Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,2,Mod(17,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("560.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.ci (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.47162251319\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 33.4 | ||
Root | \(0.587308 + 2.01725i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 560.33 |
Dual form | 560.2.ci.c.17.4 |
$q$-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 \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(351\) | \(421\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.80762 | + | 0.752300i | 1.62098 | + | 0.434341i | 0.951290 | − | 0.308298i | \(-0.0997593\pi\) |
0.669692 | + | 0.742639i | \(0.266426\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.21323 | − | 0.318742i | −0.989788 | − | 0.142546i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.559876 | + | 2.58583i | −0.211613 | + | 0.977353i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.71872 | + | 2.72435i | 1.57291 | + | 0.908118i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.83557 | + | 3.17930i | 0.553445 | + | 0.958596i | 0.998023 | + | 0.0628551i | \(0.0200206\pi\) |
−0.444577 | + | 0.895741i | \(0.646646\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.830578 | − | 0.830578i | 0.230361 | − | 0.230361i | −0.582482 | − | 0.812843i | \(-0.697918\pi\) |
0.812843 | + | 0.582482i | \(0.197918\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.97414 | − | 2.55992i | −1.54252 | − | 0.660970i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.204036 | + | 0.761471i | −0.0494859 | + | 0.184684i | −0.986245 | − | 0.165292i | \(-0.947143\pi\) |
0.936759 | + | 0.349976i | \(0.113810\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.09461 | + | 1.89593i | −0.251122 | + | 0.434955i | −0.963835 | − | 0.266500i | \(-0.914133\pi\) |
0.712713 | + | 0.701455i | \(0.247466\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.51725 | + | 6.83885i | −0.767526 | + | 1.49236i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.54529 | − | 1.21791i | 0.947759 | − | 0.253951i | 0.248348 | − | 0.968671i | \(-0.420112\pi\) |
0.699411 | + | 0.714719i | \(0.253446\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.79681 | + | 1.41090i | 0.959361 | + | 0.282180i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.03288 | + | 5.03288i | 0.968579 | + | 0.968579i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.62236i | − | 0.486960i | −0.969906 | − | 0.243480i | \(-0.921711\pi\) | ||
0.969906 | − | 0.243480i | \(-0.0782891\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.0359651 | + | 0.0207644i | −0.00645952 | + | 0.00372940i | −0.503226 | − | 0.864155i | \(-0.667854\pi\) |
0.496767 | + | 0.867884i | \(0.334520\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.76180 | + | 10.3072i | 0.480768 | + | 1.79425i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.06335 | − | 5.54460i | 0.348770 | − | 0.937208i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.0664979 | + | 0.248174i | 0.0109322 | + | 0.0407995i | 0.971176 | − | 0.238362i | \(-0.0766103\pi\) |
−0.960244 | + | 0.279161i | \(0.909944\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.95680 | − | 1.70711i | 0.473466 | − | 0.273356i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 8.98026i | − | 1.40248i | −0.712925 | − | 0.701241i | \(-0.752630\pi\) | ||
0.712925 | − | 0.701241i | \(-0.247370\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.474569 | + | 0.474569i | 0.0723711 | + | 0.0723711i | 0.742366 | − | 0.669995i | \(-0.233704\pi\) |
−0.669995 | + | 0.742366i | \(0.733704\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.57526 | − | 7.53368i | −1.42740 | − | 1.12306i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.18205 | + | 1.65648i | −0.901745 | + | 0.241622i | −0.679766 | − | 0.733429i | \(-0.737919\pi\) |
−0.221980 | + | 0.975051i | \(0.571252\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.37308 | − | 2.89549i | −0.910440 | − | 0.413642i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.14571 | + | 1.98443i | −0.160432 | + | 0.277876i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.04824 | − | 7.64413i | 0.281347 | − | 1.05000i | −0.670120 | − | 0.742252i | \(-0.733758\pi\) |
0.951468 | − | 0.307749i | \(-0.0995758\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.04917 | − | 7.62161i | −0.411150 | − | 1.02770i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.49957 | + | 4.49957i | −0.595982 | + | 0.595982i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.35616 | − | 9.27713i | −0.697312 | − | 1.20778i | −0.969395 | − | 0.245506i | \(-0.921046\pi\) |
0.272083 | − | 0.962274i | \(-0.412287\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.72539 | + | 0.996157i | 0.220914 | + | 0.127545i | 0.606373 | − | 0.795180i | \(-0.292624\pi\) |
−0.385459 | + | 0.922725i | \(0.625957\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.68662 | + | 10.6765i | −1.22040 | + | 1.34512i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.10300 | + | 1.57352i | −0.260846 | + | 0.195172i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.39671 | − | 1.71399i | −0.781482 | − | 0.209398i | −0.154044 | − | 0.988064i | \(-0.549230\pi\) |
−0.627438 | + | 0.778666i | \(0.715897\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.6777 | 1.64660 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.11777 | −0.963402 | −0.481701 | − | 0.876336i | \(-0.659981\pi\) | ||||
−0.481701 | + | 0.876336i | \(0.659981\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.52910 | + | 2.55331i | 1.11530 | + | 0.298843i | 0.768979 | − | 0.639274i | \(-0.220765\pi\) |
0.346318 | + | 0.938117i | \(0.387432\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 12.4062 | + | 7.56992i | 1.43255 | + | 0.874099i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.24884 | + | 2.96647i | −1.05400 | + | 0.338060i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.6145 | + | 6.70563i | 1.30673 | + | 0.754443i | 0.981550 | − | 0.191208i | \(-0.0612405\pi\) |
0.325184 | + | 0.945651i | \(0.394574\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.17114 | + | 3.76053i | 0.241238 | + | 0.417836i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.73033 | − | 9.73033i | 1.06804 | − | 1.06804i | 0.0705331 | − | 0.997509i | \(-0.477530\pi\) |
0.997509 | − | 0.0705331i | \(-0.0224700\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.694291 | − | 1.62028i | 0.0753065 | − | 0.175744i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.97280 | − | 7.36260i | 0.211507 | − | 0.789354i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.715130 | − | 1.23864i | 0.0758036 | − | 0.131296i | −0.825632 | − | 0.564209i | \(-0.809181\pi\) |
0.901435 | + | 0.432914i | \(0.142514\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.68272 | + | 2.61276i | 0.176397 | + | 0.273892i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.116597 | + | 0.0312422i | −0.0120906 | + | 0.00323967i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.02695 | − | 3.84723i | 0.310558 | − | 0.394717i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.16693 | − | 3.16693i | −0.321553 | − | 0.321553i | 0.527810 | − | 0.849363i | \(-0.323013\pi\) |
−0.849363 | + | 0.527810i | \(0.823013\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 20.0030i | 2.01037i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.0622734 | + | 0.0359536i | −0.00619644 | + | 0.00357751i | −0.503095 | − | 0.864231i | \(-0.667805\pi\) |
0.496899 | + | 0.867809i | \(0.334472\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.29116 | + | 16.0148i | 0.422820 | + | 1.57799i | 0.768638 | + | 0.639685i | \(0.220935\pi\) |
−0.345817 | + | 0.938302i | \(0.612398\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.96432 | − | 14.0149i | 0.972418 | − | 1.36771i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.18265 | − | 4.41372i | −0.114331 | − | 0.426690i | 0.884905 | − | 0.465772i | \(-0.154223\pi\) |
−0.999236 | + | 0.0390819i | \(0.987557\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.6773 | + | 9.05131i | −1.50162 | + | 0.866958i | −0.501617 | + | 0.865090i | \(0.667261\pi\) |
−0.999998 | + | 0.00186842i | \(0.999405\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.746804i | 0.0708835i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.52064 | + | 1.52064i | 0.143049 | + | 0.143049i | 0.775005 | − | 0.631955i | \(-0.217747\pi\) |
−0.631955 | + | 0.775005i | \(0.717747\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.4480 | + | 1.24674i | −0.974281 | + | 0.116259i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.18205 | − | 1.65648i | 0.571531 | − | 0.153141i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.85480 | − | 0.953932i | −0.170030 | − | 0.0874468i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.23864 | + | 2.14539i | −0.112604 | + | 0.195035i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.75585 | − | 25.2132i | 0.609155 | − | 2.27340i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.1667 | − | 4.65160i | −0.909341 | − | 0.416051i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.2527 | − | 13.2527i | 1.17599 | − | 1.17599i | 0.195234 | − | 0.980757i | \(-0.437453\pi\) |
0.980757 | − | 0.195234i | \(-0.0625467\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.975392 | + | 1.68943i | 0.0858785 | + | 0.148746i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.2929 | − | 7.09731i | −1.07404 | − | 0.620095i | −0.144755 | − | 0.989468i | \(-0.546239\pi\) |
−0.929281 | + | 0.369372i | \(0.879573\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.28970 | − | 3.89197i | −0.371964 | − | 0.337477i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9.53476 | − | 12.7431i | −0.820621 | − | 1.09675i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.3201 | + | 4.90887i | 1.56519 | + | 0.419393i | 0.934303 | − | 0.356479i | \(-0.116023\pi\) |
0.630891 | + | 0.775871i | \(0.282689\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.23706 | −0.698658 | −0.349329 | − | 0.937000i | \(-0.613591\pi\) | ||||
−0.349329 | + | 0.937000i | \(0.613591\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.6030 | −1.56666 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.16524 | + | 1.11607i | 0.348315 | + | 0.0933308i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.835856 | + | 5.80390i | −0.0694141 | + | 0.481988i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −15.7149 | − | 12.9239i | −1.29614 | − | 1.06595i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.19317 | + | 2.42093i | 0.343518 | + | 0.198330i | 0.661826 | − | 0.749657i | \(-0.269782\pi\) |
−0.318309 | + | 0.947987i | \(0.603115\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.02292 | + | 8.69995i | 0.408759 | + | 0.707992i | 0.994751 | − | 0.102325i | \(-0.0326282\pi\) |
−0.585992 | + | 0.810317i | \(0.699295\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.03730 | + | 3.03730i | −0.245551 | + | 0.245551i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.0862176 | − | 0.0344930i | 0.00692516 | − | 0.00277054i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.33762 | − | 23.6523i | 0.505797 | − | 1.88766i | 0.0474774 | − | 0.998872i | \(-0.484882\pi\) |
0.458320 | − | 0.888788i | \(-0.348452\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.5014 | − | 19.9209i | 0.912117 | − | 1.57983i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.604505 | + | 12.4353i | 0.0476417 | + | 0.980035i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.2171 | + | 5.68510i | −1.66185 | + | 0.445291i | −0.962895 | − | 0.269875i | \(-0.913018\pi\) |
−0.698954 | + | 0.715166i | \(0.746351\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.82718 | − | 23.6925i | −0.220096 | − | 1.84446i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.14616 | + | 3.14616i | 0.243457 | + | 0.243457i | 0.818279 | − | 0.574821i | \(-0.194928\pi\) |
−0.574821 | + | 0.818279i | \(0.694928\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.6203i | 0.893868i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.3303 | + | 5.96423i | −0.789981 | + | 0.456096i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.35273 | − | 5.04844i | −0.102846 | − | 0.383826i | 0.895246 | − | 0.445572i | \(-0.147000\pi\) |
−0.998092 | + | 0.0617463i | \(0.980333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.33397 | + | 11.6138i | −0.478803 | + | 0.877922i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.05888 | − | 30.0761i | −0.605742 | − | 2.26066i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.8847 | + | 6.28428i | −0.813560 | + | 0.469709i | −0.848191 | − | 0.529691i | \(-0.822308\pi\) |
0.0346308 | + | 0.999400i | \(0.488974\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.6742i | 0.867740i | 0.900976 | + | 0.433870i | \(0.142852\pi\) | ||||
−0.900976 | + | 0.433870i | \(0.857148\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.09485 | + | 4.09485i | 0.302700 | + | 0.302700i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.0680721 | − | 0.570462i | −0.00500476 | − | 0.0419412i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.79547 | + | 0.749044i | −0.204425 | + | 0.0547755i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −15.8320 | + | 10.1964i | −1.15161 | + | 0.741680i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.75170 | − | 13.4263i | 0.560894 | − | 0.971496i | −0.436525 | − | 0.899692i | \(-0.643791\pi\) |
0.997419 | − | 0.0718040i | \(-0.0228756\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.32883 | − | 8.69132i | 0.167633 | − | 0.625615i | −0.830057 | − | 0.557679i | \(-0.811692\pi\) |
0.997690 | − | 0.0679359i | \(-0.0216413\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.08821 | + | 2.83577i | −0.507597 | + | 0.203074i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.1951 | − | 12.1951i | 0.868865 | − | 0.868865i | −0.123482 | − | 0.992347i | \(-0.539406\pi\) |
0.992347 | + | 0.123482i | \(0.0394061\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.36557 | − | 7.56140i | −0.309467 | − | 0.536013i | 0.668779 | − | 0.743462i | \(-0.266817\pi\) |
−0.978246 | + | 0.207448i | \(0.933484\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.6701 | − | 9.62450i | −1.17582 | − | 0.678860i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.78099 | + | 1.46820i | 0.475932 | + | 0.103047i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.86239 | + | 19.8754i | −0.199918 | + | 1.38816i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 24.7660 | + | 6.63602i | 1.72135 | + | 0.461235i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.03696 | −0.555928 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.1745 | 0.769288 | 0.384644 | − | 0.923065i | \(-0.374324\pi\) | ||||
0.384644 | + | 0.923065i | \(0.374324\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −22.7916 | − | 6.10700i | −1.56166 | − | 0.418445i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.899067 | − | 1.20160i | −0.0613158 | − | 0.0819482i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.0335574 | − | 0.104625i | −0.00227803 | − | 0.00710242i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 24.8333 | + | 14.3375i | 1.67808 | + | 0.968838i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.462994 | + | 0.801929i | 0.0311443 | + | 0.0539436i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.746804 | + | 0.746804i | −0.0500097 | + | 0.0500097i | −0.731669 | − | 0.681660i | \(-0.761258\pi\) |
0.681660 | + | 0.731669i | \(0.261258\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 18.7910 | + | 19.7258i | 1.25273 | + | 1.31506i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.807609 | − | 3.01404i | 0.0536029 | − | 0.200049i | −0.933932 | − | 0.357452i | \(-0.883646\pi\) |
0.987534 | + | 0.157403i | \(0.0503122\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.21091 | − | 7.29350i | 0.278264 | − | 0.481968i | −0.692689 | − | 0.721236i | \(-0.743574\pi\) |
0.970954 | + | 0.239268i | \(0.0769075\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −28.1989 | + | 1.37081i | −1.85535 | + | 0.0901928i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.0201 | − | 5.90027i | 1.44259 | − | 0.386540i | 0.549148 | − | 0.835725i | \(-0.314952\pi\) |
0.893439 | + | 0.449186i | \(0.148286\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.2103 | − | 1.69569i | 0.926979 | − | 0.110615i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 27.5645 | + | 27.5645i | 1.79051 | + | 1.79051i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.9971i | 1.55224i | 0.630585 | + | 0.776120i | \(0.282815\pi\) | ||||
−0.630585 | + | 0.776120i | \(0.717185\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.4666 | + | 12.3937i | −1.38278 | + | 0.798350i | −0.992488 | − | 0.122340i | \(-0.960960\pi\) |
−0.390295 | + | 0.920690i | \(0.627627\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.25979 | − | 8.43364i | −0.144965 | − | 0.541018i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 13.1822 | + | 8.43977i | 0.842179 | + | 0.539197i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.665553 | + | 2.48388i | 0.0423481 | + | 0.158045i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 34.6392 | − | 19.9990i | 2.19517 | − | 1.26738i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.1158i | 0.701623i | 0.936446 | + | 0.350811i | \(0.114094\pi\) | ||||
−0.936446 | + | 0.350811i | \(0.885906\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.2153 | + | 12.2153i | 0.767970 | + | 0.767970i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.16825 | − | 4.02682i | 0.198403 | − | 0.252169i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −24.4314 | + | 6.54637i | −1.52399 | + | 0.408351i | −0.921052 | − | 0.389439i | \(-0.872669\pi\) |
−0.602935 | + | 0.797790i | \(0.706002\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.678966 | + | 0.0330060i | −0.0421889 | + | 0.00205090i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.14424 | − | 12.3742i | 0.442217 | − | 0.765943i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.93659 | + | 10.9595i | −0.181078 | + | 0.675792i | 0.814358 | + | 0.580363i | \(0.197089\pi\) |
−0.995436 | + | 0.0954297i | \(0.969577\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.96973 | + | 16.2654i | −0.428147 | + | 0.999174i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.93964 | − | 2.93964i | 0.179903 | − | 0.179903i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.03346 | − | 6.98616i | −0.245924 | − | 0.425954i | 0.716467 | − | 0.697621i | \(-0.245758\pi\) |
−0.962391 | + | 0.271668i | \(0.912425\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.27419 | − | 4.19976i | −0.441876 | − | 0.255117i | 0.262517 | − | 0.964927i | \(-0.415447\pi\) |
−0.704393 | + | 0.709810i | \(0.748781\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.75885 | + | 8.60155i | 0.166974 | + | 0.520590i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.31920 | + | 17.8403i | 0.260458 | + | 1.07581i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.48646 | − | 1.47009i | −0.329650 | − | 0.0883293i | 0.0901983 | − | 0.995924i | \(-0.471250\pi\) |
−0.419848 | + | 0.907594i | \(0.637917\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.226279 | −0.0135470 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.27627 | 0.434066 | 0.217033 | − | 0.976164i | \(-0.430362\pi\) | ||||
0.217033 | + | 0.976164i | \(0.430362\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.44729 | + | 1.99550i | 0.442696 | + | 0.118620i | 0.473280 | − | 0.880912i | \(-0.343070\pi\) |
−0.0305840 | + | 0.999532i | \(0.509737\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 11.3928 | − | 8.52440i | 0.674851 | − | 0.504942i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 23.2215 | + | 5.02784i | 1.37072 | + | 0.296784i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.1842 | + | 8.18927i | 0.834366 | + | 0.481721i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.50906 | − | 11.2740i | −0.381568 | − | 0.660895i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.35198 | − | 3.35198i | 0.195824 | − | 0.195824i | −0.602383 | − | 0.798207i | \(-0.705782\pi\) |
0.798207 | + | 0.602383i | \(0.205782\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.89741 | + | 22.2397i | 0.518027 | + | 1.29485i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.76284 | + | 25.2393i | −0.392420 | + | 1.46453i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.76365 | − | 4.78679i | 0.159826 | − | 0.276827i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.49286 | + | 0.961456i | −0.0860468 | + | 0.0554174i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.201888 | + | 0.0540958i | −0.0115982 | + | 0.00310772i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.50118 | − | 2.75468i | −0.200477 | − | 0.157733i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.06546 | + | 1.06546i | 0.0608089 | + | 0.0608089i | 0.736857 | − | 0.676048i | \(-0.236309\pi\) |
−0.676048 | + | 0.736857i | \(0.736309\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 48.1918i | 2.74154i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.9584 | + | 6.90417i | −0.678097 | + | 0.391500i | −0.799138 | − | 0.601148i | \(-0.794710\pi\) |
0.121040 | + | 0.992648i | \(0.461377\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.04266 | + | 22.5515i | 0.341551 | + | 1.27469i | 0.896590 | + | 0.442863i | \(0.146037\pi\) |
−0.555038 | + | 0.831825i | \(0.687296\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 24.8418 | − | 20.5421i | 1.39968 | − | 1.15742i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.41352 | + | 12.7394i | 0.191722 | + | 0.715518i | 0.993091 | + | 0.117347i | \(0.0374390\pi\) |
−0.801369 | + | 0.598171i | \(0.795894\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.33728 | − | 4.81353i | 0.466798 | − | 0.269506i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 13.2818i | − | 0.741316i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.22035 | − | 1.22035i | −0.0679023 | − | 0.0679023i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.15599 | − | 2.81226i | 0.286003 | − | 0.155996i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −50.8253 | + | 13.6186i | −2.81065 | + | 0.753111i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.822187 | − | 16.9132i | −0.0453286 | − | 0.932454i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.54799 | + | 16.5376i | −0.524805 | + | 0.908989i | 0.474778 | + | 0.880106i | \(0.342528\pi\) |
−0.999583 | + | 0.0288830i | \(0.990805\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.362328 | + | 1.35222i | −0.0198554 | + | 0.0741015i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13.6111 | + | 5.83237i | 0.743653 | + | 0.318656i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.488226 | − | 0.488226i | 0.0265953 | − | 0.0265953i | −0.693684 | − | 0.720279i | \(-0.744014\pi\) |
0.720279 | + | 0.693684i | \(0.244014\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.12540 | + | 5.41335i | 0.169748 | + | 0.294013i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.132033 | − | 0.0762292i | −0.00714998 | − | 0.00412804i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.0554 | − | 14.8586i | 0.596936 | − | 0.802289i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −30.2720 | − | 4.35966i | −1.62979 | − | 0.234716i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.68015 | + | 0.986094i | 0.197561 | + | 0.0529363i | 0.356243 | − | 0.934393i | \(-0.384058\pi\) |
−0.158682 | + | 0.987330i | \(0.550724\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.91303 | −0.423575 | −0.211787 | − | 0.977316i | \(-0.567928\pi\) | ||||
−0.211787 | + | 0.977316i | \(0.567928\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.36041 | 0.446246 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.9004 | − | 6.67203i | −1.32531 | − | 0.355116i | −0.474347 | − | 0.880338i | \(-0.657316\pi\) |
−0.850965 | + | 0.525222i | \(0.823982\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.9665 | + | 2.58747i | 0.953564 | + | 0.137329i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.48995 | − | 4.07365i | −0.237633 | − | 0.215601i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.99497 | − | 5.19325i | −0.474737 | − | 0.274089i | 0.243484 | − | 0.969905i | \(-0.421710\pi\) |
−0.718220 | + | 0.695816i | \(0.755043\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.10364 | + | 12.3039i | 0.373876 | + | 0.647572i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.09161 | + | 5.09161i | −0.267240 | + | 0.267240i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −20.2763 | − | 8.68840i | −1.06131 | − | 0.454772i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.24811 | − | 8.39004i | 0.117350 | − | 0.437957i | −0.882102 | − | 0.471059i | \(-0.843872\pi\) |
0.999452 | + | 0.0331020i | \(0.0105386\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 24.4654 | − | 42.3753i | 1.27362 | − | 2.20597i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.6197 | + | 9.57617i | 0.966686 | + | 0.497170i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.8560 | + | 3.44476i | −0.665660 | + | 0.178363i | −0.575799 | − | 0.817591i | \(-0.695309\pi\) |
−0.0898611 | + | 0.995954i | \(0.528642\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −25.0450 | − | 20.7084i | −1.29332 | − | 1.06938i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.17808 | − | 2.17808i | −0.112177 | − | 0.112177i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 25.3453i | − | 1.30190i | −0.759121 | − | 0.650949i | \(-0.774371\pi\) | ||
0.759121 | − | 0.650949i | \(-0.225629\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 47.1788 | − | 27.2387i | 2.41704 | − | 1.39548i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.76251 | − | 17.7739i | −0.243353 | − | 0.908205i | −0.974204 | − | 0.225668i | \(-0.927543\pi\) |
0.730851 | − | 0.682537i | \(-0.239123\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 21.4154 | − | 3.61749i | 1.09143 | − | 0.184364i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.946464 | + | 3.53225i | 0.0481114 | + | 0.179554i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.3621 | + | 11.1787i | −0.981699 | + | 0.566784i | −0.902783 | − | 0.430097i | \(-0.858479\pi\) |
−0.0789164 | + | 0.996881i | \(0.525146\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.70961i | 0.187603i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −29.1745 | − | 29.1745i | −1.47166 | − | 1.47166i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −23.5682 | − | 18.5432i | −1.18585 | − | 0.933008i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.2461 | + | 4.08518i | −0.765181 | + | 0.205029i | −0.620241 | − | 0.784411i | \(-0.712965\pi\) |
−0.144939 | + | 0.989441i | \(0.546299\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.11594 | − | 14.1543i | −0.456368 | − | 0.708603i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.98528 | + | 12.0989i | −0.348828 | + | 0.604188i | −0.986042 | − | 0.166499i | \(-0.946754\pi\) |
0.637213 | + | 0.770687i | \(0.280087\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0126253 | + | 0.0471183i | −0.000628911 | + | 0.00234713i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.60661 | − | 9.01496i | −0.179214 | − | 0.447957i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.666957 | + | 0.666957i | −0.0330598 | + | 0.0330598i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.156681 | − | 0.271379i | −0.00774737 | − | 0.0134188i | 0.862126 | − | 0.506694i | \(-0.169133\pi\) |
−0.869873 | + | 0.493276i | \(0.835799\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 47.7431 | + | 27.5645i | 2.35499 | + | 1.35966i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 26.9879 | − | 8.65608i | 1.32799 | − | 0.425938i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.6370 | + | 18.4340i | −1.20938 | + | 0.904891i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −23.1266 | − | 6.19675i | −1.13251 | − | 0.303456i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −31.6254 | −1.54500 | −0.772501 | − | 0.635014i | \(-0.780994\pi\) | ||||
−0.772501 | + | 0.635014i | \(0.780994\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.2137 | 1.18011 | 0.590053 | − | 0.807365i | \(-0.299107\pi\) | ||||
0.590053 | + | 0.807365i | \(0.299107\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −33.6842 | − | 9.02565i | −1.63778 | − | 0.438842i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.05308 | + | 3.36476i | −0.0995890 | + | 0.163215i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.54190 | + | 3.90386i | −0.171405 | + | 0.188921i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.8548 | + | 6.26703i | 0.524075 | + | 0.302575i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.779037 | + | 1.34933i | 0.0375249 | + | 0.0649950i | 0.884178 | − | 0.467150i | \(-0.154719\pi\) |
−0.846653 | + | 0.532145i | \(0.821386\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.28166 | − | 6.28166i | 0.301877 | − | 0.301877i | −0.539871 | − | 0.841748i | \(-0.681527\pi\) |
0.841748 | + | 0.539871i | \(0.181527\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.71305 | + | 15.6663i | −0.321866 | + | 0.751144i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.66628 | + | 9.95068i | −0.127545 | + | 0.476006i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.9571 | + | 20.7103i | −0.570681 | + | 0.988449i | 0.425815 | + | 0.904810i | \(0.359988\pi\) |
−0.996496 | + | 0.0836389i | \(0.973346\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −22.1844 | − | 31.0255i | −1.05640 | − | 1.47741i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.4238 | − | 3.32895i | 0.590272 | − | 0.158163i | 0.0486946 | − | 0.998814i | \(-0.484494\pi\) |
0.541578 | + | 0.840651i | \(0.317827\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.97756 | + | 2.51346i | −0.0937451 | + | 0.119149i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.95157 | + | 9.95157i | 0.470693 | + | 0.470693i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 17.8932i | − | 0.844435i | −0.906495 | − | 0.422217i | \(-0.861252\pi\) | ||
0.906495 | − | 0.422217i | \(-0.138748\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.5510 | − | 16.4839i | 1.34441 | − | 0.776197i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.55749 | + | 28.2049i | 0.355082 | + | 1.32518i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.89145 | − | 6.31900i | −0.135553 | − | 0.296239i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.85449 | + | 33.0454i | 0.414196 | + | 1.54580i | 0.786442 | + | 0.617665i | \(0.211921\pi\) |
−0.372246 | + | 0.928134i | \(0.621412\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.85928 | + | 2.80551i | −0.226812 | + | 0.130950i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.3471i | 1.08738i | 0.839286 | + | 0.543690i | \(0.182973\pi\) | ||||
−0.839286 | + | 0.543690i | \(0.817027\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.98510 | − | 3.98510i | −0.185203 | − | 0.185203i | 0.608415 | − | 0.793619i | \(-0.291805\pi\) |
−0.793619 | + | 0.608415i | \(0.791805\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.268016 | − | 0.0319818i | 0.0124289 | − | 0.00148312i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.71932 | − | 1.26454i | 0.218384 | − | 0.0585159i | −0.147968 | − | 0.988992i | \(-0.547273\pi\) |
0.366352 | + | 0.930476i | \(0.380607\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.01347 | − | 15.5812i | 0.370028 | − | 0.719473i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 35.5873 | − | 61.6390i | 1.63978 | − | 2.84017i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.637693 | + | 2.37990i | −0.0293212 | + | 0.109428i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.92561 | + | 7.55000i | −0.363652 | + | 0.346418i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 30.4904 | − | 30.4904i | 1.39606 | − | 1.39606i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.55572 | + | 14.8189i | 0.390921 | + | 0.677094i | 0.992571 | − | 0.121665i | \(-0.0388234\pi\) |
−0.601651 | + | 0.798759i | \(0.705490\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.261359 | + | 0.150896i | 0.0119170 | + | 0.00688026i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.65783 | + | 35.3683i | −0.348443 | + | 1.60931i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.99972 | + | 8.01859i | 0.272433 | + | 0.364105i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.125860 | + | 0.0337240i | 0.00570325 | + | 0.00152818i | 0.261670 | − | 0.965158i | \(-0.415727\pi\) |
−0.255966 | + | 0.966686i | \(0.582394\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −63.8465 | −2.88724 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.9895 | −1.21802 | −0.609011 | − | 0.793162i | \(-0.708433\pi\) | ||||
−0.609011 | + | 0.793162i | \(0.708433\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.99685 | + | 0.535055i | 0.0899337 | + | 0.0240977i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.37579 | − | 44.2713i | 0.286570 | − | 1.98985i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.54495 | − | 20.9912i | 0.203869 | − | 0.941584i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.0833977 | + | 0.0481497i | 0.00373339 | + | 0.00215548i | 0.501866 | − | 0.864946i | \(-0.332647\pi\) |
−0.498132 | + | 0.867101i | \(0.665981\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.46638 | + | 11.2001i | 0.288897 | + | 0.500384i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.6334 | − | 13.6334i | 0.607883 | − | 0.607883i | −0.334509 | − | 0.942392i | \(-0.608571\pi\) |
0.942392 | + | 0.334509i | \(0.108571\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.149286 | − | 0.0597245i | 0.00664312 | − | 0.00265771i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.74194 | + | 32.6254i | −0.388243 | + | 1.44894i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.16366 | + | 10.6758i | −0.273199 | + | 0.473195i | −0.969679 | − | 0.244381i | \(-0.921415\pi\) |
0.696480 | + | 0.717576i | \(0.254749\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.9376 | + | 23.2111i | −0.528087 | + | 1.02680i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −15.0510 | + | 4.03291i | −0.664520 | + | 0.178057i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.39274 | − | 36.8123i | −0.193567 | − | 1.62214i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.6140 | − | 16.6140i | −0.730684 | − | 0.730684i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 15.1918i | − | 0.666845i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.1415 | − | 8.16461i | 0.619551 | − | 0.357698i | −0.157143 | − | 0.987576i | \(-0.550228\pi\) |
0.776694 | + | 0.629878i | \(0.216895\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.09270 | + | 26.4703i | 0.310142 | + | 1.15747i | 0.928428 | + | 0.371512i | \(0.121161\pi\) |
−0.618286 | + | 0.785953i | \(0.712173\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −26.5205 | + | 27.8422i | −1.15745 | + | 1.21513i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.00847337 | − | 0.0316231i | −0.000369106 | − | 0.00137752i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.742186 | + | 0.428501i | −0.0322689 | + | 0.0186305i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 58.3682i | − | 2.53297i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.45881 | − | 7.45881i | −0.323077 | − | 0.323077i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.21065 | + | 10.1456i | 0.0523409 | + | 0.438630i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −35.2878 | + | 9.45533i | −1.52278 | + | 0.408028i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.49258 | − | 25.5768i | −0.107363 | − | 1.10167i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.5773 | − | 35.6410i | 0.884689 | − | 1.53233i | 0.0386200 | − | 0.999254i | \(-0.487704\pi\) |
0.846069 | − | 0.533073i | \(-0.178963\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.78254 | + | 32.7769i | −0.376895 | + | 1.40659i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 37.5826 | − | 15.0356i | 1.60986 | − | 0.644056i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.06541 | + | 8.06541i | −0.344852 | + | 0.344852i | −0.858188 | − | 0.513336i | \(-0.828410\pi\) |
0.513336 | + | 0.858188i | \(0.328410\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.42777 | + | 9.40117i | 0.231651 | + | 0.401232i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.97180 | + | 2.87047i | 0.211806 | + | 0.122286i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −23.8423 | + | 26.2788i | −1.01388 | + | 1.11749i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.238038 | − | 1.65285i | 0.0101041 | − | 0.0701597i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.7826 | + | 6.64049i | 1.05007 | + | 0.281367i | 0.742282 | − | 0.670087i | \(-0.233743\pi\) |
0.307792 | + | 0.951454i | \(0.400410\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.788333 | 0.0333429 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.41213 | −0.355160 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.3749 | + | 3.31584i | 0.521539 | + | 0.139746i | 0.509978 | − | 0.860187i | \(-0.329653\pi\) |
0.0115606 | + | 0.999933i | \(0.496320\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.88083 | − | 3.85022i | −0.121198 | − | 0.161980i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −10.9397 | + | 3.50878i | −0.459423 | + | 0.147355i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.8291 | − | 17.2218i | −1.25050 | − | 0.721977i | −0.279292 | − | 0.960206i | \(-0.590100\pi\) |
−0.971209 | + | 0.238229i | \(0.923433\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.11985 | − | 7.13579i | −0.172410 | − | 0.298623i | 0.766852 | − | 0.641824i | \(-0.221822\pi\) |
−0.939262 | + | 0.343201i | \(0.888489\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 31.8645 | − | 31.8645i | 1.33116 | − | 1.33116i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 23.5212 | + | 0.570889i | 0.980904 | + | 0.0238077i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.910086 | + | 3.39649i | −0.0378874 | + | 0.141398i | −0.982279 | − | 0.187426i | \(-0.939985\pi\) |
0.944391 | + | 0.328824i | \(0.106652\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.0770 | − | 22.6500i | 0.543460 | − | 0.941301i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19.7132 | + | 30.6088i | 0.817843 | + | 1.26987i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28.0627 | − | 7.51937i | 1.16224 | − | 0.311421i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −14.2103 | + | 1.69569i | −0.587524 | + | 0.0701081i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.37485 | + | 5.37485i | 0.221844 | + | 0.221844i | 0.809275 | − | 0.587431i | \(-0.199861\pi\) |
−0.587431 | + | 0.809275i | \(0.699861\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 0.0909162i | − | 0.00374613i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 43.4136 | − | 25.0649i | 1.78580 | − | 1.03103i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.190155 | + | 0.709668i | 0.00780872 | + | 0.0291426i | 0.969720 | − | 0.244218i | \(-0.0785314\pi\) |
−0.961912 | + | 0.273361i | \(0.911865\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.80106 | + | 2.70248i | 0.155828 | + | 0.110791i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.56845 | − | 24.5138i | −0.268829 | − | 1.00328i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.23778 | + | 4.17873i | −0.295727 | + | 0.170738i | −0.640522 | − | 0.767940i | \(-0.721282\pi\) |
0.344794 | + | 0.938678i | \(0.387949\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 39.9236i | − | 1.62852i | −0.580501 | − | 0.814259i | \(-0.697143\pi\) | ||
0.580501 | − | 0.814259i | \(-0.302857\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −25.5147 | − | 25.5147i | −1.03904 | − | 1.03904i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.42523 | − | 4.35344i | 0.139255 | − | 0.176993i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −33.2758 | + | 8.91623i | −1.35062 | + | 0.361899i | −0.860365 | − | 0.509678i | \(-0.829765\pi\) |
−0.490259 | + | 0.871577i | \(0.663098\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 17.9339 | + | 9.22349i | 0.726720 | + | 0.373755i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.75885 | + | 6.51051i | −0.152067 | + | 0.263387i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.46832 | + | 31.6042i | −0.342032 | + | 1.27648i | 0.554009 | + | 0.832510i | \(0.313097\pi\) |
−0.896041 | + | 0.443971i | \(0.853569\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −22.9888 | + | 53.6493i | −0.926997 | + | 2.16335i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.5005 | + | 15.5005i | −0.624025 | + | 0.624025i | −0.946558 | − | 0.322533i | \(-0.895466\pi\) |
0.322533 | + | 0.946558i | \(0.395466\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.31138 | − | 7.46752i | −0.173289 | − | 0.300145i | 0.766279 | − | 0.642508i | \(-0.222106\pi\) |
−0.939568 | + | 0.342363i | \(0.888773\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 29.0055 | + | 16.7463i | 1.16395 | + | 0.672008i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.80254 | + | 2.54269i | 0.112281 | + | 0.101871i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.0187 | + | 13.5356i | 0.840749 | + | 0.541425i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −22.5648 | − | 6.04621i | −0.901150 | − | 0.241462i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.202545 | −0.00807600 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.13675 | 0.164682 | 0.0823408 | − | 0.996604i | \(-0.473760\pi\) | ||||
0.0823408 | + | 0.996604i | \(0.473760\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 31.3739 | + | 8.40662i | 1.24700 | + | 0.334133i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −33.5556 | + | 25.1072i | −1.33161 | + | 0.996349i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.69827 | + | 2.88840i | −0.305017 | + | 0.114443i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −38.3055 | − | 22.1157i | −1.51534 | − | 0.874882i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.42807 | − | 9.40169i | −0.214396 | − | 0.371345i | 0.738690 | − | 0.674046i | \(-0.235445\pi\) |
−0.953086 | + | 0.302701i | \(0.902112\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.06230 | − | 8.06230i | 0.317946 | − | 0.317946i | −0.530032 | − | 0.847978i | \(-0.677820\pi\) |
0.847978 | + | 0.530032i | \(0.177820\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.62028 | − | 4.05000i | −0.0637984 | − | 0.159469i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.69865 | − | 10.0715i | 0.106095 | − | 0.395951i | −0.892372 | − | 0.451300i | \(-0.850960\pi\) |
0.998467 | + | 0.0553490i | \(0.0176271\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.6632 | − | 34.0577i | 0.771848 | − | 1.33688i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.0155070 | − | 0.318994i | −0.000607766 | − | 0.0125023i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.41946 | − | 1.72009i | 0.251213 | − | 0.0673123i | −0.131015 | − | 0.991380i | \(-0.541824\pi\) |
0.382228 | + | 0.924068i | \(0.375157\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.9449 | + | 19.6263i | 0.974677 | + | 0.766862i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 38.0090 | + | 38.0090i | 1.48287 | + | 1.48287i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 22.0345i | − | 0.858343i | −0.903223 | − | 0.429172i | \(-0.858806\pi\) | ||
0.903223 | − | 0.429172i | \(-0.141194\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.94278 | + | 5.74047i | −0.386729 | + | 0.223278i | −0.680742 | − | 0.732523i | \(-0.738343\pi\) |
0.294013 | + | 0.955802i | \(0.405009\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.696621 | + | 2.59983i | 0.0270545 | + | 0.100969i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.25358 | + | 9.98115i | 0.320060 | + | 0.387053i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.19379 | − | 11.9194i | −0.123664 | − | 0.461521i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.65857 | + | 1.53492i | −0.102786 | + | 0.0593436i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.31407i | 0.282356i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.2073 | − | 15.2073i | −0.586198 | − | 0.586198i | 0.350402 | − | 0.936600i | \(-0.386045\pi\) |
−0.936600 | + | 0.350402i | \(0.886045\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 17.0409 | + | 31.2427i | 0.655903 | + | 1.20253i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.54296 | + | 1.48523i | −0.213033 | + | 0.0570821i | −0.363757 | − | 0.931494i | \(-0.618506\pi\) |
0.150724 | + | 0.988576i | \(0.451840\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.96224 | − | 6.41606i | 0.382316 | − | 0.246226i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.53492 | − | 7.85472i | 0.173779 | − | 0.300993i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.02900 | + | 18.7685i | −0.192430 | + | 0.718157i | 0.800488 | + | 0.599349i | \(0.204574\pi\) |
−0.992917 | + | 0.118808i | \(0.962093\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −38.9821 | − | 16.7039i | −1.48943 | − | 0.638222i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.3095 | − | 17.3095i | 0.660400 | − | 0.660400i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.64782 | − | 8.05027i | −0.177068 | − | 0.306691i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.0914 | − | 11.0224i | −0.726270 | − | 0.419312i | 0.0907861 | − | 0.995870i | \(-0.471062\pi\) |
−0.817056 | + | 0.576558i | \(0.804395\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −51.7244 | − | 11.1992i | −1.96485 | − | 0.425422i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 18.2305 | + | 2.62550i | 0.691524 | + | 0.0995908i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.83821 | + | 1.83229i | 0.259016 | + | 0.0694031i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 66.2630 | 2.50630 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.0270 | −0.680870 | −0.340435 | − | 0.940268i | \(-0.610574\pi\) | ||||
−0.340435 | + | 0.940268i | \(0.610574\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.543308 | − | 0.145579i | −0.0204913 | − | 0.00549062i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 41.1729 | + | 5.92957i | 1.55066 | + | 0.223321i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.0581046 | − | 0.181158i | −0.00218525 | − | 0.00681316i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.0614 | − | 21.3974i | −1.39187 | − | 0.803597i | −0.398349 | − | 0.917234i | \(-0.630417\pi\) |
−0.993522 | + | 0.113637i | \(0.963750\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 36.5370 | + | 63.2840i | 1.37025 | + | 2.37334i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.138183 | + | 0.138183i | −0.00517498 | + | 0.00517498i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.86292 | − | 3.79777i | −0.331454 | − | 0.142029i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18.0530 | + | 67.3747i | −0.674202 | + | 2.51615i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.72691 | − | 4.72315i | 0.101697 | − | 0.176144i | −0.810687 | − | 0.585480i | \(-0.800906\pi\) |
0.912384 | + | 0.409336i | \(0.134240\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −43.8142 | + | 2.12990i | −1.63172 | + | 0.0793217i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −69.5938 | + | 18.6476i | −2.58822 | + | 0.693512i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.69989 | − | 12.5790i | 0.137411 | − | 0.467171i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.6781 | − | 16.6781i | −0.618555 | − | 0.618555i | 0.326606 | − | 0.945161i | \(-0.394095\pi\) |
−0.945161 | + | 0.326606i | \(0.894095\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 38.4054i | − | 1.42242i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.458200 | + | 0.264542i | −0.0169471 | + | 0.00978443i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.79960 | − | 32.8405i | −0.325021 | − | 1.21299i | −0.914291 | − | 0.405057i | \(-0.867252\pi\) |
0.589271 | − | 0.807936i | \(-0.299415\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 30.6614 | + | 33.6127i | 1.13096 | + | 1.23982i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.29231 | − | 23.4832i | −0.231780 | − | 0.865016i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.0733 | + | 14.4761i | −0.922335 | + | 0.532510i | −0.884379 | − | 0.466769i | \(-0.845418\pi\) |
−0.0379557 | + | 0.999279i | \(0.512085\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.47449i | 0.274582i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.0351 | − | 34.0351i | −1.24863 | − | 1.24863i | −0.956327 | − | 0.292300i | \(-0.905579\pi\) |
−0.292300 | − | 0.956327i | \(-0.594421\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.50881 | − | 6.69461i | −0.311739 | − | 0.245272i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 72.4235 | − | 19.4058i | 2.64984 | − | 0.710022i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.0753 | − | 0.587006i | 0.441221 | − | 0.0214487i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.30569 | + | 16.1179i | −0.339569 | + | 0.588151i | −0.984352 | − | 0.176215i | \(-0.943615\pi\) |
0.644782 | + | 0.764366i | \(0.276948\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.36242 | + | 31.2090i | −0.304743 | + | 1.13732i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.34385 | − | 20.8560i | −0.303664 | − | 0.759029i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.7422 | − | 29.7422i | 1.08100 | − | 1.08100i | 0.0845825 | − | 0.996416i | \(-0.473044\pi\) |
0.996416 | − | 0.0845825i | \(-0.0269557\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 25.1064 | + | 43.4856i | 0.911305 | + | 1.57843i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.6474 | + | 10.1887i | 0.639718 | + | 0.369341i | 0.784506 | − | 0.620122i | \(-0.212917\pi\) |
−0.144788 | + | 0.989463i | \(0.546250\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.6278 | − | 45.6066i | −0.529563 | − | 1.65107i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.69038 | − | 5.75415i | 0.278046 | − | 0.208042i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.1541 | − | 3.25668i | −0.438859 | − | 0.117592i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.9728 | 1.47752 | 0.738759 | − | 0.673970i | \(-0.235412\pi\) | ||||
0.738759 | + | 0.673970i | \(0.235412\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −73.5189 | −2.64772 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.8577 | + | 6.39265i | 0.858101 | + | 0.229928i | 0.660936 | − | 0.750443i | \(-0.270160\pi\) |
0.197166 | + | 0.980370i | \(0.436826\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.201814 | + | 0.0488599i | −0.00724938 | + | 0.00175510i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.93111 | − | 0.418118i | −0.0692783 | − | 0.0149999i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.0259 | + | 9.82991i | 0.610017 | + | 0.352193i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.9007 | − | 25.8088i | −0.533190 | − | 0.923513i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 13.1980 | − | 13.1980i | 0.471659 | − | 0.471659i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.5656 | + | 50.3280i | −0.769710 | + | 1.79628i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.12442 | + | 7.92843i | −0.0757273 | + | 0.282618i | −0.993397 | − | 0.114725i | \(-0.963401\pi\) |
0.917670 | + | 0.397343i | \(0.130068\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16.4897 | + | 28.5610i | −0.587048 | + | 1.01680i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.78348 | + | 3.08075i | −0.170081 | + | 0.109539i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.26046 | − | 0.605689i | 0.0802713 | − | 0.0215086i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −31.8048 | + | 40.4237i | −1.12800 | + | 1.43368i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.7928 | + | 11.7928i | 0.417722 | + | 0.417722i | 0.884418 | − | 0.466696i | \(-0.154556\pi\) |
−0.466696 | + | 0.884418i | \(0.654556\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 5.04544i | − | 0.178495i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.74899 | − | 3.89653i | 0.238464 | − | 0.137677i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.37358 | + | 34.9827i | 0.330786 | + | 1.23451i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.62573 | − | 27.7148i | 0.0925447 | − | 0.976819i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.06875 | − | 22.6489i | −0.213630 | − | 0.797278i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.8498 | + | 16.6564i | −1.01430 | + | 0.585609i | −0.912449 | − | 0.409191i | \(-0.865811\pi\) |
−0.101855 | + | 0.994799i | \(0.532478\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 55.2368i | − | 1.93963i | −0.243850 | − | 0.969813i | \(-0.578410\pi\) | ||
0.243850 | − | 0.969813i | \(-0.421590\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.2637 | − | 17.2637i | −0.605465 | − | 0.605465i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 48.7704 | − | 5.81968i | 1.70835 | − | 0.203855i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.41922 | + | 0.380278i | −0.0496521 | + | 0.0133042i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.822187 | + | 16.9132i | 0.0287295 | + | 0.590995i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.31457 | + | 16.1333i | −0.325081 | + | 0.563056i | −0.981529 | − | 0.191315i | \(-0.938725\pi\) |
0.656448 | + | 0.754371i | \(0.272058\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.37130 | − | 16.3139i | 0.152374 | − | 0.568668i | −0.846942 | − | 0.531685i | \(-0.821559\pi\) |
0.999316 | − | 0.0369821i | \(-0.0117745\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.29458 | + | 53.3382i | −0.0450716 | + | 1.85700i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.62716 | − | 5.62716i | 0.195675 | − | 0.195675i | −0.602468 | − | 0.798143i | \(-0.705816\pi\) |
0.798143 | + | 0.602468i | \(0.205816\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.29757 | + | 5.71155i | 0.114529 | + | 0.198370i | 0.917591 | − | 0.397525i | \(-0.130131\pi\) |
−0.803062 | + | 0.595895i | \(0.796797\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.2980 | − | 8.25494i | −0.495991 | − | 0.286361i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.50517 | − | 4.26213i | 0.121447 | − | 0.147674i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.96038 | − | 7.96601i | −0.206268 | − | 0.275675i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.285513 | − | 0.0765030i | −0.00986877 | − | 0.00264433i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −46.0930 | −1.59131 | −0.795654 | − | 0.605752i | \(-0.792872\pi\) | ||||
−0.795654 | + | 0.605752i | \(0.792872\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.1232 | 0.762870 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20.4290 | + | 5.47394i | 0.703613 | + | 0.188533i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.70387 | − | 25.7184i | 0.127417 | − | 0.884740i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.85413 | − | 4.40407i | −0.166790 | − | 0.151326i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19.4080 | + | 11.2052i | 0.666080 | + | 0.384562i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.604505 | + | 1.04703i | 0.0207222 | + | 0.0358918i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.9594 | − | 14.9594i | 0.512200 | − | 0.512200i | −0.403000 | − | 0.915200i | \(-0.632032\pi\) |
0.915200 | + | 0.403000i | \(0.132032\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 24.7645 | − | 9.90752i | 0.846929 | − | 0.338830i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.12136 | − | 11.6491i | 0.106623 | − | 0.397924i | −0.891901 | − | 0.452231i | \(-0.850628\pi\) |
0.998524 | + | 0.0543068i | \(0.0172949\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.90061 | − | 5.02401i | 0.0989677 | − | 0.171417i | −0.812290 | − | 0.583254i | \(-0.801779\pi\) |
0.911258 | + | 0.411837i | \(0.135113\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 61.4147 | + | 31.5858i | 2.09301 | + | 1.07644i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.90586 | + | 0.778623i | −0.0989167 | + | 0.0265046i | −0.307938 | − | 0.951406i | \(-0.599639\pi\) |
0.209021 | + | 0.977911i | \(0.432972\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.38475 | + | 11.6046i | 0.0470829 | + | 0.394567i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 33.6632 | + | 33.6632i | 1.14326 | + | 1.14326i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 49.2347i | 1.67017i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.73657 | + | 3.88936i | −0.228260 | + | 0.131786i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.31601 | − | 23.5717i | −0.213765 | − | 0.797780i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 17.7204 | − | 23.6852i | 0.599058 | − | 0.800706i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.07228 | + | 33.8582i | 0.306349 | + | 1.14331i | 0.931778 | + | 0.363030i | \(0.118258\pi\) |
−0.625428 | + | 0.780282i | \(0.715076\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.9328 | − | 6.88939i | 0.402483 | − | 0.232373i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 23.7116i | − | 0.798864i | −0.916763 | − | 0.399432i | \(-0.869207\pi\) | ||
0.916763 | − | 0.399432i | \(-0.130793\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.95370 | + | 7.95370i | 0.267663 | + | 0.267663i | 0.828158 | − | 0.560495i | \(-0.189389\pi\) |
−0.560495 | + | 0.828158i | \(0.689389\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.24965 | + | 69.1342i | 0.277309 | + | 2.32392i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.6954 | − | 5.27738i | 0.661308 | − | 0.177197i | 0.0874718 | − | 0.996167i | \(-0.472121\pi\) |
0.573836 | + | 0.818970i | \(0.305455\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 26.8495 | + | 41.6893i | 0.900503 | + | 1.39821i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.97057 | + | 13.8054i | −0.267024 | + | 0.462499i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.62640 | − | 13.5339i | 0.121353 | − | 0.452895i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 26.0934 | − | 10.4392i | 0.872207 | − | 0.348943i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.3604 | − | 11.3604i | 0.379313 | − | 0.379313i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.0544519 | + | 0.0943134i | 0.00181607 | + | 0.00314553i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.40287 | + | 3.11935i | 0.179996 | + | 0.103921i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.91468 | + | 1.57633i | −0.163550 | + | 0.0524570i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.72107 | − | 25.8378i | 0.123693 | − | 0.858879i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.29276 | − | 1.68614i | −0.208948 | − | 0.0559874i | 0.152827 | − | 0.988253i | \(-0.451162\pi\) |
−0.361775 | + | 0.932266i | \(0.617829\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.391801 | −0.0129952 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.2528 | 0.803531 | 0.401765 | − | 0.915743i | \(-0.368397\pi\) | ||||
0.401765 | + | 0.915743i | \(0.368397\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 48.7964 | + | 13.0749i | 1.61492 | + | 0.432718i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.75766 | − | 10.3681i | −0.256460 | − | 0.342757i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 25.2350 | − | 27.8138i | 0.833333 | − | 0.918493i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.2542 | + | 18.0446i | 1.03098 | + | 0.595236i | 0.917265 | − | 0.398277i | \(-0.130392\pi\) |
0.113714 | + | 0.993513i | \(0.463725\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.18986 | + | 3.79295i | 0.0721583 | + | 0.124982i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.74244 | + | 6.74244i | −0.221930 | + | 0.221930i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.0311706 | + | 1.28426i | −0.00102488 | + | 0.0422263i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −23.3813 | + | 87.2600i | −0.767941 | + | 2.86600i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.2041 | + | 36.7266i | −0.695685 | + | 1.20496i | 0.274264 | + | 0.961654i | \(0.411566\pi\) |
−0.969949 | + | 0.243307i | \(0.921768\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.4657 | − | 8.91344i | 0.408547 | − | 0.292126i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −38.7686 | + | 10.3880i | −1.26923 | + | 0.340089i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.42578 | − | 0.766776i | 0.210145 | − | 0.0250762i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.06709 | + | 4.06709i | 0.132866 | + | 0.132866i | 0.770412 | − | 0.637546i | \(-0.220050\pi\) |
−0.637546 | + | 0.770412i | \(0.720050\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 67.8621i | 2.21460i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.4071 | + | 10.0500i | −0.567455 | + | 0.327621i | −0.756132 | − | 0.654419i | \(-0.772913\pi\) |
0.188677 | + | 0.982039i | \(0.439580\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.9371 | − | 40.8179i | −0.356162 | − | 1.32921i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 38.2899 | − | 17.5207i | 1.24557 | − | 0.569949i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.2583 | + | 56.9449i | 0.495830 | + | 1.85046i | 0.525333 | + | 0.850897i | \(0.323941\pi\) |
−0.0295030 | + | 0.999565i | \(0.509392\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.0354 | − | 5.79393i | 0.325762 | − | 0.188079i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 38.3355i | 1.24311i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −31.1044 | − | 31.1044i | −1.00757 | − | 1.00757i | −0.999971 | − | 0.00759828i | \(-0.997581\pi\) |
−0.00759828 | − | 0.999971i | \(-0.502419\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −21.4359 | + | 27.2448i | −0.693648 | + | 0.881622i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 27.0292 | − | 7.24244i | 0.873729 | − | 0.234115i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −22.9505 | + | 44.6245i | −0.741111 | + | 1.44100i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.4991 | + | 26.8453i | −0.499972 | + | 0.865977i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.44392 | − | 24.0491i | 0.207653 | − | 0.774970i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.92454 | + | 18.4936i | −0.255100 | + | 0.595331i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.5036 | − | 21.5036i | 0.691510 | − | 0.691510i | −0.271054 | − | 0.962564i | \(-0.587372\pi\) |
0.962564 | + | 0.271054i | \(0.0873721\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.50822 | − | 4.34437i | −0.0805756 | − | 0.139561i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 45.3034 | + | 26.1559i | 1.45385 | + | 0.839384i | 0.998697 | − | 0.0510273i | \(-0.0162496\pi\) |
0.455158 | + | 0.890411i | \(0.349583\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.61174 | − | 21.2997i | 0.147845 | − | 0.682836i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 16.5917 | − | 4.01692i | 0.531361 | − | 0.128644i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −54.6658 | − | 14.6477i | −1.74891 | − | 0.468620i | −0.764520 | − | 0.644599i | \(-0.777024\pi\) |
−0.984394 | + | 0.175979i | \(0.943691\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.25068 | 0.167813 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −98.6358 | −3.14920 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.9514 | − | 4.00621i | −0.476875 | − | 0.127778i | 0.0123723 | − | 0.999923i | \(-0.496062\pi\) |
−0.489247 | + | 0.872145i | \(0.662728\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −30.8777 | + | 23.1035i | −0.983845 | + | 0.736139i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.4154 | − | 48.1044i | 0.331526 | − | 1.53118i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.73504 | + | 1.57907i | 0.0869691 | + | 0.0502116i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.8648 | − | 46.5311i | −0.853388 | − | 1.47811i | −0.878133 | − | 0.478417i | \(-0.841211\pi\) |
0.0247453 | − | 0.999694i | \(-0.492123\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −39.2484 | + | 39.2484i | −1.24551 | + | 1.24551i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.25190 | + | 18.1266i | 0.229901 | + | 0.574653i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.97217 | − | 37.2167i | 0.315822 | − | 1.17866i | −0.607400 | − | 0.794396i | \(-0.707787\pi\) |
0.923222 | − | 0.384267i | \(-0.125546\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.914352 | + | 1.58370i | −0.0289288 | + | 0.0501062i |
(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 | 560.2.ci.c.33.4 | 16 | ||
4.3 | odd | 2 | 70.2.k.a.33.1 | yes | 16 | ||
5.2 | odd | 4 | inner | 560.2.ci.c.257.4 | 16 | ||
7.3 | odd | 6 | inner | 560.2.ci.c.353.4 | 16 | ||
12.11 | even | 2 | 630.2.bv.c.523.4 | 16 | |||
20.3 | even | 4 | 350.2.o.c.257.2 | 16 | |||
20.7 | even | 4 | 70.2.k.a.47.3 | yes | 16 | ||
20.19 | odd | 2 | 350.2.o.c.243.4 | 16 | |||
28.3 | even | 6 | 70.2.k.a.3.3 | ✓ | 16 | ||
28.11 | odd | 6 | 490.2.l.c.423.4 | 16 | |||
28.19 | even | 6 | 490.2.g.c.293.1 | 16 | |||
28.23 | odd | 6 | 490.2.g.c.293.4 | 16 | |||
28.27 | even | 2 | 490.2.l.c.313.2 | 16 | |||
35.17 | even | 12 | inner | 560.2.ci.c.17.4 | 16 | ||
60.47 | odd | 4 | 630.2.bv.c.397.1 | 16 | |||
84.59 | odd | 6 | 630.2.bv.c.73.1 | 16 | |||
140.3 | odd | 12 | 350.2.o.c.157.4 | 16 | |||
140.27 | odd | 4 | 490.2.l.c.117.4 | 16 | |||
140.47 | odd | 12 | 490.2.g.c.97.4 | 16 | |||
140.59 | even | 6 | 350.2.o.c.143.2 | 16 | |||
140.67 | even | 12 | 490.2.l.c.227.2 | 16 | |||
140.87 | odd | 12 | 70.2.k.a.17.1 | yes | 16 | ||
140.107 | even | 12 | 490.2.g.c.97.1 | 16 | |||
420.227 | even | 12 | 630.2.bv.c.577.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.k.a.3.3 | ✓ | 16 | 28.3 | even | 6 | ||
70.2.k.a.17.1 | yes | 16 | 140.87 | odd | 12 | ||
70.2.k.a.33.1 | yes | 16 | 4.3 | odd | 2 | ||
70.2.k.a.47.3 | yes | 16 | 20.7 | even | 4 | ||
350.2.o.c.143.2 | 16 | 140.59 | even | 6 | |||
350.2.o.c.157.4 | 16 | 140.3 | odd | 12 | |||
350.2.o.c.243.4 | 16 | 20.19 | odd | 2 | |||
350.2.o.c.257.2 | 16 | 20.3 | even | 4 | |||
490.2.g.c.97.1 | 16 | 140.107 | even | 12 | |||
490.2.g.c.97.4 | 16 | 140.47 | odd | 12 | |||
490.2.g.c.293.1 | 16 | 28.19 | even | 6 | |||
490.2.g.c.293.4 | 16 | 28.23 | odd | 6 | |||
490.2.l.c.117.4 | 16 | 140.27 | odd | 4 | |||
490.2.l.c.227.2 | 16 | 140.67 | even | 12 | |||
490.2.l.c.313.2 | 16 | 28.27 | even | 2 | |||
490.2.l.c.423.4 | 16 | 28.11 | odd | 6 | |||
560.2.ci.c.17.4 | 16 | 35.17 | even | 12 | inner | ||
560.2.ci.c.33.4 | 16 | 1.1 | even | 1 | trivial | ||
560.2.ci.c.257.4 | 16 | 5.2 | odd | 4 | inner | ||
560.2.ci.c.353.4 | 16 | 7.3 | odd | 6 | inner | ||
630.2.bv.c.73.1 | 16 | 84.59 | odd | 6 | |||
630.2.bv.c.397.1 | 16 | 60.47 | odd | 4 | |||
630.2.bv.c.523.4 | 16 | 12.11 | even | 2 | |||
630.2.bv.c.577.4 | 16 | 420.227 | even | 12 |