Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(73,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.73");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.bv (of order \(12\), degree \(4\), 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: | \(5.03057532734\) |
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 | 577.4 | ||
Root | \(0.587308 - 2.01725i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.577 |
Dual form | 630.2.bv.c.523.4 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.258819 | − | 0.965926i | 0.183013 | − | 0.683013i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.866025 | − | 0.500000i | −0.433013 | − | 0.250000i | ||||
\(5\) | 2.21323 | − | 0.318742i | 0.989788 | − | 0.142546i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.559876 | + | 2.58583i | 0.211613 | + | 0.977353i | ||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.264946 | − | 2.22032i | 0.0837833 | − | 0.702126i | ||||
\(11\) | 1.83557 | − | 3.17930i | 0.553445 | − | 0.958596i | −0.444577 | − | 0.895741i | \(-0.646646\pi\) |
0.998023 | − | 0.0628551i | \(-0.0200206\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.830578 | + | 0.830578i | 0.230361 | + | 0.230361i | 0.812843 | − | 0.582482i | \(-0.197918\pi\) |
−0.582482 | + | 0.812843i | \(0.697918\pi\) | |||||||
\(14\) | 2.64263 | + | 0.128464i | 0.706273 | + | 0.0343335i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | 0.204036 | + | 0.761471i | 0.0494859 | + | 0.184684i | 0.986245 | − | 0.165292i | \(-0.0528565\pi\) |
−0.936759 | + | 0.349976i | \(0.886190\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.09461 | + | 1.89593i | 0.251122 | + | 0.434955i | 0.963835 | − | 0.266500i | \(-0.0858673\pi\) |
−0.712713 | + | 0.701455i | \(0.752534\pi\) | |||||||
\(20\) | −2.07609 | − | 0.830578i | −0.464227 | − | 0.185723i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.59589 | − | 2.59589i | −0.553445 | − | 0.553445i | ||||
\(23\) | 4.54529 | + | 1.21791i | 0.947759 | + | 0.253951i | 0.699411 | − | 0.714719i | \(-0.253446\pi\) |
0.248348 | + | 0.968671i | \(0.420112\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.79681 | − | 1.41090i | 0.959361 | − | 0.282180i | ||||
\(26\) | 1.01725 | − | 0.587308i | 0.199498 | − | 0.115180i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.808050 | − | 2.51934i | 0.152707 | − | 0.476110i | ||||
\(29\) | − | 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 | \(-0.332146\pi\) |
−0.496767 | + | 0.867884i | \(0.665480\pi\) | |||||||
\(32\) | 0.965926 | − | 0.258819i | 0.170753 | − | 0.0457532i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.788333 | 0.135198 | ||||||||
\(35\) | 2.06335 | + | 5.54460i | 0.348770 | + | 0.937208i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.0664979 | − | 0.248174i | 0.0109322 | − | 0.0407995i | −0.960244 | − | 0.279161i | \(-0.909944\pi\) |
0.971176 | + | 0.238362i | \(0.0766103\pi\) | |||||||
\(38\) | 2.11463 | − | 0.566614i | 0.343038 | − | 0.0919169i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.33961 | + | 1.79038i | −0.211811 | + | 0.283083i | ||||
\(41\) | − | 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 | \(-0.766296\pi\) |
0.669995 | + | 0.742366i | \(0.266296\pi\) | |||||||
\(44\) | −3.17930 | + | 1.83557i | −0.479298 | + | 0.276723i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.35282 | − | 4.07520i | 0.346904 | − | 0.600855i | ||||
\(47\) | −6.18205 | − | 1.65648i | −0.901745 | − | 0.241622i | −0.221980 | − | 0.975051i | \(-0.571252\pi\) |
−0.679766 | + | 0.733429i | \(0.737919\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.37308 | + | 2.89549i | −0.910440 | + | 0.413642i | ||||
\(50\) | −0.121320 | − | 4.99853i | −0.0171573 | − | 0.706899i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.304013 | − | 1.13459i | −0.0421590 | − | 0.157339i | ||||
\(53\) | −2.04824 | − | 7.64413i | −0.281347 | − | 1.05000i | −0.951468 | − | 0.307749i | \(-0.900424\pi\) |
0.670120 | − | 0.742252i | \(-0.266242\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.04917 | − | 7.62161i | 0.411150 | − | 1.02770i | ||||
\(56\) | −2.22435 | − | 1.43257i | −0.297242 | − | 0.191435i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.53301 | − | 0.678717i | −0.332600 | − | 0.0891199i | ||||
\(59\) | −5.35616 | + | 9.27713i | −0.697312 | + | 1.20778i | 0.272083 | + | 0.962274i | \(0.412287\pi\) |
−0.969395 | + | 0.245506i | \(0.921046\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.72539 | − | 0.996157i | 0.220914 | − | 0.127545i | −0.385459 | − | 0.922725i | \(-0.625957\pi\) |
0.606373 | + | 0.795180i | \(0.292624\pi\) | |||||||
\(62\) | 0.0293654 | − | 0.0293654i | 0.00372940 | − | 0.00372940i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 2.10300 | + | 1.57352i | 0.260846 | + | 0.195172i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.39671 | − | 1.71399i | 0.781482 | − | 0.209398i | 0.154044 | − | 0.988064i | \(-0.450770\pi\) |
0.627438 | + | 0.778666i | \(0.284103\pi\) | |||||||
\(68\) | 0.204036 | − | 0.761471i | 0.0247430 | − | 0.0923420i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.88971 | − | 0.557996i | 0.703955 | − | 0.0666933i | ||||
\(71\) | −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 | 0.346318 | − | 0.938117i | \(-0.387432\pi\) |
0.768979 | + | 0.639274i | \(0.220765\pi\) | |||||||
\(74\) | −0.222506 | − | 0.128464i | −0.0258658 | − | 0.0149336i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 2.18923i | − | 0.251122i | ||||||
\(77\) | 9.24884 | + | 2.96647i | 1.05400 | + | 0.338060i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.6145 | + | 6.70563i | −1.30673 | + | 0.754443i | −0.981550 | − | 0.191208i | \(-0.938760\pi\) |
−0.325184 | + | 0.945651i | \(0.605426\pi\) | |||||||
\(80\) | 1.38266 | + | 1.75735i | 0.154586 | + | 0.196477i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.67427 | − | 2.32426i | −0.957912 | − | 0.256672i | ||||
\(83\) | 9.73033 | + | 9.73033i | 1.06804 | + | 1.06804i | 0.997509 | + | 0.0705331i | \(0.0224700\pi\) |
0.0705331 | + | 0.997509i | \(0.477530\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.694291 | + | 1.62028i | 0.0753065 | + | 0.175744i | ||||
\(86\) | 0.335571 | + | 0.581226i | 0.0361855 | + | 0.0626752i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.950161 | + | 3.54605i | 0.101288 | + | 0.378010i | ||||
\(89\) | −0.715130 | − | 1.23864i | −0.0758036 | − | 0.131296i | 0.825632 | − | 0.564209i | \(-0.190819\pi\) |
−0.901435 | + | 0.432914i | \(0.857486\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.68272 | + | 2.61276i | −0.176397 | + | 0.273892i | ||||
\(92\) | −3.32739 | − | 3.32739i | −0.346904 | − | 0.346904i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.20007 | + | 5.54268i | −0.330062 | + | 0.571684i | ||||
\(95\) | 3.02695 | + | 3.84723i | 0.310558 | + | 0.394717i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.16693 | + | 3.16693i | −0.321553 | + | 0.321553i | −0.849363 | − | 0.527810i | \(-0.823013\pi\) |
0.527810 | + | 0.849363i | \(0.323013\pi\) | |||||||
\(98\) | 1.14736 | + | 6.90533i | 0.115901 | + | 0.697544i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.85961 | − | 1.17653i | −0.485961 | − | 0.117653i | ||||
\(101\) | 0.0622734 | + | 0.0359536i | 0.00619644 | + | 0.00357751i | 0.503095 | − | 0.864231i | \(-0.332195\pi\) |
−0.496899 | + | 0.867809i | \(0.665528\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.29116 | + | 16.0148i | −0.422820 | + | 1.57799i | 0.345817 | + | 0.938302i | \(0.387602\pi\) |
−0.768638 | + | 0.639685i | \(0.779065\pi\) | |||||||
\(104\) | −1.17462 | −0.115180 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.91378 | −0.768654 | ||||||||
\(107\) | −1.18265 | + | 4.41372i | −0.114331 | + | 0.426690i | −0.999236 | − | 0.0390819i | \(-0.987557\pi\) |
0.884905 | + | 0.465772i | \(0.154223\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.6773 | − | 9.05131i | −1.50162 | − | 0.866958i | −0.999998 | − | 0.00186842i | \(-0.999405\pi\) |
−0.501617 | − | 0.865090i | \(-0.667261\pi\) | |||||||
\(110\) | −6.57273 | − | 4.91789i | −0.626685 | − | 0.468902i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.95946 | + | 1.77778i | −0.185152 | + | 0.167985i | ||||
\(113\) | −1.52064 | + | 1.52064i | −0.143049 | + | 0.143049i | −0.775005 | − | 0.631955i | \(-0.782253\pi\) |
0.631955 | + | 0.775005i | \(0.282253\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.4480 | + | 1.24674i | 0.974281 | + | 0.116259i | ||||
\(116\) | −1.31118 | + | 2.27103i | −0.121740 | + | 0.210860i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.57475 | + | 7.57475i | 0.697312 | + | 0.697312i | ||||
\(119\) | −1.85480 | + | 0.953932i | −0.170030 | + | 0.0874468i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.23864 | − | 2.14539i | −0.112604 | − | 0.195035i | ||||
\(122\) | −0.515649 | − | 1.92443i | −0.0466846 | − | 0.174229i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.0207644 | − | 0.0359651i | −0.00186470 | − | 0.00322976i | ||||
\(125\) | 10.1667 | − | 4.65160i | 0.909341 | − | 0.416051i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.2527 | − | 13.2527i | −1.17599 | − | 1.17599i | −0.980757 | − | 0.195234i | \(-0.937453\pi\) |
−0.195234 | − | 0.980757i | \(-0.562547\pi\) | |||||||
\(128\) | −0.965926 | − | 0.258819i | −0.0853766 | − | 0.0228766i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.06420 | − | 1.62409i | 0.181043 | − | 0.142442i | ||||
\(131\) | −12.2929 | + | 7.09731i | −1.07404 | + | 0.620095i | −0.929281 | − | 0.369372i | \(-0.879573\pi\) |
−0.144755 | + | 0.989468i | \(0.546239\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.28970 | + | 3.89197i | −0.371964 | + | 0.337477i | ||||
\(134\) | − | 6.62236i | − | 0.572085i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.682717 | − | 0.394167i | −0.0585425 | − | 0.0337995i | ||||
\(137\) | −18.3201 | + | 4.90887i | −1.56519 | + | 0.419393i | −0.934303 | − | 0.356479i | \(-0.883977\pi\) |
−0.630891 | + | 0.775871i | \(0.717311\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.23706 | 0.698658 | 0.349329 | − | 0.937000i | \(-0.386409\pi\) | ||||
0.349329 | + | 0.937000i | \(0.386409\pi\) | |||||||
\(140\) | 0.985385 | − | 5.83344i | 0.0832803 | − | 0.493016i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.10103 | + | 7.84116i | −0.176315 | + | 0.658016i | ||||
\(143\) | 4.16524 | − | 1.11607i | 0.348315 | − | 0.0933308i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.835856 | − | 5.80390i | −0.0694141 | − | 0.481988i | ||||
\(146\) | − | 9.86525i | − | 0.816454i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.181676 | + | 0.181676i | −0.0149336 | + | 0.0149336i | ||||
\(149\) | −4.19317 | + | 2.42093i | −0.343518 | + | 0.198330i | −0.661826 | − | 0.749657i | \(-0.730218\pi\) |
0.318309 | + | 0.947987i | \(0.396885\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.02292 | + | 8.69995i | −0.408759 | + | 0.707992i | −0.994751 | − | 0.102325i | \(-0.967372\pi\) |
0.585992 | + | 0.810317i | \(0.300705\pi\) | |||||||
\(152\) | −2.11463 | − | 0.566614i | −0.171519 | − | 0.0459584i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.25916 | − | 8.16592i | 0.423795 | − | 0.658028i | ||||
\(155\) | 0.0862176 | + | 0.0344930i | 0.00692516 | + | 0.00277054i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.33762 | + | 23.6523i | 0.505797 | + | 1.88766i | 0.458320 | + | 0.888788i | \(0.348452\pi\) |
0.0474774 | + | 0.998872i | \(0.484882\pi\) | |||||||
\(158\) | 3.47109 | + | 12.9543i | 0.276145 | + | 1.03059i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.05532 | − | 0.880708i | 0.162488 | − | 0.0696261i | ||||
\(161\) | −0.604505 | + | 12.4353i | −0.0476417 | + | 0.980035i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.2171 | + | 5.68510i | 1.66185 | + | 0.445291i | 0.962895 | − | 0.269875i | \(-0.0869823\pi\) |
0.698954 | + | 0.715166i | \(0.253649\pi\) | |||||||
\(164\) | −4.49013 | + | 7.77713i | −0.350620 | + | 0.607292i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.9172 | − | 6.88038i | 0.924952 | − | 0.534021i | ||||
\(167\) | 3.14616 | − | 3.14616i | 0.243457 | − | 0.243457i | −0.574821 | − | 0.818279i | \(-0.694928\pi\) |
0.818279 | + | 0.574821i | \(0.194928\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 11.6203i | − | 0.893868i | ||||||
\(170\) | 1.74477 | − | 0.251275i | 0.133817 | − | 0.0192719i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.648273 | − | 0.173704i | 0.0494304 | − | 0.0132448i | ||||
\(173\) | 1.35273 | − | 5.04844i | 0.102846 | − | 0.383826i | −0.895246 | − | 0.445572i | \(-0.853000\pi\) |
0.998092 | + | 0.0617463i | \(0.0196670\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.33397 | + | 11.6138i | 0.478803 | + | 0.877922i | ||||
\(176\) | 3.67114 | 0.276723 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.38152 | + | 0.370178i | −0.103550 | + | 0.0277460i | ||||
\(179\) | −10.8847 | − | 6.28428i | −0.813560 | − | 0.469709i | 0.0346308 | − | 0.999400i | \(-0.488974\pi\) |
−0.848191 | + | 0.529691i | \(0.822308\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 11.6742i | − | 0.867740i | −0.900976 | − | 0.433870i | \(-0.857148\pi\) | ||
0.900976 | − | 0.433870i | \(-0.142852\pi\) | |||||||
\(182\) | 2.08821 | + | 2.30161i | 0.154789 | + | 0.170607i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.07520 | + | 2.35282i | −0.300428 | + | 0.173452i | ||||
\(185\) | 0.0680721 | − | 0.570462i | 0.00500476 | − | 0.0419412i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.79547 | + | 0.749044i | 0.204425 | + | 0.0547755i | ||||
\(188\) | 4.52558 | + | 4.52558i | 0.330062 | + | 0.330062i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.49957 | − | 1.92807i | 0.326433 | − | 0.139877i | ||||
\(191\) | 7.75170 | + | 13.4263i | 0.560894 | + | 0.971496i | 0.997419 | + | 0.0718040i | \(0.0228756\pi\) |
−0.436525 | + | 0.899692i | \(0.643791\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.32883 | + | 8.69132i | 0.167633 | + | 0.625615i | 0.997690 | + | 0.0679359i | \(0.0216413\pi\) |
−0.830057 | + | 0.557679i | \(0.811692\pi\) | |||||||
\(194\) | 2.23936 | + | 3.87868i | 0.160776 | + | 0.278473i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.96699 | + | 0.678966i | 0.497642 | + | 0.0484976i | ||||
\(197\) | −12.1951 | − | 12.1951i | −0.868865 | − | 0.868865i | 0.123482 | − | 0.992347i | \(-0.460594\pi\) |
−0.992347 | + | 0.123482i | \(0.960594\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.36557 | − | 7.56140i | 0.309467 | − | 0.536013i | −0.668779 | − | 0.743462i | \(-0.733183\pi\) |
0.978246 | + | 0.207448i | \(0.0665159\pi\) | |||||||
\(200\) | −2.39420 | + | 4.38951i | −0.169295 | + | 0.310385i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.0508460 | − | 0.0508460i | 0.00357751 | − | 0.00357751i | ||||
\(203\) | 6.78099 | − | 1.46820i | 0.475932 | − | 0.103047i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.86239 | − | 19.8754i | −0.199918 | − | 1.38816i | ||||
\(206\) | 14.3585 | + | 8.28988i | 1.00040 | + | 0.577583i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.304013 | + | 1.13459i | −0.0210795 | + | 0.0786697i | ||||
\(209\) | 8.03696 | 0.555928 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.1745 | −0.769288 | −0.384644 | − | 0.923065i | \(-0.625676\pi\) | ||||
−0.384644 | + | 0.923065i | \(0.625676\pi\) | |||||||
\(212\) | −2.04824 | + | 7.64413i | −0.140674 | + | 0.525001i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.95723 | + | 2.28471i | 0.270511 | + | 0.156179i | ||||
\(215\) | −0.899067 | + | 1.20160i | −0.0613158 | + | 0.0819482i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.0335574 | + | 0.104625i | −0.00227803 | + | 0.00710242i | ||||
\(218\) | −12.8005 | + | 12.8005i | −0.866958 | + | 0.866958i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.45147 | + | 5.07592i | −0.434958 | + | 0.342219i | ||||
\(221\) | −0.462994 | + | 0.801929i | −0.0311443 | + | 0.0539436i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.746804 | + | 0.746804i | 0.0500097 | + | 0.0500097i | 0.731669 | − | 0.681660i | \(-0.238742\pi\) |
−0.681660 | + | 0.731669i | \(0.738742\pi\) | |||||||
\(224\) | 1.21006 | + | 2.35282i | 0.0808507 | + | 0.157204i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.07525 | + | 1.86239i | 0.0715247 | + | 0.123884i | ||||
\(227\) | 0.807609 | + | 3.01404i | 0.0536029 | + | 0.200049i | 0.987534 | − | 0.157403i | \(-0.0503122\pi\) |
−0.933932 | + | 0.357452i | \(0.883646\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.21091 | + | 7.29350i | 0.278264 | + | 0.481968i | 0.970954 | − | 0.239268i | \(-0.0769075\pi\) |
−0.692689 | + | 0.721236i | \(0.743574\pi\) | |||||||
\(230\) | 3.90840 | − | 9.76931i | 0.257712 | − | 0.644169i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.85429 | + | 1.85429i | 0.121740 | + | 0.121740i | ||||
\(233\) | −22.0201 | − | 5.90027i | −1.44259 | − | 0.386540i | −0.549148 | − | 0.835725i | \(-0.685048\pi\) |
−0.893439 | + | 0.449186i | \(0.851714\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.2103 | − | 1.69569i | −0.926979 | − | 0.110615i | ||||
\(236\) | 9.27713 | − | 5.35616i | 0.603890 | − | 0.348656i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.441369 | + | 2.03850i | 0.0286097 | + | 0.132136i | ||||
\(239\) | − | 23.9971i | − | 1.55224i | −0.630585 | − | 0.776120i | \(-0.717185\pi\) | ||
0.630585 | − | 0.776120i | \(-0.282815\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.4666 | − | 12.3937i | −1.38278 | − | 0.798350i | −0.390295 | − | 0.920690i | \(-0.627627\pi\) |
−0.992488 | + | 0.122340i | \(0.960960\pi\) | |||||||
\(242\) | −2.39287 | + | 0.641168i | −0.153820 | + | 0.0412158i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.99231 | −0.127545 | ||||||||
\(245\) | −13.1822 | + | 8.43977i | −0.842179 | + | 0.539197i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.665553 | + | 2.48388i | −0.0423481 | + | 0.158045i | ||||
\(248\) | −0.0401138 | + | 0.0107485i | −0.00254723 | + | 0.000682528i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.86175 | − | 11.0242i | −0.117747 | − | 0.697234i | ||||
\(251\) | − | 11.1158i | − | 0.701623i | −0.936446 | − | 0.350811i | \(-0.885906\pi\) | ||
0.936446 | − | 0.350811i | \(-0.114094\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.2153 | − | 12.2153i | 0.767970 | − | 0.767970i | ||||
\(254\) | −16.2312 | + | 9.37110i | −1.01844 | + | 0.587995i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 24.4314 | + | 6.54637i | 1.52399 | + | 0.408351i | 0.921052 | − | 0.389439i | \(-0.127331\pi\) |
0.602935 | + | 0.797790i | \(0.293998\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.678966 | + | 0.0330060i | 0.0421889 | + | 0.00205090i | ||||
\(260\) | −1.03449 | − | 2.41421i | −0.0641565 | − | 0.149723i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.67384 | + | 13.7110i | 0.226971 | + | 0.847066i | ||||
\(263\) | −2.93659 | − | 10.9595i | −0.181078 | − | 0.675792i | −0.995436 | − | 0.0954297i | \(-0.969577\pi\) |
0.814358 | − | 0.580363i | \(-0.197089\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.96973 | − | 16.2654i | −0.428147 | − | 0.999174i | ||||
\(266\) | 2.64910 | + | 5.15085i | 0.162427 | + | 0.315819i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.39671 | − | 1.71399i | −0.390741 | − | 0.104699i | ||||
\(269\) | 4.03346 | − | 6.98616i | 0.245924 | − | 0.425954i | −0.716467 | − | 0.697621i | \(-0.754242\pi\) |
0.962391 | + | 0.271668i | \(0.0875752\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.27419 | − | 4.19976i | 0.441876 | − | 0.255117i | −0.262517 | − | 0.964927i | \(-0.584553\pi\) |
0.704393 | + | 0.709810i | \(0.251219\pi\) | |||||||
\(272\) | −0.557436 | + | 0.557436i | −0.0337995 | + | 0.0337995i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 18.9664i | 1.14580i | ||||||||
\(275\) | 4.31920 | − | 17.8403i | 0.260458 | − | 1.07581i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.48646 | + | 1.47009i | −0.329650 | + | 0.0883293i | −0.419848 | − | 0.907594i | \(-0.637917\pi\) |
0.0901983 | + | 0.995924i | \(0.471250\pi\) | |||||||
\(278\) | 2.13191 | − | 7.95639i | 0.127863 | − | 0.477193i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.37963 | − | 2.46161i | −0.321495 | − | 0.147110i | ||||
\(281\) | −7.27627 | −0.434066 | −0.217033 | − | 0.976164i | \(-0.569638\pi\) | ||||
−0.217033 | + | 0.976164i | \(0.569638\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.44729 | + | 1.99550i | −0.442696 | + | 0.118620i | −0.473280 | − | 0.880912i | \(-0.656930\pi\) |
0.0305840 | + | 0.999532i | \(0.490263\pi\) | |||||||
\(284\) | 7.03019 | + | 4.05888i | 0.417165 | + | 0.240850i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 4.31218i | − | 0.254984i | ||||||
\(287\) | 23.2215 | − | 5.02784i | 1.37072 | − | 0.296784i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.1842 | − | 8.18927i | 0.834366 | − | 0.481721i | ||||
\(290\) | −5.82247 | − | 0.694784i | −0.341907 | − | 0.0407991i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.52910 | − | 2.55331i | −0.557648 | − | 0.149421i | ||||
\(293\) | −3.35198 | − | 3.35198i | −0.195824 | − | 0.195824i | 0.602383 | − | 0.798207i | \(-0.294218\pi\) |
−0.798207 | + | 0.602383i | \(0.794218\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.89741 | + | 22.2397i | −0.518027 | + | 1.29485i | ||||
\(296\) | 0.128464 | + | 0.222506i | 0.00746682 | + | 0.0129329i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.25316 | + | 4.67687i | 0.0725938 | + | 0.270924i | ||||
\(299\) | 2.76365 | + | 4.78679i | 0.159826 | + | 0.276827i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.49286 | − | 0.961456i | −0.0860468 | − | 0.0554174i | ||||
\(302\) | 7.10348 | + | 7.10348i | 0.408759 | + | 0.408759i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.09461 | + | 1.89593i | −0.0627804 | + | 0.108739i | ||||
\(305\) | 3.50118 | − | 2.75468i | 0.200477 | − | 0.157733i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.06546 | + | 1.06546i | −0.0608089 | + | 0.0608089i | −0.736857 | − | 0.676048i | \(-0.763691\pi\) |
0.676048 | + | 0.736857i | \(0.263691\pi\) | |||||||
\(308\) | −6.52650 | − | 7.19345i | −0.371882 | − | 0.409885i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.0556324 | − | 0.0743524i | 0.00315971 | − | 0.00422293i | ||||
\(311\) | −11.9584 | − | 6.90417i | −0.678097 | − | 0.391500i | 0.121040 | − | 0.992648i | \(-0.461377\pi\) |
−0.799138 | + | 0.601148i | \(0.794710\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.04266 | − | 22.5515i | 0.341551 | − | 1.27469i | −0.555038 | − | 0.831825i | \(-0.687296\pi\) |
0.896590 | − | 0.442863i | \(-0.146037\pi\) | |||||||
\(314\) | 24.4867 | 1.38186 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.4113 | 0.754443 | ||||||||
\(317\) | −3.41352 | + | 12.7394i | −0.191722 | + | 0.715518i | 0.801369 | + | 0.598171i | \(0.204106\pi\) |
−0.993091 | + | 0.117347i | \(0.962561\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.33728 | − | 4.81353i | −0.466798 | − | 0.269506i | ||||
\(320\) | −0.318742 | − | 2.21323i | −0.0178182 | − | 0.123724i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 11.8551 | + | 3.80239i | 0.660658 | + | 0.211899i | ||||
\(323\) | −1.22035 | + | 1.22035i | −0.0679023 | + | 0.0679023i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.15599 | + | 2.81226i | 0.286003 | + | 0.155996i | ||||
\(326\) | 10.9828 | − | 19.0227i | 0.608279 | − | 1.05357i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.35000 | + | 6.35000i | 0.350620 | + | 0.350620i | ||||
\(329\) | 0.822187 | − | 16.9132i | 0.0453286 | − | 0.932454i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.54799 | + | 16.5376i | 0.524805 | + | 0.908989i | 0.999583 | + | 0.0288830i | \(0.00919501\pi\) |
−0.474778 | + | 0.880106i | \(0.657472\pi\) | |||||||
\(332\) | −3.56155 | − | 13.2919i | −0.195465 | − | 0.729487i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.22467 | − | 3.85325i | −0.121729 | − | 0.210840i | ||||
\(335\) | 13.6111 | − | 5.83237i | 0.743653 | − | 0.318656i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.488226 | + | 0.488226i | 0.0265953 | + | 0.0265953i | 0.720279 | − | 0.693684i | \(-0.244014\pi\) |
−0.693684 | + | 0.720279i | \(0.744014\pi\) | |||||||
\(338\) | −11.2243 | − | 3.00755i | −0.610523 | − | 0.163589i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.208866 | − | 1.75035i | 0.0113273 | − | 0.0949260i | ||||
\(341\) | 0.132033 | − | 0.0762292i | 0.00714998 | − | 0.00412804i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.0554 | − | 14.8586i | −0.596936 | − | 0.802289i | ||||
\(344\) | − | 0.671142i | − | 0.0361855i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.52631 | − | 2.61327i | −0.243336 | − | 0.140490i | ||||
\(347\) | 3.68015 | − | 0.986094i | 0.197561 | − | 0.0529363i | −0.158682 | − | 0.987330i | \(-0.550724\pi\) |
0.356243 | + | 0.934393i | \(0.384058\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.91303 | −0.423575 | −0.211787 | − | 0.977316i | \(-0.567928\pi\) | ||||
−0.211787 | + | 0.977316i | \(0.567928\pi\) | |||||||
\(350\) | 12.8574 | − | 3.11227i | 0.687259 | − | 0.166358i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.950161 | − | 3.54605i | 0.0506438 | − | 0.189005i | ||||
\(353\) | 24.9004 | − | 6.67203i | 1.32531 | − | 0.355116i | 0.474347 | − | 0.880338i | \(-0.342684\pi\) |
0.850965 | + | 0.525222i | \(0.176018\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −17.9665 | + | 2.58747i | −0.953564 | + | 0.137329i | ||||
\(356\) | 1.43026i | 0.0758036i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.88731 | + | 8.88731i | −0.469709 | + | 0.469709i | ||||
\(359\) | −8.99497 | + | 5.19325i | −0.474737 | + | 0.274089i | −0.718220 | − | 0.695816i | \(-0.755043\pi\) |
0.243484 | + | 0.969905i | \(0.421710\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.10364 | − | 12.3039i | 0.373876 | − | 0.647572i | ||||
\(362\) | −11.2765 | − | 3.02152i | −0.592677 | − | 0.158807i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.76365 | − | 1.42136i | 0.144855 | − | 0.0744994i | ||||
\(365\) | 20.2763 | − | 8.68840i | 1.06131 | − | 0.454772i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.24811 | − | 8.39004i | −0.117350 | − | 0.437957i | 0.882102 | − | 0.471059i | \(-0.156128\pi\) |
−0.999452 | + | 0.0331020i | \(0.989461\pi\) | |||||||
\(368\) | 1.21791 | + | 4.54529i | 0.0634878 | + | 0.236940i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.533405 | − | 0.213399i | −0.0277304 | − | 0.0110941i | ||||
\(371\) | 18.6197 | − | 9.57617i | 0.966686 | − | 0.497170i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.8560 | − | 3.44476i | −0.665660 | − | 0.178363i | −0.0898611 | − | 0.995954i | \(-0.528642\pi\) |
−0.575799 | + | 0.817591i | \(0.695309\pi\) | |||||||
\(374\) | 1.44704 | − | 2.50635i | 0.0748247 | − | 0.129600i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.54268 | − | 3.20007i | 0.285842 | − | 0.165031i | ||||
\(377\) | 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 | \(-0.225629\pi\) | |||||||
\(380\) | −0.697798 | − | 4.84527i | −0.0357963 | − | 0.248557i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14.9751 | − | 4.01258i | 0.766195 | − | 0.205301i | ||||
\(383\) | −4.76251 | + | 17.7739i | −0.243353 | + | 0.908205i | 0.730851 | + | 0.682537i | \(0.239123\pi\) |
−0.974204 | + | 0.225668i | \(0.927543\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 21.4154 | + | 3.61749i | 1.09143 | + | 0.184364i | ||||
\(386\) | 8.99792 | 0.457982 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.32611 | − | 1.15918i | 0.219625 | − | 0.0588483i | ||||
\(389\) | 19.3621 | + | 11.1787i | 0.981699 | + | 0.566784i | 0.902783 | − | 0.430097i | \(-0.141521\pi\) |
0.0789164 | + | 0.996881i | \(0.474854\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.70961i | 0.187603i | ||||||||
\(392\) | 2.45902 | − | 6.55387i | 0.124199 | − | 0.331020i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −14.9359 | + | 8.62324i | −0.752459 | + | 0.434432i | ||||
\(395\) | −23.5682 | + | 18.5432i | −1.18585 | + | 0.933008i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.2461 | − | 4.08518i | −0.765181 | − | 0.205029i | −0.144939 | − | 0.989441i | \(-0.546299\pi\) |
−0.620241 | + | 0.784411i | \(0.712965\pi\) | |||||||
\(398\) | −6.17385 | − | 6.17385i | −0.309467 | − | 0.309467i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.62028 | + | 3.44871i | 0.181014 | + | 0.172435i | ||||
\(401\) | 6.98528 | + | 12.0989i | 0.348828 | + | 0.604188i | 0.986042 | − | 0.166499i | \(-0.0532463\pi\) |
−0.637213 | + | 0.770687i | \(0.719913\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.0126253 | + | 0.0471183i | 0.000628911 | + | 0.00234713i | ||||
\(404\) | −0.0359536 | − | 0.0622734i | −0.00178876 | − | 0.00309822i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.336879 | − | 6.92993i | 0.0167190 | − | 0.343927i | ||||
\(407\) | −0.666957 | − | 0.666957i | −0.0330598 | − | 0.0330598i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.156681 | + | 0.271379i | −0.00774737 | + | 0.0134188i | −0.869873 | − | 0.493276i | \(-0.835799\pi\) |
0.862126 | + | 0.506694i | \(0.169133\pi\) | |||||||
\(410\) | −19.9390 | − | 2.37928i | −0.984718 | − | 0.117504i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11.7237 | − | 11.7237i | 0.577583 | − | 0.577583i | ||||
\(413\) | −26.9879 | − | 8.65608i | −1.32799 | − | 0.425938i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.6370 | + | 18.4340i | 1.20938 | + | 0.904891i | ||||
\(416\) | 1.01725 | + | 0.587308i | 0.0498746 | + | 0.0287951i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.08012 | − | 7.76311i | 0.101742 | − | 0.379706i | ||||
\(419\) | −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 | \(0.299107\pi\) | |||||||
\(422\) | −2.89219 | + | 10.7938i | −0.140789 | + | 0.525433i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.85354 | + | 3.95689i | 0.332837 | + | 0.192164i | ||||
\(425\) | 2.05308 | + | 3.36476i | 0.0995890 | + | 0.163215i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.54190 | + | 3.90386i | 0.171405 | + | 0.188921i | ||||
\(428\) | 3.23107 | − | 3.23107i | 0.156179 | − | 0.156179i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.927958 | + | 1.17943i | 0.0447501 | + | 0.0568771i | ||||
\(431\) | 0.779037 | − | 1.34933i | 0.0375249 | − | 0.0649950i | −0.846653 | − | 0.532145i | \(-0.821386\pi\) |
0.884178 | + | 0.467150i | \(0.154719\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.28166 | + | 6.28166i | 0.301877 | + | 0.301877i | 0.841748 | − | 0.539871i | \(-0.181527\pi\) |
−0.539871 | + | 0.841748i | \(0.681527\pi\) | |||||||
\(434\) | 0.0923749 | + | 0.0594930i | 0.00443414 | + | 0.00285575i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.05131 | + | 15.6773i | 0.433479 | + | 0.750808i | ||||
\(437\) | 2.66628 | + | 9.95068i | 0.127545 | + | 0.476006i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.9571 | + | 20.7103i | 0.570681 | + | 0.988449i | 0.996496 | + | 0.0836389i | \(0.0266542\pi\) |
−0.425815 | + | 0.904810i | \(0.640012\pi\) | |||||||
\(440\) | 3.23320 | + | 7.54538i | 0.154137 | + | 0.359712i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.654772 | + | 0.654772i | 0.0311443 | + | 0.0311443i | ||||
\(443\) | 12.4238 | + | 3.32895i | 0.590272 | + | 0.158163i | 0.541578 | − | 0.840651i | \(-0.317827\pi\) |
0.0486946 | + | 0.998814i | \(0.484494\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.97756 | − | 2.51346i | −0.0937451 | − | 0.119149i | ||||
\(446\) | 0.914645 | − | 0.528070i | 0.0433097 | − | 0.0250049i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.58583 | − | 0.559876i | 0.122169 | − | 0.0264517i | ||||
\(449\) | − | 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 | ||||
\(452\) | 2.07723 | − | 0.556592i | 0.0977046 | − | 0.0261799i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.12036 | 0.146446 | ||||||||
\(455\) | −2.89145 | + | 6.31900i | −0.135553 | + | 0.296239i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.85449 | − | 33.0454i | 0.414196 | − | 1.54580i | −0.372246 | − | 0.928134i | \(-0.621412\pi\) |
0.786442 | − | 0.617665i | \(-0.211921\pi\) | |||||||
\(458\) | 8.13485 | − | 2.17973i | 0.380116 | − | 0.101852i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.42486 | − | 6.30371i | −0.392811 | − | 0.293912i | ||||
\(461\) | 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 | \(-0.708195\pi\) |
0.793619 | + | 0.608415i | \(0.208195\pi\) | |||||||
\(464\) | 2.27103 | − | 1.31118i | 0.105430 | − | 0.0608700i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.3985 | + | 19.7427i | −0.528023 | + | 0.914563i | ||||
\(467\) | 4.71932 | + | 1.26454i | 0.218384 | + | 0.0585159i | 0.366352 | − | 0.930476i | \(-0.380607\pi\) |
−0.147968 | + | 0.988992i | \(0.547273\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.01347 | + | 15.5812i | 0.370028 | + | 0.719473i | ||||
\(470\) | −5.31581 | + | 13.2872i | −0.245200 | + | 0.612895i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.77255 | − | 10.3473i | −0.127617 | − | 0.476273i | ||||
\(473\) | 0.637693 | + | 2.37990i | 0.0293212 | + | 0.109428i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.92561 | + | 7.55000i | 0.363652 | + | 0.346418i | ||||
\(476\) | 2.08327 | + | 0.101272i | 0.0954867 | + | 0.00464182i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −23.1794 | − | 6.21090i | −1.06020 | − | 0.284080i | ||||
\(479\) | 8.55572 | − | 14.8189i | 0.390921 | − | 0.677094i | −0.601651 | − | 0.798759i | \(-0.705490\pi\) |
0.992571 | + | 0.121665i | \(0.0388234\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.261359 | − | 0.150896i | 0.0119170 | − | 0.00688026i | ||||
\(482\) | −17.5274 | + | 17.5274i | −0.798350 | + | 0.798350i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.47728i | 0.112604i | ||||||||
\(485\) | −5.99972 | + | 8.01859i | −0.272433 | + | 0.364105i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.125860 | + | 0.0337240i | −0.00570325 | + | 0.00152818i | −0.261670 | − | 0.965158i | \(-0.584273\pi\) |
0.255966 | + | 0.966686i | \(0.417606\pi\) | |||||||
\(488\) | −0.515649 | + | 1.92443i | −0.0233423 | + | 0.0871147i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.74039 | + | 14.9174i | 0.214149 | + | 0.673899i | ||||
\(491\) | −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 | ||||
\(494\) | 2.22698 | + | 1.28575i | 0.100197 | + | 0.0578486i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.0415289i | 0.00186470i | ||||||||
\(497\) | −4.54495 | − | 20.9912i | −0.203869 | − | 0.941584i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.0833977 | + | 0.0481497i | −0.00373339 | + | 0.00215548i | −0.501866 | − | 0.864946i | \(-0.667353\pi\) |
0.498132 | + | 0.867101i | \(0.334019\pi\) | |||||||
\(500\) | −11.1305 | − | 1.05497i | −0.497769 | − | 0.0471797i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −10.7370 | − | 2.87698i | −0.479217 | − | 0.128406i | ||||
\(503\) | 13.6334 | + | 13.6334i | 0.607883 | + | 0.607883i | 0.942392 | − | 0.334509i | \(-0.108571\pi\) |
−0.334509 | + | 0.942392i | \(0.608571\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.149286 | + | 0.0597245i | 0.00664312 | + | 0.00265771i | ||||
\(506\) | −8.63753 | − | 14.9606i | −0.383985 | − | 0.665081i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.85084 | + | 18.1036i | 0.215221 | + | 0.803217i | ||||
\(509\) | 6.16366 | + | 10.6758i | 0.273199 | + | 0.473195i | 0.969679 | − | 0.244381i | \(-0.0785848\pi\) |
−0.696480 | + | 0.717576i | \(0.745251\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.9376 | + | 23.2111i | 0.528087 | + | 1.02680i | ||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 12.6466 | − | 21.9046i | 0.557818 | − | 0.966169i | ||||
\(515\) | −4.39274 | + | 36.8123i | −0.193567 | + | 1.62214i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.6140 | + | 16.6140i | −0.730684 | + | 0.730684i | ||||
\(518\) | 0.207611 | − | 0.647288i | 0.00912189 | − | 0.0284402i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.59970 | + | 0.374399i | −0.114004 | + | 0.0164185i | ||||
\(521\) | −14.1415 | − | 8.16461i | −0.619551 | − | 0.357698i | 0.157143 | − | 0.987576i | \(-0.449772\pi\) |
−0.776694 | + | 0.629878i | \(0.783105\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.09270 | + | 26.4703i | −0.310142 | + | 1.15747i | 0.618286 | + | 0.785953i | \(0.287827\pi\) |
−0.928428 | + | 0.371512i | \(0.878839\pi\) | |||||||
\(524\) | 14.1946 | 0.620095 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.3461 | −0.494714 | ||||||||
\(527\) | −0.00847337 | + | 0.0316231i | −0.000369106 | + | 0.00137752i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.742186 | − | 0.428501i | −0.0322689 | − | 0.0186305i | ||||
\(530\) | −17.5151 | + | 2.52245i | −0.760805 | + | 0.109568i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.66098 | − | 1.22570i | 0.245435 | − | 0.0531407i | ||||
\(533\) | 7.45881 | − | 7.45881i | 0.323077 | − | 0.323077i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.21065 | + | 10.1456i | −0.0523409 | + | 0.438630i | ||||
\(536\) | −3.31118 | + | 5.73513i | −0.143021 | + | 0.247720i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.70417 | − | 5.70417i | −0.245924 | − | 0.245924i | ||||
\(539\) | −2.49258 | + | 25.5768i | −0.107363 | + | 1.10167i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.5773 | + | 35.6410i | 0.884689 | + | 1.53233i | 0.846069 | + | 0.533073i | \(0.178963\pi\) |
0.0386200 | + | 0.999254i | \(0.487704\pi\) | |||||||
\(542\) | −2.17395 | − | 8.11330i | −0.0933793 | − | 0.348496i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.394167 | + | 0.682717i | 0.0168998 | + | 0.0292712i | ||||
\(545\) | −37.5826 | − | 15.0356i | −1.60986 | − | 0.644056i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.06541 | + | 8.06541i | 0.344852 | + | 0.344852i | 0.858188 | − | 0.513336i | \(-0.171590\pi\) |
−0.513336 | + | 0.858188i | \(0.671590\pi\) | |||||||
\(548\) | 18.3201 | + | 4.90887i | 0.782597 | + | 0.209696i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −16.1145 | − | 8.78944i | −0.687126 | − | 0.374783i | ||||
\(551\) | 4.97180 | − | 2.87047i | 0.211806 | − | 0.122286i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −23.8423 | − | 26.2788i | −1.01388 | − | 1.11749i | ||||
\(554\) | 5.68000i | 0.241320i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.13350 | − | 4.11853i | −0.302528 | − | 0.174665i | ||||
\(557\) | −24.7826 | + | 6.64049i | −1.05007 | + | 0.281367i | −0.742282 | − | 0.670087i | \(-0.766257\pi\) |
−0.307792 | + | 0.951454i | \(0.599590\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.788333 | −0.0333429 | ||||||||
\(560\) | −3.77009 | + | 4.55921i | −0.159315 | + | 0.192662i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.88324 | + | 7.02834i | −0.0794396 | + | 0.296473i | ||||
\(563\) | 12.3749 | − | 3.31584i | 0.521539 | − | 0.139746i | 0.0115606 | − | 0.999933i | \(-0.496320\pi\) |
0.509978 | + | 0.860187i | \(0.329653\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.88083 | + | 3.85022i | −0.121198 | + | 0.161980i | ||||
\(566\) | 7.71000i | 0.324076i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.74013 | − | 5.74013i | 0.240850 | − | 0.240850i | ||||
\(569\) | 29.8291 | − | 17.2218i | 1.25050 | − | 0.721977i | 0.279292 | − | 0.960206i | \(-0.409900\pi\) |
0.971209 | + | 0.238229i | \(0.0765669\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.11985 | − | 7.13579i | 0.172410 | − | 0.298623i | −0.766852 | − | 0.641824i | \(-0.778178\pi\) |
0.939262 | + | 0.343201i | \(0.111511\pi\) | |||||||
\(572\) | −4.16524 | − | 1.11607i | −0.174158 | − | 0.0466654i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.15364 | − | 23.7315i | 0.0481520 | − | 0.990534i | ||||
\(575\) | 23.5212 | − | 0.570889i | 0.980904 | − | 0.0238077i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.910086 | − | 3.39649i | −0.0378874 | − | 0.141398i | 0.944391 | − | 0.328824i | \(-0.106652\pi\) |
−0.982279 | + | 0.187426i | \(0.939985\pi\) | |||||||
\(578\) | −4.23908 | − | 15.8204i | −0.176322 | − | 0.658044i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.17808 | + | 5.44425i | −0.0904397 | + | 0.226060i | ||||
\(581\) | −19.7132 | + | 30.6088i | −0.817843 | + | 1.26987i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −28.0627 | − | 7.51937i | −1.16224 | − | 0.311421i | ||||
\(584\) | −4.93262 | + | 8.54355i | −0.204113 | + | 0.353535i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.10531 | + | 2.37020i | −0.169589 | + | 0.0979122i | ||||
\(587\) | 5.37485 | − | 5.37485i | 0.221844 | − | 0.221844i | −0.587431 | − | 0.809275i | \(-0.699861\pi\) |
0.809275 | + | 0.587431i | \(0.199861\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.0909162i | 0.00374613i | ||||||||
\(590\) | 19.1791 | + | 14.3503i | 0.789590 | + | 0.590792i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.248174 | − | 0.0664979i | 0.0101999 | − | 0.00273305i | ||||
\(593\) | −0.190155 | + | 0.709668i | −0.00780872 | + | 0.0291426i | −0.969720 | − | 0.244218i | \(-0.921469\pi\) |
0.961912 | + | 0.273361i | \(0.0881353\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.80106 | + | 2.70248i | −0.155828 | + | 0.110791i | ||||
\(596\) | 4.84185 | 0.198330 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.33897 | − | 1.43057i | 0.218327 | − | 0.0585005i | ||||
\(599\) | −7.23778 | − | 4.17873i | −0.295727 | − | 0.170738i | 0.344794 | − | 0.938678i | \(-0.387949\pi\) |
−0.640522 | + | 0.767940i | \(0.721282\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.9236i | 1.62852i | 0.580501 | + | 0.814259i | \(0.302857\pi\) | ||||
−0.580501 | + | 0.814259i | \(0.697143\pi\) | |||||||
\(602\) | −1.31508 | + | 1.19315i | −0.0535985 | + | 0.0486290i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.69995 | − | 5.02292i | 0.353996 | − | 0.204380i | ||||
\(605\) | −3.42523 | − | 4.35344i | −0.139255 | − | 0.176993i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.2758 | + | 8.91623i | 1.35062 | + | 0.361899i | 0.860365 | − | 0.509678i | \(-0.170235\pi\) |
0.490259 | + | 0.871577i | \(0.336902\pi\) | |||||||
\(608\) | 1.54802 | + | 1.54802i | 0.0627804 | + | 0.0627804i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.75465 | − | 4.09485i | −0.0710436 | − | 0.165796i | ||||
\(611\) | −3.75885 | − | 6.51051i | −0.152067 | − | 0.263387i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.46832 | − | 31.6042i | −0.342032 | − | 1.27648i | −0.896041 | − | 0.443971i | \(-0.853569\pi\) |
0.554009 | − | 0.832510i | \(-0.313097\pi\) | |||||||
\(614\) | 0.753393 | + | 1.30491i | 0.0304044 | + | 0.0526620i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.63753 | + | 4.44231i | −0.348016 | + | 0.178986i | ||||
\(617\) | 15.5005 | + | 15.5005i | 0.624025 | + | 0.624025i | 0.946558 | − | 0.322533i | \(-0.104534\pi\) |
−0.322533 | + | 0.946558i | \(0.604534\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.31138 | − | 7.46752i | 0.173289 | − | 0.300145i | −0.766279 | − | 0.642508i | \(-0.777894\pi\) |
0.939568 | + | 0.342363i | \(0.111227\pi\) | |||||||
\(620\) | −0.0574201 | − | 0.0729806i | −0.00230605 | − | 0.00293097i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9.76397 | + | 9.76397i | −0.391500 | + | 0.391500i | ||||
\(623\) | 2.80254 | − | 2.54269i | 0.112281 | − | 0.101871i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.0187 | − | 13.5356i | 0.840749 | − | 0.541425i | ||||
\(626\) | −20.2191 | − | 11.6735i | −0.808119 | − | 0.466568i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.33762 | − | 23.6523i | 0.252898 | − | 0.943830i | ||||
\(629\) | 0.202545 | 0.00807600 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.13675 | −0.164682 | −0.0823408 | − | 0.996604i | \(-0.526240\pi\) | ||||
−0.0823408 | + | 0.996604i | \(0.526240\pi\) | |||||||
\(632\) | 3.47109 | − | 12.9543i | 0.138073 | − | 0.515294i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 11.4219 | + | 6.59442i | 0.453620 | + | 0.261898i | ||||
\(635\) | −33.5556 | − | 25.1072i | −1.33161 | − | 0.996349i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.69827 | − | 2.88840i | −0.305017 | − | 0.114443i | ||||
\(638\) | −6.80736 | + | 6.80736i | −0.269506 | + | 0.269506i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.22032 | − | 0.264946i | −0.0877657 | − | 0.0104729i | ||||
\(641\) | 5.42807 | − | 9.40169i | 0.214396 | − | 0.371345i | −0.738690 | − | 0.674046i | \(-0.764555\pi\) |
0.953086 | + | 0.302701i | \(0.0978884\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.06230 | − | 8.06230i | −0.317946 | − | 0.317946i | 0.530032 | − | 0.847978i | \(-0.322180\pi\) |
−0.847978 | + | 0.530032i | \(0.822180\pi\) | |||||||
\(644\) | 6.74114 | − | 10.4670i | 0.265638 | − | 0.412457i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.862920 | + | 1.49462i | 0.0339511 | + | 0.0588051i | ||||
\(647\) | 2.69865 | + | 10.0715i | 0.106095 | + | 0.395951i | 0.998467 | − | 0.0553490i | \(-0.0176271\pi\) |
−0.892372 | + | 0.451300i | \(0.850960\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.6632 | + | 34.0577i | 0.771848 | + | 1.33688i | ||||
\(650\) | 4.05090 | − | 4.25243i | 0.158889 | − | 0.166794i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15.5320 | − | 15.5320i | −0.608279 | − | 0.608279i | ||||
\(653\) | −6.41946 | − | 1.72009i | −0.251213 | − | 0.0673123i | 0.131015 | − | 0.991380i | \(-0.458176\pi\) |
−0.382228 | + | 0.924068i | \(0.624843\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −24.9449 | + | 19.6263i | −0.974677 | + | 0.766862i | ||||
\(656\) | 7.77713 | − | 4.49013i | 0.303646 | − | 0.175310i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −16.1241 | − | 5.17163i | −0.628582 | − | 0.201611i | ||||
\(659\) | 22.0345i | 0.858343i | 0.903223 | + | 0.429172i | \(0.141194\pi\) | ||||
−0.903223 | + | 0.429172i | \(0.858806\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.94278 | − | 5.74047i | −0.386729 | − | 0.223278i | 0.294013 | − | 0.955802i | \(-0.405009\pi\) |
−0.680742 | + | 0.732523i | \(0.738343\pi\) | |||||||
\(662\) | 18.4453 | − | 4.94240i | 0.716897 | − | 0.192092i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −13.7608 | −0.534021 | ||||||||
\(665\) | −8.25358 | + | 9.98115i | −0.320060 | + | 0.387053i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.19379 | − | 11.9194i | 0.123664 | − | 0.461521i | ||||
\(668\) | −4.29774 | + | 1.15158i | −0.166285 | + | 0.0445558i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.11082 | − | 14.6568i | −0.0815482 | − | 0.566243i | ||||
\(671\) | − | 7.31407i | − | 0.282356i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.2073 | + | 15.2073i | −0.586198 | + | 0.586198i | −0.936600 | − | 0.350402i | \(-0.886045\pi\) |
0.350402 | + | 0.936600i | \(0.386045\pi\) | |||||||
\(674\) | 0.597952 | − | 0.345228i | 0.0230322 | − | 0.0132977i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.81014 | + | 10.0635i | −0.223467 | + | 0.387056i | ||||
\(677\) | 5.54296 | + | 1.48523i | 0.213033 | + | 0.0570821i | 0.363757 | − | 0.931494i | \(-0.381494\pi\) |
−0.150724 | + | 0.988576i | \(0.548160\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.96224 | − | 6.41606i | −0.382316 | − | 0.246226i | ||||
\(680\) | −1.63665 | − | 0.654772i | −0.0627626 | − | 0.0251094i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.0394591 | − | 0.147264i | −0.00151097 | − | 0.00563901i | ||||
\(683\) | −5.02900 | − | 18.7685i | −0.192430 | − | 0.718157i | −0.992917 | − | 0.118808i | \(-0.962093\pi\) |
0.800488 | − | 0.599349i | \(-0.204574\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −38.9821 | + | 16.7039i | −1.48943 | + | 0.638222i | ||||
\(686\) | −17.2137 | + | 6.83301i | −0.657220 | + | 0.260886i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.648273 | − | 0.173704i | −0.0247152 | − | 0.00662241i | ||||
\(689\) | 4.64782 | − | 8.05027i | 0.177068 | − | 0.306691i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.0914 | − | 11.0224i | 0.726270 | − | 0.419312i | −0.0907861 | − | 0.995870i | \(-0.528938\pi\) |
0.817056 | + | 0.576558i | \(0.195605\pi\) | |||||||
\(692\) | −3.69572 | + | 3.69572i | −0.140490 | + | 0.140490i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 3.80998i | − | 0.144625i | ||||||
\(695\) | 18.2305 | − | 2.62550i | 0.691524 | − | 0.0995908i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.83821 | − | 1.83229i | 0.259016 | − | 0.0694031i | ||||
\(698\) | −2.04804 | + | 7.64340i | −0.0775196 | + | 0.289307i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.321526 | − | 13.2248i | 0.0121526 | − | 0.499852i | ||||
\(701\) | 18.0270 | 0.680870 | 0.340435 | − | 0.940268i | \(-0.389426\pi\) | ||||
0.340435 | + | 0.940268i | \(0.389426\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.543308 | − | 0.145579i | 0.0204913 | − | 0.00549062i | ||||
\(704\) | −3.17930 | − | 1.83557i | −0.119824 | − | 0.0691807i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 25.7787i | − | 0.970196i | ||||||
\(707\) | −0.0581046 | + | 0.181158i | −0.00218525 | + | 0.00681316i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.0614 | + | 21.3974i | −1.39187 | + | 0.803597i | −0.993522 | − | 0.113637i | \(-0.963750\pi\) |
−0.398349 | + | 0.917234i | \(0.630417\pi\) | |||||||
\(710\) | −2.15077 | + | 18.0240i | −0.0807170 | + | 0.676429i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.38152 | + | 0.370178i | 0.0517748 | + | 0.0138730i | ||||
\(713\) | 0.138183 | + | 0.138183i | 0.00517498 | + | 0.00517498i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.86292 | − | 3.79777i | 0.331454 | − | 0.142029i | ||||
\(716\) | 6.28428 | + | 10.8847i | 0.234854 | + | 0.406780i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.68822 | + | 10.0326i | 0.100324 | + | 0.374413i | ||||
\(719\) | 2.72691 | + | 4.72315i | 0.101697 | + | 0.176144i | 0.912384 | − | 0.409336i | \(-0.134240\pi\) |
−0.810687 | + | 0.585480i | \(0.800906\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −43.8142 | − | 2.12990i | −1.63172 | − | 0.0793217i | ||||
\(722\) | −10.0461 | − | 10.0461i | −0.373876 | − | 0.373876i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.83712 | + | 10.1102i | −0.216935 | + | 0.375742i | ||||
\(725\) | −3.69989 | − | 12.5790i | −0.137411 | − | 0.467171i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.6781 | − | 16.6781i | 0.618555 | − | 0.618555i | −0.326606 | − | 0.945161i | \(-0.605905\pi\) |
0.945161 | + | 0.326606i | \(0.105905\pi\) | |||||||
\(728\) | −0.657639 | − | 3.03736i | −0.0243737 | − | 0.112572i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.14447 | − | 21.8341i | −0.116382 | − | 0.808116i | ||||
\(731\) | −0.458200 | − | 0.264542i | −0.0169471 | − | 0.00978443i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.79960 | + | 32.8405i | −0.325021 | + | 1.21299i | 0.589271 | + | 0.807936i | \(0.299415\pi\) |
−0.914291 | + | 0.405057i | \(0.867252\pi\) | |||||||
\(734\) | −8.68601 | −0.320607 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.70563 | 0.173452 | ||||||||
\(737\) | 6.29231 | − | 23.4832i | 0.231780 | − | 0.865016i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.0733 | + | 14.4761i | 0.922335 | + | 0.532510i | 0.884379 | − | 0.466769i | \(-0.154582\pi\) |
0.0379557 | + | 0.999279i | \(0.487915\pi\) | |||||||
\(740\) | −0.344183 | + | 0.459998i | −0.0126524 | + | 0.0169099i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.43074 | − | 20.4637i | −0.162658 | − | 0.751247i | ||||
\(743\) | −34.0351 | + | 34.0351i | −1.24863 | + | 1.24863i | −0.292300 | + | 0.956327i | \(0.594421\pi\) |
−0.956327 | + | 0.292300i | \(0.905579\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.50881 | + | 6.69461i | −0.311739 | + | 0.245272i | ||||
\(746\) | −6.65477 | + | 11.5264i | −0.243649 | + | 0.422012i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.04643 | − | 2.04643i | −0.0748247 | − | 0.0748247i | ||||
\(749\) | −12.0753 | − | 0.587006i | −0.441221 | − | 0.0214487i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.30569 | + | 16.1179i | 0.339569 | + | 0.588151i | 0.984352 | − | 0.176215i | \(-0.0563853\pi\) |
−0.644782 | + | 0.764366i | \(0.723052\pi\) | |||||||
\(752\) | −1.65648 | − | 6.18205i | −0.0604055 | − | 0.225436i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.54013 | − | 2.66759i | −0.0560883 | − | 0.0971478i | ||||
\(755\) | −8.34385 | + | 20.8560i | −0.303664 | + | 0.759029i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.7422 | + | 29.7422i | 1.08100 | + | 1.08100i | 0.996416 | + | 0.0845825i | \(0.0269557\pi\) |
0.0845825 | + | 0.996416i | \(0.473044\pi\) | |||||||
\(758\) | −24.4816 | − | 6.55984i | −0.889213 | − | 0.238264i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.86078 | − | 0.580027i | −0.176319 | − | 0.0210398i | ||||
\(761\) | −17.6474 | + | 10.1887i | −0.639718 | + | 0.369341i | −0.784506 | − | 0.620122i | \(-0.787083\pi\) |
0.144788 | + | 0.989463i | \(0.453750\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.6278 | − | 45.6066i | 0.529563 | − | 1.65107i | ||||
\(764\) | − | 15.5034i | − | 0.560894i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.9357 | + | 9.20046i | 0.575779 | + | 0.332426i | ||||
\(767\) | −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 | \(0.235412\pi\) | |||||||
\(770\) | 9.03694 | − | 19.7494i | 0.325669 | − | 0.711719i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.32883 | − | 8.69132i | 0.0838165 | − | 0.312808i | ||||
\(773\) | −23.8577 | + | 6.39265i | −0.858101 | + | 0.229928i | −0.660936 | − | 0.750443i | \(-0.729840\pi\) |
−0.197166 | + | 0.980370i | \(0.563174\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.201814 | + | 0.0488599i | 0.00724938 | + | 0.00175510i | ||||
\(776\) | − | 4.47871i | − | 0.160776i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.8091 | − | 15.8091i | 0.566784 | − | 0.566784i | ||||
\(779\) | 17.0259 | − | 9.82991i | 0.610017 | − | 0.352193i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.9007 | + | 25.8088i | −0.533190 | + | 0.923513i | ||||
\(782\) | 3.58321 | + | 0.960117i | 0.128135 | + | 0.0343337i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.69411 | − | 4.07150i | −0.203361 | − | 0.145411i | ||||
\(785\) | 21.5656 | + | 50.3280i | 0.769710 | + | 1.79628i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.12442 | + | 7.92843i | 0.0757273 | + | 0.282618i | 0.993397 | − | 0.114725i | \(-0.0365988\pi\) |
−0.917670 | + | 0.397343i | \(0.869932\pi\) | |||||||
\(788\) | 4.46372 | + | 16.6588i | 0.159013 | + | 0.593446i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 11.8114 | + | 27.5645i | 0.420231 | + | 0.980701i | ||||
\(791\) | −4.78348 | − | 3.08075i | −0.170081 | − | 0.109539i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.26046 | + | 0.605689i | 0.0802713 | + | 0.0215086i | ||||
\(794\) | −7.89197 | + | 13.6693i | −0.280076 | + | 0.485105i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.56140 | + | 4.36557i | −0.268007 | + | 0.154734i | ||||
\(797\) | −11.7928 | + | 11.7928i | −0.417722 | + | 0.417722i | −0.884418 | − | 0.466696i | \(-0.845444\pi\) |
0.466696 | + | 0.884418i | \(0.345444\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 5.04544i | − | 0.178495i | ||||||
\(800\) | 4.26819 | − | 2.60433i | 0.150903 | − | 0.0920770i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 13.4945 | − | 3.61585i | 0.476508 | − | 0.127680i | ||||
\(803\) | 9.37358 | − | 34.9827i | 0.330786 | − | 1.23451i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.62573 | + | 27.7148i | 0.0925447 | + | 0.976819i | ||||
\(806\) | 0.0487805 | 0.00171822 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.0694570 | + | 0.0186109i | −0.00244349 | + | 0.000654730i | ||||
\(809\) | 28.8498 | + | 16.6564i | 1.01430 | + | 0.585609i | 0.912449 | − | 0.409191i | \(-0.134189\pi\) |
0.101855 | + | 0.994799i | \(0.467522\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 55.2368i | − | 1.93963i | −0.243850 | − | 0.969813i | \(-0.578410\pi\) | ||
0.243850 | − | 0.969813i | \(-0.421590\pi\) | |||||||
\(812\) | −6.60661 | − | 2.11900i | −0.231847 | − | 0.0743623i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.816852 | + | 0.471610i | −0.0286307 | + | 0.0165299i | ||||
\(815\) | 48.7704 | + | 5.81968i | 1.70835 | + | 0.203855i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.41922 | − | 0.380278i | −0.0496521 | − | 0.0133042i | ||||
\(818\) | 0.221580 | + | 0.221580i | 0.00774737 | + | 0.00774737i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.45881 | + | 18.6438i | −0.260473 | + | 0.651070i | ||||
\(821\) | 9.31457 | + | 16.1333i | 0.325081 | + | 0.563056i | 0.981529 | − | 0.191315i | \(-0.0612752\pi\) |
−0.656448 | + | 0.754371i | \(0.727942\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.37130 | − | 16.3139i | −0.152374 | − | 0.568668i | −0.999316 | − | 0.0369821i | \(-0.988226\pi\) |
0.846942 | − | 0.531685i | \(-0.178441\pi\) | |||||||
\(824\) | −8.28988 | − | 14.3585i | −0.288792 | − | 0.500202i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.3461 | + | 23.8280i | −0.533960 | + | 0.829081i | ||||
\(827\) | 5.62716 | + | 5.62716i | 0.195675 | + | 0.195675i | 0.798143 | − | 0.602468i | \(-0.205816\pi\) |
−0.602468 | + | 0.798143i | \(0.705816\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.29757 | − | 5.71155i | 0.114529 | − | 0.198370i | −0.803062 | − | 0.595895i | \(-0.796797\pi\) |
0.917591 | + | 0.397525i | \(0.130131\pi\) | |||||||
\(830\) | 24.1824 | − | 19.0264i | 0.839384 | − | 0.660416i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.830578 | − | 0.830578i | 0.0287951 | − | 0.0287951i | ||||
\(833\) | −3.50517 | − | 4.26213i | −0.121447 | − | 0.147674i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.96038 | − | 7.96601i | 0.206268 | − | 0.275675i | ||||
\(836\) | −6.96021 | − | 4.01848i | −0.240724 | − | 0.138982i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8.18525 | + | 30.5478i | −0.282755 | + | 1.05526i | ||||
\(839\) | −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 | ||||||||
\(842\) | 6.26698 | − | 23.3887i | 0.215974 | − | 0.806027i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.67744 | + | 5.58727i | 0.333111 | + | 0.192322i | ||||
\(845\) | −3.70387 | − | 25.7184i | −0.127417 | − | 0.884740i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.85413 | − | 4.40407i | 0.166790 | − | 0.151326i | ||||
\(848\) | 5.59589 | − | 5.59589i | 0.192164 | − | 0.192164i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.78148 | − | 1.11226i | 0.129704 | − | 0.0381502i | ||||
\(851\) | 0.604505 | − | 1.04703i | 0.0207222 | − | 0.0358918i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.9594 | + | 14.9594i | 0.512200 | + | 0.512200i | 0.915200 | − | 0.403000i | \(-0.132032\pi\) |
−0.403000 | + | 0.915200i | \(0.632032\pi\) | |||||||
\(854\) | 4.68755 | − | 2.41082i | 0.160405 | − | 0.0824967i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.28471 | − | 3.95723i | −0.0780897 | − | 0.135255i | ||||
\(857\) | −3.12136 | − | 11.6491i | −0.106623 | − | 0.397924i | 0.891901 | − | 0.452231i | \(-0.149372\pi\) |
−0.998524 | + | 0.0543068i | \(0.982705\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.90061 | − | 5.02401i | −0.0989677 | − | 0.171417i | 0.812290 | − | 0.583254i | \(-0.198221\pi\) |
−0.911258 | + | 0.411837i | \(0.864887\pi\) | |||||||
\(860\) | 1.37941 | − | 0.591080i | 0.0470376 | − | 0.0201557i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.10172 | − | 1.10172i | −0.0375249 | − | 0.0375249i | ||||
\(863\) | −2.90586 | − | 0.778623i | −0.0989167 | − | 0.0265046i | 0.209021 | − | 0.977911i | \(-0.432972\pi\) |
−0.307938 | + | 0.951406i | \(0.599639\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.38475 | − | 11.6046i | 0.0470829 | − | 0.394567i | ||||
\(866\) | 7.69343 | − | 4.44180i | 0.261433 | − | 0.150939i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.0813742 | − | 0.0738294i | 0.00276202 | − | 0.00250593i | ||||
\(869\) | 49.2347i | 1.67017i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.73657 | + | 3.88936i | 0.228260 | + | 0.131786i | ||||
\(872\) | 17.4858 | − | 4.68530i | 0.592143 | − | 0.158664i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 10.3017 | 0.348460 | ||||||||
\(875\) | 17.7204 | + | 23.6852i | 0.599058 | + | 0.800706i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.07228 | − | 33.8582i | 0.306349 | − | 1.14331i | −0.625428 | − | 0.780282i | \(-0.715076\pi\) |
0.931778 | − | 0.363030i | \(-0.118258\pi\) | |||||||
\(878\) | 23.0994 | − | 6.18945i | 0.779565 | − | 0.208884i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8.12509 | − | 1.17015i | 0.273897 | − | 0.0394456i | ||||
\(881\) | − | 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 | \(-0.810611\pi\) |
0.560495 | + | 0.828158i | \(0.310611\pi\) | |||||||
\(884\) | 0.801929 | − | 0.462994i | 0.0269718 | − | 0.0155722i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.43103 | − | 11.1389i | 0.216055 | − | 0.374218i | ||||
\(887\) | 19.6954 | + | 5.27738i | 0.661308 | + | 0.177197i | 0.573836 | − | 0.818970i | \(-0.305455\pi\) |
0.0874718 | + | 0.996167i | \(0.472121\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 26.8495 | − | 41.6893i | 0.900503 | − | 1.39821i | ||||
\(890\) | −2.93964 | + | 1.25964i | −0.0985371 | + | 0.0422233i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.273349 | − | 1.02015i | −0.00915241 | − | 0.0341573i | ||||
\(893\) | −3.62640 | − | 13.5339i | −0.121353 | − | 0.452895i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −26.0934 | − | 10.4392i | −0.872207 | − | 0.348943i | ||||
\(896\) | 0.128464 | − | 2.64263i | 0.00429168 | − | 0.0882841i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −17.2836 | − | 4.63111i | −0.576760 | − | 0.154542i | ||||
\(899\) | 0.0544519 | − | 0.0943134i | 0.00181607 | − | 0.00314553i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.40287 | − | 3.11935i | 0.179996 | − | 0.103921i | ||||
\(902\) | −23.3118 | + | 23.3118i | −0.776197 | + | 0.776197i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 2.15051i | − | 0.0715247i | ||||||
\(905\) | −3.72107 | − | 25.8378i | −0.123693 | − | 0.858879i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.29276 | − | 1.68614i | 0.208948 | − | 0.0559874i | −0.152827 | − | 0.988253i | \(-0.548838\pi\) |
0.361775 | + | 0.932266i | \(0.382171\pi\) | |||||||
\(908\) | 0.807609 | − | 3.01404i | 0.0268014 | − | 0.100024i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5.35532 | + | 4.42840i | 0.177527 | + | 0.146800i | ||||
\(911\) | 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 | ||||
\(914\) | −29.6277 | − | 17.1056i | −0.979997 | − | 0.565802i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 8.42181i | − | 0.278264i | ||||||
\(917\) | −25.2350 | − | 27.8138i | −0.833333 | − | 0.918493i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −31.2542 | + | 18.0446i | −1.03098 | + | 0.595236i | −0.917265 | − | 0.398277i | \(-0.869608\pi\) |
−0.113714 | + | 0.993513i | \(0.536275\pi\) | |||||||
\(920\) | −8.26943 | + | 6.50627i | −0.272635 | + | 0.214505i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 22.5515 | + | 6.04266i | 0.742695 | + | 0.199004i | ||||
\(923\) | −6.74244 | − | 6.74244i | −0.221930 | − | 0.221930i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.0311706 | − | 1.28426i | −0.00102488 | − | 0.0422263i | ||||
\(926\) | −2.81789 | − | 4.88073i | −0.0926017 | − | 0.160391i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.678717 | − | 2.53301i | −0.0222800 | − | 0.0831500i | ||||
\(929\) | 21.2041 | + | 36.7266i | 0.695685 | + | 1.20496i | 0.969949 | + | 0.243307i | \(0.0782323\pi\) |
−0.274264 | + | 0.961654i | \(0.588434\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.4657 | − | 8.91344i | −0.408547 | − | 0.292126i | ||||
\(932\) | 16.1198 | + | 16.1198i | 0.528023 | + | 0.528023i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.44290 | − | 4.23123i | 0.0799342 | − | 0.138450i | ||||
\(935\) | 6.42578 | + | 0.766776i | 0.210145 | + | 0.0250762i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.06709 | − | 4.06709i | 0.132866 | − | 0.132866i | −0.637546 | − | 0.770412i | \(-0.720050\pi\) |
0.770412 | + | 0.637546i | \(0.220050\pi\) | |||||||
\(938\) | 17.1243 | − | 3.70770i | 0.559129 | − | 0.121061i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 11.4587 | + | 8.57367i | 0.373740 | + | 0.279642i | ||||
\(941\) | 17.4071 | + | 10.0500i | 0.567455 | + | 0.327621i | 0.756132 | − | 0.654419i | \(-0.227087\pi\) |
−0.188677 | + | 0.982039i | \(0.560420\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.9371 | − | 40.8179i | 0.356162 | − | 1.32921i | ||||
\(944\) | −10.7123 | −0.348656 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.46386 | 0.0801069 | ||||||||
\(947\) | 15.2583 | − | 56.9449i | 0.495830 | − | 1.85046i | −0.0295030 | − | 0.999565i | \(-0.509392\pi\) |
0.525333 | − | 0.850897i | \(-0.323941\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.0354 | + | 5.79393i | 0.325762 | + | 0.188079i | ||||
\(950\) | 9.34404 | − | 5.70147i | 0.303161 | − | 0.184980i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.637013 | − | 1.98608i | 0.0206457 | − | 0.0643691i | ||||
\(953\) | 31.1044 | − | 31.1044i | 1.00757 | − | 1.00757i | 0.00759828 | − | 0.999971i | \(-0.497581\pi\) |
0.999971 | − | 0.00759828i | \(-0.00241863\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.4359 | + | 27.2448i | 0.693648 | + | 0.881622i | ||||
\(956\) | −11.9985 | + | 20.7821i | −0.388060 | + | 0.672140i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.0996 | − | 12.0996i | −0.390921 | − | 0.390921i | ||||
\(959\) | −22.9505 | − | 44.6245i | −0.741111 | − | 1.44100i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.4991 | − | 26.8453i | −0.499972 | − | 0.865977i | ||||
\(962\) | −0.0781094 | − | 0.291508i | −0.00251835 | − | 0.00939861i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 12.3937 | + | 21.4666i | 0.399175 | + | 0.691391i | ||||
\(965\) | 7.92454 | + | 18.4936i | 0.255100 | + | 0.595331i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.5036 | − | 21.5036i | −0.691510 | − | 0.691510i | 0.271054 | − | 0.962564i | \(-0.412628\pi\) |
−0.962564 | + | 0.271054i | \(0.912628\pi\) | |||||||
\(968\) | 2.39287 | + | 0.641168i | 0.0769098 | + | 0.0206079i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.19252 | + | 7.87065i | 0.198830 | + | 0.252711i | ||||
\(971\) | 45.3034 | − | 26.1559i | 1.45385 | − | 0.839384i | 0.455158 | − | 0.890411i | \(-0.349583\pi\) |
0.998697 | + | 0.0510273i | \(0.0162496\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.61174 | + | 21.2997i | 0.147845 | + | 0.682836i | ||||
\(974\) | 0.130300i | 0.00417507i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.72539 | + | 0.996157i | 0.0552285 | + | 0.0318862i | ||||
\(977\) | 54.6658 | − | 14.6477i | 1.74891 | − | 0.468620i | 0.764520 | − | 0.644599i | \(-0.222976\pi\) |
0.984394 | + | 0.175979i | \(0.0563092\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.25068 | −0.167813 | ||||||||
\(980\) | 15.6360 | − | 0.717962i | 0.499474 | − | 0.0229345i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6.98541 | + | 26.0699i | −0.222913 | + | 0.831924i | ||||
\(983\) | −14.9514 | + | 4.00621i | −0.476875 | + | 0.127778i | −0.489247 | − | 0.872145i | \(-0.662728\pi\) |
0.0123723 | + | 0.999923i | \(0.496062\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −30.8777 | − | 23.1035i | −0.983845 | − | 0.736139i | ||||
\(986\) | − | 2.06729i | − | 0.0658361i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.81832 | − | 1.81832i | 0.0578486 | − | 0.0578486i | ||||
\(989\) | −2.73504 | + | 1.57907i | −0.0869691 | + | 0.0502116i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.8648 | − | 46.5311i | 0.853388 | − | 1.47811i | −0.0247453 | − | 0.999694i | \(-0.507877\pi\) |
0.878133 | − | 0.478417i | \(-0.158789\pi\) | |||||||
\(992\) | 0.0401138 | + | 0.0107485i | 0.00127362 | + | 0.000341264i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −21.4523 | − | 1.04284i | −0.680424 | − | 0.0330769i | ||||
\(995\) | 7.25190 | − | 18.1266i | 0.229901 | − | 0.574653i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.97217 | + | 37.2167i | 0.315822 | + | 1.17866i | 0.923222 | + | 0.384267i | \(0.125546\pi\) |
−0.607400 | + | 0.794396i | \(0.707787\pi\) | |||||||
\(998\) | 0.0249241 | + | 0.0930180i | 0.000788959 | + | 0.00294443i | ||||
\(999\) | 0 | 0 |
(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 | 630.2.bv.c.577.4 | 16 | ||
3.2 | odd | 2 | 70.2.k.a.17.1 | yes | 16 | ||
5.3 | odd | 4 | inner | 630.2.bv.c.73.1 | 16 | ||
7.5 | odd | 6 | inner | 630.2.bv.c.397.1 | 16 | ||
12.11 | even | 2 | 560.2.ci.c.17.4 | 16 | |||
15.2 | even | 4 | 350.2.o.c.143.2 | 16 | |||
15.8 | even | 4 | 70.2.k.a.3.3 | ✓ | 16 | ||
15.14 | odd | 2 | 350.2.o.c.157.4 | 16 | |||
21.2 | odd | 6 | 490.2.l.c.117.4 | 16 | |||
21.5 | even | 6 | 70.2.k.a.47.3 | yes | 16 | ||
21.11 | odd | 6 | 490.2.g.c.97.4 | 16 | |||
21.17 | even | 6 | 490.2.g.c.97.1 | 16 | |||
21.20 | even | 2 | 490.2.l.c.227.2 | 16 | |||
35.33 | even | 12 | inner | 630.2.bv.c.523.4 | 16 | ||
60.23 | odd | 4 | 560.2.ci.c.353.4 | 16 | |||
84.47 | odd | 6 | 560.2.ci.c.257.4 | 16 | |||
105.23 | even | 12 | 490.2.l.c.313.2 | 16 | |||
105.38 | odd | 12 | 490.2.g.c.293.4 | 16 | |||
105.47 | odd | 12 | 350.2.o.c.243.4 | 16 | |||
105.53 | even | 12 | 490.2.g.c.293.1 | 16 | |||
105.68 | odd | 12 | 70.2.k.a.33.1 | yes | 16 | ||
105.83 | odd | 4 | 490.2.l.c.423.4 | 16 | |||
105.89 | even | 6 | 350.2.o.c.257.2 | 16 | |||
420.383 | even | 12 | 560.2.ci.c.33.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.k.a.3.3 | ✓ | 16 | 15.8 | even | 4 | ||
70.2.k.a.17.1 | yes | 16 | 3.2 | odd | 2 | ||
70.2.k.a.33.1 | yes | 16 | 105.68 | odd | 12 | ||
70.2.k.a.47.3 | yes | 16 | 21.5 | even | 6 | ||
350.2.o.c.143.2 | 16 | 15.2 | even | 4 | |||
350.2.o.c.157.4 | 16 | 15.14 | odd | 2 | |||
350.2.o.c.243.4 | 16 | 105.47 | odd | 12 | |||
350.2.o.c.257.2 | 16 | 105.89 | even | 6 | |||
490.2.g.c.97.1 | 16 | 21.17 | even | 6 | |||
490.2.g.c.97.4 | 16 | 21.11 | odd | 6 | |||
490.2.g.c.293.1 | 16 | 105.53 | even | 12 | |||
490.2.g.c.293.4 | 16 | 105.38 | odd | 12 | |||
490.2.l.c.117.4 | 16 | 21.2 | odd | 6 | |||
490.2.l.c.227.2 | 16 | 21.20 | even | 2 | |||
490.2.l.c.313.2 | 16 | 105.23 | even | 12 | |||
490.2.l.c.423.4 | 16 | 105.83 | odd | 4 | |||
560.2.ci.c.17.4 | 16 | 12.11 | even | 2 | |||
560.2.ci.c.33.4 | 16 | 420.383 | even | 12 | |||
560.2.ci.c.257.4 | 16 | 84.47 | odd | 6 | |||
560.2.ci.c.353.4 | 16 | 60.23 | odd | 4 | |||
630.2.bv.c.73.1 | 16 | 5.3 | odd | 4 | inner | ||
630.2.bv.c.397.1 | 16 | 7.5 | odd | 6 | inner | ||
630.2.bv.c.523.4 | 16 | 35.33 | even | 12 | inner | ||
630.2.bv.c.577.4 | 16 | 1.1 | even | 1 | trivial |