Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(26,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.t (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 3 x^{19} + 8 x^{18} - 15 x^{17} + 18 x^{16} - 45 x^{15} + 59 x^{14} - 147 x^{13} + 271 x^{12} + \cdots + 59049 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 26.8 | ||
Root | \(1.73056 + 0.0718963i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.26 |
Dual form | 525.2.t.h.101.8 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.46613 | + | 0.846473i | 1.03671 | + | 0.598547i | 0.918901 | − | 0.394489i | \(-0.129078\pi\) |
0.117813 | + | 0.993036i | \(0.462412\pi\) | |||||||
\(3\) | −1.73056 | − | 0.0718963i | −0.999138 | − | 0.0415094i | ||||
\(4\) | 0.433034 | + | 0.750036i | 0.216517 | + | 0.375018i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.47637 | − | 1.57028i | −1.01097 | − | 0.641064i | ||||
\(7\) | 1.71236 | + | 2.01688i | 0.647212 | + | 0.762310i | ||||
\(8\) | − | 1.91969i | − | 0.678712i | ||||||
\(9\) | 2.98966 | + | 0.248842i | 0.996554 | + | 0.0829472i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.399511 | − | 0.230658i | 0.120457 | − | 0.0695460i | −0.438561 | − | 0.898702i | \(-0.644512\pi\) |
0.559018 | + | 0.829156i | \(0.311178\pi\) | |||||||
\(12\) | −0.695465 | − | 1.32911i | −0.200763 | − | 0.383682i | ||||
\(13\) | 3.38501i | 0.938834i | 0.882977 | + | 0.469417i | \(0.155536\pi\) | ||||
−0.882977 | + | 0.469417i | \(0.844464\pi\) | |||||||
\(14\) | 0.803314 | + | 4.40649i | 0.214695 | + | 1.17768i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.49103 | − | 4.31459i | 0.622758 | − | 1.07865i | ||||
\(17\) | 2.75166 | + | 4.76601i | 0.667374 | + | 1.15593i | 0.978636 | + | 0.205602i | \(0.0659152\pi\) |
−0.311261 | + | 0.950324i | \(0.600751\pi\) | |||||||
\(18\) | 4.17261 | + | 2.89550i | 0.983493 | + | 0.682477i | ||||
\(19\) | 3.49334 | + | 2.01688i | 0.801428 | + | 0.462705i | 0.843970 | − | 0.536390i | \(-0.180212\pi\) |
−0.0425421 | + | 0.999095i | \(0.513546\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.81833 | − | 3.61345i | −0.615011 | − | 0.788519i | ||||
\(22\) | 0.780983 | 0.166506 | ||||||||
\(23\) | 3.90097 | + | 2.25223i | 0.813409 | + | 0.469622i | 0.848138 | − | 0.529775i | \(-0.177724\pi\) |
−0.0347292 | + | 0.999397i | \(0.511057\pi\) | |||||||
\(24\) | −0.138018 | + | 3.32213i | −0.0281729 | + | 0.678127i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.86532 | + | 4.96289i | −0.561936 | + | 0.973302i | ||||
\(27\) | −5.15589 | − | 0.645580i | −0.992252 | − | 0.124242i | ||||
\(28\) | −0.771225 | + | 2.15771i | −0.145748 | + | 0.407769i | ||||
\(29\) | − | 7.71756i | − | 1.43311i | −0.697528 | − | 0.716557i | \(-0.745717\pi\) | ||
0.697528 | − | 0.716557i | \(-0.254283\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.01611 | + | 1.74135i | −0.541710 | + | 0.312756i | −0.745772 | − | 0.666202i | \(-0.767919\pi\) |
0.204062 | + | 0.978958i | \(0.434586\pi\) | |||||||
\(32\) | 3.97938 | − | 2.29749i | 0.703461 | − | 0.406143i | ||||
\(33\) | −0.707961 | + | 0.370444i | −0.123240 | + | 0.0644860i | ||||
\(34\) | 9.31681i | 1.59782i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.10798 | + | 2.35011i | 0.184664 | + | 0.391685i | ||||
\(37\) | −2.89964 | + | 5.02232i | −0.476698 | + | 0.825665i | −0.999643 | − | 0.0267011i | \(-0.991500\pi\) |
0.522946 | + | 0.852366i | \(0.324833\pi\) | |||||||
\(38\) | 3.41448 | + | 5.91404i | 0.553901 | + | 0.959385i | ||||
\(39\) | 0.243370 | − | 5.85796i | 0.0389704 | − | 0.938025i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.25727 | 0.977221 | 0.488610 | − | 0.872502i | \(-0.337504\pi\) | ||||
0.488610 | + | 0.872502i | \(0.337504\pi\) | |||||||
\(42\) | −1.07337 | − | 7.68344i | −0.165625 | − | 1.18558i | ||||
\(43\) | −8.35453 | −1.27405 | −0.637027 | − | 0.770842i | \(-0.719836\pi\) | ||||
−0.637027 | + | 0.770842i | \(0.719836\pi\) | |||||||
\(44\) | 0.346004 | + | 0.199765i | 0.0521620 | + | 0.0301157i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.81290 | + | 6.60414i | 0.562182 | + | 0.973727i | ||||
\(47\) | 1.57980 | − | 2.73630i | 0.230438 | − | 0.399130i | −0.727499 | − | 0.686109i | \(-0.759317\pi\) |
0.957937 | + | 0.286978i | \(0.0926508\pi\) | |||||||
\(48\) | −4.62108 | + | 7.28756i | −0.666995 | + | 1.05187i | ||||
\(49\) | −1.13564 | + | 6.90727i | −0.162234 | + | 0.986752i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.41924 | − | 8.44568i | −0.618817 | − | 1.18263i | ||||
\(52\) | −2.53888 | + | 1.46582i | −0.352080 | + | 0.203273i | ||||
\(53\) | 10.0154 | − | 5.78238i | 1.37572 | − | 0.794271i | 0.384078 | − | 0.923301i | \(-0.374519\pi\) |
0.991641 | + | 0.129029i | \(0.0411861\pi\) | |||||||
\(54\) | −7.01277 | − | 5.31083i | −0.954316 | − | 0.722713i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.87179 | − | 3.28720i | 0.517389 | − | 0.439270i | ||||
\(57\) | −5.90043 | − | 3.74149i | −0.781531 | − | 0.495573i | ||||
\(58\) | 6.53271 | − | 11.3150i | 0.857786 | − | 1.48573i | ||||
\(59\) | −4.88061 | − | 8.45346i | −0.635401 | − | 1.10055i | −0.986430 | − | 0.164183i | \(-0.947501\pi\) |
0.351029 | − | 0.936365i | \(-0.385832\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.90647 | − | 3.98746i | −0.884283 | − | 0.510541i | −0.0122151 | − | 0.999925i | \(-0.503888\pi\) |
−0.872068 | + | 0.489384i | \(0.837222\pi\) | |||||||
\(62\) | −5.89604 | −0.748798 | ||||||||
\(63\) | 4.61750 | + | 6.45591i | 0.581750 | + | 0.813368i | ||||
\(64\) | −2.18506 | −0.273132 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.35154 | − | 0.0561498i | −0.166363 | − | 0.00691156i | ||||
\(67\) | 0.458116 | + | 0.793481i | 0.0559678 | + | 0.0969391i | 0.892652 | − | 0.450747i | \(-0.148842\pi\) |
−0.836684 | + | 0.547686i | \(0.815509\pi\) | |||||||
\(68\) | −2.38312 | + | 4.12768i | −0.288995 | + | 0.500555i | ||||
\(69\) | −6.58893 | − | 4.17808i | −0.793214 | − | 0.502981i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.52593i | 0.181094i | 0.995892 | + | 0.0905471i | \(0.0288616\pi\) | ||||
−0.995892 | + | 0.0905471i | \(0.971138\pi\) | |||||||
\(72\) | 0.477698 | − | 5.73922i | 0.0562972 | − | 0.676373i | ||||
\(73\) | 6.75338 | − | 3.89906i | 0.790423 | − | 0.456351i | −0.0496883 | − | 0.998765i | \(-0.515823\pi\) |
0.840112 | + | 0.542414i | \(0.182489\pi\) | |||||||
\(74\) | −8.50252 | + | 4.90893i | −0.988398 | + | 0.570652i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.49351i | 0.400733i | ||||||||
\(77\) | 1.14932 | + | 0.410798i | 0.130977 | + | 0.0468148i | ||||
\(78\) | 5.31542 | − | 8.38256i | 0.601853 | − | 0.949138i | ||||
\(79\) | 3.58521 | − | 6.20977i | 0.403368 | − | 0.698654i | −0.590762 | − | 0.806846i | \(-0.701173\pi\) |
0.994130 | + | 0.108192i | \(0.0345061\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.87616 | + | 1.48790i | 0.986240 | + | 0.165323i | ||||
\(82\) | 9.17399 | + | 5.29661i | 1.01310 | + | 0.584912i | ||||
\(83\) | −17.5632 | −1.92781 | −0.963904 | − | 0.266250i | \(-0.914215\pi\) | ||||
−0.963904 | + | 0.266250i | \(0.914215\pi\) | |||||||
\(84\) | 1.48978 | − | 3.67860i | 0.162549 | − | 0.401368i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −12.2489 | − | 7.07188i | −1.32083 | − | 0.762581i | ||||
\(87\) | −0.554864 | + | 13.3557i | −0.0594877 | + | 1.43188i | ||||
\(88\) | −0.442791 | − | 0.766937i | −0.0472017 | − | 0.0817558i | ||||
\(89\) | 1.35247 | − | 2.34254i | 0.143361 | − | 0.248309i | −0.785399 | − | 0.618990i | \(-0.787542\pi\) |
0.928760 | + | 0.370681i | \(0.120876\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.82718 | + | 5.79637i | −0.715683 | + | 0.607625i | ||||
\(92\) | 3.90116i | 0.406724i | ||||||||
\(93\) | 5.34476 | − | 2.79667i | 0.554225 | − | 0.290001i | ||||
\(94\) | 4.63241 | − | 2.67452i | 0.477796 | − | 0.275856i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −7.05172 | + | 3.68984i | −0.719713 | + | 0.376593i | ||||
\(97\) | − | 4.44253i | − | 0.451070i | −0.974235 | − | 0.225535i | \(-0.927587\pi\) | ||
0.974235 | − | 0.225535i | \(-0.0724130\pi\) | |||||||
\(98\) | −7.51181 | + | 9.16569i | −0.758808 | + | 0.925875i | ||||
\(99\) | 1.25180 | − | 0.590174i | 0.125811 | − | 0.0593148i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.36822 | + | 2.36982i | 0.136143 | + | 0.235806i | 0.926033 | − | 0.377442i | \(-0.123196\pi\) |
−0.789891 | + | 0.613248i | \(0.789863\pi\) | |||||||
\(102\) | 0.669844 | − | 16.1233i | 0.0663245 | − | 1.59644i | ||||
\(103\) | −15.9618 | − | 9.21552i | −1.57276 | − | 0.908033i | −0.995829 | − | 0.0912387i | \(-0.970917\pi\) |
−0.576930 | − | 0.816794i | \(-0.695749\pi\) | |||||||
\(104\) | 6.49817 | 0.637198 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 19.5785 | 1.90163 | ||||||||
\(107\) | 5.76162 | + | 3.32647i | 0.556997 | + | 0.321582i | 0.751939 | − | 0.659232i | \(-0.229119\pi\) |
−0.194942 | + | 0.980815i | \(0.562452\pi\) | |||||||
\(108\) | −1.74847 | − | 4.14666i | −0.168246 | − | 0.399013i | ||||
\(109\) | 3.91662 | + | 6.78379i | 0.375144 | + | 0.649769i | 0.990349 | − | 0.138599i | \(-0.0442599\pi\) |
−0.615204 | + | 0.788368i | \(0.710927\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.37908 | − | 8.48295i | 0.510560 | − | 0.805166i | ||||
\(112\) | 12.9676 | − | 2.36402i | 1.22532 | − | 0.223379i | ||||
\(113\) | − | 17.3914i | − | 1.63604i | −0.575187 | − | 0.818022i | \(-0.695071\pi\) | ||
0.575187 | − | 0.818022i | \(-0.304929\pi\) | |||||||
\(114\) | −5.48375 | − | 10.4801i | −0.513600 | − | 0.981550i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.78845 | − | 3.34196i | 0.537444 | − | 0.310293i | ||||
\(117\) | −0.842332 | + | 10.1200i | −0.0778736 | + | 0.935599i | ||||
\(118\) | − | 16.5252i | − | 1.52127i | ||||||
\(119\) | −4.90065 | + | 13.7109i | −0.449242 | + | 1.25688i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.39359 | + | 9.34198i | −0.490327 | + | 0.849271i | ||||
\(122\) | −6.75055 | − | 11.6923i | −0.611166 | − | 1.05857i | ||||
\(123\) | −10.8286 | − | 0.449874i | −0.976378 | − | 0.0405638i | ||||
\(124\) | −2.61216 | − | 1.50813i | −0.234579 | − | 0.135434i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.30512 | + | 13.3738i | 0.116269 | + | 1.19143i | ||||
\(127\) | −12.5556 | −1.11413 | −0.557065 | − | 0.830469i | \(-0.688073\pi\) | ||||
−0.557065 | + | 0.830469i | \(0.688073\pi\) | |||||||
\(128\) | −11.1623 | − | 6.44458i | −0.986621 | − | 0.569626i | ||||
\(129\) | 14.4580 | + | 0.600660i | 1.27296 | + | 0.0528851i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.36275 | + | 5.82446i | −0.293805 | + | 0.508886i | −0.974706 | − | 0.223490i | \(-0.928255\pi\) |
0.680901 | + | 0.732375i | \(0.261588\pi\) | |||||||
\(132\) | −0.584417 | − | 0.370582i | −0.0508670 | − | 0.0322550i | ||||
\(133\) | 1.91405 | + | 10.4993i | 0.165969 | + | 0.910405i | ||||
\(134\) | 1.55113i | 0.133997i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.14924 | − | 5.28232i | 0.784541 | − | 0.452955i | ||||
\(137\) | −17.6208 | + | 10.1734i | −1.50545 | + | 0.869171i | −0.505468 | + | 0.862845i | \(0.668680\pi\) |
−0.999980 | + | 0.00632592i | \(0.997986\pi\) | |||||||
\(138\) | −6.12363 | − | 11.7030i | −0.521278 | − | 0.996224i | ||||
\(139\) | − | 9.79157i | − | 0.830510i | −0.909705 | − | 0.415255i | \(-0.863692\pi\) | ||
0.909705 | − | 0.415255i | \(-0.136308\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.93067 | + | 4.62174i | −0.246807 | + | 0.389221i | ||||
\(142\) | −1.29166 | + | 2.23721i | −0.108393 | + | 0.187743i | ||||
\(143\) | 0.780781 | + | 1.35235i | 0.0652922 | + | 0.113089i | ||||
\(144\) | 8.52099 | − | 12.2793i | 0.710082 | − | 1.02327i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 13.2018 | 1.09259 | ||||||||
\(147\) | 2.46189 | − | 11.8718i | 0.203054 | − | 0.979168i | ||||
\(148\) | −5.02257 | −0.412852 | ||||||||
\(149\) | 14.1195 | + | 8.15190i | 1.15671 | + | 0.667830i | 0.950514 | − | 0.310680i | \(-0.100557\pi\) |
0.206200 | + | 0.978510i | \(0.433890\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.54351 | + | 13.0657i | 0.613882 | + | 1.06328i | 0.990580 | + | 0.136939i | \(0.0437263\pi\) |
−0.376697 | + | 0.926336i | \(0.622940\pi\) | |||||||
\(152\) | 3.87179 | − | 6.70613i | 0.314043 | − | 0.543939i | ||||
\(153\) | 7.04054 | + | 14.9335i | 0.569194 | + | 1.20730i | ||||
\(154\) | 1.33733 | + | 1.57515i | 0.107765 | + | 0.126929i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.49907 | − | 2.35416i | 0.360214 | − | 0.188484i | ||||
\(157\) | 10.7831 | − | 6.22562i | 0.860584 | − | 0.496858i | −0.00362372 | − | 0.999993i | \(-0.501153\pi\) |
0.864208 | + | 0.503135i | \(0.167820\pi\) | |||||||
\(158\) | 10.5128 | − | 6.06958i | 0.836354 | − | 0.482869i | ||||
\(159\) | −17.7479 | + | 9.28668i | −1.40750 | + | 0.736482i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.13739 | + | 11.7244i | 0.168450 | + | 0.924015i | ||||
\(162\) | 11.7542 | + | 9.69489i | 0.923495 | + | 0.761703i | ||||
\(163\) | 2.75193 | − | 4.76649i | 0.215548 | − | 0.373340i | −0.737894 | − | 0.674917i | \(-0.764180\pi\) |
0.953442 | + | 0.301577i | \(0.0975129\pi\) | |||||||
\(164\) | 2.70961 | + | 4.69317i | 0.211585 | + | 0.366475i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −25.7500 | − | 14.8667i | −1.99858 | − | 1.15388i | ||||
\(167\) | −0.799023 | −0.0618302 | −0.0309151 | − | 0.999522i | \(-0.509842\pi\) | ||||
−0.0309151 | + | 0.999522i | \(0.509842\pi\) | |||||||
\(168\) | −6.93669 | + | 5.41032i | −0.535177 | + | 0.417415i | ||||
\(169\) | 1.54168 | 0.118590 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.94203 | + | 6.89909i | 0.760286 | + | 0.527586i | ||||
\(172\) | −3.61779 | − | 6.26620i | −0.275854 | − | 0.477793i | ||||
\(173\) | −7.25944 | + | 12.5737i | −0.551925 | + | 0.955962i | 0.446211 | + | 0.894928i | \(0.352773\pi\) |
−0.998136 | + | 0.0610338i | \(0.980560\pi\) | |||||||
\(174\) | −12.1187 | + | 19.1116i | −0.918719 | + | 1.44884i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 2.29830i | − | 0.173241i | ||||||
\(177\) | 7.83840 | + | 14.9801i | 0.589171 | + | 1.12597i | ||||
\(178\) | 3.96579 | − | 2.28965i | 0.297249 | − | 0.171617i | ||||
\(179\) | 2.04442 | − | 1.18035i | 0.152807 | − | 0.0882234i | −0.421647 | − | 0.906760i | \(-0.638548\pi\) |
0.574454 | + | 0.818537i | \(0.305214\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.70696i | 0.721513i | 0.932660 | + | 0.360756i | \(0.117481\pi\) | ||||
−0.932660 | + | 0.360756i | \(0.882519\pi\) | |||||||
\(182\) | −14.9160 | + | 2.71923i | −1.10565 | + | 0.201563i | ||||
\(183\) | 11.6654 | + | 7.39707i | 0.862329 | + | 0.546807i | ||||
\(184\) | 4.32357 | − | 7.48865i | 0.318738 | − | 0.552071i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 10.2034 | + | 0.423903i | 0.748152 | + | 0.0310821i | ||||
\(187\) | 2.19863 | + | 1.26938i | 0.160780 | + | 0.0928264i | ||||
\(188\) | 2.73643 | 0.199575 | ||||||||
\(189\) | −7.52669 | − | 11.5043i | −0.547486 | − | 0.836815i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.37389 | − | 2.52527i | −0.316484 | − | 0.182722i | 0.333341 | − | 0.942807i | \(-0.391824\pi\) |
−0.649824 | + | 0.760085i | \(0.725157\pi\) | |||||||
\(192\) | 3.78137 | + | 0.157098i | 0.272897 | + | 0.0113375i | ||||
\(193\) | 6.55182 | + | 11.3481i | 0.471610 | + | 0.816853i | 0.999472 | − | 0.0324769i | \(-0.0103396\pi\) |
−0.527862 | + | 0.849330i | \(0.677006\pi\) | |||||||
\(194\) | 3.76048 | − | 6.51334i | 0.269987 | − | 0.467631i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.67247 | + | 2.13931i | −0.405176 | + | 0.152808i | ||||
\(197\) | − | 21.2925i | − | 1.51703i | −0.651655 | − | 0.758516i | \(-0.725925\pi\) | ||
0.651655 | − | 0.758516i | \(-0.274075\pi\) | |||||||
\(198\) | 2.33488 | + | 0.194341i | 0.165932 | + | 0.0138112i | ||||
\(199\) | −5.78974 | + | 3.34271i | −0.410424 | + | 0.236958i | −0.690972 | − | 0.722882i | \(-0.742817\pi\) |
0.280548 | + | 0.959840i | \(0.409484\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.735748 | − | 1.40610i | −0.0518957 | − | 0.0991787i | ||||
\(202\) | 4.63263i | 0.325951i | ||||||||
\(203\) | 15.5654 | − | 13.2153i | 1.09248 | − | 0.927529i | ||||
\(204\) | 4.42089 | − | 6.97185i | 0.309524 | − | 0.488127i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −15.6014 | − | 27.0224i | −1.08700 | − | 1.88274i | ||||
\(207\) | 11.1021 | + | 7.70412i | 0.771652 | + | 0.535474i | ||||
\(208\) | 14.6050 | + | 8.43218i | 1.01267 | + | 0.584666i | ||||
\(209\) | 1.86084 | 0.128717 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.72156 | 0.393889 | 0.196944 | − | 0.980415i | \(-0.436898\pi\) | ||||
0.196944 | + | 0.980415i | \(0.436898\pi\) | |||||||
\(212\) | 8.67399 | + | 5.00793i | 0.595732 | + | 0.343946i | ||||
\(213\) | 0.109709 | − | 2.64071i | 0.00751711 | − | 0.180938i | ||||
\(214\) | 5.63154 | + | 9.75412i | 0.384964 | + | 0.666778i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.23931 | + | 9.89770i | −0.0843245 | + | 0.673453i | ||||
\(217\) | −8.67678 | − | 3.10132i | −0.589019 | − | 0.210531i | ||||
\(218\) | 13.2613i | 0.898166i | ||||||||
\(219\) | −11.9674 | + | 6.26201i | −0.808685 | + | 0.423148i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.1330 | + | 9.31439i | −1.08522 | + | 0.626554i | ||||
\(222\) | 15.0670 | − | 7.88390i | 1.01123 | − | 0.529132i | ||||
\(223\) | 5.83493i | 0.390736i | 0.980730 | + | 0.195368i | \(0.0625901\pi\) | ||||
−0.980730 | + | 0.195368i | \(0.937410\pi\) | |||||||
\(224\) | 11.4479 | + | 4.09180i | 0.764896 | + | 0.273395i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.7213 | − | 25.4981i | 0.979249 | − | 1.69611i | ||||
\(227\) | −5.70646 | − | 9.88387i | −0.378751 | − | 0.656016i | 0.612130 | − | 0.790757i | \(-0.290313\pi\) |
−0.990881 | + | 0.134741i | \(0.956980\pi\) | |||||||
\(228\) | 0.251171 | − | 6.04573i | 0.0166342 | − | 0.400388i | ||||
\(229\) | 0.910719 | + | 0.525804i | 0.0601820 | + | 0.0347461i | 0.529789 | − | 0.848129i | \(-0.322271\pi\) |
−0.469607 | + | 0.882876i | \(0.655604\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.95943 | − | 0.793541i | −0.128921 | − | 0.0522112i | ||||
\(232\) | −14.8153 | −0.972672 | ||||||||
\(233\) | −3.36441 | − | 1.94244i | −0.220410 | − | 0.127254i | 0.385730 | − | 0.922612i | \(-0.373950\pi\) |
−0.606140 | + | 0.795358i | \(0.707283\pi\) | |||||||
\(234\) | −9.80132 | + | 14.1243i | −0.640732 | + | 0.923337i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.22694 | − | 7.32127i | 0.275150 | − | 0.476574i | ||||
\(237\) | −6.65088 | + | 10.4886i | −0.432021 | + | 0.681308i | ||||
\(238\) | −18.7909 | + | 15.9537i | −1.21803 | + | 1.03413i | ||||
\(239\) | − | 6.40306i | − | 0.414180i | −0.978322 | − | 0.207090i | \(-0.933601\pi\) | ||
0.978322 | − | 0.207090i | \(-0.0663993\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.96093 | − | 1.13215i | 0.126315 | − | 0.0729279i | −0.435511 | − | 0.900183i | \(-0.643432\pi\) |
0.561826 | + | 0.827255i | \(0.310099\pi\) | |||||||
\(242\) | −15.8155 | + | 9.13106i | −1.01666 | + | 0.586967i | ||||
\(243\) | −15.2537 | − | 3.21307i | −0.978527 | − | 0.206118i | ||||
\(244\) | − | 6.90681i | − | 0.442163i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −15.4953 | − | 9.82566i | −0.987945 | − | 0.626461i | ||||
\(247\) | −6.82718 | + | 11.8250i | −0.434403 | + | 0.752408i | ||||
\(248\) | 3.34286 | + | 5.79000i | 0.212272 | + | 0.367665i | ||||
\(249\) | 30.3941 | + | 1.26273i | 1.92615 | + | 0.0800221i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.3221 | −0.840886 | −0.420443 | − | 0.907319i | \(-0.638125\pi\) | ||||
−0.420443 | + | 0.907319i | \(0.638125\pi\) | |||||||
\(252\) | −2.84263 | + | 6.25891i | −0.179069 | + | 0.394274i | ||||
\(253\) | 2.07798 | 0.130641 | ||||||||
\(254\) | −18.4082 | − | 10.6280i | −1.15503 | − | 0.666859i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.72527 | − | 15.1126i | −0.545329 | − | 0.944538i | ||||
\(257\) | 9.79648 | − | 16.9680i | 0.611088 | − | 1.05844i | −0.379969 | − | 0.924999i | \(-0.624066\pi\) |
0.991057 | − | 0.133436i | \(-0.0426012\pi\) | |||||||
\(258\) | 20.6889 | + | 13.1190i | 1.28804 | + | 0.816750i | ||||
\(259\) | −15.0947 | + | 2.75180i | −0.937937 | + | 0.170988i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.92045 | − | 23.0729i | 0.118873 | − | 1.42818i | ||||
\(262\) | −9.86050 | + | 5.69296i | −0.609184 | + | 0.351712i | ||||
\(263\) | −14.5263 | + | 8.38678i | −0.895732 | + | 0.517151i | −0.875813 | − | 0.482651i | \(-0.839674\pi\) |
−0.0199186 | + | 0.999802i | \(0.506341\pi\) | |||||||
\(264\) | 0.711136 | + | 1.35906i | 0.0437674 | + | 0.0836446i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6.08112 | + | 17.0136i | −0.372858 | + | 1.04317i | ||||
\(267\) | −2.50894 | + | 3.95666i | −0.153545 | + | 0.242144i | ||||
\(268\) | −0.396759 | + | 0.687207i | −0.0242359 | + | 0.0419779i | ||||
\(269\) | −14.6703 | − | 25.4097i | −0.894465 | − | 1.54926i | −0.834466 | − | 0.551060i | \(-0.814224\pi\) |
−0.0599988 | − | 0.998198i | \(-0.519110\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.57129 | + | 1.48454i | 0.156195 | + | 0.0901792i | 0.576060 | − | 0.817407i | \(-0.304589\pi\) |
−0.419865 | + | 0.907586i | \(0.637923\pi\) | |||||||
\(272\) | 27.4178 | 1.66245 | ||||||||
\(273\) | 12.2316 | − | 9.54010i | 0.740288 | − | 0.577393i | ||||
\(274\) | −34.4460 | −2.08096 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.280479 | − | 6.75118i | 0.0168829 | − | 0.406374i | ||||
\(277\) | −6.51269 | − | 11.2803i | −0.391309 | − | 0.677768i | 0.601313 | − | 0.799014i | \(-0.294644\pi\) |
−0.992623 | + | 0.121246i | \(0.961311\pi\) | |||||||
\(278\) | 8.28830 | − | 14.3558i | 0.497099 | − | 0.861001i | ||||
\(279\) | −9.45048 | + | 4.45553i | −0.565786 | + | 0.266745i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 19.4404i | − | 1.15972i | −0.814717 | − | 0.579859i | \(-0.803108\pi\) | ||
0.814717 | − | 0.579859i | \(-0.196892\pi\) | |||||||
\(282\) | −8.20894 | + | 4.29536i | −0.488835 | + | 0.255785i | ||||
\(283\) | −4.88399 | + | 2.81977i | −0.290323 | + | 0.167618i | −0.638088 | − | 0.769964i | \(-0.720274\pi\) |
0.347764 | + | 0.937582i | \(0.386941\pi\) | |||||||
\(284\) | −1.14450 | + | 0.660778i | −0.0679136 | + | 0.0392099i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.64364i | 0.156322i | ||||||||
\(287\) | 10.7147 | + | 12.6202i | 0.632469 | + | 0.744945i | ||||
\(288\) | 12.4687 | − | 5.87850i | 0.734725 | − | 0.346394i | ||||
\(289\) | −6.64321 | + | 11.5064i | −0.390777 | + | 0.676846i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.319401 | + | 7.68805i | −0.0187236 | + | 0.450681i | ||||
\(292\) | 5.84888 | + | 3.37685i | 0.342280 | + | 0.197615i | ||||
\(293\) | 21.5754 | 1.26045 | 0.630226 | − | 0.776412i | \(-0.282962\pi\) | ||||
0.630226 | + | 0.776412i | \(0.282962\pi\) | |||||||
\(294\) | 13.6586 | − | 15.3217i | 0.796586 | − | 0.893579i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9.64129 | + | 5.56640i | 0.560389 | + | 0.323541i | ||||
\(297\) | −2.20875 | + | 0.931331i | −0.128164 | + | 0.0540413i | ||||
\(298\) | 13.8007 | + | 23.9036i | 0.799455 | + | 1.38470i | ||||
\(299\) | −7.62382 | + | 13.2049i | −0.440897 | + | 0.763656i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.3060 | − | 16.8501i | −0.824582 | − | 0.971224i | ||||
\(302\) | 25.5415i | 1.46975i | ||||||||
\(303\) | −2.19740 | − | 4.19948i | −0.126237 | − | 0.241254i | ||||
\(304\) | 17.4041 | − | 10.0482i | 0.998191 | − | 0.576306i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.31841 | + | 27.8541i | −0.132535 | + | 1.59231i | ||||
\(307\) | − | 22.9288i | − | 1.30861i | −0.756229 | − | 0.654307i | \(-0.772960\pi\) | ||
0.756229 | − | 0.654307i | \(-0.227040\pi\) | |||||||
\(308\) | 0.189580 | + | 1.03992i | 0.0108023 | + | 0.0592549i | ||||
\(309\) | 26.9602 | + | 17.0956i | 1.53371 | + | 0.972534i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.799023 | + | 1.38395i | 0.0453084 | + | 0.0784765i | 0.887790 | − | 0.460248i | \(-0.152240\pi\) |
−0.842482 | + | 0.538725i | \(0.818906\pi\) | |||||||
\(312\) | −11.2455 | − | 0.467195i | −0.636649 | − | 0.0264497i | ||||
\(313\) | 25.0145 | + | 14.4421i | 1.41390 | + | 0.816318i | 0.995754 | − | 0.0920593i | \(-0.0293449\pi\) |
0.418151 | + | 0.908378i | \(0.362678\pi\) | |||||||
\(314\) | 21.0793 | 1.18957 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.21007 | 0.349344 | ||||||||
\(317\) | −5.68143 | − | 3.28018i | −0.319101 | − | 0.184233i | 0.331891 | − | 0.943318i | \(-0.392313\pi\) |
−0.650992 | + | 0.759085i | \(0.725647\pi\) | |||||||
\(318\) | −33.8818 | − | 1.40762i | −1.90000 | − | 0.0789357i | ||||
\(319\) | −1.78012 | − | 3.08325i | −0.0996674 | − | 0.172629i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.73166 | − | 6.17090i | −0.543168 | − | 0.344426i | ||||
\(322\) | −6.79071 | + | 18.9988i | −0.378432 | + | 1.05876i | ||||
\(323\) | 22.1991i | 1.23519i | ||||||||
\(324\) | 2.72769 | + | 7.30175i | 0.151538 | + | 0.405653i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.06940 | − | 4.65887i | 0.446923 | − | 0.258031i | ||||
\(327\) | −6.29021 | − | 12.0213i | −0.347849 | − | 0.664781i | ||||
\(328\) | − | 12.0120i | − | 0.663251i | ||||||
\(329\) | 8.22399 | − | 1.49925i | 0.453403 | − | 0.0826566i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.76497 | − | 11.7173i | 0.371836 | − | 0.644040i | −0.618012 | − | 0.786169i | \(-0.712062\pi\) |
0.989848 | + | 0.142129i | \(0.0453949\pi\) | |||||||
\(332\) | −7.60544 | − | 13.1730i | −0.417403 | − | 0.722963i | ||||
\(333\) | −9.91871 | + | 14.2935i | −0.543542 | + | 0.783279i | ||||
\(334\) | −1.17147 | − | 0.676351i | −0.0641002 | − | 0.0370083i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −22.6111 | + | 3.15876i | −1.23354 | + | 0.172324i | ||||
\(337\) | 30.7122 | 1.67300 | 0.836501 | − | 0.547966i | \(-0.184598\pi\) | ||||
0.836501 | + | 0.547966i | \(0.184598\pi\) | |||||||
\(338\) | 2.26030 | + | 1.30499i | 0.122944 | + | 0.0709819i | ||||
\(339\) | −1.25038 | + | 30.0968i | −0.0679111 | + | 1.63463i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.803314 | + | 1.39138i | −0.0435019 | + | 0.0753475i | ||||
\(342\) | 8.73647 | + | 18.5307i | 0.472414 | + | 1.00202i | ||||
\(343\) | −15.8758 | + | 9.53729i | −0.857211 | + | 0.514965i | ||||
\(344\) | 16.0381i | 0.864715i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −21.2866 | + | 12.2898i | −1.14438 | + | 0.660706i | ||||
\(347\) | −6.77295 | + | 3.91036i | −0.363591 | + | 0.209919i | −0.670655 | − | 0.741770i | \(-0.733987\pi\) |
0.307064 | + | 0.951689i | \(0.400653\pi\) | |||||||
\(348\) | −10.2575 | + | 5.36729i | −0.549861 | + | 0.287717i | ||||
\(349\) | − | 25.1501i | − | 1.34625i | −0.739526 | − | 0.673127i | \(-0.764951\pi\) | ||
0.739526 | − | 0.673127i | \(-0.235049\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.18530 | − | 17.4528i | 0.116643 | − | 0.931560i | ||||
\(352\) | 1.05987 | − | 1.83575i | 0.0564913 | − | 0.0978458i | ||||
\(353\) | −6.13445 | − | 10.6252i | −0.326504 | − | 0.565521i | 0.655312 | − | 0.755359i | \(-0.272537\pi\) |
−0.981816 | + | 0.189837i | \(0.939204\pi\) | |||||||
\(354\) | −1.18810 | + | 28.5979i | −0.0631469 | + | 1.51996i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.34265 | 0.124160 | ||||||||
\(357\) | 9.46662 | − | 23.3752i | 0.501027 | − | 1.23714i | ||||
\(358\) | 3.99653 | 0.211223 | ||||||||
\(359\) | 7.11574 | + | 4.10828i | 0.375555 | + | 0.216827i | 0.675882 | − | 0.737010i | \(-0.263763\pi\) |
−0.300328 | + | 0.953836i | \(0.597096\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.36436 | − | 2.36315i | −0.0718086 | − | 0.124376i | ||||
\(362\) | −8.21668 | + | 14.2317i | −0.431859 | + | 0.748002i | ||||
\(363\) | 10.0056 | − | 15.7791i | 0.525157 | − | 0.828186i | ||||
\(364\) | −7.30388 | − | 2.61061i | −0.382827 | − | 0.136833i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 10.8416 | + | 20.7195i | 0.566698 | + | 1.08303i | ||||
\(367\) | 24.1666 | − | 13.9526i | 1.26149 | − | 0.728320i | 0.288125 | − | 0.957593i | \(-0.406968\pi\) |
0.973362 | + | 0.229273i | \(0.0736349\pi\) | |||||||
\(368\) | 19.4349 | − | 11.2207i | 1.01311 | − | 0.584921i | ||||
\(369\) | 18.7071 | + | 1.55707i | 0.973853 | + | 0.0810577i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 28.8123 | + | 10.2983i | 1.49586 | + | 0.534663i | ||||
\(372\) | 4.41206 | + | 2.79771i | 0.228755 | + | 0.145054i | ||||
\(373\) | −9.04199 | + | 15.6612i | −0.468176 | + | 0.810905i | −0.999339 | − | 0.0363650i | \(-0.988422\pi\) |
0.531162 | + | 0.847270i | \(0.321755\pi\) | |||||||
\(374\) | 2.14900 | + | 3.72217i | 0.111122 | + | 0.192469i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.25284 | − | 3.03273i | −0.270895 | − | 0.156401i | ||||
\(377\) | 26.1241 | 1.34546 | ||||||||
\(378\) | −1.29706 | − | 23.2380i | −0.0667135 | − | 1.19523i | ||||
\(379\) | 24.7450 | 1.27107 | 0.635534 | − | 0.772073i | \(-0.280780\pi\) | ||||
0.635534 | + | 0.772073i | \(0.280780\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 21.7282 | + | 0.902702i | 1.11317 | + | 0.0462468i | ||||
\(382\) | −4.27514 | − | 7.40476i | −0.218735 | − | 0.378861i | ||||
\(383\) | −6.46470 | + | 11.1972i | −0.330331 | + | 0.572150i | −0.982577 | − | 0.185858i | \(-0.940494\pi\) |
0.652246 | + | 0.758008i | \(0.273827\pi\) | |||||||
\(384\) | 18.8537 | + | 11.9552i | 0.962126 | + | 0.610089i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 22.1838i | 1.12912i | ||||||||
\(387\) | −24.9772 | − | 2.07895i | −1.26966 | − | 0.105679i | ||||
\(388\) | 3.33205 | − | 1.92376i | 0.169159 | − | 0.0976642i | ||||
\(389\) | −16.4024 | + | 9.46992i | −0.831634 | + | 0.480144i | −0.854412 | − | 0.519596i | \(-0.826082\pi\) |
0.0227777 | + | 0.999741i | \(0.492749\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.7894i | 1.25365i | ||||||||
\(392\) | 13.2598 | + | 2.18007i | 0.669721 | + | 0.110110i | ||||
\(393\) | 6.23820 | − | 9.83780i | 0.314675 | − | 0.496251i | ||||
\(394\) | 18.0236 | − | 31.2177i | 0.908014 | − | 1.57273i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.984724 | + | 0.683331i | 0.0494842 | + | 0.0343387i | ||||
\(397\) | 6.31044 | + | 3.64333i | 0.316712 | + | 0.182854i | 0.649926 | − | 0.759998i | \(-0.274800\pi\) |
−0.333214 | + | 0.942851i | \(0.608133\pi\) | |||||||
\(398\) | −11.3181 | −0.567323 | ||||||||
\(399\) | −2.55751 | − | 18.3073i | −0.128036 | − | 0.916510i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.7394 | + | 7.93243i | 0.686111 | + | 0.396126i | 0.802154 | − | 0.597118i | \(-0.203688\pi\) |
−0.116042 | + | 0.993244i | \(0.537021\pi\) | |||||||
\(402\) | 0.111521 | − | 2.68432i | 0.00556215 | − | 0.133882i | ||||
\(403\) | −5.89451 | − | 10.2096i | −0.293626 | − | 0.508576i | ||||
\(404\) | −1.18497 | + | 2.05242i | −0.0589543 | + | 0.102112i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 34.0073 | − | 6.19963i | 1.68776 | − | 0.307682i | ||||
\(407\) | 2.67530i | 0.132610i | ||||||||
\(408\) | −16.2131 | + | 8.48356i | −0.802667 | + | 0.419999i | ||||
\(409\) | −22.8109 | + | 13.1699i | −1.12793 | + | 0.651209i | −0.943413 | − | 0.331620i | \(-0.892405\pi\) |
−0.184515 | + | 0.982830i | \(0.559071\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 31.2253 | − | 16.3388i | 1.54023 | − | 0.805932i | ||||
\(412\) | − | 15.9625i | − | 0.786417i | ||||||
\(413\) | 8.69228 | − | 24.3190i | 0.427719 | − | 1.19666i | ||||
\(414\) | 9.75590 | + | 20.6929i | 0.479476 | + | 1.01700i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 7.77705 | + | 13.4702i | 0.381301 | + | 0.660433i | ||||
\(417\) | −0.703978 | + | 16.9449i | −0.0344739 | + | 0.829794i | ||||
\(418\) | 2.72824 | + | 1.57515i | 0.133443 | + | 0.0770432i | ||||
\(419\) | 14.3499 | 0.701039 | 0.350519 | − | 0.936555i | \(-0.386005\pi\) | ||||
0.350519 | + | 0.936555i | \(0.386005\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0679 | −0.490682 | −0.245341 | − | 0.969437i | \(-0.578900\pi\) | ||||
−0.245341 | + | 0.969437i | \(0.578900\pi\) | |||||||
\(422\) | 8.38858 | + | 4.84315i | 0.408350 | + | 0.235761i | ||||
\(423\) | 5.40398 | − | 7.78749i | 0.262751 | − | 0.378641i | ||||
\(424\) | −11.1004 | − | 19.2264i | −0.539082 | − | 0.933717i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.39613 | − | 3.77876i | 0.116093 | − | 0.183082i | ||||
\(427\) | −3.78415 | − | 20.7575i | −0.183128 | − | 1.00453i | ||||
\(428\) | 5.76190i | 0.278512i | ||||||||
\(429\) | −1.25396 | − | 2.39646i | −0.0605416 | − | 0.115702i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.13983 | − | 4.12218i | 0.343914 | − | 0.198559i | −0.318088 | − | 0.948061i | \(-0.603041\pi\) |
0.662001 | + | 0.749503i | \(0.269707\pi\) | |||||||
\(432\) | −15.6289 | + | 20.6374i | −0.751946 | + | 0.992918i | ||||
\(433\) | − | 10.7241i | − | 0.515367i | −0.966229 | − | 0.257683i | \(-0.917041\pi\) | ||
0.966229 | − | 0.257683i | \(-0.0829591\pi\) | |||||||
\(434\) | −10.0961 | − | 11.8916i | −0.484631 | − | 0.570816i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.39206 | + | 5.87521i | −0.162450 | + | 0.281372i | ||||
\(437\) | 9.08496 | + | 15.7356i | 0.434593 | + | 0.752737i | ||||
\(438\) | −22.8465 | − | 0.949162i | −1.09165 | − | 0.0453527i | ||||
\(439\) | −2.74233 | − | 1.58329i | −0.130884 | − | 0.0755661i | 0.433128 | − | 0.901332i | \(-0.357410\pi\) |
−0.564013 | + | 0.825766i | \(0.690743\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.11399 | + | 20.3678i | −0.243523 | + | 0.969895i | ||||
\(442\) | −31.5375 | −1.50009 | ||||||||
\(443\) | −15.1150 | − | 8.72667i | −0.718137 | − | 0.414617i | 0.0959297 | − | 0.995388i | \(-0.469418\pi\) |
−0.814067 | + | 0.580772i | \(0.802751\pi\) | |||||||
\(444\) | 8.69184 | + | 0.361104i | 0.412496 | + | 0.0171372i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.93911 | + | 8.55480i | −0.233874 | + | 0.405081i | ||||
\(447\) | −23.8485 | − | 15.1225i | −1.12800 | − | 0.715268i | ||||
\(448\) | −3.74161 | − | 4.40700i | −0.176774 | − | 0.208211i | ||||
\(449\) | 12.2873i | 0.579876i | 0.957046 | + | 0.289938i | \(0.0936346\pi\) | ||||
−0.957046 | + | 0.289938i | \(0.906365\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.49985 | − | 1.44329i | 0.117713 | − | 0.0679618i | ||||
\(452\) | 13.0442 | − | 7.53105i | 0.613546 | − | 0.354231i | ||||
\(453\) | −12.1151 | − | 23.1534i | −0.569217 | − | 1.08784i | ||||
\(454\) | − | 19.3215i | − | 0.906801i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.18250 | + | 11.3270i | −0.336351 | + | 0.530434i | ||||
\(457\) | 2.44467 | − | 4.23430i | 0.114357 | − | 0.198072i | −0.803165 | − | 0.595756i | \(-0.796853\pi\) |
0.917523 | + | 0.397684i | \(0.130186\pi\) | |||||||
\(458\) | 0.890158 | + | 1.54180i | 0.0415943 | + | 0.0720435i | ||||
\(459\) | −11.1104 | − | 26.3494i | −0.518589 | − | 1.22989i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.12746 | −0.238810 | −0.119405 | − | 0.992846i | \(-0.538099\pi\) | ||||
−0.119405 | + | 0.992846i | \(0.538099\pi\) | |||||||
\(462\) | −2.20107 | − | 2.82204i | −0.102403 | − | 0.131293i | ||||
\(463\) | −39.9073 | −1.85465 | −0.927325 | − | 0.374257i | \(-0.877898\pi\) | ||||
−0.927325 | + | 0.374257i | \(0.877898\pi\) | |||||||
\(464\) | −33.2981 | − | 19.2247i | −1.54583 | − | 0.892483i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.28845 | − | 5.69577i | −0.152335 | − | 0.263851i | ||||
\(467\) | −4.56309 | + | 7.90350i | −0.211155 | + | 0.365730i | −0.952076 | − | 0.305861i | \(-0.901056\pi\) |
0.740922 | + | 0.671592i | \(0.234389\pi\) | |||||||
\(468\) | −7.95516 | + | 3.75054i | −0.367727 | + | 0.173369i | ||||
\(469\) | −0.815897 | + | 2.28269i | −0.0376746 | + | 0.105405i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.1084 | + | 9.99853i | −0.880467 | + | 0.460708i | ||||
\(472\) | −16.2280 | + | 9.36925i | −0.746955 | + | 0.431254i | ||||
\(473\) | −3.33773 | + | 1.92704i | −0.153469 | + | 0.0886053i | ||||
\(474\) | −18.6294 | + | 9.74792i | −0.855677 | + | 0.447737i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −12.4058 | + | 2.26161i | −0.568619 | + | 0.103661i | ||||
\(477\) | 31.3815 | − | 14.7951i | 1.43686 | − | 0.677422i | ||||
\(478\) | 5.42002 | − | 9.38775i | 0.247906 | − | 0.429386i | ||||
\(479\) | −6.20210 | − | 10.7424i | −0.283381 | − | 0.490831i | 0.688834 | − | 0.724919i | \(-0.258123\pi\) |
−0.972215 | + | 0.234088i | \(0.924790\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.0006 | − | 9.81532i | −0.775162 | − | 0.447540i | ||||
\(482\) | 3.83332 | 0.174603 | ||||||||
\(483\) | −2.85594 | − | 20.4435i | −0.129950 | − | 0.930211i | ||||
\(484\) | −9.34243 | −0.424656 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −19.6442 | − | 17.6227i | −0.891081 | − | 0.799380i | ||||
\(487\) | 7.08208 | + | 12.2665i | 0.320920 | + | 0.555849i | 0.980678 | − | 0.195628i | \(-0.0626747\pi\) |
−0.659758 | + | 0.751478i | \(0.729341\pi\) | |||||||
\(488\) | −7.65467 | + | 13.2583i | −0.346511 | + | 0.600174i | ||||
\(489\) | −5.10507 | + | 8.05083i | −0.230859 | + | 0.364071i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 32.1216i | − | 1.44963i | −0.688946 | − | 0.724813i | \(-0.741926\pi\) | ||
0.688946 | − | 0.724813i | \(-0.258074\pi\) | |||||||
\(492\) | −4.35171 | − | 8.31662i | −0.196190 | − | 0.374942i | ||||
\(493\) | 36.7819 | − | 21.2361i | 1.65658 | − | 0.956424i | ||||
\(494\) | −20.0191 | + | 11.5580i | −0.900703 | + | 0.520021i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 17.3511i | 0.779086i | ||||||||
\(497\) | −3.07762 | + | 2.61294i | −0.138050 | + | 0.117206i | ||||
\(498\) | 43.4929 | + | 27.5791i | 1.94897 | + | 1.23585i | ||||
\(499\) | −13.3589 | + | 23.1383i | −0.598027 | + | 1.03581i | 0.395085 | + | 0.918644i | \(0.370715\pi\) |
−0.993112 | + | 0.117168i | \(0.962618\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.38276 | + | 0.0574468i | 0.0617769 | + | 0.00256653i | ||||
\(502\) | −19.5320 | − | 11.2768i | −0.871758 | − | 0.503310i | ||||
\(503\) | 9.55539 | 0.426054 | 0.213027 | − | 0.977046i | \(-0.431668\pi\) | ||||
0.213027 | + | 0.977046i | \(0.431668\pi\) | |||||||
\(504\) | 12.3933 | − | 8.86415i | 0.552042 | − | 0.394841i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.04659 | + | 1.75895i | 0.135438 | + | 0.0781950i | ||||
\(507\) | −2.66796 | − | 0.110841i | −0.118488 | − | 0.00492261i | ||||
\(508\) | −5.43700 | − | 9.41716i | −0.241228 | − | 0.417819i | ||||
\(509\) | 9.10071 | − | 15.7629i | 0.403382 | − | 0.698678i | −0.590750 | − | 0.806855i | \(-0.701168\pi\) |
0.994132 | + | 0.108177i | \(0.0345013\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.4282 | + | 6.94417i | 0.859452 | + | 0.307192i | ||||
\(512\) | − | 3.76451i | − | 0.166369i | ||||||
\(513\) | −16.7092 | − | 12.6541i | −0.737731 | − | 0.558691i | ||||
\(514\) | 28.7259 | − | 16.5849i | 1.26705 | − | 0.731530i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.81028 | + | 11.1041i | 0.255783 | + | 0.488832i | ||||
\(517\) | − | 1.45758i | − | 0.0641042i | ||||||
\(518\) | −24.4601 | − | 8.74273i | −1.07472 | − | 0.384133i | ||||
\(519\) | 13.4669 | − | 21.2376i | 0.591130 | − | 0.932228i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.93741 | + | 3.35569i | 0.0848794 | + | 0.147015i | 0.905340 | − | 0.424688i | \(-0.139616\pi\) |
−0.820460 | + | 0.571703i | \(0.806283\pi\) | |||||||
\(522\) | 22.3462 | − | 32.2024i | 0.978067 | − | 1.40946i | ||||
\(523\) | 16.3176 | + | 9.42099i | 0.713520 | + | 0.411951i | 0.812363 | − | 0.583152i | \(-0.198181\pi\) |
−0.0988429 | + | 0.995103i | \(0.531514\pi\) | |||||||
\(524\) | −5.82474 | −0.254455 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −28.3967 | −1.23816 | ||||||||
\(527\) | −16.5986 | − | 9.58321i | −0.723047 | − | 0.417451i | ||||
\(528\) | −0.165240 | + | 3.97735i | −0.00719113 | + | 0.173092i | ||||
\(529\) | −1.35494 | − | 2.34682i | −0.0589104 | − | 0.102036i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.4878 | − | 26.4875i | −0.541924 | − | 1.14946i | ||||
\(532\) | −7.04601 | + | 5.98216i | −0.305483 | + | 0.259359i | ||||
\(533\) | 21.1809i | 0.917448i | ||||||||
\(534\) | −7.02765 | + | 3.67725i | −0.304116 | + | 0.159130i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.52324 | − | 0.879440i | 0.0657937 | − | 0.0379860i | ||||
\(537\) | −3.62286 | + | 1.89568i | −0.156338 | + | 0.0818044i | ||||
\(538\) | − | 49.6721i | − | 2.14152i | ||||||
\(539\) | 1.13952 | + | 3.02147i | 0.0490824 | + | 0.130144i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.0977 | + | 19.2218i | −0.477128 | + | 0.826410i | −0.999656 | − | 0.0262117i | \(-0.991656\pi\) |
0.522528 | + | 0.852622i | \(0.324989\pi\) | |||||||
\(542\) | 2.51324 | + | 4.35306i | 0.107953 | + | 0.186980i | ||||
\(543\) | 0.697895 | − | 16.7985i | 0.0299495 | − | 0.720891i | ||||
\(544\) | 21.8997 | + | 12.6438i | 0.938944 | + | 0.542099i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 26.0086 | − | 3.63338i | 1.11306 | − | 0.155494i | ||||
\(547\) | 1.23468 | 0.0527911 | 0.0263956 | − | 0.999652i | \(-0.491597\pi\) | ||||
0.0263956 | + | 0.999652i | \(0.491597\pi\) | |||||||
\(548\) | −15.2608 | − | 8.81083i | −0.651910 | − | 0.376380i | ||||
\(549\) | −19.6558 | − | 13.6398i | −0.838888 | − | 0.582131i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.5654 | − | 26.9601i | 0.663109 | − | 1.14854i | ||||
\(552\) | −8.02060 | + | 12.6487i | −0.341379 | + | 0.538364i | ||||
\(553\) | 18.6636 | − | 3.40242i | 0.793656 | − | 0.144685i | ||||
\(554\) | − | 22.0513i | − | 0.936868i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.34403 | − | 4.24008i | 0.311456 | − | 0.179819i | ||||
\(557\) | −2.00365 | + | 1.15681i | −0.0848973 | + | 0.0490155i | −0.541848 | − | 0.840477i | \(-0.682275\pi\) |
0.456950 | + | 0.889492i | \(0.348942\pi\) | |||||||
\(558\) | −17.6272 | − | 1.46718i | −0.746217 | − | 0.0621106i | ||||
\(559\) | − | 28.2802i | − | 1.19612i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.71360 | − | 2.35481i | −0.156788 | − | 0.0994203i | ||||
\(562\) | 16.4558 | − | 28.5023i | 0.694146 | − | 1.20230i | ||||
\(563\) | 9.07818 | + | 15.7239i | 0.382600 | + | 0.662682i | 0.991433 | − | 0.130616i | \(-0.0416956\pi\) |
−0.608833 | + | 0.793298i | \(0.708362\pi\) | |||||||
\(564\) | −4.73555 | − | 0.196739i | −0.199403 | − | 0.00828422i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −9.54745 | −0.401309 | ||||||||
\(567\) | 12.1983 | + | 20.4500i | 0.512279 | + | 0.858819i | ||||
\(568\) | 2.92930 | 0.122911 | ||||||||
\(569\) | 12.9811 | + | 7.49465i | 0.544197 | + | 0.314192i | 0.746778 | − | 0.665073i | \(-0.231600\pi\) |
−0.202581 | + | 0.979265i | \(0.564933\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.6375 | − | 20.1568i | −0.487015 | − | 0.843535i | 0.512873 | − | 0.858464i | \(-0.328581\pi\) |
−0.999889 | + | 0.0149293i | \(0.995248\pi\) | |||||||
\(572\) | −0.676208 | + | 1.17123i | −0.0282737 | + | 0.0489715i | ||||
\(573\) | 7.38771 | + | 4.68459i | 0.308626 | + | 0.195701i | ||||
\(574\) | 5.02655 | + | 27.5726i | 0.209804 | + | 1.15086i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6.53258 | − | 0.543733i | −0.272191 | − | 0.0226555i | ||||
\(577\) | −23.0953 | + | 13.3341i | −0.961471 | + | 0.555105i | −0.896625 | − | 0.442790i | \(-0.853989\pi\) |
−0.0648455 | + | 0.997895i | \(0.520655\pi\) | |||||||
\(578\) | −19.4797 | + | 11.2466i | −0.810248 | + | 0.467797i | ||||
\(579\) | −10.5224 | − | 20.1096i | −0.437297 | − | 0.835725i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −30.0745 | − | 35.4229i | −1.24770 | − | 1.46959i | ||||
\(582\) | −6.97601 | + | 11.0013i | −0.289165 | + | 0.456021i | ||||
\(583\) | 2.66751 | − | 4.62026i | 0.110477 | − | 0.191351i | ||||
\(584\) | −7.48499 | − | 12.9644i | −0.309731 | − | 0.536470i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 31.6325 | + | 18.2630i | 1.30673 | + | 0.754439i | ||||
\(587\) | −45.9722 | −1.89748 | −0.948738 | − | 0.316065i | \(-0.897638\pi\) | ||||
−0.948738 | + | 0.316065i | \(0.897638\pi\) | |||||||
\(588\) | 9.97034 | − | 3.29437i | 0.411170 | − | 0.135857i | ||||
\(589\) | −14.0484 | −0.578856 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.53086 | + | 36.8480i | −0.0629710 | + | 1.51572i | ||||
\(592\) | 14.4462 | + | 25.0215i | 0.593735 | + | 1.02838i | ||||
\(593\) | 1.55298 | − | 2.68984i | 0.0637732 | − | 0.110458i | −0.832376 | − | 0.554211i | \(-0.813020\pi\) |
0.896149 | + | 0.443753i | \(0.146353\pi\) | |||||||
\(594\) | −4.02666 | − | 0.504187i | −0.165216 | − | 0.0206871i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 14.1202i | 0.578385i | ||||||||
\(597\) | 10.2598 | − | 5.36849i | 0.419906 | − | 0.219718i | ||||
\(598\) | −22.3551 | + | 12.9067i | −0.914168 | + | 0.527795i | ||||
\(599\) | −7.34708 | + | 4.24184i | −0.300193 | + | 0.173317i | −0.642530 | − | 0.766261i | \(-0.722115\pi\) |
0.342336 | + | 0.939577i | \(0.388782\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 2.63388i | − | 0.107438i | −0.998556 | − | 0.0537191i | \(-0.982892\pi\) | ||
0.998556 | − | 0.0537191i | \(-0.0171076\pi\) | |||||||
\(602\) | −6.71131 | − | 36.8141i | −0.273533 | − | 1.50043i | ||||
\(603\) | 1.17216 | + | 2.48624i | 0.0477341 | + | 0.101247i | ||||
\(604\) | −6.53319 | + | 11.3158i | −0.265832 | + | 0.460434i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.333069 | − | 8.01704i | 0.0135300 | − | 0.325670i | ||||
\(607\) | 26.2154 | + | 15.1355i | 1.06405 | + | 0.614330i | 0.926550 | − | 0.376171i | \(-0.122760\pi\) |
0.137501 | + | 0.990502i | \(0.456093\pi\) | |||||||
\(608\) | 18.5351 | 0.751698 | ||||||||
\(609\) | −27.8870 | + | 21.7507i | −1.13004 | + | 0.881381i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.26241 | + | 5.34766i | 0.374717 | + | 0.216343i | ||||
\(612\) | −8.15185 | + | 11.7474i | −0.329519 | + | 0.474859i | ||||
\(613\) | 9.01861 | + | 15.6207i | 0.364258 | + | 0.630914i | 0.988657 | − | 0.150192i | \(-0.0479893\pi\) |
−0.624399 | + | 0.781106i | \(0.714656\pi\) | |||||||
\(614\) | 19.4086 | − | 33.6167i | 0.783267 | − | 1.35666i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.788604 | − | 2.20633i | 0.0317738 | − | 0.0888956i | ||||
\(617\) | − | 11.2586i | − | 0.453254i | −0.973982 | − | 0.226627i | \(-0.927230\pi\) | ||
0.973982 | − | 0.226627i | \(-0.0727699\pi\) | |||||||
\(618\) | 25.0563 | + | 47.8855i | 1.00791 | + | 1.92624i | ||||
\(619\) | −5.23950 | + | 3.02503i | −0.210593 | + | 0.121586i | −0.601587 | − | 0.798807i | \(-0.705465\pi\) |
0.390994 | + | 0.920393i | \(0.372131\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.6590 | − | 14.1306i | −0.748760 | − | 0.567043i | ||||
\(622\) | 2.70540i | 0.108477i | ||||||||
\(623\) | 7.04054 | − | 1.28351i | 0.282073 | − | 0.0514227i | ||||
\(624\) | −24.6685 | − | 15.6424i | −0.987530 | − | 0.626198i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 24.4498 | + | 42.3482i | 0.977209 | + | 1.69258i | ||||
\(627\) | −3.22029 | − | 0.133788i | −0.128606 | − | 0.00534296i | ||||
\(628\) | 9.33888 | + | 5.39180i | 0.372662 | + | 0.215156i | ||||
\(629\) | −31.9152 | −1.27254 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 47.3970 | 1.88684 | 0.943422 | − | 0.331594i | \(-0.107586\pi\) | ||||
0.943422 | + | 0.331594i | \(0.107586\pi\) | |||||||
\(632\) | −11.9208 | − | 6.88249i | −0.474185 | − | 0.273771i | ||||
\(633\) | −9.90150 | − | 0.411359i | −0.393549 | − | 0.0163501i | ||||
\(634\) | −5.55316 | − | 9.61836i | −0.220544 | − | 0.381994i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −14.6508 | − | 9.29014i | −0.580942 | − | 0.368378i | ||||
\(637\) | −23.3812 | − | 3.84415i | −0.926397 | − | 0.152311i | ||||
\(638\) | − | 6.02728i | − | 0.238622i | ||||||
\(639\) | −0.379714 | + | 4.56201i | −0.0150213 | + | 0.180470i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.08690 | + | 1.20488i | −0.0824278 | + | 0.0475897i | −0.540647 | − | 0.841249i | \(-0.681821\pi\) |
0.458220 | + | 0.888839i | \(0.348487\pi\) | |||||||
\(642\) | −9.04442 | − | 17.2850i | −0.356955 | − | 0.682183i | ||||
\(643\) | − | 30.1631i | − | 1.18952i | −0.803904 | − | 0.594759i | \(-0.797247\pi\) | ||
0.803904 | − | 0.594759i | \(-0.202753\pi\) | |||||||
\(644\) | −7.86819 | + | 6.68020i | −0.310050 | + | 0.263237i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18.7909 | + | 32.5468i | −0.739319 | + | 1.28054i | ||||
\(647\) | 6.98967 | + | 12.1065i | 0.274792 | + | 0.475954i | 0.970083 | − | 0.242775i | \(-0.0780576\pi\) |
−0.695291 | + | 0.718729i | \(0.744724\pi\) | |||||||
\(648\) | 2.85631 | − | 17.0394i | 0.112206 | − | 0.669373i | ||||
\(649\) | −3.89972 | − | 2.25150i | −0.153077 | − | 0.0883792i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14.7927 | + | 5.99085i | 0.579772 | + | 0.234800i | ||||
\(652\) | 4.76671 | 0.186679 | ||||||||
\(653\) | 5.92653 | + | 3.42169i | 0.231923 | + | 0.133901i | 0.611459 | − | 0.791276i | \(-0.290583\pi\) |
−0.379536 | + | 0.925177i | \(0.623916\pi\) | |||||||
\(654\) | 0.953435 | − | 22.9494i | 0.0372823 | − | 0.897391i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 15.5870 | − | 26.9975i | 0.608572 | − | 1.05408i | ||||
\(657\) | 21.1606 | − | 9.97636i | 0.825552 | − | 0.389215i | ||||
\(658\) | 13.3266 | + | 4.76328i | 0.519523 | + | 0.185692i | ||||
\(659\) | 10.0735i | 0.392409i | 0.980563 | + | 0.196204i | \(0.0628616\pi\) | ||||
−0.980563 | + | 0.196204i | \(0.937138\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.84503 | + | 5.10668i | −0.344032 | + | 0.198627i | −0.662053 | − | 0.749457i | \(-0.730315\pi\) |
0.318022 | + | 0.948083i | \(0.396981\pi\) | |||||||
\(662\) | 19.8367 | − | 11.4527i | 0.770976 | − | 0.445123i | ||||
\(663\) | 28.5888 | − | 14.9592i | 1.11030 | − | 0.580967i | ||||
\(664\) | 33.7158i | 1.30843i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −26.6412 | + | 12.5603i | −1.03233 | + | 0.486701i | ||||
\(667\) | 17.3817 | − | 30.1060i | 0.673022 | − | 1.16571i | ||||
\(668\) | −0.346004 | − | 0.599296i | −0.0133873 | − | 0.0231875i | ||||
\(669\) | 0.419510 | − | 10.0977i | 0.0162192 | − | 0.390399i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.67895 | −0.142024 | ||||||||
\(672\) | −19.5171 | − | 7.90416i | −0.752888 | − | 0.304909i | ||||
\(673\) | −19.1004 | −0.736266 | −0.368133 | − | 0.929773i | \(-0.620003\pi\) | ||||
−0.368133 | + | 0.929773i | \(0.620003\pi\) | |||||||
\(674\) | 45.0282 | + | 25.9971i | 1.73442 | + | 1.00137i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.667597 | + | 1.15631i | 0.0256768 | + | 0.0444735i | ||||
\(677\) | 1.98790 | − | 3.44314i | 0.0764011 | − | 0.132331i | −0.825294 | − | 0.564704i | \(-0.808990\pi\) |
0.901695 | + | 0.432373i | \(0.142324\pi\) | |||||||
\(678\) | −27.3094 | + | 43.0675i | −1.04881 | + | 1.65400i | ||||
\(679\) | 8.96006 | − | 7.60721i | 0.343855 | − | 0.291938i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.16474 | + | 17.5149i | 0.351194 | + | 0.671172i | ||||
\(682\) | −2.35553 | + | 1.35997i | −0.0901981 | + | 0.0520759i | ||||
\(683\) | −9.21993 | + | 5.32313i | −0.352791 | + | 0.203684i | −0.665914 | − | 0.746029i | \(-0.731958\pi\) |
0.313123 | + | 0.949713i | \(0.398625\pi\) | |||||||
\(684\) | −0.869331 | + | 10.4444i | −0.0332397 | + | 0.399352i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −31.3491 | + | 0.544533i | −1.19691 | + | 0.0207904i | ||||
\(687\) | −1.53825 | − | 0.975412i | −0.0586879 | − | 0.0372143i | ||||
\(688\) | −20.8114 | + | 36.0464i | −0.793427 | + | 1.37426i | ||||
\(689\) | 19.5735 | + | 33.9022i | 0.745689 | + | 1.29157i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.3020 | + | 8.25729i | 0.544076 | + | 0.314122i | 0.746729 | − | 0.665128i | \(-0.231623\pi\) |
−0.202653 | + | 0.979251i | \(0.564956\pi\) | |||||||
\(692\) | −12.5743 | −0.478004 | ||||||||
\(693\) | 3.33385 | + | 1.51415i | 0.126642 | + | 0.0575176i | ||||
\(694\) | −13.2401 | −0.502586 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 25.6387 | + | 1.06517i | 0.971834 | + | 0.0403750i | ||||
\(697\) | 17.2178 | + | 29.8222i | 0.652172 | + | 1.12960i | ||||
\(698\) | 21.2889 | − | 36.8735i | 0.805797 | − | 1.39568i | ||||
\(699\) | 5.68265 | + | 3.60340i | 0.214938 | + | 0.136293i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.5702i | 0.739158i | 0.929199 | + | 0.369579i | \(0.120498\pi\) | ||||
−0.929199 | + | 0.369579i | \(0.879502\pi\) | |||||||
\(702\) | 17.9772 | − | 23.7383i | 0.678507 | − | 0.895945i | ||||
\(703\) | −20.2589 | + | 11.6965i | −0.764078 | + | 0.441141i | ||||
\(704\) | −0.872955 | + | 0.504001i | −0.0329007 | + | 0.0189952i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 20.7706i | − | 0.781712i | ||||||
\(707\) | −2.43677 | + | 6.81752i | −0.0916441 | + | 0.256399i | ||||
\(708\) | −7.84133 | + | 12.3660i | −0.294695 | + | 0.464742i | ||||
\(709\) | −14.1418 | + | 24.4943i | −0.531106 | + | 0.919903i | 0.468235 | + | 0.883604i | \(0.344890\pi\) |
−0.999341 | + | 0.0362991i | \(0.988443\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.2638 | − | 17.6730i | 0.459929 | − | 0.662788i | ||||
\(712\) | −4.49694 | − | 2.59631i | −0.168530 | − | 0.0973009i | ||||
\(713\) | −15.6877 | −0.587509 | ||||||||
\(714\) | 33.6658 | − | 26.2579i | 1.25991 | − | 0.982676i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.77061 | + | 1.02226i | 0.0661707 | + | 0.0382037i | ||||
\(717\) | −0.460357 | + | 11.0809i | −0.0171923 | + | 0.413823i | ||||
\(718\) | 6.95509 | + | 12.0466i | 0.259562 | + | 0.449574i | ||||
\(719\) | −9.75873 | + | 16.9026i | −0.363939 | + | 0.630361i | −0.988605 | − | 0.150531i | \(-0.951902\pi\) |
0.624666 | + | 0.780892i | \(0.285235\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.74566 | − | 47.9733i | −0.325705 | − | 1.78662i | ||||
\(722\) | − | 4.61959i | − | 0.171923i | ||||||
\(723\) | −3.47491 | + | 1.81826i | −0.129233 | + | 0.0676218i | ||||
\(724\) | −7.28057 | + | 4.20344i | −0.270580 | + | 0.156220i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 28.0261 | − | 14.6648i | 1.04015 | − | 0.544260i | ||||
\(727\) | 26.5060i | 0.983052i | 0.870863 | + | 0.491526i | \(0.163561\pi\) | ||||
−0.870863 | + | 0.491526i | \(0.836439\pi\) | |||||||
\(728\) | 11.1272 | + | 13.1061i | 0.412402 | + | 0.485743i | ||||
\(729\) | 26.1665 | + | 6.65709i | 0.969128 | + | 0.246559i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −22.9888 | − | 39.8177i | −0.850271 | − | 1.47271i | ||||
\(732\) | −0.496574 | + | 11.9526i | −0.0183539 | + | 0.441782i | ||||
\(733\) | 0.184602 | + | 0.106580i | 0.00681844 | + | 0.00393663i | 0.503405 | − | 0.864050i | \(-0.332080\pi\) |
−0.496587 | + | 0.867987i | \(0.665414\pi\) | |||||||
\(734\) | 47.2420 | 1.74373 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20.6979 | 0.762935 | ||||||||
\(737\) | 0.366045 | + | 0.211336i | 0.0134835 | + | 0.00778467i | ||||
\(738\) | 26.1091 | + | 18.1179i | 0.961090 | + | 0.666930i | ||||
\(739\) | 23.2265 | + | 40.2296i | 0.854402 | + | 1.47987i | 0.877198 | + | 0.480128i | \(0.159410\pi\) |
−0.0227959 | + | 0.999740i | \(0.507257\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.6650 | − | 19.9730i | 0.465261 | − | 0.733728i | ||||
\(742\) | 33.5255 | + | 39.4876i | 1.23076 | + | 1.44964i | ||||
\(743\) | − | 28.0937i | − | 1.03066i | −0.856992 | − | 0.515330i | \(-0.827670\pi\) | ||
0.856992 | − | 0.515330i | \(-0.172330\pi\) | |||||||
\(744\) | −5.36873 | − | 10.2603i | −0.196827 | − | 0.376159i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −26.5135 | + | 15.3076i | −0.970729 | + | 0.560451i | ||||
\(747\) | −52.5079 | − | 4.37044i | −1.92116 | − | 0.159906i | ||||
\(748\) | 2.19874i | 0.0803939i | ||||||||
\(749\) | 3.15687 | + | 17.3166i | 0.115349 | + | 0.632736i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.4832 | + | 21.6215i | −0.455518 | + | 0.788981i | −0.998718 | − | 0.0506227i | \(-0.983879\pi\) |
0.543199 | + | 0.839604i | \(0.317213\pi\) | |||||||
\(752\) | −7.87068 | − | 13.6324i | −0.287014 | − | 0.497123i | ||||
\(753\) | 23.0547 | + | 0.957813i | 0.840161 | + | 0.0349046i | ||||
\(754\) | 38.3014 | + | 22.1133i | 1.39485 | + | 0.805319i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.36933 | − | 10.6270i | 0.195281 | − | 0.386502i | ||||
\(757\) | −6.25577 | −0.227370 | −0.113685 | − | 0.993517i | \(-0.536265\pi\) | ||||
−0.113685 | + | 0.993517i | \(0.536265\pi\) | |||||||
\(758\) | 36.2796 | + | 20.9460i | 1.31773 | + | 0.760794i | ||||
\(759\) | −3.59606 | − | 0.149399i | −0.130529 | − | 0.00542284i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.3374 | + | 45.6178i | −0.954731 | + | 1.65364i | −0.219750 | + | 0.975556i | \(0.570524\pi\) |
−0.734982 | + | 0.678087i | \(0.762809\pi\) | |||||||
\(762\) | 31.0924 | + | 19.7158i | 1.12636 | + | 0.714229i | ||||
\(763\) | −6.97543 | + | 19.5157i | −0.252528 | + | 0.706514i | ||||
\(764\) | − | 4.37410i | − | 0.158249i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.9563 | + | 10.9444i | −0.684917 | + | 0.395437i | ||||
\(767\) | 28.6151 | − | 16.5209i | 1.03323 | − | 0.596536i | ||||
\(768\) | 14.0130 | + | 26.7806i | 0.505652 | + | 0.966360i | ||||
\(769\) | 5.37059i | 0.193669i | 0.995301 | + | 0.0968343i | \(0.0308717\pi\) | ||||
−0.995301 | + | 0.0968343i | \(0.969128\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.1733 | + | 28.6598i | −0.654496 | + | 1.03216i | ||||
\(772\) | −5.67432 | + | 9.82820i | −0.204223 | + | 0.353725i | ||||
\(773\) | −1.22649 | − | 2.12434i | −0.0441138 | − | 0.0764073i | 0.843125 | − | 0.537717i | \(-0.180713\pi\) |
−0.887239 | + | 0.461310i | \(0.847380\pi\) | |||||||
\(774\) | −34.8602 | − | 24.1906i | −1.25302 | − | 0.869512i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.52826 | −0.306147 | ||||||||
\(777\) | 26.3201 | − | 3.67689i | 0.944227 | − | 0.131908i | ||||
\(778\) | −32.0641 | −1.14956 | ||||||||
\(779\) | 21.8588 | + | 12.6202i | 0.783172 | + | 0.452165i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.351967 | + | 0.609625i | 0.0125944 | + | 0.0218141i | ||||
\(782\) | −20.9836 | + | 36.3446i | −0.750371 | + | 1.29968i | ||||
\(783\) | −4.98230 | + | 39.7909i | −0.178053 | + | 1.42201i | ||||
\(784\) | 26.9731 | + | 22.1060i | 0.963326 | + | 0.789501i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 17.4735 | − | 9.14307i | 0.623258 | − | 0.326122i | ||||
\(787\) | 35.6885 | − | 20.6048i | 1.27216 | − | 0.734481i | 0.296764 | − | 0.954951i | \(-0.404092\pi\) |
0.975394 | + | 0.220470i | \(0.0707590\pi\) | |||||||
\(788\) | 15.9702 | − | 9.22039i | 0.568914 | − | 0.328463i | ||||
\(789\) | 25.7416 | − | 13.4694i | 0.916426 | − | 0.479524i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 35.0764 | − | 29.7803i | 1.24717 | − | 1.05887i | ||||
\(792\) | −1.13295 | − | 2.40307i | −0.0402576 | − | 0.0853893i | ||||
\(793\) | 13.4976 | − | 23.3785i | 0.479314 | − | 0.830196i | ||||
\(794\) | 6.16797 | + | 10.6832i | 0.218893 | + | 0.379134i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.01431 | − | 2.89501i | −0.177727 | − | 0.102611i | ||||
\(797\) | −36.9407 | −1.30851 | −0.654253 | − | 0.756276i | \(-0.727017\pi\) | ||||
−0.654253 | + | 0.756276i | \(0.727017\pi\) | |||||||
\(798\) | 11.7469 | − | 29.0058i | 0.415837 | − | 1.02679i | ||||
\(799\) | 17.3883 | 0.615154 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.62634 | − | 6.66685i | 0.163464 | − | 0.235562i | ||||
\(802\) | 13.4292 | + | 23.2600i | 0.474200 | + | 0.821339i | ||||
\(803\) | 1.79870 | − | 3.11544i | 0.0634748 | − | 0.109942i | ||||
\(804\) | 0.736023 | − | 1.16073i | 0.0259575 | − | 0.0409357i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 19.9582i | − | 0.702997i | ||||||
\(807\) | 23.5610 | + | 45.0277i | 0.829385 | + | 1.58505i | ||||
\(808\) | 4.54931 | − | 2.62655i | 0.160044 | − | 0.0924016i | ||||
\(809\) | 45.9461 | − | 26.5270i | 1.61538 | − | 0.932640i | 0.627285 | − | 0.778790i | \(-0.284166\pi\) |
0.988094 | − | 0.153850i | \(-0.0491672\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 19.0686i | − | 0.669590i | −0.942291 | − | 0.334795i | \(-0.891333\pi\) | ||
0.942291 | − | 0.334795i | \(-0.108667\pi\) | |||||||
\(812\) | 16.6523 | + | 5.95198i | 0.584380 | + | 0.208873i | ||||
\(813\) | −4.34304 | − | 2.75394i | −0.152317 | − | 0.0965850i | ||||
\(814\) | −2.26457 | + | 3.92235i | −0.0793731 | + | 0.137478i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −47.4481 | − | 1.97124i | −1.66102 | − | 0.0690072i | ||||
\(817\) | −29.1852 | − | 16.8501i | −1.02106 | − | 0.589511i | ||||
\(818\) | −44.5918 | −1.55912 | ||||||||
\(819\) | −21.8533 | + | 15.6303i | −0.763617 | + | 0.546167i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.46302 | + | 5.46348i | 0.330262 | + | 0.190677i | 0.655957 | − | 0.754798i | \(-0.272265\pi\) |
−0.325696 | + | 0.945475i | \(0.605598\pi\) | |||||||
\(822\) | 59.6108 | + | 2.47654i | 2.07916 | + | 0.0863793i | ||||
\(823\) | −20.9937 | − | 36.3622i | −0.731794 | − | 1.26750i | −0.956116 | − | 0.292990i | \(-0.905350\pi\) |
0.224321 | − | 0.974515i | \(-0.427984\pi\) | |||||||
\(824\) | −17.6909 | + | 30.6416i | −0.616293 | + | 1.06745i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 33.3294 | − | 28.2971i | 1.15968 | − | 0.984584i | ||||
\(827\) | 22.1128i | 0.768937i | 0.923138 | + | 0.384468i | \(0.125615\pi\) | ||||
−0.923138 | + | 0.384468i | \(0.874385\pi\) | |||||||
\(828\) | −0.970771 | + | 11.6632i | −0.0337366 | + | 0.405323i | ||||
\(829\) | 27.1141 | − | 15.6543i | 0.941711 | − | 0.543697i | 0.0512148 | − | 0.998688i | \(-0.483691\pi\) |
0.890496 | + | 0.454990i | \(0.150357\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.4596 | + | 19.9895i | 0.362838 | + | 0.693427i | ||||
\(832\) | − | 7.39645i | − | 0.256426i | ||||||
\(833\) | −36.0450 | + | 13.5940i | −1.24888 | + | 0.471003i | ||||
\(834\) | −15.3755 | + | 24.2476i | −0.532410 | + | 0.839625i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.805806 | + | 1.39570i | 0.0278694 | + | 0.0482712i | ||||
\(837\) | 16.6749 | − | 7.03109i | 0.576370 | − | 0.243030i | ||||
\(838\) | 21.0389 | + | 12.1468i | 0.726777 | + | 0.419605i | ||||
\(839\) | −8.65688 | −0.298869 | −0.149434 | − | 0.988772i | \(-0.547745\pi\) | ||||
−0.149434 | + | 0.988772i | \(0.547745\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −30.5607 | −1.05382 | ||||||||
\(842\) | −14.7610 | − | 8.52225i | −0.508696 | − | 0.293696i | ||||
\(843\) | −1.39769 | + | 33.6428i | −0.0481391 | + | 1.15872i | ||||
\(844\) | 2.47763 | + | 4.29138i | 0.0852835 | + | 0.147715i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 14.5149 | − | 6.84318i | 0.499031 | − | 0.235273i | ||||
\(847\) | −28.0775 | + | 5.11859i | −0.964753 | + | 0.175877i | ||||
\(848\) | − | 57.6164i | − | 1.97855i | ||||||
\(849\) | 8.65476 | − | 4.52864i | 0.297031 | − | 0.155423i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.6228 | + | 13.0613i | −0.775501 | + | 0.447736i | ||||
\(852\) | 2.02813 | − | 1.06123i | 0.0694826 | − | 0.0363571i | ||||
\(853\) | 48.3400i | 1.65513i | 0.561370 | + | 0.827565i | \(0.310274\pi\) | ||||
−0.561370 | + | 0.827565i | \(0.689726\pi\) | |||||||
\(854\) | 12.0226 | − | 33.6365i | 0.411405 | − | 1.15102i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.38579 | − | 11.0605i | 0.218262 | − | 0.378041i | ||||
\(857\) | 16.8218 | + | 29.1362i | 0.574622 | + | 0.995274i | 0.996083 | + | 0.0884274i | \(0.0281841\pi\) |
−0.421461 | + | 0.906847i | \(0.638483\pi\) | |||||||
\(858\) | 0.190068 | − | 4.57497i | 0.00648881 | − | 0.156187i | ||||
\(859\) | 22.6082 | + | 13.0528i | 0.771382 | + | 0.445357i | 0.833367 | − | 0.552720i | \(-0.186410\pi\) |
−0.0619856 | + | 0.998077i | \(0.519743\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −17.6351 | − | 22.6103i | −0.601001 | − | 0.770557i | ||||
\(862\) | 13.9573 | 0.475387 | ||||||||
\(863\) | 34.0767 | + | 19.6742i | 1.15998 | + | 0.669718i | 0.951300 | − | 0.308265i | \(-0.0997485\pi\) |
0.208685 | + | 0.977983i | \(0.433082\pi\) | |||||||
\(864\) | −22.0005 | + | 9.27662i | −0.748471 | + | 0.315597i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 9.07765 | − | 15.7230i | 0.308471 | − | 0.534288i | ||||
\(867\) | 12.3237 | − | 19.4348i | 0.418536 | − | 0.660042i | ||||
\(868\) | −1.43124 | − | 7.85088i | −0.0485793 | − | 0.266476i | ||||
\(869\) | − | 3.30783i | − | 0.112211i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.68594 | + | 1.55073i | −0.0910097 | + | 0.0525445i | ||||
\(872\) | 13.0227 | − | 7.51869i | 0.441006 | − | 0.254615i | ||||
\(873\) | 1.10548 | − | 13.2817i | 0.0374150 | − | 0.449516i | ||||
\(874\) | 30.7607i | 1.04050i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −9.87904 | − | 6.26435i | −0.333782 | − | 0.211653i | ||||
\(877\) | −13.2655 | + | 22.9766i | −0.447945 | + | 0.775864i | −0.998252 | − | 0.0590984i | \(-0.981177\pi\) |
0.550307 | + | 0.834963i | \(0.314511\pi\) | |||||||
\(878\) | −2.68042 | − | 4.64262i | −0.0904597 | − | 0.156681i | ||||
\(879\) | −37.3376 | − | 1.55120i | −1.25936 | − | 0.0523205i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.2055 | −0.444904 | −0.222452 | − | 0.974944i | \(-0.571406\pi\) | ||||
−0.222452 | + | 0.974944i | \(0.571406\pi\) | |||||||
\(882\) | −24.7386 | + | 25.5331i | −0.832991 | + | 0.859743i | ||||
\(883\) | −27.3728 | −0.921169 | −0.460584 | − | 0.887616i | \(-0.652360\pi\) | ||||
−0.460584 | + | 0.887616i | \(0.652360\pi\) | |||||||
\(884\) | −13.9723 | − | 8.06689i | −0.469938 | − | 0.271319i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14.7738 | − | 25.5889i | −0.496335 | − | 0.859677i | ||||
\(887\) | 16.4606 | − | 28.5105i | 0.552692 | − | 0.957290i | −0.445387 | − | 0.895338i | \(-0.646934\pi\) |
0.998079 | − | 0.0619524i | \(-0.0197327\pi\) | |||||||
\(888\) | −16.2846 | − | 10.3262i | −0.546476 | − | 0.346523i | ||||
\(889\) | −21.4997 | − | 25.3232i | −0.721078 | − | 0.849313i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.88932 | − | 1.45292i | 0.130297 | − | 0.0486747i | ||||
\(892\) | −4.37641 | + | 2.52672i | −0.146533 | + | 0.0846009i | ||||
\(893\) | 11.0376 | − | 6.37256i | 0.369359 | − | 0.213250i | ||||
\(894\) | −22.1644 | − | 42.3587i | −0.741288 | − | 1.41669i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −6.11599 | − | 33.5486i | −0.204321 | − | 1.12078i | ||||
\(897\) | 14.1429 | − | 22.3036i | 0.472216 | − | 0.744697i | ||||
\(898\) | −10.4009 | + | 18.0149i | −0.347083 | + | 0.601165i | ||||
\(899\) | 13.4390 | + | 23.2770i | 0.448216 | + | 0.776333i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 55.1178 | + | 31.8223i | 1.83624 | + | 1.06015i | ||||
\(902\) | 4.88682 | 0.162713 | ||||||||
\(903\) | 23.5458 | + | 30.1886i | 0.783557 | + | 1.00461i | ||||
\(904\) | −33.3860 | −1.11040 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.83634 | − | 44.2011i | 0.0610083 | − | 1.46848i | ||||
\(907\) | −10.4117 | − | 18.0335i | −0.345714 | − | 0.598793i | 0.639770 | − | 0.768567i | \(-0.279030\pi\) |
−0.985483 | + | 0.169773i | \(0.945696\pi\) | |||||||
\(908\) | 4.94217 | − | 8.56010i | 0.164012 | − | 0.284077i | ||||
\(909\) | 3.50079 | + | 7.42543i | 0.116114 | + | 0.246286i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50.2293i | 1.66417i | 0.554648 | + | 0.832085i | \(0.312853\pi\) | ||||
−0.554648 | + | 0.832085i | \(0.687147\pi\) | |||||||
\(912\) | −30.8412 | + | 16.1378i | −1.02125 | + | 0.534375i | ||||
\(913\) | −7.01668 | + | 4.05108i | −0.232218 | + | 0.134071i | ||||
\(914\) | 7.16844 | − | 4.13870i | 0.237111 | − | 0.136896i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.910763i | 0.0300925i | ||||||||
\(917\) | −17.5055 | + | 3.19130i | −0.578083 | + | 0.105386i | ||||
\(918\) | 6.01475 | − | 48.0365i | 0.198516 | − | 1.58544i | ||||
\(919\) | 9.88707 | − | 17.1249i | 0.326144 | − | 0.564899i | −0.655599 | − | 0.755109i | \(-0.727584\pi\) |
0.981743 | + | 0.190211i | \(0.0609171\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.64849 | + | 39.6796i | −0.0543197 | + | 1.30749i | ||||
\(922\) | −7.51755 | − | 4.34026i | −0.247577 | − | 0.142939i | ||||
\(923\) | −5.16529 | −0.170017 | ||||||||
\(924\) | −0.253313 | − | 1.81327i | −0.00833338 | − | 0.0596522i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −58.5095 | − | 33.7805i | −1.92274 | − | 1.11009i | ||||
\(927\) | −45.4270 | − | 31.5232i | −1.49202 | − | 1.03536i | ||||
\(928\) | −17.7310 | − | 30.7111i | −0.582050 | − | 1.00814i | ||||
\(929\) | 1.84133 | − | 3.18927i | 0.0604119 | − | 0.104637i | −0.834238 | − | 0.551405i | \(-0.814092\pi\) |
0.894650 | + | 0.446769i | \(0.147425\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.8983 | + | 21.8390i | −0.586594 | + | 0.715745i | ||||
\(932\) | − | 3.36457i | − | 0.110210i | ||||||
\(933\) | −1.28325 | − | 2.45245i | −0.0420119 | − | 0.0802896i | ||||
\(934\) | −13.3802 | + | 7.72506i | −0.437814 | + | 0.252772i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 19.4273 | + | 1.61701i | 0.635002 | + | 0.0528538i | ||||
\(937\) | 36.7871i | 1.20178i | 0.799331 | + | 0.600891i | \(0.205187\pi\) | ||||
−0.799331 | + | 0.600891i | \(0.794813\pi\) | |||||||
\(938\) | −3.12845 | + | 2.65610i | −0.102148 | + | 0.0867247i | ||||
\(939\) | −42.2507 | − | 26.7914i | −1.37880 | − | 0.874305i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.1072 | − | 17.5061i | −0.329484 | − | 0.570684i | 0.652925 | − | 0.757422i | \(-0.273542\pi\) |
−0.982410 | + | 0.186739i | \(0.940208\pi\) | |||||||
\(942\) | −36.4789 | − | 1.51552i | −1.18855 | − | 0.0493784i | ||||
\(943\) | 24.4094 | + | 14.0928i | 0.794880 | + | 0.458924i | ||||
\(944\) | −48.6310 | −1.58280 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.52474 | −0.212138 | ||||||||
\(947\) | −8.50752 | − | 4.91182i | −0.276457 | − | 0.159613i | 0.355361 | − | 0.934729i | \(-0.384358\pi\) |
−0.631819 | + | 0.775116i | \(0.717691\pi\) | |||||||
\(948\) | −10.7469 | − | 0.446481i | −0.349043 | − | 0.0145010i | ||||
\(949\) | 13.1984 | + | 22.8603i | 0.428438 | + | 0.742076i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.59621 | + | 6.08501i | 0.311179 | + | 0.197320i | ||||
\(952\) | 26.3206 | + | 9.40772i | 0.853057 | + | 0.304906i | ||||
\(953\) | 24.7365i | 0.801294i | 0.916232 | + | 0.400647i | \(0.131215\pi\) | ||||
−0.916232 | + | 0.400647i | \(0.868785\pi\) | |||||||
\(954\) | 58.5332 | + | 4.87195i | 1.89508 | + | 0.157735i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4.80253 | − | 2.77274i | 0.155325 | − | 0.0896769i | ||||
\(957\) | 2.85892 | + | 5.46373i | 0.0924158 | + | 0.176617i | ||||
\(958\) | − | 20.9996i | − | 0.678468i | ||||||
\(959\) | −50.6917 | − | 18.1186i | −1.63692 | − | 0.585081i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.43537 | + | 16.3425i | −0.304367 | + | 0.527179i | ||||
\(962\) | −16.6168 | − | 28.7812i | −0.535748 | − | 0.927942i | ||||
\(963\) | 16.3975 | + | 11.3788i | 0.528403 | + | 0.366676i | ||||
\(964\) | 1.69830 | + | 0.980514i | 0.0546986 | + | 0.0315802i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 13.1177 | − | 32.3904i | 0.422054 | − | 1.04214i | ||||
\(967\) | −14.0157 | −0.450713 | −0.225357 | − | 0.974276i | \(-0.572355\pi\) | ||||
−0.225357 | + | 0.974276i | \(0.572355\pi\) | |||||||
\(968\) | 17.9337 | + | 10.3540i | 0.576410 | + | 0.332791i | ||||
\(969\) | 1.59603 | − | 38.4168i | 0.0512719 | − | 1.23412i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.0308306 | − | 0.0534003i | 0.000989403 | − | 0.00171370i | −0.865530 | − | 0.500857i | \(-0.833018\pi\) |
0.866520 | + | 0.499143i | \(0.166352\pi\) | |||||||
\(972\) | −4.19546 | − | 12.8322i | −0.134569 | − | 0.411593i | ||||
\(973\) | 19.7485 | − | 16.7667i | 0.633106 | − | 0.537516i | ||||
\(974\) | 23.9792i | 0.768342i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −34.4085 | + | 19.8657i | −1.10139 | + | 0.635887i | ||||
\(977\) | 16.5237 | − | 9.53996i | 0.528640 | − | 0.305210i | −0.211822 | − | 0.977308i | \(-0.567940\pi\) |
0.740462 | + | 0.672098i | \(0.234607\pi\) | |||||||
\(978\) | −14.2995 | + | 7.48229i | −0.457248 | + | 0.239257i | ||||
\(979\) | − | 1.24783i | − | 0.0398808i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.0213 | + | 21.2558i | 0.319955 | + | 0.678647i | ||||
\(982\) | 27.1900 | − | 47.0945i | 0.867669 | − | 1.50285i | ||||
\(983\) | −4.07300 | − | 7.05465i | −0.129909 | − | 0.225008i | 0.793732 | − | 0.608267i | \(-0.208135\pi\) |
−0.923641 | + | 0.383259i | \(0.874802\pi\) | |||||||
\(984\) | −0.863618 | + | 20.7875i | −0.0275311 | + | 0.662680i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 71.9030 | 2.28986 | ||||||||
\(987\) | −14.3399 | + | 2.00327i | −0.456444 | + | 0.0637649i | ||||
\(988\) | −11.8256 | −0.376222 | ||||||||
\(989\) | −32.5908 | − | 18.8163i | −1.03633 | − | 0.598324i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.21862 | − | 9.03891i | −0.165775 | − | 0.287130i | 0.771155 | − | 0.636647i | \(-0.219679\pi\) |
−0.936930 | + | 0.349517i | \(0.886346\pi\) | |||||||
\(992\) | −8.00150 | + | 13.8590i | −0.254048 | + | 0.440024i | ||||
\(993\) | −12.5496 | + | 19.7910i | −0.398250 | + | 0.628050i | ||||
\(994\) | −6.72398 | + | 1.22580i | −0.213272 | + | 0.0388800i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 12.2146 | + | 23.3435i | 0.387033 | + | 0.739666i | ||||
\(997\) | −11.6811 | + | 6.74411i | −0.369945 | + | 0.213588i | −0.673435 | − | 0.739247i | \(-0.735182\pi\) |
0.303489 | + | 0.952835i | \(0.401848\pi\) | |||||||
\(998\) | −39.1719 | + | 22.6159i | −1.23996 | + | 0.715894i | ||||
\(999\) | 18.1925 | − | 24.0226i | 0.575587 | − | 0.760042i |
(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 | 525.2.t.h.26.8 | yes | 20 | |
3.2 | odd | 2 | inner | 525.2.t.h.26.3 | ✓ | 20 | |
5.2 | odd | 4 | 525.2.q.g.299.6 | 40 | |||
5.3 | odd | 4 | 525.2.q.g.299.15 | 40 | |||
5.4 | even | 2 | 525.2.t.i.26.3 | yes | 20 | ||
7.3 | odd | 6 | inner | 525.2.t.h.101.3 | yes | 20 | |
15.2 | even | 4 | 525.2.q.g.299.16 | 40 | |||
15.8 | even | 4 | 525.2.q.g.299.5 | 40 | |||
15.14 | odd | 2 | 525.2.t.i.26.8 | yes | 20 | ||
21.17 | even | 6 | inner | 525.2.t.h.101.8 | yes | 20 | |
35.3 | even | 12 | 525.2.q.g.374.16 | 40 | |||
35.17 | even | 12 | 525.2.q.g.374.5 | 40 | |||
35.24 | odd | 6 | 525.2.t.i.101.8 | yes | 20 | ||
105.17 | odd | 12 | 525.2.q.g.374.15 | 40 | |||
105.38 | odd | 12 | 525.2.q.g.374.6 | 40 | |||
105.59 | even | 6 | 525.2.t.i.101.3 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.q.g.299.5 | 40 | 15.8 | even | 4 | |||
525.2.q.g.299.6 | 40 | 5.2 | odd | 4 | |||
525.2.q.g.299.15 | 40 | 5.3 | odd | 4 | |||
525.2.q.g.299.16 | 40 | 15.2 | even | 4 | |||
525.2.q.g.374.5 | 40 | 35.17 | even | 12 | |||
525.2.q.g.374.6 | 40 | 105.38 | odd | 12 | |||
525.2.q.g.374.15 | 40 | 105.17 | odd | 12 | |||
525.2.q.g.374.16 | 40 | 35.3 | even | 12 | |||
525.2.t.h.26.3 | ✓ | 20 | 3.2 | odd | 2 | inner | |
525.2.t.h.26.8 | yes | 20 | 1.1 | even | 1 | trivial | |
525.2.t.h.101.3 | yes | 20 | 7.3 | odd | 6 | inner | |
525.2.t.h.101.8 | yes | 20 | 21.17 | even | 6 | inner | |
525.2.t.i.26.3 | yes | 20 | 5.4 | even | 2 | ||
525.2.t.i.26.8 | yes | 20 | 15.14 | odd | 2 | ||
525.2.t.i.101.3 | yes | 20 | 105.59 | even | 6 | ||
525.2.t.i.101.8 | yes | 20 | 35.24 | odd | 6 |