Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(165,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.x (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 557.3 | ||
Character | \(\chi\) | \(=\) | 784.557 |
Dual form | 784.2.x.l.373.3 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.966164 | + | 1.03273i | −0.683181 | + | 0.730249i | ||||
\(3\) | −3.02670 | + | 0.811002i | −1.74747 | + | 0.468232i | −0.984082 | − | 0.177713i | \(-0.943130\pi\) |
−0.763384 | + | 0.645945i | \(0.776463\pi\) | |||||||
\(4\) | −0.133053 | − | 1.99557i | −0.0665266 | − | 0.997785i | ||||
\(5\) | 0.537019 | + | 0.143894i | 0.240162 | + | 0.0643513i | 0.376892 | − | 0.926257i | \(-0.376993\pi\) |
−0.136730 | + | 0.990608i | \(0.543659\pi\) | |||||||
\(6\) | 2.08675 | − | 3.90932i | 0.851910 | − | 1.59597i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.18943 | + | 1.79064i | 0.774081 | + | 0.633087i | ||||
\(9\) | 5.90511 | − | 3.40932i | 1.96837 | − | 1.13644i | ||||
\(10\) | −0.667452 | + | 0.415570i | −0.211067 | + | 0.131415i | ||||
\(11\) | 0.814781 | + | 3.04081i | 0.245666 | + | 0.916837i | 0.973048 | + | 0.230604i | \(0.0740703\pi\) |
−0.727382 | + | 0.686233i | \(0.759263\pi\) | |||||||
\(12\) | 2.02112 | + | 5.93208i | 0.583448 | + | 1.71244i | ||||
\(13\) | −3.16316 | − | 3.16316i | −0.877304 | − | 0.877304i | 0.115951 | − | 0.993255i | \(-0.463008\pi\) |
−0.993255 | + | 0.115951i | \(0.963008\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.74209 | −0.449807 | ||||||||
\(16\) | −3.96459 | + | 0.531034i | −0.991148 | + | 0.132758i | ||||
\(17\) | −0.490475 | + | 0.849528i | −0.118958 | + | 0.206041i | −0.919355 | − | 0.393429i | \(-0.871289\pi\) |
0.800397 | + | 0.599470i | \(0.204622\pi\) | |||||||
\(18\) | −2.18441 | + | 9.39233i | −0.514871 | + | 2.21379i | ||||
\(19\) | −1.92687 | + | 7.19116i | −0.442053 | + | 1.64977i | 0.281548 | + | 0.959547i | \(0.409152\pi\) |
−0.723601 | + | 0.690218i | \(0.757515\pi\) | |||||||
\(20\) | 0.215698 | − | 1.09080i | 0.0482315 | − | 0.243911i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.92754 | − | 2.09647i | −0.837354 | − | 0.446969i | ||||
\(23\) | −1.09077 | + | 0.629754i | −0.227441 | + | 0.131313i | −0.609391 | − | 0.792870i | \(-0.708586\pi\) |
0.381950 | + | 0.924183i | \(0.375253\pi\) | |||||||
\(24\) | −8.07896 | − | 3.64410i | −1.64911 | − | 0.743848i | ||||
\(25\) | −4.06244 | − | 2.34545i | −0.812489 | − | 0.469090i | ||||
\(26\) | 6.32282 | − | 0.210551i | 1.24001 | − | 0.0412925i | ||||
\(27\) | −8.46094 | + | 8.46094i | −1.62831 | + | 1.62831i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.17349 | + | 3.17349i | 0.589302 | + | 0.589302i | 0.937443 | − | 0.348140i | \(-0.113187\pi\) |
−0.348140 | + | 0.937443i | \(0.613187\pi\) | |||||||
\(30\) | 1.68315 | − | 1.79911i | 0.307300 | − | 0.328471i | ||||
\(31\) | 2.21570 | − | 3.83770i | 0.397951 | − | 0.689272i | −0.595522 | − | 0.803339i | \(-0.703055\pi\) |
0.993473 | + | 0.114068i | \(0.0363880\pi\) | |||||||
\(32\) | 3.28204 | − | 4.60741i | 0.580187 | − | 0.814483i | ||||
\(33\) | −4.93220 | − | 8.54282i | −0.858585 | − | 1.48711i | ||||
\(34\) | −0.403452 | − | 1.32731i | −0.0691914 | − | 0.227632i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −7.58922 | − | 11.3304i | −1.26487 | − | 1.88841i | ||||
\(37\) | −0.881285 | − | 0.236140i | −0.144882 | − | 0.0388211i | 0.185649 | − | 0.982616i | \(-0.440561\pi\) |
−0.330531 | + | 0.943795i | \(0.607228\pi\) | |||||||
\(38\) | −5.56484 | − | 8.93777i | −0.902737 | − | 1.44990i | ||||
\(39\) | 12.1393 | + | 7.00862i | 1.94384 | + | 1.12228i | ||||
\(40\) | 0.918105 | + | 1.27665i | 0.145165 | + | 0.201857i | ||||
\(41\) | 1.21375i | 0.189556i | 0.995498 | + | 0.0947779i | \(0.0302141\pi\) | ||||
−0.995498 | + | 0.0947779i | \(0.969786\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.966515 | − | 0.966515i | 0.147392 | − | 0.147392i | −0.629560 | − | 0.776952i | \(-0.716765\pi\) |
0.776952 | + | 0.629560i | \(0.216765\pi\) | |||||||
\(44\) | 5.95973 | − | 2.03054i | 0.898463 | − | 0.306116i | ||||
\(45\) | 3.66174 | − | 0.981160i | 0.545860 | − | 0.146263i | ||||
\(46\) | 0.403495 | − | 1.73491i | 0.0594921 | − | 0.255799i | ||||
\(47\) | −4.98574 | − | 8.63555i | −0.727244 | − | 1.25962i | −0.958043 | − | 0.286623i | \(-0.907467\pi\) |
0.230799 | − | 0.973001i | \(-0.425866\pi\) | |||||||
\(48\) | 11.5690 | − | 4.82257i | 1.66984 | − | 0.696078i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 6.34720 | − | 1.92931i | 0.897630 | − | 0.272845i | ||||
\(51\) | 0.795553 | − | 2.96904i | 0.111400 | − | 0.415749i | ||||
\(52\) | −5.89144 | + | 6.73318i | −0.816996 | + | 0.933724i | ||||
\(53\) | −2.95681 | − | 11.0350i | −0.406149 | − | 1.51577i | −0.801928 | − | 0.597421i | \(-0.796192\pi\) |
0.395779 | − | 0.918346i | \(-0.370475\pi\) | |||||||
\(54\) | −0.563190 | − | 16.9125i | −0.0766404 | − | 2.30150i | ||||
\(55\) | 1.75021i | 0.235999i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 23.3282i | − | 3.08989i | ||||||
\(58\) | −6.34346 | + | 0.211239i | −0.832938 | + | 0.0277370i | ||||
\(59\) | 0.663915 | + | 2.47776i | 0.0864344 | + | 0.322577i | 0.995582 | − | 0.0938966i | \(-0.0299323\pi\) |
−0.909148 | + | 0.416474i | \(0.863266\pi\) | |||||||
\(60\) | 0.231791 | + | 3.47647i | 0.0299241 | + | 0.448810i | ||||
\(61\) | −0.947210 | + | 3.53504i | −0.121278 | + | 0.452615i | −0.999680 | − | 0.0253078i | \(-0.991943\pi\) |
0.878402 | + | 0.477923i | \(0.158610\pi\) | |||||||
\(62\) | 1.82257 | + | 5.99606i | 0.231467 | + | 0.761501i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.58722 | + | 7.84097i | 0.198402 | + | 0.980121i | ||||
\(65\) | −1.24352 | − | 2.15384i | −0.154240 | − | 0.267151i | ||||
\(66\) | 13.5877 | + | 3.16015i | 1.67253 | + | 0.388987i | ||||
\(67\) | 2.17555 | − | 0.582936i | 0.265785 | − | 0.0712170i | −0.123465 | − | 0.992349i | \(-0.539401\pi\) |
0.389251 | + | 0.921132i | \(0.372734\pi\) | |||||||
\(68\) | 1.76055 | + | 0.865745i | 0.213498 | + | 0.104987i | ||||
\(69\) | 2.79069 | − | 2.79069i | 0.335960 | − | 0.335960i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.934634i | 0.110921i | 0.998461 | + | 0.0554603i | \(0.0176626\pi\) | ||||
−0.998461 | + | 0.0554603i | \(0.982337\pi\) | |||||||
\(72\) | 19.0337 | + | 3.10946i | 2.24314 | + | 0.366454i | ||||
\(73\) | −0.615321 | − | 0.355256i | −0.0720179 | − | 0.0415795i | 0.463559 | − | 0.886066i | \(-0.346572\pi\) |
−0.535577 | + | 0.844487i | \(0.679906\pi\) | |||||||
\(74\) | 1.09533 | − | 0.681978i | 0.127330 | − | 0.0792783i | ||||
\(75\) | 14.1980 | + | 3.80433i | 1.63944 | + | 0.439286i | ||||
\(76\) | 14.6068 | + | 2.88839i | 1.67552 | + | 0.331321i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −18.9665 | + | 5.76510i | −2.14754 | + | 0.652769i | ||||
\(79\) | −5.93220 | − | 10.2749i | −0.667424 | − | 1.15601i | −0.978622 | − | 0.205668i | \(-0.934063\pi\) |
0.311198 | − | 0.950345i | \(-0.399270\pi\) | |||||||
\(80\) | −2.20548 | − | 0.285305i | −0.246580 | − | 0.0318981i | ||||
\(81\) | 8.51894 | − | 14.7552i | 0.946549 | − | 1.63947i | ||||
\(82\) | −1.25347 | − | 1.17268i | −0.138423 | − | 0.129501i | ||||
\(83\) | −6.77482 | − | 6.77482i | −0.743634 | − | 0.743634i | 0.229642 | − | 0.973275i | \(-0.426245\pi\) |
−0.973275 | + | 0.229642i | \(0.926245\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.385637 | + | 0.385637i | −0.0418282 | + | 0.0418282i | ||||
\(86\) | 0.0643346 | + | 1.93196i | 0.00693738 | + | 0.208329i | ||||
\(87\) | −12.1789 | − | 7.03150i | −1.30572 | − | 0.753856i | ||||
\(88\) | −3.66108 | + | 8.11661i | −0.390272 | + | 0.865234i | ||||
\(89\) | 8.84053 | − | 5.10408i | 0.937095 | − | 0.541032i | 0.0480464 | − | 0.998845i | \(-0.484700\pi\) |
0.889048 | + | 0.457813i | \(0.151367\pi\) | |||||||
\(90\) | −2.52457 | + | 4.72954i | −0.266113 | + | 0.498537i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.40185 | + | 2.09291i | 0.146153 | + | 0.218201i | ||||
\(93\) | −3.59387 | + | 13.4125i | −0.372667 | + | 1.39081i | ||||
\(94\) | 13.7352 | + | 3.19445i | 1.41668 | + | 0.329482i | ||||
\(95\) | −2.06953 | + | 3.58453i | −0.212329 | + | 0.367765i | ||||
\(96\) | −6.19712 | + | 16.6070i | −0.632491 | + | 1.69494i | ||||
\(97\) | −3.03684 | −0.308344 | −0.154172 | − | 0.988044i | \(-0.549271\pi\) | ||||
−0.154172 | + | 0.988044i | \(0.549271\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 15.1784 | + | 15.1784i | 1.52549 | + | 1.52549i | ||||
\(100\) | −4.13999 | + | 8.41896i | −0.413999 | + | 0.841896i | ||||
\(101\) | −3.72056 | − | 13.8853i | −0.370210 | − | 1.38164i | −0.860219 | − | 0.509925i | \(-0.829673\pi\) |
0.490009 | − | 0.871717i | \(-0.336993\pi\) | |||||||
\(102\) | 2.29758 | + | 3.69017i | 0.227494 | + | 0.365382i | ||||
\(103\) | 5.24395 | − | 3.02760i | 0.516702 | − | 0.298318i | −0.218882 | − | 0.975751i | \(-0.570241\pi\) |
0.735584 | + | 0.677433i | \(0.236908\pi\) | |||||||
\(104\) | −1.26144 | − | 12.5896i | −0.123695 | − | 1.23451i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 14.2529 | + | 7.60800i | 1.38436 | + | 0.738954i | ||||
\(107\) | −17.0716 | − | 4.57432i | −1.65037 | − | 0.442216i | −0.690655 | − | 0.723184i | \(-0.742678\pi\) |
−0.959717 | + | 0.280968i | \(0.909344\pi\) | |||||||
\(108\) | 18.0102 | + | 15.7586i | 1.73303 | + | 1.51638i | ||||
\(109\) | −13.7388 | + | 3.68130i | −1.31594 | + | 0.352604i | −0.847454 | − | 0.530868i | \(-0.821866\pi\) |
−0.468483 | + | 0.883473i | \(0.655199\pi\) | |||||||
\(110\) | −1.80749 | − | 1.69099i | −0.172338 | − | 0.161230i | ||||
\(111\) | 2.85889 | 0.271354 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.01929 | 0.472175 | 0.236088 | − | 0.971732i | \(-0.424135\pi\) | ||||
0.236088 | + | 0.971732i | \(0.424135\pi\) | |||||||
\(114\) | 24.0917 | + | 22.5389i | 2.25639 | + | 2.11096i | ||||
\(115\) | −0.676380 | + | 0.181236i | −0.0630728 | + | 0.0169003i | ||||
\(116\) | 5.91068 | − | 6.75516i | 0.548793 | − | 0.627201i | ||||
\(117\) | −29.4631 | − | 7.89461i | −2.72386 | − | 0.729857i | ||||
\(118\) | −3.20031 | − | 1.70828i | −0.294612 | − | 0.157260i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.81420 | − | 3.11946i | −0.348187 | − | 0.284767i | ||||
\(121\) | 0.943649 | − | 0.544816i | 0.0857863 | − | 0.0495287i | ||||
\(122\) | −2.73557 | − | 4.39363i | −0.247667 | − | 0.397781i | ||||
\(123\) | −0.984353 | − | 3.67365i | −0.0887561 | − | 0.331242i | ||||
\(124\) | −7.95321 | − | 3.91096i | −0.714219 | − | 0.351215i | ||||
\(125\) | −3.80974 | − | 3.80974i | −0.340754 | − | 0.340754i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.3869 | −1.72031 | −0.860156 | − | 0.510031i | \(-0.829634\pi\) | ||||
−0.860156 | + | 0.510031i | \(0.829634\pi\) | |||||||
\(128\) | −9.63110 | − | 5.93650i | −0.851277 | − | 0.524717i | ||||
\(129\) | −2.14151 | + | 3.70920i | −0.188549 | + | 0.326577i | ||||
\(130\) | 3.42577 | + | 0.796745i | 0.300460 | + | 0.0698792i | ||||
\(131\) | 3.03517 | − | 11.3274i | 0.265184 | − | 0.989680i | −0.696954 | − | 0.717116i | \(-0.745462\pi\) |
0.962138 | − | 0.272564i | \(-0.0878717\pi\) | |||||||
\(132\) | −16.3915 | + | 10.9792i | −1.42670 | + | 0.955616i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.49992 | + | 2.80996i | −0.129574 | + | 0.242744i | ||||
\(135\) | −5.76117 | + | 3.32621i | −0.495842 | + | 0.286275i | ||||
\(136\) | −2.59506 | + | 0.981719i | −0.222525 | + | 0.0841817i | ||||
\(137\) | 8.98270 | + | 5.18617i | 0.767444 | + | 0.443084i | 0.831962 | − | 0.554832i | \(-0.187218\pi\) |
−0.0645179 | + | 0.997917i | \(0.520551\pi\) | |||||||
\(138\) | 0.185758 | + | 5.57829i | 0.0158128 | + | 0.474856i | ||||
\(139\) | −4.83290 | + | 4.83290i | −0.409921 | + | 0.409921i | −0.881711 | − | 0.471790i | \(-0.843608\pi\) |
0.471790 | + | 0.881711i | \(0.343608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 22.0938 | + | 22.0938i | 1.86063 | + | 1.86063i | ||||
\(142\) | −0.965222 | − | 0.903010i | −0.0809997 | − | 0.0757789i | ||||
\(143\) | 7.04128 | − | 12.1959i | 0.588821 | − | 1.01987i | ||||
\(144\) | −21.6009 | + | 16.6524i | −1.80008 | + | 1.38770i | ||||
\(145\) | 1.24758 | + | 2.16087i | 0.103606 | + | 0.179451i | ||||
\(146\) | 0.961384 | − | 0.292224i | 0.0795647 | − | 0.0241846i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.353975 | + | 1.79008i | −0.0290966 | + | 0.147144i | ||||
\(149\) | −2.37756 | − | 0.637064i | −0.194777 | − | 0.0521903i | 0.160112 | − | 0.987099i | \(-0.448815\pi\) |
−0.354889 | + | 0.934909i | \(0.615481\pi\) | |||||||
\(150\) | −17.6464 | + | 10.9870i | −1.44082 | + | 0.897086i | ||||
\(151\) | −18.0246 | − | 10.4065i | −1.46682 | − | 0.846871i | −0.467513 | − | 0.883986i | \(-0.654850\pi\) |
−0.999311 | + | 0.0371149i | \(0.988183\pi\) | |||||||
\(152\) | −17.0955 | + | 12.2942i | −1.38663 | + | 0.997194i | ||||
\(153\) | 6.68874i | 0.540753i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.74209 | − | 1.74209i | 0.139928 | − | 0.139928i | ||||
\(156\) | 12.3710 | − | 25.1573i | 0.990473 | − | 2.01420i | ||||
\(157\) | 13.8571 | − | 3.71300i | 1.10592 | − | 0.296330i | 0.340746 | − | 0.940155i | \(-0.389320\pi\) |
0.765172 | + | 0.643825i | \(0.222654\pi\) | |||||||
\(158\) | 16.3426 | + | 3.80086i | 1.30015 | + | 0.302381i | ||||
\(159\) | 17.8987 | + | 31.0015i | 1.41946 | + | 2.45858i | ||||
\(160\) | 2.42549 | − | 2.00200i | 0.191752 | − | 0.158272i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 7.00745 | + | 23.0537i | 0.550557 | + | 1.81127i | ||||
\(163\) | −4.35137 | + | 16.2395i | −0.340825 | + | 1.27198i | 0.556589 | + | 0.830788i | \(0.312110\pi\) |
−0.897414 | + | 0.441190i | \(0.854557\pi\) | |||||||
\(164\) | 2.42212 | − | 0.161493i | 0.189136 | − | 0.0126105i | ||||
\(165\) | −1.41943 | − | 5.29737i | −0.110502 | − | 0.412400i | ||||
\(166\) | 13.5421 | − | 0.450956i | 1.05107 | − | 0.0350010i | ||||
\(167\) | 1.10868i | 0.0857923i | 0.999080 | + | 0.0428962i | \(0.0136585\pi\) | ||||
−0.999080 | + | 0.0428962i | \(0.986342\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.01121i | 0.539324i | ||||||||
\(170\) | −0.0256693 | − | 0.770846i | −0.00196875 | − | 0.0591212i | ||||
\(171\) | 13.1386 | + | 49.0339i | 1.00473 | + | 3.74972i | ||||
\(172\) | −2.05735 | − | 1.80015i | −0.156871 | − | 0.137260i | ||||
\(173\) | −2.64992 | + | 9.88962i | −0.201469 | + | 0.751894i | 0.789027 | + | 0.614358i | \(0.210585\pi\) |
−0.990497 | + | 0.137536i | \(0.956082\pi\) | |||||||
\(174\) | 19.0284 | − | 5.78392i | 1.44254 | − | 0.438478i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.84505 | − | 11.6229i | −0.365209 | − | 0.876108i | ||||
\(177\) | −4.01894 | − | 6.96101i | −0.302082 | − | 0.523222i | ||||
\(178\) | −3.27028 | + | 14.0612i | −0.245118 | + | 1.05394i | ||||
\(179\) | −13.5777 | + | 3.63814i | −1.01485 | + | 0.271928i | −0.727654 | − | 0.685945i | \(-0.759389\pi\) |
−0.287194 | + | 0.957872i | \(0.592722\pi\) | |||||||
\(180\) | −2.44518 | − | 7.17671i | −0.182253 | − | 0.534920i | ||||
\(181\) | 7.35342 | − | 7.35342i | 0.546576 | − | 0.546576i | −0.378873 | − | 0.925449i | \(-0.623688\pi\) |
0.925449 | + | 0.378873i | \(0.123688\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 11.4677i | − | 0.847715i | ||||||
\(184\) | −3.51582 | − | 0.574366i | −0.259190 | − | 0.0423429i | ||||
\(185\) | −0.439288 | − | 0.253623i | −0.0322971 | − | 0.0186467i | ||||
\(186\) | −10.3792 | − | 16.6702i | −0.761040 | − | 1.22232i | ||||
\(187\) | −2.98288 | − | 0.799260i | −0.218130 | − | 0.0584477i | ||||
\(188\) | −16.5695 | + | 11.0984i | −1.20845 | + | 0.809432i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.70234 | − | 5.60050i | −0.123501 | − | 0.406303i | ||||
\(191\) | −1.77342 | − | 3.07165i | −0.128320 | − | 0.222257i | 0.794706 | − | 0.606995i | \(-0.207625\pi\) |
−0.923026 | + | 0.384738i | \(0.874292\pi\) | |||||||
\(192\) | −11.1631 | − | 22.4450i | −0.805625 | − | 1.61983i | ||||
\(193\) | −1.49697 | + | 2.59283i | −0.107754 | + | 0.186636i | −0.914860 | − | 0.403771i | \(-0.867699\pi\) |
0.807106 | + | 0.590407i | \(0.201033\pi\) | |||||||
\(194\) | 2.93409 | − | 3.13623i | 0.210655 | − | 0.225168i | ||||
\(195\) | 5.51053 | + | 5.51053i | 0.394617 | + | 0.394617i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.55345 | − | 3.55345i | 0.253173 | − | 0.253173i | −0.569097 | − | 0.822270i | \(-0.692707\pi\) |
0.822270 | + | 0.569097i | \(0.192707\pi\) | |||||||
\(198\) | −30.3401 | + | 1.01033i | −2.15618 | + | 0.0718011i | ||||
\(199\) | 1.55979 | + | 0.900545i | 0.110571 | + | 0.0638380i | 0.554265 | − | 0.832340i | \(-0.312999\pi\) |
−0.443695 | + | 0.896178i | \(0.646333\pi\) | |||||||
\(200\) | −4.69458 | − | 12.4096i | −0.331957 | − | 0.877490i | ||||
\(201\) | −6.11197 | + | 3.52875i | −0.431105 | + | 0.248899i | ||||
\(202\) | 17.9344 | + | 9.57318i | 1.26186 | + | 0.673567i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −6.03078 | − | 1.19254i | −0.422239 | − | 0.0834945i | ||||
\(205\) | −0.174651 | + | 0.651807i | −0.0121982 | + | 0.0455242i | ||||
\(206\) | −1.93984 | + | 8.34074i | −0.135155 | + | 0.581127i | ||||
\(207\) | −4.29407 | + | 7.43754i | −0.298458 | + | 0.516945i | ||||
\(208\) | 14.2204 | + | 10.8609i | 0.986008 | + | 0.753069i | ||||
\(209\) | −23.4369 | −1.62116 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.1022 | − | 15.1022i | −1.03968 | − | 1.03968i | −0.999180 | − | 0.0404953i | \(-0.987106\pi\) |
−0.0404953 | − | 0.999180i | \(-0.512894\pi\) | |||||||
\(212\) | −21.6276 | + | 7.36875i | −1.48539 | + | 0.506088i | ||||
\(213\) | −0.757990 | − | 2.82886i | −0.0519366 | − | 0.193830i | ||||
\(214\) | 21.2180 | − | 13.2108i | 1.45043 | − | 0.903069i | ||||
\(215\) | 0.658113 | − | 0.379962i | 0.0448829 | − | 0.0259132i | ||||
\(216\) | −33.6752 | + | 3.37415i | −2.29130 | + | 0.229582i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 9.47215 | − | 17.7452i | 0.641535 | − | 1.20185i | ||||
\(219\) | 2.15050 | + | 0.576226i | 0.145318 | + | 0.0389377i | ||||
\(220\) | 3.49267 | − | 0.232872i | 0.235476 | − | 0.0157002i | ||||
\(221\) | 4.23865 | − | 1.13574i | 0.285123 | − | 0.0763983i | ||||
\(222\) | −2.76216 | + | 2.95246i | −0.185384 | + | 0.198156i | ||||
\(223\) | 7.11258 | 0.476294 | 0.238147 | − | 0.971229i | \(-0.423460\pi\) | ||||
0.238147 | + | 0.971229i | \(0.423460\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −31.9856 | −2.13237 | ||||||||
\(226\) | −4.84946 | + | 5.18356i | −0.322581 | + | 0.344806i | ||||
\(227\) | 16.6228 | − | 4.45405i | 1.10329 | − | 0.295626i | 0.339187 | − | 0.940719i | \(-0.389848\pi\) |
0.764104 | + | 0.645093i | \(0.223181\pi\) | |||||||
\(228\) | −46.5530 | + | 3.10389i | −3.08305 | + | 0.205560i | ||||
\(229\) | 0.848962 | + | 0.227479i | 0.0561010 | + | 0.0150322i | 0.286760 | − | 0.958002i | \(-0.407422\pi\) |
−0.230659 | + | 0.973035i | \(0.574088\pi\) | |||||||
\(230\) | 0.466328 | − | 0.873620i | 0.0307487 | − | 0.0576048i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.26556 | + | 12.6307i | 0.0830881 | + | 0.829247i | ||||
\(233\) | 4.20619 | − | 2.42844i | 0.275556 | − | 0.159093i | −0.355854 | − | 0.934542i | \(-0.615810\pi\) |
0.631410 | + | 0.775449i | \(0.282477\pi\) | |||||||
\(234\) | 36.6191 | − | 22.7998i | 2.39387 | − | 1.49047i | ||||
\(235\) | −1.43483 | − | 5.35487i | −0.0935982 | − | 0.349313i | ||||
\(236\) | 4.85621 | − | 1.65456i | 0.316113 | − | 0.107703i | ||||
\(237\) | 26.2879 | + | 26.2879i | 1.70758 | + | 1.70758i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.91033 | 0.317623 | 0.158811 | − | 0.987309i | \(-0.449234\pi\) | ||||
0.158811 | + | 0.987309i | \(0.449234\pi\) | |||||||
\(240\) | 6.90670 | − | 0.925111i | 0.445825 | − | 0.0597157i | ||||
\(241\) | −5.42956 | + | 9.40428i | −0.349749 | + | 0.605783i | −0.986205 | − | 0.165530i | \(-0.947066\pi\) |
0.636456 | + | 0.771313i | \(0.280400\pi\) | |||||||
\(242\) | −0.349073 | + | 1.50091i | −0.0224393 | + | 0.0964824i | ||||
\(243\) | −4.52699 | + | 16.8950i | −0.290407 | + | 1.08381i | ||||
\(244\) | 7.18044 | + | 1.41987i | 0.459680 | + | 0.0908982i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.74493 | + | 2.53279i | 0.302526 | + | 0.161484i | ||||
\(247\) | 28.8418 | − | 16.6518i | 1.83516 | − | 1.05953i | ||||
\(248\) | 11.7231 | − | 4.43487i | 0.744415 | − | 0.281614i | ||||
\(249\) | 25.9998 | + | 15.0110i | 1.64767 | + | 0.951281i | ||||
\(250\) | 7.61526 | − | 0.253590i | 0.481631 | − | 0.0160384i | ||||
\(251\) | 8.18516 | − | 8.18516i | 0.516643 | − | 0.516643i | −0.399911 | − | 0.916554i | \(-0.630959\pi\) |
0.916554 | + | 0.399911i | \(0.130959\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.80370 | − | 2.80370i | −0.176267 | − | 0.176267i | ||||
\(254\) | 18.7310 | − | 20.0214i | 1.17528 | − | 1.25626i | ||||
\(255\) | 0.854454 | − | 1.47996i | 0.0535080 | − | 0.0926786i | ||||
\(256\) | 15.4360 | − | 4.21067i | 0.964750 | − | 0.263167i | ||||
\(257\) | −10.3065 | − | 17.8514i | −0.642902 | − | 1.11354i | −0.984782 | − | 0.173795i | \(-0.944397\pi\) |
0.341880 | − | 0.939744i | \(-0.388936\pi\) | |||||||
\(258\) | −1.76154 | − | 5.79529i | −0.109669 | − | 0.360799i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4.13268 | + | 2.76811i | −0.256298 | + | 0.171671i | ||||
\(261\) | 29.5593 | + | 7.92038i | 1.82967 | + | 0.490259i | ||||
\(262\) | 8.76566 | + | 14.0786i | 0.541544 | + | 0.869781i | ||||
\(263\) | 11.8037 | + | 6.81485i | 0.727846 | + | 0.420222i | 0.817634 | − | 0.575739i | \(-0.195286\pi\) |
−0.0897878 | + | 0.995961i | \(0.528619\pi\) | |||||||
\(264\) | 4.49840 | − | 27.5357i | 0.276858 | − | 1.69471i | ||||
\(265\) | − | 6.35145i | − | 0.390166i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −22.6182 | + | 22.6182i | −1.38421 | + | 1.38421i | ||||
\(268\) | −1.45275 | − | 4.26389i | −0.0887410 | − | 0.260459i | ||||
\(269\) | −6.05148 | + | 1.62149i | −0.368965 | + | 0.0988639i | −0.438537 | − | 0.898713i | \(-0.644503\pi\) |
0.0695721 | + | 0.997577i | \(0.477837\pi\) | |||||||
\(270\) | 2.13116 | − | 9.16338i | 0.129698 | − | 0.557666i | ||||
\(271\) | −6.34254 | − | 10.9856i | −0.385282 | − | 0.667328i | 0.606526 | − | 0.795063i | \(-0.292562\pi\) |
−0.991808 | + | 0.127736i | \(0.959229\pi\) | |||||||
\(272\) | 1.49341 | − | 3.62849i | 0.0905511 | − | 0.220010i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.0347 | + | 4.26600i | −0.847865 | + | 0.257718i | ||||
\(275\) | 3.82206 | − | 14.2641i | 0.230479 | − | 0.860159i | ||||
\(276\) | −5.94033 | − | 5.19771i | −0.357566 | − | 0.312865i | ||||
\(277\) | 6.25325 | + | 23.3375i | 0.375721 | + | 1.40221i | 0.852288 | + | 0.523073i | \(0.175215\pi\) |
−0.476566 | + | 0.879139i | \(0.658119\pi\) | |||||||
\(278\) | −0.321695 | − | 9.66044i | −0.0192940 | − | 0.579395i | ||||
\(279\) | − | 30.2161i | − | 1.80899i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 12.8628i | − | 0.767330i | −0.923472 | − | 0.383665i | \(-0.874662\pi\) | ||
0.923472 | − | 0.383665i | \(-0.125338\pi\) | |||||||
\(282\) | −44.1631 | + | 1.47064i | −2.62987 | + | 0.0875753i | ||||
\(283\) | −0.321770 | − | 1.20086i | −0.0191272 | − | 0.0713837i | 0.955703 | − | 0.294334i | \(-0.0950979\pi\) |
−0.974830 | + | 0.222950i | \(0.928431\pi\) | |||||||
\(284\) | 1.86513 | − | 0.124356i | 0.110675 | − | 0.00737918i | ||||
\(285\) | 3.35678 | − | 12.5277i | 0.198839 | − | 0.742076i | ||||
\(286\) | 5.79196 | + | 19.0549i | 0.342486 | + | 1.12674i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 3.67265 | − | 38.3968i | 0.216413 | − | 2.26255i | ||||
\(289\) | 8.01887 | + | 13.8891i | 0.471698 | + | 0.817005i | ||||
\(290\) | −3.43696 | − | 0.799346i | −0.201825 | − | 0.0469392i | ||||
\(291\) | 9.19160 | − | 2.46288i | 0.538821 | − | 0.144377i | ||||
\(292\) | −0.627067 | + | 1.27518i | −0.0366963 | + | 0.0746245i | ||||
\(293\) | −17.9935 | + | 17.9935i | −1.05119 | + | 1.05119i | −0.0525765 | + | 0.998617i | \(0.516743\pi\) |
−0.998617 | + | 0.0525765i | \(0.983257\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.42614i | 0.0830331i | ||||||||
\(296\) | −1.50667 | − | 2.09508i | −0.0875735 | − | 0.121774i | ||||
\(297\) | −32.6219 | − | 18.8343i | −1.89291 | − | 1.09287i | ||||
\(298\) | 2.95502 | − | 1.83986i | 0.171180 | − | 0.106580i | ||||
\(299\) | 5.44229 | + | 1.45826i | 0.314736 | + | 0.0843332i | ||||
\(300\) | 5.70272 | − | 28.8392i | 0.329247 | − | 1.66503i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 28.1619 | − | 8.56013i | 1.62053 | − | 0.492580i | ||||
\(303\) | 22.5221 | + | 39.0093i | 1.29386 | + | 2.24103i | ||||
\(304\) | 3.82049 | − | 29.5333i | 0.219120 | − | 1.69385i | ||||
\(305\) | −1.01734 | + | 1.76208i | −0.0582527 | + | 0.100897i | ||||
\(306\) | −6.90765 | − | 6.46243i | −0.394884 | − | 0.369432i | ||||
\(307\) | −1.74987 | − | 1.74987i | −0.0998702 | − | 0.0998702i | 0.655406 | − | 0.755277i | \(-0.272497\pi\) |
−0.755277 | + | 0.655406i | \(0.772497\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.4165 | + | 13.4165i | −0.763237 | + | 0.763237i | ||||
\(310\) | 0.115960 | + | 3.48226i | 0.00658608 | + | 0.197779i | ||||
\(311\) | 15.0938 | + | 8.71439i | 0.855889 | + | 0.494148i | 0.862634 | − | 0.505829i | \(-0.168813\pi\) |
−0.00674419 | + | 0.999977i | \(0.502147\pi\) | |||||||
\(312\) | 14.0282 | + | 37.0820i | 0.794191 | + | 2.09935i | ||||
\(313\) | −24.5458 | + | 14.1715i | −1.38741 | + | 0.801021i | −0.993023 | − | 0.117924i | \(-0.962376\pi\) |
−0.394386 | + | 0.918945i | \(0.629043\pi\) | |||||||
\(314\) | −9.55373 | + | 17.8980i | −0.539148 | + | 1.01004i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −19.7149 | + | 13.2052i | −1.10905 | + | 0.742851i | ||||
\(317\) | 3.01750 | − | 11.2615i | 0.169480 | − | 0.632508i | −0.827946 | − | 0.560807i | \(-0.810491\pi\) |
0.997426 | − | 0.0717003i | \(-0.0228425\pi\) | |||||||
\(318\) | −49.3092 | − | 11.4680i | −2.76512 | − | 0.643095i | ||||
\(319\) | −7.06427 | + | 12.2357i | −0.395523 | + | 0.685066i | ||||
\(320\) | −0.275901 | + | 4.43914i | −0.0154233 | + | 0.248155i | ||||
\(321\) | 55.3803 | 3.09103 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.16401 | − | 5.16401i | −0.287333 | − | 0.287333i | ||||
\(324\) | −30.5786 | − | 15.0369i | −1.69881 | − | 0.835384i | ||||
\(325\) | 5.43112 | + | 20.2692i | 0.301264 | + | 1.12433i | ||||
\(326\) | −12.5669 | − | 20.1838i | −0.696015 | − | 1.11788i | ||||
\(327\) | 38.5977 | − | 22.2844i | 2.13446 | − | 1.23233i | ||||
\(328\) | −2.17339 | + | 2.65742i | −0.120005 | + | 0.146731i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 6.84214 | + | 3.65225i | 0.376647 | + | 0.201050i | ||||
\(331\) | −0.321647 | − | 0.0861852i | −0.0176793 | − | 0.00473716i | 0.249969 | − | 0.968254i | \(-0.419580\pi\) |
−0.267648 | + | 0.963517i | \(0.586246\pi\) | |||||||
\(332\) | −12.6182 | + | 14.4210i | −0.692515 | + | 0.791458i | ||||
\(333\) | −6.00916 | + | 1.61015i | −0.329300 | + | 0.0882357i | ||||
\(334\) | −1.14497 | − | 1.07117i | −0.0626498 | − | 0.0586117i | ||||
\(335\) | 1.25219 | 0.0684146 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.22099 | 0.502299 | 0.251150 | − | 0.967948i | \(-0.419191\pi\) | ||||
0.251150 | + | 0.967948i | \(0.419191\pi\) | |||||||
\(338\) | −7.24068 | − | 6.77398i | −0.393841 | − | 0.368456i | ||||
\(339\) | −15.1919 | + | 4.07066i | −0.825111 | + | 0.221088i | ||||
\(340\) | 0.820875 | + | 0.718254i | 0.0445182 | + | 0.0389528i | ||||
\(341\) | 13.4750 | + | 3.61062i | 0.729713 | + | 0.195526i | ||||
\(342\) | −63.3327 | − | 33.8062i | −3.42464 | − | 1.82803i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.84680 | − | 0.385438i | 0.207406 | − | 0.0207814i | ||||
\(345\) | 1.90022 | − | 1.09709i | 0.102304 | − | 0.0590654i | ||||
\(346\) | −7.65303 | − | 12.2916i | −0.411430 | − | 0.660803i | ||||
\(347\) | −2.93816 | − | 10.9654i | −0.157729 | − | 0.588652i | −0.998856 | − | 0.0478151i | \(-0.984774\pi\) |
0.841127 | − | 0.540837i | \(-0.181892\pi\) | |||||||
\(348\) | −12.4114 | + | 25.2394i | −0.665321 | + | 1.35297i | ||||
\(349\) | 11.5879 | + | 11.5879i | 0.620287 | + | 0.620287i | 0.945605 | − | 0.325318i | \(-0.105471\pi\) |
−0.325318 | + | 0.945605i | \(0.605471\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 53.5267 | 2.85704 | ||||||||
\(352\) | 16.6844 | + | 6.22600i | 0.889281 | + | 0.331847i | ||||
\(353\) | −9.47403 | + | 16.4095i | −0.504252 | + | 0.873390i | 0.495736 | + | 0.868473i | \(0.334898\pi\) |
−0.999988 | + | 0.00491672i | \(0.998435\pi\) | |||||||
\(354\) | 11.0718 | + | 2.57501i | 0.588459 | + | 0.136860i | ||||
\(355\) | −0.134488 | + | 0.501916i | −0.00713789 | + | 0.0266390i | ||||
\(356\) | −11.3618 | − | 16.9628i | −0.602175 | − | 0.899026i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.36111 | − | 17.5371i | 0.494750 | − | 0.926867i | ||||
\(359\) | 3.06722 | − | 1.77086i | 0.161882 | − | 0.0934624i | −0.416871 | − | 0.908966i | \(-0.636873\pi\) |
0.578752 | + | 0.815503i | \(0.303540\pi\) | |||||||
\(360\) | 9.77403 | + | 4.40867i | 0.515137 | + | 0.232357i | ||||
\(361\) | −31.5455 | − | 18.2128i | −1.66029 | − | 0.958569i | ||||
\(362\) | 0.489470 | + | 14.6987i | 0.0257259 | + | 0.772547i | ||||
\(363\) | −2.41430 | + | 2.41430i | −0.126718 | + | 0.126718i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.279320 | − | 0.279320i | −0.0146203 | − | 0.0146203i | ||||
\(366\) | 11.8430 | + | 11.0797i | 0.619043 | + | 0.579143i | ||||
\(367\) | −5.59371 | + | 9.68859i | −0.291989 | + | 0.505740i | −0.974280 | − | 0.225341i | \(-0.927651\pi\) |
0.682291 | + | 0.731081i | \(0.260984\pi\) | |||||||
\(368\) | 3.99003 | − | 3.07595i | 0.207994 | − | 0.160345i | ||||
\(369\) | 4.13806 | + | 7.16732i | 0.215419 | + | 0.373116i | ||||
\(370\) | 0.686348 | − | 0.208623i | 0.0356815 | − | 0.0108458i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 27.2438 | + | 5.38724i | 1.41252 | + | 0.279315i | ||||
\(373\) | −18.8609 | − | 5.05377i | −0.976581 | − | 0.261674i | −0.264977 | − | 0.964255i | \(-0.585364\pi\) |
−0.711604 | + | 0.702581i | \(0.752031\pi\) | |||||||
\(374\) | 3.70737 | − | 2.30829i | 0.191704 | − | 0.119359i | ||||
\(375\) | 14.6206 | + | 8.44123i | 0.755007 | + | 0.435903i | ||||
\(376\) | 4.54723 | − | 27.8346i | 0.234506 | − | 1.43546i | ||||
\(377\) | − | 20.0765i | − | 1.03399i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.9875 | + | 10.9875i | −0.564391 | + | 0.564391i | −0.930552 | − | 0.366161i | \(-0.880672\pi\) |
0.366161 | + | 0.930552i | \(0.380672\pi\) | |||||||
\(380\) | 7.42853 | + | 3.65295i | 0.381076 | + | 0.187393i | ||||
\(381\) | 58.6784 | − | 15.7228i | 3.00619 | − | 0.805505i | ||||
\(382\) | 4.88559 | + | 1.13626i | 0.249969 | + | 0.0581362i | ||||
\(383\) | 2.41973 | + | 4.19109i | 0.123642 | + | 0.214155i | 0.921201 | − | 0.389086i | \(-0.127209\pi\) |
−0.797559 | + | 0.603241i | \(0.793876\pi\) | |||||||
\(384\) | 33.9649 | + | 10.1572i | 1.73327 | + | 0.518330i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.23137 | − | 4.05106i | −0.0626750 | − | 0.206194i | ||||
\(387\) | 2.41222 | − | 9.00254i | 0.122620 | − | 0.457625i | ||||
\(388\) | 0.404061 | + | 6.06022i | 0.0205131 | + | 0.307661i | ||||
\(389\) | 4.56824 | + | 17.0489i | 0.231619 | + | 0.864414i | 0.979644 | + | 0.200743i | \(0.0643357\pi\) |
−0.748025 | + | 0.663671i | \(0.768998\pi\) | |||||||
\(390\) | −11.0150 | + | 0.366800i | −0.557764 | + | 0.0185736i | ||||
\(391\) | − | 1.23552i | − | 0.0624827i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 36.7462i | 1.85360i | ||||||||
\(394\) | 0.236530 | + | 7.10297i | 0.0119162 | + | 0.357842i | ||||
\(395\) | −1.70721 | − | 6.37141i | −0.0858992 | − | 0.320580i | ||||
\(396\) | 28.2701 | − | 32.3092i | 1.42063 | − | 1.62360i | ||||
\(397\) | −4.30237 | + | 16.0566i | −0.215930 | + | 0.805860i | 0.769908 | + | 0.638155i | \(0.220302\pi\) |
−0.985837 | + | 0.167705i | \(0.946364\pi\) | |||||||
\(398\) | −2.43703 | + | 0.740764i | −0.122157 | + | 0.0371311i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 17.3514 | + | 7.14147i | 0.867572 | + | 0.357074i | ||||
\(401\) | 12.7912 | + | 22.1549i | 0.638760 | + | 1.10636i | 0.985705 | + | 0.168479i | \(0.0538857\pi\) |
−0.346945 | + | 0.937885i | \(0.612781\pi\) | |||||||
\(402\) | 2.26093 | − | 9.72135i | 0.112765 | − | 0.484857i | ||||
\(403\) | −19.1479 | + | 5.13066i | −0.953825 | + | 0.255577i | ||||
\(404\) | −27.2141 | + | 9.27213i | −1.35395 | + | 0.461306i | ||||
\(405\) | 6.69803 | − | 6.69803i | 0.332828 | − | 0.332828i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.87222i | − | 0.142371i | ||||||
\(408\) | 7.05829 | − | 5.07597i | 0.349438 | − | 0.251298i | ||||
\(409\) | −16.6386 | − | 9.60629i | −0.822725 | − | 0.475001i | 0.0286301 | − | 0.999590i | \(-0.490885\pi\) |
−0.851355 | + | 0.524589i | \(0.824219\pi\) | |||||||
\(410\) | −0.504397 | − | 0.810119i | −0.0249104 | − | 0.0400089i | ||||
\(411\) | −31.3939 | − | 8.41198i | −1.54855 | − | 0.414932i | ||||
\(412\) | −6.73951 | − | 10.0618i | −0.332032 | − | 0.495711i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.53218 | − | 11.6205i | −0.173597 | − | 0.571116i | ||||
\(415\) | −2.66336 | − | 4.61307i | −0.130739 | − | 0.226447i | ||||
\(416\) | −24.9556 | + | 4.19238i | −1.22355 | + | 0.205549i | ||||
\(417\) | 10.7082 | − | 18.5472i | 0.524385 | − | 0.908261i | ||||
\(418\) | 22.6439 | − | 24.2039i | 1.10755 | − | 1.18385i | ||||
\(419\) | 11.2764 | + | 11.2764i | 0.550888 | + | 0.550888i | 0.926697 | − | 0.375809i | \(-0.122635\pi\) |
−0.375809 | + | 0.926697i | \(0.622635\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.1033 | − | 27.1033i | 1.32094 | − | 1.32094i | 0.407918 | − | 0.913019i | \(-0.366255\pi\) |
0.913019 | − | 0.407918i | \(-0.133745\pi\) | |||||||
\(422\) | 30.1876 | − | 1.00525i | 1.46951 | − | 0.0489349i | ||||
\(423\) | −58.8827 | − | 33.9959i | −2.86297 | − | 1.65294i | ||||
\(424\) | 13.2859 | − | 29.4548i | 0.645220 | − | 1.43045i | ||||
\(425\) | 3.98506 | − | 2.30077i | 0.193304 | − | 0.111604i | ||||
\(426\) | 3.65378 | + | 1.95034i | 0.177026 | + | 0.0944944i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6.85694 | + | 34.6762i | −0.331443 | + | 1.67614i | ||||
\(429\) | −11.4210 | + | 42.6237i | −0.551410 | + | 2.05789i | ||||
\(430\) | −0.243448 | + | 1.04676i | −0.0117401 | + | 0.0504791i | ||||
\(431\) | 7.38092 | − | 12.7841i | 0.355526 | − | 0.615790i | −0.631682 | − | 0.775228i | \(-0.717635\pi\) |
0.987208 | + | 0.159438i | \(0.0509683\pi\) | |||||||
\(432\) | 29.0512 | − | 38.0373i | 1.39772 | − | 1.83007i | ||||
\(433\) | −30.0057 | −1.44198 | −0.720991 | − | 0.692944i | \(-0.756313\pi\) | ||||
−0.720991 | + | 0.692944i | \(0.756313\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.52852 | − | 5.52852i | −0.265072 | − | 0.265072i | ||||
\(436\) | 9.17427 | + | 26.9269i | 0.439368 | + | 1.28956i | ||||
\(437\) | −2.42690 | − | 9.05733i | −0.116095 | − | 0.433271i | ||||
\(438\) | −2.67283 | + | 1.66416i | −0.127713 | + | 0.0795165i | ||||
\(439\) | −29.2303 | + | 16.8761i | −1.39509 | + | 0.805454i | −0.993873 | − | 0.110531i | \(-0.964745\pi\) |
−0.401214 | + | 0.915984i | \(0.631412\pi\) | |||||||
\(440\) | −3.13400 | + | 3.83197i | −0.149408 | + | 0.182682i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.92232 | + | 5.47469i | −0.139001 | + | 0.260404i | ||||
\(443\) | −7.13093 | − | 1.91073i | −0.338800 | − | 0.0907813i | 0.0854075 | − | 0.996346i | \(-0.472781\pi\) |
−0.424208 | + | 0.905565i | \(0.639447\pi\) | |||||||
\(444\) | −0.380385 | − | 5.70512i | −0.0180523 | − | 0.270753i | ||||
\(445\) | 5.48198 | − | 1.46889i | 0.259871 | − | 0.0696322i | ||||
\(446\) | −6.87192 | + | 7.34536i | −0.325395 | + | 0.347813i | ||||
\(447\) | 7.71281 | 0.364803 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.59006 | −0.0750395 | −0.0375197 | − | 0.999296i | \(-0.511946\pi\) | ||||
−0.0375197 | + | 0.999296i | \(0.511946\pi\) | |||||||
\(450\) | 30.9033 | − | 33.0324i | 1.45680 | − | 1.55716i | ||||
\(451\) | −3.69078 | + | 0.988940i | −0.173792 | + | 0.0465674i | ||||
\(452\) | −0.667833 | − | 10.0163i | −0.0314122 | − | 0.471129i | ||||
\(453\) | 62.9949 | + | 16.8794i | 2.95976 | + | 0.793065i | ||||
\(454\) | −11.4605 | + | 21.4701i | −0.537867 | + | 1.00764i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 41.7724 | − | 51.0754i | 1.95617 | − | 2.39183i | ||||
\(457\) | 1.86124 | − | 1.07459i | 0.0870651 | − | 0.0502671i | −0.455835 | − | 0.890064i | \(-0.650659\pi\) |
0.542900 | + | 0.839797i | \(0.317326\pi\) | |||||||
\(458\) | −1.05516 | + | 0.656965i | −0.0493044 | + | 0.0306980i | ||||
\(459\) | −3.03793 | − | 11.3377i | −0.141798 | − | 0.529198i | ||||
\(460\) | 0.451663 | + | 1.32565i | 0.0210589 | + | 0.0618088i | ||||
\(461\) | −26.7406 | − | 26.7406i | −1.24543 | − | 1.24543i | −0.957715 | − | 0.287719i | \(-0.907103\pi\) |
−0.287719 | − | 0.957715i | \(-0.592897\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.2686 | 0.756065 | 0.378033 | − | 0.925792i | \(-0.376601\pi\) | ||||
0.378033 | + | 0.925792i | \(0.376601\pi\) | |||||||
\(464\) | −14.2668 | − | 10.8964i | −0.662321 | − | 0.505851i | ||||
\(465\) | −3.85995 | + | 6.68564i | −0.179001 | + | 0.310039i | ||||
\(466\) | −1.55595 | + | 6.69012i | −0.0720778 | + | 0.309914i | ||||
\(467\) | 6.56228 | − | 24.4908i | 0.303666 | − | 1.13330i | −0.630421 | − | 0.776253i | \(-0.717118\pi\) |
0.934087 | − | 0.357044i | \(-0.116216\pi\) | |||||||
\(468\) | −11.8341 | + | 59.8460i | −0.547030 | + | 2.76638i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 6.91641 | + | 3.69189i | 0.319030 | + | 0.170294i | ||||
\(471\) | −38.9301 | + | 22.4763i | −1.79380 | + | 1.03565i | ||||
\(472\) | −2.98319 | + | 6.61373i | −0.137312 | + | 0.304421i | ||||
\(473\) | 3.72648 | + | 2.15149i | 0.171344 | + | 0.0989255i | ||||
\(474\) | −52.5467 | + | 1.74982i | −2.41355 | + | 0.0803717i | ||||
\(475\) | 24.6943 | − | 24.6943i | 1.13305 | − | 1.13305i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −55.0819 | − | 55.0819i | −2.52203 | − | 2.52203i | ||||
\(478\) | −4.74418 | + | 5.07103i | −0.216994 | + | 0.231944i | ||||
\(479\) | 8.49302 | − | 14.7103i | 0.388056 | − | 0.672133i | −0.604132 | − | 0.796884i | \(-0.706480\pi\) |
0.992188 | + | 0.124751i | \(0.0398134\pi\) | |||||||
\(480\) | −5.71761 | + | 8.02655i | −0.260972 | + | 0.366360i | ||||
\(481\) | 2.04070 | + | 3.53460i | 0.0930479 | + | 0.161164i | ||||
\(482\) | −4.46621 | − | 14.6933i | −0.203430 | − | 0.669263i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.21277 | − | 1.81063i | −0.0551261 | − | 0.0823012i | ||||
\(485\) | −1.63084 | − | 0.436983i | −0.0740527 | − | 0.0198424i | ||||
\(486\) | −13.0741 | − | 20.9985i | −0.593053 | − | 0.952510i | ||||
\(487\) | 33.8046 | + | 19.5171i | 1.53183 | + | 0.884404i | 0.999277 | + | 0.0380089i | \(0.0121015\pi\) |
0.532555 | + | 0.846395i | \(0.321232\pi\) | |||||||
\(488\) | −8.40383 | + | 6.04360i | −0.380423 | + | 0.273581i | ||||
\(489\) | − | 52.6811i | − | 2.38232i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.8828 | + | 26.8828i | −1.21320 | + | 1.21320i | −0.243238 | + | 0.969967i | \(0.578210\pi\) |
−0.969967 | + | 0.243238i | \(0.921790\pi\) | |||||||
\(492\) | −7.20006 | + | 2.45314i | −0.324604 | + | 0.110596i | ||||
\(493\) | −4.25249 | + | 1.13945i | −0.191522 | + | 0.0513183i | ||||
\(494\) | −10.6691 | + | 45.8741i | −0.480027 | + | 2.06398i | ||||
\(495\) | 5.96703 | + | 10.3352i | 0.268198 | + | 0.464533i | ||||
\(496\) | −6.74639 | + | 16.3915i | −0.302922 | + | 0.736002i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −40.6223 | + | 12.3476i | −1.82033 | + | 0.553310i | ||||
\(499\) | 1.65798 | − | 6.18767i | 0.0742214 | − | 0.276998i | −0.918834 | − | 0.394644i | \(-0.870868\pi\) |
0.993056 | + | 0.117646i | \(0.0375347\pi\) | |||||||
\(500\) | −7.09570 | + | 8.10950i | −0.317329 | + | 0.362668i | ||||
\(501\) | −0.899143 | − | 3.35565i | −0.0401707 | − | 0.149919i | ||||
\(502\) | 0.544833 | + | 16.3613i | 0.0243171 | + | 0.730238i | ||||
\(503\) | 35.6215i | 1.58829i | 0.607731 | + | 0.794143i | \(0.292080\pi\) | ||||
−0.607731 | + | 0.794143i | \(0.707920\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 7.99206i | − | 0.355642i | ||||||
\(506\) | 5.60429 | − | 0.186624i | 0.249141 | − | 0.00829644i | ||||
\(507\) | −5.68611 | − | 21.2208i | −0.252529 | − | 0.942451i | ||||
\(508\) | 2.57949 | + | 38.6880i | 0.114447 | + | 1.71650i | ||||
\(509\) | 6.59958 | − | 24.6300i | 0.292521 | − | 1.09170i | −0.650645 | − | 0.759382i | \(-0.725501\pi\) |
0.943166 | − | 0.332322i | \(-0.107832\pi\) | |||||||
\(510\) | 0.702851 | + | 2.31230i | 0.0311228 | + | 0.102390i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −10.5652 | + | 20.0094i | −0.466922 | + | 0.884298i | ||||
\(513\) | −44.5409 | − | 77.1471i | −1.96653 | − | 3.40613i | ||||
\(514\) | 28.3934 | + | 6.60356i | 1.25238 | + | 0.291271i | ||||
\(515\) | 3.25176 | − | 0.871306i | 0.143290 | − | 0.0383943i | ||||
\(516\) | 7.68690 | + | 3.78000i | 0.338397 | + | 0.166405i | ||||
\(517\) | 22.1967 | − | 22.1967i | 0.976212 | − | 0.976212i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 32.0820i | − | 1.40824i | ||||||
\(520\) | 1.13415 | − | 6.94238i | 0.0497358 | − | 0.304444i | ||||
\(521\) | −13.4493 | − | 7.76498i | −0.589226 | − | 0.340190i | 0.175565 | − | 0.984468i | \(-0.443825\pi\) |
−0.764792 | + | 0.644278i | \(0.777158\pi\) | |||||||
\(522\) | −36.7387 | + | 22.8743i | −1.60801 | + | 1.00118i | ||||
\(523\) | −10.3555 | − | 2.77474i | −0.452814 | − | 0.121331i | 0.0252020 | − | 0.999682i | \(-0.491977\pi\) |
−0.478016 | + | 0.878351i | \(0.658644\pi\) | |||||||
\(524\) | −23.0085 | − | 4.54974i | −1.00513 | − | 0.198756i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18.4422 | + | 5.60571i | −0.804117 | + | 0.244421i | ||||
\(527\) | 2.17349 | + | 3.76460i | 0.0946787 | + | 0.163988i | ||||
\(528\) | 24.0907 | + | 31.2496i | 1.04841 | + | 1.35997i | ||||
\(529\) | −10.7068 | + | 18.5448i | −0.465514 | + | 0.806294i | ||||
\(530\) | 6.55932 | + | 6.13654i | 0.284918 | + | 0.266554i | ||||
\(531\) | 12.3680 | + | 12.3680i | 0.536725 | + | 0.536725i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.83929 | − | 3.83929i | 0.166298 | − | 0.166298i | ||||
\(534\) | −1.50555 | − | 45.2114i | −0.0651514 | − | 1.95649i | ||||
\(535\) | −8.50955 | − | 4.91299i | −0.367900 | − | 0.212407i | ||||
\(536\) | 5.80704 | + | 2.61932i | 0.250826 | + | 0.113138i | ||||
\(537\) | 38.1452 | − | 22.0231i | 1.64609 | − | 0.950368i | ||||
\(538\) | 4.17217 | − | 7.81615i | 0.179875 | − | 0.336978i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 7.40423 | + | 11.0542i | 0.318627 | + | 0.475699i | ||||
\(541\) | 6.14630 | − | 22.9383i | 0.264250 | − | 0.986194i | −0.698458 | − | 0.715651i | \(-0.746130\pi\) |
0.962708 | − | 0.270543i | \(-0.0872033\pi\) | |||||||
\(542\) | 17.4731 | + | 4.06378i | 0.750533 | + | 0.174554i | ||||
\(543\) | −16.2930 | + | 28.2202i | −0.699198 | + | 1.21105i | ||||
\(544\) | 2.30437 | + | 5.04800i | 0.0987990 | + | 0.216431i | ||||
\(545\) | −7.90771 | −0.338729 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.9159 | − | 28.9159i | −1.23636 | − | 1.23636i | −0.961480 | − | 0.274875i | \(-0.911363\pi\) |
−0.274875 | − | 0.961480i | \(-0.588637\pi\) | |||||||
\(548\) | 9.15418 | − | 18.6156i | 0.391047 | − | 0.795221i | ||||
\(549\) | 6.45868 | + | 24.1041i | 0.275650 | + | 1.02874i | ||||
\(550\) | 11.0382 | + | 17.7286i | 0.470671 | + | 0.755952i | ||||
\(551\) | −28.9360 | + | 16.7062i | −1.23271 | + | 0.711708i | ||||
\(552\) | 11.1071 | − | 1.11290i | 0.472752 | − | 0.0473683i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −30.1429 | − | 16.0899i | −1.28065 | − | 0.683595i | ||||
\(555\) | 1.53528 | + | 0.411377i | 0.0651691 | + | 0.0174620i | ||||
\(556\) | 10.2874 | + | 9.00135i | 0.436284 | + | 0.381742i | ||||
\(557\) | −16.2223 | + | 4.34676i | −0.687362 | + | 0.184178i | −0.585563 | − | 0.810627i | \(-0.699127\pi\) |
−0.101799 | + | 0.994805i | \(0.532460\pi\) | |||||||
\(558\) | 31.2050 | + | 29.1937i | 1.32101 | + | 1.23587i | ||||
\(559\) | −6.11449 | −0.258616 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.67648 | 0.408541 | ||||||||
\(562\) | 13.2838 | + | 12.4276i | 0.560342 | + | 0.524225i | ||||
\(563\) | 3.44149 | − | 0.922146i | 0.145042 | − | 0.0388638i | −0.185568 | − | 0.982631i | \(-0.559412\pi\) |
0.330609 | + | 0.943768i | \(0.392746\pi\) | |||||||
\(564\) | 41.1500 | − | 47.0293i | 1.73273 | − | 1.98029i | ||||
\(565\) | 2.69546 | + | 0.722246i | 0.113399 | + | 0.0303851i | ||||
\(566\) | 1.55104 | + | 0.827928i | 0.0651952 | + | 0.0348004i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.67359 | + | 2.04632i | −0.0702224 | + | 0.0858615i | ||||
\(569\) | 1.64887 | − | 0.951974i | 0.0691241 | − | 0.0399088i | −0.465040 | − | 0.885290i | \(-0.653960\pi\) |
0.534164 | + | 0.845381i | \(0.320627\pi\) | |||||||
\(570\) | 9.69448 | + | 15.5704i | 0.406057 | + | 0.652174i | ||||
\(571\) | 0.712086 | + | 2.65754i | 0.0297999 | + | 0.111215i | 0.979224 | − | 0.202782i | \(-0.0649984\pi\) |
−0.949424 | + | 0.313997i | \(0.898332\pi\) | |||||||
\(572\) | −25.2745 | − | 12.4287i | −1.05678 | − | 0.519669i | ||||
\(573\) | 7.85872 | + | 7.85872i | 0.328303 | + | 0.328303i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.90824 | 0.246390 | ||||||||
\(576\) | 36.1050 | + | 40.8905i | 1.50438 | + | 1.70377i | ||||
\(577\) | 0.135023 | − | 0.233867i | 0.00562108 | − | 0.00973599i | −0.863201 | − | 0.504860i | \(-0.831544\pi\) |
0.868822 | + | 0.495124i | \(0.164877\pi\) | |||||||
\(578\) | −22.0912 | − | 5.13783i | −0.918872 | − | 0.213706i | ||||
\(579\) | 2.42809 | − | 9.06176i | 0.100908 | − | 0.376594i | ||||
\(580\) | 4.14617 | − | 2.77714i | 0.172160 | − | 0.115315i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −6.33711 | + | 11.8720i | −0.262682 | + | 0.492109i | ||||
\(583\) | 31.1460 | − | 17.9821i | 1.28994 | − | 0.744744i | ||||
\(584\) | −0.711068 | − | 1.87963i | −0.0294242 | − | 0.0777795i | ||||
\(585\) | −14.6862 | − | 8.47911i | −0.607202 | − | 0.350568i | ||||
\(586\) | −1.19771 | − | 35.9671i | −0.0494770 | − | 1.48579i | ||||
\(587\) | −22.4556 | + | 22.4556i | −0.926842 | + | 0.926842i | −0.997501 | − | 0.0706582i | \(-0.977490\pi\) |
0.0706582 | + | 0.997501i | \(0.477490\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.3282 | + | 23.3282i | 0.961221 | + | 0.961221i | ||||
\(590\) | −1.47281 | − | 1.37789i | −0.0606348 | − | 0.0567267i | ||||
\(591\) | −7.87338 | + | 13.6371i | −0.323867 | + | 0.560955i | ||||
\(592\) | 3.61933 | + | 0.468205i | 0.148754 | + | 0.0192431i | ||||
\(593\) | 18.0313 | + | 31.2311i | 0.740456 | + | 1.28251i | 0.952288 | + | 0.305201i | \(0.0987238\pi\) |
−0.211832 | + | 0.977306i | \(0.567943\pi\) | |||||||
\(594\) | 50.9688 | − | 15.4926i | 2.09127 | − | 0.635667i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.954964 | + | 4.82934i | −0.0391168 | + | 0.197817i | ||||
\(597\) | −5.45136 | − | 1.46069i | −0.223109 | − | 0.0597820i | ||||
\(598\) | −6.76413 | + | 4.21149i | −0.276606 | + | 0.172221i | ||||
\(599\) | −9.29172 | − | 5.36458i | −0.379649 | − | 0.219191i | 0.298016 | − | 0.954561i | \(-0.403675\pi\) |
−0.677666 | + | 0.735370i | \(0.737008\pi\) | |||||||
\(600\) | 24.2733 | + | 33.7528i | 0.990952 | + | 1.37795i | ||||
\(601\) | 36.0677i | 1.47123i | 0.677399 | + | 0.735616i | \(0.263107\pi\) | ||||
−0.677399 | + | 0.735616i | \(0.736893\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.8594 | − | 10.8594i | 0.442230 | − | 0.442230i | ||||
\(604\) | −18.3687 | + | 37.3540i | −0.747412 | + | 1.51991i | ||||
\(605\) | 0.585153 | − | 0.156791i | 0.0237899 | − | 0.00637448i | ||||
\(606\) | −62.0460 | − | 14.4303i | −2.52045 | − | 0.586190i | ||||
\(607\) | −3.49308 | − | 6.05020i | −0.141780 | − | 0.245570i | 0.786387 | − | 0.617734i | \(-0.211949\pi\) |
−0.928167 | + | 0.372164i | \(0.878616\pi\) | |||||||
\(608\) | 26.8086 | + | 32.4795i | 1.08723 | + | 1.31722i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.836836 | − | 2.75310i | −0.0338825 | − | 0.111470i | ||||
\(611\) | −11.5450 | + | 43.0864i | −0.467059 | + | 1.74309i | ||||
\(612\) | 13.3479 | − | 0.889959i | 0.539555 | − | 0.0359745i | ||||
\(613\) | −8.54889 | − | 31.9049i | −0.345286 | − | 1.28863i | −0.892277 | − | 0.451488i | \(-0.850893\pi\) |
0.546991 | − | 0.837138i | \(-0.315773\pi\) | |||||||
\(614\) | 3.49780 | − | 0.116477i | 0.141160 | − | 0.00470064i | ||||
\(615\) | − | 2.11447i | − | 0.0852635i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.5107i | 1.67116i | 0.549370 | + | 0.835579i | \(0.314868\pi\) | ||||
−0.549370 | + | 0.835579i | \(0.685132\pi\) | |||||||
\(618\) | −0.893048 | − | 26.8181i | −0.0359237 | − | 1.07878i | ||||
\(619\) | −7.08429 | − | 26.4389i | −0.284742 | − | 1.06267i | −0.949028 | − | 0.315192i | \(-0.897931\pi\) |
0.664286 | − | 0.747478i | \(-0.268736\pi\) | |||||||
\(620\) | −3.70826 | − | 3.24468i | −0.148927 | − | 0.130309i | ||||
\(621\) | 3.90060 | − | 14.5572i | 0.156526 | − | 0.584162i | ||||
\(622\) | −23.5827 | + | 7.16822i | −0.945579 | + | 0.287420i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −51.8491 | − | 21.3399i | −2.07563 | − | 0.854282i | ||||
\(625\) | 10.2296 | + | 17.7181i | 0.409182 | + | 0.708724i | ||||
\(626\) | 9.07993 | − | 39.0411i | 0.362907 | − | 1.56040i | ||||
\(627\) | 70.9365 | − | 19.0074i | 2.83293 | − | 0.759081i | ||||
\(628\) | −9.25329 | − | 27.1588i | −0.369246 | − | 1.08375i | ||||
\(629\) | 0.632856 | − | 0.632856i | 0.0252336 | − | 0.0252336i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 2.56032i | − | 0.101925i | −0.998701 | − | 0.0509624i | \(-0.983771\pi\) | ||
0.998701 | − | 0.0509624i | \(-0.0162289\pi\) | |||||||
\(632\) | 5.41045 | − | 33.1185i | 0.215216 | − | 1.31738i | ||||
\(633\) | 57.9576 | + | 33.4618i | 2.30361 | + | 1.32999i | ||||
\(634\) | 8.71464 | + | 13.9967i | 0.346102 | + | 0.555880i | ||||
\(635\) | −10.4112 | − | 2.78966i | −0.413154 | − | 0.110704i | ||||
\(636\) | 59.4842 | − | 39.8430i | 2.35870 | − | 1.57988i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.81087 | − | 19.1171i | −0.230055 | − | 0.756854i | ||||
\(639\) | 3.18646 | + | 5.51912i | 0.126055 | + | 0.218333i | ||||
\(640\) | −4.31786 | − | 4.57387i | −0.170678 | − | 0.180798i | ||||
\(641\) | 0.327094 | − | 0.566544i | 0.0129195 | − | 0.0223771i | −0.859493 | − | 0.511147i | \(-0.829221\pi\) |
0.872413 | + | 0.488770i | \(0.162554\pi\) | |||||||
\(642\) | −53.5065 | + | 57.1928i | −2.11173 | + | 2.25722i | ||||
\(643\) | 3.21708 | + | 3.21708i | 0.126869 | + | 0.126869i | 0.767690 | − | 0.640821i | \(-0.221406\pi\) |
−0.640821 | + | 0.767690i | \(0.721406\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.68376 | + | 1.68376i | −0.0662980 | + | 0.0662980i | ||||
\(646\) | 10.3223 | − | 0.343735i | 0.406126 | − | 0.0135241i | ||||
\(647\) | 34.1274 | + | 19.7035i | 1.34169 | + | 0.774623i | 0.987055 | − | 0.160382i | \(-0.0512728\pi\) |
0.354632 | + | 0.935006i | \(0.384606\pi\) | |||||||
\(648\) | 45.0730 | − | 17.0512i | 1.77063 | − | 0.669835i | ||||
\(649\) | −6.99345 | + | 4.03767i | −0.274517 | + | 0.158493i | ||||
\(650\) | −26.1799 | − | 13.9745i | −1.02686 | − | 0.548126i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 32.9861 | + | 6.52273i | 1.29183 | + | 0.255450i | ||||
\(653\) | 9.30692 | − | 34.7339i | 0.364208 | − | 1.35924i | −0.504284 | − | 0.863538i | \(-0.668243\pi\) |
0.868491 | − | 0.495704i | \(-0.165090\pi\) | |||||||
\(654\) | −14.2780 | + | 61.3912i | −0.558314 | + | 2.40059i | ||||
\(655\) | 3.25989 | − | 5.64629i | 0.127374 | − | 0.220619i | ||||
\(656\) | −0.644542 | − | 4.81202i | −0.0251651 | − | 0.187878i | ||||
\(657\) | −4.84472 | −0.189010 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 31.8006 | + | 31.8006i | 1.23877 | + | 1.23877i | 0.960502 | + | 0.278272i | \(0.0897616\pi\) |
0.278272 | + | 0.960502i | \(0.410238\pi\) | |||||||
\(660\) | −10.3824 | + | 3.53740i | −0.404135 | + | 0.137693i | ||||
\(661\) | −1.99669 | − | 7.45175i | −0.0776622 | − | 0.289839i | 0.916162 | − | 0.400809i | \(-0.131271\pi\) |
−0.993824 | + | 0.110970i | \(0.964604\pi\) | |||||||
\(662\) | 0.399770 | − | 0.248905i | 0.0155375 | − | 0.00967397i | ||||
\(663\) | −11.9080 | + | 6.87511i | −0.462470 | + | 0.267007i | ||||
\(664\) | −2.70174 | − | 26.9643i | −0.104848 | − | 1.04642i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.14299 | − | 7.76150i | 0.160538 | − | 0.300752i | ||||
\(667\) | −5.46006 | − | 1.46302i | −0.211414 | − | 0.0566483i | ||||
\(668\) | 2.21245 | − | 0.147514i | 0.0856023 | − | 0.00570747i | ||||
\(669\) | −21.5276 | + | 5.76831i | −0.832307 | + | 0.223016i | ||||
\(670\) | −1.20982 | + | 1.29317i | −0.0467395 | + | 0.0499596i | ||||
\(671\) | −11.5211 | −0.444768 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.3929 | −1.09446 | −0.547232 | − | 0.836981i | \(-0.684319\pi\) | ||||
−0.547232 | + | 0.836981i | \(0.684319\pi\) | |||||||
\(674\) | −8.90899 | + | 9.52277i | −0.343161 | + | 0.366803i | ||||
\(675\) | 54.2168 | − | 14.5274i | 2.08681 | − | 0.559158i | ||||
\(676\) | 13.9914 | − | 0.932865i | 0.538129 | − | 0.0358794i | ||||
\(677\) | −10.3630 | − | 2.77675i | −0.398281 | − | 0.106719i | 0.0541182 | − | 0.998535i | \(-0.482765\pi\) |
−0.452400 | + | 0.891815i | \(0.649432\pi\) | |||||||
\(678\) | 10.4740 | − | 19.6220i | 0.402251 | − | 0.753579i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.53486 | + | 0.153788i | −0.0588592 | + | 0.00589752i | ||||
\(681\) | −46.6999 | + | 26.9622i | −1.78954 | + | 1.03319i | ||||
\(682\) | −16.7479 | + | 10.4276i | −0.641309 | + | 0.399292i | ||||
\(683\) | −3.89792 | − | 14.5472i | −0.149150 | − | 0.556634i | −0.999536 | − | 0.0304747i | \(-0.990298\pi\) |
0.850386 | − | 0.526160i | \(-0.176369\pi\) | |||||||
\(684\) | 96.1024 | − | 32.7431i | 3.67457 | − | 1.25196i | ||||
\(685\) | 4.07763 | + | 4.07763i | 0.155798 | + | 0.155798i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.75404 | −0.105073 | ||||||||
\(688\) | −3.31859 | + | 4.34509i | −0.126520 | + | 0.165655i | ||||
\(689\) | −25.5525 | + | 44.2582i | −0.973473 | + | 1.68610i | ||||
\(690\) | −0.702926 | + | 3.02238i | −0.0267599 | + | 0.115060i | ||||
\(691\) | 0.482439 | − | 1.80049i | 0.0183529 | − | 0.0684938i | −0.956142 | − | 0.292903i | \(-0.905379\pi\) |
0.974495 | + | 0.224409i | \(0.0720453\pi\) | |||||||
\(692\) | 20.0880 | + | 3.97225i | 0.763631 | + | 0.151002i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.1630 | + | 7.56003i | 0.537620 | + | 0.286975i | ||||
\(695\) | −3.29078 | + | 1.89994i | −0.124827 | + | 0.0720686i | ||||
\(696\) | −14.0740 | − | 37.2030i | −0.533474 | − | 1.41018i | ||||
\(697\) | −1.03111 | − | 0.595314i | −0.0390562 | − | 0.0225491i | ||||
\(698\) | −23.1630 | + | 0.771332i | −0.876733 | + | 0.0291954i | ||||
\(699\) | −10.7614 | + | 10.7614i | −0.407033 | + | 0.407033i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.77893 | + | 5.77893i | 0.218267 | + | 0.218267i | 0.807768 | − | 0.589501i | \(-0.200675\pi\) |
−0.589501 | + | 0.807768i | \(0.700675\pi\) | |||||||
\(702\) | −51.7156 | + | 55.2785i | −1.95188 | + | 2.08635i | ||||
\(703\) | 3.39624 | − | 5.88245i | 0.128091 | − | 0.221861i | ||||
\(704\) | −22.5496 | + | 11.2151i | −0.849871 | + | 0.422685i | ||||
\(705\) | 8.68562 | + | 15.0439i | 0.327119 | + | 0.566588i | ||||
\(706\) | −7.79308 | − | 25.6384i | −0.293296 | − | 0.964913i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −13.3565 | + | 8.94626i | −0.501966 | + | 0.336221i | ||||
\(709\) | 37.6192 | + | 10.0800i | 1.41282 | + | 0.378564i | 0.882931 | − | 0.469503i | \(-0.155567\pi\) |
0.529889 | + | 0.848067i | \(0.322233\pi\) | |||||||
\(710\) | −0.388405 | − | 0.623823i | −0.0145766 | − | 0.0234117i | ||||
\(711\) | −70.0606 | − | 40.4495i | −2.62748 | − | 1.51697i | ||||
\(712\) | 28.4953 | + | 4.65517i | 1.06791 | + | 0.174460i | ||||
\(713\) | 5.58138i | 0.209024i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.53621 | − | 5.53621i | 0.207043 | − | 0.207043i | ||||
\(716\) | 9.06673 | + | 26.6112i | 0.338840 | + | 0.994509i | ||||
\(717\) | −14.8621 | + | 3.98229i | −0.555035 | + | 0.148721i | ||||
\(718\) | −1.13462 | + | 4.87854i | −0.0423437 | + | 0.182066i | ||||
\(719\) | 1.89904 | + | 3.28924i | 0.0708223 | + | 0.122668i | 0.899262 | − | 0.437411i | \(-0.144104\pi\) |
−0.828440 | + | 0.560078i | \(0.810771\pi\) | |||||||
\(720\) | −13.9963 | + | 5.83441i | −0.521610 | + | 0.217436i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 49.2870 | − | 14.9814i | 1.83427 | − | 0.557548i | ||||
\(723\) | 8.80677 | − | 32.8673i | 0.327527 | − | 1.22235i | ||||
\(724\) | −15.6527 | − | 13.6959i | −0.581727 | − | 0.509003i | ||||
\(725\) | −5.44885 | − | 20.3354i | −0.202365 | − | 0.755238i | ||||
\(726\) | −0.160704 | − | 4.82592i | −0.00596428 | − | 0.179107i | ||||
\(727\) | − | 25.5053i | − | 0.945937i | −0.881079 | − | 0.472969i | \(-0.843182\pi\) | ||
0.881079 | − | 0.472969i | \(-0.156818\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 3.69376i | − | 0.136806i | ||||||
\(730\) | 0.558331 | − | 0.0185925i | 0.0206647 | − | 0.000688140i | ||||
\(731\) | 0.347030 | + | 1.29513i | 0.0128354 | + | 0.0479023i | ||||
\(732\) | −22.8845 | + | 1.52581i | −0.845837 | + | 0.0563956i | ||||
\(733\) | −10.6201 | + | 39.6348i | −0.392263 | + | 1.46395i | 0.434129 | + | 0.900851i | \(0.357056\pi\) |
−0.826392 | + | 0.563095i | \(0.809611\pi\) | |||||||
\(734\) | −4.60123 | − | 15.1376i | −0.169835 | − | 0.558737i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.678397 | + | 7.09249i | −0.0250060 | + | 0.261433i | ||||
\(737\) | 3.54519 | + | 6.14045i | 0.130589 | + | 0.226186i | ||||
\(738\) | −11.3999 | − | 2.65133i | −0.419638 | − | 0.0975967i | ||||
\(739\) | −2.28087 | + | 0.611156i | −0.0839030 | + | 0.0224817i | −0.300526 | − | 0.953774i | \(-0.597162\pi\) |
0.216623 | + | 0.976255i | \(0.430496\pi\) | |||||||
\(740\) | −0.447674 | + | 0.910375i | −0.0164568 | + | 0.0334660i | ||||
\(741\) | −73.7909 | + | 73.7909i | −2.71077 | + | 2.71077i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.1373i | 0.885513i | 0.896642 | + | 0.442756i | \(0.145999\pi\) | ||||
−0.896642 | + | 0.442756i | \(0.854001\pi\) | |||||||
\(744\) | −31.8855 | + | 22.9304i | −1.16898 | + | 0.840670i | ||||
\(745\) | −1.18512 | − | 0.684231i | −0.0434196 | − | 0.0250683i | ||||
\(746\) | 23.4419 | − | 14.5954i | 0.858269 | − | 0.534376i | ||||
\(747\) | −63.1036 | − | 16.9086i | −2.30884 | − | 0.618652i | ||||
\(748\) | −1.19810 | + | 6.05889i | −0.0438068 | + | 0.221535i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −22.8434 | + | 6.94353i | −0.834125 | + | 0.253542i | ||||
\(751\) | −8.83513 | − | 15.3029i | −0.322398 | − | 0.558410i | 0.658584 | − | 0.752507i | \(-0.271156\pi\) |
−0.980982 | + | 0.194097i | \(0.937822\pi\) | |||||||
\(752\) | 24.3522 | + | 31.5888i | 0.888033 | + | 1.15193i | ||||
\(753\) | −18.1358 | + | 31.4122i | −0.660907 | + | 1.14472i | ||||
\(754\) | 20.7336 | + | 19.3972i | 0.755073 | + | 0.706406i | ||||
\(755\) | −8.18214 | − | 8.18214i | −0.297779 | − | 0.297779i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.3436 | + | 14.3436i | −0.521327 | + | 0.521327i | −0.917972 | − | 0.396645i | \(-0.870174\pi\) |
0.396645 | + | 0.917972i | \(0.370174\pi\) | |||||||
\(758\) | −0.731367 | − | 21.9628i | −0.0265645 | − | 0.797727i | ||||
\(759\) | 10.7598 | + | 6.21215i | 0.390554 | + | 0.225487i | ||||
\(760\) | −10.9497 | + | 4.14230i | −0.397187 | + | 0.150257i | ||||
\(761\) | 11.6399 | − | 6.72028i | 0.421945 | − | 0.243610i | −0.273964 | − | 0.961740i | \(-0.588335\pi\) |
0.695909 | + | 0.718130i | \(0.255002\pi\) | |||||||
\(762\) | −40.4556 | + | 75.7897i | −1.46555 | + | 2.74557i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −5.89373 | + | 3.94767i | −0.213228 | + | 0.142822i | ||||
\(765\) | −0.962469 | + | 3.59198i | −0.0347982 | + | 0.129868i | ||||
\(766\) | −6.66610 | − | 1.55036i | −0.240856 | − | 0.0560168i | ||||
\(767\) | 5.73750 | − | 9.93765i | 0.207169 | − | 0.358828i | ||||
\(768\) | −43.3053 | + | 25.2631i | −1.56265 | + | 0.911602i | ||||
\(769\) | −42.7134 | −1.54029 | −0.770143 | − | 0.637871i | \(-0.779815\pi\) | ||||
−0.770143 | + | 0.637871i | \(0.779815\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 45.6722 | + | 45.6722i | 1.64484 | + | 1.64484i | ||||
\(772\) | 5.37335 | + | 2.64233i | 0.193391 | + | 0.0950994i | ||||
\(773\) | 6.45078 | + | 24.0746i | 0.232018 | + | 0.865905i | 0.979470 | + | 0.201589i | \(0.0646104\pi\) |
−0.747452 | + | 0.664316i | \(0.768723\pi\) | |||||||
\(774\) | 6.96657 | + | 11.1891i | 0.250408 | + | 0.402184i | ||||
\(775\) | −18.0023 | + | 10.3936i | −0.646661 | + | 0.373350i | ||||
\(776\) | −6.64895 | − | 5.43789i | −0.238683 | − | 0.195209i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −22.0206 | − | 11.7543i | −0.789475 | − | 0.421412i | ||||
\(779\) | −8.72827 | − | 2.33873i | −0.312723 | − | 0.0837938i | ||||
\(780\) | 10.2635 | − | 11.7298i | 0.367490 | − | 0.419996i | ||||
\(781\) | −2.84204 | + | 0.761522i | −0.101696 | + | 0.0272494i | ||||
\(782\) | 1.27595 | + | 1.19371i | 0.0456279 | + | 0.0426870i | ||||
\(783\) | −53.7014 | −1.91913 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.97582 | 0.284669 | ||||||||
\(786\) | −37.9488 | − | 35.5029i | −1.35359 | − | 1.26635i | ||||
\(787\) | −37.5097 | + | 10.0507i | −1.33708 | + | 0.358268i | −0.855349 | − | 0.518053i | \(-0.826657\pi\) |
−0.481727 | + | 0.876321i | \(0.659990\pi\) | |||||||
\(788\) | −7.56396 | − | 6.61836i | −0.269455 | − | 0.235769i | ||||
\(789\) | −41.2530 | − | 11.0537i | −1.46865 | − | 0.393523i | ||||
\(790\) | 8.22938 | + | 4.39274i | 0.292788 | + | 0.156287i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 6.05303 | + | 60.4113i | 0.215085 | + | 2.14662i | ||||
\(793\) | 14.1781 | − | 8.18572i | 0.503478 | − | 0.290683i | ||||
\(794\) | −12.4254 | − | 19.9565i | −0.440959 | − | 0.708231i | ||||
\(795\) | 5.15103 | + | 19.2239i | 0.182688 | + | 0.681802i | ||||
\(796\) | 1.58957 | − | 3.23249i | 0.0563406 | − | 0.114573i | ||||
\(797\) | 37.2933 | + | 37.2933i | 1.32100 | + | 1.32100i | 0.912971 | + | 0.408024i | \(0.133782\pi\) |
0.408024 | + | 0.912971i | \(0.366218\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.78152 | 0.346045 | ||||||||
\(800\) | −24.1395 | + | 11.0195i | −0.853462 | + | 0.389598i | ||||
\(801\) | 34.8029 | − | 60.2804i | 1.22970 | − | 2.12990i | ||||
\(802\) | −35.2384 | − | 8.19552i | −1.24431 | − | 0.289394i | ||||
\(803\) | 0.578911 | − | 2.16053i | 0.0204293 | − | 0.0762433i | ||||
\(804\) | 7.85507 | + | 11.7273i | 0.277027 | + | 0.413592i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 13.2014 | − | 24.7316i | 0.465001 | − | 0.871134i | ||||
\(807\) | 17.0010 | − | 9.81552i | 0.598463 | − | 0.345523i | ||||
\(808\) | 16.7177 | − | 37.0632i | 0.588127 | − | 1.30388i | ||||
\(809\) | 38.3756 | + | 22.1562i | 1.34922 | + | 0.778970i | 0.988138 | − | 0.153566i | \(-0.0490758\pi\) |
0.361077 | + | 0.932536i | \(0.382409\pi\) | |||||||
\(810\) | 0.445844 | + | 13.3886i | 0.0156654 | + | 0.470428i | ||||
\(811\) | 9.44442 | − | 9.44442i | 0.331639 | − | 0.331639i | −0.521570 | − | 0.853209i | \(-0.674653\pi\) |
0.853209 | + | 0.521570i | \(0.174653\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 28.1063 | + | 28.1063i | 0.985731 | + | 0.985731i | ||||
\(814\) | 2.96622 | + | 2.77503i | 0.103966 | + | 0.0972649i | ||||
\(815\) | −4.67354 | + | 8.09480i | −0.163707 | + | 0.283549i | ||||
\(816\) | −1.57738 | + | 12.1935i | −0.0552194 | + | 0.426858i | ||||
\(817\) | 5.08802 | + | 8.81271i | 0.178007 | + | 0.308318i | ||||
\(818\) | 25.9963 | − | 7.90187i | 0.908939 | − | 0.276283i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.32396 | + | 0.261803i | 0.0462348 | + | 0.00914257i | ||||
\(821\) | −48.2759 | − | 12.9355i | −1.68484 | − | 0.451451i | −0.715789 | − | 0.698316i | \(-0.753933\pi\) |
−0.969050 | + | 0.246865i | \(0.920600\pi\) | |||||||
\(822\) | 39.0190 | − | 24.2940i | 1.36094 | − | 0.847352i | ||||
\(823\) | 20.5366 | + | 11.8568i | 0.715861 | + | 0.413302i | 0.813227 | − | 0.581946i | \(-0.197709\pi\) |
−0.0973664 | + | 0.995249i | \(0.531042\pi\) | |||||||
\(824\) | 16.9026 | + | 2.76132i | 0.588831 | + | 0.0961950i | ||||
\(825\) | 46.2729i | 1.61102i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.8453 | − | 34.8453i | 1.21169 | − | 1.21169i | 0.241218 | − | 0.970471i | \(-0.422453\pi\) |
0.970471 | − | 0.241218i | \(-0.0775470\pi\) | |||||||
\(828\) | 15.4135 | + | 7.57952i | 0.535655 | + | 0.263406i | ||||
\(829\) | −16.3740 | + | 4.38741i | −0.568694 | + | 0.152381i | −0.531697 | − | 0.846934i | \(-0.678446\pi\) |
−0.0369962 | + | 0.999315i | \(0.511779\pi\) | |||||||
\(830\) | 7.33728 | + | 1.70646i | 0.254681 | + | 0.0592321i | ||||
\(831\) | −37.8534 | − | 65.5641i | −1.31312 | − | 2.27439i | ||||
\(832\) | 19.7816 | − | 29.8229i | 0.685805 | − | 1.03392i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 8.80831 | + | 28.9784i | 0.305007 | + | 1.00344i | ||||
\(835\) | −0.159532 | + | 0.595383i | −0.00552085 | + | 0.0206041i | ||||
\(836\) | 3.11835 | + | 46.7700i | 0.107851 | + | 1.61757i | ||||
\(837\) | 13.7237 | + | 51.2175i | 0.474360 | + | 1.77033i | ||||
\(838\) | −22.5403 | + | 0.750596i | −0.778642 | + | 0.0259289i | ||||
\(839\) | − | 1.32175i | − | 0.0456320i | −0.999740 | − | 0.0228160i | \(-0.992737\pi\) | ||
0.999740 | − | 0.0228160i | \(-0.00726318\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 8.85792i | − | 0.305445i | ||||||
\(842\) | 1.80409 | + | 54.1767i | 0.0621732 | + | 1.86705i | ||||
\(843\) | 10.4317 | + | 38.9318i | 0.359288 | + | 1.34088i | ||||
\(844\) | −28.1280 | + | 32.1468i | −0.968206 | + | 1.10654i | ||||
\(845\) | −1.00887 | + | 3.76516i | −0.0347062 | + | 0.129525i | ||||
\(846\) | 91.9989 | − | 27.9641i | 3.16299 | − | 0.961426i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 17.5825 | + | 42.1789i | 0.603784 | + | 1.44843i | ||||
\(849\) | 1.94780 | + | 3.37369i | 0.0668483 | + | 0.115785i | ||||
\(850\) | −1.47415 | + | 6.33840i | −0.0505628 | + | 0.217405i | ||||
\(851\) | 1.10999 | − | 0.297420i | 0.0380498 | − | 0.0101954i | ||||
\(852\) | −5.54433 | + | 1.88901i | −0.189945 | + | 0.0647164i | ||||
\(853\) | 33.7981 | − | 33.7981i | 1.15722 | − | 1.15722i | 0.172153 | − | 0.985070i | \(-0.444928\pi\) |
0.985070 | − | 0.172153i | \(-0.0550725\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 28.2227i | 0.965196i | ||||||||
\(856\) | −29.1861 | − | 40.5842i | −0.997560 | − | 1.38714i | ||||
\(857\) | 10.5676 | + | 6.10119i | 0.360982 | + | 0.208413i | 0.669511 | − | 0.742802i | \(-0.266504\pi\) |
−0.308530 | + | 0.951215i | \(0.599837\pi\) | |||||||
\(858\) | −32.9841 | − | 52.9762i | −1.12606 | − | 1.80858i | ||||
\(859\) | 13.1420 | + | 3.52139i | 0.448400 | + | 0.120148i | 0.475951 | − | 0.879472i | \(-0.342104\pi\) |
−0.0275506 | + | 0.999620i | \(0.508771\pi\) | |||||||
\(860\) | −0.845804 | − | 1.26276i | −0.0288417 | − | 0.0430596i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.07134 | + | 19.9740i | 0.206791 | + | 0.680319i | ||||
\(863\) | 24.2546 | + | 42.0102i | 0.825636 | + | 1.43004i | 0.901433 | + | 0.432920i | \(0.142517\pi\) |
−0.0757970 | + | 0.997123i | \(0.524150\pi\) | |||||||
\(864\) | 11.2139 | + | 66.7522i | 0.381506 | + | 2.27095i | ||||
\(865\) | −2.84611 | + | 4.92961i | −0.0967707 | + | 0.167612i | ||||
\(866\) | 28.9904 | − | 30.9877i | 0.985135 | − | 1.05301i | ||||
\(867\) | −35.5348 | − | 35.5348i | −1.20682 | − | 1.20682i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26.4104 | − | 26.4104i | 0.895913 | − | 0.895913i | ||||
\(870\) | 11.0509 | − | 0.367998i | 0.374661 | − | 0.0124763i | ||||
\(871\) | −8.72554 | − | 5.03769i | −0.295654 | − | 0.170696i | ||||
\(872\) | −36.6720 | − | 16.5413i | −1.24187 | − | 0.560158i | ||||
\(873\) | −17.9329 | + | 10.3536i | −0.606936 | + | 0.350415i | ||||
\(874\) | 11.6985 | + | 6.24454i | 0.395709 | + | 0.211225i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.863767 | − | 4.36815i | 0.0291840 | − | 0.147586i | ||||
\(877\) | −5.71771 | + | 21.3388i | −0.193073 | + | 0.720560i | 0.799684 | + | 0.600422i | \(0.205001\pi\) |
−0.992757 | + | 0.120138i | \(0.961666\pi\) | |||||||
\(878\) | 10.8128 | − | 46.4921i | 0.364916 | − | 1.56903i | ||||
\(879\) | 39.8682 | − | 69.0538i | 1.34472 | − | 2.32913i | ||||
\(880\) | −0.929423 | − | 6.93888i | −0.0313308 | − | 0.233910i | ||||
\(881\) | 22.7269 | 0.765688 | 0.382844 | − | 0.923813i | \(-0.374945\pi\) | ||||
0.382844 | + | 0.923813i | \(0.374945\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.2833 | − | 30.2833i | −1.01912 | − | 1.01912i | −0.999814 | − | 0.0193019i | \(-0.993856\pi\) |
−0.0193019 | − | 0.999814i | \(-0.506144\pi\) | |||||||
\(884\) | −2.83042 | − | 8.30741i | −0.0951973 | − | 0.279408i | ||||
\(885\) | −1.15660 | − | 4.31650i | −0.0388788 | − | 0.145098i | ||||
\(886\) | 8.86290 | − | 5.51823i | 0.297755 | − | 0.185389i | ||||
\(887\) | 33.5292 | − | 19.3581i | 1.12580 | − | 0.649980i | 0.182924 | − | 0.983127i | \(-0.441444\pi\) |
0.942875 | + | 0.333147i | \(0.108110\pi\) | |||||||
\(888\) | 6.25935 | + | 5.11925i | 0.210050 | + | 0.171791i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −3.77953 | + | 7.08059i | −0.126690 | + | 0.237342i | ||||
\(891\) | 51.8089 | + | 13.8822i | 1.73566 | + | 0.465070i | ||||
\(892\) | −0.946352 | − | 14.1936i | −0.0316862 | − | 0.475238i | ||||
\(893\) | 71.7065 | − | 19.2137i | 2.39957 | − | 0.642962i | ||||
\(894\) | −7.45184 | + | 7.96523i | −0.249227 | + | 0.266397i | ||||
\(895\) | −7.81501 | −0.261227 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −17.6548 | −0.589478 | ||||||||
\(898\) | 1.53626 | − | 1.64210i | 0.0512656 | − | 0.0547975i | ||||
\(899\) | 19.2104 | − | 5.14741i | 0.640703 | − | 0.171676i | ||||
\(900\) | 4.25578 | + | 63.8294i | 0.141859 | + | 2.12765i | ||||
\(901\) | 10.8247 | + | 2.90048i | 0.360624 | + | 0.0966290i | ||||
\(902\) | 2.54459 | − | 4.76705i | 0.0847256 | − | 0.158725i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.9894 | + | 8.98775i | 0.365502 | + | 0.298928i | ||||
\(905\) | 5.00704 | − | 2.89082i | 0.166440 | − | 0.0960940i | ||||
\(906\) | −78.2952 | + | 48.7483i | −2.60119 | + | 1.61955i | ||||
\(907\) | −9.32356 | − | 34.7960i | −0.309584 | − | 1.15538i | −0.928927 | − | 0.370262i | \(-0.879268\pi\) |
0.619344 | − | 0.785120i | \(-0.287399\pi\) | |||||||
\(908\) | −11.1001 | − | 32.5792i | −0.368369 | − | 1.08118i | ||||
\(909\) | −69.3098 | − | 69.3098i | −2.29886 | − | 2.29886i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −52.6922 | −1.74577 | −0.872886 | − | 0.487924i | \(-0.837754\pi\) | ||||
−0.872886 | + | 0.487924i | \(0.837754\pi\) | |||||||
\(912\) | 12.3881 | + | 92.4867i | 0.410209 | + | 3.06254i | ||||
\(913\) | 15.0809 | − | 26.1209i | 0.499106 | − | 0.864477i | ||||
\(914\) | −0.688507 | + | 2.96038i | −0.0227738 | + | 0.0979207i | ||||
\(915\) | 1.65013 | − | 6.15836i | 0.0545516 | − | 0.203589i | ||||
\(916\) | 0.340992 | − | 1.72443i | 0.0112667 | − | 0.0569768i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 14.6439 | + | 7.81672i | 0.483320 | + | 0.257990i | ||||
\(919\) | 22.0937 | − | 12.7558i | 0.728803 | − | 0.420775i | −0.0891810 | − | 0.996015i | \(-0.528425\pi\) |
0.817984 | + | 0.575241i | \(0.195092\pi\) | |||||||
\(920\) | −1.80542 | − | 0.814351i | −0.0595228 | − | 0.0268484i | ||||
\(921\) | 6.71547 | + | 3.87718i | 0.221282 | + | 0.127757i | ||||
\(922\) | 53.4516 | − | 1.77995i | 1.76033 | − | 0.0586194i | ||||
\(923\) | 2.95640 | − | 2.95640i | 0.0973111 | − | 0.0973111i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.02632 | + | 3.02632i | 0.0995046 | + | 0.0995046i | ||||
\(926\) | −15.7181 | + | 16.8010i | −0.516530 | + | 0.552116i | ||||
\(927\) | 20.6441 | − | 35.7566i | 0.678041 | − | 1.17440i | ||||
\(928\) | 25.0371 | − | 4.20607i | 0.821883 | − | 0.138071i | ||||
\(929\) | −24.5999 | − | 42.6083i | −0.807097 | − | 1.39793i | −0.914866 | − | 0.403757i | \(-0.867704\pi\) |
0.107770 | − | 0.994176i | \(-0.465629\pi\) | |||||||
\(930\) | −3.17509 | − | 10.4457i | −0.104115 | − | 0.342528i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −5.40577 | − | 8.07062i | −0.177072 | − | 0.264362i | ||||
\(933\) | −52.7517 | − | 14.1348i | −1.72701 | − | 0.462752i | ||||
\(934\) | 18.9521 | + | 30.4392i | 0.620130 | + | 0.996000i | ||||
\(935\) | −1.48686 | − | 0.858436i | −0.0486254 | − | 0.0280739i | ||||
\(936\) | −50.3710 | − | 70.0424i | −1.64643 | − | 2.28941i | ||||
\(937\) | 44.3522i | 1.44892i | 0.689315 | + | 0.724462i | \(0.257912\pi\) | ||||
−0.689315 | + | 0.724462i | \(0.742088\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 62.7995 | − | 62.7995i | 2.04939 | − | 2.04939i | ||||
\(940\) | −10.4951 | + | 3.57579i | −0.342313 | + | 0.116630i | ||||
\(941\) | −19.2167 | + | 5.14910i | −0.626447 | + | 0.167856i | −0.558057 | − | 0.829803i | \(-0.688453\pi\) |
−0.0683899 | + | 0.997659i | \(0.521786\pi\) | |||||||
\(942\) | 14.4010 | − | 61.9200i | 0.469209 | − | 2.01746i | ||||
\(943\) | −0.764364 | − | 1.32392i | −0.0248911 | − | 0.0431127i | ||||
\(944\) | −3.94793 | − | 9.47077i | −0.128494 | − | 0.308247i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.82230 | + | 1.76975i | −0.189299 | + | 0.0575397i | ||||
\(947\) | −8.15611 | + | 30.4390i | −0.265038 | + | 0.989136i | 0.697189 | + | 0.716887i | \(0.254434\pi\) |
−0.962227 | + | 0.272248i | \(0.912233\pi\) | |||||||
\(948\) | 48.9617 | − | 55.9571i | 1.59020 | − | 1.81740i | ||||
\(949\) | 0.822629 | + | 3.07009i | 0.0267037 | + | 0.0996594i | ||||
\(950\) | 1.64374 | + | 49.3613i | 0.0533299 | + | 1.60149i | ||||
\(951\) | 36.5323i | 1.18464i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 52.5006i | − | 1.70066i | −0.526250 | − | 0.850330i | \(-0.676402\pi\) | ||
0.526250 | − | 0.850330i | \(-0.323598\pi\) | |||||||
\(954\) | 110.103 | − | 3.66645i | 3.56471 | − | 0.118706i | ||||
\(955\) | −0.510368 | − | 1.90472i | −0.0165151 | − | 0.0616353i | ||||
\(956\) | −0.653335 | − | 9.79890i | −0.0211304 | − | 0.316919i | ||||
\(957\) | 11.4583 | − | 42.7628i | 0.370393 | − | 1.38233i | ||||
\(958\) | 6.98613 | + | 22.9836i | 0.225712 | + | 0.742566i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2.76508 | − | 13.6597i | −0.0892426 | − | 0.440865i | ||||
\(961\) | 5.68136 | + | 9.84041i | 0.183270 | + | 0.317433i | ||||
\(962\) | −5.62193 | − | 1.30751i | −0.181258 | − | 0.0421559i | ||||
\(963\) | −116.405 | + | 31.1906i | −3.75110 | + | 1.00510i | ||||
\(964\) | 19.4893 | + | 9.58380i | 0.627709 | + | 0.308673i | ||||
\(965\) | −1.17699 | + | 1.17699i | −0.0378888 | + | 0.0378888i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 22.7183i | − | 0.730572i | −0.930895 | − | 0.365286i | \(-0.880971\pi\) | ||
0.930895 | − | 0.365286i | \(-0.119029\pi\) | |||||||
\(968\) | 3.04162 | + | 0.496899i | 0.0977615 | + | 0.0159709i | ||||
\(969\) | 19.8179 | + | 11.4419i | 0.636644 | + | 0.367567i | ||||
\(970\) | 2.02694 | − | 1.26202i | 0.0650813 | − | 0.0405210i | ||||
\(971\) | 11.6299 | + | 3.11622i | 0.373221 | + | 0.100004i | 0.440554 | − | 0.897726i | \(-0.354782\pi\) |
−0.0673325 | + | 0.997731i | \(0.521449\pi\) | |||||||
\(972\) | 34.3174 | + | 6.78600i | 1.10073 | + | 0.217661i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −52.8166 | + | 16.0542i | −1.69235 | + | 0.514411i | ||||
\(975\) | −32.8768 | − | 56.9442i | −1.05290 | − | 1.82367i | ||||
\(976\) | 1.87808 | − | 14.5180i | 0.0601158 | − | 0.464709i | ||||
\(977\) | 18.8637 | − | 32.6729i | 0.603503 | − | 1.04530i | −0.388783 | − | 0.921329i | \(-0.627104\pi\) |
0.992286 | − | 0.123969i | \(-0.0395622\pi\) | |||||||
\(978\) | 54.4053 | + | 50.8986i | 1.73969 | + | 1.62756i | ||||
\(979\) | 22.7236 | + | 22.7236i | 0.726250 | + | 0.726250i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −68.5784 | + | 68.5784i | −2.18954 | + | 2.18954i | ||||
\(982\) | −1.78941 | − | 53.7359i | −0.0571025 | − | 1.71478i | ||||
\(983\) | 39.1070 | + | 22.5785i | 1.24732 | + | 0.720141i | 0.970574 | − | 0.240802i | \(-0.0774104\pi\) |
0.276747 | + | 0.960943i | \(0.410744\pi\) | |||||||
\(984\) | 4.42302 | − | 9.80584i | 0.141001 | − | 0.312599i | ||||
\(985\) | 2.41959 | − | 1.39695i | 0.0770946 | − | 0.0445106i | ||||
\(986\) | 2.93186 | − | 5.49256i | 0.0933694 | − | 0.174919i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −37.0674 | − | 55.3403i | −1.17927 | − | 1.76061i | ||||
\(989\) | −0.445575 | + | 1.66291i | −0.0141685 | + | 0.0528775i | ||||
\(990\) | −16.4386 | − | 3.82318i | −0.522453 | − | 0.121509i | ||||
\(991\) | 23.1140 | − | 40.0346i | 0.734240 | − | 1.27174i | −0.220815 | − | 0.975316i | \(-0.570872\pi\) |
0.955056 | − | 0.296426i | \(-0.0957949\pi\) | |||||||
\(992\) | −10.4099 | − | 22.8041i | −0.330514 | − | 0.724031i | ||||
\(993\) | 1.04343 | 0.0331121 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.708054 | + | 0.708054i | 0.0224468 | + | 0.0224468i | ||||
\(996\) | 26.4961 | − | 53.8816i | 0.839560 | − | 1.70730i | ||||
\(997\) | −9.97267 | − | 37.2185i | −0.315838 | − | 1.17872i | −0.923207 | − | 0.384303i | \(-0.874442\pi\) |
0.607369 | − | 0.794419i | \(-0.292225\pi\) | |||||||
\(998\) | 4.78830 | + | 7.69055i | 0.151571 | + | 0.243440i | ||||
\(999\) | 9.45447 | − | 5.45854i | 0.299126 | − | 0.172701i |
(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 | 784.2.x.l.557.3 | 24 | ||
7.2 | even | 3 | inner | 784.2.x.l.765.6 | 24 | ||
7.3 | odd | 6 | 784.2.m.h.589.2 | 12 | |||
7.4 | even | 3 | 112.2.m.d.29.2 | ✓ | 12 | ||
7.5 | odd | 6 | 784.2.x.m.765.6 | 24 | |||
7.6 | odd | 2 | 784.2.x.m.557.3 | 24 | |||
16.5 | even | 4 | inner | 784.2.x.l.165.6 | 24 | ||
28.11 | odd | 6 | 448.2.m.d.337.1 | 12 | |||
56.11 | odd | 6 | 896.2.m.h.673.6 | 12 | |||
56.53 | even | 6 | 896.2.m.g.673.1 | 12 | |||
112.5 | odd | 12 | 784.2.x.m.373.3 | 24 | |||
112.11 | odd | 12 | 448.2.m.d.113.1 | 12 | |||
112.37 | even | 12 | inner | 784.2.x.l.373.3 | 24 | ||
112.53 | even | 12 | 112.2.m.d.85.2 | yes | 12 | ||
112.67 | odd | 12 | 896.2.m.h.225.6 | 12 | |||
112.69 | odd | 4 | 784.2.x.m.165.6 | 24 | |||
112.101 | odd | 12 | 784.2.m.h.197.2 | 12 | |||
112.109 | even | 12 | 896.2.m.g.225.1 | 12 | |||
224.11 | odd | 24 | 7168.2.a.bi.1.1 | 12 | |||
224.53 | even | 24 | 7168.2.a.bj.1.12 | 12 | |||
224.123 | odd | 24 | 7168.2.a.bi.1.12 | 12 | |||
224.165 | even | 24 | 7168.2.a.bj.1.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.m.d.29.2 | ✓ | 12 | 7.4 | even | 3 | ||
112.2.m.d.85.2 | yes | 12 | 112.53 | even | 12 | ||
448.2.m.d.113.1 | 12 | 112.11 | odd | 12 | |||
448.2.m.d.337.1 | 12 | 28.11 | odd | 6 | |||
784.2.m.h.197.2 | 12 | 112.101 | odd | 12 | |||
784.2.m.h.589.2 | 12 | 7.3 | odd | 6 | |||
784.2.x.l.165.6 | 24 | 16.5 | even | 4 | inner | ||
784.2.x.l.373.3 | 24 | 112.37 | even | 12 | inner | ||
784.2.x.l.557.3 | 24 | 1.1 | even | 1 | trivial | ||
784.2.x.l.765.6 | 24 | 7.2 | even | 3 | inner | ||
784.2.x.m.165.6 | 24 | 112.69 | odd | 4 | |||
784.2.x.m.373.3 | 24 | 112.5 | odd | 12 | |||
784.2.x.m.557.3 | 24 | 7.6 | odd | 2 | |||
784.2.x.m.765.6 | 24 | 7.5 | odd | 6 | |||
896.2.m.g.225.1 | 12 | 112.109 | even | 12 | |||
896.2.m.g.673.1 | 12 | 56.53 | even | 6 | |||
896.2.m.h.225.6 | 12 | 112.67 | odd | 12 | |||
896.2.m.h.673.6 | 12 | 56.11 | odd | 6 | |||
7168.2.a.bi.1.1 | 12 | 224.11 | odd | 24 | |||
7168.2.a.bi.1.12 | 12 | 224.123 | odd | 24 | |||
7168.2.a.bj.1.1 | 12 | 224.165 | even | 24 | |||
7168.2.a.bj.1.12 | 12 | 224.53 | even | 24 |