Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(551,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.551");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.e (of order \(2\), degree \(1\), 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: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 3 x^{14} - 12 x^{13} + 15 x^{12} - 4 x^{11} + 45 x^{10} - 66 x^{9} - 32 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 551.15 | ||
Root | \(-0.462710 + 1.66910i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 690.551 |
Dual form | 690.2.e.a.551.7 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 1.66910 | + | 0.462710i | 0.963656 | + | 0.267145i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −0.462710 | + | 1.66910i | −0.188900 | + | 0.681408i | ||||
\(7\) | − | 2.82123i | − | 1.06633i | −0.846013 | − | 0.533163i | \(-0.821003\pi\) | ||
0.846013 | − | 0.533163i | \(-0.178997\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 2.57180 | + | 1.54462i | 0.857267 | + | 0.514873i | ||||
\(10\) | − | 1.00000i | − | 0.316228i | ||||||
\(11\) | 0.0884736 | 0.0266758 | 0.0133379 | − | 0.999911i | \(-0.495754\pi\) | ||||
0.0133379 | + | 0.999911i | \(0.495754\pi\) | |||||||
\(12\) | −1.66910 | − | 0.462710i | −0.481828 | − | 0.133573i | ||||
\(13\) | 5.38812 | 1.49440 | 0.747198 | − | 0.664602i | \(-0.231399\pi\) | ||||
0.747198 | + | 0.664602i | \(0.231399\pi\) | |||||||
\(14\) | 2.82123 | 0.754006 | ||||||||
\(15\) | −1.66910 | − | 0.462710i | −0.430960 | − | 0.119471i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.84233 | 0.689365 | 0.344683 | − | 0.938719i | \(-0.387987\pi\) | ||||
0.344683 | + | 0.938719i | \(0.387987\pi\) | |||||||
\(18\) | −1.54462 | + | 2.57180i | −0.364070 | + | 0.606179i | ||||
\(19\) | 5.08924i | 1.16755i | 0.811915 | + | 0.583775i | \(0.198425\pi\) | ||||
−0.811915 | + | 0.583775i | \(0.801575\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 1.30541 | − | 4.70893i | 0.284864 | − | 1.02757i | ||||
\(22\) | 0.0884736i | 0.0188626i | ||||||||
\(23\) | 4.45994 | + | 1.76321i | 0.929963 | + | 0.367654i | ||||
\(24\) | 0.462710 | − | 1.66910i | 0.0944502 | − | 0.340704i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 5.38812i | 1.05670i | ||||||||
\(27\) | 3.57789 | + | 3.76812i | 0.688564 | + | 0.725175i | ||||
\(28\) | 2.82123i | 0.533163i | ||||||||
\(29\) | 1.48542i | 0.275836i | 0.990444 | + | 0.137918i | \(0.0440410\pi\) | ||||
−0.990444 | + | 0.137918i | \(0.955959\pi\) | |||||||
\(30\) | 0.462710 | − | 1.66910i | 0.0844788 | − | 0.304735i | ||||
\(31\) | −5.56059 | −0.998712 | −0.499356 | − | 0.866397i | \(-0.666430\pi\) | ||||
−0.499356 | + | 0.866397i | \(0.666430\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0.147671 | + | 0.0409376i | 0.0257063 | + | 0.00712631i | ||||
\(34\) | 2.84233i | 0.487455i | ||||||||
\(35\) | 2.82123i | 0.476875i | ||||||||
\(36\) | −2.57180 | − | 1.54462i | −0.428633 | − | 0.257436i | ||||
\(37\) | − | 6.20488i | − | 1.02008i | −0.860152 | − | 0.510038i | \(-0.829631\pi\) | ||
0.860152 | − | 0.510038i | \(-0.170369\pi\) | |||||||
\(38\) | −5.08924 | −0.825583 | ||||||||
\(39\) | 8.99332 | + | 2.49313i | 1.44008 | + | 0.399221i | ||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | − | 0.519960i | − | 0.0812040i | −0.999175 | − | 0.0406020i | \(-0.987072\pi\) | ||
0.999175 | − | 0.0406020i | \(-0.0129276\pi\) | |||||||
\(42\) | 4.70893 | + | 1.30541i | 0.726603 | + | 0.201429i | ||||
\(43\) | 0.907222i | 0.138350i | 0.997605 | + | 0.0691750i | \(0.0220367\pi\) | ||||
−0.997605 | + | 0.0691750i | \(0.977963\pi\) | |||||||
\(44\) | −0.0884736 | −0.0133379 | ||||||||
\(45\) | −2.57180 | − | 1.54462i | −0.383381 | − | 0.230258i | ||||
\(46\) | −1.76321 | + | 4.45994i | −0.259971 | + | 0.657583i | ||||
\(47\) | − | 0.0243495i | − | 0.00355174i | −0.999998 | − | 0.00177587i | \(-0.999435\pi\) | ||
0.999998 | − | 0.00177587i | \(-0.000565277\pi\) | |||||||
\(48\) | 1.66910 | + | 0.462710i | 0.240914 | + | 0.0667864i | ||||
\(49\) | −0.959358 | −0.137051 | ||||||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | 4.74413 | + | 1.31517i | 0.664311 | + | 0.184161i | ||||
\(52\) | −5.38812 | −0.747198 | ||||||||
\(53\) | −10.2028 | −1.40147 | −0.700733 | − | 0.713424i | \(-0.747143\pi\) | ||||
−0.700733 | + | 0.713424i | \(0.747143\pi\) | |||||||
\(54\) | −3.76812 | + | 3.57789i | −0.512776 | + | 0.486889i | ||||
\(55\) | −0.0884736 | −0.0119298 | ||||||||
\(56\) | −2.82123 | −0.377003 | ||||||||
\(57\) | −2.35484 | + | 8.49445i | −0.311906 | + | 1.12512i | ||||
\(58\) | −1.48542 | −0.195045 | ||||||||
\(59\) | − | 8.85335i | − | 1.15261i | −0.817235 | − | 0.576304i | \(-0.804494\pi\) | ||
0.817235 | − | 0.576304i | \(-0.195506\pi\) | |||||||
\(60\) | 1.66910 | + | 0.462710i | 0.215480 | + | 0.0597355i | ||||
\(61\) | − | 10.4775i | − | 1.34150i | −0.741682 | − | 0.670751i | \(-0.765972\pi\) | ||
0.741682 | − | 0.670751i | \(-0.234028\pi\) | |||||||
\(62\) | − | 5.56059i | − | 0.706196i | ||||||
\(63\) | 4.35773 | − | 7.25565i | 0.549022 | − | 0.914126i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −5.38812 | −0.668314 | ||||||||
\(66\) | −0.0409376 | + | 0.147671i | −0.00503907 | + | 0.0181771i | ||||
\(67\) | 3.80095i | 0.464360i | 0.972673 | + | 0.232180i | \(0.0745859\pi\) | ||||
−0.972673 | + | 0.232180i | \(0.925414\pi\) | |||||||
\(68\) | −2.84233 | −0.344683 | ||||||||
\(69\) | 6.62825 | + | 5.00663i | 0.797947 | + | 0.602728i | ||||
\(70\) | −2.82123 | −0.337202 | ||||||||
\(71\) | − | 10.9253i | − | 1.29659i | −0.761389 | − | 0.648295i | \(-0.775482\pi\) | ||
0.761389 | − | 0.648295i | \(-0.224518\pi\) | |||||||
\(72\) | 1.54462 | − | 2.57180i | 0.182035 | − | 0.303090i | ||||
\(73\) | −5.85816 | −0.685646 | −0.342823 | − | 0.939400i | \(-0.611383\pi\) | ||||
−0.342823 | + | 0.939400i | \(0.611383\pi\) | |||||||
\(74\) | 6.20488 | 0.721302 | ||||||||
\(75\) | 1.66910 | + | 0.462710i | 0.192731 | + | 0.0534291i | ||||
\(76\) | − | 5.08924i | − | 0.583775i | ||||||
\(77\) | − | 0.249605i | − | 0.0284451i | ||||||
\(78\) | −2.49313 | + | 8.99332i | −0.282292 | + | 1.01829i | ||||
\(79\) | 9.17572i | 1.03235i | 0.856483 | + | 0.516175i | \(0.172644\pi\) | ||||
−0.856483 | + | 0.516175i | \(0.827356\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 4.22831 | + | 7.94490i | 0.469812 | + | 0.882766i | ||||
\(82\) | 0.519960 | 0.0574199 | ||||||||
\(83\) | −7.55626 | −0.829407 | −0.414703 | − | 0.909957i | \(-0.636115\pi\) | ||||
−0.414703 | + | 0.909957i | \(0.636115\pi\) | |||||||
\(84\) | −1.30541 | + | 4.70893i | −0.142432 | + | 0.513786i | ||||
\(85\) | −2.84233 | −0.308293 | ||||||||
\(86\) | −0.907222 | −0.0978283 | ||||||||
\(87\) | −0.687318 | + | 2.47932i | −0.0736883 | + | 0.265811i | ||||
\(88\) | − | 0.0884736i | − | 0.00943131i | ||||||
\(89\) | 12.3408 | 1.30813 | 0.654063 | − | 0.756440i | \(-0.273063\pi\) | ||||
0.654063 | + | 0.756440i | \(0.273063\pi\) | |||||||
\(90\) | 1.54462 | − | 2.57180i | 0.162817 | − | 0.271091i | ||||
\(91\) | − | 15.2011i | − | 1.59351i | ||||||
\(92\) | −4.45994 | − | 1.76321i | −0.464981 | − | 0.183827i | ||||
\(93\) | −9.28119 | − | 2.57294i | −0.962415 | − | 0.266801i | ||||
\(94\) | 0.0243495 | 0.00251146 | ||||||||
\(95\) | − | 5.08924i | − | 0.522145i | ||||||
\(96\) | −0.462710 | + | 1.66910i | −0.0472251 | + | 0.170352i | ||||
\(97\) | 7.83418i | 0.795440i | 0.917507 | + | 0.397720i | \(0.130198\pi\) | ||||
−0.917507 | + | 0.397720i | \(0.869802\pi\) | |||||||
\(98\) | − | 0.959358i | − | 0.0969098i | ||||||
\(99\) | 0.227536 | + | 0.136658i | 0.0228683 | + | 0.0137346i | ||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | − | 11.3714i | − | 1.13149i | −0.824579 | − | 0.565747i | \(-0.808588\pi\) | ||
0.824579 | − | 0.565747i | \(-0.191412\pi\) | |||||||
\(102\) | −1.31517 | + | 4.74413i | −0.130221 | + | 0.469739i | ||||
\(103\) | 15.3014i | 1.50770i | 0.657049 | + | 0.753848i | \(0.271805\pi\) | ||||
−0.657049 | + | 0.753848i | \(0.728195\pi\) | |||||||
\(104\) | − | 5.38812i | − | 0.528349i | ||||||
\(105\) | −1.30541 | + | 4.70893i | −0.127395 | + | 0.459544i | ||||
\(106\) | − | 10.2028i | − | 0.990986i | ||||||
\(107\) | −2.15054 | −0.207901 | −0.103950 | − | 0.994582i | \(-0.533148\pi\) | ||||
−0.103950 | + | 0.994582i | \(0.533148\pi\) | |||||||
\(108\) | −3.57789 | − | 3.76812i | −0.344282 | − | 0.362588i | ||||
\(109\) | 9.04331i | 0.866192i | 0.901348 | + | 0.433096i | \(0.142579\pi\) | ||||
−0.901348 | + | 0.433096i | \(0.857421\pi\) | |||||||
\(110\) | − | 0.0884736i | − | 0.00843562i | ||||||
\(111\) | 2.87106 | − | 10.3566i | 0.272509 | − | 0.983002i | ||||
\(112\) | − | 2.82123i | − | 0.266582i | ||||||
\(113\) | 5.46926 | 0.514505 | 0.257252 | − | 0.966344i | \(-0.417183\pi\) | ||||
0.257252 | + | 0.966344i | \(0.417183\pi\) | |||||||
\(114\) | −8.49445 | − | 2.35484i | −0.795578 | − | 0.220551i | ||||
\(115\) | −4.45994 | − | 1.76321i | −0.415892 | − | 0.164420i | ||||
\(116\) | − | 1.48542i | − | 0.137918i | ||||||
\(117\) | 13.8572 | + | 8.32259i | 1.28110 | + | 0.769424i | ||||
\(118\) | 8.85335 | 0.815017 | ||||||||
\(119\) | − | 8.01886i | − | 0.735088i | ||||||
\(120\) | −0.462710 | + | 1.66910i | −0.0422394 | + | 0.152367i | ||||
\(121\) | −10.9922 | −0.999288 | ||||||||
\(122\) | 10.4775 | 0.948585 | ||||||||
\(123\) | 0.240590 | − | 0.867865i | 0.0216933 | − | 0.0782528i | ||||
\(124\) | 5.56059 | 0.499356 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 7.25565 | + | 4.35773i | 0.646384 | + | 0.388217i | ||||
\(127\) | −1.22410 | −0.108621 | −0.0543105 | − | 0.998524i | \(-0.517296\pi\) | ||||
−0.0543105 | + | 0.998524i | \(0.517296\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −0.419780 | + | 1.51425i | −0.0369596 | + | 0.133322i | ||||
\(130\) | − | 5.38812i | − | 0.472569i | ||||||
\(131\) | 17.3758i | 1.51813i | 0.651014 | + | 0.759066i | \(0.274344\pi\) | ||||
−0.651014 | + | 0.759066i | \(0.725656\pi\) | |||||||
\(132\) | −0.147671 | − | 0.0409376i | −0.0128531 | − | 0.00356316i | ||||
\(133\) | 14.3579 | 1.24499 | ||||||||
\(134\) | −3.80095 | −0.328352 | ||||||||
\(135\) | −3.57789 | − | 3.76812i | −0.307935 | − | 0.324308i | ||||
\(136\) | − | 2.84233i | − | 0.243727i | ||||||
\(137\) | −18.2067 | −1.55550 | −0.777751 | − | 0.628573i | \(-0.783639\pi\) | ||||
−0.777751 | + | 0.628573i | \(0.783639\pi\) | |||||||
\(138\) | −5.00663 | + | 6.62825i | −0.426193 | + | 0.564234i | ||||
\(139\) | −7.87519 | −0.667965 | −0.333982 | − | 0.942579i | \(-0.608393\pi\) | ||||
−0.333982 | + | 0.942579i | \(0.608393\pi\) | |||||||
\(140\) | − | 2.82123i | − | 0.238438i | ||||||
\(141\) | 0.0112667 | − | 0.0406418i | 0.000948831 | − | 0.00342265i | ||||
\(142\) | 10.9253 | 0.916828 | ||||||||
\(143\) | 0.476706 | 0.0398642 | ||||||||
\(144\) | 2.57180 | + | 1.54462i | 0.214317 | + | 0.128718i | ||||
\(145\) | − | 1.48542i | − | 0.123357i | ||||||
\(146\) | − | 5.85816i | − | 0.484825i | ||||||
\(147\) | −1.60127 | − | 0.443904i | −0.132070 | − | 0.0366126i | ||||
\(148\) | 6.20488i | 0.510038i | ||||||||
\(149\) | −7.85015 | −0.643110 | −0.321555 | − | 0.946891i | \(-0.604205\pi\) | ||||
−0.321555 | + | 0.946891i | \(0.604205\pi\) | |||||||
\(150\) | −0.462710 | + | 1.66910i | −0.0377801 | + | 0.136282i | ||||
\(151\) | 8.89534 | 0.723892 | 0.361946 | − | 0.932199i | \(-0.382112\pi\) | ||||
0.361946 | + | 0.932199i | \(0.382112\pi\) | |||||||
\(152\) | 5.08924 | 0.412792 | ||||||||
\(153\) | 7.30989 | + | 4.39031i | 0.590970 | + | 0.354935i | ||||
\(154\) | 0.249605 | 0.0201137 | ||||||||
\(155\) | 5.56059 | 0.446637 | ||||||||
\(156\) | −8.99332 | − | 2.49313i | −0.720042 | − | 0.199611i | ||||
\(157\) | 13.4878i | 1.07644i | 0.842803 | + | 0.538222i | \(0.180904\pi\) | ||||
−0.842803 | + | 0.538222i | \(0.819096\pi\) | |||||||
\(158\) | −9.17572 | −0.729981 | ||||||||
\(159\) | −17.0295 | − | 4.72094i | −1.35053 | − | 0.374395i | ||||
\(160\) | − | 1.00000i | − | 0.0790569i | ||||||
\(161\) | 4.97442 | − | 12.5825i | 0.392039 | − | 0.991643i | ||||
\(162\) | −7.94490 | + | 4.22831i | −0.624210 | + | 0.332207i | ||||
\(163\) | −7.19796 | −0.563788 | −0.281894 | − | 0.959446i | \(-0.590963\pi\) | ||||
−0.281894 | + | 0.959446i | \(0.590963\pi\) | |||||||
\(164\) | 0.519960i | 0.0406020i | ||||||||
\(165\) | −0.147671 | − | 0.0409376i | −0.0114962 | − | 0.00318698i | ||||
\(166\) | − | 7.55626i | − | 0.586479i | ||||||
\(167\) | − | 15.7105i | − | 1.21572i | −0.794045 | − | 0.607859i | \(-0.792029\pi\) | ||
0.794045 | − | 0.607859i | \(-0.207971\pi\) | |||||||
\(168\) | −4.70893 | − | 1.30541i | −0.363301 | − | 0.100715i | ||||
\(169\) | 16.0318 | 1.23322 | ||||||||
\(170\) | − | 2.84233i | − | 0.217996i | ||||||
\(171\) | −7.86093 | + | 13.0885i | −0.601140 | + | 1.00090i | ||||
\(172\) | − | 0.907222i | − | 0.0691750i | ||||||
\(173\) | 0.427486i | 0.0325012i | 0.999868 | + | 0.0162506i | \(0.00517295\pi\) | ||||
−0.999868 | + | 0.0162506i | \(0.994827\pi\) | |||||||
\(174\) | −2.47932 | − | 0.687318i | −0.187957 | − | 0.0521055i | ||||
\(175\) | − | 2.82123i | − | 0.213265i | ||||||
\(176\) | 0.0884736 | 0.00666895 | ||||||||
\(177\) | 4.09653 | − | 14.7771i | 0.307914 | − | 1.11072i | ||||
\(178\) | 12.3408i | 0.924984i | ||||||||
\(179\) | − | 12.9141i | − | 0.965244i | −0.875829 | − | 0.482622i | \(-0.839684\pi\) | ||
0.875829 | − | 0.482622i | \(-0.160316\pi\) | |||||||
\(180\) | 2.57180 | + | 1.54462i | 0.191691 | + | 0.115129i | ||||
\(181\) | − | 24.7502i | − | 1.83967i | −0.392308 | − | 0.919834i | \(-0.628323\pi\) | ||
0.392308 | − | 0.919834i | \(-0.371677\pi\) | |||||||
\(182\) | 15.2011 | 1.12678 | ||||||||
\(183\) | 4.84802 | − | 17.4880i | 0.358376 | − | 1.29275i | ||||
\(184\) | 1.76321 | − | 4.45994i | 0.129985 | − | 0.328791i | ||||
\(185\) | 6.20488i | 0.456192i | ||||||||
\(186\) | 2.57294 | − | 9.28119i | 0.188657 | − | 0.680530i | ||||
\(187\) | 0.251471 | 0.0183894 | ||||||||
\(188\) | 0.0243495i | 0.00177587i | ||||||||
\(189\) | 10.6307 | − | 10.0940i | 0.773273 | − | 0.734234i | ||||
\(190\) | 5.08924 | 0.369212 | ||||||||
\(191\) | −15.4356 | −1.11688 | −0.558441 | − | 0.829544i | \(-0.688600\pi\) | ||||
−0.558441 | + | 0.829544i | \(0.688600\pi\) | |||||||
\(192\) | −1.66910 | − | 0.462710i | −0.120457 | − | 0.0333932i | ||||
\(193\) | 3.49474 | 0.251557 | 0.125779 | − | 0.992058i | \(-0.459857\pi\) | ||||
0.125779 | + | 0.992058i | \(0.459857\pi\) | |||||||
\(194\) | −7.83418 | −0.562461 | ||||||||
\(195\) | −8.99332 | − | 2.49313i | −0.644025 | − | 0.178537i | ||||
\(196\) | 0.959358 | 0.0685256 | ||||||||
\(197\) | − | 15.4600i | − | 1.10148i | −0.834677 | − | 0.550739i | \(-0.814346\pi\) | ||
0.834677 | − | 0.550739i | \(-0.185654\pi\) | |||||||
\(198\) | −0.136658 | + | 0.227536i | −0.00971185 | + | 0.0161703i | ||||
\(199\) | − | 1.10416i | − | 0.0782715i | −0.999234 | − | 0.0391357i | \(-0.987540\pi\) | ||
0.999234 | − | 0.0391357i | \(-0.0124605\pi\) | |||||||
\(200\) | − | 1.00000i | − | 0.0707107i | ||||||
\(201\) | −1.75874 | + | 6.34417i | −0.124052 | + | 0.447483i | ||||
\(202\) | 11.3714 | 0.800087 | ||||||||
\(203\) | 4.19072 | 0.294131 | ||||||||
\(204\) | −4.74413 | − | 1.31517i | −0.332156 | − | 0.0920804i | ||||
\(205\) | 0.519960i | 0.0363155i | ||||||||
\(206\) | −15.3014 | −1.06610 | ||||||||
\(207\) | 8.74660 | + | 11.4235i | 0.607931 | + | 0.793990i | ||||
\(208\) | 5.38812 | 0.373599 | ||||||||
\(209\) | 0.450263i | 0.0311453i | ||||||||
\(210\) | −4.70893 | − | 1.30541i | −0.324947 | − | 0.0900820i | ||||
\(211\) | −27.0611 | −1.86297 | −0.931483 | − | 0.363785i | \(-0.881484\pi\) | ||||
−0.931483 | + | 0.363785i | \(0.881484\pi\) | |||||||
\(212\) | 10.2028 | 0.700733 | ||||||||
\(213\) | 5.05523 | − | 18.2354i | 0.346378 | − | 1.24947i | ||||
\(214\) | − | 2.15054i | − | 0.147008i | ||||||
\(215\) | − | 0.907222i | − | 0.0618720i | ||||||
\(216\) | 3.76812 | − | 3.57789i | 0.256388 | − | 0.243444i | ||||
\(217\) | 15.6877i | 1.06495i | ||||||||
\(218\) | −9.04331 | −0.612490 | ||||||||
\(219\) | −9.77787 | − | 2.71063i | −0.660727 | − | 0.183167i | ||||
\(220\) | 0.0884736 | 0.00596489 | ||||||||
\(221\) | 15.3148 | 1.03018 | ||||||||
\(222\) | 10.3566 | + | 2.87106i | 0.695088 | + | 0.192693i | ||||
\(223\) | −9.23318 | −0.618299 | −0.309150 | − | 0.951013i | \(-0.600044\pi\) | ||||
−0.309150 | + | 0.951013i | \(0.600044\pi\) | |||||||
\(224\) | 2.82123 | 0.188502 | ||||||||
\(225\) | 2.57180 | + | 1.54462i | 0.171453 | + | 0.102975i | ||||
\(226\) | 5.46926i | 0.363810i | ||||||||
\(227\) | −14.7794 | −0.980945 | −0.490473 | − | 0.871457i | \(-0.663176\pi\) | ||||
−0.490473 | + | 0.871457i | \(0.663176\pi\) | |||||||
\(228\) | 2.35484 | − | 8.49445i | 0.155953 | − | 0.562559i | ||||
\(229\) | − | 26.9323i | − | 1.77974i | −0.456216 | − | 0.889869i | \(-0.650796\pi\) | ||
0.456216 | − | 0.889869i | \(-0.349204\pi\) | |||||||
\(230\) | 1.76321 | − | 4.45994i | 0.116263 | − | 0.294080i | ||||
\(231\) | 0.115494 | − | 0.416615i | 0.00759897 | − | 0.0274113i | ||||
\(232\) | 1.48542 | 0.0975226 | ||||||||
\(233\) | − | 18.5217i | − | 1.21340i | −0.794932 | − | 0.606698i | \(-0.792494\pi\) | ||
0.794932 | − | 0.606698i | \(-0.207506\pi\) | |||||||
\(234\) | −8.32259 | + | 13.8572i | −0.544065 | + | 0.905871i | ||||
\(235\) | 0.0243495i | 0.00158839i | ||||||||
\(236\) | 8.85335i | 0.576304i | ||||||||
\(237\) | −4.24569 | + | 15.3152i | −0.275787 | + | 0.994830i | ||||
\(238\) | 8.01886 | 0.519786 | ||||||||
\(239\) | 23.2974i | 1.50698i | 0.657457 | + | 0.753492i | \(0.271632\pi\) | ||||
−0.657457 | + | 0.753492i | \(0.728368\pi\) | |||||||
\(240\) | −1.66910 | − | 0.462710i | −0.107740 | − | 0.0298678i | ||||
\(241\) | − | 10.7446i | − | 0.692122i | −0.938212 | − | 0.346061i | \(-0.887519\pi\) | ||
0.938212 | − | 0.346061i | \(-0.112481\pi\) | |||||||
\(242\) | − | 10.9922i | − | 0.706604i | ||||||
\(243\) | 3.38130 | + | 15.2173i | 0.216910 | + | 0.976192i | ||||
\(244\) | 10.4775i | 0.670751i | ||||||||
\(245\) | 0.959358 | 0.0612911 | ||||||||
\(246\) | 0.867865 | + | 0.240590i | 0.0553331 | + | 0.0153395i | ||||
\(247\) | 27.4214i | 1.74478i | ||||||||
\(248\) | 5.56059i | 0.353098i | ||||||||
\(249\) | −12.6122 | − | 3.49635i | −0.799263 | − | 0.221572i | ||||
\(250\) | − | 1.00000i | − | 0.0632456i | ||||||
\(251\) | −10.1577 | −0.641147 | −0.320573 | − | 0.947224i | \(-0.603876\pi\) | ||||
−0.320573 | + | 0.947224i | \(0.603876\pi\) | |||||||
\(252\) | −4.35773 | + | 7.25565i | −0.274511 | + | 0.457063i | ||||
\(253\) | 0.394587 | + | 0.155997i | 0.0248075 | + | 0.00980747i | ||||
\(254\) | − | 1.22410i | − | 0.0768067i | ||||||
\(255\) | −4.74413 | − | 1.31517i | −0.297089 | − | 0.0823592i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.7723i | 0.921468i | 0.887538 | + | 0.460734i | \(0.152414\pi\) | ||||
−0.887538 | + | 0.460734i | \(0.847586\pi\) | |||||||
\(258\) | −1.51425 | − | 0.419780i | −0.0942728 | − | 0.0261344i | ||||
\(259\) | −17.5054 | −1.08773 | ||||||||
\(260\) | 5.38812 | 0.334157 | ||||||||
\(261\) | −2.29441 | + | 3.82020i | −0.142020 | + | 0.236465i | ||||
\(262\) | −17.3758 | −1.07348 | ||||||||
\(263\) | 24.0408 | 1.48242 | 0.741209 | − | 0.671275i | \(-0.234253\pi\) | ||||
0.741209 | + | 0.671275i | \(0.234253\pi\) | |||||||
\(264\) | 0.0409376 | − | 0.147671i | 0.00251953 | − | 0.00908854i | ||||
\(265\) | 10.2028 | 0.626754 | ||||||||
\(266\) | 14.3579i | 0.880341i | ||||||||
\(267\) | 20.5981 | + | 5.71022i | 1.26058 | + | 0.349460i | ||||
\(268\) | − | 3.80095i | − | 0.232180i | ||||||
\(269\) | − | 4.74366i | − | 0.289226i | −0.989488 | − | 0.144613i | \(-0.953806\pi\) | ||
0.989488 | − | 0.144613i | \(-0.0461937\pi\) | |||||||
\(270\) | 3.76812 | − | 3.57789i | 0.229321 | − | 0.217743i | ||||
\(271\) | −0.303443 | −0.0184329 | −0.00921643 | − | 0.999958i | \(-0.502934\pi\) | ||||
−0.00921643 | + | 0.999958i | \(0.502934\pi\) | |||||||
\(272\) | 2.84233 | 0.172341 | ||||||||
\(273\) | 7.03372 | − | 25.3723i | 0.425700 | − | 1.53560i | ||||
\(274\) | − | 18.2067i | − | 1.09991i | ||||||
\(275\) | 0.0884736 | 0.00533516 | ||||||||
\(276\) | −6.62825 | − | 5.00663i | −0.398973 | − | 0.301364i | ||||
\(277\) | 23.1558 | 1.39129 | 0.695647 | − | 0.718383i | \(-0.255118\pi\) | ||||
0.695647 | + | 0.718383i | \(0.255118\pi\) | |||||||
\(278\) | − | 7.87519i | − | 0.472322i | ||||||
\(279\) | −14.3007 | − | 8.58899i | −0.856162 | − | 0.514210i | ||||
\(280\) | 2.82123 | 0.168601 | ||||||||
\(281\) | 1.79749 | 0.107229 | 0.0536146 | − | 0.998562i | \(-0.482926\pi\) | ||||
0.0536146 | + | 0.998562i | \(0.482926\pi\) | |||||||
\(282\) | 0.0406418 | + | 0.0112667i | 0.00242018 | + | 0.000670925i | ||||
\(283\) | 25.5875i | 1.52102i | 0.649328 | + | 0.760509i | \(0.275050\pi\) | ||||
−0.649328 | + | 0.760509i | \(0.724950\pi\) | |||||||
\(284\) | 10.9253i | 0.648295i | ||||||||
\(285\) | 2.35484 | − | 8.49445i | 0.139489 | − | 0.503168i | ||||
\(286\) | 0.476706i | 0.0281882i | ||||||||
\(287\) | −1.46693 | −0.0865900 | ||||||||
\(288\) | −1.54462 | + | 2.57180i | −0.0910175 | + | 0.151545i | ||||
\(289\) | −8.92119 | −0.524776 | ||||||||
\(290\) | 1.48542 | 0.0872269 | ||||||||
\(291\) | −3.62495 | + | 13.0760i | −0.212498 | + | 0.766531i | ||||
\(292\) | 5.85816 | 0.342823 | ||||||||
\(293\) | −24.0774 | −1.40662 | −0.703308 | − | 0.710885i | \(-0.748295\pi\) | ||||
−0.703308 | + | 0.710885i | \(0.748295\pi\) | |||||||
\(294\) | 0.443904 | − | 1.60127i | 0.0258890 | − | 0.0933877i | ||||
\(295\) | 8.85335i | 0.515462i | ||||||||
\(296\) | −6.20488 | −0.360651 | ||||||||
\(297\) | 0.316548 | + | 0.333379i | 0.0183680 | + | 0.0193446i | ||||
\(298\) | − | 7.85015i | − | 0.454747i | ||||||
\(299\) | 24.0307 | + | 9.50038i | 1.38973 | + | 0.549421i | ||||
\(300\) | −1.66910 | − | 0.462710i | −0.0963656 | − | 0.0267145i | ||||
\(301\) | 2.55949 | 0.147526 | ||||||||
\(302\) | 8.89534i | 0.511869i | ||||||||
\(303\) | 5.26164 | − | 18.9800i | 0.302273 | − | 1.09037i | ||||
\(304\) | 5.08924i | 0.291888i | ||||||||
\(305\) | 10.4775i | 0.599938i | ||||||||
\(306\) | −4.39031 | + | 7.30989i | −0.250977 | + | 0.417879i | ||||
\(307\) | −18.5284 | −1.05747 | −0.528735 | − | 0.848787i | \(-0.677333\pi\) | ||||
−0.528735 | + | 0.848787i | \(0.677333\pi\) | |||||||
\(308\) | 0.249605i | 0.0142225i | ||||||||
\(309\) | −7.08013 | + | 25.5397i | −0.402774 | + | 1.45290i | ||||
\(310\) | 5.56059i | 0.315820i | ||||||||
\(311\) | 29.6815i | 1.68308i | 0.540193 | + | 0.841541i | \(0.318351\pi\) | ||||
−0.540193 | + | 0.841541i | \(0.681649\pi\) | |||||||
\(312\) | 2.49313 | − | 8.99332i | 0.141146 | − | 0.509146i | ||||
\(313\) | 8.20686i | 0.463879i | 0.972730 | + | 0.231939i | \(0.0745071\pi\) | ||||
−0.972730 | + | 0.231939i | \(0.925493\pi\) | |||||||
\(314\) | −13.4878 | −0.761161 | ||||||||
\(315\) | −4.35773 | + | 7.25565i | −0.245530 | + | 0.408809i | ||||
\(316\) | − | 9.17572i | − | 0.516175i | ||||||
\(317\) | 30.8326i | 1.73173i | 0.500274 | + | 0.865867i | \(0.333232\pi\) | ||||
−0.500274 | + | 0.865867i | \(0.666768\pi\) | |||||||
\(318\) | 4.72094 | − | 17.0295i | 0.264737 | − | 0.954970i | ||||
\(319\) | 0.131420i | 0.00735813i | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −3.58947 | − | 0.995077i | −0.200345 | − | 0.0555398i | ||||
\(322\) | 12.5825 | + | 4.97442i | 0.701198 | + | 0.277214i | ||||
\(323\) | 14.4653i | 0.804869i | ||||||||
\(324\) | −4.22831 | − | 7.94490i | −0.234906 | − | 0.441383i | ||||
\(325\) | 5.38812 | 0.298879 | ||||||||
\(326\) | − | 7.19796i | − | 0.398658i | ||||||
\(327\) | −4.18443 | + | 15.0942i | −0.231399 | + | 0.834711i | ||||
\(328\) | −0.519960 | −0.0287100 | ||||||||
\(329\) | −0.0686956 | −0.00378731 | ||||||||
\(330\) | 0.0409376 | − | 0.147671i | 0.00225354 | − | 0.00812904i | ||||
\(331\) | −18.1025 | −0.995004 | −0.497502 | − | 0.867463i | \(-0.665749\pi\) | ||||
−0.497502 | + | 0.867463i | \(0.665749\pi\) | |||||||
\(332\) | 7.55626 | 0.414703 | ||||||||
\(333\) | 9.58417 | − | 15.9577i | 0.525209 | − | 0.874477i | ||||
\(334\) | 15.7105 | 0.859642 | ||||||||
\(335\) | − | 3.80095i | − | 0.207668i | ||||||
\(336\) | 1.30541 | − | 4.70893i | 0.0712160 | − | 0.256893i | ||||
\(337\) | − | 19.1719i | − | 1.04436i | −0.852835 | − | 0.522181i | \(-0.825118\pi\) | ||
0.852835 | − | 0.522181i | \(-0.174882\pi\) | |||||||
\(338\) | 16.0318i | 0.872017i | ||||||||
\(339\) | 9.12875 | + | 2.53068i | 0.495806 | + | 0.137448i | ||||
\(340\) | 2.84233 | 0.154147 | ||||||||
\(341\) | −0.491965 | −0.0266414 | ||||||||
\(342\) | −13.0885 | − | 7.86093i | −0.707745 | − | 0.425070i | ||||
\(343\) | − | 17.0421i | − | 0.920185i | ||||||
\(344\) | 0.907222 | 0.0489141 | ||||||||
\(345\) | −6.62825 | − | 5.00663i | −0.356853 | − | 0.269548i | ||||
\(346\) | −0.427486 | −0.0229818 | ||||||||
\(347\) | 24.7654i | 1.32947i | 0.747077 | + | 0.664737i | \(0.231457\pi\) | ||||
−0.747077 | + | 0.664737i | \(0.768543\pi\) | |||||||
\(348\) | 0.687318 | − | 2.47932i | 0.0368441 | − | 0.132905i | ||||
\(349\) | 29.5558 | 1.58209 | 0.791043 | − | 0.611760i | \(-0.209538\pi\) | ||||
0.791043 | + | 0.611760i | \(0.209538\pi\) | |||||||
\(350\) | 2.82123 | 0.150801 | ||||||||
\(351\) | 19.2781 | + | 20.3031i | 1.02899 | + | 1.08370i | ||||
\(352\) | 0.0884736i | 0.00471566i | ||||||||
\(353\) | 28.0481i | 1.49285i | 0.665469 | + | 0.746425i | \(0.268231\pi\) | ||||
−0.665469 | + | 0.746425i | \(0.731769\pi\) | |||||||
\(354\) | 14.7771 | + | 4.09653i | 0.785396 | + | 0.217728i | ||||
\(355\) | 10.9253i | 0.579853i | ||||||||
\(356\) | −12.3408 | −0.654063 | ||||||||
\(357\) | 3.71040 | − | 13.3843i | 0.196375 | − | 0.708372i | ||||
\(358\) | 12.9141 | 0.682531 | ||||||||
\(359\) | 11.9019 | 0.628160 | 0.314080 | − | 0.949396i | \(-0.398304\pi\) | ||||
0.314080 | + | 0.949396i | \(0.398304\pi\) | |||||||
\(360\) | −1.54462 | + | 2.57180i | −0.0814085 | + | 0.135546i | ||||
\(361\) | −6.90033 | −0.363175 | ||||||||
\(362\) | 24.7502 | 1.30084 | ||||||||
\(363\) | −18.3471 | − | 5.08618i | −0.962970 | − | 0.266955i | ||||
\(364\) | 15.2011i | 0.796757i | ||||||||
\(365\) | 5.85816 | 0.306630 | ||||||||
\(366\) | 17.4880 | + | 4.84802i | 0.914110 | + | 0.253410i | ||||
\(367\) | − | 31.6802i | − | 1.65369i | −0.562427 | − | 0.826847i | \(-0.690132\pi\) | ||
0.562427 | − | 0.826847i | \(-0.309868\pi\) | |||||||
\(368\) | 4.45994 | + | 1.76321i | 0.232491 | + | 0.0919136i | ||||
\(369\) | 0.803139 | − | 1.33723i | 0.0418097 | − | 0.0696135i | ||||
\(370\) | −6.20488 | −0.322576 | ||||||||
\(371\) | 28.7845i | 1.49442i | ||||||||
\(372\) | 9.28119 | + | 2.57294i | 0.481207 | + | 0.133401i | ||||
\(373\) | 8.32570i | 0.431088i | 0.976494 | + | 0.215544i | \(0.0691525\pi\) | ||||
−0.976494 | + | 0.215544i | \(0.930847\pi\) | |||||||
\(374\) | 0.251471i | 0.0130032i | ||||||||
\(375\) | −1.66910 | − | 0.462710i | −0.0861920 | − | 0.0238942i | ||||
\(376\) | −0.0243495 | −0.00125573 | ||||||||
\(377\) | 8.00363i | 0.412208i | ||||||||
\(378\) | 10.0940 | + | 10.6307i | 0.519182 | + | 0.546787i | ||||
\(379\) | − | 9.50248i | − | 0.488110i | −0.969761 | − | 0.244055i | \(-0.921522\pi\) | ||
0.969761 | − | 0.244055i | \(-0.0784777\pi\) | |||||||
\(380\) | 5.08924i | 0.261072i | ||||||||
\(381\) | −2.04314 | − | 0.566402i | −0.104673 | − | 0.0290176i | ||||
\(382\) | − | 15.4356i | − | 0.789755i | ||||||
\(383\) | 37.1871 | 1.90017 | 0.950087 | − | 0.311985i | \(-0.100994\pi\) | ||||
0.950087 | + | 0.311985i | \(0.100994\pi\) | |||||||
\(384\) | 0.462710 | − | 1.66910i | 0.0236125 | − | 0.0851760i | ||||
\(385\) | 0.249605i | 0.0127210i | ||||||||
\(386\) | 3.49474i | 0.177878i | ||||||||
\(387\) | −1.40131 | + | 2.33319i | −0.0712327 | + | 0.118603i | ||||
\(388\) | − | 7.83418i | − | 0.397720i | ||||||
\(389\) | 18.6520 | 0.945696 | 0.472848 | − | 0.881144i | \(-0.343226\pi\) | ||||
0.472848 | + | 0.881144i | \(0.343226\pi\) | |||||||
\(390\) | 2.49313 | − | 8.99332i | 0.126245 | − | 0.455394i | ||||
\(391\) | 12.6766 | + | 5.01161i | 0.641084 | + | 0.253448i | ||||
\(392\) | 0.959358i | 0.0484549i | ||||||||
\(393\) | −8.03996 | + | 29.0020i | −0.405562 | + | 1.46296i | ||||
\(394\) | 15.4600 | 0.778863 | ||||||||
\(395\) | − | 9.17572i | − | 0.461681i | ||||||
\(396\) | −0.227536 | − | 0.136658i | −0.0114341 | − | 0.00686732i | ||||
\(397\) | 2.78953 | 0.140003 | 0.0700013 | − | 0.997547i | \(-0.477700\pi\) | ||||
0.0700013 | + | 0.997547i | \(0.477700\pi\) | |||||||
\(398\) | 1.10416 | 0.0553463 | ||||||||
\(399\) | 23.9648 | + | 6.64355i | 1.19974 | + | 0.332593i | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 34.5221 | 1.72395 | 0.861976 | − | 0.506949i | \(-0.169227\pi\) | ||||
0.861976 | + | 0.506949i | \(0.169227\pi\) | |||||||
\(402\) | −6.34417 | − | 1.75874i | −0.316419 | − | 0.0877178i | ||||
\(403\) | −29.9611 | −1.49247 | ||||||||
\(404\) | 11.3714i | 0.565747i | ||||||||
\(405\) | −4.22831 | − | 7.94490i | −0.210106 | − | 0.394785i | ||||
\(406\) | 4.19072i | 0.207982i | ||||||||
\(407\) | − | 0.548968i | − | 0.0272113i | ||||||
\(408\) | 1.31517 | − | 4.74413i | 0.0651107 | − | 0.234869i | ||||
\(409\) | −13.4130 | −0.663233 | −0.331616 | − | 0.943414i | \(-0.607594\pi\) | ||||
−0.331616 | + | 0.943414i | \(0.607594\pi\) | |||||||
\(410\) | −0.519960 | −0.0256790 | ||||||||
\(411\) | −30.3888 | − | 8.42440i | −1.49897 | − | 0.415545i | ||||
\(412\) | − | 15.3014i | − | 0.753848i | ||||||
\(413\) | −24.9774 | −1.22906 | ||||||||
\(414\) | −11.4235 | + | 8.74660i | −0.561436 | + | 0.429872i | ||||
\(415\) | 7.55626 | 0.370922 | ||||||||
\(416\) | 5.38812i | 0.264174i | ||||||||
\(417\) | −13.1445 | − | 3.64392i | −0.643688 | − | 0.178444i | ||||
\(418\) | −0.450263 | −0.0220231 | ||||||||
\(419\) | 39.6632 | 1.93767 | 0.968837 | − | 0.247698i | \(-0.0796741\pi\) | ||||
0.968837 | + | 0.247698i | \(0.0796741\pi\) | |||||||
\(420\) | 1.30541 | − | 4.70893i | 0.0636976 | − | 0.229772i | ||||
\(421\) | 8.88923i | 0.433234i | 0.976257 | + | 0.216617i | \(0.0695024\pi\) | ||||
−0.976257 | + | 0.216617i | \(0.930498\pi\) | |||||||
\(422\) | − | 27.0611i | − | 1.31732i | ||||||
\(423\) | 0.0376107 | − | 0.0626220i | 0.00182869 | − | 0.00304479i | ||||
\(424\) | 10.2028i | 0.495493i | ||||||||
\(425\) | 2.84233 | 0.137873 | ||||||||
\(426\) | 18.2354 | + | 5.05523i | 0.883507 | + | 0.244926i | ||||
\(427\) | −29.5594 | −1.43048 | ||||||||
\(428\) | 2.15054 | 0.103950 | ||||||||
\(429\) | 0.795671 | + | 0.220577i | 0.0384154 | + | 0.0106495i | ||||
\(430\) | 0.907222 | 0.0437501 | ||||||||
\(431\) | −40.0125 | −1.92733 | −0.963666 | − | 0.267110i | \(-0.913931\pi\) | ||||
−0.963666 | + | 0.267110i | \(0.913931\pi\) | |||||||
\(432\) | 3.57789 | + | 3.76812i | 0.172141 | + | 0.181294i | ||||
\(433\) | 24.6079i | 1.18258i | 0.806459 | + | 0.591289i | \(0.201381\pi\) | ||||
−0.806459 | + | 0.591289i | \(0.798619\pi\) | |||||||
\(434\) | −15.6877 | −0.753035 | ||||||||
\(435\) | 0.687318 | − | 2.47932i | 0.0329544 | − | 0.118874i | ||||
\(436\) | − | 9.04331i | − | 0.433096i | ||||||
\(437\) | −8.97339 | + | 22.6977i | −0.429255 | + | 1.08578i | ||||
\(438\) | 2.71063 | − | 9.77787i | 0.129519 | − | 0.467205i | ||||
\(439\) | −28.9558 | −1.38199 | −0.690993 | − | 0.722861i | \(-0.742827\pi\) | ||||
−0.690993 | + | 0.722861i | \(0.742827\pi\) | |||||||
\(440\) | 0.0884736i | 0.00421781i | ||||||||
\(441\) | −2.46728 | − | 1.48184i | −0.117489 | − | 0.0705639i | ||||
\(442\) | 15.3148i | 0.728450i | ||||||||
\(443\) | − | 3.91361i | − | 0.185941i | −0.995669 | − | 0.0929706i | \(-0.970364\pi\) | ||
0.995669 | − | 0.0929706i | \(-0.0296362\pi\) | |||||||
\(444\) | −2.87106 | + | 10.3566i | −0.136254 | + | 0.491501i | ||||
\(445\) | −12.3408 | −0.585011 | ||||||||
\(446\) | − | 9.23318i | − | 0.437204i | ||||||
\(447\) | −13.1027 | − | 3.63234i | −0.619737 | − | 0.171804i | ||||
\(448\) | 2.82123i | 0.133291i | ||||||||
\(449\) | − | 16.9735i | − | 0.801029i | −0.916290 | − | 0.400514i | \(-0.868831\pi\) | ||
0.916290 | − | 0.400514i | \(-0.131169\pi\) | |||||||
\(450\) | −1.54462 | + | 2.57180i | −0.0728140 | + | 0.121236i | ||||
\(451\) | − | 0.0460027i | − | 0.00216618i | ||||||
\(452\) | −5.46926 | −0.257252 | ||||||||
\(453\) | 14.8472 | + | 4.11596i | 0.697583 | + | 0.193385i | ||||
\(454\) | − | 14.7794i | − | 0.693633i | ||||||
\(455\) | 15.2011i | 0.712641i | ||||||||
\(456\) | 8.49445 | + | 2.35484i | 0.397789 | + | 0.110275i | ||||
\(457\) | − | 16.4848i | − | 0.771129i | −0.922681 | − | 0.385564i | \(-0.874007\pi\) | ||
0.922681 | − | 0.385564i | \(-0.125993\pi\) | |||||||
\(458\) | 26.9323 | 1.25846 | ||||||||
\(459\) | 10.1695 | + | 10.7102i | 0.474672 | + | 0.499911i | ||||
\(460\) | 4.45994 | + | 1.76321i | 0.207946 | + | 0.0822100i | ||||
\(461\) | − | 42.6536i | − | 1.98657i | −0.115674 | − | 0.993287i | \(-0.536903\pi\) | ||
0.115674 | − | 0.993287i | \(-0.463097\pi\) | |||||||
\(462\) | 0.416615 | + | 0.115494i | 0.0193827 | + | 0.00537329i | ||||
\(463\) | 9.52088 | 0.442473 | 0.221236 | − | 0.975220i | \(-0.428991\pi\) | ||||
0.221236 | + | 0.975220i | \(0.428991\pi\) | |||||||
\(464\) | 1.48542i | 0.0689589i | ||||||||
\(465\) | 9.28119 | + | 2.57294i | 0.430405 | + | 0.119317i | ||||
\(466\) | 18.5217 | 0.858001 | ||||||||
\(467\) | −18.2551 | −0.844744 | −0.422372 | − | 0.906423i | \(-0.638802\pi\) | ||||
−0.422372 | + | 0.906423i | \(0.638802\pi\) | |||||||
\(468\) | −13.8572 | − | 8.32259i | −0.640548 | − | 0.384712i | ||||
\(469\) | 10.7234 | 0.495159 | ||||||||
\(470\) | −0.0243495 | −0.00112316 | ||||||||
\(471\) | −6.24094 | + | 22.5125i | −0.287567 | + | 1.03732i | ||||
\(472\) | −8.85335 | −0.407509 | ||||||||
\(473\) | 0.0802652i | 0.00369060i | ||||||||
\(474\) | −15.3152 | − | 4.24569i | −0.703451 | − | 0.195011i | ||||
\(475\) | 5.08924i | 0.233510i | ||||||||
\(476\) | 8.01886i | 0.367544i | ||||||||
\(477\) | −26.2396 | − | 15.7595i | −1.20143 | − | 0.721576i | ||||
\(478\) | −23.2974 | −1.06560 | ||||||||
\(479\) | −6.28781 | −0.287298 | −0.143649 | − | 0.989629i | \(-0.545884\pi\) | ||||
−0.143649 | + | 0.989629i | \(0.545884\pi\) | |||||||
\(480\) | 0.462710 | − | 1.66910i | 0.0211197 | − | 0.0761837i | ||||
\(481\) | − | 33.4326i | − | 1.52440i | ||||||
\(482\) | 10.7446 | 0.489404 | ||||||||
\(483\) | 14.1249 | − | 18.6998i | 0.642704 | − | 0.850872i | ||||
\(484\) | 10.9922 | 0.499644 | ||||||||
\(485\) | − | 7.83418i | − | 0.355732i | ||||||
\(486\) | −15.2173 | + | 3.38130i | −0.690272 | + | 0.153379i | ||||
\(487\) | −2.55380 | −0.115724 | −0.0578618 | − | 0.998325i | \(-0.518428\pi\) | ||||
−0.0578618 | + | 0.998325i | \(0.518428\pi\) | |||||||
\(488\) | −10.4775 | −0.474293 | ||||||||
\(489\) | −12.0141 | − | 3.33057i | −0.543298 | − | 0.150613i | ||||
\(490\) | 0.959358i | 0.0433394i | ||||||||
\(491\) | − | 16.8062i | − | 0.758452i | −0.925304 | − | 0.379226i | \(-0.876190\pi\) | ||
0.925304 | − | 0.379226i | \(-0.123810\pi\) | |||||||
\(492\) | −0.240590 | + | 0.867865i | −0.0108466 | + | 0.0391264i | ||||
\(493\) | 4.22205i | 0.190152i | ||||||||
\(494\) | −27.4214 | −1.23375 | ||||||||
\(495\) | −0.227536 | − | 0.136658i | −0.0102270 | − | 0.00614232i | ||||
\(496\) | −5.56059 | −0.249678 | ||||||||
\(497\) | −30.8227 | −1.38259 | ||||||||
\(498\) | 3.49635 | − | 12.6122i | 0.156675 | − | 0.565164i | ||||
\(499\) | −9.17252 | −0.410619 | −0.205309 | − | 0.978697i | \(-0.565820\pi\) | ||||
−0.205309 | + | 0.978697i | \(0.565820\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 7.26941 | − | 26.2225i | 0.324773 | − | 1.17153i | ||||
\(502\) | − | 10.1577i | − | 0.453359i | ||||||
\(503\) | −5.33773 | −0.237997 | −0.118999 | − | 0.992894i | \(-0.537968\pi\) | ||||
−0.118999 | + | 0.992894i | \(0.537968\pi\) | |||||||
\(504\) | −7.25565 | − | 4.35773i | −0.323192 | − | 0.194109i | ||||
\(505\) | 11.3714i | 0.506019i | ||||||||
\(506\) | −0.155997 | + | 0.394587i | −0.00693493 | + | 0.0175415i | ||||
\(507\) | 26.7588 | + | 7.41809i | 1.18840 | + | 0.329449i | ||||
\(508\) | 1.22410 | 0.0543105 | ||||||||
\(509\) | 4.91462i | 0.217837i | 0.994051 | + | 0.108918i | \(0.0347387\pi\) | ||||
−0.994051 | + | 0.108918i | \(0.965261\pi\) | |||||||
\(510\) | 1.31517 | − | 4.74413i | 0.0582368 | − | 0.210074i | ||||
\(511\) | 16.5272i | 0.731122i | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −19.1769 | + | 18.2087i | −0.846679 | + | 0.803934i | ||||
\(514\) | −14.7723 | −0.651576 | ||||||||
\(515\) | − | 15.3014i | − | 0.674262i | ||||||
\(516\) | 0.419780 | − | 1.51425i | 0.0184798 | − | 0.0666610i | ||||
\(517\) | − | 0.00215429i | − | 9.47454e-5i | ||||||
\(518\) | − | 17.5054i | − | 0.769144i | ||||||
\(519\) | −0.197802 | + | 0.713518i | −0.00868255 | + | 0.0313200i | ||||
\(520\) | 5.38812i | 0.236285i | ||||||||
\(521\) | 39.5006 | 1.73055 | 0.865276 | − | 0.501296i | \(-0.167143\pi\) | ||||
0.865276 | + | 0.501296i | \(0.167143\pi\) | |||||||
\(522\) | −3.82020 | − | 2.29441i | −0.167206 | − | 0.100424i | ||||
\(523\) | 9.23575i | 0.403851i | 0.979401 | + | 0.201926i | \(0.0647199\pi\) | ||||
−0.979401 | + | 0.201926i | \(0.935280\pi\) | |||||||
\(524\) | − | 17.3758i | − | 0.759066i | ||||||
\(525\) | 1.30541 | − | 4.70893i | 0.0569728 | − | 0.205514i | ||||
\(526\) | 24.0408i | 1.04823i | ||||||||
\(527\) | −15.8050 | −0.688477 | ||||||||
\(528\) | 0.147671 | + | 0.0409376i | 0.00642657 | + | 0.00178158i | ||||
\(529\) | 16.7822 | + | 15.7276i | 0.729661 | + | 0.683810i | ||||
\(530\) | 10.2028i | 0.443182i | ||||||||
\(531\) | 13.6751 | − | 22.7691i | 0.593447 | − | 0.988093i | ||||
\(532\) | −14.3579 | −0.622495 | ||||||||
\(533\) | − | 2.80160i | − | 0.121351i | ||||||
\(534\) | −5.71022 | + | 20.5981i | −0.247105 | + | 0.891367i | ||||
\(535\) | 2.15054 | 0.0929761 | ||||||||
\(536\) | 3.80095 | 0.164176 | ||||||||
\(537\) | 5.97547 | − | 21.5549i | 0.257861 | − | 0.930164i | ||||
\(538\) | 4.74366 | 0.204514 | ||||||||
\(539\) | −0.0848778 | −0.00365595 | ||||||||
\(540\) | 3.57789 | + | 3.76812i | 0.153968 | + | 0.162154i | ||||
\(541\) | 36.8369 | 1.58374 | 0.791870 | − | 0.610689i | \(-0.209108\pi\) | ||||
0.791870 | + | 0.610689i | \(0.209108\pi\) | |||||||
\(542\) | − | 0.303443i | − | 0.0130340i | ||||||
\(543\) | 11.4522 | − | 41.3106i | 0.491459 | − | 1.77281i | ||||
\(544\) | 2.84233i | 0.121864i | ||||||||
\(545\) | − | 9.04331i | − | 0.387373i | ||||||
\(546\) | 25.3723 | + | 7.03372i | 1.08583 | + | 0.301015i | ||||
\(547\) | 5.76966 | 0.246693 | 0.123347 | − | 0.992364i | \(-0.460637\pi\) | ||||
0.123347 | + | 0.992364i | \(0.460637\pi\) | |||||||
\(548\) | 18.2067 | 0.777751 | ||||||||
\(549\) | 16.1837 | − | 26.9460i | 0.690703 | − | 1.15003i | ||||
\(550\) | 0.0884736i | 0.00377253i | ||||||||
\(551\) | −7.55966 | −0.322052 | ||||||||
\(552\) | 5.00663 | − | 6.62825i | 0.213096 | − | 0.282117i | ||||
\(553\) | 25.8868 | 1.10082 | ||||||||
\(554\) | 23.1558i | 0.983794i | ||||||||
\(555\) | −2.87106 | + | 10.3566i | −0.121870 | + | 0.439612i | ||||
\(556\) | 7.87519 | 0.333982 | ||||||||
\(557\) | −7.85492 | −0.332823 | −0.166412 | − | 0.986056i | \(-0.553218\pi\) | ||||
−0.166412 | + | 0.986056i | \(0.553218\pi\) | |||||||
\(558\) | 8.58899 | − | 14.3007i | 0.363601 | − | 0.605398i | ||||
\(559\) | 4.88822i | 0.206750i | ||||||||
\(560\) | 2.82123i | 0.119219i | ||||||||
\(561\) | 0.419730 | + | 0.116358i | 0.0177210 | + | 0.00491263i | ||||
\(562\) | 1.79749i | 0.0758226i | ||||||||
\(563\) | 9.90300 | 0.417362 | 0.208681 | − | 0.977984i | \(-0.433083\pi\) | ||||
0.208681 | + | 0.977984i | \(0.433083\pi\) | |||||||
\(564\) | −0.0112667 | + | 0.0406418i | −0.000474415 | + | 0.00171133i | ||||
\(565\) | −5.46926 | −0.230094 | ||||||||
\(566\) | −25.5875 | −1.07552 | ||||||||
\(567\) | 22.4144 | − | 11.9290i | 0.941317 | − | 0.500973i | ||||
\(568\) | −10.9253 | −0.458414 | ||||||||
\(569\) | −7.04866 | −0.295495 | −0.147748 | − | 0.989025i | \(-0.547202\pi\) | ||||
−0.147748 | + | 0.989025i | \(0.547202\pi\) | |||||||
\(570\) | 8.49445 | + | 2.35484i | 0.355793 | + | 0.0986333i | ||||
\(571\) | 31.1060i | 1.30175i | 0.759186 | + | 0.650874i | \(0.225597\pi\) | ||||
−0.759186 | + | 0.650874i | \(0.774403\pi\) | |||||||
\(572\) | −0.476706 | −0.0199321 | ||||||||
\(573\) | −25.7636 | − | 7.14221i | −1.07629 | − | 0.298370i | ||||
\(574\) | − | 1.46693i | − | 0.0612284i | ||||||
\(575\) | 4.45994 | + | 1.76321i | 0.185993 | + | 0.0735309i | ||||
\(576\) | −2.57180 | − | 1.54462i | −0.107158 | − | 0.0643591i | ||||
\(577\) | 8.95481 | 0.372794 | 0.186397 | − | 0.982475i | \(-0.440319\pi\) | ||||
0.186397 | + | 0.982475i | \(0.440319\pi\) | |||||||
\(578\) | − | 8.92119i | − | 0.371072i | ||||||
\(579\) | 5.83308 | + | 1.61705i | 0.242415 | + | 0.0672023i | ||||
\(580\) | 1.48542i | 0.0616787i | ||||||||
\(581\) | 21.3180i | 0.884418i | ||||||||
\(582\) | −13.0760 | − | 3.62495i | −0.542019 | − | 0.150259i | ||||
\(583\) | −0.902680 | −0.0373852 | ||||||||
\(584\) | 5.85816i | 0.242412i | ||||||||
\(585\) | −13.8572 | − | 8.32259i | −0.572923 | − | 0.344097i | ||||
\(586\) | − | 24.0774i | − | 0.994628i | ||||||
\(587\) | − | 13.8103i | − | 0.570014i | −0.958525 | − | 0.285007i | \(-0.908004\pi\) | ||
0.958525 | − | 0.285007i | \(-0.0919959\pi\) | |||||||
\(588\) | 1.60127 | + | 0.443904i | 0.0660351 | + | 0.0183063i | ||||
\(589\) | − | 28.2992i | − | 1.16605i | ||||||
\(590\) | −8.85335 | −0.364487 | ||||||||
\(591\) | 7.15348 | − | 25.8043i | 0.294255 | − | 1.06145i | ||||
\(592\) | − | 6.20488i | − | 0.255019i | ||||||
\(593\) | − | 2.50124i | − | 0.102714i | −0.998680 | − | 0.0513568i | \(-0.983645\pi\) | ||
0.998680 | − | 0.0513568i | \(-0.0163546\pi\) | |||||||
\(594\) | −0.333379 | + | 0.316548i | −0.0136787 | + | 0.0129881i | ||||
\(595\) | 8.01886i | 0.328741i | ||||||||
\(596\) | 7.85015 | 0.321555 | ||||||||
\(597\) | 0.510903 | − | 1.84295i | 0.0209099 | − | 0.0754268i | ||||
\(598\) | −9.50038 | + | 24.0307i | −0.388499 | + | 0.982689i | ||||
\(599\) | − | 0.571210i | − | 0.0233390i | −0.999932 | − | 0.0116695i | \(-0.996285\pi\) | ||
0.999932 | − | 0.0116695i | \(-0.00371460\pi\) | |||||||
\(600\) | 0.462710 | − | 1.66910i | 0.0188900 | − | 0.0681408i | ||||
\(601\) | −16.9300 | −0.690588 | −0.345294 | − | 0.938494i | \(-0.612221\pi\) | ||||
−0.345294 | + | 0.938494i | \(0.612221\pi\) | |||||||
\(602\) | 2.55949i | 0.104317i | ||||||||
\(603\) | −5.87102 | + | 9.77529i | −0.239086 | + | 0.398080i | ||||
\(604\) | −8.89534 | −0.361946 | ||||||||
\(605\) | 10.9922 | 0.446895 | ||||||||
\(606\) | 18.9800 | + | 5.26164i | 0.771009 | + | 0.213740i | ||||
\(607\) | 1.41388 | 0.0573878 | 0.0286939 | − | 0.999588i | \(-0.490865\pi\) | ||||
0.0286939 | + | 0.999588i | \(0.490865\pi\) | |||||||
\(608\) | −5.08924 | −0.206396 | ||||||||
\(609\) | 6.99473 | + | 1.93909i | 0.283441 | + | 0.0785757i | ||||
\(610\) | −10.4775 | −0.424220 | ||||||||
\(611\) | − | 0.131198i | − | 0.00530770i | ||||||
\(612\) | −7.30989 | − | 4.39031i | −0.295485 | − | 0.177468i | ||||
\(613\) | 3.59479i | 0.145192i | 0.997361 | + | 0.0725961i | \(0.0231284\pi\) | ||||
−0.997361 | + | 0.0725961i | \(0.976872\pi\) | |||||||
\(614\) | − | 18.5284i | − | 0.747744i | ||||||
\(615\) | −0.240590 | + | 0.867865i | −0.00970153 | + | 0.0349957i | ||||
\(616\) | −0.249605 | −0.0100569 | ||||||||
\(617\) | 5.75072 | 0.231515 | 0.115758 | − | 0.993277i | \(-0.463070\pi\) | ||||
0.115758 | + | 0.993277i | \(0.463070\pi\) | |||||||
\(618\) | −25.5397 | − | 7.08013i | −1.02736 | − | 0.284804i | ||||
\(619\) | − | 37.6313i | − | 1.51253i | −0.654265 | − | 0.756265i | \(-0.727022\pi\) | ||
0.654265 | − | 0.756265i | \(-0.272978\pi\) | |||||||
\(620\) | −5.56059 | −0.223319 | ||||||||
\(621\) | 9.31318 | + | 23.1142i | 0.373725 | + | 0.927539i | ||||
\(622\) | −29.6815 | −1.19012 | ||||||||
\(623\) | − | 34.8164i | − | 1.39489i | ||||||
\(624\) | 8.99332 | + | 2.49313i | 0.360021 | + | 0.0998053i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −8.20686 | −0.328012 | ||||||||
\(627\) | −0.208341 | + | 0.751534i | −0.00832034 | + | 0.0300134i | ||||
\(628\) | − | 13.4878i | − | 0.538222i | ||||||
\(629\) | − | 17.6363i | − | 0.703205i | ||||||
\(630\) | −7.25565 | − | 4.35773i | −0.289072 | − | 0.173616i | ||||
\(631\) | 18.9775i | 0.755482i | 0.925911 | + | 0.377741i | \(0.123299\pi\) | ||||
−0.925911 | + | 0.377741i | \(0.876701\pi\) | |||||||
\(632\) | 9.17572 | 0.364991 | ||||||||
\(633\) | −45.1678 | − | 12.5214i | −1.79526 | − | 0.497683i | ||||
\(634\) | −30.8326 | −1.22452 | ||||||||
\(635\) | 1.22410 | 0.0485768 | ||||||||
\(636\) | 17.0295 | + | 4.72094i | 0.675265 | + | 0.187198i | ||||
\(637\) | −5.16914 | −0.204809 | ||||||||
\(638\) | −0.131420 | −0.00520299 | ||||||||
\(639\) | 16.8754 | − | 28.0976i | 0.667579 | − | 1.11152i | ||||
\(640\) | 1.00000i | 0.0395285i | ||||||||
\(641\) | 39.5864 | 1.56357 | 0.781785 | − | 0.623548i | \(-0.214309\pi\) | ||||
0.781785 | + | 0.623548i | \(0.214309\pi\) | |||||||
\(642\) | 0.995077 | − | 3.58947i | 0.0392725 | − | 0.141665i | ||||
\(643\) | − | 8.50938i | − | 0.335577i | −0.985823 | − | 0.167789i | \(-0.946337\pi\) | ||
0.985823 | − | 0.167789i | \(-0.0536626\pi\) | |||||||
\(644\) | −4.97442 | + | 12.5825i | −0.196020 | + | 0.495822i | ||||
\(645\) | 0.419780 | − | 1.51425i | 0.0165288 | − | 0.0596234i | ||||
\(646\) | −14.4653 | −0.569128 | ||||||||
\(647\) | 18.9221i | 0.743903i | 0.928252 | + | 0.371951i | \(0.121311\pi\) | ||||
−0.928252 | + | 0.371951i | \(0.878689\pi\) | |||||||
\(648\) | 7.94490 | − | 4.22831i | 0.312105 | − | 0.166104i | ||||
\(649\) | − | 0.783288i | − | 0.0307467i | ||||||
\(650\) | 5.38812i | 0.211339i | ||||||||
\(651\) | −7.25886 | + | 26.1844i | −0.284497 | + | 1.02625i | ||||
\(652\) | 7.19796 | 0.281894 | ||||||||
\(653\) | 10.9104i | 0.426956i | 0.976948 | + | 0.213478i | \(0.0684791\pi\) | ||||
−0.976948 | + | 0.213478i | \(0.931521\pi\) | |||||||
\(654\) | −15.0942 | − | 4.18443i | −0.590230 | − | 0.163624i | ||||
\(655\) | − | 17.3758i | − | 0.678929i | ||||||
\(656\) | − | 0.519960i | − | 0.0203010i | ||||||
\(657\) | −15.0660 | − | 9.04863i | −0.587781 | − | 0.353021i | ||||
\(658\) | − | 0.0686956i | − | 0.00267803i | ||||||
\(659\) | −9.42907 | −0.367304 | −0.183652 | − | 0.982991i | \(-0.558792\pi\) | ||||
−0.183652 | + | 0.982991i | \(0.558792\pi\) | |||||||
\(660\) | 0.147671 | + | 0.0409376i | 0.00574810 | + | 0.00159349i | ||||
\(661\) | 10.2837i | 0.399991i | 0.979797 | + | 0.199995i | \(0.0640927\pi\) | ||||
−0.979797 | + | 0.199995i | \(0.935907\pi\) | |||||||
\(662\) | − | 18.1025i | − | 0.703574i | ||||||
\(663\) | 25.5619 | + | 7.08630i | 0.992744 | + | 0.275209i | ||||
\(664\) | 7.55626i | 0.293240i | ||||||||
\(665\) | −14.3579 | −0.556776 | ||||||||
\(666\) | 15.9577 | + | 9.58417i | 0.618348 | + | 0.371379i | ||||
\(667\) | −2.61911 | + | 6.62489i | −0.101412 | + | 0.256517i | ||||
\(668\) | 15.7105i | 0.607859i | ||||||||
\(669\) | −15.4111 | − | 4.27228i | −0.595828 | − | 0.165176i | ||||
\(670\) | 3.80095 | 0.146844 | ||||||||
\(671\) | − | 0.926979i | − | 0.0357856i | ||||||
\(672\) | 4.70893 | + | 1.30541i | 0.181651 | + | 0.0503573i | ||||
\(673\) | 34.9603 | 1.34762 | 0.673811 | − | 0.738904i | \(-0.264656\pi\) | ||||
0.673811 | + | 0.738904i | \(0.264656\pi\) | |||||||
\(674\) | 19.1719 | 0.738476 | ||||||||
\(675\) | 3.57789 | + | 3.76812i | 0.137713 | + | 0.145035i | ||||
\(676\) | −16.0318 | −0.616609 | ||||||||
\(677\) | 20.1189 | 0.773231 | 0.386615 | − | 0.922241i | \(-0.373644\pi\) | ||||
0.386615 | + | 0.922241i | \(0.373644\pi\) | |||||||
\(678\) | −2.53068 | + | 9.12875i | −0.0971902 | + | 0.350588i | ||||
\(679\) | 22.1020 | 0.848198 | ||||||||
\(680\) | 2.84233i | 0.108998i | ||||||||
\(681\) | −24.6684 | − | 6.83858i | −0.945294 | − | 0.262055i | ||||
\(682\) | − | 0.491965i | − | 0.0188383i | ||||||
\(683\) | 16.5961i | 0.635030i | 0.948253 | + | 0.317515i | \(0.102848\pi\) | ||||
−0.948253 | + | 0.317515i | \(0.897152\pi\) | |||||||
\(684\) | 7.86093 | − | 13.0885i | 0.300570 | − | 0.500451i | ||||
\(685\) | 18.2067 | 0.695641 | ||||||||
\(686\) | 17.0421 | 0.650669 | ||||||||
\(687\) | 12.4618 | − | 44.9528i | 0.475449 | − | 1.71506i | ||||
\(688\) | 0.907222i | 0.0345875i | ||||||||
\(689\) | −54.9740 | −2.09434 | ||||||||
\(690\) | 5.00663 | − | 6.62825i | 0.190599 | − | 0.252333i | ||||
\(691\) | −44.3960 | −1.68890 | −0.844452 | − | 0.535630i | \(-0.820074\pi\) | ||||
−0.844452 | + | 0.535630i | \(0.820074\pi\) | |||||||
\(692\) | − | 0.427486i | − | 0.0162506i | ||||||
\(693\) | 0.385544 | − | 0.641933i | 0.0146456 | − | 0.0243850i | ||||
\(694\) | −24.7654 | −0.940081 | ||||||||
\(695\) | 7.87519 | 0.298723 | ||||||||
\(696\) | 2.47932 | + | 0.687318i | 0.0939783 | + | 0.0260527i | ||||
\(697\) | − | 1.47789i | − | 0.0559792i | ||||||
\(698\) | 29.5558i | 1.11870i | ||||||||
\(699\) | 8.57017 | − | 30.9146i | 0.324153 | − | 1.16930i | ||||
\(700\) | 2.82123i | 0.106633i | ||||||||
\(701\) | 4.03643 | 0.152454 | 0.0762269 | − | 0.997090i | \(-0.475713\pi\) | ||||
0.0762269 | + | 0.997090i | \(0.475713\pi\) | |||||||
\(702\) | −20.3031 | + | 19.2781i | −0.766291 | + | 0.727604i | ||||
\(703\) | 31.5781 | 1.19099 | ||||||||
\(704\) | −0.0884736 | −0.00333447 | ||||||||
\(705\) | −0.0112667 | + | 0.0406418i | −0.000424330 | + | 0.00153066i | ||||
\(706\) | −28.0481 | −1.05560 | ||||||||
\(707\) | −32.0813 | −1.20654 | ||||||||
\(708\) | −4.09653 | + | 14.7771i | −0.153957 | + | 0.555359i | ||||
\(709\) | 32.9635i | 1.23797i | 0.785402 | + | 0.618986i | \(0.212456\pi\) | ||||
−0.785402 | + | 0.618986i | \(0.787544\pi\) | |||||||
\(710\) | −10.9253 | −0.410018 | ||||||||
\(711\) | −14.1730 | + | 23.5981i | −0.531528 | + | 0.884998i | ||||
\(712\) | − | 12.3408i | − | 0.462492i | ||||||
\(713\) | −24.7999 | − | 9.80448i | −0.928764 | − | 0.367181i | ||||
\(714\) | 13.3843 | + | 3.71040i | 0.500895 | + | 0.138858i | ||||
\(715\) | −0.476706 | −0.0178278 | ||||||||
\(716\) | 12.9141i | 0.482622i | ||||||||
\(717\) | −10.7799 | + | 38.8857i | −0.402584 | + | 1.45221i | ||||
\(718\) | 11.9019i | 0.444177i | ||||||||
\(719\) | 9.37917i | 0.349784i | 0.984588 | + | 0.174892i | \(0.0559576\pi\) | ||||
−0.984588 | + | 0.174892i | \(0.944042\pi\) | |||||||
\(720\) | −2.57180 | − | 1.54462i | −0.0958453 | − | 0.0575645i | ||||
\(721\) | 43.1690 | 1.60770 | ||||||||
\(722\) | − | 6.90033i | − | 0.256804i | ||||||
\(723\) | 4.97164 | − | 17.9339i | 0.184897 | − | 0.666968i | ||||
\(724\) | 24.7502i | 0.919834i | ||||||||
\(725\) | 1.48542i | 0.0551671i | ||||||||
\(726\) | 5.08618 | − | 18.3471i | 0.188766 | − | 0.680923i | ||||
\(727\) | − | 37.6346i | − | 1.39579i | −0.716199 | − | 0.697896i | \(-0.754120\pi\) | ||
0.716199 | − | 0.697896i | \(-0.245880\pi\) | |||||||
\(728\) | −15.2011 | −0.563392 | ||||||||
\(729\) | −1.39747 | + | 26.9638i | −0.0517583 | + | 0.998660i | ||||
\(730\) | 5.85816i | 0.216820i | ||||||||
\(731\) | 2.57862i | 0.0953737i | ||||||||
\(732\) | −4.84802 | + | 17.4880i | −0.179188 | + | 0.646374i | ||||
\(733\) | 48.8726i | 1.80515i | 0.430533 | + | 0.902575i | \(0.358326\pi\) | ||||
−0.430533 | + | 0.902575i | \(0.641674\pi\) | |||||||
\(734\) | 31.6802 | 1.16934 | ||||||||
\(735\) | 1.60127 | + | 0.443904i | 0.0590636 | + | 0.0163737i | ||||
\(736\) | −1.76321 | + | 4.45994i | −0.0649927 | + | 0.164396i | ||||
\(737\) | 0.336284i | 0.0123872i | ||||||||
\(738\) | 1.33723 | + | 0.803139i | 0.0492242 | + | 0.0295640i | ||||
\(739\) | −4.24348 | −0.156099 | −0.0780495 | − | 0.996949i | \(-0.524869\pi\) | ||||
−0.0780495 | + | 0.996949i | \(0.524869\pi\) | |||||||
\(740\) | − | 6.20488i | − | 0.228096i | ||||||
\(741\) | −12.6882 | + | 45.7691i | −0.466111 | + | 1.68137i | ||||
\(742\) | −28.7845 | −1.05671 | ||||||||
\(743\) | −13.3090 | −0.488261 | −0.244130 | − | 0.969742i | \(-0.578502\pi\) | ||||
−0.244130 | + | 0.969742i | \(0.578502\pi\) | |||||||
\(744\) | −2.57294 | + | 9.28119i | −0.0943285 | + | 0.340265i | ||||
\(745\) | 7.85015 | 0.287607 | ||||||||
\(746\) | −8.32570 | −0.304826 | ||||||||
\(747\) | −19.4332 | − | 11.6715i | −0.711023 | − | 0.427039i | ||||
\(748\) | −0.251471 | −0.00919468 | ||||||||
\(749\) | 6.06718i | 0.221690i | ||||||||
\(750\) | 0.462710 | − | 1.66910i | 0.0168958 | − | 0.0609470i | ||||
\(751\) | − | 36.2427i | − | 1.32251i | −0.750159 | − | 0.661257i | \(-0.770023\pi\) | ||
0.750159 | − | 0.661257i | \(-0.229977\pi\) | |||||||
\(752\) | − | 0.0243495i | − | 0.000887934i | ||||||
\(753\) | −16.9542 | − | 4.70005i | −0.617845 | − | 0.171279i | ||||
\(754\) | −8.00363 | −0.291475 | ||||||||
\(755\) | −8.89534 | −0.323735 | ||||||||
\(756\) | −10.6307 | + | 10.0940i | −0.386637 | + | 0.367117i | ||||
\(757\) | − | 38.6987i | − | 1.40653i | −0.710929 | − | 0.703264i | \(-0.751725\pi\) | ||
0.710929 | − | 0.703264i | \(-0.248275\pi\) | |||||||
\(758\) | 9.50248 | 0.345146 | ||||||||
\(759\) | 0.586424 | + | 0.442955i | 0.0212859 | + | 0.0160782i | ||||
\(760\) | −5.08924 | −0.184606 | ||||||||
\(761\) | 33.2491i | 1.20528i | 0.798014 | + | 0.602639i | \(0.205884\pi\) | ||||
−0.798014 | + | 0.602639i | \(0.794116\pi\) | |||||||
\(762\) | 0.566402 | − | 2.04314i | 0.0205186 | − | 0.0740153i | ||||
\(763\) | 25.5133 | 0.923643 | ||||||||
\(764\) | 15.4356 | 0.558441 | ||||||||
\(765\) | −7.30989 | − | 4.39031i | −0.264290 | − | 0.158732i | ||||
\(766\) | 37.1871i | 1.34363i | ||||||||
\(767\) | − | 47.7029i | − | 1.72245i | ||||||
\(768\) | 1.66910 | + | 0.462710i | 0.0602285 | + | 0.0166966i | ||||
\(769\) | − | 5.52635i | − | 0.199285i | −0.995023 | − | 0.0996426i | \(-0.968230\pi\) | ||
0.995023 | − | 0.0996426i | \(-0.0317700\pi\) | |||||||
\(770\) | −0.249605 | −0.00899512 | ||||||||
\(771\) | −6.83526 | + | 24.6564i | −0.246166 | + | 0.887978i | ||||
\(772\) | −3.49474 | −0.125779 | ||||||||
\(773\) | 13.0486 | 0.469327 | 0.234663 | − | 0.972077i | \(-0.424601\pi\) | ||||
0.234663 | + | 0.972077i | \(0.424601\pi\) | |||||||
\(774\) | −2.33319 | − | 1.40131i | −0.0838649 | − | 0.0503691i | ||||
\(775\) | −5.56059 | −0.199742 | ||||||||
\(776\) | 7.83418 | 0.281230 | ||||||||
\(777\) | −29.2183 | − | 8.09992i | −1.04820 | − | 0.290583i | ||||
\(778\) | 18.6520i | 0.668708i | ||||||||
\(779\) | 2.64620 | 0.0948098 | ||||||||
\(780\) | 8.99332 | + | 2.49313i | 0.322013 | + | 0.0892685i | ||||
\(781\) | − | 0.966597i | − | 0.0345876i | ||||||
\(782\) | −5.01161 | + | 12.6766i | −0.179215 | + | 0.453315i | ||||
\(783\) | −5.59724 | + | 5.31466i | −0.200029 | + | 0.189931i | ||||
\(784\) | −0.959358 | −0.0342628 | ||||||||
\(785\) | − | 13.4878i | − | 0.481401i | ||||||
\(786\) | −29.0020 | − | 8.03996i | −1.03447 | − | 0.286776i | ||||
\(787\) | − | 51.4300i | − | 1.83328i | −0.399714 | − | 0.916640i | \(-0.630890\pi\) | ||
0.399714 | − | 0.916640i | \(-0.369110\pi\) | |||||||
\(788\) | 15.4600i | 0.550739i | ||||||||
\(789\) | 40.1265 | + | 11.1239i | 1.42854 | + | 0.396021i | ||||
\(790\) | 9.17572 | 0.326457 | ||||||||
\(791\) | − | 15.4301i | − | 0.548630i | ||||||
\(792\) | 0.136658 | − | 0.227536i | 0.00485593 | − | 0.00808515i | ||||
\(793\) | − | 56.4539i | − | 2.00474i | ||||||
\(794\) | 2.78953i | 0.0989968i | ||||||||
\(795\) | 17.0295 | + | 4.72094i | 0.603976 | + | 0.167435i | ||||
\(796\) | 1.10416i | 0.0391357i | ||||||||
\(797\) | −18.9958 | −0.672867 | −0.336434 | − | 0.941707i | \(-0.609221\pi\) | ||||
−0.336434 | + | 0.941707i | \(0.609221\pi\) | |||||||
\(798\) | −6.64355 | + | 23.9648i | −0.235179 | + | 0.848346i | ||||
\(799\) | − | 0.0692092i | − | 0.00244844i | ||||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | 31.7381 | + | 19.0619i | 1.12141 | + | 0.673518i | ||||
\(802\) | 34.5221i | 1.21902i | ||||||||
\(803\) | −0.518293 | −0.0182901 | ||||||||
\(804\) | 1.75874 | − | 6.34417i | 0.0620258 | − | 0.223742i | ||||
\(805\) | −4.97442 | + | 12.5825i | −0.175325 | + | 0.443476i | ||||
\(806\) | − | 29.9611i | − | 1.05534i | ||||||
\(807\) | 2.19494 | − | 7.91765i | 0.0772655 | − | 0.278715i | ||||
\(808\) | −11.3714 | −0.400043 | ||||||||
\(809\) | − | 10.0723i | − | 0.354123i | −0.984200 | − | 0.177061i | \(-0.943341\pi\) | ||
0.984200 | − | 0.177061i | \(-0.0566591\pi\) | |||||||
\(810\) | 7.94490 | − | 4.22831i | 0.279155 | − | 0.148568i | ||||
\(811\) | 39.9165 | 1.40166 | 0.700829 | − | 0.713330i | \(-0.252814\pi\) | ||||
0.700829 | + | 0.713330i | \(0.252814\pi\) | |||||||
\(812\) | −4.19072 | −0.147065 | ||||||||
\(813\) | −0.506478 | − | 0.140406i | −0.0177629 | − | 0.00492426i | ||||
\(814\) | 0.548968 | 0.0192413 | ||||||||
\(815\) | 7.19796 | 0.252134 | ||||||||
\(816\) | 4.74413 | + | 1.31517i | 0.166078 | + | 0.0460402i | ||||
\(817\) | −4.61707 | −0.161531 | ||||||||
\(818\) | − | 13.4130i | − | 0.468976i | ||||||
\(819\) | 23.4800 | − | 39.0943i | 0.820457 | − | 1.36607i | ||||
\(820\) | − | 0.519960i | − | 0.0181578i | ||||||
\(821\) | − | 42.9606i | − | 1.49934i | −0.661814 | − | 0.749668i | \(-0.730213\pi\) | ||
0.661814 | − | 0.749668i | \(-0.269787\pi\) | |||||||
\(822\) | 8.42440 | − | 30.3888i | 0.293835 | − | 1.05993i | ||||
\(823\) | −20.1098 | −0.700985 | −0.350493 | − | 0.936565i | \(-0.613986\pi\) | ||||
−0.350493 | + | 0.936565i | \(0.613986\pi\) | |||||||
\(824\) | 15.3014 | 0.533051 | ||||||||
\(825\) | 0.147671 | + | 0.0409376i | 0.00514126 | + | 0.00142526i | ||||
\(826\) | − | 24.9774i | − | 0.869074i | ||||||
\(827\) | 17.6733 | 0.614559 | 0.307280 | − | 0.951619i | \(-0.400581\pi\) | ||||
0.307280 | + | 0.951619i | \(0.400581\pi\) | |||||||
\(828\) | −8.74660 | − | 11.4235i | −0.303965 | − | 0.396995i | ||||
\(829\) | −39.6740 | −1.37793 | −0.688967 | − | 0.724793i | \(-0.741935\pi\) | ||||
−0.688967 | + | 0.724793i | \(0.741935\pi\) | |||||||
\(830\) | 7.55626i | 0.262282i | ||||||||
\(831\) | 38.6493 | + | 10.7144i | 1.34073 | + | 0.371678i | ||||
\(832\) | −5.38812 | −0.186799 | ||||||||
\(833\) | −2.72681 | −0.0944783 | ||||||||
\(834\) | 3.64392 | − | 13.1445i | 0.126179 | − | 0.455156i | ||||
\(835\) | 15.7105i | 0.543685i | ||||||||
\(836\) | − | 0.450263i | − | 0.0155727i | ||||||
\(837\) | −19.8952 | − | 20.9530i | −0.687677 | − | 0.724241i | ||||
\(838\) | 39.6632i | 1.37014i | ||||||||
\(839\) | −31.0921 | −1.07342 | −0.536710 | − | 0.843767i | \(-0.680333\pi\) | ||||
−0.536710 | + | 0.843767i | \(0.680333\pi\) | |||||||
\(840\) | 4.70893 | + | 1.30541i | 0.162473 | + | 0.0450410i | ||||
\(841\) | 26.7935 | 0.923915 | ||||||||
\(842\) | −8.88923 | −0.306343 | ||||||||
\(843\) | 3.00019 | + | 0.831716i | 0.103332 | + | 0.0286458i | ||||
\(844\) | 27.0611 | 0.931483 | ||||||||
\(845\) | −16.0318 | −0.551512 | ||||||||
\(846\) | 0.0626220 | + | 0.0376107i | 0.00215299 | + | 0.00129308i | ||||
\(847\) | 31.0115i | 1.06557i | ||||||||
\(848\) | −10.2028 | −0.350366 | ||||||||
\(849\) | −11.8396 | + | 42.7081i | −0.406333 | + | 1.46574i | ||||
\(850\) | 2.84233i | 0.0974910i | ||||||||
\(851\) | 10.9405 | − | 27.6734i | 0.375035 | − | 0.948632i | ||||
\(852\) | −5.05523 | + | 18.2354i | −0.173189 | + | 0.624734i | ||||
\(853\) | 16.9564 | 0.580578 | 0.290289 | − | 0.956939i | \(-0.406249\pi\) | ||||
0.290289 | + | 0.956939i | \(0.406249\pi\) | |||||||
\(854\) | − | 29.5594i | − | 1.01150i | ||||||
\(855\) | 7.86093 | − | 13.0885i | 0.268838 | − | 0.447617i | ||||
\(856\) | 2.15054i | 0.0735040i | ||||||||
\(857\) | − | 41.8620i | − | 1.42998i | −0.699135 | − | 0.714990i | \(-0.746431\pi\) | ||
0.699135 | − | 0.714990i | \(-0.253569\pi\) | |||||||
\(858\) | −0.220577 | + | 0.795671i | −0.00753036 | + | 0.0271638i | ||||
\(859\) | −8.38489 | −0.286089 | −0.143044 | − | 0.989716i | \(-0.545689\pi\) | ||||
−0.143044 | + | 0.989716i | \(0.545689\pi\) | |||||||
\(860\) | 0.907222i | 0.0309360i | ||||||||
\(861\) | −2.44845 | − | 0.678761i | −0.0834430 | − | 0.0231321i | ||||
\(862\) | − | 40.0125i | − | 1.36283i | ||||||
\(863\) | − | 11.9040i | − | 0.405216i | −0.979260 | − | 0.202608i | \(-0.935058\pi\) | ||
0.979260 | − | 0.202608i | \(-0.0649416\pi\) | |||||||
\(864\) | −3.76812 | + | 3.57789i | −0.128194 | + | 0.121722i | ||||
\(865\) | − | 0.427486i | − | 0.0145350i | ||||||
\(866\) | −24.6079 | −0.836209 | ||||||||
\(867\) | −14.8904 | − | 4.12792i | −0.505703 | − | 0.140191i | ||||
\(868\) | − | 15.6877i | − | 0.532476i | ||||||
\(869\) | 0.811809i | 0.0275387i | ||||||||
\(870\) | 2.47932 | + | 0.687318i | 0.0840567 | + | 0.0233023i | ||||
\(871\) | 20.4800i | 0.693938i | ||||||||
\(872\) | 9.04331 | 0.306245 | ||||||||
\(873\) | −12.1008 | + | 20.1479i | −0.409550 | + | 0.681904i | ||||
\(874\) | −22.6977 | − | 8.97339i | −0.767761 | − | 0.303529i | ||||
\(875\) | 2.82123i | 0.0953751i | ||||||||
\(876\) | 9.77787 | + | 2.71063i | 0.330364 | + | 0.0915836i | ||||
\(877\) | 12.2166 | 0.412524 | 0.206262 | − | 0.978497i | \(-0.433870\pi\) | ||||
0.206262 | + | 0.978497i | \(0.433870\pi\) | |||||||
\(878\) | − | 28.9558i | − | 0.977212i | ||||||
\(879\) | −40.1876 | − | 11.1408i | −1.35549 | − | 0.375771i | ||||
\(880\) | −0.0884736 | −0.00298244 | ||||||||
\(881\) | 24.0770 | 0.811174 | 0.405587 | − | 0.914056i | \(-0.367067\pi\) | ||||
0.405587 | + | 0.914056i | \(0.367067\pi\) | |||||||
\(882\) | 1.48184 | − | 2.46728i | 0.0498962 | − | 0.0830775i | ||||
\(883\) | 0.670650 | 0.0225692 | 0.0112846 | − | 0.999936i | \(-0.496408\pi\) | ||||
0.0112846 | + | 0.999936i | \(0.496408\pi\) | |||||||
\(884\) | −15.3148 | −0.515092 | ||||||||
\(885\) | −4.09653 | + | 14.7771i | −0.137703 | + | 0.496728i | ||||
\(886\) | 3.91361 | 0.131480 | ||||||||
\(887\) | 49.6106i | 1.66576i | 0.553453 | + | 0.832880i | \(0.313310\pi\) | ||||
−0.553453 | + | 0.832880i | \(0.686690\pi\) | |||||||
\(888\) | −10.3566 | − | 2.87106i | −0.347544 | − | 0.0963463i | ||||
\(889\) | 3.45346i | 0.115825i | ||||||||
\(890\) | − | 12.3408i | − | 0.413666i | ||||||
\(891\) | 0.374093 | + | 0.702913i | 0.0125326 | + | 0.0235485i | ||||
\(892\) | 9.23318 | 0.309150 | ||||||||
\(893\) | 0.123920 | 0.00414683 | ||||||||
\(894\) | 3.63234 | − | 13.1027i | 0.121484 | − | 0.438220i | ||||
\(895\) | 12.9141i | 0.431670i | ||||||||
\(896\) | −2.82123 | −0.0942508 | ||||||||
\(897\) | 35.7138 | + | 26.9763i | 1.19245 | + | 0.900714i | ||||
\(898\) | 16.9735 | 0.566413 | ||||||||
\(899\) | − | 8.25982i | − | 0.275480i | ||||||
\(900\) | −2.57180 | − | 1.54462i | −0.0857267 | − | 0.0514873i | ||||
\(901\) | −28.9997 | −0.966122 | ||||||||
\(902\) | 0.0460027 | 0.00153172 | ||||||||
\(903\) | 4.27204 | + | 1.18430i | 0.142165 | + | 0.0394110i | ||||
\(904\) | − | 5.46926i | − | 0.181905i | ||||||
\(905\) | 24.7502i | 0.822724i | ||||||||
\(906\) | −4.11596 | + | 14.8472i | −0.136744 | + | 0.493266i | ||||
\(907\) | 6.74337i | 0.223910i | 0.993713 | + | 0.111955i | \(0.0357112\pi\) | ||||
−0.993713 | + | 0.111955i | \(0.964289\pi\) | |||||||
\(908\) | 14.7794 | 0.490473 | ||||||||
\(909\) | 17.5644 | − | 29.2449i | 0.582575 | − | 0.969992i | ||||
\(910\) | −15.2011 | −0.503913 | ||||||||
\(911\) | 22.2997 | 0.738821 | 0.369411 | − | 0.929266i | \(-0.379560\pi\) | ||||
0.369411 | + | 0.929266i | \(0.379560\pi\) | |||||||
\(912\) | −2.35484 | + | 8.49445i | −0.0779765 | + | 0.281279i | ||||
\(913\) | −0.668529 | −0.0221251 | ||||||||
\(914\) | 16.4848 | 0.545270 | ||||||||
\(915\) | −4.84802 | + | 17.4880i | −0.160271 | + | 0.578134i | ||||
\(916\) | 26.9323i | 0.889869i | ||||||||
\(917\) | 49.0212 | 1.61882 | ||||||||
\(918\) | −10.7102 | + | 10.1695i | −0.353490 | + | 0.335644i | ||||
\(919\) | − | 31.6892i | − | 1.04533i | −0.852538 | − | 0.522665i | \(-0.824938\pi\) | ||
0.852538 | − | 0.522665i | \(-0.175062\pi\) | |||||||
\(920\) | −1.76321 | + | 4.45994i | −0.0581313 | + | 0.147040i | ||||
\(921\) | −30.9257 | − | 8.57325i | −1.01904 | − | 0.282498i | ||||
\(922\) | 42.6536 | 1.40472 | ||||||||
\(923\) | − | 58.8667i | − | 1.93762i | ||||||
\(924\) | −0.115494 | + | 0.416615i | −0.00379949 | + | 0.0137056i | ||||
\(925\) | − | 6.20488i | − | 0.204015i | ||||||
\(926\) | 9.52088i | 0.312875i | ||||||||
\(927\) | −23.6349 | + | 39.3523i | −0.776272 | + | 1.29250i | ||||
\(928\) | −1.48542 | −0.0487613 | ||||||||
\(929\) | 29.0730i | 0.953854i | 0.878943 | + | 0.476927i | \(0.158249\pi\) | ||||
−0.878943 | + | 0.476927i | \(0.841751\pi\) | |||||||
\(930\) | −2.57294 | + | 9.28119i | −0.0843700 | + | 0.304342i | ||||
\(931\) | − | 4.88240i | − | 0.160014i | ||||||
\(932\) | 18.5217i | 0.606698i | ||||||||
\(933\) | −13.7339 | + | 49.5414i | −0.449628 | + | 1.62191i | ||||
\(934\) | − | 18.2551i | − | 0.597324i | ||||||
\(935\) | −0.251471 | −0.00822397 | ||||||||
\(936\) | 8.32259 | − | 13.8572i | 0.272032 | − | 0.452936i | ||||
\(937\) | − | 24.2016i | − | 0.790630i | −0.918546 | − | 0.395315i | \(-0.870635\pi\) | ||
0.918546 | − | 0.395315i | \(-0.129365\pi\) | |||||||
\(938\) | 10.7234i | 0.350130i | ||||||||
\(939\) | −3.79739 | + | 13.6981i | −0.123923 | + | 0.447020i | ||||
\(940\) | − | 0.0243495i | − | 0.000794193i | ||||||
\(941\) | 21.2153 | 0.691598 | 0.345799 | − | 0.938309i | \(-0.387608\pi\) | ||||
0.345799 | + | 0.938309i | \(0.387608\pi\) | |||||||
\(942\) | −22.5125 | − | 6.24094i | −0.733498 | − | 0.203341i | ||||
\(943\) | 0.916797 | − | 2.31899i | 0.0298550 | − | 0.0755167i | ||||
\(944\) | − | 8.85335i | − | 0.288152i | ||||||
\(945\) | −10.6307 | + | 10.0940i | −0.345818 | + | 0.328359i | ||||
\(946\) | −0.0802652 | −0.00260965 | ||||||||
\(947\) | 39.0946i | 1.27041i | 0.772346 | + | 0.635203i | \(0.219083\pi\) | ||||
−0.772346 | + | 0.635203i | \(0.780917\pi\) | |||||||
\(948\) | 4.24569 | − | 15.3152i | 0.137894 | − | 0.497415i | ||||
\(949\) | −31.5645 | −1.02463 | ||||||||
\(950\) | −5.08924 | −0.165117 | ||||||||
\(951\) | −14.2666 | + | 51.4628i | −0.462625 | + | 1.66880i | ||||
\(952\) | −8.01886 | −0.259893 | ||||||||
\(953\) | −20.2089 | −0.654631 | −0.327316 | − | 0.944915i | \(-0.606144\pi\) | ||||
−0.327316 | + | 0.944915i | \(0.606144\pi\) | |||||||
\(954\) | 15.7595 | − | 26.2396i | 0.510232 | − | 0.849539i | ||||
\(955\) | 15.4356 | 0.499485 | ||||||||
\(956\) | − | 23.2974i | − | 0.753492i | ||||||
\(957\) | −0.0608095 | + | 0.219354i | −0.00196569 | + | 0.00709071i | ||||
\(958\) | − | 6.28781i | − | 0.203150i | ||||||
\(959\) | 51.3653i | 1.65867i | ||||||||
\(960\) | 1.66910 | + | 0.462710i | 0.0538700 | + | 0.0149339i | ||||
\(961\) | −0.0798189 | −0.00257480 | ||||||||
\(962\) | 33.4326 | 1.07791 | ||||||||
\(963\) | −5.53076 | − | 3.32177i | −0.178226 | − | 0.107042i | ||||
\(964\) | 10.7446i | 0.346061i | ||||||||
\(965\) | −3.49474 | −0.112500 | ||||||||
\(966\) | 18.6998 | + | 14.1249i | 0.601657 | + | 0.454461i | ||||
\(967\) | 47.2295 | 1.51880 | 0.759398 | − | 0.650626i | \(-0.225493\pi\) | ||||
0.759398 | + | 0.650626i | \(0.225493\pi\) | |||||||
\(968\) | 10.9922i | 0.353302i | ||||||||
\(969\) | −6.69322 | + | 24.1440i | −0.215017 | + | 0.775617i | ||||
\(970\) | 7.83418 | 0.251540 | ||||||||
\(971\) | −14.3487 | −0.460470 | −0.230235 | − | 0.973135i | \(-0.573950\pi\) | ||||
−0.230235 | + | 0.973135i | \(0.573950\pi\) | |||||||
\(972\) | −3.38130 | − | 15.2173i | −0.108455 | − | 0.488096i | ||||
\(973\) | 22.2177i | 0.712268i | ||||||||
\(974\) | − | 2.55380i | − | 0.0818290i | ||||||
\(975\) | 8.99332 | + | 2.49313i | 0.288017 | + | 0.0798442i | ||||
\(976\) | − | 10.4775i | − | 0.335376i | ||||||
\(977\) | 23.8210 | 0.762101 | 0.381051 | − | 0.924554i | \(-0.375562\pi\) | ||||
0.381051 | + | 0.924554i | \(0.375562\pi\) | |||||||
\(978\) | 3.33057 | − | 12.0141i | 0.106500 | − | 0.384170i | ||||
\(979\) | 1.09184 | 0.0348953 | ||||||||
\(980\) | −0.959358 | −0.0306456 | ||||||||
\(981\) | −13.9685 | + | 23.2576i | −0.445979 | + | 0.742557i | ||||
\(982\) | 16.8062 | 0.536306 | ||||||||
\(983\) | −24.6498 | −0.786207 | −0.393104 | − | 0.919494i | \(-0.628599\pi\) | ||||
−0.393104 | + | 0.919494i | \(0.628599\pi\) | |||||||
\(984\) | −0.867865 | − | 0.240590i | −0.0276665 | − | 0.00766974i | ||||
\(985\) | 15.4600i | 0.492596i | ||||||||
\(986\) | −4.22205 | −0.134457 | ||||||||
\(987\) | −0.114660 | − | 0.0317861i | −0.00364967 | − | 0.00101176i | ||||
\(988\) | − | 27.4214i | − | 0.872392i | ||||||
\(989\) | −1.59962 | + | 4.04616i | −0.0508650 | + | 0.128660i | ||||
\(990\) | 0.136658 | − | 0.227536i | 0.00434327 | − | 0.00723158i | ||||
\(991\) | 41.1146 | 1.30605 | 0.653024 | − | 0.757337i | \(-0.273500\pi\) | ||||
0.653024 | + | 0.757337i | \(0.273500\pi\) | |||||||
\(992\) | − | 5.56059i | − | 0.176549i | ||||||
\(993\) | −30.2149 | − | 8.37620i | −0.958841 | − | 0.265811i | ||||
\(994\) | − | 30.8227i | − | 0.977638i | ||||||
\(995\) | 1.10416i | 0.0350041i | ||||||||
\(996\) | 12.6122 | + | 3.49635i | 0.399632 | + | 0.110786i | ||||
\(997\) | −40.8555 | −1.29391 | −0.646953 | − | 0.762530i | \(-0.723957\pi\) | ||||
−0.646953 | + | 0.762530i | \(0.723957\pi\) | |||||||
\(998\) | − | 9.17252i | − | 0.290351i | ||||||
\(999\) | 23.3807 | − | 22.2003i | 0.739734 | − | 0.702388i |
(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 | 690.2.e.a.551.15 | yes | 16 | |
3.2 | odd | 2 | 690.2.e.b.551.7 | yes | 16 | ||
23.22 | odd | 2 | 690.2.e.b.551.15 | yes | 16 | ||
69.68 | even | 2 | inner | 690.2.e.a.551.7 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.e.a.551.7 | ✓ | 16 | 69.68 | even | 2 | inner | |
690.2.e.a.551.15 | yes | 16 | 1.1 | even | 1 | trivial | |
690.2.e.b.551.7 | yes | 16 | 3.2 | odd | 2 | ||
690.2.e.b.551.15 | yes | 16 | 23.22 | odd | 2 |