Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,2,Mod(17,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([0, 10, 13]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.x (of order \(20\), degree \(8\), 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: | \(2.39551206064\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{20})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 113.3 | ||
Character | \(\chi\) | \(=\) | 300.113 |
Dual form | 300.2.x.a.77.3 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{19}{20}\right)\) |
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 | 0 | ||||||||
\(3\) | −1.21892 | − | 1.23054i | −0.703743 | − | 0.710455i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.48454 | − | 1.67217i | −0.663905 | − | 0.747817i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.245464 | + | 0.245464i | −0.0927767 | + | 0.0927767i | −0.751972 | − | 0.659195i | \(-0.770897\pi\) |
0.659195 | + | 0.751972i | \(0.270897\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.0284784 | + | 2.99986i | −0.00949280 | + | 0.999955i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.879848 | − | 1.21101i | 0.265284 | − | 0.365132i | −0.655506 | − | 0.755190i | \(-0.727545\pi\) |
0.920791 | + | 0.390057i | \(0.127545\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.29990 | − | 0.839422i | −1.46993 | − | 0.232814i | −0.630460 | − | 0.776222i | \(-0.717134\pi\) |
−0.839469 | + | 0.543408i | \(0.817134\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.248153 | + | 3.86503i | −0.0640727 | + | 0.997945i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.61182 | + | 3.36889i | −1.60360 | + | 0.817077i | −0.603802 | + | 0.797134i | \(0.706348\pi\) |
−0.999801 | + | 0.0199422i | \(0.993652\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.22097 | − | 1.04656i | −0.738940 | − | 0.240096i | −0.0847246 | − | 0.996404i | \(-0.527001\pi\) |
−0.654215 | + | 0.756308i | \(0.727001\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.601255 | + | 0.00285386i | 0.131205 | + | 0.000622763i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.61050 | − | 0.255078i | 0.335812 | − | 0.0531874i | 0.0137486 | − | 0.999905i | \(-0.495624\pi\) |
0.322063 | + | 0.946718i | \(0.395624\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.592307 | + | 4.96479i | −0.118461 | + | 0.992959i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.72618 | − | 3.62154i | 0.717104 | − | 0.696967i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.637623 | + | 1.96240i | 0.118404 | + | 0.364409i | 0.992642 | − | 0.121089i | \(-0.0386385\pi\) |
−0.874238 | + | 0.485497i | \(0.838639\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.11791 | − | 6.51825i | 0.380387 | − | 1.17071i | −0.559384 | − | 0.828908i | \(-0.688962\pi\) |
0.939772 | − | 0.341803i | \(-0.111038\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.56266 | + | 0.393426i | −0.446102 | + | 0.0684867i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.774858 | + | 0.0460576i | 0.130975 | + | 0.00778515i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.18914 | − | 7.50792i | 0.195493 | − | 1.23429i | −0.673394 | − | 0.739284i | \(-0.735164\pi\) |
0.868887 | − | 0.495010i | \(-0.164836\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.42720 | + | 7.54495i | 0.869048 | + | 1.20816i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.49942 | − | 3.44015i | −0.390343 | − | 0.537261i | 0.567944 | − | 0.823067i | \(-0.307739\pi\) |
−0.958288 | + | 0.285806i | \(0.907739\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.03773 | − | 3.03773i | −0.463250 | − | 0.463250i | 0.436469 | − | 0.899719i | \(-0.356229\pi\) |
−0.899719 | + | 0.436469i | \(0.856229\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.05856 | − | 4.40579i | 0.754086 | − | 0.656776i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.43370 | − | 2.81380i | 0.209127 | − | 0.410435i | −0.762488 | − | 0.647002i | \(-0.776022\pi\) |
0.971615 | + | 0.236567i | \(0.0760223\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.87949i | 0.982785i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.2048 | + | 4.02974i | 1.70902 | + | 0.564276i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.212713 | + | 0.108383i | 0.0292184 | + | 0.0148875i | 0.468539 | − | 0.883443i | \(-0.344781\pi\) |
−0.439320 | + | 0.898330i | \(0.644781\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.33118 | + | 0.326527i | −0.449176 | + | 0.0440289i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.63826 | + | 5.23920i | 0.349446 | + | 0.693950i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.57801 | − | 1.87303i | 0.335628 | − | 0.243848i | −0.407187 | − | 0.913345i | \(-0.633490\pi\) |
0.742815 | + | 0.669497i | \(0.233490\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.40759 | + | 2.47576i | 0.436297 | + | 0.316988i | 0.784162 | − | 0.620556i | \(-0.213093\pi\) |
−0.347865 | + | 0.937545i | \(0.613093\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.729368 | − | 0.743349i | −0.0918918 | − | 0.0936532i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.46424 | + | 10.1085i | 0.801790 | + | 1.25380i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.71895 | − | 11.2241i | −0.698681 | − | 1.37124i | −0.918391 | − | 0.395674i | \(-0.870511\pi\) |
0.219709 | − | 0.975565i | \(-0.429489\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.27695 | − | 1.67087i | −0.274113 | − | 0.201149i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.0056 | − | 4.87563i | 1.78084 | − | 0.578630i | 0.781847 | − | 0.623471i | \(-0.214278\pi\) |
0.998994 | + | 0.0448405i | \(0.0142780\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.02219 | − | 12.7676i | −0.236679 | − | 1.49433i | −0.764304 | − | 0.644856i | \(-0.776917\pi\) |
0.527625 | − | 0.849478i | \(-0.323083\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.83137 | − | 5.32281i | 0.788819 | − | 0.614626i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.0812876 | + | 0.513230i | 0.00926358 | + | 0.0584879i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.94456 | + | 3.23118i | −1.11885 | + | 0.363536i | −0.809329 | − | 0.587356i | \(-0.800169\pi\) |
−0.309521 | + | 0.950892i | \(0.600169\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.99838 | − | 0.170863i | −0.999820 | − | 0.0189847i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.61756 | + | 12.9877i | 0.726372 | + | 1.42559i | 0.897807 | + | 0.440390i | \(0.145160\pi\) |
−0.171434 | + | 0.985196i | \(0.554840\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 15.4489 | + | 6.05486i | 1.67566 | + | 0.656741i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.63761 | − | 3.17663i | 0.175570 | − | 0.340570i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.2231 | − | 7.42754i | −1.08365 | − | 0.787318i | −0.105335 | − | 0.994437i | \(-0.533591\pi\) |
−0.978316 | + | 0.207119i | \(0.933591\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.50698 | − | 1.09489i | 0.157975 | − | 0.114775i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.6025 | + | 5.33903i | −1.09943 | + | 0.553632i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.03162 | + | 6.93965i | 0.311038 | + | 0.711993i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.73153 | + | 1.39178i | 0.277345 | + | 0.141314i | 0.587131 | − | 0.809492i | \(-0.300257\pi\) |
−0.309786 | + | 0.950806i | \(0.600257\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.60780 | + | 2.67391i | 0.362598 | + | 0.268738i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 2.16240i | − | 0.215167i | −0.994196 | − | 0.107584i | \(-0.965689\pi\) | ||
0.994196 | − | 0.107584i | \(-0.0343113\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.42093 | + | 12.6018i | −0.632673 | + | 1.24169i | 0.322759 | + | 0.946481i | \(0.395390\pi\) |
−0.955432 | + | 0.295210i | \(0.904610\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.887812 | − | 1.00964i | −0.0866416 | − | 0.0985305i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.63321 | − | 1.63321i | −0.157888 | − | 0.157888i | 0.623742 | − | 0.781630i | \(-0.285612\pi\) |
−0.781630 | + | 0.623742i | \(0.785612\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.52845 | − | 3.48012i | −0.242182 | − | 0.333335i | 0.670572 | − | 0.741844i | \(-0.266049\pi\) |
−0.912754 | + | 0.408509i | \(0.866049\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.6883 | + | 7.68825i | −1.01449 | + | 0.729736i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.695637 | − | 4.39208i | 0.0654401 | − | 0.413172i | −0.933122 | − | 0.359560i | \(-0.882927\pi\) |
0.998562 | − | 0.0536118i | \(-0.0170733\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.81738 | − | 2.31436i | −0.262722 | − | 0.215815i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.66909 | − | 15.8751i | 0.246757 | − | 1.46765i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.796023 | − | 2.44991i | 0.0729713 | − | 0.224583i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.70678 | + | 8.33062i | 0.246071 | + | 0.757329i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.18668 | + | 7.26890i | −0.106999 | + | 0.655415i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.18128 | − | 6.37997i | 0.821199 | − | 0.570642i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.40727 | − | 1.48997i | 0.834760 | − | 0.132213i | 0.275600 | − | 0.961272i | \(-0.411124\pi\) |
0.559161 | + | 0.829059i | \(0.311124\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.0353179 | + | 7.44081i | −0.00310956 | + | 0.655127i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.1696 | − | 5.90366i | −1.58748 | − | 0.515805i | −0.623514 | − | 0.781812i | \(-0.714295\pi\) |
−0.963971 | + | 0.266007i | \(0.914295\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.04752 | − | 0.533739i | 0.0908317 | − | 0.0462811i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.5875 | − | 0.854494i | −0.997292 | − | 0.0735431i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.6830 | − | 2.16717i | −1.16902 | − | 0.185154i | −0.458409 | − | 0.888741i | \(-0.651580\pi\) |
−0.710609 | + | 0.703587i | \(0.751580\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.20281 | + | 8.53743i | −0.526115 | + | 0.724136i | −0.986532 | − | 0.163567i | \(-0.947700\pi\) |
0.460417 | + | 0.887703i | \(0.347700\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.21008 | + | 1.66556i | −0.438768 | + | 0.140265i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.67966 | + | 5.67966i | −0.474957 | + | 0.474957i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.33490 | − | 3.97947i | 0.193903 | − | 0.330477i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.46552 | − | 8.38554i | 0.698225 | − | 0.691628i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.21507 | −0.263389 | −0.131695 | − | 0.991290i | \(-0.542042\pi\) | ||||
−0.131695 | + | 0.991290i | \(0.542042\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.2319 | 1.07680 | 0.538400 | − | 0.842689i | \(-0.319029\pi\) | ||||
0.538400 | + | 0.842689i | \(0.319029\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.91793 | − | 19.9305i | −0.801817 | − | 1.61129i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.0437 | + | 6.13507i | −1.12802 | + | 0.492781i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.70136 | + | 6.70136i | −0.534827 | + | 0.534827i | −0.922005 | − | 0.387178i | \(-0.873450\pi\) |
0.387178 | + | 0.922005i | \(0.373450\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.125910 | − | 0.393862i | −0.00998531 | − | 0.0312353i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.332707 | + | 0.457932i | −0.0262210 | + | 0.0360901i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.95274 | + | 1.57636i | 0.779559 | + | 0.123470i | 0.533517 | − | 0.845789i | \(-0.320870\pi\) |
0.246042 | + | 0.969259i | \(0.420870\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.46224 | + | 3.70115i | 0.347385 | + | 0.288134i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.23014 | + | 4.70299i | −0.714249 | + | 0.363928i | −0.773053 | − | 0.634341i | \(-0.781271\pi\) |
0.0588037 | + | 0.998270i | \(0.481271\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.0206 | + | 4.88050i | 1.15543 | + | 0.375423i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.23125 | − | 9.63266i | 0.247100 | − | 0.736628i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.4566 | − | 3.39839i | 1.63132 | − | 0.258375i | 0.727440 | − | 0.686171i | \(-0.240710\pi\) |
0.903875 | + | 0.427796i | \(0.140710\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.07329 | − | 1.36407i | −0.0811329 | − | 0.103114i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.44722 | − | 0.889279i | −0.409438 | − | 0.0668423i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.69521 | − | 17.5280i | −0.425680 | − | 1.31011i | −0.902342 | − | 0.431021i | \(-0.858153\pi\) |
0.476662 | − | 0.879087i | \(-0.341847\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.883167 | + | 2.71811i | −0.0656453 | + | 0.202035i | −0.978499 | − | 0.206251i | \(-0.933874\pi\) |
0.912854 | + | 0.408287i | \(0.133874\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.10704 | − | 7.21094i | −0.0818349 | − | 0.533048i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −14.3198 | + | 9.15733i | −1.05282 | + | 0.673260i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.73765 | + | 10.9711i | −0.127069 | + | 0.802285i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.0256840 | + | 1.80360i | −0.00186823 | + | 0.131193i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.19912 | − | 12.6615i | −0.665625 | − | 0.916154i | 0.334026 | − | 0.942564i | \(-0.391593\pi\) |
−0.999651 | + | 0.0264098i | \(0.991593\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.21036 | + | 7.21036i | 0.519013 | + | 0.519013i | 0.917273 | − | 0.398260i | \(-0.130386\pi\) |
−0.398260 | + | 0.917273i | \(0.630386\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.55957 | − | 20.2760i | 0.326518 | − | 1.45199i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.50774 | + | 12.7722i | −0.463657 | + | 0.909979i | 0.534250 | + | 0.845326i | \(0.320594\pi\) |
−0.997908 | + | 0.0646527i | \(0.979406\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 9.24251i | − | 0.655184i | −0.944819 | − | 0.327592i | \(-0.893763\pi\) | ||
0.944819 | − | 0.327592i | \(-0.106237\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.84079 | + | 20.7187i | −0.482512 | + | 1.46138i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.638212 | − | 0.325185i | −0.0447937 | − | 0.0228235i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.04205 | + | 9.28647i | −0.142623 | + | 0.648596i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.719335 | + | 4.83854i | 0.0499972 | + | 0.336302i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.10135 | + | 2.97980i | −0.283696 | + | 0.206117i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.57544 | − | 6.23042i | −0.590358 | − | 0.428920i | 0.252085 | − | 0.967705i | \(-0.418884\pi\) |
−0.842443 | + | 0.538785i | \(0.818884\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −24.2903 | − | 12.5221i | −1.66434 | − | 0.858001i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.569984 | + | 9.58923i | −0.0388726 | + | 0.653980i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.08012 | + | 2.11986i | 0.0733237 | + | 0.143906i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.2462 | + | 18.0510i | −0.895096 | + | 1.21978i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 37.8700 | − | 12.3047i | 2.54741 | − | 0.827704i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.952406 | + | 6.01326i | 0.0637778 | + | 0.402677i | 0.998838 | + | 0.0481890i | \(0.0153450\pi\) |
−0.935060 | + | 0.354488i | \(0.884655\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −14.8768 | − | 1.91823i | −0.991789 | − | 0.127882i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.651345 | − | 4.11243i | −0.0432313 | − | 0.272952i | 0.956598 | − | 0.291410i | \(-0.0941243\pi\) |
−0.999830 | + | 0.0184580i | \(0.994124\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.6691 | − | 6.06597i | 1.23369 | − | 0.400851i | 0.381642 | − | 0.924310i | \(-0.375359\pi\) |
0.852051 | + | 0.523460i | \(0.175359\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.532469 | − | 0.725613i | 0.0350339 | − | 0.0477418i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.67158 | + | 13.0937i | 0.437070 | + | 0.857797i | 0.999520 | + | 0.0309667i | \(0.00985859\pi\) |
−0.562451 | + | 0.826831i | \(0.690141\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.83354 | + | 1.77979i | −0.445771 | + | 0.116101i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.0977 | + | 8.29867i | 1.04566 | + | 0.539057i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.39910 | + | 3.92267i | 0.349239 | + | 0.253737i | 0.748550 | − | 0.663079i | \(-0.230751\pi\) |
−0.399311 | + | 0.916816i | \(0.630751\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.2337 | + | 13.9741i | −1.23895 | + | 0.900153i | −0.997528 | − | 0.0702665i | \(-0.977615\pi\) |
−0.241426 | + | 0.970419i | \(0.577615\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.7580 | + | 11.2812i | 0.690128 | + | 0.723687i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.5037 | − | 10.2129i | 0.734944 | − | 0.652475i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.1923 | + | 8.25039i | 1.03029 | + | 0.524960i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.91567 | − | 23.9741i | 0.501635 | − | 1.51930i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.5783i | 1.67761i | 0.544435 | + | 0.838803i | \(0.316744\pi\) | ||||
−0.544435 | + | 0.838803i | \(0.683256\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.10809 | − | 2.17475i | 0.0696652 | − | 0.136726i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −11.3801 | − | 26.3909i | −0.712650 | − | 1.65266i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.0358 | + | 10.0358i | 0.626014 | + | 0.626014i | 0.947063 | − | 0.321049i | \(-0.104035\pi\) |
−0.321049 | + | 0.947063i | \(0.604035\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.55103 | + | 2.13481i | 0.0963765 | + | 0.132651i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.90510 | + | 1.85690i | −0.365516 | + | 0.114939i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.61785 | − | 22.8422i | 0.223086 | − | 1.40851i | −0.580954 | − | 0.813937i | \(-0.697320\pi\) |
0.804040 | − | 0.594575i | \(-0.202680\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.134546 | − | 0.516590i | −0.00826508 | − | 0.0317339i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.32124 | + | 21.6336i | 0.203257 | + | 1.32395i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.60045 | − | 8.00336i | 0.158552 | − | 0.487974i | −0.839951 | − | 0.542662i | \(-0.817416\pi\) |
0.998503 | + | 0.0546882i | \(0.0174165\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.11567 | − | 21.8998i | −0.432246 | − | 1.33032i | −0.895882 | − | 0.444291i | \(-0.853456\pi\) |
0.463636 | − | 0.886026i | \(-0.346544\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.18420 | − | 0.519832i | −0.192716 | − | 0.0314617i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.49126 | + | 5.08555i | 0.331135 | + | 0.306670i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.0819 | + | 1.75520i | −0.665845 | + | 0.105459i | −0.480202 | − | 0.877158i | \(-0.659437\pi\) |
−0.185643 | + | 0.982617i | \(0.559437\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 19.4935 | + | 6.53906i | 1.16705 | + | 0.391483i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.6137 | + | 4.74827i | 0.871778 | + | 0.283258i | 0.710539 | − | 0.703658i | \(-0.248451\pi\) |
0.161239 | + | 0.986915i | \(0.448451\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.57810 | − | 3.86124i | 0.450471 | − | 0.229527i | −0.214010 | − | 0.976831i | \(-0.568652\pi\) |
0.664481 | + | 0.747305i | \(0.268652\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.84425 | − | 12.1894i | 0.286949 | − | 0.722038i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.45795 | + | 0.230917i | 0.0860600 | + | 0.0136306i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 22.3744 | − | 30.7958i | 1.31614 | − | 1.81152i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.61686 | − | 5.05774i | −0.0947820 | − | 0.296490i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.65414 | − | 3.65414i | 0.213477 | − | 0.213477i | −0.592266 | − | 0.805743i | \(-0.701766\pi\) |
0.805743 | + | 0.592266i | \(0.201766\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.95917 | − | 1.53028i | −0.405178 | − | 0.0890966i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.10724 | − | 7.69884i | −0.0642488 | − | 0.446732i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.74960 | −0.506003 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.49131 | 0.0859575 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.66093 | + | 2.63579i | −0.152867 | + | 0.151422i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.918798 | − | 9.37342i | −0.0526102 | − | 0.536721i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.46729 | − | 1.46729i | 0.0837427 | − | 0.0837427i | −0.663995 | − | 0.747737i | \(-0.731140\pi\) |
0.747737 | + | 0.663995i | \(0.231140\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 23.3337 | − | 7.45931i | 1.32741 | − | 0.424345i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.3661 | − | 18.3969i | 0.757922 | − | 1.04319i | −0.239462 | − | 0.970906i | \(-0.576971\pi\) |
0.997384 | − | 0.0722845i | \(-0.0230290\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.0952 | + | 3.49953i | 1.24889 | + | 0.197805i | 0.745649 | − | 0.666339i | \(-0.232139\pi\) |
0.503245 | + | 0.864144i | \(0.332139\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.160233 | + | 2.32316i | −0.00902811 | + | 0.130895i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.91256 | + | 1.48402i | −0.163586 | + | 0.0833510i | −0.533866 | − | 0.845569i | \(-0.679261\pi\) |
0.370281 | + | 0.928920i | \(0.379261\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.93749 | + | 0.954449i | 0.164468 | + | 0.0534389i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.0189883 | + | 4.00049i | −0.00105983 | + | 0.223285i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.8222 | − | 3.93145i | 1.38114 | − | 0.218752i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.30673 | − | 25.8157i | 0.405305 | − | 1.43200i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.20046 | + | 7.35335i | −0.0663857 | + | 0.406641i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.338764 | + | 1.04261i | 0.0186767 | + | 0.0574809i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.16968 | + | 15.9106i | −0.284151 | + | 0.874527i | 0.702501 | + | 0.711683i | \(0.252067\pi\) |
−0.986652 | + | 0.162844i | \(0.947933\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 22.4889 | + | 3.78107i | 1.23238 | + | 0.207201i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.2786 | + | 26.2256i | −0.561579 | + | 1.43286i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.12579 | + | 19.7355i | −0.170273 | + | 1.07506i | 0.743471 | + | 0.668768i | \(0.233178\pi\) |
−0.913744 | + | 0.406291i | \(0.866822\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.25257 | + | 4.49757i | −0.339593 | + | 0.244275i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.03020 | − | 8.29986i | −0.326554 | − | 0.449463i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.40692 | − | 3.40692i | −0.183956 | − | 0.183956i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.586233 | + | 6.28791i | 0.0315617 | + | 0.338530i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.905384 | + | 1.77692i | −0.0486036 | + | 0.0953899i | −0.914031 | − | 0.405645i | \(-0.867047\pi\) |
0.865427 | + | 0.501035i | \(0.167047\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.7345i | 1.05636i | 0.849132 | + | 0.528181i | \(0.177126\pi\) | ||||
−0.849132 | + | 0.528181i | \(0.822874\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −22.7884 | + | 16.0660i | −1.21635 | + | 0.857540i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.2294 | − | 5.72168i | −0.597682 | − | 0.304534i | 0.128853 | − | 0.991664i | \(-0.458871\pi\) |
−0.726535 | + | 0.687129i | \(0.758871\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −30.4293 | − | 17.8539i | −1.61502 | − | 0.947588i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.98501 | + | 2.00669i | −0.210909 | + | 0.106205i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.9247 | + | 10.8434i | −0.787695 | + | 0.572294i | −0.907279 | − | 0.420530i | \(-0.861844\pi\) |
0.119583 | + | 0.992824i | \(0.461844\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.09198 | − | 4.42609i | −0.320631 | − | 0.232952i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.95185 | − | 13.4852i | 0.364877 | − | 0.707787i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.3476 | + | 22.3354i | −0.960356 | + | 1.16909i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.9237 | + | 27.3269i | 0.726814 | + | 1.42645i | 0.897449 | + | 0.441118i | \(0.145418\pi\) |
−0.170636 | + | 0.985334i | \(0.554582\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.3912 | − | 7.39994i | 0.540942 | − | 0.385225i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.0788174 | + | 0.0256093i | −0.00409200 | + | 0.00132957i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.64265 | − | 10.3713i | −0.0850532 | − | 0.537005i | −0.993018 | − | 0.117959i | \(-0.962365\pi\) |
0.907965 | − | 0.419046i | \(-0.137635\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −19.0421 | − | 3.52131i | −0.983328 | − | 0.181840i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.73206 | − | 10.9358i | −0.0892055 | − | 0.563221i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.0985 | + | 5.88056i | −0.929657 | + | 0.302064i | −0.734423 | − | 0.678693i | \(-0.762547\pi\) |
−0.195235 | + | 0.980757i | \(0.562547\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.3002 | − | 9.75992i | −0.681388 | − | 0.500016i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.02976 | − | 3.98364i | −0.103716 | − | 0.203554i | 0.833317 | − | 0.552796i | \(-0.186439\pi\) |
−0.937033 | + | 0.349242i | \(0.886439\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.737533 | − | 0.897834i | 0.0375882 | − | 0.0457579i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.19929 | − | 9.02628i | 0.467626 | − | 0.458831i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.59921 | − | 4.79461i | −0.334593 | − | 0.243096i | 0.407784 | − | 0.913079i | \(-0.366302\pi\) |
−0.742377 | + | 0.669982i | \(0.766302\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.78900 | + | 7.11213i | −0.495051 | + | 0.359676i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.8825 | + | 29.5546i | 0.750724 | + | 1.49083i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 20.1661 | + | 11.8322i | 1.01467 | + | 0.595342i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.6243 | − | 14.0753i | −1.38642 | − | 0.706418i | −0.407991 | − | 0.912986i | \(-0.633771\pi\) |
−0.978432 | + | 0.206568i | \(0.933771\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.93363 | − | 0.638438i | −0.0968028 | − | 0.0319619i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.3238i | 1.51430i | 0.653241 | + | 0.757150i | \(0.273409\pi\) | ||||
−0.653241 | + | 0.757150i | \(0.726591\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.6963 | + | 32.7683i | −0.831700 | + | 1.63230i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13.0727 | + | 15.3005i | 0.649588 | + | 0.760287i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.04588 | − | 8.04588i | −0.398819 | − | 0.398819i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.2791 | − | 32.0409i | −1.15108 | − | 1.58432i | −0.739826 | − | 0.672798i | \(-0.765092\pi\) |
−0.411250 | − | 0.911523i | \(-0.634908\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.0117 | + | 19.4791i | 0.691144 | + | 0.960835i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.173046 | + | 1.09257i | −0.00851503 | + | 0.0537618i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.8936 | − | 30.3464i | 0.583836 | − | 1.48965i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18.0664 | − | 2.77360i | 0.884716 | − | 0.135824i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.71751 | − | 17.5967i | 0.279319 | − | 0.859655i | −0.708725 | − | 0.705484i | \(-0.750729\pi\) |
0.988044 | − | 0.154171i | \(-0.0492705\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.75964 | − | 20.8040i | −0.329445 | − | 1.01393i | −0.969394 | − | 0.245510i | \(-0.921045\pi\) |
0.639949 | − | 0.768417i | \(-0.278955\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.40020 | + | 4.38105i | 0.408432 | + | 0.213014i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.8096 | − | 34.8218i | −0.621358 | − | 1.68910i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.44415 | + | 0.228731i | −0.0698873 | + | 0.0110691i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 13.9121 | + | 0.0660339i | 0.671683 | + | 0.00318815i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.6284 | − | 8.32716i | −1.23447 | − | 0.401105i | −0.382141 | − | 0.924104i | \(-0.624813\pi\) |
−0.852333 | + | 0.522999i | \(0.824813\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.736984 | − | 0.375512i | 0.0354172 | − | 0.0180460i | −0.436192 | − | 0.899854i | \(-0.643673\pi\) |
0.471609 | + | 0.881808i | \(0.343673\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.74296 | + | 1.97745i | −0.371246 | + | 0.0948116i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.45431 | − | 0.863878i | −0.260915 | − | 0.0413249i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.6409 | − | 16.0224i | 0.555591 | − | 0.764705i | −0.435167 | − | 0.900350i | \(-0.643311\pi\) |
0.990758 | + | 0.135645i | \(0.0433105\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.6376 | − | 0.195917i | −0.982741 | − | 0.00932938i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.4453 | + | 26.4453i | −1.25645 | + | 1.25645i | −0.303677 | + | 0.952775i | \(0.598214\pi\) |
−0.952775 | + | 0.303677i | \(0.901786\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.75649 | + | 28.1213i | 0.130670 | + | 1.33308i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.91891 | + | 3.95629i | 0.185358 | + | 0.187126i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.7481 | −0.884779 | −0.442390 | − | 0.896823i | \(-0.645869\pi\) | ||||
−0.442390 | + | 0.896823i | \(0.645869\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.36515 | −0.299723 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.1286 | − | 16.2825i | −0.757790 | − | 0.765018i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.06801 | − | 0.894533i | −0.190711 | − | 0.0419364i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.650828 | − | 0.650828i | 0.0304444 | − | 0.0304444i | −0.691721 | − | 0.722165i | \(-0.743147\pi\) |
0.722165 | + | 0.691721i | \(0.243147\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12.4362 | + | 36.4981i | −0.580474 | + | 1.70359i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.6563 | + | 17.4199i | −0.589464 | + | 0.811328i | −0.994693 | − | 0.102888i | \(-0.967192\pi\) |
0.405229 | + | 0.914215i | \(0.367192\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.7819 | + | 4.40022i | 1.29113 | + | 0.204495i | 0.763961 | − | 0.645263i | \(-0.223252\pi\) |
0.527172 | + | 0.849758i | \(0.323252\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 24.6676 | + | 9.80328i | 1.14393 | + | 0.454616i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.7269 | − | 13.6180i | 1.23677 | − | 0.630168i | 0.291539 | − | 0.956559i | \(-0.405833\pi\) |
0.945235 | + | 0.326391i | \(0.105833\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.15890 | + | 1.35131i | 0.192040 | + | 0.0623977i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.4147 | + | 0.0779126i | 0.756351 | + | 0.00359002i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.35146 | + | 1.00597i | −0.292040 | + | 0.0462546i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.10373 | − | 15.3715i | 0.325942 | − | 0.705295i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.331191 | + | 0.635023i | −0.0151642 | + | 0.0290757i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.94946 | − | 27.5436i | −0.408911 | − | 1.25850i | −0.917585 | − | 0.397540i | \(-0.869864\pi\) |
0.508673 | − | 0.860960i | \(-0.330136\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.6046 | + | 38.7931i | −0.574722 | + | 1.76881i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.969048 | − | 0.148771i | 0.0440932 | − | 0.00676930i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.72775 | − | 6.63374i | −0.0784533 | − | 0.301223i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.59886 | − | 16.4086i | 0.117766 | − | 0.743544i | −0.856166 | − | 0.516701i | \(-0.827160\pi\) |
0.973931 | − | 0.226842i | \(-0.0728402\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.1918 | − | 14.1687i | −0.460889 | − | 0.640732i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.7228 | − | 28.5225i | −0.935207 | − | 1.28720i | −0.957793 | − | 0.287457i | \(-0.907190\pi\) |
0.0225861 | − | 0.999745i | \(-0.492810\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.8270 | − | 10.8270i | −0.487622 | − | 0.487622i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.884671 | − | 10.0024i | −0.0397630 | − | 0.449573i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.48655 | + | 4.88013i | −0.111537 | + | 0.218904i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.09564i | 0.138580i | 0.997597 | + | 0.0692900i | \(0.0220734\pi\) | ||||
−0.997597 | + | 0.0692900i | \(0.977927\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.0380 | + | 5.62553i | 0.761202 | + | 0.251330i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.58961 | + | 2.33852i | 0.204641 | + | 0.104270i | 0.553307 | − | 0.832977i | \(-0.313366\pi\) |
−0.348667 | + | 0.937247i | \(0.613366\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.61591 | + | 3.21016i | −0.160906 | + | 0.142850i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.3032 | − | 24.4325i | −0.546406 | − | 1.08508i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.3242 | − | 16.2195i | 0.989502 | − | 0.718915i | 0.0296898 | − | 0.999559i | \(-0.490548\pi\) |
0.959812 | + | 0.280644i | \(0.0905481\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.63036 | + | 2.63761i | 0.160598 | + | 0.116681i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −15.7920 | + | 7.76522i | −0.697236 | + | 0.342843i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 30.6044 | − | 7.97091i | 1.34859 | − | 0.351240i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.14609 | − | 4.21194i | −0.0943850 | − | 0.185241i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −30.3357 | − | 22.2609i | −1.33159 | − | 0.977147i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.0428 | − | 3.91295i | 0.527606 | − | 0.171430i | −0.0330883 | − | 0.999452i | \(-0.510534\pi\) |
0.560694 | + | 0.828023i | \(0.310534\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.21583 | − | 20.3040i | −0.140619 | − | 0.887831i | −0.952617 | − | 0.304172i | \(-0.901620\pi\) |
0.811999 | − | 0.583659i | \(-0.198380\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.370297 | + | 2.98342i | −0.0161611 | + | 0.130207i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.95605 | + | 50.2325i | 0.346571 | + | 2.18816i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.3457 | + | 6.28579i | −0.841116 | + | 0.273295i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.54542 | + | 7.78701i | 0.240651 | + | 0.337927i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.3589 | + | 20.3305i | 0.448695 | + | 0.880613i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.306447 | + | 5.15557i | −0.0132489 | + | 0.222895i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14.6270 | + | 28.3735i | −0.631204 | + | 1.22440i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.33112 | + | 6.05291i | 0.358847 | + | 0.260717i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.2522 | − | 16.8937i | 0.999689 | − | 0.726317i | 0.0376677 | − | 0.999290i | \(-0.488007\pi\) |
0.962022 | + | 0.272974i | \(0.0880072\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.42126 | − | 2.22638i | 0.189735 | − | 0.0955429i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.06577 | + | 9.39436i | −0.0884879 | + | 0.402410i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.4858 | − | 11.4571i | −0.961424 | − | 0.489870i | −0.0984630 | − | 0.995141i | \(-0.531393\pi\) |
−0.862961 | + | 0.505271i | \(0.831393\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.52399 | + | 10.1518i | −0.321116 | + | 0.433268i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 6.98813i | − | 0.297705i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.64789 | − | 3.23417i | 0.0700755 | − | 0.137531i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 28.7232 | + | 6.45916i | 1.21923 | + | 0.274176i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −26.1957 | − | 26.1957i | −1.10995 | − | 1.10995i | −0.993157 | − | 0.116791i | \(-0.962739\pi\) |
−0.116791 | − | 0.993157i | \(-0.537261\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.5497 | + | 18.6496i | 0.573093 | + | 0.788795i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.6184 | − | 11.2346i | 0.659411 | − | 0.474325i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.227603 | + | 1.43703i | −0.00959232 | + | 0.0605636i | −0.992020 | − | 0.126079i | \(-0.959761\pi\) |
0.982428 | + | 0.186643i | \(0.0597607\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.37701 | + | 5.35698i | −0.352423 | + | 0.225370i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.25072 | − | 2.16684i | 0.0945213 | − | 0.0909986i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.83577 | + | 24.1160i | −0.328493 | + | 1.01100i | 0.641347 | + | 0.767251i | \(0.278376\pi\) |
−0.969839 | + | 0.243745i | \(0.921624\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.23704 | − | 9.96258i | −0.135466 | − | 0.416921i | 0.860196 | − | 0.509963i | \(-0.170341\pi\) |
−0.995662 | + | 0.0930420i | \(0.970341\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.36757 | + | 26.7532i | −0.182458 | + | 1.11763i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.312499 | + | 8.14687i | 0.0130321 | + | 0.339748i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.5173 | + | 1.98255i | −0.521102 | + | 0.0825345i | −0.411444 | − | 0.911435i | \(-0.634976\pi\) |
−0.109658 | + | 0.993969i | \(0.534976\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.0838305 | − | 17.6615i | 0.00348388 | − | 0.733987i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.81239 | − | 1.56364i | −0.199651 | − | 0.0648707i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.318407 | − | 0.162237i | 0.0131871 | − | 0.00671915i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −30.5082 | + | 19.1040i | −1.26136 | + | 0.789852i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.7688 | + | 4.39815i | 1.14614 | + | 0.181531i | 0.700481 | − | 0.713671i | \(-0.252969\pi\) |
0.445661 | + | 0.895202i | \(0.352969\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.6434 | + | 18.7785i | −0.562167 | + | 0.773756i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 23.6491 | − | 7.56015i | 0.972795 | − | 0.310983i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.3288 | − | 16.3288i | 0.670545 | − | 0.670545i | −0.287297 | − | 0.957842i | \(-0.592757\pi\) |
0.957842 | + | 0.287297i | \(0.0927567\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.27839 | + | 2.30589i | −0.216393 | + | 0.0945322i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.3733 | + | 11.2659i | −0.465479 | + | 0.461081i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 37.1895 | 1.51952 | 0.759761 | − | 0.650202i | \(-0.225316\pi\) | ||||
0.759761 | + | 0.650202i | \(0.225316\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.85996 | −0.198242 | −0.0991209 | − | 0.995075i | \(-0.531603\pi\) | ||||
−0.0991209 | + | 0.995075i | \(0.531603\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 33.8336 | − | 16.8364i | 1.37781 | − | 0.685633i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.91190 | − | 16.8933i | 0.402976 | − | 0.686810i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.8944 | − | 17.8944i | 0.726313 | − | 0.726313i | −0.243570 | − | 0.969883i | \(-0.578319\pi\) |
0.969883 | + | 0.243570i | \(0.0783187\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.377773 | + | 1.18172i | 0.0153081 | + | 0.0478858i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.96046 | + | 13.7094i | −0.402957 | + | 0.554623i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.30092 | − | 1.47312i | −0.375661 | − | 0.0594988i | −0.0342506 | − | 0.999413i | \(-0.510904\pi\) |
−0.341410 | + | 0.939914i | \(0.610904\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13.9165 | − | 8.80662i | 0.561168 | − | 0.355117i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.21730 | − | 4.69645i | 0.371075 | − | 0.189072i | −0.258501 | − | 0.966011i | \(-0.583229\pi\) |
0.629576 | + | 0.776939i | \(0.283229\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.644785 | − | 0.209503i | −0.0259161 | − | 0.00842065i | 0.296030 | − | 0.955179i | \(-0.404337\pi\) |
−0.321946 | + | 0.946758i | \(0.604337\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.07723 | − | 6.78296i | 0.203742 | − | 0.272191i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.33261 | − | 0.686218i | 0.173582 | − | 0.0274927i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.2983 | − | 5.88137i | −0.971934 | − | 0.235255i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.66598 | + | 1.41475i | 0.346086 | + | 0.0564998i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 17.4310 | + | 53.6471i | 0.695020 | + | 2.13905i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.71397 | − | 23.7411i | 0.307088 | − | 0.945120i | −0.671802 | − | 0.740731i | \(-0.734479\pi\) |
0.978890 | − | 0.204389i | \(-0.0655207\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.78595 | + | 18.1468i | 0.110732 | + | 0.721272i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.4569 | − | 13.5187i | −0.653072 | − | 0.536471i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.77480 | − | 36.4607i | 0.228806 | − | 1.44462i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.1989 | + | 45.1537i | 0.561699 | + | 1.78625i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.2750 | + | 14.1423i | 0.405836 | + | 0.558586i | 0.962197 | − | 0.272355i | \(-0.0878027\pi\) |
−0.556361 | + | 0.830941i | \(0.687803\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.1067 | − | 11.1067i | −0.438005 | − | 0.438005i | 0.453335 | − | 0.891340i | \(-0.350234\pi\) |
−0.891340 | + | 0.453335i | \(0.850234\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.4947 | − | 10.9871i | 0.491980 | − | 0.432616i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.7527 | − | 21.1033i | 0.422730 | − | 0.829655i | −0.577185 | − | 0.816614i | \(-0.695849\pi\) |
0.999915 | − | 0.0130414i | \(-0.00415134\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 4.76996i | − | 0.187237i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.29200 | − | 3.91308i | 0.0506376 | − | 0.153366i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.4248 | − | 16.0117i | −1.22975 | − | 0.626587i | −0.286309 | − | 0.958137i | \(-0.592428\pi\) |
−0.943438 | + | 0.331550i | \(0.892428\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.1015 | + | 39.1468i | 0.668210 | + | 1.52959i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 38.3586 | − | 5.70269i | 1.49651 | − | 0.222483i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.78905 | − | 2.75290i | 0.147600 | − | 0.107238i | −0.511534 | − | 0.859263i | \(-0.670923\pi\) |
0.659135 | + | 0.752025i | \(0.270923\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.2635 | + | 16.1754i | 0.865950 | + | 0.629149i | 0.929497 | − | 0.368830i | \(-0.120241\pi\) |
−0.0635475 | + | 0.997979i | \(0.520241\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −61.3019 | − | 31.6023i | −2.38077 | − | 1.22733i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.44759 | − | 0.959281i | −0.0949134 | − | 0.0371993i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.52746 | + | 2.99780i | 0.0591433 | + | 0.116075i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.23867 | − | 8.50164i | 0.241201 | − | 0.328692i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.99632 | − | 1.94832i | 0.231485 | − | 0.0752142i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.35183 | − | 14.8489i | −0.0906565 | − | 0.572383i | −0.990644 | − | 0.136468i | \(-0.956425\pi\) |
0.899988 | − | 0.435915i | \(-0.143575\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 15.7732 | + | 20.6448i | 0.607110 | + | 0.794618i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.90476 | − | 12.0262i | −0.0732060 | − | 0.462204i | −0.996874 | − | 0.0790103i | \(-0.974824\pi\) |
0.923668 | − | 0.383194i | \(-0.125176\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.01213 | + | 0.328860i | −0.0388418 | + | 0.0126205i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.26659 | + | 5.81423i | −0.163496 | + | 0.222802i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.44981 | − | 4.80802i | −0.0937393 | − | 0.183974i | 0.839376 | − | 0.543551i | \(-0.182921\pi\) |
−0.933115 | + | 0.359578i | \(0.882921\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.6890 | + | 26.0976i | 0.637655 | + | 0.997136i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −30.2206 | − | 15.5793i | −1.15299 | − | 0.594387i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.03638 | − | 0.752974i | −0.0394829 | − | 0.0286860i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.6980 | − | 12.1318i | 0.635223 | − | 0.461517i | −0.222983 | − | 0.974822i | \(-0.571579\pi\) |
0.858206 | + | 0.513306i | \(0.171579\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.54193 | + | 0.229236i | −0.0585732 | + | 0.00870795i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 23.4843 | − | 2.30197i | 0.890811 | − | 0.0873188i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 28.1152 | + | 14.3254i | 1.06494 | + | 0.542614i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.98028 | − | 24.1698i | 0.301842 | − | 0.914187i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.7969i | 1.20095i | 0.799643 | + | 0.600475i | \(0.205022\pi\) | ||||
−0.799643 | + | 0.600475i | \(0.794978\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.6876 | + | 22.9382i | −0.440807 | + | 0.865132i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.5196 | + | 6.23955i | 0.396193 | + | 0.234995i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.530792 | + | 0.530792i | 0.0199625 | + | 0.0199625i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.36185 | − | 4.62719i | −0.126257 | − | 0.173778i | 0.741209 | − | 0.671274i | \(-0.234253\pi\) |
−0.867466 | + | 0.497497i | \(0.834253\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.40991 | − | 29.9243i | −0.352899 | − | 1.12225i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.74822 | − | 11.0379i | 0.0654715 | − | 0.413371i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.9290 | + | 1.06570i | 0.670507 | + | 0.0398549i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.75403 | − | 11.4252i | −0.0655055 | − | 0.426684i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.7159 | + | 32.9803i | −0.399637 | + | 1.22996i | 0.525654 | + | 0.850699i | \(0.323821\pi\) |
−0.925291 | + | 0.379258i | \(0.876179\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.51718 | − | 4.66939i | −0.0565027 | − | 0.173897i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 40.6401 | + | 6.63465i | 1.51142 | + | 0.246745i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.1206 | + | 2.00332i | −0.375869 | + | 0.0744015i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.83595 | − | 0.290786i | 0.0680916 | − | 0.0107847i | −0.122296 | − | 0.992494i | \(-0.539026\pi\) |
0.190387 | + | 0.981709i | \(0.439026\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.768825 | − | 26.9891i | 0.0284750 | − | 0.999595i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.3187 | + | 9.85116i | 1.12138 | + | 0.364358i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.2924 | + | 17.9824i | −1.30355 | + | 0.664194i | −0.961323 | − | 0.275423i | \(-0.911182\pi\) |
−0.342230 | + | 0.939616i | \(0.611182\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −26.5894 | − | 1.70716i | −0.980766 | − | 0.0629697i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.6242 | − | 2.94979i | −0.686033 | − | 0.108657i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.54039 | + | 6.24931i | −0.167021 | + | 0.229885i | −0.884321 | − | 0.466880i | \(-0.845378\pi\) |
0.717300 | + | 0.696765i | \(0.245378\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.58462 | − | 29.9819i | −0.352100 | − | 1.10141i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.7766 | + | 15.7766i | −0.578787 | + | 0.578787i | −0.934569 | − | 0.355782i | \(-0.884215\pi\) |
0.355782 | + | 0.934569i | \(0.384215\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.77289 | + | 5.37615i | 0.174865 | + | 0.196967i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −39.1498 | + | 19.4819i | −1.43242 | + | 0.712807i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.801789 | 0.0292967 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.4943 | 0.784340 | 0.392170 | − | 0.919893i | \(-0.371725\pi\) | ||||
0.392170 | + | 0.919893i | \(0.371725\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 32.7058 | − | 32.3967i | 1.19186 | − | 1.18060i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.6433 | − | 22.1261i | −0.714892 | − | 0.805250i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.2676 | − | 20.2676i | 0.736638 | − | 0.736638i | −0.235287 | − | 0.971926i | \(-0.575603\pi\) |
0.971926 | + | 0.235287i | \(0.0756031\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.02680 | + | 1.28729i | −0.146164 | + | 0.0467257i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.5073 | − | 36.4842i | 0.960890 | − | 1.32255i | 0.0143726 | − | 0.999897i | \(-0.495425\pi\) |
0.946517 | − | 0.322654i | \(-0.104575\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.47489 | + | 0.233599i | 0.0533945 | + | 0.00845686i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −18.6037 | + | 46.1720i | −0.672618 | + | 1.66935i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.2354 | + | 7.76285i | −0.550120 | + | 0.280300i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.9117 | + | 6.79462i | 0.754095 | + | 0.245020i | 0.660742 | − | 0.750613i | \(-0.270242\pi\) |
0.0933528 | + | 0.995633i | \(0.470242\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.116680 | − | 24.5822i | 0.00420212 | − | 0.885307i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.94871 | − | 0.308646i | 0.0700904 | − | 0.0111012i | −0.121291 | − | 0.992617i | \(-0.538703\pi\) |
0.191381 | + | 0.981516i | \(0.438703\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 31.1073 | + | 14.3758i | 1.11741 | + | 0.516393i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.736401 | − | 4.51078i | 0.0264182 | − | 0.161823i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.45022 | + | 13.6964i | 0.159446 | + | 0.490724i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.29826 | − | 22.4617i | 0.261152 | − | 0.803744i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.48282 | + | 5.00308i | 0.338888 | + | 0.178795i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21.1542 | + | 1.25741i | 0.755027 | + | 0.0448788i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.81634 | + | 24.0954i | −0.136038 | + | 0.858909i | 0.821418 | + | 0.570327i | \(0.193184\pi\) |
−0.957455 | + | 0.288582i | \(0.906816\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −32.5182 | + | 23.3909i | −1.15768 | + | 0.832737i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.907344 | + | 1.24885i | 0.0322614 | + | 0.0444041i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.9817 | − | 15.9817i | −0.567527 | − | 0.567527i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.471687 | + | 0.795245i | −0.0167290 | + | 0.0282044i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.9280 | + | 25.3725i | −0.457932 | + | 0.898742i | 0.540423 | + | 0.841394i | \(0.318264\pi\) |
−0.998354 | + | 0.0573478i | \(0.981736\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.4344i | 0.829048i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 22.5728 | − | 30.4565i | 0.797570 | − | 1.07613i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −17.2409 | − | 8.78466i | −0.608417 | − | 0.310004i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.25966 | − | 0.123473i | 0.0443970 | − | 0.00435187i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.0182 | + | 6.55547i | −0.458263 | + | 0.230764i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.51664 | − | 4.73462i | 0.229113 | − | 0.166460i | −0.467306 | − | 0.884095i | \(-0.654775\pi\) |
0.696419 | + | 0.717635i | \(0.254775\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.7314 | + | 18.6950i | 0.903552 | + | 0.656469i | 0.939376 | − | 0.342889i | \(-0.111405\pi\) |
−0.0358236 | + | 0.999358i | \(0.511405\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.2752 | + | 35.4502i | −0.640940 | + | 1.24329i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.1393 | − | 18.9828i | −0.425220 | − | 0.664940i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.60528 | + | 12.9636i | 0.231089 | + | 0.453538i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.24160 | + | 4.55193i | 0.113271 | + | 0.159057i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.3635 | + | 9.86569i | −1.05969 | + | 0.344315i | −0.786465 | − | 0.617635i | \(-0.788091\pi\) |
−0.273227 | + | 0.961950i | \(0.588091\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.65807 | − | 48.3511i | −0.266943 | − | 1.68541i | −0.648615 | − | 0.761116i | \(-0.724652\pi\) |
0.381672 | − | 0.924298i | \(-0.375348\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.435396 | − | 12.9561i | −0.0151585 | − | 0.451074i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.20579 | − | 32.8681i | −0.181023 | − | 1.14294i | −0.896088 | − | 0.443877i | \(-0.853603\pi\) |
0.715065 | − | 0.699058i | \(-0.246397\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.6047 | + | 10.9188i | −1.16714 | + | 0.379226i | −0.827574 | − | 0.561357i | \(-0.810280\pi\) |
−0.339564 | + | 0.940583i | \(0.610280\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.6677 | + | 11.4973i | 0.543507 | + | 0.398836i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −23.1763 | − | 45.4860i | −0.803011 | − | 1.57600i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.5667 | + | 8.45261i | 0.746345 | + | 0.292514i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −15.7144 | − | 31.9582i | −0.543170 | − | 1.10464i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.448091 | − | 0.325557i | −0.0154698 | − | 0.0112395i | 0.580023 | − | 0.814600i | \(-0.303043\pi\) |
−0.595493 | + | 0.803360i | \(0.703043\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.0170 | − | 14.5432i | 0.690243 | − | 0.501491i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.9699 | − | 23.7705i | −0.412265 | − | 0.818700i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.1376 | − | 32.3623i | −0.486349 | − | 1.11330i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.70928 | − | 1.38045i | −0.0930921 | − | 0.0474328i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.9885 | − | 4.61866i | −0.480084 | − | 0.158512i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 12.3948i | − | 0.424889i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.8598 | + | 42.9023i | −0.748466 | + | 1.46895i | 0.130188 | + | 0.991489i | \(0.458442\pi\) |
−0.878654 | + | 0.477458i | \(0.841558\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −20.9044 | + | 8.89682i | −0.714914 | + | 0.304265i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.1939 | + | 20.1939i | 0.689811 | + | 0.689811i | 0.962190 | − | 0.272379i | \(-0.0878104\pi\) |
−0.272379 | + | 0.962190i | \(0.587810\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.6355 | − | 16.0149i | −0.396998 | − | 0.546421i | 0.562989 | − | 0.826464i | \(-0.309651\pi\) |
−0.959987 | + | 0.280043i | \(0.909651\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.49297 | − | 2.07554i | −0.0508802 | − | 0.0707342i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.15711 | + | 19.9332i | −0.107469 | + | 0.678534i | 0.873857 | + | 0.486183i | \(0.161611\pi\) |
−0.981326 | + | 0.192351i | \(0.938389\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −37.5358 | − | 30.8341i | −1.27625 | − | 1.04839i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −65.1682 | + | 10.0048i | −2.21323 | + | 0.339780i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.83671 | + | 14.8859i | −0.164074 | + | 0.504969i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.8882 | + | 64.2872i | 0.707769 | + | 2.17829i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.25296 | + | 8.15459i | −0.143941 | + | 0.275991i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.687620 | + | 3.81973i | −0.0232458 | + | 0.129130i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.4522 | + | 2.13062i | −0.454249 | + | 0.0719460i | −0.379367 | − | 0.925246i | \(-0.623858\pi\) |
−0.0748823 | + | 0.997192i | \(0.523858\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.95067 | − | 0.0424844i | −0.301898 | − | 0.00143296i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.1299 | − | 8.16520i | −0.846648 | − | 0.275093i | −0.146607 | − | 0.989195i | \(-0.546835\pi\) |
−0.700041 | + | 0.714102i | \(0.746835\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.7538 | − | 5.98887i | 0.395547 | − | 0.201541i | −0.244892 | − | 0.969550i | \(-0.578752\pi\) |
0.640439 | + | 0.768009i | \(0.278752\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.59957 | + | 10.4289i | 0.221842 | + | 0.350562i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 46.6702 | + | 7.39183i | 1.56703 | + | 0.248193i | 0.878761 | − | 0.477261i | \(-0.158371\pi\) |
0.688270 | + | 0.725455i | \(0.258371\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.94341 | + | 2.67488i | −0.0651800 | + | 0.0897126i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.12412 | + | 10.7468i | −0.272168 | + | 0.360030i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.56271 | + | 7.56271i | −0.253076 | + | 0.253076i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.8551 | + | 35.5444i | −0.697111 | + | 1.18812i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.6650 | + | 10.7668i | 0.356096 | + | 0.359492i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.1418 | 0.471657 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.77155 | −0.0590189 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.81778 | − | 1.83512i | −0.0604920 | − | 0.0610690i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.85624 | − | 2.55832i | 0.194668 | − | 0.0850416i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.53014 | − | 2.53014i | 0.0840121 | − | 0.0840121i | −0.663852 | − | 0.747864i | \(-0.731079\pi\) |
0.747864 | + | 0.663852i | \(0.231079\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.48692 | + | 0.0615818i | 0.215157 | + | 0.00204254i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.4648 | + | 32.2965i | −0.777424 | + | 1.07003i | 0.218137 | + | 0.975918i | \(0.430002\pi\) |
−0.995561 | + | 0.0941143i | \(0.969998\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.5506 | + | 3.41329i | 0.713222 | + | 0.112963i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −10.4145 | + | 12.5561i | −0.344292 | + | 0.415090i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.90912 | − | 3.01085i | 0.195136 | − | 0.0994269i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.5675 | + | 9.28213i | 0.942354 | + | 0.306189i | 0.739605 | − | 0.673042i | \(-0.235012\pi\) |
0.202749 | + | 0.979231i | \(0.435012\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.59407 | − | 0.0170593i | −0.118429 | − | 0.000562123i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −83.6211 | + | 13.2443i | −2.75242 | + | 0.435941i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 36.5709 | + | 10.3508i | 1.20244 | + | 0.340333i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −37.6208 | − | 19.6208i | −1.23563 | − | 0.644432i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.5788 | + | 41.7913i | 0.445507 | + | 1.37113i | 0.881927 | + | 0.471386i | \(0.156246\pi\) |
−0.436420 | + | 0.899743i | \(0.643754\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.19977 | − | 22.1586i | 0.235963 | − | 0.726219i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −38.9303 | + | 5.97668i | −1.27452 | + | 0.195668i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 20.9251 | − | 13.3813i | 0.684324 | − | 0.437616i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.0688669 | − | 0.434808i | 0.00224978 | − | 0.0142046i | −0.986538 | − | 0.163533i | \(-0.947711\pi\) |
0.988788 | + | 0.149328i | \(0.0477111\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.6259 | − | 31.4548i | −0.738368 | − | 1.02649i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.63450 | − | 6.37884i | −0.151080 | − | 0.207944i | 0.726768 | − | 0.686883i | \(-0.241022\pi\) |
−0.877848 | + | 0.478939i | \(0.841022\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.90281 | − | 4.90281i | −0.159657 | − | 0.159657i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.05406 | − | 2.63456i | 0.0993485 | − | 0.0857023i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.6899 | − | 30.7932i | 0.509854 | − | 1.00065i | −0.482345 | − | 0.875982i | \(-0.660215\pi\) |
0.992199 | − | 0.124664i | \(-0.0397853\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 69.3645i | 2.25167i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.37633 | + | 1.77513i | 0.174339 | + | 0.0575626i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.6912 | + | 20.7332i | 1.31812 | + | 0.671615i | 0.964576 | − | 0.263804i | \(-0.0849771\pi\) |
0.353542 | + | 0.935419i | \(0.384977\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.51576 | + | 34.1789i | −0.243204 | + | 1.10600i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.40607 | − | 4.77811i | −0.0777772 | − | 0.154454i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.89065 | − | 2.82672i | 0.125636 | − | 0.0912796i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.9225 | − | 9.38873i | −0.416854 | − | 0.302862i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.94592 | − | 4.85290i | 0.159380 | − | 0.156382i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.35291 | − | 22.7610i | 0.0435518 | − | 0.732702i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.1811 | − | 47.4582i | −0.777613 | − | 1.52615i | −0.848815 | − | 0.528690i | \(-0.822684\pi\) |
0.0712023 | − | 0.997462i | \(-0.477316\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −35.0940 | − | 25.7527i | −1.12738 | − | 0.827296i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −44.7462 | + | 14.5389i | −1.43597 | + | 0.466576i | −0.920640 | − | 0.390413i | \(-0.872332\pi\) |
−0.515334 | + | 0.856989i | \(0.672332\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.573066 | − | 3.61820i | −0.0183717 | − | 0.115994i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −40.6737 | + | 22.4760i | −1.30260 | + | 0.719808i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.14152 | − | 7.20725i | −0.0365203 | − | 0.230580i | 0.962676 | − | 0.270655i | \(-0.0872403\pi\) |
−0.999197 | + | 0.0400750i | \(0.987240\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.9896 | + | 5.84518i | −0.574951 | + | 0.186813i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.5119 | − | 7.48591i | 0.335619 | − | 0.239007i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.79016 | + | 17.2517i | 0.280363 | + | 0.550243i | 0.987649 | − | 0.156685i | \(-0.0500807\pi\) |
−0.707286 | + | 0.706928i | \(0.750081\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 31.0182 | − | 8.07868i | 0.988322 | − | 0.257408i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.870052 | − | 1.68772i | 0.0276940 | − | 0.0537207i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.66712 | − | 4.11740i | −0.180204 | − | 0.130926i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.6053 | + | 25.1423i | −1.09927 | + | 0.798670i | −0.980941 | − | 0.194304i | \(-0.937755\pi\) |
−0.118333 | + | 0.992974i | \(0.537755\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25.8801 | − | 13.0322i | 0.821282 | − | 0.413565i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.4550 | + | 13.7208i | −0.489958 | + | 0.434980i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.6440 | + | 7.46148i | 0.463779 | + | 0.236307i | 0.670236 | − | 0.742148i | \(-0.266193\pi\) |
−0.206456 | + | 0.978456i | \(0.566193\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −22.7593 | − | 32.2824i | −0.720073 | − | 1.02137i |
(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 | 300.2.x.a.113.3 | yes | 80 | |
3.2 | odd | 2 | inner | 300.2.x.a.113.9 | yes | 80 | |
25.2 | odd | 20 | inner | 300.2.x.a.77.9 | yes | 80 | |
75.2 | even | 20 | inner | 300.2.x.a.77.3 | ✓ | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.x.a.77.3 | ✓ | 80 | 75.2 | even | 20 | inner | |
300.2.x.a.77.9 | yes | 80 | 25.2 | odd | 20 | inner | |
300.2.x.a.113.3 | yes | 80 | 1.1 | even | 1 | trivial | |
300.2.x.a.113.9 | yes | 80 | 3.2 | odd | 2 | inner |