Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(214,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.214");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.h (of order \(3\), degree \(2\), 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: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 214.3 | ||
Character | \(\chi\) | \(=\) | 441.214 |
Dual form | 441.2.h.h.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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.72661 | −1.22090 | −0.610449 | − | 0.792056i | \(-0.709011\pi\) | ||||
−0.610449 | + | 0.792056i | \(0.709011\pi\) | |||||||
\(3\) | −1.70981 | + | 0.276691i | −0.987158 | + | 0.159747i | ||||
\(4\) | 0.981184 | 0.490592 | ||||||||
\(5\) | −1.75616 | + | 3.04175i | −0.785377 | + | 1.36031i | 0.143397 | + | 0.989665i | \(0.454197\pi\) |
−0.928774 | + | 0.370647i | \(0.879136\pi\) | |||||||
\(6\) | 2.95217 | − | 0.477737i | 1.20522 | − | 0.195035i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.75910 | 0.621935 | ||||||||
\(9\) | 2.84688 | − | 0.946176i | 0.948962 | − | 0.315392i | ||||
\(10\) | 3.03220 | − | 5.25192i | 0.958865 | − | 1.66080i | ||||
\(11\) | 3.04532 | + | 5.27465i | 0.918199 | + | 1.59037i | 0.802150 | + | 0.597123i | \(0.203690\pi\) |
0.116049 | + | 0.993244i | \(0.462977\pi\) | |||||||
\(12\) | −1.67764 | + | 0.271484i | −0.484292 | + | 0.0783708i | ||||
\(13\) | 0.560139 | + | 0.970190i | 0.155355 | + | 0.269082i | 0.933188 | − | 0.359388i | \(-0.117015\pi\) |
−0.777833 | + | 0.628471i | \(0.783681\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.16106 | − | 5.68672i | 0.557984 | − | 1.46831i | ||||
\(16\) | −4.99965 | −1.24991 | ||||||||
\(17\) | −0.601978 | + | 1.04266i | −0.146001 | + | 0.252881i | −0.929746 | − | 0.368202i | \(-0.879974\pi\) |
0.783745 | + | 0.621083i | \(0.213307\pi\) | |||||||
\(18\) | −4.91546 | + | 1.63368i | −1.15859 | + | 0.385061i | ||||
\(19\) | 1.10269 | + | 1.90991i | 0.252974 | + | 0.438163i | 0.964343 | − | 0.264655i | \(-0.0852581\pi\) |
−0.711370 | + | 0.702818i | \(0.751925\pi\) | |||||||
\(20\) | −1.72311 | + | 2.98452i | −0.385300 | + | 0.667359i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.25808 | − | 9.10727i | −1.12103 | − | 1.94168i | ||||
\(23\) | 0.636695 | − | 1.10279i | 0.132760 | − | 0.229947i | −0.791980 | − | 0.610548i | \(-0.790949\pi\) |
0.924740 | + | 0.380601i | \(0.124283\pi\) | |||||||
\(24\) | −3.00772 | + | 0.486726i | −0.613948 | + | 0.0993525i | ||||
\(25\) | −3.66817 | − | 6.35345i | −0.733633 | − | 1.27069i | ||||
\(26\) | −0.967143 | − | 1.67514i | −0.189672 | − | 0.328522i | ||||
\(27\) | −4.60583 | + | 2.40548i | −0.886392 | + | 0.462936i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.10262 | + | 5.37390i | −0.576142 | + | 0.997907i | 0.419774 | + | 0.907628i | \(0.362109\pi\) |
−0.995917 | + | 0.0902789i | \(0.971224\pi\) | |||||||
\(30\) | −3.73132 | + | 9.81875i | −0.681242 | + | 1.79265i | ||||
\(31\) | −0.188404 | −0.0338383 | −0.0169192 | − | 0.999857i | \(-0.505386\pi\) | ||||
−0.0169192 | + | 0.999857i | \(0.505386\pi\) | |||||||
\(32\) | 5.11425 | 0.904079 | ||||||||
\(33\) | −6.66636 | − | 8.17602i | −1.16046 | − | 1.42326i | ||||
\(34\) | 1.03938 | − | 1.80026i | 0.178252 | − | 0.308742i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.79332 | − | 0.928373i | 0.465553 | − | 0.154729i | ||||
\(37\) | −1.78835 | − | 3.09752i | −0.294003 | − | 0.509228i | 0.680749 | − | 0.732516i | \(-0.261654\pi\) |
−0.974753 | + | 0.223288i | \(0.928321\pi\) | |||||||
\(38\) | −1.90391 | − | 3.29767i | −0.308855 | − | 0.534953i | ||||
\(39\) | −1.22617 | − | 1.50385i | −0.196345 | − | 0.240809i | ||||
\(40\) | −3.08925 | + | 5.35074i | −0.488453 | + | 0.846026i | ||||
\(41\) | 1.68320 | + | 2.91538i | 0.262871 | + | 0.455307i | 0.967004 | − | 0.254762i | \(-0.0819972\pi\) |
−0.704132 | + | 0.710069i | \(0.748664\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.90276 | + | 3.29567i | −0.290168 | + | 0.502585i | −0.973849 | − | 0.227195i | \(-0.927044\pi\) |
0.683681 | + | 0.729781i | \(0.260378\pi\) | |||||||
\(44\) | 2.98802 | + | 5.17540i | 0.450461 | + | 0.780221i | ||||
\(45\) | −2.12154 | + | 10.3211i | −0.316261 | + | 1.53859i | ||||
\(46\) | −1.09932 | + | 1.90408i | −0.162086 | + | 0.280742i | ||||
\(47\) | −5.72070 | −0.834449 | −0.417225 | − | 0.908803i | \(-0.636997\pi\) | ||||
−0.417225 | + | 0.908803i | \(0.636997\pi\) | |||||||
\(48\) | 8.54843 | − | 1.38336i | 1.23386 | − | 0.199670i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 6.33349 | + | 10.9699i | 0.895691 | + | 1.55138i | ||||
\(51\) | 0.740773 | − | 1.94930i | 0.103729 | − | 0.272957i | ||||
\(52\) | 0.549600 | + | 0.951935i | 0.0762158 | + | 0.132010i | ||||
\(53\) | 4.16913 | − | 7.22115i | 0.572675 | − | 0.991901i | −0.423615 | − | 0.905842i | \(-0.639239\pi\) |
0.996290 | − | 0.0860593i | \(-0.0274275\pi\) | |||||||
\(54\) | 7.95247 | − | 4.15334i | 1.08219 | − | 0.565197i | ||||
\(55\) | −21.3922 | −2.88453 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.41384 | − | 2.96047i | −0.319720 | − | 0.392124i | ||||
\(58\) | 5.35702 | − | 9.27862i | 0.703411 | − | 1.21834i | ||||
\(59\) | −11.2685 | −1.46704 | −0.733519 | − | 0.679669i | \(-0.762123\pi\) | ||||
−0.733519 | + | 0.679669i | \(0.762123\pi\) | |||||||
\(60\) | 2.12040 | − | 5.57972i | 0.273743 | − | 0.720339i | ||||
\(61\) | 12.0022 | 1.53672 | 0.768361 | − | 0.640017i | \(-0.221073\pi\) | ||||
0.768361 | + | 0.640017i | \(0.221073\pi\) | |||||||
\(62\) | 0.325300 | 0.0413131 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.16898 | 0.146123 | ||||||||
\(65\) | −3.93477 | −0.488048 | ||||||||
\(66\) | 11.5102 | + | 14.1168i | 1.41681 | + | 1.73766i | ||||
\(67\) | −7.91303 | −0.966731 | −0.483366 | − | 0.875419i | \(-0.660586\pi\) | ||||
−0.483366 | + | 0.875419i | \(0.660586\pi\) | |||||||
\(68\) | −0.590651 | + | 1.02304i | −0.0716270 | + | 0.124062i | ||||
\(69\) | −0.783494 | + | 2.06172i | −0.0943217 | + | 0.248202i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.2052 | −1.44850 | −0.724248 | − | 0.689540i | \(-0.757813\pi\) | ||||
−0.724248 | + | 0.689540i | \(0.757813\pi\) | |||||||
\(72\) | 5.00795 | − | 1.66442i | 0.590192 | − | 0.196153i | ||||
\(73\) | 2.65737 | − | 4.60269i | 0.311021 | − | 0.538704i | −0.667563 | − | 0.744554i | \(-0.732662\pi\) |
0.978584 | + | 0.205849i | \(0.0659957\pi\) | |||||||
\(74\) | 3.08779 | + | 5.34820i | 0.358948 | + | 0.621716i | ||||
\(75\) | 8.02980 | + | 9.84823i | 0.927201 | + | 1.13718i | ||||
\(76\) | 1.08194 | + | 1.87397i | 0.124107 | + | 0.214959i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.11712 | + | 2.59657i | 0.239717 | + | 0.294003i | ||||
\(79\) | 9.21711 | 1.03701 | 0.518503 | − | 0.855076i | \(-0.326490\pi\) | ||||
0.518503 | + | 0.855076i | \(0.326490\pi\) | |||||||
\(80\) | 8.78016 | − | 15.2077i | 0.981651 | − | 1.70027i | ||||
\(81\) | 7.20950 | − | 5.38731i | 0.801056 | − | 0.598589i | ||||
\(82\) | −2.90623 | − | 5.03373i | −0.320939 | − | 0.555883i | ||||
\(83\) | 0.624950 | − | 1.08245i | 0.0685972 | − | 0.118814i | −0.829687 | − | 0.558229i | \(-0.811481\pi\) |
0.898284 | + | 0.439415i | \(0.144814\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.11433 | − | 3.66213i | −0.229332 | − | 0.397214i | ||||
\(86\) | 3.28532 | − | 5.69034i | 0.354265 | − | 0.613605i | ||||
\(87\) | 3.81798 | − | 10.0468i | 0.409330 | − | 1.07713i | ||||
\(88\) | 5.35702 | + | 9.27862i | 0.571060 | + | 0.989105i | ||||
\(89\) | −2.77066 | − | 4.79892i | −0.293689 | − | 0.508684i | 0.680990 | − | 0.732293i | \(-0.261550\pi\) |
−0.974679 | + | 0.223608i | \(0.928216\pi\) | |||||||
\(90\) | 3.66308 | − | 17.8206i | 0.386122 | − | 1.87846i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.624715 | − | 1.08204i | 0.0651310 | − | 0.112810i | ||||
\(93\) | 0.322134 | − | 0.0521295i | 0.0334038 | − | 0.00540558i | ||||
\(94\) | 9.87741 | 1.01878 | ||||||||
\(95\) | −7.74596 | −0.794718 | ||||||||
\(96\) | −8.74438 | + | 1.41506i | −0.892469 | + | 0.144424i | ||||
\(97\) | 8.24277 | − | 14.2769i | 0.836926 | − | 1.44960i | −0.0555261 | − | 0.998457i | \(-0.517684\pi\) |
0.892452 | − | 0.451142i | \(-0.148983\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.6604 | + | 12.1349i | 1.37292 | + | 1.21960i | ||||
\(100\) | −3.59915 | − | 6.23391i | −0.359915 | − | 0.623391i | ||||
\(101\) | 6.48192 | + | 11.2270i | 0.644975 | + | 1.11713i | 0.984307 | + | 0.176463i | \(0.0564657\pi\) |
−0.339332 | + | 0.940667i | \(0.610201\pi\) | |||||||
\(102\) | −1.27903 | + | 3.36569i | −0.126643 | + | 0.333253i | ||||
\(103\) | −1.35091 | + | 2.33984i | −0.133109 | + | 0.230552i | −0.924873 | − | 0.380275i | \(-0.875829\pi\) |
0.791765 | + | 0.610826i | \(0.209163\pi\) | |||||||
\(104\) | 0.985340 | + | 1.70666i | 0.0966205 | + | 0.167352i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.19847 | + | 12.4681i | −0.699177 | + | 1.21101i | ||||
\(107\) | 0.0892402 | + | 0.154569i | 0.00862718 | + | 0.0149427i | 0.870307 | − | 0.492510i | \(-0.163921\pi\) |
−0.861680 | + | 0.507453i | \(0.830587\pi\) | |||||||
\(108\) | −4.51917 | + | 2.36022i | −0.434857 | + | 0.227113i | ||||
\(109\) | −4.67927 | + | 8.10473i | −0.448192 | + | 0.776292i | −0.998268 | − | 0.0588226i | \(-0.981265\pi\) |
0.550076 | + | 0.835115i | \(0.314599\pi\) | |||||||
\(110\) | 36.9360 | 3.52171 | ||||||||
\(111\) | 3.91479 | + | 4.80134i | 0.371575 | + | 0.455723i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.21019 | + | 7.29226i | 0.396061 | + | 0.685998i | 0.993236 | − | 0.116113i | \(-0.0370434\pi\) |
−0.597175 | + | 0.802111i | \(0.703710\pi\) | |||||||
\(114\) | 4.16775 | + | 5.11159i | 0.390346 | + | 0.478744i | ||||
\(115\) | 2.23627 | + | 3.87333i | 0.208533 | + | 0.361190i | ||||
\(116\) | −3.04424 | + | 5.27278i | −0.282651 | + | 0.489565i | ||||
\(117\) | 2.51262 | + | 2.23203i | 0.232292 | + | 0.206351i | ||||
\(118\) | 19.4564 | 1.79110 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.80152 | − | 10.0035i | 0.347030 | − | 0.913190i | ||||
\(121\) | −13.0479 | + | 22.5997i | −1.18618 | + | 2.05452i | ||||
\(122\) | −20.7231 | −1.87618 | ||||||||
\(123\) | −3.68460 | − | 4.51902i | −0.332230 | − | 0.407467i | ||||
\(124\) | −0.184859 | −0.0166008 | ||||||||
\(125\) | 8.20593 | 0.733960 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.92438 | −0.880647 | −0.440323 | − | 0.897839i | \(-0.645136\pi\) | ||||
−0.440323 | + | 0.897839i | \(0.645136\pi\) | |||||||
\(128\) | −12.2469 | −1.08248 | ||||||||
\(129\) | 2.34147 | − | 6.16144i | 0.206155 | − | 0.542485i | ||||
\(130\) | 6.79381 | 0.595857 | ||||||||
\(131\) | 7.62335 | − | 13.2040i | 0.666055 | − | 1.15364i | −0.312943 | − | 0.949772i | \(-0.601315\pi\) |
0.978998 | − | 0.203870i | \(-0.0653519\pi\) | |||||||
\(132\) | −6.54093 | − | 8.02219i | −0.569314 | − | 0.698242i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 13.6627 | 1.18028 | ||||||||
\(135\) | 0.771665 | − | 18.2342i | 0.0664144 | − | 1.56935i | ||||
\(136\) | −1.05894 | + | 1.83413i | −0.0908032 | + | 0.157276i | ||||
\(137\) | −3.07350 | − | 5.32346i | −0.262587 | − | 0.454814i | 0.704342 | − | 0.709861i | \(-0.251242\pi\) |
−0.966929 | + | 0.255047i | \(0.917909\pi\) | |||||||
\(138\) | 1.35279 | − | 3.55979i | 0.115157 | − | 0.303030i | ||||
\(139\) | 0.438687 | + | 0.759829i | 0.0372090 | + | 0.0644478i | 0.884030 | − | 0.467430i | \(-0.154820\pi\) |
−0.846821 | + | 0.531878i | \(0.821487\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.78129 | − | 1.58286i | 0.823733 | − | 0.133301i | ||||
\(142\) | 21.0737 | 1.76847 | ||||||||
\(143\) | −3.41161 | + | 5.90908i | −0.285293 | + | 0.494142i | ||||
\(144\) | −14.2334 | + | 4.73054i | −1.18612 | + | 0.394212i | ||||
\(145\) | −10.8974 | − | 18.8748i | −0.904977 | − | 1.56747i | ||||
\(146\) | −4.58824 | + | 7.94706i | −0.379725 | + | 0.657703i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.75470 | − | 3.03923i | −0.144236 | − | 0.249823i | ||||
\(149\) | −2.88776 | + | 5.00175i | −0.236575 | + | 0.409760i | −0.959729 | − | 0.280927i | \(-0.909358\pi\) |
0.723154 | + | 0.690686i | \(0.242692\pi\) | |||||||
\(150\) | −13.8643 | − | 17.0041i | −1.13202 | − | 1.38838i | ||||
\(151\) | 1.01321 | + | 1.75494i | 0.0824541 | + | 0.142815i | 0.904304 | − | 0.426890i | \(-0.140391\pi\) |
−0.821849 | + | 0.569705i | \(0.807058\pi\) | |||||||
\(152\) | 1.93973 | + | 3.35972i | 0.157333 | + | 0.272509i | ||||
\(153\) | −0.727226 | + | 3.53790i | −0.0587927 | + | 0.286022i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.330866 | − | 0.573077i | 0.0265758 | − | 0.0460307i | ||||
\(156\) | −1.20310 | − | 1.47556i | −0.0963252 | − | 0.118139i | ||||
\(157\) | −3.04756 | −0.243222 | −0.121611 | − | 0.992578i | \(-0.538806\pi\) | ||||
−0.121611 | + | 0.992578i | \(0.538806\pi\) | |||||||
\(158\) | −15.9144 | −1.26608 | ||||||||
\(159\) | −5.13039 | + | 13.5003i | −0.406867 | + | 1.07065i | ||||
\(160\) | −8.98141 | + | 15.5563i | −0.710043 | + | 1.22983i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −12.4480 | + | 9.30178i | −0.978008 | + | 0.730817i | ||||
\(163\) | 2.69445 | + | 4.66693i | 0.211046 | + | 0.365542i | 0.952042 | − | 0.305967i | \(-0.0989797\pi\) |
−0.740996 | + | 0.671509i | \(0.765646\pi\) | |||||||
\(164\) | 1.65153 | + | 2.86053i | 0.128963 | + | 0.223370i | ||||
\(165\) | 36.5766 | − | 5.91903i | 2.84748 | − | 0.460796i | ||||
\(166\) | −1.07905 | + | 1.86896i | −0.0837502 | + | 0.145060i | ||||
\(167\) | −8.30480 | − | 14.3843i | −0.642645 | − | 1.11309i | −0.984840 | − | 0.173464i | \(-0.944504\pi\) |
0.342196 | − | 0.939629i | \(-0.388829\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.87249 | − | 10.1714i | 0.451730 | − | 0.782419i | ||||
\(170\) | 3.65063 | + | 6.32308i | 0.279991 | + | 0.484958i | ||||
\(171\) | 4.94633 | + | 4.39396i | 0.378255 | + | 0.336014i | ||||
\(172\) | −1.86696 | + | 3.23366i | −0.142354 | + | 0.246564i | ||||
\(173\) | −17.6503 | −1.34193 | −0.670965 | − | 0.741489i | \(-0.734120\pi\) | ||||
−0.670965 | + | 0.741489i | \(0.734120\pi\) | |||||||
\(174\) | −6.59216 | + | 17.3469i | −0.499750 | + | 1.31507i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −15.2255 | − | 26.3714i | −1.14767 | − | 1.98782i | ||||
\(177\) | 19.2670 | − | 3.11790i | 1.44820 | − | 0.234355i | ||||
\(178\) | 4.78384 | + | 8.28586i | 0.358564 | + | 0.621051i | ||||
\(179\) | −1.31422 | + | 2.27630i | −0.0982294 | + | 0.170138i | −0.910952 | − | 0.412513i | \(-0.864651\pi\) |
0.812722 | + | 0.582651i | \(0.197985\pi\) | |||||||
\(180\) | −2.08162 | + | 10.1269i | −0.155155 | + | 0.754818i | ||||
\(181\) | 3.97391 | 0.295378 | 0.147689 | − | 0.989034i | \(-0.452816\pi\) | ||||
0.147689 | + | 0.989034i | \(0.452816\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.5214 | + | 3.32089i | −1.51699 | + | 0.245487i | ||||
\(184\) | 1.12001 | − | 1.93991i | 0.0825681 | − | 0.143012i | ||||
\(185\) | 12.5625 | 0.923613 | ||||||||
\(186\) | −0.556200 | + | 0.0900074i | −0.0407826 | + | 0.00659966i | ||||
\(187\) | −7.33286 | −0.536232 | ||||||||
\(188\) | −5.61306 | −0.409374 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 13.3743 | 0.970270 | ||||||||
\(191\) | −18.2059 | −1.31733 | −0.658666 | − | 0.752435i | \(-0.728879\pi\) | ||||
−0.658666 | + | 0.752435i | \(0.728879\pi\) | |||||||
\(192\) | −1.99873 | + | 0.323446i | −0.144246 | + | 0.0233427i | ||||
\(193\) | −0.202385 | −0.0145680 | −0.00728401 | − | 0.999973i | \(-0.502319\pi\) | ||||
−0.00728401 | + | 0.999973i | \(0.502319\pi\) | |||||||
\(194\) | −14.2321 | + | 24.6506i | −1.02180 | + | 1.76981i | ||||
\(195\) | 6.72770 | − | 1.08871i | 0.481780 | − | 0.0779644i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.63136 | −0.116229 | −0.0581147 | − | 0.998310i | \(-0.518509\pi\) | ||||
−0.0581147 | + | 0.998310i | \(0.518509\pi\) | |||||||
\(198\) | −23.5862 | − | 20.9523i | −1.67620 | − | 1.48901i | ||||
\(199\) | −3.14605 | + | 5.44912i | −0.223018 | + | 0.386278i | −0.955723 | − | 0.294268i | \(-0.904924\pi\) |
0.732705 | + | 0.680546i | \(0.238257\pi\) | |||||||
\(200\) | −6.45266 | − | 11.1763i | −0.456272 | − | 0.790287i | ||||
\(201\) | 13.5298 | − | 2.18946i | 0.954316 | − | 0.154433i | ||||
\(202\) | −11.1918 | − | 19.3847i | −0.787449 | − | 1.36390i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.726835 | − | 1.91263i | 0.0508886 | − | 0.133911i | ||||
\(205\) | −11.8238 | −0.825812 | ||||||||
\(206\) | 2.33249 | − | 4.04000i | 0.162512 | − | 0.281480i | ||||
\(207\) | 0.769166 | − | 3.74193i | 0.0534607 | − | 0.260082i | ||||
\(208\) | −2.80050 | − | 4.85061i | −0.194180 | − | 0.336329i | ||||
\(209\) | −6.71607 | + | 11.6326i | −0.464560 | + | 0.804642i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.14368 | + | 14.1053i | 0.560634 | + | 0.971046i | 0.997441 | + | 0.0714912i | \(0.0227758\pi\) |
−0.436807 | + | 0.899555i | \(0.643891\pi\) | |||||||
\(212\) | 4.09069 | − | 7.08528i | 0.280950 | − | 0.486619i | ||||
\(213\) | 20.8686 | − | 3.37708i | 1.42989 | − | 0.231393i | ||||
\(214\) | −0.154083 | − | 0.266880i | −0.0105329 | − | 0.0182435i | ||||
\(215\) | −6.68308 | − | 11.5754i | −0.455782 | − | 0.789438i | ||||
\(216\) | −8.10210 | + | 4.23148i | −0.551278 | + | 0.287916i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.07927 | − | 13.9937i | 0.547197 | − | 0.947773i | ||||
\(219\) | −3.27006 | + | 8.60499i | −0.220970 | + | 0.581471i | ||||
\(220\) | −20.9897 | −1.41513 | ||||||||
\(221\) | −1.34877 | −0.0907278 | ||||||||
\(222\) | −6.75932 | − | 8.29004i | −0.453656 | − | 0.556391i | ||||
\(223\) | −9.98472 | + | 17.2940i | −0.668626 | + | 1.15809i | 0.309662 | + | 0.950847i | \(0.399784\pi\) |
−0.978288 | + | 0.207248i | \(0.933549\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −16.4543 | − | 14.6168i | −1.09695 | − | 0.974454i | ||||
\(226\) | −7.26936 | − | 12.5909i | −0.483551 | − | 0.837534i | ||||
\(227\) | −1.80642 | − | 3.12880i | −0.119896 | − | 0.207666i | 0.799830 | − | 0.600226i | \(-0.204923\pi\) |
−0.919726 | + | 0.392560i | \(0.871589\pi\) | |||||||
\(228\) | −2.36842 | − | 2.90477i | −0.156852 | − | 0.192373i | ||||
\(229\) | −6.85733 | + | 11.8772i | −0.453145 | + | 0.784870i | −0.998579 | − | 0.0532835i | \(-0.983031\pi\) |
0.545435 | + | 0.838153i | \(0.316365\pi\) | |||||||
\(230\) | −3.86117 | − | 6.68774i | −0.254598 | − | 0.440976i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.45781 | + | 9.45321i | −0.358323 | + | 0.620634i | ||||
\(233\) | 12.6271 | + | 21.8707i | 0.827227 | + | 1.43280i | 0.900205 | + | 0.435466i | \(0.143417\pi\) |
−0.0729776 | + | 0.997334i | \(0.523250\pi\) | |||||||
\(234\) | −4.33832 | − | 3.85384i | −0.283605 | − | 0.251934i | ||||
\(235\) | 10.0464 | − | 17.4009i | 0.655357 | − | 1.13511i | ||||
\(236\) | −11.0565 | −0.719717 | ||||||||
\(237\) | −15.7595 | + | 2.55029i | −1.02369 | + | 0.165659i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.49495 | − | 7.78549i | −0.290754 | − | 0.503601i | 0.683234 | − | 0.730200i | \(-0.260573\pi\) |
−0.973988 | + | 0.226598i | \(0.927240\pi\) | |||||||
\(240\) | −10.8046 | + | 28.4316i | −0.697431 | + | 1.83525i | ||||
\(241\) | −4.62862 | − | 8.01701i | −0.298156 | − | 0.516421i | 0.677558 | − | 0.735469i | \(-0.263038\pi\) |
−0.975714 | + | 0.219048i | \(0.929705\pi\) | |||||||
\(242\) | 22.5287 | − | 39.0209i | 1.44820 | − | 2.50836i | ||||
\(243\) | −10.8362 | + | 11.2061i | −0.695146 | + | 0.718869i | ||||
\(244\) | 11.7763 | 0.753903 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.36188 | + | 7.80259i | 0.405619 | + | 0.497475i | ||||
\(247\) | −1.23532 | + | 2.13963i | −0.0786013 | + | 0.136141i | ||||
\(248\) | −0.331421 | −0.0210452 | ||||||||
\(249\) | −0.769042 | + | 2.02369i | −0.0487361 | + | 0.128246i | ||||
\(250\) | −14.1684 | −0.896091 | ||||||||
\(251\) | 20.6517 | 1.30353 | 0.651763 | − | 0.758422i | \(-0.274030\pi\) | ||||
0.651763 | + | 0.758422i | \(0.274030\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.75576 | 0.487600 | ||||||||
\(254\) | 17.1355 | 1.07518 | ||||||||
\(255\) | 4.62838 | + | 5.67653i | 0.289841 | + | 0.355478i | ||||
\(256\) | 18.8076 | 1.17548 | ||||||||
\(257\) | 1.22289 | − | 2.11811i | 0.0762819 | − | 0.132124i | −0.825361 | − | 0.564605i | \(-0.809028\pi\) |
0.901643 | + | 0.432481i | \(0.142362\pi\) | |||||||
\(258\) | −4.04280 | + | 10.6384i | −0.251694 | + | 0.662318i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3.86073 | −0.239432 | ||||||||
\(261\) | −3.74815 | + | 18.2345i | −0.232005 | + | 1.12869i | ||||
\(262\) | −13.1626 | + | 22.7982i | −0.813186 | + | 1.40848i | ||||
\(263\) | 12.2814 | + | 21.2720i | 0.757302 | + | 1.31169i | 0.944222 | + | 0.329311i | \(0.106816\pi\) |
−0.186919 | + | 0.982375i | \(0.559850\pi\) | |||||||
\(264\) | −11.7268 | − | 14.3824i | −0.721733 | − | 0.885177i | ||||
\(265\) | 14.6433 | + | 25.3629i | 0.899531 | + | 1.55803i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.06510 | + | 7.43861i | 0.371178 | + | 0.455236i | ||||
\(268\) | −7.76415 | −0.474271 | ||||||||
\(269\) | 14.7851 | − | 25.6086i | 0.901466 | − | 1.56139i | 0.0758746 | − | 0.997117i | \(-0.475825\pi\) |
0.825592 | − | 0.564268i | \(-0.190842\pi\) | |||||||
\(270\) | −1.33237 | + | 31.4833i | −0.0810852 | + | 1.91601i | ||||
\(271\) | 12.3958 | + | 21.4701i | 0.752989 | + | 1.30421i | 0.946368 | + | 0.323090i | \(0.104722\pi\) |
−0.193380 | + | 0.981124i | \(0.561945\pi\) | |||||||
\(272\) | 3.00968 | − | 5.21291i | 0.182488 | − | 0.316079i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.30674 | + | 9.19154i | 0.320592 | + | 0.555281i | ||||
\(275\) | 22.3415 | − | 38.6966i | 1.34724 | − | 2.33349i | ||||
\(276\) | −0.768752 | + | 2.02293i | −0.0462735 | + | 0.121766i | ||||
\(277\) | −0.939249 | − | 1.62683i | −0.0564340 | − | 0.0977466i | 0.836428 | − | 0.548076i | \(-0.184640\pi\) |
−0.892862 | + | 0.450330i | \(0.851306\pi\) | |||||||
\(278\) | −0.757442 | − | 1.31193i | −0.0454284 | − | 0.0786842i | ||||
\(279\) | −0.536364 | + | 0.178263i | −0.0321113 | + | 0.0106723i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.03965 | − | 10.4610i | 0.360295 | − | 0.624049i | −0.627714 | − | 0.778444i | \(-0.716009\pi\) |
0.988009 | + | 0.154395i | \(0.0493427\pi\) | |||||||
\(282\) | −16.8885 | + | 2.73299i | −1.00569 | + | 0.162747i | ||||
\(283\) | −27.9719 | −1.66276 | −0.831378 | − | 0.555708i | \(-0.812447\pi\) | ||||
−0.831378 | + | 0.555708i | \(0.812447\pi\) | |||||||
\(284\) | −11.9756 | −0.710620 | ||||||||
\(285\) | 13.2441 | − | 2.14323i | 0.784513 | − | 0.126954i | ||||
\(286\) | 5.89052 | − | 10.2027i | 0.348314 | − | 0.603297i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 14.5597 | − | 4.83897i | 0.857937 | − | 0.285139i | ||||
\(289\) | 7.77524 | + | 13.4671i | 0.457367 | + | 0.792183i | ||||
\(290\) | 18.8155 | + | 32.5894i | 1.10488 | + | 1.91372i | ||||
\(291\) | −10.1433 | + | 26.6914i | −0.594609 | + | 1.56468i | ||||
\(292\) | 2.60736 | − | 4.51609i | 0.152584 | − | 0.264284i | ||||
\(293\) | −4.41163 | − | 7.64117i | −0.257730 | − | 0.446402i | 0.707903 | − | 0.706309i | \(-0.249641\pi\) |
−0.965634 | + | 0.259908i | \(0.916308\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.7893 | − | 34.2761i | 1.15218 | − | 1.99563i | ||||
\(296\) | −3.14589 | − | 5.44883i | −0.182851 | − | 0.316707i | ||||
\(297\) | −26.7143 | − | 16.9687i | −1.55012 | − | 0.984621i | ||||
\(298\) | 4.98604 | − | 8.63608i | 0.288834 | − | 0.500275i | ||||
\(299\) | 1.42655 | 0.0824996 | ||||||||
\(300\) | 7.87871 | + | 9.66293i | 0.454878 | + | 0.557889i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.74942 | − | 3.03009i | −0.100668 | − | 0.174362i | ||||
\(303\) | −14.1893 | − | 17.4026i | −0.815151 | − | 0.999751i | ||||
\(304\) | −5.51304 | − | 9.54887i | −0.316195 | − | 0.547665i | ||||
\(305\) | −21.0777 | + | 36.5076i | −1.20691 | + | 2.09042i | ||||
\(306\) | 1.25564 | − | 6.10857i | 0.0717799 | − | 0.349204i | ||||
\(307\) | 1.05532 | 0.0602304 | 0.0301152 | − | 0.999546i | \(-0.490413\pi\) | ||||
0.0301152 | + | 0.999546i | \(0.490413\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.66238 | − | 4.37446i | 0.0945696 | − | 0.248855i | ||||
\(310\) | −0.571277 | + | 0.989481i | −0.0324464 | + | 0.0561988i | ||||
\(311\) | 3.07215 | 0.174206 | 0.0871029 | − | 0.996199i | \(-0.472239\pi\) | ||||
0.0871029 | + | 0.996199i | \(0.472239\pi\) | |||||||
\(312\) | −2.15696 | − | 2.64542i | −0.122114 | − | 0.149768i | ||||
\(313\) | 28.1621 | 1.59181 | 0.795907 | − | 0.605419i | \(-0.206994\pi\) | ||||
0.795907 | + | 0.605419i | \(0.206994\pi\) | |||||||
\(314\) | 5.26196 | 0.296949 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.04368 | 0.508747 | ||||||||
\(317\) | 12.8465 | 0.721530 | 0.360765 | − | 0.932657i | \(-0.382516\pi\) | ||||
0.360765 | + | 0.932657i | \(0.382516\pi\) | |||||||
\(318\) | 8.85819 | − | 23.3098i | 0.496743 | − | 1.30715i | ||||
\(319\) | −37.7939 | −2.11605 | ||||||||
\(320\) | −2.05291 | + | 3.55575i | −0.114761 | + | 0.198772i | ||||
\(321\) | −0.195351 | − | 0.239591i | −0.0109034 | − | 0.0133726i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.65517 | −0.147738 | ||||||||
\(324\) | 7.07385 | − | 5.28594i | 0.392992 | − | 0.293663i | ||||
\(325\) | 4.10937 | − | 7.11763i | 0.227947 | − | 0.394815i | ||||
\(326\) | −4.65227 | − | 8.05797i | −0.257665 | − | 0.446290i | ||||
\(327\) | 5.75814 | − | 15.1522i | 0.318426 | − | 0.837920i | ||||
\(328\) | 2.96091 | + | 5.12845i | 0.163489 | + | 0.283171i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −63.1535 | + | 10.2199i | −3.47649 | + | 0.562585i | ||||
\(331\) | −21.5560 | −1.18483 | −0.592413 | − | 0.805634i | \(-0.701825\pi\) | ||||
−0.592413 | + | 0.805634i | \(0.701825\pi\) | |||||||
\(332\) | 0.613191 | − | 1.06208i | 0.0336532 | − | 0.0582891i | ||||
\(333\) | −8.02202 | − | 7.12617i | −0.439604 | − | 0.390512i | ||||
\(334\) | 14.3392 | + | 24.8361i | 0.784604 | + | 1.35897i | ||||
\(335\) | 13.8965 | − | 24.0695i | 0.759248 | − | 1.31506i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.30340 | + | 10.9178i | 0.343368 | + | 0.594731i | 0.985056 | − | 0.172235i | \(-0.0550989\pi\) |
−0.641688 | + | 0.766966i | \(0.721766\pi\) | |||||||
\(338\) | −10.1395 | + | 17.5621i | −0.551516 | + | 0.955254i | ||||
\(339\) | −9.21632 | − | 11.3034i | −0.500562 | − | 0.613919i | ||||
\(340\) | −2.07455 | − | 3.59323i | −0.112508 | − | 0.194870i | ||||
\(341\) | −0.573750 | − | 0.993764i | −0.0310703 | − | 0.0538153i | ||||
\(342\) | −8.54039 | − | 7.58665i | −0.461811 | − | 0.410239i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.34714 | + | 5.79741i | −0.180466 | + | 0.312575i | ||||
\(345\) | −4.89531 | − | 6.00390i | −0.263554 | − | 0.323239i | ||||
\(346\) | 30.4752 | 1.63836 | ||||||||
\(347\) | 23.1366 | 1.24204 | 0.621020 | − | 0.783795i | \(-0.286719\pi\) | ||||
0.621020 | + | 0.783795i | \(0.286719\pi\) | |||||||
\(348\) | 3.74614 | − | 9.85776i | 0.200814 | − | 0.528431i | ||||
\(349\) | 8.24346 | − | 14.2781i | 0.441262 | − | 0.764289i | −0.556521 | − | 0.830833i | \(-0.687864\pi\) |
0.997783 | + | 0.0665448i | \(0.0211975\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.91368 | − | 3.12112i | −0.262273 | − | 0.166593i | ||||
\(352\) | 15.5745 | + | 26.9759i | 0.830124 | + | 1.43782i | ||||
\(353\) | 12.2438 | + | 21.2068i | 0.651669 | + | 1.12872i | 0.982718 | + | 0.185110i | \(0.0592642\pi\) |
−0.331049 | + | 0.943614i | \(0.607402\pi\) | |||||||
\(354\) | −33.2666 | + | 5.38339i | −1.76810 | + | 0.286124i | ||||
\(355\) | 21.4343 | − | 37.1253i | 1.13761 | − | 1.97041i | ||||
\(356\) | −2.71852 | − | 4.70862i | −0.144081 | − | 0.249556i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.26915 | − | 3.93028i | 0.119928 | − | 0.207722i | ||||
\(359\) | −10.2389 | − | 17.7342i | −0.540386 | − | 0.935977i | −0.998882 | − | 0.0472797i | \(-0.984945\pi\) |
0.458495 | − | 0.888697i | \(-0.348389\pi\) | |||||||
\(360\) | −3.73200 | + | 18.1559i | −0.196694 | + | 0.956900i | ||||
\(361\) | 7.06816 | − | 12.2424i | 0.372009 | − | 0.644338i | ||||
\(362\) | −6.86139 | −0.360627 | ||||||||
\(363\) | 16.0564 | − | 42.2514i | 0.842740 | − | 2.21762i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.33349 | + | 16.1661i | 0.488537 | + | 0.846172i | ||||
\(366\) | 35.4325 | − | 5.73388i | 1.85209 | − | 0.299715i | ||||
\(367\) | −11.1269 | − | 19.2724i | −0.580821 | − | 1.00601i | −0.995382 | − | 0.0959900i | \(-0.969398\pi\) |
0.414561 | − | 0.910021i | \(-0.363935\pi\) | |||||||
\(368\) | −3.18325 | + | 5.51355i | −0.165938 | + | 0.287414i | ||||
\(369\) | 7.55034 | + | 6.70716i | 0.393055 | + | 0.349161i | ||||
\(370\) | −21.6905 | −1.12764 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.316073 | − | 0.0511487i | 0.0163876 | − | 0.00265194i | ||||
\(373\) | 16.2684 | − | 28.1777i | 0.842347 | − | 1.45899i | −0.0455576 | − | 0.998962i | \(-0.514506\pi\) |
0.887905 | − | 0.460027i | \(-0.152160\pi\) | |||||||
\(374\) | 12.6610 | 0.654685 | ||||||||
\(375\) | −14.0306 | + | 2.27050i | −0.724535 | + | 0.117248i | ||||
\(376\) | −10.0633 | −0.518973 | ||||||||
\(377\) | −6.95160 | −0.358026 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.54440 | 0.0793306 | 0.0396653 | − | 0.999213i | \(-0.487371\pi\) | ||||
0.0396653 | + | 0.999213i | \(0.487371\pi\) | |||||||
\(380\) | −7.60021 | −0.389883 | ||||||||
\(381\) | 16.9688 | − | 2.74598i | 0.869337 | − | 0.140681i | ||||
\(382\) | 31.4345 | 1.60833 | ||||||||
\(383\) | −15.8147 | + | 27.3919i | −0.808093 | + | 1.39966i | 0.106090 | + | 0.994357i | \(0.466167\pi\) |
−0.914183 | + | 0.405302i | \(0.867166\pi\) | |||||||
\(384\) | 20.9398 | − | 3.38859i | 1.06858 | − | 0.172923i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.349441 | 0.0177861 | ||||||||
\(387\) | −2.29865 | + | 11.1827i | −0.116847 | + | 0.568451i | ||||
\(388\) | 8.08767 | − | 14.0083i | 0.410589 | − | 0.711162i | ||||
\(389\) | 2.62313 | + | 4.54340i | 0.132998 | + | 0.230359i | 0.924831 | − | 0.380378i | \(-0.124206\pi\) |
−0.791833 | + | 0.610738i | \(0.790873\pi\) | |||||||
\(390\) | −11.6161 | + | 1.87978i | −0.588205 | + | 0.0951866i | ||||
\(391\) | 0.766552 | + | 1.32771i | 0.0387662 | + | 0.0671451i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.38103 | + | 24.6857i | −0.473210 | + | 1.24523i | ||||
\(394\) | 2.81672 | 0.141904 | ||||||||
\(395\) | −16.1867 | + | 28.0362i | −0.814440 | + | 1.41065i | ||||
\(396\) | 13.4034 | + | 11.9066i | 0.673546 | + | 0.598328i | ||||
\(397\) | −0.0138175 | − | 0.0239325i | −0.000693478 | − | 0.00120114i | 0.865678 | − | 0.500600i | \(-0.166887\pi\) |
−0.866372 | + | 0.499399i | \(0.833554\pi\) | |||||||
\(398\) | 5.43201 | − | 9.40851i | 0.272282 | − | 0.471606i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 18.3395 | + | 31.7650i | 0.916977 | + | 1.58825i | ||||
\(401\) | −6.06885 | + | 10.5115i | −0.303064 | + | 0.524922i | −0.976828 | − | 0.214024i | \(-0.931343\pi\) |
0.673765 | + | 0.738946i | \(0.264676\pi\) | |||||||
\(402\) | −23.3606 | + | 3.78035i | −1.16512 | + | 0.188547i | ||||
\(403\) | −0.105532 | − | 0.182787i | −0.00525694 | − | 0.00910529i | ||||
\(404\) | 6.35996 | + | 11.0158i | 0.316420 | + | 0.548055i | ||||
\(405\) | 3.72583 | + | 31.3905i | 0.185138 | + | 1.55980i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.8922 | − | 18.8659i | 0.539907 | − | 0.935146i | ||||
\(408\) | 1.30309 | − | 3.42902i | 0.0645127 | − | 0.169762i | ||||
\(409\) | 31.3453 | 1.54993 | 0.774963 | − | 0.632007i | \(-0.217769\pi\) | ||||
0.774963 | + | 0.632007i | \(0.217769\pi\) | |||||||
\(410\) | 20.4152 | 1.00823 | ||||||||
\(411\) | 6.72805 | + | 8.25168i | 0.331870 | + | 0.407025i | ||||
\(412\) | −1.32549 | + | 2.29582i | −0.0653022 | + | 0.113107i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.32805 | + | 6.46086i | −0.0652701 | + | 0.317534i | ||||
\(415\) | 2.19502 | + | 3.80189i | 0.107749 | + | 0.186627i | ||||
\(416\) | 2.86469 | + | 4.96179i | 0.140453 | + | 0.243272i | ||||
\(417\) | −0.960308 | − | 1.17778i | −0.0470265 | − | 0.0576762i | ||||
\(418\) | 11.5960 | − | 20.0849i | 0.567181 | − | 0.982385i | ||||
\(419\) | 7.44319 | + | 12.8920i | 0.363623 | + | 0.629814i | 0.988554 | − | 0.150866i | \(-0.0482061\pi\) |
−0.624931 | + | 0.780680i | \(0.714873\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.54213 | + | 7.86721i | −0.221370 | + | 0.383424i | −0.955224 | − | 0.295883i | \(-0.904386\pi\) |
0.733854 | + | 0.679307i | \(0.237720\pi\) | |||||||
\(422\) | −14.0610 | − | 24.3543i | −0.684477 | − | 1.18555i | ||||
\(423\) | −16.2862 | + | 5.41278i | −0.791860 | + | 0.263179i | ||||
\(424\) | 7.33392 | − | 12.7027i | 0.356166 | − | 0.616898i | ||||
\(425\) | 8.83262 | 0.428445 | ||||||||
\(426\) | −36.0320 | + | 5.83089i | −1.74575 | + | 0.282508i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.0875611 | + | 0.151660i | 0.00423243 | + | 0.00733078i | ||||
\(429\) | 4.19821 | − | 11.0473i | 0.202691 | − | 0.533371i | ||||
\(430\) | 11.5391 | + | 19.9863i | 0.556463 | + | 0.963823i | ||||
\(431\) | 8.31776 | − | 14.4068i | 0.400652 | − | 0.693950i | −0.593152 | − | 0.805090i | \(-0.702117\pi\) |
0.993805 | + | 0.111140i | \(0.0354502\pi\) | |||||||
\(432\) | 23.0275 | − | 12.0266i | 1.10791 | − | 0.578629i | ||||
\(433\) | 19.7423 | 0.948756 | 0.474378 | − | 0.880321i | \(-0.342673\pi\) | ||||
0.474378 | + | 0.880321i | \(0.342673\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 23.8549 | + | 29.2571i | 1.14375 | + | 1.40277i | ||||
\(436\) | −4.59122 | + | 7.95223i | −0.219880 | + | 0.380843i | ||||
\(437\) | 2.80830 | 0.134339 | ||||||||
\(438\) | 5.64612 | − | 14.8575i | 0.269782 | − | 0.709917i | ||||
\(439\) | −6.73514 | −0.321451 | −0.160725 | − | 0.986999i | \(-0.551383\pi\) | ||||
−0.160725 | + | 0.986999i | \(0.551383\pi\) | |||||||
\(440\) | −37.6310 | −1.79399 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.32879 | 0.110769 | ||||||||
\(443\) | 28.6403 | 1.36074 | 0.680372 | − | 0.732867i | \(-0.261818\pi\) | ||||
0.680372 | + | 0.732867i | \(0.261818\pi\) | |||||||
\(444\) | 3.84113 | + | 4.71100i | 0.182292 | + | 0.223574i | ||||
\(445\) | 19.4628 | 0.922626 | ||||||||
\(446\) | 17.2397 | − | 29.8601i | 0.816324 | − | 1.41392i | ||||
\(447\) | 3.55358 | − | 9.35105i | 0.168079 | − | 0.442290i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.66872 | −0.314716 | −0.157358 | − | 0.987542i | \(-0.550298\pi\) | ||||
−0.157358 | + | 0.987542i | \(0.550298\pi\) | |||||||
\(450\) | 28.4102 | + | 25.2375i | 1.33927 | + | 1.18971i | ||||
\(451\) | −10.2518 | + | 17.7566i | −0.482736 | + | 0.836124i | ||||
\(452\) | 4.13097 | + | 7.15505i | 0.194305 | + | 0.336545i | ||||
\(453\) | −2.21797 | − | 2.72026i | −0.104210 | − | 0.127809i | ||||
\(454\) | 3.11898 | + | 5.40223i | 0.146381 | + | 0.253539i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.24617 | − | 5.20776i | −0.198845 | − | 0.243876i | ||||
\(457\) | −28.6573 | −1.34053 | −0.670266 | − | 0.742121i | \(-0.733820\pi\) | ||||
−0.670266 | + | 0.742121i | \(0.733820\pi\) | |||||||
\(458\) | 11.8399 | − | 20.5074i | 0.553244 | − | 0.958246i | ||||
\(459\) | 0.264513 | − | 6.25034i | 0.0123464 | − | 0.291741i | ||||
\(460\) | 2.19419 | + | 3.80045i | 0.102305 | + | 0.177197i | ||||
\(461\) | −10.0087 | + | 17.3355i | −0.466150 | + | 0.807395i | −0.999253 | − | 0.0386554i | \(-0.987693\pi\) |
0.533103 | + | 0.846050i | \(0.321026\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.95789 | − | 8.58731i | −0.230413 | − | 0.399086i | 0.727517 | − | 0.686090i | \(-0.240674\pi\) |
−0.957930 | + | 0.287003i | \(0.907341\pi\) | |||||||
\(464\) | 15.5120 | − | 26.8676i | 0.720127 | − | 1.24730i | ||||
\(465\) | −0.407153 | + | 1.07140i | −0.0188813 | + | 0.0496850i | ||||
\(466\) | −21.8020 | − | 37.7623i | −1.00996 | − | 1.74930i | ||||
\(467\) | 8.04035 | + | 13.9263i | 0.372063 | + | 0.644432i | 0.989883 | − | 0.141888i | \(-0.0453172\pi\) |
−0.617820 | + | 0.786320i | \(0.711984\pi\) | |||||||
\(468\) | 2.46535 | + | 2.19003i | 0.113961 | + | 0.101234i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −17.3463 | + | 30.0446i | −0.800124 | + | 1.38586i | ||||
\(471\) | 5.21075 | − | 0.843232i | 0.240099 | − | 0.0388541i | ||||
\(472\) | −19.8225 | −0.912402 | ||||||||
\(473\) | −23.1780 | −1.06573 | ||||||||
\(474\) | 27.2105 | − | 4.40335i | 1.24982 | − | 0.202253i | ||||
\(475\) | 8.08967 | − | 14.0117i | 0.371180 | − | 0.642902i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.03657 | − | 24.5025i | 0.230609 | − | 1.12189i | ||||
\(478\) | 7.76103 | + | 13.4425i | 0.354981 | + | 0.614846i | ||||
\(479\) | −4.10128 | − | 7.10362i | −0.187392 | − | 0.324573i | 0.756988 | − | 0.653429i | \(-0.226670\pi\) |
−0.944380 | + | 0.328856i | \(0.893337\pi\) | |||||||
\(480\) | 11.0522 | − | 29.0833i | 0.504462 | − | 1.32746i | ||||
\(481\) | 2.00345 | − | 3.47008i | 0.0913496 | − | 0.158222i | ||||
\(482\) | 7.99183 | + | 13.8423i | 0.364018 | + | 0.630497i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.8024 | + | 22.1745i | −0.581929 | + | 1.00793i | ||||
\(485\) | 28.9512 | + | 50.1449i | 1.31460 | + | 2.27696i | ||||
\(486\) | 18.7100 | − | 19.3485i | 0.848702 | − | 0.877666i | ||||
\(487\) | −1.36840 | + | 2.37014i | −0.0620081 | + | 0.107401i | −0.895363 | − | 0.445337i | \(-0.853084\pi\) |
0.833355 | + | 0.552738i | \(0.186417\pi\) | |||||||
\(488\) | 21.1130 | 0.955741 | ||||||||
\(489\) | −5.89829 | − | 7.23402i | −0.266730 | − | 0.327134i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.85482 | + | 17.0690i | 0.444742 | + | 0.770315i | 0.998034 | − | 0.0626719i | \(-0.0199622\pi\) |
−0.553293 | + | 0.832987i | \(0.686629\pi\) | |||||||
\(492\) | −3.61528 | − | 4.43399i | −0.162989 | − | 0.199900i | ||||
\(493\) | −3.73542 | − | 6.46993i | −0.168235 | − | 0.291391i | ||||
\(494\) | 2.13291 | − | 3.69431i | 0.0959642 | − | 0.166215i | ||||
\(495\) | −60.9012 | + | 20.2408i | −2.73731 | + | 0.909756i | ||||
\(496\) | 0.941952 | 0.0422949 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.32784 | − | 3.49413i | 0.0595018 | − | 0.156576i | ||||
\(499\) | 16.5480 | − | 28.6619i | 0.740789 | − | 1.28309i | −0.211347 | − | 0.977411i | \(-0.567785\pi\) |
0.952136 | − | 0.305674i | \(-0.0988817\pi\) | |||||||
\(500\) | 8.05153 | 0.360075 | ||||||||
\(501\) | 18.1796 | + | 22.2966i | 0.812205 | + | 0.996138i | ||||
\(502\) | −35.6575 | −1.59147 | ||||||||
\(503\) | −12.1860 | −0.543346 | −0.271673 | − | 0.962390i | \(-0.587577\pi\) | ||||
−0.271673 | + | 0.962390i | \(0.587577\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −45.5331 | −2.02619 | ||||||||
\(506\) | −13.3912 | −0.595310 | ||||||||
\(507\) | −7.22648 | + | 19.0161i | −0.320939 | + | 0.844534i | ||||
\(508\) | −9.73765 | −0.432038 | ||||||||
\(509\) | 6.81965 | − | 11.8120i | 0.302276 | − | 0.523557i | −0.674375 | − | 0.738389i | \(-0.735587\pi\) |
0.976651 | + | 0.214832i | \(0.0689204\pi\) | |||||||
\(510\) | −7.99142 | − | 9.80116i | −0.353866 | − | 0.434002i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −7.97968 | −0.352656 | ||||||||
\(513\) | −9.67304 | − | 6.14422i | −0.427075 | − | 0.271274i | ||||
\(514\) | −2.11146 | + | 3.65715i | −0.0931325 | + | 0.161310i | ||||
\(515\) | −4.74481 | − | 8.21826i | −0.209081 | − | 0.362140i | ||||
\(516\) | 2.29741 | − | 6.04551i | 0.101138 | − | 0.266139i | ||||
\(517\) | −17.4214 | − | 30.1747i | −0.766190 | − | 1.32708i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 30.1787 | − | 4.88368i | 1.32470 | − | 0.214370i | ||||
\(520\) | −6.92164 | −0.303534 | ||||||||
\(521\) | −17.7745 | + | 30.7863i | −0.778714 | + | 1.34877i | 0.153969 | + | 0.988076i | \(0.450794\pi\) |
−0.932683 | + | 0.360697i | \(0.882539\pi\) | |||||||
\(522\) | 6.47160 | − | 31.4839i | 0.283254 | − | 1.37801i | ||||
\(523\) | 13.3593 | + | 23.1391i | 0.584163 | + | 1.01180i | 0.994979 | + | 0.100082i | \(0.0319105\pi\) |
−0.410816 | + | 0.911718i | \(0.634756\pi\) | |||||||
\(524\) | 7.47991 | − | 12.9556i | 0.326761 | − | 0.565967i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21.2052 | − | 36.7284i | −0.924589 | − | 1.60143i | ||||
\(527\) | 0.113415 | − | 0.196440i | 0.00494043 | − | 0.00855708i | ||||
\(528\) | 33.3294 | + | 40.8772i | 1.45048 | + | 1.77895i | ||||
\(529\) | 10.6892 | + | 18.5143i | 0.464750 | + | 0.804970i | ||||
\(530\) | −25.2833 | − | 43.7919i | −1.09824 | − | 1.90220i | ||||
\(531\) | −32.0802 | + | 10.6620i | −1.39216 | + | 0.462692i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.88565 | + | 3.26604i | −0.0816766 | + | 0.141468i | ||||
\(534\) | −10.4721 | − | 12.8436i | −0.453171 | − | 0.555796i | ||||
\(535\) | −0.626879 | −0.0271023 | ||||||||
\(536\) | −13.9198 | −0.601244 | ||||||||
\(537\) | 1.61723 | − | 4.25566i | 0.0697888 | − | 0.183645i | ||||
\(538\) | −25.5282 | + | 44.2161i | −1.10060 | + | 1.90629i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.757146 | − | 17.8911i | 0.0325824 | − | 0.769910i | ||||
\(541\) | −18.7927 | − | 32.5500i | −0.807963 | − | 1.39943i | −0.914272 | − | 0.405100i | \(-0.867237\pi\) |
0.106309 | − | 0.994333i | \(-0.466097\pi\) | |||||||
\(542\) | −21.4026 | − | 37.0705i | −0.919322 | − | 1.59231i | ||||
\(543\) | −6.79462 | + | 1.09954i | −0.291585 | + | 0.0471859i | ||||
\(544\) | −3.07866 | + | 5.33240i | −0.131997 | + | 0.228625i | ||||
\(545\) | −16.4350 | − | 28.4663i | −0.704000 | − | 1.21936i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.13381 | + | 15.8202i | −0.390533 | + | 0.676424i | −0.992520 | − | 0.122082i | \(-0.961043\pi\) |
0.601986 | + | 0.798506i | \(0.294376\pi\) | |||||||
\(548\) | −3.01567 | − | 5.22329i | −0.128823 | − | 0.223128i | ||||
\(549\) | 34.1688 | − | 11.3562i | 1.45829 | − | 0.484669i | ||||
\(550\) | −38.5750 | + | 66.8139i | −1.64485 | + | 2.84896i | ||||
\(551\) | −13.6849 | −0.582995 | ||||||||
\(552\) | −1.37824 | + | 3.62677i | −0.0586619 | + | 0.154366i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.62172 | + | 2.80890i | 0.0689002 | + | 0.119339i | ||||
\(555\) | −21.4794 | + | 3.47592i | −0.911752 | + | 0.147545i | ||||
\(556\) | 0.430433 | + | 0.745532i | 0.0182544 | + | 0.0316176i | ||||
\(557\) | 1.94636 | − | 3.37119i | 0.0824698 | − | 0.142842i | −0.821840 | − | 0.569718i | \(-0.807053\pi\) |
0.904310 | + | 0.426876i | \(0.140386\pi\) | |||||||
\(558\) | 0.926091 | − | 0.307791i | 0.0392046 | − | 0.0130298i | ||||
\(559\) | −4.26324 | −0.180316 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.5378 | − | 2.02893i | 0.529346 | − | 0.0856617i | ||||
\(562\) | −10.4281 | + | 18.0620i | −0.439884 | + | 0.761901i | ||||
\(563\) | 3.32855 | 0.140282 | 0.0701409 | − | 0.997537i | \(-0.477655\pi\) | ||||
0.0701409 | + | 0.997537i | \(0.477655\pi\) | |||||||
\(564\) | 9.59725 | − | 1.55308i | 0.404117 | − | 0.0653965i | ||||
\(565\) | −29.5750 | −1.24423 | ||||||||
\(566\) | 48.2965 | 2.03006 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −21.4702 | −0.900870 | ||||||||
\(569\) | −36.6244 | −1.53538 | −0.767688 | − | 0.640824i | \(-0.778593\pi\) | ||||
−0.767688 | + | 0.640824i | \(0.778593\pi\) | |||||||
\(570\) | −22.8674 | + | 3.70053i | −0.957810 | + | 0.154998i | ||||
\(571\) | −22.5824 | −0.945044 | −0.472522 | − | 0.881319i | \(-0.656656\pi\) | ||||
−0.472522 | + | 0.881319i | \(0.656656\pi\) | |||||||
\(572\) | −3.34742 | + | 5.79789i | −0.139962 | + | 0.242422i | ||||
\(573\) | 31.1286 | − | 5.03740i | 1.30042 | − | 0.210441i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.34201 | −0.389589 | ||||||||
\(576\) | 3.32795 | − | 1.10606i | 0.138665 | − | 0.0460859i | ||||
\(577\) | −11.2725 | + | 19.5245i | −0.469279 | + | 0.812815i | −0.999383 | − | 0.0351177i | \(-0.988819\pi\) |
0.530104 | + | 0.847932i | \(0.322153\pi\) | |||||||
\(578\) | −13.4248 | − | 23.2525i | −0.558399 | − | 0.967175i | ||||
\(579\) | 0.346040 | − | 0.0559981i | 0.0143809 | − | 0.00232720i | ||||
\(580\) | −10.6923 | − | 18.5197i | −0.443975 | − | 0.768987i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 17.5135 | − | 46.0857i | 0.725957 | − | 1.91031i | ||||
\(583\) | 50.7854 | 2.10332 | ||||||||
\(584\) | 4.67457 | − | 8.09659i | 0.193435 | − | 0.335039i | ||||
\(585\) | −11.2018 | + | 3.72298i | −0.463139 | + | 0.153926i | ||||
\(586\) | 7.61717 | + | 13.1933i | 0.314662 | + | 0.545011i | ||||
\(587\) | −12.1198 | + | 20.9921i | −0.500237 | + | 0.866436i | 0.499763 | + | 0.866162i | \(0.333421\pi\) |
−1.00000 | 0.000273884i | \(0.999913\pi\) | ||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.207750 | − | 0.359834i | −0.00856020 | − | 0.0148267i | ||||
\(590\) | −34.1684 | + | 59.1814i | −1.40669 | + | 2.43646i | ||||
\(591\) | 2.78931 | − | 0.451381i | 0.114737 | − | 0.0185673i | ||||
\(592\) | 8.94112 | + | 15.4865i | 0.367478 | + | 0.636490i | ||||
\(593\) | 22.8663 | + | 39.6056i | 0.939007 | + | 1.62641i | 0.767328 | + | 0.641255i | \(0.221586\pi\) |
0.171680 | + | 0.985153i | \(0.445081\pi\) | |||||||
\(594\) | 46.1252 | + | 29.2983i | 1.89254 | + | 1.20212i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.83343 | + | 4.90764i | −0.116062 | + | 0.201025i | ||||
\(597\) | 3.87142 | − | 10.1874i | 0.158447 | − | 0.416944i | ||||
\(598\) | −2.46310 | −0.100724 | ||||||||
\(599\) | −30.1668 | −1.23258 | −0.616290 | − | 0.787519i | \(-0.711365\pi\) | ||||
−0.616290 | + | 0.787519i | \(0.711365\pi\) | |||||||
\(600\) | 14.1252 | + | 17.3240i | 0.576659 | + | 0.707249i | ||||
\(601\) | 7.36933 | − | 12.7641i | 0.300601 | − | 0.520657i | −0.675671 | − | 0.737203i | \(-0.736146\pi\) |
0.976272 | + | 0.216547i | \(0.0694794\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −22.5275 | + | 7.48712i | −0.917391 | + | 0.304899i | ||||
\(604\) | 0.994149 | + | 1.72192i | 0.0404513 | + | 0.0700638i | ||||
\(605\) | −45.8285 | − | 79.3772i | −1.86319 | − | 3.22714i | ||||
\(606\) | 24.4993 | + | 30.0474i | 0.995217 | + | 1.22059i | ||||
\(607\) | 3.03918 | − | 5.26401i | 0.123356 | − | 0.213660i | −0.797733 | − | 0.603011i | \(-0.793967\pi\) |
0.921089 | + | 0.389351i | \(0.127301\pi\) | |||||||
\(608\) | 5.63941 | + | 9.76774i | 0.228708 | + | 0.396134i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 36.3930 | − | 63.0345i | 1.47351 | − | 2.55219i | ||||
\(611\) | −3.20439 | − | 5.55016i | −0.129636 | − | 0.224535i | ||||
\(612\) | −0.713543 | + | 3.47133i | −0.0288432 | + | 0.140320i | ||||
\(613\) | −5.88668 | + | 10.1960i | −0.237761 | + | 0.411814i | −0.960071 | − | 0.279755i | \(-0.909747\pi\) |
0.722311 | + | 0.691569i | \(0.243080\pi\) | |||||||
\(614\) | −1.82213 | −0.0735352 | ||||||||
\(615\) | 20.2165 | − | 3.27154i | 0.815207 | − | 0.131921i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.0319 | − | 27.7680i | −0.645418 | − | 1.11790i | −0.984205 | − | 0.177034i | \(-0.943350\pi\) |
0.338786 | − | 0.940863i | \(-0.389984\pi\) | |||||||
\(618\) | −2.87029 | + | 7.55300i | −0.115460 | + | 0.303826i | ||||
\(619\) | 6.27588 | + | 10.8701i | 0.252249 | + | 0.436908i | 0.964145 | − | 0.265377i | \(-0.0854965\pi\) |
−0.711896 | + | 0.702285i | \(0.752163\pi\) | |||||||
\(620\) | 0.324641 | − | 0.562294i | 0.0130379 | − | 0.0225823i | ||||
\(621\) | −0.279767 | + | 6.61081i | −0.0112267 | + | 0.265283i | ||||
\(622\) | −5.30441 | −0.212688 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 6.13043 | + | 7.51873i | 0.245414 | + | 0.300990i | ||||
\(625\) | 3.92995 | − | 6.80687i | 0.157198 | − | 0.272275i | ||||
\(626\) | −48.6249 | −1.94344 | ||||||||
\(627\) | 8.26456 | − | 21.7477i | 0.330055 | − | 0.868521i | ||||
\(628\) | −2.99022 | −0.119323 | ||||||||
\(629\) | 4.30619 | 0.171699 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.4642 | 1.33219 | 0.666095 | − | 0.745867i | \(-0.267964\pi\) | ||||
0.666095 | + | 0.745867i | \(0.267964\pi\) | |||||||
\(632\) | 16.2138 | 0.644950 | ||||||||
\(633\) | −17.8269 | − | 21.8640i | −0.708556 | − | 0.869016i | ||||
\(634\) | −22.1809 | −0.880915 | ||||||||
\(635\) | 17.4288 | − | 30.1875i | 0.691639 | − | 1.19795i | ||||
\(636\) | −5.03386 | + | 13.2463i | −0.199606 | + | 0.525251i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 65.2553 | 2.58348 | ||||||||
\(639\) | −34.7469 | + | 11.5483i | −1.37457 | + | 0.456844i | ||||
\(640\) | 21.5074 | − | 37.2519i | 0.850155 | − | 1.47251i | ||||
\(641\) | 9.49183 | + | 16.4403i | 0.374905 | + | 0.649354i | 0.990313 | − | 0.138855i | \(-0.0443421\pi\) |
−0.615408 | + | 0.788209i | \(0.711009\pi\) | |||||||
\(642\) | 0.337296 | + | 0.413680i | 0.0133120 | + | 0.0163266i | ||||
\(643\) | 4.81347 | + | 8.33718i | 0.189825 | + | 0.328786i | 0.945192 | − | 0.326516i | \(-0.105875\pi\) |
−0.755367 | + | 0.655302i | \(0.772541\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.6296 | + | 17.9426i | 0.576039 | + | 0.706490i | ||||
\(646\) | 4.58445 | 0.180373 | ||||||||
\(647\) | 3.90607 | − | 6.76551i | 0.153564 | − | 0.265980i | −0.778972 | − | 0.627059i | \(-0.784258\pi\) |
0.932535 | + | 0.361079i | \(0.117592\pi\) | |||||||
\(648\) | 12.6822 | − | 9.47680i | 0.498205 | − | 0.372284i | ||||
\(649\) | −34.3163 | − | 59.4375i | −1.34703 | − | 2.33313i | ||||
\(650\) | −7.09528 | + | 12.2894i | −0.278300 | + | 0.482029i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.64376 | + | 4.57912i | 0.103537 | + | 0.179332i | ||||
\(653\) | −15.8714 | + | 27.4901i | −0.621097 | + | 1.07577i | 0.368185 | + | 0.929753i | \(0.379979\pi\) |
−0.989282 | + | 0.146019i | \(0.953354\pi\) | |||||||
\(654\) | −9.94207 | + | 26.1620i | −0.388766 | + | 1.02302i | ||||
\(655\) | 26.7756 | + | 46.3767i | 1.04621 | + | 1.81209i | ||||
\(656\) | −8.41540 | − | 14.5759i | −0.328566 | − | 0.569093i | ||||
\(657\) | 3.21026 | − | 15.6177i | 0.125244 | − | 0.609303i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.10685 | − | 5.38122i | 0.121026 | − | 0.209623i | −0.799147 | − | 0.601136i | \(-0.794715\pi\) |
0.920172 | + | 0.391513i | \(0.128048\pi\) | |||||||
\(660\) | 35.8884 | − | 5.80766i | 1.39695 | − | 0.226063i | ||||
\(661\) | 27.5263 | 1.07065 | 0.535324 | − | 0.844647i | \(-0.320190\pi\) | ||||
0.535324 | + | 0.844647i | \(0.320190\pi\) | |||||||
\(662\) | 37.2189 | 1.44655 | ||||||||
\(663\) | 2.30613 | − | 0.373191i | 0.0895627 | − | 0.0144935i | ||||
\(664\) | 1.09935 | − | 1.90413i | 0.0426630 | − | 0.0738945i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 13.8509 | + | 12.3041i | 0.536712 | + | 0.476775i | ||||
\(667\) | 3.95084 | + | 6.84306i | 0.152977 | + | 0.264964i | ||||
\(668\) | −8.14854 | − | 14.1137i | −0.315276 | − | 0.546075i | ||||
\(669\) | 12.2868 | − | 32.3322i | 0.475037 | − | 1.25003i | ||||
\(670\) | −23.9939 | + | 41.5586i | −0.926965 | + | 1.60555i | ||||
\(671\) | 36.5505 | + | 63.3073i | 1.41102 | + | 2.44395i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.10894 | + | 14.0451i | −0.312577 | + | 0.541399i | −0.978919 | − | 0.204247i | \(-0.934526\pi\) |
0.666343 | + | 0.745646i | \(0.267859\pi\) | |||||||
\(674\) | −10.8835 | − | 18.8508i | −0.419217 | − | 0.726106i | ||||
\(675\) | 32.1781 | + | 20.4392i | 1.23853 | + | 0.786704i | ||||
\(676\) | 5.76199 | − | 9.98006i | 0.221615 | − | 0.383849i | ||||
\(677\) | −20.5090 | −0.788225 | −0.394112 | − | 0.919062i | \(-0.628948\pi\) | ||||
−0.394112 | + | 0.919062i | \(0.628948\pi\) | |||||||
\(678\) | 15.9130 | + | 19.5167i | 0.611135 | + | 0.749532i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.71932 | − | 6.44205i | −0.142629 | − | 0.247041i | ||||
\(681\) | 3.95433 | + | 4.84983i | 0.151530 | + | 0.185846i | ||||
\(682\) | 0.990642 | + | 1.71584i | 0.0379337 | + | 0.0657030i | ||||
\(683\) | 0.0561542 | − | 0.0972618i | 0.00214868 | − | 0.00372162i | −0.864949 | − | 0.501860i | \(-0.832649\pi\) |
0.867098 | + | 0.498138i | \(0.165983\pi\) | |||||||
\(684\) | 4.85326 | + | 4.31128i | 0.185569 | + | 0.164846i | ||||
\(685\) | 21.5902 | 0.824918 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.43839 | − | 22.2052i | 0.321945 | − | 0.847179i | ||||
\(688\) | 9.51311 | − | 16.4772i | 0.362684 | − | 0.628187i | ||||
\(689\) | 9.34118 | 0.355871 | ||||||||
\(690\) | 8.45229 | + | 10.3664i | 0.321773 | + | 0.394642i | ||||
\(691\) | 18.8670 | 0.717735 | 0.358868 | − | 0.933388i | \(-0.383163\pi\) | ||||
0.358868 | + | 0.933388i | \(0.383163\pi\) | |||||||
\(692\) | −17.3182 | −0.658340 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −39.9480 | −1.51640 | ||||||||
\(695\) | −3.08161 | −0.116892 | ||||||||
\(696\) | 6.71620 | − | 17.6733i | 0.254577 | − | 0.669905i | ||||
\(697\) | −4.05299 | −0.153518 | ||||||||
\(698\) | −14.2332 | + | 24.6527i | −0.538736 | + | 0.933118i | ||||
\(699\) | −27.6413 | − | 33.9010i | −1.04549 | − | 1.28225i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.16006 | −0.119354 | −0.0596770 | − | 0.998218i | \(-0.519007\pi\) | ||||
−0.0596770 | + | 0.998218i | \(0.519007\pi\) | |||||||
\(702\) | 8.48402 | + | 5.38896i | 0.320209 | + | 0.203393i | ||||
\(703\) | 3.94398 | − | 6.83118i | 0.148750 | − | 0.257643i | ||||
\(704\) | 3.55992 | + | 6.16596i | 0.134170 | + | 0.232388i | ||||
\(705\) | −12.3628 | + | 32.5320i | −0.465610 | + | 1.22523i | ||||
\(706\) | −21.1402 | − | 36.6159i | −0.795622 | − | 1.37806i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 18.9045 | − | 3.05923i | 0.710475 | − | 0.114973i | ||||
\(709\) | −21.5211 | −0.808243 | −0.404121 | − | 0.914705i | \(-0.632423\pi\) | ||||
−0.404121 | + | 0.914705i | \(0.632423\pi\) | |||||||
\(710\) | −37.0087 | + | 64.1009i | −1.38891 | + | 2.40567i | ||||
\(711\) | 26.2400 | − | 8.72100i | 0.984079 | − | 0.327063i | ||||
\(712\) | −4.87385 | − | 8.44176i | −0.182655 | − | 0.316368i | ||||
\(713\) | −0.119956 | + | 0.207769i | −0.00449237 | + | 0.00778102i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.9826 | − | 20.7545i | −0.448125 | − | 0.776175i | ||||
\(716\) | −1.28949 | + | 2.23347i | −0.0481906 | + | 0.0834685i | ||||
\(717\) | 9.83968 | + | 12.0680i | 0.367469 | + | 0.450687i | ||||
\(718\) | 17.6785 | + | 30.6201i | 0.659757 | + | 1.14273i | ||||
\(719\) | 9.41508 | + | 16.3074i | 0.351123 | + | 0.608163i | 0.986447 | − | 0.164083i | \(-0.0524665\pi\) |
−0.635323 | + | 0.772246i | \(0.719133\pi\) | |||||||
\(720\) | 10.6070 | − | 51.6021i | 0.395298 | − | 1.92310i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −12.2040 | + | 21.1379i | −0.454185 | + | 0.786671i | ||||
\(723\) | 10.1323 | + | 12.4268i | 0.376824 | + | 0.462159i | ||||
\(724\) | 3.89914 | 0.144910 | ||||||||
\(725\) | 45.5237 | 1.69071 | ||||||||
\(726\) | −27.7231 | + | 72.9517i | −1.02890 | + | 2.70749i | ||||
\(727\) | −19.5426 | + | 33.8489i | −0.724797 | + | 1.25538i | 0.234261 | + | 0.972174i | \(0.424733\pi\) |
−0.959058 | + | 0.283211i | \(0.908600\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.4273 | − | 22.1585i | 0.571381 | − | 0.820685i | ||||
\(730\) | −16.1153 | − | 27.9125i | −0.596454 | − | 1.03309i | ||||
\(731\) | −2.29084 | − | 3.96784i | −0.0847296 | − | 0.146756i | ||||
\(732\) | −20.1353 | + | 3.25841i | −0.744222 | + | 0.120434i | ||||
\(733\) | −9.29924 | + | 16.1068i | −0.343475 | + | 0.594917i | −0.985076 | − | 0.172123i | \(-0.944937\pi\) |
0.641600 | + | 0.767039i | \(0.278271\pi\) | |||||||
\(734\) | 19.2119 | + | 33.2759i | 0.709123 | + | 1.22824i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.25621 | − | 5.63993i | 0.120026 | − | 0.207890i | ||||
\(737\) | −24.0977 | − | 41.7385i | −0.887651 | − | 1.53746i | ||||
\(738\) | −13.0365 | − | 11.5807i | −0.479880 | − | 0.426290i | ||||
\(739\) | −2.75068 | + | 4.76432i | −0.101185 | + | 0.175258i | −0.912173 | − | 0.409805i | \(-0.865597\pi\) |
0.810988 | + | 0.585063i | \(0.198930\pi\) | |||||||
\(740\) | 12.3261 | 0.453117 | ||||||||
\(741\) | 1.52014 | − | 4.00016i | 0.0558436 | − | 0.146949i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.2326 | + | 17.7234i | 0.375399 | + | 0.650210i | 0.990387 | − | 0.138327i | \(-0.0441725\pi\) |
−0.614988 | + | 0.788537i | \(0.710839\pi\) | |||||||
\(744\) | 0.566666 | − | 0.0917010i | 0.0207750 | − | 0.00336192i | ||||
\(745\) | −10.1427 | − | 17.5677i | −0.371601 | − | 0.643631i | ||||
\(746\) | −28.0892 | + | 48.6520i | −1.02842 | + | 1.78128i | ||||
\(747\) | 0.754977 | − | 3.67291i | 0.0276232 | − | 0.134385i | ||||
\(748\) | −7.19489 | −0.263071 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 24.2253 | − | 3.92027i | 0.884583 | − | 0.143148i | ||||
\(751\) | −19.0230 | + | 32.9488i | −0.694159 | + | 1.20232i | 0.276305 | + | 0.961070i | \(0.410890\pi\) |
−0.970463 | + | 0.241248i | \(0.922443\pi\) | |||||||
\(752\) | 28.6015 | 1.04299 | ||||||||
\(753\) | −35.3105 | + | 5.71414i | −1.28679 | + | 0.208235i | ||||
\(754\) | 12.0027 | 0.437113 | ||||||||
\(755\) | −7.11744 | −0.259030 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −51.0780 | −1.85646 | −0.928230 | − | 0.372006i | \(-0.878670\pi\) | ||||
−0.928230 | + | 0.372006i | \(0.878670\pi\) | |||||||
\(758\) | −2.66658 | −0.0968546 | ||||||||
\(759\) | −13.2609 | + | 2.14595i | −0.481338 | + | 0.0778929i | ||||
\(760\) | −13.6259 | −0.494263 | ||||||||
\(761\) | 20.0375 | − | 34.7059i | 0.726357 | − | 1.25809i | −0.232055 | − | 0.972703i | \(-0.574545\pi\) |
0.958413 | − | 0.285385i | \(-0.0921216\pi\) | |||||||
\(762\) | −29.2985 | + | 4.74124i | −1.06137 | + | 0.171757i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −17.8633 | −0.646273 | ||||||||
\(765\) | −9.48429 | − | 8.42514i | −0.342905 | − | 0.304612i | ||||
\(766\) | 27.3058 | − | 47.2951i | 0.986599 | − | 1.70884i | ||||
\(767\) | −6.31195 | − | 10.9326i | −0.227911 | − | 0.394754i | ||||
\(768\) | −32.1574 | + | 5.20389i | −1.16038 | + | 0.187779i | ||||
\(769\) | 22.4828 | + | 38.9414i | 0.810751 | + | 1.40426i | 0.912339 | + | 0.409436i | \(0.134274\pi\) |
−0.101587 | + | 0.994827i | \(0.532392\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.50485 | + | 3.95993i | −0.0541958 | + | 0.142613i | ||||
\(772\) | −0.198577 | −0.00714695 | ||||||||
\(773\) | 12.1781 | − | 21.0930i | 0.438014 | − | 0.758663i | −0.559522 | − | 0.828816i | \(-0.689015\pi\) |
0.997536 | + | 0.0701524i | \(0.0223485\pi\) | |||||||
\(774\) | 3.96887 | − | 19.3082i | 0.142658 | − | 0.694020i | ||||
\(775\) | 0.691096 | + | 1.19701i | 0.0248249 | + | 0.0429980i | ||||
\(776\) | 14.4998 | − | 25.1145i | 0.520514 | − | 0.901556i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.52913 | − | 7.84468i | −0.162377 | − | 0.281245i | ||||
\(779\) | −3.71208 | + | 6.42951i | −0.132999 | + | 0.230361i | ||||
\(780\) | 6.60111 | − | 1.06823i | 0.236358 | − | 0.0382487i | ||||
\(781\) | −37.1689 | − | 64.3784i | −1.33001 | − | 2.30364i | ||||
\(782\) | −1.32354 | − | 2.29243i | −0.0473296 | − | 0.0819773i | ||||
\(783\) | 1.36331 | − | 32.2145i | 0.0487207 | − | 1.15125i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.35200 | − | 9.26993i | 0.191021 | − | 0.330858i | ||||
\(786\) | 16.1974 | − | 42.6225i | 0.577742 | − | 1.52030i | ||||
\(787\) | 41.5233 | 1.48015 | 0.740073 | − | 0.672526i | \(-0.234791\pi\) | ||||
0.740073 | + | 0.672526i | \(0.234791\pi\) | |||||||
\(788\) | −1.60066 | −0.0570212 | ||||||||
\(789\) | −26.8846 | − | 32.9728i | −0.957115 | − | 1.17386i | ||||
\(790\) | 27.9481 | − | 48.4075i | 0.994349 | − | 1.72226i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 24.0300 | + | 21.3465i | 0.853869 | + | 0.758515i | ||||
\(793\) | 6.72289 | + | 11.6444i | 0.238737 | + | 0.413504i | ||||
\(794\) | 0.0238574 | + | 0.0413222i | 0.000846666 | + | 0.00146647i | ||||
\(795\) | −32.0549 | − | 39.3141i | −1.13687 | − | 1.39433i | ||||
\(796\) | −3.08686 | + | 5.34659i | −0.109411 | + | 0.189505i | ||||
\(797\) | −17.3018 | − | 29.9676i | −0.612861 | − | 1.06151i | −0.990756 | − | 0.135657i | \(-0.956685\pi\) |
0.377895 | − | 0.925848i | \(-0.376648\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.44373 | − | 5.96472i | 0.121831 | − | 0.211017i | ||||
\(800\) | −18.7599 | − | 32.4931i | −0.663263 | − | 1.14880i | ||||
\(801\) | −12.4284 | − | 11.0404i | −0.439134 | − | 0.390095i | ||||
\(802\) | 10.4785 | − | 18.1494i | 0.370010 | − | 0.640876i | ||||
\(803\) | 32.3701 | 1.14232 | ||||||||
\(804\) | 13.2752 | − | 2.14827i | 0.468180 | − | 0.0757635i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.182213 | + | 0.315603i | 0.00641819 | + | 0.0111166i | ||||
\(807\) | −18.1941 | + | 47.8767i | −0.640462 | + | 1.68534i | ||||
\(808\) | 11.4023 | + | 19.7494i | 0.401133 | + | 0.694782i | ||||
\(809\) | 5.62597 | − | 9.74446i | 0.197799 | − | 0.342597i | −0.750016 | − | 0.661420i | \(-0.769954\pi\) |
0.947814 | + | 0.318823i | \(0.103287\pi\) | |||||||
\(810\) | −6.43306 | − | 54.1991i | −0.226035 | − | 1.90436i | ||||
\(811\) | −29.6803 | −1.04222 | −0.521108 | − | 0.853491i | \(-0.674481\pi\) | ||||
−0.521108 | + | 0.853491i | \(0.674481\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −27.1349 | − | 33.2799i | −0.951664 | − | 1.16718i | ||||
\(814\) | −18.8066 | + | 32.5740i | −0.659171 | + | 1.14172i | ||||
\(815\) | −18.9275 | −0.663002 | ||||||||
\(816\) | −3.70360 | + | 9.74583i | −0.129652 | + | 0.341172i | ||||
\(817\) | −8.39258 | −0.293619 | ||||||||
\(818\) | −54.1211 | −1.89230 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.6014 | −0.405137 | ||||||||
\(821\) | 34.6431 | 1.20905 | 0.604526 | − | 0.796585i | \(-0.293362\pi\) | ||||
0.604526 | + | 0.796585i | \(0.293362\pi\) | |||||||
\(822\) | −11.6167 | − | 14.2474i | −0.405179 | − | 0.496937i | ||||
\(823\) | 36.3870 | 1.26837 | 0.634186 | − | 0.773180i | \(-0.281335\pi\) | ||||
0.634186 | + | 0.773180i | \(0.281335\pi\) | |||||||
\(824\) | −2.37638 | + | 4.11601i | −0.0827851 | + | 0.143388i | ||||
\(825\) | −27.4927 | + | 72.3454i | −0.957171 | + | 2.51874i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.3576 | −0.846997 | −0.423498 | − | 0.905897i | \(-0.639198\pi\) | ||||
−0.423498 | + | 0.905897i | \(0.639198\pi\) | |||||||
\(828\) | 0.754693 | − | 3.67153i | 0.0262274 | − | 0.127594i | ||||
\(829\) | −19.5851 | + | 33.9224i | −0.680219 | + | 1.17817i | 0.294694 | + | 0.955592i | \(0.404782\pi\) |
−0.974914 | + | 0.222583i | \(0.928551\pi\) | |||||||
\(830\) | −3.78994 | − | 6.56438i | −0.131551 | − | 0.227853i | ||||
\(831\) | 2.05606 | + | 2.52168i | 0.0713240 | + | 0.0874761i | ||||
\(832\) | 0.654792 | + | 1.13413i | 0.0227008 | + | 0.0393190i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.65808 | + | 2.03357i | 0.0574146 | + | 0.0704167i | ||||
\(835\) | 58.3381 | 2.01887 | ||||||||
\(836\) | −6.58970 | + | 11.4137i | −0.227910 | + | 0.394751i | ||||
\(837\) | 0.867755 | − | 0.453202i | 0.0299940 | − | 0.0156650i | ||||
\(838\) | −12.8515 | − | 22.2594i | −0.443947 | − | 0.768939i | ||||
\(839\) | −17.1739 | + | 29.7460i | −0.592907 | + | 1.02695i | 0.400931 | + | 0.916108i | \(0.368687\pi\) |
−0.993839 | + | 0.110838i | \(0.964647\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.75250 | − | 8.23157i | −0.163879 | − | 0.283847i | ||||
\(842\) | 7.84250 | − | 13.5836i | 0.270270 | − | 0.468122i | ||||
\(843\) | −7.43218 | + | 19.5574i | −0.255978 | + | 0.673591i | ||||
\(844\) | 7.99045 | + | 13.8399i | 0.275043 | + | 0.476388i | ||||
\(845\) | 20.6260 | + | 35.7253i | 0.709556 | + | 1.22899i | ||||
\(846\) | 28.1199 | − | 9.34577i | 0.966781 | − | 0.321314i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −20.8442 | + | 36.1032i | −0.715793 | + | 1.23979i | ||||
\(849\) | 47.8265 | − | 7.73956i | 1.64140 | − | 0.265621i | ||||
\(850\) | −15.2505 | −0.523088 | ||||||||
\(851\) | −4.55454 | −0.156127 | ||||||||
\(852\) | 20.4760 | − | 3.31353i | 0.701495 | − | 0.113520i | ||||
\(853\) | −16.3371 | + | 28.2967i | −0.559373 | + | 0.968862i | 0.438176 | + | 0.898889i | \(0.355625\pi\) |
−0.997549 | + | 0.0699730i | \(0.977709\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −22.0518 | + | 7.32904i | −0.754157 | + | 0.250648i | ||||
\(856\) | 0.156982 | + | 0.271901i | 0.00536555 | + | 0.00929340i | ||||
\(857\) | 28.8340 | + | 49.9419i | 0.984950 | + | 1.70598i | 0.642159 | + | 0.766571i | \(0.278039\pi\) |
0.342791 | + | 0.939412i | \(0.388628\pi\) | |||||||
\(858\) | −7.24867 | + | 19.0745i | −0.247465 | + | 0.651191i | ||||
\(859\) | −14.9884 | + | 25.9607i | −0.511397 | + | 0.885766i | 0.488515 | + | 0.872555i | \(0.337539\pi\) |
−0.999913 | + | 0.0132108i | \(0.995795\pi\) | |||||||
\(860\) | −6.55733 | − | 11.3576i | −0.223603 | − | 0.387292i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −14.3615 | + | 24.8749i | −0.489156 | + | 0.847243i | ||||
\(863\) | 11.5888 | + | 20.0724i | 0.394487 | + | 0.683272i | 0.993036 | − | 0.117815i | \(-0.0375889\pi\) |
−0.598548 | + | 0.801087i | \(0.704256\pi\) | |||||||
\(864\) | −23.5553 | + | 12.3022i | −0.801369 | + | 0.418531i | ||||
\(865\) | 30.9967 | − | 53.6879i | 1.05392 | − | 1.82544i | ||||
\(866\) | −34.0873 | −1.15833 | ||||||||
\(867\) | −17.0204 | − | 20.8748i | −0.578043 | − | 0.708947i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.0690 | + | 48.6170i | 0.952177 | + | 1.64922i | ||||
\(870\) | −41.1881 | − | 50.5156i | −1.39641 | − | 1.71264i | ||||
\(871\) | −4.43240 | − | 7.67715i | −0.150186 | − | 0.260130i | ||||
\(872\) | −8.23129 | + | 14.2570i | −0.278747 | + | 0.482803i | ||||
\(873\) | 9.95776 | − | 48.4438i | 0.337019 | − | 1.63957i | ||||
\(874\) | −4.84884 | −0.164014 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.20853 | + | 8.44308i | −0.108406 | + | 0.285265i | ||||
\(877\) | 0.369978 | − | 0.640820i | 0.0124933 | − | 0.0216390i | −0.859711 | − | 0.510780i | \(-0.829357\pi\) |
0.872204 | + | 0.489141i | \(0.162690\pi\) | |||||||
\(878\) | 11.6290 | 0.392458 | ||||||||
\(879\) | 9.65728 | + | 11.8443i | 0.325732 | + | 0.399497i | ||||
\(880\) | 106.954 | 3.60540 | ||||||||
\(881\) | −18.0285 | −0.607395 | −0.303697 | − | 0.952769i | \(-0.598221\pi\) | ||||
−0.303697 | + | 0.952769i | \(0.598221\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.0928 | 1.45019 | 0.725095 | − | 0.688649i | \(-0.241796\pi\) | ||||
0.725095 | + | 0.688649i | \(0.241796\pi\) | |||||||
\(884\) | −1.32339 | −0.0445104 | ||||||||
\(885\) | −24.3520 | + | 64.0810i | −0.818584 | + | 2.15406i | ||||
\(886\) | −49.4507 | −1.66133 | ||||||||
\(887\) | 15.4763 | − | 26.8058i | 0.519645 | − | 0.900051i | −0.480094 | − | 0.877217i | \(-0.659398\pi\) |
0.999739 | − | 0.0228344i | \(-0.00726904\pi\) | |||||||
\(888\) | 6.88650 | + | 8.44602i | 0.231096 | + | 0.283430i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −33.6047 | −1.12643 | ||||||||
\(891\) | 50.3714 | + | 21.6215i | 1.68751 | + | 0.724349i | ||||
\(892\) | −9.79685 | + | 16.9686i | −0.328023 | + | 0.568152i | ||||
\(893\) | −6.30813 | − | 10.9260i | −0.211094 | − | 0.365625i | ||||
\(894\) | −6.13565 | + | 16.1456i | −0.205207 | + | 0.539991i | ||||
\(895\) | −4.61595 | − | 7.99506i | −0.154294 | − | 0.267245i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.43913 | + | 0.394713i | −0.0814401 | + | 0.0131791i | ||||
\(898\) | 11.5143 | 0.384236 | ||||||||
\(899\) | 0.584545 | − | 1.01246i | 0.0194957 | − | 0.0337675i | ||||
\(900\) | −16.1447 | − | 14.3418i | −0.538157 | − | 0.478059i | ||||
\(901\) | 5.01945 | + | 8.69395i | 0.167222 | + | 0.289637i | ||||
\(902\) | 17.7008 | − | 30.6587i | 0.589372 | − | 1.02082i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.40614 | + | 12.8278i | 0.246324 | + | 0.426646i | ||||
\(905\) | −6.97880 | + | 12.0876i | −0.231983 | + | 0.401807i | ||||
\(906\) | 3.82958 | + | 4.69683i | 0.127229 | + | 0.156042i | ||||
\(907\) | 21.4042 | + | 37.0731i | 0.710714 | + | 1.23099i | 0.964590 | + | 0.263755i | \(0.0849611\pi\) |
−0.253876 | + | 0.967237i | \(0.581706\pi\) | |||||||
\(908\) | −1.77243 | − | 3.06993i | −0.0588200 | − | 0.101879i | ||||
\(909\) | 29.0760 | + | 25.8290i | 0.964391 | + | 0.856694i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.04869 | − | 5.28049i | 0.101008 | − | 0.174950i | −0.811092 | − | 0.584918i | \(-0.801127\pi\) |
0.912100 | + | 0.409968i | \(0.134460\pi\) | |||||||
\(912\) | 12.0683 | + | 14.8013i | 0.399622 | + | 0.490121i | ||||
\(913\) | 7.61269 | 0.251943 | ||||||||
\(914\) | 49.4800 | 1.63665 | ||||||||
\(915\) | 25.9375 | − | 68.2530i | 0.857467 | − | 2.25638i | ||||
\(916\) | −6.72830 | + | 11.6538i | −0.222309 | + | 0.385051i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.456710 | + | 10.7919i | −0.0150737 | + | 0.356186i | ||||
\(919\) | −12.4307 | − | 21.5305i | −0.410050 | − | 0.710227i | 0.584845 | − | 0.811145i | \(-0.301155\pi\) |
−0.994895 | + | 0.100918i | \(0.967822\pi\) | |||||||
\(920\) | 3.93382 | + | 6.81357i | 0.129694 | + | 0.224637i | ||||
\(921\) | −1.80440 | + | 0.291998i | −0.0594569 | + | 0.00962165i | ||||
\(922\) | 17.2811 | − | 29.9317i | 0.569121 | − | 0.985747i | ||||
\(923\) | −6.83664 | − | 11.8414i | −0.225031 | − | 0.389764i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.1199 | + | 22.7244i | −0.431381 | + | 0.747174i | ||||
\(926\) | 8.56034 | + | 14.8269i | 0.281310 | + | 0.487244i | ||||
\(927\) | −1.63198 | + | 7.93946i | −0.0536012 | + | 0.260766i | ||||
\(928\) | −15.8676 | + | 27.4834i | −0.520878 | + | 0.902188i | ||||
\(929\) | −41.8402 | −1.37273 | −0.686366 | − | 0.727256i | \(-0.740795\pi\) | ||||
−0.686366 | + | 0.727256i | \(0.740795\pi\) | |||||||
\(930\) | 0.702994 | − | 1.84989i | 0.0230521 | − | 0.0606603i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 12.3895 | + | 21.4592i | 0.405831 | + | 0.702920i | ||||
\(933\) | −5.25279 | + | 0.850036i | −0.171969 | + | 0.0278289i | ||||
\(934\) | −13.8826 | − | 24.0453i | −0.454251 | − | 0.786786i | ||||
\(935\) | 12.8776 | − | 22.3047i | 0.421144 | − | 0.729443i | ||||
\(936\) | 4.41995 | + | 3.92636i | 0.144471 | + | 0.128337i | ||||
\(937\) | −29.2537 | −0.955676 | −0.477838 | − | 0.878448i | \(-0.658579\pi\) | ||||
−0.477838 | + | 0.878448i | \(0.658579\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −48.1517 | + | 7.79218i | −1.57137 | + | 0.254288i | ||||
\(940\) | 9.85740 | − | 17.0735i | 0.321513 | − | 0.556877i | ||||
\(941\) | −3.35737 | −0.109447 | −0.0547236 | − | 0.998502i | \(-0.517428\pi\) | ||||
−0.0547236 | + | 0.998502i | \(0.517428\pi\) | |||||||
\(942\) | −8.99693 | + | 1.45593i | −0.293136 | + | 0.0474369i | ||||
\(943\) | 4.28673 | 0.139595 | ||||||||
\(944\) | 56.3387 | 1.83367 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 40.0194 | 1.30114 | ||||||||
\(947\) | 5.26601 | 0.171122 | 0.0855612 | − | 0.996333i | \(-0.472732\pi\) | ||||
0.0855612 | + | 0.996333i | \(0.472732\pi\) | |||||||
\(948\) | −15.4630 | + | 2.50230i | −0.502214 | + | 0.0812710i | ||||
\(949\) | 5.95398 | 0.193274 | ||||||||
\(950\) | −13.9677 | + | 24.1928i | −0.453173 | + | 0.784918i | ||||
\(951\) | −21.9650 | + | 3.55450i | −0.712264 | + | 0.115263i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 56.2520 | 1.82218 | 0.911090 | − | 0.412208i | \(-0.135242\pi\) | ||||
0.911090 | + | 0.412208i | \(0.135242\pi\) | |||||||
\(954\) | −8.69619 | + | 42.3063i | −0.281549 | + | 1.36972i | ||||
\(955\) | 31.9724 | − | 55.3778i | 1.03460 | − | 1.79198i | ||||
\(956\) | −4.41038 | − | 7.63900i | −0.142642 | − | 0.247063i | ||||
\(957\) | 64.6203 | − | 10.4572i | 2.08888 | − | 0.338034i | ||||
\(958\) | 7.08131 | + | 12.2652i | 0.228787 | + | 0.396270i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.52624 | − | 6.64767i | 0.0815341 | − | 0.214553i | ||||
\(961\) | −30.9645 | −0.998855 | ||||||||
\(962\) | −3.45918 | + | 5.99148i | −0.111528 | + | 0.193173i | ||||
\(963\) | 0.400306 | + | 0.355602i | 0.0128997 | + | 0.0114591i | ||||
\(964\) | −4.54153 | − | 7.86616i | −0.146273 | − | 0.253352i | ||||
\(965\) | 0.355420 | − | 0.615606i | 0.0114414 | − | 0.0198171i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.88641 | − | 11.9276i | −0.221452 | − | 0.383566i | 0.733797 | − | 0.679369i | \(-0.237746\pi\) |
−0.955249 | + | 0.295803i | \(0.904413\pi\) | |||||||
\(968\) | −22.9526 | + | 39.7551i | −0.737725 | + | 1.27778i | ||||
\(969\) | 4.53983 | − | 0.734661i | 0.145840 | − | 0.0236007i | ||||
\(970\) | −49.9874 | − | 86.5807i | −1.60500 | − | 2.77994i | ||||
\(971\) | −25.6627 | − | 44.4491i | −0.823555 | − | 1.42644i | −0.903019 | − | 0.429602i | \(-0.858654\pi\) |
0.0794635 | − | 0.996838i | \(-0.474679\pi\) | |||||||
\(972\) | −10.6324 | + | 10.9952i | −0.341033 | + | 0.352671i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.36269 | − | 4.09230i | 0.0757055 | − | 0.131126i | ||||
\(975\) | −5.05685 | + | 13.3068i | −0.161949 | + | 0.426159i | ||||
\(976\) | −60.0066 | −1.92077 | ||||||||
\(977\) | 17.6850 | 0.565794 | 0.282897 | − | 0.959150i | \(-0.408704\pi\) | ||||
0.282897 | + | 0.959150i | \(0.408704\pi\) | |||||||
\(978\) | 10.1841 | + | 12.4903i | 0.325650 | + | 0.399397i | ||||
\(979\) | 16.8751 | − | 29.2285i | 0.539329 | − | 0.934146i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.65284 | + | 27.5006i | −0.180481 | + | 0.878027i | ||||
\(982\) | −17.0154 | − | 29.4716i | −0.542984 | − | 0.940476i | ||||
\(983\) | −8.00207 | − | 13.8600i | −0.255226 | − | 0.442065i | 0.709731 | − | 0.704473i | \(-0.248817\pi\) |
−0.964957 | + | 0.262408i | \(0.915483\pi\) | |||||||
\(984\) | −6.48158 | − | 7.94940i | −0.206625 | − | 0.253418i | ||||
\(985\) | 2.86492 | − | 4.96218i | 0.0912839 | − | 0.158108i | ||||
\(986\) | 6.44961 | + | 11.1711i | 0.205397 | + | 0.355759i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.21207 | + | 2.09937i | −0.0385612 | + | 0.0667899i | ||||
\(989\) | 2.42295 | + | 4.19667i | 0.0770454 | + | 0.133446i | ||||
\(990\) | 105.153 | − | 34.9480i | 3.34197 | − | 1.11072i | ||||
\(991\) | 5.43319 | − | 9.41055i | 0.172591 | − | 0.298936i | −0.766734 | − | 0.641965i | \(-0.778120\pi\) |
0.939325 | + | 0.343029i | \(0.111453\pi\) | |||||||
\(992\) | −0.963543 | −0.0305925 | ||||||||
\(993\) | 36.8567 | − | 5.96435i | 1.16961 | − | 0.189273i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.0499 | − | 19.1390i | −0.350306 | − | 0.606748i | ||||
\(996\) | −0.754572 | + | 1.98561i | −0.0239095 | + | 0.0629166i | ||||
\(997\) | 20.5187 | + | 35.5395i | 0.649835 | + | 1.12555i | 0.983162 | + | 0.182736i | \(0.0584954\pi\) |
−0.333327 | + | 0.942811i | \(0.608171\pi\) | |||||||
\(998\) | −28.5719 | + | 49.4880i | −0.904428 | + | 1.56652i | ||||
\(999\) | 15.6879 | + | 9.96477i | 0.496342 | + | 0.315271i |
(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 | 441.2.h.h.214.3 | 24 | ||
3.2 | odd | 2 | 1323.2.h.h.802.9 | 24 | |||
7.2 | even | 3 | 441.2.g.h.79.10 | 24 | |||
7.3 | odd | 6 | 441.2.f.h.295.9 | yes | 24 | ||
7.4 | even | 3 | 441.2.f.h.295.10 | yes | 24 | ||
7.5 | odd | 6 | 441.2.g.h.79.9 | 24 | |||
7.6 | odd | 2 | inner | 441.2.h.h.214.4 | 24 | ||
9.4 | even | 3 | 441.2.g.h.67.10 | 24 | |||
9.5 | odd | 6 | 1323.2.g.h.361.3 | 24 | |||
21.2 | odd | 6 | 1323.2.g.h.667.3 | 24 | |||
21.5 | even | 6 | 1323.2.g.h.667.4 | 24 | |||
21.11 | odd | 6 | 1323.2.f.h.883.4 | 24 | |||
21.17 | even | 6 | 1323.2.f.h.883.3 | 24 | |||
21.20 | even | 2 | 1323.2.h.h.802.10 | 24 | |||
63.4 | even | 3 | 441.2.f.h.148.10 | yes | 24 | ||
63.5 | even | 6 | 1323.2.h.h.226.10 | 24 | |||
63.11 | odd | 6 | 3969.2.a.bi.1.9 | 12 | |||
63.13 | odd | 6 | 441.2.g.h.67.9 | 24 | |||
63.23 | odd | 6 | 1323.2.h.h.226.9 | 24 | |||
63.25 | even | 3 | 3969.2.a.bh.1.4 | 12 | |||
63.31 | odd | 6 | 441.2.f.h.148.9 | ✓ | 24 | ||
63.32 | odd | 6 | 1323.2.f.h.442.4 | 24 | |||
63.38 | even | 6 | 3969.2.a.bi.1.10 | 12 | |||
63.40 | odd | 6 | inner | 441.2.h.h.373.4 | 24 | ||
63.41 | even | 6 | 1323.2.g.h.361.4 | 24 | |||
63.52 | odd | 6 | 3969.2.a.bh.1.3 | 12 | |||
63.58 | even | 3 | inner | 441.2.h.h.373.3 | 24 | ||
63.59 | even | 6 | 1323.2.f.h.442.3 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.9 | ✓ | 24 | 63.31 | odd | 6 | ||
441.2.f.h.148.10 | yes | 24 | 63.4 | even | 3 | ||
441.2.f.h.295.9 | yes | 24 | 7.3 | odd | 6 | ||
441.2.f.h.295.10 | yes | 24 | 7.4 | even | 3 | ||
441.2.g.h.67.9 | 24 | 63.13 | odd | 6 | |||
441.2.g.h.67.10 | 24 | 9.4 | even | 3 | |||
441.2.g.h.79.9 | 24 | 7.5 | odd | 6 | |||
441.2.g.h.79.10 | 24 | 7.2 | even | 3 | |||
441.2.h.h.214.3 | 24 | 1.1 | even | 1 | trivial | ||
441.2.h.h.214.4 | 24 | 7.6 | odd | 2 | inner | ||
441.2.h.h.373.3 | 24 | 63.58 | even | 3 | inner | ||
441.2.h.h.373.4 | 24 | 63.40 | odd | 6 | inner | ||
1323.2.f.h.442.3 | 24 | 63.59 | even | 6 | |||
1323.2.f.h.442.4 | 24 | 63.32 | odd | 6 | |||
1323.2.f.h.883.3 | 24 | 21.17 | even | 6 | |||
1323.2.f.h.883.4 | 24 | 21.11 | odd | 6 | |||
1323.2.g.h.361.3 | 24 | 9.5 | odd | 6 | |||
1323.2.g.h.361.4 | 24 | 63.41 | even | 6 | |||
1323.2.g.h.667.3 | 24 | 21.2 | odd | 6 | |||
1323.2.g.h.667.4 | 24 | 21.5 | even | 6 | |||
1323.2.h.h.226.9 | 24 | 63.23 | odd | 6 | |||
1323.2.h.h.226.10 | 24 | 63.5 | even | 6 | |||
1323.2.h.h.802.9 | 24 | 3.2 | odd | 2 | |||
1323.2.h.h.802.10 | 24 | 21.20 | even | 2 | |||
3969.2.a.bh.1.3 | 12 | 63.52 | odd | 6 | |||
3969.2.a.bh.1.4 | 12 | 63.25 | even | 3 | |||
3969.2.a.bi.1.9 | 12 | 63.11 | odd | 6 | |||
3969.2.a.bi.1.10 | 12 | 63.38 | even | 6 |