Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(353,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.353");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.m (of order \(6\), degree \(2\), 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: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 353.2 | ||
Character | \(\chi\) | \(=\) | 684.353 |
Dual form | 684.3.m.a.653.2 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(3\) | −2.99460 | − | 0.179992i | −0.998199 | − | 0.0599974i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 0.944063i | − | 0.188813i | −0.995534 | − | 0.0944063i | \(-0.969905\pi\) | ||
0.995534 | − | 0.0944063i | \(-0.0300953\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.01764 | + | 8.69081i | −0.716806 | + | 1.24154i | 0.245453 | + | 0.969408i | \(0.421063\pi\) |
−0.962259 | + | 0.272135i | \(0.912270\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.93521 | + | 1.07801i | 0.992801 | + | 0.119779i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.50935 | + | 1.44878i | 0.228123 | + | 0.131707i | 0.609706 | − | 0.792628i | \(-0.291288\pi\) |
−0.381583 | + | 0.924335i | \(0.624621\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.63747 | − | 6.30028i | 0.279805 | − | 0.484637i | −0.691531 | − | 0.722347i | \(-0.743063\pi\) |
0.971336 | + | 0.237710i | \(0.0763967\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.169924 | + | 2.82709i | −0.0113283 | + | 0.188472i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 15.0969 | + | 8.71618i | 0.888051 | + | 0.512717i | 0.873305 | − | 0.487175i | \(-0.161972\pi\) |
0.0147468 | + | 0.999891i | \(0.495306\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −18.3970 | + | 4.74856i | −0.968265 | + | 0.249924i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 16.5901 | − | 25.1223i | 0.790004 | − | 1.19630i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −11.5334 | − | 6.65879i | −0.501450 | − | 0.289512i | 0.227862 | − | 0.973693i | \(-0.426826\pi\) |
−0.729312 | + | 0.684181i | \(0.760160\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.1087 | 0.964350 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −26.5633 | − | 4.83646i | −0.983826 | − | 0.179128i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 16.6225i | − | 0.573190i | −0.958052 | − | 0.286595i | \(-0.907477\pi\) | ||
0.958052 | − | 0.286595i | \(-0.0925234\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.71890 | + | 8.17338i | 0.152223 | + | 0.263657i | 0.932044 | − | 0.362344i | \(-0.118024\pi\) |
−0.779822 | + | 0.626002i | \(0.784690\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.25373 | − | 4.79016i | −0.219810 | − | 0.145156i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.20467 | + | 4.73697i | 0.234419 | + | 0.135342i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −63.1336 | −1.70631 | −0.853156 | − | 0.521655i | \(-0.825315\pi\) | ||||
−0.853156 | + | 0.521655i | \(0.825315\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12.0267 | + | 18.2121i | −0.308378 | + | 0.466976i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 34.1661i | 0.833319i | 0.909063 | + | 0.416659i | \(0.136799\pi\) | ||||
−0.909063 | + | 0.416659i | \(0.863201\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −23.8541 | − | 41.3166i | −0.554747 | − | 0.960850i | −0.997923 | − | 0.0644157i | \(-0.979482\pi\) |
0.443176 | − | 0.896435i | \(-0.353852\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.01771 | − | 8.43540i | 0.0226157 | − | 0.187453i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 42.6230i | − | 0.906873i | −0.891289 | − | 0.453437i | \(-0.850198\pi\) | ||
0.891289 | − | 0.453437i | \(-0.149802\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −25.8534 | − | 44.7794i | −0.527620 | − | 0.913865i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −43.6402 | − | 28.8188i | −0.855690 | − | 0.565074i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −69.9633 | + | 40.3933i | −1.32006 | + | 0.762138i | −0.983738 | − | 0.179609i | \(-0.942517\pi\) |
−0.336323 | + | 0.941747i | \(0.609183\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.36774 | − | 2.36899i | 0.0248679 | − | 0.0430725i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 55.9464 | − | 10.9087i | 0.981516 | − | 0.191381i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 92.1179i | 1.56132i | 0.624955 | + | 0.780661i | \(0.285117\pi\) | ||||
−0.624955 | + | 0.780661i | \(0.714883\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −56.9441 | −0.933509 | −0.466755 | − | 0.884387i | \(-0.654577\pi\) | ||||
−0.466755 | + | 0.884387i | \(0.654577\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −54.2024 | + | 72.2451i | −0.860355 | + | 1.14675i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.94786 | − | 3.43400i | −0.0915056 | − | 0.0528308i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −39.6354 | + | 68.6505i | −0.591573 | + | 1.02463i | 0.402448 | + | 0.915443i | \(0.368160\pi\) |
−0.994021 | + | 0.109192i | \(0.965174\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 33.3392 | + | 22.0163i | 0.483177 | + | 0.319077i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −61.9380 | − | 35.7599i | −0.872366 | − | 0.503661i | −0.00423248 | − | 0.999991i | \(-0.501347\pi\) |
−0.868134 | + | 0.496330i | \(0.834681\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 63.6907 | − | 110.316i | 0.872475 | − | 1.51117i | 0.0130472 | − | 0.999915i | \(-0.495847\pi\) |
0.859428 | − | 0.511257i | \(-0.170820\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −72.1959 | − | 4.33938i | −0.962613 | − | 0.0578584i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −25.1820 | + | 14.5389i | −0.327040 | + | 0.188816i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.36504 | − | 5.82843i | −0.0425955 | − | 0.0737776i | 0.843942 | − | 0.536435i | \(-0.180229\pi\) |
−0.886537 | + | 0.462657i | \(0.846896\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 78.6758 | + | 19.2644i | 0.971306 | + | 0.237832i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −101.821 | − | 58.7865i | −1.22676 | − | 0.708271i | −0.260410 | − | 0.965498i | \(-0.583858\pi\) |
−0.966351 | + | 0.257227i | \(0.917191\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.22863 | − | 14.2524i | 0.0968074 | − | 0.167675i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.99192 | + | 49.7777i | −0.0343899 | + | 0.572157i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −87.6080 | + | 50.5805i | −0.984360 | + | 0.568320i | −0.903584 | − | 0.428412i | \(-0.859073\pi\) |
−0.0807762 | + | 0.996732i | \(0.525740\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 36.5030 | + | 63.2251i | 0.401132 | + | 0.694781i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.6601 | − | 25.3253i | −0.136130 | − | 0.272315i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.48294 | + | 17.3680i | 0.0471889 | + | 0.182821i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −42.5419 | − | 73.6847i | −0.438576 | − | 0.759637i | 0.559004 | − | 0.829165i | \(-0.311184\pi\) |
−0.997580 | + | 0.0695287i | \(0.977850\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 20.8598 | + | 15.6502i | 0.210705 | + | 0.158083i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 196.653i | − | 1.94706i | −0.228552 | − | 0.973532i | \(-0.573399\pi\) | ||
0.228552 | − | 0.973532i | \(-0.426601\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −32.8937 | − | 56.9735i | −0.319356 | − | 0.553141i | 0.660998 | − | 0.750388i | \(-0.270133\pi\) |
−0.980354 | + | 0.197247i | \(0.936800\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −23.7170 | − | 15.6621i | −0.225877 | − | 0.149163i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 2.00186i | − | 0.0187090i | −0.999956 | − | 0.00935448i | \(-0.997022\pi\) | ||
0.999956 | − | 0.00935448i | \(-0.00297767\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 33.9399 | − | 58.7857i | 0.311375 | − | 0.539318i | −0.667285 | − | 0.744802i | \(-0.732544\pi\) |
0.978660 | + | 0.205485i | \(0.0658770\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 189.060 | + | 11.3635i | 1.70324 | + | 0.102374i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −92.2373 | + | 53.2532i | −0.816260 | + | 0.471268i | −0.849125 | − | 0.528192i | \(-0.822870\pi\) |
0.0328653 | + | 0.999460i | \(0.489537\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.28631 | + | 10.8882i | −0.0546636 | + | 0.0946801i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 39.2933 | − | 52.3731i | 0.335840 | − | 0.447633i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −151.501 | + | 87.4693i | −1.27312 | + | 0.735036i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −56.3021 | − | 97.5181i | −0.465307 | − | 0.805935i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.14962 | − | 102.314i | 0.0499969 | − | 0.831818i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 46.3617i | − | 0.370894i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.57128 | − | 14.8459i | −0.0674904 | − | 0.116897i | 0.830306 | − | 0.557308i | \(-0.188166\pi\) |
−0.897796 | + | 0.440412i | \(0.854833\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 63.9968 | + | 128.020i | 0.496099 | + | 0.992403i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 175.291i | 1.33810i | 0.743218 | + | 0.669049i | \(0.233298\pi\) | ||||
−0.743218 | + | 0.669049i | \(0.766702\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 51.0409 | − | 183.712i | 0.383766 | − | 1.38129i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.56592 | + | 25.0774i | −0.0338217 | + | 0.185759i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 171.435i | 1.25135i | 0.780084 | + | 0.625675i | \(0.215176\pi\) | ||||
−0.780084 | + | 0.625675i | \(0.784824\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 31.9396 | − | 55.3210i | 0.229781 | − | 0.397993i | −0.727962 | − | 0.685618i | \(-0.759532\pi\) |
0.957743 | + | 0.287625i | \(0.0928655\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.67181 | + | 127.639i | −0.0544100 | + | 0.905240i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 18.2554 | − | 10.5398i | 0.127660 | − | 0.0737046i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15.6927 | −0.108225 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 69.3605 | + | 138.750i | 0.471840 | + | 0.943875i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 161.148i | 1.08153i | 0.841173 | + | 0.540766i | \(0.181866\pi\) | ||||
−0.841173 | + | 0.540766i | \(0.818134\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 97.2259 | − | 168.400i | 0.643880 | − | 1.11523i | −0.340679 | − | 0.940180i | \(-0.610657\pi\) |
0.984559 | − | 0.175053i | \(-0.0560098\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 125.498 | + | 94.1554i | 0.820246 | + | 0.615395i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.71618 | − | 4.45494i | 0.0497818 | − | 0.0287415i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −60.0978 | −0.382789 | −0.191394 | − | 0.981513i | \(-0.561301\pi\) | ||||
−0.191394 | + | 0.981513i | \(0.561301\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 216.782 | − | 108.369i | 1.36341 | − | 0.681565i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 115.740 | − | 66.8228i | 0.718885 | − | 0.415048i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 37.0420 | 0.227252 | 0.113626 | − | 0.993524i | \(-0.463753\pi\) | ||||
0.113626 | + | 0.993524i | \(0.463753\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.52221 | + | 6.84798i | −0.0274073 | + | 0.0415029i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.3428 | + | 11.1676i | 0.115825 | + | 0.0668718i | 0.556793 | − | 0.830651i | \(-0.312031\pi\) |
−0.440968 | + | 0.897523i | \(0.645365\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 58.0376 | + | 100.524i | 0.343418 | + | 0.594817i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −169.500 | + | 22.5972i | −0.991230 | + | 0.132148i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 189.603 | − | 109.467i | 1.09597 | − | 0.632759i | 0.160811 | − | 0.986985i | \(-0.448589\pi\) |
0.935160 | + | 0.354227i | \(0.115256\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −120.969 | + | 209.524i | −0.691251 | + | 1.19728i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.5805 | − | 275.856i | 0.0936751 | − | 1.55851i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 71.3531i | 0.398621i | 0.979936 | + | 0.199310i | \(0.0638702\pi\) | ||||
−0.979936 | + | 0.199310i | \(0.936130\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 42.9974 | + | 74.4737i | 0.237555 | + | 0.411457i | 0.960012 | − | 0.279959i | \(-0.0903207\pi\) |
−0.722457 | + | 0.691416i | \(0.756987\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 170.524 | + | 10.2495i | 0.931827 | + | 0.0560081i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 59.6021i | 0.322173i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 25.2556 | + | 43.7440i | 0.135057 | + | 0.233925i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 175.318 | − | 206.589i | 0.927607 | − | 1.09306i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 276.487 | + | 159.630i | 1.44757 | + | 0.835757i | 0.998337 | − | 0.0576547i | \(-0.0183623\pi\) |
0.449238 | + | 0.893412i | \(0.351696\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 112.770 | 0.584300 | 0.292150 | − | 0.956372i | \(-0.405629\pi\) | ||||
0.292150 | + | 0.956372i | \(0.405629\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 17.1933 | + | 11.3540i | 0.0881710 | + | 0.0582257i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 94.3781i | 0.479077i | 0.970887 | + | 0.239538i | \(0.0769961\pi\) | ||||
−0.970887 | + | 0.239538i | \(0.923004\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 149.404 | + | 258.776i | 0.750775 | + | 1.30038i | 0.947447 | + | 0.319911i | \(0.103653\pi\) |
−0.196672 | + | 0.980469i | \(0.563013\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 131.049 | − | 198.446i | 0.651983 | − | 0.987296i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 144.463 | + | 83.4057i | 0.711640 | + | 0.410866i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 32.2549 | 0.157341 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −95.8747 | − | 71.9307i | −0.463163 | − | 0.347491i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −53.0443 | − | 14.7374i | −0.253800 | − | 0.0705137i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −32.9241 | −0.156039 | −0.0780193 | − | 0.996952i | \(-0.524860\pi\) | ||||
−0.0780193 | + | 0.996952i | \(0.524860\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 179.043 | + | 118.235i | 0.840577 | + | 0.555093i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −39.0054 | + | 22.5198i | −0.181421 | + | 0.104743i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −94.7110 | −0.436456 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −210.584 | + | 318.887i | −0.961570 | + | 1.45610i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 109.829 | − | 63.4097i | 0.496963 | − | 0.286922i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −122.138 | − | 211.549i | −0.547704 | − | 0.948652i | −0.998431 | − | 0.0559898i | \(-0.982169\pi\) |
0.450727 | − | 0.892662i | \(-0.351165\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 215.417 | + | 25.9894i | 0.957407 | + | 0.115508i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −376.013 | − | 217.091i | −1.65644 | − | 0.956348i | −0.974337 | − | 0.225095i | \(-0.927731\pi\) |
−0.682107 | − | 0.731253i | \(-0.738936\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −202.602 | − | 350.917i | −0.884724 | − | 1.53239i | −0.846030 | − | 0.533136i | \(-0.821014\pi\) |
−0.0386942 | − | 0.999251i | \(-0.512320\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 78.0269 | − | 39.0054i | 0.337779 | − | 0.168855i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 200.063 | + | 115.506i | 0.858639 | + | 0.495735i | 0.863556 | − | 0.504253i | \(-0.168232\pi\) |
−0.00491747 | + | 0.999988i | \(0.501565\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −40.2388 | −0.171229 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.02788 | + | 18.0595i | 0.0380923 | + | 0.0762003i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −83.8959 | + | 48.4373i | −0.351029 | + | 0.202667i | −0.665138 | − | 0.746720i | \(-0.731627\pi\) |
0.314110 | + | 0.949387i | \(0.398294\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −298.299 | −1.23775 | −0.618877 | − | 0.785488i | \(-0.712412\pi\) | ||||
−0.618877 | + | 0.785488i | \(0.712412\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −232.135 | − | 71.8502i | −0.955287 | − | 0.295680i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −42.2746 | + | 24.4072i | −0.172549 | + | 0.0996214i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −37.0014 | + | 133.179i | −0.149803 | + | 0.539187i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 294.332 | + | 194.369i | 1.18206 | + | 0.780597i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.82420 | + | 1.63055i | −0.0112518 | + | 0.00649622i | −0.505615 | − | 0.862759i | \(-0.668734\pi\) |
0.494364 | + | 0.869255i | \(0.335401\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.2942 | − | 33.4185i | −0.0762615 | − | 0.132089i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −27.2067 | + | 41.1991i | −0.106693 | + | 0.161565i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −75.6315 | − | 43.6659i | −0.294286 | − | 0.169906i | 0.345587 | − | 0.938387i | \(-0.387680\pi\) |
−0.639873 | + | 0.768481i | \(0.721013\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 316.781 | − | 548.682i | 1.22309 | − | 2.11846i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 17.9192 | − | 148.526i | 0.0686559 | − | 0.569063i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −146.393 | + | 84.5202i | −0.556629 | + | 0.321370i | −0.751791 | − | 0.659401i | \(-0.770810\pi\) |
0.195163 | + | 0.980771i | \(0.437477\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 38.1338 | + | 66.0497i | 0.143901 | + | 0.249244i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 271.455 | − | 135.699i | 1.01668 | − | 0.508238i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −28.8312 | − | 16.6457i | −0.107179 | − | 0.0618798i | 0.445452 | − | 0.895306i | \(-0.353043\pi\) |
−0.552631 | + | 0.833426i | \(0.686376\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 101.879 | − | 176.460i | 0.375938 | − | 0.651144i | −0.614529 | − | 0.788894i | \(-0.710654\pi\) |
0.990467 | + | 0.137750i | \(0.0439871\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −97.9317 | − | 195.904i | −0.358724 | − | 0.717596i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 60.4973 | + | 34.9282i | 0.219990 | + | 0.127011i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 69.4690 | − | 120.324i | 0.250791 | − | 0.434382i | −0.712953 | − | 0.701212i | \(-0.752643\pi\) |
0.963744 | + | 0.266830i | \(0.0859761\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 33.3534 | + | 78.1178i | 0.119546 | + | 0.279992i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 145.827i | 0.518956i | 0.965749 | + | 0.259478i | \(0.0835505\pi\) | ||||
−0.965749 | + | 0.259478i | \(0.916450\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −333.171 | −1.17728 | −0.588641 | − | 0.808395i | \(-0.700337\pi\) | ||||
−0.588641 | + | 0.808395i | \(0.700337\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10.2985 | − | 52.8169i | −0.0361351 | − | 0.185323i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −296.931 | − | 171.433i | −1.03460 | − | 0.597328i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.44374 | + | 12.8929i | 0.0257569 | + | 0.0446123i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 114.133 | + | 228.313i | 0.392210 | + | 0.784582i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −163.865 | + | 94.6077i | −0.559267 | + | 0.322893i | −0.752851 | − | 0.658191i | \(-0.771322\pi\) |
0.193584 | + | 0.981084i | \(0.437989\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 86.9651 | 0.294797 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −59.6497 | − | 50.6206i | −0.200841 | − | 0.170440i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −83.9044 | + | 48.4423i | −0.280617 | + | 0.162014i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 478.766 | 1.59058 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −35.3960 | + | 588.897i | −0.116819 | + | 1.94356i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 53.7588i | 0.176258i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 42.5147 | − | 73.6377i | 0.138484 | − | 0.239862i | −0.788439 | − | 0.615113i | \(-0.789110\pi\) |
0.926923 | + | 0.375251i | \(0.122444\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 88.2485 | + | 176.533i | 0.285594 | + | 0.571305i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 119.243 | − | 68.8452i | 0.383420 | − | 0.221367i | −0.295885 | − | 0.955223i | \(-0.595615\pi\) |
0.679305 | + | 0.733856i | \(0.262281\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 38.4710 | 0.122910 | 0.0614552 | − | 0.998110i | \(-0.480426\pi\) | ||||
0.0614552 | + | 0.998110i | \(0.480426\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 68.2039 | + | 51.1705i | 0.216520 | + | 0.162446i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 343.114i | 1.08238i | 0.840901 | + | 0.541189i | \(0.182026\pi\) | ||||
−0.840901 | + | 0.541189i | \(0.817974\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.0823 | − | 41.7117i | 0.0754930 | − | 0.130758i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.360319 | + | 5.99476i | −0.00112249 | + | 0.0186753i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −319.127 | − | 88.6636i | −0.988010 | − | 0.274500i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 87.6948 | − | 151.892i | 0.269830 | − | 0.467360i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −112.217 | + | 169.930i | −0.343172 | + | 0.519665i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 370.429 | + | 213.867i | 1.12592 | + | 0.650052i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −59.9385 | + | 103.817i | −0.181083 | + | 0.313645i | −0.942250 | − | 0.334911i | \(-0.891294\pi\) |
0.761167 | + | 0.648556i | \(0.224627\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −564.111 | − | 68.0584i | −1.69403 | − | 0.204380i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 64.8104 | + | 37.4183i | 0.193464 | + | 0.111696i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −228.092 | −0.676830 | −0.338415 | − | 0.940997i | \(-0.609891\pi\) | ||||
−0.338415 | + | 0.940997i | \(0.609891\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 285.799 | − | 142.870i | 0.843064 | − | 0.421445i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 27.3465i | 0.0801951i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 27.1635 | 0.0791938 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 20.7848 | − | 31.4743i | 0.0602457 | − | 0.0912299i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 153.282i | − | 0.441734i | −0.975304 | − | 0.220867i | \(-0.929111\pi\) | ||
0.975304 | − | 0.220867i | \(-0.0708887\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −166.507 | + | 288.398i | −0.477097 | + | 0.826356i | −0.999655 | − | 0.0262473i | \(-0.991644\pi\) |
0.522559 | + | 0.852603i | \(0.324978\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −127.094 | + | 149.764i | −0.362092 | + | 0.426677i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −158.739 | − | 91.6479i | −0.449685 | − | 0.259626i | 0.258012 | − | 0.966142i | \(-0.416933\pi\) |
−0.707697 | + | 0.706516i | \(0.750266\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −33.7596 | + | 58.4734i | −0.0950975 | + | 0.164714i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 469.429 | − | 234.666i | 1.31493 | − | 0.657328i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 420.734 | + | 242.911i | 1.17196 | + | 0.676633i | 0.954141 | − | 0.299356i | \(-0.0967719\pi\) |
0.217821 | + | 0.975989i | \(0.430105\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 315.902 | − | 174.719i | 0.875076 | − | 0.483986i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 151.050 | + | 302.161i | 0.416114 | + | 0.832400i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −104.145 | − | 60.1280i | −0.285328 | − | 0.164734i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −173.687 | −0.473262 | −0.236631 | − | 0.971600i | \(-0.576043\pi\) | ||||
−0.236631 | + | 0.971600i | \(0.576043\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −36.8313 | + | 305.281i | −0.0998137 | + | 0.827319i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 810.716i | − | 2.18522i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 69.7815 | + | 120.865i | 0.187082 | + | 0.324035i | 0.944276 | − | 0.329155i | \(-0.106764\pi\) |
−0.757194 | + | 0.653190i | \(0.773430\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.34475 | + | 138.835i | −0.0222527 | + | 0.370226i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −104.726 | − | 60.4639i | −0.277789 | − | 0.160382i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 307.458 | 0.811234 | 0.405617 | − | 0.914043i | \(-0.367057\pi\) | ||||
0.405617 | + | 0.914043i | \(0.367057\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 22.9954 | + | 46.0002i | 0.0603553 | + | 0.120735i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 187.428i | 0.489369i | 0.969603 | + | 0.244685i | \(0.0786844\pi\) | ||||
−0.969603 | + | 0.244685i | \(0.921316\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.7256 | + | 23.7734i | 0.0356509 | + | 0.0617492i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −168.602 | − | 394.887i | −0.435664 | − | 1.02038i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 658.884i | − | 1.69379i | −0.531761 | − | 0.846895i | \(-0.678469\pi\) | ||
0.531761 | − | 0.846895i | \(-0.321531\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −116.078 | − | 201.054i | −0.296876 | − | 0.514204i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 31.5510 | − | 524.925i | 0.0802824 | − | 1.33569i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.50240 | + | 3.17681i | −0.0139301 | + | 0.00804257i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −357.219 | + | 618.721i | −0.899796 | + | 1.55849i | −0.0720408 | + | 0.997402i | \(0.522951\pi\) |
−0.827755 | + | 0.561090i | \(0.810382\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −185.913 | + | 540.955i | −0.465948 | + | 1.35578i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 712.138i | 1.77590i | 0.459936 | + | 0.887952i | \(0.347872\pi\) | ||||
−0.459936 | + | 0.887952i | \(0.652128\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 68.6594 | 0.170371 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.1868 | − | 74.2749i | 0.0449058 | − | 0.183395i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −158.424 | − | 91.4664i | −0.389249 | − | 0.224733i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −35.7805 | + | 61.9736i | −0.0874828 | + | 0.151525i | −0.906446 | − | 0.422321i | \(-0.861216\pi\) |
0.818964 | + | 0.573845i | \(0.194549\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 30.8569 | − | 513.378i | 0.0750777 | − | 1.24910i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −800.579 | − | 462.215i | −1.93845 | − | 1.11916i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −55.4981 | + | 96.1256i | −0.133730 | + | 0.231628i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −105.604 | + | 159.915i | −0.253246 | + | 0.383490i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −339.757 | + | 196.159i | −0.810875 | + | 0.468159i | −0.847260 | − | 0.531179i | \(-0.821749\pi\) |
0.0363848 | + | 0.999338i | \(0.488416\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 100.615 | + | 174.271i | 0.238991 | + | 0.413945i | 0.960425 | − | 0.278538i | \(-0.0898499\pi\) |
−0.721434 | + | 0.692484i | \(0.756517\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 45.9479 | − | 380.846i | 0.108624 | − | 0.900344i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 363.967 | + | 210.136i | 0.856392 | + | 0.494438i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 285.725 | − | 494.890i | 0.669144 | − | 1.15899i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −56.5646 | + | 28.2765i | −0.131852 | + | 0.0659125i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −158.719 | + | 91.6364i | −0.368257 | + | 0.212613i | −0.672697 | − | 0.739918i | \(-0.734864\pi\) |
0.304440 | + | 0.952532i | \(0.401531\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −341.233 | − | 591.034i | −0.788068 | − | 1.36497i | −0.927149 | − | 0.374693i | \(-0.877748\pi\) |
0.139081 | − | 0.990281i | \(-0.455585\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 46.9933 | + | 2.82456i | 0.108031 | + | 0.00649324i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 243.799 | + | 67.7351i | 0.557893 | + | 0.155000i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 135.974 | + | 235.514i | 0.309736 | + | 0.536478i | 0.978304 | − | 0.207172i | \(-0.0664261\pi\) |
−0.668569 | + | 0.743650i | \(0.733093\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −182.733 | − | 427.983i | −0.414360 | − | 0.970484i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 139.879i | − | 0.315754i | −0.987459 | − | 0.157877i | \(-0.949535\pi\) | ||
0.987459 | − | 0.157877i | \(-0.0504649\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 47.7512 | + | 82.7075i | 0.107306 | + | 0.185860i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 29.0054 | − | 482.574i | 0.0648890 | − | 1.07958i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 290.887i | − | 0.647855i | −0.946082 | − | 0.323928i | \(-0.894997\pi\) | ||
0.946082 | − | 0.323928i | \(-0.105003\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −49.4990 | + | 85.7347i | −0.109754 | + | 0.190099i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −321.463 | + | 486.791i | −0.709631 | + | 1.07459i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 59.6884 | − | 34.4611i | 0.131183 | − | 0.0757388i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −256.031 | + | 443.459i | −0.560244 | + | 0.970371i | 0.437231 | + | 0.899349i | \(0.355959\pi\) |
−0.997475 | + | 0.0710214i | \(0.977374\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −358.867 | − | 304.546i | −0.781846 | − | 0.663499i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 655.852 | − | 378.657i | 1.42267 | − | 0.821381i | 0.426147 | − | 0.904654i | \(-0.359871\pi\) |
0.996527 | + | 0.0832733i | \(0.0265375\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.97566 | + | 5.15400i | 0.00642692 | + | 0.0111318i | 0.869221 | − | 0.494424i | \(-0.164621\pi\) |
−0.862794 | + | 0.505556i | \(0.831288\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −23.9087 | + | 11.9519i | −0.0514166 | + | 0.0257030i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 329.416i | 0.705387i | 0.935739 | + | 0.352693i | \(0.114734\pi\) | ||||
−0.935739 | + | 0.352693i | \(0.885266\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −397.752 | − | 688.927i | −0.848086 | − | 1.46893i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 179.969 | + | 10.8171i | 0.382099 | + | 0.0229663i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 138.237i | − | 0.292256i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −443.530 | + | 114.482i | −0.933747 | + | 0.241014i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −668.680 | + | 285.502i | −1.40185 | + | 0.598536i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 63.0086i | − | 0.131542i | −0.997835 | − | 0.0657710i | \(-0.979049\pi\) | ||
0.997835 | − | 0.0657710i | \(-0.0209507\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −229.646 | + | 397.759i | −0.477435 | + | 0.826942i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −358.623 | + | 179.275i | −0.742491 | + | 0.371169i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −69.5630 | + | 40.1622i | −0.143429 | + | 0.0828087i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −83.6068 | −0.171677 | −0.0858386 | − | 0.996309i | \(-0.527357\pi\) | ||||
−0.0858386 | + | 0.996309i | \(0.527357\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −110.926 | − | 6.66727i | −0.226842 | − | 0.0136345i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 15.2612i | − | 0.0310819i | −0.999879 | − | 0.0155409i | \(-0.995053\pi\) | ||
0.999879 | − | 0.0155409i | \(-0.00494703\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 144.885 | − | 250.948i | 0.293884 | − | 0.509022i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.7748 | − | 19.6930i | 0.0298480 | − | 0.0397837i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 621.565 | − | 358.861i | 1.25063 | − | 0.722054i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 38.5770 | 0.0773086 | 0.0386543 | − | 0.999253i | \(-0.487693\pi\) | ||||
0.0386543 | + | 0.999253i | \(0.487693\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −55.9139 | − | 36.9240i | −0.111605 | − | 0.0737005i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −146.505 | + | 84.5850i | −0.291263 | + | 0.168161i | −0.638511 | − | 0.769612i | \(-0.720449\pi\) |
0.347248 | + | 0.937773i | \(0.387116\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −185.653 | −0.367630 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −155.706 | − | 311.475i | −0.307112 | − | 0.614350i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −403.328 | − | 232.861i | −0.792392 | − | 0.457488i | 0.0484118 | − | 0.998827i | \(-0.484584\pi\) |
−0.840804 | + | 0.541340i | \(0.817917\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 639.154 | + | 1107.05i | 1.25079 | + | 2.16643i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 511.652 | − | 37.1609i | 0.997373 | − | 0.0724384i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −53.7866 | + | 31.0537i | −0.104440 | + | 0.0602984i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 61.7512 | − | 106.956i | 0.119441 | − | 0.206879i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −587.487 | + | 293.683i | −1.13196 | + | 0.565863i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 940.532i | 1.80524i | 0.430433 | + | 0.902622i | \(0.358361\pi\) | ||||
−0.430433 | + | 0.902622i | \(0.641639\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 180.183 | + | 312.086i | 0.344518 | + | 0.596723i | 0.985266 | − | 0.171028i | \(-0.0547090\pi\) |
−0.640748 | + | 0.767751i | \(0.721376\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 399.966 | − | 605.667i | 0.761840 | − | 1.15365i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 164.523i | 0.312188i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −175.821 | − | 304.531i | −0.332365 | − | 0.575673i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −99.3038 | + | 823.093i | −0.187013 | + | 1.55008i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 215.256 | + | 124.278i | 0.403857 | + | 0.233167i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.88988 | −0.00353249 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.8430 | − | 213.674i | 0.0239162 | − | 0.397903i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 149.823i | − | 0.277965i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 242.147 | + | 419.411i | 0.447591 | + | 0.775251i | 0.998229 | − | 0.0594939i | \(-0.0189487\pi\) |
−0.550638 | + | 0.834744i | \(0.685615\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −115.355 | − | 230.758i | −0.212441 | − | 0.424969i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −55.4974 | − | 32.0414i | −0.101830 | − | 0.0587916i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.1222 | 0.0568961 | 0.0284481 | − | 0.999595i | \(-0.490943\pi\) | ||||
0.0284481 | + | 0.999595i | \(0.490943\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −508.807 | − | 61.3861i | −0.926788 | − | 0.111814i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 78.9330 | + | 305.805i | 0.143254 | + | 0.555000i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 67.5383 | 0.122131 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.7279 | − | 178.484i | 0.0193295 | − | 0.321593i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −267.742 | + | 154.581i | −0.480685 | + | 0.277524i | −0.720702 | − | 0.693245i | \(-0.756180\pi\) |
0.240017 | + | 0.970769i | \(0.422847\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −347.075 | −0.620885 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −67.7567 | − | 135.541i | −0.120778 | − | 0.241607i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 694.453 | − | 400.943i | 1.23349 | − | 0.712154i | 0.265732 | − | 0.964047i | \(-0.414386\pi\) |
0.967755 | + | 0.251893i | \(0.0810530\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 50.2744 | + | 87.0778i | 0.0889813 | + | 0.154120i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −562.190 | + | 587.094i | −0.991517 | + | 1.03544i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 94.4488 | + | 54.5300i | 0.165991 | + | 0.0958349i | 0.580694 | − | 0.814122i | \(-0.302781\pi\) |
−0.414703 | + | 0.909957i | \(0.636115\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 240.420 | + | 416.419i | 0.421050 | + | 0.729281i | 0.996043 | − | 0.0888782i | \(-0.0283282\pi\) |
−0.574992 | + | 0.818159i | \(0.694995\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −799.234 | − | 527.792i | −1.39482 | − | 0.921103i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −278.055 | − | 160.535i | −0.483573 | − | 0.279191i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1108.78 | −1.92164 | −0.960818 | − | 0.277179i | \(-0.910601\pi\) | ||||
−0.960818 | + | 0.277179i | \(0.910601\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −337.700 | − | 20.2977i | −0.583248 | − | 0.0350565i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1021.80 | − | 589.939i | 1.75870 | − | 1.01538i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −234.083 | −0.401515 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −49.4435 | − | 37.0953i | −0.0845188 | − | 0.0634108i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 840.894 | − | 485.490i | 1.43253 | − | 0.827070i | 0.435215 | − | 0.900327i | \(-0.356672\pi\) |
0.997313 | + | 0.0732563i | \(0.0233391\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −125.626 | − | 127.958i | −0.213286 | − | 0.217246i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.9873 | − | 282.624i | 0.0287433 | − | 0.478214i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −399.441 | + | 230.618i | −0.673594 | + | 0.388900i | −0.797437 | − | 0.603402i | \(-0.793811\pi\) |
0.123843 | + | 0.992302i | \(0.460478\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 82.5765 | + | 143.027i | 0.138784 | + | 0.240381i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −400.828 | − | 801.820i | −0.671403 | − | 1.34308i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −930.550 | − | 537.253i | −1.55351 | − | 0.896917i | −0.997852 | − | 0.0655020i | \(-0.979135\pi\) |
−0.555653 | − | 0.831415i | \(-0.687532\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −352.905 | + | 611.249i | −0.587196 | + | 1.01705i | 0.407401 | + | 0.913249i | \(0.366435\pi\) |
−0.994598 | + | 0.103805i | \(0.966898\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −428.156 | + | 570.679i | −0.710043 | + | 0.946400i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −92.0632 | + | 53.1527i | −0.152171 | + | 0.0878557i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 499.764 | + | 865.617i | 0.823335 | + | 1.42606i | 0.903185 | + | 0.429251i | \(0.141222\pi\) |
−0.0798504 | + | 0.996807i | \(0.525444\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −417.596 | − | 275.769i | −0.685707 | − | 0.452822i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −268.537 | − | 155.040i | −0.439504 | − | 0.253748i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.0192 | + | 45.0666i | −0.0424457 | + | 0.0735181i | −0.886468 | − | 0.462790i | \(-0.846848\pi\) |
0.844022 | + | 0.536308i | \(0.180182\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −96.5904 | − | 5.80563i | −0.157058 | − | 0.00944005i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1025.06 | + | 591.821i | 1.66137 | + | 0.959191i | 0.972063 | + | 0.234721i | \(0.0754175\pi\) |
0.689305 | + | 0.724471i | \(0.257916\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −94.2234 | + | 163.200i | −0.152219 | + | 0.263650i | −0.932043 | − | 0.362348i | \(-0.881975\pi\) |
0.779824 | + | 0.625999i | \(0.215308\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 274.159 | + | 232.660i | 0.441480 | + | 0.374654i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 1015.18i | − | 1.62950i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 558.950 | 0.894320 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 156.194 | + | 53.6800i | 0.249112 | + | 0.0856140i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −953.120 | − | 550.284i | −1.51529 | − | 0.874855i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 80.3672 | + | 139.200i | 0.127365 | + | 0.220602i | 0.922655 | − | 0.385627i | \(-0.126015\pi\) |
−0.795290 | + | 0.606229i | \(0.792681\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 98.5945 | + | 5.92608i | 0.155757 | + | 0.00936190i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.0155 | + | 8.09183i | −0.0220716 | + | 0.0127430i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −376.164 | −0.590524 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −514.879 | − | 386.292i | −0.805758 | − | 0.604526i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29.1362 | + | 16.8218i | −0.0454543 | + | 0.0262430i | −0.522555 | − | 0.852606i | \(-0.675021\pi\) |
0.477101 | + | 0.878849i | \(0.341688\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −681.548 | −1.05995 | −0.529975 | − | 0.848013i | \(-0.677799\pi\) | ||||
−0.529975 | + | 0.848013i | \(0.677799\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 120.859 | − | 60.4170i | 0.187378 | − | 0.0936698i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 823.205i | − | 1.27234i | −0.771548 | − | 0.636171i | \(-0.780517\pi\) | ||
0.771548 | − | 0.636171i | \(-0.219483\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −133.458 | + | 231.156i | −0.205637 | + | 0.356173i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 283.621 | + | 17.0472i | 0.435670 | + | 0.0261862i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −252.547 | + | 145.808i | −0.386750 | + | 0.223290i | −0.680751 | − | 0.732515i | \(-0.738346\pi\) |
0.294001 | + | 0.955805i | \(0.405013\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 165.486 | 0.252650 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 688.010 | − | 917.033i | 1.04720 | − | 1.39579i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 578.433i | − | 0.877743i | −0.898550 | − | 0.438871i | \(-0.855378\pi\) | ||
0.898550 | − | 0.438871i | \(-0.144622\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 552.534 | − | 957.017i | 0.835906 | − | 1.44783i | −0.0573850 | − | 0.998352i | \(-0.518276\pi\) |
0.893291 | − | 0.449479i | \(-0.148390\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −340.306 | + | 170.118i | −0.513282 | + | 0.256588i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −173.435 | − | 48.1858i | −0.260805 | − | 0.0724599i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −110.686 | + | 191.713i | −0.165946 | + | 0.287426i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 327.677 | + | 655.488i | 0.489801 | + | 0.979803i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −142.893 | − | 82.4991i | −0.212955 | − | 0.122950i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −373.740 | + | 647.337i | −0.555334 | + | 0.961867i | 0.442543 | + | 0.896747i | \(0.354076\pi\) |
−0.997877 | + | 0.0651201i | \(0.979257\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −640.408 | − | 116.601i | −0.948752 | − | 0.172742i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 630.167 | + | 363.827i | 0.930823 | + | 0.537411i | 0.887072 | − | 0.461632i | \(-0.152736\pi\) |
0.0437512 | + | 0.999042i | \(0.486069\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 853.840 | 1.25750 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1086.93 | + | 717.779i | 1.59608 | + | 1.05401i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 123.112i | − | 0.180252i | −0.995930 | − | 0.0901260i | \(-0.971273\pi\) | ||
0.995930 | − | 0.0901260i | \(-0.0287270\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 161.845 | 0.236271 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 543.548 | + | 1087.32i | 0.791191 | + | 1.58271i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 587.718i | 0.853001i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 471.063 | − | 815.905i | 0.681712 | − | 1.18076i | −0.292746 | − | 0.956190i | \(-0.594569\pi\) |
0.974458 | − | 0.224569i | \(-0.0720975\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −240.680 | + | 102.761i | −0.347301 | + | 0.148285i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −52.2265 | − | 30.1530i | −0.0751461 | − | 0.0433856i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −297.798 | + | 515.801i | −0.427257 | + | 0.740030i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −578.317 | − | 381.904i | −0.827349 | − | 0.546358i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 557.020 | + | 321.596i | 0.794608 | + | 0.458767i | 0.841582 | − | 0.540129i | \(-0.181625\pi\) |
−0.0469742 | + | 0.998896i | \(0.514958\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1161.47 | − | 299.794i | 1.65216 | − | 0.426449i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 120.499 | + | 7.24267i | 0.170921 | + | 0.0102733i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1709.08 | + | 986.736i | 2.41736 | + | 1.39567i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 508.567 | 0.717301 | 0.358651 | − | 0.933472i | \(-0.383237\pi\) | ||||
0.358651 | + | 0.933472i | \(0.383237\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −23.7843 | − | 55.7057i | −0.0334519 | − | 0.0783485i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 125.689i | − | 0.176281i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.95019 | − | 17.2342i | −0.0139163 | − | 0.0241038i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 259.952 | − | 129.950i | 0.362556 | − | 0.181241i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −581.261 | − | 335.591i | −0.808430 | − | 0.466747i | 0.0379806 | − | 0.999278i | \(-0.487907\pi\) |
−0.846410 | + | 0.532531i | \(0.821241\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 660.194 | 0.915665 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 893.284 | + | 53.6914i | 1.23552 | + | 0.0742620i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 400.748i | − | 0.552756i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −243.419 | − | 421.613i | −0.334826 | − | 0.579936i | 0.648625 | − | 0.761108i | \(-0.275344\pi\) |
−0.983451 | + | 0.181172i | \(0.942011\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 682.217 | + | 256.945i | 0.935826 | + | 0.352462i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 831.668i | − | 1.13771i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 244.666 | + | 423.774i | 0.333787 | + | 0.578136i | 0.983251 | − | 0.182256i | \(-0.0583400\pi\) |
−0.649464 | + | 0.760392i | \(0.725007\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 130.988 | − | 65.4807i | 0.178215 | − | 0.0890894i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −198.918 | + | 114.846i | −0.269903 | + | 0.155828i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −313.307 | + | 542.664i | −0.423961 | + | 0.734322i | −0.996323 | − | 0.0856793i | \(-0.972694\pi\) |
0.572362 | + | 0.820001i | \(0.306027\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 134.775 | − | 392.158i | 0.181883 | − | 0.529228i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1256.65i | 1.69132i | 0.533725 | + | 0.845658i | \(0.320792\pi\) | ||||
−0.533725 | + | 0.845658i | \(0.679208\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 152.134 | 0.204207 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −846.421 | − | 635.033i | −1.13309 | − | 0.850111i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.3978 | + | 10.0446i | 0.0232280 | + | 0.0134107i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 396.432 | − | 686.641i | 0.527873 | − | 0.914302i | −0.471599 | − | 0.881813i | \(-0.656323\pi\) |
0.999472 | − | 0.0324894i | \(-0.0103435\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.75082 | − | 4.37451i | 0.0116213 | − | 0.00580944i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −158.980 | − | 91.7874i | −0.210570 | − | 0.121573i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 341.349 | − | 591.233i | 0.450923 | − | 0.781021i | −0.547521 | − | 0.836792i | \(-0.684428\pi\) |
0.998444 | + | 0.0557708i | \(0.0177616\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 51.7632 | + | 103.548i | 0.0681992 | + | 0.136426i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 931.990 | − | 538.085i | 1.22469 | − | 0.707076i | 0.258777 | − | 0.965937i | \(-0.416681\pi\) |
0.965915 | + | 0.258861i | \(0.0833472\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 340.596 | + | 589.930i | 0.446391 | + | 0.773172i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 88.8887 | − | 118.478i | 0.116194 | − | 0.154873i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 580.369 | + | 335.076i | 0.756674 | + | 0.436866i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.6952 | − | 25.4528i | 0.0191095 | − | 0.0330986i | −0.856313 | − | 0.516458i | \(-0.827250\pi\) |
0.875422 | + | 0.483359i | \(0.160584\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 218.626 | + | 144.375i | 0.283562 | + | 0.187256i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −587.271 | + | 339.061i | −0.759729 | + | 0.438630i | −0.829198 | − | 0.558954i | \(-0.811203\pi\) |
0.0694693 | + | 0.997584i | \(0.477869\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 113.767 | + | 197.050i | 0.146796 | + | 0.254258i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1047.39 | + | 1586.06i | −1.34799 | + | 2.04126i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −162.240 | − | 628.555i | −0.208267 | − | 0.806874i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −103.616 | − | 179.469i | −0.132671 | − | 0.229793i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −80.3941 | + | 441.549i | −0.102674 | + | 0.563919i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 56.7361i | 0.0722753i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 472.469 | + | 818.341i | 0.600342 | + | 1.03982i | 0.992769 | + | 0.120040i | \(0.0383022\pi\) |
−0.392427 | + | 0.919783i | \(0.628364\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 453.602 | − | 226.754i | 0.574907 | − | 0.287395i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1068.82i | − | 1.35123i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −207.132 | + | 358.764i | −0.261201 | + | 0.452413i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −102.307 | − | 204.656i | −0.128688 | − | 0.257429i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1032.66 | − | 596.209i | 1.29569 | − | 0.748066i | 0.316032 | − | 0.948748i | \(-0.397649\pi\) |
0.979656 | + | 0.200682i | \(0.0643158\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 371.510 | − | 643.475i | 0.464969 | − | 0.805350i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −837.322 | + | 357.505i | −1.04535 | + | 0.446324i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 319.645 | − | 184.547i | 0.398063 | − | 0.229822i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −63.0849 | − | 109.266i | −0.0783663 | − | 0.135734i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 83.3416 | + | 55.0364i | 0.103273 | + | 0.0681988i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1351.83i | 1.67099i | 0.549502 | + | 0.835493i | \(0.314818\pi\) | ||||
−0.549502 | + | 0.835493i | \(0.685182\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −79.2739 | − | 137.307i | −0.0977484 | − | 0.169305i | 0.813004 | − | 0.582258i | \(-0.197831\pi\) |
−0.910752 | + | 0.412953i | \(0.864497\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −336.849 | + | 510.089i | −0.414328 | + | 0.627416i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 34.9700i | − | 0.0429080i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 635.040 | + | 646.830i | 0.777282 | + | 0.791713i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 258.005 | + | 604.280i | 0.315024 | + | 0.737826i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 975.246i | 1.18788i | 0.804511 | + | 0.593938i | \(0.202427\pi\) | ||||
−0.804511 | + | 0.593938i | \(0.797573\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −59.2050 | + | 102.546i | −0.0719380 | + | 0.124600i | −0.899751 | − | 0.436404i | \(-0.856252\pi\) |
0.827813 | + | 0.561005i | \(0.189585\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −174.878 | − | 115.485i | −0.211974 | − | 0.139982i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 893.922 | − | 516.106i | 1.08092 | − | 0.624070i | 0.149777 | − | 0.988720i | \(-0.452145\pi\) |
0.931145 | + | 0.364650i | \(0.118811\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.5992 | 0.0260546 | 0.0130273 | − | 0.999915i | \(-0.495853\pi\) | ||||
0.0130273 | + | 0.999915i | \(0.495853\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −229.689 | + | 347.817i | −0.276400 | + | 0.418553i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 901.372i | − | 1.08208i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.5429 | − | 18.2609i | 0.0126262 | − | 0.0218693i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −85.8194 | − | 239.935i | −0.102532 | − | 0.286660i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1030.30 | − | 594.841i | 1.22800 | − | 0.708988i | 0.261392 | − | 0.965233i | \(-0.415818\pi\) |
0.966612 | + | 0.256244i | \(0.0824852\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 564.692 | 0.671453 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 26.2476 | − | 436.692i | 0.0311360 | − | 0.518021i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 94.9011 | − | 54.7912i | 0.112309 | − | 0.0648416i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1130.01 | 1.33414 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 997.711 | + | 59.9681i | 1.17516 | + | 0.0706338i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 728.142 | + | 420.393i | 0.855631 | + | 0.493999i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 320.869 | + | 555.761i | 0.376165 | + | 0.651537i | 0.990501 | − | 0.137508i | \(-0.0439093\pi\) |
−0.614336 | + | 0.789045i | \(0.710576\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 21.3332 | + | 160.019i | 0.0249511 | + | 0.187157i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −217.083 | + | 125.333i | −0.253305 | + | 0.146246i | −0.621277 | − | 0.783591i | \(-0.713386\pi\) |
0.367972 | + | 0.929837i | \(0.380052\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.1802 | + | 33.2211i | −0.0223285 | + | 0.0386741i | −0.876974 | − | 0.480538i | \(-0.840441\pi\) |
0.854645 | + | 0.519212i | \(0.173775\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 858.331 | + | 566.818i | 0.996900 | + | 0.658325i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1063.03i | − | 1.23178i | −0.787832 | − | 0.615890i | \(-0.788796\pi\) | ||
0.787832 | − | 0.615890i | \(-0.211204\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −103.344 | − | 178.997i | −0.119473 | − | 0.206933i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −19.9704 | − | 39.9490i | −0.0230339 | − | 0.0460772i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 19.5008i | − | 0.0224405i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 288.345 | + | 499.428i | 0.331051 | + | 0.573396i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −300.688 | − | 704.249i | −0.344431 | − | 0.806700i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 402.921 | + | 232.626i | 0.460481 | + | 0.265859i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1249.88 | −1.42518 | −0.712588 | − | 0.701583i | \(-0.752477\pi\) | ||||
−0.712588 | + | 0.701583i | \(0.752477\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 507.739 | − | 253.817i | 0.577632 | − | 0.288757i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1354.58i | 1.53755i | 0.639522 | + | 0.768773i | \(0.279132\pi\) | ||||
−0.639522 | + | 0.768773i | \(0.720868\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 124.127 | + | 214.994i | 0.140574 | + | 0.243481i | 0.927713 | − | 0.373294i | \(-0.121772\pi\) |
−0.787139 | + | 0.616776i | \(0.788439\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −260.425 | − | 15.6530i | −0.294266 | − | 0.0176870i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 323.107 | + | 186.546i | 0.364269 | + | 0.210311i | 0.670952 | − | 0.741501i | \(-0.265886\pi\) |
−0.306683 | + | 0.951812i | \(0.599219\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 172.030 | 0.193510 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 169.515 | + | 162.325i | 0.190253 | + | 0.182183i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 202.398 | + | 784.138i | 0.226650 | + | 0.878094i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 67.3618 | 0.0752646 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 259.979 | − | 129.963i | 0.289832 | − | 0.144886i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 135.862 | − | 78.4400i | 0.151126 | − | 0.0872525i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1408.30 | −1.56304 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1433.71 | − | 86.1740i | −1.58772 | − | 0.0954308i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 70.3079 | − | 40.5923i | 0.0776883 | − | 0.0448533i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 418.749 | + | 725.295i | 0.461686 | + | 0.799664i | 0.999045 | − | 0.0436898i | \(-0.0139113\pi\) |
−0.537359 | + | 0.843354i | \(0.680578\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 211.994 | − | 1757.14i | 0.233216 | − | 1.93305i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −806.747 | − | 465.775i | −0.885562 | − | 0.511279i | −0.0130736 | − | 0.999915i | \(-0.504162\pi\) |
−0.872488 | + | 0.488635i | \(0.837495\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −170.337 | − | 295.032i | −0.186568 | − | 0.323146i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.67615 | − | 160.986i | 0.0105750 | − | 0.175941i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1523.42 | − | 879.546i | −1.66131 | − | 0.959156i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −72.4463 | −0.0788316 | −0.0394158 | − | 0.999223i | \(-0.512550\pi\) | ||||
−0.0394158 | + | 0.999223i | \(0.512550\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −140.569 | + | 212.863i | −0.152626 | + | 0.231121i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −450.595 | + | 260.151i | −0.488185 | + | 0.281854i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1522.07 | −1.64548 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −232.494 | − | 544.530i | −0.250803 | − | 0.587411i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −788.117 | + | 455.020i | −0.848350 | + | 0.489795i | −0.860094 | − | 0.510136i | \(-0.829595\pi\) |
0.0117435 | + | 0.999931i | \(0.496262\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 688.264 | + | 701.042i | 0.739274 | + | 0.752999i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −369.478 | + | 184.701i | −0.396010 | + | 0.197964i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 41.2970 | − | 23.8429i | 0.0441680 | − | 0.0255004i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −248.636 | − | 430.651i | −0.265354 | − | 0.459606i | 0.702303 | − | 0.711879i | \(-0.252155\pi\) |
−0.967656 | + | 0.252273i | \(0.918822\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −115.205 | − | 6.92447i | −0.122689 | − | 0.00737430i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1037.45 | − | 598.972i | −1.10250 | − | 0.636527i | −0.165622 | − | 0.986189i | \(-0.552963\pi\) |
−0.936876 | + | 0.349662i | \(0.886296\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 227.505 | − | 394.049i | 0.241256 | − | 0.417868i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −195.033 | − | 165.511i | −0.206384 | − | 0.175144i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −282.836 | + | 163.295i | −0.298665 | + | 0.172434i | −0.641843 | − | 0.766836i | \(-0.721830\pi\) |
0.343178 | + | 0.939270i | \(0.388497\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −463.346 | − | 802.539i | −0.488246 | − | 0.845668i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 61.7577 | − | 1027.49i | 0.0649398 | − | 1.08043i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.86935 | − | 2.23397i | −0.00406018 | − | 0.00234415i | 0.497969 | − | 0.867195i | \(-0.334079\pi\) |
−0.502029 | + | 0.864851i | \(0.667413\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 150.700 | − | 261.021i | 0.157802 | − | 0.273320i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −79.6245 | + | 120.575i | −0.0832022 | + | 0.125993i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1489.91 | − | 860.199i | −1.55361 | − | 0.896975i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 435.964 | − | 755.112i | 0.453657 | − | 0.785756i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.15802 | − | 17.8870i | 0.00224093 | − | 0.0185743i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 106.462i | − | 0.110323i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −68.7657 | −0.0711124 | −0.0355562 | − | 0.999368i | \(-0.511320\pi\) | ||||
−0.0355562 | + | 0.999368i | \(0.511320\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 939.698 | + | 322.952i | 0.969761 | + | 0.333284i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1310.58 | + | 756.661i | 1.34972 | + | 0.779260i | 0.988209 | − | 0.153109i | \(-0.0489287\pi\) |
0.361508 | + | 0.932369i | \(0.382262\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 320.523 | + | 555.162i | 0.329417 | + | 0.570567i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −289.950 | + | 439.070i | −0.297384 | + | 0.450329i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −360.077 | + | 207.891i | −0.368554 | + | 0.212785i | −0.672826 | − | 0.739800i | \(-0.734920\pi\) |
0.304273 | + | 0.952585i | \(0.401587\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −293.119 | −0.299407 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 366.631 | − | 488.675i | 0.373732 | − | 0.498139i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1468.69 | − | 847.950i | 1.49409 | − | 0.862615i | 0.494115 | − | 0.869396i | \(-0.335492\pi\) |
0.999977 | + | 0.00678179i | \(0.00215873\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 89.0989 | 0.0904557 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1070.79 | − | 707.119i | −1.08489 | − | 0.716433i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 635.358i | 0.642425i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 488.526 | − | 846.152i | 0.492963 | − | 0.853837i | −0.507004 | − | 0.861944i | \(-0.669247\pi\) |
0.999967 | + | 0.00810664i | \(0.00258045\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 198.178 | − | 300.100i | 0.199575 | − | 0.302216i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 244.301 | − | 141.047i | 0.245528 | − | 0.141756i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −219.619 | −0.220280 | −0.110140 | − | 0.993916i | \(-0.535130\pi\) | ||||
−0.110140 | + | 0.993916i | \(0.535130\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1677.04 | + | 305.343i | 1.67871 | + | 0.305649i |
(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 | 684.3.m.a.353.2 | ✓ | 80 | |
3.2 | odd | 2 | 2052.3.m.a.1493.23 | 80 | |||
9.4 | even | 3 | 2052.3.be.a.125.18 | 80 | |||
9.5 | odd | 6 | 684.3.be.a.581.28 | yes | 80 | ||
19.7 | even | 3 | 684.3.be.a.425.28 | yes | 80 | ||
57.26 | odd | 6 | 2052.3.be.a.197.18 | 80 | |||
171.121 | even | 3 | 2052.3.m.a.881.18 | 80 | |||
171.140 | odd | 6 | inner | 684.3.m.a.653.2 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.m.a.353.2 | ✓ | 80 | 1.1 | even | 1 | trivial | |
684.3.m.a.653.2 | yes | 80 | 171.140 | odd | 6 | inner | |
684.3.be.a.425.28 | yes | 80 | 19.7 | even | 3 | ||
684.3.be.a.581.28 | yes | 80 | 9.5 | odd | 6 | ||
2052.3.m.a.881.18 | 80 | 171.121 | even | 3 | |||
2052.3.m.a.1493.23 | 80 | 3.2 | odd | 2 | |||
2052.3.be.a.125.18 | 80 | 9.4 | even | 3 | |||
2052.3.be.a.197.18 | 80 | 57.26 | odd | 6 |