Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(47,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(42))
chi = DirichletCharacter(H, H._module([21, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.bp (of order \(42\), degree \(12\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(120\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{42})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{42}]$ |
Embedding invariants
Embedding label | 495.10 | ||
Character | \(\chi\) | \(=\) | 784.495 |
Dual form | 784.2.bp.c.255.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{29}{42}\right)\) |
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 | ||||||||
\(3\) | 2.52689 | + | 1.72281i | 1.45890 | + | 0.994663i | 0.994009 | + | 0.109296i | \(0.0348596\pi\) |
0.464893 | + | 0.885367i | \(0.346093\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.607633 | − | 0.0455358i | −0.271742 | − | 0.0203642i | −0.0618378 | − | 0.998086i | \(-0.519696\pi\) |
−0.209904 | + | 0.977722i | \(0.567315\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.56115 | + | 0.663712i | −0.968024 | + | 0.250859i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.32110 | + | 5.91407i | 0.773701 | + | 1.97136i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.84067 | + | 2.29229i | 1.76103 | + | 0.691152i | 0.999051 | + | 0.0435474i | \(0.0138659\pi\) |
0.761976 | + | 0.647605i | \(0.224229\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.03918 | + | 0.828717i | −0.288216 | + | 0.229845i | −0.756915 | − | 0.653513i | \(-0.773294\pi\) |
0.468699 | + | 0.883358i | \(0.344723\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.45698 | − | 1.16190i | −0.376189 | − | 0.300001i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.89256 | − | 2.03969i | −0.459012 | − | 0.494698i | 0.460554 | − | 0.887631i | \(-0.347651\pi\) |
−0.919567 | + | 0.392934i | \(0.871460\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.73256 | + | 4.73293i | −0.626892 | + | 1.08581i | 0.361279 | + | 0.932458i | \(0.382340\pi\) |
−0.988172 | + | 0.153352i | \(0.950993\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.61520 | − | 2.73524i | −1.66177 | − | 0.596878i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.76777 | − | 5.13843i | 0.994148 | − | 1.07144i | −0.00329681 | − | 0.999995i | \(-0.501049\pi\) |
0.997445 | − | 0.0714421i | \(-0.0227601\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.57701 | − | 0.689873i | −0.915402 | − | 0.137975i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.28201 | + | 9.99815i | −0.439173 | + | 1.92414i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.81141 | + | 7.93629i | 0.336370 | + | 1.47373i | 0.806552 | + | 0.591163i | \(0.201331\pi\) |
−0.470182 | + | 0.882569i | \(0.655812\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.65442 | − | 4.59759i | −0.476748 | − | 0.825751i | 0.522897 | − | 0.852396i | \(-0.324851\pi\) |
−0.999645 | + | 0.0266446i | \(0.991518\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 10.8096 | + | 15.8547i | 1.88170 | + | 2.75995i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.58646 | − | 0.286669i | 0.268161 | − | 0.0484560i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.69524 | + | 2.06521i | 1.10069 | + | 0.339518i | 0.791307 | − | 0.611419i | \(-0.209401\pi\) |
0.309384 | + | 0.950937i | \(0.399877\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.05361 | + | 0.303776i | −0.649097 | + | 0.0486431i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.41792 | + | 2.94434i | 0.221442 | + | 0.459828i | 0.981861 | − | 0.189605i | \(-0.0607206\pi\) |
−0.760419 | + | 0.649433i | \(0.775006\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.22494 | − | 2.54362i | 0.186802 | − | 0.387898i | −0.786445 | − | 0.617660i | \(-0.788081\pi\) |
0.973247 | + | 0.229762i | \(0.0737949\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.14108 | − | 3.69928i | −0.170102 | − | 0.551456i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.120128 | − | 0.0181063i | 0.0175224 | − | 0.00264108i | −0.140275 | − | 0.990113i | \(-0.544799\pi\) |
0.157798 | + | 0.987471i | \(0.449561\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.11897 | − | 3.39973i | 0.874139 | − | 0.485676i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.26829 | − | 8.41459i | −0.177597 | − | 1.17828i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.13106 | + | 1.58272i | −0.704806 | + | 0.217404i | −0.626382 | − | 0.779516i | \(-0.715465\pi\) |
−0.0784237 | + | 0.996920i | \(0.524989\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.44460 | − | 1.65883i | −0.464470 | − | 0.223677i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −15.0588 | + | 7.25194i | −1.99459 | + | 0.960543i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.675569 | − | 9.01484i | −0.0879515 | − | 1.17363i | −0.850240 | − | 0.526395i | \(-0.823543\pi\) |
0.762289 | − | 0.647237i | \(-0.224076\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.474172 | + | 1.53723i | −0.0607115 | + | 0.196822i | −0.980848 | − | 0.194777i | \(-0.937602\pi\) |
0.920136 | + | 0.391599i | \(0.128078\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.86993 | − | 13.6063i | −1.24349 | − | 1.71423i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.669176 | − | 0.456236i | 0.0830010 | − | 0.0565891i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.76814 | − | 5.06229i | 1.07120 | − | 0.618457i | 0.142690 | − | 0.989767i | \(-0.454425\pi\) |
0.928509 | + | 0.371311i | \(0.121092\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 20.9002 | − | 4.77032i | 2.51608 | − | 0.574279i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.66850 | − | 1.29380i | −0.672727 | − | 0.153546i | −0.127506 | − | 0.991838i | \(-0.540697\pi\) |
−0.545221 | + | 0.838292i | \(0.683554\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.427054 | − | 2.83332i | 0.0499829 | − | 0.331615i | −0.949839 | − | 0.312739i | \(-0.898753\pi\) |
0.999822 | − | 0.0188753i | \(-0.00600854\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −10.3771 | − | 9.62854i | −1.19824 | − | 1.11181i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −16.4802 | − | 1.99439i | −1.87810 | − | 0.227281i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.97875 | + | 5.18389i | 1.01019 | + | 0.583233i | 0.911247 | − | 0.411860i | \(-0.135121\pi\) |
0.0989419 | + | 0.995093i | \(0.468454\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.01949 | + | 8.36887i | −1.00217 | + | 0.929874i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.22316 | − | 10.3115i | 0.902609 | − | 1.13184i | −0.0881376 | − | 0.996108i | \(-0.528092\pi\) |
0.990746 | − | 0.135727i | \(-0.0433370\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.05710 | + | 1.32556i | 0.114659 | + | 0.143778i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.09546 | + | 23.1749i | −0.975136 | + | 2.48461i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.82948 | + | 3.46532i | −0.935923 | + | 0.367323i | −0.783782 | − | 0.621036i | \(-0.786712\pi\) |
−0.152141 | + | 0.988359i | \(0.548617\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.11146 | − | 2.81218i | 0.221341 | − | 0.294797i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.21332 | − | 16.1907i | 0.125816 | − | 1.67889i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.87591 | − | 2.75146i | 0.192465 | − | 0.282294i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 15.8417i | − | 1.60848i | −0.594307 | − | 0.804239i | \(-0.702573\pi\) | ||
0.594307 | − | 0.804239i | \(-0.297427\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 39.8628i | 4.00636i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.06548 | − | 13.2966i | 0.902049 | − | 1.32306i | −0.0439975 | − | 0.999032i | \(-0.514009\pi\) |
0.946046 | − | 0.324031i | \(-0.105038\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.527915 | − | 7.04454i | 0.0520171 | − | 0.694119i | −0.908852 | − | 0.417118i | \(-0.863040\pi\) |
0.960869 | − | 0.277002i | \(-0.0893407\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.50270 | + | 2.00879i | 0.439418 | + | 0.196037i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.67577 | + | 2.22758i | −0.548698 | + | 0.215348i | −0.623463 | − | 0.781853i | \(-0.714275\pi\) |
0.0747648 | + | 0.997201i | \(0.476179\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.74772 | + | 9.54904i | −0.358967 | + | 0.914633i | 0.631311 | + | 0.775530i | \(0.282517\pi\) |
−0.990278 | + | 0.139103i | \(0.955578\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.3602 | + | 16.7532i | 1.26809 | + | 1.59014i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.32036 | + | 2.90965i | −0.218282 | + | 0.273716i | −0.878901 | − | 0.477005i | \(-0.841722\pi\) |
0.660619 | + | 0.750721i | \(0.270294\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.13104 | + | 2.90518i | −0.291971 | + | 0.270909i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.31313 | − | 4.22224i | −0.676099 | − | 0.390346i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.20089 | + | 3.96784i | 0.568434 | + | 0.363731i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.7952 | + | 19.2951i | 1.89047 | + | 1.75410i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.48960 | + | 9.88283i | −0.134312 | + | 0.891105i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.72003 | + | 1.30556i | 0.511615 | + | 0.116773i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.8208 | − | 2.69803i | 1.04893 | − | 0.239411i | 0.336885 | − | 0.941546i | \(-0.390627\pi\) |
0.712045 | + | 0.702134i | \(0.247769\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.47745 | − | 4.31711i | 0.658353 | − | 0.380100i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.568703 | − | 0.387735i | 0.0496878 | − | 0.0338765i | −0.538221 | − | 0.842803i | \(-0.680904\pi\) |
0.587909 | + | 0.808927i | \(0.299951\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.85719 | − | 13.9354i | 0.334461 | − | 1.20835i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.84190 | − | 5.97130i | 0.158526 | − | 0.513927i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.714708 | − | 9.53712i | −0.0610616 | − | 0.814811i | −0.940716 | − | 0.339197i | \(-0.889845\pi\) |
0.879654 | − | 0.475614i | \(-0.157774\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.6115 | − | 5.59179i | 0.984872 | − | 0.474289i | 0.129094 | − | 0.991632i | \(-0.458793\pi\) |
0.855778 | + | 0.517343i | \(0.173079\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.334744 | + | 0.161204i | 0.0281905 | + | 0.0135758i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.96916 | + | 2.45816i | −0.666414 | + | 0.205562i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.739286 | − | 4.90484i | −0.0613943 | − | 0.407325i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 21.3191 | + | 1.95106i | 1.75837 | + | 0.160920i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.1030 | + | 1.82424i | −0.991517 | + | 0.149447i | −0.624716 | − | 0.780852i | \(-0.714785\pi\) |
−0.366801 | + | 0.930299i | \(0.619547\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.19312 | − | 16.8357i | −0.422610 | − | 1.37007i | −0.877524 | − | 0.479533i | \(-0.840806\pi\) |
0.454913 | − | 0.890536i | \(-0.349670\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.67006 | − | 15.9270i | 0.620088 | − | 1.28763i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.40356 | + | 2.91452i | 0.112737 | + | 0.234100i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.802185 | − | 0.0601155i | 0.0640214 | − | 0.00479774i | −0.0426809 | − | 0.999089i | \(-0.513590\pi\) |
0.106702 | + | 0.994291i | \(0.465971\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −15.6924 | − | 4.84045i | −1.24449 | − | 0.383873i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.80053 | + | 16.3247i | −0.693579 | + | 1.28657i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.74712 | + | 2.56256i | 0.136845 | + | 0.200715i | 0.888544 | − | 0.458792i | \(-0.151718\pi\) |
−0.751699 | + | 0.659507i | \(0.770765\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.84629 | − | 10.1261i | −0.455133 | − | 0.788314i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.44560 | + | 15.0961i | 0.266628 | + | 1.16818i | 0.913908 | + | 0.405922i | \(0.133050\pi\) |
−0.647279 | + | 0.762253i | \(0.724093\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.49965 | + | 10.9517i | −0.192281 | + | 0.842438i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −34.3335 | − | 5.17494i | −2.62555 | − | 0.395737i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.90407 | − | 3.12985i | 0.220793 | − | 0.237958i | −0.612936 | − | 0.790133i | \(-0.710011\pi\) |
0.833728 | + | 0.552175i | \(0.186202\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.1803 | − | 1.27095i | 0.920743 | − | 0.0960745i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.8237 | − | 23.9434i | 1.03906 | − | 1.79970i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.21331 | + | 1.30763i | 0.0906868 | + | 0.0977372i | 0.776765 | − | 0.629791i | \(-0.216859\pi\) |
−0.686078 | + | 0.727528i | \(0.740669\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.9292 | − | 12.7031i | −1.18401 | − | 0.944215i | −0.184752 | − | 0.982785i | \(-0.559148\pi\) |
−0.999256 | + | 0.0385704i | \(0.987720\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.84653 | + | 3.06751i | −0.284344 | + | 0.226757i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.97421 | − | 1.55976i | −0.292190 | − | 0.114676i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.37822 | − | 16.2514i | −0.466422 | − | 1.18842i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.791313 | − | 27.1214i | −0.0575595 | − | 1.97279i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.94239 | + | 0.745079i | 0.719406 | + | 0.0539121i | 0.429402 | − | 0.903113i | \(-0.358724\pi\) |
0.290004 | + | 0.957025i | \(0.406343\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.73424 | − | 5.95491i | −0.628705 | − | 0.428644i | 0.206604 | − | 0.978425i | \(-0.433759\pi\) |
−0.835309 | + | 0.549781i | \(0.814711\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.47694 | 0.177377 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.34180 | −0.594328 | −0.297164 | − | 0.954826i | \(-0.596041\pi\) | ||||
−0.297164 | + | 0.954826i | \(0.596041\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.25104 | + | 2.89831i | 0.301348 | + | 0.205456i | 0.704548 | − | 0.709656i | \(-0.251150\pi\) |
−0.403200 | + | 0.915112i | \(0.632102\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 30.8775 | + | 2.31395i | 2.17793 | + | 0.163213i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.90669 | − | 19.1238i | −0.695314 | − | 1.34223i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.727502 | − | 1.85364i | −0.0508109 | − | 0.129464i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 41.4555 | + | 16.2701i | 2.88136 | + | 1.13085i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −26.8092 | + | 21.3797i | −1.85443 | + | 1.47886i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.01958 | − | 3.20551i | −0.276719 | − | 0.220676i | 0.475289 | − | 0.879830i | \(-0.342343\pi\) |
−0.752008 | + | 0.659153i | \(0.770915\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.0947 | − | 13.0350i | −0.828717 | − | 0.893144i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.860141 | + | 1.48981i | −0.0586611 | + | 0.101604i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.84983 | + | 10.0133i | 0.668650 | + | 0.679750i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.96037 | − | 6.42376i | 0.402765 | − | 0.434077i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.65703 | + | 0.551208i | 0.245998 | + | 0.0370783i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.82015 | + | 16.7372i | −0.255816 | + | 1.12080i | 0.669860 | + | 0.742487i | \(0.266354\pi\) |
−0.925676 | + | 0.378317i | \(0.876503\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.54375 | − | 28.6700i | −0.436250 | − | 1.91134i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.23237 | + | 9.06272i | 0.347284 | + | 0.601514i | 0.985766 | − | 0.168123i | \(-0.0537705\pi\) |
−0.638482 | + | 0.769637i | \(0.720437\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.80204 | − | 7.04330i | −0.317328 | − | 0.465435i | 0.634124 | − | 0.773231i | \(-0.281361\pi\) |
−0.951452 | + | 0.307797i | \(0.900408\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −38.2079 | − | 33.4319i | −2.51389 | − | 2.19966i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.46866 | − | 1.99532i | −0.423776 | − | 0.130718i | 0.0755296 | − | 0.997144i | \(-0.475935\pi\) |
−0.499305 | + | 0.866426i | \(0.666411\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.0738181 | + | 0.00553190i | −0.00481536 | + | 0.000360862i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.7575 | + | 28.5678i | 0.893647 | + | 1.85568i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.36736 | + | 13.2219i | −0.411870 | + | 0.855257i | 0.587084 | + | 0.809526i | \(0.300276\pi\) |
−0.998954 | + | 0.0457307i | \(0.985438\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.71383 | + | 12.0399i | 0.239229 | + | 0.775561i | 0.992968 | + | 0.118387i | \(0.0377723\pi\) |
−0.753739 | + | 0.657174i | \(0.771751\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.78704 | + | 1.02298i | −0.435389 | + | 0.0656243i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.87290 | + | 1.78716i | −0.247431 | + | 0.114177i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.08264 | − | 7.18288i | −0.0688870 | − | 0.457036i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 38.5438 | − | 11.8892i | 2.44261 | − | 0.753446i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.8830 | − | 11.0199i | −1.44437 | − | 0.695570i | −0.462758 | − | 0.886484i | \(-0.653140\pi\) |
−0.981607 | + | 0.190915i | \(0.938855\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 39.6257 | − | 19.0827i | 2.49125 | − | 1.19972i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.387493 | + | 5.17074i | 0.0242658 | + | 0.323804i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.69048 | + | 15.2062i | −0.292584 | + | 0.948535i | 0.683280 | + | 0.730156i | \(0.260553\pi\) |
−0.975864 | + | 0.218378i | \(0.929923\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.5182 | − | 0.845598i | −1.15067 | − | 0.0525429i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −42.7314 | + | 29.1337i | −2.64500 | + | 1.80333i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.06421 | − | 1.76912i | 0.188947 | − | 0.109089i | −0.402543 | − | 0.915401i | \(-0.631873\pi\) |
0.591490 | + | 0.806313i | \(0.298540\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.18988 | − | 0.728068i | 0.195952 | − | 0.0447249i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −28.2812 | − | 6.45501i | −1.73078 | − | 0.395040i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.24235 | − | 8.24243i | 0.0757472 | − | 0.502550i | −0.918498 | − | 0.395425i | \(-0.870597\pi\) |
0.994246 | − | 0.107125i | \(-0.0341645\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.72109 | + | 1.59694i | 0.104549 | + | 0.0970072i | 0.730716 | − | 0.682682i | \(-0.239187\pi\) |
−0.626167 | + | 0.779689i | \(0.715377\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.1803 | − | 3.46844i | 0.616139 | − | 0.209920i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −25.1514 | − | 14.5212i | −1.51669 | − | 0.875659i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.6463 | − | 11.7341i | 0.759845 | − | 0.705033i | −0.201771 | − | 0.979433i | \(-0.564670\pi\) |
0.961616 | + | 0.274400i | \(0.0884792\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 21.0293 | − | 26.3699i | 1.25899 | − | 1.57872i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.08750 | + | 1.36368i | 0.0648747 | + | 0.0813503i | 0.813210 | − | 0.581970i | \(-0.197718\pi\) |
−0.748335 | + | 0.663321i | \(0.769147\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.0232741 | − | 0.0593014i | 0.00138350 | − | 0.00352510i | −0.930180 | − | 0.367103i | \(-0.880350\pi\) |
0.931564 | + | 0.363578i | \(0.118445\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.48046 | − | 3.72081i | 0.561574 | − | 0.220402i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.58569 | − | 6.59980i | −0.329713 | − | 0.389574i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.691843 | − | 9.23201i | 0.0406967 | − | 0.543059i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 27.2921 | − | 40.0302i | 1.59989 | − | 2.34661i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.65962i | 0.155377i | 0.996978 | + | 0.0776883i | \(0.0247539\pi\) | ||||
−0.996978 | + | 0.0776883i | \(0.975246\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.50848i | 0.320716i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −36.2472 | + | 53.1648i | −2.10327 | + | 3.08494i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.696255 | + | 9.29087i | −0.0402654 | + | 0.537305i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.44903 | + | 7.32759i | −0.0835207 | + | 0.422355i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 45.8150 | − | 17.9811i | 2.63200 | − | 1.03298i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.358122 | − | 0.912480i | 0.0205060 | − | 0.0522484i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.5505 | + | 18.2458i | 0.830443 | + | 1.04134i | 0.998455 | + | 0.0555575i | \(0.0176936\pi\) |
−0.168013 | + | 0.985785i | \(0.553735\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.4704 | − | 16.8913i | 0.766302 | − | 0.960913i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.4105 | − | 10.5874i | 0.647028 | − | 0.600354i | −0.286838 | − | 0.957979i | \(-0.592604\pi\) |
0.933865 | + | 0.357625i | \(0.116414\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.7466 | − | 13.1327i | −1.28571 | − | 0.742307i | −0.307827 | − | 0.951442i | \(-0.599602\pi\) |
−0.977887 | + | 0.209136i | \(0.932935\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.37773 | + | 8.71707i | 0.303001 | + | 0.491151i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.8582 | + | 10.0749i | 0.609857 | + | 0.565865i | 0.923463 | − | 0.383689i | \(-0.125346\pi\) |
−0.313605 | + | 0.949553i | \(0.601537\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.61248 | + | 50.5055i | −0.426217 | + | 2.82777i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.1798 | − | 4.14941i | −1.01470 | − | 0.231598i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.8252 | − | 3.38376i | 0.824899 | − | 0.188278i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.32804 | − | 3.07614i | 0.295546 | − | 0.170634i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −25.9213 | + | 17.6728i | −1.43345 | + | 0.977309i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.295648 | + | 0.126103i | −0.0162996 | + | 0.00695230i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.99942 | − | 25.9335i | 0.439688 | − | 1.42543i | −0.416673 | − | 0.909056i | \(-0.636804\pi\) |
0.856361 | − | 0.516377i | \(-0.172720\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.32655 | + | 44.3897i | 0.182294 | + | 2.43254i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.55833 | + | 2.67675i | −0.303684 | + | 0.146246i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.94647 | + | 4.30839i | 0.487345 | + | 0.234693i | 0.661386 | − | 0.750045i | \(-0.269968\pi\) |
−0.174041 | + | 0.984738i | \(0.555683\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.8761 | + | 3.35482i | −0.590707 | + | 0.182209i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.96456 | − | 32.9377i | −0.268846 | − | 1.78368i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.4152 | + | 12.7684i | −0.724351 | + | 0.689431i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12.9169 | + | 1.94690i | −0.695420 | + | 0.104818i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.46062 | + | 4.73522i | 0.0784103 | + | 0.254200i | 0.986287 | − | 0.165036i | \(-0.0527741\pi\) |
−0.907877 | + | 0.419236i | \(0.862298\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.1471 | + | 29.3769i | −0.757279 | + | 1.57251i | 0.0613041 | + | 0.998119i | \(0.480474\pi\) |
−0.818583 | + | 0.574388i | \(0.805240\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.91422 | − | 12.2810i | −0.315678 | − | 0.655511i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.7410 | + | 1.70420i | −1.21038 | + | 0.0907055i | −0.664585 | − | 0.747213i | \(-0.731392\pi\) |
−0.545796 | + | 0.837918i | \(0.683773\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.38546 | + | 1.04427i | 0.179681 | + | 0.0554243i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.83315 | + | 20.7092i | 0.467500 | + | 1.09605i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.26707 | − | 13.5923i | −0.489097 | − | 0.717374i | 0.499773 | − | 0.866157i | \(-0.333417\pi\) |
−0.988870 | + | 0.148783i | \(0.952465\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.43377 | − | 9.41157i | −0.285988 | − | 0.495346i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 19.3055 | + | 84.5829i | 1.01328 | + | 4.43945i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.388510 | + | 1.70217i | −0.0203355 | + | 0.0890957i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.02290 | + | 0.757080i | 0.262193 | + | 0.0395193i | 0.278823 | − | 0.960342i | \(-0.410056\pi\) |
−0.0166301 | + | 0.999862i | \(0.505294\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −14.1219 | + | 15.2198i | −0.735157 | + | 0.792311i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.0909 | − | 7.45914i | 0.627731 | − | 0.387259i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.03849 | + | 3.53076i | −0.105549 | + | 0.182816i | −0.913962 | − | 0.405799i | \(-0.866993\pi\) |
0.808413 | + | 0.588615i | \(0.200327\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.2047 | + | 13.1535i | 0.630247 | + | 0.679244i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.45931 | − | 6.74608i | −0.435677 | − | 0.347441i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.1361 | + | 17.6530i | −1.13706 | + | 0.906771i | −0.996524 | − | 0.0833047i | \(-0.973453\pi\) |
−0.140531 | + | 0.990076i | \(0.544881\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 34.5182 | + | 13.5474i | 1.76842 | + | 0.694054i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.40912 | + | 16.3302i | 0.327491 | + | 0.834433i | 0.995885 | + | 0.0906260i | \(0.0288868\pi\) |
−0.668394 | + | 0.743807i | \(0.733018\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.92313 | + | 1.96230i | 0.505730 | + | 0.100008i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 17.8863 | + | 1.34040i | 0.909214 | + | 0.0681362i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.44430 | − | 3.71186i | −0.276037 | − | 0.188199i | 0.417387 | − | 0.908729i | \(-0.362946\pi\) |
−0.693423 | + | 0.720530i | \(0.743898\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.5041 | −0.986363 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.10504 | 0.106185 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.21974 | − | 3.55876i | −0.262634 | − | 0.179061i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.3892 | − | 1.45302i | −0.973117 | − | 0.0729250i | −0.421327 | − | 0.906909i | \(-0.638436\pi\) |
−0.551789 | + | 0.833984i | \(0.686055\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 33.7547 | − | 28.5680i | 1.68985 | − | 1.43019i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.98388 | − | 17.7946i | −0.348758 | − | 0.888622i | −0.992373 | − | 0.123272i | \(-0.960661\pi\) |
0.643615 | − | 0.765350i | \(-0.277434\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.56851 | + | 2.57795i | 0.327201 | + | 0.128417i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.86163 | − | 4.67449i | 0.291267 | − | 0.232277i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 34.3706 | + | 27.4097i | 1.70369 | + | 1.35865i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.0745 | + | 24.8684i | 1.14096 | + | 1.22966i | 0.969663 | + | 0.244445i | \(0.0786059\pi\) |
0.171299 | + | 0.985219i | \(0.445204\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.6246 | − | 25.3306i | 0.721379 | − | 1.24947i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.71348 | + | 22.6400i | 0.379556 | + | 1.11404i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.46621 | + | 5.89117i | −0.268326 | + | 0.289186i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 38.9745 | + | 5.87446i | 1.90859 | + | 0.287674i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.42669 | − | 6.25073i | 0.0696983 | − | 0.305368i | −0.928049 | − | 0.372459i | \(-0.878515\pi\) |
0.997747 | + | 0.0670910i | \(0.0213718\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.61140 | + | 24.5852i | 0.273483 | + | 1.19821i | 0.905870 | + | 0.423555i | \(0.139218\pi\) |
−0.632388 | + | 0.774652i | \(0.717925\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.385911 | + | 0.668418i | 0.0187636 | + | 0.0324996i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.25512 | + | 10.6413i | 0.351925 | + | 0.516179i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.194150 | − | 4.25179i | 0.00939556 | − | 0.205758i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −24.3721 | − | 7.51781i | −1.17670 | − | 0.362963i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.7399 | + | 1.47930i | −0.950839 | + | 0.0712556i | −0.541110 | − | 0.840952i | \(-0.681996\pi\) |
−0.409729 | + | 0.912207i | \(0.634377\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.13296 | + | 2.35262i | 0.0544467 | + | 0.113060i | 0.926417 | − | 0.376499i | \(-0.122872\pi\) |
−0.871970 | + | 0.489559i | \(0.837158\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.58199 | − | 13.6677i | 0.315582 | − | 0.655314i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.2916 | + | 36.6066i | 0.540152 | + | 1.75113i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.4158 | + | 3.83081i | −1.21303 | + | 0.182835i | −0.724228 | − | 0.689560i | \(-0.757804\pi\) |
−0.488801 | + | 0.872395i | \(0.662566\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 34.3090 | + | 28.2969i | 1.63376 | + | 1.34747i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.49472 | + | 36.4551i | 0.261062 | + | 1.73203i | 0.607817 | + | 0.794077i | \(0.292046\pi\) |
−0.346755 | + | 0.937956i | \(0.612716\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.52289 | − | 1.70358i | 0.261810 | − | 0.0807577i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −33.7258 | − | 16.2415i | −1.59518 | − | 0.768197i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.9520 | + | 11.5347i | −1.13037 | + | 0.544356i | −0.903080 | − | 0.429472i | \(-0.858700\pi\) |
−0.227286 | + | 0.973828i | \(0.572985\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.53231 | + | 20.4472i | 0.0721534 | + | 0.962821i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.8822 | − | 51.4887i | 0.746210 | − | 2.41915i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.41105 | + | 1.61263i | −0.0661510 | + | 0.0756012i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.5712 | − | 18.7977i | 1.28972 | − | 0.879319i | 0.292684 | − | 0.956209i | \(-0.405451\pi\) |
0.997040 | + | 0.0768901i | \(0.0244991\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 24.7120 | − | 14.2675i | 1.15346 | − | 0.665948i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −37.3408 | + | 8.52280i | −1.73914 | + | 0.396947i | −0.970186 | − | 0.242362i | \(-0.922078\pi\) |
−0.768950 | + | 0.639308i | \(0.779221\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.2163 | − | 4.15776i | −0.846585 | − | 0.193228i | −0.222840 | − | 0.974855i | \(-0.571533\pi\) |
−0.623745 | + | 0.781628i | \(0.714390\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.47451 | + | 9.78274i | −0.0683788 | + | 0.453664i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.88925 | + | 3.60869i | 0.179973 | + | 0.166990i | 0.765015 | − | 0.644013i | \(-0.222732\pi\) |
−0.585042 | + | 0.811003i | \(0.698922\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.0966 | + | 18.7848i | −0.881799 | + | 0.867401i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.13060 | + | 1.23010i | 0.0981730 | + | 0.0566802i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.9852 | − | 12.0485i | 0.597060 | − | 0.553990i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.7721 | − | 19.7776i | 0.723673 | − | 0.907457i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −21.2701 | − | 26.6718i | −0.973889 | − | 1.22122i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.96234 | − | 4.99996i | 0.0896616 | − | 0.228454i | −0.879008 | − | 0.476807i | \(-0.841794\pi\) |
0.968670 | + | 0.248353i | \(0.0798893\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.66902 | + | 3.40234i | −0.395273 | + | 0.155133i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −50.3623 | + | 26.0892i | −2.29156 | + | 1.18710i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.721363 | + | 9.62592i | −0.0327554 | + | 0.437091i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.08858 | − | 5.99685i | 0.185271 | − | 0.271743i | −0.722355 | − | 0.691523i | \(-0.756940\pi\) |
0.907626 | + | 0.419779i | \(0.137893\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.48527i | 0.428939i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.4661i | 0.788235i | 0.919060 | + | 0.394118i | \(0.128950\pi\) | ||||
−0.919060 | + | 0.394118i | \(0.871050\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.7594 | − | 18.7146i | 0.574654 | − | 0.842863i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.81518 | − | 24.2220i | 0.0815865 | − | 1.08870i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.3766 | − | 0.448639i | 0.689734 | − | 0.0201242i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.6176 | + | 5.34453i | −0.609610 | + | 0.239254i | −0.650005 | − | 0.759930i | \(-0.725233\pi\) |
0.0403958 | + | 0.999184i | \(0.487138\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.3011 | + | 44.0824i | −0.772955 | + | 1.96946i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.82683 | − | 11.0685i | −0.393569 | − | 0.493520i | 0.545085 | − | 0.838381i | \(-0.316497\pi\) |
−0.938654 | + | 0.344861i | \(0.887926\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.11396 | + | 7.66666i | −0.272068 | + | 0.341162i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −25.1840 | + | 23.3673i | −1.11846 | + | 1.03778i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.0982 | − | 12.7584i | −0.979487 | − | 0.565507i | −0.0773715 | − | 0.997002i | \(-0.524653\pi\) |
−0.902115 | + | 0.431495i | \(0.857986\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.786756 | + | 7.53999i | 0.0348041 | + | 0.333549i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −41.0848 | − | 38.1212i | −1.81394 | − | 1.68309i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.641558 | + | 4.25646i | −0.0282704 | + | 0.187562i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.743131 | + | 0.169615i | 0.0326829 | + | 0.00745965i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.7304 | − | 2.90563i | 0.558803 | − | 0.127543i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.44592 | − | 4.87625i | 0.370022 | − | 0.213632i | −0.303446 | − | 0.952849i | \(-0.598137\pi\) |
0.673468 | + | 0.739216i | \(0.264804\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.3622 | − | 22.7460i | 1.45883 | − | 0.994611i | 0.464807 | − | 0.885412i | \(-0.346124\pi\) |
0.994020 | − | 0.109199i | \(-0.0348285\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 32.9679 | + | 17.7727i | 1.43884 | + | 0.775665i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.35402 | + | 14.1154i | −0.189664 | + | 0.614876i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.95307 | − | 26.0620i | −0.0849163 | − | 1.13313i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 51.7463 | − | 24.9197i | 2.24560 | − | 1.08142i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.91349 | − | 1.88464i | −0.169512 | − | 0.0816328i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.55022 | − | 1.09510i | 0.153490 | − | 0.0473453i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.813097 | + | 5.39455i | 0.0350877 | + | 0.232792i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 43.5321 | − | 5.83021i | 1.87506 | − | 0.251125i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.8606 | + | 2.69206i | −0.767889 | + | 0.115741i | −0.521293 | − | 0.853378i | \(-0.674550\pi\) |
−0.246596 | + | 0.969118i | \(0.579312\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18.3664 | − | 59.5423i | −0.788177 | − | 2.55521i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.71207 | − | 5.63166i | 0.116172 | − | 0.241234i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.70505 | − | 5.61708i | −0.115659 | − | 0.240169i | 0.835101 | − | 0.550097i | \(-0.185409\pi\) |
−0.950760 | + | 0.309928i | \(0.899695\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.1919 | + | 0.763776i | −0.434979 | + | 0.0325972i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −42.5117 | − | 13.1131i | −1.81106 | − | 0.558638i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −26.4365 | − | 7.31740i | −1.12420 | − | 0.311168i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.35524 | − | 10.7882i | −0.312212 | − | 0.457932i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.43462 | − | 2.48483i | −0.0607866 | − | 0.105286i | 0.834031 | − | 0.551718i | \(-0.186028\pi\) |
−0.894817 | + | 0.446433i | \(0.852694\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.835006 | + | 3.65840i | 0.0353170 | + | 0.154734i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.8810 | − | 52.0541i | 0.501617 | − | 2.19773i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.7424 | − | 2.82497i | −0.789899 | − | 0.119058i | −0.258312 | − | 0.966062i | \(-0.583166\pi\) |
−0.531587 | + | 0.847004i | \(0.678404\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.54242 | − | 1.66234i | 0.0648903 | − | 0.0699351i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 17.5458 | − | 27.4203i | 0.736852 | − | 1.15154i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.4374 | + | 28.4704i | −0.689092 | + | 1.19354i | 0.283040 | + | 0.959108i | \(0.408657\pi\) |
−0.972132 | + | 0.234435i | \(0.924676\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.4504 | − | 28.5068i | −1.10692 | − | 1.19297i | −0.979568 | − | 0.201112i | \(-0.935544\pi\) |
−0.127347 | − | 0.991858i | \(-0.540646\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.8397 | + | 19.0116i | 0.995919 | + | 0.794219i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −25.3670 | + | 20.2295i | −1.05788 | + | 0.843628i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.7313 | − | 7.35150i | −0.779795 | − | 0.306047i | −0.0581477 | − | 0.998308i | \(-0.518519\pi\) |
−0.721647 | + | 0.692261i | \(0.756615\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.8113 | − | 30.0948i | −0.490863 | − | 1.25070i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.2169 | + | 31.8671i | −0.589815 | + | 1.32207i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −33.5969 | − | 2.51774i | −1.39144 | − | 0.104274i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.25144 | + | 2.89858i | 0.175775 | + | 0.119842i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.40317 | −0.264287 | −0.132144 | − | 0.991231i | \(-0.542186\pi\) | ||||
−0.132144 | + | 0.991231i | \(0.542186\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 29.0134 | 1.19548 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21.0788 | − | 14.3713i | −0.867067 | − | 0.591156i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26.8607 | − | 2.01293i | −1.10304 | − | 0.0826612i | −0.489258 | − | 0.872139i | \(-0.662732\pi\) |
−0.613779 | + | 0.789478i | \(0.710351\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.58719 | − | 2.69335i | −0.147060 | − | 0.110417i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.74870 | + | 14.6474i | 0.235279 | + | 0.599480i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 43.5263 | + | 17.0828i | 1.77844 | + | 0.697984i | 0.997285 | + | 0.0736413i | \(0.0234620\pi\) |
0.781150 | + | 0.624343i | \(0.214633\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.9633 | − | 12.7303i | 0.651155 | − | 0.519279i | −0.241280 | − | 0.970456i | \(-0.577567\pi\) |
0.892434 | + | 0.451177i | \(0.148996\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 50.2905 | + | 40.1053i | 2.04799 | + | 1.63321i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11.7573 | − | 12.6713i | −0.478000 | − | 0.515162i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.44788 | + | 12.9001i | −0.302300 | + | 0.523599i | −0.976657 | − | 0.214807i | \(-0.931088\pi\) |
0.674356 | + | 0.738406i | \(0.264421\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.91342 | − | 65.3911i | 0.320668 | − | 2.64978i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.109829 | + | 0.118368i | −0.00444321 | + | 0.00478864i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.0781 | + | 6.34226i | 1.69952 | + | 0.256161i | 0.925976 | − | 0.377581i | \(-0.123244\pi\) |
0.773544 | + | 0.633743i | \(0.218482\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.35515 | − | 5.93731i | 0.0546450 | − | 0.239415i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.09852 | + | 13.5755i | 0.124742 | + | 0.546530i | 0.998219 | + | 0.0596637i | \(0.0190028\pi\) |
−0.873477 | + | 0.486866i | \(0.838140\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.6473 | − | 20.1738i | −0.468146 | − | 0.810853i | 0.531191 | − | 0.847252i | \(-0.321745\pi\) |
−0.999337 | + | 0.0363992i | \(0.988411\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 40.4947 | + | 59.3948i | 1.62500 | + | 2.38343i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20.3137 | − | 14.7354i | 0.813849 | − | 0.590362i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.6991 | + | 5.76791i | 0.747964 | + | 0.230716i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −104.577 | + | 7.83697i | −4.17641 | + | 0.312978i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.45873 | − | 17.5647i | −0.337272 | − | 0.700352i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.8283 | − | 37.0208i | 0.709733 | − | 1.47378i | −0.163535 | − | 0.986538i | \(-0.552290\pi\) |
0.873269 | − | 0.487239i | \(-0.161996\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.63457 | − | 15.0249i | −0.184208 | − | 0.597187i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.30559 | + | 1.10114i | −0.289914 | + | 0.0436975i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.54129 | + | 8.60382i | −0.140311 | + | 0.340896i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.50555 | − | 36.5270i | −0.217796 | − | 1.44498i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.1898 | + | 4.06852i | −0.520967 | + | 0.160697i | −0.544076 | − | 0.839036i | \(-0.683120\pi\) |
0.0231091 | + | 0.999733i | \(0.492643\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.8339 | + | 7.14362i | 0.584991 | + | 0.281717i | 0.702878 | − | 0.711310i | \(-0.251898\pi\) |
−0.117887 | + | 0.993027i | \(0.537612\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.74013 | + | 2.28273i | −0.186643 | + | 0.0898823i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.276330 | − | 3.68737i | −0.0108637 | − | 0.144966i | 0.989134 | − | 0.147015i | \(-0.0469666\pi\) |
−0.999998 | + | 0.00204962i | \(0.999348\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.7189 | − | 54.2013i | 0.656273 | − | 2.12759i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.63843 | + | 42.2720i | 0.299374 | + | 1.65677i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 36.3023 | − | 24.7505i | 1.42062 | − | 0.968561i | 0.422556 | − | 0.906337i | \(-0.361133\pi\) |
0.998062 | − | 0.0622243i | \(-0.0198194\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.363218 | + | 0.209704i | −0.0141921 | + | 0.00819382i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 17.7477 | − | 4.05079i | 0.692403 | − | 0.158036i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.48701 | − | 0.339401i | −0.0579258 | − | 0.0132212i | 0.193460 | − | 0.981108i | \(-0.438029\pi\) |
−0.251386 | + | 0.967887i | \(0.580886\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.38988 | − | 22.4904i | 0.131851 | − | 0.874775i | −0.820911 | − | 0.571056i | \(-0.806534\pi\) |
0.952762 | − | 0.303718i | \(-0.0982281\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.29129 | + | 7.69320i | 0.322007 | + | 0.298779i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.97832 | + | 8.29196i | −0.115494 | + | 0.321549i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 49.4164 | + | 28.5306i | 1.91341 | + | 1.10471i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −38.4880 | + | 35.7117i | −1.48803 | + | 1.38069i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.29326 | + | 7.89150i | −0.242949 | + | 0.304648i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.72482 | − | 10.9406i | −0.336317 | − | 0.421728i | 0.584701 | − | 0.811249i | \(-0.301212\pi\) |
−0.921018 | + | 0.389521i | \(0.872641\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 17.3422 | − | 44.1873i | 0.667503 | − | 1.70077i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.1872 | − | 5.56808i | 0.545260 | − | 0.213999i | −0.0766911 | − | 0.997055i | \(-0.524436\pi\) |
0.621951 | + | 0.783056i | \(0.286340\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.5143 | + | 40.5729i | 0.403502 | + | 1.55704i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.39169 | + | 31.9149i | −0.0916498 | + | 1.22298i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.93609 | − | 13.1068i | 0.341930 | − | 0.501519i | −0.616303 | − | 0.787509i | \(-0.711370\pi\) |
0.958232 | + | 0.285990i | \(0.0923226\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.82762i | 0.222662i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 26.0707i | − | 0.994658i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.02046 | − | 5.89693i | 0.153167 | − | 0.224655i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.23813 | + | 16.5217i | −0.0471007 | + | 0.628515i | 0.922842 | + | 0.385180i | \(0.125861\pi\) |
−0.969942 | + | 0.243335i | \(0.921758\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −26.4574 | − | 102.095i | −1.00503 | − | 3.87825i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.31014 | + | 2.86902i | −0.277290 | + | 0.108828i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.32205 | − | 8.46444i | 0.125832 | − | 0.320614i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.9081 | − | 16.1862i | −0.488228 | − | 0.612218i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.6510 | − | 19.6257i | 0.591128 | − | 0.741252i | −0.392838 | − | 0.919608i | \(-0.628507\pi\) |
0.983966 | + | 0.178356i | \(0.0570780\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −28.0696 | + | 26.0448i | −1.05867 | + | 0.982299i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.196061 | − | 0.113196i | −0.00738408 | − | 0.00426320i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.3929 | + | 40.0715i | −0.541302 | + | 1.50704i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.2783 | − | 15.1041i | −0.611345 | − | 0.567245i | 0.312546 | − | 0.949903i | \(-0.398818\pi\) |
−0.923890 | + | 0.382658i | \(0.875009\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.81727 | + | 65.1333i | −0.368176 | + | 2.44269i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −36.2800 | − | 8.28068i | −1.35870 | − | 0.310114i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.95426 | − | 1.13078i | 0.185279 | − | 0.0422887i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −38.8685 | + | 22.4407i | −1.45157 | + | 0.838064i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.1147 | + | 16.4411i | −0.899327 | + | 0.613151i | −0.922253 | − | 0.386586i | \(-0.873654\pi\) |
0.0229263 | + | 0.999737i | \(0.492702\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.32347 | + | 18.3925i | 0.123773 | + | 0.684973i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.3580 | + | 36.8219i | −0.422410 | + | 1.36942i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.81579 | − | 37.5741i | −0.104576 | − | 1.39547i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.7019 | − | 20.0826i | 1.54664 | − | 0.744822i | 0.550688 | − | 0.834711i | \(-0.314366\pi\) |
0.995952 | + | 0.0898890i | \(0.0286512\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14.3441 | + | 6.90776i | 0.531263 | + | 0.255843i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.50646 | + | 2.31544i | −0.277636 | + | 0.0856395i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.70029 | + | 37.8190i | 0.210545 | + | 1.39688i | 0.805252 | + | 0.592933i | \(0.202030\pi\) |
−0.594707 | + | 0.803943i | \(0.702732\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −12.8653 | − | 2.15631i | −0.474545 | − | 0.0795366i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 62.8160 | − | 9.46799i | 2.31386 | − | 0.348758i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.50652 | + | 8.12593i | 0.0922038 | + | 0.298917i | 0.989914 | − | 0.141669i | \(-0.0452468\pi\) |
−0.897710 | + | 0.440586i | \(0.854771\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.63898 | − | 20.0156i | 0.354097 | − | 0.735290i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.0659 | − | 29.2081i | −0.516026 | − | 1.07154i | −0.982372 | − | 0.186937i | \(-0.940144\pi\) |
0.466346 | − | 0.884603i | \(-0.345570\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.43726 | − | 0.557346i | 0.272480 | − | 0.0204196i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 80.0698 | + | 24.6983i | 2.92960 | + | 0.903662i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.0580 | − | 9.47224i | 0.477130 | − | 0.346108i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.9137 | + | 38.0084i | 0.945604 | + | 1.38695i | 0.921985 | + | 0.387226i | \(0.126567\pi\) |
0.0236197 | + | 0.999721i | \(0.492481\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −38.8379 | − | 67.2691i | −1.41533 | − | 2.45142i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.38889 | + | 10.4664i | 0.0869405 | + | 0.380911i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.25933 | + | 31.8052i | −0.263845 | + | 1.15598i | 0.653197 | + | 0.757188i | \(0.273428\pi\) |
−0.917042 | + | 0.398792i | \(0.869430\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 133.006 | + | 20.0474i | 4.82781 | + | 0.727675i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.5193 | + | 33.9697i | −1.14257 | + | 1.23140i | −0.173444 | + | 0.984844i | \(0.555489\pi\) |
−0.969129 | + | 0.246556i | \(0.920701\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.26067 | − | 26.9439i | 0.118044 | − | 0.975436i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.38584 | + | 9.32854i | −0.194725 | + | 0.337274i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.17278 | + | 8.80817i | 0.295102 | + | 0.318044i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.6859 | + | 21.2813i | 0.962318 | + | 0.767423i | 0.972591 | − | 0.232524i | \(-0.0746986\pi\) |
−0.0102728 | + | 0.999947i | \(0.503270\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −38.0496 | + | 30.3436i | −1.37032 | + | 1.09280i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.0838 | + | 9.84467i | 0.902202 | + | 0.354088i | 0.770678 | − | 0.637225i | \(-0.219918\pi\) |
0.131524 | + | 0.991313i | \(0.458013\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.97754 | + | 22.8744i | 0.322483 | + | 0.821673i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −45.3368 | − | 34.0400i | −1.62645 | − | 1.22118i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17.8099 | − | 1.33467i | −0.638106 | − | 0.0478194i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.1421 | − | 20.5505i | −1.07857 | − | 0.735355i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −83.4819 | −2.98340 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.490172 | −0.0174950 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.32684 | − | 1.58642i | −0.0829431 | − | 0.0565496i | 0.521138 | − | 0.853472i | \(-0.325508\pi\) |
−0.604082 | + | 0.796923i | \(0.706460\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.7908 | + | 0.808656i | 0.384162 | + | 0.0287889i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.01164 | − | 8.99209i | 0.142637 | − | 0.319722i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.781178 | − | 1.99041i | −0.0277404 | − | 0.0706815i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.31479 | + | 3.65579i | 0.330362 | + | 0.129657i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.1223 | − | 18.4394i | 0.819035 | − | 0.653159i | −0.121600 | − | 0.992579i | \(-0.538802\pi\) |
0.940635 | + | 0.339420i | \(0.110231\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.264280 | − | 0.210756i | −0.00934955 | − | 0.00745602i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −40.9883 | − | 44.1749i | −1.44825 | − | 1.56084i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.98907 | − | 15.5695i | 0.317217 | − | 0.549437i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.09085 | − | 9.51870i | 0.214674 | − | 0.335490i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17.3394 | − | 18.6874i | 0.610375 | − | 0.657828i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.3566 | − | 4.57552i | −1.06728 | − | 0.160867i | −0.408165 | − | 0.912908i | \(-0.633831\pi\) |
−0.659116 | + | 0.752042i | \(0.729069\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.05296 | + | 30.9010i | −0.247663 | + | 1.08508i | 0.686189 | + | 0.727423i | \(0.259282\pi\) |
−0.933852 | + | 0.357659i | \(0.883575\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.59780 | + | 7.00040i | 0.0560372 | + | 0.245515i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.944922 | − | 1.63665i | −0.0330992 | − | 0.0573295i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.69154 | + | 12.7482i | 0.304079 | + | 0.446001i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 21.5324 | + | 5.95997i | 0.752402 | + | 0.208258i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.9051 | + | 9.53295i | 1.07859 | + | 0.332702i | 0.782624 | − | 0.622495i | \(-0.213881\pi\) |
0.295970 | + | 0.955197i | \(0.404357\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.15835 | − | 0.686324i | 0.319240 | − | 0.0239237i | 0.0858535 | − | 0.996308i | \(-0.472638\pi\) |
0.233387 | + | 0.972384i | \(0.425019\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −38.5377 | − | 80.0244i | −1.34171 | − | 2.78609i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.39789 | − | 4.97927i | 0.0833829 | − | 0.173146i | −0.855108 | − | 0.518449i | \(-0.826510\pi\) |
0.938491 | + | 0.345303i | \(0.112224\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.95903 | − | 19.3187i | −0.206966 | − | 0.670966i | −0.998229 | − | 0.0594903i | \(-0.981052\pi\) |
0.791263 | − | 0.611476i | \(-0.209424\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 52.1715 | − | 7.86359i | 1.80981 | − | 0.272785i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.5149 | − | 6.04663i | −0.641503 | − | 0.209503i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.40624 | − | 9.32982i | −0.0486651 | − | 0.322872i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 52.0248 | − | 16.0475i | 1.79824 | − | 0.554683i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −46.2048 | − | 22.2511i | −1.59517 | − | 0.768192i | −0.595779 | − | 0.803148i | \(-0.703157\pi\) |
−0.999389 | + | 0.0349560i | \(0.988871\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −33.5754 | + | 16.1691i | −1.15777 | + | 0.557555i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.398635 | + | 5.31942i | 0.0137297 | + | 0.183211i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.01757 | − | 6.54079i | 0.0694064 | − | 0.225010i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −66.0661 | − | 35.6157i | −2.27006 | − | 1.22377i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.160976 | − | 0.109752i | 0.00552468 | − | 0.00376666i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 42.5333 | − | 24.5566i | 1.45802 | − | 0.841789i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −48.4003 | + | 11.0470i | −1.65719 | + | 0.378244i | −0.945851 | − | 0.324602i | \(-0.894770\pi\) |
−0.711342 | + | 0.702846i | \(0.751912\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 20.6265 | + | 4.70787i | 0.705412 | + | 0.161006i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.05860 | − | 40.1962i | 0.206958 | − | 1.37308i | −0.608175 | − | 0.793803i | \(-0.708098\pi\) |
0.815133 | − | 0.579274i | \(-0.196664\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.0542 | − | 17.6797i | −0.650121 | − | 0.603225i | 0.284583 | − | 0.958652i | \(-0.408145\pi\) |
−0.934704 | + | 0.355427i | \(0.884335\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.74427 | − | 26.3001i | −0.0935244 | − | 0.896304i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.61799 | + | 3.24355i | 0.191238 | + | 0.110412i | 0.592562 | − | 0.805525i | \(-0.298116\pi\) |
−0.401324 | + | 0.915936i | \(0.631450\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.90713 | + | 1.76956i | −0.0648445 | + | 0.0601669i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17.6532 | − | 22.1364i | 0.599533 | − | 0.751791i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 40.5589 | + | 50.8593i | 1.37587 | + | 1.72528i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.91645 | + | 12.5269i | −0.166588 | + | 0.424458i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 93.6887 | − | 36.7701i | 3.17088 | − | 1.24448i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15.5164 | + | 0.452717i | −0.524549 | + | 0.0153046i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.47450 | + | 19.6758i | −0.0497902 | + | 0.664404i | 0.915348 | + | 0.402663i | \(0.131915\pi\) |
−0.965138 | + | 0.261740i | \(0.915704\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.58201 | + | 6.72057i | −0.154547 | + | 0.226679i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45.8724i | 1.54548i | 0.634722 | + | 0.772740i | \(0.281115\pi\) | ||||
−0.634722 | + | 0.772740i | \(0.718885\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 45.4282i | − | 1.52878i | −0.644754 | − | 0.764391i | \(-0.723040\pi\) | ||
0.644754 | − | 0.764391i | \(-0.276960\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.49004 | + | 13.9193i | −0.319004 | + | 0.467893i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.00255 | + | 40.0662i | −0.100816 | + | 1.34529i | 0.685773 | + | 0.727815i | \(0.259464\pi\) |
−0.786589 | + | 0.617477i | \(0.788155\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −28.4842 | + | 14.7557i | −0.955330 | + | 0.494890i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −71.8637 | + | 28.2044i | −2.40753 | + | 0.944884i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.242560 | + | 0.618033i | −0.00811697 | + | 0.0206817i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.677702 | − | 0.849811i | −0.0226531 | − | 0.0284061i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −17.7657 | + | 22.2775i | −0.593181 | + | 0.743825i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 31.6796 | − | 29.3943i | 1.05657 | − | 0.980356i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.9391 | + | 7.47039i | 0.431063 | + | 0.248875i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −16.2856 | + | 16.0196i | −0.541950 | + | 0.533100i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.10067 | + | 8.44418i | 0.302516 | + | 0.280694i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.64835 | − | 10.9361i | 0.0547326 | − | 0.363127i | −0.944653 | − | 0.328072i | \(-0.893601\pi\) |
0.999385 | − | 0.0350554i | \(-0.0111608\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 99.6791 | + | 22.7511i | 3.30615 | + | 0.754606i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.258695 | + | 0.0590454i | −0.00857095 | + | 0.00195626i | −0.226804 | − | 0.973940i | \(-0.572828\pi\) |
0.218233 | + | 0.975897i | \(0.429971\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 71.6657 | − | 41.3762i | 2.37179 | − | 1.36935i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.47696 | − | 1.68876i | 0.0818858 | − | 0.0558288i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.19919 | + | 1.37050i | −0.0396007 | + | 0.0452579i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.46079 | − | 24.1873i | 0.246109 | − | 0.797865i | −0.745261 | − | 0.666773i | \(-0.767675\pi\) |
0.991370 | − | 0.131093i | \(-0.0418486\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.33367 | + | 71.1729i | 0.175750 | + | 2.34523i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.96277 | − | 3.35309i | 0.229182 | − | 0.110368i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −29.2195 | − | 14.0713i | −0.960730 | − | 0.462663i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 42.8873 | − | 13.2290i | 1.40860 | − | 0.434497i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.0246981 | + | 0.163861i | 0.000810320 | + | 0.00537612i | 0.989232 | − | 0.146354i | \(-0.0467537\pi\) |
−0.988422 | + | 0.151730i | \(0.951516\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.629773 | + | 38.2507i | −0.0206400 | + | 1.25361i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 47.0730 | − | 7.09511i | 1.54110 | − | 0.232283i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.13560 | + | 10.1654i | 0.102545 | + | 0.332443i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.08630 | + | 8.48530i | −0.133494 | + | 0.277203i | −0.956991 | − | 0.290118i | \(-0.906306\pi\) |
0.823497 | + | 0.567320i | \(0.192020\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −34.8530 | − | 72.3730i | −1.13738 | − | 2.36180i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.474846 | − | 0.0355848i | 0.0154796 | − | 0.00116003i | −0.0669881 | − | 0.997754i | \(-0.521339\pi\) |
0.0824676 | + | 0.996594i | \(0.473720\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 21.8896 | + | 6.75204i | 0.712823 | + | 0.219877i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.754165 | + | 16.5159i | −0.0245330 | + | 0.537261i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.0072 | − | 41.0791i | −0.910113 | − | 1.33489i | −0.942075 | − | 0.335401i | \(-0.891128\pi\) |
0.0319629 | − | 0.999489i | \(-0.489824\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.90423 | + | 3.29823i | 0.0618140 | + | 0.107065i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.0803 | + | 44.1649i | 0.326877 | + | 1.43214i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.40190 | + | 19.2860i | −0.142592 | + | 0.624734i | 0.852236 | + | 0.523157i | \(0.175246\pi\) |
−0.994828 | + | 0.101577i | \(0.967611\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.00740 | − | 0.905470i | −0.194395 | − | 0.0293003i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −106.247 | + | 114.507i | −3.43448 | + | 3.70149i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.16037 | + | 23.9516i | 0.263512 | + | 0.773438i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.40813 | − | 2.43895i | 0.0454235 | − | 0.0786758i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −26.3481 | − | 28.3965i | −0.849056 | − | 0.915065i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.03606 | + | 4.01612i | 0.162116 | + | 0.129284i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.38500 | − | 5.88934i | 0.237486 | − | 0.189388i | −0.497514 | − | 0.867456i | \(-0.665754\pi\) |
0.735000 | + | 0.678067i | \(0.237182\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 43.2914 | + | 16.9906i | 1.39072 | + | 0.545817i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.1629 | + | 43.7304i | 0.550784 | + | 1.40338i | 0.887079 | + | 0.461618i | \(0.152731\pi\) |
−0.336294 | + | 0.941757i | \(0.609174\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −26.0274 | + | 22.0281i | −0.834399 | + | 0.706188i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18.7630 | + | 1.40609i | 0.600896 | + | 0.0450309i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −29.8813 | − | 20.3727i | −0.955987 | − | 0.651781i | −0.0185100 | − | 0.999829i | \(-0.505892\pi\) |
−0.937477 | + | 0.348048i | \(0.886845\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −59.5136 | −1.90206 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −65.1726 | −2.08080 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.72256 | − | 4.58337i | −0.214416 | − | 0.146187i | 0.451350 | − | 0.892347i | \(-0.350943\pi\) |
−0.665766 | + | 0.746161i | \(0.731895\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.06875 | + | 0.379851i | 0.161504 | + | 0.0121030i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.964322 | − | 0.190694i | −0.0306947 | − | 0.00606987i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.22996 | − | 18.4216i | −0.229899 | − | 0.585774i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.64904 | − | 3.00203i | −0.242980 | − | 0.0953625i | 0.240726 | − | 0.970593i | \(-0.422614\pi\) |
−0.483706 | + | 0.875231i | \(0.660710\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 64.8921 | − | 51.7497i | 2.05929 | − | 1.64223i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.45110 | − | 1.95469i | −0.0777050 | − | 0.0619677i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.4673 | − | 36.0692i | −1.05992 | − | 1.14232i | −0.989460 | − | 0.144809i | \(-0.953743\pi\) |
−0.0704619 | − | 0.997514i | \(-0.522447\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −35.9269 | + | 62.2272i | −1.13668 | + | 1.96878i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 784.2.bp.c.495.10 | yes | 120 | |
4.3 | odd | 2 | inner | 784.2.bp.c.495.1 | yes | 120 | |
49.10 | odd | 42 | inner | 784.2.bp.c.255.1 | ✓ | 120 | |
196.59 | even | 42 | inner | 784.2.bp.c.255.10 | yes | 120 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
784.2.bp.c.255.1 | ✓ | 120 | 49.10 | odd | 42 | inner | |
784.2.bp.c.255.10 | yes | 120 | 196.59 | even | 42 | inner | |
784.2.bp.c.495.1 | yes | 120 | 4.3 | odd | 2 | inner | |
784.2.bp.c.495.10 | yes | 120 | 1.1 | even | 1 | trivial |