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 | 113.9 | ||
Character | \(\chi\) | \(=\) | 300.113 |
Dual form | 300.2.x.a.77.9 |
$q$-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 | ||||||||
\(3\) | 1.71199 | + | 0.262830i | 0.988420 | + | 0.151745i | ||||
\(4\) | 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 | ||||||||
\(9\) | 2.86184 | + | 0.899925i | 0.953947 | + | 0.299975i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.879848 | + | 1.21101i | −0.265284 | + | 0.365132i | −0.920791 | − | 0.390057i | \(-0.872455\pi\) |
0.655506 | + | 0.755190i | \(0.272455\pi\) | |||||||
\(12\) | 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 | ||||||||
\(15\) | 2.10202 | + | 3.25292i | 0.542739 | + | 0.839901i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.61182 | − | 3.36889i | 1.60360 | − | 0.817077i | 0.603802 | − | 0.797134i | \(-0.293652\pi\) |
0.999801 | − | 0.0199422i | \(-0.00634822\pi\) | |||||||
\(18\) | 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 | ||||||||
\(21\) | −0.484748 | + | 0.355717i | −0.105781 | + | 0.0776239i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.61050 | + | 0.255078i | −0.335812 | + | 0.0531874i | −0.322063 | − | 0.946718i | \(-0.604376\pi\) |
−0.0137486 | + | 0.999905i | \(0.504376\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.592307 | + | 4.96479i | −0.118461 | + | 0.992959i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.66293 | + | 2.29284i | 0.897381 | + | 0.441257i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.637623 | − | 1.96240i | −0.118404 | − | 0.364409i | 0.874238 | − | 0.485497i | \(-0.161361\pi\) |
−0.992642 | + | 0.121089i | \(0.961361\pi\) | |||||||
\(30\) | 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 | ||||||||
\(33\) | −1.82458 | + | 1.84199i | −0.317619 | + | 0.320649i | ||||
\(34\) | 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 | ||||||||
\(39\) | −8.85278 | − | 2.83006i | −1.41758 | − | 0.453172i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.49942 | + | 3.44015i | 0.390343 | + | 0.537261i | 0.958288 | − | 0.285806i | \(-0.0922612\pi\) |
−0.567944 | + | 0.823067i | \(0.692261\pi\) | |||||||
\(42\) | 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 | ||||||||
\(45\) | 2.74368 | + | 6.12146i | 0.409003 | + | 0.912533i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.43370 | + | 2.81380i | −0.209127 | + | 0.410435i | −0.971615 | − | 0.236567i | \(-0.923978\pi\) |
0.762488 | + | 0.647002i | \(0.223978\pi\) | |||||||
\(48\) | 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 | 0.439320 | − | 0.898330i | \(-0.355219\pi\) |
−0.468539 | + | 0.883443i | \(0.655219\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.33118 | + | 0.326527i | −0.449176 | + | 0.0440289i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.23920 | − | 2.63826i | −0.693950 | − | 0.349446i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.57801 | + | 1.87303i | −0.335628 | + | 0.243848i | −0.742815 | − | 0.669497i | \(-0.766510\pi\) |
0.407187 | + | 0.913345i | \(0.366510\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | −0.923378 | + | 0.481580i | −0.116335 | + | 0.0606734i | ||||
\(64\) | 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 | ||||||||
\(69\) | −2.82420 | + | 0.0134051i | −0.339994 | + | 0.00161379i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.0056 | + | 4.87563i | −1.78084 | + | 0.578630i | −0.998994 | − | 0.0448405i | \(-0.985722\pi\) |
−0.781847 | + | 0.623471i | \(0.785722\pi\) | |||||||
\(72\) | 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 | ||||||||
\(75\) | −2.31892 | + | 8.34402i | −0.267766 | + | 0.963484i | ||||
\(76\) | 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 | ||||||||
\(81\) | 7.38027 | + | 5.15088i | 0.820030 | + | 0.572320i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.61756 | − | 12.9877i | −0.726372 | − | 1.42559i | −0.897807 | − | 0.440390i | \(-0.854840\pi\) |
0.171434 | − | 0.985196i | \(-0.445160\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 15.4489 | + | 6.05486i | 1.67566 | + | 0.656741i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.575829 | − | 3.52720i | −0.0617354 | − | 0.378156i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.2231 | + | 7.42754i | 1.08365 | + | 0.787318i | 0.978316 | − | 0.207119i | \(-0.0664086\pi\) |
0.105335 | + | 0.994437i | \(0.466409\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.50698 | − | 1.09489i | 0.157975 | − | 0.114775i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.33903 | − | 10.6025i | 0.553632 | − | 1.09943i | ||||
\(94\) | 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 | \(0.0343113\pi\) | ||||
−0.994196 | + | 0.107584i | \(0.965689\pi\) | |||||||
\(102\) | 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 | ||||||||
\(105\) | −1.31445 | − | 0.282506i | −0.128277 | − | 0.0275697i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.63321 | + | 1.63321i | 0.157888 | + | 0.157888i | 0.781630 | − | 0.623742i | \(-0.214388\pi\) |
−0.623742 | + | 0.781630i | \(0.714388\pi\) | |||||||
\(108\) | 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 | ||||||||
\(111\) | 4.00910 | − | 12.5410i | 0.380527 | − | 1.19034i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.695637 | + | 4.39208i | −0.0654401 | + | 0.413172i | 0.933122 | + | 0.359560i | \(0.117073\pi\) |
−0.998562 | + | 0.0536118i | \(0.982927\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.81738 | − | 2.31436i | −0.262722 | − | 0.215815i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −14.4121 | − | 7.17181i | −1.33240 | − | 0.663034i | ||||
\(118\) | 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 | ||||||||
\(123\) | 3.37481 | + | 6.54643i | 0.304296 | + | 0.590272i | ||||
\(124\) | 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 | ||||||||
\(129\) | −4.40217 | − | 5.99898i | −0.387590 | − | 0.528181i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.1696 | + | 5.90366i | 1.58748 | + | 0.515805i | 0.963971 | − | 0.266007i | \(-0.0857045\pi\) |
0.623514 | + | 0.781812i | \(0.285705\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.04752 | − | 0.533739i | 0.0908317 | − | 0.0462811i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.08826 | + | 11.2010i | 0.265795 | + | 0.964030i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.6830 | + | 2.16717i | 1.16902 | + | 0.185154i | 0.710609 | − | 0.703587i | \(-0.248420\pi\) |
0.458409 | + | 0.888741i | \(0.348420\pi\) | |||||||
\(138\) | 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 | ||||||||
\(141\) | −3.19404 | + | 4.44039i | −0.268987 | + | 0.373948i | ||||
\(142\) | 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 | ||||||||
\(147\) | −1.80813 | + | 11.7776i | −0.149132 | + | 0.971404i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.21507 | 0.263389 | 0.131695 | − | 0.991290i | \(-0.457958\pi\) | ||||
0.131695 | + | 0.991290i | \(0.457958\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.2319 | 1.07680 | 0.538400 | − | 0.842689i | \(-0.319029\pi\) | ||||
0.538400 | + | 0.842689i | \(0.319029\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 21.9537 | − | 3.69109i | 1.77485 | − | 0.298407i | ||||
\(154\) | 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 | ||||||||
\(159\) | −0.335677 | − | 0.241458i | −0.0266209 | − | 0.0191488i | ||||
\(160\) | 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 | ||||||||
\(165\) | −5.78877 | − | 0.316519i | −0.450655 | − | 0.0246410i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.23014 | − | 4.70299i | 0.714249 | − | 0.363928i | −0.0588037 | − | 0.998270i | \(-0.518729\pi\) |
0.773053 | + | 0.634341i | \(0.218729\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.0206 | + | 4.88050i | 1.15543 | + | 0.375423i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.27607 | − | 5.89370i | −0.632887 | − | 0.450703i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −21.4566 | + | 3.39839i | −1.63132 | + | 0.258375i | −0.903875 | − | 0.427796i | \(-0.859290\pi\) |
−0.727440 | + | 0.686171i | \(0.759290\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.07329 | − | 1.36407i | −0.0811329 | − | 0.103114i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.90582 | + | 2.52904i | −0.368744 | + | 0.190094i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.69521 | + | 17.5280i | 0.425680 | + | 1.31011i | 0.902342 | + | 0.431021i | \(0.141847\pi\) |
−0.476662 | + | 0.879087i | \(0.658153\pi\) | |||||||
\(180\) | 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 | ||||||||
\(183\) | 5.18307 | + | 5.13410i | 0.383143 | + | 0.379523i | ||||
\(184\) | 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 | ||||||||
\(189\) | −1.70739 | + | 0.581770i | −0.124194 | + | 0.0423176i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.19912 | + | 12.6615i | 0.665625 | + | 0.916154i | 0.999651 | − | 0.0264098i | \(-0.00840749\pi\) |
−0.334026 | + | 0.942564i | \(0.608407\pi\) | |||||||
\(192\) | 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 | ||||||||
\(195\) | −8.40992 | − | 19.0047i | −0.602247 | − | 1.36095i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.50774 | − | 12.7722i | 0.463657 | − | 0.909979i | −0.534250 | − | 0.845326i | \(-0.679406\pi\) |
0.997908 | − | 0.0646527i | \(-0.0205940\pi\) | |||||||
\(198\) | 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 | ||||||||
\(207\) | −4.83854 | − | 0.719335i | −0.336302 | − | 0.0499972i | ||||
\(208\) | 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 | ||||||||
\(213\) | −26.9710 | + | 4.40311i | −1.84802 | + | 0.301696i | ||||
\(214\) | 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 | ||||||||
\(219\) | −0.106272 | − | 22.3895i | −0.00718120 | − | 1.51294i | ||||
\(220\) | 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 | ||||||||
\(225\) | −6.16303 | + | 13.6754i | −0.410869 | + | 0.911695i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.651345 | + | 4.11243i | 0.0432313 | + | 0.272952i | 0.999830 | − | 0.0184580i | \(-0.00587571\pi\) |
−0.956598 | + | 0.291410i | \(0.905876\pi\) | |||||||
\(228\) | 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 | ||||||||
\(231\) | −0.00427191 | − | 0.900010i | −0.000281071 | − | 0.0592163i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.67158 | − | 13.0937i | −0.437070 | − | 0.857797i | −0.999520 | − | 0.0309667i | \(-0.990141\pi\) |
0.562451 | − | 0.826831i | \(-0.309859\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.83354 | + | 1.77979i | −0.445771 | + | 0.116101i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −17.8743 | + | 2.91804i | −1.16106 | + | 0.189547i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.39910 | − | 3.92267i | −0.349239 | − | 0.253737i | 0.399311 | − | 0.916816i | \(-0.369249\pi\) |
−0.748550 | + | 0.663079i | \(0.769249\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | 11.2812 | + | 10.7580i | 0.723687 | + | 0.690128i | ||||
\(244\) | 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 | \(-0.683256\pi\) | ||
0.544435 | − | 0.838803i | \(-0.316744\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.10809 | − | 2.17475i | 0.0696652 | − | 0.136726i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 24.8569 | + | 14.4263i | 1.55660 | + | 0.903409i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.0358 | − | 10.0358i | −0.626014 | − | 0.626014i | 0.321049 | − | 0.947063i | \(-0.395965\pi\) |
−0.947063 | + | 0.321049i | \(0.895965\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.55103 | + | 2.13481i | 0.0963765 | + | 0.132651i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.0587621 | − | 6.18989i | −0.00363728 | − | 0.383145i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.61785 | + | 22.8422i | −0.223086 | + | 1.40851i | 0.580954 | + | 0.813937i | \(0.302680\pi\) |
−0.804040 | + | 0.594575i | \(0.797320\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.134546 | − | 0.516590i | −0.00826508 | − | 0.0317339i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.5498 | + | 15.4028i | 0.951630 | + | 0.942639i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.60045 | + | 8.00336i | −0.158552 | + | 0.487974i | −0.998503 | − | 0.0546882i | \(-0.982584\pi\) |
0.839951 | + | 0.542662i | \(0.182584\pi\) | |||||||
\(270\) | 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 | ||||||||
\(273\) | 2.86771 | − | 1.47836i | 0.173562 | − | 0.0894744i | ||||
\(274\) | 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 | ||||||||
\(279\) | 11.9270 | − | 16.7482i | 0.714053 | − | 1.00269i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.6137 | − | 4.74827i | −0.871778 | − | 0.283258i | −0.161239 | − | 0.986915i | \(-0.551549\pi\) |
−0.710539 | + | 0.703658i | \(0.751549\pi\) | |||||||
\(282\) | 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 | ||||||||
\(285\) | −3.36617 | − | 12.6774i | −0.199395 | − | 0.750946i | ||||
\(286\) | 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 | ||||||||
\(291\) | 4.31056 | + | 3.10065i | 0.252690 | + | 0.181764i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.65414 | + | 3.65414i | −0.213477 | + | 0.213477i | −0.805743 | − | 0.592266i | \(-0.798234\pi\) |
0.592266 | + | 0.805743i | \(0.298234\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.95917 | − | 1.53028i | −0.405178 | − | 0.0890966i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.87931 | + | 3.62948i | −0.399178 | + | 0.210604i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.74960 | 0.506003 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.49131 | 0.0859575 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.568343 | + | 3.70202i | −0.0326505 | + | 0.212675i | ||||
\(304\) | 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 | ||||||||
\(309\) | −14.3047 | + | 19.8866i | −0.813767 | + | 1.13131i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.3661 | + | 18.3969i | −0.757922 | + | 1.04319i | 0.239462 | + | 0.970906i | \(0.423029\pi\) |
−0.997384 | + | 0.0722845i | \(0.976971\pi\) | |||||||
\(312\) | 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 | ||||||||
\(315\) | −2.17607 | − | 0.829123i | −0.122608 | − | 0.0467158i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.91256 | − | 1.48402i | 0.163586 | − | 0.0833510i | −0.370281 | − | 0.928920i | \(-0.620739\pi\) |
0.533866 | + | 0.845569i | \(0.320739\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.93749 | + | 0.954449i | 0.164468 | + | 0.0534389i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.36679 | + | 3.22530i | 0.132101 | + | 0.180019i | ||||
\(322\) | 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 | ||||||||
\(327\) | −3.41402 | − | 6.62249i | −0.188796 | − | 0.366225i | ||||
\(328\) | 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 | ||||||||
\(333\) | 10.1597 | − | 20.4163i | 0.556747 | − | 1.11881i | ||||
\(334\) | 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 | ||||||||
\(339\) | −2.34529 | + | 7.33638i | −0.127379 | + | 0.398457i | ||||
\(340\) | 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 | ||||||||
\(345\) | −4.21505 | − | 4.70265i | −0.226931 | − | 0.253182i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.905384 | − | 1.77692i | 0.0486036 | − | 0.0953899i | −0.865427 | − | 0.501035i | \(-0.832953\pi\) |
0.914031 | + | 0.405645i | \(0.132953\pi\) | |||||||
\(348\) | 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 | 0.726535 | − | 0.687129i | \(-0.241129\pi\) |
−0.128853 | + | 0.991664i | \(0.541129\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −30.4293 | − | 17.8539i | −1.61502 | − | 0.947588i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.00669 | + | 3.98501i | −0.106205 | + | 0.210909i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.9247 | − | 10.8434i | 0.787695 | − | 0.572294i | −0.119583 | − | 0.992824i | \(-0.538156\pi\) |
0.907279 | + | 0.420530i | \(0.138156\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.09198 | − | 4.42609i | −0.320631 | − | 0.232952i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.44446 | + | 14.9734i | 0.128301 | + | 0.785899i | ||||
\(364\) | 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 | ||||||||
\(369\) | 4.05705 | + | 12.0945i | 0.211202 | + | 0.629612i | ||||
\(370\) | 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 | ||||||||
\(375\) | −17.3951 | + | 8.50936i | −0.898281 | + | 0.439421i | ||||
\(376\) | 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 | ||||||||
\(381\) | 16.4968 | − | 0.0783022i | 0.845156 | − | 0.00401154i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.02976 | + | 3.98364i | 0.103716 | + | 0.203554i | 0.937033 | − | 0.349242i | \(-0.113561\pi\) |
−0.833317 | + | 0.552796i | \(0.813561\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.737533 | − | 0.897834i | 0.0375882 | − | 0.0457579i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.95978 | − | 11.4272i | −0.302952 | − | 0.580879i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.59921 | + | 4.79461i | 0.334593 | + | 0.243096i | 0.742377 | − | 0.669982i | \(-0.233698\pi\) |
−0.407784 | + | 0.913079i | \(0.633698\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.78900 | + | 7.11213i | −0.495051 | + | 0.359676i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 29.5546 | + | 14.8825i | 1.49083 | + | 0.750724i | ||||
\(394\) | 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 | \(-0.726591\pi\) | ||
0.653241 | − | 0.757150i | \(-0.273409\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.6963 | + | 32.7683i | −0.831700 | + | 1.63230i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.34312 | + | 19.9877i | 0.116431 | + | 0.993199i | ||||
\(406\) | 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 | ||||||||
\(411\) | 22.8556 | + | 7.30648i | 1.12738 | + | 0.360402i | ||||
\(412\) | 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 | ||||||||
\(417\) | −12.8631 | + | 12.9857i | −0.629906 | + | 0.635915i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.71751 | + | 17.5967i | −0.279319 | + | 0.859655i | 0.708725 | + | 0.705484i | \(0.249271\pi\) |
−0.988044 | + | 0.154171i | \(0.950729\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | −6.63524 | + | 6.76243i | −0.322617 | + | 0.328801i | ||||
\(424\) | 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 | ||||||||
\(429\) | 11.2163 | − | 8.23075i | 0.541529 | − | 0.397384i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.6284 | + | 8.32716i | 1.23447 | + | 0.401105i | 0.852333 | − | 0.522999i | \(-0.175187\pi\) |
0.382141 | + | 0.924104i | \(0.375187\pi\) | |||||||
\(432\) | 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 | ||||||||
\(435\) | 5.04325 | − | 6.19914i | 0.241805 | − | 0.297226i | ||||
\(436\) | 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 | ||||||||
\(441\) | −6.19103 | + | 19.6880i | −0.294811 | + | 0.937525i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.4453 | − | 26.4453i | 1.25645 | − | 1.25645i | 0.303677 | − | 0.952775i | \(-0.401786\pi\) |
0.952775 | − | 0.303677i | \(-0.0982142\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.75649 | + | 28.1213i | 0.130670 | + | 1.33308i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.50418 | + | 0.845016i | 0.260339 | + | 0.0399679i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.7481 | 0.884779 | 0.442390 | − | 0.896823i | \(-0.354131\pi\) | ||||
0.442390 | + | 0.896823i | \(0.354131\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.36515 | −0.299723 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 22.6530 | + | 3.47774i | 1.06433 | + | 0.163399i | ||||
\(454\) | 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 | ||||||||
\(459\) | 38.5548 | − | 0.549035i | 1.79958 | − | 0.0256268i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.6563 | − | 17.4199i | 0.589464 | − | 0.811328i | −0.405229 | − | 0.914215i | \(-0.632808\pi\) |
0.994693 | + | 0.102888i | \(0.0328082\pi\) | |||||||
\(462\) | 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 | ||||||||
\(465\) | 25.6552 | − | 6.81209i | 1.18973 | − | 0.315903i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −26.7269 | + | 13.6180i | −1.23677 | + | 0.630168i | −0.945235 | − | 0.326391i | \(-0.894167\pi\) |
−0.291539 | + | 0.956559i | \(0.594167\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.15890 | + | 1.35131i | 0.192040 | + | 0.0623977i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.2340 | + | 9.71137i | −0.609790 | + | 0.447476i | ||||
\(472\) | 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 | ||||||||
\(477\) | −0.511214 | − | 0.501600i | −0.0234069 | − | 0.0229667i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.94946 | + | 27.5436i | 0.408911 | + | 1.25850i | 0.917585 | + | 0.397540i | \(0.130136\pi\) |
−0.508673 | + | 0.860960i | \(0.669864\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.6046 | + | 38.7931i | −0.574722 | + | 1.76881i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.689950 | − | 0.696531i | 0.0313938 | − | 0.0316932i | ||||
\(484\) | 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 | ||||||||
\(489\) | 16.6247 | + | 5.31459i | 0.751795 | + | 0.240334i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.7228 | + | 28.5225i | 0.935207 | + | 1.28720i | 0.957793 | + | 0.287457i | \(0.0928100\pi\) |
−0.0225861 | + | 0.999745i | \(0.507190\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.8270 | − | 10.8270i | −0.487622 | − | 0.487622i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.82715 | − | 2.06334i | −0.441697 | − | 0.0927401i | ||||
\(496\) | 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 | 0.348667 | − | 0.937247i | \(-0.386634\pi\) |
−0.553307 | + | 0.832977i | \(0.686634\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.61591 | + | 3.21016i | −0.160906 | + | 0.142850i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 24.4325 | + | 12.3032i | 1.08508 | + | 0.546406i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.3242 | + | 16.2195i | −0.989502 | + | 0.718915i | −0.959812 | − | 0.280644i | \(-0.909452\pi\) |
−0.0296898 | + | 0.999559i | \(0.509452\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.63036 | + | 2.63761i | 0.160598 | + | 0.116681i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.6195 | − | 12.2652i | −0.557166 | − | 0.541521i | ||||
\(514\) | 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 | ||||||||
\(519\) | −37.6268 | + | 0.178596i | −1.65163 | + | 0.00783948i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.0428 | + | 3.91295i | −0.527606 | + | 0.171430i | −0.560694 | − | 0.828023i | \(-0.689466\pi\) |
0.0330883 | + | 0.999452i | \(0.489466\pi\) | |||||||
\(522\) | 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 | ||||||||
\(525\) | −1.47894 | − | 2.61737i | −0.0645464 | − | 0.114231i | ||||
\(526\) | 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 | ||||||||
\(531\) | −9.06343 | + | 3.04031i | −0.393319 | + | 0.131938i | ||||
\(532\) | 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 | ||||||||
\(537\) | 5.14327 | + | 31.5048i | 0.221948 | + | 1.35953i | ||||
\(538\) | 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 | ||||||||
\(543\) | −2.22638 | + | 4.42126i | −0.0955429 | + | 0.189735i | ||||
\(544\) | 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 | ||||||||
\(555\) | 26.9223 | − | 11.9136i | 1.14279 | − | 0.505705i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.1957 | + | 26.1957i | 1.10995 | + | 1.10995i | 0.993157 | + | 0.116791i | \(0.0372606\pi\) |
0.116791 | + | 0.993157i | \(0.462739\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.5497 | + | 18.6496i | 0.573093 | + | 0.788795i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.85837 | + | 18.3257i | −0.247340 | + | 0.773712i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.227603 | − | 1.43703i | 0.00959232 | − | 0.0605636i | −0.982428 | − | 0.186643i | \(-0.940239\pi\) |
0.992020 | + | 0.126079i | \(0.0402393\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.37701 | + | 5.35698i | −0.352423 | + | 0.225370i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.07595 | + | 0.547235i | −0.129178 | + | 0.0229817i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.83577 | − | 24.1160i | 0.328493 | − | 1.01100i | −0.641347 | − | 0.767251i | \(-0.721624\pi\) |
0.969839 | − | 0.243745i | \(-0.0783761\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | 12.4210 | + | 24.0942i | 0.518895 | + | 1.00655i | ||||
\(574\) | 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 | ||||||||
\(579\) | 10.4490 | + | 14.2392i | 0.434245 | + | 0.591760i | ||||
\(580\) | 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 | ||||||||
\(585\) | −9.40274 | − | 34.7462i | −0.388756 | − | 1.43658i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.7688 | − | 4.39815i | −1.14614 | − | 0.181531i | −0.445661 | − | 0.895202i | \(-0.647031\pi\) |
−0.700481 | + | 0.713671i | \(0.747031\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.6434 | + | 18.7785i | −0.562167 | + | 0.773756i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.4981 | − | 20.1554i | 0.596373 | − | 0.829084i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16.3288 | + | 16.3288i | −0.670545 | + | 0.670545i | −0.957842 | − | 0.287297i | \(-0.907243\pi\) |
0.287297 | + | 0.957842i | \(0.407243\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.27839 | + | 2.30589i | −0.216393 | + | 0.0945322i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.42920 | − | 15.8231i | 0.0994207 | − | 0.647597i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.1895 | −1.51952 | −0.759761 | − | 0.650202i | \(-0.774684\pi\) | ||||
−0.759761 | + | 0.650202i | \(0.774684\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.85996 | −0.198242 | −0.0991209 | − | 0.995075i | \(-0.531603\pi\) | ||||
−0.0991209 | + | 0.995075i | \(0.531603\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.26591 | − | 37.2682i | −0.255168 | − | 1.51768i | ||||
\(604\) | 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 | ||||||||
\(609\) | 1.00715 | + | 0.724456i | 0.0408117 | + | 0.0293565i | ||||
\(610\) | 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 | ||||||||
\(615\) | −5.93673 | + | 15.3617i | −0.239392 | + | 0.619442i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.21730 | + | 4.69645i | −0.371075 | + | 0.189072i | −0.629576 | − | 0.776939i | \(-0.716771\pi\) |
0.258501 | + | 0.966011i | \(0.416771\pi\) | |||||||
\(618\) | 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 | ||||||||
\(621\) | −8.09449 | − | 2.50321i | −0.324821 | − | 0.100450i | ||||
\(622\) | 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 | ||||||||
\(627\) | 7.80465 | − | 4.02345i | 0.311688 | − | 0.160681i | ||||
\(628\) | 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 | ||||||||
\(633\) | −13.0436 | − | 12.9203i | −0.518435 | − | 0.513537i | ||||
\(634\) | 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 | ||||||||
\(639\) | −47.3314 | + | 0.449328i | −1.87240 | + | 0.0177751i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.2750 | − | 14.1423i | −0.405836 | − | 0.558586i | 0.556361 | − | 0.830941i | \(-0.312197\pi\) |
−0.962197 | + | 0.272355i | \(0.912197\pi\) | |||||||
\(642\) | 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 | ||||||||
\(645\) | 3.49614 | − | 16.2669i | 0.137660 | − | 0.640508i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.7527 | + | 21.1033i | −0.422730 | + | 0.829655i | 0.577185 | + | 0.816614i | \(0.304151\pi\) |
−0.999915 | + | 0.0130414i | \(0.995849\pi\) | |||||||
\(648\) | 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 | 0.943438 | − | 0.331550i | \(-0.107572\pi\) |
0.286309 | + | 0.958137i | \(0.407572\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.1015 | + | 39.1468i | 0.668210 | + | 1.52959i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.70269 | − | 38.3586i | 0.222483 | − | 1.49651i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.78905 | + | 2.75290i | −0.147600 | + | 0.107238i | −0.659135 | − | 0.752025i | \(-0.729077\pi\) |
0.511534 | + | 0.859263i | \(0.329077\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | −68.0672 | + | 11.1122i | −2.64351 | + | 0.431563i | ||||
\(664\) | 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 | ||||||||
\(669\) | 0.0500518 | + | 10.5450i | 0.00193511 | + | 0.407692i | ||||
\(670\) | 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 | ||||||||
\(675\) | −14.1454 | + | 21.7924i | −0.544455 | + | 0.838790i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.90476 | + | 12.0262i | 0.0732060 | + | 0.462204i | 0.996874 | + | 0.0790103i | \(0.0251760\pi\) |
−0.923668 | + | 0.383194i | \(0.874824\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.01213 | + | 0.328860i | −0.0388418 | + | 0.0126205i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.0342301 | + | 7.21165i | 0.00131170 | + | 0.276351i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.44981 | + | 4.80802i | 0.0937393 | + | 0.183974i | 0.933115 | − | 0.359578i | \(-0.117079\pi\) |
−0.839376 | + | 0.543551i | \(0.817079\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.6890 | + | 26.0976i | 0.637655 | + | 0.997136i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 33.5558 | − | 5.47810i | 1.28023 | − | 0.209003i | ||||
\(688\) | 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 | ||||||||
\(693\) | 0.229236 | − | 1.54193i | 0.00870795 | − | 0.0585732i | ||||
\(694\) | 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 | \(-0.794978\pi\) | ||
0.799643 | − | 0.600475i | \(-0.205022\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.6876 | + | 22.9382i | −0.440807 | + | 0.865132i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.1668 | + | 1.25094i | −0.458227 | + | 0.0471130i | ||||
\(706\) | 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 | ||||||||
\(711\) | −31.3676 | + | 0.297780i | −1.17638 | + | 0.0111676i | ||||
\(712\) | 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 | ||||||||
\(717\) | −8.21222 | − | 8.13463i | −0.306691 | − | 0.303793i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.7159 | − | 32.9803i | 0.399637 | − | 1.22996i | −0.525654 | − | 0.850699i | \(-0.676179\pi\) |
0.925291 | − | 0.379258i | \(-0.123821\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.51718 | − | 4.66939i | −0.0565027 | − | 0.173897i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −36.6008 | + | 18.8684i | −1.36120 | + | 0.701724i | ||||
\(724\) | 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 | ||||||||
\(729\) | 16.4858 | + | 21.3827i | 0.610584 | + | 0.791952i | ||||
\(730\) | 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 | ||||||||
\(735\) | −22.3785 | + | 14.4608i | −0.825442 | + | 0.533396i | ||||
\(736\) | 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 | ||||||||
\(741\) | 25.5527 | + | 18.3804i | 0.938701 | + | 0.675222i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.7766 | − | 15.7766i | 0.578787 | − | 0.578787i | −0.355782 | − | 0.934569i | \(-0.615785\pi\) |
0.934569 | + | 0.355782i | \(0.115785\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.77289 | + | 5.37615i | 0.174865 | + | 0.196967i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.25047 | − | 43.1241i | −0.265281 | − | 1.57783i | ||||
\(748\) | 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 | ||||||||
\(753\) | 6.98556 | − | 45.5018i | 0.254568 | − | 1.65818i | ||||
\(754\) | 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 | ||||||||
\(759\) | 2.46864 | − | 3.43192i | 0.0896058 | − | 0.124571i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.5073 | + | 36.4842i | −0.960890 | + | 1.32255i | −0.0143726 | + | 0.999897i | \(0.504575\pi\) |
−0.946517 | + | 0.322654i | \(0.895425\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.47489 | + | 0.233599i | 0.0533945 | + | 0.00845686i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 38.7633 | + | 31.2308i | 1.40149 | + | 1.12915i | ||||
\(766\) | 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 | ||||||||
\(771\) | −14.5435 | − | 19.8189i | −0.523770 | − | 0.713759i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.94871 | + | 0.308646i | −0.0700904 | + | 0.0111012i | −0.191381 | − | 0.981516i | \(-0.561297\pi\) |
0.121291 | + | 0.992617i | \(0.461297\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 31.1073 | + | 14.3758i | 1.11741 | + | 0.516393i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.09427 | + | 4.06244i | 0.0751314 | + | 0.145739i | ||||
\(778\) | 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 | ||||||||
\(783\) | 1.52629 | − | 10.6125i | 0.0545450 | − | 0.379260i | ||||
\(784\) | 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 | ||||||||
\(789\) | −12.1974 | + | 38.1549i | −0.434237 | + | 1.35835i | ||||
\(790\) | 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 | ||||||||
\(795\) | −0.0945661 | − | 0.919761i | −0.00335392 | − | 0.0326206i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.9280 | − | 25.3725i | 0.457932 | − | 0.898742i | −0.540423 | − | 0.841394i | \(-0.681736\pi\) |
0.998354 | − | 0.0573478i | \(-0.0182644\pi\) | |||||||
\(798\) | 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 | ||||||||
\(807\) | −6.55547 | + | 13.0182i | −0.230764 | + | 0.458263i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.51664 | + | 4.73462i | −0.229113 | + | 0.166460i | −0.696419 | − | 0.717635i | \(-0.745225\pi\) |
0.467306 | + | 0.884095i | \(0.345225\pi\) | |||||||
\(810\) | 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 | ||||||||
\(813\) | −6.42607 | − | 39.3625i | −0.225372 | − | 1.38050i | ||||
\(814\) | 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 | ||||||||
\(819\) | 5.29806 | − | 1.77722i | 0.185129 | − | 0.0621012i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.3635 | − | 9.86569i | 1.05969 | − | 0.344315i | 0.273227 | − | 0.961950i | \(-0.411909\pi\) |
0.786465 | + | 0.617635i | \(0.211909\pi\) | |||||||
\(822\) | 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 | ||||||||
\(825\) | −8.06436 | − | 10.1497i | −0.280765 | − | 0.353367i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.20579 | + | 32.8681i | 0.181023 | + | 1.14294i | 0.896088 | + | 0.443877i | \(0.146397\pi\) |
−0.715065 | + | 0.699058i | \(0.753603\pi\) | |||||||
\(828\) | 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 | ||||||||
\(831\) | −19.4334 | + | 0.0922408i | −0.674137 | + | 0.00319980i | ||||
\(832\) | 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 | ||||||||
\(837\) | 24.8209 | − | 25.5381i | 0.857937 | − | 0.882725i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.448091 | + | 0.325557i | 0.0154698 | + | 0.0112395i | 0.595493 | − | 0.803360i | \(-0.296957\pi\) |
−0.580023 | + | 0.814600i | \(0.696957\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.0170 | − | 14.5432i | 0.690243 | − | 0.501491i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −23.7705 | − | 11.9699i | −0.818700 | − | 0.412265i | ||||
\(844\) | 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 | ||||||||
\(855\) | −2.43085 | − | 22.5884i | −0.0831334 | − | 0.772507i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.1939 | − | 20.1939i | −0.689811 | − | 0.689811i | 0.272379 | − | 0.962190i | \(-0.412190\pi\) |
−0.962190 | + | 0.272379i | \(0.912190\pi\) | |||||||
\(858\) | 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 | ||||||||
\(861\) | −2.43531 | − | 0.778520i | −0.0829951 | − | 0.0265319i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.15711 | − | 19.9332i | 0.107469 | − | 0.678534i | −0.873857 | − | 0.486183i | \(-0.838389\pi\) |
0.981326 | − | 0.192351i | \(-0.0616112\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −37.5358 | − | 30.8341i | −1.27625 | − | 1.04839i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 46.3989 | − | 46.8415i | 1.57579 | − | 1.59082i | ||||
\(868\) | 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 | ||||||||
\(873\) | 6.56471 | + | 6.44124i | 0.222182 | + | 0.218003i | ||||
\(874\) | 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 | ||||||||
\(879\) | −7.21627 | + | 5.29544i | −0.243399 | + | 0.178611i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.1299 | + | 8.16520i | 0.846648 | + | 0.275093i | 0.700041 | − | 0.714102i | \(-0.253165\pi\) |
0.146607 | + | 0.989195i | \(0.453165\pi\) | |||||||
\(882\) | 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 | ||||||||
\(885\) | −11.5118 | − | 4.44891i | −0.386966 | − | 0.149548i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −46.6702 | − | 7.39183i | −1.56703 | − | 0.248193i | −0.688270 | − | 0.725455i | \(-0.741629\pi\) |
−0.878761 | + | 0.477261i | \(0.841629\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.94341 | + | 2.67488i | −0.0651800 | + | 0.0897126i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −12.7313 | + | 4.40557i | −0.426514 | + | 0.147592i | ||||
\(892\) | 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 | ||||||||
\(897\) | 14.9793 | + | 2.29965i | 0.500143 | + | 0.0767832i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −14.1418 | −0.471657 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.77155 | −0.0590189 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.55311 | + | 0.391960i | 0.0849621 | + | 0.0130436i | ||||
\(904\) | 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 | ||||||||
\(909\) | −1.94600 | + | 6.18845i | −0.0645447 | + | 0.205258i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.4648 | − | 32.2965i | 0.777424 | − | 1.07003i | −0.218137 | − | 0.975918i | \(-0.569998\pi\) |
0.995561 | − | 0.0941143i | \(-0.0300019\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.5506 | + | 3.41329i | 0.713222 | + | 0.112963i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.890636 | + | 16.2887i | −0.0294435 | + | 0.538489i | ||||
\(916\) | 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 | ||||||||
\(921\) | 2.89764 | − | 2.12634i | 0.0954804 | − | 0.0700654i | ||||
\(922\) | 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 | ||||||||
\(927\) | −29.7164 | + | 30.2860i | −0.976013 | + | 0.994722i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.5788 | − | 41.7913i | −0.445507 | − | 1.37113i | −0.881927 | − | 0.471386i | \(-0.843754\pi\) |
0.436420 | − | 0.899743i | \(-0.356246\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.19977 | − | 22.1586i | 0.235963 | − | 0.726219i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −27.7179 | + | 27.9823i | −0.907444 | + | 0.916099i | ||||
\(934\) | 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 | ||||||||
\(939\) | 36.9070 | + | 11.7984i | 1.20442 | + | 0.385028i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.63450 | + | 6.37884i | 0.151080 | + | 0.207944i | 0.877848 | − | 0.478939i | \(-0.158978\pi\) |
−0.726768 | + | 0.686883i | \(0.758978\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.90281 | − | 4.90281i | −0.159657 | − | 0.159657i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.50750 | − | 1.99139i | −0.114099 | − | 0.0647799i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.6899 | + | 30.7932i | −0.509854 | + | 1.00065i | 0.482345 | + | 0.875982i | \(0.339785\pi\) |
−0.992199 | + | 0.124664i | \(0.960215\pi\) | |||||||
\(948\) | 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 | −0.353542 | − | 0.935419i | \(-0.615023\pi\) |
−0.964576 | + | 0.263804i | \(0.915023\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.51576 | + | 34.1789i | −0.243204 | + | 1.10600i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.77811 | + | 2.40607i | 0.154454 | + | 0.0777772i | ||||
\(958\) | 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 | ||||||||
\(963\) | 3.20422 | + | 6.14376i | 0.103255 | + | 0.197980i | ||||
\(964\) | 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 | ||||||||
\(969\) | −43.5287 | + | 0.206609i | −1.39834 | + | 0.00663725i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 44.7462 | − | 14.5389i | 1.43597 | − | 0.466576i | 0.515334 | − | 0.856989i | \(-0.327668\pi\) |
0.920640 | + | 0.390413i | \(0.127668\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.573066 | − | 3.61820i | −0.0183717 | − | 0.115994i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 19.2942 | − | 42.2759i | 0.617909 | − | 1.35391i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.14152 | + | 7.20725i | 0.0365203 | + | 0.230580i | 0.999197 | − | 0.0400750i | \(-0.0127597\pi\) |
−0.962676 | + | 0.270655i | \(0.912760\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.9896 | + | 5.84518i | −0.574951 | + | 0.186813i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.10419 | − | 12.2350i | −0.131037 | − | 0.390632i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.79016 | − | 17.2517i | −0.280363 | − | 0.550243i | 0.707286 | − | 0.706928i | \(-0.249919\pi\) |
−0.987649 | + | 0.156685i | \(0.949919\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 31.0182 | − | 8.07868i | 0.988322 | − | 0.257408i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.305934 | − | 1.87398i | −0.00973798 | − | 0.0596494i | ||||
\(988\) | 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 | ||||||||
\(993\) | −13.0322 | + | 25.8801i | −0.413565 | + | 0.821282i | ||||
\(994\) | 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.113.9 | yes | 80 | |
3.2 | odd | 2 | inner | 300.2.x.a.113.3 | yes | 80 | |
25.2 | odd | 20 | inner | 300.2.x.a.77.3 | ✓ | 80 | |
75.2 | even | 20 | inner | 300.2.x.a.77.9 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.x.a.77.3 | ✓ | 80 | 25.2 | odd | 20 | inner | |
300.2.x.a.77.9 | yes | 80 | 75.2 | even | 20 | inner | |
300.2.x.a.113.3 | yes | 80 | 3.2 | odd | 2 | inner | |
300.2.x.a.113.9 | yes | 80 | 1.1 | even | 1 | trivial |