Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(25,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.bj (of order \(6\), 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: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 11x^{14} + 88x^{12} - 303x^{10} + 758x^{8} - 968x^{6} + 867x^{4} - 30x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 25.7 | ||
Root | \(1.34967 + 0.779232i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.25 |
Dual form | 273.2.bj.c.142.7 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.34967 | − | 0.779232i | 0.954360 | − | 0.551000i | 0.0599273 | − | 0.998203i | \(-0.480913\pi\) |
0.894433 | + | 0.447203i | \(0.147580\pi\) | |||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0.214404 | − | 0.371358i | 0.107202 | − | 0.185679i | ||||
\(5\) | −1.85159 | + | 1.06902i | −0.828057 | + | 0.478079i | −0.853187 | − | 0.521605i | \(-0.825333\pi\) |
0.0251298 | + | 0.999684i | \(0.492000\pi\) | |||||||
\(6\) | 1.55846i | 0.636240i | ||||||||
\(7\) | 1.34967 | + | 2.27561i | 0.510127 | + | 0.860099i | ||||
\(8\) | 2.44865i | 0.865727i | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −1.66602 | + | 2.88564i | −0.526843 | + | 0.912519i | ||||
\(11\) | 4.76616 | + | 2.75174i | 1.43705 | + | 0.829682i | 0.997644 | − | 0.0686064i | \(-0.0218553\pi\) |
0.439407 | + | 0.898288i | \(0.355189\pi\) | |||||||
\(12\) | 0.214404 | + | 0.371358i | 0.0618930 | + | 0.107202i | ||||
\(13\) | −2.90324 | − | 2.13803i | −0.805214 | − | 0.592984i | ||||
\(14\) | 3.59483 | + | 2.01961i | 0.960759 | + | 0.539764i | ||||
\(15\) | − | 2.13803i | − | 0.552038i | ||||||
\(16\) | 2.33687 | + | 4.04758i | 0.584217 | + | 1.01189i | ||||
\(17\) | 3.71730 | − | 6.43855i | 0.901577 | − | 1.56158i | 0.0761300 | − | 0.997098i | \(-0.475744\pi\) |
0.825447 | − | 0.564479i | \(-0.190923\pi\) | |||||||
\(18\) | −1.34967 | − | 0.779232i | −0.318120 | − | 0.183667i | ||||
\(19\) | −3.20126 | + | 1.84825i | −0.734420 | + | 0.424017i | −0.820037 | − | 0.572311i | \(-0.806047\pi\) |
0.0856172 | + | 0.996328i | \(0.472714\pi\) | |||||||
\(20\) | 0.916805i | 0.205004i | ||||||||
\(21\) | −2.64557 | + | 0.0310431i | −0.577311 | + | 0.00677416i | ||||
\(22\) | 8.57698 | 1.82862 | ||||||||
\(23\) | −1.88525 | − | 3.26535i | −0.393102 | − | 0.680872i | 0.599755 | − | 0.800184i | \(-0.295265\pi\) |
−0.992857 | + | 0.119312i | \(0.961931\pi\) | |||||||
\(24\) | −2.12059 | − | 1.22432i | −0.432863 | − | 0.249914i | ||||
\(25\) | −0.214404 | + | 0.371358i | −0.0428808 | + | 0.0742716i | ||||
\(26\) | −5.58444 | − | 0.623342i | −1.09520 | − | 0.122247i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.13444 | − | 0.0133115i | 0.214389 | − | 0.00251564i | ||||
\(29\) | 0.903241 | 0.167728 | 0.0838638 | − | 0.996477i | \(-0.473274\pi\) | ||||
0.0838638 | + | 0.996477i | \(0.473274\pi\) | |||||||
\(30\) | −1.66602 | − | 2.88564i | −0.304173 | − | 0.526843i | ||||
\(31\) | 2.62251 | + | 1.51411i | 0.471017 | + | 0.271942i | 0.716665 | − | 0.697417i | \(-0.245667\pi\) |
−0.245648 | + | 0.969359i | \(0.579001\pi\) | |||||||
\(32\) | 2.06682 | + | 1.19328i | 0.365366 | + | 0.210944i | ||||
\(33\) | −4.76616 | + | 2.75174i | −0.829682 | + | 0.479017i | ||||
\(34\) | − | 11.5865i | − | 1.98708i | ||||||
\(35\) | −4.93170 | − | 2.77068i | −0.833610 | − | 0.468330i | ||||
\(36\) | −0.428808 | −0.0714679 | ||||||||
\(37\) | −0.824689 | + | 0.476134i | −0.135578 | + | 0.0782760i | −0.566255 | − | 0.824230i | \(-0.691608\pi\) |
0.430677 | + | 0.902506i | \(0.358275\pi\) | |||||||
\(38\) | −2.88043 | + | 4.98905i | −0.467267 | + | 0.809330i | ||||
\(39\) | 3.30321 | − | 1.44526i | 0.528937 | − | 0.231427i | ||||
\(40\) | −2.61764 | − | 4.53389i | −0.413886 | − | 0.716872i | ||||
\(41\) | − | 4.86183i | − | 0.759290i | −0.925132 | − | 0.379645i | \(-0.876046\pi\) | ||
0.925132 | − | 0.379645i | \(-0.123954\pi\) | |||||||
\(42\) | −3.54645 | + | 2.10341i | −0.547229 | + | 0.324563i | ||||
\(43\) | 4.89360 | 0.746267 | 0.373133 | − | 0.927778i | \(-0.378283\pi\) | ||||
0.373133 | + | 0.927778i | \(0.378283\pi\) | |||||||
\(44\) | 2.04376 | − | 1.17997i | 0.308109 | − | 0.177887i | ||||
\(45\) | 1.85159 | + | 1.06902i | 0.276019 | + | 0.159360i | ||||
\(46\) | −5.08892 | − | 2.93809i | −0.750321 | − | 0.433198i | ||||
\(47\) | 4.55629 | − | 2.63057i | 0.664603 | − | 0.383709i | −0.129426 | − | 0.991589i | \(-0.541313\pi\) |
0.794029 | + | 0.607880i | \(0.207980\pi\) | |||||||
\(48\) | −4.67374 | −0.674596 | ||||||||
\(49\) | −3.35679 | + | 6.14264i | −0.479541 | + | 0.877519i | ||||
\(50\) | 0.668281i | 0.0945092i | ||||||||
\(51\) | 3.71730 | + | 6.43855i | 0.520526 | + | 0.901577i | ||||
\(52\) | −1.41644 | + | 0.619740i | −0.196425 | + | 0.0859424i | ||||
\(53\) | 6.49807 | − | 11.2550i | 0.892579 | − | 1.54599i | 0.0558062 | − | 0.998442i | \(-0.482227\pi\) |
0.836773 | − | 0.547550i | \(-0.184440\pi\) | |||||||
\(54\) | 1.34967 | − | 0.779232i | 0.183667 | − | 0.106040i | ||||
\(55\) | −11.7666 | −1.58661 | ||||||||
\(56\) | −5.57216 | + | 3.30486i | −0.744611 | + | 0.441631i | ||||
\(57\) | − | 3.69650i | − | 0.489613i | ||||||
\(58\) | 1.21908 | − | 0.703834i | 0.160073 | − | 0.0924179i | ||||
\(59\) | 7.30419 | + | 4.21708i | 0.950925 | + | 0.549017i | 0.893368 | − | 0.449326i | \(-0.148336\pi\) |
0.0575566 | + | 0.998342i | \(0.481669\pi\) | |||||||
\(60\) | −0.793977 | − | 0.458403i | −0.102502 | − | 0.0591795i | ||||
\(61\) | 1.81406 | + | 3.14204i | 0.232266 | + | 0.402297i | 0.958475 | − | 0.285178i | \(-0.0920526\pi\) |
−0.726208 | + | 0.687475i | \(0.758719\pi\) | |||||||
\(62\) | 4.71936 | 0.599360 | ||||||||
\(63\) | 1.29590 | − | 2.30665i | 0.163268 | − | 0.290611i | ||||
\(64\) | −5.62811 | −0.703514 | ||||||||
\(65\) | 7.66121 | + | 0.855154i | 0.950257 | + | 0.106069i | ||||
\(66\) | −4.28849 | + | 7.42788i | −0.527877 | + | 0.914309i | ||||
\(67\) | −1.52883 | − | 0.882669i | −0.186776 | − | 0.107835i | 0.403696 | − | 0.914893i | \(-0.367725\pi\) |
−0.590472 | + | 0.807058i | \(0.701059\pi\) | |||||||
\(68\) | −1.59401 | − | 2.76090i | −0.193302 | − | 0.334808i | ||||
\(69\) | 3.77050 | 0.453915 | ||||||||
\(70\) | −8.81516 | + | 0.103437i | −1.05361 | + | 0.0123631i | ||||
\(71\) | − | 11.7994i | − | 1.40033i | −0.713979 | − | 0.700167i | \(-0.753109\pi\) | ||
0.713979 | − | 0.700167i | \(-0.246891\pi\) | |||||||
\(72\) | 2.12059 | − | 1.22432i | 0.249914 | − | 0.144288i | ||||
\(73\) | 6.43323 | + | 3.71423i | 0.752953 | + | 0.434718i | 0.826760 | − | 0.562555i | \(-0.190181\pi\) |
−0.0738068 | + | 0.997273i | \(0.523515\pi\) | |||||||
\(74\) | −0.742038 | + | 1.28525i | −0.0862601 | + | 0.149407i | ||||
\(75\) | −0.214404 | − | 0.371358i | −0.0247572 | − | 0.0428808i | ||||
\(76\) | 1.58509i | 0.181822i | ||||||||
\(77\) | 0.170845 | + | 14.5599i | 0.0194696 | + | 1.65925i | ||||
\(78\) | 3.33205 | − | 4.52459i | 0.377280 | − | 0.512309i | ||||
\(79\) | −7.64418 | − | 13.2401i | −0.860037 | − | 1.48963i | −0.871892 | − | 0.489698i | \(-0.837107\pi\) |
0.0118547 | − | 0.999930i | \(-0.496226\pi\) | |||||||
\(80\) | −8.65386 | − | 4.99631i | −0.967531 | − | 0.558604i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −3.78849 | − | 6.56186i | −0.418369 | − | 0.724636i | ||||
\(83\) | 10.4833i | 1.15069i | 0.817910 | + | 0.575346i | \(0.195133\pi\) | ||||
−0.817910 | + | 0.575346i | \(0.804867\pi\) | |||||||
\(84\) | −0.555692 | + | 0.989110i | −0.0606310 | + | 0.107921i | ||||
\(85\) | 15.8954i | 1.72410i | ||||||||
\(86\) | 6.60474 | − | 3.81325i | 0.712207 | − | 0.411193i | ||||
\(87\) | −0.451620 | + | 0.782230i | −0.0484188 | + | 0.0838638i | ||||
\(88\) | −6.73804 | + | 11.6706i | −0.718278 | + | 1.24409i | ||||
\(89\) | −4.49716 | + | 2.59644i | −0.476698 | + | 0.275222i | −0.719039 | − | 0.694969i | \(-0.755418\pi\) |
0.242341 | + | 0.970191i | \(0.422085\pi\) | |||||||
\(90\) | 3.33205 | 0.351229 | ||||||||
\(91\) | 0.946917 | − | 9.49228i | 0.0992638 | − | 0.995061i | ||||
\(92\) | −1.61682 | −0.168565 | ||||||||
\(93\) | −2.62251 | + | 1.51411i | −0.271942 | + | 0.157006i | ||||
\(94\) | 4.09965 | − | 7.10081i | 0.422847 | − | 0.732392i | ||||
\(95\) | 3.95162 | − | 6.84441i | 0.405428 | − | 0.702221i | ||||
\(96\) | −2.06682 | + | 1.19328i | −0.210944 | + | 0.121789i | ||||
\(97\) | 7.06195i | 0.717032i | 0.933524 | + | 0.358516i | \(0.116717\pi\) | ||||
−0.933524 | + | 0.358516i | \(0.883283\pi\) | |||||||
\(98\) | 0.255983 | + | 10.9062i | 0.0258582 | + | 1.10170i | ||||
\(99\) | − | 5.50349i | − | 0.553121i | ||||||
\(100\) | 0.0919380 | + | 0.159241i | 0.00919380 | + | 0.0159241i | ||||
\(101\) | −5.05417 | + | 8.75407i | −0.502908 | + | 0.871063i | 0.497086 | + | 0.867701i | \(0.334403\pi\) |
−0.999994 | + | 0.00336163i | \(0.998930\pi\) | |||||||
\(102\) | 10.0342 | + | 5.79327i | 0.993538 | + | 0.573619i | ||||
\(103\) | −5.93170 | − | 10.2740i | −0.584468 | − | 1.01233i | −0.994942 | − | 0.100456i | \(-0.967970\pi\) |
0.410474 | − | 0.911872i | \(-0.365363\pi\) | |||||||
\(104\) | 5.23529 | − | 7.10901i | 0.513362 | − | 0.697096i | ||||
\(105\) | 4.86533 | − | 2.88564i | 0.474808 | − | 0.281609i | ||||
\(106\) | − | 20.2540i | − | 1.96724i | ||||||
\(107\) | 5.77885 | + | 10.0093i | 0.558662 | + | 0.967631i | 0.997608 | + | 0.0691181i | \(0.0220185\pi\) |
−0.438946 | + | 0.898513i | \(0.644648\pi\) | |||||||
\(108\) | 0.214404 | − | 0.371358i | 0.0206310 | − | 0.0357340i | ||||
\(109\) | −10.7460 | − | 6.20423i | −1.02928 | − | 0.594257i | −0.112504 | − | 0.993651i | \(-0.535887\pi\) |
−0.916779 | + | 0.399394i | \(0.869220\pi\) | |||||||
\(110\) | −15.8811 | + | 9.16894i | −1.51420 | + | 0.874224i | ||||
\(111\) | − | 0.952269i | − | 0.0903853i | ||||||
\(112\) | −6.05670 | + | 10.7807i | −0.572304 | + | 1.01868i | ||||
\(113\) | −5.09290 | −0.479100 | −0.239550 | − | 0.970884i | \(-0.577000\pi\) | ||||
−0.239550 | + | 0.970884i | \(0.577000\pi\) | |||||||
\(114\) | −2.88043 | − | 4.98905i | −0.269777 | − | 0.467267i | ||||
\(115\) | 6.98143 | + | 4.03073i | 0.651021 | + | 0.375867i | ||||
\(116\) | 0.193658 | − | 0.335426i | 0.0179807 | − | 0.0311435i | ||||
\(117\) | −0.399972 | + | 3.58330i | −0.0369774 | + | 0.331276i | ||||
\(118\) | 13.1443 | 1.21003 | ||||||||
\(119\) | 19.6687 | − | 0.230793i | 1.80303 | − | 0.0211568i | ||||
\(120\) | 5.23529 | 0.477914 | ||||||||
\(121\) | 9.64418 | + | 16.7042i | 0.876743 | + | 1.51856i | ||||
\(122\) | 4.89675 | + | 2.82714i | 0.443331 | + | 0.255957i | ||||
\(123\) | 4.21047 | + | 2.43091i | 0.379645 | + | 0.219188i | ||||
\(124\) | 1.12455 | − | 0.649261i | 0.100988 | − | 0.0583054i | ||||
\(125\) | − | 11.6070i | − | 1.03816i | ||||||
\(126\) | −0.0483796 | − | 4.12302i | −0.00430999 | − | 0.367308i | ||||
\(127\) | 19.0019 | 1.68615 | 0.843074 | − | 0.537797i | \(-0.180743\pi\) | ||||
0.843074 | + | 0.537797i | \(0.180743\pi\) | |||||||
\(128\) | −11.7297 | + | 6.77216i | −1.03677 | + | 0.598580i | ||||
\(129\) | −2.44680 | + | 4.23798i | −0.215429 | + | 0.373133i | ||||
\(130\) | 11.0065 | − | 4.81569i | 0.965331 | − | 0.422364i | ||||
\(131\) | −5.47526 | − | 9.48343i | −0.478376 | − | 0.828571i | 0.521317 | − | 0.853363i | \(-0.325441\pi\) |
−0.999693 | + | 0.0247922i | \(0.992108\pi\) | |||||||
\(132\) | 2.35994i | 0.205406i | ||||||||
\(133\) | −8.52653 | − | 4.79029i | −0.739344 | − | 0.415371i | ||||
\(134\) | −2.75121 | −0.237669 | ||||||||
\(135\) | −1.85159 | + | 1.06902i | −0.159360 | + | 0.0920064i | ||||
\(136\) | 15.7657 | + | 9.10234i | 1.35190 | + | 0.780520i | ||||
\(137\) | 1.42665 | + | 0.823676i | 0.121887 | + | 0.0703714i | 0.559704 | − | 0.828693i | \(-0.310915\pi\) |
−0.437817 | + | 0.899064i | \(0.644248\pi\) | |||||||
\(138\) | 5.08892 | − | 2.93809i | 0.433198 | − | 0.250107i | ||||
\(139\) | 2.81778 | 0.239001 | 0.119500 | − | 0.992834i | \(-0.461871\pi\) | ||||
0.119500 | + | 0.992834i | \(0.461871\pi\) | |||||||
\(140\) | −2.08629 | + | 1.23738i | −0.176324 | + | 0.104578i | ||||
\(141\) | 5.26115i | 0.443069i | ||||||||
\(142\) | −9.19448 | − | 15.9253i | −0.771584 | − | 1.33642i | ||||
\(143\) | −7.95398 | − | 18.1792i | −0.665146 | − | 1.52022i | ||||
\(144\) | 2.33687 | − | 4.04758i | 0.194739 | − | 0.337298i | ||||
\(145\) | −1.67243 | + | 0.965580i | −0.138888 | + | 0.0801871i | ||||
\(146\) | 11.5770 | 0.958118 | ||||||||
\(147\) | −3.64128 | − | 5.97838i | −0.300328 | − | 0.493089i | ||||
\(148\) | 0.408340i | 0.0335653i | ||||||||
\(149\) | −5.72160 | + | 3.30336i | −0.468731 | + | 0.270622i | −0.715709 | − | 0.698399i | \(-0.753896\pi\) |
0.246977 | + | 0.969021i | \(0.420563\pi\) | |||||||
\(150\) | −0.578748 | − | 0.334140i | −0.0472546 | − | 0.0272824i | ||||
\(151\) | −16.0349 | − | 9.25774i | −1.30490 | − | 0.753384i | −0.323660 | − | 0.946174i | \(-0.604913\pi\) |
−0.981240 | + | 0.192789i | \(0.938247\pi\) | |||||||
\(152\) | −4.52571 | − | 7.83875i | −0.367083 | − | 0.635807i | ||||
\(153\) | −7.43460 | −0.601051 | ||||||||
\(154\) | 11.5761 | + | 19.5178i | 0.932827 | + | 1.57279i | ||||
\(155\) | −6.47443 | −0.520039 | ||||||||
\(156\) | 0.171511 | − | 1.53655i | 0.0137319 | − | 0.123022i | ||||
\(157\) | 0.00564763 | − | 0.00978198i | 0.000450730 | − | 0.000780687i | −0.865800 | − | 0.500390i | \(-0.833190\pi\) |
0.866251 | + | 0.499610i | \(0.166523\pi\) | |||||||
\(158\) | −20.6342 | − | 11.9132i | −1.64157 | − | 0.947761i | ||||
\(159\) | 6.49807 | + | 11.2550i | 0.515331 | + | 0.892579i | ||||
\(160\) | −5.10255 | −0.403392 | ||||||||
\(161\) | 4.88619 | − | 8.69723i | 0.385086 | − | 0.685437i | ||||
\(162\) | 1.55846i | 0.122444i | ||||||||
\(163\) | −1.58260 | + | 0.913712i | −0.123958 | + | 0.0715674i | −0.560697 | − | 0.828021i | \(-0.689467\pi\) |
0.436739 | + | 0.899588i | \(0.356133\pi\) | |||||||
\(164\) | −1.80548 | − | 1.04239i | −0.140984 | − | 0.0813973i | ||||
\(165\) | 5.88332 | − | 10.1902i | 0.458016 | − | 0.793307i | ||||
\(166\) | 8.16892 | + | 14.1490i | 0.634031 | + | 1.09817i | ||||
\(167\) | 9.06078i | 0.701145i | 0.936536 | + | 0.350572i | \(0.114013\pi\) | ||||
−0.936536 | + | 0.350572i | \(0.885987\pi\) | |||||||
\(168\) | −0.0760136 | − | 6.47806i | −0.00586458 | − | 0.499793i | ||||
\(169\) | 3.85762 | + | 12.4145i | 0.296740 | + | 0.954958i | ||||
\(170\) | 12.3862 | + | 21.4536i | 0.949979 | + | 1.64541i | ||||
\(171\) | 3.20126 | + | 1.84825i | 0.244807 | + | 0.141339i | ||||
\(172\) | 1.04921 | − | 1.81728i | 0.0800012 | − | 0.138566i | ||||
\(173\) | 3.12811 | + | 5.41805i | 0.237826 | + | 0.411927i | 0.960090 | − | 0.279690i | \(-0.0902318\pi\) |
−0.722264 | + | 0.691617i | \(0.756899\pi\) | |||||||
\(174\) | 1.40767i | 0.106715i | ||||||||
\(175\) | −1.13444 | + | 0.0133115i | −0.0857556 | + | 0.00100626i | ||||
\(176\) | 25.7219i | 1.93886i | ||||||||
\(177\) | −7.30419 | + | 4.21708i | −0.549017 | + | 0.316975i | ||||
\(178\) | −4.04645 | + | 7.00866i | −0.303294 | + | 0.525321i | ||||
\(179\) | −0.191591 | + | 0.331845i | −0.0143202 | + | 0.0248033i | −0.873097 | − | 0.487547i | \(-0.837892\pi\) |
0.858777 | + | 0.512350i | \(0.171225\pi\) | |||||||
\(180\) | 0.793977 | − | 0.458403i | 0.0591795 | − | 0.0341673i | ||||
\(181\) | 10.0096 | 0.744011 | 0.372005 | − | 0.928231i | \(-0.378670\pi\) | ||||
0.372005 | + | 0.928231i | \(0.378670\pi\) | |||||||
\(182\) | −6.11866 | − | 13.5493i | −0.453545 | − | 1.00434i | ||||
\(183\) | −3.62811 | −0.268198 | ||||||||
\(184\) | 7.99568 | − | 4.61631i | 0.589449 | − | 0.340319i | ||||
\(185\) | 1.01799 | − | 1.76321i | 0.0748442 | − | 0.129634i | ||||
\(186\) | −2.35968 | + | 4.08709i | −0.173020 | + | 0.299680i | ||||
\(187\) | 35.4345 | − | 20.4581i | 2.59122 | − | 1.49604i | ||||
\(188\) | − | 2.25602i | − | 0.164537i | ||||||
\(189\) | 1.34967 | + | 2.27561i | 0.0981740 | + | 0.165526i | ||||
\(190\) | − | 12.3169i | − | 0.893563i | ||||||
\(191\) | 5.29331 | + | 9.16828i | 0.383011 | + | 0.663394i | 0.991491 | − | 0.130175i | \(-0.0415540\pi\) |
−0.608480 | + | 0.793569i | \(0.708221\pi\) | |||||||
\(192\) | 2.81406 | − | 4.87409i | 0.203087 | − | 0.351757i | ||||
\(193\) | −6.56628 | − | 3.79104i | −0.472651 | − | 0.272885i | 0.244698 | − | 0.969599i | \(-0.421311\pi\) |
−0.717349 | + | 0.696714i | \(0.754645\pi\) | |||||||
\(194\) | 5.50289 | + | 9.53129i | 0.395085 | + | 0.684307i | ||||
\(195\) | −4.57119 | + | 6.20723i | −0.327350 | + | 0.444509i | ||||
\(196\) | 1.56141 | + | 2.56358i | 0.111529 | + | 0.183113i | ||||
\(197\) | 5.77227i | 0.411257i | 0.978630 | + | 0.205628i | \(0.0659238\pi\) | ||||
−0.978630 | + | 0.205628i | \(0.934076\pi\) | |||||||
\(198\) | −4.28849 | − | 7.42788i | −0.304770 | − | 0.527877i | ||||
\(199\) | −12.8653 | + | 22.2834i | −0.911999 | + | 1.57963i | −0.100763 | + | 0.994910i | \(0.532128\pi\) |
−0.811236 | + | 0.584718i | \(0.801205\pi\) | |||||||
\(200\) | −0.909325 | − | 0.524999i | −0.0642990 | − | 0.0371230i | ||||
\(201\) | 1.52883 | − | 0.882669i | 0.107835 | − | 0.0622587i | ||||
\(202\) | 15.7535i | 1.10841i | ||||||||
\(203\) | 1.21908 | + | 2.05542i | 0.0855624 | + | 0.144262i | ||||
\(204\) | 3.18801 | 0.223205 | ||||||||
\(205\) | 5.19738 | + | 9.00212i | 0.363001 | + | 0.628736i | ||||
\(206\) | −16.0117 | − | 9.24434i | −1.11559 | − | 0.644084i | ||||
\(207\) | −1.88525 | + | 3.26535i | −0.131034 | + | 0.226957i | ||||
\(208\) | 1.86936 | − | 16.7474i | 0.129617 | − | 1.16122i | ||||
\(209\) | −20.3436 | −1.40720 | ||||||||
\(210\) | 4.31800 | − | 7.68588i | 0.297971 | − | 0.530376i | ||||
\(211\) | 2.62646 | 0.180813 | 0.0904065 | − | 0.995905i | \(-0.471183\pi\) | ||||
0.0904065 | + | 0.995905i | \(0.471183\pi\) | |||||||
\(212\) | −2.78642 | − | 4.82623i | −0.191372 | − | 0.331467i | ||||
\(213\) | 10.2186 | + | 5.89971i | 0.700167 | + | 0.404242i | ||||
\(214\) | 15.5991 | + | 9.00612i | 1.06633 | + | 0.615646i | ||||
\(215\) | −9.06095 | + | 5.23134i | −0.617952 | + | 0.356775i | ||||
\(216\) | 2.44865i | 0.166609i | ||||||||
\(217\) | 0.0940053 | + | 8.01136i | 0.00638150 | + | 0.543846i | ||||
\(218\) | −19.3381 | −1.30974 | ||||||||
\(219\) | −6.43323 | + | 3.71423i | −0.434718 | + | 0.250984i | ||||
\(220\) | −2.52281 | + | 4.36964i | −0.170088 | + | 0.294601i | ||||
\(221\) | −24.5581 | + | 10.7449i | −1.65195 | + | 0.722783i | ||||
\(222\) | −0.742038 | − | 1.28525i | −0.0498023 | − | 0.0862601i | ||||
\(223\) | − | 6.46813i | − | 0.433138i | −0.976267 | − | 0.216569i | \(-0.930513\pi\) | ||
0.976267 | − | 0.216569i | \(-0.0694866\pi\) | |||||||
\(224\) | 0.0740863 | + | 6.31381i | 0.00495010 | + | 0.421859i | ||||
\(225\) | 0.428808 | 0.0285872 | ||||||||
\(226\) | −6.87373 | + | 3.96855i | −0.457234 | + | 0.263984i | ||||
\(227\) | −6.18745 | − | 3.57233i | −0.410675 | − | 0.237104i | 0.280404 | − | 0.959882i | \(-0.409531\pi\) |
−0.691080 | + | 0.722778i | \(0.742865\pi\) | |||||||
\(228\) | −1.37272 | − | 0.792543i | −0.0909109 | − | 0.0524875i | ||||
\(229\) | −11.2457 | + | 6.49269i | −0.743134 | + | 0.429049i | −0.823208 | − | 0.567740i | \(-0.807818\pi\) |
0.0800736 | + | 0.996789i | \(0.474484\pi\) | |||||||
\(230\) | 12.5635 | 0.828412 | ||||||||
\(231\) | −12.6946 | − | 7.13197i | −0.835245 | − | 0.469249i | ||||
\(232\) | 2.21172i | 0.145206i | ||||||||
\(233\) | −9.85968 | − | 17.0775i | −0.645929 | − | 1.11878i | −0.984086 | − | 0.177693i | \(-0.943137\pi\) |
0.338157 | − | 0.941090i | \(-0.390197\pi\) | |||||||
\(234\) | 2.25239 | + | 5.14794i | 0.147243 | + | 0.336531i | ||||
\(235\) | −5.62426 | + | 9.74150i | −0.366886 | + | 0.635466i | ||||
\(236\) | 3.13209 | − | 1.80831i | 0.203882 | − | 0.117711i | ||||
\(237\) | 15.2884 | 0.993085 | ||||||||
\(238\) | 26.3664 | − | 15.6380i | 1.70908 | − | 1.01366i | ||||
\(239\) | − | 20.8752i | − | 1.35031i | −0.737677 | − | 0.675153i | \(-0.764077\pi\) | ||
0.737677 | − | 0.675153i | \(-0.235923\pi\) | |||||||
\(240\) | 8.65386 | − | 4.99631i | 0.558604 | − | 0.322510i | ||||
\(241\) | −14.8824 | − | 8.59237i | −0.958661 | − | 0.553483i | −0.0629006 | − | 0.998020i | \(-0.520035\pi\) |
−0.895761 | + | 0.444536i | \(0.853368\pi\) | |||||||
\(242\) | 26.0329 | + | 15.0301i | 1.67346 | + | 0.966171i | ||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 1.55576 | 0.0995975 | ||||||||
\(245\) | −0.351180 | − | 14.9621i | −0.0224360 | − | 0.955895i | ||||
\(246\) | 7.57698 | 0.483091 | ||||||||
\(247\) | 13.2457 | + | 1.47850i | 0.842801 | + | 0.0940744i | ||||
\(248\) | −3.70752 | + | 6.42160i | −0.235427 | + | 0.407772i | ||||
\(249\) | −9.07880 | − | 5.24165i | −0.575346 | − | 0.332176i | ||||
\(250\) | −9.04452 | − | 15.6656i | −0.572026 | − | 0.990778i | ||||
\(251\) | −22.3931 | −1.41344 | −0.706720 | − | 0.707493i | \(-0.749826\pi\) | ||||
−0.706720 | + | 0.707493i | \(0.749826\pi\) | |||||||
\(252\) | −0.578748 | − | 0.975798i | −0.0364577 | − | 0.0614695i | ||||
\(253\) | − | 20.7509i | − | 1.30460i | ||||||
\(254\) | 25.6463 | − | 14.8069i | 1.60919 | − | 0.929068i | ||||
\(255\) | −13.7658 | − | 7.94771i | −0.862050 | − | 0.497705i | ||||
\(256\) | −4.92605 | + | 8.53218i | −0.307878 | + | 0.533261i | ||||
\(257\) | −10.2903 | − | 17.8233i | −0.641890 | − | 1.11179i | −0.985010 | − | 0.172495i | \(-0.944817\pi\) |
0.343120 | − | 0.939292i | \(-0.388516\pi\) | |||||||
\(258\) | 7.62649i | 0.474805i | ||||||||
\(259\) | −2.19655 | − | 1.23405i | −0.136487 | − | 0.0766798i | ||||
\(260\) | 1.96016 | − | 2.66171i | 0.121564 | − | 0.165072i | ||||
\(261\) | −0.451620 | − | 0.782230i | −0.0279546 | − | 0.0484188i | ||||
\(262\) | −14.7796 | − | 8.53299i | −0.913085 | − | 0.527170i | ||||
\(263\) | −2.52474 | + | 4.37298i | −0.155682 | + | 0.269649i | −0.933307 | − | 0.359079i | \(-0.883091\pi\) |
0.777625 | + | 0.628728i | \(0.216424\pi\) | |||||||
\(264\) | −6.73804 | − | 11.6706i | −0.414698 | − | 0.718278i | ||||
\(265\) | 27.7862i | 1.70689i | ||||||||
\(266\) | −15.2407 | + | 0.178835i | −0.934470 | + | 0.0109651i | ||||
\(267\) | − | 5.19287i | − | 0.317799i | ||||||
\(268\) | −0.655573 | + | 0.378495i | −0.0400455 | + | 0.0231203i | ||||
\(269\) | 7.45079 | − | 12.9052i | 0.454283 | − | 0.786841i | −0.544364 | − | 0.838849i | \(-0.683229\pi\) |
0.998647 | + | 0.0520082i | \(0.0165622\pi\) | |||||||
\(270\) | −1.66602 | + | 2.88564i | −0.101391 | + | 0.175614i | ||||
\(271\) | 5.41883 | − | 3.12856i | 0.329170 | − | 0.190047i | −0.326302 | − | 0.945265i | \(-0.605803\pi\) |
0.655473 | + | 0.755219i | \(0.272469\pi\) | |||||||
\(272\) | 34.7474 | 2.10687 | ||||||||
\(273\) | 7.74710 | + | 5.56619i | 0.468876 | + | 0.336881i | ||||
\(274\) | 2.56734 | 0.155099 | ||||||||
\(275\) | −2.04376 | + | 1.17997i | −0.123244 | + | 0.0711548i | ||||
\(276\) | 0.808409 | − | 1.40021i | 0.0486605 | − | 0.0842825i | ||||
\(277\) | 1.45934 | − | 2.52764i | 0.0876830 | − | 0.151871i | −0.818848 | − | 0.574010i | \(-0.805387\pi\) |
0.906531 | + | 0.422139i | \(0.138720\pi\) | |||||||
\(278\) | 3.80307 | − | 2.19570i | 0.228093 | − | 0.131689i | ||||
\(279\) | − | 3.02822i | − | 0.181295i | ||||||
\(280\) | 6.78441 | − | 12.0760i | 0.405446 | − | 0.721678i | ||||
\(281\) | 3.53952i | 0.211150i | 0.994411 | + | 0.105575i | \(0.0336683\pi\) | ||||
−0.994411 | + | 0.105575i | \(0.966332\pi\) | |||||||
\(282\) | 4.09965 | + | 7.10081i | 0.244131 | + | 0.422847i | ||||
\(283\) | 13.2715 | − | 22.9869i | 0.788907 | − | 1.36643i | −0.137731 | − | 0.990470i | \(-0.543981\pi\) |
0.926637 | − | 0.375957i | \(-0.122686\pi\) | |||||||
\(284\) | −4.38181 | − | 2.52984i | −0.260013 | − | 0.150118i | ||||
\(285\) | 3.95162 | + | 6.84441i | 0.234074 | + | 0.405428i | ||||
\(286\) | −24.9010 | − | 18.3379i | −1.47243 | − | 1.08434i | ||||
\(287\) | 11.0636 | − | 6.56186i | 0.653065 | − | 0.387334i | ||||
\(288\) | − | 2.38656i | − | 0.140629i | ||||||
\(289\) | −19.1366 | − | 33.1456i | −1.12568 | − | 1.94974i | ||||
\(290\) | −1.50482 | + | 2.60643i | −0.0883661 | + | 0.153055i | ||||
\(291\) | −6.11583 | − | 3.53097i | −0.358516 | − | 0.206989i | ||||
\(292\) | 2.75862 | − | 1.59269i | 0.161436 | − | 0.0932051i | ||||
\(293\) | 3.08146i | 0.180021i | 0.995941 | + | 0.0900105i | \(0.0286901\pi\) | ||||
−0.995941 | + | 0.0900105i | \(0.971310\pi\) | |||||||
\(294\) | −9.57307 | − | 5.23143i | −0.558313 | − | 0.305103i | ||||
\(295\) | −18.0325 | −1.04989 | ||||||||
\(296\) | −1.16588 | − | 2.01937i | −0.0677656 | − | 0.117374i | ||||
\(297\) | 4.76616 | + | 2.75174i | 0.276561 | + | 0.159672i | ||||
\(298\) | −5.14817 | + | 8.91690i | −0.298226 | + | 0.516542i | ||||
\(299\) | −1.50809 | + | 13.5108i | −0.0872153 | + | 0.781351i | ||||
\(300\) | −0.183876 | −0.0106161 | ||||||||
\(301\) | 6.60474 | + | 11.1359i | 0.380691 | + | 0.641863i | ||||
\(302\) | −28.8557 | −1.66046 | ||||||||
\(303\) | −5.05417 | − | 8.75407i | −0.290354 | − | 0.502908i | ||||
\(304\) | −14.9619 | − | 8.63823i | −0.858121 | − | 0.495437i | ||||
\(305\) | −6.71779 | − | 3.87852i | −0.384659 | − | 0.222083i | ||||
\(306\) | −10.0342 | + | 5.79327i | −0.573619 | + | 0.331179i | ||||
\(307\) | − | 25.3997i | − | 1.44963i | −0.688941 | − | 0.724817i | \(-0.741924\pi\) | ||
0.688941 | − | 0.724817i | \(-0.258076\pi\) | |||||||
\(308\) | 5.44355 | + | 3.05824i | 0.310175 | + | 0.174260i | ||||
\(309\) | 11.8634 | 0.674885 | ||||||||
\(310\) | −8.73834 | + | 5.04508i | −0.496304 | + | 0.286541i | ||||
\(311\) | 10.4629 | − | 18.1222i | 0.593295 | − | 1.02762i | −0.400491 | − | 0.916301i | \(-0.631160\pi\) |
0.993785 | − | 0.111315i | \(-0.0355064\pi\) | |||||||
\(312\) | 3.53894 | + | 8.08840i | 0.200353 | + | 0.457915i | ||||
\(313\) | 6.35583 | + | 11.0086i | 0.359253 | + | 0.622244i | 0.987836 | − | 0.155498i | \(-0.0496983\pi\) |
−0.628584 | + | 0.777742i | \(0.716365\pi\) | |||||||
\(314\) | − | 0.0176032i | − | 0.000993408i | ||||||
\(315\) | 0.0663713 | + | 5.65632i | 0.00373960 | + | 0.318697i | ||||
\(316\) | −6.55576 | −0.368790 | ||||||||
\(317\) | −11.1455 | + | 6.43484i | −0.625992 | + | 0.361417i | −0.779198 | − | 0.626778i | \(-0.784373\pi\) |
0.153206 | + | 0.988194i | \(0.451040\pi\) | |||||||
\(318\) | 17.5405 | + | 10.1270i | 0.983622 | + | 0.567894i | ||||
\(319\) | 4.30499 | + | 2.48549i | 0.241033 | + | 0.139161i | ||||
\(320\) | 10.4210 | − | 6.01655i | 0.582550 | − | 0.336335i | ||||
\(321\) | −11.5577 | −0.645088 | ||||||||
\(322\) | −0.182415 | − | 15.5458i | −0.0101656 | − | 0.866336i | ||||
\(323\) | 27.4820i | 1.52914i | ||||||||
\(324\) | 0.214404 | + | 0.371358i | 0.0119113 | + | 0.0206310i | ||||
\(325\) | 1.41644 | − | 0.619740i | 0.0785701 | − | 0.0343770i | ||||
\(326\) | −1.42399 | + | 2.46642i | −0.0788673 | + | 0.136602i | ||||
\(327\) | 10.7460 | − | 6.20423i | 0.594257 | − | 0.343094i | ||||
\(328\) | 11.9049 | 0.657338 | ||||||||
\(329\) | 12.1356 | + | 6.81792i | 0.669059 | + | 0.375884i | ||||
\(330\) | − | 18.3379i | − | 1.00947i | ||||||
\(331\) | −23.7769 | + | 13.7276i | −1.30689 | + | 0.754536i | −0.981577 | − | 0.191068i | \(-0.938805\pi\) |
−0.325318 | + | 0.945605i | \(0.605471\pi\) | |||||||
\(332\) | 3.89306 | + | 2.24766i | 0.213659 | + | 0.123356i | ||||
\(333\) | 0.824689 | + | 0.476134i | 0.0451927 | + | 0.0260920i | ||||
\(334\) | 7.06045 | + | 12.2291i | 0.386331 | + | 0.669144i | ||||
\(335\) | 3.77435 | 0.206215 | ||||||||
\(336\) | −6.30800 | − | 10.6356i | −0.344130 | − | 0.580220i | ||||
\(337\) | 16.5012 | 0.898875 | 0.449438 | − | 0.893312i | \(-0.351624\pi\) | ||||
0.449438 | + | 0.893312i | \(0.351624\pi\) | |||||||
\(338\) | 14.8802 | + | 13.7494i | 0.809378 | + | 0.747871i | ||||
\(339\) | 2.54645 | − | 4.41058i | 0.138304 | − | 0.239550i | ||||
\(340\) | 5.90290 | + | 3.40804i | 0.320129 | + | 0.184827i | ||||
\(341\) | 8.33287 | + | 14.4330i | 0.451250 | + | 0.781589i | ||||
\(342\) | 5.76086 | 0.311511 | ||||||||
\(343\) | −18.5088 | + | 0.651786i | −0.999381 | + | 0.0351931i | ||||
\(344\) | 11.9827i | 0.646063i | ||||||||
\(345\) | −6.98143 | + | 4.03073i | −0.375867 | + | 0.217007i | ||||
\(346\) | 8.44383 | + | 4.87505i | 0.453943 | + | 0.262084i | ||||
\(347\) | 4.41936 | − | 7.65455i | 0.237244 | − | 0.410918i | −0.722679 | − | 0.691184i | \(-0.757089\pi\) |
0.959922 | + | 0.280266i | \(0.0904227\pi\) | |||||||
\(348\) | 0.193658 | + | 0.335426i | 0.0103812 | + | 0.0179807i | ||||
\(349\) | 27.2777i | 1.46014i | 0.683370 | + | 0.730072i | \(0.260514\pi\) | ||||
−0.683370 | + | 0.730072i | \(0.739486\pi\) | |||||||
\(350\) | −1.52075 | + | 0.901958i | −0.0812873 | + | 0.0482117i | ||||
\(351\) | −2.90324 | − | 2.13803i | −0.154964 | − | 0.114120i | ||||
\(352\) | 6.56720 | + | 11.3747i | 0.350033 | + | 0.606275i | ||||
\(353\) | −2.03841 | − | 1.17687i | −0.108493 | − | 0.0626387i | 0.444771 | − | 0.895644i | \(-0.353285\pi\) |
−0.553265 | + | 0.833005i | \(0.686618\pi\) | |||||||
\(354\) | −6.57216 | + | 11.3833i | −0.349306 | + | 0.605016i | ||||
\(355\) | 12.6138 | + | 21.8477i | 0.669470 | + | 1.15956i | ||||
\(356\) | 2.22674i | 0.118017i | ||||||||
\(357\) | −9.63450 | + | 17.1490i | −0.509912 | + | 0.907622i | ||||
\(358\) | 0.597175i | 0.0315617i | ||||||||
\(359\) | −3.01674 | + | 1.74172i | −0.159218 | + | 0.0919244i | −0.577492 | − | 0.816396i | \(-0.695968\pi\) |
0.418274 | + | 0.908321i | \(0.362635\pi\) | |||||||
\(360\) | −2.61764 | + | 4.53389i | −0.137962 | + | 0.238957i | ||||
\(361\) | −2.66795 | + | 4.62103i | −0.140419 | + | 0.243212i | ||||
\(362\) | 13.5097 | − | 7.79983i | 0.710054 | − | 0.409950i | ||||
\(363\) | −19.2884 | −1.01238 | ||||||||
\(364\) | −3.32201 | − | 2.38683i | −0.174121 | − | 0.125104i | ||||
\(365\) | −15.8823 | −0.831318 | ||||||||
\(366\) | −4.89675 | + | 2.82714i | −0.255957 | + | 0.147777i | ||||
\(367\) | −2.91178 | + | 5.04335i | −0.151994 | + | 0.263261i | −0.931960 | − | 0.362560i | \(-0.881903\pi\) |
0.779967 | + | 0.625821i | \(0.215236\pi\) | |||||||
\(368\) | 8.81116 | − | 15.2614i | 0.459314 | − | 0.795555i | ||||
\(369\) | −4.21047 | + | 2.43091i | −0.219188 | + | 0.126548i | ||||
\(370\) | − | 3.17301i | − | 0.164957i | ||||||
\(371\) | 34.3822 | − | 0.403441i | 1.78503 | − | 0.0209456i | ||||
\(372\) | 1.29852i | 0.0673252i | ||||||||
\(373\) | −4.36340 | − | 7.55764i | −0.225928 | − | 0.391320i | 0.730669 | − | 0.682732i | \(-0.239208\pi\) |
−0.956598 | + | 0.291412i | \(0.905875\pi\) | |||||||
\(374\) | 31.8832 | − | 55.2233i | 1.64864 | − | 2.85553i | ||||
\(375\) | 10.0519 | + | 5.80349i | 0.519080 | + | 0.299691i | ||||
\(376\) | 6.44134 | + | 11.1567i | 0.332187 | + | 0.575365i | ||||
\(377\) | −2.62233 | − | 1.93116i | −0.135057 | − | 0.0994598i | ||||
\(378\) | 3.59483 | + | 2.01961i | 0.184898 | + | 0.103878i | ||||
\(379\) | 18.8676i | 0.969162i | 0.874747 | + | 0.484581i | \(0.161028\pi\) | ||||
−0.874747 | + | 0.484581i | \(0.838972\pi\) | |||||||
\(380\) | −1.69448 | − | 2.93493i | −0.0869252 | − | 0.150559i | ||||
\(381\) | −9.50097 | + | 16.4562i | −0.486749 | + | 0.843074i | ||||
\(382\) | 14.2884 | + | 8.24943i | 0.731060 | + | 0.422078i | ||||
\(383\) | 12.4544 | − | 7.19054i | 0.636389 | − | 0.367420i | −0.146833 | − | 0.989161i | \(-0.546908\pi\) |
0.783222 | + | 0.621742i | \(0.213575\pi\) | |||||||
\(384\) | − | 13.5443i | − | 0.691181i | ||||||
\(385\) | −15.8811 | − | 26.7763i | −0.809374 | − | 1.36465i | ||||
\(386\) | −11.8164 | −0.601439 | ||||||||
\(387\) | −2.44680 | − | 4.23798i | −0.124378 | − | 0.215429i | ||||
\(388\) | 2.62251 | + | 1.51411i | 0.133138 | + | 0.0768672i | ||||
\(389\) | −1.37671 | + | 2.38453i | −0.0698019 | + | 0.120900i | −0.898814 | − | 0.438330i | \(-0.855570\pi\) |
0.829012 | + | 0.559231i | \(0.188903\pi\) | |||||||
\(390\) | −1.33273 | + | 11.9397i | −0.0674852 | + | 0.604591i | ||||
\(391\) | −28.0321 | −1.41765 | ||||||||
\(392\) | −15.0411 | − | 8.21959i | −0.759692 | − | 0.415152i | ||||
\(393\) | 10.9505 | 0.552381 | ||||||||
\(394\) | 4.49793 | + | 7.79065i | 0.226603 | + | 0.392487i | ||||
\(395\) | 28.3078 | + | 16.3435i | 1.42432 | + | 0.822332i | ||||
\(396\) | −2.04376 | − | 1.17997i | −0.102703 | − | 0.0592956i | ||||
\(397\) | −8.62315 | + | 4.97858i | −0.432783 | + | 0.249868i | −0.700532 | − | 0.713621i | \(-0.747054\pi\) |
0.267748 | + | 0.963489i | \(0.413720\pi\) | |||||||
\(398\) | 40.1003i | 2.01005i | ||||||||
\(399\) | 8.41178 | − | 4.98905i | 0.421116 | − | 0.249765i | ||||
\(400\) | −2.00413 | −0.100207 | ||||||||
\(401\) | 1.52399 | − | 0.879875i | 0.0761043 | − | 0.0439388i | −0.461465 | − | 0.887158i | \(-0.652676\pi\) |
0.537569 | + | 0.843220i | \(0.319343\pi\) | |||||||
\(402\) | 1.37561 | − | 2.38262i | 0.0686090 | − | 0.118834i | ||||
\(403\) | −4.37657 | − | 10.0028i | −0.218012 | − | 0.498277i | ||||
\(404\) | 2.16727 | + | 3.75381i | 0.107825 | + | 0.186759i | ||||
\(405\) | − | 2.13803i | − | 0.106240i | ||||||
\(406\) | 3.24700 | + | 1.82420i | 0.161146 | + | 0.0905334i | ||||
\(407\) | −5.24080 | −0.259777 | ||||||||
\(408\) | −15.7657 | + | 9.10234i | −0.780520 | + | 0.450633i | ||||
\(409\) | 13.5151 | + | 7.80292i | 0.668277 | + | 0.385830i | 0.795423 | − | 0.606054i | \(-0.207249\pi\) |
−0.127147 | + | 0.991884i | \(0.540582\pi\) | |||||||
\(410\) | 14.0295 | + | 8.09992i | 0.692867 | + | 0.400027i | ||||
\(411\) | −1.42665 | + | 0.823676i | −0.0703714 | + | 0.0406289i | ||||
\(412\) | −5.08712 | −0.250624 | ||||||||
\(413\) | 0.261822 | + | 22.3131i | 0.0128834 | + | 1.09796i | ||||
\(414\) | 5.87618i | 0.288799i | ||||||||
\(415\) | −11.2068 | − | 19.4108i | −0.550122 | − | 0.952839i | ||||
\(416\) | −3.44921 | − | 7.88331i | −0.169111 | − | 0.386511i | ||||
\(417\) | −1.40889 | + | 2.44027i | −0.0689936 | + | 0.119500i | ||||
\(418\) | −27.4572 | + | 15.8524i | −1.34297 | + | 0.775366i | ||||
\(419\) | 5.58634 | 0.272911 | 0.136455 | − | 0.990646i | \(-0.456429\pi\) | ||||
0.136455 | + | 0.990646i | \(0.456429\pi\) | |||||||
\(420\) | −0.0284605 | − | 2.42547i | −0.00138873 | − | 0.118351i | ||||
\(421\) | − | 12.3229i | − | 0.600582i | −0.953848 | − | 0.300291i | \(-0.902916\pi\) | ||
0.953848 | − | 0.300291i | \(-0.0970838\pi\) | |||||||
\(422\) | 3.54485 | − | 2.04662i | 0.172561 | − | 0.0996280i | ||||
\(423\) | −4.55629 | − | 2.63057i | −0.221534 | − | 0.127903i | ||||
\(424\) | 27.5595 | + | 15.9115i | 1.33841 | + | 0.772730i | ||||
\(425\) | 1.59401 | + | 2.76090i | 0.0773206 | + | 0.133923i | ||||
\(426\) | 18.3890 | 0.890948 | ||||||||
\(427\) | −4.70167 | + | 8.36879i | −0.227530 | + | 0.404994i | ||||
\(428\) | 4.95603 | 0.239559 | ||||||||
\(429\) | 19.7206 | + | 2.20124i | 0.952121 | + | 0.106277i | ||||
\(430\) | −8.15285 | + | 14.1212i | −0.393166 | + | 0.680983i | ||||
\(431\) | 0.338321 | + | 0.195330i | 0.0162964 | + | 0.00940871i | 0.508126 | − | 0.861283i | \(-0.330338\pi\) |
−0.491830 | + | 0.870691i | \(0.663672\pi\) | |||||||
\(432\) | 2.33687 | + | 4.04758i | 0.112433 | + | 0.194739i | ||||
\(433\) | 21.9621 | 1.05543 | 0.527715 | − | 0.849421i | \(-0.323049\pi\) | ||||
0.527715 | + | 0.849421i | \(0.323049\pi\) | |||||||
\(434\) | 6.36958 | + | 10.7394i | 0.305750 | + | 0.515509i | ||||
\(435\) | − | 1.93116i | − | 0.0925921i | ||||||
\(436\) | −4.60798 | + | 2.66042i | −0.220682 | + | 0.127411i | ||||
\(437\) | 12.0703 | + | 6.96882i | 0.577403 | + | 0.333364i | ||||
\(438\) | −5.78849 | + | 10.0260i | −0.276585 | + | 0.479059i | ||||
\(439\) | 0.180296 | + | 0.312281i | 0.00860504 | + | 0.0149044i | 0.870296 | − | 0.492529i | \(-0.163928\pi\) |
−0.861691 | + | 0.507434i | \(0.830594\pi\) | |||||||
\(440\) | − | 28.8123i | − | 1.37357i | ||||||
\(441\) | 6.99807 | − | 0.164253i | 0.333242 | − | 0.00782159i | ||||
\(442\) | −24.7724 | + | 33.6385i | −1.17830 | + | 1.60002i | ||||
\(443\) | 18.2334 | + | 31.5811i | 0.866293 | + | 1.50046i | 0.865757 | + | 0.500464i | \(0.166837\pi\) |
0.000535780 | 1.00000i | \(0.499829\pi\) | ||||||||
\(444\) | −0.353633 | − | 0.204170i | −0.0167827 | − | 0.00968948i | ||||
\(445\) | 5.55127 | − | 9.61509i | 0.263156 | − | 0.455799i | ||||
\(446\) | −5.04017 | − | 8.72983i | −0.238659 | − | 0.413369i | ||||
\(447\) | − | 6.60673i | − | 0.312488i | ||||||
\(448\) | −7.59609 | − | 12.8074i | −0.358881 | − | 0.605092i | ||||
\(449\) | 25.8905i | 1.22185i | 0.791689 | + | 0.610924i | \(0.209202\pi\) | ||||
−0.791689 | + | 0.610924i | \(0.790798\pi\) | |||||||
\(450\) | 0.578748 | − | 0.334140i | 0.0272824 | − | 0.0157515i | ||||
\(451\) | 13.3785 | − | 23.1722i | 0.629969 | − | 1.09114i | ||||
\(452\) | −1.09194 | + | 1.89129i | −0.0513604 | + | 0.0889589i | ||||
\(453\) | 16.0349 | − | 9.25774i | 0.753384 | − | 0.434967i | ||||
\(454\) | −11.1347 | −0.522576 | ||||||||
\(455\) | 8.39411 | + | 18.5881i | 0.393522 | + | 0.871424i | ||||
\(456\) | 9.05141 | 0.423871 | ||||||||
\(457\) | 34.8434 | − | 20.1168i | 1.62990 | − | 0.941026i | 0.645784 | − | 0.763520i | \(-0.276530\pi\) |
0.984120 | − | 0.177506i | \(-0.0568028\pi\) | |||||||
\(458\) | −10.1186 | + | 17.5259i | −0.472812 | + | 0.818934i | ||||
\(459\) | 3.71730 | − | 6.43855i | 0.173509 | − | 0.300526i | ||||
\(460\) | 2.99369 | − | 1.72841i | 0.139581 | − | 0.0805874i | ||||
\(461\) | − | 26.6895i | − | 1.24305i | −0.783393 | − | 0.621527i | \(-0.786513\pi\) | ||
0.783393 | − | 0.621527i | \(-0.213487\pi\) | |||||||
\(462\) | −22.6910 | + | 0.266256i | −1.05568 | + | 0.0123874i | ||||
\(463\) | − | 4.61949i | − | 0.214686i | −0.994222 | − | 0.107343i | \(-0.965766\pi\) | ||
0.994222 | − | 0.107343i | \(-0.0342343\pi\) | |||||||
\(464\) | 2.11076 | + | 3.65594i | 0.0979894 | + | 0.169723i | ||||
\(465\) | 3.23722 | − | 5.60702i | 0.150122 | − | 0.260019i | ||||
\(466\) | −26.6146 | − | 15.3660i | −1.23290 | − | 0.711814i | ||||
\(467\) | −8.57973 | − | 14.8605i | −0.397023 | − | 0.687664i | 0.596334 | − | 0.802736i | \(-0.296623\pi\) |
−0.993357 | + | 0.115073i | \(0.963290\pi\) | |||||||
\(468\) | 1.24493 | + | 0.916805i | 0.0575470 | + | 0.0423793i | ||||
\(469\) | −0.0548016 | − | 4.67032i | −0.00253050 | − | 0.215655i | ||||
\(470\) | 17.5304i | 0.808617i | ||||||||
\(471\) | 0.00564763 | + | 0.00978198i | 0.000260229 | + | 0.000450730i | ||||
\(472\) | −10.3261 | + | 17.8854i | −0.475298 | + | 0.823241i | ||||
\(473\) | 23.3237 | + | 13.4659i | 1.07242 | + | 0.619164i | ||||
\(474\) | 20.6342 | − | 11.9132i | 0.947761 | − | 0.547190i | ||||
\(475\) | − | 1.58509i | − | 0.0727287i | ||||||
\(476\) | 4.13134 | − | 7.35363i | 0.189360 | − | 0.337053i | ||||
\(477\) | −12.9961 | −0.595053 | ||||||||
\(478\) | −16.2666 | − | 28.1747i | −0.744019 | − | 1.28868i | ||||
\(479\) | −24.7932 | − | 14.3144i | −1.13283 | − | 0.654040i | −0.188185 | − | 0.982134i | \(-0.560261\pi\) |
−0.944645 | + | 0.328093i | \(0.893594\pi\) | |||||||
\(480\) | 2.55127 | − | 4.41894i | 0.116449 | − | 0.201696i | ||||
\(481\) | 3.41226 | + | 0.380881i | 0.155586 | + | 0.0173667i | ||||
\(482\) | −26.7818 | −1.21988 | ||||||||
\(483\) | 5.08892 | + | 8.58018i | 0.231554 | + | 0.390412i | ||||
\(484\) | 8.27099 | 0.375954 | ||||||||
\(485\) | −7.54935 | − | 13.0759i | −0.342798 | − | 0.593744i | ||||
\(486\) | −1.34967 | − | 0.779232i | −0.0612222 | − | 0.0353467i | ||||
\(487\) | 13.6192 | + | 7.86303i | 0.617144 | + | 0.356308i | 0.775756 | − | 0.631033i | \(-0.217369\pi\) |
−0.158612 | + | 0.987341i | \(0.550702\pi\) | |||||||
\(488\) | −7.69374 | + | 4.44198i | −0.348279 | + | 0.201079i | ||||
\(489\) | − | 1.82742i | − | 0.0826390i | ||||||
\(490\) | −12.1329 | − | 19.9203i | −0.548110 | − | 0.899906i | ||||
\(491\) | 34.2012 | 1.54348 | 0.771740 | − | 0.635938i | \(-0.219387\pi\) | ||||
0.771740 | + | 0.635938i | \(0.219387\pi\) | |||||||
\(492\) | 1.80548 | − | 1.04239i | 0.0813973 | − | 0.0469948i | ||||
\(493\) | 3.35762 | − | 5.81556i | 0.151219 | − | 0.261920i | ||||
\(494\) | 19.0293 | − | 8.32595i | 0.856170 | − | 0.374602i | ||||
\(495\) | 5.88332 | + | 10.1902i | 0.264436 | + | 0.458016i | ||||
\(496\) | 14.1531i | 0.635493i | ||||||||
\(497\) | 26.8509 | − | 15.9253i | 1.20443 | − | 0.714348i | ||||
\(498\) | −16.3378 | −0.732116 | ||||||||
\(499\) | −11.9087 | + | 6.87551i | −0.533108 | + | 0.307790i | −0.742281 | − | 0.670089i | \(-0.766256\pi\) |
0.209173 | + | 0.977879i | \(0.432923\pi\) | |||||||
\(500\) | −4.31035 | − | 2.48858i | −0.192765 | − | 0.111293i | ||||
\(501\) | −7.84687 | − | 4.53039i | −0.350572 | − | 0.202403i | ||||
\(502\) | −30.2233 | + | 17.4494i | −1.34893 | + | 0.778805i | ||||
\(503\) | −31.7971 | −1.41776 | −0.708882 | − | 0.705327i | \(-0.750800\pi\) | ||||
−0.708882 | + | 0.705327i | \(0.750800\pi\) | |||||||
\(504\) | 5.64817 | + | 3.17320i | 0.251590 | + | 0.141346i | ||||
\(505\) | − | 21.6120i | − | 0.961720i | ||||||
\(506\) | −16.1697 | − | 28.0068i | −0.718833 | − | 1.24505i | ||||
\(507\) | −12.6800 | − | 2.86644i | −0.563141 | − | 0.127303i | ||||
\(508\) | 4.07409 | − | 7.05652i | 0.180758 | − | 0.313083i | ||||
\(509\) | 22.4013 | − | 12.9334i | 0.992921 | − | 0.573263i | 0.0867751 | − | 0.996228i | \(-0.472344\pi\) |
0.906146 | + | 0.422964i | \(0.139011\pi\) | |||||||
\(510\) | −24.7724 | −1.09694 | ||||||||
\(511\) | 0.230603 | + | 19.6525i | 0.0102013 | + | 0.869376i | ||||
\(512\) | − | 11.7345i | − | 0.518597i | ||||||
\(513\) | −3.20126 | + | 1.84825i | −0.141339 | + | 0.0816022i | ||||
\(514\) | −27.7769 | − | 16.0370i | −1.22519 | − | 0.707363i | ||||
\(515\) | 21.9662 | + | 12.6822i | 0.967946 | + | 0.558844i | ||||
\(516\) | 1.04921 | + | 1.81728i | 0.0461887 | + | 0.0800012i | ||||
\(517\) | 28.9547 | 1.27342 | ||||||||
\(518\) | −3.92622 | + | 0.0460703i | −0.172508 | + | 0.00202421i | ||||
\(519\) | −6.25623 | −0.274618 | ||||||||
\(520\) | −2.09397 | + | 18.7596i | −0.0918266 | + | 0.822663i | ||||
\(521\) | −0.391998 | + | 0.678960i | −0.0171737 | + | 0.0297458i | −0.874485 | − | 0.485053i | \(-0.838800\pi\) |
0.857311 | + | 0.514799i | \(0.172134\pi\) | |||||||
\(522\) | −1.21908 | − | 0.703834i | −0.0533575 | − | 0.0308060i | ||||
\(523\) | 17.6130 | + | 30.5065i | 0.770161 | + | 1.33396i | 0.937474 | + | 0.348054i | \(0.113158\pi\) |
−0.167313 | + | 0.985904i | \(0.553509\pi\) | |||||||
\(524\) | −4.69567 | −0.205131 | ||||||||
\(525\) | 0.555692 | − | 0.989110i | 0.0242524 | − | 0.0431683i | ||||
\(526\) | 7.86943i | 0.343123i | ||||||||
\(527\) | 19.4973 | − | 11.2568i | 0.849317 | − | 0.490353i | ||||
\(528\) | −22.2758 | − | 12.8609i | −0.969429 | − | 0.559700i | ||||
\(529\) | 4.39167 | − | 7.60660i | 0.190942 | − | 0.330722i | ||||
\(530\) | 21.6519 | + | 37.5022i | 0.940498 | + | 1.62899i | ||||
\(531\) | − | 8.43415i | − | 0.366011i | ||||||
\(532\) | −3.60704 | + | 2.13934i | −0.156385 | + | 0.0927522i | ||||
\(533\) | −10.3948 | + | 14.1151i | −0.450247 | + | 0.611391i | ||||
\(534\) | −4.04645 | − | 7.00866i | −0.175107 | − | 0.303294i | ||||
\(535\) | −21.4001 | − | 12.3554i | −0.925209 | − | 0.534170i | ||||
\(536\) | 2.16134 | − | 3.74356i | 0.0933558 | − | 0.161697i | ||||
\(537\) | −0.191591 | − | 0.331845i | −0.00826776 | − | 0.0143202i | ||||
\(538\) | − | 23.2236i | − | 1.00124i | ||||||
\(539\) | −32.9019 | + | 20.0398i | −1.41719 | + | 0.863173i | ||||
\(540\) | 0.916805i | 0.0394530i | ||||||||
\(541\) | −33.7367 | + | 19.4779i | −1.45045 | + | 0.837419i | −0.998507 | − | 0.0546260i | \(-0.982603\pi\) |
−0.451946 | + | 0.892045i | \(0.649270\pi\) | |||||||
\(542\) | 4.87575 | − | 8.44504i | 0.209431 | − | 0.362746i | ||||
\(543\) | −5.00482 | + | 8.66860i | −0.214777 | + | 0.372005i | ||||
\(544\) | 15.3660 | − | 8.87155i | 0.658811 | − | 0.380365i | ||||
\(545\) | 26.5297 | 1.13641 | ||||||||
\(546\) | 14.7934 | + | 1.47573i | 0.633098 | + | 0.0631556i | ||||
\(547\) | −14.5121 | −0.620491 | −0.310246 | − | 0.950656i | \(-0.600411\pi\) | ||||
−0.310246 | + | 0.950656i | \(0.600411\pi\) | |||||||
\(548\) | 0.611758 | − | 0.353199i | 0.0261330 | − | 0.0150879i | ||||
\(549\) | 1.81406 | − | 3.14204i | 0.0774221 | − | 0.134099i | ||||
\(550\) | −1.83894 | + | 3.18513i | −0.0784125 | + | 0.135814i | ||||
\(551\) | −2.89151 | + | 1.66941i | −0.123182 | + | 0.0711194i | ||||
\(552\) | 9.23261i | 0.392966i | ||||||||
\(553\) | 19.8122 | − | 35.2649i | 0.842500 | − | 1.49962i | ||||
\(554\) | − | 4.54864i | − | 0.193253i | ||||||
\(555\) | 1.01799 | + | 1.76321i | 0.0432113 | + | 0.0748442i | ||||
\(556\) | 0.604142 | − | 1.04640i | 0.0256213 | − | 0.0443774i | ||||
\(557\) | −3.15836 | − | 1.82348i | −0.133824 | − | 0.0772634i | 0.431593 | − | 0.902068i | \(-0.357952\pi\) |
−0.565417 | + | 0.824805i | \(0.691285\pi\) | |||||||
\(558\) | −2.35968 | − | 4.08709i | −0.0998933 | − | 0.173020i | ||||
\(559\) | −14.2073 | − | 10.4627i | −0.600905 | − | 0.442524i | ||||
\(560\) | −0.310202 | − | 26.4362i | −0.0131084 | − | 1.11713i | ||||
\(561\) | 40.9162i | 1.72748i | ||||||||
\(562\) | 2.75810 | + | 4.77717i | 0.116344 | + | 0.201513i | ||||
\(563\) | −0.134670 | + | 0.233255i | −0.00567566 | + | 0.00983053i | −0.868849 | − | 0.495077i | \(-0.835140\pi\) |
0.863174 | + | 0.504907i | \(0.168473\pi\) | |||||||
\(564\) | 1.95377 | + | 1.12801i | 0.0822686 | + | 0.0474978i | ||||
\(565\) | 9.42998 | − | 5.44440i | 0.396722 | − | 0.229048i | ||||
\(566\) | − | 41.3662i | − | 1.73875i | ||||||
\(567\) | −2.64557 | + | 0.0310431i | −0.111103 | + | 0.00130369i | ||||
\(568\) | 28.8926 | 1.21231 | ||||||||
\(569\) | −22.8066 | − | 39.5022i | −0.956103 | − | 1.65602i | −0.731823 | − | 0.681495i | \(-0.761330\pi\) |
−0.224280 | − | 0.974525i | \(-0.572003\pi\) | |||||||
\(570\) | 10.6668 | + | 6.15846i | 0.446781 | + | 0.257949i | ||||
\(571\) | 10.7183 | − | 18.5646i | 0.448545 | − | 0.776903i | −0.549746 | − | 0.835332i | \(-0.685276\pi\) |
0.998292 | + | 0.0584283i | \(0.0186089\pi\) | |||||||
\(572\) | −8.45635 | − | 0.943908i | −0.353578 | − | 0.0394668i | ||||
\(573\) | −10.5866 | −0.442262 | ||||||||
\(574\) | 9.81901 | − | 17.4775i | 0.409838 | − | 0.729495i | ||||
\(575\) | 1.61682 | 0.0674260 | ||||||||
\(576\) | 2.81406 | + | 4.87409i | 0.117252 | + | 0.203087i | ||||
\(577\) | −2.10289 | − | 1.21410i | −0.0875445 | − | 0.0505438i | 0.455589 | − | 0.890190i | \(-0.349429\pi\) |
−0.543133 | + | 0.839647i | \(0.682762\pi\) | |||||||
\(578\) | −51.6561 | − | 29.8237i | −2.14861 | − | 1.24050i | ||||
\(579\) | 6.56628 | − | 3.79104i | 0.272885 | − | 0.157550i | ||||
\(580\) | 0.828096i | 0.0343848i | ||||||||
\(581\) | −23.8559 | + | 14.1490i | −0.989709 | + | 0.586999i | ||||
\(582\) | −11.0058 | −0.456205 | ||||||||
\(583\) | 61.9417 | − | 35.7621i | 2.56536 | − | 1.48111i | ||||
\(584\) | −9.09483 | + | 15.7527i | −0.376347 | + | 0.651852i | ||||
\(585\) | −3.09002 | − | 7.06238i | −0.127757 | − | 0.291994i | ||||
\(586\) | 2.40117 | + | 4.15895i | 0.0991916 | + | 0.171805i | ||||
\(587\) | 3.50483i | 0.144660i | 0.997381 | + | 0.0723299i | \(0.0230434\pi\) | ||||
−0.997381 | + | 0.0723299i | \(0.976957\pi\) | |||||||
\(588\) | −3.00083 | + | 0.0704331i | −0.123752 | + | 0.00290461i | ||||
\(589\) | −11.1938 | −0.461232 | ||||||||
\(590\) | −24.3379 | + | 14.0515i | −1.00198 | + | 0.578491i | ||||
\(591\) | −4.99893 | − | 2.88613i | −0.205628 | − | 0.118720i | ||||
\(592\) | −3.85438 | − | 2.22533i | −0.158414 | − | 0.0914604i | ||||
\(593\) | 3.28590 | − | 1.89711i | 0.134936 | − | 0.0779051i | −0.431013 | − | 0.902346i | \(-0.641844\pi\) |
0.565948 | + | 0.824441i | \(0.308510\pi\) | |||||||
\(594\) | 8.57698 | 0.351918 | ||||||||
\(595\) | −36.1718 | + | 21.4536i | −1.48290 | + | 0.879510i | ||||
\(596\) | 2.83302i | 0.116045i | ||||||||
\(597\) | −12.8653 | − | 22.2834i | −0.526543 | − | 0.911999i | ||||
\(598\) | 8.49263 | + | 19.4103i | 0.347289 | + | 0.793745i | ||||
\(599\) | 2.21344 | − | 3.83379i | 0.0904386 | − | 0.156644i | −0.817257 | − | 0.576273i | \(-0.804506\pi\) |
0.907696 | + | 0.419629i | \(0.137840\pi\) | |||||||
\(600\) | 0.909325 | − | 0.524999i | 0.0371230 | − | 0.0214330i | ||||
\(601\) | 0.00578763 | 0.000236082 | 0.000118041 | − | 1.00000i | \(-0.499962\pi\) | ||||
0.000118041 | 1.00000i | \(0.499962\pi\) | ||||||||
\(602\) | 17.5917 | + | 9.88318i | 0.716983 | + | 0.402808i | ||||
\(603\) | 1.76534i | 0.0718901i | ||||||||
\(604\) | −6.87588 | + | 3.96979i | −0.279775 | + | 0.161528i | ||||
\(605\) | −35.7142 | − | 20.6196i | −1.45199 | − | 0.838305i | ||||
\(606\) | −13.6429 | − | 7.87673i | −0.554205 | − | 0.319970i | ||||
\(607\) | −0.0179917 | − | 0.0311626i | −0.000730261 | − | 0.00126485i | 0.865660 | − | 0.500632i | \(-0.166899\pi\) |
−0.866390 | + | 0.499367i | \(0.833566\pi\) | |||||||
\(608\) | −8.82191 | −0.357776 | ||||||||
\(609\) | −2.38959 | + | 0.0280394i | −0.0968309 | + | 0.00113621i | ||||
\(610\) | −12.0890 | −0.489471 | ||||||||
\(611\) | −18.8523 | − | 2.10431i | −0.762681 | − | 0.0851313i | ||||
\(612\) | −1.59401 | + | 2.76090i | −0.0644338 | + | 0.111603i | ||||
\(613\) | 37.8958 | + | 21.8792i | 1.53060 | + | 0.883691i | 0.999334 | + | 0.0364845i | \(0.0116160\pi\) |
0.531264 | + | 0.847207i | \(0.321717\pi\) | |||||||
\(614\) | −19.7922 | − | 34.2811i | −0.798749 | − | 1.38347i | ||||
\(615\) | −10.3948 | −0.419157 | ||||||||
\(616\) | −35.6519 | + | 0.418340i | −1.43646 | + | 0.0168554i | ||||
\(617\) | − | 30.0459i | − | 1.20960i | −0.796376 | − | 0.604802i | \(-0.793252\pi\) | ||
0.796376 | − | 0.604802i | \(-0.206748\pi\) | |||||||
\(618\) | 16.0117 | − | 9.24434i | 0.644084 | − | 0.371862i | ||||
\(619\) | 27.5160 | + | 15.8864i | 1.10596 | + | 0.638526i | 0.937780 | − | 0.347230i | \(-0.112878\pi\) |
0.168180 | + | 0.985756i | \(0.446211\pi\) | |||||||
\(620\) | −1.38814 | + | 2.40433i | −0.0557492 | + | 0.0965604i | ||||
\(621\) | −1.88525 | − | 3.26535i | −0.0756524 | − | 0.131034i | ||||
\(622\) | − | 32.6120i | − | 1.30762i | ||||||
\(623\) | −11.9782 | − | 6.72945i | −0.479895 | − | 0.269610i | ||||
\(624\) | 13.5690 | + | 9.99262i | 0.543194 | + | 0.400025i | ||||
\(625\) | 11.3360 | + | 19.6346i | 0.453442 | + | 0.785384i | ||||
\(626\) | 17.1565 | + | 9.90532i | 0.685713 | + | 0.395896i | ||||
\(627\) | 10.1718 | − | 17.6181i | 0.406223 | − | 0.703599i | ||||
\(628\) | −0.00242175 | − | 0.00419459i | −9.66382e−5 | − | 0.000167382i | ||||
\(629\) | 7.07973i | 0.282287i | ||||||||
\(630\) | 4.49716 | + | 7.58244i | 0.179171 | + | 0.302092i | ||||
\(631\) | − | 19.7990i | − | 0.788185i | −0.919071 | − | 0.394092i | \(-0.871059\pi\) | ||
0.919071 | − | 0.394092i | \(-0.128941\pi\) | |||||||
\(632\) | 32.4203 | − | 18.7179i | 1.28961 | − | 0.744557i | ||||
\(633\) | −1.31323 | + | 2.27458i | −0.0521962 | + | 0.0904065i | ||||
\(634\) | −10.0285 | + | 17.3698i | −0.398281 | + | 0.689843i | ||||
\(635\) | −35.1838 | + | 20.3134i | −1.39623 | + | 0.806113i | ||||
\(636\) | 5.57285 | 0.220978 | ||||||||
\(637\) | 22.8787 | − | 10.6566i | 0.906488 | − | 0.422231i | ||||
\(638\) | 7.74708 | 0.306710 | ||||||||
\(639\) | −10.2186 | + | 5.89971i | −0.404242 | + | 0.233389i | ||||
\(640\) | 14.4791 | − | 25.0786i | 0.572337 | − | 0.991318i | ||||
\(641\) | −9.10916 | + | 15.7775i | −0.359790 | + | 0.623175i | −0.987926 | − | 0.154929i | \(-0.950485\pi\) |
0.628135 | + | 0.778104i | \(0.283818\pi\) | |||||||
\(642\) | −15.5991 | + | 9.00612i | −0.615646 | + | 0.355443i | ||||
\(643\) | 24.7132i | 0.974592i | 0.873237 | + | 0.487296i | \(0.162017\pi\) | ||||
−0.873237 | + | 0.487296i | \(0.837983\pi\) | |||||||
\(644\) | −2.18217 | − | 3.67925i | −0.0859895 | − | 0.144983i | ||||
\(645\) | − | 10.4627i | − | 0.411968i | ||||||
\(646\) | 21.4148 | + | 37.0915i | 0.842555 | + | 1.45935i | ||||
\(647\) | −14.5947 | + | 25.2788i | −0.573777 | + | 0.993810i | 0.422397 | + | 0.906411i | \(0.361189\pi\) |
−0.996173 | + | 0.0873994i | \(0.972144\pi\) | |||||||
\(648\) | −2.12059 | − | 1.22432i | −0.0833046 | − | 0.0480959i | ||||
\(649\) | 23.2086 | + | 40.1985i | 0.911018 | + | 1.57793i | ||||
\(650\) | 1.42881 | − | 1.94018i | 0.0560424 | − | 0.0761001i | ||||
\(651\) | −6.98504 | − | 3.92427i | −0.273765 | − | 0.153804i | ||||
\(652\) | 0.783613i | 0.0306887i | ||||||||
\(653\) | 11.6140 | + | 20.1160i | 0.454490 | + | 0.787200i | 0.998659 | − | 0.0517758i | \(-0.0164881\pi\) |
−0.544168 | + | 0.838976i | \(0.683155\pi\) | |||||||
\(654\) | 9.66906 | − | 16.7473i | 0.378090 | − | 0.654871i | ||||
\(655\) | 20.2759 | + | 11.7063i | 0.792245 | + | 0.457403i | ||||
\(656\) | 19.6786 | − | 11.3615i | 0.768321 | − | 0.443590i | ||||
\(657\) | − | 7.42846i | − | 0.289812i | ||||||
\(658\) | 21.6918 | − | 0.254532i | 0.845636 | − | 0.00992269i | ||||
\(659\) | 48.4141 | 1.88594 | 0.942972 | − | 0.332872i | \(-0.108018\pi\) | ||||
0.942972 | + | 0.332872i | \(0.108018\pi\) | |||||||
\(660\) | −2.52281 | − | 4.36964i | −0.0982004 | − | 0.170088i | ||||
\(661\) | 22.3988 | + | 12.9319i | 0.871212 | + | 0.502994i | 0.867751 | − | 0.497000i | \(-0.165565\pi\) |
0.00346104 | + | 0.999994i | \(0.498898\pi\) | |||||||
\(662\) | −21.3939 | + | 37.0554i | −0.831499 | + | 1.44020i | ||||
\(663\) | 2.97363 | − | 26.6404i | 0.115486 | − | 1.03463i | ||||
\(664\) | −25.6699 | −0.996185 | ||||||||
\(665\) | 20.9086 | − | 0.245341i | 0.810800 | − | 0.00951393i | ||||
\(666\) | 1.48408 | 0.0575068 | ||||||||
\(667\) | −1.70283 | − | 2.94940i | −0.0659340 | − | 0.114201i | ||||
\(668\) | 3.36480 | + | 1.94267i | 0.130188 | + | 0.0751640i | ||||
\(669\) | 5.60156 | + | 3.23406i | 0.216569 | + | 0.125036i | ||||
\(670\) | 5.09413 | − | 2.94110i | 0.196803 | − | 0.113624i | ||||
\(671\) | 19.9673i | 0.770828i | ||||||||
\(672\) | −5.50496 | − | 3.09274i | −0.212358 | − | 0.119305i | ||||
\(673\) | −33.2032 | −1.27989 | −0.639944 | − | 0.768421i | \(-0.721043\pi\) | ||||
−0.639944 | + | 0.768421i | \(0.721043\pi\) | |||||||
\(674\) | 22.2711 | − | 12.8582i | 0.857851 | − | 0.495280i | ||||
\(675\) | −0.214404 | + | 0.371358i | −0.00825241 | + | 0.0142936i | ||||
\(676\) | 5.43730 | + | 1.22915i | 0.209127 | + | 0.0472750i | ||||
\(677\) | −19.1718 | − | 33.2066i | −0.736833 | − | 1.27623i | −0.953915 | − | 0.300078i | \(-0.902987\pi\) |
0.217082 | − | 0.976153i | \(-0.430346\pi\) | |||||||
\(678\) | − | 7.93710i | − | 0.304823i | ||||||
\(679\) | −16.0702 | + | 9.53129i | −0.616719 | + | 0.365777i | ||||
\(680\) | −38.9223 | −1.49260 | ||||||||
\(681\) | 6.18745 | − | 3.57233i | 0.237104 | − | 0.136892i | ||||
\(682\) | 22.4932 | + | 12.9865i | 0.861311 | + | 0.497278i | ||||
\(683\) | 9.67577 | + | 5.58631i | 0.370233 | + | 0.213754i | 0.673560 | − | 0.739132i | \(-0.264764\pi\) |
−0.303327 | + | 0.952886i | \(0.598098\pi\) | |||||||
\(684\) | 1.37272 | − | 0.792543i | 0.0524875 | − | 0.0303036i | ||||
\(685\) | −3.52210 | −0.134572 | ||||||||
\(686\) | −24.4728 | + | 15.3023i | −0.934377 | + | 0.584246i | ||||
\(687\) | − | 12.9854i | − | 0.495423i | ||||||
\(688\) | 11.4357 | + | 19.8072i | 0.435982 | + | 0.755143i | ||||
\(689\) | −42.9290 | + | 18.7828i | −1.63547 | + | 0.715570i | ||||
\(690\) | −6.28174 | + | 10.8803i | −0.239142 | + | 0.414206i | ||||
\(691\) | −11.6191 | + | 6.70831i | −0.442013 | + | 0.255196i | −0.704451 | − | 0.709753i | \(-0.748807\pi\) |
0.262438 | + | 0.964949i | \(0.415473\pi\) | |||||||
\(692\) | 2.68272 | 0.101982 | ||||||||
\(693\) | 12.5238 | − | 7.42788i | 0.475739 | − | 0.282162i | ||||
\(694\) | − | 13.7748i | − | 0.522885i | ||||||
\(695\) | −5.21737 | + | 3.01225i | −0.197906 | + | 0.114261i | ||||
\(696\) | −1.91540 | − | 1.10586i | −0.0726032 | − | 0.0419175i | ||||
\(697\) | −31.3031 | − | 18.0729i | −1.18569 | − | 0.684558i | ||||
\(698\) | 21.2557 | + | 36.8159i | 0.804539 | + | 1.39350i | ||||
\(699\) | 19.7194 | 0.745855 | ||||||||
\(700\) | −0.238285 | + | 0.424138i | −0.00900632 | + | 0.0160309i | ||||
\(701\) | −17.9203 | −0.676841 | −0.338421 | − | 0.940995i | \(-0.609893\pi\) | ||||
−0.338421 | + | 0.940995i | \(0.609893\pi\) | |||||||
\(702\) | −5.58444 | − | 0.623342i | −0.210771 | − | 0.0235265i | ||||
\(703\) | 1.76003 | − | 3.04846i | 0.0663808 | − | 0.114975i | ||||
\(704\) | −26.8245 | − | 15.4871i | −1.01099 | − | 0.583693i | ||||
\(705\) | −5.62426 | − | 9.74150i | −0.211822 | − | 0.366886i | ||||
\(706\) | −3.66823 | −0.138056 | ||||||||
\(707\) | −26.7423 | + | 0.313794i | −1.00575 | + | 0.0118014i | ||||
\(708\) | 3.61663i | 0.135921i | ||||||||
\(709\) | −26.4757 | + | 15.2857i | −0.994315 | + | 0.574068i | −0.906561 | − | 0.422074i | \(-0.861302\pi\) |
−0.0877539 | + | 0.996142i | \(0.527969\pi\) | |||||||
\(710\) | 34.0489 | + | 19.6581i | 1.27783 | + | 0.737756i | ||||
\(711\) | −7.64418 | + | 13.2401i | −0.286679 | + | 0.496543i | ||||
\(712\) | −6.35776 | − | 11.0120i | −0.238267 | − | 0.412690i | ||||
\(713\) | − | 11.4179i | − | 0.427603i | ||||||
\(714\) | 0.359682 | + | 30.6530i | 0.0134608 | + | 1.14716i | ||||
\(715\) | 34.1614 | + | 25.1575i | 1.27756 | + | 0.940837i | ||||
\(716\) | 0.0821556 | + | 0.142298i | 0.00307030 | + | 0.00531792i | ||||
\(717\) | 18.0785 | + | 10.4376i | 0.675153 | + | 0.389800i | ||||
\(718\) | −2.71440 | + | 4.70149i | −0.101301 | + | 0.175458i | ||||
\(719\) | 1.77518 | + | 3.07470i | 0.0662030 | + | 0.114667i | 0.897227 | − | 0.441570i | \(-0.145578\pi\) |
−0.831024 | + | 0.556237i | \(0.812245\pi\) | |||||||
\(720\) | 9.99262i | 0.372403i | ||||||||
\(721\) | 15.3738 | − | 27.3647i | 0.572550 | − | 1.01912i | ||||
\(722\) | 8.31581i | 0.309482i | ||||||||
\(723\) | 14.8824 | − | 8.59237i | 0.553483 | − | 0.319554i | ||||
\(724\) | 2.14611 | − | 3.71716i | 0.0797594 | − | 0.138147i | ||||
\(725\) | −0.193658 | + | 0.335426i | −0.00719229 | + | 0.0124574i | ||||
\(726\) | −26.0329 | + | 15.0301i | −0.966171 | + | 0.557819i | ||||
\(727\) | 8.34296 | 0.309423 | 0.154712 | − | 0.987960i | \(-0.450555\pi\) | ||||
0.154712 | + | 0.987960i | \(0.450555\pi\) | |||||||
\(728\) | 23.2432 | + | 2.31866i | 0.861451 | + | 0.0859354i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −21.4358 | + | 12.3760i | −0.793376 | + | 0.458056i | ||||
\(731\) | 18.1910 | − | 31.5077i | 0.672817 | − | 1.16535i | ||||
\(732\) | −0.777881 | + | 1.34733i | −0.0287513 | + | 0.0497987i | ||||
\(733\) | 4.48482 | − | 2.58931i | 0.165651 | − | 0.0956385i | −0.414883 | − | 0.909875i | \(-0.636177\pi\) |
0.580533 | + | 0.814236i | \(0.302844\pi\) | |||||||
\(734\) | 9.07581i | 0.334994i | ||||||||
\(735\) | 13.1332 | + | 7.17693i | 0.484424 | + | 0.264725i | ||||
\(736\) | − | 8.99852i | − | 0.331690i | ||||||
\(737\) | −4.85776 | − | 8.41388i | −0.178938 | − | 0.309929i | ||||
\(738\) | −3.78849 | + | 6.56186i | −0.139456 | + | 0.241545i | ||||
\(739\) | −5.18606 | − | 2.99417i | −0.190772 | − | 0.110142i | 0.401572 | − | 0.915828i | \(-0.368464\pi\) |
−0.592344 | + | 0.805685i | \(0.701797\pi\) | |||||||
\(740\) | −0.436523 | − | 0.756079i | −0.0160469 | − | 0.0277940i | ||||
\(741\) | −7.90324 | + | 10.7318i | −0.290333 | + | 0.394243i | ||||
\(742\) | 46.0902 | − | 27.3362i | 1.69202 | − | 1.00354i | ||||
\(743\) | 21.3134i | 0.781912i | 0.920409 | + | 0.390956i | \(0.127856\pi\) | ||||
−0.920409 | + | 0.390956i | \(0.872144\pi\) | |||||||
\(744\) | −3.70752 | − | 6.42160i | −0.135924 | − | 0.235427i | ||||
\(745\) | 7.06271 | − | 12.2330i | 0.258758 | − | 0.448181i | ||||
\(746\) | −11.7783 | − | 6.80020i | −0.431234 | − | 0.248973i | ||||
\(747\) | 9.07880 | − | 5.24165i | 0.332176 | − | 0.191782i | ||||
\(748\) | − | 17.5452i | − | 0.641515i | ||||||
\(749\) | −14.9776 | + | 26.6596i | −0.547270 | + | 0.974120i | ||||
\(750\) | 18.0890 | 0.660519 | ||||||||
\(751\) | −7.70605 | − | 13.3473i | −0.281198 | − | 0.487049i | 0.690482 | − | 0.723349i | \(-0.257398\pi\) |
−0.971680 | + | 0.236300i | \(0.924065\pi\) | |||||||
\(752\) | 21.2949 | + | 12.2946i | 0.776545 | + | 0.448339i | ||||
\(753\) | 11.1966 | − | 19.3930i | 0.408025 | − | 0.706720i | ||||
\(754\) | −5.04409 | − | 0.563028i | −0.183695 | − | 0.0205043i | ||||
\(755\) | 39.5867 | 1.44071 | ||||||||
\(756\) | 1.13444 | − | 0.0133115i | 0.0412592 | − | 0.000484136i | ||||
\(757\) | −31.6188 | −1.14920 | −0.574602 | − | 0.818433i | \(-0.694843\pi\) | ||||
−0.574602 | + | 0.818433i | \(0.694843\pi\) | |||||||
\(758\) | 14.7022 | + | 25.4650i | 0.534008 | + | 0.924929i | ||||
\(759\) | 17.9708 | + | 10.3754i | 0.652298 | + | 0.376605i | ||||
\(760\) | 16.7595 | + | 9.67612i | 0.607932 | + | 0.350990i | ||||
\(761\) | 6.39264 | − | 3.69079i | 0.231733 | − | 0.133791i | −0.379638 | − | 0.925135i | \(-0.623952\pi\) |
0.611371 | + | 0.791344i | \(0.290618\pi\) | |||||||
\(762\) | 29.6138i | 1.07280i | ||||||||
\(763\) | −0.385197 | − | 32.8274i | −0.0139451 | − | 1.18843i | ||||
\(764\) | 4.53962 | 0.164238 | ||||||||
\(765\) | 13.7658 | − | 7.94771i | 0.497705 | − | 0.287350i | ||||
\(766\) | 11.2062 | − | 19.4097i | 0.404896 | − | 0.701301i | ||||
\(767\) | −12.1896 | − | 27.8598i | −0.440140 | − | 1.00596i | ||||
\(768\) | −4.92605 | − | 8.53218i | −0.177754 | − | 0.307878i | ||||
\(769\) | 40.4051i | 1.45704i | 0.685022 | + | 0.728522i | \(0.259792\pi\) | ||||
−0.685022 | + | 0.728522i | \(0.740208\pi\) | |||||||
\(770\) | −42.2991 | − | 23.7641i | −1.52435 | − | 0.856398i | ||||
\(771\) | 20.5806 | 0.741191 | ||||||||
\(772\) | −2.81567 | + | 1.62563i | −0.101338 | + | 0.0585076i | ||||
\(773\) | −24.1100 | − | 13.9199i | −0.867176 | − | 0.500664i | −0.000767212 | − | 1.00000i | \(-0.500244\pi\) |
−0.866409 | + | 0.499335i | \(0.833578\pi\) | |||||||
\(774\) | −6.60474 | − | 3.81325i | −0.237402 | − | 0.137064i | ||||
\(775\) | −1.12455 | + | 0.649261i | −0.0403951 | + | 0.0233222i | ||||
\(776\) | −17.2922 | −0.620754 | ||||||||
\(777\) | 2.16699 | − | 1.28525i | 0.0777404 | − | 0.0461080i | ||||
\(778\) | 4.29110i | 0.153843i | ||||||||
\(779\) | 8.98587 | + | 15.5640i | 0.321952 | + | 0.557637i | ||||
\(780\) | 1.32502 | + | 3.02840i | 0.0474435 | + | 0.108434i | ||||
\(781\) | 32.4690 | − | 56.2379i | 1.16183 | − | 2.01235i | ||||
\(782\) | −37.8341 | + | 21.8435i | −1.35294 | + | 0.781123i | ||||
\(783\) | 0.903241 | 0.0322792 | ||||||||
\(784\) | −32.7072 | + | 0.767678i | −1.16811 | + | 0.0274171i | ||||
\(785\) | 0.0241497i | 0.000861938i | ||||||||
\(786\) | 14.7796 | − | 8.53299i | 0.527170 | − | 0.304362i | ||||
\(787\) | −19.7457 | − | 11.4002i | −0.703859 | − | 0.406373i | 0.104924 | − | 0.994480i | \(-0.466540\pi\) |
−0.808783 | + | 0.588107i | \(0.799873\pi\) | |||||||
\(788\) | 2.14358 | + | 1.23760i | 0.0763618 | + | 0.0440875i | ||||
\(789\) | −2.52474 | − | 4.37298i | −0.0898831 | − | 0.155682i | ||||
\(790\) | 50.9415 | 1.81242 | ||||||||
\(791\) | −6.87373 | − | 11.5895i | −0.244402 | − | 0.412074i | ||||
\(792\) | 13.4761 | 0.478852 | ||||||||
\(793\) | 1.45114 | − | 13.0006i | 0.0515316 | − | 0.461665i | ||||
\(794\) | −7.75893 | + | 13.4389i | −0.275354 | + | 0.476927i | ||||
\(795\) | −24.0636 | − | 13.8931i | −0.853447 | − | 0.492738i | ||||
\(796\) | 5.51675 | + | 9.55529i | 0.195536 | + | 0.338678i | ||||
\(797\) | 8.63198 | 0.305760 | 0.152880 | − | 0.988245i | \(-0.451145\pi\) | ||||
0.152880 | + | 0.988245i | \(0.451145\pi\) | |||||||
\(798\) | 7.46550 | − | 13.2883i | 0.264276 | − | 0.470400i | ||||
\(799\) | − | 39.1145i | − | 1.38377i | ||||||
\(800\) | −0.886268 | + | 0.511687i | −0.0313343 | + | 0.0180909i | ||||
\(801\) | 4.49716 | + | 2.59644i | 0.158899 | + | 0.0917406i | ||||
\(802\) | 1.37125 | − | 2.37508i | 0.0484206 | − | 0.0838669i | ||||
\(803\) | 20.4412 | + | 35.4052i | 0.721355 | + | 1.24942i | ||||
\(804\) | − | 0.756990i | − | 0.0266970i | ||||||
\(805\) | 0.250253 | + | 21.3271i | 0.00882025 | + | 0.751683i | ||||
\(806\) | −13.7015 | − | 10.0902i | −0.482613 | − | 0.355411i | ||||
\(807\) | 7.45079 | + | 12.9052i | 0.262280 | + | 0.454283i | ||||
\(808\) | −21.4356 | − | 12.3759i | −0.754103 | − | 0.435381i | ||||
\(809\) | −14.0190 | + | 24.2815i | −0.492880 | + | 0.853694i | −0.999966 | − | 0.00820168i | \(-0.997389\pi\) |
0.507086 | + | 0.861895i | \(0.330723\pi\) | |||||||
\(810\) | −1.66602 | − | 2.88564i | −0.0585381 | − | 0.101391i | ||||
\(811\) | 36.2095i | 1.27149i | 0.771901 | + | 0.635743i | \(0.219306\pi\) | ||||
−0.771901 | + | 0.635743i | \(0.780694\pi\) | |||||||
\(812\) | 1.02467 | − | 0.0120235i | 0.0359590 | − | 0.000421943i | ||||
\(813\) | 6.25712i | 0.219447i | ||||||||
\(814\) | −7.07334 | + | 4.08379i | −0.247920 | + | 0.143137i | ||||
\(815\) | 1.95355 | − | 3.38364i | 0.0684298 | − | 0.118524i | ||||
\(816\) | −17.3737 | + | 30.0921i | −0.608200 | + | 1.05343i | ||||
\(817\) | −15.6657 | + | 9.04459i | −0.548073 | + | 0.316430i | ||||
\(818\) | 24.3211 | 0.850369 | ||||||||
\(819\) | −8.69401 | + | 3.92609i | −0.303793 | + | 0.137189i | ||||
\(820\) | 4.45735 | 0.155657 | ||||||||
\(821\) | −13.9062 | + | 8.02877i | −0.485331 | + | 0.280206i | −0.722635 | − | 0.691229i | \(-0.757069\pi\) |
0.237305 | + | 0.971435i | \(0.423736\pi\) | |||||||
\(822\) | −1.28367 | + | 2.22338i | −0.0447731 | + | 0.0775493i | ||||
\(823\) | 15.5112 | − | 26.8663i | 0.540688 | − | 0.936499i | −0.458177 | − | 0.888861i | \(-0.651497\pi\) |
0.998865 | − | 0.0476379i | \(-0.0151693\pi\) | |||||||
\(824\) | 25.1574 | − | 14.5246i | 0.876400 | − | 0.505990i | ||||
\(825\) | − | 2.35994i | − | 0.0821624i | ||||||
\(826\) | 17.7405 | + | 29.9113i | 0.617270 | + | 1.04075i | ||||
\(827\) | 5.74395i | 0.199737i | 0.995001 | + | 0.0998683i | \(0.0318422\pi\) | ||||
−0.995001 | + | 0.0998683i | \(0.968158\pi\) | |||||||
\(828\) | 0.808409 | + | 1.40021i | 0.0280942 | + | 0.0486605i | ||||
\(829\) | −13.1223 | + | 22.7285i | −0.455757 | + | 0.789395i | −0.998731 | − | 0.0503545i | \(-0.983965\pi\) |
0.542974 | + | 0.839750i | \(0.317298\pi\) | |||||||
\(830\) | −30.2510 | − | 17.4654i | −1.05003 | − | 0.606234i | ||||
\(831\) | 1.45934 | + | 2.52764i | 0.0506238 | + | 0.0876830i | ||||
\(832\) | 16.3398 | + | 12.0331i | 0.566480 | + | 0.417173i | ||||
\(833\) | 27.0715 | + | 44.4468i | 0.937971 | + | 1.53999i | ||||
\(834\) | 4.39140i | 0.152062i | ||||||||
\(835\) | −9.68614 | − | 16.7769i | −0.335203 | − | 0.580588i | ||||
\(836\) | −4.36175 | + | 7.55477i | −0.150854 | + | 0.261287i | ||||
\(837\) | 2.62251 | + | 1.51411i | 0.0906473 | + | 0.0523352i | ||||
\(838\) | 7.53971 | − | 4.35305i | 0.260455 | − | 0.150374i | ||||
\(839\) | 14.9188i | 0.515055i | 0.966271 | + | 0.257528i | \(0.0829078\pi\) | ||||
−0.966271 | + | 0.257528i | \(0.917092\pi\) | |||||||
\(840\) | 7.06591 | + | 11.9135i | 0.243797 | + | 0.411054i | ||||
\(841\) | −28.1842 | −0.971867 | ||||||||
\(842\) | −9.60241 | − | 16.6319i | −0.330921 | − | 0.573172i | ||||
\(843\) | −3.06531 | − | 1.76976i | −0.105575 | − | 0.0609537i | ||||
\(844\) | 0.563123 | − | 0.975358i | 0.0193835 | − | 0.0335732i | ||||
\(845\) | −20.4140 | − | 18.8627i | −0.702263 | − | 0.648895i | ||||
\(846\) | −8.19931 | −0.281898 | ||||||||
\(847\) | −24.9958 | + | 44.4915i | −0.858865 | + | 1.52875i | ||||
\(848\) | 60.7406 | 2.08584 | ||||||||
\(849\) | 13.2715 | + | 22.9869i | 0.455475 | + | 0.788907i | ||||
\(850\) | 4.30276 | + | 2.48420i | 0.147583 | + | 0.0852073i | ||||
\(851\) | 3.10949 | + | 1.79526i | 0.106592 | + | 0.0615408i | ||||
\(852\) | 4.38181 | − | 2.52984i | 0.150118 | − | 0.0866709i | ||||
\(853\) | 24.1400i | 0.826537i | 0.910609 | + | 0.413268i | \(0.135613\pi\) | ||||
−0.910609 | + | 0.413268i | \(0.864387\pi\) | |||||||
\(854\) | 0.175527 | + | 14.9588i | 0.00600639 | + | 0.511879i | ||||
\(855\) | −7.90324 | −0.270285 | ||||||||
\(856\) | −24.5091 | + | 14.1504i | −0.837705 | + | 0.483649i | ||||
\(857\) | −0.669552 | + | 1.15970i | −0.0228715 | + | 0.0396146i | −0.877235 | − | 0.480062i | \(-0.840614\pi\) |
0.854363 | + | 0.519676i | \(0.173948\pi\) | |||||||
\(858\) | 28.3316 | − | 12.3960i | 0.967225 | − | 0.423192i | ||||
\(859\) | −20.2107 | − | 35.0059i | −0.689580 | − | 1.19439i | −0.971974 | − | 0.235089i | \(-0.924462\pi\) |
0.282394 | − | 0.959298i | \(-0.408871\pi\) | |||||||
\(860\) | 4.48648i | 0.152988i | ||||||||
\(861\) | 0.150926 | + | 12.8623i | 0.00514356 | + | 0.438346i | ||||
\(862\) | 0.608829 | 0.0207368 | ||||||||
\(863\) | −11.7479 | + | 6.78268i | −0.399905 | + | 0.230885i | −0.686443 | − | 0.727184i | \(-0.740829\pi\) |
0.286538 | + | 0.958069i | \(0.407495\pi\) | |||||||
\(864\) | 2.06682 | + | 1.19328i | 0.0703147 | + | 0.0405962i | ||||
\(865\) | −11.5840 | − | 6.68802i | −0.393867 | − | 0.227399i | ||||
\(866\) | 29.6416 | − | 17.1136i | 1.00726 | − | 0.581542i | ||||
\(867\) | 38.2732 | 1.29983 | ||||||||
\(868\) | 2.99524 | + | 1.68276i | 0.101665 | + | 0.0571165i | ||||
\(869\) | − | 84.1392i | − | 2.85423i | ||||||
\(870\) | −1.50482 | − | 2.60643i | −0.0510182 | − | 0.0883661i | ||||
\(871\) | 2.55138 | + | 5.83129i | 0.0864501 | + | 0.197586i | ||||
\(872\) | 15.1920 | − | 26.3132i | 0.514464 | − | 0.891078i | ||||
\(873\) | 6.11583 | − | 3.53097i | 0.206989 | − | 0.119505i | ||||
\(874\) | 21.7213 | 0.734734 | ||||||||
\(875\) | 26.4129 | − | 15.6656i | 0.892920 | − | 0.529593i | ||||
\(876\) | 3.18538i | 0.107624i | ||||||||
\(877\) | −15.8608 | + | 9.15722i | −0.535580 | + | 0.309217i | −0.743286 | − | 0.668974i | \(-0.766734\pi\) |
0.207706 | + | 0.978191i | \(0.433400\pi\) | |||||||
\(878\) | 0.486679 | + | 0.280984i | 0.0164246 | + | 0.00948276i | ||||
\(879\) | −2.66863 | − | 1.54073i | −0.0900105 | − | 0.0519676i | ||||
\(880\) | −27.4971 | − | 47.6264i | −0.926927 | − | 1.60549i | ||||
\(881\) | −19.5050 | −0.657141 | −0.328570 | − | 0.944480i | \(-0.606567\pi\) | ||||
−0.328570 | + | 0.944480i | \(0.606567\pi\) | |||||||
\(882\) | 9.31709 | − | 5.67481i | 0.313723 | − | 0.191081i | ||||
\(883\) | 9.06232 | 0.304972 | 0.152486 | − | 0.988306i | \(-0.451272\pi\) | ||||
0.152486 | + | 0.988306i | \(0.451272\pi\) | |||||||
\(884\) | −1.27511 | + | 11.4236i | −0.0428868 | + | 0.384217i | ||||
\(885\) | 9.01626 | − | 15.6166i | 0.303078 | − | 0.524947i | ||||
\(886\) | 49.2180 | + | 28.4160i | 1.65351 | + | 0.954655i | ||||
\(887\) | 4.07510 | + | 7.05829i | 0.136829 | + | 0.236994i | 0.926295 | − | 0.376800i | \(-0.122976\pi\) |
−0.789466 | + | 0.613794i | \(0.789642\pi\) | |||||||
\(888\) | 2.33177 | 0.0782490 | ||||||||
\(889\) | 25.6463 | + | 43.2410i | 0.860150 | + | 1.45026i | ||||
\(890\) | − | 17.3029i | − | 0.579995i | ||||||
\(891\) | −4.76616 | + | 2.75174i | −0.159672 | + | 0.0921869i | ||||
\(892\) | −2.40199 | − | 1.38679i | −0.0804247 | − | 0.0464332i | ||||
\(893\) | −9.72391 | + | 16.8423i | −0.325398 | + | 0.563606i | ||||
\(894\) | −5.14817 | − | 8.91690i | −0.172181 | − | 0.298226i | ||||
\(895\) | − | 0.819256i | − | 0.0273847i | ||||||
\(896\) | −31.2420 | − | 17.5521i | −1.04372 | − | 0.586374i | ||||
\(897\) | −10.9467 | − | 8.06146i | −0.365499 | − | 0.269164i | ||||
\(898\) | 20.1747 | + | 34.9436i | 0.673239 | + | 1.16608i | ||||
\(899\) | 2.36876 | + | 1.36760i | 0.0790026 | + | 0.0456122i | ||||
\(900\) | 0.0919380 | − | 0.159241i | 0.00306460 | − | 0.00530804i | ||||
\(901\) | −48.3105 | − | 83.6763i | −1.60946 | − | 2.78766i | ||||
\(902\) | − | 41.6998i | − | 1.38845i | ||||||
\(903\) | −12.9464 | + | 0.151913i | −0.430828 | + | 0.00505533i | ||||
\(904\) | − | 12.4707i | − | 0.414770i | ||||||
\(905\) | −18.5338 | + | 10.7005i | −0.616084 | + | 0.355696i | ||||
\(906\) | 14.4278 | − | 24.9898i | 0.479333 | − | 0.830229i | ||||
\(907\) | −12.2060 | + | 21.1414i | −0.405294 | + | 0.701989i | −0.994356 | − | 0.106099i | \(-0.966164\pi\) |
0.589062 | + | 0.808088i | \(0.299497\pi\) | |||||||
\(908\) | −2.65322 | + | 1.53184i | −0.0880504 | + | 0.0508359i | ||||
\(909\) | 10.1083 | 0.335272 | ||||||||
\(910\) | 25.8137 | + | 18.5468i | 0.855716 | + | 0.614821i | ||||
\(911\) | 11.3864 | 0.377248 | 0.188624 | − | 0.982049i | \(-0.439597\pi\) | ||||
0.188624 | + | 0.982049i | \(0.439597\pi\) | |||||||
\(912\) | 14.9619 | − | 8.63823i | 0.495437 | − | 0.286040i | ||||
\(913\) | −28.8473 | + | 49.9651i | −0.954708 | + | 1.65360i | ||||
\(914\) | 31.3513 | − | 54.3021i | 1.03701 | − | 1.79615i | ||||
\(915\) | 6.71779 | − | 3.87852i | 0.222083 | − | 0.128220i | ||||
\(916\) | 5.56823i | 0.183979i | ||||||||
\(917\) | 14.1908 | − | 25.2590i | 0.468621 | − | 0.834127i | ||||
\(918\) | − | 11.5865i | − | 0.382413i | ||||||
\(919\) | 16.3008 | + | 28.2337i | 0.537712 | + | 0.931345i | 0.999027 | + | 0.0441082i | \(0.0140446\pi\) |
−0.461315 | + | 0.887237i | \(0.652622\pi\) | |||||||
\(920\) | −9.86982 | + | 17.0950i | −0.325398 | + | 0.563607i | ||||
\(921\) | 21.9967 | + | 12.6998i | 0.724817 | + | 0.418473i | ||||
\(922\) | −20.7973 | − | 36.0220i | −0.684923 | − | 1.18632i | ||||
\(923\) | −25.2276 | + | 34.2566i | −0.830376 | + | 1.12757i | ||||
\(924\) | −5.37029 | + | 3.18513i | −0.176670 | + | 0.104783i | ||||
\(925\) | − | 0.408340i | − | 0.0134261i | ||||||
\(926\) | −3.59965 | − | 6.23478i | −0.118292 | − | 0.204888i | ||||
\(927\) | −5.93170 | + | 10.2740i | −0.194823 | + | 0.337443i | ||||
\(928\) | 1.86684 | + | 1.07782i | 0.0612819 | + | 0.0353811i | ||||
\(929\) | 19.5941 | − | 11.3127i | 0.642863 | − | 0.371157i | −0.142854 | − | 0.989744i | \(-0.545628\pi\) |
0.785717 | + | 0.618587i | \(0.212294\pi\) | |||||||
\(930\) | − | 10.0902i | − | 0.330870i | ||||||
\(931\) | −0.607163 | − | 25.8684i | −0.0198989 | − | 0.847801i | ||||
\(932\) | −8.45581 | −0.276979 | ||||||||
\(933\) | 10.4629 | + | 18.1222i | 0.342539 | + | 0.593295i | ||||
\(934\) | −23.1596 | − | 13.3712i | −0.757805 | − | 0.437519i | ||||
\(935\) | −43.7401 | + | 75.7601i | −1.43045 | + | 2.47762i | ||||
\(936\) | −8.77423 | − | 0.979390i | −0.286795 | − | 0.0320123i | ||||
\(937\) | 9.49113 | 0.310062 | 0.155031 | − | 0.987910i | \(-0.450452\pi\) | ||||
0.155031 | + | 0.987910i | \(0.450452\pi\) | |||||||
\(938\) | −3.71323 | − | 6.26069i | −0.121241 | − | 0.204419i | ||||
\(939\) | −12.7117 | −0.414829 | ||||||||
\(940\) | 2.41172 | + | 4.17723i | 0.0786618 | + | 0.136246i | ||||
\(941\) | 48.6155 | + | 28.0682i | 1.58482 | + | 0.914997i | 0.994141 | + | 0.108090i | \(0.0344736\pi\) |
0.590680 | + | 0.806906i | \(0.298860\pi\) | |||||||
\(942\) | 0.0152449 | + | 0.00880162i | 0.000496704 | + | 0.000286772i | ||||
\(943\) | −15.8756 | + | 9.16576i | −0.516979 | + | 0.298478i | ||||
\(944\) | 39.4190i | 1.28298i | ||||||||
\(945\) | −4.93170 | − | 2.77068i | −0.160428 | − | 0.0901302i | ||||
\(946\) | 41.9723 | 1.36464 | ||||||||
\(947\) | −20.7809 | + | 11.9978i | −0.675288 | + | 0.389878i | −0.798077 | − | 0.602555i | \(-0.794149\pi\) |
0.122789 | + | 0.992433i | \(0.460816\pi\) | |||||||
\(948\) | 3.27788 | − | 5.67746i | 0.106461 | − | 0.184395i | ||||
\(949\) | −10.7361 | − | 24.5378i | −0.348508 | − | 0.796530i | ||||
\(950\) | −1.23515 | − | 2.13934i | −0.0400735 | − | 0.0694094i | ||||
\(951\) | − | 12.8697i | − | 0.417328i | ||||||
\(952\) | 0.565130 | + | 48.1618i | 0.0183160 | + | 1.56093i | ||||
\(953\) | 35.6072 | 1.15343 | 0.576715 | − | 0.816946i | \(-0.304334\pi\) | ||||
0.576715 | + | 0.816946i | \(0.304334\pi\) | |||||||
\(954\) | −17.5405 | + | 10.1270i | −0.567894 | + | 0.327874i | ||||
\(955\) | −19.6021 | − | 11.3173i | −0.634309 | − | 0.366219i | ||||
\(956\) | −7.75219 | − | 4.47573i | −0.250724 | − | 0.144755i | ||||
\(957\) | −4.30499 | + | 2.48549i | −0.139161 | + | 0.0803444i | ||||
\(958\) | −44.6168 | −1.44150 | ||||||||
\(959\) | 0.0511390 | + | 4.35818i | 0.00165136 | + | 0.140733i | ||||
\(960\) | 12.0331i | 0.388367i | ||||||||
\(961\) | −10.9150 | − | 18.9052i | −0.352095 | − | 0.609847i | ||||
\(962\) | 4.90222 | − | 2.14488i | 0.158054 | − | 0.0691537i | ||||
\(963\) | 5.77885 | − | 10.0093i | 0.186221 | − | 0.322544i | ||||
\(964\) | −6.38170 | + | 3.68447i | −0.205541 | + | 0.118669i | ||||
\(965\) | 16.2108 | 0.521843 | ||||||||
\(966\) | 13.5543 | + | 7.61495i | 0.436103 | + | 0.245007i | ||||
\(967\) | − | 54.8608i | − | 1.76420i | −0.471058 | − | 0.882102i | \(-0.656128\pi\) | ||
0.471058 | − | 0.882102i | \(-0.343872\pi\) | |||||||
\(968\) | −40.9027 | + | 23.6152i | −1.31466 | + | 0.759020i | ||||
\(969\) | −23.8001 | − | 13.7410i | −0.764569 | − | 0.441424i | ||||
\(970\) | −20.3782 | − | 11.7654i | −0.654306 | − | 0.377764i | ||||
\(971\) | −12.8520 | − | 22.2604i | −0.412441 | − | 0.714369i | 0.582715 | − | 0.812677i | \(-0.301990\pi\) |
−0.995156 | + | 0.0983076i | \(0.968657\pi\) | |||||||
\(972\) | −0.428808 | −0.0137540 | ||||||||
\(973\) | 3.80307 | + | 6.41216i | 0.121921 | + | 0.205564i | ||||
\(974\) | 24.5085 | 0.785303 | ||||||||
\(975\) | −0.171511 | + | 1.53655i | −0.00549275 | + | 0.0492088i | ||||
\(976\) | −8.47843 | + | 14.6851i | −0.271388 | + | 0.470058i | ||||
\(977\) | 34.0689 | + | 19.6697i | 1.08996 | + | 0.629289i | 0.933566 | − | 0.358406i | \(-0.116680\pi\) |
0.156394 | + | 0.987695i | \(0.450013\pi\) | |||||||
\(978\) | −1.42399 | − | 2.46642i | −0.0455341 | − | 0.0788673i | ||||
\(979\) | −28.5789 | −0.913386 | ||||||||
\(980\) | −5.63160 | − | 3.07752i | −0.179895 | − | 0.0983078i | ||||
\(981\) | 12.4085i | 0.396171i | ||||||||
\(982\) | 46.1603 | − | 26.6507i | 1.47304 | − | 0.850458i | ||||
\(983\) | −32.5998 | − | 18.8215i | −1.03977 | − | 0.600314i | −0.120004 | − | 0.992773i | \(-0.538291\pi\) |
−0.919769 | + | 0.392460i | \(0.871624\pi\) | |||||||
\(984\) | −5.95245 | + | 10.3099i | −0.189757 | + | 0.328669i | ||||
\(985\) | −6.17065 | − | 10.6879i | −0.196613 | − | 0.340544i | ||||
\(986\) | − | 10.4654i | − | 0.333287i | ||||||
\(987\) | −11.9723 | + | 7.10081i | −0.381083 | + | 0.226021i | ||||
\(988\) | 3.38897 | − | 4.60189i | 0.107817 | − | 0.146406i | ||||
\(989\) | −9.22565 | − | 15.9793i | −0.293359 | − | 0.508112i | ||||
\(990\) | 15.8811 | + | 9.16894i | 0.504734 | + | 0.291408i | ||||
\(991\) | −30.3909 | + | 52.6386i | −0.965399 | + | 1.67212i | −0.256859 | + | 0.966449i | \(0.582688\pi\) |
−0.708540 | + | 0.705671i | \(0.750646\pi\) | |||||||
\(992\) | 3.61351 | + | 6.25878i | 0.114729 | + | 0.198717i | ||||
\(993\) | − | 27.4552i | − | 0.871263i | ||||||
\(994\) | 23.8303 | − | 42.4169i | 0.755850 | − | 1.34538i | ||||
\(995\) | − | 55.0130i | − | 1.74403i | ||||||
\(996\) | −3.89306 | + | 2.24766i | −0.123356 | + | 0.0712198i | ||||
\(997\) | −9.03612 | + | 15.6510i | −0.286177 | + | 0.495673i | −0.972894 | − | 0.231252i | \(-0.925718\pi\) |
0.686717 | + | 0.726925i | \(0.259051\pi\) | |||||||
\(998\) | −10.7152 | + | 18.5593i | −0.339185 | + | 0.587485i | ||||
\(999\) | −0.824689 | + | 0.476134i | −0.0260920 | + | 0.0150642i |
(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 | 273.2.bj.c.25.7 | yes | 16 | |
3.2 | odd | 2 | 819.2.dl.f.298.2 | 16 | |||
7.2 | even | 3 | inner | 273.2.bj.c.142.2 | yes | 16 | |
7.3 | odd | 6 | 1911.2.c.k.883.7 | 8 | |||
7.4 | even | 3 | 1911.2.c.n.883.7 | 8 | |||
13.12 | even | 2 | inner | 273.2.bj.c.25.2 | ✓ | 16 | |
21.2 | odd | 6 | 819.2.dl.f.415.7 | 16 | |||
39.38 | odd | 2 | 819.2.dl.f.298.7 | 16 | |||
91.25 | even | 6 | 1911.2.c.n.883.2 | 8 | |||
91.38 | odd | 6 | 1911.2.c.k.883.2 | 8 | |||
91.51 | even | 6 | inner | 273.2.bj.c.142.7 | yes | 16 | |
273.233 | odd | 6 | 819.2.dl.f.415.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.bj.c.25.2 | ✓ | 16 | 13.12 | even | 2 | inner | |
273.2.bj.c.25.7 | yes | 16 | 1.1 | even | 1 | trivial | |
273.2.bj.c.142.2 | yes | 16 | 7.2 | even | 3 | inner | |
273.2.bj.c.142.7 | yes | 16 | 91.51 | even | 6 | inner | |
819.2.dl.f.298.2 | 16 | 3.2 | odd | 2 | |||
819.2.dl.f.298.7 | 16 | 39.38 | odd | 2 | |||
819.2.dl.f.415.2 | 16 | 273.233 | odd | 6 | |||
819.2.dl.f.415.7 | 16 | 21.2 | odd | 6 | |||
1911.2.c.k.883.2 | 8 | 91.38 | odd | 6 | |||
1911.2.c.k.883.7 | 8 | 7.3 | odd | 6 | |||
1911.2.c.n.883.2 | 8 | 91.25 | even | 6 | |||
1911.2.c.n.883.7 | 8 | 7.4 | even | 3 |