Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(239,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.p (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} + 8 x^{18} - 20 x^{17} + 56 x^{16} - 140 x^{15} + 288 x^{14} - 532 x^{13} + \cdots + 59049 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 239.10 | ||
Root | \(-1.39758 + 1.02312i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.239 |
Dual form | 546.2.p.c.281.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | 1.71169 | + | 0.264783i | 0.988246 | + | 0.152873i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0.790081 | + | 0.790081i | 0.353335 | + | 0.353335i | 0.861349 | − | 0.508014i | \(-0.169620\pi\) |
−0.508014 | + | 0.861349i | \(0.669620\pi\) | |||||||
\(6\) | 1.02312 | + | 1.39758i | 0.417687 | + | 0.570559i | ||||
\(7\) | −0.707107 | − | 0.707107i | −0.267261 | − | 0.267261i | ||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 2.85978 | + | 0.906454i | 0.953260 | + | 0.302151i | ||||
\(10\) | 1.11734i | 0.353335i | ||||||||
\(11\) | −3.45508 | + | 3.45508i | −1.04174 | + | 1.04174i | −0.0426547 | + | 0.999090i | \(0.513582\pi\) |
−0.999090 | + | 0.0426547i | \(0.986418\pi\) | |||||||
\(12\) | −0.264783 | + | 1.71169i | −0.0764363 | + | 0.494123i | ||||
\(13\) | −1.18766 | + | 3.40433i | −0.329399 | + | 0.944191i | ||||
\(14\) | − | 1.00000i | − | 0.267261i | ||||||
\(15\) | 1.14317 | + | 1.56157i | 0.295166 | + | 0.403197i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 0.401161 | 0.0972959 | 0.0486480 | − | 0.998816i | \(-0.484509\pi\) | ||||
0.0486480 | + | 0.998816i | \(0.484509\pi\) | |||||||
\(18\) | 1.38121 | + | 2.66313i | 0.325554 | + | 0.627706i | ||||
\(19\) | 4.88536 | − | 4.88536i | 1.12078 | − | 1.12078i | 0.129153 | − | 0.991625i | \(-0.458774\pi\) |
0.991625 | − | 0.129153i | \(-0.0412258\pi\) | |||||||
\(20\) | −0.790081 | + | 0.790081i | −0.176667 | + | 0.176667i | ||||
\(21\) | −1.02312 | − | 1.39758i | −0.223263 | − | 0.304977i | ||||
\(22\) | −4.88622 | −1.04174 | ||||||||
\(23\) | 6.12089 | 1.27629 | 0.638147 | − | 0.769915i | \(-0.279701\pi\) | ||||
0.638147 | + | 0.769915i | \(0.279701\pi\) | |||||||
\(24\) | −1.39758 | + | 1.02312i | −0.285280 | + | 0.208843i | ||||
\(25\) | − | 3.75155i | − | 0.750309i | ||||||
\(26\) | −3.24703 | + | 1.56742i | −0.636795 | + | 0.307396i | ||||
\(27\) | 4.65505 | + | 2.30879i | 0.895865 | + | 0.444327i | ||||
\(28\) | 0.707107 | − | 0.707107i | 0.133631 | − | 0.133631i | ||||
\(29\) | − | 1.16528i | − | 0.216388i | −0.994130 | − | 0.108194i | \(-0.965493\pi\) | ||
0.994130 | − | 0.108194i | \(-0.0345067\pi\) | |||||||
\(30\) | −0.295853 | + | 1.91255i | −0.0540152 | + | 0.349182i | ||||
\(31\) | 2.88418 | − | 2.88418i | 0.518014 | − | 0.518014i | −0.398956 | − | 0.916970i | \(-0.630627\pi\) |
0.916970 | + | 0.398956i | \(0.130627\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | −6.82887 | + | 4.99918i | −1.18875 | + | 0.870246i | ||||
\(34\) | 0.283664 | + | 0.283664i | 0.0486480 | + | 0.0486480i | ||||
\(35\) | − | 1.11734i | − | 0.188865i | ||||||
\(36\) | −0.906454 | + | 2.85978i | −0.151076 | + | 0.476630i | ||||
\(37\) | −4.48595 | − | 4.48595i | −0.737486 | − | 0.737486i | 0.234605 | − | 0.972091i | \(-0.424620\pi\) |
−0.972091 | + | 0.234605i | \(0.924620\pi\) | |||||||
\(38\) | 6.90894 | 1.12078 | ||||||||
\(39\) | −2.93432 | + | 5.51269i | −0.469868 | + | 0.882737i | ||||
\(40\) | −1.11734 | −0.176667 | ||||||||
\(41\) | −6.76896 | − | 6.76896i | −1.05713 | − | 1.05713i | −0.998266 | − | 0.0588688i | \(-0.981251\pi\) |
−0.0588688 | − | 0.998266i | \(-0.518749\pi\) | |||||||
\(42\) | 0.264783 | − | 1.71169i | 0.0408569 | − | 0.264120i | ||||
\(43\) | 2.74375i | 0.418418i | 0.977871 | + | 0.209209i | \(0.0670889\pi\) | ||||
−0.977871 | + | 0.209209i | \(0.932911\pi\) | |||||||
\(44\) | −3.45508 | − | 3.45508i | −0.520872 | − | 0.520872i | ||||
\(45\) | 1.54328 | + | 2.97563i | 0.230059 | + | 0.443580i | ||||
\(46\) | 4.32812 | + | 4.32812i | 0.638147 | + | 0.638147i | ||||
\(47\) | −5.67285 | + | 5.67285i | −0.827471 | + | 0.827471i | −0.987166 | − | 0.159696i | \(-0.948949\pi\) |
0.159696 | + | 0.987166i | \(0.448949\pi\) | |||||||
\(48\) | −1.71169 | − | 0.264783i | −0.247061 | − | 0.0382181i | ||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 2.65274 | − | 2.65274i | 0.375155 | − | 0.375155i | ||||
\(51\) | 0.686665 | + | 0.106221i | 0.0961523 | + | 0.0148739i | ||||
\(52\) | −3.40433 | − | 1.18766i | −0.472095 | − | 0.164699i | ||||
\(53\) | − | 3.46244i | − | 0.475603i | −0.971314 | − | 0.237801i | \(-0.923573\pi\) | ||
0.971314 | − | 0.237801i | \(-0.0764267\pi\) | |||||||
\(54\) | 1.65905 | + | 4.92418i | 0.225769 | + | 0.670096i | ||||
\(55\) | −5.45958 | −0.736169 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 9.65578 | − | 7.06867i | 1.27894 | − | 0.936268i | ||||
\(58\) | 0.823979 | − | 0.823979i | 0.108194 | − | 0.108194i | ||||
\(59\) | 8.03324 | − | 8.03324i | 1.04584 | − | 1.04584i | 0.0469418 | − | 0.998898i | \(-0.485052\pi\) |
0.998898 | − | 0.0469418i | \(-0.0149475\pi\) | |||||||
\(60\) | −1.56157 | + | 1.14317i | −0.201598 | + | 0.147583i | ||||
\(61\) | −0.717748 | −0.0918983 | −0.0459491 | − | 0.998944i | \(-0.514631\pi\) | ||||
−0.0459491 | + | 0.998944i | \(0.514631\pi\) | |||||||
\(62\) | 4.07885 | 0.518014 | ||||||||
\(63\) | −1.38121 | − | 2.66313i | −0.174016 | − | 0.335523i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −3.62804 | + | 1.75134i | −0.450003 | + | 0.217228i | ||||
\(66\) | −8.36370 | − | 1.29379i | −1.02950 | − | 0.159254i | ||||
\(67\) | −0.693547 | + | 0.693547i | −0.0847303 | + | 0.0847303i | −0.748202 | − | 0.663471i | \(-0.769082\pi\) |
0.663471 | + | 0.748202i | \(0.269082\pi\) | |||||||
\(68\) | 0.401161i | 0.0486480i | ||||||||
\(69\) | 10.4771 | + | 1.62071i | 1.26129 | + | 0.195110i | ||||
\(70\) | 0.790081 | − | 0.790081i | 0.0944327 | − | 0.0944327i | ||||
\(71\) | −5.15463 | − | 5.15463i | −0.611742 | − | 0.611742i | 0.331658 | − | 0.943400i | \(-0.392392\pi\) |
−0.943400 | + | 0.331658i | \(0.892392\pi\) | |||||||
\(72\) | −2.66313 | + | 1.38121i | −0.313853 | + | 0.162777i | ||||
\(73\) | −0.0455596 | − | 0.0455596i | −0.00533235 | − | 0.00533235i | 0.704436 | − | 0.709768i | \(-0.251200\pi\) |
−0.709768 | + | 0.704436i | \(0.751200\pi\) | |||||||
\(74\) | − | 6.34409i | − | 0.737486i | ||||||
\(75\) | 0.993346 | − | 6.42149i | 0.114702 | − | 0.741490i | ||||
\(76\) | 4.88536 | + | 4.88536i | 0.560389 | + | 0.560389i | ||||
\(77\) | 4.88622 | 0.556836 | ||||||||
\(78\) | −5.97294 | + | 1.82318i | −0.676302 | + | 0.206435i | ||||
\(79\) | −4.24647 | −0.477765 | −0.238882 | − | 0.971048i | \(-0.576781\pi\) | ||||
−0.238882 | + | 0.971048i | \(0.576781\pi\) | |||||||
\(80\) | −0.790081 | − | 0.790081i | −0.0883337 | − | 0.0883337i | ||||
\(81\) | 7.35668 | + | 5.18452i | 0.817409 | + | 0.576058i | ||||
\(82\) | − | 9.57276i | − | 1.05713i | ||||||
\(83\) | 1.74175 | + | 1.74175i | 0.191182 | + | 0.191182i | 0.796207 | − | 0.605025i | \(-0.206837\pi\) |
−0.605025 | + | 0.796207i | \(0.706837\pi\) | |||||||
\(84\) | 1.39758 | − | 1.02312i | 0.152488 | − | 0.111631i | ||||
\(85\) | 0.316950 | + | 0.316950i | 0.0343780 | + | 0.0343780i | ||||
\(86\) | −1.94012 | + | 1.94012i | −0.209209 | + | 0.209209i | ||||
\(87\) | 0.308547 | − | 1.99461i | 0.0330797 | − | 0.213844i | ||||
\(88\) | − | 4.88622i | − | 0.520872i | ||||||
\(89\) | −8.55005 | + | 8.55005i | −0.906304 | + | 0.906304i | −0.995972 | − | 0.0896678i | \(-0.971419\pi\) |
0.0896678 | + | 0.995972i | \(0.471419\pi\) | |||||||
\(90\) | −1.01282 | + | 3.19535i | −0.106761 | + | 0.336820i | ||||
\(91\) | 3.24703 | − | 1.56742i | 0.340381 | − | 0.164310i | ||||
\(92\) | 6.12089i | 0.638147i | ||||||||
\(93\) | 5.70051 | − | 4.17315i | 0.591115 | − | 0.432735i | ||||
\(94\) | −8.02263 | −0.827471 | ||||||||
\(95\) | 7.71965 | 0.792019 | ||||||||
\(96\) | −1.02312 | − | 1.39758i | −0.104422 | − | 0.142640i | ||||
\(97\) | −7.03452 | + | 7.03452i | −0.714247 | + | 0.714247i | −0.967421 | − | 0.253174i | \(-0.918525\pi\) |
0.253174 | + | 0.967421i | \(0.418525\pi\) | |||||||
\(98\) | −0.707107 | + | 0.707107i | −0.0714286 | + | 0.0714286i | ||||
\(99\) | −13.0126 | + | 6.74889i | −1.30782 | + | 0.678289i | ||||
\(100\) | 3.75155 | 0.375155 | ||||||||
\(101\) | 3.38548 | 0.336868 | 0.168434 | − | 0.985713i | \(-0.446129\pi\) | ||||
0.168434 | + | 0.985713i | \(0.446129\pi\) | |||||||
\(102\) | 0.410436 | + | 0.560655i | 0.0406392 | + | 0.0555131i | ||||
\(103\) | 13.1959i | 1.30023i | 0.759835 | + | 0.650116i | \(0.225280\pi\) | ||||
−0.759835 | + | 0.650116i | \(0.774720\pi\) | |||||||
\(104\) | −1.56742 | − | 3.24703i | −0.153698 | − | 0.318397i | ||||
\(105\) | 0.295853 | − | 1.91255i | 0.0288723 | − | 0.186645i | ||||
\(106\) | 2.44831 | − | 2.44831i | 0.237801 | − | 0.237801i | ||||
\(107\) | − | 18.9481i | − | 1.83178i | −0.401432 | − | 0.915889i | \(-0.631487\pi\) | ||
0.401432 | − | 0.915889i | \(-0.368513\pi\) | |||||||
\(108\) | −2.30879 | + | 4.65505i | −0.222164 | + | 0.447932i | ||||
\(109\) | −5.81740 | + | 5.81740i | −0.557206 | + | 0.557206i | −0.928511 | − | 0.371305i | \(-0.878910\pi\) |
0.371305 | + | 0.928511i | \(0.378910\pi\) | |||||||
\(110\) | −3.86050 | − | 3.86050i | −0.368085 | − | 0.368085i | ||||
\(111\) | −6.49076 | − | 8.86637i | −0.616076 | − | 0.841559i | ||||
\(112\) | 0.707107 | + | 0.707107i | 0.0668153 | + | 0.0668153i | ||||
\(113\) | − | 14.8579i | − | 1.39771i | −0.715262 | − | 0.698856i | \(-0.753693\pi\) | ||
0.715262 | − | 0.698856i | \(-0.246307\pi\) | |||||||
\(114\) | 11.8260 | + | 1.82937i | 1.10760 | + | 0.171336i | ||||
\(115\) | 4.83599 | + | 4.83599i | 0.450959 | + | 0.450959i | ||||
\(116\) | 1.16528 | 0.108194 | ||||||||
\(117\) | −6.48232 | + | 8.65907i | −0.599291 | + | 0.800531i | ||||
\(118\) | 11.3607 | 1.04584 | ||||||||
\(119\) | −0.283664 | − | 0.283664i | −0.0260034 | − | 0.0260034i | ||||
\(120\) | −1.91255 | − | 0.295853i | −0.174591 | − | 0.0270076i | ||||
\(121\) | − | 12.8751i | − | 1.17046i | ||||||
\(122\) | −0.507525 | − | 0.507525i | −0.0459491 | − | 0.0459491i | ||||
\(123\) | −9.79407 | − | 13.3787i | −0.883102 | − | 1.20632i | ||||
\(124\) | 2.88418 | + | 2.88418i | 0.259007 | + | 0.259007i | ||||
\(125\) | 6.91443 | − | 6.91443i | 0.618445 | − | 0.618445i | ||||
\(126\) | 0.906454 | − | 2.85978i | 0.0807534 | − | 0.254769i | ||||
\(127\) | 2.26219i | 0.200737i | 0.994950 | + | 0.100368i | \(0.0320021\pi\) | ||||
−0.994950 | + | 0.100368i | \(0.967998\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | −0.726498 | + | 4.69645i | −0.0639646 | + | 0.413500i | ||||
\(130\) | −3.80380 | − | 1.32703i | −0.333615 | − | 0.116388i | ||||
\(131\) | 12.7200i | 1.11135i | 0.831400 | + | 0.555675i | \(0.187540\pi\) | ||||
−0.831400 | + | 0.555675i | \(0.812460\pi\) | |||||||
\(132\) | −4.99918 | − | 6.82887i | −0.435123 | − | 0.594377i | ||||
\(133\) | −6.90894 | −0.599081 | ||||||||
\(134\) | −0.980824 | −0.0847303 | ||||||||
\(135\) | 1.85373 | + | 5.50200i | 0.159544 | + | 0.473536i | ||||
\(136\) | −0.283664 | + | 0.283664i | −0.0243240 | + | 0.0243240i | ||||
\(137\) | 15.4491 | − | 15.4491i | 1.31991 | − | 1.31991i | 0.406065 | − | 0.913844i | \(-0.366901\pi\) |
0.913844 | − | 0.406065i | \(-0.133099\pi\) | |||||||
\(138\) | 6.26240 | + | 8.55442i | 0.533091 | + | 0.728201i | ||||
\(139\) | 2.96141 | 0.251184 | 0.125592 | − | 0.992082i | \(-0.459917\pi\) | ||||
0.125592 | + | 0.992082i | \(0.459917\pi\) | |||||||
\(140\) | 1.11734 | 0.0944327 | ||||||||
\(141\) | −11.2123 | + | 8.20810i | −0.944242 | + | 0.691247i | ||||
\(142\) | − | 7.28975i | − | 0.611742i | ||||||
\(143\) | −7.65875 | − | 15.8657i | −0.640457 | − | 1.32676i | ||||
\(144\) | −2.85978 | − | 0.906454i | −0.238315 | − | 0.0755379i | ||||
\(145\) | 0.920667 | − | 0.920667i | 0.0764572 | − | 0.0764572i | ||||
\(146\) | − | 0.0644310i | − | 0.00533235i | ||||||
\(147\) | −0.264783 | + | 1.71169i | −0.0218389 | + | 0.141178i | ||||
\(148\) | 4.48595 | − | 4.48595i | 0.368743 | − | 0.368743i | ||||
\(149\) | −3.74411 | − | 3.74411i | −0.306730 | − | 0.306730i | 0.536910 | − | 0.843640i | \(-0.319591\pi\) |
−0.843640 | + | 0.536910i | \(0.819591\pi\) | |||||||
\(150\) | 5.24308 | − | 3.83828i | 0.428096 | − | 0.313394i | ||||
\(151\) | 12.1505 | + | 12.1505i | 0.988794 | + | 0.988794i | 0.999938 | − | 0.0111437i | \(-0.00354723\pi\) |
−0.0111437 | + | 0.999938i | \(0.503547\pi\) | |||||||
\(152\) | 6.90894i | 0.560389i | ||||||||
\(153\) | 1.14723 | + | 0.363634i | 0.0927483 | + | 0.0293981i | ||||
\(154\) | 3.45508 | + | 3.45508i | 0.278418 | + | 0.278418i | ||||
\(155\) | 4.55747 | 0.366065 | ||||||||
\(156\) | −5.51269 | − | 2.93432i | −0.441368 | − | 0.234934i | ||||
\(157\) | 20.3675 | 1.62550 | 0.812750 | − | 0.582613i | \(-0.197970\pi\) | ||||
0.812750 | + | 0.582613i | \(0.197970\pi\) | |||||||
\(158\) | −3.00271 | − | 3.00271i | −0.238882 | − | 0.238882i | ||||
\(159\) | 0.916795 | − | 5.92663i | 0.0727066 | − | 0.470012i | ||||
\(160\) | − | 1.11734i | − | 0.0883337i | ||||||
\(161\) | −4.32812 | − | 4.32812i | −0.341104 | − | 0.341104i | ||||
\(162\) | 1.53595 | + | 8.86797i | 0.120676 | + | 0.696733i | ||||
\(163\) | 8.52261 | + | 8.52261i | 0.667542 | + | 0.667542i | 0.957147 | − | 0.289604i | \(-0.0935237\pi\) |
−0.289604 | + | 0.957147i | \(0.593524\pi\) | |||||||
\(164\) | 6.76896 | − | 6.76896i | 0.528567 | − | 0.528567i | ||||
\(165\) | −9.34511 | − | 1.44560i | −0.727516 | − | 0.112540i | ||||
\(166\) | 2.46321i | 0.191182i | ||||||||
\(167\) | −12.4225 | + | 12.4225i | −0.961284 | + | 0.961284i | −0.999278 | − | 0.0379938i | \(-0.987903\pi\) |
0.0379938 | + | 0.999278i | \(0.487903\pi\) | |||||||
\(168\) | 1.71169 | + | 0.264783i | 0.132060 | + | 0.0204285i | ||||
\(169\) | −10.1789 | − | 8.08639i | −0.782993 | − | 0.622030i | ||||
\(170\) | 0.448235i | 0.0343780i | ||||||||
\(171\) | 18.3994 | − | 9.54269i | 1.40704 | − | 0.729748i | ||||
\(172\) | −2.74375 | −0.209209 | ||||||||
\(173\) | −21.8487 | −1.66112 | −0.830562 | − | 0.556926i | \(-0.811981\pi\) | ||||
−0.830562 | + | 0.556926i | \(0.811981\pi\) | |||||||
\(174\) | 1.62857 | − | 1.19222i | 0.123462 | − | 0.0903822i | ||||
\(175\) | −2.65274 | + | 2.65274i | −0.200529 | + | 0.200529i | ||||
\(176\) | 3.45508 | − | 3.45508i | 0.260436 | − | 0.260436i | ||||
\(177\) | 15.8775 | − | 11.6234i | 1.19343 | − | 0.873666i | ||||
\(178\) | −12.0916 | −0.906304 | ||||||||
\(179\) | 13.0946 | 0.978737 | 0.489369 | − | 0.872077i | \(-0.337227\pi\) | ||||
0.489369 | + | 0.872077i | \(0.337227\pi\) | |||||||
\(180\) | −2.97563 | + | 1.54328i | −0.221790 | + | 0.115030i | ||||
\(181\) | 18.6617i | 1.38711i | 0.720403 | + | 0.693556i | \(0.243957\pi\) | ||||
−0.720403 | + | 0.693556i | \(0.756043\pi\) | |||||||
\(182\) | 3.40433 | + | 1.18766i | 0.252346 | + | 0.0880355i | ||||
\(183\) | −1.22856 | − | 0.190048i | −0.0908181 | − | 0.0140487i | ||||
\(184\) | −4.32812 | + | 4.32812i | −0.319073 | + | 0.319073i | ||||
\(185\) | − | 7.08853i | − | 0.521159i | ||||||
\(186\) | 6.98173 | + | 1.08001i | 0.511925 | + | 0.0791901i | ||||
\(187\) | −1.38604 | + | 1.38604i | −0.101358 | + | 0.101358i | ||||
\(188\) | −5.67285 | − | 5.67285i | −0.413735 | − | 0.413735i | ||||
\(189\) | −1.65905 | − | 4.92418i | −0.120678 | − | 0.358181i | ||||
\(190\) | 5.45862 | + | 5.45862i | 0.396010 | + | 0.396010i | ||||
\(191\) | − | 7.22379i | − | 0.522695i | −0.965245 | − | 0.261347i | \(-0.915833\pi\) | ||
0.965245 | − | 0.261347i | \(-0.0841668\pi\) | |||||||
\(192\) | 0.264783 | − | 1.71169i | 0.0191091 | − | 0.123531i | ||||
\(193\) | −19.1571 | − | 19.1571i | −1.37896 | − | 1.37896i | −0.846387 | − | 0.532568i | \(-0.821227\pi\) |
−0.532568 | − | 0.846387i | \(-0.678773\pi\) | |||||||
\(194\) | −9.94831 | −0.714247 | ||||||||
\(195\) | −6.67382 | + | 2.03712i | −0.477922 | + | 0.145881i | ||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | 17.1364 | + | 17.1364i | 1.22092 | + | 1.22092i | 0.967307 | + | 0.253610i | \(0.0816179\pi\) |
0.253610 | + | 0.967307i | \(0.418382\pi\) | |||||||
\(198\) | −13.9735 | − | 4.42913i | −0.993053 | − | 0.314765i | ||||
\(199\) | 9.75133i | 0.691253i | 0.938372 | + | 0.345627i | \(0.112334\pi\) | ||||
−0.938372 | + | 0.345627i | \(0.887666\pi\) | |||||||
\(200\) | 2.65274 | + | 2.65274i | 0.187577 | + | 0.187577i | ||||
\(201\) | −1.37078 | + | 1.00350i | −0.0966873 | + | 0.0707814i | ||||
\(202\) | 2.39390 | + | 2.39390i | 0.168434 | + | 0.168434i | ||||
\(203\) | −0.823979 | + | 0.823979i | −0.0578320 | + | 0.0578320i | ||||
\(204\) | −0.106221 | + | 0.686665i | −0.00743694 | + | 0.0480762i | ||||
\(205\) | − | 10.6961i | − | 0.747045i | ||||||
\(206\) | −9.33092 | + | 9.33092i | −0.650116 | + | 0.650116i | ||||
\(207\) | 17.5044 | + | 5.54830i | 1.21664 | + | 0.385634i | ||||
\(208\) | 1.18766 | − | 3.40433i | 0.0823496 | − | 0.236048i | ||||
\(209\) | 33.7586i | 2.33513i | ||||||||
\(210\) | 1.56157 | − | 1.14317i | 0.107759 | − | 0.0788865i | ||||
\(211\) | 7.32056 | 0.503968 | 0.251984 | − | 0.967731i | \(-0.418917\pi\) | ||||
0.251984 | + | 0.967731i | \(0.418917\pi\) | |||||||
\(212\) | 3.46244 | 0.237801 | ||||||||
\(213\) | −7.45828 | − | 10.1880i | −0.511033 | − | 0.698070i | ||||
\(214\) | 13.3983 | − | 13.3983i | 0.915889 | − | 0.915889i | ||||
\(215\) | −2.16778 | + | 2.16778i | −0.147842 | + | 0.147842i | ||||
\(216\) | −4.92418 | + | 1.65905i | −0.335048 | + | 0.112884i | ||||
\(217\) | −4.07885 | −0.276890 | ||||||||
\(218\) | −8.22704 | −0.557206 | ||||||||
\(219\) | −0.0659206 | − | 0.0900475i | −0.00445450 | − | 0.00608484i | ||||
\(220\) | − | 5.45958i | − | 0.368085i | ||||||
\(221\) | −0.476445 | + | 1.36569i | −0.0320491 | + | 0.0918659i | ||||
\(222\) | 1.67981 | − | 10.8591i | 0.112741 | − | 0.728818i | ||||
\(223\) | −5.34679 | + | 5.34679i | −0.358047 | + | 0.358047i | −0.863093 | − | 0.505045i | \(-0.831476\pi\) |
0.505045 | + | 0.863093i | \(0.331476\pi\) | |||||||
\(224\) | 1.00000i | 0.0668153i | ||||||||
\(225\) | 3.40060 | − | 10.7286i | 0.226707 | − | 0.715240i | ||||
\(226\) | 10.5061 | − | 10.5061i | 0.698856 | − | 0.698856i | ||||
\(227\) | 3.12944 | + | 3.12944i | 0.207708 | + | 0.207708i | 0.803293 | − | 0.595584i | \(-0.203079\pi\) |
−0.595584 | + | 0.803293i | \(0.703079\pi\) | |||||||
\(228\) | 7.06867 | + | 9.65578i | 0.468134 | + | 0.639470i | ||||
\(229\) | −18.3485 | − | 18.3485i | −1.21250 | − | 1.21250i | −0.970201 | − | 0.242300i | \(-0.922098\pi\) |
−0.242300 | − | 0.970201i | \(-0.577902\pi\) | |||||||
\(230\) | 6.83913i | 0.450959i | ||||||||
\(231\) | 8.36370 | + | 1.29379i | 0.550291 | + | 0.0851249i | ||||
\(232\) | 0.823979 | + | 0.823979i | 0.0540969 | + | 0.0540969i | ||||
\(233\) | −11.2420 | −0.736486 | −0.368243 | − | 0.929730i | \(-0.620041\pi\) | ||||
−0.368243 | + | 0.929730i | \(0.620041\pi\) | |||||||
\(234\) | −10.7066 | + | 1.53919i | −0.699911 | + | 0.100620i | ||||
\(235\) | −8.96402 | −0.584748 | ||||||||
\(236\) | 8.03324 | + | 8.03324i | 0.522920 | + | 0.522920i | ||||
\(237\) | −7.26864 | − | 1.12439i | −0.472149 | − | 0.0730372i | ||||
\(238\) | − | 0.401161i | − | 0.0260034i | ||||||
\(239\) | −5.38574 | − | 5.38574i | −0.348375 | − | 0.348375i | 0.511129 | − | 0.859504i | \(-0.329227\pi\) |
−0.859504 | + | 0.511129i | \(0.829227\pi\) | |||||||
\(240\) | −1.14317 | − | 1.56157i | −0.0737916 | − | 0.100799i | ||||
\(241\) | −6.88932 | − | 6.88932i | −0.443780 | − | 0.443780i | 0.449500 | − | 0.893280i | \(-0.351602\pi\) |
−0.893280 | + | 0.449500i | \(0.851602\pi\) | |||||||
\(242\) | 9.10407 | − | 9.10407i | 0.585232 | − | 0.585232i | ||||
\(243\) | 11.2196 | + | 10.8222i | 0.719738 | + | 0.694246i | ||||
\(244\) | − | 0.717748i | − | 0.0459491i | ||||||
\(245\) | −0.790081 | + | 0.790081i | −0.0504764 | + | 0.0504764i | ||||
\(246\) | 2.53471 | − | 16.3856i | 0.161607 | − | 1.04471i | ||||
\(247\) | 10.8292 | + | 22.4335i | 0.689045 | + | 1.42741i | ||||
\(248\) | 4.07885i | 0.259007i | ||||||||
\(249\) | 2.52015 | + | 3.44253i | 0.159708 | + | 0.218161i | ||||
\(250\) | 9.77847 | 0.618445 | ||||||||
\(251\) | −7.66247 | −0.483651 | −0.241825 | − | 0.970320i | \(-0.577746\pi\) | ||||
−0.241825 | + | 0.970320i | \(0.577746\pi\) | |||||||
\(252\) | 2.66313 | − | 1.38121i | 0.167761 | − | 0.0870080i | ||||
\(253\) | −21.1481 | + | 21.1481i | −1.32957 | + | 1.32957i | ||||
\(254\) | −1.59961 | + | 1.59961i | −0.100368 | + | 0.100368i | ||||
\(255\) | 0.458598 | + | 0.626443i | 0.0287185 | + | 0.0392294i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 16.8782 | 1.05283 | 0.526417 | − | 0.850227i | \(-0.323535\pi\) | ||||
0.526417 | + | 0.850227i | \(0.323535\pi\) | |||||||
\(258\) | −3.83461 | + | 2.80718i | −0.238732 | + | 0.174768i | ||||
\(259\) | 6.34409i | 0.394203i | ||||||||
\(260\) | −1.75134 | − | 3.62804i | −0.108614 | − | 0.225002i | ||||
\(261\) | 1.05628 | − | 3.33245i | 0.0653818 | − | 0.206274i | ||||
\(262\) | −8.99439 | + | 8.99439i | −0.555675 | + | 0.555675i | ||||
\(263\) | 8.93905i | 0.551206i | 0.961272 | + | 0.275603i | \(0.0888774\pi\) | ||||
−0.961272 | + | 0.275603i | \(0.911123\pi\) | |||||||
\(264\) | 1.29379 | − | 8.36370i | 0.0796271 | − | 0.514750i | ||||
\(265\) | 2.73561 | − | 2.73561i | 0.168047 | − | 0.168047i | ||||
\(266\) | −4.88536 | − | 4.88536i | −0.299540 | − | 0.299540i | ||||
\(267\) | −16.8990 | + | 12.3712i | −1.03420 | + | 0.757102i | ||||
\(268\) | −0.693547 | − | 0.693547i | −0.0423651 | − | 0.0423651i | ||||
\(269\) | 12.7919i | 0.779934i | 0.920829 | + | 0.389967i | \(0.127514\pi\) | ||||
−0.920829 | + | 0.389967i | \(0.872486\pi\) | |||||||
\(270\) | −2.57971 | + | 5.20128i | −0.156996 | + | 0.316540i | ||||
\(271\) | 8.84670 | + | 8.84670i | 0.537399 | + | 0.537399i | 0.922764 | − | 0.385365i | \(-0.125925\pi\) |
−0.385365 | + | 0.922764i | \(0.625925\pi\) | |||||||
\(272\) | −0.401161 | −0.0243240 | ||||||||
\(273\) | 5.97294 | − | 1.82318i | 0.361499 | − | 0.110344i | ||||
\(274\) | 21.8484 | 1.31991 | ||||||||
\(275\) | 12.9619 | + | 12.9619i | 0.781630 | + | 0.781630i | ||||
\(276\) | −1.62071 | + | 10.4771i | −0.0975551 | + | 0.630646i | ||||
\(277\) | − | 20.8417i | − | 1.25226i | −0.779720 | − | 0.626128i | \(-0.784639\pi\) | ||
0.779720 | − | 0.626128i | \(-0.215361\pi\) | |||||||
\(278\) | 2.09403 | + | 2.09403i | 0.125592 | + | 0.125592i | ||||
\(279\) | 10.8625 | − | 5.63374i | 0.650321 | − | 0.337283i | ||||
\(280\) | 0.790081 | + | 0.790081i | 0.0472163 | + | 0.0472163i | ||||
\(281\) | −16.1377 | + | 16.1377i | −0.962693 | + | 0.962693i | −0.999329 | − | 0.0366360i | \(-0.988336\pi\) |
0.0366360 | + | 0.999329i | \(0.488336\pi\) | |||||||
\(282\) | −13.7323 | − | 2.12426i | −0.817745 | − | 0.126498i | ||||
\(283\) | 10.2026i | 0.606483i | 0.952914 | + | 0.303242i | \(0.0980690\pi\) | ||||
−0.952914 | + | 0.303242i | \(0.901931\pi\) | |||||||
\(284\) | 5.15463 | − | 5.15463i | 0.305871 | − | 0.305871i | ||||
\(285\) | 13.2137 | + | 2.04403i | 0.782710 | + | 0.121078i | ||||
\(286\) | 5.80318 | − | 16.6343i | 0.343149 | − | 0.983606i | ||||
\(287\) | 9.57276i | 0.565062i | ||||||||
\(288\) | −1.38121 | − | 2.66313i | −0.0813886 | − | 0.156926i | ||||
\(289\) | −16.8391 | −0.990534 | ||||||||
\(290\) | 1.30202 | 0.0764572 | ||||||||
\(291\) | −13.9035 | + | 10.1783i | −0.815040 | + | 0.596663i | ||||
\(292\) | 0.0455596 | − | 0.0455596i | 0.00266618 | − | 0.00266618i | ||||
\(293\) | −21.5130 | + | 21.5130i | −1.25680 | + | 1.25680i | −0.304189 | + | 0.952612i | \(0.598386\pi\) |
−0.952612 | + | 0.304189i | \(0.901614\pi\) | |||||||
\(294\) | −1.39758 | + | 1.02312i | −0.0815085 | + | 0.0596695i | ||||
\(295\) | 12.6938 | 0.739063 | ||||||||
\(296\) | 6.34409 | 0.368743 | ||||||||
\(297\) | −24.0606 | + | 8.10650i | −1.39614 | + | 0.470387i | ||||
\(298\) | − | 5.29497i | − | 0.306730i | ||||||
\(299\) | −7.26955 | + | 20.8375i | −0.420409 | + | 1.20506i | ||||
\(300\) | 6.42149 | + | 0.993346i | 0.370745 | + | 0.0573508i | ||||
\(301\) | 1.94012 | − | 1.94012i | 0.111827 | − | 0.111827i | ||||
\(302\) | 17.1834i | 0.988794i | ||||||||
\(303\) | 5.79490 | + | 0.896418i | 0.332908 | + | 0.0514979i | ||||
\(304\) | −4.88536 | + | 4.88536i | −0.280194 | + | 0.280194i | ||||
\(305\) | −0.567079 | − | 0.567079i | −0.0324709 | − | 0.0324709i | ||||
\(306\) | 0.554088 | + | 1.06834i | 0.0316751 | + | 0.0610732i | ||||
\(307\) | 6.55827 | + | 6.55827i | 0.374300 | + | 0.374300i | 0.869041 | − | 0.494741i | \(-0.164737\pi\) |
−0.494741 | + | 0.869041i | \(0.664737\pi\) | |||||||
\(308\) | 4.88622i | 0.278418i | ||||||||
\(309\) | −3.49405 | + | 22.5873i | −0.198770 | + | 1.28495i | ||||
\(310\) | 3.22262 | + | 3.22262i | 0.183032 | + | 0.183032i | ||||
\(311\) | 13.0914 | 0.742343 | 0.371171 | − | 0.928564i | \(-0.378956\pi\) | ||||
0.371171 | + | 0.928564i | \(0.378956\pi\) | |||||||
\(312\) | −1.82318 | − | 5.97294i | −0.103217 | − | 0.338151i | ||||
\(313\) | 4.62512 | 0.261427 | 0.130714 | − | 0.991420i | \(-0.458273\pi\) | ||||
0.130714 | + | 0.991420i | \(0.458273\pi\) | |||||||
\(314\) | 14.4020 | + | 14.4020i | 0.812750 | + | 0.812750i | ||||
\(315\) | 1.01282 | − | 3.19535i | 0.0570659 | − | 0.180038i | ||||
\(316\) | − | 4.24647i | − | 0.238882i | ||||||
\(317\) | 10.8188 | + | 10.8188i | 0.607643 | + | 0.607643i | 0.942330 | − | 0.334686i | \(-0.108630\pi\) |
−0.334686 | + | 0.942330i | \(0.608630\pi\) | |||||||
\(318\) | 4.83903 | − | 3.54249i | 0.271359 | − | 0.198653i | ||||
\(319\) | 4.02614 | + | 4.02614i | 0.225421 | + | 0.225421i | ||||
\(320\) | 0.790081 | − | 0.790081i | 0.0441668 | − | 0.0441668i | ||||
\(321\) | 5.01712 | − | 32.4332i | 0.280029 | − | 1.81025i | ||||
\(322\) | − | 6.12089i | − | 0.341104i | ||||||
\(323\) | 1.95982 | − | 1.95982i | 0.109047 | − | 0.109047i | ||||
\(324\) | −5.18452 | + | 7.35668i | −0.288029 | + | 0.408705i | ||||
\(325\) | 12.7715 | + | 4.45557i | 0.708435 | + | 0.247151i | ||||
\(326\) | 12.0528i | 0.667542i | ||||||||
\(327\) | −11.4979 | + | 8.41725i | −0.635838 | + | 0.465475i | ||||
\(328\) | 9.57276 | 0.528567 | ||||||||
\(329\) | 8.02263 | 0.442302 | ||||||||
\(330\) | −5.58580 | − | 7.63019i | −0.307488 | − | 0.420028i | ||||
\(331\) | −4.19602 | + | 4.19602i | −0.230634 | + | 0.230634i | −0.812957 | − | 0.582323i | \(-0.802144\pi\) |
0.582323 | + | 0.812957i | \(0.302144\pi\) | |||||||
\(332\) | −1.74175 | + | 1.74175i | −0.0955910 | + | 0.0955910i | ||||
\(333\) | −8.76253 | − | 16.8951i | −0.480183 | − | 0.925848i | ||||
\(334\) | −17.5681 | −0.961284 | ||||||||
\(335\) | −1.09592 | −0.0598763 | ||||||||
\(336\) | 1.02312 | + | 1.39758i | 0.0558157 | + | 0.0762442i | ||||
\(337\) | 13.8715i | 0.755631i | 0.925881 | + | 0.377815i | \(0.123325\pi\) | ||||
−0.925881 | + | 0.377815i | \(0.876675\pi\) | |||||||
\(338\) | −1.47963 | − | 12.9155i | −0.0804815 | − | 0.702512i | ||||
\(339\) | 3.93412 | − | 25.4321i | 0.213672 | − | 1.38128i | ||||
\(340\) | −0.316950 | + | 0.316950i | −0.0171890 | + | 0.0171890i | ||||
\(341\) | 19.9301i | 1.07928i | ||||||||
\(342\) | 19.7580 | + | 6.26263i | 1.06839 | + | 0.338644i | ||||
\(343\) | 0.707107 | − | 0.707107i | 0.0381802 | − | 0.0381802i | ||||
\(344\) | −1.94012 | − | 1.94012i | −0.104604 | − | 0.104604i | ||||
\(345\) | 6.99724 | + | 9.55822i | 0.376719 | + | 0.514597i | ||||
\(346\) | −15.4494 | − | 15.4494i | −0.830562 | − | 0.830562i | ||||
\(347\) | − | 31.5445i | − | 1.69340i | −0.532072 | − | 0.846699i | \(-0.678586\pi\) | ||
0.532072 | − | 0.846699i | \(-0.321414\pi\) | |||||||
\(348\) | 1.99461 | + | 0.308547i | 0.106922 | + | 0.0165399i | ||||
\(349\) | −17.5248 | − | 17.5248i | −0.938083 | − | 0.938083i | 0.0601086 | − | 0.998192i | \(-0.480855\pi\) |
−0.998192 | + | 0.0601086i | \(0.980855\pi\) | |||||||
\(350\) | −3.75155 | −0.200529 | ||||||||
\(351\) | −13.3885 | + | 13.1053i | −0.714626 | + | 0.699507i | ||||
\(352\) | 4.88622 | 0.260436 | ||||||||
\(353\) | 13.8691 | + | 13.8691i | 0.738177 | + | 0.738177i | 0.972225 | − | 0.234048i | \(-0.0751972\pi\) |
−0.234048 | + | 0.972225i | \(0.575197\pi\) | |||||||
\(354\) | 19.4461 | + | 3.00813i | 1.03355 | + | 0.159880i | ||||
\(355\) | − | 8.14514i | − | 0.432299i | ||||||
\(356\) | −8.55005 | − | 8.55005i | −0.453152 | − | 0.453152i | ||||
\(357\) | −0.410436 | − | 0.560655i | −0.0217226 | − | 0.0296730i | ||||
\(358\) | 9.25929 | + | 9.25929i | 0.489369 | + | 0.489369i | ||||
\(359\) | 3.97606 | − | 3.97606i | 0.209848 | − | 0.209848i | −0.594355 | − | 0.804203i | \(-0.702592\pi\) |
0.804203 | + | 0.594355i | \(0.202592\pi\) | |||||||
\(360\) | −3.19535 | − | 1.01282i | −0.168410 | − | 0.0533803i | ||||
\(361\) | − | 28.7334i | − | 1.51228i | ||||||
\(362\) | −13.1958 | + | 13.1958i | −0.693556 | + | 0.693556i | ||||
\(363\) | 3.40911 | − | 22.0382i | 0.178932 | − | 1.15671i | ||||
\(364\) | 1.56742 | + | 3.24703i | 0.0821551 | + | 0.170191i | ||||
\(365\) | − | 0.0719915i | − | 0.00376821i | ||||||
\(366\) | −0.734342 | − | 1.00311i | −0.0383847 | − | 0.0524334i | ||||
\(367\) | −0.717511 | −0.0374538 | −0.0187269 | − | 0.999825i | \(-0.505961\pi\) | ||||
−0.0187269 | + | 0.999825i | \(0.505961\pi\) | |||||||
\(368\) | −6.12089 | −0.319073 | ||||||||
\(369\) | −13.2220 | − | 25.4935i | −0.688309 | − | 1.32714i | ||||
\(370\) | 5.01235 | − | 5.01235i | 0.260579 | − | 0.260579i | ||||
\(371\) | −2.44831 | + | 2.44831i | −0.127110 | + | 0.127110i | ||||
\(372\) | 4.17315 | + | 5.70051i | 0.216368 | + | 0.295558i | ||||
\(373\) | −9.28116 | −0.480560 | −0.240280 | − | 0.970704i | \(-0.577239\pi\) | ||||
−0.240280 | + | 0.970704i | \(0.577239\pi\) | |||||||
\(374\) | −1.96016 | −0.101358 | ||||||||
\(375\) | 13.6662 | − | 10.0045i | 0.705719 | − | 0.516632i | ||||
\(376\) | − | 8.02263i | − | 0.413735i | ||||||
\(377\) | 3.96701 | + | 1.38396i | 0.204311 | + | 0.0712777i | ||||
\(378\) | 2.30879 | − | 4.65505i | 0.118751 | − | 0.239430i | ||||
\(379\) | 12.4251 | − | 12.4251i | 0.638236 | − | 0.638236i | −0.311884 | − | 0.950120i | \(-0.600960\pi\) |
0.950120 | + | 0.311884i | \(0.100960\pi\) | |||||||
\(380\) | 7.71965i | 0.396010i | ||||||||
\(381\) | −0.598989 | + | 3.87217i | −0.0306871 | + | 0.198377i | ||||
\(382\) | 5.10799 | − | 5.10799i | 0.261347 | − | 0.261347i | ||||
\(383\) | −13.7627 | − | 13.7627i | −0.703243 | − | 0.703243i | 0.261863 | − | 0.965105i | \(-0.415663\pi\) |
−0.965105 | + | 0.261863i | \(0.915663\pi\) | |||||||
\(384\) | 1.39758 | − | 1.02312i | 0.0713199 | − | 0.0522108i | ||||
\(385\) | 3.86050 | + | 3.86050i | 0.196749 | + | 0.196749i | ||||
\(386\) | − | 27.0922i | − | 1.37896i | ||||||
\(387\) | −2.48708 | + | 7.84652i | −0.126426 | + | 0.398861i | ||||
\(388\) | −7.03452 | − | 7.03452i | −0.357123 | − | 0.357123i | ||||
\(389\) | −4.94989 | −0.250970 | −0.125485 | − | 0.992096i | \(-0.540049\pi\) | ||||
−0.125485 | + | 0.992096i | \(0.540049\pi\) | |||||||
\(390\) | −6.15956 | − | 3.27864i | −0.311902 | − | 0.166021i | ||||
\(391\) | 2.45546 | 0.124178 | ||||||||
\(392\) | −0.707107 | − | 0.707107i | −0.0357143 | − | 0.0357143i | ||||
\(393\) | −3.36804 | + | 21.7727i | −0.169895 | + | 1.09829i | ||||
\(394\) | 24.2345i | 1.22092i | ||||||||
\(395\) | −3.35505 | − | 3.35505i | −0.168811 | − | 0.168811i | ||||
\(396\) | −6.74889 | − | 13.0126i | −0.339144 | − | 0.653909i | ||||
\(397\) | 9.83277 | + | 9.83277i | 0.493493 | + | 0.493493i | 0.909405 | − | 0.415912i | \(-0.136538\pi\) |
−0.415912 | + | 0.909405i | \(0.636538\pi\) | |||||||
\(398\) | −6.89523 | + | 6.89523i | −0.345627 | + | 0.345627i | ||||
\(399\) | −11.8260 | − | 1.82937i | −0.592039 | − | 0.0915830i | ||||
\(400\) | 3.75155i | 0.187577i | ||||||||
\(401\) | −1.18747 | + | 1.18747i | −0.0592992 | + | 0.0592992i | −0.736134 | − | 0.676835i | \(-0.763351\pi\) |
0.676835 | + | 0.736134i | \(0.263351\pi\) | |||||||
\(402\) | −1.67887 | − | 0.259706i | −0.0837343 | − | 0.0129529i | ||||
\(403\) | 6.39326 | + | 13.2441i | 0.318471 | + | 0.659737i | ||||
\(404\) | 3.38548i | 0.168434i | ||||||||
\(405\) | 1.71618 | + | 9.90856i | 0.0852778 | + | 0.492360i | ||||
\(406\) | −1.16528 | −0.0578320 | ||||||||
\(407\) | 30.9986 | 1.53654 | ||||||||
\(408\) | −0.560655 | + | 0.410436i | −0.0277565 | + | 0.0203196i | ||||
\(409\) | −1.16592 | + | 1.16592i | −0.0576512 | + | 0.0576512i | −0.735345 | − | 0.677693i | \(-0.762980\pi\) |
0.677693 | + | 0.735345i | \(0.262980\pi\) | |||||||
\(410\) | 7.56325 | − | 7.56325i | 0.373522 | − | 0.373522i | ||||
\(411\) | 30.5348 | − | 22.3535i | 1.50617 | − | 1.10262i | ||||
\(412\) | −13.1959 | −0.650116 | ||||||||
\(413\) | −11.3607 | −0.559025 | ||||||||
\(414\) | 8.45423 | + | 16.3007i | 0.415503 | + | 0.801137i | ||||
\(415\) | 2.75225i | 0.135102i | ||||||||
\(416\) | 3.24703 | − | 1.56742i | 0.159199 | − | 0.0768491i | ||||
\(417\) | 5.06902 | + | 0.784131i | 0.248231 | + | 0.0383991i | ||||
\(418\) | −23.8709 | + | 23.8709i | −1.16756 | + | 1.16756i | ||||
\(419\) | − | 13.3819i | − | 0.653748i | −0.945068 | − | 0.326874i | \(-0.894005\pi\) | ||
0.945068 | − | 0.326874i | \(-0.105995\pi\) | |||||||
\(420\) | 1.91255 | + | 0.295853i | 0.0933227 | + | 0.0144362i | ||||
\(421\) | −25.6047 | + | 25.6047i | −1.24790 | + | 1.24790i | −0.291253 | + | 0.956646i | \(0.594072\pi\) |
−0.956646 | + | 0.291253i | \(0.905928\pi\) | |||||||
\(422\) | 5.17642 | + | 5.17642i | 0.251984 | + | 0.251984i | ||||
\(423\) | −21.3653 | + | 11.0809i | −1.03882 | + | 0.538773i | ||||
\(424\) | 2.44831 | + | 2.44831i | 0.118901 | + | 0.118901i | ||||
\(425\) | − | 1.50498i | − | 0.0730020i | ||||||
\(426\) | 1.93020 | − | 12.4778i | 0.0935186 | − | 0.604551i | ||||
\(427\) | 0.507525 | + | 0.507525i | 0.0245608 | + | 0.0245608i | ||||
\(428\) | 18.9481 | 0.915889 | ||||||||
\(429\) | −8.90845 | − | 29.1851i | −0.430104 | − | 1.40907i | ||||
\(430\) | −3.06571 | −0.147842 | ||||||||
\(431\) | 1.57749 | + | 1.57749i | 0.0759852 | + | 0.0759852i | 0.744078 | − | 0.668093i | \(-0.232889\pi\) |
−0.668093 | + | 0.744078i | \(0.732889\pi\) | |||||||
\(432\) | −4.65505 | − | 2.30879i | −0.223966 | − | 0.111082i | ||||
\(433\) | 4.98342i | 0.239488i | 0.992805 | + | 0.119744i | \(0.0382074\pi\) | ||||
−0.992805 | + | 0.119744i | \(0.961793\pi\) | |||||||
\(434\) | −2.88418 | − | 2.88418i | −0.138445 | − | 0.138445i | ||||
\(435\) | 1.81968 | − | 1.33212i | 0.0872468 | − | 0.0638703i | ||||
\(436\) | −5.81740 | − | 5.81740i | −0.278603 | − | 0.278603i | ||||
\(437\) | 29.9027 | − | 29.9027i | 1.43044 | − | 1.43044i | ||||
\(438\) | 0.0170602 | − | 0.110286i | 0.000815170 | − | 0.00526967i | ||||
\(439\) | − | 16.2436i | − | 0.775265i | −0.921814 | − | 0.387633i | \(-0.873293\pi\) | ||
0.921814 | − | 0.387633i | \(-0.126707\pi\) | |||||||
\(440\) | 3.86050 | − | 3.86050i | 0.184042 | − | 0.184042i | ||||
\(441\) | −0.906454 | + | 2.85978i | −0.0431645 | + | 0.136180i | ||||
\(442\) | −1.30258 | + | 0.628788i | −0.0619575 | + | 0.0299084i | ||||
\(443\) | 36.6212i | 1.73993i | 0.493115 | + | 0.869964i | \(0.335858\pi\) | ||||
−0.493115 | + | 0.869964i | \(0.664142\pi\) | |||||||
\(444\) | 8.86637 | − | 6.49076i | 0.420779 | − | 0.308038i | ||||
\(445\) | −13.5105 | −0.640457 | ||||||||
\(446\) | −7.56150 | −0.358047 | ||||||||
\(447\) | −5.41739 | − | 7.40014i | −0.256234 | − | 0.350015i | ||||
\(448\) | −0.707107 | + | 0.707107i | −0.0334077 | + | 0.0334077i | ||||
\(449\) | 15.8676 | − | 15.8676i | 0.748839 | − | 0.748839i | −0.225422 | − | 0.974261i | \(-0.572376\pi\) |
0.974261 | + | 0.225422i | \(0.0723762\pi\) | |||||||
\(450\) | 9.99085 | − | 5.18167i | 0.470973 | − | 0.244266i | ||||
\(451\) | 46.7746 | 2.20253 | ||||||||
\(452\) | 14.8579 | 0.698856 | ||||||||
\(453\) | 17.5807 | + | 24.0152i | 0.826012 | + | 1.12833i | ||||
\(454\) | 4.42570i | 0.207708i | ||||||||
\(455\) | 3.80380 | + | 1.32703i | 0.178325 | + | 0.0622120i | ||||
\(456\) | −1.82937 | + | 11.8260i | −0.0856681 | + | 0.553802i | ||||
\(457\) | 4.36244 | − | 4.36244i | 0.204066 | − | 0.204066i | −0.597673 | − | 0.801740i | \(-0.703908\pi\) |
0.801740 | + | 0.597673i | \(0.203908\pi\) | |||||||
\(458\) | − | 25.9487i | − | 1.21250i | ||||||
\(459\) | 1.86743 | + | 0.926198i | 0.0871640 | + | 0.0432312i | ||||
\(460\) | −4.83599 | + | 4.83599i | −0.225479 | + | 0.225479i | ||||
\(461\) | −10.1936 | − | 10.1936i | −0.474762 | − | 0.474762i | 0.428690 | − | 0.903452i | \(-0.358975\pi\) |
−0.903452 | + | 0.428690i | \(0.858975\pi\) | |||||||
\(462\) | 4.99918 | + | 6.82887i | 0.232583 | + | 0.317708i | ||||
\(463\) | −26.1202 | − | 26.1202i | −1.21391 | − | 1.21391i | −0.969730 | − | 0.244181i | \(-0.921481\pi\) |
−0.244181 | − | 0.969730i | \(-0.578519\pi\) | |||||||
\(464\) | 1.16528i | 0.0540969i | ||||||||
\(465\) | 7.80098 | + | 1.20674i | 0.361762 | + | 0.0559613i | ||||
\(466\) | −7.94927 | − | 7.94927i | −0.368243 | − | 0.368243i | ||||
\(467\) | 12.0016 | 0.555368 | 0.277684 | − | 0.960673i | \(-0.410433\pi\) | ||||
0.277684 | + | 0.960673i | \(0.410433\pi\) | |||||||
\(468\) | −8.65907 | − | 6.48232i | −0.400266 | − | 0.299646i | ||||
\(469\) | 0.980824 | 0.0452902 | ||||||||
\(470\) | −6.33852 | − | 6.33852i | −0.292374 | − | 0.292374i | ||||
\(471\) | 34.8628 | + | 5.39296i | 1.60639 | + | 0.248494i | ||||
\(472\) | 11.3607i | 0.522920i | ||||||||
\(473\) | −9.47986 | − | 9.47986i | −0.435885 | − | 0.435885i | ||||
\(474\) | −4.34464 | − | 5.93477i | −0.199556 | − | 0.272593i | ||||
\(475\) | −18.3276 | − | 18.3276i | −0.840930 | − | 0.840930i | ||||
\(476\) | 0.283664 | − | 0.283664i | 0.0130017 | − | 0.0130017i | ||||
\(477\) | 3.13854 | − | 9.90181i | 0.143704 | − | 0.453373i | ||||
\(478\) | − | 7.61659i | − | 0.348375i | ||||||
\(479\) | −27.0032 | + | 27.0032i | −1.23381 | + | 1.23381i | −0.271317 | + | 0.962490i | \(0.587459\pi\) |
−0.962490 | + | 0.271317i | \(0.912541\pi\) | |||||||
\(480\) | 0.295853 | − | 1.91255i | 0.0135038 | − | 0.0872954i | ||||
\(481\) | 20.5995 | − | 9.94386i | 0.939254 | − | 0.453401i | ||||
\(482\) | − | 9.74296i | − | 0.443780i | ||||||
\(483\) | −6.26240 | − | 8.55442i | −0.284949 | − | 0.389240i | ||||
\(484\) | 12.8751 | 0.585232 | ||||||||
\(485\) | −11.1157 | −0.504736 | ||||||||
\(486\) | 0.280987 | + | 15.5859i | 0.0127458 | + | 0.706992i | ||||
\(487\) | −25.0734 | + | 25.0734i | −1.13618 | + | 1.13618i | −0.147055 | + | 0.989128i | \(0.546980\pi\) |
−0.989128 | + | 0.147055i | \(0.953020\pi\) | |||||||
\(488\) | 0.507525 | − | 0.507525i | 0.0229746 | − | 0.0229746i | ||||
\(489\) | 12.3314 | + | 16.8447i | 0.557647 | + | 0.761745i | ||||
\(490\) | −1.11734 | −0.0504764 | ||||||||
\(491\) | 5.26963 | 0.237815 | 0.118907 | − | 0.992905i | \(-0.462061\pi\) | ||||
0.118907 | + | 0.992905i | \(0.462061\pi\) | |||||||
\(492\) | 13.3787 | − | 9.79407i | 0.603158 | − | 0.441551i | ||||
\(493\) | − | 0.467466i | − | 0.0210536i | ||||||
\(494\) | −8.20549 | + | 23.5203i | −0.369182 | + | 1.05823i | ||||
\(495\) | −15.6132 | − | 4.94886i | −0.701761 | − | 0.222435i | ||||
\(496\) | −2.88418 | + | 2.88418i | −0.129503 | + | 0.129503i | ||||
\(497\) | 7.28975i | 0.326990i | ||||||||
\(498\) | −0.652216 | + | 4.21625i | −0.0292265 | + | 0.188935i | ||||
\(499\) | 2.56674 | − | 2.56674i | 0.114903 | − | 0.114903i | −0.647317 | − | 0.762221i | \(-0.724109\pi\) |
0.762221 | + | 0.647317i | \(0.224109\pi\) | |||||||
\(500\) | 6.91443 | + | 6.91443i | 0.309223 | + | 0.309223i | ||||
\(501\) | −24.5528 | + | 17.9743i | −1.09694 | + | 0.803031i | ||||
\(502\) | −5.41818 | − | 5.41818i | −0.241825 | − | 0.241825i | ||||
\(503\) | − | 9.03215i | − | 0.402724i | −0.979517 | − | 0.201362i | \(-0.935463\pi\) | ||
0.979517 | − | 0.201362i | \(-0.0645367\pi\) | |||||||
\(504\) | 2.85978 | + | 0.906454i | 0.127385 | + | 0.0403767i | ||||
\(505\) | 2.67480 | + | 2.67480i | 0.119027 | + | 0.119027i | ||||
\(506\) | −29.9080 | −1.32957 | ||||||||
\(507\) | −15.2820 | − | 16.5366i | −0.678698 | − | 0.734417i | ||||
\(508\) | −2.26219 | −0.100368 | ||||||||
\(509\) | −13.7882 | − | 13.7882i | −0.611152 | − | 0.611152i | 0.332094 | − | 0.943246i | \(-0.392245\pi\) |
−0.943246 | + | 0.332094i | \(0.892245\pi\) | |||||||
\(510\) | −0.118685 | + | 0.767240i | −0.00525546 | + | 0.0339740i | ||||
\(511\) | 0.0644310i | 0.00285026i | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 34.0208 | − | 11.4623i | 1.50206 | − | 0.506073i | ||||
\(514\) | 11.9347 | + | 11.9347i | 0.526417 | + | 0.526417i | ||||
\(515\) | −10.4258 | + | 10.4258i | −0.459417 | + | 0.459417i | ||||
\(516\) | −4.69645 | − | 0.726498i | −0.206750 | − | 0.0319823i | ||||
\(517\) | − | 39.2003i | − | 1.72403i | ||||||
\(518\) | −4.48595 | + | 4.48595i | −0.197101 | + | 0.197101i | ||||
\(519\) | −37.3982 | − | 5.78516i | −1.64160 | − | 0.253940i | ||||
\(520\) | 1.32703 | − | 3.80380i | 0.0581940 | − | 0.166808i | ||||
\(521\) | − | 23.1627i | − | 1.01477i | −0.861718 | − | 0.507387i | \(-0.830611\pi\) | ||
0.861718 | − | 0.507387i | \(-0.169389\pi\) | |||||||
\(522\) | 3.10330 | − | 1.60950i | 0.135828 | − | 0.0704459i | ||||
\(523\) | 32.4378 | 1.41840 | 0.709202 | − | 0.705005i | \(-0.249055\pi\) | ||||
0.709202 | + | 0.705005i | \(0.249055\pi\) | |||||||
\(524\) | −12.7200 | −0.555675 | ||||||||
\(525\) | −5.24308 | + | 3.83828i | −0.228827 | + | 0.167516i | ||||
\(526\) | −6.32086 | + | 6.32086i | −0.275603 | + | 0.275603i | ||||
\(527\) | 1.15702 | − | 1.15702i | 0.0504007 | − | 0.0504007i | ||||
\(528\) | 6.82887 | − | 4.99918i | 0.297189 | − | 0.217561i | ||||
\(529\) | 14.4653 | 0.628925 | ||||||||
\(530\) | 3.86873 | 0.168047 | ||||||||
\(531\) | 30.2551 | − | 15.6915i | 1.31296 | − | 0.680955i | ||||
\(532\) | − | 6.90894i | − | 0.299540i | ||||||
\(533\) | 31.0830 | − | 15.0045i | 1.34636 | − | 0.649918i | ||||
\(534\) | −20.6971 | − | 3.20165i | −0.895651 | − | 0.138549i | ||||
\(535\) | 14.9705 | − | 14.9705i | 0.647231 | − | 0.647231i | ||||
\(536\) | − | 0.980824i | − | 0.0423651i | ||||||
\(537\) | 22.4139 | + | 3.46723i | 0.967233 | + | 0.149622i | ||||
\(538\) | −9.04522 | + | 9.04522i | −0.389967 | + | 0.389967i | ||||
\(539\) | −3.45508 | − | 3.45508i | −0.148821 | − | 0.148821i | ||||
\(540\) | −5.50200 | + | 1.85373i | −0.236768 | + | 0.0797719i | ||||
\(541\) | −4.03020 | − | 4.03020i | −0.173272 | − | 0.173272i | 0.615143 | − | 0.788415i | \(-0.289098\pi\) |
−0.788415 | + | 0.615143i | \(0.789098\pi\) | |||||||
\(542\) | 12.5111i | 0.537399i | ||||||||
\(543\) | −4.94130 | + | 31.9431i | −0.212051 | + | 1.37081i | ||||
\(544\) | −0.283664 | − | 0.283664i | −0.0121620 | − | 0.0121620i | ||||
\(545\) | −9.19243 | −0.393760 | ||||||||
\(546\) | 5.51269 | + | 2.93432i | 0.235921 | + | 0.125577i | ||||
\(547\) | −26.2318 | −1.12159 | −0.560795 | − | 0.827955i | \(-0.689505\pi\) | ||||
−0.560795 | + | 0.827955i | \(0.689505\pi\) | |||||||
\(548\) | 15.4491 | + | 15.4491i | 0.659955 | + | 0.659955i | ||||
\(549\) | −2.05260 | − | 0.650606i | −0.0876029 | − | 0.0277672i | ||||
\(550\) | 18.3309i | 0.781630i | ||||||||
\(551\) | −5.69282 | − | 5.69282i | −0.242522 | − | 0.242522i | ||||
\(552\) | −8.55442 | + | 6.26240i | −0.364100 | + | 0.266545i | ||||
\(553\) | 3.00271 | + | 3.00271i | 0.127688 | + | 0.127688i | ||||
\(554\) | 14.7373 | − | 14.7373i | 0.626128 | − | 0.626128i | ||||
\(555\) | 1.87692 | − | 12.1334i | 0.0796709 | − | 0.515033i | ||||
\(556\) | 2.96141i | 0.125592i | ||||||||
\(557\) | −16.9451 | + | 16.9451i | −0.717988 | + | 0.717988i | −0.968193 | − | 0.250205i | \(-0.919502\pi\) |
0.250205 | + | 0.968193i | \(0.419502\pi\) | |||||||
\(558\) | 11.6646 | + | 3.69729i | 0.493802 | + | 0.156519i | ||||
\(559\) | −9.34063 | − | 3.25865i | −0.395066 | − | 0.137826i | ||||
\(560\) | 1.11734i | 0.0472163i | ||||||||
\(561\) | −2.73948 | + | 2.00548i | −0.115661 | + | 0.0846714i | ||||
\(562\) | −22.8221 | −0.962693 | ||||||||
\(563\) | −43.2433 | −1.82249 | −0.911243 | − | 0.411869i | \(-0.864876\pi\) | ||||
−0.911243 | + | 0.411869i | \(0.864876\pi\) | |||||||
\(564\) | −8.20810 | − | 11.2123i | −0.345623 | − | 0.472121i | ||||
\(565\) | 11.7389 | − | 11.7389i | 0.493860 | − | 0.493860i | ||||
\(566\) | −7.21435 | + | 7.21435i | −0.303242 | + | 0.303242i | ||||
\(567\) | −1.53595 | − | 8.86797i | −0.0645039 | − | 0.372420i | ||||
\(568\) | 7.28975 | 0.305871 | ||||||||
\(569\) | −12.0354 | −0.504549 | −0.252274 | − | 0.967656i | \(-0.581179\pi\) | ||||
−0.252274 | + | 0.967656i | \(0.581179\pi\) | |||||||
\(570\) | 7.89812 | + | 10.7888i | 0.330816 | + | 0.451894i | ||||
\(571\) | − | 35.0986i | − | 1.46883i | −0.678699 | − | 0.734416i | \(-0.737456\pi\) | ||
0.678699 | − | 0.734416i | \(-0.262544\pi\) | |||||||
\(572\) | 15.8657 | − | 7.65875i | 0.663378 | − | 0.320228i | ||||
\(573\) | 1.91274 | − | 12.3649i | 0.0799057 | − | 0.516551i | ||||
\(574\) | −6.76896 | + | 6.76896i | −0.282531 | + | 0.282531i | ||||
\(575\) | − | 22.9628i | − | 0.957615i | ||||||
\(576\) | 0.906454 | − | 2.85978i | 0.0377689 | − | 0.119157i | ||||
\(577\) | 8.36869 | − | 8.36869i | 0.348393 | − | 0.348393i | −0.511118 | − | 0.859511i | \(-0.670768\pi\) |
0.859511 | + | 0.511118i | \(0.170768\pi\) | |||||||
\(578\) | −11.9070 | − | 11.9070i | −0.495267 | − | 0.495267i | ||||
\(579\) | −27.7185 | − | 37.8635i | −1.15194 | − | 1.57355i | ||||
\(580\) | 0.920667 | + | 0.920667i | 0.0382286 | + | 0.0382286i | ||||
\(581\) | − | 2.46321i | − | 0.102191i | ||||||
\(582\) | −17.0284 | − | 2.63414i | −0.705851 | − | 0.109189i | ||||
\(583\) | 11.9630 | + | 11.9630i | 0.495456 | + | 0.495456i | ||||
\(584\) | 0.0644310 | 0.00266618 | ||||||||
\(585\) | −11.9629 | + | 1.71980i | −0.494606 | + | 0.0711051i | ||||
\(586\) | −30.4239 | −1.25680 | ||||||||
\(587\) | 23.2366 | + | 23.2366i | 0.959076 | + | 0.959076i | 0.999195 | − | 0.0401193i | \(-0.0127738\pi\) |
−0.0401193 | + | 0.999195i | \(0.512774\pi\) | |||||||
\(588\) | −1.71169 | − | 0.264783i | −0.0705890 | − | 0.0109195i | ||||
\(589\) | − | 28.1805i | − | 1.16116i | ||||||
\(590\) | 8.97589 | + | 8.97589i | 0.369531 | + | 0.369531i | ||||
\(591\) | 24.7948 | + | 33.8696i | 1.01992 | + | 1.39321i | ||||
\(592\) | 4.48595 | + | 4.48595i | 0.184371 | + | 0.184371i | ||||
\(593\) | 14.2518 | − | 14.2518i | 0.585250 | − | 0.585250i | −0.351091 | − | 0.936341i | \(-0.614189\pi\) |
0.936341 | + | 0.351091i | \(0.114189\pi\) | |||||||
\(594\) | −22.7456 | − | 11.2813i | −0.933262 | − | 0.462875i | ||||
\(595\) | − | 0.448235i | − | 0.0183758i | ||||||
\(596\) | 3.74411 | − | 3.74411i | 0.153365 | − | 0.153365i | ||||
\(597\) | −2.58199 | + | 16.6913i | −0.105674 | + | 0.683128i | ||||
\(598\) | −19.8747 | + | 9.59400i | −0.812737 | + | 0.392328i | ||||
\(599\) | 13.6271i | 0.556787i | 0.960467 | + | 0.278394i | \(0.0898020\pi\) | ||||
−0.960467 | + | 0.278394i | \(0.910198\pi\) | |||||||
\(600\) | 3.83828 | + | 5.24308i | 0.156697 | + | 0.214048i | ||||
\(601\) | −8.52974 | −0.347936 | −0.173968 | − | 0.984751i | \(-0.555659\pi\) | ||||
−0.173968 | + | 0.984751i | \(0.555659\pi\) | |||||||
\(602\) | 2.74375 | 0.111827 | ||||||||
\(603\) | −2.61206 | + | 1.35472i | −0.106371 | + | 0.0551686i | ||||
\(604\) | −12.1505 | + | 12.1505i | −0.494397 | + | 0.494397i | ||||
\(605\) | 10.1724 | − | 10.1724i | 0.413566 | − | 0.413566i | ||||
\(606\) | 3.46375 | + | 4.73148i | 0.140705 | + | 0.192203i | ||||
\(607\) | −7.46360 | −0.302938 | −0.151469 | − | 0.988462i | \(-0.548400\pi\) | ||||
−0.151469 | + | 0.988462i | \(0.548400\pi\) | |||||||
\(608\) | −6.90894 | −0.280194 | ||||||||
\(609\) | −1.62857 | + | 1.19222i | −0.0659932 | + | 0.0483113i | ||||
\(610\) | − | 0.801971i | − | 0.0324709i | ||||||
\(611\) | −12.5748 | − | 26.0497i | −0.508723 | − | 1.05386i | ||||
\(612\) | −0.363634 | + | 1.14723i | −0.0146991 | + | 0.0463742i | ||||
\(613\) | 30.4690 | − | 30.4690i | 1.23063 | − | 1.23063i | 0.266910 | − | 0.963721i | \(-0.413997\pi\) |
0.963721 | − | 0.266910i | \(-0.0860026\pi\) | |||||||
\(614\) | 9.27479i | 0.374300i | ||||||||
\(615\) | 2.83213 | − | 18.3083i | 0.114203 | − | 0.738264i | ||||
\(616\) | −3.45508 | + | 3.45508i | −0.139209 | + | 0.139209i | ||||
\(617\) | −21.2814 | − | 21.2814i | −0.856755 | − | 0.856755i | 0.134199 | − | 0.990954i | \(-0.457154\pi\) |
−0.990954 | + | 0.134199i | \(0.957154\pi\) | |||||||
\(618\) | −18.4423 | + | 13.5010i | −0.741859 | + | 0.543089i | ||||
\(619\) | 1.08316 | + | 1.08316i | 0.0435359 | + | 0.0435359i | 0.728540 | − | 0.685004i | \(-0.240199\pi\) |
−0.685004 | + | 0.728540i | \(0.740199\pi\) | |||||||
\(620\) | 4.55747i | 0.183032i | ||||||||
\(621\) | 28.4930 | + | 14.1319i | 1.14339 | + | 0.567092i | ||||
\(622\) | 9.25699 | + | 9.25699i | 0.371171 | + | 0.371171i | ||||
\(623\) | 12.0916 | 0.484440 | ||||||||
\(624\) | 2.93432 | − | 5.51269i | 0.117467 | − | 0.220684i | ||||
\(625\) | −7.83182 | −0.313273 | ||||||||
\(626\) | 3.27045 | + | 3.27045i | 0.130714 | + | 0.130714i | ||||
\(627\) | −8.93869 | + | 57.7842i | −0.356977 | + | 2.30768i | ||||
\(628\) | 20.3675i | 0.812750i | ||||||||
\(629\) | −1.79959 | − | 1.79959i | −0.0717544 | − | 0.0717544i | ||||
\(630\) | 2.97563 | − | 1.54328i | 0.118552 | − | 0.0614859i | ||||
\(631\) | −7.38311 | − | 7.38311i | −0.293917 | − | 0.293917i | 0.544709 | − | 0.838625i | \(-0.316640\pi\) |
−0.838625 | + | 0.544709i | \(0.816640\pi\) | |||||||
\(632\) | 3.00271 | − | 3.00271i | 0.119441 | − | 0.119441i | ||||
\(633\) | 12.5305 | + | 1.93836i | 0.498044 | + | 0.0770429i | ||||
\(634\) | 15.3001i | 0.607643i | ||||||||
\(635\) | −1.78731 | + | 1.78731i | −0.0709272 | + | 0.0709272i | ||||
\(636\) | 5.92663 | + | 0.916795i | 0.235006 | + | 0.0363533i | ||||
\(637\) | −3.40433 | − | 1.18766i | −0.134884 | − | 0.0470569i | ||||
\(638\) | 5.69382i | 0.225421i | ||||||||
\(639\) | −10.0687 | − | 19.4135i | −0.398310 | − | 0.767988i | ||||
\(640\) | 1.11734 | 0.0441668 | ||||||||
\(641\) | −18.4812 | −0.729964 | −0.364982 | − | 0.931015i | \(-0.618925\pi\) | ||||
−0.364982 | + | 0.931015i | \(0.618925\pi\) | |||||||
\(642\) | 26.4814 | − | 19.3861i | 1.04514 | − | 0.765109i | ||||
\(643\) | 29.6076 | − | 29.6076i | 1.16761 | − | 1.16761i | 0.184844 | − | 0.982768i | \(-0.440822\pi\) |
0.982768 | − | 0.184844i | \(-0.0591779\pi\) | |||||||
\(644\) | 4.32812 | − | 4.32812i | 0.170552 | − | 0.170552i | ||||
\(645\) | −4.28457 | + | 3.13659i | −0.168705 | + | 0.123503i | ||||
\(646\) | 2.77160 | 0.109047 | ||||||||
\(647\) | 22.8592 | 0.898690 | 0.449345 | − | 0.893358i | \(-0.351657\pi\) | ||||
0.449345 | + | 0.893358i | \(0.351657\pi\) | |||||||
\(648\) | −8.86797 | + | 1.53595i | −0.348367 | + | 0.0603378i | ||||
\(649\) | 55.5109i | 2.17900i | ||||||||
\(650\) | 5.88024 | + | 12.1814i | 0.230642 | + | 0.477793i | ||||
\(651\) | −6.98173 | − | 1.08001i | −0.273636 | − | 0.0423289i | ||||
\(652\) | −8.52261 | + | 8.52261i | −0.333771 | + | 0.333771i | ||||
\(653\) | 20.8455i | 0.815748i | 0.913038 | + | 0.407874i | \(0.133730\pi\) | ||||
−0.913038 | + | 0.407874i | \(0.866270\pi\) | |||||||
\(654\) | −14.0822 | − | 2.17838i | −0.550656 | − | 0.0851815i | ||||
\(655\) | −10.0498 | + | 10.0498i | −0.392679 | + | 0.392679i | ||||
\(656\) | 6.76896 | + | 6.76896i | 0.264284 | + | 0.264284i | ||||
\(657\) | −0.0889928 | − | 0.171588i | −0.00347194 | − | 0.00669429i | ||||
\(658\) | 5.67285 | + | 5.67285i | 0.221151 | + | 0.221151i | ||||
\(659\) | − | 20.6669i | − | 0.805067i | −0.915405 | − | 0.402534i | \(-0.868130\pi\) | ||
0.915405 | − | 0.402534i | \(-0.131870\pi\) | |||||||
\(660\) | 1.44560 | − | 9.34511i | 0.0562700 | − | 0.363758i | ||||
\(661\) | 8.65092 | + | 8.65092i | 0.336482 | + | 0.336482i | 0.855041 | − | 0.518560i | \(-0.173532\pi\) |
−0.518560 | + | 0.855041i | \(0.673532\pi\) | |||||||
\(662\) | −5.93406 | −0.230634 | ||||||||
\(663\) | −1.17714 | + | 2.21148i | −0.0457162 | + | 0.0858867i | ||||
\(664\) | −2.46321 | −0.0955910 | ||||||||
\(665\) | −5.45862 | − | 5.45862i | −0.211676 | − | 0.211676i | ||||
\(666\) | 5.75063 | − | 18.1427i | 0.222832 | − | 0.703016i | ||||
\(667\) | − | 7.13256i | − | 0.276174i | ||||||
\(668\) | −12.4225 | − | 12.4225i | −0.480642 | − | 0.480642i | ||||
\(669\) | −10.5678 | + | 7.73631i | −0.408574 | + | 0.299103i | ||||
\(670\) | −0.774930 | − | 0.774930i | −0.0299381 | − | 0.0299381i | ||||
\(671\) | 2.47988 | − | 2.47988i | 0.0957345 | − | 0.0957345i | ||||
\(672\) | −0.264783 | + | 1.71169i | −0.0102142 | + | 0.0660300i | ||||
\(673\) | 31.6297i | 1.21924i | 0.792696 | + | 0.609618i | \(0.208677\pi\) | ||||
−0.792696 | + | 0.609618i | \(0.791323\pi\) | |||||||
\(674\) | −9.80866 | + | 9.80866i | −0.377815 | + | 0.377815i | ||||
\(675\) | 8.66154 | − | 17.4636i | 0.333383 | − | 0.672175i | ||||
\(676\) | 8.08639 | − | 10.1789i | 0.311015 | − | 0.391497i | ||||
\(677\) | − | 13.4729i | − | 0.517805i | −0.965903 | − | 0.258903i | \(-0.916639\pi\) | ||
0.965903 | − | 0.258903i | \(-0.0833609\pi\) | |||||||
\(678\) | 20.7651 | − | 15.2014i | 0.797478 | − | 0.583806i | ||||
\(679\) | 9.94831 | 0.381781 | ||||||||
\(680\) | −0.448235 | −0.0171890 | ||||||||
\(681\) | 4.52802 | + | 6.18526i | 0.173514 | + | 0.237020i | ||||
\(682\) | −14.0927 | + | 14.0927i | −0.539638 | + | 0.539638i | ||||
\(683\) | 4.78530 | − | 4.78530i | 0.183104 | − | 0.183104i | −0.609603 | − | 0.792707i | \(-0.708671\pi\) |
0.792707 | + | 0.609603i | \(0.208671\pi\) | |||||||
\(684\) | 9.54269 | + | 18.3994i | 0.364874 | + | 0.703518i | ||||
\(685\) | 24.4121 | 0.932739 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −26.5486 | − | 36.2653i | −1.01289 | − | 1.38361i | ||||
\(688\) | − | 2.74375i | − | 0.104604i | ||||||
\(689\) | 11.7873 | + | 4.11221i | 0.449060 | + | 0.156663i | ||||
\(690\) | −1.81089 | + | 11.7065i | −0.0689392 | + | 0.445658i | ||||
\(691\) | 23.2258 | − | 23.2258i | 0.883552 | − | 0.883552i | −0.110342 | − | 0.993894i | \(-0.535195\pi\) |
0.993894 | + | 0.110342i | \(0.0351946\pi\) | |||||||
\(692\) | − | 21.8487i | − | 0.830562i | ||||||
\(693\) | 13.9735 | + | 4.42913i | 0.530809 | + | 0.168249i | ||||
\(694\) | 22.3053 | − | 22.3053i | 0.846699 | − | 0.846699i | ||||
\(695\) | 2.33975 | + | 2.33975i | 0.0887519 | + | 0.0887519i | ||||
\(696\) | 1.19222 | + | 1.62857i | 0.0451911 | + | 0.0617310i | ||||
\(697\) | −2.71545 | − | 2.71545i | −0.102855 | − | 0.102855i | ||||
\(698\) | − | 24.7839i | − | 0.938083i | ||||||
\(699\) | −19.2428 | − | 2.97668i | −0.727829 | − | 0.112589i | ||||
\(700\) | −2.65274 | − | 2.65274i | −0.100264 | − | 0.100264i | ||||
\(701\) | 4.56217 | 0.172311 | 0.0861554 | − | 0.996282i | \(-0.472542\pi\) | ||||
0.0861554 | + | 0.996282i | \(0.472542\pi\) | |||||||
\(702\) | −18.7339 | − | 0.200301i | −0.707066 | − | 0.00755986i | ||||
\(703\) | −43.8309 | −1.65312 | ||||||||
\(704\) | 3.45508 | + | 3.45508i | 0.130218 | + | 0.130218i | ||||
\(705\) | −15.3436 | − | 2.37352i | −0.577875 | − | 0.0893920i | ||||
\(706\) | 19.6139i | 0.738177i | ||||||||
\(707\) | −2.39390 | − | 2.39390i | −0.0900318 | − | 0.0900318i | ||||
\(708\) | 11.6234 | + | 15.8775i | 0.436833 | + | 0.596713i | ||||
\(709\) | −6.99329 | − | 6.99329i | −0.262638 | − | 0.262638i | 0.563487 | − | 0.826125i | \(-0.309460\pi\) |
−0.826125 | + | 0.563487i | \(0.809460\pi\) | |||||||
\(710\) | 5.75949 | − | 5.75949i | 0.216150 | − | 0.216150i | ||||
\(711\) | −12.1440 | − | 3.84923i | −0.455434 | − | 0.144357i | ||||
\(712\) | − | 12.0916i | − | 0.453152i | ||||||
\(713\) | 17.6537 | − | 17.6537i | 0.661138 | − | 0.661138i | ||||
\(714\) | 0.106221 | − | 0.686665i | 0.00397521 | − | 0.0256978i | ||||
\(715\) | 6.48414 | − | 18.5862i | 0.242493 | − | 0.695084i | ||||
\(716\) | 13.0946i | 0.489369i | ||||||||
\(717\) | −7.79268 | − | 10.6448i | −0.291023 | − | 0.397537i | ||||
\(718\) | 5.62299 | 0.209848 | ||||||||
\(719\) | −16.1959 | −0.604005 | −0.302002 | − | 0.953307i | \(-0.597655\pi\) | ||||
−0.302002 | + | 0.953307i | \(0.597655\pi\) | |||||||
\(720\) | −1.54328 | − | 2.97563i | −0.0575148 | − | 0.110895i | ||||
\(721\) | 9.33092 | − | 9.33092i | 0.347502 | − | 0.347502i | ||||
\(722\) | 20.3176 | − | 20.3176i | 0.756142 | − | 0.756142i | ||||
\(723\) | −9.96821 | − | 13.6166i | −0.370722 | − | 0.506405i | ||||
\(724\) | −18.6617 | −0.693556 | ||||||||
\(725\) | −4.37161 | −0.162358 | ||||||||
\(726\) | 17.9940 | − | 13.1728i | 0.667819 | − | 0.488887i | ||||
\(727\) | 11.3030i | 0.419205i | 0.977787 | + | 0.209602i | \(0.0672169\pi\) | ||||
−0.977787 | + | 0.209602i | \(0.932783\pi\) | |||||||
\(728\) | −1.18766 | + | 3.40433i | −0.0440177 | + | 0.126173i | ||||
\(729\) | 16.3390 | + | 21.4951i | 0.605147 | + | 0.796114i | ||||
\(730\) | 0.0509057 | − | 0.0509057i | 0.00188410 | − | 0.00188410i | ||||
\(731\) | 1.10069i | 0.0407104i | ||||||||
\(732\) | 0.190048 | − | 1.22856i | 0.00702436 | − | 0.0454090i | ||||
\(733\) | −9.73470 | + | 9.73470i | −0.359559 | + | 0.359559i | −0.863650 | − | 0.504091i | \(-0.831828\pi\) |
0.504091 | + | 0.863650i | \(0.331828\pi\) | |||||||
\(734\) | −0.507357 | − | 0.507357i | −0.0187269 | − | 0.0187269i | ||||
\(735\) | −1.56157 | + | 1.14317i | −0.0575995 | + | 0.0421666i | ||||
\(736\) | −4.32812 | − | 4.32812i | −0.159537 | − | 0.159537i | ||||
\(737\) | − | 4.79252i | − | 0.176535i | ||||||
\(738\) | 8.67727 | − | 27.3760i | 0.319415 | − | 1.00772i | ||||
\(739\) | 36.2462 | + | 36.2462i | 1.33334 | + | 1.33334i | 0.902366 | + | 0.430971i | \(0.141829\pi\) |
0.430971 | + | 0.902366i | \(0.358171\pi\) | |||||||
\(740\) | 7.08853 | 0.260579 | ||||||||
\(741\) | 12.5962 | + | 41.2667i | 0.462734 | + | 1.51597i | ||||
\(742\) | −3.46244 | −0.127110 | ||||||||
\(743\) | −2.02620 | − | 2.02620i | −0.0743340 | − | 0.0743340i | 0.668962 | − | 0.743296i | \(-0.266739\pi\) |
−0.743296 | + | 0.668962i | \(0.766739\pi\) | |||||||
\(744\) | −1.08001 | + | 6.98173i | −0.0395951 | + | 0.255963i | ||||
\(745\) | − | 5.91630i | − | 0.216756i | ||||||
\(746\) | −6.56277 | − | 6.56277i | −0.240280 | − | 0.240280i | ||||
\(747\) | 3.40221 | + | 6.55984i | 0.124480 | + | 0.240012i | ||||
\(748\) | −1.38604 | − | 1.38604i | −0.0506788 | − | 0.0506788i | ||||
\(749\) | −13.3983 | + | 13.3983i | −0.489563 | + | 0.489563i | ||||
\(750\) | 16.7377 | + | 2.58917i | 0.611176 | + | 0.0945433i | ||||
\(751\) | 21.0845i | 0.769385i | 0.923045 | + | 0.384692i | \(0.125692\pi\) | ||||
−0.923045 | + | 0.384692i | \(0.874308\pi\) | |||||||
\(752\) | 5.67285 | − | 5.67285i | 0.206868 | − | 0.206868i | ||||
\(753\) | −13.1158 | − | 2.02889i | −0.477966 | − | 0.0739369i | ||||
\(754\) | 1.82649 | + | 3.78371i | 0.0665167 | + | 0.137794i | ||||
\(755\) | 19.1998i | 0.698751i | ||||||||
\(756\) | 4.92418 | − | 1.65905i | 0.179091 | − | 0.0603392i | ||||
\(757\) | 6.62915 | 0.240941 | 0.120470 | − | 0.992717i | \(-0.461560\pi\) | ||||
0.120470 | + | 0.992717i | \(0.461560\pi\) | |||||||
\(758\) | 17.5718 | 0.638236 | ||||||||
\(759\) | −41.7988 | + | 30.5994i | −1.51720 | + | 1.11069i | ||||
\(760\) | −5.45862 | + | 5.45862i | −0.198005 | + | 0.198005i | ||||
\(761\) | 13.3011 | − | 13.3011i | 0.482165 | − | 0.482165i | −0.423658 | − | 0.905822i | \(-0.639254\pi\) |
0.905822 | + | 0.423658i | \(0.139254\pi\) | |||||||
\(762\) | −3.16158 | + | 2.31449i | −0.114532 | + | 0.0838450i | ||||
\(763\) | 8.22704 | 0.297839 | ||||||||
\(764\) | 7.22379 | 0.261347 | ||||||||
\(765\) | 0.619106 | + | 1.19371i | 0.0223838 | + | 0.0431586i | ||||
\(766\) | − | 19.4634i | − | 0.703243i | ||||||
\(767\) | 17.8070 | + | 36.8886i | 0.642974 | + | 1.33197i | ||||
\(768\) | 1.71169 | + | 0.264783i | 0.0617654 | + | 0.00955454i | ||||
\(769\) | −30.0658 | + | 30.0658i | −1.08420 | + | 1.08420i | −0.0880872 | + | 0.996113i | \(0.528075\pi\) |
−0.996113 | + | 0.0880872i | \(0.971925\pi\) | |||||||
\(770\) | 5.45958i | 0.196749i | ||||||||
\(771\) | 28.8903 | + | 4.46906i | 1.04046 | + | 0.160949i | ||||
\(772\) | 19.1571 | − | 19.1571i | 0.689478 | − | 0.689478i | ||||
\(773\) | −9.37726 | − | 9.37726i | −0.337276 | − | 0.337276i | 0.518065 | − | 0.855341i | \(-0.326653\pi\) |
−0.855341 | + | 0.518065i | \(0.826653\pi\) | |||||||
\(774\) | −7.30696 | + | 3.78969i | −0.262643 | + | 0.136218i | ||||
\(775\) | −10.8201 | − | 10.8201i | −0.388671 | − | 0.388671i | ||||
\(776\) | − | 9.94831i | − | 0.357123i | ||||||
\(777\) | −1.67981 | + | 10.8591i | −0.0602628 | + | 0.389569i | ||||
\(778\) | −3.50010 | − | 3.50010i | −0.125485 | − | 0.125485i | ||||
\(779\) | −66.1376 | −2.36963 | ||||||||
\(780\) | −2.03712 | − | 6.67382i | −0.0729405 | − | 0.238961i | ||||
\(781\) | 35.6193 | 1.27456 | ||||||||
\(782\) | 1.73628 | + | 1.73628i | 0.0620891 | + | 0.0620891i | ||||
\(783\) | 2.69040 | − | 5.42445i | 0.0961469 | − | 0.193854i | ||||
\(784\) | − | 1.00000i | − | 0.0357143i | ||||||
\(785\) | 16.0919 | + | 16.0919i | 0.574345 | + | 0.574345i | ||||
\(786\) | −17.7772 | + | 13.0141i | −0.634091 | + | 0.464196i | ||||
\(787\) | 19.9564 | + | 19.9564i | 0.711370 | + | 0.711370i | 0.966822 | − | 0.255452i | \(-0.0822242\pi\) |
−0.255452 | + | 0.966822i | \(0.582224\pi\) | |||||||
\(788\) | −17.1364 | + | 17.1364i | −0.610458 | + | 0.610458i | ||||
\(789\) | −2.36691 | + | 15.3009i | −0.0842642 | + | 0.544727i | ||||
\(790\) | − | 4.74476i | − | 0.168811i | ||||||
\(791\) | −10.5061 | + | 10.5061i | −0.373554 | + | 0.373554i | ||||
\(792\) | 4.42913 | − | 13.9735i | 0.157382 | − | 0.496527i | ||||
\(793\) | 0.852444 | − | 2.44345i | 0.0302712 | − | 0.0867695i | ||||
\(794\) | 13.9056i | 0.493493i | ||||||||
\(795\) | 5.40686 | − | 3.95817i | 0.191761 | − | 0.140382i | ||||
\(796\) | −9.75133 | −0.345627 | ||||||||
\(797\) | 45.7135 | 1.61926 | 0.809628 | − | 0.586943i | \(-0.199669\pi\) | ||||
0.809628 | + | 0.586943i | \(0.199669\pi\) | |||||||
\(798\) | −7.06867 | − | 9.65578i | −0.250228 | − | 0.341811i | ||||
\(799\) | −2.27573 | + | 2.27573i | −0.0805095 | + | 0.0805095i | ||||
\(800\) | −2.65274 | + | 2.65274i | −0.0937886 | + | 0.0937886i | ||||
\(801\) | −32.2015 | + | 16.7010i | −1.13778 | + | 0.590102i | ||||
\(802\) | −1.67933 | −0.0592992 | ||||||||
\(803\) | 0.314824 | 0.0111099 | ||||||||
\(804\) | −1.00350 | − | 1.37078i | −0.0353907 | − | 0.0483436i | ||||
\(805\) | − | 6.83913i | − | 0.241048i | ||||||
\(806\) | −4.84430 | + | 13.8857i | −0.170633 | + | 0.489104i | ||||
\(807\) | −3.38707 | + | 21.8958i | −0.119231 | + | 0.770767i | ||||
\(808\) | −2.39390 | + | 2.39390i | −0.0842170 | + | 0.0842170i | ||||
\(809\) | 4.26659i | 0.150005i | 0.997183 | + | 0.0750026i | \(0.0238965\pi\) | ||||
−0.997183 | + | 0.0750026i | \(0.976103\pi\) | |||||||
\(810\) | −5.79288 | + | 8.21993i | −0.203541 | + | 0.288819i | ||||
\(811\) | −32.9674 | + | 32.9674i | −1.15764 | + | 1.15764i | −0.172660 | + | 0.984981i | \(0.555236\pi\) |
−0.984981 | + | 0.172660i | \(0.944764\pi\) | |||||||
\(812\) | −0.823979 | − | 0.823979i | −0.0289160 | − | 0.0289160i | ||||
\(813\) | 12.8004 | + | 17.4853i | 0.448929 | + | 0.613236i | ||||
\(814\) | 21.9193 | + | 21.9193i | 0.768272 | + | 0.768272i | ||||
\(815\) | 13.4671i | 0.471732i | ||||||||
\(816\) | −0.686665 | − | 0.106221i | −0.0240381 | − | 0.00371847i | ||||
\(817\) | 13.4042 | + | 13.4042i | 0.468953 | + | 0.468953i | ||||
\(818\) | −1.64886 | −0.0576512 | ||||||||
\(819\) | 10.7066 | − | 1.53919i | 0.374118 | − | 0.0537837i | ||||
\(820\) | 10.6961 | 0.373522 | ||||||||
\(821\) | 17.3300 | + | 17.3300i | 0.604822 | + | 0.604822i | 0.941588 | − | 0.336766i | \(-0.109333\pi\) |
−0.336766 | + | 0.941588i | \(0.609333\pi\) | |||||||
\(822\) | 37.3977 | + | 5.78508i | 1.30439 | + | 0.201778i | ||||
\(823\) | 39.4252i | 1.37428i | 0.726526 | + | 0.687139i | \(0.241134\pi\) | ||||
−0.726526 | + | 0.687139i | \(0.758866\pi\) | |||||||
\(824\) | −9.33092 | − | 9.33092i | −0.325058 | − | 0.325058i | ||||
\(825\) | 18.7547 | + | 25.6188i | 0.652953 | + | 0.891933i | ||||
\(826\) | −8.03324 | − | 8.03324i | −0.279512 | − | 0.279512i | ||||
\(827\) | 18.4845 | − | 18.4845i | 0.642768 | − | 0.642768i | −0.308467 | − | 0.951235i | \(-0.599816\pi\) |
0.951235 | + | 0.308467i | \(0.0998160\pi\) | |||||||
\(828\) | −5.54830 | + | 17.5044i | −0.192817 | + | 0.608320i | ||||
\(829\) | − | 12.9895i | − | 0.451143i | −0.974227 | − | 0.225571i | \(-0.927575\pi\) | ||
0.974227 | − | 0.225571i | \(-0.0724248\pi\) | |||||||
\(830\) | −1.94613 | + | 1.94613i | −0.0675512 | + | 0.0675512i | ||||
\(831\) | 5.51853 | − | 35.6746i | 0.191436 | − | 1.23754i | ||||
\(832\) | 3.40433 | + | 1.18766i | 0.118024 | + | 0.0411748i | ||||
\(833\) | 0.401161i | 0.0138994i | ||||||||
\(834\) | 3.02988 | + | 4.13880i | 0.104916 | + | 0.143315i | ||||
\(835\) | −19.6296 | −0.679310 | ||||||||
\(836\) | −33.7586 | −1.16756 | ||||||||
\(837\) | 20.0850 | − | 6.76703i | 0.694238 | − | 0.233903i | ||||
\(838\) | 9.46243 | − | 9.46243i | 0.326874 | − | 0.326874i | ||||
\(839\) | 3.51977 | − | 3.51977i | 0.121516 | − | 0.121516i | −0.643734 | − | 0.765250i | \(-0.722616\pi\) |
0.765250 | + | 0.643734i | \(0.222616\pi\) | |||||||
\(840\) | 1.14317 | + | 1.56157i | 0.0394433 | + | 0.0538794i | ||||
\(841\) | 27.6421 | 0.953176 | ||||||||
\(842\) | −36.2106 | −1.24790 | ||||||||
\(843\) | −31.8957 | + | 23.3497i | −1.09855 | + | 0.804208i | ||||
\(844\) | 7.32056i | 0.251984i | ||||||||
\(845\) | −1.65326 | − | 14.4311i | −0.0568738 | − | 0.496444i | ||||
\(846\) | −22.9429 | − | 7.27214i | −0.788795 | − | 0.250021i | ||||
\(847\) | −9.10407 | + | 9.10407i | −0.312820 | + | 0.312820i | ||||
\(848\) | 3.46244i | 0.118901i | ||||||||
\(849\) | −2.70148 | + | 17.4638i | −0.0927147 | + | 0.599355i | ||||
\(850\) | 1.06418 | − | 1.06418i | 0.0365010 | − | 0.0365010i | ||||
\(851\) | −27.4580 | − | 27.4580i | −0.941248 | − | 0.941248i | ||||
\(852\) | 10.1880 | − | 7.45828i | 0.349035 | − | 0.255516i | ||||
\(853\) | 22.3026 | + | 22.3026i | 0.763626 | + | 0.763626i | 0.976976 | − | 0.213350i | \(-0.0684373\pi\) |
−0.213350 | + | 0.976976i | \(0.568437\pi\) | |||||||
\(854\) | 0.717748i | 0.0245608i | ||||||||
\(855\) | 22.0765 | + | 6.99751i | 0.755000 | + | 0.239310i | ||||
\(856\) | 13.3983 | + | 13.3983i | 0.457944 | + | 0.457944i | ||||
\(857\) | −0.612444 | −0.0209207 | −0.0104603 | − | 0.999945i | \(-0.503330\pi\) | ||||
−0.0104603 | + | 0.999945i | \(0.503330\pi\) | |||||||
\(858\) | 14.3377 | − | 26.9362i | 0.489482 | − | 0.919586i | ||||
\(859\) | 26.4751 | 0.903319 | 0.451659 | − | 0.892190i | \(-0.350832\pi\) | ||||
0.451659 | + | 0.892190i | \(0.350832\pi\) | |||||||
\(860\) | −2.16778 | − | 2.16778i | −0.0739208 | − | 0.0739208i | ||||
\(861\) | −2.53471 | + | 16.3856i | −0.0863825 | + | 0.558420i | ||||
\(862\) | 2.23091i | 0.0759852i | ||||||||
\(863\) | 36.8495 | + | 36.8495i | 1.25437 | + | 1.25437i | 0.953741 | + | 0.300630i | \(0.0971968\pi\) |
0.300630 | + | 0.953741i | \(0.402803\pi\) | |||||||
\(864\) | −1.65905 | − | 4.92418i | −0.0564422 | − | 0.167524i | ||||
\(865\) | −17.2622 | − | 17.2622i | −0.586933 | − | 0.586933i | ||||
\(866\) | −3.52381 | + | 3.52381i | −0.119744 | + | 0.119744i | ||||
\(867\) | −28.8233 | − | 4.45870i | −0.978891 | − | 0.151425i | ||||
\(868\) | − | 4.07885i | − | 0.138445i | ||||||
\(869\) | 14.6719 | − | 14.6719i | 0.497709 | − | 0.497709i | ||||
\(870\) | 2.22866 | + | 0.344753i | 0.0755586 | + | 0.0116882i | ||||
\(871\) | −1.53736 | − | 3.18476i | −0.0520915 | − | 0.107912i | ||||
\(872\) | − | 8.22704i | − | 0.278603i | ||||||
\(873\) | −26.4936 | + | 13.7407i | −0.896674 | + | 0.465052i | ||||
\(874\) | 42.2888 | 1.43044 | ||||||||
\(875\) | −9.77847 | −0.330573 | ||||||||
\(876\) | 0.0900475 | − | 0.0659206i | 0.00304242 | − | 0.00222725i | ||||
\(877\) | 39.5160 | − | 39.5160i | 1.33436 | − | 1.33436i | 0.432934 | − | 0.901426i | \(-0.357478\pi\) |
0.901426 | − | 0.432934i | \(-0.142522\pi\) | |||||||
\(878\) | 11.4860 | − | 11.4860i | 0.387633 | − | 0.387633i | ||||
\(879\) | −42.5198 | + | 31.1273i | −1.43416 | + | 1.04990i | ||||
\(880\) | 5.45958 | 0.184042 | ||||||||
\(881\) | −12.5247 | −0.421968 | −0.210984 | − | 0.977489i | \(-0.567667\pi\) | ||||
−0.210984 | + | 0.977489i | \(0.567667\pi\) | |||||||
\(882\) | −2.66313 | + | 1.38121i | −0.0896722 | + | 0.0465078i | ||||
\(883\) | − | 54.3967i | − | 1.83059i | −0.402780 | − | 0.915297i | \(-0.631956\pi\) | ||
0.402780 | − | 0.915297i | \(-0.368044\pi\) | |||||||
\(884\) | −1.36569 | − | 0.476445i | −0.0459330 | − | 0.0160246i | ||||
\(885\) | 21.7279 | + | 3.36111i | 0.730376 | + | 0.112982i | ||||
\(886\) | −25.8951 | + | 25.8951i | −0.869964 | + | 0.869964i | ||||
\(887\) | − | 17.4377i | − | 0.585499i | −0.956189 | − | 0.292750i | \(-0.905430\pi\) | ||
0.956189 | − | 0.292750i | \(-0.0945702\pi\) | |||||||
\(888\) | 10.8591 | + | 1.67981i | 0.364409 | + | 0.0563707i | ||||
\(889\) | 1.59961 | − | 1.59961i | 0.0536491 | − | 0.0536491i | ||||
\(890\) | −9.55334 | − | 9.55334i | −0.320229 | − | 0.320229i | ||||
\(891\) | −43.3308 | + | 7.50499i | −1.45164 | + | 0.251426i | ||||
\(892\) | −5.34679 | − | 5.34679i | −0.179024 | − | 0.179024i | ||||
\(893\) | 55.4278i | 1.85482i | ||||||||
\(894\) | 1.40202 | − | 9.06337i | 0.0468905 | − | 0.303124i | ||||
\(895\) | 10.3458 | + | 10.3458i | 0.345822 | + | 0.345822i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −17.9607 | + | 33.7426i | −0.599689 | + | 1.12663i | ||||
\(898\) | 22.4402 | 0.748839 | ||||||||
\(899\) | −3.36088 | − | 3.36088i | −0.112092 | − | 0.112092i | ||||
\(900\) | 10.7286 | + | 3.40060i | 0.357620 | + | 0.113353i | ||||
\(901\) | − | 1.38900i | − | 0.0462742i | ||||||
\(902\) | 33.0746 | + | 33.0746i | 1.10126 | + | 1.10126i | ||||
\(903\) | 3.83461 | − | 2.80718i | 0.127608 | − | 0.0934172i | ||||
\(904\) | 10.5061 | + | 10.5061i | 0.349428 | + | 0.349428i | ||||
\(905\) | −14.7442 | + | 14.7442i | −0.490115 | + | 0.490115i | ||||
\(906\) | −4.54988 | + | 29.4127i | −0.151160 | + | 0.977172i | ||||
\(907\) | 8.21025i | 0.272617i | 0.990666 | + | 0.136308i | \(0.0435238\pi\) | ||||
−0.990666 | + | 0.136308i | \(0.956476\pi\) | |||||||
\(908\) | −3.12944 | + | 3.12944i | −0.103854 | + | 0.103854i | ||||
\(909\) | 9.68173 | + | 3.06878i | 0.321123 | + | 0.101785i | ||||
\(910\) | 1.75134 | + | 3.62804i | 0.0580565 | + | 0.120268i | ||||
\(911\) | 12.8821i | 0.426803i | 0.976965 | + | 0.213401i | \(0.0684542\pi\) | ||||
−0.976965 | + | 0.213401i | \(0.931546\pi\) | |||||||
\(912\) | −9.65578 | + | 7.06867i | −0.319735 | + | 0.234067i | ||||
\(913\) | −12.0358 | −0.398326 | ||||||||
\(914\) | 6.16942 | 0.204066 | ||||||||
\(915\) | −0.820512 | − | 1.12082i | −0.0271253 | − | 0.0370531i | ||||
\(916\) | 18.3485 | − | 18.3485i | 0.606251 | − | 0.606251i | ||||
\(917\) | 8.99439 | − | 8.99439i | 0.297021 | − | 0.297021i | ||||
\(918\) | 0.665549 | + | 1.97539i | 0.0219664 | + | 0.0651976i | ||||
\(919\) | −9.54855 | −0.314978 | −0.157489 | − | 0.987521i | \(-0.550340\pi\) | ||||
−0.157489 | + | 0.987521i | \(0.550340\pi\) | |||||||
\(920\) | −6.83913 | −0.225479 | ||||||||
\(921\) | 9.48921 | + | 12.9622i | 0.312680 | + | 0.427121i | ||||
\(922\) | − | 14.4159i | − | 0.474762i | ||||||
\(923\) | 23.6700 | − | 11.4261i | 0.779108 | − | 0.376094i | ||||
\(924\) | −1.29379 | + | 8.36370i | −0.0425625 | + | 0.275145i | ||||
\(925\) | −16.8293 | + | 16.8293i | −0.553342 | + | 0.553342i | ||||
\(926\) | − | 36.9396i | − | 1.21391i | ||||||
\(927\) | −11.9615 | + | 37.7374i | −0.392867 | + | 1.23946i | ||||
\(928\) | −0.823979 | + | 0.823979i | −0.0270484 | + | 0.0270484i | ||||
\(929\) | 16.1245 | + | 16.1245i | 0.529029 | + | 0.529029i | 0.920283 | − | 0.391254i | \(-0.127959\pi\) |
−0.391254 | + | 0.920283i | \(0.627959\pi\) | |||||||
\(930\) | 4.66283 | + | 6.36942i | 0.152900 | + | 0.208862i | ||||
\(931\) | 4.88536 | + | 4.88536i | 0.160111 | + | 0.160111i | ||||
\(932\) | − | 11.2420i | − | 0.368243i | ||||||
\(933\) | 22.4084 | + | 3.46637i | 0.733617 | + | 0.113484i | ||||
\(934\) | 8.48641 | + | 8.48641i | 0.277684 | + | 0.277684i | ||||
\(935\) | −2.19017 | −0.0716263 | ||||||||
\(936\) | −1.53919 | − | 10.7066i | −0.0503100 | − | 0.349956i | ||||
\(937\) | −6.42931 | −0.210037 | −0.105018 | − | 0.994470i | \(-0.533490\pi\) | ||||
−0.105018 | + | 0.994470i | \(0.533490\pi\) | |||||||
\(938\) | 0.693547 | + | 0.693547i | 0.0226451 | + | 0.0226451i | ||||
\(939\) | 7.91678 | + | 1.22465i | 0.258354 | + | 0.0399651i | ||||
\(940\) | − | 8.96402i | − | 0.292374i | ||||||
\(941\) | 2.88070 | + | 2.88070i | 0.0939081 | + | 0.0939081i | 0.752500 | − | 0.658592i | \(-0.228848\pi\) |
−0.658592 | + | 0.752500i | \(0.728848\pi\) | |||||||
\(942\) | 20.8383 | + | 28.4651i | 0.678949 | + | 0.927444i | ||||
\(943\) | −41.4321 | − | 41.4321i | −1.34921 | − | 1.34921i | ||||
\(944\) | −8.03324 | + | 8.03324i | −0.261460 | + | 0.261460i | ||||
\(945\) | 2.57971 | − | 5.20128i | 0.0839180 | − | 0.169198i | ||||
\(946\) | − | 13.4066i | − | 0.435885i | ||||||
\(947\) | 28.0551 | − | 28.0551i | 0.911669 | − | 0.911669i | −0.0847346 | − | 0.996404i | \(-0.527004\pi\) |
0.996404 | + | 0.0847346i | \(0.0270042\pi\) | |||||||
\(948\) | 1.12439 | − | 7.26864i | 0.0365186 | − | 0.236075i | ||||
\(949\) | 0.209209 | − | 0.100990i | 0.00679123 | − | 0.00327829i | ||||
\(950\) | − | 25.9192i | − | 0.840930i | ||||||
\(951\) | 15.6538 | + | 21.3830i | 0.507609 | + | 0.693393i | ||||
\(952\) | 0.401161 | 0.0130017 | ||||||||
\(953\) | 9.21108 | 0.298376 | 0.149188 | − | 0.988809i | \(-0.452334\pi\) | ||||
0.149188 | + | 0.988809i | \(0.452334\pi\) | |||||||
\(954\) | 9.22092 | − | 4.78235i | 0.298538 | − | 0.154834i | ||||
\(955\) | 5.70737 | − | 5.70737i | 0.184686 | − | 0.184686i | ||||
\(956\) | 5.38574 | − | 5.38574i | 0.174187 | − | 0.174187i | ||||
\(957\) | 5.82546 | + | 7.95757i | 0.188310 | + | 0.257232i | ||||
\(958\) | −38.1883 | −1.23381 | ||||||||
\(959\) | −21.8484 | −0.705521 | ||||||||
\(960\) | 1.56157 | − | 1.14317i | 0.0503996 | − | 0.0368958i | ||||
\(961\) | 14.3630i | 0.463323i | ||||||||
\(962\) | 21.5974 | + | 7.53465i | 0.696328 | + | 0.242927i | ||||
\(963\) | 17.1755 | − | 54.1873i | 0.553474 | − | 1.74616i | ||||
\(964\) | 6.88932 | − | 6.88932i | 0.221890 | − | 0.221890i | ||||
\(965\) | − | 30.2712i | − | 0.974466i | ||||||
\(966\) | 1.62071 | − | 10.4771i | 0.0521454 | − | 0.337094i | ||||
\(967\) | −18.1772 | + | 18.1772i | −0.584539 | + | 0.584539i | −0.936147 | − | 0.351608i | \(-0.885635\pi\) |
0.351608 | + | 0.936147i | \(0.385635\pi\) | |||||||
\(968\) | 9.10407 | + | 9.10407i | 0.292616 | + | 0.292616i | ||||
\(969\) | 3.87353 | − | 2.83568i | 0.124436 | − | 0.0910950i | ||||
\(970\) | −7.85996 | − | 7.85996i | −0.252368 | − | 0.252368i | ||||
\(971\) | − | 12.9466i | − | 0.415476i | −0.978184 | − | 0.207738i | \(-0.933390\pi\) | ||
0.978184 | − | 0.207738i | \(-0.0666102\pi\) | |||||||
\(972\) | −10.8222 | + | 11.2196i | −0.347123 | + | 0.359869i | ||||
\(973\) | −2.09403 | − | 2.09403i | −0.0671316 | − | 0.0671316i | ||||
\(974\) | −35.4591 | −1.13618 | ||||||||
\(975\) | 20.6811 | + | 11.0082i | 0.662325 | + | 0.352546i | ||||
\(976\) | 0.717748 | 0.0229746 | ||||||||
\(977\) | −6.63981 | − | 6.63981i | −0.212426 | − | 0.212426i | 0.592871 | − | 0.805297i | \(-0.297994\pi\) |
−0.805297 | + | 0.592871i | \(0.797994\pi\) | |||||||
\(978\) | −3.19138 | + | 20.6307i | −0.102049 | + | 0.659696i | ||||
\(979\) | − | 59.0822i | − | 1.88827i | ||||||
\(980\) | −0.790081 | − | 0.790081i | −0.0252382 | − | 0.0252382i | ||||
\(981\) | −21.9097 | + | 11.3633i | −0.699522 | + | 0.362801i | ||||
\(982\) | 3.72619 | + | 3.72619i | 0.118907 | + | 0.118907i | ||||
\(983\) | 19.2743 | − | 19.2743i | 0.614756 | − | 0.614756i | −0.329426 | − | 0.944181i | \(-0.606855\pi\) |
0.944181 | + | 0.329426i | \(0.106855\pi\) | |||||||
\(984\) | 16.3856 | + | 2.53471i | 0.522354 | + | 0.0808034i | ||||
\(985\) | 27.0782i | 0.862784i | ||||||||
\(986\) | 0.330549 | − | 0.330549i | 0.0105268 | − | 0.0105268i | ||||
\(987\) | 13.7323 | + | 2.12426i | 0.437103 | + | 0.0676158i | ||||
\(988\) | −22.4335 | + | 10.8292i | −0.713705 | + | 0.344523i | ||||
\(989\) | 16.7942i | 0.534024i | ||||||||
\(990\) | −7.54082 | − | 14.5396i | −0.239663 | − | 0.462098i | ||||
\(991\) | −26.9609 | −0.856442 | −0.428221 | − | 0.903674i | \(-0.640859\pi\) | ||||
−0.428221 | + | 0.903674i | \(0.640859\pi\) | |||||||
\(992\) | −4.07885 | −0.129503 | ||||||||
\(993\) | −8.29332 | + | 6.07126i | −0.263181 | + | 0.192665i | ||||
\(994\) | −5.15463 | + | 5.15463i | −0.163495 | + | 0.163495i | ||||
\(995\) | −7.70434 | + | 7.70434i | −0.244244 | + | 0.244244i | ||||
\(996\) | −3.44253 | + | 2.52015i | −0.109081 | + | 0.0798541i | ||||
\(997\) | 48.0588 | 1.52204 | 0.761018 | − | 0.648730i | \(-0.224700\pi\) | ||||
0.761018 | + | 0.648730i | \(0.224700\pi\) | |||||||
\(998\) | 3.62992 | 0.114903 | ||||||||
\(999\) | −10.5252 | − | 31.2395i | −0.333002 | − | 0.988373i |
(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.p.c.239.10 | ✓ | 20 | |
3.2 | odd | 2 | 546.2.p.d.239.5 | yes | 20 | ||
13.8 | odd | 4 | 546.2.p.d.281.5 | yes | 20 | ||
39.8 | even | 4 | inner | 546.2.p.c.281.10 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.p.c.239.10 | ✓ | 20 | 1.1 | even | 1 | trivial | |
546.2.p.c.281.10 | yes | 20 | 39.8 | even | 4 | inner | |
546.2.p.d.239.5 | yes | 20 | 3.2 | odd | 2 | ||
546.2.p.d.281.5 | yes | 20 | 13.8 | odd | 4 |