 | − | 0.999988i | \(-0.498442\pi\) | ||||
0.00489336 | + | 0.999988i | \(0.498442\pi\) | |||||||
\(62\) | −3.63304 | − | 6.29261i | −0.461397 | − | 0.799163i | ||||
\(63\) | 1.44928 | − | 2.21350i | 0.182593 | − | 0.278875i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.278825 | + | 7.95162i | 0.0345840 | + | 0.986278i | ||||
\(66\) | 0.527733 | − | 0.914061i | 0.0649595 | − | 0.112513i | ||||
\(67\) | −11.7062 | −1.43013 | −0.715067 | − | 0.699056i | \(-0.753604\pi\) | ||||
−0.715067 | + | 0.699056i | \(0.753604\pi\) | |||||||
\(68\) | 0.472267 | − | 0.817990i | 0.0572707 | − | 0.0991958i | ||||
\(69\) | −3.11385 | + | 5.39335i | −0.374864 | + | 0.649284i | ||||
\(70\) | 3.19819 | − | 4.88461i | 0.382257 | − | 0.583823i | ||||
\(71\) | −4.20868 | + | 7.28964i | −0.499478 | + | 0.865121i | −1.00000 | 0.000602515i | \(-0.999808\pi\) | |
0.500522 | + | 0.865724i | \(0.333142\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 6.57264 | − | 11.3841i | 0.769269 | − | 1.33241i | −0.168690 | − | 0.985669i | \(-0.553954\pi\) |
0.937960 | − | 0.346745i | \(-0.112713\pi\) | |||||||
\(74\) | 1.13110 | + | 1.95913i | 0.131488 | + | 0.227744i | ||||
\(75\) | −0.0651512 | + | 0.112845i | −0.00752301 | + | 0.0130302i | ||||
\(76\) | −1.96372 | − | 3.40126i | −0.225254 | − | 0.390152i | ||||
\(77\) | −1.52967 | + | 2.33627i | −0.174322 | + | 0.266243i | ||||
\(78\) | −3.05741 | + | 1.91109i | −0.346183 | + | 0.216389i | ||||
\(79\) | 3.00194 | + | 5.19951i | 0.337744 | + | 0.584991i | 0.984008 | − | 0.178124i | \(-0.0570027\pi\) |
−0.646264 | + | 0.763114i | \(0.723669\pi\) | |||||||
\(80\) | −2.20674 | −0.246721 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.26221 | −0.360250 | ||||||||
\(83\) | −1.77617 | −0.194960 | −0.0974799 | − | 0.995237i | \(-0.531078\pi\) | ||||
−0.0974799 | + | 0.995237i | \(0.531078\pi\) | |||||||
\(84\) | 2.64159 | + | 0.148368i | 0.288221 | + | 0.0161883i | ||||
\(85\) | −1.04217 | + | 1.80509i | −0.113039 | + | 0.195789i | ||||
\(86\) | −0.537418 | − | 0.930835i | −0.0579512 | − | 0.100374i | ||||
\(87\) | −0.888084 | − | 1.53821i | −0.0952126 | − | 0.164913i | ||||
\(88\) | 1.05547 | 0.112513 | ||||||||
\(89\) | −6.66765 | + | 11.5487i | −0.706769 | + | 1.22416i | 0.259280 | + | 0.965802i | \(0.416515\pi\) |
−0.966049 | + | 0.258358i | \(0.916819\pi\) | |||||||
\(90\) | 2.20674 | 0.232611 | ||||||||
\(91\) | 8.35995 | − | 4.59470i | 0.876361 | − | 0.481655i | ||||
\(92\) | −6.22771 | −0.649284 | ||||||||
\(93\) | −3.63304 | + | 6.29261i | −0.376729 | + | 0.652513i | ||||
\(94\) | 4.85355 | 0.500606 | ||||||||
\(95\) | 4.33342 | + | 7.50570i | 0.444599 | + | 0.770069i | ||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | −8.99467 | + | 15.5792i | −0.913270 | + | 1.58183i | −0.103855 | + | 0.994592i | \(0.533118\pi\) |
−0.809415 | + | 0.587238i | \(0.800215\pi\) | |||||||
\(98\) | −6.95597 | − | 0.783854i | −0.702659 | − | 0.0791812i | ||||
\(99\) | −1.05547 | −0.106078 | ||||||||
\(100\) | −0.130302 | −0.0130302 | ||||||||
\(101\) | 13.5004 | 1.34334 | 0.671668 | − | 0.740852i | \(-0.265578\pi\) | ||||
0.671668 | + | 0.740852i | \(0.265578\pi\) | |||||||
\(102\) | −0.944533 | −0.0935227 | ||||||||
\(103\) | 1.46258 | + | 2.53327i | 0.144113 | + | 0.249610i | 0.929041 | − | 0.369976i | \(-0.120634\pi\) |
−0.784929 | + | 0.619586i | \(0.787301\pi\) | |||||||
\(104\) | −3.18376 | − | 1.69224i | −0.312193 | − | 0.165938i | ||||
\(105\) | −5.82930 | − | 0.327409i | −0.568881 | − | 0.0319519i | ||||
\(106\) | 4.94074 | + | 8.55761i | 0.479887 | + | 0.831188i | ||||
\(107\) | −7.05459 | + | 12.2189i | −0.681993 | + | 1.18125i | 0.292378 | + | 0.956303i | \(0.405553\pi\) |
−0.974372 | + | 0.224944i | \(0.927780\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | 0.723832 | − | 1.25371i | 0.0693306 | − | 0.120084i | −0.829276 | − | 0.558839i | \(-0.811247\pi\) |
0.898607 | + | 0.438755i | \(0.144580\pi\) | |||||||
\(110\) | −2.32914 | −0.222075 | ||||||||
\(111\) | 1.13110 | − | 1.95913i | 0.107360 | − | 0.185952i | ||||
\(112\) | 1.19230 | + | 2.36187i | 0.112662 | + | 0.223175i | ||||
\(113\) | −1.67707 | + | 2.90477i | −0.157765 | + | 0.273257i | −0.934062 | − | 0.357110i | \(-0.883762\pi\) |
0.776297 | + | 0.630367i | \(0.217096\pi\) | |||||||
\(114\) | −1.96372 | + | 3.40126i | −0.183919 | + | 0.318557i | ||||
\(115\) | 13.7429 | 1.28153 | ||||||||
\(116\) | 0.888084 | − | 1.53821i | 0.0824565 | − | 0.142819i | ||||
\(117\) | 3.18376 | + | 1.69224i | 0.294338 | + | 0.156448i | ||||
\(118\) | 1.01937 | 0.0938405 | ||||||||
\(119\) | 2.49507 | + | 0.140138i | 0.228722 | + | 0.0128465i | ||||
\(120\) | 1.10337 | + | 1.91109i | 0.100723 | + | 0.174458i | ||||
\(121\) | −9.88599 | −0.898726 | ||||||||
\(122\) | 0.0382184 | − | 0.0661962i | 0.00346013 | − | 0.00599312i | ||||
\(123\) | 1.63110 | + | 2.82515i | 0.147072 | + | 0.254735i | ||||
\(124\) | −7.26608 | −0.652513 | ||||||||
\(125\) | 11.3212 | 1.01260 | ||||||||
\(126\) | −1.19230 | − | 2.36187i | −0.106219 | − | 0.210412i | ||||
\(127\) | −4.80963 | − | 8.33053i | −0.426786 | − | 0.739215i | 0.569799 | − | 0.821784i | \(-0.307021\pi\) |
−0.996585 | + | 0.0825687i | \(0.973688\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −0.537418 | + | 0.930835i | −0.0473170 | + | 0.0819554i | ||||
\(130\) | 7.02572 | + | 3.73434i | 0.616197 | + | 0.327523i | ||||
\(131\) | −3.27649 | − | 5.67504i | −0.286268 | − | 0.495831i | 0.686648 | − | 0.726990i | \(-0.259081\pi\) |
−0.972916 | + | 0.231159i | \(0.925748\pi\) | |||||||
\(132\) | −0.527733 | − | 0.914061i | −0.0459333 | − | 0.0795588i | ||||
\(133\) | 5.69198 | − | 8.69338i | 0.493557 | − | 0.753812i | ||||
\(134\) | −5.85308 | + | 10.1378i | −0.505629 | + | 0.875775i | ||||
\(135\) | −1.10337 | − | 1.91109i | −0.0949629 | − | 0.164481i | ||||
\(136\) | −0.472267 | − | 0.817990i | −0.0404965 | − | 0.0701420i | ||||
\(137\) | −3.56234 | − | 6.17015i | −0.304351 | − | 0.527152i | 0.672766 | − | 0.739856i | \(-0.265106\pi\) |
−0.977117 | + | 0.212704i | \(0.931773\pi\) | |||||||
\(138\) | 3.11385 | + | 5.39335i | 0.265069 | + | 0.459113i | ||||
\(139\) | −3.09957 | + | 5.36862i | −0.262902 | + | 0.455360i | −0.967012 | − | 0.254731i | \(-0.918013\pi\) |
0.704109 | + | 0.710091i | \(0.251346\pi\) | |||||||
\(140\) | −2.63110 | − | 5.21202i | −0.222369 | − | 0.440496i | ||||
\(141\) | −2.42678 | − | 4.20330i | −0.204371 | − | 0.353982i | ||||
\(142\) | 4.20868 | + | 7.28964i | 0.353184 | + | 0.611733i | ||||
\(143\) | −3.36035 | − | 1.78611i | −0.281007 | − | 0.149362i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | −1.95977 | + | 3.39442i | −0.162750 | + | 0.281891i | ||||
\(146\) | −6.57264 | − | 11.3841i | −0.543956 | − | 0.942159i | ||||
\(147\) | 2.79915 | + | 6.41598i | 0.230870 | + | 0.529181i | ||||
\(148\) | 2.26221 | 0.185952 | ||||||||
\(149\) | −21.8748 | −1.79206 | −0.896028 | − | 0.443997i | \(-0.853560\pi\) | ||||
−0.896028 | + | 0.443997i | \(0.853560\pi\) | |||||||
\(150\) | 0.0651512 | + | 0.112845i | 0.00531957 | + | 0.00921377i | ||||
\(151\) | 7.25658 | − | 12.5688i | 0.590532 | − | 1.02283i | −0.403629 | − | 0.914923i | \(-0.632251\pi\) |
0.994161 | − | 0.107909i | \(-0.0344154\pi\) | |||||||
\(152\) | −3.92744 | −0.318557 | ||||||||
\(153\) | 0.472267 | + | 0.817990i | 0.0381805 | + | 0.0661305i | ||||
\(154\) | 1.25844 | + | 2.49287i | 0.101408 | + | 0.200881i | ||||
\(155\) | 16.0343 | 1.28791 | ||||||||
\(156\) | 0.126352 | + | 3.60334i | 0.0101162 | + | 0.288498i | ||||
\(157\) | 2.13538 | − | 3.69859i | 0.170422 | − | 0.295179i | −0.768146 | − | 0.640275i | \(-0.778820\pi\) |
0.938567 | + | 0.345096i | \(0.112154\pi\) | |||||||
\(158\) | 6.00388 | 0.477643 | ||||||||
\(159\) | 4.94074 | − | 8.55761i | 0.391826 | − | 0.678663i | ||||
\(160\) | −1.10337 | + | 1.91109i | −0.0872290 | + | 0.151085i | ||||
\(161\) | −7.42532 | − | 14.7090i | −0.585197 | − | 1.15923i | ||||
\(162\) | 0.500000 | − | 0.866025i | 0.0392837 | − | 0.0680414i | ||||
\(163\) | 6.06417 | 0.474982 | 0.237491 | − | 0.971390i | \(-0.423675\pi\) | ||||
0.237491 | + | 0.971390i | \(0.423675\pi\) | |||||||
\(164\) | −1.63110 | + | 2.82515i | −0.127368 | + | 0.220607i | ||||
\(165\) | 1.16457 | + | 2.01709i | 0.0906617 | + | 0.157031i | ||||
\(166\) | −0.888084 | + | 1.53821i | −0.0689287 | + | 0.119388i | ||||
\(167\) | −7.86930 | − | 13.6300i | −0.608944 | − | 1.05472i | −0.991415 | − | 0.130755i | \(-0.958260\pi\) |
0.382470 | − | 0.923968i | \(-0.375073\pi\) | |||||||
\(168\) | 1.44928 | − | 2.21350i | 0.111815 | − | 0.170775i | ||||
\(169\) | 7.27262 | + | 10.7754i | 0.559432 | + | 0.828876i | ||||
\(170\) | 1.04217 | + | 1.80509i | 0.0799307 | + | 0.138444i | ||||
\(171\) | 3.92744 | 0.300339 | ||||||||
\(172\) | −1.07484 | −0.0819554 | ||||||||
\(173\) | −10.5844 | −0.804717 | −0.402358 | − | 0.915482i | \(-0.631809\pi\) | ||||
−0.402358 | + | 0.915482i | \(0.631809\pi\) | |||||||
\(174\) | −1.77617 | −0.134651 | ||||||||
\(175\) | −0.155360 | − | 0.307757i | −0.0117441 | − | 0.0232642i | ||||
\(176\) | 0.527733 | − | 0.914061i | 0.0397794 | − | 0.0689000i | ||||
\(177\) | −0.509684 | − | 0.882799i | −0.0383102 | − | 0.0663552i | ||||
\(178\) | 6.66765 | + | 11.5487i | 0.499761 | + | 0.865612i | ||||
\(179\) | 14.2382 | 1.06421 | 0.532105 | − | 0.846678i | \(-0.321401\pi\) | ||||
0.532105 | + | 0.846678i | \(0.321401\pi\) | |||||||
\(180\) | 1.10337 | − | 1.91109i | 0.0822403 | − | 0.142444i | ||||
\(181\) | −13.7312 | −1.02063 | −0.510314 | − | 0.859988i | \(-0.670471\pi\) | ||||
−0.510314 | + | 0.859988i | \(0.670471\pi\) | |||||||
\(182\) | 0.200850 | − | 9.53728i | 0.0148880 | − | 0.706950i | ||||
\(183\) | −0.0764368 | −0.00565037 | ||||||||
\(184\) | −3.11385 | + | 5.39335i | −0.229556 | + | 0.397603i | ||||
\(185\) | −4.99210 | −0.367026 | ||||||||
\(186\) | 3.63304 | + | 6.29261i | 0.266388 | + | 0.461397i | ||||
\(187\) | −0.498462 | − | 0.863361i | −0.0364511 | − | 0.0631352i | ||||
\(188\) | 2.42678 | − | 4.20330i | 0.176991 | − | 0.306557i | ||||
\(189\) | −1.44928 | + | 2.21350i | −0.105420 | + | 0.161008i | ||||
\(190\) | 8.66684 | 0.628758 | ||||||||
\(191\) | 0.875997 | 0.0633850 | 0.0316925 | − | 0.999498i | \(-0.489910\pi\) | ||||
0.0316925 | + | 0.999498i | \(0.489910\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −22.6625 | −1.63128 | −0.815640 | − | 0.578560i | \(-0.803615\pi\) | ||||
−0.815640 | + | 0.578560i | \(0.803615\pi\) | |||||||
\(194\) | 8.99467 | + | 15.5792i | 0.645779 | + | 1.11852i | ||||
\(195\) | −0.278825 | − | 7.95162i | −0.0199671 | − | 0.569428i | ||||
\(196\) | −4.15682 | + | 5.63212i | −0.296916 | + | 0.402295i | ||||
\(197\) | 8.44249 | + | 14.6228i | 0.601502 | + | 1.04183i | 0.992594 | + | 0.121481i | \(0.0387642\pi\) |
−0.391092 | + | 0.920352i | \(0.627902\pi\) | |||||||
\(198\) | −0.527733 | + | 0.914061i | −0.0375044 | + | 0.0649595i | ||||
\(199\) | 2.95042 | + | 5.11028i | 0.209150 | + | 0.362258i | 0.951447 | − | 0.307813i | \(-0.0995970\pi\) |
−0.742297 | + | 0.670071i | \(0.766264\pi\) | |||||||
\(200\) | −0.0651512 | + | 0.112845i | −0.00460688 | + | 0.00797936i | ||||
\(201\) | 11.7062 | 0.825689 | ||||||||
\(202\) | 6.75018 | − | 11.6917i | 0.474941 | − | 0.822622i | ||||
\(203\) | 4.69190 | + | 0.263526i | 0.329307 | + | 0.0184959i | ||||
\(204\) | −0.472267 | + | 0.817990i | −0.0330653 | + | 0.0572707i | ||||
\(205\) | 3.59942 | − | 6.23438i | 0.251394 | − | 0.435428i | ||||
\(206\) | 2.92516 | 0.203806 | ||||||||
\(207\) | 3.11385 | − | 5.39335i | 0.216428 | − | 0.374864i | ||||
\(208\) | −3.05741 | + | 1.91109i | −0.211993 | + | 0.132510i | ||||
\(209\) | −4.14528 | −0.286735 | ||||||||
\(210\) | −3.19819 | + | 4.88461i | −0.220696 | + | 0.337070i | ||||
\(211\) | −11.7856 | − | 20.4132i | −0.811353 | − | 1.40531i | −0.911917 | − | 0.410375i | \(-0.865398\pi\) |
0.100564 | − | 0.994931i | \(-0.467935\pi\) | |||||||
\(212\) | 9.88148 | 0.678663 | ||||||||
\(213\) | 4.20868 | − | 7.28964i | 0.288374 | − | 0.499478i | ||||
\(214\) | 7.05459 | + | 12.2189i | 0.482242 | + | 0.835268i | ||||
\(215\) | 2.37188 | 0.161761 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −8.66338 | − | 17.1615i | −0.588108 | − | 1.16500i | ||||
\(218\) | −0.723832 | − | 1.25371i | −0.0490241 | − | 0.0849123i | ||||
\(219\) | −6.57264 | + | 11.3841i | −0.444138 | + | 0.769269i | ||||
\(220\) | −1.16457 | + | 2.01709i | −0.0785153 | + | 0.135992i | ||||
\(221\) | 0.119343 | + | 3.40347i | 0.00802791 | + | 0.228942i | ||||
\(222\) | −1.13110 | − | 1.95913i | −0.0759147 | − | 0.131488i | ||||
\(223\) | −2.87906 | − | 4.98667i | −0.192796 | − | 0.333932i | 0.753380 | − | 0.657586i | \(-0.228422\pi\) |
−0.946176 | + | 0.323653i | \(0.895089\pi\) | |||||||
\(224\) | 2.64159 | + | 0.148368i | 0.176499 | + | 0.00991325i | ||||
\(225\) | 0.0651512 | − | 0.112845i | 0.00434341 | − | 0.00752301i | ||||
\(226\) | 1.67707 | + | 2.90477i | 0.111557 | + | 0.193222i | ||||
\(227\) | −9.84025 | − | 17.0438i | −0.653121 | − | 1.13124i | −0.982361 | − | 0.186992i | \(-0.940126\pi\) |
0.329241 | − | 0.944246i | \(-0.393207\pi\) | |||||||
\(228\) | 1.96372 | + | 3.40126i | 0.130051 | + | 0.225254i | ||||
\(229\) | 10.0430 | + | 17.3951i | 0.663663 | + | 1.14950i | 0.979646 | + | 0.200733i | \(0.0643324\pi\) |
−0.315983 | + | 0.948765i | \(0.602334\pi\) | |||||||
\(230\) | 6.87146 | − | 11.9017i | 0.453091 | − | 0.784777i | ||||
\(231\) | 1.52967 | − | 2.33627i | 0.100645 | − | 0.153716i | ||||
\(232\) | −0.888084 | − | 1.53821i | −0.0583056 | − | 0.100988i | ||||
\(233\) | −2.82261 | − | 4.88890i | −0.184915 | − | 0.320282i | 0.758633 | − | 0.651518i | \(-0.225868\pi\) |
−0.943548 | + | 0.331236i | \(0.892534\pi\) | |||||||
\(234\) | 3.05741 | − | 1.91109i | 0.199869 | − | 0.124932i | ||||
\(235\) | −5.35526 | + | 9.27559i | −0.349339 | + | 0.605073i | ||||
\(236\) | 0.509684 | − | 0.882799i | 0.0331776 | − | 0.0574653i | ||||
\(237\) | −3.00194 | − | 5.19951i | −0.194997 | − | 0.337744i | ||||
\(238\) | 1.36890 | − | 2.09072i | 0.0887324 | − | 0.135521i | ||||
\(239\) | 8.20960 | 0.531035 | 0.265517 | − | 0.964106i | \(-0.414457\pi\) | ||||
0.265517 | + | 0.964106i | \(0.414457\pi\) | |||||||
\(240\) | 2.20674 | 0.142444 | ||||||||
\(241\) | 10.5084 | + | 18.2011i | 0.676908 | + | 1.17244i | 0.975907 | + | 0.218186i | \(0.0700139\pi\) |
−0.298999 | + | 0.954253i | \(0.596653\pi\) | |||||||
\(242\) | −4.94299 | + | 8.56152i | −0.317748 | + | 0.550355i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −0.0382184 | − | 0.0661962i | −0.00244668 | − | 0.00423778i | ||||
\(245\) | 9.17303 | − | 12.4286i | 0.586043 | − | 0.794036i | ||||
\(246\) | 3.26221 | 0.207991 | ||||||||
\(247\) | 12.5040 | + | 6.64619i | 0.795611 | + | 0.422887i | ||||
\(248\) | −3.63304 | + | 6.29261i | −0.230698 | + | 0.399581i | ||||
\(249\) | 1.77617 | 0.112560 | ||||||||
\(250\) | 5.66062 | − | 9.80448i | 0.358009 | − | 0.620090i | ||||
\(251\) | −12.0281 | + | 20.8333i | −0.759209 | + | 1.31499i | 0.184045 | + | 0.982918i | \(0.441081\pi\) |
−0.943254 | + | 0.332071i | \(0.892253\pi\) | |||||||
\(252\) | −2.64159 | − | 0.148368i | −0.166404 | − | 0.00934630i | ||||
\(253\) | −3.28657 | + | 5.69251i | −0.206625 | + | 0.357885i | ||||
\(254\) | −9.61927 | −0.603567 | ||||||||
\(255\) | 1.04217 | − | 1.80509i | 0.0652632 | − | 0.113039i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 1.79955 | − | 3.11691i | 0.112253 | − | 0.194428i | −0.804425 | − | 0.594054i | \(-0.797527\pi\) |
0.916678 | + | 0.399626i | \(0.130860\pi\) | |||||||
\(258\) | 0.537418 | + | 0.930835i | 0.0334582 | + | 0.0579512i | ||||
\(259\) | 2.69724 | + | 5.34303i | 0.167598 | + | 0.332000i | ||||
\(260\) | 6.74690 | − | 4.21728i | 0.418425 | − | 0.261545i | ||||
\(261\) | 0.888084 | + | 1.53821i | 0.0549710 | + | 0.0952126i | ||||
\(262\) | −6.55297 | −0.404844 | ||||||||
\(263\) | −30.2393 | −1.86463 | −0.932317 | − | 0.361643i | \(-0.882216\pi\) | ||||
−0.932317 | + | 0.361643i | \(0.882216\pi\) | |||||||
\(264\) | −1.05547 | −0.0649595 | ||||||||
\(265\) | −21.8058 | −1.33952 | ||||||||
\(266\) | −4.68270 | − | 9.27609i | −0.287115 | − | 0.568753i | ||||
\(267\) | 6.66765 | − | 11.5487i | 0.408053 | − | 0.706769i | ||||
\(268\) | 5.85308 | + | 10.1378i | 0.357534 | + | 0.619266i | ||||
\(269\) | −5.21964 | − | 9.04068i | −0.318247 | − | 0.551220i | 0.661875 | − | 0.749614i | \(-0.269761\pi\) |
−0.980122 | + | 0.198394i | \(0.936427\pi\) | |||||||
\(270\) | −2.20674 | −0.134298 | ||||||||
\(271\) | 5.33456 | − | 9.23972i | 0.324051 | − | 0.561273i | −0.657269 | − | 0.753656i | \(-0.728288\pi\) |
0.981320 | + | 0.192383i | \(0.0616217\pi\) | |||||||
\(272\) | −0.944533 | −0.0572707 | ||||||||
\(273\) | −8.35995 | + | 4.59470i | −0.505967 | + | 0.278084i | ||||
\(274\) | −7.12468 | −0.430417 | ||||||||
\(275\) | −0.0687649 | + | 0.119104i | −0.00414668 | + | 0.00718226i | ||||
\(276\) | 6.22771 | 0.374864 | ||||||||
\(277\) | −9.53530 | − | 16.5156i | −0.572920 | − | 0.992327i | −0.996264 | − | 0.0863582i | \(-0.972477\pi\) |
0.423344 | − | 0.905969i | \(-0.360856\pi\) | |||||||
\(278\) | 3.09957 | + | 5.36862i | 0.185900 | + | 0.321988i | ||||
\(279\) | 3.63304 | − | 6.29261i | 0.217504 | − | 0.376729i | ||||
\(280\) | −5.82930 | − | 0.327409i | −0.348367 | − | 0.0195664i | ||||
\(281\) | 23.3309 | 1.39181 | 0.695903 | − | 0.718136i | \(-0.255005\pi\) | ||||
0.695903 | + | 0.718136i | \(0.255005\pi\) | |||||||
\(282\) | −4.85355 | −0.289025 | ||||||||
\(283\) | 8.22931 | 0.489182 | 0.244591 | − | 0.969626i | \(-0.421346\pi\) | ||||
0.244591 | + | 0.969626i | \(0.421346\pi\) | |||||||
\(284\) | 8.41735 | 0.499478 | ||||||||
\(285\) | −4.33342 | − | 7.50570i | −0.256690 | − | 0.444599i | ||||
\(286\) | −3.22699 | + | 2.01709i | −0.190816 | + | 0.119273i | ||||
\(287\) | −8.61740 | − | 0.484007i | −0.508669 | − | 0.0285700i | ||||
\(288\) | 0.500000 | + | 0.866025i | 0.0294628 | + | 0.0510310i | ||||
\(289\) | 8.05393 | − | 13.9498i | 0.473761 | − | 0.820577i | ||||
\(290\) | 1.95977 | + | 3.39442i | 0.115082 | + | 0.199327i | ||||
\(291\) | 8.99467 | − | 15.5792i | 0.527277 | − | 0.913270i | ||||
\(292\) | −13.1453 | −0.769269 | ||||||||
\(293\) | 9.34471 | − | 16.1855i | 0.545924 | − | 0.945568i | −0.452624 | − | 0.891701i | \(-0.649512\pi\) |
0.998548 | − | 0.0538667i | \(-0.0171546\pi\) | |||||||
\(294\) | 6.95597 | + | 0.783854i | 0.405681 | + | 0.0457153i | ||||
\(295\) | −1.12474 | + | 1.94811i | −0.0654849 | + | 0.113423i | ||||
\(296\) | 1.13110 | − | 1.95913i | 0.0657440 | − | 0.113872i | ||||
\(297\) | 1.05547 | 0.0612444 | ||||||||
\(298\) | −10.9374 | + | 18.9442i | −0.633588 | + | 1.09741i | ||||
\(299\) | 19.0406 | − | 11.9017i | 1.10115 | − | 0.688295i | ||||
\(300\) | 0.130302 | 0.00752301 | ||||||||
\(301\) | −1.28153 | − | 2.53862i | −0.0738662 | − | 0.146323i | ||||
\(302\) | −7.25658 | − | 12.5688i | −0.417569 | − | 0.723251i | ||||
\(303\) | −13.5004 | −0.775576 | ||||||||
\(304\) | −1.96372 | + | 3.40126i | −0.112627 | + | 0.195076i | ||||
\(305\) | 0.0843380 | + | 0.146078i | 0.00482918 | + | 0.00836439i | ||||
\(306\) | 0.944533 | 0.0539954 | ||||||||
\(307\) | 18.0495 | 1.03014 | 0.515069 | − | 0.857149i | \(-0.327766\pi\) | ||||
0.515069 | + | 0.857149i | \(0.327766\pi\) | |||||||
\(308\) | 2.78811 | + | 0.156597i | 0.158867 | + | 0.00892297i | ||||
\(309\) | −1.46258 | − | 2.53327i | −0.0832034 | − | 0.144113i | ||||
\(310\) | 8.01717 | − | 13.8862i | 0.455345 | − | 0.788681i | ||||
\(311\) | −8.46321 | + | 14.6587i | −0.479905 | + | 0.831219i | −0.999734 | − | 0.0230506i | \(-0.992662\pi\) |
0.519830 | + | 0.854270i | \(0.325995\pi\) | |||||||
\(312\) | 3.18376 | + | 1.69224i | 0.180245 | + | 0.0958045i | ||||
\(313\) | −11.0035 | − | 19.0587i | −0.621957 | − | 1.07726i | −0.989121 | − | 0.147105i | \(-0.953004\pi\) |
0.367163 | − | 0.930156i | \(-0.380329\pi\) | |||||||
\(314\) | −2.13538 | − | 3.69859i | −0.120506 | − | 0.208723i | ||||
\(315\) | 5.82930 | + | 0.327409i | 0.328444 | + | 0.0184474i | ||||
\(316\) | 3.00194 | − | 5.19951i | 0.168872 | − | 0.292495i | ||||
\(317\) | 4.46606 | + | 7.73544i | 0.250839 | + | 0.434466i | 0.963757 | − | 0.266782i | \(-0.0859602\pi\) |
−0.712918 | + | 0.701247i | \(0.752627\pi\) | |||||||
\(318\) | −4.94074 | − | 8.55761i | −0.277063 | − | 0.479887i | ||||
\(319\) | −0.937343 | − | 1.62353i | −0.0524811 | − | 0.0909000i | ||||
\(320\) | 1.10337 | + | 1.91109i | 0.0616802 | + | 0.106833i | ||||
\(321\) | 7.05459 | − | 12.2189i | 0.393749 | − | 0.681993i | ||||
\(322\) | −16.4510 | − | 0.923992i | −0.916781 | − | 0.0514921i | ||||
\(323\) | 1.85480 | + | 3.21260i | 0.103204 | + | 0.178754i | ||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 0.398387 | − | 0.249020i | 0.0220985 | − | 0.0138131i | ||||
\(326\) | 3.03208 | − | 5.25172i | 0.167932 | − | 0.290866i | ||||
\(327\) | −0.723832 | + | 1.25371i | −0.0400280 | + | 0.0693306i | ||||
\(328\) | 1.63110 | + | 2.82515i | 0.0900626 | + | 0.155993i | ||||
\(329\) | 12.8211 | + | 0.720111i | 0.706849 | + | 0.0397010i | ||||
\(330\) | 2.32914 | 0.128215 | ||||||||
\(331\) | 4.32850 | 0.237916 | 0.118958 | − | 0.992899i | \(-0.462045\pi\) | ||||
0.118958 | + | 0.992899i | \(0.462045\pi\) | |||||||
\(332\) | 0.888084 | + | 1.53821i | 0.0487399 | + | 0.0844200i | ||||
\(333\) | −1.13110 | + | 1.95913i | −0.0619841 | + | 0.107360i | ||||
\(334\) | −15.7386 | −0.861178 | ||||||||
\(335\) | −12.9162 | − | 22.3715i | −0.705688 | − | 1.22229i | ||||
\(336\) | −1.19230 | − | 2.36187i | −0.0650455 | − | 0.128850i | ||||
\(337\) | −0.416096 | −0.0226662 | −0.0113331 | − | 0.999936i | \(-0.503608\pi\) | ||||
−0.0113331 | + | 0.999936i | \(0.503608\pi\) | |||||||
\(338\) | 12.9681 | − | 0.910576i | 0.705370 | − | 0.0495288i | ||||
\(339\) | 1.67707 | − | 2.90477i | 0.0910858 | − | 0.157765i | ||||
\(340\) | 2.08434 | 0.113039 | ||||||||
\(341\) | −3.83456 | + | 6.64164i | −0.207653 | + | 0.359665i | ||||
\(342\) | 1.96372 | − | 3.40126i | 0.106186 | − | 0.183919i | ||||
\(343\) | −18.2585 | − | 3.10266i | −0.985867 | − | 0.167528i | ||||
\(344\) | −0.537418 | + | 0.930835i | −0.0289756 | + | 0.0501872i | ||||
\(345\) | −13.7429 | −0.739894 | ||||||||
\(346\) | −5.29220 | + | 9.16635i | −0.284510 | + | 0.492786i | ||||
\(347\) | −10.8726 | − | 18.8319i | −0.583671 | − | 1.01095i | −0.995040 | − | 0.0994787i | \(-0.968282\pi\) |
0.411369 | − | 0.911469i | \(-0.365051\pi\) | |||||||
\(348\) | −0.888084 | + | 1.53821i | −0.0476063 | + | 0.0824565i | ||||
\(349\) | 15.8128 | + | 27.3885i | 0.846438 | + | 1.46607i | 0.884366 | + | 0.466794i | \(0.154591\pi\) |
−0.0379278 | + | 0.999280i | \(0.512076\pi\) | |||||||
\(350\) | −0.344205 | − | 0.0193327i | −0.0183985 | − | 0.00103338i | ||||
\(351\) | −3.18376 | − | 1.69224i | −0.169936 | − | 0.0903253i | ||||
\(352\) | −0.527733 | − | 0.914061i | −0.0281283 | − | 0.0487196i | ||||
\(353\) | 27.7887 | 1.47905 | 0.739523 | − | 0.673131i | \(-0.235051\pi\) | ||||
0.739523 | + | 0.673131i | \(0.235051\pi\) | |||||||
\(354\) | −1.01937 | −0.0541788 | ||||||||
\(355\) | −18.5749 | −0.985854 | ||||||||
\(356\) | 13.3353 | 0.706769 | ||||||||
\(357\) | −2.49507 | − | 0.140138i | −0.132053 | − | 0.00741691i | ||||
\(358\) | 7.11908 | − | 12.3306i | 0.376255 | − | 0.651693i | ||||
\(359\) | 4.17747 | + | 7.23559i | 0.220478 | + | 0.381880i | 0.954953 | − | 0.296756i | \(-0.0959048\pi\) |
−0.734475 | + | 0.678636i | \(0.762572\pi\) | |||||||
\(360\) | −1.10337 | − | 1.91109i | −0.0581527 | − | 0.100723i | ||||
\(361\) | −3.57522 | −0.188169 | ||||||||
\(362\) | −6.86558 | + | 11.8915i | −0.360847 | + | 0.625005i | ||||
\(363\) | 9.88599 | 0.518880 | ||||||||
\(364\) | −8.15910 | − | 4.94258i | −0.427653 | − | 0.259062i | ||||
\(365\) | 29.0082 | 1.51836 | ||||||||
\(366\) | −0.0382184 | + | 0.0661962i | −0.00199771 | + | 0.00346013i | ||||
\(367\) | −20.7810 | −1.08476 | −0.542379 | − | 0.840134i | \(-0.682476\pi\) | ||||
−0.542379 | + | 0.840134i | \(0.682476\pi\) | |||||||
\(368\) | 3.11385 | + | 5.39335i | 0.162321 | + | 0.281148i | ||||
\(369\) | −1.63110 | − | 2.82515i | −0.0849118 | − | 0.147072i | ||||
\(370\) | −2.49605 | + | 4.32328i | −0.129763 | + | 0.224757i | ||||
\(371\) | 11.7817 | + | 23.3387i | 0.611676 | + | 1.21169i | ||||
\(372\) | 7.26608 | 0.376729 | ||||||||
\(373\) | 15.4568 | 0.800323 | 0.400161 | − | 0.916445i | \(-0.368954\pi\) | ||||
0.400161 | + | 0.916445i | \(0.368954\pi\) | |||||||
\(374\) | −0.996923 | −0.0515497 | ||||||||
\(375\) | −11.3212 | −0.584626 | ||||||||
\(376\) | −2.42678 | − | 4.20330i | −0.125151 | − | 0.216769i | ||||
\(377\) | 0.224422 | + | 6.40013i | 0.0115583 | + | 0.329623i | ||||
\(378\) | 1.19230 | + | 2.36187i | 0.0613255 | + | 0.121481i | ||||
\(379\) | 12.1123 | + | 20.9792i | 0.622169 | + | 1.07763i | 0.989081 | + | 0.147372i | \(0.0470816\pi\) |
−0.366912 | + | 0.930256i | \(0.619585\pi\) | |||||||
\(380\) | 4.33342 | − | 7.50570i | 0.222300 | − | 0.385034i | ||||
\(381\) | 4.80963 | + | 8.33053i | 0.246405 | + | 0.426786i | ||||
\(382\) | 0.437999 | − | 0.758636i | 0.0224100 | − | 0.0388152i | ||||
\(383\) | 14.9993 | 0.766431 | 0.383215 | − | 0.923659i | \(-0.374817\pi\) | ||||
0.383215 | + | 0.923659i | \(0.374817\pi\) | |||||||
\(384\) | −0.500000 | + | 0.866025i | −0.0255155 | + | 0.0441942i | ||||
\(385\) | −6.15263 | − | 0.345570i | −0.313567 | − | 0.0176119i | ||||
\(386\) | −11.3312 | + | 19.6263i | −0.576745 | + | 0.998951i | ||||
\(387\) | 0.537418 | − | 0.930835i | 0.0273185 | − | 0.0473170i | ||||
\(388\) | 17.9893 | 0.913270 | ||||||||
\(389\) | 4.37986 | − | 7.58613i | 0.222068 | − | 0.384632i | −0.733368 | − | 0.679832i | \(-0.762053\pi\) |
0.955436 | + | 0.295200i | \(0.0953861\pi\) | |||||||
\(390\) | −7.02572 | − | 3.73434i | −0.355761 | − | 0.189096i | ||||
\(391\) | 5.88228 | 0.297480 | ||||||||
\(392\) | 2.79915 | + | 6.41598i | 0.141378 | + | 0.324056i | ||||
\(393\) | 3.27649 | + | 5.67504i | 0.165277 | + | 0.286268i | ||||
\(394\) | 16.8850 | 0.850653 | ||||||||
\(395\) | −6.62449 | + | 11.4740i | −0.333315 | + | 0.577318i | ||||
\(396\) | 0.527733 | + | 0.914061i | 0.0265196 | + | 0.0459333i | ||||
\(397\) | 34.8800 | 1.75058 | 0.875289 | − | 0.483601i | \(-0.160671\pi\) | ||||
0.875289 | + | 0.483601i | \(0.160671\pi\) | |||||||
\(398\) | 5.90084 | 0.295783 | ||||||||
\(399\) | −5.69198 | + | 8.69338i | −0.284955 | + | 0.435213i | ||||
\(400\) | 0.0651512 | + | 0.112845i | 0.00325756 | + | 0.00564226i | ||||
\(401\) | 6.47372 | − | 11.2128i | 0.323282 | − | 0.559941i | −0.657881 | − | 0.753122i | \(-0.728547\pi\) |
0.981163 | + | 0.193181i | \(0.0618803\pi\) | |||||||
\(402\) | 5.85308 | − | 10.1378i | 0.291925 | − | 0.505629i | ||||
\(403\) | 22.2154 | − | 13.8862i | 1.10663 | − | 0.691719i | ||||
\(404\) | −6.75018 | − | 11.6917i | −0.335834 | − | 0.581682i | ||||
\(405\) | 1.10337 | + | 1.91109i | 0.0548269 | + | 0.0949629i | ||||
\(406\) | 2.57417 | − | 3.93154i | 0.127754 | − | 0.195119i | ||||
\(407\) | 1.19384 | − | 2.06779i | 0.0591765 | − | 0.102497i | ||||
\(408\) | 0.472267 | + | 0.817990i | 0.0233807 | + | 0.0404965i | ||||
\(409\) | 17.0621 | + | 29.5524i | 0.843666 | + | 1.46127i | 0.886775 | + | 0.462201i | \(0.152940\pi\) |
−0.0431093 | + | 0.999070i | \(0.513726\pi\) | |||||||
\(410\) | −3.59942 | − | 6.23438i | −0.177763 | − | 0.307894i | ||||
\(411\) | 3.56234 | + | 6.17015i | 0.175717 | + | 0.304351i | ||||
\(412\) | 1.46258 | − | 2.53327i | 0.0720563 | − | 0.124805i | ||||
\(413\) | 2.69275 | + | 0.151242i | 0.132502 | + | 0.00744211i | ||||
\(414\) | −3.11385 | − | 5.39335i | −0.153038 | − | 0.265069i | ||||
\(415\) | −1.95977 | − | 3.39442i | −0.0962013 | − | 0.166626i | ||||
\(416\) | 0.126352 | + | 3.60334i | 0.00619490 | + | 0.176668i | ||||
\(417\) | 3.09957 | − | 5.36862i | 0.151787 | − | 0.262902i | ||||
\(418\) | −2.07264 | + | 3.58992i | −0.101376 | + | 0.175589i | ||||
\(419\) | 11.0690 | + | 19.1720i | 0.540754 | + | 0.936613i | 0.998861 | + | 0.0477160i | \(0.0151943\pi\) |
−0.458107 | + | 0.888897i | \(0.651472\pi\) | |||||||
\(420\) | 2.63110 | + | 5.21202i | 0.128385 | + | 0.254321i | ||||
\(421\) | −31.1012 | −1.51578 | −0.757890 | − | 0.652382i | \(-0.773770\pi\) | ||||
−0.757890 | + | 0.652382i | \(0.773770\pi\) | |||||||
\(422\) | −23.5712 | −1.14743 | ||||||||
\(423\) | 2.42678 | + | 4.20330i | 0.117994 | + | 0.204371i | ||||
\(424\) | 4.94074 | − | 8.55761i | 0.239943 | − | 0.415594i | ||||
\(425\) | 0.123075 | 0.00597001 | ||||||||
\(426\) | −4.20868 | − | 7.28964i | −0.203911 | − | 0.353184i | ||||
\(427\) | 0.110779 | − | 0.169193i | 0.00536095 | − | 0.00818781i | ||||
\(428\) | 14.1092 | 0.681993 | ||||||||
\(429\) | 3.36035 | + | 1.78611i | 0.162239 | + | 0.0862341i | ||||
\(430\) | 1.18594 | − | 2.05411i | 0.0571911 | − | 0.0990580i | ||||
\(431\) | 11.3146 | 0.545005 | 0.272502 | − | 0.962155i | \(-0.412149\pi\) | ||||
0.272502 | + | 0.962155i | \(0.412149\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | −19.0285 | + | 32.9583i | −0.914450 | + | 1.58387i | −0.106746 | + | 0.994286i | \(0.534043\pi\) |
−0.807704 | + | 0.589588i | \(0.799290\pi\) | |||||||
\(434\) | −19.1940 | − | 1.07805i | −0.921341 | − | 0.0517482i | ||||
\(435\) | 1.95977 | − | 3.39442i | 0.0939637 | − | 0.162750i | ||||
\(436\) | −1.44766 | −0.0693306 | ||||||||
\(437\) | 12.2295 | − | 21.1821i | 0.585015 | − | 1.01328i | ||||
\(438\) | 6.57264 | + | 11.3841i | 0.314053 | + | 0.543956i | ||||
\(439\) | 1.48304 | − | 2.56871i | 0.0707818 | − | 0.122598i | −0.828462 | − | 0.560045i | \(-0.810784\pi\) |
0.899244 | + | 0.437447i | \(0.144117\pi\) | |||||||
\(440\) | 1.16457 | + | 2.01709i | 0.0555187 | + | 0.0961612i | ||||
\(441\) | −2.79915 | − | 6.41598i | −0.133293 | − | 0.305523i | ||||
\(442\) | 3.00716 | + | 1.59838i | 0.143036 | + | 0.0760272i | ||||
\(443\) | −10.1253 | − | 17.5375i | −0.481067 | − | 0.833233i | 0.518697 | − | 0.854958i | \(-0.326417\pi\) |
−0.999764 | + | 0.0217253i | \(0.993084\pi\) | |||||||
\(444\) | −2.26221 | −0.107360 | ||||||||
\(445\) | −29.4275 | −1.39500 | ||||||||
\(446\) | −5.75811 | −0.272654 | ||||||||
\(447\) | 21.8748 | 1.03464 | ||||||||
\(448\) | 1.44928 | − | 2.21350i | 0.0684722 | − | 0.104578i | ||||
\(449\) | 5.97830 | − | 10.3547i | 0.282133 | − | 0.488669i | −0.689777 | − | 0.724022i | \(-0.742291\pi\) |
0.971910 | + | 0.235353i | \(0.0756246\pi\) | |||||||
\(450\) | −0.0651512 | − | 0.112845i | −0.00307126 | − | 0.00531957i | ||||
\(451\) | 1.72158 | + | 2.98186i | 0.0810658 | + | 0.140410i | ||||
\(452\) | 3.35413 | 0.157765 | ||||||||
\(453\) | −7.25658 | + | 12.5688i | −0.340944 | + | 0.590532i | ||||
\(454\) | −19.6805 | −0.923652 | ||||||||
\(455\) | 18.0050 | + | 10.9070i | 0.844088 | + | 0.511327i | ||||
\(456\) | 3.92744 | 0.183919 | ||||||||
\(457\) | −11.5421 | + | 19.9915i | −0.539916 | + | 0.935162i | 0.458992 | + | 0.888440i | \(0.348211\pi\) |
−0.998908 | + | 0.0467216i | \(0.985123\pi\) | |||||||
\(458\) | 20.0861 | 0.938561 | ||||||||
\(459\) | −0.472267 | − | 0.817990i | −0.0220435 | − | 0.0381805i | ||||
\(460\) | −6.87146 | − | 11.9017i | −0.320384 | − | 0.554921i | ||||
\(461\) | −9.46131 | + | 16.3875i | −0.440657 | + | 0.763240i | −0.997738 | − | 0.0672176i | \(-0.978588\pi\) |
0.557081 | + | 0.830458i | \(0.311921\pi\) | |||||||
\(462\) | −1.25844 | − | 2.49287i | −0.0585478 | − | 0.115979i | ||||
\(463\) | −32.7770 | −1.52328 | −0.761638 | − | 0.648002i | \(-0.775605\pi\) | ||||
−0.761638 | + | 0.648002i | \(0.775605\pi\) | |||||||
\(464\) | −1.77617 | −0.0824565 | ||||||||
\(465\) | −16.0343 | −0.743575 | ||||||||
\(466\) | −5.64521 | −0.261509 | ||||||||
\(467\) | −10.7307 | − | 18.5861i | −0.496557 | − | 0.860061i | 0.503436 | − | 0.864033i | \(-0.332069\pi\) |
−0.999992 | + | 0.00397163i | \(0.998736\pi\) | |||||||
\(468\) | −0.126352 | − | 3.60334i | −0.00584061 | − | 0.166564i | ||||
\(469\) | −16.9655 | + | 25.9116i | −0.783396 | + | 1.19648i | ||||
\(470\) | 5.35526 | + | 9.27559i | 0.247020 | + | 0.427851i | ||||
\(471\) | −2.13538 | + | 3.69859i | −0.0983931 | + | 0.170422i | ||||
\(472\) | −0.509684 | − | 0.882799i | −0.0234601 | − | 0.0406341i | ||||
\(473\) | −0.567227 | + | 0.982465i | −0.0260811 | + | 0.0451738i | ||||
\(474\) | −6.00388 | −0.275767 | ||||||||
\(475\) | 0.255877 | − | 0.443193i | 0.0117405 | − | 0.0203351i | ||||
\(476\) | −1.12617 | − | 2.23086i | −0.0516179 | − | 0.102251i | ||||
\(477\) | −4.94074 | + | 8.55761i | −0.226221 | + | 0.391826i | ||||
\(478\) | 4.10480 | − | 7.10972i | 0.187749 | − | 0.325191i | ||||
\(479\) | −31.8921 | −1.45719 | −0.728593 | − | 0.684947i | \(-0.759826\pi\) | ||||
−0.728593 | + | 0.684947i | \(0.759826\pi\) | |||||||
\(480\) | 1.10337 | − | 1.91109i | 0.0503617 | − | 0.0872290i | ||||
\(481\) | −6.91648 | + | 4.32328i | −0.315364 | + | 0.197125i | ||||
\(482\) | 21.0169 | 0.957293 | ||||||||
\(483\) | 7.42532 | + | 14.7090i | 0.337864 | + | 0.669283i | ||||
\(484\) | 4.94299 | + | 8.56152i | 0.224682 | + | 0.389160i | ||||
\(485\) | −39.6978 | −1.80258 | ||||||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | −0.372339 | − | 0.644911i | −0.0168723 | − | 0.0292237i | 0.857466 | − | 0.514541i | \(-0.172038\pi\) |
−0.874338 | + | 0.485317i | \(0.838704\pi\) | |||||||
\(488\) | −0.0764368 | −0.00346013 | ||||||||
\(489\) | −6.06417 | −0.274231 | ||||||||
\(490\) | −6.17699 | − | 14.1584i | −0.279048 | − | 0.639611i | ||||
\(491\) | −20.5033 | − | 35.5127i | −0.925301 | − | 1.60267i | −0.791077 | − | 0.611717i | \(-0.790479\pi\) |
−0.134224 | − | 0.990951i | \(-0.542854\pi\) | |||||||
\(492\) | 1.63110 | − | 2.82515i | 0.0735358 | − | 0.127368i | ||||
\(493\) | −0.838824 | + | 1.45289i | −0.0377788 | + | 0.0654347i | ||||
\(494\) | 12.0078 | − | 7.50570i | 0.540255 | − | 0.337697i | ||||
\(495\) | −1.16457 | − | 2.01709i | −0.0523435 | − | 0.0906617i | ||||
\(496\) | 3.63304 | + | 6.29261i | 0.163128 | + | 0.282547i | ||||
\(497\) | 10.0360 | + | 19.8807i | 0.450178 | + | 0.891770i | ||||
\(498\) | 0.888084 | − | 1.53821i | 0.0397960 | − | 0.0689287i | ||||
\(499\) | 5.61372 | + | 9.72324i | 0.251305 | + | 0.435272i | 0.963885 | − | 0.266318i | \(-0.0858071\pi\) |
−0.712581 | + | 0.701590i | \(0.752474\pi\) | |||||||
\(500\) | −5.66062 | − | 9.80448i | −0.253151 | − | 0.438470i | ||||
\(501\) | 7.86930 | + | 13.6300i | 0.351574 | + | 0.608944i | ||||
\(502\) | 12.0281 | + | 20.8333i | 0.536842 | + | 0.929837i | ||||
\(503\) | −19.4719 | + | 33.7264i | −0.868211 | + | 1.50379i | −0.00438828 | + | 0.999990i | \(0.501397\pi\) |
−0.863823 | + | 0.503796i | \(0.831936\pi\) | |||||||
\(504\) | −1.44928 | + | 2.21350i | −0.0645563 | + | 0.0985971i | ||||
\(505\) | 14.8959 | + | 25.8004i | 0.662859 | + | 1.14810i | ||||
\(506\) | 3.28657 | + | 5.69251i | 0.146106 | + | 0.253063i | ||||
\(507\) | −7.27262 | − | 10.7754i | −0.322988 | − | 0.478552i | ||||
\(508\) | −4.80963 | + | 8.33053i | −0.213393 | + | 0.369608i | ||||
\(509\) | 10.8076 | − | 18.7194i | 0.479039 | − | 0.829721i | −0.520672 | − | 0.853757i | \(-0.674318\pi\) |
0.999711 | + | 0.0240364i | \(0.00765175\pi\) | |||||||
\(510\) | −1.04217 | − | 1.80509i | −0.0461480 | − | 0.0799307i | ||||
\(511\) | −15.6732 | − | 31.0474i | −0.693340 | − | 1.37346i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −3.92744 | −0.173401 | ||||||||
\(514\) | −1.79955 | − | 3.11691i | −0.0793747 | − | 0.137481i | ||||
\(515\) | −3.22754 | + | 5.59026i | −0.142222 | + | 0.246336i | ||||
\(516\) | 1.07484 | 0.0473170 | ||||||||
\(517\) | −2.56138 | − | 4.43644i | −0.112649 | − | 0.195115i | ||||
\(518\) | 5.97582 | + | 0.335639i | 0.262562 | + | 0.0147471i | ||||
\(519\) | 10.5844 | 0.464603 | ||||||||
\(520\) | −0.278825 | − | 7.95162i | −0.0122273 | − | 0.348702i | ||||
\(521\) | 3.75964 | − | 6.51188i | 0.164713 | − | 0.285291i | −0.771840 | − | 0.635816i | \(-0.780664\pi\) |
0.936553 | + | 0.350525i | \(0.113997\pi\) | |||||||
\(522\) | 1.77617 | 0.0777407 | ||||||||
\(523\) | −16.8098 | + | 29.1154i | −0.735041 | + | 1.27313i | 0.219665 | + | 0.975575i | \(0.429504\pi\) |
−0.954705 | + | 0.297553i | \(0.903830\pi\) | |||||||
\(524\) | −3.27649 | + | 5.67504i | −0.143134 | + | 0.247915i | ||||
\(525\) | 0.155360 | + | 0.307757i | 0.00678047 | + | 0.0134316i | ||||
\(526\) | −15.1196 | + | 26.1880i | −0.659247 | + | 1.14185i | ||||
\(527\) | 6.86306 | 0.298959 | ||||||||
\(528\) | −0.527733 | + | 0.914061i | −0.0229667 | + | 0.0397794i | ||||
\(529\) | −7.89218 | − | 13.6697i | −0.343138 | − | 0.594333i | ||||
\(530\) | −10.9029 | + | 18.8844i | −0.473593 | + | 0.820286i | ||||
\(531\) | 0.509684 | + | 0.882799i | 0.0221184 | + | 0.0383102i | ||||
\(532\) | −10.3747 | − | 0.582706i | −0.449799 | − | 0.0252635i | ||||
\(533\) | −0.412185 | − | 11.7548i | −0.0178537 | − | 0.509158i | ||||
\(534\) | −6.66765 | − | 11.5487i | −0.288537 | − | 0.499761i | ||||
\(535\) | −31.1353 | −1.34610 | ||||||||
\(536\) | 11.7062 | 0.505629 | ||||||||
\(537\) | −14.2382 | −0.614422 | ||||||||
\(538\) | −10.4393 | −0.450069 | ||||||||
\(539\) | 2.95441 | + | 6.77185i | 0.127255 | + | 0.291684i | ||||
\(540\) | −1.10337 | + | 1.91109i | −0.0474815 | + | 0.0822403i | ||||
\(541\) | 3.62006 | + | 6.27013i | 0.155639 | + | 0.269574i | 0.933291 | − | 0.359120i | \(-0.116923\pi\) |
−0.777653 | + | 0.628694i | \(0.783590\pi\) | |||||||
\(542\) | −5.33456 | − | 9.23972i | −0.229139 | − | 0.396880i | ||||
\(543\) | 13.7312 | 0.589260 | ||||||||
\(544\) | −0.472267 | + | 0.817990i | −0.0202483 | + | 0.0350710i | ||||
\(545\) | 3.19462 | 0.136842 | ||||||||
\(546\) | −0.200850 | + | 9.53728i | −0.00859560 | + | 0.408158i | ||||
\(547\) | 13.7236 | 0.586779 | 0.293390 | − | 0.955993i | \(-0.405217\pi\) | ||||
0.293390 | + | 0.955993i | \(0.405217\pi\) | |||||||
\(548\) | −3.56234 | + | 6.17015i | −0.152176 | + | 0.263576i | ||||
\(549\) | 0.0764368 | 0.00326224 | ||||||||
\(550\) | 0.0687649 | + | 0.119104i | 0.00293215 | + | 0.00507863i | ||||
\(551\) | 3.48790 | + | 6.04121i | 0.148589 | + | 0.257364i | ||||
\(552\) | 3.11385 | − | 5.39335i | 0.132534 | − | 0.229556i | ||||
\(553\) | 15.8598 | + | 0.890783i | 0.674426 | + | 0.0378799i | ||||
\(554\) | −19.0706 | −0.810232 | ||||||||
\(555\) | 4.99210 | 0.211903 | ||||||||
\(556\) | 6.19915 | 0.262902 | ||||||||
\(557\) | −23.2244 | −0.984048 | −0.492024 | − | 0.870582i | \(-0.663743\pi\) | ||||
−0.492024 | + | 0.870582i | \(0.663743\pi\) | |||||||
\(558\) | −3.63304 | − | 6.29261i | −0.153799 | − | 0.266388i | ||||
\(559\) | 3.28621 | − | 2.05411i | 0.138992 | − | 0.0868796i | ||||
\(560\) | −3.19819 | + | 4.88461i | −0.135148 | + | 0.206413i | ||||
\(561\) | 0.498462 | + | 0.863361i | 0.0210451 | + | 0.0364511i | ||||
\(562\) | 11.6655 | − | 20.2052i | 0.492077 | − | 0.852303i | ||||
\(563\) | 7.80616 | + | 13.5207i | 0.328990 | + | 0.569828i | 0.982312 | − | 0.187253i | \(-0.0599583\pi\) |
−0.653321 | + | 0.757081i | \(0.726625\pi\) | |||||||
\(564\) | −2.42678 | + | 4.20330i | −0.102186 | + | 0.176991i | ||||
\(565\) | −7.40170 | −0.311392 | ||||||||
\(566\) | 4.11466 | − | 7.12679i | 0.172952 | − | 0.299561i | ||||
\(567\) | 1.44928 | − | 2.21350i | 0.0608642 | − | 0.0929582i | ||||
\(568\) | 4.20868 | − | 7.28964i | 0.176592 | − | 0.305867i | ||||
\(569\) | 6.65159 | − | 11.5209i | 0.278849 | − | 0.482981i | −0.692250 | − | 0.721658i | \(-0.743380\pi\) |
0.971099 | + | 0.238677i | \(0.0767137\pi\) | |||||||
\(570\) | −8.66684 | −0.363014 | ||||||||
\(571\) | 15.4972 | − | 26.8420i | 0.648539 | − | 1.12330i | −0.334933 | − | 0.942242i | \(-0.608714\pi\) |
0.983472 | − | 0.181061i | \(-0.0579530\pi\) | |||||||
\(572\) | 0.133360 | + | 3.80320i | 0.00557607 | + | 0.159020i | ||||
\(573\) | −0.875997 | −0.0365953 | ||||||||
\(574\) | −4.72786 | + | 7.22089i | −0.197337 | + | 0.301394i | ||||
\(575\) | −0.405743 | − | 0.702767i | −0.0169206 | − | 0.0293074i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −22.8416 | + | 39.5629i | −0.950910 | + | 1.64702i | −0.207449 | + | 0.978246i | \(0.566516\pi\) |
−0.743462 | + | 0.668779i | \(0.766817\pi\) | |||||||
\(578\) | −8.05393 | − | 13.9498i | −0.334999 | − | 0.580236i | ||||
\(579\) | 22.6625 | 0.941820 | ||||||||
\(580\) | 3.91954 | 0.162750 | ||||||||
\(581\) | −2.57417 | + | 3.93154i | −0.106795 | + | 0.163108i | ||||
\(582\) | −8.99467 | − | 15.5792i | −0.372841 | − | 0.645779i | ||||
\(583\) | 5.21479 | − | 9.03227i | 0.215974 | − | 0.374079i | ||||
\(584\) | −6.57264 | + | 11.3841i | −0.271978 | + | 0.471079i | ||||
\(585\) | 0.278825 | + | 7.95162i | 0.0115280 | + | 0.328759i | ||||
\(586\) | −9.34471 | − | 16.1855i | −0.386027 | − | 0.668618i | ||||
\(587\) | −1.75183 | − | 3.03426i | −0.0723057 | − | 0.125237i | 0.827606 | − | 0.561310i | \(-0.189702\pi\) |
−0.899911 | + | 0.436073i | \(0.856369\pi\) | |||||||
\(588\) | 4.15682 | − | 5.63212i | 0.171425 | − | 0.232265i | ||||
\(589\) | 14.2686 | − | 24.7139i | 0.587925 | − | 1.01832i | ||||
\(590\) | 1.12474 | + | 1.94811i | 0.0463048 | + | 0.0802023i | ||||
\(591\) | −8.44249 | − | 14.6228i | −0.347277 | − | 0.601502i | ||||
\(592\) | −1.13110 | − | 1.95913i | −0.0464880 | − | 0.0805197i | ||||
\(593\) | −6.29875 | − | 10.9098i | −0.258659 | − | 0.448010i | 0.707224 | − | 0.706989i | \(-0.249947\pi\) |
−0.965883 | + | 0.258979i | \(0.916614\pi\) | |||||||
\(594\) | 0.527733 | − | 0.914061i | 0.0216532 | − | 0.0375044i | ||||
\(595\) | 2.48516 | + | 4.92293i | 0.101882 | + | 0.201820i | ||||
\(596\) | 10.9374 | + | 18.9442i | 0.448014 | + | 0.775983i | ||||
\(597\) | −2.95042 | − | 5.11028i | −0.120753 | − | 0.209150i | ||||
\(598\) | −0.786882 | − | 22.4405i | −0.0321780 | − | 0.917662i | ||||
\(599\) | −15.2844 | + | 26.4733i | −0.624503 | + | 1.08167i | 0.364134 | + | 0.931347i | \(0.381365\pi\) |
−0.988637 | + | 0.150324i | \(0.951968\pi\) | |||||||
\(600\) | 0.0651512 | − | 0.112845i | 0.00265979 | − | 0.00460688i | ||||
\(601\) | 7.11682 | + | 12.3267i | 0.290301 | + | 0.502817i | 0.973881 | − | 0.227059i | \(-0.0729112\pi\) |
−0.683580 | + | 0.729876i | \(0.739578\pi\) | |||||||
\(602\) | −2.83927 | − | 0.159471i | −0.115720 | − | 0.00649956i | ||||
\(603\) | −11.7062 | −0.476712 | ||||||||
\(604\) | −14.5132 | −0.590532 | ||||||||
\(605\) | −10.9079 | − | 18.8930i | −0.443469 | − | 0.768111i | ||||
\(606\) | −6.75018 | + | 11.6917i | −0.274207 | + | 0.474941i | ||||
\(607\) | 2.41963 | 0.0982098 | 0.0491049 | − | 0.998794i | \(-0.484363\pi\) | ||||
0.0491049 | + | 0.998794i | \(0.484363\pi\) | |||||||
\(608\) | 1.96372 | + | 3.40126i | 0.0796394 | + | 0.137939i | ||||
\(609\) | −4.69190 | − | 0.263526i | −0.190125 | − | 0.0106786i | ||||
\(610\) | 0.168676 | 0.00682949 | ||||||||
\(611\) | 0.613255 | + | 17.4890i | 0.0248096 | + | 0.707529i | ||||
\(612\) | 0.472267 | − | 0.817990i | 0.0190902 | − | 0.0330653i | ||||
\(613\) | 0.538956 | 0.0217682 | 0.0108841 | − | 0.999941i | \(-0.496535\pi\) | ||||
0.0108841 | + | 0.999941i | \(0.496535\pi\) | |||||||
\(614\) | 9.02474 | − | 15.6313i | 0.364209 | − | 0.630828i | ||||
\(615\) | −3.59942 | + | 6.23438i | −0.145143 | + | 0.251394i | ||||
\(616\) | 1.52967 | − | 2.33627i | 0.0616322 | − | 0.0941312i | ||||
\(617\) | 22.1866 | − | 38.4283i | 0.893198 | − | 1.54706i | 0.0571781 | − | 0.998364i | \(-0.481790\pi\) |
0.836020 | − | 0.548700i | \(-0.184877\pi\) | |||||||
\(618\) | −2.92516 | −0.117667 | ||||||||
\(619\) | 9.10976 | − | 15.7786i | 0.366152 | − | 0.634194i | −0.622808 | − | 0.782375i | \(-0.714008\pi\) |
0.988960 | + | 0.148180i | \(0.0473416\pi\) | |||||||
\(620\) | −8.01717 | − | 13.8862i | −0.321977 | − | 0.557681i | ||||
\(621\) | −3.11385 | + | 5.39335i | −0.124955 | + | 0.216428i | ||||
\(622\) | 8.46321 | + | 14.6587i | 0.339344 | + | 0.587761i | ||||
\(623\) | 15.8997 | + | 31.4962i | 0.637009 | + | 1.26187i | ||||
\(624\) | 3.05741 | − | 1.91109i | 0.122394 | − | 0.0765049i | ||||
\(625\) | 12.1658 | + | 21.0717i | 0.486630 | + | 0.842868i | ||||
\(626\) | −22.0071 | −0.879581 | ||||||||
\(627\) | 4.14528 | 0.165547 | ||||||||
\(628\) | −4.27076 | −0.170422 | ||||||||
\(629\) | −2.13673 | −0.0851969 | ||||||||
\(630\) | 3.19819 | − | 4.88461i | 0.127419 | − | 0.194608i | ||||
\(631\) | −1.76140 | + | 3.05083i | −0.0701200 | + | 0.121451i | −0.898954 | − | 0.438044i | \(-0.855672\pi\) |
0.828834 | + | 0.559495i | \(0.189005\pi\) | |||||||
\(632\) | −3.00194 | − | 5.19951i | −0.119411 | − | 0.206825i | ||||
\(633\) | 11.7856 | + | 20.4132i | 0.468435 | + | 0.811353i | ||||
\(634\) | 8.93212 | 0.354740 | ||||||||
\(635\) | 10.6136 | − | 18.3833i | 0.421188 | − | 0.729519i | ||||
\(636\) | −9.88148 | −0.391826 | ||||||||
\(637\) | 1.94559 | − | 25.1638i | 0.0770871 | − | 0.997024i | ||||
\(638\) | −1.87469 | −0.0742195 | ||||||||
\(639\) | −4.20868 | + | 7.28964i | −0.166493 | + | 0.288374i | ||||
\(640\) | 2.20674 | 0.0872290 | ||||||||
\(641\) | 13.6088 | + | 23.5711i | 0.537515 | + | 0.931003i | 0.999037 | + | 0.0438742i | \(0.0139701\pi\) |
−0.461522 | + | 0.887129i | \(0.652697\pi\) | |||||||
\(642\) | −7.05459 | − | 12.2189i | −0.278423 | − | 0.482242i | ||||
\(643\) | −20.1450 | + | 34.8922i | −0.794442 | + | 1.37601i | 0.128750 | + | 0.991677i | \(0.458903\pi\) |
−0.923193 | + | 0.384338i | \(0.874430\pi\) | |||||||
\(644\) | −9.02572 | + | 13.7850i | −0.355663 | + | 0.543206i | ||||
\(645\) | −2.37188 | −0.0933927 | ||||||||
\(646\) | 3.70960 | 0.145952 | ||||||||
\(647\) | −31.1858 | −1.22604 | −0.613020 | − | 0.790068i | \(-0.710045\pi\) | ||||
−0.613020 | + | 0.790068i | \(0.710045\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −0.537955 | − | 0.931765i | −0.0211166 | − | 0.0365750i | ||||
\(650\) | −0.0164639 | − | 0.469523i | −0.000645768 | − | 0.0184162i | ||||
\(651\) | 8.66338 | + | 17.1615i | 0.339544 | + | 0.672613i | ||||
\(652\) | −3.03208 | − | 5.25172i | −0.118746 | − | 0.205673i | ||||
\(653\) | −0.232998 | + | 0.403565i | −0.00911792 | + | 0.0157927i | −0.870548 | − | 0.492083i | \(-0.836236\pi\) |
0.861430 | + | 0.507876i | \(0.169569\pi\) | |||||||
\(654\) | 0.723832 | + | 1.25371i | 0.0283041 | + | 0.0490241i | ||||
\(655\) | 7.23035 | − | 12.5233i | 0.282513 | − | 0.489327i | ||||
\(656\) | 3.26221 | 0.127368 | ||||||||
\(657\) | 6.57264 | − | 11.3841i | 0.256423 | − | 0.444138i | ||||
\(658\) | 7.03418 | − | 10.7433i | 0.274221 | − | 0.418819i | ||||
\(659\) | −22.1490 | + | 38.3632i | −0.862803 | + | 1.49442i | 0.00640903 | + | 0.999979i | \(0.497960\pi\) |
−0.869212 | + | 0.494439i | \(0.835373\pi\) | |||||||
\(660\) | 1.16457 | − | 2.01709i | 0.0453308 | − | 0.0785153i | ||||
\(661\) | 31.9836 | 1.24402 | 0.622008 | − | 0.783011i | \(-0.286317\pi\) | ||||
0.622008 | + | 0.783011i | \(0.286317\pi\) | |||||||
\(662\) | 2.16425 | − | 3.74859i | 0.0841160 | − | 0.145693i | ||||
\(663\) | −0.119343 | − | 3.40347i | −0.00463491 | − | 0.132180i | ||||
\(664\) | 1.77617 | 0.0689287 | ||||||||
\(665\) | 22.8942 | + | 1.28588i | 0.887799 | + | 0.0498643i | ||||
\(666\) | 1.13110 | + | 1.95913i | 0.0438294 | + | 0.0759147i | ||||
\(667\) | 11.0615 | 0.428301 | ||||||||
\(668\) | −7.86930 | + | 13.6300i | −0.304472 | + | 0.527361i | ||||
\(669\) | 2.87906 | + | 4.98667i | 0.111311 | + | 0.192796i | ||||
\(670\) | −25.8324 | −0.997994 | ||||||||
\(671\) | −0.0806765 | −0.00311448 | ||||||||
\(672\) | −2.64159 | − | 0.148368i | −0.101901 | − | 0.00572342i | ||||
\(673\) | 2.49379 | + | 4.31938i | 0.0961286 | + | 0.166500i | 0.910079 | − | 0.414435i | \(-0.136021\pi\) |
−0.813950 | + | 0.580934i | \(0.802687\pi\) | |||||||
\(674\) | −0.208048 | + | 0.360350i | −0.00801371 | + | 0.0138802i | ||||
\(675\) | −0.0651512 | + | 0.112845i | −0.00250767 | + | 0.00434341i | ||||
\(676\) | 5.69545 | − | 11.6860i | 0.219056 | − | 0.449460i | ||||
\(677\) | −17.6543 | − | 30.5782i | −0.678511 | − | 1.17522i | −0.975429 | − | 0.220312i | \(-0.929292\pi\) |
0.296919 | − | 0.954903i | \(-0.404041\pi\) | |||||||
\(678\) | −1.67707 | − | 2.90477i | −0.0644074 | − | 0.111557i | ||||
\(679\) | 21.4487 | + | 42.4884i | 0.823127 | + | 1.63056i | ||||
\(680\) | 1.04217 | − | 1.80509i | 0.0399654 | − | 0.0692220i | ||||
\(681\) | 9.84025 | + | 17.0438i | 0.377079 | + | 0.653121i | ||||
\(682\) | 3.83456 | + | 6.64164i | 0.146833 | + | 0.254322i | ||||
\(683\) | 17.8038 | + | 30.8371i | 0.681243 | + | 1.17995i | 0.974602 | + | 0.223945i | \(0.0718937\pi\) |
−0.293359 | + | 0.956003i | \(0.594773\pi\) | |||||||
\(684\) | −1.96372 | − | 3.40126i | −0.0750847 | − | 0.130051i | ||||
\(685\) | 7.86115 | − | 13.6159i | 0.300359 | − | 0.520237i | ||||
\(686\) | −11.8162 | + | 14.2610i | −0.451146 | + | 0.544488i | ||||
\(687\) | −10.0430 | − | 17.3951i | −0.383166 | − | 0.663663i | ||||
\(688\) | 0.537418 | + | 0.930835i | 0.0204889 | + | 0.0354877i | ||||
\(689\) | −30.2117 | + | 18.8844i | −1.15097 | + | 0.719439i | ||||
\(690\) | −6.87146 | + | 11.9017i | −0.261592 | + | 0.453091i | ||||
\(691\) | 8.50855 | − | 14.7372i | 0.323680 | − | 0.560631i | −0.657564 | − | 0.753399i | \(-0.728413\pi\) |
0.981244 | + | 0.192768i | \(0.0617464\pi\) | |||||||
\(692\) | 5.29220 | + | 9.16635i | 0.201179 | + | 0.348452i | ||||
\(693\) | −1.52967 | + | 2.33627i | −0.0581074 | + | 0.0887477i | ||||
\(694\) | −21.7452 | −0.825435 | ||||||||
\(695\) | −13.6799 | −0.518908 | ||||||||
\(696\) | 0.888084 | + | 1.53821i | 0.0336627 | + | 0.0583056i | ||||
\(697\) | 1.54063 | − | 2.66845i | 0.0583555 | − | 0.101075i | ||||
\(698\) | 31.6255 | 1.19704 | ||||||||
\(699\) | 2.82261 | + | 4.88890i | 0.106761 | + | 0.184915i | ||||
\(700\) | −0.188845 | + | 0.288424i | −0.00713768 | + | 0.0109014i | ||||
\(701\) | −24.2469 | −0.915792 | −0.457896 | − | 0.889006i | \(-0.651397\pi\) | ||||
−0.457896 | + | 0.889006i | \(0.651397\pi\) | |||||||
\(702\) | −3.05741 | + | 1.91109i | −0.115394 | + | 0.0721295i | ||||
\(703\) | −4.44234 | + | 7.69436i | −0.167546 | + | 0.290198i | ||||
\(704\) | −1.05547 | −0.0397794 | ||||||||
\(705\) | 5.35526 | − | 9.27559i | 0.201691 | − | 0.349339i | ||||
\(706\) | 13.8944 | − | 24.0658i | 0.522922 | − | 0.905727i | ||||
\(707\) | 19.5659 | − | 29.8830i | 0.735850 | − | 1.12387i | ||||
\(708\) | −0.509684 | + | 0.882799i | −0.0191551 | + | 0.0331776i | ||||
\(709\) | 6.27866 | 0.235800 | 0.117900 | − | 0.993025i | \(-0.462384\pi\) | ||||
0.117900 | + | 0.993025i | \(0.462384\pi\) | |||||||
\(710\) | −9.28745 | + | 16.0863i | −0.348552 | + | 0.603710i | ||||
\(711\) | 3.00194 | + | 5.19951i | 0.112581 | + | 0.194997i | ||||
\(712\) | 6.66765 | − | 11.5487i | 0.249881 | − | 0.432806i | ||||
\(713\) | −22.6255 | − | 39.1886i | −0.847333 | − | 1.46762i | ||||
\(714\) | −1.36890 | + | 2.09072i | −0.0512297 | + | 0.0782433i | ||||
\(715\) | −0.294291 | − | 8.39268i | −0.0110059 | − | 0.313868i | ||||
\(716\) | −7.11908 | − | 12.3306i | −0.266053 | − | 0.460816i | ||||
\(717\) | −8.20960 | −0.306593 | ||||||||
\(718\) | 8.35493 | 0.311803 | ||||||||
\(719\) | −19.9288 | −0.743218 | −0.371609 | − | 0.928389i | \(-0.621194\pi\) | ||||
−0.371609 | + | 0.928389i | \(0.621194\pi\) | |||||||
\(720\) | −2.20674 | −0.0822403 | ||||||||
\(721\) | 7.72708 | + | 0.434001i | 0.287771 | + | 0.0161630i | ||||
\(722\) | −1.78761 | + | 3.09623i | −0.0665279 | + | 0.115230i | ||||
\(723\) | −10.5084 | − | 18.2011i | −0.390813 | − | 0.676908i | ||||
\(724\) | 6.86558 | + | 11.8915i | 0.255157 | + | 0.441945i | ||||
\(725\) | 0.231439 | 0.00859542 | ||||||||
\(726\) | 4.94299 | − | 8.56152i | 0.183452 | − | 0.317748i | ||||
\(727\) | 10.1916 | 0.377984 | 0.188992 | − | 0.981979i | \(-0.439478\pi\) | ||||
0.188992 | + | 0.981979i | \(0.439478\pi\) | |||||||
\(728\) | −8.35995 | + | 4.59470i | −0.309840 | + | 0.170291i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 14.5041 | − | 25.1218i | 0.536821 | − | 0.929801i | ||||
\(731\) | 1.01522 | 0.0375492 | ||||||||
\(732\) | 0.0382184 | + | 0.0661962i | 0.00141259 | + | 0.00244668i | ||||
\(733\) | 14.7321 | + | 25.5168i | 0.544144 | + | 0.942485i | 0.998660 | + | 0.0517467i | \(0.0164788\pi\) |
−0.454516 | + | 0.890738i | \(0.650188\pi\) | |||||||
\(734\) | −10.3905 | + | 17.9969i | −0.383520 | + | 0.664276i | ||||
\(735\) | −9.17303 | + | 12.4286i | −0.338352 | + | 0.458437i | ||||
\(736\) | 6.22771 | 0.229556 | ||||||||
\(737\) | 12.3555 | 0.455119 | ||||||||
\(738\) | −3.26221 | −0.120083 | ||||||||
\(739\) | 32.6951 | 1.20271 | 0.601354 | − | 0.798983i | \(-0.294628\pi\) | ||||
0.601354 | + | 0.798983i | \(0.294628\pi\) | |||||||
\(740\) | 2.49605 | + | 4.32328i | 0.0917566 | + | 0.158927i | ||||
\(741\) | −12.5040 | − | 6.64619i | −0.459346 | − | 0.244154i | ||||
\(742\) | 26.1028 | + | 1.46609i | 0.958263 | + | 0.0538220i | ||||
\(743\) | −10.7085 | − | 18.5477i | −0.392857 | − | 0.680448i | 0.599968 | − | 0.800024i | \(-0.295180\pi\) |
−0.992825 | + | 0.119576i | \(0.961846\pi\) | |||||||
\(744\) | 3.63304 | − | 6.29261i | 0.133194 | − | 0.230698i | ||||
\(745\) | −24.1360 | − | 41.8048i | −0.884276 | − | 1.53161i | ||||
\(746\) | 7.72840 | − | 13.3860i | 0.282957 | − | 0.490096i | ||||
\(747\) | −1.77617 | −0.0649866 | ||||||||
\(748\) | −0.498462 | + | 0.863361i | −0.0182256 | + | 0.0315676i | ||||
\(749\) | 16.8224 | + | 33.3240i | 0.614678 | + | 1.21763i | ||||
\(750\) | −5.66062 | + | 9.80448i | −0.206697 | + | 0.358009i | ||||
\(751\) | 15.7078 | − | 27.2067i | 0.573185 | − | 0.992785i | −0.423051 | − | 0.906106i | \(-0.639041\pi\) |
0.996236 | − | 0.0866797i | \(-0.0276257\pi\) | |||||||
\(752\) | −4.85355 | −0.176991 | ||||||||
\(753\) | 12.0281 | − | 20.8333i | 0.438330 | − | 0.759209i | ||||
\(754\) | 5.65489 | + | 3.00571i | 0.205939 | + | 0.109461i | ||||
\(755\) | 32.0268 | 1.16557 | ||||||||
\(756\) | 2.64159 | + | 0.148368i | 0.0960736 | + | 0.00539609i | ||||
\(757\) | −9.28891 | − | 16.0889i | −0.337611 | − | 0.584760i | 0.646372 | − | 0.763023i | \(-0.276286\pi\) |
−0.983983 | + | 0.178263i | \(0.942952\pi\) | |||||||
\(758\) | 24.2247 | 0.879880 | ||||||||
\(759\) | 3.28657 | − | 5.69251i | 0.119295 | − | 0.206625i | ||||
\(760\) | −4.33342 | − | 7.50570i | −0.157190 | − | 0.272260i | ||||
\(761\) | 25.8283 | 0.936275 | 0.468137 | − | 0.883656i | \(-0.344925\pi\) | ||||
0.468137 | + | 0.883656i | \(0.344925\pi\) | |||||||
\(762\) | 9.61927 | 0.348469 | ||||||||
\(763\) | −1.72606 | − | 3.41919i | −0.0624874 | − | 0.123783i | ||||
\(764\) | −0.437999 | − | 0.758636i | −0.0158462 | − | 0.0274465i | ||||
\(765\) | −1.04217 | + | 1.80509i | −0.0376797 | + | 0.0652632i | ||||
\(766\) | 7.49967 | − | 12.9898i | 0.270974 | − | 0.469341i | ||||
\(767\) | 0.128799 | + | 3.67313i | 0.00465066 | + | 0.132629i | ||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | −9.92009 | − | 17.1821i | −0.357727 | − | 0.619602i | 0.629853 | − | 0.776714i | \(-0.283115\pi\) |
−0.987581 | + | 0.157112i | \(0.949782\pi\) | |||||||
\(770\) | −3.37559 | + | 5.15555i | −0.121648 | + | 0.185793i | ||||
\(771\) | −1.79955 | + | 3.11691i | −0.0648092 | + | 0.112253i | ||||
\(772\) | 11.3312 | + | 19.6263i | 0.407820 | + | 0.706365i | ||||
\(773\) | −21.5162 | − | 37.2672i | −0.773885 | − | 1.34041i | −0.935419 | − | 0.353541i | \(-0.884978\pi\) |
0.161534 | − | 0.986867i | \(-0.448356\pi\) | |||||||
\(774\) | −0.537418 | − | 0.930835i | −0.0193171 | − | 0.0334582i | ||||
\(775\) | −0.473394 | − | 0.819942i | −0.0170048 | − | 0.0294532i | ||||
\(776\) | 8.99467 | − | 15.5792i | 0.322890 | − | 0.559261i | ||||
\(777\) | −2.69724 | − | 5.34303i | −0.0967628 | − | 0.191680i | ||||
\(778\) | −4.37986 | − | 7.58613i | −0.157025 | − | 0.271976i | ||||
\(779\) | −6.40606 | − | 11.0956i | −0.229521 | − | 0.397542i | ||||
\(780\) | −6.74690 | + | 4.21728i | −0.241578 | + | 0.151003i | ||||
\(781\) | 4.44212 | − | 7.69398i | 0.158952 | − | 0.275312i | ||||
\(782\) | 2.94114 | − | 5.09420i | 0.105175 | − | 0.182168i | ||||
\(783\) | −0.888084 | − | 1.53821i | −0.0317375 | − | 0.0549710i | ||||
\(784\) | 6.95597 | + | 0.783854i | 0.248428 | + | 0.0279948i | ||||
\(785\) | 9.42445 | 0.336373 | ||||||||
\(786\) | 6.55297 | 0.233737 | ||||||||
\(787\) | 4.64127 | + | 8.03891i | 0.165443 | + | 0.286556i | 0.936813 | − | 0.349831i | \(-0.113761\pi\) |
−0.771369 | + | 0.636388i | \(0.780428\pi\) | |||||||
\(788\) | 8.44249 | − | 14.6228i | 0.300751 | − | 0.520916i | ||||
\(789\) | 30.2393 | 1.07655 | ||||||||
\(790\) | 6.62449 | + | 11.4740i | 0.235689 | + | 0.408225i | ||||
\(791\) | 3.99915 | + | 7.92202i | 0.142193 | + | 0.281675i | ||||
\(792\) | 1.05547 | 0.0375044 | ||||||||
\(793\) | 0.243356 | + | 0.129350i | 0.00864183 | + | 0.00459334i | ||||
\(794\) | 17.4400 | − | 30.2070i | 0.618922 | − | 1.07201i | ||||
\(795\) | 21.8058 | 0.773373 | ||||||||
\(796\) | 2.95042 | − | 5.11028i | 0.104575 | − | 0.181129i | ||||
\(797\) | 19.2169 | − | 33.2847i | 0.680698 | − | 1.17900i | −0.294071 | − | 0.955784i | \(-0.595010\pi\) |
0.974768 | − | 0.223219i | \(-0.0716566\pi\) | |||||||
\(798\) | 4.68270 | + | 9.27609i | 0.165766 | + | 0.328370i | ||||
\(799\) | −2.29217 | + | 3.97016i | −0.0810912 | + | 0.140454i | ||||
\(800\) | 0.130302 | 0.00460688 | ||||||||
\(801\) | −6.66765 | + | 11.5487i | −0.235590 | + | 0.408053i | ||||
\(802\) | −6.47372 | − | 11.2128i | −0.228595 | − | 0.395938i | ||||
\(803\) | −6.93721 | + | 12.0156i | −0.244809 | + | 0.424021i | ||||
\(804\) | −5.85308 | − | 10.1378i | −0.206422 | − | 0.357534i | ||||
\(805\) | 19.9174 | − | 30.4200i | 0.701997 | − | 1.07216i | ||||
\(806\) | −0.918082 | − | 26.1821i | −0.0323381 | − | 0.922227i | ||||
\(807\) | 5.21964 | + | 9.04068i | 0.183740 | + | 0.318247i | ||||
\(808\) | −13.5004 | −0.474941 | ||||||||
\(809\) | 31.4702 | 1.10643 | 0.553217 | − | 0.833037i | \(-0.313400\pi\) | ||||
0.553217 | + | 0.833037i | \(0.313400\pi\) | |||||||
\(810\) | 2.20674 | 0.0775369 | ||||||||
\(811\) | 50.9386 | 1.78870 | 0.894348 | − | 0.447373i | \(-0.147640\pi\) | ||||
0.894348 | + | 0.447373i | \(0.147640\pi\) | |||||||
\(812\) | −2.11773 | − | 4.19507i | −0.0743178 | − | 0.147218i | ||||
\(813\) | −5.33456 | + | 9.23972i | −0.187091 | + | 0.324051i | ||||
\(814\) | −1.19384 | − | 2.06779i | −0.0418441 | − | 0.0724762i | ||||
\(815\) | 6.69102 | + | 11.5892i | 0.234376 | + | 0.405951i | ||||
\(816\) | 0.944533 | 0.0330653 | ||||||||
\(817\) | 2.11068 | − | 3.65580i | 0.0738432 | − | 0.127900i | ||||
\(818\) | 34.1242 | 1.19312 | ||||||||
\(819\) | 8.35995 | − | 4.59470i | 0.292120 | − | 0.160552i | ||||
\(820\) | −7.19884 | −0.251394 | ||||||||
\(821\) | −20.1627 | + | 34.9228i | −0.703682 | + | 1.21881i | 0.263483 | + | 0.964664i | \(0.415129\pi\) |
−0.967165 | + | 0.254149i | \(0.918204\pi\) | |||||||
\(822\) | 7.12468 | 0.248502 | ||||||||
\(823\) | −10.7358 | − | 18.5949i | −0.374225 | − | 0.648177i | 0.615986 | − | 0.787757i | \(-0.288758\pi\) |
−0.990211 | + | 0.139581i | \(0.955425\pi\) | |||||||
\(824\) | −1.46258 | − | 2.53327i | −0.0509515 | − | 0.0882505i | ||||
\(825\) | 0.0687649 | − | 0.119104i | 0.00239409 | − | 0.00414668i | ||||
\(826\) | 1.47735 | − | 2.25637i | 0.0514037 | − | 0.0785092i | ||||
\(827\) | −48.0554 | −1.67105 | −0.835525 | − | 0.549452i | \(-0.814836\pi\) | ||||
−0.835525 | + | 0.549452i | \(0.814836\pi\) | |||||||
\(828\) | −6.22771 | −0.216428 | ||||||||
\(829\) | 8.83025 | 0.306687 | 0.153344 | − | 0.988173i | \(-0.450996\pi\) | ||||
0.153344 | + | 0.988173i | \(0.450996\pi\) | |||||||
\(830\) | −3.91954 | −0.136049 | ||||||||
\(831\) | 9.53530 | + | 16.5156i | 0.330776 | + | 0.572920i | ||||
\(832\) | 3.18376 | + | 1.69224i | 0.110377 | + | 0.0586680i | ||||
\(833\) | 3.92626 | − | 5.31973i | 0.136037 | − | 0.184318i | ||||
\(834\) | −3.09957 | − | 5.36862i | −0.107329 | − | 0.185900i | ||||
\(835\) | 17.3655 | − | 30.0779i | 0.600957 | − | 1.04089i | ||||
\(836\) | 2.07264 | + | 3.58992i | 0.0716838 | + | 0.124160i | ||||
\(837\) | −3.63304 | + | 6.29261i | −0.125576 | + | 0.217504i | ||||
\(838\) | 22.1379 | 0.764741 | ||||||||
\(839\) | −10.3799 | + | 17.9786i | −0.358355 | + | 0.620689i | −0.987686 | − | 0.156448i | \(-0.949996\pi\) |
0.629331 | + | 0.777137i | \(0.283329\pi\) | |||||||
\(840\) | 5.82930 | + | 0.327409i | 0.201130 | + | 0.0112967i | ||||
\(841\) | 12.9226 | − | 22.3826i | 0.445607 | − | 0.771815i | ||||
\(842\) | −15.5506 | + | 26.9344i | −0.535909 | + | 0.928222i | ||||
\(843\) | −23.3309 | −0.803559 | ||||||||
\(844\) | −11.7856 | + | 20.4132i | −0.405677 | + | 0.702653i | ||||
\(845\) | −12.5684 | + | 25.7879i | −0.432365 | + | 0.887130i | ||||
\(846\) | 4.85355 | 0.166869 | ||||||||
\(847\) | −14.3276 | + | 21.8826i | −0.492303 | + | 0.751896i | ||||
\(848\) | −4.94074 | − | 8.55761i | −0.169666 | − | 0.293869i | ||||
\(849\) | −8.22931 | −0.282429 | ||||||||
\(850\) | 0.0615374 | − | 0.106586i | 0.00211072 | − | 0.00365587i | ||||
\(851\) | 7.04418 | + | 12.2009i | 0.241471 | + | 0.418241i | ||||
\(852\) | −8.41735 | −0.288374 | ||||||||
\(853\) | 9.67377 | 0.331224 | 0.165612 | − | 0.986191i | \(-0.447040\pi\) | ||||
0.165612 | + | 0.986191i | \(0.447040\pi\) | |||||||
\(854\) | −0.0911359 | − | 0.180533i | −0.00311860 | − | 0.00617773i | ||||
\(855\) | 4.33342 | + | 7.50570i | 0.148200 | + | 0.256690i | ||||
\(856\) | 7.05459 | − | 12.2189i | 0.241121 | − | 0.417634i | ||||
\(857\) | 5.94275 | − | 10.2931i | 0.203000 | − | 0.351607i | −0.746493 | − | 0.665393i | \(-0.768264\pi\) |
0.949494 | + | 0.313786i | \(0.101597\pi\) | |||||||
\(858\) | 3.22699 | − | 2.01709i | 0.110168 | − | 0.0688625i | ||||
\(859\) | −12.4094 | − | 21.4937i | −0.423404 | − | 0.733357i | 0.572866 | − | 0.819649i | \(-0.305832\pi\) |
−0.996270 | + | 0.0862919i | \(0.972498\pi\) | |||||||
\(860\) | −1.18594 | − | 2.05411i | −0.0404402 | − | 0.0700446i | ||||
\(861\) | 8.61740 | + | 0.484007i | 0.293680 | + | 0.0164949i | ||||
\(862\) | 5.65730 | − | 9.79873i | 0.192688 | − | 0.333746i | ||||
\(863\) | −19.3325 | − | 33.4848i | −0.658084 | − | 1.13984i | −0.981111 | − | 0.193446i | \(-0.938034\pi\) |
0.323027 | − | 0.946390i | \(-0.395300\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | −11.6785 | − | 20.2278i | −0.397081 | − | 0.687764i | ||||
\(866\) | 19.0285 | + | 32.9583i | 0.646614 | + | 1.11997i | ||||
\(867\) | −8.05393 | + | 13.9498i | −0.273526 | + | 0.473761i | ||||
\(868\) | −10.5306 | + | 16.0835i | −0.357433 | + | 0.545908i | ||||
\(869\) | −3.16845 | − | 5.48791i | −0.107482 | − | 0.186165i | ||||
\(870\) | −1.95977 | − | 3.39442i | −0.0664424 | − | 0.115082i | ||||
\(871\) | −37.2696 | − | 19.8097i | −1.26283 | − | 0.671225i | ||||
\(872\) | −0.723832 | + | 1.25371i | −0.0245121 | + | 0.0424561i | ||||
\(873\) | −8.99467 | + | 15.5792i | −0.304423 | + | 0.527277i | ||||
\(874\) | −12.2295 | − | 21.1821i | −0.413668 | − | 0.716494i | ||||
\(875\) | 16.4077 | − | 25.0595i | 0.554681 | − | 0.847167i | ||||
\(876\) | 13.1453 | 0.444138 | ||||||||
\(877\) | 55.6952 | 1.88069 | 0.940347 | − | 0.340217i | \(-0.110501\pi\) | ||||
0.940347 | + | 0.340217i | \(0.110501\pi\) | |||||||
\(878\) | −1.48304 | − | 2.56871i | −0.0500503 | − | 0.0866897i | ||||
\(879\) | −9.34471 | + | 16.1855i | −0.315189 | + | 0.545924i | ||||
\(880\) | 2.32914 | 0.0785153 | ||||||||
\(881\) | −1.98870 | − | 3.44454i | −0.0670011 | − | 0.116049i | 0.830579 | − | 0.556901i | \(-0.188010\pi\) |
−0.897580 | + | 0.440852i | \(0.854676\pi\) | |||||||
\(882\) | −6.95597 | − | 0.783854i | −0.234220 | − | 0.0263937i | ||||
\(883\) | −10.3816 | −0.349370 | −0.174685 | − | 0.984624i | \(-0.555891\pi\) | ||||
−0.174685 | + | 0.984624i | \(0.555891\pi\) | |||||||
\(884\) | 2.88782 | − | 1.80509i | 0.0971279 | − | 0.0607117i | ||||
\(885\) | 1.12474 | − | 1.94811i | 0.0378077 | − | 0.0654849i | ||||
\(886\) | −20.2506 | −0.680332 | ||||||||
\(887\) | 0.675474 | − | 1.16996i | 0.0226802 | − | 0.0392832i | −0.854463 | − | 0.519513i | \(-0.826113\pi\) |
0.877143 | + | 0.480230i | \(0.159447\pi\) | |||||||
\(888\) | −1.13110 | + | 1.95913i | −0.0379573 | + | 0.0657440i | ||||
\(889\) | −25.4101 | − | 1.42719i | −0.852229 | − | 0.0478664i | ||||
\(890\) | −14.7138 | + | 25.4850i | −0.493206 | + | 0.854258i | ||||
\(891\) | −1.05547 | −0.0353595 | ||||||||
\(892\) | −2.87906 | + | 4.98667i | −0.0963979 | + | 0.166966i | ||||
\(893\) | 9.53102 | + | 16.5082i | 0.318943 | + | 0.552426i | ||||
\(894\) | 10.9374 | − | 18.9442i | 0.365802 | − | 0.633588i | ||||
\(895\) | 15.7100 | + | 27.2104i | 0.525126 | + | 0.909545i | ||||
\(896\) | −1.19230 | − | 2.36187i | −0.0398321 | − | 0.0789044i | ||||
\(897\) | −19.0406 | + | 11.9017i | −0.635748 | + | 0.397387i | ||||
\(898\) | −5.97830 | − | 10.3547i | −0.199498 | − | 0.345541i | ||||
\(899\) | 12.9058 | 0.430432 | ||||||||
\(900\) | −0.130302 | −0.00434341 | ||||||||
\(901\) | −9.33338 | −0.310940 | ||||||||
\(902\) | 3.44315 | 0.114644 | ||||||||
\(903\) | 1.28153 | + | 2.53862i | 0.0426467 | + | 0.0844799i | ||||
\(904\) | 1.67707 | − | 2.90477i | 0.0557784 | − | 0.0966111i | ||||
\(905\) | −15.1505 | − | 26.2415i | −0.503621 | − | 0.872297i | ||||
\(906\) | 7.25658 | + | 12.5688i | 0.241084 | + | 0.417569i | ||||
\(907\) | 26.7461 | 0.888091 | 0.444045 | − | 0.896004i | \(-0.353543\pi\) | ||||
0.444045 | + | 0.896004i | \(0.353543\pi\) | |||||||
\(908\) | −9.84025 | + | 17.0438i | −0.326560 | + | 0.565619i | ||||
\(909\) | 13.5004 | 0.447779 | ||||||||
\(910\) | 18.4482 | − | 10.1393i | 0.611553 | − | 0.336114i | ||||
\(911\) | −13.3116 | −0.441034 | −0.220517 | − | 0.975383i | \(-0.570774\pi\) | ||||
−0.220517 | + | 0.975383i | \(0.570774\pi\) | |||||||
\(912\) | 1.96372 | − | 3.40126i | 0.0650253 | − | 0.112627i | ||||
\(913\) | 1.87469 | 0.0620431 | ||||||||
\(914\) | 11.5421 | + | 19.9915i | 0.381778 | + | 0.661259i | ||||
\(915\) | −0.0843380 | − | 0.146078i | −0.00278813 | − | 0.00482918i | ||||
\(916\) | 10.0430 | − | 17.3951i | 0.331831 | − | 0.574749i | ||||
\(917\) | −17.3103 | − | 0.972251i | −0.571635 | − | 0.0321065i | ||||
\(918\) | −0.944533 | −0.0311742 | ||||||||
\(919\) | 32.8634 | 1.08406 | 0.542032 | − | 0.840358i | \(-0.317655\pi\) | ||||
0.542032 | + | 0.840358i | \(0.317655\pi\) | |||||||
\(920\) | −13.7429 | −0.453091 | ||||||||
\(921\) | −18.0495 | −0.594751 | ||||||||
\(922\) | 9.46131 | + | 16.3875i | 0.311592 | + | 0.539692i | ||||
\(923\) | −25.7353 | + | 16.0863i | −0.847087 | + | 0.529488i | ||||
\(924\) | −2.78811 | − | 0.156597i | −0.0917220 | − | 0.00515168i | ||||
\(925\) | 0.147385 | + | 0.255279i | 0.00484600 | + | 0.00839352i | ||||
\(926\) | −16.3885 | + | 28.3857i | −0.538560 | + | 0.932813i | ||||
\(927\) | 1.46258 | + | 2.53327i | 0.0480375 | + | 0.0832034i | ||||
\(928\) | −0.888084 | + | 1.53821i | −0.0291528 | + | 0.0504941i | ||||
\(929\) | 44.7305 | 1.46756 | 0.733780 | − | 0.679387i | \(-0.237754\pi\) | ||||
0.733780 | + | 0.679387i | \(0.237754\pi\) | |||||||
\(930\) | −8.01717 | + | 13.8862i | −0.262894 | + | 0.455345i | ||||
\(931\) | −10.9935 | − | 25.1984i | −0.360297 | − | 0.825843i | ||||
\(932\) | −2.82261 | + | 4.88890i | −0.0924575 | + | 0.160141i | ||||
\(933\) | 8.46321 | − | 14.6587i | 0.277073 | − | 0.479905i | ||||
\(934\) | −21.4614 | −0.702237 | ||||||||
\(935\) | 1.09997 | − | 1.90521i | 0.0359730 | − | 0.0623071i | ||||
\(936\) | −3.18376 | − | 1.69224i | −0.104064 | − | 0.0553127i | ||||
\(937\) | 26.6286 | 0.869917 | 0.434958 | − | 0.900451i | \(-0.356763\pi\) | ||||
0.434958 | + | 0.900451i | \(0.356763\pi\) | |||||||
\(938\) | 13.9573 | + | 27.6484i | 0.455722 | + | 0.902751i | ||||
\(939\) | 11.0035 | + | 19.0587i | 0.359087 | + | 0.621957i | ||||
\(940\) | 10.7105 | 0.349339 | ||||||||
\(941\) | −5.48027 | + | 9.49210i | −0.178652 | + | 0.309434i | −0.941419 | − | 0.337239i | \(-0.890507\pi\) |
0.762767 | + | 0.646673i | \(0.223840\pi\) | |||||||
\(942\) | 2.13538 | + | 3.69859i | 0.0695745 | + | 0.120506i | ||||
\(943\) | −20.3161 | −0.661582 | ||||||||
\(944\) | −1.01937 | −0.0331776 | ||||||||
\(945\) | −5.82930 | − | 0.327409i | −0.189627 | − | 0.0106506i | ||||
\(946\) | 0.567227 | + | 0.982465i | 0.0184421 | + | 0.0319427i | ||||
\(947\) | 26.8500 | − | 46.5055i | 0.872507 | − | 1.51123i | 0.0131120 | − | 0.999914i | \(-0.495826\pi\) |
0.859395 | − | 0.511312i | \(-0.170840\pi\) | |||||||
\(948\) | −3.00194 | + | 5.19951i | −0.0974984 | + | 0.168872i | ||||
\(949\) | 40.1905 | − | 25.1218i | 1.30464 | − | 0.815490i | ||||
\(950\) | −0.255877 | − | 0.443193i | −0.00830176 | − | 0.0143791i | ||||
\(951\) | −4.46606 | − | 7.73544i | −0.144822 | − | 0.250839i | ||||
\(952\) | −2.49507 | − | 0.140138i | −0.0808656 | − | 0.00454191i | ||||
\(953\) | 15.5264 | − | 26.8924i | 0.502948 | − | 0.871131i | −0.497046 | − | 0.867724i | \(-0.665582\pi\) |
0.999994 | − | 0.00340721i | \(-0.00108455\pi\) | |||||||
\(954\) | 4.94074 | + | 8.55761i | 0.159962 | + | 0.277063i | ||||
\(955\) | 0.966549 | + | 1.67411i | 0.0312768 | + | 0.0541730i | ||||
\(956\) | −4.10480 | − | 7.10972i | −0.132759 | − | 0.229945i | ||||
\(957\) | 0.937343 | + | 1.62353i | 0.0303000 | + | 0.0524811i | ||||
\(958\) | −15.9460 | + | 27.6194i | −0.515193 | + | 0.892341i | ||||
\(959\) | −18.8205 | − | 1.05707i | −0.607744 | − | 0.0341347i | ||||
\(960\) | −1.10337 | − | 1.91109i | −0.0356111 | − | 0.0616802i | ||||
\(961\) | −10.8980 | − | 18.8759i | −0.351548 | − | 0.608898i | ||||
\(962\) | 0.285834 | + | 8.15149i | 0.00921565 | + | 0.262815i | ||||
\(963\) | −7.05459 | + | 12.2189i | −0.227331 | + | 0.393749i | ||||
\(964\) | 10.5084 | − | 18.2011i | 0.338454 | − | 0.586220i | ||||
\(965\) | −25.0051 | − | 43.3101i | −0.804942 | − | 1.39420i | ||||
\(966\) | 16.4510 | + | 0.923992i | 0.529304 | + | 0.0297290i | ||||
\(967\) | −49.7062 | −1.59844 | −0.799221 | − | 0.601037i | \(-0.794754\pi\) | ||||
−0.799221 | + | 0.601037i | \(0.794754\pi\) | |||||||
\(968\) | 9.88599 | 0.317748 | ||||||||
\(969\) | −1.85480 | − | 3.21260i | −0.0595847 | − | 0.103204i | ||||
\(970\) | −19.8489 | + | 34.3793i | −0.637309 | + | 1.10385i | ||||
\(971\) | −51.1140 | −1.64033 | −0.820163 | − | 0.572130i | \(-0.806117\pi\) | ||||
−0.820163 | + | 0.572130i | \(0.806117\pi\) | |||||||
\(972\) | 0.500000 | + | 0.866025i | 0.0160375 | + | 0.0277778i | ||||
\(973\) | 7.39127 | + | 14.6416i | 0.236953 | + | 0.469387i | ||||
\(974\) | −0.744679 | −0.0238610 | ||||||||
\(975\) | −0.398387 | + | 0.249020i | −0.0127586 | + | 0.00797502i | ||||
\(976\) | −0.0382184 | + | 0.0661962i | −0.00122334 | + | 0.00211889i | ||||
\(977\) | −4.63586 | −0.148314 | −0.0741571 | − | 0.997247i | \(-0.523627\pi\) | ||||
−0.0741571 | + | 0.997247i | \(0.523627\pi\) | |||||||
\(978\) | −3.03208 | + | 5.25172i | −0.0969554 | + | 0.167932i | ||||
\(979\) | 7.03748 | − | 12.1893i | 0.224919 | − | 0.389571i | ||||
\(980\) | −15.3500 | − | 1.72976i | −0.490338 | − | 0.0552552i | ||||
\(981\) | 0.723832 | − | 1.25371i | 0.0231102 | − | 0.0400280i | ||||
\(982\) | −41.0066 | −1.30857 | ||||||||
\(983\) | 5.80348 | − | 10.0519i | 0.185102 | − | 0.320607i | −0.758509 | − | 0.651663i | \(-0.774072\pi\) |
0.943611 | + | 0.331056i | \(0.107405\pi\) | |||||||
\(984\) | −1.63110 | − | 2.82515i | −0.0519977 | − | 0.0900626i | ||||
\(985\) | −18.6304 | + | 32.2687i | −0.593613 | + | 1.02817i | ||||
\(986\) | 0.838824 | + | 1.45289i | 0.0267136 | + | 0.0462693i | ||||
\(987\) | −12.8211 | − | 0.720111i | −0.408100 | − | 0.0229214i | ||||
\(988\) | −0.496239 | − | 14.1519i | −0.0157875 | − | 0.450232i | ||||
\(989\) | −3.34688 | − | 5.79697i | −0.106425 | − | 0.184333i | ||||
\(990\) | −2.32914 | −0.0740249 | ||||||||
\(991\) | −47.4955 | −1.50875 | −0.754373 | − | 0.656446i | \(-0.772059\pi\) | ||||
−0.754373 | + | 0.656446i | \(0.772059\pi\) | |||||||
\(992\) | 7.26608 | 0.230698 | ||||||||
\(993\) | −4.32850 | −0.137361 | ||||||||
\(994\) | 22.2352 | + | 1.24887i | 0.705257 | + | 0.0396116i | ||||
\(995\) | −6.51081 | + | 11.2771i | −0.206407 | + | 0.357507i | ||||
\(996\) | −0.888084 | − | 1.53821i | −0.0281400 | − | 0.0487399i | ||||
\(997\) | −0.737548 | − | 1.27747i | −0.0233584 | − | 0.0404579i | 0.854110 | − | 0.520093i | \(-0.174103\pi\) |
−0.877468 | + | 0.479635i | \(0.840769\pi\) | |||||||
\(998\) | 11.2274 | 0.355398 | ||||||||
\(999\) | 1.13110 | − | 1.95913i | 0.0357865 | − | 0.0619841i |
(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.k.e.445.5 | yes | 10 | |
3.2 | odd | 2 | 1638.2.p.j.991.1 | 10 | |||
7.2 | even | 3 | 546.2.j.e.289.5 | ✓ | 10 | ||
13.9 | even | 3 | 546.2.j.e.529.5 | yes | 10 | ||
21.2 | odd | 6 | 1638.2.m.k.289.1 | 10 | |||
39.35 | odd | 6 | 1638.2.m.k.1621.1 | 10 | |||
91.9 | even | 3 | inner | 546.2.k.e.373.5 | yes | 10 | |
273.191 | odd | 6 | 1638.2.p.j.919.1 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.j.e.289.5 | ✓ | 10 | 7.2 | even | 3 | ||
546.2.j.e.529.5 | yes | 10 | 13.9 | even | 3 | ||
546.2.k.e.373.5 | yes | 10 | 91.9 | even | 3 | inner | |
546.2.k.e.445.5 | yes | 10 | 1.1 | even | 1 | trivial | |
1638.2.m.k.289.1 | 10 | 21.2 | odd | 6 | |||
1638.2.m.k.1621.1 | 10 | 39.35 | odd | 6 | |||
1638.2.p.j.919.1 | 10 | 273.191 | odd | 6 | |||
1638.2.p.j.991.1 | 10 | 3.2 | odd | 2 |