Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(246,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.246");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.c (of order \(2\), degree \(1\), 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 10x^{14} + 121x^{12} + 296x^{10} + 3468x^{8} - 1748x^{6} + 40192x^{4} - 65056x^{2} + 228484 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 246.6 | ||
Root | \(1.41421 - 1.52340i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.246 |
Dual form | 637.2.c.g.246.12 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.52340i | − | 1.07720i | −0.842561 | − | 0.538602i | \(-0.818953\pi\) | ||
0.842561 | − | 0.538602i | \(-0.181047\pi\) | |||||||
\(3\) | 2.99510 | 1.72922 | 0.864611 | − | 0.502442i | \(-0.167565\pi\) | ||||
0.864611 | + | 0.502442i | \(0.167565\pi\) | |||||||
\(4\) | −0.320733 | −0.160367 | ||||||||
\(5\) | 2.94606i | 1.31752i | 0.752354 | + | 0.658759i | \(0.228918\pi\) | ||||
−0.752354 | + | 0.658759i | \(0.771082\pi\) | |||||||
\(6\) | − | 4.56272i | − | 1.86272i | ||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 2.55819i | − | 0.904456i | ||||||
\(9\) | 5.97063 | 1.99021 | ||||||||
\(10\) | 4.48801 | 1.41923 | ||||||||
\(11\) | − | 2.37108i | − | 0.714908i | −0.933931 | − | 0.357454i | \(-0.883645\pi\) | ||
0.933931 | − | 0.357454i | \(-0.116355\pi\) | |||||||
\(12\) | −0.960628 | −0.277309 | ||||||||
\(13\) | 2.32734 | + | 2.75381i | 0.645489 | + | 0.763770i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.82374i | 2.27828i | ||||||||
\(16\) | −4.53860 | −1.13465 | ||||||||
\(17\) | −5.36994 | −1.30240 | −0.651201 | − | 0.758905i | \(-0.725735\pi\) | ||||
−0.651201 | + | 0.758905i | \(0.725735\pi\) | |||||||
\(18\) | − | 9.09563i | − | 2.14386i | ||||||
\(19\) | 5.35438i | 1.22838i | 0.789159 | + | 0.614189i | \(0.210517\pi\) | ||||
−0.789159 | + | 0.614189i | \(0.789483\pi\) | |||||||
\(20\) | − | 0.944899i | − | 0.211286i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.61209 | −0.770101 | ||||||||
\(23\) | −2.79056 | −0.581873 | −0.290936 | − | 0.956742i | \(-0.593967\pi\) | ||||
−0.290936 | + | 0.956742i | \(0.593967\pi\) | |||||||
\(24\) | − | 7.66203i | − | 1.56400i | ||||||
\(25\) | −3.67927 | −0.735853 | ||||||||
\(26\) | 4.19514 | − | 3.54546i | 0.822735 | − | 0.695323i | ||||
\(27\) | 8.89733 | 1.71229 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.585818 | 0.108784 | 0.0543918 | − | 0.998520i | \(-0.482678\pi\) | ||||
0.0543918 | + | 0.998520i | \(0.482678\pi\) | |||||||
\(30\) | 13.4421 | 2.45417 | ||||||||
\(31\) | − | 8.33379i | − | 1.49679i | −0.663252 | − | 0.748397i | \(-0.730824\pi\) | ||
0.663252 | − | 0.748397i | \(-0.269176\pi\) | |||||||
\(32\) | 1.79770i | 0.317792i | ||||||||
\(33\) | − | 7.10163i | − | 1.23623i | ||||||
\(34\) | 8.18054i | 1.40295i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.91498 | −0.319163 | ||||||||
\(37\) | 0.675710i | 0.111086i | 0.998456 | + | 0.0555430i | \(0.0176890\pi\) | ||||
−0.998456 | + | 0.0555430i | \(0.982311\pi\) | |||||||
\(38\) | 8.15683 | 1.32321 | ||||||||
\(39\) | 6.97063 | + | 8.24794i | 1.11619 | + | 1.32073i | ||||
\(40\) | 7.53657 | 1.19164 | ||||||||
\(41\) | − | 11.2799i | − | 1.76162i | −0.473473 | − | 0.880808i | \(-0.657000\pi\) | ||
0.473473 | − | 0.880808i | \(-0.343000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.5271 | −1.60536 | −0.802682 | − | 0.596408i | \(-0.796594\pi\) | ||||
−0.802682 | + | 0.596408i | \(0.796594\pi\) | |||||||
\(44\) | 0.760484i | 0.114647i | ||||||||
\(45\) | 17.5898i | 2.62214i | ||||||||
\(46\) | 4.25113i | 0.626795i | ||||||||
\(47\) | 0.537744i | 0.0784380i | 0.999231 | + | 0.0392190i | \(0.0124870\pi\) | ||||
−0.999231 | + | 0.0392190i | \(0.987513\pi\) | |||||||
\(48\) | −13.5936 | −1.96206 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 5.60498i | 0.792664i | ||||||||
\(51\) | −16.0835 | −2.25214 | ||||||||
\(52\) | −0.746456 | − | 0.883239i | −0.103515 | − | 0.122483i | ||||
\(53\) | 7.90345 | 1.08562 | 0.542811 | − | 0.839855i | \(-0.317360\pi\) | ||||
0.542811 | + | 0.839855i | \(0.317360\pi\) | |||||||
\(54\) | − | 13.5541i | − | 1.84449i | ||||||
\(55\) | 6.98535 | 0.941904 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 16.0369i | 2.12414i | ||||||||
\(58\) | − | 0.892432i | − | 0.117182i | ||||||
\(59\) | − | 6.14603i | − | 0.800145i | −0.916484 | − | 0.400072i | \(-0.868985\pi\) | ||
0.916484 | − | 0.400072i | \(-0.131015\pi\) | |||||||
\(60\) | − | 2.83007i | − | 0.365360i | ||||||
\(61\) | −2.78689 | −0.356824 | −0.178412 | − | 0.983956i | \(-0.557096\pi\) | ||||
−0.178412 | + | 0.983956i | \(0.557096\pi\) | |||||||
\(62\) | −12.6957 | −1.61235 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.33858 | −0.792323 | ||||||||
\(65\) | −8.11289 | + | 6.85649i | −1.00628 | + | 0.850443i | ||||
\(66\) | −10.8186 | −1.33168 | ||||||||
\(67\) | − | 4.21353i | − | 0.514765i | −0.966310 | − | 0.257382i | \(-0.917140\pi\) | ||
0.966310 | − | 0.257382i | \(-0.0828600\pi\) | |||||||
\(68\) | 1.72232 | 0.208862 | ||||||||
\(69\) | −8.35802 | −1.00619 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.25151i | − | 0.148527i | −0.997239 | − | 0.0742637i | \(-0.976339\pi\) | ||
0.997239 | − | 0.0742637i | \(-0.0236607\pi\) | |||||||
\(72\) | − | 15.2740i | − | 1.80006i | ||||||
\(73\) | 10.8620i | 1.27130i | 0.771977 | + | 0.635650i | \(0.219268\pi\) | ||||
−0.771977 | + | 0.635650i | \(0.780732\pi\) | |||||||
\(74\) | 1.02937 | 0.119662 | ||||||||
\(75\) | −11.0198 | −1.27245 | ||||||||
\(76\) | − | 1.71733i | − | 0.196991i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 12.5649 | − | 10.6190i | 1.42269 | − | 1.20237i | ||||
\(79\) | 6.29136 | 0.707833 | 0.353917 | − | 0.935277i | \(-0.384850\pi\) | ||||
0.353917 | + | 0.935277i | \(0.384850\pi\) | |||||||
\(80\) | − | 13.3710i | − | 1.49492i | ||||||
\(81\) | 8.73651 | 0.970723 | ||||||||
\(82\) | −17.1837 | −1.89762 | ||||||||
\(83\) | 1.74725i | 0.191786i | 0.995392 | + | 0.0958928i | \(0.0305706\pi\) | ||||
−0.995392 | + | 0.0958928i | \(0.969429\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 15.8202i | − | 1.71594i | ||||||
\(86\) | 16.0369i | 1.72930i | ||||||||
\(87\) | 1.75458 | 0.188111 | ||||||||
\(88\) | −6.06567 | −0.646602 | ||||||||
\(89\) | 10.2343i | 1.08483i | 0.840110 | + | 0.542416i | \(0.182490\pi\) | ||||
−0.840110 | + | 0.542416i | \(0.817510\pi\) | |||||||
\(90\) | 26.7963 | 2.82457 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.895027 | 0.0933130 | ||||||||
\(93\) | − | 24.9605i | − | 2.58829i | ||||||
\(94\) | 0.819196 | 0.0844936 | ||||||||
\(95\) | −15.7743 | −1.61841 | ||||||||
\(96\) | 5.38430i | 0.549533i | ||||||||
\(97\) | 9.90640i | 1.00584i | 0.864332 | + | 0.502921i | \(0.167741\pi\) | ||||
−0.864332 | + | 0.502921i | \(0.832259\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 14.1568i | − | 1.42282i | ||||||
\(100\) | 1.18006 | 0.118006 | ||||||||
\(101\) | 2.05077 | 0.204059 | 0.102030 | − | 0.994781i | \(-0.467466\pi\) | ||||
0.102030 | + | 0.994781i | \(0.467466\pi\) | |||||||
\(102\) | 24.5016i | 2.42602i | ||||||||
\(103\) | 3.02962 | 0.298517 | 0.149259 | − | 0.988798i | \(-0.452311\pi\) | ||||
0.149259 | + | 0.988798i | \(0.452311\pi\) | |||||||
\(104\) | 7.04476 | − | 5.95378i | 0.690796 | − | 0.583816i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 12.0401i | − | 1.16944i | ||||||
\(107\) | −12.4305 | −1.20170 | −0.600852 | − | 0.799360i | \(-0.705172\pi\) | ||||
−0.600852 | + | 0.799360i | \(0.705172\pi\) | |||||||
\(108\) | −2.85367 | −0.274594 | ||||||||
\(109\) | 3.53782i | 0.338862i | 0.985542 | + | 0.169431i | \(0.0541929\pi\) | ||||
−0.985542 | + | 0.169431i | \(0.945807\pi\) | |||||||
\(110\) | − | 10.6414i | − | 1.01462i | ||||||
\(111\) | 2.02382i | 0.192092i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.3848 | 0.976921 | 0.488460 | − | 0.872586i | \(-0.337559\pi\) | ||||
0.488460 | + | 0.872586i | \(0.337559\pi\) | |||||||
\(114\) | 24.4305 | 2.28813 | ||||||||
\(115\) | − | 8.22117i | − | 0.766628i | ||||||
\(116\) | −0.187891 | −0.0174453 | ||||||||
\(117\) | 13.8957 | + | 16.4420i | 1.28466 | + | 1.52006i | ||||
\(118\) | −9.36283 | −0.861918 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 22.5728 | 2.06060 | ||||||||
\(121\) | 5.37797 | 0.488907 | ||||||||
\(122\) | 4.24553i | 0.384372i | ||||||||
\(123\) | − | 33.7843i | − | 3.04623i | ||||||
\(124\) | 2.67292i | 0.240036i | ||||||||
\(125\) | 3.89096i | 0.348018i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.09504 | −0.452112 | −0.226056 | − | 0.974114i | \(-0.572583\pi\) | ||||
−0.226056 | + | 0.974114i | \(0.572583\pi\) | |||||||
\(128\) | 13.2516i | 1.17128i | ||||||||
\(129\) | −31.5296 | −2.77603 | ||||||||
\(130\) | 10.4451 | + | 12.3591i | 0.916100 | + | 1.08397i | ||||
\(131\) | −22.5443 | −1.96971 | −0.984854 | − | 0.173386i | \(-0.944529\pi\) | ||||
−0.984854 | + | 0.173386i | \(0.944529\pi\) | |||||||
\(132\) | 2.27773i | 0.198251i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −6.41887 | −0.554506 | ||||||||
\(135\) | 26.2121i | 2.25597i | ||||||||
\(136\) | 13.7373i | 1.17797i | ||||||||
\(137\) | 1.03479i | 0.0884082i | 0.999023 | + | 0.0442041i | \(0.0140752\pi\) | ||||
−0.999023 | + | 0.0442041i | \(0.985925\pi\) | |||||||
\(138\) | 12.7326i | 1.08387i | ||||||||
\(139\) | −8.49456 | −0.720499 | −0.360249 | − | 0.932856i | \(-0.617308\pi\) | ||||
−0.360249 | + | 0.932856i | \(0.617308\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.61060i | 0.135637i | ||||||||
\(142\) | −1.90655 | −0.159994 | ||||||||
\(143\) | 6.52951 | − | 5.51832i | 0.546025 | − | 0.461465i | ||||
\(144\) | −27.0983 | −2.25819 | ||||||||
\(145\) | 1.72585i | 0.143324i | ||||||||
\(146\) | 16.5471 | 1.36945 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 0.216723i | − | 0.0178145i | ||||||
\(149\) | − | 4.31343i | − | 0.353370i | −0.984267 | − | 0.176685i | \(-0.943463\pi\) | ||
0.984267 | − | 0.176685i | \(-0.0565374\pi\) | |||||||
\(150\) | 16.7875i | 1.37069i | ||||||||
\(151\) | 12.2447i | 0.996463i | 0.867044 | + | 0.498232i | \(0.166017\pi\) | ||||
−0.867044 | + | 0.498232i | \(0.833983\pi\) | |||||||
\(152\) | 13.6975 | 1.11101 | ||||||||
\(153\) | −32.0619 | −2.59205 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 24.5518 | 1.97205 | ||||||||
\(156\) | −2.23571 | − | 2.64539i | −0.179000 | − | 0.211801i | ||||
\(157\) | 22.2040 | 1.77207 | 0.886035 | − | 0.463619i | \(-0.153449\pi\) | ||||
0.886035 | + | 0.463619i | \(0.153449\pi\) | |||||||
\(158\) | − | 9.58423i | − | 0.762480i | ||||||
\(159\) | 23.6716 | 1.87728 | ||||||||
\(160\) | −5.29614 | −0.418697 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 13.3092i | − | 1.04567i | ||||||
\(163\) | 11.3644i | 0.890127i | 0.895499 | + | 0.445063i | \(0.146819\pi\) | ||||
−0.895499 | + | 0.445063i | \(0.853181\pi\) | |||||||
\(164\) | 3.61782i | 0.282505i | ||||||||
\(165\) | 20.9218 | 1.62876 | ||||||||
\(166\) | 2.66175 | 0.206592 | ||||||||
\(167\) | 1.88127i | 0.145577i | 0.997347 | + | 0.0727885i | \(0.0231898\pi\) | ||||
−0.997347 | + | 0.0727885i | \(0.976810\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.16695 | + | 12.8181i | −0.166688 | + | 0.986010i | ||||
\(170\) | −24.1004 | −1.84841 | ||||||||
\(171\) | 31.9690i | 2.44473i | ||||||||
\(172\) | 3.37638 | 0.257447 | ||||||||
\(173\) | −5.57113 | −0.423565 | −0.211783 | − | 0.977317i | \(-0.567927\pi\) | ||||
−0.211783 | + | 0.977317i | \(0.567927\pi\) | |||||||
\(174\) | − | 2.67292i | − | 0.202634i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 10.7614i | 0.811170i | ||||||||
\(177\) | − | 18.4080i | − | 1.38363i | ||||||
\(178\) | 15.5909 | 1.16858 | ||||||||
\(179\) | 4.66142 | 0.348411 | 0.174205 | − | 0.984709i | \(-0.444264\pi\) | ||||
0.174205 | + | 0.984709i | \(0.444264\pi\) | |||||||
\(180\) | − | 5.64164i | − | 0.420503i | ||||||
\(181\) | 12.5360 | 0.931794 | 0.465897 | − | 0.884839i | \(-0.345732\pi\) | ||||
0.465897 | + | 0.884839i | \(0.345732\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.34701 | −0.617029 | ||||||||
\(184\) | 7.13879i | 0.526278i | ||||||||
\(185\) | −1.99068 | −0.146358 | ||||||||
\(186\) | −38.0248 | −2.78811 | ||||||||
\(187\) | 12.7326i | 0.931098i | ||||||||
\(188\) | − | 0.172472i | − | 0.0125788i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 24.0305i | 1.74336i | ||||||||
\(191\) | −1.31764 | −0.0953408 | −0.0476704 | − | 0.998863i | \(-0.515180\pi\) | ||||
−0.0476704 | + | 0.998863i | \(0.515180\pi\) | |||||||
\(192\) | −18.9847 | −1.37010 | ||||||||
\(193\) | − | 15.1445i | − | 1.09012i | −0.838396 | − | 0.545061i | \(-0.816506\pi\) | ||
0.838396 | − | 0.545061i | \(-0.183494\pi\) | |||||||
\(194\) | 15.0914 | 1.08350 | ||||||||
\(195\) | −24.2989 | + | 20.5359i | −1.74008 | + | 1.47061i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 9.90571i | − | 0.705753i | −0.935670 | − | 0.352876i | \(-0.885204\pi\) | ||
0.935670 | − | 0.352876i | \(-0.114796\pi\) | |||||||
\(198\) | −21.5665 | −1.53266 | ||||||||
\(199\) | −8.57326 | −0.607742 | −0.303871 | − | 0.952713i | \(-0.598279\pi\) | ||||
−0.303871 | + | 0.952713i | \(0.598279\pi\) | |||||||
\(200\) | 9.41225i | 0.665547i | ||||||||
\(201\) | − | 12.6199i | − | 0.890142i | ||||||
\(202\) | − | 3.12413i | − | 0.219813i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 5.15852 | 0.361169 | ||||||||
\(205\) | 33.2311 | 2.32096 | ||||||||
\(206\) | − | 4.61530i | − | 0.321564i | ||||||
\(207\) | −16.6614 | −1.15805 | ||||||||
\(208\) | −10.5629 | − | 12.4984i | −0.732403 | − | 0.866611i | ||||
\(209\) | 12.6957 | 0.878177 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.44515 | −0.0994881 | −0.0497440 | − | 0.998762i | \(-0.515841\pi\) | ||||
−0.0497440 | + | 0.998762i | \(0.515841\pi\) | |||||||
\(212\) | −2.53490 | −0.174098 | ||||||||
\(213\) | − | 3.74841i | − | 0.256837i | ||||||
\(214\) | 18.9366i | 1.29448i | ||||||||
\(215\) | − | 31.0134i | − | 2.11510i | ||||||
\(216\) | − | 22.7610i | − | 1.54869i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 5.38950 | 0.365023 | ||||||||
\(219\) | 32.5328i | 2.19836i | ||||||||
\(220\) | −2.24043 | −0.151050 | ||||||||
\(221\) | −12.4977 | − | 14.7878i | −0.840686 | − | 0.994735i | ||||
\(222\) | 3.08307 | 0.206922 | ||||||||
\(223\) | 14.9949i | 1.00413i | 0.864829 | + | 0.502067i | \(0.167427\pi\) | ||||
−0.864829 | + | 0.502067i | \(0.832573\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −21.9675 | −1.46450 | ||||||||
\(226\) | − | 15.8202i | − | 1.05234i | ||||||
\(227\) | 1.14220i | 0.0758105i | 0.999281 | + | 0.0379052i | \(0.0120685\pi\) | ||||
−0.999281 | + | 0.0379052i | \(0.987932\pi\) | |||||||
\(228\) | − | 5.14356i | − | 0.340641i | ||||||
\(229\) | − | 6.26935i | − | 0.414290i | −0.978310 | − | 0.207145i | \(-0.933583\pi\) | ||
0.978310 | − | 0.207145i | \(-0.0664172\pi\) | |||||||
\(230\) | −12.5241 | −0.825814 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 1.49863i | − | 0.0983900i | ||||||
\(233\) | 6.16695 | 0.404010 | 0.202005 | − | 0.979384i | \(-0.435254\pi\) | ||||
0.202005 | + | 0.979384i | \(0.435254\pi\) | |||||||
\(234\) | 25.0476 | − | 21.1686i | 1.63741 | − | 1.38384i | ||||
\(235\) | −1.58423 | −0.103343 | ||||||||
\(236\) | 1.97124i | 0.128317i | ||||||||
\(237\) | 18.8433 | 1.22400 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 27.4589i | − | 1.77617i | −0.459684 | − | 0.888083i | \(-0.652037\pi\) | ||
0.459684 | − | 0.888083i | \(-0.347963\pi\) | |||||||
\(240\) | − | 40.0474i | − | 2.58505i | ||||||
\(241\) | 9.79378i | 0.630873i | 0.948947 | + | 0.315436i | \(0.102151\pi\) | ||||
−0.948947 | + | 0.315436i | \(0.897849\pi\) | |||||||
\(242\) | − | 8.19278i | − | 0.526652i | ||||||
\(243\) | −0.525262 | −0.0336956 | ||||||||
\(244\) | 0.893848 | 0.0572227 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −51.4668 | −3.28140 | ||||||||
\(247\) | −14.7449 | + | 12.4615i | −0.938198 | + | 0.792904i | ||||
\(248\) | −21.3194 | −1.35378 | ||||||||
\(249\) | 5.23319i | 0.331640i | ||||||||
\(250\) | 5.92747 | 0.374886 | ||||||||
\(251\) | 12.4945 | 0.788644 | 0.394322 | − | 0.918972i | \(-0.370979\pi\) | ||||
0.394322 | + | 0.918972i | \(0.370979\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.61665i | 0.415985i | ||||||||
\(254\) | 7.76176i | 0.487016i | ||||||||
\(255\) | − | 47.3830i | − | 2.96724i | ||||||
\(256\) | 7.51022 | 0.469389 | ||||||||
\(257\) | 19.1929 | 1.19722 | 0.598610 | − | 0.801040i | \(-0.295720\pi\) | ||||
0.598610 | + | 0.801040i | \(0.295720\pi\) | |||||||
\(258\) | 48.0321i | 2.99035i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.60207 | − | 2.19910i | 0.161374 | − | 0.136383i | ||||
\(261\) | 3.49770 | 0.216502 | ||||||||
\(262\) | 34.3439i | 2.12178i | ||||||||
\(263\) | 28.8153 | 1.77683 | 0.888415 | − | 0.459041i | \(-0.151807\pi\) | ||||
0.888415 | + | 0.459041i | \(0.151807\pi\) | |||||||
\(264\) | −18.1673 | −1.11812 | ||||||||
\(265\) | 23.2840i | 1.43033i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 30.6527i | 1.87592i | ||||||||
\(268\) | 1.35142i | 0.0825511i | ||||||||
\(269\) | −8.15419 | −0.497170 | −0.248585 | − | 0.968610i | \(-0.579965\pi\) | ||||
−0.248585 | + | 0.968610i | \(0.579965\pi\) | |||||||
\(270\) | 39.9313 | 2.43014 | ||||||||
\(271\) | 18.5788i | 1.12858i | 0.825577 | + | 0.564290i | \(0.190850\pi\) | ||||
−0.825577 | + | 0.564290i | \(0.809150\pi\) | |||||||
\(272\) | 24.3720 | 1.47777 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.57640 | 0.0952336 | ||||||||
\(275\) | 8.72384i | 0.526067i | ||||||||
\(276\) | 2.68069 | 0.161359 | ||||||||
\(277\) | 17.2342 | 1.03550 | 0.517752 | − | 0.855531i | \(-0.326769\pi\) | ||||
0.517752 | + | 0.855531i | \(0.326769\pi\) | |||||||
\(278\) | 12.9406i | 0.776124i | ||||||||
\(279\) | − | 49.7580i | − | 2.97893i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.4691i | 0.684191i | 0.939665 | + | 0.342096i | \(0.111137\pi\) | ||||
−0.939665 | + | 0.342096i | \(0.888863\pi\) | |||||||
\(282\) | 2.45358 | 0.146108 | ||||||||
\(283\) | 1.45575 | 0.0865355 | 0.0432678 | − | 0.999064i | \(-0.486223\pi\) | ||||
0.0432678 | + | 0.999064i | \(0.486223\pi\) | |||||||
\(284\) | 0.401402i | 0.0238188i | ||||||||
\(285\) | −47.2456 | −2.79859 | ||||||||
\(286\) | −8.40658 | − | 9.94702i | −0.497092 | − | 0.588180i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 10.7334i | 0.632472i | ||||||||
\(289\) | 11.8363 | 0.696252 | ||||||||
\(290\) | 2.62916 | 0.154389 | ||||||||
\(291\) | 29.6707i | 1.73932i | ||||||||
\(292\) | − | 3.48380i | − | 0.203874i | ||||||
\(293\) | − | 30.6962i | − | 1.79329i | −0.442750 | − | 0.896645i | \(-0.645997\pi\) | ||
0.442750 | − | 0.896645i | \(-0.354003\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.1066 | 1.05421 | ||||||||
\(296\) | 1.72859 | 0.100472 | ||||||||
\(297\) | − | 21.0963i | − | 1.22413i | ||||||
\(298\) | −6.57107 | −0.380652 | ||||||||
\(299\) | −6.49460 | − | 7.68469i | −0.375592 | − | 0.444417i | ||||
\(300\) | 3.53441 | 0.204059 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 18.6536 | 1.07339 | ||||||||
\(303\) | 6.14226 | 0.352864 | ||||||||
\(304\) | − | 24.3013i | − | 1.39378i | ||||||
\(305\) | − | 8.21034i | − | 0.470123i | ||||||
\(306\) | 48.8430i | 2.79217i | ||||||||
\(307\) | − | 21.2602i | − | 1.21339i | −0.794936 | − | 0.606693i | \(-0.792496\pi\) | ||
0.794936 | − | 0.606693i | \(-0.207504\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.07401 | 0.516202 | ||||||||
\(310\) | − | 37.4022i | − | 2.12430i | ||||||
\(311\) | 4.44647 | 0.252136 | 0.126068 | − | 0.992022i | \(-0.459764\pi\) | ||||
0.126068 | + | 0.992022i | \(0.459764\pi\) | |||||||
\(312\) | 21.0998 | − | 17.8322i | 1.19454 | − | 1.00955i | ||||
\(313\) | 2.28687 | 0.129261 | 0.0646307 | − | 0.997909i | \(-0.479413\pi\) | ||||
0.0646307 | + | 0.997909i | \(0.479413\pi\) | |||||||
\(314\) | − | 33.8254i | − | 1.90888i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.01785 | −0.113513 | ||||||||
\(317\) | − | 8.10086i | − | 0.454990i | −0.973779 | − | 0.227495i | \(-0.926947\pi\) | ||
0.973779 | − | 0.227495i | \(-0.0730535\pi\) | |||||||
\(318\) | − | 36.0613i | − | 2.02222i | ||||||
\(319\) | − | 1.38902i | − | 0.0777703i | ||||||
\(320\) | − | 18.6738i | − | 1.04390i | ||||||
\(321\) | −37.2307 | −2.07801 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 28.7527i | − | 1.59984i | ||||||
\(324\) | −2.80209 | −0.155672 | ||||||||
\(325\) | −8.56292 | − | 10.1320i | −0.474985 | − | 0.562022i | ||||
\(326\) | 17.3124 | 0.958847 | ||||||||
\(327\) | 10.5961i | 0.585967i | ||||||||
\(328\) | −28.8560 | −1.59330 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − | 31.8722i | − | 1.75451i | ||||||
\(331\) | − | 11.7858i | − | 0.647804i | −0.946091 | − | 0.323902i | \(-0.895005\pi\) | ||
0.946091 | − | 0.323902i | \(-0.104995\pi\) | |||||||
\(332\) | − | 0.560401i | − | 0.0307560i | ||||||
\(333\) | 4.03441i | 0.221084i | ||||||||
\(334\) | 2.86592 | 0.156816 | ||||||||
\(335\) | 12.4133 | 0.678212 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.63045 | −0.143290 | −0.0716450 | − | 0.997430i | \(-0.522825\pi\) | ||||
−0.0716450 | + | 0.997430i | \(0.522825\pi\) | |||||||
\(338\) | 19.5271 | + | 3.30112i | 1.06213 | + | 0.179557i | ||||
\(339\) | 31.1035 | 1.68931 | ||||||||
\(340\) | 5.07405i | 0.275179i | ||||||||
\(341\) | −19.7601 | −1.07007 | ||||||||
\(342\) | 48.7014 | 2.63347 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 26.9302i | 1.45198i | ||||||||
\(345\) | − | 24.6232i | − | 1.32567i | ||||||
\(346\) | 8.48704i | 0.456266i | ||||||||
\(347\) | 4.82463 | 0.259000 | 0.129500 | − | 0.991579i | \(-0.458663\pi\) | ||||
0.129500 | + | 0.991579i | \(0.458663\pi\) | |||||||
\(348\) | −0.562753 | −0.0301667 | ||||||||
\(349\) | − | 17.5231i | − | 0.937991i | −0.883201 | − | 0.468995i | \(-0.844616\pi\) | ||
0.883201 | − | 0.468995i | \(-0.155384\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 20.7071 | + | 24.5016i | 1.10527 | + | 1.30780i | ||||
\(352\) | 4.26250 | 0.227192 | ||||||||
\(353\) | 6.59724i | 0.351136i | 0.984467 | + | 0.175568i | \(0.0561761\pi\) | ||||
−0.984467 | + | 0.175568i | \(0.943824\pi\) | |||||||
\(354\) | −28.0426 | −1.49045 | ||||||||
\(355\) | 3.68704 | 0.195688 | ||||||||
\(356\) | − | 3.28248i | − | 0.173971i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 7.10118i | − | 0.375309i | ||||||
\(359\) | − | 23.0484i | − | 1.21645i | −0.793764 | − | 0.608225i | \(-0.791882\pi\) | ||
0.793764 | − | 0.608225i | \(-0.208118\pi\) | |||||||
\(360\) | 44.9981 | 2.37161 | ||||||||
\(361\) | −9.66934 | −0.508912 | ||||||||
\(362\) | − | 19.0973i | − | 1.00373i | ||||||
\(363\) | 16.1076 | 0.845428 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −32.0001 | −1.67496 | ||||||||
\(366\) | 12.7158i | 0.664665i | ||||||||
\(367\) | 15.9318 | 0.831631 | 0.415815 | − | 0.909449i | \(-0.363496\pi\) | ||||
0.415815 | + | 0.909449i | \(0.363496\pi\) | |||||||
\(368\) | 12.6652 | 0.660222 | ||||||||
\(369\) | − | 67.3478i | − | 3.50599i | ||||||
\(370\) | 3.03259i | 0.157657i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 8.00568i | 0.415075i | ||||||||
\(373\) | 23.4289 | 1.21310 | 0.606552 | − | 0.795044i | \(-0.292552\pi\) | ||||
0.606552 | + | 0.795044i | \(0.292552\pi\) | |||||||
\(374\) | 19.3967 | 1.00298 | ||||||||
\(375\) | 11.6538i | 0.601800i | ||||||||
\(376\) | 1.37565 | 0.0709437 | ||||||||
\(377\) | 1.36340 | + | 1.61323i | 0.0702186 | + | 0.0830856i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 30.1041i | − | 1.54634i | −0.634196 | − | 0.773172i | \(-0.718669\pi\) | ||
0.634196 | − | 0.773172i | \(-0.281331\pi\) | |||||||
\(380\) | 5.05934 | 0.259539 | ||||||||
\(381\) | −15.2602 | −0.781802 | ||||||||
\(382\) | 2.00728i | 0.102701i | ||||||||
\(383\) | − | 12.8597i | − | 0.657101i | −0.944486 | − | 0.328551i | \(-0.893440\pi\) | ||
0.944486 | − | 0.328551i | \(-0.106560\pi\) | |||||||
\(384\) | 39.6898i | 2.02541i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −23.0710 | −1.17428 | ||||||||
\(387\) | −62.8532 | −3.19501 | ||||||||
\(388\) | − | 3.17731i | − | 0.161304i | ||||||
\(389\) | −36.8531 | −1.86853 | −0.934264 | − | 0.356582i | \(-0.883942\pi\) | ||||
−0.934264 | + | 0.356582i | \(0.883942\pi\) | |||||||
\(390\) | 31.2843 | + | 37.0169i | 1.58414 | + | 1.87442i | ||||
\(391\) | 14.9852 | 0.757833 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −67.5226 | −3.40606 | ||||||||
\(394\) | −15.0903 | −0.760239 | ||||||||
\(395\) | 18.5347i | 0.932583i | ||||||||
\(396\) | 4.54057i | 0.228172i | ||||||||
\(397\) | 20.3087i | 1.01926i | 0.860393 | + | 0.509631i | \(0.170218\pi\) | ||||
−0.860393 | + | 0.509631i | \(0.829782\pi\) | |||||||
\(398\) | 13.0605i | 0.654662i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.6987 | 0.834935 | ||||||||
\(401\) | 19.6699i | 0.982268i | 0.871084 | + | 0.491134i | \(0.163417\pi\) | ||||
−0.871084 | + | 0.491134i | \(0.836583\pi\) | |||||||
\(402\) | −19.2252 | −0.958864 | ||||||||
\(403\) | 22.9497 | − | 19.3956i | 1.14321 | − | 0.966163i | ||||
\(404\) | −0.657750 | −0.0327243 | ||||||||
\(405\) | 25.7383i | 1.27895i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.60216 | 0.0794162 | ||||||||
\(408\) | 41.1446i | 2.03696i | ||||||||
\(409\) | 23.1755i | 1.14595i | 0.819572 | + | 0.572976i | \(0.194211\pi\) | ||||
−0.819572 | + | 0.572976i | \(0.805789\pi\) | |||||||
\(410\) | − | 50.6241i | − | 2.50015i | ||||||
\(411\) | 3.09931i | 0.152877i | ||||||||
\(412\) | −0.971699 | −0.0478722 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 25.3819i | 1.24745i | ||||||||
\(415\) | −5.14750 | −0.252681 | ||||||||
\(416\) | −4.95053 | + | 4.18387i | −0.242720 | + | 0.205131i | ||||
\(417\) | −25.4421 | −1.24590 | ||||||||
\(418\) | − | 19.3405i | − | 0.945975i | ||||||
\(419\) | −28.6478 | −1.39953 | −0.699767 | − | 0.714371i | \(-0.746713\pi\) | ||||
−0.699767 | + | 0.714371i | \(0.746713\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 36.3249i | 1.77037i | 0.465241 | + | 0.885184i | \(0.345968\pi\) | ||||
−0.465241 | + | 0.885184i | \(0.654032\pi\) | |||||||
\(422\) | 2.20153i | 0.107169i | ||||||||
\(423\) | 3.21067i | 0.156108i | ||||||||
\(424\) | − | 20.2185i | − | 0.981898i | ||||||
\(425\) | 19.7575 | 0.958377 | ||||||||
\(426\) | −5.71031 | −0.276666 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.98688 | 0.192713 | ||||||||
\(429\) | 19.5565 | − | 16.5279i | 0.944198 | − | 0.797976i | ||||
\(430\) | −47.2456 | −2.27839 | ||||||||
\(431\) | − | 7.93131i | − | 0.382038i | −0.981586 | − | 0.191019i | \(-0.938821\pi\) | ||
0.981586 | − | 0.191019i | \(-0.0611792\pi\) | |||||||
\(432\) | −40.3814 | −1.94285 | ||||||||
\(433\) | 9.60994 | 0.461824 | 0.230912 | − | 0.972975i | \(-0.425829\pi\) | ||||
0.230912 | + | 0.972975i | \(0.425829\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.16911i | 0.247840i | ||||||||
\(436\) | − | 1.13470i | − | 0.0543421i | ||||||
\(437\) | − | 14.9417i | − | 0.714760i | ||||||
\(438\) | 49.5603 | 2.36808 | ||||||||
\(439\) | 3.46690 | 0.165466 | 0.0827332 | − | 0.996572i | \(-0.473635\pi\) | ||||
0.0827332 | + | 0.996572i | \(0.473635\pi\) | |||||||
\(440\) | − | 17.8698i | − | 0.851910i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −22.5277 | + | 19.0389i | −1.07153 | + | 0.905590i | ||||
\(443\) | 2.45667 | 0.116720 | 0.0583600 | − | 0.998296i | \(-0.481413\pi\) | ||||
0.0583600 | + | 0.998296i | \(0.481413\pi\) | |||||||
\(444\) | − | 0.649106i | − | 0.0308052i | ||||||
\(445\) | −30.1508 | −1.42929 | ||||||||
\(446\) | 22.8432 | 1.08166 | ||||||||
\(447\) | − | 12.9192i | − | 0.611056i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 22.7487i | − | 1.07358i | −0.843716 | − | 0.536790i | \(-0.819637\pi\) | ||
0.843716 | − | 0.536790i | \(-0.180363\pi\) | |||||||
\(450\) | 33.4652i | 1.57757i | ||||||||
\(451\) | −26.7454 | −1.25939 | ||||||||
\(452\) | −3.33075 | −0.156665 | ||||||||
\(453\) | 36.6742i | 1.72311i | ||||||||
\(454\) | 1.74002 | 0.0816633 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 41.0254 | 1.92119 | ||||||||
\(457\) | − | 12.2568i | − | 0.573349i | −0.958028 | − | 0.286675i | \(-0.907450\pi\) | ||
0.958028 | − | 0.286675i | \(-0.0925499\pi\) | |||||||
\(458\) | −9.55070 | −0.446275 | ||||||||
\(459\) | −47.7781 | −2.23009 | ||||||||
\(460\) | 2.63680i | 0.122942i | ||||||||
\(461\) | 24.0650i | 1.12082i | 0.828216 | + | 0.560409i | \(0.189356\pi\) | ||||
−0.828216 | + | 0.560409i | \(0.810644\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.3956i | 0.901390i | 0.892678 | + | 0.450695i | \(0.148824\pi\) | ||||
−0.892678 | + | 0.450695i | \(0.851176\pi\) | |||||||
\(464\) | −2.65879 | −0.123431 | ||||||||
\(465\) | 73.5352 | 3.41012 | ||||||||
\(466\) | − | 9.39470i | − | 0.435201i | ||||||
\(467\) | 17.8782 | 0.827307 | 0.413653 | − | 0.910434i | \(-0.364253\pi\) | ||||
0.413653 | + | 0.910434i | \(0.364253\pi\) | |||||||
\(468\) | −4.45681 | − | 5.27349i | −0.206016 | − | 0.243767i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.41340i | 0.111322i | ||||||||
\(471\) | 66.5031 | 3.06430 | ||||||||
\(472\) | −15.7227 | −0.723696 | ||||||||
\(473\) | 24.9605i | 1.14769i | ||||||||
\(474\) | − | 28.7057i | − | 1.31850i | ||||||
\(475\) | − | 19.7002i | − | 0.903906i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 47.1886 | 2.16062 | ||||||||
\(478\) | −41.8307 | −1.91329 | ||||||||
\(479\) | 20.7671i | 0.948875i | 0.880289 | + | 0.474437i | \(0.157348\pi\) | ||||
−0.880289 | + | 0.474437i | \(0.842652\pi\) | |||||||
\(480\) | −15.8625 | −0.724019 | ||||||||
\(481\) | −1.86078 | + | 1.57261i | −0.0848441 | + | 0.0717048i | ||||
\(482\) | 14.9198 | 0.679578 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.72490 | −0.0784043 | ||||||||
\(485\) | −29.1848 | −1.32522 | ||||||||
\(486\) | 0.800181i | 0.0362970i | ||||||||
\(487\) | 19.1987i | 0.869977i | 0.900436 | + | 0.434988i | \(0.143248\pi\) | ||||
−0.900436 | + | 0.434988i | \(0.856752\pi\) | |||||||
\(488\) | 7.12938i | 0.322732i | ||||||||
\(489\) | 34.0374i | 1.53923i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.91648 | −0.357266 | −0.178633 | − | 0.983916i | \(-0.557167\pi\) | ||||
−0.178633 | + | 0.983916i | \(0.557167\pi\) | |||||||
\(492\) | 10.8357i | 0.488513i | ||||||||
\(493\) | −3.14581 | −0.141680 | ||||||||
\(494\) | 18.9837 | + | 22.4624i | 0.854119 | + | 1.01063i | ||||
\(495\) | 41.7069 | 1.87459 | ||||||||
\(496\) | 37.8237i | 1.69833i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 7.97222 | 0.357244 | ||||||||
\(499\) | − | 39.1750i | − | 1.75371i | −0.480753 | − | 0.876856i | \(-0.659637\pi\) | ||
0.480753 | − | 0.876856i | \(-0.340363\pi\) | |||||||
\(500\) | − | 1.24796i | − | 0.0558105i | ||||||
\(501\) | 5.63459i | 0.251735i | ||||||||
\(502\) | − | 19.0340i | − | 0.849530i | ||||||
\(503\) | 16.1533 | 0.720239 | 0.360120 | − | 0.932906i | \(-0.382736\pi\) | ||||
0.360120 | + | 0.932906i | \(0.382736\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.04169i | 0.268852i | ||||||||
\(506\) | 10.0798 | 0.448101 | ||||||||
\(507\) | −6.49022 | + | 38.3916i | −0.288241 | + | 1.70503i | ||||
\(508\) | 1.63415 | 0.0725036 | ||||||||
\(509\) | 24.3177i | 1.07786i | 0.842350 | + | 0.538930i | \(0.181171\pi\) | ||||
−0.842350 | + | 0.538930i | \(0.818829\pi\) | |||||||
\(510\) | −72.1830 | −3.19632 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 15.0621i | 0.665658i | ||||||||
\(513\) | 47.6396i | 2.10334i | ||||||||
\(514\) | − | 29.2384i | − | 1.28965i | ||||||
\(515\) | 8.92543i | 0.393302i | ||||||||
\(516\) | 10.1126 | 0.445183 | ||||||||
\(517\) | 1.27503 | 0.0560759 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.6861 | −0.732439 | ||||||||
\(520\) | 17.5402 | + | 20.7543i | 0.769188 | + | 0.910136i | ||||
\(521\) | −34.4550 | −1.50950 | −0.754750 | − | 0.656012i | \(-0.772242\pi\) | ||||
−0.754750 | + | 0.656012i | \(0.772242\pi\) | |||||||
\(522\) | − | 5.32838i | − | 0.233217i | ||||||
\(523\) | 34.6865 | 1.51674 | 0.758368 | − | 0.651827i | \(-0.225997\pi\) | ||||
0.758368 | + | 0.651827i | \(0.225997\pi\) | |||||||
\(524\) | 7.23072 | 0.315875 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 43.8971i | − | 1.91401i | ||||||
\(527\) | 44.7520i | 1.94943i | ||||||||
\(528\) | 32.2314i | 1.40269i | ||||||||
\(529\) | −15.2128 | −0.661424 | ||||||||
\(530\) | 35.4708 | 1.54075 | ||||||||
\(531\) | − | 36.6956i | − | 1.59246i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 31.0626 | − | 26.2521i | 1.34547 | − | 1.13710i | ||||
\(534\) | 46.6962 | 2.02074 | ||||||||
\(535\) | − | 36.6211i | − | 1.58327i | ||||||
\(536\) | −10.7790 | −0.465582 | ||||||||
\(537\) | 13.9614 | 0.602480 | ||||||||
\(538\) | 12.4221i | 0.535553i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | − | 8.40708i | − | 0.361783i | ||||||
\(541\) | − | 12.2568i | − | 0.526961i | −0.964665 | − | 0.263481i | \(-0.915129\pi\) | ||
0.964665 | − | 0.263481i | \(-0.0848705\pi\) | |||||||
\(542\) | 28.3028 | 1.21571 | ||||||||
\(543\) | 37.5466 | 1.61128 | ||||||||
\(544\) | − | 9.65356i | − | 0.413893i | ||||||
\(545\) | −10.4226 | −0.446456 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.4110 | −0.701686 | −0.350843 | − | 0.936434i | \(-0.614105\pi\) | ||||
−0.350843 | + | 0.936434i | \(0.614105\pi\) | |||||||
\(548\) | − | 0.331892i | − | 0.0141777i | ||||||
\(549\) | −16.6395 | −0.710155 | ||||||||
\(550\) | 13.2899 | 0.566681 | ||||||||
\(551\) | 3.13669i | 0.133627i | ||||||||
\(552\) | 21.3814i | 0.910052i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 26.2545i | − | 1.11545i | ||||||
\(555\) | −5.96229 | −0.253085 | ||||||||
\(556\) | 2.72449 | 0.115544 | ||||||||
\(557\) | 35.6541i | 1.51071i | 0.655315 | + | 0.755356i | \(0.272536\pi\) | ||||
−0.655315 | + | 0.755356i | \(0.727464\pi\) | |||||||
\(558\) | −75.8010 | −3.20891 | ||||||||
\(559\) | −24.5001 | − | 28.9896i | −1.03624 | − | 1.22613i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 38.1353i | 1.61007i | ||||||||
\(562\) | 17.4720 | 0.737013 | ||||||||
\(563\) | −10.7748 | −0.454103 | −0.227052 | − | 0.973883i | \(-0.572909\pi\) | ||||
−0.227052 | + | 0.973883i | \(0.572909\pi\) | |||||||
\(564\) | − | 0.516572i | − | 0.0217516i | ||||||
\(565\) | 30.5943i | 1.28711i | ||||||||
\(566\) | − | 2.21769i | − | 0.0932163i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.20161 | −0.134336 | ||||||||
\(569\) | −20.9328 | −0.877550 | −0.438775 | − | 0.898597i | \(-0.644587\pi\) | ||||
−0.438775 | + | 0.898597i | \(0.644587\pi\) | |||||||
\(570\) | 71.9738i | 3.01465i | ||||||||
\(571\) | −32.2668 | −1.35032 | −0.675161 | − | 0.737670i | \(-0.735926\pi\) | ||||
−0.675161 | + | 0.737670i | \(0.735926\pi\) | |||||||
\(572\) | −2.09423 | + | 1.76991i | −0.0875642 | + | 0.0740036i | ||||
\(573\) | −3.94645 | −0.164865 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.2672 | 0.428173 | ||||||||
\(576\) | −37.8453 | −1.57689 | ||||||||
\(577\) | − | 0.197896i | − | 0.00823851i | −0.999992 | − | 0.00411925i | \(-0.998689\pi\) | ||
0.999992 | − | 0.00411925i | \(-0.00131120\pi\) | |||||||
\(578\) | − | 18.0313i | − | 0.750005i | ||||||
\(579\) | − | 45.3592i | − | 1.88506i | ||||||
\(580\) | − | 0.553539i | − | 0.0229844i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 45.2001 | 1.87361 | ||||||||
\(583\) | − | 18.7397i | − | 0.776120i | ||||||
\(584\) | 27.7870 | 1.14984 | ||||||||
\(585\) | −48.4390 | + | 40.9376i | −2.00271 | + | 1.69256i | ||||
\(586\) | −46.7624 | −1.93174 | ||||||||
\(587\) | − | 10.1251i | − | 0.417907i | −0.977926 | − | 0.208954i | \(-0.932994\pi\) | ||
0.977926 | − | 0.208954i | \(-0.0670058\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 44.6222 | 1.83863 | ||||||||
\(590\) | − | 27.5835i | − | 1.13559i | ||||||
\(591\) | − | 29.6686i | − | 1.22040i | ||||||
\(592\) | − | 3.06677i | − | 0.126044i | ||||||
\(593\) | 29.9345i | 1.22926i | 0.788815 | + | 0.614631i | \(0.210695\pi\) | ||||
−0.788815 | + | 0.614631i | \(0.789305\pi\) | |||||||
\(594\) | −32.1380 | −1.31864 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.38346i | 0.0566688i | ||||||||
\(597\) | −25.6778 | −1.05092 | ||||||||
\(598\) | −11.7068 | + | 9.89384i | −0.478727 | + | 0.404589i | ||||
\(599\) | 26.8872 | 1.09858 | 0.549291 | − | 0.835631i | \(-0.314898\pi\) | ||||
0.549291 | + | 0.835631i | \(0.314898\pi\) | |||||||
\(600\) | 28.1906i | 1.15088i | ||||||||
\(601\) | 24.7432 | 1.00930 | 0.504649 | − | 0.863325i | \(-0.331622\pi\) | ||||
0.504649 | + | 0.863325i | \(0.331622\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 25.1574i | − | 1.02449i | ||||||
\(604\) | − | 3.92730i | − | 0.159799i | ||||||
\(605\) | 15.8438i | 0.644143i | ||||||||
\(606\) | − | 9.35709i | − | 0.380106i | ||||||
\(607\) | −3.09235 | −0.125515 | −0.0627573 | − | 0.998029i | \(-0.519989\pi\) | ||||
−0.0627573 | + | 0.998029i | \(0.519989\pi\) | |||||||
\(608\) | −9.62557 | −0.390369 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.5076 | −0.506417 | ||||||||
\(611\) | −1.48084 | + | 1.25151i | −0.0599086 | + | 0.0506308i | ||||
\(612\) | 10.2833 | 0.415679 | ||||||||
\(613\) | − | 31.3605i | − | 1.26664i | −0.773891 | − | 0.633319i | \(-0.781692\pi\) | ||
0.773891 | − | 0.633319i | \(-0.218308\pi\) | |||||||
\(614\) | −32.3877 | −1.30706 | ||||||||
\(615\) | 99.5305 | 4.01346 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 12.5311i | − | 0.504484i | −0.967664 | − | 0.252242i | \(-0.918832\pi\) | ||
0.967664 | − | 0.252242i | \(-0.0811678\pi\) | |||||||
\(618\) | − | 13.8233i | − | 0.556055i | ||||||
\(619\) | 11.6112i | 0.466692i | 0.972394 | + | 0.233346i | \(0.0749675\pi\) | ||||
−0.972394 | + | 0.233346i | \(0.925032\pi\) | |||||||
\(620\) | −7.87459 | −0.316251 | ||||||||
\(621\) | −24.8286 | −0.996336 | ||||||||
\(622\) | − | 6.77374i | − | 0.271602i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −31.6369 | − | 37.4341i | −1.26649 | − | 1.49856i | ||||
\(625\) | −29.8593 | −1.19437 | ||||||||
\(626\) | − | 3.48380i | − | 0.139241i | ||||||
\(627\) | 38.0248 | 1.51856 | ||||||||
\(628\) | −7.12155 | −0.284181 | ||||||||
\(629\) | − | 3.62852i | − | 0.144679i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 12.7037i | − | 0.505728i | −0.967502 | − | 0.252864i | \(-0.918628\pi\) | ||
0.967502 | − | 0.252864i | \(-0.0813725\pi\) | |||||||
\(632\) | − | 16.0945i | − | 0.640204i | ||||||
\(633\) | −4.32836 | −0.172037 | ||||||||
\(634\) | −12.3408 | −0.490116 | ||||||||
\(635\) | − | 15.0103i | − | 0.595665i | ||||||
\(636\) | −7.59228 | −0.301054 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.11603 | −0.0837744 | ||||||||
\(639\) | − | 7.47233i | − | 0.295601i | ||||||
\(640\) | −39.0399 | −1.54319 | ||||||||
\(641\) | 40.3015 | 1.59181 | 0.795906 | − | 0.605420i | \(-0.206995\pi\) | ||||
0.795906 | + | 0.605420i | \(0.206995\pi\) | |||||||
\(642\) | 56.7170i | 2.23844i | ||||||||
\(643\) | 11.6643i | 0.459997i | 0.973191 | + | 0.229998i | \(0.0738721\pi\) | ||||
−0.973191 | + | 0.229998i | \(0.926128\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 92.8882i | − | 3.65747i | ||||||
\(646\) | −43.8017 | −1.72336 | ||||||||
\(647\) | −11.0387 | −0.433977 | −0.216988 | − | 0.976174i | \(-0.569623\pi\) | ||||
−0.216988 | + | 0.976174i | \(0.569623\pi\) | |||||||
\(648\) | − | 22.3496i | − | 0.877976i | ||||||
\(649\) | −14.5727 | −0.572030 | ||||||||
\(650\) | −15.4350 | + | 13.0447i | −0.605412 | + | 0.511656i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 3.64493i | − | 0.142747i | ||||||
\(653\) | 19.1260 | 0.748458 | 0.374229 | − | 0.927336i | \(-0.377907\pi\) | ||||
0.374229 | + | 0.927336i | \(0.377907\pi\) | |||||||
\(654\) | 16.1421 | 0.631206 | ||||||||
\(655\) | − | 66.4170i | − | 2.59513i | ||||||
\(656\) | 51.1947i | 1.99882i | ||||||||
\(657\) | 64.8529i | 2.53015i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.8233 | 1.12279 | 0.561397 | − | 0.827546i | \(-0.310264\pi\) | ||||
0.561397 | + | 0.827546i | \(0.310264\pi\) | |||||||
\(660\) | −6.71032 | −0.261199 | ||||||||
\(661\) | − | 48.2385i | − | 1.87626i | −0.346281 | − | 0.938131i | \(-0.612556\pi\) | ||
0.346281 | − | 0.938131i | \(-0.387444\pi\) | |||||||
\(662\) | −17.9544 | −0.697816 | ||||||||
\(663\) | −37.4319 | − | 44.2910i | −1.45373 | − | 1.72012i | ||||
\(664\) | 4.46979 | 0.173462 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.14600 | 0.238153 | ||||||||
\(667\) | −1.63476 | −0.0632982 | ||||||||
\(668\) | − | 0.603386i | − | 0.0233457i | ||||||
\(669\) | 44.9112i | 1.73637i | ||||||||
\(670\) | − | 18.9104i | − | 0.730572i | ||||||
\(671\) | 6.60794i | 0.255097i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33.0426 | 1.27370 | 0.636849 | − | 0.770989i | \(-0.280238\pi\) | ||||
0.636849 | + | 0.770989i | \(0.280238\pi\) | |||||||
\(674\) | 4.00722i | 0.154352i | ||||||||
\(675\) | −32.7356 | −1.26000 | ||||||||
\(676\) | 0.695012 | − | 4.11120i | 0.0267312 | − | 0.158123i | ||||
\(677\) | −15.7186 | −0.604117 | −0.302058 | − | 0.953289i | \(-0.597674\pi\) | ||||
−0.302058 | + | 0.953289i | \(0.597674\pi\) | |||||||
\(678\) | − | 47.3830i | − | 1.81973i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −40.4710 | −1.55199 | ||||||||
\(681\) | 3.42100i | 0.131093i | ||||||||
\(682\) | 30.1024i | 1.15268i | ||||||||
\(683\) | 33.3629i | 1.27660i | 0.769789 | + | 0.638298i | \(0.220361\pi\) | ||||
−0.769789 | + | 0.638298i | \(0.779639\pi\) | |||||||
\(684\) | − | 10.2535i | − | 0.392053i | ||||||
\(685\) | −3.04856 | −0.116479 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 18.7773i | − | 0.716400i | ||||||
\(688\) | 47.7781 | 1.82152 | ||||||||
\(689\) | 18.3941 | + | 21.7646i | 0.700758 | + | 0.829166i | ||||
\(690\) | −37.5109 | −1.42802 | ||||||||
\(691\) | − | 45.3507i | − | 1.72522i | −0.505869 | − | 0.862610i | \(-0.668828\pi\) | ||
0.505869 | − | 0.862610i | \(-0.331172\pi\) | |||||||
\(692\) | 1.78685 | 0.0679257 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 7.34981i | − | 0.278995i | ||||||
\(695\) | − | 25.0255i | − | 0.949270i | ||||||
\(696\) | − | 4.48855i | − | 0.170138i | ||||||
\(697\) | 60.5721i | 2.29433i | ||||||||
\(698\) | −26.6946 | −1.01041 | ||||||||
\(699\) | 18.4706 | 0.698623 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.5681 | −0.890155 | −0.445077 | − | 0.895492i | \(-0.646824\pi\) | ||||
−0.445077 | + | 0.895492i | \(0.646824\pi\) | |||||||
\(702\) | 37.3256 | − | 31.5452i | 1.40876 | − | 1.19060i | ||||
\(703\) | −3.61800 | −0.136456 | ||||||||
\(704\) | 15.0293i | 0.566438i | ||||||||
\(705\) | −4.74491 | −0.178704 | ||||||||
\(706\) | 10.0502 | 0.378244 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 5.90405i | 0.221888i | ||||||||
\(709\) | 8.66932i | 0.325583i | 0.986660 | + | 0.162792i | \(0.0520498\pi\) | ||||
−0.986660 | + | 0.162792i | \(0.947950\pi\) | |||||||
\(710\) | − | 5.61681i | − | 0.210795i | ||||||
\(711\) | 37.5634 | 1.40874 | ||||||||
\(712\) | 26.1812 | 0.981183 | ||||||||
\(713\) | 23.2560i | 0.870943i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.2573 | + | 19.2363i | 0.607988 | + | 0.719398i | ||||
\(716\) | −1.49507 | −0.0558735 | ||||||||
\(717\) | − | 82.2420i | − | 3.07138i | ||||||
\(718\) | −35.1119 | −1.31036 | ||||||||
\(719\) | 11.0038 | 0.410373 | 0.205186 | − | 0.978723i | \(-0.434220\pi\) | ||||
0.205186 | + | 0.978723i | \(0.434220\pi\) | |||||||
\(720\) | − | 79.8331i | − | 2.97520i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 14.7302i | 0.548202i | ||||||||
\(723\) | 29.3333i | 1.09092i | ||||||||
\(724\) | −4.02071 | −0.149429 | ||||||||
\(725\) | −2.15538 | −0.0800488 | ||||||||
\(726\) | − | 24.5382i | − | 0.910698i | ||||||
\(727\) | −40.7049 | −1.50966 | −0.754831 | − | 0.655919i | \(-0.772281\pi\) | ||||
−0.754831 | + | 0.655919i | \(0.772281\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.7827 | −1.02899 | ||||||||
\(730\) | 48.7488i | 1.80427i | ||||||||
\(731\) | 56.5298 | 2.09083 | ||||||||
\(732\) | 2.67716 | 0.0989508 | ||||||||
\(733\) | − | 10.3536i | − | 0.382418i | −0.981549 | − | 0.191209i | \(-0.938759\pi\) | ||
0.981549 | − | 0.191209i | \(-0.0612409\pi\) | |||||||
\(734\) | − | 24.2704i | − | 0.895835i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 5.01660i | − | 0.184914i | ||||||
\(737\) | −9.99062 | −0.368009 | ||||||||
\(738\) | −102.597 | −3.77666 | ||||||||
\(739\) | − | 48.5321i | − | 1.78528i | −0.450770 | − | 0.892640i | \(-0.648850\pi\) | ||
0.450770 | − | 0.892640i | \(-0.351150\pi\) | |||||||
\(740\) | 0.638477 | 0.0234709 | ||||||||
\(741\) | −44.1626 | + | 37.3234i | −1.62235 | + | 1.37111i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.5215i | 0.899608i | 0.893127 | + | 0.449804i | \(0.148506\pi\) | ||||
−0.893127 | + | 0.449804i | \(0.851494\pi\) | |||||||
\(744\) | −63.8537 | −2.34099 | ||||||||
\(745\) | 12.7076 | 0.465572 | ||||||||
\(746\) | − | 35.6915i | − | 1.30676i | ||||||
\(747\) | 10.4322i | 0.381694i | ||||||||
\(748\) | − | 4.08376i | − | 0.149317i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 17.7534 | 0.648261 | ||||||||
\(751\) | 28.0663 | 1.02415 | 0.512077 | − | 0.858939i | \(-0.328876\pi\) | ||||
0.512077 | + | 0.858939i | \(0.328876\pi\) | |||||||
\(752\) | − | 2.44060i | − | 0.0889996i | ||||||
\(753\) | 37.4222 | 1.36374 | ||||||||
\(754\) | 2.45759 | − | 2.07700i | 0.0895001 | − | 0.0756397i | ||||
\(755\) | −36.0738 | −1.31286 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.70864 | 0.207484 | 0.103742 | − | 0.994604i | \(-0.466918\pi\) | ||||
0.103742 | + | 0.994604i | \(0.466918\pi\) | |||||||
\(758\) | −45.8605 | −1.66573 | ||||||||
\(759\) | 19.8175i | 0.719331i | ||||||||
\(760\) | 40.3536i | 1.46378i | ||||||||
\(761\) | − | 7.69598i | − | 0.278979i | −0.990224 | − | 0.139490i | \(-0.955454\pi\) | ||
0.990224 | − | 0.139490i | \(-0.0445462\pi\) | |||||||
\(762\) | 23.2473i | 0.842159i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.422610 | 0.0152895 | ||||||||
\(765\) | − | 94.4563i | − | 3.41508i | ||||||
\(766\) | −19.5904 | −0.707832 | ||||||||
\(767\) | 16.9250 | − | 14.3039i | 0.611126 | − | 0.516485i | ||||
\(768\) | 22.4939 | 0.811677 | ||||||||
\(769\) | − | 15.0754i | − | 0.543634i | −0.962349 | − | 0.271817i | \(-0.912375\pi\) | ||
0.962349 | − | 0.271817i | \(-0.0876245\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 57.4847 | 2.07026 | ||||||||
\(772\) | 4.85733i | 0.174819i | ||||||||
\(773\) | − | 21.2624i | − | 0.764755i | −0.924006 | − | 0.382378i | \(-0.875105\pi\) | ||
0.924006 | − | 0.382378i | \(-0.124895\pi\) | |||||||
\(774\) | 95.7503i | 3.44167i | ||||||||
\(775\) | 30.6622i | 1.10142i | ||||||||
\(776\) | 25.3424 | 0.909740 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 56.1419i | 2.01278i | ||||||||
\(779\) | 60.3966 | 2.16393 | ||||||||
\(780\) | 7.79347 | − | 6.58654i | 0.279051 | − | 0.235836i | ||||
\(781\) | −2.96744 | −0.106183 | ||||||||
\(782\) | − | 22.8283i | − | 0.816340i | ||||||
\(783\) | 5.21221 | 0.186269 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 65.4142i | 2.33473i | ||||||||
\(786\) | 102.864i | 3.66902i | ||||||||
\(787\) | 9.28939i | 0.331131i | 0.986199 | + | 0.165565i | \(0.0529449\pi\) | ||||
−0.986199 | + | 0.165565i | \(0.947055\pi\) | |||||||
\(788\) | 3.17709i | 0.113179i | ||||||||
\(789\) | 86.3048 | 3.07253 | ||||||||
\(790\) | 28.2357 | 1.00458 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −36.2158 | −1.28687 | ||||||||
\(793\) | −6.48604 | − | 7.67456i | −0.230326 | − | 0.272532i | ||||
\(794\) | 30.9381 | 1.09795 | ||||||||
\(795\) | 69.7381i | 2.47335i | ||||||||
\(796\) | 2.74973 | 0.0974615 | ||||||||
\(797\) | −49.7686 | −1.76289 | −0.881447 | − | 0.472283i | \(-0.843430\pi\) | ||||
−0.881447 | + | 0.472283i | \(0.843430\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 2.88765i | − | 0.102158i | ||||||
\(800\) | − | 6.61423i | − | 0.233848i | ||||||
\(801\) | 61.1051i | 2.15904i | ||||||||
\(802\) | 29.9650 | 1.05810 | ||||||||
\(803\) | 25.7547 | 0.908863 | ||||||||
\(804\) | 4.04764i | 0.142749i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −29.5472 | − | 34.9614i | −1.04075 | − | 1.23146i | ||||
\(807\) | −24.4226 | −0.859717 | ||||||||
\(808\) | − | 5.24625i | − | 0.184563i | ||||||
\(809\) | −9.59433 | −0.337319 | −0.168659 | − | 0.985674i | \(-0.553944\pi\) | ||||
−0.168659 | + | 0.985674i | \(0.553944\pi\) | |||||||
\(810\) | 39.2096 | 1.37768 | ||||||||
\(811\) | 35.6060i | 1.25030i | 0.780506 | + | 0.625148i | \(0.214962\pi\) | ||||
−0.780506 | + | 0.625148i | \(0.785038\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 55.6453i | 1.95157i | ||||||||
\(814\) | − | 2.44073i | − | 0.0855474i | ||||||
\(815\) | −33.4801 | −1.17276 | ||||||||
\(816\) | 72.9966 | 2.55539 | ||||||||
\(817\) | − | 56.3659i | − | 1.97199i | ||||||
\(818\) | 35.3054 | 1.23442 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.6583 | −0.372205 | ||||||||
\(821\) | − | 0.296780i | − | 0.0103577i | −0.999987 | − | 0.00517884i | \(-0.998352\pi\) | ||
0.999987 | − | 0.00517884i | \(-0.00164848\pi\) | |||||||
\(822\) | 4.72147 | 0.164680 | ||||||||
\(823\) | −22.9119 | −0.798658 | −0.399329 | − | 0.916808i | \(-0.630757\pi\) | ||||
−0.399329 | + | 0.916808i | \(0.630757\pi\) | |||||||
\(824\) | − | 7.75033i | − | 0.269995i | ||||||
\(825\) | 26.1288i | 0.909687i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 8.50142i | − | 0.295623i | −0.989016 | − | 0.147812i | \(-0.952777\pi\) | ||
0.989016 | − | 0.147812i | \(-0.0472230\pi\) | |||||||
\(828\) | 5.34387 | 0.185712 | ||||||||
\(829\) | 54.3605 | 1.88802 | 0.944009 | − | 0.329919i | \(-0.107022\pi\) | ||||
0.944009 | + | 0.329919i | \(0.107022\pi\) | |||||||
\(830\) | 7.84168i | 0.272189i | ||||||||
\(831\) | 51.6182 | 1.79061 | ||||||||
\(832\) | −14.7521 | − | 17.4553i | −0.511436 | − | 0.605152i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 38.7583i | 1.34209i | ||||||||
\(835\) | −5.54233 | −0.191800 | ||||||||
\(836\) | −4.07192 | −0.140830 | ||||||||
\(837\) | − | 74.1485i | − | 2.56295i | ||||||
\(838\) | 43.6419i | 1.50758i | ||||||||
\(839\) | 17.0486i | 0.588585i | 0.955715 | + | 0.294292i | \(0.0950839\pi\) | ||||
−0.955715 | + | 0.294292i | \(0.904916\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.6568 | −0.988166 | ||||||||
\(842\) | 55.3372 | 1.90705 | ||||||||
\(843\) | 34.3512i | 1.18312i | ||||||||
\(844\) | 0.463507 | 0.0159546 | ||||||||
\(845\) | −37.7630 | − | 6.38395i | −1.29909 | − | 0.219615i | ||||
\(846\) | 4.89112 | 0.168160 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −35.8706 | −1.23180 | ||||||||
\(849\) | 4.36013 | 0.149639 | ||||||||
\(850\) | − | 30.0984i | − | 1.03237i | ||||||
\(851\) | − | 1.88561i | − | 0.0646379i | ||||||
\(852\) | 1.20224i | 0.0411881i | ||||||||
\(853\) | − | 45.0401i | − | 1.54214i | −0.636747 | − | 0.771072i | \(-0.719721\pi\) | ||
0.636747 | − | 0.771072i | \(-0.280279\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −94.1825 | −3.22097 | ||||||||
\(856\) | 31.7996i | 1.08689i | ||||||||
\(857\) | −39.7927 | −1.35929 | −0.679646 | − | 0.733541i | \(-0.737866\pi\) | ||||
−0.679646 | + | 0.733541i | \(0.737866\pi\) | |||||||
\(858\) | −25.1786 | − | 29.7923i | −0.859582 | − | 1.01709i | ||||
\(859\) | −22.3379 | −0.762158 | −0.381079 | − | 0.924542i | \(-0.624447\pi\) | ||||
−0.381079 | + | 0.924542i | \(0.624447\pi\) | |||||||
\(860\) | 9.94702i | 0.339191i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12.0825 | −0.411532 | ||||||||
\(863\) | 14.1624i | 0.482094i | 0.970513 | + | 0.241047i | \(0.0774908\pi\) | ||||
−0.970513 | + | 0.241047i | \(0.922509\pi\) | |||||||
\(864\) | 15.9947i | 0.544152i | ||||||||
\(865\) | − | 16.4129i | − | 0.558055i | ||||||
\(866\) | − | 14.6397i | − | 0.497479i | ||||||
\(867\) | 35.4509 | 1.20397 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 14.9173i | − | 0.506036i | ||||||
\(870\) | 7.87459 | 0.266974 | ||||||||
\(871\) | 11.6033 | − | 9.80633i | 0.393162 | − | 0.332275i | ||||
\(872\) | 9.05041 | 0.306485 | ||||||||
\(873\) | 59.1474i | 2.00184i | ||||||||
\(874\) | −22.7622 | −0.769941 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 10.4343i | − | 0.352544i | ||||||
\(877\) | 43.9546i | 1.48424i | 0.670266 | + | 0.742121i | \(0.266180\pi\) | ||||
−0.670266 | + | 0.742121i | \(0.733820\pi\) | |||||||
\(878\) | − | 5.28147i | − | 0.178241i | ||||||
\(879\) | − | 91.9382i | − | 3.10100i | ||||||
\(880\) | −31.7037 | −1.06873 | ||||||||
\(881\) | 15.3849 | 0.518331 | 0.259165 | − | 0.965833i | \(-0.416553\pi\) | ||||
0.259165 | + | 0.965833i | \(0.416553\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.5262 | 1.49842 | 0.749212 | − | 0.662330i | \(-0.230432\pi\) | ||||
0.749212 | + | 0.662330i | \(0.230432\pi\) | |||||||
\(884\) | 4.00843 | + | 4.74294i | 0.134818 | + | 0.159522i | ||||
\(885\) | 54.2310 | 1.82295 | ||||||||
\(886\) | − | 3.74248i | − | 0.125731i | ||||||
\(887\) | −16.1072 | −0.540826 | −0.270413 | − | 0.962744i | \(-0.587160\pi\) | ||||
−0.270413 | + | 0.962744i | \(0.587160\pi\) | |||||||
\(888\) | 5.17731 | 0.173739 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 45.9316i | 1.53963i | ||||||||
\(891\) | − | 20.7150i | − | 0.693978i | ||||||
\(892\) | − | 4.80936i | − | 0.161029i | ||||||
\(893\) | −2.87928 | −0.0963515 | ||||||||
\(894\) | −19.6810 | −0.658231 | ||||||||
\(895\) | 13.7328i | 0.459037i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −19.4520 | − | 23.0164i | −0.649483 | − | 0.768495i | ||||
\(898\) | −34.6553 | −1.15646 | ||||||||
\(899\) | − | 4.88208i | − | 0.162827i | ||||||
\(900\) | 7.04572 | 0.234857 | ||||||||
\(901\) | −42.4411 | −1.41392 | ||||||||
\(902\) | 40.7439i | 1.35662i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 26.5663i | − | 0.883582i | ||||||
\(905\) | 36.9318i | 1.22766i | ||||||||
\(906\) | 55.8694 | 1.85614 | ||||||||
\(907\) | −18.6037 | −0.617725 | −0.308862 | − | 0.951107i | \(-0.599948\pi\) | ||||
−0.308862 | + | 0.951107i | \(0.599948\pi\) | |||||||
\(908\) | − | 0.366341i | − | 0.0121575i | ||||||
\(909\) | 12.2444 | 0.406121 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.1801 | 1.26496 | 0.632481 | − | 0.774576i | \(-0.282037\pi\) | ||||
0.632481 | + | 0.774576i | \(0.282037\pi\) | |||||||
\(912\) | − | 72.7850i | − | 2.41015i | ||||||
\(913\) | 4.14287 | 0.137109 | ||||||||
\(914\) | −18.6720 | −0.617614 | ||||||||
\(915\) | − | 24.5908i | − | 0.812946i | ||||||
\(916\) | 2.01079i | 0.0664383i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 72.7850i | 2.40226i | ||||||||
\(919\) | −16.7629 | −0.552956 | −0.276478 | − | 0.961020i | \(-0.589167\pi\) | ||||
−0.276478 | + | 0.961020i | \(0.589167\pi\) | |||||||
\(920\) | −21.0313 | −0.693381 | ||||||||
\(921\) | − | 63.6765i | − | 2.09821i | ||||||
\(922\) | 36.6605 | 1.20735 | ||||||||
\(923\) | 3.44643 | − | 2.91270i | 0.113441 | − | 0.0958728i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 2.48612i | − | 0.0817430i | ||||||
\(926\) | 29.5472 | 0.970980 | ||||||||
\(927\) | 18.0887 | 0.594111 | ||||||||
\(928\) | 1.05313i | 0.0345706i | ||||||||
\(929\) | − | 6.58871i | − | 0.216169i | −0.994142 | − | 0.108084i | \(-0.965528\pi\) | ||
0.994142 | − | 0.108084i | \(-0.0344716\pi\) | |||||||
\(930\) | − | 112.023i | − | 3.67339i | ||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.97794 | −0.0647897 | ||||||||
\(933\) | 13.3176 | 0.436000 | ||||||||
\(934\) | − | 27.2356i | − | 0.891177i | ||||||
\(935\) | −37.5109 | −1.22674 | ||||||||
\(936\) | 42.0617 | − | 35.5478i | 1.37483 | − | 1.16192i | ||||
\(937\) | −39.0958 | −1.27721 | −0.638603 | − | 0.769537i | \(-0.720487\pi\) | ||||
−0.638603 | + | 0.769537i | \(0.720487\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.84940 | 0.223522 | ||||||||
\(940\) | 0.508114 | 0.0165728 | ||||||||
\(941\) | 13.2351i | 0.431452i | 0.976454 | + | 0.215726i | \(0.0692118\pi\) | ||||
−0.976454 | + | 0.215726i | \(0.930788\pi\) | |||||||
\(942\) | − | 101.311i | − | 3.30088i | ||||||
\(943\) | 31.4771i | 1.02504i | ||||||||
\(944\) | 27.8943i | 0.907884i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 38.0248 | 1.23629 | ||||||||
\(947\) | − | 50.1427i | − | 1.62942i | −0.579870 | − | 0.814709i | \(-0.696897\pi\) | ||
0.579870 | − | 0.814709i | \(-0.303103\pi\) | |||||||
\(948\) | −6.04366 | −0.196289 | ||||||||
\(949\) | −29.9119 | + | 25.2796i | −0.970981 | + | 0.820610i | ||||
\(950\) | −30.0112 | −0.973690 | ||||||||
\(951\) | − | 24.2629i | − | 0.786778i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.9832 | −0.971252 | −0.485626 | − | 0.874167i | \(-0.661408\pi\) | ||||
−0.485626 | + | 0.874167i | \(0.661408\pi\) | |||||||
\(954\) | − | 71.8869i | − | 2.32742i | ||||||
\(955\) | − | 3.88184i | − | 0.125613i | ||||||
\(956\) | 8.80697i | 0.284838i | ||||||||
\(957\) | − | 4.16026i | − | 0.134482i | ||||||
\(958\) | 31.6366 | 1.02213 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | − | 55.9300i | − | 1.80513i | ||||||
\(961\) | −38.4521 | −1.24039 | ||||||||
\(962\) | 2.39570 | + | 2.83470i | 0.0772406 | + | 0.0913943i | ||||
\(963\) | −74.2180 | −2.39164 | ||||||||
\(964\) | − | 3.14119i | − | 0.101171i | ||||||
\(965\) | 44.6165 | 1.43626 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.8356i | 1.21671i | 0.793665 | + | 0.608356i | \(0.208171\pi\) | ||||
−0.793665 | + | 0.608356i | \(0.791829\pi\) | |||||||
\(968\) | − | 13.7579i | − | 0.442195i | ||||||
\(969\) | − | 86.1172i | − | 2.76648i | ||||||
\(970\) | 44.4600i | 1.42753i | ||||||||
\(971\) | 15.3432 | 0.492388 | 0.246194 | − | 0.969221i | \(-0.420820\pi\) | ||||
0.246194 | + | 0.969221i | \(0.420820\pi\) | |||||||
\(972\) | 0.168469 | 0.00540364 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 29.2472 | 0.937142 | ||||||||
\(975\) | −25.6468 | − | 30.3464i | −0.821355 | − | 0.971862i | ||||
\(976\) | 12.6486 | 0.404871 | ||||||||
\(977\) | 26.5487i | 0.849367i | 0.905342 | + | 0.424684i | \(0.139615\pi\) | ||||
−0.905342 | + | 0.424684i | \(0.860385\pi\) | |||||||
\(978\) | 51.8525 | 1.65806 | ||||||||
\(979\) | 24.2663 | 0.775555 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 21.1230i | 0.674406i | ||||||||
\(982\) | 12.0599i | 0.384848i | ||||||||
\(983\) | 8.02003i | 0.255799i | 0.991787 | + | 0.127900i | \(0.0408235\pi\) | ||||
−0.991787 | + | 0.127900i | \(0.959176\pi\) | |||||||
\(984\) | −86.4265 | −2.75518 | ||||||||
\(985\) | 29.1828 | 0.929842 | ||||||||
\(986\) | 4.79231i | 0.152618i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.72919 | − | 3.99681i | 0.150456 | − | 0.127155i | ||||
\(989\) | 29.3765 | 0.934117 | ||||||||
\(990\) | − | 63.5361i | − | 2.01931i | ||||||
\(991\) | 49.0958 | 1.55958 | 0.779789 | − | 0.626042i | \(-0.215326\pi\) | ||||
0.779789 | + | 0.626042i | \(0.215326\pi\) | |||||||
\(992\) | 14.9817 | 0.475669 | ||||||||
\(993\) | − | 35.2995i | − | 1.12020i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 25.2573i | − | 0.800711i | ||||||
\(996\) | − | 1.67846i | − | 0.0531840i | ||||||
\(997\) | 19.9476 | 0.631746 | 0.315873 | − | 0.948801i | \(-0.397703\pi\) | ||||
0.315873 | + | 0.948801i | \(0.397703\pi\) | |||||||
\(998\) | −59.6790 | −1.88910 | ||||||||
\(999\) | 6.01201i | 0.190212i |
(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 | 637.2.c.g.246.6 | yes | 16 | |
7.2 | even | 3 | 637.2.r.g.116.5 | 32 | |||
7.3 | odd | 6 | 637.2.r.g.324.12 | 32 | |||
7.4 | even | 3 | 637.2.r.g.324.11 | 32 | |||
7.5 | odd | 6 | 637.2.r.g.116.6 | 32 | |||
7.6 | odd | 2 | inner | 637.2.c.g.246.5 | ✓ | 16 | |
13.5 | odd | 4 | 8281.2.a.cs.1.6 | 16 | |||
13.8 | odd | 4 | 8281.2.a.cs.1.12 | 16 | |||
13.12 | even | 2 | inner | 637.2.c.g.246.12 | yes | 16 | |
91.12 | odd | 6 | 637.2.r.g.116.12 | 32 | |||
91.25 | even | 6 | 637.2.r.g.324.5 | 32 | |||
91.34 | even | 4 | 8281.2.a.cs.1.11 | 16 | |||
91.38 | odd | 6 | 637.2.r.g.324.6 | 32 | |||
91.51 | even | 6 | 637.2.r.g.116.11 | 32 | |||
91.83 | even | 4 | 8281.2.a.cs.1.5 | 16 | |||
91.90 | odd | 2 | inner | 637.2.c.g.246.11 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.c.g.246.5 | ✓ | 16 | 7.6 | odd | 2 | inner | |
637.2.c.g.246.6 | yes | 16 | 1.1 | even | 1 | trivial | |
637.2.c.g.246.11 | yes | 16 | 91.90 | odd | 2 | inner | |
637.2.c.g.246.12 | yes | 16 | 13.12 | even | 2 | inner | |
637.2.r.g.116.5 | 32 | 7.2 | even | 3 | |||
637.2.r.g.116.6 | 32 | 7.5 | odd | 6 | |||
637.2.r.g.116.11 | 32 | 91.51 | even | 6 | |||
637.2.r.g.116.12 | 32 | 91.12 | odd | 6 | |||
637.2.r.g.324.5 | 32 | 91.25 | even | 6 | |||
637.2.r.g.324.6 | 32 | 91.38 | odd | 6 | |||
637.2.r.g.324.11 | 32 | 7.4 | even | 3 | |||
637.2.r.g.324.12 | 32 | 7.3 | odd | 6 | |||
8281.2.a.cs.1.5 | 16 | 91.83 | even | 4 | |||
8281.2.a.cs.1.6 | 16 | 13.5 | odd | 4 | |||
8281.2.a.cs.1.11 | 16 | 91.34 | even | 4 | |||
8281.2.a.cs.1.12 | 16 | 13.8 | odd | 4 |